LMFDB - Embedded newform 968.2.o.d.493.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [968,2,Mod(245,968)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(968, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 5, 8]))

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

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

chi := DirichletCharacter("968.245");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 968 = 2^{3} \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	968.o (of order $10$, degree $4$, not 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:	$7.72951891566$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$10$ over $\Q(\zeta_{10})$
Twist minimal:	no (minimal twist has level 88)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			493.5
Character	$\chi$	$=$	968.493
Dual form			968.2.o.d.269.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.227030 + 1.39587i) q^{2} +(0.510574 + 0.702745i) q^{3} +(-1.89691 - 0.633809i) q^{4} +(-3.49435 + 1.13538i) q^{5} +(-1.09686 + 0.553152i) q^{6} +(-0.967003 - 0.702569i) q^{7} +(1.31537 - 2.50396i) q^{8} +(0.693886 - 2.13556i) q^{9} +(-0.791527 - 5.13543i) q^{10} +(-0.523110 - 1.65665i) q^{12} +(-3.78569 - 1.23005i) q^{13} +(1.20023 - 1.19031i) q^{14} +(-2.58201 - 1.87594i) q^{15} +(3.19657 + 2.40456i) q^{16} +(0.982622 + 3.02420i) q^{17} +(2.82344 + 1.45341i) q^{18} +(2.53106 + 3.48370i) q^{19} +(7.34810 + 0.0610261i) q^{20} -1.03827i q^{21} +2.46096 q^{23} +(2.43124 - 0.354084i) q^{24} +(6.87629 - 4.99592i) q^{25} +(2.57645 - 5.00509i) q^{26} +(4.33342 - 1.40801i) q^{27} +(1.38903 + 1.94561i) q^{28} +(2.25727 - 3.10687i) q^{29} +(3.20476 - 3.17826i) q^{30} +(2.82708 - 8.70085i) q^{31} +(-4.08218 + 3.91610i) q^{32} +(-4.44448 + 0.685031i) q^{34} +(4.17673 + 1.35710i) q^{35} +(-2.66978 + 3.61119i) q^{36} +(3.13311 - 4.31236i) q^{37} +(-5.43743 + 2.74213i) q^{38} +(-1.06847 - 3.28841i) q^{39} +(-1.75342 + 10.2431i) q^{40} +(0.431229 - 0.313306i) q^{41} +(1.44929 + 0.235718i) q^{42} +6.51729i q^{43} +8.25022i q^{45} +(-0.558711 + 3.43518i) q^{46} +(-0.290335 + 0.210940i) q^{47} +(-0.0577087 + 3.47409i) q^{48} +(-1.72163 - 5.29862i) q^{49} +(5.41254 + 10.7326i) q^{50} +(-1.62354 + 2.23461i) q^{51} +(6.40153 + 4.73270i) q^{52} +(2.30524 + 0.749017i) q^{53} +(0.981589 + 6.36855i) q^{54} +(-3.03117 + 1.49719i) q^{56} +(-1.15586 + 3.55738i) q^{57} +(3.82432 + 3.85621i) q^{58} +(-0.350132 + 0.481916i) q^{59} +(3.70886 + 5.19500i) q^{60} +(-6.93255 + 2.25252i) q^{61} +(11.5034 + 5.92159i) q^{62} +(-2.17137 + 1.57759i) q^{63} +(-4.53959 - 6.58727i) q^{64} +14.6251 q^{65} -11.2692i q^{67} +(0.0528154 - 6.35945i) q^{68} +(1.25650 + 1.72943i) q^{69} +(-2.84258 + 5.52207i) q^{70} +(1.72651 + 5.31364i) q^{71} +(-4.43463 - 4.54652i) q^{72} +(-2.16144 - 1.57038i) q^{73} +(5.30819 + 5.35246i) q^{74} +(7.02172 + 2.28149i) q^{75} +(-2.59320 - 8.21250i) q^{76} +(4.83277 - 0.744878i) q^{78} +(3.55369 - 10.9371i) q^{79} +(-13.9000 - 4.77305i) q^{80} +(-2.24785 - 1.63316i) q^{81} +(0.339433 + 0.673070i) q^{82} +(0.953750 - 0.309892i) q^{83} +(-0.658065 + 1.96951i) q^{84} +(-6.86725 - 9.45196i) q^{85} +(-9.09731 - 1.47962i) q^{86} +3.33584 q^{87} +13.6469 q^{89} +(-11.5163 - 1.87305i) q^{90} +(2.79658 + 3.84917i) q^{91} +(-4.66823 - 1.55978i) q^{92} +(7.55791 - 2.45571i) q^{93} +(-0.228531 - 0.453160i) q^{94} +(-12.7997 - 9.29955i) q^{95} +(-4.83627 - 0.869275i) q^{96} +(-1.83886 + 5.65943i) q^{97} +(7.78706 - 1.20022i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 5 q^{2} - q^{4} - 8 q^{6} - 5 q^{8} + 10 q^{9} + 20 q^{10} - 6 q^{12} + 2 q^{14} + 22 q^{15} - 25 q^{16} - 4 q^{17} - 25 q^{18} + 8 q^{20} - 8 q^{23} + 40 q^{24} + 6 q^{25} - 20 q^{26} + 18 q^{28}+ \cdots + 144 q^{98}+O(q^{100}) $ 40 * q - 5 * q^2 - q^4 - 8 * q^6 - 5 * q^8 + 10 * q^9 + 20 * q^10 - 6 * q^12 + 2 * q^14 + 22 * q^15 - 25 * q^16 - 4 * q^17 - 25 * q^18 + 8 * q^20 - 8 * q^23 + 40 * q^24 + 6 * q^25 - 20 * q^26 + 18 * q^28 - 12 * q^30 + 4 * q^31 - 20 * q^32 + 10 * q^34 - 27 * q^36 - 33 * q^38 - 6 * q^39 + 20 * q^40 - 16 * q^41 - 20 * q^42 + 42 * q^46 + 4 * q^47 + 23 * q^48 + 6 * q^49 + 39 * q^50 - 108 * q^54 - 32 * q^56 - 4 * q^57 - 16 * q^58 + 94 * q^60 + 52 * q^62 + 30 * q^63 + 11 * q^64 + 36 * q^65 - 63 * q^68 + 52 * q^70 + 12 * q^71 - 44 * q^72 - 4 * q^73 + 26 * q^74 + 134 * q^76 - 12 * q^78 + 16 * q^79 + 16 * q^80 + 16 * q^81 + 54 * q^82 - 72 * q^84 - 10 * q^86 - 68 * q^87 - 16 * q^89 - 126 * q^90 - 64 * q^92 - 40 * q^94 - 26 * q^95 + 5 * q^96 - 20 * q^97 + 144 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/968\mathbb{Z}\right)^\times$.

$n$	$485$	$727$	$849$
$\chi(n)$	$-1$	$1$	$e\left(\frac{3}{5}\right)$

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 $

$2$	−0.227030	+	1.39587i	−0.160534	+	0.987030i
$2$	−0.227030	+	1.39587i	−0.160534	+	0.987030i
$3$	0.510574	+	0.702745i	0.294780	+	0.405730i	0.930559	−	0.366141i	$-0.119321\pi$
$3$	0.510574	+	0.702745i	0.294780	+	0.405730i	−0.635779	+	0.771871i	$0.719321\pi$
$4$	−1.89691	−	0.633809i	−0.948457	−	0.316905i
$5$	−3.49435	+	1.13538i	−1.56272	+	0.507759i	−0.957533	−	0.288325i	$-0.906902\pi$
$5$	−3.49435	+	1.13538i	−1.56272	+	0.507759i	−0.605187	+	0.796083i	$0.706902\pi$
$6$	−1.09686	+	0.553152i	−0.447790	+	0.225823i
$7$	−0.967003	−	0.702569i	−0.365493	−	0.265546i	0.389847	−	0.920880i	$-0.372528\pi$
$7$	−0.967003	−	0.702569i	−0.365493	−	0.265546i	−0.755339	+	0.655334i	$0.772528\pi$
$8$	1.31537	−	2.50396i	0.465054	−	0.885282i
$9$	0.693886	−	2.13556i	0.231295	−	0.711854i
$10$	−0.791527	−	5.13543i	−0.250303	−	1.62396i
$11$		0			0
$11$		0			0
$12$	−0.523110	−	1.65665i	−0.151009	−	0.478235i
$13$	−3.78569	−	1.23005i	−1.04996	−	0.341154i	−0.267309	−	0.963611i	$-0.586134\pi$
$13$	−3.78569	−	1.23005i	−1.04996	−	0.341154i	−0.782654	+	0.622457i	$0.786134\pi$
$14$	1.20023	−	1.19031i	0.320776	−	0.318123i
$15$	−2.58201	−	1.87594i	−0.666672	−	0.484366i
$16$	3.19657	+	2.40456i	0.799143	+	0.601141i
$17$	0.982622	+	3.02420i	0.238321	+	0.733476i	0.996664	+	0.0816201i	$0.0260094\pi$
$17$	0.982622	+	3.02420i	0.238321	+	0.733476i	−0.758343	+	0.651856i	$0.773991\pi$
$18$	2.82344	+	1.45341i	0.665491	+	0.342573i
$19$	2.53106	+	3.48370i	0.580665	+	0.799216i	0.993768	−	0.111468i	$-0.0355552\pi$
$19$	2.53106	+	3.48370i	0.580665	+	0.799216i	−0.413103	+	0.910684i	$0.635555\pi$
$20$	7.34810	+	0.0610261i	1.64308	+	0.0136459i
$21$		−	1.03827i		−	0.226569i
$22$		0			0
$23$	2.46096			0.513145			0.256573	−	0.966525i	$-0.417407\pi$
$23$	2.46096			0.513145			0.256573	+	0.966525i	$0.417407\pi$
$24$	2.43124	−	0.354084i	0.496275	−	0.0722770i
$25$	6.87629	−	4.99592i	1.37526	−	0.999184i
$26$	2.57645	−	5.00509i	0.505284	−	0.981578i
$27$	4.33342	−	1.40801i	0.833967	−	0.270972i
$28$	1.38903	+	1.94561i	0.262501	+	0.367685i
$29$	2.25727	−	3.10687i	0.419165	−	0.576931i	−0.546259	−	0.837616i	$-0.683949\pi$
$29$	2.25727	−	3.10687i	0.419165	−	0.576931i	0.965424	+	0.260686i	$0.0839486\pi$
$30$	3.20476	−	3.17826i	0.585107	−	0.580268i
$31$	2.82708	−	8.70085i	0.507758	−	1.56272i	−0.288326	−	0.957532i	$-0.593099\pi$
$31$	2.82708	−	8.70085i	0.507758	−	1.56272i	0.796084	−	0.605186i	$-0.206901\pi$
$32$	−4.08218	+	3.91610i	−0.721634	+	0.692274i
$33$		0			0
$34$	−4.44448	+	0.685031i	−0.762222	+	0.117482i
$35$	4.17673	+	1.35710i	0.705996	+	0.229392i
$36$	−2.66978	+	3.61119i	−0.444964	+	0.601865i
$37$	3.13311	−	4.31236i	0.515080	−	0.708947i	−0.469685	−	0.882834i	$-0.655633\pi$
$37$	3.13311	−	4.31236i	0.515080	−	0.708947i	0.984766	+	0.173887i	$0.0556326\pi$
$38$	−5.43743	+	2.74213i	−0.882067	+	0.444832i
$39$	−1.06847	−	3.28841i	−0.171092	−	0.526567i
$40$	−1.75342	+	10.2431i	−0.277240	+	1.61958i
$41$	0.431229	−	0.313306i	0.0673466	−	0.0489302i	−0.553603	−	0.832781i	$-0.686747\pi$
$41$	0.431229	−	0.313306i	0.0673466	−	0.0489302i	0.620949	+	0.783851i	$0.286747\pi$
$42$	1.44929	+	0.235718i	0.223631	+	0.0363721i
$43$			6.51729i			0.993878i	0.867785	+	0.496939i	$0.165543\pi$
$43$			6.51729i			0.993878i	−0.867785	+	0.496939i	$0.834457\pi$
$44$		0			0
$45$			8.25022i			1.22987i
$46$	−0.558711	+	3.43518i	−0.0823775	+	0.506490i
$47$	−0.290335	+	0.210940i	−0.0423497	+	0.0307688i	−0.608759	−	0.793355i	$-0.708332\pi$
$47$	−0.290335	+	0.210940i	−0.0423497	+	0.0307688i	0.566409	+	0.824124i	$0.308332\pi$
$48$	−0.0577087	+	3.47409i	−0.00832953	+	0.501441i
$49$	−1.72163	−	5.29862i	−0.245947	−	0.756946i
$50$	5.41254	+	10.7326i	0.765448	+	1.51782i
$51$	−1.62354	+	2.23461i	−0.227341	+	0.312908i
$52$	6.40153	+	4.73270i	0.887732	+	0.656308i
$53$	2.30524	+	0.749017i	0.316649	+	0.102885i	0.463029	−	0.886343i	$-0.346762\pi$
$53$	2.30524	+	0.749017i	0.316649	+	0.102885i	−0.146381	+	0.989228i	$0.546762\pi$
$54$	0.981589	+	6.36855i	0.133577	+	0.866651i
$55$		0			0
$56$	−3.03117	+	1.49719i	−0.405057	+	0.200071i
$57$	−1.15586	+	3.55738i	−0.153098	+	0.471186i
$58$	3.82432	+	3.85621i	0.502158	+	0.506345i
$59$	−0.350132	+	0.481916i	−0.0455833	+	0.0627401i	−0.831200	−	0.555973i	$-0.812346\pi$
$59$	−0.350132	+	0.481916i	−0.0455833	+	0.0627401i	0.785617	+	0.618713i	$0.212346\pi$
$60$	3.70886	+	5.19500i	0.478812	+	0.670672i
$61$	−6.93255	+	2.25252i	−0.887622	+	0.288406i	−0.717118	−	0.696951i	$-0.754539\pi$
