LMFDB - Embedded newform 175.4.e.f.51.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [175,4,Mod(51,175)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(175, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("175.51");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 175 = 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	175.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:	$10.3253342510$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - x^{15} + 46 x^{14} - 7 x^{13} + 1485 x^{12} - 175 x^{11} + 21701 x^{10} + 4916 x^{9} + \cdots + 1498176 $ x^16 - x^15 + 46x^14 - 7x^13 + 1485x^12 - 175x^11 + 21701x^10 + 4916x^9 + 225012x^8 + 16322x^7 + 1117997x^6 - 98710x^5 + 3998444x^4 - 474528x^3 + 2777872x^2 + 460224x + 1498176
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			51.2
Root			$-1.46047 + 2.52961i$ of defining polynomial
Character	$\chi$	$=$	175.51
Dual form			175.4.e.f.151.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.46047 + 2.52961i) q^{2} +(-5.02414 - 8.70206i) q^{3} +(-0.265967 - 0.460668i) q^{4} +29.3505 q^{6} +(-18.3734 + 2.32782i) q^{7} -21.8138 q^{8} +(-36.9839 + 64.0580i) q^{9} +(-7.79680 - 13.5045i) q^{11} +(-2.67251 + 4.62892i) q^{12} +63.9123 q^{13} +(20.9454 - 49.8773i) q^{14} +(33.9863 - 58.8659i) q^{16} +(5.28883 + 9.16053i) q^{17} +(-108.028 - 187.110i) q^{18} +(19.3864 - 33.5782i) q^{19} +(112.567 + 148.191i) q^{21} +45.5481 q^{22} +(-12.0614 + 20.8909i) q^{23} +(109.596 + 189.825i) q^{24} +(-93.3422 + 161.673i) q^{26} +471.945 q^{27} +(5.95906 + 7.84491i) q^{28} +226.731 q^{29} +(71.5651 + 123.954i) q^{31} +(12.0168 + 20.8136i) q^{32} +(-78.3444 + 135.697i) q^{33} -30.8968 q^{34} +39.3460 q^{36} +(-142.626 + 247.036i) q^{37} +(56.6265 + 98.0800i) q^{38} +(-321.104 - 556.168i) q^{39} +32.0457 q^{41} +(-539.268 + 68.3225i) q^{42} +235.711 q^{43} +(-4.14738 + 7.18348i) q^{44} +(-35.2306 - 61.0212i) q^{46} +(72.1481 - 124.964i) q^{47} -683.006 q^{48} +(332.163 - 85.5397i) q^{49} +(53.1436 - 92.0475i) q^{51} +(-16.9985 - 29.4423i) q^{52} +(159.291 + 275.900i) q^{53} +(-689.263 + 1193.84i) q^{54} +(400.794 - 50.7786i) q^{56} -389.599 q^{57} +(-331.135 + 573.542i) q^{58} +(-224.161 - 388.258i) q^{59} +(-83.3473 + 144.362i) q^{61} -418.076 q^{62} +(530.404 - 1263.05i) q^{63} +473.580 q^{64} +(-228.840 - 396.362i) q^{66} +(370.521 + 641.761i) q^{67} +(2.81331 - 4.87279i) q^{68} +242.392 q^{69} -373.652 q^{71} +(806.760 - 1397.35i) q^{72} +(118.657 + 205.520i) q^{73} +(-416.604 - 721.580i) q^{74} -20.6245 q^{76} +(174.690 + 229.973i) q^{77} +1875.86 q^{78} +(232.695 - 403.040i) q^{79} +(-1372.55 - 2377.33i) q^{81} +(-46.8018 + 81.0631i) q^{82} -691.289 q^{83} +(38.3277 - 91.2700i) q^{84} +(-344.249 + 596.257i) q^{86} +(-1139.13 - 1973.03i) q^{87} +(170.078 + 294.584i) q^{88} +(-506.590 + 877.440i) q^{89} +(-1174.28 + 148.776i) q^{91} +12.8317 q^{92} +(719.105 - 1245.53i) q^{93} +(210.741 + 365.014i) q^{94} +(120.748 - 209.141i) q^{96} +1151.67 q^{97} +(-268.732 + 965.172i) q^{98} +1153.42 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + q^{2} - 6 q^{3} - 27 q^{4} + 8 q^{6} - 16 q^{7} - 84 q^{8} - 42 q^{9} - 103 q^{12} + 276 q^{13} - 65 q^{14} - 191 q^{16} - 138 q^{17} - 81 q^{18} + 42 q^{19} + 302 q^{21} + 254 q^{22} - 124 q^{23}+ \cdots + 8172 q^{99}+O(q^{100}) $ 16 * q + q^2 - 6 * q^3 - 27 * q^4 + 8 * q^6 - 16 * q^7 - 84 * q^8 - 42 * q^9 - 103 * q^12 + 276 * q^13 - 65 * q^14 - 191 * q^16 - 138 * q^17 - 81 * q^18 + 42 * q^19 + 302 * q^21 + 254 * q^22 - 124 * q^23 + 292 * q^24 - 23 * q^26 + 408 * q^27 + 619 * q^28 + 576 * q^29 - 18 * q^31 + 562 * q^32 - 236 * q^33 - 976 * q^34 - 1422 * q^36 - 220 * q^37 - 1104 * q^38 - 22 * q^39 + 336 * q^41 - 1299 * q^42 + 120 * q^43 + 880 * q^44 + 98 * q^46 - 1098 * q^47 + 676 * q^48 - 1114 * q^49 - 628 * q^51 - 1370 * q^52 + 734 * q^53 - 2163 * q^54 + 3051 * q^56 + 1828 * q^57 - 924 * q^58 - 558 * q^59 + 1496 * q^61 + 1602 * q^62 + 130 * q^63 + 4872 * q^64 + 682 * q^66 + 1166 * q^67 - 2455 * q^68 + 1644 * q^69 - 1448 * q^71 + 2191 * q^72 - 892 * q^73 - 235 * q^74 - 3018 * q^76 - 3474 * q^77 + 4244 * q^78 + 840 * q^79 - 2392 * q^81 - 4154 * q^82 + 2292 * q^83 - 5271 * q^84 - 1816 * q^86 - 4286 * q^87 + 788 * q^88 - 2678 * q^89 + 2046 * q^91 + 13864 * q^92 + 1986 * q^93 - 3625 * q^94 + 6601 * q^96 + 1328 * q^97 - 6502 * q^98 + 8172 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/175\mathbb{Z}\right)^\times$.

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

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 $

$2$	−1.46047	+	2.52961i	−0.516355	+	0.894354i	0.483464	+	0.875364i	$0.339378\pi$
$2$	−1.46047	+	2.52961i	−0.516355	+	0.894354i	−0.999820	+	0.0189897i	$0.993955\pi$
$3$	−5.02414	−	8.70206i	−0.966895	−	1.67471i	−0.704434	−	0.709770i	$-0.748799\pi$
$3$	−5.02414	−	8.70206i	−0.966895	−	1.67471i	−0.262462	−	0.964942i	$-0.584534\pi$
$4$	−0.265967	−	0.460668i	−0.0332459	−	0.0575835i
$5$		0			0
$5$		0			0
$6$	29.3505			1.99705
$7$	−18.3734	+	2.32782i	−0.992070	+	0.125690i
$7$	−18.3734	+	2.32782i	−0.992070	+	0.125690i
$8$	−21.8138			−0.964044
$9$	−36.9839	+	64.0580i	−1.36977	+	2.37252i
$10$		0			0
$11$	−7.79680	−	13.5045i	−0.213711	−	0.370159i	0.739162	−	0.673528i	$-0.235222\pi$
$11$	−7.79680	−	13.5045i	−0.213711	−	0.370159i	−0.952873	+	0.303369i	$0.901889\pi$
$12$	−2.67251	+	4.62892i	−0.0642905	+	0.111354i
$13$	63.9123			1.36354			0.681772	−	0.731565i	$-0.261210\pi$
$13$	63.9123			1.36354			0.681772	+	0.731565i	$0.261210\pi$
$14$	20.9454	−	49.8773i	0.399849	−	0.952162i
$15$		0			0
$16$	33.9863	−	58.8659i	0.531035	−	0.919780i
$17$	5.28883	+	9.16053i	0.0754547	+	0.130691i	0.901284	−	0.433229i	$-0.142626\pi$
$17$	5.28883	+	9.16053i	0.0754547	+	0.130691i	−0.825829	+	0.563920i	$0.809292\pi$
$18$	−108.028	−	187.110i	−1.41458	−	2.45012i
$19$	19.3864	−	33.5782i	0.234081	−	0.405440i	−0.724924	−	0.688829i	$-0.758125\pi$
$19$	19.3864	−	33.5782i	0.234081	−	0.405440i	0.959005	+	0.283389i	$0.0914586\pi$
$20$		0			0
$21$	112.567	+	148.191i	1.16972	+	1.53990i
$22$	45.5481			0.441404
$23$	−12.0614	+	20.8909i	−0.109346	+	0.189394i	−0.915506	−	0.402305i	$-0.868209\pi$
$23$	−12.0614	+	20.8909i	−0.109346	+	0.189394i	0.806159	+	0.591699i	$0.201542\pi$
$24$	109.596	+	189.825i	0.932130	+	1.61450i
$25$		0			0
$26$	−93.3422	+	161.673i	−0.704073	+	1.21949i
$27$	471.945			3.36392
$28$	5.95906	+	7.84491i	0.0402199	+	0.0529482i
$29$	226.731			1.45182			0.725912	−	0.687787i	$-0.241418\pi$
$29$	226.731			1.45182			0.725912	+	0.687787i	$0.241418\pi$
$30$		0			0
$31$	71.5651	+	123.954i	0.414628	+	0.718157i	0.995389	−	0.0959171i	$-0.0305784\pi$
$31$	71.5651	+	123.954i	0.414628	+	0.718157i	−0.580761	+	0.814074i	$0.697245\pi$
$32$	12.0168	+	20.8136i	0.0663838	+	0.114980i
$33$	−78.3444	+	135.697i	−0.413273	+	0.715810i
$34$	−30.8968			−0.155846
$35$		0			0
$36$	39.3460			0.182157
$37$	−142.626	+	247.036i	−0.633720	+	1.09764i	0.353065	+	0.935599i	$0.385140\pi$
$37$	−142.626	+	247.036i	−0.633720	+	1.09764i	−0.986785	+	0.162036i	$0.948194\pi$
$38$	56.6265	+	98.0800i	0.241738	+	0.418702i
$39$	−321.104	−	556.168i	−1.31840	−	2.28354i
$40$		0			0
$41$	32.0457			0.122066			0.0610328	−	0.998136i	$-0.480561\pi$
$41$	32.0457			0.122066			0.0610328	+	0.998136i	$0.480561\pi$
$42$	−539.268	+	68.3225i	−1.98121	+	0.251009i
$43$	235.711			0.835942			0.417971	−	0.908460i	$-0.362741\pi$
$43$	235.711			0.835942			0.417971	+	0.908460i	$0.362741\pi$
$44$	−4.14738	+	7.18348i	−0.0142100	+	0.0246125i
$45$		0			0
$46$	−35.2306	−	61.0212i	−0.112923	−	0.195589i
$47$	72.1481	−	124.964i	0.223912	−	0.387828i	−0.732080	−	0.681219i	$-0.761450\pi$
$47$	72.1481	−	124.964i	0.223912	−	0.387828i	0.955993	+	0.293391i	$0.0947837\pi$
$48$	−683.006			−2.05382
$49$	332.163	−	85.5397i	0.968404	−	0.249387i
$50$		0			0
$51$	53.1436	−	92.0475i	0.145914	−	0.252730i
$52$	−16.9985	−	29.4423i	−0.0453322	−	0.0785177i
$53$	159.291	+	275.900i	0.412835	+	0.715051i	0.995198	−	0.0978773i	$-0.0312053\pi$
