LMFDB - Embedded newform 445.2.o.b.16.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [445,2,Mod(16,445)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(445, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 16]))

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

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

chi := DirichletCharacter("445.16");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 445 = 5 \cdot 89 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	445.o (of order $11$, degree $10$, 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:	$3.55334288995$
Analytic rank:	$0$
Dimension:	$160$
Relative dimension:	$16$ over $\Q(\zeta_{11})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			16.7
Character	$\chi$	$=$	445.16
Dual form			445.2.o.b.306.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.253332 + 0.554720i) q^{2} +(-2.20686 + 2.54685i) q^{3} +(1.06618 + 1.23044i) q^{4} +(-0.959493 + 0.281733i) q^{5} +(-0.853719 - 1.86938i) q^{6} +(-3.40176 + 0.998847i) q^{7} +(-2.12290 + 0.623340i) q^{8} +(-1.18928 - 8.27159i) q^{9} +(0.0867877 - 0.603621i) q^{10} +(0.380364 + 0.111685i) q^{11} -5.48667 q^{12} +(2.57520 - 2.97194i) q^{13} +(0.307695 - 2.14006i) q^{14} +(1.39993 - 3.06543i) q^{15} +(-0.271388 + 1.88755i) q^{16} +(0.0194207 + 0.0425254i) q^{17} +(4.88970 + 1.43574i) q^{18} +(0.782901 + 5.44520i) q^{19} +(-1.36965 - 0.880222i) q^{20} +(4.96329 - 10.8681i) q^{21} +(-0.158312 + 0.182702i) q^{22} +(1.02544 + 7.13210i) q^{23} +(3.09739 - 6.78233i) q^{24} +(0.841254 - 0.540641i) q^{25} +(0.996214 + 2.18141i) q^{26} +(15.1861 + 9.75949i) q^{27} +(-4.85593 - 3.12072i) q^{28} +(-4.93733 + 1.44973i) q^{29} +(1.34580 + 1.55314i) q^{30} +(1.09007 - 7.58161i) q^{31} +(-4.70090 - 3.02108i) q^{32} +(-1.12385 + 0.722257i) q^{33} -0.0285096 q^{34} +(2.98256 - 1.91677i) q^{35} +(8.90973 - 10.2824i) q^{36} +1.06169 q^{37} +(-3.21889 - 0.945152i) q^{38} +(1.88598 + 13.1173i) q^{39} +(1.86129 - 1.19618i) q^{40} +(-3.62585 - 4.18445i) q^{41} +(4.77138 + 5.50647i) q^{42} +(-4.40848 - 1.29445i) q^{43} +(0.268117 + 0.587094i) q^{44} +(3.47148 + 7.60148i) q^{45} +(-4.21609 - 1.23796i) q^{46} +(-8.64467 - 9.97648i) q^{47} +(-4.20838 - 4.85673i) q^{48} +(4.68551 - 3.01120i) q^{49} +(0.0867877 + 0.603621i) q^{50} +(-0.151165 - 0.0443859i) q^{51} +6.40245 q^{52} +(-1.45266 + 1.67646i) q^{53} +(-9.26090 + 5.95162i) q^{54} -0.396422 q^{55} +(6.59898 - 4.24091i) q^{56} +(-15.5958 - 10.0228i) q^{57} +(0.446590 - 3.10610i) q^{58} +(-3.51770 - 4.05964i) q^{59} +(5.26442 - 1.54577i) q^{60} +(5.45273 + 3.50426i) q^{61} +(3.92952 + 2.52535i) q^{62} +(12.3077 + 26.9501i) q^{63} +(-0.341727 + 0.219615i) q^{64} +(-1.63360 + 3.57708i) q^{65} +(-0.115942 - 0.806395i) q^{66} +(4.28732 - 4.94783i) q^{67} +(-0.0316190 + 0.0692361i) q^{68} +(-20.4274 - 13.1279i) q^{69} +(0.307695 + 2.14006i) q^{70} +(-2.97633 - 0.873930i) q^{71} +(7.68073 + 16.8185i) q^{72} +(0.641276 - 4.46017i) q^{73} +(-0.268960 + 0.588941i) q^{74} +(-0.479596 + 3.33566i) q^{75} +(-5.86529 + 6.76890i) q^{76} -1.40547 q^{77} +(-7.75421 - 2.27684i) q^{78} +(-1.91000 + 13.2843i) q^{79} +(-0.271388 - 1.88755i) q^{80} +(-34.3150 + 10.0758i) q^{81} +(3.23974 - 0.951274i) q^{82} +(-0.619556 - 1.35664i) q^{83} +(18.6643 - 5.48034i) q^{84} +(-0.0306148 - 0.0353314i) q^{85} +(1.83486 - 2.11755i) q^{86} +(7.20374 - 15.7740i) q^{87} -0.877094 q^{88} +(-5.63476 + 7.56634i) q^{89} -5.09612 q^{90} +(-5.79171 + 12.6821i) q^{91} +(-7.68233 + 8.86588i) q^{92} +(16.9036 + 19.5078i) q^{93} +(7.72412 - 2.26801i) q^{94} +(-2.28528 - 5.00406i) q^{95} +(18.0684 - 5.30537i) q^{96} +(-11.1581 + 3.27632i) q^{97} +(0.483379 + 3.36198i) q^{98} +(0.471455 - 3.27904i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 160 q - 2 q^{2} - 2 q^{3} - 22 q^{4} - 16 q^{5} - 6 q^{6} - 2 q^{7} - 6 q^{8} - 32 q^{9} - 2 q^{10} - q^{11} - 16 q^{12} - 8 q^{13} + 27 q^{14} - 2 q^{15} - 34 q^{16} + 19 q^{17} + 53 q^{18} - 14 q^{19}+ \cdots + 50 q^{99}+O(q^{100}) $ 160 * q - 2 * q^2 - 2 * q^3 - 22 * q^4 - 16 * q^5 - 6 * q^6 - 2 * q^7 - 6 * q^8 - 32 * q^9 - 2 * q^10 - q^11 - 16 * q^12 - 8 * q^13 + 27 * q^14 - 2 * q^15 - 34 * q^16 + 19 * q^17 + 53 * q^18 - 14 * q^19 - 22 * q^20 - 26 * q^21 + 34 * q^22 + 33 * q^23 + 50 * q^24 - 16 * q^25 - 35 * q^26 + 7 * q^27 + 49 * q^28 - 17 * q^29 - 6 * q^30 + 20 * q^31 + 11 * q^32 - 20 * q^33 + 2 * q^34 - 2 * q^35 - 102 * q^36 + 130 * q^37 - 19 * q^38 + 3 * q^39 - 6 * q^40 - 52 * q^41 - 92 * q^42 - 26 * q^43 + 14 * q^44 + q^45 + 102 * q^46 - 4 * q^47 + 3 * q^48 - 68 * q^49 - 2 * q^50 + 46 * q^51 - 66 * q^52 - 2 * q^53 - 79 * q^54 + 32 * q^55 + 199 * q^56 - 86 * q^57 - 74 * q^58 - 47 * q^59 - 16 * q^60 - 24 * q^61 + 41 * q^62 + 94 * q^63 + 70 * q^64 + 25 * q^65 - 130 * q^66 + 21 * q^67 - 57 * q^68 + 64 * q^69 + 27 * q^70 - 26 * q^71 - 66 * q^72 + 12 * q^73 - 70 * q^74 - 2 * q^75 - 137 * q^76 - 100 * q^77 - 170 * q^78 - 59 * q^79 - 34 * q^80 - 84 * q^81 + 359 * q^82 - 39 * q^83 + 202 * q^84 - 14 * q^85 - 108 * q^86 + 133 * q^87 + 48 * q^88 + 42 * q^90 + 22 * q^91 + 57 * q^92 + 69 * q^93 - 74 * q^94 - 3 * q^95 - 116 * q^96 - 37 * q^97 + 3 * q^98 + 50 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/445\mathbb{Z}\right)^\times$.

$n$	$181$	$357$
$\chi(n)$	$e\left(\frac{8}{11}\right)$	$1$

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 $

$2$	−0.253332	+	0.554720i	−0.179133	+	0.392246i	−0.977804	−	0.209522i	$-0.932809\pi$
$2$	−0.253332	+	0.554720i	−0.179133	+	0.392246i	0.798671	+	0.601768i	$0.205537\pi$
$3$	−2.20686	+	2.54685i	−1.27413	+	1.47042i	−0.462075	+	0.886841i	$0.652895\pi$
$3$	−2.20686	+	2.54685i	−1.27413	+	1.47042i	−0.812054	+	0.583583i	$0.801650\pi$
$4$	1.06618	+	1.23044i	0.533092	+	0.615221i
$5$	−0.959493	+	0.281733i	−0.429098	+	0.125995i
$5$	−0.959493	+	0.281733i	−0.429098	+	0.125995i
$6$	−0.853719	−	1.86938i	−0.348529	−	0.763173i
$7$	−3.40176	+	0.998847i	−1.28575	+	0.377529i	−0.852017	−	0.523515i	$-0.824620\pi$
$7$	−3.40176	+	0.998847i	−1.28575	+	0.377529i	−0.433728	+	0.901044i	$0.642802\pi$
$8$	−2.12290	+	0.623340i	−0.750559	+	0.220384i
$9$	−1.18928	−	8.27159i	−0.396425	−	2.75720i
$10$	0.0867877	−	0.603621i	0.0274447	−	0.190882i
$11$	0.380364	+	0.111685i	0.114684	+	0.0336743i	0.338571	−	0.940941i	$-0.390056\pi$
$11$	0.380364	+	0.111685i	0.114684	+	0.0336743i	−0.223887	+	0.974615i	$0.571875\pi$
$12$	−5.48667			−1.58386
$13$	2.57520	−	2.97194i	0.714233	−	0.824269i	−0.276368	−	0.961052i	$-0.589131\pi$
$13$	2.57520	−	2.97194i	0.714233	−	0.824269i	0.990601	+	0.136783i	$0.0436762\pi$
$14$	0.307695	−	2.14006i	0.0822349	−	0.571956i
$15$	1.39993	−	3.06543i	0.361461	−	0.791490i
$16$	−0.271388	+	1.88755i	−0.0678471	+	0.471887i
$17$	0.0194207	+	0.0425254i	0.00471022	+	0.0103139i	0.911972	−	0.410251i	$-0.134559\pi$
$17$	0.0194207	+	0.0425254i	0.00471022	+	0.0103139i	−0.907262	+	0.420565i	$0.861832\pi$
$18$	4.88970	+	1.43574i	1.15251	+	0.338408i
$19$	0.782901	+	5.44520i	0.179610	+	1.24921i	0.857667	+	0.514205i	$0.171913\pi$
$19$	0.782901	+	5.44520i	0.179610	+	1.24921i	−0.678057	+	0.735009i	$0.737178\pi$
$20$	−1.36965	−	0.880222i	−0.306264	−	0.196824i
$21$	4.96329	−	10.8681i	1.08308	−	2.37161i
$22$	−0.158312	+	0.182702i	−0.0337523	+	0.0389522i
$23$	1.02544	+	7.13210i	0.213819	+	1.48715i	0.760244	+	0.649637i	$0.225079\pi$
$23$	1.02544	+	7.13210i	0.213819	+	1.48715i	−0.546425	+	0.837508i	$0.684012\pi$
$24$	3.09739	−	6.78233i	0.632251	−	1.38444i
$25$	0.841254	−	0.540641i	0.168251	−	0.108128i
$26$	0.996214	+	2.18141i	0.195374	+	0.427809i
$27$	15.1861	+	9.75949i	2.92256	+	1.87821i
$28$	−4.85593	−	3.12072i	−0.917685	−	0.589760i
$29$	−4.93733	+	1.44973i	−0.916840	+	0.269208i	−0.705917	−	0.708294i	$-0.749465\pi$
$29$	−4.93733	+	1.44973i	−0.916840	+	0.269208i	−0.210922	+	0.977503i	$0.567647\pi$
$30$	1.34580	+	1.55314i	0.245709	+	0.283563i
$31$	1.09007	−	7.58161i	0.195782	−	1.36170i	−0.620574	−	0.784148i	$-0.713100\pi$
$31$	1.09007	−	7.58161i	0.195782	−	1.36170i	0.816356	−	0.577549i	$-0.195991\pi$
$32$	−4.70090	−	3.02108i	−0.831009	−	0.534057i
$33$	−1.12385	+	0.722257i	−0.195638	+	0.125729i
$34$	−0.0285096			−0.00488935
$35$	2.98256	−	1.91677i	0.504144	−	0.323994i
$36$	8.90973	−	10.2824i	1.48496	−	1.71373i
$37$	1.06169			0.174541			0.0872704	−	0.996185i	$-0.472186\pi$
$37$	1.06169			0.174541			0.0872704	+	0.996185i	$0.472186\pi$
$38$	−3.21889	−	0.945152i	−0.522173	−	0.153324i
$39$	1.88598	+	13.1173i	0.301999	+	2.10045i
$40$	1.86129	−	1.19618i	0.294296	−	0.189133i
$41$	−3.62585	−	4.18445i	−0.566262	−	0.653502i	0.398331	−	0.917242i	$-0.369589\pi$
$41$	−3.62585	−	4.18445i	−0.566262	−	0.653502i	−0.964594	+	0.263740i	$0.915044\pi$
$42$	4.77138	+	5.50647i	0.736240	+	0.849666i
$43$	−4.40848	−	1.29445i	−0.672287	−	0.197401i	−0.0722659	−	0.997385i	$-0.523023\pi$
$43$	−4.40848	−	1.29445i	−0.672287	−	0.197401i	−0.600021	+	0.799984i	$0.704841\pi$
$44$	0.268117	+	0.587094i	0.0404201	+	0.0885077i
$45$	3.47148	+	7.60148i	0.517497	+	1.13316i
$46$	−4.21609	−	1.23796i	−0.621629	−	0.182527i
$47$	−8.64467	−	9.97648i	−1.26096	−	1.45522i	−0.834784	−	0.550577i	$-0.814408\pi$
$47$	−8.64467	−	9.97648i	−1.26096	−	1.45522i	−0.426171	−	0.904643i	$-0.640138\pi$
$48$	−4.20838	−	4.85673i	−0.607427	−	0.701009i
$49$	4.68551	−	3.01120i	0.669359	−	0.430171i
$50$	0.0867877	+	0.603621i	0.0122736	+	0.0853650i
$51$	−0.151165	−	0.0443859i	−0.0211673	−	0.00621527i
$52$	6.40245			0.887860
$53$	−1.45266	+	1.67646i	−0.199539	+	0.230280i	−0.846696	−	0.532076i	$-0.821412\pi$
$53$	−1.45266	+	1.67646i	−0.199539	+	0.230280i	0.647158	+	0.762356i	$0.275957\pi$