$61$	−6.93255	+	2.25252i	−0.887622	+	0.288406i	−0.170503	+	0.985357i	$0.554539\pi$
$62$	11.5034	+	5.92159i	1.46094	+	0.752042i
$63$	−2.17137	+	1.57759i	−0.273567	+	0.198758i
$64$	−4.53959	−	6.58727i	−0.567449	−	0.823409i
$65$	14.6251			1.81402
$66$		0			0
$67$		−	11.2692i		−	1.37675i	−0.725353	−	0.688377i	$-0.758323\pi$
$67$		−	11.2692i		−	1.37675i	0.725353	−	0.688377i	$-0.241677\pi$
$68$	0.0528154	−	6.35945i	0.00640480	−	0.771196i
$69$	1.25650	+	1.72943i	0.151265	+	0.208199i
$70$	−2.84258	+	5.52207i	−0.339753	+	0.660014i
$71$	1.72651	+	5.31364i	0.204899	+	0.630613i	0.999718	+	0.0237665i	$0.00756584\pi$
$71$	1.72651	+	5.31364i	0.204899	+	0.630613i	−0.794819	+	0.606847i	$0.792434\pi$
$72$	−4.43463	−	4.54652i	−0.522627	−	0.535813i
$73$	−2.16144	−	1.57038i	−0.252978	−	0.183799i	0.454068	−	0.890967i	$-0.349972\pi$
$73$	−2.16144	−	1.57038i	−0.252978	−	0.183799i	−0.707045	+	0.707168i	$0.749972\pi$
$74$	5.30819	+	5.35246i	0.617064	+	0.622210i
$75$	7.02172	+	2.28149i	0.810798	+	0.263444i
$76$	−2.59320	−	8.21250i	−0.297460	−	0.942038i
$77$		0			0
$78$	4.83277	−	0.744878i	0.547204	−	0.0843408i
$79$	3.55369	−	10.9371i	0.399822	−	1.23053i	−0.525320	−	0.850905i	$-0.676055\pi$
$79$	3.55369	−	10.9371i	0.399822	−	1.23053i	0.925142	−	0.379621i	$-0.123945\pi$
$80$	−13.9000	−	4.77305i	−1.55407	−	0.533644i
$81$	−2.24785	−	1.63316i	−0.249761	−	0.181462i
$82$	0.339433	+	0.673070i	0.0374841	+	0.0743281i
$83$	0.953750	−	0.309892i	0.104688	−	0.0340151i	−0.256205	−	0.966623i	$-0.582472\pi$
$83$	0.953750	−	0.309892i	0.104688	−	0.0340151i	0.360892	+	0.932607i	$0.382472\pi$
$84$	−0.658065	+	1.96951i	−0.0718008	+	0.214891i
$85$	−6.86725	−	9.45196i	−0.744858	−	1.02521i
$86$	−9.09731	−	1.47962i	−0.980988	−	0.159552i
$87$	3.33584			0.357640
$88$		0			0
$89$	13.6469			1.44657			0.723283	−	0.690551i	$-0.242632\pi$
$89$	13.6469			1.44657			0.723283	+	0.690551i	$0.242632\pi$
$90$	−11.5163	−	1.87305i	−1.21392	−	0.197437i
$91$	2.79658	+	3.84917i	0.293162	+	0.403502i
$92$	−4.66823	−	1.55978i	−0.486697	−	0.162618i
$93$	7.55791	−	2.45571i	0.783719	−	0.254646i
$94$	−0.228531	−	0.453160i	−0.0235712	−	0.0467399i
$95$	−12.7997	−	9.29955i	−1.31323	−	0.954114i
$96$	−4.83627	−	0.869275i	−0.493600	−	0.0887200i
$97$	−1.83886	+	5.65943i	−0.186708	+	0.574628i	−0.999974	−	0.00726443i	$-0.997688\pi$
$97$	−1.83886	+	5.65943i	−0.186708	+	0.574628i	0.813266	+	0.581893i	$0.197688\pi$
$98$	7.78706	−	1.20022i	0.786612	−	0.121241i
$99$		0			0
$100$	−16.2102	+	5.11857i	−1.62102	+	0.511857i
$101$	5.68268	+	1.84641i	0.565448	+	0.183725i	0.577771	−	0.816199i	$-0.303923\pi$
$101$	5.68268	+	1.84641i	0.565448	+	0.183725i	−0.0123233	+	0.999924i	$0.503923\pi$
$102$	−2.75064	−	2.77358i	−0.272354	−	0.274625i
$103$	3.17591	+	2.30743i	0.312932	+	0.227358i	0.733153	−	0.680063i	$-0.238048\pi$
$103$	3.17591	+	2.30743i	0.312932	+	0.227358i	−0.420222	+	0.907421i	$0.638048\pi$
$104$	−8.05958	+	7.86124i	−0.790307	+	0.770858i
$105$	1.17883	+	3.62808i	0.115042	+	0.354064i
$106$	−1.56889	+	3.04776i	−0.152384	+	0.296025i
$107$	−7.53003	−	10.3642i	−0.727955	−	1.00194i	−0.999222	−	0.0394404i	$-0.987442\pi$
$107$	−7.53003	−	10.3642i	−0.727955	−	1.00194i	0.271266	−	0.962504i	$-0.412558\pi$
$108$	−9.11253	−	0.0756798i	−0.876854	−	0.00728229i
$109$			5.65346i			0.541504i	0.962649	+	0.270752i	$0.0872723\pi$
$109$			5.65346i			0.541504i	−0.962649	+	0.270752i	$0.912728\pi$
$110$		0			0
$111$	4.63018			0.439477
$112$	−1.40172	−	4.57103i	−0.132450	−	0.431922i
$113$	12.9433	−	9.40385i	1.21760	−	0.884640i	0.221704	−	0.975114i	$-0.428838\pi$
$113$	12.9433	−	9.40385i	1.21760	−	0.884640i	0.995899	+	0.0904741i	$0.0288382\pi$
$114$	−4.70323	−	2.42107i	−0.440498	−	0.226754i
$115$	−8.59945	+	2.79413i	−0.801903	+	0.260554i
$116$	−6.25101	+	4.46278i	−0.580392	+	0.414359i
$117$	−5.25368	+	7.23107i	−0.485703	+	0.668513i
$118$	−0.593202	−	0.598149i	−0.0546086	−	0.0550641i
$119$	1.17451	−	3.61477i	0.107667	−	0.331365i
$120$	−8.09358	+	3.99768i	−0.738839	+	0.364936i
$121$		0			0
$122$	−1.57033	−	10.1883i	−0.142171	−	0.922408i
$123$	0.440349	+	0.143078i	0.0397049	+	0.0129009i
$124$	−10.8774	+	14.7129i	−0.976819	+	1.32126i
$125$	−7.55775	+	10.4024i	−0.675986	+	0.930414i
$126$	−1.70915	−	3.38911i	−0.152263	−	0.301926i
$127$	−2.86054	−	8.80385i	−0.253832	−	0.781215i	−0.994058	−	0.108856i	$-0.965281\pi$
$127$	−2.86054	−	8.80385i	−0.253832	−	0.781215i	0.740225	−	0.672359i	$-0.234719\pi$
$128$	10.2256	−	4.84118i	0.903824	−	0.427904i
$129$	−4.58000	+	3.32756i	−0.403246	+	0.292976i
$130$	−3.32034	+	20.4148i	−0.291213	+	1.79049i
$131$		−	13.3281i		−	1.16448i	−0.813016	−	0.582241i	$-0.802176\pi$
$131$		−	13.3281i		−	1.16448i	0.813016	−	0.582241i	$-0.197824\pi$
$132$		0			0
$133$		−	5.14699i		−	0.446301i
$134$	15.7304	+	2.55845i	1.35890	+	0.221016i
$135$	−13.5438	+	9.84017i	−1.16567	+	0.846907i
$136$	8.86498	+	1.51751i	0.760166	+	0.130125i
$137$	−3.00021	−	9.23371i	−0.256325	−	0.788889i	−0.993566	−	0.113258i	$-0.963871\pi$
$137$	−3.00021	−	9.23371i	−0.256325	−	0.788889i	0.737240	−	0.675631i	$-0.236129\pi$
$138$	−2.69932	+	1.36128i	−0.229782	+	0.115880i
$139$	13.0811	−	18.0046i	1.10953	−	1.52713i	0.287418	−	0.957805i	$-0.407203\pi$
$139$	13.0811	−	18.0046i	1.10953	−	1.52713i	0.822110	−	0.569329i	$-0.192797\pi$
$140$	−7.06275	−	5.22155i	−0.596912	−	0.441302i
$141$	−0.296475	−	0.0963305i	−0.0249677	−	0.00811249i
$142$	−7.80913	+	1.20363i	−0.655328	+	0.101006i
$143$		0			0
$144$	7.35315	−	5.15798i	0.612763	−	0.429832i
$145$	−4.36021	+	13.4193i	−0.362096	+	1.11442i
$146$	2.68276	−	2.66057i	0.222027	−	0.220190i
$147$	2.84456	−	3.91521i	0.234616	−	0.322921i
$148$	−8.67646	+	6.19438i	−0.713200	+	0.509175i
$149$	11.9845	−	3.89401i	0.981811	−	0.319010i	0.226237	−	0.974072i	$-0.427358\pi$
$149$	11.9845	−	3.89401i	0.981811	−	0.319010i	0.755575	+	0.655062i	$0.227358\pi$
$150$	−4.77881	+	9.28345i	−0.390188	+	0.757990i
$151$	−12.2699	+	8.91459i	−0.998509	+	0.725459i	−0.961768	−	0.273866i	$-0.911698\pi$
$151$	−12.2699	+	8.91459i	−0.998509	+	0.725459i	−0.0367411	+	0.999325i	$0.511698\pi$
$152$	12.0523	−	1.75529i	0.977572	−	0.142373i
$153$	7.14020			0.577251
$154$		0			0
$155$			33.6136i			2.69991i
$156$	−0.0574296	+	6.91504i	−0.00459805	+	0.553646i
$157$	−0.897329	−	1.23507i	−0.0716147	−	0.0985691i	0.771707	−	0.635978i	$-0.219403\pi$
$157$	−0.897329	−	1.23507i	−0.0716147	−	0.0985691i	−0.843322	+	0.537409i	$0.819403\pi$
$158$	14.4601	+	7.44356i	1.15038	+	0.592178i
$159$	0.650627	+	2.00242i	0.0515980	+	0.158802i
$160$	9.81829	−	18.3190i	0.776204	−	1.44825i
$161$	−2.37975	−	1.72899i	−0.187551	−	0.136264i
$162$	2.79000	−	2.76693i	0.219203	−	0.217390i
$163$	−14.7758	−	4.80095i	−1.15733	−	0.376039i	−0.333430	−	0.942775i	$-0.608206\pi$
$163$	−14.7758	−	4.80095i	−1.15733	−	0.376039i	−0.823900	+	0.566735i	$0.808206\pi$
$164$	−1.01658	+	0.320998i	−0.0793816	+	0.0250657i
$165$		0			0
$166$	0.216040	+	1.40167i	0.0167679	+	0.108791i
$167$	2.59371	−	7.98263i	0.200707	−	0.617714i	−0.799155	−	0.601125i	$-0.794719\pi$
$167$	2.59371	−	7.98263i	0.200707	−	0.617714i	0.999862	−	0.0165890i	$-0.00528067\pi$
$168$	−2.59978	−	1.36571i	−0.200578	−	0.105367i
$169$	2.30125	+	1.67195i	0.177019	+	0.128612i
$170$	14.7528	−	7.43992i	1.13149	−	0.570616i
$171$	9.19593	−	2.98794i	0.703230	−	0.228493i
$172$	4.13072	−	12.3628i	0.314965	−	0.942651i
$173$	14.6137	+	20.1141i	1.11106	+	1.52925i	0.819843	+	0.572589i	$0.194061\pi$
$173$	14.6137	+	20.1141i	1.11106	+	1.52925i	0.291219	+	0.956656i	$0.405939\pi$
$174$	−0.757336	+	4.65641i	−0.0574135	+	0.353001i
$175$	−10.1594			−0.767976
$176$		0			0
$177$	−0.517432			−0.0388926
$178$	−3.09825	+	19.0493i	−0.232224	+	1.42781i
$179$	−9.69021	−	13.3374i	−0.724280	−	0.996886i	−0.999371	−	0.0354679i	$-0.988708\pi$
$179$	−9.69021	−	13.3374i	−0.724280	−	0.996886i	0.275091	−	0.961418i	$-0.411292\pi$
$180$	5.22907	−	15.6500i	0.389752	−	1.16648i
$181$	8.72980	−	2.83648i	0.648881	−	0.210834i	0.0339603	−	0.999423i	$-0.489188\pi$
$181$	8.72980	−	2.83648i	0.648881	−	0.210834i	0.614921	+	0.788589i	$0.289188\pi$
$182$	−6.00785	+	3.02980i	−0.445332	+	0.224583i
$183$	−5.12253	−	3.72174i	−0.378668	−	0.275119i
$184$	3.23708	−	6.16213i	0.238641	−	0.454278i
$185$	−6.05201	+	18.6262i	−0.444952	+	1.36942i
$186$	1.71199	+	11.1074i	0.125529	+	0.814434i
$187$		0			0
$188$	0.684436	−	0.216119i	0.0499176	−	0.0157621i
$189$	−5.17965	−	1.68297i	−0.376764	−	0.122418i
$190$	15.8869	−	15.7555i	1.15256	−	1.14302i
$191$	1.99813	+	1.45172i	0.144579	+	0.105043i	0.657724	−	0.753259i	$-0.271519\pi$
$191$	1.99813	+	1.45172i	0.144579	+	0.105043i	−0.513144	+	0.858302i	$0.671519\pi$
$192$	2.31138	−	6.55347i	0.166809	−	0.472956i
$193$	3.09207	+	9.51643i	0.222572	+	0.685007i	0.998529	+	0.0542210i	$0.0172675\pi$
$193$	3.09207	+	9.51643i	0.222572	+	0.685007i	−0.775957	+	0.630786i	$0.782732\pi$
$194$	−7.48236	−	3.85167i	−0.537202	−	0.276534i
$195$	7.46721	+	10.2777i	0.534738	+	0.736003i
$196$	−0.0925364	+	11.1422i	−0.00660974	+	0.795873i
$197$			11.7936i			0.840260i	0.907464	+	0.420130i	$0.138015\pi$
$197$			11.7936i			0.840260i	−0.907464	+	0.420130i	$0.861985\pi$
$198$		0			0
$199$	−14.7867			−1.04820			−0.524101	−	0.851656i	$-0.675598\pi$
