LMFDB - Embedded newform 175.4.x.a.103.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [175,4,Mod(3,175)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(175, base_ring=CyclotomicField(60))

chi = DirichletCharacter(H, H._module([21, 10]))

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

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

chi := DirichletCharacter("175.3");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 175 = 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	175.x (of order $60$, degree $16$, 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:	$928$
Relative dimension:	$58$ over $\Q(\zeta_{60})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{60}]$

Embedding invariants

Embedding label			103.8
Character	$\chi$	$=$	175.103
Dual form			175.4.x.a.17.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-4.55296 - 0.238611i) q^{2} +(1.16184 + 1.43476i) q^{3} +(12.7163 + 1.33654i) q^{4} +(0.739681 + 11.1558i) q^{5} +(-4.94748 - 6.80963i) q^{6} +(4.38567 - 17.9935i) q^{7} +(-21.5535 - 3.41373i) q^{8} +(4.90497 - 23.0761i) q^{9} +O(q^{10})$	\(q+(-4.55296 - 0.238611i) q^{2} +(1.16184 + 1.43476i) q^{3} +(12.7163 + 1.33654i) q^{4} +(0.739681 + 11.1558i) q^{5} +(-4.94748 - 6.80963i) q^{6} +(4.38567 - 17.9935i) q^{7} +(-21.5535 - 3.41373i) q^{8} +(4.90497 - 23.0761i) q^{9} +(-0.705835 - 50.9686i) q^{10} +(-29.1757 + 6.20148i) q^{11} +(12.8568 + 19.7977i) q^{12} +(33.5772 + 17.1084i) q^{13} +(-24.2612 + 80.8772i) q^{14} +(-15.1465 + 14.0226i) q^{15} +(-2.73824 - 0.582032i) q^{16} +(-1.86788 - 4.86599i) q^{17} +(-27.8383 + 103.894i) q^{18} +(-10.3818 - 98.7763i) q^{19} +(-5.50421 + 142.850i) q^{20} +(30.9118 - 14.6133i) q^{21} +(134.316 - 21.2735i) q^{22} +(-6.71157 + 128.064i) q^{23} +(-20.1439 - 34.8902i) q^{24} +(-123.906 + 16.5035i) q^{25} +(-148.793 - 85.9059i) q^{26} +(83.2215 - 42.4035i) q^{27} +(79.8187 - 222.950i) q^{28} +(148.907 - 204.953i) q^{29} +(72.3076 - 60.2303i) q^{30} +(48.2050 - 108.270i) q^{31} +(180.957 + 48.4872i) q^{32} +(-42.7952 - 34.6549i) q^{33} +(7.34330 + 22.6004i) q^{34} +(203.977 + 35.6164i) q^{35} +(93.2153 - 286.887i) q^{36} +(241.596 - 156.894i) q^{37} +(23.6989 + 452.202i) q^{38} +(14.4650 + 68.0525i) q^{39} +(22.1404 - 242.972i) q^{40} +(373.584 - 121.385i) q^{41} +(-144.227 + 59.1578i) q^{42} +(257.326 + 257.326i) q^{43} +(-379.297 + 39.8657i) q^{44} +(261.061 + 37.6501i) q^{45} +(61.1150 - 581.471i) q^{46} +(-294.443 - 113.026i) q^{47} +(-2.34634 - 4.60495i) q^{48} +(-304.532 - 157.827i) q^{49} +(568.076 - 45.5747i) q^{50} +(4.81134 - 8.33348i) q^{51} +(404.113 + 262.434i) q^{52} +(293.082 - 237.333i) q^{53} +(-389.022 + 173.204i) q^{54} +(-90.7635 - 320.892i) q^{55} +(-155.951 + 372.851i) q^{56} +(129.658 - 129.658i) q^{57} +(-726.870 + 897.610i) q^{58} +(-191.477 + 212.657i) q^{59} +(-211.350 + 158.072i) q^{60} +(-36.1653 + 32.5634i) q^{61} +(-245.310 + 481.448i) q^{62} +(-393.707 - 189.461i) q^{63} +(-791.020 - 257.018i) q^{64} +(-166.023 + 387.237i) q^{65} +(186.576 + 167.994i) q^{66} +(571.777 - 219.485i) q^{67} +(-17.2490 - 64.3741i) q^{68} +(-191.539 + 139.161i) q^{69} +(-920.199 - 210.831i) q^{70} +(775.979 + 563.782i) q^{71} +(-184.495 + 480.625i) q^{72} +(86.5291 - 133.243i) q^{73} +(-1137.41 + 656.686i) q^{74} +(-167.638 - 158.600i) q^{75} -1269.95i q^{76} +(-16.3685 + 552.170i) q^{77} +(-49.6205 - 313.292i) q^{78} +(148.229 + 332.928i) q^{79} +(4.46763 - 30.9779i) q^{80} +(-424.375 - 188.944i) q^{81} +(-1729.88 + 463.519i) q^{82} +(-104.113 + 657.345i) q^{83} +(412.616 - 144.512i) q^{84} +(52.9026 - 24.4370i) q^{85} +(-1110.19 - 1233.00i) q^{86} +(467.064 - 24.4778i) q^{87} +(650.008 - 34.0655i) q^{88} +(-276.345 - 306.913i) q^{89} +(-1179.62 - 233.711i) q^{90} +(455.099 - 529.139i) q^{91} +(-256.510 + 1619.54i) q^{92} +(211.348 - 56.6306i) q^{93} +(1313.62 + 584.860i) q^{94} +(1094.25 - 188.881i) q^{95} +(140.676 + 315.964i) q^{96} +(43.0516 + 271.817i) q^{97} +(1348.86 + 791.245i) q^{98} +703.678i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 928 q - 8 q^{2} - 24 q^{3} - 10 q^{4} - 24 q^{7} + 84 q^{8} - 10 q^{9}+O(q^{10}) $ 928 * q - 8 * q^2 - 24 * q^3 - 10 * q^4 - 24 * q^7 + 84 * q^8 - 10 * q^9	\( 928 q - 8 q^{2} - 24 q^{3} - 10 q^{4} - 24 q^{7} + 84 q^{8} - 10 q^{9} - 96 q^{10} - 6 q^{11} - 72 q^{12} - 20 q^{14} - 368 q^{15} - 1670 q^{16} + 120 q^{17} - 14 q^{18} - 30 q^{19} - 12 q^{21} - 880 q^{22} + 296 q^{23} + 32 q^{25} - 48 q^{26} + 226 q^{28} - 200 q^{29} - 38 q^{30} - 18 q^{31} - 964 q^{32} - 1092 q^{33} + 288 q^{35} + 7400 q^{36} - 392 q^{37} + 5424 q^{38} + 2430 q^{39} + 2172 q^{40} - 2098 q^{42} + 1560 q^{43} - 10 q^{44} - 4224 q^{45} - 6 q^{46} + 96 q^{47} + 6232 q^{50} - 16 q^{51} - 8928 q^{52} - 2384 q^{53} - 30 q^{54} + 244 q^{56} + 1556 q^{57} + 640 q^{58} + 4890 q^{59} + 3676 q^{60} - 18 q^{61} + 224 q^{63} - 9700 q^{64} - 1116 q^{65} - 2610 q^{66} - 2404 q^{67} - 13614 q^{68} - 1700 q^{70} - 24 q^{71} - 518 q^{72} - 4200 q^{73} - 16104 q^{75} - 722 q^{77} - 356 q^{78} - 10 q^{79} + 6414 q^{80} - 6810 q^{81} + 1692 q^{82} + 20620 q^{84} + 2712 q^{85} - 6 q^{86} + 9102 q^{87} + 1650 q^{88} + 20370 q^{89} - 12 q^{91} + 1612 q^{92} - 4604 q^{93} - 30 q^{94} + 1652 q^{95} - 2610 q^{96} - 19478 q^{98}+O(q^{100}) \) 928 * q - 8 * q^2 - 24 * q^3 - 10 * q^4 - 24 * q^7 + 84 * q^8 - 10 * q^9 - 96 * q^10 - 6 * q^11 - 72 * q^12 - 20 * q^14 - 368 * q^15 - 1670 * q^16 + 120 * q^17 - 14 * q^18 - 30 * q^19 - 12 * q^21 - 880 * q^22 + 296 * q^23 + 32 * q^25 - 48 * q^26 + 226 * q^28 - 200 * q^29 - 38 * q^30 - 18 * q^31 - 964 * q^32 - 1092 * q^33 + 288 * q^35 + 7400 * q^36 - 392 * q^37 + 5424 * q^38 + 2430 * q^39 + 2172 * q^40 - 2098 * q^42 + 1560 * q^43 - 10 * q^44 - 4224 * q^45 - 6 * q^46 + 96 * q^47 + 6232 * q^50 - 16 * q^51 - 8928 * q^52 - 2384 * q^53 - 30 * q^54 + 244 * q^56 + 1556 * q^57 + 640 * q^58 + 4890 * q^59 + 3676 * q^60 - 18 * q^61 + 224 * q^63 - 9700 * q^64 - 1116 * q^65 - 2610 * q^66 - 2404 * q^67 - 13614 * q^68 - 1700 * q^70 - 24 * q^71 - 518 * q^72 - 4200 * q^73 - 16104 * q^75 - 722 * q^77 - 356 * q^78 - 10 * q^79 + 6414 * q^80 - 6810 * q^81 + 1692 * q^82 + 20620 * q^84 + 2712 * q^85 - 6 * q^86 + 9102 * q^87 + 1650 * q^88 + 20370 * q^89 - 12 * q^91 + 1612 * q^92 - 4604 * q^93 - 30 * q^94 + 1652 * q^95 - 2610 * q^96 - 19478 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{7}{20}\right)$

Coefficient data

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

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

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

$2$	−4.55296	−	0.238611i	−1.60971	−	0.0843616i	−0.773876	−	0.633337i	$-0.781685\pi$
$2$	−4.55296	−	0.238611i	−1.60971	−	0.0843616i	−0.835839	+	0.548975i	$0.815018\pi$
$3$	1.16184	+	1.43476i	0.223597	+	0.276119i	0.876583	−	0.481251i	$-0.159817\pi$
$3$	1.16184	+	1.43476i	0.223597	+	0.276119i	−0.652986	+	0.757370i	$0.726484\pi$
$4$	12.7163	+	1.33654i	1.58954	+	0.167068i
$5$	0.739681	+	11.1558i	0.0661591	+	0.997809i
$5$	0.739681	+	11.1558i	0.0661591	+	0.997809i
$6$	−4.94748	−	6.80963i	−0.336634	−	0.463336i
$7$	4.38567	−	17.9935i	0.236804	−	0.971557i
$7$	4.38567	−	17.9935i	0.236804	−	0.971557i
$8$	−21.5535	−	3.41373i	−0.952538	−	0.150867i
$9$	4.90497	−	23.0761i	0.181665	−	0.854669i
$10$	−0.705835	−	50.9686i	−0.0223205	−	1.61177i
$11$	−29.1757	+	6.20148i	−0.799709	+	0.169983i	−0.589601	−	0.807695i	$-0.700715\pi$
$11$	−29.1757	+	6.20148i	−0.799709	+	0.169983i	−0.210108	+	0.977678i	$0.567382\pi$
$12$	12.8568	+	19.7977i	0.309286	+	0.476259i
$13$	33.5772	+	17.1084i	0.716357	+	0.365002i	0.773871	−	0.633343i	$-0.218318\pi$
$13$	33.5772	+	17.1084i	0.716357	+	0.365002i	−0.0575149	+	0.998345i	$0.518318\pi$
$14$	−24.2612	+	80.8772i	−0.463149	+	1.54395i
$15$	−15.1465	+	14.0226i	−0.260721	+	0.241375i
$16$	−2.73824	−	0.582032i	−0.0427851	−	0.00909425i
$17$	−1.86788	−	4.86599i	−0.0266487	−	0.0694221i	0.919611	−	0.392831i	$-0.128504\pi$
$17$	−1.86788	−	4.86599i	−0.0266487	−	0.0694221i	−0.946259	+	0.323409i	$0.895171\pi$