$54$	−9.26090	+	5.95162i	−1.26025	+	0.809912i
$55$	−0.396422			−0.0534536
$56$	6.59898	−	4.24091i	0.881826	−	0.566715i
$57$	−15.5958	−	10.0228i	−2.06572	−	1.32756i
$58$	0.446590	−	3.10610i	0.0586401	−	0.407851i
$59$	−3.51770	−	4.05964i	−0.457965	−	0.528520i	0.479060	−	0.877782i	$-0.340978\pi$
$59$	−3.51770	−	4.05964i	−0.457965	−	0.528520i	−0.937025	+	0.349262i	$0.886432\pi$
$60$	5.26442	−	1.54577i	0.679633	−	0.199558i
$61$	5.45273	+	3.50426i	0.698151	+	0.448674i	0.840975	−	0.541074i	$-0.181982\pi$
$61$	5.45273	+	3.50426i	0.698151	+	0.448674i	−0.142825	+	0.989748i	$0.545618\pi$
$62$	3.92952	+	2.52535i	0.499049	+	0.320719i
$63$	12.3077	+	26.9501i	1.55062	+	3.39539i
$64$	−0.341727	+	0.219615i	−0.0427159	+	0.0274518i
$65$	−1.63360	+	3.57708i	−0.202623	+	0.443682i
$66$	−0.115942	−	0.806395i	−0.0142715	−	0.0992604i
$67$	4.28732	−	4.94783i	0.523779	−	0.604474i	−0.430794	−	0.902450i	$-0.641766\pi$
$67$	4.28732	−	4.94783i	0.523779	−	0.604474i	0.954573	+	0.297977i	$0.0963118\pi$
$68$	−0.0316190	+	0.0692361i	−0.00383437	+	0.00839611i
$69$	−20.4274	−	13.1279i	−2.45917	−	1.58041i
$70$	0.307695	+	2.14006i	0.0367766	+	0.255787i
$71$	−2.97633	−	0.873930i	−0.353226	−	0.103716i	0.100306	−	0.994957i	$-0.468018\pi$
$71$	−2.97633	−	0.873930i	−0.353226	−	0.103716i	−0.453531	+	0.891240i	$0.649836\pi$
$72$	7.68073	+	16.8185i	0.905183	+	1.98207i
$73$	0.641276	−	4.46017i	0.0750557	−	0.522024i	−0.917260	−	0.398289i	$-0.869604\pi$
$73$	0.641276	−	4.46017i	0.0750557	−	0.522024i	0.992315	−	0.123734i	$-0.0394870\pi$
$74$	−0.268960	+	0.588941i	−0.0312660	+	0.0684629i
$75$	−0.479596	+	3.33566i	−0.0553789	+	0.385169i
$76$	−5.86529	+	6.76890i	−0.672795	+	0.776446i
$77$	−1.40547			−0.160168
$78$	−7.75421	−	2.27684i	−0.877991	−	0.257802i
$79$	−1.91000	+	13.2843i	−0.214892	+	1.49460i	0.541620	+	0.840624i	$0.317811\pi$
$79$	−1.91000	+	13.2843i	−0.214892	+	1.49460i	−0.756511	+	0.653980i	$0.773098\pi$
$80$	−0.271388	−	1.88755i	−0.0303421	−	0.211034i
$81$	−34.3150	+	10.0758i	−3.81277	+	1.11953i
$82$	3.23974	−	0.951274i	0.357770	−	0.105051i
$83$	−0.619556	−	1.35664i	−0.0680051	−	0.148910i	0.872577	−	0.488476i	$-0.162447\pi$
$83$	−0.619556	−	1.35664i	−0.0680051	−	0.148910i	−0.940582	+	0.339566i	$0.889720\pi$
$84$	18.6643	−	5.48034i	2.03645	−	0.597954i
$85$	−0.0306148	−	0.0353314i	−0.00332065	−	0.00383223i
$86$	1.83486	−	2.11755i	0.197859	−	0.228341i
$87$	7.20374	−	15.7740i	0.772322	−	1.69115i
$88$	−0.877094			−0.0934986
$89$	−5.63476	+	7.56634i	−0.597283	+	0.802030i
$89$	−5.63476	+	7.56634i	−0.597283	+	0.802030i
$90$	−5.09612			−0.537179
$91$	−5.79171	+	12.6821i	−0.607137	+	1.32944i
$92$	−7.68233	+	8.86588i	−0.800938	+	0.924332i
$93$	16.9036	+	19.5078i	1.75282	+	2.02286i
$94$	7.72412	−	2.26801i	0.796683	−	0.233927i
$95$	−2.28528	−	5.00406i	−0.234465	−	0.513406i
$96$	18.0684	−	5.30537i	1.84410	−	0.541477i
$97$	−11.1581	+	3.27632i	−1.13294	+	0.332660i	−0.793861	−	0.608099i	$-0.791932\pi$
$97$	−11.1581	+	3.27632i	−1.13294	+	0.332660i	−0.339075	+	0.940759i	$0.610114\pi$
$98$	0.483379	+	3.36198i	0.0488287	+	0.339611i
$99$	0.471455	−	3.27904i	0.0473830	−	0.329556i
$100$	1.56216	+	0.458691i	0.156216	+	0.0458691i
$101$	3.00441			0.298950			0.149475	−	0.988766i	$-0.452242\pi$
$101$	3.00441			0.298950			0.149475	+	0.988766i	$0.452242\pi$
$102$	0.0629166	−	0.0726096i	0.00622967	−	0.00718942i
$103$	−0.371156	+	2.58145i	−0.0365711	+	0.254357i	−0.999903	−	0.0139566i	$-0.995557\pi$
$103$	−0.371156	+	2.58145i	−0.0365711	+	0.254357i	0.963332	+	0.268314i	$0.0864664\pi$
$104$	−3.61437	+	7.91438i	−0.354419	+	0.776068i
$105$	−1.70035	+	11.8262i	−0.165937	+	1.15412i
$106$	−0.561961	−	1.23052i	−0.0545824	−	0.119519i
$107$	−11.5037	−	3.37780i	−1.11211	−	0.326545i	−0.326456	−	0.945212i	$-0.605855\pi$
$107$	−11.5037	−	3.37780i	−1.11211	−	0.326545i	−0.785653	+	0.618668i	$0.787673\pi$
$108$	4.18265	+	29.0910i	0.402476	+	2.79928i
$109$	12.8836	+	8.27977i	1.23402	+	0.793058i	0.984513	−	0.175314i	$-0.0560940\pi$
$109$	12.8836	+	8.27977i	1.23402	+	0.793058i	0.249510	+	0.968372i	$0.419730\pi$
$110$	0.100426	−	0.219903i	0.00957529	−	0.0209670i
$111$	−2.34300	+	2.70396i	−0.222388	+	0.256649i
$112$	−0.962173	−	6.69206i	−0.0909168	−	0.632340i
$113$	−2.34087	+	5.12580i	−0.220211	+	0.482195i	−0.987204	−	0.159460i	$-0.949025\pi$
$113$	−2.34087	+	5.12580i	−0.220211	+	0.482195i	0.766993	+	0.641655i	$0.221752\pi$
$114$	9.51079	−	6.11222i	0.890767	−	0.572461i
$115$	−2.99325	−	6.55430i	−0.279122	−	0.611192i
$116$	−7.04792	−	4.52942i	−0.654383	−	0.420546i
$117$	−27.6453	−	17.7666i	−2.55581	−	1.64252i
$118$	3.14311	−	0.922899i	0.289346	−	0.0849598i
$119$	−0.108541	−	0.125263i	−0.00994994	−	0.0114828i
$120$	−1.06112	+	7.38023i	−0.0968663	+	0.673720i
$121$	−9.12159	−	5.86209i	−0.829235	−	0.532917i
$122$	−3.32523	+	2.13700i	−0.301052	+	0.193475i
$123$	18.6589			1.68242
$124$	10.4909	−	6.74212i	0.942115	−	0.605461i
$125$	−0.654861	+	0.755750i	−0.0585725	+	0.0675963i
$126$	−18.0677			−1.60960
$127$	15.0286	+	4.41280i	1.33358	+	0.391573i	0.869373	−	0.494156i	$-0.164523\pi$
$127$	15.0286	+	4.41280i	1.33358	+	0.391573i	0.464202	+	0.885729i	$0.346341\pi$
$128$	−1.62576	−	11.3074i	−0.143698	−	0.999440i
$129$	13.0256	−	8.37107i	1.14684	−	0.737032i
$130$	−1.57043	−	1.81238i	−0.137736	−	0.158956i
$131$	−3.14806	−	3.63305i	−0.275047	−	0.317421i	0.601373	−	0.798968i	$-0.294620\pi$
$131$	−3.14806	−	3.63305i	−0.275047	−	0.317421i	−0.876420	+	0.481547i	$0.840075\pi$
$132$	−2.08693	−	0.612779i	−0.181644	−	0.0533355i
$133$	−8.10217	−	17.7413i	−0.702547	−	1.53836i
$134$	1.65854	+	3.63170i	0.143276	+	0.313731i
$135$	−17.3205	−	5.08575i	−1.49071	−	0.437712i
$136$	−0.0677361	−	0.0781716i	−0.00580832	−	0.00670316i
$137$	13.0350	+	15.0432i	1.11365	+	1.28522i	0.954579	+	0.297956i	$0.0963050\pi$
$137$	13.0350	+	15.0432i	1.11365	+	1.28522i	0.159073	+	0.987267i	$0.449150\pi$
$138$	12.4572	−	8.00575i	1.06043	−	0.681495i
$139$	0.599102	+	4.16685i	0.0508152	+	0.353427i	0.999327	+	0.0366853i	$0.0116799\pi$
$139$	0.599102	+	4.16685i	0.0508152	+	0.353427i	−0.948512	+	0.316742i	$0.897411\pi$
$140$	5.53844	+	1.62623i	0.468083	+	0.137442i
$141$	44.4861			3.74641
$142$	1.23879	−	1.42964i	0.103957	−	0.119972i
$143$	1.31144	−	0.842810i	0.109668	−	0.0704793i
$144$	15.9358			1.32798
$145$	4.32890	−	2.78201i	0.359496	−	0.231034i
$146$	2.31169	+	1.48563i	0.191317	+	0.122952i
$147$	−2.67119	+	18.5786i	−0.220316	+	1.53233i
$148$	1.13196	+	1.30635i	0.0930464	+	0.107381i
$149$	2.19729	−	0.645183i	0.180009	−	0.0528554i	−0.190486	−	0.981690i	$-0.561006\pi$
$149$	2.19729	−	0.645183i	0.180009	−	0.0528554i	0.370495	+	0.928835i	$0.379188\pi$
$150$	−1.72886	−	1.11107i	−0.141161	−	0.0907186i
$151$	−1.32465	−	0.851301i	−0.107798	−	0.0692779i	0.485631	−	0.874164i	$-0.338590\pi$
$151$	−1.32465	−	0.851301i	−0.107798	−	0.0692779i	−0.593429	+	0.804886i	$0.702226\pi$
$152$	−5.05623	−	11.0716i	−0.410115	−	0.898026i
$153$	0.328656	−	0.211215i	0.0265703	−	0.0170757i
$154$	0.356049	−	0.779639i	0.0286913	−	0.0628251i
$155$	1.09007	+	7.58161i	0.0875566	+	0.608969i
$156$	−14.1293	+	16.3061i	−1.13125	+	1.30553i
$157$	9.28761	−	20.3370i	0.741232	−	1.62307i	−0.0402848	−	0.999188i	$-0.512827\pi$
$157$	9.28761	−	20.3370i	0.741232	−	1.62307i	0.781517	−	0.623884i	$-0.214446\pi$
$158$	−6.88522	−	4.42486i	−0.547758	−	0.352023i
$159$	−1.06388	−	7.39942i	−0.0843709	−	0.586812i
$160$	5.36161	+	1.57431i	0.423873	+	0.124460i
$161$	−10.6122	−	23.2374i	−0.836357	−	1.83137i
$162$	3.10384	−	21.5877i	0.243861	−	1.69609i
$163$	−6.72692	+	14.7299i	−0.526893	+	1.15374i	0.439870	+	0.898062i	$0.355025\pi$
$163$	−6.72692	+	14.7299i	−0.526893	+	1.15374i	−0.966763	+	0.255674i	$0.917703\pi$
$164$	1.28290	−	8.92280i	0.100178	−	0.696753i
$165$	0.874847	−	1.00963i	0.0681067	−	0.0785994i
$166$	0.909507			0.0705914
$167$	−6.82664	−	2.00448i	−0.528261	−	0.155112i	0.00671674	−	0.999977i	$-0.497862\pi$
$167$	−6.82664	−	2.00448i	−0.528261	−	0.155112i	−0.534978	+	0.844866i	$0.679680\pi$
$168$	−3.76206	+	26.1657i	−0.290249	+	2.01873i
$169$	−0.350683	−	2.43906i	−0.0269756	−	0.187620i
$170$	0.0273547	−	0.00803208i	0.00209801	−	0.000616032i
$171$	44.1094	−	12.9517i	3.37313	−	0.990440i
$172$	−3.10751	−	6.80450i	−0.236946	−	0.518839i
$173$	−11.7688	+	3.45564i	−0.894768	+	0.262728i	−0.696616	−	0.717444i	$-0.745312\pi$
$173$	−11.7688	+	3.45564i	−0.894768	+	0.262728i	−0.198152	+	0.980171i	$0.563494\pi$
$174$	6.92520	+	7.99211i	0.524998	+	0.605880i
$175$	−2.32173	+	2.67941i	−0.175506	+	0.202545i
$176$	−0.314037	+	0.687646i	−0.0236714	+	0.0518332i
$177$	18.1023			1.36065
$178$	−2.76973	−	5.04251i	−0.207600	−	0.377952i
$179$	−17.2789			−1.29148			−0.645741	−	0.763556i	$-0.723452\pi$
$179$	−17.2789			−1.29148			−0.645741	+	0.763556i	$0.723452\pi$
$180$	−5.65194	+	12.3760i	−0.421271	+	0.922455i
$181$	−9.88327	+	11.4059i	−0.734618	+	0.847794i	−0.992984	−	0.118253i	$-0.962271\pi$
$181$	−9.88327	+	11.4059i	−0.734618	+	0.847794i	0.258366	+	0.966047i	$0.416816\pi$
$182$	−5.56778	−	6.42556i	−0.412711	−	0.476294i
$183$	−20.9582	+	6.15388i	−1.54927	+	0.454908i
$184$	−6.62264	−	14.5015i	−0.488227	−	1.06907i
$185$	−1.01868	+	0.299113i	−0.0748952	+	0.0219912i
$186$	−15.1036	+	4.43480i	−1.10745	+	0.325176i
$187$	0.00263749	+	0.0183442i	0.000192873	+	0.00134146i
$188$	3.05867	−	21.2735i	0.223077	−	1.55153i
$189$	−61.4076	−	18.0309i	−4.46675	−	1.31156i
$190$	3.35479			0.243382
$191$	−8.78026	+	10.1330i	−0.635317	+	0.733195i	−0.978540	−	0.206059i	$-0.933936\pi$
$191$	−8.78026	+	10.1330i	−0.635317	+	0.733195i	0.343222	+	0.939254i	$0.388482\pi$