$199$	−14.7867			−1.04820			−0.524101	+	0.851656i	$0.675598\pi$
$200$	−3.46467	−	23.7894i	−0.244989	−	1.68217i
$201$	7.91939	−	5.75378i	0.558591	−	0.405840i
$202$	−3.86750	+	7.51310i	−0.272116	+	0.528620i
$203$	−4.36557	+	1.41846i	−0.306403	+	0.0995565i
$204$	4.49604	−	3.20985i	0.314786	−	0.224735i
$205$	−1.15114	+	1.58441i	−0.0803992	+	0.110660i
$206$	−3.94191	+	3.90930i	−0.274646	+	0.272374i
$207$	1.70763	−	5.25553i	0.118688	−	0.365285i
$208$	−9.14352	−	13.0349i	−0.633989	−	0.903806i
$209$		0			0
$210$	−5.33196	+	0.821819i	−0.367940	+	0.0567109i
$211$	−8.08990	−	2.62857i	−0.556932	−	0.180958i	0.0170085	−	0.999855i	$-0.494586\pi$
$211$	−8.08990	−	2.62857i	−0.556932	−	0.180958i	−0.573940	+	0.818897i	$0.694586\pi$
$212$	−3.89810	−	2.88190i	−0.267723	−	0.197930i
$213$	−2.85263	+	3.92630i	−0.195459	+	0.269026i
$214$	16.1766	−	8.15797i	1.10581	−	0.557667i
$215$	−7.39962	−	22.7737i	−0.504650	−	1.55315i
$216$	2.17446	−	12.7027i	0.147953	−	0.864312i
$217$	−8.84673	+	6.42753i	−0.600555	+	0.436329i
$218$	−7.89151	−	1.28351i	−0.534480	−	0.0869300i
$219$		−	2.32074i		−	0.156821i
$220$		0			0
$221$		−	12.6574i		−	0.851427i
$222$	−1.05119	+	6.46313i	−0.0705512	+	0.433777i
$223$	−4.06365	+	2.95241i	−0.272122	+	0.197708i	−0.715474	−	0.698639i	$-0.753789\pi$
$223$	−4.06365	+	2.95241i	−0.272122	+	0.197708i	0.443352	+	0.896348i	$0.353789\pi$
$224$	6.69880	−	0.918863i	0.447583	−	0.0613941i
$225$	−5.89773	−	18.1513i	−0.393182	−	1.21009i
$226$	10.1881	+	20.2021i	0.677699	+	1.34383i
$227$	−10.6228	+	14.6211i	−0.705062	+	0.970434i	0.294828	+	0.955550i	$0.404738\pi$
$227$	−10.6228	+	14.6211i	−0.705062	+	0.970434i	−0.999889	+	0.0148837i	$0.995262\pi$
$228$	4.44727	−	6.01545i	0.294528	−	0.398383i
$229$	−3.78767	−	1.23069i	−0.250296	−	0.0813262i	0.181182	−	0.983450i	$-0.442008\pi$
$229$	−3.78767	−	1.23069i	−0.250296	−	0.0813262i	−0.431478	+	0.902123i	$0.642008\pi$
$230$	−1.94791	−	12.6381i	−0.128442	−	0.833330i
$231$		0			0
$232$	−4.81031	−	9.73880i	−0.315812	−	0.639383i
$233$	−3.79638	+	11.6841i	−0.248709	+	0.765448i	0.746295	+	0.665615i	$0.231831\pi$
$233$	−3.79638	+	11.6841i	−0.248709	+	0.765448i	−0.995004	+	0.0998327i	$0.968169\pi$
$234$	−8.90091	−	8.97513i	−0.581870	−	0.586723i
$235$	0.775032	−	1.06674i	0.0505575	−	0.0695865i
$236$	0.969613	−	0.692236i	0.0631165	−	0.0450607i
$237$	9.50046	−	3.08689i	0.617121	−	0.200515i
$238$	4.77911	+	2.46013i	0.309783	+	0.159466i
$239$	16.9458	−	12.3118i	1.09613	−	0.796386i	0.115707	−	0.993283i	$-0.463087\pi$
$239$	16.9458	−	12.3118i	1.09613	−	0.796386i	0.980424	+	0.196898i	$0.0630866\pi$
$240$	−3.74276	−	12.2052i	−0.241594	−	0.787841i
$241$	−17.4490			−1.12399			−0.561996	−	0.827140i	$-0.689966\pi$
$241$	−17.4490			−1.12399			−0.561996	+	0.827140i	$0.689966\pi$
$242$		0			0
$243$		−	16.0828i		−	1.03171i
$244$	14.5781	+	0.121072i	0.933268	+	0.00775082i
$245$	12.0319	+	16.5605i	0.768692	+	1.05801i
$246$	−0.299691	+	0.582187i	−0.0191076	+	0.0371189i
$247$	−5.29670	−	16.3016i	−0.337021	−	1.03724i
$248$	−18.0679	−	18.5237i	−1.14731	−	1.17626i
$249$	0.704736	+	0.512021i	0.0446608	+	0.0324480i
$250$	−12.8045	−	12.9113i	−0.809828	−	0.816582i
$251$	5.66665	+	1.84121i	0.357676	+	0.116216i	0.482342	−	0.875983i	$-0.339786\pi$
$251$	5.66665	+	1.84121i	0.357676	+	0.116216i	−0.124667	+	0.992199i	$0.539786\pi$
$252$	5.11879	−	1.61632i	0.322454	−	0.101819i
$253$		0			0
$254$	12.9385	−	1.99421i	0.811832	−	0.125128i
$255$	3.13608	−	9.65186i	0.196389	−	0.604423i
$256$	4.43614	+	15.3727i	0.277259	+	0.960795i
$257$	11.4623	+	8.32787i	0.715000	+	0.519478i	0.884783	−	0.466003i	$-0.154307\pi$
$257$	11.4623	+	8.32787i	0.715000	+	0.519478i	−0.169783	+	0.985482i	$0.554307\pi$
$258$	−3.60506	−	7.14855i	−0.224441	−	0.445049i
$259$	−6.05945	+	1.96884i	−0.376516	+	0.122338i
$260$	−27.7426	−	9.26953i	−1.72052	−	0.574872i
$261$	−5.06862	−	6.97635i	−0.313740	−	0.431825i
$262$	18.6043	+	3.02588i	1.14938	+	0.186939i
$263$	−11.0152			−0.679225			−0.339612	−	0.940566i	$-0.610296\pi$
$263$	−11.0152			−0.679225			−0.339612	+	0.940566i	$0.610296\pi$
$264$		0			0
$265$	−8.90572			−0.547074
$266$	7.18454	+	1.16852i	0.440512	+	0.0716466i
$267$	6.96775	+	9.59029i	0.426419	+	0.586916i
$268$	−7.14254	+	21.3768i	−0.436300	+	1.30579i
$269$	−2.36175	+	0.767379i	−0.143998	+	0.0467879i	−0.380129	−	0.924933i	$-0.624121\pi$
$269$	−2.36175	+	0.767379i	−0.143998	+	0.0467879i	0.236131	+	0.971721i	$0.424121\pi$
$270$	−10.6608	−	21.1395i	−0.648793	−	1.28651i
$271$	0.248958	+	0.180879i	0.0151231	+	0.0109876i	0.595321	−	0.803488i	$-0.297025\pi$
$271$	0.248958	+	0.180879i	0.0151231	+	0.0109876i	−0.580198	+	0.814475i	$0.697025\pi$
$272$	−4.13086	+	12.0299i	−0.250470	+	0.729417i
$273$	−1.27712	+	3.93057i	−0.0772949	+	0.237889i
$274$	13.5702	−	2.09158i	0.819806	−	0.126357i
$275$		0			0
$276$	−1.28735	−	4.07696i	−0.0774895	−	0.245404i
$277$	2.37765	+	0.772546i	0.142859	+	0.0464178i	0.379574	−	0.925161i	$-0.376071\pi$
$277$	2.37765	+	0.772546i	0.142859	+	0.0464178i	−0.236715	+	0.971579i	$0.576071\pi$
$278$	22.1624	+	22.3472i	1.32921	+	1.34030i
$279$	−16.6195	−	12.0748i	−0.994985	−	0.722899i
$280$	8.89208	−	8.67325i	0.531403	−	0.518326i
$281$	0.384151	+	1.18230i	0.0229166	+	0.0705299i	0.961861	−	0.273540i	$-0.0881944\pi$
$281$	0.384151	+	1.18230i	0.0229166	+	0.0705299i	−0.938944	+	0.344069i	$0.888194\pi$
$282$	0.201774	−	0.391971i	0.0120155	−	0.0233415i
$283$	−8.11251	−	11.1659i	−0.482239	−	0.663745i	0.496694	−	0.867926i	$-0.334547\pi$
$283$	−8.11251	−	11.1659i	−0.482239	−	0.663745i	−0.978933	+	0.204181i	$0.934547\pi$
$284$	0.0927987	−	11.1738i	0.00550659	−	0.663043i
$285$		−	13.7431i		−	0.814069i
$286$		0			0
$287$	−0.637118			−0.0376079
$288$	5.53050	+	11.4351i	0.325888	+	0.673818i
$289$	5.57305	−	4.04906i	0.327826	−	0.238180i
$290$	−17.7418	−	9.13288i	−1.04183	−	0.536301i
$291$	−4.91602	+	1.59731i	−0.288182	+	0.0936360i
$292$	3.10475	+	4.34882i	0.181692	+	0.254495i
$293$	8.74894	−	12.0419i	0.511118	−	0.703494i	−0.472989	−	0.881068i	$-0.656825\pi$
$293$	8.74894	−	12.0419i	0.511118	−	0.703494i	0.984107	+	0.177574i	$0.0568250\pi$
$294$	4.81933	+	4.85952i	0.281069	+	0.283413i
$295$	0.676325	−	2.08151i	0.0393772	−	0.121190i
$296$	−6.67674	−	13.5175i	−0.388078	−	0.785690i
$297$		0			0
$298$	2.71469	+	17.6129i	0.157258	+	1.02029i
$299$	−9.31644	−	3.02709i	−0.538784	−	0.175061i
$300$	−11.8736	−	8.77823i	−0.685521	−	0.506811i
$301$	4.57885	−	6.30224i	0.263920	−	0.363255i
$302$	−9.65800	−	19.1511i	−0.555755	−	1.10202i
$303$	1.60387	+	4.93621i	0.0921400	+	0.283578i
$304$	−0.286078	+	17.2220i	−0.0164077	+	0.987749i
$305$	21.6673	−	15.7422i	1.24066	−	0.901395i
$306$	−1.62104	+	9.96680i	−0.0926686	+	0.569764i
$307$		−	8.40361i		−	0.479619i	−0.970820	−	0.239810i	$-0.922915\pi$
$307$		−	8.40361i		−	0.479619i	0.970820	−	0.239810i	$-0.0770850\pi$
$308$		0			0
$309$			3.40997i			0.193986i
$310$	−46.9203	−	7.63129i	−2.66489	−	0.433428i
$311$	−20.7482	+	15.0745i	−1.17652	+	0.854795i	−0.991775	−	0.127991i	$-0.959147\pi$
$311$	−20.7482	+	15.0745i	−1.17652	+	0.854795i	−0.184749	+	0.982786i	$0.559147\pi$
$312$	−9.63947	−	1.65009i	−0.545727	−	0.0934177i
$313$	5.83498	+	17.9582i	0.329812	+	1.01506i	0.969221	+	0.246191i	$0.0791791\pi$
$313$	5.83498	+	17.9582i	0.329812	+	1.01506i	−0.639409	+	0.768867i	$0.720821\pi$
$314$	1.92772	−	0.972159i	0.108787	−	0.0548621i
$315$	5.79635	−	7.97799i	0.326587	−	0.449509i
$316$	−13.6731	+	18.4945i	−0.769173	+	1.04040i
$317$	−18.9857	−	6.16884i	−1.06634	−	0.346476i	−0.277282	−	0.960789i	$-0.589434\pi$
$317$	−18.9857	−	6.16884i	−1.06634	−	0.346476i	−0.789063	+	0.614312i	$0.789434\pi$
$318$	−2.94284	+	0.453581i	−0.165026	+	0.0254356i
$319$		0			0
$320$	23.3420	+	17.8640i	1.30486	+	0.998631i
$321$	3.43875	−	10.5834i	0.191932	−	0.590707i
$322$	2.95373	−	2.92930i	0.164605	−	0.163243i
$323$	−8.04834	+	11.0776i	−0.447822	+	0.616374i
$324$	3.22886	+	4.52266i	0.179381	+	0.251259i
$325$	−32.1768	+	10.4549i	−1.78485	+	0.579931i
$326$	10.0561	−	19.5352i	0.556953	−	1.08195i
$327$	−3.97295	+	2.88651i	−0.219704	+	0.159625i
$328$	−0.217278	−	1.49189i	−0.0119972	−	0.0823759i
$329$	0.428955			0.0236490
$330$		0			0
$331$		−	18.8624i		−	1.03677i	−0.855147	−	0.518386i	$-0.826533\pi$
$331$		−	18.8624i		−	1.03677i	0.855147	−	0.518386i	$-0.173467\pi$
$332$	−2.00560	−	0.0166565i	−0.110071	−	0.000914145i
$333$	−7.03528	−	9.68324i	−0.385531	−	0.530638i
$334$	10.5539	+	5.43278i	0.577482	+	0.297269i
$335$	12.7949	+	39.3786i	0.699059	+	2.15148i
$336$	2.49659	−	3.31891i	0.136200	−	0.181061i
$337$	17.2189	+	12.5102i	0.937972	+	0.681476i	0.947932	−	0.318474i	$-0.103170\pi$
$337$	17.2189	+	12.5102i	0.937972	+	0.681476i	−0.00995978	+	0.999950i	$0.503170\pi$
$338$	−2.85628	+	2.83266i	−0.155361	+	0.154076i
$339$	13.2170	+	4.29447i	0.717850	+	0.233244i
$340$	7.03585	+	22.2821i	0.381572	+	1.20842i
$341$		0			0
$342$	2.08303	+	13.5147i	0.112637	+	0.730791i
$343$	−4.64336	+	14.2908i	−0.250718	+	0.771631i
$344$	16.3190	+	8.57267i	0.879862	+	0.462207i
$345$	−6.35422	−	4.61661i	−0.342100	−	0.248550i
$346$	−31.3944	+	15.8324i	−1.68778	+	0.851155i
$347$	−5.18044	+	1.68323i	−0.278100	+	0.0903603i	−0.444747	−	0.895656i	$-0.646706\pi$
$347$	−5.18044	+	1.68323i	−0.278100	+	0.0903603i	0.166646	+	0.986017i	$0.446706\pi$
