LMFDB - Embedded newform 175.2.x.a.17.13

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [175,2,Mod(3,175)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://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);

sage: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")

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:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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			17.13
Character	$\chi$	$=$	175.17
Dual form			175.2.x.a.103.13

$q$-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} +(-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} - 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}+ \cdots + 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

Character values

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

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{13}{20}\right)$

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	0.253282	−	0.967393i	$-0.418490\pi$
$2$	0.857433	−	0.0449361i	0.606296	−	0.0317746i	0.353014	+	0.935618i	$0.385157\pi$
$3$	−1.95506	+	2.41430i	−1.12875	+	1.39390i	−0.220546	+	0.975377i	$0.570784\pi$
$3$	−1.95506	+	2.41430i	−1.12875	+	1.39390i	−0.908208	+	0.418519i	$0.862549\pi$
$4$	−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	0.557025	−	0.830496i	$-0.311943\pi$
$11$	2.41483	+	0.513288i	0.728099	+	0.154762i	0.171074	+	0.985258i	$0.445276\pi$
$12$	2.13662	−	3.29011i	0.616790	−	0.949774i
$13$	−3.07959	+	1.56913i	−0.854124	+	0.435198i	−0.825506	−	0.564393i	$-0.809110\pi$
$13$	−3.07959	+	1.56913i	−0.854124	+	0.435198i	−0.0286171	+	0.999590i	$0.509110\pi$
$14$	−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	0.678864	+	0.734264i	$0.262472\pi$
$17$	−1.30681	+	3.40436i	−0.316949	+	0.825679i	−0.995813	+	0.0914154i	$0.970861\pi$
$18$	−1.47803	−	5.51610i	−0.348376	−	1.30016i
$19$	−0.742133	+	7.06093i	−0.170257	+	1.61989i	0.491989	+	0.870601i	$0.336270\pi$
$19$	−0.742133	+	7.06093i	−0.170257	+	1.61989i	−0.662246	+	0.749286i	$0.730397\pi$
$20$	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	−0.986729	−	0.162375i	$-0.948085\pi$
$23$	−0.107322	−	2.04783i	−0.0223782	−	0.427001i	0.964351	−	0.264627i	$-0.0852487\pi$
$24$	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	0.860608	−	0.509269i	$-0.170084\pi$
$29$	0.594101	+	0.817710i	0.110322	+	0.151845i	−0.750286	+	0.661114i	$0.770084\pi$
$30$	5.50976	+	2.28407i	1.00594	+	0.417013i
$31$	−1.48256	−	3.32988i	−0.266275	−	0.598063i	0.730081	−	0.683361i	$-0.239482\pi$
$31$	−1.48256	−	3.32988i	−0.266275	−	0.598063i	−0.996355	+	0.0852978i	$0.972816\pi$
$32$	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	0.605426	−	0.795902i	$-0.293003\pi$
$37$	0.757805	+	0.492125i	0.124582	+	0.0809048i	−0.480843	+	0.876806i	$0.659669\pi$
$38$	−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	0.478629	−	0.878017i	$-0.341134\pi$
$41$	2.23957	+	0.727680i	0.349762	+	0.113644i	−0.128867	+	0.991662i	$0.541134\pi$
$42$	−0.186678	−	7.05474i	−0.0288051	−	1.08857i
$43$	1.54846	−	1.54846i	0.236138	−	0.236138i	−0.579111	−	0.815249i	$-0.696600\pi$
$43$	1.54846	−	1.54846i	0.236138	−	0.236138i	0.815249	+	0.579111i	$0.196600\pi$
$44$	−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	−0.534908	−	0.844910i	$-0.679654\pi$
$47$	−2.51648	+	0.965986i	−0.367066	+	0.140904i	0.167842	+	0.985814i	$0.446320\pi$
$48$	−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	0.581193	−	0.813766i	$-0.302586\pi$
$53$	−0.683987	−	0.553882i	−0.0939528	−	0.0760815i	−0.675146	+	0.737684i	$0.735919\pi$
$54$	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	0.686982	−	0.726674i	$-0.258935\pi$
$59$	−0.825876	−	0.917228i	−0.107520	−	0.119413i	−0.794502	+	0.607261i	$0.792268\pi$
$60$	−8.26812	−	2.93057i	−1.06741	−	0.378335i
$61$	−8.07138	−	7.26750i	−1.03343	−	0.930508i	−0.0358074	−	0.999359i	$-0.511400\pi$
$61$	−8.07138	−	7.26750i	−1.03343	−	0.930508i	−0.997627	+	0.0688502i	$0.978067\pi$
$62$	−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	0.629321	−	0.777145i	$-0.283333\pi$
$67$	4.72283	+	1.81293i	0.576986	+	0.221484i	−0.0523352	+	0.998630i	$0.516666\pi$
$68$	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	−0.421057	+	0.907034i	$0.638341\pi$
$71$	−11.9130	+	8.65529i	−1.41381	+	1.02719i	−0.992754	+	0.120161i	$0.961659\pi$
$72$	6.67739	+	17.3952i	0.786938	+	2.05004i
$73$	4.49475	+	6.92130i	0.526070	+	0.810077i	0.997414	−	0.0718724i	$-0.0228974\pi$
$73$	4.49475	+	6.92130i	0.526070	+	0.810077i	−0.471343	+	0.881950i	$0.656231\pi$
$74$	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	0.128350	+	0.991729i	$0.459032\pi$
$79$	−6.17313	+	13.8651i	−0.694531	+	1.55994i	−0.822881	+	0.568214i	$0.807635\pi$
$80$	−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	0.999920	+	0.0126222i	$0.00401788\pi$
$83$	0.481396	+	3.03941i	0.0528401	+	0.333619i	−0.947080	+	0.320997i	$0.895982\pi$
$84$	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	−0.977749	−	0.209778i	$-0.932726\pi$
$89$	−6.29169	+	6.98763i	−0.666918	+	0.740687i	0.310831	+	0.950465i	$0.399393\pi$
$90$	−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	−0.280021	−	0.959994i	$-0.590341\pi$
$97$	2.78673	−	17.5947i	0.282949	−	1.78647i	0.562970	−	0.826477i	$-0.309659\pi$
$98$	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	0.969848	−	0.243711i	$-0.0783649\pi$
