LMFDB - Embedded newform 175.2.x.a.3.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [175,2,Mod(3,175)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("175.3"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(175, base_ring=CyclotomicField(60)) chi = DirichletCharacter(H, H._module([21, 10])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 175 = 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	175.x (of order $60$, degree $16$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$1.39738203537$
Analytic rank:	$0$
Dimension:	$288$
Relative dimension:	$18$ over $\Q(\zeta_{60})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{60}]$

Embedding invariants

Embedding label			3.4
Character	$\chi$	$=$	175.3
Dual form			175.2.x.a.117.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.09978 + 1.69351i) q^{2} +(0.0195422 - 0.0509090i) q^{3} +(-0.844998 - 1.89790i) q^{4} +(1.92424 - 1.13899i) q^{5} +(0.0647231 + 0.0890837i) q^{6} +(-0.0453616 + 2.64536i) q^{7} +(0.154579 + 0.0244829i) q^{8} +(2.22722 + 2.00540i) q^{9} +(-0.187337 + 4.51137i) q^{10} +(2.53998 + 2.82093i) q^{11} +(-0.113133 + 0.00592906i) q^{12} +(-2.72389 - 1.38789i) q^{13} +(-4.43007 - 2.98614i) q^{14} +(-0.0203814 - 0.120220i) q^{15} +(2.56878 - 2.85292i) q^{16} +(-2.13519 + 2.63674i) q^{17} +(-5.84563 + 1.56633i) q^{18} +(-3.38312 - 1.50626i) q^{19} +(-3.78767 - 2.68956i) q^{20} +(0.133786 + 0.0540054i) q^{21} +(-7.57071 + 1.19908i) q^{22} +(4.81891 + 3.12944i) q^{23} +(0.00426721 - 0.00739102i) q^{24} +(2.40538 - 4.38339i) q^{25} +(5.34609 - 3.08657i) q^{26} +(0.291380 - 0.148466i) q^{27} +(5.05895 - 2.14923i) q^{28} +(1.14694 - 1.57863i) q^{29} +(0.226008 + 0.0976989i) q^{30} +(-4.49990 + 0.472959i) q^{31} +(2.08738 + 7.79020i) q^{32} +(0.193248 - 0.0741808i) q^{33} +(-2.11711 - 6.51580i) q^{34} +(2.92577 + 5.14197i) q^{35} +(1.92404 - 5.92160i) q^{36} +(-0.428655 - 8.17923i) q^{37} +(6.27156 - 4.07280i) q^{38} +(-0.123887 + 0.111548i) q^{39} +(0.325333 - 0.128954i) q^{40} +(7.75457 - 2.51961i) q^{41} +(-0.238595 + 0.167175i) q^{42} +(5.09273 + 5.09273i) q^{43} +(3.20756 - 7.20430i) q^{44} +(6.56985 + 1.32207i) q^{45} +(-10.5995 + 4.71920i) q^{46} +(7.25711 - 5.87669i) q^{47} +(-0.0950399 - 0.186526i) q^{48} +(-6.99588 - 0.239996i) q^{49} +(4.77794 + 8.89432i) q^{50} +(0.0925076 + 0.160228i) q^{51} +(-0.332392 + 6.34242i) q^{52} +(-6.21509 - 2.38575i) q^{53} +(-0.0690257 + 0.656736i) q^{54} +(8.10055 + 2.53512i) q^{55} +(-0.0717781 + 0.407807i) q^{56} +(-0.142796 + 0.142796i) q^{57} +(1.41205 + 3.67851i) q^{58} +(-3.16655 - 0.673070i) q^{59} +(-0.210942 + 0.140267i) q^{60} +(-2.94484 - 13.8544i) q^{61} +(4.14794 - 8.14080i) q^{62} +(-5.40605 + 5.80085i) q^{63} +(-8.18628 - 2.65988i) q^{64} +(-6.82221 + 0.431863i) q^{65} +(-0.0869038 + 0.408850i) q^{66} +(-10.9566 - 8.87250i) q^{67} +(6.80848 + 1.82433i) q^{68} +(0.253489 - 0.184170i) q^{69} +(-11.9257 - 0.700216i) q^{70} +(1.76180 + 1.28002i) q^{71} +(0.295184 + 0.364522i) q^{72} +(2.19250 + 0.114904i) q^{73} +(14.3231 + 8.26943i) q^{74} +(-0.176148 - 0.208117i) q^{75} +7.69359i q^{76} +(-7.57761 + 6.59120i) q^{77} +(-0.0526601 - 0.332483i) q^{78} +(6.51601 + 0.684861i) q^{79} +(1.69348 - 8.41552i) q^{80} +(0.937960 + 8.92409i) q^{81} +(-4.26133 + 15.9035i) q^{82} +(1.08205 - 6.83177i) q^{83} +(-0.0105526 - 0.299547i) q^{84} +(-1.10538 + 7.50568i) q^{85} +(-14.2255 + 3.02372i) q^{86} +(-0.0579529 - 0.0892396i) q^{87} +(0.323563 + 0.498243i) q^{88} +(-3.73767 + 0.794467i) q^{89} +(-9.46435 + 9.67214i) q^{90} +(3.79503 - 7.14272i) q^{91} +(1.86738 - 11.7902i) q^{92} +(-0.0638599 + 0.238328i) q^{93} +(1.97103 + 18.7531i) q^{94} +(-8.22555 + 0.954948i) q^{95} +(0.437383 + 0.0459708i) q^{96} +(-0.674820 - 4.26064i) q^{97} +(8.10037 - 11.5837i) q^{98} +11.3765i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 288 q - 8 q^{2} - 24 q^{3} - 10 q^{4} - 30 q^{5} - 10 q^{7} - 36 q^{8} - 10 q^{9} - 36 q^{10} - 6 q^{11} - 36 q^{12} - 20 q^{14} - 28 q^{15} - 30 q^{16} - 42 q^{17} - 14 q^{18} - 30 q^{19} - 12 q^{21} + 32 q^{22}+ \cdots + 222 q^{98}+O(q^{100}) $ 288 * q - 8 * q^2 - 24 * q^3 - 10 * q^4 - 30 * q^5 - 10 * q^7 - 36 * q^8 - 10 * q^9 - 36 * q^10 - 6 * q^11 - 36 * q^12 - 20 * q^14 - 28 * q^15 - 30 * q^16 - 42 * q^17 - 14 * q^18 - 30 * q^19 - 12 * q^21 + 32 * q^22 - 40 * q^23 + 2 * q^25 - 48 * q^26 + 22 * q^28 - 58 * q^30 - 18 * q^31 + 8 * q^32 - 30 * q^33 - 2 * q^35 + 40 * q^36 - 10 * q^37 + 72 * q^38 + 30 * q^39 - 48 * q^40 + 6 * q^42 - 108 * q^43 - 10 * q^44 + 186 * q^45 - 6 * q^46 - 54 * q^47 - 248 * q^50 - 16 * q^51 + 216 * q^52 + 50 * q^53 - 30 * q^54 + 4 * q^56 - 216 * q^57 - 4 * q^58 + 90 * q^59 + 96 * q^60 - 18 * q^61 - 66 * q^63 - 100 * q^64 + 14 * q^65 - 90 * q^66 + 4 * q^67 + 342 * q^68 - 60 * q^70 - 24 * q^71 + 58 * q^72 - 6 * q^73 + 216 * q^75 - 80 * q^77 - 132 * q^78 - 10 * q^79 - 6 * q^80 - 10 * q^81 + 216 * q^82 + 20 * q^84 - 48 * q^85 - 6 * q^86 - 48 * q^87 - 122 * q^88 + 120 * q^89 - 12 * q^91 - 4 * q^92 + 106 * q^93 - 30 * q^94 - 98 * q^95 - 90 * q^96 + 222 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/175\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{7}{20}\right)$

Coefficient data

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

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

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

$2$	−1.09978	+	1.69351i	−0.777662	+	1.19749i	0.198425	+	0.980116i	$0.436417\pi$
$2$	−1.09978	+	1.69351i	−0.777662	+	1.19749i	−0.976087	+	0.217379i	$0.930249\pi$
$3$	0.0195422	−	0.0509090i	0.0112827	−	0.0293923i	−0.927823	−	0.373020i	$-0.878322\pi$
$3$	0.0195422	−	0.0509090i	0.0112827	−	0.0293923i	0.939106	+	0.343627i	$0.111656\pi$
$4$	−0.844998	−	1.89790i	−0.422499	−	0.948948i
$5$	1.92424	−	1.13899i	0.860545	−	0.509374i
$5$	1.92424	−	1.13899i	0.860545	−	0.509374i
$6$	0.0647231	+	0.0890837i	0.0264231	+	0.0363683i
$7$	−0.0453616	+	2.64536i	−0.0171451	+	0.999853i
$7$	−0.0453616	+	2.64536i	−0.0171451	+	0.999853i
$8$	0.154579	+	0.0244829i	0.0546519	+	0.00865601i
$9$	2.22722	+	2.00540i	0.742408	+	0.668467i
$10$	−0.187337	+	4.51137i	−0.0592410	+	1.42662i
$11$	2.53998	+	2.82093i	0.765832	+	0.850543i	0.992349	−	0.123464i	$-0.0394004\pi$
$11$	2.53998	+	2.82093i	0.765832	+	0.850543i	−0.226517	+	0.974007i	$0.572734\pi$
$12$	−0.113133	+	0.00592906i	−0.0326587	+	0.00171157i
$13$	−2.72389	−	1.38789i	−0.755471	−	0.384932i	0.0334387	−	0.999441i	$-0.489354\pi$
$13$	−2.72389	−	1.38789i	−0.755471	−	0.384932i	−0.788910	+	0.614509i	$0.789354\pi$
$14$	−4.43007	−	2.98614i	−1.18399	−	0.798079i
$15$	−0.0203814	−	0.120220i	−0.00526245	−	0.0310405i
$16$	2.56878	−	2.85292i	0.642195	−	0.713230i
$17$	−2.13519	+	2.63674i	−0.517859	+	0.639503i	−0.967248	−	0.253834i	$-0.918308\pi$
$17$	−2.13519	+	2.63674i	−0.517859	+	0.639503i	0.449389	+	0.893336i	$0.351642\pi$
$18$	−5.84563	+	1.56633i	−1.37783	+	0.369188i
$19$	−3.38312	−	1.50626i	−0.776140	−	0.345560i	−0.0198559	−	0.999803i	$-0.506321\pi$
$19$	−3.38312	−	1.50626i	−0.776140	−	0.345560i	−0.756284	+	0.654243i	$0.772987\pi$
$20$	−3.78767	−	2.68956i	−0.846949	−	0.601403i
$21$	0.133786	+	0.0540054i	0.0291946	+	0.0117849i
$22$	−7.57071	+	1.19908i	−1.61408	+	0.255645i
$23$	4.81891	+	3.12944i	1.00481	+	0.652533i	0.938505	−	0.345266i	$-0.112211\pi$
$23$	4.81891	+	3.12944i	1.00481	+	0.652533i	0.0663077	+	0.997799i	$0.478878\pi$
$24$	0.00426721	−	0.00739102i	0.000871040	−	0.00150869i
$25$	2.40538	−	4.38339i	0.481077	−	0.876679i
$26$	5.34609	−	3.08657i	1.04846	−	0.605326i
$27$	0.291380	−	0.148466i	0.0560761	−	0.0285722i
$28$	5.05895	−	2.14923i	0.956052	−	0.406167i
$29$	1.14694	−	1.57863i	0.212982	−	0.293144i	−0.689138	−	0.724630i	$-0.742011\pi$
$29$	1.14694	−	1.57863i	0.212982	−	0.293144i	0.902120	+	0.431486i	$0.142011\pi$
$30$	0.226008	+	0.0976989i	0.0412633	+	0.0178373i
$31$	−4.49990	+	0.472959i	−0.808206	+	0.0849459i	−0.499614	−	0.866248i	$-0.666525\pi$
$31$	−4.49990	+	0.472959i	−0.808206	+	0.0849459i	−0.308593	+	0.951194i	$0.599858\pi$
$32$	2.08738	+	7.79020i	0.369000	+	1.37712i
$33$	0.193248	−	0.0741808i	0.0336401	−	0.0129132i
$34$	−2.11711	−	6.51580i	−0.363082	−	1.11745i
$35$	2.92577	+	5.14197i	0.494545	+	0.869152i
$36$	1.92404	−	5.92160i	0.320674	−	0.986933i
$37$	−0.428655	−	8.17923i	−0.0704705	−	1.34466i	−0.773636	−	0.633631i	$-0.781564\pi$
$37$	−0.428655	−	8.17923i	−0.0704705	−	1.34466i	0.703165	−	0.711027i	$-0.251769\pi$
$38$	6.27156	−	4.07280i	1.01738	−	0.660695i
$39$	−0.123887	+	0.111548i	−0.0198378	+	0.0178620i
$40$	0.325333	−	0.128954i	0.0514396	−	0.0203894i
$41$	7.75457	−	2.51961i	1.21106	−	0.393497i	0.367242	−	0.930126i	$-0.380302\pi$
$41$	7.75457	−	2.51961i	1.21106	−	0.393497i	0.843819	+	0.536628i	$0.180302\pi$
$42$	−0.238595	+	0.167175i	−0.0368159	+	0.0257957i
$43$	5.09273	+	5.09273i	0.776634	+	0.776634i	0.979257	−	0.202623i	$-0.0649464\pi$
$43$	5.09273	+	5.09273i	0.776634	+	0.776634i	−0.202623	+	0.979257i	$0.564946\pi$
$44$	3.20756	−	7.20430i	0.483558	−	1.08609i
$45$	6.56985	+	1.32207i	0.979376	+	0.197083i
$46$	−10.5995	+	4.71920i	−1.56281	+	0.695808i
$47$	7.25711	−	5.87669i	1.05856	−	0.857204i	0.0684709	−	0.997653i	$-0.478188\pi$
$47$	7.25711	−	5.87669i	1.05856	−	0.857204i	0.990088	+	0.140449i	$0.0448546\pi$
$48$	−0.0950399	−	0.186526i	−0.0137178	−	0.0269228i
$49$	−6.99588	−	0.239996i	−0.999412	−	0.0342851i
$50$	4.77794	+	8.89432i	0.675703	+	1.25785i
$51$	0.0925076	+	0.160228i	0.0129537	+	0.0224364i
$52$	−0.332392	+	6.34242i	−0.0460945	+	0.879536i
$53$	−6.21509	−	2.38575i	−0.853708	−	0.327708i	−0.108139	−	0.994136i	$-0.534489\pi$
$53$	−6.21509	−	2.38575i	−0.853708	−	0.327708i	−0.745569	+	0.666428i	$0.767822\pi$
$54$	−0.0690257	+	0.656736i	−0.00939321	+	0.0893704i
$55$	8.10055	+	2.53512i	1.09228	+	0.341836i
$56$	−0.0717781	+	0.407807i	−0.00959175	+	0.0544955i
$57$	−0.142796	+	0.142796i	−0.0189138	+	0.0189138i
$58$	1.41205	+	3.67851i	0.185411	+	0.483012i
$59$	−3.16655	−	0.673070i	−0.412249	−	0.0876263i	−0.00288177	−	0.999996i	$-0.500917\pi$