$348$	−6.32781	−	2.11429i	−0.339206	−	0.113338i
$349$	−6.00038	−	8.25881i	−0.321193	−	0.442084i	0.617638	−	0.786462i	$-0.288090\pi$
$349$	−6.00038	−	8.25881i	−0.321193	−	0.442084i	−0.938831	+	0.344379i	$0.888090\pi$
$350$	2.30648	−	14.1812i	0.123287	−	0.758016i
$351$	−18.1369			−0.968077
$352$		0			0
$353$	5.11121			0.272042			0.136021	−	0.990706i	$-0.456569\pi$
$353$	5.11121			0.272042			0.136021	+	0.990706i	$0.456569\pi$
$354$	0.117473	−	0.722269i	0.00624360	−	0.0383882i
$355$	−12.0660	−	16.6075i	−0.640399	−	0.881433i
$356$	−25.8870	−	8.64952i	−1.37201	−	0.458424i
$357$	3.13994	−	1.02023i	0.166183	−	0.0539962i
$358$	20.8173	−	10.4983i	1.10023	−	0.554852i
$359$	16.9733	+	12.3318i	0.895815	+	0.650848i	0.937388	−	0.348288i	$-0.113237\pi$
$359$	16.9733	+	12.3318i	0.895815	+	0.650848i	−0.0415725	+	0.999135i	$0.513237\pi$
$360$	20.6582	+	10.8521i	1.08878	+	0.571957i
$361$	0.141394	−	0.435166i	0.00744178	−	0.0229035i
$362$	1.97744	+	12.8296i	0.103932	+	0.674311i
$363$		0			0
$364$	−2.86524	−	9.07405i	−0.150180	−	0.475609i
$365$	9.33581	+	3.03339i	0.488659	+	0.158775i
$366$	6.35803	−	6.30545i	0.332340	−	0.329591i
$367$	25.5075	+	18.5323i	1.33148	+	0.967378i	0.999712	+	0.0240171i	$0.00764560\pi$
$367$	25.5075	+	18.5323i	1.33148	+	0.967378i	0.331769	+	0.943361i	$0.392354\pi$
$368$	7.86663	+	5.91753i	0.410077	+	0.308473i
$369$	−0.369861	−	1.13831i	−0.0192542	−	0.0592583i
$370$	−24.6257	−	12.6765i	−1.28023	−	0.659021i
$371$	−1.70293	−	2.34389i	−0.0884119	−	0.121689i
$372$	−15.8932	−	0.131993i	−0.824023	−	0.00684353i
$373$		−	24.8244i		−	1.28536i	−0.766136	−	0.642678i	$-0.777823\pi$
$373$		−	24.8244i		−	1.28536i	0.766136	−	0.642678i	$-0.222177\pi$
$374$		0			0
$375$	−11.1690			−0.576765
$376$	0.146287	+	1.00445i	0.00754419	+	0.0518006i
$377$	−12.3669	+	8.98510i	−0.636929	+	0.462756i
$378$	3.52515	−	6.84804i	0.181314	−	0.352225i
$379$	33.9918	−	11.0446i	1.74604	−	0.567324i	0.750434	−	0.660945i	$-0.229844\pi$
$379$	33.9918	−	11.0446i	1.74604	−	0.567324i	0.995608	+	0.0936215i	$0.0298443\pi$
$380$	18.3859	+	25.7530i	0.943175	+	1.32110i
$381$	4.72634	−	6.50525i	0.242138	−	0.333274i
$382$	−2.48005	+	2.45954i	−0.126891	+	0.125841i
$383$	−5.88298	+	18.1060i	−0.300606	+	0.925171i	0.680674	+	0.732586i	$0.261687\pi$
$383$	−5.88298	+	18.1060i	−0.300606	+	0.925171i	−0.981280	+	0.192585i	$0.938313\pi$
$384$	8.62305	+	4.71422i	0.440043	+	0.240571i
$385$		0			0
$386$	−13.9857	+	2.15562i	−0.711853	+	0.109718i
$387$	13.9181	+	4.52226i	0.707496	+	0.229879i
$388$	7.07516	−	9.56997i	0.359187	−	0.485842i
$389$	19.1441	−	26.3496i	0.970643	−	1.33598i	0.0289221	−	0.999582i	$-0.490793\pi$
$389$	19.1441	−	26.3496i	0.970643	−	1.33598i	0.941721	−	0.336394i	$-0.109207\pi$
$390$	−16.0417	+	8.08991i	−0.812301	+	0.409648i
$391$	2.41819	+	7.44243i	0.122293	+	0.376380i
$392$	−15.5321	−	2.65879i	−0.784490	−	0.134289i
$393$	9.36627	−	6.80499i	0.472466	−	0.343266i
$394$	−16.4624	−	2.67750i	−0.829362	−	0.134891i
$395$			42.2530i			2.12598i
$396$		0			0
$397$			13.0143i			0.653167i	0.945168	+	0.326584i	$0.105897\pi$
$397$			13.0143i			0.653167i	−0.945168	+	0.326584i	$0.894103\pi$
$398$	3.35702	−	20.6403i	0.168272	−	1.03461i
$399$	3.61702	−	2.62792i	0.181078	−	0.131561i
$400$	33.9936	+	0.564674i	1.69968	+	0.0282337i
$401$	6.35150	+	19.5479i	0.317179	+	0.976175i	0.974848	+	0.222869i	$0.0715422\pi$
$401$	6.35150	+	19.5479i	0.317179	+	0.976175i	−0.657670	+	0.753306i	$0.728458\pi$
$402$	6.23359	+	12.3607i	0.310903	+	0.616497i
$403$	−21.4049	+	29.4613i	−1.06625	+	1.46757i
$404$	−9.60928	−	7.10422i	−0.478080	−	0.353448i
$405$	9.70901	+	3.15465i	0.482445	+	0.156756i
$406$	−0.988874	−	6.41581i	−0.0490770	−	0.318412i
$407$		0			0
$408$	3.45981	+	7.00462i	0.171286	+	0.346781i
$409$	−3.04719	+	9.37828i	−0.150674	+	0.463726i	−0.997697	−	0.0678299i	$-0.978392\pi$
$409$	−3.04719	+	9.37828i	−0.150674	+	0.463726i	0.847023	+	0.531556i	$0.178392\pi$
$410$	−1.95029	−	1.96655i	−0.0963179	−	0.0971212i
$411$	4.95711	−	6.82288i	0.244516	−	0.336548i
$412$	−4.56196	−	6.38992i	−0.224751	−	0.314809i
$413$	0.677157	−	0.220022i	0.0333207	−	0.0108266i
$414$	6.94836	+	3.57679i	0.341493	+	0.175790i
$415$	−2.98089	+	2.16574i	−0.146326	+	0.106312i
$416$	20.2709	−	9.80387i	0.993861	−	0.480674i
$417$	19.3316			0.946671
$418$		0			0
$419$			0.169087i			0.00826046i	0.999991	+	0.00413023i	$0.00131470\pi$
$419$			0.169087i			0.00826046i	−0.999991	+	0.00413023i	$0.998685\pi$
$420$	0.0633616	−	7.62931i	0.00309173	−	0.372272i
$421$	−13.8205	−	19.0223i	−0.673569	−	0.927089i	0.326265	−	0.945278i	$-0.394210\pi$
$421$	−13.8205	−	19.0223i	−0.673569	−	0.927089i	−0.999835	+	0.0181896i	$0.994210\pi$
$422$	5.50579	−	10.6957i	0.268018	−	0.520658i
$423$	0.249017	+	0.766396i	0.0121076	+	0.0372635i
$424$	4.90775	−	4.78697i	0.238341	−	0.232476i
$425$	21.8655	+	15.8862i	1.06063	+	0.770593i
$426$	−4.83299	−	4.87329i	−0.234159	−	0.236112i
$427$	8.28634	+	2.69240i	0.401004	+	0.130294i
$428$	7.71490	+	24.4326i	0.372914	+	1.18099i
$429$		0			0
$430$	33.4691	−	5.15861i	1.61402	−	0.248770i
$431$	2.25358	−	6.93580i	0.108551	−	0.334086i	−0.881996	−	0.471256i	$-0.843801\pi$
$431$	2.25358	−	6.93580i	0.108551	−	0.334086i	0.990547	+	0.137170i	$0.0438008\pi$
$432$	17.2377	+	5.91917i	0.829351	+	0.284786i
$433$	−1.89173	−	1.37442i	−0.0909105	−	0.0660504i	0.541401	−	0.840764i	$-0.317894\pi$
$433$	−1.89173	−	1.37442i	−0.0909105	−	0.0660504i	−0.632312	+	0.774714i	$0.717894\pi$
$434$	−6.96353	−	13.8081i	−0.334260	−	0.662812i
$435$	−11.6566	+	3.78746i	−0.558891	+	0.181595i
$436$	3.58322	−	10.7241i	0.171605	−	0.513593i
$437$	6.22883	+	8.57325i	0.297965	+	0.410114i
$438$	3.23945	+	0.526877i	0.154787	+	0.0251752i
$439$	1.21401			0.0579413			0.0289707	−	0.999580i	$-0.490777\pi$
$439$	1.21401			0.0579413			0.0289707	+	0.999580i	$0.490777\pi$
$440$		0			0
$441$	−12.5102			−0.595722
$442$	17.6681	+	2.87360i	0.840384	+	0.136683i
$443$	2.71484	+	3.73666i	0.128986	+	0.177534i	0.868625	−	0.495469i	$-0.165004\pi$
$443$	2.71484	+	3.73666i	0.128986	+	0.177534i	−0.739639	+	0.673003i	$0.765004\pi$
$444$	−8.78305	−	2.93465i	−0.416825	−	0.139272i
$445$	−47.6870	+	15.4944i	−2.26058	+	0.734507i
$446$	−3.19862	−	6.34262i	−0.151459	−	0.300332i
$447$	8.85550	+	6.43389i	0.418851	+	0.304313i
$448$	−0.238214	+	9.55928i	−0.0112546	+	0.451634i
$449$	1.81356	−	5.58157i	0.0855872	−	0.263410i	−0.899099	−	0.437745i	$-0.855777\pi$
$449$	1.81356	−	5.58157i	0.0855872	−	0.263410i	0.984687	+	0.174334i	$0.0557774\pi$
$450$	26.6759	−	4.11157i	1.25751	−	0.193821i
$451$		0			0
$452$	−30.5126	+	9.63473i	−1.43519	+	0.453180i
$453$	−12.5294	−	4.07104i	−0.588682	−	0.191274i
$454$	−17.9974	−	18.1475i	−0.844661	−	0.851705i
$455$	−14.1425	−	10.2751i	−0.663012	−	0.481706i
$456$	7.38713	+	7.57351i	0.345934	+	0.354662i
$457$	7.57010	+	23.2984i	0.354115	+	1.08985i	0.956521	+	0.291663i	$0.0942086\pi$
$457$	7.57010	+	23.2984i	0.354115	+	1.08985i	−0.602407	+	0.798189i	$0.705791\pi$
$458$	2.57780	−	5.00770i	0.120453	−	0.233994i
$459$	8.51622	+	11.7216i	0.397503	+	0.547116i
$460$	18.0834	+	0.150183i	0.843141	+	0.00700231i
$461$			6.59878i			0.307336i	0.988123	+	0.153668i	$0.0491086\pi$
$461$			6.59878i			0.307336i	−0.988123	+	0.153668i	$0.950891\pi$
$462$		0			0
$463$	−14.4202			−0.670163			−0.335081	−	0.942189i	$-0.608764\pi$
$463$	−14.4202			−0.670163			−0.335081	+	0.942189i	$0.608764\pi$
$464$	14.6862	−	4.50357i	0.681789	−	0.209073i
$465$	−23.6218	+	17.1622i	−1.09544	+	0.795880i
$466$	−15.4475	−	7.95189i	−0.715594	−	0.368364i
$467$	−5.22015	+	1.69613i	−0.241560	+	0.0784876i	−0.427295	−	0.904112i	$-0.640533\pi$
$467$	−5.22015	+	1.69613i	−0.241560	+	0.0784876i	0.185735	+	0.982600i	$0.440533\pi$
$468$	14.5489	−	10.3869i	0.672523	−	0.480134i
$469$	−7.91740	+	10.8974i	−0.365592	+	0.503194i
$470$	1.31308	+	1.32403i	0.0605677	+	0.0610728i
$471$	0.409785	−	1.26119i	0.0188819	−	0.0581125i
$472$	0.746141	+	1.51061i	0.0343439	+	0.0695316i
$473$		0			0
$474$	2.15201	+	13.9622i	0.0988450	+	0.641307i
$475$	34.8086	+	11.3100i	1.59713	+	0.518938i
$476$	−4.51902	+	6.11249i	−0.207129	+	0.280166i
$477$	3.19914	−	4.40324i	0.146479	−	0.201611i
$478$	13.3385	+	26.4493i	0.610090	+	1.20976i
$479$	9.22841	+	28.4021i	0.421657	+	1.29773i	0.906160	+	0.422936i	$0.139001\pi$
$479$	9.22841	+	28.4021i	0.421657	+	1.29773i	−0.484503	+	0.874790i	$0.660999\pi$
$480$	17.8866	−	2.45347i	0.816407	−	0.111985i
$481$	−17.1654	+	12.4714i	−0.782675	+	0.568647i
$482$	3.96145	−	24.3566i	0.180439	−	1.10941i
$483$		−	2.55514i		−	0.116263i
$484$		0			0
$485$		−	21.8638i		−	0.992786i
$486$	22.4495	+	3.65127i	1.01833	+	0.165625i
$487$	2.40887	−	1.75015i	0.109156	−	0.0793068i	−0.531868	−	0.846827i	$-0.678510\pi$
$487$	2.40887	−	1.75015i	0.109156	−	0.0793068i	0.641024	+	0.767520i	$0.278510\pi$
$488$	−3.47867	+	20.3217i	−0.157472	+	0.919920i
$489$	−4.17030	−	12.8349i	−0.188588	−	0.580413i
$490$	−25.8480	+	13.0353i	−1.16769	+	0.588875i
$491$	1.75193	−	2.41132i	0.0790633	−	0.108821i	−0.767654	−	0.640865i	$-0.778576\pi$
$491$	1.75193	−	2.41132i	0.0790633	−	0.108821i	0.846717	+	0.532044i	$0.178576\pi$
$492$	−0.744620	−	0.550504i	−0.0335701	−	0.0248186i
$493$	11.6138	+	3.77356i	0.523061	+	0.169953i
