LMFDB - Embedded newform 175.2.x.a.103.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [175,2,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, 2, names="a")

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

chi := DirichletCharacter("175.3");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 175 = 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
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:	$1.39738203537$
Analytic rank:	$0$
Dimension:	$288$
Relative dimension:	$18$ over $\Q(\zeta_{60})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{60}]$

Embedding invariants

Embedding label			103.13
Character	$\chi$	$=$	175.103
Dual form			175.2.x.a.17.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.857433 + 0.0449361i) q^{2} +(-1.95506 - 2.41430i) q^{3} +(-1.25587 - 0.131998i) q^{4} +(-0.521374 + 2.17444i) q^{5} +(-1.56784 - 2.15795i) q^{6} +(-2.09857 - 1.61121i) q^{7} +(-2.76697 - 0.438245i) q^{8} +(-1.38284 + 6.50575i) q^{9} +O(q^{10})$	\(q+(0.857433 + 0.0449361i) q^{2} +(-1.95506 - 2.41430i) q^{3} +(-1.25587 - 0.131998i) q^{4} +(-0.521374 + 2.17444i) q^{5} +(-1.56784 - 2.15795i) q^{6} +(-2.09857 - 1.61121i) q^{7} +(-2.76697 - 0.438245i) q^{8} +(-1.38284 + 6.50575i) q^{9} +(-0.544753 + 1.84100i) q^{10} +(2.41483 - 0.513288i) q^{11} +(2.13662 + 3.29011i) q^{12} +(-3.07959 - 1.56913i) q^{13} +(-1.72698 - 1.47580i) q^{14} +(6.26905 - 2.99240i) q^{15} +(0.117592 + 0.0249949i) q^{16} +(-1.30681 - 3.40436i) q^{17} +(-1.47803 + 5.51610i) q^{18} +(-0.742133 - 7.06093i) q^{19} +(0.941799 - 2.66199i) q^{20} +(0.212895 + 8.21659i) q^{21} +(2.09362 - 0.331597i) q^{22} +(-0.107322 + 2.04783i) q^{23} +(4.35154 + 7.53709i) q^{24} +(-4.45634 - 2.26739i) q^{25} +(-2.57003 - 1.48381i) q^{26} +(10.1063 - 5.14941i) q^{27} +(2.42286 + 2.30048i) q^{28} +(0.594101 - 0.817710i) q^{29} +(5.50976 - 2.28407i) q^{30} +(-1.48256 + 3.32988i) q^{31} +(5.51171 + 1.47686i) q^{32} +(-5.96037 - 4.82661i) q^{33} +(-0.967525 - 2.97773i) q^{34} +(4.59761 - 3.72317i) q^{35} +(2.59541 - 7.98786i) q^{36} +(0.757805 - 0.492125i) q^{37} +(-0.319038 - 6.08762i) q^{38} +(2.23243 + 10.5028i) q^{39} +(2.39556 - 5.78811i) q^{40} +(2.23957 - 0.727680i) q^{41} +(-0.186678 + 7.05474i) q^{42} +(1.54846 + 1.54846i) q^{43} +(-3.10047 + 0.325873i) q^{44} +(-13.4254 - 6.39882i) q^{45} +(-0.184043 + 1.75105i) q^{46} +(-2.51648 - 0.965986i) q^{47} +(-0.169554 - 0.332768i) q^{48} +(1.80801 + 6.76248i) q^{49} +(-3.71912 - 2.14438i) q^{50} +(-5.66425 + 9.81076i) q^{51} +(3.66045 + 2.37712i) q^{52} +(-0.683987 + 0.553882i) q^{53} +(8.89685 - 3.96114i) q^{54} +(-0.142917 + 5.51851i) q^{55} +(5.10058 + 5.37786i) q^{56} +(-15.5963 + 15.5963i) q^{57} +(0.546147 - 0.674435i) q^{58} +(-0.825876 + 0.917228i) q^{59} +(-8.26812 + 2.93057i) q^{60} +(-8.07138 + 7.26750i) q^{61} +(-1.42082 + 2.78852i) q^{62} +(13.3841 - 11.4247i) q^{63} +(4.43089 + 1.43968i) q^{64} +(5.01758 - 5.87826i) q^{65} +(-4.89372 - 4.40633i) q^{66} +(4.72283 - 1.81293i) q^{67} +(1.19182 + 4.44794i) q^{68} +(5.15389 - 3.74452i) q^{69} +(4.10945 - 2.98577i) q^{70} +(-11.9130 - 8.65529i) q^{71} +(6.67739 - 17.3952i) q^{72} +(4.49475 - 6.92130i) q^{73} +(0.671881 - 0.387911i) q^{74} +(3.23826 + 15.1918i) q^{75} +8.96558i q^{76} +(-5.89471 - 2.81362i) q^{77} +(1.44221 + 9.10574i) q^{78} +(-6.17313 - 13.8651i) q^{79} +(-0.115659 + 0.242664i) q^{80} +(-13.9624 - 6.21645i) q^{81} +(1.95298 - 0.523299i) q^{82} +(0.481396 - 3.03941i) q^{83} +(0.817199 - 10.3471i) q^{84} +(8.08390 - 1.06663i) q^{85} +(1.25812 + 1.39728i) q^{86} +(-3.13570 + 0.164335i) q^{87} +(-6.90671 + 0.361965i) q^{88} +(-6.29169 - 6.98763i) q^{89} +(-11.2238 - 6.08984i) q^{90} +(3.93454 + 8.25478i) q^{91} +(0.405091 - 2.55764i) q^{92} +(10.9378 - 2.93077i) q^{93} +(-2.11430 - 0.941349i) q^{94} +(15.7405 + 2.06766i) q^{95} +(-7.21015 - 16.1943i) q^{96} +(2.78673 + 17.5947i) q^{97} +(1.24637 + 5.87961i) q^{98} +16.4201i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 288 q - 8 q^{2} - 24 q^{3} - 10 q^{4} - 30 q^{5} - 10 q^{7} - 36 q^{8} - 10 q^{9}+O(q^{10}) $ 288 * q - 8 * q^2 - 24 * q^3 - 10 * q^4 - 30 * q^5 - 10 * q^7 - 36 * q^8 - 10 * q^9	$ 288 q - 8 q^{2} - 24 q^{3} - 10 q^{4} - 30 q^{5} - 10 q^{7} - 36 q^{8} - 10 q^{9} - 36 q^{10} - 6 q^{11} - 36 q^{12} - 20 q^{14} - 28 q^{15} - 30 q^{16} - 42 q^{17} - 14 q^{18} - 30 q^{19} - 12 q^{21} + 32 q^{22} - 40 q^{23} + 2 q^{25} - 48 q^{26} + 22 q^{28} - 58 q^{30} - 18 q^{31} + 8 q^{32} - 30 q^{33} - 2 q^{35} + 40 q^{36} - 10 q^{37} + 72 q^{38} + 30 q^{39} - 48 q^{40} + 6 q^{42} - 108 q^{43} - 10 q^{44} + 186 q^{45} - 6 q^{46} - 54 q^{47} - 248 q^{50} - 16 q^{51} + 216 q^{52} + 50 q^{53} - 30 q^{54} + 4 q^{56} - 216 q^{57} - 4 q^{58} + 90 q^{59} + 96 q^{60} - 18 q^{61} - 66 q^{63} - 100 q^{64} + 14 q^{65} - 90 q^{66} + 4 q^{67} + 342 q^{68} - 60 q^{70} - 24 q^{71} + 58 q^{72} - 6 q^{73} + 216 q^{75} - 80 q^{77} - 132 q^{78} - 10 q^{79} - 6 q^{80} - 10 q^{81} + 216 q^{82} + 20 q^{84} - 48 q^{85} - 6 q^{86} - 48 q^{87} - 122 q^{88} + 120 q^{89} - 12 q^{91} - 4 q^{92} + 106 q^{93} - 30 q^{94} - 98 q^{95} - 90 q^{96} + 222 q^{98}+O(q^{100}) $ 288 * q - 8 * q^2 - 24 * q^3 - 10 * q^4 - 30 * q^5 - 10 * q^7 - 36 * q^8 - 10 * q^9 - 36 * q^10 - 6 * q^11 - 36 * q^12 - 20 * q^14 - 28 * q^15 - 30 * q^16 - 42 * q^17 - 14 * q^18 - 30 * q^19 - 12 * q^21 + 32 * q^22 - 40 * q^23 + 2 * q^25 - 48 * q^26 + 22 * q^28 - 58 * q^30 - 18 * q^31 + 8 * q^32 - 30 * q^33 - 2 * q^35 + 40 * q^36 - 10 * q^37 + 72 * q^38 + 30 * q^39 - 48 * q^40 + 6 * q^42 - 108 * q^43 - 10 * q^44 + 186 * q^45 - 6 * q^46 - 54 * q^47 - 248 * q^50 - 16 * q^51 + 216 * q^52 + 50 * q^53 - 30 * q^54 + 4 * q^56 - 216 * q^57 - 4 * q^58 + 90 * q^59 + 96 * q^60 - 18 * q^61 - 66 * q^63 - 100 * q^64 + 14 * q^65 - 90 * q^66 + 4 * q^67 + 342 * q^68 - 60 * q^70 - 24 * q^71 + 58 * q^72 - 6 * q^73 + 216 * q^75 - 80 * q^77 - 132 * q^78 - 10 * q^79 - 6 * q^80 - 10 * q^81 + 216 * q^82 + 20 * q^84 - 48 * q^85 - 6 * q^86 - 48 * q^87 - 122 * q^88 + 120 * q^89 - 12 * q^91 - 4 * q^92 + 106 * q^93 - 30 * q^94 - 98 * q^95 - 90 * q^96 + 222 * 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 $

$2$	0.857433	+	0.0449361i	0.606296	+	0.0317746i	0.353014	−	0.935618i	$-0.385157\pi$
$2$	0.857433	+	0.0449361i	0.606296	+	0.0317746i	0.253282	+	0.967393i	$0.418490\pi$
$3$	−1.95506	−	2.41430i	−1.12875	−	1.39390i	−0.908208	−	0.418519i	$-0.862549\pi$
$3$	−1.95506	−	2.41430i	−1.12875	−	1.39390i	−0.220546	−	0.975377i	$-0.570784\pi$
$4$	−1.25587	−	0.131998i	−0.627936	−	0.0659988i
$5$	−0.521374	+	2.17444i	−0.233165	+	0.972437i
$5$	−0.521374	+	2.17444i	−0.233165	+	0.972437i
$6$	−1.56784	−	2.15795i	−0.640069	−	0.880979i
$7$	−2.09857	−	1.61121i	−0.793186	−	0.608980i
$7$	−2.09857	−	1.61121i	−0.793186	−	0.608980i
$8$	−2.76697	−	0.438245i	−0.978272	−	0.154943i
$9$	−1.38284	+	6.50575i	−0.460946	+	2.16858i
$10$	−0.544753	+	1.84100i	−0.172266	+	0.582176i
$11$	2.41483	−	0.513288i	0.728099	−	0.154762i	0.171074	−	0.985258i	$-0.445276\pi$
$11$	2.41483	−	0.513288i	0.728099	−	0.154762i	0.557025	+	0.830496i	$0.311943\pi$
$12$	2.13662	+	3.29011i	0.616790	+	0.949774i
$13$	−3.07959	−	1.56913i	−0.854124	−	0.435198i	−0.0286171	−	0.999590i	$-0.509110\pi$
$13$	−3.07959	−	1.56913i	−0.854124	−	0.435198i	−0.825506	+	0.564393i	$0.809110\pi$
$14$	−1.72698	−	1.47580i	−0.461556	−	0.394425i
$15$	6.26905	−	2.99240i	1.61866	−	0.772634i
$16$	0.117592	+	0.0249949i	0.0293980	+	0.00624873i
$17$	−1.30681	−	3.40436i	−0.316949	−	0.825679i	−0.995813	−	0.0914154i	$-0.970861\pi$
$17$	−1.30681	−	3.40436i	−0.316949	−	0.825679i	0.678864	−	0.734264i	$-0.262472\pi$
$18$	−1.47803	+	5.51610i	−0.348376	+	1.30016i
$19$	−0.742133	−	7.06093i	−0.170257	−	1.61989i	−0.662246	−	0.749286i	$-0.730397\pi$
$19$	−0.742133	−	7.06093i	−0.170257	−	1.61989i	0.491989	−	0.870601i	$-0.336270\pi$
$20$	0.941799	−	2.66199i	0.210593	−	0.595240i
$21$	0.212895	+	8.21659i	0.0464576	+	1.79301i
$22$	2.09362	−	0.331597i	0.446361	−	0.0706967i
$23$	−0.107322	+	2.04783i	−0.0223782	+	0.427001i	0.964351	+	0.264627i	$0.0852487\pi$
