LMFDB - Embedded newform 175.4.e.a.51.1

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:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 7)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			51.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	175.51
Dual form			175.4.e.a.151.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.00000 - 1.73205i) q^{2} +(3.50000 + 6.06218i) q^{3} +(2.00000 + 3.46410i) q^{4} +14.0000 q^{6} +(-14.0000 + 12.1244i) q^{7} +24.0000 q^{8} +(-11.0000 + 19.0526i) q^{9} +O(q^{10})$	\(q+(1.00000 - 1.73205i) q^{2} +(3.50000 + 6.06218i) q^{3} +(2.00000 + 3.46410i) q^{4} +14.0000 q^{6} +(-14.0000 + 12.1244i) q^{7} +24.0000 q^{8} +(-11.0000 + 19.0526i) q^{9} +(2.50000 + 4.33013i) q^{11} +(-14.0000 + 24.2487i) q^{12} +14.0000 q^{13} +(7.00000 + 36.3731i) q^{14} +(8.00000 - 13.8564i) q^{16} +(-10.5000 - 18.1865i) q^{17} +(22.0000 + 38.1051i) q^{18} +(-24.5000 + 42.4352i) q^{19} +(-122.500 - 42.4352i) q^{21} +10.0000 q^{22} +(-79.5000 + 137.698i) q^{23} +(84.0000 + 145.492i) q^{24} +(14.0000 - 24.2487i) q^{26} +35.0000 q^{27} +(-70.0000 - 24.2487i) q^{28} +58.0000 q^{29} +(-73.5000 - 127.306i) q^{31} +(80.0000 + 138.564i) q^{32} +(-17.5000 + 30.3109i) q^{33} -42.0000 q^{34} -88.0000 q^{36} +(109.500 - 189.660i) q^{37} +(49.0000 + 84.8705i) q^{38} +(49.0000 + 84.8705i) q^{39} +350.000 q^{41} +(-196.000 + 169.741i) q^{42} +124.000 q^{43} +(-10.0000 + 17.3205i) q^{44} +(159.000 + 275.396i) q^{46} +(262.500 - 454.663i) q^{47} +112.000 q^{48} +(49.0000 - 339.482i) q^{49} +(73.5000 - 127.306i) q^{51} +(28.0000 + 48.4974i) q^{52} +(151.500 + 262.406i) q^{53} +(35.0000 - 60.6218i) q^{54} +(-336.000 + 290.985i) q^{56} -343.000 q^{57} +(58.0000 - 100.459i) q^{58} +(52.5000 + 90.9327i) q^{59} +(206.500 - 357.668i) q^{61} -294.000 q^{62} +(-77.0000 - 400.104i) q^{63} +448.000 q^{64} +(35.0000 + 60.6218i) q^{66} +(207.500 + 359.401i) q^{67} +(42.0000 - 72.7461i) q^{68} -1113.00 q^{69} -432.000 q^{71} +(-264.000 + 457.261i) q^{72} +(-556.500 - 963.886i) q^{73} +(-219.000 - 379.319i) q^{74} -196.000 q^{76} +(-87.5000 - 30.3109i) q^{77} +196.000 q^{78} +(51.5000 - 89.2006i) q^{79} +(419.500 + 726.595i) q^{81} +(350.000 - 606.218i) q^{82} -1092.00 q^{83} +(-98.0000 - 509.223i) q^{84} +(124.000 - 214.774i) q^{86} +(203.000 + 351.606i) q^{87} +(60.0000 + 103.923i) q^{88} +(164.500 - 284.922i) q^{89} +(-196.000 + 169.741i) q^{91} -636.000 q^{92} +(514.500 - 891.140i) q^{93} +(-525.000 - 909.327i) q^{94} +(-560.000 + 969.948i) q^{96} +882.000 q^{97} +(-539.000 - 424.352i) q^{98} -110.000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{2} + 7 q^{3} + 4 q^{4} + 28 q^{6} - 28 q^{7} + 48 q^{8} - 22 q^{9}+O(q^{10}) $ 2 * q + 2 * q^2 + 7 * q^3 + 4 * q^4 + 28 * q^6 - 28 * q^7 + 48 * q^8 - 22 * q^9	$ 2 q + 2 q^{2} + 7 q^{3} + 4 q^{4} + 28 q^{6} - 28 q^{7} + 48 q^{8} - 22 q^{9} + 5 q^{11} - 28 q^{12} + 28 q^{13} + 14 q^{14} + 16 q^{16} - 21 q^{17} + 44 q^{18} - 49 q^{19} - 245 q^{21} + 20 q^{22} - 159 q^{23} + 168 q^{24} + 28 q^{26} + 70 q^{27} - 140 q^{28} + 116 q^{29} - 147 q^{31} + 160 q^{32} - 35 q^{33} - 84 q^{34} - 176 q^{36} + 219 q^{37} + 98 q^{38} + 98 q^{39} + 700 q^{41} - 392 q^{42} + 248 q^{43} - 20 q^{44} + 318 q^{46} + 525 q^{47} + 224 q^{48} + 98 q^{49} + 147 q^{51} + 56 q^{52} + 303 q^{53} + 70 q^{54} - 672 q^{56} - 686 q^{57} + 116 q^{58} + 105 q^{59} + 413 q^{61} - 588 q^{62} - 154 q^{63} + 896 q^{64} + 70 q^{66} + 415 q^{67} + 84 q^{68} - 2226 q^{69} - 864 q^{71} - 528 q^{72} - 1113 q^{73} - 438 q^{74} - 392 q^{76} - 175 q^{77} + 392 q^{78} + 103 q^{79} + 839 q^{81} + 700 q^{82} - 2184 q^{83} - 196 q^{84} + 248 q^{86} + 406 q^{87} + 120 q^{88} + 329 q^{89} - 392 q^{91} - 1272 q^{92} + 1029 q^{93} - 1050 q^{94} - 1120 q^{96} + 1764 q^{97} - 1078 q^{98} - 220 q^{99}+O(q^{100}) $ 2 * q + 2 * q^2 + 7 * q^3 + 4 * q^4 + 28 * q^6 - 28 * q^7 + 48 * q^8 - 22 * q^9 + 5 * q^11 - 28 * q^12 + 28 * q^13 + 14 * q^14 + 16 * q^16 - 21 * q^17 + 44 * q^18 - 49 * q^19 - 245 * q^21 + 20 * q^22 - 159 * q^23 + 168 * q^24 + 28 * q^26 + 70 * q^27 - 140 * q^28 + 116 * q^29 - 147 * q^31 + 160 * q^32 - 35 * q^33 - 84 * q^34 - 176 * q^36 + 219 * q^37 + 98 * q^38 + 98 * q^39 + 700 * q^41 - 392 * q^42 + 248 * q^43 - 20 * q^44 + 318 * q^46 + 525 * q^47 + 224 * q^48 + 98 * q^49 + 147 * q^51 + 56 * q^52 + 303 * q^53 + 70 * q^54 - 672 * q^56 - 686 * q^57 + 116 * q^58 + 105 * q^59 + 413 * q^61 - 588 * q^62 - 154 * q^63 + 896 * q^64 + 70 * q^66 + 415 * q^67 + 84 * q^68 - 2226 * q^69 - 864 * q^71 - 528 * q^72 - 1113 * q^73 - 438 * q^74 - 392 * q^76 - 175 * q^77 + 392 * q^78 + 103 * q^79 + 839 * q^81 + 700 * q^82 - 2184 * q^83 - 196 * q^84 + 248 * q^86 + 406 * q^87 + 120 * q^88 + 329 * q^89 - 392 * q^91 - 1272 * q^92 + 1029 * q^93 - 1050 * q^94 - 1120 * q^96 + 1764 * q^97 - 1078 * q^98 - 220 * q^99

Display 100 coefficients 10 coefficients

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 $

$2$	1.00000	−	1.73205i	0.353553	−	0.612372i	−0.633316	−	0.773893i	$-0.718307\pi$
$2$	1.00000	−	1.73205i	0.353553	−	0.612372i	0.986869	+	0.161521i	$0.0516399\pi$
$3$	3.50000	+	6.06218i	0.673575	+	1.16667i	0.976883	+	0.213774i	$0.0685756\pi$
$3$	3.50000	+	6.06218i	0.673575	+	1.16667i	−0.303308	+	0.952893i	$0.598091\pi$
$4$	2.00000	+	3.46410i	0.250000	+	0.433013i
$5$		0			0
$5$		0			0
$6$	14.0000			0.952579
$7$	−14.0000	+	12.1244i	−0.755929	+	0.654654i
$7$	−14.0000	+	12.1244i	−0.755929	+	0.654654i
$8$	24.0000			1.06066
$9$	−11.0000	+	19.0526i	−0.407407	+	0.705650i
$10$		0			0
$11$	2.50000	+	4.33013i	0.0685253	+	0.118689i	0.898252	−	0.439480i	$-0.144837\pi$
$11$	2.50000	+	4.33013i	0.0685253	+	0.118689i	−0.829727	+	0.558169i	$0.811504\pi$
$12$	−14.0000	+	24.2487i	−0.336788	+	0.583333i
$13$	14.0000			0.298685			0.149342	−	0.988786i	$-0.452284\pi$
$13$	14.0000			0.298685			0.149342	+	0.988786i	$0.452284\pi$
$14$	7.00000	+	36.3731i	0.133631	+	0.694365i
$15$		0			0
$16$	8.00000	−	13.8564i	0.125000	−	0.216506i
$17$	−10.5000	−	18.1865i	−0.149801	−	0.259464i	0.781353	−	0.624090i	$-0.214530\pi$
$17$	−10.5000	−	18.1865i	−0.149801	−	0.259464i	−0.931154	+	0.364626i	$0.881197\pi$
$18$	22.0000	+	38.1051i	0.288081	+	0.498970i
$19$	−24.5000	+	42.4352i	−0.295826	+	0.512385i	−0.975177	−	0.221429i	$-0.928928\pi$
$19$	−24.5000	+	42.4352i	−0.295826	+	0.512385i	0.679351	+	0.733813i	$0.262261\pi$
$20$		0			0
$21$	−122.500	−	42.4352i	−1.27294	−	0.440959i
$22$	10.0000			0.0969094
$23$	−79.5000	+	137.698i	−0.720735	+	1.24835i	0.239971	+	0.970780i	$0.422862\pi$
$23$	−79.5000	+	137.698i	−0.720735	+	1.24835i	−0.960706	+	0.277569i	$0.910471\pi$
$24$	84.0000	+	145.492i	0.714435	+	1.23744i
$25$		0			0
$26$	14.0000	−	24.2487i	0.105601	−	0.182906i
$27$	35.0000			0.249472
$28$	−70.0000	−	24.2487i	−0.472456	−	0.163663i
$29$	58.0000			0.371391			0.185695	−	0.982607i	$-0.440546\pi$
$29$	58.0000			0.371391			0.185695	+	0.982607i	$0.440546\pi$
$30$		0			0
$31$	−73.5000	−	127.306i	−0.425838	−	0.737574i	0.570660	−	0.821186i	$-0.306687\pi$
$31$	−73.5000	−	127.306i	−0.425838	−	0.737574i	−0.996498	+	0.0836128i	$0.973354\pi$
$32$	80.0000	+	138.564i	0.441942	+	0.765466i
$33$	−17.5000	+	30.3109i	−0.0923139	+	0.159892i
$34$	−42.0000			−0.211851
$35$		0			0
$36$	−88.0000			−0.407407
$37$	109.500	−	189.660i	0.486532	−	0.842698i	−0.513348	−	0.858181i	$-0.671595\pi$
$37$	109.500	−	189.660i	0.486532	−	0.842698i	0.999880	+	0.0154821i	$0.00492832\pi$
$38$	49.0000	+	84.8705i	0.209180	+	0.362311i
$39$	49.0000	+	84.8705i	0.201187	+	0.348466i
$40$		0			0
$41$	350.000			1.33319			0.666595	−	0.745420i	$-0.267751\pi$
$41$	350.000			1.33319			0.666595	+	0.745420i	$0.267751\pi$
$42$	−196.000	+	169.741i	−0.720082	+	0.623610i
$43$	124.000			0.439763			0.219882	−	0.975527i	$-0.429433\pi$
$43$	124.000			0.439763			0.219882	+	0.975527i	$0.429433\pi$
$44$	−10.0000	+	17.3205i	−0.0342627	+	0.0593447i
$45$		0			0
$46$	159.000	+	275.396i	0.509636	+	0.882716i
$47$	262.500	−	454.663i	0.814671	−	1.41105i	−0.0948921	−	0.995488i	$-0.530251\pi$
$47$	262.500	−	454.663i	0.814671	−	1.41105i	0.909564	−	0.415565i	$-0.136416\pi$
$48$	112.000			0.336788
$49$	49.0000	−	339.482i	0.142857	−	0.989743i
$50$		0			0
$51$	73.5000	−	127.306i	0.201805	−	0.349537i
$52$	28.0000	+	48.4974i	0.0746712	+	0.129334i
$53$	151.500	+	262.406i	0.392644	+	0.680079i	0.992797	−	0.119806i	$-0.0382272\pi$
