LMFDB - Embedded newform 750.2.m.d.61.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [750,2,Mod(31,750)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(750, base_ring=CyclotomicField(50)) chi = DirichletCharacter(H, H._module([0, 24])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("750.31"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 750 = 2 \cdot 3 \cdot 5^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	750.m (of order $25$, degree $20$, minimal)

Newform invariants

comment:select newform

sage:traces = [140,0,0,0,-20,0,5,0,0,20] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(10)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$5.98878015160$
Analytic rank:	$0$
Dimension:	$140$
Relative dimension:	$7$ over $\Q(\zeta_{25})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{25}]$

Embedding invariants

Embedding label			61.6
Character	$\chi$	$=$	750.61
Dual form			750.2.m.d.541.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.187381 - 0.982287i) q^{2} +(0.968583 - 0.248690i) q^{3} +(-0.929776 - 0.368125i) q^{4} +(1.98800 + 1.02364i) q^{5} +(-0.0627905 - 0.998027i) q^{6} +(1.12925 - 3.47548i) q^{7} +(-0.535827 + 0.844328i) q^{8} +(0.876307 - 0.481754i) q^{9} +(1.37802 - 1.76098i) q^{10} +(0.303692 - 1.59201i) q^{11} +(-0.992115 - 0.125333i) q^{12} +(-0.0409670 + 0.0225218i) q^{13} +(-3.20232 - 1.76049i) q^{14} +(2.18012 + 0.497085i) q^{15} +(0.728969 + 0.684547i) q^{16} +(-2.06734 + 0.818516i) q^{17} +(-0.309017 - 0.951057i) q^{18} +(0.659733 + 0.169391i) q^{19} +(-1.47157 - 1.68359i) q^{20} +(0.229458 - 3.64713i) q^{21} +(-1.50690 - 0.596626i) q^{22} +(0.222543 + 0.472928i) q^{23} +(-0.309017 + 0.951057i) q^{24} +(2.90432 + 4.07000i) q^{25} +(0.0144464 + 0.0444616i) q^{26} +(0.728969 - 0.684547i) q^{27} +(-2.32936 + 2.81571i) q^{28} +(-1.41864 + 1.71484i) q^{29} +(0.896793 - 2.04836i) q^{30} +(5.61641 - 2.22369i) q^{31} +(0.809017 - 0.587785i) q^{32} +(-0.101766 - 1.61752i) q^{33} +(0.416638 + 2.18409i) q^{34} +(5.80260 - 5.75332i) q^{35} +(-0.992115 + 0.125333i) q^{36} +(-5.17108 - 4.85597i) q^{37} +(0.290012 - 0.616306i) q^{38} +(-0.0340790 + 0.0320023i) q^{39} +(-1.92951 + 1.13003i) q^{40} +(1.79087 - 3.80579i) q^{41} +(-3.53953 - 0.908797i) q^{42} +(-1.98699 - 1.44363i) q^{43} +(-0.868423 + 1.36842i) q^{44} +(2.23524 - 0.0607045i) q^{45} +(0.506252 - 0.129983i) q^{46} +(1.41081 + 2.22308i) q^{47} +(0.876307 + 0.481754i) q^{48} +(-5.14064 - 3.73489i) q^{49} +(4.54213 - 2.09023i) q^{50} +(-1.79883 + 1.30693i) q^{51} +(0.0463810 - 0.00585929i) q^{52} +(-0.419376 + 6.66579i) q^{53} +(-0.535827 - 0.844328i) q^{54} +(2.23339 - 2.85405i) q^{55} +(2.32936 + 2.81571i) q^{56} +0.681132 q^{57} +(1.41864 + 1.71484i) q^{58} +(6.14368 + 0.776127i) q^{59} +(-1.84403 - 1.26473i) q^{60} +(0.930153 + 1.97668i) q^{61} +(-1.13190 - 5.93360i) q^{62} +(-0.684754 - 3.58961i) q^{63} +(-0.425779 - 0.904827i) q^{64} +(-0.104497 + 0.00283791i) q^{65} +(-1.60794 - 0.203130i) q^{66} +(-4.64704 - 5.61731i) q^{67} +2.22348 q^{68} +(0.333164 + 0.402726i) q^{69} +(-4.56411 - 6.77789i) q^{70} +(4.85222 + 7.64587i) q^{71} +(-0.0627905 + 0.998027i) q^{72} +(-9.49155 + 1.19906i) q^{73} +(-5.73892 + 4.16957i) q^{74} +(3.82524 + 3.21986i) q^{75} +(-0.551047 - 0.400359i) q^{76} +(-5.19005 - 2.85326i) q^{77} +(0.0250497 + 0.0394720i) q^{78} +(-9.61421 + 2.46851i) q^{79} +(0.748462 + 2.10708i) q^{80} +(0.535827 - 0.844328i) q^{81} +(-3.40281 - 2.47228i) q^{82} +(3.25636 + 0.836091i) q^{83} +(-1.55594 + 3.30654i) q^{84} +(-4.94774 - 0.488997i) q^{85} +(-1.79038 + 1.68128i) q^{86} +(-0.947609 + 2.01377i) q^{87} +(1.18145 + 1.10946i) q^{88} +(2.80212 - 0.353991i) q^{89} +(0.359214 - 2.20703i) q^{90} +(0.0320120 + 0.167813i) q^{91} +(-0.0328189 - 0.521641i) q^{92} +(4.88695 - 3.55057i) q^{93} +(2.44806 - 0.969257i) q^{94} +(1.13816 + 1.01208i) q^{95} +(0.637424 - 0.770513i) q^{96} +(-7.53305 + 9.10590i) q^{97} +(-4.63199 + 4.34973i) q^{98} +(-0.500829 - 1.54139i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 140 q - 20 q^{5} + 5 q^{7} + 20 q^{10} + 5 q^{11} - 10 q^{13} + 20 q^{14} - 5 q^{17} + 35 q^{18} - 5 q^{19} - 5 q^{23} + 35 q^{24} - 40 q^{25} - 10 q^{26} + 25 q^{29} + 5 q^{30} + 30 q^{31} + 35 q^{32}+ \cdots - 10 q^{99}+O(q^{100}) $ 140 * q - 20 * q^5 + 5 * q^7 + 20 * q^10 + 5 * q^11 - 10 * q^13 + 20 * q^14 - 5 * q^17 + 35 * q^18 - 5 * q^19 - 5 * q^23 + 35 * q^24 - 40 * q^25 - 10 * q^26 + 25 * q^29 + 5 * q^30 + 30 * q^31 + 35 * q^32 - 15 * q^34 - 25 * q^37 + 35 * q^38 - 10 * q^39 + 5 * q^40 + 55 * q^41 + 35 * q^43 + 25 * q^44 + 20 * q^46 + 10 * q^47 - 60 * q^49 - 5 * q^51 + 40 * q^52 + 40 * q^55 + 20 * q^57 - 25 * q^58 + 75 * q^59 + 50 * q^61 + 5 * q^62 + 5 * q^63 - 35 * q^65 + 20 * q^66 - 95 * q^67 + 20 * q^68 - 20 * q^69 + 65 * q^70 - 50 * q^71 + 20 * q^73 + 30 * q^74 + 35 * q^75 - 5 * q^76 + 15 * q^77 + 5 * q^78 + 70 * q^79 - 15 * q^82 + 25 * q^83 + 5 * q^84 - 95 * q^85 - 5 * q^86 - 5 * q^88 - 105 * q^89 - 5 * q^90 - 65 * q^91 + 55 * q^92 - 30 * q^93 - 10 * q^94 + 125 * q^95 - 5 * q^97 + 70 * q^98 - 10 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/750\mathbb{Z}\right)^\times$.

$n$	$127$	$251$
$\chi(n)$	$e\left(\frac{14}{25}\right)$	$1$

Coefficient data

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

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

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

$2$	0.187381	−	0.982287i	0.132499	−	0.694582i
$2$	0.187381	−	0.982287i	0.132499	−	0.694582i
$3$	0.968583	−	0.248690i	0.559212	−	0.143581i
$3$	0.968583	−	0.248690i	0.559212	−	0.143581i
$4$	−0.929776	−	0.368125i	−0.464888	−	0.184062i
$5$	1.98800	+	1.02364i	0.889062	+	0.457786i
$5$	1.98800	+	1.02364i	0.889062	+	0.457786i
$6$	−0.0627905	−	0.998027i	−0.0256341	−	0.407443i
$7$	1.12925	−	3.47548i	0.426817	−	1.31361i	−0.474426	−	0.880295i	$-0.657344\pi$
$7$	1.12925	−	3.47548i	0.426817	−	1.31361i	0.901244	−	0.433313i	$-0.142656\pi$
$8$	−0.535827	+	0.844328i	−0.189443	+	0.298515i
$9$	0.876307	−	0.481754i	0.292102	−	0.160585i
$10$	1.37802	−	1.76098i	0.435770	−	0.556871i
$11$	0.303692	−	1.59201i	0.0915666	−	0.480009i	−0.906732	−	0.421707i	$-0.861431\pi$
$11$	0.303692	−	1.59201i	0.0915666	−	0.480009i	0.998299	−	0.0583023i	$-0.0185687\pi$
$12$	−0.992115	−	0.125333i	−0.286399	−	0.0361806i
$13$	−0.0409670	+	0.0225218i	−0.0113622	+	0.00624643i	−0.487425	−	0.873165i	$-0.662064\pi$
$13$	−0.0409670	+	0.0225218i	−0.0113622	+	0.00624643i	0.476062	+	0.879411i	$0.342064\pi$
$14$	−3.20232	−	1.76049i	−0.855856	−	0.470511i
$15$	2.18012	+	0.497085i	0.562904	+	0.128347i
$16$	0.728969	+	0.684547i	0.182242	+	0.171137i
$17$	−2.06734	+	0.818516i	−0.501403	+	0.198519i	−0.605191	−	0.796080i	$-0.706903\pi$
$17$	−2.06734	+	0.818516i	−0.501403	+	0.198519i	0.103789	+	0.994599i	$0.466903\pi$
$18$	−0.309017	−	0.951057i	−0.0728360	−	0.224166i
$19$	0.659733	+	0.169391i	0.151353	+	0.0388609i	0.323606	−	0.946192i	$-0.395105\pi$
$19$	0.659733	+	0.169391i	0.151353	+	0.0388609i	−0.172253	+	0.985053i	$0.555105\pi$
$20$	−1.47157	−	1.68359i	−0.329053	−	0.376462i
$21$	0.229458	−	3.64713i	0.0500718	−	0.795868i
$22$	−1.50690	−	0.596626i	−0.321273	−	0.127201i
$23$	0.222543	+	0.472928i	0.0464034	+	0.0986123i	0.926684	−	0.375840i	$-0.122646\pi$
$23$	0.222543	+	0.472928i	0.0464034	+	0.0986123i	−0.880281	+	0.474453i	$0.842646\pi$
$24$	−0.309017	+	0.951057i	−0.0630778	+	0.194134i
$25$	2.90432	+	4.07000i	0.580863	+	0.814001i
$26$	0.0144464	+	0.0444616i	0.00283318	+	0.00871963i
$27$	0.728969	−	0.684547i	0.140290	−	0.131741i
$28$	−2.32936	+	2.81571i	−0.440208	+	0.532120i
$29$	−1.41864	+	1.71484i	−0.263435	+	0.318439i	−0.885601	−	0.464447i	$-0.846253\pi$
$29$	−1.41864	+	1.71484i	−0.263435	+	0.318439i	0.622166	+	0.782886i	$0.286253\pi$
$30$	0.896793	−	2.04836i	0.163731	−	0.373977i
$31$	5.61641	−	2.22369i	1.00874	−	0.399387i	0.195114	−	0.980781i	$-0.437492\pi$
$31$	5.61641	−	2.22369i	1.00874	−	0.399387i	0.813622	+	0.581394i	$0.197492\pi$
$32$	0.809017	−	0.587785i	0.143015	−	0.103907i
$33$	−0.101766	−	1.61752i	−0.0177151	−	0.281574i
$34$	0.416638	+	2.18409i	0.0714528	+	0.374569i
$35$	5.80260	−	5.75332i	0.980819	−	0.972488i
$36$	−0.992115	+	0.125333i	−0.165352	+	0.0208889i
$37$	−5.17108	−	4.85597i	−0.850121	−	0.798316i	0.131067	−	0.991374i	$-0.458160\pi$
$37$	−5.17108	−	4.85597i	−0.850121	−	0.798316i	−0.981188	+	0.193057i	$0.938160\pi$
$38$	0.290012	−	0.616306i	0.0470461	−	0.0999781i
$39$	−0.0340790	+	0.0320023i	−0.00545701	+	0.00512448i
$40$	−1.92951	+	1.13003i	−0.305083	+	0.178674i
$41$	1.79087	−	3.80579i	0.279687	−	0.594365i	−0.714788	−	0.699341i	$-0.753477\pi$
$41$	1.79087	−	3.80579i	0.279687	−	0.594365i	0.994475	+	0.104976i	$0.0334767\pi$
$42$	−3.53953	−	0.908797i	−0.546161	−	0.140230i
$43$	−1.98699	−	1.44363i	−0.303013	−	0.220151i	0.425880	−	0.904780i	$-0.359965\pi$
$43$	−1.98699	−	1.44363i	−0.303013	−	0.220151i	−0.728892	+	0.684628i	$0.759965\pi$
$44$	−0.868423	+	1.36842i	−0.130920	+	0.206297i
$45$	2.23524	−	0.0607045i	0.333210	−	0.00904929i
$46$	0.506252	−	0.129983i	0.0746427	−	0.0191650i
$47$	1.41081	+	2.22308i	0.205788	+	0.324270i	0.931508	−	0.363720i	$-0.118493\pi$
$47$	1.41081	+	2.22308i	0.205788	+	0.324270i	−0.725721	+	0.687990i	$0.758493\pi$
$48$	0.876307	+	0.481754i	0.126484	+	0.0695352i
$49$	−5.14064	−	3.73489i	−0.734377	−	0.533556i
$50$	4.54213	−	2.09023i	0.642354	−	0.295603i
$51$	−1.79883	+	1.30693i	−0.251887	+	0.183006i
$52$	0.0463810	−	0.00585929i	0.00643189	−	0.000812537i
$53$	−0.419376	+	6.66579i	−0.0576057	+	0.915617i	0.858028	+	0.513603i	$0.171690\pi$
$53$	−0.419376	+	6.66579i	−0.0576057	+	0.915617i	−0.915634	+	0.402014i	$0.868310\pi$
$54$	−0.535827	−	0.844328i	−0.0729168	−	0.114898i
$55$	2.23339	−	2.85405i	0.301150	−	0.384840i
$56$	2.32936	+	2.81571i	0.311274	+	0.376266i