$192$	0.194817	−	1.35498i	0.0140597	−	0.0977876i
$193$	−3.04010	+	6.65689i	−0.218831	+	0.479173i	−0.986928	−	0.161160i	$-0.948476\pi$
$193$	−3.04010	+	6.65689i	−0.218831	+	0.479173i	0.768097	+	0.640333i	$0.221204\pi$
$194$	1.00927	−	7.01963i	0.0724614	−	0.503980i
$195$	−5.50516	−	12.0546i	−0.394233	−	0.863250i
$196$	8.70072	+	2.55476i	0.621480	+	0.182483i
$197$	0.790628	+	5.49894i	0.0563299	+	0.391783i	0.998409	+	0.0563916i	$0.0179595\pi$
$197$	0.790628	+	5.49894i	0.0563299	+	0.391783i	−0.942079	+	0.335392i	$0.891131\pi$
$198$	1.69951	+	1.09221i	0.120779	+	0.0776201i
$199$	−8.77043	+	19.2046i	−0.621720	+	1.36138i	0.292542	+	0.956253i	$0.405499\pi$
$199$	−8.77043	+	19.2046i	−0.621720	+	1.36138i	−0.914262	+	0.405124i	$0.867229\pi$
$200$	−1.44890	+	1.67211i	−0.102452	+	0.118236i
$201$	3.13987	+	21.8383i	0.221470	+	1.54036i
$202$	−0.761113	+	1.66660i	−0.0535517	+	0.117262i
$203$	15.3476	−	9.86328i	1.07719	−	0.692267i
$204$	−0.106555	−	0.233323i	−0.00746034	−	0.0163359i
$205$	4.65787	+	2.99343i	0.325320	+	0.209070i
$206$	−1.33795	−	0.859850i	−0.0932196	−	0.0599086i
$207$	57.7743	−	16.9641i	4.01559	−	1.17908i
$208$	4.91080	+	5.66737i	0.340503	+	0.392961i
$209$	−0.310360	+	2.15860i	−0.0214680	+	0.149313i
$210$	−6.12946	−	3.93916i	−0.422973	−	0.271828i
$211$	−7.42440	+	4.77137i	−0.511117	+	0.328475i	−0.770649	−	0.637260i	$-0.780068\pi$
$211$	−7.42440	+	4.77137i	−0.511117	+	0.328475i	0.259533	+	0.965734i	$0.416432\pi$
$212$	−3.61160			−0.248046
$213$	8.79410	−	5.65163i	0.602562	−	0.387243i
$214$	4.78800	−	5.52565i	0.327301	−	0.377725i
$215$	4.59459			0.313349
$216$	−38.3220	−	11.2524i	−2.60748	−	0.765626i
$217$	3.86471	+	26.8796i	0.262353	+	1.82471i
$218$	−7.85677	+	5.04924i	−0.532128	+	0.341978i
$219$	9.94417	+	11.4762i	0.671965	+	0.775489i
$220$	−0.422659	−	0.487775i	−0.0284957	−	0.0328858i
$221$	0.176396	+	0.0517944i	0.0118657	+	0.00348407i
$222$	−0.906386	−	1.98471i	−0.0608326	−	0.133205i
$223$	4.58591	+	10.0417i	0.307095	+	0.672445i	0.998761	−	0.0497732i	$-0.0158499\pi$
$223$	4.58591	+	10.0417i	0.307095	+	0.672445i	−0.691665	+	0.722218i	$0.743123\pi$
$224$	19.0089	+	5.58153i	1.27009	+	0.372931i
$225$	−5.47244	−	6.31553i	−0.364829	−	0.421036i
$226$	−2.25036	−	2.59706i	−0.149692	−	0.172754i
$227$	18.5998	−	11.9534i	1.23451	−	0.793374i	0.249926	−	0.968265i	$-0.419594\pi$
$227$	18.5998	−	11.9534i	1.23451	−	0.793374i	0.984588	+	0.174891i	$0.0559574\pi$
$228$	−4.29552	−	29.8760i	−0.284478	−	1.97859i
$229$	−8.78834	−	2.58049i	−0.580750	−	0.170523i	−0.0218535	−	0.999761i	$-0.506957\pi$
$229$	−8.78834	−	2.58049i	−0.580750	−	0.170523i	−0.558896	+	0.829238i	$0.688775\pi$
$230$	4.39408			0.289737
$231$	3.10166	−	3.57951i	0.204074	−	0.235514i
$232$	9.57780	−	6.15528i	0.628813	−	0.404114i
$233$	−12.5197			−0.820191			−0.410095	−	0.912043i	$-0.634505\pi$
$233$	−12.5197			−0.820191			−0.410095	+	0.912043i	$0.634505\pi$
$234$	16.8589	−	10.8346i	1.10210	−	0.708278i
$235$	11.1052	+	7.13688i	0.724424	+	0.465559i
$236$	1.24464	−	8.65665i	0.0810191	−	0.563500i
$237$	−29.6181	−	34.1811i	−1.92390	−	2.22030i
$238$	0.0969828	−	0.0284767i	0.00628646	−	0.00184587i
$239$	8.02336	+	5.15630i	0.518988	+	0.333534i	0.773772	−	0.633465i	$-0.218368\pi$
$239$	8.02336	+	5.15630i	0.518988	+	0.333534i	−0.254783	+	0.966998i	$0.582004\pi$
$240$	5.40621	+	3.47436i	0.348969	+	0.224269i
$241$	−2.13502	−	4.67505i	−0.137529	−	0.301146i	0.828319	−	0.560257i	$-0.189298\pi$
$241$	−2.13502	−	4.67505i	−0.137529	−	0.301146i	−0.965848	+	0.259111i	$0.916570\pi$
$242$	5.56260	−	3.57487i	0.357578	−	0.229801i
$243$	27.5699	−	60.3696i	1.76861	−	3.87271i
$244$	1.50183	+	10.4455i	0.0961448	+	0.668702i
$245$	−3.64736	+	4.20928i	−0.233021	+	0.268921i
$246$	−4.72689	+	10.3505i	−0.301376	+	0.659921i
$247$	18.1990	+	11.6958i	1.15797	+	0.744184i
$248$	2.41181	+	16.7745i	0.153150	+	1.06518i
$249$	4.82242	+	1.41599i	0.305609	+	0.0897348i
$250$	−0.253332	−	0.554720i	−0.0160221	−	0.0350836i
$251$	−1.82956	+	12.7249i	−0.115481	+	0.803189i	0.846952	+	0.531669i	$0.178435\pi$
$251$	−1.82956	+	12.7249i	−0.115481	+	0.803189i	−0.962433	+	0.271519i	$0.912474\pi$
$252$	−20.0383	+	43.8777i	−1.26229	+	2.76403i
$253$	−0.406508	+	2.82732i	−0.0255569	+	0.177752i
$254$	−6.25510	+	7.21877i	−0.392480	+	0.452946i
$255$	0.157546			0.00986593
$256$	5.90477	+	1.73380i	0.369048	+	0.108362i
$257$	−1.02065	+	7.09875i	−0.0636662	+	0.442808i	0.932909	+	0.360113i	$0.117262\pi$
$257$	−1.02065	+	7.09875i	−0.0636662	+	0.442808i	−0.996575	+	0.0826951i	$0.973647\pi$
$258$	1.34379	+	9.34624i	0.0836605	+	0.581872i
$259$	−3.61162	+	1.06047i	−0.224415	+	0.0658942i
$260$	−6.14311	+	1.80378i	−0.380979	+	0.111866i
$261$	17.8634	+	39.1155i	1.10572	+	2.42119i
$262$	2.81283	−	0.825921i	0.173777	−	0.0510256i
$263$	4.67351	+	5.39352i	0.288181	+	0.332579i	0.881319	−	0.472523i	$-0.156656\pi$
$263$	4.67351	+	5.39352i	0.288181	+	0.332579i	−0.593138	+	0.805101i	$0.702111\pi$
$264$	1.93562	−	2.23383i	0.119129	−	0.137482i
$265$	0.921506	−	2.01782i	0.0566076	−	0.123953i
$266$	11.8940			0.729266
$267$	−6.83521	−	31.0487i	−0.418308	−	1.90015i
$268$	10.6591			0.651108
$269$	5.54855	−	12.1496i	0.338301	−	0.740775i	−0.661658	−	0.749805i	$-0.730147\pi$
$269$	5.54855	−	12.1496i	0.338301	−	0.740775i	0.999959	+	0.00902998i	$0.00287437\pi$
$270$	7.20900	−	8.31963i	0.438726	−	0.506317i
$271$	−16.7371	−	19.3156i	−1.01671	−	1.17334i	−0.984772	−	0.173851i	$-0.944379\pi$
$271$	−16.7371	−	19.3156i	−1.01671	−	1.17334i	−0.0319335	−	0.999490i	$-0.510166\pi$
$272$	−0.0855393	+	0.0251166i	−0.00518658	+	0.00152292i
$273$	−19.5179	−	42.7382i	−1.18127	−	2.58663i
$274$	−11.6469	+	3.41984i	−0.703615	+	0.206600i
$275$	0.380364	−	0.111685i	0.0229368	−	0.00673486i
$276$	−5.62625	−	39.1315i	−0.338661	−	2.35544i
$277$	−1.73158	+	12.0434i	−0.104041	+	0.723619i	0.869305	+	0.494276i	$0.164567\pi$
$277$	−1.73158	+	12.0434i	−0.104041	+	0.723619i	−0.973346	+	0.229343i	$0.926342\pi$
$278$	−2.46320	−	0.723262i	−0.147733	−	0.0433784i
$279$	−64.0083			−3.83208
$280$	−5.13688	+	5.92827i	−0.306987	+	0.354282i
$281$	−2.33924	+	16.2698i	−0.139547	+	0.970574i	0.792921	+	0.609324i	$0.208559\pi$
$281$	−2.33924	+	16.2698i	−0.139547	+	0.970574i	−0.932469	+	0.361250i	$0.882350\pi$
$282$	−11.2698	+	24.6773i	−0.671105	+	1.46951i
$283$	−0.326482	+	2.27073i	−0.0194074	+	0.134981i	−0.997222	−	0.0744931i	$-0.976266\pi$
$283$	−0.326482	+	2.27073i	−0.0194074	+	0.134981i	0.977814	+	0.209474i	$0.0671752\pi$
$284$	−2.09800	−	4.59398i	−0.124493	−	0.272602i
$285$	17.7879	+	5.22299i	1.05366	+	0.309383i
$286$	0.135294	+	0.940991i	0.00800011	+	0.0556420i
$287$	16.5139	+	10.6128i	0.974785	+	0.626456i
$288$	−19.3985	+	42.4768i	−1.14307	+	2.50297i
$289$	11.1312	−	12.8461i	0.654777	−	0.755652i
$290$	0.446590	+	3.10610i	0.0262246	+	0.182396i
$291$	16.2801	−	35.6484i	0.954356	−	2.08975i
$292$	6.17170	−	3.96631i	0.361172	−	0.232111i
$293$	−6.48253	−	14.1948i	−0.378713	−	0.829266i	−0.998992	−	0.0448851i	$-0.985708\pi$
$293$	−6.48253	−	14.1948i	−0.378713	−	0.829266i	0.620279	−	0.784381i	$-0.287019\pi$
$294$	−9.62919	−	6.18831i	−0.561586	−	0.360909i
$295$	4.51894	+	2.90415i	0.263103	+	0.169086i
$296$	−2.25386	+	0.661794i	−0.131003	+	0.0384660i
$297$	4.68625	+	5.40822i	0.271924	+	0.313817i
$298$	−0.198748	+	1.38233i	−0.0115132	+	0.0800760i
$299$	23.8369	+	15.3191i	1.37853	+	0.885924i
$300$	−4.61568	+	2.96632i	−0.266486	+	0.171260i
$301$	16.2896			0.938914
$302$	0.807809	−	0.519148i	0.0464842	−	0.0298736i
$303$	−6.63030	+	7.65177i	−0.380901	+	0.439583i
$304$	−10.4905			−0.601674
$305$	−6.21912	−	1.82610i	−0.356106	−	0.104562i
$306$	0.0339057	+	0.235820i	0.00193826	+	0.0134809i
$307$	7.11508	−	4.57258i	0.406079	−	0.260971i	−0.321618	−	0.946869i	$-0.604227\pi$
$307$	7.11508	−	4.57258i	0.406079	−	0.260971i	0.727698	+	0.685898i	$0.240590\pi$
$308$	−1.49849	−	1.72934i	−0.0853841	−	0.0985386i
$309$	−5.75546	−	6.64216i	−0.327417	−	0.377859i
$310$	−4.48182	−	1.31598i	−0.254550	−	0.0747426i
$311$	2.16552	+	4.74182i	0.122795	+	0.268884i	0.961040	−	0.276411i	$-0.0891450\pi$
$311$	2.16552	+	4.74182i	0.122795	+	0.268884i	−0.838244	+	0.545295i	$0.816418\pi$
$312$	−12.1803	−	26.6712i	−0.689574	−	1.50996i
$313$	1.62922	+	0.478381i	0.0920887	+	0.0270397i	0.327452	−	0.944868i	$-0.393810\pi$
$313$	1.62922	+	0.478381i	0.0920887	+	0.0270397i	−0.235364	+	0.971907i	$0.575628\pi$
$314$	8.92850	+	10.3040i	0.503865	+	0.581491i
$315$	−19.4019	−	22.3909i	−1.09317	−	1.26159i
$316$	−18.3820	+	11.8134i	−1.03407	+	0.664556i
$317$	−0.00485763	−	0.0337856i	−0.000272832	−	0.00189759i	0.989685	−	0.143264i	$-0.0457597\pi$
$317$	−0.00485763	−	0.0337856i	−0.000272832	−	0.00189759i	−0.989957	+	0.141366i	$0.954851\pi$
$318$	4.37412	+	1.28436i	0.245288	+	0.0720232i
$319$	−2.03990			−0.114212
$320$	0.266012	−	0.306994i	0.0148705	−	0.0171615i
$321$	33.9899	−	21.8440i	1.89713	−	1.21921i
$322$	15.5787			0.868165
$323$	−0.216355	+	0.139043i	−0.0120383	+	0.00773655i
$324$	−48.9838	−	31.4799i	−2.72132	−	1.74889i
$325$	0.559646	−	3.89242i	0.0310435	−	0.215913i
$326$	−6.46682	−	7.46311i	−0.358164	−	0.413344i
$327$	−49.5195	+	14.5402i	−2.73844	+	0.804077i
$328$	10.3057	+	6.62304i	0.569035	+	0.365696i
$329$	39.3721	+	25.3029i	2.17065	+	1.39499i
$330$	0.338433	+	0.741066i	0.0186301	+	0.0407943i
$331$	6.83352	−	4.39164i	0.375604	−	0.241386i	−0.339195	−	0.940716i	$-0.610155\pi$
$331$	6.83352	−	4.39164i	0.375604	−	0.241386i	0.714799	+	0.699330i	$0.246518\pi$
$332$	1.00870	−	2.20875i	0.0553598	−	0.121221i
$333$	−1.26264	−	8.78187i	−0.0691924	−	0.481243i
$334$	2.84133	−	3.27907i	0.155471	−	0.179423i