$18$	−27.8383	+	103.894i	−0.364531	+	1.36045i
$19$	−10.3818	−	98.7763i	−0.125355	−	1.19268i	−0.858577	−	0.512685i	$-0.828651\pi$
$19$	−10.3818	−	98.7763i	−0.125355	−	1.19268i	0.733221	−	0.679990i	$-0.238016\pi$
$20$	−5.50421	+	142.850i	−0.0615390	+	1.59711i
$21$	30.9118	−	14.6133i	0.321214	−	0.151851i
$22$	134.316	−	21.2735i	1.30164	−	0.206160i
$23$	−6.71157	+	128.064i	−0.0608460	+	1.16101i	0.782149	+	0.623091i	$0.214123\pi$
$23$	−6.71157	+	128.064i	−0.0608460	+	1.16101i	−0.842995	+	0.537921i	$0.819210\pi$
$24$	−20.1439	−	34.8902i	−0.171327	−	0.296748i
$25$	−123.906	+	16.5035i	−0.991246	+	0.132028i
$26$	−148.793	−	85.9059i	−1.12234	−	0.647982i
$27$	83.2215	−	42.4035i	0.593184	−	0.302243i
$28$	79.8187	−	222.950i	0.538726	−	1.50477i
$29$	148.907	−	204.953i	0.953493	−	1.31237i	0.00353442	−	0.999994i	$-0.498875\pi$
$29$	148.907	−	204.953i	0.953493	−	1.31237i	0.949958	−	0.312376i	$-0.101125\pi$
$30$	72.3076	−	60.2303i	0.440050	−	0.366550i
$31$	48.2050	−	108.270i	0.279286	−	0.627287i	−0.718374	−	0.695657i	$-0.755113\pi$
$31$	48.2050	−	108.270i	0.279286	−	0.627287i	0.997660	+	0.0683701i	$0.0217799\pi$
$32$	180.957	+	48.4872i	0.999654	+	0.267857i
$33$	−42.7952	−	34.6549i	−0.225748	−	0.182807i
$34$	7.34330	+	22.6004i	0.0370402	+	0.113998i
$35$	203.977	+	35.6164i	0.985096	+	0.172008i
$36$	93.2153	−	286.887i	0.431552	−	1.32818i
$37$	241.596	−	156.894i	1.07346	−	0.697115i	0.118235	−	0.992986i	$-0.462276\pi$
$37$	241.596	−	156.894i	1.07346	−	0.697115i	0.955228	+	0.295871i	$0.0956097\pi$
$38$	23.6989	+	452.202i	0.101170	+	1.93044i
$39$	14.4650	+	68.0525i	0.0593911	+	0.279413i
$40$	22.1404	−	242.972i	0.0875176	−	0.960432i
$41$	373.584	−	121.385i	1.42302	−	0.462369i	0.506463	−	0.862262i	$-0.330953\pi$
$41$	373.584	−	121.385i	1.42302	−	0.462369i	0.916562	+	0.399893i	$0.130953\pi$
$42$	−144.227	+	59.1578i	−0.529874	+	0.217339i
$43$	257.326	+	257.326i	0.912601	+	0.912601i	0.996476	−	0.0838754i	$-0.0267298\pi$
$43$	257.326	+	257.326i	0.912601	+	0.912601i	−0.0838754	+	0.996476i	$0.526730\pi$
$44$	−379.297	+	39.8657i	−1.29957	+	0.136590i
$45$	261.061	+	37.6501i	0.864815	+	0.124723i
$46$	61.1150	−	581.471i	0.195890	−	1.86376i
$47$	−294.443	−	113.026i	−0.913806	−	0.350777i	−0.144386	−	0.989521i	$-0.546121\pi$
$47$	−294.443	−	113.026i	−0.913806	−	0.350777i	−0.769419	+	0.638744i	$0.779454\pi$
$48$	−2.34634	−	4.60495i	−0.00705552	−	0.0138472i
$49$	−304.532	−	157.827i	−0.887848	−	0.460137i
$50$	568.076	−	45.5747i	1.60676	−	0.128905i
$51$	4.81134	−	8.33348i	0.0132102	−	0.0228808i
$52$	404.113	+	262.434i	1.07770	+	0.699866i
$53$	293.082	−	237.333i	0.759582	−	0.615098i	−0.169261	−	0.985571i	$-0.554138\pi$
$53$	293.082	−	237.333i	0.759582	−	0.615098i	0.928843	+	0.370474i	$0.120805\pi$
$54$	−389.022	+	173.204i	−0.980355	+	0.436482i
$55$	−90.7635	−	320.892i	−0.222519	−	0.786711i
$56$	−155.951	+	372.851i	−0.372141	+	0.889719i
$57$	129.658	−	129.658i	0.301292	−	0.301292i
$58$	−726.870	+	897.610i	−1.64556	+	2.03210i
$59$	−191.477	+	212.657i	−0.422512	+	0.469247i	−0.916391	−	0.400284i	$-0.868912\pi$
$59$	−191.477	+	212.657i	−0.422512	+	0.469247i	0.493880	+	0.869530i	$0.335578\pi$
$60$	−211.350	+	158.072i	−0.454754	+	0.340118i
$61$	−36.1653	+	32.5634i	−0.0759098	+	0.0683495i	−0.706212	−	0.708000i	$-0.749598\pi$
$61$	−36.1653	+	32.5634i	−0.0759098	+	0.0683495i	0.630302	+	0.776350i	$0.282931\pi$
$62$	−245.310	+	481.448i	−0.502490	+	0.986193i
$63$	−393.707	−	189.461i	−0.787341	−	0.378887i
$64$	−791.020	−	257.018i	−1.54496	−	0.501988i
$65$	−166.023	+	387.237i	−0.316809	+	0.738935i
$66$	186.576	+	167.994i	0.347969	+	0.313312i
$67$	571.777	−	219.485i	1.04259	−	0.400214i	0.224000	−	0.974589i	$-0.428088\pi$
$67$	571.777	−	219.485i	1.04259	−	0.400214i	0.818592	+	0.574376i	$0.194755\pi$
$68$	−17.2490	−	64.3741i	−0.0307610	−	0.114802i
$69$	−191.539	+	139.161i	−0.334183	+	0.242798i
$70$	−920.199	−	210.831i	−1.57121	−	0.359988i
$71$	775.979	+	563.782i	1.29707	+	0.942375i	0.999922	−	0.0124577i	$-0.00396550\pi$
$71$	775.979	+	563.782i	1.29707	+	0.942375i	0.297145	+	0.954832i	$0.403965\pi$
$72$	−184.495	+	480.625i	−0.301985	+	0.786697i
$73$	86.5291	−	133.243i	0.138732	−	0.213629i	−0.762474	−	0.647018i	$-0.776016\pi$
$73$	86.5291	−	133.243i	0.138732	−	0.213629i	0.901207	+	0.433389i	$0.142682\pi$
$74$	−1137.41	+	656.686i	−1.78678	+	1.03160i
$75$	−167.638	−	158.600i	−0.258095	−	0.244181i
$76$		−	1269.95i		−	1.91675i
$77$	−16.3685	+	552.170i	−0.0242255	+	0.817216i
$78$	−49.6205	−	313.292i	−0.0720310	−	0.454786i
$79$	148.229	+	332.928i	0.211102	+	0.474144i	0.987800	−	0.155730i	$-0.0497731\pi$
$79$	148.229	+	332.928i	0.211102	+	0.474144i	−0.776697	+	0.629874i	$0.783106\pi$
$80$	4.46763	−	30.9779i	0.00624370	−	0.0432930i
$81$	−424.375	−	188.944i	−0.582132	−	0.259182i
$82$	−1729.88	+	463.519i	−2.32967	+	0.624233i
$83$	−104.113	+	657.345i	−0.137686	+	0.869313i	0.818063	+	0.575129i	$0.195048\pi$
$83$	−104.113	+	657.345i	−0.137686	+	0.869313i	−0.955749	+	0.294184i	$0.904952\pi$
$84$	412.616	−	144.512i	0.535954	−	0.187710i
$85$	52.9026	−	24.4370i	0.0675070	−	0.0311832i
$86$	−1110.19	−	1233.00i	−1.39204	−	1.54602i
$87$	467.064	−	24.4778i	0.575569	−	0.0301643i
$88$	650.008	−	34.0655i	0.787398	−	0.0412658i
$89$	−276.345	−	306.913i	−0.329130	−	0.365536i	0.555755	−	0.831346i	$-0.312429\pi$
$89$	−276.345	−	306.913i	−0.329130	−	0.365536i	−0.884884	+	0.465811i	$0.845763\pi$
$90$	−1179.62	−	233.711i	−1.38158	−	0.273726i
$91$	455.099	−	529.139i	0.524256	−	0.609548i
$92$	−256.510	+	1619.54i	−0.290685	+	1.83531i
$93$	211.348	−	56.6306i	0.235654	−	0.0631432i
$94$	1313.62	+	584.860i	1.44137	+	0.641741i
$95$	1094.25	−	188.881i	1.18177	−	0.203987i
$96$	140.676	+	315.964i	0.149559	+	0.335916i
$97$	43.0516	+	271.817i	0.0450642	+	0.284524i	0.999921	−	0.0125413i	$-0.00399213\pi$
$97$	43.0516	+	271.817i	0.0450642	+	0.284524i	−0.954857	+	0.297065i	$0.903992\pi$
$98$	1348.86	+	791.245i	1.39036	+	0.815590i
$99$			703.678i			0.714367i
$100$	−1597.69	+	44.2593i	−1.59769	+	0.0442593i
$101$	1250.48	−	721.966i	1.23196	−	0.711271i	0.264519	−	0.964380i	$-0.414787\pi$
$101$	1250.48	−	721.966i	1.23196	−	0.711271i	0.967438	+	0.253110i	$0.0814534\pi$
$102$	−23.8943	+	36.7940i	−0.0231950	+	0.0357171i
$103$	556.788	−	1450.48i	0.532640	−	1.38757i	−0.358365	−	0.933582i	$-0.616666\pi$
$103$	556.788	−	1450.48i	0.532640	−	1.38757i	0.891005	−	0.453993i	$-0.150001\pi$
$104$	−665.301	−	483.370i	−0.627290	−	0.455753i
$105$	185.888	+	334.038i	0.172770	+	0.310464i
$106$	−1391.02	+	1010.63i	−1.27460	+	0.926052i
$107$	269.736	+	1006.67i	0.243705	+	0.909518i	0.974030	+	0.226418i	$0.0727017\pi$
$107$	269.736	+	1006.67i	0.243705	+	0.909518i	−0.730326	+	0.683099i	$0.760632\pi$
$108$	1114.95	−	427.988i	0.993387	−	0.381325i
$109$	−1022.55	−	920.712i	−0.898559	−	0.809066i	0.0837203	−	0.996489i	$-0.473320\pi$
$109$	−1022.55	−	920.712i	−0.898559	−	0.809066i	−0.982279	+	0.187423i	$0.939986\pi$
$110$	336.674	+	1482.67i	0.291824	+	1.28515i
$111$	505.802	+	164.345i	0.432510	+	0.140531i
$112$	−22.4818	+	46.7180i	−0.0189672	+	0.0394146i
$113$	−89.2825	+	175.227i	−0.0743274	+	0.145876i	−0.925180	−	0.379529i	$-0.876086\pi$
$113$	−89.2825	+	175.227i	−0.0743274	+	0.145876i	0.850852	+	0.525405i	$0.176086\pi$
$114$	−621.266	+	559.390i	−0.510411	+	0.459576i
$115$	−1433.63	+	19.8535i	−1.16249	+	0.0160987i
$116$	2167.48	−	2407.23i	1.73487	−	1.92677i
$117$	559.490	−	690.913i	0.442093	−	0.545939i
$118$	922.529	−	922.529i	0.719710	−	0.719710i
$119$	−95.7481	+	12.2690i	−0.0737581	+	0.00945128i
$120$	374.330	−	250.530i	0.284763	−	0.190584i
$121$	−403.167	+	179.501i	−0.302905	+	0.134862i
$122$	172.429	−	139.631i	0.127959	−	0.103619i
$123$	608.204	+	394.973i	0.445853	+	0.289540i
$124$	757.699	−	1312.37i	0.548737	−	0.950440i
$125$	−275.761	−	1370.07i	−0.197319	−	0.980339i
$126$	1747.33	+	956.553i	1.23543	+	0.676322i
$127$	−753.542	−	1478.91i	−0.526504	−	1.03332i	−0.989168	−	0.146789i	$-0.953106\pi$
$127$	−753.542	−	1478.91i	−0.526504	−	1.03332i	0.462664	−	0.886534i	$-0.346894\pi$
$128$	2140.98	+	821.845i	1.47842	+	0.567512i
$129$	−70.2278	+	668.173i	−0.0479319	+	0.456042i