$59$	−3.16655	−	0.673070i	−0.412249	−	0.0876263i	−0.409368	+	0.912370i	$0.634251\pi$
$60$	−0.210942	+	0.140267i	−0.0272325	+	0.0181084i
$61$	−2.94484	−	13.8544i	−0.377048	−	1.77387i	−0.600979	−	0.799265i	$-0.705222\pi$
$61$	−2.94484	−	13.8544i	−0.377048	−	1.77387i	0.223931	−	0.974605i	$-0.428111\pi$
$62$	4.14794	−	8.14080i	0.526789	−	1.03388i
$63$	−5.40605	+	5.80085i	−0.681098	+	0.730838i
$64$	−8.18628	−	2.65988i	−1.02329	−	0.332485i
$65$	−6.82221	+	0.431863i	−0.846191	+	0.0535660i
$66$	−0.0869038	+	0.408850i	−0.0106971	+	0.0503260i
$67$	−10.9566	−	8.87250i	−1.33856	−	1.08395i	−0.989139	−	0.146984i	$-0.953043\pi$
$67$	−10.9566	−	8.87250i	−1.33856	−	1.08395i	−0.349426	−	0.936964i	$-0.613623\pi$
$68$	6.80848	+	1.82433i	0.825650	+	0.221232i
$69$	0.253489	−	0.184170i	0.0305164	−	0.0221715i
$70$	−11.9257	−	0.700216i	−1.42539	−	0.0836918i
$71$	1.76180	+	1.28002i	0.209087	+	0.151910i	0.687400	−	0.726279i	$-0.258752\pi$
$71$	1.76180	+	1.28002i	0.209087	+	0.151910i	−0.478314	+	0.878189i	$0.658752\pi$
$72$	0.295184	+	0.364522i	0.0347878	+	0.0429593i
$73$	2.19250	+	0.114904i	0.256613	+	0.0134485i	0.180209	−	0.983628i	$-0.442323\pi$
$73$	2.19250	+	0.114904i	0.256613	+	0.0134485i	0.0764042	+	0.997077i	$0.475656\pi$
$74$	14.3231	+	8.26943i	1.66502	+	0.961301i
$75$	−0.176148	−	0.208117i	−0.0203398	−	0.0240312i
$76$			7.69359i			0.882515i
$77$	−7.57761	+	6.59120i	−0.863548	+	0.751137i
$78$	−0.0526601	−	0.332483i	−0.00596258	−	0.0376463i
$79$	6.51601	+	0.684861i	0.733109	+	0.0770529i	0.463724	−	0.885980i	$-0.346513\pi$
$79$	6.51601	+	0.684861i	0.733109	+	0.0770529i	0.269385	+	0.963033i	$0.413180\pi$
$80$	1.69348	−	8.41552i	0.189337	−	0.940884i
$81$	0.937960	+	8.92409i	0.104218	+	0.991566i
$82$	−4.26133	+	15.9035i	−0.470585	+	1.75625i
$83$	1.08205	−	6.83177i	0.118770	−	0.749884i	−0.854369	−	0.519667i	$-0.826056\pi$
$83$	1.08205	−	6.83177i	0.118770	−	0.749884i	0.973139	−	0.230218i	$-0.0739438\pi$
$84$	−0.0105526	−	0.299547i	−0.00115138	−	0.0326833i
$85$	−1.10538	+	7.50568i	−0.119895	+	0.814105i
$86$	−14.2255	+	3.02372i	−1.53398	+	0.326056i
$87$	−0.0579529	−	0.0892396i	−0.00621320	−	0.00956749i
$88$	0.323563	+	0.498243i	0.0344919	+	0.0531129i
$89$	−3.73767	+	0.794467i	−0.396193	+	0.0842133i	−0.401700	−	0.915772i	$-0.631580\pi$
$89$	−3.73767	+	0.794467i	−0.396193	+	0.0842133i	0.00550702	+	0.999985i	$0.498247\pi$
$90$	−9.46435	+	9.67214i	−0.997630	+	1.01953i
$91$	3.79503	−	7.14272i	0.397828	−	0.748760i
$92$	1.86738	−	11.7902i	0.194688	−	1.22921i
$93$	−0.0638599	+	0.238328i	−0.00662196	+	0.0247135i
$94$	1.97103	+	18.7531i	0.203296	+	1.93423i
$95$	−8.22555	+	0.954948i	−0.843923	+	0.0979756i
$96$	0.437383	+	0.0459708i	0.0446402	+	0.00469188i
$97$	−0.674820	−	4.26064i	−0.0685176	−	0.432603i	−0.997971	−	0.0636644i	$-0.979721\pi$
$97$	−0.674820	−	4.26064i	−0.0685176	−	0.432603i	0.929454	−	0.368939i	$-0.120279\pi$
$98$	8.10037	−	11.5837i	0.818261	−	1.17013i
$99$			11.3765i			1.14338i
$100$	−10.3518	−	0.861209i	−1.03518	−	0.0861209i
$101$	−6.04964	−	3.49276i	−0.601962	−	0.347543i	0.167851	−	0.985812i	$-0.446317\pi$
$101$	−6.04964	−	3.49276i	−0.601962	−	0.347543i	−0.769813	+	0.638270i	$0.779651\pi$
$102$	−0.373086	−	0.0195526i	−0.0369410	−	0.00193600i
$103$	6.06984	+	7.49562i	0.598079	+	0.738566i	0.982842	−	0.184450i	$-0.0590502\pi$
$103$	6.06984	+	7.49562i	0.598079	+	0.738566i	−0.384763	+	0.923015i	$0.625717\pi$
$104$	−0.387076	−	0.281228i	−0.0379560	−	0.0275766i
$105$	0.318949	−	0.0484628i	0.0311262	−	0.00472948i
$106$	10.8755	−	7.90153i	1.05632	−	0.767465i
$107$	−3.20223	−	0.858034i	−0.309571	−	0.0829493i	0.100689	−	0.994918i	$-0.467895\pi$
$107$	−3.20223	−	0.858034i	−0.309571	−	0.0829493i	−0.410260	+	0.911969i	$0.634562\pi$
$108$	−0.527988	−	0.427556i	−0.0508057	−	0.0411416i
$109$	−2.02932	+	9.54720i	−0.194374	+	0.914456i	0.767519	+	0.641027i	$0.221491\pi$
$109$	−2.02932	+	9.54720i	−0.194374	+	0.914456i	−0.961892	+	0.273429i	$0.911842\pi$
$110$	−13.2021	+	10.9303i	−1.25877	+	1.04216i
$111$	−0.424774	−	0.138017i	−0.0403177	−	0.0131000i
$112$	7.43048	+	6.92477i	0.702115	+	0.654329i
$113$	−2.12247	+	4.16559i	−0.199666	+	0.391866i	−0.969030	−	0.246945i	$-0.920573\pi$
$113$	−2.12247	+	4.16559i	−0.199666	+	0.391866i	0.769364	+	0.638811i	$0.220573\pi$
$114$	−0.0847825	−	0.398870i	−0.00794061	−	0.0373576i
$115$	12.8371	+	0.533068i	1.19707	+	0.0497089i
$116$	−3.96524	−	0.842838i	−0.368163	−	0.0782556i
$117$	−3.28343	−	8.55364i	−0.303554	−	0.790784i
$118$	4.62236	−	4.62236i	0.425523	−	0.425523i
$119$	−6.87827	−	5.76795i	−0.630530	−	0.528747i
$120$	−0.000207210	−	0.0190824i	−1.89156e−5	−	0.00174198i
$121$	−0.356354	+	3.39048i	−0.0323958	+	0.308225i
$122$	26.7012	+	10.2496i	2.41742	+	0.927959i
$123$	0.0232699	−	0.444016i	0.00209818	−	0.0400356i
$124$	4.70003	+	8.14070i	0.422075	+	0.731056i
$125$	−0.364133	−	11.1744i	−0.0325690	−	0.999469i
$126$	−3.87835	−	15.5349i	−0.345511	−	1.38396i
$127$	−5.56395	−	10.9199i	−0.493721	−	0.968982i	−0.994631	−	0.103483i	$-0.967001\pi$
$127$	−5.56395	−	10.9199i	−0.493721	−	0.968982i	0.500910	−	0.865499i	$-0.332999\pi$
$128$	0.972292	−	0.787347i	0.0859393	−	0.0695923i
$129$	0.358789	−	0.159743i	0.0315896	−	0.0140646i
$130$	6.77157	−	12.0285i	0.593906	−	1.05497i
$131$	−4.18789	+	9.40615i	−0.365898	+	0.821819i	0.632967	+	0.774179i	$0.281837\pi$
$131$	−4.18789	+	9.40615i	−0.365898	+	0.821819i	−0.998865	+	0.0476406i	$0.984830\pi$
$132$	−0.304081	−	0.304081i	−0.0264669	−	0.0264669i
$133$	4.13807	−	8.88125i	0.358816	−	0.770102i
$134$	27.0756	−	8.79739i	2.33897	−	0.759979i
$135$	0.391583	−	0.617564i	0.0337021	−	0.0531514i
$136$	−0.394610	+	0.355309i	−0.0338375	+	0.0304675i
$137$	15.6084	−	10.1362i	1.33351	−	0.865993i	0.336384	−	0.941725i	$-0.390796\pi$
$137$	15.6084	−	10.1362i	1.33351	−	0.865993i	0.997128	+	0.0757320i	$0.0241294\pi$
$138$	0.0331130	+	0.631833i	0.00281876	+	0.0537852i
$139$	−4.94661	+	15.2241i	−0.419566	+	1.29129i	0.488537	+	0.872543i	$0.337531\pi$
$139$	−4.94661	+	15.2241i	−0.419566	+	1.29129i	−0.908103	+	0.418747i	$0.862469\pi$
$140$	7.28666	−	9.89776i	0.615835	−	0.836513i
$141$	−0.157357	−	0.484296i	−0.0132519	−	0.0407851i
$142$	−4.10532	+	1.57588i	−0.344511	+	0.132245i
$143$	−3.00348	−	11.2091i	−0.251163	−	0.937354i
$144$	11.4425	−	1.20266i	0.953542	−	0.100221i
$145$	0.408938	−	4.34402i	0.0339605	−	0.360752i
$146$	−2.60586	+	3.58666i	−0.215663	+	0.296834i
$147$	−0.148933	+	0.351464i	−0.0122838	+	0.0289882i
$148$	−15.1611	+	7.72497i	−1.24624	+	0.634989i
$149$	1.52167	−	0.878534i	0.124660	−	0.0719723i	−0.436373	−	0.899766i	$-0.643737\pi$
$149$	1.52167	−	0.878534i	0.124660	−	0.0719723i	0.561033	+	0.827793i	$0.310404\pi$
$150$	0.546173	−	0.0694264i	0.0445948	−	0.00566864i
$151$	0.749583	−	1.29832i	0.0610002	−	0.105655i	−0.833913	−	0.551897i	$-0.813904\pi$
$151$	0.749583	−	1.29832i	0.0610002	−	0.105655i	0.894913	+	0.446241i	$0.147238\pi$
$152$	−0.486081	−	0.315665i	−0.0394264	−	0.0256038i
$153$	−10.0433	+	1.59070i	−0.811949	+	0.128600i
$154$	−2.82859	−	20.0817i	−0.227934	−	1.61823i
$155$	−8.12018	+	6.03545i	−0.652229	+	0.484779i
$156$	0.316391	+	0.140866i	0.0253316	+	0.0112783i
$157$	3.82995	−	1.02623i	0.305664	−	0.0819023i	−0.102727	−	0.994710i	$-0.532757\pi$
$157$	3.82995	−	1.02623i	0.305664	−	0.0819023i	0.408391	+	0.912807i	$0.366090\pi$
$158$	−8.32601	+	10.2818i	−0.662382	+	0.817973i
$159$	−0.242912	+	0.269781i	−0.0192642	+	0.0213951i
$160$	12.8896	+	12.6127i	1.01901	+	0.997120i
$161$	−8.49709	+	12.6058i	−0.669665	+	0.993477i
$162$	−16.1446	−	8.22609i	−1.26844	−	0.646303i
$163$	10.8248	−	0.567303i	0.847862	−	0.0444346i	0.376545	−	0.926398i	$-0.377112\pi$
$163$	10.8248	−	0.567303i	0.847862	−	0.0444346i	0.471317	+	0.881964i	$0.343779\pi$
$164$	−11.3346	−	12.5883i	−0.885080	−	0.982981i
$165$	0.287363	−	0.362850i	0.0223712	−	0.0282478i
$166$	10.3797	+	9.34591i	0.805620	+	0.725383i
$167$	12.4850	+	1.97743i	0.966117	+	0.153018i	0.619507	−	0.784991i	$-0.287333\pi$
$167$	12.4850	+	1.97743i	0.966117	+	0.153018i	0.346610	+	0.938009i	$0.387333\pi$
$168$	0.0193584	+	0.0116236i	0.00149353	+	0.000896778i
$169$	−2.14788	−	2.95630i	−0.165221	−	0.227407i
$170$	−11.4953	−	10.1266i	−0.881648	−	0.776673i
$171$	−4.51430	−	10.1393i	−0.345217	−	0.775371i
$172$	5.36213	−	13.9688i	0.408858	−	1.06511i
$173$	−7.30558	+	11.2496i	−0.555433	+	0.855292i	−0.999165	−	0.0408678i	$-0.986988\pi$
$173$	−7.30558	+	11.2496i	−0.555433	+	0.855292i	0.443731	+	0.896160i	$0.353654\pi$
$174$	0.214864			0.0162888
$175$	11.4866	+	6.56195i	0.868302	+	0.496037i
$176$	14.5725			1.09845
$177$	−0.0961465	+	0.148053i	−0.00722681	+	0.0111283i
$178$	2.76518	−	7.20354i	0.207259	−	0.539928i
$179$	2.19411	+	4.92806i	0.163996	+	0.368340i	0.976786	−	0.214215i	$-0.0687194\pi$
$179$	2.19411	+	4.92806i	0.163996	+	0.368340i	−0.812791	+	0.582556i	$0.802053\pi$
$180$	−3.04235	−	13.5860i	−0.226763	−	1.01264i
$181$	12.4457	+	17.1301i	0.925085	+	1.27327i	0.961746	+	0.273942i	$0.0883276\pi$
$181$	12.4457	+	17.1301i	0.925085	+	1.27327i	−0.0366616	+	0.999328i	$0.511672\pi$
$182$	7.92258	+	14.2824i	0.587261	+	1.05868i
$183$	−0.762861	−	0.120825i	−0.0563923	−	0.00893166i
$184$	0.668285	+	0.601726i	0.0492666	+	0.0443598i
$185$	−10.1409	−	15.2505i	−0.745576	−	1.12124i
$186$	−0.333380	−	0.370256i	−0.0244446	−	0.0271485i
$187$	−12.8614	+	0.674037i	−0.940518	+	0.0492905i
$188$	−17.2856	−	8.80745i	−1.26068	−	0.642349i
$189$	0.379528	+	0.777541i	0.0276066	+	0.0565578i
$190$	7.42908	−	14.9803i	0.538962	−	1.08679i
$191$	−10.1181	+	11.2373i	−0.732121	+	0.813103i	−0.988138	−	0.153570i	$-0.950923\pi$
$191$	−10.1181	+	11.2373i	−0.732121	+	0.813103i	0.256017	+	0.966672i	$0.417590\pi$
$192$	−0.295390	+	0.364776i	−0.0213179	+	0.0263254i
$193$	−12.9143	+	3.46038i	−0.929593	+	0.249084i	−0.691681	−	0.722203i	$-0.743130\pi$
$193$	−12.9143	+	3.46038i	−0.929593	+	0.249084i	−0.237912	+	0.971287i	$0.576463\pi$
$194$	7.95761	+	3.54296i	0.571323	+	0.254370i
$195$	−0.111335	+	0.355752i	−0.00797286	+	0.0254759i