$57$	0.681132			0.0902181
$58$	1.41864	+	1.71484i	0.186277	+	0.225170i
$59$	6.14368	+	0.776127i	0.799839	+	0.101043i	0.514619	−	0.857419i	$-0.327933\pi$
$59$	6.14368	+	0.776127i	0.799839	+	0.101043i	0.285220	+	0.958462i	$0.407933\pi$
$60$	−1.84403	−	1.26473i	−0.238063	−	0.163276i
$61$	0.930153	+	1.97668i	0.119094	+	0.253087i	0.955481	−	0.295051i	$-0.0953367\pi$
$61$	0.930153	+	1.97668i	0.119094	+	0.253087i	−0.836388	+	0.548139i	$0.815337\pi$
$62$	−1.13190	−	5.93360i	−0.143751	−	0.753568i
$63$	−0.684754	−	3.58961i	−0.0862709	−	0.452248i
$64$	−0.425779	−	0.904827i	−0.0532224	−	0.113103i
$65$	−0.104497	+	0.00283791i	−0.0129612	+	0.000352000i
$66$	−1.60794	−	0.203130i	−0.197923	−	0.0250035i
$67$	−4.64704	−	5.61731i	−0.567727	−	0.686264i	0.406029	−	0.913860i	$-0.366913\pi$
$67$	−4.64704	−	5.61731i	−0.567727	−	0.686264i	−0.973756	+	0.227597i	$0.926913\pi$
$68$	2.22348			0.269636
$69$	0.333164	+	0.402726i	0.0401082	+	0.0484825i
$70$	−4.56411	−	6.77789i	−0.545516	−	0.810112i
$71$	4.85222	+	7.64587i	0.575852	+	0.907398i	0.999998	+	0.00180415i	$0.000574278\pi$
$71$	4.85222	+	7.64587i	0.575852	+	0.907398i	−0.424146	+	0.905594i	$0.639426\pi$
$72$	−0.0627905	+	0.998027i	−0.00739993	+	0.117619i
$73$	−9.49155	+	1.19906i	−1.11090	+	0.140340i	−0.659300	−	0.751880i	$-0.729147\pi$
$73$	−9.49155	+	1.19906i	−1.11090	+	0.140340i	−0.451602	+	0.892219i	$0.649147\pi$
$74$	−5.73892	+	4.16957i	−0.667136	+	0.484703i
$75$	3.82524	+	3.21986i	0.441701	+	0.371798i
$76$	−0.551047	−	0.400359i	−0.0632094	−	0.0459244i
$77$	−5.19005	−	2.85326i	−0.591461	−	0.325159i
$78$	0.0250497	+	0.0394720i	0.00283632	+	0.00446933i
$79$	−9.61421	+	2.46851i	−1.08168	+	0.277729i	−0.747150	−	0.664655i	$-0.768578\pi$
$79$	−9.61421	+	2.46851i	−1.08168	+	0.277729i	−0.334533	+	0.942384i	$0.608578\pi$
$80$	0.748462	+	2.10708i	0.0836806	+	0.235579i
$81$	0.535827	−	0.844328i	0.0595363	−	0.0938142i
$82$	−3.40281	−	2.47228i	−0.375777	−	0.273018i
$83$	3.25636	+	0.836091i	0.357432	+	0.0917729i	0.423136	−	0.906066i	$-0.360929\pi$
$83$	3.25636	+	0.836091i	0.357432	+	0.0917729i	−0.0657040	+	0.997839i	$0.520929\pi$
$84$	−1.55594	+	3.30654i	−0.169767	+	0.360773i
$85$	−4.94774	−	0.488997i	−0.536658	−	0.0530392i
$86$	−1.79038	+	1.68128i	−0.193062	+	0.181297i
$87$	−0.947609	+	2.01377i	−0.101594	+	0.215899i
$88$	1.18145	+	1.10946i	0.125943	+	0.118268i
$89$	2.80212	−	0.353991i	0.297025	−	0.0375229i	0.0245913	−	0.999698i	$-0.492172\pi$
$89$	2.80212	−	0.353991i	0.297025	−	0.0375229i	0.272433	+	0.962175i	$0.412172\pi$
$90$	0.359214	−	2.20703i	0.0378644	−	0.232641i
$91$	0.0320120	+	0.167813i	0.00335577	+	0.0175916i
$92$	−0.0328189	−	0.521641i	−0.00342160	−	0.0543848i
$93$	4.88695	−	3.55057i	0.506753	−	0.368177i
$94$	2.44806	−	0.969257i	0.252499	−	0.0999713i
$95$	1.13816	+	1.01208i	0.116772	+	0.103837i
$96$	0.637424	−	0.770513i	0.0650568	−	0.0786402i
$97$	−7.53305	+	9.10590i	−0.764866	+	0.924564i	−0.998863	−	0.0476735i	$-0.984819\pi$
$97$	−7.53305	+	9.10590i	−0.764866	+	0.924564i	0.233997	+	0.972237i	$0.424819\pi$
$98$	−4.63199	+	4.34973i	−0.467902	+	0.439389i
$99$	−0.500829	−	1.54139i	−0.0503352	−	0.154916i
$100$	−1.20210	−	4.85335i	−0.120210	−	0.485335i
$101$	−4.61884	+	14.2153i	−0.459592	+	1.41448i	0.406067	+	0.913843i	$0.366900\pi$
$101$	−4.61884	+	14.2153i	−0.459592	+	1.41448i	−0.865659	+	0.500634i	$0.833100\pi$
$102$	0.946710	+	2.01186i	0.0937383	+	0.199204i
$103$	0.948154	+	0.375401i	0.0934244	+	0.0369893i	0.414372	−	0.910108i	$-0.364001\pi$
$103$	0.948154	+	0.375401i	0.0934244	+	0.0369893i	−0.320947	+	0.947097i	$0.604001\pi$
$104$	0.00293544	−	0.0466574i	0.000287843	−	0.00457514i
$105$	4.18951	−	7.01562i	0.408854	−	0.684654i
$106$	6.46914	+	1.66099i	0.628338	+	0.161330i
$107$	3.16059	+	9.72730i	0.305546	+	0.940373i	0.979473	+	0.201576i	$0.0646062\pi$
$107$	3.16059	+	9.72730i	0.305546	+	0.940373i	−0.673927	+	0.738798i	$0.735394\pi$
$108$	−0.929776	+	0.368125i	−0.0894678	+	0.0354228i
$109$	−9.77390	−	9.17830i	−0.936170	−	0.879122i	0.0566921	−	0.998392i	$-0.481945\pi$
$109$	−9.77390	−	9.17830i	−0.936170	−	0.879122i	−0.992862	+	0.119270i	$0.961945\pi$
$110$	−2.38500	−	2.72862i	−0.227401	−	0.260164i
$111$	−6.21625	−	3.41741i	−0.590021	−	0.324367i
$112$	3.20232	−	1.76049i	0.302591	−	0.166351i
$113$	17.1170	+	2.16238i	1.61023	+	0.203419i	0.878351	−	0.478017i	$-0.158644\pi$
$113$	17.1170	+	2.16238i	1.61023	+	0.203419i	0.731878	+	0.681436i	$0.238644\pi$
$114$	0.127631	−	0.669067i	0.0119538	−	0.0626639i
$115$	−0.0416922	+	1.16799i	−0.00388782	+	0.108915i
$116$	1.95030	−	1.07218i	0.181081	−	0.0995499i
$117$	−0.0250497	+	0.0394720i	−0.00231585	+	0.00364919i
$118$	1.91359	−	5.88942i	0.176160	−	0.542165i
$119$	0.510194	+	8.10930i	0.0467694	+	0.743378i
$120$	−1.58787	+	1.57438i	−0.144952	+	0.143721i
$121$	7.78528	+	3.08241i	0.707752	+	0.280219i
$122$	2.11596	−	0.543285i	0.191570	−	0.0491868i
$123$	0.788144	−	4.13160i	0.0710646	−	0.372534i
$124$	−6.04060			−0.542462
$125$	1.60757	+	11.0642i	0.143785	+	0.989609i
$126$	−3.65434			−0.325554
$127$	0.345040	−	1.80876i	0.0306173	−	0.160502i	−0.963695	−	0.267006i	$-0.913966\pi$
$127$	0.345040	−	1.80876i	0.0306173	−	0.160502i	0.994312	+	0.106504i	$0.0339657\pi$
$128$	−0.968583	+	0.248690i	−0.0856115	+	0.0219813i
$129$	−2.28358	−	0.904132i	−0.201058	−	0.0796044i
$130$	−0.0167931	+	0.103178i	−0.00147285	+	0.00904929i
$131$	0.619731	+	9.85034i	0.0541461	+	0.860628i	0.927566	+	0.373660i	$0.121897\pi$
$131$	0.619731	+	9.85034i	0.0541461	+	0.860628i	−0.873420	+	0.486968i	$0.838103\pi$
$132$	−0.500829	+	1.54139i	−0.0435916	+	0.134161i
$133$	1.33372	−	2.10160i	0.115648	−	0.182232i
$134$	−6.38858	+	3.51215i	−0.551889	+	0.303404i
$135$	2.14992	−	0.614680i	0.185036	−	0.0529032i
$136$	0.416638	−	2.18409i	0.0357264	−	0.187284i
$137$	−19.2925	−	2.43721i	−1.64827	−	0.208225i	−0.754358	−	0.656463i	$-0.772052\pi$
$137$	−19.2925	−	2.43721i	−1.64827	−	0.208225i	−0.893914	+	0.448238i	$0.852052\pi$
$138$	0.458021	−	0.251799i	0.0389894	−	0.0214346i
$139$	3.67454	+	2.02010i	0.311671	+	0.171342i	0.629910	−	0.776668i	$-0.283092\pi$
$139$	3.67454	+	2.02010i	0.311671	+	0.171342i	−0.318240	+	0.948010i	$0.603092\pi$
$140$	−7.51306	+	3.21322i	−0.634970	+	0.271567i
$141$	1.91935	+	1.80239i	0.161638	+	0.151788i
$142$	8.41966	−	3.33358i	0.706562	−	0.279748i
$143$	0.0234136	+	0.0720596i	0.00195794	+	0.00602593i
$144$	0.968583	+	0.248690i	0.0807153	+	0.0207242i
$145$	−4.57565	+	1.95694i	−0.379987	+	0.162515i
$146$	−0.600716	+	9.54811i	−0.0497156	+	0.790208i
$147$	−5.90796	−	2.33913i	−0.487281	−	0.192928i
$148$	3.02035	+	6.41857i	0.248271	+	0.527603i
$149$	4.79879	−	14.7692i	0.393133	−	1.20994i	−0.537274	−	0.843408i	$-0.680546\pi$
$149$	4.79879	−	14.7692i	0.393133	−	1.20994i	0.930406	−	0.366530i	$-0.119454\pi$
$150$	3.87961	−	3.15414i	0.316769	−	0.257535i
$151$	5.89363	+	18.1387i	0.479617	+	1.47611i	0.839629	+	0.543161i	$0.182773\pi$
$151$	5.89363	+	18.1387i	0.479617	+	1.47611i	−0.360012	+	0.932948i	$0.617227\pi$
$152$	−0.496524	+	0.466267i	−0.0402734	+	0.0378192i
$153$	−1.41730	+	1.71322i	−0.114582	+	0.138505i
$154$	−3.77524	+	4.56348i	−0.304217	+	0.367735i
$155$	13.4417	+	1.32848i	1.07966	+	0.106706i
$156$	0.0434667	−	0.0172097i	0.00348012	−	0.00137788i
$157$	13.4945	−	9.80431i	1.07698	−	0.782469i	0.0998233	−	0.995005i	$-0.468172\pi$
$157$	13.4945	−	9.80431i	1.07698	−	0.782469i	0.977153	+	0.212536i	$0.0681723\pi$
$158$	0.623262	+	9.90647i	0.0495841	+	0.788116i
$159$	1.25151	+	6.56067i	0.0992515	+	0.520295i
$160$	2.21001	−	0.340376i	0.174717	−	0.0269091i
$161$	1.89496	−	0.239389i	0.149344	−	0.0188665i
$162$	−0.728969	−	0.684547i	−0.0572732	−	0.0537831i
$163$	6.38756	−	13.5743i	0.500313	−	1.06322i	−0.482035	−	0.876152i	$-0.660102\pi$
$163$	6.38756	−	13.5743i	0.500313	−	1.06322i	0.982347	−	0.187066i	$-0.0598979\pi$
$164$	−3.06611	+	2.87927i	−0.239423	+	0.224833i
$165$	1.45345	−	3.31980i	0.113151	−	0.258446i
$166$	1.43146	−	3.04201i	0.111103	−	0.236106i
$167$	−13.3077	−	3.41683i	−1.02978	−	0.264403i	−0.304249	−	0.952592i	$-0.598406\pi$
$167$	−13.3077	−	3.41683i	−1.02978	−	0.264403i	−0.725531	+	0.688190i	$0.758406\pi$
$168$	2.95642	+	2.14797i	0.228093	+	0.165719i
$169$	−6.96458	+	10.9744i	−0.535737	+	0.844186i
$170$	−1.40745	+	4.76847i	−0.107946	+	0.365725i
$171$	0.659733	−	0.169391i	0.0504510	−	0.0129536i
$172$	1.31602	+	2.07371i	0.100345	+	0.158119i
$173$	8.97264	+	4.93275i	0.682177	+	0.375030i	0.784851	−	0.619685i	$-0.212740\pi$
$173$	8.97264	+	4.93275i	0.682177	+	0.375030i	−0.102673	+	0.994715i	$0.532740\pi$
$174$	1.80054	+	1.30817i	0.136498	+	0.0991719i
$175$	17.4249	−	5.49784i	1.31720	−	0.415597i
$176$	1.31119	−	0.952633i	0.0988345	−	0.0718074i
$177$	6.14368	−	0.776127i	0.461787	−	0.0583373i
$178$	0.177345	−	2.81882i	0.0132926	−	0.211280i
$179$	12.1547	+	19.1527i	0.908482	+	1.43154i	0.902085	+	0.431559i	$0.142036\pi$
$179$	12.1547	+	19.1527i	0.908482	+	1.43154i	0.00639692	+	0.999980i	$0.497964\pi$
$180$	−2.10062	−	0.766407i	−0.156571	−	0.0571246i
$181$	3.29114	+	3.97831i	0.244629	+	0.295705i	0.878509	−	0.477726i	$-0.158539\pi$
$181$	3.29114	+	3.97831i	0.244629	+	0.295705i	−0.633880	+	0.773431i	$0.718539\pi$
$182$	0.170839			0.0126634
$183$	1.39251	+	1.68326i	0.102937	+	0.124430i
$184$	−0.518551	−	0.0655082i	−0.0382281	−	0.00482933i
$185$	−5.30936	−	14.9470i	−0.390352	−	1.09893i
$186$	−2.57196	−	5.46570i	−0.188585	−	0.400764i
$187$	0.675252	+	3.53979i	0.0493793	+	0.258855i
$188$	−0.493368	−	2.58632i	−0.0359825	−	0.188627i
$189$	−1.55594	−	3.30654i	−0.113178	−	0.240516i
$190$	1.20742	−	0.928351i	0.0875955	−	0.0673497i
$191$	−8.77458	−	1.10849i	−0.634906	−	0.0802073i	−0.198709	−	0.980058i	$-0.563675\pi$
$191$	−8.77458	−	1.10849i	−0.634906	−	0.0802073i	−0.436197	+	0.899851i	$0.643675\pi$
$192$	−0.637424	−	0.770513i	−0.0460021	−	0.0556070i
