LMFDB - Embedded newform 225.4.e.f.151.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [225,4,Mod(76,225)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(225, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 0]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("225.76");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 225 = 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	225.e (of order $3$, degree $2$, 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:	$13.2754297513$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			151.8
Character	$\chi$	$=$	225.151
Dual form			225.4.e.f.76.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.07290 - 1.85832i) q^{2} +(-2.66146 + 4.46280i) q^{3} +(1.69777 + 2.94063i) q^{4} +(5.43782 + 9.73398i) q^{6} +(11.6282 - 20.1406i) q^{7} +24.4526 q^{8} +(-12.8333 - 23.7552i) q^{9} +O(q^{10})$	\(q+(1.07290 - 1.85832i) q^{2} +(-2.66146 + 4.46280i) q^{3} +(1.69777 + 2.94063i) q^{4} +(5.43782 + 9.73398i) q^{6} +(11.6282 - 20.1406i) q^{7} +24.4526 q^{8} +(-12.8333 - 23.7552i) q^{9} +(-6.24976 + 10.8249i) q^{11} +(-17.6420 - 0.249540i) q^{12} +(25.3078 + 43.8344i) q^{13} +(-24.9518 - 43.2178i) q^{14} +(12.6529 - 21.9155i) q^{16} +63.6794 q^{17} +(-57.9134 - 1.63865i) q^{18} +5.41153 q^{19} +(58.9358 + 105.498i) q^{21} +(13.4107 + 23.2281i) q^{22} +(44.2335 + 76.6146i) q^{23} +(-65.0795 + 109.127i) q^{24} +108.611 q^{26} +(140.170 + 5.95112i) q^{27} +78.9683 q^{28} +(-72.2845 + 125.200i) q^{29} +(138.980 + 240.720i) q^{31} +(70.6596 + 122.386i) q^{32} +(-31.6759 - 56.7015i) q^{33} +(68.3216 - 118.337i) q^{34} +(48.0672 - 78.0687i) q^{36} +243.269 q^{37} +(5.80603 - 10.0563i) q^{38} +(-262.980 - 3.71976i) q^{39} +(-234.286 - 405.796i) q^{41} +(259.281 + 3.66743i) q^{42} +(249.205 - 431.637i) q^{43} -42.4427 q^{44} +189.832 q^{46} +(-226.262 + 391.897i) q^{47} +(64.1294 + 114.795i) q^{48} +(-98.9304 - 171.352i) q^{49} +(-169.480 + 284.189i) q^{51} +(-85.9339 + 148.842i) q^{52} -223.885 q^{53} +(161.447 - 254.095i) q^{54} +(284.339 - 492.490i) q^{56} +(-14.4026 + 24.1506i) q^{57} +(155.108 + 268.655i) q^{58} +(-57.9657 - 100.400i) q^{59} +(-41.3965 + 71.7008i) q^{61} +596.444 q^{62} +(-627.672 - 17.7599i) q^{63} +505.689 q^{64} +(-139.354 - 1.97112i) q^{66} +(-405.064 - 701.592i) q^{67} +(108.113 + 187.258i) q^{68} +(-459.642 - 6.50146i) q^{69} -134.171 q^{71} +(-313.806 - 580.874i) q^{72} +707.508 q^{73} +(261.003 - 452.070i) q^{74} +(9.18755 + 15.9133i) q^{76} +(145.347 + 251.748i) q^{77} +(-289.064 + 484.710i) q^{78} +(-208.821 + 361.689i) q^{79} +(-399.615 + 609.712i) q^{81} -1005.46 q^{82} +(461.443 - 799.243i) q^{83} +(-210.171 + 352.420i) q^{84} +(-534.745 - 926.205i) q^{86} +(-366.363 - 655.808i) q^{87} +(-152.823 + 264.696i) q^{88} +114.544 q^{89} +1177.14 q^{91} +(-150.197 + 260.149i) q^{92} +(-1444.17 - 20.4273i) q^{93} +(485.513 + 840.932i) q^{94} +(-734.242 - 10.3856i) q^{96} +(-180.777 + 313.115i) q^{97} -424.569 q^{98} +(337.352 + 9.54534i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 4 q^{2} + q^{3} - 48 q^{4} - 13 q^{6} - 6 q^{7} - 90 q^{8} - 61 q^{9}+O(q^{10}) $ 24 * q + 4 * q^2 + q^3 - 48 * q^4 - 13 * q^6 - 6 * q^7 - 90 * q^8 - 61 * q^9	\( 24 q + 4 q^{2} + q^{3} - 48 q^{4} - 13 q^{6} - 6 q^{7} - 90 q^{8} - 61 q^{9} - 29 q^{11} + 77 q^{12} - 24 q^{13} + 69 q^{14} - 192 q^{16} - 158 q^{17} - 125 q^{18} - 150 q^{19} - 60 q^{21} + 18 q^{22} + 318 q^{23} + 342 q^{24} - 308 q^{26} + 394 q^{27} + 192 q^{28} - 106 q^{29} - 60 q^{31} + 914 q^{32} + 80 q^{33} + 108 q^{34} + 1303 q^{36} - 168 q^{37} + 640 q^{38} - 410 q^{39} + 353 q^{41} - 1521 q^{42} + 426 q^{43} + 1142 q^{44} + 540 q^{46} + 1210 q^{47} - 2680 q^{48} - 666 q^{49} - 1369 q^{51} + 75 q^{52} - 896 q^{53} - 2128 q^{54} + 570 q^{56} - 1544 q^{57} - 594 q^{58} - 482 q^{59} - 402 q^{61} - 5088 q^{62} + 1038 q^{63} + 1950 q^{64} + 2041 q^{66} + 201 q^{67} + 3437 q^{68} + 2856 q^{69} - 1888 q^{71} + 5493 q^{72} - 906 q^{73} - 10 q^{74} + 462 q^{76} + 2652 q^{77} + 4589 q^{78} - 258 q^{79} + 3071 q^{81} + 1746 q^{82} + 3012 q^{83} - 2703 q^{84} - 1952 q^{86} - 2708 q^{87} + 216 q^{88} - 1476 q^{89} - 1236 q^{91} + 5232 q^{92} - 3024 q^{93} - 63 q^{94} - 10424 q^{96} + 318 q^{97} - 15022 q^{98} - 1697 q^{99}+O(q^{100}) \) 24 * q + 4 * q^2 + q^3 - 48 * q^4 - 13 * q^6 - 6 * q^7 - 90 * q^8 - 61 * q^9 - 29 * q^11 + 77 * q^12 - 24 * q^13 + 69 * q^14 - 192 * q^16 - 158 * q^17 - 125 * q^18 - 150 * q^19 - 60 * q^21 + 18 * q^22 + 318 * q^23 + 342 * q^24 - 308 * q^26 + 394 * q^27 + 192 * q^28 - 106 * q^29 - 60 * q^31 + 914 * q^32 + 80 * q^33 + 108 * q^34 + 1303 * q^36 - 168 * q^37 + 640 * q^38 - 410 * q^39 + 353 * q^41 - 1521 * q^42 + 426 * q^43 + 1142 * q^44 + 540 * q^46 + 1210 * q^47 - 2680 * q^48 - 666 * q^49 - 1369 * q^51 + 75 * q^52 - 896 * q^53 - 2128 * q^54 + 570 * q^56 - 1544 * q^57 - 594 * q^58 - 482 * q^59 - 402 * q^61 - 5088 * q^62 + 1038 * q^63 + 1950 * q^64 + 2041 * q^66 + 201 * q^67 + 3437 * q^68 + 2856 * q^69 - 1888 * q^71 + 5493 * q^72 - 906 * q^73 - 10 * q^74 + 462 * q^76 + 2652 * q^77 + 4589 * q^78 - 258 * q^79 + 3071 * q^81 + 1746 * q^82 + 3012 * q^83 - 2703 * q^84 - 1952 * q^86 - 2708 * q^87 + 216 * q^88 - 1476 * q^89 - 1236 * q^91 + 5232 * q^92 - 3024 * q^93 - 63 * q^94 - 10424 * q^96 + 318 * q^97 - 15022 * q^98 - 1697 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/225\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	1.07290	−	1.85832i	0.379327	−	0.657014i	−0.611637	−	0.791138i	$-0.709489\pi$
$2$	1.07290	−	1.85832i	0.379327	−	0.657014i	0.990965	+	0.134124i	$0.0428221\pi$
$3$	−2.66146	+	4.46280i	−0.512198	+	0.858867i
$3$	−2.66146	+	4.46280i	−0.512198	+	0.858867i
$4$	1.69777	+	2.94063i	0.212222	+	0.367579i
$5$		0			0
$5$		0			0
$6$	5.43782	+	9.73398i	0.369997	+	0.662313i
$7$	11.6282	−	20.1406i	0.627864	−	1.08749i	−0.360115	−	0.932908i	$-0.617263\pi$
$7$	11.6282	−	20.1406i	0.627864	−	1.08749i	0.987980	−	0.154585i	$-0.0494040\pi$
$8$	24.4526			1.08066
$9$	−12.8333	−	23.7552i	−0.475306	−	0.879821i
$10$		0			0
$11$	−6.24976	+	10.8249i	−0.171307	+	0.296712i	−0.938877	−	0.344253i	$-0.888132\pi$
$11$	−6.24976	+	10.8249i	−0.171307	+	0.296712i	0.767570	+	0.640965i	$0.221466\pi$
$12$	−17.6420	−	0.249540i	−0.424401	−	0.00600299i
$13$	25.3078	+	43.8344i	0.539933	+	0.935191i	0.998907	+	0.0467417i	$0.0148838\pi$
$13$	25.3078	+	43.8344i	0.539933	+	0.935191i	−0.458974	+	0.888450i	$0.651783\pi$
$14$	−24.9518	−	43.2178i	−0.476332	−	0.825031i
$15$		0			0
$16$	12.6529	−	21.9155i	0.197702	−	0.342430i
$17$	63.6794			0.908502			0.454251	−	0.890874i	$-0.349907\pi$
$17$	63.6794			0.908502			0.454251	+	0.890874i	$0.349907\pi$
$18$	−57.9134	−	1.63865i	−0.758351	−	0.0214575i
$19$	5.41153			0.0653416			0.0326708	−	0.999466i	$-0.489599\pi$
$19$	5.41153			0.0653416			0.0326708	+	0.999466i	$0.489599\pi$
$20$		0			0
$21$	58.9358	+	105.498i	0.612421	+	1.09626i
$22$	13.4107	+	23.2281i	0.129963	+	0.225102i
$23$	44.2335	+	76.6146i	0.401014	+	0.694576i	0.993849	−	0.110748i	$-0.0353247\pi$
$23$	44.2335	+	76.6146i	0.401014	+	0.694576i	−0.592835	+	0.805324i	$0.701991\pi$
$24$	−65.0795	+	109.127i	−0.553512	+	0.928144i
$25$		0			0
$26$	108.611			0.819245
$27$	140.170	+	5.95112i	0.999100	+	0.0424183i
$28$	78.9683			0.532986
$29$	−72.2845	+	125.200i	−0.462858	+	0.801694i	−0.999102	−	0.0423690i	$-0.986510\pi$
$29$	−72.2845	+	125.200i	−0.462858	+	0.801694i	0.536244	+	0.844063i	$0.319843\pi$
$30$		0			0
$31$	138.980	+	240.720i	0.805208	+	1.39466i	0.916150	+	0.400835i	$0.131280\pi$
$31$	138.980	+	240.720i	0.805208	+	1.39466i	−0.110942	+	0.993827i	$0.535387\pi$
$32$	70.6596	+	122.386i	0.390343	+	0.676093i
$33$	−31.6759	−	56.7015i	−0.167093	−	0.299105i
$34$	68.3216	−	118.337i	0.344619	−	0.596898i
$35$		0			0
$36$	48.0672	−	78.0687i	0.222533	−	0.361429i
$37$	243.269			1.08090			0.540448	−	0.841378i	$-0.318255\pi$
$37$	243.269			1.08090			0.540448	+	0.841378i	$0.318255\pi$
$38$	5.80603	−	10.0563i	0.0247858	−	0.0429303i
$39$	−262.980	−	3.71976i	−1.07976	−	0.0152728i
$40$		0			0
$41$	−234.286	−	405.796i	−0.892424	−	1.54572i	−0.836961	−	0.547263i	$-0.815670\pi$
$41$	−234.286	−	405.796i	−0.892424	−	1.54572i	−0.0554628	−	0.998461i	$-0.517663\pi$
$42$	259.281	+	3.66743i	0.952569	+	0.0134737i
$43$	249.205	−	431.637i	0.883802	−	1.53079i	0.0367211	−	0.999326i	$-0.488309\pi$
$43$	249.205	−	431.637i	0.883802	−	1.53079i	0.847081	−	0.531464i	$-0.178358\pi$