$196$	5.45602	+	13.4803i	0.389716	+	0.962875i
$197$	−9.33538	+	1.47858i	−0.665118	+	0.105344i	−0.479859	−	0.877345i	$-0.659312\pi$
$197$	−9.33538	+	1.47858i	−0.665118	+	0.105344i	−0.185259	+	0.982690i	$0.559312\pi$
$198$	−19.2663	−	12.5117i	−1.36920	−	0.889167i
$199$	−6.97072	+	12.0736i	−0.494141	+	0.855878i	−0.999977	−	0.00675174i	$-0.997851\pi$
$199$	−6.97072	+	12.0736i	−0.494141	+	0.855878i	0.505836	+	0.862630i	$0.331184\pi$
$200$	0.479140	−	0.618690i	0.0338803	−	0.0437480i
$201$	−0.665806	+	0.384403i	−0.0469624	+	0.0271137i
$202$	12.5683	−	6.40388i	0.884304	−	0.450575i
$203$	4.12402	+	3.10569i	0.289450	+	0.217977i
$204$	0.225927	−	0.310962i	0.0158181	−	0.0217717i
$205$	12.0518	−	13.6807i	0.841735	−	0.955505i
$206$	−19.3694	+	2.03581i	−1.34953	+	0.141842i
$207$	4.45702	+	16.6338i	0.309784	+	1.15613i
$208$	−10.9566	+	4.20585i	−0.759705	+	0.291623i
$209$	−4.34399	−	13.3694i	−0.300480	−	0.924782i
$210$	−0.268701	+	0.593442i	−0.0185421	+	0.0409514i
$211$	−1.35065	+	4.15686i	−0.0929824	+	0.286170i	−0.986723	−	0.162415i	$-0.948072\pi$
$211$	−1.35065	+	4.15686i	−0.0929824	+	0.286170i	0.893740	+	0.448585i	$0.148072\pi$
$212$	0.723832	+	13.8115i	0.0497130	+	0.948580i
$213$	0.0995938	−	0.0646770i	0.00682406	−	0.00443159i
$214$	4.97484	−	4.47937i	0.340073	−	0.306203i
$215$	15.6002	+	3.99903i	1.06393	+	0.272732i
$216$	0.0486761	−	0.0158158i	0.00331199	−	0.00107613i
$217$	−1.04702	−	11.9253i	−0.0710767	−	0.809544i
$218$	−13.9365	−	13.9365i	−0.943899	−	0.943899i
$219$	0.0486958	−	0.109373i	0.00329056	−	0.00739072i
$220$	−2.03355	−	17.5162i	−0.137102	−	1.18094i
$221$	9.47552	−	4.21877i	0.637392	−	0.283785i
$222$	0.700892	−	0.567571i	0.0470408	−	0.0380929i
$223$	2.56478	+	5.03366i	0.171750	+	0.337079i	0.960796	−	0.277255i	$-0.0894247\pi$
$223$	2.56478	+	5.03366i	0.171750	+	0.337079i	−0.789046	+	0.614334i	$0.789425\pi$
$224$	−20.7026	+	5.16849i	−1.38325	+	0.345334i
$225$	14.1478	−	4.93904i	0.943186	−	0.329269i
$226$	−4.72023	−	8.17568i	−0.313985	−	0.543838i
$227$	−0.865117	+	16.5074i	−0.0574198	+	1.09564i	0.806249	+	0.591576i	$0.201494\pi$
$227$	−0.865117	+	16.5074i	−0.0574198	+	1.09564i	−0.863669	+	0.504060i	$0.831839\pi$
$228$	0.391673	+	0.150349i	0.0259392	+	0.00995713i
$229$	2.91929	−	27.7751i	0.192912	−	1.83543i	−0.286780	−	0.957996i	$-0.592585\pi$
$229$	2.91929	−	27.7751i	0.192912	−	1.83543i	0.479692	−	0.877437i	$-0.340748\pi$
$230$	−15.0208	+	21.1536i	−0.990442	+	1.39483i
$231$	0.187469	+	0.514575i	0.0123346	+	0.0338565i
$232$	0.215943	−	0.215943i	0.0141773	−	0.0141773i
$233$	5.77338	+	15.0402i	0.378227	+	0.985314i	0.982121	+	0.188250i	$0.0602815\pi$
$233$	5.77338	+	15.0402i	0.378227	+	0.985314i	−0.603894	+	0.797064i	$0.706385\pi$
$234$	18.0968	+	3.84659i	1.18302	+	0.251459i
$235$	7.27089	−	19.5740i	0.474300	−	1.27687i
$236$	1.39831	+	6.57852i	0.0910221	+	0.428225i
$237$	0.162203	−	0.318340i	0.0105362	−	0.0206784i
$238$	17.3327	−	5.30496i	1.12351	−	0.343870i
$239$	−14.3559	−	4.66452i	−0.928606	−	0.301722i	−0.194614	−	0.980880i	$-0.562345\pi$
$239$	−14.3559	−	4.66452i	−0.928606	−	0.301722i	−0.733993	+	0.679157i	$0.762345\pi$
$240$	−0.395332	−	0.250671i	−0.0255186	−	0.0161807i
$241$	−5.19859	+	24.4574i	−0.334871	+	1.57544i	0.412451	+	0.910980i	$0.364673\pi$
$241$	−5.19859	+	24.4574i	−0.334871	+	1.57544i	−0.747322	+	0.664462i	$0.768661\pi$
$242$	−5.34991	−	4.33227i	−0.343905	−	0.278489i
$243$	1.42029	+	0.380565i	0.0911115	+	0.0244133i
$244$	−23.8058	+	17.2959i	−1.52401	+	1.10726i
$245$	−13.7351	+	7.50647i	−0.877503	+	0.479571i
$246$	0.726356	+	0.527729i	0.0463108	+	0.0336467i
$247$	7.12471	+	8.79829i	0.453335	+	0.559822i
$248$	−0.707170	−	0.0370612i	−0.0449053	−	0.00235339i
$249$	−0.326653	−	0.188593i	−0.0207008	−	0.0119516i
$250$	19.3245	+	11.6727i	1.22219	+	0.738249i
$251$		−	12.4908i		−	0.788410i	−0.919023	−	0.394205i	$-0.871020\pi$
$251$		−	12.4908i		−	0.788410i	0.919023	−	0.394205i	$-0.128980\pi$
$252$	15.5775	+	5.35841i	0.981290	+	0.337548i
$253$	3.41200	+	21.5425i	0.214511	+	1.35437i
$254$	24.6121	+	2.58683i	1.54430	+	0.162312i
$255$	0.360505	+	0.202951i	0.0225757	+	0.0127093i
$256$	−1.53540	−	14.6083i	−0.0959623	−	0.913020i
$257$	1.49102	−	5.56457i	0.0930075	−	0.347109i	−0.903702	−	0.428161i	$-0.859162\pi$
$257$	1.49102	−	5.56457i	0.0930075	−	0.347109i	0.996710	+	0.0810527i	$0.0258282\pi$
$258$	−0.124062	+	0.783297i	−0.00772376	+	0.0487659i
$259$	21.6565	−	0.762926i	1.34567	−	0.0474059i
$260$	6.58438	+	12.5829i	0.408346	+	0.780360i
$261$	5.72029	−	1.21589i	0.354077	−	0.0752614i
$262$	−11.3237	−	17.4370i	−0.699580	−	1.07726i
$263$	3.52255	+	5.42424i	0.217209	+	0.334473i	0.930432	−	0.366464i	$-0.119432\pi$
$263$	3.52255	+	5.42424i	0.217209	+	0.334473i	−0.713223	+	0.700938i	$0.752765\pi$
$264$	0.0316882	−	0.00673553i	0.00195027	−	0.000414543i
$265$	−14.6767	+	2.48820i	−0.901580	+	0.152849i
$266$	10.4895	+	16.7753i	0.643155	+	1.02856i
$267$	−0.0325966	+	0.205807i	−0.00199488	+	0.0125952i
$268$	−7.58076	+	28.2918i	−0.463068	+	1.72819i
$269$	−1.59755	−	15.1996i	−0.0974041	−	0.926738i	−0.928681	−	0.370880i	$-0.879056\pi$
$269$	−1.59755	−	15.1996i	−0.0974041	−	0.926738i	0.831277	−	0.555859i	$-0.187610\pi$
$270$	0.615197	+	1.34234i	0.0374397	+	0.0816920i
$271$	−4.48618	−	0.471517i	−0.272516	−	0.0286426i	−0.0327154	−	0.999465i	$-0.510415\pi$
$271$	−4.48618	−	0.471517i	−0.272516	−	0.0286426i	−0.239801	+	0.970822i	$0.577082\pi$
$272$	2.03757	+	12.8647i	0.123546	+	0.780038i
$273$	−0.289466	−	0.332786i	−0.0175193	−	0.0201411i
$274$			37.5806i			2.27032i
$275$	18.4749	−	4.34830i	1.11408	−	0.262213i
$276$	−0.563733	−	0.325471i	−0.0339327	−	0.0195911i
$277$	5.65708	+	0.296475i	0.339901	+	0.0178134i	0.221523	−	0.975155i	$-0.428897\pi$
$277$	5.65708	+	0.296475i	0.339901	+	0.0178134i	0.118378	+	0.992969i	$0.462231\pi$
$278$	−20.3420	−	25.1203i	−1.22003	−	1.50662i
$279$	−10.9708	−	7.97073i	−0.656803	−	0.477195i
$280$	0.326372	+	0.866472i	0.0195044	+	0.0517816i
$281$	8.30707	−	6.03544i	0.495558	−	0.360044i	−0.311760	−	0.950161i	$-0.600918\pi$
$281$	8.30707	−	6.03544i	0.495558	−	0.360044i	0.807318	+	0.590117i	$0.200918\pi$
$282$	0.993220	+	0.266133i	0.0591454	+	0.0158480i
$283$	−21.9867	−	17.8045i	−1.30697	−	1.05837i	−0.994088	−	0.108575i	$-0.965371\pi$
$283$	−21.9867	−	17.8045i	−1.30697	−	1.05837i	−0.312885	−	0.949791i	$-0.601296\pi$
$284$	0.940630	−	4.42532i	0.0558161	−	0.262594i
$285$	−0.112129	+	0.437416i	−0.00664197	+	0.0259103i
$286$	22.2860	+	7.24115i	1.31780	+	0.428178i
$287$	6.31353	+	20.6279i	0.372676	+	1.21763i
$288$	−10.9734	+	21.5365i	−0.646615	+	1.26905i
$289$	1.14114	+	5.36865i	0.0671260	+	0.315803i
$290$	6.90692	+	5.47001i	0.405588	+	0.321210i
$291$	−0.230093	−	0.0489077i	−0.0134883	−	0.00286702i
$292$	−1.63458	−	4.25823i	−0.0956567	−	0.249194i
$293$	13.4826	−	13.4826i	0.787661	−	0.787661i	−0.193449	−	0.981110i	$-0.561968\pi$
$293$	13.4826	−	13.4826i	0.787661	−	0.787661i	0.981110	+	0.193449i	$0.0619675\pi$
$294$	−0.431415	−	0.638752i	−0.0251607	−	0.0372528i
$295$	−6.85981	+	2.31153i	−0.399394	+	0.134583i
$296$	0.133990	−	1.27483i	0.00778802	−	0.0740981i
$297$	1.15891	+	0.444864i	0.0672468	+	0.0258136i
$298$	−0.185689	+	3.54315i	−0.0107567	+	0.205249i
$299$	−8.78286	−	15.2124i	−0.507926	−	0.879754i
$300$	−0.246139	+	0.510169i	−0.0142108	+	0.0294546i
$301$	−13.7031	+	13.2411i	−0.789836	+	0.763205i
$302$	1.37434	+	2.69729i	0.0790843	+	0.155212i
$303$	−0.296036	+	0.239725i	−0.0170068	+	0.0137719i
$304$	−12.9877	+	5.78251i	−0.744897	+	0.331650i
$305$	−21.4466	−	23.3049i	−1.22803	−	1.33444i
$306$	8.35152	−	18.7578i	0.477424	−	1.07231i
$307$	−13.9902	−	13.9902i	−0.798461	−	0.798461i	0.184392	−	0.982853i	$-0.440968\pi$
$307$	−13.9902	−	13.9902i	−0.798461	−	0.798461i	−0.982853	+	0.184392i	$0.940968\pi$
$308$	18.9125	+	8.81196i	1.07764	+	0.502108i
$309$	0.500213	−	0.162529i	0.0284561	−	0.00924595i
$310$	−1.29069	−	20.3893i	−0.0733065	−	1.15804i
$311$	−0.132551	+	0.119349i	−0.00751626	+	0.00676767i	−0.672880	−	0.739751i	$-0.734943\pi$
$311$	−0.132551	+	0.119349i	−0.00751626	+	0.00676767i	0.665364	+	0.746519i	$0.268276\pi$
$312$	−0.0218813	+	0.0142099i	−0.00123879	+	0.000804477i
$313$	−0.719241	−	13.7239i	−0.0406539	−	0.775723i	−0.940558	−	0.339634i	$-0.889697\pi$
$313$	−0.719241	−	13.7239i	−0.0406539	−	0.775723i	0.899904	−	0.436089i	$-0.143637\pi$
$314$	−2.47417	+	7.61471i	−0.139625	+	0.429723i
$315$	−3.79538	+	17.3197i	−0.213846	+	0.975853i
$316$	−4.20622	−	12.9454i	−0.236619	−	0.728237i
$317$	11.3955	−	4.37431i	0.640034	−	0.245686i	−0.0166391	−	0.999862i	$-0.505297\pi$
$317$	11.3955	−	4.37431i	0.640034	−	0.245686i	0.656673	+	0.754176i	$0.271963\pi$
$318$	−0.189728	−	0.708076i	−0.0106394	−	0.0397069i
$319$	7.36642	−	0.774242i	0.412440	−	0.0433492i
$320$	−18.7819	+	4.20588i	−1.04994	+	0.235116i
$321$	−0.106260	+	0.146254i	−0.00593086	+	0.00816313i
$322$	−12.0032	−	28.2536i	−0.668911	−	1.57451i
$323$	11.1952	−	5.70424i	0.622918	−	0.317392i
$324$	16.1444	−	9.32098i	0.896912	−	0.517832i
$325$	−12.6357	+	8.60147i	−0.700901	+	0.477124i
$326$	−10.9441	+	18.9558i	−0.606140	+	1.04987i
$327$	0.446381	+	0.289883i	0.0246849	+	0.0160306i
$328$	1.26038	−	0.199625i	0.0695929	−	0.0110224i
$329$	15.2168	+	19.4643i	0.838929	+	1.07310i
$330$	0.298455	+	0.885708i	0.0164294	+	0.0487566i
$331$	7.85181	+	3.49585i	0.431574	+	0.192149i	0.611014	−	0.791620i	$-0.290762\pi$
$331$	7.85181	+	3.49585i	0.431574	+	0.192149i	−0.179440	+	0.983769i	$0.557429\pi$
$332$	−13.8803	+	3.71922i	−0.761781	+	0.204119i
$333$	15.4479	−	19.0766i	0.846542	−	1.04539i
$334$	−17.0795	+	18.9688i	−0.934551	+	1.03792i
$335$	−31.1889	−	4.59326i	−1.70403	−	0.250957i
$336$	0.497741	−	0.242954i	0.0271540	−	0.0132542i
$337$	−6.18213	−	3.14995i	−0.336762	−	0.171589i	0.277429	−	0.960746i	$-0.410518\pi$
$337$	−6.18213	−	3.14995i	−0.336762	−	0.171589i	−0.614191	+	0.789157i	$0.710518\pi$
$338$	7.36872	−	0.386178i	0.400806	−	0.0210053i
$339$	0.170589	+	0.189458i	0.00926510	+	0.0102899i
$340$	15.1790	−	4.24438i	0.823199	−	0.230184i
$341$	−12.7638	−	11.4926i	−0.691201	−	0.622360i
