LMFDB - Embedded newform 722.2.i.b.11.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [722,2,Mod(7,722)] 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("722.7"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(722, base_ring=CyclotomicField(114)) chi = DirichletCharacter(H, H._module([50])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 722 = 2 \cdot 19^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	722.i (of order $57$, degree $36$, minimal)

Newform invariants

comment:select newform

sage:traces = [612] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$5.76519902594$
Analytic rank:	$0$
Dimension:	$612$
Relative dimension:	$17$ over $\Q(\zeta_{57})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{57}]$

Embedding invariants

Embedding label			11.1
Character	$\chi$	$=$	722.11
Dual form			722.2.i.b.197.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.592235 - 0.805765i) q^{2} +(-0.447948 - 3.23037i) q^{3} +(-0.298515 + 0.954405i) q^{4} +(2.48156 + 1.72067i) q^{5} +(-2.33763 + 2.27408i) q^{6} +(-1.96145 + 2.13070i) q^{7} +(0.945817 - 0.324699i) q^{8} +(-7.34782 + 2.07777i) q^{9} +(-0.0832070 - 3.01860i) q^{10} +(1.20197 + 4.74649i) q^{11} +(3.21680 + 0.536789i) q^{12} +(-0.399546 - 0.162282i) q^{13} +(2.87848 + 0.318590i) q^{14} +(4.44680 - 8.78712i) q^{15} +(-0.821778 - 0.569808i) q^{16} +(-0.0937829 - 0.299841i) q^{17} +(6.02583 + 4.69009i) q^{18} +(2.96631 + 3.19390i) q^{19} +(-2.38300 + 1.85476i) q^{20} +(7.76157 + 5.38176i) q^{21} +(3.11270 - 3.77954i) q^{22} +(-0.983949 + 7.09573i) q^{23} +(-1.47258 - 2.90989i) q^{24} +(1.44422 + 3.85734i) q^{25} +(0.105864 + 0.418049i) q^{26} +(6.07327 + 13.8457i) q^{27} +(-1.44803 - 2.50806i) q^{28} +(-5.10291 - 1.14359i) q^{29} +(-9.71390 + 1.62096i) q^{30} +(4.16530 + 9.49593i) q^{31} +(0.0275543 + 0.999620i) q^{32} +(14.7945 - 6.00900i) q^{33} +(-0.186060 + 0.253143i) q^{34} +(-8.53368 + 1.91244i) q^{35} +(0.210403 - 7.63304i) q^{36} +(-2.80869 - 11.0913i) q^{37} +(0.816775 - 4.28169i) q^{38} +(-0.345253 + 1.36337i) q^{39} +(2.90580 + 0.821682i) q^{40} +(-0.277621 + 0.0153168i) q^{41} +(-0.260247 - 9.44127i) q^{42} +(0.149356 - 5.41836i) q^{43} +(-4.88888 - 0.269727i) q^{44} +(-21.8092 - 7.48711i) q^{45} +(6.30022 - 3.40951i) q^{46} +(1.31011 - 1.27450i) q^{47} +(-1.47258 + 2.90989i) q^{48} +(-0.114551 - 1.38242i) q^{49} +(2.25279 - 3.44816i) q^{50} +(-0.926586 + 0.437266i) q^{51} +(0.274153 - 0.332885i) q^{52} +(-2.19634 + 2.13664i) q^{53} +(7.55955 - 13.0935i) q^{54} +(-5.18439 + 13.8469i) q^{55} +(-1.16333 + 2.65213i) q^{56} +(8.98871 - 11.0130i) q^{57} +(2.10066 + 4.78902i) q^{58} +(3.04730 - 0.168124i) q^{59} +(7.05903 + 6.86713i) q^{60} +(1.52463 + 7.80526i) q^{61} +(5.18465 - 8.98008i) q^{62} +(9.98527 - 19.7314i) q^{63} +(0.789141 - 0.614213i) q^{64} +(-0.712262 - 1.09020i) q^{65} +(-13.6037 - 8.36213i) q^{66} +(-9.60814 - 8.36774i) q^{67} +0.314165 q^{68} +23.3626 q^{69} +(6.59493 + 5.74353i) q^{70} +(-1.42764 + 7.30874i) q^{71} +(-6.27505 + 4.35102i) q^{72} +(-0.664388 - 2.12417i) q^{73} +(-7.27354 + 8.83177i) q^{74} +(11.8137 - 6.39326i) q^{75} +(-3.93376 + 1.87764i) q^{76} +(-12.4709 - 6.74894i) q^{77} +(1.30303 - 0.529245i) q^{78} +(0.0133285 - 0.483534i) q^{79} +(-1.05884 - 2.82802i) q^{80} +(22.4905 - 13.8248i) q^{81} +(0.176759 + 0.214626i) q^{82} +(-0.226778 - 2.73680i) q^{83} +(-7.45332 + 5.80115i) q^{84} +(0.283200 - 0.905441i) q^{85} +(-4.45438 + 3.08860i) q^{86} +(-1.40837 + 16.9966i) q^{87} +(2.67803 + 4.09903i) q^{88} +(3.22738 - 10.3185i) q^{89} +(6.88332 + 22.0072i) q^{90} +(1.12946 - 0.533006i) q^{91} +(-6.47847 - 3.05727i) q^{92} +(28.8095 - 17.7091i) q^{93} +(-1.80284 - 0.300840i) q^{94} +(1.86542 + 13.0299i) q^{95} +(3.21680 - 0.536789i) q^{96} +(-12.1106 + 10.5471i) q^{97} +(-1.04606 + 0.911019i) q^{98} +(-18.6940 - 32.3789i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 612 q + 17 q^{2} - 19 q^{3} + 17 q^{4} + q^{5} - 2 q^{7} - 34 q^{8} + 4 q^{9} + q^{10} - 28 q^{11} + 4 q^{13} - 18 q^{14} - 52 q^{15} + 17 q^{16} + 18 q^{17} - 46 q^{18} - 12 q^{19} - 2 q^{20} - 65 q^{21}+ \cdots - 116 q^{99}+O(q^{100}) $ 612 * q + 17 * q^2 - 19 * q^3 + 17 * q^4 + q^5 - 2 * q^7 - 34 * q^8 + 4 * q^9 + q^10 - 28 * q^11 + 4 * q^13 - 18 * q^14 - 52 * q^15 + 17 * q^16 + 18 * q^17 - 46 * q^18 - 12 * q^19 - 2 * q^20 - 65 * q^21 + 33 * q^22 + 39 * q^23 + 20 * q^25 - 8 * q^26 + 158 * q^27 - 37 * q^28 - 42 * q^29 - 29 * q^30 + 12 * q^31 + 17 * q^32 + 60 * q^33 - q^34 - 14 * q^35 + 23 * q^36 - 6 * q^37 + 76 * q^38 - 108 * q^39 + q^40 + 8 * q^41 + 11 * q^42 + 7 * q^43 - 5 * q^44 - 101 * q^45 - 21 * q^46 + 105 * q^47 - 62 * q^49 - 78 * q^50 - 3 * q^51 + 4 * q^52 + 146 * q^53 - 79 * q^54 + 4 * q^55 - 21 * q^56 - 28 * q^57 + 8 * q^58 - 4 * q^59 - 14 * q^60 - 93 * q^61 - 6 * q^62 - 95 * q^63 - 34 * q^64 - 76 * q^65 - 16 * q^66 - 6 * q^67 + 78 * q^68 + 38 * q^69 + 81 * q^70 - 151 * q^71 + 23 * q^72 + 7 * q^73 - 35 * q^74 - 12 * q^75 - 7 * q^76 + 78 * q^77 - 3 * q^78 - 10 * q^79 + q^80 + 58 * q^81 - 30 * q^82 + 67 * q^83 - 22 * q^84 - 6 * q^85 - 12 * q^86 - 109 * q^87 + 10 * q^88 - 25 * q^89 - 73 * q^90 + 37 * q^91 + q^92 + 56 * q^93 - 39 * q^94 - 29 * q^95 - 153 * q^97 + 164 * q^98 - 116 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/722\mathbb{Z}\right)^\times$.

$n$	$363$
$\chi(n)$	$e\left(\frac{17}{57}\right)$

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 $

$2$	−0.592235	−	0.805765i	−0.418774	−	0.569762i
$2$	−0.592235	−	0.805765i	−0.418774	−	0.569762i
$3$	−0.447948	−	3.23037i	−0.258623	−	1.86505i	−0.463268	−	0.886218i	$-0.653323\pi$
$3$	−0.447948	−	3.23037i	−0.258623	−	1.86505i	0.204645	−	0.978836i	$-0.434396\pi$
$4$	−0.298515	+	0.954405i	−0.149257	+	0.477203i
$5$	2.48156	+	1.72067i	1.10979	+	0.769509i	0.975185	−	0.221391i	$-0.0710598\pi$
$5$	2.48156	+	1.72067i	1.10979	+	0.769509i	0.134601	+	0.990900i	$0.457025\pi$
$6$	−2.33763	+	2.27408i	−0.954333	+	0.928389i
$7$	−1.96145	+	2.13070i	−0.741357	+	0.805329i	−0.986431	−	0.164176i	$-0.947504\pi$
$7$	−1.96145	+	2.13070i	−0.741357	+	0.805329i	0.245074	+	0.969504i	$0.421188\pi$
$8$	0.945817	−	0.324699i	0.334397	−	0.114799i
$9$	−7.34782	+	2.07777i	−2.44927	+	0.692589i
$10$	−0.0832070	−	3.01860i	−0.0263124	−	0.954564i
$11$	1.20197	+	4.74649i	0.362409	+	1.43112i	0.835201	+	0.549945i	$0.185351\pi$
$11$	1.20197	+	4.74649i	0.362409	+	1.43112i	−0.472792	+	0.881174i	$0.656754\pi$
$12$	3.21680	+	0.536789i	0.928610	+	0.154958i
$13$	−0.399546	−	0.162282i	−0.110814	−	0.0450088i	0.320229	−	0.947340i	$-0.396240\pi$
$13$	−0.399546	−	0.162282i	−0.110814	−	0.0450088i	−0.431043	+	0.902331i	$0.641854\pi$
$14$	2.87848	+	0.318590i	0.769307	+	0.0851468i
$15$	4.44680	−	8.78712i	1.14816	−	2.26882i
$16$	−0.821778	−	0.569808i	−0.205444	−	0.142452i
$17$	−0.0937829	−	0.299841i	−0.0227457	−	0.0727220i	0.942339	−	0.334659i	$-0.108621\pi$
$17$	−0.0937829	−	0.299841i	−0.0227457	−	0.0727220i	−0.965085	+	0.261937i	$0.915639\pi$
$18$	6.02583	+	4.69009i	1.42030	+	1.10547i
$19$	2.96631	+	3.19390i	0.680519	+	0.732730i
$19$	2.96631	+	3.19390i	0.680519	+	0.732730i
$20$	−2.38300	+	1.85476i	−0.532855	+	0.414738i
$21$	7.76157	+	5.38176i	1.69371	+	1.17440i
$22$	3.11270	−	3.77954i	0.663630	−	0.805802i
$23$	−0.983949	+	7.09573i	−0.205168	+	1.47956i	0.556095	+	0.831118i	$0.312299\pi$
$23$	−0.983949	+	7.09573i	−0.205168	+	1.47956i	−0.761263	+	0.648443i	$0.775420\pi$
$24$	−1.47258	−	2.90989i	−0.300588	−	0.593979i
$25$	1.44422	+	3.85734i	0.288844	+	0.771469i
$26$	0.105864	+	0.418049i	0.0207617	+	0.0819861i
$27$	6.07327	+	13.8457i	1.16880	+	2.66460i
$28$	−1.44803	−	2.50806i	−0.273652	−	0.473979i
$29$	−5.10291	−	1.14359i	−0.947587	−	0.212359i	−0.282620	−	0.959232i	$-0.591203\pi$
$29$	−5.10291	−	1.14359i	−0.947587	−	0.212359i	−0.664967	+	0.746873i	$0.731554\pi$
$30$	−9.71390	+	1.62096i	−1.77351	+	0.295946i
$31$	4.16530	+	9.49593i	0.748110	+	1.70552i	0.707884	+	0.706329i	$0.249650\pi$
$31$	4.16530	+	9.49593i	0.748110	+	1.70552i	0.0402261	+	0.999191i	$0.487192\pi$
$32$	0.0275543	+	0.999620i	0.00487097	+	0.176710i
$33$	14.7945	−	6.00900i	2.57539	−	1.04603i
$34$	−0.186060	+	0.253143i	−0.0319089	+	0.0434137i
$35$	−8.53368	+	1.91244i	−1.44246	+	0.323262i
$36$	0.210403	−	7.63304i	0.0350672	−	1.27217i
$37$	−2.80869	−	11.0913i	−0.461745	−	1.82339i	−0.560340	−	0.828263i	$-0.689329\pi$
$37$	−2.80869	−	11.0913i	−0.461745	−	1.82339i	0.0985947	−	0.995128i	$-0.468565\pi$
$38$	0.816775	−	4.28169i	0.132498	−	0.694582i
$39$	−0.345253	+	1.36337i	−0.0552848	+	0.218315i
$40$	2.90580	+	0.821682i	0.459448	+	0.129919i
$41$	−0.277621	+	0.0153168i	−0.0433571	+	0.00239208i	−0.0767533	−	0.997050i	$-0.524455\pi$
$41$	−0.277621	+	0.0153168i	−0.0433571	+	0.00239208i	0.0333962	+	0.999442i	$0.489368\pi$
$42$	−0.260247	−	9.44127i	−0.0401570	−	1.45682i
$43$	0.149356	−	5.41836i	0.0227766	−	0.826292i	−0.898860	−	0.438237i	$-0.855603\pi$
$43$	0.149356	−	5.41836i	0.0227766	−	0.826292i	0.921636	−	0.388055i	$-0.126853\pi$
$44$	−4.88888	−	0.269727i	−0.737026	−	0.0406629i
$45$	−21.8092	−	7.48711i	−3.25112	−	1.11611i
$46$	6.30022	−	3.40951i	0.928917	−	0.502705i
$47$	1.31011	−	1.27450i	0.191099	−	0.185904i	−0.595524	−	0.803338i	$-0.703056\pi$
$47$	1.31011	−	1.27450i	0.191099	−	0.185904i	0.786623	+	0.617433i	$0.211827\pi$
$48$	−1.47258	+	2.90989i	−0.212548	+	0.420006i
$49$	−0.114551	−	1.38242i	−0.0163644	−	0.197489i
$50$	2.25279	−	3.44816i	0.318593	−	0.487643i
$51$	−0.926586	+	0.437266i	−0.129748	+	0.0612295i
$52$	0.274153	−	0.332885i	0.0380181	−	0.0461629i
$53$	−2.19634	+	2.13664i	−0.301691	+	0.293490i	−0.832526	−	0.553985i	$-0.813106\pi$
$53$	−2.19634	+	2.13664i	−0.301691	+	0.293490i	0.530835	+	0.847475i	$0.321878\pi$
$54$	7.55955	−	13.0935i	1.02872	−	1.78180i
$55$	−5.18439	+	13.8469i	−0.699063	+	1.86711i