$101$	12.4991	+	7.21639i	1.24371	+	0.718057i	0.273864	+	0.961769i	$0.411698\pi$
$102$	−5.29757	−	8.15754i	−0.524537	−	0.807717i
$103$	−5.37411	−	14.0000i	−0.529527	−	1.37946i	−0.893923	−	0.448220i	$-0.852058\pi$
$103$	−5.37411	−	14.0000i	−0.529527	−	1.37946i	0.364397	−	0.931244i	$-0.381275\pi$
$104$	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	0.635089	+	0.772439i	$0.280963\pi$
$107$	−3.11495	+	11.6252i	−0.301134	+	1.12385i	−0.936223	+	0.351408i	$0.885703\pi$
$108$	−13.3719	−	5.13300i	−1.28671	−	0.493923i
$109$	−0.551684	+	0.496739i	−0.0528417	+	0.0475789i	−0.695128	−	0.718886i	$-0.744653\pi$
$109$	−0.551684	+	0.496739i	−0.0528417	+	0.0475789i	0.642287	+	0.766464i	$0.277986\pi$
$110$	−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	1.00000		0.000375885i	$-0.000119648\pi$
$113$	4.37867	+	8.59362i	0.411911	+	0.808420i	−0.588089	+	0.808796i	$0.700120\pi$
$114$	−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	0.551416	+	0.834230i	$0.314088\pi$
$127$	−5.04425	+	9.89989i	−0.447605	+	0.878473i	−0.999021	+	0.0442431i	$0.985912\pi$
$128$	−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	0.702430	−	0.711753i	$-0.252099\pi$
$131$	14.2099	+	1.49352i	1.24153	+	0.130490i	0.539098	+	0.842243i	$0.318765\pi$
$132$	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	−0.991959	−	0.126561i	$-0.959606\pi$
$137$	0.0912401	−	1.74096i	0.00779517	−	0.148741i	0.999754	−	0.0221797i	$-0.00706059\pi$
$138$	4.58737	+	2.97907i	0.390503	+	0.253596i
$139$	3.24021	+	9.97233i	0.274831	+	0.845842i	0.989264	+	0.146138i	$0.0466845\pi$
$139$	3.24021	+	9.97233i	0.274831	+	0.845842i	−0.714433	+	0.699703i	$0.753315\pi$
$140$	−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	−0.00357448	−	0.999994i	$-0.501138\pi$
$149$	10.5057	−	6.06545i	0.860658	−	0.496901i	0.864233	+	0.503092i	$0.167804\pi$
$150$	2.09393	−	13.1715i	0.170969	−	1.07545i
$151$	2.51055	−	4.34839i	0.204305	−	0.353867i	−0.745606	−	0.666387i	$-0.767840\pi$
$151$	2.51055	−	4.34839i	0.204305	−	0.353867i	0.949911	+	0.312520i	$0.101173\pi$
$152$	−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	0.898883	−	0.438189i	$-0.144380\pi$
$157$	−1.23630	−	4.61392i	−0.0986672	−	0.368231i	−0.997550	+	0.0699583i	$0.977713\pi$
$158$	−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	−0.814018	−	0.580840i	$-0.802724\pi$
$163$	0.608954	−	0.937707i	0.0476969	−	0.0734469i	0.861715	+	0.507393i	$0.169391\pi$
$164$	−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	−0.872195	−	0.489158i	$-0.837304\pi$
$167$	−20.0374	+	3.17362i	−1.55054	+	0.245582i	−0.678349	+	0.734740i	$0.737304\pi$
$168$	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	−0.387486	−	0.921876i	$-0.626656\pi$
$173$	−8.89779	+	0.466313i	−0.676486	+	0.0354531i	−0.289001	+	0.957329i	$0.593323\pi$
$174$	−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	0.112323	−	0.993672i	$-0.464171\pi$
$179$	5.73678	−	0.602960i	0.428787	−	0.0450674i	0.316464	+	0.948604i	$0.397504\pi$
$180$	16.0159	−	9.80821i	1.19375	−	0.731061i
$181$	−3.29233	+	4.53150i	−0.244717	+	0.336824i	−0.913652	−	0.406497i	$-0.866750\pi$
$181$	−3.29233	+	4.53150i	−0.244717	+	0.336824i	0.668935	+	0.743321i	$0.266750\pi$
$182$	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	0.455535	−	0.890218i	$-0.349448\pi$
$191$	17.0510	−	3.62431i	1.23377	−	0.262246i	0.778236	+	0.627972i	$0.216115\pi$
$192$	−5.18683	+	13.5121i	−0.374327	+	0.975155i
$193$	−3.72157	−	13.8891i	−0.267885	−	0.999759i	−0.960461	−	0.278415i	$-0.910191\pi$
$193$	−3.72157	−	13.8891i	−0.267885	−	0.999759i	0.692576	−	0.721345i	$-0.256476\pi$
$194$	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	0.429530	−	0.903052i	$-0.358679\pi$
$197$	7.84565	+	1.24263i	0.558979	+	0.0885336i	0.129449	+	0.991586i	$0.458679\pi$
$198$	−0.737855	−	14.0791i	−0.0524371	−	1.00056i
$199$	3.08282	−	5.33960i	0.218535	−	0.378514i	−0.735825	−	0.677172i	$-0.763205\pi$
$199$	3.08282	−	5.33960i	0.218535	−	0.378514i	0.954360	+	0.298657i	$0.0965388\pi$
$200$	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	0.943379	+	0.331717i	$0.107628\pi$
$211$	5.44934	+	16.7713i	0.375148	+	1.15459i	−0.568231	+	0.822869i	$0.692372\pi$
$212$	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	−0.721733	−	0.692172i	$-0.756654\pi$
$223$	3.91951	−	7.69248i	0.262470	−	0.515126i	0.984203	+	0.177046i	$0.0566540\pi$
$224$	−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	−0.203936	−	0.978984i	$-0.565373\pi$
$227$	9.15235	−	5.94360i	0.607463	−	0.394491i	0.811398	+	0.584493i	$0.198707\pi$
$228$	21.6456	+	17.5282i	1.43351	+	1.16084i
$229$	−8.95229	−	3.98582i	−0.591584	−	0.263390i	0.0890341	−	0.996029i	$-0.471622\pi$
$229$	−8.95229	−	3.98582i	−0.591584	−	0.263390i	−0.680618	+	0.732638i	$0.738289\pi$
$230$	−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	0.841974	−	0.539518i	$-0.181394\pi$
$233$	2.12463	+	2.62370i	0.139189	+	0.171884i	−0.702785	+	0.711402i	$0.748060\pi$
$234$	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	−0.730061	−	0.683382i	$-0.760508\pi$
$239$	−14.2076	+	4.61631i	−0.919010	+	0.298604i	−0.188949	+	0.981987i	$0.560508\pi$
$240$	0.811984	+	0.195188i	0.0524134	+	0.0125993i
$241$	−19.7392	+	17.7732i	−1.27151	+	1.14487i	−0.289271	+	0.957247i	$0.593413\pi$
$241$	−19.7392	+	17.7732i	−1.27151	+	1.14487i	−0.982240	+	0.187627i	$0.939920\pi$
