LMFDB - Embedded newform 810.2.w.a.23.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [810,2,Mod(23,810)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(810, base_ring=CyclotomicField(108))

chi = DirichletCharacter(H, H._module([22, 81]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("810.23");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 810 = 2 \cdot 3^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	810.w (of order $108$, degree $36$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$6.46788256372$
Analytic rank:	$0$
Dimension:	$1944$
Relative dimension:	$54$ over $\Q(\zeta_{108})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{108}]$

Embedding invariants

Embedding label			23.15
Character	$\chi$	$=$	810.23
Dual form			810.2.w.a.317.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.989442 + 0.144932i) q^{2} +(0.128776 - 1.72726i) q^{3} +(0.957990 - 0.286803i) q^{4} +(-1.90840 + 1.16533i) q^{5} +(0.122918 + 1.72768i) q^{6} +(3.82371 + 0.111259i) q^{7} +(-0.906308 + 0.422618i) q^{8} +(-2.96683 - 0.444858i) q^{9} +(1.71936 - 1.42962i) q^{10} +(0.153943 - 0.306525i) q^{11} +(-0.372017 - 1.69163i) q^{12} +(2.95082 - 1.17229i) q^{13} +(-3.79946 + 0.444093i) q^{14} +(1.76707 + 3.44637i) q^{15} +(0.835488 - 0.549509i) q^{16} +(0.312269 + 3.56925i) q^{17} +(2.99998 + 0.0101720i) q^{18} +(-0.721623 - 0.859996i) q^{19} +(-1.49401 + 1.66371i) q^{20} +(0.684573 - 6.59020i) q^{21} +(-0.107892 + 0.325600i) q^{22} +(-0.0186617 - 0.641360i) q^{23} +(0.613260 + 1.61985i) q^{24} +(2.28400 - 4.44785i) q^{25} +(-2.74976 + 1.58758i) q^{26} +(-1.15044 + 5.06720i) q^{27} +(3.69498 - 0.990067i) q^{28} +(8.92278 + 1.04292i) q^{29} +(-2.24790 - 3.15387i) q^{30} +(2.10447 + 0.498769i) q^{31} +(-0.747025 + 0.664796i) q^{32} +(-0.509623 - 0.305372i) q^{33} +(-0.826270 - 3.48631i) q^{34} +(-7.42682 + 4.24357i) q^{35} +(-2.96978 + 0.424728i) q^{36} +(1.34911 + 1.92672i) q^{37} +(0.838644 + 0.746330i) q^{38} +(-1.64484 - 5.24778i) q^{39} +(1.23711 - 1.86268i) q^{40} +(8.70655 - 6.48178i) q^{41} +(0.277785 + 6.61983i) q^{42} +(-2.70148 + 3.03563i) q^{43} +(0.0595631 - 0.337799i) q^{44} +(6.18032 - 2.60838i) q^{45} +(0.111418 + 0.631883i) q^{46} +(-2.95836 - 1.82474i) q^{47} +(-0.841553 - 1.51387i) q^{48} +(7.62020 + 0.443826i) q^{49} +(-1.61525 + 4.73191i) q^{50} +(6.20523 - 0.0797358i) q^{51} +(2.49064 - 1.96934i) q^{52} +(-3.34859 - 12.4971i) q^{53} +(0.403895 - 5.18043i) q^{54} +(0.0634192 + 0.764367i) q^{55} +(-3.51248 + 1.51513i) q^{56} +(-1.57836 + 1.13568i) q^{57} +(-8.97972 + 0.261283i) q^{58} +(5.50193 - 2.76317i) q^{59} +(2.68127 + 2.79478i) q^{60} +(1.53050 - 5.11223i) q^{61} +(-2.15454 - 0.188498i) q^{62} +(-11.2948 - 2.03109i) q^{63} +(0.642788 - 0.766044i) q^{64} +(-4.26525 + 5.67588i) q^{65} +(0.548501 + 0.228287i) q^{66} +(2.45280 - 3.10207i) q^{67} +(1.32282 + 3.32975i) q^{68} +(-1.11020 - 0.0503581i) q^{69} +(6.73338 - 5.27514i) q^{70} +(-2.40056 - 6.59548i) q^{71} +(2.87687 - 0.850660i) q^{72} +(-3.99025 - 8.55712i) q^{73} +(-1.61411 - 1.71085i) q^{74} +(-7.38845 - 4.51783i) q^{75} +(-0.937957 - 0.616904i) q^{76} +(0.622735 - 1.15493i) q^{77} +(2.38805 + 4.95399i) q^{78} +(-5.22366 - 3.88887i) q^{79} +(-0.954086 + 2.02231i) q^{80} +(8.60420 + 2.63964i) q^{81} +(-7.67520 + 7.67520i) q^{82} +(-0.340388 - 2.32381i) q^{83} +(-1.23428 - 6.50968i) q^{84} +(-4.75530 - 6.44767i) q^{85} +(2.23300 - 3.39511i) q^{86} +(2.95043 - 15.2776i) q^{87} +(-0.00997635 + 0.342865i) q^{88} +(14.7404 + 5.36507i) q^{89} +(-5.73703 + 3.47657i) q^{90} +(11.4135 - 4.15417i) q^{91} +(-0.201822 - 0.609064i) q^{92} +(1.13251 - 3.57073i) q^{93} +(3.19158 + 1.37671i) q^{94} +(2.37933 + 0.800288i) q^{95} +(1.05207 + 1.37591i) q^{96} +(-2.95099 + 14.2917i) q^{97} +(-7.60407 + 0.665270i) q^{98} +(-0.593082 + 0.840926i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 1944 q + 36 q^{20} + 108 q^{30} + 108 q^{35} + 36 q^{41} + 216 q^{51} + 108 q^{67} - 144 q^{72} - 576 q^{77} - 576 q^{87} - 144 q^{92} + 36 q^{93} + 108 q^{97}+O(q^{100}) $ 1944 * q + 36 * q^20 + 108 * q^30 + 108 * q^35 + 36 * q^41 + 216 * q^51 + 108 * q^67 - 144 * q^72 - 576 * q^77 - 576 * q^87 - 144 * q^92 + 36 * q^93 + 108 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/810\mathbb{Z}\right)^\times$.

$n$	$487$	$731$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{11}{54}\right)$

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 $

$2$	−0.989442	+	0.144932i	−0.699641	+	0.102482i
$2$	−0.989442	+	0.144932i	−0.699641	+	0.102482i
$3$	0.128776	−	1.72726i	0.0743487	−	0.997232i
$3$	0.128776	−	1.72726i	0.0743487	−	0.997232i
$4$	0.957990	−	0.286803i	0.478995	−	0.143402i
$5$	−1.90840	+	1.16533i	−0.853463	+	0.521153i
$5$	−1.90840	+	1.16533i	−0.853463	+	0.521153i
$6$	0.122918	+	1.72768i	0.0501813	+	0.705324i
$7$	3.82371	+	0.111259i	1.44523	+	0.0420518i	0.742708	−	0.669615i	$-0.233541\pi$
$7$	3.82371	+	0.111259i	1.44523	+	0.0420518i	0.702517	+	0.711667i	$0.252059\pi$
$8$	−0.906308	+	0.422618i	−0.320428	+	0.149418i
$9$	−2.96683	−	0.444858i	−0.988945	−	0.148286i
$10$	1.71936	−	1.42962i	0.543709	−	0.452085i
$11$	0.153943	−	0.306525i	0.0464155	−	0.0924208i	−0.869229	−	0.494409i	$-0.835384\pi$
$11$	0.153943	−	0.306525i	0.0464155	−	0.0924208i	0.915645	+	0.401988i	$0.131681\pi$
$12$	−0.372017	−	1.69163i	−0.107392	−	0.488331i
$13$	2.95082	−	1.17229i	0.818410	−	0.325133i	0.0777155	−	0.996976i	$-0.475237\pi$
$13$	2.95082	−	1.17229i	0.818410	−	0.325133i	0.740694	+	0.671842i	$0.234497\pi$
$14$	−3.79946	+	0.444093i	−1.01545	+	0.118689i
$15$	1.76707	+	3.44637i	0.456256	+	0.889848i
$16$	0.835488	−	0.549509i	0.208872	−	0.137377i
$17$	0.312269	+	3.56925i	0.0757364	+	0.865671i	0.935118	+	0.354336i	$0.115293\pi$
$17$	0.312269	+	3.56925i	0.0757364	+	0.865671i	−0.859382	+	0.511335i	$0.829151\pi$
$18$	2.99998	+	0.0101720i	0.707103	+	0.00239757i
$19$	−0.721623	−	0.859996i	−0.165552	−	0.197297i	0.676890	−	0.736084i	$-0.263327\pi$
$19$	−0.721623	−	0.859996i	−0.165552	−	0.197297i	−0.842442	+	0.538787i	$0.818883\pi$
$20$	−1.49401	+	1.66371i	−0.334070	+	0.372017i
$21$	0.684573	−	6.59020i	0.149386	−	1.43810i
$22$	−0.107892	+	0.325600i	−0.0230027	+	0.0694181i
$23$	−0.0186617	−	0.641360i	−0.00389123	−	0.133733i	−0.999284	−	0.0378468i	$-0.987950\pi$
$23$	−0.0186617	−	0.641360i	−0.00389123	−	0.133733i	0.995392	−	0.0958860i	$-0.0305684\pi$
$24$	0.613260	+	1.61985i	0.125181	+	0.330650i
$25$	2.28400	−	4.44785i	0.456800	−	0.889570i
$26$	−2.74976	+	1.58758i	−0.539273	+	0.311349i
$27$	−1.15044	+	5.06720i	−0.221402	+	0.975183i
$28$	3.69498	−	0.990067i	0.698286	−	0.187105i
$29$	8.92278	+	1.04292i	1.65692	+	0.193666i	0.892497	−	0.451052i	$-0.148951\pi$
$29$	8.92278	+	1.04292i	1.65692	+	0.193666i	0.764420	+	0.644718i	$0.223025\pi$
$30$	−2.24790	−	3.15387i	−0.410409	−	0.575816i
$31$	2.10447	+	0.498769i	0.377974	+	0.0895815i	0.415211	−	0.909725i	$-0.363708\pi$
$31$	2.10447	+	0.498769i	0.377974	+	0.0895815i	−0.0372373	+	0.999306i	$0.511856\pi$
$32$	−0.747025	+	0.664796i	−0.132057	+	0.117520i
$33$	−0.509623	−	0.305372i	−0.0887140	−	0.0531584i
$34$	−0.826270	−	3.48631i	−0.141704	−	0.597897i
$35$	−7.42682	+	4.24357i	−1.25536	+	0.717294i
$36$	−2.96978	+	0.424728i	−0.494964	+	0.0707881i
$37$	1.34911	+	1.92672i	0.221792	+	0.316751i	0.914592	−	0.404378i	$-0.132512\pi$
$37$	1.34911	+	1.92672i	0.221792	+	0.316751i	−0.692800	+	0.721130i	$0.743623\pi$
$38$	0.838644	+	0.746330i	0.136046	+	0.121071i
$39$	−1.64484	−	5.24778i	−0.263386	−	0.840318i
$40$	1.23711	−	1.86268i	0.195604	−	0.294515i
$41$	8.70655	−	6.48178i	1.35973	−	1.01228i	0.362978	−	0.931798i	$-0.381760\pi$
$41$	8.70655	−	6.48178i	1.35973	−	1.01228i	0.996756	−	0.0804869i	$-0.0256475\pi$
$42$	0.277785	+	6.61983i	0.0428631	+	1.02146i
$43$	−2.70148	+	3.03563i	−0.411973	+	0.462930i	−0.916247	−	0.400614i	$-0.868797\pi$
$43$	−2.70148	+	3.03563i	−0.411973	+	0.462930i	0.504275	+	0.863543i	$0.331760\pi$
$44$	0.0595631	−	0.337799i	0.00897947	−	0.0509251i
$45$	6.18032	−	2.60838i	0.921308	−	0.388835i
$46$	0.111418	+	0.631883i	0.0164277	+	0.0931661i
$47$	−2.95836	−	1.82474i	−0.431521	−	0.266166i	0.292068	−	0.956398i	$-0.405657\pi$
$47$	−2.95836	−	1.82474i	−0.431521	−	0.266166i	−0.723588	+	0.690232i	$0.757509\pi$
$48$	−0.841553	−	1.51387i	−0.121468	−	0.218508i
$49$	7.62020	+	0.443826i	1.08860	+	0.0634037i
$50$	−1.61525	+	4.73191i	−0.228431	+	0.669193i
$51$	6.20523	−	0.0797358i	0.868906	−	0.0111652i
$52$	2.49064	−	1.96934i	0.345389	−	0.273099i
$53$	−3.34859	−	12.4971i	−0.459965	−	1.71661i	−0.673067	−	0.739581i	$-0.735024\pi$
$53$	−3.34859	−	12.4971i	−0.459965	−	1.71661i	0.213103	−	0.977030i	$-0.431643\pi$
$54$	0.403895	−	5.18043i	0.0549631	−	0.704967i
$55$	0.0634192	+	0.764367i	0.00855145	+	0.103067i
$56$	−3.51248	+	1.51513i	−0.469374	+	0.202468i
$57$	−1.57836	+	1.13568i	−0.209059	+	0.150425i
$58$	−8.97972	+	0.261283i	−1.17909	+	0.0343082i
$59$	5.50193	−	2.76317i	0.716290	−	0.359734i	−0.0530344	−	0.998593i	$-0.516889\pi$
$59$	5.50193	−	2.76317i	0.716290	−	0.359734i	0.769324	+	0.638858i	$0.220593\pi$
$60$	2.68127	+	2.79478i	0.346150	+	0.360805i
$61$	1.53050	−	5.11223i	0.195961	−	0.654554i	−0.802372	−	0.596825i	$-0.796429\pi$
$61$	1.53050	−	5.11223i	0.195961	−	0.654554i	0.998332	−	0.0577292i	$-0.0183860\pi$
$62$	−2.15454	−	0.188498i	−0.273627	−	0.0239392i
$63$	−11.2948	−	2.03109i	−1.42301	−	0.255893i
$64$	0.642788	−	0.766044i	0.0803485	−	0.0957556i
$65$	−4.26525	+	5.67588i	−0.529039	+	0.704006i
$66$	0.548501	+	0.228287i	0.0675158	+	0.0281001i
$67$	2.45280	−	3.10207i	0.299657	−	0.378979i	−0.611356	−	0.791356i	$-0.709376\pi$