$130$	848.293	−	1723.46i	0.572309	−	1.16275i
$131$	−2378.90	+	250.032i	−1.58661	+	0.166759i	−0.856343	−	0.516407i	$-0.827269\pi$
$131$	−2378.90	+	250.032i	−1.58661	+	0.166759i	−0.730263	+	0.683166i	$0.760602\pi$
$132$	−497.881	−	497.881i	−0.328295	−	0.328295i
$133$	−1822.86	−	246.395i	−1.18844	−	0.160640i
$134$	−2655.65	+	862.873i	−1.71204	+	0.556275i
$135$	534.604	+	897.041i	0.340825	+	0.571889i
$136$	23.6481	+	111.255i	0.0149103	+	0.0701476i
$137$	−3.53437	−	67.4397i	−0.00220410	−	0.0420567i	0.997306	−	0.0733527i	$-0.0233699\pi$
$137$	−3.53437	−	67.4397i	−0.00220410	−	0.0420567i	−0.999510	+	0.0312960i	$0.990037\pi$
$138$	905.276	−	587.893i	0.558422	−	0.362643i
$139$	377.402	−	1161.52i	0.230294	−	0.708771i	−0.767417	−	0.641148i	$-0.778459\pi$
$139$	377.402	−	1161.52i	0.230294	−	0.708771i	0.997711	−	0.0676229i	$-0.0215415\pi$
$140$	2546.23	+	725.533i	1.53711	+	0.437991i
$141$	−179.932	−	553.772i	−0.107468	−	0.330752i
$142$	−3398.48	−	2752.03i	−2.00841	−	1.62638i
$143$	−1085.74	−	290.922i	−0.634921	−	0.170127i
$144$	−26.8620	+	60.3330i	−0.0155451	+	0.0349149i
$145$	2396.56	+	1509.58i	1.37258	+	0.864579i
$146$	−425.757	+	586.004i	−0.241342	+	0.332178i
$147$	−127.375	−	620.300i	−0.0714674	−	0.348037i
$148$	3281.91	−	1672.22i	1.82278	−	0.928753i
$149$	568.347	+	328.135i	0.312488	+	0.180415i	0.648039	−	0.761607i	$-0.275589\pi$
$149$	568.347	+	328.135i	0.312488	+	0.180415i	−0.335551	+	0.942022i	$0.608923\pi$
$150$	725.404	+	762.101i	0.394860	+	0.414835i
$151$	616.881	+	1068.47i	0.332457	+	0.575833i	0.982993	−	0.183643i	$-0.0587889\pi$
$151$	616.881	+	1068.47i	0.332457	+	0.575833i	−0.650536	+	0.759476i	$0.725456\pi$
$152$	−113.432	+	2164.41i	−0.0605300	+	1.15498i
$153$	−121.450	+	19.2358i	−0.0641741	+	0.0101642i
$154$	206.279	−	2510.10i	0.107938	−	1.31344i
$155$	1243.50	+	457.682i	0.644390	+	0.237174i
$156$	92.9869	+	884.712i	0.0477238	+	0.454062i
$157$	217.342	−	811.133i	0.110483	−	0.412328i	−0.888426	−	0.459019i	$-0.848201\pi$
$157$	217.342	−	811.133i	0.110483	−	0.412328i	0.998909	+	0.0466912i	$0.0148677\pi$
$158$	−595.442	−	1551.18i	−0.299815	−	0.781045i
$159$	681.031	+	144.758i	0.339681	+	0.0722014i
$160$	−407.066	+	2054.59i	−0.201134	+	1.01519i
$161$	2274.89	+	682.413i	1.11358	+	0.334047i
$162$	1887.08	+	961.514i	0.915202	+	0.466319i
$163$	23.4246	+	36.0708i	0.0112562	+	0.0173330i	0.844254	−	0.535943i	$-0.180044\pi$
$163$	23.4246	+	36.0708i	0.0112562	+	0.0173330i	−0.832998	+	0.553276i	$0.813377\pi$
$164$	4912.86	−	1044.26i	2.33921	−	0.497214i
$165$	354.950	−	503.051i	0.167472	−	0.237348i
$166$	630.873	−	2968.02i	0.294971	−	1.38773i
$167$	−1085.00	−	171.846i	−0.502751	−	0.0796280i	−0.100092	−	0.994978i	$-0.531914\pi$
$167$	−1085.00	−	171.846i	−0.502751	−	0.0796280i	−0.402659	+	0.915350i	$0.631914\pi$
$168$	−716.142	+	209.442i	−0.328878	+	0.0961833i
$169$	−456.635	−	628.505i	−0.207845	−	0.286074i
$170$	−246.694	+	98.6378i	−0.111298	+	0.0445010i
$171$	−2330.29	−	244.923i	−1.04212	−	0.109531i
$172$	2928.32	+	3616.17i	1.29815	+	1.60308i
$173$	−2949.13	−	154.557i	−1.29606	−	0.0679235i	−0.608208	−	0.793778i	$-0.708111\pi$
$173$	−2949.13	−	154.557i	−1.29606	−	0.0679235i	−0.687849	+	0.725854i	$0.741445\pi$
$174$	−2132.36			−0.929047
$175$	−246.453	+	2301.88i	−0.106458	+	0.994317i
$176$	83.4996			0.0357615
$177$	−527.578	−	27.6492i	−0.224040	−	0.0117415i
$178$	1184.96	+	1463.30i	0.498968	+	0.616174i
$179$	−1030.19	−	108.277i	−0.430167	−	0.0452123i	−0.113029	−	0.993592i	$-0.536055\pi$
$179$	−1030.19	−	108.277i	−0.430167	−	0.0452123i	−0.317138	+	0.948379i	$0.602722\pi$
$180$	3269.42	+	827.691i	1.35382	+	0.342736i
$181$	−60.9428	−	83.8806i	−0.0250268	−	0.0344464i	0.796320	−	0.604875i	$-0.206777\pi$
$181$	−60.9428	−	83.8806i	−0.0250268	−	0.0344464i	−0.821347	+	0.570429i	$0.806777\pi$
$182$	−2198.31	+	2300.56i	−0.895325	+	0.936971i
$183$	−88.7391	−	14.0549i	−0.0358458	−	0.00567742i
$184$	581.835	−	2737.32i	0.233117	−	1.09673i
$185$	1928.99	+	2579.16i	0.766607	+	1.02499i
$186$	−975.773	+	207.407i	−0.384662	+	0.0817625i
$187$	84.6730	+	130.385i	0.0331118	+	0.0509877i
$188$	−3593.17	−	1830.81i	−1.39393	−	0.710243i
$189$	−398.005	−	1683.41i	−0.153178	−	0.647885i
$190$	−5027.16	+	598.866i	−1.91952	+	0.228665i
$191$	−4305.57	−	915.177i	−1.63110	−	0.346701i	−0.700759	−	0.713398i	$-0.747155\pi$
$191$	−4305.57	−	915.177i	−1.63110	−	0.346701i	−0.930341	+	0.366697i	$0.880489\pi$
$192$	−550.284	−	1433.54i	−0.206840	−	0.538837i
$193$	−524.065	+	1955.84i	−0.195456	+	0.729452i	0.796692	+	0.604385i	$0.206581\pi$
$193$	−524.065	+	1955.84i	−0.195456	+	0.729452i	−0.992148	+	0.125067i	$0.960086\pi$
$194$	−131.154	−	1247.84i	−0.0485376	−	0.461804i
$195$	−748.483	+	211.706i	−0.274872	+	0.0777467i
$196$	−3661.59	−	2414.00i	−1.33440	−	0.879738i
$197$	1686.70	−	267.147i	0.610013	−	0.0966165i	0.156218	−	0.987723i	$-0.450070\pi$
$197$	1686.70	−	267.147i	0.610013	−	0.0966165i	0.453795	+	0.891106i	$0.350070\pi$
$198$	167.905	−	3203.82i	0.0602651	−	1.14993i
$199$	1666.36	+	2886.22i	0.593594	+	1.02813i	0.993744	+	0.111685i	$0.0356247\pi$
$199$	1666.36	+	2886.22i	0.593594	+	1.02813i	−0.400150	+	0.916450i	$0.631042\pi$
$200$	2726.94	+	67.2730i	0.964118	+	0.0237846i
$201$	979.223	+	565.355i	0.343627	+	0.198393i
$202$	−5865.66	+	2988.71i	−2.04310	+	1.04101i
$203$	−3034.76	−	3578.21i	−1.04925	−	1.23715i
$204$	72.3206	−	99.5408i	0.0248209	−	0.0341630i
$205$	1630.48	+	4077.86i	0.555502	+	1.38932i
$206$	−2881.13	+	6471.13i	−0.974456	+	2.18866i
$207$	2922.30	+	783.028i	0.981227	+	0.262919i
$208$	−81.9849	−	66.3900i	−0.0273299	−	0.0221314i
$209$	915.456	+	2817.48i	0.302983	+	0.932485i
$210$	−766.637	−	1565.22i	−0.251919	−	0.514334i
$211$	1122.56	−	3454.89i	0.366258	−	1.12723i	−0.582932	−	0.812521i	$-0.698095\pi$
$211$	1122.56	−	3454.89i	0.366258	−	1.12723i	0.949190	−	0.314704i	$-0.101905\pi$
$212$	4044.13	−	2626.29i	1.31015	−	0.850822i
$213$	92.6763	+	1768.37i	0.0298126	+	0.568858i
$214$	−987.896	−	4647.69i	−0.315566	−	1.48462i
$215$	−2680.35	+	3061.03i	−0.850225	+	0.970978i
$216$	−1938.47	+	629.846i	−0.610629	+	0.198405i
$217$	−1736.75	−	1342.21i	−0.543310	−	0.419887i
$218$	4435.96	+	4435.96i	1.37817	+	1.37817i
$219$	291.705	−	30.6595i	0.0900074	−	0.00946015i
$220$	−725.294	−	4201.89i	−0.222269	−	1.28769i
$221$	20.5313	−	195.343i	0.00624927	−	0.0594578i
$222$	−2263.68	−	868.947i	−0.684362	−	0.262702i
$223$	2008.20	+	3941.31i	0.603045	+	1.18354i	0.967630	+	0.252372i	$0.0812107\pi$
$223$	2008.20	+	3941.31i	0.603045	+	1.18354i	−0.364586	+	0.931170i	$0.618789\pi$
$224$	1666.07	−	3043.40i	0.496960	−	0.907792i
$225$	−226.917	+	2940.20i	−0.0672347	+	0.871172i
$226$	448.311	−	776.497i	0.131952	−	0.228548i
$227$	−3638.51	−	2362.88i	−1.06386	−	0.690880i	−0.110857	−	0.993836i	$-0.535360\pi$
$227$	−3638.51	−	2362.88i	−1.06386	−	0.690880i	−0.953004	+	0.302956i	$0.902026\pi$
$228$	1822.07	−	1475.48i	0.529252	−	0.428580i
$229$	1682.88	−	749.265i	0.485623	−	0.216213i	−0.149295	−	0.988793i	$-0.547700\pi$
$229$	1682.88	−	749.265i	0.485623	−	0.216213i	0.634918	+	0.772579i	$0.281034\pi$
$230$	6532.00	+	251.687i	1.87264	+	0.0721555i
$231$	−811.249	+	618.051i	−0.231066	+	0.176038i
$232$	−3909.11	+	3909.11i	−1.10623	+	1.10623i
$233$	3218.38	−	3974.36i	0.904905	−	1.11746i	−0.0877087	−	0.996146i	$-0.527954\pi$
$233$	3218.38	−	3974.36i	0.904905	−	1.11746i	0.992614	−	0.121318i	$-0.0387122\pi$
$234$	−2712.19	+	3012.20i	−0.757700	+	0.841511i
$235$	1043.11	−	3368.36i	0.289552	−	0.935011i
$236$	−2719.11	+	2448.30i	−0.749996	+	0.675300i
$237$	−305.452	+	599.484i	−0.0837184	+	0.164307i
$238$	438.865	−	33.0140i	0.119527	−	0.00899151i
$239$	−1919.14	−	623.565i	−0.519408	−	0.168766i	0.0375685	−	0.999294i	$-0.488039\pi$
$239$	−1919.14	−	623.565i	−0.519408	−	0.168766i	−0.556977	+	0.830528i	$0.688039\pi$
$240$	49.6366	−	29.5816i	0.0133501	−	0.00795618i
$241$	4127.47	+	3716.39i	1.10321	+	0.993334i	0.999999	−	0.00132541i	$-0.000421891\pi$
$241$	4127.47	+	3716.39i	1.10321	+	0.993334i	0.103210	+	0.994660i	$0.467089\pi$
$242$	1878.43	−	721.063i	0.498968	−	0.191536i
