LMFDB - Embedded newform 155.2.p.c.37.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [155,2,Mod(37,155)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(155, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([3, 10]))

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

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

chi := DirichletCharacter("155.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 155 = 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	155.p (of order $12$, degree $4$, 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:	$1.23768123133$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$12$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			37.3
Character	$\chi$	$=$	155.37
Dual form			155.2.p.c.88.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.51649 - 1.51649i) q^{2} +(0.852101 - 3.18009i) q^{3} +2.59946i q^{4} +(-1.57889 + 1.58338i) q^{5} +(-6.11475 + 3.53035i) q^{6} +(0.903022 - 3.37012i) q^{7} +(0.909067 - 0.909067i) q^{8} +(-6.78879 - 3.91951i) q^{9} +O(q^{10})$	\(q+(-1.51649 - 1.51649i) q^{2} +(0.852101 - 3.18009i) q^{3} +2.59946i q^{4} +(-1.57889 + 1.58338i) q^{5} +(-6.11475 + 3.53035i) q^{6} +(0.903022 - 3.37012i) q^{7} +(0.909067 - 0.909067i) q^{8} +(-6.78879 - 3.91951i) q^{9} +(4.79554 - 0.00681153i) q^{10} +(2.73771 + 1.58062i) q^{11} +(8.26649 + 2.21500i) q^{12} +(-2.14217 + 0.573993i) q^{13} +(-6.48016 + 3.74132i) q^{14} +(3.68992 + 6.37021i) q^{15} +2.44174 q^{16} +(2.29741 + 0.615590i) q^{17} +(4.35122 + 16.2390i) q^{18} +(2.05712 - 1.18768i) q^{19} +(-4.11594 - 4.10426i) q^{20} +(-9.94781 - 5.74337i) q^{21} +(-1.75471 - 6.54868i) q^{22} +(-1.57327 - 1.57327i) q^{23} +(-2.11629 - 3.66553i) q^{24} +(-0.0142038 - 4.99998i) q^{25} +(4.11903 + 2.37812i) q^{26} +(-11.2652 + 11.2652i) q^{27} +(8.76049 + 2.34737i) q^{28} -2.26875 q^{29} +(4.06463 - 15.2560i) q^{30} +(2.33854 - 5.05284i) q^{31} +(-5.52100 - 5.52100i) q^{32} +(7.35930 - 7.35930i) q^{33} +(-2.55046 - 4.41753i) q^{34} +(3.91042 + 6.75089i) q^{35} +(10.1886 - 17.6472i) q^{36} +(3.52258 + 0.943873i) q^{37} +(-4.92069 - 1.31850i) q^{38} +7.30139i q^{39} +(0.00408322 + 2.87472i) q^{40} +(0.995477 - 1.72422i) q^{41} +(6.37597 + 23.7955i) q^{42} +(0.494912 - 1.84704i) q^{43} +(-4.10875 + 7.11656i) q^{44} +(16.9248 - 4.56077i) q^{45} +4.77169i q^{46} +(-2.97173 - 2.97173i) q^{47} +(2.08061 - 7.76494i) q^{48} +(-4.48011 - 2.58659i) q^{49} +(-7.56086 + 7.60394i) q^{50} +(3.91526 - 6.78143i) q^{51} +(-1.49207 - 5.56848i) q^{52} +(-1.25560 + 0.336436i) q^{53} +34.1669 q^{54} +(-6.82527 + 1.83922i) q^{55} +(-2.24276 - 3.88458i) q^{56} +(-2.02405 - 7.55384i) q^{57} +(3.44053 + 3.44053i) q^{58} +(1.22692 - 0.708363i) q^{59} +(-16.5591 + 9.59178i) q^{60} +5.71128i q^{61} +(-11.2089 + 4.11620i) q^{62} +(-19.3397 + 19.3397i) q^{63} +11.8615i q^{64} +(2.47341 - 4.29815i) q^{65} -22.3206 q^{66} +(7.80274 - 2.09074i) q^{67} +(-1.60020 + 5.97203i) q^{68} +(-6.34373 + 3.66256i) q^{69} +(4.30752 - 16.1677i) q^{70} +(1.08550 - 1.88015i) q^{71} +(-9.73457 + 2.60837i) q^{72} +(-3.40783 + 0.913126i) q^{73} +(-3.91058 - 6.77332i) q^{74} +(-15.9125 - 4.21532i) q^{75} +(3.08732 + 5.34740i) q^{76} +(7.79909 - 7.79909i) q^{77} +(11.0725 - 11.0725i) q^{78} +(2.13513 + 3.69815i) q^{79} +(-3.85524 + 3.86621i) q^{80} +(14.4666 + 25.0569i) q^{81} +(-4.12438 + 1.10512i) q^{82} +(16.7926 - 4.49956i) q^{83} +(14.9296 - 25.8589i) q^{84} +(-4.60208 + 2.66574i) q^{85} +(-3.55153 + 2.05048i) q^{86} +(-1.93321 + 7.21483i) q^{87} +(3.92565 - 1.05187i) q^{88} +10.1402 q^{89} +(-32.5826 - 18.7499i) q^{90} +7.73771i q^{91} +(4.08966 - 4.08966i) q^{92} +(-14.0758 - 11.7423i) q^{93} +9.01316i q^{94} +(-1.36742 + 5.13243i) q^{95} +(-22.2617 + 12.8528i) q^{96} +(8.87120 + 8.87120i) q^{97} +(2.87149 + 10.7165i) q^{98} +(-12.3905 - 21.4610i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 6 q^{3} - 4 q^{5} - 48 q^{6} - 8 q^{7} + 36 q^{8}+O(q^{10}) $ 48 * q + 6 * q^3 - 4 * q^5 - 48 * q^6 - 8 * q^7 + 36 * q^8	$ 48 q + 6 q^{3} - 4 q^{5} - 48 q^{6} - 8 q^{7} + 36 q^{8} - 6 q^{10} - 12 q^{11} - 56 q^{16} - 12 q^{17} + 2 q^{18} + 34 q^{20} - 24 q^{21} - 60 q^{22} + 12 q^{25} - 24 q^{26} + 28 q^{28} + 32 q^{31} + 52 q^{32} + 20 q^{33} + 48 q^{35} + 4 q^{36} + 42 q^{37} - 10 q^{38} - 16 q^{40} + 4 q^{41} + 78 q^{42} - 72 q^{43} - 42 q^{45} - 36 q^{47} + 24 q^{48} - 22 q^{50} + 8 q^{51} + 60 q^{52} - 72 q^{53} - 42 q^{55} + 36 q^{56} + 6 q^{57} - 78 q^{62} - 64 q^{63} - 36 q^{65} + 32 q^{66} + 26 q^{67} + 96 q^{68} - 88 q^{70} - 4 q^{71} + 22 q^{72} + 12 q^{73} - 24 q^{75} - 28 q^{76} + 4 q^{78} + 18 q^{80} + 60 q^{81} - 32 q^{82} + 90 q^{83} + 48 q^{86} + 2 q^{87} + 78 q^{88} - 118 q^{90} - 6 q^{93} - 52 q^{95} - 120 q^{96} + 4 q^{97} - 42 q^{98}+O(q^{100}) $ 48 * q + 6 * q^3 - 4 * q^5 - 48 * q^6 - 8 * q^7 + 36 * q^8 - 6 * q^10 - 12 * q^11 - 56 * q^16 - 12 * q^17 + 2 * q^18 + 34 * q^20 - 24 * q^21 - 60 * q^22 + 12 * q^25 - 24 * q^26 + 28 * q^28 + 32 * q^31 + 52 * q^32 + 20 * q^33 + 48 * q^35 + 4 * q^36 + 42 * q^37 - 10 * q^38 - 16 * q^40 + 4 * q^41 + 78 * q^42 - 72 * q^43 - 42 * q^45 - 36 * q^47 + 24 * q^48 - 22 * q^50 + 8 * q^51 + 60 * q^52 - 72 * q^53 - 42 * q^55 + 36 * q^56 + 6 * q^57 - 78 * q^62 - 64 * q^63 - 36 * q^65 + 32 * q^66 + 26 * q^67 + 96 * q^68 - 88 * q^70 - 4 * q^71 + 22 * q^72 + 12 * q^73 - 24 * q^75 - 28 * q^76 + 4 * q^78 + 18 * q^80 + 60 * q^81 - 32 * q^82 + 90 * q^83 + 48 * q^86 + 2 * q^87 + 78 * q^88 - 118 * q^90 - 6 * q^93 - 52 * q^95 - 120 * q^96 + 4 * q^97 - 42 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/155\mathbb{Z}\right)^\times$.

$n$	$32$	$96$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$	−1.51649	−	1.51649i	−1.07232	−	1.07232i	−0.997173	−	0.0751445i	$-0.976058\pi$
$2$	−1.51649	−	1.51649i	−1.07232	−	1.07232i	−0.0751445	−	0.997173i	$-0.523942\pi$
$3$	0.852101	−	3.18009i	0.491961	−	1.83602i	−0.0544651	−	0.998516i	$-0.517345\pi$
$3$	0.852101	−	3.18009i	0.491961	−	1.83602i	0.546426	−	0.837507i	$-0.315988\pi$
$4$			2.59946i			1.29973i
$5$	−1.57889	+	1.58338i	−0.706102	+	0.708110i
$5$	−1.57889	+	1.58338i	−0.706102	+	0.708110i
$6$	−6.11475	+	3.53035i	−2.49634	+	1.44126i
$7$	0.903022	−	3.37012i	0.341310	−	1.27379i	−0.555554	−	0.831481i	$-0.687494\pi$
$7$	0.903022	−	3.37012i	0.341310	−	1.27379i	0.896864	−	0.442306i	$-0.145840\pi$
$8$	0.909067	−	0.909067i	0.321404	−	0.321404i
$9$	−6.78879	−	3.91951i	−2.26293	−	1.30650i
$10$	4.79554	−	0.00681153i	1.51648	−	0.00215400i
$11$	2.73771	+	1.58062i	0.825451	+	0.476574i	0.852292	−	0.523066i	$-0.175212\pi$
$11$	2.73771	+	1.58062i	0.825451	+	0.476574i	−0.0268419	+	0.999640i	$0.508545\pi$
$12$	8.26649	+	2.21500i	2.38633	+	0.639416i
$13$	−2.14217	+	0.573993i	−0.594132	+	0.159197i	−0.543341	−	0.839512i	$-0.682841\pi$
$13$	−2.14217	+	0.573993i	−0.594132	+	0.159197i	−0.0507909	+	0.998709i	$0.516174\pi$
$14$	−6.48016	+	3.74132i	−1.73190	+	0.999911i
$15$	3.68992	+	6.37021i	0.952733	+	1.64478i
$16$	2.44174			0.610435
$17$	2.29741	+	0.615590i	0.557205	+	0.149303i	0.526422	−	0.850223i	$-0.323533\pi$
$17$	2.29741	+	0.615590i	0.557205	+	0.149303i	0.0307830	+	0.999526i	$0.490200\pi$
$18$	4.35122	+	16.2390i	1.02559	+	3.82756i
$19$	2.05712	−	1.18768i	0.471936	−	0.272472i	−0.245114	−	0.969494i	$-0.578825\pi$
$19$	2.05712	−	1.18768i	0.471936	−	0.272472i	0.717050	+	0.697022i	$0.245492\pi$
$20$	−4.11594	−	4.10426i	−0.920351	−	0.917740i
$21$	−9.94781	−	5.74337i	−2.17079	−	1.25331i
$22$	−1.75471	−	6.54868i	−0.374106	−	1.39618i
$23$	−1.57327	−	1.57327i	−0.328050	−	0.328050i	0.523794	−	0.851845i	$-0.324516\pi$
$23$	−1.57327	−	1.57327i	−0.328050	−	0.328050i	−0.851845	+	0.523794i	$0.824516\pi$
$24$	−2.11629	−	3.66553i	−0.431987	−	0.748223i
$25$	−0.0142038	−	4.99998i	−0.00284077	−	0.999996i
$26$	4.11903	+	2.37812i	0.807808	+	0.466388i
$27$	−11.2652	+	11.2652i	−2.16798	+	2.16798i
$28$	8.76049	+	2.34737i	1.65558	+	0.443611i
$29$	−2.26875			−0.421297			−0.210649	−	0.977562i	$-0.567558\pi$
$29$	−2.26875			−0.421297			−0.210649	+	0.977562i	$0.567558\pi$
$30$	4.06463	−	15.2560i	0.742096	−	2.78536i
$31$	2.33854	−	5.05284i	0.420014	−	0.907518i
$31$	2.33854	−	5.05284i	0.420014	−	0.907518i
$32$	−5.52100	−	5.52100i	−0.975983	−	0.975983i
$33$	7.35930	−	7.35930i	1.28109	−	1.28109i
$34$	−2.55046	−	4.41753i	−0.437401	−	0.757600i
$35$	3.91042	+	6.75089i	0.660982	+	1.14111i
$36$	10.1886	−	17.6472i	1.69810	−	2.94119i
$37$	3.52258	+	0.943873i	0.579109	+	0.155172i	0.536471	−	0.843919i	$-0.319757\pi$
$37$	3.52258	+	0.943873i	0.579109	+	0.155172i	0.0426381	+	0.999091i	$0.486424\pi$
$38$	−4.92069	−	1.31850i	−0.798242	−	0.213888i
$39$			7.30139i			1.16916i
$40$	0.00408322	+	2.87472i	0.000645613	+	0.454533i
$41$	0.995477	−	1.72422i	0.155467	−	0.269277i	−0.777762	−	0.628559i	$-0.783645\pi$
$41$	0.995477	−	1.72422i	0.155467	−	0.269277i	0.933229	+	0.359282i	$0.116978\pi$
$42$	6.37597	+	23.7955i	0.983834	+	3.67172i
$43$	0.494912	−	1.84704i	0.0754734	−	0.281671i	−0.917867	−	0.396889i	$-0.870090\pi$
$43$	0.494912	−	1.84704i	0.0754734	−	0.281671i	0.993340	+	0.115218i	$0.0367566\pi$
$44$	−4.10875	+	7.11656i	−0.619417	+	1.07286i
$45$	16.9248	−	4.56077i	2.52301	−	0.679880i
$46$			4.77169i			0.703548i
$47$	−2.97173	−	2.97173i	−0.433471	−	0.433471i	0.456336	−	0.889807i	$-0.349161\pi$
$47$	−2.97173	−	2.97173i	−0.433471	−	0.433471i	−0.889807	+	0.456336i	$0.849161\pi$
$48$	2.08061	−	7.76494i	0.300310	−	1.12077i
$49$	−4.48011	−	2.58659i	−0.640015	−	0.369513i
$50$	−7.56086	+	7.60394i	−1.06927	+	1.07536i
