LMFDB - Embedded newform 175.2.x.a.108.7

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			108.7
Character	$\chi$	$=$	175.108
Dual form			175.2.x.a.47.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.0571879 - 1.09121i) q^{2} +(-2.14107 - 1.73380i) q^{3} +(0.801576 - 0.0842491i) q^{4} +(-1.85562 + 1.24767i) q^{5} +(-1.76950 + 2.43551i) q^{6} +(-2.33490 - 1.24428i) q^{7} +(-0.479648 - 3.02838i) q^{8} +(0.954369 + 4.48995i) q^{9} +(1.46759 + 1.95352i) q^{10} +(-2.33390 - 0.496086i) q^{11} +(-1.86230 - 1.20939i) q^{12} +(1.87090 + 3.67184i) q^{13} +(-1.22424 + 2.61902i) q^{14} +(6.13623 + 0.545928i) q^{15} +(-1.70041 + 0.361432i) q^{16} +(-4.38143 - 1.68187i) q^{17} +(4.84490 - 1.29819i) q^{18} +(0.387149 - 3.68347i) q^{19} +(-1.38230 + 1.15644i) q^{20} +(2.84185 + 6.71235i) q^{21} +(-0.407863 + 2.57515i) q^{22} +(3.37458 - 0.176854i) q^{23} +(-4.22365 + 7.31558i) q^{24} +(1.88664 - 4.63040i) q^{25} +(3.89975 - 2.25152i) q^{26} +(1.98904 - 3.90371i) q^{27} +(-1.97643 - 0.800672i) q^{28} +(-4.02782 - 5.54382i) q^{29} +(0.244804 - 6.72713i) q^{30} +(-3.81411 - 8.56663i) q^{31} +(-1.09550 - 4.08847i) q^{32} +(4.13693 + 5.10869i) q^{33} +(-1.58471 + 4.87724i) q^{34} +(5.88514 - 0.604282i) q^{35} +(1.14327 + 3.51863i) q^{36} +(1.82239 - 2.80623i) q^{37} +(-4.04158 - 0.211810i) q^{38} +(2.36053 - 11.1054i) q^{39} +(4.66846 + 5.02107i) q^{40} +(4.39294 + 1.42735i) q^{41} +(7.16206 - 3.48492i) q^{42} +(3.92655 + 3.92655i) q^{43} +(-1.91260 - 0.201022i) q^{44} +(-7.37292 - 7.14090i) q^{45} +(-0.385971 - 3.67226i) q^{46} +(-2.93204 - 7.63822i) q^{47} +(4.26734 + 2.17432i) q^{48} +(3.90354 + 5.81054i) q^{49} +(-5.16063 - 1.79391i) q^{50} +(6.46492 + 11.1976i) q^{51} +(1.80902 + 2.78564i) q^{52} +(-3.29547 + 4.06957i) q^{53} +(-4.37351 - 1.94721i) q^{54} +(4.94978 - 1.99140i) q^{55} +(-2.64822 + 7.66778i) q^{56} +(-7.21534 + 7.21534i) q^{57} +(-5.81913 + 4.71224i) q^{58} +(3.33935 + 3.70872i) q^{59} +(4.96465 - 0.0793685i) q^{60} +(2.25986 + 2.03478i) q^{61} +(-9.12986 + 4.65190i) q^{62} +(3.35840 - 11.6711i) q^{63} +(-7.70535 + 2.50362i) q^{64} +(-8.05292 - 4.47927i) q^{65} +(5.33807 - 4.80642i) q^{66} +(-4.08532 + 10.6426i) q^{67} +(-3.65375 - 0.979019i) q^{68} +(-7.53185 - 5.47221i) q^{69} +(-0.995957 - 6.38736i) q^{70} +(-2.61763 + 1.90182i) q^{71} +(13.1395 - 5.04378i) q^{72} +(12.8107 - 8.31934i) q^{73} +(-3.16640 - 1.82812i) q^{74} +(-12.0676 + 6.64296i) q^{75} -2.98520i q^{76} +(4.83217 + 4.06234i) q^{77} +(-12.2533 - 1.94074i) q^{78} +(0.754949 - 1.69564i) q^{79} +(2.70436 - 2.79223i) q^{80} +(1.55330 - 0.691572i) q^{81} +(1.30632 - 4.87525i) q^{82} +(4.83083 - 0.765128i) q^{83} +(2.84347 + 5.14104i) q^{84} +(10.2287 - 2.34567i) q^{85} +(4.06014 - 4.50924i) q^{86} +(-0.988053 + 18.8532i) q^{87} +(-0.382885 + 7.30589i) q^{88} +(-2.32462 + 2.58176i) q^{89} +(-7.37057 + 8.45378i) q^{90} +(0.200436 - 10.9013i) q^{91} +(2.69009 - 0.426068i) q^{92} +(-6.68658 + 24.9547i) q^{93} +(-8.16722 + 3.63628i) q^{94} +(3.87736 + 7.31815i) q^{95} +(-4.74306 + 10.6531i) q^{96} +(-3.70443 - 0.586724i) q^{97} +(6.11728 - 4.59187i) q^{98} -10.9526i 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 $\left(\mathbb{Z}/175\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{3}{20}\right)$

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 $

$2$	−0.0571879	−	1.09121i	−0.0404379	−	0.771602i	−0.941315	−	0.337528i	$-0.890409\pi$
$2$	−0.0571879	−	1.09121i	−0.0404379	−	0.771602i	0.900878	−	0.434073i	$-0.142924\pi$
$3$	−2.14107	−	1.73380i	−1.23615	−	1.00101i	−0.999568	−	0.0294004i	$-0.990640\pi$
$3$	−2.14107	−	1.73380i	−1.23615	−	1.00101i	−0.236580	−	0.971612i	$-0.576026\pi$
$4$	0.801576	−	0.0842491i	0.400788	−	0.0421245i
$5$	−1.85562	+	1.24767i	−0.829858	+	0.557975i
$5$	−1.85562	+	1.24767i	−0.829858	+	0.557975i
$6$	−1.76950	+	2.43551i	−0.722396	+	0.994292i
$7$	−2.33490	−	1.24428i	−0.882510	−	0.470293i
$7$	−2.33490	−	1.24428i	−0.882510	−	0.470293i
$8$	−0.479648	−	3.02838i	−0.169581	−	1.07069i
$9$	0.954369	+	4.48995i	0.318123	+	1.49665i
$10$	1.46759	+	1.95352i	0.464092	+	0.617756i
$11$	−2.33390	−	0.496086i	−0.703698	−	0.149576i	−0.157854	−	0.987462i	$-0.550458\pi$
$11$	−2.33390	−	0.496086i	−0.703698	−	0.149576i	−0.545844	+	0.837887i	$0.683791\pi$
$12$	−1.86230	−	1.20939i	−0.537600	−	0.349122i
$13$	1.87090	+	3.67184i	0.518893	+	1.01839i	0.990621	+	0.136641i	$0.0436306\pi$
$13$	1.87090	+	3.67184i	0.518893	+	1.01839i	−0.471727	+	0.881744i	$0.656369\pi$
$14$	−1.22424	+	2.61902i	−0.327192	+	0.699964i
$15$	6.13623	+	0.545928i	1.58437	+	0.140958i
$16$	−1.70041	+	0.361432i	−0.425102	+	0.0903581i
$17$	−4.38143	−	1.68187i	−1.06265	−	0.407915i	−0.236659	−	0.971593i	$-0.576052\pi$
$17$	−4.38143	−	1.68187i	−1.06265	−	0.407915i	−0.825995	+	0.563678i	$0.809386\pi$
$18$	4.84490	−	1.29819i	1.14195	−	0.305986i
$19$	0.387149	−	3.68347i	0.0888180	−	0.845047i	−0.855895	−	0.517149i	$-0.826993\pi$
$19$	0.387149	−	3.68347i	0.0888180	−	0.845047i	0.944713	−	0.327898i	$-0.106340\pi$
$20$	−1.38230	+	1.15644i	−0.309093	+	0.258587i
$21$	2.84185	+	6.71235i	0.620143	+	1.46476i
$22$	−0.407863	+	2.57515i	−0.0869567	+	0.549023i
$23$	3.37458	−	0.176854i	0.703649	−	0.0368767i	0.302844	−	0.953040i	$-0.402064\pi$
$23$	3.37458	−	0.176854i	0.703649	−	0.0368767i	0.400805	+	0.916163i	$0.368730\pi$
$24$	−4.22365	+	7.31558i	−0.862150	+	1.49329i
$25$	1.88664	−	4.63040i	0.377327	−	0.926080i
$26$	3.89975	−	2.25152i	0.764805	−	0.441560i
$27$	1.98904	−	3.90371i	0.382791	−	0.751269i
$28$	−1.97643	−	0.800672i	−0.373510	−	0.151313i
$29$	−4.02782	−	5.54382i	−0.747948	−	1.02946i	−0.998122	−	0.0612613i	$-0.980488\pi$
$29$	−4.02782	−	5.54382i	−0.747948	−	1.02946i	0.250174	−	0.968201i	$-0.419512\pi$
$30$	0.244804	−	6.72713i	0.0446949	−	1.22820i
$31$	−3.81411	−	8.56663i	−0.685034	−	1.53861i	−0.835197	−	0.549951i	$-0.814647\pi$
$31$	−3.81411	−	8.56663i	−0.685034	−	1.53861i	0.150163	−	0.988661i	$-0.452020\pi$
$32$	−1.09550	−	4.08847i	−0.193659	−	0.722747i
$33$	4.13693	+	5.10869i	0.720148	+	0.889308i
$34$	−1.58471	+	4.87724i	−0.271776	+	0.836441i
$35$	5.88514	−	0.604282i	0.994770	−	0.102142i
$36$	1.14327	+	3.51863i	0.190546	+	0.586439i
$37$	1.82239	−	2.80623i	0.299599	−	0.461341i	−0.656525	−	0.754304i	$-0.727974\pi$
$37$	1.82239	−	2.80623i	0.299599	−	0.461341i	0.956124	+	0.292963i	$0.0946412\pi$
$38$	−4.04158	−	0.211810i	−0.655631	−	0.0343602i
$39$	2.36053	−	11.1054i	0.377988	−	1.77829i
$40$	4.66846	+	5.02107i	0.738148	+	0.793901i
$41$	4.39294	+	1.42735i	0.686063	+	0.222915i	0.631248	−	0.775581i	$-0.282543\pi$
$41$	4.39294	+	1.42735i	0.686063	+	0.222915i	0.0548149	+	0.998497i	$0.482543\pi$
$42$	7.16206	−	3.48492i	1.10513	−	0.537735i
$43$	3.92655	+	3.92655i	0.598794	+	0.598794i	0.939992	−	0.341198i	$-0.110833\pi$
$43$	3.92655	+	3.92655i	0.598794	+	0.598794i	−0.341198	+	0.939992i	$0.610833\pi$
$44$	−1.91260	−	0.201022i	−0.288335	−	0.0303052i
$45$	−7.37292	−	7.14090i	−1.09909	−	1.06450i
$46$	−0.385971	−	3.67226i	−0.0569082	−	0.541446i
$47$	−2.93204	−	7.63822i	−0.427682	−	1.11415i	−0.963001	−	0.269499i	$-0.913142\pi$
$47$	−2.93204	−	7.63822i	−0.427682	−	1.11415i	0.535319	−	0.844650i	$-0.320191\pi$
$48$	4.26734	+	2.17432i	0.615938	+	0.313836i
$49$	3.90354	+	5.81054i	0.557648	+	0.830077i
$50$	−5.16063	−	1.79391i	−0.729823	−	0.253697i
$51$	6.46492	+	11.1976i	0.905269	+	1.56797i
$52$	1.80902	+	2.78564i	0.250865	+	0.386299i
$53$	−3.29547	+	4.06957i	−0.452668	+	0.558998i	−0.951479	−	0.307712i	$-0.900437\pi$
$53$	−3.29547	+	4.06957i	−0.452668	+	0.558998i	0.498812	+	0.866710i	$0.333770\pi$
$54$	−4.37351	−	1.94721i	−0.595159	−	0.264982i
$55$	4.94978	−	1.99140i	0.667429	−	0.268520i
$56$	−2.64822	+	7.66778i	−0.353883	+	1.02465i
$57$	−7.21534	+	7.21534i	−0.955695	+	0.955695i
$58$	−5.81913	+	4.71224i	−0.764089	+	0.618747i
$59$	3.33935	+	3.70872i	0.434746	+	0.482835i	0.920212	−	0.391421i	$-0.128016\pi$
$59$	3.33935	+	3.70872i	0.434746	+	0.482835i	−0.485465	+	0.874256i	$0.661350\pi$
$60$	4.96465	−	0.0793685i	0.640933	−	0.0102464i
$61$	2.25986	+	2.03478i	0.289345	+	0.260527i	0.801001	−	0.598663i	$-0.204301\pi$
$61$	2.25986	+	2.03478i	0.289345	+	0.260527i	−0.511656	+	0.859190i	$0.670968\pi$
$62$	−9.12986	+	4.65190i	−1.15949	+	0.590792i
$63$	3.35840	−	11.6711i	0.423118	−	1.47042i
$64$	−7.70535	+	2.50362i	−0.963169	+	0.312953i
$65$	−8.05292	−	4.47927i	−0.998841	−	0.555585i
$66$	5.33807	−	4.80642i	0.657070	−	0.591629i
$67$	−4.08532	+	10.6426i	−0.499102	+	1.30020i	0.420478	+	0.907303i	$0.361862\pi$
$67$	−4.08532	+	10.6426i	−0.499102	+	1.30020i	−0.919580	+	0.392902i	$0.871471\pi$
$68$	−3.65375	−	0.979019i	−0.443082	−	0.118724i
$69$	−7.53185	−	5.47221i	−0.906729	−	0.658777i
$70$	−0.995957	−	6.38736i	−0.119040	−	0.763435i
$71$	−2.61763	+	1.90182i	−0.310655	+	0.225704i	−0.732178	−	0.681114i	$-0.761496\pi$
$71$	−2.61763	+	1.90182i	−0.310655	+	0.225704i	0.421522	+	0.906818i	$0.361496\pi$
$72$	13.1395	−	5.04378i	1.54851	−	0.594416i
$73$	12.8107	−	8.31934i	1.49938	−	0.973706i	0.505544	−	0.862801i	$-0.331292\pi$
$73$	12.8107	−	8.31934i	1.49938	−	0.973706i	0.993831	−	0.110905i	$-0.0353748\pi$
$74$	−3.16640	−	1.82812i	−0.368087	−	0.212515i
$75$	−12.0676	+	6.64296i	−1.39345	+	0.767062i
$76$		−	2.98520i		−	0.342426i
$77$	4.83217	+	4.06234i	0.550676	+	0.462947i
$78$	−12.2533	−	1.94074i	−1.38742	−	0.219746i
$79$	0.754949	−	1.69564i	0.0849384	−	0.190775i	−0.866083	−	0.499901i	$-0.833370\pi$