$53$	159.291	+	275.900i	0.412835	+	0.715051i	−0.582364	+	0.812928i	$0.697872\pi$
$54$	−689.263	+	1193.84i	−1.73698	+	3.00854i
$55$		0			0
$56$	400.794	−	50.7786i	0.956399	−	0.121171i
$57$	−389.599			−0.905327
$58$	−331.135	+	573.542i	−0.749657	+	1.29844i
$59$	−224.161	−	388.258i	−0.494632	−	0.856727i	0.505349	−	0.862915i	$-0.331364\pi$
$59$	−224.161	−	388.258i	−0.494632	−	0.856727i	−0.999981	+	0.00618772i	$0.998030\pi$
$60$		0			0
$61$	−83.3473	+	144.362i	−0.174943	+	0.303010i	−0.940142	−	0.340784i	$-0.889307\pi$
$61$	−83.3473	+	144.362i	−0.174943	+	0.303010i	0.765198	+	0.643794i	$0.222641\pi$
$62$	−418.076			−0.856382
$63$	530.404	−	1263.05i	1.06071	−	2.52587i
$64$	473.580			0.924960
$65$		0			0
$66$	−228.840	−	396.362i	−0.426792	−	0.739225i
$67$	370.521	+	641.761i	0.675617	+	1.17020i	0.976288	+	0.216475i	$0.0694561\pi$
$67$	370.521	+	641.761i	0.675617	+	1.17020i	−0.300671	+	0.953728i	$0.597211\pi$
$68$	2.81331	−	4.87279i	0.00501711	−	0.00868990i
$69$	242.392			0.422906
$70$		0			0
$71$	−373.652			−0.624567			−0.312284	−	0.949989i	$-0.601094\pi$
$71$	−373.652			−0.624567			−0.312284	+	0.949989i	$0.601094\pi$
$72$	806.760	−	1397.35i	1.32052	−	2.28721i
$73$	118.657	+	205.520i	0.190243	+	0.329511i	0.945331	−	0.326113i	$-0.105739\pi$
$73$	118.657	+	205.520i	0.190243	+	0.329511i	−0.755088	+	0.655624i	$0.772406\pi$
$74$	−416.604	−	721.580i	−0.654450	−	1.13354i
$75$		0			0
$76$	−20.6245			−0.0311289
$77$	174.690	+	229.973i	0.258542	+	0.340362i
$78$	1875.86			2.72306
$79$	232.695	−	403.040i	0.331396	−	0.573994i	−0.651390	−	0.758743i	$-0.725814\pi$
$79$	232.695	−	403.040i	0.331396	−	0.573994i	0.982786	+	0.184749i	$0.0591472\pi$
$80$		0			0
$81$	−1372.55	−	2377.33i	−1.88279	−	3.26108i
$82$	−46.8018	+	81.0631i	−0.0630292	+	0.109170i
$83$	−691.289			−0.914202			−0.457101	−	0.889415i	$-0.651112\pi$
$83$	−691.289			−0.914202			−0.457101	+	0.889415i	$0.651112\pi$
$84$	38.3277	−	91.2700i	0.0497845	−	0.118552i
$85$		0			0
$86$	−344.249	+	596.257i	−0.431643	+	0.747628i
$87$	−1139.13	−	1973.03i	−1.40376	−	2.43139i
$88$	170.078	+	294.584i	0.206027	+	0.356850i
$89$	−506.590	+	877.440i	−0.603353	+	1.04504i	0.388956	+	0.921256i	$0.372836\pi$
$89$	−506.590	+	877.440i	−0.603353	+	1.04504i	−0.992309	+	0.123782i	$0.960498\pi$
$90$		0			0
$91$	−1174.28	+	148.776i	−1.35273	+	0.171384i
$92$	12.8317			0.0145413
$93$	719.105	−	1245.53i	0.801804	−	1.38876i
$94$	210.741	+	365.014i	0.231237	+	0.400514i
$95$		0			0
$96$	120.748	−	209.141i	0.128372	−	0.222348i
$97$	1151.67			1.20551			0.602757	−	0.797925i	$-0.294069\pi$
$97$	1151.67			1.20551			0.602757	+	0.797925i	$0.294069\pi$
$98$	−268.732	+	965.172i	−0.277000	+	0.994868i
$99$	1153.42			1.17094
$100$		0			0
$101$	600.514	+	1040.12i	0.591618	+	1.02471i	0.994015	+	0.109247i	$0.0348438\pi$
$101$	600.514	+	1040.12i	0.591618	+	1.02471i	−0.402397	+	0.915465i	$0.631823\pi$
$102$	155.230	+	268.866i	0.150687	+	0.260997i
$103$	−514.525	+	891.184i	−0.492211	+	0.852534i	−0.999960	−	0.00897107i	$-0.997144\pi$
$103$	−514.525	+	891.184i	−0.492211	+	0.852534i	0.507749	+	0.861505i	$0.330478\pi$
$104$	−1394.17			−1.31452
$105$		0			0
$106$	−930.559			−0.852678
$107$	288.369	−	499.469i	0.260539	−	0.451266i	−0.705846	−	0.708365i	$-0.749433\pi$
$107$	288.369	−	499.469i	0.260539	−	0.451266i	0.966385	+	0.257098i	$0.0827665\pi$
$108$	−125.522	−	217.410i	−0.111836	−	0.193706i
$109$	95.6623	+	165.692i	0.0840623	+	0.145600i	0.904991	−	0.425430i	$-0.139877\pi$
$109$	95.6623	+	165.692i	0.0840623	+	0.145600i	−0.820929	+	0.571030i	$0.806544\pi$
$110$		0			0
$111$	2866.30			2.45096
$112$	−487.414	+	1160.68i	−0.411217	+	0.979232i
$113$	−2091.69			−1.74132			−0.870662	−	0.491882i	$-0.836309\pi$
$113$	−2091.69			−1.74132			−0.870662	+	0.491882i	$0.836309\pi$
$114$	568.999	−	985.535i	0.467470	−	0.809682i
$115$		0			0
$116$	−60.3030	−	104.448i	−0.0482671	−	0.0836012i
$117$	−2363.72	+	4094.09i	−1.86775	+	3.23503i
$118$	1309.52			1.02162
$119$	−118.498	−	155.998i	−0.0912830	−	0.120171i
$120$		0			0
$121$	543.920	−	942.097i	0.408655	−	0.707811i
$122$	−243.453	−	421.673i	−0.180666	−	0.312922i
$123$	−161.002	−	278.863i	−0.118025	−	0.204425i
$124$	38.0679	−	65.9355i	0.0275693	−	0.0477515i
$125$		0			0
$126$	2420.40	+	3186.37i	1.71132	+	2.25290i
$127$	498.841			0.348543			0.174271	−	0.984698i	$-0.444243\pi$
$127$	498.841			0.348543			0.174271	+	0.984698i	$0.444243\pi$
$128$	−787.784	+	1364.48i	−0.543992	+	0.942222i
$129$	−1184.24	−	2051.17i	−0.808269	−	1.39996i
$130$		0			0
$131$	−155.825	+	269.897i	−0.103928	+	0.180008i	−0.913300	−	0.407289i	$-0.866474\pi$
$131$	−155.825	+	269.897i	−0.103928	+	0.180008i	0.809372	+	0.587296i	$0.199808\pi$
$132$	83.3481			0.0549585
$133$	−278.029	+	662.072i	−0.181265	+	0.431646i
$134$	−2164.55			−1.39543
$135$		0			0
$136$	−115.370	−	199.826i	−0.0727417	−	0.125992i
$137$	−511.345	−	885.675i	−0.318884	−	0.552324i	0.661371	−	0.750059i	$-0.269975\pi$
$137$	−511.345	−	885.675i	−0.318884	−	0.552324i	−0.980255	+	0.197735i	$0.936641\pi$
$138$	−354.007	+	613.157i	−0.218370	+	0.378228i
$139$	1141.29			0.696424			0.348212	−	0.937416i	$-0.386789\pi$
$139$	1141.29			0.696424			0.348212	+	0.937416i	$0.386789\pi$
$140$		0			0
$141$	−1449.93			−0.866000
$142$	545.708	−	945.194i	0.322499	−	0.558584i
$143$	−498.311	−	863.101i	−0.291405	−	0.504728i
$144$	2513.89	+	4354.18i	1.45480	+	2.51978i
$145$		0			0
$146$	−693.182			−0.392932
$147$	−2413.20	−	2460.73i	−1.35400	−	1.38067i
$148$	151.736			0.0842743
$149$	−645.485	+	1118.01i	−0.354900	+	0.614705i	−0.987101	−	0.160099i	$-0.948819\pi$
$149$	−645.485	+	1118.01i	−0.354900	+	0.614705i	0.632201	+	0.774805i	$0.282152\pi$
$150$		0			0
$151$	574.974	+	995.885i	0.309873	+	0.536715i	0.978334	−	0.207032i	$-0.0663803\pi$
$151$	574.974	+	995.885i	0.309873	+	0.536715i	−0.668462	+	0.743747i	$0.733047\pi$
$152$	−422.891	+	732.468i	−0.225664	+	0.390862i
$153$	−782.407			−0.413424
$154$	−836.873	+	106.028i	−0.437904	+	0.0554802i
$155$		0			0
$156$	−170.806	+	295.845i	−0.0876630	+	0.151837i
$157$	1811.17	+	3137.03i	0.920681	+	1.59467i	0.798364	+	0.602175i	$0.205699\pi$
$157$	1811.17	+	3137.03i	0.920681	+	1.59467i	0.122317	+	0.992491i	$0.460968\pi$
$158$	679.690	+	1177.26i	0.342236	+	0.592770i
$159$	1600.60	−	2772.31i	0.798337	−	1.38276i
$160$		0			0
$161$	172.978	−	411.913i	0.0846743	−	0.201635i
$162$	8018.30			3.88875
$163$	1352.86	−	2343.22i	0.650086	−	1.12598i	−0.333016	−	0.942921i	$-0.608066\pi$
$163$	1352.86	−	2343.22i	0.650086	−	1.12598i	0.983102	−	0.183060i	$-0.0586003\pi$
$164$	−8.52308	−	14.7624i	−0.00405818	−	0.00702897i
$165$		0			0
$166$	1009.61	−	1748.69i	0.472053	−	0.817620i
$167$	3397.98			1.57451			0.787256	−	0.616627i	$-0.211501\pi$
$167$	3397.98			1.57451			0.787256	+	0.616627i	$0.211501\pi$
$168$	−2455.52	−	3232.61i	−1.12766	−	1.48453i
$169$	1887.78			0.859253
$170$		0			0
$171$	1433.97	+	2483.70i	0.641275	+	1.11072i
$172$	−62.6912	−	108.584i	−0.0277916	−	0.0481365i
$173$	2093.40	−	3625.88i	0.919991	−	1.59347i	0.120566	−	0.992705i	$-0.461529\pi$
$173$	2093.40	−	3625.88i	0.919991	−	1.59347i	0.799425	−	0.600766i	$-0.205138\pi$
$174$	6654.67			2.89936
$175$		0			0
$176$	−1059.94			−0.453953
$177$	−2252.43	+	3901.32i	−0.956514	+	1.65673i
$178$	−1479.72	−	2562.96i	−0.623089	−	1.07922i
$179$	−458.926	−	794.884i	−0.191630	−	0.331913i	0.754161	−	0.656690i	$-0.228044\pi$
$179$	−458.926	−	794.884i	−0.191630	−	0.331913i	−0.945791	+	0.324777i	$0.894711\pi$
$180$		0			0
$181$	262.339			0.107732			0.0538661	−	0.998548i	$-0.482846\pi$
$181$	262.339			0.107732			0.0538661	+	0.998548i	$0.482846\pi$
$182$	1338.67	−	3187.77i	0.545212	−	1.29832i
$183$	1674.99			0.676607
$184$	263.104	−	455.710i	0.105415	−	0.182584i
$185$		0			0
$186$	2100.47	+	3638.12i	0.828031	+	1.43419i
$187$	82.4720	−	142.846i	0.0322511	−	0.0558605i
$188$	−76.7560			−0.0297766
$189$	−8671.23	+	1098.60i	−3.33724	+	0.422812i
$190$		0			0
$191$	−723.091	+	1252.43i	−0.273932	+	0.474464i	−0.969865	−	0.243642i	$-0.921658\pi$