$23$	−0.107322	+	2.04783i	−0.0223782	+	0.427001i	−0.986729	+	0.162375i	$0.948085\pi$
$24$	4.35154	+	7.53709i	0.888254	+	1.53850i
$25$	−4.45634	−	2.26739i	−0.891268	−	0.453477i
$26$	−2.57003	−	1.48381i	−0.504024	−	0.290998i
$27$	10.1063	−	5.14941i	1.94496	−	0.991005i
$28$	2.42286	+	2.30048i	0.457878	+	0.434750i
$29$	0.594101	−	0.817710i	0.110322	−	0.151845i	−0.750286	−	0.661114i	$-0.770084\pi$
$29$	0.594101	−	0.817710i	0.110322	−	0.151845i	0.860608	+	0.509269i	$0.170084\pi$
$30$	5.50976	−	2.28407i	1.00594	−	0.417013i
$31$	−1.48256	+	3.32988i	−0.266275	+	0.598063i	−0.996355	−	0.0852978i	$-0.972816\pi$
$31$	−1.48256	+	3.32988i	−0.266275	+	0.598063i	0.730081	+	0.683361i	$0.239482\pi$
$32$	5.51171	+	1.47686i	0.974342	+	0.261074i
$33$	−5.96037	−	4.82661i	−1.03757	−	0.840205i
$34$	−0.967525	−	2.97773i	−0.165929	−	0.510677i
$35$	4.59761	−	3.72317i	0.777138	−	0.629330i
$36$	2.59541	−	7.98786i	0.432569	−	1.33131i
$37$	0.757805	−	0.492125i	0.124582	−	0.0809048i	−0.480843	−	0.876806i	$-0.659669\pi$
$37$	0.757805	−	0.492125i	0.124582	−	0.0809048i	0.605426	+	0.795902i	$0.293003\pi$
$38$	−0.319038	−	6.08762i	−0.0517549	−	0.987542i
$39$	2.23243	+	10.5028i	0.357475	+	1.68179i
$40$	2.39556	−	5.78811i	0.378772	−	0.915181i
$41$	2.23957	−	0.727680i	0.349762	−	0.113644i	−0.128867	−	0.991662i	$-0.541134\pi$
$41$	2.23957	−	0.727680i	0.349762	−	0.113644i	0.478629	+	0.878017i	$0.341134\pi$
$42$	−0.186678	+	7.05474i	−0.0288051	+	1.08857i
$43$	1.54846	+	1.54846i	0.236138	+	0.236138i	0.815249	−	0.579111i	$-0.196600\pi$
$43$	1.54846	+	1.54846i	0.236138	+	0.236138i	−0.579111	+	0.815249i	$0.696600\pi$
$44$	−3.10047	+	0.325873i	−0.467414	+	0.0491272i
$45$	−13.4254	−	6.39882i	−2.00133	−	0.953880i
$46$	−0.184043	+	1.75105i	−0.0271356	+	0.258178i
$47$	−2.51648	−	0.965986i	−0.367066	−	0.140904i	0.167842	−	0.985814i	$-0.446320\pi$
$47$	−2.51648	−	0.965986i	−0.367066	−	0.140904i	−0.534908	+	0.844910i	$0.679654\pi$
$48$	−0.169554	−	0.332768i	−0.0244730	−	0.0480310i
$49$	1.80801	+	6.76248i	0.258287	+	0.966068i
$50$	−3.71912	−	2.14438i	−0.525963	−	0.303261i
$51$	−5.66425	+	9.81076i	−0.793153	+	1.37378i
$52$	3.66045	+	2.37712i	0.507613	+	0.329647i
$53$	−0.683987	+	0.553882i	−0.0939528	+	0.0760815i	−0.675146	−	0.737684i	$-0.735919\pi$
$53$	−0.683987	+	0.553882i	−0.0939528	+	0.0760815i	0.581193	+	0.813766i	$0.302586\pi$
$54$	8.89685	−	3.96114i	1.21071	−	0.539042i
$55$	−0.142917	+	5.51851i	−0.0192709	+	0.744115i
$56$	5.10058	+	5.37786i	0.681594	+	0.718647i
$57$	−15.5963	+	15.5963i	−2.06578	+	2.06578i
$58$	0.546147	−	0.674435i	0.0717126	−	0.0885576i
$59$	−0.825876	+	0.917228i	−0.107520	+	0.119413i	−0.794502	−	0.607261i	$-0.792268\pi$
$59$	−0.825876	+	0.917228i	−0.107520	+	0.119413i	0.686982	+	0.726674i	$0.258935\pi$
$60$	−8.26812	+	2.93057i	−1.06741	+	0.378335i
$61$	−8.07138	+	7.26750i	−1.03343	+	0.930508i	−0.997627	−	0.0688502i	$-0.978067\pi$
$61$	−8.07138	+	7.26750i	−1.03343	+	0.930508i	−0.0358074	+	0.999359i	$0.511400\pi$
$62$	−1.42082	+	2.78852i	−0.180445	+	0.354143i
$63$	13.3841	−	11.4247i	1.68624	−	1.43938i
$64$	4.43089	+	1.43968i	0.553861	+	0.179960i
$65$	5.01758	−	5.87826i	0.622354	−	0.729108i
$66$	−4.89372	−	4.40633i	−0.602376	−	0.542382i
$67$	4.72283	−	1.81293i	0.576986	−	0.221484i	−0.0523352	−	0.998630i	$-0.516666\pi$
$67$	4.72283	−	1.81293i	0.576986	−	0.221484i	0.629321	+	0.777145i	$0.283333\pi$
$68$	1.19182	+	4.44794i	0.144530	+	0.539392i
$69$	5.15389	−	3.74452i	0.620455	−	0.450787i
$70$	4.10945	−	2.98577i	0.491173	−	0.356867i
$71$	−11.9130	−	8.65529i	−1.41381	−	1.02719i	−0.992754	−	0.120161i	$-0.961659\pi$
$71$	−11.9130	−	8.65529i	−1.41381	−	1.02719i	−0.421057	−	0.907034i	$-0.638341\pi$
$72$	6.67739	−	17.3952i	0.786938	−	2.05004i
$73$	4.49475	−	6.92130i	0.526070	−	0.810077i	−0.471343	−	0.881950i	$-0.656231\pi$
$73$	4.49475	−	6.92130i	0.526070	−	0.810077i	0.997414	+	0.0718724i	$0.0228974\pi$
$74$	0.671881	−	0.387911i	0.0781046	−	0.0450937i
$75$	3.23826	+	15.1918i	0.373922	+	1.75420i
$76$			8.96558i			1.02842i
$77$	−5.89471	−	2.81362i	−0.671765	−	0.320642i
$78$	1.44221	+	9.10574i	0.163298	+	1.03102i
$79$	−6.17313	−	13.8651i	−0.694531	−	1.55994i	−0.822881	−	0.568214i	$-0.807635\pi$
$79$	−6.17313	−	13.8651i	−0.694531	−	1.55994i	0.128350	−	0.991729i	$-0.459032\pi$
$80$	−0.115659	+	0.242664i	−0.0129311	+	0.0271307i
$81$	−13.9624	−	6.21645i	−1.55138	−	0.690717i
$82$	1.95298	−	0.523299i	0.215670	−	0.0577887i
$83$	0.481396	−	3.03941i	0.0528401	−	0.333619i	−0.947080	−	0.320997i	$-0.895982\pi$
$83$	0.481396	−	3.03941i	0.0528401	−	0.333619i	0.999920	−	0.0126222i	$-0.00401788\pi$
$84$	0.817199	−	10.3471i	0.0891638	−	1.12896i
$85$	8.08390	−	1.06663i	0.876822	−	0.115693i
$86$	1.25812	+	1.39728i	0.135667	+	0.150673i
$87$	−3.13570	+	0.164335i	−0.336182	+	0.0176186i
$88$	−6.90671	+	0.361965i	−0.736258	+	0.0385856i
$89$	−6.29169	−	6.98763i	−0.666918	−	0.740687i	0.310831	−	0.950465i	$-0.399393\pi$
$89$	−6.29169	−	6.98763i	−0.666918	−	0.740687i	−0.977749	+	0.209778i	$0.932726\pi$
$90$	−11.2238	−	6.08984i	−1.18309	−	0.641926i
$91$	3.93454	+	8.25478i	0.412452	+	0.865337i
$92$	0.405091	−	2.55764i	0.0422336	−	0.266653i
$93$	10.9378	−	2.93077i	1.13420	−	0.303907i
$94$	−2.11430	−	0.941349i	−0.218074	−	0.0970927i
$95$	15.7405	+	2.06766i	1.61494	+	0.212137i
$96$	−7.21015	−	16.1943i	−0.735883	−	1.65282i
$97$	2.78673	+	17.5947i	0.282949	+	1.78647i	0.562970	+	0.826477i	$0.309659\pi$
$97$	2.78673	+	17.5947i	0.282949	+	1.78647i	−0.280021	+	0.959994i	$0.590341\pi$
$98$	1.24637	+	5.87961i	0.125902	+	0.593931i
$99$			16.4201i			1.65028i
$100$	5.29730	+	3.43577i	0.529730	+	0.343577i
$101$	12.4991	−	7.21639i	1.24371	−	0.718057i	0.273864	−	0.961769i	$-0.411698\pi$
$101$	12.4991	−	7.21639i	1.24371	−	0.718057i	0.969848	+	0.243711i	$0.0783649\pi$
$102$	−5.29757	+	8.15754i	−0.524537	+	0.807717i
$103$	−5.37411	+	14.0000i	−0.529527	+	1.37946i	0.364397	+	0.931244i	$0.381275\pi$
$103$	−5.37411	+	14.0000i	−0.529527	+	1.37946i	−0.893923	+	0.448220i	$0.852058\pi$
$104$	7.83346	+	5.69134i	0.768134	+	0.558082i
$105$	−17.9774	−	3.82098i	−1.75442	−	0.372890i
$106$	−0.611362	+	0.444181i	−0.0593807	+	0.0431426i
$107$	−3.11495	−	11.6252i	−0.301134	−	1.12385i	−0.936223	−	0.351408i	$-0.885703\pi$
$107$	−3.11495	−	11.6252i	−0.301134	−	1.12385i	0.635089	−	0.772439i	$-0.280963\pi$
$108$	−13.3719	+	5.13300i	−1.28671	+	0.493923i
$109$	−0.551684	−	0.496739i	−0.0528417	−	0.0475789i	0.642287	−	0.766464i	$-0.277986\pi$
$109$	−0.551684	−	0.496739i	−0.0528417	−	0.0475789i	−0.695128	+	0.718886i	$0.744653\pi$
$110$	−0.370522	+	4.72533i	−0.0353279	+	0.450542i
$111$	−2.66969	−	0.867435i	−0.253396	−	0.0823333i
$112$	−0.206503	−	0.241919i	−0.0195127	−	0.0228592i
$113$	4.37867	−	8.59362i	0.411911	−	0.808420i	−0.588089	−	0.808796i	$-0.700120\pi$
$113$	4.37867	−	8.59362i	0.411911	−	0.808420i	1.00000		0.000375885i	$0.000119648\pi$
$114$	−14.0736	+	12.6719i	−1.31811	+	1.18683i
$115$	−4.39691	−	1.30105i	−0.410014	−	0.121323i
$116$	−0.854051	+	0.948520i	−0.0792967	+	0.0880679i
$117$	14.4669	−	17.8652i	1.33747	−	1.65163i
$118$	−0.749350	+	0.749350i	−0.0689833	+	0.0689833i
$119$	−2.74270	+	9.24985i	−0.251423	+	0.847932i
$120$	−18.6577	+	5.53250i	−1.70321	+	0.505046i
$121$	−4.48106	+	1.99510i	−0.407369	+	0.181372i
$122$	−7.24724	+	5.86870i	−0.656134	+	0.531327i
$123$	−6.13532	−	3.98433i	−0.553203	−	0.359255i
$124$	2.30144	−	3.98620i	0.206675	−	0.357972i
$125$	7.25370	−	8.50787i	0.648791	−	0.760967i
$126$	11.9894	−	9.19451i	1.06810	−	0.819112i
$127$	−5.04425	−	9.89989i	−0.447605	−	0.878473i	−0.999021	−	0.0442431i	$-0.985912\pi$
$127$	−5.04425	−	9.89989i	−0.447605	−	0.878473i	0.551416	−	0.834230i	$-0.314088\pi$
$128$	−6.91980	−	2.65626i	−0.611629	−	0.234783i
$129$	0.711112	−	6.76578i	0.0626100	−	0.595694i
$130$	4.56638	−	4.81474i	0.400498	−	0.422281i
$131$	14.2099	−	1.49352i	1.24153	−	0.130490i	0.539098	−	0.842243i	$-0.318765\pi$
$131$	14.2099	−	1.49352i	1.24153	−	0.130490i	0.702430	+	0.711753i	$0.252099\pi$
$132$	6.84836	+	6.84836i	0.596073	+	0.596073i