$51$	3.91526	−	6.78143i	0.548246	−	0.949590i
$52$	−1.49207	−	5.56848i	−0.206913	−	0.772210i
$53$	−1.25560	+	0.336436i	−0.172469	+	0.0462130i	−0.344020	−	0.938962i	$-0.611789\pi$
$53$	−1.25560	+	0.336436i	−0.172469	+	0.0462130i	0.171551	+	0.985175i	$0.445122\pi$
$54$	34.1669			4.64953
$55$	−6.82527	+	1.83922i	−0.920319	+	0.248000i
$56$	−2.24276	−	3.88458i	−0.299702	−	0.519098i
$57$	−2.02405	−	7.55384i	−0.268092	−	1.00053i
$58$	3.44053	+	3.44053i	0.451764	+	0.451764i
$59$	1.22692	−	0.708363i	0.159731	−	0.0922210i	−0.418004	−	0.908445i	$-0.637270\pi$
$59$	1.22692	−	0.708363i	0.159731	−	0.0922210i	0.577735	+	0.816224i	$0.303937\pi$
$60$	−16.5591	+	9.59178i	−2.13777	+	1.23829i
$61$			5.71128i			0.731254i	0.930761	+	0.365627i	$0.119145\pi$
$61$			5.71128i			0.731254i	−0.930761	+	0.365627i	$0.880855\pi$
$62$	−11.2089	+	4.11620i	−1.42353	+	0.522758i
$63$	−19.3397	+	19.3397i	−2.43657	+	2.43657i
$64$			11.8615i			1.48269i
$65$	2.47341	−	4.29815i	0.306788	−	0.533120i
$66$	−22.3206			−2.74747
$67$	7.80274	−	2.09074i	0.953256	−	0.255424i	0.251513	−	0.967854i	$-0.419072\pi$
$67$	7.80274	−	2.09074i	0.953256	−	0.255424i	0.701743	+	0.712430i	$0.252405\pi$
$68$	−1.60020	+	5.97203i	−0.194053	+	0.724215i
$69$	−6.34373	+	3.66256i	−0.763696	+	0.440920i
$70$	4.30752	−	16.1677i	0.514848	−	1.93241i
$71$	1.08550	−	1.88015i	0.128826	−	0.223132i	−0.794396	−	0.607400i	$-0.792213\pi$
$71$	1.08550	−	1.88015i	0.128826	−	0.223132i	0.923222	+	0.384267i	$0.125546\pi$
$72$	−9.73457	+	2.60837i	−1.14723	+	0.307399i
$73$	−3.40783	+	0.913126i	−0.398857	+	0.106873i	−0.452671	−	0.891678i	$-0.649529\pi$
$73$	−3.40783	+	0.913126i	−0.398857	+	0.106873i	0.0538143	+	0.998551i	$0.482862\pi$
$74$	−3.91058	−	6.77332i	−0.454595	−	0.787382i
$75$	−15.9125	−	4.21532i	−1.83741	−	0.486743i
$76$	3.08732	+	5.34740i	0.354140	+	0.613389i
$77$	7.79909	−	7.79909i	0.888788	−	0.888788i
$78$	11.0725	−	11.0725i	1.25371	−	1.25371i
$79$	2.13513	+	3.69815i	0.240221	+	0.416075i	0.960777	−	0.277322i	$-0.0894468\pi$
$79$	2.13513	+	3.69815i	0.240221	+	0.416075i	−0.720556	+	0.693396i	$0.756114\pi$
$80$	−3.85524	+	3.86621i	−0.431029	+	0.432255i
$81$	14.4666	+	25.0569i	1.60740	+	2.78409i
$82$	−4.12438	+	1.10512i	−0.455461	+	0.122040i
$83$	16.7926	−	4.49956i	1.84322	−	0.493891i	0.844119	−	0.536156i	$-0.180124\pi$
$83$	16.7926	−	4.49956i	1.84322	−	0.493891i	0.999106	+	0.0422658i	$0.0134576\pi$
$84$	14.9296	−	25.8589i	1.62896	−	2.82144i
$85$	−4.60208	+	2.66574i	−0.499166	+	0.289140i
$86$	−3.55153	+	2.05048i	−0.382972	+	0.221109i
$87$	−1.93321	+	7.21483i	−0.207262	+	0.773511i
$88$	3.92565	−	1.05187i	0.418476	−	0.112130i
$89$	10.1402			1.07486			0.537431	−	0.843308i	$-0.319395\pi$
$89$	10.1402			1.07486			0.537431	+	0.843308i	$0.319395\pi$
$90$	−32.5826	−	18.7499i	−3.43451	−	1.97642i
$91$			7.73771i			0.811133i
$92$	4.08966	−	4.08966i	0.426376	−	0.426376i
$93$	−14.0758	−	11.7423i	−1.45959	−	1.21762i
$94$			9.01316i			0.929637i
$95$	−1.36742	+	5.13243i	−0.140294	+	0.526576i
$96$	−22.2617	+	12.8528i	−2.27207	+	1.31178i
$97$	8.87120	+	8.87120i	0.900734	+	0.900734i	0.995500	−	0.0947656i	$-0.0302102\pi$
$97$	8.87120	+	8.87120i	0.900734	+	0.900734i	−0.0947656	+	0.995500i	$0.530210\pi$
$98$	2.87149	+	10.7165i	0.290064	+	1.08253i
$99$	−12.3905	−	21.4610i	−1.24529	−	2.15691i
$100$	12.9972	−	0.0369223i	1.29972	−	0.00369223i
$101$	−2.73864			−0.272505			−0.136252	−	0.990674i	$-0.543506\pi$
$101$	−2.73864			−0.272505			−0.136252	+	0.990674i	$0.543506\pi$
$102$	−16.2214	+	4.34650i	−1.60616	+	0.430368i
$103$	4.57705	+	17.0818i	0.450991	+	1.68312i	0.699615	+	0.714520i	$0.253355\pi$
$103$	4.57705	+	17.0818i	0.450991	+	1.68312i	−0.248625	+	0.968600i	$0.579979\pi$
$104$	−1.42558	+	2.46918i	−0.139790	+	0.242123i
$105$	24.8005	−	6.68304i	2.42028	−	0.652198i
$106$	2.41429	+	1.39389i	0.234497	+	0.135387i
$107$	0.0243170	−	0.0907522i	0.00235081	−	0.00877335i	−0.964740	−	0.263203i	$-0.915221\pi$
$107$	0.0243170	−	0.0907522i	0.00235081	−	0.00877335i	0.967091	+	0.254430i	$0.0818877\pi$
$108$	−29.2833	−	29.2833i	−2.81779	−	2.81779i
$109$			10.4443i			1.00038i	0.865915	+	0.500191i	$0.166737\pi$
$109$			10.4443i			1.00038i	−0.865915	+	0.500191i	$0.833263\pi$
$110$	13.1396	+	7.56127i	1.25281	+	0.720939i
$111$	6.00319	−	10.3978i	0.569798	−	0.986919i
$112$	2.20494	−	8.22896i	0.208348	−	0.777564i
$113$	4.12491	+	15.3944i	0.388039	+	1.44818i	0.833320	+	0.552791i	$0.186437\pi$
$113$	4.12491	+	15.3944i	0.388039	+	1.44818i	−0.445280	+	0.895391i	$0.646896\pi$
$114$	−8.38586	+	14.5247i	−0.785408	+	1.36037i
$115$	4.97512	−	0.00706661i	0.463933	−	0.000658964i
$116$		−	5.89753i		−	0.547572i
$117$	16.7925	+	4.49954i	1.55247	+	0.415983i
$118$	−2.93483	−	0.786385i	−0.270173	−	0.0723926i
$119$	4.14923	−	7.18668i	0.380359	−	0.658802i
$120$	9.14534	+	2.43657i	0.834851	+	0.222427i
$121$	−0.503297	−	0.871736i	−0.0457543	−	0.0792488i
$122$	8.66107	−	8.66107i	0.784136	−	0.784136i
$123$	−4.63491	−	4.63491i	−0.417916	−	0.417916i
$124$	13.1346	+	6.07893i	1.17953	+	0.545904i
$125$	7.93931	+	7.87194i	0.710113	+	0.704087i
$126$	58.6566			5.22555
$127$	−15.0108	−	4.02213i	−1.33199	−	0.356906i	−0.478534	−	0.878069i	$-0.658832\pi$
$127$	−15.0108	−	4.02213i	−1.33199	−	0.356906i	−0.853457	+	0.521163i	$0.825498\pi$
$128$	6.94587	−	6.94587i	0.613934	−	0.613934i
$129$	−5.45202	−	3.14773i	−0.480024	−	0.277142i
$130$	−10.2690	+	2.76720i	−0.900648	+	0.242700i
$131$	−5.06937	−	8.78040i	−0.442913	−	0.767147i	0.554992	−	0.831856i	$-0.312721\pi$
$131$	−5.06937	−	8.78040i	−0.442913	−	0.767147i	−0.997904	+	0.0647088i	$0.979388\pi$
$132$	19.1302	+	19.1302i	1.66507	+	1.66507i
$133$	−2.14500	−	8.00525i	−0.185995	−	0.694144i
$134$	−15.0033	−	8.66217i	−1.29609	−	0.748297i
$135$	−0.0505992	−	35.6235i	−0.00435489	−	3.06598i
$136$	2.64812	−	1.52889i	0.227074	−	0.131101i
$137$	−4.69186	−	17.5103i	−0.400853	−	1.49600i	−0.811579	−	0.584243i	$-0.801391\pi$
$137$	−4.69186	−	17.5103i	−0.400853	−	1.49600i	0.410726	−	0.911759i	$-0.365275\pi$
$138$	15.1744	+	4.06597i	1.29173	+	0.346118i
$139$	6.58472			0.558509			0.279254	−	0.960217i	$-0.409913\pi$
$139$	6.58472			0.558509			0.279254	+	0.960217i	$0.409913\pi$
$140$	−17.5486	+	10.1650i	−1.48313	+	0.859097i
$141$	−11.9826	+	6.91813i	−1.00911	+	0.582612i
$142$	−4.49737	+	1.20507i	−0.377411	+	0.101127i
$143$	−6.77191	−	1.81453i	−0.566296	−	0.151738i
$144$	−16.5764	−	9.57042i	−1.38137	−	0.797535i
$145$	3.58212	−	3.59231i	0.297479	−	0.298325i
$146$	6.55267	+	3.78319i	0.542303	+	0.313099i
$147$	−12.0431	+	12.0431i	−0.993297	+	0.993297i
$148$	−2.45356	+	9.15680i	−0.201681	+	0.752684i
$149$	9.30735	−	5.37360i	0.762488	−	0.440222i	−0.0677006	−	0.997706i	$-0.521566\pi$
$149$	9.30735	−	5.37360i	0.762488	−	0.440222i	0.830188	+	0.557483i	$0.188233\pi$
$150$	17.7386	+	30.5235i	1.44835	+	2.49223i
$151$			9.14787i			0.744443i	0.928144	+	0.372222i	$0.121404\pi$
$151$			9.14787i			0.744443i	−0.928144	+	0.372222i	$0.878596\pi$
$152$	0.790381	−	2.94974i	0.0641084	−	0.239256i
$153$	−13.1839	−	13.1839i	−1.06585	−	1.06585i
$154$	−23.6544			−1.90613
$155$	4.30829	+	11.6807i	0.346050	+	0.938216i
$156$	−18.9797			−1.51959
$157$	5.74150	+	5.74150i	0.458222	+	0.458222i	0.898071	−	0.439850i	$-0.144968\pi$
$157$	5.74150	+	5.74150i	0.458222	+	0.458222i	−0.439850	+	0.898071i	$0.644968\pi$
$158$	2.37030	−	8.84608i	0.188571	−	0.703757i
$159$			4.27958i			0.339393i
$160$	17.4589	−	0.0247984i	1.38025	−	0.00196049i
$161$	−6.72283	+	3.88143i	−0.529833	+	0.305899i
$162$	16.0600	−	59.9367i	1.26179	−	4.70907i
$163$	9.87710	−	9.87710i	0.773634	−	0.773634i	−0.205106	−	0.978740i	$-0.565754\pi$
$163$	9.87710	−	9.87710i	0.773634	−	0.773634i	0.978740	+	0.205106i	$0.0657539\pi$
$164$	4.48203	+	2.58770i	0.349987	+	0.202065i
$165$	0.0330555	+	23.2721i	0.00257336	+	1.81173i
$166$	−32.2892	−	18.6422i	−2.50613	−	1.44691i
$167$	−14.7632	−	3.95578i	−1.14241	−	0.306107i	−0.362489	−	0.931988i	$-0.618073\pi$
$167$	−14.7632	−	3.95578i	−1.14241	−	0.306107i	−0.779919	+	0.625881i	$0.784740\pi$
$168$	−14.2643	+	3.82212i	−1.10052	+	0.294883i
$169$	−6.99890	+	4.04081i	−0.538377	+	0.310832i
$170$	11.0215	+	2.93644i	0.845314	+	0.225215i
$171$	−18.6205			−1.42394
$172$	4.80130	+	1.28650i	0.366095	+	0.0980950i
$173$	−4.29839	−	16.0418i	−0.326800	−	1.21964i	−0.912490	−	0.409100i	$-0.865843\pi$
$173$	−4.29839	−	16.0418i	−0.326800	−	1.21964i	0.585689	−	0.810536i	$-0.300824\pi$
$174$	13.8729	−	8.00951i	1.05170	−	0.607199i
$175$	−16.8634	−	4.46722i	−1.27475	−	0.337690i
$176$	6.68477	+	3.85945i	0.503884	+	0.290917i
$177$	−1.20719	−	4.50531i	−0.0907382	−	0.338640i
$178$	−15.3775	−	15.3775i	−1.15259	−	1.15259i
$179$	9.72573	+	16.8455i	0.726935	+	1.25909i	0.958173	+	0.286191i	$0.0923891\pi$
$179$	9.72573	+	16.8455i	0.726935	+	1.25909i	−0.231238	+	0.972897i	$0.574278\pi$
$180$	11.8555	+	43.9954i	0.883659	+	3.27922i
$181$	10.3202	+	5.95835i	0.767092	+	0.442881i	0.831836	−	0.555021i	$-0.187290\pi$
$181$	10.3202	+	5.95835i	0.767092	+	0.442881i	−0.0647444	+	0.997902i	$0.520623\pi$
$182$	11.7341	−	11.7341i	0.869792	−	0.869792i
$183$	18.1623	+	4.86659i	1.34260	+	0.359748i
$184$	−2.86042			−0.210873
$185$	−7.05629	+	4.08732i	−0.518789	+	0.300506i
$186$	3.53874	+	39.1528i	0.259473	+	2.87082i
$187$	5.31664	+	5.31664i	0.388791	+	0.388791i
$188$	7.72488	−	7.72488i	0.563395	−	0.563395i
$189$	27.7923	+	48.1377i	2.02159	+	3.50150i
$190$	9.85693	−	5.70958i	0.715097	−	0.414217i
$191$	−8.72140	+	15.1059i	−0.631058	+	1.09303i	0.356277	+	0.934380i	$0.384046\pi$