$243$	−874.670	−	3264.31i	−0.230906	−	0.861752i
$244$	−503.413	+	365.751i	−0.132081	+	0.0959623i
$245$	1535.44	−	3514.05i	0.400390	−	0.916345i
$246$	−2674.89	−	1943.42i	−0.693270	−	0.503690i
$247$	1341.32	−	3494.25i	0.345530	−	0.900136i
$248$	−1408.59	+	2169.04i	−0.360668	+	0.555380i
$249$	−1064.09	+	614.355i	−0.270820	+	0.156358i
$250$	928.619	+	6303.66i	0.234924	+	1.59471i
$251$		−	1146.84i		−	0.288399i	−0.989549	−	0.144199i	$-0.953939\pi$
$251$		−	1146.84i		−	0.288399i	0.989549	−	0.144199i	$-0.0460607\pi$
$252$	−4753.29	−	2935.46i	−1.18821	−	0.733797i
$253$	−598.375	−	3777.99i	−0.148694	−	0.938815i
$254$	3077.96	+	6913.22i	0.760349	+	1.70777i
$255$	96.5259	+	47.5104i	0.0237046	+	0.0116675i
$256$	−3473.12	−	1546.33i	−0.847931	−	0.377523i
$257$	−5272.91	+	1412.87i	−1.27982	+	0.342928i	−0.833787	−	0.552086i	$-0.813832\pi$
$257$	−5272.91	+	1412.87i	−1.27982	+	0.342928i	−0.446038	+	0.895014i	$0.647165\pi$
$258$	479.178	−	3025.41i	0.115629	−	0.730053i
$259$	−1763.52	−	5035.24i	−0.423087	−	1.20801i
$260$	−2628.76	+	4702.34i	−0.627033	+	1.12164i
$261$	−3999.11	−	4441.47i	−0.948425	−	1.05333i
$262$	10890.7	−	570.757i	2.56805	−	0.134586i
$263$	−4227.86	+	221.573i	−0.991260	+	0.0519497i	−0.541065	−	0.840981i	$-0.681979\pi$
$263$	−4227.86	+	221.573i	−0.991260	+	0.0519497i	−0.450195	+	0.892930i	$0.648645\pi$
$264$	804.083	+	893.025i	0.187454	+	0.208189i
$265$	2864.44	+	3094.02i	0.664003	+	0.717224i
$266$	8240.63	+	1556.78i	1.89949	+	0.358844i
$267$	119.275	−	753.073i	0.0273390	−	0.172612i
$268$	7564.26	−	2026.84i	1.72411	−	0.461973i
$269$	2324.34	+	1034.86i	0.526830	+	0.234560i	0.652876	−	0.757464i	$-0.273562\pi$
$269$	2324.34	+	1034.86i	0.526830	+	0.234560i	−0.126046	+	0.992024i	$0.540229\pi$
$270$	−2219.99	−	4211.75i	−0.500385	−	0.949330i
$271$	3457.92	+	7766.62i	0.775106	+	1.74092i	0.664803	+	0.747019i	$0.268516\pi$
$271$	3457.92	+	7766.62i	0.775106	+	1.74092i	0.110303	+	0.993898i	$0.464818\pi$
$272$	2.28255	+	14.4114i	0.000508823	+	0.00321258i
$273$	1287.94	+	38.1797i	0.285530	+	0.00846424i
$274$			307.894i			0.0678852i
$275$	3512.69	−	1249.90i	0.770266	−	0.274080i
$276$	−2621.67	+	1513.62i	−0.571762	+	0.330107i
$277$	−1235.39	+	1902.34i	−0.267969	+	0.412636i	−0.946881	−	0.321583i	$-0.895785\pi$
$277$	−1235.39	+	1902.34i	−0.267969	+	0.412636i	0.678912	+	0.734220i	$0.262452\pi$
$278$	−1995.45	+	5198.32i	−0.430500	+	1.12149i
$279$	−2262.01	−	1643.44i	−0.485386	−	0.352654i
$280$	−4274.82	−	1463.98i	−0.912390	−	0.312462i
$281$	5649.25	−	4104.42i	1.19931	−	0.871349i	0.205093	−	0.978743i	$-0.434250\pi$
$281$	5649.25	−	4104.42i	1.19931	−	0.871349i	0.994217	+	0.107393i	$0.0342504\pi$
$282$	687.085	+	2564.24i	0.145090	+	0.541483i
$283$	−7181.64	+	2756.77i	−1.50850	+	0.579057i	−0.965437	−	0.260638i	$-0.916067\pi$
$283$	−7181.64	+	2756.77i	−1.50850	+	0.579057i	−0.543059	+	0.839695i	$0.682734\pi$
$284$	9114.10	+	8206.37i	1.90430	+	1.71464i
$285$	1542.35	+	1350.54i	0.320565	+	0.280698i
$286$	4873.89	+	1583.62i	1.00769	+	0.327418i
$287$	−545.721	−	7254.44i	−0.112240	−	1.49204i
$288$	2006.48	−	3937.94i	0.410531	−	0.805713i
$289$	3630.88	−	3269.26i	0.739036	−	0.665431i
$290$	−10551.3	−	7444.91i	−2.13652	−	1.50752i
$291$	−339.972	+	377.577i	−0.0684863	+	0.0760618i
$292$	1278.42	−	1578.72i	0.256212	−	0.316395i
$293$	−3230.91	+	3230.91i	−0.644203	+	0.644203i	−0.951586	−	0.307383i	$-0.900547\pi$
$293$	−3230.91	+	3230.91i	−0.644203	+	0.644203i	0.307383	+	0.951586i	$0.400547\pi$
$294$	431.923	+	2854.59i	0.0856812	+	0.566270i
$295$	−2514.00	−	1978.79i	−0.496172	−	0.390541i
$296$	−5742.83	+	2556.87i	−1.12769	+	0.502078i
$297$	−2165.08	+	1753.25i	−0.422999	+	0.342538i
$298$	−2509.36	−	1629.60i	−0.487797	−	0.316779i
$299$	−2416.34	+	4185.22i	−0.467359	+	0.809489i
$300$	−1919.76	−	2240.87i	−0.369459	−	0.431256i
$301$	5758.74	−	3501.65i	1.10275	−	0.670537i
$302$	−2553.69	−	5011.89i	−0.486583	−	0.954974i
$303$	2488.71	+	955.327i	0.471857	+	0.181129i
$304$	−29.0630	+	276.516i	−0.00548315	+	0.0521687i
$305$	−390.023	−	379.368i	−0.0732218	−	0.0712215i
$306$	557.546	−	58.6004i	0.104159	−	0.0109476i
$307$	3724.17	+	3724.17i	0.692344	+	0.692344i	0.962747	−	0.270403i	$-0.0871570\pi$
$307$	3724.17	+	3724.17i	0.692344	+	0.692344i	−0.270403	+	0.962747i	$0.587157\pi$
$308$	−946.146	+	6999.71i	−0.175038	+	1.29495i
$309$	2727.99	−	886.378i	0.502233	−	0.163185i
$310$	−5552.41	−	2380.52i	−1.01728	−	0.436144i
$311$	−608.551	−	2863.01i	−0.110957	−	0.522013i	−0.998160	−	0.0606336i	$-0.980688\pi$
$311$	−608.551	−	2863.01i	−0.110957	−	0.522013i	0.887203	−	0.461380i	$-0.152645\pi$
$312$	−79.4579	−	1516.15i	−0.0144180	−	0.275112i
$313$	−79.1983	+	51.4320i	−0.0143021	+	0.00928789i	−0.551770	−	0.833996i	$-0.686047\pi$
$313$	−79.1983	+	51.4320i	−0.0143021	+	0.00928789i	0.537468	+	0.843284i	$0.319381\pi$
$314$	−1183.10	+	3641.20i	−0.212631	+	0.654409i
$315$	1822.38	−	4532.28i	0.325967	−	0.810682i
$316$	1439.96	+	4431.74i	0.256342	+	0.788940i
$317$	875.326	+	708.825i	0.155089	+	0.125589i	0.703724	−	0.710473i	$-0.251519\pi$
$317$	875.326	+	708.825i	0.155089	+	0.125589i	−0.548635	+	0.836062i	$0.684852\pi$
$318$	−3066.16	−	821.576i	−0.540698	−	0.144880i
$319$	−3073.45	+	6903.08i	−0.539436	+	1.21159i
$320$	2282.15	−	9014.61i	0.398675	−	1.57479i
$321$	−1130.94	+	1556.60i	−0.196644	+	0.270657i
$322$	−10194.7	−	3649.81i	−1.76437	−	0.631665i
$323$	−461.253	+	235.020i	−0.0794575	+	0.0404856i
$324$	−5143.96	−	2969.87i	−0.882023	−	0.509236i
$325$	−4442.76	−	1565.69i	−0.758276	−	0.267227i
$326$	−98.0446	−	169.818i	−0.0166570	−	0.0288508i
$327$	132.950	−	2536.84i	0.0224837	−	0.429014i
$328$	−8466.41	+	1340.95i	−1.42524	+	0.225736i
$329$	−3325.06	+	4802.36i	−0.557193	+	0.804749i
$330$	−1736.11	+	2205.68i	−0.289605	+	0.367935i
$331$	361.653	+	3440.90i	0.0600552	+	0.571387i	0.982631	+	0.185571i	$0.0594134\pi$
$331$	361.653	+	3440.90i	0.0600552	+	0.571387i	−0.922576	+	0.385816i	$0.873920\pi$
$332$	−2202.51	+	8219.87i	−0.364091	+	1.35881i
$333$	−2435.48	−	6344.64i	−0.400791	−	1.04410i
$334$	4898.94	+	1041.30i	0.802568	+	0.170591i
$335$	2871.47	+	6216.30i	0.468314	+	1.01383i
$336$	−93.1494	+	22.0231i	−0.0151242	+	0.00357576i
$337$	7416.98	+	3779.14i	1.19890	+	0.610869i	0.935332	−	0.353772i	$-0.115101\pi$
$337$	7416.98	+	3779.14i	1.19890	+	0.610869i	0.263566	+	0.964641i	$0.415101\pi$
$338$	1929.07	+	2970.51i	0.310437	+	0.478032i
$339$	−355.141	+	75.4875i	−0.0568985	+	0.0120941i
$340$	705.389	−	240.043i	0.112515	−	0.0382888i
$341$	−734.978	+	3457.80i	−0.116719	+	0.549122i
$342$	10551.3	+	1671.16i	1.66827	+	0.264228i
$343$	−4175.44	+	4787.42i	−0.657295	+	0.753633i
$344$	−4667.82	−	6424.71i	−0.731605	−	1.00697i
$345$	−1694.14	−	2033.85i	−0.264375	−	0.317387i
$346$	13390.4	+	1407.38i	2.08055	+	0.218675i
$347$	3115.07	+	3846.79i	0.481918	+	0.595119i	0.958883	−	0.283803i	$-0.0915962\pi$
$347$	3115.07	+	3846.79i	0.481918	+	0.595119i	−0.476964	+	0.878923i	$0.658263\pi$
$348$	5972.06	+	312.982i	0.919931	+	0.0482115i
$349$	−4289.89			−0.657973			−0.328987	−	0.944335i	$-0.606707\pi$
$349$	−4289.89			−0.657973			−0.328987	+	0.944335i	$0.606707\pi$
$350$	1671.34	−	10421.5i	0.255249	−	1.59159i
$351$	3519.80			0.535251
$352$	−5580.23	−	292.447i	−0.844964	−	0.0442827i
$353$	−2515.12	−	3105.91i	−0.379224	−	0.468303i	0.551420	−	0.834228i	$-0.314086\pi$
$353$	−2515.12	−	3105.91i	−0.379224	−	0.468303i	−0.930644	+	0.365925i	$0.880753\pi$
$354$	2395.44	+	251.771i	0.359651	+	0.0378008i
$355$	−5715.49	+	9073.72i	−0.854497	+	1.35657i
$356$	−3103.90	−	4272.15i	−0.462097	−	0.636021i
$357$	−128.848	−	123.121i	−0.0191018	−	0.0182528i
$358$	4664.57	+	738.795i	0.688631	+	0.109069i
$359$	−2143.06	+	10082.3i	−0.315060	+	1.48224i	0.480837	+	0.876810i	$0.340333\pi$
$359$	−2143.06	+	10082.3i	−0.315060	+	1.48224i	−0.795897	+	0.605431i	$0.793001\pi$
$360$	−5498.24	−	1702.68i	−0.804952	−	0.249276i
$361$	−2939.86	+	624.886i	−0.428613	+	0.0911046i
$362$	257.455	+	396.447i	0.0373800	+	0.0575601i
$363$	−725.958	−	369.894i	−0.104967	−	0.0534832i
$364$	6494.41	−	6120.45i	0.935163	−	0.881316i
$365$	1550.44	+	866.748i	0.222340	+	0.124295i