$53$	151.500	+	262.406i	0.392644	+	0.680079i	−0.600153	+	0.799885i	$0.704894\pi$
$54$	35.0000	−	60.6218i	0.0882018	−	0.152770i
$55$		0			0
$56$	−336.000	+	290.985i	−0.801784	+	0.694365i
$57$	−343.000			−0.797043
$58$	58.0000	−	100.459i	0.131306	−	0.227429i
$59$	52.5000	+	90.9327i	0.115846	+	0.200651i	0.918118	−	0.396308i	$-0.129709\pi$
$59$	52.5000	+	90.9327i	0.115846	+	0.200651i	−0.802272	+	0.596959i	$0.796375\pi$
$60$		0			0
$61$	206.500	−	357.668i	0.433436	−	0.750734i	−0.563730	−	0.825959i	$-0.690634\pi$
$61$	206.500	−	357.668i	0.433436	−	0.750734i	0.997167	+	0.0752252i	$0.0239676\pi$
$62$	−294.000			−0.602226
$63$	−77.0000	−	400.104i	−0.153986	−	0.800132i
$64$	448.000			0.875000
$65$		0			0
$66$	35.0000	+	60.6218i	0.0652758	+	0.113061i
$67$	207.500	+	359.401i	0.378361	+	0.655340i	0.990824	−	0.135159i	$-0.0431546\pi$
$67$	207.500	+	359.401i	0.378361	+	0.655340i	−0.612463	+	0.790499i	$0.709821\pi$
$68$	42.0000	−	72.7461i	0.0749007	−	0.129732i
$69$	−1113.00			−1.94188
$70$		0			0
$71$	−432.000			−0.722098			−0.361049	−	0.932547i	$-0.617581\pi$
$71$	−432.000			−0.722098			−0.361049	+	0.932547i	$0.617581\pi$
$72$	−264.000	+	457.261i	−0.432121	+	0.748455i
$73$	−556.500	−	963.886i	−0.892238	−	1.54540i	−0.837186	−	0.546919i	$-0.815801\pi$
$73$	−556.500	−	963.886i	−0.892238	−	1.54540i	−0.0550526	−	0.998483i	$-0.517533\pi$
$74$	−219.000	−	379.319i	−0.344030	−	0.595878i
$75$		0			0
$76$	−196.000			−0.295826
$77$	−87.5000	−	30.3109i	−0.129501	−	0.0448603i
$78$	196.000			0.284521
$79$	51.5000	−	89.2006i	0.0733443	−	0.127036i	−0.827021	−	0.562171i	$-0.809966\pi$
$79$	51.5000	−	89.2006i	0.0733443	−	0.127036i	0.900365	+	0.435135i	$0.143299\pi$
$80$		0			0
$81$	419.500	+	726.595i	0.575446	+	0.996701i
$82$	350.000	−	606.218i	0.471354	−	0.816409i
$83$	−1092.00			−1.44413			−0.722064	−	0.691827i	$-0.756806\pi$
$83$	−1092.00			−1.44413			−0.722064	+	0.691827i	$0.756806\pi$
$84$	−98.0000	−	509.223i	−0.127294	−	0.661438i
$85$		0			0
$86$	124.000	−	214.774i	0.155480	−	0.269299i
$87$	203.000	+	351.606i	0.250160	+	0.433289i
$88$	60.0000	+	103.923i	0.0726821	+	0.125889i
$89$	164.500	−	284.922i	0.195921	−	0.339345i	−0.751281	−	0.659982i	$-0.770564\pi$
$89$	164.500	−	284.922i	0.195921	−	0.339345i	0.947202	+	0.320637i	$0.103897\pi$
$90$		0			0
$91$	−196.000	+	169.741i	−0.225784	+	0.195535i
$92$	−636.000			−0.720735
$93$	514.500	−	891.140i	0.573668	−	0.993623i
$94$	−525.000	−	909.327i	−0.576060	−	0.997765i
$95$		0			0
$96$	−560.000	+	969.948i	−0.595362	+	1.03120i
$97$	882.000			0.923232			0.461616	−	0.887080i	$-0.347270\pi$
$97$	882.000			0.923232			0.461616	+	0.887080i	$0.347270\pi$
$98$	−539.000	−	424.352i	−0.555584	−	0.437409i
$99$	−110.000			−0.111671
$100$		0			0
$101$	−689.500	−	1194.25i	−0.679285	−	1.17656i	−0.975196	−	0.221341i	$-0.928957\pi$
$101$	−689.500	−	1194.25i	−0.679285	−	1.17656i	0.295911	−	0.955215i	$-0.404377\pi$
$102$	−147.000	−	254.611i	−0.142698	−	0.247160i
$103$	−339.500	+	588.031i	−0.324776	+	0.562529i	−0.981467	−	0.191631i	$-0.938622\pi$
$103$	−339.500	+	588.031i	−0.324776	+	0.562529i	0.656691	+	0.754160i	$0.271956\pi$
$104$	336.000			0.316803
$105$		0			0
$106$	606.000			0.555282
$107$	228.500	−	395.774i	0.206448	−	0.357578i	−0.744145	−	0.668018i	$-0.767143\pi$
$107$	228.500	−	395.774i	0.206448	−	0.357578i	0.950593	+	0.310440i	$0.100476\pi$
$108$	70.0000	+	121.244i	0.0623681	+	0.108025i
$109$	562.500	+	974.279i	0.494291	+	0.856137i	0.999978	−	0.00657959i	$-0.00209436\pi$
$109$	562.500	+	974.279i	0.494291	+	0.856137i	−0.505687	+	0.862717i	$0.668761\pi$
$110$		0			0
$111$	1533.00			1.31086
$112$	56.0000	+	290.985i	0.0472456	+	0.245495i
$113$	1538.00			1.28038			0.640190	−	0.768217i	$-0.278856\pi$
$113$	1538.00			1.28038			0.640190	+	0.768217i	$0.278856\pi$
$114$	−343.000	+	594.093i	−0.281797	+	0.488087i
$115$		0			0
$116$	116.000	+	200.918i	0.0928477	+	0.160817i
$117$	−154.000	+	266.736i	−0.121686	+	0.210767i
$118$	210.000			0.163831
$119$	367.500	+	127.306i	0.283098	+	0.0980680i
$120$		0			0
$121$	653.000	−	1131.03i	0.490609	−	0.849759i
$122$	−413.000	−	715.337i	−0.306486	−	0.530849i
$123$	1225.00	+	2121.76i	0.898004	+	1.55539i
$124$	294.000	−	509.223i	0.212919	−	0.368787i
$125$		0			0
$126$	−770.000	−	266.736i	−0.544421	−	0.188593i
$127$	−72.0000			−0.0503068			−0.0251534	−	0.999684i	$-0.508007\pi$
$127$	−72.0000			−0.0503068			−0.0251534	+	0.999684i	$0.508007\pi$
$128$	−192.000	+	332.554i	−0.132583	+	0.229640i
$129$	434.000	+	751.710i	0.296214	+	0.513057i
$130$		0			0
$131$	−1074.50	+	1861.09i	−0.716637	+	1.24125i	0.245687	+	0.969349i	$0.420986\pi$
$131$	−1074.50	+	1861.09i	−0.716637	+	1.24125i	−0.962325	+	0.271903i	$0.912347\pi$
$132$	−140.000			−0.0923139
$133$	−171.500	−	891.140i	−0.111812	−	0.580990i
$134$	830.000			0.535083
$135$		0			0
$136$	−252.000	−	436.477i	−0.158888	−	0.275203i
$137$	−562.500	−	974.279i	−0.350786	−	0.607578i	0.635602	−	0.772017i	$-0.280752\pi$
$137$	−562.500	−	974.279i	−0.350786	−	0.607578i	−0.986387	+	0.164439i	$0.947419\pi$
$138$	−1113.00	+	1927.77i	−0.686557	+	1.18915i
$139$	252.000			0.153772			0.0768862	−	0.997040i	$-0.475502\pi$
$139$	252.000			0.153772			0.0768862	+	0.997040i	$0.475502\pi$
$140$		0			0
$141$	3675.00			2.19497
$142$	−432.000	+	748.246i	−0.255300	+	0.442193i
$143$	35.0000	+	60.6218i	0.0204675	+	0.0354507i
$144$	176.000	+	304.841i	0.101852	+	0.176413i
$145$		0			0
$146$	−2226.00			−1.26182
$147$	2229.50	−	891.140i	1.25093	−	0.500000i
$148$	876.000			0.486532
$149$	100.500	−	174.071i	0.0552569	−	0.0957078i	−0.837074	−	0.547090i	$-0.815736\pi$
$149$	100.500	−	174.071i	0.0552569	−	0.0957078i	0.892331	+	0.451382i	$0.149069\pi$
$150$		0			0
$151$	−809.500	−	1402.10i	−0.436266	−	0.755635i	0.561132	−	0.827726i	$-0.310366\pi$
$151$	−809.500	−	1402.10i	−0.436266	−	0.755635i	−0.997398	+	0.0720914i	$0.977033\pi$
$152$	−588.000	+	1018.45i	−0.313770	+	0.543466i
$153$	462.000			0.244121
$154$	−140.000	+	121.244i	−0.0732566	+	0.0634421i
$155$		0			0
$156$	−196.000	+	339.482i	−0.100593	+	0.174233i
$157$	339.500	+	588.031i	0.172580	+	0.298917i	0.939321	−	0.343039i	$-0.111456\pi$
$157$	339.500	+	588.031i	0.172580	+	0.298917i	−0.766741	+	0.641956i	$0.778123\pi$
$158$	−103.000	−	178.401i	−0.0518623	−	0.0898281i
$159$	−1060.50	+	1836.84i	−0.528950	+	0.916169i
$160$		0			0
$161$	−556.500	−	2891.66i	−0.272412	−	1.41549i
$162$	1678.00			0.813803
$163$	−233.500	+	404.434i	−0.112203	+	0.194342i	−0.916658	−	0.399672i	$-0.869124\pi$
$163$	−233.500	+	404.434i	−0.112203	+	0.194342i	0.804455	+	0.594014i	$0.202457\pi$
$164$	700.000	+	1212.44i	0.333298	+	0.577288i
$165$		0			0
$166$	−1092.00	+	1891.40i	−0.510576	+	0.884344i
$167$	−1204.00			−0.557894			−0.278947	−	0.960306i	$-0.589985\pi$
$167$	−1204.00			−0.557894			−0.278947	+	0.960306i	$0.589985\pi$
$168$	−2940.00	−	1018.45i	−1.35015	−	0.467707i
$169$	−2001.00			−0.910787
$170$		0			0
$171$	−539.000	−	933.575i	−0.241043	−	0.417499i
$172$	248.000	+	429.549i	0.109941	+	0.190423i
$173$	−1410.50	+	2443.06i	−0.619875	+	1.07365i	0.369633	+	0.929178i	$0.379483\pi$
$173$	−1410.50	+	2443.06i	−0.619875	+	1.07365i	−0.989508	+	0.144477i	$0.953850\pi$
$174$	812.000			0.353779
$175$		0			0
$176$	80.0000			0.0342627
$177$	−367.500	+	636.529i	−0.156062	+	0.270307i
$178$	−329.000	−	569.845i	−0.138537	−	0.239953i
$179$	1626.50	+	2817.18i	0.679164	+	1.17635i	0.975233	+	0.221180i	$0.0709907\pi$
$179$	1626.50	+	2817.18i	0.679164	+	1.17635i	−0.296069	+	0.955166i	$0.595676\pi$
$180$		0			0
$181$	1582.00			0.649664			0.324832	−	0.945772i	$-0.394692\pi$
$181$	1582.00			0.649664			0.324832	+	0.945772i	$0.394692\pi$
$182$	98.0000	+	509.223i	0.0399134	+	0.207396i
$183$	2891.00			1.16781
$184$	−1908.00	+	3304.75i	−0.764454	+	1.32407i
$185$		0			0
$186$	−1029.00	−	1782.28i	−0.405645	−	0.702597i
$187$	52.5000	−	90.9327i	0.0205304	−	0.0355597i
$188$	2100.00			0.814671
$189$	−490.000	+	424.352i	−0.188583	+	0.163318i
$190$		0			0
$191$	−1278.50	+	2214.43i	−0.484340	+	0.838902i	−0.999838	−	0.0179887i	$-0.994274\pi$
$191$	−1278.50	+	2214.43i	−0.484340	+	0.838902i	0.515498	+	0.856891i	$0.327607\pi$
$192$	1568.00	+	2715.86i	0.589378	+	1.02083i
$193$	−198.500	−	343.812i	−0.0740329	−	0.128229i	0.826632	−	0.562742i	$-0.190254\pi$
$193$	−198.500	−	343.812i	−0.0740329	−	0.128229i	−0.900665	+	0.434514i	$0.856920\pi$
