LMFDB - Embedded newform 51.2.i.a.41.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [51,2,Mod(5,51)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(51, base_ring=CyclotomicField(16)) chi = DirichletCharacter(H, H._module([8, 5])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("51.5"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 51 = 3 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	51.i (of order $16$, degree $8$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$0.407237050309$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$4$ over $\Q(\zeta_{16})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			41.3
Character	$\chi$	$=$	51.41
Dual form			51.2.i.a.5.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.419490 + 0.173759i) q^{2} +(1.73140 + 0.0473558i) q^{3} +(-1.26843 - 1.26843i) q^{4} +(-3.00087 + 0.596910i) q^{5} +(0.718078 + 0.320711i) q^{6} +(-0.464975 + 2.33759i) q^{7} +(-0.659211 - 1.59148i) q^{8} +(2.99551 + 0.163984i) q^{9} +(-1.36255 - 0.271029i) q^{10} +(0.172899 + 0.258762i) q^{11} +(-2.13610 - 2.25624i) q^{12} +(1.45541 - 1.45541i) q^{13} +(-0.601228 + 0.899802i) q^{14} +(-5.22398 + 0.891383i) q^{15} +2.80552i q^{16} +(-2.58814 - 3.20960i) q^{17} +(1.22810 + 0.589286i) q^{18} +(0.427451 - 1.03196i) q^{19} +(4.56354 + 3.04926i) q^{20} +(-0.915758 + 4.02529i) q^{21} +(0.0275675 + 0.138591i) q^{22} +(4.71932 - 3.15335i) q^{23} +(-1.06599 - 2.78671i) q^{24} +(4.02951 - 1.66908i) q^{25} +(0.863423 - 0.357641i) q^{26} +(5.17868 + 0.425777i) q^{27} +(3.55487 - 2.37529i) q^{28} +(1.62296 + 8.15918i) q^{29} +(-2.34629 - 0.533785i) q^{30} +(-5.25259 - 3.50967i) q^{31} +(-1.80591 + 4.35984i) q^{32} +(0.287105 + 0.456210i) q^{33} +(-0.528006 - 1.79611i) q^{34} -7.29234i q^{35} +(-3.59161 - 4.00761i) q^{36} +(-6.02262 + 9.01349i) q^{37} +(0.358623 - 0.358623i) q^{38} +(2.58883 - 2.45099i) q^{39} +(2.92817 + 4.38232i) q^{40} +(5.42232 + 1.07857i) q^{41} +(-1.08358 + 1.52945i) q^{42} +(-1.13048 - 2.72921i) q^{43} +(0.108911 - 0.547534i) q^{44} +(-9.08703 + 1.29596i) q^{45} +(2.52763 - 0.502777i) q^{46} +(-4.50710 - 4.50710i) q^{47} +(-0.132858 + 4.85749i) q^{48} +(1.21904 + 0.504943i) q^{49} +1.98036 q^{50} +(-4.32913 - 5.67967i) q^{51} -3.69219 q^{52} +(-5.31572 - 2.20184i) q^{53} +(2.09842 + 1.07845i) q^{54} +(-0.673306 - 0.673306i) q^{55} +(4.02673 - 0.800967i) q^{56} +(0.788959 - 1.76649i) q^{57} +(-0.736910 + 3.70470i) q^{58} +(-0.337607 - 0.815054i) q^{59} +(7.75693 + 5.49561i) q^{60} +(-3.27882 - 0.652199i) q^{61} +(-1.59358 - 2.38495i) q^{62} +(-1.77617 + 6.92603i) q^{63} +(2.45248 - 2.45248i) q^{64} +(-3.49876 + 5.23626i) q^{65} +(0.0411673 + 0.241262i) q^{66} -2.49028i q^{67} +(-0.788274 + 7.35405i) q^{68} +(8.32038 - 5.23624i) q^{69} +(1.26711 - 3.05907i) q^{70} +(0.997325 + 0.666391i) q^{71} +(-1.71370 - 4.87539i) q^{72} +(-0.197828 - 0.994547i) q^{73} +(-4.09260 + 2.73459i) q^{74} +(7.05575 - 2.69903i) q^{75} +(-1.85116 + 0.766777i) q^{76} +(-0.685274 + 0.283850i) q^{77} +(1.51187 - 0.578333i) q^{78} +(11.0957 - 7.41392i) q^{79} +(-1.67464 - 8.41899i) q^{80} +(8.94622 + 0.982433i) q^{81} +(2.08720 + 1.39462i) q^{82} +(-1.56322 + 3.77396i) q^{83} +(6.26739 - 3.94423i) q^{84} +(9.68252 + 8.08669i) q^{85} -1.34131i q^{86} +(2.42362 + 14.2037i) q^{87} +(0.297837 - 0.445745i) q^{88} +(0.687749 - 0.687749i) q^{89} +(-4.03710 - 1.03531i) q^{90} +(2.72543 + 4.07889i) q^{91} +(-9.98596 - 1.98633i) q^{92} +(-8.92815 - 6.32540i) q^{93} +(-1.10754 - 2.67383i) q^{94} +(-0.666738 + 3.35192i) q^{95} +(-3.33321 + 7.46312i) q^{96} +(-6.12098 + 1.21754i) q^{97} +(0.423637 + 0.423637i) q^{98} +(0.475490 + 0.803479i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 8 q^{3} - 16 q^{4} - 8 q^{6} - 16 q^{7} - 8 q^{9} - 16 q^{10} + 16 q^{12} - 16 q^{13} + 16 q^{15} + 16 q^{18} - 16 q^{19} + 16 q^{21} - 16 q^{22} + 16 q^{24} + 16 q^{25} - 8 q^{27} + 32 q^{28} - 8 q^{30}+ \cdots - 64 q^{99}+O(q^{100}) $ 32 * q - 8 * q^3 - 16 * q^4 - 8 * q^6 - 16 * q^7 - 8 * q^9 - 16 * q^10 + 16 * q^12 - 16 * q^13 + 16 * q^15 + 16 * q^18 - 16 * q^19 + 16 * q^21 - 16 * q^22 + 16 * q^24 + 16 * q^25 - 8 * q^27 + 32 * q^28 - 8 * q^30 + 16 * q^31 + 96 * q^34 + 8 * q^36 + 16 * q^37 - 24 * q^39 + 16 * q^40 - 56 * q^42 + 16 * q^43 - 40 * q^45 - 32 * q^46 - 64 * q^48 - 48 * q^49 - 40 * q^51 - 96 * q^52 - 24 * q^54 - 48 * q^55 + 8 * q^57 - 48 * q^58 + 32 * q^60 - 32 * q^61 + 64 * q^63 + 16 * q^64 + 72 * q^66 + 80 * q^69 + 48 * q^70 + 64 * q^72 + 48 * q^73 + 88 * q^75 + 48 * q^76 + 96 * q^78 + 16 * q^79 + 48 * q^81 + 112 * q^82 - 56 * q^87 + 16 * q^88 - 88 * q^90 + 16 * q^91 - 72 * q^93 - 48 * q^94 - 112 * q^96 - 16 * q^97 - 64 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/51\mathbb{Z}\right)^\times$.

$n$	$35$	$37$
$\chi(n)$	$-1$	$e\left(\frac{11}{16}\right)$

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 $

$2$	0.419490	+	0.173759i	0.296624	+	0.122866i	0.526032	−	0.850465i	$-0.323679\pi$
$2$	0.419490	+	0.173759i	0.296624	+	0.122866i	−0.229408	+	0.973330i	$0.573679\pi$
$3$	1.73140	+	0.0473558i	0.999626	+	0.0273409i
$3$	1.73140	+	0.0473558i	0.999626	+	0.0273409i
$4$	−1.26843	−	1.26843i	−0.634217	−	0.634217i
$5$	−3.00087	+	0.596910i	−1.34203	+	0.266946i	−0.813300	−	0.581845i	$-0.802331\pi$
$5$	−3.00087	+	0.596910i	−1.34203	+	0.266946i	−0.528729	+	0.848791i	$0.677331\pi$
$6$	0.718078	+	0.320711i	0.293154	+	0.130930i
$7$	−0.464975	+	2.33759i	−0.175744	+	0.883525i	0.787791	+	0.615943i	$0.211225\pi$
$7$	−0.464975	+	2.33759i	−0.175744	+	0.883525i	−0.963535	+	0.267582i	$0.913775\pi$
$8$	−0.659211	−	1.59148i	−0.233066	−	0.562672i
$9$	2.99551	+	0.163984i	0.998505	+	0.0546613i
$10$	−1.36255	−	0.271029i	−0.430877	−	0.0857068i
$11$	0.172899	+	0.258762i	0.0521312	+	0.0780198i	0.856620	−	0.515949i	$-0.172560\pi$
$11$	0.172899	+	0.258762i	0.0521312	+	0.0780198i	−0.804488	+	0.593968i	$0.797560\pi$
$12$	−2.13610	−	2.25624i	−0.616640	−	0.651320i
$13$	1.45541	−	1.45541i	0.403659	−	0.403659i	−0.475861	−	0.879520i	$-0.657864\pi$
$13$	1.45541	−	1.45541i	0.403659	−	0.403659i	0.879520	+	0.475861i	$0.157864\pi$
$14$	−0.601228	+	0.899802i	−0.160685	+	0.240482i
$15$	−5.22398	+	0.891383i	−1.34883	+	0.230154i
$16$			2.80552i			0.701380i
$17$	−2.58814	−	3.20960i	−0.627717	−	0.778442i
$17$	−2.58814	−	3.20960i	−0.627717	−	0.778442i
$18$	1.22810	+	0.589286i	0.289465	+	0.138896i
$19$	0.427451	−	1.03196i	0.0980640	−	0.236747i	−0.867233	−	0.497903i	$-0.834104\pi$
$19$	0.427451	−	1.03196i	0.0980640	−	0.236747i	0.965297	+	0.261156i	$0.0841036\pi$
$20$	4.56354	+	3.04926i	1.02044	+	0.681836i
$21$	−0.915758	+	4.02529i	−0.199835	+	0.878390i
$22$	0.0275675	+	0.138591i	0.00587740	+	0.0295477i
$23$	4.71932	−	3.15335i	0.984047	−	0.657519i	0.0441670	−	0.999024i	$-0.485937\pi$
$23$	4.71932	−	3.15335i	0.984047	−	0.657519i	0.939880	+	0.341505i	$0.110937\pi$
$24$	−1.06599	−	2.78671i	−0.217595	−	0.568834i
$25$	4.02951	−	1.66908i	0.805902	−	0.333816i
$26$	0.863423	−	0.357641i	0.169331	−	0.0701392i
$27$	5.17868	+	0.425777i	0.996637	+	0.0819409i
$28$	3.55487	−	2.37529i	0.671806	−	0.448887i
$29$	1.62296	+	8.15918i	0.301376	+	1.51512i	0.773618	+	0.633652i	$0.218445\pi$
$29$	1.62296	+	8.15918i	0.301376	+	1.51512i	−0.472242	+	0.881469i	$0.656555\pi$
$30$	−2.34629	−	0.533785i	−0.428373	−	0.0974553i
$31$	−5.25259	−	3.50967i	−0.943394	−	0.630355i	−0.0141803	−	0.999899i	$-0.504514\pi$
$31$	−5.25259	−	3.50967i	−0.943394	−	0.630355i	−0.929213	+	0.369544i	$0.879514\pi$
$32$	−1.80591	+	4.35984i	−0.319242	+	0.770718i
$33$	0.287105	+	0.456210i	0.0499785	+	0.0794159i
$34$	−0.528006	−	1.79611i	−0.0905522	−	0.308030i
$35$		−	7.29234i		−	1.23263i
$36$	−3.59161	−	4.00761i	−0.598601	−	0.667936i
$37$	−6.02262	+	9.01349i	−0.990113	+	1.48181i	−0.117694	+	0.993050i	$0.537550\pi$
$37$	−6.02262	+	9.01349i	−0.990113	+	1.48181i	−0.872419	+	0.488758i	$0.837450\pi$
$38$	0.358623	−	0.358623i	0.0581763	−	0.0581763i
$39$	2.58883	−	2.45099i	0.414545	−	0.392472i
$40$	2.92817	+	4.38232i	0.462985	+	0.692906i
$41$	5.42232	+	1.07857i	0.846824	+	0.168444i	0.599386	−	0.800460i	$-0.295411\pi$
$41$	5.42232	+	1.07857i	0.846824	+	0.168444i	0.247438	+	0.968904i	$0.420411\pi$
$42$	−1.08358	+	1.52945i	−0.167200	+	0.235999i
$43$	−1.13048	−	2.72921i	−0.172396	−	0.416201i	0.813939	−	0.580950i	$-0.197319\pi$
$43$	−1.13048	−	2.72921i	−0.172396	−	0.416201i	−0.986336	+	0.164749i	$0.947319\pi$
$44$	0.108911	−	0.547534i	0.0164190	−	0.0825439i
$45$	−9.08703	+	1.29596i	−1.35461	+	0.193190i
$46$	2.52763	−	0.502777i	0.372679	−	0.0741304i
$47$	−4.50710	−	4.50710i	−0.657428	−	0.657428i	0.297343	−	0.954771i	$-0.403900\pi$
$47$	−4.50710	−	4.50710i	−0.657428	−	0.657428i	−0.954771	+	0.297343i	$0.903900\pi$
$48$	−0.132858	+	4.85749i	−0.0191764	+	0.701118i
$49$	1.21904	+	0.504943i	0.174148	+	0.0721347i
$50$	1.98036			0.280065
$51$	−4.32913	−	5.67967i	−0.606199	−	0.795313i
$52$	−3.69219			−0.512015
$53$	−5.31572	−	2.20184i	−0.730170	−	0.302447i	−0.0135484	−	0.999908i	$-0.504313\pi$
$53$	−5.31572	−	2.20184i	−0.730170	−	0.302447i	−0.716622	+	0.697462i	$0.754313\pi$
$54$	2.09842	+	1.07845i	0.285559	+	0.146758i
$55$	−0.673306	−	0.673306i	−0.0907886	−	0.0907886i
$56$	4.02673	−	0.800967i	0.538095	−	0.107034i
$57$	0.788959	−	1.76649i	0.104500	−	0.233978i
$58$	−0.736910	+	3.70470i	−0.0967610	+	0.486451i
$59$	−0.337607	−	0.815054i	−0.0439526	−	0.106111i	0.900379	−	0.435107i	$-0.143290\pi$
$59$	−0.337607	−	0.815054i	−0.0439526	−	0.106111i	−0.944331	+	0.328996i	$0.893290\pi$
$60$	7.75693	+	5.49561i	1.00142	+	0.709480i
$61$	−3.27882	−	0.652199i	−0.419810	−	0.0835055i	−0.0193351	−	0.999813i	$-0.506155\pi$
$61$	−3.27882	−	0.652199i	−0.419810	−	0.0835055i	−0.400475	+	0.916308i	$0.631155\pi$
$62$	−1.59358	−	2.38495i	−0.202384	−	0.302890i
$63$	−1.77617	+	6.92603i	−0.223776	+	0.872598i