$191$	−8.72140	+	15.1059i	−0.631058	+	1.09303i	−0.987336	+	0.158645i	$0.949288\pi$
$192$	37.7207	+	10.1072i	2.72226	+	0.729427i
$193$	−24.2765	−	6.50486i	−1.74746	−	0.468230i	−0.763379	−	0.645951i	$-0.776461\pi$
$193$	−24.2765	−	6.50486i	−1.74746	−	0.468230i	−0.984081	+	0.177721i	$0.943128\pi$
$194$		−	26.9061i		−	1.93175i
$195$	−11.5609	−	11.5281i	−0.827893	−	0.825545i
$196$	6.72373	−	11.6458i	0.480266	−	0.831846i
$197$	6.15659	+	22.9767i	0.438639	+	1.63702i	0.732205	+	0.681084i	$0.238491\pi$
$197$	6.15659	+	22.9767i	0.438639	+	1.63702i	−0.293566	+	0.955939i	$0.594842\pi$
$198$	−13.7552	+	51.3352i	−0.977542	+	3.64824i
$199$	8.29048	−	14.3595i	0.587697	−	1.01792i	−0.406836	−	0.913501i	$-0.633368\pi$
$199$	8.29048	−	14.3595i	0.587697	−	1.01792i	0.994533	−	0.104420i	$-0.0332985\pi$
$200$	−4.55823	−	4.53241i	−0.322316	−	0.320490i
$201$		−	26.5949i		−	1.87586i
$202$	4.15310	+	4.15310i	0.292211	+	0.292211i
$203$	−2.04874	+	7.64598i	−0.143793	+	0.536643i
$204$	17.6280	+	10.1775i	1.23421	+	0.712571i
$205$	1.15835	+	4.29857i	0.0809023	+	0.300225i
$206$	18.9633	−	32.8453i	1.32123	−	2.28844i
$207$	4.51416	+	16.8471i	0.313756	+	1.17095i
$208$	−5.23062	+	1.40154i	−0.362679	+	0.0971794i
$209$	7.50907			0.519413
$210$	−47.7443	−	27.4748i	−3.29467	−	1.89594i
$211$	−3.47162	−	6.01302i	−0.238996	−	0.413954i	0.721430	−	0.692487i	$-0.243485\pi$
$211$	−3.47162	−	6.01302i	−0.238996	−	0.413954i	−0.960427	+	0.278533i	$0.910152\pi$
$212$	−0.874550	−	3.26387i	−0.0600644	−	0.224163i
$213$	−5.05407	−	5.05407i	−0.346299	−	0.346299i
$214$	−0.174501	+	0.100748i	−0.0119286	+	0.00688700i
$215$	2.14316	+	3.69991i	0.146162	+	0.252332i
$216$			20.4816i			1.39359i
$217$	−14.9170	−	12.4440i	−1.01263	−	0.844753i
$218$	15.8386	−	15.8386i	1.07273	−	1.07273i
$219$			11.6153i			0.784887i
$220$	−4.78097	−	17.7420i	−0.322333	−	1.19616i
$221$	−5.27480			−0.354822
$222$	−24.8719	+	6.66441i	−1.66929	+	0.447286i
$223$	−5.71846	+	21.3416i	−0.382936	+	1.42914i	0.458458	+	0.888716i	$0.348402\pi$
$223$	−5.71846	+	21.3416i	−0.382936	+	1.42914i	−0.841394	+	0.540422i	$0.818265\pi$
$224$	−23.5920	+	13.6209i	−1.57631	+	0.910082i
$225$	−19.5010	+	33.9995i	−1.30007	+	2.26663i
$226$	17.0900	−	29.6007i	1.13681	−	1.96901i
$227$	−23.4122	+	6.27329i	−1.55392	+	0.416373i	−0.930734	−	0.365697i	$-0.880831\pi$
$227$	−23.4122	+	6.27329i	−1.55392	+	0.416373i	−0.623191	+	0.782070i	$0.714164\pi$
$228$	19.6359	−	5.26142i	1.30042	−	0.348446i
$229$	−8.32847	−	14.4253i	−0.550361	−	0.953253i	−0.998248	−	0.0591633i	$-0.981157\pi$
$229$	−8.32847	−	14.4253i	−0.550361	−	0.953253i	0.447887	−	0.894090i	$-0.352177\pi$
$230$	−7.55542	−	7.53399i	−0.498190	−	0.496776i
$231$	−18.1562	−	31.4474i	−1.19459	−	2.06909i
$232$	−2.06245	+	2.06245i	−0.135407	+	0.135407i
$233$	4.66612	−	4.66612i	0.305687	−	0.305687i	−0.537547	−	0.843234i	$-0.680649\pi$
$233$	4.66612	−	4.66612i	0.305687	−	0.305687i	0.843234	+	0.537547i	$0.180649\pi$
$234$	−18.6421	−	32.2891i	−1.21867	−	2.11081i
$235$	9.39742	−	0.0133480i	0.613020	−	0.000870726i
$236$	1.84136	+	3.18933i	0.119862	+	0.207607i
$237$	13.5798	−	3.63869i	0.882102	−	0.236358i
$238$	−17.1907	+	4.60625i	−1.11431	+	0.298579i
$239$	−6.51760	+	11.2888i	−0.421588	+	0.730213i	−0.996095	−	0.0882873i	$-0.971861\pi$
$239$	−6.51760	+	11.2888i	−0.421588	+	0.730213i	0.574507	+	0.818500i	$0.305194\pi$
$240$	9.00981	+	15.5544i	0.581581	+	1.00403i
$241$	19.8611	−	11.4668i	1.27936	−	0.738642i	0.302633	−	0.953107i	$-0.402134\pi$
$241$	19.8611	−	11.4668i	1.27936	−	0.738642i	0.976732	+	0.214466i	$0.0688010\pi$
$242$	−0.558733	+	2.08522i	−0.0359167	+	0.134043i
$243$	45.8444	−	12.2840i	2.94092	−	0.788018i
$244$	−14.8462			−0.950432
$245$	11.1692	−	3.00978i	0.713572	−	0.192288i
$246$			14.0575i			0.896276i
$247$	−3.72499	+	3.72499i	−0.237015	+	0.237015i
$248$	−2.46749	−	6.71927i	−0.156686	−	0.426674i
$249$		−	57.2359i		−	3.62718i
$250$	−0.102173	−	23.9775i	−0.00646197	−	1.51647i
$251$	−3.62281	+	2.09163i	−0.228670	+	0.132023i	−0.609958	−	0.792434i	$-0.708814\pi$
$251$	−3.62281	+	2.09163i	−0.228670	+	0.132023i	0.381288	+	0.924456i	$0.375480\pi$
$252$	−50.2726	−	50.2726i	−3.16688	−	3.16688i
$253$	−1.82042	−	6.79391i	−0.114449	−	0.427130i
$254$	16.6641	+	28.8631i	1.04560	+	1.81103i
$255$	4.55583	+	16.9065i	0.285297	+	1.05873i
$256$	2.65647			0.166029
$257$	14.2029	−	3.80565i	0.885951	−	0.237390i	0.212978	−	0.977057i	$-0.431684\pi$
$257$	14.2029	−	3.80565i	0.885951	−	0.237390i	0.672973	+	0.739667i	$0.265017\pi$
$258$	3.49443	+	13.0414i	0.217554	+	0.811922i
$259$	6.36194	−	11.0192i	0.395312	−	0.684700i
$260$	11.1729	+	6.42951i	0.692911	+	0.398741i
$261$	15.4021	+	8.89241i	0.953366	+	0.550426i
$262$	−5.62773	+	21.0030i	−0.347682	+	1.29757i
$263$	−10.5051	−	10.5051i	−0.647771	−	0.647771i	0.304683	−	0.952454i	$-0.401450\pi$
$263$	−10.5051	−	10.5051i	−0.647771	−	0.647771i	−0.952454	+	0.304683i	$0.901450\pi$
$264$		−	13.3802i		−	0.823495i
$265$	1.44974	−	2.51928i	0.0890570	−	0.154758i
$266$	−8.88699	+	15.3927i	−0.544896	+	0.943788i
$267$	8.64050	−	32.2468i	0.528790	−	1.97347i
$268$	5.43478	+	20.2829i	0.331982	+	1.23897i
$269$	3.49959	−	6.06147i	0.213374	−	0.369574i	−0.739394	−	0.673273i	$-0.764888\pi$
$269$	3.49959	−	6.06147i	0.213374	−	0.369574i	0.952768	+	0.303698i	$0.0982214\pi$
$270$	−53.9458	+	54.0993i	−3.28304	+	3.29238i
$271$		−	4.25678i		−	0.258581i	−0.991607	−	0.129290i	$-0.958730\pi$
$271$		−	4.25678i		−	0.258581i	0.991607	−	0.129290i	$-0.0412700\pi$
$272$	5.60969	+	1.50311i	0.340137	+	0.0911395i
$273$	24.6066	+	6.59332i	1.48926	+	0.399046i
$274$	−19.4389	+	33.6692i	−1.17435	+	2.03403i
$275$	7.86417	−	13.7109i	0.474227	−	0.826801i
$276$	−9.52066	−	16.4903i	−0.573076	−	0.992597i
$277$	−10.3362	+	10.3362i	−0.621040	+	0.621040i	−0.945797	−	0.324758i	$-0.894717\pi$
$277$	−10.3362	+	10.3362i	−0.621040	+	0.621040i	0.324758	+	0.945797i	$0.394717\pi$
$278$	−9.98563	−	9.98563i	−0.598899	−	0.598899i
$279$	−35.6805	+	25.1368i	−2.13614	+	1.50490i
$280$	9.69185	+	2.58217i	0.579199	+	0.154314i
$281$	−12.8965			−0.769340			−0.384670	−	0.923054i	$-0.625685\pi$
$281$	−12.8965			−0.769340			−0.384670	+	0.923054i	$0.625685\pi$
$282$	28.6626	+	7.68013i	1.70683	+	0.457345i
$283$	−21.8798	+	21.8798i	−1.30062	+	1.30062i	−0.372649	+	0.927972i	$0.621550\pi$
$283$	−21.8798	+	21.8798i	−1.30062	+	1.30062i	−0.927972	+	0.372649i	$0.878450\pi$
$284$	4.88736	+	2.82172i	0.290012	+	0.167438i
$285$	15.1564	+	8.72186i	0.897786	+	0.516638i
$286$	7.51780	+	13.0212i	0.444537	+	0.769960i
$287$	−4.91189	−	4.91189i	−0.289939	−	0.289939i
$288$	15.8413	+	59.1205i	0.933457	+	3.48371i
$289$	−9.82327	−	5.67147i	−0.577839	−	0.333616i
$290$	−10.8799	+	0.0154537i	−0.638890	+	0.000907472i
$291$	35.7703	−	20.6520i	2.09689	−	1.21064i
$292$	−2.37363	−	8.85851i	−0.138906	−	0.518405i
$293$	12.8163	+	3.43411i	0.748734	+	0.200623i	0.612956	−	0.790117i	$-0.289980\pi$
$293$	12.8163	+	3.43411i	0.748734	+	0.200623i	0.135778	+	0.990739i	$0.456647\pi$
$294$	36.5263			2.13026
$295$	−0.815564	+	3.06111i	−0.0474840	+	0.178225i
$296$	4.06031	−	2.34422i	0.236001	−	0.136255i
$297$	−48.6466	+	13.0348i	−2.82276	+	0.756357i
$298$	−22.2634	−	5.96547i	−1.28969	−	0.345570i
$299$	4.27327	+	2.46718i	0.247130	+	0.142680i
$300$	10.9575	−	41.3638i	0.632634	−	2.38814i
$301$	−5.77783	−	3.33583i	−0.333029	−	0.192274i
$302$	13.8726	−	13.8726i	0.798279	−	0.798279i
$303$	−2.33360	+	8.70910i	−0.134062	+	0.500325i
$304$	5.02295	−	2.90000i	0.288086	−	0.166327i
$305$	−9.04314	−	9.01749i	−0.517809	−	0.516340i
$306$			39.9862i			2.28586i
$307$	−2.64371	+	9.86647i	−0.150885	+	0.563109i	0.848538	+	0.529134i	$0.177483\pi$
$307$	−2.64371	+	9.86647i	−0.150885	+	0.563109i	−0.999423	+	0.0339749i	$0.989183\pi$
$308$	20.2734	+	20.2734i	1.15518	+	1.15518i
$309$	58.2217			3.31212
$310$	11.1801	−	24.2471i	0.634990	−	1.37714i
$311$	−5.69962			−0.323196			−0.161598	−	0.986857i	$-0.551665\pi$
$311$	−5.69962			−0.323196			−0.161598	+	0.986857i	$0.551665\pi$
$312$	6.63746	+	6.63746i	0.375772	+	0.375772i
$313$	2.01857	−	7.53341i	0.114096	−	0.425813i	−0.885121	−	0.465360i	$-0.845925\pi$
$313$	2.01857	−	7.53341i	0.114096	−	0.425813i	0.999218	+	0.0395469i	$0.0125915\pi$
$314$		−	17.4138i		−	0.982718i
$315$	−0.0868671	−	61.1573i	−0.00489441	−	3.44582i
$316$	−9.61318	+	5.55017i	−0.540784	+	0.312222i
$317$	−3.72893	+	13.9165i	−0.209437	+	0.781631i	0.778614	+	0.627504i	$0.215923\pi$
$317$	−3.72893	+	13.9165i	−0.209437	+	0.781631i	−0.988051	+	0.154127i	$0.950743\pi$
$318$	6.48992	−	6.48992i	0.363937	−	0.363937i
$319$	−6.21119	−	3.58603i	−0.347760	−	0.200779i
$320$	−18.7814	−	18.7281i	−1.04991	−	1.04693i
$321$	−0.267879	−	0.154660i	−0.0149516	−	0.00863229i
$322$	16.0812	+	4.30894i	0.896170	+	0.240128i
$323$	5.45718	−	1.46225i	0.303646	−	0.0813617i
$324$	−65.1342	+	37.6052i	−3.61857	+	2.08918i
$325$	2.90038	+	10.7027i	0.160884	+	0.593677i
$326$	−29.9569			−1.65916
$327$	33.2138	+	8.89960i	1.83673	+	0.492149i
$328$	−0.662473	−	2.47238i	−0.0365790	−	0.136515i
$329$	−12.6986	+	7.33155i	−0.700098	+	0.404202i
$330$	35.2417	−	35.3420i	1.93999	−	1.94551i
$331$	28.6558	+	16.5444i	1.57507	+	0.909364i	0.995533	+	0.0944152i	$0.0300981\pi$
$331$	28.6558	+	16.5444i	1.57507	+	0.909364i	0.579532	+	0.814949i	$0.303235\pi$
$332$	11.6964	+	43.6516i	0.641924	+	2.39569i
$333$	−20.2146	−	20.2146i	−1.10775	−	1.10775i
$334$	16.3892	+	28.3870i	0.896779	+	1.55327i
$335$	−9.00924	+	15.6558i	−0.492227	+	0.855366i
$336$	−24.2900	−	14.0238i	−1.32513	−	0.765062i
$337$	−15.8086	+	15.8086i	−0.861147	+	0.861147i	−0.991471	−	0.130325i	$-0.958398\pi$