$193$	7.14212			0.514101			0.257050	−	0.966398i	$-0.417249\pi$
$193$	7.14212			0.514101			0.257050	+	0.966398i	$0.417249\pi$
$194$	7.53305	+	9.10590i	0.540842	+	0.653765i
$195$	−0.100508	+	0.0287361i	−0.00719754	+	0.00205783i
$196$	3.40474	+	5.36501i	0.243196	+	0.383215i
$197$	−0.275611	+	4.38072i	−0.0196365	+	0.312113i	0.975932	+	0.218075i	$0.0699777\pi$
$197$	−0.275611	+	4.38072i	−0.0196365	+	0.312113i	−0.995569	+	0.0940385i	$0.970022\pi$
$198$	−1.60794	+	0.203130i	−0.114271	+	0.0144358i
$199$	−17.6124	+	12.7962i	−1.24851	+	0.907095i	−0.998134	−	0.0610539i	$-0.980554\pi$
$199$	−17.6124	+	12.7962i	−1.24851	+	0.907095i	−0.250375	+	0.968149i	$0.580554\pi$
$200$	−4.99263	+	0.271379i	−0.353032	+	0.0191894i
$201$	−5.89802	−	4.28516i	−0.416014	−	0.302252i
$202$	13.0980	+	7.20071i	0.921575	+	0.506640i
$203$	4.35790	+	6.86696i	0.305865	+	0.481966i
$204$	2.15362	−	0.552956i	0.150784	−	0.0387147i
$205$	7.45602	−	5.73272i	0.520751	−	0.400391i
$206$	0.546418	−	0.861017i	0.0380707	−	0.0599899i
$207$	0.422851	+	0.307219i	0.0293902	+	0.0213532i
$208$	−0.0452809	−	0.0116262i	−0.00313967	−	0.000806130i
$209$	0.470027	−	0.998858i	0.0325124	−	0.0690925i
$210$	−6.10631	−	5.42990i	−0.421376	−	0.374699i
$211$	−12.0539	+	11.3193i	−0.829822	+	0.779255i	−0.977757	−	0.209742i	$-0.932738\pi$
$211$	−12.0539	+	11.3193i	−0.829822	+	0.779255i	0.147934	+	0.988997i	$0.452738\pi$
$212$	2.84377	−	6.04331i	0.195311	−	0.415056i
$213$	6.60123	+	6.19896i	0.452309	+	0.424746i
$214$	10.1472	−	1.28189i	0.693651	−	0.0876285i
$215$	−2.47238	−	4.90390i	−0.168615	−	0.334443i
$216$	0.187381	+	0.982287i	0.0127497	+	0.0668362i
$217$	−1.38606	−	22.0308i	−0.0940920	−	1.49555i
$218$	−10.8472	+	7.88093i	−0.734663	+	0.533764i
$219$	−8.89516	+	3.52184i	−0.601080	+	0.237984i
$220$	−3.12720	+	1.83146i	−0.210836	+	0.123477i
$221$	0.0662582	−	0.0800924i	0.00445701	−	0.00538760i
$222$	−4.52169	+	5.46579i	−0.303476	+	0.366840i
$223$	2.50929	−	2.35638i	0.168035	−	0.157795i	−0.595968	−	0.803008i	$-0.703231\pi$
$223$	2.50929	−	2.35638i	0.168035	−	0.157795i	0.764003	+	0.645213i	$0.223231\pi$
$224$	−1.12925	−	3.47548i	−0.0754513	−	0.232215i
$225$	4.50581	+	2.16741i	0.300388	+	0.144494i
$226$	5.33147	−	16.4086i	0.354644	−	1.09148i
$227$	−7.98281	−	16.9643i	−0.529838	−	1.12596i	−0.973272	−	0.229655i	$-0.926240\pi$
$227$	−7.98281	−	16.9643i	−0.529838	−	1.12596i	0.443434	−	0.896307i	$-0.353760\pi$
$228$	−0.633300	−	0.250741i	−0.0419413	−	0.0166057i
$229$	0.575927	−	9.15410i	0.0380583	−	0.604920i	−0.932062	−	0.362298i	$-0.881992\pi$
$229$	0.575927	−	9.15410i	0.0380583	−	0.604920i	0.970121	−	0.242622i	$-0.0780076\pi$
$230$	1.13949	+	0.259813i	0.0751355	+	0.0171315i
$231$	−5.73657	−	1.47290i	−0.377439	−	0.0969098i
$232$	−0.687744	−	2.11666i	−0.0451526	−	0.138966i
$233$	−13.0110	+	5.15140i	−0.852376	+	0.337479i	−0.753362	−	0.657607i	$-0.771569\pi$
$233$	−13.0110	+	5.15140i	−0.852376	+	0.337479i	−0.0990143	+	0.995086i	$0.531569\pi$
$234$	0.0340790	+	0.0320023i	0.00222782	+	0.00209206i
$235$	0.529059	+	5.86366i	0.0345120	+	0.382503i
$236$	−5.42653	−	2.98326i	−0.353237	−	0.194194i
$237$	−8.69827	+	4.78191i	−0.565013	+	0.310619i
$238$	8.06126	+	1.01837i	0.522534	+	0.0660114i
$239$	−1.28190	+	6.71995i	−0.0829191	+	0.434677i	0.916482	+	0.400076i	$0.131016\pi$
$239$	−1.28190	+	6.71995i	−0.0829191	+	0.434677i	−0.999401	+	0.0346015i	$0.988984\pi$
$240$	1.24896	+	1.85475i	0.0806199	+	0.119724i
$241$	−11.9750	+	6.58333i	−0.771380	+	0.424070i	−0.818273	−	0.574830i	$-0.805068\pi$
$241$	−11.9750	+	6.58333i	−0.771380	+	0.424070i	0.0468928	+	0.998900i	$0.485068\pi$
$242$	4.48663	−	7.06979i	0.288411	−	0.454463i
$243$	0.309017	−	0.951057i	0.0198234	−	0.0610103i
$244$	−0.137172	−	2.18028i	−0.00878151	−	0.139578i
$245$	−6.39642	−	12.6871i	−0.408652	−	0.810552i
$246$	−3.91073	−	1.54837i	−0.249339	−	0.0987204i
$247$	−0.0308423	+	0.00791895i	−0.00196245	+	0.000503871i
$248$	−1.13190	+	5.93360i	−0.0718754	+	0.376784i
$249$	3.36198			0.213057
$250$	11.1694	+	0.494123i	0.706416	+	0.0312511i
$251$	12.5979			0.795173			0.397587	−	0.917565i	$-0.369848\pi$
$251$	12.5979			0.795173			0.397587	+	0.917565i	$0.369848\pi$
$252$	−0.684754	+	3.58961i	−0.0431355	+	0.226124i
$253$	0.820491	−	0.210666i	0.0515838	−	0.0132445i
$254$	−1.71207	−	0.677856i	−0.107425	−	0.0425325i
$255$	−4.91390	+	0.756818i	−0.307721	+	0.0473938i
$256$	0.0627905	+	0.998027i	0.00392441	+	0.0623767i
$257$	0.325228	−	1.00095i	0.0202871	−	0.0624374i	−0.940400	−	0.340069i	$-0.889550\pi$
$257$	0.325228	−	1.00095i	0.0202871	−	0.0624374i	0.960688	+	0.277632i	$0.0895495\pi$
$258$	−1.31602	+	2.07371i	−0.0819317	+	0.129104i
$259$	−22.7163	+	12.4884i	−1.41152	+	0.775990i
$260$	0.0982035	+	0.0358292i	0.00609032	+	0.00222204i
$261$	−0.417034	+	2.18617i	−0.0258137	+	0.135320i
$262$	9.79199	+	1.23702i	0.604951	+	0.0764231i
$263$	7.68357	−	4.22408i	0.473789	−	0.260468i	−0.226922	−	0.973913i	$-0.572866\pi$
$263$	7.68357	−	4.22408i	0.473789	−	0.260468i	0.700711	+	0.713445i	$0.252866\pi$
$264$	1.42024	+	0.780786i	0.0874100	+	0.0480541i
$265$	−7.65710	+	12.8223i	−0.470372	+	0.787669i
$266$	−1.81446	−	1.70390i	−0.111252	−	0.104473i
$267$	2.62606	−	1.03973i	0.160712	−	0.0636304i
$268$	2.25284	+	6.93353i	0.137614	+	0.423533i
$269$	29.1226	+	7.47741i	1.77564	+	0.455906i	0.987237	−	0.159258i	$-0.0509102\pi$
$269$	29.1226	+	7.47741i	1.77564	+	0.455906i	0.788399	+	0.615164i	$0.210910\pi$
$270$	−0.200937	−	2.22702i	−0.0122286	−	0.135532i
$271$	−0.469907	+	7.46897i	−0.0285448	+	0.453707i	0.957630	+	0.288001i	$0.0929905\pi$
$271$	−0.469907	+	7.46897i	−0.0285448	+	0.453707i	−0.986175	+	0.165707i	$0.947009\pi$
$272$	−2.06734	−	0.818516i	−0.125351	−	0.0496298i
$273$	0.0727397	+	0.154580i	0.00440241	+	0.00935559i
$274$	−6.00910	+	18.4941i	−0.363023	+	1.11727i
$275$	7.36150	−	3.38767i	0.443915	−	0.204284i
$276$	−0.161515	−	0.497091i	−0.00972204	−	0.0299214i
$277$	−4.13222	+	3.88041i	−0.248281	+	0.233151i	−0.798688	−	0.601745i	$-0.794472\pi$
$277$	−4.13222	+	3.88041i	−0.248281	+	0.233151i	0.550407	+	0.834896i	$0.314472\pi$
$278$	2.67286	−	3.23093i	0.160307	−	0.193778i
$279$	3.85042	−	4.65436i	0.230519	−	0.278649i
$280$	1.74850	+	7.98208i	0.104493	+	0.477021i
$281$	−16.5476	+	6.55165i	−0.987146	+	0.390839i	−0.805546	−	0.592534i	$-0.798128\pi$
$281$	−16.5476	+	6.55165i	−0.987146	+	0.390839i	−0.181600	+	0.983372i	$0.558128\pi$
$282$	2.13011	−	1.54762i	0.126846	−	0.0921591i
$283$	−1.42843	−	22.7042i	−0.0849112	−	1.34963i	−0.777769	−	0.628551i	$-0.783649\pi$
$283$	−1.42843	−	22.7042i	−0.0849112	−	1.34963i	0.692858	−	0.721075i	$-0.256351\pi$
$284$	−1.69684	−	8.89517i	−0.100689	−	0.527831i
$285$	1.35409	+	0.697235i	0.0802095	+	0.0413006i
$286$	0.0751705	−	0.00949624i	0.00444493	−	0.000561525i
$287$	−11.2046	−	10.5218i	−0.661387	−	0.621084i
$288$	0.425779	−	0.904827i	0.0250893	−	0.0533174i
$289$	−8.78856	+	8.25300i	−0.516974	+	0.485471i
$290$	1.06488	+	4.86130i	0.0625320	+	0.285465i
$291$	−5.03184	+	10.6932i	−0.294972	+	0.626847i
$292$	9.26643	+	2.37921i	0.542277	+	0.139233i
$293$	−19.7353	−	14.3386i	−1.15295	−	0.837667i	−0.164080	−	0.986447i	$-0.552465\pi$
$293$	−19.7353	−	14.3386i	−1.15295	−	0.837667i	−0.988870	+	0.148780i	$0.952465\pi$
$294$	−3.40474	+	5.36501i	−0.198568	+	0.312894i
$295$	11.4192	+	7.83186i	0.664850	+	0.455989i
$296$	6.87083	−	1.76413i	0.399359	−	0.102538i
$297$	−0.868423	−	1.36842i	−0.0503910	−	0.0794036i
$298$	−13.6084	−	7.48126i	−0.788311	−	0.433378i
$299$	−0.0197681	−	0.0143624i	−0.00114322	−	0.000830599i
$300$	−2.37131	−	4.40192i	−0.136908	−	0.254145i
$301$	−7.26112	+	5.27551i	−0.418524	+	0.304075i
$302$	18.9218	−	2.39038i	1.08883	−	0.137551i
$303$	−0.938522	+	14.9174i	−0.0539167	+	0.856981i
$304$	0.364969	+	0.575099i	0.0209324	+	0.0329842i
$305$	−0.174259	+	4.88178i	−0.00997805	+	0.279530i
$306$	1.41730	+	1.71322i	0.0810215	+	0.0979381i
$307$	13.4570			0.768029			0.384015	−	0.923327i	$-0.374541\pi$
$307$	13.4570			0.768029			0.384015	+	0.923327i	$0.374541\pi$
$308$	3.77524	+	4.56348i	0.215114	+	0.260028i
$309$	1.01172	+	0.127811i	0.0575550	+	0.00727089i
$310$	3.82367	−	12.9547i	0.217170	−	0.735776i
$311$	2.79383	+	5.93719i	0.158423	+	0.336667i	0.968243	−	0.250013i	$-0.0804348\pi$
$311$	2.79383	+	5.93719i	0.158423	+	0.336667i	−0.809819	+	0.586680i	$0.800435\pi$
$312$	−0.00876001	−	0.0459216i	−0.000495938	−	0.00259980i
$313$	−0.221252	−	1.15984i	−0.0125059	−	0.0655582i	0.975487	−	0.220056i	$-0.0706240\pi$
$313$	−0.221252	−	1.15984i	−0.0125059	−	0.0655582i	−0.987993	+	0.154498i	$0.950624\pi$
$314$	−7.10204	−	15.0926i	−0.400791	−	0.851725i
$315$	2.31318	−	7.83710i	0.130333	−	0.441570i
$316$	9.84778	+	1.24406i	0.553981	+	0.0699841i
$317$	−14.6459	−	17.7039i	−0.822598	−	0.994350i	−0.999948	−	0.0102023i	$-0.996752\pi$
$317$	−14.6459	−	17.7039i	−0.822598	−	0.994350i	0.177350	−	0.984148i	$-0.443248\pi$
$318$	6.67897			0.374538
$319$	2.29922	+	2.77928i	0.128731	+	0.155610i
$320$	0.0797674	−	2.23464i	0.00445914	−	0.124920i
$321$	5.48038	+	8.63569i	0.305885	+	0.481997i
$322$	0.119931	−	1.90625i	0.00668350	−	0.106231i
$323$	−1.50254	+	0.189815i	−0.0836035	+	0.0105616i
$324$	−0.809017	+	0.587785i	−0.0449454	+	0.0326547i
$325$	−0.210645	−	0.101326i	−0.0116845	−	0.00562053i
$326$	−12.1369	−	8.81799i	−0.672202	−	0.488383i
$327$	−11.7494	−	6.45928i	−0.649743	−	0.357199i
$328$	2.25374	+	3.55133i	0.124442	+	0.196089i
$329$	9.31944	−	2.39283i	0.513797	−	0.131921i
$330$	−2.98865	−	2.04977i	−0.164520	−	0.112836i
$331$	8.68189	−	13.6805i	0.477200	−	0.751947i	−0.517398	−	0.855745i	$-0.673099\pi$
$331$	8.68189	−	13.6805i	0.477200	−	0.751947i	0.994598	+	0.103798i	$0.0330995\pi$
$332$	−2.71990	−	1.97612i	−0.149274	−	0.108454i
$333$	−6.87083	−	1.76413i	−0.376519	−	0.0966737i
$334$	−5.84993	+	12.4317i	−0.320094	+	0.680234i
$335$	−3.48823	−	15.9241i	−0.190582	−	0.870029i