$64$	2.45248	−	2.45248i	0.306561	−	0.306561i
$65$	−3.49876	+	5.23626i	−0.433967	+	0.649478i
$66$	0.0411673	+	0.241262i	0.00506735	+	0.0296974i
$67$		−	2.49028i		−	0.304236i	−0.988362	−	0.152118i	$-0.951391\pi$
$67$		−	2.49028i		−	0.304236i	0.988362	−	0.152118i	$-0.0486095\pi$
$68$	−0.788274	+	7.35405i	−0.0955923	+	0.891809i
$69$	8.32038	−	5.23624i	1.00166	−	0.630369i
$70$	1.26711	−	3.05907i	0.151448	−	0.365628i
$71$	0.997325	+	0.666391i	0.118361	+	0.0790861i	0.613342	−	0.789818i	$-0.289825\pi$
$71$	0.997325	+	0.666391i	0.118361	+	0.0790861i	−0.494981	+	0.868904i	$0.664825\pi$
$72$	−1.71370	−	4.87539i	−0.201962	−	0.574571i
$73$	−0.197828	−	0.994547i	−0.0231540	−	0.116403i	0.967480	−	0.252948i	$-0.0814001\pi$
$73$	−0.197828	−	0.994547i	−0.0231540	−	0.116403i	−0.990634	+	0.136545i	$0.956400\pi$
$74$	−4.09260	+	2.73459i	−0.475755	+	0.317889i
$75$	7.05575	−	2.69903i	0.814728	−	0.311657i
$76$	−1.85116	+	0.766777i	−0.212343	+	0.0879554i
$77$	−0.685274	+	0.283850i	−0.0780942	+	0.0323477i
$78$	1.51187	−	0.578333i	0.171185	−	0.0654834i
$79$	11.0957	−	7.41392i	1.24836	−	0.834131i	0.257147	−	0.966372i	$-0.417217\pi$
$79$	11.0957	−	7.41392i	1.24836	−	0.834131i	0.991218	+	0.132242i	$0.0422175\pi$
$80$	−1.67464	−	8.41899i	−0.187231	−	0.941272i
$81$	8.94622	+	0.982433i	0.994024	+	0.109159i
$82$	2.08720	+	1.39462i	0.230493	+	0.154010i
$83$	−1.56322	+	3.77396i	−0.171586	+	0.414246i	−0.986156	−	0.165820i	$-0.946973\pi$
$83$	−1.56322	+	3.77396i	−0.171586	+	0.414246i	0.814570	+	0.580065i	$0.196973\pi$
$84$	6.26739	−	3.94423i	0.683828	−	0.430351i
$85$	9.68252	+	8.08669i	1.05022	+	0.877125i
$86$		−	1.34131i		−	0.144637i
$87$	2.42362	+	14.2037i	0.259839	+	1.52279i
$88$	0.297837	−	0.445745i	0.0317495	−	0.0475165i
$89$	0.687749	−	0.687749i	0.0729012	−	0.0729012i	−0.669716	−	0.742617i	$-0.733584\pi$
$89$	0.687749	−	0.687749i	0.0729012	−	0.0729012i	0.742617	+	0.669716i	$0.233584\pi$
$90$	−4.03710	−	1.03531i	−0.425548	−	0.109131i
$91$	2.72543	+	4.07889i	0.285703	+	0.427584i
$92$	−9.98596	−	1.98633i	−1.04111	−	0.207089i
$93$	−8.92815	−	6.32540i	−0.925806	−	0.655913i
$94$	−1.10754	−	2.67383i	−0.114234	−	0.275785i
$95$	−0.666738	+	3.35192i	−0.0684059	+	0.343900i
$96$	−3.33321	+	7.46312i	−0.340195	+	0.761702i
$97$	−6.12098	+	1.21754i	−0.621491	+	0.123622i	−0.495785	−	0.868445i	$-0.665120\pi$
$97$	−6.12098	+	1.21754i	−0.621491	+	0.123622i	−0.125706	+	0.992068i	$0.540120\pi$
$98$	0.423637	+	0.423637i	0.0427938	+	0.0427938i
$99$	0.475490	+	0.803479i	0.0477886	+	0.0807527i
$100$	−7.22828	−	2.99405i	−0.722828	−	0.299405i
$101$	3.89961			0.388026			0.194013	−	0.980999i	$-0.437850\pi$
$101$	3.89961			0.388026			0.194013	+	0.980999i	$0.437850\pi$
$102$	−0.829134	−	3.13479i	−0.0820965	−	0.310390i
$103$	−8.34664			−0.822419			−0.411210	−	0.911541i	$-0.634894\pi$
$103$	−8.34664			−0.822419			−0.411210	+	0.911541i	$0.634894\pi$
$104$	−3.27568	−	1.35683i	−0.321207	−	0.133048i
$105$	0.345335	−	12.6260i	0.0337012	−	1.23217i
$106$	−1.84730	−	1.84730i	−0.179426	−	0.179426i
$107$	−5.14612	+	1.02363i	−0.497494	+	0.0989577i	−0.437459	−	0.899239i	$-0.644121\pi$
$107$	−5.14612	+	1.02363i	−0.497494	+	0.0989577i	−0.0600352	+	0.998196i	$0.519121\pi$
$108$	−6.02874	−	7.10888i	−0.580116	−	0.684052i
$109$	−0.476511	+	2.39558i	−0.0456415	+	0.229455i	−0.996873	−	0.0790234i	$-0.974820\pi$
$109$	−0.476511	+	2.39558i	−0.0456415	+	0.229455i	0.951231	+	0.308479i	$0.0998198\pi$
$110$	−0.165453	−	0.399438i	−0.0157753	−	0.0380849i
$111$	−10.8544	+	15.3208i	−1.03026	+	1.45418i
$112$	−6.55815	−	1.30450i	−0.619687	−	0.123263i
$113$	4.29629	+	6.42985i	0.404161	+	0.604870i	0.976596	−	0.215080i	$-0.0690013\pi$
$113$	4.29629	+	6.42985i	0.404161	+	0.604870i	−0.572435	+	0.819950i	$0.694001\pi$
$114$	0.637904	−	0.603938i	0.0597452	−	0.0565640i
$115$	−12.2798	+	12.2798i	−1.14510	+	1.14510i
$116$	8.29075	−	12.4080i	0.769777	−	1.15205i
$117$	4.59838	−	4.12105i	0.425120	−	0.380991i
$118$		−	0.400569i		−	0.0368754i
$119$	8.70614	−	4.55763i	0.798091	−	0.417797i
$120$	4.86232	+	7.72623i	0.443867	+	0.705305i
$121$	4.17245	−	10.0732i	0.379314	−	0.915745i
$122$	−1.26211	−	0.843314i	−0.114266	−	0.0763501i
$123$	9.33714	+	2.12421i	0.841902	+	0.191534i
$124$	2.21078	+	11.1143i	0.198534	+	0.998098i
$125$	1.62433	−	1.08534i	0.145284	−	0.0970757i
$126$	−1.94854	+	2.59678i	−0.173590	+	0.231339i
$127$	11.7962	−	4.88615i	1.04674	−	0.433576i	0.208016	−	0.978125i	$-0.433299\pi$
$127$	11.7962	−	4.88615i	1.04674	−	0.433576i	0.838729	+	0.544550i	$0.183299\pi$
$128$	10.1746	−	4.21446i	0.899318	−	0.372510i
$129$	−1.82807	−	4.77890i	−0.160952	−	0.420759i
$130$	−2.37754	+	1.58862i	−0.208524	+	0.139331i
$131$	−2.00825	−	10.0962i	−0.175462	−	0.882107i	−0.963751	−	0.266802i	$-0.914033\pi$
$131$	−2.00825	−	10.0962i	−0.175462	−	0.882107i	0.788289	−	0.615305i	$-0.210967\pi$
$132$	0.214498	−	0.942845i	0.0186697	−	0.0820641i
$133$	2.21354	+	1.47904i	0.191938	+	0.128249i
$134$	0.432708	−	1.04465i	0.0373803	−	0.0902439i
$135$	−15.7947	+	1.81350i	−1.35939	+	0.156081i
$136$	−3.40187	+	6.23477i	−0.291708	+	0.534627i
$137$			19.0290i			1.62576i	0.582434	+	0.812878i	$0.302100\pi$
$137$			19.0290i			1.62576i	−0.582434	+	0.812878i	$0.697900\pi$
$138$	4.40016	−	0.750812i	0.374566	−	0.0639134i
$139$	1.03770	−	1.55303i	0.0880167	−	0.131726i	−0.784849	−	0.619688i	$-0.787259\pi$
$139$	1.03770	−	1.55303i	0.0880167	−	0.131726i	0.872865	+	0.487961i	$0.162259\pi$
$140$	−9.24985	+	9.24985i	−0.781755	+	0.781755i
$141$	−7.59017	−	8.01704i	−0.639207	−	0.675157i
$142$	0.302577	+	0.452838i	0.0253917	+	0.0380013i
$143$	0.628247	+	0.124966i	0.0525366	+	0.0104502i
$144$	−0.460060	+	8.40398i	−0.0383384	+	0.700331i
$145$	−9.74058	−	23.5158i	−0.808911	−	1.95288i
$146$	0.0898242	−	0.451577i	0.00743391	−	0.0373728i
$147$	2.08674	+	0.931988i	0.172111	+	0.0768691i
$148$	19.0723	−	3.79372i	1.56773	−	0.311842i
$149$	5.87087	+	5.87087i	0.480960	+	0.480960i	0.905438	−	0.424478i	$-0.139542\pi$
$149$	5.87087	+	5.87087i	0.480960	+	0.480960i	−0.424478	+	0.905438i	$0.639542\pi$
$150$	3.42880	+	0.0937814i	0.279960	+	0.00765722i
$151$	14.9344	+	6.18603i	1.21534	+	0.503412i	0.895927	−	0.444202i	$-0.146513\pi$
$151$	14.9344	+	6.18603i	1.21534	+	0.503412i	0.319418	+	0.947614i	$0.396513\pi$
$152$	−1.92412			−0.156067
$153$	−7.22650	−	10.0388i	−0.584228	−	0.811590i
$154$	−0.336787			−0.0271391
$155$	17.8573	+	7.39673i	1.43433	+	0.594120i
$156$	−6.39268	−	0.174847i	−0.511824	−	0.0139989i
$157$	3.33169	+	3.33169i	0.265898	+	0.265898i	0.827445	−	0.561547i	$-0.189794\pi$
$157$	3.33169	+	3.33169i	0.265898	+	0.265898i	−0.561547	+	0.827445i	$0.689794\pi$
$158$	5.94277	−	1.18209i	0.472782	−	0.0940421i
$159$	−9.09939	−	4.06401i	−0.721628	−	0.322297i
$160$	2.81685	−	14.1613i	0.222692	−	1.11955i
$161$	5.17687	+	12.4981i	0.407994	+	0.984986i
$162$	3.58214	+	1.96660i	0.281440	+	0.154511i
$163$	−3.23758	−	0.643995i	−0.253587	−	0.0504416i	0.0666598	−	0.997776i	$-0.478766\pi$
$163$	−3.23758	−	0.643995i	−0.253587	−	0.0504416i	−0.320247	+	0.947334i	$0.603766\pi$
$164$	−5.50976	−	8.24594i	−0.430240	−	0.643900i
$165$	−1.13388	−	1.19765i	−0.0882724	−	0.0932369i
$166$	−1.31151	+	1.31151i	−0.101793	+	0.101793i
$167$	3.69262	−	5.52640i	0.285743	−	0.427645i	−0.660634	−	0.750708i	$-0.729712\pi$
$167$	3.69262	−	5.52640i	0.285743	−	0.427645i	0.946378	+	0.323063i	$0.104712\pi$
$168$	7.00983	−	1.19611i	0.540820	−	0.0922817i
$169$			8.76354i			0.674118i
$170$	2.65659	+	5.07471i	0.203751	+	0.389212i
$171$	1.44966	−	3.02115i	0.110858	−	0.231033i
$172$	−2.02789	+	4.89576i	−0.154625	+	0.373298i
$173$	−12.5940	−	8.41505i	−0.957505	−	0.639784i	−0.0245198	−	0.999699i	$-0.507806\pi$
$173$	−12.5940	−	8.41505i	−0.957505	−	0.639784i	−0.932985	+	0.359915i	$0.882806\pi$
$174$	−1.45133	+	6.37943i	−0.110025	+	0.483623i
$175$	2.02799	+	10.1954i	0.153302	+	0.770701i
$176$	−0.725963	+	0.485073i	−0.0547215	+	0.0365637i
$177$	−0.545936	−	1.42718i	−0.0410350	−	0.107273i
$178$	0.408006	−	0.169002i	0.0305813	−	0.0126672i
$179$	−17.6614	+	7.31558i	−1.32007	+	0.546792i	−0.927807	−	0.373059i	$-0.878309\pi$
$179$	−17.6614	+	7.31558i	−1.32007	+	0.546792i	−0.392266	+	0.919852i	$0.628309\pi$
$180$	13.1701	+	9.88246i	0.981643	+	0.736595i
$181$	−6.27270	+	4.19128i	−0.466246	+	0.311535i	−0.766410	−	0.642352i	$-0.777959\pi$
$181$	−6.27270	+	4.19128i	−0.466246	+	0.311535i	0.300164	+	0.953888i	$0.402959\pi$
$182$	0.434548	+	2.18462i	0.0322109	+	0.161935i
$183$	−5.64608	−	1.28449i	−0.417370	−	0.0949522i
$184$	−8.12952	−	5.43197i	−0.599316	−	0.400450i
$185$	12.6929	−	30.6433i	0.933197	−	2.25294i
$186$	−2.64618	−	4.20478i	−0.194027	−	0.308310i
$187$	0.383034	−	1.22465i	0.0280103	−	0.0895554i
$188$			11.4339i			0.833904i
$189$	−3.40325	+	11.9076i	−0.247550	+	0.866154i
$190$	−0.862115	+	1.29025i	−0.0625444	+	0.0936043i
$191$	11.3186	−	11.3186i	0.818985	−	0.818985i	−0.166976	−	0.985961i	$-0.553400\pi$
$191$	11.3186	−	11.3186i	0.818985	−	0.818985i	0.985961	+	0.166976i	$0.0534002\pi$
$192$	4.36238	−	4.13010i	0.314828	−	0.298064i
$193$	−6.02621	−	9.01886i	−0.433776	−	0.649192i	0.548605	−	0.836082i	$-0.315159\pi$
$193$	−6.02621	−	9.01886i	−0.433776	−	0.649192i	−0.982381	+	0.186890i	$0.940159\pi$
$194$	−2.77925	−	0.552827i	−0.199538	−	0.0396906i
$195$	−6.30572	+	8.90039i	−0.451562	+	0.637370i
$196$	−0.905784	−	2.18676i	−0.0646989	−	0.156197i
$197$	1.09663	−	5.51314i	0.0781318	−	0.392795i	−0.921854	−	0.387536i	$-0.873326\pi$
$197$	1.09663	−	5.51314i	0.0781318	−	0.392795i	0.999986	−	0.00525859i	$-0.00167387\pi$
$198$	0.0598520	+	0.419672i	0.00425350	+	0.0298248i
$199$	−8.28425	+	1.64784i	−0.587255	+	0.116812i	−0.479770	−	0.877394i	$-0.659280\pi$
$199$	−8.28425	+	1.64784i	−0.587255	+	0.116812i	−0.107485	+	0.994207i	$0.534280\pi$
$200$	−5.31260	−	5.31260i	−0.375657	−	0.375657i