$133$	−9.81921	+	16.0136i	−0.851433	+	1.38855i
$134$	4.13098	−	1.34224i	0.356862	−	0.115952i
$135$	5.92791	+	24.6602i	0.510193	+	2.12242i
$136$	2.12397	+	9.99248i	0.182129	+	0.856848i
$137$	0.0912401	+	1.74096i	0.00779517	+	0.148741i	0.999754	+	0.0221797i	$0.00706059\pi$
$137$	0.0912401	+	1.74096i	0.00779517	+	0.148741i	−0.991959	+	0.126561i	$0.959606\pi$
$138$	4.58737	−	2.97907i	0.390503	−	0.253596i
$139$	3.24021	−	9.97233i	0.274831	−	0.845842i	−0.714433	−	0.699703i	$-0.753315\pi$
$139$	3.24021	−	9.97233i	0.274831	−	0.845842i	0.989264	−	0.146138i	$-0.0466845\pi$
$140$	−6.26546	+	4.06895i	−0.529528	+	0.343889i
$141$	2.58769	+	7.96409i	0.217923	+	0.670697i
$142$	−9.82565	−	7.95666i	−0.824550	−	0.667708i
$143$	−8.24209	−	2.20846i	−0.689238	−	0.184681i
$144$	−0.325221	+	0.730459i	−0.0271018	+	0.0608716i
$145$	1.46831	+	1.71817i	0.121936	+	0.142686i
$146$	4.16496	−	5.73258i	0.344695	−	0.474431i
$147$	12.7919	−	17.5861i	1.05506	−	1.45048i
$148$	−1.01667	+	0.518017i	−0.0835694	+	0.0425808i
$149$	10.5057	+	6.06545i	0.860658	+	0.496901i	0.864233	−	0.503092i	$-0.167804\pi$
$149$	10.5057	+	6.06545i	0.860658	+	0.496901i	−0.00357448	+	0.999994i	$0.501138\pi$
$150$	2.09393	+	13.1715i	0.170969	+	1.07545i
$151$	2.51055	+	4.34839i	0.204305	+	0.353867i	0.949911	−	0.312520i	$-0.101173\pi$
$151$	2.51055	+	4.34839i	0.204305	+	0.353867i	−0.745606	+	0.666387i	$0.767840\pi$
$152$	−1.04096	+	19.8626i	−0.0844326	+	1.61107i
$153$	23.9550	−	3.79410i	1.93665	−	0.306735i
$154$	−4.92788	−	2.67738i	−0.397100	−	0.215749i
$155$	−6.46763	−	4.95983i	−0.519493	−	0.398383i
$156$	−1.41731	−	13.4848i	−0.113476	−	1.07965i
$157$	−1.23630	+	4.61392i	−0.0986672	+	0.368231i	−0.997550	−	0.0699583i	$-0.977713\pi$
$157$	−1.23630	+	4.61392i	−0.0986672	+	0.368231i	0.898883	+	0.438189i	$0.144380\pi$
$158$	−4.67000	−	12.1658i	−0.371525	−	0.967856i
$159$	2.67447	+	0.568476i	0.212099	+	0.0450831i
$160$	−6.08500	+	11.2149i	−0.481061	+	0.886613i
$161$	3.52470	−	4.12459i	0.277785	−	0.325064i
$162$	−11.6925	−	5.95761i	−0.918646	−	0.468074i
$163$	0.608954	+	0.937707i	0.0476969	+	0.0734469i	0.861715	−	0.507393i	$-0.169391\pi$
$163$	0.608954	+	0.937707i	0.0476969	+	0.0734469i	−0.814018	+	0.580840i	$0.802724\pi$
$164$	−2.90866	+	0.618255i	−0.227128	+	0.0482776i
$165$	13.6027	−	10.4440i	1.05897	−	0.813062i
$166$	0.549344	−	2.58446i	0.0426374	−	0.200593i
$167$	−20.0374	−	3.17362i	−1.55054	−	0.245582i	−0.678349	−	0.734740i	$-0.737304\pi$
$167$	−20.0374	−	3.17362i	−1.55054	−	0.245582i	−0.872195	+	0.489158i	$0.837304\pi$
$168$	3.01180	−	22.8284i	0.232366	−	1.76125i
$169$	−0.619519	−	0.852694i	−0.0476553	−	0.0655919i
$170$	6.97933	−	0.551308i	0.535290	−	0.0422834i
$171$	46.9629	+	4.93599i	3.59134	+	0.377465i
$172$	−1.74028	−	2.14906i	−0.132695	−	0.163865i
$173$	−8.89779	−	0.466313i	−0.676486	−	0.0354531i	−0.289001	−	0.957329i	$-0.593323\pi$
$173$	−8.89779	−	0.466313i	−0.676486	−	0.0354531i	−0.387486	+	0.921876i	$0.626656\pi$
$174$	−2.69604			−0.204386
$175$	5.69872	+	11.9384i	0.430782	+	0.902456i
$176$	0.296794			0.0223717
$177$	3.82910	+	0.200675i	0.287813	+	0.0150836i
$178$	−5.08070	−	6.27414i	−0.380815	−	0.470267i
$179$	5.73678	+	0.602960i	0.428787	+	0.0450674i	0.316464	−	0.948604i	$-0.397504\pi$
$179$	5.73678	+	0.602960i	0.428787	+	0.0450674i	0.112323	+	0.993672i	$0.464171\pi$
$180$	16.0159	+	9.80821i	1.19375	+	0.731061i
$181$	−3.29233	−	4.53150i	−0.244717	−	0.336824i	0.668935	−	0.743321i	$-0.266750\pi$
$181$	−3.29233	−	4.53150i	−0.244717	−	0.336824i	−0.913652	+	0.406497i	$0.866750\pi$
$182$	3.00267	+	7.25472i	0.222572	+	0.537756i
$183$	33.3259	+	5.27831i	2.46352	+	0.390184i
$184$	1.19441	−	5.61925i	0.0880529	−	0.414256i
$185$	0.674994	+	1.90438i	0.0496265	+	0.140013i
$186$	9.51012	−	2.02144i	0.697316	−	0.148219i
$187$	−4.90315	−	7.55019i	−0.358554	−	0.552124i
$188$	3.03287	+	1.54532i	0.221195	+	0.112704i
$189$	−29.5056	−	5.47693i	−2.14621	−	0.398388i
$190$	13.4035	+	2.48019i	0.972390	+	0.179932i
$191$	17.0510	+	3.62431i	1.23377	+	0.262246i	0.778236	−	0.627972i	$-0.216115\pi$
$191$	17.0510	+	3.62431i	1.23377	+	0.262246i	0.455535	+	0.890218i	$0.349448\pi$
$192$	−5.18683	−	13.5121i	−0.374327	−	0.975155i
$193$	−3.72157	+	13.8891i	−0.267885	+	0.999759i	0.692576	+	0.721345i	$0.256476\pi$
$193$	−3.72157	+	13.8891i	−0.267885	+	0.999759i	−0.960461	+	0.278415i	$0.910191\pi$
$194$	1.59879	+	15.2115i	0.114787	+	1.09212i
$195$	−24.0015	−	0.621586i	−1.71879	−	0.0445127i
$196$	−1.37800	−	8.73146i	−0.0984286	−	0.623676i
$197$	7.84565	−	1.24263i	0.558979	−	0.0885336i	0.129449	−	0.991586i	$-0.458679\pi$
$197$	7.84565	−	1.24263i	0.558979	−	0.0885336i	0.429530	+	0.903052i	$0.358679\pi$
$198$	−0.737855	+	14.0791i	−0.0524371	+	1.00056i
$199$	3.08282	+	5.33960i	0.218535	+	0.378514i	0.954360	−	0.298657i	$-0.0965388\pi$
$199$	3.08282	+	5.33960i	0.218535	+	0.378514i	−0.735825	+	0.677172i	$0.763205\pi$
$200$	11.3369	+	8.22676i	0.801639	+	0.581720i
$201$	−13.6104	−	7.85795i	−0.960001	−	0.554257i
$202$	11.0415	−	5.62590i	0.776874	−	0.395837i
$203$	−2.56427	+	0.758803i	−0.179976	+	0.0532575i
$204$	8.40857	−	11.5734i	0.588718	−	0.810300i
$205$	0.414641	+	5.24919i	0.0289598	+	0.366619i
$206$	−5.23704	+	11.7626i	−0.364882	+	0.819539i
$207$	−13.1742	−	3.53003i	−0.915673	−	0.245354i
$208$	−0.322914	−	0.261491i	−0.0223901	−	0.0181311i
$209$	−5.41641	−	16.6700i	−0.374661	−	1.15309i
$210$	−15.2427	−	4.08407i	−1.05185	−	0.281828i
$211$	5.44934	−	16.7713i	0.375148	−	1.15459i	−0.568231	−	0.822869i	$-0.692372\pi$
$211$	5.44934	−	16.7713i	0.375148	−	1.15459i	0.943379	−	0.331717i	$-0.107628\pi$
$212$	0.932111	−	0.605320i	0.0640177	−	0.0415736i
$213$	2.39415	+	45.6831i	0.164045	+	3.13016i
$214$	−2.14847	−	10.1078i	−0.146867	−	0.690953i
$215$	−4.17436	+	2.55970i	−0.284689	+	0.174570i
$216$	−30.2205	+	9.81924i	−2.05625	+	0.668115i
$217$	8.47638	−	4.59928i	0.575414	−	0.312219i
$218$	−0.450710	−	0.450710i	−0.0305260	−	0.0305260i
$219$	−25.4976	+	2.67990i	−1.72297	+	0.181091i
$220$	0.907915	−	6.91168i	0.0612116	−	0.465985i
$221$	−1.31744	+	12.5346i	−0.0886204	+	0.843167i
$222$	−2.25010	−	0.863733i	−0.151017	−	0.0579699i
$223$	3.91951	+	7.69248i	0.262470	+	0.515126i	0.984203	−	0.177046i	$-0.0566540\pi$
$223$	3.91951	+	7.69248i	0.262470	+	0.515126i	−0.721733	+	0.692172i	$0.756654\pi$
$224$	−9.18720	−	11.9798i	−0.613846	−	0.800435i
$225$	20.9134	−	25.8564i	1.39423	−	1.72376i
$226$	4.14058	−	7.17169i	0.275427	−	0.477054i
$227$	9.15235	+	5.94360i	0.607463	+	0.394491i	0.811398	−	0.584493i	$-0.198707\pi$
$227$	9.15235	+	5.94360i	0.607463	+	0.394491i	−0.203936	+	0.978984i	$0.565373\pi$
$228$	21.6456	−	17.5282i	1.43351	−	1.16084i
$229$	−8.95229	+	3.98582i	−0.591584	+	0.263390i	−0.680618	−	0.732638i	$-0.738289\pi$
$229$	−8.95229	+	3.98582i	−0.591584	+	0.263390i	0.0890341	+	0.996029i	$0.471622\pi$
$230$	−3.71159	−	1.31314i	−0.244735	−	0.0865860i
$231$	4.73158	+	19.7324i	0.311315	+	1.29830i
$232$	−2.00222	+	2.00222i	−0.131452	+	0.131452i
$233$	2.12463	−	2.62370i	0.139189	−	0.171884i	−0.702785	−	0.711402i	$-0.748060\pi$
$233$	2.12463	−	2.62370i	0.139189	−	0.171884i	0.841974	+	0.539518i	$0.181394\pi$
$234$	13.2072	−	14.6681i	0.863382	−	0.958883i
$235$	3.41250	−	4.96828i	0.222607	−	0.324095i
$236$	1.15827	−	1.04291i	0.0753968	−	0.0678875i
$237$	−21.4056	+	42.0108i	−1.39044	+	2.72890i
$238$	−2.76733	+	7.80787i	−0.179380	+	0.506109i
$239$	−14.2076	−	4.61631i	−0.919010	−	0.298604i	−0.188949	−	0.981987i	$-0.560508\pi$
$239$	−14.2076	−	4.61631i	−0.919010	−	0.298604i	−0.730061	+	0.683382i	$0.760508\pi$
$240$	0.811984	−	0.195188i	0.0524134	−	0.0125993i
$241$	−19.7392	−	17.7732i	−1.27151	−	1.14487i	−0.982240	−	0.187627i	$-0.939920\pi$
$241$	−19.7392	−	17.7732i	−1.27151	−	1.14487i	−0.289271	−	0.957247i	$-0.593413\pi$
$242$	−3.93186	+	1.50930i	−0.252749	+	0.0970214i
$243$	3.48192	+	12.9947i	0.223365	+	0.833610i
$244$	11.0959	−	8.06166i	0.710343	−	0.516095i
$245$	−15.6472	+	0.405625i	−0.999664	+	0.0259144i
$246$	−5.08159	−	3.69199i	−0.323990	−	0.235393i
$247$	−8.79403	+	22.9092i	−0.559551	+	1.45768i
$248$	5.56149	−	8.56395i	0.353155	−	0.543811i