$194$	882.000	−	1527.67i	0.326412	−	0.565362i
$195$		0			0
$196$	1274.00	−	509.223i	0.464286	−	0.185577i
$197$	−2914.00			−1.05388			−0.526939	−	0.849903i	$-0.676660\pi$
$197$	−2914.00			−1.05388			−0.526939	+	0.849903i	$0.676660\pi$
$198$	−110.000	+	190.526i	−0.0394816	+	0.0683842i
$199$	−1669.50	−	2891.66i	−0.594712	−	1.03007i	−0.993587	−	0.113066i	$-0.963933\pi$
$199$	−1669.50	−	2891.66i	−0.594712	−	1.03007i	0.398875	−	0.917005i	$-0.369401\pi$
$200$		0			0
$201$	−1452.50	+	2515.80i	−0.509709	+	0.882841i
$202$	−2758.00			−0.960654
$203$	−812.000	+	703.213i	−0.280745	+	0.243132i
$204$	588.000			0.201805
$205$		0			0
$206$	679.000	+	1176.06i	0.229651	+	0.397768i
$207$	−1749.00	−	3029.36i	−0.587265	−	1.01717i
$208$	112.000	−	193.990i	0.0373356	−	0.0646671i
$209$	−245.000			−0.0810861
$210$		0			0
$211$	1780.00			0.580759			0.290380	−	0.956911i	$-0.406218\pi$
$211$	1780.00			0.580759			0.290380	+	0.956911i	$0.406218\pi$
$212$	−606.000	+	1049.62i	−0.196322	+	0.340040i
$213$	−1512.00	−	2618.86i	−0.486387	−	0.842448i
$214$	−457.000	−	791.547i	−0.145981	−	0.252846i
$215$		0			0
$216$	840.000			0.264605
$217$	2572.50	+	891.140i	0.804759	+	0.278777i
$218$	2250.00			0.699033
$219$	3895.50	−	6747.20i	1.20198	−	2.08189i
$220$		0			0
$221$	−147.000	−	254.611i	−0.0447434	−	0.0774978i
$222$	1533.00	−	2655.23i	0.463460	−	0.802737i
$223$	1400.00			0.420408			0.210204	−	0.977658i	$-0.432587\pi$
$223$	1400.00			0.420408			0.210204	+	0.977658i	$0.432587\pi$
$224$	−2800.00	−	969.948i	−0.835191	−	0.289319i
$225$		0			0
$226$	1538.00	−	2663.89i	0.452682	−	0.784069i
$227$	−1102.50	−	1909.59i	−0.322359	−	0.558342i	0.658615	−	0.752480i	$-0.271142\pi$
$227$	−1102.50	−	1909.59i	−0.322359	−	0.558342i	−0.980974	+	0.194138i	$0.937809\pi$
$228$	−686.000	−	1188.19i	−0.199261	−	0.345130i
$229$	−143.500	+	248.549i	−0.0414094	+	0.0717231i	−0.885987	−	0.463710i	$-0.846518\pi$
$229$	−143.500	+	248.549i	−0.0414094	+	0.0717231i	0.844578	+	0.535433i	$0.179851\pi$
$230$		0			0
$231$	−122.500	−	636.529i	−0.0348914	−	0.181301i
$232$	1392.00			0.393919
$233$	2293.50	−	3972.46i	0.644859	−	1.11693i	−0.339475	−	0.940615i	$-0.610249\pi$
$233$	2293.50	−	3972.46i	0.644859	−	1.11693i	0.984334	−	0.176314i	$-0.0564173\pi$
$234$	308.000	+	533.472i	0.0860453	+	0.149035i
$235$		0			0
$236$	−210.000	+	363.731i	−0.0579230	+	0.100326i
$237$	721.000			0.197612
$238$	588.000	−	509.223i	0.160144	−	0.138689i
$239$	1668.00			0.451439			0.225720	−	0.974192i	$-0.427527\pi$
$239$	1668.00			0.451439			0.225720	+	0.974192i	$0.427527\pi$
$240$		0			0
$241$	1704.50	+	2952.28i	0.455587	+	0.789100i	0.998722	−	0.0505456i	$-0.0160960\pi$
$241$	1704.50	+	2952.28i	0.455587	+	0.789100i	−0.543135	+	0.839646i	$0.682763\pi$
$242$	−1306.00	−	2262.06i	−0.346913	−	0.600870i
$243$	−2464.00	+	4267.77i	−0.650476	+	1.12666i
$244$	1652.00			0.433436
$245$		0			0
$246$	4900.00			1.26997
$247$	−343.000	+	594.093i	−0.0883586	+	0.153042i
$248$	−1764.00	−	3055.34i	−0.451670	−	0.782315i
$249$	−3822.00	−	6619.90i	−0.972729	−	1.68482i
$250$		0			0
$251$	−4760.00			−1.19701			−0.598503	−	0.801121i	$-0.704238\pi$
$251$	−4760.00			−1.19701			−0.598503	+	0.801121i	$0.704238\pi$
$252$	1232.00	−	1066.94i	0.307971	−	0.266711i
$253$	−795.000			−0.197554
$254$	−72.0000	+	124.708i	−0.0177861	+	0.0308065i
$255$		0			0
$256$	2176.00	+	3768.94i	0.531250	+	0.920152i
$257$	−402.500	+	697.150i	−0.0976936	+	0.169210i	−0.910730	−	0.413003i	$-0.864480\pi$
$257$	−402.500	+	697.150i	−0.0976936	+	0.169210i	0.813036	+	0.582213i	$0.197813\pi$
$258$	1736.00			0.418909
$259$	766.500	+	3982.85i	0.183892	+	0.955530i
$260$		0			0
$261$	−638.000	+	1105.05i	−0.151307	+	0.262072i
$262$	2149.00	+	3722.18i	0.506739	+	0.877698i
$263$	−128.500	−	222.569i	−0.0301279	−	0.0521831i	0.850568	−	0.525865i	$-0.176258\pi$
$263$	−128.500	−	222.569i	−0.0301279	−	0.0521831i	−0.880696	+	0.473681i	$0.842925\pi$
$264$	−420.000	+	727.461i	−0.0979137	+	0.169591i
$265$		0			0
$266$	−1715.00	−	594.093i	−0.395314	−	0.136941i
$267$	2303.00			0.527870
$268$	−830.000	+	1437.60i	−0.189180	+	0.327670i
$269$	−1795.50	−	3109.90i	−0.406965	−	0.704884i	0.587583	−	0.809164i	$-0.300080\pi$
$269$	−1795.50	−	3109.90i	−0.406965	−	0.704884i	−0.994548	+	0.104280i	$0.966746\pi$
$270$		0			0
$271$	−696.500	+	1206.37i	−0.156123	+	0.270413i	−0.933467	−	0.358662i	$-0.883233\pi$
$271$	−696.500	+	1206.37i	−0.156123	+	0.270413i	0.777344	+	0.629075i	$0.216566\pi$
$272$	−336.000			−0.0749007
$273$	−1715.00	−	594.093i	−0.380207	−	0.131708i
$274$	−2250.00			−0.496086
$275$		0			0
$276$	−2226.00	−	3855.55i	−0.485469	−	0.840857i
$277$	207.500	+	359.401i	0.0450089	+	0.0779577i	0.887652	−	0.460514i	$-0.152335\pi$
$277$	207.500	+	359.401i	0.0450089	+	0.0779577i	−0.842643	+	0.538472i	$0.819002\pi$
$278$	252.000	−	436.477i	0.0543667	−	0.0941660i
$279$	3234.00			0.693959
$280$		0			0
$281$	−4954.00			−1.05171			−0.525856	−	0.850574i	$-0.676255\pi$
$281$	−4954.00			−1.05171			−0.525856	+	0.850574i	$0.676255\pi$
$282$	3675.00	−	6365.29i	0.776039	−	1.34414i
$283$	−2138.50	−	3703.99i	−0.449190	−	0.778019i	0.549144	−	0.835728i	$-0.314954\pi$
$283$	−2138.50	−	3703.99i	−0.449190	−	0.778019i	−0.998333	+	0.0577087i	$0.981621\pi$
$284$	−864.000	−	1496.49i	−0.180525	−	0.312678i
$285$		0			0
$286$	140.000			0.0289454
$287$	−4900.00	+	4243.52i	−1.00780	+	0.872778i
$288$	−3520.00			−0.720201
$289$	2236.00	−	3872.87i	0.455119	−	0.788289i
$290$		0			0
$291$	3087.00	+	5346.84i	0.621866	+	1.07710i
$292$	2226.00	−	3855.55i	0.446119	−	0.772701i
$293$	−7742.00			−1.54366			−0.771830	−	0.635829i	$-0.780658\pi$
$293$	−7742.00			−1.54366			−0.771830	+	0.635829i	$0.780658\pi$
$294$	686.000	−	4752.75i	0.136083	−	0.942809i
$295$		0			0
$296$	2628.00	−	4551.83i	0.516045	−	0.893817i
$297$	87.5000	+	151.554i	0.0170952	+	0.0296097i
$298$	−201.000	−	348.142i	−0.0390725	−	0.0676756i
$299$	−1113.00	+	1927.77i	−0.215272	+	0.372863i
$300$		0			0
$301$	−1736.00	+	1503.42i	−0.332430	+	0.287893i
$302$	−3238.00			−0.616973
$303$	4826.50	−	8359.74i	0.915100	−	1.58500i
$304$	392.000	+	678.964i	0.0739564	+	0.128096i
$305$		0			0
$306$	462.000	−	800.207i	0.0863097	−	0.149493i
$307$	7364.00			1.36901			0.684504	−	0.729009i	$-0.260019\pi$
$307$	7364.00			1.36901			0.684504	+	0.729009i	$0.260019\pi$
$308$	−70.0000	−	363.731i	−0.0129501	−	0.0672905i
$309$	−4753.00			−0.875044
$310$		0			0
$311$	−4987.50	−	8638.60i	−0.909374	−	1.57508i	−0.814936	−	0.579550i	$-0.803228\pi$
$311$	−4987.50	−	8638.60i	−0.909374	−	1.57508i	−0.0944372	−	0.995531i	$-0.530105\pi$
$312$	1176.00	+	2036.89i	0.213391	+	0.369603i
$313$	−2376.50	+	4116.22i	−0.429162	+	0.743330i	−0.996799	−	0.0799485i	$-0.974524\pi$
$313$	−2376.50	+	4116.22i	−0.429162	+	0.743330i	0.567637	+	0.823279i	$0.307858\pi$
$314$	1358.00			0.244065
$315$		0			0
$316$	412.000			0.0733443
$317$	−1738.50	+	3011.17i	−0.308025	+	0.533515i	−0.977930	−	0.208932i	$-0.933001\pi$
$317$	−1738.50	+	3011.17i	−0.308025	+	0.533515i	0.669905	+	0.742447i	$0.266335\pi$
$318$	2121.00	+	3673.68i	0.374024	+	0.647829i
$319$	145.000	+	251.147i	0.0254497	+	0.0440801i
$320$		0			0
$321$	3199.00			0.556233
$322$	−5565.00	−	1927.77i	−0.963122	−	0.333635i
$323$	1029.00			0.177260
$324$	−1678.00	+	2906.38i	−0.287723	+	0.498351i
$325$		0			0
$326$	467.000	+	808.868i	0.0793397	+	0.137420i
$327$	−3937.50	+	6819.95i	−0.665885	+	1.15335i
$328$	8400.00			1.41406
$329$	1837.50	+	9547.93i	0.307917	+	1.59998i
$330$		0			0
$331$	−1670.50	+	2893.39i	−0.277399	+	0.480469i	−0.970738	−	0.240143i	$-0.922806\pi$
$331$	−1670.50	+	2893.39i	−0.277399	+	0.480469i	0.693339	+	0.720612i	$0.256139\pi$
$332$	−2184.00	−	3782.80i	−0.361032	−	0.625325i
$333$	2409.00	+	4172.51i	0.396434	+	0.686643i
$334$	−1204.00	+	2085.39i	−0.197245	+	0.341639i
$335$		0			0
$336$	−1568.00	+	1357.93i	−0.254588	+	0.220479i
$337$	−7366.00			−1.19066			−0.595329	−	0.803482i	$-0.702978\pi$
$337$	−7366.00			−1.19066			−0.595329	+	0.803482i	$0.702978\pi$
$338$	−2001.00	+	3465.83i	−0.322012	+	0.557741i
$339$	5383.00	+	9323.63i	0.862432	+	1.49378i
$340$		0			0
$341$	367.500	−	636.529i	0.0583614	−	0.101085i
$342$	−2156.00			−0.340886
$343$	3430.00	+	5346.84i	0.539949	+	0.841698i
$344$	2976.00			0.466439
$345$		0			0
$346$	2821.00	+	4886.12i	0.438318	+	0.759188i