$335$	−2.71969	+	5.95529i	−0.148592	+	0.325372i
$336$	19.1670	+	12.3179i	1.04565	+	0.671997i
$337$	−3.45543	−	24.0331i	−0.188229	−	1.30916i	−0.836589	−	0.547831i	$-0.815454\pi$
$337$	−3.45543	−	24.0331i	−0.188229	−	1.30916i	0.648360	−	0.761334i	$-0.275455\pi$
$338$	1.44183	+	0.423360i	0.0784253	+	0.0230277i
$339$	−7.88866	−	17.2738i	−0.428453	−	0.938182i
$340$	0.0108322	−	0.0753396i	0.000587459	−	0.00408586i
$341$	1.26138	−	2.76203i	0.0683074	−	0.149572i
$342$	−3.98976	+	27.7494i	−0.215742	+	1.50052i
$343$	3.32082	−	3.83243i	0.179307	−	0.206932i
$344$	10.1657			0.548095
$345$	23.2985	+	6.84105i	1.25435	+	0.368310i
$346$	1.06451	−	7.40383i	0.0572284	−	0.398032i
$347$	1.07701	+	7.49077i	0.0578169	+	0.402125i	0.998094	+	0.0617149i	$0.0196570\pi$
$347$	1.07701	+	7.49077i	0.0578169	+	0.402125i	−0.940277	+	0.340411i	$0.889434\pi$
$348$	27.0895	−	7.95419i	1.45215	−	0.426390i
$349$	28.1597	−	8.26845i	1.50736	−	0.442600i	0.579324	−	0.815098i	$-0.303317\pi$
$349$	28.1597	−	8.26845i	1.50736	−	0.442600i	0.928033	+	0.372498i	$0.121499\pi$
$350$	−0.898157	−	1.96669i	−0.0480085	−	0.105124i
$351$	68.1119	−	19.9995i	3.63554	−	1.06749i
$352$	−1.45064	−	1.67413i	−0.0773196	−	0.0892316i
$353$	−18.8222	+	21.7220i	−1.00181	+	1.15615i	−0.0140873	+	0.999901i	$0.504484\pi$
$353$	−18.8222	+	21.7220i	−1.00181	+	1.15615i	−0.987718	+	0.156245i	$0.950061\pi$
$354$	−4.58590	+	10.0417i	−0.243738	+	0.533711i
$355$	3.10198			0.164636
$356$	−15.3176	+	1.13387i	−0.811833	+	0.0600949i
$357$	0.558561			0.0295622
$358$	4.37729	−	9.58492i	0.231347	−	0.506579i
$359$	−9.53010	+	10.9983i	−0.502980	+	0.580470i	−0.949287	−	0.314410i	$-0.898193\pi$
$359$	−9.53010	+	10.9983i	−0.502980	+	0.580470i	0.446308	+	0.894880i	$0.352739\pi$
$360$	−12.1079	−	13.9733i	−0.638143	−	0.736456i
$361$	−10.8069	+	3.17319i	−0.568784	+	0.167010i
$362$	−3.82333	−	8.37193i	−0.200950	−	0.440019i
$363$	35.0599	−	10.2945i	1.84017	−	0.540322i
$364$	−21.7796	+	6.39507i	−1.14156	+	0.335193i
$365$	0.641276	+	4.46017i	0.0335659	+	0.233456i
$366$	1.89570	−	13.1849i	0.0990900	−	0.689186i
$367$	0.229791	+	0.0674728i	0.0119950	+	0.00352205i	0.287725	−	0.957713i	$-0.407101\pi$
$367$	0.229791	+	0.0674728i	0.0119950	+	0.00352205i	−0.275730	+	0.961235i	$0.588919\pi$
$368$	−13.7405			−0.716271
$369$	−30.2999	+	34.9680i	−1.57735	+	1.82036i
$370$	0.0921416	−	0.640859i	0.00479022	−	0.0333167i
$371$	3.26708	−	7.15391i	0.169618	−	0.371413i
$372$	−5.98085	+	41.5978i	−0.310093	+	2.15674i
$373$	−12.5705	−	27.5255i	−0.650875	−	1.42522i	−0.890786	−	0.454422i	$-0.849846\pi$
$373$	−12.5705	−	27.5255i	−0.650875	−	1.42522i	0.239912	−	0.970795i	$-0.422882\pi$
$374$	−0.0108440	−	0.00318410i	−0.000560732	−	0.000164646i
$375$	−0.479596	−	3.33566i	−0.0247662	−	0.172253i
$376$	24.5705	+	15.7905i	1.26713	+	0.814334i
$377$	−8.40612	+	18.4068i	−0.432937	+	0.948000i
$378$	25.5586	−	29.4962i	1.31459	−	1.51712i
$379$	3.90991	+	27.1940i	0.200838	+	1.39686i	0.801804	+	0.597587i	$0.203874\pi$
$379$	3.90991	+	27.1940i	0.200838	+	1.39686i	−0.600966	+	0.799275i	$0.705217\pi$
$380$	3.72068	−	8.14716i	0.190867	−	0.417940i
$381$	−44.4048	+	28.5372i	−2.27492	+	1.46201i
$382$	−3.39663	−	7.43758i	−0.173787	−	0.380540i
$383$	14.4535	+	9.28868i	0.738538	+	0.474629i	0.855041	−	0.518561i	$-0.173532\pi$
$383$	14.4535	+	9.28868i	0.738538	+	0.474629i	−0.116503	+	0.993190i	$0.537168\pi$
$384$	32.3860	+	20.8132i	1.65269	+	1.06212i
$385$	1.34853	−	0.395965i	0.0687277	−	0.0201803i
$386$	−2.92255	−	3.37281i	−0.148754	−	0.171671i
$387$	−5.46424	+	38.0046i	−0.277763	+	1.93188i
$388$	−15.9280	−	10.2363i	−0.808619	−	0.519668i
$389$	18.9565	−	12.1826i	0.961132	−	0.617682i	0.0368210	−	0.999322i	$-0.488277\pi$
$389$	18.9565	−	12.1826i	0.961132	−	0.617682i	0.924311	+	0.381640i	$0.124640\pi$
$390$	8.08157			0.409226
$391$	−0.283381	+	0.182118i	−0.0143312	+	0.00921009i
$392$	−8.06988	+	9.31314i	−0.407591	+	0.470385i
$393$	16.2001			0.817189
$394$	−3.25066	−	0.954480i	−0.163766	−	0.0480860i
$395$	−1.91000	−	13.2843i	−0.0961025	−	0.668407i
$396$	4.53733	−	2.91597i	0.228010	−	0.146533i
$397$	16.2788	+	18.7868i	0.817011	+	0.942881i	0.999184	−	0.0403858i	$-0.0128587\pi$
$397$	16.2788	+	18.7868i	0.817011	+	0.942881i	−0.182173	+	0.983266i	$0.558313\pi$
$398$	−8.43132	−	9.73027i	−0.422624	−	0.487734i
$399$	63.0646	+	18.5174i	3.15718	+	0.927032i
$400$	0.792179	+	1.73463i	0.0396089	+	0.0867315i
$401$	9.43834	+	20.6671i	0.471328	+	1.03206i	0.984757	+	0.173933i	$0.0556476\pi$
$401$	9.43834	+	20.6671i	0.471328	+	1.03206i	−0.513429	+	0.858132i	$0.671625\pi$
$402$	−12.9096	−	3.79059i	−0.643871	−	0.189057i
$403$	−19.7250	−	22.7638i	−0.982570	−	1.13395i
$404$	3.20325	+	3.69675i	0.159368	+	0.183920i
$405$	30.0863	−	19.3353i	1.49500	−	0.960778i
$406$	1.58333	+	11.0123i	0.0785792	+	0.546530i
$407$	0.403829	+	0.118575i	0.0200171	+	0.00587754i
$408$	0.348575			0.0172570
$409$	−16.4418	+	18.9748i	−0.812995	+	0.938246i	−0.999018	−	0.0442994i	$-0.985894\pi$
$409$	−16.4418	+	18.9748i	−0.812995	+	0.938246i	0.186024	+	0.982545i	$0.440440\pi$
$410$	−2.84050	+	1.82548i	−0.140282	+	0.0901541i
$411$	−67.0789			−3.30876
$412$	−3.57204	+	2.29561i	−0.175982	+	0.113097i
$413$	16.0213	+	10.2963i	0.788358	+	0.506647i
$414$	−5.22577	+	36.3461i	−0.256833	+	1.78631i
$415$	0.976668	+	1.12714i	0.0479428	+	0.0553289i
$416$	−21.0843	+	6.19090i	−1.03374	+	0.303534i
$417$	−11.9345	−	7.66981i	−0.584433	−	0.375592i
$418$	−1.11879	−	0.719005i	−0.0547219	−	0.0351677i
$419$	−2.30233	−	5.04140i	−0.112476	−	0.246288i	0.845020	−	0.534735i	$-0.179589\pi$
$419$	−2.30233	−	5.04140i	−0.112476	−	0.246288i	−0.957496	+	0.288446i	$0.906861\pi$
$420$	−16.3643	+	10.5167i	−0.798496	+	0.513162i
$421$	6.97576	−	15.2748i	0.339978	−	0.744448i	−0.659999	−	0.751267i	$-0.729443\pi$
$421$	6.97576	−	15.2748i	0.339978	−	0.744448i	0.999977	+	0.00681895i	$0.00217056\pi$
$422$	−0.765936	−	5.32720i	−0.0372852	−	0.259324i
$423$	−72.2405	+	83.3700i	−3.51245	+	4.05359i
$424$	2.03885	−	4.46447i	0.0990155	−	0.216814i
$425$	0.0393287	+	0.0252750i	0.00190772	+	0.00122602i
$426$	0.907241	+	6.31000i	0.0439560	+	0.305721i
$427$	−22.0491	−	6.47420i	−1.06703	−	0.313309i
$428$	−8.10892	−	17.7561i	−0.391960	−	0.858272i
$429$	−0.747646	+	5.19999i	−0.0360967	+	0.251058i
$430$	−1.16396	+	2.54871i	−0.0561310	+	0.122910i
$431$	4.94566	−	34.3978i	0.238224	−	1.65688i	−0.422580	−	0.906326i	$-0.638875\pi$
$431$	4.94566	−	34.3978i	0.238224	−	1.65688i	0.660804	−	0.750559i	$-0.270215\pi$
$432$	−22.5428	+	26.0158i	−1.08459	+	1.25169i
$433$	35.3155			1.69716			0.848578	−	0.529070i	$-0.177459\pi$
$433$	35.3155			1.69716			0.848578	+	0.529070i	$0.177459\pi$
$434$	−15.8897	−	4.66564i	−0.762731	−	0.223958i
$435$	−2.46789	+	17.1646i	−0.118326	+	0.822977i
$436$	3.54849	+	24.6803i	0.169942	+	1.18197i
$437$	−38.0329	+	11.1675i	−1.81936	+	0.534212i
$438$	−8.88524	+	2.60894i	−0.424553	+	0.124660i
$439$	−6.91829	−	15.1489i	−0.330192	−	0.723019i	0.669614	−	0.742709i	$-0.266459\pi$
$439$	−6.91829	−	15.1489i	−0.330192	−	0.723019i	−0.999806	+	0.0196899i	$0.993732\pi$
$440$	0.841566	−	0.247106i	0.0401201	−	0.0117803i
$441$	−30.4797	−	35.1755i	−1.45142	−	1.67502i
$442$	−0.0734180	+	0.0847289i	−0.00349214	+	0.00403014i
$443$	4.26900	−	9.34780i	0.202826	−	0.444127i	−0.780697	−	0.624910i	$-0.785136\pi$
$443$	4.26900	−	9.34780i	0.202826	−	0.444127i	0.983523	+	0.180783i	$0.0578630\pi$
$444$	−5.82514			−0.276449
$445$	3.27483	−	8.84734i	0.155242	−	0.419404i
$446$	−6.73211			−0.318775
$447$	−3.20592	+	7.01999i	−0.151635	+	0.332034i
$448$	0.943112	−	1.08841i	0.0445579	−	0.0514225i
$449$	7.93778	+	9.16069i	0.374607	+	0.432320i	0.911481	−	0.411343i	$-0.134940\pi$
$449$	7.93778	+	9.16069i	0.374607	+	0.432320i	−0.536873	+	0.843663i	$0.680395\pi$
$450$	4.88970	−	1.43574i	0.230502	−	0.0676816i
$451$	−0.911803	−	1.99657i	−0.0429351	−	0.0940148i
$452$	−8.80281	+	2.58474i	−0.414049	+	0.121576i
$453$	5.09144	−	1.49498i	0.239217	−	0.0702404i
$454$	1.91884	+	13.3459i	0.0900559	+	0.626352i
$455$	1.98415	−	13.8001i	0.0930185	−	0.646958i
$456$	39.3561	+	11.5560i	1.84302	+	0.541159i
$457$	−21.7395			−1.01693			−0.508466	−	0.861082i	$-0.669787\pi$
$457$	−21.7395			−1.01693			−0.508466	+	0.861082i	$0.669787\pi$
$458$	3.65781	−	4.22134i	0.170918	−	0.197250i
$459$	−0.120102	+	0.835330i	−0.00560590	+	0.0389899i
$460$	4.87333	−	10.6711i	0.227220	−	0.497543i
$461$	0.792026	−	5.50866i	0.0368883	−	0.256564i	−0.963029	−	0.269397i	$-0.913176\pi$
$461$	0.792026	−	5.50866i	0.0368883	−	0.256564i	0.999918	+	0.0128327i	$0.00408488\pi$
$462$	1.19987	+	2.62736i	0.0558231	+	0.122236i
$463$	−32.8316	−	9.64023i	−1.52581	−	0.448020i	−0.592048	−	0.805903i	$-0.701680\pi$
$463$	−32.8316	−	9.64023i	−1.52581	−	0.448020i	−0.933766	+	0.357883i	$0.883499\pi$
$464$	−1.39650	−	9.71289i	−0.0648310	−	0.450909i
$465$	−21.7148	−	13.9553i	−1.00700	−	0.647160i
$466$	3.17163	−	6.94491i	0.146923	−	0.321717i
$467$	−12.3134	+	14.2104i	−0.569794	+	0.657578i	−0.965379	−	0.260852i	$-0.915997\pi$
$467$	−12.3134	+	14.2104i	−0.569794	+	0.657578i	0.395585	+	0.918430i	$0.370542\pi$
$468$	−7.61428	−	52.9585i	−0.351970	−	2.44801i
$469$	−9.64231	+	21.1137i	−0.445241	+	0.974941i
$470$	−6.77227	+	4.35227i	−0.312382	+	0.200755i
$471$	31.2989	+	68.5351i	1.44218	+	3.15793i
$472$	9.99826	+	6.42549i	0.460207	+	0.295757i
$473$	−1.53226	−	0.984723i	−0.0704533	−	0.0452776i
$474$	26.4641	−	7.77057i	1.21554	−	0.356914i
$475$	3.60252	+	4.15752i	0.165295	+	0.190760i
$476$	0.0384042	−	0.267107i	0.00176025	−	0.0122428i
$477$	15.5946	+	10.0221i	0.714029	+	0.458878i