$44$	−42.4427			−0.145420
$45$		0			0
$46$	189.832			0.608462
$47$	−226.262	+	391.897i	−0.702206	+	1.21626i	0.265484	+	0.964115i	$0.414468\pi$
$47$	−226.262	+	391.897i	−0.702206	+	1.21626i	−0.967690	+	0.252142i	$0.918865\pi$
$48$	64.1294	+	114.795i	0.192839	+	0.345192i
$49$	−98.9304	−	171.352i	−0.288427	−	0.499570i
$50$		0			0
$51$	−169.480	+	284.189i	−0.465333	+	0.780282i
$52$	−85.9339	+	148.842i	−0.229171	+	0.396936i
$53$	−223.885			−0.580244			−0.290122	−	0.956990i	$-0.593696\pi$
$53$	−223.885			−0.580244			−0.290122	+	0.956990i	$0.593696\pi$
$54$	161.447	−	254.095i	0.406855	−	0.640332i
$55$		0			0
$56$	284.339	−	492.490i	0.678508	−	1.17521i
$57$	−14.4026	+	24.1506i	−0.0334679	+	0.0561197i
$58$	155.108	+	268.655i	0.351150	+	0.608209i
$59$	−57.9657	−	100.400i	−0.127907	−	0.221541i	0.794959	−	0.606663i	$-0.207492\pi$
$59$	−57.9657	−	100.400i	−0.127907	−	0.221541i	−0.922865	+	0.385123i	$0.874159\pi$
$60$		0			0
$61$	−41.3965	+	71.7008i	−0.0868898	+	0.150497i	−0.906195	−	0.422860i	$-0.861026\pi$
$61$	−41.3965	+	71.7008i	−0.0868898	+	0.150497i	0.819305	+	0.573358i	$0.194359\pi$
$62$	596.444			1.22175
$63$	−627.672	−	17.7599i	−1.25523	−	0.0355165i
$64$	505.689			0.987675
$65$		0			0
$66$	−139.354	−	1.97112i	−0.259899	−	0.00367617i
$67$	−405.064	−	701.592i	−0.738604	−	1.27930i	−0.953124	−	0.302580i	$-0.902152\pi$
$67$	−405.064	−	701.592i	−0.738604	−	1.27930i	0.214520	−	0.976720i	$-0.431181\pi$
$68$	108.113	+	187.258i	0.192804	+	0.333946i
$69$	−459.642	−	6.50146i	−0.801947	−	0.0113432i
$70$		0			0
$71$	−134.171			−0.224270			−0.112135	−	0.993693i	$-0.535769\pi$
$71$	−134.171			−0.224270			−0.112135	+	0.993693i	$0.535769\pi$
$72$	−313.806	−	580.874i	−0.513644	−	0.950787i
$73$	707.508			1.13435			0.567175	−	0.823597i	$-0.308036\pi$
$73$	707.508			1.13435			0.567175	+	0.823597i	$0.308036\pi$
$74$	261.003	−	452.070i	0.410013	−	0.710163i
$75$		0			0
$76$	9.18755	+	15.9133i	0.0138669	+	0.0240182i
$77$	145.347	+	251.748i	0.215115	+	0.372589i
$78$	−289.064	+	484.710i	−0.419616	+	0.703623i
$79$	−208.821	+	361.689i	−0.297396	+	0.515104i	−0.975539	−	0.219825i	$-0.929451\pi$
$79$	−208.821	+	361.689i	−0.297396	+	0.515104i	0.678144	+	0.734929i	$0.262785\pi$
$80$		0			0
$81$	−399.615	+	609.712i	−0.548169	+	0.836368i
$82$	−1005.46			−1.35408
$83$	461.443	−	799.243i	0.610240	−	1.05697i	−0.380959	−	0.924592i	$-0.624406\pi$
$83$	461.443	−	799.243i	0.610240	−	1.05697i	0.991200	−	0.132376i	$-0.0422605\pi$
$84$	−210.171	+	352.420i	−0.272994	+	0.457764i
$85$		0			0
$86$	−534.745	−	926.205i	−0.670500	−	1.16134i
$87$	−366.363	−	655.808i	−0.451474	−	0.808160i
$88$	−152.823	+	264.696i	−0.185124	+	0.320645i
$89$	114.544			0.136423			0.0682116	−	0.997671i	$-0.478271\pi$
$89$	114.544			0.136423			0.0682116	+	0.997671i	$0.478271\pi$
$90$		0			0
$91$	1177.14			1.35602
$92$	−150.197	+	260.149i	−0.170208	+	0.294808i
$93$	−1444.17	−	20.4273i	−1.61026	−	0.0227765i
$94$	485.513	+	840.932i	0.532732	+	0.922719i
$95$		0			0
$96$	−734.242	−	10.3856i	−0.780607	−	0.0110414i
$97$	−180.777	+	313.115i	−0.189228	+	0.327753i	−0.944993	−	0.327090i	$-0.893932\pi$
$97$	−180.777	+	313.115i	−0.189228	+	0.327753i	0.755765	+	0.654843i	$0.227265\pi$
$98$	−424.569			−0.437633
$99$	337.352	+	9.54534i	0.342476	+	0.00969033i
$100$		0			0
$101$	−144.611	+	250.473i	−0.142469	+	0.246763i	−0.928426	−	0.371518i	$-0.878837\pi$
$101$	−144.611	+	250.473i	−0.142469	+	0.246763i	0.785957	+	0.618281i	$0.212171\pi$
$102$	346.277	+	619.854i	0.336143	+	0.601713i
$103$	241.404	+	418.124i	0.230934	+	0.399990i	0.958083	−	0.286490i	$-0.0924884\pi$
$103$	241.404	+	418.124i	0.230934	+	0.399990i	−0.727149	+	0.686480i	$0.759155\pi$
$104$	618.841	+	1071.86i	0.583484	+	1.01062i
$105$		0			0
$106$	−240.206	+	416.049i	−0.220102	+	0.381229i
$107$	−1796.65			−1.62326			−0.811628	−	0.584175i	$-0.801418\pi$
$107$	−1796.65			−1.62326			−0.811628	+	0.584175i	$0.801418\pi$
$108$	220.477	+	422.291i	0.196439	+	0.376250i
$109$	1507.20			1.32443			0.662216	−	0.749313i	$-0.269616\pi$
$109$	1507.20			1.32443			0.662216	+	0.749313i	$0.269616\pi$
$110$		0			0
$111$	−647.450	+	1085.66i	−0.553633	+	0.928346i
$112$	−294.262	−	509.677i	−0.248260	−	0.429999i
$113$	−1075.02	−	1861.98i	−0.894948	−	1.55010i	−0.833869	−	0.551962i	$-0.813879\pi$
$113$	−1075.02	−	1861.98i	−0.894948	−	1.55010i	−0.0610790	−	0.998133i	$-0.519454\pi$
$114$	29.4269	+	52.6757i	0.0241762	+	0.0432766i
$115$		0			0
$116$	−490.891			−0.392914
$117$	716.512	−	1163.73i	0.566168	−	0.919546i
$118$	−248.765			−0.194074
$119$	740.478	−	1282.54i	0.570416	−	0.987989i
$120$		0			0
$121$	587.381	+	1017.37i	0.441308	+	0.764368i
$122$	88.8285	+	153.855i	0.0659193	+	0.114176i
$123$	2434.53	+	34.4355i	1.78467	+	0.0252435i
$124$	−471.912	+	817.375i	−0.341765	+	0.591955i
$125$		0			0
$126$	−706.432	+	1147.36i	−0.499476	+	0.811229i
$127$	−1288.35			−0.900180			−0.450090	−	0.892983i	$-0.648608\pi$
$127$	−1288.35			−0.900180			−0.450090	+	0.892983i	$0.648608\pi$
$128$	−22.7226	+	39.3567i	−0.0156907	+	0.0271772i
$129$	1263.06	+	2260.94i	0.862063	+	1.54314i
$130$		0			0
$131$	−851.472	−	1474.79i	−0.567889	−	0.983612i	−0.996774	−	0.0802534i	$-0.974427\pi$
$131$	−851.472	−	1474.79i	−0.567889	−	0.983612i	0.428886	−	0.903359i	$-0.358906\pi$
$132$	112.960	−	189.414i	0.0744839	−	0.124896i
$133$	62.9264	−	108.992i	0.0410256	−	0.0710585i
$134$	−1738.37			−1.12069
$135$		0			0
$136$	1557.12			0.981782
$137$	110.241	−	190.944i	0.0687486	−	0.119076i	−0.829602	−	0.558355i	$-0.811433\pi$
$137$	110.241	−	190.944i	0.0687486	−	0.119076i	0.898351	+	0.439279i	$0.144766\pi$
$138$	−505.231	+	847.184i	−0.311653	+	0.522588i
$139$	−1512.99	−	2620.58i	−0.923241	−	1.59910i	−0.794366	−	0.607440i	$-0.792197\pi$
$139$	−1512.99	−	2620.58i	−0.923241	−	1.59910i	−0.128875	−	0.991661i	$-0.541137\pi$
$140$		0			0
$141$	−1146.77	−	2052.78i	−0.684934	−	1.22607i
$142$	−143.952	+	249.332i	−0.0850716	+	0.147348i
$143$	−632.671			−0.369976
$144$	−682.985	−	19.3250i	−0.395246	−	0.0111834i
$145$		0			0
$146$	759.085	−	1314.77i	0.430290	−	0.745284i
$147$	1028.01	+	14.5408i	0.576796	+	0.00815856i
$148$	413.015	+	715.363i	0.229390	+	0.397314i
$149$	−964.264	−	1670.15i	−0.530172	−	0.918284i	−0.999380	−	0.0351969i	$-0.988794\pi$
$149$	−964.264	−	1670.15i	−0.530172	−	0.918284i	0.469209	−	0.883087i	$-0.344539\pi$
$150$		0			0
$151$	546.916	−	947.285i	0.294751	−	0.510523i	−0.680176	−	0.733049i	$-0.738097\pi$
$151$	546.916	−	947.285i	0.294751	−	0.510523i	0.974927	+	0.222526i	$0.0714301\pi$
$152$	132.326			0.0706121
$153$	−817.214	−	1512.72i	−0.431816	−	0.799319i
$154$	623.771			0.326395
$155$		0			0
$156$	−435.543	−	779.643i	−0.223534	−	0.400137i
$157$	−287.034	−	497.157i	−0.145910	−	0.252723i	0.783802	−	0.621010i	$-0.213278\pi$
$157$	−287.034	−	497.157i	−0.145910	−	0.252723i	−0.929712	+	0.368288i	$0.879944\pi$
$158$	448.089	+	776.113i	0.225620	+	0.390786i
$159$	595.861	−	999.154i	0.297200	−	0.498353i
$160$		0			0
$161$	2057.42			1.00713
$162$	704.291	+	1396.77i	0.341570	+	0.677412i
$163$	−2279.16			−1.09520			−0.547601	−	0.836740i	$-0.684459\pi$
$163$	−2279.16			−1.09520			−0.547601	+	0.836740i	$0.684459\pi$
$164$	795.530	−	1377.90i	0.378783	−	0.656072i
$165$		0			0
$166$	−990.164	−	1715.01i	−0.462962	−	0.801873i
$167$	1567.06	+	2714.23i	0.726125	+	1.25769i	0.958509	+	0.285061i	$0.0920140\pi$
$167$	1567.06	+	2714.23i	0.726125	+	1.25769i	−0.232384	+	0.972624i	$0.574653\pi$
$168$	1441.13	+	2579.69i	0.661819	+	1.18469i
$169$	−182.472	+	316.051i	−0.0830552	+	0.143856i
$170$		0			0
$171$	−69.4475	−	128.552i	−0.0310572	−	0.0574889i
$172$	1692.38			0.750248
$173$	2091.71	−	3622.95i	0.919249	−	1.59219i	0.118690	−	0.992931i	$-0.462130\pi$
$173$	2091.71	−	3622.95i	0.919249	−	1.59219i	0.800559	−	0.599254i	$-0.204536\pi$
$174$	−1611.77	−	22.7979i	−0.702229	−	0.00993276i
$175$		0			0
$176$	158.156	+	273.934i	0.0677354	+	0.117321i
$177$	602.337	+	8.51982i	0.255788	+	0.00361802i
$178$	122.894	−	212.859i	0.0517490	−	0.0896319i
$179$	−2760.46			−1.15266			−0.576331	−	0.817216i	$-0.695516\pi$
$179$	−2760.46			−1.15266			−0.576331	+	0.817216i	$0.695516\pi$
$180$		0			0
$181$	2563.75			1.05283			0.526414	−	0.850229i	$-0.323536\pi$
$181$	2563.75			1.05283			0.526414	+	0.850229i	$0.323536\pi$
$182$	1262.95	−	2187.50i	0.514375	−	0.890923i
$183$	−209.812	−	375.573i	−0.0847525	−	0.151711i
$184$	1081.62	+	1873.42i	0.433360	+	0.750601i
$185$		0			0
$186$	−1587.41	+	2661.81i	−0.625778	+	1.04932i