$191$	−723.091	+	1252.43i	−0.273932	+	0.474464i	0.695933	+	0.718107i	$0.254991\pi$
$192$	−2379.33	−	4121.12i	−0.894340	−	1.54904i
$193$	2032.93	+	3521.13i	0.758204	+	1.31325i	0.943766	+	0.330615i	$0.107256\pi$
$193$	2032.93	+	3521.13i	0.758204	+	1.31325i	−0.185562	+	0.982633i	$0.559411\pi$
$194$	−1681.99	+	2913.29i	−0.622474	+	1.07816i
$195$		0			0
$196$	−127.750	−	130.266i	−0.0465560	−	0.0474730i
$197$	1073.07			0.388088			0.194044	−	0.980993i	$-0.437840\pi$
$197$	1073.07			0.388088			0.194044	+	0.980993i	$0.437840\pi$
$198$	−1684.55	+	2917.72i	−0.604624	+	1.04724i
$199$	1488.51	+	2578.18i	0.530240	+	0.918403i	0.999378	+	0.0352775i	$0.0112315\pi$
$199$	1488.51	+	2578.18i	0.530240	+	0.918403i	−0.469138	+	0.883125i	$0.655435\pi$
$200$		0			0
$201$	3723.10	−	6448.59i	1.30650	−	2.26293i
$202$	−3508.14			−1.22194
$203$	−4165.82	+	527.788i	−1.44031	+	0.182480i
$204$	−56.5378			−0.0194041
$205$		0			0
$206$	−1502.90	−	2603.10i	−0.508311	−	0.880421i
$207$	−892.152	−	1545.25i	−0.299560	−	0.518853i
$208$	2172.14	−	3762.26i	0.724090	−	1.25416i
$209$	−604.607			−0.200103
$210$		0			0
$211$	−521.629			−0.170192			−0.0850958	−	0.996373i	$-0.527120\pi$
$211$	−521.629			−0.170192			−0.0850958	+	0.996373i	$0.527120\pi$
$212$	84.7321	−	146.760i	0.0274501	−	0.0475450i
$213$	1877.28	+	3251.54i	0.603891	+	1.04597i
$214$	842.310	+	1458.92i	0.269061	+	0.466028i
$215$		0			0
$216$	−10294.9			−3.24297
$217$	−1603.44	−	2110.87i	−0.501605	−	0.660347i
$218$	−558.849			−0.173624
$219$	1192.30	−	2065.12i	0.367890	−	0.637205i
$220$		0			0
$221$	338.021	+	585.470i	0.102886	+	0.178204i
$222$	−4186.15	+	7250.63i	−1.26557	+	2.19203i
$223$	2381.79			0.715229			0.357615	−	0.933869i	$-0.383590\pi$
$223$	2381.79			0.715229			0.357615	+	0.933869i	$0.383590\pi$
$224$	−269.239	−	354.444i	−0.0803093	−	0.105725i
$225$		0			0
$226$	3054.86	−	5291.17i	0.899142	−	1.55736i
$227$	170.517	+	295.343i	0.0498572	+	0.0863552i	0.889877	−	0.456201i	$-0.150790\pi$
$227$	170.517	+	295.343i	0.0498572	+	0.0863552i	−0.840020	+	0.542556i	$0.817457\pi$
$228$	103.620	+	179.476i	0.0300984	+	0.0521319i
$229$	−387.522	+	671.208i	−0.111826	+	0.193688i	−0.916507	−	0.400020i	$-0.869003\pi$
$229$	−387.522	+	671.208i	−0.111826	+	0.193688i	0.804680	+	0.593708i	$0.202337\pi$
$230$		0			0
$231$	1123.58	−	2675.58i	0.320025	−	0.762078i
$232$	−4945.87			−1.39962
$233$	1249.92	−	2164.93i	0.351438	−	0.608709i	−0.635063	−	0.772460i	$-0.719026\pi$
$233$	1249.92	−	2164.93i	0.351438	−	0.608709i	0.986502	+	0.163751i	$0.0523594\pi$
$234$	−6904.31	−	11958.6i	−1.92884	−	3.34085i
$235$		0			0
$236$	−119.239	+	206.528i	−0.0328889	+	0.0569653i
$237$	−4676.37			−1.28170
$238$	567.679	−	71.9221i	0.154610	−	0.0195883i
$239$	−2181.70			−0.590470			−0.295235	−	0.955425i	$-0.595398\pi$
$239$	−2181.70			−0.590470			−0.295235	+	0.955425i	$0.595398\pi$
$240$		0			0
$241$	1135.07	+	1966.00i	0.303387	+	0.525481i	0.976901	−	0.213693i	$-0.0685492\pi$
$241$	1135.07	+	1966.00i	0.303387	+	0.525481i	−0.673514	+	0.739174i	$0.735216\pi$
$242$	1588.76	+	2751.81i	0.422022	+	0.730964i
$243$	−7420.51	+	12852.7i	−1.95895	+	3.39301i
$244$	88.6705			0.0232645
$245$		0			0
$246$	940.555			0.243771
$247$	1239.03	−	2146.06i	0.319180	−	0.552835i
$248$	−1561.11	−	2703.92i	−0.399720	−	0.692335i
$249$	3473.13	+	6015.64i	0.883938	+	1.53103i
$250$		0			0
$251$	2943.81			0.740286			0.370143	−	0.928975i	$-0.379309\pi$
$251$	2943.81			0.740286			0.370143	+	0.928975i	$0.379309\pi$
$252$	−722.918	+	91.5901i	−0.180713	+	0.0228954i
$253$	376.160			0.0934743
$254$	−728.544	+	1261.87i	−0.179972	+	0.311721i
$255$		0			0
$256$	−406.759	−	704.527i	−0.0993064	−	0.172004i
$257$	1811.81	−	3138.15i	0.439757	−	0.761682i	−0.557913	−	0.829899i	$-0.688398\pi$
$257$	1811.81	−	3138.15i	0.439757	−	0.761682i	0.997670	+	0.0682171i	$0.0217311\pi$
$258$	6918.22			1.66942
$259$	2045.48	−	4870.90i	0.490732	−	1.16858i
$260$		0			0
$261$	−8385.40	+	14523.9i	−1.98867	+	3.44448i
$262$	−455.157	−	788.355i	−0.107327	−	0.185896i
$263$	230.615	+	399.436i	0.0540696	+	0.0936514i	0.891793	−	0.452443i	$-0.149447\pi$
$263$	230.615	+	399.436i	0.0540696	+	0.0936514i	−0.837724	+	0.546094i	$0.816114\pi$
$264$	1708.99	−	2960.06i	0.398413	−	0.690072i
$265$		0			0
$266$	−1268.73	−	1670.25i	−0.292447	−	0.384998i
$267$	10180.7			2.33352
$268$	197.093	−	341.374i	0.0449229	−	0.0778088i
$269$	2865.16	+	4962.61i	0.649413	+	1.12482i	0.983263	+	0.182190i	$0.0583186\pi$
$269$	2865.16	+	4962.61i	0.649413	+	1.12482i	−0.333851	+	0.942626i	$0.608348\pi$
$270$		0			0
$271$	217.608	−	376.908i	0.0487777	−	0.0844854i	−0.840606	−	0.541648i	$-0.817801\pi$
$271$	217.608	−	376.908i	0.0487777	−	0.0844854i	0.889383	+	0.457162i	$0.151134\pi$
$272$	718.991			0.160277
$273$	7194.42	+	9471.22i	1.59497	+	2.09972i
$274$	2987.22			0.658630
$275$		0			0
$276$	−64.4681	−	111.662i	−0.0140599	−	0.0243524i
$277$	−53.7502	−	93.0980i	−0.0116590	−	0.0201939i	0.860137	−	0.510063i	$-0.170378\pi$
$277$	−53.7502	−	93.0980i	−0.0116590	−	0.0201939i	−0.871796	+	0.489869i	$0.837045\pi$
$278$	−1666.82	+	2887.02i	−0.359602	+	0.622849i
$279$	−10587.0			−2.27179
$280$		0			0
$281$	−8058.94			−1.71088			−0.855438	−	0.517905i	$-0.826712\pi$
$281$	−8058.94			−1.71088			−0.855438	+	0.517905i	$0.826712\pi$
$282$	2117.58	−	3667.76i	0.447164	−	0.774510i
$283$	−2898.18	−	5019.80i	−0.608760	−	1.05440i	−0.991445	−	0.130525i	$-0.958334\pi$
$283$	−2898.18	−	5019.80i	−0.608760	−	1.05440i	0.382685	−	0.923879i	$-0.374999\pi$
$284$	99.3789	+	172.129i	0.0207643	+	0.0359648i
$285$		0			0
$286$	2911.08			0.601874
$287$	−588.787	+	74.5964i	−0.121098	+	0.0153425i
$288$	−1777.71			−0.363723
$289$	2400.56	−	4157.89i	0.488613	−	0.846303i
$290$		0			0
$291$	−5786.17	−	10021.9i	−1.16561	−	2.01889i
$292$	63.1176	−	109.323i	0.0126496	−	0.0219097i
$293$	1250.96			0.249427			0.124713	−	0.992193i	$-0.460199\pi$
$293$	1250.96			0.249427			0.124713	+	0.992193i	$0.460199\pi$
$294$	9749.13	−	2510.63i	1.93395	−	0.498037i
$295$		0			0
$296$	3111.23	−	5388.81i	0.610934	−	1.05817i
$297$	−3679.66	−	6373.36i	−0.718908	−	1.24519i
$298$	−1885.43	−	3265.65i	−0.366509	−	0.634813i
$299$	−770.869	+	1335.18i	−0.149099	+	0.258246i
$300$		0			0
$301$	−4330.80	+	548.691i	−0.829313	+	0.105070i
$302$	−3358.94			−0.640018
$303$	6034.13	−	10451.4i	1.14406	−	1.98158i
$304$	−1317.74	−	2282.39i	−0.248610	−	0.430606i
$305$		0			0
$306$	1142.68	−	1979.19i	0.213474	−	0.369747i
$307$	−493.727			−0.0917865			−0.0458933	−	0.998946i	$-0.514613\pi$
$307$	−493.727			−0.0917865			−0.0458933	+	0.998946i	$0.514613\pi$
$308$	59.4796	−	141.639i	0.0110038	−	0.0262034i
$309$	10340.2			1.90367
$310$		0			0
$311$	52.7320	+	91.3345i	0.00961466	+	0.0166531i	0.870793	−	0.491650i	$-0.163606\pi$
$311$	52.7320	+	91.3345i	0.00961466	+	0.0166531i	−0.861178	+	0.508303i	$0.830273\pi$
$312$	7004.51	+	12132.2i	1.27100	+	2.20144i
$313$	1855.32	−	3213.50i	0.335044	−	0.580312i	−0.648450	−	0.761258i	$-0.724582\pi$
$313$	1855.32	−	3213.50i	0.335044	−	0.580312i	0.983493	+	0.180945i	$0.0579156\pi$
$314$	−10580.7			−1.90159
$315$		0			0
$316$	−247.557			−0.0440701
$317$	3250.70	−	5630.38i	0.575955	−	0.997583i	−0.419983	−	0.907532i	$-0.637964\pi$
$317$	3250.70	−	5630.38i	0.575955	−	0.997583i	0.995937	−	0.0900506i	$-0.0287029\pi$
$318$	4675.26	+	8097.78i	0.824451	+	1.42799i
$319$	−1767.78	−	3061.88i	−0.310271	−	0.537406i
$320$		0			0
$321$	−5795.21			−1.00766
$322$	789.351	+	1039.16i	0.136611	+	0.179844i
$323$	410.125			0.0706500
$324$	−730.106	+	1264.58i	−0.125190	+	0.216835i
$325$		0			0
$326$	3951.62	+	6844.42i	0.671350	+	1.16281i
$327$	961.241	−	1664.92i	0.162559	−	0.281560i
$328$	−699.038			−0.117677
$329$	−1034.71	+	2463.96i	−0.173391	+	0.412896i
$330$		0			0
$331$	54.3441	−	94.1268i	0.00902424	−	0.0156304i	−0.861478	−	0.507795i	$-0.830461\pi$
$331$	54.3441	−	94.1268i	0.00902424	−	0.0156304i	0.870502	+	0.492164i	$0.163794\pi$
$332$	183.860	+	318.455i	0.0303934	+	0.0526430i
$333$	−10549.8	−	18272.7i	−1.73611	−	3.00702i
$334$	−4962.66	+	8595.57i	−0.813007	+	1.40817i
$335$		0			0