$249$	−8.27921	+	4.78000i	−0.524673	+	0.302920i
$250$	6.60187	−	6.96897i	0.417539	−	0.440756i
$251$		−	6.13565i		−	0.387279i	−0.981073	−	0.193639i	$-0.937971\pi$
$251$		−	6.13565i		−	0.387279i	0.981073	−	0.193639i	$-0.0620292\pi$
$252$	−18.3168	+	12.5813i	−1.15385	+	0.792550i
$253$	0.791961	+	5.00024i	0.0497901	+	0.314363i
$254$	−3.88024	−	8.71516i	−0.243468	−	0.546838i
$255$	−18.3797	−	17.4316i	−1.15098	−	1.09161i
$256$	−14.3262	−	6.37841i	−0.895384	−	0.398651i
$257$	−15.5655	+	4.17077i	−0.970951	+	0.260166i	−0.709230	−	0.704978i	$-0.750957\pi$
$257$	−15.5655	+	4.17077i	−0.970951	+	0.260166i	−0.261722	+	0.965143i	$0.584290\pi$
$258$	0.913759	−	5.76925i	0.0568882	−	0.359178i
$259$	−2.38323	−	0.188224i	−0.148086	−	0.0116957i
$260$	−7.07736	+	6.72004i	−0.438919	+	0.416759i
$261$	4.49827	+	4.99584i	0.278436	+	0.309234i
$262$	12.2512	−	0.642057i	0.756880	−	0.0396664i
$263$	−20.8879	+	1.09469i	−1.28800	+	0.0675012i	−0.683999	−	0.729483i	$-0.739761\pi$
$263$	−20.8879	+	1.09469i	−1.28800	+	0.0675012i	−0.604001	+	0.796984i	$0.706428\pi$
$264$	14.3769	+	15.9672i	0.884839	+	0.982713i
$265$	−0.847767	−	1.77607i	−0.0520779	−	0.109103i
$266$	−9.13890	+	13.2893i	−0.560342	+	0.814822i
$267$	−4.56959	+	28.8512i	−0.279654	+	1.76567i
$268$	−6.17058	+	1.65340i	−0.376928	+	0.100998i
$269$	20.6897	+	9.21166i	1.26148	+	0.561645i	0.924971	−	0.380037i	$-0.124089\pi$
$269$	20.6897	+	9.21166i	1.26148	+	0.561645i	0.336504	+	0.941682i	$0.390755\pi$
$270$	3.97465	+	21.4109i	0.241889	+	1.30302i
$271$	4.69544	+	10.5461i	0.285228	+	0.640632i	0.998162	−	0.0605988i	$-0.0193010\pi$
$271$	4.69544	+	10.5461i	0.285228	+	0.640632i	−0.712935	+	0.701231i	$0.752634\pi$
$272$	−0.0685787	−	0.432989i	−0.00415820	−	0.0262538i
$273$	12.2372	−	25.6377i	0.740632	−	1.55167i
$274$			1.49686i			0.0904286i
$275$	−11.9251	−	3.18797i	−0.719112	−	0.192242i
$276$	−6.96689	+	4.02234i	−0.419357	+	0.242116i
$277$	13.8337	−	21.3021i	0.831189	−	1.27992i	−0.126457	−	0.991972i	$-0.540360\pi$
$277$	13.8337	−	21.3021i	0.831189	−	1.27992i	0.957646	−	0.287947i	$-0.0929728\pi$
$278$	3.22638	−	8.40500i	0.193505	−	0.504098i
$279$	−19.6132	−	14.2498i	−1.17421	−	0.853114i
$280$	−14.3531	+	8.28702i	−0.857763	+	0.495244i
$281$	1.65462	−	1.20215i	0.0987061	−	0.0717142i	−0.537337	−	0.843367i	$-0.680570\pi$
$281$	1.65462	−	1.20215i	0.0987061	−	0.0717142i	0.636044	+	0.771653i	$0.280570\pi$
$282$	1.86089	+	6.94495i	0.110815	+	0.413566i
$283$	19.3529	−	7.42890i	1.15041	−	0.441602i	0.292940	−	0.956131i	$-0.405366\pi$
$283$	19.3529	−	7.42890i	1.15041	−	0.441602i	0.857473	+	0.514528i	$0.172033\pi$
$284$	13.8187	+	12.4424i	0.819990	+	0.738322i
$285$	−25.7816	−	42.0445i	−1.52717	−	2.49050i
$286$	−6.96780	−	2.26398i	−0.412015	−	0.133872i
$287$	−5.87234	−	2.08132i	−0.346633	−	0.122857i
$288$	−17.2299	+	33.8156i	−1.01528	+	1.99260i
$289$	2.75154	−	2.47750i	0.161855	−	0.145735i
$290$	1.18177	+	1.53919i	0.0693959	+	0.0903845i
$291$	37.0306	−	41.1267i	2.17077	−	2.41089i
$292$	−6.55842	+	8.09898i	−0.383803	+	0.473957i
$293$	12.1262	−	12.1262i	0.708422	−	0.708422i	−0.257781	−	0.966203i	$-0.582991\pi$
$293$	12.1262	−	12.1262i	0.708422	−	0.708422i	0.966203	+	0.257781i	$0.0829914\pi$
$294$	11.7584	−	14.5041i	0.685765	−	0.845896i
$295$	−1.56386	−	2.27403i	−0.0910517	−	0.132399i
$296$	−2.31250	+	1.02959i	−0.134411	+	0.0598437i
$297$	21.7618	−	17.6224i	1.26275	−	1.02255i
$298$	8.73535	+	5.67280i	0.506025	+	0.328617i
$299$	3.54381	−	6.13806i	0.204944	−	0.354973i
$300$	−2.06157	−	19.5064i	−0.119025	−	1.12620i
$301$	−0.754663	−	5.74445i	−0.0434981	−	0.331105i
$302$	1.95722	+	3.84127i	0.112626	+	0.221040i
$303$	−41.8591	−	16.0682i	−2.40474	−	0.923094i
$304$	0.0892185	−	0.848857i	0.00511703	−	0.0486853i
$305$	−11.5945	−	21.3398i	−0.663900	−	1.22191i
$306$	20.7103	−	2.17674i	1.18393	−	0.124436i
$307$	3.57700	+	3.57700i	0.204150	+	0.204150i	0.801775	−	0.597625i	$-0.203889\pi$
$307$	3.57700	+	3.57700i	0.204150	+	0.204150i	−0.597625	+	0.801775i	$0.703889\pi$
$308$	7.03161	+	4.31164i	0.400663	+	0.245679i
$309$	44.3069	−	14.3962i	2.52053	−	0.818971i
$310$	−5.32268	−	4.54335i	−0.302308	−	0.258045i
$311$	−0.644209	−	3.03077i	−0.0365298	−	0.171859i	0.956101	−	0.293037i	$-0.0946660\pi$
$311$	−0.644209	−	3.03077i	−0.0365298	−	0.171859i	−0.992631	+	0.121178i	$0.961333\pi$
$312$	−1.57429	−	30.0392i	−0.0891266	−	1.70064i
$313$	−0.292086	+	0.189683i	−0.0165097	+	0.0107215i	−0.552867	−	0.833269i	$-0.686466\pi$
$313$	−0.292086	+	0.189683i	−0.0165097	+	0.0107215i	0.536358	+	0.843991i	$0.319800\pi$
$314$	−1.26737	+	3.90057i	−0.0715220	+	0.220122i
$315$	17.8642	+	35.0594i	1.00654	+	1.97538i
$316$	5.92251	+	18.2276i	0.333167	+	1.02538i
$317$	1.07690	+	0.872053i	0.0604845	+	0.0489794i	0.659086	−	0.752068i	$-0.270943\pi$
$317$	1.07690	+	0.872053i	0.0604845	+	0.0489794i	−0.598601	+	0.801047i	$0.704277\pi$
$318$	2.26763	+	0.607611i	0.127163	+	0.0340731i
$319$	1.01493	−	2.27958i	0.0568253	−	0.127632i
$320$	−5.44064	+	8.88407i	−0.304141	+	0.496634i
$321$	−21.9767	+	30.2483i	−1.22662	+	1.68830i
$322$	3.20754	−	3.37818i	0.178749	−	0.188258i
$323$	−23.0681	+	11.7538i	−1.28354	+	0.653999i
$324$	16.7144	+	9.65007i	0.928579	+	0.536115i
$325$	10.1659	+	13.9752i	0.563901	+	0.775203i
$326$	0.480000	+	0.831384i	0.0265847	+	0.0460461i
$327$	−0.120699	+	2.30308i	−0.00667470	+	0.127361i
$328$	−6.51572	+	1.03199i	−0.359771	+	0.0569821i
$329$	3.72461	+	6.08177i	0.205344	+	0.335299i
$330$	12.1327	−	8.34374i	0.667885	−	0.459308i
$331$	−1.33440	−	12.6959i	−0.0733450	−	0.697831i	−0.967979	−	0.251031i	$-0.919230\pi$
$331$	−1.33440	−	12.6959i	−0.0733450	−	0.697831i	0.894634	−	0.446800i	$-0.147436\pi$
$332$	−1.00577	+	3.75357i	−0.0551986	+	0.206004i
$333$	2.15372	+	5.61062i	0.118023	+	0.307460i
$334$	−17.0381	−	3.62157i	−0.932286	−	0.198163i
$335$	1.47973	+	11.2147i	0.0808463	+	0.612725i
$336$	−0.180338	+	0.971525i	−0.00983826	+	0.0530011i
$337$	2.29665	+	1.17020i	0.125106	+	0.0637448i	0.515423	−	0.856936i	$-0.327635\pi$
$337$	2.29665	+	1.17020i	0.125106	+	0.0637448i	−0.390317	+	0.920680i	$0.627635\pi$
$338$	−0.492879	−	0.758967i	−0.0268091	−	0.0412823i
$339$	−29.3081	+	6.22963i	−1.59180	+	0.338347i
$340$	−10.2931	+	0.272502i	−0.558224	+	0.0147785i
$341$	−1.87094	+	8.80206i	−0.101317	+	0.476658i
$342$	40.0457	+	6.34261i	2.16542	+	0.342969i
$343$	7.10152	−	17.1046i	0.383446	−	0.923563i
$344$	−3.60594	−	4.96315i	−0.194419	−	0.267595i
$345$	5.45511	+	13.1591i	0.293693	+	0.708461i
$346$	−7.60830	−	0.799664i	−0.409025	−	0.0429902i
$347$	3.91924	+	4.83986i	0.210396	+	0.259818i	0.871409	−	0.490557i	$-0.163207\pi$
$347$	3.91924	+	4.83986i	0.210396	+	0.259818i	−0.661013	+	0.750374i	$0.729873\pi$
$348$	3.95973	+	0.207521i	0.212264	+	0.0111243i
$349$	−6.37223			−0.341098			−0.170549	−	0.985349i	$-0.554554\pi$
$349$	−6.37223			−0.341098			−0.170549	+	0.985349i	$0.554554\pi$
$350$	4.34980	+	10.4924i	0.232507	+	0.560844i
$351$	−39.2033			−2.09252
$352$	14.0679	+	0.737268i	0.749822	+	0.0392965i
$353$	0.415853	+	0.513536i	0.0221336	+	0.0273328i	0.788093	−	0.615557i	$-0.211069\pi$
$353$	0.415853	+	0.513536i	0.0221336	+	0.0273328i	−0.765959	+	0.642889i	$0.777735\pi$
$354$	3.27418	+	0.344130i	0.174021	+	0.0182903i
$355$	25.0315	−	21.3914i	1.32853	−	1.13534i
$356$	6.97921	+	9.60606i	0.369897	+	0.509120i
$357$	27.6940	−	11.4623i	1.46572	−	0.606650i
$358$	4.89181	+	0.774787i	0.258540	+	0.0409488i
$359$	−3.89736	+	18.3356i	−0.205695	+	0.967717i	0.747243	+	0.664551i	$0.231377\pi$
$359$	−3.89736	+	18.3356i	−0.205695	+	0.967717i	−0.952938	+	0.303166i	$0.901956\pi$
$360$	34.3433	+	23.5889i	1.81005	+	1.24325i
$361$	−30.7211	+	6.52997i	−1.61690	+	0.343683i
$362$	−2.61932	−	4.03340i	−0.137669	−	0.211991i
$363$	13.5775	+	6.91808i	0.712633	+	0.363105i
$364$	−3.85167	−	10.8863i	−0.201882	−	0.570597i
$365$	12.7065	+	13.3821i	0.665088	+	0.700452i
$366$	28.3376	+	6.02334i	1.48123	+	0.314845i
$367$	−11.1627	−	29.0797i	−0.582686	−	1.51795i	−0.834969	−	0.550296i	$-0.814515\pi$
$367$	−11.1627	−	29.0797i	−0.582686	−	1.51795i	0.252283	−	0.967654i	$-0.418819\pi$