$337$	−15.8086	+	15.8086i	−0.861147	+	0.861147i	0.130325	+	0.991471i	$0.458398\pi$
$338$	16.7416	+	4.48589i	0.910621	+	0.244000i
$339$	52.4703			2.84980
$340$	−6.92947	−	11.9629i	−0.375803	−	0.648780i
$341$	14.3889	−	10.1369i	0.779200	−	0.548943i
$342$	28.2377	+	28.2377i	1.52692	+	1.52692i
$343$	4.50695	−	4.50695i	0.243352	−	0.243352i
$344$	−1.22917	−	2.12899i	−0.0662726	−	0.114787i
$345$	4.21684	−	15.8273i	0.227027	−	0.852115i
$346$	−17.8087	+	30.8456i	−0.957403	+	1.65827i
$347$	−6.78452	−	1.81791i	−0.364212	−	0.0975903i	0.0720718	−	0.997399i	$-0.477039\pi$
$347$	−6.78452	−	1.81791i	−0.364212	−	0.0975903i	−0.436284	+	0.899809i	$0.643706\pi$
$348$	−18.7546	−	5.02529i	−1.00535	−	0.269384i
$349$		−	11.4291i		−	0.611788i	−0.952066	−	0.305894i	$-0.901045\pi$
$349$		−	11.4291i		−	0.611788i	0.952066	−	0.305894i	$-0.0989553\pi$
$350$	18.7986	+	32.3475i	1.00483	+	1.72905i
$351$	17.6658	−	30.5980i	0.942930	−	1.63320i
$352$	−6.38830	−	23.8415i	−0.340498	−	1.27075i
$353$	0.839974	−	3.13483i	0.0447073	−	0.166850i	−0.939963	−	0.341277i	$-0.889141\pi$
$353$	0.839974	−	3.13483i	0.0447073	−	0.166850i	0.984670	+	0.174427i	$0.0558073\pi$
$354$	−5.00154	+	8.66292i	−0.265829	+	0.460429i
$355$	1.26310	+	4.68732i	0.0670384	+	0.248777i
$356$			26.3591i			1.39703i
$357$	−19.3187	−	19.3187i	−1.02245	−	1.02245i
$358$	10.7970	−	40.2948i	0.570637	−	2.12965i
$359$	−20.6059	−	11.8968i	−1.08754	−	0.627891i	−0.154619	−	0.987974i	$-0.549415\pi$
$359$	−20.6059	−	11.8968i	−1.08754	−	0.627891i	−0.932920	+	0.360083i	$0.882748\pi$
$360$	11.2398	−	19.5319i	0.592388	−	1.02942i
$361$	−6.67883	+	11.5681i	−0.351518	+	0.608846i
$362$	−6.61463	−	24.6861i	−0.347657	−	1.29747i
$363$	−3.20106	+	0.857720i	−0.168012	+	0.0450186i
$364$	−20.1139			−1.05425
$365$	3.93477	−	6.83763i	0.205955	−	0.357898i
$366$	−20.1628	−	34.9230i	−1.05393	−	1.82546i
$367$	6.96869	+	26.0075i	0.363762	+	1.35758i	0.869091	+	0.494653i	$0.164705\pi$
$367$	6.96869	+	26.0075i	0.363762	+	1.35758i	−0.505328	+	0.862927i	$0.668629\pi$
$368$	−3.84152	−	3.84152i	−0.200253	−	0.200253i
$369$	−13.5162	+	7.80356i	−0.703623	+	0.406237i
$370$	16.8991	+	4.50239i	0.878544	+	0.234068i
$371$			4.53532i			0.235462i
$372$	30.5236	−	36.5894i	1.58257	−	1.89707i
$373$	−6.23018	+	6.23018i	−0.322587	+	0.322587i	−0.849759	−	0.527172i	$-0.823252\pi$
$373$	−6.23018	+	6.23018i	−0.322587	+	0.322587i	0.527172	+	0.849759i	$0.323252\pi$
$374$		−	16.1252i		−	0.833815i
$375$	31.7985	−	18.5400i	1.64207	−	0.957401i
$376$	−5.40300			−0.278639
$377$	4.86006	−	1.30225i	0.250306	−	0.0670693i
$378$	30.8535	−	115.147i	1.58693	−	5.92251i
$379$	29.0795	−	16.7891i	1.49372	−	0.862397i	0.493741	−	0.869609i	$-0.335629\pi$
$379$	29.0795	−	16.7891i	1.49372	−	0.862397i	0.999974	+	0.00721222i	$0.00229574\pi$
$380$	−13.3415	−	3.55455i	−0.684406	−	0.182344i
$381$	−25.5814	+	44.3083i	−1.31058	+	2.26998i
$382$	36.1338	−	9.68201i	1.84876	−	0.495375i
$383$	20.5469	−	5.50552i	1.04990	−	0.281319i	0.307687	−	0.951487i	$-0.400445\pi$
$383$	20.5469	−	5.50552i	1.04990	−	0.281319i	0.742209	+	0.670169i	$0.233778\pi$
$384$	−16.1699	−	28.0070i	−0.825165	−	1.42923i
$385$	0.0350308	+	24.6629i	0.00178534	+	1.25694i
$386$	26.9504	+	46.6795i	1.37174	+	2.37592i
$387$	−10.5993	+	10.5993i	−0.538795	+	0.538795i
$388$	−23.0603	+	23.0603i	−1.17071	+	1.17071i
$389$	0.808511	+	1.40038i	0.0409931	+	0.0710022i	0.885794	−	0.464079i	$-0.153614\pi$
$389$	0.808511	+	1.40038i	0.0409931	+	0.0710022i	−0.844801	+	0.535081i	$0.820281\pi$
$390$	0.0497337	+	35.0141i	0.00251836	+	1.77301i
$391$	−2.64597	−	4.58295i	−0.133812	−	0.231770i
$392$	−6.42410	+	1.72133i	−0.324466	+	0.0869405i
$393$	−32.2420	+	8.63923i	−1.62640	+	0.435791i
$394$	25.5075	−	44.1802i	1.28505	−	2.22577i
$395$	−9.22673	−	2.45825i	−0.464247	−	0.123688i
$396$	55.7868	−	32.2085i	2.80339	−	1.61854i
$397$	6.04529	−	22.5613i	0.303404	−	1.13232i	−0.630906	−	0.775859i	$-0.717317\pi$
$397$	6.04529	−	22.5613i	0.303404	−	1.13232i	0.934310	−	0.356461i	$-0.116017\pi$
$398$	−34.3484	+	9.20363i	−1.72173	+	0.461337i
$399$	−27.2851			−1.36597
$400$	−0.0346821	−	12.2086i	−0.00173410	−	0.610432i
$401$		−	18.3291i		−	0.915313i	−0.889129	−	0.457656i	$-0.848689\pi$
$401$		−	18.3291i		−	0.915313i	0.889129	−	0.457656i	$-0.151311\pi$
$402$	−40.3308	+	40.3308i	−2.01152	+	2.01152i
$403$	−2.10925	+	12.1664i	−0.105069	+	0.606050i
$404$		−	7.11897i		−	0.354182i
$405$	−62.5158	−	16.6559i	−3.10643	−	0.827639i
$406$	14.7019	−	8.48815i	0.729643	−	0.421260i
$407$	8.15191	+	8.15191i	0.404075	+	0.404075i
$408$	−2.60554	−	9.72401i	−0.128993	−	0.481410i
$409$	7.15772	+	12.3975i	0.353927	+	0.613019i	0.986934	−	0.161127i	$-0.0515129\pi$
$409$	7.15772	+	12.3975i	0.353927	+	0.613019i	−0.633007	+	0.774146i	$0.718180\pi$
$410$	4.76211	−	8.27534i	0.235184	−	0.408690i
$411$	−59.6820			−2.94390
$412$	−44.4034	+	11.8979i	−2.18760	+	0.586165i
$413$	−1.27933	−	4.77454i	−0.0629519	−	0.234940i
$414$	18.7027	−	32.3940i	0.919188	−	1.59208i
$415$	−19.3891	+	33.6934i	−0.951775	+	1.65394i
$416$	14.9959	+	8.65791i	0.735236	+	0.424489i
$417$	5.61085	−	20.9400i	0.274764	−	1.02543i
$418$	−11.3874	−	11.3874i	−0.556976	−	0.556976i
$419$			17.9605i			0.877429i	0.898627	+	0.438714i	$0.144566\pi$
$419$			17.9605i			0.877429i	−0.898627	+	0.438714i	$0.855434\pi$
$420$	17.3723	+	64.4678i	0.847680	+	3.14570i
$421$	3.18350	−	5.51398i	0.155154	−	0.268735i	−0.777961	−	0.628313i	$-0.783746\pi$
$421$	3.18350	−	5.51398i	0.155154	−	0.268735i	0.933115	+	0.359578i	$0.117079\pi$
$422$	−3.85400	+	14.3833i	−0.187610	+	0.700169i
$423$	8.52672	+	31.8221i	0.414583	+	1.54725i
$424$	−0.835578	+	1.44726i	−0.0405793	+	0.0702853i
$425$	3.04531	−	11.4958i	0.147719	−	0.557627i
$426$			15.3288i			0.742685i
$427$	19.2477	+	5.15741i	0.931462	+	0.249584i
$428$	0.235907	+	0.0632110i	0.0114030	+	0.00305542i
$429$	−11.5407	+	19.9891i	−0.557191	+	0.965082i
$430$	2.36079	−	8.86092i	0.113848	−	0.427312i
$431$	−6.93886	−	12.0185i	−0.334233	−	0.578909i	0.649104	−	0.760700i	$-0.275144\pi$
$431$	−6.93886	−	12.0185i	−0.334233	−	0.578909i	−0.983337	+	0.181791i	$0.941811\pi$
$432$	−27.5066	+	27.5066i	−1.32341	+	1.32341i
$433$	−11.0732	−	11.0732i	−0.532144	−	0.532144i	0.389066	−	0.921210i	$-0.372798\pi$
$433$	−11.0732	−	11.0732i	−0.532144	−	0.532144i	−0.921210	+	0.389066i	$0.872798\pi$
$434$	3.75021	+	41.4925i	0.180016	+	1.99170i
$435$	−8.37152	−	14.4524i	−0.401384	−	0.692942i
$436$	−27.1495			−1.30023
$437$	−5.10496	−	1.36787i	−0.244203	−	0.0654341i
$438$	17.6144	−	17.6144i	0.841648	−	0.841648i
$439$	0.111541	+	0.0643985i	0.00532358	+	0.00307357i	0.502659	−	0.864485i	$-0.332355\pi$
$439$	0.111541	+	0.0643985i	0.00532358	+	0.00307357i	−0.497336	+	0.867558i	$0.665688\pi$
$440$	−4.53265	+	7.87660i	−0.216086	+	0.375502i
$441$	20.2763	+	35.1196i	0.965539	+	1.67236i
$442$	7.99916	+	7.99916i	0.380481	+	0.380481i
$443$	−2.41025	−	8.99518i	−0.114515	−	0.427374i	0.884736	−	0.466093i	$-0.154339\pi$
$443$	−2.41025	−	8.99518i	−0.114515	−	0.427374i	−0.999250	+	0.0387192i	$0.987672\pi$
$444$	27.0287	+	15.6050i	1.28273	+	0.740583i
$445$	−16.0103	+	16.0559i	−0.758962	+	0.761121i
$446$	41.0362	−	23.6922i	1.94312	−	1.12186i
$447$	−9.15770	−	34.1770i	−0.433144	−	1.61652i
$448$	39.9749	+	10.7112i	1.88863	+	0.506058i
$449$	−10.2251			−0.482553			−0.241277	−	0.970456i	$-0.577566\pi$
$449$	−10.2251			−0.482553			−0.241277	+	0.970456i	$0.577566\pi$
$450$	81.1328	−	21.9867i	3.82464	−	1.03646i
$451$	5.45065	−	3.14694i	0.256661	−	0.148183i
$452$	−40.0171	+	10.7225i	−1.88224	+	0.504346i
$453$	29.0910	+	7.79491i	1.36681	+	0.366237i
$454$	45.0177	+	25.9910i	2.11278	+	1.21982i
$455$	−12.2518	−	12.2170i	−0.574372	−	0.572742i
$456$	−8.70695	−	5.02696i	−0.407740	−	0.235409i
$457$	2.04136	−	2.04136i	0.0954909	−	0.0954909i	−0.657748	−	0.753238i	$-0.728491\pi$
$457$	2.04136	−	2.04136i	0.0954909	−	0.0954909i	0.753238	+	0.657748i	$0.228491\pi$
$458$	−9.24581	+	34.5058i	−0.432028	+	1.61235i
$459$	−32.8155	+	18.9460i	−1.53169	+	0.884324i
$460$	0.0183693	+	12.9326i	0.000856475	+	0.602987i
$461$		−	1.31351i		−	0.0611761i	−0.999532	−	0.0305881i	$-0.990262\pi$
$461$		−	1.31351i		−	0.0611761i	0.999532	−	0.0305881i	$-0.00973800\pi$
$462$	−20.1559	+	75.2230i	−0.937740	+	3.49969i
$463$	−4.13598	−	4.13598i	−0.192215	−	0.192215i	0.604437	−	0.796653i	$-0.293398\pi$
$463$	−4.13598	−	4.13598i	−0.192215	−	0.192215i	−0.796653	+	0.604437i	$0.793398\pi$
$464$	−5.53971			−0.257174
$465$	40.8167	−	3.74759i	1.89283	−	0.173790i
$466$	−14.1522			−0.655588
$467$	11.4248	+	11.4248i	0.528678	+	0.528678i	0.920178	−	0.391500i	$-0.128044\pi$
$467$	11.4248	+	11.4248i	0.528678	+	0.528678i	−0.391500	+	0.920178i	$0.628044\pi$
$468$	−11.6964	+	43.6515i	−0.540665	+	2.01779i
$469$		−	28.1842i		−	1.30142i
$470$	−14.2713	−	14.2308i	−0.658286	−	0.656418i
$471$	23.1508	−	13.3661i	1.06673	−	0.615879i
$472$	0.471404	−	1.75930i	0.0216981	−	0.0809785i
$473$	4.27439	−	4.27439i	0.196537	−	0.196537i
$474$	−26.1116	−	15.0755i	−1.19934	−	0.692442i
$475$	−5.96759	−	10.2687i	−0.273812	−	0.471160i
$476$	18.6815	+	10.7857i	0.856263	+	0.494364i
$477$	9.84264	+	2.63733i	0.450663	+	0.120755i
$478$	27.0032	−	7.23548i	1.23510	−	0.330943i
$479$	22.3558	−	12.9071i	1.02146	−	0.589741i	0.106935	−	0.994266i	$-0.465896\pi$
$479$	22.3558	−	12.9071i	1.02146	−	0.589741i	0.914527	+	0.404525i	$0.132563\pi$
$480$	14.7979	−	55.5419i	0.675428	−	2.53513i
$481$	−8.08776			−0.368770
$482$	−47.5083	−	12.7298i	−2.16394	−	0.579827i
$483$	6.61474	+	24.6865i	0.300981	+	1.12328i