$347$	3707.50	+	6421.58i	0.573571	+	0.993454i	0.996195	+	0.0871487i	$0.0277755\pi$
$347$	3707.50	+	6421.58i	0.573571	+	0.993454i	−0.422625	+	0.906305i	$0.638891\pi$
$348$	−812.000	+	1406.43i	−0.125080	+	0.216645i
$349$	−3878.00			−0.594798			−0.297399	−	0.954753i	$-0.596119\pi$
$349$	−3878.00			−0.594798			−0.297399	+	0.954753i	$0.596119\pi$
$350$		0			0
$351$	490.000			0.0745136
$352$	−400.000	+	692.820i	−0.0605684	+	0.104908i
$353$	633.500	+	1097.25i	0.0955179	+	0.165442i	0.909825	−	0.414993i	$-0.136216\pi$
$353$	633.500	+	1097.25i	0.0955179	+	0.165442i	−0.814307	+	0.580435i	$0.802883\pi$
$354$	735.000	+	1273.06i	0.110353	+	0.191136i
$355$		0			0
$356$	1316.00			0.195921
$357$	514.500	+	2673.42i	0.0762751	+	0.396337i
$358$	6506.00			0.960483
$359$	−2342.50	+	4057.33i	−0.344380	+	0.596484i	−0.985241	−	0.171173i	$-0.945244\pi$
$359$	−2342.50	+	4057.33i	−0.344380	+	0.596484i	0.640861	+	0.767657i	$0.278578\pi$
$360$		0			0
$361$	2229.00	+	3860.74i	0.324974	+	0.562872i
$362$	1582.00	−	2740.10i	0.229691	−	0.397836i
$363$	9142.00			1.32185
$364$	−980.000	−	339.482i	−0.141115	−	0.0488838i
$365$		0			0
$366$	2891.00	−	5007.36i	0.412882	−	0.715133i
$367$	−2320.50	−	4019.22i	−0.330052	−	0.571667i	0.652470	−	0.757815i	$-0.273733\pi$
$367$	−2320.50	−	4019.22i	−0.330052	−	0.571667i	−0.982522	+	0.186148i	$0.940400\pi$
$368$	1272.00	+	2203.17i	0.180184	+	0.312087i
$369$	−3850.00	+	6668.40i	−0.543152	+	0.940766i
$370$		0			0
$371$	−5302.50	−	1836.84i	−0.742027	−	0.257046i
$372$	4116.00			0.573668
$373$	−4398.50	+	7618.43i	−0.610578	+	1.05755i	0.380565	+	0.924754i	$0.375730\pi$
$373$	−4398.50	+	7618.43i	−0.610578	+	1.05755i	−0.991143	+	0.132798i	$0.957604\pi$
$374$	−105.000	−	181.865i	−0.0145172	−	0.0251445i
$375$		0			0
$376$	6300.00	−	10911.9i	0.864090	−	1.49665i
$377$	812.000			0.110929
$378$	245.000	+	1273.06i	0.0333371	+	0.173225i
$379$	13680.0			1.85407			0.927037	−	0.374969i	$-0.122347\pi$
$379$	13680.0			1.85407			0.927037	+	0.374969i	$0.122347\pi$
$380$		0			0
$381$	−252.000	−	436.477i	−0.0338854	−	0.0586913i
$382$	2557.00	+	4428.85i	0.342480	+	0.593193i
$383$	4882.50	−	8456.74i	0.651395	−	1.12825i	−0.331390	−	0.943494i	$-0.607518\pi$
$383$	4882.50	−	8456.74i	0.651395	−	1.12825i	0.982785	−	0.184755i	$-0.0591490\pi$
$384$	−2688.00			−0.357217
$385$		0			0
$386$	−794.000			−0.104698
$387$	−1364.00	+	2362.52i	−0.179163	+	0.310319i
$388$	1764.00	+	3055.34i	0.230808	+	0.399771i
$389$	−865.500	−	1499.09i	−0.112809	−	0.195390i	0.804093	−	0.594504i	$-0.202651\pi$
$389$	−865.500	−	1499.09i	−0.112809	−	0.195390i	−0.916902	+	0.399113i	$0.869318\pi$
$390$		0			0
$391$	3339.00			0.431868
$392$	1176.00	−	8147.57i	0.151523	−	1.04978i
$393$	−15043.0			−1.93084
$394$	−2914.00	+	5047.20i	−0.372602	+	0.645366i
$395$		0			0
$396$	−220.000	−	381.051i	−0.0279177	−	0.0483549i
$397$	5491.50	−	9511.56i	0.694233	−	1.20245i	−0.276206	−	0.961099i	$-0.589077\pi$
$397$	5491.50	−	9511.56i	0.694233	−	1.20245i	0.970439	−	0.241348i	$-0.0775896\pi$
$398$	−6678.00			−0.841050
$399$	4802.00	−	4158.65i	0.602508	−	0.521787i
$400$		0			0
$401$	−3301.50	+	5718.37i	−0.411145	+	0.712124i	−0.995015	−	0.0997232i	$-0.968204\pi$
$401$	−3301.50	+	5718.37i	−0.411145	+	0.712124i	0.583870	+	0.811847i	$0.301538\pi$
$402$	2905.00	+	5031.61i	0.360418	+	0.624263i
$403$	−1029.00	−	1782.28i	−0.127191	−	0.220302i
$404$	2758.00	−	4777.00i	0.339643	−	0.588278i
$405$		0			0
$406$	406.000	+	2109.64i	0.0496292	+	0.257881i
$407$	1095.00			0.133359
$408$	1764.00	−	3055.34i	0.214047	−	0.370740i
$409$	−5477.50	−	9487.31i	−0.662213	−	1.14699i	−0.980033	−	0.198835i	$-0.936284\pi$
$409$	−5477.50	−	9487.31i	−0.662213	−	1.14699i	0.317820	−	0.948151i	$-0.397049\pi$
$410$		0			0
$411$	3937.50	−	6819.95i	0.472561	−	0.818500i
$412$	−2716.00			−0.324776
$413$	−1837.50	−	636.529i	−0.218928	−	0.0758391i
$414$	−6996.00			−0.830518
$415$		0			0
$416$	1120.00	+	1939.90i	0.132001	+	0.228633i
$417$	882.000	+	1527.67i	0.103577	+	0.179401i
$418$	−245.000	+	424.352i	−0.0286683	+	0.0496549i
$419$	6636.00			0.773723			0.386861	−	0.922138i	$-0.373559\pi$
$419$	6636.00			0.773723			0.386861	+	0.922138i	$0.373559\pi$
$420$		0			0
$421$	−16630.0			−1.92517			−0.962585	−	0.270980i	$-0.912652\pi$
$421$	−16630.0			−1.92517			−0.962585	+	0.270980i	$0.912652\pi$
$422$	1780.00	−	3083.05i	0.205329	−	0.355641i
$423$	5775.00	+	10002.6i	0.663806	+	1.14975i
$424$	3636.00	+	6297.74i	0.416462	+	0.721333i
$425$		0			0
$426$	−6048.00			−0.687856
$427$	1445.50	+	7511.04i	0.163824	+	0.851252i
$428$	1828.00			0.206448
$429$	−245.000	+	424.352i	−0.0275728	+	0.0477574i
$430$		0			0
$431$	−2461.50	−	4263.44i	−0.275096	−	0.476480i	0.695064	−	0.718948i	$-0.255376\pi$
$431$	−2461.50	−	4263.44i	−0.275096	−	0.476480i	−0.970159	+	0.242468i	$0.922043\pi$
$432$	280.000	−	484.974i	0.0311840	−	0.0540123i
$433$	−8974.00			−0.995988			−0.497994	−	0.867180i	$-0.665930\pi$
$433$	−8974.00			−0.995988			−0.497994	+	0.867180i	$0.665930\pi$
$434$	4116.00	−	3564.56i	0.455240	−	0.394250i
$435$		0			0
$436$	−2250.00	+	3897.11i	−0.247146	+	0.428069i
$437$	−3895.50	−	6747.20i	−0.426423	−	0.738587i
$438$	−7791.00	−	13494.4i	−0.849928	−	1.47212i
$439$	2089.50	−	3619.12i	0.227167	−	0.393465i	−0.729800	−	0.683660i	$-0.760387\pi$
$439$	2089.50	−	3619.12i	0.227167	−	0.393465i	0.956967	+	0.290195i	$0.0937203\pi$
$440$		0			0
$441$	5929.00	+	4667.88i	0.640212	+	0.504036i
$442$	−588.000			−0.0632767
$443$	−6463.50	+	11195.1i	−0.693206	+	1.20067i	0.277576	+	0.960704i	$0.410469\pi$
$443$	−6463.50	+	11195.1i	−0.693206	+	1.20067i	−0.970782	+	0.239964i	$0.922864\pi$
$444$	3066.00	+	5310.47i	0.327716	+	0.567621i
$445$		0			0
$446$	1400.00	−	2424.87i	0.148637	−	0.257446i
$447$	1407.00			0.148879
$448$	−6272.00	+	5431.71i	−0.661438	+	0.572822i
$449$	−2826.00			−0.297032			−0.148516	−	0.988910i	$-0.547450\pi$
$449$	−2826.00			−0.297032			−0.148516	+	0.988910i	$0.547450\pi$
$450$		0			0
$451$	875.000	+	1515.54i	0.0913573	+	0.158235i
$452$	3076.00	+	5327.79i	0.320095	+	0.554421i
$453$	5666.50	−	9814.67i	0.587716	−	1.01795i
$454$	−4410.00			−0.455884
$455$		0			0
$456$	−8232.00			−0.845392
$457$	4239.50	−	7343.03i	0.433951	−	0.751625i	−0.563259	−	0.826281i	$-0.690453\pi$
$457$	4239.50	−	7343.03i	0.433951	−	0.751625i	0.997209	+	0.0746560i	$0.0237859\pi$
$458$	287.000	+	497.099i	0.0292808	+	0.0507159i
$459$	−367.500	−	636.529i	−0.0373713	−	0.0647290i
$460$		0			0
$461$	9338.00			0.943414			0.471707	−	0.881755i	$-0.343638\pi$
$461$	9338.00			0.943414			0.471707	+	0.881755i	$0.343638\pi$
$462$	−1225.00	−	424.352i	−0.123360	−	0.0427330i
$463$	4016.00			0.403109			0.201554	−	0.979477i	$-0.435401\pi$
$463$	4016.00			0.403109			0.201554	+	0.979477i	$0.435401\pi$
$464$	464.000	−	803.672i	0.0464238	−	0.0804084i
$465$		0			0
$466$	−4587.00	−	7944.92i	−0.455984	−	0.789788i
$467$	−2929.50	+	5074.04i	−0.290281	+	0.502781i	−0.973876	−	0.227080i	$-0.927082\pi$
$467$	−2929.50	+	5074.04i	−0.290281	+	0.502781i	0.683595	+	0.729861i	$0.260415\pi$
$468$	−1232.00			−0.121686
$469$	−7262.50	−	2515.80i	−0.715034	−	0.247695i
$470$		0			0
$471$	−2376.50	+	4116.22i	−0.232491	+	0.402687i
$472$	1260.00	+	2182.38i	0.122873	+	0.212823i
$473$	310.000	+	536.936i	0.0301349	+	0.0521952i
$474$	721.000	−	1248.81i	0.0698663	−	0.121012i
$475$		0			0
$476$	294.000	+	1527.67i	0.0283098	+	0.147102i
$477$	−6666.00			−0.639864
$478$	1668.00	−	2889.06i	0.159608	−	0.276449i
$479$	−3251.50	−	5631.76i	−0.310156	−	0.537206i	0.668240	−	0.743946i	$-0.267048\pi$
$479$	−3251.50	−	5631.76i	−0.310156	−	0.537206i	−0.978396	+	0.206740i	$0.933715\pi$
$480$		0			0
$481$	1533.00	−	2655.23i	0.145320	−	0.251701i
$482$	6818.00			0.644297
$483$	15582.0	−	13494.4i	1.46792	−	1.27126i
$484$	5224.00			0.490609
$485$		0			0
$486$	4928.00	+	8535.55i	0.459956	+	0.796667i
$487$	−8024.50	−	13898.8i	−0.746663	−	1.29326i	−0.949414	−	0.314028i	$-0.898322\pi$
$487$	−8024.50	−	13898.8i	−0.746663	−	1.29326i	0.202751	−	0.979230i	$-0.435012\pi$
$488$	4956.00	−	8584.04i	0.459729	−	0.796273i
$489$	−3269.00			−0.302309
$490$		0			0
$491$	8864.00			0.814718			0.407359	−	0.913268i	$-0.366450\pi$
$491$	8864.00			0.814718			0.407359	+	0.913268i	$0.366450\pi$
$492$	−4900.00	+	8487.05i	−0.449002	+	0.777695i
$493$	−609.000	−	1054.82i	−0.0556348	−	0.0963624i
$494$	686.000	+	1188.19i	0.0624789	+	0.108217i