$201$	0.117929	−	4.31168i	0.00831810	−	0.304123i
$202$	1.63585	+	0.677590i	0.115098	+	0.0476751i
$203$	−19.8274			−1.39161
$204$	−1.71308	+	12.6955i	−0.119939	+	0.888862i
$205$	−16.9155			−1.18143
$206$	−3.50133	−	1.45030i	−0.243950	−	0.101047i
$207$	14.6539	−	8.67202i	1.01852	−	0.602747i
$208$	4.08319	+	4.08319i	0.283119	+	0.283119i
$209$	0.340938	−	0.0678168i	0.0235832	−	0.00469098i
$210$	2.33874	−	5.23647i	0.161388	−	0.361351i
$211$	−2.32730	+	11.7002i	−0.160218	+	0.805472i	0.814175	+	0.580620i	$0.197190\pi$
$211$	−2.32730	+	11.7002i	−0.160218	+	0.805472i	−0.974393	+	0.224852i	$0.927810\pi$
$212$	3.94975	+	9.53553i	0.271270	+	0.654903i
$213$	1.69521	+	1.20102i	0.116154	+	0.0822926i
$214$	−2.33661	−	0.464780i	−0.159727	−	0.0317717i
$215$	5.02150	+	7.51521i	0.342464	+	0.512533i
$216$	−2.73623	−	8.52242i	−0.186177	−	0.579878i
$217$	10.6465	−	10.6465i	0.722731	−	0.722731i
$218$	−0.616144	+	0.922125i	−0.0417306	+	0.0624542i
$219$	−0.295422	−	1.73133i	−0.0199628	−	0.116992i
$220$			1.70809i			0.115159i
$221$	−8.43812	−	0.904474i	−0.567609	−	0.0608415i
$222$	−7.21544	+	4.54087i	−0.484269	+	0.304763i
$223$	−2.08637	+	5.03695i	−0.139714	+	0.337299i	−0.978213	−	0.207604i	$-0.933434\pi$
$223$	−2.08637	+	5.03695i	−0.139714	+	0.337299i	0.838499	+	0.544903i	$0.183434\pi$
$224$	−9.35181	−	6.24868i	−0.624844	−	0.417508i
$225$	12.3442	−	4.33897i	0.822944	−	0.289265i
$226$	0.685010	+	3.44378i	0.0455662	+	0.229077i
$227$	−20.1039	+	13.4330i	−1.33434	+	0.891579i	−0.998728	−	0.0504205i	$-0.983944\pi$
$227$	−20.1039	+	13.4330i	−1.33434	+	0.891579i	−0.335614	+	0.942000i	$0.608944\pi$
$228$	−3.24142	+	1.23994i	−0.214668	+	0.0821168i
$229$	−6.34884	+	2.62978i	−0.419543	+	0.173781i	−0.582460	−	0.812859i	$-0.697910\pi$
$229$	−6.34884	+	2.62978i	−0.419543	+	0.173781i	0.162917	+	0.986640i	$0.447910\pi$
$230$	−7.28498	+	3.01754i	−0.480357	+	0.198970i
$231$	−1.19993	+	0.459007i	−0.0789494	+	0.0302004i
$232$	11.9153	−	7.96153i	0.782275	−	0.522700i
$233$	1.91961	+	9.65051i	0.125758	+	0.632226i	0.991325	+	0.131434i	$0.0419580\pi$
$233$	1.91961	+	9.65051i	0.125758	+	0.632226i	−0.865567	+	0.500792i	$0.833042\pi$
$234$	2.64504	−	0.929733i	0.172912	−	0.0607785i
$235$	16.2155	+	10.8349i	1.05779	+	0.706789i
$236$	−0.605611	+	1.46207i	−0.0394219	+	0.0951729i
$237$	19.5622	−	12.3110i	1.27070	−	0.799687i
$238$	4.44407	−	0.399115i	0.288066	−	0.0258708i
$239$		−	15.3938i		−	0.995745i	−0.867250	−	0.497872i	$-0.834115\pi$
$239$		−	15.3938i		−	0.995745i	0.867250	−	0.497872i	$-0.165885\pi$
$240$	−2.50079	−	14.6560i	−0.161425	−	0.946039i
$241$	8.31553	−	12.4451i	0.535650	−	0.801657i	−0.460652	−	0.887581i	$-0.652384\pi$
$241$	8.31553	−	12.4451i	0.535650	−	0.801657i	0.996302	+	0.0859240i	$0.0273842\pi$
$242$	3.50061	−	3.50061i	0.225028	−	0.225028i
$243$	15.4430	+	2.12464i	0.990668	+	0.136296i
$244$	3.33170	+	4.98624i	0.213290	+	0.319211i
$245$	−3.95958	−	0.787610i	−0.252968	−	0.0503185i
$246$	3.54774	+	2.51349i	0.226196	+	0.160255i
$247$	−0.879808	−	2.12405i	−0.0559809	−	0.135150i
$248$	−2.12299	+	10.6730i	−0.134810	+	0.677736i
$249$	−2.88529	+	6.46021i	−0.182848	+	0.409399i
$250$	0.869976	−	0.173049i	0.0550221	−	0.0109446i
$251$	18.8524	+	18.8524i	1.18995	+	1.18995i	0.977081	+	0.212869i	$0.0682809\pi$
$251$	18.8524	+	18.8524i	1.18995	+	1.18995i	0.212869	+	0.977081i	$0.431719\pi$
$252$	11.0382	−	6.53226i	0.695339	−	0.411494i
$253$	1.63194	+	0.675970i	0.102599	+	0.0424979i
$254$	5.79740			0.363761
$255$	16.3814	+	14.4598i	1.02584	+	0.905511i
$256$	−1.93622			−0.121014
$257$	−2.18812	−	0.906350i	−0.136491	−	0.0565366i	0.313392	−	0.949624i	$-0.398535\pi$
$257$	−2.18812	−	0.906350i	−0.136491	−	0.0565366i	−0.449884	+	0.893087i	$0.648535\pi$
$258$	0.0635187	−	2.32234i	0.00395450	−	0.144583i
$259$	−18.2695	−	18.2695i	−1.13521	−	1.13521i
$260$	11.0798	−	2.20391i	0.687139	−	0.136680i
$261$	3.52363	+	24.7071i	0.218107	+	1.52933i
$262$	0.911854	−	4.58420i	0.0563345	−	0.283213i
$263$	−12.1218	−	29.2646i	−0.747461	−	1.80453i	−0.572405	−	0.819971i	$-0.693990\pi$
$263$	−12.1218	−	29.2646i	−0.747461	−	1.80453i	−0.175055	−	0.984559i	$-0.556010\pi$
$264$	0.536785	−	0.757659i	0.0330368	−	0.0466307i
$265$	17.2661	+	3.43444i	1.06065	+	0.210976i
$266$	0.671562	+	1.00506i	0.0411761	+	0.0616244i
$267$	1.22334	−	1.15820i	0.0748672	−	0.0708808i
$268$	−3.15876	+	3.15876i	−0.192952	+	0.192952i
$269$	−10.6861	+	15.9929i	−0.651546	+	0.975107i	0.347750	+	0.937587i	$0.386946\pi$
$269$	−10.6861	+	15.9929i	−0.651546	+	0.975107i	−0.999296	+	0.0375200i	$0.988054\pi$
$270$	−6.94082	−	1.98371i	−0.422405	−	0.120725i
$271$		−	14.1909i		−	0.862033i	−0.902344	−	0.431017i	$-0.858155\pi$
$271$		−	14.1909i		−	0.862033i	0.902344	−	0.431017i	$-0.141845\pi$
$272$	9.00459	−	7.26109i	0.545983	−	0.440268i
$273$	4.52566	+	7.19127i	0.273905	+	0.435236i
$274$	−3.30645	+	7.98247i	−0.199750	+	0.482239i
$275$	1.12859	+	0.754103i	0.0680568	+	0.0454741i
$276$	−17.1957	−	3.91204i	−1.03506	−	0.235477i
$277$	−3.04146	−	15.2905i	−0.182744	−	0.918715i	−0.957934	−	0.286987i	$-0.907346\pi$
$277$	−3.04146	−	15.2905i	−0.182744	−	0.918715i	0.775191	−	0.631727i	$-0.217654\pi$
$278$	0.705158	−	0.471171i	0.0422926	−	0.0282590i
$279$	−15.1587	−	11.3746i	−0.907527	−	0.680980i
$280$	−11.6056	+	4.80719i	−0.693567	+	0.287285i
$281$	−2.87379	+	1.19036i	−0.171436	+	0.0710112i	−0.466751	−	0.884389i	$-0.654576\pi$
$281$	−2.87379	+	1.19036i	−0.171436	+	0.0710112i	0.295315	+	0.955400i	$0.404576\pi$
$282$	−1.79097	−	4.68193i	−0.106651	−	0.278805i
$283$	−6.70804	+	4.48217i	−0.398752	+	0.266437i	−0.738738	−	0.673993i	$-0.764578\pi$
$283$	−6.70804	+	4.48217i	−0.398752	+	0.266437i	0.339986	+	0.940431i	$0.389578\pi$
$284$	−0.419767	−	2.11031i	−0.0249086	−	0.125224i
$285$	−1.31313	+	5.77195i	−0.0777829	+	0.341901i
$286$	0.241829	+	0.161585i	0.0142997	+	0.00955474i
$287$	−5.04249	+	12.1736i	−0.297649	+	0.718587i
$288$	−6.12456	+	12.7638i	−0.360893	+	0.752116i
$289$	−3.60303	+	16.6138i	−0.211943	+	0.977282i
$290$		−	11.5572i		−	0.678661i
$291$	−10.6555	+	1.81819i	−0.624639	+	0.106584i
$292$	−1.01059	+	1.51245i	−0.0591400	+	0.0885093i
$293$	8.86520	−	8.86520i	0.517910	−	0.517910i	−0.399028	−	0.916939i	$-0.630652\pi$
$293$	8.86520	−	8.86520i	0.517910	−	0.517910i	0.916939	+	0.399028i	$0.130652\pi$
$294$	0.713425	+	0.753548i	0.0416078	+	0.0439478i
$295$	1.49963	+	2.24435i	0.0873117	+	0.130671i
$296$	18.3149	+	3.64307i	1.06453	+	0.211749i
$297$	0.785216	+	1.41366i	0.0455628	+	0.0820291i
$298$	1.44266	+	3.48288i	0.0835709	+	0.201758i
$299$	2.27914	−	11.4580i	0.131806	−	0.662634i
$300$	−12.3733	−	5.52621i	−0.714372	−	0.319056i
$301$	6.90542	−	1.37357i	0.398022	−	0.0791714i
$302$	5.18996	+	5.18996i	0.298649	+	0.298649i
$303$	6.75180	+	0.184669i	0.387881	+	0.0106090i
$304$	2.89518	+	1.19922i	0.166050	+	0.0687801i
$305$	10.2286			0.585689
$306$	−1.28712	−	5.46685i	−0.0735795	−	0.312519i
$307$	18.0205			1.02849			0.514243	−	0.857645i	$-0.328073\pi$
$307$	18.0205			1.02849			0.514243	+	0.857645i	$0.328073\pi$
$308$	1.22927	+	0.509180i	0.0700441	+	0.0290132i
$309$	−14.4514	−	0.395262i	−0.822112	−	0.0224857i
$310$	6.20571	+	6.20571i	0.352461	+	0.352461i
$311$	−10.5180	+	2.09217i	−0.596424	+	0.118636i	−0.484065	−	0.875032i	$-0.660840\pi$
$311$	−10.5180	+	2.09217i	−0.596424	+	0.118636i	−0.112358	+	0.993668i	$0.535840\pi$
$312$	−5.60728	−	2.50435i	−0.317450	−	0.141781i
$313$	−3.99371	+	20.0777i	−0.225738	+	1.13486i	0.687108	+	0.726556i	$0.258880\pi$
$313$	−3.99371	+	20.0777i	−0.225738	+	1.13486i	−0.912846	+	0.408305i	$0.866120\pi$
$314$	0.818702	+	1.97652i	0.0462020	+	0.111542i
$315$	1.19583	−	21.8443i	0.0673773	−	1.23079i
$316$	−23.4782	−	4.67011i	−1.32075	−	0.262714i
$317$	−4.70443	−	7.04068i	−0.264227	−	0.395444i	0.675505	−	0.737356i	$-0.263926\pi$
$317$	−4.70443	−	7.04068i	−0.264227	−	0.395444i	−0.939732	+	0.341911i	$0.888926\pi$
$318$	−3.11095	−	3.28591i	−0.174453	−	0.184265i
$319$	−1.83068	+	1.83068i	−0.102498	+	0.102498i
$320$	−5.89567	+	8.82350i	−0.329578	+	0.493248i
$321$	−8.95848	+	1.52861i	−0.500013	+	0.0853187i
$322$			6.14234i			0.342299i
$323$	−4.41847	+	1.29891i	−0.245850	+	0.0722732i
$324$	−10.1015	−	12.5938i	−0.561196	−	0.699658i
$325$	3.43541	−	8.29381i	0.190562	−	0.460058i
$326$	−1.24623	−	0.832707i	−0.0690225	−	0.0461194i
$327$	−0.938477	+	4.12515i	−0.0518979	+	0.228121i
$328$	−1.85794	−	9.34050i	−0.102588	−	0.515743i
$329$	12.6314	−	8.44005i	0.696393	−	0.465315i
$330$	−0.267550	−	0.699424i	−0.0147281	−	0.0385020i
$331$	13.8877	−	5.75246i	0.763335	−	0.316184i	0.0331656	−	0.999450i	$-0.489441\pi$
$331$	13.8877	−	5.75246i	0.763335	−	0.316184i	0.730169	+	0.683266i	$0.239441\pi$
$332$	6.76986	−	2.80417i	0.371544	−	0.153899i
$333$	−19.5189	+	26.0124i	−1.06963	+	1.42547i
$334$	2.50928	−	1.67664i	0.137301	−	0.0917419i
$335$	1.48647	+	7.47301i	0.0812148	+	0.408294i
$336$	−11.2930	−	2.56918i	−0.616085	−	0.140160i
$337$	−22.9447	−	15.3312i	−1.24988	−	0.835143i	−0.258481	−	0.966016i	$-0.583222\pi$
$337$	−22.9447	−	15.3312i	−1.24988	−	0.835143i	−0.991399	+	0.130873i	$0.958222\pi$
$338$	−1.52274	+	3.67622i	−0.0828261	+	0.199960i
$339$	7.13412	+	11.3361i	0.387472	+	0.615694i
$340$	−2.02420	−	22.5391i	−0.109778	−	1.22235i
$341$		−	1.96599i		−	0.106465i
$342$	1.13307	−	1.01545i	0.0612693	−	0.0549094i
$343$	−11.0161	+	16.4868i	−0.594815	+	0.890204i
$344$	−3.59825	+	3.59825i	−0.194005	+	0.194005i
$345$	−21.8428	+	20.6798i	−1.17598	+	1.11336i
$346$	−3.82088	−	5.71835i	−0.205412	−	0.307420i
$347$	16.6581	+	3.31350i	0.894252	+	0.177878i	0.620764	−	0.783997i	$-0.286823\pi$
$347$	16.6581	+	3.31350i	0.894252	+	0.177878i	0.273488	+	0.961875i	$0.411823\pi$
$348$	14.9422	−	21.0906i	0.800988	−	1.13058i
$349$	13.5795	+	32.7838i	0.726894	+	1.75488i	0.652677	+	0.757636i	$0.273646\pi$