$484$	2.26604	−	1.30830i	0.103002	−	0.0594681i
$485$	−28.0532	+	0.0398464i	−1.27383	+	0.00180933i
$486$	−88.1509	−	50.8939i	−3.99861	−	2.30860i
$487$	−2.48587	−	9.27738i	−0.112645	−	0.420398i	0.886455	−	0.462815i	$-0.153161\pi$
$487$	−2.48587	−	9.27738i	−0.112645	−	0.420398i	−0.999100	+	0.0424174i	$0.986494\pi$
$488$	5.19194	+	5.19194i	0.235028	+	0.235028i
$489$	−22.9937	−	39.8263i	−1.03981	−	1.80101i
$490$	−21.5022	−	12.3736i	−0.971369	−	0.558982i
$491$	0.674672	+	0.389522i	0.0304475	+	0.0175789i	0.515147	−	0.857102i	$-0.327738\pi$
$491$	0.674672	+	0.389522i	0.0304475	+	0.0175789i	−0.484699	+	0.874681i	$0.661071\pi$
$492$	12.0482	−	12.0482i	0.543177	−	0.543177i
$493$	−5.21227	−	1.39662i	−0.234749	−	0.0629008i
$494$	11.2978			0.508311
$495$	53.5442	+	14.2656i	2.40663	+	0.641192i
$496$	5.71010	−	12.3377i	0.256391	−	0.553980i
$497$	−5.35609	−	5.35609i	−0.240254	−	0.240254i
$498$	−86.7974	+	86.7974i	−3.88949	+	3.88949i
$499$	−1.23395	−	2.13726i	−0.0552392	−	0.0956771i	0.837084	−	0.547075i	$-0.184259\pi$
$499$	−1.23395	−	2.13726i	−0.0552392	−	0.0956771i	−0.892323	+	0.451398i	$0.850925\pi$
$500$	−20.4628	+	20.6379i	−0.915122	+	0.922955i
$501$	−25.1594	+	43.5774i	−1.12404	+	1.94689i
$502$	8.66587	+	2.32201i	0.386776	+	0.103636i
$503$	39.0086	+	10.4523i	1.73931	+	0.466046i	0.982293	−	0.187351i	$-0.0599902\pi$
$503$	39.0086	+	10.4523i	1.73931	+	0.466046i	0.757015	+	0.653397i	$0.226657\pi$
$504$			35.1621i			1.56624i
$505$	4.32401	−	4.33631i	0.192416	−	0.192963i
$506$	−7.54222	+	13.0635i	−0.335293	+	0.580744i
$507$	6.88637	+	25.7003i	0.305834	+	1.14139i
$508$	10.4553	−	39.0199i	0.463881	−	1.73123i
$509$	−20.7660	+	35.9678i	−0.920439	+	1.59425i	−0.121702	+	0.992567i	$0.538835\pi$
$509$	−20.7660	+	35.9678i	−0.920439	+	1.59425i	−0.798737	+	0.601680i	$0.794498\pi$
$510$	18.7296	−	32.5473i	0.829361	−	1.44122i
$511$			12.3094i			0.544535i
$512$	−17.9202	−	17.9202i	−0.791970	−	0.791970i
$513$	−9.79440	+	36.5532i	−0.432433	+	1.61386i
$514$	−27.3097	−	15.7672i	−1.20458	−	0.695463i
$515$	−34.2737	−	19.7231i	−1.51028	−	0.869103i
$516$	8.18238	−	14.1723i	0.360209	−	0.623901i
$517$	−3.43856	−	12.8329i	−0.151228	−	0.564390i
$518$	−26.3582	+	7.06267i	−1.15811	+	0.310316i
$519$	−54.6770			−2.40005
$520$	−1.65882	−	6.15580i	−0.0727440	−	0.269950i
$521$	0.934138	+	1.61797i	0.0409253	+	0.0708848i	0.885763	−	0.464139i	$-0.153636\pi$
$521$	0.934138	+	1.61797i	0.0409253	+	0.0708848i	−0.844837	+	0.535023i	$0.820303\pi$
$522$	−9.87186	−	36.8423i	−0.432079	−	1.61254i
$523$	19.7451	+	19.7451i	0.863393	+	0.863393i	0.991731	−	0.128338i	$-0.0409642\pi$
$523$	19.7451	+	19.7451i	0.863393	+	0.863393i	−0.128338	+	0.991731i	$0.540964\pi$
$524$	22.8243	−	13.1776i	0.997083	−	0.575666i
$525$	−28.5755	+	49.8204i	−1.24713	+	2.17434i
$526$			31.8616i			1.38923i
$527$	8.48308	−	10.1689i	0.369529	−	0.442964i
$528$	17.9695	−	17.9695i	0.782022	−	0.782022i
$529$		−	18.0496i		−	0.784766i
$530$	−6.01897	+	1.62195i	−0.261447	+	0.0704528i
$531$	−11.1057			−0.481948
$532$	20.8093	−	5.57584i	0.902198	−	0.241743i
$533$	−1.14279	+	4.26497i	−0.0494999	+	0.184736i
$534$	−62.0050	+	35.7986i	−2.68322	+	1.54916i
$535$	0.105302	+	0.181791i	0.00455259	+	0.00785951i
$536$	5.19259	−	8.99384i	0.224286	−	0.388475i
$537$	61.8573	−	16.5746i	2.66934	−	0.715247i
$538$	−14.4992	+	3.88505i	−0.625106	+	0.167497i
$539$	−8.17682	−	14.1627i	−0.352201	−	0.610029i
$540$	92.6018	−	0.131530i	3.98495	−	0.00566017i
$541$	−16.3319	−	28.2877i	−0.702165	−	1.21619i	−0.967705	−	0.252085i	$-0.918884\pi$
$541$	−16.3319	−	28.2877i	−0.702165	−	1.21619i	0.265540	−	0.964100i	$-0.414450\pi$
$542$	−6.45534	+	6.45534i	−0.277281	+	0.277281i
$543$	27.7419	−	27.7419i	1.19052	−	1.19052i
$544$	−9.28534	−	16.0827i	−0.398106	−	0.689540i
$545$	−16.5373	−	16.4904i	−0.708381	−	0.706372i
$546$	−27.3169	−	47.3142i	−1.16905	−	2.02486i
$547$	−25.7171	+	6.89089i	−1.09959	+	0.294633i	−0.762596	−	0.646875i	$-0.776075\pi$
$547$	−25.7171	+	6.89089i	−1.09959	+	0.294633i	−0.336990	+	0.941508i	$0.609409\pi$
$548$	45.5172	−	12.1963i	1.94440	−	0.520999i
$549$	22.3854	−	38.7727i	0.955386	−	1.65478i
$550$	−32.7183	+	8.86655i	−1.39511	+	0.378071i
$551$	−4.66710	+	2.69455i	−0.198825	+	0.114792i
$552$	−2.43737	+	9.09639i	−0.103741	+	0.387168i
$553$	14.3913	−	3.85614i	0.611980	−	0.163980i
$554$	31.3493			1.33190
$555$	6.98537	+	25.9224i	0.296512	+	1.10035i
$556$			17.1167i			0.725910i
$557$	25.3436	−	25.3436i	1.07384	−	1.07384i	0.0767940	−	0.997047i	$-0.475532\pi$
$557$	25.3436	−	25.3436i	1.07384	−	1.07384i	0.997047	−	0.0767940i	$-0.0244684\pi$
$558$	92.2285	+	15.9894i	3.90435	+	0.676887i
$559$			4.24075i			0.179365i
$560$	9.54823	+	16.4839i	0.403486	+	0.696572i
$561$	21.4377	−	12.3771i	0.905100	−	0.522560i
$562$	19.5573	+	19.5573i	0.824976	+	0.824976i
$563$	−2.35164	−	8.77645i	−0.0991100	−	0.369883i	0.898501	−	0.438972i	$-0.144657\pi$
$563$	−2.35164	−	8.77645i	−0.0991100	−	0.369883i	−0.997610	+	0.0690890i	$0.977991\pi$
$564$	−17.9834	−	31.1481i	−0.757237	−	1.31157i
$565$	−30.8880	−	17.7748i	−1.29947	−	0.747789i
$566$	66.3609			2.78936
$567$	97.5083	−	26.1273i	4.09496	−	1.09724i
$568$	−0.722385	−	2.69598i	−0.0303106	−	0.113121i
$569$	−13.3886	+	23.1898i	−0.561280	+	0.972166i	0.436105	+	0.899896i	$0.356358\pi$
$569$	−13.3886	+	23.1898i	−0.561280	+	0.972166i	−0.997385	+	0.0722701i	$0.976976\pi$
$570$	−9.75786	−	36.2110i	−0.408712	−	1.51671i
$571$	−5.08259	−	2.93443i	−0.212700	−	0.122802i	0.389866	−	0.920872i	$-0.372521\pi$
$571$	−5.08259	−	2.93443i	−0.212700	−	0.122802i	−0.602565	+	0.798069i	$0.705855\pi$
$572$	4.71679	−	17.6033i	0.197219	−	0.736030i
$573$	40.6066	+	40.6066i	1.69636	+	1.69636i
$574$			14.8976i			0.621814i
$575$	−7.84399	+	7.88868i	−0.327117	+	0.328981i
$576$	46.4914	−	80.5255i	1.93714	−	3.35523i
$577$	−4.38825	+	16.3772i	−0.182685	+	0.681790i	0.812429	+	0.583060i	$0.198145\pi$
$577$	−4.38825	+	16.3772i	−0.182685	+	0.681790i	−0.995114	+	0.0987302i	$0.968522\pi$
$578$	6.29615	+	23.4975i	0.261885	+	0.977369i
$579$	−41.3720	+	71.6585i	−1.71936	+	2.97803i
$580$	9.33805	+	9.31156i	0.387741	+	0.386641i
$581$		−	60.6563i		−	2.51645i
$582$	−85.5637	−	22.9267i	−3.54673	−	0.950343i
$583$	−3.96923	−	1.06355i	−0.164389	−	0.0440478i
$584$	−2.26786	+	3.92804i	−0.0938446	+	0.162544i
$585$	−33.6381	+	19.4847i	−1.39076	+	0.805594i
$586$	−14.2279	−	24.6434i	−0.587749	−	1.01801i
$587$	7.56157	−	7.56157i	0.312100	−	0.312100i	−0.533623	−	0.845722i	$-0.679170\pi$
$587$	7.56157	−	7.56157i	0.312100	−	0.312100i	0.845722	+	0.533623i	$0.179170\pi$
$588$	−31.3055	−	31.3055i	−1.29102	−	1.29102i
$589$	−1.19050	−	13.1717i	−0.0490538	−	0.542732i
$590$	5.87892	−	3.40534i	0.242031	−	0.140196i
$591$	78.3140			3.22141
$592$	8.60123	+	2.30469i	0.353508	+	0.0947222i
$593$	1.50511	−	1.50511i	0.0618076	−	0.0618076i	−0.675527	−	0.737335i	$-0.736084\pi$
$593$	1.50511	−	1.50511i	0.0618076	−	0.0618076i	0.737335	+	0.675527i	$0.236084\pi$
$594$	93.5390	+	54.0048i	3.83795	+	2.21584i
$595$	4.82808	+	17.9168i	0.197932	+	0.734518i
$596$	13.9684	+	24.1940i	0.572170	+	0.991027i
$597$	−38.6002	−	38.6002i	−1.57980	−	1.57980i
$598$	−2.73892	−	10.2218i	−0.112003	−	0.418000i
$599$	−6.33256	−	3.65611i	−0.258742	−	0.149384i	0.365019	−	0.931000i	$-0.381063\pi$
$599$	−6.33256	−	3.65611i	−0.258742	−	0.149384i	−0.623760	+	0.781616i	$0.714396\pi$
$600$	−18.2975	+	10.6335i	−0.746993	+	0.434111i
$601$	−19.3298	+	11.1601i	−0.788480	+	0.455229i	−0.839427	−	0.543472i	$-0.817109\pi$
$601$	−19.3298	+	11.1601i	−0.788480	+	0.455229i	0.0509474	+	0.998701i	$0.483776\pi$
$602$	3.70325	+	13.8207i	0.150933	+	0.563291i
$603$	−61.1658	−	16.3893i	−2.49086	−	0.667425i
$604$	−23.7795			−0.967574
$605$	2.17494	+	0.579465i	0.0884241	+	0.0235586i
$606$	16.7461	−	9.66836i	0.680263	−	0.392750i
$607$	6.94701	−	1.86145i	0.281970	−	0.0755537i	−0.115062	−	0.993358i	$-0.536707\pi$
$607$	6.94701	−	1.86145i	0.281970	−	0.0755537i	0.397032	+	0.917805i	$0.370040\pi$
$608$	−17.9145	−	4.80018i	−0.726530	−	0.194673i
$609$	22.5692	+	13.0303i	0.914548	+	0.528015i
$610$	0.0389025	+	27.3887i	0.00157512	+	1.10894i
$611$	8.07170	+	4.66020i	0.326546	+	0.188532i
$612$	34.2709	−	34.2709i	1.38532	−	1.38532i
$613$	2.76534	−	10.3204i	0.111691	−	0.416837i	−0.887327	−	0.461141i	$-0.847440\pi$
$613$	2.76534	−	10.3204i	0.111691	−	0.416837i	0.999018	+	0.0443040i	$0.0141070\pi$
$614$	18.9715	−	10.9532i	0.765628	−	0.442036i
$615$	14.6569	−	0.0208184i	0.591021	−	0.000839480i
$616$		−	14.1798i		−	0.571320i
$617$	−8.99710	+	33.5776i	−0.362210	+	1.35178i	0.508955	+	0.860793i	$0.330032\pi$
$617$	−8.99710	+	33.5776i	−0.362210	+	1.35178i	−0.871164	+	0.490992i	$0.836635\pi$
$618$	−88.2924	−	88.2924i	−3.55164	−	3.55164i
$619$	21.1960			0.851938			0.425969	−	0.904738i	$-0.359933\pi$
$619$	21.1960			0.851938			0.425969	+	0.904738i	$0.359933\pi$
$620$	−30.3635	+	11.1992i	−1.21943	+	0.449771i
$621$	35.4464			1.42241
$622$	8.64339	+	8.64339i	0.346568	+	0.346568i
$623$	9.15684	−	34.1738i	0.366861	−	1.36914i
$624$			17.8281i			0.713695i
$625$	−24.9996	+	0.142038i	−0.999984	+	0.00568152i
$626$	−14.4854	+	8.36317i	−0.578954	+	0.334259i
$627$	6.39849	−	23.8795i	0.255531	−	0.953654i
$628$	−14.9248	+	14.9248i	−0.595564	+	0.595564i
$629$	7.51179	+	4.33694i	0.299515	+	0.172925i
$630$	−92.6124	+	92.8759i	−3.68977	+	3.70026i
$631$	2.93300	+	1.69337i	0.116761	+	0.0674118i	0.557243	−	0.830349i	$-0.311859\pi$
$631$	2.93300	+	1.69337i	0.116761	+	0.0674118i	−0.440482	+	0.897761i	$0.645193\pi$
$632$	5.30284	+	1.42089i	0.210936	+	0.0565201i