$56$	−1.16333	+	2.65213i	−0.155457	+	0.354406i
$57$	8.98871	−	11.0130i	1.19058	−	1.45871i
$58$	2.10066	+	4.78902i	0.275830	+	0.628829i
$59$	3.04730	−	0.168124i	0.396725	−	0.0218879i	0.144373	−	0.989523i	$-0.453884\pi$
$59$	3.04730	−	0.168124i	0.396725	−	0.0218879i	0.252352	+	0.967635i	$0.418796\pi$
$60$	7.05903	+	6.86713i	0.911317	+	0.886543i
$61$	1.52463	+	7.80526i	0.195209	+	0.999361i	0.942333	+	0.334676i	$0.108627\pi$
$61$	1.52463	+	7.80526i	0.195209	+	0.999361i	−0.747124	+	0.664685i	$0.768566\pi$
$62$	5.18465	−	8.98008i	0.658451	−	1.14047i
$63$	9.98527	−	19.7314i	1.25803	−	2.48593i
$64$	0.789141	−	0.614213i	0.0986426	−	0.0767766i
$65$	−0.712262	−	1.09020i	−0.0883453	−	0.135223i
$66$	−13.6037	−	8.36213i	−1.67449	−	1.02931i
$67$	−9.60814	−	8.36774i	−1.17382	−	1.02228i	−0.999292	−	0.0376302i	$-0.988019\pi$
$67$	−9.60814	−	8.36774i	−1.17382	−	1.02228i	−0.174530	−	0.984652i	$-0.555841\pi$
$68$	0.314165			0.0380981
$69$	23.3626			2.81252
$70$	6.59493	+	5.74353i	0.788245	+	0.686483i
$71$	−1.42764	+	7.30874i	−0.169430	+	0.867388i	0.795715	+	0.605672i	$0.207095\pi$
$71$	−1.42764	+	7.30874i	−0.169430	+	0.867388i	−0.965145	+	0.261716i	$0.915712\pi$
$72$	−6.27505	+	4.35102i	−0.739521	+	0.512773i
$73$	−0.664388	−	2.12417i	−0.0777607	−	0.248615i	0.907395	−	0.420279i	$-0.138068\pi$
$73$	−0.664388	−	2.12417i	−0.0777607	−	0.248615i	−0.985155	+	0.171665i	$0.945085\pi$
$74$	−7.27354	+	8.83177i	−0.845532	+	1.02667i
$75$	11.8137	−	6.39326i	1.36413	−	0.738230i
$76$	−3.93376	+	1.87764i	−0.451233	+	0.215380i
$77$	−12.4709	−	6.74894i	−1.42120	−	0.769113i
$78$	1.30303	−	0.529245i	0.147539	−	0.0599252i
$79$	0.0133285	−	0.483534i	0.00149957	−	0.0544018i	−0.998500	−	0.0547450i	$-0.982565\pi$
$79$	0.0133285	−	0.483534i	0.00149957	−	0.0544018i	1.00000		0.000343245i	$0.000109258\pi$
$80$	−1.05884	−	2.82802i	−0.118381	−	0.316183i
$81$	22.4905	−	13.8248i	2.49894	−	1.53609i
$82$	0.176759	+	0.214626i	0.0195197	+	0.0237015i
$83$	−0.226778	−	2.73680i	−0.0248921	−	0.300403i	−0.997647	−	0.0685655i	$-0.978158\pi$
$83$	−0.226778	−	2.73680i	−0.0248921	−	0.300403i	0.972755	−	0.231838i	$-0.0744738\pi$
$84$	−7.45332	+	5.80115i	−0.813224	+	0.632957i
$85$	0.283200	−	0.905441i	0.0307174	−	0.0982089i
$86$	−4.45438	+	3.08860i	−0.480328	+	0.333052i
$87$	−1.40837	+	16.9966i	−0.150994	+	1.82222i
$88$	2.67803	+	4.09903i	0.285479	+	0.436958i
$89$	3.22738	−	10.3185i	0.342101	−	1.09376i	−0.611133	−	0.791528i	$-0.709286\pi$
$89$	3.22738	−	10.3185i	0.342101	−	1.09376i	0.953235	−	0.302232i	$-0.0977316\pi$
$90$	6.88332	+	22.0072i	0.725566	+	2.31976i
$91$	1.12946	−	0.533006i	0.118400	−	0.0558742i
$92$	−6.47847	−	3.05727i	−0.675428	−	0.318742i
$93$	28.8095	−	17.7091i	2.98741	−	1.83635i
$94$	−1.80284	−	0.300840i	−0.185949	−	0.0310293i
$95$	1.86542	+	13.0299i	0.191388	+	1.33684i
$96$	3.21680	−	0.536789i	0.328313	−	0.0547858i
$97$	−12.1106	+	10.5471i	−1.22964	+	1.07090i	−0.234534	+	0.972108i	$0.575356\pi$
$97$	−12.1106	+	10.5471i	−1.22964	+	1.07090i	−0.995108	+	0.0987885i	$0.968503\pi$
$98$	−1.04606	+	0.911019i	−0.105669	+	0.0920268i
$99$	−18.6940	−	32.3789i	−1.87881	−	3.25420i
$100$	−4.11259	+	0.226898i	−0.411259	+	0.0226898i
$101$	11.7136	−	3.31230i	1.16555	−	0.329586i	0.366250	−	0.930517i	$-0.380642\pi$
$101$	11.7136	−	3.31230i	1.16555	−	0.329586i	0.799302	+	0.600930i	$0.205203\pi$
$102$	0.901091	+	0.487646i	0.0892213	+	0.0482841i
$103$	−1.20788	−	1.31210i	−0.119016	−	0.129286i	0.673371	−	0.739305i	$-0.264846\pi$
$103$	−1.20788	−	1.31210i	−0.119016	−	0.129286i	−0.792386	+	0.610019i	$0.791162\pi$
$104$	−0.430590	−	0.0237563i	−0.0422228	−	0.00232950i
$105$	10.0005	+	26.7103i	0.975953	+	2.60666i
$106$	3.02238	+	0.504346i	0.293560	+	0.0489864i
$107$	6.13969	−	13.9971i	0.593546	−	1.35315i	−0.320388	−	0.947286i	$-0.603813\pi$
$107$	6.13969	−	13.9971i	0.593546	−	1.35315i	0.913934	−	0.405862i	$-0.133029\pi$
$108$	−15.0273	+	1.66322i	−1.44601	+	0.160044i
$109$	−2.01081	−	1.95615i	−0.192601	−	0.187365i	0.594674	−	0.803967i	$-0.297281\pi$
$109$	−2.01081	−	1.95615i	−0.192601	−	0.187365i	−0.787275	+	0.616601i	$0.788509\pi$
$110$	14.2277	−	4.02321i	1.35656	−	0.383598i
$111$	−34.5707	+	14.0414i	−3.28130	+	1.33275i
$112$	2.82596	−	0.633313i	0.267028	−	0.0598425i
$113$	7.49075	+	8.13712i	0.704670	+	0.765476i	0.980667	−	0.195683i	$-0.0626922\pi$
$113$	7.49075	+	8.13712i	0.704670	+	0.765476i	−0.275997	+	0.961158i	$0.589008\pi$
$114$	−14.1973	−	0.720509i	−1.32970	−	0.0674819i
$115$	−14.6512	+	15.9154i	−1.36623	+	1.48412i
$116$	2.61474	−	4.52886i	0.242773	−	0.420495i
$117$	3.27297	+	0.362253i	0.302587	+	0.0334903i
$118$	−1.94019	−	2.35584i	−0.178609	−	0.216872i
$119$	0.822820	+	0.388298i	0.0754278	+	0.0355952i
$120$	1.35269	−	9.75488i	0.123483	−	0.890495i
$121$	−11.4102	+	6.17488i	−1.03729	+	0.561353i
$122$	5.38627	−	5.85104i	0.487650	−	0.529729i
$123$	0.173839	+	0.889956i	0.0156745	+	0.0802447i
$124$	−10.3064	+	1.14071i	−0.925539	+	0.102439i
$125$	0.653204	−	2.57944i	0.0584243	−	0.230712i
$126$	−21.8125	+	3.63987i	−1.94321	+	0.324265i
$127$	7.98706	+	13.8340i	0.708737	+	1.22757i	0.965326	+	0.261048i	$0.0840680\pi$
$127$	7.98706	+	13.8340i	0.708737	+	1.22757i	−0.256589	+	0.966521i	$0.582599\pi$
$128$	−0.962268	−	0.272103i	−0.0850533	−	0.0240508i
$129$	−17.5702	+	1.94467i	−1.54697	+	0.171219i
$130$	−0.456617	+	1.21957i	−0.0400480	+	0.106963i
$131$	7.93987	+	0.878785i	0.693710	+	0.0767798i	0.449947	−	0.893055i	$-0.351443\pi$
$131$	7.93987	+	0.878785i	0.693710	+	0.0767798i	0.243763	+	0.969835i	$0.421618\pi$
$132$	1.31865	+	15.9137i	0.114773	+	1.38511i
$133$	−12.6235	+	0.0556633i	−1.09460	+	0.00482662i
$134$	−1.05215	+	12.6976i	−0.0908920	+	1.09690i
$135$	−8.75270	+	44.8089i	−0.753312	+	3.85654i
$136$	−0.186060	−	0.253143i	−0.0159545	−	0.0217068i
$137$	2.88772	+	2.51492i	0.246714	+	0.214864i	0.771263	−	0.636517i	$-0.219625\pi$
$137$	2.88772	+	2.51492i	0.246714	+	0.214864i	−0.524548	+	0.851381i	$0.675766\pi$
$138$	−13.8361	−	18.8247i	−1.17781	−	1.60247i
$139$	7.33496	+	4.50878i	0.622143	+	0.382430i	0.798586	−	0.601881i	$-0.205582\pi$
$139$	7.33496	+	4.50878i	0.622143	+	0.382430i	−0.176443	+	0.984311i	$0.556459\pi$
$140$	0.722185	−	8.71548i	0.0610358	−	0.736593i
$141$	−4.70395	−	3.66123i	−0.396144	−	0.308331i
$142$	6.73463	−	3.17815i	0.565157	−	0.266704i
$143$	0.290023	−	2.09150i	0.0242530	−	0.174900i
$144$	7.22220	+	2.47939i	0.601850	+	0.206615i
$145$	−10.6954	−	11.6183i	−0.888206	−	0.964849i
$146$	−1.31811	+	1.79335i	−0.109087	+	0.148418i
$147$	−4.41441	+	0.989293i	−0.364095	+	0.0815955i
$148$	11.4240	+	0.630279i	0.939045	+	0.0518086i
$149$	0.196956	+	0.389196i	0.0161353	+	0.0318841i	0.900179	−	0.435519i	$-0.143435\pi$
$149$	0.196956	+	0.389196i	0.0161353	+	0.0318841i	−0.884044	+	0.467403i	$0.845190\pi$
$150$	−12.1480	−	5.73276i	−0.991877	−	0.468078i
$151$	−9.78200	+	14.9725i	−0.796048	+	1.21844i	0.176169	+	0.984360i	$0.443629\pi$
$151$	−9.78200	+	14.9725i	−0.796048	+	1.21844i	−0.972217	+	0.234082i	$0.924792\pi$
$152$	3.84265	+	2.05768i	0.311680	+	0.166900i
$153$	1.31210	+	2.00832i	0.106077	+	0.162363i
$154$	1.94767	+	14.0456i	0.156948	+	1.13183i
$155$	−6.00296	+	30.7318i	−0.482169	+	2.46844i
$156$	−1.19815	−	0.736499i	−0.0959286	−	0.0589671i
$157$	2.40015	+	17.3086i	0.191553	+	1.38138i	0.805764	+	0.592237i	$0.201755\pi$
$157$	2.40015	+	17.3086i	0.191553	+	1.38138i	−0.614211	+	0.789142i	$0.710526\pi$
$158$	−0.397508	+	0.275626i	−0.0316241	+	0.0219276i
$159$	7.88597	+	6.13790i	0.625398	+	0.486767i
$160$	−1.65164	+	2.52803i	−0.130574	+	0.199858i
$161$	−13.1889	−	16.0144i	−1.03943	−	1.26211i
$162$	−24.4592	−	9.93448i	−1.92170	−	0.780526i
$163$	−0.554251	+	1.26357i	−0.0434123	+	0.0989701i	−0.936142	−	0.351623i	$-0.885630\pi$
$163$	−0.554251	+	1.26357i	−0.0434123	+	0.0989701i	0.892729	+	0.450594i	$0.148788\pi$
$164$	0.0682555	−	0.269535i	0.00532986	−	0.0210471i
$165$	47.0529	+	10.5448i	3.66306	+	0.820911i
$166$	−2.07091	+	1.80356i	−0.160734	+	0.139983i
$167$	17.5385	+	3.93046i	1.35717	+	0.304148i	0.835730	−	0.549141i	$-0.185045\pi$
$167$	17.5385	+	3.93046i	1.35717	+	0.304148i	0.521438	+	0.853289i	$0.325396\pi$
$168$	9.08848	+	2.56998i	0.701192	+	0.198278i
$169$	−9.18487	−	8.93518i	−0.706529	−	0.687322i
$170$	−0.897294	+	0.308041i	−0.0688193	+	0.0236257i
$171$	−28.4321	−	17.3049i	−2.17426	−	1.32334i
$172$	5.12672	+	1.76001i	0.390909	+	0.134199i
$173$	−10.5844	−	20.9153i	−0.804715	−	1.59016i	−0.807284	−	0.590163i	$-0.799064\pi$
$173$	−10.5844	−	20.9153i	−0.804715	−	1.59016i	0.00256997	−	0.999997i	$-0.499182\pi$
$174$	14.5293	−	8.93114i	1.10146	−	0.677068i
$175$	−11.0516	−	4.48877i	−0.835423	−	0.339319i
$176$	1.71683	−	4.58545i	0.129411	−	0.345641i
$177$	−1.90814	−	9.76859i	−0.143424	−	0.734252i
$178$	−10.2257	+	3.51047i	−0.766446	+	0.263121i
$179$	−10.3809	−	5.61789i	−0.775908	−	0.419901i	0.0391838	−	0.999232i	$-0.487524\pi$
$179$	−10.3809	−	5.61789i	−0.775908	−	0.419901i	−0.815092	+	0.579331i	$0.803314\pi$
$180$	13.6561	−	18.5798i	1.01787	−	1.38486i
$181$	6.24089	−	8.49104i	0.463882	−	0.631134i	−0.509460	−	0.860495i	$-0.670155\pi$
$181$	6.24089	−	8.49104i	0.463882	−	0.631134i	0.973342	+	0.229360i	$0.0736634\pi$
$182$	−1.09838	−	0.594416i	−0.0814177	−	0.0440610i
$183$	24.5309	−	8.42147i	1.81338	−	0.622533i
$184$	1.37334	+	7.03075i	0.101244	+	0.518314i
$185$	12.1145	−	32.3564i	0.890676	−	2.37889i
$186$	−31.3314	−	12.7257i	−2.29733	−	0.933095i
$187$	1.31046	−	0.805540i	0.0958307	−	0.0589069i
$188$	0.825297	+	1.63083i	0.0601910	+	0.118941i
$189$	−41.4134	−	14.2172i	−3.01238	−	1.03415i
$190$	9.39427	−	9.21986i	0.681532	−	0.668879i
$191$	12.7752	−	4.38573i	0.924381	−	0.317341i	0.178900	−	0.983867i	$-0.442746\pi$
$191$	12.7752	−	4.38573i	0.924381	−	0.317341i	0.745481	+	0.666527i	$0.232220\pi$
$192$	−2.33763	−	2.27408i	−0.168704	−	0.164118i