$495$		0			0
$496$	−2352.00			−0.212919
$497$	6048.00	−	5237.72i	0.545855	−	0.472724i
$498$	−15288.0			−1.37565
$499$	5105.50	−	8842.99i	0.458023	−	0.793319i	−0.540833	−	0.841130i	$-0.681891\pi$
$499$	5105.50	−	8842.99i	0.458023	−	0.793319i	0.998856	+	0.0478104i	$0.0152243\pi$
$500$		0			0
$501$	−4214.00	−	7298.86i	−0.375784	−	0.650876i
$502$	−4760.00	+	8244.56i	−0.423206	+	0.733014i
$503$	1680.00			0.148921			0.0744607	−	0.997224i	$-0.476276\pi$
$503$	1680.00			0.148921			0.0744607	+	0.997224i	$0.476276\pi$
$504$	−1848.00	−	9602.49i	−0.163326	−	0.848668i
$505$		0			0
$506$	−795.000	+	1376.98i	−0.0698460	+	0.120977i
$507$	−7003.50	−	12130.4i	−0.613484	−	1.06259i
$508$	−144.000	−	249.415i	−0.0125767	−	0.0217835i
$509$	4728.50	−	8190.00i	0.411762	−	0.713193i	−0.583320	−	0.812242i	$-0.698247\pi$
$509$	4728.50	−	8190.00i	0.411762	−	0.713193i	0.995083	+	0.0990489i	$0.0315800\pi$
$510$		0			0
$511$	19477.5	+	6747.20i	1.68617	+	0.584107i
$512$	5632.00			0.486136
$513$	−857.500	+	1485.23i	−0.0738003	+	0.127826i
$514$	805.000	+	1394.30i	0.0690798	+	0.119650i
$515$		0			0
$516$	−1736.00	+	3006.84i	−0.148107	+	0.256529i
$517$	2625.00			0.223302
$518$	7665.00	+	2655.23i	0.650156	+	0.225221i
$519$	−19747.0			−1.67013
$520$		0			0
$521$	9040.50	+	15658.6i	0.760214	+	1.31673i	0.942740	+	0.333528i	$0.108239\pi$
$521$	9040.50	+	15658.6i	0.760214	+	1.31673i	−0.182526	+	0.983201i	$0.558427\pi$
$522$	1276.00	+	2210.10i	0.106990	+	0.185313i
$523$	10188.5	−	17647.0i	0.851839	−	1.47543i	−0.0277071	−	0.999616i	$-0.508821\pi$
$523$	10188.5	−	17647.0i	0.851839	−	1.47543i	0.879546	−	0.475813i	$-0.157846\pi$
$524$	−8596.00			−0.716637
$525$		0			0
$526$	−514.000			−0.0426073
$527$	−1543.50	+	2673.42i	−0.127582	+	0.220979i
$528$	280.000	+	484.974i	0.0230785	+	0.0399731i
$529$	−6557.00	−	11357.1i	−0.538917	−	0.933431i
$530$		0			0
$531$	−2310.00			−0.188786
$532$	2744.00	−	2376.37i	0.223623	−	0.193663i
$533$	4900.00			0.398204
$534$	2303.00	−	3988.91i	0.186630	−	0.323253i
$535$		0			0
$536$	4980.00	+	8625.61i	0.401312	+	0.695093i
$537$	−11385.5	+	19720.3i	−0.914936	+	1.58472i
$538$	−7182.00			−0.575535
$539$	1592.50	−	636.529i	0.127261	−	0.0508668i
$540$		0			0
$541$	3096.50	−	5363.30i	0.246079	−	0.426222i	−0.716355	−	0.697736i	$-0.754191\pi$
$541$	3096.50	−	5363.30i	0.246079	−	0.426222i	0.962435	+	0.271514i	$0.0875243\pi$
$542$	1393.00	+	2412.75i	0.110396	+	0.191211i
$543$	5537.00	+	9590.37i	0.437597	+	0.757941i
$544$	1680.00	−	2909.85i	0.132407	−	0.229336i
$545$		0			0
$546$	−2744.00	+	2376.37i	−0.215078	+	0.186263i
$547$	18464.0			1.44326			0.721630	−	0.692279i	$-0.243393\pi$
$547$	18464.0			1.44326			0.721630	+	0.692279i	$0.243393\pi$
$548$	2250.00	−	3897.11i	0.175393	−	0.303789i
$549$	4543.00	+	7868.71i	0.353170	+	0.611709i
$550$		0			0
$551$	−1421.00	+	2461.24i	−0.109867	+	0.190295i
$552$	−26712.0			−2.05967
$553$	360.500	+	1873.21i	0.0277216	+	0.144045i
$554$	830.000			0.0636522
$555$		0			0
$556$	504.000	+	872.954i	0.0384431	+	0.0665854i
$557$	−4706.50	−	8151.90i	−0.358027	−	0.620120i	0.629604	−	0.776916i	$-0.283217\pi$
$557$	−4706.50	−	8151.90i	−0.358027	−	0.620120i	−0.987631	+	0.156796i	$0.949884\pi$
$558$	3234.00	−	5601.45i	0.245351	−	0.424961i
$559$	1736.00			0.131351
$560$		0			0
$561$	735.000			0.0553150
$562$	−4954.00	+	8580.58i	−0.371836	+	0.644039i
$563$	1599.50	+	2770.42i	0.119735	+	0.207387i	0.919663	−	0.392709i	$-0.128462\pi$
$563$	1599.50	+	2770.42i	0.119735	+	0.207387i	−0.799928	+	0.600097i	$0.795129\pi$
$564$	7350.00	+	12730.6i	0.548743	+	0.950450i
$565$		0			0
$566$	−8554.00			−0.635250
$567$	−14682.5	−	5086.17i	−1.08749	−	0.376718i
$568$	−10368.0			−0.765901
$569$	−10791.5	+	18691.4i	−0.795085	+	1.37713i	0.127701	+	0.991813i	$0.459240\pi$
$569$	−10791.5	+	18691.4i	−0.795085	+	1.37713i	−0.922785	+	0.385314i	$0.874093\pi$
$570$		0			0
$571$	−10133.5	−	17551.7i	−0.742686	−	1.28637i	−0.951268	−	0.308365i	$-0.900218\pi$
$571$	−10133.5	−	17551.7i	−0.742686	−	1.28637i	0.208582	−	0.978005i	$-0.433115\pi$
$572$	−140.000	+	242.487i	−0.0102337	+	0.0177253i
$573$	−17899.0			−1.30496
$574$	2450.00	+	12730.6i	0.178155	+	0.925721i
$575$		0			0
$576$	−4928.00	+	8535.55i	−0.356481	+	0.617444i
$577$	6975.50	+	12081.9i	0.503282	+	0.871710i	0.999993	+	0.00379418i	$0.00120773\pi$
$577$	6975.50	+	12081.9i	0.503282	+	0.871710i	−0.496711	+	0.867916i	$0.665459\pi$
$578$	−4472.00	−	7745.73i	−0.321818	−	0.557405i
$579$	1389.50	−	2406.68i	0.0997334	−	0.172743i
$580$		0			0
$581$	15288.0	−	13239.8i	1.09166	−	0.945403i
$582$	12348.0			0.879452
$583$	−757.500	+	1312.03i	−0.0538121	+	0.0932053i
$584$	−13356.0	−	23133.3i	−0.946362	−	1.63915i
$585$		0			0
$586$	−7742.00	+	13409.5i	−0.545766	+	0.945295i
$587$	20972.0			1.47463			0.737314	−	0.675550i	$-0.236094\pi$
$587$	20972.0			1.47463			0.737314	+	0.675550i	$0.236094\pi$
$588$	7546.00	+	5940.93i	0.529238	+	0.416667i
$589$	7203.00			0.503895
$590$		0			0
$591$	−10199.0	−	17665.2i	−0.709866	−	1.22952i
$592$	−1752.00	−	3034.55i	−0.121633	−	0.210675i
$593$	−94.5000	+	163.679i	−0.00654410	+	0.0113347i	−0.869279	−	0.494322i	$-0.835416\pi$
$593$	−94.5000	+	163.679i	−0.00654410	+	0.0113347i	0.862735	+	0.505657i	$0.168750\pi$
$594$	350.000			0.0241762
$595$		0			0
$596$	804.000			0.0552569
$597$	11686.5	−	20241.6i	0.801167	−	1.38766i
$598$	2226.00	+	3855.55i	0.152221	+	0.263654i
$599$	5140.50	+	8903.61i	0.350643	+	0.607331i	0.986362	−	0.164589i	$-0.0526297\pi$
$599$	5140.50	+	8903.61i	0.350643	+	0.607331i	−0.635719	+	0.771920i	$0.719296\pi$
$600$		0			0
$601$	−6090.00			−0.413338			−0.206669	−	0.978411i	$-0.566262\pi$
$601$	−6090.00			−0.413338			−0.206669	+	0.978411i	$0.566262\pi$
$602$	868.000	+	4510.26i	0.0587658	+	0.305356i
$603$	−9130.00			−0.616588
$604$	3238.00	−	5608.38i	0.218133	−	0.377817i
$605$		0			0
$606$	−9653.00	−	16719.5i	−0.647073	−	1.12076i
$607$	2474.50	−	4285.96i	0.165464	−	0.286593i	−0.771356	−	0.636404i	$-0.780421\pi$
$607$	2474.50	−	4285.96i	0.165464	−	0.286593i	0.936820	+	0.349812i	$0.113754\pi$
$608$	−7840.00			−0.522951
$609$	−7105.00	−	2461.24i	−0.472757	−	0.163768i
$610$		0			0
$611$	3675.00	−	6365.29i	0.243330	−	0.421460i
$612$	924.000	+	1600.41i	0.0610302	+	0.105707i
$613$	−7898.50	−	13680.6i	−0.520420	−	0.901394i	−0.999718	−	0.0237416i	$-0.992442\pi$
$613$	−7898.50	−	13680.6i	−0.520420	−	0.901394i	0.479298	−	0.877652i	$-0.340891\pi$
$614$	7364.00	−	12754.8i	0.484018	−	0.838343i
$615$		0			0
$616$	−2100.00	−	727.461i	−0.137356	−	0.0475816i
$617$	9378.00			0.611903			0.305951	−	0.952047i	$-0.401025\pi$
$617$	9378.00			0.611903			0.305951	+	0.952047i	$0.401025\pi$
$618$	−4753.00	+	8232.44i	−0.309375	+	0.535853i
$619$	12176.5	+	21090.3i	0.790654	+	1.36945i	0.925562	+	0.378595i	$0.123593\pi$
$619$	12176.5	+	21090.3i	0.790654	+	1.36945i	−0.134908	+	0.990858i	$0.543074\pi$
$620$		0			0
$621$	−2782.50	+	4819.43i	−0.179803	+	0.311429i
$622$	−19950.0			−1.28605
$623$	1151.50	+	5983.37i	0.0740512	+	0.384781i
$624$	1568.00			0.100593
$625$		0			0
$626$	4753.00	+	8232.44i	0.303463	+	0.525614i
$627$	−857.500	−	1485.23i	−0.0546176	−	0.0946005i
$628$	−1358.00	+	2352.12i	−0.0862900	+	0.149459i
$629$	−4599.00			−0.291533
$630$		0			0
$631$	−12640.0			−0.797449			−0.398725	−	0.917071i	$-0.630547\pi$
$631$	−12640.0			−0.797449			−0.398725	+	0.917071i	$0.630547\pi$
$632$	1236.00	−	2140.81i	0.0777934	−	0.134742i
$633$	6230.00	+	10790.7i	0.391185	+	0.677553i
$634$	3477.00	+	6022.34i	0.217806	+	0.377252i
$635$		0			0
$636$	−8484.00			−0.528950
$637$	686.000	−	4752.75i	0.0426692	−	0.295621i
$638$	580.000			0.0359913
$639$	4752.00	−	8230.71i	0.294188	−	0.509549i
$640$		0			0
$641$	520.500	+	901.532i	0.0320726	+	0.0555513i	0.881616	−	0.471967i	$-0.156456\pi$
$641$	520.500	+	901.532i	0.0320726	+	0.0555513i	−0.849544	+	0.527518i	$0.823123\pi$
$642$	3199.00	−	5540.83i	0.196658	−	0.340622i
$643$	−9548.00			−0.585593			−0.292797	−	0.956175i	$-0.594586\pi$
$643$	−9548.00			−0.585593			−0.292797	+	0.956175i	$0.594586\pi$
$644$	8904.00	−	7711.09i	0.544824	−	0.471832i
$645$		0			0
$646$	1029.00	−	1782.28i	0.0626710	−	0.108549i
$647$	−1620.50	−	2806.79i	−0.0984674	−	0.170551i	0.812583	−	0.582845i	$-0.198061\pi$
$647$	−1620.50	−	2806.79i	−0.0984674	−	0.170551i	−0.911050	+	0.412295i	$0.864727\pi$
$648$	10068.0	+	17438.3i	0.610352	+	1.05716i