$633$	−22.0801	+	5.91635i	−0.877605	+	0.235154i
$634$	26.7591	−	15.4494i	1.06274	−	0.613573i
$635$	30.0690	−	17.4173i	1.19325	−	0.691185i
$636$	−11.1246			−0.441118
$637$	11.0818	+	2.96937i	0.439079	+	0.117651i
$638$	3.98102	+	14.8574i	0.157610	+	0.588208i
$639$	−14.7385	+	8.50928i	−0.583046	+	0.336622i
$640$	0.0311984	+	21.9647i	0.00123323	+	0.868233i
$641$	−7.77706	−	4.49009i	−0.307175	−	0.177348i	0.338486	−	0.940971i	$-0.390085\pi$
$641$	−7.77706	−	4.49009i	−0.307175	−	0.177348i	−0.645662	+	0.763623i	$0.723418\pi$
$642$	0.171695	+	0.640775i	0.00677627	+	0.0252894i
$643$	13.5906	+	13.5906i	0.535961	+	0.535961i	0.922340	−	0.386379i	$-0.126274\pi$
$643$	13.5906	+	13.5906i	0.535961	+	0.535961i	−0.386379	+	0.922340i	$0.626274\pi$
$644$	−10.0896	−	17.4757i	−0.397586	−	0.688639i
$645$	13.5922	−	3.66272i	0.535193	−	0.144220i
$646$	−10.4932	−	6.05826i	−0.412850	−	0.238359i
$647$	29.4619	−	29.4619i	1.15827	−	1.15827i	0.173418	−	0.984848i	$-0.444519\pi$
$647$	29.4619	−	29.4619i	1.15827	−	1.15827i	0.984848	−	0.173418i	$-0.0554811\pi$
$648$	35.9295	+	9.62727i	1.41144	+	0.378195i
$649$	4.47860			0.175800
$650$	11.8321	−	20.6288i	0.464091	−	0.809129i
$651$	−52.2837	+	36.8337i	−2.04916	+	1.44362i
$652$	25.6751	+	25.6751i	1.00551	+	1.00551i
$653$	−8.60028	+	8.60028i	−0.336555	+	0.336555i	−0.855069	−	0.518514i	$-0.826485\pi$
$653$	−8.60028	+	8.60028i	−0.336555	+	0.336555i	0.518514	+	0.855069i	$0.326485\pi$
$654$	−36.8721	−	63.8643i	−1.44181	−	2.49729i
$655$	21.9067	+	5.83655i	0.855966	+	0.228053i
$656$	2.43069	−	4.21009i	0.0949027	−	0.164376i
$657$	26.7141	+	7.15801i	1.04221	+	0.279261i
$658$	30.3755	+	8.13908i	1.18416	+	0.317295i
$659$			43.6699i			1.70114i	0.525862	+	0.850570i	$0.323743\pi$
$659$			43.6699i			1.70114i	−0.525862	+	0.850570i	$0.676257\pi$
$660$	−60.4949	+	0.0859262i	−2.35476	+	0.00334467i
$661$	−13.0996	+	22.6892i	−0.509516	+	0.882508i	0.490423	+	0.871484i	$0.336842\pi$
$661$	−13.0996	+	22.6892i	−0.509516	+	0.882508i	−0.999939	+	0.0110232i	$0.996491\pi$
$662$	−18.3667	−	68.5455i	−0.713843	−	2.66410i
$663$	−4.49467	+	16.7743i	−0.174558	+	0.651461i
$664$	11.1752	−	19.3560i	0.433681	−	0.751158i
$665$	16.0621	+	9.24307i	0.622862	+	0.358431i
$666$			61.3102i			2.37572i
$667$	3.56937	+	3.56937i	0.138207	+	0.138207i
$668$	10.2829	−	38.3762i	0.397856	−	1.48482i
$669$	62.9953	+	36.3704i	2.43554	+	1.40616i
$670$	37.4041	−	10.0794i	1.44505	−	0.389400i
$671$	−9.02734	+	15.6358i	−0.348497	+	0.603614i
$672$	23.2127	+	86.6310i	0.895449	+	3.34186i
$673$	29.3067	−	7.85271i	1.12969	−	0.302700i	0.354892	−	0.934907i	$-0.384518\pi$
$673$	29.3067	−	7.85271i	1.12969	−	0.302700i	0.774799	+	0.632207i	$0.217851\pi$
$674$	47.9469			1.84684
$675$	56.4856	+	56.1656i	2.17413	+	2.16181i
$676$	−10.5039	−	18.1933i	−0.403997	−	0.699743i
$677$	−7.35187	−	27.4376i	−0.282555	−	1.05451i	−0.950607	−	0.310396i	$-0.899538\pi$
$677$	−7.35187	−	27.4376i	−0.282555	−	1.05451i	0.668052	−	0.744115i	$-0.267128\pi$
$678$	−79.5705	−	79.5705i	−3.05589	−	3.05589i
$679$	37.9079	−	21.8862i	1.45477	−	0.839913i
$680$	−1.76027	+	6.60694i	−0.0675033	+	0.253365i
$681$			79.7984i			3.05788i
$682$	−37.1929	−	6.44805i	−1.42419	−	0.246909i
$683$	0.444110	−	0.444110i	0.0169934	−	0.0169934i	−0.698559	−	0.715552i	$-0.746175\pi$
$683$	0.444110	−	0.444110i	0.0169934	−	0.0169934i	0.715552	+	0.698559i	$0.246175\pi$
$684$		−	48.4031i		−	1.85074i
$685$	35.1334	+	20.2178i	1.34238	+	0.772482i
$686$	−13.6694			−0.521902
$687$	−52.9705	+	14.1934i	−2.02095	+	0.541512i
$688$	1.20845	−	4.50998i	0.0460716	−	0.171942i
$689$	2.49659	−	1.44141i	0.0951125	−	0.0549132i
$690$	−30.3967	+	17.6072i	−1.15718	+	0.670293i
$691$	−7.17221	+	12.4226i	−0.272844	+	0.472579i	−0.969589	−	0.244739i	$-0.921298\pi$
$691$	−7.17221	+	12.4226i	−0.272844	+	0.472579i	0.696745	+	0.717319i	$0.254631\pi$
$692$	41.7000	−	11.1735i	1.58519	−	0.424752i
$693$	−83.5150	+	22.3778i	−3.17247	+	0.850061i
$694$	7.53179	+	13.0455i	0.285903	+	0.495199i
$695$	−10.3966	+	10.4261i	−0.394364	+	0.395486i
$696$	4.80135	+	8.31619i	0.181995	+	0.315224i
$697$	3.34843	−	3.34843i	0.126831	−	0.126831i
$698$	−17.3321	+	17.3321i	−0.656031	+	0.656031i
$699$	−10.8626	−	18.8147i	−0.410863	−	0.711635i
$700$	11.6124	−	43.8356i	0.438906	−	1.65683i
$701$	−9.37172	−	16.2323i	−0.353965	−	0.613085i	0.632975	−	0.774172i	$-0.281833\pi$
$701$	−9.37172	−	16.2323i	−0.353965	−	0.613085i	−0.986940	+	0.161087i	$0.948500\pi$
$702$	−73.1914	+	19.6116i	−2.76243	+	0.740191i
$703$	8.36740	−	2.24204i	0.315582	−	0.0845601i
$704$	−18.7486	+	32.4735i	−0.706613	+	1.22389i
$705$	7.96510	−	29.8960i	0.299983	−	1.12595i
$706$	−6.02773	+	3.48011i	−0.226857	+	0.130976i
$707$	−2.47305	+	9.22954i	−0.0930086	+	0.347113i
$708$	11.7114	−	3.13805i	0.440140	−	0.117935i
$709$	−12.5934			−0.472953			−0.236477	−	0.971637i	$-0.575993\pi$
$709$	−12.5934			−0.472953			−0.236477	+	0.971637i	$0.575993\pi$
$710$	5.19277	−	9.02372i	0.194881	−	0.338654i
$711$		−	33.4746i		−	1.25540i
$712$	9.21815	−	9.21815i	0.345465	−	0.345465i
$713$	−11.6287	+	4.27035i	−0.435497	+	0.159926i
$714$			58.5930i			2.19279i
$715$	13.5652	−	7.85759i	0.507310	−	0.293857i
$716$	−43.7890	+	25.2816i	−1.63647	+	0.944818i
$717$	30.3457	+	30.3457i	1.13328	+	1.13328i
$718$	13.2072	+	49.2900i	0.492888	+	1.83948i
$719$	−15.2258	−	26.3718i	−0.567825	−	0.983503i	−0.996781	−	0.0801768i	$-0.974452\pi$
$719$	−15.2258	−	26.3718i	−0.567825	−	0.983503i	0.428955	−	0.903326i	$-0.358882\pi$
$720$	41.3260	−	11.1362i	1.54013	−	0.415022i
$721$	61.7010			2.29786
$722$	27.6712	−	7.41447i	1.02981	−	0.275938i
$723$	−19.5418	−	72.9308i	−0.726766	−	2.71233i
$724$	−15.4885	+	26.8268i	−0.575624	+	0.997011i
$725$	0.0322251	+	11.3437i	0.00119681	+	0.421296i
$726$	6.15508	+	3.55363i	0.228436	+	0.131888i
$727$	−10.0065	+	37.3448i	−0.371121	+	1.38504i	0.487809	+	0.872950i	$0.337796\pi$
$727$	−10.0065	+	37.3448i	−0.371121	+	1.38504i	−0.858930	+	0.512092i	$0.828871\pi$
$728$	7.03410	+	7.03410i	0.260701	+	0.260701i
$729$		−	69.4569i		−	2.57248i
$730$	−16.3362	+	4.40215i	−0.604629	+	0.162931i
$731$	2.27404	−	3.93875i	0.0841083	−	0.145680i
$732$	−12.6505	+	47.2122i	−0.467575	+	1.74501i
$733$	3.90930	+	14.5897i	0.144393	+	0.538883i	0.999782	+	0.0208957i	$0.00665180\pi$
$733$	3.90930	+	14.5897i	0.144393	+	0.538883i	−0.855388	+	0.517987i	$0.826682\pi$
$734$	28.8721	−	50.0079i	1.06569	−	1.84583i
$735$	−0.0540934	−	38.0835i	−0.00199526	−	1.40473i
$736$			17.3721i			0.640343i
$737$	24.6663	+	6.60931i	0.908594	+	0.243457i
$738$	32.3311	+	8.66308i	1.19012	+	0.318892i
$739$	3.69591	−	6.40150i	0.135956	−	0.235483i	−0.790006	−	0.613099i	$-0.789923\pi$
$739$	3.69591	−	6.40150i	0.135956	−	0.235483i	0.925962	+	0.377616i	$0.123256\pi$
$740$	−10.6248	−	18.3425i	−0.390576	−	0.674284i
$741$	8.67171	+	15.0198i	0.318563	+	0.551768i
$742$	6.87775	−	6.87775i	0.252490	−	0.252490i
$743$	−12.7045	−	12.7045i	−0.466083	−	0.466083i	0.434560	−	0.900643i	$-0.356904\pi$
$743$	−12.7045	−	12.7045i	−0.466083	−	0.466083i	−0.900643	+	0.434560i	$0.856904\pi$
$744$	−23.4704	+	2.12132i	−0.860466	+	0.0777714i
$745$	−6.18682	+	23.2214i	−0.226668	+	0.850767i
$746$	18.8960			0.691830
$747$	−131.637	−	35.2721i	−4.81636	−	1.29054i
$748$	−13.8204	+	13.8204i	−0.505323	+	0.505323i
$749$	−0.283888	−	0.163903i	−0.0103730	−	0.00598887i
$750$	−76.3376	−	20.1064i	−2.78746	−	0.734180i
$751$	−1.27703	−	2.21188i	−0.0465995	−	0.0807127i	0.841785	−	0.539813i	$-0.181505\pi$
$751$	−1.27703	−	2.21188i	−0.0465995	−	0.0807127i	−0.888384	+	0.459100i	$0.848172\pi$
$752$	−7.25618	−	7.25618i	−0.264606	−	0.264606i
$753$	3.56456	+	13.3031i	0.129900	+	0.484793i
$754$	−9.34506	−	5.39537i	−0.340327	−	0.196488i
$755$	−14.4846	−	14.4435i	−0.527148	−	0.525653i
$756$	−125.132	+	72.2449i	−4.55100	+	2.62752i
$757$	−4.78920	−	17.8735i	−0.174066	−	0.649624i	−0.996709	−	0.0810653i	$-0.974168\pi$
$757$	−4.78920	−	17.8735i	−0.174066	−	0.649624i	0.822643	−	0.568559i	$-0.192499\pi$
$758$	−69.5591	−	18.6383i	−2.52650	−	0.676973i
$759$	−23.1564			−0.840524
$760$	3.42265	+	5.90880i	0.124152	+	0.214335i
$761$	−5.41655	+	3.12725i	−0.196350	+	0.113363i	−0.594952	−	0.803761i	$-0.702829\pi$
$761$	−5.41655	+	3.12725i	−0.196350	+	0.113363i	0.398602	+	0.917124i	$0.369496\pi$
$762$	105.987	−	28.3991i	3.83949	−	1.02879i
$763$	35.1986	+	9.43143i	1.27427	+	0.341441i
$764$	−39.2671	−	22.6709i	−1.42064	−	0.820204i
$765$	41.6910	−	0.0592173i	1.50734	−	0.00214101i
$766$	−39.5081	−	22.8100i	−1.42748	−	0.824159i
$767$	−2.22168	+	2.22168i	−0.0802202	+	0.0802202i
$768$	2.26358	−	8.44781i	0.0816800	−	0.304834i
$769$	−30.1941	+	17.4326i	−1.08883	+	0.628634i	−0.933264	−	0.359192i	$-0.883052\pi$
$769$	−30.1941	+	17.4326i	−1.08883	+	0.628634i	−0.155563	+	0.987826i	$0.549719\pi$
$770$	37.3477	−	37.4540i	1.34592	−	1.34975i
$771$		−	48.4091i		−	1.74341i
$772$	16.9091	−	63.1057i	0.608572	−	2.27122i
$773$	30.6773	+	30.6773i	1.10339	+	1.10339i	0.993999	+	0.109387i	$0.0348886\pi$
$773$	30.6773	+	30.6773i	1.10339	+	1.10339i	0.109387	+	0.993999i	$0.465111\pi$
$774$	32.1475			1.15552
$775$	−25.2973	−	11.6209i	−0.908707	−	0.417434i
$776$	16.1290			0.578999
$777$	−29.6210	−	29.6210i	−1.06265	−	1.06265i
$778$	0.897564	−	3.34975i	0.0321792	−	0.120094i
$779$		−	4.72923i		−	0.169442i
$780$	29.9668	−	30.0521i	1.07298	−	1.07604i
$781$	5.94359	−	3.43153i	0.212678	−	0.122790i
$782$	−2.93741	+	10.9626i	−0.105042	+	0.392020i
$783$	25.5579	−	25.5579i	0.913364	−	0.913364i
$784$	−10.9392	−	6.31578i	−0.390687	−	0.225563i
$785$	−18.1562	+	0.0257889i	−0.648023	+	0.000920444i