$193$	20.0774	+	5.67735i	1.44520	+	0.408665i	0.902292	−	0.431125i	$-0.141883\pi$
$193$	20.0774	+	5.67735i	1.44520	+	0.408665i	0.542912	+	0.839790i	$0.317322\pi$
$194$	15.6708	+	3.51191i	1.12510	+	0.252140i
$195$	−3.20269	+	2.78922i	−0.229349	+	0.199740i
$196$	1.35358	+	0.303345i	0.0966845	+	0.0216675i
$197$	−4.87006	+	19.2314i	−0.346978	+	1.37018i	0.512358	+	0.858772i	$0.328772\pi$
$197$	−4.87006	+	19.2314i	−0.346978	+	1.37018i	−0.859336	+	0.511412i	$0.829123\pi$
$198$	−15.0186	+	34.2389i	−1.06732	+	2.43325i
$199$	12.3614	+	5.02076i	0.876274	+	0.355912i	0.769710	−	0.638394i	$-0.220401\pi$
$199$	12.3614	+	5.02076i	0.876274	+	0.355912i	0.106565	+	0.994306i	$0.466015\pi$
$200$	2.61845	+	3.17940i	0.185152	+	0.224818i
$201$	−22.7269	+	34.7862i	−1.60303	+	2.45363i
$202$	−9.60617	−	7.47678i	−0.675888	−	0.526065i
$203$	12.4457	−	8.62968i	0.873519	−	0.605685i
$204$	−0.140730	−	1.01487i	−0.00985304	−	0.0710550i
$205$	−0.715287	−	0.439685i	−0.0499578	−	0.0307090i
$206$	−0.341901	+	1.75034i	−0.0238213	+	0.121952i
$207$	−7.51338	−	54.1826i	−0.522216	−	3.76595i
$208$	0.235869	+	0.361024i	0.0163545	+	0.0250325i
$209$	−11.5944	+	17.9185i	−0.801999	+	1.23945i
$210$	15.5995	−	23.8769i	1.07647	−	1.64766i
$211$	0.698664	+	0.329707i	0.0480980	+	0.0226980i	0.450675	−	0.892688i	$-0.351184\pi$
$211$	0.698664	+	0.329707i	0.0480980	+	0.0226980i	−0.402577	+	0.915386i	$0.631885\pi$
$212$	−1.38358	−	2.73402i	−0.0950244	−	0.187773i
$213$	24.2494	+	1.33788i	1.66154	+	0.0916699i
$214$	−14.9145	+	3.34242i	−1.01953	+	0.228483i
$215$	9.69386	−	13.1890i	0.661116	−	0.899481i
$216$	10.2399	+	11.1235i	0.696736	+	0.756857i
$217$	−28.4030	−	9.75076i	−1.92812	−	0.661925i
$218$	−0.385322	+	2.77874i	−0.0260973	+	0.188200i
$219$	−6.56423	+	3.09773i	−0.443570	+	0.209325i
$220$	−11.6679	−	9.08150i	−0.786651	−	0.612275i
$221$	−0.0111880	+	0.135019i	−0.000752587	+	0.00908238i
$222$	31.7880	+	19.5400i	2.13347	+	1.31144i
$223$	−4.61095	−	6.27343i	−0.308772	−	0.420100i	0.623519	−	0.781808i	$-0.285702\pi$
$223$	−4.61095	−	6.27343i	−0.308772	−	0.420100i	−0.932291	+	0.361708i	$0.882194\pi$
$224$	−2.18394	−	1.90199i	−0.145920	−	0.127082i
$225$	−18.6265	−	25.3423i	−1.24177	−	1.68949i
$226$	2.12032	−	10.8549i	0.141042	−	0.722055i
$227$	−0.538536	+	6.49917i	−0.0357439	+	0.431365i	0.955093	+	0.296305i	$0.0957544\pi$
$227$	−0.538536	+	6.49917i	−0.0357439	+	0.431365i	−0.990837	+	0.135060i	$0.956877\pi$
$228$	7.82759	+	11.8664i	0.518395	+	0.785872i
$229$	0.389734	+	4.70339i	0.0257544	+	0.310809i	0.997270	+	0.0738353i	$0.0235239\pi$
$229$	0.389734	+	4.70339i	0.0257544	+	0.310809i	−0.971516	+	0.236974i	$0.923845\pi$
$230$	21.5010	+	2.37973i	1.41773	+	0.156915i
$231$	−16.2152	+	43.3089i	−1.06688	+	2.84952i
$232$	−5.19774	+	0.575286i	−0.341249	+	0.0377694i
$233$	21.5709	+	6.09967i	1.41316	+	0.399603i	0.891294	−	0.453426i	$-0.149798\pi$
$233$	21.5709	+	6.09967i	1.41316	+	0.399603i	0.521864	+	0.853029i	$0.325237\pi$
$234$	−1.64648	−	2.85179i	−0.107634	−	0.186427i
$235$	5.44411	−	0.908460i	0.355134	−	0.0592614i
$236$	−0.749205	+	2.95855i	−0.0487691	+	0.192585i
$237$	−1.56796	+	0.173542i	−0.101850	+	0.0112728i
$238$	−0.174426	−	0.892964i	−0.0113064	−	0.0578823i
$239$	0.910176	−	0.988715i	0.0588744	−	0.0639546i	−0.705591	−	0.708619i	$-0.749319\pi$
$239$	0.910176	−	0.988715i	0.0588744	−	0.0639546i	0.764466	+	0.644664i	$0.223003\pi$
$240$	−8.66125	+	4.68724i	−0.559081	+	0.302560i
$241$	−1.41698	+	10.2185i	−0.0912757	+	0.658232i	0.888609	+	0.458666i	$0.151673\pi$
$241$	−1.41698	+	10.2185i	−0.0912757	+	0.658232i	−0.979884	+	0.199566i	$0.936047\pi$
$242$	11.7330	+	5.53694i	0.754227	+	0.355928i
$243$	−25.8992	−	31.4477i	−1.66143	−	2.01737i
$244$	−7.90450	−	0.874870i	−0.506034	−	0.0560078i
$245$	2.09443	−	3.62766i	0.133808	−	0.231763i
$246$	0.614142	−	0.667137i	0.0391563	−	0.0425351i
$247$	−0.666868	−	1.75749i	−0.0424318	−	0.111826i
$248$	7.02294	+	7.62894i	0.445957	+	0.484438i
$249$	−8.73929	+	1.95852i	−0.553830	+	0.124116i
$250$	−2.46528	+	1.00131i	−0.155918	+	0.0633283i
$251$	−4.19903	+	1.18737i	−0.265040	+	0.0749463i	−0.402031	−	0.915626i	$-0.631696\pi$
$251$	−4.19903	+	1.18737i	−0.265040	+	0.0749463i	0.136991	+	0.990572i	$0.456257\pi$
$252$	15.8510	+	15.4201i	0.998521	+	0.971376i
$253$	−34.8625	+	3.85858i	−2.19178	+	0.242587i
$254$	6.41673	−	14.6287i	0.402621	−	0.917884i
$255$	−3.05177	−	0.509250i	−0.191109	−	0.0318905i
$256$	0.350638	+	0.936511i	0.0219148	+	0.0585320i
$257$	−4.37857	−	0.241572i	−0.273128	−	0.0150689i	−0.0819937	−	0.996633i	$-0.526129\pi$
$257$	−4.37857	−	0.241572i	−0.273128	−	0.0150689i	−0.191134	+	0.981564i	$0.561216\pi$
$258$	11.9726	+	13.0058i	0.745384	+	0.809703i
$259$	29.1412	+	15.7704i	1.81075	+	0.979927i
$260$	1.25311	−	0.354346i	0.0777147	−	0.0219756i
$261$	39.8714	−	2.19977i	2.46798	−	0.136162i
$262$	−3.99418	−	6.91812i	−0.246761	−	0.427403i
$263$	5.44034	−	4.73800i	0.335466	−	0.292157i	−0.472567	−	0.881295i	$-0.656673\pi$
$263$	5.44034	−	4.73800i	0.335466	−	0.292157i	0.808033	+	0.589137i	$0.200532\pi$
$264$	12.0418	−	10.4872i	0.741119	−	0.645441i
$265$	−9.12681	+	1.52300i	−0.560655	+	0.0935568i
$266$	7.52094	+	10.1386i	0.461138	+	0.621638i
$267$	−34.7783	−	5.80347i	−2.12840	−	0.355166i
$268$	10.8544	−	6.67217i	0.663037	−	0.407567i
$269$	−6.12680	−	2.89131i	−0.373558	−	0.176286i	0.230796	−	0.973002i	$-0.425867\pi$
$269$	−6.12680	−	2.89131i	−0.373558	−	0.176286i	−0.604354	+	0.796716i	$0.706569\pi$
$270$	41.2891	−	19.4848i	2.51278	−	1.18581i
$271$	−3.03101	−	9.69068i	−0.184121	−	0.588667i	−0.999946	−	0.0103685i	$-0.996700\pi$
$271$	−3.03101	−	9.69068i	−0.184121	−	0.588667i	0.815826	−	0.578298i	$-0.196283\pi$
$272$	−0.0937829	+	0.299841i	−0.00568642	+	0.0181805i
$273$	−2.22775	−	3.40982i	−0.134829	−	0.206372i
$274$	0.316223	−	3.81624i	0.0191037	−	0.230548i
$275$	−16.5729	+	11.4914i	−0.999384	+	0.692958i
$276$	−6.97408	+	22.2974i	−0.419790	+	1.34214i
$277$	17.0988	−	13.3085i	1.02737	−	0.799630i	0.0474154	−	0.998875i	$-0.484902\pi$
$277$	17.0988	−	13.3085i	1.02737	−	0.799630i	0.979950	+	0.199245i	$0.0638489\pi$
$278$	−0.711002	−	8.58052i	−0.0426431	−	0.514625i
$279$	−50.3362	−	61.1199i	−3.01355	−	3.65915i
$280$	−7.45034	+	4.57970i	−0.445243	+	0.273690i
$281$	−8.99976	−	24.0373i	−0.536880	−	1.43394i	−0.870939	−	0.491392i	$-0.836488\pi$
$281$	−8.99976	−	24.0373i	−0.536880	−	1.43394i	0.334058	−	0.942552i	$-0.391582\pi$
$282$	−0.164247	+	5.95859i	−0.00978079	+	0.354829i
$283$	0.235209	−	0.0955338i	0.0139817	−	0.00567890i	−0.369308	−	0.929307i	$-0.620405\pi$
$283$	0.235209	−	0.0955338i	0.0139817	−	0.00567890i	0.383290	+	0.923628i	$0.374791\pi$
$284$	−6.54933	−	3.54432i	−0.388631	−	0.210317i
$285$	41.2558	−	11.8627i	2.44378	−	0.702687i
$286$	−1.85702	+	1.00497i	−0.109808	+	0.0594250i
$287$	0.511903	−	0.621570i	0.0302167	−	0.0366901i
$288$	−2.27944	−	7.28778i	−0.134317	−	0.429437i
$289$	13.8891	−	9.63050i	0.817007	−	0.566500i
$290$	−3.02743	+	15.4988i	−0.177777	+	0.910120i
$291$	39.4960	+	34.3971i	2.31529	+	2.01639i
$292$	2.22564			0.130246
$293$	20.9424			1.22347			0.611735	−	0.791063i	$-0.290472\pi$
$293$	20.9424			1.22347			0.611735	+	0.791063i	$0.290472\pi$
$294$	3.41151	+	2.97109i	0.198963	+	0.173277i
$295$	7.85133	+	4.82620i	0.457122	+	0.280992i
$296$	−6.25783	−	9.57832i	−0.363729	−	0.556728i
$297$	−58.4183	+	45.4688i	−3.38978	+	2.63837i
$298$	0.196956	−	0.389196i	0.0114094	−	0.0225455i
$299$	1.54464	−	2.67539i	0.0893287	−	0.154722i
$300$	2.57519	+	13.1835i	0.148679	+	0.761152i
$301$	11.2519	+	10.9461i	0.648551	+	0.630920i
$302$	17.8575	−	0.985228i	1.02759	−	0.0566935i
$303$	−15.9471	−	36.3557i	−0.916135	−	2.08858i
$304$	−0.617743	−	4.31490i	−0.0354300	−	0.247477i
$305$	−9.64684	+	21.9926i	−0.552377	+	1.25929i
$306$	0.841160	−	2.24664i	0.0480859	−	0.128432i
$307$	−3.04798	+	5.27926i	−0.173957	+	0.301303i	−0.939800	−	0.341725i	$-0.888989\pi$
$307$	−3.04798	+	5.27926i	−0.173957	+	0.301303i	0.765843	+	0.643028i	$0.222322\pi$
$308$	10.1640	−	9.88767i	0.579147	−	0.563403i
$309$	−3.69752	+	4.48964i	−0.210344	+	0.255407i
$310$	28.3178	−	13.3635i	1.60834	−	0.758995i
$311$	−1.02194	+	1.56419i	−0.0579487	+	0.0886971i	−0.864965	−	0.501832i	$-0.832660\pi$
$311$	−1.02194	+	1.56419i	−0.0579487	+	0.0886971i	0.807017	+	0.590529i	$0.201081\pi$
$312$	0.116140	+	1.40161i	0.00657516	+	0.0793503i
$313$	−7.19982	+	14.2272i	−0.406958	+	0.804171i	−0.999999	−	0.00100083i	$-0.999681\pi$
$313$	−7.19982	+	14.2272i	−0.406958	+	0.804171i	0.593041	+	0.805172i	$0.297927\pi$
$314$	12.5252	−	12.1847i	0.706840	−	0.687625i
$315$	58.7304	−	31.7833i	3.30908	−	1.79079i
$316$	0.457508	+	0.157063i	0.0257368	+	0.00883547i
$317$	12.4667	+	0.687809i	0.700201	+	0.0386312i	0.401691	−	0.915775i	$-0.368423\pi$
$317$	12.4667	+	0.687809i	0.700201	+	0.0386312i	0.298510	+	0.954406i	$0.403510\pi$
$318$	0.275354	−	9.98932i	0.0154411	−	0.560173i
$319$	−0.705534	−	25.5955i	−0.0395023	−	1.43307i
$320$	3.01516	−	0.166351i	0.168552	−	0.00929929i
$321$	−47.9660	−	13.5635i	−2.67720	−	0.757040i
$322$	−5.09291	+	20.1114i	−0.283817	+	1.12077i
$323$	0.679470	−	1.18895i	0.0378067	−	0.0661552i
$324$	6.48076	+	25.5919i	0.360042	+	1.42177i
$325$	0.0489429	−	1.77556i	0.00271486	−	0.0984901i
$326$	1.34638	−	0.301732i	0.0745693	−	0.0167114i
$327$	−5.41834	+	7.37192i	−0.299635	+	0.407668i
$328$	−0.257605	+	0.104630i	−0.0142239	+	0.00577724i
$329$	0.145854	+	5.29131i	0.00804119	+	0.291719i
$330$	−19.3697	−	44.1586i	−1.06627	−	2.43085i
$331$	−21.5858	+	3.60204i	−1.18646	+	0.197986i	−0.724730	−	0.689033i	$-0.758036\pi$
$331$	−21.5858	+	3.60204i	−1.18646	+	0.197986i	−0.461734	+	0.887019i	$0.652772\pi$
$332$	2.67971	+	0.600538i	0.147068	+	0.0329588i
$333$	43.6827	+	75.6607i	2.39380	+	4.14618i
$334$	−7.21987	−	16.4596i	−0.395054	−	0.900632i
$335$	−9.44501	−	37.2975i	−0.516036	−	2.03778i