$366$	400.672	+	85.1655i	0.0572226	+	0.0121630i
$367$	−3825.31	−	9965.28i	−0.544086	−	1.41739i	−0.879762	−	0.475415i	$-0.842298\pi$
$367$	−3825.31	−	9965.28i	−0.544086	−	1.41739i	0.335675	−	0.941978i	$-0.391035\pi$
$368$	92.9154	−	346.765i	0.0131618	−	0.0491206i
$369$	−968.665	−	9216.23i	−0.136658	−	1.30021i
$370$	−8167.21	−	12203.1i	−1.14755	−	1.71461i
$371$	−2985.09	−	6314.43i	−0.417731	−	0.883635i
$372$	2763.27	−	437.658i	0.385131	−	0.0609987i
$373$	−219.317	+	4184.82i	−0.0304445	+	0.580916i	0.940233	+	0.340531i	$0.110607\pi$
$373$	−219.317	+	4184.82i	−0.0304445	+	0.580916i	−0.970678	+	0.240384i	$0.922726\pi$
$374$	−354.402	−	613.842i	−0.0489991	−	0.0848690i
$375$	1645.32	−	1987.45i	0.226571	−	0.273685i
$376$	5960.42	+	3441.25i	0.817514	+	0.471992i
$377$	8506.29	−	4334.17i	1.16206	−	0.592098i
$378$	1410.42	+	7759.48i	0.191916	+	1.05583i
$379$	−894.591	+	1231.30i	−0.121245	+	0.166880i	−0.865325	−	0.501211i	$-0.832888\pi$
$379$	−894.591	+	1231.30i	−0.121245	+	0.166880i	0.744080	+	0.668091i	$0.232888\pi$
$380$	14167.4	−	939.357i	1.91255	−	0.126810i
$381$	1246.38	−	2799.41i	0.167596	−	0.376426i
$382$	19384.7	+	5194.12i	2.59636	+	0.695692i
$383$	8705.31	+	7049.42i	1.16141	+	0.940493i	0.998931	−	0.0462191i	$-0.0147172\pi$
$383$	8705.31	+	7049.42i	1.16141	+	0.940493i	0.162480	+	0.986712i	$0.448051\pi$
$384$	1308.34	+	4026.64i	0.173869	+	0.535114i
$385$	−6172.03	+	225.825i	−0.817028	+	0.0298938i
$386$	2852.73	−	8779.80i	0.376166	−	1.15772i
$387$	7200.24	−	4675.89i	0.945759	−	0.614183i
$388$	184.164	+	3514.06i	0.0240967	+	0.459792i
$389$	1018.36	+	4791.02i	0.132733	+	0.624458i	0.993343	+	0.115194i	$0.0367490\pi$
$389$	1018.36	+	4791.02i	0.132733	+	0.624458i	−0.860610	+	0.509264i	$0.829918\pi$
$390$	3458.33	−	785.295i	0.449024	−	0.101961i
$391$	635.697	−	206.550i	0.0822214	−	0.0267153i
$392$	6024.94	+	4441.31i	0.776289	+	0.572245i
$393$	−3122.65	−	3122.65i	−0.400806	−	0.400806i
$394$	−7743.23	+	813.846i	−0.990097	+	0.104063i
$395$	−3604.45	+	1899.88i	−0.459139	+	0.242009i
$396$	−940.494	+	8948.21i	−0.119348	+	1.13552i
$397$	5036.95	+	1933.50i	0.636769	+	0.244433i	0.655268	−	0.755396i	$-0.272555\pi$
$397$	5036.95	+	1933.50i	0.636769	+	0.244433i	−0.0184992	+	0.999829i	$0.505889\pi$
$398$	−6898.19	−	13538.5i	−0.868781	−	1.70508i
$399$	−1764.36	−	2901.64i	−0.221375	−	0.364069i
$400$	348.890	+	26.9264i	0.0436112	+	0.00336580i
$401$	5287.18	−	9157.66i	0.658426	−	1.14043i	−0.322597	−	0.946536i	$-0.604556\pi$
$401$	5287.18	−	9157.66i	0.658426	−	1.14043i	0.981023	−	0.193891i	$-0.0621109\pi$
$402$	−4323.46	−	2807.69i	−0.536405	−	0.348345i
$403$	3470.92	−	2810.70i	0.429030	−	0.347421i
$404$	16866.5	−	7509.45i	2.07708	−	0.924775i
$405$	1793.93	−	4874.01i	0.220101	−	0.598004i
$406$	12963.3	+	17015.6i	1.58463	+	2.07997i
$407$	−6075.75	+	6075.75i	−0.739960	+	0.739960i
$408$	−132.149	+	163.191i	−0.0160352	+	0.0198018i
$409$	7026.38	−	7803.59i	0.849467	−	0.943429i	−0.149505	−	0.988761i	$-0.547768\pi$
$409$	7026.38	−	7803.59i	0.849467	−	0.943429i	0.998972	+	0.0453320i	$0.0144346\pi$
$410$	−6450.50	−	18955.4i	−0.776994	−	2.28327i
$411$	92.6533	−	83.4254i	0.0111198	−	0.0100123i
$412$	9018.93	−	17700.6i	1.07847	−	2.11662i
$413$	2986.68	+	4377.98i	0.355848	+	0.521614i
$414$	−13118.3	−	4262.39i	−1.55731	−	0.506002i
$415$	−7410.25	−	675.246i	−0.876518	−	0.0798711i
$416$	5246.48	+	4723.95i	0.618341	+	0.556756i
$417$	2104.99	−	808.029i	0.247198	−	0.0948905i
$418$	−3495.75	−	13046.3i	−0.409050	−	1.52660i
$419$	−1524.45	+	1107.58i	−0.177743	+	0.129138i	−0.673099	−	0.739552i	$-0.735037\pi$
$419$	−1524.45	+	1107.58i	−0.177743	+	0.129138i	0.495357	+	0.868690i	$0.335037\pi$
$420$	1917.36	+	4496.19i	0.222756	+	0.522361i
$421$	−4322.16	−	3140.23i	−0.500354	−	0.363529i	0.308798	−	0.951128i	$-0.400073\pi$
$421$	−4322.16	−	3140.23i	−0.500354	−	0.363529i	−0.809152	+	0.587599i	$0.800073\pi$
$422$	−5935.35	+	15462.1i	−0.684665	+	1.78361i
$423$	−4052.42	+	6240.18i	−0.465805	+	0.717277i
$424$	−7127.12	+	4114.84i	−0.816329	+	0.471308i
$425$	311.747	+	572.098i	0.0355811	+	0.0652960i
$426$		−	8073.43i		−	0.918214i
$427$	427.321	+	793.553i	0.0484297	+	0.0899361i
$428$	2084.60	+	13161.7i	0.235428	+	1.48643i
$429$	−844.053	−	1895.77i	−0.0949913	−	0.213354i
$430$	12933.9	−	13297.2i	1.45053	−	1.49127i
$431$	−7597.30	−	3382.53i	−0.849069	−	0.378030i	−0.0643847	−	0.997925i	$-0.520508\pi$
$431$	−7597.30	−	3382.53i	−0.849069	−	0.378030i	−0.784685	+	0.619895i	$0.787175\pi$
$432$	−252.561	+	67.6735i	−0.0281281	+	0.00753690i
$433$	−2205.37	+	13924.1i	−0.244765	+	1.54539i	0.492820	+	0.870131i	$0.335966\pi$
$433$	−2205.37	+	13924.1i	−0.244765	+	1.54539i	−0.737585	+	0.675254i	$0.764034\pi$
$434$	7587.08	+	6525.45i	0.839151	+	0.721732i
$435$	618.549	+	5192.39i	0.0681773	+	0.572312i
$436$	−11772.6	−	13074.8i	−1.29313	−	1.43617i
$437$	12719.4	−	666.596i	1.39234	−	0.0729693i
$438$	−1335.44	+	69.9873i	−0.145684	+	0.00763499i
$439$	−3124.11	−	3469.68i	−0.339649	−	0.377218i	0.548988	−	0.835830i	$-0.315013\pi$
$439$	−3124.11	−	3469.68i	−0.339649	−	0.377218i	−0.888636	+	0.458612i	$0.848347\pi$
$440$	860.827	+	7226.19i	0.0932689	+	0.782943i
$441$	−5135.74	+	6253.26i	−0.554556	+	0.675225i
$442$	−140.089	+	884.489i	−0.0150755	+	0.0951829i
$443$	−1777.06	+	476.163i	−0.190589	+	0.0510681i	−0.352851	−	0.935680i	$-0.614788\pi$
$443$	−1777.06	+	476.163i	−0.190589	+	0.0510681i	0.162262	+	0.986748i	$0.448121\pi$
$444$	6212.30	+	2765.89i	0.664015	+	0.295639i
$445$	3219.46	−	3309.88i	0.342960	−	0.352592i
$446$	−8202.81	−	18423.8i	−0.870885	−	1.95604i
$447$	189.536	+	1196.68i	0.0200553	+	0.126624i
$448$	−8093.81	+	13106.0i	−0.853563	+	1.38215i
$449$		−	5058.52i		−	0.531684i	−0.964017	−	0.265842i	$-0.914350\pi$
$449$		−	5058.52i		−	0.531684i	0.964017	−	0.265842i	$-0.0856500\pi$
$450$	1734.71	−	13332.5i	0.181722	−	1.39667i
$451$	−10146.8	+	5858.26i	−1.05941	+	0.611651i
$452$	−1369.55	+	2108.91i	−0.142518	+	0.219458i
$453$	−816.275	+	2126.47i	−0.0846622	+	0.220552i
$454$	16002.2	+	11626.3i	1.65423	+	1.20187i
$455$	6239.62	+	4685.62i	0.642897	+	0.482781i
$456$	−3237.20	+	2351.96i	−0.332447	+	0.241537i
$457$	2684.58	+	10019.0i	0.274791	+	1.02553i	0.955981	+	0.293428i	$0.0947961\pi$
$457$	2684.58	+	10019.0i	0.274791	+	1.02553i	−0.681190	+	0.732107i	$0.738537\pi$
$458$	−7840.86	+	3009.82i	−0.799955	+	0.307074i
$459$	−361.782	−	325.750i	−0.0367899	−	0.0331258i
$460$	−18257.1	−	1663.64i	−1.85052	−	0.168626i
$461$	−2417.37	−	785.450i	−0.244226	−	0.0793537i	0.184346	−	0.982861i	$-0.440983\pi$
$461$	−2417.37	−	785.450i	−0.244226	−	0.0793537i	−0.428572	+	0.903508i	$0.640983\pi$
$462$	3841.06	−	2620.39i	0.386801	−	0.263878i
$463$	−1223.32	+	2400.90i	−0.122792	+	0.240992i	−0.944217	−	0.329324i	$-0.893179\pi$
$463$	−1223.32	+	2400.90i	−0.122792	+	0.240992i	0.821425	+	0.570316i	$0.193179\pi$
$464$	−527.032	+	474.542i	−0.0527303	+	0.0474785i
$465$	788.093	+	2315.88i	0.0785955	+	0.230960i
$466$	−15601.5	+	17327.2i	−1.55091	+	1.72246i
$467$	4566.58	−	5639.25i	0.452497	−	0.558787i	−0.498938	−	0.866638i	$-0.666276\pi$
$467$	4566.58	−	5639.25i	0.452497	−	0.558787i	0.951435	+	0.307851i	$0.0996097\pi$
$468$	8038.10	−	8038.10i	0.793934	−	0.793934i
$469$	−1441.67	−	11250.9i	−0.141941	−	1.10771i
$470$	−5552.95	+	15087.1i	−0.544975	+	1.48067i
$471$	1416.30	−	630.576i	0.138555	−	0.0616888i
$472$	4852.95	−	3929.84i	0.473252	−	0.383232i
$473$	−9103.46	−	5911.86i	−0.884942	−	0.574688i
$474$	1533.76	−	2656.54i	0.148624	−	0.257424i
$475$	2916.52	+	12067.6i	0.281725	+	1.16568i
$476$	−1233.96	+	28.0461i	−0.118821	+	0.00270062i
$477$	−4039.15	−	7927.28i	−0.387715	−	0.760933i
$478$	8588.96	+	3296.99i	0.821862	+	0.315483i
$479$	264.798	−	2519.39i	0.0252587	−	0.240321i	−0.974607	−	0.223923i	$-0.928114\pi$
$479$	264.798	−	2519.39i	0.0252587	−	0.240321i	0.999866	−	0.0163977i	$-0.00521978\pi$
$480$	−3420.79	+	1803.07i	−0.325285	+	0.171456i
$481$	10796.3	−	1134.74i	1.02343	−	0.107567i
$482$	−17905.4	−	17905.4i	−1.69205	−	1.69205i
$483$	1663.97	+	4056.78i	0.156756	+	0.382173i
$484$	−5366.71	+	1743.75i	−0.504011	+	0.163763i
