LMFDB - Embedded newform 1001.2.i.d.144.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1001,2,Mod(144,1001)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1001, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 0, 0]))

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

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

chi := DirichletCharacter("1001.144");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1001 = 7 \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1001.i (of order $3$, degree $2$, 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:	$7.99302524233$
Analytic rank:	$0$
Dimension:	$50$
Relative dimension:	$25$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			144.11
Character	$\chi$	$=$	1001.144
Dual form			1001.2.i.d.716.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.510452 - 0.884128i) q^{2} +(0.692979 - 1.20028i) q^{3} +(0.478878 - 0.829442i) q^{4} +(-1.61918 - 2.80451i) q^{5} -1.41493 q^{6} +(2.64329 + 0.114204i) q^{7} -3.01958 q^{8} +(0.539560 + 0.934545i) q^{9} +O(q^{10})$	\(q+(-0.510452 - 0.884128i) q^{2} +(0.692979 - 1.20028i) q^{3} +(0.478878 - 0.829442i) q^{4} +(-1.61918 - 2.80451i) q^{5} -1.41493 q^{6} +(2.64329 + 0.114204i) q^{7} -3.01958 q^{8} +(0.539560 + 0.934545i) q^{9} +(-1.65303 + 2.86313i) q^{10} +(-0.500000 + 0.866025i) q^{11} +(-0.663705 - 1.14957i) q^{12} -1.00000 q^{13} +(-1.24830 - 2.39530i) q^{14} -4.48824 q^{15} +(0.583594 + 1.01082i) q^{16} +(-2.39701 + 4.15174i) q^{17} +(0.550838 - 0.954080i) q^{18} +(-4.10227 - 7.10534i) q^{19} -3.10157 q^{20} +(1.96882 - 3.09353i) q^{21} +1.02090 q^{22} +(-3.03187 - 5.25136i) q^{23} +(-2.09251 + 3.62433i) q^{24} +(-2.74350 + 4.75189i) q^{25} +(0.510452 + 0.884128i) q^{26} +5.65349 q^{27} +(1.36054 - 2.13776i) q^{28} -7.24736 q^{29} +(2.29103 + 3.96818i) q^{30} +(3.04092 - 5.26703i) q^{31} +(-2.42379 + 4.19813i) q^{32} +(0.692979 + 1.20028i) q^{33} +4.89423 q^{34} +(-3.95968 - 7.59803i) q^{35} +1.03353 q^{36} +(-0.858684 - 1.48728i) q^{37} +(-4.18802 + 7.25387i) q^{38} +(-0.692979 + 1.20028i) q^{39} +(4.88926 + 8.46844i) q^{40} +4.92464 q^{41} +(-3.74006 - 0.161591i) q^{42} -7.44999 q^{43} +(0.478878 + 0.829442i) q^{44} +(1.74729 - 3.02640i) q^{45} +(-3.09525 + 5.36113i) q^{46} +(4.63713 + 8.03175i) q^{47} +1.61768 q^{48} +(6.97391 + 0.603747i) q^{49} +5.60170 q^{50} +(3.32215 + 5.75414i) q^{51} +(-0.478878 + 0.829442i) q^{52} +(-2.08134 + 3.60499i) q^{53} +(-2.88583 - 4.99841i) q^{54} +3.23836 q^{55} +(-7.98162 - 0.344848i) q^{56} -11.3712 q^{57} +(3.69943 + 6.40760i) q^{58} +(0.801895 - 1.38892i) q^{59} +(-2.14932 + 3.72273i) q^{60} +(5.96310 + 10.3284i) q^{61} -6.20897 q^{62} +(1.31948 + 2.53189i) q^{63} +7.28329 q^{64} +(1.61918 + 2.80451i) q^{65} +(0.707465 - 1.22536i) q^{66} +(6.31355 - 10.9354i) q^{67} +(2.29575 + 3.97636i) q^{68} -8.40410 q^{69} +(-4.69641 + 7.37929i) q^{70} +3.44987 q^{71} +(-1.62925 - 2.82194i) q^{72} +(4.28998 - 7.43046i) q^{73} +(-0.876633 + 1.51837i) q^{74} +(3.80238 + 6.58592i) q^{75} -7.85796 q^{76} +(-1.42055 + 2.23205i) q^{77} +1.41493 q^{78} +(-4.73235 - 8.19667i) q^{79} +(1.88989 - 3.27339i) q^{80} +(2.29907 - 3.98211i) q^{81} +(-2.51379 - 4.35401i) q^{82} +5.15030 q^{83} +(-1.62308 - 3.11444i) q^{84} +15.5248 q^{85} +(3.80286 + 6.58675i) q^{86} +(-5.02227 + 8.69883i) q^{87} +(1.50979 - 2.61504i) q^{88} +(-7.76640 - 13.4518i) q^{89} -3.56763 q^{90} +(-2.64329 - 0.114204i) q^{91} -5.80760 q^{92} +(-4.21459 - 7.29988i) q^{93} +(4.73407 - 8.19964i) q^{94} +(-13.2847 + 23.0097i) q^{95} +(3.35927 + 5.81843i) q^{96} +11.7633 q^{97} +(-3.02606 - 6.47402i) q^{98} -1.07912 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 50 q - 6 q^{2} + 2 q^{3} - 30 q^{4} + q^{5} + 4 q^{6} + q^{7} + 42 q^{8} - 37 q^{9}+O(q^{10}) $ 50 * q - 6 * q^2 + 2 * q^3 - 30 * q^4 + q^5 + 4 * q^6 + q^7 + 42 * q^8 - 37 * q^9	\( 50 q - 6 q^{2} + 2 q^{3} - 30 q^{4} + q^{5} + 4 q^{6} + q^{7} + 42 q^{8} - 37 q^{9} + 3 q^{10} - 25 q^{11} - 9 q^{12} - 50 q^{13} + 22 q^{14} - 32 q^{16} + q^{17} - 44 q^{18} - 5 q^{19} + 8 q^{20} + 2 q^{21} + 12 q^{22} - 15 q^{23} + 4 q^{24} - 50 q^{25} + 6 q^{26} - 34 q^{27} + 12 q^{28} + 48 q^{29} - q^{30} + 12 q^{31} - 48 q^{32} + 2 q^{33} - 16 q^{34} + 20 q^{35} + 60 q^{36} - 33 q^{37} - 16 q^{38} - 2 q^{39} + 21 q^{40} + 24 q^{41} - 42 q^{42} + 76 q^{43} - 30 q^{44} + 22 q^{45} - 39 q^{46} - 4 q^{47} + 164 q^{48} + 23 q^{49} + 32 q^{50} - 51 q^{51} + 30 q^{52} - 2 q^{53} - 10 q^{54} - 2 q^{55} - 72 q^{56} + 76 q^{57} - 17 q^{58} + 4 q^{59} + 33 q^{60} + 22 q^{61} + 84 q^{62} - 19 q^{63} + 82 q^{64} - q^{65} - 2 q^{66} - 24 q^{67} - 14 q^{68} - 60 q^{69} - 124 q^{70} + 18 q^{71} - 102 q^{72} - 11 q^{73} - 39 q^{74} + 16 q^{75} + 116 q^{76} + q^{77} - 4 q^{78} - 19 q^{79} + 33 q^{80} - 73 q^{81} + 32 q^{82} + 32 q^{83} - 109 q^{84} + 28 q^{85} - 27 q^{86} + 11 q^{87} - 21 q^{88} - 13 q^{89} + 80 q^{90} - q^{91} - 17 q^{93} + 56 q^{94} - 15 q^{95} - 55 q^{96} + 68 q^{97} - 22 q^{98} + 74 q^{99}+O(q^{100}) \) 50 * q - 6 * q^2 + 2 * q^3 - 30 * q^4 + q^5 + 4 * q^6 + q^7 + 42 * q^8 - 37 * q^9 + 3 * q^10 - 25 * q^11 - 9 * q^12 - 50 * q^13 + 22 * q^14 - 32 * q^16 + q^17 - 44 * q^18 - 5 * q^19 + 8 * q^20 + 2 * q^21 + 12 * q^22 - 15 * q^23 + 4 * q^24 - 50 * q^25 + 6 * q^26 - 34 * q^27 + 12 * q^28 + 48 * q^29 - q^30 + 12 * q^31 - 48 * q^32 + 2 * q^33 - 16 * q^34 + 20 * q^35 + 60 * q^36 - 33 * q^37 - 16 * q^38 - 2 * q^39 + 21 * q^40 + 24 * q^41 - 42 * q^42 + 76 * q^43 - 30 * q^44 + 22 * q^45 - 39 * q^46 - 4 * q^47 + 164 * q^48 + 23 * q^49 + 32 * q^50 - 51 * q^51 + 30 * q^52 - 2 * q^53 - 10 * q^54 - 2 * q^55 - 72 * q^56 + 76 * q^57 - 17 * q^58 + 4 * q^59 + 33 * q^60 + 22 * q^61 + 84 * q^62 - 19 * q^63 + 82 * q^64 - q^65 - 2 * q^66 - 24 * q^67 - 14 * q^68 - 60 * q^69 - 124 * q^70 + 18 * q^71 - 102 * q^72 - 11 * q^73 - 39 * q^74 + 16 * q^75 + 116 * q^76 + q^77 - 4 * q^78 - 19 * q^79 + 33 * q^80 - 73 * q^81 + 32 * q^82 + 32 * q^83 - 109 * q^84 + 28 * q^85 - 27 * q^86 + 11 * q^87 - 21 * q^88 - 13 * q^89 + 80 * q^90 - q^91 - 17 * q^93 + 56 * q^94 - 15 * q^95 - 55 * q^96 + 68 * q^97 - 22 * q^98 + 74 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1001\mathbb{Z}\right)^\times$.

$n$	$365$	$430$	$925$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$1$

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 $

$2$	−0.510452	−	0.884128i	−0.360944	−	0.625173i	0.627173	−	0.778880i	$-0.284212\pi$
$2$	−0.510452	−	0.884128i	−0.360944	−	0.625173i	−0.988116	+	0.153707i	$0.950879\pi$
$3$	0.692979	−	1.20028i	0.400092	−	0.692979i	−0.593645	−	0.804727i	$-0.702312\pi$
$3$	0.692979	−	1.20028i	0.400092	−	0.692979i	0.993737	+	0.111748i	$0.0356449\pi$
$4$	0.478878	−	0.829442i	0.239439	−	0.414721i
$5$	−1.61918	−	2.80451i	−0.724120	−	1.25421i	−0.959335	−	0.282270i	$-0.908913\pi$
$5$	−1.61918	−	2.80451i	−0.724120	−	1.25421i	0.235215	−	0.971943i	$-0.424421\pi$
$6$	−1.41493			−0.577642
$7$	2.64329	+	0.114204i	0.999068	+	0.0431650i
$7$	2.64329	+	0.114204i	0.999068	+	0.0431650i
$8$	−3.01958			−1.06758
$9$	0.539560	+	0.934545i	0.179853	+	0.311515i
$10$	−1.65303	+	2.86313i	−0.522734	+	0.905401i
$11$	−0.500000	+	0.866025i	−0.150756	+	0.261116i
$11$	−0.500000	+	0.866025i	−0.150756	+	0.261116i
$12$	−0.663705	−	1.14957i	−0.191595	−	0.331853i
$13$	−1.00000			−0.277350
$13$	−1.00000			−0.277350
$14$	−1.24830	−	2.39530i	−0.333622	−	0.640170i
$15$	−4.48824			−1.15886
$16$	0.583594	+	1.01082i	0.145899	+	0.252704i
$17$	−2.39701	+	4.15174i	−0.581360	+	1.00694i	0.413959	+	0.910296i	$0.364146\pi$
$17$	−2.39701	+	4.15174i	−0.581360	+	1.00694i	−0.995319	+	0.0966492i	$0.969187\pi$
$18$	0.550838	−	0.954080i	0.129834	−	0.224879i
$19$	−4.10227	−	7.10534i	−0.941126	−	1.63008i	−0.763329	−	0.646010i	$-0.776436\pi$
$19$	−4.10227	−	7.10534i	−0.941126	−	1.63008i	−0.177797	−	0.984067i	$-0.556897\pi$
$20$	−3.10157			−0.693531
$21$	1.96882	−	3.09353i	0.429631	−	0.675063i
$22$	1.02090			0.217657
$23$	−3.03187	−	5.25136i	−0.632190	−	1.09498i	−0.987103	−	0.160085i	$-0.948823\pi$
$23$	−3.03187	−	5.25136i	−0.632190	−	1.09498i	0.354914	−	0.934899i	$-0.384510\pi$
$24$	−2.09251	+	3.62433i	−0.427131	+	0.739813i
$25$	−2.74350	+	4.75189i	−0.548701	+	0.950378i
$26$	0.510452	+	0.884128i	0.100108	+	0.173392i
$27$	5.65349			1.08801
$28$	1.36054	−	2.13776i	0.257117	−	0.403999i
$29$	−7.24736			−1.34580			−0.672901	−	0.739733i	$-0.734952\pi$
$29$	−7.24736			−1.34580			−0.672901	+	0.739733i	$0.734952\pi$
$30$	2.29103	+	3.96818i	0.418283	+	0.724487i
$31$	3.04092	−	5.26703i	0.546165	−	0.945986i	−0.452367	−	0.891832i	$-0.649420\pi$
$31$	3.04092	−	5.26703i	0.546165	−	0.945986i	0.998533	−	0.0541544i	$-0.0172463\pi$
$32$	−2.42379	+	4.19813i	−0.428470	+	0.742131i
$33$	0.692979	+	1.20028i	0.120632	+	0.208941i
$34$	4.89423			0.839353
$35$	−3.95968	−	7.59803i	−0.669307	−	1.28430i
$36$	1.03353			0.172256
$37$	−0.858684	−	1.48728i	−0.141167	−	0.244508i	0.786769	−	0.617247i	$-0.211752\pi$
$37$	−0.858684	−	1.48728i	−0.141167	−	0.244508i	−0.927936	+	0.372739i	$0.878419\pi$
$38$	−4.18802	+	7.25387i	−0.679387	+	1.17673i
$39$	−0.692979	+	1.20028i	−0.110965	+	0.192198i