$478$	−4.89288	+	3.14446i	−0.223795	+	0.143824i
$479$	28.0749			1.28278			0.641388	−	0.767217i	$-0.278359\pi$
$479$	28.0749			1.28278			0.641388	+	0.767217i	$0.278359\pi$
$480$	−15.8418	+	10.1809i	−0.723078	+	0.464694i
$481$	2.73407	−	3.15529i	0.124663	−	0.143869i
$482$	3.13421			0.142759
$483$	82.6018	+	24.2541i	3.75851	+	1.10360i
$484$	−2.51233	−	17.4737i	−0.114197	−	0.794257i
$485$	9.78310	−	6.28722i	0.444228	−	0.285488i
$486$	26.5039	+	30.5871i	1.20224	+	1.38746i
$487$	19.0347	+	21.9672i	0.862544	+	0.995429i	0.999988	+	0.00491965i	$0.00156598\pi$
$487$	19.0347	+	21.9672i	0.862544	+	0.995429i	−0.137444	+	0.990510i	$0.543889\pi$
$488$	−13.7600	−	4.04029i	−0.622884	−	0.182895i
$489$	−22.6695	−	49.6392i	−1.02515	−	2.24476i
$490$	−1.41098	−	3.08961i	−0.0637415	−	0.139574i
$491$	5.52292	+	1.62167i	0.249246	+	0.0731852i	0.403969	−	0.914773i	$-0.367630\pi$
$491$	5.52292	+	1.62167i	0.249246	+	0.0731852i	−0.154723	+	0.987958i	$0.549449\pi$
$492$	19.8938	+	22.9587i	0.896883	+	1.03506i
$493$	−0.157537	−	0.181807i	−0.00709511	−	0.00818819i
$494$	−11.0982	+	7.13241i	−0.499334	+	0.320902i
$495$	0.471455	+	3.27904i	0.0211903	+	0.147382i
$496$	14.0148	+	4.11512i	0.629283	+	0.184774i
$497$	10.9977			0.493314
$498$	−2.00715	+	2.31638i	−0.0899426	+	0.103799i
$499$	−3.72546	+	2.39421i	−0.166774	+	0.107179i	−0.621366	−	0.783521i	$-0.713422\pi$
$499$	−3.72546	+	2.39421i	−0.166774	+	0.107179i	0.454591	+	0.890700i	$0.349785\pi$
$500$	−1.62811			−0.0728112
$501$	20.1705	−	12.9628i	0.901153	−	0.579136i
$502$	−6.59527	−	4.23852i	−0.294361	−	0.189174i
$503$	−4.74312	+	32.9891i	−0.211485	+	1.47091i	0.556716	+	0.830703i	$0.312061\pi$
$503$	−4.74312	+	32.9891i	−0.211485	+	1.47091i	−0.768201	+	0.640208i	$0.778848\pi$
$504$	−42.9271	−	49.5405i	−1.91212	−	2.20671i
$505$	−2.88271	+	0.846440i	−0.128279	+	0.0376661i
$506$	−1.46539	−	0.941749i	−0.0651445	−	0.0418659i
$507$	6.98581	+	4.48951i	0.310251	+	0.199386i
$508$	10.5936	+	23.1967i	0.470015	+	1.02919i
$509$	14.1071	−	9.06609i	0.625286	−	0.401847i	−0.189275	−	0.981924i	$-0.560614\pi$
$509$	14.1071	−	9.06609i	0.625286	−	0.401847i	0.814562	+	0.580077i	$0.196977\pi$
$510$	−0.0399115	+	0.0873940i	−0.00176731	+	0.00386987i
$511$	2.27356	+	15.8130i	0.100576	+	0.699525i
$512$	12.5042	−	14.4306i	0.552611	−	0.637747i
$513$	−41.2532	+	90.3319i	−1.82137	+	3.98825i
$514$	−3.67926	−	2.36451i	−0.162285	−	0.104294i
$515$	−0.371156	−	2.58145i	−0.0163551	−	0.113752i
$516$	24.1879	+	7.10220i	1.06481	+	0.312657i
$517$	−2.17390	−	4.76018i	−0.0956081	−	0.209352i
$518$	0.326677	−	2.27209i	0.0143533	−	0.0998297i
$519$	17.1711	−	37.5995i	0.753729	−	1.65044i
$520$	1.23823	−	8.61208i	0.0543000	−	0.377665i
$521$	−4.61855	+	5.33009i	−0.202342	+	0.233516i	−0.847847	−	0.530241i	$-0.822102\pi$
$521$	−4.61855	+	5.33009i	−0.202342	+	0.233516i	0.645505	+	0.763756i	$0.276647\pi$
$522$	−26.2235			−1.14777
$523$	−30.6245	−	8.99217i	−1.33912	−	0.393200i	−0.467762	−	0.883855i	$-0.654940\pi$
$523$	−30.6245	−	8.99217i	−1.33912	−	0.393200i	−0.871354	+	0.490655i	$0.836758\pi$
$524$	1.11385	−	7.74701i	0.0486588	−	0.338430i
$525$	−1.70035	−	11.8262i	−0.0742092	−	0.516136i
$526$	−4.17584	+	1.22614i	−0.182075	+	0.0534621i
$527$	0.343581	−	0.100885i	0.0149666	−	0.00439460i
$528$	−1.05829	−	2.31734i	−0.0460563	−	0.100849i
$529$	−27.7470	+	8.14724i	−1.20639	+	0.354228i
$530$	0.885875	+	1.02235i	0.0384800	+	0.0444083i
$531$	−29.3962	+	33.9250i	−1.27568	+	1.47222i
$532$	13.1912	−	28.8847i	0.571911	−	1.25231i
$533$	−21.7733			−0.943105
$534$	18.9549	+	4.07400i	0.820259	+	0.176299i
$535$	11.9894			0.518347
$536$	−6.01738	+	13.1762i	−0.259911	+	0.569126i
$537$	38.1320	−	44.0066i	1.64552	−	1.89903i
$538$	5.33401	+	6.15577i	0.229965	+	0.265394i
$539$	2.11851	−	0.622050i	0.0912506	−	0.0267936i
$540$	−12.2091	−	26.7342i	−0.525396	−	1.15046i
$541$	8.64742	−	2.53911i	0.371782	−	0.109165i	−0.0905038	−	0.995896i	$-0.528848\pi$
$541$	8.64742	−	2.53911i	0.371782	−	0.109165i	0.462285	+	0.886731i	$0.347030\pi$
$542$	14.9548	−	4.39112i	0.642363	−	0.188615i
$543$	−7.23814	−	50.3424i	−0.310618	−	2.16040i
$544$	0.0371781	−	0.258579i	0.00159400	−	0.0110865i
$545$	−14.6944	−	4.31466i	−0.629438	−	0.184820i
$546$	28.6522			1.22620
$547$	14.8605	−	17.1499i	0.635390	−	0.733279i	−0.343163	−	0.939276i	$-0.611498\pi$
$547$	14.8605	−	17.1499i	0.635390	−	0.733279i	0.978553	+	0.205997i	$0.0660438\pi$
$548$	−4.61206	+	32.0776i	−0.197017	+	1.37029i
$549$	22.5010	−	49.2703i	0.960318	−	2.10280i
$550$	−0.0344046	+	0.239289i	−0.00146702	+	0.0102033i
$551$	−11.7595	−	25.7498i	−0.500972	−	1.09698i
$552$	51.5484	+	15.1360i	2.19405	+	0.644230i
$553$	−6.77166	−	47.0979i	−0.287960	−	2.00281i
$554$	−6.24206	−	4.01153i	−0.265200	−	0.170433i
$555$	1.48630	−	3.25453i	0.0630897	−	0.138147i
$556$	−4.48831	+	5.17979i	−0.190347	+	0.219672i
$557$	−1.30183	−	9.05445i	−0.0551605	−	0.383650i	−0.998636	−	0.0522080i	$-0.983374\pi$
$557$	−1.30183	−	9.05445i	−0.0551605	−	0.383650i	0.943476	−	0.331442i	$-0.107535\pi$
$558$	16.2154	−	35.5067i	0.686451	−	1.50312i
$559$	−15.1998	+	9.76830i	−0.642882	+	0.413155i
$560$	2.80857	+	6.14991i	0.118684	+	0.259881i
$561$	−0.0525404	−	0.0337657i	−0.00221826	−	0.00142559i
$562$	−8.43257	−	5.41928i	−0.355706	−	0.228599i
$563$	−1.82289	+	0.535247i	−0.0768254	+	0.0225580i	−0.319919	−	0.947445i	$-0.603656\pi$
$563$	−1.82289	+	0.535247i	−0.0768254	+	0.0225580i	0.243094	+	0.970003i	$0.421838\pi$
$564$	47.4304	+	54.7376i	1.99718	+	2.30487i
$565$	0.801948	−	5.57767i	0.0337382	−	0.234654i
$566$	−1.17691	−	0.756356i	−0.0494693	−	0.0317920i
$567$	106.667	−	68.5508i	4.47960	−	2.87886i
$568$	6.86322			0.287974
$569$	−27.5612	+	17.7125i	−1.15543	+	0.742548i	−0.970713	−	0.240244i	$-0.922773\pi$
$569$	−27.5612	+	17.7125i	−1.15543	+	0.742548i	−0.184715	+	0.982792i	$0.559136\pi$
$570$	−7.40353	+	8.54413i	−0.310100	+	0.357874i
$571$	−37.0436			−1.55023			−0.775113	−	0.631823i	$-0.782307\pi$
$571$	−37.0436			−1.55023			−0.775113	+	0.631823i	$0.782307\pi$
$572$	2.43526	+	0.715058i	0.101824	+	0.0298981i
$573$	−6.43034	−	44.7240i	−0.268631	−	1.86837i
$574$	−10.0706	+	6.47201i	−0.420341	+	0.270137i
$575$	4.71856	+	5.44551i	0.196778	+	0.227093i
$576$	2.22297	+	2.56544i	0.0926237	+	0.106894i
$577$	−13.1071	−	3.84858i	−0.545655	−	0.160219i	−0.00272410	−	0.999996i	$-0.500867\pi$
$577$	−13.1071	−	3.84858i	−0.545655	−	0.160219i	−0.542930	+	0.839778i	$0.682685\pi$
$578$	4.30609	+	9.42902i	0.179110	+	0.392196i
$579$	−10.2450	−	22.4335i	−0.425769	−	0.932303i
$580$	8.03852	+	2.36032i	0.333781	+	0.0980070i
$581$	3.46266	+	3.99612i	0.143655	+	0.165787i
$582$	15.6506	+	18.0618i	0.648739	+	0.748685i
$583$	−0.739777	+	0.475426i	−0.0306384	+	0.0196901i
$584$	1.41884	+	9.86824i	0.0587120	+	0.408351i
$585$	31.5309	+	9.25832i	1.30364	+	0.382784i
$586$	9.51634			0.393116
$587$	6.99734	−	8.07536i	0.288811	−	0.333306i	−0.592740	−	0.805394i	$-0.701954\pi$
$587$	6.99734	−	8.07536i	0.288811	−	0.333306i	0.881552	+	0.472088i	$0.156499\pi$
$588$	−25.7078	+	16.5214i	−1.06017	+	0.681332i
$589$	42.1368			1.73622
$590$	−2.75578	+	1.77103i	−0.113454	+	0.0729122i
$591$	−15.7498	−	10.1218i	−0.647859	−	0.416354i
$592$	−0.288130	+	2.00399i	−0.0118421	+	0.0823635i
$593$	−20.4437	−	23.5933i	−0.839523	−	0.968861i	0.160312	−	0.987066i	$-0.448750\pi$
$593$	−20.4437	−	23.5933i	−0.839523	−	0.968861i	−0.999834	+	0.0182057i	$0.994205\pi$
$594$	−4.18722	+	1.22948i	−0.171804	+	0.0504461i
$595$	0.139435	+	0.0896095i	0.00571628	+	0.00367363i
$596$	3.13658	+	2.01576i	0.128479	+	0.0825686i
$597$	−29.5560	−	64.7187i	−1.20965	−	2.64876i
$598$	−14.5364	+	9.34200i	−0.594439	+	0.382023i
$599$	19.1625	−	41.9600i	0.782959	−	1.71444i	0.0871701	−	0.996193i	$-0.472218\pi$
$599$	19.1625	−	41.9600i	0.782959	−	1.71444i	0.695789	−	0.718247i	$-0.255055\pi$
$600$	−1.06112	−	7.38023i	−0.0433199	−	0.301297i
$601$	17.9824	−	20.7528i	0.733519	−	0.846526i	−0.259345	−	0.965785i	$-0.583507\pi$
$601$	17.9824	−	20.7528i	0.733519	−	0.846526i	0.992863	+	0.119259i	$0.0380520\pi$
$602$	−4.12667	+	9.03614i	−0.168190	+	0.368285i
$603$	−46.0252	−	29.5786i	−1.87429	−	1.20453i
$604$	−0.364844	−	2.53755i	−0.0148453	−	0.103251i
$605$	10.4036	+	3.05478i	0.422968	+	0.124195i
$606$	−2.56492	−	5.61639i	−0.104193	−	0.228150i
$607$	0.392040	−	2.72670i	0.0159124	−	0.110673i	−0.980317	−	0.197429i	$-0.936741\pi$
$607$	0.392040	−	2.72670i	0.0159124	−	0.110673i	0.996230	+	0.0867556i	$0.0276499\pi$
$608$	12.7701	−	27.9625i	0.517894	−	1.13403i
$609$	−8.74959	+	60.8548i	−0.354551	+	2.46596i
$610$	2.58847	−	2.98726i	0.104804	−	0.120951i
$611$	−51.9114			−2.10011
$612$	0.610296	+	0.179199i	0.0246698	+	0.00724369i
$613$	−4.05246	+	28.1855i	−0.163677	+	1.13840i	0.727949	+	0.685631i	$0.240474\pi$
$613$	−4.05246	+	28.1855i	−0.163677	+	1.13840i	−0.891627	+	0.452771i	$0.850436\pi$
$614$	0.734025	+	5.10526i	0.0296228	+	0.206031i
$615$	−17.9031	+	5.25682i	−0.721922	+	0.211975i
$616$	2.98367	−	0.876083i	0.120215	−	0.0352984i
$617$	13.3674	+	29.2705i	0.538150	+	1.17839i	0.962099	+	0.272699i	$0.0879163\pi$
$617$	13.3674	+	29.2705i	0.538150	+	1.17839i	−0.423949	+	0.905686i	$0.639356\pi$
$618$	5.14258	−	1.51000i	0.206865	−	0.0607410i
$619$	−8.96217	−	10.3429i	−0.360220	−	0.415716i	0.546493	−	0.837464i	$-0.315962\pi$
$619$	−8.96217	−	10.3429i	−0.360220	−	0.415716i	−0.906713	+	0.421747i	$0.861417\pi$
$620$	−8.16652	+	9.42466i	−0.327975	+	0.378504i
$621$	−54.0332	+	118.316i	−2.16828	+	4.74787i
$622$	−3.17898			−0.127465
$623$	11.6105	−	31.3671i	0.465164	−	1.25670i
$624$	−25.2714			−1.01166
$625$	0.415415	−	0.909632i	0.0166166	−	0.0363853i