$342$	22.1358	+	3.50596i	1.19697	+	0.189581i
$343$	0.952220	−	18.4958i	0.0514151	−	0.998677i
$344$	0.662544	+	0.911914i	0.0357220	+	0.0491671i
$345$	0.278003	−	0.643109i	0.0149672	−	0.0346238i
$346$	−11.0168	−	24.7442i	−0.592268	−	1.33026i
$347$	−5.47365	+	14.2593i	−0.293841	+	0.765481i	0.704597	+	0.709608i	$0.251128\pi$
$347$	−5.47365	+	14.2593i	−0.293841	+	0.765481i	−0.998438	+	0.0558738i	$0.982206\pi$
$348$	−0.120397	+	0.185396i	−0.00645398	+	0.00993826i
$349$	27.7967			1.48792			0.743961	−	0.668224i	$-0.232945\pi$
$349$	27.7967			1.48792			0.743961	+	0.668224i	$0.232945\pi$
$350$	−23.7454	+	12.2359i	−1.26925	+	0.654038i
$351$	−0.999742			−0.0533623
$352$	−16.6737	+	25.6753i	−0.888712	+	1.36850i
$353$	−4.45506	+	11.6058i	−0.237119	+	0.617716i	−0.999570	−	0.0293301i	$-0.990663\pi$
$353$	−4.45506	+	11.6058i	−0.237119	+	0.617716i	0.762451	+	0.647046i	$0.223996\pi$
$354$	−0.144989	−	0.325651i	−0.00770608	−	0.0173081i
$355$	4.84805	+	0.456386i	0.257308	+	0.0242225i
$356$	4.66614	+	6.42239i	0.247305	+	0.340386i
$357$	−0.428057	+	0.237448i	−0.0226552	+	0.0125671i
$358$	−10.7588	−	1.70402i	−0.568619	−	0.0900604i
$359$	−27.4274	−	24.6957i	−1.44756	−	1.30339i	−0.875533	−	0.483159i	$-0.839489\pi$
$359$	−27.4274	−	24.6957i	−1.44756	−	1.30339i	−0.572030	−	0.820232i	$-0.693844\pi$
$360$	0.983193	+	0.365214i	0.0518188	+	0.0192485i
$361$	−3.53682	−	3.92804i	−0.186148	−	0.206739i
$362$	−42.6976	+	2.23769i	−2.24414	+	0.117610i
$363$	0.165642	+	0.0843988i	0.00869395	+	0.00442979i
$364$	−16.7629	−	1.16700i	−0.878616	−	0.0611675i
$365$	4.34977	−	2.27614i	0.227677	−	0.119139i
$366$	1.04360	−	1.15903i	0.0545498	−	0.0605837i
$367$	−9.11853	+	11.2604i	−0.475983	+	0.587791i	−0.957423	−	0.288689i	$-0.906781\pi$
$367$	−9.11853	+	11.2604i	−0.475983	+	0.587791i	0.481440	+	0.876479i	$0.340114\pi$
$368$	21.3068	−	5.70913i	1.11069	−	0.297609i
$369$	22.3240	+	9.93929i	1.16214	+	0.517419i
$370$	36.9798	−	0.401552i	1.92249	−	0.0208757i
$371$	6.59309	−	16.3329i	0.342296	−	0.847964i
$372$	0.506284	−	0.0801875i	0.0262496	−	0.00415753i
$373$	22.2573	+	14.4541i	1.15244	+	0.748404i	0.971953	−	0.235173i	$-0.0755657\pi$
$373$	22.2573	+	14.4541i	1.15244	+	0.748404i	0.180488	+	0.983577i	$0.442232\pi$
$374$	13.0032	−	22.5222i	0.672380	−	1.16460i
$375$	−0.575994	−	0.199834i	−0.0297442	−	0.0103194i
$376$	1.26568	−	0.730738i	0.0652722	−	0.0376849i
$377$	−5.31511	+	2.70819i	−0.273742	+	0.139479i
$378$	−1.73417	−	0.212389i	−0.0891963	−	0.0109241i
$379$	−0.369609	+	0.508723i	−0.0189855	+	0.0261314i	−0.818404	−	0.574643i	$-0.805141\pi$
$379$	−0.369609	+	0.508723i	−0.0189855	+	0.0261314i	0.799419	+	0.600774i	$0.205141\pi$
$380$	8.76296	+	14.8043i	0.449530	+	0.759445i
$381$	−0.664652	+	0.0698577i	−0.0340512	+	0.00357892i
$382$	−7.90282	−	29.4937i	−0.404344	−	1.50903i
$383$	10.9688	−	4.21053i	0.560480	−	0.215148i	−0.0616015	−	0.998101i	$-0.519621\pi$
$383$	10.9688	−	4.21053i	0.560480	−	0.215148i	0.622081	+	0.782953i	$0.286287\pi$
$384$	−0.0210824	−	0.0648849i	−0.00107586	−	0.00331114i
$385$	−7.07377	+	21.3139i	−0.360513	+	1.08626i
$386$	8.34271	−	25.6762i	0.424633	−	1.30689i
$387$	1.12968	+	21.5556i	0.0574250	+	1.09573i
$388$	−7.51604	+	4.88097i	−0.381569	+	0.247794i
$389$	−3.77113	+	3.39554i	−0.191204	+	0.172161i	−0.759173	−	0.650889i	$-0.774396\pi$
$389$	−3.77113	+	3.39554i	−0.191204	+	0.172161i	0.567969	+	0.823050i	$0.307730\pi$
$390$	−0.480027	−	0.579796i	−0.0243071	−	0.0293591i
$391$	−18.5408	+	6.02427i	−0.937648	+	0.304660i
$392$	−1.07554	−	0.208378i	−0.0543230	−	0.0105247i
$393$	0.397018	+	0.397018i	0.0200269	+	0.0200269i
$394$	7.76288	−	17.4357i	0.391088	−	0.878398i
$395$	13.3184	−	6.10387i	0.670122	−	0.307119i
$396$	21.5915	−	9.61314i	1.08501	−	0.483078i
$397$	23.1860	−	18.7756i	1.16367	−	0.942323i	0.164641	−	0.986354i	$-0.447353\pi$
$397$	23.1860	−	18.7756i	1.16367	−	0.942323i	0.999030	+	0.0440310i	$0.0140200\pi$
$398$	−12.7806	−	25.0834i	−0.640634	−	1.25732i
$399$	−0.371269	−	0.384224i	−0.0185867	−	0.0192352i
$400$	−6.32657	−	18.1223i	−0.316328	−	0.906117i
$401$	8.26123	+	14.3089i	0.412546	+	0.714551i	0.995167	−	0.0981931i	$-0.0313063\pi$
$401$	8.26123	+	14.3089i	0.412546	+	0.714551i	−0.582621	+	0.812744i	$0.697973\pi$
$402$	0.0812484	−	1.55031i	0.00405230	−	0.0773225i
$403$	12.9137	+	4.95709i	0.643275	+	0.246930i
$404$	−1.51697	+	14.4330i	−0.0754719	+	0.718067i
$405$	11.9693	+	16.1037i	0.594762	+	0.800201i
$406$	−9.79505	+	3.56852i	−0.486120	+	0.177102i
$407$	21.9843	−	21.9843i	1.08972	−	1.08972i
$408$	0.0103769	+	0.0270327i	0.000513732	+	0.00133832i
$409$	−18.8781	−	4.01266i	−0.933461	−	0.198413i	−0.284014	−	0.958820i	$-0.591666\pi$
$409$	−18.8781	−	4.01266i	−0.933461	−	0.198413i	−0.649447	+	0.760407i	$0.725000\pi$
$410$	9.91418	+	35.4557i	0.489627	+	1.75103i
$411$	−0.211003	−	0.992690i	−0.0104080	−	0.0489658i
$412$	9.09692	−	17.8537i	0.448173	−	0.879589i
$413$	1.92415	−	8.34613i	0.0946815	−	0.410686i
$414$	−33.0713	−	10.7455i	−1.62537	−	0.528114i
$415$	−5.69924	−	14.3784i	−0.279765	−	0.705808i
$416$	5.12616	−	24.1167i	0.251331	−	1.18242i
$417$	0.678376	+	0.549338i	0.0332202	+	0.0269012i
$418$	27.4187	+	7.34682i	1.34109	+	0.359345i
$419$	−19.1402	+	13.9062i	−0.935062	+	0.679362i	−0.947227	−	0.320564i	$-0.896128\pi$
$419$	−19.1402	+	13.9062i	−0.935062	+	0.679362i	0.0121653	+	0.999926i	$0.496128\pi$
$420$	−0.361488	−	0.564380i	−0.0176388	−	0.0275389i
$421$	−0.268667	−	0.195198i	−0.0130940	−	0.00951338i	0.581219	−	0.813747i	$-0.302576\pi$
$421$	−0.268667	−	0.195198i	−0.0130940	−	0.00951338i	−0.594313	+	0.804234i	$0.702576\pi$
$422$	−5.55429	−	6.85898i	−0.270379	−	0.333890i
$423$	27.9484	+	1.46471i	1.35890	+	0.0712167i
$424$	−0.902312	−	0.520950i	−0.0438201	−	0.0252996i
$425$	6.42191	+	15.7017i	0.311508	+	0.761646i
$426$			0.239794i			0.0116181i
$427$	36.7834	−	7.16170i	1.78007	−	0.346579i
$428$	1.07742	+	6.80253i	0.0520788	+	0.328813i
$429$	−0.629340	−	0.0661463i	−0.0303848	−	0.00319357i
$430$	−23.9292	+	22.0211i	−1.15397	+	1.06195i
$431$	−3.57389	−	34.0033i	−0.172148	−	1.63788i	−0.650352	−	0.759633i	$-0.725378\pi$
$431$	−3.57389	−	34.0033i	−0.172148	−	1.63788i	0.478203	−	0.878249i	$-0.341288\pi$
$432$	0.324931	−	1.21266i	0.0156333	−	0.0583441i
$433$	−0.570691	+	3.60320i	−0.0274256	+	0.173159i	−0.997599	−	0.0692529i	$-0.977938\pi$
$433$	−0.570691	+	3.60320i	−0.0274256	+	0.173159i	0.970173	+	0.242412i	$0.0779384\pi$
$434$	21.3472	+	11.3421i	1.02470	+	0.544438i
$435$	−0.213159	−	0.105710i	−0.0102202	−	0.00506842i
$436$	19.8344	−	4.21592i	0.949893	−	0.201906i
$437$	−11.5892	−	17.8458i	−0.554386	−	0.853680i
$438$	0.131669	+	0.202753i	0.00629140	+	0.00968791i
$439$	30.0361	−	6.38437i	1.43355	−	0.304710i	0.575297	−	0.817944i	$-0.304886\pi$
$439$	30.0361	−	6.38437i	1.43355	−	0.304710i	0.858248	+	0.513235i	$0.171553\pi$
$440$	1.19011	+	0.590202i	0.0567362	+	0.0281368i
$441$	−15.1001	−	14.5641i	−0.719053	−	0.693528i
$442$	−3.27644	+	20.6866i	−0.155844	+	0.983963i
$443$	−1.67479	+	6.25039i	−0.0795715	+	0.296965i	−0.994231	−	0.107260i	$-0.965792\pi$
$443$	−1.67479	+	6.25039i	−0.0795715	+	0.296965i	0.914659	+	0.404225i	$0.132459\pi$
$444$	0.0969902	+	0.922800i	0.00460295	+	0.0437942i
$445$	−6.28728	+	5.78593i	−0.298046	+	0.274280i
$446$	−11.3453	−	1.19244i	−0.537214	−	0.0564635i
$447$	−0.0149887	−	0.0946350i	−0.000708941	−	0.00447608i
$448$	7.40770	−	21.5350i	0.349981	−	1.01743i
$449$			33.2556i			1.56943i	0.619856	+	0.784715i	$0.287191\pi$
$449$			33.2556i			1.56943i	−0.619856	+	0.784715i	$0.712809\pi$
$450$	−7.19513	+	29.3913i	−0.339182	+	1.38552i
$451$	26.8041	+	15.4754i	1.26216	+	0.728706i
$452$	9.69935	+	0.508321i	0.456219	+	0.0239094i
$453$	−0.0514476	−	0.0635324i	−0.00241722	−	0.00298501i
$454$	−27.0041	−	19.6196i	−1.26737	−	0.920795i
$455$	−0.832968	−	18.0668i	−0.0390501	−	0.846985i
$456$	−0.0255693	+	0.0185772i	−0.00119739	+	0.000869955i
$457$	−26.8112	−	7.18403i	−1.25417	−	0.336055i	−0.430226	−	0.902721i	$-0.641566\pi$
$457$	−26.8112	−	7.18403i	−1.25417	−	0.336055i	−0.823947	+	0.566666i	$0.808233\pi$
$458$	43.8270	+	35.4904i	2.04790	+	1.65836i
$459$	−0.230687	+	1.08529i	−0.0107675	+	0.0506572i
$460$	−9.83565	−	24.8140i	−0.458589	−	1.15696i
$461$	−5.61141	−	1.82326i	−0.261350	−	0.0849176i	0.175411	−	0.984495i	$-0.443874\pi$
$461$	−5.61141	−	1.82326i	−0.261350	−	0.0849176i	−0.436761	+	0.899578i	$0.643874\pi$
$462$	−1.07761	−	0.248438i	−0.0501352	−	0.0115584i
$463$	10.0954	−	19.8133i	0.469173	−	0.920804i	−0.528252	−	0.849088i	$-0.677152\pi$
$463$	10.0954	−	19.8133i	0.469173	−	0.920804i	0.997425	−	0.0717166i	$-0.0228477\pi$
$464$	−1.55746	−	7.32729i	−0.0723034	−	0.340161i
$465$	0.148573	+	0.531336i	0.00688991	+	0.0246401i
$466$	−31.8202	−	6.76359i	−1.47404	−	0.313317i
$467$	4.71248	+	12.2764i	0.218068	+	0.568085i	0.998355	−	0.0573358i	$-0.0182606\pi$
$467$	4.71248	+	12.2764i	0.218068	+	0.568085i	−0.780287	+	0.625421i	$0.784927\pi$
$468$	−13.4594	+	13.4594i	−0.622162	+	0.622162i
$469$	23.9680	−	28.5818i	1.10674	−	1.31978i
$470$	25.1524	+	33.8404i	1.16019	+	1.56094i
$471$	0.0226010	−	0.215034i	0.00104140	−	0.00990825i
$472$	−0.473003	−	0.181569i	−0.0217717	−	0.00835738i
$473$	−1.43082	+	27.3017i	−0.0657892	+	1.25533i
$474$	0.360727	+	0.624797i	0.0165687	+	0.0286979i
$475$	−14.7402	+	11.2064i	−0.676328	+	0.514185i
$476$	−5.13485	+	17.9281i	−0.235355	+	0.821735i
$477$	−9.05801	−	17.7773i	−0.414738	−	0.813969i
$478$	23.6878	−	19.1820i	1.08345	−	0.877363i
$479$	9.63545	−	4.28998i	0.440255	−	0.196014i	−0.174625	−	0.984635i	$-0.555871\pi$
$479$	9.63545	−	4.28998i	0.440255	−	0.196014i	0.614880	+	0.788621i	$0.289205\pi$
$480$	0.893990	−	0.409718i	0.0408049	−	0.0187010i
$481$	−10.1843	+	22.8742i	−0.464363	+	1.04298i
$482$	−35.7017	−	35.7017i	−1.62617	−	1.62617i
$483$	0.475698	+	0.678923i	0.0216450	+	0.0308921i
$484$	6.73589	−	2.18862i	0.306177	−	0.0994829i
$485$	−6.15137	−	7.42988i	−0.279319	−	0.337373i
$486$	−2.20650	+	1.98674i	−0.100089	+	0.0901203i
$487$	−31.0226	+	20.1463i	−1.40577	+	0.912916i	−0.999999	−	0.00106056i	$-0.999662\pi$