$40$	4.88926	+	8.46844i	0.773059	+	1.33898i
$41$	4.92464			0.769099			0.384550	−	0.923104i	$-0.374357\pi$
$41$	4.92464			0.769099			0.384550	+	0.923104i	$0.374357\pi$
$42$	−3.74006	−	0.161591i	−0.577104	−	0.0249340i
$43$	−7.44999			−1.13611			−0.568057	−	0.822990i	$-0.692305\pi$
$43$	−7.44999			−1.13611			−0.568057	+	0.822990i	$0.692305\pi$
$44$	0.478878	+	0.829442i	0.0721936	+	0.125043i
$45$	1.74729	−	3.02640i	0.260471	−	0.451149i
$46$	−3.09525	+	5.36113i	−0.456370	+	0.790456i
$47$	4.63713	+	8.03175i	0.676396	+	1.17155i	0.976059	+	0.217506i	$0.0697923\pi$
$47$	4.63713	+	8.03175i	0.676396	+	1.17155i	−0.299663	+	0.954045i	$0.596874\pi$
$48$	1.61768			0.233491
$49$	6.97391	+	0.603747i	0.996274	+	0.0862496i
$50$	5.60170			0.792201
$51$	3.32215	+	5.75414i	0.465195	+	0.805741i
$52$	−0.478878	+	0.829442i	−0.0664085	+	0.115023i
$53$	−2.08134	+	3.60499i	−0.285894	+	0.495184i	−0.972826	−	0.231539i	$-0.925624\pi$
$53$	−2.08134	+	3.60499i	−0.285894	+	0.495184i	0.686931	+	0.726722i	$0.258957\pi$
$54$	−2.88583	−	4.99841i	−0.392712	−	0.680197i
$55$	3.23836			0.436661
$56$	−7.98162	−	0.344848i	−1.06659	−	0.0460823i
$57$	−11.3712			−1.50615
$58$	3.69943	+	6.40760i	0.485759	+	0.841359i
$59$	0.801895	−	1.38892i	0.104398	−	0.180822i	−0.809094	−	0.587679i	$-0.800042\pi$
$59$	0.801895	−	1.38892i	0.104398	−	0.180822i	0.913492	+	0.406857i	$0.133375\pi$
$60$	−2.14932	+	3.72273i	−0.277476	+	0.480603i
$61$	5.96310	+	10.3284i	0.763496	+	1.32241i	0.941038	+	0.338301i	$0.109852\pi$
$61$	5.96310	+	10.3284i	0.763496	+	1.32241i	−0.177542	+	0.984113i	$0.556814\pi$
$62$	−6.20897			−0.788540
$63$	1.31948	+	2.53189i	0.166239	+	0.318988i
$64$	7.28329			0.910411
$65$	1.61918	+	2.80451i	0.200835	+	0.347856i
$66$	0.707465	−	1.22536i	0.0870829	−	0.150832i
$67$	6.31355	−	10.9354i	0.771322	−	1.33597i	−0.165516	−	0.986207i	$-0.552929\pi$
$67$	6.31355	−	10.9354i	0.771322	−	1.33597i	0.936838	−	0.349763i	$-0.113738\pi$
$68$	2.29575	+	3.97636i	0.278401	+	0.482204i
$69$	−8.40410			−1.01174
$70$	−4.69641	+	7.37929i	−0.561328	+	0.881993i
$71$	3.44987			0.409424			0.204712	−	0.978822i	$-0.434374\pi$
$71$	3.44987			0.409424			0.204712	+	0.978822i	$0.434374\pi$
$72$	−1.62925	−	2.82194i	−0.192008	−	0.332568i
$73$	4.28998	−	7.43046i	0.502104	−	0.869670i	−0.497893	−	0.867239i	$-0.665893\pi$
$73$	4.28998	−	7.43046i	0.502104	−	0.869670i	0.999997	−	0.00243138i	$-0.000773934\pi$
$74$	−0.876633	+	1.51837i	−0.101907	+	0.176507i
$75$	3.80238	+	6.58592i	0.439061	+	0.760476i
$76$	−7.85796			−0.901369
$77$	−1.42055	+	2.23205i	−0.161886	+	0.254366i
$78$	1.41493			0.160209
$79$	−4.73235	−	8.19667i	−0.532431	−	0.922197i	−0.999283	−	0.0378619i	$-0.987945\pi$
$79$	−4.73235	−	8.19667i	−0.532431	−	0.922197i	0.466852	−	0.884335i	$-0.345388\pi$
$80$	1.88989	−	3.27339i	0.211296	−	0.365976i
$81$	2.29907	−	3.98211i	0.255452	−	0.442456i
$82$	−2.51379	−	4.35401i	−0.277602	−	0.480820i
$83$	5.15030			0.565319			0.282659	−	0.959220i	$-0.408783\pi$
$83$	5.15030			0.565319			0.282659	+	0.959220i	$0.408783\pi$
$84$	−1.62308	−	3.11444i	−0.177092	−	0.339814i
$85$	15.5248			1.68390
$86$	3.80286	+	6.58675i	0.410073	+	0.710267i
$87$	−5.02227	+	8.69883i	−0.538444	+	0.932612i
$88$	1.50979	−	2.61504i	0.160944	−	0.278764i
$89$	−7.76640	−	13.4518i	−0.823237	−	1.42589i	−0.903259	−	0.429095i	$-0.858832\pi$
$89$	−7.76640	−	13.4518i	−0.823237	−	1.42589i	0.0800221	−	0.996793i	$-0.474501\pi$
$90$	−3.56763			−0.376061
$91$	−2.64329	−	0.114204i	−0.277092	−	0.0119718i
$92$	−5.80760			−0.605484
$93$	−4.21459	−	7.29988i	−0.437032	−	0.756962i
$94$	4.73407	−	8.19964i	0.488282	−	0.845728i
$95$	−13.2847	+	23.0097i	−1.36298	+	2.36074i
$96$	3.35927	+	5.81843i	0.342854	+	0.593841i
$97$	11.7633			1.19438			0.597191	−	0.802099i	$-0.296284\pi$
$97$	11.7633			1.19438			0.597191	+	0.802099i	$0.296284\pi$
$98$	−3.02606	−	6.47402i	−0.305678	−	0.653975i
$99$	−1.07912			−0.108456
$100$	2.62761	+	4.55115i	0.262761	+	0.455115i
$101$	0.605188	−	1.04822i	0.0602184	−	0.104301i	−0.834345	−	0.551243i	$-0.814154\pi$
$101$	0.605188	−	1.04822i	0.0602184	−	0.104301i	0.894563	+	0.446942i	$0.147487\pi$
$102$	3.39160	−	5.87442i	0.335818	−	0.581654i
$103$	−1.36138	−	2.35797i	−0.134141	−	0.232338i	0.791128	−	0.611650i	$-0.209494\pi$
$103$	−1.36138	−	2.35797i	−0.134141	−	0.232338i	−0.925269	+	0.379312i	$0.876161\pi$
$104$	3.01958			0.296094
$105$	−11.8637	−	0.512575i	−1.15778	−	0.0500222i
$106$	4.24970			0.412767
$107$	−7.57455	−	13.1195i	−0.732260	−	1.26831i	−0.955915	−	0.293643i	$-0.905132\pi$
$107$	−7.57455	−	13.1195i	−0.732260	−	1.26831i	0.223655	−	0.974668i	$-0.428201\pi$
$108$	2.70733	−	4.68924i	0.260513	−	0.451222i
$109$	−1.83055	+	3.17060i	−0.175334	+	0.303688i	−0.940277	−	0.340410i	$-0.889434\pi$
$109$	−1.83055	+	3.17060i	−0.175334	+	0.303688i	0.764942	+	0.644099i	$0.222767\pi$
$110$	−1.65303	−	2.86313i	−0.157610	−	0.272989i
$111$	−2.38020			−0.225919
$112$	1.42717	+	2.73852i	0.134855	+	0.258766i
$113$	12.8965			1.21320			0.606600	−	0.795007i	$-0.292533\pi$
$113$	12.8965			1.21320			0.606600	+	0.795007i	$0.292533\pi$
$114$	5.80442	+	10.0536i	0.543634	+	0.941602i
$115$	−9.81832	+	17.0058i	−0.915563	+	1.58580i
$116$	−3.47061	+	6.01126i	−0.322238	+	0.558132i
$117$	−0.539560	−	0.934545i	−0.0498823	−	0.0863987i
$118$	−1.63731			−0.150727
$119$	−6.81012	+	10.7005i	−0.624283	+	0.980912i
$120$	13.5526			1.23718
$121$	−0.500000	−	0.866025i	−0.0454545	−	0.0787296i
$122$	6.08774	−	10.5443i	0.551158	−	0.954635i
$123$	3.41267	−	5.91092i	0.307710	−	0.532970i
$124$	−2.91246	−	5.04453i	−0.261547	−	0.453012i
$125$	1.57711			0.141061
$126$	1.56498	−	2.45900i	0.139420	−	0.219065i
$127$	18.2556			1.61992			0.809959	−	0.586486i	$-0.199489\pi$
$127$	18.2556			1.61992			0.809959	+	0.586486i	$0.199489\pi$
$128$	1.12981	+	1.95690i	0.0998624	+	0.172967i
$129$	−5.16269	+	8.94204i	−0.454549	+	0.787303i
$130$	1.65303	−	2.86313i	0.144980	−	0.251113i
$131$	−3.24022	−	5.61223i	−0.283100	−	0.490343i	0.689047	−	0.724717i	$-0.258029\pi$
$131$	−3.24022	−	5.61223i	−0.283100	−	0.490343i	−0.972147	+	0.234374i	$0.924696\pi$
$132$	1.32741			0.115536
$133$	−10.0320	−	19.2499i	−0.869886	−	1.66918i
$134$	−12.8910			−1.11362
$135$	−9.15403	−	15.8552i	−0.787854	−	1.36460i
$136$	7.23797	−	12.5365i	0.620651	−	1.07500i
$137$	−0.527476	+	0.913616i	−0.0450653	+	0.0780554i	−0.887678	−	0.460464i	$-0.847683\pi$
$137$	−0.527476	+	0.913616i	−0.0450653	+	0.0780554i	0.842613	+	0.538520i	$0.181016\pi$
$138$	4.28989	+	7.43030i	0.365180	+	0.632509i
$139$	−9.17581			−0.778282			−0.389141	−	0.921178i	$-0.627228\pi$
$139$	−9.17581			−0.778282			−0.389141	+	0.921178i	$0.627228\pi$
$140$	−8.19832	−	0.354211i	−0.692885	−	0.0299363i
$141$	12.8538			1.08248
$142$	−1.76099	−	3.05013i	−0.147779	−	0.255961i
$143$	0.500000	−	0.866025i	0.0418121	−	0.0724207i
$144$	−0.629768	+	1.09079i	−0.0524807	+	0.0908992i
$145$	11.7348	+	20.3253i	0.974522	+	1.68792i
$146$	−8.75931			−0.724926
$147$	5.55744	−	7.95223i	0.458370	−	0.655889i
$148$	−1.64482			−0.135203
$149$	−3.44307	−	5.96357i	−0.282067	−	0.488554i	0.689827	−	0.723975i	$-0.257687\pi$
$149$	−3.44307	−	5.96357i	−0.282067	−	0.488554i	−0.971894	+	0.235420i	$0.924353\pi$
$150$	3.88186	−	6.72359i	0.316953	−	0.548978i
$151$	−8.40576	+	14.5592i	−0.684051	+	1.18481i	0.289683	+	0.957123i	$0.406450\pi$
$151$	−8.40576	+	14.5592i	−0.684051	+	1.18481i	−0.973734	+	0.227689i	$0.926883\pi$
$152$	12.3872	+	21.4552i	1.00473	+	1.74024i
$153$	−5.17332			−0.418238
$154$	2.69854	+	0.116591i	0.217454	+	0.00939518i
$155$	−19.6952			−1.58196
$156$	0.663705	+	1.14957i	0.0531390	+	0.0920394i
$157$	2.00042	−	3.46483i	0.159651	−	0.276524i	−0.775092	−	0.631849i	$-0.782296\pi$
$157$	2.00042	−	3.46483i	0.159651	−	0.276524i	0.934743	+	0.355325i	$0.115630\pi$
$158$	−4.83127	+	8.36801i	−0.384355	+	0.665723i
$159$	2.88465	+	4.99637i	0.228768	+	0.396238i
$160$	15.6982			1.24105
$161$	−7.41438	−	14.2271i	−0.584335	−	1.12125i
$162$	−4.69426			−0.368816
$163$	−1.39916	−	2.42341i	−0.109591	−	0.189816i	0.806014	−	0.591897i	$-0.201621\pi$
$163$	−1.39916	−	2.42341i	−0.109591	−	0.189816i	−0.915604	+	0.402080i	$0.868287\pi$
$164$	2.35830	−	4.08470i	0.184153	−	0.318962i
$165$	2.24412	−	3.88693i	0.174704	−	0.302597i
$166$	−2.62898	−	4.55352i	−0.204048	−	0.353422i
$167$	15.3965			1.19142			0.595710	−	0.803200i	$-0.296871\pi$
$167$	15.3965			1.19142			0.595710	+	0.803200i	$0.296871\pi$
$168$	−5.94501	+	9.34117i	−0.458667	+	0.720687i
$169$	1.00000			0.0769231
$170$	−7.92465	−	13.7259i	−0.607793	−	1.05273i
$171$	4.42684	−	7.66752i	0.338529	−	0.586350i
$172$	−3.56764	+	6.17933i	−0.272030	+	0.471170i
$173$	4.13475	+	7.16159i	0.314359	+	0.544486i	0.979301	−	0.202409i	$-0.0648771\pi$
$173$	4.13475	+	7.16159i	0.314359	+	0.544486i	−0.664942	+	0.746895i	$0.731544\pi$
$174$	10.2545			0.777392
$175$	−7.79455	+	12.2473i	−0.589212	+	0.925807i
$176$	−1.16719			−0.0879802
$177$	−1.11139	−	1.92499i	−0.0835374	−	0.144691i
$178$	−7.92875	+	13.7330i	−0.594285	+	1.02933i
$179$	4.56881	−	7.91342i	0.341489	−	0.591477i	−0.643220	−	0.765681i	$-0.722402\pi$
$179$	4.56881	−	7.91342i	0.341489	−	0.591477i	0.984709	+	0.174205i	$0.0557354\pi$