$368$	−0.0638055	+	0.238125i	−0.00332609	+	0.0124131i
$369$	1.63714	+	15.5763i	0.0852260	+	0.810871i
$370$	0.493186	+	1.66321i	0.0256395	+	0.0864661i
$371$	2.32782	−	0.0603148i	0.120854	−	0.00313139i
$372$	−14.1233	+	2.23692i	−0.732260	+	0.115979i
$373$	−0.422082	+	8.05381i	−0.0218546	+	0.417010i	0.965693	+	0.259688i	$0.0836196\pi$
$373$	−0.422082	+	8.05381i	−0.0218546	+	0.417010i	−0.987547	+	0.157323i	$0.949714\pi$
$374$	−3.86484	−	6.69411i	−0.199846	−	0.346144i
$375$	−34.7219	−	0.879210i	−1.79303	−	0.0454022i
$376$	6.53969	+	3.77569i	0.337259	+	0.194716i
$377$	−3.11268	+	1.58599i	−0.160311	+	0.0816826i
$378$	−25.0529	−	6.02197i	−1.28858	−	0.309737i
$379$	−8.68157	+	11.9492i	−0.445942	+	0.613787i	−0.971520	−	0.236959i	$-0.923849\pi$
$379$	−8.68157	+	11.9492i	−0.445942	+	0.613787i	0.525577	+	0.850746i	$0.323849\pi$
$380$	−19.4951	−	4.67442i	−1.00008	−	0.239793i
$381$	−14.0395	+	31.5332i	−0.719264	+	1.61549i
$382$	14.4573	+	3.87381i	0.739698	+	0.198201i
$383$	19.3346	+	15.6568i	0.987950	+	0.800026i	0.979808	−	0.199941i	$-0.0640749\pi$
$383$	19.3346	+	15.6568i	0.987950	+	0.800026i	0.00814217	+	0.999967i	$0.497408\pi$
$384$	7.11561	+	21.8996i	0.363117	+	1.11756i
$385$	9.19139	−	11.3507i	0.468437	−	0.578486i
$386$	−3.81512	+	11.7417i	−0.194185	+	0.597639i
$387$	−12.2152	+	7.93263i	−0.620932	+	0.403238i
$388$	−1.17732	−	22.4645i	−0.0597692	−	1.14046i
$389$	5.93602	+	27.9268i	0.300968	+	1.41594i	0.825427	+	0.564508i	$0.190934\pi$
$389$	5.93602	+	27.9268i	0.300968	+	1.41594i	−0.524459	+	0.851436i	$0.675732\pi$
$390$	−20.5518	−	1.61150i	−1.04068	−	0.0816017i
$391$	7.11180	−	2.31076i	0.359659	−	0.116860i
$392$	−2.03909	−	19.5039i	−0.102990	−	0.985097i
$393$	−31.3871	−	31.3871i	−1.58327	−	1.58327i
$394$	6.78295	−	0.712917i	0.341720	−	0.0359162i
$395$	33.3672	−	6.19419i	1.67889	−	0.311663i
$396$	2.16741	−	20.6215i	0.108916	−	1.03627i
$397$	−7.23706	−	2.77805i	−0.363218	−	0.139426i	0.169913	−	0.985459i	$-0.445651\pi$
$397$	−7.23706	−	2.77805i	−0.363218	−	0.139426i	−0.533131	+	0.846033i	$0.678985\pi$
$398$	2.40337	+	4.71688i	0.120470	+	0.236436i
$399$	57.8587	−	7.60104i	2.89656	−	0.380528i
$400$	−0.467356	−	0.378012i	−0.0233678	−	0.0189006i
$401$	18.2018	−	31.5265i	0.908956	−	1.57436i	0.0934398	−	0.995625i	$-0.470214\pi$
$401$	18.2018	−	31.5265i	0.908956	−	1.57436i	0.815517	−	0.578734i	$-0.196453\pi$
$402$	−11.3169	−	7.34926i	−0.564434	−	0.366548i
$403$	9.79066	−	7.92832i	0.487707	−	0.394938i
$404$	−16.6499	+	7.41300i	−0.828362	+	0.368811i
$405$	20.7969	−	27.1192i	1.03341	−	1.34756i
$406$	−2.23278	+	0.535394i	−0.110811	+	0.0265712i
$407$	1.57737	−	1.57737i	0.0781873	−	0.0781873i
$408$	19.9723	−	24.6638i	0.988778	−	1.22104i
$409$	−7.87770	+	8.74907i	−0.389527	+	0.432614i	−0.905732	−	0.423852i	$-0.860678\pi$
$409$	−7.87770	+	8.74907i	−0.389527	+	0.432614i	0.516204	+	0.856465i	$0.327344\pi$
$410$	0.119649	+	4.51946i	0.00590902	+	0.223200i
$411$	4.02483	−	3.62397i	0.198530	−	0.178757i
$412$	8.59716	−	16.8729i	0.423552	−	0.831267i
$413$	3.21101	−	0.594211i	0.158003	−	0.0292392i
$414$	−11.1374	−	3.61876i	−0.547373	−	0.177852i
$415$	6.35802	+	2.63143i	0.312103	+	0.129172i
$416$	−14.6564	−	13.1967i	−0.718590	−	0.647021i
$417$	−30.4110	+	11.6737i	−1.48923	+	0.571662i
$418$	−3.89512	−	14.5368i	−0.190517	−	0.711018i
$419$	4.95298	−	3.59855i	0.241969	−	0.175801i	−0.460191	−	0.887820i	$-0.652219\pi$
$419$	4.95298	−	3.59855i	0.241969	−	0.175801i	0.702160	+	0.712019i	$0.252219\pi$
$420$	22.0730	+	7.17165i	1.07705	+	0.349940i
$421$	−19.6842	−	14.3014i	−0.959351	−	0.697009i	−0.00635102	−	0.999980i	$-0.502022\pi$
$421$	−19.6842	−	14.3014i	−0.959351	−	0.697009i	−0.953000	+	0.302971i	$0.902022\pi$
$422$	5.42608	−	14.1354i	0.264137	−	0.688101i
$423$	9.76435	−	15.0358i	0.474759	−	0.731065i
$424$	2.13531	−	1.23282i	0.103700	−	0.0598711i
$425$	−1.89541	+	18.1340i	−0.0919407	+	0.879630i
$426$			39.2778i			1.90301i
$427$	28.6478	−	2.24670i	1.38637	−	0.108725i
$428$	2.37749	+	15.0109i	0.114920	+	0.725578i
$429$	10.7819	+	24.2165i	0.520555	+	1.16919i
$430$	−3.69425	+	2.00719i	−0.178153	+	0.0967955i
$431$	2.01719	+	0.898112i	0.0971648	+	0.0432605i	0.454743	−	0.890622i	$-0.349731\pi$
$431$	2.01719	+	0.898112i	0.0971648	+	0.0432605i	−0.357579	+	0.933883i	$0.616398\pi$
$432$	1.31713	−	0.352923i	0.0633703	−	0.0169800i
$433$	−4.68698	+	29.5924i	−0.225242	+	1.42212i	0.572887	+	0.819635i	$0.305824\pi$
$433$	−4.68698	+	29.5924i	−0.225242	+	1.42212i	−0.798129	+	0.602487i	$0.794176\pi$
$434$	7.47459	−	3.56267i	0.358792	−	0.171014i
$435$	1.27753	−	6.90406i	0.0612531	−	0.331024i
$436$	0.627277	+	0.696661i	0.0300411	+	0.0333640i
$437$	14.5392	−	0.761967i	0.695504	−	0.0364498i
$438$	−21.9829	+	1.15207i	−1.05038	+	0.0550482i
$439$	−3.48497	−	3.87046i	−0.166329	−	0.184727i	0.654218	−	0.756306i	$-0.272998\pi$
$439$	−3.48497	−	3.87046i	−0.166329	−	0.184727i	−0.820547	+	0.571579i	$0.806331\pi$
$440$	2.81391	−	15.2069i	0.134148	−	0.724961i
$441$	−46.4952	+	2.41104i	−2.21406	+	0.114811i
$442$	−1.69287	+	10.6884i	−0.0805216	+	0.508393i
$443$	−34.0081	+	9.11243i	−1.61577	+	0.432945i	−0.949756	−	0.312992i	$-0.898669\pi$
$443$	−34.0081	+	9.11243i	−1.61577	+	0.432945i	−0.666016	+	0.745937i	$0.732002\pi$
$444$	3.23829	+	1.44178i	0.153682	+	0.0684239i
$445$	18.4745	−	10.0377i	0.875774	−	0.475833i
$446$	3.01505	+	6.77191i	0.142767	+	0.320659i
$447$	−5.89541	−	37.2221i	−0.278843	−	1.76055i
$448$	−6.97891	−	10.1604i	−0.329722	−	0.480032i
$449$			11.0263i			0.520361i	0.965560	+	0.260181i	$0.0837821\pi$
$449$			11.0263i			0.520361i	−0.965560	+	0.260181i	$0.916218\pi$
$450$	19.0938	−	21.2303i	0.900088	−	1.00081i
$451$	5.03467	−	2.90677i	0.237073	−	0.136874i
$452$	−6.63339	+	10.2145i	−0.312008	+	0.480451i
$453$	5.59005	−	14.5626i	0.262643	−	0.684210i
$454$	7.58044	+	5.50751i	0.355768	+	0.258480i
$455$	−20.0009	+	4.25158i	−0.937655	+	0.199317i
$456$	49.9894	−	36.3194i	2.34097	−	1.70081i
$457$	1.28162	+	4.78308i	0.0599518	+	0.223743i	0.989401	−	0.145206i	$-0.0463844\pi$
$457$	1.28162	+	4.78308i	0.0599518	+	0.223743i	−0.929450	+	0.368949i	$0.879718\pi$
$458$	−7.85509	+	3.01529i	−0.367044	+	0.140895i
$459$	−30.7375	−	27.6762i	−1.43470	−	1.29181i
$460$	5.35023	+	2.21433i	0.249456	+	0.103244i
$461$	9.15490	+	2.97461i	0.426386	+	0.138541i	0.514346	−	0.857583i	$-0.328035\pi$
$461$	9.15490	+	2.97461i	0.426386	+	0.138541i	−0.0879597	+	0.996124i	$0.528035\pi$
$462$	3.17032	+	17.1318i	0.147496	+	0.797044i
$463$	9.49875	−	18.6423i	0.441444	−	0.866383i	−0.557891	−	0.829914i	$-0.688389\pi$
$463$	9.49875	−	18.6423i	0.441444	−	0.866383i	0.999335	−	0.0364685i	$-0.0116109\pi$
$464$	0.0903001	−	0.0813066i	0.00419208	−	0.00377456i
$465$	0.670100	+	25.3116i	0.0310752	+	1.17380i
$466$	1.93962	−	2.15417i	0.0898513	−	0.0997900i
$467$	−0.189940	+	0.234556i	−0.00878937	+	0.0108540i	−0.781522	−	0.623878i	$-0.785556\pi$
$467$	−0.189940	+	0.234556i	−0.00878937	+	0.0108540i	0.772732	+	0.634732i	$0.218890\pi$
$468$	−20.5268	+	20.5268i	−0.948850	+	0.948850i
$469$	−12.8322	−	3.80492i	−0.592536	−	0.175695i
$470$	3.14924	−	4.10662i	0.145264	−	0.189424i
$471$	13.5564	−	6.03570i	0.624647	−	0.278111i
$472$	2.68715	−	2.17601i	0.123686	−	0.100159i
$473$	4.53408	+	2.94447i	0.208477	+	0.135387i
$474$	−20.2416	+	35.0596i	−0.929730	+	1.61034i
$475$	−12.7026	+	33.1486i	−0.582838	+	1.52096i
$476$	4.66544	−	11.2546i	0.213840	−	0.515854i
$477$	−2.65757	−	5.21578i	−0.121682	−	0.238814i
$478$	−11.9746	−	4.59661i	−0.547704	−	0.210244i
$479$	−1.64916	+	15.6907i	−0.0753519	+	0.716926i	0.889998	+	0.455965i	$0.150706\pi$
$479$	−1.64916	+	15.6907i	−0.0753519	+	0.716926i	−0.965350	+	0.260960i	$0.915961\pi$
$480$	38.9726	−	7.23475i	1.77885	−	0.330219i
$481$	−3.10593	+	0.326447i	−0.141618	+	0.0148847i
$482$	−16.1263	−	16.1263i	−0.734535	−	0.734535i
$483$	−16.8490	−	0.445848i	−0.766656	−	0.0202868i
$484$	5.89098	−	1.91410i	0.267772	−	0.0870044i
$485$	−39.7115	−	3.11385i	−1.80320	−	0.141393i
$486$	2.40158	+	11.2985i	0.108938	+	0.512512i
$487$	−0.370620	−	7.07185i	−0.0167944	−	0.320456i	−0.994089	−	0.108570i	$-0.965373\pi$