$349$	13.5795	+	32.7838i	0.726894	+	1.75488i	0.0742177	+	0.997242i	$0.476354\pi$
$350$	−0.920817	+	4.62926i	−0.0492197	+	0.247444i
$351$	8.15681	−	6.91744i	0.435378	−	0.369226i
$352$	−1.44040	+	0.286514i	−0.0767737	+	0.0152712i
$353$	−16.3117	−	16.3117i	−0.868187	−	0.868187i	0.124085	−	0.992272i	$-0.460400\pi$
$353$	−16.3117	−	16.3117i	−0.868187	−	0.868187i	−0.992272	+	0.124085i	$0.960400\pi$
$354$	0.0189693	−	0.693547i	0.00100821	−	0.0368616i
$355$	−3.39062	−	1.40444i	−0.179955	−	0.0745399i
$356$	−1.74473			−0.0924704
$357$	15.2897	−	7.47881i	0.809215	−	0.395820i
$358$	−8.67992			−0.458748
$359$	14.5670	+	6.03383i	0.768814	+	0.318453i	0.732392	−	0.680883i	$-0.238404\pi$
$359$	14.5670	+	6.03383i	0.768814	+	0.318453i	0.0364222	+	0.999336i	$0.488404\pi$
$360$	8.05276	+	13.6075i	0.424418	+	0.717177i
$361$	12.5528	+	12.5528i	0.660674	+	0.660674i
$362$	−3.35960	+	0.668267i	−0.176577	+	0.0351233i
$363$	7.70123	−	17.2432i	0.404209	−	0.905032i
$364$	1.71678	−	8.63083i	0.0899836	−	0.452378i
$365$	1.18731	+	2.86642i	0.0621466	+	0.150035i
$366$	−2.14528	−	1.51989i	−0.112136	−	0.0794457i
$367$	17.1344	+	3.40824i	0.894408	+	0.177909i	0.620834	−	0.783942i	$-0.286794\pi$
$367$	17.1344	+	3.40824i	0.894408	+	0.177909i	0.273574	+	0.961851i	$0.411794\pi$
$368$	8.84679	+	13.2402i	0.461171	+	0.690191i
$369$	16.0658	+	4.12003i	0.836350	+	0.214480i
$370$	10.6491	−	10.6491i	0.553618	−	0.553618i
$371$	7.61868	−	11.4022i	0.395542	−	0.591971i
$372$	3.30143	+	19.3481i	0.171171	+	1.00315i
$373$		−	9.88473i		−	0.511812i	−0.966702	−	0.255906i	$-0.917626\pi$
$373$		−	9.88473i		−	0.511812i	0.966702	−	0.255906i	$-0.0823738\pi$
$374$	0.373473	−	0.447174i	0.0193118	−	0.0231228i
$375$	2.86376	−	1.80224i	0.147884	−	0.0930672i
$376$	−4.20181	+	10.1441i	−0.216692	+	0.523141i
$377$	14.2371	+	9.51290i	0.733246	+	0.489939i
$378$	−3.49668	+	4.40380i	−0.179850	+	0.226507i
$379$	−4.33652	−	21.8012i	−0.222752	−	1.11985i	−0.916624	−	0.399751i	$-0.869096\pi$
$379$	−4.33652	−	21.8012i	−0.222752	−	1.11985i	0.693872	−	0.720099i	$-0.255904\pi$
$380$	5.09740	−	3.40597i	0.261491	−	0.174723i
$381$	20.6554	−	7.90128i	1.05821	−	0.404795i
$382$	6.71474	−	2.78134i	0.343556	−	0.142306i
$383$	17.3935	−	7.20462i	0.888765	−	0.368139i	0.108875	−	0.994055i	$-0.465275\pi$
$383$	17.3935	−	7.20462i	0.888765	−	0.368139i	0.779890	+	0.625917i	$0.215275\pi$
$384$	17.8159	−	6.81511i	0.909166	−	0.347782i
$385$	1.88698	−	1.26084i	0.0961696	−	0.0642585i
$386$	−0.960832	−	4.83043i	−0.0489050	−	0.245862i
$387$	−2.93881	−	8.36078i	−0.149388	−	0.425002i
$388$	9.30842	+	6.21969i	0.472563	+	0.315757i
$389$	−4.70975	+	11.3703i	−0.238794	+	0.576499i	−0.997159	−	0.0753313i	$-0.975999\pi$
$389$	−4.70975	+	11.3703i	−0.238794	+	0.576499i	0.758365	+	0.651830i	$0.225999\pi$
$390$	−4.19171	+	2.63795i	−0.212255	+	0.133578i
$391$	−22.3353	−	6.98581i	−1.12954	−	0.353287i
$392$		−	2.27294i		−	0.114801i
$393$	−2.99899	−	17.5757i	−0.151279	−	0.886575i
$394$	1.41798	−	2.12216i	0.0714369	−	0.106913i
$395$	−28.8713	+	28.8713i	−1.45267	+	1.45267i
$396$	0.416032	−	1.62229i	0.0209064	−	0.0815230i
$397$	−3.63413	−	5.43887i	−0.182392	−	0.272969i	0.728995	−	0.684519i	$-0.239988\pi$
$397$	−3.63413	−	5.43887i	−0.182392	−	0.272969i	−0.911387	+	0.411550i	$0.864988\pi$
$398$	−3.76149	−	0.748206i	−0.188546	−	0.0375042i
$399$	3.76249	+	2.66564i	0.188360	+	0.133449i
$400$	4.68263	+	11.3049i	0.234132	+	0.565244i
$401$	1.04712	−	5.26423i	0.0522907	−	0.262883i	−0.945792	−	0.324772i	$-0.894712\pi$
$401$	1.04712	−	5.26423i	0.0522907	−	0.262883i	0.998083	+	0.0618889i	$0.0197125\pi$
$402$	0.798662	−	1.78822i	0.0398336	−	0.0891882i
$403$	−12.7527	+	2.53667i	−0.635259	+	0.126361i
$404$	−4.94640	−	4.94640i	−0.246092	−	0.246092i
$405$	−27.4328	+	2.39193i	−1.36315	+	0.118856i
$406$	−8.31741	−	3.44518i	−0.412786	−	0.170982i
$407$	−3.37366			−0.167226
$408$	−6.18526	+	10.6338i	−0.306216	+	0.526452i
$409$	29.6457			1.46589			0.732943	−	0.680290i	$-0.238146\pi$
$409$	29.6457			1.46589			0.732943	+	0.680290i	$0.238146\pi$
$410$	−7.09587	−	2.93921i	−0.350440	−	0.145157i
$411$	−0.901133	+	32.9468i	−0.0444496	+	1.62515i
$412$	10.5872	+	10.5872i	0.521592	+	0.521592i
$413$	2.06224	−	0.410205i	0.101476	−	0.0201849i
$414$	7.65400	−	1.09159i	0.376174	−	0.0536485i
$415$	2.43832	−	12.2583i	0.119692	−	0.601734i
$416$	3.71704	+	8.97372i	0.182243	+	0.439973i
$417$	1.87023	−	2.63978i	0.0915853	−	0.129271i
$418$	0.154804	+	0.0307924i	0.00757170	+	0.00150611i
$419$	−15.8338	−	23.6969i	−0.773530	−	1.15767i	−0.983667	−	0.179998i	$-0.942391\pi$
$419$	−15.8338	−	23.6969i	−0.773530	−	1.15767i	0.210137	−	0.977672i	$-0.432609\pi$
$420$	−16.4533	+	15.5772i	−0.802837	+	0.760089i
$421$	−10.1384	+	10.1384i	−0.494115	+	0.494115i	−0.909600	−	0.415485i	$-0.863612\pi$
$421$	−10.1384	+	10.1384i	−0.494115	+	0.494115i	0.415485	+	0.909600i	$0.363612\pi$
$422$	−3.00928	+	4.50371i	−0.146490	+	0.219237i
$423$	−12.7620	−	14.2402i	−0.620509	−	0.692381i
$424$			9.91133i			0.481337i
$425$	−15.7860	−	8.61329i	−0.765734	−	0.417806i
$426$	0.502438	+	0.798374i	0.0243432	+	0.0386814i
$427$	3.04914	−	7.36128i	0.147558	−	0.356237i
$428$	7.82591	+	5.22910i	0.378280	+	0.252758i
$429$	1.08183	+	0.246118i	0.0522313	+	0.0118827i
$430$	0.800640	+	4.02509i	0.0386103	+	0.194107i
$431$	14.2217	−	9.50263i	0.685035	−	0.457726i	−0.163724	−	0.986506i	$-0.552351\pi$
$431$	14.2217	−	9.50263i	0.685035	−	0.457726i	0.848759	+	0.528781i	$0.177351\pi$
$432$	−1.19453	+	14.5289i	−0.0574717	+	0.699021i
$433$	−24.9557	+	10.3370i	−1.19929	+	0.496763i	−0.890770	−	0.454454i	$-0.849835\pi$
$433$	−24.9557	+	10.3370i	−1.19929	+	0.496763i	−0.308522	+	0.951217i	$0.599835\pi$
$434$	6.31602	−	2.61618i	0.303178	−	0.125581i
$435$	−15.7513	−	41.1767i	−0.755215	−	1.97427i
$436$	3.64306	−	2.43421i	0.174471	−	0.116578i
$437$	−1.23685	−	6.21805i	−0.0591664	−	0.297450i
$438$	0.176907	−	0.777608i	0.00845293	−	0.0371555i
$439$	−3.58289	−	2.39401i	−0.171002	−	0.114260i	0.467124	−	0.884192i	$-0.345290\pi$
$439$	−3.58289	−	2.39401i	−0.171002	−	0.114260i	−0.638126	+	0.769932i	$0.720290\pi$
$440$	−0.627700	+	1.51540i	−0.0299244	+	0.0722440i
$441$	3.56885	+	1.71247i	0.169945	+	0.0815460i
$442$	−3.38255	−	1.84561i	−0.160891	−	0.0877868i
$443$			18.4676i			0.877421i	0.898628	+	0.438711i	$0.144565\pi$
$443$			18.4676i			0.877421i	−0.898628	+	0.438711i	$0.855435\pi$
$444$	33.2015	−	5.66527i	1.57567	−	0.268862i
$445$	−1.65332	+	2.47437i	−0.0783748	+	0.117296i
$446$	−1.75043	+	1.75043i	−0.0828851	+	0.0828851i
$447$	9.88682	+	10.4429i	0.467631	+	0.493930i
$448$	4.59256	+	6.87324i	0.216978	+	0.324730i
$449$	−34.5644	−	6.87529i	−1.63120	−	0.324465i	−0.707243	−	0.706971i	$-0.750061\pi$
$449$	−34.5644	−	6.87529i	−1.63120	−	0.324465i	−0.923953	+	0.382506i	$0.875061\pi$
$450$	5.93219	+	0.324747i	0.279646	+	0.0153087i
$451$	0.658424	+	1.58958i	0.0310040	+	0.0748502i
$452$	2.70628	−	13.6054i	0.127293	−	0.639944i
$453$	25.5645	+	11.4177i	1.20113	+	0.536452i
$454$	−10.7675	+	2.14179i	−0.505343	+	0.100519i
$455$	−10.6134	−	10.6134i	−0.497563	−	0.497563i
$456$	−3.33142	−	0.0911182i	−0.156008	−	0.00426700i
$457$	−7.09930	−	2.94063i	−0.332091	−	0.137557i	0.210406	−	0.977614i	$-0.432521\pi$
$457$	−7.09930	−	2.94063i	−0.332091	−	0.137557i	−0.542498	+	0.840057i	$0.682521\pi$
$458$	−3.12022			−0.145798
$459$	−12.0366	−	17.7234i	−0.561820	−	0.827260i
$460$	31.1522			1.45248
$461$	−28.6159	−	11.8531i	−1.33278	−	0.552054i	−0.401330	−	0.915933i	$-0.631452\pi$
$461$	−28.6159	−	11.8531i	−1.33278	−	0.552054i	−0.931446	+	0.363879i	$0.881452\pi$
$462$	−0.583114	−	0.0159488i	−0.0271289	−	0.000742006i
$463$	−13.2795	−	13.2795i	−0.617149	−	0.617149i	0.327650	−	0.944799i	$-0.393743\pi$
$463$	−13.2795	−	13.2795i	−0.617149	−	0.617149i	−0.944799	+	0.327650i	$0.893743\pi$
$464$	−22.8907	+	4.55325i	−1.06268	+	0.211379i
$465$	30.5679	+	13.6524i	1.41755	+	0.633114i
$466$	−0.871602	+	4.38184i	−0.0403762	+	0.202985i
$467$	−4.24049	−	10.2375i	−0.196227	−	0.473733i	0.794886	−	0.606759i	$-0.207531\pi$
$467$	−4.24049	−	10.2375i	−0.196227	−	0.473733i	−0.991113	+	0.133026i	$0.957531\pi$
$468$	−11.0600	−	0.605461i	−0.511250	−	0.0279874i
$469$	5.82126	+	1.15792i	0.268801	+	0.0534678i
$470$	4.91961	+	7.36271i	0.226925	+	0.339617i
$471$	5.61072	+	5.92627i	0.258529	+	0.273068i
$472$	−1.07459	+	1.07459i	−0.0494618	+	0.0494618i
$473$	0.510759	−	0.764404i	0.0234847	−	0.0351473i
$474$	10.3453	−	1.76525i	0.475176	−	0.0810807i
$475$		−	4.87173i		−	0.223531i
$476$	−16.8242	−	5.26211i	−0.771136	−	0.241188i
$477$	−15.5623	−	7.46735i	−0.712547	−	0.341906i
$478$	2.67481	−	6.45756i	0.122343	−	0.295362i
$479$	33.4090	+	22.3232i	1.52650	+	1.01997i	0.983640	+	0.180145i	$0.0576569\pi$
$479$	33.4090	+	22.3232i	1.52650	+	1.01997i	0.542855	+	0.839826i	$0.317343\pi$
$480$	5.54773	−	24.3855i	0.253218	−	1.11304i
$481$	4.35295	+	21.8838i	0.198478	+	0.997814i
$482$	5.65072	−	3.77569i	0.257383	−	0.171978i
$483$	8.37139	+	21.8843i	0.380911	+	0.995772i
$484$	−18.0697	+	7.48470i	−0.821348	+	0.340214i
$485$	17.6415	−	7.30734i	0.801058	−	0.331809i
$486$	6.10901	+	3.57462i	0.277110	+	0.162148i
$487$	−33.7348	+	22.5409i	−1.52867	+	1.02143i	−0.545632	+	0.838025i	$0.683710\pi$
$487$	−33.7348	+	22.5409i	−1.52867	+	1.02143i	−0.983038	+	0.183400i	$0.941290\pi$
$488$	1.12348	+	5.64811i	0.0508575	+	0.255678i
$489$	−5.57506	−	1.26833i	−0.252113	−	0.0573560i
$490$	−1.52415	−	1.01841i	−0.0688541	−	0.0460069i
$491$	−12.9778	+	31.3311i	−0.585679	+	1.41395i	0.301918	+	0.953334i	$0.402373\pi$
$491$	−12.9778	+	31.3311i	−0.585679	+	1.41395i	−0.887597	+	0.460620i	$0.847627\pi$
$492$	−9.14913	−	14.5380i	−0.412474	−	0.655422i
$493$	21.9872	−	26.3262i	0.990254	−	1.18567i
$494$		−	1.04389i		−	0.0469668i
$495$	−1.90649	−	2.12731i	−0.0856902	−	0.0956155i
$496$	9.84645	−	14.7363i	0.442119	−	0.661677i