$336$	2.66390	−	2.50157i	0.145327	−	0.136472i
$337$	−11.1462	+	23.6868i	−0.607171	+	1.29030i	0.330837	+	0.943688i	$0.392669\pi$
$337$	−11.1462	+	23.6868i	−0.607171	+	1.29030i	−0.938007	+	0.346615i	$0.887331\pi$
$338$	9.47500	+	8.89762i	0.515372	+	0.483967i
$339$	17.1170	−	2.16238i	0.929666	−	0.117444i
$340$	4.42028	+	2.27604i	0.239723	+	0.123436i
$341$	−1.83448	−	9.61669i	−0.0993427	−	0.520773i
$342$	−0.0427686	−	0.679788i	−0.00231266	−	0.0367587i
$343$	1.90933	−	1.38721i	0.103094	−	0.0749022i
$344$	2.28358	−	0.904132i	0.123122	−	0.0487475i
$345$	0.250084	+	1.14166i	0.0134641	+	0.0614650i
$346$	6.52668	−	7.88941i	0.350877	−	0.424137i
$347$	−6.60665	+	7.98607i	−0.354664	+	0.428715i	−0.917427	−	0.397903i	$-0.869738\pi$
$347$	−6.60665	+	7.98607i	−0.354664	+	0.428715i	0.562764	+	0.826618i	$0.309738\pi$
$348$	1.62238	−	1.52352i	0.0869689	−	0.0816692i
$349$	−9.35983	−	28.8066i	−0.501020	−	1.54198i	−0.807360	−	0.590060i	$-0.799104\pi$
$349$	−9.35983	−	28.8066i	−0.501020	−	1.54198i	0.306339	−	0.951922i	$-0.400896\pi$
$350$	−2.13535	−	18.1465i	−0.114139	−	0.969970i
$351$	−0.0144464	+	0.0444616i	−0.000771094	+	0.00237318i
$352$	−0.690068	−	1.46647i	−0.0367807	−	0.0781630i
$353$	25.1664	+	9.96410i	1.33947	+	0.530335i	0.925084	−	0.379764i	$-0.123995\pi$
$353$	25.1664	+	9.96410i	1.33947	+	0.530335i	0.414391	+	0.910099i	$0.363995\pi$
$354$	0.388831	−	6.18029i	0.0206661	−	0.328479i
$355$	1.81960	+	20.1669i	0.0965742	+	1.07035i
$356$	−2.73566	−	0.702399i	−0.144990	−	0.0372271i
$357$	2.51087	+	7.72765i	0.132889	+	0.408991i
$358$	21.0910	−	8.35051i	1.11469	−	0.441338i
$359$	−11.7522	−	11.0360i	−0.620256	−	0.582459i	0.309380	−	0.950938i	$-0.399878\pi$
$359$	−11.7522	−	11.0360i	−0.620256	−	0.582459i	−0.929636	+	0.368480i	$0.879878\pi$
$360$	−1.14645	+	1.91981i	−0.0604232	+	0.101183i
$361$	−16.2433	−	8.92981i	−0.854909	−	0.469990i
$362$	4.52454	−	2.48739i	0.237805	−	0.130734i
$363$	8.30725	+	1.04945i	0.436018	+	0.0550818i
$364$	0.0320120	−	0.167813i	0.00167789	−	0.00879579i
$365$	−20.0967	−	7.33221i	−1.05191	−	0.383785i
$366$	1.91437	−	1.05243i	0.100066	−	0.0550116i
$367$	15.9755	−	25.1734i	0.833916	−	1.31404i	−0.113337	−	0.993557i	$-0.536154\pi$
$367$	15.9755	−	25.1734i	0.833916	−	1.31404i	0.947254	−	0.320485i	$-0.103846\pi$
$368$	−0.161515	+	0.497091i	−0.00841953	+	0.0259127i
$369$	−0.264103	−	4.19780i	−0.0137487	−	0.218529i
$370$	−15.6771	+	2.41452i	−0.815016	+	0.125525i
$371$	22.6932	+	8.98489i	1.17817	+	0.466472i
$372$	−5.85082	+	1.50224i	−0.303351	+	0.0778873i
$373$	5.43955	−	28.5151i	0.281649	−	1.47646i	−0.507177	−	0.861842i	$-0.669311\pi$
$373$	5.43955	−	28.5151i	0.281649	−	1.47646i	0.788827	−	0.614616i	$-0.210689\pi$
$374$	3.60362			0.186339
$375$	4.30861	+	10.3168i	0.222496	+	0.532756i
$376$	−2.63296			−0.135785
$377$	0.0194962	−	0.102203i	0.00100410	−	0.00526370i
$378$	−3.53953	+	0.908797i	−0.182054	+	0.0467435i
$379$	11.3659	+	4.50009i	0.583828	+	0.231154i	0.641425	−	0.767186i	$-0.278344\pi$
$379$	11.3659	+	4.50009i	0.583828	+	0.231154i	−0.0575965	+	0.998340i	$0.518344\pi$
$380$	−0.685660	−	1.35999i	−0.0351736	−	0.0697660i
$381$	−0.115621	−	1.83774i	−0.00592344	−	0.0941504i
$382$	−2.73305	+	8.41145i	−0.139835	+	0.430367i
$383$	1.58985	−	2.50520i	0.0812376	−	0.128010i	−0.801280	−	0.598290i	$-0.795847\pi$
$383$	1.58985	−	2.50520i	0.0812376	−	0.128010i	0.882517	+	0.470280i	$0.155847\pi$
$384$	−0.876307	+	0.481754i	−0.0447188	+	0.0245844i
$385$	−7.39713	−	10.9850i	−0.376993	−	0.559849i
$386$	1.33830	−	7.01561i	0.0681176	−	0.357085i
$387$	−2.43668	−	0.307825i	−0.123864	−	0.0156476i
$388$	10.3562	−	5.69335i	0.525754	−	0.289036i
$389$	−14.2000	−	7.80654i	−0.719971	−	0.395807i	0.0792419	−	0.996855i	$-0.474750\pi$
$389$	−14.2000	−	7.80654i	−0.719971	−	0.395807i	−0.799213	+	0.601048i	$0.794750\pi$
$390$	0.00939373	+	0.104113i	0.000475670	+	0.00527194i
$391$	−0.847171	−	0.795546i	−0.0428433	−	0.0402325i
$392$	5.90796	−	2.33913i	0.298397	−	0.118144i
$393$	3.04994	+	9.38675i	0.153849	+	0.473499i
$394$	4.25148	+	1.09159i	0.214186	+	0.0549937i
$395$	−21.6399	−	4.93409i	−1.08882	−	0.248261i
$396$	−0.101766	+	1.61752i	−0.00511392	+	0.0812834i
$397$	−35.3121	−	13.9811i	−1.77227	−	0.701690i	−0.997594	−	0.0693263i	$-0.977915\pi$
$397$	−35.3121	−	13.9811i	−1.77227	−	0.701690i	−0.774672	−	0.632363i	$-0.782085\pi$
$398$	9.26926	+	19.6982i	0.464626	+	0.987381i
$399$	0.769169	−	2.36726i	0.0385066	−	0.118511i
$400$	−0.668954	+	4.95505i	−0.0334477	+	0.247752i
$401$	−3.64755	−	11.2260i	−0.182150	−	0.560600i	0.817738	−	0.575591i	$-0.195228\pi$
$401$	−3.64755	−	11.2260i	−0.182150	−	0.560600i	−0.999888	+	0.0149909i	$0.995228\pi$
$402$	−5.31444	+	4.99059i	−0.265060	+	0.248908i
$403$	−0.180006	+	0.217590i	−0.00896673	+	0.0108389i
$404$	9.52750	−	11.5168i	0.474011	−	0.572981i
$405$	1.92951	−	1.13003i	0.0958783	−	0.0561518i
$406$	7.56191	−	2.99397i	0.375292	−	0.148588i
$407$	−9.30116	+	6.75769i	−0.461042	+	0.334966i
$408$	−0.139613	−	2.21909i	−0.00691188	−	0.109861i
$409$	−6.53168	−	34.2403i	−0.322971	−	1.69307i	−0.659747	−	0.751487i	$-0.729337\pi$
$409$	−6.53168	−	34.2403i	−0.322971	−	1.69307i	0.336777	−	0.941585i	$-0.390663\pi$
$410$	−4.23406	−	8.39816i	−0.209105	−	0.414756i
$411$	−19.2925	+	2.43721i	−0.951630	+	0.120219i
$412$	−0.743377	−	0.698078i	−0.0366236	−	0.0343918i
$413$	9.63517	−	20.4758i	0.474116	−	1.00755i
$414$	0.381012	−	0.357794i	0.0187257	−	0.0175846i
$415$	5.61780	+	4.99550i	0.275767	+	0.245219i
$416$	−0.0199050	+	0.0423004i	−0.000975925	+	0.00207395i
$417$	4.06148	+	1.04281i	0.198891	+	0.0510666i
$418$	−0.893091	−	0.648869i	−0.0436825	−	0.0317372i
$419$	7.71100	−	12.1506i	0.376707	−	0.593596i	−0.602090	−	0.798428i	$-0.705665\pi$
$419$	7.71100	−	12.1506i	0.376707	−	0.593596i	0.978797	+	0.204833i	$0.0656651\pi$
$420$	−6.47793	+	4.98069i	−0.316091	+	0.243033i
$421$	−11.1136	+	2.85348i	−0.541642	+	0.139070i	−0.509592	−	0.860416i	$-0.670204\pi$
$421$	−11.1136	+	2.85348i	−0.541642	+	0.139070i	−0.0320499	+	0.999486i	$0.510204\pi$
$422$	8.86017	+	13.9614i	0.431306	+	0.679630i
$423$	2.30728	+	1.26844i	0.112184	+	0.0616736i
$424$	−5.40340	−	3.92580i	−0.262412	−	0.190654i
$425$	−9.33556	−	6.03684i	−0.452841	−	0.292830i
$426$	7.32611	−	5.32273i	0.354951	−	0.257887i
$427$	7.92028	−	1.00056i	0.383289	−	0.0484207i
$428$	0.642214	−	10.2077i	0.0310426	−	0.493408i
$429$	0.0405985	+	0.0639730i	0.00196011	+	0.00308865i
$430$	−5.28032	+	1.50968i	−0.254640	+	0.0728034i
$431$	−4.98541	−	6.02632i	−0.240139	−	0.290278i	0.636651	−	0.771152i	$-0.280319\pi$
$431$	−4.98541	−	6.02632i	−0.240139	−	0.290278i	−0.876789	+	0.480874i	$0.840319\pi$
$432$	1.00000			0.0481125
$433$	−20.0943	−	24.2898i	−0.965670	−	1.16729i	−0.985872	−	0.167499i	$-0.946431\pi$
$433$	−20.0943	−	24.2898i	−0.965670	−	1.16729i	0.0202022	−	0.999796i	$-0.493569\pi$
$434$	−21.9003	−	2.76665i	−1.05125	−	0.132804i
$435$	−3.94523	+	3.03337i	−0.189159	+	0.145439i
$436$	5.70878	+	12.1318i	0.273401	+	0.581007i
$437$	0.0667094	+	0.349703i	0.00319114	+	0.0167286i
$438$	1.79268	+	9.39753i	0.0856574	+	0.449032i
$439$	−3.14805	−	6.68995i	−0.150248	−	0.319294i	0.815508	−	0.578746i	$-0.196458\pi$
$439$	−3.14805	−	6.68995i	−0.150248	−	0.319294i	−0.965756	+	0.259452i	$0.916458\pi$
$440$	1.21304	+	3.41499i	0.0578296	+	0.162803i
$441$	−6.30407	−	0.796389i	−0.300194	−	0.0379233i
$442$	−0.0662582	−	0.0800924i	−0.00315158	−	0.00380961i
$443$	−34.4465			−1.63660			−0.818302	−	0.574789i	$-0.805084\pi$
$443$	−34.4465			−1.63660			−0.818302	+	0.574789i	$0.805084\pi$
$444$	4.52169	+	5.46579i	0.214590	+	0.259395i
$445$	5.93299	+	2.16464i	0.281251	+	0.102614i
$446$	−1.84445	−	2.90639i	−0.0873372	−	0.137621i
$447$	0.975088	−	15.4986i	0.0461201	−	0.733058i
$448$	−3.62552	+	0.458010i	−0.171290	+	0.0216389i
$449$	20.8201	−	15.1267i	0.982560	−	0.713872i	0.0242808	−	0.999705i	$-0.492270\pi$
$449$	20.8201	−	15.1267i	0.982560	−	0.713872i	0.958279	+	0.285833i	$0.0922704\pi$
$450$	2.97332	−	4.01987i	0.140164	−	0.189499i
$451$	−5.51498	−	4.00687i	−0.259690	−	0.188676i
$452$	−15.1189	−	8.31170i	−0.711135	−	0.390950i
$453$	10.2194	+	16.1032i	0.480149	+	0.756593i
$454$	−18.1597	+	4.66261i	−0.852276	+	0.218827i
$455$	−0.108140	+	0.366382i	−0.00506969	+	0.0171762i
$456$	−0.364969	+	0.575099i	−0.0170912	+	0.0269315i
$457$	19.3051	+	14.0260i	0.903053	+	0.656106i	0.939248	−	0.343238i	$-0.111524\pi$
$457$	19.3051	+	14.0260i	0.903053	+	0.656106i	−0.0361953	+	0.999345i	$0.511524\pi$
$458$	−8.88404	−	2.28103i	−0.415124	−	0.106586i
$459$	−0.946710	+	2.01186i	−0.0441886	+	0.0939057i
$460$	0.468729	−	1.07062i	0.0218546	−	0.0499179i
$461$	−17.6935	+	16.6153i	−0.824068	+	0.773852i	−0.976740	−	0.214425i	$-0.931212\pi$
$461$	−17.6935	+	16.6153i	−0.824068	+	0.773852i	0.152672	+	0.988277i	$0.451212\pi$
$462$	−2.52174	+	5.35897i	−0.117322	+	0.249322i
$463$	−2.79518	−	2.62485i	−0.129903	−	0.121987i	0.616873	−	0.787063i	$-0.288399\pi$
$463$	−2.79518	−	2.62485i	−0.129903	−	0.121987i	−0.746776	+	0.665076i	$0.768399\pi$
$464$	−2.20804	+	0.278940i	−0.102506	+	0.0129495i
$465$	13.3498	−	2.05608i	0.619081	−	0.0953482i
$466$	2.62215	+	13.7458i	0.121469	+	0.636760i
$467$	1.58743	+	25.2314i	0.0734574	+	1.16757i	0.846205	+	0.532858i	$0.178882\pi$
$467$	1.58743	+	25.2314i	0.0734574	+	1.16757i	−0.772748	+	0.634713i	$0.781118\pi$
$468$	0.0378213	−	0.0274788i	0.00174829	−	0.00127021i
$469$	−24.7705	+	9.80735i	−1.14380	+	0.452861i
$470$	5.85893	+	0.579053i	0.270252	+	0.0267097i
$471$	10.6323	−	12.8522i	0.489910	−	0.592200i
$472$	−3.94725	+	4.77141i	−0.181687	+	0.219622i
$473$	−2.90170	+	2.72488i	−0.133420	+	0.125290i
$474$	3.06732	+	9.44024i	0.140887	+	0.433604i
$475$	1.22665	+	3.17708i	0.0562827	+	0.145774i
$476$	2.51087	−	7.72765i	0.115085	−	0.354196i
$477$	2.84377	+	6.04331i	0.130207	+	0.276704i
$478$	6.36071	+	2.51839i	0.290932	+	0.115188i