$187$	−397.981	+	689.323i	−0.155632	+	0.269563i
$188$	−1536.57			−0.596094
$189$	1749.78	−	2753.91i	0.673429	−	1.05988i
$190$		0			0
$191$	−2180.95	+	3777.51i	−0.826219	+	1.43105i	0.0747649	+	0.997201i	$0.476179\pi$
$191$	−2180.95	+	3777.51i	−0.826219	+	1.43105i	−0.900984	+	0.433852i	$0.857154\pi$
$192$	−1345.87	+	2256.79i	−0.505885	+	0.848281i
$193$	1384.57	+	2398.15i	0.516393	+	0.894419i	0.999819	+	0.0190333i	$0.00605887\pi$
$193$	1384.57	+	2398.15i	0.516393	+	0.894419i	−0.483426	+	0.875385i	$0.660608\pi$
$194$	387.911	+	671.882i	0.143559	+	0.248651i
$195$		0			0
$196$	335.923	−	581.835i	0.122421	−	0.212039i
$197$	547.622			0.198053			0.0990264	−	0.995085i	$-0.468427\pi$
$197$	547.622			0.198053			0.0990264	+	0.995085i	$0.468427\pi$
$198$	379.683	−	616.665i	0.136277	−	0.221336i
$199$	−2077.15			−0.739927			−0.369963	−	0.929046i	$-0.620630\pi$
$199$	−2077.15			−0.739927			−0.369963	+	0.929046i	$0.620630\pi$
$200$		0			0
$201$	4209.13	+	59.5365i	1.47706	+	0.0208925i
$202$	310.306	+	537.466i	0.108084	+	0.187208i
$203$	1681.08	+	2911.71i	0.581224	+	1.00671i
$204$	−1123.43	−	15.8905i	−0.385569	−	0.00545373i
$205$		0			0
$206$	1036.01			0.350399
$207$	1252.33	−	2033.99i	0.420498	−	0.682956i
$208$	1280.87			0.426984
$209$	−33.8208	+	58.5793i	−0.0111934	+	0.0193876i
$210$		0			0
$211$	305.993	+	529.995i	0.0998360	+	0.172921i	0.911617	−	0.411041i	$-0.134835\pi$
$211$	305.993	+	529.995i	0.0998360	+	0.172921i	−0.811781	+	0.583962i	$0.801502\pi$
$212$	−380.106	−	658.363i	−0.123140	−	0.213286i
$213$	357.090	−	598.778i	0.114871	−	0.192618i
$214$	−1927.62	+	3338.74i	−0.615745	+	1.06650i
$215$		0			0
$216$	3427.51	+	145.520i	1.07969	+	0.0458398i
$217$	6464.33			2.02225
$218$	1617.07	−	2800.85i	0.502393	−	0.870171i
$219$	−1883.01	+	3157.47i	−0.581012	+	0.974256i
$220$		0			0
$221$	1611.59	+	2791.35i	0.490530	+	0.849623i
$222$	1322.85	+	2367.97i	0.399928	+	0.715891i
$223$	−89.6685	+	155.310i	−0.0269267	+	0.0466384i	−0.879175	−	0.476500i	$-0.841905\pi$
$223$	−89.6685	+	155.310i	−0.0269267	+	0.0466384i	0.852248	+	0.523138i	$0.175239\pi$
$224$	3286.58			0.980328
$225$		0			0
$226$	−4613.54			−1.35791
$227$	106.893	−	185.144i	0.0312544	−	0.0541342i	−0.849975	−	0.526823i	$-0.823383\pi$
$227$	106.893	−	185.144i	0.0312544	−	0.0541342i	0.881230	+	0.472689i	$0.156716\pi$
$228$	−95.4703	−	1.35039i	−0.0277310	−	0.000392245i
$229$	−1452.45	−	2515.72i	−0.419130	−	0.725955i	0.576722	−	0.816941i	$-0.304332\pi$
$229$	−1452.45	−	2515.72i	−0.419130	−	0.725955i	−0.995852	+	0.0909854i	$0.970998\pi$
$230$		0			0
$231$	−1510.34	−	21.3632i	−0.430186	−	0.00608482i
$232$	−1767.54	+	3061.47i	−0.500193	+	0.866359i
$233$	−2683.70			−0.754570			−0.377285	−	0.926097i	$-0.623142\pi$
$233$	−2683.70			−0.754570			−0.377285	+	0.926097i	$0.623142\pi$
$234$	−1393.83	−	2580.07i	−0.389392	−	0.720789i
$235$		0			0
$236$	196.825	−	340.911i	0.0542891	−	0.0940315i
$237$	−1058.38	−	1894.55i	−0.290081	−	0.519259i
$238$	−1588.92	−	2752.08i	−0.432748	−	0.749542i
$239$	1999.45	+	3463.14i	0.541144	+	0.937289i	0.998839	+	0.0481794i	$0.0153419\pi$
$239$	1999.45	+	3463.14i	0.541144	+	0.937289i	−0.457695	+	0.889109i	$0.651325\pi$
$240$		0			0
$241$	−1221.72	+	2116.09i	−0.326548	+	0.565598i	−0.981824	−	0.189791i	$-0.939219\pi$
$241$	−1221.72	+	2116.09i	−0.326548	+	0.565598i	0.655276	+	0.755389i	$0.272552\pi$
$242$	2520.80			0.669601
$243$	−1657.47	−	3406.13i	−0.437557	−	0.899190i
$244$	−281.127			−0.0737596
$245$		0			0
$246$	2676.00	−	4487.18i	0.693559	−	1.16298i
$247$	136.954	+	237.211i	0.0352801	+	0.0611069i
$248$	3398.40	+	5886.21i	0.870157	+	1.50716i
$249$	2338.75	+	4186.48i	0.595230	+	1.06549i
$250$		0			0
$251$	665.021			0.167234			0.0836170	−	0.996498i	$-0.473353\pi$
$251$	665.021			0.167234			0.0836170	+	0.996498i	$0.473353\pi$
$252$	−1013.42	−	1875.90i	−0.253331	−	0.468932i
$253$	−1105.79			−0.274785
$254$	−1382.27	+	2394.17i	−0.341463	+	0.591431i
$255$		0			0
$256$	2071.52	+	3587.97i	0.505741	+	0.875969i
$257$	−1000.94	−	1733.67i	−0.242944	−	0.420792i	0.718607	−	0.695416i	$-0.244780\pi$
$257$	−1000.94	−	1733.67i	−0.242944	−	0.420792i	−0.961552	+	0.274624i	$0.911447\pi$
$258$	5556.68	+	78.5971i	1.34087	+	0.0189660i
$259$	2828.78	−	4899.59i	0.678656	−	1.17547i
$260$		0			0
$261$	3901.80	+	110.401i	0.925347	+	0.0261826i
$262$	−3654.17			−0.861663
$263$	−2190.68	+	3794.37i	−0.513624	+	0.889623i	0.486251	+	0.873819i	$0.338364\pi$
$263$	−2190.68	+	3794.37i	−0.513624	+	0.889623i	−0.999875	+	0.0158039i	$0.994969\pi$
$264$	−774.557	−	1386.50i	−0.180571	−	0.323231i
$265$		0			0
$266$	−135.027	−	233.874i	−0.0311243	−	0.0539088i
$267$	−304.855	+	511.188i	−0.0698757	+	0.117169i
$268$	1375.41	−	2382.29i	0.313496	−	0.542990i
$269$	−99.0813			−0.0224576			−0.0112288	−	0.999937i	$-0.503574\pi$
$269$	−99.0813			−0.0224576			−0.0112288	+	0.999937i	$0.503574\pi$
$270$		0			0
$271$	−7951.92			−1.78245			−0.891227	−	0.453558i	$-0.850155\pi$
$271$	−7951.92			−1.78245			−0.891227	+	0.453558i	$0.850155\pi$
$272$	805.732	−	1395.57i	0.179613	−	0.311098i
$273$	−3132.91	+	5253.34i	−0.694550	+	1.16464i
$274$	−236.556	−	409.727i	−0.0521564	−	0.0903375i
$275$		0			0
$276$	−761.249	−	1362.67i	−0.166021	−	0.297186i
$277$	2882.82	−	4993.20i	0.625314	−	1.08308i	−0.363166	−	0.931725i	$-0.618304\pi$
$277$	2882.82	−	4993.20i	0.625314	−	1.08308i	0.988480	−	0.151352i	$-0.0483625\pi$
$278$	−6493.16			−1.40084
$279$	3934.77	−	6390.70i	0.844332	−	1.37133i
$280$		0			0
$281$	−2789.94	+	4832.31i	−0.592290	+	1.02588i	0.401633	+	0.915801i	$0.368443\pi$
$281$	−2789.94	+	4832.31i	−0.592290	+	1.02588i	−0.993923	+	0.110076i	$0.964890\pi$
$282$	−5045.09	−	71.3609i	−1.06536	−	0.0150691i
$283$	−377.022	−	653.022i	−0.0791931	−	0.137167i	0.823709	−	0.567013i	$-0.191901\pi$
$283$	−377.022	−	653.022i	−0.0791931	−	0.137167i	−0.902902	+	0.429846i	$0.858568\pi$
$284$	−227.792	−	394.547i	−0.0475949	−	0.0824368i
$285$		0			0
$286$	−678.793	+	1175.70i	−0.140342	+	0.243080i
$287$	−10897.3			−2.24128
$288$	2000.51	−	3249.14i	0.409309	−	0.664782i
$289$	−857.930			−0.174625
$290$		0			0
$291$	−916.240	−	1640.12i	−0.184574	−	0.330396i
$292$	1201.19	+	2080.52i	0.240734	+	0.416963i
$293$	4834.85	+	8374.21i	0.964010	+	1.66971i	0.712251	+	0.701925i	$0.247676\pi$
$293$	4834.85	+	8374.21i	0.964010	+	1.66971i	0.251759	+	0.967790i	$0.418991\pi$
$294$	1129.97	−	1894.77i	0.224155	−	0.375868i
$295$		0			0
$296$	5948.54			1.16808
$297$	−940.448	+	1480.13i	−0.183738	+	0.289178i
$298$	−4138.23			−0.804434
$299$	−2238.91	+	3877.90i	−0.433041	+	0.750049i
$300$		0			0
$301$	−5795.63	−	10038.3i	−1.10981	−	1.92226i
$302$	−1173.57	−	2032.68i	−0.223614	−	0.387311i
$303$	−732.938	−	1312.00i	−0.138964	−	0.248753i
$304$	68.4717	−	118.597i	0.0129182	−	0.0223749i
$305$		0			0
$306$	−3687.89	−	104.349i	−0.688963	−	0.0194941i
$307$	1601.00			0.297635			0.148817	−	0.988865i	$-0.452453\pi$
$307$	1601.00			0.297635			0.148817	+	0.988865i	$0.452453\pi$
$308$	−493.533	+	854.824i	−0.0913040	+	0.158143i
$309$	−2508.49	−	35.4817i	−0.461822	−	0.00653230i
$310$		0			0
$311$	−2980.08	−	5161.64i	−0.543359	−	0.941125i	−0.998708	−	0.0508122i	$-0.983819\pi$
$311$	−2980.08	−	5161.64i	−0.543359	−	0.941125i	0.455349	−	0.890313i	$-0.349514\pi$
$312$	−6430.54	−	90.9576i	−1.16685	−	0.0165047i
$313$	1835.78	−	3179.67i	0.331517	−	0.574204i	−0.651293	−	0.758826i	$-0.725773\pi$
$313$	1835.78	−	3179.67i	0.331517	−	0.574204i	0.982809	+	0.184623i	$0.0591064\pi$
$314$	−1231.83			−0.221390
$315$		0			0
$316$	−1418.13			−0.252455
$317$	1171.21	−	2028.59i	0.207512	−	0.359422i	−0.743418	−	0.668827i	$-0.766797\pi$
$317$	1171.21	−	2028.59i	0.207512	−	0.359422i	0.950930	+	0.309405i	$0.100130\pi$
$318$	−1217.45	−	2179.29i	−0.214689	−	0.384303i
$319$	−903.521	−	1564.94i	−0.158581	−	0.274671i
$320$		0			0
$321$	4781.70	−	8018.08i	0.831429	−	1.39416i
$322$	2207.41	−	3823.34i	0.382031	−	0.661697i
$323$	344.603			0.0593629
$324$	−2471.39	−	139.968i	−0.423764	−	0.0240000i
$325$		0			0
$326$	−2445.31	+	4235.41i	−0.415440	+	0.719563i
$327$	−4011.34	+	6726.32i	−0.678372	+	1.13751i
$328$	−5728.90	−	9922.74i	−0.964407	−	1.67040i
$329$	5262.04	+	9114.12i	0.881780	+	1.52729i
$330$		0			0
$331$	672.393	−	1164.62i	0.111656	−	0.193394i	−0.804782	−	0.593570i	$-0.797718\pi$
$331$	672.393	−	1164.62i	0.111656	−	0.193394i	0.916438	+	0.400177i	$0.131051\pi$
$332$	3133.70			0.518025
$333$	−3121.93	−	5778.89i	−0.513756	−	0.950994i