$180$	−1.67348	−	2.89855i	−0.124734	−	0.216045i
$181$	19.2760			1.43277			0.716387	−	0.697703i	$-0.245795\pi$
$181$	19.2760			1.43277			0.716387	+	0.697703i	$0.245795\pi$
$182$	1.24830	+	2.39530i	0.0925300	+	0.177551i
$183$	16.5292			1.22187
$184$	9.15500	+	15.8569i	0.674915	+	1.16899i
$185$	−2.78073	+	4.81637i	−0.204444	+	0.354107i
$186$	−4.30269	+	7.45247i	−0.315488	+	0.546442i
$187$	−2.39701	−	4.15174i	−0.175287	−	0.303605i
$188$	8.88249			0.647822
$189$	14.9438	+	0.645651i	1.08700	+	0.0469642i
$190$	27.1247			1.96783
$191$	−1.11030	−	1.92309i	−0.0803383	−	0.139150i	0.823057	−	0.567959i	$-0.192267\pi$
$191$	−1.11030	−	1.92309i	−0.0803383	−	0.139150i	−0.903395	+	0.428809i	$0.858933\pi$
$192$	5.04717	−	8.74195i	0.364248	−	0.630896i
$193$	−7.96453	+	13.7950i	−0.573299	+	0.992983i	0.422925	+	0.906165i	$0.361003\pi$
$193$	−7.96453	+	13.7950i	−0.573299	+	0.992983i	−0.996224	+	0.0868185i	$0.972330\pi$
$194$	−6.00459	−	10.4003i	−0.431105	−	0.746695i
$195$	4.48824			0.321409
$196$	3.84043	−	5.49533i	0.274316	−	0.392524i
$197$	−9.02193			−0.642786			−0.321393	−	0.946946i	$-0.604151\pi$
$197$	−9.02193			−0.642786			−0.321393	+	0.946946i	$0.604151\pi$
$198$	0.550838	+	0.954080i	0.0391464	+	0.0678035i
$199$	−6.02956	+	10.4435i	−0.427424	+	0.740320i	−0.996643	−	0.0818654i	$-0.973912\pi$
$199$	−6.02956	+	10.4435i	−0.427424	+	0.740320i	0.569219	+	0.822186i	$0.307246\pi$
$200$	8.28424	−	14.3487i	0.585784	−	1.01461i
$201$	−8.75031	−	15.1560i	−0.617199	−	1.06902i
$202$	−1.23568			−0.0869419
$203$	−19.1568	−	0.827677i	−1.34455	−	0.0580916i
$204$	6.36363			0.445543
$205$	−7.97389	−	13.8112i	−0.556921	−	0.964615i
$206$	−1.38983	+	2.40726i	−0.0968344	+	0.167722i
$207$	3.27176	−	5.66685i	0.227403	−	0.393873i
$208$	−0.583594	−	1.01082i	−0.0404650	−	0.0700874i
$209$	8.20454			0.567520
$210$	5.60266	+	10.7507i	0.386620	+	0.741867i
$211$	−19.6827			−1.35501			−0.677505	−	0.735518i	$-0.736939\pi$
$211$	−19.6827			−1.35501			−0.677505	+	0.735518i	$0.736939\pi$
$212$	1.99342	+	3.45271i	0.136909	+	0.237133i
$213$	2.39069	−	4.14079i	0.163807	−	0.283723i
$214$	−7.73289	+	13.3938i	−0.528609	+	0.915578i
$215$	12.0629	+	20.8935i	0.822683	+	1.42493i
$216$	−17.0712			−1.16155
$217$	8.63953	−	13.5750i	0.586490	−	0.921529i
$218$	3.73762			0.253144
$219$	−5.94573	−	10.2983i	−0.401775	−	0.695895i
$220$	1.55078	−	2.68603i	0.104554	−	0.181092i
$221$	2.39701	−	4.15174i	0.161240	−	0.279276i
$222$	1.21498	+	2.10440i	0.0815439	+	0.141238i
$223$	−27.5664			−1.84598			−0.922992	−	0.384819i	$-0.874264\pi$
$223$	−27.5664			−1.84598			−0.922992	+	0.384819i	$0.874264\pi$
$224$	−6.88621	+	10.8200i	−0.460104	+	0.722944i
$225$	−5.92114			−0.394742
$226$	−6.58304	−	11.4022i	−0.437897	−	0.758460i
$227$	7.66372	−	13.2740i	0.508659	−	0.881023i	−0.491291	−	0.870996i	$-0.663475\pi$
$227$	7.66372	−	13.2740i	0.508659	−	0.881023i	0.999950	−	0.0100276i	$-0.00319195\pi$
$228$	−5.44540	+	9.43171i	−0.360630	+	0.624630i
$229$	−10.8211	−	18.7427i	−0.715078	−	1.23855i	−0.962929	−	0.269754i	$-0.913058\pi$
$229$	−10.8211	−	18.7427i	−0.715078	−	1.23855i	0.247851	−	0.968798i	$-0.420276\pi$
$230$	20.0471			1.32187
$231$	1.69467	+	3.25181i	0.111501	+	0.213953i
$232$	21.8840			1.43676
$233$	−5.69401	−	9.86232i	−0.373027	−	0.646102i	0.617002	−	0.786961i	$-0.288347\pi$
$233$	−5.69401	−	9.86232i	−0.373027	−	0.646102i	−0.990030	+	0.140859i	$0.955014\pi$
$234$	−0.550838	+	0.954080i	−0.0360094	+	0.0623702i
$235$	15.0167	−	26.0097i	0.979584	−	1.69669i
$236$	−0.768021	−	1.33025i	−0.0499939	−	0.0865919i
$237$	−13.1177			−0.852085
$238$	12.9368	+	0.558940i	0.838571	+	0.0362307i
$239$	19.9330			1.28936			0.644680	−	0.764453i	$-0.276991\pi$
$239$	19.9330			1.28936			0.644680	+	0.764453i	$0.276991\pi$
$240$	−2.61931	−	4.53678i	−0.169076	−	0.292848i
$241$	8.51455	−	14.7476i	0.548470	−	0.949978i	−0.449910	−	0.893074i	$-0.648544\pi$
$241$	8.51455	−	14.7476i	0.548470	−	0.949978i	0.998380	−	0.0569040i	$-0.0181229\pi$
$242$	−0.510452	+	0.884128i	−0.0328131	+	0.0568339i
$243$	5.29382	+	9.16916i	0.339599	+	0.588202i
$244$	11.4224			0.731244
$245$	−9.59883	−	20.5360i	−0.613247	−	1.31199i
$246$	−6.96802			−0.444264
$247$	4.10227	+	7.10534i	0.261021	+	0.452102i
$248$	−9.18231	+	15.9042i	−0.583077	+	1.00992i
$249$	3.56905	−	6.18178i	0.226179	−	0.391754i
$250$	−0.805038	−	1.39437i	−0.0509150	−	0.0881874i
$251$	−9.48244			−0.598526			−0.299263	−	0.954171i	$-0.596741\pi$
$251$	−9.48244			−0.598526			−0.299263	+	0.954171i	$0.596741\pi$
$252$	2.73193	+	0.118034i	0.172095	+	0.00743542i
$253$	6.06375			0.381225
$254$	−9.31858	−	16.1402i	−0.584699	−	1.01273i
$255$	10.7583	−	18.6340i	0.673714	−	1.16691i
$256$	8.43672	−	14.6128i	0.527295	−	0.913302i
$257$	−2.27174	−	3.93478i	−0.141707	−	0.245445i	0.786432	−	0.617677i	$-0.211926\pi$
$257$	−2.27174	−	3.93478i	−0.141707	−	0.245445i	−0.928140	+	0.372232i	$0.878593\pi$
$258$	10.5412			0.656267
$259$	−2.09989	−	4.02938i	−0.130481	−	0.250374i
$260$	3.10157			0.192351
$261$	−3.91039	−	6.77299i	−0.242047	−	0.419237i
$262$	−3.30795	+	5.72954i	−0.204366	+	0.353972i
$263$	8.96395	−	15.5260i	0.552741	−	0.957375i	−0.445335	−	0.895364i	$-0.646915\pi$
$263$	8.96395	−	15.5260i	0.552741	−	0.957375i	0.998075	−	0.0620110i	$-0.0197514\pi$
$264$	−2.09251	−	3.62433i	−0.128785	−	0.223062i
$265$	13.4803			0.828088
$266$	−11.8986	+	18.6958i	−0.729547	+	1.14631i
$267$	−21.5278			−1.31748
$268$	−6.04684	−	10.4734i	−0.369370	−	0.639767i
$269$	−6.53573	+	11.3202i	−0.398491	+	0.690206i	−0.993540	−	0.113483i	$-0.963799\pi$
$269$	−6.53573	+	11.3202i	−0.398491	+	0.690206i	0.595049	+	0.803689i	$0.297133\pi$
$270$	−9.34538	+	16.1867i	−0.568742	+	0.985090i
$271$	3.87272	+	6.70775i	0.235251	+	0.407467i	0.959346	−	0.282234i	$-0.0910755\pi$
$271$	3.87272	+	6.70775i	0.235251	+	0.407467i	−0.724095	+	0.689701i	$0.757742\pi$
$272$	−5.59552			−0.339278
$273$	−1.96882	+	3.09353i	−0.119158	+	0.187229i
$274$	1.07700			0.0650642
$275$	−2.74350	−	4.75189i	−0.165440	−	0.286550i
$276$	−4.02454	+	6.97071i	−0.242249	+	0.419588i
$277$	−8.74306	+	15.1434i	−0.525320	+	0.909880i	0.474245	+	0.880393i	$0.342721\pi$
$277$	−8.74306	+	15.1434i	−0.525320	+	0.909880i	−0.999565	+	0.0294877i	$0.990612\pi$
$278$	4.68381	+	8.11259i	0.280916	+	0.486561i
$279$	6.56303			0.392918
$280$	11.9566	+	22.9429i	0.714542	+	1.37110i
$281$	22.7675			1.35820			0.679098	−	0.734048i	$-0.262371\pi$
$281$	22.7675			1.35820			0.679098	+	0.734048i	$0.262371\pi$
$282$	−6.56122	−	11.3644i	−0.390715	−	0.676738i
$283$	3.04236	−	5.26952i	0.180849	−	0.313240i	−0.761321	−	0.648376i	$-0.775449\pi$
$283$	3.04236	−	5.26952i	0.180849	−	0.313240i	0.942170	+	0.335135i	$0.108782\pi$
$284$	1.65207	−	2.86147i	0.0980322	−	0.169797i
$285$	18.4120	+	31.8905i	1.09063	+	1.88903i
$286$	−1.02090			−0.0603673
$287$	13.0172	+	0.562413i	0.768383	+	0.0331982i
$288$	−5.23112			−0.308247
$289$	−2.99130	−	5.18108i	−0.175959	−	0.304770i
$290$	11.9801	−	20.7501i	0.703496	−	1.21849i
$291$	8.15172	−	14.1192i	0.477862	−	0.827681i
$292$	−4.10876	−	7.11658i	−0.240447	−	0.416466i
$293$	32.3607			1.89053			0.945265	−	0.326302i	$-0.105803\pi$
$293$	32.3607			1.89053			0.945265	+	0.326302i	$0.105803\pi$
$294$	−9.86760	−	0.854260i	−0.575490	−	0.0498214i
$295$	−5.19366			−0.302387
$296$	2.59287	+	4.49098i	0.150707	+	0.261033i
$297$	−2.82674	+	4.89607i	−0.164024	+	0.284099i
$298$	−3.51504	+	6.08822i	−0.203621	+	0.352681i
$299$	3.03187	+	5.25136i	0.175338	+	0.303694i
$300$	7.28351			0.420514
$301$	−19.6925	−	0.850818i	−1.13505	−	0.0490404i
$302$	17.1629			0.987616
$303$	−0.838765	−	1.45278i	−0.0481858	−	0.0834602i
$304$	4.78813	−	8.29328i	0.274618	−	0.475652i
$305$	19.3107	−	33.4471i	1.10573	−	1.91517i
$306$	2.64073	+	4.57388i	0.150960	+	0.261471i
$307$	19.5270			1.11447			0.557233	−	0.830356i	$-0.311863\pi$
$307$	19.5270			1.11447			0.557233	+	0.830356i	$0.311863\pi$
$308$	1.17109	+	2.24714i	0.0667289	+	0.128043i
$309$	−3.77362			−0.214674
$310$	10.0535	+	17.4131i	0.570998	+	0.988997i
$311$	−1.68253	+	2.91422i	−0.0954074	+	0.165250i	−0.909779	−	0.415094i	$-0.863749\pi$
$311$	−1.68253	+	2.91422i	−0.0954074	+	0.165250i	0.814371	+	0.580344i	$0.197082\pi$
$312$	2.09251	−	3.62433i	0.118465	−	0.205187i
$313$	−0.614288	−	1.06398i	−0.0347216	−	0.0601396i	0.848142	−	0.529768i	$-0.177721\pi$
$313$	−0.614288	−	1.06398i	−0.0347216	−	0.0601396i	−0.882864	+	0.469629i	$0.844388\pi$
$314$	−4.08447			−0.230500
$315$	4.96422	−	7.80009i	0.279702	−	0.439485i
$316$	−9.06488			−0.509939
$317$	−0.410160	−	0.710418i	−0.0230369	−	0.0399010i	0.854277	−	0.519818i	$-0.174000\pi$
$317$	−0.410160	−	0.710418i	−0.0230369	−	0.0399010i	−0.877314	+	0.479917i	$0.840667\pi$
$318$	2.94495	−	5.10081i	0.165145	−	0.286039i
$319$	3.62368	−	6.27640i	0.202887	−	0.351411i
$320$	−11.7930	−	20.4260i	−0.659247	−	1.14185i
$321$	−20.9960			−1.17188
$322$	−8.79389	+	13.8175i	−0.490064	+	0.770020i
$323$	39.3327			2.18853
$324$	−2.20195	−	3.81389i	−0.122331	−	0.211883i
$325$	2.74350	−	4.75189i	0.152182	−	0.263587i
$326$	−1.42840	+	2.47407i	−0.0791120	+	0.137026i
$327$	2.53706	+	4.39432i	0.140300	+	0.243006i
$328$	−14.8704			−0.821078
$329$	11.3400	+	21.7598i	0.625195	+	1.19966i