$79$	0.754949	−	1.69564i	0.0849384	−	0.190775i	0.951021	+	0.309126i	$0.100036\pi$
$80$	2.70436	−	2.79223i	0.302356	−	0.312181i
$81$	1.55330	−	0.691572i	0.172589	−	0.0768414i
$82$	1.30632	−	4.87525i	0.144259	−	0.538381i
$83$	4.83083	−	0.765128i	0.530252	−	0.0839837i	0.114433	−	0.993431i	$-0.463495\pi$
$83$	4.83083	−	0.765128i	0.530252	−	0.0839837i	0.415819	+	0.909447i	$0.363495\pi$
$84$	2.84347	+	5.14104i	0.310248	+	0.560934i
$85$	10.2287	−	2.34567i	1.10946	−	0.254424i
$86$	4.06014	−	4.50924i	0.437816	−	0.486244i
$87$	−0.988053	+	18.8532i	−0.105930	+	2.02127i
$88$	−0.382885	+	7.30589i	−0.0408157	+	0.778810i
$89$	−2.32462	+	2.58176i	−0.246410	+	0.273666i	−0.853644	−	0.520857i	$-0.825612\pi$
$89$	−2.32462	+	2.58176i	−0.246410	+	0.273666i	0.607234	+	0.794523i	$0.292279\pi$
$90$	−7.37057	+	8.45378i	−0.776926	+	0.891106i
$91$	0.200436	−	10.9013i	0.0210114	−	1.14277i
$92$	2.69009	−	0.426068i	0.280461	−	0.0444207i
$93$	−6.68658	+	24.9547i	−0.693366	+	2.58768i
$94$	−8.16722	+	3.63628i	−0.842384	+	0.375054i
$95$	3.87736	+	7.31815i	0.397809	+	0.750827i
$96$	−4.74306	+	10.6531i	−0.484087	+	1.08728i
$97$	−3.70443	−	0.586724i	−0.376128	−	0.0595728i	−0.0344914	−	0.999405i	$-0.510981\pi$
$97$	−3.70443	−	0.586724i	−0.376128	−	0.0595728i	−0.341636	+	0.939832i	$0.610981\pi$
$98$	6.11728	−	4.59187i	0.617939	−	0.463849i
$99$		−	10.9526i		−	1.10077i
$100$	1.12218	−	3.87057i	0.112218	−	0.387057i
$101$	−11.0295	−	6.36787i	−1.09747	−	0.633627i	−0.161918	−	0.986804i	$-0.551768\pi$
$101$	−11.0295	−	6.36787i	−1.09747	−	0.633627i	−0.935556	+	0.353177i	$0.885101\pi$
$102$	11.8492	−	7.69494i	1.17324	−	0.761913i
$103$	11.1059	−	4.26315i	1.09430	−	0.420061i	0.256778	−	0.966470i	$-0.417339\pi$
$103$	11.1059	−	4.26315i	1.09430	−	0.420061i	0.837518	+	0.546409i	$0.184006\pi$
$104$	10.2223	−	7.42697i	1.00238	−	0.728274i
$105$	−13.6482	−	8.90987i	−1.33193	−	0.869514i
$106$	4.62921	+	3.36332i	0.449629	+	0.326674i
$107$	−5.06438	−	1.35700i	−0.489592	−	0.131186i	0.00557325	−	0.999984i	$-0.498226\pi$
$107$	−5.06438	−	1.35700i	−0.489592	−	0.131186i	−0.495166	+	0.868799i	$0.664893\pi$
$108$	1.26548	−	3.29669i	0.121771	−	0.317225i
$109$	−3.72213	+	3.35142i	−0.356515	+	0.321007i	−0.827853	−	0.560945i	$-0.810438\pi$
$109$	−3.72213	+	3.35142i	−0.356515	+	0.321007i	0.471338	+	0.881953i	$0.343771\pi$
$110$	−2.45610	−	5.28737i	−0.234180	−	0.504131i
$111$	−8.76731	+	2.84867i	−0.832156	+	0.270384i
$112$	4.42001	+	1.27187i	0.417651	+	0.120181i
$113$	−3.08610	+	1.57245i	−0.290316	+	0.147923i	−0.593083	−	0.805141i	$-0.702089\pi$
$113$	−3.08610	+	1.57245i	−0.290316	+	0.147923i	0.302767	+	0.953064i	$0.402089\pi$
$114$	8.28607	+	7.46081i	0.776062	+	0.698769i
$115$	−6.04128	+	4.53854i	−0.563353	+	0.423221i
$116$	−3.69567	−	4.10446i	−0.343134	−	0.381089i
$117$	−14.7009	+	11.9045i	−1.35909	+	1.10057i
$118$	3.85602	−	3.85602i	0.354976	−	0.354976i
$119$	8.13750	+	9.37874i	0.745963	+	0.859748i
$120$	−1.28995	−	18.8447i	−0.117756	−	1.72027i
$121$	−4.84800	−	2.15847i	−0.440727	−	0.196224i
$122$	2.09114	−	2.58234i	0.189323	−	0.233794i
$123$	−6.93085	−	10.6726i	−0.624934	−	0.962313i
$124$	−3.77903	−	6.54547i	−0.339367	−	0.587801i
$125$	2.27634	+	10.9462i	0.203602	+	0.979054i
$126$	−12.9277	−	2.99727i	−1.15169	−	0.267018i
$127$	−5.16052	−	2.62941i	−0.457922	−	0.233323i	0.209785	−	0.977748i	$-0.432724\pi$
$127$	−5.16052	−	2.62941i	−0.457922	−	0.233323i	−0.667706	+	0.744425i	$0.732724\pi$
$128$	0.138901	+	0.361848i	0.0122772	+	0.0319832i
$129$	−1.59915	−	15.2149i	−0.140797	−	1.33960i
$130$	−4.42729	+	9.04358i	−0.388299	+	0.793174i
$131$	8.67156	+	0.911418i	0.757638	+	0.0796310i	0.475468	−	0.879733i	$-0.342279\pi$
$131$	8.67156	+	0.911418i	0.757638	+	0.0796310i	0.282171	+	0.959364i	$0.408946\pi$
$132$	3.74647	+	3.74647i	0.326088	+	0.326088i
$133$	−5.48723	+	8.11883i	−0.475803	+	0.703992i
$134$	11.8470	+	3.84932i	1.02342	+	0.332530i
$135$	1.17965	+	9.72545i	0.101528	+	0.837034i
$136$	−2.99181	+	14.0753i	−0.256545	+	1.20695i
$137$	11.5728	+	0.606504i	0.988730	+	0.0518171i	0.539838	−	0.841769i	$-0.318486\pi$
$137$	11.5728	+	0.606504i	0.988730	+	0.0518171i	0.448892	+	0.893586i	$0.351819\pi$
$138$	−5.54060	+	8.53177i	−0.471647	+	0.726273i
$139$	2.43621	+	7.49788i	0.206636	+	0.635962i	0.999642	+	0.0267475i	$0.00851502\pi$
$139$	2.43621	+	7.49788i	0.206636	+	0.635962i	−0.793006	+	0.609214i	$0.791485\pi$
$140$	4.66648	−	0.980196i	0.394389	−	0.0828416i
$141$	−6.96548	+	21.4375i	−0.586599	+	1.80537i
$142$	2.22498	+	2.74762i	0.186716	+	0.230575i
$143$	−2.54494	−	9.49785i	−0.212819	−	0.794250i
$144$	−3.24563	−	7.28980i	−0.270469	−	0.607483i
$145$	14.3910	+	5.26182i	1.19510	+	0.436970i
$146$	−9.81076	−	13.5034i	−0.811944	−	1.11755i
$147$	1.71660	−	19.2087i	0.141583	−	1.58431i
$148$	1.22436	−	2.40294i	0.100642	−	0.197521i
$149$	10.9467	−	6.32008i	0.896788	−	0.517761i	0.0206316	−	0.999787i	$-0.493432\pi$
$149$	10.9467	−	6.32008i	0.896788	−	0.517761i	0.876157	+	0.482026i	$0.160099\pi$
$150$	7.93898	+	12.7884i	0.648215	+	1.04417i
$151$	0.469302	−	0.812854i	0.0381912	−	0.0661491i	−0.846298	−	0.532710i	$-0.821174\pi$
$151$	0.469302	−	0.812854i	0.0381912	−	0.0661491i	0.884489	+	0.466561i	$0.154507\pi$
$152$	−11.3406	+	0.594338i	−0.919848	+	0.0482072i
$153$	3.37003	−	21.2776i	0.272451	−	1.72019i
$154$	4.15652	−	5.50522i	0.334942	−	0.443623i
$155$	17.7659	+	11.1376i	1.42699	+	0.894596i
$156$	0.956525	−	9.10073i	0.0765833	−	0.728641i
$157$	1.89004	−	0.506435i	0.150842	−	0.0404179i	−0.182608	−	0.983186i	$-0.558454\pi$
$157$	1.89004	−	0.506435i	0.150842	−	0.0404179i	0.333450	+	0.942768i	$0.391787\pi$
$158$	−1.89348	−	0.726837i	−0.150637	−	0.0578241i
$159$	14.1117	−	2.99953i	1.11913	−	0.237878i
$160$	7.13390	+	6.21981i	0.563984	+	0.491720i
$161$	−8.09938	−	3.78599i	−0.638321	−	0.298378i
$162$	−0.843480	−	1.65542i	−0.0662700	−	0.130062i
$163$	−12.0806	−	7.84523i	−0.946225	−	0.614486i	−0.0234087	−	0.999726i	$-0.507452\pi$
$163$	−12.0806	−	7.84523i	−0.946225	−	0.614486i	−0.922816	+	0.385240i	$0.874119\pi$
$164$	3.64153	+	0.774032i	0.284356	+	0.0604417i
$165$	−14.0505	−	4.31824i	−1.09383	−	0.336175i
$166$	−1.11118	−	5.22769i	−0.0862443	−	0.405747i
$167$	−2.98613	−	18.8537i	−0.231074	−	1.45894i	−0.781420	−	0.624005i	$-0.785504\pi$
$167$	−2.98613	−	18.8537i	−0.231074	−	1.45894i	0.550346	−	0.834937i	$-0.314496\pi$
$168$	18.9645	−	11.8258i	1.46314	−	0.912378i
$169$	−2.34095	+	3.22204i	−0.180073	+	0.247849i
$170$	−3.14457	−	11.0275i	−0.241178	−	0.845771i
$171$	16.9081	−	1.77711i	1.29299	−	0.135899i
$172$	3.47824	+	2.81662i	0.265213	+	0.214766i
$173$	0.761408	+	14.5285i	0.0578887	+	1.10458i	0.860951	+	0.508688i	$0.169869\pi$
$173$	0.761408	+	14.5285i	0.0578887	+	1.10458i	−0.803062	+	0.595895i	$0.796797\pi$
$174$	20.6293			1.56390
$175$	−10.1666	+	8.46403i	−0.768524	+	0.639821i
$176$	4.14788			0.312659
$177$	−0.719581	−	13.7304i	−0.0540870	−	1.03204i
$178$	2.95018	+	2.38901i	0.221125	+	0.179064i
$179$	13.7083	−	1.44080i	1.02461	−	0.107690i	0.422710	−	0.906265i	$-0.361079\pi$
$179$	13.7083	−	1.44080i	1.02461	−	0.107690i	0.601896	+	0.798575i	$0.294412\pi$
$180$	−6.51158	−	5.10281i	−0.485344	−	0.380341i
$181$	−3.00729	+	4.13918i	−0.223530	+	0.307663i	−0.906022	−	0.423230i	$-0.860896\pi$
$181$	−3.00729	+	4.13918i	−0.223530	+	0.307663i	0.682492	+	0.730893i	$0.260896\pi$
$182$	−11.9071	+	0.404705i	−0.882611	+	0.0299987i
$183$	−1.31059	−	8.27476i	−0.0968818	−	0.611688i
$184$	−2.15419	−	10.1347i	−0.158809	−	0.747139i
$185$	0.119597	+	7.48103i	0.00879296	+	0.550016i
$186$	27.6132	+	5.86936i	2.02470	+	0.430362i
$187$	9.39149	+	6.09890i	0.686773	+	0.445996i
$188$	−2.99376	−	5.87559i	−0.218343	−	0.428522i
$189$	−9.50151	+	6.63986i	−0.691133	+	0.482978i
$190$	7.76390	−	4.64952i	0.563252	−	0.337312i
$191$	−5.74487	+	1.22111i	−0.415685	+	0.0883565i	−0.411006	−	0.911633i	$-0.634823\pi$
$191$	−5.74487	+	1.22111i	−0.415685	+	0.0883565i	−0.00467839	+	0.999989i	$0.501489\pi$
$192$	20.8385	+	7.99915i	1.50389	+	0.577289i
$193$	−20.4549	+	5.48087i	−1.47237	+	0.394521i	−0.903744	−	0.428072i	$-0.859193\pi$
$193$	−20.4549	+	5.48087i	−1.47237	+	0.394521i	−0.568629	+	0.822594i	$0.692526\pi$
$194$	−0.428390	+	4.07586i	−0.0307566	+	0.292630i
$195$	9.47568	+	23.5526i	0.678568	+	1.68664i
$196$	3.61852	+	4.32872i	0.258465	+	0.309195i
$197$	2.44928	−	15.4641i	0.174504	−	1.10178i	−0.732535	−	0.680729i	$-0.761663\pi$
$197$	2.44928	−	15.4641i	0.174504	−	1.10178i	0.907039	−	0.421046i	$-0.138337\pi$
$198$	−11.9515	+	0.626353i	−0.849359	+	0.0445130i
$199$	2.32152	−	4.02100i	0.164569	−	0.285041i	−0.771933	−	0.635703i	$-0.780710\pi$
$199$	2.32152	−	4.02100i	0.164569	−	0.285041i	0.936502	+	0.350662i	$0.114044\pi$
$200$	−14.9275	−	3.49248i	−1.05554	−	0.246956i
$201$	27.1992	−	15.7035i	1.91848	−	1.10764i
$202$	−6.31793	+	12.3996i	−0.444528	+	0.872435i
$203$	2.50651	+	17.9560i	0.175922	+	1.26027i
$204$	6.12551	+	8.43104i	0.428871	+	0.590291i
$205$	−9.93249	+	2.83232i	−0.693715	+	0.197818i
$206$	−5.28712	−	11.8751i	−0.368371	−	0.827374i
$207$	4.01467	+	14.9829i	0.279039	+	1.04139i
$208$	−4.50841	−	5.56742i	−0.312602	−	0.386031i
$209$	−2.73089	+	8.40481i	−0.188900	+	0.581373i
$210$	−8.94202	+	15.4026i	−0.617058	+	1.06288i
$211$	−6.92366	−	21.3088i	−0.476645	−	1.46696i	−0.843727	−	0.536773i	$-0.819643\pi$
$211$	−6.92366	−	21.3088i	−0.476645	−	1.46696i	0.367082	−	0.930188i	$-0.380357\pi$
$212$	−2.29871	+	3.53971i	−0.157876	+	0.243108i