$485$	−3000.50	+	681.334i	−0.280919	+	0.0637893i
$486$	3203.44	+	15071.0i	0.298994	+	1.40665i
$487$	−293.375	−	5597.93i	−0.0272979	−	0.520875i	−0.977720	−	0.209913i	$-0.932682\pi$
$487$	−293.375	−	5597.93i	−0.0272979	−	0.520875i	0.950422	−	0.310962i	$-0.100651\pi$
$488$	890.651	−	578.396i	0.0826186	−	0.0536532i
$489$	−24.5371	+	75.5173i	−0.00226913	+	0.00698366i
$490$	−7829.28	+	15633.0i	−0.721818	+	1.44128i
$491$	1400.14	+	4309.20i	0.128692	+	0.396073i	0.994556	−	0.104207i	$-0.0332305\pi$
$491$	1400.14	+	4309.20i	0.128692	+	0.396073i	−0.865864	+	0.500280i	$0.833231\pi$
$492$	7206.24	+	5835.50i	0.660330	+	0.534725i
$493$	−1275.44	−	341.752i	−0.116517	−	0.0312206i
$494$	−6940.72	+	15589.1i	−0.632141	+	1.41981i
$495$	−7850.12	+	520.497i	−0.712801	+	0.0472618i
$496$	−195.014	+	268.413i	−0.0176540	+	0.0242986i
$497$	13547.6	−	11490.0i	1.22272	−	1.03702i
$498$	4991.37	−	2543.23i	0.449134	−	0.228845i
$499$	−7896.51	−	4559.05i	−0.708410	−	0.409000i	0.102062	−	0.994778i	$-0.467456\pi$
$499$	−7896.51	−	4559.05i	−0.708410	−	0.409000i	−0.810472	+	0.585778i	$0.800789\pi$
$500$	−1675.53	−	17790.8i	−0.149864	−	1.59126i
$501$	−1014.04	−	1756.36i	−0.0904269	−	0.156624i
$502$	−273.649	+	5221.53i	−0.0243298	+	0.464240i
$503$	−3966.01	+	628.155i	−0.351562	+	0.0556820i	−0.329718	−	0.944079i	$-0.606954\pi$
$503$	−3966.01	+	628.155i	−0.351562	+	0.0556820i	−0.0218440	+	0.999761i	$0.506954\pi$
$504$	7838.99	+	5427.56i	0.692810	+	0.479688i
$505$	8979.10	+	13416.2i	0.791217	+	1.18220i
$506$	1822.91	+	17343.8i	0.160154	+	1.52377i
$507$	371.213	−	1385.39i	0.0325171	−	0.121355i
$508$	−7605.67	−	19813.5i	−0.664266	−	1.73047i
$509$	−12427.8	−	2641.61i	−1.08222	−	0.230034i	−0.367911	−	0.929861i	$-0.619927\pi$
$509$	−12427.8	−	2641.61i	−1.08222	−	0.230034i	−0.714312	+	0.699827i	$0.753260\pi$
$510$	−428.142	−	239.345i	−0.0371734	−	0.0207811i
$511$	−2018.02	−	2141.32i	−0.174701	−	0.185375i
$512$	−902.730	−	459.964i	−0.0779207	−	0.0397026i
$513$	−5052.45	−	7780.08i	−0.434836	−	0.669589i
$514$	24344.5	−	5174.58i	2.08908	−	0.444048i
$515$	16593.2	+	5138.54i	1.41977	+	0.439672i
$516$	−1786.08	+	8402.86i	−0.152380	+	0.716890i
$517$	9291.49	+	1471.63i	0.790405	+	0.125188i
$518$	6827.76	+	23346.1i	0.579140	+	1.98024i
$519$	−3204.67	−	4410.85i	−0.271040	−	0.373054i
$520$	4900.29	−	7779.54i	0.413253	−	0.656068i
$521$	−19453.5	−	2044.64i	−1.63584	−	0.171934i	−0.758456	−	0.651724i	$-0.774046\pi$
$521$	−19453.5	−	2044.64i	−1.63584	−	0.171934i	−0.877383	+	0.479791i	$0.840713\pi$
$522$	17148.0	+	21176.1i	1.43783	+	1.77558i
$523$	−19322.1	−	1012.63i	−1.61548	−	0.0846637i	−0.776965	−	0.629544i	$-0.783242\pi$
$523$	−19322.1	−	1012.63i	−1.61548	−	0.0846637i	−0.838514	+	0.544880i	$0.816575\pi$
$524$	−30585.1			−2.54984
$525$	−3588.98	+	2320.82i	−0.298354	+	0.192931i
$526$	19302.2			1.60003
$527$	−616.883	−	32.3295i	−0.0509902	−	0.00267228i
$528$	97.0136	+	119.802i	0.00799616	+	0.00987444i
$529$	−4255.09	−	447.228i	−0.349724	−	0.0367575i
$530$	−12303.4	−	14770.4i	−1.00835	−	1.21054i
$531$	3968.09	+	5461.61i	0.324295	+	0.446353i
$532$	−22850.8	−	5569.57i	−1.86223	−	0.453894i
$533$	14620.6	+	2315.68i	1.18816	+	0.188186i
$534$	−722.746	+	3400.25i	−0.0585698	+	0.275549i
$535$	−11030.7	+	3753.75i	−0.891402	+	0.303343i
$536$	−13073.0	+	2778.76i	−1.05349	+	0.223926i
$537$	−1041.57	−	1603.87i	−0.0837000	−	0.128887i
$538$	−10335.7	−	5266.30i	−0.828259	−	0.422019i
$539$	9863.69	+	2716.16i	0.788236	+	0.217056i
$540$	5599.27	+	12121.6i	0.446212	+	0.965982i
$541$	−1764.74	−	375.107i	−0.140244	−	0.0298098i	0.137255	−	0.990536i	$-0.456172\pi$
$541$	−1764.74	−	375.107i	−0.140244	−	0.0298098i	−0.277499	+	0.960726i	$0.589505\pi$
$542$	−13890.6	−	36186.2i	−1.10083	−	2.86777i
$543$	49.5423	−	184.894i	0.00391540	−	0.0146125i
$544$	−102.067	−	971.102i	−0.00804427	−	0.0765361i
$545$	9514.96	−	12088.5i	0.747846	−	0.950117i
$546$	−5854.83	−	481.147i	−0.458908	−	0.0377128i
$547$	−13626.3	+	2158.19i	−1.06512	+	0.168698i	−0.664304	−	0.747463i	$-0.731272\pi$
$547$	−13626.3	+	2158.19i	−1.06512	+	0.168698i	−0.400812	+	0.916160i	$0.631272\pi$
$548$	45.1918	−	862.310i	0.00352280	−	0.0672191i
$549$	574.045	+	994.276i	0.0446260	+	0.0772944i
$550$	−16291.4	+	4852.59i	−1.26303	+	0.376209i
$551$	−21790.4	−	12580.7i	−1.68476	−	0.972695i
$552$	4603.39	−	2345.55i	0.354952	−	0.180857i
$553$	6640.63	−	1207.05i	0.510648	−	0.0928191i
$554$	6078.60	−	8366.48i	0.466165	−	0.641621i
$555$	−1459.28	+	5764.21i	−0.111609	+	0.440860i
$556$	6351.60	−	14265.9i	0.484474	−	1.08815i
$557$	−13960.5	−	3740.71i	−1.06199	−	0.284558i	−0.314790	−	0.949161i	$-0.601934\pi$
$557$	−13960.5	−	3740.71i	−1.06199	−	0.284558i	−0.747197	+	0.664603i	$0.768601\pi$
$558$	9906.68	+	8022.27i	0.751583	+	0.608620i
$559$	4237.84	+	13042.7i	0.320647	+	0.986849i
$560$	−537.808	−	216.247i	−0.0405831	−	0.0163181i
$561$	−88.6941	+	272.972i	−0.00667499	+	0.0205435i
$562$	−26700.2	+	17339.3i	−2.00405	+	1.30145i
$563$	125.535	+	2395.36i	0.00939731	+	0.179311i	0.999295	+	0.0375311i	$0.0119493\pi$
$563$	125.535	+	2395.36i	0.00939731	+	0.179311i	−0.989898	+	0.141780i	$0.954717\pi$
$564$	−1547.93	−	7282.45i	−0.115567	−	0.543699i
$565$	−2020.84	−	866.410i	−0.150474	−	0.0645135i
$566$	33355.5	−	10837.9i	2.47710	−	0.804858i
$567$	−5260.92	+	6807.34i	−0.389661	+	0.504200i
$568$	−14800.4	−	14800.4i	−1.09333	−	1.09333i
$569$	25693.9	−	2700.53i	1.89305	−	0.198967i	0.914441	−	0.404718i	$-0.132630\pi$
$569$	25693.9	−	2700.53i	1.89305	−	0.198967i	0.978604	+	0.205751i	$0.0659637\pi$
$570$	−6700.01	−	6516.98i	−0.492338	−	0.478888i
$571$	−757.194	+	7204.22i	−0.0554949	+	0.527998i	0.931095	+	0.364778i	$0.118855\pi$
$571$	−757.194	+	7204.22i	−0.0554949	+	0.527998i	−0.986590	+	0.163221i	$0.947812\pi$
$572$	−13417.7	−	5150.59i	−0.980812	−	0.376498i
$573$	−3689.34	−	7240.75i	−0.268978	−	0.527900i
$574$	753.663	+	33159.4i	0.0548036	+	2.41123i
$575$	−1281.91	−	15978.7i	−0.0929729	−	1.15888i
$576$	−9810.89	+	16993.0i	−0.709700	+	1.22924i
$577$	8129.87	+	5279.60i	0.586570	+	0.380923i	0.803536	−	0.595256i	$-0.202949\pi$
$577$	8129.87	+	5279.60i	0.586570	+	0.380923i	−0.216966	+	0.976179i	$0.569616\pi$
$578$	−17311.3	+	14018.4i	−1.24577	+	1.00881i
$579$	−3415.03	+	1520.47i	−0.245119	+	0.109134i
$580$	28457.9	+	22399.5i	2.03733	+	1.60360i
$581$	11371.3	+	4756.26i	0.811983	+	0.339626i
$582$	1637.97	−	1637.97i	0.116660	−	0.116660i
$583$	−7079.04	+	8741.89i	−0.502889	+	0.621016i
$584$	−2319.86	+	2576.47i	−0.164378	+	0.182560i
$585$	8121.56	+	5730.53i	0.573992	+	0.405005i
$586$	15481.1	−	13939.3i	1.09133	−	0.982637i
$587$	−1987.56	+	3900.82i	−0.139754	+	0.274283i	−0.950266	−	0.311439i	$-0.899189\pi$
$587$	−1987.56	+	3900.82i	−0.139754	+	0.274283i	0.810512	+	0.585722i	$0.199189\pi$
$588$	−790.687	−	8058.19i	−0.0554547	−	0.565160i
$589$	−11195.0	−	3637.47i	−0.783160	−	0.254464i
$590$	10974.0	+	9609.22i	0.765748	+	0.670517i
$591$	2342.98	+	2109.63i	0.163075	+	0.146833i
$592$	−752.866	+	288.998i	−0.0522679	+	0.0200638i
$593$	3353.54	+	12515.6i	0.232232	+	0.866700i	0.979377	+	0.202040i	$0.0647570\pi$
$593$	3353.54	+	12515.6i	0.232232	+	0.866700i	−0.747146	+	0.664660i	$0.768576\pi$
$594$	10275.9	−	7465.85i	0.709804	−	0.515703i
$595$	−207.695	−	1059.08i	−0.0143103	−	0.0729712i
$596$	6788.72	+	4932.30i	0.466572	+	0.338985i
$597$	−2204.98	+	5744.16i	−0.151162	+	0.393791i
$598$	12000.1	−	18478.6i	0.820604	−	1.26362i
$599$	10130.3	−	5848.76i	0.691009	−	0.398955i	−0.112981	−	0.993597i	$-0.536040\pi$
$599$	10130.3	−	5848.76i	0.691009	−	0.398955i	0.803990	+	0.594643i	$0.202706\pi$
$600$	3071.76	+	3990.66i	0.209007	+	0.271530i
$601$			3575.72i			0.242690i	0.992610	+	0.121345i	$0.0387207\pi$
$601$			3575.72i			0.242690i	−0.992610	+	0.121345i	$0.961279\pi$
$602$	−27054.8	+	14568.8i	−1.83168	+	0.986343i
$603$	−2260.29	−	14270.9i	−0.152647	−	0.963776i
$604$	6416.42	+	14411.5i	0.432252	+	0.970854i
$605$	−2300.70	−	4364.89i	−0.154606	−	0.293319i
$606$	−11103.1	−	4943.40i	−0.744276	−	0.331373i
$607$	6286.53	−	1684.47i	0.420367	−	0.112637i	−0.0424340	−	0.999099i	$-0.513511\pi$