$330$	−4.58206			−0.252234
$331$	−3.86809	−	6.69972i	−0.212609	−	0.368250i	0.739921	−	0.672694i	$-0.234863\pi$
$331$	−3.86809	−	6.69972i	−0.212609	−	0.368250i	−0.952530	+	0.304444i	$0.901529\pi$
$332$	2.46637	−	4.27187i	0.135359	−	0.234449i
$333$	0.926623	−	1.60496i	0.0507786	−	0.0879512i
$334$	−7.85918	−	13.6125i	−0.430035	−	0.744843i
$335$	−40.8911			−2.23412
$336$	4.27598	+	0.184745i	0.233274	+	0.0100787i
$337$	4.64723			0.253151			0.126575	−	0.991957i	$-0.459601\pi$
$337$	4.64723			0.253151			0.126575	+	0.991957i	$0.459601\pi$
$338$	−0.510452	−	0.884128i	−0.0277649	−	0.0480902i
$339$	8.93700	−	15.4793i	0.485391	−	0.840722i
$340$	7.43448	−	12.8769i	0.403191	−	0.698348i
$341$	3.04092	+	5.26703i	0.164675	+	0.285226i
$342$	−9.03875			−0.488760
$343$	18.3651	+	2.39232i	0.991622	+	0.129173i
$344$	22.4959			1.21290
$345$	13.6078	+	23.5694i	0.732618	+	1.26893i
$346$	4.22117	−	7.31129i	0.226932	−	0.393057i
$347$	4.42799	−	7.66950i	0.237707	−	0.411720i	−0.722349	−	0.691529i	$-0.756938\pi$
$347$	4.42799	−	7.66950i	0.237707	−	0.411720i	0.960056	+	0.279808i	$0.0902709\pi$
$348$	4.81011	+	8.33136i	0.257849	+	0.446608i
$349$	−18.7943			−1.00604			−0.503019	−	0.864275i	$-0.667777\pi$
$349$	−18.7943			−1.00604			−0.503019	+	0.864275i	$0.667777\pi$
$350$	14.8069	+	0.639737i	0.791462	+	0.0341954i
$351$	−5.65349			−0.301761
$352$	−2.42379	−	4.19813i	−0.129188	−	0.223761i
$353$	−9.36994	+	16.2292i	−0.498712	+	0.863794i	−0.999999	−	0.00148692i	$-0.999527\pi$
$353$	−9.36994	+	16.2292i	−0.498712	+	0.863794i	0.501287	+	0.865281i	$0.332860\pi$
$354$	−1.13463	+	1.96523i	−0.0603046	+	0.104451i
$355$	−5.58597	−	9.67519i	−0.296473	−	0.513506i
$356$	−14.8766			−0.788461
$357$	8.12426	+	15.5892i	0.429981	+	0.825070i
$358$	−9.32863			−0.493034
$359$	−17.5522	−	30.4012i	−0.926367	−	1.60451i	−0.789348	−	0.613947i	$-0.789581\pi$
$359$	−17.5522	−	30.4012i	−0.926367	−	1.60451i	−0.137020	−	0.990568i	$-0.543752\pi$
$360$	−5.27609	+	9.13846i	−0.278074	+	0.481639i
$361$	−24.1573	+	41.8416i	−1.27144	+	2.20219i
$362$	−9.83946	−	17.0424i	−0.517151	−	0.895731i
$363$	−1.38596			−0.0727439
$364$	−1.36054	+	2.13776i	−0.0713115	+	0.112049i
$365$	−27.7850			−1.45434
$366$	−8.43736	−	14.6139i	−0.441028	−	0.763883i
$367$	−1.73465	+	3.00450i	−0.0905479	+	0.156833i	−0.907742	−	0.419529i	$-0.862195\pi$
$367$	−1.73465	+	3.00450i	−0.0905479	+	0.156833i	0.817194	+	0.576363i	$0.195528\pi$
$368$	3.53877	−	6.12933i	0.184471	−	0.319513i
$369$	2.65714	+	4.60230i	0.138325	+	0.239586i
$370$	5.67772			0.295171
$371$	−5.91329	+	9.29133i	−0.307003	+	0.482382i
$372$	−8.07310			−0.418571
$373$	8.68381	+	15.0408i	0.449631	+	0.778783i	0.998362	−	0.0572155i	$-0.0182222\pi$
$373$	8.68381	+	15.0408i	0.449631	+	0.778783i	−0.548731	+	0.835999i	$0.684889\pi$
$374$	−2.44711	+	4.23853i	−0.126537	+	0.219169i
$375$	1.09290	−	1.89296i	0.0564373	−	0.0977522i
$376$	−14.0022	−	24.2525i	−0.722109	−	1.25073i
$377$	7.24736			0.373258
$378$	−7.05724	−	13.5418i	−0.362985	−	0.696515i
$379$	2.41786			0.124197			0.0620985	−	0.998070i	$-0.480221\pi$
$379$	2.41786			0.124197			0.0620985	+	0.998070i	$0.480221\pi$
$380$	12.7235	+	22.0377i	0.652700	+	1.13051i
$381$	12.6507	−	21.9117i	0.648116	−	1.12257i
$382$	−1.13351	+	1.96329i	−0.0579952	+	0.100451i
$383$	−0.581540	−	1.00726i	−0.0297153	−	0.0514684i	0.850785	−	0.525513i	$-0.176127\pi$
$383$	−0.581540	−	1.00726i	−0.0297153	−	0.0514684i	−0.880501	+	0.474045i	$0.842793\pi$
$384$	3.13175			0.159816
$385$	8.55992	+	0.369834i	0.436254	+	0.0188485i
$386$	16.2620			0.827715
$387$	−4.01972	−	6.96235i	−0.204334	−	0.353916i
$388$	5.63319	−	9.75697i	0.285982	−	0.495335i
$389$	−10.7069	+	18.5448i	−0.542860	+	0.940261i	0.455879	+	0.890042i	$0.349325\pi$
$389$	−10.7069	+	18.5448i	−0.542860	+	0.940261i	−0.998738	+	0.0502186i	$0.984008\pi$
$390$	−2.29103	−	3.96818i	−0.116011	−	0.200937i
$391$	29.0697			1.47012
$392$	−21.0583	−	1.82306i	−1.06361	−	0.0920787i
$393$	−8.98163			−0.453063
$394$	4.60526	+	7.97654i	0.232010	+	0.401852i
$395$	−15.3251	+	26.5438i	−0.771088	+	1.33556i
$396$	−0.516767	+	0.895067i	−0.0259685	+	0.0449788i
$397$	−3.66128	−	6.34152i	−0.183754	−	0.318272i	0.759402	−	0.650622i	$-0.225492\pi$
$397$	−3.66128	−	6.34152i	−0.183754	−	0.318272i	−0.943156	+	0.332350i	$0.892158\pi$
$398$	12.3112			0.617104
$399$	−30.0572	−	1.29863i	−1.50474	−	0.0650129i
$400$	−6.40437			−0.320219
$401$	−9.39973	−	16.2808i	−0.469400	−	0.813025i	0.529988	−	0.848005i	$-0.322196\pi$
$401$	−9.39973	−	16.2808i	−0.469400	−	0.813025i	−0.999388	+	0.0349804i	$0.988863\pi$
$402$	−8.93322	+	15.4728i	−0.445549	+	0.771713i
$403$	−3.04092	+	5.26703i	−0.151479	+	0.262369i
$404$	−0.579623	−	1.00394i	−0.0288373	−	0.0499477i
$405$	−14.8905			−0.739913
$406$	9.04687	+	17.3596i	0.448989	+	0.861542i
$407$	1.71737			0.0851268
$408$	−10.0315	−	17.3751i	−0.496634	−	0.860196i
$409$	−4.39208	+	7.60730i	−0.217174	+	0.376157i	−0.953943	−	0.299988i	$-0.903017\pi$
$409$	−4.39208	+	7.60730i	−0.217174	+	0.376157i	0.736769	+	0.676145i	$0.236351\pi$
$410$	−8.14057	+	14.0999i	−0.402034	+	0.696343i
$411$	0.731060	+	1.26623i	0.0360605	+	0.0624587i
$412$	−2.60774			−0.128474
$413$	2.27826	−	3.57974i	0.112106	−	0.176148i
$414$	−6.68029			−0.328318
$415$	−8.33927	−	14.4440i	−0.409359	−	0.709030i
$416$	2.42379	−	4.19813i	0.118836	−	0.205830i
$417$	−6.35865	+	11.0135i	−0.311384	+	0.539333i
$418$	−4.18802	−	7.25387i	−0.204843	−	0.354798i
$419$	38.2464			1.86846			0.934229	−	0.356673i	$-0.116089\pi$
$419$	38.2464			1.86846			0.934229	+	0.356673i	$0.116089\pi$
$420$	−6.10642	+	9.59478i	−0.297963	+	0.468177i
$421$	−7.24846			−0.353268			−0.176634	−	0.984277i	$-0.556521\pi$
$421$	−7.24846			−0.353268			−0.176634	+	0.984277i	$0.556521\pi$
$422$	10.0470	+	17.4020i	0.489083	+	0.847116i
$423$	−5.00402	+	8.66722i	−0.243304	+	0.421415i
$424$	6.28479	−	10.8856i	0.305216	−	0.528650i
$425$	−13.1524	−	22.7806i	−0.637985	−	1.10502i
$426$	−4.88132			−0.236501
$427$	14.5826	+	27.9819i	0.705703	+	1.35414i
$428$	−14.5092			−0.701327
$429$	−0.692979	−	1.20028i	−0.0334573	−	0.0579498i
$430$	12.3150	−	21.3303i	0.593884	−	1.02864i
$431$	−2.18656	+	3.78723i	−0.105323	+	0.182424i	−0.913870	−	0.406007i	$-0.866921\pi$
$431$	−2.18656	+	3.78723i	−0.105323	+	0.182424i	0.808547	+	0.588431i	$0.200254\pi$
$432$	3.29934	+	5.71463i	0.158740	+	0.274945i
$433$	4.82105			0.231685			0.115842	−	0.993268i	$-0.463043\pi$
$433$	4.82105			0.231685			0.115842	+	0.993268i	$0.463043\pi$
$434$	−16.4121	−	0.709089i	−0.787805	−	0.0340374i
$435$	32.5279			1.55959
$436$	1.75322	+	3.03666i	0.0839639	+	0.145430i
$437$	−24.8751	+	43.0850i	−1.18994	+	2.06104i
$438$	−6.07002	+	10.5136i	−0.290037	+	0.502358i
$439$	19.0206	+	32.9447i	0.907805	+	1.57236i	0.817107	+	0.576486i	$0.195577\pi$
$439$	19.0206	+	32.9447i	0.907805	+	1.57236i	0.0906985	+	0.995878i	$0.471090\pi$
$440$	−9.77851			−0.466172
$441$	3.19862	+	6.84319i	0.152315	+	0.325866i
$442$	−4.89423			−0.232795
$443$	−5.89624	−	10.2126i	−0.280139	−	0.485215i	0.691280	−	0.722587i	$-0.257047\pi$
$443$	−5.89624	−	10.2126i	−0.280139	−	0.485215i	−0.971419	+	0.237372i	$0.923714\pi$
$444$	−1.13983	+	1.97424i	−0.0540938	+	0.0936932i
$445$	−25.1504	+	43.5619i	−1.19225	+	2.06503i
$446$	14.0713	+	24.3722i	0.666297	+	1.15406i
$447$	−9.54389			−0.451411
$448$	19.2518	+	0.831780i	0.909562	+	0.0392979i
$449$	−26.1941			−1.23617			−0.618087	−	0.786109i	$-0.712092\pi$
$449$	−26.1941			−1.23617			−0.618087	+	0.786109i	$0.712092\pi$
$450$	3.02245	+	5.23504i	0.142480	+	0.246782i
$451$	−2.46232	+	4.26486i	−0.115946	+	0.200825i
$452$	6.17585	−	10.6969i	0.290488	−	0.503139i
$453$	11.6500	+	20.1785i	0.547367	+	0.948067i
$454$	−15.6478			−0.734389
$455$	3.95968	+	7.59803i	0.185632	+	0.356201i
$456$	34.3362			1.60794
$457$	16.6831	+	28.8959i	0.780402	+	1.35170i	0.931708	+	0.363208i	$0.118319\pi$
$457$	16.6831	+	28.8959i	0.780402	+	1.35170i	−0.151306	+	0.988487i	$0.548348\pi$
$458$	−11.0473	+	19.1345i	−0.516206	+	0.894095i
$459$	−13.5515	+	23.4718i	−0.632528	+	1.09557i
$460$	9.40356	+	16.2874i	0.438443	+	0.759406i
$461$	−34.1948			−1.59261			−0.796304	−	0.604896i	$-0.793215\pi$
$461$	−34.1948			−1.59261			−0.796304	+	0.604896i	$0.793215\pi$
$462$	2.00997	−	3.15819i	0.0935124	−	0.146932i
$463$	9.03569			0.419924			0.209962	−	0.977710i	$-0.432666\pi$
$463$	9.03569			0.419924			0.209962	+	0.977710i	$0.432666\pi$
$464$	−4.22952	−	7.32574i	−0.196351	−	0.340089i
$465$	−13.6484	+	23.6397i	−0.632928	+	1.09626i
$466$	−5.81304	+	10.0685i	−0.269284	+	0.466413i
$467$	12.4321	+	21.5331i	0.575291	+	0.996433i	0.996010	+	0.0892421i	$0.0284445\pi$
$467$	12.4321	+	21.5331i	0.575291	+	0.996433i	−0.420719	+	0.907191i	$0.638222\pi$
$468$	−1.03353			−0.0477751
$469$	17.9374	−	28.1843i	0.828271	−	1.30143i
$470$	−30.6613			−1.41430
$471$	−2.77250	−	4.80211i	−0.127750	−	0.221270i
$472$	−2.42139	+	4.19397i	−0.111453	+	0.193043i
$473$	3.72500	−	6.45188i	0.171275	−	0.296658i
$474$	6.69594	+	11.5977i	0.307555	+	0.532700i
$475$	45.0184			2.06559
$476$	5.61421	+	10.7728i	0.257327	+	0.493772i
$477$	−4.49204			−0.205676
$478$	−10.1748	−	17.6233i	−0.465386	−	0.806073i