$479$	2.73756	−	43.5123i	0.125082	−	1.98813i	−0.0263185	−	0.999654i	$-0.508378\pi$
$479$	2.73756	−	43.5123i	0.125082	−	1.98813i	0.151401	−	0.988472i	$-0.451622\pi$
$480$	2.05593	−	0.879290i	0.0938400	−	0.0401339i
$481$	0.321209	+	0.0824725i	0.0146459	+	0.00376042i
$482$	4.22282	+	12.9965i	0.192344	+	0.591975i
$483$	1.77589	−	0.703126i	0.0808059	−	0.0319933i
$484$	−6.10386	−	5.73190i	−0.277448	−	0.260541i
$485$	−24.2969	+	10.3914i	−1.10327	+	0.471850i
$486$	−0.876307	−	0.481754i	−0.0397501	−	0.0218528i
$487$	19.6685	−	10.8128i	0.891264	−	0.489976i	0.0308217	−	0.999525i	$-0.490188\pi$
$487$	19.6685	−	10.8128i	0.891264	−	0.489976i	0.860442	+	0.509549i	$0.170188\pi$
$488$	−2.16736	−	0.273802i	−0.0981120	−	0.0123944i
$489$	2.81110	−	14.7363i	0.127123	−	0.666400i
$490$	−13.6610	+	3.90578i	−0.617141	+	0.176445i
$491$	30.2472	−	16.6285i	1.36504	−	0.750435i	0.380362	−	0.924838i	$-0.375799\pi$
$491$	30.2472	−	16.6285i	1.36504	−	0.750435i	0.984674	+	0.174403i	$0.0557995\pi$
$492$	−2.25374	+	3.55133i	−0.101606	+	0.160106i
$493$	1.52918	−	4.70634i	0.0688709	−	0.211963i
$494$	0.00199942	+	0.0317798i	8.99581e−5	+	0.00142984i
$495$	0.582184	−	3.57696i	0.0261672	−	0.160773i
$496$	5.61641	+	2.22369i	0.252184	+	0.0998467i
$497$	32.0525	−	8.22967i	1.43775	−	0.369151i
$498$	0.629973	−	3.30243i	0.0282297	−	0.147986i
$499$	25.9954			1.16371			0.581856	−	0.813292i	$-0.302327\pi$
$499$	25.9954			1.16371			0.581856	+	0.813292i	$0.302327\pi$
$500$	2.57831	−	10.8790i	0.115306	−	0.486523i
$501$	−13.7393			−0.613828
$502$	2.36061	−	12.3748i	0.105359	−	0.552313i
$503$	16.4791	−	4.23110i	0.734765	−	0.188656i	0.137276	−	0.990533i	$-0.456165\pi$
$503$	16.4791	−	4.23110i	0.734765	−	0.188656i	0.597489	+	0.801877i	$0.296165\pi$
$504$	3.39772	+	1.34525i	0.151346	+	0.0599222i
$505$	−23.7337	+	23.5321i	−1.05613	+	1.04716i
$506$	−0.0531901	−	0.845432i	−0.00236459	−	0.0375840i
$507$	−4.01655	+	12.3617i	−0.178381	+	0.549000i
$508$	−0.986659	+	1.55473i	−0.0437759	+	0.0689798i
$509$	2.15817	−	1.18646i	0.0956590	−	0.0525890i	−0.433206	−	0.901295i	$-0.642618\pi$
$509$	2.15817	−	1.18646i	0.0956590	−	0.0525890i	0.528865	+	0.848706i	$0.322618\pi$
$510$	−0.177361	+	4.96868i	−0.00785368	+	0.220017i
$511$	−6.55104	+	34.3418i	−0.289801	+	1.51919i
$512$	0.992115	+	0.125333i	0.0438457	+	0.00553900i
$513$	0.596880	−	0.328138i	0.0263529	−	0.0144876i
$514$	−0.922276	−	0.507026i	−0.0406799	−	0.0223639i
$515$	1.50066	+	1.71687i	0.0661269	+	0.0756542i
$516$	1.79038	+	1.68128i	0.0788172	+	0.0740143i
$517$	3.96762	−	1.57089i	0.174496	−	0.0690877i
$518$	8.01057	+	24.6540i	0.351964	+	1.08323i
$519$	9.91747	+	2.54637i	0.435329	+	0.111773i
$520$	0.0535961	−	0.0897503i	0.00235034	−	0.00393581i
$521$	−0.678410	+	10.7830i	−0.0297217	+	0.472413i	0.954811	+	0.297213i	$0.0960572\pi$
$521$	−0.678410	+	10.7830i	−0.0297217	+	0.472413i	−0.984533	+	0.175200i	$0.943943\pi$
$522$	2.06930	+	0.819293i	0.0905708	+	0.0358595i
$523$	−12.9379	−	27.4945i	−0.565737	−	1.20225i	−0.959152	−	0.282891i	$-0.908706\pi$
$523$	−12.9379	−	27.4945i	−0.565737	−	1.20225i	0.393415	−	0.919361i	$-0.371294\pi$
$524$	3.04994	−	9.38675i	0.133237	−	0.410062i
$525$	15.5102	−	9.65852i	0.676922	−	0.421532i
$526$	−2.70950	−	8.33899i	−0.118140	−	0.363597i
$527$	−9.79087	+	9.19424i	−0.426497	+	0.400507i
$528$	1.03308	−	1.24878i	0.0449592	−	0.0543463i
$529$	14.4866	−	17.5113i	0.629853	−	0.761361i
$530$	11.1604	+	9.92413i	0.484777	+	0.431077i
$531$	5.75765	−	2.27961i	0.249861	−	0.0989268i
$532$	−2.01371	+	1.46305i	−0.0873055	+	0.0634311i
$533$	0.0123467	+	0.196246i	0.000534796	+	0.00850035i
$534$	−0.529239	−	2.77437i	−0.0229024	−	0.120059i
$535$	−3.67400	+	22.5732i	−0.158841	+	0.975925i
$536$	7.23286	−	0.913723i	0.312412	−	0.0394668i
$537$	16.5359	+	15.5282i	0.713576	+	0.670092i
$538$	12.8020	−	27.2056i	0.551933	−	1.17292i
$539$	−7.50715	+	7.04968i	−0.323356	+	0.303651i
$540$	−2.22523	−	0.219925i	−0.0957585	−	0.00946405i
$541$	7.68490	−	16.3313i	0.330400	−	0.702135i	−0.668745	−	0.743492i	$-0.733168\pi$
$541$	7.68490	−	16.3313i	0.330400	−	0.702135i	0.999144	+	0.0413569i	$0.0131681\pi$
$542$	7.24862	+	1.86113i	0.311355	+	0.0799423i
$543$	4.17711	+	3.03485i	0.179257	+	0.130238i
$544$	−1.19140	+	1.87734i	−0.0510808	+	0.0804904i
$545$	−10.0353	−	28.2515i	−0.429863	−	1.21016i
$546$	0.165472	−	0.0424859i	0.00708154	−	0.00181823i
$547$	10.2182	+	16.1014i	0.436900	+	0.688444i	0.989424	−	0.145053i	$-0.0463352\pi$
$547$	10.2182	+	16.1014i	0.436900	+	0.688444i	−0.552524	+	0.833497i	$0.686335\pi$
$548$	17.0405	+	9.36812i	0.727936	+	0.400186i
$549$	1.76737	+	1.28407i	0.0754295	+	0.0548028i
$550$	−1.94826	−	7.86590i	−0.0830740	−	0.335403i
$551$	−1.22640	+	0.891034i	−0.0522466	+	0.0379593i
$552$	−0.518551	+	0.0655082i	−0.0220710	+	0.00278822i
$553$	−2.27761	+	36.2016i	−0.0968538	+	1.53945i
$554$	3.03738	+	4.78614i	0.129046	+	0.203344i
$555$	−8.85973	−	13.1570i	−0.376075	−	0.558485i
$556$	−2.67286	−	3.23093i	−0.113354	−	0.137022i
$557$	2.98430			0.126449			0.0632245	−	0.997999i	$-0.479862\pi$
$557$	2.98430			0.126449			0.0632245	+	0.997999i	$0.479862\pi$
$558$	−3.85042	−	4.65436i	−0.163001	−	0.197035i
$559$	0.113914	+	0.0143907i	0.00481805	+	0.000608662i
$560$	8.16833	−	0.221835i	0.345175	−	0.00937422i
$561$	1.53435	+	3.26066i	0.0647803	+	0.137665i
$562$	3.33490	+	17.4821i	0.140674	+	0.737439i
$563$	−3.74242	−	19.6185i	−0.157724	−	0.826820i	−0.969918	−	0.243432i	$-0.921727\pi$
$563$	−3.74242	−	19.6185i	−0.157724	−	0.826820i	0.812194	−	0.583388i	$-0.198273\pi$
$564$	−1.12106	−	2.38237i	−0.0472051	−	0.100316i
$565$	31.8151	+	21.8204i	1.33847	+	0.917993i
$566$	−22.5697	−	2.85122i	−0.948676	−	0.119846i
$567$	−2.32936	−	2.81571i	−0.0978240	−	0.118249i
$568$	−9.05557			−0.379963
$569$	29.7779	+	35.9953i	1.24836	+	1.50900i	0.780443	+	0.625227i	$0.214994\pi$
$569$	29.7779	+	35.9953i	1.24836	+	1.50900i	0.467912	+	0.883775i	$0.345006\pi$
$570$	0.938616	−	1.19946i	0.0393143	−	0.0502398i
$571$	22.3098	+	35.1547i	0.933638	+	1.47118i	0.881305	+	0.472548i	$0.156666\pi$
$571$	22.3098	+	35.1547i	0.933638	+	1.47118i	0.0523326	+	0.998630i	$0.483334\pi$
$572$	0.00475751	−	0.0756184i	0.000198921	−	0.00316177i
$573$	−8.77458	+	1.10849i	−0.366563	+	0.0463077i
$574$	−12.4350	+	9.03456i	−0.519027	+	0.377095i
$575$	−1.27848	+	2.27928i	−0.0533165	+	0.0950527i
$576$	−0.809017	−	0.587785i	−0.0337090	−	0.0244911i
$577$	18.4434	+	10.1394i	0.767810	+	0.422107i	0.816967	−	0.576684i	$-0.195654\pi$
$577$	18.4434	+	10.1394i	0.767810	+	0.422107i	−0.0491574	+	0.998791i	$0.515654\pi$
$578$	6.46001	+	10.1793i	0.268701	+	0.423405i
$579$	6.91773	−	1.77617i	0.287491	−	0.0738152i
$580$	4.97473	−	0.135103i	0.206564	−	0.00560985i
$581$	6.58307	−	10.3733i	0.273112	−	0.430355i
$582$	9.56093	+	6.94642i	0.396313	+	0.287939i
$583$	10.4846	+	2.69200i	0.434229	+	0.111491i
$584$	4.07343	−	8.65647i	0.168560	−	0.358207i
$585$	−0.0902042	+	0.0528286i	−0.00372948	+	0.00218420i
$586$	−17.7826	+	16.6990i	−0.734593	+	0.689829i
$587$	−4.38580	+	9.32030i	−0.181021	+	0.384690i	−0.974657	−	0.223703i	$-0.928185\pi$
$587$	−4.38580	+	9.32030i	−0.181021	+	0.384690i	0.793636	+	0.608393i	$0.208185\pi$
$588$	4.63199	+	4.34973i	0.191020	+	0.179380i
$589$	4.08200	−	0.515676i	0.168196	−	0.0212481i
$590$	9.83288	−	9.74937i	0.404813	−	0.401375i
$591$	0.822488	+	4.31163i	0.0338326	+	0.177357i
$592$	−0.445417	−	7.07970i	−0.0183065	−	0.290974i
$593$	−19.8519	+	14.4233i	−0.815221	+	0.592293i	−0.915340	−	0.402683i	$-0.868078\pi$
$593$	−19.8519	+	14.4233i	−0.815221	+	0.592293i	0.100119	+	0.994975i	$0.468078\pi$
$594$	−1.50690	+	0.596626i	−0.0618290	+	0.0244798i
$595$	−7.28674	+	16.6436i	−0.298727	+	0.682320i
$596$	−9.89870	+	11.9655i	−0.405467	+	0.490125i
$597$	−13.8768	+	16.7742i	−0.567939	+	0.686521i
$598$	−0.0178122	+	0.0167267i	−0.000728394	+	0.000684007i
$599$	−6.51850	−	20.0619i	−0.266339	−	0.819706i	−0.991382	−	0.131003i	$-0.958180\pi$
$599$	−6.51850	−	20.0619i	−0.266339	−	0.819706i	0.725043	−	0.688703i	$-0.241820\pi$
$600$	−4.76829	+	1.50447i	−0.194665	+	0.0614197i
$601$	−0.263225	+	0.810123i	−0.0107372	+	0.0330456i	−0.956282	−	0.292448i	$-0.905530\pi$
$601$	−0.263225	+	0.810123i	−0.0107372	+	0.0330456i	0.945544	+	0.325493i	$0.105530\pi$
$602$	3.82147	+	8.12103i	0.155751	+	0.330989i
$603$	−6.77840	−	2.68376i	−0.276038	−	0.109291i
$604$	1.19755	−	19.0345i	0.0487277	−	0.774505i
$605$	12.3219	+	14.0972i	0.500956	+	0.573131i
$606$	14.4773	+	3.71714i	0.588100	+	0.150998i
$607$	7.56811	+	23.2923i	0.307180	+	0.945403i	0.978855	+	0.204557i	$0.0655754\pi$
$607$	7.56811	+	23.2923i	0.307180	+	0.945403i	−0.671674	+	0.740846i	$0.734425\pi$
$608$	0.633300	−	0.250741i	0.0256837	−	0.0101689i
$609$	5.92874	+	5.56745i	0.240244	+	0.225605i
$610$	4.76266	+	1.08593i	0.192834	+	0.0439679i
$611$	−0.107865	−	0.0592991i	−0.00436373	−	0.00239898i
$612$	1.94845	−	1.07117i	0.0787613	−	0.0432994i
$613$	−26.4126	−	3.33669i	−1.06680	−	0.134768i	−0.427720	−	0.903911i	$-0.640683\pi$
$613$	−26.4126	−	3.33669i	−1.06680	−	0.134768i	−0.639076	+	0.769143i	$0.720683\pi$
$614$	2.52158	−	13.2186i	0.101763	−	0.533459i
$615$	5.79611	−	7.40685i	0.233722	−	0.298673i
$616$	5.19005	−	2.85326i	0.209113	−	0.114961i
$617$	−7.00337	+	11.0355i	−0.281945	+	0.444274i	−0.955555	−	0.294813i	$-0.904743\pi$
$617$	−7.00337	+	11.0355i	−0.281945	+	0.444274i	0.673610	+	0.739087i	$0.264743\pi$
$618$	0.315125	−	0.969855i	0.0126762	−	0.0390133i
$619$	1.18354	+	18.8118i	0.0475703	+	0.756108i	0.947437	+	0.319943i	$0.103664\pi$
$619$	1.18354	+	18.8118i	0.0475703	+	0.756108i	−0.899867	+	0.436165i	$0.856336\pi$
$620$	−12.0087	−	6.18340i	−0.482282	−	0.248332i
$621$	0.485969	+	0.192409i	0.0195012	+	0.00772109i
$622$	6.35553	−	1.63182i	0.254834	−	0.0654302i
$623$	1.93402	−	10.1385i	0.0774848	−	0.406189i
$624$	−0.0467497			−0.00187148