$497$	−2.02148	+	2.02148i	−0.0906757	+	0.0906757i
$498$	−2.33287	+	2.20865i	−0.104538	+	0.0989721i
$499$	0.488815	+	0.731563i	0.0218824	+	0.0327493i	0.842250	−	0.539088i	$-0.181231\pi$
$499$	0.488815	+	0.731563i	0.0218824	+	0.0327493i	−0.820367	+	0.571837i	$0.806231\pi$
$500$	−3.43703	−	0.683668i	−0.153709	−	0.0305746i
$501$	6.65512	−	9.39355i	0.297329	−	0.419673i
$502$	4.63262	+	11.1841i	0.206764	+	0.499172i
$503$	−0.915226	+	4.60115i	−0.0408079	+	0.205155i	−0.995810	−	0.0914427i	$-0.970852\pi$
$503$	−0.915226	+	4.60115i	−0.0408079	+	0.205155i	0.955002	+	0.296598i	$0.0958522\pi$
$504$	12.1935	−	1.73899i	0.543141	−	0.0774607i
$505$	−11.7022	+	2.32772i	−0.520742	+	0.103582i
$506$	0.567126	+	0.567126i	0.0252118	+	0.0252118i
$507$	−0.415004	+	15.1732i	−0.0184310	+	0.673866i
$508$	−21.1605	−	8.76495i	−0.938844	−	0.388882i
$509$	23.4235			1.03823			0.519114	−	0.854705i	$-0.326262\pi$
$509$	23.4235			1.03823			0.519114	+	0.854705i	$0.326262\pi$
$510$	4.35931	+	8.91217i	0.193033	+	0.394637i
$511$	2.41683			0.106914
$512$	−21.1615	−	8.76536i	−0.935213	−	0.387378i
$513$	2.65302	−	5.16218i	0.117134	−	0.227916i
$514$	−0.760410	−	0.760410i	−0.0335402	−	0.0335402i
$515$	25.0472	−	4.98219i	1.10371	−	0.219542i
$516$	−3.74294	+	8.38050i	−0.164774	+	0.368931i
$517$	0.386992	−	1.94554i	0.0170199	−	0.0855649i
$518$	−4.48938	−	10.8383i	−0.197252	−	0.476209i
$519$	−21.4068	−	15.1662i	−0.939655	−	0.665724i
$520$	10.6398	+	2.11639i	0.466586	+	0.0928098i
$521$	−1.87377	−	2.80429i	−0.0820913	−	0.122858i	0.788152	−	0.615481i	$-0.211038\pi$
$521$	−1.87377	−	2.80429i	−0.0820913	−	0.122858i	−0.870243	+	0.492623i	$0.836038\pi$
$522$	−2.81494	+	10.9766i	−0.123206	+	0.480434i
$523$	29.9264	−	29.9264i	1.30859	−	1.30859i	0.386158	−	0.922433i	$-0.373802\pi$
$523$	29.9264	−	29.9264i	1.30859	−	1.30859i	0.922433	−	0.386158i	$-0.126198\pi$
$524$	−10.2590	+	15.3537i	−0.448166	+	0.670728i
$525$	3.02846	+	17.7484i	0.132173	+	0.774604i
$526$		−	14.3825i		−	0.627105i
$527$	2.32983	+	25.9422i	0.101489	+	1.13006i
$528$	−1.27991	+	0.805478i	−0.0557007	+	0.0350539i
$529$	3.52667	−	8.51414i	0.153334	−	0.370180i
$530$	6.64619	+	4.44084i	0.288692	+	0.192898i
$531$	−0.877650	−	2.49687i	−0.0380868	−	0.108355i
$532$	−0.931664	−	4.68379i	−0.0403928	−	0.203068i
$533$	9.46148	−	6.32196i	0.409822	−	0.273834i
$534$	0.714426	−	0.273289i	0.0309162	−	0.0118264i
$535$	14.8318	−	6.14353i	0.641235	−	0.265608i
$536$	−3.96323	+	1.64162i	−0.171185	+	0.0709073i
$537$	−30.9254	+	11.8299i	−1.33453	+	0.510496i
$538$	−7.26164	+	4.85208i	−0.313072	+	0.209188i
$539$	0.0801111	+	0.402746i	0.00345063	+	0.0173475i
$540$	22.3348	+	17.7342i	0.961137	+	0.763158i
$541$	26.5506	+	17.7405i	1.14150	+	0.762725i	0.974755	−	0.223275i	$-0.0716749\pi$
$541$	26.5506	+	17.7405i	1.14150	+	0.762725i	0.166743	+	0.986000i	$0.446675\pi$
$542$	2.46578	−	5.95292i	0.105914	−	0.255700i
$543$	−11.0590	+	6.95975i	−0.474589	+	0.298671i
$544$	18.6673	−	5.48766i	0.800353	−	0.235282i
$545$		−	7.47326i		−	0.320119i
$546$	0.648924	+	3.80304i	0.0277714	+	0.162755i
$547$	2.57308	−	3.85088i	0.110017	−	0.164652i	−0.772376	−	0.635166i	$-0.780932\pi$
$547$	2.57308	−	3.85088i	0.110017	−	0.164652i	0.882392	+	0.470514i	$0.155932\pi$
$548$	24.1370	−	24.1370i	1.03108	−	1.03108i
$549$	−9.71481	−	2.49135i	−0.414618	−	0.106328i
$550$	0.342403	+	0.512442i	0.0146001	+	0.0218506i
$551$	9.11366	+	1.81282i	0.388255	+	0.0772287i
$552$	−13.8182	−	9.78991i	−0.588143	−	0.416686i
$553$	12.1715	+	29.3845i	0.517583	+	1.24956i
$554$	1.38098	−	6.94268i	0.0586724	−	0.294966i
$555$	23.4276	−	52.4547i	0.994445	−	2.22658i
$556$	−3.28617	+	0.653660i	−0.139365	+	0.0277214i
$557$	−11.8460	−	11.8460i	−0.501933	−	0.501933i	0.410105	−	0.912038i	$-0.365492\pi$
$557$	−11.8460	−	11.8460i	−0.501933	−	0.501933i	−0.912038	+	0.410105i	$0.865492\pi$
$558$	−4.38249	−	7.40549i	−0.185525	−	0.313499i
$559$	−5.61745	−	2.32682i	−0.237593	−	0.0984141i
$560$	20.4588			0.864543
$561$	0.721182	−	2.10223i	0.0304483	−	0.0887561i
$562$	−1.41236			−0.0595770
$563$	12.3385	+	5.11078i	0.520006	+	0.215394i	0.627220	−	0.778842i	$-0.284193\pi$
$563$	12.3385	+	5.11078i	0.520006	+	0.215394i	−0.107214	+	0.994236i	$0.534193\pi$
$564$	−0.541462	+	19.7967i	−0.0227997	+	0.833592i
$565$	−16.7306	−	16.7306i	−0.703863	−	0.703863i
$566$	−3.59277	+	0.714647i	−0.151015	+	0.0300388i
$567$	−6.45629	+	20.4558i	−0.271139	+	0.859062i
$568$	0.403098	−	2.02651i	0.0169136	−	0.0850305i
$569$	14.8059	+	35.7445i	0.620694	+	1.49849i	0.850890	+	0.525345i	$0.176064\pi$
$569$	14.8059	+	35.7445i	0.620694	+	1.49849i	−0.230195	+	0.973144i	$0.573936\pi$
$570$	−1.55377	+	2.19311i	−0.0650802	+	0.0918593i
$571$	19.3864	+	3.85620i	0.811297	+	0.161377i	0.583270	−	0.812278i	$-0.301773\pi$
$571$	19.3864	+	3.85620i	0.811297	+	0.161377i	0.228026	+	0.973655i	$0.426773\pi$
$572$	−0.638378	−	0.955401i	−0.0266919	−	0.0399473i
$573$	20.1331	−	19.0611i	0.841071	−	0.796287i
$574$	−4.23055	+	4.23055i	−0.176580	+	0.176580i
$575$	13.7534	−	20.5834i	0.573555	−	0.858386i
$576$	7.74862	−	6.94429i	0.322859	−	0.289345i
$577$			34.4403i			1.43377i	0.697192	+	0.716884i	$0.254432\pi$
$577$			34.4403i			1.43377i	−0.697192	+	0.716884i	$0.745568\pi$
$578$	−4.39822	+	6.34327i	−0.182942	+	0.263845i
$579$	−10.0067	−	15.9007i	−0.415864	−	0.660809i
$580$	−17.4730	+	42.1836i	−0.725527	+	1.75158i
$581$	−8.09510	−	5.40897i	−0.335841	−	0.224402i
$582$	−4.78582	−	1.08878i	−0.198379	−	0.0451313i
$583$	−0.349331	−	1.75621i	−0.0144678	−	0.0727346i
$584$	−1.45239	+	0.970455i	−0.0601002	+	0.0401577i
$585$	−11.3392	+	15.1115i	−0.468820	+	0.624786i
$586$	5.25927	−	2.17846i	0.217258	−	0.0899913i
$587$	7.71494	−	3.19563i	0.318430	−	0.131898i	−0.217743	−	0.976006i	$-0.569870\pi$
$587$	7.71494	−	3.19563i	0.318430	−	0.131898i	0.536173	+	0.844108i	$0.319870\pi$
$588$	−1.46472	−	3.82905i	−0.0604041	−	0.157907i
$589$	−5.86706	+	3.92024i	−0.241748	+	0.161531i
$590$	0.239104	+	1.20206i	0.00984375	+	0.0494879i
$591$	2.15979	−	9.49354i	0.0888419	−	0.390512i
$592$	−25.2875	−	16.8966i	−1.03931	−	0.694445i
$593$	−0.0555800	+	0.134182i	−0.00228240	+	0.00551019i	−0.925017	−	0.379927i	$-0.875949\pi$
$593$	−0.0555800	+	0.134182i	−0.00228240	+	0.00551019i	0.922734	+	0.385437i	$0.125949\pi$
$594$	0.0837541	+	0.729456i	0.00343647	+	0.0299299i
$595$	−23.4055	+	18.8736i	−0.959531	+	0.773743i
$596$		−	14.8936i		−	0.610066i
$597$	−14.4214	+	2.46077i	−0.590229	+	0.100712i
$598$	2.94700	−	4.41050i	0.120512	−	0.180359i
$599$	−19.5023	+	19.5023i	−0.796842	+	0.796842i	−0.982596	−	0.185754i	$-0.940527\pi$
$599$	−19.5023	+	19.5023i	−0.796842	+	0.796842i	0.185754	+	0.982596i	$0.440527\pi$
$600$	−8.94667	−	9.44983i	−0.365246	−	0.385788i
$601$	−17.1815	−	25.7140i	−0.700849	−	1.04889i	−0.995635	−	0.0933313i	$-0.970248\pi$
$601$	−17.1815	−	25.7140i	−0.700849	−	1.04889i	0.294786	−	0.955563i	$-0.404752\pi$
$602$	3.13542	+	0.623675i	0.127790	+	0.0254191i
$603$	0.408367	−	7.45968i	0.0166300	−	0.303782i
$604$	−11.0967	−	26.7899i	−0.451519	−	1.09006i
$605$	−6.50820	+	32.7189i	−0.264596	+	1.33021i
$606$	2.80022	+	1.25065i	0.113751	+	0.0508041i
$607$	−9.07485	+	1.80510i	−0.368337	+	0.0732668i	−0.375788	−	0.926705i	$-0.622628\pi$
$607$	−9.07485	+	1.80510i	−0.368337	+	0.0732668i	0.00745155	+	0.999972i	$0.497628\pi$
$608$	3.72724	+	3.72724i	0.151159	+	0.151159i
$609$	−34.3293	−	0.938944i	−1.39109	−	0.0380479i
$610$	4.29081	+	1.77731i	0.173730	+	0.0719612i
$611$	−13.1194			−0.530754
$612$	−3.56723	+	21.8999i	−0.144197	+	0.885251i
$613$	−19.1051			−0.771649			−0.385824	−	0.922572i	$-0.626083\pi$
$613$	−19.1051			−0.771649			−0.385824	+	0.922572i	$0.626083\pi$
$614$	7.55944	+	3.13122i	0.305074	+	0.126366i
$615$	−29.2875	−	0.801046i	−1.18099	−	0.0323013i
$616$	0.903480	+	0.903480i	0.0364023	+	0.0364023i
$617$	11.8884	−	2.36475i	0.478610	−	0.0952014i	0.0501108	−	0.998744i	$-0.484043\pi$
$617$	11.8884	−	2.36475i	0.478610	−	0.0952014i	0.428499	+	0.903542i	$0.359043\pi$
$618$	−5.99354	−	2.67686i	−0.241096	−	0.107679i
$619$	7.99128	−	40.1749i	0.321197	−	1.61476i	−0.396244	−	0.918145i	$-0.629687\pi$
$619$	7.99128	−	40.1749i	0.321197	−	1.61476i	0.717441	−	0.696619i	$-0.245313\pi$
$620$	−13.2685	−	32.0331i	−0.532877	−	1.28648i
$621$	25.7825	−	14.3208i	1.03462	−	0.574674i
$622$	−4.77575	−	0.949955i	−0.191490	−	0.0380897i
$623$	1.28789	+	1.92746i	0.0515981	+	0.0772220i
$624$	6.87629	+	7.26302i	0.275272	+	0.290753i
$625$	−19.6468	+	19.6468i	−0.785872	+	0.785872i
$626$	−5.16400	+	7.72847i	−0.206395	+	0.308892i
$627$	0.593513	−	0.101273i	0.0237026	−	0.00404445i
$628$		−	8.45205i		−	0.337274i
$629$	44.5171	−	3.99801i	1.77501	−	0.159411i
$630$	4.29727	−	8.95569i	0.171208	−	0.356803i
$631$	2.60197	−	6.28172i	0.103583	−	0.250071i	−0.863588	−	0.504198i	$-0.831788\pi$
$631$	2.60197	−	6.28172i	0.103583	−	0.250071i	0.967171	+	0.254127i	$0.0817881\pi$
$632$	−19.1135	−	12.7712i	−0.760294	−	0.508012i
$633$	−4.58357	+	20.1475i	−0.182181	+	0.800790i
$634$	−0.750085	−	3.77093i	−0.0297897	−	0.149763i
$635$	−32.4823	+	21.7040i	−1.28902	+	0.861296i
$636$	6.38704	+	16.6969i	0.253263	+	0.662075i
$637$	2.50911	−	1.03931i	0.0994145	−	0.0411788i
$638$	−1.08605	+	0.449856i	−0.0429970	+	0.0178100i
$639$	2.87822	+	2.15973i	0.113861	+	0.0854376i
$640$	−28.0170	+	18.7204i	−1.10747	+	0.739988i
$641$	−3.06190	−	15.3932i	−0.120938	−	0.607995i	−0.992952	−	0.118515i	$-0.962187\pi$
$641$	−3.06190	−	15.3932i	−0.120938	−	0.607995i	0.872014	−	0.489480i	$-0.162813\pi$
$642$	−4.02360	−	0.915374i	−0.158799	−	0.0361269i
$643$	32.5931	+	21.7780i	1.28535	+	0.858842i	0.995173	−	0.0981314i	$-0.0312865\pi$
$643$	32.5931	+	21.7780i	1.28535	+	0.858842i	0.290175	+	0.956974i	$0.406287\pi$
$644$	9.28645	−	22.4195i	0.365937	−	0.883451i
$645$	8.33836	+	13.2497i	0.328323	+	0.521705i
$646$	−2.07920	−	0.222868i	−0.0818051	−	0.00876862i