$479$	−2.53822	+	4.39633i	−0.115974	+	0.200874i	−0.918169	−	0.396189i	$-0.870332\pi$
$479$	−2.53822	+	4.39633i	−0.115974	+	0.200874i	0.802194	+	0.597063i	$0.203666\pi$
$480$	10.8785	−	18.8422i	0.496535	−	0.860025i
$481$	0.858684	+	1.48728i	0.0391526	+	0.0678143i
$482$	−17.3851			−0.791867
$483$	−22.2144	−	0.959782i	−1.01079	−	0.0436716i
$484$	−0.957757			−0.0435344
$485$	−19.0469	−	32.9902i	−0.864876	−	1.49801i
$486$	5.40448	−	9.36083i	0.245152	−	0.424616i
$487$	−5.43626	+	9.41588i	−0.246340	+	0.426674i	−0.962508	−	0.271255i	$-0.912561\pi$
$487$	−5.43626	+	9.41588i	−0.246340	+	0.426674i	0.716167	+	0.697929i	$0.245895\pi$
$488$	−18.0061	−	31.1874i	−0.815096	−	1.41179i
$489$	−3.87835			−0.175385
$490$	−13.2567	+	18.9692i	−0.598876	+	0.856942i
$491$	−10.2761			−0.463753			−0.231876	−	0.972745i	$-0.574487\pi$
$491$	−10.2761			−0.463753			−0.231876	+	0.972745i	$0.574487\pi$
$492$	−3.26851	−	5.66122i	−0.147356	−	0.255228i
$493$	17.3720	−	30.0892i	0.782395	−	1.35515i
$494$	4.18802	−	7.25387i	0.188428	−	0.326367i
$495$	1.74729	+	3.02640i	0.0785349	+	0.136026i
$496$	7.09866			0.318739
$497$	9.11899	+	0.393989i	0.409043	+	0.0176728i
$498$	−7.28731			−0.326552
$499$	8.15589	+	14.1264i	0.365108	+	0.632385i	0.988793	−	0.149290i	$-0.0476988\pi$
$499$	8.15589	+	14.1264i	0.365108	+	0.632385i	−0.623686	+	0.781675i	$0.714365\pi$
$500$	0.755243	−	1.30812i	0.0337755	−	0.0585009i
$501$	10.6695	−	18.4801i	0.476677	−	0.825629i
$502$	4.84033	+	8.38369i	0.216034	+	0.374182i
$503$	20.6109			0.918994			0.459497	−	0.888179i	$-0.348030\pi$
$503$	20.6109			0.918994			0.459497	+	0.888179i	$0.348030\pi$
$504$	−3.98429	−	7.64525i	−0.177474	−	0.340546i
$505$	−3.91964			−0.174422
$506$	−3.09525	−	5.36113i	−0.137601	−	0.238331i
$507$	0.692979	−	1.20028i	0.0307763	−	0.0533061i
$508$	8.74219	−	15.1419i	0.387872	−	0.671814i
$509$	−6.87377	−	11.9057i	−0.304675	−	0.527712i	0.672514	−	0.740084i	$-0.265214\pi$
$509$	−6.87377	−	11.9057i	−0.304675	−	0.527712i	−0.977189	+	0.212372i	$0.931881\pi$
$510$	−21.9665			−0.972691
$511$	12.1882	−	19.1509i	0.539176	−	0.847186i
$512$	−12.7069			−0.561570
$513$	−23.1922	−	40.1700i	−1.02396	−	1.77355i
$514$	−2.31923	+	4.01702i	−0.102297	+	0.177183i
$515$	−4.40864	+	7.63598i	−0.194268	+	0.336482i
$516$	4.94460	+	8.56430i	0.217674	+	0.377022i
$517$	−9.27427			−0.407882
$518$	−2.49060	+	3.91338i	−0.109431	+	0.171944i
$519$	11.4612			0.503089
$520$	−4.88926	−	8.46844i	−0.214408	−	0.371366i
$521$	2.68755	−	4.65497i	0.117744	−	0.203938i	−0.801130	−	0.598491i	$-0.795767\pi$
$521$	2.68755	−	4.65497i	0.117744	−	0.203938i	0.918873	+	0.394553i	$0.129101\pi$
$522$	−3.99213	+	6.91456i	−0.174731	+	0.302642i
$523$	15.8721	+	27.4913i	0.694040	+	1.20211i	0.970503	+	0.241088i	$0.0775043\pi$
$523$	15.8721	+	27.4913i	0.694040	+	1.20211i	−0.276463	+	0.961025i	$0.589162\pi$
$524$	−6.20669			−0.271140
$525$	9.29864	+	17.8427i	0.405826	+	0.778720i
$526$	−18.3027			−0.798034
$527$	14.5782	+	25.2502i	0.635037	+	1.09992i
$528$	−0.808838	+	1.40095i	−0.0352001	+	0.0609684i
$529$	−6.88453	+	11.9243i	−0.299327	+	0.518450i
$530$	−6.88104	−	11.9183i	−0.298893	−	0.517698i
$531$	1.73068			0.0751052
$532$	−20.7708	−	0.897410i	−0.900529	−	0.0389076i
$533$	−4.92464			−0.213310
$534$	10.9889	+	19.0334i	0.475537	+	0.823654i
$535$	−24.5292	+	42.4858i	−1.06049	+	1.83682i
$536$	−19.0643	+	33.0203i	−0.823451	+	1.42626i
$537$	−6.33219	−	10.9677i	−0.273254	−	0.473290i
$538$	13.3447			0.575331
$539$	−4.00982	+	5.73771i	−0.172715	+	0.247141i
$540$	−17.5347			−0.754572
$541$	−9.97823	−	17.2828i	−0.428997	−	0.743045i	0.567787	−	0.823176i	$-0.307800\pi$
$541$	−9.97823	−	17.2828i	−0.428997	−	0.743045i	−0.996784	+	0.0801302i	$0.974466\pi$
$542$	3.95367	−	6.84796i	0.169825	−	0.294145i
$543$	13.3579	−	23.1365i	0.573241	−	0.992882i
$544$	−11.6197	−	20.1259i	−0.498190	−	0.862891i
$545$	11.8560			0.507853
$546$	3.74006	+	0.161591i	0.160060	+	0.00691544i
$547$	−11.4257			−0.488528			−0.244264	−	0.969709i	$-0.578546\pi$
$547$	−11.4257			−0.488528			−0.244264	+	0.969709i	$0.578546\pi$
$548$	0.505194	+	0.875021i	0.0215808	+	0.0373791i
$549$	−6.43489	+	11.1456i	−0.274635	+	0.475681i
$550$	−2.80085	+	4.85122i	−0.119429	+	0.206857i
$551$	29.7307	+	51.4950i	1.26657	+	2.19376i
$552$	25.3769			1.08011
$553$	−11.5729	−	22.2066i	−0.492128	−	0.944320i
$554$	17.8516			0.758444
$555$	3.85398	+	6.67529i	0.163592	+	0.283350i
$556$	−4.39410	+	7.61080i	−0.186351	+	0.322770i
$557$	5.45247	−	9.44396i	0.231029	−	0.400154i	−0.727082	−	0.686550i	$-0.759124\pi$
$557$	5.45247	−	9.44396i	0.231029	−	0.400154i	0.958111	+	0.286397i	$0.0924575\pi$
$558$	−3.35011	−	5.80256i	−0.141821	−	0.245642i
$559$	7.44999			0.315101
$560$	5.36936	−	8.43667i	0.226897	−	0.356514i
$561$	−6.64431			−0.280523
$562$	−11.6217	−	20.1294i	−0.490232	−	0.849107i
$563$	12.0094	−	20.8010i	0.506138	−	0.876656i	−0.493837	−	0.869554i	$-0.664406\pi$
$563$	12.0094	−	20.8010i	0.506138	−	0.876656i	0.999975	−	0.00710170i	$-0.00226056\pi$
$564$	6.15538	−	10.6614i	0.259188	−	0.448927i
$565$	−20.8818	−	36.1683i	−0.878503	−	1.52161i
$566$	−6.21190			−0.261106
$567$	6.53187	−	10.2633i	0.274313	−	0.431017i
$568$	−10.4172			−0.437095
$569$	3.69581	+	6.40134i	0.154937	+	0.268358i	0.933036	−	0.359783i	$-0.117149\pi$
$569$	3.69581	+	6.40134i	0.154937	+	0.268358i	−0.778099	+	0.628141i	$0.783816\pi$
$570$	18.7968	−	32.5571i	0.787313	−	1.36367i
$571$	−9.25182	+	16.0246i	−0.387176	+	0.670609i	−0.992069	−	0.125698i	$-0.959883\pi$
$571$	−9.25182	+	16.0246i	−0.387176	+	0.670609i	0.604892	+	0.796307i	$0.293216\pi$
$572$	−0.478878	−	0.829442i	−0.0200229	−	0.0346807i
$573$	−3.07765			−0.128571
$574$	−6.14742	−	11.7960i	−0.256588	−	0.492355i
$575$	33.2718			1.38753
$576$	3.92977	+	6.80656i	0.163740	+	0.283607i
$577$	3.24929	−	5.62793i	0.135270	−	0.234294i	−0.790431	−	0.612551i	$-0.790143\pi$
$577$	3.24929	−	5.62793i	0.135270	−	0.234294i	0.925700	+	0.378258i	$0.123477\pi$
$578$	−3.05383	+	5.28938i	−0.127022	+	0.220009i
$579$	11.0385	+	19.1192i	0.458744	+	0.794569i
$580$	22.4782			0.933355
$581$	13.6137	+	0.588184i	0.564792	+	0.0244020i
$582$	−16.6442			−0.689925
$583$	−2.08134	−	3.60499i	−0.0862004	−	0.149304i
$584$	−12.9540	+	22.4369i	−0.536038	+	0.928446i
$585$	−1.74729	+	3.02640i	−0.0722416	+	0.125126i
$586$	−16.5186	−	28.6110i	−0.682375	−	1.18191i
$587$	34.8019			1.43643			0.718215	−	0.695821i	$-0.244959\pi$
$587$	34.8019			1.43643			0.718215	+	0.695821i	$0.244959\pi$
$588$	−3.93457	−	8.41772i	−0.162259	−	0.347141i
$589$	−49.8987			−2.05604
$590$	2.65111	+	4.59186i	0.109145	+	0.189044i
$591$	−6.25201	+	10.8288i	−0.257173	+	0.445437i
$592$	1.00225	−	1.73594i	0.0411921	−	0.0713468i
$593$	−10.3107	−	17.8587i	−0.423411	−	0.733369i	0.572860	−	0.819654i	$-0.305834\pi$
$593$	−10.3107	−	17.8587i	−0.423411	−	0.733369i	−0.996271	+	0.0862842i	$0.972501\pi$
$594$	5.77167			0.236814
$595$	41.0364	+	1.77299i	1.68233	+	0.0726855i
$596$	−6.59524			−0.270152
$597$	8.35672	+	14.4743i	0.342018	+	0.592392i
$598$	3.09525	−	5.36113i	0.126574	−	0.219233i
$599$	9.82046	−	17.0095i	0.401253	−	0.694991i	−0.592624	−	0.805479i	$-0.701908\pi$
$599$	9.82046	−	17.0095i	0.401253	−	0.694991i	0.993877	+	0.110488i	$0.0352414\pi$
$600$	−11.4816	−	19.8867i	−0.468735	−	0.811872i
$601$	3.17432			0.129483			0.0647417	−	0.997902i	$-0.479378\pi$
$601$	3.17432			0.129483			0.0647417	+	0.997902i	$0.479378\pi$
$602$	9.29981	+	17.8450i	0.379032	+	0.727306i
$603$	13.6261			0.554899
$604$	8.05068	+	13.9442i	0.327577	+	0.567381i
$605$	−1.61918	+	2.80451i	−0.0658291	+	0.114019i
$606$	−0.856298	+	1.48315i	−0.0347847	+	0.0602489i
$607$	18.3922	+	31.8562i	0.746516	+	1.29300i	0.949483	+	0.313818i	$0.101608\pi$
$607$	18.3922	+	31.8562i	0.746516	+	1.29300i	−0.202967	+	0.979186i	$0.565058\pi$
$608$	39.7722			1.61297
$609$	−14.2687	+	22.4199i	−0.578198	+	0.908501i
$610$	−39.4287			−1.59642
$611$	−4.63713	−	8.03175i	−0.187598	−	0.324930i
$612$	−2.47739	+	4.29096i	−0.100143	+	0.173452i
$613$	4.62195	−	8.00544i	0.186679	−	0.323337i	−0.757462	−	0.652879i	$-0.773561\pi$
$613$	4.62195	−	8.00544i	0.186679	−	0.323337i	0.944141	+	0.329542i	$0.106894\pi$
$614$	−9.96761	−	17.2644i	−0.402260	−	0.696735i
$615$	−22.1030			−0.891277
$616$	4.28946	−	6.73986i	0.172827	−	0.271557i
$617$	−43.4223			−1.74812			−0.874058	−	0.485822i	$-0.838520\pi$
$617$	−43.4223			−1.74812			−0.874058	+	0.485822i	$0.838520\pi$
$618$	1.92625	+	3.33637i	0.0774852	+	0.134208i
$619$	19.2263	−	33.3009i	0.772770	−	1.33848i	−0.163270	−	0.986581i	$-0.552204\pi$
$619$	19.2263	−	33.3009i	0.772770	−	1.33848i	0.936039	−	0.351895i	$-0.114463\pi$
$620$	−9.43161	+	16.3360i	−0.378783	+	0.656071i
$621$	−17.1407	−	29.6885i	−0.687831	−	1.19136i
$622$	3.43539			0.137747
$623$	−18.9926	−	36.4439i	−0.760921	−	1.46009i
$624$	−1.61768			−0.0647588
$625$	11.1639	+	19.3364i	0.446556	+	0.773457i
$626$	−0.627129	+	1.08622i	−0.0250651	+	0.0434140i
$627$	5.68558	−	9.84771i	0.227060	−	0.393280i
$628$	−1.91592	−	3.31846i	−0.0764534	−	0.132421i
$629$	8.23309			0.328275
$630$	−9.43027	−	0.407438i	−0.375711	−	0.0162327i
$631$	−24.8342			−0.988633			−0.494317	−	0.869282i	$-0.664582\pi$
$631$	−24.8342			−0.988633			−0.494317	+	0.869282i	$0.664582\pi$