$334$	6725.20			1.10176
$335$		0			0
$336$	3057.75	+	43.2508i	0.496471	+	0.00702239i
$337$	−968.133	−	1676.86i	−0.156491	−	0.271051i	0.777110	−	0.629365i	$-0.216685\pi$
$337$	−968.133	−	1676.86i	−0.156491	−	0.271051i	−0.933601	+	0.358314i	$0.883352\pi$
$338$	391.549	+	678.183i	0.0630102	+	0.109137i
$339$	11170.8	+	158.007i	1.78972	+	0.0253149i
$340$		0			0
$341$	−3474.35			−0.551750
$342$	−313.400	−	8.86762i	−0.0495519	−	0.00140206i
$343$	3375.42			0.531357
$344$	6093.71	−	10554.6i	0.955090	−	1.65426i
$345$		0			0
$346$	−4488.40	−	7774.13i	−0.697392	−	1.20792i
$347$	1895.80	+	3283.61i	0.293290	+	0.507993i	0.974586	−	0.224015i	$-0.0719165\pi$
$347$	1895.80	+	3283.61i	0.293290	+	0.507993i	−0.681296	+	0.732008i	$0.738583\pi$
$348$	1306.49	−	2190.75i	0.201250	−	0.337461i
$349$	−451.754	+	782.461i	−0.0692890	+	0.120012i	−0.898589	−	0.438792i	$-0.855406\pi$
$349$	−451.754	+	782.461i	−0.0692890	+	0.120012i	0.829300	+	0.558804i	$0.188740\pi$
$350$		0			0
$351$	3286.53	+	6294.88i	0.499778	+	0.957253i
$352$	−1766.42			−0.267473
$353$	4041.75	−	7000.51i	0.609406	−	1.05552i	−0.381932	−	0.924190i	$-0.624741\pi$
$353$	4041.75	−	7000.51i	0.609406	−	1.05552i	0.991338	−	0.131332i	$-0.0419255\pi$
$354$	662.079	−	1110.19i	0.0994043	−	0.166684i
$355$		0			0
$356$	194.470	+	336.832i	0.0289520	+	0.0501463i
$357$	3752.99	+	6718.05i	0.556385	+	0.995958i
$358$	−2961.70	+	5129.81i	−0.437236	+	0.757316i
$359$	−3688.92			−0.542322			−0.271161	−	0.962534i	$-0.587408\pi$
$359$	−3688.92			−0.542322			−0.271161	+	0.962534i	$0.587408\pi$
$360$		0			0
$361$	−6829.72			−0.995730
$362$	2750.64	−	4764.25i	0.399366	−	0.691722i
$363$	−6103.63	−	86.3336i	−0.882528	−	0.0124830i
$364$	1998.52	+	3461.53i	0.287777	+	0.498444i
$365$		0			0
$366$	−923.040	−	13.0561i	−0.131825	−	0.00186462i
$367$	−1518.23	+	2629.65i	−0.215943	+	0.374024i	−0.953564	−	0.301191i	$-0.902616\pi$
$367$	−1518.23	+	2629.65i	−0.215943	+	0.374024i	0.737621	+	0.675215i	$0.235949\pi$
$368$	2238.73			0.317125
$369$	−6633.09	+	10773.2i	−0.935785	+	1.51986i
$370$		0			0
$371$	−2603.38	+	4509.18i	−0.364315	+	0.631011i
$372$	−2391.81	−	4281.46i	−0.333359	−	0.596729i
$373$	2490.02	+	4312.84i	0.345653	+	0.598688i	0.985472	−	0.169837i	$-0.0543242\pi$
$373$	2490.02	+	4312.84i	0.345653	+	0.598688i	−0.639819	+	0.768525i	$0.720991\pi$
$374$	853.987	+	1479.15i	0.118071	+	0.204505i
$375$		0			0
$376$	−5532.68	+	9582.89i	−0.758846	+	1.31436i
$377$	−7317.45			−0.999650
$378$	−3240.29	−	6206.32i	−0.440907	−	0.844494i
$379$	−6027.99			−0.816984			−0.408492	−	0.912762i	$-0.633945\pi$
$379$	−6027.99			−0.816984			−0.408492	+	0.912762i	$0.633945\pi$
$380$		0			0
$381$	3428.90	−	5749.67i	0.461071	−	0.773135i
$382$	4679.88	+	8105.78i	0.626815	+	1.08568i
$383$	1892.57	+	3278.03i	0.252496	+	0.437335i	0.964212	−	0.265131i	$-0.0854153\pi$
$383$	1892.57	+	3278.03i	0.252496	+	0.437335i	−0.711717	+	0.702467i	$0.752082\pi$
$384$	−115.166	−	206.153i	−0.0153048	−	0.0273964i
$385$		0			0
$386$	5942.03			0.783527
$387$	−13451.7	−	380.615i	−1.76690	−	0.0499942i
$388$	−1227.67			−0.160633
$389$	−2871.46	+	4973.51i	−0.374264	+	0.648244i	−0.990217	−	0.139539i	$-0.955438\pi$
$389$	−2871.46	+	4973.51i	−0.374264	+	0.648244i	0.615953	+	0.787783i	$0.288771\pi$
$390$		0			0
$391$	2816.76	+	4878.77i	0.364322	+	0.631024i
$392$	−2419.10	−	4190.00i	−0.311691	−	0.539865i
$393$	8847.87	+	125.150i	1.13566	+	0.0160635i
$394$	587.543	−	1017.65i	0.0751269	−	0.130124i
$395$		0			0
$396$	544.678	+	1008.23i	0.0691189	+	0.127944i
$397$	−899.327			−0.113693			−0.0568463	−	0.998383i	$-0.518104\pi$
$397$	−899.327			−0.113693			−0.0568463	+	0.998383i	$0.518104\pi$
$398$	−2228.58	+	3860.01i	−0.280674	+	0.486142i
$399$	318.933	+	570.905i	0.0400165	+	0.0716316i
$400$		0			0
$401$	2838.95	+	4917.20i	0.353542	+	0.612352i	0.986867	−	0.161533i	$-0.0516439\pi$
$401$	2838.95	+	4917.20i	0.353542	+	0.612352i	−0.633326	+	0.773886i	$0.718311\pi$
$402$	4626.61	−	7758.02i	0.574016	−	0.962524i
$403$	−7034.54	+	12184.2i	−0.869517	+	1.50605i
$404$	−982.067			−0.120940
$405$		0			0
$406$	7214.51			0.881897
$407$	−1520.37	+	2633.36i	−0.185165	+	0.320714i
$408$	−4144.23	+	6949.14i	−0.502867	+	0.843220i
$409$	1815.75	+	3144.97i	0.219518	+	0.380217i	0.954661	−	0.297696i	$-0.0962180\pi$
$409$	1815.75	+	3144.97i	0.219518	+	0.380217i	−0.735142	+	0.677913i	$0.762885\pi$
$410$		0			0
$411$	558.741	+	1000.17i	0.0670576	+	0.120036i
$412$	−819.699	+	1419.76i	−0.0980186	+	0.169773i
$413$	−2696.15			−0.321232
$414$	−2436.16	−	4509.49i	−0.289205	−	0.535337i
$415$		0			0
$416$	−3576.48	+	6194.64i	−0.421518	+	0.730090i
$417$	15721.9	+	222.381i	1.84630	+	0.0261152i
$418$	72.5725	+	125.699i	0.00849196	+	0.0147085i
$419$	1459.14	+	2527.31i	0.170128	+	0.294671i	0.938465	−	0.345376i	$-0.112248\pi$
$419$	1459.14	+	2527.31i	0.170128	+	0.294671i	−0.768336	+	0.640046i	$0.778915\pi$
$420$		0			0
$421$	7154.67	−	12392.3i	0.828260	−	1.43459i	−0.0711420	−	0.997466i	$-0.522664\pi$
$421$	7154.67	−	12392.3i	0.828260	−	1.43459i	0.899402	−	0.437122i	$-0.144002\pi$
$422$	1313.20			0.151482
$423$	12213.3	+	345.573i	1.40385	+	0.0397218i
$424$	−5474.56			−0.627047
$425$		0			0
$426$	−729.597	−	1306.02i	−0.0829791	−	0.148537i
$427$	962.733	+	1667.50i	0.109110	+	0.188984i
$428$	−3050.30	−	5283.27i	−0.344490	−	0.596674i
$429$	1683.83	−	2823.49i	0.189501	−	0.317761i
$430$		0			0
$431$	−3222.12			−0.360102			−0.180051	−	0.983657i	$-0.557626\pi$
$431$	−3222.12			−0.360102			−0.180051	+	0.983657i	$0.557626\pi$
$432$	1903.98	−	2996.60i	0.212050	−	0.333736i
$433$	−997.716			−0.110732			−0.0553662	−	0.998466i	$-0.517633\pi$
$433$	−997.716			−0.110732			−0.0553662	+	0.998466i	$0.517633\pi$
$434$	6935.58	−	12012.8i	0.767093	−	1.32864i
$435$		0			0
$436$	2558.88	+	4432.10i	0.281073	+	0.486833i
$437$	239.371	+	414.602i	0.0262029	+	0.0453847i
$438$	3847.30	+	6886.87i	0.419706	+	0.751295i
$439$	4468.16	−	7739.08i	0.485771	−	0.841380i	−0.514095	−	0.857733i	$-0.671872\pi$
$439$	4468.16	−	7739.08i	0.485771	−	0.841380i	0.999866	+	0.0163529i	$0.00520553\pi$
$440$		0			0
$441$	−2800.91	+	4549.12i	−0.302441	+	0.491212i
$442$	6916.29			0.744286
$443$	3346.27	−	5795.91i	0.358885	−	0.621607i	−0.628890	−	0.777494i	$-0.716490\pi$
$443$	3346.27	−	5795.91i	0.358885	−	0.621607i	0.987775	+	0.155887i	$0.0498236\pi$
$444$	−4291.75	−	60.7052i	−0.458733	−	0.00648861i
$445$		0			0
$446$	192.411	+	333.265i	0.0204280	+	0.0353824i
$447$	10019.9	+	141.728i	1.06024	+	0.0149967i
$448$	5880.26	−	10184.9i	0.620125	−	1.07409i
$449$	−17877.3			−1.87903			−0.939513	−	0.342514i	$-0.888721\pi$
$449$	−17877.3			−1.87903			−0.939513	+	0.342514i	$0.888721\pi$
$450$		0			0
$451$	5856.93			0.611513
$452$	3650.27	−	6322.46i	0.379855	−	0.657928i
$453$	2771.96	+	4961.94i	0.287501	+	0.514641i
$454$	−229.371	−	397.282i	−0.0237113	−	0.0410691i
$455$		0			0
$456$	−352.180	+	590.544i	−0.0361674	+	0.0606464i
$457$	4579.33	−	7931.63i	0.468735	−	0.811873i	−0.530626	−	0.847606i	$-0.678043\pi$
$457$	4579.33	−	7931.63i	0.468735	−	0.811873i	0.999361	+	0.0357331i	$0.0113766\pi$
$458$	−6233.35			−0.635950
$459$	8925.94	+	378.964i	0.907684	+	0.0385371i
$460$		0			0
$461$	8436.12	−	14611.8i	0.852298	−	1.47622i	−0.0268321	−	0.999640i	$-0.508542\pi$
$461$	8436.12	−	14611.8i	0.852298	−	1.47622i	0.879130	−	0.476583i	$-0.158125\pi$
$462$	−1660.14	+	2783.77i	−0.167179	+	0.280330i
$463$	490.023	+	848.746i	0.0491864	+	0.0851934i	0.889570	−	0.456798i	$-0.151004\pi$
$463$	490.023	+	848.746i	0.0491864	+	0.0851934i	−0.840384	+	0.541992i	$0.817670\pi$
$464$	1829.22	+	3168.31i	0.183016	+	0.316993i
$465$		0			0
$466$	−2879.34	+	4987.16i	−0.286229	+	0.495763i
$467$	7396.39			0.732900			0.366450	−	0.930438i	$-0.380573\pi$
$467$	7396.39			0.732900			0.366450	+	0.930438i	$0.380573\pi$
$468$	4638.58	+	131.248i	0.458159	+	0.0129636i
$469$	−18840.7			−1.85497
$470$		0			0
$471$	2982.65	+	42.1884i	0.291790	+	0.00412726i
$472$	−1417.41	−	2455.02i	−0.138224	−	0.239410i
$473$	3114.95	+	5395.25i	0.302802	+	0.524469i
$474$	−4656.21	−	65.8603i	−0.451196	−	0.00638199i
$475$		0			0
$476$	5028.65			0.484218
$477$	2873.17	+	5318.42i	0.275793	+	0.510511i
$478$	8580.82			0.821082
$479$	2256.79	−	3908.88i	0.215273	−	0.372863i	−0.738084	−	0.674708i	$-0.764269\pi$
$479$	2256.79	−	3908.88i	0.215273	−	0.372863i	0.953357	+	0.301846i	$0.0976027\pi$
$480$		0			0
$481$	6156.60	+	10663.5i	0.583611	+	1.01084i
$482$	2621.57	+	4540.69i	0.247737	+	0.429093i