$336$	12549.1	−	1589.91i	2.03753	−	0.258145i
$337$	−8207.88			−1.32674			−0.663370	−	0.748291i	$-0.730875\pi$
$337$	−8207.88			−1.32674			−0.663370	+	0.748291i	$0.730875\pi$
$338$	−2757.05	+	4775.35i	−0.443680	+	0.768476i
$339$	10508.9	+	18202.0i	1.68368	+	2.91621i
$340$		0			0
$341$	1115.96	−	1932.90i	0.177221	−	0.306956i
$342$	−8377.08			−1.32450
$343$	−5903.83	+	2344.87i	−0.929379	+	0.369128i
$344$	−5141.75			−0.805885
$345$		0			0
$346$	6114.72	+	10591.0i	0.950085	+	1.64560i
$347$	4701.28	+	8142.85i	0.727313	+	1.25974i	0.958015	+	0.286719i	$0.0925646\pi$
$347$	4701.28	+	8142.85i	0.727313	+	1.25974i	−0.230701	+	0.973025i	$0.574102\pi$
$348$	−605.941	+	1049.52i	−0.0933386	+	0.161667i
$349$	−690.530			−0.105912			−0.0529559	−	0.998597i	$-0.516864\pi$
$349$	−690.530			−0.105912			−0.0529559	+	0.998597i	$0.516864\pi$
$350$		0			0
$351$	30163.1			4.58685
$352$	187.385	−	324.560i	0.0283740	−	0.0491451i
$353$	−1800.69	−	3118.89i	−0.271505	−	0.470260i	0.697743	−	0.716349i	$-0.254188\pi$
$353$	−1800.69	−	3118.89i	−0.271505	−	0.470260i	−0.969247	+	0.246088i	$0.920855\pi$
$354$	−6579.23	−	11395.6i	−0.987803	−	1.71092i
$355$		0			0
$356$	538.945			0.0802360
$357$	−762.159	+	1814.93i	−0.112991	+	0.269066i
$358$	2681.00			0.395797
$359$	−4031.95	+	6983.55i	−0.592753	+	1.02668i	0.401107	+	0.916031i	$0.368626\pi$
$359$	−4031.95	+	6983.55i	−0.592753	+	1.02668i	−0.993860	+	0.110647i	$0.964708\pi$
$360$		0			0
$361$	2677.84	+	4638.15i	0.390412	+	0.676214i
$362$	−383.140	+	663.618i	−0.0556281	+	0.0963508i
$363$	−10930.9			−1.58051
$364$	380.857	+	501.386i	0.0548416	+	0.0721972i
$365$		0			0
$366$	−2446.28	+	4237.09i	−0.349370	+	0.605126i
$367$	−1694.81	−	2935.50i	−0.241059	−	0.417526i	0.719958	−	0.694018i	$-0.244161\pi$
$367$	−1694.81	−	2935.50i	−0.241059	−	0.417526i	−0.961016	+	0.276493i	$0.910828\pi$
$368$	819.841	+	1420.01i	0.116134	+	0.201149i
$369$	−1185.17	+	2052.78i	−0.167202	+	0.289603i
$370$		0			0
$371$	−3568.95	−	4698.41i	−0.499436	−	0.657491i
$372$	−765.033			−0.106627
$373$	−4420.62	+	7656.74i	−0.613649	+	1.06287i	0.376971	+	0.926225i	$0.376966\pi$
$373$	−4420.62	+	7656.74i	−0.613649	+	1.06287i	−0.990620	+	0.136646i	$0.956368\pi$
$374$	240.896	+	417.245i	0.0333060	+	0.0576877i
$375$		0			0
$376$	−1573.83	+	2725.95i	−0.215862	+	0.373883i
$377$	14490.9			1.97963
$378$	9885.06	−	23539.3i	1.34506	−	3.20300i
$379$	3038.06			0.411754			0.205877	−	0.978578i	$-0.433995\pi$
$379$	3038.06			0.411754			0.205877	+	0.978578i	$0.433995\pi$
$380$		0			0
$381$	−2506.24	−	4340.94i	−0.337005	−	0.583709i
$382$	−2112.11	−	3658.28i	−0.282893	−	0.489984i
$383$	−1409.34	+	2441.05i	−0.188026	+	0.325671i	−0.944592	−	0.328247i	$-0.893542\pi$
$383$	−1409.34	+	2441.05i	−0.188026	+	0.325671i	0.756566	+	0.653917i	$0.226876\pi$
$384$	15831.7			2.10393
$385$		0			0
$386$	−11876.1			−1.56601
$387$	−8717.49	+	15099.1i	−1.14505	+	1.98329i
$388$	−306.307	−	530.540i	−0.0400783	−	0.0694177i
$389$	−6094.35	−	10555.7i	−0.794334	−	1.37583i	−0.923261	−	0.384173i	$-0.874487\pi$
$389$	−6094.35	−	10555.7i	−0.794334	−	1.37583i	0.128927	−	0.991654i	$-0.458847\pi$
$390$		0			0
$391$	−255.162			−0.0330028
$392$	−7245.74	+	1865.95i	−0.933584	+	0.240420i
$393$	3131.55			0.401948
$394$	−1567.19	+	2714.46i	−0.200391	+	0.347088i
$395$		0			0
$396$	−306.773	−	531.346i	−0.0389291	−	0.0674271i
$397$	5195.17	−	8998.29i	0.656771	−	1.13756i	−0.324676	−	0.945825i	$-0.605255\pi$
$397$	5195.17	−	8998.29i	0.656771	−	1.13756i	0.981447	−	0.191735i	$-0.0614114\pi$
$398$	−8695.73			−1.09517
$399$	7158.25	−	906.914i	0.898147	−	0.113791i
$400$		0			0
$401$	−751.138	+	1301.01i	−0.0935413	+	0.162018i	−0.908999	−	0.416799i	$-0.863152\pi$
$401$	−751.138	+	1301.01i	−0.0935413	+	0.162018i	0.815458	+	0.578817i	$0.196485\pi$
$402$	10875.0	+	18836.0i	1.34924	+	2.33695i
$403$	4573.89	+	7922.20i	0.565364	+	0.979238i
$404$	319.434	−	553.275i	0.0393377	−	0.0681348i
$405$		0			0
$406$	4748.97	−	11308.7i	0.580510	−	1.38237i
$407$	4448.12			0.541733
$408$	−1159.27	+	2007.91i	−0.140667	+	0.243643i
$409$	−7048.61	−	12208.5i	−0.852155	−	1.47598i	−0.879260	−	0.476343i	$-0.841962\pi$
$409$	−7048.61	−	12208.5i	−0.852155	−	1.47598i	0.0271048	−	0.999633i	$-0.491371\pi$
$410$		0			0
$411$	−5138.13	+	8899.50i	−0.616655	+	1.06808i
$412$	547.387			0.0654559
$413$	5022.39	+	6611.81i	0.598391	+	0.787763i
$414$	5211.86			0.618717
$415$		0			0
$416$	768.018	+	1330.25i	0.0905173	+	0.156781i
$417$	−5733.99	−	9931.57i	−0.673369	−	1.16631i
$418$	883.012	−	1529.42i	0.103324	−	0.178963i
$419$	11529.9			1.34433			0.672163	−	0.740403i	$-0.265365\pi$
$419$	11529.9			1.34433			0.672163	+	0.740403i	$0.265365\pi$
$420$		0			0
$421$	−3370.05			−0.390134			−0.195067	−	0.980790i	$-0.562492\pi$
$421$	−3370.05			−0.390134			−0.195067	+	0.980790i	$0.562492\pi$
$422$	761.826	−	1319.52i	0.0878794	−	0.152212i
$423$	5336.64	+	9243.33i	0.613419	+	1.06247i
$424$	−3474.74	−	6018.42i	−0.397991	−	0.689341i
$425$		0			0
$426$	−10966.9			−1.24729
$427$	1195.32	−	2846.43i	0.135470	−	0.322596i
$428$	−306.786			−0.0346473
$429$	−5007.17	+	8672.67i	−0.563516	+	0.976039i
$430$		0			0
$431$	4163.53	+	7211.45i	0.465314	+	0.805948i	0.999216	−	0.0395991i	$-0.0126081\pi$
$431$	4163.53	+	7211.45i	0.465314	+	0.805948i	−0.533902	+	0.845547i	$0.679275\pi$
$432$	16039.6	−	27781.5i	1.78636	−	3.09407i
$433$	818.149			0.0908031			0.0454015	−	0.998969i	$-0.485543\pi$
$433$	818.149			0.0908031			0.0454015	+	0.998969i	$0.485543\pi$
$434$	7681.46	−	973.203i	0.849590	−	0.107639i
$435$		0			0
$436$	50.8860	−	88.1372i	0.00558945	−	0.00968120i
$437$	467.652	+	809.997i	0.0511918	+	0.0886668i
$438$	3482.64	+	6032.11i	0.379924	+	0.658048i
$439$	−4232.89	+	7331.58i	−0.460193	+	0.797078i	−0.998970	−	0.0453707i	$-0.985553\pi$
$439$	−4232.89	+	7331.58i	−0.460193	+	0.797078i	0.538777	+	0.842448i	$0.318886\pi$
$440$		0			0
$441$	−6805.16	+	24441.3i	−0.734819	+	2.63916i
$442$	−1974.69			−0.212503
$443$	−7284.47	+	12617.1i	−0.781254	+	1.35317i	0.149957	+	0.988693i	$0.452086\pi$
$443$	−7284.47	+	12617.1i	−0.781254	+	1.35317i	−0.931211	+	0.364480i	$0.881247\pi$
$444$	−762.340	−	1320.41i	−0.0814844	−	0.141135i
$445$		0			0
$446$	−3478.54	+	6025.00i	−0.369313	+	0.639668i
$447$	12972.0			1.37261
$448$	−8701.26	+	1102.41i	−0.917625	+	0.116258i
$449$	−841.211			−0.0884169			−0.0442084	−	0.999022i	$-0.514077\pi$
$449$	−841.211			−0.0884169			−0.0442084	+	0.999022i	$0.514077\pi$
$450$		0			0
$451$	−249.854	−	432.759i	−0.0260868	−	0.0451837i
$452$	556.320	+	963.574i	0.0578918	+	0.100272i
$453$	5777.50	−	10006.9i	0.599229	−	1.03789i
$454$	−996.140			−0.102976
$455$		0			0
$456$	8498.64			0.872775
$457$	−6938.33	+	12017.5i	−0.710200	+	1.23010i	0.254581	+	0.967051i	$0.418062\pi$
$457$	−6938.33	+	12017.5i	−0.710200	+	1.23010i	−0.964782	+	0.263052i	$0.915271\pi$
$458$	−1131.93	−	1960.56i	−0.115484	−	0.200024i
$459$	2496.04	+	4323.27i	0.253824	+	0.439636i
$460$		0			0
$461$	3053.09			0.308452			0.154226	−	0.988036i	$-0.450712\pi$
$461$	3053.09			0.308452			0.154226	+	0.988036i	$0.450712\pi$
$462$	5127.22	+	6749.82i	0.516320	+	0.679719i
$463$	9935.80			0.997312			0.498656	−	0.866800i	$-0.333827\pi$
$463$	9935.80			0.997312			0.498656	+	0.866800i	$0.333827\pi$
$464$	7705.74	−	13346.7i	0.770970	−	1.33536i
$465$		0			0
$466$	3650.96	+	6323.64i	0.362934	+	0.628620i
$467$	−4963.63	+	8597.26i	−0.491840	+	0.851892i	−0.999956	−	0.00939651i	$-0.997009\pi$
$467$	−4963.63	+	8597.26i	−0.491840	+	0.851892i	0.508116	+	0.861289i	$0.330342\pi$
$468$	2514.69			0.248379
$469$	−8301.63	−	10928.8i	−0.817342	−	1.07600i
$470$		0			0
$471$	18199.1	−	31521.8i	1.78040	−	3.08375i
$472$	4889.81	+	8469.40i	0.476847	+	0.825923i
$473$	−1837.79	−	3183.14i	−0.178650	−	0.309432i
$474$	6829.71	−	11829.4i	0.661813	−	1.14629i
$475$		0			0
$476$	−40.3470	+	96.0786i	−0.00388509	+	0.00925159i
$477$	−23564.8			−2.26196
$478$	3186.32	−	5518.86i	0.304893	−	0.528089i
$479$	6587.12	+	11409.2i	0.628336	+	1.08831i	0.987886	+	0.155184i	$0.0495972\pi$