$632$	14.2897	+	24.7505i	0.568415	+	0.984523i
$633$	−13.6397	+	23.6246i	−0.542129	+	0.938994i
$634$	−0.418734	+	0.725268i	−0.0166300	+	0.0288041i
$635$	−29.5591	−	51.1978i	−1.17302	−	2.03172i
$636$	5.52559			0.219104
$637$	−6.97391	−	0.603747i	−0.276317	−	0.0239213i
$638$	−7.39886			−0.292924
$639$	1.86141	+	3.22406i	0.0736363	+	0.127542i
$640$	3.65875	−	6.33714i	0.144625	−	0.250498i
$641$	4.71483	−	8.16632i	0.186224	−	0.322550i	−0.757764	−	0.652529i	$-0.773708\pi$
$641$	4.71483	−	8.16632i	0.186224	−	0.322550i	0.943988	+	0.329978i	$0.107041\pi$
$642$	10.7175	+	18.5632i	0.422984	+	0.732630i
$643$	26.8222			1.05776			0.528882	−	0.848695i	$-0.322611\pi$
$643$	26.8222			1.05776			0.528882	+	0.848695i	$0.322611\pi$
$644$	−15.3511	−	0.663250i	−0.604919	−	0.0261357i
$645$	33.4373			1.31659
$646$	−20.0775	−	34.7752i	−0.789937	−	1.36821i
$647$	14.1596	−	24.5251i	0.556671	−	0.964183i	−0.441100	−	0.897458i	$-0.645412\pi$
$647$	14.1596	−	24.5251i	0.556671	−	0.964183i	0.997771	−	0.0667249i	$-0.0212550\pi$
$648$	−6.94224	+	12.0243i	−0.272717	+	0.472359i
$649$	0.801895	+	1.38892i	0.0314771	+	0.0545200i
$650$	−5.60170			−0.219717
$651$	−10.3067	−	19.7770i	−0.403951	−	0.775121i
$652$	−2.68011			−0.104961
$653$	3.86584	+	6.69583i	0.151282	+	0.262028i	0.931699	−	0.363231i	$-0.118327\pi$
$653$	3.86584	+	6.69583i	0.151282	+	0.262028i	−0.780417	+	0.625259i	$0.784993\pi$
$654$	2.59009	−	4.48617i	0.101281	−	0.175423i
$655$	−10.4930	+	18.1744i	−0.409996	+	0.710134i
$656$	2.87399	+	4.97790i	0.112211	+	0.194354i
$657$	9.25880			0.361220
$658$	13.4499	−	21.1333i	0.524332	−	0.823864i
$659$	−8.34168			−0.324946			−0.162473	−	0.986713i	$-0.551947\pi$
$659$	−8.34168			−0.324946			−0.162473	+	0.986713i	$0.551947\pi$
$660$	−2.14932	−	3.72273i	−0.0836622	−	0.144907i
$661$	7.75901	−	13.4390i	0.301790	−	0.522716i	−0.674751	−	0.738045i	$-0.735749\pi$
$661$	7.75901	−	13.4390i	0.301790	−	0.522716i	0.976542	+	0.215329i	$0.0690824\pi$
$662$	−3.94894	+	6.83977i	−0.153480	+	0.265835i
$663$	−3.32215	−	5.75414i	−0.129022	−	0.223472i
$664$	−15.5518			−0.603525
$665$	−37.7429	+	59.3040i	−1.46361	+	2.29971i
$666$	−1.89198			−0.0733129
$667$	21.9731	+	38.0585i	0.850802	+	1.47363i
$668$	7.37306	−	12.7705i	0.285272	−	0.494106i
$669$	−19.1030	+	33.0873i	−0.738563	+	1.27923i
$670$	20.8729	+	36.1530i	0.806392	+	1.39671i
$671$	−11.9262			−0.460406
$672$	8.21503	+	15.7634i	0.316902	+	0.608087i
$673$	29.8481			1.15056			0.575280	−	0.817957i	$-0.304893\pi$
$673$	29.8481			1.15056			0.575280	+	0.817957i	$0.304893\pi$
$674$	−2.37218	−	4.10874i	−0.0913731	−	0.158263i
$675$	−15.5104	+	26.8647i	−0.596994	+	1.03402i
$676$	0.478878	−	0.829442i	0.0184184	−	0.0319016i
$677$	3.08673	+	5.34637i	0.118633	+	0.205478i	0.919226	−	0.393730i	$-0.128816\pi$
$677$	3.08673	+	5.34637i	0.118633	+	0.205478i	−0.800593	+	0.599208i	$0.795482\pi$
$678$	−18.2476			−0.700796
$679$	31.0937	+	1.34341i	1.19327	+	0.0515555i
$680$	−46.8784			−1.79770
$681$	−10.6216	−	18.3971i	−0.407021	−	0.704980i
$682$	3.10448	−	5.37713i	0.118877	−	0.205901i
$683$	1.61130	−	2.79085i	0.0616545	−	0.106789i	−0.833551	−	0.552443i	$-0.813696\pi$
$683$	1.61130	−	2.79085i	0.0616545	−	0.106789i	0.895205	+	0.445654i	$0.147029\pi$
$684$	−4.23984	−	7.34361i	−0.162114	−	0.280790i
$685$	3.41632			0.130531
$686$	−7.25937	−	17.4583i	−0.277164	−	0.666560i
$687$	−29.9952			−1.14439
$688$	−4.34777	−	7.53056i	−0.165757	−	0.287100i
$689$	2.08134	−	3.60499i	0.0792929	−	0.137339i
$690$	13.8922	−	24.0620i	0.528868	−	0.916026i
$691$	3.21347	+	5.56590i	0.122246	+	0.211737i	0.920653	−	0.390381i	$-0.127657\pi$
$691$	3.21347	+	5.56590i	0.122246	+	0.211737i	−0.798407	+	0.602118i	$0.794324\pi$
$692$	7.92016			0.301079
$693$	−2.85242	−	0.123240i	−0.108355	−	0.00468149i
$694$	−9.04109			−0.343195
$695$	14.8573	+	25.7336i	0.563570	+	0.976132i
$696$	15.1652	−	26.2668i	0.574834	−	0.995642i
$697$	−11.8044	+	20.4458i	−0.447124	+	0.774441i
$698$	9.59360	+	16.6166i	0.363123	+	0.628948i
$699$	−15.7833			−0.596980
$700$	6.42576	+	12.3301i	0.242871	+	0.466033i
$701$	36.5622			1.38093			0.690467	−	0.723364i	$-0.257405\pi$
$701$	36.5622			1.38093			0.690467	+	0.723364i	$0.257405\pi$
$702$	2.88583	+	4.99841i	0.108919	+	0.188653i
$703$	−7.04511	+	12.2025i	−0.265711	+	0.460226i
$704$	−3.64164	+	6.30751i	−0.137250	+	0.237723i
$705$	−20.8126	−	36.0484i	−0.783847	−	1.35766i
$706$	19.1316			0.720028
$707$	1.71939	−	2.70162i	0.0646645	−	0.101605i
$708$	−2.12889			−0.0800085
$709$	24.1750	+	41.8723i	0.907910	+	1.57255i	0.816963	+	0.576690i	$0.195656\pi$
$709$	24.1750	+	41.8723i	0.907910	+	1.57255i	0.0909467	+	0.995856i	$0.471011\pi$
$710$	−5.70274	+	9.87743i	−0.214020	+	0.370693i
$711$	5.10677	−	8.84519i	0.191519	−	0.331720i
$712$	23.4513	+	40.6188i	0.878875	+	1.52226i
$713$	−36.8787			−1.38112
$714$	9.63584	−	15.1404i	0.360612	−	0.566616i
$715$	−3.23836			−0.121108
$716$	−4.37581	−	7.57913i	−0.163532	−	0.283245i
$717$	13.8132	−	23.9251i	0.515862	−	0.893499i
$718$	−17.9190	+	31.0367i	−0.668733	+	1.15828i
$719$	−7.77996	−	13.4753i	−0.290143	−	0.502543i	0.683700	−	0.729763i	$-0.260370\pi$
$719$	−7.77996	−	13.4753i	−0.290143	−	0.502543i	−0.973843	+	0.227220i	$0.927036\pi$
$720$	4.07884			0.152009
$721$	−3.32922	−	6.38828i	−0.123987	−	0.237912i
$722$	49.3245			1.83567
$723$	−11.8008	−	20.4396i	−0.438877	−	0.760157i
$724$	9.23086	−	15.9883i	0.343062	−	0.594201i
$725$	19.8832	−	34.4387i	0.738442	−	1.27902i
$726$	0.707465	+	1.22536i	0.0262565	+	0.0454775i
$727$	−21.7131			−0.805294			−0.402647	−	0.915355i	$-0.631910\pi$
$727$	−21.7131			−0.805294			−0.402647	+	0.915355i	$0.631910\pi$
$728$	7.98162	+	0.344848i	0.295819	+	0.0127809i
$729$	28.4684			1.05439
$730$	14.1829	+	24.5655i	0.524933	+	0.909211i
$731$	17.8577	−	30.9304i	0.660491	−	1.14400i
$732$	7.91548	−	13.7100i	0.292565	−	0.506737i
$733$	−4.31276	−	7.46992i	−0.159295	−	0.275908i	0.775319	−	0.631569i	$-0.217589\pi$
$733$	−4.31276	−	7.46992i	−0.159295	−	0.275908i	−0.934615	+	0.355662i	$0.884256\pi$
$734$	3.54181			0.130731
$735$	−31.3006	−	2.70976i	−1.15454	−	0.0999511i
$736$	29.3945			1.08350
$737$	6.31355	+	10.9354i	0.232562	+	0.402810i
$738$	2.71268	−	4.69850i	0.0998551	−	0.172954i
$739$	3.53940	−	6.13042i	0.130199	−	0.225511i	−0.793554	−	0.608500i	$-0.791772\pi$
$739$	3.53940	−	6.13042i	0.130199	−	0.225511i	0.923753	+	0.382988i	$0.125105\pi$
$740$	2.66327	+	4.61291i	0.0979036	+	0.169574i
$741$	11.3712			0.417730
$742$	11.2332	+	0.485332i	0.412383	+	0.0178171i
$743$	−29.4927			−1.08198			−0.540991	−	0.841028i	$-0.681951\pi$
$743$	−29.4927			−1.08198			−0.540991	+	0.841028i	$0.681951\pi$
$744$	12.7263	+	22.0426i	0.466569	+	0.808121i
$745$	−11.1499	+	19.3122i	−0.408501	+	0.707544i
$746$	8.86533	−	15.3552i	0.324583	−	0.562194i
$747$	2.77889	+	4.81319i	0.101674	+	0.176105i
$748$	−4.59150			−0.167882
$749$	−18.5234	−	35.5437i	−0.676831	−	1.29874i
$750$	−2.23150			−0.0814827
$751$	15.6877	+	27.1718i	0.572451	+	0.991515i	0.996313	+	0.0857880i	$0.0273408\pi$
$751$	15.6877	+	27.1718i	0.572451	+	0.991515i	−0.423862	+	0.905727i	$0.639326\pi$
$752$	−5.41241	+	9.37457i	−0.197370	+	0.341855i
$753$	−6.57113	+	11.3815i	−0.239465	+	0.414766i
$754$	−3.69943	−	6.40760i	−0.134725	−	0.233351i
$755$	54.4419			1.98134
$756$	7.69179	−	12.0858i	0.279748	−	0.439557i
$757$	−5.32246			−0.193448			−0.0967240	−	0.995311i	$-0.530836\pi$
$757$	−5.32246			−0.193448			−0.0967240	+	0.995311i	$0.530836\pi$
$758$	−1.23420	−	2.13769i	−0.0448281	−	0.0776446i
$759$	4.20205	−	7.27817i	0.152525	−	0.264181i
$760$	40.1141	−	69.4797i	1.45509	−	2.52029i
$761$	−19.6035	−	33.9542i	−0.710626	−	1.23084i	−0.964623	−	0.263635i	$-0.915079\pi$
$761$	−19.6035	−	33.9542i	−0.710626	−	1.23084i	0.253997	−	0.967205i	$-0.418255\pi$
$762$	−25.8303			−0.935734
$763$	−5.20075	+	8.17174i	−0.188280	+	0.295837i
$764$	−2.12679			−0.0769445
$765$	8.37655	+	14.5086i	0.302855	+	0.524560i
$766$	−0.593696	+	1.02831i	−0.0214511	+	0.0371544i
$767$	−0.801895	+	1.38892i	−0.0289548	+	0.0501511i
$768$	−11.6929	−	20.2528i	−0.421933	−	0.730809i
$769$	5.94544			0.214398			0.107199	−	0.994238i	$-0.465812\pi$
$769$	5.94544			0.214398			0.107199	+	0.994238i	$0.465812\pi$
$770$	−4.04245	−	7.75685i	−0.145680	−	0.279537i
$771$	−6.29708			−0.226784
$772$	7.62808	+	13.2122i	0.274540	+	0.475518i
$773$	−27.4984	+	47.6287i	−0.989050	+	1.71308i	−0.366713	+	0.930334i	$0.619517\pi$
$773$	−27.4984	+	47.6287i	−0.989050	+	1.71308i	−0.622336	+	0.782750i	$0.713816\pi$
$774$	−4.10374	+	7.10789i	−0.147506	+	0.255488i
$775$	16.6856	+	28.9002i	0.599363	+	1.03813i
$776$	−35.5202			−1.27510
$777$	−6.29155	−	0.271828i	−0.225708	−	0.00975179i
$778$	21.8613			0.783767
$779$	−20.2022	−	34.9913i	−0.723819	−	1.25369i
$780$	2.14932	−	3.72273i	0.0769580	−	0.133295i
$781$	−1.72494	+	2.98768i	−0.0617230	+	0.106907i
$782$	−14.8387	−	25.7014i	−0.530630	−	0.919078i
$783$	−40.9729			−1.46425
$784$	3.45966	+	7.40168i	0.123559	+	0.264346i
$785$	−12.9562			−0.462426
$786$	4.58469	+	7.94091i	0.163530	+	0.283243i
$787$	22.3458	−	38.7041i	0.796542	−	1.37965i	−0.125314	−	0.992117i	$-0.539994\pi$
$787$	22.3458	−	38.7041i	0.796542	−	1.37965i	0.921855	−	0.387534i	$-0.126673\pi$