$786$	61.9958	+	35.7933i	2.21132	+	1.27671i
$787$	10.3874	+	2.78331i	0.370273	+	0.0992142i	0.439157	−	0.898410i	$-0.355277\pi$
$787$	10.3874	+	2.78331i	0.370273	+	0.0992142i	−0.0688843	+	0.997625i	$0.521944\pi$
$788$	−59.7270	+	16.0038i	−2.12769	+	0.570112i
$789$	−42.3584	+	24.4557i	−1.50800	+	0.870644i
$790$	10.2643	+	17.7201i	0.365187	+	0.630453i
$791$	55.6059			1.97712
$792$	−30.7732	−	8.24567i	−1.09348	−	0.292997i
$793$	−3.27824	−	12.2345i	−0.116414	−	0.434461i
$794$	−43.3815	+	25.0463i	−1.53955	+	0.888861i
$795$	−6.77621	−	6.75699i	−0.240327	−	0.239646i
$796$	37.3270	+	21.5508i	1.32302	+	0.763846i
$797$	4.93638	+	18.4228i	0.174855	+	0.652569i	0.996576	+	0.0826790i	$0.0263476\pi$
$797$	4.93638	+	18.4228i	0.174855	+	0.652569i	−0.821721	+	0.569890i	$0.806986\pi$
$798$	41.3775	+	41.3775i	1.46475	+	1.46475i
$799$	−4.99792	−	8.65666i	−0.176814	−	0.306251i
$800$	−27.5264	+	27.6833i	−0.973207	+	0.978752i
$801$	−68.8398	−	39.7447i	−2.43234	−	1.40431i
$802$	−27.7958	+	27.7958i	−0.981505	+	0.981505i
$803$	−10.7730	−	2.88661i	−0.380169	−	0.101866i
$804$	69.1323			2.43811
$805$	4.46883	−	16.7732i	0.157506	−	0.591176i
$806$	21.6488	−	15.2515i	0.762546	−	0.537210i
$807$	−16.2940	−	16.2940i	−0.573576	−	0.573576i
$808$	−2.48961	+	2.48961i	−0.0875840	+	0.0875840i
$809$	−7.20327	−	12.4764i	−0.253253	−	0.438648i	0.711166	−	0.703024i	$-0.248167\pi$
$809$	−7.20327	−	12.4764i	−0.253253	−	0.438648i	−0.964420	+	0.264376i	$0.914834\pi$
$810$	69.5458	+	120.063i	2.44359	+	4.21857i
$811$	−3.88878	+	6.73556i	−0.136553	+	0.236518i	−0.926190	−	0.377058i	$-0.876936\pi$
$811$	−3.88878	+	6.73556i	−0.136553	+	0.236518i	0.789636	+	0.613575i	$0.210269\pi$
$812$	−19.8754	−	5.32560i	−0.697490	−	0.186892i
$813$	−13.5369	−	3.62721i	−0.474761	−	0.127212i
$814$		−	24.7245i		−	0.866593i
$815$	0.0443645	+	31.2341i	0.00155402	+	1.09408i
$816$	9.56004	−	16.5585i	0.334668	−	0.579663i
$817$	−1.17559	−	4.38738i	−0.0411289	−	0.153495i
$818$	7.94611	−	29.6553i	0.277829	−	1.03687i
$819$	30.3280	−	52.5297i	1.05975	−	1.83554i
$820$	−11.1740	+	3.01107i	−0.390211	+	0.105151i
$821$			6.13858i			0.214238i	0.994246	+	0.107119i	$0.0341626\pi$
$821$			6.13858i			0.214238i	−0.994246	+	0.107119i	$0.965837\pi$
$822$	90.5070	+	90.5070i	3.15679	+	3.15679i
$823$	6.29111	−	23.4787i	0.219294	−	0.818417i	−0.765316	−	0.643654i	$-0.777417\pi$
$823$	6.29111	−	23.4787i	0.219294	−	0.818417i	0.984611	−	0.174763i	$-0.0559159\pi$
$824$	19.6894	+	11.3677i	0.685911	+	0.396011i
$825$	−36.9009	−	36.6918i	−1.28472	−	1.27745i
$826$	−5.30043	+	9.18061i	−0.184425	+	0.319434i
$827$	−4.12326	−	15.3882i	−0.143380	−	0.535101i	−0.999822	−	0.0188580i	$-0.993997\pi$
$827$	−4.12326	−	15.3882i	−0.143380	−	0.535101i	0.856442	−	0.516243i	$-0.172670\pi$
$828$	−43.7933	+	11.7344i	−1.52192	+	0.407798i
$829$	1.50851			0.0523928			0.0261964	−	0.999657i	$-0.491660\pi$
$829$	1.50851			0.0523928			0.0261964	+	0.999657i	$0.491660\pi$
$830$	80.4989	−	21.6922i	2.79416	−	0.752948i
$831$	24.0624	+	41.6773i	0.834716	+	1.44577i
$832$	−6.80845	−	25.4095i	−0.236040	−	0.880915i
$833$	−8.70038	−	8.70038i	−0.301450	−	0.301450i
$834$	−40.2639	+	23.2464i	−1.39423	+	0.804957i
$835$	29.5729	−	17.1300i	1.02341	−	0.592808i
$836$			19.5195i			0.675096i
$837$	30.5771	+	83.2651i	1.05690	+	2.87806i
$838$	27.2369	−	27.2369i	0.940882	−	0.940882i
$839$		−	1.19346i		−	0.0412027i	−0.999788	−	0.0206013i	$-0.993442\pi$
$839$		−	1.19346i		−	0.0412027i	0.999788	−	0.0206013i	$-0.00655807\pi$
$840$	16.4700	−	28.6206i	0.568268	−	0.987506i
$841$	−23.8528			−0.822509
$842$	−13.1896	+	3.53414i	−0.454544	+	0.121795i
$843$	−10.9891	+	41.0119i	−0.378485	+	1.41253i
$844$	15.6306	−	9.02433i	0.538027	−	0.310630i
$845$	4.65234	−	17.4619i	0.160045	−	0.600709i
$846$	35.3272	−	61.1885i	1.21457	−	2.10370i
$847$	−3.39235	+	0.908977i	−0.116562	+	0.0312328i
$848$	−3.06584	+	0.821488i	−0.105281	+	0.0282100i
$849$	50.9359	+	88.2236i	1.74812	+	3.02783i
$850$	−22.0513	+	12.8150i	−0.756354	+	0.439551i
$851$	−4.05702	−	7.02696i	−0.139073	−	0.240881i
$852$	13.1378	−	13.1378i	0.450095	−	0.450095i
$853$	−35.6376	+	35.6376i	−1.22021	+	1.22021i	−0.252652	+	0.967557i	$0.581303\pi$
$853$	−35.6376	+	35.6376i	−1.22021	+	1.22021i	−0.967557	+	0.252652i	$0.918697\pi$
$854$	−21.3677	−	37.0100i	−0.731189	−	1.26646i
$855$	29.3997	−	29.4834i	1.00545	−	1.00831i
$856$	−0.0603941	−	0.104606i	−0.00206423	−	0.00357535i
$857$	−7.17879	+	1.92355i	−0.245223	+	0.0657073i	−0.379337	−	0.925259i	$-0.623848\pi$
$857$	−7.17879	+	1.92355i	−0.245223	+	0.0657073i	0.134114	+	0.990966i	$0.457181\pi$
$858$	47.8145	−	12.8119i	1.63236	−	0.437389i
$859$	18.3116	−	31.7166i	0.624783	−	1.08216i	−0.363800	−	0.931477i	$-0.618521\pi$
$859$	18.3116	−	31.7166i	0.624783	−	1.08216i	0.988583	−	0.150679i	$-0.0481460\pi$
$860$	−9.61775	+	5.57104i	−0.327963	+	0.189971i
$861$	−19.8056	+	11.4348i	−0.674974	+	0.389697i
$862$	−7.70314	+	28.7485i	−0.262370	+	0.979178i
$863$	−37.3561	+	10.0095i	−1.27162	+	0.340729i	−0.830650	−	0.556795i	$-0.812031\pi$
$863$	−37.3561	+	10.0095i	−1.27162	+	0.340729i	−0.440966	+	0.897524i	$0.645364\pi$
$864$	124.390			4.23183
$865$	32.1870	+	18.5223i	1.09439	+	0.629776i
$866$			33.5847i			1.14125i
$867$	−26.4062	+	26.4062i	−0.896801	+	0.896801i
$868$	32.3476	−	38.7760i	1.09795	−	1.31614i
$869$			13.4993i			0.457932i
$870$	−9.22164	+	34.6122i	−0.312643	+	1.17346i
$871$	−15.5147	+	8.95744i	−0.525697	+	0.303511i
$872$	9.49457	+	9.49457i	0.321527	+	0.321527i
$873$	−25.4540	−	94.9955i	−0.861486	−	3.21511i
$874$	5.66724	+	9.81596i	0.191697	+	0.332030i
$875$	33.6988	−	19.6479i	1.13923	−	0.664221i
$876$	−30.1934			−1.02014
$877$	−35.3955	+	9.48419i	−1.19522	+	0.320258i	−0.800947	−	0.598735i	$-0.795670\pi$
$877$	−35.3955	+	9.48419i	−1.19522	+	0.320258i	−0.394273	+	0.918993i	$0.629004\pi$
$878$	−0.0714916	−	0.266810i	−0.00241272	−	0.00900441i
$879$	21.8415	−	37.8306i	0.736696	−	1.27599i
$880$	−16.6655	+	4.49089i	−0.561795	+	0.151388i
$881$	8.52128	+	4.91976i	0.287089	+	0.165751i	0.636628	−	0.771171i	$-0.280329\pi$
$881$	8.52128	+	4.91976i	0.287089	+	0.165751i	−0.349539	+	0.936922i	$0.613662\pi$
$882$	22.5097	−	84.0072i	0.757939	−	2.82867i
$883$	−40.2708	−	40.2708i	−1.35522	−	1.35522i	−0.879712	−	0.475507i	$-0.842265\pi$
$883$	−40.2708	−	40.2708i	−1.35522	−	1.35522i	−0.475507	−	0.879712i	$-0.657735\pi$
$884$		−	13.7116i		−	0.461172i
$885$	9.03965	+	5.20194i	0.303865	+	0.174861i
$886$	−9.98595	+	17.2962i	−0.335485	+	0.581076i
$887$	−11.6772	+	43.5800i	−0.392083	+	1.46327i	0.434609	+	0.900619i	$0.356886\pi$
$887$	−11.6772	+	43.5800i	−0.392083	+	1.46327i	−0.826692	+	0.562654i	$0.809780\pi$
$888$	−3.99503	−	14.9096i	−0.134064	−	0.500335i
$889$	−27.1101	+	46.9561i	−0.909244	+	1.57486i
$890$	48.6279	−	0.0690705i	1.63001	−	0.00231525i
$891$			91.4645i			3.06418i
$892$	−55.4765	−	14.8649i	−1.85749	−	0.497713i
$893$	−9.64266	−	2.58374i	−0.322679	−	0.0864617i
$894$	−37.9414	+	65.7165i	−1.26895	+	2.19789i
$895$	−42.0287	−	11.1976i	−1.40486	−	0.374294i
$896$	−17.1362	−	29.6807i	−0.572479	−	0.991563i
$897$	11.4871	−	11.4871i	0.383543	−	0.383543i
$898$	15.5063	+	15.5063i	0.517450	+	0.517450i
$899$	−5.30557	+	11.4637i	−0.176951	+	0.382335i
$900$	−88.3802	−	50.6921i	−2.94601	−	1.68974i
$901$	−3.09173			−0.103000
$902$	−13.0381	−	3.49355i	−0.434122	−	0.116323i
$903$	−15.5315	+	15.5315i	−0.516857	+	0.516857i
$904$	17.7444	+	10.2447i	0.590169	+	0.340734i
$905$	−25.7288	+	6.93319i	−0.855253	+	0.230467i
$906$	−32.2952	−	55.9370i	−1.07294	−	1.85838i
$907$	19.6804	+	19.6804i	0.653478	+	0.653478i	0.953829	−	0.300351i	$-0.0971037\pi$
$907$	19.6804	+	19.6804i	0.653478	+	0.653478i	−0.300351	+	0.953829i	$0.597104\pi$
$908$	−16.3071	−	60.8591i	−0.541172	−	2.01968i
$909$	18.5920	+	10.7341i	0.616659	+	0.356028i
$910$	0.0527057	+	37.1065i	0.00174718	+	1.23007i
$911$	3.25420	−	1.87881i	0.107816	−	0.0622478i	−0.445122	−	0.895470i	$-0.646840\pi$
$911$	3.25420	−	1.87881i	0.107816	−	0.0622478i	0.552939	+	0.833222i	$0.313506\pi$
$912$	−4.94219	−	18.4445i	−0.163652	−	0.610759i
$913$	53.0853	+	14.2242i	1.75687	+	0.470751i
$914$	−6.19139			−0.204793
$915$	−36.3820	+	21.0741i	−1.20275	+	0.696690i
$916$	37.4980	−	21.6495i	1.23897	−	0.715320i
$917$	−34.1688	+	9.15550i	−1.12835	+	0.302341i
$918$	78.4955	+	21.0328i	2.59074	+	0.694186i
$919$	−10.1472	−	5.85849i	−0.334725	−	0.193254i	0.323212	−	0.946327i	$-0.395237\pi$
$919$	−10.1472	−	5.85849i	−0.334725	−	0.193254i	−0.657937	+	0.753073i	$0.728571\pi$
$920$	4.51630	−	4.52915i	0.148898	−	0.149322i
$921$	29.1235	+	16.8145i	0.959652	+	0.554056i
$922$	−1.99191	+	1.99191i	−0.0656002	+	0.0656002i
$923$	−1.24614	+	4.65067i	−0.0410173	+	0.153079i
$924$	81.7461	−	47.1961i	2.68925	−	1.55264i
$925$	4.66931	−	17.6263i	0.153526	−	0.579548i
$926$			12.5443i			0.412231i
$927$	35.8796	−	133.905i	1.17844	−	4.39800i
$928$	12.5258	+	12.5258i	0.411179	+	0.411179i
$929$	51.0477			1.67482			0.837411	−	0.546574i	$-0.184068\pi$
$929$	51.0477			1.67482			0.837411	+	0.546574i	$0.184068\pi$
$930$	−67.5811	−	56.2148i	−2.21607	−	1.84336i
$931$	−12.2882			−0.402728
$932$	12.1294	+	12.1294i	0.397311	+	0.397311i
$933$	−4.85665	+	18.1253i	−0.159000	+	0.593395i
$934$		−	34.6512i		−	1.13382i
$935$	−16.8127	+	0.0238805i	−0.549833	+	0.000780977i
$936$	19.3559	−	11.1752i	0.632668	−	0.365271i
$937$	3.56387	−	13.3006i	0.116427	−	0.434510i	−0.882963	−	0.469443i	$-0.844455\pi$
$937$	3.56387	−	13.3006i	0.116427	−	0.434510i	0.999390	+	0.0349323i	$0.0111216\pi$
$938$	−42.7409	+	42.7409i	−1.39554	+	1.39554i