$607$	6286.53	−	1684.47i	0.420367	−	0.112637i	0.462801	+	0.886462i	$0.346845\pi$
$608$	2910.73	−	18377.6i	0.194154	−	1.22584i
$609$	1607.95	−	8511.46i	0.106991	−	0.566341i
$610$	1685.24	+	1820.31i	0.111858	+	0.120823i
$611$	−7952.86	−	8832.54i	−0.526576	−	0.584822i
$612$	−1570.11	+	82.2858i	−0.103706	+	0.00543497i
$613$	20669.8	−	1083.26i	1.36190	−	0.0713741i	0.642668	−	0.766145i	$-0.277828\pi$
$613$	20669.8	−	1083.26i	1.36190	−	0.0713741i	0.719231	+	0.694771i	$0.244494\pi$
$614$	−16067.4	−	17844.6i	−1.05607	−	1.17288i
$615$	−3956.38	+	7077.19i	−0.259409	+	0.464032i
$616$	2237.76	−	11845.3i	0.146367	−	0.774774i
$617$	−2032.48	+	12832.6i	−0.132617	+	0.837311i	0.828262	+	0.560341i	$0.189330\pi$
$617$	−2032.48	+	12832.6i	−0.132617	+	0.837311i	−0.960879	+	0.276969i	$0.910670\pi$
$618$	−12631.9	+	3384.72i	−0.822218	+	0.220313i
$619$	12783.8	+	5691.70i	0.830086	+	0.369578i	0.777379	−	0.629032i	$-0.216549\pi$
$619$	12783.8	+	5691.70i	0.830086	+	0.369578i	0.0527064	+	0.998610i	$0.483215\pi$
$620$	15201.1	+	7482.04i	0.984662	+	0.484654i
$621$	4871.83	+	10942.3i	0.314814	+	0.707084i
$622$	2087.56	+	13180.4i	0.134572	+	0.849653i
$623$	−6734.39	+	3626.40i	−0.433078	+	0.233208i
$624$		−	194.763i		−	0.0124948i
$625$	15080.3	−	4089.76i	0.965137	−	0.261745i
$626$	372.859	−	215.270i	0.0238058	−	0.0137443i
$627$	−2978.79	+	4586.94i	−0.189731	+	0.292160i
$628$	3847.91	−	10024.2i	0.244504	−	0.636954i
$629$	−1214.72	−	882.544i	−0.0770016	−	0.0559449i
$630$	−9378.69	+	20200.4i	−0.593105	+	1.27747i
$631$	14962.9	−	10871.2i	0.944000	−	0.685856i	−0.00538002	−	0.999986i	$-0.501713\pi$
$631$	14962.9	−	10871.2i	0.944000	−	0.685856i	0.949380	+	0.314129i	$0.101713\pi$
$632$	−2058.33	−	7681.77i	−0.129550	−	0.483488i
$633$	6261.18	−	2403.44i	0.393143	−	0.150913i
$634$	−3816.19	−	3436.12i	−0.239054	−	0.215245i
$635$	15941.1	−	9500.32i	0.996226	−	0.593714i
$636$	8466.74	+	2751.01i	0.527874	+	0.171517i
$637$	−7525.15	−	10509.4i	−0.468065	−	0.653688i
$638$	15640.4	−	30696.1i	0.970550	−	1.90481i
$639$	16816.0	−	15141.2i	1.04105	−	0.937366i
$640$	−7584.73	+	24492.3i	−0.468458	+	1.51273i
$641$	−18245.1	+	20263.2i	−1.12424	+	1.24860i	−0.158987	+	0.987281i	$0.550823\pi$
$641$	−18245.1	+	20263.2i	−1.12424	+	1.24860i	−0.965254	+	0.261315i	$0.915844\pi$
$642$	5520.53	−	6817.28i	0.339373	−	0.419091i
$643$	10430.4	−	10430.4i	0.639711	−	0.639711i	−0.310773	−	0.950484i	$-0.600588\pi$
$643$	10430.4	−	10430.4i	0.639711	−	0.639711i	0.950484	+	0.310773i	$0.100588\pi$
$644$	28016.2	+	11718.3i	1.71428	+	0.717026i
$645$	−7505.98	−	289.216i	−0.458214	−	0.0176556i
$646$	2156.14	−	959.977i	0.131319	−	0.0584672i
$647$	−7541.93	+	6107.33i	−0.458275	+	0.371104i	−0.830481	−	0.557046i	$-0.811935\pi$
$647$	−7541.93	+	6107.33i	−0.458275	+	0.371104i	0.372207	+	0.928150i	$0.378601\pi$
$648$	8501.74	+	5521.09i	0.515401	+	0.334705i
$649$	4267.69	−	7391.85i	0.258122	−	0.447081i
$650$	19854.1	+	8188.62i	1.19806	+	0.494129i
$651$	−92.0790	−	4051.26i	−0.00554357	−	0.243904i
$652$	249.666	+	489.996i	0.0149964	+	0.0294321i
$653$	2456.09	+	942.803i	0.147188	+	0.0565004i	0.430847	−	0.902425i	$-0.358215\pi$
$653$	2456.09	+	942.803i	0.147188	+	0.0565004i	−0.283658	+	0.958925i	$0.591548\pi$
$654$	−1210.63	+	11518.4i	−0.0723846	+	0.688694i
$655$	−4548.95	−	26353.7i	−0.271362	−	1.57210i
$656$	−1093.61	+	114.943i	−0.0650891	+	0.00684114i
$657$	−2650.30	−	2650.30i	−0.157379	−	0.157379i
$658$	16284.8	−	21071.5i	0.964811	−	1.24841i
$659$	10653.1	−	3461.41i	0.629723	−	0.204609i	0.0232705	−	0.999729i	$-0.492592\pi$
$659$	10653.1	−	3461.41i	0.629723	−	0.204609i	0.606452	+	0.795120i	$0.292592\pi$
$660$	5186.01	−	5922.56i	0.305856	−	0.349296i
$661$	5341.55	+	25130.0i	0.314315	+	1.47874i	0.797554	+	0.603248i	$0.206127\pi$
$661$	5341.55	+	25130.0i	0.314315	+	1.47874i	−0.483238	+	0.875489i	$0.660540\pi$
$662$	−825.558	−	15752.6i	−0.0484686	−	0.924836i
$663$	304.124	−	197.500i	0.0178148	−	0.0115690i
$664$	4488.00	−	13812.7i	0.262302	−	0.807281i
$665$	1400.41	−	20517.8i	0.0816625	−	1.19646i
$666$	9574.75	+	29468.0i	0.557078	+	1.71451i
$667$	25247.7	+	20445.2i	1.46566	+	1.18687i
$668$	−13567.5	−	3635.40i	−0.785841	−	0.210566i
$669$	−3321.62	+	7460.47i	−0.191960	+	0.431149i
$670$	−11590.4	−	28987.8i	−0.668323	−	1.67148i
$671$	853.207	−	1174.34i	0.0490875	−	0.0675631i
$672$	6302.25	−	1145.54i	0.361778	−	0.0657594i
$673$	28190.4	−	14363.8i	1.61465	−	0.822707i	0.615245	−	0.788336i	$-0.289057\pi$
$673$	28190.4	−	14363.8i	1.61465	−	0.822707i	0.999409	−	0.0343709i	$-0.0109428\pi$
$674$	−32867.5	−	18976.0i	−1.87835	−	1.08447i
$675$	−9611.81	+	6627.48i	−0.548087	+	0.377914i
$676$	−4966.71	−	8602.59i	−0.282585	−	0.489451i
$677$	−1006.65	+	19208.1i	−0.0571475	+	1.09044i	0.808084	+	0.589067i	$0.200505\pi$
$677$	−1006.65	+	19208.1i	−0.0571475	+	1.09044i	−0.865232	+	0.501372i	$0.832829\pi$
$678$	1634.95	−	258.951i	0.0926106	−	0.0146681i
$679$	5079.74	+	417.450i	0.287103	+	0.0235939i
$680$	−1223.66	+	346.108i	−0.0690075	+	0.0195186i
$681$	−837.227	−	7965.69i	−0.0471110	−	0.448232i
$682$	4171.40	−	15567.9i	0.234210	−	0.874082i
$683$	−1345.79	−	3505.89i	−0.0753954	−	0.196412i	0.890703	−	0.454586i	$-0.150213\pi$
$683$	−1345.79	−	3505.89i	−0.0753954	−	0.196412i	−0.966098	+	0.258174i	$0.916879\pi$
$684$	−29305.4	−	6229.06i	−1.63819	−	0.348207i
$685$	749.733	−	89.3127i	0.0418187	−	0.00498170i
$686$	20152.9	−	20800.6i	1.12164	−	1.15768i
$687$	3030.26	+	1543.99i	0.168285	+	0.0857453i
$688$	−554.849	−	854.393i	−0.0307463	−	0.0473451i
$689$	13901.2	−	2954.80i	0.768643	−	0.163380i
$690$	7228.06	+	9664.27i	0.398794	+	0.533206i
$691$	5627.10	−	26473.4i	0.309790	−	1.45745i	−0.497589	−	0.867413i	$-0.665781\pi$
$691$	5627.10	−	26473.4i	0.309790	−	1.45745i	0.807378	−	0.590034i	$-0.200886\pi$
$692$	−37295.5	−	5907.03i	−2.04879	−	0.324496i
$693$	12661.6	+	3086.10i	0.694048	+	0.169165i
$694$	−13264.9	−	18257.6i	−0.725546	−	0.998628i
$695$	13236.9	+	3351.08i	0.722454	+	0.182897i
$696$	−10150.4	−	1066.85i	−0.552802	−	0.0581018i
$697$	−1288.47	−	1591.12i	−0.0700203	−	0.0864679i
$698$	19531.7	+	1023.61i	1.05915	+	0.0555077i
$699$	9441.50			0.510888
$700$	−6210.54	+	28942.1i	−0.335338	+	1.56272i
$701$	−12815.5			−0.690491			−0.345245	−	0.938512i	$-0.612204\pi$
$701$	−12815.5			−0.690491			−0.345245	+	0.938512i	$0.612204\pi$
$702$	−16025.5	−	839.861i	−0.861601	−	0.0451546i
$703$	−18005.6	−	22235.1i	−0.965996	−	1.19291i
$704$	24672.5	+	2593.18i	1.32085	+	0.138827i
$705$	6044.71	−	2416.90i	0.322918	−	0.129115i
$706$	10710.1	+	14741.2i	0.570936	+	0.785826i
$707$	−7506.50	−	25666.9i	−0.399308	−	1.36535i
$708$	−6671.90	−	1056.73i	−0.354160	−	0.0560935i
$709$	4102.88	−	19302.5i	0.217330	−	1.02246i	−0.725252	−	0.688483i	$-0.758277\pi$
$709$	4102.88	−	19302.5i	0.217330	−	1.02246i	0.942582	−	0.333974i	$-0.108390\pi$
$710$	28187.5	−	39948.5i	1.48994	−	2.11161i
$711$	8409.73	−	1787.54i	0.443586	−	0.0942871i
$712$	4908.48	+	7558.40i	0.258361	+	0.397841i
$713$	13542.0	+	6900.01i	0.711294	+	0.362423i
$714$	557.260	+	591.308i	0.0292086	+	0.0309932i
$715$	2442.38	−	12327.5i	0.127748	−	0.644786i
$716$	−12955.5	−	2753.78i	−0.676215	−	0.143734i
$717$	−1335.07	−	3477.98i	−0.0695386	−	0.181154i
$718$	12163.0	−	45393.1i	0.632201	−	2.35941i
$719$	3525.63	+	33544.1i	0.182870	+	1.73990i	0.573373	+	0.819294i	$0.305635\pi$
$719$	3525.63	+	33544.1i	0.182870	+	1.73990i	−0.390503	+	0.920602i	$0.627699\pi$
$720$	−692.935	−	255.041i	−0.0358669	−	0.0132011i
$721$	−23657.3	−	16379.9i	−1.22198	−	0.846073i
$722$	13534.2	−	2143.60i	0.697631	−	0.110494i
$723$	−536.644	+	10239.8i	−0.0276044	+	0.526724i
$724$	−662.860	−	1148.11i	−0.0340262	−	0.0589352i
$725$	−15068.0	+	27852.3i	−0.771876	+	1.42677i
$726$	3217.00	+	1857.33i	0.164454	+	0.0949478i
$727$	−2372.21	+	1208.70i	−0.121018	+	0.0616619i	−0.513452	−	0.858119i	$-0.671633\pi$
$727$	−2372.21	+	1208.70i	−0.121018	+	0.0616619i	0.392433	+	0.919780i	$0.371633\pi$
$728$	−11615.3	+	9851.19i	−0.591335	+	0.501524i
$729$	−3705.01	+	5099.50i	−0.188234	+	0.259082i
$730$	−6852.30	−	4316.22i	−0.347418	−	0.218836i