$487$	−0.370620	−	7.07185i	−0.0167944	−	0.320456i	0.977294	−	0.211886i	$-0.0679605\pi$
$488$	25.5182	−	16.5717i	1.15516	−	0.750167i
$489$	1.07336	−	3.30347i	0.0485391	−	0.149388i
$490$	−13.4347	−	0.355329i	−0.606916	−	0.0160521i
$491$	−6.72096	−	20.6850i	−0.303313	−	0.933500i	−0.980301	−	0.197507i	$-0.936715\pi$
$491$	−6.72096	−	20.6850i	−0.303313	−	0.933500i	0.676989	−	0.735993i	$-0.263285\pi$
$492$	7.17926	+	5.81365i	0.323666	+	0.262100i
$493$	−3.56016	−	0.953942i	−0.160342	−	0.0429634i
$494$	−8.56974	+	19.2480i	−0.385571	+	0.866006i
$495$	−35.7044	−	8.56099i	−1.60479	−	0.384788i
$496$	−0.257567	+	0.354510i	−0.0115651	+	0.0159180i
$497$	11.0548	+	37.3581i	0.495875	+	1.67574i
$498$	−7.31366	+	3.72649i	−0.327733	+	0.166988i
$499$	3.54008	+	2.04386i	0.158476	+	0.0914959i	0.577141	−	0.816645i	$-0.304168\pi$
$499$	3.54008	+	2.04386i	0.158476	+	0.0914959i	−0.418665	+	0.908141i	$0.637502\pi$
$500$	−10.2327	+	9.72732i	−0.457622	+	0.435019i
$501$	31.5123	+	54.5810i	1.40787	+	2.43850i
$502$	0.275713	−	5.26091i	0.0123057	−	0.234806i
$503$	37.4748	−	5.93543i	1.67092	−	0.264648i	0.752020	−	0.659140i	$-0.229079\pi$
$503$	37.4748	−	5.93543i	1.67092	−	0.264648i	0.918899	+	0.394492i	$0.129079\pi$
$504$	−42.0403	+	25.7464i	−1.87262	+	1.14684i
$505$	9.17484	+	30.9410i	0.408275	+	1.37686i
$506$	0.454361	+	4.32296i	0.0201988	+	0.192179i
$507$	−0.847462	+	3.16277i	−0.0376371	+	0.140464i
$508$	5.02817	+	13.0988i	0.223089	+	0.581167i
$509$	28.4939	+	6.05656i	1.26297	+	0.268452i	0.790263	−	0.612768i	$-0.209944\pi$
$509$	28.4939	+	6.05656i	1.26297	+	0.268452i	0.472706	+	0.881220i	$0.343277\pi$
$510$	−14.9760	−	15.7723i	−0.663150	−	0.698411i
$511$	−20.5842	+	7.28288i	−0.910592	+	0.322176i
$512$	1.21138	+	0.617229i	0.0535360	+	0.0272779i
$513$	−43.8598	−	67.5382i	−1.93646	−	2.98188i
$514$	−13.5338	+	2.87670i	−0.596951	+	0.126886i
$515$	−27.6402	−	18.9849i	−1.21797	−	0.836575i
$516$	−1.78613	+	8.40309i	−0.0786301	+	0.369926i
$517$	−6.57270	−	1.04101i	−0.289067	−	0.0457837i
$518$	−2.03500	−	0.268482i	−0.0894126	−	0.0117964i
$519$	16.2699	+	22.3936i	0.714169	+	0.982969i
$520$	−16.4596	+	14.0660i	−0.721802	+	0.616837i
$521$	−10.3649	−	1.08939i	−0.454093	−	0.0477271i	−0.125278	−	0.992122i	$-0.539982\pi$
$521$	−10.3649	−	1.08939i	−0.454093	−	0.0477271i	−0.328815	+	0.944395i	$0.606649\pi$
$522$	3.63247	+	4.48573i	0.158989	+	0.196335i
$523$	−13.4776	−	0.706329i	−0.589333	−	0.0308856i	−0.244661	−	0.969609i	$-0.578677\pi$
$523$	−13.4776	−	0.706329i	−0.589333	−	0.0308856i	−0.344672	+	0.938723i	$0.612010\pi$
$524$	−18.0430			−0.788212
$525$	17.6814	−	37.0986i	0.771681	−	1.61912i
$526$	−17.9591			−0.783055
$527$	13.2735	+	0.695636i	0.578204	+	0.0303024i
$528$	−0.580250	−	0.716549i	−0.0252521	−	0.0311838i
$529$	18.6919	+	1.96460i	0.812692	+	0.0854174i
$530$	−0.647094	−	1.56095i	−0.0281080	−	0.0678034i
$531$	−4.82520	−	6.64132i	−0.209396	−	0.288209i
$532$	14.4454	−	18.8149i	0.626289	−	0.815730i
$533$	−8.03876	−	1.27322i	−0.348198	−	0.0551491i
$534$	−5.21458	+	24.5327i	−0.225657	+	1.06163i
$535$	26.9022	−	0.712212i	1.16308	−	0.0307916i
$536$	−13.8624	+	2.94655i	−0.598767	+	0.127272i
$537$	−9.76003	−	15.0291i	−0.421176	−	0.648555i
$538$	17.3261	+	8.82810i	0.746982	+	0.380606i
$539$	7.83714	+	15.4022i	0.337569	+	0.663420i
$540$	−4.18961	−	31.7526i	−0.180292	−	1.36641i
$541$	11.0515	+	2.34907i	0.475141	+	0.100994i	0.439257	−	0.898362i	$-0.355242\pi$
$541$	11.0515	+	2.34907i	0.475141	+	0.100994i	0.0358843	+	0.999356i	$0.488575\pi$
$542$	3.55212	+	9.25359i	0.152577	+	0.397476i
$543$	−4.50370	+	16.8080i	−0.193272	+	0.721301i
$544$	−2.17501	−	20.6938i	−0.0932528	−	0.887241i
$545$	1.36776	−	0.940615i	0.0585884	−	0.0402915i
$546$	11.6447	−	21.4327i	0.498346	−	0.917237i
$547$	−30.3524	+	4.80735i	−1.29778	+	0.205547i	−0.766826	−	0.641856i	$-0.778165\pi$
$547$	−30.3524	+	4.80735i	−1.29778	+	0.205547i	−0.530950	+	0.847403i	$0.678165\pi$
$548$	0.115217	−	2.19847i	0.00492183	−	0.0939141i
$549$	−36.1191	−	62.5602i	−1.54153	−	2.67000i
$550$	−10.0817	−	3.26934i	−0.429887	−	0.139405i
$551$	−6.21469	−	3.58806i	−0.264755	−	0.152856i
$552$	−15.9017	+	8.10230i	−0.676820	+	0.344857i
$553$	−9.38478	+	39.0431i	−0.399081	+	1.66028i
$554$	12.8187	−	17.6435i	0.544616	−	0.749600i
$555$	3.27809	−	5.35281i	0.139147	−	0.227214i
$556$	−5.38561	+	12.0963i	−0.228401	+	0.512996i
$557$	3.01658	+	0.808291i	0.127817	+	0.0342484i	0.322160	−	0.946685i	$-0.395591\pi$
$557$	3.01658	+	0.808291i	0.127817	+	0.0342484i	−0.194344	+	0.980934i	$0.562258\pi$
$558$	−16.1767	−	13.0996i	−0.684813	−	0.554550i
$559$	−2.33889	−	7.19835i	−0.0989244	−	0.304458i
$560$	0.633702	−	0.322897i	0.0267788	−	0.0136449i
$561$	−8.64245	+	26.5987i	−0.364885	+	1.12300i
$562$	1.47274	−	0.956410i	0.0621239	−	0.0403437i
$563$	1.54206	+	29.4243i	0.0649902	+	1.24009i	0.815315	+	0.579018i	$0.196564\pi$
$563$	1.54206	+	29.4243i	0.0649902	+	1.24009i	−0.750325	+	0.661070i	$0.770103\pi$
$564$	−2.19857	−	10.3435i	−0.0925764	−	0.435538i
$565$	16.4034	+	14.0016i	0.690094	+	0.589053i
$566$	16.9277	−	5.50014i	0.711523	−	0.231188i
$567$	19.2851	+	35.5420i	0.809897	+	1.49262i
$568$	29.1698	+	29.1698i	1.22394	+	1.22394i
$569$	7.94274	−	0.834815i	0.332977	−	0.0349973i	0.0634350	−	0.997986i	$-0.479794\pi$
$569$	7.94274	−	0.834815i	0.332977	−	0.0349973i	0.269542	+	0.962989i	$0.413128\pi$
$570$	−20.2167	−	37.2089i	−0.846782	−	1.55851i
$571$	−3.24397	+	30.8643i	−0.135756	+	1.29163i	0.688426	+	0.725307i	$0.258302\pi$
$571$	−3.24397	+	30.8643i	−0.135756	+	1.29163i	−0.824182	+	0.566325i	$0.808365\pi$
$572$	10.0595	+	3.86148i	0.420609	+	0.161457i
$573$	−24.5856	−	48.2521i	−1.02708	−	2.01576i
$574$	−4.94161	−	2.04847i	−0.206259	−	0.0855017i
$575$	5.12148	−	8.88247i	0.213580	−	0.370425i
$576$	−15.4934	+	26.8354i	−0.645559	+	1.11814i
$577$	27.5508	+	17.8917i	1.14695	+	0.744840i	0.970887	−	0.239538i	$-0.0769959\pi$
$577$	27.5508	+	17.8917i	1.14695	+	0.744840i	0.176067	+	0.984378i	$0.443663\pi$
$578$	2.47059	−	2.00064i	0.102763	−	0.0832157i
$579$	40.8083	−	18.1690i	1.69594	−	0.755079i
$580$	−1.61722	−	2.35161i	−0.0671512	−	0.0976454i
$581$	−5.90738	+	5.60280i	−0.245079	+	0.232443i
$582$	33.5993	−	33.5993i	1.39274	−	1.39274i
$583$	−1.36741	+	1.68861i	−0.0566324	+	0.0699352i
$584$	−15.4701	+	17.1812i	−0.640156	+	0.710965i
$585$	31.3040	+	40.7718i	1.29426	+	1.68571i
$586$	10.9423	−	9.85252i	0.452023	−	0.407004i
$587$	17.4894	−	34.3249i	0.721865	−	1.41674i	−0.179534	−	0.983752i	$-0.557459\pi$
$587$	17.4894	−	34.3249i	0.721865	−	1.41674i	0.901399	−	0.432989i	$-0.142541\pi$
$588$	−18.3863	+	20.3974i	−0.758237	+	0.841176i
$589$	24.6123	+	7.99701i	1.01413	+	0.329511i
$590$	−1.23872	−	2.02010i	−0.0509974	−	0.0831664i
$591$	−18.3388	−	16.5123i	−0.754357	−	0.679226i
$592$	0.101412	−	0.0389286i	0.00416802	−	0.00159995i
$593$	5.96985	+	22.2798i	0.245153	+	0.914922i	0.973307	+	0.229508i	$0.0737118\pi$
$593$	5.96985	+	22.2798i	0.245153	+	0.914922i	−0.728154	+	0.685413i	$0.759622\pi$
$594$	19.4512	−	14.1321i	0.798092	−	0.579848i
$595$	−18.6832	−	10.7864i	−0.765938	−	0.442201i
$596$	−12.3932	−	9.00416i	−0.507644	−	0.368825i
$597$	6.86429	−	17.8821i	0.280937	−	0.731865i
$598$	3.31440	−	5.10373i	0.135536	−	0.208707i
$599$	15.2982	−	8.83240i	0.625066	−	0.360882i	−0.153773	−	0.988106i	$-0.549142\pi$
$599$	15.2982	−	8.83240i	0.625066	−	0.360882i	0.778839	+	0.627224i	$0.215809\pi$
$600$	−2.30245	−	43.4544i	−0.0939970	−	1.77402i
$601$		−	22.6811i		−	0.925181i	−0.886572	−	0.462591i	$-0.846920\pi$
$601$		−	22.6811i		−	0.925181i	0.886572	−	0.462591i	$-0.153080\pi$
$602$	−0.388939	−	4.95939i	−0.0158520	−	0.202130i
$603$	5.26352	+	33.2325i	0.214347	+	1.35333i
$604$	−2.57895	−	5.79241i	−0.104936	−	0.235690i
$605$	−2.00190	−	10.7840i	−0.0813889	−	0.438430i
$606$	−35.1693	−	15.6584i	−1.42865	−	0.636078i
$607$	−13.6007	+	3.64430i	−0.552036	+	0.147917i	−0.524045	−	0.851691i	$-0.675578\pi$
$607$	−13.6007	+	3.64430i	−0.552036	+	0.147917i	−0.0279907	+	0.999608i	$0.508911\pi$
$608$	6.33757	−	40.0138i	0.257022	−	1.62277i