$649$	−262.500	+	454.663i	−0.0158768	+	0.0274994i
$650$		0			0
$651$	3601.50	+	18713.9i	0.216826	+	1.12666i
$652$	−1868.00			−0.112203
$653$	−4426.50	+	7666.92i	−0.265272	+	0.459464i	−0.967635	−	0.252355i	$-0.918795\pi$
$653$	−4426.50	+	7666.92i	−0.265272	+	0.459464i	0.702363	+	0.711819i	$0.252128\pi$
$654$	7875.00	+	13639.9i	0.470851	+	0.815539i
$655$		0			0
$656$	2800.00	−	4849.74i	0.166649	−	0.288644i
$657$	24486.0			1.45402
$658$	18375.0	+	6365.29i	1.08865	+	0.377120i
$659$	7044.00			0.416381			0.208191	−	0.978088i	$-0.433243\pi$
$659$	7044.00			0.416381			0.208191	+	0.978088i	$0.433243\pi$
$660$		0			0
$661$	6044.50	+	10469.4i	0.355679	+	0.616054i	0.987234	−	0.159277i	$-0.0509163\pi$
$661$	6044.50	+	10469.4i	0.355679	+	0.616054i	−0.631555	+	0.775331i	$0.717583\pi$
$662$	3341.00	+	5786.78i	0.196151	+	0.339743i
$663$	1029.00	−	1782.28i	0.0602761	−	0.104401i
$664$	−26208.0			−1.53173
$665$		0			0
$666$	9636.00			0.560642
$667$	−4611.00	+	7986.49i	−0.267674	+	0.463625i
$668$	−2408.00	−	4170.78i	−0.139474	−	0.241575i
$669$	4900.00	+	8487.05i	0.283176	+	0.490476i
$670$		0			0
$671$	2065.00			0.118805
$672$	−3920.00	−	20368.9i	−0.225026	−	1.16927i
$673$	−982.000			−0.0562456			−0.0281228	−	0.999604i	$-0.508953\pi$
$673$	−982.000			−0.0562456			−0.0281228	+	0.999604i	$0.508953\pi$
$674$	−7366.00	+	12758.3i	−0.420961	+	0.729126i
$675$		0			0
$676$	−4002.00	−	6931.67i	−0.227697	−	0.394383i
$677$	−15256.5	+	26425.0i	−0.866108	+	1.50014i	−0.000164659		1.00000i	$0.500052\pi$
$677$	−15256.5	+	26425.0i	−0.866108	+	1.50014i	−0.865943	+	0.500143i	$0.833281\pi$
$678$	21532.0			1.21966
$679$	−12348.0	+	10693.7i	−0.697898	+	0.604397i
$680$		0			0
$681$	7717.50	−	13367.1i	0.434266	−	0.752171i
$682$	−735.000	−	1273.06i	−0.0412677	−	0.0714778i
$683$	5737.50	+	9937.64i	0.321434	+	0.556740i	0.980784	−	0.195096i	$-0.0625019\pi$
$683$	5737.50	+	9937.64i	0.321434	+	0.556740i	−0.659350	+	0.751836i	$0.729169\pi$
$684$	2156.00	−	3734.30i	0.120522	−	0.208749i
$685$		0			0
$686$	12691.0	−	594.093i	0.706333	−	0.0330650i
$687$	−2009.00			−0.111569
$688$	992.000	−	1718.19i	0.0549704	−	0.0952116i
$689$	2121.00	+	3673.68i	0.117277	+	0.203129i
$690$		0			0
$691$	14157.5	−	24521.5i	0.779416	−	1.34999i	−0.152862	−	0.988248i	$-0.548849\pi$
$691$	14157.5	−	24521.5i	0.779416	−	1.34999i	0.932279	−	0.361741i	$-0.117818\pi$
$692$	−11284.0			−0.619875
$693$	1540.00	−	1333.68i	0.0844152	−	0.0731057i
$694$	14830.0			0.811151
$695$		0			0
$696$	4872.00	+	8438.55i	0.265334	+	0.459573i
$697$	−3675.00	−	6365.29i	−0.199714	−	0.345915i
$698$	−3878.00	+	6716.89i	−0.210293	+	0.364238i
$699$	32109.0			1.73744
$700$		0			0
$701$	10614.0			0.571876			0.285938	−	0.958248i	$-0.407695\pi$
$701$	10614.0			0.571876			0.285938	+	0.958248i	$0.407695\pi$
$702$	490.000	−	848.705i	0.0263445	−	0.0456301i
$703$	5365.50	+	9293.32i	0.287857	+	0.498583i
$704$	1120.00	+	1939.90i	0.0599596	+	0.103853i
$705$		0			0
$706$	2534.00			0.135083
$707$	24132.5	+	8359.74i	1.28373	+	0.444697i
$708$	−2940.00			−0.156062
$709$	−5149.50	+	8919.20i	−0.272769	+	0.472451i	−0.969570	−	0.244814i	$-0.921273\pi$
$709$	−5149.50	+	8919.20i	−0.272769	+	0.472451i	0.696801	+	0.717265i	$0.254606\pi$
$710$		0			0
$711$	1133.00	+	1962.41i	0.0597621	+	0.103511i
$712$	3948.00	−	6838.14i	0.207806	−	0.359930i
$713$	23373.0			1.22767
$714$	5145.00	+	1782.28i	0.269673	+	0.0934176i
$715$		0			0
$716$	−6506.00	+	11268.7i	−0.339582	+	0.588173i
$717$	5838.00	+	10111.7i	0.304078	+	0.526679i
$718$	4685.00	+	8114.66i	0.243513	+	0.421778i
$719$	−16264.5	+	28170.9i	−0.843621	+	1.46119i	0.0431924	+	0.999067i	$0.486247\pi$
$719$	−16264.5	+	28170.9i	−0.843621	+	1.46119i	−0.886813	+	0.462128i	$0.847086\pi$
$720$		0			0
$721$	−2376.50	−	12348.7i	−0.122754	−	0.637847i
$722$	8916.00			0.459583
$723$	−11931.5	+	20666.0i	−0.613744	+	1.06304i
$724$	3164.00	+	5480.21i	0.162416	+	0.281313i
$725$		0			0
$726$	9142.00	−	15834.4i	0.467344	−	0.809463i
$727$	−29456.0			−1.50270			−0.751350	−	0.659904i	$-0.770597\pi$
$727$	−29456.0			−1.50270			−0.751350	+	0.659904i	$0.770597\pi$
$728$	−4704.00	+	4073.78i	−0.239481	+	0.207396i
$729$	−11843.0			−0.601687
$730$		0			0
$731$	−1302.00	−	2255.13i	−0.0658772	−	0.114103i
$732$	5782.00	+	10014.7i	0.291952	+	0.505676i
$733$	13933.5	−	24133.5i	0.702109	−	1.21609i	−0.265616	−	0.964079i	$-0.585575\pi$
$733$	13933.5	−	24133.5i	0.702109	−	1.21609i	0.967725	−	0.252009i	$-0.0810912\pi$
$734$	−9282.00			−0.466764
$735$		0			0
$736$	−25440.0			−1.27409
$737$	−1037.50	+	1797.00i	−0.0518546	+	0.0898147i
$738$	7700.00	+	13336.8i	0.384066	+	0.665222i
$739$	−9769.50	−	16921.3i	−0.486302	−	0.842299i	0.513574	−	0.858045i	$-0.328321\pi$
$739$	−9769.50	−	16921.3i	−0.486302	−	0.842299i	−0.999876	+	0.0157460i	$0.994988\pi$
$740$		0			0
$741$	−4802.00			−0.238065
$742$	−8484.00	+	7347.36i	−0.419754	+	0.363518i
$743$	−1248.00			−0.0616214			−0.0308107	−	0.999525i	$-0.509809\pi$
$743$	−1248.00			−0.0616214			−0.0308107	+	0.999525i	$0.509809\pi$
$744$	12348.0	−	21387.4i	0.608467	−	1.05390i
$745$		0			0
$746$	8797.00	+	15236.9i	0.431744	+	0.747803i
$747$	12012.0	−	20805.4i	0.588348	−	1.01905i
$748$	420.000			0.0205304
$749$	1599.50	+	8311.25i	0.0780300	+	0.405456i
$750$		0			0
$751$	−14046.5	+	24329.3i	−0.682509	+	1.18214i	0.291704	+	0.956509i	$0.405778\pi$
$751$	−14046.5	+	24329.3i	−0.682509	+	1.18214i	−0.974213	+	0.225631i	$0.927556\pi$
$752$	−4200.00	−	7274.61i	−0.203668	−	0.352763i
$753$	−16660.0	−	28856.0i	−0.806274	−	1.39651i
$754$	812.000	−	1406.43i	0.0392192	−	0.0679297i
$755$		0			0
$756$	−2450.00	−	848.705i	−0.117865	−	0.0408295i
$757$	−35954.0			−1.72625			−0.863124	−	0.504991i	$-0.831496\pi$
$757$	−35954.0			−1.72625			−0.863124	+	0.504991i	$0.831496\pi$
$758$	13680.0	−	23694.5i	0.655514	−	1.13538i
$759$	−2782.50	−	4819.43i	−0.133068	−	0.230480i
$760$		0			0
$761$	430.500	−	745.648i	0.0205067	−	0.0355187i	−0.855590	−	0.517654i	$-0.826805\pi$
$761$	430.500	−	745.648i	0.0205067	−	0.0355187i	0.876097	+	0.482136i	$0.160139\pi$
$762$	−1008.00			−0.0479212
$763$	−19687.5	−	6819.95i	−0.934122	−	0.323589i
$764$	−10228.0			−0.484340
$765$		0			0
$766$	−9765.00	−	16913.5i	−0.460605	−	0.797792i
$767$	735.000	+	1273.06i	0.0346014	+	0.0599315i
$768$	−15232.0	+	26382.6i	−0.715674	+	1.23958i
$769$	24710.0			1.15873			0.579366	−	0.815067i	$-0.303300\pi$
$769$	24710.0			1.15873			0.579366	+	0.815067i	$0.303300\pi$
$770$		0			0
$771$	−5635.00			−0.263216
$772$	794.000	−	1375.25i	0.0370164	−	0.0641143i
$773$	8249.50	+	14288.6i	0.383847	+	0.664843i	0.991609	−	0.129277i	$-0.0412656\pi$
$773$	8249.50	+	14288.6i	0.383847	+	0.664843i	−0.607761	+	0.794120i	$0.707932\pi$
$774$	2728.00	+	4725.03i	0.126687	+	0.219429i
$775$		0			0
$776$	21168.0			0.979236
$777$	−21462.0	+	18586.6i	−0.990920	+	0.858162i
$778$	−3462.00			−0.159536
$779$	−8575.00	+	14852.3i	−0.394392	+	0.683107i
$780$		0			0
$781$	−1080.00	−	1870.61i	−0.0494820	−	0.0857053i
$782$	3339.00	−	5783.32i	0.152688	−	0.264464i
$783$	2030.00			0.0926517
$784$	−4312.00	−	3394.82i	−0.196429	−	0.154647i
$785$		0			0
$786$	−15043.0	+	26055.2i	−0.682654	+	1.18239i
$787$	8235.50	+	14264.3i	0.373016	+	0.646083i	0.990028	−	0.140871i	$-0.0449902\pi$
$787$	8235.50	+	14264.3i	0.373016	+	0.646083i	−0.617012	+	0.786954i	$0.711657\pi$
$788$	−5828.00	−	10094.4i	−0.263469	−	0.456342i
$789$	899.500	−	1557.98i	0.0405869	−	0.0702985i
$790$		0			0
$791$	−21532.0	+	18647.3i	−0.967876	+	0.838205i
$792$	−2640.00			−0.118445
$793$	2891.00	−	5007.36i	0.129461	−	0.224233i
$794$	−10983.0	−	19023.1i	−0.490897	−	0.850258i
$795$		0			0
$796$	6678.00	−	11566.6i	0.297356	−	0.515036i
$797$	36470.0			1.62087			0.810435	−	0.585828i	$-0.199231\pi$
$797$	36470.0			1.62087			0.810435	+	0.585828i	$0.199231\pi$
$798$	−2401.00	−	12476.0i	−0.106509	−	0.553439i
$799$	−11025.0			−0.488156
$800$		0			0
$801$	3619.00	+	6268.29i	0.159639	+	0.276503i
$802$	6603.00	+	11436.7i	0.290723	+	0.503547i
$803$	2782.50	−	4819.43i	0.122282	−	0.211798i
$804$	−11620.0			−0.509709
$805$		0			0
$806$	−4116.00			−0.179876
$807$	12568.5	−	21769.3i	0.548243	−	0.949585i
$808$	−16548.0	−	28662.0i	−0.720491	−	1.24793i
$809$	−17875.5	−	30961.3i	−0.776847	−	1.34554i	−0.933751	−	0.357924i	$-0.883485\pi$
$809$	−17875.5	−	30961.3i	−0.776847	−	1.34554i	0.156904	−	0.987614i	$-0.449849\pi$
$810$		0			0