$336$	−3.31172	−	8.84521i	−0.180669	−	0.482546i
$337$	4.08082	+	8.06392i	0.222296	+	0.439270i	0.975948	−	0.218005i	$-0.0699548\pi$
$337$	4.08082	+	8.06392i	0.222296	+	0.439270i	−0.753651	+	0.657274i	$0.771709\pi$
$338$	−1.76005	+	12.6926i	−0.0957342	+	0.690385i
$339$	22.9304	−	27.8429i	1.24541	−	1.51222i
$340$	0.779618	+	0.540575i	0.0422807	+	0.0293168i
$341$	−40.0657	+	31.1844i	−2.16968	+	1.68873i
$342$	2.89483	+	33.1582i	0.156535	+	1.79299i
$343$	−12.8276	−	9.98410i	−0.692624	−	0.539091i
$344$	−1.61807	−	5.17327i	−0.0872407	−	0.278924i
$345$	57.9756	+	40.1994i	3.12130	+	2.16426i
$346$	−10.5844	+	20.9153i	−0.569019	+	1.12441i
$347$	−4.24411	−	0.469738i	−0.227836	−	0.0252169i	−0.00463472	−	0.999989i	$-0.501475\pi$
$347$	−4.24411	−	0.469738i	−0.227836	−	0.0252169i	−0.223201	+	0.974772i	$0.571651\pi$
$348$	−15.8012	−	6.41788i	−0.847032	−	0.344035i
$349$	−2.63325	−	0.439411i	−0.140954	−	0.0235211i	0.0936967	−	0.995601i	$-0.470132\pi$
$349$	−2.63325	−	0.439411i	−0.140954	−	0.0235211i	−0.234651	+	0.972080i	$0.575395\pi$
$350$	2.92825	+	11.5634i	0.156522	+	0.618090i
$351$	−0.179655	−	6.51756i	−0.00958929	−	0.347881i
$352$	−4.71156	+	1.33230i	−0.251127	+	0.0710120i
$353$	1.73867	−	0.596885i	0.0925399	−	0.0317690i	−0.278041	−	0.960569i	$-0.589685\pi$
$353$	1.73867	−	0.596885i	0.0925399	−	0.0317690i	0.370581	+	0.928800i	$0.379159\pi$
$354$	−6.74112	+	7.32281i	−0.358287	+	0.389203i
$355$	−16.1187	+	15.6805i	−0.855494	+	0.832237i
$356$	8.88461	+	6.16045i	0.470884	+	0.326503i
$357$	0.885766	−	2.83195i	0.0468797	−	0.149883i
$358$	1.62126	+	11.6917i	0.0856865	+	0.617926i
$359$	3.63647	+	4.94760i	0.191926	+	0.261124i	0.891080	−	0.453847i	$-0.149949\pi$
$359$	3.63647	+	4.94760i	0.191926	+	0.261124i	−0.699154	+	0.714971i	$0.746440\pi$
$360$	−23.0586			−1.21529
$361$	−1.40196	+	18.9482i	−0.0737874	+	0.997274i
$362$	−10.5379			−0.553858
$363$	25.0583	+	34.0931i	1.31522	+	1.78942i
$364$	0.171542	+	1.23707i	0.00899126	+	0.0648403i
$365$	2.00628	−	6.41444i	0.105014	−	0.335747i
$366$	−21.3138	−	14.7787i	−1.11409	−	0.772493i
$367$	9.43194	−	9.17554i	0.492343	−	0.478959i	−0.408712	−	0.912664i	$-0.634022\pi$
$367$	9.43194	−	9.17554i	0.492343	−	0.478959i	0.901055	+	0.433704i	$0.142794\pi$
$368$	4.85179	−	5.27045i	0.252917	−	0.274741i
$369$	2.00808	−	0.689376i	0.104537	−	0.0358875i
$370$	−33.2463	+	9.40116i	−1.72839	+	0.488743i
$371$	−0.244518	−	8.87065i	−0.0126947	−	0.460541i
$372$	8.30163	+	32.7824i	0.430419	+	1.69969i
$373$	9.23641	+	1.54128i	0.478243	+	0.0798047i	0.398806	−	0.917035i	$-0.369425\pi$
$373$	9.23641	+	1.54128i	0.478243	+	0.0798047i	0.0794370	+	0.996840i	$0.474688\pi$
$374$	−1.42518	−	0.578858i	−0.0736942	−	0.0299320i
$375$	−8.62515	−	0.954632i	−0.445401	−	0.0492970i
$376$	0.825297	−	1.63083i	0.0425615	−	0.0841037i
$377$	1.85326	+	1.28502i	0.0954479	+	0.0661821i
$378$	13.0707	+	41.7894i	0.672285	+	2.14941i
$379$	12.9212	+	10.0569i	0.663715	+	0.516590i	0.889119	−	0.457675i	$-0.151318\pi$
$379$	12.9212	+	10.0569i	0.663715	+	0.516590i	−0.225404	+	0.974265i	$0.572370\pi$
$380$	−12.9927	−	2.10925i	−0.666509	−	0.108202i
$381$	41.1111	−	31.9981i	2.10619	−	1.63931i
$382$	−11.0998	−	7.69643i	−0.567915	−	0.393783i
$383$	9.47425	−	11.5039i	0.484112	−	0.587824i	−0.471717	−	0.881750i	$-0.656365\pi$
$383$	9.47425	−	11.5039i	0.484112	−	0.587824i	0.955828	+	0.293926i	$0.0949619\pi$
$384$	−0.447948	+	3.23037i	−0.0228593	+	0.164849i
$385$	−19.3346	−	38.2063i	−0.985385	−	1.94717i
$386$	−7.31594	−	19.5400i	−0.372372	−	0.994561i
$387$	10.1606	+	40.1235i	0.516494	+	2.03959i
$388$	−6.45103	−	14.7069i	−0.327501	−	0.746628i
$389$	3.31852	+	5.74785i	0.168256	+	0.291428i	0.937807	−	0.347158i	$-0.112853\pi$
$389$	3.31852	+	5.74785i	0.168256	+	0.291428i	−0.769551	+	0.638586i	$0.779520\pi$
$390$	4.14420	+	0.928738i	0.209850	+	0.0470285i
$391$	2.21986	−	0.370430i	0.112263	−	0.0187334i
$392$	−0.557215	−	1.27032i	−0.0281436	−	0.0641610i
$393$	−0.717853	−	26.0424i	−0.0362109	−	1.31366i
$394$	18.3803	−	7.46541i	0.925984	−	0.376102i
$395$	0.865079	−	1.17698i	0.0435269	−	0.0592204i
$396$	36.4830	−	8.17604i	1.83334	−	0.410861i
$397$	0.220408	−	7.99599i	0.0110620	−	0.401307i	−0.973744	−	0.227647i	$-0.926897\pi$
$397$	0.220408	−	7.99599i	0.0110620	−	0.401307i	0.984806	−	0.173660i	$-0.0555594\pi$
$398$	−3.27529	−	12.9338i	−0.164175	−	0.648314i
$399$	5.83449	+	40.7536i	0.292090	+	2.04023i
$400$	1.01112	−	3.99281i	0.0505558	−	0.199640i
$401$	−28.5477	−	8.07251i	−1.42560	−	0.403122i	−0.530008	−	0.847993i	$-0.677811\pi$
$401$	−28.5477	−	8.07251i	−1.42560	−	0.403122i	−0.895595	+	0.444871i	$0.853250\pi$
$402$	41.4892	−	2.28902i	2.06929	−	0.114166i
$403$	−0.123215	−	4.47001i	−0.00613778	−	0.222667i
$404$	−0.335418	+	12.1683i	−0.0166877	+	0.605397i
$405$	79.5994	+	4.39162i	3.95533	+	0.218221i
$406$	−14.3243	−	4.91754i	−0.710903	−	0.244053i
$407$	49.2685	−	26.6628i	2.44215	−	1.32162i
$408$	−0.734401	+	0.714436i	−0.0363582	+	0.0353698i
$409$	2.94560	−	5.82067i	0.145651	−	0.287813i	−0.807748	−	0.589529i	$-0.799314\pi$
$409$	2.94560	−	5.82067i	0.145651	−	0.287813i	0.953398	+	0.301715i	$0.0975592\pi$
$410$	0.0693351	+	0.836750i	0.00342422	+	0.0413242i
$411$	6.83056	−	10.4549i	0.336927	−	0.515704i
$412$	1.61285	−	0.761122i	0.0794593	−	0.0374978i
$413$	−5.61889	+	6.82265i	−0.276488	+	0.335721i
$414$	−39.2087	+	38.1428i	−1.92700	+	1.87462i
$415$	4.14638	−	7.18174i	0.203538	−	0.352538i
$416$	0.151211	−	0.403866i	0.00741371	−	0.0198011i
$417$	11.2794	−	25.7143i	0.552352	−	1.25924i
$418$	21.3047	−	1.26967i	1.04205	−	0.0621014i
$419$	−7.87522	−	17.9537i	−0.384730	−	0.877096i	−0.996303	−	0.0859078i	$-0.972621\pi$
$419$	−7.87522	−	17.9537i	−0.384730	−	0.877096i	0.611573	−	0.791188i	$-0.290537\pi$
$420$	−28.4777	+	1.57116i	−1.38957	+	0.0766647i
$421$	−23.7165	−	23.0717i	−1.15587	−	1.12445i	−0.990400	−	0.138232i	$-0.955858\pi$
$421$	−23.7165	−	23.0717i	−1.15587	−	1.12445i	−0.165469	−	0.986215i	$-0.552914\pi$
$422$	−0.148107	−	0.758223i	−0.00720971	−	0.0369097i
$423$	−6.97836	+	12.0869i	−0.339299	+	0.587684i
$424$	−1.38358	+	2.73402i	−0.0671924	+	0.132776i
$425$	1.02114	−	0.794789i	0.0495328	−	0.0385529i
$426$	−13.2834	−	20.3317i	−0.643581	−	0.985074i
$427$	−19.6211	−	12.0611i	−0.949534	−	0.583676i
$428$	11.5261	+	10.0381i	0.557135	+	0.485209i
$429$	−6.88622			−0.332470
$430$	−16.3683			−0.789348
$431$	22.3821	+	19.4926i	1.07811	+	0.938924i	0.998323	−	0.0578880i	$-0.0184366\pi$
$431$	22.3821	+	19.4926i	1.07811	+	0.938924i	0.0797839	+	0.996812i	$0.474577\pi$
$432$	2.89849	−	14.8387i	0.139454	−	0.713925i
$433$	−32.8995	+	22.8120i	−1.58105	+	1.09627i	−0.634873	+	0.772617i	$0.718947\pi$
$433$	−32.8995	+	22.8120i	−1.58105	+	1.09627i	−0.946175	+	0.323657i	$0.895088\pi$
$434$	8.96443	+	28.6609i	0.430307	+	1.37577i
$435$	−32.7405	+	39.7546i	−1.56979	+	1.90609i
$436$	2.46722	−	1.33519i	0.118158	−	0.0639440i
$437$	−25.5817	+	17.9055i	−1.22374	+	0.856537i
$438$	6.38361	+	3.45464i	0.305021	+	0.165069i
$439$	−32.8354	+	13.3366i	−1.56715	+	0.636521i	−0.984370	−	0.176110i	$-0.943648\pi$
$439$	−32.8354	+	13.3366i	−1.56715	+	0.636521i	−0.582778	+	0.812631i	$0.698034\pi$
$440$	−0.407407	+	14.7800i	−0.0194224	+	0.704608i
$441$	3.71404	+	9.91976i	0.176859	+	0.472370i
$442$	0.115420	−	0.0709483i	0.00548996	−	0.00337466i
$443$	−19.7721	−	24.0079i	−0.939399	−	1.14065i	−0.989878	−	0.141924i	$-0.954671\pi$
$443$	−19.7721	−	24.0079i	−0.939399	−	1.14065i	0.0504785	−	0.998725i	$-0.483925\pi$
$444$	−3.08132	−	37.1860i	−0.146233	−	1.76477i
$445$	25.7637	−	20.0527i	1.22132	−	0.950589i
$446$	−2.32414	+	7.43069i	−0.110051	+	0.351853i
$447$	1.16902	−	0.810580i	0.0552927	−	0.0383391i
$448$	−0.239155	+	2.88617i	−0.0112990	+	0.136359i
$449$	−18.9461	−	28.9992i	−0.894122	−	1.36856i	−0.929359	−	0.369176i	$-0.879640\pi$
$449$	−18.9461	−	28.9992i	−0.894122	−	1.36856i	0.0352378	−	0.999379i	$-0.488781\pi$
$450$	−9.38866	+	30.0172i	−0.442586	+	1.41503i
$451$	−0.406394	−	1.29931i	−0.0191363	−	0.0611823i
$452$	−10.0022	+	4.72016i	−0.470464	+	0.222017i
$453$	52.7484	+	24.8926i	2.47834	+	1.16956i
$454$	5.55574	−	3.41510i	0.260744	−	0.160279i
$455$	3.71995	+	0.620750i	0.174394	+	0.0291012i
$456$	4.92577	−	13.3349i	0.230670	−	0.624464i
$457$	4.76059	−	0.794402i	0.222691	−	0.0371605i	−0.0521970	−	0.998637i	$-0.516622\pi$
$457$	4.76059	−	0.794402i	0.222691	−	0.0371605i	0.274888	+	0.961476i	$0.411359\pi$
$458$	3.55902	−	3.09955i	0.166302	−	0.144832i
$459$	3.58192	−	3.11950i	0.167190	−	0.145606i
$460$	−10.8161	−	18.7341i	−0.504306	−	0.873483i
$461$	20.6240	−	1.13786i	0.960555	−	0.0529953i	0.431981	−	0.901883i	$-0.357815\pi$
$461$	20.6240	−	1.13786i	0.960555	−	0.0529953i	0.528574	+	0.848887i	$0.322727\pi$
$462$	44.5000	−	12.5834i	2.07033	−	0.585433i
$463$	−30.7388	−	16.6350i	−1.42855	−	0.773094i	−0.436594	−	0.899658i	$-0.643816\pi$
$463$	−30.7388	−	16.6350i	−1.42855	−	0.773094i	−0.991958	+	0.126564i	$0.959605\pi$
$464$	3.54183	+	3.84746i	0.164425	+	0.178614i
$465$	101.964	+	5.62552i	4.72847	+	0.260877i
$466$	−7.86015	−	20.9935i	−0.364115	−	0.972507i
$467$	−0.138461	−	0.0231050i	−0.00640721	−	0.00106917i	0.161390	−	0.986891i	$-0.448402\pi$
$467$	−0.138461	−	0.0231050i	−0.00640721	−	0.00106917i	−0.167797	+	0.985822i	$0.553665\pi$
$468$	−1.32277	+	3.01561i	−0.0611449	+	0.139396i
$469$	36.6750	−	4.05919i	1.69349	−	0.187436i
$470$	−3.95620	−	3.84865i	−0.182486	−	0.177525i
$471$	54.8381	−	15.5067i	2.52681	−	0.714513i
$472$	2.82760	−	1.14847i	0.130151	−	0.0528627i
$473$	25.8977	−	5.80381i	1.19078	−	0.266859i
$474$	1.06844	+	1.16063i	0.0490749	+	0.0533096i
$475$	−8.03595	+	16.0548i	−0.368714	+	0.736644i
$476$	−0.616218	+	0.669391i	−0.0282443	+	0.0306815i
$477$	11.6989	−	20.2631i	0.535657	−	0.927784i
$478$	−1.33571	−	0.147836i	−0.0610940	−	0.00676188i
$479$	12.9118	+	15.6779i	0.589956	+	0.716344i	0.978767	−	0.204974i	$-0.0657109\pi$