$487$	−31.0226	+	20.1463i	−1.40577	+	0.912916i	−0.405768	+	0.913976i	$0.632996\pi$
$488$	−0.116015	−	2.21369i	−0.00525174	−	0.100209i
$489$	0.182659	−	0.562165i	0.00826011	−	0.0254220i
$490$	2.39329	−	31.5160i	0.108118	−	1.42375i
$491$	−8.54554	−	26.3005i	−0.385655	−	1.18692i	−0.936004	−	0.351989i	$-0.885506\pi$
$491$	−8.54554	−	26.3005i	−0.385655	−	1.18692i	0.550350	−	0.834934i	$-0.314494\pi$
$492$	−0.862360	+	0.331029i	−0.0388782	+	0.0149239i
$493$	1.71350	+	6.39486i	0.0771720	+	0.288010i
$494$	−22.7356	+	2.38961i	−1.02292	+	0.107514i
$495$	12.9578	+	21.8911i	0.582410	+	0.983934i
$496$	−10.2099	+	14.0528i	−0.458440	+	0.630989i
$497$	−3.46603	+	4.60252i	−0.155473	+	0.206451i
$498$	0.678633	−	0.345781i	0.0304103	−	0.0154948i
$499$	−29.8613	+	17.2404i	−1.33678	+	0.771788i	−0.986328	−	0.164794i	$-0.947304\pi$
$499$	−29.8613	+	17.2404i	−1.33678	+	0.771788i	−0.350448	+	0.936582i	$0.613971\pi$
$500$	−20.9002	+	10.1334i	−0.934684	+	0.453181i
$501$	0.344652	−	0.596956i	0.0153979	−	0.0266700i
$502$	21.1533	+	13.7371i	0.944117	+	0.613117i
$503$	4.83025	−	0.765036i	0.215370	−	0.0341113i	−0.0478169	−	0.998856i	$-0.515226\pi$
$503$	4.83025	−	0.765036i	0.215370	−	0.0341113i	0.263187	+	0.964745i	$0.415226\pi$
$504$	−0.977683	+	0.764333i	−0.0435494	+	0.0340461i
$505$	−15.6192	+	0.169604i	−0.695045	+	0.00754727i
$506$	−40.2350	−	17.9138i	−1.78866	−	0.796365i
$507$	−0.192476	+	0.0515739i	−0.00854817	+	0.00229048i
$508$	−16.0233	+	19.7871i	−0.710917	+	0.877909i
$509$	−19.6524	+	21.8262i	−0.871079	+	0.967431i	−0.999706	−	0.0242622i	$-0.992276\pi$
$509$	−19.6524	+	21.8262i	−0.871079	+	0.967431i	0.128627	+	0.991693i	$0.458943\pi$
$510$	−0.740177	+	0.387319i	−0.0327756	+	0.0171508i
$511$	−0.403418	+	5.79475i	−0.0178462	+	0.256344i
$512$	28.6575	+	14.6017i	1.26649	+	0.645311i
$513$	−1.20940	+	0.0633820i	−0.0533964	+	0.00279839i
$514$	7.78388	+	8.64488i	0.343332	+	0.381309i
$515$	20.2173	+	7.50985i	0.890880	+	0.330924i
$516$	−0.606352	−	0.545962i	−0.0266932	−	0.0240346i
$517$	35.0107	+	5.54515i	1.53977	+	0.243875i
$518$	−22.5253	+	37.5146i	−0.989707	+	1.64830i
$519$	0.429940	+	0.591762i	0.0188723	+	0.0259755i
$520$	−1.06514	−	0.100271i	−0.0467096	−	0.00439716i
$521$	16.7254	+	37.5659i	0.732753	+	1.64579i	0.763124	+	0.646252i	$0.223664\pi$
$521$	16.7254	+	37.5659i	0.732753	+	1.64579i	−0.0303715	+	0.999539i	$0.509669\pi$
$522$	−4.23195	+	11.0246i	−0.185227	+	0.482533i
$523$	−9.04956	+	13.9351i	−0.395710	+	0.609339i	−0.979228	−	0.202760i	$-0.935009\pi$
$523$	−9.04956	+	13.9351i	−0.395710	+	0.609339i	0.583519	+	0.812100i	$0.301675\pi$
$524$	21.3907			0.934455
$525$	0.558534	−	0.456535i	0.0243764	−	0.0199248i
$526$	−13.0601			−0.569446
$527$	8.36107	−	12.8749i	0.364214	−	0.560840i
$528$	0.284779	−	0.741874i	0.0123934	−	0.0322859i
$529$	4.07358	+	9.14942i	0.177112	+	0.397801i
$530$	11.9273	−	27.5916i	0.518089	−	1.19850i
$531$	−5.70284	−	7.84928i	−0.247482	−	0.340630i
$532$	−20.3523	−	0.348994i	−0.882386	−	0.0151308i
$533$	−24.6195	−	3.89935i	−1.06639	−	0.168900i
$534$	−0.312688	−	0.281545i	−0.0135313	−	0.0121837i
$535$	−7.13914	+	1.99626i	−0.308652	+	0.0863057i
$536$	−1.47644	−	1.63975i	−0.0637724	−	0.0708265i
$537$	0.293760	−	0.0153953i	0.0126767	−	0.000664358i
$538$	27.4977	+	14.0108i	1.18551	+	0.604048i
$539$	−17.0924	−	20.3445i	−0.736221	−	0.876300i
$540$	−1.50296	−	0.221344i	−0.0646770	−	0.00952515i
$541$	4.47384	−	4.96870i	0.192345	−	0.213621i	−0.639256	−	0.768994i	$-0.720758\pi$
$541$	4.47384	−	4.96870i	0.192345	−	0.213621i	0.831602	+	0.555373i	$0.187424\pi$
$542$	5.73234	−	7.07885i	0.246225	−	0.304063i
$543$	1.11529	−	0.298842i	0.0478618	−	0.0128245i
$544$	−24.9976	−	11.1297i	−1.07176	−	0.477180i
$545$	6.96931	+	20.6825i	0.298533	+	0.885939i
$546$	0.881926	−	0.124223i	0.0377429	−	0.00531626i
$547$	−9.20536	+	1.45799i	−0.393593	+	0.0623389i	−0.350094	−	0.936715i	$-0.613850\pi$
$547$	−9.20536	+	1.45799i	−0.393593	+	0.0623389i	−0.0434985	+	0.999053i	$0.513850\pi$
$548$	−32.4265	−	21.0580i	−1.38519	−	0.899553i
$549$	21.2248	−	36.7624i	0.905851	−	1.56898i
$550$	−12.9544	+	36.0696i	−0.552377	+	1.53801i
$551$	−6.25807	+	3.61310i	−0.266603	+	0.153923i
$552$	0.0436930	−	0.0222627i	0.00185970	−	0.000947564i
$553$	−2.10728	+	17.2062i	−0.0896107	+	0.731680i
$554$	−6.72363	+	9.25428i	−0.285660	+	0.393177i
$555$	−0.974567	+	0.218237i	−0.0413680	+	0.00926363i
$556$	33.0736	−	3.47618i	1.40263	−	0.147423i
$557$	7.10767	+	26.5262i	0.301162	+	1.12395i	0.936199	+	0.351469i	$0.114318\pi$
$557$	7.10767	+	26.5262i	0.301162	+	1.12395i	−0.635038	+	0.772481i	$0.719015\pi$
$558$	25.5640	−	9.81309i	1.08221	−	0.415421i
$559$	−6.80388	−	20.9402i	−0.287774	−	0.885676i
$560$	22.1853	+	4.86162i	0.937499	+	0.205441i
$561$	−0.217025	+	0.667933i	−0.00916279	+	0.0282002i
$562$	1.08514	+	20.7058i	0.0457741	+	0.873421i
$563$	−25.5643	+	16.6016i	−1.07741	+	0.699676i	−0.956130	−	0.292943i	$-0.905365\pi$
$563$	−25.5643	+	16.6016i	−1.07741	+	0.699676i	−0.121276	+	0.992619i	$0.538699\pi$
$564$	−0.786177	+	0.707877i	−0.0331040	+	0.0298070i
$565$	0.660440	+	10.4331i	0.0277849	+	0.438923i
$566$	54.3327	−	17.6538i	2.28377	−	0.742043i
$567$	−23.6500	+	2.07643i	−0.993207	+	0.0872020i
$568$	0.240998	+	0.240998i	0.0101120	+	0.0101120i
$569$	−3.62068	+	8.13218i	−0.151787	+	0.340919i	−0.973395	−	0.229134i	$-0.926411\pi$
$569$	−3.62068	+	8.13218i	−0.151787	+	0.340919i	0.821608	+	0.570053i	$0.193077\pi$
$570$	−0.617453	−	0.670955i	−0.0258623	−	0.0281032i
$571$	39.4472	−	17.5630i	1.65081	−	0.734989i	0.651100	−	0.758992i	$-0.274308\pi$
$571$	39.4472	−	17.5630i	1.65081	−	0.734989i	0.999712	+	0.0240028i	$0.00764107\pi$
$572$	−18.7358	+	15.1720i	−0.783384	+	0.634372i
$573$	0.374351	+	0.734705i	0.0156387	+	0.0306927i
$574$	−41.8772	−	11.9942i	−1.74792	−	0.500627i
$575$	25.3089	−	13.5957i	1.05545	−	0.566979i
$576$	−12.8985	−	22.3409i	−0.537440	−	0.930873i
$577$	0.145877	−	2.78350i	0.00607295	−	0.115879i	−0.993911	−	0.110187i	$-0.964855\pi$
$577$	0.145877	−	2.78350i	0.00607295	−	0.115879i	0.999984	−	0.00569159i	$-0.00181170\pi$
$578$	−10.3469	−	3.97180i	−0.430374	−	0.165205i
$579$	−0.0762088	+	0.725079i	−0.00316713	+	0.0301332i
$580$	−8.59006	+	2.89457i	−0.356683	+	0.120190i
$581$	18.0234	+	3.17230i	0.747738	+	0.131609i
$582$	0.335877	−	0.335877i	0.0139226	−	0.0139226i
$583$	−9.05615	−	23.5921i	−0.375068	−	0.977085i
$584$	0.336101	+	0.0714405i	0.0139080	+	0.00295623i
$585$	−16.0607	−	12.7194i	−0.664026	−	0.525883i
$586$	8.00505	+	37.6608i	0.330686	+	1.55575i
$587$	−14.5534	+	28.5627i	−0.600684	+	1.17891i	0.367817	+	0.929898i	$0.380105\pi$
$587$	−14.5534	+	28.5627i	−0.600684	+	1.17891i	−0.968501	+	0.249011i	$0.919895\pi$
$588$	0.792889	−	0.0143275i	0.0326982	−	0.000590857i
$589$	15.9361	+	5.17795i	0.656635	+	0.213354i
$590$	3.62968	−	14.1594i	0.149431	−	0.582932i
$591$	−0.107160	+	0.504150i	−0.00440799	+	0.0207380i
$592$	−24.4358	−	19.7877i	−1.00431	−	0.813271i
$593$	−13.2874	−	3.56036i	−0.545650	−	0.146206i	−0.0245444	−	0.999699i	$-0.507814\pi$
$593$	−13.2874	−	3.56036i	−0.545650	−	0.146206i	−0.521105	+	0.853492i	$0.674480\pi$
$594$	−2.02793	+	1.47338i	−0.0832070	+	0.0604535i
$595$	−19.8051	−	3.26460i	−0.811930	−	0.133836i
$596$	−2.95317	−	2.14560i	−0.120967	−	0.0878873i
$597$	0.478435	+	0.590818i	0.0195810	+	0.0241806i
$598$	35.4216	+	1.85637i	1.44850	+	0.0759125i
$599$	−27.9160	−	16.1173i	−1.14062	−	0.658535i	−0.194033	−	0.980995i	$-0.562157\pi$
$599$	−27.9160	−	16.1173i	−1.14062	−	0.658535i	−0.946583	+	0.322460i	$0.895490\pi$
$600$	−0.0221335	−	0.0364831i	−0.000903595	−	0.00148942i
$601$			12.7293i			0.519238i	0.965711	+	0.259619i	$0.0835970\pi$
$601$			12.7293i			0.519238i	−0.965711	+	0.259619i	$0.916403\pi$
$602$	−7.35355	−	37.7688i	−0.299708	−	1.53934i
$603$	−6.60993	−	41.7335i	−0.269177	−	1.69952i
$604$	−3.09746	−	0.325557i	−0.126034	−	0.0132467i
$605$	3.17603	+	6.92997i	0.129124	+	0.281743i
$606$	−0.0804033	−	0.764987i	−0.00326616	−	0.0310755i
$607$	−3.01036	+	11.2348i	−0.122187	+	0.456007i	−0.999724	−	0.0235020i	$-0.992518\pi$
$607$	−3.01036	+	11.2348i	−0.122187	+	0.456007i	0.877537	+	0.479509i	$0.159185\pi$
$608$	4.67223	−	29.4993i	0.189484	−	1.19635i
$609$	0.238700	−	0.149258i	0.00967261	−	0.00604825i
$610$	63.0538	−	10.6898i	2.55297	−	0.432818i
$611$	−27.9238	+	5.93538i	−1.12968	+	0.240120i
$612$	11.5055	+	17.7169i	0.465083	+	0.716164i
$613$	−13.0570	−	20.1061i	−0.527369	−	0.812077i	0.470142	−	0.882591i	$-0.344203\pi$
$613$	−13.0570	−	20.1061i	−0.527369	−	0.812077i	−0.997511	+	0.0705139i	$0.977536\pi$
$614$	39.0786	−	8.30642i	1.57709	−	0.335220i
$615$	−0.460955	−	0.880897i	−0.0185875	−	0.0355212i
$616$	−1.33271	+	0.833340i	−0.0536964	+	0.0335762i
$617$	−7.33373	+	46.3033i	−0.295245	+	1.86410i	0.179194	+	0.983814i	$0.442651\pi$
$617$	−7.33373	+	46.3033i	−0.295245	+	1.86410i	−0.474439	+	0.880288i	$0.657349\pi$
$618$	−0.274879	+	1.02586i	−0.0110573	+	0.0412663i
$619$	−0.396520	−	3.77263i	−0.0159375	−	0.151635i	0.983659	−	0.180042i	$-0.0576233\pi$
$619$	−0.396520	−	3.77263i	−0.0159375	−	0.151635i	−0.999596	+	0.0284068i	$0.990957\pi$
$620$	18.3162	+	10.3113i	0.735596	+	0.414113i
$621$	1.86875	+	0.196413i	0.0749903	+	0.00788180i
$622$	−0.0563428	−	0.355734i	−0.00225914	−	0.0142637i
$623$	−1.93211	−	9.92354i	−0.0774082	−	0.397578i
$624$			0.639982i			0.0256198i
$625$	−13.4283	−	21.0875i	−0.537131	−	0.843499i
$626$	24.0327	+	13.8753i	0.960539	+	0.554568i
$627$	−0.765515	−	0.0401189i	−0.0305717	−	0.00160220i
$628$	−5.18399	−	6.40169i	−0.206864	−	0.255455i
$629$	22.4817	+	16.3339i	0.896406	+	0.651277i
$630$	−25.1570	−	25.4754i	−1.00228	−	1.01496i
$631$	−16.4374	+	11.9425i	−0.654362	+	0.475422i	−0.864754	−	0.502195i	$-0.832526\pi$
$631$	−16.4374	+	11.9425i	−0.654362	+	0.475422i	0.210392	+	0.977617i	$0.432526\pi$
$632$	0.990471	+	0.265396i	0.0393988	+	0.0105569i
$633$	0.185227	+	0.149994i	0.00736213	+	0.00596174i
$634$	−5.12456	+	24.1092i	−0.203522	+	0.957498i
$635$	−23.1440	−	14.6751i	−0.918444	−	0.582364i