$647$		−	26.5289i		−	1.04296i	−0.853264	−	0.521479i	$-0.825381\pi$
$647$		−	26.5289i		−	1.04296i	0.853264	−	0.521479i	$-0.174619\pi$
$648$	−4.33393	−	14.8853i	−0.170253	−	0.584751i
$649$	0.152533	−	0.228282i	0.00598746	−	0.00896087i
$650$	2.88224	−	2.88224i	0.113051	−	0.113051i
$651$	18.9375	−	17.9292i	0.742221	−	0.702701i
$652$	3.28979	+	4.92352i	0.128838	+	0.192820i
$653$	31.6152	+	6.28866i	1.23720	+	0.246094i	0.769992	−	0.638054i	$-0.220260\pi$
$653$	31.6152	+	6.28866i	1.23720	+	0.246094i	0.467207	+	0.884148i	$0.345260\pi$
$654$	−1.11046	+	1.56739i	−0.0434225	+	0.0612899i
$655$	12.0530	+	29.0985i	0.470950	+	1.13697i
$656$	−3.02594	+	15.2124i	−0.118143	+	0.593945i
$657$	−0.429506	−	3.01162i	−0.0167566	−	0.117495i
$658$	6.76529	−	1.34570i	0.263739	−	0.0524608i
$659$	31.2044	+	31.2044i	1.21555	+	1.21555i	0.969174	+	0.246379i	$0.0792407\pi$
$659$	31.2044	+	31.2044i	1.21555	+	1.21555i	0.246379	+	0.969174i	$0.420759\pi$
$660$	−0.0808879	+	2.95739i	−0.00314856	+	0.115116i
$661$	1.00677	+	0.417016i	0.0391587	+	0.0162201i	0.402177	−	0.915562i	$-0.368254\pi$
$661$	1.00677	+	0.417016i	0.0391587	+	0.0162201i	−0.363018	+	0.931782i	$0.618254\pi$
$662$	6.82528			0.265272
$663$	−14.5669	−	1.96560i	−0.565733	−	0.0763377i
$664$	7.03666			0.273075
$665$	−7.52539	−	3.11712i	−0.291822	−	0.120877i
$666$	−12.7079	+	7.52038i	−0.492420	+	0.291409i
$667$	33.3880	+	33.3880i	1.29279	+	1.29279i
$668$	−11.6937	+	2.32602i	−0.452443	+	0.0899965i
$669$	−3.85088	+	8.62219i	−0.148884	+	0.333353i
$670$	−0.674938	+	3.39314i	−0.0260751	+	0.131089i
$671$	−0.398142	−	0.961201i	−0.0153701	−	0.0371067i
$672$	−15.8958	−	11.2619i	−0.613196	−	0.434435i
$673$	30.1550	+	5.99820i	1.16239	+	0.231214i	0.738342	−	0.674426i	$-0.235609\pi$
$673$	30.1550	+	5.99820i	1.16239	+	0.231214i	0.424048	+	0.905640i	$0.360609\pi$
$674$	−6.96117	−	10.4181i	−0.268134	−	0.401291i
$675$	21.5782	−	6.92794i	0.830545	−	0.266657i
$676$	11.1160	−	11.1160i	0.427537	−	0.427537i
$677$	6.61301	−	9.89706i	0.254158	−	0.380375i	−0.682347	−	0.731029i	$-0.739041\pi$
$677$	6.61301	−	9.89706i	0.254158	−	0.380375i	0.936505	+	0.350654i	$0.114041\pi$
$678$	1.02295	+	5.99500i	0.0392860	+	0.230237i
$679$		−	14.8744i		−	0.570829i
$680$	6.48696	−	20.7403i	0.248763	−	0.795356i
$681$	−35.4441	+	22.3059i	−1.35822	+	0.854764i
$682$	0.341608	−	0.824715i	0.0130808	−	0.0315800i
$683$	−31.5197	−	21.0608i	−1.20607	−	0.805869i	−0.220540	−	0.975378i	$-0.570782\pi$
$683$	−31.5197	−	21.0608i	−1.20607	−	0.805869i	−0.985529	+	0.169509i	$0.945782\pi$
$684$	−5.67093	+	1.99333i	−0.216833	+	0.0762169i
$685$	−11.3586	−	57.1035i	−0.433989	−	2.18181i
$686$	−7.48588	+	5.00191i	−0.285812	+	0.190974i
$687$	−11.1169	+	4.25255i	−0.424138	+	0.162245i
$688$	7.65686	−	3.17157i	0.291915	−	0.120915i
$689$	−10.9412	+	4.53198i	−0.416826	+	0.172655i
$690$	−12.7561	+	4.87959i	−0.485617	+	0.185763i
$691$	−11.3597	+	7.59031i	−0.432143	+	0.288749i	−0.752555	−	0.658529i	$-0.771179\pi$
$691$	−11.3597	+	7.59031i	−0.432143	+	0.288749i	0.320412	+	0.947278i	$0.396179\pi$
$692$	5.30074	+	26.6486i	0.201504	+	1.01303i
$693$	−2.09929	+	0.737902i	−0.0797456	+	0.0280306i
$694$	6.41215	+	4.28446i	0.243402	+	0.162636i
$695$	−2.18699	+	5.27985i	−0.0829571	+	0.200276i
$696$	21.0072	−	13.2204i	0.796274	−	0.501116i
$697$	−10.5720	−	20.1949i	−0.400442	−	0.764938i
$698$			16.1121i			0.609850i
$699$	2.86660	+	16.7998i	0.108425	+	0.635428i
$700$	10.3598	−	15.5046i	0.391565	−	0.586018i
$701$	19.2749	−	19.2749i	0.728005	−	0.728005i	−0.242217	−	0.970222i	$-0.577875\pi$
$701$	19.2749	−	19.2749i	0.728005	−	0.728005i	0.970222	+	0.242217i	$0.0778747\pi$
$702$	4.62366	−	1.48448i	0.174509	−	0.0560282i
$703$	6.72717	+	10.0679i	0.253720	+	0.379719i
$704$	1.05864	+	0.210577i	0.0398992	+	0.00793643i
$705$	27.5625	+	19.5274i	1.03807	+	0.735446i
$706$	−4.00831	−	9.67692i	−0.150855	−	0.364196i
$707$	−1.81322	+	9.11568i	−0.0681932	+	0.342831i
$708$	−1.11779	+	2.50276i	−0.0420093	+	0.0940595i
$709$	29.7252	−	5.91272i	1.11635	−	0.222057i	0.397762	−	0.917488i	$-0.369787\pi$
$709$	29.7252	−	5.91272i	1.11635	−	0.222057i	0.718592	+	0.695432i	$0.244787\pi$
$710$	−1.17830	−	1.17830i	−0.0442207	−	0.0442207i
$711$	34.4531	−	20.3890i	1.29209	−	0.764646i
$712$	−1.54791	−	0.641164i	−0.0580103	−	0.0240287i
$713$	−35.8559			−1.34281
$714$	7.71337	−	0.480576i	0.288666	−	0.0179851i
$715$	−1.95988			−0.0732953
$716$	31.6816	+	13.1230i	1.18400	+	0.490428i
$717$	0.728988	−	26.6529i	0.0272245	−	0.995372i
$718$	5.06226	+	5.06226i	0.188922	+	0.188922i
$719$	0.877852	−	0.174616i	0.0327384	−	0.00651206i	−0.178694	−	0.983905i	$-0.557187\pi$
$719$	0.877852	−	0.174616i	0.0327384	−	0.00651206i	0.211432	+	0.977393i	$0.432187\pi$
$720$	−3.63583	−	25.4938i	−0.135500	−	0.950099i
$721$	3.88098	−	19.5110i	0.144535	−	0.726628i
$722$	3.08462	+	7.44693i	0.114798	+	0.277146i
$723$	14.9869	−	21.1536i	0.557368	−	0.786712i
$724$	13.2729	+	2.64014i	0.493282	+	0.0981199i
$725$	20.1580	+	30.1686i	0.748651	+	1.12043i
$726$	6.22674	−	5.89519i	0.231096	−	0.218791i
$727$	−30.4698	+	30.4698i	−1.13006	+	1.13006i	−0.139898	+	0.990166i	$0.544677\pi$
$727$	−30.4698	+	30.4698i	−1.13006	+	1.13006i	−0.990166	+	0.139898i	$0.955323\pi$
$728$	4.69483	−	7.02631i	0.174002	−	0.260412i
$729$	26.6374	+	4.40993i	0.986571	+	0.163331i
$730$			1.40874i			0.0521398i
$731$	−5.83384	+	10.6920i	−0.215772	+	0.395457i
$732$	5.53239	+	8.79097i	0.204483	+	0.324924i
$733$	2.03359	−	4.90952i	0.0751123	−	0.181337i	−0.881864	−	0.471505i	$-0.843711\pi$
$733$	2.03359	−	4.90952i	0.0751123	−	0.181337i	0.956976	+	0.290168i	$0.0937110\pi$
$734$	6.59550	+	4.40697i	0.243444	+	0.162664i
$735$	−6.81833	−	1.55118i	−0.251498	−	0.0572161i
$736$	5.22546	+	26.2702i	0.192613	+	0.968331i
$737$	0.644391	−	0.430569i	0.0237365	−	0.0158602i
$738$	6.02354	+	4.51988i	0.221730	+	0.166379i
$739$	−24.1993	+	10.0237i	−0.890186	+	0.368727i	−0.780438	−	0.625233i	$-0.785004\pi$
$739$	−24.1993	+	10.0237i	−0.890186	+	0.368727i	−0.109747	+	0.993960i	$0.535004\pi$
$740$	−54.9690	+	22.7689i	−2.02070	+	0.837001i
$741$	−1.42272	−	3.71924i	−0.0522648	−	0.136630i
$742$	5.17719	−	3.45928i	0.190060	−	0.126994i
$743$	1.23104	+	6.18886i	0.0451625	+	0.227047i	0.996774	−	0.0802553i	$-0.0255736\pi$
$743$	1.23104	+	6.18886i	0.0451625	+	0.227047i	−0.951612	+	0.307303i	$0.900574\pi$
$744$	−4.18118	+	18.3787i	−0.153290	+	0.673797i
$745$	−21.1221	−	14.1133i	−0.773853	−	0.517072i
$746$	1.71756	−	4.14655i	0.0628842	−	0.151816i
$747$	−5.30153	+	11.0486i	−0.193973	+	0.404247i
$748$	−2.03924	+	1.06754i	−0.0745621	+	0.0390330i
$749$		−	12.5055i		−	0.456940i
$750$	1.51447	−	0.258419i	0.0553008	−	0.00943613i
$751$	15.1572	−	22.6843i	0.553093	−	0.827762i	−0.444594	−	0.895732i	$-0.646652\pi$
$751$	15.1572	−	22.6843i	0.553093	−	0.827762i	0.997687	+	0.0679697i	$0.0216521\pi$
$752$	12.6448	−	12.6448i	0.461107	−	0.461107i
$753$	31.7483	+	33.5338i	1.15697	+	1.22204i
$754$	4.31936	+	6.46438i	0.157302	+	0.235419i
$755$	−48.5087	−	9.64897i	−1.76541	−	0.351162i
$756$	19.4209	−	10.7873i	0.706330	−	0.392329i
$757$	−5.39949	−	13.0355i	−0.196248	−	0.473784i	0.794868	−	0.606782i	$-0.207540\pi$
$757$	−5.39949	−	13.0355i	−0.196248	−	0.473784i	−0.991116	+	0.132997i	$0.957540\pi$
$758$	1.96901	−	9.89888i	0.0715176	−	0.359543i
$759$	2.79353	+	1.24766i	0.101399	+	0.0452872i
$760$	5.77402	−	1.14852i	0.209446	−	0.0416614i
$761$	−31.4843	−	31.4843i	−1.14131	−	1.14131i	−0.988212	−	0.153094i	$-0.951076\pi$
$761$	−31.4843	−	31.4843i	−1.14131	−	1.14131i	−0.153094	−	0.988212i	$-0.548924\pi$
$762$	10.0376	+	0.274541i	0.363625	+	0.00994556i
$763$	−5.37832	−	2.22777i	−0.194708	−	0.0806508i
$764$	−28.7138			−1.03883
$765$	27.6780	+	25.8116i	1.00070	+	0.933220i
$766$	8.54826			0.308861
$767$	−1.67760	−	0.694885i	−0.0605746	−	0.0250908i
$768$	−3.35239	−	0.0916915i	−0.120969	−	0.00330863i
$769$	−16.1543	−	16.1543i	−0.582537	−	0.582537i	0.353062	−	0.935600i	$-0.385140\pi$
$769$	−16.1543	−	16.1543i	−0.582537	−	0.582537i	−0.935600	+	0.353062i	$0.885140\pi$
$770$	1.01065	−	0.201031i	0.0364214	−	0.00724467i
$771$	−3.74560	−	1.67288i	−0.134895	−	0.0602472i
$772$	−3.79598	+	19.0837i	−0.136620	+	0.686836i
$773$	3.98178	+	9.61286i	0.143215	+	0.345751i	0.979169	−	0.203049i	$-0.0650850\pi$
$773$	3.98178	+	9.61286i	0.143215	+	0.345751i	−0.835954	+	0.548799i	$0.815085\pi$
$774$	0.219953	−	4.01791i	0.00790605	−	0.144421i
$775$	−27.0233	−	5.37527i	−0.970705	−	0.193085i
$776$	5.97270	+	8.93878i	0.214407	+	0.320883i
$777$	−30.7666	−	32.4970i	−1.10375	−	1.16582i
$778$	−3.95139	+	3.95139i	−0.141664	+	0.141664i
$779$	3.43081	−	5.13457i	0.122922	−	0.183965i
$780$	19.2879	−	3.29116i	0.690619	−	0.117842i
$781$			0.373289i			0.0133573i
$782$	−8.15558	−	6.81142i	−0.291643	−	0.243576i
$783$	4.93080	+	42.9448i	0.176212	+	1.53472i
$784$	−1.41663	+	3.42004i	−0.0505938	+	0.122144i
$785$	−11.9867	−	8.00924i	−0.427823	−	0.285862i
$786$	1.79587	−	7.89391i	0.0640567	−	0.281567i
$787$	7.55680	+	37.9906i	0.269371	+	1.35422i	0.844236	+	0.535971i	$0.180054\pi$
$787$	7.55680	+	37.9906i	0.269371	+	1.35422i	−0.574865	+	0.818248i	$0.694946\pi$
$788$	−8.38406	+	5.60205i	−0.298670	+	0.199565i
$789$	−19.6018	−	51.2428i	−0.697844	−	1.82429i
$790$	−17.1279	+	7.09460i	−0.609382	+	0.252414i
$791$	−17.0280	+	7.05323i	−0.605446	+	0.250784i
$792$	0.965270	−	1.28639i	0.0342994	−	0.0457100i
$793$	−5.72127	+	3.82283i	−0.203168	+	0.135753i
$794$	−0.579434	−	2.91301i	−0.0205634	−	0.103379i
$795$	29.7319	+	6.76404i	1.05448	+	0.239896i
$796$	12.5982	+	8.41784i	0.446531	+	0.298362i
$797$	10.9971	−	26.5493i	0.389537	−	0.940426i	−0.600501	−	0.799624i	$-0.705032\pi$
$797$	10.9971	−	26.5493i	0.389537	−	0.940426i	0.990038	−	0.140802i	$-0.0449680\pi$
$798$	1.11515	+	1.77197i	0.0394759	+	0.0627272i
$799$	−2.80096	+	26.1310i	−0.0990908	+	0.924448i