$242$	−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	$0.0620292\pi$
$251$			6.13565i			0.387279i	−0.981073	+	0.193639i	$0.937971\pi$
$252$	−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	−0.261722	−	0.965143i	$-0.584290\pi$
$257$	−15.5655	−	4.17077i	−0.970951	−	0.260166i	−0.709230	+	0.704978i	$0.750957\pi$
$258$	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	−0.604001	−	0.796984i	$-0.706428\pi$
$263$	−20.8879	−	1.09469i	−1.28800	−	0.0675012i	−0.683999	+	0.729483i	$0.739761\pi$
$264$	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	0.336504	−	0.941682i	$-0.390755\pi$
$269$	20.6897	−	9.21166i	1.26148	−	0.561645i	0.924971	+	0.380037i	$0.124089\pi$
$270$	3.97465	−	21.4109i	0.241889	−	1.30302i
$271$	4.69544	−	10.5461i	0.285228	−	0.640632i	−0.712935	−	0.701231i	$-0.752634\pi$
$271$	4.69544	−	10.5461i	0.285228	−	0.640632i	0.998162	+	0.0605988i	$0.0193010\pi$
$272$	−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	0.957646	+	0.287947i	$0.0929728\pi$
$277$	13.8337	+	21.3021i	0.831189	+	1.27992i	−0.126457	+	0.991972i	$0.540360\pi$
$278$	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	0.636044	−	0.771653i	$-0.280570\pi$
$281$	1.65462	+	1.20215i	0.0987061	+	0.0717142i	−0.537337	+	0.843367i	$0.680570\pi$
$282$	1.86089	−	6.94495i	0.110815	−	0.413566i
$283$	19.3529	+	7.42890i	1.15041	+	0.441602i	0.857473	−	0.514528i	$-0.172033\pi$
$283$	19.3529	+	7.42890i	1.15041	+	0.441602i	0.292940	+	0.956131i	$0.405366\pi$
$284$	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	0.966203	−	0.257781i	$-0.0829914\pi$
$293$	12.1262	+	12.1262i	0.708422	+	0.708422i	−0.257781	+	0.966203i	$0.582991\pi$
$294$	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	−0.597625	−	0.801775i	$-0.703889\pi$
$307$	3.57700	−	3.57700i	0.204150	−	0.204150i	0.801775	+	0.597625i	$0.203889\pi$
$308$	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	−0.992631	−	0.121178i	$-0.961333\pi$
$311$	−0.644209	+	3.03077i	−0.0365298	+	0.171859i	0.956101	+	0.293037i	$0.0946660\pi$
$312$	−1.57429	+	30.0392i	−0.0891266	+	1.70064i
$313$	−0.292086	−	0.189683i	−0.0165097	−	0.0107215i	0.536358	−	0.843991i	$-0.319800\pi$
$313$	−0.292086	−	0.189683i	−0.0165097	−	0.0107215i	−0.552867	+	0.833269i	$0.686466\pi$
$314$	−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	−0.598601	−	0.801047i	$-0.704277\pi$
$317$	1.07690	−	0.872053i	0.0604845	−	0.0489794i	0.659086	+	0.752068i	$0.270943\pi$
$318$	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	0.894634	+	0.446800i	$0.147436\pi$
$331$	−1.33440	+	12.6959i	−0.0733450	+	0.697831i	−0.967979	+	0.251031i	$0.919230\pi$
$332$	−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	−0.390317	−	0.920680i	$-0.627635\pi$
$337$	2.29665	−	1.17020i	0.125106	−	0.0637448i	0.515423	+	0.856936i	$0.327635\pi$
$338$	−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	−0.661013	−	0.750374i	$-0.729873\pi$
$347$	3.91924	−	4.83986i	0.210396	−	0.259818i	0.871409	+	0.490557i	$0.163207\pi$
$348$	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	−0.765959	−	0.642889i	$-0.777735\pi$
$353$	0.415853	−	0.513536i	0.0221336	−	0.0273328i	0.788093	+	0.615557i	$0.211069\pi$
$354$	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	−0.952938	−	0.303166i	$-0.901956\pi$
$359$	−3.89736	−	18.3356i	−0.205695	−	0.967717i	0.747243	−	0.664551i	$-0.231377\pi$
$360$	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	0.252283	+	0.967654i	$0.418819\pi$
$367$	−11.1627	+	29.0797i	−0.582686	+	1.51795i	−0.834969	+	0.550296i	$0.814515\pi$
$368$	−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	−0.987547	−	0.157323i	$-0.949714\pi$
$373$	−0.422082	−	8.05381i	−0.0218546	−	0.417010i	0.965693	−	0.259688i	$-0.0836196\pi$
$374$	−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	0.525577	−	0.850746i	$-0.323849\pi$
$379$	−8.68157	−	11.9492i	−0.445942	−	0.613787i	−0.971520	+	0.236959i	$0.923849\pi$
$380$	−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	0.00814217	−	0.999967i	$-0.497408\pi$
$383$	19.3346	−	15.6568i	0.987950	−	0.800026i	0.979808	+	0.199941i	$0.0640749\pi$
$384$	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	−0.524459	−	0.851436i	$-0.675732\pi$
$389$	5.93602	−	27.9268i	0.300968	−	1.41594i	0.825427	−	0.564508i	$-0.190934\pi$
$390$	−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	−0.533131	−	0.846033i	$-0.678985\pi$
$397$	−7.23706	+	2.77805i	−0.363218	+	0.139426i	0.169913	+	0.985459i	$0.445651\pi$
$398$	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	0.815517	+	0.578734i	$0.196453\pi$
$401$	18.2018	+	31.5265i	0.908956	+	1.57436i	0.0934398	+	0.995625i	$0.470214\pi$
$402$	−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	0.516204	−	0.856465i	$-0.327344\pi$
$409$	−7.87770	−	8.74907i	−0.389527	−	0.432614i	−0.905732	+	0.423852i	$0.860678\pi$
$410$	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	0.702160	−	0.712019i	$-0.252219\pi$
$419$	4.95298	+	3.59855i	0.241969	+	0.175801i	−0.460191	+	0.887820i	$0.652219\pi$
$420$	22.0730	−	7.17165i	1.07705	−	0.349940i
$421$	−19.6842	+	14.3014i	−0.959351	+	0.697009i	−0.953000	−	0.302971i	$-0.902022\pi$
$421$	−19.6842	+	14.3014i	−0.959351	+	0.697009i	−0.00635102	+	0.999980i	$0.502022\pi$
$422$	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	−0.357579	−	0.933883i	$-0.616398\pi$