$479$	6587.12	+	11409.2i	0.628336	+	1.08831i	−0.359549	+	0.933126i	$0.617069\pi$
$480$		0			0
$481$	−9115.58	+	15788.6i	−0.864105	+	1.49667i
$482$	−6630.96			−0.626622
$483$	−4453.56	+	564.243i	−0.419552	+	0.0531552i
$484$	−578.658			−0.0543443
$485$		0			0
$486$	−21674.9	−	37542.1i	−2.02303	−	3.50400i
$487$	−4236.88	−	7338.50i	−0.394233	−	0.682832i	0.598770	−	0.800921i	$-0.295656\pi$
$487$	−4236.88	−	7338.50i	−0.394233	−	0.682832i	−0.993003	+	0.118089i	$0.962323\pi$
$488$	1818.12	−	3149.08i	0.168653	−	0.292115i
$489$	−27187.8			−2.51426
$490$		0			0
$491$	−10831.1			−0.995523			−0.497762	−	0.867314i	$-0.665845\pi$
$491$	−10831.1			−0.995523			−0.497762	+	0.867314i	$0.665845\pi$
$492$	−85.6422	+	148.337i	−0.00784766	+	0.0135926i
$493$	1199.14	+	2076.98i	0.109547	+	0.189741i
$494$	3619.13	+	6268.52i	0.329620	+	0.570919i
$495$		0			0
$496$	9728.92			0.880728
$497$	6865.24	−	869.792i	0.619614	−	0.0785020i
$498$	−20289.7			−1.82571
$499$	6046.05	−	10472.1i	0.542402	−	0.939467i	−0.456364	−	0.889793i	$-0.650848\pi$
$499$	6046.05	−	10472.1i	0.542402	−	0.939467i	0.998765	−	0.0496738i	$-0.0158182\pi$
$500$		0			0
$501$	−17071.9	−	29569.4i	−1.52239	−	2.63685i
$502$	−4299.36	+	7446.71i	−0.382251	+	0.662078i
$503$	18398.5			1.63091			0.815455	−	0.578821i	$-0.196487\pi$
$503$	18398.5			1.63091			0.815455	+	0.578821i	$0.196487\pi$
$504$	−11570.1	+	27552.0i	−1.02257	+	2.43505i
$505$		0			0
$506$	−549.372	+	951.540i	−0.0482660	+	0.0835991i
$507$	−9484.46	−	16427.6i	−0.830808	−	1.43900i
$508$	−132.675	−	229.800i	−0.0115876	−	0.0200703i
$509$	10351.4	−	17929.1i	0.901406	−	1.56128i	0.0757355	−	0.997128i	$-0.475870\pi$
$509$	10351.4	−	17929.1i	0.901406	−	1.56128i	0.825670	−	0.564153i	$-0.190797\pi$
$510$		0			0
$511$	−2658.54	−	3499.88i	−0.230151	−	0.302986i
$512$	−10228.3			−0.882874
$513$	9149.30	−	15847.0i	0.787429	−	1.36387i
$514$	5292.20	+	9166.37i	0.454142	+	0.786598i
$515$		0			0
$516$	−629.938	+	1091.08i	−0.0537432	+	0.0930859i
$517$	−2250.10			−0.191411
$518$	9334.14	+	12288.1i	0.791734	+	1.04229i
$519$	−42070.2			−3.55814
$520$		0			0
$521$	7236.53	+	12534.0i	0.608518	+	1.05398i	0.991485	+	0.130222i	$0.0415691\pi$
$521$	7236.53	+	12534.0i	0.608518	+	1.05398i	−0.382967	+	0.923762i	$0.625098\pi$
$522$	−24493.3	−	42423.7i	−2.05372	−	3.55715i
$523$	−7958.97	+	13785.3i	−0.665433	+	1.15256i	0.313734	+	0.949511i	$0.398420\pi$
$523$	−7958.97	+	13785.3i	−0.665433	+	1.15256i	−0.979168	+	0.203053i	$0.934914\pi$
$524$	165.777			0.0138206
$525$		0			0
$526$	−1347.23			−0.111677
$527$	−756.992	+	1311.15i	−0.0625713	+	0.108377i
$528$	5325.27	+	9223.63i	0.438925	+	0.760241i
$529$	5792.55	+	10033.0i	0.476087	+	0.824606i
$530$		0			0
$531$	33161.4			2.71013
$532$	378.942	−	48.0101i	0.0308820	−	0.00391260i
$533$	2048.11			0.166442
$534$	−14868.7	+	25753.3i	−1.20492	+	2.08699i
$535$		0			0
$536$	−8082.48	−	13999.3i	−0.651325	−	1.12813i
$537$	−4611.42	+	7987.21i	−0.370572	+	0.641850i
$538$	−16738.0			−1.34131
$539$	−3744.97	−	3818.74i	−0.299272	−	0.305167i
$540$		0			0
$541$	4419.67	−	7655.09i	0.351232	−	0.608351i	−0.635234	−	0.772320i	$-0.719096\pi$
$541$	4419.67	−	7655.09i	0.351232	−	0.608351i	0.986466	+	0.163969i	$0.0524296\pi$
$542$	635.622	+	1100.93i	0.0503732	+	0.0872490i
$543$	−1318.03	−	2282.89i	−0.104166	−	0.180421i
$544$	−127.109	+	220.160i	−0.0100179	+	0.0173516i
$545$		0			0
$546$	−34465.8	+	4366.65i	−2.70147	+	0.342262i
$547$	−11349.6			−0.887155			−0.443577	−	0.896236i	$-0.646291\pi$
$547$	−11349.6			−0.887155			−0.443577	+	0.896236i	$0.646291\pi$
$548$	−272.001	+	471.120i	−0.0212032	+	0.0367249i
$549$	−6165.02	−	10678.1i	−0.479265	−	0.830111i
$550$		0			0
$551$	4395.49	−	7613.21i	0.339844	−	0.588628i
$552$	−5287.49			−0.407700
$553$	−3337.20	+	7946.88i	−0.256622	+	0.611095i
$554$	314.003			0.0240807
$555$		0			0
$556$	−303.545	−	525.756i	−0.0231532	−	0.0401025i
$557$	−3305.43	−	5725.18i	−0.251446	−	0.435518i	0.712478	−	0.701695i	$-0.247573\pi$
$557$	−3305.43	−	5725.18i	−0.251446	−	0.435518i	−0.963924	+	0.266177i	$0.914240\pi$
$558$	15462.1	−	26781.1i	1.17305	−	2.03178i
$559$	15064.8			1.13984
$560$		0			0
$561$	−1657.40			−0.124734
$562$	11769.9	−	20386.0i	0.883420	−	1.53013i
$563$	−6424.96	−	11128.4i	−0.480959	−	0.833045i	0.518802	−	0.854894i	$-0.326378\pi$
$563$	−6424.96	−	11128.4i	−0.480959	−	0.833045i	−0.999761	+	0.0218488i	$0.993045\pi$
$564$	385.633	+	667.936i	0.0287909	+	0.0498673i
$565$		0			0
$566$	16930.9			1.25735
$567$	30752.4	+	40484.5i	2.27774	+	2.99857i
$568$	8150.77			0.602110
$569$	4486.52	−	7770.88i	0.330553	−	0.572535i	−0.652067	−	0.758161i	$-0.726098\pi$
$569$	4486.52	−	7770.88i	0.330553	−	0.572535i	0.982620	+	0.185626i	$0.0594314\pi$
$570$		0			0
$571$	−661.018	−	1144.92i	−0.0484461	−	0.0839112i	0.840785	−	0.541368i	$-0.182094\pi$
$571$	−661.018	−	1144.92i	−0.0484461	−	0.0839112i	−0.889232	+	0.457457i	$0.848760\pi$
$572$	−265.069	+	459.112i	−0.0193760	+	0.0335602i
$573$	14531.6			1.05945
$574$	671.208	−	1598.35i	0.0488078	−	0.116226i
$575$		0			0
$576$	−17514.8	+	30336.5i	−1.26699	+	2.19448i
$577$	11616.3	+	20120.0i	0.838116	+	1.45166i	0.891468	+	0.453084i	$0.149676\pi$
$577$	11616.3	+	20120.0i	0.838116	+	1.45166i	−0.0533512	+	0.998576i	$0.516990\pi$
$578$	7011.90	+	12145.0i	0.504596	+	0.873986i
$579$	20427.4	−	35381.3i	1.46621	−	2.53955i
$580$		0			0
$581$	12701.3	−	1609.19i	0.906952	−	0.114906i
$582$	33802.2			2.40747
$583$	2483.92	−	4302.27i	0.176455	−	0.305629i
$584$	−2588.36	−	4483.18i	−0.183403	−	0.317663i
$585$		0			0
$586$	−1827.00	+	3164.46i	−0.128793	+	0.223076i
$587$	−13229.8			−0.930244			−0.465122	−	0.885247i	$-0.653990\pi$
$587$	−13229.8			−0.930244			−0.465122	+	0.885247i	$0.653990\pi$
$588$	−491.750	+	1766.16i	−0.0344889	+	0.123869i
$589$	5549.55			0.388226
$590$		0			0
$591$	−5391.26	−	9337.94i	−0.375240	−	0.649935i
$592$	9694.68	+	16791.7i	0.673055	+	1.16577i
$593$	13172.6	−	22815.7i	0.912201	−	1.57998i	0.101252	−	0.994861i	$-0.467715\pi$
$593$	13172.6	−	22815.7i	0.912201	−	1.57998i	0.810949	−	0.585117i	$-0.198951\pi$
$594$	21496.2			1.48485
$595$		0			0
$596$	686.710			0.0471959
$597$	14957.0	−	25906.2i	1.02537	−	1.77600i
$598$	−2251.67	−	3900.00i	−0.153976	−	0.266694i
$599$	6294.29	+	10902.0i	0.429345	+	0.743647i	0.996815	−	0.0797468i	$-0.0254112\pi$
$599$	6294.29	+	10902.0i	0.429345	+	0.743647i	−0.567470	+	0.823394i	$0.692078\pi$
$600$		0			0
$601$	−5027.54			−0.341227			−0.170614	−	0.985338i	$-0.554575\pi$
$601$	−5027.54			−0.341227			−0.170614	+	0.985338i	$0.554575\pi$
$602$	4937.04	−	11756.6i	0.334251	−	0.795953i
$603$	−54813.2			−3.70177
$604$	305.848	−	529.745i	0.0206040	−	0.0356871i
$605$		0			0
$606$	17625.4	+	30528.0i	1.18149	+	2.04640i
$607$	980.794	−	1698.78i	0.0655835	−	0.113594i	−0.831369	−	0.555721i	$-0.812442\pi$
$607$	980.794	−	1698.78i	0.0655835	−	0.113594i	0.896953	+	0.442127i	$0.145776\pi$
$608$	931.845			0.0621567
$609$	25522.5	+	33599.5i	1.69823	+	2.23567i
$610$		0			0
$611$	4611.15	−	7986.75i	0.305315	−	0.528820i
$612$	208.094	+	360.430i	0.0137446	+	0.0238064i
$613$	4657.33	+	8066.73i	0.306864	+	0.531504i	0.977675	−	0.210124i	$-0.0673869\pi$
$613$	4657.33	+	8066.73i	0.306864	+	0.531504i	−0.670810	+	0.741629i	$0.734054\pi$
$614$	721.075	−	1248.94i	0.0473945	−	0.0820896i
$615$		0			0
$616$	−3810.65	−	5016.59i	−0.249246	−	0.328124i
$617$	−20829.3			−1.35909			−0.679544	−	0.733635i	$-0.737822\pi$
$617$	−20829.3			−1.35909			−0.679544	+	0.733635i	$0.737822\pi$
$618$	−15101.6	+	26156.7i	−0.982968	+	1.70255i
$619$	−6682.39	−	11574.2i	−0.433906	−	0.751548i	0.563299	−	0.826253i	$-0.309532\pi$
$619$	−6682.39	−	11574.2i	−0.433906	−	0.751548i	−0.997206	+	0.0747050i	$0.976198\pi$
$620$		0			0
$621$	−5692.30	+	9859.35i	−0.367833	+	0.637105i
$622$	−308.055			−0.0198583
$623$	7265.26	−	17300.8i	0.467217	−	1.11259i
$624$	−43652.5			−2.80048
$625$		0			0
$626$	5419.28	+	9386.47i	0.346003	+	0.599295i
$627$	3037.63	+	5261.32i	0.193479	+	0.335115i
$628$	963.421	−	1668.69i	0.0612176	−	0.106032i
$629$	−3017.31			−0.191269