$800$			20.5822i			0.727691i
$801$	2.17294	−	1.94738i	0.0767771	−	0.0688074i
$802$	1.35396	−	2.02635i	0.0478100	−	0.0715528i
$803$	0.223147	−	0.223147i	0.00787469	−	0.00787469i
$804$	−5.61867	+	5.31950i	−0.198155	+	0.187604i
$805$	−22.9953	−	34.4149i	−0.810478	−	1.21297i
$806$	−5.79041	−	1.15178i	−0.203959	−	0.0405699i
$807$	−19.2594	+	27.1842i	−0.677963	+	0.956929i
$808$	−2.57067	−	6.20614i	−0.0904357	−	0.218331i
$809$	8.48221	−	42.6430i	0.298219	−	1.49925i	−0.483350	−	0.875427i	$-0.660580\pi$
$809$	8.48221	−	42.6430i	0.298219	−	1.49925i	0.781569	−	0.623819i	$-0.214420\pi$
$810$	−11.9234	−	3.76330i	−0.418947	−	0.132229i
$811$	−33.1881	+	6.60153i	−1.16539	+	0.231811i	−0.739624	−	0.673020i	$-0.764997\pi$
$811$	−33.1881	+	6.60153i	−1.16539	+	0.231811i	−0.425770	+	0.904832i	$0.639997\pi$
$812$	25.1498	+	25.1498i	0.882584	+	0.882584i
$813$	0.672019	−	24.5701i	0.0235688	−	0.861711i
$814$	−1.41522	−	0.586202i	−0.0496033	−	0.0205464i
$815$	10.1000			0.353786
$816$	15.9344	−	12.1454i	0.557817	−	0.425176i
$817$	−3.29966			−0.115440
$818$	12.4361	+	5.15119i	0.434817	+	0.180107i
$819$	7.49519	+	12.6653i	0.261903	+	0.442562i
$820$	21.4561	+	21.4561i	0.749281	+	0.749281i
$821$	−22.3951	+	4.45467i	−0.781595	+	0.155469i	−0.569732	−	0.821830i	$-0.692953\pi$
$821$	−22.3951	+	4.45467i	−0.781595	+	0.155469i	−0.211863	+	0.977299i	$0.567953\pi$
$822$	−6.10281	+	13.6643i	−0.212860	+	0.476597i
$823$	−1.56241	+	7.85479i	−0.0544624	+	0.273801i	−0.998415	−	0.0562801i	$-0.982076\pi$
$823$	−1.56241	+	7.85479i	−0.0544624	+	0.273801i	0.943953	+	0.330081i	$0.107076\pi$
$824$	5.50220	+	13.2835i	0.191678	+	0.462752i
$825$	1.91834	+	1.35910i	0.0667881	+	0.0473179i
$826$	0.936366	+	0.186255i	0.0325803	+	0.00648063i
$827$	−7.25454	−	10.8572i	−0.252265	−	0.377541i	0.683625	−	0.729833i	$-0.260402\pi$
$827$	−7.25454	−	10.8572i	−0.252265	−	0.377541i	−0.935890	+	0.352292i	$0.885402\pi$
$828$	−29.5874	−	7.58763i	−1.02823	−	0.263688i
$829$	24.5541	−	24.5541i	0.852800	−	0.852800i	−0.137678	−	0.990477i	$-0.543964\pi$
$829$	24.5541	−	24.5541i	0.852800	−	0.852800i	0.990477	+	0.137678i	$0.0439638\pi$
$830$	3.15283	−	4.71854i	0.109436	−	0.163783i
$831$	−4.54191	−	26.6180i	−0.157557	−	0.923368i
$832$		−	7.13876i		−	0.247492i
$833$	−1.53439	−	5.21949i	−0.0531633	−	0.180845i
$834$	1.24323	−	0.782394i	0.0430494	−	0.0270921i
$835$	−7.78231	+	18.7881i	−0.269318	+	0.650191i
$836$	−0.518478	−	0.346436i	−0.0179319	−	0.0119817i
$837$	−25.7072	−	20.4119i	−0.888569	−	0.705538i
$838$	−2.52457	−	12.6919i	−0.0872098	−	0.438433i
$839$	26.1126	−	17.4479i	0.901507	−	0.602368i	−0.0160941	−	0.999870i	$-0.505123\pi$
$839$	26.1126	−	17.4479i	0.901507	−	0.602368i	0.917601	+	0.397503i	$0.130123\pi$
$840$	−20.3216	+	7.77360i	−0.701162	+	0.268215i
$841$	−37.1456	+	15.3862i	−1.28088	+	0.530560i
$842$	−6.01459	+	2.49133i	−0.207277	+	0.0858568i
$843$	−5.03207	+	1.92491i	−0.173314	+	0.0662974i
$844$	17.7929	−	11.8888i	0.612457	−	0.409231i
$845$	−5.23104	−	26.2982i	−0.179953	−	0.904686i
$846$	−2.87918	−	8.19112i	−0.0989881	−	0.281616i
$847$	21.6069	+	14.4373i	0.742422	+	0.496070i
$848$	6.17732	−	14.9134i	0.212130	−	0.512127i
$849$	−11.8266	+	7.44278i	−0.405887	+	0.255436i
$850$	−5.12544	−	6.35615i	−0.175801	−	0.218014i
$851$			61.5290i			2.10919i
$852$	−0.626851	−	3.67368i	−0.0214756	−	0.125858i
$853$	14.9568	−	22.3845i	0.512112	−	0.766430i	−0.481838	−	0.876260i	$-0.660031\pi$
$853$	14.9568	−	22.3845i	0.512112	−	0.766430i	0.993950	+	0.109830i	$0.0350307\pi$
$854$	2.55817	−	2.55817i	0.0875388	−	0.0875388i
$855$	−2.54689	+	9.93139i	−0.0871016	+	0.339646i
$856$	5.02145	+	7.51514i	0.171630	+	0.256862i
$857$	17.9881	+	3.57805i	0.614462	+	0.122224i	0.492502	−	0.870311i	$-0.336082\pi$
$857$	17.9881	+	3.57805i	0.614462	+	0.122224i	0.121959	+	0.992535i	$0.461082\pi$
$858$	0.411052	+	0.291221i	0.0140331	+	0.00994213i
$859$	3.04555	+	7.35261i	0.103913	+	0.250868i	0.967281	−	0.253706i	$-0.0816496\pi$
$859$	3.04555	+	7.35261i	0.103913	+	0.250868i	−0.863368	+	0.504574i	$0.831650\pi$
$860$	3.16310	−	15.9020i	0.107861	−	0.542254i
$861$	−9.30707	+	20.8387i	−0.317184	+	0.710181i
$862$	7.61702	−	1.51512i	0.259437	−	0.0516052i
$863$	−1.39363	−	1.39363i	−0.0474397	−	0.0474397i	0.682989	−	0.730429i	$-0.260680\pi$
$863$	−1.39363	−	1.39363i	−0.0474397	−	0.0474397i	−0.730429	+	0.682989i	$0.760680\pi$
$864$	−11.2085	+	21.8093i	−0.381322	+	0.741968i
$865$	42.8160	+	17.7350i	1.45579	+	0.603007i
$866$	−12.2648			−0.416775
$867$	−7.02506	+	28.5946i	−0.238584	+	0.971122i
$868$	−27.0087			−0.916736
$869$	3.83688	+	1.58929i	0.130157	+	0.0539130i
$870$	0.547299	−	20.0101i	0.0185552	−	0.678407i
$871$	−3.62439	−	3.62439i	−0.122808	−	0.122808i
$872$	4.12663	−	0.820839i	0.139745	−	0.0277971i
$873$	−18.5351	+	2.64341i	−0.627319	+	0.0894659i
$874$	0.561594	−	2.82332i	0.0189962	−	0.0955003i
$875$	1.78181	+	4.30166i	0.0602360	+	0.145423i
$876$	−1.82135	+	2.57080i	−0.0615379	+	0.0868593i
$877$	−2.25554	−	0.448655i	−0.0761643	−	0.0151500i	0.156861	−	0.987621i	$-0.449863\pi$
$877$	−2.25554	−	0.448655i	−0.0761643	−	0.0151500i	−0.233025	+	0.972471i	$0.574863\pi$
$878$	−1.08701	−	1.62682i	−0.0366847	−	0.0549026i
$879$	15.7691	−	14.9294i	0.531877	−	0.503557i
$880$	1.88897	−	1.88897i	0.0636773	−	0.0636773i
$881$	−12.3943	+	18.5493i	−0.417573	+	0.624942i	−0.979308	−	0.202375i	$-0.935134\pi$
$881$	−12.3943	+	18.5493i	−0.417573	+	0.624942i	0.561735	+	0.827317i	$0.310134\pi$
$882$	1.19954	+	1.33848i	0.0403906	+	0.0450690i
$883$		−	36.1867i		−	1.21778i	−0.793255	−	0.608890i	$-0.791615\pi$
$883$		−	36.1867i		−	1.21778i	0.793255	−	0.608890i	$-0.208385\pi$
$884$	9.55592	+	11.8505i	0.321401	+	0.398574i
$885$	2.49018	+	3.95689i	0.0837063	+	0.133009i
$886$	−3.20890	+	7.74697i	−0.107805	+	0.260264i
$887$	3.25224	+	2.17308i	0.109200	+	0.0729648i	0.608971	−	0.793193i	$-0.291583\pi$
$887$	3.25224	+	2.17308i	0.109200	+	0.0729648i	−0.499771	+	0.866157i	$0.666583\pi$
$888$	31.5380	+	7.17494i	1.05835	+	0.240775i
$889$	5.93686	+	29.8466i	0.199116	+	1.00102i
$890$	−1.12349	+	0.750694i	−0.0376596	+	0.0251633i
$891$	1.29258	+	2.48481i	0.0433031	+	0.0832442i
$892$	9.03546	−	3.74261i	0.302530	−	0.125312i
$893$	−6.57770	+	2.72457i	−0.220114	+	0.0911743i
$894$	2.33289	+	6.09860i	0.0780234	+	0.203968i
$895$	48.6327	−	32.4954i	1.62561	−	1.08620i
$896$	5.12074	+	25.7437i	0.171072	+	0.860036i
$897$	4.48871	−	19.7305i	0.149874	−	0.658782i
$898$	−13.3048	−	8.88998i	−0.443987	−	0.296662i
$899$	20.1113	−	48.5529i	0.670748	−	1.61933i
$900$	−21.1614	−	10.1540i	−0.705382	−	0.338468i
$901$	6.69081	+	22.7600i	0.222903	+	0.758246i
$902$			0.781218i			0.0260117i
$903$	12.0211	−	2.05120i	0.400038	−	0.0682596i
$904$	7.40080	−	11.0761i	0.246147	−	0.368385i
$905$	16.3217	−	16.3217i	0.542552	−	0.542552i
$906$	8.74014	+	9.23168i	0.290372	+	0.306702i
$907$	−16.6035	−	24.8490i	−0.551311	−	0.825096i	0.446249	−	0.894909i	$-0.352760\pi$
$907$	−16.6035	−	24.8490i	−0.551311	−	0.825096i	−0.997560	+	0.0698131i	$0.977760\pi$
$908$	42.5393	+	8.46160i	1.41172	+	0.280808i
$909$	11.6813	+	0.639474i	0.387446	+	0.0212100i
$910$	−2.60804	−	6.29637i	−0.0864558	−	0.208723i
$911$	−3.57313	+	17.9633i	−0.118383	+	0.595151i	0.875361	+	0.483470i	$0.160624\pi$
$911$	−3.57313	+	17.9633i	−0.118383	+	0.595151i	−0.993744	+	0.111682i	$0.964376\pi$
$912$	4.95593	+	2.21344i	0.164107	+	0.0732943i
$913$	−1.24684	+	0.248012i	−0.0412643	+	0.00820799i
$914$	−2.46713	−	2.46713i	−0.0816053	−	0.0816053i
$915$	17.7099	+	0.484385i	0.585470	+	0.0160133i
$916$	11.3888	+	4.71739i	0.376296	+	0.155867i
$917$	24.5345			0.810200
$918$	−1.96963	−	9.52627i	−0.0650075	−	0.314414i
$919$	18.9782			0.626034			0.313017	−	0.949747i	$-0.398660\pi$
$919$	18.9782			0.626034			0.313017	+	0.949747i	$0.398660\pi$
$920$	27.6380	+	11.4480i	0.911198	+	0.377431i
$921$	31.2008	+	0.853377i	1.02810	+	0.0281197i
$922$	−9.94452	−	9.94452i	−0.327505	−	0.327505i
$923$	2.42140	−	0.481646i	0.0797012	−	0.0158536i
$924$	2.10425	+	0.939809i	0.0692247	+	0.0309174i
$925$	−9.22400	+	46.3722i	−0.303283	+	1.52471i
$926$	−3.26319	−	7.87803i	−0.107235	−	0.258888i
$927$	−25.0025	−	1.36872i	−0.821190	−	0.0449545i
$928$	−38.5036	−	7.65885i	−1.26394	−	0.251414i
$929$	16.9777	+	25.4089i	0.557019	+	0.833638i	0.997956	−	0.0639000i	$-0.0203539\pi$
$929$	16.9777	+	25.4089i	0.557019	+	0.833638i	−0.440937	+	0.897538i	$0.645354\pi$
$930$	10.4507	+	11.0385i	0.342692	+	0.361966i
$931$	1.04216	−	1.04216i	0.0341554	−	0.0341554i
$932$	9.80614	−	14.6759i	0.321211	−	0.480726i
$933$	−18.3101	+	3.12430i	−0.599444	+	0.102285i
$934$		−	5.03134i		−	0.164630i
$935$	−0.418429	+	3.90366i	−0.0136841	+	0.127663i
$936$	−9.58986	−	4.60157i	−0.313454	−	0.150407i
$937$	14.2347	−	34.3655i	0.465026	−	1.12267i	−0.501282	−	0.865284i	$-0.667138\pi$
$937$	14.2347	−	34.3655i	0.465026	−	1.12267i	0.966308	−	0.257388i	$-0.0828618\pi$
$938$	2.24076	+	1.49723i	0.0731634	+	0.0488863i
$939$	−7.86552	+	34.5735i	−0.256682	+	1.12826i
$940$	−6.82501	−	34.3117i	−0.222607	−	1.11912i
$941$	−37.1328	+	24.8113i	−1.21049	+	0.808826i	−0.986178	−	0.165690i	$-0.947015\pi$
$941$	−37.1328	+	24.8113i	−1.21049	+	0.808826i	−0.224316	+	0.974516i	$0.572015\pi$
$942$	1.32390	+	3.46092i	0.0431351	+	0.112763i
$943$	28.9908	−	12.0084i	0.944069	−	0.391046i
$944$	2.28665	−	0.947162i	0.0744242	−	0.0308275i
$945$	3.10492	−	37.7647i	0.101003	−	1.22849i
$946$	0.347080	−	0.231911i	0.0112845	−	0.00754009i
$947$	−6.99454	−	35.1639i	−0.227292	−	1.14267i	−0.910837	−	0.412766i	$-0.864563\pi$
$947$	−6.99454	−	35.1639i	−0.227292	−	1.14267i	0.683545	−	0.729908i	$-0.260437\pi$
$948$	−40.4291	−	9.19767i	−1.31308	−	0.298727i
$949$	−1.73540	−	1.15956i	−0.0563334	−	0.0376408i
$950$	0.846505	−	2.04364i	0.0274643	−	0.0663046i
$951$	−7.81186	−	12.4130i	−0.253317	−	0.402521i
$952$	−12.9925	−	10.8512i	−0.421091	−	0.351689i