$626$	−0.678100	+	0.782569i	−0.0271023	+	0.0312777i
$627$	−4.81270	−	5.55415i	−0.192201	−	0.221812i
$628$	34.9259	−	10.2552i	1.39369	−	0.409225i
$629$	0.0206188	+	0.0451489i	0.000822125	+	0.00180020i
$630$	17.3358	−	5.09025i	0.690675	−	0.202800i
$631$	14.8873	−	4.37131i	0.592655	−	0.174019i	0.0283673	−	0.999598i	$-0.490969\pi$
$631$	14.8873	−	4.37131i	0.592655	−	0.174019i	0.564287	+	0.825578i	$0.309151\pi$
$632$	−4.22592	−	29.3919i	−0.168098	−	1.16915i
$633$	4.23262	−	29.4385i	0.168232	−	1.17008i
$634$	0.0199721	+	0.00586434i	0.000793194	+	0.000232903i
$635$	−15.6631			−0.621571
$636$	7.97028	−	9.19819i	0.316042	−	0.364732i
$637$	3.11705	−	21.6795i	0.123502	−	0.858974i
$638$	0.516772	−	1.13157i	0.0204592	−	0.0447994i
$639$	−3.68911	+	25.6583i	−0.145939	+	1.01503i
$640$	4.74556	+	10.3913i	0.187585	+	0.410753i
$641$	26.6294	+	7.81910i	1.05180	+	0.308836i	0.761544	−	0.648114i	$-0.224442\pi$
$641$	26.6294	+	7.81910i	1.05180	+	0.308836i	0.290254	+	0.956950i	$0.406260\pi$
$642$	3.50655	+	24.3886i	0.138393	+	0.962542i
$643$	−19.5221	−	12.5461i	−0.769877	−	0.494770i	0.0957832	−	0.995402i	$-0.469464\pi$
$643$	−19.5221	−	12.5461i	−0.769877	−	0.494770i	−0.865660	+	0.500632i	$0.833101\pi$
$644$	17.2778	−	37.8331i	0.680840	−	1.49083i
$645$	−10.1396	+	11.7017i	−0.399247	+	0.460755i
$646$	−0.0223202	−	0.155240i	−0.000878176	−	0.00610785i
$647$	−18.2273	+	39.9121i	−0.716587	+	1.56911i	0.102039	+	0.994780i	$0.467463\pi$
$647$	−18.2273	+	39.9121i	−0.716587	+	1.56911i	−0.818626	+	0.574327i	$0.805264\pi$
$648$	66.5667	−	42.7798i	2.61499	−	1.68055i
$649$	−0.884606	−	1.93702i	−0.0347238	−	0.0760345i
$650$	2.01743	+	1.29652i	0.0791300	+	0.0508537i
$651$	−76.9872	−	49.4767i	−3.01737	−	1.93914i
$652$	−25.2964	+	7.42771i	−0.990685	+	0.290891i
$653$	25.4689	+	29.3927i	0.996674	+	1.15022i	0.988647	+	0.150256i	$0.0480097\pi$
$653$	25.4689	+	29.3927i	0.996674	+	1.15022i	0.00802719	+	0.999968i	$0.497445\pi$
$654$	4.47912	−	31.1530i	0.175147	−	1.21818i
$655$	4.04409	+	2.59898i	0.158016	+	0.101550i
$656$	8.88236	−	5.70835i	0.346798	−	0.222874i
$657$	−37.6554			−1.46908
$658$	−24.0102	+	15.4304i	−0.936016	+	0.601541i
$659$	−6.63201	+	7.65375i	−0.258347	+	0.298148i	−0.870074	−	0.492921i	$-0.835929\pi$
$659$	−6.63201	+	7.65375i	−0.258347	+	0.298148i	0.611728	+	0.791068i	$0.290475\pi$
$660$	2.17504			0.0846632
$661$	1.60352	+	0.470837i	0.0623699	+	0.0183134i	0.312769	−	0.949829i	$-0.398744\pi$
$661$	1.60352	+	0.470837i	0.0623699	+	0.0183134i	−0.250399	+	0.968143i	$0.580562\pi$
$662$	0.704978	+	4.90323i	0.0273998	+	0.190569i
$663$	−0.521192	+	0.334950i	−0.0202414	+	0.0130084i
$664$	2.16090	+	2.49382i	0.0838593	+	0.0967788i
$665$	12.7723	+	14.7400i	0.495287	+	0.571592i
$666$	5.19134	+	1.52432i	0.201160	+	0.0590660i
$667$	−15.4026	−	33.7269i	−0.596390	−	1.30591i
$668$	−4.81206	−	10.5369i	−0.186184	−	0.407686i
$669$	−35.6953	−	10.4811i	−1.38006	−	0.405222i
$670$	−2.61453	−	3.01733i	−0.101008	−	0.116570i
$671$	1.68265	+	1.94188i	0.0649580	+	0.0749656i
$672$	−56.1653	+	36.0952i	−2.16662	+	1.39240i
$673$	2.23969	+	15.5774i	0.0863338	+	0.600465i	0.986357	+	0.164622i	$0.0526405\pi$
$673$	2.23969	+	15.5774i	0.0863338	+	0.600465i	−0.900023	+	0.435843i	$0.856450\pi$
$674$	14.2070	+	4.17155i	0.547233	+	0.160682i
$675$	18.0517			0.694811
$676$	2.62722	−	3.03198i	0.101047	−	0.116615i
$677$	18.0745	−	11.6158i	0.694660	−	0.446431i	−0.145079	−	0.989420i	$-0.546344\pi$
$677$	18.0745	−	11.6158i	0.694660	−	0.446431i	0.839740	+	0.542989i	$0.182707\pi$
$678$	11.5805			0.444748
$679$	34.6847	−	22.2905i	1.33108	−	0.855432i
$680$	0.0870158	+	0.0559217i	0.00333690	+	0.00214450i
$681$	−10.6037	+	73.7503i	−0.406334	+	2.82612i
$682$	1.21260	+	1.39942i	0.0464330	+	0.0535866i
$683$	14.3442	−	4.21183i	0.548865	−	0.161161i	0.00446930	−	0.999990i	$-0.498577\pi$
$683$	14.3442	−	4.21183i	0.548865	−	0.161161i	0.544395	+	0.838829i	$0.316759\pi$
$684$	62.9650	+	40.4652i	2.40753	+	1.54722i
$685$	−16.7451	−	10.7614i	−0.639798	−	0.411173i
$686$	1.28465	+	2.81300i	0.0490483	+	0.107401i
$687$	25.9667	−	16.6878i	0.990692	−	0.636679i
$688$	3.63974	−	7.96992i	0.138764	−	0.303850i
$689$	1.24145	+	8.63447i	0.0472954	+	0.328947i
$690$	−9.69711	+	11.1911i	−0.369163	+	0.426036i
$691$	1.90260	−	4.16611i	0.0723783	−	0.158486i	−0.869985	−	0.493079i	$-0.835871\pi$
$691$	1.90260	−	4.16611i	0.0723783	−	0.158486i	0.942363	+	0.334592i	$0.108599\pi$
$692$	−16.7997	−	10.7965i	−0.638630	−	0.410422i
$693$	1.67149	+	11.6254i	0.0634945	+	0.441614i
$694$	−4.42812	−	1.30021i	−0.168089	−	0.0493554i
$695$	−1.74877	−	3.82927i	−0.0663347	−	0.145253i
$696$	−5.46027	+	37.9770i	−0.206971	+	1.43951i
$697$	0.107529	−	0.235456i	0.00407295	−	0.00891853i
$698$	−2.54709	+	17.7154i	−0.0964089	+	0.670539i
$699$	27.6291	−	31.8857i	1.04503	−	1.20603i
$700$	−5.77226			−0.218171
$701$	−13.9109	−	4.08461i	−0.525408	−	0.154274i	0.00826308	−	0.999966i	$-0.497370\pi$
$701$	−13.9109	−	4.08461i	−0.525408	−	0.154274i	−0.533671	+	0.845692i	$0.679188\pi$
$702$	−6.16083	+	42.8495i	−0.232526	+	1.61725i
$703$	0.831199	+	5.78112i	0.0313493	+	0.218039i
$704$	−0.154508	+	0.0453678i	−0.00582326	+	0.00170986i
$705$	−42.6841	+	12.5332i	−1.60758	+	0.472027i
$706$	−7.28135	−	15.9439i	−0.274037	−	0.600058i
$707$	−10.2203	+	3.00095i	−0.384373	+	0.112862i
$708$	19.3004	+	22.2739i	0.725355	+	0.837104i
$709$	−9.56567	+	11.0394i	−0.359246	+	0.414592i	−0.906387	−	0.422448i	$-0.861171\pi$
$709$	−9.56567	+	11.0394i	−0.359246	+	0.414592i	0.547141	+	0.837041i	$0.315716\pi$
$710$	−0.785832	+	1.72073i	−0.0294917	+	0.0645779i
$711$	112.154			4.20611
$712$	7.24564	−	19.5750i	0.271542	−	0.733603i
$713$	55.1906			2.06690
$714$	−0.141501	+	0.309845i	−0.00529555	+	0.0115956i
$715$	−1.02087	+	1.17815i	−0.0381783	+	0.0440601i
$716$	−18.4225	−	21.2606i	−0.688479	−	0.794548i
$717$	−30.8387	+	9.05507i	−1.15169	+	0.338168i
$718$	−3.68671	−	8.07276i	−0.137587	−	0.301273i
$719$	31.7007	−	9.30816i	1.18224	−	0.347136i	0.369201	−	0.929350i	$-0.379632\pi$
$719$	31.7007	−	9.30816i	1.18224	−	0.347136i	0.813036	+	0.582214i	$0.197813\pi$
$720$	−15.2903	+	4.48963i	−0.569834	+	0.167318i
$721$	−1.31589	−	9.15219i	−0.0490062	−	0.340845i
$722$	0.977500	−	6.79866i	0.0363788	−	0.253020i
$723$	16.6183	+	4.87958i	0.618042	+	0.181474i
$724$	−24.5717			−0.913200
$725$	−3.36976	+	3.88892i	−0.125150	+	0.144431i
$726$	−3.17122	+	22.0563i	−0.117695	+	0.818587i
$727$	4.06052	−	8.89130i	0.150596	−	0.329760i	−0.819266	−	0.573414i	$-0.805619\pi$
$727$	4.06052	−	8.89130i	0.150596	−	0.329760i	0.969862	+	0.243654i	$0.0783460\pi$
$728$	4.38999	−	30.5330i	0.162704	−	1.13163i
$729$	48.3391	+	105.848i	1.79034	+	3.92029i
$730$	−2.63660	−	0.774176i	−0.0975850	−	0.0286535i
$731$	−0.0305690	−	0.212612i	−0.00113063	−	0.00786373i
$732$	−29.9173	−	19.2267i	−1.10578	−	0.710639i
$733$	−4.05533	+	8.87994i	−0.149787	+	0.327988i	−0.969621	−	0.244614i	$-0.921339\pi$
$733$	−4.05533	+	8.87994i	−0.149787	+	0.327988i	0.819833	+	0.572602i	$0.194066\pi$
$734$	−0.0956419	+	0.110377i	−0.00353021	+	0.00407408i
$735$	−2.67119	−	18.5786i	−0.0985285	−	0.685280i
$736$	16.7262	−	36.6252i	0.616535	−	1.35002i
$737$	2.18334	−	1.40315i	0.0804245	−	0.0516857i
$738$	−11.7215	−	25.6665i	−0.431474	−	0.944796i
$739$	−34.2364	−	22.0024i	−1.25940	−	0.809370i	−0.271202	−	0.962522i	$-0.587421\pi$
$739$	−34.2364	−	22.0024i	−1.25940	−	0.809370i	−0.988203	+	0.153152i	$0.951058\pi$
$740$	−1.45415	−	0.934523i	−0.0534555	−	0.0343538i
$741$	−69.9498	+	20.5391i	−2.56967	+	0.754523i
$742$	3.14076	+	3.62463i	0.115301	+	0.133064i
$743$	1.52116	−	10.5799i	0.0558058	−	0.388138i	−0.942707	−	0.333622i	$-0.891729\pi$
$743$	1.52116	−	10.5799i	0.0558058	−	0.388138i	0.998513	−	0.0545164i	$-0.0173617\pi$
$744$	−48.0446	−	30.8764i	−1.76140	−	1.13198i
$745$	−1.92652	+	1.23810i	−0.0705821	+	0.0453603i
$746$	18.4534			0.675629
$747$	−10.4847	+	6.73813i	−0.383616	+	0.246535i
$748$	−0.0197594	+	0.0228036i	−0.000722475	+	0.000833781i
$749$	42.5069			1.55317
$750$	1.97185	+	0.578989i	0.0720019	+	0.0211417i
$751$	6.97750	+	48.5296i	0.254612	+	1.77087i	0.569746	+	0.821821i	$0.307042\pi$
$751$	6.97750	+	48.5296i	0.254612	+	1.77087i	−0.315133	+	0.949047i	$0.602049\pi$
$752$	21.1771	−	13.6097i	0.772251	−	0.496296i
$753$	−28.3708	−	32.7416i	−1.03389	−	1.19317i
$754$	−8.08109	−	9.32608i	−0.294296	−	0.339636i
$755$	1.51083	+	0.443620i	0.0549848	+	0.0161450i
$756$	−43.2859	−	94.7828i	−1.57429	−	3.44722i
$757$	8.13403	+	17.8110i	0.295636	+	0.647353i	0.997915	−	0.0645493i	$-0.0205610\pi$
$757$	8.13403	+	17.8110i	0.295636	+	0.647353i	−0.702278	+	0.711903i	$0.747834\pi$
$758$	−16.0755	−	4.72021i	−0.583890	−	0.171446i
$759$	−6.30366	−	7.27481i	−0.228808	−	0.264059i
$760$	7.97065	+	9.19863i	0.289126	+	0.333669i
$761$	−19.0389	+	12.2355i	−0.690158	+	0.443538i	−0.838142	−	0.545452i	$-0.816358\pi$
$761$	−19.0389	+	12.2355i	−0.690158	+	0.443538i	0.147984	+	0.988990i	$0.452722\pi$
$762$	−4.58100	−	31.8616i	−0.165952	−	1.15422i
$763$	−52.0971	−	15.2971i	−1.88604	−	0.553792i
$764$	−21.8294			−0.789760
$765$	−0.255838	+	0.295252i	−0.00924983	+	0.0106749i
$766$	−8.81414	+	5.66450i	−0.318468	+	0.204667i
$767$	−21.1238			−0.762737
$768$	−17.4467	+	11.2123i	−0.629553	+	0.404589i
$769$	−7.78024	−	5.00005i	−0.280562	−	0.180307i	0.392790	−	0.919628i	$-0.371510\pi$
$769$	−7.78024	−	5.00005i	−0.280562	−	0.180307i	−0.673352	+	0.739322i	$0.735146\pi$
$770$	−0.121977	+	0.848369i	−0.00439575	+	0.0305731i
$771$	−15.8270	−	18.2654i	−0.569996	−	0.657811i
$772$	−11.4322	+	3.35680i	−0.411455	+	0.120814i
$773$	36.7050	+	23.5889i	1.32019	+	0.848433i	0.995255	−	0.0973034i	$-0.0310217\pi$