$630$		0			0
$631$	−29261.9			−1.84612			−0.923058	−	0.384661i	$-0.874318\pi$
$631$	−29261.9			−1.84612			−0.923058	+	0.384661i	$0.874318\pi$
$632$	−5075.97	+	8791.84i	−0.319480	+	0.553356i
$633$	2620.74	+	4539.25i	0.164558	+	0.285022i
$634$	9495.13	+	16446.0i	0.594795	+	1.03021i
$635$		0			0
$636$	−1702.82			−0.106166
$637$	21229.3	−	5467.04i	1.32046	−	0.340050i
$638$	10327.2			0.640841
$639$	13819.1	−	23935.4i	0.855516	−	1.48180i
$640$		0			0
$641$	6224.26	+	10780.7i	0.383531	+	0.664296i	0.991564	−	0.129616i	$-0.0413745\pi$
$641$	6224.26	+	10780.7i	0.383531	+	0.664296i	−0.608033	+	0.793912i	$0.708041\pi$
$642$	8463.76	−	14659.7i	0.520308	−	0.901200i
$643$	−13458.0			−0.825397			−0.412698	−	0.910868i	$-0.635414\pi$
$643$	−13458.0			−0.825397			−0.412698	+	0.910868i	$0.635414\pi$
$644$	−235.762	+	29.8698i	−0.0144259	+	0.00182769i
$645$		0			0
$646$	−598.977	+	1037.46i	−0.0364805	+	0.0631861i
$647$	918.898	+	1591.58i	0.0558356	+	0.0967101i	0.892592	−	0.450865i	$-0.148884\pi$
$647$	918.898	+	1591.58i	0.0558356	+	0.0967101i	−0.836757	+	0.547575i	$0.815551\pi$
$648$	29940.6	+	51858.6i	1.81509	+	3.14383i
$649$	−3495.48	+	6054.35i	−0.211417	+	0.366185i
$650$		0			0
$651$	−10313.0	+	24558.5i	−0.620891	+	1.47853i
$652$	−1439.26			−0.0864506
$653$	−6064.19	+	10503.5i	−0.363415	+	0.629454i	−0.988520	−	0.151087i	$-0.951723\pi$
$653$	−6064.19	+	10503.5i	−0.363415	+	0.629454i	0.625105	+	0.780540i	$0.285056\pi$
$654$	2807.73	+	4863.14i	0.167876	+	0.290770i
$655$		0			0
$656$	1089.11	−	1886.40i	0.0648211	−	0.112274i
$657$	−17553.6			−1.04236
$658$	−4721.71	−	6215.98i	−0.279744	−	0.368273i
$659$	4131.14			0.244198			0.122099	−	0.992518i	$-0.461038\pi$
$659$	4131.14			0.244198			0.122099	+	0.992518i	$0.461038\pi$
$660$		0			0
$661$	−10681.3	−	18500.6i	−0.628525	−	1.08864i	−0.987848	−	0.155424i	$-0.950326\pi$
$661$	−10681.3	−	18500.6i	−0.628525	−	1.08864i	0.359323	−	0.933213i	$-0.383008\pi$
$662$	158.736	+	274.939i	0.00931943	+	0.0161417i
$663$	3396.53	−	5882.96i	0.198960	−	0.344608i
$664$	15079.7			0.881331
$665$		0			0
$666$	61630.6			3.58579
$667$	−2734.69	+	4736.61i	−0.158752	+	0.274966i
$668$	−903.749	−	1565.34i	−0.0523460	−	0.0906659i
$669$	−11966.4	−	20726.4i	−0.691552	−	1.19780i
$670$		0			0
$671$	2599.37			0.149549
$672$	−1731.70	+	4123.71i	−0.0994075	+	0.236719i
$673$	26260.3			1.50410			0.752052	−	0.659104i	$-0.229064\pi$
$673$	26260.3			1.50410			0.752052	+	0.659104i	$0.229064\pi$
$674$	11987.4	−	20762.8i	0.685070	−	1.18658i
$675$		0			0
$676$	−502.086	−	869.639i	−0.0285666	−	0.0494788i
$677$	−15258.3	+	26428.1i	−0.866208	+	1.50032i	−0.000364836		1.00000i	$0.500116\pi$
$677$	−15258.3	+	26428.1i	−0.866208	+	1.50032i	−0.865843	+	0.500316i	$0.833217\pi$
$678$	−61392.1			−3.47750
$679$	−21160.2	+	2680.89i	−1.19595	+	0.151521i
$680$		0			0
$681$	1713.40	−	2967.69i	0.0964134	−	0.166993i
$682$	3259.65	+	5645.89i	0.183018	+	0.316997i
$683$	−14603.7	−	25294.3i	−0.818147	−	1.41707i	−0.907046	−	0.421031i	$-0.861668\pi$
$683$	−14603.7	−	25294.3i	−0.818147	−	1.41707i	0.0888993	−	0.996041i	$-0.471665\pi$
$684$	762.775	−	1321.16i	0.0426395	−	0.0738538i
$685$		0			0
$686$	2690.78	−	18359.0i	0.149759	−	1.02179i
$687$	7787.85			0.432497
$688$	8010.92	−	13875.3i	0.443915	−	0.768883i
$689$	10180.6	+	17633.4i	0.562919	+	0.975004i
$690$		0			0
$691$	−5312.39	+	9201.33i	−0.292464	+	0.506563i	−0.974392	−	0.224857i	$-0.927809\pi$
$691$	−5312.39	+	9201.33i	−0.292464	+	0.506563i	0.681928	+	0.731420i	$0.261142\pi$
$692$	−2227.10			−0.122344
$693$	−21192.3	+	2684.96i	−1.16166	+	0.147176i
$694$	−27464.4			−1.50221
$695$		0			0
$696$	24848.7	+	43039.3i	1.35329	+	2.34397i
$697$	169.484	+	293.555i	0.00921043	+	0.0159529i
$698$	1008.50	−	1746.78i	0.0546881	−	0.0947227i
$699$	−25119.1			−1.35922
$700$		0			0
$701$	22033.0			1.18712			0.593562	−	0.804788i	$-0.297721\pi$
$701$	22033.0			1.18712			0.593562	+	0.804788i	$0.297721\pi$
$702$	−44052.4	+	76301.0i	−2.36845	+	4.10227i
$703$	5530.01	+	9578.27i	0.296683	+	0.513871i
$704$	−3692.41	−	6395.44i	−0.197674	−	0.342382i
$705$		0			0
$706$	10519.5			0.560772
$707$	−13454.7	−	17712.7i	−0.715722	−	0.942225i
$708$	2396.29			0.127201
$709$	−12433.7	+	21535.8i	−0.658614	+	1.14075i	0.322361	+	0.946617i	$0.395523\pi$
$709$	−12433.7	+	21535.8i	−0.658614	+	1.14075i	−0.980975	+	0.194136i	$0.937810\pi$
$710$		0			0
$711$	17211.9	+	29812.0i	0.907874	+	1.57248i
$712$	11050.7	−	19140.3i	0.581659	−	1.00746i
$713$	−3452.69			−0.181352
$714$	−3477.97	−	4578.63i	−0.182296	−	0.239987i
$715$		0			0
$716$	−244.118	+	422.825i	−0.0127418	+	0.0220694i
$717$	10961.2	+	18985.3i	0.570923	+	0.988868i
$718$	−11777.1	−	20398.6i	−0.612142	−	1.06026i
$719$	702.482	−	1216.74i	0.0364370	−	0.0631107i	−0.847232	−	0.531223i	$-0.821733\pi$
$719$	702.482	−	1216.74i	0.0364370	−	0.0631107i	0.883669	+	0.468113i	$0.155066\pi$
$720$		0			0
$721$	7379.06	−	17571.8i	0.381152	−	0.907639i
$722$	−15643.6			−0.806366
$723$	11405.5	−	19754.9i	0.586687	−	1.01617i
$724$	−69.7736	−	120.851i	−0.00358165	−	0.00620360i
$725$		0			0
$726$	15964.3	−	27651.0i	0.816103	−	1.41353i
$727$	28384.6			1.44804			0.724020	−	0.689779i	$-0.242292\pi$
$727$	28384.6			1.44804			0.724020	+	0.689779i	$0.242292\pi$
$728$	25615.6	−	3245.37i	1.30409	−	0.165222i
$729$	75008.8			3.81084
$730$		0			0
$731$	1246.63	+	2159.23i	0.0630758	+	0.109251i
$732$	−445.493	−	771.616i	−0.0224944	−	0.0389614i
$733$	−10235.9	+	17729.1i	−0.515787	+	0.893369i	0.484045	+	0.875043i	$0.339167\pi$
$733$	−10235.9	+	17729.1i	−0.515787	+	0.893369i	−0.999832	+	0.0183260i	$0.994166\pi$
$734$	9900.91			0.497887
$735$		0			0
$736$	−579.754			−0.0290353
$737$	5777.76	−	10007.4i	0.288774	−	0.500171i
$738$	−3461.83	−	5996.06i	−0.172672	−	0.299076i
$739$	16590.5	+	28735.6i	0.825834	+	1.43039i	0.901280	+	0.433236i	$0.142628\pi$
$739$	16590.5	+	28735.6i	0.825834	+	1.43039i	−0.0754464	+	0.997150i	$0.524038\pi$
$740$		0			0
$741$	−24900.1			−1.23445
$742$	17097.5	−	2166.17i	0.845916	−	0.107173i
$743$	−30844.1			−1.52296			−0.761481	−	0.648188i	$-0.775527\pi$
$743$	−30844.1			−1.52296			−0.761481	+	0.648188i	$0.775527\pi$
$744$	−15686.4	+	27169.7i	−0.772974	+	1.33883i
$745$		0			0
$746$	−12912.4	−	22364.9i	−0.633722	−	1.09764i
$747$	25566.5	−	44282.6i	1.25225	−	2.16896i
$748$	−87.7393			−0.00428886
$749$	−4135.64	+	9848.21i	−0.201753	+	0.480435i
$750$		0			0
$751$	12346.5	−	21384.7i	0.599906	−	1.03907i	−0.392928	−	0.919569i	$-0.628538\pi$
$751$	12346.5	−	21384.7i	0.599906	−	1.03907i	0.992834	−	0.119499i	$-0.0381289\pi$
$752$	−4904.09	−	8494.13i	−0.237811	−	0.411900i
$753$	−14790.1	−	25617.2i	−0.715779	−	1.23977i
$754$	−21163.6	+	36656.4i	−1.02219	+	1.77049i
$755$		0			0
$756$	2812.35	+	3702.37i	0.135297	+	0.178113i
$757$	6870.57			0.329875			0.164937	−	0.986304i	$-0.447258\pi$
$757$	6870.57			0.329875			0.164937	+	0.986304i	$0.447258\pi$
$758$	−4437.01	+	7685.12i	−0.212611	+	0.368253i
$759$	−1889.88	−	3273.37i	−0.0903799	−	0.156542i
$760$		0			0
$761$	−15441.3	+	26745.1i	−0.735540	+	1.27399i	0.218946	+	0.975737i	$0.429738\pi$
$761$	−15441.3	+	26745.1i	−0.735540	+	1.27399i	−0.954486	+	0.298256i	$0.903595\pi$
$762$	14641.2			0.696057
$763$	−2143.34	−	2821.64i	−0.101696	−	0.133880i
$764$	769.273			0.0364284
$765$		0			0
$766$	−4116.62	−	7130.19i	−0.194177	−	0.336324i
$767$	−14326.6	−	24814.5i	−0.674452	−	1.16819i
$768$	−4087.22	+	7079.28i	−0.192038	+	0.332619i
$769$	−13536.3			−0.634761			−0.317380	−	0.948298i	$-0.602803\pi$
$769$	−13536.3			−0.634761			−0.317380	+	0.948298i	$0.602803\pi$
$770$		0			0
$771$	−36411.1			−1.70080
$772$	1081.38	−	1873.01i	0.0504143	−	0.0873201i
$773$	−7142.87	−	12371.8i	−0.332356	−	0.575657i	0.650617	−	0.759406i	$-0.274510\pi$
$773$	−7142.87	−	12371.8i	−0.332356	−	0.575657i	−0.982973	+	0.183748i	$0.941177\pi$
$774$	−25463.3	−	44103.8i	−1.18251	−	2.04816i
$775$		0			0
$776$	−25122.4			−1.16217
$777$	−52663.6	+	6672.22i	−2.43153	+	0.308062i
$778$	35602.6			1.64064
$779$	621.249	−	1076.03i	0.0285732	−	0.0494903i