$811$	−16492.0			−0.714072			−0.357036	−	0.934091i	$-0.616213\pi$
$811$	−16492.0			−0.714072			−0.357036	+	0.934091i	$0.616213\pi$
$812$	−4060.00	−	1406.43i	−0.175466	−	0.0607831i
$813$	−9751.00			−0.420643
$814$	1095.00	−	1896.60i	0.0471495	−	0.0816654i
$815$		0			0
$816$	−1176.00	−	2036.89i	−0.0504513	−	0.0873842i
$817$	−3038.00	+	5261.97i	−0.130093	+	0.225328i
$818$	−21910.0			−0.936510
$819$	−1078.00	−	5601.45i	−0.0459931	−	0.238987i
$820$		0			0
$821$	20736.5	−	35916.7i	0.881497	−	1.52680i	0.0318198	−	0.999494i	$-0.489870\pi$
$821$	20736.5	−	35916.7i	0.881497	−	1.52680i	0.849677	−	0.527304i	$-0.176797\pi$
$822$	−7875.00	−	13639.9i	−0.334151	−	0.578767i
$823$	−12532.5	−	21706.9i	−0.530809	−	0.919387i	−0.999354	−	0.0359479i	$-0.988555\pi$
$823$	−12532.5	−	21706.9i	−0.530809	−	0.919387i	0.468545	−	0.883440i	$-0.344778\pi$
$824$	−8148.00	+	14112.7i	−0.344477	+	0.596652i
$825$		0			0
$826$	−2940.00	+	2546.11i	−0.123845	+	0.107253i
$827$	−9732.00			−0.409208			−0.204604	−	0.978845i	$-0.565591\pi$
$827$	−9732.00			−0.409208			−0.204604	+	0.978845i	$0.565591\pi$
$828$	6996.00	−	12117.4i	0.293633	−	0.508587i
$829$	−13877.5	−	24036.5i	−0.581406	−	1.00702i	−0.995313	−	0.0967055i	$-0.969170\pi$
$829$	−13877.5	−	24036.5i	−0.581406	−	1.00702i	0.413907	−	0.910319i	$-0.364164\pi$
$830$		0			0
$831$	−1452.50	+	2515.80i	−0.0606338	+	0.105021i
$832$	6272.00			0.261349
$833$	−6688.50	+	2673.42i	−0.278203	+	0.111199i
$834$	3528.00			0.146480
$835$		0			0
$836$	−490.000	−	848.705i	−0.0202715	−	0.0351113i
$837$	−2572.50	−	4455.70i	−0.106235	−	0.184004i
$838$	6636.00	−	11493.9i	0.273552	−	0.473806i
$839$	21112.0			0.868733			0.434367	−	0.900736i	$-0.356972\pi$
$839$	21112.0			0.868733			0.434367	+	0.900736i	$0.356972\pi$
$840$		0			0
$841$	−21025.0			−0.862069
$842$	−16630.0	+	28804.0i	−0.680650	+	1.17892i
$843$	−17339.0	−	30032.0i	−0.708407	−	1.22700i
$844$	3560.00	+	6166.10i	0.145190	+	0.251476i
$845$		0			0
$846$	23100.0			0.938764
$847$	4571.00	+	23751.6i	0.185433	+	0.963536i
$848$	4848.00			0.196322
$849$	14969.5	−	25927.9i	0.605126	−	1.04811i
$850$		0			0
$851$	17410.5	+	30155.9i	0.701321	+	1.21472i
$852$	6048.00	−	10475.4i	0.243194	−	0.421224i
$853$	21238.0			0.852492			0.426246	−	0.904607i	$-0.359836\pi$
$853$	21238.0			0.852492			0.426246	+	0.904607i	$0.359836\pi$
$854$	14455.0	+	5007.36i	0.579204	+	0.200642i
$855$		0			0
$856$	5484.00	−	9498.57i	0.218971	−	0.379269i
$857$	−17804.5	−	30838.3i	−0.709673	−	1.22919i	−0.964978	−	0.262330i	$-0.915509\pi$
$857$	−17804.5	−	30838.3i	−0.709673	−	1.22919i	0.255305	−	0.966861i	$-0.417824\pi$
$858$	490.000	+	848.705i	0.0194969	+	0.0337696i
$859$	−1088.50	+	1885.34i	−0.0432353	+	0.0748858i	−0.886833	−	0.462090i	$-0.847100\pi$
$859$	−1088.50	+	1885.34i	−0.0432353	+	0.0748858i	0.843598	+	0.536975i	$0.180433\pi$
$860$		0			0
$861$	−42875.0	−	14852.3i	−1.69707	−	0.587882i
$862$	−9846.00			−0.389044
$863$	−16123.5	+	27926.7i	−0.635980	+	1.10155i	0.350327	+	0.936627i	$0.386070\pi$
$863$	−16123.5	+	27926.7i	−0.635980	+	1.10155i	−0.986307	+	0.164921i	$0.947263\pi$
$864$	2800.00	+	4849.74i	0.110252	+	0.190962i
$865$		0			0
$866$	−8974.00	+	15543.4i	−0.352135	+	0.609916i
$867$	31304.0			1.22623
$868$	2058.00	+	10693.7i	0.0804759	+	0.418165i
$869$	515.000			0.0201038
$870$		0			0
$871$	2905.00	+	5031.61i	0.113011	+	0.195740i
$872$	13500.0	+	23382.7i	0.524275	+	0.908071i
$873$	−9702.00	+	16804.4i	−0.376132	+	0.651479i
$874$	−15582.0			−0.603054
$875$		0			0
$876$	31164.0			1.20198
$877$	13815.5	−	23929.1i	0.531946	−	0.921357i	−0.467359	−	0.884068i	$-0.654794\pi$
$877$	13815.5	−	23929.1i	0.531946	−	0.921357i	0.999305	−	0.0372891i	$-0.0118723\pi$
$878$	−4179.00	−	7238.24i	−0.160631	−	0.278222i
$879$	−27097.0	−	46933.4i	−1.03977	−	1.80094i
$880$		0			0
$881$	24402.0			0.933172			0.466586	−	0.884476i	$-0.345484\pi$
$881$	24402.0			0.933172			0.466586	+	0.884476i	$0.345484\pi$
$882$	14014.0	−	5601.45i	0.535007	−	0.213844i
$883$	19612.0			0.747448			0.373724	−	0.927540i	$-0.378081\pi$
$883$	19612.0			0.747448			0.373724	+	0.927540i	$0.378081\pi$
$884$	588.000	−	1018.45i	0.0223717	−	0.0387489i
$885$		0			0
$886$	12927.0	+	22390.2i	0.490170	+	0.849000i
$887$	1130.50	−	1958.08i	0.0427942	−	0.0741218i	−0.843835	−	0.536603i	$-0.819707\pi$
$887$	1130.50	−	1958.08i	0.0427942	−	0.0741218i	0.886629	+	0.462481i	$0.153041\pi$
$888$	36792.0			1.39038
$889$	1008.00	−	872.954i	0.0380284	−	0.0329335i
$890$		0			0
$891$	−2097.50	+	3632.98i	−0.0788652	+	0.136599i
$892$	2800.00	+	4849.74i	0.105102	+	0.182042i
$893$	12862.5	+	22278.5i	0.482001	+	0.834851i
$894$	1407.00	−	2437.00i	0.0526366	−	0.0911693i
$895$		0			0
$896$	−1344.00	−	6983.63i	−0.0501115	−	0.260387i
$897$	−15582.0			−0.580009
$898$	−2826.00	+	4894.78i	−0.105017	+	0.181894i
$899$	−4263.00	−	7383.73i	−0.158152	−	0.273928i
$900$		0			0
$901$	3181.50	−	5510.52i	0.117637	−	0.203754i
$902$	3500.00			0.129199
$903$	−15190.0	−	5261.97i	−0.559791	−	0.193917i
$904$	36912.0			1.35805
$905$		0			0
$906$	−11333.0	−	19629.3i	−0.415578	−	0.719802i
$907$	−11916.5	−	20640.0i	−0.436252	−	0.755611i	0.561145	−	0.827718i	$-0.310361\pi$
$907$	−11916.5	−	20640.0i	−0.436252	−	0.755611i	−0.997397	+	0.0721066i	$0.977028\pi$
$908$	4410.00	−	7638.34i	0.161180	−	0.279171i
$909$	30338.0			1.10698
$910$		0			0
$911$	31824.0			1.15738			0.578692	−	0.815546i	$-0.303563\pi$
$911$	31824.0			1.15738			0.578692	+	0.815546i	$0.303563\pi$
$912$	−2744.00	+	4752.75i	−0.0996304	+	0.172565i
$913$	−2730.00	−	4728.50i	−0.0989593	−	0.171402i
$914$	−8479.00	−	14686.1i	−0.306849	−	0.531479i
$915$		0			0
$916$	−1148.00			−0.0414094
$917$	−7521.50	−	39082.9i	−0.270863	−	1.40745i
$918$	−1470.00			−0.0528510
$919$	8409.50	−	14565.7i	0.301854	−	0.522826i	−0.674702	−	0.738090i	$-0.735728\pi$
$919$	8409.50	−	14565.7i	0.301854	−	0.522826i	0.976556	+	0.215264i	$0.0690612\pi$
$920$		0			0
$921$	25774.0	+	44641.9i	0.922130	+	1.59718i
$922$	9338.00	−	16173.9i	0.333547	−	0.577721i
$923$	−6048.00			−0.215680
$924$	1960.00	−	1697.41i	0.0697828	−	0.0604336i
$925$		0			0
$926$	4016.00	−	6955.92i	0.142520	−	0.246853i
$927$	−7469.00	−	12936.7i	−0.264632	−	0.458357i
$928$	4640.00	+	8036.72i	0.164133	+	0.284287i
$929$	−899.500	+	1557.98i	−0.0317671	+	0.0550222i	−0.881472	−	0.472237i	$-0.843447\pi$
$929$	−899.500	+	1557.98i	−0.0317671	+	0.0550222i	0.849705	+	0.527259i	$0.176780\pi$
$930$		0			0
$931$	13205.5	+	10396.6i	0.464869	+	0.365989i
$932$	18348.0			0.644859
$933$	34912.5	−	60470.2i	1.22506	−	2.12187i
$934$	5859.00	+	10148.1i	0.205259	+	0.355520i
$935$		0			0
$936$	−3696.00	+	6401.66i	−0.129068	+	0.223552i
$937$	−14154.0			−0.493480			−0.246740	−	0.969082i	$-0.579359\pi$
$937$	−14154.0			−0.493480			−0.246740	+	0.969082i	$0.579359\pi$
$938$	−11620.0	+	10063.2i	−0.404484	+	0.350294i
$939$	−33271.0			−1.15629
$940$		0			0
$941$	−6023.50	−	10433.0i	−0.208672	−	0.361431i	0.742624	−	0.669708i	$-0.233581\pi$
$941$	−6023.50	−	10433.0i	−0.208672	−	0.361431i	−0.951296	+	0.308277i	$0.900247\pi$
$942$	4753.00	+	8232.44i	0.164396	+	0.284742i
$943$	−27825.0	+	48194.3i	−0.960877	+	1.66429i
$944$	1680.00			0.0579230
$945$		0			0
$946$	1240.00			0.0426172
$947$	−12189.5	+	21112.8i	−0.418274	+	0.724472i	−0.995766	−	0.0919245i	$-0.970698\pi$
$947$	−12189.5	+	21112.8i	−0.418274	+	0.724472i	0.577492	+	0.816396i	$0.304031\pi$
$948$	1442.00	+	2497.62i	0.0494029	+	0.0855684i
$949$	−7791.00	−	13494.4i	−0.266498	−	0.461588i
$950$		0			0
$951$	−24339.0			−0.829912
$952$	8820.00	+	3055.34i	0.300271	+	0.104017i
$953$	52330.0			1.77874			0.889368	−	0.457192i	$-0.151145\pi$
$953$	52330.0			1.77874			0.889368	+	0.457192i	$0.151145\pi$
$954$	−6666.00	+	11545.9i	−0.226226	+	0.391835i
$955$		0			0
$956$	3336.00	+	5778.12i	0.112860	+	0.195479i
$957$	−1015.00	+	1758.03i	−0.0342845	+	0.0593825i
$958$	−13006.0			−0.438627
$959$	19687.5	+	6819.95i	0.662922	+	0.229643i
$960$		0			0
$961$	4091.00	−	7085.82i	0.137323	−	0.237851i
$962$	−3066.00	−	5310.47i	−0.102757	−	0.177980i
$963$	5027.00	+	8707.02i	0.168217	+	0.291360i
$964$	−6818.00	+	11809.1i	−0.227794	+	0.394550i
$965$		0			0
$966$	−7791.00	−	40483.2i	−0.259494	−	1.34837i
$967$	12416.0			0.412897			0.206449	−	0.978457i	$-0.433809\pi$
$967$	12416.0			0.412897			0.206449	+	0.978457i	$0.433809\pi$
$968$	15672.0	−	27144.7i	0.520369	−	0.901305i