$431$	2.01719	−	0.898112i	0.0971648	−	0.0432605i	0.454743	+	0.890622i	$0.349731\pi$
$432$	1.31713	+	0.352923i	0.0633703	+	0.0169800i
$433$	−4.68698	−	29.5924i	−0.225242	−	1.42212i	−0.798129	−	0.602487i	$-0.794176\pi$
$433$	−4.68698	−	29.5924i	−0.225242	−	1.42212i	0.572887	−	0.819635i	$-0.305824\pi$
$434$	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	−0.820547	−	0.571579i	$-0.806331\pi$
$439$	−3.48497	+	3.87046i	−0.166329	+	0.184727i	0.654218	+	0.756306i	$0.272998\pi$
$440$	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	−0.666016	−	0.745937i	$-0.732002\pi$
$443$	−34.0081	−	9.11243i	−1.61577	−	0.432945i	−0.949756	+	0.312992i	$0.898669\pi$
$444$	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	$-0.916218\pi$
$449$		−	11.0263i		−	0.520361i	0.965560	−	0.260181i	$-0.0837821\pi$
$450$	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	−0.929450	−	0.368949i	$-0.879718\pi$
$457$	1.28162	−	4.78308i	0.0599518	−	0.223743i	0.989401	+	0.145206i	$0.0463844\pi$
$458$	−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	−0.0879597	−	0.996124i	$-0.528035\pi$
$461$	9.15490	−	2.97461i	0.426386	−	0.138541i	0.514346	+	0.857583i	$0.328035\pi$
$462$	3.17032	−	17.1318i	0.147496	−	0.797044i
$463$	9.49875	+	18.6423i	0.441444	+	0.866383i	0.999335	+	0.0364685i	$0.0116109\pi$
$463$	9.49875	+	18.6423i	0.441444	+	0.866383i	−0.557891	+	0.829914i	$0.688389\pi$
$464$	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	0.772732	−	0.634732i	$-0.218890\pi$
$467$	−0.189940	−	0.234556i	−0.00878937	−	0.0108540i	−0.781522	+	0.623878i	$0.785556\pi$
$468$	−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	−0.965350	−	0.260960i	$-0.915961\pi$
$479$	−1.64916	−	15.6907i	−0.0753519	−	0.716926i	0.889998	−	0.455965i	$-0.150706\pi$
$480$	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	0.977294	+	0.211886i	$0.0679605\pi$
$487$	−0.370620	+	7.07185i	−0.0167944	+	0.320456i	−0.994089	+	0.108570i	$0.965373\pi$
$488$	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	0.676989	+	0.735993i	$0.263285\pi$
$491$	−6.72096	+	20.6850i	−0.303313	+	0.933500i	−0.980301	+	0.197507i	$0.936715\pi$
$492$	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	−0.418665	−	0.908141i	$-0.637502\pi$
$499$	3.54008	−	2.04386i	0.158476	−	0.0914959i	0.577141	+	0.816645i	$0.304168\pi$
$500$	−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	0.918899	−	0.394492i	$-0.129079\pi$
$503$	37.4748	+	5.93543i	1.67092	+	0.264648i	0.752020	+	0.659140i	$0.229079\pi$
$504$	−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	0.472706	−	0.881220i	$-0.343277\pi$
$509$	28.4939	−	6.05656i	1.26297	−	0.268452i	0.790263	+	0.612768i	$0.209944\pi$
$510$	−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	−0.328815	−	0.944395i	$-0.606649\pi$
$521$	−10.3649	+	1.08939i	−0.454093	+	0.0477271i	−0.125278	+	0.992122i	$0.539982\pi$
$522$	3.63247	−	4.48573i	0.158989	−	0.196335i
$523$	−13.4776	+	0.706329i	−0.589333	+	0.0308856i	−0.344672	−	0.938723i	$-0.612010\pi$
$523$	−13.4776	+	0.706329i	−0.589333	+	0.0308856i	−0.244661	+	0.969609i	$0.578677\pi$
$524$	−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	0.0358843	−	0.999356i	$-0.488575\pi$
$541$	11.0515	−	2.34907i	0.475141	−	0.100994i	0.439257	+	0.898362i	$0.355242\pi$
$542$	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	−0.530950	−	0.847403i	$-0.678165\pi$
$547$	−30.3524	−	4.80735i	−1.29778	−	0.205547i	−0.766826	+	0.641856i	$0.778165\pi$
$548$	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	−0.194344	−	0.980934i	$-0.562258\pi$
$557$	3.01658	−	0.808291i	0.127817	−	0.0342484i	0.322160	+	0.946685i	$0.395591\pi$
$558$	−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	−0.750325	−	0.661070i	$-0.770103\pi$
$563$	1.54206	−	29.4243i	0.0649902	−	1.24009i	0.815315	−	0.579018i	$-0.196564\pi$
$564$	−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	0.269542	−	0.962989i	$-0.413128\pi$
$569$	7.94274	+	0.834815i	0.332977	+	0.0349973i	0.0634350	+	0.997986i	$0.479794\pi$
$570$	−20.2167	+	37.2089i	−0.846782	+	1.55851i
$571$	−3.24397	−	30.8643i	−0.135756	−	1.29163i	−0.824182	−	0.566325i	$-0.808365\pi$
$571$	−3.24397	−	30.8643i	−0.135756	−	1.29163i	0.688426	−	0.725307i	$-0.258302\pi$
$572$	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	0.176067	−	0.984378i	$-0.443663\pi$
$577$	27.5508	−	17.8917i	1.14695	−	0.744840i	0.970887	+	0.239538i	$0.0769959\pi$
$578$	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	0.901399	+	0.432989i	$0.142541\pi$
$587$	17.4894	+	34.3249i	0.721865	+	1.41674i	−0.179534	+	0.983752i	$0.557459\pi$
$588$	−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	−0.728154	−	0.685413i	$-0.759622\pi$
$593$	5.96985	−	22.2798i	0.245153	−	0.914922i	0.973307	−	0.229508i	$-0.0737118\pi$
$594$	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	0.778839	−	0.627224i	$-0.215809\pi$
$599$	15.2982	+	8.83240i	0.625066	+	0.360882i	−0.153773	+	0.988106i	$0.549142\pi$
$600$	−2.30245	+	43.4544i	−0.0939970	+	1.77402i
$601$			22.6811i			0.925181i	0.886572	+	0.462591i	$0.153080\pi$
$601$			22.6811i			0.925181i	−0.886572	+	0.462591i	$0.846920\pi$
$602$	−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	−0.0279907	−	0.999608i	$-0.508911\pi$
$607$	−13.6007	−	3.64430i	−0.552036	−	0.147917i	−0.524045	+	0.851691i	$0.675578\pi$
$608$	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	0.300013	−	0.953935i	$-0.403009\pi$