$636$	0.717277	+	0.233058i	0.0284419	+	0.00924133i
$637$	18.7229	+	10.3632i	0.741829	+	0.410607i
$638$	−6.79026	+	13.3266i	−0.268829	+	0.527606i
$639$	1.35696	+	6.38400i	0.0536805	+	0.252547i
$640$	0.974138	−	2.62248i	0.0385062	−	0.103663i
$641$	10.7436	+	2.28363i	0.424348	+	0.0901981i	0.415136	−	0.909760i	$-0.363734\pi$
$641$	10.7436	+	2.28363i	0.424348	+	0.0901981i	0.00921279	+	0.999958i	$0.497067\pi$
$642$	−0.130821	−	0.340801i	−0.00516310	−	0.0134503i
$643$	−1.99706	+	1.99706i	−0.0787564	+	0.0787564i	−0.745388	−	0.666631i	$-0.767736\pi$
$643$	−1.99706	+	1.99706i	−0.0787564	+	0.0787564i	0.666631	+	0.745388i	$0.267736\pi$
$644$	31.1045	+	5.47471i	1.22569	+	0.215734i
$645$	0.508449	−	0.716043i	0.0200202	−	0.0281942i
$646$	−2.65206	+	25.2326i	−0.104344	+	0.992765i
$647$	−20.9821	−	8.05429i	−0.824893	−	0.316647i	−0.0909482	−	0.995856i	$-0.528990\pi$
$647$	−20.9821	−	8.05429i	−0.824893	−	0.316647i	−0.733945	+	0.679209i	$0.762323\pi$
$648$	−0.0734988	+	1.40244i	−0.00288731	+	0.0550931i
$649$	−6.14428	−	10.6422i	−0.241184	−	0.417743i
$650$	−0.670242	−	30.8584i	−0.0262891	−	1.21037i
$651$	−0.627568	−	0.179743i	−0.0245963	−	0.00704470i
$652$	−10.2236	−	20.0649i	−0.400387	−	0.785803i
$653$	5.90474	−	4.78157i	0.231070	−	0.187117i	−0.506792	−	0.862068i	$-0.669169\pi$
$653$	5.90474	−	4.78157i	0.231070	−	0.187117i	0.737862	+	0.674951i	$0.235835\pi$
$654$	−0.981843	+	0.437145i	−0.0383931	+	0.0170937i
$655$	2.65506	+	22.8697i	0.103742	+	0.893592i
$656$	12.7315	−	28.5955i	0.497083	−	1.11647i
$657$	4.65276	+	4.65276i	0.181522	+	0.181522i
$658$	−49.6981	+	4.36342i	−1.93744	+	0.170104i
$659$	39.6715	−	12.8900i	1.54538	−	0.502125i	0.592526	−	0.805551i	$-0.298131\pi$
$659$	39.6715	−	12.8900i	1.54538	−	0.502125i	0.952855	+	0.303426i	$0.0981306\pi$
$660$	−0.931472	−	0.238778i	−0.0362575	−	0.00929441i
$661$	32.5603	−	29.3174i	1.26645	−	1.14031i	0.283001	−	0.959120i	$-0.408670\pi$
$661$	32.5603	−	29.3174i	1.26645	−	1.14031i	0.983447	−	0.181195i	$-0.0579965\pi$
$662$	−14.5555	+	9.45247i	−0.565717	+	0.367381i
$663$	−0.0296017	−	0.564834i	−0.00114963	−	0.0219363i
$664$	0.334523	−	1.02956i	0.0129820	−	0.0399545i
$665$	−2.15306	−	21.8029i	−0.0834921	−	0.845479i
$666$	15.3172	+	47.1414i	0.593528	+	1.82669i
$667$	10.4672	−	4.01800i	0.405293	−	0.155578i
$668$	−6.79683	−	25.3661i	−0.262977	−	0.981445i
$669$	0.306380	−	0.0322019i	0.0118453	−	0.00124500i
$670$	42.0797	−	47.7672i	1.62568	−	1.84541i
$671$	31.6024	−	43.4970i	1.22000	−	1.67918i
$672$	−0.141450	+	1.15495i	−0.00545655	+	0.0445532i
$673$	25.6305	−	13.0594i	0.987982	−	0.503402i	0.116163	−	0.993230i	$-0.462940\pi$
$673$	25.6305	−	13.0594i	0.987982	−	0.503402i	0.871819	+	0.489828i	$0.162940\pi$
$674$	12.1335	−	7.00526i	0.467364	−	0.269833i
$675$	0.0500977	−	1.63435i	0.00192826	−	0.0629062i
$676$	−3.79579	+	6.57451i	−0.145992	+	0.252866i
$677$	34.8273	+	22.6171i	1.33852	+	0.869245i	0.997490	−	0.0708068i	$-0.0225574\pi$
$677$	34.8273	+	22.6171i	1.33852	+	0.869245i	0.341030	+	0.940052i	$0.389224\pi$
$678$	−0.508459	+	0.0805320i	−0.0195273	+	0.00309281i
$679$	11.3016	−	1.59187i	0.433714	−	0.0610905i
$680$	−0.354629	+	1.13316i	−0.0135994	+	0.0434546i
$681$	0.823471	+	0.366633i	0.0315555	+	0.0140494i
$682$	33.5003	−	8.97638i	1.28279	−	0.343724i
$683$	2.90769	−	3.59070i	0.111260	−	0.137394i	−0.718474	−	0.695554i	$-0.755159\pi$
$683$	2.90769	−	3.59070i	0.111260	−	0.137394i	0.829734	+	0.558160i	$0.188492\pi$
$684$	−15.4287	+	17.1354i	−0.589933	+	0.655187i
$685$	18.4891	−	37.2823i	0.706433	−	1.42448i
$686$	30.2756	+	21.9539i	1.15593	+	0.838203i
$687$	−1.35696	−	0.691404i	−0.0517711	−	0.0263787i
$688$	27.6113	−	1.44705i	1.05267	−	0.0551681i
$689$	13.6181	+	15.1244i	0.518806	+	0.576193i
$690$	0.783372	+	1.17808i	0.0298225	+	0.0448488i
$691$	−0.175360	−	0.157895i	−0.00667101	−	0.00600660i	0.665788	−	0.746141i	$-0.268095\pi$
$691$	−0.175360	−	0.157895i	−0.00667101	−	0.00600660i	−0.672459	+	0.740134i	$0.734762\pi$
$692$	27.5238	+	4.35934i	1.04630	+	0.165717i
$693$	−30.0950	−	0.516058i	−1.14322	−	0.0196034i
$694$	−18.1286	−	24.9518i	−0.688151	−	0.947159i
$695$	7.82171	+	34.9289i	0.296694	+	1.32493i
$696$	−0.00677345	−	0.0152134i	−0.000256747	−	0.000576663i
$697$	−9.91391	+	25.8266i	−0.375516	+	0.978252i
$698$	−30.5702	+	47.0740i	−1.15710	+	1.78178i
$699$	0.878505			0.0332281
$700$	2.74778	−	27.3451i	0.103856	−	1.03355i
$701$	−8.97311			−0.338910			−0.169455	−	0.985538i	$-0.554201\pi$
$701$	−8.97311			−0.338910			−0.169455	+	0.985538i	$0.554201\pi$
$702$	1.09950	−	1.69308i	0.0414978	−	0.0639010i
$703$	−10.8699	+	28.3170i	−0.409965	+	1.06799i
$704$	−13.2896	−	29.8490i	−0.500872	−	1.12498i
$705$	−0.854403	−	0.752671i	−0.0321787	−	0.0283472i
$706$	−14.7550	−	20.3086i	−0.555313	−	0.764323i
$707$	9.51404	−	15.8451i	0.357812	−	0.595915i
$708$	0.362232	+	0.0573719i	0.0136135	+	0.00215617i
$709$	13.1569	+	11.8465i	0.494119	+	0.444906i	0.878130	−	0.478422i	$-0.158791\pi$
$709$	13.1569	+	11.8465i	0.494119	+	0.444906i	−0.384011	+	0.923328i	$0.625458\pi$
$710$	−6.10468	+	7.70831i	−0.229105	+	0.289288i
$711$	13.1392	+	14.5926i	0.492759	+	0.547264i
$712$	−0.597217	+	0.0312988i	−0.0223816	+	0.00117297i
$713$	−23.1647	−	11.8030i	−0.867526	−	0.442026i
$714$	0.0686475	−	0.986061i	0.00256907	−	0.0369024i
$715$	−18.5465	−	18.1481i	−0.693601	−	0.678700i
$716$	7.49892	−	8.32840i	0.280248	−	0.311247i
$717$	−0.518011	+	0.639691i	−0.0193455	+	0.0238897i
$718$	71.9867	−	19.2888i	2.68652	−	0.719851i
$719$	−0.351469	−	0.156484i	−0.0131076	−	0.00583587i	0.400172	−	0.916440i	$-0.368950\pi$
$719$	−0.351469	−	0.156484i	−0.0131076	−	0.00583587i	−0.413280	+	0.910604i	$0.635617\pi$
$720$	20.6483	−	15.3471i	0.769516	−	0.571954i
$721$	−20.1040	+	15.7169i	−0.748711	+	0.585328i
$722$	10.5419	−	1.66967i	0.392329	−	0.0621388i
$723$	1.14351	+	0.742606i	0.0425277	+	0.0276178i
$724$	21.9945	−	38.0956i	0.817419	−	1.41581i
$725$	−4.16092	−	8.82471i	−0.154533	−	0.327742i
$726$	−0.325100	+	0.187697i	−0.0120656	+	0.00696608i
$727$	−29.7326	+	15.1495i	−1.10272	+	0.561864i	−0.907990	−	0.418992i	$-0.862383\pi$
$727$	−29.7326	+	15.1495i	−1.10272	+	0.561864i	−0.194731	+	0.980857i	$0.562383\pi$
$728$	0.761507	−	1.01120i	0.0282233	−	0.0374776i
$729$	−15.7759	+	21.7137i	−0.584292	+	0.804210i
$730$	−0.929110	+	9.86965i	−0.0343879	+	0.365292i
$731$	−24.3021	+	2.55426i	−0.898847	+	0.0944726i
$732$	0.415302	+	1.54993i	0.0153500	+	0.0572870i
$733$	−45.7741	+	17.5710i	−1.69070	+	0.649001i	−0.997428	−	0.0716715i	$-0.977167\pi$
$733$	−45.7741	+	17.5710i	−1.69070	+	0.649001i	−0.693276	+	0.720672i	$0.743833\pi$
$734$	−9.04134	−	27.8264i	−0.333722	−	1.02709i
$735$	0.113734	+	0.845933i	0.00419513	+	0.0312027i
$736$	−14.3200	+	44.0726i	−0.527844	+	1.62454i
$737$	−2.80087	−	53.4438i	−0.103172	−	1.96863i
$738$	−41.3838	+	26.8750i	−1.52336	+	0.989281i
$739$	1.05689	−	0.951626i	0.0388782	−	0.0350061i	−0.649463	−	0.760394i	$-0.725006\pi$
$739$	1.05689	−	0.951626i	0.0388782	−	0.0350061i	0.688341	+	0.725387i	$0.258339\pi$
$740$	−20.3749	+	32.1331i	−0.748996	+	1.18124i
$741$	0.587145	−	0.190775i	0.0215693	−	0.00700829i
$742$	20.4091	+	29.1281i	0.749241	+	1.06933i
$743$	−28.2843	−	28.2843i	−1.03765	−	1.03765i	−0.999263	−	0.0383888i	$-0.987777\pi$
$743$	−28.2843	−	28.2843i	−1.03765	−	1.03765i	−0.0383888	−	0.999263i	$-0.512223\pi$
$744$	−0.0157064	+	0.0352771i	−0.000575823	+	0.00129332i
$745$	1.92740	−	3.42368i	0.0706145	−	0.125434i
$746$	−48.9564	+	21.7968i	−1.79242	+	0.798037i
$747$	16.1104	−	13.0460i	0.589449	−	0.477326i
$748$	12.1471	+	23.8400i	0.444142	+	0.871677i
$749$	2.41507	−	8.43213i	0.0882447	−	0.308103i
$750$	0.971890	−	0.755680i	0.0354884	−	0.0275935i
$751$	−14.2895	−	24.7501i	−0.521430	−	0.903143i	−0.999689	−	0.0249242i	$-0.992066\pi$
$751$	−14.2895	−	24.7501i	−0.521430	−	0.903143i	0.478260	−	0.878218i	$-0.341268\pi$
$752$	1.87619	−	35.7999i	0.0684177	−	1.30549i
$753$	−0.635893	−	0.244096i	−0.0231732	−	0.00889537i
$754$	1.25911	−	11.9796i	0.0458541	−	0.436272i
$755$	−0.0363987	−	3.35204i	−0.00132469	−	0.121993i
$756$	1.15499	−	1.37732i	0.0420066	−	0.0500928i
$757$	9.94771	−	9.94771i	0.361556	−	0.361556i	−0.502830	−	0.864385i	$-0.667708\pi$
$757$	9.94771	−	9.94771i	0.361556	−	0.361556i	0.864385	+	0.502830i	$0.167708\pi$
$758$	−0.455041	−	1.18542i	−0.0165278	−	0.0430565i
$759$	1.16339	+	0.247286i	0.0422283	+	0.00897590i
$760$	−1.29488	−	0.0537703i	−0.0469701	−	0.00195046i
$761$	−4.97651	−	23.4126i	−0.180398	−	0.848708i	−0.971503	−	0.237027i	$-0.923827\pi$
$761$	−4.97651	−	23.4126i	−0.180398	−	0.848708i	0.791105	−	0.611681i	$-0.209506\pi$
$762$	0.612666	−	1.20243i	0.0221946	−	0.0435593i
$763$	−25.1637	−	5.80136i	−0.910989	−	0.210023i
$764$	29.8770	+	9.70763i	1.08091	+	0.351210i
$765$	−17.5138	+	14.5001i	−0.633214	+	0.524252i
$766$	−4.93269	+	23.2065i	−0.178225	+	0.838484i
$767$	7.69118	+	6.22819i	0.277712	+	0.224887i
$768$	−0.773701	−	0.207313i	−0.0279185	−	0.00748075i
$769$	−18.1484	+	13.1856i	−0.654450	+	0.475486i	−0.864784	−	0.502144i	$-0.832545\pi$
$769$	−18.1484	+	13.1856i	−0.654450	+	0.475486i	0.210334	+	0.977630i	$0.432545\pi$
$770$	−28.3158	−	35.4201i	−1.02043	−	1.27645i
$771$	−0.254149	−	0.184650i	−0.00915296	−	0.00665002i
$772$	17.4800	+	21.5860i	0.629119	+	0.776897i
$773$	0.888166	+	0.0465468i	0.0319451	+	0.00167417i	0.0683018	−	0.997665i	$-0.478242\pi$
$773$	0.888166	+	0.0465468i	0.0319451	+	0.00167417i	−0.0363567	+	0.999339i	$0.511575\pi$
$774$	−37.7472	−	21.7933i	−1.35679	−	0.783345i
$775$	−8.75082	+	20.8625i	−0.314339	+	0.749403i
$776$		−	0.675128i		−	0.0242357i
$777$	0.384374	−	1.11742i	0.0137893	−	0.0400872i
$778$	−1.60298	−	10.1208i	−0.0574696	−	0.362849i
$779$	−30.0298	−	3.15626i	−1.07593	−	0.113085i
$780$	0.769258	−	0.0893073i	0.0275438	−	0.00319771i
$781$	0.864075	+	8.22113i	0.0309190	+	0.294175i
$782$	10.1886	−	38.0244i	0.364344	−	1.35975i
$783$	0.0998239	−	0.630263i	0.00356742	−	0.0225238i
$784$	−18.6556	+	19.3422i	−0.666271	+	0.690793i
$785$	6.20087	−	6.33701i	0.221319	−	0.226178i