$625$	−8.12988	+	23.6412i	−0.325195	+	0.945647i
$626$	−1.18076			−0.0471925
$627$	0.206854	−	1.08437i	0.00826096	−	0.0433055i
$628$	−16.1561	+	4.14817i	−0.644697	+	0.165530i
$629$	14.6651	+	5.80630i	0.584734	+	0.231513i
$630$	−7.26483	−	3.74073i	−0.289438	−	0.149034i
$631$	−0.246858	−	3.92370i	−0.00982727	−	0.156200i	−0.999880	−	0.0155021i	$-0.995065\pi$
$631$	−0.246858	−	3.92370i	−0.00982727	−	0.156200i	0.990053	−	0.140698i	$-0.0449347\pi$
$632$	3.06732	−	9.44024i	0.122011	−	0.375512i
$633$	−8.86017	+	13.9614i	−0.352160	+	0.554915i
$634$	−20.1347	+	11.0691i	−0.799651	+	0.439612i
$635$	2.53746	−	3.24263i	0.100696	−	0.128680i
$636$	1.25151	−	6.56067i	0.0496258	−	0.260147i
$637$	0.294713	+	0.0372309i	0.0116770	+	0.00147514i
$638$	3.16088	−	1.73771i	0.125140	−	0.0687965i
$639$	7.93546	+	4.36255i	0.313922	+	0.172580i
$640$	−2.18012	−	0.497085i	−0.0861767	−	0.0196490i
$641$	2.35194	+	2.20861i	0.0928959	+	0.0872350i	0.729604	−	0.683870i	$-0.239704\pi$
$641$	2.35194	+	2.20861i	0.0928959	+	0.0872350i	−0.636708	+	0.771105i	$0.719704\pi$
$642$	9.50965	−	3.76514i	0.375316	−	0.148598i
$643$	7.84811	+	24.1540i	0.309499	+	0.952540i	0.977960	+	0.208793i	$0.0669535\pi$
$643$	7.84811	+	24.1540i	0.309499	+	0.952540i	−0.668461	+	0.743747i	$0.733047\pi$
$644$	−1.85001	−	0.475003i	−0.0729008	−	0.0187177i
$645$	−3.61425	−	4.13498i	−0.142311	−	0.162815i
$646$	−0.0950950	+	1.51149i	−0.00374146	+	0.0594688i
$647$	−8.01338	−	3.17272i	−0.315038	−	0.124733i	0.205284	−	0.978702i	$-0.434188\pi$
$647$	−8.01338	−	3.17272i	−0.315038	−	0.124733i	−0.520322	+	0.853970i	$0.674188\pi$
$648$	0.425779	+	0.904827i	0.0167262	+	0.0355450i
$649$	3.10139	−	9.54509i	0.121740	−	0.374677i
$650$	−0.139002	+	0.187928i	−0.00545210	+	0.00737113i
$651$	−6.82136	−	20.9940i	−0.267350	−	0.822819i
$652$	−10.9360	+	10.2696i	−0.428288	+	0.402189i
$653$	7.98311	−	9.64992i	0.312403	−	0.377630i	−0.590819	−	0.806804i	$-0.701195\pi$
$653$	7.98311	−	9.64992i	0.312403	−	0.377630i	0.903222	+	0.429174i	$0.141195\pi$
$654$	−8.54648	+	10.3309i	−0.334194	+	0.403971i
$655$	−8.85118	+	20.2169i	−0.345844	+	0.789939i
$656$	3.91073	−	1.54837i	0.152688	−	0.0604536i
$657$	−7.73986	+	5.62334i	−0.301961	+	0.219387i
$658$	−0.604153	−	9.60274i	−0.0235523	−	0.374354i
$659$	−0.207846	−	1.08957i	−0.00809653	−	0.0424435i	0.978010	−	0.208559i	$-0.0668774\pi$
$659$	−0.207846	−	1.08957i	−0.00809653	−	0.0424435i	−0.986106	+	0.166116i	$0.946877\pi$
$660$	−2.57348	+	2.55163i	−0.100173	+	0.0993219i
$661$	−32.4954	+	4.10512i	−1.26392	+	0.159671i	−0.728579	−	0.684962i	$-0.759819\pi$
$661$	−32.4954	+	4.10512i	−1.26392	+	0.159671i	−0.535346	+	0.844633i	$0.679819\pi$
$662$	−11.8113	−	11.0916i	−0.459060	−	0.431086i
$663$	0.0442584	−	0.0940538i	0.00171885	−	0.00365275i
$664$	−2.45078	+	2.30144i	−0.0951087	+	0.0893130i
$665$	4.80273	−	2.81275i	0.186242	−	0.109074i
$666$	−3.02035	+	6.41857i	−0.117036	+	0.248714i
$667$	−1.12671	−	0.289289i	−0.0436263	−	0.0112013i
$668$	11.1154	+	8.07578i	0.430066	+	0.312461i
$669$	1.84445	−	2.90639i	0.0713105	−	0.112367i
$670$	−16.2957	+	0.442557i	−0.629558	+	0.0170975i
$671$	3.42937	−	0.880512i	0.132389	−	0.0339918i
$672$	−1.95809	−	3.08546i	−0.0755350	−	0.119024i
$673$	0.530783	+	0.291801i	0.0204602	+	0.0112481i	0.491951	−	0.870623i	$-0.336284\pi$
$673$	0.530783	+	0.291801i	0.0204602	+	0.0112481i	−0.471491	+	0.881871i	$0.656284\pi$
$674$	21.1787	+	15.3872i	0.815772	+	0.592693i
$675$	4.90327	+	0.978764i	0.188727	+	0.0376726i
$676$	10.5155	−	7.63992i	0.404440	−	0.293843i
$677$	2.91935	−	0.368800i	0.112200	−	0.0141741i	−0.0690329	−	0.997614i	$-0.521991\pi$
$677$	2.91935	−	0.368800i	0.112200	−	0.0141741i	0.181233	+	0.983440i	$0.441991\pi$
$678$	1.08333	−	17.2190i	0.0416049	−	0.661290i
$679$	23.1407	+	36.4638i	0.888057	+	1.39935i
$680$	3.06400	−	3.91550i	0.117499	−	0.150152i
$681$	−11.9509	−	14.4461i	−0.457958	−	0.553577i
$682$	−9.79010			−0.374882
$683$	−27.2735	−	32.9679i	−1.04359	−	1.26148i	−0.964351	−	0.264628i	$-0.914751\pi$
$683$	−27.2735	−	32.9679i	−1.04359	−	1.26148i	−0.0792391	−	0.996856i	$-0.525249\pi$
$684$	−0.675761	−	0.0853684i	−0.0258384	−	0.00326414i
$685$	−35.8588	−	24.5938i	−1.37009	−	0.939682i
$686$	−1.00486	−	2.13544i	−0.0383659	−	0.0815317i
$687$	−1.71870	−	9.00973i	−0.0655724	−	0.343743i
$688$	−0.460218	−	2.41255i	−0.0175456	−	0.0919775i
$689$	−0.132945	−	0.282523i	−0.00506481	−	0.0107633i
$690$	1.16830	−	0.0317285i	0.0444764	−	0.00120789i
$691$	49.9165	+	6.30592i	1.89891	+	0.239888i	0.985813	−	0.167849i	$-0.0536821\pi$
$691$	49.9165	+	6.30592i	1.89891	+	0.239888i	0.913099	+	0.407737i	$0.133682\pi$
$692$	−6.52668	−	7.88941i	−0.248107	−	0.299910i
$693$	−5.92264			−0.224983
$694$	6.60665	+	7.98607i	0.250785	+	0.303147i
$695$	5.23715	+	7.77737i	0.198656	+	0.295013i
$696$	−1.19253	−	1.87913i	−0.0452027	−	0.0712281i
$697$	−0.587227	+	9.33371i	−0.0222428	+	0.353539i
$698$	−30.0502	+	3.79623i	−1.13742	+	0.143689i
$699$	−11.3211	+	8.22525i	−0.428203	+	0.311108i
$700$	−18.2252	−	1.30278i	−0.688847	−	0.0492406i
$701$	−15.7242	−	11.4243i	−0.593894	−	0.431489i	0.249812	−	0.968294i	$-0.419631\pi$
$701$	−15.7242	−	11.4243i	−0.593894	−	0.431489i	−0.843706	+	0.536805i	$0.819631\pi$
$702$	0.0409670	+	0.0225218i	0.00154620	+	0.000850031i
$703$	−2.58898	−	4.07957i	−0.0976451	−	0.153864i
$704$	−1.56980	+	0.403056i	−0.0591640	+	0.0151907i
$705$	1.97067	+	5.54787i	0.0742197	+	0.208945i
$706$	14.5033	−	22.8536i	0.545840	−	0.860106i
$707$	44.1893	+	32.1054i	1.66191	+	1.20745i
$708$	−5.99796	−	1.54001i	−0.225417	−	0.0578773i
$709$	−2.21306	+	4.70298i	−0.0831131	+	0.176624i	−0.942064	−	0.335434i	$-0.891117\pi$
$709$	−2.21306	+	4.70298i	−0.0831131	+	0.176624i	0.858951	+	0.512059i	$0.171117\pi$
$710$	20.1507	+	1.99154i	0.756242	+	0.0747412i
$711$	−7.23578	+	6.79485i	−0.271363	+	0.254827i
$712$	−1.20257	+	2.55559i	−0.0450682	+	0.0957748i
$713$	2.30154	+	2.16129i	0.0861933	+	0.0809409i
$714$	8.06126	−	1.01837i	0.301685	−	0.0381117i
$715$	−0.0272169	+	0.167222i	−0.00101785	+	0.00625374i
$716$	−4.25054	−	22.2821i	−0.158850	−	0.832723i
$717$	0.429558	+	6.82762i	0.0160421	+	0.254982i
$718$	−13.0427	+	9.47606i	−0.486748	+	0.353643i
$719$	−31.7024	+	12.5519i	−1.18230	+	0.468106i	−0.875289	−	0.483600i	$-0.839329\pi$
$719$	−31.7024	+	12.5519i	−1.18230	+	0.468106i	−0.307011	+	0.951706i	$0.599329\pi$
$720$	1.67098	+	1.48588i	0.0622737	+	0.0553754i
$721$	2.37540	−	2.87137i	0.0884646	−	0.106935i
$722$	−11.8153	+	14.2823i	−0.439721	+	0.531531i
$723$	−9.96161	+	9.35457i	−0.370476	+	0.347900i
$724$	−1.59551	−	4.91049i	−0.0592968	−	0.182497i
$725$	−11.0996	−	0.793430i	−0.412229	−	0.0294673i
$726$	2.58749	−	7.96346i	0.0960306	−	0.295552i
$727$	−7.06531	−	15.0146i	−0.262038	−	0.556859i	0.729904	−	0.683549i	$-0.239565\pi$
$727$	−7.06531	−	15.0146i	−0.262038	−	0.556859i	−0.991942	+	0.126690i	$0.959565\pi$
$728$	−0.158842	−	0.0628900i	−0.00588708	−	0.00233086i
$729$	0.0627905	−	0.998027i	0.00232557	−	0.0369640i
$730$	−10.9681	+	18.3668i	−0.405946	+	0.679785i
$731$	5.28940	+	1.35809i	0.195636	+	0.0502307i
$732$	−0.675075	−	2.07767i	−0.0249515	−	0.0767928i
$733$	−15.0695	+	5.96643i	−0.556604	+	0.220375i	−0.629549	−	0.776961i	$-0.716760\pi$
$733$	−15.0695	+	5.96643i	−0.556604	+	0.220375i	0.0729449	+	0.997336i	$0.476760\pi$
$734$	−21.7340	−	20.4096i	−0.802217	−	0.753332i
$735$	−9.35063	−	10.6978i	−0.344903	−	0.394595i
$736$	0.458021	+	0.251799i	0.0168829	+	0.00928145i
$737$	−10.3541	+	5.69220i	−0.381397	+	0.209675i
$738$	−4.17293	−	0.527164i	−0.153608	−	0.0194052i
$739$	2.14787	−	11.2595i	0.0790106	−	0.414188i	−0.920703	−	0.390264i	$-0.872384\pi$
$739$	2.14787	−	11.2595i	0.0790106	−	0.414188i	0.999714	−	0.0239244i	$-0.00761610\pi$
$740$	−0.565846	+	15.8519i	−0.0208009	+	0.582727i
$741$	−0.0279040	+	0.0153403i	−0.00102508	+	0.000563541i
$742$	13.0780	−	20.6077i	0.480110	−	0.756532i
$743$	−5.16031	+	15.8818i	−0.189313	+	0.582647i	−0.999996	−	0.00283911i	$-0.999096\pi$
$743$	−5.16031	+	15.8818i	−0.189313	+	0.582647i	0.810683	+	0.585486i	$0.199096\pi$
$744$	0.379292	+	6.02868i	0.0139055	+	0.221022i
$745$	24.6584	−	24.4489i	0.903412	−	0.895739i
$746$	−26.9908	−	10.6864i	−0.988203	−	0.391257i
$747$	3.25636	−	0.836091i	0.119144	−	0.0305910i
$748$	0.675252	−	3.53979i	0.0246897	−	0.129428i
$749$	37.3761			1.36569
$750$	10.9414	−	2.29912i	0.399523	−	0.0839520i
$751$	40.2303			1.46803			0.734013	−	0.679136i	$-0.237645\pi$
$751$	40.2303			1.46803			0.734013	+	0.679136i	$0.237645\pi$
$752$	−0.493368	+	2.58632i	−0.0179913	+	0.0943135i
$753$	12.2021	−	3.13297i	0.444670	−	0.114172i
$754$	−0.0967390	−	0.0383017i	−0.00352303	−	0.00139487i
$755$	−6.85099	+	42.0928i	−0.249333	+	1.53191i
$756$	0.229458	+	3.64713i	0.00834530	+	0.132645i
$757$	−0.394994	+	1.21567i	−0.0143563	+	0.0441842i	−0.957978	−	0.286842i	$-0.907395\pi$
$757$	−0.394994	+	1.21567i	−0.0143563	+	0.0441842i	0.943622	+	0.331026i	$0.107395\pi$
$758$	6.55014	−	10.3214i	0.237912	−	0.374889i
$759$	0.742323	−	0.408095i	0.0269446	−	0.0148129i
$760$	−1.46438	+	0.418678i	−0.0531187	+	0.0151870i
$761$	4.00143	−	20.9762i	0.145052	−	0.760388i	−0.833201	−	0.552970i	$-0.813494\pi$
$761$	4.00143	−	20.9762i	0.145052	−	0.760388i	0.978253	−	0.207417i	$-0.0665057\pi$
$762$	−1.82686	−	0.230786i	−0.0661800	−	0.00836048i
$763$	−42.9362	+	23.6044i	−1.55440	+	0.854536i
$764$	7.75034	+	4.26078i	0.280397	+	0.154150i
$765$	−4.57131	+	1.95508i	−0.165276	+	0.0706861i
$766$	−2.16292	−	2.03112i	−0.0781495	−	0.0733873i
$767$	−0.269168	+	0.106571i	−0.00971909	+	0.00384806i
$768$	0.309017	+	0.951057i	0.0111507	+	0.0343183i
$769$	9.95633	+	2.55635i	0.359034	+	0.0921843i	0.423898	−	0.905710i	$-0.360661\pi$
$769$	9.95633	+	2.55635i	0.359034	+	0.0921843i	−0.0648641	+	0.997894i	$0.520661\pi$
$770$	−12.1765	+	5.20772i	−0.438812	+	0.187673i