$613$	12.3464	+	0.647050i	0.498668	+	0.0261341i	0.198656	+	0.980069i	$0.436342\pi$
$614$	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	0.918454	+	0.395527i	$0.129438\pi$
$617$	4.15259	+	26.2184i	0.167177	+	1.05551i	−0.751277	+	0.659987i	$0.770562\pi$
$618$	38.6371	+	10.3528i	1.55421	+	0.416450i
$619$	−36.0574	+	16.0538i	−1.44927	+	0.645255i	−0.972315	−	0.233674i	$-0.924925\pi$
$619$	−36.0574	+	16.0538i	−1.44927	+	0.645255i	−0.476952	+	0.878929i	$0.658259\pi$
$620$	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	0.535514	−	0.844526i	$-0.320118\pi$
$631$	−2.56712	−	1.86512i	−0.102195	−	0.0742493i	−0.637709	+	0.770277i	$0.720118\pi$
$632$	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	0.675193	−	0.737641i	$-0.264060\pi$
$641$	−3.26561	−	3.62683i	−0.128984	−	0.143251i	−0.804177	+	0.594390i	$0.797394\pi$
$642$	−20.2028	−	24.9483i	−0.797339	−	0.984632i
$643$	−0.430113	−	0.430113i	−0.0169620	−	0.0169620i	0.698575	−	0.715537i	$-0.253818\pi$
$643$	−0.430113	−	0.430113i	−0.0169620	−	0.0169620i	−0.715537	+	0.698575i	$0.753818\pi$
$644$	−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	0.347432	−	0.937705i	$-0.387054\pi$
$647$	−12.6557	−	10.2484i	−0.497547	−	0.402905i	−0.844979	+	0.534800i	$0.820387\pi$
$648$	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	0.729648	−	0.683823i	$-0.239684\pi$
$653$	44.1941	−	16.9645i	1.72945	−	0.663873i	0.999801	+	0.0199493i	$0.00635048\pi$
$654$	−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	0.0561901	−	0.998420i	$-0.482105\pi$
$659$	−12.4558	−	4.04712i	−0.485208	−	0.157654i	−0.541398	+	0.840767i	$0.682105\pi$
$660$	−18.4619	−	11.3208i	−0.718627	−	0.440660i
$661$	−6.32141	+	29.7399i	−0.245874	+	1.15675i	0.665895	+	0.746045i	$0.268050\pi$
$661$	−6.32141	+	29.7399i	−0.245874	+	1.15675i	−0.911769	+	0.410702i	$0.865284\pi$
$662$	−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	0.684214	−	0.729282i	$-0.260146\pi$
$673$	12.8773	+	6.56131i	0.496383	+	0.252920i	−0.187830	+	0.982201i	$0.560146\pi$
$674$	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	0.946424	+	0.322927i	$0.104667\pi$
$677$	1.01318	+	19.3326i	0.0389397	+	0.743014i	−0.907484	+	0.420086i	$0.862000\pi$
$678$	−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	0.182581	+	0.983191i	$0.441555\pi$
$683$	−15.9677	+	41.5972i	−0.610986	+	1.59167i	−0.793567	+	0.608483i	$0.791778\pi$
$684$	−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	0.964745	−	0.263187i	$-0.0847735\pi$
$691$	−0.621449	−	2.92369i	−0.0236410	−	0.111222i	−0.988386	+	0.151964i	$0.951440\pi$
$692$	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	−0.944881	−	0.327414i	$-0.893823\pi$
$709$	−5.72110	−	26.9157i	−0.214861	−	1.01084i	0.730020	−	0.683425i	$-0.239511\pi$
$710$	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	−0.988879	−	0.148721i	$-0.952484\pi$
$719$	0.249681	−	2.37555i	0.00931152	−	0.0885932i	0.998191	+	0.0601281i	$0.0191509\pi$
$720$	−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	−0.566457	−	0.824091i	$-0.691686\pi$
$727$	−42.2271	−	21.5158i	−1.56612	−	0.797976i	−0.999659	+	0.0261149i	$0.991686\pi$
$728$	−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	−0.790565	−	0.612378i	$-0.790213\pi$
$733$	−9.63660	+	7.80357i	−0.355936	+	0.288231i	0.434629	+	0.900610i	$0.356880\pi$
$734$	−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	−0.988661	−	0.150162i	$-0.952020\pi$
$739$	−0.663245	+	3.12032i	−0.0243979	+	0.114783i	0.964264	+	0.264945i	$0.0853538\pi$
$740$	−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	−0.921879	−	0.387478i	$-0.873346\pi$
$743$	−14.5667	+	14.5667i	−0.534401	+	0.534401i	0.387478	+	0.921879i	$0.373346\pi$
$744$	−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	0.753588	−	0.657347i	$-0.228321\pi$
$751$	−5.27493	−	9.13644i	−0.192485	−	0.333394i	−0.946073	+	0.323953i	$0.894988\pi$
$752$	−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	0.959072	−	0.283161i	$-0.0913830\pi$
$757$	18.5968	+	18.5968i	0.675912	+	0.675912i	−0.283161	+	0.959072i	$0.591383\pi$
$758$	−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	0.992937	−	0.118641i	$-0.0378537\pi$
$761$	26.9997	+	24.3106i	0.978737	+	0.881259i	−0.0142005	+	0.999899i	$0.504520\pi$
$762$	−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
$767$	3.98261	+	1.52878i	0.143804	+	0.0552010i
$768$	12.6091	−	47.0578i	0.454991	−	1.69805i
$769$	−12.1604	−	8.83501i	−0.438514	−	0.318599i	0.346530	−	0.938039i	$-0.387360\pi$
$769$	−12.1604	−	8.83501i	−0.438514	−	0.318599i	−0.785044	+	0.619440i	$0.787360\pi$
$770$	8.39106	+	9.31945i	0.302393	+	0.335850i
$771$	40.5010	−	29.4257i	1.45861	−	1.05974i
$772$	6.50715	+	16.9517i	0.234197	+	0.610105i
$773$	24.0690	+	37.0631i	0.865703	+	1.33307i	0.941873	+	0.335970i	$0.109064\pi$
$773$	24.0690	+	37.0631i	0.865703	+	1.33307i	−0.0761698	+	0.997095i	$0.524269\pi$
$774$	−10.8302	−	6.25279i	−0.389282	−	0.224752i
$775$	14.1569	+	11.4775i	0.508530	+	0.412285i
$776$			49.9053i			1.79150i
$777$	4.20492	−	6.12180i	0.150851	−	0.219618i
$778$	3.83482	−	24.2121i	0.137485	−	0.868045i
$779$	−6.80015	+	15.2734i	−0.243641	+	0.547226i
$780$	30.0608	−	3.94878i	1.07635	−	0.141389i
$781$	−33.2105	+	14.7863i	−1.18837	+	0.529094i
$782$	6.20172	+	1.66175i	0.221773	+	0.0594239i
$783$	1.79343	+	11.3233i	0.0640921	+	0.404661i