$483$	−5475.75	+	9181.88i	−0.515850	+	0.864989i
$484$	−1994.48	+	3454.54i	−0.187310	+	0.324431i
$485$		0			0
$486$	−8107.96	−	574.340i	−0.756758	−	0.0536061i
$487$	−14036.0			−1.30602			−0.653012	−	0.757348i	$-0.726495\pi$
$487$	−14036.0			−1.30602			−0.653012	+	0.757348i	$0.726495\pi$
$488$	−1012.25	+	1753.27i	−0.0938983	+	0.162637i
$489$	6065.91	−	10171.5i	0.560961	−	0.940633i
$490$		0			0
$491$	3597.57	+	6231.17i	0.330664	+	0.572727i	0.982642	−	0.185511i	$-0.0593940\pi$
$491$	3597.57	+	6231.17i	0.330664	+	0.572727i	−0.651978	+	0.758238i	$0.726061\pi$
$492$	4032.02	+	7217.52i	0.369467	+	0.661364i
$493$	−4603.04	+	7972.69i	−0.420508	+	0.728341i
$494$	587.752			0.0535308
$495$		0			0
$496$	7034.00			0.636766
$497$	−1560.17	+	2702.29i	−0.140811	+	0.243892i
$498$	10289.1	+	145.535i	0.925831	+	0.0130955i
$499$	2738.51	+	4743.24i	0.245676	+	0.425524i	0.962322	−	0.271914i	$-0.0876566\pi$
$499$	2738.51	+	4743.24i	0.245676	+	0.425524i	−0.716645	+	0.697438i	$0.754323\pi$
$500$		0			0
$501$	−16283.8	−	230.328i	−1.45210	−	0.0205395i
$502$	713.500	−	1235.82i	0.0634364	−	0.109875i
$503$	−1253.89			−0.111149			−0.0555747	−	0.998455i	$-0.517699\pi$
$503$	−1253.89			−0.111149			−0.0555747	+	0.998455i	$0.517699\pi$
$504$	−15348.2	−	434.275i	−1.35647	−	0.0383813i
$505$		0			0
$506$	−1186.41	+	2054.91i	−0.104234	+	0.180538i
$507$	−924.833	−	1655.50i	−0.0810124	−	0.145016i
$508$	−2187.33	−	3788.57i	−0.191038	−	0.330887i
$509$	−6341.09	−	10983.1i	−0.552188	−	0.956418i	−0.998116	−	0.0613492i	$-0.980460\pi$
$509$	−6341.09	−	10983.1i	−0.552188	−	0.956418i	0.445928	−	0.895069i	$-0.352874\pi$
$510$		0			0
$511$	8227.05	−	14249.7i	0.712218	−	1.23360i
$512$	8526.55			0.735984
$513$	758.533	+	32.2047i	0.0652828	+	0.00277168i
$514$	−4295.61			−0.368621
$515$		0			0
$516$	−4504.20	+	7552.75i	−0.384276	+	0.644363i
$517$	−2828.17	−	4898.53i	−0.240585	−	0.416706i
$518$	−6069.99	−	10513.5i	−0.514865	−	0.891772i
$519$	10601.5	+	18977.3i	0.896638	+	1.60503i
$520$		0			0
$521$	10532.9			0.885710			0.442855	−	0.896593i	$-0.353966\pi$
$521$	10532.9			0.885710			0.442855	+	0.896593i	$0.353966\pi$
$522$	4391.40	−	7132.33i	0.368211	−	0.598034i
$523$	4327.58			0.361820			0.180910	−	0.983500i	$-0.442096\pi$
$523$	4327.58			0.361820			0.180910	+	0.983500i	$0.442096\pi$
$524$	2891.21	−	5007.73i	0.241037	−	0.417488i
$525$		0			0
$526$	4700.76	+	8141.95i	0.389663	+	0.674916i
$527$	8850.14	+	15328.9i	0.731533	+	1.26705i
$528$	−1643.44	−	23.2458i	−0.135457	−	0.00191599i
$529$	2170.30	−	3759.07i	0.178376	−	0.308956i
$530$		0			0
$531$	−1641.12	+	2665.44i	−0.134121	+	0.217834i
$532$	427.339			0.0348261
$533$	11858.6	−	20539.6i	0.963698	−	1.66917i
$534$	622.871	+	1114.97i	0.0504761	+	0.0903548i
$535$		0			0
$536$	−9904.85	−	17155.7i	−0.798180	−	1.38249i
$537$	7346.86	−	12319.4i	0.590392	−	0.989984i
$538$	−106.304	+	184.124i	−0.00851877	+	0.0147549i
$539$	2473.16			0.197638
$540$		0			0
$541$	−9235.00			−0.733907			−0.366953	−	0.930239i	$-0.619599\pi$
$541$	−9235.00			−0.733907			−0.366953	+	0.930239i	$0.619599\pi$
$542$	−8531.61	+	14777.2i	−0.676133	+	1.17110i
$543$	−6823.31	+	11441.5i	−0.539256	+	0.904239i
$544$	4499.56	+	7793.47i	0.354627	+	0.614232i
$545$		0			0
$546$	6401.07	+	11458.2i	0.501723	+	0.898109i
$547$	−10390.8	+	17997.3i	−0.812206	+	1.40678i	0.0991101	+	0.995076i	$0.468400\pi$
$547$	−10390.8	+	17997.3i	−0.812206	+	1.40678i	−0.911317	+	0.411706i	$0.864933\pi$
$548$	748.660			0.0583598
$549$	2234.52	+	63.2254i	0.173710	+	0.00491511i
$550$		0			0
$551$	−391.170	+	677.526i	−0.0302439	+	0.0523840i
$552$	−11239.4	−	158.977i	−0.866632	−	0.0122582i
$553$	4856.44	+	8411.60i	0.373448	+	0.646831i
$554$	−6185.96	−	10714.4i	−0.474397	−	0.821680i
$555$		0			0
$556$	5137.44	−	8898.31i	0.391864	−	0.678728i
$557$	14486.4			1.10199			0.550996	−	0.834508i	$-0.314248\pi$
$557$	14486.4			1.10199			0.550996	+	0.834508i	$0.314248\pi$
$558$	−7654.32	−	14168.6i	−0.580705	−	1.07492i
$559$	25227.4			1.90878
$560$		0			0
$561$	−2017.10	−	3610.72i	−0.151804	−	0.271737i
$562$	5986.64	+	10369.2i	0.449344	+	0.778286i
$563$	−10947.8	−	18962.2i	−0.819532	−	1.41947i	−0.906027	−	0.423219i	$-0.860900\pi$
$563$	−10947.8	−	18962.2i	−0.819532	−	1.41947i	0.0864949	−	0.996252i	$-0.472433\pi$
$564$	4089.51	−	6857.40i	0.305318	−	0.511965i
$565$		0			0
$566$	−1618.03			−0.120160
$567$	7633.18	+	15138.4i	0.565368	+	1.12125i
$568$	−3280.82			−0.242359
$569$	−9961.73	+	17254.2i	−0.733950	+	1.27124i	0.221233	+	0.975221i	$0.428992\pi$
$569$	−9961.73	+	17254.2i	−0.733950	+	1.27124i	−0.955183	+	0.296017i	$0.904341\pi$
$570$		0			0
$571$	−1225.64	−	2122.86i	−0.0898271	−	0.155585i	0.817611	−	0.575771i	$-0.195298\pi$
$571$	−1225.64	−	2122.86i	−0.0898271	−	0.155585i	−0.907438	+	0.420186i	$0.861965\pi$
$572$	−1074.13	−	1860.45i	−0.0785170	−	0.135996i
$573$	−11053.8	−	19786.8i	−0.805897	−	1.44260i
$574$	−11691.7	+	20250.7i	−0.850180	+	1.47255i
$575$		0			0
$576$	−6489.64	−	12012.7i	−0.469447	−	0.868977i
$577$	−4268.82			−0.307995			−0.153998	−	0.988071i	$-0.549215\pi$
$577$	−4268.82			−0.307995			−0.153998	+	0.988071i	$0.549215\pi$
$578$	−920.473	+	1594.31i	−0.0662398	+	0.114731i
$579$	−14387.5	−	203.505i	−1.03268	−	0.0146069i
$580$		0			0
$581$	−10731.5	−	18587.5i	−0.766296	−	1.32726i
$582$	−4030.89	−	57.0153i	−0.287089	−	0.00406076i
$583$	1399.23	−	2423.53i	0.0993997	−	0.172165i
$584$	17300.4			1.22585
$585$		0			0
$586$	20749.2			1.46270
$587$	1407.06	−	2437.09i	0.0989360	−	0.171362i	−0.812309	−	0.583228i	$-0.801789\pi$
$587$	1407.06	−	2437.09i	0.0989360	−	0.171362i	0.911244	+	0.411866i	$0.135123\pi$
$588$	1702.57	+	3047.69i	0.119410	+	0.213749i
$589$	752.092	+	1302.66i	0.0526136	+	0.0911294i
$590$		0			0
$591$	−1457.47	+	2443.93i	−0.101442	+	0.170101i
$592$	3078.06	−	5331.36i	0.213695	−	0.370131i
$593$	7066.19			0.489331			0.244666	−	0.969607i	$-0.421322\pi$
$593$	7066.19			0.489331			0.244666	+	0.969607i	$0.421322\pi$
$594$	1741.55	+	3335.68i	0.120297	+	0.230412i
$595$		0			0
$596$	3274.20	−	5671.09i	0.225028	−	0.389760i
$597$	5528.26	−	9269.92i	0.378989	−	0.635499i
$598$	4804.24	+	8321.19i	0.328528	+	0.569028i
$599$	−3623.12	−	6275.43i	−0.247140	−	0.428059i	0.715591	−	0.698519i	$-0.246157\pi$
$599$	−3623.12	−	6275.43i	−0.247140	−	0.428059i	−0.962731	+	0.270461i	$0.912824\pi$
$600$		0			0
$601$	−928.919	+	1608.93i	−0.0630472	+	0.109201i	−0.895826	−	0.444405i	$-0.853415\pi$
$601$	−928.919	+	1608.93i	−0.0630472	+	0.109201i	0.832779	+	0.553606i	$0.186749\pi$
$602$	−24872.5			−1.68393
$603$	−11468.1	+	18626.1i	−0.774492	+	1.25790i
$604$	3714.16			0.250210
$605$		0			0
$606$	−3224.47	−	45.6089i	−0.216147	−	0.00305732i
$607$	−7826.04	−	13555.1i	−0.523310	−	0.906400i	−0.999632	−	0.0271286i	$-0.991364\pi$
$607$	−7826.04	−	13555.1i	−0.523310	−	0.906400i	0.476322	−	0.879271i	$-0.341970\pi$
$608$	382.376	+	662.295i	0.0255056	+	0.0441770i
$609$	−17468.5	−	247.086i	−1.16233	−	0.0164408i
$610$		0			0
$611$	−22904.8			−1.51658
$612$	3060.89	−	4971.37i	0.202172	−	0.328359i
$613$	−421.560			−0.0277760			−0.0138880	−	0.999904i	$-0.504421\pi$
$613$	−421.560			−0.0277760			−0.0138880	+	0.999904i	$0.504421\pi$
$614$	1717.71	−	2975.16i	0.112901	−	0.195550i
$615$		0			0
$616$	3554.10	+	6155.89i	0.232466	+	0.402643i
$617$	−7436.70	−	12880.7i	−0.485235	−	0.840452i	0.514621	−	0.857418i	$-0.327933\pi$
$617$	−7436.70	−	12880.7i	−0.485235	−	0.840452i	−0.999856	+	0.0169657i	$0.994599\pi$
$618$	−2757.30	+	4623.50i	−0.179474	+	0.300946i
$619$	11751.5	−	20354.1i	0.763054	−	1.32165i	−0.178215	−	0.983992i	$-0.557032\pi$
$619$	11751.5	−	20354.1i	0.763054	−	1.32165i	0.941269	−	0.337657i	$-0.109635\pi$
$620$		0			0
$621$	5744.25	+	11002.3i	0.371190	+	0.710961i
$622$	−12789.3			−0.824443
$623$	1331.94	−	2306.99i	0.0856552	−	0.148359i
$624$	−3408.99	+	5716.29i	−0.218700	+	0.366722i
$625$		0			0
$626$	−3939.22	−	6822.94i	−0.251507	−	0.435622i
$627$	−171.415	−	306.842i	−0.0109181	−	0.0195440i
$628$	974.637	−	1688.12i	0.0619304	−	0.107267i
$629$	15491.2			0.981995
$630$		0			0
$631$	−3402.59			−0.214667			−0.107333	−	0.994223i	$-0.534231\pi$
$631$	−3402.59			−0.214667			−0.107333	+	0.994223i	$0.534231\pi$
$632$	−5106.22	+	8844.23i	−0.321384	+	0.556653i
$633$	−3179.65	−	44.9750i	−0.199652	−	0.00282400i
$634$	−2513.17	−	4352.94i	−0.157430	−	0.272677i
$635$		0			0
$636$	3949.78	+	55.8681i	0.246256	+	0.00348320i
$637$	5007.43	−	8673.12i	0.311462	−	0.539468i
$638$	−3877.55			−0.240617