$773$	36.7050	+	23.5889i	1.32019	+	0.848433i	0.324933	+	0.945737i	$0.394658\pi$
$774$	−19.6976	−	12.6589i	−0.708017	−	0.455015i
$775$	−3.18190	−	6.96739i	−0.114297	−	0.250276i
$776$	21.6453	−	13.9106i	0.777023	−	0.499362i
$777$	5.26947	−	11.5385i	0.189041	−	0.413943i
$778$	1.95564	+	13.6018i	0.0701131	+	0.487647i
$779$	19.9465	−	23.0195i	0.714657	−	0.824758i
$780$	8.96300	−	19.6262i	0.320927	−	0.702732i
$781$	−1.03449	−	0.664824i	−0.0370168	−	0.0237893i
$782$	−0.0292349	−	0.203333i	−0.00104544	−	0.00727118i
$783$	−89.1273	−	26.1701i	−3.18515	−	0.935244i
$784$	4.41218	+	9.66132i	0.157578	+	0.345047i
$785$	−3.18179	+	22.1299i	−0.113563	+	0.789849i
$786$	−4.10401	+	8.98653i	−0.146385	+	0.320539i
$787$	−3.01980	+	21.0032i	−0.107644	+	0.748682i	0.862483	+	0.506086i	$0.168908\pi$
$787$	−3.01980	+	21.0032i	−0.107644	+	0.748682i	−0.970127	+	0.242596i	$0.922001\pi$
$788$	−5.92317	+	6.83571i	−0.211004	+	0.243512i
$789$	−24.0502			−0.856211
$790$	7.85294	+	2.30583i	0.279395	+	0.0820378i
$791$	2.84321	−	19.7749i	0.101093	−	0.703116i
$792$	1.04311	+	7.25496i	0.0370652	+	0.257794i
$793$	24.4564	−	7.18103i	0.868471	−	0.255006i
$794$	−14.5453	+	4.27090i	−0.516195	+	0.151568i
$795$	3.10544	+	6.79997i	0.110139	+	0.241170i
$796$	−32.9810	+	9.68410i	−1.16898	+	0.343244i
$797$	−2.85860	−	3.29900i	−0.101257	−	0.116857i	0.702859	−	0.711329i	$-0.251906\pi$
$797$	−2.85860	−	3.29900i	−0.101257	−	0.116857i	−0.804116	+	0.594472i	$0.797361\pi$
$798$	−26.2483	+	30.2921i	−0.929179	+	1.07233i
$799$	0.256369	−	0.561369i	0.00906967	−	0.0198598i
$800$	−5.58797			−0.197564
$801$	69.2869	+	37.6100i	2.44813	+	1.32888i
$802$	−13.8555			−0.489254
$803$	0.742053	−	1.62487i	0.0261865	−	0.0573404i
$804$	−23.5231	+	27.1471i	−0.829596	+	0.957404i
$805$	16.7291	+	19.3064i	0.589622	+	0.680460i
$806$	17.6245	−	5.17502i	0.620797	−	0.182282i
$807$	18.6984	+	40.9438i	0.658215	+	1.44129i
$808$	−6.37806	+	1.87277i	−0.224380	+	0.0658838i
$809$	−8.44782	+	2.48050i	−0.297009	+	0.0872098i	−0.426842	−	0.904326i	$-0.640374\pi$
$809$	−8.44782	+	2.48050i	−0.297009	+	0.0872098i	0.129833	+	0.991536i	$0.458556\pi$
$810$	3.10384	+	21.5877i	0.109058	+	0.758514i
$811$	0.746582	−	5.19259i	0.0262160	−	0.182336i	−0.972506	−	0.232878i	$-0.925186\pi$
$811$	0.746582	−	5.19259i	0.0262160	−	0.182336i	0.998722	+	0.0505416i	$0.0160948\pi$
$812$	28.4995	+	8.36822i	1.00014	+	0.293667i
$813$	86.1303			3.02072
$814$	−0.168079	+	0.193973i	−0.00589116	+	0.00679876i
$815$	2.30454	−	16.0284i	0.0807246	−	0.561452i
$816$	0.124805	−	0.273284i	0.00436904	−	0.00956687i
$817$	3.59711	−	25.0185i	0.125847	−	0.875286i
$818$	−6.36049	−	13.9275i	−0.222389	−	0.486965i
$819$	111.789	+	32.8242i	3.90622	+	1.14697i
$820$	1.28290	+	8.92280i	0.0448010	+	0.311598i
$821$	−25.8314	−	16.6008i	−0.901523	−	0.579373i	0.00571876	−	0.999984i	$-0.498180\pi$
$821$	−25.8314	−	16.6008i	−0.901523	−	0.579373i	−0.907241	+	0.420610i	$0.861816\pi$
$822$	16.9932	−	37.2100i	0.592707	−	1.29785i
$823$	−31.9084	+	36.8242i	−1.11226	+	1.28361i	−0.157075	+	0.987587i	$0.550206\pi$
$823$	−31.9084	+	36.8242i	−1.11226	+	1.28361i	−0.955180	+	0.296024i	$0.904339\pi$
$824$	−0.821191	−	5.71151i	−0.0286076	−	0.198970i
$825$	−0.554965	+	1.21520i	−0.0193214	+	0.0423079i
$826$	−9.77026	+	6.27897i	−0.339951	+	0.218473i
$827$	12.4834	+	27.3348i	0.434089	+	0.950523i	0.992646	+	0.121056i	$0.0386282\pi$
$827$	12.4834	+	27.3348i	0.434089	+	0.950523i	−0.558556	+	0.829467i	$0.688645\pi$
$828$	82.4713	+	53.0011i	2.86608	+	1.84192i
$829$	6.92411	+	4.44986i	0.240484	+	0.154550i	0.655332	−	0.755341i	$-0.272529\pi$
$829$	6.92411	+	4.44986i	0.240484	+	0.154550i	−0.414848	+	0.909891i	$0.636165\pi$
$830$	−0.872666	+	0.256238i	−0.0302907	+	0.00889414i
$831$	−26.8514	−	30.9882i	−0.931465	−	1.07497i
$832$	−0.227335	+	1.58115i	−0.00788141	+	0.0548164i
$833$	0.219048	+	0.140774i	0.00758958	+	0.00487752i
$834$	7.27798	−	4.67727i	0.252016	−	0.161961i
$835$	7.11484			0.246219
$836$	−2.98693	+	1.91958i	−0.103305	+	0.0663902i
$837$	90.5465	−	104.496i	3.12975	−	3.61192i
$838$	3.37982			0.116754
$839$	−6.04728	−	1.77564i	−0.208775	−	0.0613020i	0.175673	−	0.984449i	$-0.443790\pi$
$839$	−6.04728	−	1.77564i	−0.208775	−	0.0613020i	−0.384448	+	0.923147i	$0.625608\pi$
$840$	−3.76206	−	26.1657i	−0.129803	−	0.902802i
$841$	−2.12082	+	1.36297i	−0.0731318	+	0.0469989i
$842$	6.70604	+	7.73918i	0.231105	+	0.266710i
$843$	−36.2743	−	41.8628i	−1.24935	−	1.44183i
$844$	−13.7867	−	4.04813i	−0.474557	−	0.139343i
$845$	1.02364	+	2.24146i	0.0352143	+	0.0771085i
$846$	−27.9461	−	61.1935i	−0.960808	−	2.10388i
$847$	36.8848	+	10.8304i	1.26738	+	0.372135i
$848$	−2.77017	−	3.19694i	−0.0951279	−	0.109783i
$849$	−5.06272	−	5.84269i	−0.173752	−	0.200520i
$850$	−0.0239838	+	0.0154134i	−0.000822637	+	0.000528677i
$851$	1.08870	+	7.57208i	0.0373202	+	0.259568i
$852$	16.3301	+	4.79496i	0.559461	+	0.164273i
$853$	8.32940			0.285193			0.142597	−	0.989781i	$-0.454455\pi$
$853$	8.32940			0.285193			0.142597	+	0.989781i	$0.454455\pi$
$854$	9.17711	−	10.5909i	0.314034	−	0.362415i
$855$	−38.6737	+	24.8541i	−1.32261	+	0.849992i
$856$	26.5268			0.906669
$857$	14.9595	−	9.61391i	0.511008	−	0.328405i	−0.259598	−	0.965717i	$-0.583590\pi$
$857$	14.9595	−	9.61391i	0.511008	−	0.328405i	0.770606	+	0.637312i	$0.219954\pi$
$858$	−2.69514	−	1.73206i	−0.0920104	−	0.0591315i
$859$	−4.32641	+	30.0909i	−0.147615	+	1.02669i	0.772493	+	0.635023i	$0.219009\pi$
$859$	−4.32641	+	30.0909i	−0.147615	+	1.02669i	−0.920108	+	0.391664i	$0.871900\pi$
$860$	4.89869	+	5.65339i	0.167044	+	0.192779i
$861$	−63.4731	+	18.6374i	−2.16316	+	0.635160i
$862$	17.8282	+	11.4575i	0.607233	+	0.390245i
$863$	11.0700	+	7.11423i	0.376826	+	0.242171i	0.715320	−	0.698797i	$-0.246281\pi$
$863$	11.0700	+	7.11423i	0.376826	+	0.242171i	−0.338494	+	0.940969i	$0.609917\pi$
$864$	−41.9039	−	91.7567i	−1.42560	−	3.12163i
$865$	10.3185	−	6.63133i	0.350841	−	0.225472i
$866$	−8.94655	+	19.5902i	−0.304016	+	0.665703i
$867$	8.15208	+	56.6990i	0.276859	+	1.92560i
$868$	−28.9534	+	33.4140i	−0.982741	+	1.13414i
$869$	−2.21016	+	4.83957i	−0.0749744	+	0.164171i
$870$	−8.89632	−	5.71732i	−0.301614	−	0.193835i
$871$	−3.66395	−	25.4834i	−0.124148	−	0.863471i
$872$	−32.5117	−	9.54629i	−1.10098	−	0.323278i
$873$	40.3705	+	88.3990i	1.36633	+	2.99185i
$874$	3.44013	−	23.9267i	0.116364	−	0.809331i
$875$	1.47280	−	3.22499i	0.0497898	−	0.109024i
$876$	−3.51847	+	24.4715i	−0.118878	+	0.826814i
$877$	13.4009	−	15.4655i	0.452517	−	0.522232i	−0.482950	−	0.875648i	$-0.660435\pi$
$877$	13.4009	−	15.4655i	0.452517	−	0.522232i	0.935466	+	0.353416i	$0.114980\pi$
$878$	10.1560			0.342750
$879$	50.4579	+	14.8158i	1.70190	+	0.499724i
$880$	0.107584	−	0.748266i	0.00362667	−	0.0252240i
$881$	−1.75024	−	12.1732i	−0.0589672	−	0.410126i	−0.997830	−	0.0658358i	$-0.979029\pi$
$881$	−1.75024	−	12.1732i	−0.0589672	−	0.410126i	0.938863	−	0.344290i	$-0.111880\pi$
$882$	27.2340	−	7.99663i	0.917017	−	0.269261i
$883$	−32.5099	+	9.54576i	−1.09404	+	0.321240i	−0.778484	−	0.627665i	$-0.784011\pi$
$883$	−32.5099	+	9.54576i	−1.09404	+	0.321240i	−0.315561	+	0.948905i	$0.602193\pi$
$884$	0.124340	+	0.272267i	0.00418201	+	0.00915733i
$885$	−17.3691	+	5.10002i	−0.583855	+	0.171435i
$886$	4.10393	+	4.73619i	0.137874	+	0.159115i
$887$	−13.9061	+	16.0485i	−0.466922	+	0.538857i	−0.939553	−	0.342403i	$-0.888759\pi$
$887$	−13.9061	+	16.0485i	−0.466922	+	0.538857i	0.472631	+	0.881261i	$0.343304\pi$
$888$	3.28847	−	7.20074i	0.110354	−	0.241641i
$889$	−55.5315			−1.86247
$890$	4.07818	+	4.05793i	0.136701	+	0.136022i
$891$	−14.1775			−0.474964
$892$	−7.46636	+	16.3491i	−0.249992	+	0.547407i
$893$	47.5560	−	54.8826i	1.59140	−	1.83658i
$894$	−3.08196	−	3.55678i	−0.103076	−	0.118956i
$895$	16.5789	−	4.86802i	0.554173	−	0.162720i
$896$	16.8248	+	36.8411i	0.562076	+	1.23078i
$897$	−91.6200	+	26.9021i	−3.05910	+	0.898234i
$898$	−7.09251	+	2.08255i	−0.236680	+	0.0694955i
$899$	5.60926	+	39.0132i	0.187079	+	1.30116i
$900$	1.93627	−	13.4671i	0.0645423	−	0.448902i
$901$	−0.0995041	−	0.0292170i	−0.00331496	−	0.000973360i
$902$	1.33853			0.0445680
$903$	−35.9487	+	41.4870i	−1.19630	+	1.38060i
$904$	1.77433	−	12.3407i	0.0590133	−	0.410447i
$905$	6.26952	−	13.7283i	0.208406	−	0.456345i
$906$	−0.460529	+	3.20305i	−0.0153001	+	0.106414i
$907$	3.84211	+	8.41304i	0.127575	+	0.279350i	0.962632	−	0.270813i	$-0.0872926\pi$
$907$	3.84211	+	8.41304i	0.127575	+	0.279350i	−0.835057	+	0.550164i	$0.814565\pi$
$908$	34.5388	+	10.1415i	1.14621	+	0.336558i
$909$	−3.57307	−	24.8512i	−0.118511	−	0.824263i
$910$	7.15253	+	4.59665i	0.237104	+	0.152378i
$911$	14.2264	−	31.1515i	0.471342	−	1.03210i	−0.513412	−	0.858142i	$-0.671619\pi$
$911$	14.2264	−	31.1515i	0.471342	−	1.03210i	0.984754	−	0.173953i	$-0.0556542\pi$
$912$	23.1511	−	26.7178i	0.766610	−	0.884715i
$913$	−0.0841408	−	0.585212i	−0.00278465	−	0.0193677i
$914$	5.50732	−	12.0593i	0.182166	−	0.398888i
$915$	18.3755	−	11.8092i	0.607475	−	0.390401i
$916$	−6.19485	−	13.5648i	−0.204683	−	0.448194i
$917$	14.3378	+	9.21435i	0.473476	+	0.304284i
$918$	−0.432948	−	0.278239i	−0.0142894	−	0.00918326i
$919$	−47.9869	+	14.0902i	−1.58294	+	0.464793i	−0.950734	−	0.310007i	$-0.899669\pi$
$919$	−47.9869	+	14.0902i	−1.58294	+	0.464793i	−0.632206	+	0.774800i	$0.717851\pi$
$920$	10.4399	+	12.0483i	0.344194	+	0.397221i
$921$	−4.05628	+	28.2121i	−0.133659	+	0.929619i
$922$	2.85512	+	1.83487i	0.0940282	+	0.0604283i
$923$	−10.2619	+	6.59495i	−0.337776	+	0.217075i
$924$	7.71132			0.253684
$925$	0.893151	−	0.573993i	0.0293666	−	0.0188728i