$494$	23.9574	−	3.69257i	1.07789	−	0.166136i
$495$		0			0
$496$	29.9587	−	21.0150i	1.34519	−	0.943601i
$497$	2.06366	−	6.35130i	0.0925678	−	0.284895i
$498$	−0.874711	+	0.867477i	−0.0391967	+	0.0388726i
$499$	−8.93099	+	12.2925i	−0.399806	+	0.550286i	−0.960695	−	0.277605i	$-0.910459\pi$
$499$	−8.93099	+	12.2925i	−0.399806	+	0.550286i	0.560889	+	0.827891i	$0.310459\pi$
$500$	20.9295	−	14.9422i	0.935996	−	0.668236i
$501$	6.93404	−	2.25300i	0.309790	−	0.100657i
$502$	−3.85659	+	7.49191i	−0.172128	+	0.334380i
$503$	26.6342	−	19.3508i	1.18756	−	0.862812i	0.194554	−	0.980892i	$-0.437674\pi$
$503$	26.6342	−	19.3508i	1.18756	−	0.862812i	0.993004	+	0.118080i	$0.0376740\pi$
$504$	1.09406	+	7.51213i	0.0487333	+	0.334617i
$505$	−21.9536			−0.976924
$506$		0			0
$507$			2.47085i			0.109734i
$508$	−0.153752	+	18.5132i	−0.00682166	+	0.821390i
$509$	7.92281	+	10.9048i	0.351172	+	0.483347i	0.947663	−	0.319273i	$-0.103439\pi$
$509$	7.92281	+	10.9048i	0.351172	+	0.483347i	−0.596490	+	0.802620i	$0.703439\pi$
$510$	12.7608	+	6.56882i	0.565056	+	0.290872i
$511$	0.986821	+	3.03712i	0.0436544	+	0.134354i
$512$	−22.4655	+	2.70222i	−0.992844	+	0.119422i
$513$	15.8732	+	11.5326i	0.700820	+	0.509176i
$514$	−14.2269	+	14.1093i	−0.627523	+	0.622333i
$515$	−13.7176	−	4.45710i	−0.604468	−	0.196403i
$516$	10.7969	−	3.40926i	0.475307	−	0.150084i
$517$		0			0
$518$	−1.37256	−	8.90520i	−0.0603070	−	0.391272i
$519$	−6.67368	+	20.5395i	−0.292942	+	0.901583i
$520$	19.2375	−	36.6206i	0.843619	−	1.60592i
$521$	−7.52914	−	5.47024i	−0.329857	−	0.239655i	0.410513	−	0.911855i	$-0.365350\pi$
$521$	−7.52914	−	5.47024i	−0.329857	−	0.239655i	−0.740370	+	0.672199i	$0.765350\pi$
$522$	10.8888	−	5.49130i	0.476591	−	0.240348i
$523$	13.6298	−	4.42859i	0.595989	−	0.193649i	0.00453848	−	0.999990i	$-0.498555\pi$
$523$	13.6298	−	4.42859i	0.595989	−	0.193649i	0.591451	+	0.806341i	$0.298555\pi$
$524$	−8.44748	+	25.2823i	−0.369030	+	1.10446i
$525$	−5.18711	−	7.13945i	−0.226384	−	0.311591i
$526$	2.50077	−	15.3758i	0.109039	−	0.670415i
$527$	29.0911			1.26723
$528$		0			0
$529$	−16.9437			−0.736682
$530$	2.02186	−	12.4312i	0.0878242	−	0.539978i
$531$	0.786209	+	1.08212i	0.0341186	+	0.0469602i
$532$	−3.26221	+	9.76340i	−0.141435	+	0.423297i
$533$	−2.01788	+	0.655649i	−0.0874041	+	0.0283993i
$534$	−14.9687	+	7.54880i	−0.647759	+	0.326669i
$535$	38.0799	+	27.6666i	1.64634	+	1.19613i
$536$	−28.2176	−	14.8232i	−1.21882	−	0.640266i
$537$	4.42524	−	13.6195i	0.190963	−	0.587725i
$538$	−0.534975	−	3.47092i	−0.0230644	−	0.149642i
$539$		0			0
$540$	31.9283	−	10.0818i	1.37398	−	0.433850i
$541$	−21.9923	−	7.14572i	−0.945521	−	0.307218i	−0.204627	−	0.978840i	$-0.565598\pi$
$541$	−21.9923	−	7.14572i	−0.945521	−	0.307218i	−0.740894	+	0.671622i	$0.765598\pi$
$542$	−0.309004	+	0.306448i	−0.0132729	+	0.0131631i
$543$	6.45054	+	4.68659i	0.276819	+	0.201121i
$544$	−15.8543	−	8.49729i	−0.679747	−	0.364318i
$545$	−6.41884	−	19.7552i	−0.274953	−	0.846219i
$546$	−5.19663	−	2.67505i	−0.222395	−	0.114482i
$547$	5.31444	+	7.31470i	0.227229	+	0.312754i	0.907374	−	0.420323i	$-0.138083\pi$
$547$	5.31444	+	7.31470i	0.227229	+	0.312754i	−0.680145	+	0.733077i	$0.738083\pi$
$548$	−0.161260	+	19.4171i	−0.00688867	+	0.829458i
$549$			16.3679i			0.698564i
$550$		0			0
$551$	16.5367			0.704487
$552$	5.98318	−	0.871385i	0.254661	−	0.0370886i
$553$	−11.1205	+	8.07954i	−0.472893	+	0.343577i
$554$	−1.61817	+	3.14351i	−0.0687496	+	0.133555i
$555$	−16.1794	+	5.25702i	−0.686779	+	0.223148i
$556$	−36.2253	+	25.8623i	−1.53630	+	1.09681i
$557$	−16.3446	+	22.4964i	−0.692542	+	0.953203i	0.307456	+	0.951562i	$0.400522\pi$
$557$	−16.3446	+	22.4964i	−0.692542	+	0.953203i	−0.999999	+	0.00164059i	$0.999478\pi$
$558$	20.6280	−	20.4574i	0.873253	−	0.866030i
$559$	8.01658	−	24.6725i	0.339065	−	1.04353i
$560$	10.0880	+	14.3813i	0.426295	+	0.607720i
$561$		0			0
$562$	−1.73755	+	0.267809i	−0.0732940	+	0.0112969i
$563$	−33.6052	−	10.9190i	−1.41629	−	0.460181i	−0.501869	−	0.864943i	$-0.667354\pi$
$563$	−33.6052	−	10.9190i	−1.41629	−	0.460181i	−0.914422	+	0.404762i	$0.867354\pi$
$564$	0.501332	+	0.370639i	0.0211099	+	0.0156067i
$565$	−34.5514	+	47.5559i	−1.45359	+	2.00069i
$566$	17.4280	−	8.78903i	0.732552	−	0.369430i
$567$	1.02627	+	3.15853i	0.0430993	+	0.132646i
$568$	15.5761	+	2.66632i	0.653560	+	0.111876i
$569$	26.4592	−	19.2237i	1.10923	−	0.805901i	0.126686	−	0.991943i	$-0.459566\pi$
$569$	26.4592	−	19.2237i	1.10923	−	0.805901i	0.982542	+	0.186042i	$0.0595660\pi$
$570$	19.1836	+	3.12009i	0.803511	+	0.130686i
$571$		−	32.0987i		−	1.34329i	−0.740874	−	0.671644i	$-0.765588\pi$
$571$		−	32.0987i		−	1.34329i	0.740874	−	0.671644i	$-0.234412\pi$
$572$		0			0
$573$			2.14539i			0.0896249i
$574$	0.144645	−	0.889335i	0.00603736	−	0.0371201i
$575$	16.9223	−	12.2948i	0.705708	−	0.512727i
$576$	−17.2175	+	5.12376i	−0.717395	+	0.213490i
$577$	6.54916	+	20.1562i	0.272645	+	0.839116i	0.989833	+	0.142236i	$0.0454290\pi$
$577$	6.54916	+	20.1562i	0.272645	+	0.839116i	−0.717188	+	0.696880i	$0.754571\pi$
$578$	4.38671	+	8.69851i	0.182463	+	0.361811i
$579$	−5.10889	+	7.03178i	−0.212318	+	0.292231i
$580$	16.7762	−	22.6918i	0.696596	−	0.942226i
$581$	−1.14000	−	0.370408i	−0.0472952	−	0.0153671i
$582$	−1.11356	−	7.22476i	−0.0461584	−	0.299476i
$583$		0			0
$584$	−6.77526	+	3.34652i	−0.280362	+	0.138480i
$585$	10.1482	−	31.2328i	0.419575	−	1.29132i
$586$	14.8226	+	14.9463i	0.612318	+	0.617424i
$587$	−3.97489	+	5.47096i	−0.164061	+	0.225811i	−0.883130	−	0.469128i	$-0.844568\pi$
$587$	−3.97489	+	5.47096i	−0.164061	+	0.225811i	0.719069	+	0.694939i	$0.244568\pi$
$588$	−7.87739	+	5.62390i	−0.324858	+	0.231926i
$589$	37.4667	−	12.1737i	1.54379	−	0.501607i
$590$	2.75198	+	1.41663i	0.113297	+	0.0583217i
$591$	−8.28790	+	6.02151i	−0.340919	+	0.247692i
$592$	20.3846	−	6.25099i	0.837800	−	0.256914i
$593$	−8.93648			−0.366977			−0.183489	−	0.983022i	$-0.558739\pi$
$593$	−8.93648			−0.366977			−0.183489	+	0.983022i	$0.558739\pi$
$594$		0			0
$595$			13.9648i			0.572500i
$596$	−25.2017	−	0.209301i	−1.03230	−	0.00857329i
$597$	−7.54971	−	10.3913i	−0.308989	−	0.425287i
$598$	6.34055	−	12.3173i	0.259284	−	0.503692i
$599$	−1.75023	−	5.38664i	−0.0715123	−	0.220092i	0.908912	−	0.416987i	$-0.136914\pi$
$599$	−1.75023	−	5.38664i	−0.0715123	−	0.220092i	−0.980425	+	0.196895i	$0.936914\pi$
$600$	14.9489	−	14.5811i	0.610288	−	0.595269i
$601$	−27.7733	−	20.1785i	−1.13290	−	0.823099i	−0.146784	−	0.989169i	$-0.546892\pi$
$601$	−27.7733	−	20.1785i	−1.13290	−	0.823099i	−0.986114	+	0.166070i	$0.946892\pi$
$602$	7.75758	+	7.82228i	0.316176	+	0.318812i
$603$	−24.0661	−	7.81956i	−0.980048	−	0.318437i
$604$	28.9251	−	9.13346i	1.17694	−	0.371635i
$605$		0			0
$606$	−7.25444	+	1.11813i	−0.294691	+	0.0454210i
$607$	12.4984	−	38.4660i	0.507293	−	1.56129i	−0.289588	−	0.957151i	$-0.593518\pi$
$607$	12.4984	−	38.4660i	0.507293	−	1.56129i	0.796881	−	0.604136i	$-0.206482\pi$
$608$	−23.9747	−	4.30924i	−0.972304	−	0.174763i
$609$	−3.22577	−	2.34366i	−0.130715	−	0.0949698i
$610$	17.0550	+	33.8187i	0.690535	+	1.36928i
$611$	1.35858	−	0.441431i	0.0549625	−	0.0178584i
$612$	−13.5443	−	4.52552i	−0.547498	−	0.182933i
$613$	8.52308	+	11.7310i	0.344244	+	0.473811i	0.945675	−	0.325114i	$-0.105403\pi$
$613$	8.52308	+	11.7310i	0.344244	+	0.473811i	−0.601431	+	0.798925i	$0.705403\pi$
$614$	11.7304	+	1.90787i	0.473399	+	0.0769954i
$615$	−1.70118			−0.0685982
$616$		0			0
$617$	−17.5018			−0.704595			−0.352297	−	0.935888i	$-0.614599\pi$
$617$	−17.5018			−0.704595			−0.352297	+	0.935888i	$0.614599\pi$
$618$	−4.75988	−	0.774166i	−0.191471	−	0.0311415i
$619$	16.5014	+	22.7122i	0.663245	+	0.912879i	0.999583	−	0.0288623i	$-0.00918843\pi$
$619$	16.5014	+	22.7122i	0.663245	+	0.912879i	−0.336338	+	0.941741i	$0.609188\pi$
$620$	21.3046	−	63.7621i	0.855614	−	2.56075i
$621$	10.6644	−	3.46506i	0.427946	−	0.139048i
$622$	−16.3316	−	32.3842i	−0.654836	−	1.29849i
$623$	−13.1966	−	9.58787i	−0.528710	−	0.384130i
$624$	4.49175	−	13.0808i	0.179814	−	0.523653i
$625$	1.46621	−	4.51254i	0.0586486	−	0.180502i
$626$	−26.3921	+	4.06783i	−1.05484	+	0.162583i
$627$		0			0
$628$	0.919360	+	2.91155i	0.0366864	+	0.116184i
$629$	16.1201	+	5.23774i	0.642750	+	0.208842i
$630$	9.82030	+	9.90220i	0.391250	+	0.394513i
$631$	−14.5008	−	10.5355i	−0.577268	−	0.419410i	0.260470	−	0.965482i	$-0.416123\pi$
$631$	−14.5008	−	10.5355i	−0.577268	−	0.419410i	−0.837738	+	0.546072i	$0.816123\pi$
$632$	−22.7117	−	23.2847i	−0.903423	−	0.926216i
$633$	−2.28328	−	7.02722i	−0.0907523	−	0.279307i
$634$	12.9212	−	25.1011i	0.513168	−	0.996893i
$635$	19.9915	+	27.5159i	0.793337	+	1.09193i
$636$	0.0349708	−	4.21080i	0.00138668	−	0.166969i
$637$			22.1767i			0.878671i
$638$		0			0
$639$	12.5456			0.496297
$640$	−30.2352	+	28.5267i	−1.19515	+	1.12762i
$641$	−2.86764	+	2.08347i	−0.113265	+	0.0822919i	−0.642976	−	0.765886i	$-0.722300\pi$
$641$	−2.86764	+	2.08347i	−0.113265	+	0.0822919i	0.529711	+	0.848178i	$0.322300\pi$
$642$	13.9924	+	7.20280i	0.552234	+	0.284272i
$643$	−14.8746	+	4.83306i	−0.586598	+	0.190597i	−0.587254	−	0.809403i	$-0.699791\pi$
$643$	−14.8746	+	4.83306i	−0.586598	+	0.190597i	0.000656291		1.00000i	$0.499791\pi$