$639$	1721.85	+	3187.25i	0.106597	+	0.197317i
$640$		0			0
$641$	4328.19	−	7496.64i	0.266697	−	0.461933i	−0.701310	−	0.712857i	$-0.747401\pi$
$641$	4328.19	−	7496.64i	0.266697	−	0.461933i	0.968007	+	0.250923i	$0.0807342\pi$
$642$	−9769.85	−	17488.5i	−0.600600	−	1.07510i
$643$	5641.51	+	9771.38i	0.346002	+	0.599293i	0.985535	−	0.169470i	$-0.0542056\pi$
$643$	5641.51	+	9771.38i	0.346002	+	0.599293i	−0.639533	+	0.768764i	$0.720872\pi$
$644$	3493.04	+	6050.12i	0.213735	+	0.370199i
$645$		0			0
$646$	369.725	−	640.382i	0.0225180	−	0.0390023i
$647$	−18232.2			−1.10785			−0.553927	−	0.832565i	$-0.686871\pi$
$647$	−18232.2			−1.10785			−0.553927	+	0.832565i	$0.686871\pi$
$648$	−9771.61	+	14909.0i	−0.592385	+	0.903829i
$649$	1449.09			0.0876450
$650$		0			0
$651$	−17204.6	+	28849.0i	−1.03579	+	1.73684i
$652$	−3869.51	−	6702.18i	−0.232426	−	0.402573i
$653$	9852.12	+	17064.4i	0.590418	+	1.02263i	0.994176	+	0.107769i	$0.0343706\pi$
$653$	9852.12	+	17064.4i	0.590418	+	1.02263i	−0.403758	+	0.914866i	$0.632296\pi$
$654$	8195.86	+	14671.0i	0.490036	+	0.877189i
$655$		0			0
$656$	−11857.6			−0.705736
$657$	−9079.63	−	16807.0i	−0.539163	−	0.998025i
$658$	22582.6			1.33793
$659$	2227.87	−	3858.79i	0.131693	−	0.228099i	−0.792636	−	0.609695i	$-0.791292\pi$
$659$	2227.87	−	3858.79i	0.131693	−	0.228099i	0.924329	+	0.381596i	$0.124625\pi$
$660$		0			0
$661$	8793.82	+	15231.3i	0.517458	+	0.896264i	0.999794	+	0.0202777i	$0.00645502\pi$
$661$	8793.82	+	15231.3i	0.517458	+	0.896264i	−0.482336	+	0.875986i	$0.660212\pi$
$662$	−1442.82	−	2499.04i	−0.0847082	−	0.146719i
$663$	−16746.4	−	236.872i	−0.980962	−	0.0138753i
$664$	11283.5	−	19543.5i	0.659463	−	1.14222i
$665$		0			0
$666$	−14088.5	−	398.633i	−0.819698	−	0.0231933i
$667$	−12789.6			−0.742450
$668$	−5321.03	+	9216.30i	−0.308199	+	0.533816i
$669$	−454.471	−	813.526i	−0.0262644	−	0.0470145i
$670$		0			0
$671$	−517.436	−	896.225i	−0.0297696	−	0.0515624i
$672$	−8747.09	+	14667.3i	−0.502123	+	0.841972i
$673$	3885.57	−	6730.00i	0.222552	−	0.385472i	−0.733030	−	0.680196i	$-0.761895\pi$
$673$	3885.57	−	6730.00i	0.222552	−	0.385472i	0.955582	+	0.294725i	$0.0952279\pi$
$674$	−4154.84			−0.237446
$675$		0			0
$676$	−1239.19			−0.0705045
$677$	724.033	−	1254.06i	0.0411032	−	0.0711928i	−0.844742	−	0.535174i	$-0.820246\pi$
$677$	724.033	−	1254.06i	0.0411032	−	0.0711928i	0.885845	+	0.463981i	$0.153579\pi$
$678$	12278.8	−	20589.3i	0.695521	−	1.16627i
$679$	4204.22	+	7281.93i	0.237619	+	0.411568i
$680$		0			0
$681$	541.771	+	969.797i	0.0304856	+	0.0545708i
$682$	−3727.63	+	6456.45i	−0.209294	+	0.362508i
$683$	−19014.6			−1.06526			−0.532630	−	0.846348i	$-0.678796\pi$
$683$	−19014.6			−1.06526			−0.532630	+	0.846348i	$0.678796\pi$
$684$	260.117	−	422.471i	0.0145407	−	0.0236164i
$685$		0			0
$686$	3621.48	−	6272.59i	0.201558	−	0.349109i
$687$	15092.8	+	213.482i	0.838177	+	0.0118557i
$688$	−6306.36	−	10922.9i	−0.349459	−	0.605281i
$689$	−5666.04	−	9813.87i	−0.313293	−	0.542639i
$690$		0			0
$691$	−16149.2	+	27971.2i	−0.889064	+	1.53990i	−0.0480796	+	0.998844i	$0.515310\pi$
$691$	−16149.2	+	27971.2i	−0.889064	+	1.53990i	−0.840984	+	0.541060i	$0.818023\pi$
$692$	14205.0			0.780338
$693$	4115.05	−	6683.49i	0.225567	−	0.366356i
$694$	8135.99			0.445012
$695$		0			0
$696$	−8958.50	−	16036.2i	−0.487890	−	0.873347i
$697$	−14919.2	−	25840.8i	−0.810769	−	1.40429i
$698$	969.374	+	1679.00i	0.0525664	+	0.0910476i
$699$	7142.55	−	11976.8i	0.386490	−	0.648075i
$700$		0			0
$701$	8389.52			0.452022			0.226011	−	0.974125i	$-0.427431\pi$
$701$	8389.52			0.452022			0.226011	+	0.974125i	$0.427431\pi$
$702$	15224.0	+	646.357i	0.818508	+	0.0347510i
$703$	1316.46			0.0706274
$704$	−3160.44	+	5474.04i	−0.169195	+	0.293055i
$705$		0			0
$706$	−8672.77	−	15021.7i	−0.462329	−	0.800777i
$707$	3363.13	+	5825.11i	0.178902	+	0.309867i
$708$	997.578	+	1785.71i	0.0529538	+	0.0947899i
$709$	76.8578	−	133.122i	0.00407117	−	0.00705147i	−0.863983	−	0.503522i	$-0.832037\pi$
$709$	76.8578	−	133.122i	0.00407117	−	0.00705147i	0.868054	+	0.496470i	$0.165371\pi$
$710$		0			0
$711$	11271.8	+	318.936i	0.594553	+	0.0168228i
$712$	2800.90			0.147427
$713$	−12295.1	+	21295.7i	−0.645799	+	1.11856i
$714$	16510.8	+	233.540i	0.865410	+	0.0122409i
$715$		0			0
$716$	−4686.64	−	8117.50i	−0.244620	−	0.423694i
$717$	−20776.8	−	293.880i	−1.08218	−	0.0153070i
$718$	−3957.83	+	6855.17i	−0.205717	+	0.356313i
$719$	−271.312			−0.0140726			−0.00703632	−	0.999975i	$-0.502240\pi$
$719$	−271.312			−0.0140726			−0.00703632	+	0.999975i	$0.502240\pi$
$720$		0			0
$721$	11228.4			0.579982
$722$	−7327.60	+	12691.8i	−0.377708	+	0.654209i
$723$	−6192.11	−	11084.2i	−0.318516	−	0.570160i
$724$	4352.66	+	7539.03i	0.223433	+	0.386997i
$725$		0			0
$726$	−6709.02	+	11249.9i	−0.342968	+	0.575098i
$727$	8057.68	−	13956.3i	0.411063	−	0.711982i	−0.583943	−	0.811795i	$-0.698491\pi$
$727$	8057.68	−	13956.3i	0.411063	−	0.711982i	0.995006	+	0.0998123i	$0.0318242\pi$
$728$	28784.0			1.46540
$729$	19612.2	+	1668.34i	0.996401	+	0.0847602i
$730$		0			0
$731$	15869.3	−	27486.4i	0.802936	−	1.39073i
$732$	748.210	−	1254.62i	0.0377795	−	0.0633497i
$733$	−13007.0	−	22528.8i	−0.655424	−	1.13523i	−0.981787	−	0.189983i	$-0.939157\pi$
$733$	−13007.0	−	22528.8i	−0.655424	−	1.13523i	0.326364	−	0.945244i	$-0.394177\pi$
$734$	3257.82	+	5642.71i	0.163826	+	0.283755i
$735$		0			0
$736$	−6251.03	+	10827.1i	−0.313065	+	0.542245i
$737$	10126.2			0.506111
$738$	12903.4	+	23884.9i	0.643603	+	1.19135i
$739$	16758.4			0.834192			0.417096	−	0.908862i	$-0.363048\pi$
$739$	16758.4			0.834192			0.417096	+	0.908862i	$0.363048\pi$
$740$		0			0
$741$	−1423.13	−	20.1296i	−0.0705531	−	0.000997947i
$742$	5586.33	+	9675.80i	0.276389	+	0.478720i
$743$	−12022.9	−	20824.3i	−0.593645	−	1.02822i	−0.993737	−	0.111748i	$-0.964355\pi$
$743$	−12022.9	−	20824.3i	−0.593645	−	1.02822i	0.400092	−	0.916475i	$-0.368978\pi$
$744$	−35313.7	−	499.499i	−1.74014	−	0.0246136i
$745$		0			0
$746$	10686.2			0.524462
$747$	−24908.0	−	704.768i	−1.21999	−	0.0345196i
$748$	−2702.73			−0.132114
$749$	−20891.8	+	36185.6i	−1.01918	+	1.76528i
$750$		0			0
$751$	−8658.97	−	14997.8i	−0.420733	−	0.728730i	0.575279	−	0.817958i	$-0.304894\pi$
$751$	−8658.97	−	14997.8i	−0.420733	−	0.728730i	−0.996011	+	0.0892271i	$0.971560\pi$
$752$	5725.76	+	9917.30i	0.277655	+	0.480913i
$753$	−1769.93	+	2967.86i	−0.0856570	+	0.143632i
$754$	−7850.89	+	13598.1i	−0.379194	+	0.656784i
$755$		0			0
$756$	11069.0	+	469.950i	0.532506	+	0.0226083i
$757$	9907.10			0.475667			0.237833	−	0.971306i	$-0.423563\pi$
$757$	9907.10			0.475667			0.237833	+	0.971306i	$0.423563\pi$
$758$	−6467.43	+	11201.9i	−0.309904	+	0.536770i
$759$	2943.03	−	4934.94i	0.140745	−	0.236004i
$760$		0			0
$761$	15587.5	+	26998.3i	0.742504	+	1.28606i	0.951352	+	0.308107i	$0.0996955\pi$
$761$	15587.5	+	26998.3i	0.742504	+	1.28606i	−0.208847	+	0.977948i	$0.566971\pi$
$762$	−7005.84	−	12540.8i	−0.333064	−	0.596201i
$763$	17526.0	−	30355.9i	0.831564	−	1.44031i
$764$	−14811.0			−0.701367
$765$		0			0
$766$	8122.15			0.383114
$767$	2933.97	−	5081.79i	0.138122	−	0.239234i
$768$	−21525.7	−	304.472i	−1.01138	−	0.0143056i
$769$	−12703.5	−	22003.0i	−0.595706	−	1.03179i	−0.993447	−	0.114296i	$-0.963539\pi$
$769$	−12703.5	−	22003.0i	−0.595706	−	1.03179i	0.397740	−	0.917498i	$-0.369794\pi$
$770$		0			0
$771$	10401.0	+	147.118i	0.485840	+	0.00687202i
$772$	−4701.39	+	8143.04i	−0.219180	+	0.379630i
$773$	18107.2			0.842521			0.421261	−	0.906940i	$-0.361588\pi$
$773$	18107.2			0.842521			0.421261	+	0.906940i	$0.361588\pi$
$774$	−15139.6	+	24589.2i	−0.703079	+	1.14191i
$775$		0			0
$776$	−4420.46	+	7656.46i	−0.204491	+	0.354189i
$777$	14337.2	+	25664.4i	0.661963	+	1.18495i
$778$	6161.57	+	10672.2i	0.283937	+	0.491793i
$779$	−1267.85	−	2195.98i	−0.0583124	−	0.101000i
$780$		0			0
$781$	838.535	−	1452.39i	0.0384189	−	0.0665434i
$782$	12088.4			0.552788
$783$	−10877.2	+	17119.1i	−0.496448	+	0.781339i
$784$	−5007.04			−0.228090
$785$		0			0
$786$	9725.44	−	16307.9i	0.441342	−	0.740054i
$787$	6101.80	+	10568.6i	0.276373	+	0.478693i	0.970481	−	0.241179i	$-0.0775340\pi$
$787$	6101.80	+	10568.6i	0.276373	+	0.478693i	−0.694107	+	0.719871i	$0.744201\pi$
$788$	929.738	+	1610.35i	0.0420311	+	0.0728000i
$789$	−11103.1	−	19875.1i	−0.500991	−	0.896798i
$790$		0			0
$791$	−50002.1			−2.24762
$792$	8249.12	+	233.408i	0.370100	+	0.0104720i
$793$	−4190.62			−0.187659