$67$	2.45280	−	3.10207i	0.299657	−	0.378979i	0.911013	+	0.412377i	$0.135301\pi$
$68$	1.32282	+	3.32975i	0.160416	+	0.403791i
$69$	−1.11020	−	0.0503581i	−0.133652	−	0.00606240i
$70$	6.73338	−	5.27514i	0.804793	−	0.630500i
$71$	−2.40056	−	6.59548i	−0.284894	−	0.782739i	−0.996761	−	0.0804249i	$-0.974372\pi$
$71$	−2.40056	−	6.59548i	−0.284894	−	0.782739i	0.711867	−	0.702314i	$-0.247850\pi$
$72$	2.87687	−	0.850660i	0.339042	−	0.100251i
$73$	−3.99025	−	8.55712i	−0.467024	−	1.00154i	−0.988909	−	0.148520i	$-0.952549\pi$
$73$	−3.99025	−	8.55712i	−0.467024	−	1.00154i	0.521886	−	0.853015i	$-0.325229\pi$
$74$	−1.61411	−	1.71085i	−0.187636	−	0.198883i
$75$	−7.38845	−	4.51783i	−0.853145	−	0.521674i
$76$	−0.937957	−	0.616904i	−0.107591	−	0.0707637i
$77$	0.622735	−	1.15493i	0.0709673	−	0.131617i
$78$	2.38805	+	4.95399i	0.270393	+	0.560928i
$79$	−5.22366	−	3.88887i	−0.587707	−	0.437532i	0.261790	−	0.965125i	$-0.415687\pi$
$79$	−5.22366	−	3.88887i	−0.587707	−	0.437532i	−0.849497	+	0.527593i	$0.823095\pi$
$80$	−0.954086	+	2.02231i	−0.106670	+	0.226101i
$81$	8.60420	+	2.63964i	0.956023	+	0.293293i
$82$	−7.67520	+	7.67520i	−0.847584	+	0.847584i
$83$	−0.340388	−	2.32381i	−0.0373625	−	0.255071i	0.962507	−	0.271259i	$-0.0874398\pi$
$83$	−0.340388	−	2.32381i	−0.0373625	−	0.255071i	−0.999869	+	0.0161871i	$0.994847\pi$
$84$	−1.23428	−	6.50968i	−0.134671	−	0.710264i
$85$	−4.75530	−	6.44767i	−0.515785	−	0.699348i
$86$	2.23300	−	3.39511i	0.240791	−	0.366104i
$87$	2.95043	−	15.2776i	0.316320	−	1.63793i
$88$	−0.00997635	+	0.342865i	−0.00106348	+	0.0365495i
$89$	14.7404	+	5.36507i	1.56248	+	0.568696i	0.971303	−	0.237845i	$-0.0764411\pi$
$89$	14.7404	+	5.36507i	1.56248	+	0.568696i	0.591177	+	0.806542i	$0.298663\pi$
$90$	−5.73703	+	3.47657i	−0.604736	+	0.366462i
$91$	11.4135	−	4.15417i	1.19646	−	0.435476i
$92$	−0.201822	−	0.609064i	−0.0210414	−	0.0634993i
$93$	1.13251	−	3.57073i	0.117435	−	0.370268i
$94$	3.19158	+	1.37671i	0.329187	+	0.141997i
$95$	2.37933	+	0.800288i	0.244114	+	0.0821078i
$96$	1.05207	+	1.37591i	0.107377	+	0.140429i
$97$	−2.95099	+	14.2917i	−0.299628	+	1.45110i	0.507974	+	0.861372i	$0.330395\pi$
$97$	−2.95099	+	14.2917i	−0.299628	+	1.45110i	−0.807602	+	0.589728i	$0.799235\pi$
$98$	−7.60407	+	0.665270i	−0.768127	+	0.0672024i
$99$	−0.593082	+	0.840926i	−0.0596070	+	0.0845163i
$100$	0.912389	−	4.91605i	0.0912389	−	0.491605i
$101$	−10.0340	−	3.00398i	−0.998420	−	0.298907i	−0.254425	−	0.967092i	$-0.581886\pi$
$101$	−10.0340	−	3.00398i	−0.998420	−	0.298907i	−0.743995	+	0.668185i	$0.767071\pi$
$102$	−6.12815	+	0.978229i	−0.606778	+	0.0968591i
$103$	5.75922	+	1.90840i	0.567473	+	0.188040i	0.583901	−	0.811825i	$-0.301526\pi$
$103$	5.75922	+	1.90840i	0.567473	+	0.188040i	−0.0164280	+	0.999865i	$0.505229\pi$
$104$	−2.17892	+	2.30952i	−0.213661	+	0.226467i
$105$	6.37333	+	13.3745i	0.621974	+	1.30522i
$106$	5.12447	+	11.8798i	0.497732	+	1.15387i
$107$	−4.14367	+	15.4644i	−0.400583	+	1.49500i	0.411475	+	0.911421i	$0.365014\pi$
$107$	−4.14367	+	15.4644i	−0.400583	+	1.49500i	−0.812058	+	0.583576i	$0.801653\pi$
$108$	0.351179	+	5.18427i	0.0337922	+	0.498857i
$109$	1.02729	+	0.593105i	0.0983963	+	0.0568091i	0.548391	−	0.836222i	$-0.315241\pi$
$109$	1.02729	+	0.593105i	0.0983963	+	0.0568091i	−0.449994	+	0.893031i	$0.648574\pi$
$110$	−0.173531	−	0.747106i	−0.0165455	−	0.0712337i
$111$	3.50168	−	2.08214i	0.332365	−	0.197628i
$112$	3.25580	−	2.00821i	0.307644	−	0.189758i
$113$	5.41904	+	6.08932i	0.509780	+	0.572835i	0.944826	−	0.327573i	$-0.106231\pi$
$113$	5.41904	+	6.08932i	0.509780	+	0.572835i	−0.435046	+	0.900408i	$0.643268\pi$
$114$	1.39710	−	1.35245i	0.130850	−	0.126668i
$115$	0.783012	+	1.20223i	0.0730162	+	0.112108i
$116$	8.84704	−	1.55997i	0.821427	−	0.144840i
$117$	−9.27609	+	2.16528i	−0.857575	+	0.200180i
$118$	−5.04337	+	3.53140i	−0.464279	+	0.325092i
$119$	0.796916	+	13.6825i	0.0730531	+	1.25427i
$120$	−3.05801	−	2.37667i	−0.279157	−	0.216960i
$121$	6.49849	+	8.72898i	0.590771	+	0.793544i
$122$	−0.773416	+	5.28007i	−0.0700218	+	0.478035i
$123$	−10.0745	−	15.8731i	−0.908388	−	1.43123i
$124$	2.15911	−	0.125754i	0.193894	−	0.0112930i
$125$	0.824437	+	11.1499i	0.0737399	+	0.997278i
$126$	11.4699	+	0.372668i	1.02182	+	0.0331999i
$127$	10.4043	+	7.28518i	0.923233	+	0.646455i	0.935446	−	0.353471i	$-0.114999\pi$
$127$	10.4043	+	7.28518i	0.923233	+	0.646455i	−0.0122125	+	0.999925i	$0.503887\pi$
$128$	−0.524977	+	0.851117i	−0.0464018	+	0.0752288i
$129$	4.89543	+	5.05707i	0.431019	+	0.445251i
$130$	3.39760	−	6.23412i	0.297989	−	0.546769i
$131$	2.16744	−	9.14515i	0.189370	−	0.799015i	−0.792563	−	0.609789i	$-0.791254\pi$
$131$	2.16744	−	9.14515i	0.189370	−	0.799015i	0.981934	−	0.189226i	$-0.0605979\pi$
$132$	−0.575795	−	0.146381i	−0.0501166	−	0.0127408i
$133$	−2.66359	−	3.36866i	−0.230963	−	0.292100i
$134$	−1.97732	+	3.42481i	−0.170814	+	0.295859i
$135$	−3.70947	−	11.0109i	−0.319260	−	0.947667i
$136$	−1.79144	−	3.10287i	−0.153615	−	0.266069i
$137$	1.02883	−	2.58972i	0.0878988	−	0.221255i	−0.878790	−	0.477208i	$-0.841649\pi$
$137$	1.02883	−	2.58972i	0.0878988	−	0.221255i	0.966689	+	0.255954i	$0.0823895\pi$
$138$	1.10577	−	0.111076i	0.0941296	−	0.00945545i
$139$	−11.3513	−	10.7094i	−0.962805	−	0.908360i	0.0330370	−	0.999454i	$-0.489482\pi$
$139$	−11.3513	−	10.7094i	−0.962805	−	0.908360i	−0.995842	+	0.0910942i	$0.970964\pi$
$140$	−5.89775	+	6.19533i	−0.498451	+	0.523601i
$141$	−3.53276	+	4.87486i	−0.297512	+	0.410537i
$142$	3.33111	+	6.17792i	0.279540	+	0.518440i
$143$	0.0949221	−	1.08496i	0.00793778	−	0.0907293i
$144$	−2.72321	+	1.25863i	−0.226934	+	0.104886i
$145$	−18.2436	+	8.40769i	−1.51505	+	0.698220i
$146$	5.18832	+	7.88846i	0.429389	+	0.652854i
$147$	1.74790	−	13.1049i	0.144164	−	1.08087i
$148$	1.84502	+	1.45885i	0.151660	+	0.119917i
$149$	−0.0965525	+	0.223834i	−0.00790989	+	0.0183372i	−0.922125	−	0.386891i	$-0.873549\pi$
$149$	−0.0965525	+	0.223834i	−0.00790989	+	0.0183372i	0.914215	+	0.405229i	$0.132808\pi$
$150$	7.96522	+	3.39930i	0.650358	+	0.277552i
$151$	14.7369	+	7.40116i	1.19927	+	0.602298i	0.932398	−	0.361434i	$-0.117713\pi$
$151$	14.7369	+	7.40116i	1.19927	+	0.602298i	0.266875	+	0.963731i	$0.414009\pi$
$152$	1.01746	+	0.474451i	0.0825271	+	0.0384830i
$153$	0.661359	−	10.7283i	0.0534677	−	0.867331i
$154$	−0.448773	+	1.23299i	−0.0361632	+	0.0993575i
$155$	−4.59741	+	1.50056i	−0.369273	+	0.120528i
$156$	−3.08082	−	4.55558i	−0.246663	−	0.364738i
$157$	4.74602	−	0.979974i	0.378774	−	0.0782105i	−0.00901360	−	0.999959i	$-0.502869\pi$
$157$	4.74602	−	0.979974i	0.378774	−	0.0782105i	0.387787	+	0.921749i	$0.373240\pi$
$158$	5.73213	+	3.09073i	0.456023	+	0.245886i
$159$	−22.0169	+	4.17455i	−1.74606	+	0.331064i
$160$	0.650916	−	2.13923i	0.0514594	−	0.169121i
$161$		−	2.45445i		−	0.193438i
$162$	−8.89592	−	1.36474i	−0.698930	−	0.107224i
$163$	−0.0991899	−	0.0991899i	−0.00776915	−	0.00776915i	0.703212	−	0.710981i	$-0.251749\pi$
$163$	−0.0991899	−	0.0991899i	−0.00776915	−	0.00776915i	−0.710981	+	0.703212i	$0.751749\pi$
$164$	6.48178	−	8.70655i	0.506142	−	0.679867i
$165$	1.32843	−	0.0111093i	0.103418	−	0.000864857i
$166$	0.673589	+	2.24994i	0.0522806	+	0.174629i
$167$	3.09990	+	15.0128i	0.239878	+	1.16173i	0.908421	+	0.418056i	$0.137288\pi$
$167$	3.09990	+	15.0128i	0.239878	+	1.16173i	−0.668544	+	0.743673i	$0.733082\pi$
$168$	2.16470	+	6.26206i	0.167011	+	0.483128i
$169$	−2.12278	+	2.00274i	−0.163291	+	0.154057i
$170$	5.63957	+	5.69040i	0.432535	+	0.436434i
$171$	1.75836	+	2.87249i	0.134465	+	0.219664i
$172$	−1.71736	+	3.68290i	−0.130948	+	0.280818i
$173$	−16.6026	+	5.50150i	−1.26227	+	0.418271i	−0.866084	−	0.499898i	$-0.833371\pi$
$173$	−16.6026	+	5.50150i	−1.26227	+	0.418271i	−0.396188	+	0.918170i	$0.629667\pi$
$174$	−0.705067	+	15.5439i	−0.0534510	+	1.17838i
$175$	9.22820	−	16.7532i	0.697586	−	1.26642i
$176$	−0.0398210	−	0.340691i	−0.00300162	−	0.0256805i
$177$	−4.06419	−	9.85907i	−0.305484	−	0.741053i
$178$	−15.3623	−	3.17207i	−1.15146	−	0.237757i
$179$	−6.97995	−	5.85687i	−0.521706	−	0.437763i	0.343520	−	0.939145i	$-0.388381\pi$
$179$	−6.97995	−	5.85687i	−0.521706	−	0.437763i	−0.865226	+	0.501382i	$0.832825\pi$
$180$	5.17259	−	4.27134i	0.385542	−	0.318367i
$181$	−7.33147	+	6.15184i	−0.544944	+	0.457262i	−0.873225	−	0.487318i	$-0.837975\pi$
$181$	−7.33147	+	6.15184i	−0.544944	+	0.457262i	0.328281	+	0.944580i	$0.393531\pi$
$182$	−10.6909	+	5.76449i	−0.792463	+	0.427292i
$183$	−8.63304	−	3.30190i	−0.638173	−	0.244083i
$184$	0.287964	+	0.573383i	0.0212290	+	0.0422703i
$185$	−4.81991	−	2.10481i	−0.354367	−	0.154748i
$186$	−0.603036	+	3.69717i	−0.0442168	+	0.271089i
$187$	1.14214	+	0.453742i	0.0835213	+	0.0331809i
$188$	−3.35742	−	0.899617i	−0.244865	−	0.0656113i
$189$	−4.96271	+	19.2475i	−0.360984	+	1.40005i
$190$	−2.47019	−	0.446998i	−0.179207	−	0.0324286i
$191$	−0.646676	+	5.53267i	−0.0467919	+	0.400330i	0.949464	+	0.313876i	$0.101628\pi$
$191$	−0.646676	+	5.53267i	−0.0467919	+	0.400330i	−0.996256	+	0.0864540i	$0.972446\pi$
$192$	−1.24038	−	1.20891i	−0.0895167	−	0.0872454i
$193$	6.72677	+	10.9058i	0.484204	+	0.785014i	0.997309	−	0.0733120i	$-0.0233569\pi$
$193$	6.72677	+	10.9058i	0.484204	+	0.785014i	−0.513105	+	0.858326i	$0.671505\pi$
$194$	0.848517	−	14.5685i	0.0609200	−	1.04596i
$195$	9.25444	+	8.09809i	0.662724	+	0.579916i
$196$	7.42736	−	1.76032i	0.530526	−	0.125737i
$197$	2.88592	−	4.12152i	0.205613	−	0.293646i	−0.703080	−	0.711111i	$-0.748192\pi$
$197$	2.88592	−	4.12152i	0.205613	−	0.293646i	0.908693	+	0.417465i	$0.137081\pi$
$198$	0.464943	−	0.918004i	0.0330421	−	0.0652397i
$199$	3.41998	+	0.603035i	0.242436	+	0.0427480i	0.293546	−	0.955945i	$-0.405165\pi$