$786$	−1.10899	+	0.235723i	−0.0395563	+	0.00840795i
$787$	−6.24286	−	9.61316i	−0.222534	−	0.342672i	0.709716	−	0.704488i	$-0.248823\pi$
$787$	−6.24286	−	9.61316i	−0.222534	−	0.342672i	−0.932249	+	0.361816i	$0.882157\pi$
$788$	10.6946	+	16.4682i	0.380978	+	0.586655i
$789$	0.344981	−	0.0733280i	0.0122817	−	0.00261055i
$790$	−4.31035	+	29.2678i	−0.153355	+	1.04130i
$791$	−10.9232	−	5.80367i	−0.388385	−	0.206355i
$792$	−0.278530	+	1.75857i	−0.00989715	+	0.0624881i
$793$	−11.2069	+	41.8249i	−0.397970	+	1.48524i
$794$	6.29731	+	59.9149i	0.223483	+	2.12630i
$795$	−0.160141	+	0.795800i	−0.00567963	+	0.0282241i
$796$	28.8048	+	3.02750i	1.02096	+	0.107307i
$797$	−1.06473	−	6.72244i	−0.0377146	−	0.238121i	0.961629	−	0.274354i	$-0.0884641\pi$
$797$	−1.06473	−	6.72244i	−0.0377146	−	0.238121i	−0.999343	+	0.0362333i	$0.988464\pi$
$798$	1.05900	−	0.206187i	0.0374883	−	0.00729894i
$799$			31.6829i			1.12086i
$800$	39.1684	+	9.58861i	1.38481	+	0.339009i
$801$	−9.91786	−	5.72608i	−0.350430	−	0.202321i
$802$	−33.3178	−	1.74611i	−1.17649	−	0.0616573i
$803$	5.24477	+	6.47675i	0.185084	+	0.228560i
$804$	1.29216	+	0.938811i	0.0455711	+	0.0331093i
$805$	−1.99247	+	33.9347i	−0.0702254	+	1.19604i
$806$	−22.5971	+	16.4177i	−0.795948	+	0.578290i
$807$	−0.805018	−	0.215704i	−0.0283380	−	0.00759314i
$808$	−0.849634	−	0.688020i	−0.0298900	−	0.0242045i
$809$	4.20054	−	19.7620i	0.147683	−	0.694794i	−0.840537	−	0.541754i	$-0.817760\pi$
$809$	4.20054	−	19.7620i	0.147683	−	0.694794i	0.988220	−	0.153040i	$-0.0489063\pi$
$810$	−40.4356	+	2.55967i	−1.42076	+	0.0899377i
$811$	−44.8838	−	14.5836i	−1.57608	−	0.512101i	−0.615041	−	0.788495i	$-0.710860\pi$
$811$	−44.8838	−	14.5836i	−1.57608	−	0.512101i	−0.961044	+	0.276394i	$0.910860\pi$
$812$	2.40948	−	10.4513i	0.0845562	−	0.366768i
$813$	−0.111674	+	0.219173i	−0.00391658	+	0.00768673i
$814$	13.0528	+	61.4086i	0.457500	+	2.15237i
$815$	20.1833	−	13.4210i	0.706990	−	0.470117i
$816$	0.694749	+	0.147673i	0.0243211	+	0.00516960i
$817$	−9.55833	−	24.9003i	−0.334404	−	0.871151i
$818$	27.5572	−	27.5572i	0.963517	−	0.963517i
$819$	22.7764	−	8.29787i	0.795872	−	0.289951i
$820$	−36.1484	−	11.3129i	−1.26236	−	0.395063i
$821$	4.44023	−	42.2460i	0.154965	−	1.47439i	−0.590061	−	0.807359i	$-0.700896\pi$
$821$	4.44023	−	42.2460i	0.154965	−	1.47439i	0.745026	−	0.667036i	$-0.232437\pi$
$822$	1.91319	+	0.734405i	0.0667302	+	0.0256153i
$823$	−0.576213	+	10.9948i	−0.0200855	+	0.383255i	0.970029	+	0.242991i	$0.0781285\pi$
$823$	−0.576213	+	10.9948i	−0.0200855	+	0.383255i	−0.990114	+	0.140264i	$0.955205\pi$
$824$	0.754754	+	1.30727i	0.0262931	+	0.0455410i
$825$	0.139671	−	1.02551i	0.00486271	−	0.0357038i
$826$	12.0181	+	12.4375i	0.418165	+	0.432756i
$827$	−6.91433	−	13.5701i	−0.240435	−	0.471880i	0.738983	−	0.673724i	$-0.235307\pi$
$827$	−6.91433	−	13.5701i	−0.240435	−	0.471880i	−0.979418	+	0.201844i	$0.935307\pi$
$828$	27.8031	−	22.5145i	0.966224	−	0.782433i
$829$	22.8989	−	10.1953i	0.795312	−	0.354096i	0.0314750	−	0.999505i	$-0.489980\pi$
$829$	22.8989	−	10.1953i	0.795312	−	0.354096i	0.763837	+	0.645409i	$0.223313\pi$
$830$	30.6179	+	6.16135i	1.06276	+	0.213864i
$831$	0.125645	−	0.282203i	0.00435857	−	0.00978950i
$832$	18.6069	+	18.6069i	0.645078	+	0.645078i
$833$	15.5703	−	17.9339i	0.539480	−	0.621372i
$834$	−1.67638	+	0.544688i	−0.0580482	+	0.0188610i
$835$	26.2764	−	10.4153i	0.909331	−	0.360436i
$836$	−21.7031	+	19.5416i	−0.750617	+	0.675859i
$837$	−1.24096	+	0.805892i	−0.0428940	+	0.0278557i
$838$	−2.50027	−	47.7080i	−0.0863704	−	1.64805i
$839$	−5.42302	+	16.6903i	−0.187223	+	0.576214i	−0.999980	−	0.00638981i	$-0.997966\pi$
$839$	−5.42302	+	16.6903i	−0.187223	+	0.576214i	0.812756	+	0.582604i	$0.197966\pi$
$840$	0.0504893		0.000317463i	0.00174205		1.09535e-5i
$841$	7.78489	+	23.9594i	0.268445	+	0.826188i
$842$	0.626046	−	0.240316i	0.0215750	−	0.00828185i
$843$	−0.144920	−	0.540850i	−0.00499132	−	0.0186279i
$844$	9.03059	−	0.949153i	0.310846	−	0.0326712i
$845$	−7.50023	−	3.24220i	−0.258016	−	0.111535i
$846$	−33.2176	+	45.7201i	−1.14204	+	1.57189i
$847$	−8.95288	−	1.09648i	−0.307624	−	0.0376756i
$848$	−22.7715	+	11.6027i	−0.781978	+	0.398438i
$849$	−1.33608	+	0.771384i	−0.0458540	+	0.0264738i
$850$	−33.6538	−	6.39286i	−1.15432	−	0.219273i
$851$	23.5307	−	40.7564i	0.806623	−	1.39711i
$852$	−0.206907	−	0.134367i	−0.00708851	−	0.00460333i
$853$	−17.0873	+	2.70636i	−0.585057	+	0.0926639i	−0.441944	−	0.897043i	$-0.645711\pi$
$853$	−17.0873	+	2.70636i	−0.585057	+	0.0926639i	−0.143113	+	0.989706i	$0.545711\pi$
$854$	−28.3252	+	70.1695i	−0.969269	+	2.40115i
$855$	−20.2352	−	14.3686i	−0.692029	−	0.491397i
$856$	−0.473990	−	0.211034i	−0.0162006	−	0.00721299i
$857$	−29.2405	+	7.83496i	−0.998836	+	0.267637i	−0.720958	−	0.692979i	$-0.756298\pi$
$857$	−29.2405	+	7.83496i	−0.998836	+	0.267637i	−0.277878	+	0.960616i	$0.589631\pi$
$858$	0.804156	−	0.993050i	0.0274534	−	0.0339022i
$859$	−16.3706	+	18.1814i	−0.558558	+	0.620342i	−0.954600	−	0.297891i	$-0.903717\pi$
$859$	−16.3706	+	18.1814i	−0.558558	+	0.620342i	0.396042	+	0.918233i	$0.370384\pi$
$860$	−5.59240	−	32.9868i	−0.190699	−	1.12484i
$861$	1.17353	+	0.0816986i	0.0399938	+	0.00278428i
$862$	61.5156	+	31.3438i	2.09523	+	1.06757i
$863$	32.6665	−	1.71198i	1.11198	−	0.0582764i	0.512515	−	0.858678i	$-0.328714\pi$
$863$	32.6665	−	1.71198i	1.11198	−	0.0582764i	0.599464	+	0.800402i	$0.295380\pi$
$864$	1.76480	+	1.96001i	0.0600396	+	0.0666807i
$865$	−1.24443	+	29.9679i	−0.0423120	+	1.01894i
$866$	−5.47443	−	4.92920i	−0.186029	−	0.167501i
$867$	0.295613	+	0.0468206i	0.0100396	+	0.00159011i
$868$	−21.7483	+	12.0640i	−0.738185	+	0.409479i
$869$	14.6186	+	20.1208i	0.495902	+	0.682550i
$870$	0.413449	−	0.244729i	0.0140172	−	0.00829709i
$871$	17.5306	+	39.3743i	0.594001	+	1.33415i
$872$	−0.547433	+	1.42611i	−0.0185384	+	0.0482943i
$873$	7.04133	−	10.8427i	0.238313	−	0.366970i
$874$	42.9677			1.45340
$875$	29.5769	−	0.456374i	0.999881	−	0.0154282i
$876$	−0.248726			−0.00840366
$877$	2.01433	−	3.10180i	0.0680191	−	0.104740i	−0.803024	−	0.595946i	$-0.796777\pi$
$877$	2.01433	−	3.10180i	0.0680191	−	0.104740i	0.871043	+	0.491206i	$0.163444\pi$
$878$	−22.2211	+	57.8880i	−0.749926	+	1.95362i
$879$	−0.422907	−	0.949864i	−0.0142643	−	0.0320381i
$880$	28.0410	−	16.5980i	0.945263	−	0.559520i
$881$	13.7300	+	18.8977i	0.462575	+	0.636680i	0.975040	−	0.222028i	$-0.0712676\pi$
$881$	13.7300	+	18.8977i	0.462575	+	0.636680i	−0.512465	+	0.858708i	$0.671268\pi$
$882$	41.2713	−	9.55496i	1.38968	−	0.321732i
$883$	44.4188	+	7.03524i	1.49481	+	0.236755i	0.849672	−	0.527311i	$-0.176800\pi$
$883$	44.4188	+	7.03524i	1.49481	+	0.236755i	0.645139	+	0.764066i	$0.276800\pi$
$884$	−16.0136	−	14.4187i	−0.538595	−	0.484953i
$885$	−0.0163776	+	0.394399i	−0.000550527	+	0.0132576i
$886$	−8.74322	−	9.71033i	−0.293734	−	0.326225i
$887$	51.5648	−	2.70240i	1.73138	−	0.0907376i	0.839598	−	0.543208i	$-0.182791\pi$
$887$	51.5648	−	2.70240i	1.73138	−	0.0907376i	0.891779	+	0.452471i	$0.149457\pi$
$888$	−0.0622820	−	0.0317343i	−0.00209005	−	0.00106493i
$889$	29.1394	−	14.2233i	0.977305	−	0.477035i
$890$	−2.88393	−	17.0108i	−0.0966695	−	0.570205i
$891$	−22.7919	+	25.3129i	−0.763556	+	0.848015i
$892$	7.38613	−	9.12112i	0.247306	−	0.305398i
$893$	−33.4035	+	8.95044i	−1.11781	+	0.299515i
$894$	0.176750	+	0.0786941i	0.00591140	+	0.00263192i
$895$	9.83503	+	6.98367i	0.328749	+	0.233438i
$896$	2.03871	+	2.60778i	0.0681086	+	0.0871198i
$897$	−0.946083	+	0.149845i	−0.0315888	+	0.00500317i
$898$	−56.3189	−	36.5739i	−1.87938	−	1.22049i
$899$	−4.41450	+	7.64614i	−0.147232	+	0.255013i
$900$	−21.3286	−	22.6776i	−0.710955	−	0.755919i
$901$	19.5610	−	11.2935i	0.651670	−	0.376242i
$902$	−55.6864	+	28.3736i	−1.85415	+	0.944738i
$903$	0.406303	+	0.956373i	0.0135209	+	0.0318261i
$904$	−0.430076	+	0.591949i	−0.0143041	+	0.0196879i
$905$	43.4596	+	18.7867i	1.44465	+	0.624492i
$906$	0.164174	−	0.0172554i	0.00545432	−	0.000573272i
$907$	−0.506638	−	1.89080i	−0.0168226	−	0.0627830i	0.957004	−	0.290074i	$-0.0936799\pi$
$907$	−0.506638	−	1.89080i	−0.0168226	−	0.0627830i	−0.973827	+	0.227291i	$0.927013\pi$
$908$	32.0604	−	12.3068i	1.06396	−	0.408416i
$909$	−6.46952	−	19.9111i	−0.214580	−	0.660410i
$910$	31.5125	+	18.4589i	1.04463	+	0.611906i
$911$	12.2158	−	37.5963i	0.404726	−	1.24562i	−0.516397	−	0.856349i	$-0.672727\pi$
$911$	12.2158	−	37.5963i	0.404726	−	1.24562i	0.921124	−	0.389270i	$-0.127273\pi$
$912$	0.0405739	+	0.774195i	0.00134353	+	0.0256362i
$913$	22.0203	−	14.3002i	0.728767	−	0.473267i
$914$	41.6527	−	37.5042i	1.37775	−	1.24053i
$915$	−1.60555	+	0.636398i	−0.0530777	+	0.0210387i
$916$	−55.1811	+	17.9294i	−1.82324	+	0.592405i
$917$	−24.6927	−	11.5052i	−0.815425	−	0.379934i
$918$	−1.58426	−	1.58426i	−0.0522883	−	0.0522883i
$919$	1.55562	−	3.49397i	0.0513151	−	0.115256i	−0.886068	−	0.463554i	$-0.846574\pi$
$919$	1.55562	−	3.49397i	0.0513151	−	0.115256i	0.937384	+	0.348299i	$0.113241\pi$
$920$	1.97130	+	0.396692i	0.0649919	+	0.0130785i
$921$	−0.985624	+	0.438828i	−0.0324774	+	0.0144599i
$922$	9.25904	−	7.49782i	0.304930	−	0.246928i
$923$	−3.02241	−	5.93181i	−0.0994838	−	0.195248i
$924$	0.818199	−	0.790611i	0.0269168	−	0.0260092i
$925$	−36.8839	−	17.7952i	−1.21273	−	0.585103i
$926$	22.4514	+	38.8870i	0.737800	+	1.27791i
$927$	−1.51285	+	28.8669i	−0.0496885	+	0.948113i
$928$	14.6919	+	5.63971i	0.482287	+	0.185133i
$929$	−1.91707	+	18.2397i	−0.0628971	+	0.598426i	0.916995	+	0.398899i	$0.130607\pi$
$929$	−1.91707	+	18.2397i	−0.0628971	+	0.598426i	−0.979892	+	0.199528i	$0.936059\pi$
$930$	−1.06322	−	0.332743i	−0.0348645	−	0.0109111i
$931$	23.3064	+	11.3496i	0.763837	+	0.371967i
$932$	23.6662	−	23.6662i	0.775212	−	0.775212i
$933$	0.00348563	+	0.00908037i	0.000114114	+	0.000297278i
$934$	−25.9730	−	5.52073i	−0.849862	−	0.180644i
$935$	−23.9806	+	15.9461i	−0.784251	+	0.521492i
$936$	−0.298132	−	1.40260i	−0.00974475	−	0.0458454i
$937$	16.8884	−	33.1453i	0.551720	−	1.08281i	−0.431793	−	0.901973i	$-0.642119\pi$