$780$		0			0
$781$	2913.29	+	5045.96i	0.133477	+	0.231189i
$782$	372.658	−	645.462i	0.0170412	−	0.0295162i
$783$	107005.			4.88382
$784$	6253.59	−	22460.2i	0.284876	−	1.02315i
$785$		0			0
$786$	−4573.54	+	7921.61i	−0.207548	+	0.359484i
$787$	4226.82	+	7321.06i	0.191448	+	0.331598i	0.945730	−	0.324952i	$-0.105348\pi$
$787$	4226.82	+	7321.06i	0.191448	+	0.331598i	−0.754282	+	0.656550i	$0.772015\pi$
$788$	−285.402	−	494.330i	−0.0129023	−	0.0223474i
$789$	2317.28	−	4013.65i	0.104559	−	0.181102i
$790$		0			0
$791$	38431.4	−	4869.07i	1.72751	−	0.218867i
$792$	−25160.6			−1.12884
$793$	−5326.92	+	9226.49i	−0.238543	+	0.413168i
$794$	15174.8	+	26283.5i	0.678254	+	1.17477i
$795$		0			0
$796$	791.789	−	1371.42i	0.0352566	−	0.0610662i
$797$	5465.35			0.242902			0.121451	−	0.992597i	$-0.461245\pi$
$797$	5465.35			0.242902			0.121451	+	0.992597i	$0.461245\pi$
$798$	−8160.29	+	19432.1i	−0.361994	+	0.862018i
$799$	1526.32			0.0675810
$800$		0			0
$801$	−37471.3	−	64902.3i	−1.65291	−	2.86293i
$802$	−2194.04	−	3800.18i	−0.0966011	−	0.167318i
$803$	1850.29	−	3204.80i	0.0813142	−	0.140840i
$804$	−3960.88			−0.173743
$805$		0			0
$806$	−26720.2			−1.16771
$807$	28789.9	−	49865.6i	1.25583	−	2.17516i
$808$	−13099.5	−	22689.0i	−0.570346	−	0.987867i
$809$	−8300.53	−	14376.9i	−0.360731	−	0.624804i	0.627350	−	0.778737i	$-0.284139\pi$
$809$	−8300.53	−	14376.9i	−0.360731	−	0.624804i	−0.988081	+	0.153933i	$0.950806\pi$
$810$		0			0
$811$	−24613.6			−1.06572			−0.532861	−	0.846203i	$-0.678883\pi$
$811$	−24613.6			−1.06572			−0.532861	+	0.846203i	$0.678883\pi$
$812$	1351.10	+	1778.69i	0.0583922	+	0.0768714i
$813$	−4373.17			−0.188652
$814$	−6496.37	+	11252.0i	−0.279727	+	0.484501i
$815$		0			0
$816$	−3612.31	−	6256.70i	−0.154971	−	0.268417i
$817$	4569.57	−	7914.73i	0.195678	−	0.338924i
$818$	41177.2			1.76006
$819$	33899.3	−	80724.6i	1.44632	−	3.44413i
$820$		0			0
$821$	8970.29	−	15537.0i	0.381322	−	0.660469i	−0.609930	−	0.792456i	$-0.708802\pi$
$821$	8970.29	−	15537.0i	0.381322	−	0.660469i	0.991251	+	0.131987i	$0.0421357\pi$
$822$	−15008.2	−	25995.0i	−0.636827	−	1.10302i
$823$	−22954.5	−	39758.4i	−0.972229	−	1.68395i	−0.688791	−	0.724960i	$-0.741858\pi$
$823$	−22954.5	−	39758.4i	−0.972229	−	1.68395i	−0.283439	−	0.958990i	$-0.591475\pi$
$824$	11223.8	−	19440.1i	0.474513	−	0.821880i
$825$		0			0
$826$	−24060.4	+	3048.33i	−1.01352	+	0.128408i
$827$	36696.8			1.54301			0.771507	−	0.636221i	$-0.219503\pi$
$827$	36696.8			1.54301			0.771507	+	0.636221i	$0.219503\pi$
$828$	−474.566	+	821.972i	−0.0199182	+	0.0344994i
$829$	−14460.2	−	25045.9i	−0.605820	−	1.04931i	−0.991921	−	0.126855i	$-0.959512\pi$
$829$	−14460.2	−	25045.9i	−0.605820	−	1.04931i	0.386101	−	0.922457i	$-0.373822\pi$
$830$		0			0
$831$	−540.096	+	935.474i	−0.0225460	+	0.0390508i
$832$	30267.5			1.26122
$833$	2540.34	+	2590.38i	0.105663	+	0.107745i
$834$	33497.4			1.39079
$835$		0			0
$836$	160.805	+	278.523i	0.00665259	+	0.0115226i
$837$	33774.8	+	58499.6i	1.39478	+	2.41582i
$838$	−16839.1	+	29166.2i	−0.694150	+	1.20230i
$839$	5852.41			0.240820			0.120410	−	0.992724i	$-0.461579\pi$
$839$	5852.41			0.240820			0.120410	+	0.992724i	$0.461579\pi$
$840$		0			0
$841$	27018.0			1.10779
$842$	4921.87	−	8524.93i	0.201448	−	0.348918i
$843$	40489.2	+	70129.4i	1.65424	+	2.86523i
$844$	138.736	+	240.298i	0.00565817	+	0.00980023i
$845$		0			0
$846$	−31176.1			−1.26697
$847$	−7800.62	+	18575.6i	−0.316449	+	0.753562i
$848$	21654.8			0.876920
$849$	−29121.7	+	50440.3i	−1.17721	+	2.03900i
$850$		0			0
$851$	−3440.54	−	5959.19i	−0.138590	−	0.240045i
$852$	998.586	−	1729.60i	0.0401538	−	0.0695484i
$853$	18715.7			0.751245			0.375623	−	0.926773i	$-0.377429\pi$
$853$	18715.7			0.751245			0.375623	+	0.926773i	$0.377429\pi$
$854$	5454.64	+	7180.85i	0.218564	+	0.287733i
$855$		0			0
$856$	−6290.42	+	10895.3i	−0.251171	+	0.435041i
$857$	8648.57	+	14979.8i	0.344725	+	0.597081i	0.985304	−	0.170811i	$-0.0546388\pi$
$857$	8648.57	+	14979.8i	0.344725	+	0.597081i	−0.640579	+	0.767893i	$0.721305\pi$
$858$	−14625.7	−	25332.4i	−0.581949	−	1.00797i
$859$	−15366.4	+	26615.3i	−0.610354	+	1.05716i	0.380827	+	0.924646i	$0.375639\pi$
$859$	−15366.4	+	26615.3i	−0.610354	+	1.05716i	−0.991181	+	0.132518i	$0.957694\pi$
$860$		0			0
$861$	3607.29	+	4748.88i	0.142783	+	0.187969i
$862$	−24322.9			−0.961070
$863$	5396.51	−	9347.02i	0.212861	−	0.368686i	−0.739748	−	0.672884i	$-0.765055\pi$
$863$	5396.51	−	9347.02i	0.212861	−	0.368686i	0.952609	+	0.304198i	$0.0983885\pi$
$864$	5671.25	+	9822.89i	0.223310	+	0.386784i
$865$		0			0
$866$	−1194.89	+	2069.60i	−0.0468867	+	0.0812101i
$867$	−48242.9			−1.88975
$868$	−545.950	+	1300.07i	−0.0213488	+	0.0508380i
$869$	−7257.12			−0.283292
$870$		0			0
$871$	23680.8	+	41016.4i	0.921234	+	1.59562i
$872$	−2086.76	−	3614.38i	−0.0810398	−	0.140365i
$873$	−42593.4	+	73773.9i	−1.65128	+	2.86010i
$874$	−2731.97			−0.105733
$875$		0			0
$876$	−1268.45			−0.0489233
$877$	−9783.36	+	16945.3i	−0.376694	+	0.652453i	−0.990579	−	0.136942i	$-0.956272\pi$
$877$	−9783.36	+	16945.3i	−0.376694	+	0.652453i	0.613885	+	0.789395i	$0.289606\pi$
$878$	−12364.0	−	21415.1i	−0.475246	−	0.823151i
$879$	−6285.01	−	10886.0i	−0.241170	−	0.417718i
$880$		0			0
$881$	27700.5			1.05931			0.529656	−	0.848213i	$-0.322321\pi$
$881$	27700.5			1.05931			0.529656	+	0.848213i	$0.322321\pi$
$882$	−51888.2	−	52910.2i	−1.98091	−	2.01993i
$883$	−5071.61			−0.193288			−0.0966440	−	0.995319i	$-0.530811\pi$
$883$	−5071.61			−0.193288			−0.0966440	+	0.995319i	$0.530811\pi$
$884$	179.805	−	311.431i	0.00684106	−	0.0118491i
$885$		0			0
$886$	−21277.6	−	36853.8i	−0.806810	−	1.39744i
$887$	−11274.4	+	19527.9i	−0.426784	+	0.739212i	−0.996585	−	0.0825707i	$-0.973687\pi$
$887$	−11274.4	+	19527.9i	−0.426784	+	0.739212i	0.569801	+	0.821783i	$0.307020\pi$
$888$	−62525.0			−2.36284
$889$	−9165.39	+	1161.21i	−0.345779	+	0.0438084i
$890$		0			0
$891$	−21403.0	+	37071.1i	−0.804745	+	1.39386i
$892$	−633.476	−	1097.21i	−0.0237784	−	0.0411854i
$893$	−2797.38	−	4845.20i	−0.104827	−	0.181566i
$894$	−18945.3	+	32814.2i	−0.708753	+	1.22760i
$895$		0			0
$896$	11298.0	−	26904.0i	0.421250	−	1.00312i
$897$	15491.8			0.576651
$898$	1228.57	−	2127.94i	0.0456545	−	0.0790760i
$899$	16226.0	+	28104.3i	0.601967	+	1.04264i
$900$		0			0
$901$	−1684.92	+	2918.37i	−0.0623007	+	0.107908i
$902$	1459.62			0.0538803
$903$	26533.3	+	34930.2i	0.977821	+	1.28727i
$904$	45627.7			1.67871
$905$		0			0
$906$	16875.8	+	29229.7i	0.618830	+	1.07185i
$907$	−12121.1	−	20994.3i	−0.443742	−	0.768584i	0.554222	−	0.832369i	$-0.313016\pi$
$907$	−12121.1	−	20994.3i	−0.443742	−	0.768584i	−0.997964	+	0.0637854i	$0.979683\pi$
$908$	90.7035	−	157.103i	0.00331509	−	0.00574191i
$909$	−88837.4			−3.24153
$910$		0			0
$911$	6574.69			0.239110			0.119555	−	0.992828i	$-0.461853\pi$
$911$	6574.69			0.239110			0.119555	+	0.992828i	$0.461853\pi$
$912$	−13241.0	+	22934.1i	−0.480760	+	0.832702i
$913$	5389.84	+	9335.48i	0.195375	+	0.338400i
$914$	−20266.5	−	35102.6i	−0.733432	−	1.27034i
$915$		0			0
$916$	412.272			0.0148710
$917$	2234.76	−	5321.66i	0.0804781	−	0.191643i
$918$	−14581.6			−0.524253
$919$	20956.1	−	36297.1i	0.752208	−	1.30286i	−0.194542	−	0.980894i	$-0.562322\pi$
$919$	20956.1	−	36297.1i	0.752208	−	1.30286i	0.946750	−	0.321969i	$-0.104345\pi$
$920$		0			0
$921$	2480.55	+	4296.44i	0.0887480	+	0.153716i
$922$	−4458.95	+	7723.13i	−0.159271	+	0.275865i
$923$	−23880.9			−0.851625
$924$	−1531.39	+	194.019i	−0.0545226	+	0.00690774i
$925$		0			0
$926$	−14511.0	+	25133.7i	−0.514968	+	0.891950i
$927$	−38058.3	−	65918.9i	−1.34843	−	2.33556i
$928$	2724.57	+	4719.10i	0.0963777	+	0.166931i
$929$	24085.7	−	41717.7i	0.850621	−	1.47332i	−0.0300283	−	0.999549i	$-0.509560\pi$
$929$	24085.7	−	41717.7i	0.850621	−	1.47332i	0.880649	−	0.473769i	$-0.157107\pi$
$930$		0			0
$931$	3567.16	−	12811.7i	0.125573	−	0.451006i
$932$	−1329.75			−0.0467355
$933$	529.866	−	917.754i	0.0185927	−	0.0322036i
$934$	−14498.5	−	25112.1i	−0.507929	−	0.879759i