$199$	3.41998	+	0.603035i	0.242436	+	0.0427480i	−0.0511097	+	0.998693i	$0.516276\pi$
$200$	−0.190263	+	4.99638i	−0.0134537	+	0.353297i
$201$	−5.04222	−	4.63609i	−0.355651	−	0.327005i
$202$	10.3634	+	1.51802i	0.729168	+	0.106807i
$203$	34.0020	+	4.98057i	2.38648	+	0.349567i
$204$	5.92167	−	1.85607i	0.414600	−	0.129951i
$205$	−9.06216	+	22.5159i	−0.632928	+	1.57258i
$206$	−5.97500	−	1.05355i	−0.416298	−	0.0734045i
$207$	−0.229948	+	1.91111i	−0.0159825	+	0.132831i
$208$	1.82119	−	2.60093i	0.126277	−	0.180342i
$209$	−0.374699	+	0.0888053i	−0.0259185	+	0.00614279i
$210$	−8.24443	−	12.3096i	−0.568920	−	0.849443i
$211$	1.13127	−	19.4232i	0.0778801	−	1.33715i	−0.702428	−	0.711754i	$-0.747901\pi$
$211$	1.13127	−	19.4232i	0.0778801	−	1.33715i	0.780309	−	0.625395i	$-0.215062\pi$
$212$	−6.79213	−	11.0117i	−0.466485	−	0.756288i
$213$	−11.7012	+	3.29704i	−0.801755	+	0.225910i
$214$	1.85864	−	15.9016i	0.127054	−	1.08701i
$215$	1.61800	−	8.94134i	0.110346	−	0.609794i
$216$	−1.09884	−	5.07864i	−0.0747664	−	0.345557i
$217$	7.99139	+	2.14129i	0.542491	+	0.145360i
$218$	−1.10240	−	0.437956i	−0.0746640	−	0.0296621i
$219$	−15.2942	+	5.79024i	−1.03349	+	0.391268i
$220$	0.279978	+	0.714067i	0.0188761	+	0.0481424i
$221$	5.10563	+	10.1661i	0.343442	+	0.683849i
$222$	−3.16294	+	2.56766i	−0.212283	+	0.172330i
$223$	−25.3769	+	13.6831i	−1.69936	+	0.916289i	−0.725791	+	0.687915i	$0.758526\pi$
$223$	−25.3769	+	13.6831i	−1.69936	+	0.916289i	−0.973573	+	0.228374i	$0.926659\pi$
$224$	−2.93037	+	2.45887i	−0.195794	+	0.164290i
$225$	−8.75490	+	12.1800i	−0.583660	+	0.811998i
$226$	−6.24436	−	5.23964i	−0.415369	−	0.348536i
$227$	−24.8614	−	5.13346i	−1.65011	−	0.340720i	−0.716106	−	0.697991i	$-0.754077\pi$
$227$	−24.8614	−	5.13346i	−1.65011	−	0.340720i	−0.934000	+	0.357272i	$0.883707\pi$
$228$	−1.18634	+	1.54065i	−0.0785671	+	0.102032i
$229$	0.506210	+	4.33090i	0.0334513	+	0.286194i	0.999602	+	0.0282153i	$0.00898240\pi$
$229$	0.506210	+	4.33090i	0.0334513	+	0.286194i	−0.966151	+	0.257979i	$0.916944\pi$
$230$	−0.948985	−	1.07605i	−0.0625742	−	0.0709525i
$231$	−1.91468	−	1.22435i	−0.125976	−	0.0805564i
$232$	−8.52754	+	2.82572i	−0.559860	+	0.185518i
$233$	−11.5729	+	24.8181i	−0.758163	+	1.62589i	0.0215647	+	0.999767i	$0.493135\pi$
$233$	−11.5729	+	24.8181i	−0.758163	+	1.62589i	−0.779728	+	0.626119i	$0.784643\pi$
$234$	8.86433	−	3.48682i	0.579479	−	0.227941i
$235$	7.77216	+	0.0348702i	0.507000	+	0.00227468i
$236$	4.47830	−	4.22506i	0.291513	−	0.275028i
$237$	−7.38976	+	8.52181i	−0.480016	+	0.553551i
$238$	−2.77153	−	13.4226i	−0.179652	−	0.870055i
$239$	−7.41847	−	24.7794i	−0.479861	−	1.60285i	−0.764777	−	0.644295i	$-0.777151\pi$
$239$	−7.41847	−	24.7794i	−0.479861	−	1.60285i	0.284917	−	0.958552i	$-0.408034\pi$
$240$	3.37018	+	1.90838i	0.217544	+	0.123185i
$241$	−3.20651	+	4.30709i	−0.206549	+	0.277444i	−0.893311	−	0.449438i	$-0.851624\pi$
$241$	−3.20651	+	4.30709i	−0.206549	+	0.277444i	0.686762	+	0.726882i	$0.259032\pi$
$242$	−7.69498	−	7.69498i	−0.494652	−	0.494652i
$243$	5.66735	−	14.5217i	0.363560	−	0.931571i
$244$		−	5.33641i		−	0.341629i
$245$	−15.0596	+	8.03307i	−0.962124	+	0.513214i
$246$	12.2687	+	14.2454i	0.782222	+	0.908255i
$247$	−3.13754	−	1.69175i	−0.199637	−	0.107643i
$248$	−2.11809	+	0.437350i	−0.134499	+	0.0277717i
$249$	−4.05765	+	0.288687i	−0.257143	+	0.0182948i
$250$	−2.43171	−	10.9127i	−0.153795	−	0.690179i
$251$	−7.03101	+	19.3175i	−0.443794	+	1.21931i	0.493185	+	0.869925i	$0.335833\pi$
$251$	−7.03101	+	19.3175i	−0.443794	+	1.21931i	−0.936978	+	0.349388i	$0.886390\pi$
$252$	−11.4028	+	1.29362i	−0.718311	+	0.0814906i
$253$	−0.199466	−	0.0930124i	−0.0125403	−	0.00584764i
$254$	−11.3503	−	5.70034i	−0.712182	−	0.357671i
$255$	−11.7492	+	7.38332i	−0.735760	+	0.462362i
$256$	0.396080	−	0.918216i	0.0247550	−	0.0573885i
$257$	7.74500	+	6.12395i	0.483120	+	0.382001i	0.831654	−	0.555295i	$-0.187395\pi$
$257$	7.74500	+	6.12395i	0.483120	+	0.382001i	−0.348534	+	0.937296i	$0.613320\pi$
$258$	−5.57668	−	4.29418i	−0.347189	−	0.267344i
$259$	4.94422	+	7.51733i	0.307219	+	0.467104i
$260$	−2.45820	+	6.66072i	−0.152451	+	0.413080i
$261$	−26.0084	−	7.06354i	−1.60988	−	0.437222i
$262$	−0.819132	+	9.36272i	−0.0506062	+	0.578431i
$263$	3.46527	+	6.42674i	0.213678	+	0.396290i	0.964448	−	0.264274i	$-0.0851322\pi$
$263$	3.46527	+	6.42674i	0.213678	+	0.396290i	−0.750770	+	0.660564i	$0.770317\pi$
$264$	0.590931	+	0.0613844i	0.0363693	+	0.00377795i
$265$	20.9538	+	19.9473i	1.28718	+	1.22535i
$266$	3.12369	+	2.94705i	0.191526	+	0.180695i
$267$	11.1651	−	24.7696i	0.683291	−	1.51587i
$268$	1.46007	−	3.67523i	0.0891882	−	0.224500i
$269$	4.60189	+	7.97070i	0.280582	+	0.485982i	0.971528	−	0.236924i	$-0.0761392\pi$
$269$	4.60189	+	7.97070i	0.280582	+	0.485982i	−0.690946	+	0.722906i	$0.742806\pi$
$270$	5.26613	+	10.3570i	0.320487	+	0.630308i
$271$	−10.1432	+	17.5685i	−0.616154	+	1.06721i	0.374027	+	0.927418i	$0.377977\pi$
$271$	−10.1432	+	17.5685i	−0.616154	+	1.06721i	−0.990181	+	0.139792i	$0.955357\pi$
$272$	2.22223	+	2.81047i	0.134743	+	0.170410i
$273$	−5.70554	−	20.2490i	−0.345315	−	1.22552i
$274$	−0.642634	+	2.71149i	−0.0388229	+	0.163807i
$275$	−1.01177	−	1.38482i	−0.0610121	−	0.0835076i
$276$	−1.07800	+	0.270165i	−0.0648879	+	0.0162620i
$277$	−11.8268	+	19.1742i	−0.710605	+	1.15207i	0.271264	+	0.962505i	$0.412558\pi$
$277$	−11.8268	+	19.1742i	−0.710605	+	1.15207i	−0.981869	+	0.189561i	$0.939293\pi$
$278$	12.7836	+	8.95117i	0.766709	+	0.536855i
$279$	−6.02173	−	2.41595i	−0.360512	−	0.144639i
$280$	4.93758	−	6.98469i	0.295077	−	0.417415i
$281$	−18.2173	+	1.06104i	−1.08675	+	0.0632961i	−0.592153	−	0.805825i	$-0.701722\pi$
$281$	−18.2173	+	1.06104i	−1.08675	+	0.0632961i	−0.494599	+	0.869121i	$0.664685\pi$
$282$	2.78894	−	5.33540i	0.166079	−	0.317718i
$283$	4.62425	−	31.5695i	0.274883	−	1.87661i	−0.176528	−	0.984296i	$-0.556487\pi$
$283$	4.62425	−	31.5695i	0.274883	−	1.87661i	0.451411	−	0.892316i	$-0.350921\pi$
$284$	−4.19131	−	5.62991i	−0.248709	−	0.334074i
$285$	1.68870	−	4.00665i	0.100030	−	0.237334i
$286$	0.0633261	+	1.08727i	0.00374455	+	0.0642914i
$287$	34.0124	−	23.8158i	2.00769	−	1.40580i
$288$	2.51204	−	1.64002i	0.148023	−	0.0966390i
$289$	4.09969	−	0.722886i	0.241158	−	0.0425227i
$290$	16.8324	−	10.9630i	0.988434	−	0.643769i
$291$	24.3054	+	6.93755i	1.42481	+	0.406686i
$292$	−6.27683	−	7.05322i	−0.367324	−	0.412758i
$293$	11.5562	−	7.12798i	0.675121	−	0.416421i	−0.144361	−	0.989525i	$-0.546113\pi$
$293$	11.5562	−	7.12798i	0.675121	−	0.416421i	0.819483	+	0.573104i	$0.194261\pi$
$294$	0.169872	+	13.2199i	0.00990715	+	0.770998i
$295$	−7.27988	+	11.6848i	−0.423851	+	0.680317i
$296$	−2.03697	−	1.17605i	−0.118397	−	0.0683564i
$297$	1.37612	+	1.13270i	0.0798506	+	0.0657257i
$298$	0.0630924	−	0.235464i	0.00365485	−	0.0136401i
$299$	−0.806924	−	1.87066i	−0.0466656	−	0.108183i
$300$	−8.37379	−	2.20900i	−0.483461	−	0.127537i
$301$	−10.6674	+	11.3068i	−0.614860	+	0.651714i
$302$	−15.6540	−	5.18716i	−0.900785	−	0.298488i
$303$	−6.48079	+	16.9445i	−0.372311	+	0.973434i
$304$	−1.07548	−	0.321978i	−0.0616832	−	0.0184667i
$305$	3.03664	+	11.5397i	0.173877	+	0.660763i
$306$	0.900495	+	10.7109i	0.0514779	+	0.612300i
$307$	−20.0868	+	1.75737i	−1.14642	+	0.100298i	−0.644490	−	0.764613i	$-0.722930\pi$
$307$	−20.0868	+	1.75737i	−1.14642	+	0.100298i	−0.501925	+	0.864911i	$0.667375\pi$
$308$	0.265335	−	1.28502i	0.0151189	−	0.0732207i
$309$	4.03794	−	9.70190i	0.229710	−	0.551922i
$310$	4.33139	−	2.15103i	0.246006	−	0.122170i
$311$	14.9078	+	6.43060i	0.845344	+	0.364646i	0.774293	−	0.632827i	$-0.218106\pi$
$311$	14.9078	+	6.43060i	0.845344	+	0.364646i	0.0710504	+	0.997473i	$0.477365\pi$
$312$	3.70854	+	4.06097i	0.209955	+	0.229907i
$313$	4.45315	+	13.4388i	0.251707	+	0.759609i	0.995802	+	0.0915348i	$0.0291773\pi$
$313$	4.45315	+	13.4388i	0.251707	+	0.759609i	−0.744095	+	0.668074i	$0.767119\pi$
$314$	−4.55388	+	1.65748i	−0.256990	+	0.0935368i
$315$	23.9219	−	9.28607i	1.34785	−	0.523211i
$316$	−6.11955	−	2.22733i	−0.344252	−	0.125297i
$317$	1.02620	−	35.2683i	0.0576373	−	1.98087i	−0.106073	−	0.994358i	$-0.533828\pi$
$317$	1.02620	−	35.2683i	0.0576373	−	1.98087i	0.163711	−	0.986508i	$-0.447654\pi$
$318$	21.1795	−	7.32143i	1.18769	−	0.410566i
$319$	1.69328	−	2.57450i	0.0948053	−	0.144145i
$320$	−0.334000	+	2.21098i	−0.0186712	+	0.123598i
$321$	26.1773	+	9.14861i	1.46108	+	0.510626i
$322$	0.355728	+	2.42853i	0.0198239	+	0.135337i
$323$	2.84420	−	2.84420i	0.158256	−	0.158256i
$324$	8.99979	+	0.0610317i	0.499989	+	0.00339065i
$325$	1.52552	−	15.8023i	0.0846205	−	0.876553i
$326$	0.112518	+	0.0837668i	0.00623182	+	0.00463942i
$327$	1.15673	−	1.69801i	0.0639675	−	0.0939003i
$328$	−5.15149	+	9.55404i	−0.284443	+	0.527533i
$329$	−11.1089	−	7.30642i	−0.612452	−	0.402816i
$330$	−1.31279	+	0.203523i	−0.0722667	+	0.0112036i
$331$	2.51394	+	2.66462i	0.138179	+	0.146461i	0.792767	−	0.609525i	$-0.208640\pi$
$331$	2.51394	+	2.66462i	0.138179	+	0.146461i	−0.654589	+	0.755985i	$0.727158\pi$
$332$	−0.992565	−	2.12856i	−0.0544741	−	0.116820i
$333$	−3.14546	−	6.31643i	−0.172370	−	0.346138i
$334$	−5.24301	−	14.4051i	−0.286885	−	0.788209i
$335$	−1.06598	+	8.77834i	−0.0582409	+	0.479612i
$336$	−3.04942	−	5.88221i	−0.166360	−	0.320901i
$337$	−10.2036	−	25.6840i	−0.555826	−	1.39910i	−0.889729	−	0.456490i	$-0.849107\pi$
$337$	−10.2036	−	25.6840i	−0.555826	−	1.39910i	0.333903	−	0.942607i	$-0.391634\pi$
$338$	1.81010	−	2.28925i	0.0984567	−	0.124519i
$339$	11.2157	−	8.57592i	0.609152	−	0.465780i
$340$	−6.40474	−	4.81296i	−0.347346	−	0.261020i
$341$	0.476853	−	0.568291i	0.0258230	−	0.0307747i