$794$	−964.888	+	1671.23i	−0.0431267	+	0.0746976i
$795$		0			0
$796$	−3526.53	−	6108.14i	−0.157029	−	0.271981i
$797$	7226.25	+	12516.2i	0.321163	+	0.556270i	0.980728	−	0.195377i	$-0.0625930\pi$
$797$	7226.25	+	12516.2i	0.321163	+	0.556270i	−0.659565	+	0.751647i	$0.729260\pi$
$798$	1403.11	+	19.8464i	0.0622423	+	0.000880394i
$799$	−14408.2	+	24955.8i	−0.637956	+	1.10497i
$800$		0			0
$801$	−1469.97	−	2721.02i	−0.0648427	−	0.120028i
$802$	12183.6			0.536432
$803$	−4421.76	+	7658.71i	−0.194322	+	0.336575i
$804$	6971.08	+	12478.6i	0.305785	+	0.547370i
$805$		0			0
$806$	15094.7	+	26144.8i	0.659663	+	1.14257i
$807$	263.701	−	442.180i	0.0115027	−	0.0192881i
$808$	−3536.11	+	6124.72i	−0.153960	+	0.266667i
$809$	38826.9			1.68737			0.843683	−	0.536841i	$-0.180382\pi$
$809$	38826.9			1.68737			0.843683	+	0.536841i	$0.180382\pi$
$810$		0			0
$811$	8619.51			0.373208			0.186604	−	0.982435i	$-0.440252\pi$
$811$	8619.51			0.373208			0.186604	+	0.982435i	$0.440252\pi$
$812$	−5708.18	+	9886.86i	−0.246697	+	0.427292i
$813$	21163.7	−	35487.9i	0.912970	−	1.53089i
$814$	3262.41	+	5650.66i	0.140476	+	0.243311i
$815$		0			0
$816$	4083.73	+	7310.07i	0.175195	+	0.313608i
$817$	1348.58	−	2335.81i	0.0577490	−	0.100024i
$818$	7792.47			0.333077
$819$	−15106.5	−	27963.1i	−0.644523	−	1.19305i
$820$		0			0
$821$	10933.8	−	18937.9i	0.464789	−	0.805039i	−0.534403	−	0.845230i	$-0.679463\pi$
$821$	10933.8	−	18937.9i	0.464789	−	0.805039i	0.999192	+	0.0401913i	$0.0127967\pi$
$822$	2458.11	+	34.7691i	0.104302	+	0.00147532i
$823$	1125.97	+	1950.24i	0.0476900	+	0.0826015i	0.888885	−	0.458130i	$-0.151481\pi$
$823$	1125.97	+	1950.24i	0.0476900	+	0.0826015i	−0.841195	+	0.540732i	$0.818147\pi$
$824$	5902.94	+	10224.2i	0.249562	+	0.432253i
$825$		0			0
$826$	−2892.70	+	5010.29i	−0.121852	+	0.211054i
$827$	−11573.5			−0.486637			−0.243319	−	0.969946i	$-0.578236\pi$
$827$	−11573.5			−0.486637			−0.243319	+	0.969946i	$0.578236\pi$
$828$	8107.38	+	229.398i	0.340279	+	0.00962816i
$829$	−10513.6			−0.440473			−0.220236	−	0.975447i	$-0.570683\pi$
$829$	−10513.6			−0.440473			−0.220236	+	0.975447i	$0.570683\pi$
$830$		0			0
$831$	14611.1	+	26154.7i	0.609934	+	1.09181i
$832$	12797.9	+	22166.6i	0.533278	+	0.923665i
$833$	−6299.83	−	10911.6i	−0.262036	−	0.453860i
$834$	17281.3	−	28977.7i	0.717509	−	1.20314i
$835$		0			0
$836$	−229.680			−0.00950197
$837$	18048.2	+	34568.7i	0.745324	+	1.42756i
$838$	6262.05			0.258137
$839$	23352.5	−	40447.8i	0.960928	−	1.66438i	0.240751	−	0.970587i	$-0.422606\pi$
$839$	23352.5	−	40447.8i	0.960928	−	1.66438i	0.720178	−	0.693790i	$-0.244060\pi$
$840$		0			0
$841$	1744.40	+	3021.39i	0.0715242	+	0.123883i
$842$	−15352.5	−	26591.3i	−0.628363	−	1.08836i
$843$	−14140.4	−	25311.9i	−0.577722	−	1.03415i
$844$	−1039.01	+	1799.62i	−0.0423747	+	0.0733952i
$845$		0			0
$846$	13745.8	−	22325.3i	0.558617	−	0.907282i
$847$	27320.8			1.10833
$848$	−2832.80	+	4906.55i	−0.114716	+	0.198693i
$849$	3917.74	+	55.4150i	0.158370	+	0.00224009i
$850$		0			0
$851$	10760.6	+	18637.9i	0.433454	+	0.750764i
$852$	2367.04	+	33.4809i	0.0951803	+	0.00134629i
$853$	−290.122	+	502.505i	−0.0116455	+	0.0201705i	−0.871789	−	0.489881i	$-0.837040\pi$
$853$	−290.122	+	502.505i	−0.0116455	+	0.0201705i	0.860144	+	0.510051i	$0.170374\pi$
$854$	4131.66			0.165553
$855$		0			0
$856$	−43932.6			−1.75419
$857$	17487.2	−	30288.8i	0.697027	−	1.20729i	−0.272465	−	0.962166i	$-0.587839\pi$
$857$	17487.2	−	30288.8i	0.697027	−	1.20729i	0.969493	−	0.245121i	$-0.0788276\pi$
$858$	−3440.35	−	6158.41i	−0.136890	−	0.245040i
$859$	−19155.9	−	33179.1i	−0.760876	−	1.31788i	−0.942400	−	0.334489i	$-0.891436\pi$
$859$	−19155.9	−	33179.1i	−0.760876	−	1.31788i	0.181524	−	0.983387i	$-0.441897\pi$
$860$		0			0
$861$	29002.8	−	48632.6i	1.14798	−	1.92496i
$862$	−3457.01	+	5987.72i	−0.136597	+	0.236592i
$863$	26886.0			1.06050			0.530248	−	0.847842i	$-0.322099\pi$
$863$	26886.0			1.06050			0.530248	+	0.847842i	$0.322099\pi$
$864$	9176.00	+	17575.3i	0.361313	+	0.692042i
$865$		0			0
$866$	−1070.45	+	1854.07i	−0.0420038	+	0.0727528i
$867$	2283.35	−	3828.78i	0.0894424	−	0.149979i
$868$	10975.0	+	19009.2i	0.429164	+	0.743335i
$869$	−2610.17	−	4520.94i	−0.101892	−	0.176482i
$870$		0			0
$871$	20502.6	−	35511.5i	0.797593	−	1.38147i
$872$	36854.8			1.43126
$873$	9758.05	+	276.103i	0.378305	+	0.0107041i
$874$	1027.28			0.0397578
$875$		0			0
$876$	−12481.9	−	176.551i	−0.481419	−	0.00680949i
$877$	18014.4	+	31201.8i	0.693617	+	1.20138i	0.970645	+	0.240517i	$0.0773171\pi$
$877$	18014.4	+	31201.8i	0.693617	+	1.20138i	−0.277028	+	0.960862i	$0.589350\pi$
$878$	−9587.77	−	16606.5i	−0.368532	−	0.638317i
$879$	−50240.2	−	710.629i	−1.92783	−	0.0272684i
$880$		0			0
$881$	18790.0			0.718560			0.359280	−	0.933230i	$-0.383022\pi$
$881$	18790.0			0.718560			0.359280	+	0.933230i	$0.383022\pi$
$882$	5448.61	+	10085.7i	0.208009	+	0.385038i
$883$	−21532.1			−0.820624			−0.410312	−	0.911945i	$-0.634580\pi$
$883$	−21532.1			−0.820624			−0.410312	+	0.911945i	$0.634580\pi$
$884$	−5472.22	+	9478.17i	−0.208202	+	0.360617i
$885$		0			0
$886$	−7180.42	−	12436.9i	−0.272270	−	0.471585i
$887$	4296.63	+	7441.98i	0.162646	+	0.281710i	0.935817	−	0.352487i	$-0.114664\pi$
$887$	4296.63	+	7441.98i	0.162646	+	0.281710i	−0.773171	+	0.634197i	$0.781331\pi$
$888$	−15831.8	+	26547.2i	−0.598289	+	1.00323i
$889$	−14981.2	+	25948.3i	−0.565191	+	0.978939i
$890$		0			0
$891$	−4102.57	−	8136.35i	−0.154255	−	0.305924i
$892$	−608.947			−0.0228577
$893$	−1224.42	+	2120.76i	−0.0458833	+	0.0794722i
$894$	11013.7	−	18468.1i	0.412030	−	0.690902i
$895$		0			0
$896$	528.447	+	915.297i	0.0197033	+	0.0341271i
$897$	−11347.5	−	20312.7i	−0.422390	−	0.756099i
$898$	−19180.6	+	33221.7i	−0.712765	+	1.23455i
$899$	−40184.3			−1.49079
$900$		0			0
$901$	−14256.9			−0.527153
$902$	6283.90	−	10884.0i	0.231963	−	0.401772i
$903$	60223.9	+	851.844i	2.21941	+	0.0313927i
$904$	−26286.9	−	45530.3i	−0.967135	−	1.67513i
$905$		0			0
$906$	12194.9	+	172.492i	0.447183	+	0.00632523i
$907$	−22443.0	+	38872.5i	−0.821620	+	1.42309i	0.0828560	+	0.996562i	$0.473596\pi$
$907$	−22443.0	+	38872.5i	−0.821620	+	1.42309i	−0.904476	+	0.426525i	$0.859737\pi$
$908$	725.921			0.0265314
$909$	7805.87	+	220.866i	0.284823	+	0.00805904i
$910$		0			0
$911$	−24541.7	+	42507.5i	−0.892540	+	1.54592i	−0.0557198	+	0.998446i	$0.517745\pi$
$911$	−24541.7	+	42507.5i	−0.892540	+	1.54592i	−0.836820	+	0.547478i	$0.815588\pi$
$912$	347.038	+	621.216i	0.0126004	+	0.0225554i
$913$	5767.82	+	9990.15i	0.209076	+	0.362131i
$914$	−9826.31	−	17019.7i	−0.355608	−	0.615931i
$915$		0			0
$916$	4931.88	−	8542.26i	0.177897	−	0.308127i
$917$	−39604.4			−1.42623
$918$	10280.9	−	16180.6i	0.369629	−	0.581743i
$919$	−3203.42			−0.114985			−0.0574924	−	0.998346i	$-0.518311\pi$
$919$	−3203.42			−0.114985			−0.0574924	+	0.998346i	$0.518311\pi$
$920$		0			0
$921$	−4261.00	+	7144.95i	−0.152448	+	0.255629i
$922$	−18102.2	−	31353.9i	−0.646599	−	1.11994i
$923$	−3395.57	−	5881.30i	−0.121091	−	0.209735i
$924$	−2501.39	−	4477.62i	−0.0890582	−	0.159419i
$925$		0			0
$926$	2102.98			0.0746310
$927$	6834.60	−	11100.5i	0.242155	−	0.393298i
$928$	−20430.4			−0.722693
$929$	−3350.68	+	5803.55i	−0.118334	+	0.204961i	−0.919108	−	0.394007i	$-0.871089\pi$
$929$	−3350.68	+	5803.55i	−0.118334	+	0.204961i	0.800774	+	0.598967i	$0.204422\pi$
$930$		0			0
$931$	−535.365	−	927.279i	−0.0188463	−	0.0326427i
$932$	−4556.31	−	7891.76i	−0.160136	−	0.277364i
$933$	30966.8	+	438.013i	1.08661	+	0.0153697i
$934$	7935.58	−	13744.8i	0.278009	−	0.481525i
$935$		0			0
$936$	17520.6	−	28456.2i	0.611835	−	0.993717i
$937$	44589.7			1.55462			0.777312	−	0.629116i	$-0.216583\pi$
$937$	44589.7			1.55462			0.777312	+	0.629116i	$0.216583\pi$
$938$	−20214.2	+	35011.9i	−0.703641	+	1.21874i
$939$	9304.39	+	16655.3i	0.323362	+	0.578835i
$940$		0			0
$941$	22110.7	+	38296.8i	0.765980	+	1.32672i	0.939727	+	0.341926i	$0.111079\pi$
$941$	22110.7	+	38296.8i	0.765980	+	1.32672i	−0.173747	+	0.984790i	$0.555588\pi$
$942$	3278.48	−	5497.43i	0.113396	−	0.190144i
$943$	20726.6	−	35899.5i	0.715748	−	1.23971i
$944$	−2933.74			−0.101150
$945$		0			0
$946$	13368.1			0.459445
$947$	12589.2	−	21805.1i	0.431988	−	0.748225i	−0.565056	−	0.825052i	$-0.691146\pi$
$947$	12589.2	−	21805.1i	0.431988	−	0.748225i	0.997044	+	0.0768272i	$0.0244790\pi$
$948$	3774.29	−	6328.82i	0.129307	−	0.216826i
$949$	17905.5	+	31013.2i	0.612473	+	1.06083i
$950$		0			0