$644$	3.41834	+	4.78806i	0.134701	+	0.188676i
$645$	12.2261	−	16.8277i	0.481400	−	0.662591i
$646$	−13.6357	−	13.7494i	−0.536489	−	0.540963i
$647$	−8.57099	+	26.3788i	−0.336960	+	1.03706i	0.628788	+	0.777577i	$0.283551\pi$
$647$	−8.57099	+	26.3788i	−0.336960	+	1.03706i	−0.965748	+	0.259481i	$0.916449\pi$
$648$	−7.04611	+	3.48030i	−0.276797	+	0.136719i
$649$		0			0
$650$	−7.28856	−	47.2882i	−0.285881	−	1.85480i
$651$	−9.03383	−	2.93527i	−0.354064	−	0.115042i
$652$	24.9856	+	18.4720i	0.978510	+	0.723421i
$653$	2.60741	−	3.58879i	0.102036	−	0.140440i	−0.754946	−	0.655787i	$-0.772337\pi$
$653$	2.60741	−	3.58879i	0.102036	−	0.140440i	0.856982	+	0.515347i	$0.172337\pi$
$654$	−3.12723	−	6.20105i	−0.122284	−	0.242480i
$655$	15.1325	+	46.5731i	0.591276	+	1.81976i
$656$	2.13182	+	0.0354120i	0.0832335	+	0.00138261i
$657$	−4.85344	+	3.52623i	−0.189351	+	0.137571i
$658$	−0.0973855	+	0.598765i	−0.00379648	+	0.0233423i
$659$		−	14.0037i		−	0.545506i	−0.962084	−	0.272753i	$-0.912066\pi$
$659$		−	14.0037i		−	0.545506i	0.962084	−	0.272753i	$-0.0879341\pi$
$660$		0			0
$661$			33.4719i			1.30191i	0.759118	+	0.650953i	$0.225631\pi$
$661$			33.4719i			1.30191i	−0.759118	+	0.650953i	$0.774369\pi$
$662$	26.3295	+	4.28233i	1.02332	+	0.166437i
$663$	8.89491	−	6.46253i	0.345450	−	0.250984i
$664$	0.478581	−	2.79577i	0.0185725	−	0.108497i
$665$	5.84380	+	17.9854i	0.226613	+	0.697443i
$666$	15.1138	−	7.62197i	0.585647	−	0.295345i
$667$	5.55505	−	7.64587i	0.215092	−	0.296049i
$668$	−9.97951	+	13.4984i	−0.386119	+	0.522270i
$669$	−4.14959	−	1.34828i	−0.160432	−	0.0521277i
$670$	−57.8723	+	8.91989i	−2.23580	+	0.344605i
$671$		0			0
$672$	4.06597	+	4.23841i	0.156848	+	0.163500i
$673$	0.312128	−	0.960631i	0.0120317	−	0.0370296i	−0.944860	−	0.327473i	$-0.893803\pi$
$673$	0.312128	−	0.960631i	0.0120317	−	0.0370296i	0.956892	+	0.290444i	$0.0938029\pi$
$674$	−21.3719	+	21.1951i	−0.823215	+	0.816406i
$675$	22.7635	−	31.3313i	0.876168	−	1.20594i
$676$	−3.30557	−	4.63011i	−0.127137	−	0.178081i
$677$	−29.7611	+	9.66997i	−1.14381	+	0.371647i	−0.818809	−	0.574066i	$-0.805365\pi$
$677$	−29.7611	+	9.66997i	−1.14381	+	0.371647i	−0.325003	+	0.945713i	$0.605365\pi$
$678$	−8.99519	+	17.4743i	−0.345458	+	0.671096i
$679$	5.75432	−	4.18076i	0.220831	−	0.160443i
$680$	−32.7003	+	4.76244i	−1.25400	+	0.182631i
$681$	−15.6986			−0.601573
$682$		0			0
$683$		−	12.2698i		−	0.469491i	−0.972057	−	0.234745i	$-0.924574\pi$
$683$		−	12.2698i		−	0.469491i	0.972057	−	0.234745i	$-0.0754256\pi$
$684$	−19.3377	−	0.160600i	−0.739395	−	0.00614069i
$685$	20.9676	+	28.8594i	0.801130	+	1.10266i
$686$	−18.8939	−	9.72598i	−0.721374	−	0.371340i
$687$	−1.06903	−	3.29013i	−0.0407859	−	0.125526i
$688$	−15.6713	+	20.8330i	−0.597461	+	0.794251i
$689$	−7.80559	−	5.67110i	−0.297369	−	0.216052i
$690$	7.88680	−	7.82157i	0.300245	−	0.297762i
$691$	9.98898	+	3.24562i	0.379999	+	0.123469i	0.492787	−	0.870150i	$-0.335978\pi$
$691$	9.98898	+	3.24562i	0.379999	+	0.123469i	−0.112788	+	0.993619i	$0.535978\pi$
$692$	−14.9725	−	47.4170i	−0.569170	−	1.80252i
$693$		0			0
$694$	−1.17345	−	7.61337i	−0.0445437	−	0.288999i
$695$	−25.2679	+	77.7666i	−0.958466	+	2.94986i
$696$	4.38787	−	8.35280i	0.166322	−	0.316612i
$697$	1.37124	+	0.996261i	0.0519392	+	0.0377361i
$698$	12.8905	−	6.50076i	0.487913	−	0.246057i
$699$	−10.1492	+	3.29769i	−0.383880	+	0.124730i
$700$	19.2715	+	6.43910i	0.728393	+	0.243375i
$701$	3.40536	+	4.68708i	0.128619	+	0.177028i	0.868470	−	0.495742i	$-0.165104\pi$
$701$	3.40536	+	4.68708i	0.128619	+	0.177028i	−0.739851	+	0.672771i	$0.765104\pi$
$702$	4.11762	−	25.3168i	0.155410	−	0.955521i
$703$	22.9531			0.865691
$704$		0			0
$705$	1.14536			0.0431367
$706$	−1.16040	+	7.13459i	−0.0436721	+	0.268514i
$707$	−4.19793	−	5.77796i	−0.157880	−	0.217303i
$708$	0.981525	+	0.327953i	0.0368880	+	0.0123252i
$709$	43.3278	−	14.0781i	1.62721	−	0.528713i	0.653583	−	0.756855i	$-0.273265\pi$
$709$	43.3278	−	14.0781i	1.62721	−	0.528713i	0.973628	+	0.228142i	$0.0732650\pi$
$710$	25.9212	−	13.0722i	0.972807	−	0.490592i
$711$	−20.8911	−	15.1783i	−0.783477	−	0.569230i
$712$	17.9507	−	34.1712i	0.672732	−	1.28062i
$713$	6.95732	−	21.4124i	0.260554	−	0.801902i
$714$	0.711247	+	4.61457i	0.0266177	+	0.172696i
$715$		0			0
$716$	9.92812	+	31.4417i	0.371031	+	1.17503i
$717$	17.3042	+	5.62246i	0.646236	+	0.209975i
$718$	−21.0671	+	20.8928i	−0.786216	+	0.779713i
$719$	−2.37119	−	1.72277i	−0.0884304	−	0.0642485i	0.542692	−	0.839932i	$-0.317405\pi$
$719$	−2.37119	−	1.72277i	−0.0884304	−	0.0642485i	−0.631122	+	0.775684i	$0.717405\pi$
$720$	−19.8382	+	26.3724i	−0.739326	+	0.982842i
$721$	−1.44998	−	4.46259i	−0.0540002	−	0.166195i
$722$	0.575335	+	0.296163i	0.0214117	+	0.0110221i
$723$	−8.90903	−	12.2622i	−0.331331	−	0.456037i
$724$	−18.3575	−	0.152459i	−0.682250	−	0.00566611i
$725$		−	32.6409i		−	1.21225i
$726$		0			0
$727$	−24.5751			−0.911438			−0.455719	−	0.890124i	$-0.650618\pi$
$727$	−24.5751			−0.911438			−0.455719	+	0.890124i	$0.650618\pi$
$728$	13.3167	−	1.93943i	0.493550	−	0.0718802i
$729$	4.55856	−	3.31199i	0.168836	−	0.122666i
$730$	−6.35373	+	12.3429i	−0.235162	+	0.456832i
$731$	−19.7096	+	6.40404i	−0.728986	+	0.236862i
$732$	7.35813	+	10.3065i	0.271964	+	0.380940i
$733$	−12.2285	+	16.8312i	−0.451672	+	0.621673i	−0.972756	−	0.231833i	$-0.925528\pi$
$733$	−12.2285	+	16.8312i	−0.451672	+	0.621673i	0.521084	+	0.853505i	$0.325528\pi$
$734$	−31.6597	+	31.3978i	−1.16858	+	1.15891i
$735$	−5.49464	+	16.9108i	−0.202673	+	0.623763i
$736$	−10.0461	+	9.63735i	−0.370303	+	0.355237i
$737$		0			0
$738$	1.67291	−	0.257847i	0.0615807	−	0.00949147i
$739$	−2.61653	−	0.850163i	−0.0962507	−	0.0312737i	0.260496	−	0.965475i	$-0.416114\pi$
$739$	−2.61653	−	0.850163i	−0.0962507	−	0.0312737i	−0.356746	+	0.934201i	$0.616114\pi$
$740$	23.2856	−	31.4964i	0.855995	−	1.15783i
$741$	8.75148	−	12.0454i	0.321494	−	0.442498i
$742$	3.65838	−	1.84494i	0.134303	−	0.0677300i
$743$	−13.8990	−	42.7766i	−0.509903	−	1.56932i	−0.792368	−	0.610043i	$-0.791152\pi$
$743$	−13.8990	−	42.7766i	−0.509903	−	1.56932i	0.282465	−	0.959278i	$-0.408848\pi$
$744$	3.79247	−	22.1549i	0.139039	−	0.812237i
$745$	−37.4570	+	27.2141i	−1.37232	+	0.997046i
$746$	34.6516	+	5.63587i	1.26869	+	0.206344i
$747$		−	2.25182i		−	0.0823899i
$748$		0			0
$749$			15.3126i			0.559509i
$750$	2.53570	−	15.5905i	0.0925905	−	0.569284i
$751$	28.5391	−	20.7349i	1.04141	−	0.756626i	0.0708463	−	0.997487i	$-0.477430\pi$
$751$	28.5391	−	20.7349i	1.04141	−	0.756626i	0.970559	+	0.240862i	$0.0774300\pi$
$752$	−1.43530	−	0.0238420i	−0.0523398	−	0.000869427i
$753$	1.59935	+	4.92229i	0.0582835	+	0.179378i
$754$	−9.73438	−	19.3025i	−0.354505	−	0.702957i
$755$	32.7538	−	45.0817i	1.19203	−	1.64069i
$756$	8.75867	+	6.47536i	0.318550	+	0.235507i
$757$	44.5991	+	14.4911i	1.62098	+	0.526689i	0.972173	−	0.234263i	$-0.0752677\pi$
$757$	44.5991	+	14.4911i	1.62098	+	0.526689i	0.648808	+	0.760952i	$0.275268\pi$
$758$	7.69970	+	49.9557i	0.279666	+	1.81447i
$759$		0			0
$760$	−40.1221	+	19.8176i	−1.45538	+	0.718860i
$761$	−1.36665	+	4.20610i	−0.0495409	+	0.152471i	−0.972767	−	0.231787i	$-0.925543\pi$
$761$	−1.36665	+	4.20610i	−0.0495409	+	0.152471i	0.923226	+	0.384258i	$0.125543\pi$
$762$	8.00748	+	8.07425i	0.290080	+	0.292499i
$763$	3.97195	−	5.46691i	0.143794	−	0.197916i
$764$	−2.87016	−	4.02023i	−0.103839	−	0.145447i
$765$	−24.9503	+	8.10685i	−0.902081	+	0.293104i
$766$	−23.9380	−	12.3225i	−0.864914	−	0.445229i
$767$	1.91827	−	1.39371i	0.0692648	−	0.0503238i
$768$	−8.53813	+	10.9664i	−0.308093	+	0.395716i
$769$	−53.6158			−1.93344			−0.966718	−	0.255844i	$-0.917647\pi$
$769$	−53.6158			−1.93344			−0.966718	+	0.255844i	$0.917647\pi$
$770$		0			0
$771$			12.3071i			0.443229i
$772$	0.166197	−	20.0116i	0.00598156	−	0.720234i
$773$	−25.2658	−	34.7754i	−0.908749	−	1.25079i	−0.967592	−	0.252518i	$-0.918741\pi$
$773$	−25.2658	−	34.7754i	−0.908749	−	1.25079i	0.0588433	−	0.998267i	$-0.481259\pi$
$774$	−9.47232	+	18.4012i	−0.340475	+	0.661416i
$775$	−24.0289	−	73.9534i	−0.863144	−	2.65648i
$776$	11.7522	+	12.0487i	0.421879	+	0.432523i
$777$	−4.47739	−	3.25302i	−0.160626	−	0.116701i
$778$	32.4343	+	32.7048i	1.16283	+	1.17252i
$779$	2.18293	+	0.709277i	0.0782116	+	0.0254125i
$780$	−7.65054	−	24.2288i	−0.273933	−	0.867529i
$781$		0			0
$782$	−10.9377	+	1.68583i	−0.391131	+	0.0602852i
$783$	5.40719	−	16.6416i	0.193237	−	0.594723i
$784$	7.23758	−	21.0772i	0.258485	−	0.752757i
$785$	4.53786	+	3.29694i	0.161963	+	0.117673i
$786$	7.37247	+	14.6190i	0.262967	+	0.521444i
$787$	14.4914	−	4.70853i	0.516562	−	0.167841i	−0.0391226	−	0.999234i	$-0.512456\pi$
$787$	14.4914	−	4.70853i	0.516562	−	0.167841i	0.555684	+	0.831393i	$0.312456\pi$
$788$	7.47490	−	22.3715i	0.266282	−	0.796951i
$789$	−5.62407	−	7.74086i	−0.200222	−	0.275582i
$790$	−58.9798	−	9.59270i	−2.09841	−	0.341293i
$791$	−19.1230			−0.679937
$792$		0			0
$793$	29.0152			1.03036
$794$	−18.1662	−	2.95463i	−0.644696	−	0.104856i
$795$	−4.54703	−	6.25845i	−0.161267	−	0.221964i
$796$	28.0491	+	9.37194i	0.994174	+	0.332180i
$797$	30.7264	−	9.98362i	1.08839	−	0.353638i	0.290764	−	0.956795i	$-0.406091\pi$
$797$	30.7264	−	9.98362i	1.08839	−	0.353638i	0.797623	+	0.603157i	$0.206091\pi$