$342$	−2.15611	−	2.58731i	−0.116589	−	0.139906i
$343$	2.41266	+	0.211080i	0.130271	+	0.0113973i
$344$	1.16546	−	3.89291i	0.0628375	−	0.209892i
$345$	2.17739	−	1.19764i	0.117226	−	0.0644790i
$346$	15.6300	−	7.84966i	0.840272	−	0.422000i
$347$	30.6229	−	0.891035i	1.64392	−	0.0478333i	0.805411	−	0.592717i	$-0.201945\pi$
$347$	30.6229	−	0.891035i	1.64392	−	0.0478333i	0.838512	+	0.544883i	$0.183426\pi$
$348$	−1.55519	−	15.4820i	−0.0833668	−	0.829922i
$349$	31.8115	−	13.7221i	1.70283	−	0.734530i	0.703106	−	0.711085i	$-0.251796\pi$
$349$	31.8115	−	13.7221i	1.70283	−	0.734530i	0.999725	−	0.0234442i	$-0.00746320\pi$
$350$	−6.70270	+	17.9137i	−0.358274	+	0.957529i
$351$	2.54546	+	16.3010i	0.135867	+	0.870084i
$352$	0.0887775	+	0.331322i	0.00473186	+	0.0176595i
$353$	8.56779	−	6.77453i	0.456018	−	0.360572i	−0.365446	−	0.930832i	$-0.619084\pi$
$353$	8.56779	−	6.77453i	0.456018	−	0.360572i	0.821464	+	0.570260i	$0.193158\pi$
$354$	5.45018	+	9.16595i	0.289674	+	0.487165i
$355$	12.2672	+	9.78938i	0.651073	+	0.519566i
$356$	15.6599	+	0.912084i	0.829972	+	0.0483404i
$357$	23.7358	+	0.385498i	1.25623	+	0.0204027i
$358$	7.75510	+	4.78342i	0.409870	+	0.252812i
$359$	−3.03357	−	17.2042i	−0.160106	−	0.908005i	−0.953968	−	0.299908i	$-0.903044\pi$
$359$	−3.03357	−	17.2042i	−0.160106	−	0.908005i	0.793862	−	0.608098i	$-0.208067\pi$
$360$	−4.49892	+	4.97591i	−0.237114	+	0.262254i
$361$	3.08046	−	17.4702i	0.162130	−	0.919482i
$362$	6.36247	−	7.14945i	0.334404	−	0.375767i
$363$	15.9140	−	10.1005i	0.835270	−	0.530137i
$364$	9.74258	−	7.25308i	0.510650	−	0.380165i
$365$	17.5869	+	11.6805i	0.920541	+	0.611383i
$366$	9.02044	+	2.01583i	0.471506	+	0.105369i
$367$	17.5149	+	15.5869i	0.914268	+	0.813630i	0.982924	−	0.184011i	$-0.0589081\pi$
$367$	17.5149	+	15.5869i	0.914268	+	0.813630i	−0.0686559	+	0.997640i	$0.521871\pi$
$368$	−0.368025	−	0.525594i	−0.0191846	−	0.0273985i
$369$	−28.7143	+	15.3572i	−1.49481	+	0.799464i
$370$	5.07408	+	1.38402i	0.263789	+	0.0719520i
$371$	−11.4136	−	48.1579i	−0.592566	−	2.50023i
$372$	0.0608318	−	3.74553i	0.00315398	−	0.194197i
$373$	−15.9877	+	14.2278i	−0.827810	+	0.736688i	−0.967327	−	0.253532i	$-0.918408\pi$
$373$	−15.9877	+	14.2278i	−0.827810	+	0.736688i	0.139517	+	0.990220i	$0.455445\pi$
$374$	−1.19584	−	0.283419i	−0.0618354	−	0.0146552i
$375$	19.3649	+	0.0118220i	1.00000	+	0.000610486i
$376$	3.45235	+	0.403522i	0.178041	+	0.0208100i
$377$	27.5521	−	7.38256i	1.41901	−	0.380221i
$378$	2.12074	−	19.7635i	0.109079	−	1.01653i
$379$	−5.20618	+	3.00579i	−0.267423	+	0.154397i	−0.627716	−	0.778442i	$-0.716010\pi$
$379$	−5.20618	+	3.00579i	−0.267423	+	0.154397i	0.360293	+	0.932839i	$0.382677\pi$
$380$	2.50890	+	0.0842687i	0.128704	+	0.00432289i
$381$	13.9232	−	17.0328i	0.713307	−	0.872615i
$382$	−0.162012	−	5.56798i	−0.00828924	−	0.284883i
$383$	−0.642960	+	1.94034i	−0.0328537	+	0.0991469i	−0.964374	−	0.264542i	$-0.914779\pi$
$383$	−0.642960	+	1.94034i	−0.0328537	+	0.0991469i	0.931520	+	0.363689i	$0.118483\pi$
$384$	1.40249	+	1.01637i	0.0715707	+	0.0518666i
$385$	0.157454	+	2.92977i	0.00802461	+	0.149315i
$386$	−8.23634	−	9.81569i	−0.419219	−	0.499605i
$387$	9.36528	−	7.80444i	0.476064	−	0.396722i
$388$	1.27188	+	14.5376i	0.0645698	+	0.738036i
$389$	25.7563	−	16.9402i	1.30590	−	0.858902i	0.310119	−	0.950698i	$-0.399631\pi$
$389$	25.7563	−	16.9402i	1.30590	−	0.858902i	0.995778	+	0.0917960i	$0.0292608\pi$
$390$	−10.3304	−	6.67133i	−0.523100	−	0.337816i
$391$	2.28335	−	0.266885i	0.115474	−	0.0134970i
$392$	−7.09382	+	2.81819i	−0.358292	+	0.142340i
$393$	−15.5169	−	4.92140i	−0.782725	−	0.248252i
$394$	−2.25811	+	4.49627i	−0.113762	+	0.226519i
$395$	14.5007	+	1.33423i	0.729608	+	0.0671322i
$396$	−0.326986	+	0.975696i	−0.0164317	+	0.0490306i
$397$	−20.2114	+	9.42472i	−1.01438	+	0.473013i	−0.857434	−	0.514594i	$-0.827943\pi$
$397$	−20.2114	+	9.42472i	−1.01438	+	0.473013i	−0.156946	+	0.987607i	$0.550165\pi$
$398$	−3.47127	−	0.101004i	−0.173999	−	0.00506286i
$399$	−6.16155	+	4.16691i	−0.308463	+	0.208606i
$400$	−0.535880	−	4.97120i	−0.0267940	−	0.248560i
$401$	−1.52282	+	0.455901i	−0.0760458	+	0.0227666i	−0.324600	−	0.945851i	$-0.605230\pi$
$401$	−1.52282	+	0.455901i	−0.0760458	+	0.0227666i	0.248554	+	0.968618i	$0.420045\pi$
$402$	5.66090	+	3.85636i	0.282340	+	0.192338i
$403$	6.79461	−	0.995264i	0.338464	−	0.0495776i
$404$	−10.4740			−0.521102
$405$	−19.4963	+	4.98927i	−0.968781	+	0.247919i
$406$	−34.3649			−1.70550
$407$	0.798274	−	0.116930i	0.0395690	−	0.00579600i
$408$	−5.59015	+	2.69471i	−0.276754	+	0.133408i
$409$	−9.84195	+	2.94649i	−0.486653	+	0.145694i	−0.520724	−	0.853725i	$-0.674338\pi$
$409$	−9.84195	+	2.94649i	−0.486653	+	0.145694i	0.0340709	+	0.999419i	$0.489153\pi$
$410$	5.70321	−	23.5915i	0.281661	−	1.16510i
$411$	−4.34062	−	2.11055i	−0.214107	−	0.104106i
$412$	6.06461	+	0.176462i	0.298782	+	0.00869366i
$413$	21.3452	−	9.95343i	1.05033	−	0.489776i
$414$	−0.0494608	−	1.92426i	−0.00243086	−	0.0945721i
$415$	3.35761	+	4.03810i	0.164819	+	0.198223i
$416$	−1.42501	+	2.83742i	−0.0698666	+	0.139116i
$417$	−19.9597	+	18.2275i	−0.977429	+	0.892605i
$418$	0.357872	−	0.142173i	0.0175041	−	0.00695393i
$419$	22.5748	−	2.63862i	1.10285	−	0.128905i	0.454868	−	0.890559i	$-0.349687\pi$
$419$	22.5748	−	2.63862i	1.10285	−	0.128905i	0.647984	+	0.761654i	$0.275613\pi$
$420$	9.94144	+	10.9847i	0.485093	+	0.536000i
$421$	−12.6476	+	8.31843i	−0.616404	+	0.405415i	−0.818956	−	0.573856i	$-0.805447\pi$
$421$	−12.6476	+	8.31843i	−0.616404	+	0.405415i	0.202552	+	0.979271i	$0.435076\pi$
$422$	1.69571	+	19.3821i	0.0825460	+	0.943506i
$423$	7.96520	+	6.72975i	0.387281	+	0.327212i
$424$	8.31636	+	9.91106i	0.403878	+	0.481324i
$425$	16.5887	+	6.76324i	0.804671	+	0.328065i
$426$	11.0998	−	4.95811i	0.537789	−	0.240221i
$427$	6.42097	−	19.3774i	0.310732	−	0.937737i
$428$	0.465643	+	16.0031i	0.0225077	+	0.773540i
$429$	−1.86179	−	0.303672i	−0.0898880	−	0.0146614i
$430$	−0.305027	+	9.08143i	−0.0147097	+	0.437946i
$431$	−30.6239	+	17.6807i	−1.47510	+	0.851650i	−0.999606	−	0.0280680i	$-0.991065\pi$
$431$	−30.6239	+	17.6807i	−1.47510	+	0.851650i	−0.475495	+	0.879718i	$0.657731\pi$
$432$	1.82329	+	4.86576i	0.0877232	+	0.234104i
$433$	−31.4330	+	8.42244i	−1.51057	+	0.404757i	−0.916625	−	0.399747i	$-0.869098\pi$
$433$	−31.4330	+	8.42244i	−1.51057	+	0.404757i	−0.593947	+	0.804504i	$0.702431\pi$
$434$	−8.21735	−	0.960471i	−0.394446	−	0.0461041i
$435$	12.1729	+	32.5941i	0.583646	+	1.56277i
$436$	1.15424	+	0.273559i	0.0552778	+	0.0131011i
$437$	−0.538100	+	0.478869i	−0.0257408	+	0.0229074i
$438$	14.2935	−	7.94572i	0.682971	−	0.379661i
$439$	2.80794	+	11.8476i	0.134016	+	0.565456i	0.998072	+	0.0620619i	$0.0197676\pi$
$439$	2.80794	+	11.8476i	0.134016	+	0.565456i	−0.864057	+	0.503395i	$0.832084\pi$
$440$	−0.380513	−	0.665950i	−0.0181402	−	0.0317479i
$441$	−22.4104	−	4.70666i	−1.06716	−	0.224127i
$442$	−6.52512	−	9.31884i	−0.310368	−	0.443252i
$443$	−6.09803	−	5.42678i	−0.289726	−	0.257834i	0.507313	−	0.861762i	$-0.330639\pi$
$443$	−6.09803	−	5.42678i	−0.289726	−	0.257834i	−0.797039	+	0.603927i	$0.793602\pi$
$444$	2.75741	−	2.99896i	0.130861	−	0.142324i
$445$	−34.3827	+	6.93877i	−1.62990	+	0.328929i
$446$	23.1259	−	17.2166i	1.09504	−	0.815228i
$447$	0.374185	+	0.195595i	0.0176983	+	0.00925135i
$448$	2.54306	−	2.85761i	0.120148	−	0.135010i
$449$	4.44042	−	25.1829i	0.209556	−	1.18845i	−0.680551	−	0.732701i	$-0.738259\pi$
$449$	4.44042	−	25.1829i	0.209556	−	1.18845i	0.890107	−	0.455752i	$-0.150629\pi$
$450$	6.89720	−	13.3202i	0.325137	−	0.627922i
$451$	−0.646520	−	3.66660i	−0.0304434	−	0.172653i
$452$	6.93782	+	4.27931i	0.326328	+	0.201282i
$453$	14.6815	−	24.5013i	0.689795	−	1.15117i
$454$	25.3429	+	1.47605i	1.18940	+	0.0692746i
$455$	−16.9405	+	21.2284i	−0.794185	+	0.995201i
$456$	0.950522	−	1.69632i	0.0445123	−	0.0794375i
$457$	−11.0496	+	8.73687i	−0.516877	+	0.408694i	−0.844045	−	0.536273i	$-0.819832\pi$
$457$	−11.0496	+	8.73687i	−0.516877	+	0.408694i	0.327167	+	0.944966i	$0.393906\pi$
$458$	−1.12855	−	4.21181i	−0.0527337	−	0.196805i
$459$	−18.4453	−	2.52388i	−0.860955	−	0.117805i
$460$	1.09492	+	0.927149i	0.0510509	+	0.0432285i
$461$	−12.6894	+	5.47365i	−0.591002	+	0.254933i	−0.670510	−	0.741901i	$-0.733924\pi$
$461$	−12.6894	+	5.47365i	−0.591002	+	0.254933i	0.0795075	+	0.996834i	$0.474665\pi$
$462$	2.07191	+	0.933927i	0.0963938	+	0.0434502i
$463$	−24.9427	+	0.725758i	−1.15918	+	0.0337288i	−0.603288	−	0.797523i	$-0.706143\pi$
$463$	−24.9427	+	0.725758i	−1.15918	+	0.0337288i	−0.555896	+	0.831252i	$0.687625\pi$
$464$	8.02797	−	4.03180i	0.372689	−	0.187171i
$465$	1.99981	+	8.13414i	0.0927392	+	0.377212i
$466$	7.85374	−	26.2333i	0.363817	−	1.21523i
$467$	4.47633	+	0.391628i	0.207140	+	0.0181224i	0.190253	−	0.981735i	$-0.439069\pi$
$467$	4.47633	+	0.391628i	0.207140	+	0.0181224i	0.0168864	+	0.999857i	$0.494625\pi$
$468$	−8.26539	+	4.73473i	−0.382068	+	0.218863i
$469$	9.72393	−	11.5885i	0.449009	−	0.535109i
$470$	−7.69516	+	1.09193i	−0.354951	+	0.0503671i
$471$	−1.08150	−	8.32379i	−0.0498327	−	0.383540i
$472$	−3.81867	+	4.82950i	−0.175769	+	0.222296i
$473$	0.514624	+	1.29539i	0.0236624	+	0.0595619i
$474$	6.07665	−	9.50284i	0.279110	−	0.436480i
$475$	−5.47332	+	1.24544i	−0.251133	+	0.0571446i
$476$	4.68763	+	12.8791i	0.214857	+	0.590315i
$477$	4.37528	+	38.5665i	0.200330	+	1.76584i
$478$	10.9315	+	23.4426i	0.499994	+	1.07224i
$479$	12.5077	+	13.2574i	0.571492	+	0.605746i	0.947063	−	0.321047i	$-0.104035\pi$
$479$	12.5077	+	13.2574i	0.571492	+	0.605746i	−0.375571	+	0.926794i	$0.622553\pi$
$480$	−3.61118	−	1.39978i	−0.164827	−	0.0638909i