$784$	0.0435797	−	0.840404i	0.00155642	−	0.0300144i
$785$	−9.38810	+	5.09382i	−0.335076	+	0.181806i
$786$	−25.5019	+	28.3227i	−0.909622	+	1.01024i
$787$	−3.01076	−	0.157787i	−0.107322	−	0.00562450i	−0.00140060	−	0.999999i	$-0.500446\pi$
$787$	−3.01076	−	0.157787i	−0.107322	−	0.00562450i	−0.105921	+	0.994375i	$0.533779\pi$
$788$	−10.0172	−	0.524977i	−0.356846	−	0.0187015i
$789$	43.4799	−	48.2893i	1.54793	−	1.71914i
$790$	28.8885	+	3.81170i	1.02781	+	0.135614i
$791$	−23.0351	−	10.9794i	−0.819033	−	0.390382i
$792$	7.19602	+	45.4339i	0.255699	+	1.61442i
$793$	36.2602	+	9.71588i	1.28764	+	0.345021i
$794$	−6.08046	+	2.70719i	−0.215787	+	0.0960747i
$795$	−2.63051	−	5.51908i	−0.0932947	−	0.195741i
$796$	−3.16681	+	7.11278i	−0.112245	+	0.252106i
$797$	−0.278785	+	1.76018i	−0.00987509	+	0.0623488i	−0.992134	−	0.125182i	$-0.960048\pi$
$797$	−0.278785	+	1.76018i	−0.00987509	+	0.0623488i	0.982259	+	0.187531i	$0.0600485\pi$
$798$	49.9515	+	3.91743i	1.76826	+	0.138676i
$799$		−	9.82937i		−	0.347738i
$800$	−21.2135	+	19.0786i	−0.750009	+	0.674529i
$801$	54.1601	+	31.2694i	1.91365	+	1.10485i
$802$	17.0235	+	26.2139i	0.601122	+	0.925646i
$803$	7.30143	+	19.0209i	0.257662	+	0.671232i
$804$	16.0556	−	11.6651i	0.566239	−	0.411397i
$805$	7.13098	−	9.81469i	0.251334	−	0.345922i
$806$	8.75110	+	6.35804i	0.308244	+	0.223953i
$807$	−18.2100	+	67.9605i	−0.641021	+	2.39232i
$808$	−37.7473	−	14.4898i	−1.32795	−	0.509751i
$809$	−25.7296	+	23.1670i	−0.904603	+	0.814508i	−0.983225	−	0.182396i	$-0.941615\pi$
$809$	−25.7296	+	23.1670i	−0.904603	+	0.814508i	0.0786219	+	0.996905i	$0.474948\pi$
$810$	19.0506	+	22.3184i	0.669369	+	0.784187i
$811$	−47.4403	+	15.4143i	−1.66585	+	0.541269i	−0.982086	−	0.188432i	$-0.939660\pi$
$811$	−47.4403	+	15.4143i	−1.66585	+	0.541269i	−0.683767	+	0.729700i	$0.739660\pi$
$812$	3.32055	+	0.614483i	0.116529	+	0.0215641i
$813$	16.2816	+	31.9545i	0.571022	+	1.12069i
$814$	1.42337	+	1.28161i	0.0498891	+	0.0449203i
$815$	−2.35648	−	0.835235i	−0.0825437	−	0.0292570i
$816$	−0.911289	−	1.01209i	−0.0319015	−	0.0354302i
$817$	9.78441	+	12.0827i	0.342313	+	0.422721i
$818$	−7.14775	−	7.14775i	−0.249915	−	0.249915i
$819$	−59.1444	−	14.1821i	−2.06667	−	0.495562i
$820$	0.172144	+	6.64704i	0.00601151	+	0.232125i
$821$	14.0947	+	6.27537i	0.491908	+	0.219012i	0.637672	−	0.770308i	$-0.279897\pi$
$821$	14.0947	+	6.27537i	0.491908	+	0.219012i	−0.145764	+	0.989319i	$0.546564\pi$
$822$	3.61386	+	2.92645i	0.126048	+	0.102072i
$823$	−17.7541	+	11.5297i	−0.618869	+	0.401898i	−0.815647	−	0.578550i	$-0.803619\pi$
$823$	−17.7541	+	11.5297i	−0.618869	+	0.401898i	0.196778	+	0.980448i	$0.436952\pi$
$824$	21.0054	+	36.3825i	0.731759	+	1.26744i
$825$	15.6176	−	35.0235i	0.543736	−	1.21936i
$826$	2.77992	+	0.365205i	0.0967259	+	0.0127071i
$827$	−0.614015	+	1.20507i	−0.0213514	+	0.0419045i	−0.901436	−	0.432913i	$-0.857486\pi$
$827$	−0.614015	+	1.20507i	−0.0213514	+	0.0419045i	0.880084	+	0.474817i	$0.157486\pi$
$828$	16.0792	−	6.17223i	0.558791	−	0.214500i
$829$	−3.42782	−	32.6135i	−0.119053	−	1.13271i	−0.877031	−	0.480433i	$-0.840479\pi$
$829$	−3.42782	−	32.6135i	−0.119053	−	1.13271i	0.757978	−	0.652280i	$-0.226187\pi$
$830$	5.33333	−	2.54198i	0.185123	−	0.0882335i
$831$	−78.4754	−	8.24810i	−2.72228	−	0.286123i
$832$	−11.3863	+	11.3863i	−0.394747	+	0.394747i
$833$	20.6592	+	14.9924i	0.715799	+	0.519456i
$834$	−26.5999	−	8.64284i	−0.921080	−	0.299277i
$835$	17.3478	+	41.9155i	0.600346	+	1.45054i
$836$	4.60193	−	21.6504i	0.159161	−	0.748793i
$837$	2.16376	−	41.2870i	0.0747904	−	1.42709i
$838$	4.40856	+	2.86295i	0.152291	+	0.0988989i
$839$	8.80454	+	27.0976i	0.303966	+	0.935512i	0.980061	+	0.198697i	$0.0636711\pi$
$839$	8.80454	+	27.0976i	0.303966	+	0.935512i	−0.676094	+	0.736815i	$0.736329\pi$
$840$	48.0685	−	18.4511i	1.65852	−	0.636623i
$841$	8.64580	−	26.6090i	0.298131	−	0.917553i
$842$	−16.2353	+	13.1470i	−0.559504	+	0.453077i
$843$	−6.13722	+	1.64446i	−0.211377	+	0.0566383i
$844$	−9.05744	−	20.3434i	−0.311770	−	0.700247i
$845$	2.17713	+	0.902531i	0.0748955	+	0.0310480i
$846$	9.04792	+	12.4534i	0.311074	+	0.428157i
$847$	12.6183	−	3.03307i	0.433571	−	0.104217i
$848$	−0.0942756	−	0.0480358i	−0.00323744	−	0.00164956i
$849$	−55.7717	+	32.1998i	−1.91408	+	1.10510i
$850$	−2.44006	−	15.4635i	−0.0836933	−	0.530395i
$851$	0.926457	−	1.60467i	0.0317585	−	0.0550074i
$852$	3.02331	+	57.6882i	0.103577	+	1.97636i
$853$	9.12263	+	1.44488i	0.312353	+	0.0494718i	0.310643	−	0.950527i	$-0.399456\pi$
$853$	9.12263	+	1.44488i	0.312353	+	0.0494718i	0.00170994	+	0.999999i	$0.499456\pi$
$854$	24.6646	+	0.639070i	0.844004	+	0.0218685i
$855$	−35.2182	−	99.5442i	−1.20444	−	3.40434i
$856$	3.52431	−	33.5316i	0.120459	−	1.14609i
$857$	7.74225	+	28.8945i	0.264470	+	0.987016i	0.962574	+	0.271019i	$0.0873607\pi$
$857$	7.74225	+	28.8945i	0.264470	+	0.987016i	−0.698104	+	0.715997i	$0.745973\pi$
$858$	8.15655	−	21.2485i	0.278460	−	0.725413i
$859$	−51.9291	+	11.0379i	−1.77180	+	0.376608i	−0.974041	−	0.226370i	$-0.927314\pi$
$859$	−51.9291	+	11.0379i	−1.77180	+	0.376608i	−0.797758	+	0.602978i	$0.793981\pi$
$860$	5.58033	+	2.66366i	0.190288	+	0.0908299i
$861$	6.45584	−	18.2467i	0.220014	−	0.621845i
$862$	1.68925	−	0.860716i	0.0575361	−	0.0293161i
$863$	4.16714	−	6.41683i	0.141851	−	0.218431i	−0.760603	−	0.649217i	$-0.775097\pi$