$926$	13.6649	−	15.7702i	0.449057	−	0.518240i
$927$	21.7941			0.715811
$928$	27.5897	+	8.10105i	0.905675	+	0.265930i
$929$	0.299616	+	2.08387i	0.00983007	+	0.0683697i	0.994146	−	0.108045i	$-0.0344591\pi$
$929$	0.299616	+	2.08387i	0.00983007	+	0.0683697i	−0.984316	+	0.176415i	$0.943550\pi$
$930$	13.2423	−	8.51033i	0.434233	−	0.279065i
$931$	20.0648	+	23.1561i	0.657599	+	0.758910i
$932$	−13.3483	−	15.4047i	−0.437237	−	0.504599i
$933$	−16.8557	−	4.94927i	−0.551830	−	0.162032i
$934$	−4.76341	−	10.4304i	−0.155863	−	0.341293i
$935$	−0.00769881	−	0.0168580i	−0.000251778	−	0.000551317i
$936$	69.7630	+	20.4843i	2.28027	+	0.669549i
$937$	2.55984	+	2.95421i	0.0836262	+	0.0965097i	0.796021	−	0.605270i	$-0.206935\pi$
$937$	2.55984	+	2.95421i	0.0836262	+	0.0965097i	−0.712394	+	0.701779i	$0.752389\pi$
$938$	−9.26949	−	10.6976i	−0.302660	−	0.349288i
$939$	−4.81381	+	3.09365i	−0.157093	+	0.100957i
$940$	3.05867	+	21.2735i	0.0997630	+	0.693867i
$941$	40.4709	+	11.8833i	1.31931	+	0.387386i	0.864245	−	0.503071i	$-0.167797\pi$
$941$	40.4709	+	11.8833i	1.31931	+	0.387386i	0.455069	+	0.890456i	$0.349615\pi$
$942$	−45.9468			−1.49703
$943$	26.1258	−	30.1508i	0.850774	−	0.981846i
$944$	8.61742	−	5.53808i	0.280473	−	0.180249i
$945$	64.0001			2.08192
$946$	0.934415	−	0.600512i	0.0303805	−	0.0195243i
$947$	39.3311	+	25.2766i	1.27809	+	0.821378i	0.990651	−	0.136422i	$-0.0435602\pi$
$947$	39.3311	+	25.2766i	1.27809	+	0.821378i	0.287438	+	0.957799i	$0.407197\pi$
$948$	10.4795	−	72.8867i	0.340359	−	2.36725i
$949$	−11.6040	−	13.3917i	−0.376681	−	0.434713i
$950$	−3.21889	+	0.945152i	−0.104435	+	0.0306648i
$951$	0.0967668	+	0.0621882i	0.00313788	+	0.00201659i
$952$	0.308504	+	0.198263i	0.00999866	+	0.00642575i
$953$	1.76150	+	3.85714i	0.0570605	+	0.124945i	0.936014	−	0.351962i	$-0.114485\pi$
$953$	1.76150	+	3.85714i	0.0570605	+	0.124945i	−0.878954	+	0.476907i	$0.841758\pi$
$954$	−9.51005	+	6.11174i	−0.307899	+	0.197875i
$955$	5.56981	−	12.1962i	0.180235	−	0.394659i
$956$	2.20985	+	15.3699i	0.0714717	+	0.497097i
$957$	4.50176	−	5.19531i	0.145521	−	0.167941i
$958$	−7.11227	+	15.5737i	−0.229787	+	0.503163i
$959$	−59.3677	−	38.1533i	−1.91708	−	1.23203i
$960$	0.194817	+	1.35498i	0.00628770	+	0.0437319i
$961$	−26.5482	−	7.79526i	−0.856395	−	0.251460i
$962$	1.05767	+	2.31598i	0.0341007	+	0.0746701i
$963$	−14.2587	+	99.1714i	−0.459480	+	3.19575i
$964$	3.47605	−	7.61149i	0.111956	−	0.245149i
$965$	1.04149	−	7.24373i	0.0335268	−	0.233184i
$966$	−34.3799	+	39.6765i	−1.10615	+	1.27657i
$967$	29.3623			0.944227			0.472113	−	0.881538i	$-0.343491\pi$
$967$	29.3623			0.944227			0.472113	+	0.881538i	$0.343491\pi$
$968$	23.0183	+	6.75878i	0.739836	+	0.217236i
$969$	0.123343	−	0.857871i	0.00396236	−	0.0275588i
$970$	1.00927	+	7.01963i	0.0324057	+	0.225387i
$971$	36.4281	−	10.6963i	1.16903	−	0.343259i	0.361096	−	0.932528i	$-0.382403\pi$
$971$	36.4281	−	10.6963i	1.16903	−	0.343259i	0.807937	+	0.589269i	$0.200584\pi$
$972$	103.676	−	30.4420i	3.32540	−	0.976427i
$973$	−6.20005	−	13.5762i	−0.198764	−	0.435233i
$974$	−17.0077	+	4.99392i	−0.544963	+	0.160016i
$975$	8.67834	+	10.0153i	0.277929	+	0.320748i
$976$	−8.09426	+	9.34127i	−0.259091	+	0.299007i
$977$	7.32111	−	16.0310i	0.234223	−	0.512877i	−0.755625	−	0.655004i	$-0.772667\pi$
$977$	7.32111	−	16.0310i	0.234223	−	0.512877i	0.989848	+	0.142127i	$0.0453941\pi$
$978$	33.2788			1.06414
$979$	−2.98831	+	2.24865i	−0.0955068	+	0.0718671i
$980$	−9.06804			−0.289668
$981$	53.1648	−	116.415i	1.69742	−	3.71683i
$982$	−2.29871	+	2.65285i	−0.0733547	+	0.0846558i
$983$	8.11605	+	9.36643i	0.258862	+	0.298743i	0.870272	−	0.492571i	$-0.163943\pi$
$983$	8.11605	+	9.36643i	0.258862	+	0.298743i	−0.611410	+	0.791314i	$0.709397\pi$
$984$	−39.6110	+	11.6308i	−1.26275	+	0.370778i
$985$	−2.30783	−	5.05345i	−0.0735336	−	0.161016i
$986$	0.140761	−	0.0413313i	0.00448275	−	0.00131626i
$987$	−151.331	+	44.4349i	−4.81693	+	1.41438i
$988$	5.01249	+	34.8626i	0.159469	+	1.10913i
$989$	4.71149	−	32.7691i	0.149817	−	1.04200i
$990$	−1.93838	−	0.569161i	−0.0616059	−	0.0180891i
$991$	−4.77353			−0.151636			−0.0758181	−	0.997122i	$-0.524157\pi$
$991$	−4.77353			−0.151636			−0.0758181	+	0.997122i	$0.524157\pi$
$992$	−28.0290	+	32.3472i	−0.889921	+	1.02702i
$993$	−3.89577	+	27.0956i	−0.123628	+	0.859854i
$994$	−2.78607	+	6.10064i	−0.0883687	+	0.193500i
$995$	3.00462	−	20.8976i	0.0952528	−	0.662498i
$996$	3.39930	+	7.44342i	0.107711	+	0.235854i
$997$	−24.7130	−	7.25641i	−0.782670	−	0.229813i	−0.134100	−	0.990968i	$-0.542814\pi$
$997$	−24.7130	−	7.25641i	−0.782670	−	0.229813i	−0.648570	+	0.761155i	$0.724633\pi$
$998$	−0.384336	−	2.67312i	−0.0121659	−	0.0846160i
$999$	16.1229	+	10.3616i	0.510106	+	0.327825i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	445.2.o.b.16.7	✓	160
89.39	even	11	inner	445.2.o.b.306.7	yes	160

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
445.2.o.b.16.7	✓	160	1.1	even	1	trivial
445.2.o.b.306.7	yes	160	89.39	even	11	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 445 = 5 \cdot 89 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	445.o (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.253332 + 0.554720i) q^{2} +(-2.20686 + 2.54685i) q^{3} +(1.06618 + 1.23044i) q^{4} +(-0.959493 + 0.281733i) q^{5} +(-0.853719 - 1.86938i) q^{6} +(-3.40176 + 0.998847i) q^{7} +(-2.12290 + 0.623340i) q^{8} +(-1.18928 - 8.27159i) q^{9} +(0.0867877 - 0.603621i) q^{10} +(0.380364 + 0.111685i) q^{11} -5.48667 q^{12} +(2.57520 - 2.97194i) q^{13} +(0.307695 - 2.14006i) q^{14} +(1.39993 - 3.06543i) q^{15} +(-0.271388 + 1.88755i) q^{16} +(0.0194207 + 0.0425254i) q^{17} +(4.88970 + 1.43574i) q^{18} +(0.782901 + 5.44520i) q^{19} +(-1.36965 - 0.880222i) q^{20} +(4.96329 - 10.8681i) q^{21} +(-0.158312 + 0.182702i) q^{22} +(1.02544 + 7.13210i) q^{23} +(3.09739 - 6.78233i) q^{24} +(0.841254 - 0.540641i) q^{25} +(0.996214 + 2.18141i) q^{26} +(15.1861 + 9.75949i) q^{27} +(-4.85593 - 3.12072i) q^{28} +(-4.93733 + 1.44973i) q^{29} +(1.34580 + 1.55314i) q^{30} +(1.09007 - 7.58161i) q^{31} +(-4.70090 - 3.02108i) q^{32} +(-1.12385 + 0.722257i) q^{33} -0.0285096 q^{34} +(2.98256 - 1.91677i) q^{35} +(8.90973 - 10.2824i) q^{36} +1.06169 q^{37} +(-3.21889 - 0.945152i) q^{38} +(1.88598 + 13.1173i) q^{39} +(1.86129 - 1.19618i) q^{40} +(-3.62585 - 4.18445i) q^{41} +(4.77138 + 5.50647i) q^{42} +(-4.40848 - 1.29445i) q^{43} +(0.268117 + 0.587094i) q^{44} +(3.47148 + 7.60148i) q^{45} +(-4.21609 - 1.23796i) q^{46} +(-8.64467 - 9.97648i) q^{47} +(-4.20838 - 4.85673i) q^{48} +(4.68551 - 3.01120i) q^{49} +(0.0867877 + 0.603621i) q^{50} +(-0.151165 - 0.0443859i) q^{51} +6.40245 q^{52} +(-1.45266 + 1.67646i) q^{53} +(-9.26090 + 5.95162i) q^{54} -0.396422 q^{55} +(6.59898 - 4.24091i) q^{56} +(-15.5958 - 10.0228i) q^{57} +(0.446590 - 3.10610i) q^{58} +(-3.51770 - 4.05964i) q^{59} +(5.26442 - 1.54577i) q^{60} +(5.45273 + 3.50426i) q^{61} +(3.92952 + 2.52535i) q^{62} +(12.3077 + 26.9501i) q^{63} +(-0.341727 + 0.219615i) q^{64} +(-1.63360 + 3.57708i) q^{65} +(-0.115942 - 0.806395i) q^{66} +(4.28732 - 4.94783i) q^{67} +(-0.0316190 + 0.0692361i) q^{68} +(-20.4274 - 13.1279i) q^{69} +(0.307695 + 2.14006i) q^{70} +(-2.97633 - 0.873930i) q^{71} +(7.68073 + 16.8185i) q^{72} +(0.641276 - 4.46017i) q^{73} +(-0.268960 + 0.588941i) q^{74} +(-0.479596 + 3.33566i) q^{75} +(-5.86529 + 6.76890i) q^{76} -1.40547 q^{77} +(-7.75421 - 2.27684i) q^{78} +(-1.91000 + 13.2843i) q^{79} +(-0.271388 - 1.88755i) q^{80} +(-34.3150 + 10.0758i) q^{81} +(3.23974 - 0.951274i) q^{82} +(-0.619556 - 1.35664i) q^{83} +(18.6643 - 5.48034i) q^{84} +(-0.0306148 - 0.0353314i) q^{85} +(1.83486 - 2.11755i) q^{86} +(7.20374 - 15.7740i) q^{87} -0.877094 q^{88} +(-5.63476 + 7.56634i) q^{89} -5.09612 q^{90} +(-5.79171 + 12.6821i) q^{91} +(-7.68233 + 8.86588i) q^{92} +(16.9036 + 19.5078i) q^{93} +(7.72412 - 2.26801i) q^{94} +(-2.28528 - 5.00406i) q^{95} +(18.0684 - 5.30537i) q^{96} +(-11.1581 + 3.27632i) q^{97} +(0.483379 + 3.36198i) q^{98} +(0.471455 - 3.27904i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 160 q - 2 q^{2} - 2 q^{3} - 22 q^{4} - 16 q^{5} - 6 q^{6} - 2 q^{7} - 6 q^{8} - 32 q^{9} - 2 q^{10} - q^{11} - 16 q^{12} - 8 q^{13} + 27 q^{14} - 2 q^{15} - 34 q^{16} + 19 q^{17} + 53 q^{18} - 14 q^{19}+ \cdots + 50 q^{99}+O(q^{100}) \) 160 * q - 2 * q^2 - 2 * q^3 - 22 * q^4 - 16 * q^5 - 6 * q^6 - 2 * q^7 - 6 * q^8 - 32 * q^9 - 2 * q^10 - q^11 - 16 * q^12 - 8 * q^13 + 27 * q^14 - 2 * q^15 - 34 * q^16 + 19 * q^17 + 53 * q^18 - 14 * q^19 - 22 * q^20 - 26 * q^21 + 34 * q^22 + 33 * q^23 + 50 * q^24 - 16 * q^25 - 35 * q^26 + 7 * q^27 + 49 * q^28 - 17 * q^29 - 6 * q^30 + 20 * q^31 + 11 * q^32 - 20 * q^33 + 2 * q^34 - 2 * q^35 - 102 * q^36 + 130 * q^37 - 19 * q^38 + 3 * q^39 - 6 * q^40 - 52 * q^41 - 92 * q^42 - 26 * q^43 + 14 * q^44 + q^45 + 102 * q^46 - 4 * q^47 + 3 * q^48 - 68 * q^49 - 2 * q^50 + 46 * q^51 - 66 * q^52 - 2 * q^53 - 79 * q^54 + 32 * q^55 + 199 * q^56 - 86 * q^57 - 74 * q^58 - 47 * q^59 - 16 * q^60 - 24 * q^61 + 41 * q^62 + 94 * q^63 + 70 * q^64 + 25 * q^65 - 130 * q^66 + 21 * q^67 - 57 * q^68 + 64 * q^69 + 27 * q^70 - 26 * q^71 - 66 * q^72 + 12 * q^73 - 70 * q^74 - 2 * q^75 - 137 * q^76 - 100 * q^77 - 170 * q^78 - 59 * q^79 - 34 * q^80 - 84 * q^81 + 359 * q^82 - 39 * q^83 + 202 * q^84 - 14 * q^85 - 108 * q^86 + 133 * q^87 + 48 * q^88 + 42 * q^90 + 22 * q^91 + 57 * q^92 + 69 * q^93 - 74 * q^94 - 3 * q^95 - 116 * q^96 - 37 * q^97 + 3 * q^98 + 50 * q^99

Introduction

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