$213$	8.90191	+	0.466529i	0.609949	+	0.0319661i
$214$	−1.19115	+	5.60391i	−0.0814251	+	0.383075i
$215$	−12.1852	−	2.38714i	−0.831026	−	0.162801i
$216$	−12.7759	−	4.15115i	−0.869292	−	0.282450i
$217$	−1.75371	+	24.7481i	−0.119050	+	1.68001i
$218$	3.86996	+	3.86996i	0.262107	+	0.262107i
$219$	−41.8527	−	4.39889i	−2.82814	−	0.297249i
$220$	3.79986	−	2.01327i	0.256186	−	0.135735i
$221$	−2.02163	−	19.2345i	−0.135990	−	1.29386i
$222$	3.60988	+	9.40406i	0.242279	+	0.631159i
$223$	−15.4190	−	7.85636i	−1.03253	−	0.526100i	−0.146249	−	0.989248i	$-0.546720\pi$
$223$	−15.4190	−	7.85636i	−1.03253	−	0.526100i	−0.886281	+	0.463147i	$0.846720\pi$
$224$	−2.52931	+	10.9093i	−0.168997	+	0.728908i
$225$	22.5908	+	4.05179i	1.50605	+	0.270119i
$226$	1.89235	+	3.27765i	0.125878	+	0.218026i
$227$	−0.393311	−	0.605646i	−0.0261050	−	0.0401981i	0.825377	−	0.564582i	$-0.190962\pi$
$227$	−0.393311	−	0.605646i	−0.0261050	−	0.0401981i	−0.851482	+	0.524384i	$0.824296\pi$
$228$	−5.17576	+	6.39153i	−0.342773	+	0.423289i
$229$	−13.4740	−	5.99900i	−0.890385	−	0.396425i	−0.0900217	−	0.995940i	$-0.528694\pi$
$229$	−13.4740	−	5.99900i	−0.890385	−	0.396425i	−0.800364	+	0.599515i	$0.795360\pi$
$230$	5.29799	+	6.33275i	0.349339	+	0.417569i
$231$	−3.30270	−	17.0758i	−0.217302	−	1.12350i
$232$	−14.8569	+	14.8569i	−0.975400	+	0.975400i
$233$	13.2440	−	10.7248i	0.867646	−	0.702606i	−0.0883174	−	0.996092i	$-0.528149\pi$
$233$	13.2440	−	10.7248i	0.867646	−	0.702606i	0.955963	+	0.293487i	$0.0948157\pi$
$234$	13.8310	+	15.3609i	0.904163	+	1.00417i
$235$	14.9707	+	10.5154i	0.976582	+	0.685949i
$236$	2.98920	+	2.69149i	0.194580	+	0.175201i
$237$	−4.55631	+	2.32156i	−0.295964	+	0.150801i
$238$	9.76880	−	9.41606i	0.633218	−	0.610353i
$239$	5.99181	−	1.94686i	0.387578	−	0.125932i	−0.108745	−	0.994070i	$-0.534683\pi$
$239$	5.99181	−	1.94686i	0.387578	−	0.125932i	0.496323	+	0.868138i	$0.334683\pi$
$240$	−10.6314	+	1.28953i	−0.686253	+	0.0832389i
$241$	17.3746	−	15.6441i	1.11920	−	1.00773i	0.119306	−	0.992858i	$-0.461933\pi$
$241$	17.3746	−	15.6441i	1.11920	−	1.00773i	0.999889	−	0.0148706i	$-0.00473364\pi$
$242$	−2.07809	+	5.41362i	−0.133585	+	0.348001i
$243$	−17.2206	−	4.61425i	−1.10470	−	0.296004i
$244$	1.98287	+	1.44064i	0.126941	+	0.0922277i
$245$	−14.4931	−	5.91182i	−0.925931	−	0.377692i
$246$	−11.2497	+	8.17335i	−0.717252	+	0.521114i
$247$	14.2494	−	5.46985i	0.906670	−	0.348038i
$248$	−24.1136	+	15.6595i	−1.53121	+	0.994381i
$249$	−11.6697	−	6.73752i	−0.739539	−	0.426973i
$250$	11.8144	−	3.10995i	0.747206	−	0.196691i
$251$			20.4139i			1.28851i	0.764809	+	0.644257i	$0.222833\pi$
$251$			20.4139i			1.28851i	−0.764809	+	0.644257i	$0.777167\pi$
$252$	1.70873	−	9.63822i	0.107640	−	0.607151i
$253$	−7.96369	−	1.26132i	−0.500673	−	0.0792988i
$254$	−2.57412	+	5.78157i	−0.161515	+	0.362768i
$255$	−25.9673	−	12.7123i	−1.62613	−	0.796076i
$256$	−14.4160	+	6.41841i	−0.900998	+	0.401150i
$257$	2.85695	−	10.6623i	0.178212	−	0.665096i	−0.817770	−	0.575545i	$-0.804790\pi$
$257$	2.85695	−	10.6623i	0.178212	−	0.665096i	0.995982	−	0.0895510i	$-0.0285432\pi$
$258$	−16.5112	+	2.61512i	−1.02794	+	0.162810i
$259$	−7.74683	+	4.28471i	−0.481365	+	0.266239i
$260$	−6.83240	−	2.91203i	−0.423728	−	0.180596i
$261$	21.0475	−	23.3756i	1.30281	−	1.44691i
$262$	0.498640	−	9.51461i	0.0308061	−	0.587815i
$263$	−1.01782	+	19.4212i	−0.0627617	+	1.19756i	0.767819	+	0.640666i	$0.221342\pi$
$263$	−1.01782	+	19.4212i	−0.0627617	+	1.19756i	−0.830581	+	0.556898i	$0.811992\pi$
$264$	13.4868	−	14.9786i	0.830053	−	0.921867i
$265$	1.03765	−	11.6632i	0.0637426	−	0.716466i
$266$	9.17315	+	5.52341i	0.562442	+	0.338662i
$267$	9.45344	−	1.49728i	0.578541	−	0.0916319i
$268$	−2.37807	+	8.87507i	−0.145264	+	0.542131i
$269$	−4.64556	+	2.06834i	−0.283245	+	0.126109i	−0.543442	−	0.839447i	$-0.682879\pi$
$269$	−4.64556	+	2.06834i	−0.283245	+	0.126109i	0.260197	+	0.965556i	$0.416212\pi$
$270$	10.5450	−	1.84342i	0.641751	−	0.112187i
$271$	0.642671	−	1.44346i	0.0390395	−	0.0876842i	−0.892973	−	0.450110i	$-0.851385\pi$
$271$	0.642671	−	1.44346i	0.0390395	−	0.0876842i	0.932013	+	0.362426i	$0.118051\pi$
$272$	8.05810	+	1.27628i	0.488594	+	0.0773857i
$273$	−19.3299	+	22.9929i	−1.16990	+	1.39160i
$274$		−	12.6630i		−	0.765001i
$275$	−6.70030	+	9.87097i	−0.404043	+	0.595242i
$276$	−6.49838	−	3.75184i	−0.391157	−	0.225834i
$277$	−8.81379	+	5.72374i	−0.529569	+	0.343906i	−0.781567	−	0.623822i	$-0.785579\pi$
$277$	−8.81379	+	5.72374i	−0.529569	+	0.343906i	0.251998	+	0.967728i	$0.418913\pi$
$278$	8.04243	−	3.08720i	0.482353	−	0.185158i
$279$	34.8237	−	25.3009i	2.08484	−	1.51472i
$280$	−4.65279	−	17.5326i	−0.278057	−	1.04777i
$281$	18.9491	+	13.7673i	1.13041	+	0.821289i	0.985754	−	0.168194i	$-0.0537934\pi$
$281$	18.9491	+	13.7673i	1.13041	+	0.821289i	0.144653	+	0.989482i	$0.453793\pi$
$282$	23.7912	+	6.37483i	1.41674	+	0.379615i
$283$	−8.82370	+	22.9865i	−0.524515	+	1.36641i	0.373985	+	0.927435i	$0.377991\pi$
$283$	−8.82370	+	22.9865i	−0.524515	+	1.36641i	−0.898500	+	0.438973i	$0.855342\pi$
$284$	−1.93800	+	1.74499i	−0.114999	+	0.103546i
$285$	4.38654	−	22.3913i	0.259836	−	1.32634i
$286$	−10.2186	+	3.32022i	−0.604238	+	0.196329i
$287$	−8.48107	−	8.79878i	−0.500622	−	0.519376i
$288$	17.3115	−	8.82066i	1.02009	−	0.519763i
$289$	3.73480	+	3.36283i	0.219694	+	0.197813i
$290$	4.91876	−	16.0045i	0.288839	−	0.939815i
$291$	6.91418	+	7.67897i	0.405316	+	0.450149i
$292$	9.56783	−	7.74788i	0.559915	−	0.453410i
$293$	17.1698	−	17.1698i	1.00307	−	1.00307i	0.00307618	−	0.999995i	$-0.499021\pi$
$293$	17.1698	−	17.1698i	1.00307	−	1.00307i	0.999995	−	0.00307618i	$-0.000979181\pi$
$294$	−21.0589	−	0.774659i	−1.22818	−	0.0451791i
$295$	−10.8238	−	2.71556i	−0.630187	−	0.158106i
$296$	−9.37243	−	4.17287i	−0.544761	−	0.242543i
$297$	−6.57880	+	8.12414i	−0.381741	+	0.471410i
$298$	−7.52255	−	11.5837i	−0.435770	−	0.671026i
$299$	6.96288	+	12.0601i	0.402674	+	0.697451i
$300$	−9.11346	+	6.34152i	−0.526166	+	0.366128i
$301$	−4.28239	−	14.0538i	−0.246833	−	0.810050i
$302$	−0.913833	−	0.465621i	−0.0525852	−	0.0267935i
$303$	12.5742	+	32.7570i	0.722371	+	1.88184i
$304$	0.673017	+	6.40333i	0.0386002	+	0.367256i
$305$	−6.73217	−	0.956224i	−0.385483	−	0.0547532i
$306$	−23.4110	−	2.46059i	−1.33832	−	0.140663i
$307$	−19.3107	−	19.3107i	−1.10212	−	1.10212i	−0.994155	−	0.107964i	$-0.965567\pi$
$307$	−19.3107	−	19.3107i	−1.10212	−	1.10212i	−0.107964	−	0.994155i	$-0.534433\pi$
$308$	4.21560	+	2.84917i	0.240206	+	0.162347i
$309$	−31.1700	−	10.1277i	−1.77320	−	0.576147i
$310$	11.1375	−	20.0232i	0.632568	−	1.13724i
$311$	−5.61842	+	26.4326i	−0.318591	+	1.49885i	0.469299	+	0.883039i	$0.344507\pi$
$311$	−5.61842	+	26.4326i	−0.318591	+	1.49885i	−0.787890	+	0.615815i	$0.788827\pi$
$312$	−34.7637	−	1.82189i	−1.96811	−	0.103144i
$313$	9.47367	−	14.5882i	0.535484	−	0.824573i	−0.462593	−	0.886571i	$-0.653081\pi$
$313$	9.47367	−	14.5882i	0.535484	−	0.824573i	0.998076	+	0.0619984i	$0.0197474\pi$
$314$	−0.660715	−	2.03347i	−0.0372863	−	0.114755i
$315$	8.32979	+	25.8473i	0.469330	+	1.45633i
$316$	0.462293	−	1.42279i	0.0260060	−	0.0800383i
$317$	14.8498	+	18.3380i	0.834050	+	1.02997i	0.999046	+	0.0436721i	$0.0139057\pi$
$317$	14.8498	+	18.3380i	0.834050	+	1.02997i	−0.164996	+	0.986294i	$0.552761\pi$
$318$	−4.08013	−	15.2272i	−0.228802	−	0.853902i
$319$	6.65033	+	14.9369i	0.372347	+	0.836306i
$320$	11.1745	−	14.2595i	0.624673	−	0.797131i
$321$	8.49043	+	11.6861i	0.473890	+	0.652253i
$322$	−3.66812	+	9.05463i	−0.204416	+	0.504595i
$323$	−7.89141	+	15.4878i	−0.439090	+	0.861762i
$324$	1.18682	−	0.685212i	0.0659345	−	0.0380673i
$325$	20.5318	−	1.73557i	1.13890	−	0.0962724i
$326$	−7.86992	+	13.6311i	−0.435875	+	0.754957i
$327$	13.7800	−	0.722181i	0.762038	−	0.0399367i
$328$	2.21550	−	13.9881i	0.122331	−	0.772365i
$329$	−2.65806	+	21.4828i	−0.146543	+	1.18438i
$330$	−3.90858	+	15.5790i	−0.215161	+	0.857597i
$331$	0.252912	−	2.40630i	0.0139013	−	0.132262i	−0.985370	−	0.170428i	$-0.945485\pi$
$331$	0.252912	−	2.40630i	0.0139013	−	0.132262i	0.999271	+	0.0381660i	$0.0121516\pi$
$332$	3.80782	−	1.02030i	0.208981	−	0.0559963i
$333$	14.3391	+	5.50425i	0.785776	+	0.301631i
$334$	−20.4025	+	4.33670i	−1.11638	+	0.237293i
$335$	−5.69770	−	24.8458i	−0.311299	−	1.35747i
$336$	−7.25837	−	10.3866i	−0.395976	−	0.566635i
$337$	0.574984	+	1.12847i	0.0313214	+	0.0614716i	0.906137	−	0.422985i	$-0.139018\pi$
$337$	0.574984	+	1.12847i	0.0313214	+	0.0614716i	−0.874816	+	0.484456i	$0.839018\pi$
$338$	3.64980	+	2.37021i	0.198523	+	0.128922i
$339$	9.33386	+	1.98397i	0.506946	+	0.107755i
$340$	8.00146	−	2.74199i	0.433940	−	0.148705i
$341$	4.65197	+	21.8858i	0.251918	+	1.18518i
$342$	−2.90614	−	18.3486i	−0.157146	−	0.992181i
$343$	−1.88444	−	18.4241i	−0.101750	−	0.994810i
$344$	10.0077	−	13.7744i	0.539580	−	0.742668i
$345$	20.8038	+	0.757060i	1.12004	+	0.0407588i
$346$	15.8101	−	1.66171i	0.849957	−	0.0893341i
$347$	17.3398	+	14.0415i	0.930851	+	0.753788i	0.969405	−	0.245468i	$-0.0789417\pi$
$347$	17.3398	+	14.0415i	0.930851	+	0.753788i	−0.0385536	+	0.999257i	$0.512275\pi$
$348$	0.796363	+	15.1955i	0.0426895	+	0.814564i
$349$	−16.3537			−0.875393			−0.437696	−	0.899123i	$-0.644206\pi$
$349$	−16.3537			−0.875393			−0.437696	+	0.899123i	$0.644206\pi$
$350$	9.81744	+	10.6099i	0.524764	+	0.567122i
$351$	18.0551			0.963709
$352$	0.528562	+	10.0856i	0.0281724	+	0.537562i