$798$	2.84707	+	5.64552i	0.100785	+	0.199849i
$799$	−0.923216	−	0.670755i	−0.0326610	−	0.0237296i
$800$	−8.50577	+	47.3225i	−0.300724	+	1.67310i
$801$	9.46938	−	29.1438i	0.334584	−	1.02974i
$802$	−28.7283	+	4.42792i	−1.01443	+	0.156355i
$803$		0			0
$804$	−18.6692	+	5.89504i	−0.658412	+	0.207902i
$805$	10.2788	+	3.33977i	0.362279	+	0.117711i
$806$	−36.2647	−	36.5671i	−1.27737	−	1.28802i
$807$	−1.74512	−	1.26790i	−0.0614312	−	0.0446324i
$808$	12.0982	−	11.8005i	0.425612	−	0.415138i
$809$	−15.5606	−	47.8907i	−0.547082	−	1.68375i	−0.715987	−	0.698113i	$-0.754023\pi$
$809$	−15.5606	−	47.8907i	−0.547082	−	1.68375i	0.168905	−	0.985632i	$-0.445977\pi$
$810$	−6.60772	+	12.8363i	−0.232172	+	0.451023i
$811$	−25.6617	−	35.3204i	−0.901106	−	1.24027i	−0.970114	−	0.242649i	$-0.921984\pi$
$811$	−25.6617	−	35.3204i	−0.901106	−	1.24027i	0.0690084	−	0.997616i	$-0.478016\pi$
$812$	9.18016	+	0.0762414i	0.322160	+	0.00267555i
$813$			0.267306i			0.00937483i
$814$		0			0
$815$	57.0827			1.99952
$816$	−10.5630	+	3.23919i	−0.369780	+	0.113394i
$817$	−22.7043	+	16.4957i	−0.794323	+	0.577110i
$818$	−12.3991	−	6.38263i	−0.433523	−	0.223164i
$819$	10.1606	−	3.30139i	0.355042	−	0.115360i
$820$	3.18783	−	2.27589i	0.111324	−	0.0794774i
$821$	−11.1672	+	15.3703i	−0.389736	+	0.536426i	−0.958131	−	0.286330i	$-0.907565\pi$
$821$	−11.1672	+	15.3703i	−0.389736	+	0.536426i	0.568395	+	0.822756i	$0.307565\pi$
$822$	8.39845	+	8.46849i	0.292930	+	0.295373i
$823$	−4.08288	+	12.5658i	−0.142320	+	0.438017i	−0.996657	−	0.0817036i	$-0.973964\pi$
$823$	−4.08288	+	12.5658i	−0.142320	+	0.438017i	0.854336	+	0.519720i	$0.173964\pi$
$824$	9.95521	−	4.91720i	0.346806	−	0.171299i
$825$		0			0
$826$	0.153387	+	0.995176i	0.00533702	+	0.0346266i
$827$	−16.8815	−	5.48515i	−0.587029	−	0.190737i	0.000418135	−	1.00000i	$-0.499867\pi$
$827$	−16.8815	−	5.48515i	−0.587029	−	0.190737i	−0.587447	+	0.809263i	$0.699867\pi$
$828$	−6.57022	+	8.88699i	−0.228331	+	0.308844i
$829$	5.03360	−	6.92816i	0.174824	−	0.240625i	−0.712609	−	0.701562i	$-0.752486\pi$
$829$	5.03360	−	6.92816i	0.174824	−	0.240625i	0.887433	+	0.460937i	$0.152486\pi$
$830$	−2.34635	−	4.65263i	−0.0814429	−	0.161495i
$831$	0.671065	+	2.06533i	0.0232790	+	0.0716454i
$832$	9.08285	+	30.5213i	0.314891	+	1.05814i
$833$	14.3324	−	10.4131i	0.496588	−	0.360792i
$834$	−4.38885	+	26.9844i	−0.151973	+	0.934393i
$835$			30.8389i			1.06723i
$836$		0			0
$837$		−	41.6850i		−	1.44084i
$838$	−0.236024	−	0.0383879i	−0.00815333	−	0.00132609i
$839$	30.7967	−	22.3751i	1.06322	−	0.772474i	0.0885383	−	0.996073i	$-0.471780\pi$
$839$	30.7967	−	22.3751i	1.06322	−	0.772474i	0.974681	+	0.223598i	$0.0717804\pi$
$840$	10.6352	+	1.82053i	0.366948	+	0.0628141i
$841$	4.40414	+	13.5546i	0.151867	+	0.467398i
$842$	29.6903	−	14.9730i	1.02320	−	0.516004i
$843$	−0.634715	+	0.873611i	−0.0218608	+	0.0300888i
$844$	13.6798	+	10.1136i	0.470879	+	0.348125i
$845$	−9.93967	−	3.22959i	−0.341935	−	0.111101i
$846$	−1.12633	+	0.173601i	−0.0387239	+	0.00596853i
$847$		0			0
$848$	5.56779	+	7.93737i	0.191199	+	0.272571i
$849$	3.70476	−	11.4021i	0.127147	−	0.391318i
$850$	−27.1392	+	26.9147i	−0.930866	+	0.923168i
$851$	7.71046	−	10.6125i	0.264311	−	0.363793i
$852$	7.89972	−	5.63984i	0.270640	−	0.193218i
$853$	32.5718	−	10.5832i	1.11524	−	0.362362i	0.307288	−	0.951616i	$-0.400578\pi$
$853$	32.5718	−	10.5832i	1.11524	−	0.362362i	0.807948	+	0.589254i	$0.200578\pi$
$854$	−5.63949	+	10.9554i	−0.192979	+	0.374887i
$855$	−28.7413	+	20.8818i	−0.982933	+	0.714142i
$856$	−35.8563	+	5.22208i	−1.22554	+	0.178487i
$857$	52.8215			1.80435			0.902174	−	0.431371i	$-0.141970\pi$
$857$	52.8215			1.80435			0.902174	+	0.431371i	$0.141970\pi$
$858$		0			0
$859$		−	8.91497i		−	0.304175i	−0.988367	−	0.152087i	$-0.951400\pi$
$859$		−	8.91497i		−	0.304175i	0.988367	−	0.152087i	$-0.0485995\pi$
$860$	−0.397725	+	47.8897i	−0.0135623	+	1.63303i
$861$	−0.325296	−	0.447732i	−0.0110861	−	0.0152587i
$862$	9.16985	+	4.72034i	0.312326	+	0.160775i
$863$	−0.324037	−	0.997282i	−0.0110303	−	0.0339479i	0.945390	−	0.325942i	$-0.105681\pi$
$863$	−0.324037	−	0.997282i	−0.0110303	−	0.0339479i	−0.956420	+	0.291994i	$0.905681\pi$
$864$	−12.1759	+	22.7178i	−0.414232	+	0.772876i
$865$	−73.9027	−	53.6934i	−2.51277	−	1.82563i
$866$	2.34799	−	2.32857i	0.0797880	−	0.0791281i
$867$	5.69091	+	1.84909i	0.193273	+	0.0627984i
$868$	20.8553	−	6.58533i	0.707876	−	0.223521i
$869$		0			0
$870$	−2.64041	−	17.1310i	−0.0895182	−	0.580794i
$871$	−13.8617	+	42.6618i	−0.469685	+	1.44554i
$872$	14.1560	+	7.43641i	0.479383	+	0.251829i
$873$	10.8101	+	7.85400i	0.365867	+	0.265818i
$874$	−13.3813	+	6.74826i	−0.452629	+	0.228263i
$875$	14.6167	−	4.74926i	0.494136	−	0.160554i
$876$	−1.47091	+	4.40224i	−0.0496973	+	0.148738i
$877$	−7.10243	−	9.77565i	−0.239832	−	0.330100i	0.672086	−	0.740473i	$-0.265399\pi$
$877$	−7.10243	−	9.77565i	−0.239832	−	0.330100i	−0.911918	+	0.410373i	$0.865399\pi$
$878$	−0.275616	+	1.69460i	−0.00930158	+	0.0571899i
$879$	12.9294			0.436096
$880$		0			0
$881$	11.8356			0.398752			0.199376	−	0.979923i	$-0.436109\pi$
$881$	11.8356			0.398752			0.199376	+	0.979923i	$0.436109\pi$
$882$	2.84018	−	17.4626i	0.0956338	−	0.587995i
$883$	30.0534	+	41.3650i	1.01138	+	1.39204i	0.918075	+	0.396406i	$0.129743\pi$
$883$	30.0534	+	41.3650i	1.01138	+	1.39204i	0.0933036	+	0.995638i	$0.470257\pi$
$884$	−8.02236	+	24.0100i	−0.269821	+	0.807542i
$885$	1.80809	−	0.587484i	0.0607783	−	0.0197481i
$886$	−5.83224	+	2.94124i	−0.195938	+	0.0988127i
$887$	13.7419	+	9.98405i	0.461407	+	0.335232i	0.794083	−	0.607810i	$-0.207952\pi$
$887$	13.7419	+	9.98405i	0.461407	+	0.335232i	−0.332676	+	0.943041i	$0.607952\pi$
$888$	6.09041	−	11.5938i	0.204381	−	0.389061i
$889$	−3.41915	+	10.5231i	−0.114675	+	0.352932i
$890$	−10.8019	−	70.0826i	−0.362080	−	2.34917i
$891$		0			0
$892$	9.57966	−	3.02490i	0.320751	−	0.101281i
$893$	−1.46971	−	0.477537i	−0.0491819	−	0.0159802i
$894$	−10.9914	+	10.9004i	−0.367606	+	0.364566i
$895$	49.0041	+	35.6035i	1.63802	+	1.19009i
$896$	−13.2894	−	2.50276i	−0.443969	−	0.0836113i
$897$	−2.62946	−	8.09264i	−0.0877951	−	0.270205i
$898$	7.37942	+	3.79868i	0.246254	+	0.126764i
$899$	−20.6509	−	28.4235i	−0.688746	−	0.947978i
$900$	−0.316999	+	38.1696i	−0.0105666	+	1.27232i
$901$			7.70750i			0.256774i
$902$		0			0
$903$	6.76671			0.225182
$904$	−6.52158	−	44.7790i	−0.216904	−	1.48933i
$905$	−27.2845	+	19.8233i	−0.906966	+	0.658950i
$906$	8.52720	−	16.5652i	0.283297	−	0.550340i
$907$	13.6986	−	4.45094i	0.454855	−	0.147791i	−0.0726243	−	0.997359i	$-0.523137\pi$
$907$	13.6986	−	4.45094i	0.454855	−	0.147791i	0.527479	+	0.849568i	$0.323137\pi$
$908$	29.4176	−	21.0021i	0.976256	−	0.696978i
$909$	7.88626	−	10.8545i	0.261571	−	0.360021i
$910$	17.5536	−	17.4084i	0.581895	−	0.577082i
$911$	−12.3572	+	38.0317i	−0.409414	+	1.26005i	0.507739	+	0.861511i	$0.330481\pi$
$911$	−12.3572	+	38.0317i	−0.409414	+	1.26005i	−0.917153	+	0.398535i	$0.869519\pi$
$912$	−12.2487	+	8.59207i	−0.405596	+	0.284512i
$913$		0			0
$914$	−34.2402	+	5.27746i	−1.13256	+	0.174563i
$915$	22.1255	+	7.18901i	0.731446	+	0.237661i
$916$	6.40487	+	4.73517i	0.211623	+	0.156455i
$917$	−9.36391	+	12.8883i	−0.309224	+	0.425610i
$918$	−18.2953	+	9.22641i	−0.603833	+	0.304517i
$919$	2.18755	+	6.73259i	0.0721607	+	0.222088i	0.980632	−	0.195860i	$-0.0627497\pi$
$919$	2.18755	+	6.73259i	0.0721607	+	0.222088i	−0.908471	+	0.417947i	$0.862750\pi$
$920$	−4.31510	+	25.2080i	−0.142265	+	0.831082i
$921$	5.90560	−	4.29067i	0.194596	−	0.141382i
$922$	−9.21105	−	1.49812i	−0.303350	−	0.0493380i
$923$		−	22.2395i		−	0.732022i
$924$		0			0
$925$		−	45.3058i		−	1.48965i
$926$	3.27381	−	20.1287i	0.107584	−	0.661471i
$927$	7.13138	−	5.18125i	0.234225	−	0.170175i
$928$	2.95220	+	21.5225i	0.0969107	+	0.706510i
$929$	−11.8469	−	36.4610i	−0.388684	−	1.19625i	−0.933772	−	0.357867i	$-0.883504\pi$
$929$	−11.8469	−	36.4610i	−0.388684	−	1.19625i	0.545089	−	0.838378i	$-0.316496\pi$
$930$	−18.5934	−	36.8694i	−0.609703	−	1.20899i
$931$	14.1013	−	19.4088i	0.462151	−	0.636097i
$932$	14.6069	−	19.7575i	0.478464	−	0.647178i
$933$	−21.1870	−	6.88409i	−0.693632	−	0.225375i
$934$	−1.18245	−	7.67174i	−0.0386909	−	0.251027i
$935$		0			0
$936$	11.1957	+	22.6665i	0.365944	+	0.740879i
$937$	17.9279	−	55.1764i	0.585679	−	1.80253i	−0.0108493	−	0.999941i	$-0.503454\pi$
$937$	17.9279	−	55.1764i	0.585679	−	1.80253i	0.596528	−	0.802592i	$-0.296546\pi$
$938$	−13.4138	−	13.5257i	−0.437977	−	0.441630i
$939$	−9.64086	+	13.2695i	−0.314618	+	0.433034i
$940$	−2.14628	+	1.53229i	−0.0700039	+	0.0499779i
$941$	10.4977	−	3.41092i	0.342216	−	0.111193i	−0.132867	−	0.991134i	$-0.542418\pi$
$941$	10.4977	−	3.41092i	0.342216	−	0.111193i	0.475083	+	0.879941i	$0.342418\pi$
$942$	1.66742	+	0.858334i	0.0543276	+	0.0279660i
$943$	1.06124	−	0.771033i	0.0345586	−	0.0251083i
$944$	−2.27802	+	0.698562i	−0.0741432	+	0.0227363i
$945$	20.0103			0.650936
$946$		0			0
$947$		−	15.5478i		−	0.505235i	−0.967566	−	0.252617i	$-0.918709\pi$
$947$		−	15.5478i		−	0.505235i	0.967566	−	0.252617i	$-0.0812914\pi$
$948$	−19.9781	−	0.165918i	−0.648857	−	0.00538877i
$949$	6.25092	+	8.60365i	0.202913	+	0.279286i
$950$	−23.6899	+	46.0206i	−0.768602	+	1.49311i