$953$			38.2262i			1.23827i	0.785286	+	0.619134i	$0.212516\pi$
$953$			38.2262i			1.23827i	−0.785286	+	0.619134i	$0.787484\pi$
$954$	−5.23070	−	5.83655i	−0.169350	−	0.188965i
$955$	−27.2094	+	40.7218i	−0.880477	+	1.31773i
$956$	−19.5261	+	19.5261i	−0.631518	+	0.631518i
$957$	−3.25634	+	3.08295i	−0.105262	+	0.0996576i
$958$	10.1359	+	15.1694i	0.327476	+	0.490102i
$959$	−44.4819	−	8.84801i	−1.43640	−	0.285717i
$960$	−10.6256	+	14.9978i	−0.342941	+	0.484053i
$961$	3.40876	+	8.22947i	0.109960	+	0.265467i
$962$	−1.97647	+	9.93639i	−0.0637240	+	0.320362i
$963$	−15.5831	+	2.22241i	−0.502159	+	0.0716160i
$964$	−26.3334	+	5.23804i	−0.848143	+	0.168706i
$965$	23.4673	+	23.4673i	0.755439	+	0.755439i
$966$	−0.290875	+	10.6349i	−0.00935877	+	0.342171i
$967$	17.2448	+	7.14301i	0.554554	+	0.229704i	0.642319	−	0.766437i	$-0.277972\pi$
$967$	17.2448	+	7.14301i	0.554554	+	0.229704i	−0.0877650	+	0.996141i	$0.527972\pi$
$968$	−18.7818			−0.603669
$969$	−7.71167	+	2.03970i	−0.247735	+	0.0655244i
$970$	8.67014			0.278381
$971$	12.3249	+	5.10513i	0.395524	+	0.163831i	0.571575	−	0.820550i	$-0.306333\pi$
$971$	12.3249	+	5.10513i	0.395524	+	0.163831i	−0.176051	+	0.984381i	$0.556333\pi$
$972$	−16.8934	−	22.2834i	−0.541857	−	0.714740i
$973$	3.14784	+	3.14784i	0.100915	+	0.100915i
$974$	−18.0681	+	3.59397i	−0.578939	+	0.115158i
$975$	6.34084	−	14.1972i	0.203069	−	0.454676i
$976$	1.82976	−	9.19880i	0.0585691	−	0.294447i
$977$	1.38266	+	3.33804i	0.0442352	+	0.106793i	0.944453	−	0.328647i	$-0.106593\pi$
$977$	1.38266	+	3.33804i	0.0442352	+	0.106793i	−0.900218	+	0.435440i	$0.856593\pi$
$978$	−2.11830	−	1.50077i	−0.0677358	−	0.0479893i
$979$	0.296875	+	0.0590521i	0.00948816	+	0.00188731i
$980$	4.02344	+	6.02150i	0.128524	+	0.192350i
$981$	−1.82023	+	7.09786i	−0.0581156	+	0.226617i
$982$	−10.8881	+	10.8881i	−0.347453	+	0.347453i
$983$	25.6445	−	38.3798i	0.817934	−	1.22412i	−0.153813	−	0.988100i	$-0.549155\pi$
$983$	25.6445	−	38.3798i	0.817934	−	1.22412i	0.971747	−	0.236024i	$-0.0758445\pi$
$984$	−2.77452	−	16.2602i	−0.0884484	−	0.518355i
$985$			17.1988i			0.547999i
$986$	13.7978	−	7.22310i	0.439412	−	0.230030i
$987$	22.2698	−	14.0150i	0.708855	−	0.446101i
$988$	−1.57823	+	3.81019i	−0.0502102	+	0.121218i
$989$	−13.9412	−	9.31524i	−0.443306	−	0.296208i
$990$	−0.430114	−	1.22365i	−0.0136699	−	0.0388903i
$991$	−1.66369	−	8.36392i	−0.0528488	−	0.265689i	0.945323	−	0.326137i	$-0.105747\pi$
$991$	−1.66369	−	8.36392i	−0.0528488	−	0.265689i	−0.998171	+	0.0604481i	$0.980747\pi$
$992$	24.7873	−	16.5623i	0.786997	−	0.525855i
$993$	24.3176	−	9.30217i	0.771694	−	0.295195i
$994$	−1.19924	+	0.496741i	−0.0380376	+	0.0157557i
$995$	23.8763	−	9.88990i	0.756930	−	0.313531i
$996$	11.8542	−	4.53455i	0.375613	−	0.143683i
$997$	−11.0513	+	7.38423i	−0.349998	+	0.233861i	−0.718125	−	0.695915i	$-0.754999\pi$
$997$	−11.0513	+	7.38423i	−0.349998	+	0.233861i	0.368127	+	0.929776i	$0.379999\pi$
$998$	0.0779377	+	0.391819i	0.00246708	+	0.0124028i
$999$	−35.0270	+	44.1137i	−1.10820	+	1.39569i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	51.2.i.a.41.3	yes	32
3.2	odd	2	inner	51.2.i.a.41.2	yes	32
4.3	odd	2		816.2.cj.c.449.1		32
12.11	even	2		816.2.cj.c.449.3		32
17.2	even	8		867.2.i.g.827.2		32
17.3	odd	16		867.2.i.d.131.3		32
17.4	even	4		867.2.i.c.503.2		32
17.5	odd	16	inner	51.2.i.a.5.2	✓	32
17.6	odd	16		867.2.i.f.65.3		32
17.7	odd	16		867.2.i.b.224.2		32
17.8	even	8		867.2.i.b.329.3		32
17.9	even	8		867.2.i.i.329.3		32
17.10	odd	16		867.2.i.i.224.2		32
17.11	odd	16		867.2.i.g.65.3		32
17.12	odd	16		867.2.i.h.158.2		32
17.13	even	4		867.2.i.d.503.2		32
17.14	odd	16		867.2.i.c.131.3		32
17.15	even	8		867.2.i.f.827.2		32
17.16	even	2		867.2.i.h.653.3		32
51.2	odd	8		867.2.i.g.827.3		32
51.5	even	16	inner	51.2.i.a.5.3	yes	32
51.8	odd	8		867.2.i.b.329.2		32
51.11	even	16		867.2.i.g.65.2		32
51.14	even	16		867.2.i.c.131.2		32
51.20	even	16		867.2.i.d.131.2		32
51.23	even	16		867.2.i.f.65.2		32
51.26	odd	8		867.2.i.i.329.2		32
51.29	even	16		867.2.i.h.158.3		32
51.32	odd	8		867.2.i.f.827.3		32
51.38	odd	4		867.2.i.c.503.3		32
51.41	even	16		867.2.i.b.224.3		32
51.44	even	16		867.2.i.i.224.3		32
51.47	odd	4		867.2.i.d.503.3		32
51.50	odd	2		867.2.i.h.653.2		32
68.39	even	16		816.2.cj.c.209.3		32
204.107	odd	16		816.2.cj.c.209.1		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
51.2.i.a.5.2	✓	32	17.5	odd	16	inner
51.2.i.a.5.3	yes	32	51.5	even	16	inner
51.2.i.a.41.2	yes	32	3.2	odd	2	inner
51.2.i.a.41.3	yes	32	1.1	even	1	trivial
816.2.cj.c.209.1		32	204.107	odd	16
816.2.cj.c.209.3		32	68.39	even	16
816.2.cj.c.449.1		32	4.3	odd	2
816.2.cj.c.449.3		32	12.11	even	2
867.2.i.b.224.2		32	17.7	odd	16
867.2.i.b.224.3		32	51.41	even	16
867.2.i.b.329.2		32	51.8	odd	8
867.2.i.b.329.3		32	17.8	even	8
867.2.i.c.131.2		32	51.14	even	16
867.2.i.c.131.3		32	17.14	odd	16
867.2.i.c.503.2		32	17.4	even	4
867.2.i.c.503.3		32	51.38	odd	4
867.2.i.d.131.2		32	51.20	even	16
867.2.i.d.131.3		32	17.3	odd	16
867.2.i.d.503.2		32	17.13	even	4
867.2.i.d.503.3		32	51.47	odd	4
867.2.i.f.65.2		32	51.23	even	16
867.2.i.f.65.3		32	17.6	odd	16
867.2.i.f.827.2		32	17.15	even	8
867.2.i.f.827.3		32	51.32	odd	8
867.2.i.g.65.2		32	51.11	even	16
867.2.i.g.65.3		32	17.11	odd	16
867.2.i.g.827.2		32	17.2	even	8
867.2.i.g.827.3		32	51.2	odd	8
867.2.i.h.158.2		32	17.12	odd	16
867.2.i.h.158.3		32	51.29	even	16
867.2.i.h.653.2		32	51.50	odd	2
867.2.i.h.653.3		32	17.16	even	2
867.2.i.i.224.2		32	17.10	odd	16
867.2.i.i.224.3		32	51.44	even	16
867.2.i.i.329.2		32	51.26	odd	8
867.2.i.i.329.3		32	17.9	even	8

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:	\( N \)	\(=\)	\( 51 = 3 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	51.i (of order \(16\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.419490 + 0.173759i) q^{2} +(1.73140 + 0.0473558i) q^{3} +(-1.26843 - 1.26843i) q^{4} +(-3.00087 + 0.596910i) q^{5} +(0.718078 + 0.320711i) q^{6} +(-0.464975 + 2.33759i) q^{7} +(-0.659211 - 1.59148i) q^{8} +(2.99551 + 0.163984i) q^{9} +(-1.36255 - 0.271029i) q^{10} +(0.172899 + 0.258762i) q^{11} +(-2.13610 - 2.25624i) q^{12} +(1.45541 - 1.45541i) q^{13} +(-0.601228 + 0.899802i) q^{14} +(-5.22398 + 0.891383i) q^{15} +2.80552i q^{16} +(-2.58814 - 3.20960i) q^{17} +(1.22810 + 0.589286i) q^{18} +(0.427451 - 1.03196i) q^{19} +(4.56354 + 3.04926i) q^{20} +(-0.915758 + 4.02529i) q^{21} +(0.0275675 + 0.138591i) q^{22} +(4.71932 - 3.15335i) q^{23} +(-1.06599 - 2.78671i) q^{24} +(4.02951 - 1.66908i) q^{25} +(0.863423 - 0.357641i) q^{26} +(5.17868 + 0.425777i) q^{27} +(3.55487 - 2.37529i) q^{28} +(1.62296 + 8.15918i) q^{29} +(-2.34629 - 0.533785i) q^{30} +(-5.25259 - 3.50967i) q^{31} +(-1.80591 + 4.35984i) q^{32} +(0.287105 + 0.456210i) q^{33} +(-0.528006 - 1.79611i) q^{34} -7.29234i q^{35} +(-3.59161 - 4.00761i) q^{36} +(-6.02262 + 9.01349i) q^{37} +(0.358623 - 0.358623i) q^{38} +(2.58883 - 2.45099i) q^{39} +(2.92817 + 4.38232i) q^{40} +(5.42232 + 1.07857i) q^{41} +(-1.08358 + 1.52945i) q^{42} +(-1.13048 - 2.72921i) q^{43} +(0.108911 - 0.547534i) q^{44} +(-9.08703 + 1.29596i) q^{45} +(2.52763 - 0.502777i) q^{46} +(-4.50710 - 4.50710i) q^{47} +(-0.132858 + 4.85749i) q^{48} +(1.21904 + 0.504943i) q^{49} +1.98036 q^{50} +(-4.32913 - 5.67967i) q^{51} -3.69219 q^{52} +(-5.31572 - 2.20184i) q^{53} +(2.09842 + 1.07845i) q^{54} +(-0.673306 - 0.673306i) q^{55} +(4.02673 - 0.800967i) q^{56} +(0.788959 - 1.76649i) q^{57} +(-0.736910 + 3.70470i) q^{58} +(-0.337607 - 0.815054i) q^{59} +(7.75693 + 5.49561i) q^{60} +(-3.27882 - 0.652199i) q^{61} +(-1.59358 - 2.38495i) q^{62} +(-1.77617 + 6.92603i) q^{63} +(2.45248 - 2.45248i) q^{64} +(-3.49876 + 5.23626i) q^{65} +(0.0411673 + 0.241262i) q^{66} -2.49028i q^{67} +(-0.788274 + 7.35405i) q^{68} +(8.32038 - 5.23624i) q^{69} +(1.26711 - 3.05907i) q^{70} +(0.997325 + 0.666391i) q^{71} +(-1.71370 - 4.87539i) q^{72} +(-0.197828 - 0.994547i) q^{73} +(-4.09260 + 2.73459i) q^{74} +(7.05575 - 2.69903i) q^{75} +(-1.85116 + 0.766777i) q^{76} +(-0.685274 + 0.283850i) q^{77} +(1.51187 - 0.578333i) q^{78} +(11.0957 - 7.41392i) q^{79} +(-1.67464 - 8.41899i) q^{80} +(8.94622 + 0.982433i) q^{81} +(2.08720 + 1.39462i) q^{82} +(-1.56322 + 3.77396i) q^{83} +(6.26739 - 3.94423i) q^{84} +(9.68252 + 8.08669i) q^{85} -1.34131i q^{86} +(2.42362 + 14.2037i) q^{87} +(0.297837 - 0.445745i) q^{88} +(0.687749 - 0.687749i) q^{89} +(-4.03710 - 1.03531i) q^{90} +(2.72543 + 4.07889i) q^{91} +(-9.98596 - 1.98633i) q^{92} +(-8.92815 - 6.32540i) q^{93} +(-1.10754 - 2.67383i) q^{94} +(-0.666738 + 3.35192i) q^{95} +(-3.33321 + 7.46312i) q^{96} +(-6.12098 + 1.21754i) q^{97} +(0.423637 + 0.423637i) q^{98} +(0.475490 + 0.803479i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 8 q^{3} - 16 q^{4} - 8 q^{6} - 16 q^{7} - 8 q^{9} - 16 q^{10} + 16 q^{12} - 16 q^{13} + 16 q^{15} + 16 q^{18} - 16 q^{19} + 16 q^{21} - 16 q^{22} + 16 q^{24} + 16 q^{25} - 8 q^{27} + 32 q^{28} - 8 q^{30}+ \cdots - 64 q^{99}+O(q^{100}) \) 32 * q - 8 * q^3 - 16 * q^4 - 8 * q^6 - 16 * q^7 - 8 * q^9 - 16 * q^10 + 16 * q^12 - 16 * q^13 + 16 * q^15 + 16 * q^18 - 16 * q^19 + 16 * q^21 - 16 * q^22 + 16 * q^24 + 16 * q^25 - 8 * q^27 + 32 * q^28 - 8 * q^30 + 16 * q^31 + 96 * q^34 + 8 * q^36 + 16 * q^37 - 24 * q^39 + 16 * q^40 - 56 * q^42 + 16 * q^43 - 40 * q^45 - 32 * q^46 - 64 * q^48 - 48 * q^49 - 40 * q^51 - 96 * q^52 - 24 * q^54 - 48 * q^55 + 8 * q^57 - 48 * q^58 + 32 * q^60 - 32 * q^61 + 64 * q^63 + 16 * q^64 + 72 * q^66 + 80 * q^69 + 48 * q^70 + 64 * q^72 + 48 * q^73 + 88 * q^75 + 48 * q^76 + 96 * q^78 + 16 * q^79 + 48 * q^81 + 112 * q^82 - 56 * q^87 + 16 * q^88 - 88 * q^90 + 16 * q^91 - 72 * q^93 - 48 * q^94 - 112 * q^96 - 16 * q^97 - 64 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more