$353$	14.7109	+	11.9127i	0.782984	+	0.634048i	0.935128	−	0.354310i	$-0.115284\pi$
$353$	14.7109	+	11.9127i	0.782984	+	0.634048i	−0.152144	+	0.988358i	$0.548618\pi$
$354$	−14.9416	+	1.57043i	−0.794138	+	0.0834672i
$355$	2.48447	−	6.79499i	0.131862	−	0.360640i
$356$	−1.64585	+	2.26532i	−0.0872300	+	0.120062i
$357$	−1.16205	−	34.1894i	−0.0615021	−	1.80949i
$358$	−2.35616	−	14.8762i	−0.124527	−	0.786232i
$359$	−1.02937	−	4.84281i	−0.0543281	−	0.255594i	0.942599	−	0.333926i	$-0.108374\pi$
$359$	−1.02937	−	4.84281i	−0.0543281	−	0.255594i	−0.996927	+	0.0783326i	$0.975040\pi$
$360$	−18.0889	+	25.7531i	−0.953370	+	1.35731i
$361$	5.16671	+	1.09822i	0.271932	+	0.0578010i
$362$	4.68869	+	3.04487i	0.246432	+	0.160035i
$363$	6.63754	+	13.0269i	0.348381	+	0.683736i
$364$	−0.757760	−	8.75512i	−0.0397174	−	0.458893i
$365$	−13.3919	+	31.4210i	−0.700964	+	1.64465i
$366$	−8.95455	+	1.90335i	−0.468062	+	0.0994896i
$367$	−7.15585	−	2.74687i	−0.373532	−	0.143386i	0.164357	−	0.986401i	$-0.447445\pi$
$367$	−7.15585	−	2.74687i	−0.373532	−	0.143386i	−0.537890	+	0.843015i	$0.680778\pi$
$368$	−5.67424	+	1.52041i	−0.295790	+	0.0792568i
$369$	−2.21626	+	21.0863i	−0.115374	+	1.09771i
$370$	8.15653	−	0.558330i	0.424038	−	0.0290262i
$371$	12.7583	−	5.40156i	0.662377	−	0.280435i
$372$	−3.25740	+	20.5664i	−0.168888	+	1.06632i
$373$	25.5614	−	1.33961i	1.32352	−	0.0693626i	0.622563	−	0.782570i	$-0.286091\pi$
$373$	25.5614	−	1.33961i	1.32352	−	0.0693626i	0.700954	+	0.713207i	$0.252758\pi$
$374$	6.11810	−	10.5969i	0.316359	−	0.547951i
$375$	14.1047	−	27.3832i	0.728363	−	1.41406i
$376$	−21.7251	+	12.5430i	−1.12038	+	0.646854i
$377$	12.8204	−	25.1614i	0.660284	−	1.29588i
$378$	7.78884	+	9.98842i	0.400615	+	0.513749i
$379$	−7.41911	−	10.2115i	−0.381094	−	0.524531i	0.574780	−	0.818308i	$-0.305088\pi$
$379$	−7.41911	−	10.2115i	−0.381094	−	0.524531i	−0.955874	+	0.293777i	$0.905088\pi$
$380$	3.72455	+	5.53939i	0.191065	+	0.284165i
$381$	6.49014	+	14.5771i	0.332500	+	0.746807i
$382$	1.66102	+	6.19903i	0.0849854	+	0.317170i
$383$	−17.4475	−	21.5459i	−0.891526	−	1.10094i	−0.994340	−	0.106243i	$-0.966118\pi$
$383$	−17.4475	−	21.5459i	−0.891526	−	1.10094i	0.102814	−	0.994701i	$-0.467215\pi$
$384$	0.329978	−	1.01557i	0.0168391	−	0.0518255i
$385$	−14.0351	−	1.50920i	−0.715296	−	0.0769160i
$386$	7.15054	+	22.0071i	0.363953	+	1.12013i
$387$	−13.8827	+	21.3774i	−0.705695	+	1.08667i
$388$	−3.01881	−	0.158209i	−0.153257	−	0.00803186i
$389$	2.97603	−	14.0011i	0.150891	−	0.709885i	−0.836031	−	0.548683i	$-0.815130\pi$
$389$	2.97603	−	14.0011i	0.150891	−	0.709885i	0.986921	−	0.161202i	$-0.0515371\pi$
$390$	25.1589	−	11.6869i	1.27397	−	0.591788i
$391$	−15.0830	−	4.90075i	−0.762778	−	0.247842i
$392$	15.7242	−	14.6084i	0.794192	−	0.737835i
$393$	−16.9862	−	16.9862i	−0.856841	−	0.856841i
$394$	−17.0147	−	1.78832i	−0.857188	−	0.0900941i
$395$	0.714708	+	4.08840i	0.0359609	+	0.205709i
$396$	−0.922743	−	8.77931i	−0.0463696	−	0.441177i
$397$	10.6083	+	27.6357i	0.532418	+	1.38700i	0.891215	+	0.453580i	$0.149854\pi$
$397$	10.6083	+	27.6357i	0.532418	+	1.38700i	−0.358798	+	0.933415i	$0.616813\pi$
$398$	−4.52051	−	2.30332i	−0.226593	−	0.115455i
$399$	25.8250	−	7.86921i	1.29287	−	0.393953i
$400$	−1.53447	+	8.55545i	−0.0767235	+	0.427773i
$401$	−4.39681	−	7.61549i	−0.219566	−	0.380299i	0.735109	−	0.677949i	$-0.237131\pi$
$401$	−4.39681	−	7.61549i	−0.219566	−	0.380299i	−0.954675	+	0.297649i	$0.903797\pi$
$402$	−18.6912	−	28.7820i	−0.932234	−	1.43552i
$403$	24.3195	−	30.0321i	1.21144	−	1.49600i
$404$	−9.37745	−	4.17511i	−0.466546	−	0.207720i
$405$	−2.01947	+	3.22130i	−0.100348	+	0.160068i
$406$	19.4504	−	3.76199i	0.965309	−	0.186705i
$407$	−5.64541	+	5.64541i	−0.279832	+	0.279832i
$408$	30.8096	−	24.9491i	1.52530	−	1.23516i
$409$	12.1567	+	13.5014i	0.601110	+	0.667600i	0.964514	−	0.264031i	$-0.0850522\pi$
$409$	12.1567	+	13.5014i	0.601110	+	0.667600i	−0.363404	+	0.931632i	$0.618386\pi$
$410$	3.65868	+	10.6765i	0.180689	+	0.527273i
$411$	−23.7266	−	21.3635i	−1.17035	−	1.05378i
$412$	8.54306	−	4.35290i	0.420886	−	0.214452i
$413$	−3.18237	−	12.8146i	−0.156594	−	0.630565i
$414$	16.1199	−	5.23768i	0.792251	−	0.257418i
$415$	−8.00954	+	7.44707i	−0.393173	+	0.365562i
$416$	12.9626	−	11.6716i	0.635546	−	0.572248i
$417$	7.78376	−	20.2774i	0.381172	−	0.992988i
$418$	9.32758	+	2.49932i	0.456227	+	0.122246i
$419$	1.99482	+	1.44932i	0.0974532	+	0.0708039i	0.635445	−	0.772146i	$-0.280817\pi$
$419$	1.99482	+	1.44932i	0.0974532	+	0.0708039i	−0.537992	+	0.842950i	$0.680817\pi$
$420$	−11.6907	−	5.99209i	−0.570449	−	0.292384i
$421$	−12.4642	+	9.05577i	−0.607468	+	0.441351i	−0.848522	−	0.529160i	$-0.822507\pi$
$421$	−12.4642	+	9.05577i	−0.607468	+	0.441351i	0.241054	+	0.970512i	$0.422507\pi$
$422$	−22.8565	+	8.77377i	−1.11263	+	0.427101i
$423$	31.4970	−	20.4544i	1.53144	−	0.994526i
$424$	13.9049	+	8.02797i	0.675279	+	0.389873i
$425$	−16.0539	+	17.1147i	−0.778730	+	0.830185i
$426$		−	9.74052i		−	0.471930i
$427$	−2.74470	−	7.56291i	−0.132825	−	0.365995i
$428$	−4.17382	−	0.661067i	−0.201749	−	0.0319539i
$429$	−11.0185	+	24.7480i	−0.531979	+	1.19484i
$430$	−1.90802	+	13.4332i	−0.0920128	+	0.647804i
$431$	−6.11271	+	2.72155i	−0.294439	+	0.131093i	−0.548640	−	0.836059i	$-0.684854\pi$
$431$	−6.11271	+	2.72155i	−0.294439	+	0.131093i	0.254201	+	0.967151i	$0.418187\pi$
$432$	−1.97125	+	7.35679i	−0.0948416	+	0.353954i
$433$	32.4446	−	5.13871i	1.55919	−	0.246951i	0.683543	−	0.729910i	$-0.260438\pi$
$433$	32.4446	−	5.13871i	1.55919	−	0.246951i	0.875643	+	0.482959i	$0.160438\pi$
$434$	27.1056	+	0.498375i	1.30111	+	0.0239228i
$435$	−21.6891	−	36.2171i	−1.03991	−	1.73647i
$436$	−2.70121	+	3.00000i	−0.129365	+	0.143674i
$437$	0.655027	−	12.4987i	0.0313342	−	0.597892i
$438$	−2.40665	+	45.9216i	−0.114994	+	2.19422i
$439$	10.8562	−	12.0570i	0.518137	−	0.575449i	−0.426117	−	0.904668i	$-0.640119\pi$
$439$	10.8562	−	12.0570i	0.518137	−	0.575449i	0.944254	+	0.329219i	$0.106785\pi$
$440$	−8.40485	−	14.0346i	−0.400686	−	0.669076i
$441$	−22.3636	+	23.0721i	−1.06494	+	1.09867i
$442$	−20.8733	+	3.30601i	−0.992841	+	0.157251i
$443$	6.95157	−	25.9436i	0.330279	−	1.23262i	−0.578618	−	0.815598i	$-0.696408\pi$
$443$	6.95157	−	25.9436i	0.330279	−	1.23262i	0.908897	−	0.417020i	$-0.136925\pi$
$444$	−6.78767	+	3.02207i	−0.322129	+	0.143421i
$445$	1.09243	−	7.69112i	0.0517862	−	0.364594i
$446$	−7.69115	+	17.2746i	−0.364187	+	0.817976i
$447$	−34.3954	−	5.44770i	−1.62685	−	0.257667i
$448$	21.1064	+	3.74190i	0.997186	+	0.176788i
$449$		−	14.5437i		−	0.686358i	−0.939270	−	0.343179i	$-0.888496\pi$
$449$		−	14.5437i		−	0.686358i	0.939270	−	0.343179i	$-0.111504\pi$
$450$	3.12943	−	24.8830i	0.147523	−	1.17300i
$451$	−9.54462	−	5.51059i	−0.449438	−	0.259483i
$452$	−2.34127	+	1.52044i	−0.110124	+	0.0715153i
$453$	−2.41414	+	0.926701i	−0.113426	+	0.0435402i
$454$	−0.638394	+	0.463820i	−0.0299613	+	0.0217682i
$455$	13.2293	+	20.4787i	0.620200	+	0.960058i
$456$	25.3116	+	18.3899i	1.18532	+	0.861188i
$457$	−9.79222	−	2.62382i	−0.458061	−	0.122737i	0.0224079	−	0.999749i	$-0.492867\pi$
$457$	−9.79222	−	2.62382i	−0.458061	−	0.122737i	−0.480469	+	0.877012i	$0.659533\pi$
$458$	−5.77562	+	15.0460i	−0.269877	+	0.703053i
$459$	−15.2804	+	13.7585i	−0.713227	+	0.642193i
$460$	−4.46018	+	4.14696i	−0.207957	+	0.193353i
$461$	4.22493	−	1.37276i	0.196775	−	0.0639359i	−0.208972	−	0.977922i	$-0.567012\pi$
$461$	4.22493	−	1.37276i	0.196775	−	0.0639359i	0.405746	+	0.913986i	$0.367012\pi$
$462$	−18.4444	+	4.58047i	−0.858110	+	0.213103i
$463$	−10.6819	+	5.44272i	−0.496431	+	0.252944i	−0.684234	−	0.729262i	$-0.739863\pi$
$463$	−10.6819	+	5.44272i	−0.496431	+	0.252944i	0.187803	+	0.982207i	$0.439863\pi$
$464$	8.85265	+	7.97097i	0.410974	+	0.370043i
$465$	−18.7275	−	54.6490i	−0.868466	−	2.53429i
$466$	−12.4604	−	13.8387i	−0.577217	−	0.641065i
$467$	−1.25232	+	1.01411i	−0.0579504	+	0.0469273i	−0.657858	−	0.753142i	$-0.728537\pi$
$467$	−1.25232	+	1.01411i	−0.0579504	+	0.0469273i	0.599908	+	0.800069i	$0.295204\pi$
$468$	−10.7809	+	10.7809i	−0.498348	+	0.498348i
$469$	22.7812	−	19.7662i	1.05194	−	0.912720i
$470$	10.6184	−	16.9375i	0.489788	−	0.781271i
$471$	−4.92477	−	2.19265i	−0.226922	−	0.101032i
$472$	9.62970	−	11.8917i	0.443243	−	0.547360i
$473$	−7.21628	−	11.1121i	−0.331805	−	0.510935i
$474$	2.79387	+	4.83913i	0.128327	+	0.222269i
$475$	−16.3255	−	8.74202i	−0.749068	−	0.401112i
$476$	7.31298	+	6.83220i	0.335190	+	0.313153i
$477$	−21.4173	−	10.9126i	−0.980629	−	0.499655i
$478$	−2.46709	−	6.42698i	−0.112842	−	0.293963i
$479$	−0.644677	−	6.13369i	−0.0294560	−	0.280256i	−0.999328	−	0.0366421i	$-0.988334\pi$
$479$	−0.644677	−	6.13369i	−0.0294560	−	0.280256i	0.969872	−	0.243613i	$-0.0783328\pi$
$480$	−4.49024	−	25.6858i	−0.204951	−	1.17239i
$481$	13.7135	+	1.44135i	0.625283	+	0.0657199i
$482$	−18.0647	−	18.0647i	−0.822823	−	0.822823i
$483$	10.7772	+	22.1488i	0.490379	+	1.00781i
$484$	−4.06789	−	1.32174i	−0.184904	−	0.0600790i
$485$	7.60604	−	3.53317i	0.345373	−	0.160433i
$486$	−4.05030	+	19.0552i	−0.183725	+	0.864360i
$487$	31.9361	+	1.67370i	1.44716	+	0.0758425i	0.759651	−	0.650331i	$-0.225370\pi$
$487$	31.9361	+	1.67370i	1.44716	+	0.0758425i	0.687511	+	0.726174i	$0.258703\pi$
$488$	5.07816	−	7.81967i	0.229877	−	0.353980i
$489$	12.2633	+	37.7426i	0.554566	+	1.70678i
$490$	−5.62220	+	16.1531i	−0.253985	+	0.729723i
$491$	2.30750	−	7.10175i	0.104136	−	0.320498i	−0.885391	−	0.464848i	$-0.846109\pi$