$951$	−5.35850	−	16.4918i	−0.173761	−	0.534783i
$952$	−7.50630	−	7.69569i	−0.243281	−	0.249419i
$953$	6.33105	+	4.59978i	0.205083	+	0.149001i	0.685586	−	0.727992i	$-0.259546\pi$
$953$	6.33105	+	4.59978i	0.205083	+	0.149001i	−0.480503	+	0.876993i	$0.659546\pi$
$954$	5.42006	+	5.46526i	0.175481	+	0.176944i
$955$	−8.63041	−	2.80419i	−0.279274	−	0.0907415i
$956$	−39.9480	+	12.6141i	−1.29201	+	0.407969i
$957$		0			0
$958$	−41.7408	+	6.43354i	−1.34858	+	0.207858i
$959$	−3.58610	+	11.0369i	−0.115801	+	0.356399i
$960$	−0.636059	+	25.5244i	−0.0205287	+	0.823796i
$961$	−42.6329	−	30.9746i	−1.37525	−	0.999180i
$962$	−13.5114	−	26.7921i	−0.435625	−	0.863811i
$963$	−27.3584	+	8.88927i	−0.881611	+	0.286453i
$964$	33.0993	+	11.0594i	1.06606	+	0.356198i
$965$	−21.6096	−	29.7430i	−0.695637	−	0.957462i
$966$	3.56665	+	0.580093i	0.114755	+	0.0186642i
$967$	47.0564			1.51323			0.756615	−	0.653860i	$-0.226852\pi$
$967$	47.0564			1.51323			0.756615	+	0.653860i	$0.226852\pi$
$968$		0			0
$969$	−11.8940			−0.382090
$970$	30.5191	+	4.96375i	0.979910	+	0.159376i
$971$	−22.7992	−	31.3804i	−0.731662	−	1.00705i	−0.999055	−	0.0434585i	$-0.986162\pi$
$971$	−22.7992	−	31.3804i	−0.731662	−	1.00705i	0.267394	−	0.963587i	$-0.413838\pi$
$972$	−10.1934	+	30.5077i	−0.326954	+	0.978534i
$973$	−25.2990	+	8.22014i	−0.811049	+	0.263526i
$974$	1.89610	+	3.75981i	0.0607549	+	0.120472i
$975$	−23.7757	−	17.2741i	−0.761433	−	0.553213i
$976$	−27.5767	−	9.46941i	−0.882709	−	0.303108i
$977$	−12.0635	+	37.1276i	−0.385945	+	1.18782i	0.549847	+	0.835265i	$0.314686\pi$
$977$	−12.0635	+	37.1276i	−0.385945	+	1.18782i	−0.935792	+	0.352552i	$0.885314\pi$
$978$	18.8626	−	2.90731i	0.603160	−	0.0929654i
$979$		0			0
$980$	−12.3273	−	39.0399i	−0.393782	−	1.24708i
$981$	12.0733	+	3.92286i	0.385471	+	0.125247i
$982$	2.96815	+	2.99291i	0.0947176	+	0.0955075i
$983$	−4.54996	−	3.30574i	−0.145121	−	0.105437i	0.512856	−	0.858475i	$-0.328588\pi$
$983$	−4.54996	−	3.30574i	−0.145121	−	0.105437i	−0.657977	+	0.753038i	$0.728588\pi$
$984$	0.937484	−	0.914413i	0.0298859	−	0.0291504i
$985$	−13.3903	−	41.2110i	−0.426649	−	1.31309i
$986$	−7.90410	+	15.3547i	−0.251718	+	0.488994i
$987$	0.219013	+	0.301446i	0.00697127	+	0.00959513i
$988$	−0.284694	+	34.2798i	−0.00905733	+	1.09058i
$989$			16.0388i			0.510004i
$990$		0			0
$991$	7.34032			0.233173			0.116586	−	0.993181i	$-0.462805\pi$
$991$	7.34032			0.233173			0.116586	+	0.993181i	$0.462805\pi$
$992$	22.5327	+	46.5895i	0.715414	+	1.47922i
$993$	13.2555	−	9.63066i	0.420650	−	0.305620i
$994$	8.39708	+	4.32254i	0.266339	+	0.137103i
$995$	51.6699	−	16.7886i	1.63804	−	0.532233i
$996$	−1.01230	−	1.41793i	−0.0320760	−	0.0449287i
$997$	33.4680	−	46.0647i	1.05994	−	1.45888i	0.180081	−	0.983652i	$-0.442364\pi$
$997$	33.4680	−	46.0647i	1.05994	−	1.45888i	0.879861	−	0.475232i	$-0.157636\pi$
$998$	−15.1311	−	15.2573i	−0.478966	−	0.482960i
$999$	7.50522	−	23.0987i	0.237455	−	0.730811i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	968.2.o.d.493.5		40
8.5	even	2	inner	968.2.o.d.493.4		40
11.2	odd	10		88.2.o.a.69.4	yes	40
11.3	even	5		968.2.o.i.565.8		40
11.4	even	5		968.2.c.i.485.2		20
11.5	even	5	inner	968.2.o.d.269.4		40
11.6	odd	10		968.2.o.j.269.7		40
11.7	odd	10		968.2.c.h.485.19		20
11.8	odd	10		88.2.o.a.37.3	✓	40
11.9	even	5		968.2.o.i.245.7		40
11.10	odd	2		968.2.o.j.493.6		40
33.2	even	10		792.2.br.b.685.7		40
33.8	even	10		792.2.br.b.37.8		40
44.7	even	10		3872.2.c.h.1937.14		20
44.15	odd	10		3872.2.c.i.1937.14		20
44.19	even	10		352.2.w.a.81.7		40
44.35	even	10		352.2.w.a.113.4		40
88.5	even	10	inner	968.2.o.d.269.5		40
88.13	odd	10		88.2.o.a.69.3	yes	40
88.19	even	10		352.2.w.a.81.4		40
88.21	odd	2		968.2.o.j.493.7		40
88.29	odd	10		968.2.c.h.485.20		20
88.35	even	10		352.2.w.a.113.7		40
88.37	even	10		968.2.c.i.485.1		20
88.51	even	10		3872.2.c.h.1937.7		20
88.53	even	10		968.2.o.i.245.8		40
88.59	odd	10		3872.2.c.i.1937.7		20
88.61	odd	10		968.2.o.j.269.6		40
88.69	even	10		968.2.o.i.565.7		40
88.85	odd	10		88.2.o.a.37.4	yes	40
264.101	even	10		792.2.br.b.685.8		40
264.173	even	10		792.2.br.b.37.7		40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
88.2.o.a.37.3	✓	40	11.8	odd	10
88.2.o.a.37.4	yes	40	88.85	odd	10
88.2.o.a.69.3	yes	40	88.13	odd	10
88.2.o.a.69.4	yes	40	11.2	odd	10
352.2.w.a.81.4		40	88.19	even	10
352.2.w.a.81.7		40	44.19	even	10
352.2.w.a.113.4		40	44.35	even	10
352.2.w.a.113.7		40	88.35	even	10
792.2.br.b.37.7		40	264.173	even	10
792.2.br.b.37.8		40	33.8	even	10
792.2.br.b.685.7		40	33.2	even	10
792.2.br.b.685.8		40	264.101	even	10
968.2.c.h.485.19		20	11.7	odd	10
968.2.c.h.485.20		20	88.29	odd	10
968.2.c.i.485.1		20	88.37	even	10
968.2.c.i.485.2		20	11.4	even	5
968.2.o.d.269.4		40	11.5	even	5	inner
968.2.o.d.269.5		40	88.5	even	10	inner
968.2.o.d.493.4		40	8.5	even	2	inner
968.2.o.d.493.5		40	1.1	even	1	trivial
968.2.o.i.245.7		40	11.9	even	5
968.2.o.i.245.8		40	88.53	even	10
968.2.o.i.565.7		40	88.69	even	10
968.2.o.i.565.8		40	11.3	even	5
968.2.o.j.269.6		40	88.61	odd	10
968.2.o.j.269.7		40	11.6	odd	10
968.2.o.j.493.6		40	11.10	odd	2
968.2.o.j.493.7		40	88.21	odd	2
3872.2.c.h.1937.7		20	88.51	even	10
3872.2.c.h.1937.14		20	44.7	even	10
3872.2.c.i.1937.7		20	88.59	odd	10
3872.2.c.i.1937.14		20	44.15	odd	10

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:	\( N \)	\(=\)	\( 968 = 2^{3} \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	968.o (of order \(10\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.227030 + 1.39587i) q^{2} +(0.510574 + 0.702745i) q^{3} +(-1.89691 - 0.633809i) q^{4} +(-3.49435 + 1.13538i) q^{5} +(-1.09686 + 0.553152i) q^{6} +(-0.967003 - 0.702569i) q^{7} +(1.31537 - 2.50396i) q^{8} +(0.693886 - 2.13556i) q^{9} +(-0.791527 - 5.13543i) q^{10} +(-0.523110 - 1.65665i) q^{12} +(-3.78569 - 1.23005i) q^{13} +(1.20023 - 1.19031i) q^{14} +(-2.58201 - 1.87594i) q^{15} +(3.19657 + 2.40456i) q^{16} +(0.982622 + 3.02420i) q^{17} +(2.82344 + 1.45341i) q^{18} +(2.53106 + 3.48370i) q^{19} +(7.34810 + 0.0610261i) q^{20} -1.03827i q^{21} +2.46096 q^{23} +(2.43124 - 0.354084i) q^{24} +(6.87629 - 4.99592i) q^{25} +(2.57645 - 5.00509i) q^{26} +(4.33342 - 1.40801i) q^{27} +(1.38903 + 1.94561i) q^{28} +(2.25727 - 3.10687i) q^{29} +(3.20476 - 3.17826i) q^{30} +(2.82708 - 8.70085i) q^{31} +(-4.08218 + 3.91610i) q^{32} +(-4.44448 + 0.685031i) q^{34} +(4.17673 + 1.35710i) q^{35} +(-2.66978 + 3.61119i) q^{36} +(3.13311 - 4.31236i) q^{37} +(-5.43743 + 2.74213i) q^{38} +(-1.06847 - 3.28841i) q^{39} +(-1.75342 + 10.2431i) q^{40} +(0.431229 - 0.313306i) q^{41} +(1.44929 + 0.235718i) q^{42} +6.51729i q^{43} +8.25022i q^{45} +(-0.558711 + 3.43518i) q^{46} +(-0.290335 + 0.210940i) q^{47} +(-0.0577087 + 3.47409i) q^{48} +(-1.72163 - 5.29862i) q^{49} +(5.41254 + 10.7326i) q^{50} +(-1.62354 + 2.23461i) q^{51} +(6.40153 + 4.73270i) q^{52} +(2.30524 + 0.749017i) q^{53} +(0.981589 + 6.36855i) q^{54} +(-3.03117 + 1.49719i) q^{56} +(-1.15586 + 3.55738i) q^{57} +(3.82432 + 3.85621i) q^{58} +(-0.350132 + 0.481916i) q^{59} +(3.70886 + 5.19500i) q^{60} +(-6.93255 + 2.25252i) q^{61} +(11.5034 + 5.92159i) q^{62} +(-2.17137 + 1.57759i) q^{63} +(-4.53959 - 6.58727i) q^{64} +14.6251 q^{65} -11.2692i q^{67} +(0.0528154 - 6.35945i) q^{68} +(1.25650 + 1.72943i) q^{69} +(-2.84258 + 5.52207i) q^{70} +(1.72651 + 5.31364i) q^{71} +(-4.43463 - 4.54652i) q^{72} +(-2.16144 - 1.57038i) q^{73} +(5.30819 + 5.35246i) q^{74} +(7.02172 + 2.28149i) q^{75} +(-2.59320 - 8.21250i) q^{76} +(4.83277 - 0.744878i) q^{78} +(3.55369 - 10.9371i) q^{79} +(-13.9000 - 4.77305i) q^{80} +(-2.24785 - 1.63316i) q^{81} +(0.339433 + 0.673070i) q^{82} +(0.953750 - 0.309892i) q^{83} +(-0.658065 + 1.96951i) q^{84} +(-6.86725 - 9.45196i) q^{85} +(-9.09731 - 1.47962i) q^{86} +3.33584 q^{87} +13.6469 q^{89} +(-11.5163 - 1.87305i) q^{90} +(2.79658 + 3.84917i) q^{91} +(-4.66823 - 1.55978i) q^{92} +(7.55791 - 2.45571i) q^{93} +(-0.228531 - 0.453160i) q^{94} +(-12.7997 - 9.29955i) q^{95} +(-4.83627 - 0.869275i) q^{96} +(-1.83886 + 5.65943i) q^{97} +(7.78706 - 1.20022i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 5 q^{2} - q^{4} - 8 q^{6} - 5 q^{8} + 10 q^{9} + 20 q^{10} - 6 q^{12} + 2 q^{14} + 22 q^{15} - 25 q^{16} - 4 q^{17} - 25 q^{18} + 8 q^{20} - 8 q^{23} + 40 q^{24} + 6 q^{25} - 20 q^{26} + 18 q^{28}+ \cdots + 144 q^{98}+O(q^{100}) \) 40 * q - 5 * q^2 - q^4 - 8 * q^6 - 5 * q^8 + 10 * q^9 + 20 * q^10 - 6 * q^12 + 2 * q^14 + 22 * q^15 - 25 * q^16 - 4 * q^17 - 25 * q^18 + 8 * q^20 - 8 * q^23 + 40 * q^24 + 6 * q^25 - 20 * q^26 + 18 * q^28 - 12 * q^30 + 4 * q^31 - 20 * q^32 + 10 * q^34 - 27 * q^36 - 33 * q^38 - 6 * q^39 + 20 * q^40 - 16 * q^41 - 20 * q^42 + 42 * q^46 + 4 * q^47 + 23 * q^48 + 6 * q^49 + 39 * q^50 - 108 * q^54 - 32 * q^56 - 4 * q^57 - 16 * q^58 + 94 * q^60 + 52 * q^62 + 30 * q^63 + 11 * q^64 + 36 * q^65 - 63 * q^68 + 52 * q^70 + 12 * q^71 - 44 * q^72 - 4 * q^73 + 26 * q^74 + 134 * q^76 - 12 * q^78 + 16 * q^79 + 16 * q^80 + 16 * q^81 + 54 * q^82 - 72 * q^84 - 10 * q^86 - 68 * q^87 - 16 * q^89 - 126 * q^90 - 64 * q^92 - 40 * q^94 - 26 * q^95 + 5 * q^96 - 20 * q^97 + 144 * q^98

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