$731$	771.492	−	1732.80i	0.0390351	−	0.0876743i
$732$	−1109.65	−	297.330i	−0.0560299	−	0.0150132i
$733$	26264.7	+	21268.7i	1.32348	+	1.07173i	0.991727	+	0.128363i	$0.0409723\pi$
$733$	26264.7	+	21268.7i	1.32348	+	1.07173i	0.331750	+	0.943367i	$0.392361\pi$
$734$	15038.7	+	46284.3i	0.756250	+	2.32750i
$735$	6825.75	−	1879.80i	0.342547	−	0.0943367i
$736$	−7423.99	+	22848.7i	−0.371810	+	1.14431i
$737$	−15320.9	+	9949.48i	−0.765741	+	0.497278i
$738$	2211.20	+	42192.3i	0.110292	+	2.10450i
$739$	−2451.08	−	11531.4i	−0.122009	−	0.574005i	−0.996099	−	0.0882420i	$-0.971875\pi$
$739$	−2451.08	−	11531.4i	−0.122009	−	0.574005i	0.874091	−	0.485763i	$-0.161458\pi$
$740$	21082.6	+	35375.6i	1.04731	+	1.75734i
$741$	6571.80	−	2135.31i	0.325804	−	0.105860i
$742$	12084.3	+	29461.6i	0.597882	+	1.45764i
$743$	12667.3	+	12667.3i	0.625463	+	0.625463i	0.946923	−	0.321460i	$-0.104174\pi$
$743$	12667.3	+	12667.3i	0.625463	+	0.625463i	−0.321460	+	0.946923i	$0.604174\pi$
$744$	−4748.61	+	499.099i	−0.233995	+	0.0245939i
$745$	−3240.23	+	6583.10i	−0.159346	+	0.323740i
$746$	1997.08	−	19001.0i	0.0980139	−	0.932540i
$747$	14658.3	+	5626.78i	0.717962	+	0.275600i
$748$	902.466	+	1771.19i	0.0441142	+	0.0865790i
$749$	19296.5	−	438.580i	0.941359	−	0.0213957i
$750$	−7965.31	+	8656.21i	−0.387803	+	0.421440i
$751$	−4859.13	+	8416.26i	−0.236101	+	0.408940i	−0.959592	−	0.281394i	$-0.909203\pi$
$751$	−4859.13	+	8416.26i	−0.236101	+	0.408940i	0.723491	+	0.690334i	$0.242536\pi$
$752$	740.471	+	480.867i	0.0359072	+	0.0233184i
$753$	1645.44	−	1332.45i	0.0796325	−	0.0644851i
$754$	−39763.0	+	17703.6i	−1.92053	+	0.855076i
$755$	−11463.4	+	7672.15i	−0.552576	+	0.369826i
$756$	−2811.21	−	21938.8i	−0.135242	−	1.05543i
$757$	−2045.34	+	2045.34i	−0.0982025	+	0.0982025i	−0.754501	−	0.656299i	$-0.772121\pi$
$757$	−2045.34	+	2045.34i	−0.0982025	+	0.0982025i	0.656299	+	0.754501i	$0.272121\pi$
$758$	4366.84	−	5392.60i	0.209249	−	0.258401i
$759$	4725.28	−	5247.96i	0.225977	−	0.250973i
$760$	−24229.8	+	335.544i	−1.15645	+	0.0160151i
$761$	499.725	−	449.955i	0.0238042	−	0.0214334i	−0.657143	−	0.753766i	$-0.728235\pi$
$761$	499.725	−	449.955i	0.0238042	−	0.0214334i	0.680947	+	0.732333i	$0.261568\pi$
$762$	−6342.69	+	12448.2i	−0.301537	+	0.591800i
$763$	−21051.4	+	14361.4i	−0.998836	+	0.681412i
$764$	−53527.9	−	17392.3i	−2.53478	−	0.823600i
$765$	−304.425	−	1340.65i	−0.0143876	−	0.0633610i

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.x (of order \(60\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(-4.55296 - 0.238611i) q^{2} +(1.16184 + 1.43476i) q^{3} +(12.7163 + 1.33654i) q^{4} +(0.739681 + 11.1558i) q^{5} +(-4.94748 - 6.80963i) q^{6} +(4.38567 - 17.9935i) q^{7} +(-21.5535 - 3.41373i) q^{8} +(4.90497 - 23.0761i) q^{9} +O(q^{10})\)	\(q+(-4.55296 - 0.238611i) q^{2} +(1.16184 + 1.43476i) q^{3} +(12.7163 + 1.33654i) q^{4} +(0.739681 + 11.1558i) q^{5} +(-4.94748 - 6.80963i) q^{6} +(4.38567 - 17.9935i) q^{7} +(-21.5535 - 3.41373i) q^{8} +(4.90497 - 23.0761i) q^{9} +(-0.705835 - 50.9686i) q^{10} +(-29.1757 + 6.20148i) q^{11} +(12.8568 + 19.7977i) q^{12} +(33.5772 + 17.1084i) q^{13} +(-24.2612 + 80.8772i) q^{14} +(-15.1465 + 14.0226i) q^{15} +(-2.73824 - 0.582032i) q^{16} +(-1.86788 - 4.86599i) q^{17} +(-27.8383 + 103.894i) q^{18} +(-10.3818 - 98.7763i) q^{19} +(-5.50421 + 142.850i) q^{20} +(30.9118 - 14.6133i) q^{21} +(134.316 - 21.2735i) q^{22} +(-6.71157 + 128.064i) q^{23} +(-20.1439 - 34.8902i) q^{24} +(-123.906 + 16.5035i) q^{25} +(-148.793 - 85.9059i) q^{26} +(83.2215 - 42.4035i) q^{27} +(79.8187 - 222.950i) q^{28} +(148.907 - 204.953i) q^{29} +(72.3076 - 60.2303i) q^{30} +(48.2050 - 108.270i) q^{31} +(180.957 + 48.4872i) q^{32} +(-42.7952 - 34.6549i) q^{33} +(7.34330 + 22.6004i) q^{34} +(203.977 + 35.6164i) q^{35} +(93.2153 - 286.887i) q^{36} +(241.596 - 156.894i) q^{37} +(23.6989 + 452.202i) q^{38} +(14.4650 + 68.0525i) q^{39} +(22.1404 - 242.972i) q^{40} +(373.584 - 121.385i) q^{41} +(-144.227 + 59.1578i) q^{42} +(257.326 + 257.326i) q^{43} +(-379.297 + 39.8657i) q^{44} +(261.061 + 37.6501i) q^{45} +(61.1150 - 581.471i) q^{46} +(-294.443 - 113.026i) q^{47} +(-2.34634 - 4.60495i) q^{48} +(-304.532 - 157.827i) q^{49} +(568.076 - 45.5747i) q^{50} +(4.81134 - 8.33348i) q^{51} +(404.113 + 262.434i) q^{52} +(293.082 - 237.333i) q^{53} +(-389.022 + 173.204i) q^{54} +(-90.7635 - 320.892i) q^{55} +(-155.951 + 372.851i) q^{56} +(129.658 - 129.658i) q^{57} +(-726.870 + 897.610i) q^{58} +(-191.477 + 212.657i) q^{59} +(-211.350 + 158.072i) q^{60} +(-36.1653 + 32.5634i) q^{61} +(-245.310 + 481.448i) q^{62} +(-393.707 - 189.461i) q^{63} +(-791.020 - 257.018i) q^{64} +(-166.023 + 387.237i) q^{65} +(186.576 + 167.994i) q^{66} +(571.777 - 219.485i) q^{67} +(-17.2490 - 64.3741i) q^{68} +(-191.539 + 139.161i) q^{69} +(-920.199 - 210.831i) q^{70} +(775.979 + 563.782i) q^{71} +(-184.495 + 480.625i) q^{72} +(86.5291 - 133.243i) q^{73} +(-1137.41 + 656.686i) q^{74} +(-167.638 - 158.600i) q^{75} -1269.95i q^{76} +(-16.3685 + 552.170i) q^{77} +(-49.6205 - 313.292i) q^{78} +(148.229 + 332.928i) q^{79} +(4.46763 - 30.9779i) q^{80} +(-424.375 - 188.944i) q^{81} +(-1729.88 + 463.519i) q^{82} +(-104.113 + 657.345i) q^{83} +(412.616 - 144.512i) q^{84} +(52.9026 - 24.4370i) q^{85} +(-1110.19 - 1233.00i) q^{86} +(467.064 - 24.4778i) q^{87} +(650.008 - 34.0655i) q^{88} +(-276.345 - 306.913i) q^{89} +(-1179.62 - 233.711i) q^{90} +(455.099 - 529.139i) q^{91} +(-256.510 + 1619.54i) q^{92} +(211.348 - 56.6306i) q^{93} +(1313.62 + 584.860i) q^{94} +(1094.25 - 188.881i) q^{95} +(140.676 + 315.964i) q^{96} +(43.0516 + 271.817i) q^{97} +(1348.86 + 791.245i) q^{98} +703.678i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 928 q - 8 q^{2} - 24 q^{3} - 10 q^{4} - 24 q^{7} + 84 q^{8} - 10 q^{9}+O(q^{10}) \) 928 * q - 8 * q^2 - 24 * q^3 - 10 * q^4 - 24 * q^7 + 84 * q^8 - 10 * q^9	\( 928 q - 8 q^{2} - 24 q^{3} - 10 q^{4} - 24 q^{7} + 84 q^{8} - 10 q^{9} - 96 q^{10} - 6 q^{11} - 72 q^{12} - 20 q^{14} - 368 q^{15} - 1670 q^{16} + 120 q^{17} - 14 q^{18} - 30 q^{19} - 12 q^{21} - 880 q^{22} + 296 q^{23} + 32 q^{25} - 48 q^{26} + 226 q^{28} - 200 q^{29} - 38 q^{30} - 18 q^{31} - 964 q^{32} - 1092 q^{33} + 288 q^{35} + 7400 q^{36} - 392 q^{37} + 5424 q^{38} + 2430 q^{39} + 2172 q^{40} - 2098 q^{42} + 1560 q^{43} - 10 q^{44} - 4224 q^{45} - 6 q^{46} + 96 q^{47} + 6232 q^{50} - 16 q^{51} - 8928 q^{52} - 2384 q^{53} - 30 q^{54} + 244 q^{56} + 1556 q^{57} + 640 q^{58} + 4890 q^{59} + 3676 q^{60} - 18 q^{61} + 224 q^{63} - 9700 q^{64} - 1116 q^{65} - 2610 q^{66} - 2404 q^{67} - 13614 q^{68} - 1700 q^{70} - 24 q^{71} - 518 q^{72} - 4200 q^{73} - 16104 q^{75} - 722 q^{77} - 356 q^{78} - 10 q^{79} + 6414 q^{80} - 6810 q^{81} + 1692 q^{82} + 20620 q^{84} + 2712 q^{85} - 6 q^{86} + 9102 q^{87} + 1650 q^{88} + 20370 q^{89} - 12 q^{91} + 1612 q^{92} - 4604 q^{93} - 30 q^{94} + 1652 q^{95} - 2610 q^{96} - 19478 q^{98}+O(q^{100}) \) 928 * q - 8 * q^2 - 24 * q^3 - 10 * q^4 - 24 * q^7 + 84 * q^8 - 10 * q^9 - 96 * q^10 - 6 * q^11 - 72 * q^12 - 20 * q^14 - 368 * q^15 - 1670 * q^16 + 120 * q^17 - 14 * q^18 - 30 * q^19 - 12 * q^21 - 880 * q^22 + 296 * q^23 + 32 * q^25 - 48 * q^26 + 226 * q^28 - 200 * q^29 - 38 * q^30 - 18 * q^31 - 964 * q^32 - 1092 * q^33 + 288 * q^35 + 7400 * q^36 - 392 * q^37 + 5424 * q^38 + 2430 * q^39 + 2172 * q^40 - 2098 * q^42 + 1560 * q^43 - 10 * q^44 - 4224 * q^45 - 6 * q^46 + 96 * q^47 + 6232 * q^50 - 16 * q^51 - 8928 * q^52 - 2384 * q^53 - 30 * q^54 + 244 * q^56 + 1556 * q^57 + 640 * q^58 + 4890 * q^59 + 3676 * q^60 - 18 * q^61 + 224 * q^63 - 9700 * q^64 - 1116 * q^65 - 2610 * q^66 - 2404 * q^67 - 13614 * q^68 - 1700 * q^70 - 24 * q^71 - 518 * q^72 - 4200 * q^73 - 16104 * q^75 - 722 * q^77 - 356 * q^78 - 10 * q^79 + 6414 * q^80 - 6810 * q^81 + 1692 * q^82 + 20620 * q^84 + 2712 * q^85 - 6 * q^86 + 9102 * q^87 + 1650 * q^88 + 20370 * q^89 - 12 * q^91 + 1612 * q^92 - 4604 * q^93 - 30 * q^94 + 1652 * q^95 - 2610 * q^96 - 19478 * q^98

Introduction

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