$479$	12.9118	+	15.6779i	0.589956	+	0.716344i	−0.388812	+	0.921317i	$0.627114\pi$
$480$	8.90631	+	4.20299i	0.406516	+	0.191839i
$481$	−0.677706	+	4.88726i	−0.0309007	+	0.222840i
$482$	9.07291	−	4.91001i	0.413260	−	0.223645i
$483$	−45.8245	+	49.7786i	−2.08509	+	2.26501i
$484$	−2.48723	−	12.7332i	−0.113056	−	0.578783i
$485$	−48.2012	+	5.33491i	−2.18870	+	0.242246i
$486$	−10.0010	+	39.4931i	−0.453655	+	1.79144i
$487$	24.0307	−	4.01002i	1.08894	−	0.181711i	0.407222	−	0.913329i	$-0.366498\pi$
$487$	24.0307	−	4.01002i	1.08894	−	0.181711i	0.681715	+	0.731618i	$0.261234\pi$
$488$	3.97639	+	6.88730i	0.180003	+	0.311773i
$489$	4.33006	+	1.22442i	0.195812	+	0.0553704i
$490$	−4.16344	+	0.460809i	−0.188085	+	0.0208172i
$491$	9.88898	−	26.4123i	0.446283	−	1.19197i	−0.499254	−	0.866456i	$-0.666392\pi$
$491$	9.88898	−	26.4123i	0.446283	−	1.19197i	0.945537	−	0.325514i	$-0.105537\pi$
$492$	−0.901272	−	0.0997528i	−0.0406325	−	0.00449720i
$493$	0.135671	+	1.63731i	0.00611033	+	0.0737407i
$494$	−1.02118	+	1.57818i	−0.0459450	+	0.0710059i
$495$	9.32337	−	112.516i	0.419054	−	5.05723i
$496$	1.98791	−	10.1770i	0.0892596	−	0.456959i
$497$	−12.7725	−	17.3776i	−0.572924	−	0.779491i
$498$	6.75383	+	5.88191i	0.302646	+	0.263575i
$499$	−2.01584	−	2.74265i	−0.0902415	−	0.122778i	0.758302	−	0.651903i	$-0.226029\pi$
$499$	−2.01584	−	2.74265i	−0.0902415	−	0.122778i	−0.848544	+	0.529125i	$0.822520\pi$
$500$	2.26684	+	1.39342i	0.101376	+	0.0623158i
$501$	4.84052	−	58.4164i	0.216258	−	2.60985i
$502$	3.44356	+	2.68023i	0.153693	+	0.119624i
$503$	−18.7598	+	8.85295i	−0.836457	+	0.394733i	−0.796626	−	0.604473i	$-0.793384\pi$
$503$	−18.7598	+	8.85295i	−0.836457	+	0.394733i	−0.0398311	+	0.999206i	$0.512682\pi$
$504$	3.03745	−	21.9045i	0.135299	−	0.975706i
$505$	34.7675	+	11.9357i	1.54713	+	0.531131i
$506$	23.7559	+	25.8058i	1.05608	+	1.14721i
$507$	−24.7496	+	33.6730i	−1.09917	+	1.49547i
$508$	−15.5875	+	3.49324i	−0.691583	+	0.154987i
$509$	8.54438	+	0.471406i	0.378723	+	0.0208947i	0.243449	−	0.969914i	$-0.421721\pi$
$509$	8.54438	+	0.471406i	0.378723	+	0.0208947i	0.135273	+	0.990808i	$0.456809\pi$
$510$	1.39703	+	2.76060i	0.0618615	+	0.122242i
$511$	5.82912	+	2.75083i	0.257865	+	0.121690i
$512$	0.546948	−	0.837166i	0.0241719	−	0.0369979i
$513$	−26.2064	+	60.4680i	−1.15704	+	2.66973i
$514$	2.39849	+	3.67117i	0.105793	+	0.161928i
$515$	−0.739713	−	5.33443i	−0.0325957	−	0.235063i
$516$	3.38896	−	17.3496i	0.149191	−	0.763773i
$517$	7.62409	+	4.68651i	0.335307	+	0.206113i
$518$	−4.55119	−	32.8208i	−0.199968	−	1.44206i
$519$	−62.8228	+	43.5604i	−2.75762	+	1.91209i
$520$	−1.02766	−	0.799858i	−0.0450657	−	0.0350761i
$521$	19.9397	−	30.5200i	0.873573	−	1.33710i	−0.0670846	−	0.997747i	$-0.521370\pi$
$521$	19.9397	−	30.5200i	0.873573	−	1.33710i	0.940658	−	0.339356i	$-0.110209\pi$
$522$	−25.3857	−	30.8242i	−1.11110	−	1.34914i
$523$	30.1117	+	12.2303i	1.31669	+	0.534794i	0.923124	−	0.384502i	$-0.125627\pi$
$523$	30.1117	+	12.2303i	1.31669	+	0.534794i	0.393567	+	0.919296i	$0.371241\pi$
$524$	−3.20889	+	7.31552i	−0.140181	+	0.319580i
$525$	−9.54985	+	37.7115i	−0.416790	+	1.64586i
$526$	−7.03967	−	1.57763i	−0.306944	−	0.0687878i
$527$	2.45663	−	2.13948i	0.107013	−	0.0931973i
$528$	−15.5817	−	3.49195i	−0.678109	−	0.151968i
$529$	−27.2490	−	7.70529i	−1.18474	−	0.335013i
$530$	6.63239	+	6.45209i	0.288093	+	0.280261i
$531$	−22.0417	+	7.56692i	−0.956528	+	0.328376i
$532$	3.71518	−	12.0646i	0.161073	−	0.523065i
$533$	0.113408	+	0.0389330i	0.00491224	+	0.00168637i
$534$	15.9207	+	31.4601i	0.688956	+	1.36141i
$535$	39.3204	−	24.1702i	1.69997	−	1.04497i
$536$	−11.8045	−	4.79459i	−0.509879	−	0.207095i
$537$	−13.4977	+	36.0508i	−0.582470	+	1.55571i
$538$	1.29879	+	6.64910i	0.0559950	+	0.286663i
$539$	6.42395	−	2.20534i	0.276699	−	0.0949909i
$540$	−40.1530	−	21.7297i	−1.72791	−	0.935099i
$541$	1.49409	−	2.03278i	0.0642360	−	0.0873962i	−0.772461	−	0.635062i	$-0.780975\pi$
$541$	1.49409	−	2.03278i	0.0642360	−	0.0873962i	0.836697	+	0.547666i	$0.184483\pi$
$542$	−6.01334	+	8.18144i	−0.258295	+	0.351423i
$543$	−30.2248	−	16.3568i	−1.29707	−	0.701939i
$544$	0.297143	−	0.102009i	0.0127399	−	0.00437361i
$545$	−1.62405	−	8.31425i	−0.0695668	−	0.356143i
$546$	−1.42816	+	3.81445i	−0.0611197	+	0.163244i
$547$	−9.18769	−	3.73172i	−0.392837	−	0.159557i	0.171337	−	0.985213i	$-0.445191\pi$
$547$	−9.18769	−	3.73172i	−0.392837	−	0.159557i	−0.564174	+	0.825656i	$0.690805\pi$
$548$	−3.26227	+	2.00531i	−0.139357	+	0.0856627i
$549$	−27.4202	−	54.1838i	−1.17027	−	2.31251i
$550$	19.0744	+	6.54826i	0.813337	+	0.279219i
$551$	−11.4843	−	19.6904i	−0.489249	−	0.838840i
$552$	22.0967	−	7.58582i	0.940499	−	0.322874i
$553$	1.00412	+	0.976825i	0.0426996	+	0.0415388i
$554$	−20.8500	−	5.89582i	−0.885832	−	0.250490i
$555$	−109.950	−	24.6403i	−4.66711	−	1.04592i
$556$	−6.49280	+	5.65459i	−0.275356	+	0.239808i
$557$	−2.83529	−	0.635403i	−0.120135	−	0.0269229i	0.158199	−	0.987407i	$-0.449431\pi$
$557$	−2.83529	−	0.635403i	−0.120135	−	0.0269229i	−0.278334	+	0.960484i	$0.589782\pi$
$558$	−19.4374	+	76.7565i	−0.822850	+	3.24936i
$559$	−0.938974	+	2.14065i	−0.0397144	+	0.0905396i
$560$	8.10252	+	3.29096i	0.342394	+	0.139068i
$561$	−3.18921	−	3.87244i	−0.134649	−	0.163495i
$562$	−14.0384	+	21.4874i	−0.592175	+	0.906392i
$563$	−12.5839	−	9.79447i	−0.530350	−	0.412788i	0.313322	−	0.949647i	$-0.398558\pi$
$563$	−12.5839	−	9.79447i	−0.530350	−	0.412788i	−0.843672	+	0.536859i	$0.819611\pi$
$564$	4.89850	−	3.39654i	0.206264	−	0.143020i
$565$	4.58739	+	33.0819i	0.192993	+	1.39176i
$566$	−0.216277	−	0.132945i	−0.00909081	−	0.00558810i
$567$	−14.6573	+	75.0371i	−0.615548	+	3.15126i
$568$	1.02285	+	7.37629i	0.0429180	+	0.309502i
$569$	−11.2217	−	17.1761i	−0.470439	−	0.720060i	0.520576	−	0.853816i	$-0.325717\pi$
$569$	−11.2217	−	17.1761i	−0.470439	−	0.720060i	−0.991014	+	0.133755i	$0.957296\pi$
$570$	−33.9917	−	26.2169i	−1.42376	−	1.09811i
$571$	−2.54810	+	3.90015i	−0.106635	+	0.163216i	−0.886497	−	0.462735i	$-0.846868\pi$
$571$	−2.54810	+	3.90015i	−0.106635	+	0.163216i	0.779862	+	0.625951i	$0.215289\pi$
$572$	1.90956	+	0.901143i	0.0798427	+	0.0376787i
$573$	−19.8902	−	39.3040i	−0.830924	−	1.64195i
$574$	−0.804006	−	0.0443583i	−0.0335586	−	0.00185148i
$575$	−28.7917	+	6.45237i	−1.20070	+	0.269082i
$576$	−4.52227	+	6.15277i	−0.188428	+	0.256366i
$577$	9.29128	+	10.0930i	0.386801	+	0.420178i	0.898491	−	0.438992i	$-0.144665\pi$
$577$	9.29128	+	10.0930i	0.386801	+	0.420178i	−0.511690	+	0.859170i	$0.670980\pi$
$578$	−15.9855	−	5.48784i	−0.664911	−	0.228264i
$579$	9.34630	−	67.4006i	0.388419	−	2.80107i
$580$	14.2813	−	6.73952i	0.593000	−	0.279843i
$581$	6.27612	+	4.88490i	0.260377	+	0.202660i
$582$	4.32505	−	52.1956i	0.179279	−	2.16358i
$583$	−12.7815	−	7.85674i	−0.529354	−	0.325393i
$584$	−1.31811	−	1.79335i	−0.0545436	−	0.0742092i
$585$	7.49875	+	6.53067i	0.310035	+	0.270010i
$586$	−12.4028	−	16.8747i	−0.512357	−	0.697086i
$587$	0.880888	−	4.50965i	0.0363581	−	0.186133i	−0.958850	−	0.283913i	$-0.908367\pi$
$587$	0.880888	−	4.50965i	0.0363581	−	0.186133i	0.995208	+	0.0977801i	$0.0311742\pi$
$588$	0.373581	−	4.50846i	0.0154062	−	0.185926i
$589$	−17.9734	+	41.4715i	−0.740582	+	1.70880i
$590$	−0.761056	−	9.18458i	−0.0313322	−	0.378123i
$591$	64.3062	+	7.11741i	2.64520	+	0.292771i
$592$	−4.01177	+	10.7150i	−0.164883	+	0.440382i
$593$	−21.2877	+	2.35612i	−0.874181	+	0.0967543i	−0.535891	−	0.844287i	$-0.680024\pi$
$593$	−21.2877	+	2.35612i	−0.874181	+	0.0967543i	−0.338290	+	0.941042i	$0.609849\pi$
$594$	71.2346	+	20.1432i	2.92279	+	0.826486i
$595$	1.37374	+	2.37939i	0.0563179	+	0.0975455i
$596$	−0.430244	+	0.0717951i	−0.0176235	+	0.00294084i
$597$	10.6816	−	42.1808i	0.437170	−	1.72635i
$598$	−3.07053	+	0.339846i	−0.125563	+	0.0138973i
$599$	−2.92628	−	14.9809i	−0.119564	−	0.612103i	−0.992295	−	0.123900i	$-0.960460\pi$
$599$	−2.92628	−	14.9809i	−0.119564	−	0.612103i	0.872730	−	0.488203i	$-0.162347\pi$
$600$	9.09772	−	9.88276i	0.371413	−	0.403462i
$601$	5.32030	−	2.87920i	0.217020	−	0.117445i	−0.363801	−	0.931477i	$-0.618521\pi$
$601$	5.32030	−	2.87920i	0.217020	−	0.117445i	0.580821	+	0.814032i	$0.302732\pi$
$602$	2.15615	−	15.5491i	0.0878783	−	0.633732i
$603$	87.9851	+	41.5212i	3.58303	+	1.69087i
$604$	−11.3697	−	13.8055i	−0.462628	−	0.561738i
$605$	−38.9400	−	4.30987i	−1.58313	−	0.175221i
$606$	−19.8497	+	34.3807i	−0.806339	+	1.39662i
$607$	−10.2393	+	11.1228i	−0.415599	+	0.451461i	−0.908039	−	0.418886i	$-0.862421\pi$
$607$	−10.2393	+	11.1228i	−0.415599	+	0.451461i	0.492440	+	0.870346i	$0.336105\pi$
$608$	−3.11095	+	3.05319i	−0.126166	+	0.123823i
$609$	−33.4521	−	36.3387i	−1.35555	−	1.47252i
$610$	23.4341	−	5.25170i	0.948817	−	0.212635i
$611$	−0.730276	+	0.296613i	−0.0295438	+	0.0119997i
$612$	−2.30843	+	0.652761i	−0.0933126	+	0.0263863i
$613$	23.0073	+	22.3818i	0.929255	+	0.903993i	0.995591	−	0.0938041i	$-0.0299027\pi$
$613$	23.0073	+	22.3818i	0.929255	+	0.903993i	−0.0663356	+	0.997797i	$0.521131\pi$
$614$	6.05896	−	0.670606i	0.244520	−	0.0270634i
$615$	−1.09993	+	2.50760i	−0.0443536	+	0.101116i
$616$	−13.9866	−	2.33395i	−0.563537	−	0.0940376i
$617$	−2.57106	−	6.86700i	−0.103507	−	0.276455i	0.874500	−	0.485025i	$-0.161189\pi$
$617$	−2.57106	−	6.86700i	−0.103507	−	0.276455i	−0.978008	+	0.208570i	$0.933119\pi$
$618$	5.80740	+	0.320403i	0.233608	+	0.0128885i
$619$	−7.44788	−	8.09056i	−0.299356	−	0.325187i	0.567855	−	0.823129i	$-0.307773\pi$
$619$	−7.44788	−	8.09056i	−0.299356	−	0.325187i	−0.867210	+	0.497942i	$0.834089\pi$
$620$	−27.5386	−	14.9032i	−1.10598	−	0.598525i
$621$	−104.221	+	29.4708i	−4.18224	+	1.18262i
$622$	1.86560	−	0.102928i	0.0748037	−	0.00412703i
$623$	15.6553	+	27.1158i	0.627217	+	1.08637i
$624$	1.06058	−	0.923663i	0.0424573	−	0.0369761i