$771$	0.0660844	−	1.05038i	0.00237997	−	0.0378286i
$772$	−6.64057	−	2.62919i	−0.238999	−	0.0946266i
$773$	−16.2357	−	34.5027i	−0.583958	−	1.24097i	−0.950544	−	0.310590i	$-0.899473\pi$
$773$	−16.2357	−	34.5027i	−0.583958	−	1.24097i	0.366586	−	0.930384i	$-0.380527\pi$
$774$	−0.758961	+	2.33584i	−0.0272803	+	0.0839601i
$775$	25.3623	+	16.4005i	0.911039	+	0.589123i
$776$	−3.65195	−	11.2396i	−0.131097	−	0.403476i
$777$	−18.8969	+	17.7453i	−0.677922	+	0.636611i
$778$	−10.3291	+	12.4857i	−0.370316	+	0.447635i
$779$	1.82616	−	2.20745i	0.0654290	−	0.0790901i
$780$	0.104029	+	0.0102814i	0.00372482	+	0.000368133i
$781$	13.6459	−	5.40278i	0.488288	−	0.193327i
$782$	−0.940199	+	0.683094i	−0.0336214	+	0.0244274i
$783$	0.139746	+	2.22120i	0.00499411	+	0.0793791i
$784$	−1.19065	−	6.24163i	−0.0425234	−	0.222915i
$785$	36.8632	−	5.67750i	1.31570	−	0.202639i
$786$	9.79199	−	1.23702i	0.349269	−	0.0441229i
$787$	−10.5049	−	9.86479i	−0.374460	−	0.351642i	0.474353	−	0.880335i	$-0.342682\pi$
$787$	−10.5049	−	9.86479i	−0.374460	−	0.351642i	−0.848813	+	0.528693i	$0.822682\pi$
$788$	1.86891	−	3.97163i	0.0665770	−	0.141483i
$789$	6.39169	−	6.00220i	0.227550	−	0.213684i
$790$	−8.90162	+	20.3321i	−0.316705	+	0.723383i
$791$	26.8447	−	57.0478i	0.954486	−	2.02839i
$792$	1.56980	+	0.403056i	0.0557804	+	0.0143220i
$793$	−0.0826240	−	0.0600298i	−0.00293406	−	0.00213172i
$794$	−20.3503	+	32.0669i	−0.722204	+	1.13801i
$795$	−4.22775	+	14.3237i	−0.149943	+	0.508010i
$796$	21.0862	−	5.41401i	0.747379	−	0.191894i
$797$	21.6802	+	34.1625i	0.767950	+	1.21010i	0.972878	+	0.231319i	$0.0743041\pi$
$797$	21.6802	+	34.1625i	0.767950	+	1.21010i	−0.204927	+	0.978777i	$0.565696\pi$
$798$	−2.18120	−	1.19913i	−0.0772137	−	0.0424486i
$799$	−4.73625	−	3.44109i	−0.167556	−	0.121737i
$800$	4.74193	+	1.58559i	0.167653	+	0.0560590i
$801$	2.28498	−	1.66014i	0.0807359	−	0.0586581i
$802$	−11.7107	+	1.47940i	−0.413518	+	0.0522394i
$803$	−0.973591	+	15.4748i	−0.0343573	+	0.546093i
$804$	3.90636	+	6.15545i	0.137767	+	0.217086i
$805$	4.01224	+	1.46385i	0.141413	+	0.0515940i
$806$	0.180006	+	0.217590i	0.00634044	+	0.00766427i
$807$	30.0672			1.05842
$808$	−9.52750	−	11.5168i	−0.335176	−	0.405158i
$809$	18.9108	+	2.38899i	0.664869	+	0.0839925i	0.450522	−	0.892765i	$-0.351238\pi$
$809$	18.9108	+	2.38899i	0.664869	+	0.0839925i	0.214347	+	0.976758i	$0.431238\pi$
$810$	−0.748462	−	2.10708i	−0.0262983	−	0.0740354i
$811$	−14.7237	−	31.2895i	−0.517020	−	1.09872i	−0.977477	−	0.211042i	$-0.932314\pi$
$811$	−14.7237	−	31.2895i	−0.517020	−	1.09872i	0.460457	−	0.887682i	$-0.347686\pi$
$812$	−1.52398	−	7.98899i	−0.0534812	−	0.280358i
$813$	1.40231	+	7.35118i	0.0491812	+	0.257817i
$814$	4.89513	+	10.4027i	0.171574	+	0.364614i
$815$	26.5937	−	20.4471i	0.931536	−	0.716231i
$816$	−2.20594	−	0.278675i	−0.0772235	−	0.00975559i
$817$	−1.06634	−	1.28899i	−0.0373066	−	0.0450959i
$818$	−34.8577			−1.21877
$819$	0.108897	+	0.131634i	0.00380517	+	0.00459965i
$820$	−9.04279	+	2.58540i	−0.315788	+	0.0902862i
$821$	8.88589	+	14.0019i	0.310120	+	0.488670i	0.963261	−	0.268565i	$-0.0865495\pi$
$821$	8.88589	+	14.0019i	0.310120	+	0.488670i	−0.653142	+	0.757236i	$0.726549\pi$
$822$	−1.22102	+	19.4075i	−0.0425878	+	0.676914i
$823$	15.2415	−	1.92545i	0.531286	−	0.0671170i	0.144886	−	0.989448i	$-0.453719\pi$
$823$	15.2415	−	1.92545i	0.531286	−	0.0671170i	0.386400	+	0.922331i	$0.373719\pi$
$824$	−0.825008	+	0.599403i	−0.0287405	+	0.0208812i
$825$	6.28775	−	5.11197i	0.218911	−	0.177976i
$826$	−18.3077	−	13.3013i	−0.637005	−	0.462811i
$827$	−45.5429	−	25.0374i	−1.58368	−	0.870636i	−0.998201	−	0.0599488i	$-0.980906\pi$
$827$	−45.5429	−	25.0374i	−1.58368	−	0.870636i	−0.585480	−	0.810687i	$-0.699094\pi$
$828$	−0.280062	−	0.441307i	−0.00973282	−	0.0153365i
$829$	45.0930	−	11.5779i	1.56614	−	0.402117i	0.636709	−	0.771104i	$-0.280295\pi$
$829$	45.0930	−	11.5779i	1.56614	−	0.402117i	0.929434	+	0.368987i	$0.120295\pi$
$830$	5.95968	−	4.58223i	0.206864	−	0.159051i
$831$	−3.03738	+	4.78614i	−0.105365	+	0.166029i
$832$	0.0378213	+	0.0274788i	0.00131122	+	0.000952655i
$833$	13.6845	+	3.51358i	0.474140	+	0.121738i
$834$	1.78538	−	3.79413i	0.0618228	−	0.131380i
$835$	−22.9581	−	20.4150i	−0.794499	−	0.706490i
$836$	−0.804724	+	0.755686i	−0.0278320	+	0.0261360i
$837$	2.57196	−	5.46570i	0.0889000	−	0.188922i
$838$	−10.4905	−	9.85122i	−0.362388	−	0.340305i
$839$	−28.0278	+	3.54073i	−0.967627	+	0.122240i	−0.593234	−	0.805030i	$-0.702149\pi$
$839$	−28.0278	+	3.54073i	−0.967627	+	0.122240i	−0.374393	+	0.927270i	$0.622149\pi$
$840$	3.67863	+	7.29648i	0.126925	+	0.251752i
$841$	4.50591	+	23.6208i	0.155376	+	0.814511i
$842$	0.720461	+	11.4514i	0.0248287	+	0.394641i
$843$	−14.3984	+	10.4610i	−0.495906	+	0.360297i
$844$	15.3743	−	6.08713i	0.529206	−	0.209528i
$845$	−25.0795	+	14.6880i	−0.862760	+	0.505281i
$846$	1.67831	−	2.02873i	0.0577016	−	0.0697492i
$847$	19.5044	−	23.5768i	0.670179	−	0.810107i
$848$	−4.86876	+	4.57207i	−0.167194	+	0.157006i
$849$	−7.02986	−	21.6357i	−0.241264	−	0.742535i
$850$	−7.67922	+	8.03902i	−0.263395	+	0.275736i
$851$	1.14574	−	3.52621i	0.0392753	−	0.120877i
$852$	−3.85567	−	8.19372i	−0.132093	−	0.280712i
$853$	−10.9265	−	4.32612i	−0.374117	−	0.148124i	0.173539	−	0.984827i	$-0.444480\pi$
$853$	−10.9265	−	4.32612i	−0.374117	−	0.148124i	−0.547656	+	0.836703i	$0.684480\pi$
$854$	0.501271	−	7.96747i	0.0171531	−	0.272641i
$855$	1.48495	+	0.338581i	0.0507841	+	0.0115792i
$856$	−9.90656	−	2.54357i	−0.338599	−	0.0869375i
$857$	−3.95266	−	12.1650i	−0.135020	−	0.415550i	0.860573	−	0.509327i	$-0.170106\pi$
$857$	−3.95266	−	12.1650i	−0.135020	−	0.415550i	−0.995593	+	0.0937774i	$0.970106\pi$
$858$	0.0704473	−	0.0278920i	0.00240503	−	0.000952219i
$859$	7.31646	+	6.87061i	0.249634	+	0.234422i	0.799255	−	0.600992i	$-0.205228\pi$
$859$	7.31646	+	6.87061i	0.249634	+	0.234422i	−0.549621	+	0.835414i	$0.685228\pi$
$860$	0.493511	+	5.46968i	0.0168286	+	0.186514i
$861$	−13.4693	−	7.40480i	−0.459032	−	0.252355i
$862$	−6.85375	+	3.76788i	−0.233440	+	0.128335i
$863$	−26.6220	−	3.36314i	−0.906225	−	0.114483i	−0.341614	−	0.939840i	$-0.610974\pi$
$863$	−26.6220	−	3.36314i	−0.906225	−	0.114483i	−0.564610	+	0.825358i	$0.690974\pi$
$864$	0.187381	−	0.982287i	0.00637484	−	0.0334181i
$865$	12.7883	+	18.9911i	0.434814	+	0.645716i
$866$	−27.6249	+	15.1869i	−0.938732	+	0.516072i
$867$	−6.46001	+	10.1793i	−0.219393	+	0.345709i
$868$	−6.82136	+	20.9940i	−0.231532	+	0.712582i
$869$	1.01013	+	16.0556i	0.0342664	+	0.544648i
$870$	2.24038	+	4.44375i	0.0759561	+	0.150657i
$871$	0.316888	+	0.125465i	0.0107373	+	0.00425121i
$872$	12.9866	−	3.33440i	0.439782	−	0.112917i
$873$	−2.21447	+	11.6086i	−0.0749483	+	0.392893i
$874$	0.356009			0.0120422
$875$	40.2686	+	6.90716i	1.36133	+	0.233504i
$876$	9.56699			0.323239
$877$	9.03427	−	47.3593i	0.305066	−	1.59921i	−0.418011	−	0.908442i	$-0.637273\pi$
$877$	9.03427	−	47.3593i	0.305066	−	1.59921i	0.723077	−	0.690768i	$-0.242727\pi$
$878$	−7.16134	+	1.83872i	−0.241684	+	0.0620538i
$879$	−22.6812	−	8.98011i	−0.765017	−	0.302891i
$880$	3.58180	−	0.551653i	0.120742	−	0.0185962i
$881$	0.475065	+	7.55094i	0.0160053	+	0.254398i	0.997890	+	0.0649203i	$0.0206793\pi$
$881$	0.475065	+	7.55094i	0.0160053	+	0.254398i	−0.981885	+	0.189477i	$0.939321\pi$
$882$	−1.96355	+	6.04318i	−0.0661161	+	0.203484i
$883$	−20.4286	+	32.1903i	−0.687477	+	1.08329i	0.303958	+	0.952686i	$0.401692\pi$
$883$	−20.4286	+	32.1903i	−0.687477	+	1.08329i	−0.991435	+	0.130605i	$0.958308\pi$
$884$	−0.0910892	+	0.0500767i	−0.00306366	+	0.00168426i
$885$	13.0081	+	4.74598i	0.437263	+	0.159534i
$886$	−6.45464	+	33.8364i	−0.216848	+	1.13676i
$887$	−30.9940	−	3.91545i	−1.04068	−	0.131468i	−0.413626	−	0.910447i	$-0.635738\pi$
$887$	−30.9940	−	3.91545i	−1.04068	−	0.131468i	−0.627050	+	0.778979i	$0.715738\pi$
$888$	6.21625	−	3.41741i	0.208604	−	0.114681i
$889$	−5.89668	−	3.24173i	−0.197768	−	0.108724i
$890$	3.23803	−	5.42229i	0.108539	−	0.181756i
$891$	−1.18145	−	1.10946i	−0.0395801	−	0.0371682i
$892$	−3.20052	+	1.26718i	−0.107161	+	0.0424282i
$893$	0.554189	+	1.70562i	0.0185452	+	0.0570763i
$894$	−15.0413	−	3.86196i	−0.503058	−	0.129163i
$895$	4.55804	+	50.5176i	0.152358	+	1.68862i
$896$	−0.229458	+	3.64713i	−0.00766564	+	0.121842i
$897$	−0.0227189	−	0.00899503i	−0.000758561	−	0.000300335i
$898$	−10.9574	−	23.2857i	−0.365655	−	0.777056i
$899$	−4.15439	+	12.7859i	−0.138557	+	0.426433i
$900$	−3.39152	−	3.67390i	−0.113051	−	0.122463i
$901$	−4.58907	−	14.1237i	−0.152884	−	0.470528i
$902$	−4.96930	+	4.66649i	−0.165460	+	0.155377i
$903$	−5.72103	+	6.91554i	−0.190384	+	0.230135i
$904$	−10.9975	+	13.2937i	−0.365771	+	0.442141i
$905$	2.47044	+	11.2778i	0.0821204	+	0.374888i
$906$	17.7329	−	7.02094i	0.589135	−	0.233255i
$907$	26.6656	−	19.3737i	0.885418	−	0.643294i	−0.0492616	−	0.998786i	$-0.515687\pi$
$907$	26.6656	−	19.3737i	0.885418	−	0.643294i	0.934679	+	0.355492i	$0.115687\pi$
$908$	1.17724	+	18.7117i	0.0390681	+	0.620970i
$909$	2.80077	+	14.6821i	0.0928955	+	0.486975i
$910$	0.339629	+	0.174878i	0.0112586	+	0.00579714i
$911$	−14.3024	+	1.80682i	−0.473861	+	0.0598626i	−0.358637	−	0.933477i	$-0.616759\pi$
$911$	−14.3024	+	1.80682i	−0.473861	+	0.0598626i	−0.115224	+	0.993340i	$0.536759\pi$
$912$	0.496524	+	0.466267i	0.0164415	+	0.0154396i
$913$	2.31999	−	4.93024i	0.0767806	−	0.163167i
$914$	17.3949	−	16.3349i	0.575373	−	0.540311i
$915$	1.04527	+	4.77175i	0.0345554	+	0.157749i
$916$	−3.90533	+	8.29925i	−0.129036	+	0.274215i
$917$	34.9345	+	8.96965i	1.15364	+	0.296204i
$918$	1.79883	+	1.30693i	0.0593702	+	0.0431350i
$919$	14.4188	−	22.7205i	0.475634	−	0.749479i	−0.518794	−	0.854899i	$-0.673619\pi$
$919$	14.4188	−	22.7205i	0.475634	−	0.749479i	0.994428	+	0.105421i	$0.0336189\pi$
$920$	−0.963824	−	0.661041i	−0.0317763	−	0.0217939i
$921$	13.0342	−	3.34661i	0.429491	−	0.110275i