$491$	2.30750	−	7.10175i	0.104136	−	0.320498i	0.989527	+	0.144350i	$0.0461091\pi$
$492$	−6.45476	−	7.97096i	−0.291003	−	0.359359i
$493$	8.32363	+	31.0642i	0.374877	+	1.39906i
$494$	−6.78364	−	15.2363i	−0.305211	−	0.685514i
$495$	13.6652	+	20.3238i	0.614205	+	0.913485i
$496$	9.58179	+	13.1882i	0.430235	+	0.592168i
$497$	8.47830	−	1.18350i	0.380304	−	0.0530872i
$498$	−6.68468	+	13.1194i	−0.299548	+	0.587895i
$499$	−24.3866	+	14.0796i	−1.09169	+	0.630289i	−0.934027	−	0.357204i	$-0.883730\pi$
$499$	−24.3866	+	14.0796i	−1.09169	+	0.630289i	−0.157666	+	0.987493i	$0.550397\pi$
$500$	2.74686	+	8.58240i	0.122844	+	0.383816i
$501$	−26.2951	+	45.5444i	−1.17478	+	2.03478i
$502$	22.2759	−	1.16743i	0.994220	−	0.0521049i
$503$	−4.65980	+	29.4208i	−0.207770	+	1.31181i	0.634571	+	0.772865i	$0.281177\pi$
$503$	−4.65980	+	29.4208i	−0.207770	+	1.31181i	−0.842341	+	0.538945i	$0.818823\pi$
$504$	−36.9553	−	4.57248i	−1.64612	−	0.203674i
$505$	28.4115	−	1.94482i	1.26430	−	0.0865434i
$506$	−0.920943	+	8.76218i	−0.0409409	+	0.389527i
$507$	10.5985	−	2.83987i	0.470697	−	0.126123i
$508$	−4.35807	−	1.67291i	−0.193358	−	0.0742233i
$509$	−7.73428	+	1.64397i	−0.342816	+	0.0728678i	−0.376103	−	0.926578i	$-0.622736\pi$
$509$	−7.73428	+	1.64397i	−0.342816	+	0.0728678i	0.0332865	+	0.999446i	$0.489403\pi$
$510$	−12.3868	+	29.0627i	−0.548496	+	1.28692i
$511$	−40.2632	+	3.48481i	−1.78114	+	0.154159i
$512$	8.18017	+	16.0545i	0.361516	+	0.709515i
$513$	−13.6091	−	8.83788i	−0.600859	−	0.390202i
$514$	−11.7982	−	2.50778i	−0.520395	−	0.110613i
$515$	−15.2893	+	21.7673i	−0.673726	+	0.959181i
$516$	−2.56368	−	12.0612i	−0.112860	−	0.530964i
$517$	3.05387	+	19.2814i	0.134309	+	0.847995i
$518$	5.11854	+	8.20838i	0.224896	+	0.360655i
$519$	23.5594	−	32.4267i	1.03414	−	1.42337i
$520$	−9.70236	+	26.5357i	−0.425476	+	1.16367i
$521$	−8.53022	+	0.896563i	−0.373716	+	0.0392791i	−0.289525	−	0.957170i	$-0.593497\pi$
$521$	−8.53022	+	0.896563i	−0.373716	+	0.0392791i	−0.0841911	+	0.996450i	$0.526831\pi$
$522$	−26.7113	−	21.6304i	−1.16912	−	0.946737i
$523$	−0.581347	−	11.0928i	−0.0254205	−	0.485053i	−0.981442	−	0.191757i	$-0.938581\pi$
$523$	−0.581347	−	11.0928i	−0.0254205	−	0.485053i	0.956022	−	0.293296i	$-0.0947520\pi$
$524$	7.02771			0.307007
$525$	36.4424	−	0.495151i	1.59048	−	0.0216101i
$526$	21.2508			0.926580
$527$	2.30327	+	43.9490i	0.100332	+	1.91445i
$528$	−8.88091	−	7.19162i	−0.386492	−	0.312975i
$529$	−11.5175	+	1.21053i	−0.500759	+	0.0526319i
$530$	−12.7864	−	0.465303i	−0.555404	−	0.0202115i
$531$	−13.4650	+	18.5330i	−0.584332	+	0.804264i
$532$	−3.71443	+	6.97016i	−0.161041	+	0.302195i
$533$	2.97773	+	18.8006i	0.128980	+	0.814345i
$534$	−2.17447	−	10.2301i	−0.0940983	−	0.442698i
$535$	11.0906	−	3.80061i	0.479490	−	0.164315i
$536$	34.1894	+	7.26719i	1.47676	+	0.313895i
$537$	−31.8485	−	20.6826i	−1.37436	−	0.892521i
$538$	2.52266	+	4.95100i	0.108760	+	0.213453i
$539$	−6.22795	−	15.4977i	−0.268257	−	0.667535i
$540$	1.76494	+	7.69631i	0.0759508	+	0.331196i
$541$	30.9839	−	6.58584i	1.33210	−	0.283147i	0.513788	−	0.857917i	$-0.328242\pi$
$541$	30.9839	−	6.58584i	1.33210	−	0.283147i	0.818315	+	0.574770i	$0.194908\pi$
$542$	−1.61187	−	0.618741i	−0.0692359	−	0.0265772i
$543$	13.6154	−	3.64822i	0.584291	−	0.156560i
$544$	−2.07643	+	19.7559i	−0.0890260	+	0.847026i
$545$	2.72538	−	10.8629i	0.116742	−	0.465317i
$546$	26.1956	+	19.7780i	1.12107	+	0.846422i
$547$	−1.94023	+	12.2501i	−0.0829582	+	0.523777i	0.910856	+	0.412724i	$0.135423\pi$
$547$	−1.94023	+	12.2501i	−0.0829582	+	0.523777i	−0.993814	+	0.111054i	$0.964577\pi$
$548$	9.32757	−	0.488837i	0.398454	−	0.0208821i
$549$	−6.97934	+	12.0886i	−0.297871	+	0.515928i
$550$	11.1545	+	6.74693i	0.475628	+	0.287690i
$551$	−21.9799	+	12.6901i	−0.936375	+	0.540616i
$552$	−12.9593	+	25.4340i	−0.551584	+	1.08254i
$553$	−3.87259	+	3.01979i	−0.164679	+	0.128415i
$554$	6.74984	+	9.29036i	0.286773	+	0.394710i
$555$	12.7146	−	16.2248i	0.539704	−	0.688703i
$556$	2.58450	+	5.80487i	0.109607	+	0.246181i
$557$	−5.23372	−	19.5325i	−0.221760	−	0.827619i	−0.983677	−	0.179944i	$-0.942408\pi$
$557$	−5.23372	−	19.5325i	−0.221760	−	0.827619i	0.761917	−	0.647675i	$-0.224258\pi$
$558$	−29.6001	−	36.5530i	−1.25307	−	1.54741i
$559$	−7.07150	+	21.7639i	−0.299093	+	0.920513i
$560$	−9.78872	+	3.15460i	−0.413649	+	0.133306i
$561$	−9.53353	−	29.3412i	−0.402506	−	1.23879i
$562$	13.9394	−	21.4647i	0.587996	−	0.905435i
$563$	−15.4767	−	0.811099i	−0.652264	−	0.0341837i	−0.276666	−	0.960966i	$-0.589230\pi$
$563$	−15.4767	−	0.811099i	−0.652264	−	0.0341837i	−0.375599	+	0.926782i	$0.622563\pi$
$564$	−3.77727	+	17.7707i	−0.159052	+	0.748280i
$565$	3.76472	−	6.76829i	0.158383	−	0.284744i
$566$	25.5877	+	8.31396i	1.07553	+	0.349462i
$567$	−4.48731	−	0.317982i	−0.188449	−	0.0133540i
$568$	7.01496	+	7.01496i	0.294341	+	0.294341i
$569$	−39.8255	−	4.18583i	−1.66957	−	0.175479i	−0.777970	−	0.628301i	$-0.783750\pi$
$569$	−39.8255	−	4.18583i	−1.66957	−	0.175479i	−0.891601	+	0.452823i	$0.850417\pi$
$570$	−24.6844	−	3.50613i	−1.03392	−	0.146856i
$571$	−2.39094	−	22.7482i	−0.100058	−	0.951984i	−0.923244	−	0.384213i	$-0.874473\pi$
$571$	−2.39094	−	22.7482i	−0.100058	−	0.951984i	0.823187	−	0.567771i	$-0.192194\pi$
$572$	−2.84015	−	7.39884i	−0.118753	−	0.309361i
$573$	14.4173	+	7.34600i	0.602293	+	0.306884i
$574$	−9.11630	+	9.75781i	−0.380507	+	0.407283i
$575$	5.54770	−	15.9593i	0.231355	−	0.665550i
$576$	−18.5949	−	32.2073i	−0.774787	−	1.34197i
$577$	−1.20049	−	1.84859i	−0.0499770	−	0.0769579i	0.812799	−	0.582544i	$-0.197943\pi$
$577$	−1.20049	−	1.84859i	−0.0499770	−	0.0769579i	−0.862776	+	0.505587i	$0.831276\pi$
$578$	3.45596	−	4.26776i	0.143749	−	0.177515i
$579$	53.2981	+	23.7298i	2.21499	+	0.986178i
$580$	11.9788	+	3.00533i	0.497391	+	0.124789i
$581$	−12.2315	−	4.22440i	−0.507450	−	0.175258i
$582$	7.98396	−	7.98396i	0.330946	−	0.330946i
$583$	9.71017	−	7.86314i	0.402154	−	0.325658i
$584$	−31.3387	−	34.8052i	−1.29681	−	1.44025i
$585$	12.4263	−	40.4321i	0.513762	−	1.67166i
$586$	−19.7178	−	17.7540i	−0.814534	−	0.733409i
$587$	37.0311	−	18.8683i	1.52844	−	0.778777i	0.530800	−	0.847497i	$-0.321892\pi$
$587$	37.0311	−	18.8683i	1.52844	−	0.778777i	0.997636	+	0.0687201i	$0.0218915\pi$
$588$	−0.242336	−	15.5419i	−0.00999376	−	0.640937i
$589$	−33.0316	+	10.7326i	−1.36104	+	0.442229i
$590$	−2.34426	+	11.9664i	−0.0965116	+	0.492647i
$591$	−32.0559	+	28.8633i	−1.31860	+	1.18728i
$592$	−2.08454	+	5.43040i	−0.0856739	+	0.223188i
$593$	16.2429	+	4.35228i	0.667017	+	0.178727i	0.576411	−	0.817160i	$-0.304453\pi$
$593$	16.2429	+	4.35228i	0.667017	+	0.178727i	0.0906063	+	0.995887i	$0.471120\pi$
$594$	9.24136	+	6.71424i	0.379178	+	0.275489i
$595$	−26.8017	−	7.25044i	−1.09876	−	0.297239i
$596$	8.24215	−	5.98828i	0.337612	−	0.245289i
$597$	−11.9422	+	4.58417i	−0.488761	+	0.187618i
$598$	12.7619	−	8.28765i	0.521871	−	0.338907i
$599$	−33.4463	−	19.3103i	−1.36658	−	0.788996i	−0.376091	−	0.926583i	$-0.622732\pi$
$599$	−33.4463	−	19.3103i	−1.36658	−	0.788996i	−0.990490	+	0.137587i	$0.956065\pi$
$600$	25.9056	+	33.3590i	1.05759	+	1.36188i
$601$			17.0869i			0.696991i	0.937310	+	0.348495i	$0.113307\pi$
$601$			17.0869i			0.696991i	−0.937310	+	0.348495i	$0.886693\pi$
$602$	−15.0908	+	5.47669i	−0.615055	+	0.223213i
$603$	−51.6838	−	8.18591i	−2.10473	−	0.333356i
$604$	0.307699	−	0.691103i	0.0125201	−	0.0281206i
$605$	11.6891	−	2.04341i	0.475229	−	0.0830766i
$606$	35.0257	−	15.5944i	1.42282	−	0.633481i
$607$	−1.59515	+	5.95317i	−0.0647450	+	0.241632i	−0.990713	−	0.135971i	$-0.956585\pi$
$607$	−1.59515	+	5.95317i	−0.0647450	+	0.241632i	0.925968	+	0.377602i	$0.123251\pi$
$608$	−15.4839	+	2.45241i	−0.627955	+	0.0994583i
$609$	25.7656	−	42.7909i	1.04408	−	1.73398i
$610$	−0.658442	+	7.40089i	−0.0266595	+	0.299653i
$611$	22.5608	−	25.0563i	0.912711	−	1.01367i
$612$	0.908725	−	17.3395i	0.0367330	−	0.700908i
$613$	1.54042	−	29.3930i	0.0622171	−	1.18717i	−0.771958	−	0.635673i	$-0.780722\pi$
$613$	1.54042	−	29.3930i	0.0622171	−	1.18717i	0.834175	−	0.551500i	$-0.185944\pi$
$614$	−19.9677	+	22.1763i	−0.805829	+	0.894964i
$615$	26.1769	+	11.1568i	1.05555	+	0.449885i
$616$	9.98456	−	16.5821i	0.402290	−	0.668112i
$617$	32.5489	−	5.15524i	1.31037	−	0.207542i	0.538123	−	0.842866i	$-0.319133\pi$
$617$	32.5489	−	5.15524i	1.31037	−	0.207542i	0.772246	+	0.635324i	$0.219133\pi$
$618$	−9.26894	+	34.5922i	−0.372851	+	1.39150i
$619$	5.43927	−	2.42172i	0.218623	−	0.0973370i	−0.294503	−	0.955651i	$-0.595154\pi$
$619$	5.43927	−	2.42172i	0.218623	−	0.0973370i	0.513126	+	0.858313i	$0.328487\pi$
$620$	15.1790	+	7.43091i	0.609604	+	0.298432i
$621$	6.02179	−	13.5252i	0.241646	−	0.542746i
$622$	29.1648	+	4.61925i	1.16940	+	0.185215i
$623$	8.64019	−	3.13567i	0.346162	−	0.125628i
$624$			19.7369i			0.790109i
$625$	−17.8812	−	17.4718i	−0.715249	−	0.698870i
$626$	−16.4605	−	9.50349i	−0.657895	−	0.379836i
$627$	20.4193	−	13.2605i	0.815469	−	0.529572i
$628$	1.47235	−	0.565181i	0.0587530	−	0.0225532i
$629$	−12.7044	+	9.23028i	−0.506557	+	0.368035i
$630$	27.7284	−	10.5677i	1.10473	−	0.421027i
$631$	−22.9678	−	16.6871i	−0.914335	−	0.664303i	0.0277723	−	0.999614i	$-0.491159\pi$
$631$	−22.9678	−	16.6871i	−0.914335	−	0.664303i	−0.942108	+	0.335311i	$0.891159\pi$
$632$	−5.49716	−	1.47296i	−0.218665	−	0.0585912i
$633$	−22.1213	+	57.6280i	−0.879243	+	2.29051i
$634$	19.1614	−	17.2530i	0.760996	−	0.685204i