$939$	−22.2368	−	12.8385i	−0.725672	−	0.418967i
$940$	0.0346975	+	24.4282i	0.00113171	+	0.796759i
$941$	22.2783	+	12.8624i	0.726253	+	0.419303i	0.817050	−	0.576567i	$-0.195608\pi$
$941$	22.2783	+	12.8624i	0.726253	+	0.419303i	−0.0907966	+	0.995869i	$0.528941\pi$
$942$	−55.3774	−	14.8383i	−1.80429	−	0.483459i
$943$	−4.27882	+	1.14651i	−0.139338	+	0.0373354i
$944$	2.99582	−	1.72964i	0.0975056	−	0.0562949i
$945$	−120.101	−	31.9983i	−3.90690	−	1.04090i
$946$	−12.9641			−0.421499
$947$	−0.387562	−	0.103847i	−0.0125941	−	0.00337457i	0.252517	−	0.967593i	$-0.418742\pi$
$947$	−0.387562	−	0.103847i	−0.0125941	−	0.00337457i	−0.265111	+	0.964218i	$0.585408\pi$
$948$	9.45862	+	35.3001i	0.307202	+	1.14649i
$949$	6.77604	−	3.91215i	0.219959	−	0.126994i
$950$	−6.52256	+	24.6221i	−0.211620	+	0.798846i
$951$	41.0784	+	23.7166i	1.33206	+	0.769064i
$952$	−2.76124	−	10.3051i	−0.0894925	−	0.333990i
$953$	26.4721	+	26.4721i	0.857515	+	0.857515i	0.991045	−	0.133530i	$-0.0426313\pi$
$953$	26.4721	+	26.4721i	0.857515	+	0.857515i	−0.133530	+	0.991045i	$0.542631\pi$
$954$	−10.9267	−	18.9257i	−0.353767	−	0.612742i
$955$	−10.1483	−	37.6599i	−0.328391	−	1.21865i
$956$	−29.3448	−	16.9422i	−0.949078	−	0.547950i
$957$	−16.6965	+	16.6965i	−0.539720	+	0.539720i
$958$	−53.4757	−	14.3288i	−1.72772	−	0.462942i
$959$	−63.2486			−2.04240
$960$	−75.5605	+	43.7681i	−2.43871	+	1.41261i
$961$	−20.0625	−	23.6325i	−0.647176	−	0.762340i
$962$	12.2650	+	12.2650i	0.395438	+	0.395438i
$963$	−0.520787	+	0.520787i	−0.0167821	+	0.0167821i
$964$	29.8075	+	51.6280i	0.960033	+	1.66283i
$965$	48.6296	−	28.1685i	1.56544	−	0.906776i
$966$	27.4056	−	47.4679i	0.881761	−	1.52726i
$967$	55.3767	+	14.8381i	1.78079	+	0.477162i	0.990728	−	0.135860i	$-0.0433796\pi$
$967$	55.3767	+	14.8381i	1.78079	+	0.477162i	0.790066	+	0.613022i	$0.210046\pi$
$968$	−1.25000	−	0.334936i	−0.0401765	−	0.0107653i
$969$		−	18.6003i		−	0.597528i
$970$	42.6027	+	42.4818i	1.36789	+	1.36401i
$971$	−30.2698	+	52.4288i	−0.971404	+	1.68252i	−0.280077	+	0.959977i	$0.590360\pi$
$971$	−30.2698	+	52.4288i	−0.971404	+	1.68252i	−0.691326	+	0.722543i	$0.742973\pi$
$972$	31.9317	+	119.171i	1.02421	+	3.82240i
$973$	5.94615	−	22.1913i	0.190625	−	0.711421i
$974$	−10.2992	+	17.8388i	−0.330009	+	0.571592i
$975$	36.5068	−	0.103708i	1.16915	−	0.00332131i
$976$			13.9454i			0.446383i
$977$	−21.5177	−	21.5177i	−0.688411	−	0.688411i	0.273470	−	0.961881i	$-0.411829\pi$
$977$	−21.5177	−	21.5177i	−0.688411	−	0.688411i	−0.961881	+	0.273470i	$0.911829\pi$
$978$	−25.5264	+	95.2657i	−0.816243	+	3.04626i
$979$	27.7610	+	16.0278i	0.887245	+	0.512251i
$980$	7.82379	+	29.0338i	0.249922	+	0.927449i
$981$	40.9365	−	70.9042i	1.30700	−	2.26380i
$982$	−0.432426	−	1.61384i	−0.0137993	−	0.0514995i
$983$	−4.02183	+	1.07765i	−0.128277	+	0.0343716i	−0.322386	−	0.946608i	$-0.604485\pi$
$983$	−4.02183	+	1.07765i	−0.128277	+	0.0343716i	0.194110	+	0.980980i	$0.437818\pi$
$984$	−8.42689			−0.268639
$985$	−46.1015	−	26.5295i	−1.46892	−	0.845300i
$986$	5.78637	+	10.0223i	0.184276	+	0.319175i
$987$	12.4945	+	46.6299i	0.397703	+	1.48425i
$988$	−9.68295	−	9.68295i	−0.308056	−	0.308056i
$989$	−3.68453	+	2.12726i	−0.117161	+	0.0676431i
$990$	−59.5653	−	102.833i	−1.89311	−	3.26823i
$991$		−	45.9581i		−	1.45991i	−0.683496	−	0.729954i	$-0.739542\pi$
$991$		−	45.9581i		−	1.45991i	0.683496	−	0.729954i	$-0.260458\pi$
$992$	−40.8078	+	14.9857i	−1.29565	+	0.475795i
$993$	77.0304	−	77.0304i	2.44448	−	2.44448i
$994$			16.2449i			0.515256i
$995$	9.64688	+	35.7992i	0.305827	+	1.13491i
$996$	148.782			4.71435
$997$	49.0182	−	13.1344i	1.55242	−	0.415970i	0.622167	−	0.782884i	$-0.286252\pi$
$997$	49.0182	−	13.1344i	1.55242	−	0.415970i	0.930255	+	0.366914i	$0.119586\pi$
$998$	−1.36986	+	5.11240i	−0.0433622	+	0.161830i
$999$	−50.3153	+	29.0496i	−1.59191	+	0.919088i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	155.2.p.c.37.3	✓	48
5.2	odd	4		775.2.bj.f.68.10		48
5.3	odd	4	inner	155.2.p.c.68.3	yes	48
5.4	even	2		775.2.bj.f.657.10		48
31.26	odd	6	inner	155.2.p.c.57.3	yes	48
155.57	even	12		775.2.bj.f.243.10		48
155.88	even	12	inner	155.2.p.c.88.3	yes	48
155.119	odd	6		775.2.bj.f.57.10		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
155.2.p.c.37.3	✓	48	1.1	even	1	trivial
155.2.p.c.57.3	yes	48	31.26	odd	6	inner
155.2.p.c.68.3	yes	48	5.3	odd	4	inner
155.2.p.c.88.3	yes	48	155.88	even	12	inner
775.2.bj.f.57.10		48	155.119	odd	6
775.2.bj.f.68.10		48	5.2	odd	4
775.2.bj.f.243.10		48	155.57	even	12
775.2.bj.f.657.10		48	5.4	even	2

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:	\( N \)	\(=\)	\( 155 = 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	155.p (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.51649 - 1.51649i) q^{2} +(0.852101 - 3.18009i) q^{3} +2.59946i q^{4} +(-1.57889 + 1.58338i) q^{5} +(-6.11475 + 3.53035i) q^{6} +(0.903022 - 3.37012i) q^{7} +(0.909067 - 0.909067i) q^{8} +(-6.78879 - 3.91951i) q^{9} +O(q^{10})\)	\(q+(-1.51649 - 1.51649i) q^{2} +(0.852101 - 3.18009i) q^{3} +2.59946i q^{4} +(-1.57889 + 1.58338i) q^{5} +(-6.11475 + 3.53035i) q^{6} +(0.903022 - 3.37012i) q^{7} +(0.909067 - 0.909067i) q^{8} +(-6.78879 - 3.91951i) q^{9} +(4.79554 - 0.00681153i) q^{10} +(2.73771 + 1.58062i) q^{11} +(8.26649 + 2.21500i) q^{12} +(-2.14217 + 0.573993i) q^{13} +(-6.48016 + 3.74132i) q^{14} +(3.68992 + 6.37021i) q^{15} +2.44174 q^{16} +(2.29741 + 0.615590i) q^{17} +(4.35122 + 16.2390i) q^{18} +(2.05712 - 1.18768i) q^{19} +(-4.11594 - 4.10426i) q^{20} +(-9.94781 - 5.74337i) q^{21} +(-1.75471 - 6.54868i) q^{22} +(-1.57327 - 1.57327i) q^{23} +(-2.11629 - 3.66553i) q^{24} +(-0.0142038 - 4.99998i) q^{25} +(4.11903 + 2.37812i) q^{26} +(-11.2652 + 11.2652i) q^{27} +(8.76049 + 2.34737i) q^{28} -2.26875 q^{29} +(4.06463 - 15.2560i) q^{30} +(2.33854 - 5.05284i) q^{31} +(-5.52100 - 5.52100i) q^{32} +(7.35930 - 7.35930i) q^{33} +(-2.55046 - 4.41753i) q^{34} +(3.91042 + 6.75089i) q^{35} +(10.1886 - 17.6472i) q^{36} +(3.52258 + 0.943873i) q^{37} +(-4.92069 - 1.31850i) q^{38} +7.30139i q^{39} +(0.00408322 + 2.87472i) q^{40} +(0.995477 - 1.72422i) q^{41} +(6.37597 + 23.7955i) q^{42} +(0.494912 - 1.84704i) q^{43} +(-4.10875 + 7.11656i) q^{44} +(16.9248 - 4.56077i) q^{45} +4.77169i q^{46} +(-2.97173 - 2.97173i) q^{47} +(2.08061 - 7.76494i) q^{48} +(-4.48011 - 2.58659i) q^{49} +(-7.56086 + 7.60394i) q^{50} +(3.91526 - 6.78143i) q^{51} +(-1.49207 - 5.56848i) q^{52} +(-1.25560 + 0.336436i) q^{53} +34.1669 q^{54} +(-6.82527 + 1.83922i) q^{55} +(-2.24276 - 3.88458i) q^{56} +(-2.02405 - 7.55384i) q^{57} +(3.44053 + 3.44053i) q^{58} +(1.22692 - 0.708363i) q^{59} +(-16.5591 + 9.59178i) q^{60} +5.71128i q^{61} +(-11.2089 + 4.11620i) q^{62} +(-19.3397 + 19.3397i) q^{63} +11.8615i q^{64} +(2.47341 - 4.29815i) q^{65} -22.3206 q^{66} +(7.80274 - 2.09074i) q^{67} +(-1.60020 + 5.97203i) q^{68} +(-6.34373 + 3.66256i) q^{69} +(4.30752 - 16.1677i) q^{70} +(1.08550 - 1.88015i) q^{71} +(-9.73457 + 2.60837i) q^{72} +(-3.40783 + 0.913126i) q^{73} +(-3.91058 - 6.77332i) q^{74} +(-15.9125 - 4.21532i) q^{75} +(3.08732 + 5.34740i) q^{76} +(7.79909 - 7.79909i) q^{77} +(11.0725 - 11.0725i) q^{78} +(2.13513 + 3.69815i) q^{79} +(-3.85524 + 3.86621i) q^{80} +(14.4666 + 25.0569i) q^{81} +(-4.12438 + 1.10512i) q^{82} +(16.7926 - 4.49956i) q^{83} +(14.9296 - 25.8589i) q^{84} +(-4.60208 + 2.66574i) q^{85} +(-3.55153 + 2.05048i) q^{86} +(-1.93321 + 7.21483i) q^{87} +(3.92565 - 1.05187i) q^{88} +10.1402 q^{89} +(-32.5826 - 18.7499i) q^{90} +7.73771i q^{91} +(4.08966 - 4.08966i) q^{92} +(-14.0758 - 11.7423i) q^{93} +9.01316i q^{94} +(-1.36742 + 5.13243i) q^{95} +(-22.2617 + 12.8528i) q^{96} +(8.87120 + 8.87120i) q^{97} +(2.87149 + 10.7165i) q^{98} +(-12.3905 - 21.4610i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 6 q^{3} - 4 q^{5} - 48 q^{6} - 8 q^{7} + 36 q^{8}+O(q^{10}) \) 48 * q + 6 * q^3 - 4 * q^5 - 48 * q^6 - 8 * q^7 + 36 * q^8	\( 48 q + 6 q^{3} - 4 q^{5} - 48 q^{6} - 8 q^{7} + 36 q^{8} - 6 q^{10} - 12 q^{11} - 56 q^{16} - 12 q^{17} + 2 q^{18} + 34 q^{20} - 24 q^{21} - 60 q^{22} + 12 q^{25} - 24 q^{26} + 28 q^{28} + 32 q^{31} + 52 q^{32} + 20 q^{33} + 48 q^{35} + 4 q^{36} + 42 q^{37} - 10 q^{38} - 16 q^{40} + 4 q^{41} + 78 q^{42} - 72 q^{43} - 42 q^{45} - 36 q^{47} + 24 q^{48} - 22 q^{50} + 8 q^{51} + 60 q^{52} - 72 q^{53} - 42 q^{55} + 36 q^{56} + 6 q^{57} - 78 q^{62} - 64 q^{63} - 36 q^{65} + 32 q^{66} + 26 q^{67} + 96 q^{68} - 88 q^{70} - 4 q^{71} + 22 q^{72} + 12 q^{73} - 24 q^{75} - 28 q^{76} + 4 q^{78} + 18 q^{80} + 60 q^{81} - 32 q^{82} + 90 q^{83} + 48 q^{86} + 2 q^{87} + 78 q^{88} - 118 q^{90} - 6 q^{93} - 52 q^{95} - 120 q^{96} + 4 q^{97} - 42 q^{98}+O(q^{100}) \) 48 * q + 6 * q^3 - 4 * q^5 - 48 * q^6 - 8 * q^7 + 36 * q^8 - 6 * q^10 - 12 * q^11 - 56 * q^16 - 12 * q^17 + 2 * q^18 + 34 * q^20 - 24 * q^21 - 60 * q^22 + 12 * q^25 - 24 * q^26 + 28 * q^28 + 32 * q^31 + 52 * q^32 + 20 * q^33 + 48 * q^35 + 4 * q^36 + 42 * q^37 - 10 * q^38 - 16 * q^40 + 4 * q^41 + 78 * q^42 - 72 * q^43 - 42 * q^45 - 36 * q^47 + 24 * q^48 - 22 * q^50 + 8 * q^51 + 60 * q^52 - 72 * q^53 - 42 * q^55 + 36 * q^56 + 6 * q^57 - 78 * q^62 - 64 * q^63 - 36 * q^65 + 32 * q^66 + 26 * q^67 + 96 * q^68 - 88 * q^70 - 4 * q^71 + 22 * q^72 + 12 * q^73 - 24 * q^75 - 28 * q^76 + 4 * q^78 + 18 * q^80 + 60 * q^81 - 32 * q^82 + 90 * q^83 + 48 * q^86 + 2 * q^87 + 78 * q^88 - 118 * q^90 - 6 * q^93 - 52 * q^95 - 120 * q^96 + 4 * q^97 - 42 * q^98

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