$609$	6.84527	+	4.70740i	0.277384	+	0.190753i
$610$	−8.98259	−	18.8184i	−0.363694	−	0.761936i
$611$	6.23396	+	6.92351i	0.252199	+	0.280095i
$612$	−30.5853	+	1.60291i	−1.23634	+	0.0647937i
$613$	12.3464	−	0.647050i	0.498668	−	0.0261341i	0.198656	−	0.980069i	$-0.436342\pi$
$613$	12.3464	−	0.647050i	0.498668	−	0.0261341i	0.300013	+	0.953935i	$0.403009\pi$
$614$	2.90630	+	3.22777i	0.117289	+	0.130262i
$615$	11.8625	−	11.2635i	0.478340	−	0.454190i
$616$	15.0774	+	10.3685i	0.607487	+	0.417761i
$617$	4.15259	−	26.2184i	0.167177	−	1.05551i	−0.751277	−	0.659987i	$-0.770562\pi$
$617$	4.15259	−	26.2184i	0.167177	−	1.05551i	0.918454	−	0.395527i	$-0.129438\pi$
$618$	38.6371	−	10.3528i	1.55421	−	0.416450i
$619$	−36.0574	−	16.0538i	−1.44927	−	0.645255i	−0.476952	−	0.878929i	$-0.658259\pi$
$619$	−36.0574	−	16.0538i	−1.44927	−	0.645255i	−0.972315	+	0.233674i	$0.924925\pi$
$620$	7.46784	+	7.08263i	0.299916	+	0.284445i
$621$	9.46048	+	21.2486i	0.379636	+	0.852676i
$622$	−0.416175	−	2.62763i	−0.0166871	−	0.105358i
$623$	1.94503	+	24.8013i	0.0779261	+	0.993642i
$624$			1.29084i			0.0516750i
$625$	14.7179	+	20.2085i	0.588717	+	0.808339i
$626$	−0.258967	+	0.149515i	−0.0103504	+	0.00597581i
$627$	−29.6570	+	45.6677i	−1.18438	+	1.82379i
$628$	2.16166	−	5.63131i	0.0862595	−	0.224714i
$629$	−2.66568	−	1.93673i	−0.106288	−	0.0772225i
$630$	13.7419	+	30.8639i	0.547492	+	1.22965i
$631$	−2.56712	+	1.86512i	−0.102195	+	0.0742493i	−0.637709	−	0.770277i	$-0.720118\pi$
$631$	−2.56712	+	1.86512i	−0.102195	+	0.0742493i	0.535514	+	0.844526i	$0.320118\pi$
$632$	11.0046	+	41.0696i	0.437738	+	1.63366i
$633$	−51.1448	+	19.6326i	−2.03282	+	0.780327i
$634$	0.884179	+	0.796119i	0.0351152	+	0.0316179i
$635$	24.1566	−	5.80685i	0.958626	−	0.230438i
$636$	−3.28376	−	1.06696i	−0.130209	−	0.0423076i
$637$	5.04327	−	23.6626i	0.199821	−	0.937548i
$638$	0.972672	−	1.90898i	0.0385085	−	0.0755771i
$639$	72.7829	−	65.5340i	2.87925	−	2.59249i
$640$	9.38367	−	13.6617i	0.370922	−	0.540028i
$641$	−3.26561	+	3.62683i	−0.128984	+	0.143251i	−0.804177	−	0.594390i	$-0.797394\pi$
$641$	−3.26561	+	3.62683i	−0.128984	+	0.143251i	0.675193	+	0.737641i	$0.264060\pi$
$642$	−20.2028	+	24.9483i	−0.797339	+	0.984632i
$643$	−0.430113	+	0.430113i	−0.0169620	+	0.0169620i	−0.715537	−	0.698575i	$-0.753818\pi$
$643$	−0.430113	+	0.430113i	−0.0169620	+	0.0169620i	0.698575	+	0.715537i	$0.253818\pi$
$644$	−4.97101	+	4.71471i	−0.195885	+	0.185786i
$645$	14.3410	+	5.07377i	0.564676	+	0.199779i
$646$	−20.3075	+	9.04149i	−0.798989	+	0.355733i
$647$	−12.6557	+	10.2484i	−0.497547	+	0.402905i	−0.844979	−	0.534800i	$-0.820387\pi$
$647$	−12.6557	+	10.2484i	−0.497547	+	0.402905i	0.347432	+	0.937705i	$0.387054\pi$
$648$	35.9092	+	23.3197i	1.41065	+	0.916084i
$649$	−1.52355	+	2.63886i	−0.0598045	+	0.103584i
$650$	8.08855	+	12.4396i	0.317259	+	0.487921i
$651$	−27.6758	−	11.4726i	−1.08470	−	0.449648i
$652$	−0.640993	−	1.25802i	−0.0251032	−	0.0492679i
$653$	44.1941	+	16.9645i	1.72945	+	0.663873i	0.999801	−	0.0199493i	$-0.00635048\pi$
$653$	44.1941	+	16.9645i	1.72945	+	0.663873i	0.729648	+	0.683823i	$0.239684\pi$
$654$	−0.206983	+	1.96931i	−0.00809369	+	0.0770063i
$655$	−4.16111	+	31.6773i	−0.162588	+	1.23773i
$656$	0.281543	−	0.0295914i	0.0109924	−	0.00115535i
$657$	38.8127	+	38.8127i	1.51423	+	1.51423i
$658$	2.92031	+	5.38207i	0.113846	+	0.209815i
$659$	−12.4558	+	4.04712i	−0.485208	+	0.157654i	−0.541398	−	0.840767i	$-0.682105\pi$
$659$	−12.4558	+	4.04712i	−0.485208	+	0.157654i	0.0561901	+	0.998420i	$0.482105\pi$
$660$	−18.4619	+	11.3208i	−0.718627	+	0.440660i
$661$	−6.32141	−	29.7399i	−0.245874	−	1.15675i	−0.911769	−	0.410702i	$-0.865284\pi$
$661$	−6.32141	−	29.7399i	−0.245874	−	1.15675i	0.665895	−	0.746045i	$-0.268050\pi$
$662$	−0.573649	−	10.9459i	−0.0222955	−	0.425423i
$663$	32.8379	−	21.3252i	1.27532	−	0.828201i
$664$	−2.66402	+	8.19900i	−0.103384	+	0.318183i
$665$	−29.7011	−	29.7003i	−1.15176	−	1.15173i
$666$	1.59455	+	4.90751i	0.0617874	+	0.190162i
$667$	1.61077	+	1.30438i	0.0623692	+	0.0505056i
$668$	24.7456	+	6.63055i	0.957434	+	0.256544i
$669$	10.9090	−	24.5021i	0.421768	−	0.947307i
$670$	0.764823	+	9.68235i	0.0295477	+	0.374062i
$671$	−15.7607	+	21.6927i	−0.608435	+	0.837439i
$672$	−10.9613	+	45.6019i	−0.422842	+	1.75913i
$673$	12.8773	−	6.56131i	0.496383	−	0.252920i	−0.187830	−	0.982201i	$-0.560146\pi$
$673$	12.8773	−	6.56131i	0.496383	−	0.252920i	0.684214	+	0.729282i	$0.260146\pi$
$674$	1.91663	+	1.10657i	0.0738260	+	0.0426235i
$675$	−56.7127	+	0.0326626i	−2.18287	+	0.00125719i
$676$	0.665483	+	1.15265i	0.0255955	+	0.0443327i
$677$	1.01318	−	19.3326i	0.0389397	−	0.743014i	−0.907484	−	0.420086i	$-0.862000\pi$
$677$	1.01318	−	19.3326i	0.0389397	−	0.743014i	0.946424	−	0.322927i	$-0.104667\pi$
$678$	−25.4097	+	4.02450i	−0.975853	+	0.154560i
$679$	22.5006	−	41.4137i	0.863493	−	1.58931i
$680$	−22.8354	−	0.591385i	−0.875697	−	0.0226786i
$681$	−3.54376	−	33.7166i	−0.135797	−	1.29202i
$682$	−1.99973	+	7.46310i	−0.0765737	+	0.285777i
$683$	−15.9677	−	41.5972i	−0.610986	−	1.59167i	−0.793567	−	0.608483i	$-0.791778\pi$
$683$	−15.9677	−	41.5972i	−0.610986	−	1.59167i	0.182581	−	0.983191i	$-0.441555\pi$
$684$	−58.3278	−	12.3980i	−2.23022	−	0.474048i
$685$	−3.83318	−	0.709297i	−0.146458	−	0.0271008i
$686$	6.85769	−	14.3470i	0.261828	−	0.547769i
$687$	27.1252	+	13.8210i	1.03489	+	0.527303i
$688$	0.143383	+	0.220790i	0.00546642	+	0.00841755i
$689$	2.97551	−	0.632464i	0.113358	−	0.0240950i
$690$	4.08607	+	11.5282i	0.155554	+	0.438869i
$691$	−0.621449	+	2.92369i	−0.0236410	+	0.111222i	−0.988386	−	0.151964i	$-0.951440\pi$
$691$	−0.621449	+	2.92369i	−0.0236410	+	0.111222i	0.964745	+	0.263187i	$0.0847735\pi$
$692$	11.1129	+	1.76012i	0.422450	+	0.0669096i
$693$	26.4562	−	34.4587i	1.00499	−	1.30898i
$694$	3.14300	+	4.32597i	0.119307	+	0.164212i
$695$	19.9948	+	12.2449i	0.758447	+	0.464477i
$696$	8.74841	+	0.919495i	0.331608	+	0.0348534i
$697$	−5.40398	−	6.67336i	−0.204690	−	0.252772i
$698$	−5.46376	−	0.286343i	−0.206806	−	0.0108383i
$699$	−10.4882			−0.396698
$700$	−5.58103	−	15.7453i	−0.210943	−	0.595116i
$701$	−27.5603			−1.04094			−0.520469	−	0.853880i	$-0.674243\pi$
$701$	−27.5603			−1.04094			−0.520469	+	0.853880i	$0.674243\pi$
$702$	−33.6142	−	1.76164i	−1.26868	−	0.0664889i
$703$	−4.03725	−	4.98559i	−0.152268	−	0.188035i
$704$	11.4388	+	1.20227i	0.431117	+	0.0453122i
$705$	−18.6666	+	1.47450i	−0.703023	+	0.0555328i
$706$	0.333490	+	0.459010i	0.0125511	+	0.0172751i
$707$	−37.8575	−	4.99463i	−1.42378	−	0.187842i
$708$	−4.78237	−	0.757453i	−0.179733	−	0.0284668i
$709$	−5.72110	+	26.9157i	−0.214861	+	1.01084i	0.730020	+	0.683425i	$0.239511\pi$
$709$	−5.72110	+	26.9157i	−0.214861	+	1.01084i	−0.944881	+	0.327414i	$0.893823\pi$
$710$	22.4241	−	17.2169i	0.841560	−	0.646137i
$711$	98.7391	−	20.9877i	3.70301	−	0.787098i
$712$	14.3466	+	22.0919i	0.537663	+	0.827928i
$713$	−6.65990	−	3.39339i	−0.249415	−	0.127083i
$714$	24.2608	−	8.58370i	0.907939	−	0.321237i
$715$	9.09937	−	16.7705i	0.340297	−	0.627180i
$716$	−7.12508	−	1.51448i	−0.266277	−	0.0565989i
$717$	16.6315	+	43.3264i	0.621113	+	1.61805i
$718$	−4.16565	+	15.5464i	−0.155461	+	0.580188i
$719$	0.249681	+	2.37555i	0.00931152	+	0.0885932i	0.998191	−	0.0601281i	$-0.0191509\pi$
$719$	0.249681	+	2.37555i	0.00931152	+	0.0885932i	−0.988879	+	0.148721i	$0.952484\pi$
$720$	−1.41877	−	1.08802i	−0.0528746	−	0.0405479i
$721$	33.8349	−	20.7213i	1.26008	−	0.771700i
$722$	−26.6347	+	4.21852i	−0.991241	+	0.156997i
$723$	−4.31861	+	82.4039i	−0.160611	+	3.06464i
$724$	3.53660	+	6.12557i	0.131437	+	0.227655i
$725$	−4.50158	+	2.29694i	−0.167185	+	0.0853061i
$726$	11.3309	+	6.54190i	0.420530	+	0.242793i
$727$	−42.2271	+	21.5158i	−1.56612	+	0.797976i	−0.999659	−	0.0261149i	$-0.991686\pi$
$727$	−42.2271	+	21.5158i	−1.56612	+	0.797976i	−0.566457	+	0.824091i	$0.691686\pi$
$728$	−7.26914	−	24.5650i	−0.269412	−	0.910441i
$729$	−2.38496	+	3.28261i	−0.0883317	+	0.121578i
$730$	10.2936	+	12.0452i	0.380984	+	0.445815i
$731$	3.24798	−	7.29507i	0.120131	−	0.269818i