$635$	12.8566	−	1.55944i	0.510198	−	0.0618844i
$636$	11.0589	−	3.59325i	0.438513	−	0.142481i
$637$	−14.0323	+	25.2041i	−0.555979	+	0.998622i
$638$	15.9190	−	8.11112i	0.630238	−	0.321122i
$639$	−11.0373	−	9.93799i	−0.436627	−	0.393141i
$640$	−0.709214	−	0.498150i	−0.0280341	−	0.0196911i
$641$	23.8137	+	26.4478i	0.940584	+	1.04462i	0.998926	+	0.0463281i	$0.0147520\pi$
$641$	23.8137	+	26.4478i	0.940584	+	1.04462i	−0.0583420	+	0.998297i	$0.518581\pi$
$642$	12.2664	−	9.93314i	0.484116	−	0.392030i
$643$	−8.34509	+	8.34509i	−0.329098	+	0.329098i	−0.852243	−	0.523145i	$-0.824758\pi$
$643$	−8.34509	+	8.34509i	−0.329098	+	0.329098i	0.523145	+	0.852243i	$0.324758\pi$
$644$	−6.81124	−	2.35239i	−0.268400	−	0.0926973i
$645$	21.9506	+	26.2378i	0.864304	+	1.03311i
$646$	17.3517	+	7.72547i	0.682693	+	0.303954i
$647$	−3.80662	+	4.70079i	−0.149654	+	0.184807i	−0.846460	−	0.532453i	$-0.821270\pi$
$647$	−3.80662	+	4.70079i	−0.149654	+	0.184807i	0.696806	+	0.717260i	$0.254604\pi$
$648$	−2.83938	−	4.37226i	−0.111541	−	0.171759i
$649$	−5.95387	−	10.3124i	−0.233710	−	0.404797i
$650$	−3.06804	−	22.3052i	−0.120339	−	0.874883i
$651$	46.6631	−	49.9467i	1.82887	−	1.95757i
$652$	−10.3445	−	5.27077i	−0.405121	−	0.206419i
$653$	0.271008	+	0.705999i	0.0106053	+	0.0276279i	0.938781	−	0.344515i	$-0.111957\pi$
$653$	0.271008	+	0.705999i	0.0106053	+	0.0276279i	−0.928176	+	0.372143i	$0.878623\pi$
$654$	−1.57610	−	14.9956i	−0.0616304	−	0.586374i
$655$	−17.2283	+	9.12801i	−0.673164	+	0.356661i
$656$	−7.98568	−	0.839329i	−0.311788	−	0.0327703i
$657$	49.5795	+	49.5795i	1.93428	+	1.93428i
$658$	23.5942	+	1.67194i	0.919798	+	0.0651792i
$659$	33.3711	+	10.8429i	1.29995	+	0.422380i	0.875565	−	0.483100i	$-0.160489\pi$
$659$	33.3711	+	10.8429i	1.29995	+	0.422380i	0.424388	+	0.905480i	$0.360489\pi$
$660$	−11.6264	−	2.27766i	−0.452556	−	0.0886576i
$661$	1.45007	−	6.82204i	0.0564011	−	0.265346i	−0.940908	−	0.338664i	$-0.890025\pi$
$661$	1.45007	−	6.82204i	0.0564011	−	0.265346i	0.997309	+	0.0733171i	$0.0233585\pi$
$662$	−2.64024	−	0.138369i	−0.102616	−	0.00537787i
$663$	−29.0205	+	44.6876i	−1.12706	+	1.73552i
$664$	−4.63419	−	14.2626i	−0.179842	−	0.553495i
$665$	0.0525662	−	21.9117i	0.00203843	−	0.849699i
$666$	5.18627	−	15.9617i	0.200964	−	0.618503i
$667$	−14.5727	−	17.9958i	−0.564256	−	0.696799i
$668$	−3.98202	−	14.8611i	−0.154069	−	0.574993i
$669$	19.3917	+	43.5545i	0.749727	+	1.68391i
$670$	−26.7861	+	7.63827i	−1.03484	+	0.295092i
$671$	−4.26485	−	5.87007i	−0.164643	−	0.226611i
$672$	24.3300	−	18.9722i	0.938551	−	0.731870i
$673$	4.08127	−	8.00994i	0.157321	−	0.308760i	−0.798870	−	0.601504i	$-0.794568\pi$
$673$	4.08127	−	8.00994i	0.157321	−	0.308760i	0.956191	+	0.292744i	$0.0945683\pi$
$674$	1.19851	−	0.691962i	0.0461650	−	0.0266534i
$675$	−14.3231	−	16.5749i	−0.551298	−	0.637969i
$676$	−1.60500	+	2.77994i	−0.0617306	+	0.106921i
$677$	−18.5552	+	0.972439i	−0.713136	+	0.0373739i	−0.405454	−	0.914115i	$-0.632887\pi$
$677$	−18.5552	+	0.972439i	−0.713136	+	0.0373739i	−0.307682	+	0.951489i	$0.599553\pi$
$678$	1.63115	−	10.2987i	0.0626438	−	0.395518i
$679$	7.91943	+	5.97929i	0.303920	+	0.229464i
$680$	−12.0097	−	29.8512i	−0.460553	−	1.14474i
$681$	−0.207965	+	1.97865i	−0.00796923	+	0.0758222i
$682$	23.6160	−	6.32788i	0.904302	−	0.242307i
$683$	−8.12312	−	3.11817i	−0.310822	−	0.119314i	0.197956	−	0.980211i	$-0.436570\pi$
$683$	−8.12312	−	3.11817i	−0.310822	−	0.119314i	−0.508779	+	0.860897i	$0.669903\pi$
$684$	13.4034	−	2.84898i	0.512492	−	0.108934i
$685$	−22.2314	+	13.3136i	−0.849417	+	0.508686i
$686$	−19.9968	+	3.10995i	−0.763482	+	0.118739i
$687$	18.4476	+	36.2055i	0.703821	+	1.38133i
$688$	−8.09592	−	5.25755i	−0.308654	−	0.200442i
$689$	−21.1083	−	4.48670i	−0.804162	−	0.170930i
$690$	−0.363611	−	22.7446i	−0.0138424	−	0.865870i
$691$	8.72219	+	41.0347i	0.331808	+	1.56103i	0.755451	+	0.655205i	$0.227418\pi$
$691$	8.72219	+	41.0347i	0.331808	+	1.56103i	−0.423644	+	0.905829i	$0.639249\pi$
$692$	1.83434	+	11.5816i	0.0697312	+	0.440265i
$693$	−13.6280	+	25.5732i	−0.517687	+	0.971444i
$694$	14.3306	−	19.7244i	0.543983	−	0.748728i
$695$	−13.8756	−	10.8736i	−0.526330	−	0.412460i
$696$	57.5684	−	6.05069i	2.18213	−	0.229351i
$697$	−16.8468	−	13.6422i	−0.638117	−	0.516737i
$698$	0.935232	+	17.8453i	0.0353991	+	0.675454i
$699$	−46.9511			−1.77586
$700$	−7.43624	+	7.64109i	−0.281063	+	0.288806i
$701$	30.6923			1.15923			0.579616	−	0.814890i	$-0.303203\pi$
$701$	30.6923			1.15923			0.579616	+	0.814890i	$0.303203\pi$
$702$	−1.03253	−	19.7019i	−0.0389704	−	0.743599i
$703$	−9.63114	−	7.79914i	−0.363245	−	0.294150i
$704$	19.2256	−	2.02069i	0.724590	−	0.0761575i
$705$	−13.8217	−	48.4705i	−0.520556	−	1.82550i
$706$	12.1579	−	16.7340i	0.457570	−	0.629791i
$707$	17.8293	+	28.5921i	0.670541	+	1.07532i
$708$	−1.73357	−	10.9454i	−0.0651517	−	0.411352i
$709$	5.28472	+	24.8627i	0.198472	+	0.933737i	0.958774	+	0.284168i	$0.0917174\pi$
$709$	5.28472	+	24.8627i	0.198472	+	0.933737i	−0.760302	+	0.649569i	$0.774949\pi$
$710$	−7.55683	−	2.32249i	−0.283603	−	0.0871616i
$711$	8.33386	+	1.77142i	0.312544	+	0.0664333i
$712$	8.93353	+	5.80150i	0.334798	+	0.217420i
$713$	−14.3861	−	28.2343i	−0.538763	−	1.05738i
$714$	−37.2413	+	3.22326i	−1.39372	+	0.120627i
$715$	16.5726	+	14.4491i	0.619781	+	0.540367i
$716$	10.8668	−	2.30982i	0.406113	−	0.0863220i
$717$	−16.2044	−	6.22027i	−0.605163	−	0.232300i
$718$	−5.22565	+	1.40021i	−0.195020	+	0.0522554i
$719$	−0.209637	+	1.99456i	−0.00781814	+	0.0743846i	−0.997735	−	0.0672630i	$-0.978573\pi$
$719$	−0.209637	+	1.99456i	−0.00781814	+	0.0743846i	0.989917	+	0.141648i	$0.0452400\pi$
$720$	15.1179	+	9.47761i	0.563412	+	0.353210i
$721$	−31.2357	−	3.86479i	−1.16328	−	0.143932i
$722$	0.902913	−	5.70077i	0.0336029	−	0.212161i
$723$	−64.3241	+	3.37108i	−2.39224	+	0.125372i
$724$	−2.06185	+	3.57123i	−0.0766281	+	0.132724i
$725$	−33.2692	+	8.19126i	−1.23559	+	0.304216i
$726$	13.8355	−	7.98793i	0.513484	−	0.296460i
$727$	−15.4939	+	30.4086i	−0.574638	+	1.12779i	0.402547	+	0.915399i	$0.368125\pi$
$727$	−15.4939	+	30.4086i	−0.574638	+	1.12779i	−0.977185	+	0.212391i	$0.931875\pi$
$728$	−33.1094	+	4.62179i	−1.22712	+	0.171295i
$729$	25.8721	+	35.6099i	0.958226	+	1.31888i
$730$	35.0528	+	12.8165i	1.29736	+	0.474359i
$731$	−10.6000	−	23.8079i	−0.392054	−	0.880567i
$732$	−1.74768	−	6.52244i	−0.0645962	−	0.241076i
$733$	−10.0391	−	12.3973i	−0.370803	−	0.457903i	0.557254	−	0.830342i	$-0.311855\pi$
$733$	−10.0391	−	12.3973i	−0.370803	−	0.457903i	−0.928057	+	0.372439i	$0.878522\pi$
$734$	−2.58819	+	7.96562i	−0.0955317	+	0.294016i
$735$	20.7808	+	37.7858i	0.766513	+	1.39375i
$736$	−4.41993	−	13.6031i	−0.162921	−	0.501419i
$737$	14.8144	−	22.8122i	0.545696	−	0.840298i
$738$	23.1363	+	1.21252i	0.851661	+	0.0446336i
$739$	2.82573	−	13.2940i	0.103946	−	0.489029i	−0.895120	−	0.445825i	$-0.852910\pi$
$739$	2.82573	−	13.2940i	0.103946	−	0.489029i	0.999066	−	0.0432034i	$-0.0137564\pi$
$740$	0.726136	+	5.98654i	0.0266933	+	0.220070i
$741$	−39.9927	−	12.9944i	−1.46917	−	0.477362i
$742$	−6.62385	−	13.6131i	−0.243169	−	0.499751i
$743$	8.39691	+	8.39691i	0.308053	+	0.308053i	0.844154	−	0.536101i	$-0.180103\pi$
$743$	8.39691	+	8.39691i	0.308053	+	0.308053i	−0.536101	+	0.844154i	$0.680103\pi$
$744$	78.7794	+	8.28004i	2.88819	+	0.303561i
$745$	−12.4275	+	25.3855i	−0.455309	+	0.930054i
$746$	−2.92360	−	27.8162i	−0.107041	−	1.01842i
$747$	8.04578	+	20.9600i	0.294380	+	0.766885i
$748$	8.04182	+	4.09751i	0.294038	+	0.149820i
$749$	10.1364	+	9.46996i	0.370374	+	0.346025i
$750$	−30.6874	−	13.8252i	−1.12055	−	0.504824i
$751$	9.47113	+	16.4045i	0.345606	+	0.598608i	0.985464	−	0.169886i	$-0.0543399\pi$
$751$	9.47113	+	16.4045i	0.345606	+	0.598608i	−0.639857	+	0.768494i	$0.721007\pi$
$752$	7.74635	+	11.9283i	0.282480	+	0.434982i
$753$	35.3937	−	43.7076i	1.28982	−	1.59279i
$754$	−28.1896	−	12.5508i	−1.02660	−	0.457073i
$755$	0.143330	+	2.09388i	0.00521631	+	0.0762041i
$756$	−7.05679	+	6.12284i	−0.256653	+	0.222686i
$757$	7.38774	−	7.38774i	0.268512	−	0.268512i	−0.559988	−	0.828500i	$-0.689194\pi$
$757$	7.38774	−	7.38774i	0.268512	−	0.268512i	0.828500	+	0.559988i	$0.189194\pi$
$758$	−10.7186	+	8.67978i	−0.389318	+	0.315264i
$759$	14.8639	+	16.5081i	0.539526	+	0.599205i
$760$	20.3024	−	15.2523i	0.736444	−	0.553257i
$761$	4.54661	+	4.09379i	0.164815	+	0.148400i	0.747411	−	0.664362i	$-0.231297\pi$
$761$	4.54661	+	4.09379i	0.164815	+	0.148400i	−0.582597	+	0.812762i	$0.697963\pi$
$762$	15.5355	−	7.91573i	0.562792	−	0.286757i
$763$	12.8609	−	3.19387i	0.465596	−	0.115626i
$764$	−4.50208	+	1.46281i	−0.162879	+	0.0529227i
$765$	20.2939	+	43.6877i	0.733727	+	1.57953i
$766$	−22.5133	+	20.2711i	−0.813438	+	0.732423i
$767$	−7.37027	+	19.2002i	−0.266125	+	0.693279i
$768$	41.9939	+	11.2522i	1.51532	+	0.406030i
$769$	19.2318	+	13.9727i	0.693517	+	0.503870i	0.877814	−	0.479001i	$-0.159001\pi$
$769$	19.2318	+	13.9727i	0.693517	+	0.503870i	−0.184297	+	0.982871i	$0.559001\pi$
$770$	−0.844216	+	15.4016i	−0.0304234	+	0.555034i
$771$	−24.6033	+	17.8753i	−0.886065	+	0.643764i
$772$	−15.9344	+	6.11664i	−0.573491	+	0.220143i
$773$	43.5595	−	28.2879i	1.56673	−	1.01744i	0.588856	−	0.808238i	$-0.299579\pi$
$773$	43.5595	−	28.2879i	1.56673	−	1.01744i	0.977871	−	0.209207i	$-0.0670882\pi$
$774$	24.1212	+	13.9264i	0.867017	+	0.500572i
$775$	−46.8627	+	1.49875i	−1.68336	+	0.0538366i
$776$			11.4998i			0.412820i