$922$	13.0056	+	20.4935i	0.428316	+	0.674917i
$923$	−0.370980	−	0.203948i	−0.0122110	−	0.00671303i
$924$	4.79152	+	3.48124i	0.157629	+	0.114524i
$925$	4.74536	−	35.1496i	0.156026	−	1.15571i
$926$	−3.10212	+	2.25382i	−0.101942	+	0.0740652i
$927$	1.01172	−	0.127811i	0.0332294	−	0.00419785i
$928$	−0.139746	+	2.22120i	−0.00458738	+	0.0729143i
$929$	24.1393	+	38.0375i	0.791986	+	1.24797i	0.964792	+	0.263014i	$0.0847165\pi$
$929$	24.1393	+	38.0375i	0.791986	+	1.24797i	−0.172806	+	0.984956i	$0.555284\pi$
$930$	0.481843	−	13.4986i	0.0158003	−	0.442636i
$931$	−2.75879	−	3.33481i	−0.0904157	−	0.109294i
$932$	13.9936			0.458377
$933$	4.18257	+	5.05586i	0.136931	+	0.165521i
$934$	25.0820	+	3.16859i	0.820707	+	0.103679i
$935$	−2.28108	+	7.72834i	−0.0745992	+	0.252744i
$936$	−0.0199050	−	0.0423004i	−0.000650617	−	0.00138263i
$937$	8.13969	+	42.6698i	0.265912	+	1.39396i	0.825131	+	0.564941i	$0.191101\pi$
$937$	8.13969	+	42.6698i	0.265912	+	1.39396i	−0.559219	+	0.829020i	$0.688899\pi$
$938$	4.99210	+	26.1695i	0.162998	+	0.854464i
$939$	−0.502742	−	1.06838i	−0.0164064	−	0.0348653i
$940$	1.66665	−	5.64665i	0.0543601	−	0.184173i
$941$	−42.8629	−	5.41484i	−1.39729	−	0.176519i	−0.609658	−	0.792664i	$-0.708693\pi$
$941$	−42.8629	−	5.41484i	−1.39729	−	0.176519i	−0.787632	+	0.616146i	$0.788693\pi$
$942$	−10.6323	−	12.8522i	−0.346419	−	0.418748i
$943$	2.19841			0.0715901
$944$	3.94725	+	4.77141i	0.128472	+	0.155296i
$945$	0.291497	−	8.16614i	0.00948240	−	0.265645i
$946$	2.13289	+	3.36090i	0.0693463	+	0.109272i
$947$	0.126868	−	2.01651i	0.00412265	−	0.0655277i	−0.995427	−	0.0955205i	$-0.969548\pi$
$947$	0.126868	−	2.01651i	0.00412265	−	0.0655277i	0.999550	+	0.0299928i	$0.00954844\pi$
$948$	9.84778	−	1.24406i	0.319841	−	0.0404053i
$949$	0.361836	−	0.262889i	0.0117457	−	0.00853374i
$950$	3.35066	−	0.609600i	0.108710	−	0.0197780i
$951$	−18.5886	−	13.5054i	−0.602776	−	0.437943i
$952$	−7.12028	−	3.91441i	−0.230770	−	0.126867i
$953$	15.6408	+	24.6459i	0.506654	+	0.798359i	0.997333	−	0.0729815i	$-0.0232514\pi$
$953$	15.6408	+	24.6459i	0.506654	+	0.798359i	−0.490680	+	0.871340i	$0.663251\pi$
$954$	6.46914	−	1.66099i	0.209446	−	0.0537766i
$955$	−16.3092	−	11.1857i	−0.527754	−	0.361961i
$956$	3.66566	−	5.77615i	0.118556	−	0.186814i
$957$	2.91816	+	2.12017i	0.0943308	+	0.0685353i
$958$	−42.2286	−	10.8425i	−1.36434	−	0.350304i
$959$	−30.2566	+	64.2986i	−0.977037	+	2.07631i
$960$	−0.478472	−	2.18428i	−0.0154426	−	0.0704972i
$961$	4.00118	−	3.75736i	0.129070	−	0.121205i
$962$	0.141200	−	0.300066i	0.00455248	−	0.00967451i
$963$	7.45581	+	7.00147i	0.240260	+	0.225619i
$964$	13.5576	−	1.71272i	0.436661	−	0.0551631i
$965$	14.1986	+	7.31097i	0.457068	+	0.235348i
$966$	−0.357902	−	1.87619i	−0.0115153	−	0.0603654i
$967$	−2.85414	−	45.3652i	−0.0917828	−	1.45885i	−0.727066	−	0.686567i	$-0.759117\pi$
$967$	−2.85414	−	45.3652i	−0.0917828	−	1.45885i	0.635284	−	0.772279i	$-0.280883\pi$
$968$	−6.77412	+	4.92169i	−0.217729	+	0.158189i
$969$	−1.40813	+	0.557517i	−0.0452356	+	0.0179100i
$970$	5.65457	+	25.8137i	0.181557	+	0.828828i
$971$	−10.0961	+	12.2041i	−0.323999	+	0.391647i	−0.907213	−	0.420671i	$-0.861795\pi$
$971$	−10.0961	+	12.2041i	−0.323999	+	0.391647i	0.583215	+	0.812318i	$0.301795\pi$
$972$	−0.637424	+	0.770513i	−0.0204454	+	0.0247142i
$973$	11.1703	−	10.4896i	0.358103	−	0.336281i
$974$	−6.93580	−	21.3462i	−0.222238	−	0.683977i
$975$	−0.229226	−	0.0457569i	−0.00734111	−	0.00146539i
$976$	−0.675075	+	2.07767i	−0.0216086	+	0.0665046i
$977$	14.9060	+	31.6768i	0.476884	+	1.01343i	0.988076	+	0.153964i	$0.0492039\pi$
$977$	14.9060	+	31.6768i	0.476884	+	1.01343i	−0.511192	+	0.859466i	$0.670796\pi$
$978$	−13.9486	−	5.52262i	−0.446026	−	0.176594i
$979$	0.287426	−	4.56851i	0.00918619	−	0.146010i
$980$	1.27679	+	14.1509i	0.0407855	+	0.452033i
$981$	−12.9866	−	3.33440i	−0.414631	−	0.106459i
$982$	−10.6662	−	32.8273i	−0.340373	−	1.04756i
$983$	15.7141	−	6.22166i	0.501203	−	0.198440i	−0.103900	−	0.994588i	$-0.533132\pi$
$983$	15.7141	−	6.22166i	0.501203	−	0.198440i	0.605102	+	0.796148i	$0.293132\pi$
$984$	3.06611	+	2.87927i	0.0977442	+	0.0917879i
$985$	−5.03220	+	8.42676i	−0.160339	+	0.268499i
$986$	−4.33644	−	2.38398i	−0.138100	−	0.0759213i
$987$	8.43158	−	4.63530i	0.268380	−	0.147543i
$988$	0.0315916	+	0.00399095i	0.00100506	+	0.000126969i
$989$	0.240543	−	1.26097i	0.00764883	−	0.0400966i
$990$	−3.40452	−	1.24213i	−0.108203	−	0.0394774i
$991$	49.9596	−	27.4655i	1.58702	−	0.872471i	0.589096	−	0.808063i	$-0.299484\pi$
$991$	49.9596	−	27.4655i	1.58702	−	0.872471i	0.997924	−	0.0644079i	$-0.0205159\pi$
$992$	3.23671	−	5.10025i	0.102766	−	0.161933i
$993$	5.00694	−	15.4098i	0.158890	−	0.489014i
$994$	−2.07787	−	33.0268i	−0.0659060	−	1.04755i
$995$	−48.1122	+	7.41003i	−1.52526	+	0.234914i
$996$	−3.12589	−	1.23763i	−0.0990477	−	0.0392157i
$997$	−19.5849	+	5.02854i	−0.620260	+	0.159256i	−0.545727	−	0.837963i	$-0.683746\pi$
$997$	−19.5849	+	5.02854i	−0.620260	+	0.159256i	−0.0745326	+	0.997219i	$0.523746\pi$
$998$	4.87104	−	25.5349i	0.154190	−	0.808293i
$999$	−7.09370			−0.224435

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	750.2.m.d.61.6	✓	140
125.41	even	25	inner	750.2.m.d.541.6	yes	140

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
750.2.m.d.61.6	✓	140	1.1	even	1	trivial
750.2.m.d.541.6	yes	140	125.41	even	25	inner

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:	\( N \)	\(=\)	\( 750 = 2 \cdot 3 \cdot 5^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	750.m (of order \(25\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(0.187381 - 0.982287i) q^{2} +(0.968583 - 0.248690i) q^{3} +(-0.929776 - 0.368125i) q^{4} +(1.98800 + 1.02364i) q^{5} +(-0.0627905 - 0.998027i) q^{6} +(1.12925 - 3.47548i) q^{7} +(-0.535827 + 0.844328i) q^{8} +(0.876307 - 0.481754i) q^{9} +(1.37802 - 1.76098i) q^{10} +(0.303692 - 1.59201i) q^{11} +(-0.992115 - 0.125333i) q^{12} +(-0.0409670 + 0.0225218i) q^{13} +(-3.20232 - 1.76049i) q^{14} +(2.18012 + 0.497085i) q^{15} +(0.728969 + 0.684547i) q^{16} +(-2.06734 + 0.818516i) q^{17} +(-0.309017 - 0.951057i) q^{18} +(0.659733 + 0.169391i) q^{19} +(-1.47157 - 1.68359i) q^{20} +(0.229458 - 3.64713i) q^{21} +(-1.50690 - 0.596626i) q^{22} +(0.222543 + 0.472928i) q^{23} +(-0.309017 + 0.951057i) q^{24} +(2.90432 + 4.07000i) q^{25} +(0.0144464 + 0.0444616i) q^{26} +(0.728969 - 0.684547i) q^{27} +(-2.32936 + 2.81571i) q^{28} +(-1.41864 + 1.71484i) q^{29} +(0.896793 - 2.04836i) q^{30} +(5.61641 - 2.22369i) q^{31} +(0.809017 - 0.587785i) q^{32} +(-0.101766 - 1.61752i) q^{33} +(0.416638 + 2.18409i) q^{34} +(5.80260 - 5.75332i) q^{35} +(-0.992115 + 0.125333i) q^{36} +(-5.17108 - 4.85597i) q^{37} +(0.290012 - 0.616306i) q^{38} +(-0.0340790 + 0.0320023i) q^{39} +(-1.92951 + 1.13003i) q^{40} +(1.79087 - 3.80579i) q^{41} +(-3.53953 - 0.908797i) q^{42} +(-1.98699 - 1.44363i) q^{43} +(-0.868423 + 1.36842i) q^{44} +(2.23524 - 0.0607045i) q^{45} +(0.506252 - 0.129983i) q^{46} +(1.41081 + 2.22308i) q^{47} +(0.876307 + 0.481754i) q^{48} +(-5.14064 - 3.73489i) q^{49} +(4.54213 - 2.09023i) q^{50} +(-1.79883 + 1.30693i) q^{51} +(0.0463810 - 0.00585929i) q^{52} +(-0.419376 + 6.66579i) q^{53} +(-0.535827 - 0.844328i) q^{54} +(2.23339 - 2.85405i) q^{55} +(2.32936 + 2.81571i) q^{56} +0.681132 q^{57} +(1.41864 + 1.71484i) q^{58} +(6.14368 + 0.776127i) q^{59} +(-1.84403 - 1.26473i) q^{60} +(0.930153 + 1.97668i) q^{61} +(-1.13190 - 5.93360i) q^{62} +(-0.684754 - 3.58961i) q^{63} +(-0.425779 - 0.904827i) q^{64} +(-0.104497 + 0.00283791i) q^{65} +(-1.60794 - 0.203130i) q^{66} +(-4.64704 - 5.61731i) q^{67} +2.22348 q^{68} +(0.333164 + 0.402726i) q^{69} +(-4.56411 - 6.77789i) q^{70} +(4.85222 + 7.64587i) q^{71} +(-0.0627905 + 0.998027i) q^{72} +(-9.49155 + 1.19906i) q^{73} +(-5.73892 + 4.16957i) q^{74} +(3.82524 + 3.21986i) q^{75} +(-0.551047 - 0.400359i) q^{76} +(-5.19005 - 2.85326i) q^{77} +(0.0250497 + 0.0394720i) q^{78} +(-9.61421 + 2.46851i) q^{79} +(0.748462 + 2.10708i) q^{80} +(0.535827 - 0.844328i) q^{81} +(-3.40281 - 2.47228i) q^{82} +(3.25636 + 0.836091i) q^{83} +(-1.55594 + 3.30654i) q^{84} +(-4.94774 - 0.488997i) q^{85} +(-1.79038 + 1.68128i) q^{86} +(-0.947609 + 2.01377i) q^{87} +(1.18145 + 1.10946i) q^{88} +(2.80212 - 0.353991i) q^{89} +(0.359214 - 2.20703i) q^{90} +(0.0320120 + 0.167813i) q^{91} +(-0.0328189 - 0.521641i) q^{92} +(4.88695 - 3.55057i) q^{93} +(2.44806 - 0.969257i) q^{94} +(1.13816 + 1.01208i) q^{95} +(0.637424 - 0.770513i) q^{96} +(-7.53305 + 9.10590i) q^{97} +(-4.63199 + 4.34973i) q^{98} +(-0.500829 - 1.54139i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 140 q - 20 q^{5} + 5 q^{7} + 20 q^{10} + 5 q^{11} - 10 q^{13} + 20 q^{14} - 5 q^{17} + 35 q^{18} - 5 q^{19} - 5 q^{23} + 35 q^{24} - 40 q^{25} - 10 q^{26} + 25 q^{29} + 5 q^{30} + 30 q^{31} + 35 q^{32}+ \cdots - 10 q^{99}+O(q^{100}) \) 140 * q - 20 * q^5 + 5 * q^7 + 20 * q^10 + 5 * q^11 - 10 * q^13 + 20 * q^14 - 5 * q^17 + 35 * q^18 - 5 * q^19 - 5 * q^23 + 35 * q^24 - 40 * q^25 - 10 * q^26 + 25 * q^29 + 5 * q^30 + 30 * q^31 + 35 * q^32 - 15 * q^34 - 25 * q^37 + 35 * q^38 - 10 * q^39 + 5 * q^40 + 55 * q^41 + 35 * q^43 + 25 * q^44 + 20 * q^46 + 10 * q^47 - 60 * q^49 - 5 * q^51 + 40 * q^52 + 40 * q^55 + 20 * q^57 - 25 * q^58 + 75 * q^59 + 50 * q^61 + 5 * q^62 + 5 * q^63 - 35 * q^65 + 20 * q^66 - 95 * q^67 + 20 * q^68 - 20 * q^69 + 65 * q^70 - 50 * q^71 + 20 * q^73 + 30 * q^74 + 35 * q^75 - 5 * q^76 + 15 * q^77 + 5 * q^78 + 70 * q^79 - 15 * q^82 + 25 * q^83 + 5 * q^84 - 95 * q^85 - 5 * q^86 - 5 * q^88 - 105 * q^89 - 5 * q^90 - 65 * q^91 + 55 * q^92 - 30 * q^93 - 10 * q^94 + 125 * q^95 - 5 * q^97 + 70 * q^98 - 10 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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