$481$	6.23964	+	4.10388i	0.284503	+	0.187121i
$482$	2.54842	−	4.72634i	0.116077	−	0.215279i
$483$	−4.23946	−	0.316073i	−0.192902	−	0.0143818i
$484$	8.72898	+	6.49849i	0.396772	+	0.295386i
$485$	−11.0229	−	30.7132i	−0.500523	−	1.39461i
$486$	−3.50284	+	15.1898i	−0.158892	+	0.689023i
$487$	0.178071	−	0.178071i	0.00806916	−	0.00806916i	−0.703061	−	0.711130i	$-0.748184\pi$
$487$	0.178071	−	0.178071i	0.00806916	−	0.00806916i	0.711130	+	0.703061i	$0.248184\pi$
$488$	0.773416	+	5.28007i	0.0350109	+	0.239018i
$489$	−0.184100	+	0.158553i	−0.00832528	+	0.00717002i
$490$	13.7364	−	10.1309i	0.620546	−	0.457666i
$491$	−21.3743	+	32.4980i	−0.964609	+	1.46662i	−0.0819306	+	0.996638i	$0.526109\pi$
$491$	−21.3743	+	32.4980i	−0.964609	+	1.46662i	−0.882678	+	0.469978i	$0.844262\pi$
$492$	−14.2037	−	12.3169i	−0.640354	−	0.555289i
$493$	−0.936147	+	32.1733i	−0.0421620	+	1.44901i
$494$	3.34960	+	1.21915i	0.150706	+	0.0548524i
$495$	0.151880	−	2.29596i	0.00682652	−	0.103196i
$496$	2.03234	−	0.739710i	0.0912546	−	0.0332140i
$497$	−8.44523	−	25.4863i	−0.378820	−	1.14322i
$498$	3.97297	−	0.873722i	0.178033	−	0.0391524i
$499$	−28.0600	−	12.1039i	−1.25614	−	0.541845i	−0.339140	−	0.940736i	$-0.610136\pi$
$499$	−28.0600	−	12.1039i	−1.25614	−	0.541845i	−0.916998	+	0.398891i	$0.869395\pi$
$500$	3.98763	+	10.4450i	0.178332	+	0.467116i
$501$	26.3302	−	3.42104i	1.17635	−	0.152841i
$502$	4.15705	−	20.1326i	0.185538	−	0.898562i
$503$	−44.6636	+	3.90756i	−1.99145	+	0.174229i	−0.993051	+	0.117689i	$0.962451\pi$
$503$	−44.6636	+	3.90756i	−1.99145	+	0.174229i	−0.998400	+	0.0565404i	$0.981993\pi$
$504$	11.0949	−	2.93260i	0.494208	−	0.130628i
$505$	22.6495	−	5.96014i	1.00789	−	0.265223i
$506$	0.210840	+	0.0631214i	0.00937298	+	0.00280609i
$507$	3.18588	+	3.92449i	0.141490	+	0.174293i
$508$	12.0566	+	3.99513i	0.534926	+	0.177255i
$509$	−21.6111	+	22.9064i	−0.957895	+	1.01531i	0.0419743	+	0.999119i	$0.486635\pi$
$509$	−21.6111	+	22.9064i	−0.957895	+	1.01531i	−0.999869	+	0.0161903i	$0.994846\pi$
$510$	10.5550	−	9.00819i	0.467384	−	0.398890i
$511$	−14.3055	−	33.1639i	−0.632838	−	1.46708i
$512$	−0.258819	+	0.965926i	−0.0114383	+	0.0426883i
$513$	5.18795	−	2.66723i	0.229054	−	0.117761i
$514$	−8.55078	−	4.93679i	−0.377159	−	0.217753i
$515$	−13.2148	+	3.06942i	−0.582315	+	0.135255i
$516$	6.14016	+	3.44060i	0.270305	+	0.151464i
$517$	−1.01475	+	0.625905i	−0.0446285	+	0.0275273i
$518$	−5.98152	−	6.72138i	−0.262813	−	0.295321i
$519$	7.36449	+	29.3854i	0.323265	+	1.28988i
$520$	1.46690	−	6.94666i	0.0643277	−	0.304631i
$521$	11.8303	−	2.08600i	0.518295	−	0.0913894i	0.0916192	−	0.995794i	$-0.470796\pi$
$521$	11.8303	−	2.08600i	0.518295	−	0.0913894i	0.426676	+	0.904405i	$0.359685\pi$
$522$	26.7576	+	3.21951i	1.17115	+	0.140914i
$523$	29.7541	−	20.8340i	1.30105	−	0.911008i	0.301950	−	0.953324i	$-0.402363\pi$
$523$	29.7541	−	20.8340i	1.30105	−	0.911008i	0.999104	+	0.0423160i	$0.0134736\pi$
$524$	−0.546473	−	9.38259i	−0.0238728	−	0.409880i
$525$	−27.7486	−	18.0969i	−1.21105	−	0.789812i
$526$	−4.36012	−	5.85666i	−0.190110	−	0.255362i
$527$	−1.12307	+	7.66713i	−0.0489217	+	0.333986i
$528$	−0.593589	+	0.0249085i	−0.0258326	+	0.00108400i
$529$	22.5501	−	1.31339i	0.980439	−	0.0571041i
$530$	−23.6235	−	16.6998i	−1.02614	−	0.725394i
$531$	−17.5525	+	5.75030i	−0.761715	+	0.249542i
$532$	−3.51784	−	2.46322i	−0.152518	−	0.106794i
$533$	18.0929	−	29.3331i	0.783692	−	1.27056i
$534$	−7.45728	+	26.1262i	−0.322708	+	1.13059i
$535$	−10.1134	−	34.3410i	−0.437239	−	1.48469i
$536$	−0.912001	+	3.84803i	−0.0393924	+	0.166210i
$537$	−11.0152	+	11.3019i	−0.475340	+	0.487715i
$538$	−5.70851	−	7.21958i	−0.246111	−	0.311258i
$539$	1.30912	−	2.26746i	0.0563877	−	0.0976664i
$540$	−6.71159	−	9.48443i	−0.288821	−	0.408145i
$541$	−2.54055	−	4.40036i	−0.109227	−	0.189186i	0.806230	−	0.591602i	$-0.201504\pi$
$541$	−2.54055	−	4.40036i	−0.109227	−	0.189186i	−0.915457	+	0.402415i	$0.868171\pi$
$542$	7.48984	−	18.8531i	0.321716	−	0.809809i
$543$	9.68169	+	13.4555i	0.415481	+	0.577433i
$544$	−2.60610	−	2.45873i	−0.111735	−	0.105417i
$545$	−2.65164	+	0.0652497i	−0.113584	+	0.00279499i
$546$	8.58002	+	19.2083i	0.367191	+	0.822039i
$547$	4.89313	+	9.07487i	0.209215	+	0.388013i	0.963162	−	0.268922i	$-0.0866673\pi$
$547$	4.89313	+	9.07487i	0.209215	+	0.388013i	−0.753947	+	0.656935i	$0.771853\pi$
$548$	0.242868	−	2.77600i	0.0103748	−	0.118585i
$549$	−6.81496	+	14.4863i	−0.290855	+	0.618259i
$550$	1.20179	+	1.22356i	0.0512446	+	0.0521726i
$551$	−5.54197	−	8.42615i	−0.236096	−	0.358966i
$552$	1.02746	−	0.423549i	0.0437317	−	0.0180275i
$553$	−19.5411	−	15.4511i	−0.830971	−	0.657047i
$554$	8.92300	−	20.6858i	0.379102	−	0.878857i
$555$	−4.25623	+	8.05418i	−0.180667	+	0.341881i
$556$	−13.9459	−	7.00391i	−0.591439	−	0.297032i
$557$	5.74770	+	2.68020i	0.243538	+	0.113564i	0.540555	−	0.841309i	$-0.318214\pi$
$557$	5.74770	+	2.68020i	0.243538	+	0.113564i	−0.297017	+	0.954872i	$0.595992\pi$
$558$	6.30830	+	1.51770i	0.267052	+	0.0642495i
$559$	−4.41296	+	12.1245i	−0.186648	+	0.512812i
$560$	−3.87314	+	7.62655i	−0.163670	+	0.322281i
$561$	0.930808	−	1.91433i	0.0392987	−	0.0808232i
$562$	17.8712	−	3.69010i	0.753849	−	0.155657i
$563$	29.6301	+	15.9764i	1.24876	+	0.673325i	0.958900	−	0.283744i	$-0.0915765\pi$
$563$	29.6301	+	15.9764i	1.24876	+	0.673325i	0.289860	+	0.957069i	$0.406391\pi$
$564$	−1.98622	+	5.68327i	−0.0836351	+	0.239309i
$565$	−17.4378	−	5.30590i	−0.733614	−	0.223221i
$566$			31.9064i			1.34112i
$567$	32.6063	+	11.0505i	1.36933	+	0.464077i
$568$	4.96301	+	4.96301i	0.208243	+	0.208243i
$569$	14.0514	−	18.8743i	0.589066	−	0.791253i	−0.403236	−	0.915096i	$-0.632115\pi$
$569$	14.0514	−	18.8743i	0.589066	−	0.791253i	0.992302	+	0.123843i	$0.0395220\pi$
$570$	−1.09018	+	4.20910i	−0.0456627	+	0.176300i
$571$	−4.08591	−	13.6479i	−0.170990	−	0.571146i	−0.999930	−	0.0118093i	$-0.996241\pi$
$571$	−4.08591	−	13.6479i	−0.170990	−	0.571146i	0.828940	−	0.559337i	$-0.188944\pi$
$572$	−0.220237	−	1.06661i	−0.00920857	−	0.0445971i
$573$	9.47307	+	1.82945i	0.395743	+	0.0764264i
$574$	−30.2017	+	28.4938i	−1.26059	+	1.18931i
$575$	−2.89529	−	1.38186i	−0.120742	−	0.0576276i
$576$	−2.24782	+	1.98678i	−0.0936594	+	0.0827824i
$577$	−16.1327	+	34.5968i	−0.671615	+	1.44028i	0.214457	+	0.976733i	$0.431202\pi$
$577$	−16.1327	+	34.5968i	−0.671615	+	1.44028i	−0.886071	+	0.463549i	$0.846576\pi$
$578$	−3.95163	+	1.30943i	−0.164366	+	0.0544651i
$579$	19.7033	−	10.2145i	0.818841	−	0.424499i
$580$	−15.0658	+	13.2868i	−0.625574	+	0.551704i
$581$	−1.04300	−	8.92344i	−0.0432710	−	0.370207i
$582$	−25.0542	−	3.34167i	−1.03853	−	0.138517i
$583$	−4.34617	−	0.897412i	−0.180000	−	0.0371670i
$584$	7.23279	+	6.06903i	0.299295	+	0.251138i
$585$	15.1792	−	14.9420i	0.627584	−	0.617774i
$586$	−10.4011	+	8.72758i	−0.429667	+	0.360533i
$587$	−17.8065	+	9.60120i	−0.734955	+	0.396284i	−0.798737	−	0.601680i	$-0.794498\pi$
$587$	−17.8065	+	9.60120i	−0.734955	+	0.396284i	0.0637826	+	0.997964i	$0.479684\pi$
$588$	−2.08406	−	13.0557i	−0.0859450	−	0.538406i
$589$	−1.08969	−	2.16976i	−0.0449001	−	0.0894034i
$590$	5.50951	−	12.6165i	0.226823	−	0.519415i
$591$	−6.74729	−	5.51548i	−0.277547	−	0.226877i
$592$	2.18591	+	0.868408i	0.0898405	+	0.0356914i
$593$	25.3370	+	6.78902i	1.04046	+	0.278792i	0.738306	−	0.674466i	$-0.235626\pi$
$593$	25.3370	+	6.78902i	1.04046	+	0.278792i	0.302159	+	0.953258i	$0.402293\pi$
$594$	−1.52576	−	0.921293i	−0.0626025	−	0.0378011i
$595$	−17.4655	−	25.1831i	−0.716017	−	1.03241i
$596$	−0.0283000	+	0.242122i	−0.00115921	+	0.00991771i
$597$	1.48201	−	5.82953i	0.0606545	−	0.238587i
$598$	1.06952	+	1.73396i	0.0437360	+	0.0709069i
$599$	1.26859	−	21.7808i	0.0518330	−	0.889939i	−0.867740	−	0.497019i	$-0.834428\pi$
$599$	1.26859	−	21.7808i	0.0518330	−	0.889939i	0.919573	−	0.392920i	$-0.128535\pi$
$600$	8.60553	+	0.972046i	0.351319	+	0.0396836i
$601$	42.1114	−	9.98058i	1.71776	−	0.407116i	0.750493	−	0.660879i	$-0.229816\pi$
$601$	42.1114	−	9.98058i	1.71776	−	0.407116i	0.967267	+	0.253762i	$0.0816681\pi$
$602$	8.91608	−	12.7335i	0.363392	−	0.518978i
$603$	−8.65704	+	8.11219i	−0.352542	+	0.330354i
$604$	16.2405	+	2.86364i	0.660816	+	0.116520i
$605$	−22.5739	−	9.08551i	−0.917759	−	0.369378i
$606$	3.95657	−	17.7048i	0.160725	−	0.719209i
$607$	−2.72797	−	0.399589i	−0.110725	−	0.0162188i	0.0893423	−	0.996001i	$-0.471524\pi$
$607$	−2.72797	−	0.399589i	−0.110725	−	0.0162188i	−0.200067	+	0.979782i	$0.564116\pi$
$608$	1.11079	+	0.162707i	0.0450486	+	0.00659864i
$609$	12.9814	−	58.0889i	0.526031	−	2.35388i
$610$	−4.67705	−	10.9778i	−0.189368	−	0.444478i
$611$	−10.8687	−	1.91644i	−0.439700	−	0.0775310i
$612$	−2.44333	−	10.4673i	−0.0987659	−	0.423114i
$613$	−17.4092	+	24.8629i	−0.703150	+	1.00420i	0.295653	+	0.955295i	$0.404463\pi$
$613$	−17.4092	+	24.8629i	−0.703150	+	1.00420i	−0.998803	+	0.0489071i	$0.984426\pi$
$614$	19.6200	−	4.65003i	0.791800	−	0.187660i
$615$	37.7237	+	18.5522i	1.52117	+	0.748096i
$616$	−0.0762933	+	1.30991i	−0.00307394	+	0.0527776i
$617$	7.36345	+	11.9380i	0.296441	+	0.480604i	0.964710	−	0.263316i	$-0.0848161\pi$
$617$	7.36345	+	11.9380i	0.296441	+	0.480604i	−0.668269	+	0.743920i	$0.732964\pi$
$618$	−2.58919	+	10.1847i	−0.104153	+	0.409688i
$619$	−0.444549	+	3.80336i	−0.0178679	+	0.152870i	−0.999227	−	0.0393137i	$-0.987483\pi$
$619$	−0.444549	+	3.80336i	−0.0178679	+	0.152870i	0.981359	+	0.192184i	$0.0615569\pi$
$620$	−3.97390	+	2.75607i	−0.159596	+	0.110686i
$621$	3.27137	+	0.643284i	0.131275	+	0.0258141i
$622$	−15.6824	−	4.20208i	−0.628807	−	0.168488i
$623$	55.7661	+	22.1545i	2.23422	+	0.887600i