$863$	4.16714	−	6.41683i	0.141851	−	0.218431i	0.902454	+	0.430785i	$0.141763\pi$
$864$	63.3079	+	13.4565i	2.15378	+	0.457800i
$865$	5.65304	+	19.1045i	0.192209	+	0.649574i
$866$	−5.34854	−	25.1629i	−0.181751	−	0.855070i
$867$	−11.3608	+	1.79938i	−0.385834	+	0.0611101i
$868$	−11.2523	−	4.65724i	−0.381929	−	0.158077i
$869$	−22.0238	+	30.3132i	−0.747108	+	1.02831i
$870$	1.40564	+	5.86236i	0.0476557	+	0.198752i
$871$	−17.3891	+	1.82767i	−0.589207	+	0.0619281i
$872$	1.30880	−	1.61623i	0.0443216	−	0.0547326i
$873$	−118.320	+	6.20090i	−4.00453	+	0.209869i
$874$	12.5006			0.422840
$875$	−28.9304	−	6.16714i	−0.978025	−	0.208487i
$876$	32.3755			1.09387
$877$	−55.5748	+	2.91255i	−1.87663	+	0.0983499i	−0.956227	−	0.292626i	$-0.905471\pi$
$877$	−55.5748	+	2.91255i	−1.87663	+	0.0983499i	−0.920401	+	0.390976i	$0.872137\pi$
$878$	−2.81421	+	3.47526i	−0.0949749	+	0.117284i
$879$	−52.9838	+	5.56882i	−1.78710	+	0.187832i
$880$	−0.154741	−	0.645360i	−0.00521630	−	0.0217551i
$881$	29.7627	−	40.9648i	1.00273	−	1.38014i	0.0790948	−	0.996867i	$-0.474797\pi$
$881$	29.7627	−	40.9648i	1.00273	−	1.38014i	0.923635	−	0.383273i	$-0.125203\pi$
$882$	−39.9748	+	0.0220087i	−1.34602	+	0.000741073i
$883$	−29.5527	+	4.68068i	−0.994527	+	0.157518i	−0.632425	−	0.774621i	$-0.717941\pi$
$883$	−29.5527	+	4.68068i	−0.994527	+	0.157518i	−0.362101	+	0.932139i	$0.617941\pi$
$884$	3.30907	+	15.5679i	0.111296	+	0.523606i
$885$	−2.43275	−	8.22150i	−0.0817758	−	0.276363i
$886$	−29.5691	−	6.28511i	−0.993393	−	0.211152i
$887$	−0.624447	+	0.961564i	−0.0209669	+	0.0322861i	−0.848999	−	0.528395i	$-0.822794\pi$
$887$	−0.624447	+	0.961564i	−0.0209669	+	0.0322861i	0.828032	+	0.560681i	$0.189461\pi$
$888$	7.00681	−	3.57015i	0.235133	−	0.119806i
$889$	−5.36508	−	28.9030i	−0.179939	−	0.969375i
$890$	16.2917	+	7.77649i	0.546098	+	0.260668i
$891$	−36.9076	+	7.84496i	−1.23645	+	0.262816i
$892$	−3.90702	+	10.1781i	−0.130817	+	0.340789i
$893$	−4.95319	−	18.4856i	−0.165752	−	0.618596i
$894$	−3.38230	+	32.1804i	−0.113121	+	1.07627i
$895$	−4.30211	−	12.1599i	−0.143804	−	0.406461i
$896$	10.2419	−	16.7236i	0.342158	−	0.558696i
$897$	−21.7475	−	3.44446i	−0.726126	−	0.115007i
$898$	−0.495478	−	9.45428i	−0.0165343	−	0.315493i
$899$	1.84208	−	3.19058i	0.0614370	−	0.106412i
$900$	−29.6776	−	29.7118i	−0.989253	−	0.990393i
$901$	2.77946	−	1.60472i	0.0925971	−	0.0534610i
$902$	4.44751	+	2.26612i	0.148086	+	0.0754535i
$903$	−12.3934	−	13.0527i	−0.412427	−	0.434368i
$904$	−15.8818	−	21.8594i	−0.528220	−	0.727032i
$905$	11.5700	+	4.79635i	0.384600	+	0.159436i
$906$	5.44748	+	12.2352i	0.180980	+	0.406488i
$907$	34.2261	−	9.17085i	1.13646	−	0.304513i	0.358932	−	0.933364i	$-0.383141\pi$
$907$	34.2261	−	9.17085i	1.13646	−	0.304513i	0.777526	+	0.628851i	$0.216474\pi$
$908$	−10.7096	+	8.67250i	−0.355412	+	0.287807i
$909$	29.6637	−	91.2954i	0.983882	−	3.02808i
$910$	−17.3404	−	2.74668i	−0.574830	−	0.0910516i
$911$	−1.99352	−	6.13541i	−0.0660482	−	0.203275i	0.912586	−	0.408885i	$-0.134082\pi$
$911$	−1.99352	−	6.13541i	−0.0660482	−	0.203275i	−0.978634	+	0.205610i	$0.934082\pi$
$912$	−2.22382	−	1.44417i	−0.0736381	−	0.0478211i
$913$	−0.397605	+	7.58676i	−0.0131588	+	0.251085i
$914$	0.883972	−	4.15876i	0.0292392	−	0.137560i
$915$	−28.8526	−	69.7131i	−0.953838	−	2.30465i
$916$	11.7691	+	3.82400i	0.388860	+	0.126348i
$917$	−32.2270	+	19.7609i	−1.06423	+	0.652563i
$918$	−25.1117	+	25.1117i	−0.828808	+	0.828808i
$919$	25.9062	+	2.72286i	0.854568	+	0.0898187i	0.521673	−	0.853145i	$-0.325308\pi$
$919$	25.9062	+	2.72286i	0.854568	+	0.0898187i	0.332895	+	0.942964i	$0.391975\pi$
$920$	11.5960	−	5.52689i	0.382307	−	0.182216i
$921$	1.64269	+	15.6292i	0.0541286	+	0.514999i
$922$	7.71605	−	2.96191i	0.254114	−	0.0975454i
$923$	23.1058	−	45.3477i	0.760537	−	1.49264i
$924$	−3.33764	+	25.4059i	−0.109800	+	0.835793i
$925$	−4.49288	−	0.474837i	−0.147725	−	0.0156125i
$926$	8.98225	+	15.5577i	0.295175	+	0.511258i
$927$	−83.6491	+	54.3224i	−2.74740	+	1.78418i
$928$	4.48216	+	3.62958i	0.147134	+	0.119147i
$929$	41.1452	+	18.3190i	1.34993	+	0.601027i	0.949056	−	0.315107i	$-0.102040\pi$
$929$	41.1452	+	18.3190i	1.34993	+	0.601027i	0.400873	+	0.916134i	$0.368707\pi$
$930$	−0.562838	−	21.7331i	−0.0184562	−	0.712655i
$931$	46.4076	+	17.7849i	1.52095	+	0.582876i
$932$	−3.01458	−	3.01458i	−0.0987459	−	0.0987459i
$933$	−6.05770	−	7.48064i	−0.198320	−	0.244905i
$934$	−0.173401	−	0.192581i	−0.00567384	−	0.00630144i
$935$	18.9738	+	6.72511i	0.620509	+	0.219935i
$936$	−47.8589	−	43.0923i	−1.56432	−	1.40852i
$937$	−1.89104	−	3.71138i	−0.0617776	−	0.121245i	0.858053	−	0.513561i	$-0.171674\pi$
$937$	−1.89104	−	3.71138i	−0.0617776	−	0.121245i	−0.919831	+	0.392316i	$0.871674\pi$
$938$	−10.8318	+	3.83909i	−0.353670	+	0.125351i
$939$	1.02899	−	0.334341i	0.0335800	−	0.0109108i
$940$	−4.94147	−	5.78909i	−0.161173	−	0.188819i
$941$	−33.9281	+	30.5490i	−1.10602	+	0.995868i	−0.106025	+	0.994363i	$0.533812\pi$
$941$	−33.9281	+	30.5490i	−1.10602	+	0.995868i	−0.999999	+	0.00150480i	$0.999521\pi$
$942$	11.8949	+	4.56604i	0.387558	+	0.148770i
$943$	1.24981	−	4.66434i	0.0406993	−	0.151892i
$944$	−0.120042	−	0.0872159i	−0.00390705	−	0.00283864i
$945$	27.2927	+	61.3024i	0.887830	+	1.99417i
$946$	3.75535	−	2.72842i	0.122097	−	0.0887087i
$947$	−11.3958	−	29.6870i	−0.370313	−	0.964698i	−0.984476	−	0.175519i	$-0.943840\pi$