$935$		0			0
$936$	51561.9	−	89307.8i	1.80059	−	3.11871i
$937$	−48696.8			−1.69782			−0.848909	−	0.528539i	$-0.822740\pi$
$937$	−48696.8			−1.69782			−0.848909	+	0.528539i	$0.822740\pi$
$938$	39770.0	−	5038.66i	1.38437	−	0.175392i
$939$	−37285.4			−1.29581
$940$		0			0
$941$	1000.15	+	1732.31i	0.0346482	+	0.0600124i	0.882830	−	0.469694i	$-0.155636\pi$
$941$	1000.15	+	1732.31i	0.0346482	+	0.0600124i	−0.848181	+	0.529706i	$0.822302\pi$
$942$	53158.6	+	92073.4i	1.83864	+	3.18462i
$943$	−386.514	+	669.462i	−0.0133474	+	0.0231184i
$944$	−30473.6			−1.05067
$945$		0			0
$946$	10736.2			0.368988
$947$	−21247.7	+	36802.1i	−0.729101	+	1.26284i	0.228163	+	0.973623i	$0.426728\pi$
$947$	−21247.7	+	36802.1i	−0.729101	+	1.26284i	−0.957264	+	0.289216i	$0.906605\pi$
$948$	1243.76	+	2154.25i	0.0426112	+	0.0738048i
$949$	7583.64	+	13135.2i	0.259405	+	0.449303i
$950$		0			0
$951$	−65327.9			−2.22755
$952$	2584.89	+	3402.92i	0.0880008	+	0.115850i
$953$	51166.5			1.73919			0.869594	−	0.493768i	$-0.164381\pi$
$953$	51166.5			1.73919			0.869594	+	0.493768i	$0.164381\pi$
$954$	34415.7	−	59609.7i	1.16798	−	2.02299i
$955$		0			0
$956$	580.260	+	1005.04i	0.0196307	+	0.0340014i
$957$	−17763.1	+	30766.6i	−0.600000	+	1.03923i
$958$	−38481.3			−1.29778
$959$	11456.8	+	15082.5i	0.385777	+	0.507863i
$960$		0			0
$961$	4652.38	−	8058.16i	0.156167	−	0.270490i
$962$	−26626.1	−	46117.8i	−0.892371	−	1.54563i
$963$	21330.0	+	36944.6i	0.713758	+	1.23627i
$964$	603.782	−	1045.78i	0.0201727	−	0.0349402i
$965$		0			0
$966$	5076.98	−	12089.8i	0.169099	−	0.402675i
$967$	−26324.2			−0.875418			−0.437709	−	0.899117i	$-0.644210\pi$
$967$	−26324.2			−0.875418			−0.437709	+	0.899117i	$0.644210\pi$
$968$	−11865.0	+	20550.7i	−0.393961	+	0.682361i
$969$	−2060.52	−	3568.93i	−0.0683112	−	0.118318i
$970$		0			0
$971$	2617.28	−	4533.27i	0.0865012	−	0.149824i	−0.819529	−	0.573038i	$-0.805765\pi$
$971$	2617.28	−	4533.27i	0.0865012	−	0.149824i	0.906030	+	0.423214i	$0.139098\pi$
$972$	7894.44			0.260508
$973$	−20969.3	+	2656.71i	−0.690901	+	0.0875337i
$974$	24751.4			0.814257
$975$		0			0
$976$	5665.33	+	9812.63i	0.185802	+	0.321818i
$977$	22490.3	+	38954.3i	0.736467	+	1.27560i	0.954077	+	0.299562i	$0.0968406\pi$
$977$	22490.3	+	38954.3i	0.736467	+	1.27560i	−0.217610	+	0.976036i	$0.569826\pi$
$978$	39707.0	−	68774.5i	1.29825	−	2.24864i
$979$	15799.1			0.515774
$980$		0			0
$981$	−14151.9			−0.460585
$982$	15818.6	−	27398.6i	0.514044	−	0.890350i
$983$	−8196.66	−	14197.0i	−0.265954	−	0.460646i	0.701859	−	0.712316i	$-0.252354\pi$
$983$	−8196.66	−	14197.0i	−0.265954	−	0.460646i	−0.967813	+	0.251670i	$0.919020\pi$
$984$	3512.06	+	6083.07i	0.113781	+	0.197074i
$985$		0			0
$986$	−7005.27			−0.226261
$987$	26640.1	−	3375.17i	0.859132	−	0.108848i
$988$	−1318.16			−0.0424456
$989$	−2842.99	+	4924.20i	−0.0914073	+	0.158322i
$990$		0			0
$991$	1941.67	+	3363.07i	0.0622393	+	0.107802i	0.895466	−	0.445130i	$-0.146842\pi$
$991$	1941.67	+	3363.07i	0.0622393	+	0.107802i	−0.833227	+	0.552931i	$0.813509\pi$
$992$	−1719.96	+	2979.06i	−0.0550492	+	0.0953480i
$993$	−1092.13			−0.0349020
$994$	−7826.27	+	18636.7i	−0.249733	+	0.594689i
$995$		0			0
$996$	1847.47	−	3199.92i	0.0587746	−	0.101801i
$997$	6981.81	+	12092.9i	0.221781	+	0.384137i	0.955349	−	0.295480i	$-0.0954795\pi$
$997$	6981.81	+	12092.9i	0.221781	+	0.384137i	−0.733567	+	0.679617i	$0.762146\pi$
$998$	17660.2	+	30588.4i	0.560144	+	0.970198i
$999$	−67311.8	+	116588.i	−2.13178	+	3.69236i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	175.4.e.f.51.2	yes	16
5.2	odd	4		175.4.k.e.149.4		32
5.3	odd	4		175.4.k.e.149.13		32
5.4	even	2		175.4.e.e.51.7	✓	16
7.2	even	3		1225.4.a.bl.1.7		8
7.4	even	3	inner	175.4.e.f.151.2	yes	16
7.5	odd	6		1225.4.a.bk.1.7		8
35.4	even	6		175.4.e.e.151.7	yes	16
35.9	even	6		1225.4.a.bn.1.2		8
35.18	odd	12		175.4.k.e.74.4		32
35.19	odd	6		1225.4.a.bo.1.2		8
35.32	odd	12		175.4.k.e.74.13		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
175.4.e.e.51.7	✓	16	5.4	even	2
175.4.e.e.151.7	yes	16	35.4	even	6
175.4.e.f.51.2	yes	16	1.1	even	1	trivial
175.4.e.f.151.2	yes	16	7.4	even	3	inner
175.4.k.e.74.4		32	35.18	odd	12
175.4.k.e.74.13		32	35.32	odd	12
175.4.k.e.149.4		32	5.2	odd	4
175.4.k.e.149.13		32	5.3	odd	4
1225.4.a.bk.1.7		8	7.5	odd	6
1225.4.a.bl.1.7		8	7.2	even	3
1225.4.a.bn.1.2		8	35.9	even	6
1225.4.a.bo.1.2		8	35.19	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:	\( N \)	\(=\)	\( 175 = 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	175.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.46047 + 2.52961i) q^{2} +(-5.02414 - 8.70206i) q^{3} +(-0.265967 - 0.460668i) q^{4} +29.3505 q^{6} +(-18.3734 + 2.32782i) q^{7} -21.8138 q^{8} +(-36.9839 + 64.0580i) q^{9} +(-7.79680 - 13.5045i) q^{11} +(-2.67251 + 4.62892i) q^{12} +63.9123 q^{13} +(20.9454 - 49.8773i) q^{14} +(33.9863 - 58.8659i) q^{16} +(5.28883 + 9.16053i) q^{17} +(-108.028 - 187.110i) q^{18} +(19.3864 - 33.5782i) q^{19} +(112.567 + 148.191i) q^{21} +45.5481 q^{22} +(-12.0614 + 20.8909i) q^{23} +(109.596 + 189.825i) q^{24} +(-93.3422 + 161.673i) q^{26} +471.945 q^{27} +(5.95906 + 7.84491i) q^{28} +226.731 q^{29} +(71.5651 + 123.954i) q^{31} +(12.0168 + 20.8136i) q^{32} +(-78.3444 + 135.697i) q^{33} -30.8968 q^{34} +39.3460 q^{36} +(-142.626 + 247.036i) q^{37} +(56.6265 + 98.0800i) q^{38} +(-321.104 - 556.168i) q^{39} +32.0457 q^{41} +(-539.268 + 68.3225i) q^{42} +235.711 q^{43} +(-4.14738 + 7.18348i) q^{44} +(-35.2306 - 61.0212i) q^{46} +(72.1481 - 124.964i) q^{47} -683.006 q^{48} +(332.163 - 85.5397i) q^{49} +(53.1436 - 92.0475i) q^{51} +(-16.9985 - 29.4423i) q^{52} +(159.291 + 275.900i) q^{53} +(-689.263 + 1193.84i) q^{54} +(400.794 - 50.7786i) q^{56} -389.599 q^{57} +(-331.135 + 573.542i) q^{58} +(-224.161 - 388.258i) q^{59} +(-83.3473 + 144.362i) q^{61} -418.076 q^{62} +(530.404 - 1263.05i) q^{63} +473.580 q^{64} +(-228.840 - 396.362i) q^{66} +(370.521 + 641.761i) q^{67} +(2.81331 - 4.87279i) q^{68} +242.392 q^{69} -373.652 q^{71} +(806.760 - 1397.35i) q^{72} +(118.657 + 205.520i) q^{73} +(-416.604 - 721.580i) q^{74} -20.6245 q^{76} +(174.690 + 229.973i) q^{77} +1875.86 q^{78} +(232.695 - 403.040i) q^{79} +(-1372.55 - 2377.33i) q^{81} +(-46.8018 + 81.0631i) q^{82} -691.289 q^{83} +(38.3277 - 91.2700i) q^{84} +(-344.249 + 596.257i) q^{86} +(-1139.13 - 1973.03i) q^{87} +(170.078 + 294.584i) q^{88} +(-506.590 + 877.440i) q^{89} +(-1174.28 + 148.776i) q^{91} +12.8317 q^{92} +(719.105 - 1245.53i) q^{93} +(210.741 + 365.014i) q^{94} +(120.748 - 209.141i) q^{96} +1151.67 q^{97} +(-268.732 + 965.172i) q^{98} +1153.42 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + q^{2} - 6 q^{3} - 27 q^{4} + 8 q^{6} - 16 q^{7} - 84 q^{8} - 42 q^{9} - 103 q^{12} + 276 q^{13} - 65 q^{14} - 191 q^{16} - 138 q^{17} - 81 q^{18} + 42 q^{19} + 302 q^{21} + 254 q^{22} - 124 q^{23}+ \cdots + 8172 q^{99}+O(q^{100}) \) 16 * q + q^2 - 6 * q^3 - 27 * q^4 + 8 * q^6 - 16 * q^7 - 84 * q^8 - 42 * q^9 - 103 * q^12 + 276 * q^13 - 65 * q^14 - 191 * q^16 - 138 * q^17 - 81 * q^18 + 42 * q^19 + 302 * q^21 + 254 * q^22 - 124 * q^23 + 292 * q^24 - 23 * q^26 + 408 * q^27 + 619 * q^28 + 576 * q^29 - 18 * q^31 + 562 * q^32 - 236 * q^33 - 976 * q^34 - 1422 * q^36 - 220 * q^37 - 1104 * q^38 - 22 * q^39 + 336 * q^41 - 1299 * q^42 + 120 * q^43 + 880 * q^44 + 98 * q^46 - 1098 * q^47 + 676 * q^48 - 1114 * q^49 - 628 * q^51 - 1370 * q^52 + 734 * q^53 - 2163 * q^54 + 3051 * q^56 + 1828 * q^57 - 924 * q^58 - 558 * q^59 + 1496 * q^61 + 1602 * q^62 + 130 * q^63 + 4872 * q^64 + 682 * q^66 + 1166 * q^67 - 2455 * q^68 + 1644 * q^69 - 1448 * q^71 + 2191 * q^72 - 892 * q^73 - 235 * q^74 - 3018 * q^76 - 3474 * q^77 + 4244 * q^78 + 840 * q^79 - 2392 * q^81 - 4154 * q^82 + 2292 * q^83 - 5271 * q^84 - 1816 * q^86 - 4286 * q^87 + 788 * q^88 - 2678 * q^89 + 2046 * q^91 + 13864 * q^92 + 1986 * q^93 - 3625 * q^94 + 6601 * q^96 + 1328 * q^97 - 6502 * q^98 + 8172 * q^99

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