$625$	21.5896	−	18.8024i	0.863583	−	0.752095i
$626$	15.7278	−	2.62451i	0.628609	−	0.104896i
$627$	63.0772	+	29.4275i	2.51906	+	1.17522i
$628$	−17.2359	−	2.87617i	−0.687788	−	0.114772i
$629$	−3.06220	+	1.88233i	−0.122098	+	0.0750533i
$630$	−60.3921	−	28.4997i	−2.40608	−	1.13546i
$631$	−36.2352	+	17.0998i	−1.44250	+	0.680733i	−0.978717	−	0.205215i	$-0.934211\pi$
$631$	−36.2352	+	17.0998i	−1.44250	+	0.680733i	−0.463785	+	0.885948i	$0.653509\pi$
$632$	−0.144397	−	0.461662i	−0.00574380	−	0.0183639i
$633$	0.752111	−	2.40463i	0.0298937	−	0.0955756i
$634$	−6.82902	−	10.4526i	−0.271215	−	0.415126i
$635$	−3.98344	+	48.0730i	−0.158078	+	1.90772i
$636$	−8.21212	+	5.69416i	−0.325632	+	0.225788i
$637$	−0.178573	+	0.570930i	−0.00707532	+	0.0226211i
$638$	−20.2061	+	15.7270i	−0.799967	+	0.622639i
$639$	−4.69578	−	56.6696i	−0.185762	−	2.24182i
$640$	−1.91972	−	2.33099i	−0.0758837	−	0.0921404i
$641$	25.5998	−	15.7361i	1.01113	−	0.621540i	0.0840741	−	0.996460i	$-0.473207\pi$
$641$	25.5998	−	15.7361i	1.01113	−	0.621540i	0.927057	+	0.374919i	$0.122330\pi$
$642$	17.4782	+	46.6821i	0.689808	+	1.84240i
$643$	0.997857	−	36.2004i	0.0393516	−	1.42760i	−0.680130	−	0.733092i	$-0.738077\pi$
$643$	0.997857	−	36.2004i	0.0393516	−	1.42760i	0.719481	−	0.694512i	$-0.244380\pi$
$644$	19.2213	−	7.80702i	0.757425	−	0.307640i
$645$	−46.9476	−	25.4068i	−1.84856	−	1.00039i
$646$	−1.36042	+	0.156647i	−0.0535252	+	0.00616319i
$647$	16.2632	−	8.80122i	0.639373	−	0.346012i	−0.123704	−	0.992319i	$-0.539477\pi$
$647$	16.2632	−	8.80122i	0.639373	−	0.346012i	0.763077	+	0.646308i	$0.223688\pi$
$648$	16.7830	−	20.3784i	0.659297	−	0.800540i
$649$	4.46077	+	14.2619i	0.175101	+	0.559828i
$650$	−1.45967	+	1.01211i	−0.0572528	+	0.0396982i
$651$	−18.7755	+	96.1200i	−0.735869	+	3.76724i
$652$	−1.04050	−	0.906173i	−0.0407492	−	0.0354885i
$653$	−18.9856			−0.742962			−0.371481	−	0.928441i	$-0.621150\pi$
$653$	−18.9856			−0.742962			−0.371481	+	0.928441i	$0.621150\pi$
$654$	9.14897			0.357753
$655$	18.1911	+	15.8427i	0.710787	+	0.619025i
$656$	0.236870	+	0.145604i	0.00924823	+	0.00568486i
$657$	9.29532	+	14.2276i	0.362645	+	0.555070i
$658$	4.17717	−	3.25122i	0.162843	−	0.126746i
$659$	−15.1999	+	30.0359i	−0.592106	+	1.17003i	0.377649	+	0.925949i	$0.376733\pi$
$659$	−15.1999	+	30.0359i	−0.592106	+	1.17003i	−0.969754	+	0.244084i	$0.921513\pi$
$660$	−24.1100	+	41.7597i	−0.938480	+	1.62549i
$661$	5.98226	+	30.6258i	0.232683	+	1.19121i	0.896408	+	0.443230i	$0.146168\pi$
$661$	5.98226	+	30.6258i	0.232683	+	1.19121i	−0.663725	+	0.747977i	$0.731025\pi$
$662$	15.6863	+	15.2598i	0.609664	+	0.593091i
$663$	0.441174	−	0.0243402i	0.0171338	−	0.000945296i
$664$	−1.10313	−	2.51488i	−0.0428097	−	0.0975963i
$665$	−31.4217	−	21.5828i	−1.21848	−	0.836945i
$666$	35.0943	−	80.0070i	1.35988	−	3.10021i
$667$	13.1356	−	35.0836i	0.508613	−	1.35844i
$668$	−8.98675	+	15.5655i	−0.347708	+	0.602247i
$669$	−18.2000	+	17.7052i	−0.703653	+	0.684525i
$670$	−24.4594	+	29.6994i	−0.944947	+	1.14739i
$671$	−35.2150	+	16.6184i	−1.35946	+	0.641544i
$672$	−5.16585	+	7.90692i	−0.199277	+	0.305016i
$673$	3.98125	+	48.0466i	0.153466	+	1.85206i	0.445038	+	0.895512i	$0.353190\pi$
$673$	3.98125	+	48.0466i	0.153466	+	1.85206i	−0.291572	+	0.956549i	$0.594178\pi$
$674$	4.08082	−	8.06392i	0.157187	−	0.310611i
$675$	−44.6363	+	43.4229i	−1.71805	+	1.67135i
$676$	11.2696	−	6.09880i	0.433446	−	0.234569i
$677$	23.5780	+	8.09435i	0.906178	+	0.311091i	0.738107	−	0.674684i	$-0.235720\pi$
$677$	23.5780	+	8.09435i	0.906178	+	0.311091i	0.168071	+	0.985775i	$0.446246\pi$
$678$	−36.0150	−	1.98701i	−1.38315	−	0.0763105i
$679$	1.28153	−	46.4916i	0.0491807	−	1.78418i
$680$	−0.0261407	−	0.948337i	−0.00100245	−	0.0363671i
$681$	21.2359	−	1.17162i	0.813763	−	0.0448966i
$682$	48.8556	+	13.8151i	1.87078	+	0.529006i
$683$	−5.13757	+	20.2878i	−0.196584	+	0.776292i	0.790010	+	0.613094i	$0.210076\pi$
$683$	−5.13757	+	20.2878i	−0.196584	+	0.776292i	−0.986593	+	0.163198i	$0.947819\pi$
$684$	25.0033	−	21.9700i	0.956024	−	0.840044i
$685$	2.83869	+	11.2097i	0.108461	+	0.428302i
$686$	−0.447899	+	16.2490i	−0.0171009	+	0.620388i
$687$	15.0191	−	3.36586i	0.573015	−	0.128416i
$688$	−3.21016	+	4.36758i	−0.122386	+	0.166513i
$689$	1.22428	−	0.497258i	0.0466412	−	0.0189440i
$690$	−1.94393	−	70.5222i	−0.0740042	−	2.68473i
$691$	9.18048	+	20.9294i	0.349242	+	0.796192i	0.999339	+	0.0363408i	$0.0115702\pi$
$691$	9.18048	+	20.9294i	0.349242	+	0.796192i	−0.650097	+	0.759851i	$0.725272\pi$
$692$	23.1212	−	3.85825i	0.878938	−	0.146669i
$693$	105.657	+	23.6783i	4.01358	+	0.899464i
$694$	2.13502	+	3.69796i	0.0810441	+	0.140372i
$695$	10.4440	+	23.8099i	0.396163	+	0.903160i
$696$	4.18671	+	16.5329i	0.158697	+	0.626679i
$697$	0.0306287	+	0.0818055i	0.00116014	+	0.00309861i
$698$	1.20544	+	2.38201i	0.0456265	+	0.0901605i
$699$	10.0415	−	72.4143i	0.379806	−	2.73896i
$700$	7.58318	−	9.20774i	0.286617	−	0.348020i
$701$	36.4843	+	25.2977i	1.37799	+	0.955480i	0.999554	+	0.0298535i	$0.00950408\pi$
$701$	36.4843	+	25.2977i	1.37799	+	0.955480i	0.378439	+	0.925626i	$0.376461\pi$
$702$	−5.14522	+	4.00469i	−0.194194	+	0.151147i
$703$	27.0929	−	41.8708i	1.02183	−	1.57919i
$704$	3.86388	+	3.00738i	0.145625	+	0.113345i
$705$	−5.37334	−	17.1795i	−0.202372	−	0.647018i
$706$	−1.51065	−	1.04746i	−0.0568540	−	0.0394217i
$707$	−15.9182	+	31.4552i	−0.598665	+	1.18299i
$708$	9.89280	+	1.09493i	0.371794	+	0.0411502i
$709$	28.1026	+	11.4143i	1.05542	+	0.428673i	0.837012	−	0.547185i	$-0.184301\pi$
$709$	28.1026	+	11.4143i	1.05542	+	0.428673i	0.218405	+	0.975858i	$0.429915\pi$
$710$	22.1809	+	3.70134i	0.832435	+	0.138909i
$711$	0.906734	+	3.58061i	0.0340052	+	0.134283i
$712$	−0.297902	−	10.8073i	−0.0111644	−	0.405023i
$713$	−71.4790	+	20.2123i	−2.67691	+	0.756958i
$714$	−2.80647	+	0.963462i	−0.105029	+	0.0360567i
$715$	4.31849	−	4.69113i	0.161502	−	0.175438i
$716$	8.46060	−	8.23060i	0.316188	−	0.307592i
$717$	−3.60162	−	2.49731i	−0.134505	−	0.0932638i
$718$	1.83295	−	5.86028i	0.0684052	−	0.218704i
$719$	1.27592	+	9.20124i	0.0475836	+	0.343148i	0.999341	+	0.0362968i	$0.0115562\pi$
$719$	1.27592	+	9.20124i	0.0475836	+	0.343148i	−0.951757	+	0.306851i	$0.900725\pi$
$720$	13.6561	+	18.5798i	0.508933	+	0.692428i
$721$	5.16489			0.192351
$722$	16.0981	−	10.0921i	0.599109	−	0.375591i
$723$	33.6443			1.25125
$724$	6.24089	+	8.49104i	0.231941	+	0.315567i
$725$	−2.95852	−	21.3353i	−0.109877	−	0.792372i
$726$	12.6306	−	40.3822i	0.468765	−	1.49872i
$727$	−10.6117	−	7.35798i	−0.393566	−	0.272892i	0.356447	−	0.934315i	$-0.383988\pi$
$727$	−10.6117	−	7.35798i	−0.393566	−	0.272892i	−0.750013	+	0.661423i	$0.769953\pi$
$728$	0.895197	−	0.870862i	0.0331782	−	0.0322763i
$729$	−36.3458	+	39.4821i	−1.34614	+	1.46230i
$730$	−6.35672	+	2.18226i	−0.235273	+	0.0807692i
$731$	−1.63865	+	0.463366i	−0.0606077	+	0.0171382i
$732$	0.714655	+	25.9264i	0.0264144	+	0.958266i
$733$	−8.16942	−	32.2603i	−0.301745	−	1.19156i	−0.915583	−	0.402130i	$-0.868270\pi$
$733$	−8.16942	−	32.2603i	−0.301745	−	1.19156i	0.613838	−	0.789432i	$-0.289625\pi$
$734$	−12.9793	−	2.16585i	−0.479073	−	0.0799432i
$735$	−12.6569	−	5.14078i	−0.466856	−	0.189620i
$736$	−7.12015	−	0.788058i	−0.262452	−	0.0290482i
$737$	28.1686	−	55.6627i	1.03760	−	2.05036i
$738$	−1.74473	−	1.20977i	−0.0642245	−	0.0445323i
$739$	3.95561	+	12.6468i	0.145510	+	0.465220i	0.998380	−	0.0569030i	$-0.0181226\pi$
$739$	3.95561	+	12.6468i	0.145510	+	0.465220i	−0.852870	+	0.522123i	$0.825140\pi$
$740$	27.2648	+	21.2210i	1.00227	+	0.780100i
$741$	−5.37861	+	2.94149i	−0.197588	+	0.108058i
$742$	−7.00285	+	5.45054i	−0.257083	+	0.200096i
$743$	11.6040	+	8.04605i	0.425710	+	0.295181i	0.763217	−	0.646142i	$-0.223619\pi$
$743$	11.6040	+	8.04605i	0.425710	+	0.295181i	−0.337507	+	0.941323i	$0.609584\pi$
$744$	21.4984	−	26.1040i	0.788169	−	0.957021i
$745$	−0.180921	+	1.30471i	−0.00662843	+	0.0478008i
$746$	−4.22822	−	8.35518i	−0.154806	−	0.305905i
$747$	7.35276	+	19.6383i	0.269023	+	0.718529i
$748$	0.377618	+	1.49118i	0.0138071	+	0.0545229i
$749$	17.7809	+	40.5364i	0.649700	+	1.48117i
$750$	4.33891	+	7.51521i	0.158435	+	0.274417i
$751$	−15.7954	−	3.53984i	−0.576384	−	0.129171i	−0.0792656	−	0.996854i	$-0.525258\pi$
$751$	−15.7954	−	3.53984i	−0.576384	−	0.129171i	−0.497118	+	0.867683i	$0.665608\pi$
$752$	−1.80284	+	0.300840i	−0.0657427	+	0.0109705i
$753$	5.71660	+	13.0325i	0.208325	+	0.474932i
$754$	−0.0621402	−	2.25433i	−0.00226301	−	0.0820979i
$755$	−50.0373	+	20.3234i	−1.82104	+	0.739644i
$756$	25.9315	−	35.2811i	0.943119	−	1.28316i
$757$	20.7078	−	4.64073i	0.752638	−	0.168670i	0.174554	−	0.984648i	$-0.444152\pi$
$757$	20.7078	−	4.64073i	0.752638	−	0.168670i	0.578084	+	0.815977i	$0.303801\pi$
$758$	0.451167	−	16.3675i	0.0163871	−	0.594494i
$759$	28.0812	+	110.890i	1.01928	+	4.02506i
$760$	5.99515	+	11.7182i	0.217467	+	0.425064i
$761$	2.09490	−	8.27256i	0.0759399	−	0.299880i	−0.919764	−	0.392471i	$-0.871620\pi$
$761$	2.09490	−	8.27256i	0.0759399	−	0.299880i	0.995704	+	0.0925913i	$0.0295150\pi$
$762$	−50.1304	−	14.1755i	−1.81603	−	0.513525i
$763$	8.11207	−	0.447555i	0.293677	−	0.0162026i
$764$	0.372178	+	13.5019i	0.0134649	+	0.488482i
$765$	−0.199609	+	7.24144i	−0.00721688	+	0.261815i
$766$	−14.8805	−	0.820978i	−0.537653	−	0.0296631i
$767$	−1.24482	−	0.427347i	−0.0449478	−	0.0154306i
$768$	2.86821	−	1.55220i	0.103498	−	0.0560101i
$769$	15.3432	−	14.9261i	0.553290	−	0.538249i	−0.366624	−	0.930369i	$-0.619486\pi$
$769$	15.3432	−	14.9261i	0.553290	−	0.538249i	0.919914	+	0.392120i	$0.128258\pi$
$770$	−19.3346	+	38.2063i	−0.696772	+	1.37686i
$771$	1.18100	+	14.2526i	0.0425328	+	0.513295i
$772$	−11.4119	+	17.4672i	−0.410723	+	0.628659i
$773$	−44.5141	+	21.0067i	−1.60106	+	0.755560i	−0.999077	−	0.0429476i	$-0.986325\pi$
$773$	−44.5141	+	21.0067i	−1.60106	+	0.755560i	−0.601985	+	0.798507i	$0.705623\pi$