$777$	24.0154	+	4.25762i	0.861546	+	0.152741i
$778$	−15.4483	−	2.44678i	−0.553850	−	0.0877212i
$779$	6.95834	−	15.6287i	0.249309	−	0.559956i
$780$	9.57977	+	18.0809i	0.343011	+	0.647400i
$781$	7.05276	−	3.14009i	0.252367	−	0.112361i
$782$	−4.48518	+	16.7389i	−0.160390	+	0.598583i
$783$	−29.6530	+	4.69657i	−1.05971	+	0.167842i
$784$	−8.73772	−	8.46942i	−0.312061	−	0.302479i
$785$	−2.87533	+	3.29790i	−0.102625	+	0.117707i
$786$	−17.5641	+	19.5069i	−0.626491	+	0.695789i
$787$	1.22089	−	23.2960i	0.0435202	−	0.830414i	−0.886460	−	0.462805i	$-0.846843\pi$
$787$	1.22089	−	23.2960i	0.0435202	−	0.830414i	0.929980	−	0.367609i	$-0.119824\pi$
$788$	0.660445	−	12.6020i	0.0235274	−	0.448929i
$789$	35.8518	−	39.8175i	1.27636	−	1.41754i
$790$	4.42042	−	1.01370i	0.157272	−	0.0360659i
$791$	9.16230	+	0.168462i	0.325774	+	0.00598982i
$792$	−33.1685	+	5.25337i	−1.17859	+	0.186670i
$793$	−3.24344	+	12.1047i	−0.115178	+	0.429850i
$794$	29.5497	−	13.1564i	1.04868	−	0.466902i
$795$	−22.4434	+	23.1727i	−0.795987	+	0.821851i
$796$	1.52211	−	3.41872i	0.0539499	−	0.121173i
$797$	−26.6088	−	4.21442i	−0.942532	−	0.149282i	−0.333787	−	0.942648i	$-0.608327\pi$
$797$	−26.6088	−	4.21442i	−0.942532	−	0.149282i	−0.608745	+	0.793366i	$0.708327\pi$
$798$	−10.0638	−	27.7305i	−0.356256	−	0.981648i
$799$			38.3977i			1.35841i
$800$	−20.9981	−	2.64084i	−0.742394	−	0.0933678i
$801$	−13.8105	−	7.97350i	−0.487970	−	0.281730i
$802$	−8.05865	+	5.23335i	−0.284561	+	0.184796i
$803$	−34.0260	+	13.0613i	−1.20075	+	0.460925i
$804$	20.4792	−	14.8790i	0.722247	−	0.524743i
$805$	19.7530	−	3.08001i	0.696203	−	0.108556i
$806$	−34.1621	−	24.8202i	−1.20331	−	0.874254i
$807$	13.5326	+	3.62604i	0.476369	+	0.127643i
$808$	−13.9941	+	36.4558i	−0.492309	+	1.28251i
$809$	22.5688	−	20.3211i	0.793478	−	0.714451i	−0.169057	−	0.985606i	$-0.554072\pi$
$809$	22.5688	−	20.3211i	0.793478	−	0.714451i	0.962536	+	0.271155i	$0.0874056\pi$
$810$	3.63060	+	2.01945i	0.127566	+	0.0709561i
$811$	36.4823	−	11.8538i	1.28107	−	0.416244i	0.412112	−	0.911133i	$-0.364791\pi$
$811$	36.4823	−	11.8538i	1.28107	−	0.416244i	0.868956	+	0.494889i	$0.164791\pi$
$812$	3.52194	+	14.1820i	0.123596	+	0.497689i
$813$	−3.87869	+	1.97629i	−0.136032	+	0.0693115i
$814$	6.48317	+	5.83747i	0.227235	+	0.204603i
$815$	32.2052	−	0.514856i	1.12810	−	0.0180346i
$816$	−15.0401	−	16.7038i	−0.526510	−	0.584749i
$817$	15.9835	−	12.9432i	0.559192	−	0.452825i
$818$	14.0376	−	14.0376i	0.490814	−	0.490814i
$819$	49.1376	−	9.50392i	1.71701	−	0.332094i
$820$	−7.72303	+	3.10713i	−0.269700	+	0.108506i
$821$	−23.6704	−	10.5387i	−0.826101	−	0.367804i	−0.0502631	−	0.998736i	$-0.516006\pi$
$821$	−23.6704	−	10.5387i	−0.826101	−	0.367804i	−0.775838	+	0.630932i	$0.782673\pi$
$822$	−21.9552	+	27.1124i	−0.765775	+	0.945654i
$823$	11.4540	+	17.6377i	0.399262	+	0.614810i	0.979933	−	0.199329i	$-0.0638762\pi$
$823$	11.4540	+	17.6377i	0.399262	+	0.614810i	−0.580670	+	0.814139i	$0.697210\pi$
$824$	−18.2374	−	31.5880i	−0.635328	−	1.10042i
$825$	31.4602	−	9.51743i	1.09530	−	0.331354i
$826$	−13.8014	+	4.20547i	−0.480213	+	0.146327i
$827$	−21.2916	−	10.8486i	−0.740382	−	0.377243i	0.0427610	−	0.999085i	$-0.486385\pi$
$827$	−21.2916	−	10.8486i	−0.740382	−	0.377243i	−0.783143	+	0.621842i	$0.786385\pi$
$828$	4.48036	+	11.6717i	0.155703	+	0.405621i
$829$	−5.76680	−	54.8674i	−0.200289	−	1.90562i	−0.385141	−	0.922858i	$-0.625847\pi$
$829$	−5.76680	−	54.8674i	−0.200289	−	1.90562i	0.184852	−	0.982766i	$-0.440820\pi$
$830$	8.58436	+	8.31421i	0.297968	+	0.288590i
$831$	28.7948	+	3.02645i	0.998880	+	0.104987i
$832$	−23.6088	−	23.6088i	−0.818488	−	0.818488i
$833$	−7.33048	−	32.0238i	−0.253986	−	1.10956i
$834$	−22.5720	−	7.33409i	−0.781605	−	0.253959i
$835$	29.0643	+	31.2595i	1.00581	+	1.08178i
$836$	−1.48092	+	6.96717i	−0.0512186	+	0.240965i
$837$	−41.0280	−	2.15019i	−1.41814	−	0.0743213i
$838$	1.46743	−	2.25965i	0.0506916	−	0.0780582i
$839$	−3.08363	−	9.49044i	−0.106459	−	0.327646i	0.883611	−	0.468221i	$-0.155105\pi$
$839$	−3.08363	−	9.49044i	−0.106459	−	0.327646i	−0.990070	+	0.140575i	$0.955105\pi$
$840$	−20.4361	+	45.6055i	−0.705113	+	1.57354i
$841$	−5.54913	+	17.0785i	−0.191349	+	0.588912i
$842$	10.5945	+	13.0832i	0.365112	+	0.450876i
$843$	−16.7015	−	62.3308i	−0.575229	−	2.14679i
$844$	−7.34509	−	16.4974i	−0.252829	−	0.567862i
$845$	0.323862	−	8.89961i	0.0111412	−	0.306156i
$846$	−24.1213	−	33.2001i	−0.829306	−	1.14144i
$847$	8.63387	+	11.0721i	0.296663	+	0.380441i
$848$	4.13276	−	8.11101i	0.141920	−	0.278533i
$849$	58.7463	−	33.9172i	2.01617	−	1.16404i
$850$	19.5938	+	16.5394i	0.672062	+	0.567298i
$851$	5.65350	−	9.79216i	0.193800	−	0.335671i
$852$	7.17486	−	0.376019i	0.245807	−	0.0128822i
$853$	5.83957	−	36.8696i	0.199943	−	1.26239i	−0.659713	−	0.751517i	$-0.729322\pi$
$853$	5.83957	−	36.8696i	0.199943	−	1.26239i	0.859656	−	0.510873i	$-0.170678\pi$
$854$	−8.09575	+	3.42755i	−0.277031	+	0.117288i
$855$	−29.1577	+	24.3934i	−0.997173	+	0.834236i
$856$	−1.68038	+	15.9877i	−0.0574342	+	0.546450i
$857$	−5.88159	+	1.57597i	−0.200911	+	0.0538340i	−0.357871	−	0.933771i	$-0.616497\pi$
$857$	−5.88159	+	1.57597i	−0.200911	+	0.0538340i	0.156960	+	0.987605i	$0.449831\pi$
$858$	27.6354	+	10.6082i	0.943455	+	0.362159i
$859$	−26.5387	+	5.64097i	−0.905488	+	0.192467i	−0.637044	−	0.770828i	$-0.719843\pi$
$859$	−26.5387	+	5.64097i	−0.905488	+	0.192467i	−0.268444	+	0.963295i	$0.586510\pi$
$860$	−9.96850	−	0.886878i	−0.339923	−	0.0302423i
$861$	2.90319	+	33.5433i	0.0989406	+	1.14315i
$862$	3.31936	+	6.51460i	0.113058	+	0.221888i
$863$	22.1204	+	14.3652i	0.752988	+	0.488996i	0.863169	−	0.504916i	$-0.168476\pi$
$863$	22.1204	+	14.3652i	0.752988	+	0.488996i	−0.110181	+	0.993912i	$0.535143\pi$
$864$	−18.1392	−	3.85560i	−0.617108	−	0.131170i
$865$	−19.5397	−	26.0094i	−0.664369	−	0.884346i
$866$	−7.46285	−	35.1099i	−0.253598	−	1.19308i
$867$	−2.16598	−	13.6755i	−0.0735605	−	0.464443i
$868$	0.679269	+	19.9852i	0.0230559	+	0.678342i
$869$	−2.60316	+	3.58295i	−0.0883063	+	0.121543i
$870$	−38.2800	+	25.7385i	−1.29781	+	0.872618i
$871$	−46.7213	+	4.91060i	−1.58309	+	0.166389i
$872$	11.9347	+	9.66450i	0.404159	+	0.327281i
$873$	−0.901029	−	17.1927i	−0.0304952	−	0.581883i
$874$	−13.6761			−0.462602
$875$	8.30504	−	28.3906i	0.280762	−	0.959778i
$876$	−33.9187			−1.14601
$877$	0.325237	+	6.20589i	0.0109825	+	0.209558i	0.998609	+	0.0527319i	$0.0167929\pi$
$877$	0.325237	+	6.20589i	0.0109825	+	0.209558i	−0.987626	+	0.156826i	$0.949874\pi$
$878$	−13.7775	−	11.1568i	−0.464970	−	0.376525i
$879$	−66.5309	+	6.99268i	−2.24403	+	0.235857i
$880$	−7.69689	+	5.17519i	−0.259462	+	0.174456i
$881$	−21.7017	+	29.8698i	−0.731149	+	1.00634i	0.267931	+	0.963438i	$0.413660\pi$
$881$	−21.7017	+	29.8698i	−0.731149	+	1.00634i	−0.999079	+	0.0429017i	$0.986340\pi$
$882$	26.4554	+	23.0840i	0.890800	+	0.777278i
$883$	1.39512	+	8.80845i	0.0469496	+	0.296428i	0.999979	−	0.00644911i	$-0.00205283\pi$
$883$	1.39512	+	8.80845i	0.0469496	+	0.296428i	−0.953030	+	0.302877i	$0.902053\pi$
$884$	−3.24098	−	15.2476i	−0.109006	−	0.512833i
$885$	18.4663	+	24.5806i	0.620738	+	0.826268i
$886$	−28.7075	−	6.10196i	−0.964446	−	0.204999i
$887$	−29.9050	−	19.4206i	−1.00411	−	0.652078i	−0.0657880	−	0.997834i	$-0.520956\pi$
$887$	−29.9050	−	19.4206i	−1.00411	−	0.652078i	−0.938325	+	0.345755i	$0.887623\pi$
$888$	12.8321	+	25.1844i	0.430616	+	0.845132i
$889$	8.77757	+	12.5605i	0.294390	+	0.421267i
$890$	−8.45509	−	0.752233i	−0.283415	−	0.0252149i
$891$	−3.96832	+	0.843493i	−0.132944	+	0.0282581i
$892$	−13.0214	−	4.99843i	−0.435988	−	0.167360i
$893$	−29.2703	+	7.84295i	−0.979493	+	0.262454i
$894$	−3.97758	+	37.8442i	−0.133030	+	1.26570i
$895$	−23.6397	+	19.7770i	−0.790188	+	0.661072i
$896$	0.125921	−	1.01771i	0.00420673	−	0.0339993i
$897$	6.00177	−	37.8937i	0.200393	−	1.26523i
$898$	−15.8702	+	0.831722i	−0.529595	+	0.0277549i
$899$	−32.1293	+	55.6496i	−1.07157	+	1.85602i
$900$	18.4496	+	1.34456i	0.614988	+	0.0448188i
$901$	21.2834	−	12.2880i	0.709053	−	0.409372i
$902$	−5.46737	+	10.7303i	−0.182043	+	0.357280i
$903$	−15.1977	+	37.5151i	−0.505749	+	1.24842i
$904$	6.24220	+	8.59165i	0.207612	+	0.285754i
$905$	0.416048	−	11.4328i	0.0138299	−	0.380041i
$906$	1.14928	+	2.58133i	0.0381824	+	0.0857591i
$907$	11.1347	+	41.5553i	0.369722	+	1.37982i	0.860905	+	0.508765i	$0.169898\pi$
$907$	11.1347	+	41.5553i	0.369722	+	1.37982i	−0.491183	+	0.871056i	$0.663436\pi$
$908$	−0.366294	−	0.452335i	−0.0121559	−	0.0150113i
$909$	18.0652	−	55.5991i	0.599186	−	1.84411i
$910$	21.5900	−	15.6071i	0.715703	−	0.517370i
$911$	−2.10979	−	6.49326i	−0.0699004	−	0.215131i	0.910004	−	0.414600i	$-0.136078\pi$
$911$	−2.10979	−	6.49326i	−0.0699004	−	0.215131i	−0.979904	+	0.199469i	$0.936078\pi$
$912$	9.66114	−	14.8769i	0.319912	−	0.492622i
$913$	−11.6543	−	0.610774i	−0.385700	−	0.0202137i
$914$	−2.30314	+	10.8354i	−0.0761811	+	0.358404i
$915$	12.7561	+	13.7196i	0.421705	+	0.453556i
$916$	−11.3058	−	3.67349i	−0.373555	−	0.121375i
$917$	−19.1132	−	12.9179i	−0.631173	−	0.426587i
$918$	15.8873	+	15.8873i	0.524358	+	0.524358i
$919$	49.3154	+	5.18326i	1.62676	+	0.170980i	0.873530	−	0.486771i	$-0.161825\pi$
$919$	49.3154	+	5.18326i	1.62676	+	0.170980i	0.753235	+	0.657751i	$0.228492\pi$
$920$	16.6421	+	16.1184i	0.548674	+	0.531407i
$921$	7.86458	+	74.8265i	0.259147	+	2.46562i
$922$	−1.73959	−	4.53178i	−0.0572902	−	0.149246i
$923$	−11.8805	−	6.05341i	−0.391051	−	0.199250i