$788$	−4.32041	+	7.48316i	−0.153908	+	0.266577i
$789$	−12.4237	−	21.5184i	−0.442294	−	0.766076i
$790$	31.2908			1.11328
$791$	34.0891	+	1.47283i	1.21207	+	0.0523678i
$792$	3.25849			0.115785
$793$	−5.96310	−	10.3284i	−0.211756	−	0.366772i
$794$	−3.73781	+	6.47408i	−0.132650	+	0.229757i
$795$	9.34157	−	16.1801i	0.331311	−	0.573848i
$796$	5.77485	+	10.0023i	0.204684	+	0.354523i
$797$	2.57155			0.0910891			0.0455446	−	0.998962i	$-0.485498\pi$
$797$	2.57155			0.0910891			0.0455446	+	0.998962i	$0.485498\pi$
$798$	14.1946	+	27.2373i	0.502483	+	0.964190i
$799$	−44.4610			−1.57292
$800$	−13.2994	−	23.0352i	−0.470203	−	0.814416i
$801$	8.38088	−	14.5161i	0.296124	−	0.512901i
$802$	−9.59621	+	16.6211i	−0.338854	+	0.586912i
$803$	4.28998	+	7.43046i	0.151390	+	0.262215i
$804$	−16.7613			−0.591127
$805$	−27.8947	+	43.8300i	−0.983160	+	1.54480i
$806$	6.20897			0.218702
$807$	9.05825	+	15.6894i	0.318866	+	0.552291i
$808$	−1.82741	+	3.16517i	−0.0642882	+	0.111350i
$809$	−19.8460	+	34.3742i	−0.697747	+	1.20853i	0.271499	+	0.962439i	$0.412481\pi$
$809$	−19.8460	+	34.3742i	−0.697747	+	1.20853i	−0.969246	+	0.246095i	$0.920853\pi$
$810$	7.60086	+	13.1651i	0.267067	+	0.462574i
$811$	33.8232			1.18769			0.593846	−	0.804579i	$-0.297609\pi$
$811$	33.8232			1.18769			0.593846	+	0.804579i	$0.297609\pi$
$812$	−9.86031	+	15.4931i	−0.346029	+	0.543702i
$813$	10.7349			0.376488
$814$	−0.876633	−	1.51837i	−0.0307260	−	0.0532190i
$815$	−4.53098	+	7.84789i	−0.158713	+	0.274900i
$816$	−3.87758	+	6.71617i	−0.135742	+	0.235113i
$817$	30.5619	+	52.9347i	1.06923	+	1.85195i
$818$	8.96777			0.313551
$819$	−1.31948	−	2.53189i	−0.0461064	−	0.0884714i
$820$	−15.2741			−0.533394
$821$	−2.97652	−	5.15548i	−0.103881	−	0.179928i	0.809399	−	0.587259i	$-0.199793\pi$
$821$	−2.97652	−	5.15548i	−0.103881	−	0.179928i	−0.913281	+	0.407331i	$0.866460\pi$
$822$	0.746341	−	1.29270i	0.0260316	−	0.0450881i
$823$	−14.0224	+	24.2875i	−0.488789	+	0.846607i	−0.999917	−	0.0128973i	$-0.995895\pi$
$823$	−14.0224	+	24.2875i	−0.488789	+	0.846607i	0.511128	+	0.859505i	$0.329228\pi$
$824$	4.11079	+	7.12010i	0.143206	+	0.248040i
$825$	−7.60476			−0.264764
$826$	−4.32789	−	0.186988i	−0.150587	−	0.00650614i
$827$	13.1813			0.458357			0.229179	−	0.973384i	$-0.426396\pi$
$827$	13.1813			0.458357			0.229179	+	0.973384i	$0.426396\pi$
$828$	−3.13355	−	5.42746i	−0.108898	−	0.188617i
$829$	17.0175	−	29.4753i	0.591044	−	1.02372i	−0.403048	−	0.915179i	$-0.632049\pi$
$829$	17.0175	−	29.4753i	0.591044	−	1.02372i	0.994092	−	0.108539i	$-0.0346173\pi$
$830$	−8.51359	+	14.7460i	−0.295511	+	0.511840i
$831$	12.1175	+	20.9882i	0.420352	+	0.728071i
$832$	−7.28329			−0.252503
$833$	−19.2231	+	27.5067i	−0.666042	+	0.953051i
$834$	12.9831			0.449569
$835$	−24.9298	−	43.1797i	−0.862731	−	1.49429i
$836$	3.92898	−	6.80519i	0.135887	−	0.235362i
$837$	17.1918	−	29.7771i	0.594236	−	1.02925i
$838$	−19.5229	−	33.8147i	−0.674409	−	1.16811i
$839$	21.0786			0.727714			0.363857	−	0.931455i	$-0.381460\pi$
$839$	21.0786			0.727714			0.363857	+	0.931455i	$0.381460\pi$
$840$	35.8234	+	1.54776i	1.23603	+	0.0534028i
$841$	23.5243			0.811182
$842$	3.69999	+	6.40856i	0.127510	+	0.220854i
$843$	15.7774	−	27.3273i	0.543403	−	0.941202i
$844$	−9.42560	+	16.3256i	−0.324443	+	0.561951i
$845$	−1.61918	−	2.80451i	−0.0557016	−	0.0964780i
$846$	10.2172			0.351276
$847$	−1.22274	−	2.34625i	−0.0420138	−	0.0806182i
$848$	−4.85864			−0.166846
$849$	−4.21658	−	7.30333i	−0.144713	−	0.250650i
$850$	−13.4273	+	23.2568i	−0.460554	+	0.797702i
$851$	−5.20685	+	9.01852i	−0.178488	+	0.309151i
$852$	−2.28970	−	3.96587i	−0.0784438	−	0.135869i
$853$	−6.34612			−0.217287			−0.108643	−	0.994081i	$-0.534651\pi$
$853$	−6.34612			−0.217287			−0.108643	+	0.994081i	$0.534651\pi$
$854$	17.2958	−	27.1763i	0.591852	−	0.929954i
$855$	−28.6715			−0.980543
$856$	22.8720	+	39.6155i	0.781749	+	1.35403i
$857$	−16.6235	+	28.7927i	−0.567848	+	0.983541i	0.428931	+	0.903337i	$0.358890\pi$
$857$	−16.6235	+	28.7927i	−0.567848	+	0.983541i	−0.996779	+	0.0802035i	$0.974443\pi$
$858$	−0.707465	+	1.22536i	−0.0241524	+	0.0418333i
$859$	−15.0222	−	26.0192i	−0.512550	−	0.887762i	−0.999894	−	0.0145523i	$-0.995368\pi$
$859$	−15.0222	−	26.0192i	−0.512550	−	0.887762i	0.487344	−	0.873210i	$-0.337966\pi$
$860$	23.1066			0.787930
$861$	9.69572	−	15.2345i	0.330429	−	0.519191i
$862$	4.46453			0.152062
$863$	2.18558	+	3.78553i	0.0743979	+	0.128861i	0.900824	−	0.434184i	$-0.142963\pi$
$863$	2.18558	+	3.78553i	0.0743979	+	0.128861i	−0.826426	+	0.563045i	$0.809630\pi$
$864$	−13.7029	+	23.7341i	−0.466181	+	0.807449i
$865$	13.3898	−	23.1918i	0.455267	−	0.788546i
$866$	−2.46091	−	4.26242i	−0.0836251	−	0.144843i
$867$	−8.29163			−0.281599
$868$	−7.12236	−	13.6667i	−0.241749	−	0.463880i
$869$	9.46470			0.321068
$870$	−16.6039	−	28.7588i	−0.562926	−	0.975016i
$871$	−6.31355	+	10.9354i	−0.213926	+	0.370531i
$872$	5.52749	−	9.57389i	0.187184	−	0.324213i
$873$	6.34700	+	10.9933i	0.214813	+	0.372068i
$874$	50.7902			1.71801
$875$	4.16875	+	0.180112i	0.140929	+	0.00608890i
$876$	−11.3891			−0.384803
$877$	−0.616511	−	1.06783i	−0.0208181	−	0.0360580i	0.855429	−	0.517921i	$-0.173294\pi$
$877$	−0.616511	−	1.06783i	−0.0208181	−	0.0360580i	−0.876247	+	0.481863i	$0.839960\pi$
$878$	19.4182	−	33.6334i	0.655333	−	1.13507i
$879$	22.4253	−	38.8417i	0.756386	−	1.31010i
$880$	1.88989	+	3.27339i	0.0637082	+	0.110346i
$881$	31.0801			1.04711			0.523557	−	0.851991i	$-0.324605\pi$
$881$	31.0801			1.04711			0.523557	+	0.851991i	$0.324605\pi$
$882$	4.41752	−	6.32111i	0.148746	−	0.212843i
$883$	31.3597			1.05534			0.527670	−	0.849450i	$-0.323066\pi$
$883$	31.3597			1.05534			0.527670	+	0.849450i	$0.323066\pi$
$884$	−2.29575	−	3.97636i	−0.0772145	−	0.133739i
$885$	−3.59910	+	6.23382i	−0.120982	+	0.209548i
$886$	−6.01949	+	10.4261i	−0.202229	+	0.350271i
$887$	27.1595	+	47.0416i	0.911925	+	1.57950i	0.811342	+	0.584572i	$0.198738\pi$
$887$	27.1595	+	47.0416i	0.911925	+	1.57950i	0.100583	+	0.994929i	$0.467929\pi$
$888$	7.18721			0.241187
$889$	48.2546	+	2.08486i	1.61841	+	0.0699238i
$890$	51.3523			1.72133
$891$	2.29907	+	3.98211i	0.0770218	+	0.133406i
$892$	−13.2010	+	22.8647i	−0.442001	+	0.765568i
$893$	38.0456	−	65.8969i	1.27315	−	2.20515i
$894$	4.87170	+	8.43802i	0.162934	+	0.282210i
$895$	−29.5910			−0.989117
$896$	2.76294	+	5.30166i	0.0923032	+	0.177116i
$897$	8.40410			0.280605
$898$	13.3708	+	23.1589i	0.446190	+	0.772823i
$899$	−22.0387	+	38.1721i	−0.735030	+	1.27311i
$900$	−2.83550	+	4.91124i	−0.0945168	+	0.163708i
$901$	−9.97799	−	17.2824i	−0.332415	−	0.575760i
$902$	5.02758			0.167400
$903$	−14.6677	+	23.0468i	−0.488110	+	0.766948i
$904$	−38.9420			−1.29519
$905$	−31.2114	−	54.0596i	−1.03750	−	1.79700i
$906$	11.8936	−	20.6003i	0.395137	−	0.684398i
$907$	−15.4354	+	26.7348i	−0.512523	+	0.887716i	0.487372	+	0.873195i	$0.337956\pi$
$907$	−15.4354	+	26.7348i	−0.512523	+	0.887716i	−0.999895	+	0.0145210i	$0.995378\pi$
$908$	−7.33998	−	12.7132i	−0.243586	−	0.421903i
$909$	1.30614			0.0433219
$910$	4.69641	−	7.37929i	0.155684	−	0.244621i
$911$	8.81171			0.291945			0.145972	−	0.989289i	$-0.453369\pi$
$911$	8.81171			0.291945			0.145972	+	0.989289i	$0.453369\pi$
$912$	−6.63614	−	11.4941i	−0.219745	−	0.380609i
$913$	−2.57515	+	4.46029i	−0.0852250	+	0.147614i
$914$	17.0318	−	29.5000i	0.563362	−	0.975772i
$915$	−26.7638	−	46.3563i	−0.884784	−	1.53249i
$916$	−20.7280			−0.684871
$917$	−7.92389	−	15.2048i	−0.261670	−	0.502106i
$918$	27.6695			0.913228
$919$	−27.8515	−	48.2402i	−0.918736	−	1.59130i	−0.801338	−	0.598212i	$-0.795878\pi$
$919$	−27.8515	−	48.2402i	−0.918736	−	1.59130i	−0.117398	−	0.993085i	$-0.537455\pi$
$920$	29.6472	−	51.3505i	0.977440	−	1.69298i
$921$	13.5318	−	23.4378i	0.445889	−	0.772302i
$922$	17.4548	+	30.2325i	0.574842	+	0.995656i
$923$	−3.44987			−0.113554
$924$	3.50873	+	0.151596i	0.115429	+	0.00498713i
$925$	9.42321			0.309833
$926$	−4.61228	−	7.98870i	−0.151569	−	0.262525i
$927$	1.46909	−	2.54454i	0.0482512	−	0.0835736i
$928$	17.5661	−	30.4254i	0.576635	−	0.998761i
$929$	3.90257	+	6.75945i	0.128039	+	0.221770i	0.922917	−	0.384999i	$-0.125798\pi$
$929$	3.90257	+	6.75945i	0.128039	+	0.221770i	−0.794878	+	0.606770i	$0.792465\pi$
$930$	27.8673			0.913806
$931$	−24.3191	−	52.0288i	−0.797025	−	1.70517i
$932$	−10.9070			−0.357269
$933$	2.33191	+	4.03899i	0.0763434	+	0.132231i
$934$	12.6920	−	21.9832i	0.415295	−	0.719313i
$935$	−7.76239	+	13.4449i	−0.253857	+	0.439694i
$936$	1.62925	+	2.82194i	0.0532536	+	0.0922379i
$937$	−0.225318			−0.00736081			−0.00368041	−	0.999993i	$-0.501172\pi$
$937$	−0.225318			−0.00736081			−0.00368041	+	0.999993i	$0.501172\pi$
$938$	−34.0747	−	1.47221i	−1.11258	−	0.0480693i
$939$	−1.70276			−0.0555673
$940$	−14.3824	−	24.9110i	−0.469101	−	0.812507i
$941$	7.89461	−	13.6739i	0.257357	−	0.445755i	−0.708176	−	0.706036i	$-0.750482\pi$
$941$	7.89461	−	13.6739i	0.257357	−	0.445755i	0.965533	+	0.260280i	$0.0838150\pi$
$942$	−2.83045	+	4.90249i	−0.0922212	+	0.159732i
$943$	−14.9309	−	25.8611i	−0.486217	−	0.842152i
$944$	1.87193			0.0609260
$945$	−22.3860	−	42.9554i	−0.728216	−	1.39734i