$774$	26.3126	−	31.9496i	0.945786	−	1.14841i
$775$	−30.6134	+	29.7812i	−1.09967	+	1.06977i
$776$	−8.02975	+	13.9079i	−0.288251	+	0.499266i
$777$	37.8906	−	101.201i	1.35932	−	3.63057i
$778$	2.66607	−	6.07803i	0.0955833	−	0.217908i
$779$	−0.872431	−	0.841258i	−0.0312581	−	0.0301412i
$780$	−1.70600	−	3.88929i	−0.0610846	−	0.139259i
$781$	−36.4068	+	2.00862i	−1.30274	+	0.0718741i
$782$	−1.61316	−	1.56931i	−0.0576865	−	0.0561183i
$783$	−15.1576	−	77.5985i	−0.541689	−	2.77314i
$784$	−0.693579	+	1.20131i	−0.0247707	+	0.0429041i
$785$	−23.8264	+	47.0822i	−0.850400	+	1.68044i
$786$	−20.5589	+	16.0016i	−0.733311	+	0.570759i
$787$	−15.1172	−	23.1387i	−0.538872	−	0.824804i	0.459105	−	0.888382i	$-0.348170\pi$
$787$	−15.1172	−	23.1387i	−0.538872	−	0.824804i	−0.997977	+	0.0635774i	$0.979749\pi$
$788$	−16.9008	−	10.3889i	−0.602066	−	0.370089i
$789$	−17.7425	−	15.4519i	−0.631648	−	0.550103i
$790$	−1.46070			−0.0519694
$791$	−32.0305			−1.13887
$792$	−28.1945	−	24.5546i	−1.00185	−	0.872510i
$793$	0.657489	−	3.36598i	0.0233481	−	0.119529i
$794$	−6.57342	+	4.55791i	−0.233282	+	0.161754i
$795$	9.00817	+	28.8007i	0.319487	+	1.02146i
$796$	−8.48189	+	10.2990i	−0.300633	+	0.365038i
$797$	35.9153	−	19.4364i	1.27219	−	0.688473i	0.307419	−	0.951574i	$-0.400535\pi$
$797$	35.9153	−	19.4364i	1.27219	−	0.688473i	0.964768	+	0.263101i	$0.0847453\pi$
$798$	29.3825	−	28.8370i	1.04013	−	1.02082i
$799$	−0.505011	−	0.273298i	−0.0178660	−	0.00966861i
$800$	−3.81608	+	1.54996i	−0.134919	+	0.0547993i
$801$	−2.27477	+	82.5243i	−0.0803749	+	2.91585i
$802$	10.4024	+	27.7835i	0.367321	+	0.981071i
$803$	9.28375	−	5.70670i	0.327616	−	0.201385i
$804$	−26.4158	−	32.0749i	−0.931612	−	1.13119i
$805$	−5.17347	−	62.4344i	−0.182341	−	2.20052i
$806$	−3.52881	+	2.74658i	−0.124297	+	0.0967442i
$807$	−6.59550	+	21.0870i	−0.232173	+	0.742297i
$808$	10.0035	−	6.93625i	0.351921	−	0.244016i
$809$	−2.65141	+	31.9978i	−0.0932187	+	1.12498i	0.776060	+	0.630660i	$0.217216\pi$
$809$	−2.65141	+	31.9978i	−0.0932187	+	1.12498i	−0.869278	+	0.494323i	$0.835416\pi$
$810$	−43.6030	−	66.7393i	−1.53205	−	2.34498i
$811$	0.166698	−	0.532964i	0.00585357	−	0.0187149i	−0.951432	−	0.307858i	$-0.900388\pi$
$811$	0.166698	−	0.532964i	0.00585357	−	0.0187149i	0.957286	+	0.289143i	$0.0933703\pi$
$812$	4.52097	+	14.4544i	0.158655	+	0.507249i
$813$	−29.9467	+	14.1322i	−1.05028	+	0.495638i
$814$	−50.6625	−	23.9082i	−1.77572	−	0.837982i
$815$	−3.54959	+	2.18192i	−0.124337	+	0.0764295i
$816$	1.01061	+	0.168640i	0.0353783	+	0.00590359i
$817$	17.7487	−	15.5955i	0.620949	−	0.545618i
$818$	−6.43458	+	1.07374i	−0.224980	+	0.0375425i
$819$	−7.19162	+	6.26319i	−0.251296	+	0.218853i
$820$	0.633162	−	0.551421i	0.0221110	−	0.0192565i
$821$	−15.9754	−	27.6701i	−0.557544	−	0.965694i	−0.997701	−	0.0677734i	$-0.978411\pi$
$821$	−15.9754	−	27.6701i	−0.557544	−	0.965694i	0.440157	−	0.897921i	$-0.354923\pi$
$822$	−12.4695	+	0.687963i	−0.434925	+	0.0239955i
$823$	0.539569	−	0.152576i	0.0188082	−	0.00531845i	−0.262686	−	0.964881i	$-0.584608\pi$
$823$	0.539569	−	0.152576i	0.0188082	−	0.00531845i	0.281495	+	0.959563i	$0.409170\pi$
$824$	−1.56847	−	0.848814i	−0.0546403	−	0.0295698i
$825$	44.5453	+	48.3891i	1.55087	+	1.68469i
$826$	8.82516	+	0.486898i	0.307067	+	0.0169413i
$827$	−8.13323	−	21.7229i	−0.282820	−	0.755379i	−0.998384	−	0.0568313i	$-0.981900\pi$
$827$	−8.13323	−	21.7229i	−0.282820	−	0.755379i	0.715564	−	0.698547i	$-0.246170\pi$
$828$	53.9550	+	9.00349i	1.87506	+	0.312893i
$829$	1.27905	−	2.91594i	0.0444233	−	0.101275i	−0.892161	−	0.451718i	$-0.850811\pi$
$829$	1.27905	−	2.91594i	0.0444233	−	0.101275i	0.936584	+	0.350443i	$0.113969\pi$
$830$	−8.24243	+	0.912272i	−0.286099	+	0.0316654i
$831$	−50.6507	−	49.2738i	−1.75705	−	1.70929i
$832$	−0.414973	+	0.117343i	−0.0143866	+	0.00406815i
$833$	−0.403763	+	0.163994i	−0.0139895	+	0.00568206i
$834$	−27.3997	+	6.14043i	−0.948776	+	0.212626i
$835$	36.7597	+	39.9317i	1.27212	+	1.38189i
$836$	−13.6405	−	16.4147i	−0.471765	−	0.567713i
$837$	−106.180	+	115.343i	−3.67013	+	3.98683i
$838$	−9.80248	+	16.9784i	−0.338621	+	0.586509i
$839$	−1.95190	−	0.216036i	−0.0673871	−	0.00745840i	0.0762514	−	0.997089i	$-0.475705\pi$
$839$	−1.95190	−	0.216036i	−0.0673871	−	0.00745840i	−0.143639	+	0.989630i	$0.545880\pi$
$840$	18.1315	+	22.0159i	0.625596	+	0.759619i
$841$	−1.49446	−	0.705252i	−0.0515331	−	0.0243190i
$842$	−4.54467	+	32.7738i	−0.156620	+	1.12946i
$843$	−73.6179	+	39.8400i	−2.53553	+	1.37216i
$844$	−0.523236	+	0.568385i	−0.0180105	+	0.0195646i
$845$	−7.41825	−	37.9773i	−0.255196	−	1.30646i
$846$	13.8720	−	1.53535i	0.476929	−	0.0527865i
$847$	9.22365	−	36.4234i	0.316928	−	1.25152i
$848$	3.02238	−	0.504346i	0.103789	−	0.0173193i
$849$	−0.413971	−	0.717019i	−0.0142075	−	0.0246080i
$850$	−1.24517	−	0.352101i	−0.0427090	−	0.0120770i
$851$	81.4641	−	9.01644i	2.79255	−	0.309080i
$852$	−8.51569	+	22.7444i	−0.291743	+	0.779211i
$853$	13.3006	+	1.47211i	0.455402	+	0.0504039i	0.334784	−	0.942295i	$-0.391337\pi$
$853$	13.3006	+	1.47211i	0.455402	+	0.0504039i	0.120619	+	0.992699i	$0.461512\pi$
$854$	1.90194	+	22.9530i	0.0650831	+	0.785436i
$855$	−40.7799	−	91.8654i	−1.39464	−	3.14173i
$856$	1.26218	−	15.2322i	0.0431404	−	0.520627i
$857$	−0.886990	+	4.54090i	−0.0302990	+	0.155114i	−0.993532	−	0.113554i	$-0.963776\pi$
$857$	−0.886990	+	4.54090i	−0.0302990	+	0.155114i	0.963233	+	0.268668i	$0.0865835\pi$
$858$	4.07826	+	5.54868i	0.139230	+	0.189429i
$859$	1.54577	+	1.34621i	0.0527409	+	0.0459321i	0.682721	−	0.730679i	$-0.260797\pi$
$859$	1.54577	+	1.34621i	0.0527409	+	0.0459321i	−0.629980	+	0.776611i	$0.716937\pi$
$860$	9.69386	+	13.1890i	0.330558	+	0.449740i
$861$	−2.23721	−	1.37520i	−0.0762437	−	0.0468669i
$862$	2.45098	−	29.5789i	0.0834806	−	1.00746i
$863$	2.85944	+	2.22559i	0.0973363	+	0.0757599i	0.661712	−	0.749758i	$-0.269830\pi$
$863$	2.85944	+	2.22559i	0.0973363	+	0.0757599i	−0.564375	+	0.825518i	$0.690883\pi$
$864$	−13.6731	+	6.45247i	−0.465167	+	0.219518i
$865$	9.72265	−	70.1147i	0.330580	−	2.38397i
$866$	37.8653	+	12.9992i	1.28672	+	0.441730i
$867$	−37.3317	−	40.5530i	−1.26785	−	1.37725i
$868$	17.7849	−	24.1972i	0.603658	−	0.821307i
$869$	2.31111	−	0.517931i	0.0783989	−	0.0175696i
$870$	51.4229	+	2.83708i	1.74340	+	0.0961860i
$871$	2.48096	+	4.90252i	0.0840643	+	0.166116i
$872$	−2.53702	−	1.19725i	−0.0859144	−	0.0405440i
$873$	67.0719	−	102.661i	2.27004	−	3.47455i
$874$	29.5780	+	10.0086i	1.00049	+	0.338545i
$875$	4.21479	+	6.45122i	0.142486	+	0.218091i
$876$	−0.996974	−	7.18965i	−0.0336846	−	0.242916i
$877$	4.78192	−	24.4807i	0.161474	−	0.826656i	−0.809436	−	0.587209i	$-0.800227\pi$
$877$	4.78192	−	24.4807i	0.161474	−	0.826656i	0.970909	−	0.239447i	$-0.0769662\pi$
$878$	30.1925	+	18.5592i	1.01895	+	0.626344i
$879$	−9.38112	−	67.6518i	−0.316417	−	2.28184i
$880$	12.1505	−	8.42495i	0.409593	−	0.284005i
$881$	33.1955	+	25.8371i	1.11839	+	0.870475i	0.992582	−	0.121580i	$-0.0387962\pi$
$881$	33.1955	+	25.8371i	1.11839	+	0.870475i	0.125804	+	0.992055i	$0.459849\pi$
$882$	5.79341	−	8.86748i	0.195074	−	0.298584i
$883$	−1.39773	−	1.69717i	−0.0470373	−	0.0571143i	0.747870	−	0.663846i	$-0.231077\pi$
$883$	−1.39773	−	1.69717i	−0.0470373	−	0.0571143i	−0.794907	+	0.606731i	$0.792480\pi$
$884$	−0.125523	−	0.0509832i	−0.00422181	−	0.00171475i
$885$	12.0734	−	27.5246i	0.405843	−	0.925229i
$886$	−7.63501	+	30.1500i	−0.256503	+	1.01291i
$887$	34.7502	+	7.78771i	1.16680	+	0.261486i	0.758692	−	0.651449i	$-0.225839\pi$
$887$	34.7502	+	7.78771i	1.16680	+	0.261486i	0.408106	+	0.912935i	$0.366189\pi$
$888$	−28.1383	+	24.5057i	−0.944260	+	0.822357i
$889$	−45.1423	−	10.1166i	−1.51402	−	0.339301i
$890$	−31.4159	−	8.88358i	−1.05306	−	0.297778i
$891$	92.6524	+	90.1336i	3.10397	+	3.01959i
$892$	7.36383	−	2.52801i	0.246559	−	0.0846439i
$893$	7.95681	+	0.403806i	0.266264	+	0.0135128i
$894$	−1.34547	−	0.461901i	−0.0449993	−	0.0154483i
$895$	−16.0944	−	31.8033i	−0.537975	−	1.06307i
$896$	2.46721	−	1.51659i	0.0824237	−	0.0506656i
$897$	−9.33442	−	3.79131i	−0.311667	−	0.126588i
$898$	−12.1460	+	32.4404i	−0.405316	+	1.08255i
$899$	−10.3957	−	53.2203i	−0.346717	−	1.77500i
$900$	29.7471	−	10.2122i	0.991571	−	0.340407i
$901$	0.846630	+	0.458173i	0.0282053	+	0.0152640i
$902$	−0.806260	+	1.09696i	−0.0268455	+	0.0365247i
$903$	30.3195	−	41.2512i	1.00897	−	1.37275i
$904$	9.72700	+	5.26399i	0.323515	+	0.175078i
$905$	30.0974	−	10.3325i	1.00047	−	0.343463i
$906$	−11.1819	−	57.2451i	−0.371494	−	1.90184i
$907$	−16.7961	+	44.8604i	−0.557706	+	1.48957i	0.288907	+	0.957357i	$0.406708\pi$
$907$	−16.7961	+	44.8604i	−0.557706	+	1.48957i	−0.846613	+	0.532209i	$0.821362\pi$
$908$	−6.04208	−	2.45408i	−0.200513	−	0.0814415i
$909$	−79.1876	+	48.6764i	−2.62649	+	1.61449i
$910$	−1.70291	−	3.36504i	−0.0564508	−	0.111550i
$911$	26.6104	+	9.13538i	0.881643	+	0.302669i	0.728098	−	0.685473i	$-0.240405\pi$
$911$	26.6104	+	9.13538i	0.881643	+	0.302669i	0.153545	+	0.988142i	$0.450931\pi$
$912$	−13.6620	+	3.92839i	−0.452394	+	0.130082i
$913$	12.7176	−	4.36596i	0.420891	−	0.144492i
$914$	−3.45949	−	3.36544i	−0.114430	−	0.111319i
$915$	75.3655	+	21.3113i	2.49151	+	0.704531i
$916$	−4.60528	−	1.03207i	−0.152163	−	0.0341005i
$917$	−17.4461	+	15.1938i	−0.576120	+	0.501743i
$918$	−4.63492	−	1.03871i	−0.152975	−	0.0342826i
$919$	3.03577	−	11.9880i	0.100141	−	0.395448i	−0.898951	−	0.438049i	$-0.855670\pi$
$919$	3.03577	−	11.9880i	0.100141	−	0.395448i	0.999092	+	0.0426011i	$0.0135645\pi$
$920$	−8.68960	+	19.8103i	−0.286487	+	0.653126i
$921$	18.4193	+	7.48127i	0.606936	+	0.246516i
$922$	−13.1311	−	15.9442i	−0.432450	−	0.525094i
$923$	1.75648	−	2.68850i	0.0578153	−	0.0884930i
$924$	−36.4938	−	28.4042i	−1.20056	−	0.934431i
$925$	38.7264	−	26.8523i	1.27332	−	0.882898i