$624$	−4.25795	−	3.48060i	−0.170454	−	0.139336i
$625$	−14.5667	−	20.3178i	−0.582668	−	0.812710i
$626$	−6.35385	−	12.6516i	−0.253951	−	0.505658i
$627$	0.105137	+	0.658637i	0.00419878	+	0.0263034i
$628$	4.26558	−	2.29998i	0.170215	−	0.0917792i
$629$	−6.45568	+	5.41696i	−0.257405	+	0.215988i
$630$	−22.3235	+	12.6551i	−0.889390	+	0.504190i
$631$	−16.3387	−	13.7098i	−0.650431	−	0.545777i	0.256770	−	0.966472i	$-0.417342\pi$
$631$	−16.3387	−	13.7098i	−0.650431	−	0.545777i	−0.907202	+	0.420696i	$0.861786\pi$
$632$	6.37775	+	1.31690i	0.253693	+	0.0523834i
$633$	−33.4032	−	4.45524i	−1.32766	−	0.177080i
$634$	4.09614	+	35.0447i	0.162678	+	1.39180i
$635$	−28.3453	−	1.77856i	−1.12485	−	0.0705800i
$636$	−19.8947	+	10.3137i	−0.788877	+	0.408965i
$637$	23.0061	−	7.62340i	0.911536	−	0.302050i
$638$	−1.30227	+	2.79273i	−0.0515574	+	0.110565i
$639$	4.18801	+	20.6356i	0.165675	+	0.816332i
$640$	0.0100321	−	2.23605i	0.000396555	−	0.0883875i
$641$	14.4684	−	13.6503i	0.571469	−	0.539153i	−0.345341	−	0.938477i	$-0.612237\pi$
$641$	14.4684	−	13.6503i	0.571469	−	0.539153i	0.916810	+	0.399324i	$0.130755\pi$
$642$	−27.2269	−	5.25809i	−1.07456	−	0.207520i
$643$	−7.37710	−	35.7273i	−0.290924	−	1.40895i	−0.825774	−	0.564001i	$-0.809261\pi$
$643$	−7.37710	−	35.7273i	−0.290924	−	1.40895i	0.534850	−	0.844947i	$-0.320368\pi$
$644$	−0.703944	−	2.35134i	−0.0277393	−	0.0926556i
$645$	−15.2356	−	3.94612i	−0.599902	−	0.155378i
$646$	−2.40196	+	3.22639i	−0.0945037	+	0.126941i
$647$	−30.5406	−	30.5406i	−1.20067	−	1.20067i	−0.973962	−	0.226712i	$-0.927202\pi$
$647$	−30.5406	−	30.5406i	−1.20067	−	1.20067i	−0.226712	−	0.973962i	$-0.572798\pi$
$648$	−8.91362	+	1.24397i	−0.350160	+	0.0488677i
$649$		−	2.11185i		−	0.0828973i
$650$	0.780845	+	15.8565i	0.0306273	+	0.621945i
$651$	4.72765	−	13.5274i	0.185291	−	0.530182i
$652$	−0.123471	−	0.0665749i	−0.00483549	−	0.00260727i
$653$	−20.2878	+	4.18910i	−0.793924	+	0.163932i	−0.581823	−	0.813315i	$-0.697660\pi$
$653$	−20.2878	+	4.18910i	−0.793924	+	0.163932i	−0.212101	+	0.977248i	$0.568031\pi$
$654$	−0.898425	+	1.84773i	−0.0351312	+	0.0722520i
$655$	6.52080	+	19.9784i	0.254789	+	0.780621i
$656$	3.71241	−	10.1998i	0.144945	−	0.398234i
$657$	8.03171	+	27.1627i	0.313347	+	1.05972i
$658$	12.0505	+	5.61925i	0.469778	+	0.219061i
$659$	−32.3833	−	16.2635i	−1.26147	−	0.633535i	−0.312807	−	0.949817i	$-0.601269\pi$
$659$	−32.3833	−	16.2635i	−1.26147	−	0.633535i	−0.948665	+	0.316281i	$0.897566\pi$
$660$	1.26943	−	0.391639i	0.0494126	−	0.0152445i
$661$	−14.9992	+	34.7721i	−0.583402	+	1.35248i	0.329445	+	0.944175i	$0.393138\pi$
$661$	−14.9992	+	34.7721i	−0.583402	+	1.35248i	−0.912847	+	0.408302i	$0.866121\pi$
$662$	−2.87358	−	2.27213i	−0.111685	−	0.0883090i
$663$	18.2170	−	7.50958i	0.707491	−	0.291648i
$664$	1.29058	+	1.96223i	0.0500843	+	0.0761494i
$665$	9.00882	+	3.32479i	0.349347	+	0.128930i
$666$	4.02770	+	5.79386i	0.156070	+	0.224508i
$667$	0.502375	−	5.74217i	0.0194520	−	0.222338i
$668$	7.27540	+	13.4931i	0.281494	+	0.522063i
$669$	20.3663	+	45.5945i	0.787408	+	1.76279i
$670$	−0.217532	−	8.84015i	−0.00840399	−	0.341525i
$671$	−1.33142	−	1.25613i	−0.0513988	−	0.0484922i
$672$	3.86974	+	5.37814i	0.149279	+	0.207466i
$673$	11.8879	−	29.9236i	0.458244	−	1.15347i	−0.499619	−	0.866245i	$-0.666527\pi$
$673$	11.8879	−	29.9236i	0.458244	−	1.15347i	0.957863	−	0.287224i	$-0.0927326\pi$
$674$	13.8183	+	23.9340i	0.532261	+	0.921903i
$675$	19.9105	+	16.6905i	0.766356	+	0.642416i
$676$	−1.45921	+	2.52742i	−0.0561234	+	0.0972085i
$677$	−10.2219	−	12.9278i	−0.392861	−	0.496854i	0.547607	−	0.836736i	$-0.315539\pi$
$677$	−10.2219	−	12.9278i	−0.392861	−	0.496854i	−0.940468	+	0.339882i	$0.889613\pi$
$678$	−9.85433	+	10.1109i	−0.378453	+	0.388306i
$679$	−12.8738	+	54.3189i	−0.494051	+	2.08457i
$680$	7.03467	+	3.83390i	0.269767	+	0.147023i
$681$	−12.0683	+	42.2809i	−0.462460	+	1.62021i
$682$	−0.389455	+	0.631402i	−0.0149130	+	0.0241776i
$683$	−0.437141	−	0.306089i	−0.0167267	−	0.0117122i	0.565183	−	0.824965i	$-0.308805\pi$
$683$	−0.437141	−	0.306089i	−0.0167267	−	0.0117122i	−0.581910	+	0.813253i	$0.697694\pi$
$684$	2.50833	+	2.24751i	0.0959083	+	0.0859356i
$685$	1.05446	+	6.14115i	0.0402890	+	0.234641i
$686$	−2.41778	+	0.140820i	−0.0923112	+	0.00537651i
$687$	7.54577	−	0.316639i	0.287889	−	0.0120805i
$688$	−0.588949	+	4.02072i	−0.0224535	+	0.153289i
$689$	−24.5313	−	32.9512i	−0.934567	−	1.25534i
$690$	−1.98082	+	1.50057i	−0.0754085	+	0.0571258i
$691$	−1.91056	−	32.8031i	−0.0726812	−	1.24789i	−0.815644	−	0.578555i	$-0.803617\pi$
$691$	−1.91056	−	32.8031i	−0.0726812	−	1.24789i	0.742963	−	0.669333i	$-0.233420\pi$
$692$	−14.3273	+	10.0321i	−0.544641	+	0.381362i
$693$	−2.36133	+	3.14947i	−0.0896996	+	0.119638i
$694$	−30.1704	+	5.31986i	−1.14525	+	0.201939i
$695$	34.1429	+	7.20980i	1.29511	+	0.273483i
$696$	3.78260	+	15.0931i	0.143379	+	0.572104i
$697$	25.8539	+	29.0518i	0.979286	+	1.10042i
$698$	−29.4869	+	18.1878i	−1.11609	+	0.688417i
$699$	41.3769	+	23.1853i	1.56502	+	0.876947i
$700$	4.03566	−	18.6960i	0.152534	−	0.706643i
$701$	1.93114	+	1.11494i	0.0729380	+	0.0421108i	0.536025	−	0.844202i	$-0.319925\pi$
$701$	1.93114	+	1.11494i	0.0729380	+	0.0421108i	−0.463087	+	0.886313i	$0.653258\pi$
$702$	−4.88112	−	15.7600i	−0.184226	−	0.594823i
$703$	0.683430	−	2.55059i	0.0257760	−	0.0961975i
$704$	−0.135859	−	0.314957i	−0.00512039	−	0.0118704i
$705$	1.06110	−	13.4200i	0.0399632	−	0.505428i
$706$	−7.49549	+	7.94475i	−0.282096	+	0.299005i
$707$	−38.0329	−	12.6027i	−1.43037	−	0.473974i
$708$	−6.72107	−	8.27927i	−0.252593	−	0.311154i
$709$	7.93141	+	2.37451i	0.297870	+	0.0891765i	0.432251	−	0.901753i	$-0.357719\pi$
$709$	7.93141	+	2.37451i	0.297870	+	0.0891765i	−0.134381	+	0.990930i	$0.542905\pi$
$710$	−13.5564	−	7.90812i	−0.508764	−	0.296786i
$711$	13.7677	+	13.8614i	0.516330	+	0.519844i
$712$	−15.6267	+	1.36716i	−0.585636	+	0.0512365i
$713$	0.280617	−	1.35903i	0.0105092	−	0.0508961i
$714$	−23.5411	+	3.05865i	−0.881004	+	0.114467i
$715$	1.08320	+	2.18116i	0.0405092	+	0.0815709i
$716$	−8.36649	−	3.60895i	−0.312670	−	0.134873i
$717$	−43.7557	+	9.62261i	−1.63409	+	0.359363i
$718$	5.49499	+	16.5829i	0.205071	+	0.618870i
$719$	−38.1899	+	13.9000i	−1.42424	+	0.518382i	−0.935276	−	0.353919i	$-0.884849\pi$
$719$	−38.1899	+	13.9000i	−1.42424	+	0.518382i	−0.488968	+	0.872302i	$0.662627\pi$
$720$	3.73025	−	5.57541i	0.139018	−	0.207783i
$721$	21.8092	+	7.93791i	0.812219	+	0.295623i
$722$	−0.515953	+	17.7322i	−0.0192018	+	0.659923i
$723$	7.02653	+	6.09311i	0.261319	+	0.226605i
$724$	−5.25911	+	7.99608i	−0.195453	+	0.297172i
$725$	25.0184	−	37.3051i	0.929159	−	1.38548i
$726$	−14.2821	+	12.3003i	−0.530060	+	0.456506i
$727$	−1.55414	−	10.6100i	−0.0576399	−	0.393504i	−0.998502	−	0.0547147i	$-0.982575\pi$
$727$	−1.55414	−	10.6100i	−0.0576399	−	0.393504i	0.940862	−	0.338790i	$-0.110018\pi$
$728$	−8.58851	+	8.58851i	−0.318311	+	0.318311i
$729$	−24.3530	−	11.6590i	−0.901962	−	0.431815i
$730$	−19.0941	−	9.00823i	−0.706704	−	0.333410i
$731$	−11.6785	−	8.69434i	−0.431946	−	0.321572i
$732$	−9.21736	−	0.687201i	−0.340683	−	0.0253997i
$733$	−8.96152	+	16.6202i	−0.331001	+	0.613880i	−0.990450	−	0.137869i	$-0.955975\pi$
$733$	−8.96152	+	16.6202i	−0.331001	+	0.613880i	0.659449	+	0.751749i	$0.270790\pi$
$734$	−19.5890	−	12.8839i	−0.723042	−	0.475552i
$735$	11.9359	+	27.0463i	0.440261	+	0.997618i
$736$	0.440314	+	0.466706i	0.0162302	+	0.0172030i
$737$	−0.573272	−	1.22939i	−0.0211168	−	0.0452850i
$738$	26.1854	−	19.3567i	0.963899	−	0.712529i
$739$	−15.8500	−	43.5474i	−0.583050	−	1.60192i	−0.782939	−	0.622098i	$-0.786280\pi$
$739$	−15.8500	−	43.5474i	−0.583050	−	1.60192i	0.199889	−	0.979818i	$-0.435942\pi$
$740$	−5.22109	−	0.634015i	−0.191931	−	0.0233069i
$741$	−3.32612	+	5.20148i	−0.122188	+	0.191081i
$742$	18.2727	+	45.9952i	0.670813	+	1.68854i
$743$	21.5489	−	27.2531i	0.790554	−	0.999818i	−0.209206	−	0.977872i	$-0.567088\pi$
$743$	21.5489	−	27.2531i	0.790554	−	0.999818i	0.999759	−	0.0219463i	$-0.00698628\pi$
$744$	0.482657	+	3.71480i	0.0176951	+	0.136191i
$745$	−0.0765800	−	0.539681i	−0.00280567	−	0.0197724i
$746$	13.7568	−	16.3947i	0.503672	−	0.600253i
$747$	−0.0238901	+	7.04579i	−0.000874092	+	0.257792i
$748$	1.22429	+	0.107111i	0.0447644	+	0.00391638i
$749$	−17.5647	+	58.6702i	−0.641800	+	2.14376i
$750$	−19.1622	+	2.79490i	−0.699703	+	0.102055i
$751$	3.42873	−	1.72198i	0.125116	−	0.0628358i	−0.385140	−	0.922858i	$-0.625847\pi$
$751$	3.42873	−	1.72198i	0.125116	−	0.0628358i	0.510256	+	0.860022i	$0.329551\pi$
$752$	−3.47438	+	0.101094i	−0.126698	+	0.00368653i
$753$	32.4609	+	14.6320i	1.18294	+	0.533220i
$754$	−26.1912	+	11.2978i	−0.953828	+	0.411441i
$755$	−36.7488	+	3.04903i	−1.33742	+	0.110966i
$756$	0.766012	+	19.8622i	0.0278596	+	0.722382i
$757$	−10.0079	−	37.3501i	−0.363744	−	1.35751i	−0.869115	−	0.494610i	$-0.835311\pi$
$757$	−10.0079	−	37.3501i	−0.363744	−	1.35751i	0.505371	−	0.862902i	$-0.331356\pi$
$758$	4.71557	−	3.72859i	0.171277	−	0.135429i
$759$	−0.186343	+	0.332551i	−0.00676381	+	0.0120708i
$760$	−2.49462	+	0.280240i	−0.0904894	+	0.0101654i
$761$	−17.0506	−	0.993085i	−0.618084	−	0.0359993i	−0.253753	−	0.967269i	$-0.581665\pi$
$761$	−17.0506	−	0.993085i	−0.618084	−	0.0359993i	−0.364331	+	0.931270i	$0.618702\pi$
$762$	−11.3076	+	18.8708i	−0.409631	+	0.683618i
$763$	3.86206	+	2.38215i	0.139816	+	0.0862398i
$764$	0.967279	+	5.48571i	0.0349949	+	0.198466i
$765$	11.2399	+	21.2446i	0.406379	+	0.768100i
$766$	0.354954	−	2.01304i	0.0128250	−	0.0727341i
$767$	12.9960	−	14.6035i	0.469257	−	0.527300i
$768$	−1.53499	−	0.802376i	−0.0553892	−	0.0289532i