$947$	−11.3958	−	29.6870i	−0.370313	−	0.964698i	0.614163	−	0.789179i	$-0.289494\pi$
$948$	32.4280	+	49.9347i	1.05321	+	1.62181i
$949$	−24.7024	−	14.2619i	−0.801873	−	0.462962i
$950$	−12.3812	−	27.8519i	−0.401700	−	0.903634i
$951$			4.30486i			0.139595i
$952$	11.6427	+	24.3921i	0.377341	+	0.790552i
$953$	−5.01517	+	31.6645i	−0.162457	+	1.02571i	0.762872	+	0.646549i	$0.223789\pi$
$953$	−5.01517	+	31.6645i	−0.162457	+	1.02571i	−0.925329	+	0.379165i	$0.876211\pi$
$954$	−2.04431	+	4.59160i	−0.0661870	+	0.148658i
$955$	−16.7708	−	35.1868i	−0.542690	−	1.13862i
$956$	17.2335	−	7.67286i	0.557372	−	0.248158i
$957$	−7.48783	−	2.00636i	−0.242047	−	0.0648564i
$958$	−2.11912	−	13.3796i	−0.0684657	−	0.432275i
$959$	2.61358	+	3.80055i	0.0843970	+	0.122726i
$960$	32.0856	+	4.23354i	1.03556	+	0.136637i
$961$	11.8530	−	13.1640i	0.382353	−	0.424646i
$962$	−2.67780	−	0.140337i	−0.0863357	−	0.00452466i
$963$	79.9378	+	4.18936i	2.57596	+	0.135000i
$964$	22.4439	−	24.9264i	0.722868	−	0.802826i
$965$	−28.2606	+	15.3337i	−0.909742	+	0.493610i
$966$	−14.4268	+	1.13941i	−0.464176	+	0.0366600i
$967$	−2.94641	−	18.6029i	−0.0947502	−	0.598229i	−0.988682	−	0.150026i	$-0.952064\pi$
$967$	−2.94641	−	18.6029i	−0.0947502	−	0.598229i	0.893932	−	0.448203i	$-0.147936\pi$
$968$	13.2733	+	3.55657i	0.426620	+	0.114312i
$969$	73.4767	−	32.7139i	2.36041	−	1.05092i
$970$	−33.9100	+	4.45440i	−1.08878	+	0.143022i
$971$	−18.9161	+	42.4862i	−0.607045	+	1.36345i	0.304605	+	0.952479i	$0.401476\pi$
$971$	−18.9161	+	42.4862i	−0.607045	+	1.36345i	−0.911650	+	0.410967i	$0.865191\pi$
$972$	−2.65758	+	16.7793i	−0.0852418	+	0.538196i
$973$	−22.8673	−	15.7070i	−0.733092	−	0.503543i
$974$			6.08029i			0.194825i
$975$	13.8654	+	51.8657i	0.444047	+	1.66103i
$976$	−1.13078	−	0.652856i	−0.0361954	−	0.0208974i
$977$	21.7345	+	33.4682i	0.695348	+	1.07074i	0.993233	+	0.116140i	$0.0370522\pi$
$977$	21.7345	+	33.4682i	0.695348	+	1.07074i	−0.297885	+	0.954602i	$0.596281\pi$
$978$	1.06878	+	2.78427i	0.0341758	+	0.0890311i
$979$	−18.7800	+	13.6445i	−0.600212	+	0.436080i
$980$	19.7045	−	1.55598i	0.629436	−	0.0497040i
$981$	3.99455	+	2.90221i	0.127536	+	0.0926604i
$982$	−4.83327	+	18.0380i	−0.154236	+	0.575616i
$983$	40.9055	+	15.7021i	1.30468	+	0.500820i	0.908704	−	0.417440i	$-0.137073\pi$
$983$	40.9055	+	15.7021i	1.30468	+	0.500820i	0.395977	+	0.918260i	$0.370406\pi$
$984$	15.2302	−	13.7133i	0.485520	−	0.437164i
$985$	−1.38850	−	17.7077i	−0.0442412	−	0.564215i
$986$	−3.00973	+	0.977921i	−0.0958494	+	0.0311434i
$987$	7.40136	+	20.8825i	0.235588	+	0.664698i
$988$	14.0681	+	27.6103i	0.447567	+	0.878400i
$989$	−3.33717	−	3.00480i	−0.106116	−	0.0955470i
$990$	−30.2294	+	8.94489i	−0.960754	+	0.284287i
$991$	21.6051	+	23.9949i	0.686310	+	0.762224i	0.981134	−	0.193327i	$-0.0619279\pi$
$991$	21.6051	+	23.9949i	0.686310	+	0.762224i	−0.294825	+	0.955551i	$0.595261\pi$
$992$	−13.0892	−	16.1638i	−0.415582	−	0.513201i
$993$	−28.0429	−	28.0429i	−0.889916	−	0.889916i
$994$	7.80000	−	32.5288i	0.247401	−	1.03175i
$995$	−13.2179	−	3.91947i	−0.419036	−	0.124255i
$996$	11.0286	+	4.91024i	0.349454	+	0.155587i
$997$	−26.3192	−	21.3129i	−0.833539	−	0.674986i	0.114402	−	0.993435i	$-0.463505\pi$
$997$	−26.3192	−	21.3129i	−0.833539	−	0.674986i	−0.947940	+	0.318448i	$0.896838\pi$
$998$	2.94353	−	1.91155i	0.0931759	−	0.0605092i
$999$	5.12445	+	8.87580i	0.162130	+	0.280818i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	175.2.x.a.17.13	yes	288
5.2	odd	4		875.2.bb.a.143.13		288
5.3	odd	4		875.2.bb.b.143.6		288
5.4	even	2		875.2.bb.c.857.6		288
7.5	odd	6	inner	175.2.x.a.117.6	yes	288
25.3	odd	20	inner	175.2.x.a.3.6	✓	288
25.4	even	10		875.2.bb.a.507.13		288
25.21	even	5		875.2.bb.b.507.6		288
25.22	odd	20		875.2.bb.c.493.13		288
35.12	even	12		875.2.bb.a.768.13		288
35.19	odd	6		875.2.bb.c.607.13		288
35.33	even	12		875.2.bb.b.768.6		288
175.47	even	60		875.2.bb.c.243.6		288
175.54	odd	30		875.2.bb.a.257.13		288
175.96	odd	30		875.2.bb.b.257.6		288
175.103	even	60	inner	175.2.x.a.103.13	yes	288

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
175.2.x.a.3.6	✓	288	25.3	odd	20	inner
175.2.x.a.17.13	yes	288	1.1	even	1	trivial
175.2.x.a.103.13	yes	288	175.103	even	60	inner
175.2.x.a.117.6	yes	288	7.5	odd	6	inner
875.2.bb.a.143.13		288	5.2	odd	4
875.2.bb.a.257.13		288	175.54	odd	30
875.2.bb.a.507.13		288	25.4	even	10
875.2.bb.a.768.13		288	35.12	even	12
875.2.bb.b.143.6		288	5.3	odd	4
875.2.bb.b.257.6		288	175.96	odd	30
875.2.bb.b.507.6		288	25.21	even	5
875.2.bb.b.768.6		288	35.33	even	12
875.2.bb.c.243.6		288	175.47	even	60
875.2.bb.c.493.13		288	25.22	odd	20
875.2.bb.c.607.13		288	35.19	odd	6
875.2.bb.c.857.6		288	5.4	even	2

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 $\F_{q}$
Belyi maps

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} +(-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})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 288 q - 8 q^{2} - 24 q^{3} - 10 q^{4} - 30 q^{5} - 10 q^{7} - 36 q^{8} - 10 q^{9} - 36 q^{10} - 6 q^{11} - 36 q^{12} - 20 q^{14} - 28 q^{15} - 30 q^{16} - 42 q^{17} - 14 q^{18} - 30 q^{19} - 12 q^{21} + 32 q^{22}+ \cdots + 222 q^{98}+O(q^{100}) \) 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

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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