$924$	−4.08599	−	13.4093i	−0.134419	−	0.441133i
$925$	−9.55579	−	13.7327i	−0.314192	−	0.451529i
$926$	6.55002	+	11.3450i	0.215247	+	0.372819i
$927$	29.7405	+	45.7963i	0.976805	+	1.50415i
$928$	−18.2533	+	22.5409i	−0.599193	+	0.739942i
$929$	−15.5782	−	6.93586i	−0.511104	−	0.227558i	0.134946	−	0.990853i	$-0.456914\pi$
$929$	−15.5782	−	6.93586i	−0.511104	−	0.227558i	−0.646050	+	0.763295i	$0.723580\pi$
$930$	−58.5625	+	23.5608i	−1.92034	+	0.772591i
$931$	22.9142	−	12.1290i	0.750983	−	0.397513i
$932$	9.71255	−	9.71255i	0.318145	−	0.318145i
$933$	57.8584	−	46.8528i	1.89420	−	1.53389i
$934$	1.17822	+	1.30855i	0.0385526	+	0.0428170i
$935$	−25.0364	+	0.400251i	−0.818779	+	0.0130896i
$936$	43.1026	+	38.8098i	1.40885	+	1.26854i
$937$	−25.7159	+	13.1029i	−0.840101	+	0.428053i	−0.820425	−	0.571754i	$-0.806263\pi$
$937$	−25.7159	+	13.1029i	−0.840101	+	0.428053i	−0.0196757	+	0.999806i	$0.506263\pi$
$938$	−22.8719	−	23.7287i	−0.746794	−	0.774770i
$939$	−45.5768	+	14.8088i	−1.48734	+	0.483267i
$940$	12.8861	+	7.16762i	0.420298	+	0.233782i
$941$	0.522224	−	0.470213i	0.0170240	−	0.0153285i	−0.660575	−	0.750760i	$-0.729687\pi$
$941$	0.522224	−	0.470213i	0.0170240	−	0.0153285i	0.677599	+	0.735432i	$0.263021\pi$
$942$	−2.11100	+	5.49935i	−0.0687802	+	0.179179i
$943$	15.0768	+	4.03982i	0.490968	+	0.131554i
$944$	−7.01870	−	5.09939i	−0.228439	−	0.165971i
$945$	9.34682	−	24.1758i	0.304052	−	0.786439i
$946$	−11.7129	+	8.50996i	−0.380821	+	0.276683i
$947$	17.7573	−	6.81639i	0.577035	−	0.221503i	−0.0523074	−	0.998631i	$-0.516658\pi$
$947$	17.7573	−	6.81639i	0.577035	−	0.221503i	0.629343	+	0.777128i	$0.283324\pi$
$948$	−3.45664	+	2.24477i	−0.112267	+	0.0729068i
$949$	54.5147	+	31.4741i	1.76962	+	1.02169i
$950$	−8.60576	+	18.3145i	−0.279208	+	0.594202i
$951$		−	65.0097i		−	2.10809i
$952$	24.4992	−	29.1419i	0.794025	−	0.944495i
$953$	34.0918	+	5.39961i	1.10434	+	0.174910i	0.681875	−	0.731469i	$-0.261165\pi$
$953$	34.0918	+	5.39961i	1.10434	+	0.174910i	0.422466	+	0.906379i	$0.361165\pi$
$954$	−10.6832	+	23.9948i	−0.345880	+	0.776860i
$955$	9.13675	−	9.43363i	0.295658	−	0.305265i
$956$	4.63887	−	2.06536i	0.150032	−	0.0667985i
$957$	11.6588	−	43.5113i	0.376876	−	1.40652i
$958$	−6.65627	+	1.05425i	−0.215054	+	0.0340613i
$959$	−26.2667	−	15.8159i	−0.848195	−	0.510722i
$960$	−48.6486	+	11.1562i	−1.57013	+	0.360065i
$961$	−38.0966	+	42.3106i	−1.22892	+	1.36486i
$962$	0.788567	−	15.0468i	0.0254244	−	0.485127i
$963$	1.25956	−	24.0339i	0.0405889	−	0.774482i
$964$	12.6091	−	14.0038i	0.406110	−	0.451031i
$965$	31.1181	−	35.6913i	1.00173	−	1.14894i
$966$	23.5527	−	13.0268i	0.757795	−	0.419131i
$967$	44.4029	−	7.03273i	1.42790	−	0.226157i	0.605853	−	0.795576i	$-0.292832\pi$
$967$	44.4029	−	7.03273i	1.42790	−	0.226157i	0.822047	+	0.569419i	$0.192832\pi$
$968$	−4.21132	+	15.7169i	−0.135357	+	0.505159i
$969$	43.7488	−	19.4782i	1.40541	−	0.625731i
$970$	−4.29040	−	8.09773i	−0.137757	−	0.260002i
$971$	14.5419	−	32.6617i	0.466673	−	1.04816i	−0.514931	−	0.857232i	$-0.672182\pi$
$971$	14.5419	−	32.6617i	0.466673	−	1.04816i	0.981603	−	0.190932i	$-0.0611510\pi$
$972$	−14.1924	−	2.24785i	−0.455221	−	0.0720999i
$973$	3.64115	−	20.5381i	0.116730	−	0.658422i
$974$		−	34.9447i		−	1.11970i
$975$	−46.9691	−	31.8821i	−1.50422	−	1.02105i
$976$	−4.57811	−	2.64317i	−0.146542	−	0.0846059i
$977$	−13.4154	+	8.71205i	−0.429196	+	0.278723i	−0.741105	−	0.671389i	$-0.765698\pi$
$977$	−13.4154	+	8.71205i	−0.429196	+	0.278723i	0.311909	+	0.950112i	$0.399031\pi$
$978$	40.4837	−	15.5402i	1.29453	−	0.496922i
$979$	6.70622	−	4.87235i	0.214332	−	0.155721i
$980$	−12.1154	−	3.51774i	−0.387012	−	0.112370i
$981$	−18.6000	−	13.5137i	−0.593852	−	0.431458i
$982$	−7.88146	−	2.11183i	−0.251507	−	0.0673912i
$983$	−12.4094	+	32.3275i	−0.395797	+	1.03109i	0.580425	+	0.814314i	$0.302886\pi$
$983$	−12.4094	+	32.3275i	−0.395797	+	1.03109i	−0.976222	+	0.216773i	$0.930447\pi$
$984$	−28.9962	+	26.1083i	−0.924365	+	0.832302i
$985$	14.7492	+	31.7514i	0.469950	+	1.01169i
$986$	33.4215	−	10.8593i	1.06436	−	0.345831i
$987$	42.9380	−	41.3876i	1.36673	−	1.31738i
$988$	10.9612	−	5.58500i	0.348722	−	0.177683i
$989$	13.9449	+	12.5561i	0.443422	+	0.399259i
$990$	21.3960	−	16.0739i	0.680010	−	0.510861i
$991$	−22.7867	−	25.3072i	−0.723842	−	0.803908i	0.263136	−	0.964759i	$-0.415243\pi$
$991$	−22.7867	−	25.3072i	−0.723842	−	0.803908i	−0.986979	+	0.160850i	$0.948576\pi$
$992$	−30.8461	+	24.9786i	−0.979363	+	0.793073i
$993$	−4.71356	+	4.71356i	−0.149580	+	0.149580i
$994$	−1.77630	−	9.18392i	−0.0563408	−	0.291296i
$995$	0.709020	+	10.3579i	0.0224774	+	0.328369i
$996$	−9.92181	−	4.41747i	−0.314384	−	0.139973i
$997$	−2.60430	+	3.21604i	−0.0824789	+	0.101853i	−0.816715	−	0.577041i	$-0.804207\pi$
$997$	−2.60430	+	3.21604i	−0.0824789	+	0.101853i	0.734236	+	0.678894i	$0.237541\pi$
$998$	16.7584	+	25.8057i	0.530478	+	0.816864i
$999$	−7.32990	−	12.6958i	−0.231908	−	0.401676i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	175.2.x.a.108.7	yes	288
5.2	odd	4		875.2.bb.b.857.12		288
5.3	odd	4		875.2.bb.a.857.7		288
5.4	even	2		875.2.bb.c.143.12		288
7.5	odd	6	inner	175.2.x.a.33.7	✓	288
25.3	odd	20		875.2.bb.c.507.12		288
25.4	even	10		875.2.bb.a.493.12		288
25.21	even	5		875.2.bb.b.493.7		288
25.22	odd	20	inner	175.2.x.a.122.7	yes	288
35.12	even	12		875.2.bb.b.607.7		288
35.19	odd	6		875.2.bb.c.768.12		288
35.33	even	12		875.2.bb.a.607.12		288
175.47	even	60	inner	175.2.x.a.47.7	yes	288
175.54	odd	30		875.2.bb.a.243.7		288
175.96	odd	30		875.2.bb.b.243.12		288
175.103	even	60		875.2.bb.c.257.12		288

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
175.2.x.a.33.7	✓	288	7.5	odd	6	inner
175.2.x.a.47.7	yes	288	175.47	even	60	inner
175.2.x.a.108.7	yes	288	1.1	even	1	trivial
175.2.x.a.122.7	yes	288	25.22	odd	20	inner
875.2.bb.a.243.7		288	175.54	odd	30
875.2.bb.a.493.12		288	25.4	even	10
875.2.bb.a.607.12		288	35.33	even	12
875.2.bb.a.857.7		288	5.3	odd	4
875.2.bb.b.243.12		288	175.96	odd	30
875.2.bb.b.493.7		288	25.21	even	5
875.2.bb.b.607.7		288	35.12	even	12
875.2.bb.b.857.12		288	5.2	odd	4
875.2.bb.c.143.12		288	5.4	even	2
875.2.bb.c.257.12		288	175.103	even	60
875.2.bb.c.507.12		288	25.3	odd	20
875.2.bb.c.768.12		288	35.19	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
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+(-0.0571879 - 1.09121i) q^{2} +(-2.14107 - 1.73380i) q^{3} +(0.801576 - 0.0842491i) q^{4} +(-1.85562 + 1.24767i) q^{5} +(-1.76950 + 2.43551i) q^{6} +(-2.33490 - 1.24428i) q^{7} +(-0.479648 - 3.02838i) q^{8} +(0.954369 + 4.48995i) q^{9} +(1.46759 + 1.95352i) q^{10} +(-2.33390 - 0.496086i) q^{11} +(-1.86230 - 1.20939i) q^{12} +(1.87090 + 3.67184i) q^{13} +(-1.22424 + 2.61902i) q^{14} +(6.13623 + 0.545928i) q^{15} +(-1.70041 + 0.361432i) q^{16} +(-4.38143 - 1.68187i) q^{17} +(4.84490 - 1.29819i) q^{18} +(0.387149 - 3.68347i) q^{19} +(-1.38230 + 1.15644i) q^{20} +(2.84185 + 6.71235i) q^{21} +(-0.407863 + 2.57515i) q^{22} +(3.37458 - 0.176854i) q^{23} +(-4.22365 + 7.31558i) q^{24} +(1.88664 - 4.63040i) q^{25} +(3.89975 - 2.25152i) q^{26} +(1.98904 - 3.90371i) q^{27} +(-1.97643 - 0.800672i) q^{28} +(-4.02782 - 5.54382i) q^{29} +(0.244804 - 6.72713i) q^{30} +(-3.81411 - 8.56663i) q^{31} +(-1.09550 - 4.08847i) q^{32} +(4.13693 + 5.10869i) q^{33} +(-1.58471 + 4.87724i) q^{34} +(5.88514 - 0.604282i) q^{35} +(1.14327 + 3.51863i) q^{36} +(1.82239 - 2.80623i) q^{37} +(-4.04158 - 0.211810i) q^{38} +(2.36053 - 11.1054i) q^{39} +(4.66846 + 5.02107i) q^{40} +(4.39294 + 1.42735i) q^{41} +(7.16206 - 3.48492i) q^{42} +(3.92655 + 3.92655i) q^{43} +(-1.91260 - 0.201022i) q^{44} +(-7.37292 - 7.14090i) q^{45} +(-0.385971 - 3.67226i) q^{46} +(-2.93204 - 7.63822i) q^{47} +(4.26734 + 2.17432i) q^{48} +(3.90354 + 5.81054i) q^{49} +(-5.16063 - 1.79391i) q^{50} +(6.46492 + 11.1976i) q^{51} +(1.80902 + 2.78564i) q^{52} +(-3.29547 + 4.06957i) q^{53} +(-4.37351 - 1.94721i) q^{54} +(4.94978 - 1.99140i) q^{55} +(-2.64822 + 7.66778i) q^{56} +(-7.21534 + 7.21534i) q^{57} +(-5.81913 + 4.71224i) q^{58} +(3.33935 + 3.70872i) q^{59} +(4.96465 - 0.0793685i) q^{60} +(2.25986 + 2.03478i) q^{61} +(-9.12986 + 4.65190i) q^{62} +(3.35840 - 11.6711i) q^{63} +(-7.70535 + 2.50362i) q^{64} +(-8.05292 - 4.47927i) q^{65} +(5.33807 - 4.80642i) q^{66} +(-4.08532 + 10.6426i) q^{67} +(-3.65375 - 0.979019i) q^{68} +(-7.53185 - 5.47221i) q^{69} +(-0.995957 - 6.38736i) q^{70} +(-2.61763 + 1.90182i) q^{71} +(13.1395 - 5.04378i) q^{72} +(12.8107 - 8.31934i) q^{73} +(-3.16640 - 1.82812i) q^{74} +(-12.0676 + 6.64296i) q^{75} -2.98520i q^{76} +(4.83217 + 4.06234i) q^{77} +(-12.2533 - 1.94074i) q^{78} +(0.754949 - 1.69564i) q^{79} +(2.70436 - 2.79223i) q^{80} +(1.55330 - 0.691572i) q^{81} +(1.30632 - 4.87525i) q^{82} +(4.83083 - 0.765128i) q^{83} +(2.84347 + 5.14104i) q^{84} +(10.2287 - 2.34567i) q^{85} +(4.06014 - 4.50924i) q^{86} +(-0.988053 + 18.8532i) q^{87} +(-0.382885 + 7.30589i) q^{88} +(-2.32462 + 2.58176i) q^{89} +(-7.37057 + 8.45378i) q^{90} +(0.200436 - 10.9013i) q^{91} +(2.69009 - 0.426068i) q^{92} +(-6.68658 + 24.9547i) q^{93} +(-8.16722 + 3.63628i) q^{94} +(3.87736 + 7.31815i) q^{95} +(-4.74306 + 10.6531i) q^{96} +(-3.70443 - 0.586724i) q^{97} +(6.11728 - 4.59187i) q^{98} -10.9526i 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

Fields

Representations

Groups

Database

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