$969$	3601.50	+	6237.98i	0.119398	+	0.206804i
$970$		0			0
$971$	−18406.5	+	31881.0i	−0.608334	+	1.05367i	0.383181	+	0.923673i	$0.374829\pi$
$971$	−18406.5	+	31881.0i	−0.608334	+	1.05367i	−0.991515	+	0.129993i	$0.958505\pi$
$972$	−19712.0			−0.650476
$973$	−3528.00	+	3055.34i	−0.116241	+	0.100668i
$974$	−32098.0			−1.05594
$975$		0			0
$976$	−3304.00	−	5722.70i	−0.108359	−	0.187683i
$977$	17497.5	+	30306.6i	0.572973	+	0.992418i	0.996259	+	0.0864221i	$0.0275434\pi$
$977$	17497.5	+	30306.6i	0.572973	+	0.992418i	−0.423286	+	0.905996i	$0.639123\pi$
$978$	−3269.00	+	5662.07i	−0.106883	+	0.185126i
$979$	1645.00			0.0537022
$980$		0			0
$981$	−24750.0			−0.805511
$982$	8864.00	−	15352.9i	0.288046	−	0.498911i
$983$	−7150.50	−	12385.0i	−0.232010	−	0.401853i	0.726390	−	0.687283i	$-0.241197\pi$
$983$	−7150.50	−	12385.0i	−0.232010	−	0.401853i	−0.958399	+	0.285430i	$0.907863\pi$
$984$	29400.0	+	50922.3i	0.952477	+	1.64974i
$985$		0			0
$986$	−2436.00			−0.0786796
$987$	−51450.0	+	44557.0i	−1.65924	+	1.43695i
$988$	−2744.00			−0.0883586
$989$	−9858.00	+	17074.6i	−0.316953	+	0.548978i
$990$		0			0
$991$	1332.50	+	2307.96i	0.0427127	+	0.0739805i	0.886591	−	0.462553i	$-0.153067\pi$
$991$	1332.50	+	2307.96i	0.0427127	+	0.0739805i	−0.843879	+	0.536534i	$0.819733\pi$
$992$	11760.0	−	20368.9i	0.376392	−	0.651929i
$993$	−23387.0			−0.747396
$994$	−3024.00	−	15713.2i	−0.0964944	−	0.501400i
$995$		0			0
$996$	15288.0	−	26479.6i	0.486364	−	0.842408i
$997$	12435.5	+	21538.9i	0.395021	+	0.684197i	0.993104	−	0.117237i	$-0.0374039\pi$
$997$	12435.5	+	21538.9i	0.395021	+	0.684197i	−0.598083	+	0.801434i	$0.704071\pi$
$998$	−10211.0	−	17686.0i	−0.323871	−	0.560962i
$999$	3832.50	−	6638.08i	0.121376	−	0.210230i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	175.4.e.a.51.1		2
5.2	odd	4		175.4.k.a.149.2		4
5.3	odd	4		175.4.k.a.149.1		4
5.4	even	2		7.4.c.a.2.1	✓	2
7.2	even	3		1225.4.a.c.1.1		1
7.4	even	3	inner	175.4.e.a.151.1		2
7.5	odd	6		1225.4.a.d.1.1		1
15.14	odd	2		63.4.e.b.37.1		2
20.19	odd	2		112.4.i.c.65.1		2
35.4	even	6		7.4.c.a.4.1	yes	2
35.9	even	6		49.4.a.d.1.1		1
35.18	odd	12		175.4.k.a.74.2		4
35.19	odd	6		49.4.a.c.1.1		1
35.24	odd	6		49.4.c.a.18.1		2
35.32	odd	12		175.4.k.a.74.1		4
35.34	odd	2		49.4.c.a.30.1		2
40.19	odd	2		448.4.i.a.65.1		2
40.29	even	2		448.4.i.f.65.1		2
105.44	odd	6		441.4.a.d.1.1		1
105.59	even	6		441.4.e.k.361.1		2
105.74	odd	6		63.4.e.b.46.1		2
105.89	even	6		441.4.a.e.1.1		1
105.104	even	2		441.4.e.k.226.1		2
140.19	even	6		784.4.a.r.1.1		1
140.39	odd	6		112.4.i.c.81.1		2
140.79	odd	6		784.4.a.b.1.1		1
280.109	even	6		448.4.i.f.193.1		2
280.179	odd	6		448.4.i.a.193.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
7.4.c.a.2.1	✓	2	5.4	even	2
7.4.c.a.4.1	yes	2	35.4	even	6
49.4.a.c.1.1		1	35.19	odd	6
49.4.a.d.1.1		1	35.9	even	6
49.4.c.a.18.1		2	35.24	odd	6
49.4.c.a.30.1		2	35.34	odd	2
63.4.e.b.37.1		2	15.14	odd	2
63.4.e.b.46.1		2	105.74	odd	6
112.4.i.c.65.1		2	20.19	odd	2
112.4.i.c.81.1		2	140.39	odd	6
175.4.e.a.51.1		2	1.1	even	1	trivial
175.4.e.a.151.1		2	7.4	even	3	inner
175.4.k.a.74.1		4	35.32	odd	12
175.4.k.a.74.2		4	35.18	odd	12
175.4.k.a.149.1		4	5.3	odd	4
175.4.k.a.149.2		4	5.2	odd	4
441.4.a.d.1.1		1	105.44	odd	6
441.4.a.e.1.1		1	105.89	even	6
441.4.e.k.226.1		2	105.104	even	2
441.4.e.k.361.1		2	105.59	even	6
448.4.i.a.65.1		2	40.19	odd	2
448.4.i.a.193.1		2	280.179	odd	6
448.4.i.f.65.1		2	40.29	even	2
448.4.i.f.193.1		2	280.109	even	6
784.4.a.b.1.1		1	140.79	odd	6
784.4.a.r.1.1		1	140.19	even	6
1225.4.a.c.1.1		1	7.2	even	3
1225.4.a.d.1.1		1	7.5	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 175 = 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	175.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.00000 - 1.73205i) q^{2} +(3.50000 + 6.06218i) q^{3} +(2.00000 + 3.46410i) q^{4} +14.0000 q^{6} +(-14.0000 + 12.1244i) q^{7} +24.0000 q^{8} +(-11.0000 + 19.0526i) q^{9} +O(q^{10})\)	\(q+(1.00000 - 1.73205i) q^{2} +(3.50000 + 6.06218i) q^{3} +(2.00000 + 3.46410i) q^{4} +14.0000 q^{6} +(-14.0000 + 12.1244i) q^{7} +24.0000 q^{8} +(-11.0000 + 19.0526i) q^{9} +(2.50000 + 4.33013i) q^{11} +(-14.0000 + 24.2487i) q^{12} +14.0000 q^{13} +(7.00000 + 36.3731i) q^{14} +(8.00000 - 13.8564i) q^{16} +(-10.5000 - 18.1865i) q^{17} +(22.0000 + 38.1051i) q^{18} +(-24.5000 + 42.4352i) q^{19} +(-122.500 - 42.4352i) q^{21} +10.0000 q^{22} +(-79.5000 + 137.698i) q^{23} +(84.0000 + 145.492i) q^{24} +(14.0000 - 24.2487i) q^{26} +35.0000 q^{27} +(-70.0000 - 24.2487i) q^{28} +58.0000 q^{29} +(-73.5000 - 127.306i) q^{31} +(80.0000 + 138.564i) q^{32} +(-17.5000 + 30.3109i) q^{33} -42.0000 q^{34} -88.0000 q^{36} +(109.500 - 189.660i) q^{37} +(49.0000 + 84.8705i) q^{38} +(49.0000 + 84.8705i) q^{39} +350.000 q^{41} +(-196.000 + 169.741i) q^{42} +124.000 q^{43} +(-10.0000 + 17.3205i) q^{44} +(159.000 + 275.396i) q^{46} +(262.500 - 454.663i) q^{47} +112.000 q^{48} +(49.0000 - 339.482i) q^{49} +(73.5000 - 127.306i) q^{51} +(28.0000 + 48.4974i) q^{52} +(151.500 + 262.406i) q^{53} +(35.0000 - 60.6218i) q^{54} +(-336.000 + 290.985i) q^{56} -343.000 q^{57} +(58.0000 - 100.459i) q^{58} +(52.5000 + 90.9327i) q^{59} +(206.500 - 357.668i) q^{61} -294.000 q^{62} +(-77.0000 - 400.104i) q^{63} +448.000 q^{64} +(35.0000 + 60.6218i) q^{66} +(207.500 + 359.401i) q^{67} +(42.0000 - 72.7461i) q^{68} -1113.00 q^{69} -432.000 q^{71} +(-264.000 + 457.261i) q^{72} +(-556.500 - 963.886i) q^{73} +(-219.000 - 379.319i) q^{74} -196.000 q^{76} +(-87.5000 - 30.3109i) q^{77} +196.000 q^{78} +(51.5000 - 89.2006i) q^{79} +(419.500 + 726.595i) q^{81} +(350.000 - 606.218i) q^{82} -1092.00 q^{83} +(-98.0000 - 509.223i) q^{84} +(124.000 - 214.774i) q^{86} +(203.000 + 351.606i) q^{87} +(60.0000 + 103.923i) q^{88} +(164.500 - 284.922i) q^{89} +(-196.000 + 169.741i) q^{91} -636.000 q^{92} +(514.500 - 891.140i) q^{93} +(-525.000 - 909.327i) q^{94} +(-560.000 + 969.948i) q^{96} +882.000 q^{97} +(-539.000 - 424.352i) q^{98} -110.000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{2} + 7 q^{3} + 4 q^{4} + 28 q^{6} - 28 q^{7} + 48 q^{8} - 22 q^{9}+O(q^{10}) \) 2 * q + 2 * q^2 + 7 * q^3 + 4 * q^4 + 28 * q^6 - 28 * q^7 + 48 * q^8 - 22 * q^9	\( 2 q + 2 q^{2} + 7 q^{3} + 4 q^{4} + 28 q^{6} - 28 q^{7} + 48 q^{8} - 22 q^{9} + 5 q^{11} - 28 q^{12} + 28 q^{13} + 14 q^{14} + 16 q^{16} - 21 q^{17} + 44 q^{18} - 49 q^{19} - 245 q^{21} + 20 q^{22} - 159 q^{23} + 168 q^{24} + 28 q^{26} + 70 q^{27} - 140 q^{28} + 116 q^{29} - 147 q^{31} + 160 q^{32} - 35 q^{33} - 84 q^{34} - 176 q^{36} + 219 q^{37} + 98 q^{38} + 98 q^{39} + 700 q^{41} - 392 q^{42} + 248 q^{43} - 20 q^{44} + 318 q^{46} + 525 q^{47} + 224 q^{48} + 98 q^{49} + 147 q^{51} + 56 q^{52} + 303 q^{53} + 70 q^{54} - 672 q^{56} - 686 q^{57} + 116 q^{58} + 105 q^{59} + 413 q^{61} - 588 q^{62} - 154 q^{63} + 896 q^{64} + 70 q^{66} + 415 q^{67} + 84 q^{68} - 2226 q^{69} - 864 q^{71} - 528 q^{72} - 1113 q^{73} - 438 q^{74} - 392 q^{76} - 175 q^{77} + 392 q^{78} + 103 q^{79} + 839 q^{81} + 700 q^{82} - 2184 q^{83} - 196 q^{84} + 248 q^{86} + 406 q^{87} + 120 q^{88} + 329 q^{89} - 392 q^{91} - 1272 q^{92} + 1029 q^{93} - 1050 q^{94} - 1120 q^{96} + 1764 q^{97} - 1078 q^{98} - 220 q^{99}+O(q^{100}) \) 2 * q + 2 * q^2 + 7 * q^3 + 4 * q^4 + 28 * q^6 - 28 * q^7 + 48 * q^8 - 22 * q^9 + 5 * q^11 - 28 * q^12 + 28 * q^13 + 14 * q^14 + 16 * q^16 - 21 * q^17 + 44 * q^18 - 49 * q^19 - 245 * q^21 + 20 * q^22 - 159 * q^23 + 168 * q^24 + 28 * q^26 + 70 * q^27 - 140 * q^28 + 116 * q^29 - 147 * q^31 + 160 * q^32 - 35 * q^33 - 84 * q^34 - 176 * q^36 + 219 * q^37 + 98 * q^38 + 98 * q^39 + 700 * q^41 - 392 * q^42 + 248 * q^43 - 20 * q^44 + 318 * q^46 + 525 * q^47 + 224 * q^48 + 98 * q^49 + 147 * q^51 + 56 * q^52 + 303 * q^53 + 70 * q^54 - 672 * q^56 - 686 * q^57 + 116 * q^58 + 105 * q^59 + 413 * q^61 - 588 * q^62 - 154 * q^63 + 896 * q^64 + 70 * q^66 + 415 * q^67 + 84 * q^68 - 2226 * q^69 - 864 * q^71 - 528 * q^72 - 1113 * q^73 - 438 * q^74 - 392 * q^76 - 175 * q^77 + 392 * q^78 + 103 * q^79 + 839 * q^81 + 700 * q^82 - 2184 * q^83 - 196 * q^84 + 248 * q^86 + 406 * q^87 + 120 * q^88 + 329 * q^89 - 392 * q^91 - 1272 * q^92 + 1029 * q^93 - 1050 * q^94 - 1120 * q^96 + 1764 * q^97 - 1078 * q^98 - 220 * q^99

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