$946$	−7.60572			−0.247283
$947$	24.1720	+	41.8671i	0.785484	+	1.36050i	0.928709	+	0.370808i	$0.120919\pi$
$947$	24.1720	+	41.8671i	0.785484	+	1.36050i	−0.143225	+	0.989690i	$0.545747\pi$
$948$	−6.28177	+	10.8803i	−0.204022	+	0.353377i
$949$	−4.28998	+	7.43046i	−0.139259	+	0.241203i
$950$	−22.9797	−	39.8020i	−0.745560	−	1.29135i
$951$	−1.13693			−0.0368675
$952$	20.5637	−	32.3110i	0.666474	−	1.04721i
$953$	31.2361			1.01184			0.505919	−	0.862581i	$-0.331154\pi$
$953$	31.2361			1.01184			0.505919	+	0.862581i	$0.331154\pi$
$954$	2.29297	+	3.97154i	0.0742376	+	0.128583i
$955$	−3.59555	+	6.22767i	−0.116349	+	0.201523i
$956$	9.54549	−	16.5333i	0.308723	−	0.534724i
$957$	−5.02227	−	8.69883i	−0.162347	−	0.281193i
$958$	5.18256			0.167441
$959$	−1.49861	+	2.35471i	−0.0483926	+	0.0760374i
$960$	−32.6891			−1.05504
$961$	−2.99439	−	5.18643i	−0.0965931	−	0.167304i
$962$	0.876633	−	1.51837i	0.0282638	−	0.0489543i
$963$	8.17385	−	14.1575i	0.263399	−	0.456220i
$964$	−8.15486	−	14.1246i	−0.262650	−	0.454924i
$965$	51.5841			1.66055
$966$	10.4908	+	20.1303i	0.337537	+	0.647683i
$967$	17.1528			0.551598			0.275799	−	0.961215i	$-0.411058\pi$
$967$	17.1528			0.551598			0.275799	+	0.961215i	$0.411058\pi$
$968$	1.50979	+	2.61504i	0.0485265	+	0.0840504i
$969$	27.2568	−	47.2101i	0.875613	−	1.51661i
$970$	−19.4451	+	33.6798i	−0.624343	+	1.08139i
$971$	0.827752	+	1.43371i	0.0265638	+	0.0460099i	0.879002	−	0.476819i	$-0.158210\pi$
$971$	0.827752	+	1.43371i	0.0265638	+	0.0460099i	−0.852438	+	0.522829i	$0.824877\pi$
$972$	10.1404			0.325253
$973$	−24.2543	−	1.04791i	−0.777557	−	0.0335946i
$974$	11.0998			0.355660
$975$	−3.80238	−	6.58592i	−0.121774	−	0.210918i
$976$	−6.96006	+	12.0552i	−0.222786	+	0.385877i
$977$	−4.48536	+	7.76888i	−0.143500	+	0.248548i	−0.928812	−	0.370551i	$-0.879169\pi$
$977$	−4.48536	+	7.76888i	−0.143500	+	0.248548i	0.785313	+	0.619099i	$0.212502\pi$
$978$	1.97971	+	3.42896i	0.0633041	+	0.109646i
$979$	15.5328			0.496431
$980$	−21.6301	−	1.87256i	−0.690947	−	0.0598168i
$981$	−3.95076			−0.126138
$982$	5.24544	+	9.08537i	0.167389	+	0.289926i
$983$	−5.21180	+	9.02711i	−0.166231	+	0.287920i	−0.937092	−	0.349083i	$-0.886493\pi$
$983$	−5.21180	+	9.02711i	−0.166231	+	0.287920i	0.770861	+	0.637004i	$0.219826\pi$
$984$	−10.3048	+	17.8485i	−0.328507	+	0.568990i
$985$	14.6082	+	25.3021i	0.465454	+	0.806191i
$986$	−35.4702			−1.12960
$987$	33.9761	+	1.46795i	1.08147	+	0.0467253i
$988$	7.85796			0.249995
$989$	22.5874	+	39.1226i	0.718239	+	1.24403i
$990$	1.78382	−	3.08966i	0.0566934	−	0.0981958i
$991$	3.60346	−	6.24138i	0.114468	−	0.198264i	−0.803099	−	0.595845i	$-0.796817\pi$
$991$	3.60346	−	6.24138i	0.114468	−	0.198264i	0.917567	+	0.397582i	$0.130150\pi$
$992$	14.7411	+	25.5323i	0.468030	+	0.810652i
$993$	−10.7220			−0.340253
$994$	−4.30647	−	8.26347i	−0.136593	−	0.262101i
$995$	39.0518			1.23803
$996$	−3.41828	−	5.92064i	−0.108312	−	0.187603i
$997$	−16.9145	+	29.2968i	−0.535689	+	0.927841i	0.463441	+	0.886128i	$0.346615\pi$
$997$	−16.9145	+	29.2968i	−0.535689	+	0.927841i	−0.999130	+	0.0417126i	$0.986719\pi$
$998$	8.32637	−	14.4217i	0.263567	−	0.456511i
$999$	−4.85456	−	8.40835i	−0.153592	−	0.266028i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1001.2.i.d.144.11	✓	50
7.2	even	3	inner	1001.2.i.d.716.11	yes	50
7.3	odd	6		7007.2.a.bi.1.15		25
7.4	even	3		7007.2.a.bh.1.15		25

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1001.2.i.d.144.11	✓	50	1.1	even	1	trivial
1001.2.i.d.716.11	yes	50	7.2	even	3	inner
7007.2.a.bh.1.15		25	7.4	even	3
7007.2.a.bi.1.15		25	7.3	odd	6

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:	\( N \)	\(=\)	\( 1001 = 7 \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1001.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.510452 - 0.884128i) q^{2} +(0.692979 - 1.20028i) q^{3} +(0.478878 - 0.829442i) q^{4} +(-1.61918 - 2.80451i) q^{5} -1.41493 q^{6} +(2.64329 + 0.114204i) q^{7} -3.01958 q^{8} +(0.539560 + 0.934545i) q^{9} +O(q^{10})\)	\(q+(-0.510452 - 0.884128i) q^{2} +(0.692979 - 1.20028i) q^{3} +(0.478878 - 0.829442i) q^{4} +(-1.61918 - 2.80451i) q^{5} -1.41493 q^{6} +(2.64329 + 0.114204i) q^{7} -3.01958 q^{8} +(0.539560 + 0.934545i) q^{9} +(-1.65303 + 2.86313i) q^{10} +(-0.500000 + 0.866025i) q^{11} +(-0.663705 - 1.14957i) q^{12} -1.00000 q^{13} +(-1.24830 - 2.39530i) q^{14} -4.48824 q^{15} +(0.583594 + 1.01082i) q^{16} +(-2.39701 + 4.15174i) q^{17} +(0.550838 - 0.954080i) q^{18} +(-4.10227 - 7.10534i) q^{19} -3.10157 q^{20} +(1.96882 - 3.09353i) q^{21} +1.02090 q^{22} +(-3.03187 - 5.25136i) q^{23} +(-2.09251 + 3.62433i) q^{24} +(-2.74350 + 4.75189i) q^{25} +(0.510452 + 0.884128i) q^{26} +5.65349 q^{27} +(1.36054 - 2.13776i) q^{28} -7.24736 q^{29} +(2.29103 + 3.96818i) q^{30} +(3.04092 - 5.26703i) q^{31} +(-2.42379 + 4.19813i) q^{32} +(0.692979 + 1.20028i) q^{33} +4.89423 q^{34} +(-3.95968 - 7.59803i) q^{35} +1.03353 q^{36} +(-0.858684 - 1.48728i) q^{37} +(-4.18802 + 7.25387i) q^{38} +(-0.692979 + 1.20028i) q^{39} +(4.88926 + 8.46844i) q^{40} +4.92464 q^{41} +(-3.74006 - 0.161591i) q^{42} -7.44999 q^{43} +(0.478878 + 0.829442i) q^{44} +(1.74729 - 3.02640i) q^{45} +(-3.09525 + 5.36113i) q^{46} +(4.63713 + 8.03175i) q^{47} +1.61768 q^{48} +(6.97391 + 0.603747i) q^{49} +5.60170 q^{50} +(3.32215 + 5.75414i) q^{51} +(-0.478878 + 0.829442i) q^{52} +(-2.08134 + 3.60499i) q^{53} +(-2.88583 - 4.99841i) q^{54} +3.23836 q^{55} +(-7.98162 - 0.344848i) q^{56} -11.3712 q^{57} +(3.69943 + 6.40760i) q^{58} +(0.801895 - 1.38892i) q^{59} +(-2.14932 + 3.72273i) q^{60} +(5.96310 + 10.3284i) q^{61} -6.20897 q^{62} +(1.31948 + 2.53189i) q^{63} +7.28329 q^{64} +(1.61918 + 2.80451i) q^{65} +(0.707465 - 1.22536i) q^{66} +(6.31355 - 10.9354i) q^{67} +(2.29575 + 3.97636i) q^{68} -8.40410 q^{69} +(-4.69641 + 7.37929i) q^{70} +3.44987 q^{71} +(-1.62925 - 2.82194i) q^{72} +(4.28998 - 7.43046i) q^{73} +(-0.876633 + 1.51837i) q^{74} +(3.80238 + 6.58592i) q^{75} -7.85796 q^{76} +(-1.42055 + 2.23205i) q^{77} +1.41493 q^{78} +(-4.73235 - 8.19667i) q^{79} +(1.88989 - 3.27339i) q^{80} +(2.29907 - 3.98211i) q^{81} +(-2.51379 - 4.35401i) q^{82} +5.15030 q^{83} +(-1.62308 - 3.11444i) q^{84} +15.5248 q^{85} +(3.80286 + 6.58675i) q^{86} +(-5.02227 + 8.69883i) q^{87} +(1.50979 - 2.61504i) q^{88} +(-7.76640 - 13.4518i) q^{89} -3.56763 q^{90} +(-2.64329 - 0.114204i) q^{91} -5.80760 q^{92} +(-4.21459 - 7.29988i) q^{93} +(4.73407 - 8.19964i) q^{94} +(-13.2847 + 23.0097i) q^{95} +(3.35927 + 5.81843i) q^{96} +11.7633 q^{97} +(-3.02606 - 6.47402i) q^{98} -1.07912 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 50 q - 6 q^{2} + 2 q^{3} - 30 q^{4} + q^{5} + 4 q^{6} + q^{7} + 42 q^{8} - 37 q^{9}+O(q^{10}) \) 50 * q - 6 * q^2 + 2 * q^3 - 30 * q^4 + q^5 + 4 * q^6 + q^7 + 42 * q^8 - 37 * q^9	\( 50 q - 6 q^{2} + 2 q^{3} - 30 q^{4} + q^{5} + 4 q^{6} + q^{7} + 42 q^{8} - 37 q^{9} + 3 q^{10} - 25 q^{11} - 9 q^{12} - 50 q^{13} + 22 q^{14} - 32 q^{16} + q^{17} - 44 q^{18} - 5 q^{19} + 8 q^{20} + 2 q^{21} + 12 q^{22} - 15 q^{23} + 4 q^{24} - 50 q^{25} + 6 q^{26} - 34 q^{27} + 12 q^{28} + 48 q^{29} - q^{30} + 12 q^{31} - 48 q^{32} + 2 q^{33} - 16 q^{34} + 20 q^{35} + 60 q^{36} - 33 q^{37} - 16 q^{38} - 2 q^{39} + 21 q^{40} + 24 q^{41} - 42 q^{42} + 76 q^{43} - 30 q^{44} + 22 q^{45} - 39 q^{46} - 4 q^{47} + 164 q^{48} + 23 q^{49} + 32 q^{50} - 51 q^{51} + 30 q^{52} - 2 q^{53} - 10 q^{54} - 2 q^{55} - 72 q^{56} + 76 q^{57} - 17 q^{58} + 4 q^{59} + 33 q^{60} + 22 q^{61} + 84 q^{62} - 19 q^{63} + 82 q^{64} - q^{65} - 2 q^{66} - 24 q^{67} - 14 q^{68} - 60 q^{69} - 124 q^{70} + 18 q^{71} - 102 q^{72} - 11 q^{73} - 39 q^{74} + 16 q^{75} + 116 q^{76} + q^{77} - 4 q^{78} - 19 q^{79} + 33 q^{80} - 73 q^{81} + 32 q^{82} + 32 q^{83} - 109 q^{84} + 28 q^{85} - 27 q^{86} + 11 q^{87} - 21 q^{88} - 13 q^{89} + 80 q^{90} - q^{91} - 17 q^{93} + 56 q^{94} - 15 q^{95} - 55 q^{96} + 68 q^{97} - 22 q^{98} + 74 q^{99}+O(q^{100}) \) 50 * q - 6 * q^2 + 2 * q^3 - 30 * q^4 + q^5 + 4 * q^6 + q^7 + 42 * q^8 - 37 * q^9 + 3 * q^10 - 25 * q^11 - 9 * q^12 - 50 * q^13 + 22 * q^14 - 32 * q^16 + q^17 - 44 * q^18 - 5 * q^19 + 8 * q^20 + 2 * q^21 + 12 * q^22 - 15 * q^23 + 4 * q^24 - 50 * q^25 + 6 * q^26 - 34 * q^27 + 12 * q^28 + 48 * q^29 - q^30 + 12 * q^31 - 48 * q^32 + 2 * q^33 - 16 * q^34 + 20 * q^35 + 60 * q^36 - 33 * q^37 - 16 * q^38 - 2 * q^39 + 21 * q^40 + 24 * q^41 - 42 * q^42 + 76 * q^43 - 30 * q^44 + 22 * q^45 - 39 * q^46 - 4 * q^47 + 164 * q^48 + 23 * q^49 + 32 * q^50 - 51 * q^51 + 30 * q^52 - 2 * q^53 - 10 * q^54 - 2 * q^55 - 72 * q^56 + 76 * q^57 - 17 * q^58 + 4 * q^59 + 33 * q^60 + 22 * q^61 + 84 * q^62 - 19 * q^63 + 82 * q^64 - q^65 - 2 * q^66 - 24 * q^67 - 14 * q^68 - 60 * q^69 - 124 * q^70 + 18 * q^71 - 102 * q^72 - 11 * q^73 - 39 * q^74 + 16 * q^75 + 116 * q^76 + q^77 - 4 * q^78 - 19 * q^79 + 33 * q^80 - 73 * q^81 + 32 * q^82 + 32 * q^83 - 109 * q^84 + 28 * q^85 - 27 * q^86 + 11 * q^87 - 21 * q^88 - 13 * q^89 + 80 * q^90 - q^91 - 17 * q^93 + 56 * q^94 - 15 * q^95 - 55 * q^96 + 68 * q^97 - 22 * q^98 + 74 * q^99

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