$769$	−16.7236	+	12.4503i	−0.603069	+	0.448968i	−0.854893	−	0.518805i	$-0.826377\pi$
$769$	−16.7236	+	12.4503i	−0.603069	+	0.448968i	0.251824	+	0.967773i	$0.418970\pi$
$770$	−0.580409	−	2.87602i	−0.0209165	−	0.103645i
$771$	11.5750	−	12.5890i	0.416863	−	0.453381i
$772$	9.57198	+	8.51834i	0.344503	+	0.306582i
$773$	14.4624	+	20.6544i	0.520176	+	0.742889i	0.990183	−	0.139774i	$-0.0446375\pi$
$773$	14.4624	+	20.6544i	0.520176	+	0.742889i	−0.470007	+	0.882663i	$0.655749\pi$
$774$	−8.13529	+	9.07937i	−0.292417	+	0.326351i
$775$	7.02505	−	8.22118i	0.252347	−	0.295313i
$776$	−3.36542	−	14.1998i	−0.120811	−	0.509743i
$777$	13.6211	−	7.57190i	0.488653	−	0.271640i
$778$	−23.0292	+	20.4942i	−0.825636	+	0.734754i
$779$	−11.8572	−	2.81020i	−0.424827	−	0.100686i
$780$	11.1882	+	5.10368i	0.400602	+	0.182741i
$781$	−2.39123	−	0.279494i	−0.0855649	−	0.0100011i
$782$	−2.22056	+	0.594997i	−0.0794070	+	0.0212770i
$783$	−15.5498	+	44.0136i	−0.555705	+	1.57292i
$784$	6.61047	−	3.81656i	0.236088	−	0.136306i
$785$	−7.91532	+	7.40088i	−0.282510	+	0.264149i
$786$	16.0663	+	2.62054i	0.573068	+	0.0934717i
$787$	−0.238127	−	8.18389i	−0.00848831	−	0.291724i	−0.993121	−	0.117089i	$-0.962644\pi$
$787$	−0.238127	−	8.18389i	−0.00848831	−	0.291724i	0.984633	−	0.174636i	$-0.0558747\pi$
$788$	1.58262	−	4.77607i	0.0563784	−	0.170140i
$789$	11.5469	−	5.15780i	0.411080	−	0.183623i
$790$	−14.5409	+	0.781470i	−0.517343	+	0.0278035i
$791$	20.0433	+	23.8867i	0.712659	+	0.849314i
$792$	0.182124	−	1.01279i	0.00647151	−	0.0359878i
$793$	−1.47676	−	16.8794i	−0.0524413	−	0.599407i
$794$	18.6320	−	12.2545i	0.661226	−	0.434895i
$795$	37.1525	−	33.6238i	1.31766	−	1.19251i
$796$	3.44926	−	0.403161i	0.122256	−	0.0142896i
$797$	18.8003	−	7.46889i	0.665941	−	0.264562i	−0.0117249	−	0.999931i	$-0.503732\pi$
$797$	18.8003	−	7.46889i	0.665941	−	0.264562i	0.677666	+	0.735370i	$0.262991\pi$
$798$	5.49258	−	5.01591i	0.194435	−	0.177561i
$799$	5.58916	−	11.1289i	0.197730	−	0.393713i
$800$	1.25071	+	4.84105i	0.0442192	+	0.171157i
$801$	−41.3457	−	22.4747i	−1.46088	−	0.794103i
$802$	1.44066	−	0.671792i	0.0508716	−	0.0237218i
$803$	−3.23724	−	0.0941941i	−0.114240	−	0.00332404i
$804$	−6.16004	−	2.99520i	−0.217248	−	0.105633i
$805$	2.86025	+	4.68407i	0.100811	+	0.165092i
$806$	−6.57863	+	1.96951i	−0.231722	+	0.0693731i
$807$	14.3601	−	6.92221i	0.505498	−	0.243673i
$808$	10.3634	−	1.51802i	0.364584	−	0.0534037i
$809$	12.4868			0.439012			0.219506	−	0.975611i	$-0.429556\pi$
$809$	12.4868			0.439012			0.219506	+	0.975611i	$0.429556\pi$
$810$	18.5674	−	7.76223i	0.652391	−	0.272737i
$811$	−42.0938			−1.47811			−0.739057	−	0.673643i	$-0.764729\pi$
$811$	−42.0938			−1.47811			−0.739057	+	0.673643i	$0.764729\pi$
$812$	34.0020	−	4.98057i	1.19324	−	0.174784i
$813$	29.0391	+	19.7823i	1.01845	+	0.693794i
$814$	−0.772899	+	0.231391i	−0.0270901	+	0.00811024i
$815$	0.304883	+	0.0737050i	0.0106796	+	0.00258177i
$816$	5.14058	−	3.47645i	0.179956	−	0.121700i
$817$	4.56009	+	0.132685i	0.159537	+	0.00464206i
$818$	9.31100	−	4.34179i	0.325551	−	0.151807i
$819$	−35.7100	+	7.24736i	−1.24781	+	0.253243i
$820$	−2.22382	+	24.1690i	−0.0776593	+	0.844019i
$821$	−20.2836	+	40.3879i	−0.707902	+	1.40955i	0.195478	+	0.980708i	$0.437374\pi$
$821$	−20.2836	+	40.3879i	−0.707902	+	1.40955i	−0.903380	+	0.428841i	$0.858922\pi$
$822$	4.60068	+	1.45917i	0.160467	+	0.0508943i
$823$	50.4103	−	20.0267i	1.75719	−	0.698088i	0.758258	−	0.651955i	$-0.226051\pi$
$823$	50.4103	−	20.0267i	1.75719	−	0.698088i	0.998935	−	0.0461336i	$-0.0146900\pi$
$824$	−6.02615	+	0.704356i	−0.209931	+	0.0245374i
$825$	−2.52222	+	1.56926i	−0.0878126	+	0.0546346i
$826$	−19.6773	+	12.9419i	−0.684659	+	0.450307i
$827$	−1.02791	−	11.7490i	−0.0357439	−	0.408554i	−0.992897	−	0.118974i	$-0.962040\pi$
$827$	−1.02791	−	11.7490i	−0.0357439	−	0.408554i	0.957154	−	0.289581i	$-0.0935159\pi$
$828$	0.327825	+	1.89677i	0.0113927	+	0.0659174i
$829$	−0.0749146	−	0.0892798i	−0.00260189	−	0.00310082i	0.764742	−	0.644337i	$-0.222866\pi$
$829$	−0.0749146	−	0.0892798i	−0.00260189	−	0.00310082i	−0.767344	+	0.641236i	$0.778422\pi$
$830$	−3.90741	−	3.50884i	−0.135628	−	0.121794i
$831$	31.5958	+	22.8971i	1.09605	+	0.794293i
$832$	0.998727	−	3.01399i	0.0346246	−	0.104491i
$833$	0.795426	+	27.3370i	0.0275599	+	0.947171i
$834$	17.1072	−	20.9279i	0.592373	−	0.724672i
$835$	−23.4108	−	25.0381i	−0.810165	−	0.866480i
$836$	−0.333488	+	0.192539i	−0.0115339	+	0.00665911i
$837$	−4.94843	+	10.0900i	−0.171043	+	0.348760i
$838$	−21.9540	+	5.88256i	−0.758389	+	0.203210i
$839$	−19.4811	−	2.27701i	−0.672561	−	0.0786111i	−0.227044	−	0.973884i	$-0.572906\pi$
$839$	−19.4811	−	2.27701i	−0.672561	−	0.0786111i	−0.445517	+	0.895273i	$0.646980\pi$
$840$	−11.4285	−	9.42793i	−0.394321	−	0.325294i
$841$	50.3099	+	11.9237i	1.73483	+	0.411161i
$842$	11.3084	−	10.0636i	0.389714	−	0.346816i
$843$	−0.513263	+	31.6026i	−0.0176777	+	1.08845i
$844$	−4.48689	−	18.9317i	−0.154445	−	0.651656i
$845$	1.71726	−	6.29577i	0.0590755	−	0.216581i
$846$	−8.85646	−	5.50428i	−0.304491	−	0.189241i
$847$	23.8771	+	34.1001i	0.820428	+	1.17169i
$848$	−9.66499	−	8.60111i	−0.331897	−	0.295363i
$849$	−53.9331	−	12.0527i	−1.85098	−	0.413646i
$850$	−17.3938	−	4.28760i	−0.596601	−	0.147063i
$851$	1.21055	−	0.901219i	0.0414970	−	0.0308934i
$852$	−10.2640	+	6.51448i	−0.351640	+	0.223182i
$853$	−7.65008	+	8.59632i	−0.261934	+	0.294332i	−0.863352	−	0.504602i	$-0.831639\pi$
$853$	−7.65008	+	8.59632i	−0.261934	+	0.294332i	0.601419	+	0.798934i	$0.294602\pi$
$854$	−3.54477	+	20.1034i	−0.121300	+	0.687924i
$855$	−6.70306	−	3.43278i	−0.229240	−	0.117399i
$856$	−2.78009	−	15.7667i	−0.0950215	−	0.538894i
$857$	4.90500	+	3.02545i	0.167552	+	0.103347i	0.606203	−	0.795310i	$-0.292692\pi$
$857$	4.90500	+	3.02545i	0.167552	+	0.103347i	−0.438651	+	0.898657i	$0.644544\pi$
$858$	1.88614	+	0.0306332i	0.0643919	+	0.00104580i
$859$	4.49551	+	0.261834i	0.153385	+	0.00893366i	0.134665	−	0.990891i	$-0.457004\pi$
$859$	4.49551	+	0.261834i	0.153385	+	0.00893366i	0.0187195	+	0.999825i	$0.494041\pi$
$860$	−1.01438	−	9.02975i	−0.0345902	−	0.307912i
$861$	−36.7560	−	61.8151i	−1.25264	−	2.10665i
$862$	27.7381	−	21.9324i	0.944762	−	0.747021i
$863$	12.9549	+	48.3482i	0.440989	+	1.64579i	0.726315	+	0.687362i	$0.241231\pi$
$863$	12.9549	+	48.3482i	0.440989	+	1.64579i	−0.285326	+	0.958430i	$0.592102\pi$
$864$	−2.50924	−	4.55013i	−0.0853662	−	0.154799i
$865$	25.2733	−	29.8466i	0.859320	−	1.01482i
$866$	29.8804	−	12.8892i	1.01538	−	0.437991i
$867$	−0.720669	−	7.17431i	−0.0244752	−	0.243652i
$868$	8.26979	−	0.240626i	0.280695	−	0.00816739i
$869$	−1.99618	+	1.00252i	−0.0677158	+	0.0340081i
$870$	−16.7683	−	30.4857i	−0.568499	−	1.03356i
$871$	3.60126	−	12.0290i	0.122024	−	0.407589i
$872$	−1.18170	−	0.103385i	−0.0400173	−	0.00350106i
$873$	15.1129	−	41.0883i	0.511493	−	1.39063i
$874$	0.463016	−	0.551801i	0.0156617	−	0.0186649i
$875$	1.91189	+	42.7257i	0.0646335	+	1.44439i
$876$	−12.9910	+	9.93342i	−0.438926	+	0.335619i
$877$	−10.5153	+	13.2988i	−0.355078	+	0.449069i	−0.929132	−	0.369748i	$-0.879444\pi$
$877$	−10.5153	+	13.2988i	−0.355078	+	0.449069i	0.574054	+	0.818817i	$0.305370\pi$
$878$	−4.49539	−	11.3156i	−0.151712	−	0.381882i
$879$	−10.8237	−	20.8785i	−0.365074	−	0.704213i
$880$	0.473013	+	0.603770i	0.0159453	+	0.0203531i
$881$	3.21682	+	8.83815i	0.108378	+	0.297765i	0.982012	−	0.188818i	$-0.0604655\pi$
$881$	3.21682	+	8.83815i	0.108378	+	0.297765i	−0.873635	+	0.486582i	$0.838243\pi$
$882$	22.8560	+	1.40898i	0.769600	+	0.0474430i
$883$	16.8918	+	36.2245i	0.568453	+	1.21905i	0.954952	+	0.296761i	$0.0959066\pi$
$883$	16.8918	+	36.2245i	0.568453	+	1.21905i	−0.386499	+	0.922290i	$0.626316\pi$
$884$	7.80682	+	8.27475i	0.262572	+	0.278310i
$885$	19.2452	+	14.0789i	0.646921	+	0.473258i
$886$	6.82016	+	4.48569i	0.229128	+	0.150700i
$887$	−2.66200	+	4.93698i	−0.0893811	+	0.165768i	−0.920981	−	0.389608i	$-0.872611\pi$
$887$	−2.66200	+	4.93698i	−0.0893811	+	0.165768i	0.831600	+	0.555375i	$0.187425\pi$
$888$	−2.29365	+	3.36693i	−0.0769698	+	0.112987i
$889$	38.9725	+	29.0139i	1.30710	+	0.973097i
$890$	33.0141	−	11.8487i	1.10663	−	0.397168i
$891$	2.13367	−	2.23105i	0.0714806	−	0.0747430i
$892$	−20.3865	+	20.3865i	−0.682589	+	0.682589i
$893$	0.565546	+	3.86095i	0.0189253	+	0.129202i
$894$	−0.398582	−	0.139299i	−0.0133306	−	0.00465885i
$895$	20.1458	+	3.04330i	0.673399	+	0.101726i
$896$	−2.10205	+	3.19601i	−0.0702246	+	0.106771i
$897$	−3.33502	+	1.15287i	−0.111353	+	0.0384932i
$898$	−0.743735	+	25.5605i	−0.0248188	+	0.852966i
$899$	18.2575	+	6.64520i	0.608923	+	0.221630i
$900$	−4.89385	+	14.1792i	−0.163128	+	0.472641i
$901$	43.5597	−	15.8544i	1.45118	−	0.528188i
$902$	1.17110	+	3.53418i	0.0389934	+	0.117675i
$903$	18.1561	+	19.8814i	0.604196	+	0.661613i
$904$	−7.48478	−	3.22862i	−0.248940	−	0.107382i
$905$	6.82246	−	20.2838i	0.226786	−	0.674256i
$906$	−10.9754	+	26.3705i	−0.364634	+	0.876100i
$907$	5.95600	−	28.8449i	0.197766	−	0.957780i	−0.755384	−	0.655282i	$-0.772550\pi$
$907$	5.95600	−	28.8449i	0.197766	−	0.957780i	0.953150	−	0.302498i	$-0.0978205\pi$
$908$	−25.2892	+	2.21252i	−0.839252	+	0.0734250i
$909$	28.4329	+	13.3760i	0.943059	+	0.443654i
$910$	13.6850	−	23.4594i	0.453654	−	0.777673i
$911$	−30.5259	−	9.13885i	−1.01137	−	0.302784i	−0.262093	−	0.965043i	$-0.584413\pi$
$911$	−30.5259	−	9.13885i	−1.01137	−	0.302784i	−0.749275	+	0.662259i	$0.769598\pi$
$912$	−0.694635	+	1.81617i	−0.0230017	+	0.0601395i
$913$	−0.764707	−	0.253396i	−0.0253081	−	0.00838619i
$914$	9.66666	−	10.2461i	0.319745	−	0.338910i
$915$	20.3231	−	3.75902i	0.671862	−	0.124269i
$916$	1.72706	+	4.00378i	0.0570637	+	0.132289i