$937$	16.8884	−	33.1453i	0.551720	−	1.08281i	0.983513	−	0.180838i	$-0.0578810\pi$
$938$	22.0441	+	72.0238i	0.719765	+	2.35166i
$939$	−0.712728	−	0.231579i	−0.0232590	−	0.00755731i
$940$	−43.2932	+	2.74057i	−1.41207	+	0.0893875i
$941$	3.62373	−	17.0483i	0.118130	−	0.555758i	−0.878781	−	0.477225i	$-0.841643\pi$
$941$	3.62373	−	17.0483i	0.118130	−	0.555758i	0.996911	−	0.0785338i	$-0.0250239\pi$
$942$	0.339307	+	0.274765i	0.0110552	+	0.00895234i
$943$	45.2536	+	12.1257i	1.47366	+	0.394866i
$944$	−10.0544	+	7.30493i	−0.327242	+	0.237755i
$945$	1.61592	+	1.06389i	0.0525658	+	0.0346085i
$946$	−44.6622	−	32.4490i	−1.45209	−	1.05501i
$947$	−14.9613	−	18.4756i	−0.486175	−	0.600377i	0.473741	−	0.880664i	$-0.342903\pi$
$947$	−14.9613	−	18.4756i	−0.486175	−	0.600377i	−0.959916	+	0.280288i	$0.909570\pi$
$948$	−0.741238	−	0.0388466i	−0.0240743	−	0.00126168i
$949$	−5.81265	−	3.35594i	−0.188687	−	0.108938i
$950$	−2.76718	−	37.2874i	−0.0897790	−	1.20976i
$951$		−	0.665616i		−	0.0215841i
$952$	−0.922020	−	1.06000i	−0.0298828	−	0.0343549i
$953$	4.35463	+	27.4941i	0.141060	+	0.890621i	0.952135	+	0.305678i	$0.0988830\pi$
$953$	4.35463	+	27.4941i	0.141060	+	0.890621i	−0.811075	+	0.584943i	$0.801117\pi$
$954$	40.0680	+	4.21132i	1.29725	+	0.136346i
$955$	−6.67043	+	33.1477i	−0.215850	+	1.07264i
$956$	3.27794	+	31.1875i	0.106016	+	1.00868i
$957$	0.104540	−	0.390148i	0.00337929	−	0.0126117i
$958$	−3.33174	+	21.0358i	−0.107644	+	0.679636i
$959$	26.1059	+	41.7496i	0.843002	+	1.34816i
$960$	−0.152922	+	1.03836i	−0.00493554	+	0.0335130i
$961$	−10.2971	+	2.18873i	−0.332166	+	0.0706041i
$962$	−27.5374	−	42.4039i	−0.887841	−	1.36716i
$963$	−5.41138	−	8.33279i	−0.174379	−	0.268520i
$964$	50.8105	−	10.8001i	1.63650	−	0.347848i
$965$	−20.9089	+	21.3679i	−0.673080	+	0.687858i
$966$	−1.67293	+	0.0589348i	−0.0538256	+	0.00189620i
$967$	2.80338	−	17.6999i	0.0901507	−	0.569189i	−0.900723	−	0.434394i	$-0.856962\pi$
$967$	2.80338	−	17.6999i	0.0901507	−	0.569189i	0.990874	−	0.134795i	$-0.0430376\pi$
$968$	−0.138094	+	0.515372i	−0.00443849	+	0.0165647i
$969$	−0.0716191	−	0.681410i	−0.00230074	−	0.0218901i
$970$	19.3478	−	2.24619i	0.621219	−	0.0721207i
$971$	−15.8054	−	1.66122i	−0.507221	−	0.0533110i	−0.152538	−	0.988298i	$-0.548745\pi$
$971$	−15.8054	−	1.66122i	−0.507221	−	0.0533110i	−0.354683	+	0.934987i	$0.615411\pi$
$972$	−0.477867	−	3.01714i	−0.0153276	−	0.0967747i
$973$	−40.0488	−	13.7762i	−1.28391	−	0.441643i
$974$		−	74.6937i		−	2.39334i
$975$	0.190964	+	0.811361i	0.00611576	+	0.0259843i
$976$	−47.0900	−	27.1874i	−1.50731	−	0.870249i
$977$	−5.44914	−	0.285577i	−0.174333	−	0.00913643i	−0.0350305	−	0.999386i	$-0.511153\pi$
$977$	−5.44914	−	0.285577i	−0.174333	−	0.00913643i	−0.139303	+	0.990250i	$0.544486\pi$
$978$	0.751150	+	0.927593i	0.0240191	+	0.0296612i
$979$	−11.7347	−	8.52579i	−0.375044	−	0.272486i
$980$	25.8526	+	19.7248i	0.825832	+	0.630087i
$981$	−23.6657	+	17.1942i	−0.755588	+	0.548967i
$982$	53.9384	+	14.4527i	1.72124	+	0.461206i
$983$	−16.3947	−	13.2762i	−0.522910	−	0.423444i	0.331182	−	0.943567i	$-0.392553\pi$
$983$	−16.3947	−	13.2762i	−0.522910	−	0.423444i	−0.854091	+	0.520123i	$0.825886\pi$
$984$	0.0144678	−	0.0680659i	0.000461218	−	0.00216986i
$985$	−16.2794	+	13.4781i	−0.518705	+	0.429447i
$986$	−12.7143	−	4.13111i	−0.404904	−	0.131561i
$987$	1.28828	−	0.394299i	0.0410063	−	0.0125507i
$988$	10.6779	−	20.9565i	0.339708	−	0.666715i
$989$	8.60404	+	40.4788i	0.273592	+	1.28715i
$990$	−51.3237	−	2.13124i	−1.63117	−	0.0677353i
$991$	3.91217	+	0.831558i	0.124274	+	0.0264153i	0.269629	−	0.962964i	$-0.413099\pi$
$991$	3.91217	+	0.831558i	0.124274	+	0.0264153i	−0.145355	+	0.989380i	$0.546432\pi$
$992$	−13.0774	−	34.0679i	−0.415209	−	1.08166i
$993$	0.331412	−	0.331412i	0.0105170	−	0.0105170i
$994$	−3.98256	−	10.9315i	−0.126319	−	0.346727i
$995$	0.338489	+	31.1722i	0.0107308	+	0.988225i
$996$	−0.0819093	+	0.779315i	−0.00259540	+	0.0246935i
$997$	2.65118	+	1.01769i	0.0839636	+	0.0322306i	0.399987	−	0.916521i	$-0.369015\pi$
$997$	2.65118	+	1.01769i	0.0839636	+	0.0322306i	−0.316024	+	0.948751i	$0.602348\pi$
$998$	3.64398	−	69.5313i	0.115348	−	2.20097i
$999$	−1.33924	−	2.31963i	−0.0423716	−	0.0733897i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	175.2.x.a.3.4	✓	288
5.2	odd	4		875.2.bb.b.507.4		288
5.3	odd	4		875.2.bb.a.507.15		288
5.4	even	2		875.2.bb.c.493.15		288
7.5	odd	6	inner	175.2.x.a.103.15	yes	288
25.6	even	5		875.2.bb.b.143.4		288
25.8	odd	20		875.2.bb.c.857.4		288
25.17	odd	20	inner	175.2.x.a.17.15	yes	288
25.19	even	10		875.2.bb.a.143.15		288
35.12	even	12		875.2.bb.b.257.4		288
35.19	odd	6		875.2.bb.c.243.4		288
35.33	even	12		875.2.bb.a.257.15		288
175.19	odd	30		875.2.bb.a.768.15		288
175.33	even	60		875.2.bb.c.607.15		288
175.117	even	60	inner	175.2.x.a.117.4	yes	288
175.131	odd	30		875.2.bb.b.768.4		288

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
175.2.x.a.3.4	✓	288	1.1	even	1	trivial
175.2.x.a.17.15	yes	288	25.17	odd	20	inner
175.2.x.a.103.15	yes	288	7.5	odd	6	inner
175.2.x.a.117.4	yes	288	175.117	even	60	inner
875.2.bb.a.143.15		288	25.19	even	10
875.2.bb.a.257.15		288	35.33	even	12
875.2.bb.a.507.15		288	5.3	odd	4
875.2.bb.a.768.15		288	175.19	odd	30
875.2.bb.b.143.4		288	25.6	even	5
875.2.bb.b.257.4		288	35.12	even	12
875.2.bb.b.507.4		288	5.2	odd	4
875.2.bb.b.768.4		288	175.131	odd	30
875.2.bb.c.243.4		288	35.19	odd	6
875.2.bb.c.493.15		288	5.4	even	2
875.2.bb.c.607.15		288	175.33	even	60
875.2.bb.c.857.4		288	25.8	odd	20

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 175 = 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	175.x (of order \(60\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.09978 + 1.69351i) q^{2} +(0.0195422 - 0.0509090i) q^{3} +(-0.844998 - 1.89790i) q^{4} +(1.92424 - 1.13899i) q^{5} +(0.0647231 + 0.0890837i) q^{6} +(-0.0453616 + 2.64536i) q^{7} +(0.154579 + 0.0244829i) q^{8} +(2.22722 + 2.00540i) q^{9} +(-0.187337 + 4.51137i) q^{10} +(2.53998 + 2.82093i) q^{11} +(-0.113133 + 0.00592906i) q^{12} +(-2.72389 - 1.38789i) q^{13} +(-4.43007 - 2.98614i) q^{14} +(-0.0203814 - 0.120220i) q^{15} +(2.56878 - 2.85292i) q^{16} +(-2.13519 + 2.63674i) q^{17} +(-5.84563 + 1.56633i) q^{18} +(-3.38312 - 1.50626i) q^{19} +(-3.78767 - 2.68956i) q^{20} +(0.133786 + 0.0540054i) q^{21} +(-7.57071 + 1.19908i) q^{22} +(4.81891 + 3.12944i) q^{23} +(0.00426721 - 0.00739102i) q^{24} +(2.40538 - 4.38339i) q^{25} +(5.34609 - 3.08657i) q^{26} +(0.291380 - 0.148466i) q^{27} +(5.05895 - 2.14923i) q^{28} +(1.14694 - 1.57863i) q^{29} +(0.226008 + 0.0976989i) q^{30} +(-4.49990 + 0.472959i) q^{31} +(2.08738 + 7.79020i) q^{32} +(0.193248 - 0.0741808i) q^{33} +(-2.11711 - 6.51580i) q^{34} +(2.92577 + 5.14197i) q^{35} +(1.92404 - 5.92160i) q^{36} +(-0.428655 - 8.17923i) q^{37} +(6.27156 - 4.07280i) q^{38} +(-0.123887 + 0.111548i) q^{39} +(0.325333 - 0.128954i) q^{40} +(7.75457 - 2.51961i) q^{41} +(-0.238595 + 0.167175i) q^{42} +(5.09273 + 5.09273i) q^{43} +(3.20756 - 7.20430i) q^{44} +(6.56985 + 1.32207i) q^{45} +(-10.5995 + 4.71920i) q^{46} +(7.25711 - 5.87669i) q^{47} +(-0.0950399 - 0.186526i) q^{48} +(-6.99588 - 0.239996i) q^{49} +(4.77794 + 8.89432i) q^{50} +(0.0925076 + 0.160228i) q^{51} +(-0.332392 + 6.34242i) q^{52} +(-6.21509 - 2.38575i) q^{53} +(-0.0690257 + 0.656736i) q^{54} +(8.10055 + 2.53512i) q^{55} +(-0.0717781 + 0.407807i) q^{56} +(-0.142796 + 0.142796i) q^{57} +(1.41205 + 3.67851i) q^{58} +(-3.16655 - 0.673070i) q^{59} +(-0.210942 + 0.140267i) q^{60} +(-2.94484 - 13.8544i) q^{61} +(4.14794 - 8.14080i) q^{62} +(-5.40605 + 5.80085i) q^{63} +(-8.18628 - 2.65988i) q^{64} +(-6.82221 + 0.431863i) q^{65} +(-0.0869038 + 0.408850i) q^{66} +(-10.9566 - 8.87250i) q^{67} +(6.80848 + 1.82433i) q^{68} +(0.253489 - 0.184170i) q^{69} +(-11.9257 - 0.700216i) q^{70} +(1.76180 + 1.28002i) q^{71} +(0.295184 + 0.364522i) q^{72} +(2.19250 + 0.114904i) q^{73} +(14.3231 + 8.26943i) q^{74} +(-0.176148 - 0.208117i) q^{75} +7.69359i q^{76} +(-7.57761 + 6.59120i) q^{77} +(-0.0526601 - 0.332483i) q^{78} +(6.51601 + 0.684861i) q^{79} +(1.69348 - 8.41552i) q^{80} +(0.937960 + 8.92409i) q^{81} +(-4.26133 + 15.9035i) q^{82} +(1.08205 - 6.83177i) q^{83} +(-0.0105526 - 0.299547i) q^{84} +(-1.10538 + 7.50568i) q^{85} +(-14.2255 + 3.02372i) q^{86} +(-0.0579529 - 0.0892396i) q^{87} +(0.323563 + 0.498243i) q^{88} +(-3.73767 + 0.794467i) q^{89} +(-9.46435 + 9.67214i) q^{90} +(3.79503 - 7.14272i) q^{91} +(1.86738 - 11.7902i) q^{92} +(-0.0638599 + 0.238328i) q^{93} +(1.97103 + 18.7531i) q^{94} +(-8.22555 + 0.954948i) q^{95} +(0.437383 + 0.0459708i) q^{96} +(-0.674820 - 4.26064i) q^{97} +(8.10037 - 11.5837i) q^{98} +11.3765i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 288 q - 8 q^{2} - 24 q^{3} - 10 q^{4} - 30 q^{5} - 10 q^{7} - 36 q^{8} - 10 q^{9} - 36 q^{10} - 6 q^{11} - 36 q^{12} - 20 q^{14} - 28 q^{15} - 30 q^{16} - 42 q^{17} - 14 q^{18} - 30 q^{19} - 12 q^{21} + 32 q^{22}+ \cdots + 222 q^{98}+O(q^{100}) \) 288 * q - 8 * q^2 - 24 * q^3 - 10 * q^4 - 30 * q^5 - 10 * q^7 - 36 * q^8 - 10 * q^9 - 36 * q^10 - 6 * q^11 - 36 * q^12 - 20 * q^14 - 28 * q^15 - 30 * q^16 - 42 * q^17 - 14 * q^18 - 30 * q^19 - 12 * q^21 + 32 * q^22 - 40 * q^23 + 2 * q^25 - 48 * q^26 + 22 * q^28 - 58 * q^30 - 18 * q^31 + 8 * q^32 - 30 * q^33 - 2 * q^35 + 40 * q^36 - 10 * q^37 + 72 * q^38 + 30 * q^39 - 48 * q^40 + 6 * q^42 - 108 * q^43 - 10 * q^44 + 186 * q^45 - 6 * q^46 - 54 * q^47 - 248 * q^50 - 16 * q^51 + 216 * q^52 + 50 * q^53 - 30 * q^54 + 4 * q^56 - 216 * q^57 - 4 * q^58 + 90 * q^59 + 96 * q^60 - 18 * q^61 - 66 * q^63 - 100 * q^64 + 14 * q^65 - 90 * q^66 + 4 * q^67 + 342 * q^68 - 60 * q^70 - 24 * q^71 + 58 * q^72 - 6 * q^73 + 216 * q^75 - 80 * q^77 - 132 * q^78 - 10 * q^79 - 6 * q^80 - 10 * q^81 + 216 * q^82 + 20 * q^84 - 48 * q^85 - 6 * q^86 - 48 * q^87 - 122 * q^88 + 120 * q^89 - 12 * q^91 - 4 * q^92 + 106 * q^93 - 30 * q^94 - 98 * q^95 - 90 * q^96 + 222 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more