$926$	4.80069	+	34.6201i	0.157761	+	1.13769i
$927$	11.6015	+	7.13142i	0.381044	+	0.234227i
$928$	1.00255	−	5.13248i	0.0329102	−	0.168482i
$929$	1.29865	+	9.36515i	0.0426072	+	0.307261i	0.999839	+	0.0179389i	$0.00571043\pi$
$929$	1.29865	+	9.36515i	0.0426072	+	0.307261i	−0.957232	+	0.289322i	$0.906570\pi$
$930$	−55.8539	−	85.4908i	−1.83152	−	2.80335i
$931$	4.07551	−	4.46655i	0.133570	−	0.146385i
$932$	−12.2608	+	18.7665i	−0.401616	+	0.614719i
$933$	5.51069	+	2.60056i	0.180412	+	0.0851384i
$934$	0.0633842	+	0.125251i	0.00207399	+	0.00409833i
$935$	4.63806	+	0.255889i	0.151681	+	0.00836847i
$936$	3.21326	−	0.720108i	0.105029	−	0.0235375i
$937$	32.7358	−	44.5387i	1.06943	−	1.45502i	0.188320	−	0.982108i	$-0.439696\pi$
$937$	32.7358	−	44.5387i	1.06943	−	1.45502i	0.881112	−	0.472907i	$-0.156795\pi$
$938$	−24.9910	−	27.1474i	−0.815985	−	0.886396i
$939$	49.1844	+	16.8850i	1.60507	+	0.551022i
$940$	−0.758107	+	5.46707i	−0.0247267	+	0.178316i
$941$	37.0173	−	17.4689i	1.20673	−	0.569470i	0.285459	−	0.958391i	$-0.407854\pi$
$941$	37.0173	−	17.4689i	1.20673	−	0.569470i	0.921271	+	0.388921i	$0.127152\pi$
$942$	−44.9719	−	35.0030i	−1.46526	−	1.14046i
$943$	0.164481	−	1.98499i	0.00535624	−	0.0646402i
$944$	−2.60000	−	1.59821i	−0.0846228	−	0.0520175i
$945$	−78.3064	−	106.540i	−2.54731	−	3.46574i
$946$	−20.0140	−	17.4302i	−0.650712	−	0.566706i
$947$	4.69809	+	6.39198i	0.152667	+	0.207712i	0.875378	−	0.483440i	$-0.160613\pi$
$947$	4.69809	+	6.39198i	0.152667	+	0.207712i	−0.722710	+	0.691151i	$0.757104\pi$
$948$	0.302431	−	1.54828i	0.00982249	−	0.0502857i
$949$	−0.0792595	+	0.956520i	−0.00257287	+	0.0310499i
$950$	17.6956	−	3.03313i	0.574120	−	0.0984076i
$951$	−3.36257	−	40.5802i	−0.109039	−	1.31590i
$952$	0.904318	+	0.100090i	0.0293091	+	0.00324393i
$953$	2.78804	−	7.44653i	0.0903136	−	0.241217i	−0.883556	−	0.468326i	$-0.844857\pi$
$953$	2.78804	−	7.44653i	0.0903136	−	0.241217i	0.973869	+	0.227109i	$0.0729274\pi$
$954$	−23.2558	+	2.57395i	−0.752935	+	0.0833348i
$955$	39.2488	+	11.0985i	1.27006	+	0.359139i
$956$	0.671933	+	1.16382i	0.0217319	+	0.0376407i
$957$	−82.3667	+	13.7446i	−2.66254	+	0.444299i
$958$	4.98591	−	19.6889i	0.161087	−	0.636120i
$959$	−11.0226	+	1.21999i	−0.355940	+	0.0393954i
$960$	−1.88801	−	9.66555i	−0.0609352	−	0.311954i
$961$	−51.8272	+	56.2994i	−1.67185	+	1.81611i
$962$	4.33935	−	2.34834i	0.139906	−	0.0757134i
$963$	−16.0307	+	115.605i	−0.516581	+	3.72532i
$964$	−9.32961	−	4.40275i	−0.300487	−	0.141803i
$965$	40.0544	+	48.6354i	1.28940	+	1.56563i
$966$	67.2488	+	7.44309i	2.16369	+	0.239478i
$967$	6.65244	−	11.5224i	0.213928	−	0.370534i	−0.739012	−	0.673692i	$-0.764708\pi$
$967$	6.65244	−	11.5224i	0.213928	−	0.370534i	0.952940	+	0.303158i	$0.0980409\pi$
$968$	−8.78696	+	9.54519i	−0.282424	+	0.306794i
$969$	−4.14513	−	1.66235i	−0.133161	−	0.0534024i
$970$	32.8451	+	35.6793i	1.05459	+	1.14559i
$971$	29.5046	−	6.61214i	0.946849	−	0.212194i	0.282205	−	0.959354i	$-0.408934\pi$
$971$	29.5046	−	6.61214i	0.946849	−	0.212194i	0.664644	+	0.747160i	$0.268583\pi$
$972$	37.7451	−	15.3307i	1.21067	−	0.491733i
$973$	−23.9940	+	6.78486i	−0.769213	+	0.217513i
$974$	−17.4630	−	16.9883i	−0.559550	−	0.544339i
$975$	−5.75762	+	0.637254i	−0.184392	+	0.0204085i
$976$	3.19459	−	7.28294i	0.102256	−	0.233121i
$977$	18.4979	+	3.08676i	0.591801	+	0.0987541i	0.452914	−	0.891554i	$-0.350384\pi$
$977$	18.4979	+	3.08676i	0.591801	+	0.0987541i	0.138887	+	0.990308i	$0.455648\pi$
$978$	−1.57782	−	4.21416i	−0.0504530	−	0.134754i
$979$	52.8559	+	2.91614i	1.68928	+	0.0932002i
$980$	2.83704	+	3.08184i	0.0906258	+	0.0984459i
$981$	18.8395	+	10.1954i	0.601499	+	0.325515i
$982$	−27.1387	+	7.67409i	−0.866031	+	0.244890i
$983$	21.8394	−	1.20492i	0.696570	−	0.0384308i	0.296657	−	0.954984i	$-0.404128\pi$
$983$	21.8394	−	1.20492i	0.696570	−	0.0384308i	0.399913	+	0.916553i	$0.369040\pi$
$984$	0.453388	+	0.785291i	0.0144535	+	0.0250342i
$985$	−45.1764	+	39.3441i	−1.43944	+	1.25361i
$986$	1.23894	−	1.07899i	0.0394558	−	0.0343621i
$987$	17.0275	−	2.84139i	0.541993	−	0.0904426i
$988$	1.87642	−	0.111826i	0.0596970	−	0.00355767i
$989$	38.3002	+	6.39118i	1.21788	+	0.203228i
$990$	−96.1834	+	59.1237i	−3.05691	+	1.87907i
$991$	47.6587	+	22.4907i	1.51393	+	0.714439i	0.990485	−	0.137622i	$-0.0439458\pi$
$991$	47.6587	+	22.4907i	1.51393	+	0.714439i	0.523442	+	0.852061i	$0.324648\pi$
$992$	−9.37755	+	4.42537i	−0.297738	+	0.140506i
$993$	21.3052	+	68.1166i	0.676101	+	2.16162i
$994$	−6.43794	+	20.5832i	−0.204199	+	0.652861i
$995$	22.0364	+	33.7292i	0.698600	+	1.06929i
$996$	0.739586	−	8.92547i	0.0234347	−	0.282814i
$997$	2.63375	−	1.82620i	0.0834118	−	0.0578364i	−0.527368	−	0.849637i	$-0.676821\pi$
$997$	2.63375	−	1.82620i	0.0834118	−	0.0578364i	0.610780	+	0.791801i	$0.290856\pi$
$998$	−1.01608	+	3.24859i	−0.0321635	+	0.102832i
$999$	136.508	−	106.248i	4.31892	−	3.36155i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	722.2.i.b.11.1	✓	612
361.197	even	57	inner	722.2.i.b.197.1	yes	612

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
722.2.i.b.11.1	✓	612	1.1	even	1	trivial
722.2.i.b.197.1	yes	612	361.197	even	57	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:	\( N \)	\(=\)	\( 722 = 2 \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	722.i (of order \(57\), degree \(36\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.592235 - 0.805765i) q^{2} +(-0.447948 - 3.23037i) q^{3} +(-0.298515 + 0.954405i) q^{4} +(2.48156 + 1.72067i) q^{5} +(-2.33763 + 2.27408i) q^{6} +(-1.96145 + 2.13070i) q^{7} +(0.945817 - 0.324699i) q^{8} +(-7.34782 + 2.07777i) q^{9} +(-0.0832070 - 3.01860i) q^{10} +(1.20197 + 4.74649i) q^{11} +(3.21680 + 0.536789i) q^{12} +(-0.399546 - 0.162282i) q^{13} +(2.87848 + 0.318590i) q^{14} +(4.44680 - 8.78712i) q^{15} +(-0.821778 - 0.569808i) q^{16} +(-0.0937829 - 0.299841i) q^{17} +(6.02583 + 4.69009i) q^{18} +(2.96631 + 3.19390i) q^{19} +(-2.38300 + 1.85476i) q^{20} +(7.76157 + 5.38176i) q^{21} +(3.11270 - 3.77954i) q^{22} +(-0.983949 + 7.09573i) q^{23} +(-1.47258 - 2.90989i) q^{24} +(1.44422 + 3.85734i) q^{25} +(0.105864 + 0.418049i) q^{26} +(6.07327 + 13.8457i) q^{27} +(-1.44803 - 2.50806i) q^{28} +(-5.10291 - 1.14359i) q^{29} +(-9.71390 + 1.62096i) q^{30} +(4.16530 + 9.49593i) q^{31} +(0.0275543 + 0.999620i) q^{32} +(14.7945 - 6.00900i) q^{33} +(-0.186060 + 0.253143i) q^{34} +(-8.53368 + 1.91244i) q^{35} +(0.210403 - 7.63304i) q^{36} +(-2.80869 - 11.0913i) q^{37} +(0.816775 - 4.28169i) q^{38} +(-0.345253 + 1.36337i) q^{39} +(2.90580 + 0.821682i) q^{40} +(-0.277621 + 0.0153168i) q^{41} +(-0.260247 - 9.44127i) q^{42} +(0.149356 - 5.41836i) q^{43} +(-4.88888 - 0.269727i) q^{44} +(-21.8092 - 7.48711i) q^{45} +(6.30022 - 3.40951i) q^{46} +(1.31011 - 1.27450i) q^{47} +(-1.47258 + 2.90989i) q^{48} +(-0.114551 - 1.38242i) q^{49} +(2.25279 - 3.44816i) q^{50} +(-0.926586 + 0.437266i) q^{51} +(0.274153 - 0.332885i) q^{52} +(-2.19634 + 2.13664i) q^{53} +(7.55955 - 13.0935i) q^{54} +(-5.18439 + 13.8469i) q^{55} +(-1.16333 + 2.65213i) q^{56} +(8.98871 - 11.0130i) q^{57} +(2.10066 + 4.78902i) q^{58} +(3.04730 - 0.168124i) q^{59} +(7.05903 + 6.86713i) q^{60} +(1.52463 + 7.80526i) q^{61} +(5.18465 - 8.98008i) q^{62} +(9.98527 - 19.7314i) q^{63} +(0.789141 - 0.614213i) q^{64} +(-0.712262 - 1.09020i) q^{65} +(-13.6037 - 8.36213i) q^{66} +(-9.60814 - 8.36774i) q^{67} +0.314165 q^{68} +23.3626 q^{69} +(6.59493 + 5.74353i) q^{70} +(-1.42764 + 7.30874i) q^{71} +(-6.27505 + 4.35102i) q^{72} +(-0.664388 - 2.12417i) q^{73} +(-7.27354 + 8.83177i) q^{74} +(11.8137 - 6.39326i) q^{75} +(-3.93376 + 1.87764i) q^{76} +(-12.4709 - 6.74894i) q^{77} +(1.30303 - 0.529245i) q^{78} +(0.0133285 - 0.483534i) q^{79} +(-1.05884 - 2.82802i) q^{80} +(22.4905 - 13.8248i) q^{81} +(0.176759 + 0.214626i) q^{82} +(-0.226778 - 2.73680i) q^{83} +(-7.45332 + 5.80115i) q^{84} +(0.283200 - 0.905441i) q^{85} +(-4.45438 + 3.08860i) q^{86} +(-1.40837 + 16.9966i) q^{87} +(2.67803 + 4.09903i) q^{88} +(3.22738 - 10.3185i) q^{89} +(6.88332 + 22.0072i) q^{90} +(1.12946 - 0.533006i) q^{91} +(-6.47847 - 3.05727i) q^{92} +(28.8095 - 17.7091i) q^{93} +(-1.80284 - 0.300840i) q^{94} +(1.86542 + 13.0299i) q^{95} +(3.21680 - 0.536789i) q^{96} +(-12.1106 + 10.5471i) q^{97} +(-1.04606 + 0.911019i) q^{98} +(-18.6940 - 32.3789i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 612 q + 17 q^{2} - 19 q^{3} + 17 q^{4} + q^{5} - 2 q^{7} - 34 q^{8} + 4 q^{9} + q^{10} - 28 q^{11} + 4 q^{13} - 18 q^{14} - 52 q^{15} + 17 q^{16} + 18 q^{17} - 46 q^{18} - 12 q^{19} - 2 q^{20} - 65 q^{21}+ \cdots - 116 q^{99}+O(q^{100}) \) 612 * q + 17 * q^2 - 19 * q^3 + 17 * q^4 + q^5 - 2 * q^7 - 34 * q^8 + 4 * q^9 + q^10 - 28 * q^11 + 4 * q^13 - 18 * q^14 - 52 * q^15 + 17 * q^16 + 18 * q^17 - 46 * q^18 - 12 * q^19 - 2 * q^20 - 65 * q^21 + 33 * q^22 + 39 * q^23 + 20 * q^25 - 8 * q^26 + 158 * q^27 - 37 * q^28 - 42 * q^29 - 29 * q^30 + 12 * q^31 + 17 * q^32 + 60 * q^33 - q^34 - 14 * q^35 + 23 * q^36 - 6 * q^37 + 76 * q^38 - 108 * q^39 + q^40 + 8 * q^41 + 11 * q^42 + 7 * q^43 - 5 * q^44 - 101 * q^45 - 21 * q^46 + 105 * q^47 - 62 * q^49 - 78 * q^50 - 3 * q^51 + 4 * q^52 + 146 * q^53 - 79 * q^54 + 4 * q^55 - 21 * q^56 - 28 * q^57 + 8 * q^58 - 4 * q^59 - 14 * q^60 - 93 * q^61 - 6 * q^62 - 95 * q^63 - 34 * q^64 - 76 * q^65 - 16 * q^66 - 6 * q^67 + 78 * q^68 + 38 * q^69 + 81 * q^70 - 151 * q^71 + 23 * q^72 + 7 * q^73 - 35 * q^74 - 12 * q^75 - 7 * q^76 + 78 * q^77 - 3 * q^78 - 10 * q^79 + q^80 + 58 * q^81 - 30 * q^82 + 67 * q^83 - 22 * q^84 - 6 * q^85 - 12 * q^86 - 109 * q^87 + 10 * q^88 - 25 * q^89 - 73 * q^90 + 37 * q^91 + q^92 + 56 * q^93 - 39 * q^94 - 29 * q^95 - 153 * q^97 + 164 * q^98 - 116 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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