$917$	9.30513	−	34.7272i	0.307283	−	1.14679i
$918$	18.6164	−	0.176086i	0.614432	−	0.00581172i
$919$	8.84722	+	5.10794i	0.291843	+	0.168496i	0.638773	−	0.769396i	$-0.279442\pi$
$919$	8.84722	+	5.10794i	0.291843	+	0.168496i	−0.346930	+	0.937891i	$0.612776\pi$
$920$	−1.21773	−	0.758671i	−0.0401474	−	0.0250126i
$921$	0.448732	+	34.9214i	0.0147862	+	1.15070i
$922$	11.7621	−	7.25495i	0.387363	−	0.238929i
$923$	−14.8154	−	16.6479i	−0.487655	−	0.547973i
$924$	−2.18539	−	0.623781i	−0.0718940	−	0.0205209i
$925$	11.6511	−	1.59999i	0.383087	−	0.0526073i
$926$	24.5741	−	4.33308i	0.807556	−	0.142394i
$927$	−16.2377	−	8.22393i	−0.533315	−	0.270109i
$928$	−7.35887	+	5.15273i	−0.241567	+	0.169147i
$929$	0.993948	+	17.0654i	0.0326104	+	0.559899i	0.974558	+	0.224138i	$0.0719565\pi$
$929$	0.993948	+	17.0654i	0.0326104	+	0.559899i	−0.941947	+	0.335761i	$0.891006\pi$
$930$	−3.15760	−	7.75842i	−0.103542	−	0.254409i
$931$	−5.11722	−	6.87362i	−0.167710	−	0.225274i
$932$	−3.96877	+	27.0946i	−0.130001	+	0.887513i
$933$	13.0271	−	24.9215i	0.426487	−	0.815893i
$934$	−4.48582	+	0.261269i	−0.146781	+	0.00854899i
$935$	−2.70842	+	0.465047i	−0.0885747	+	0.0152087i
$936$	7.49190	−	5.88266i	0.244881	−	0.192281i
$937$	33.3956	+	23.3838i	1.09099	+	0.763916i	0.973392	−	0.229145i	$-0.0735931\pi$
$937$	33.3956	+	23.3838i	1.09099	+	0.763916i	0.117594	+	0.993062i	$0.462482\pi$
$938$	−7.94171	+	12.8755i	−0.259306	+	0.420399i
$939$	23.7858	−	5.96114i	0.776220	−	0.194534i
$940$	7.45565	−	2.19568i	0.243177	−	0.0716151i
$941$	−9.34997	+	39.4506i	−0.304800	+	1.28605i	0.577896	+	0.816110i	$0.303874\pi$
$941$	−9.34997	+	39.4506i	−0.304800	+	1.28605i	−0.882696	+	0.469944i	$0.844274\pi$
$942$	2.27646	+	8.07916i	0.0741710	+	0.263233i
$943$	−4.31963	−	5.46307i	−0.140667	−	0.177902i
$944$	3.07841	−	5.33196i	0.100194	−	0.173540i
$945$	−12.9589	−	42.5152i	−0.421552	−	1.38302i
$946$	−0.696933	−	1.20712i	−0.0226592	−	0.0392470i
$947$	−1.04568	+	2.63213i	−0.0339800	+	0.0855329i	−0.945353	−	0.326049i	$-0.894283\pi$
$947$	−1.04568	+	2.63213i	−0.0339800	+	0.0855329i	0.911373	+	0.411581i	$0.135023\pi$
$948$	−4.63523	+	10.2832i	−0.150545	+	0.333983i
$949$	−21.8059	−	20.5728i	−0.707850	−	0.667822i
$950$	5.23503	−	2.02555i	0.169847	−	0.0657174i
$951$	−60.7853	−	6.31422i	−1.97110	−	0.204753i
$952$	−6.50473	−	12.0638i	−0.210820	−	0.390989i
$953$	−1.41382	+	16.1600i	−0.0457981	+	0.523475i	0.938297	+	0.345831i	$0.112403\pi$
$953$	−1.41382	+	16.1600i	−0.0457981	+	0.523475i	−0.984095	+	0.177644i	$0.943153\pi$
$954$	−9.91860	−	37.5252i	−0.321126	−	1.21492i
$955$	−5.21328	−	11.3122i	−0.168698	−	0.366053i
$956$	−14.2136	−	21.6108i	−0.459702	−	0.698942i
$957$	−4.22878	−	3.25626i	−0.136697	−	0.105260i
$958$	−14.2971	−	11.3047i	−0.461918	−	0.365237i
$959$	4.22207	−	9.78786i	0.136338	−	0.316067i
$960$	3.77592	+	0.861626i	0.121867	+	0.0278088i
$961$	−23.5226	−	11.8135i	−0.758793	−	0.381080i
$962$	−6.76854	−	3.15622i	−0.218227	−	0.101761i
$963$	19.1730	−	44.0369i	0.617842	−	1.41907i
$964$	−1.83652	+	5.04578i	−0.0591502	+	0.162514i
$965$	−25.5462	−	12.9736i	−0.822362	−	0.417636i
$966$	4.24051	−	0.301697i	0.136436	−	0.00970694i
$967$	−6.15780	+	1.27148i	−0.198022	+	0.0408882i	−0.300192	−	0.953879i	$-0.597051\pi$
$967$	−6.15780	+	1.27148i	−0.198022	+	0.0408882i	0.102171	+	0.994767i	$0.467421\pi$
$968$	−9.57865	−	5.16476i	−0.307870	−	0.166002i
$969$	−4.54640	−	5.27893i	−0.146052	−	0.169584i
$970$	15.3578	+	28.7913i	0.493110	+	0.924433i
$971$			18.7383i			0.601340i	0.953728	+	0.300670i	$0.0972102\pi$
$971$			18.7383i			0.601340i	−0.953728	+	0.300670i	$0.902790\pi$
$972$	1.26437	−	15.5371i	0.0405548	−	0.498353i
$973$	−42.2126	−	42.2126i	−1.35327	−	1.35327i
$974$	−0.150383	+	0.201999i	−0.00481857	+	0.00647246i
$975$	−27.0982	−	4.66991i	−0.867836	−	0.149557i
$976$	−1.53050	−	5.11223i	−0.0489901	−	0.163638i
$977$	−0.158202	−	0.766172i	−0.00506132	−	0.0245120i	0.976733	−	0.214458i	$-0.0687984\pi$
$977$	−0.158202	−	0.766172i	−0.00506132	−	0.0245120i	−0.981795	+	0.189946i	$0.939169\pi$
$978$	0.159177	−	0.183561i	0.00508990	−	0.00586963i
$979$	3.91371	−	3.69239i	0.125083	−	0.118009i
$980$	−12.1230	+	12.0147i	−0.387256	+	0.383797i
$981$	−2.78394	−	2.21664i	−0.0888845	−	0.0707719i
$982$	16.4386	−	35.2527i	0.524577	−	1.12496i
$983$	−26.9953	+	8.94525i	−0.861015	+	0.285309i	−0.710843	−	0.703351i	$-0.751686\pi$
$983$	−26.9953	+	8.94525i	−0.861015	+	0.285309i	−0.150172	+	0.988660i	$0.547983\pi$
$984$	15.8389	+	10.1283i	0.504925	+	0.322878i
$985$	−0.704552	+	11.2286i	−0.0224489	+	0.357772i
$986$	−3.73667	−	31.9693i	−0.119000	−	1.01811i
$987$	−14.0506	+	18.2470i	−0.447236	+	0.580808i
$988$	−3.49093	−	0.720819i	−0.111061	−	0.0229323i
$989$	1.99735	+	1.67597i	0.0635120	+	0.0532929i
$990$	0.182481	+	2.29373i	0.00579964	+	0.0728997i
$991$	−10.7115	+	8.98803i	−0.340263	+	0.285514i	−0.796866	−	0.604156i	$-0.793510\pi$
$991$	−10.7115	+	8.98803i	−0.340263	+	0.285514i	0.456603	+	0.889670i	$0.349066\pi$
$992$	−1.90367	+	1.02645i	−0.0604416	+	0.0325898i
$993$	4.92621	−	3.99908i	0.156329	−	0.126907i
$994$	12.0498	+	23.9932i	0.382197	+	0.761018i
$995$	−7.22944	+	2.83458i	−0.229189	+	0.0898624i
$996$	−3.80439	+	1.44031i	−0.120547	+	0.0456379i
$997$	15.3997	+	6.11789i	0.487712	+	0.193756i	0.600125	−	0.799906i	$-0.295117\pi$
$997$	15.3997	+	6.11789i	0.487712	+	0.193756i	−0.112413	+	0.993662i	$0.535858\pi$
$998$	29.5180	+	7.90932i	0.934375	+	0.250365i
$999$	−11.3152	+	4.61961i	−0.357996	+	0.146158i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	810.2.w.a.23.15	✓	1944
5.2	odd	4	inner	810.2.w.a.347.2	yes	1944
81.74	odd	54	inner	810.2.w.a.803.2	yes	1944
405.317	even	108	inner	810.2.w.a.317.15	yes	1944

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
810.2.w.a.23.15	✓	1944	1.1	even	1	trivial
810.2.w.a.317.15	yes	1944	405.317	even	108	inner
810.2.w.a.347.2	yes	1944	5.2	odd	4	inner
810.2.w.a.803.2	yes	1944	81.74	odd	54	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 810 = 2 \cdot 3^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	810.w (of order \(108\), degree \(36\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.989442 + 0.144932i) q^{2} +(0.128776 - 1.72726i) q^{3} +(0.957990 - 0.286803i) q^{4} +(-1.90840 + 1.16533i) q^{5} +(0.122918 + 1.72768i) q^{6} +(3.82371 + 0.111259i) q^{7} +(-0.906308 + 0.422618i) q^{8} +(-2.96683 - 0.444858i) q^{9} +(1.71936 - 1.42962i) q^{10} +(0.153943 - 0.306525i) q^{11} +(-0.372017 - 1.69163i) q^{12} +(2.95082 - 1.17229i) q^{13} +(-3.79946 + 0.444093i) q^{14} +(1.76707 + 3.44637i) q^{15} +(0.835488 - 0.549509i) q^{16} +(0.312269 + 3.56925i) q^{17} +(2.99998 + 0.0101720i) q^{18} +(-0.721623 - 0.859996i) q^{19} +(-1.49401 + 1.66371i) q^{20} +(0.684573 - 6.59020i) q^{21} +(-0.107892 + 0.325600i) q^{22} +(-0.0186617 - 0.641360i) q^{23} +(0.613260 + 1.61985i) q^{24} +(2.28400 - 4.44785i) q^{25} +(-2.74976 + 1.58758i) q^{26} +(-1.15044 + 5.06720i) q^{27} +(3.69498 - 0.990067i) q^{28} +(8.92278 + 1.04292i) q^{29} +(-2.24790 - 3.15387i) q^{30} +(2.10447 + 0.498769i) q^{31} +(-0.747025 + 0.664796i) q^{32} +(-0.509623 - 0.305372i) q^{33} +(-0.826270 - 3.48631i) q^{34} +(-7.42682 + 4.24357i) q^{35} +(-2.96978 + 0.424728i) q^{36} +(1.34911 + 1.92672i) q^{37} +(0.838644 + 0.746330i) q^{38} +(-1.64484 - 5.24778i) q^{39} +(1.23711 - 1.86268i) q^{40} +(8.70655 - 6.48178i) q^{41} +(0.277785 + 6.61983i) q^{42} +(-2.70148 + 3.03563i) q^{43} +(0.0595631 - 0.337799i) q^{44} +(6.18032 - 2.60838i) q^{45} +(0.111418 + 0.631883i) q^{46} +(-2.95836 - 1.82474i) q^{47} +(-0.841553 - 1.51387i) q^{48} +(7.62020 + 0.443826i) q^{49} +(-1.61525 + 4.73191i) q^{50} +(6.20523 - 0.0797358i) q^{51} +(2.49064 - 1.96934i) q^{52} +(-3.34859 - 12.4971i) q^{53} +(0.403895 - 5.18043i) q^{54} +(0.0634192 + 0.764367i) q^{55} +(-3.51248 + 1.51513i) q^{56} +(-1.57836 + 1.13568i) q^{57} +(-8.97972 + 0.261283i) q^{58} +(5.50193 - 2.76317i) q^{59} +(2.68127 + 2.79478i) q^{60} +(1.53050 - 5.11223i) q^{61} +(-2.15454 - 0.188498i) q^{62} +(-11.2948 - 2.03109i) q^{63} +(0.642788 - 0.766044i) q^{64} +(-4.26525 + 5.67588i) q^{65} +(0.548501 + 0.228287i) q^{66} +(2.45280 - 3.10207i) q^{67} +(1.32282 + 3.32975i) q^{68} +(-1.11020 - 0.0503581i) q^{69} +(6.73338 - 5.27514i) q^{70} +(-2.40056 - 6.59548i) q^{71} +(2.87687 - 0.850660i) q^{72} +(-3.99025 - 8.55712i) q^{73} +(-1.61411 - 1.71085i) q^{74} +(-7.38845 - 4.51783i) q^{75} +(-0.937957 - 0.616904i) q^{76} +(0.622735 - 1.15493i) q^{77} +(2.38805 + 4.95399i) q^{78} +(-5.22366 - 3.88887i) q^{79} +(-0.954086 + 2.02231i) q^{80} +(8.60420 + 2.63964i) q^{81} +(-7.67520 + 7.67520i) q^{82} +(-0.340388 - 2.32381i) q^{83} +(-1.23428 - 6.50968i) q^{84} +(-4.75530 - 6.44767i) q^{85} +(2.23300 - 3.39511i) q^{86} +(2.95043 - 15.2776i) q^{87} +(-0.00997635 + 0.342865i) q^{88} +(14.7404 + 5.36507i) q^{89} +(-5.73703 + 3.47657i) q^{90} +(11.4135 - 4.15417i) q^{91} +(-0.201822 - 0.609064i) q^{92} +(1.13251 - 3.57073i) q^{93} +(3.19158 + 1.37671i) q^{94} +(2.37933 + 0.800288i) q^{95} +(1.05207 + 1.37591i) q^{96} +(-2.95099 + 14.2917i) q^{97} +(-7.60407 + 0.665270i) q^{98} +(-0.593082 + 0.840926i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1944 q + 36 q^{20} + 108 q^{30} + 108 q^{35} + 36 q^{41} + 216 q^{51} + 108 q^{67} - 144 q^{72} - 576 q^{77} - 576 q^{87} - 144 q^{92} + 36 q^{93} + 108 q^{97}+O(q^{100}) \) 1944 * q + 36 * q^20 + 108 * q^30 + 108 * q^35 + 36 * q^41 + 216 * q^51 + 108 * q^67 - 144 * q^72 - 576 * q^77 - 576 * q^87 - 144 * q^92 + 36 * q^93 + 108 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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