$732$	−41.1564	−	11.0278i	−1.52118	−	0.407600i
$733$	−9.63660	−	7.80357i	−0.355936	−	0.288231i	0.434629	−	0.900610i	$-0.356880\pi$
$733$	−9.63660	−	7.80357i	−0.355936	−	0.288231i	−0.790565	+	0.612378i	$0.790213\pi$
$734$	−8.26450	−	25.4355i	−0.305048	−	0.938842i
$735$	31.5705	+	36.9840i	1.16450	+	1.36418i
$736$	−3.61588	+	11.1285i	−0.133283	+	0.410203i
$737$	10.4743	−	6.80208i	0.385825	−	0.250558i
$738$	0.703795	+	13.4292i	0.0259071	+	0.494336i
$739$	−0.663245	−	3.12032i	−0.0243979	−	0.114783i	0.964264	−	0.264945i	$-0.0853538\pi$
$739$	−0.663245	−	3.12032i	−0.0243979	−	0.114783i	−0.988661	+	0.150162i	$0.952020\pi$
$740$	−0.596332	−	2.48076i	−0.0219216	−	0.0911944i
$741$	72.5025	−	23.5575i	2.66345	−	0.865407i
$742$	1.99866	+	0.0528872i	0.0733729	+	0.00194155i
$743$	−14.5667	−	14.5667i	−0.534401	−	0.534401i	0.387478	−	0.921879i	$-0.373346\pi$
$743$	−14.5667	−	14.5667i	−0.534401	−	0.534401i	−0.921879	+	0.387478i	$0.873346\pi$
$744$	−31.5490	+	3.31593i	−1.15664	+	0.121568i
$745$	−18.6663	+	19.6815i	−0.683881	+	0.721076i
$746$	−0.723814	+	6.88663i	−0.0265007	+	0.252138i
$747$	19.1080	+	7.33486i	0.699124	+	0.268369i
$748$	5.16112	+	10.1293i	0.188709	+	0.370363i
$749$	−12.1936	+	29.4151i	−0.445545	+	1.07480i
$750$	−29.7322	−	2.31413i	−1.08567	−	0.0845002i
$751$	−5.27493	+	9.13644i	−0.192485	+	0.333394i	−0.946073	−	0.323953i	$-0.894988\pi$
$751$	−5.27493	+	9.13644i	−0.192485	+	0.333394i	0.753588	+	0.657347i	$0.228321\pi$
$752$	−0.271773	−	0.176491i	−0.00991054	−	0.00643598i
$753$	−14.8133	+	11.9956i	−0.539826	+	0.437143i
$754$	−2.74018	+	1.22001i	−0.0997915	+	0.0444300i
$755$	−10.7642	+	3.19188i	−0.391751	+	0.116165i
$756$	36.3323	+	10.7730i	1.32139	+	0.391810i
$757$	18.5968	−	18.5968i	0.675912	−	0.675912i	−0.283161	−	0.959072i	$-0.591383\pi$
$757$	18.5968	−	18.5968i	0.675912	−	0.675912i	0.959072	+	0.283161i	$0.0913830\pi$
$758$	−7.98081	+	9.85548i	−0.289876	+	0.357967i
$759$	10.5237	−	11.6878i	0.381988	−	0.424240i
$760$	−42.6472	−	12.6193i	−1.54698	−	0.457751i
$761$	26.9997	−	24.3106i	0.978737	−	0.881259i	−0.0142005	−	0.999899i	$-0.504520\pi$
$761$	26.9997	−	24.3106i	0.978737	−	0.881259i	0.992937	+	0.118641i	$0.0378537\pi$
$762$	−13.4549	+	26.4067i	−0.487419	+	0.956614i
$763$	0.357399	+	1.93132i	0.0129387	+	0.0699185i
$764$	−20.9355	−	6.80237i	−0.757421	−	0.246101i
$765$	−4.23949	+	54.0668i	−0.153279	+	1.95479i
$766$	15.8745	+	14.2935i	0.573570	+	0.516445i

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:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	175.x (of order \(60\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(0.857433 + 0.0449361i) q^{2} +(-1.95506 - 2.41430i) q^{3} +(-1.25587 - 0.131998i) q^{4} +(-0.521374 + 2.17444i) q^{5} +(-1.56784 - 2.15795i) q^{6} +(-2.09857 - 1.61121i) q^{7} +(-2.76697 - 0.438245i) q^{8} +(-1.38284 + 6.50575i) q^{9} +O(q^{10})\)	\(q+(0.857433 + 0.0449361i) q^{2} +(-1.95506 - 2.41430i) q^{3} +(-1.25587 - 0.131998i) q^{4} +(-0.521374 + 2.17444i) q^{5} +(-1.56784 - 2.15795i) q^{6} +(-2.09857 - 1.61121i) q^{7} +(-2.76697 - 0.438245i) q^{8} +(-1.38284 + 6.50575i) q^{9} +(-0.544753 + 1.84100i) q^{10} +(2.41483 - 0.513288i) q^{11} +(2.13662 + 3.29011i) q^{12} +(-3.07959 - 1.56913i) q^{13} +(-1.72698 - 1.47580i) q^{14} +(6.26905 - 2.99240i) q^{15} +(0.117592 + 0.0249949i) q^{16} +(-1.30681 - 3.40436i) q^{17} +(-1.47803 + 5.51610i) q^{18} +(-0.742133 - 7.06093i) q^{19} +(0.941799 - 2.66199i) q^{20} +(0.212895 + 8.21659i) q^{21} +(2.09362 - 0.331597i) q^{22} +(-0.107322 + 2.04783i) q^{23} +(4.35154 + 7.53709i) q^{24} +(-4.45634 - 2.26739i) q^{25} +(-2.57003 - 1.48381i) q^{26} +(10.1063 - 5.14941i) q^{27} +(2.42286 + 2.30048i) q^{28} +(0.594101 - 0.817710i) q^{29} +(5.50976 - 2.28407i) q^{30} +(-1.48256 + 3.32988i) q^{31} +(5.51171 + 1.47686i) q^{32} +(-5.96037 - 4.82661i) q^{33} +(-0.967525 - 2.97773i) q^{34} +(4.59761 - 3.72317i) q^{35} +(2.59541 - 7.98786i) q^{36} +(0.757805 - 0.492125i) q^{37} +(-0.319038 - 6.08762i) q^{38} +(2.23243 + 10.5028i) q^{39} +(2.39556 - 5.78811i) q^{40} +(2.23957 - 0.727680i) q^{41} +(-0.186678 + 7.05474i) q^{42} +(1.54846 + 1.54846i) q^{43} +(-3.10047 + 0.325873i) q^{44} +(-13.4254 - 6.39882i) q^{45} +(-0.184043 + 1.75105i) q^{46} +(-2.51648 - 0.965986i) q^{47} +(-0.169554 - 0.332768i) q^{48} +(1.80801 + 6.76248i) q^{49} +(-3.71912 - 2.14438i) q^{50} +(-5.66425 + 9.81076i) q^{51} +(3.66045 + 2.37712i) q^{52} +(-0.683987 + 0.553882i) q^{53} +(8.89685 - 3.96114i) q^{54} +(-0.142917 + 5.51851i) q^{55} +(5.10058 + 5.37786i) q^{56} +(-15.5963 + 15.5963i) q^{57} +(0.546147 - 0.674435i) q^{58} +(-0.825876 + 0.917228i) q^{59} +(-8.26812 + 2.93057i) q^{60} +(-8.07138 + 7.26750i) q^{61} +(-1.42082 + 2.78852i) q^{62} +(13.3841 - 11.4247i) q^{63} +(4.43089 + 1.43968i) q^{64} +(5.01758 - 5.87826i) q^{65} +(-4.89372 - 4.40633i) q^{66} +(4.72283 - 1.81293i) q^{67} +(1.19182 + 4.44794i) q^{68} +(5.15389 - 3.74452i) q^{69} +(4.10945 - 2.98577i) q^{70} +(-11.9130 - 8.65529i) q^{71} +(6.67739 - 17.3952i) q^{72} +(4.49475 - 6.92130i) q^{73} +(0.671881 - 0.387911i) q^{74} +(3.23826 + 15.1918i) q^{75} +8.96558i q^{76} +(-5.89471 - 2.81362i) q^{77} +(1.44221 + 9.10574i) q^{78} +(-6.17313 - 13.8651i) q^{79} +(-0.115659 + 0.242664i) q^{80} +(-13.9624 - 6.21645i) q^{81} +(1.95298 - 0.523299i) q^{82} +(0.481396 - 3.03941i) q^{83} +(0.817199 - 10.3471i) q^{84} +(8.08390 - 1.06663i) q^{85} +(1.25812 + 1.39728i) q^{86} +(-3.13570 + 0.164335i) q^{87} +(-6.90671 + 0.361965i) q^{88} +(-6.29169 - 6.98763i) q^{89} +(-11.2238 - 6.08984i) q^{90} +(3.93454 + 8.25478i) q^{91} +(0.405091 - 2.55764i) q^{92} +(10.9378 - 2.93077i) q^{93} +(-2.11430 - 0.941349i) q^{94} +(15.7405 + 2.06766i) q^{95} +(-7.21015 - 16.1943i) q^{96} +(2.78673 + 17.5947i) q^{97} +(1.24637 + 5.87961i) q^{98} +16.4201i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 288 q - 8 q^{2} - 24 q^{3} - 10 q^{4} - 30 q^{5} - 10 q^{7} - 36 q^{8} - 10 q^{9}+O(q^{10}) \) 288 * q - 8 * q^2 - 24 * q^3 - 10 * q^4 - 30 * q^5 - 10 * q^7 - 36 * q^8 - 10 * q^9	\( 288 q - 8 q^{2} - 24 q^{3} - 10 q^{4} - 30 q^{5} - 10 q^{7} - 36 q^{8} - 10 q^{9} - 36 q^{10} - 6 q^{11} - 36 q^{12} - 20 q^{14} - 28 q^{15} - 30 q^{16} - 42 q^{17} - 14 q^{18} - 30 q^{19} - 12 q^{21} + 32 q^{22} - 40 q^{23} + 2 q^{25} - 48 q^{26} + 22 q^{28} - 58 q^{30} - 18 q^{31} + 8 q^{32} - 30 q^{33} - 2 q^{35} + 40 q^{36} - 10 q^{37} + 72 q^{38} + 30 q^{39} - 48 q^{40} + 6 q^{42} - 108 q^{43} - 10 q^{44} + 186 q^{45} - 6 q^{46} - 54 q^{47} - 248 q^{50} - 16 q^{51} + 216 q^{52} + 50 q^{53} - 30 q^{54} + 4 q^{56} - 216 q^{57} - 4 q^{58} + 90 q^{59} + 96 q^{60} - 18 q^{61} - 66 q^{63} - 100 q^{64} + 14 q^{65} - 90 q^{66} + 4 q^{67} + 342 q^{68} - 60 q^{70} - 24 q^{71} + 58 q^{72} - 6 q^{73} + 216 q^{75} - 80 q^{77} - 132 q^{78} - 10 q^{79} - 6 q^{80} - 10 q^{81} + 216 q^{82} + 20 q^{84} - 48 q^{85} - 6 q^{86} - 48 q^{87} - 122 q^{88} + 120 q^{89} - 12 q^{91} - 4 q^{92} + 106 q^{93} - 30 q^{94} - 98 q^{95} - 90 q^{96} + 222 q^{98}+O(q^{100}) \) 288 * q - 8 * q^2 - 24 * q^3 - 10 * q^4 - 30 * q^5 - 10 * q^7 - 36 * q^8 - 10 * q^9 - 36 * q^10 - 6 * q^11 - 36 * q^12 - 20 * q^14 - 28 * q^15 - 30 * q^16 - 42 * q^17 - 14 * q^18 - 30 * q^19 - 12 * q^21 + 32 * q^22 - 40 * q^23 + 2 * q^25 - 48 * q^26 + 22 * q^28 - 58 * q^30 - 18 * q^31 + 8 * q^32 - 30 * q^33 - 2 * q^35 + 40 * q^36 - 10 * q^37 + 72 * q^38 + 30 * q^39 - 48 * q^40 + 6 * q^42 - 108 * q^43 - 10 * q^44 + 186 * q^45 - 6 * q^46 - 54 * q^47 - 248 * q^50 - 16 * q^51 + 216 * q^52 + 50 * q^53 - 30 * q^54 + 4 * q^56 - 216 * q^57 - 4 * q^58 + 90 * q^59 + 96 * q^60 - 18 * q^61 - 66 * q^63 - 100 * q^64 + 14 * q^65 - 90 * q^66 + 4 * q^67 + 342 * q^68 - 60 * q^70 - 24 * q^71 + 58 * q^72 - 6 * q^73 + 216 * q^75 - 80 * q^77 - 132 * q^78 - 10 * q^79 - 6 * q^80 - 10 * q^81 + 216 * q^82 + 20 * q^84 - 48 * q^85 - 6 * q^86 - 48 * q^87 - 122 * q^88 + 120 * q^89 - 12 * q^91 - 4 * q^92 + 106 * q^93 - 30 * q^94 - 98 * q^95 - 90 * q^96 + 222 * q^98

Introduction

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