$951$	5936.07	+	10625.9i	0.202408	+	0.362321i
$952$	18106.6	−	31361.5i	0.616426	−	1.06768i
$953$	37290.3			1.26753			0.633763	−	0.773527i	$-0.281509\pi$
$953$	37290.3			1.26753			0.633763	+	0.773527i	$0.281509\pi$
$954$	12965.9	+	366.870i	0.440029	+	0.0124506i
$955$		0			0
$956$	−6789.21	+	11759.3i	−0.229685	+	0.397826i
$957$	9388.73	+	132.800i	0.317131	+	0.00448570i
$958$	−4842.63	−	8387.67i	−0.163317	−	0.282874i
$959$	−2563.82	−	4440.66i	−0.0863295	−	0.149527i
$960$		0			0
$961$	−23735.1	+	41110.4i	−0.796721	+	1.37996i
$962$	26421.7			0.885518
$963$	23056.8	+	42679.6i	0.771543	+	1.42817i
$964$	−8296.83			−0.277202
$965$		0			0
$966$	11187.9	+	20026.9i	0.372634	+	0.667034i
$967$	−6374.65	−	11041.2i	−0.211991	−	0.367179i	0.740347	−	0.672225i	$-0.234661\pi$
$967$	−6374.65	−	11041.2i	−0.211991	−	0.367179i	−0.952337	+	0.305047i	$0.901328\pi$
$968$	14363.0	+	24877.4i	0.476904	+	0.826022i
$969$	−917.148	+	1537.90i	−0.0304056	+	0.0509849i
$970$		0			0
$971$	40358.9			1.33386			0.666930	−	0.745121i	$-0.267608\pi$
$971$	40358.9			1.33386			0.666930	+	0.745121i	$0.267608\pi$
$972$	7202.17	−	10656.8i	0.237664	−	0.351665i
$973$	−70373.6			−2.31868
$974$	−15059.2	+	26083.4i	−0.495410	+	0.858075i
$975$		0			0
$976$	1047.57	+	1814.45i	0.0343566	+	0.0595073i
$977$	−19301.7	−	33431.5i	−0.632052	−	1.09475i	−0.987132	−	0.159910i	$-0.948880\pi$
$977$	−19301.7	−	33431.5i	−0.632052	−	1.09475i	0.355079	−	0.934836i	$-0.384454\pi$
$978$	−12393.7	−	22185.3i	−0.405221	−	0.725367i
$979$	−715.874	+	1239.93i	−0.0233702	+	0.0404784i
$980$		0			0
$981$	−19342.2	−	35803.7i	−0.629510	−	1.16526i
$982$	15439.3			0.501719
$983$	−14737.9	+	25526.7i	−0.478194	+	0.828257i	−0.999687	−	0.0249984i	$-0.992042\pi$
$983$	−14737.9	+	25526.7i	−0.478194	+	0.828257i	0.521493	+	0.853256i	$0.325375\pi$
$984$	59530.5	+	842.036i	1.92862	+	0.0272796i
$985$		0			0
$986$	9877.19	+	17107.8i	0.319020	+	0.552559i
$987$	−54679.3	−	773.417i	−1.76338	−	0.0249424i
$988$	−465.034	+	805.463i	−0.0149744	+	0.0259364i
$989$	44092.9			1.41767
$990$		0			0
$991$	−30568.9			−0.979873			−0.489936	−	0.871758i	$-0.662980\pi$
$991$	−30568.9			−0.979873			−0.489936	+	0.871758i	$0.662980\pi$
$992$	−19640.5	+	34018.3i	−0.628614	+	1.08879i
$993$	3407.92	+	6100.35i	0.108909	+	0.194953i
$994$	3347.80	+	5798.56i	0.106827	+	0.185029i
$995$		0			0
$996$	−8340.23	+	13985.1i	−0.265332	+	0.444915i
$997$	−5509.08	+	9542.00i	−0.174999	+	0.303108i	−0.940161	−	0.340731i	$-0.889326\pi$
$997$	−5509.08	+	9542.00i	−0.174999	+	0.303108i	0.765162	+	0.643838i	$0.222659\pi$
$998$	11752.6			0.372767
$999$	34098.9	+	1447.72i	1.07992	+	0.0458497i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	225.4.e.f.151.8	yes	24
5.2	odd	4		225.4.k.e.124.17		48
5.3	odd	4		225.4.k.e.124.8		48
5.4	even	2		225.4.e.e.151.5	yes	24
9.2	odd	6		2025.4.a.bj.1.8		12
9.4	even	3	inner	225.4.e.f.76.8	yes	24
9.7	even	3		2025.4.a.bf.1.5		12
45.4	even	6		225.4.e.e.76.5	✓	24
45.13	odd	12		225.4.k.e.49.17		48
45.22	odd	12		225.4.k.e.49.8		48
45.29	odd	6		2025.4.a.be.1.5		12
45.34	even	6		2025.4.a.bi.1.8		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
225.4.e.e.76.5	✓	24	45.4	even	6
225.4.e.e.151.5	yes	24	5.4	even	2
225.4.e.f.76.8	yes	24	9.4	even	3	inner
225.4.e.f.151.8	yes	24	1.1	even	1	trivial
225.4.k.e.49.8		48	45.22	odd	12
225.4.k.e.49.17		48	45.13	odd	12
225.4.k.e.124.8		48	5.3	odd	4
225.4.k.e.124.17		48	5.2	odd	4
2025.4.a.be.1.5		12	45.29	odd	6
2025.4.a.bf.1.5		12	9.7	even	3
2025.4.a.bi.1.8		12	45.34	even	6
2025.4.a.bj.1.8		12	9.2	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 225 = 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	225.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.07290 - 1.85832i) q^{2} +(-2.66146 + 4.46280i) q^{3} +(1.69777 + 2.94063i) q^{4} +(5.43782 + 9.73398i) q^{6} +(11.6282 - 20.1406i) q^{7} +24.4526 q^{8} +(-12.8333 - 23.7552i) q^{9} +O(q^{10})\)	\(q+(1.07290 - 1.85832i) q^{2} +(-2.66146 + 4.46280i) q^{3} +(1.69777 + 2.94063i) q^{4} +(5.43782 + 9.73398i) q^{6} +(11.6282 - 20.1406i) q^{7} +24.4526 q^{8} +(-12.8333 - 23.7552i) q^{9} +(-6.24976 + 10.8249i) q^{11} +(-17.6420 - 0.249540i) q^{12} +(25.3078 + 43.8344i) q^{13} +(-24.9518 - 43.2178i) q^{14} +(12.6529 - 21.9155i) q^{16} +63.6794 q^{17} +(-57.9134 - 1.63865i) q^{18} +5.41153 q^{19} +(58.9358 + 105.498i) q^{21} +(13.4107 + 23.2281i) q^{22} +(44.2335 + 76.6146i) q^{23} +(-65.0795 + 109.127i) q^{24} +108.611 q^{26} +(140.170 + 5.95112i) q^{27} +78.9683 q^{28} +(-72.2845 + 125.200i) q^{29} +(138.980 + 240.720i) q^{31} +(70.6596 + 122.386i) q^{32} +(-31.6759 - 56.7015i) q^{33} +(68.3216 - 118.337i) q^{34} +(48.0672 - 78.0687i) q^{36} +243.269 q^{37} +(5.80603 - 10.0563i) q^{38} +(-262.980 - 3.71976i) q^{39} +(-234.286 - 405.796i) q^{41} +(259.281 + 3.66743i) q^{42} +(249.205 - 431.637i) q^{43} -42.4427 q^{44} +189.832 q^{46} +(-226.262 + 391.897i) q^{47} +(64.1294 + 114.795i) q^{48} +(-98.9304 - 171.352i) q^{49} +(-169.480 + 284.189i) q^{51} +(-85.9339 + 148.842i) q^{52} -223.885 q^{53} +(161.447 - 254.095i) q^{54} +(284.339 - 492.490i) q^{56} +(-14.4026 + 24.1506i) q^{57} +(155.108 + 268.655i) q^{58} +(-57.9657 - 100.400i) q^{59} +(-41.3965 + 71.7008i) q^{61} +596.444 q^{62} +(-627.672 - 17.7599i) q^{63} +505.689 q^{64} +(-139.354 - 1.97112i) q^{66} +(-405.064 - 701.592i) q^{67} +(108.113 + 187.258i) q^{68} +(-459.642 - 6.50146i) q^{69} -134.171 q^{71} +(-313.806 - 580.874i) q^{72} +707.508 q^{73} +(261.003 - 452.070i) q^{74} +(9.18755 + 15.9133i) q^{76} +(145.347 + 251.748i) q^{77} +(-289.064 + 484.710i) q^{78} +(-208.821 + 361.689i) q^{79} +(-399.615 + 609.712i) q^{81} -1005.46 q^{82} +(461.443 - 799.243i) q^{83} +(-210.171 + 352.420i) q^{84} +(-534.745 - 926.205i) q^{86} +(-366.363 - 655.808i) q^{87} +(-152.823 + 264.696i) q^{88} +114.544 q^{89} +1177.14 q^{91} +(-150.197 + 260.149i) q^{92} +(-1444.17 - 20.4273i) q^{93} +(485.513 + 840.932i) q^{94} +(-734.242 - 10.3856i) q^{96} +(-180.777 + 313.115i) q^{97} -424.569 q^{98} +(337.352 + 9.54534i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 4 q^{2} + q^{3} - 48 q^{4} - 13 q^{6} - 6 q^{7} - 90 q^{8} - 61 q^{9}+O(q^{10}) \) 24 * q + 4 * q^2 + q^3 - 48 * q^4 - 13 * q^6 - 6 * q^7 - 90 * q^8 - 61 * q^9	\( 24 q + 4 q^{2} + q^{3} - 48 q^{4} - 13 q^{6} - 6 q^{7} - 90 q^{8} - 61 q^{9} - 29 q^{11} + 77 q^{12} - 24 q^{13} + 69 q^{14} - 192 q^{16} - 158 q^{17} - 125 q^{18} - 150 q^{19} - 60 q^{21} + 18 q^{22} + 318 q^{23} + 342 q^{24} - 308 q^{26} + 394 q^{27} + 192 q^{28} - 106 q^{29} - 60 q^{31} + 914 q^{32} + 80 q^{33} + 108 q^{34} + 1303 q^{36} - 168 q^{37} + 640 q^{38} - 410 q^{39} + 353 q^{41} - 1521 q^{42} + 426 q^{43} + 1142 q^{44} + 540 q^{46} + 1210 q^{47} - 2680 q^{48} - 666 q^{49} - 1369 q^{51} + 75 q^{52} - 896 q^{53} - 2128 q^{54} + 570 q^{56} - 1544 q^{57} - 594 q^{58} - 482 q^{59} - 402 q^{61} - 5088 q^{62} + 1038 q^{63} + 1950 q^{64} + 2041 q^{66} + 201 q^{67} + 3437 q^{68} + 2856 q^{69} - 1888 q^{71} + 5493 q^{72} - 906 q^{73} - 10 q^{74} + 462 q^{76} + 2652 q^{77} + 4589 q^{78} - 258 q^{79} + 3071 q^{81} + 1746 q^{82} + 3012 q^{83} - 2703 q^{84} - 1952 q^{86} - 2708 q^{87} + 216 q^{88} - 1476 q^{89} - 1236 q^{91} + 5232 q^{92} - 3024 q^{93} - 63 q^{94} - 10424 q^{96} + 318 q^{97} - 15022 q^{98} - 1697 q^{99}+O(q^{100}) \) 24 * q + 4 * q^2 + q^3 - 48 * q^4 - 13 * q^6 - 6 * q^7 - 90 * q^8 - 61 * q^9 - 29 * q^11 + 77 * q^12 - 24 * q^13 + 69 * q^14 - 192 * q^16 - 158 * q^17 - 125 * q^18 - 150 * q^19 - 60 * q^21 + 18 * q^22 + 318 * q^23 + 342 * q^24 - 308 * q^26 + 394 * q^27 + 192 * q^28 - 106 * q^29 - 60 * q^31 + 914 * q^32 + 80 * q^33 + 108 * q^34 + 1303 * q^36 - 168 * q^37 + 640 * q^38 - 410 * q^39 + 353 * q^41 - 1521 * q^42 + 426 * q^43 + 1142 * q^44 + 540 * q^46 + 1210 * q^47 - 2680 * q^48 - 666 * q^49 - 1369 * q^51 + 75 * q^52 - 896 * q^53 - 2128 * q^54 + 570 * q^56 - 1544 * q^57 - 594 * q^58 - 482 * q^59 - 402 * q^61 - 5088 * q^62 + 1038 * q^63 + 1950 * q^64 + 2041 * q^66 + 201 * q^67 + 3437 * q^68 + 2856 * q^69 - 1888 * q^71 + 5493 * q^72 - 906 * q^73 - 10 * q^74 + 462 * q^76 + 2652 * q^77 + 4589 * q^78 - 258 * q^79 + 3071 * q^81 + 1746 * q^82 + 3012 * q^83 - 2703 * q^84 - 1952 * q^86 - 2708 * q^87 + 216 * q^88 - 1476 * q^89 - 1236 * q^91 + 5232 * q^92 - 3024 * q^93 - 63 * q^94 - 10424 * q^96 + 318 * q^97 - 15022 * q^98 - 1697 * q^99

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