LMFDB - Embedded newform 155.2.h.b.66.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [155,2,Mod(16,155)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(155, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 2]))

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

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

chi := DirichletCharacter("155.16");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 155 = 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	155.h (of order $5$, 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:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			66.5
Character	$\chi$	$=$	155.66
Dual form			155.2.h.b.101.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.420591 + 1.29445i) q^{2} +(-0.973089 + 2.99486i) q^{3} +(0.119342 - 0.0867070i) q^{4} -1.00000 q^{5} -4.28595 q^{6} +(-0.741309 + 0.538593i) q^{7} +(2.36467 + 1.71804i) q^{8} +(-5.59523 - 4.06517i) q^{9} +O(q^{10})$	\(q+(0.420591 + 1.29445i) q^{2} +(-0.973089 + 2.99486i) q^{3} +(0.119342 - 0.0867070i) q^{4} -1.00000 q^{5} -4.28595 q^{6} +(-0.741309 + 0.538593i) q^{7} +(2.36467 + 1.71804i) q^{8} +(-5.59523 - 4.06517i) q^{9} +(-0.420591 - 1.29445i) q^{10} +(4.53839 - 3.29733i) q^{11} +(0.143545 + 0.441786i) q^{12} +(-0.592172 + 1.82252i) q^{13} +(-1.00897 - 0.733057i) q^{14} +(0.973089 - 2.99486i) q^{15} +(-1.13817 + 3.50294i) q^{16} +(-1.86192 - 1.35276i) q^{17} +(2.90884 - 8.95250i) q^{18} +(1.97142 + 6.06741i) q^{19} +(-0.119342 + 0.0867070i) q^{20} +(-0.891650 - 2.74422i) q^{21} +(6.17702 + 4.48787i) q^{22} +(-2.98754 - 2.17057i) q^{23} +(-7.44631 + 5.41006i) q^{24} +1.00000 q^{25} -2.60821 q^{26} +(9.97655 - 7.24839i) q^{27} +(-0.0417696 + 0.128554i) q^{28} +(0.643286 + 1.97983i) q^{29} +4.28595 q^{30} +(5.54716 + 0.478553i) q^{31} +0.832724 q^{32} +(5.45879 + 16.8004i) q^{33} +(0.967971 - 2.97911i) q^{34} +(0.741309 - 0.538593i) q^{35} -1.02023 q^{36} +8.06343 q^{37} +(-7.02476 + 5.10379i) q^{38} +(-4.88195 - 3.54694i) q^{39} +(-2.36467 - 1.71804i) q^{40} +(-0.782302 - 2.40768i) q^{41} +(3.17722 - 2.30838i) q^{42} +(-2.94598 - 9.06681i) q^{43} +(0.255718 - 0.787020i) q^{44} +(5.59523 + 4.06517i) q^{45} +(1.55316 - 4.78013i) q^{46} +(1.28959 - 3.96894i) q^{47} +(-9.38327 - 6.81735i) q^{48} +(-1.90366 + 5.85887i) q^{49} +(0.420591 + 1.29445i) q^{50} +(5.86314 - 4.25982i) q^{51} +(0.0873542 + 0.268848i) q^{52} +(-6.25519 - 4.54466i) q^{53} +(13.5787 + 9.86549i) q^{54} +(-4.53839 + 3.29733i) q^{55} -2.67828 q^{56} -20.0894 q^{57} +(-2.29222 + 1.66540i) q^{58} +(3.04742 - 9.37899i) q^{59} +(-0.143545 - 0.441786i) q^{60} -6.81609 q^{61} +(1.71362 + 7.38177i) q^{62} +6.33727 q^{63} +(2.62658 + 8.08380i) q^{64} +(0.592172 - 1.82252i) q^{65} +(-19.4513 + 14.1322i) q^{66} +0.414188 q^{67} -0.339499 q^{68} +(9.40770 - 6.83509i) q^{69} +(1.00897 + 0.733057i) q^{70} +(4.68617 + 3.40470i) q^{71} +(-6.24678 - 19.2256i) q^{72} +(5.11470 - 3.71605i) q^{73} +(3.39140 + 10.4377i) q^{74} +(-0.973089 + 2.99486i) q^{75} +(0.761360 + 0.553160i) q^{76} +(-1.58843 + 4.88869i) q^{77} +(2.53802 - 7.81123i) q^{78} +(-8.59071 - 6.24151i) q^{79} +(1.13817 - 3.50294i) q^{80} +(5.58827 + 17.1989i) q^{81} +(2.78758 - 2.02529i) q^{82} +(-3.10371 - 9.55223i) q^{83} +(-0.344354 - 0.250188i) q^{84} +(1.86192 + 1.35276i) q^{85} +(10.4974 - 7.62683i) q^{86} -6.55529 q^{87} +16.3967 q^{88} +(1.86543 - 1.35532i) q^{89} +(-2.90884 + 8.95250i) q^{90} +(-0.542612 - 1.66999i) q^{91} -0.544743 q^{92} +(-6.83108 + 16.1473i) q^{93} +5.67996 q^{94} +(-1.97142 - 6.06741i) q^{95} +(-0.810314 + 2.49389i) q^{96} +(-9.18599 + 6.67401i) q^{97} -8.38465 q^{98} -38.7976 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 2 q^{2} - 6 q^{4} - 24 q^{5} - 16 q^{6} - 9 q^{7} + 11 q^{8} - 6 q^{9}+O(q^{10}) $ 24 * q + 2 * q^2 - 6 * q^4 - 24 * q^5 - 16 * q^6 - 9 * q^7 + 11 * q^8 - 6 * q^9	\( 24 q + 2 q^{2} - 6 q^{4} - 24 q^{5} - 16 q^{6} - 9 q^{7} + 11 q^{8} - 6 q^{9} - 2 q^{10} + q^{11} + 18 q^{12} - 5 q^{13} + 6 q^{14} - 24 q^{16} + 7 q^{17} - 18 q^{18} + 2 q^{19} + 6 q^{20} - 10 q^{21} + 28 q^{22} - 15 q^{23} - 32 q^{24} + 24 q^{25} + 22 q^{26} + 9 q^{27} + 38 q^{28} + 15 q^{29} + 16 q^{30} + 6 q^{31} + 74 q^{32} + 5 q^{33} - 20 q^{34} + 9 q^{35} - 58 q^{36} - 56 q^{37} - 21 q^{38} - 10 q^{39} - 11 q^{40} - 24 q^{41} - 38 q^{42} + 21 q^{43} + 41 q^{44} + 6 q^{45} + 48 q^{46} - 8 q^{47} - 26 q^{48} - 23 q^{49} + 2 q^{50} + 26 q^{51} - 27 q^{52} + 26 q^{53} + 11 q^{54} - q^{55} - 48 q^{56} + 62 q^{57} + 52 q^{58} + 10 q^{59} - 18 q^{60} - 40 q^{61} - 28 q^{62} + 26 q^{63} + 9 q^{64} + 5 q^{65} - 2 q^{66} - 26 q^{67} - 8 q^{68} + 64 q^{69} - 6 q^{70} - 7 q^{71} - 127 q^{72} - 51 q^{73} - q^{74} + 43 q^{76} - 39 q^{77} - 31 q^{78} + 31 q^{79} + 24 q^{80} + 34 q^{81} + 58 q^{82} + 6 q^{83} + 113 q^{84} - 7 q^{85} - 22 q^{86} + 4 q^{87} - 28 q^{88} + 13 q^{89} + 18 q^{90} + 54 q^{91} - 2 q^{92} - 72 q^{93} - 10 q^{94} - 2 q^{95} + 101 q^{96} - 39 q^{97} - 220 q^{98} - 170 q^{99}+O(q^{100}) \) 24 * q + 2 * q^2 - 6 * q^4 - 24 * q^5 - 16 * q^6 - 9 * q^7 + 11 * q^8 - 6 * q^9 - 2 * q^10 + q^11 + 18 * q^12 - 5 * q^13 + 6 * q^14 - 24 * q^16 + 7 * q^17 - 18 * q^18 + 2 * q^19 + 6 * q^20 - 10 * q^21 + 28 * q^22 - 15 * q^23 - 32 * q^24 + 24 * q^25 + 22 * q^26 + 9 * q^27 + 38 * q^28 + 15 * q^29 + 16 * q^30 + 6 * q^31 + 74 * q^32 + 5 * q^33 - 20 * q^34 + 9 * q^35 - 58 * q^36 - 56 * q^37 - 21 * q^38 - 10 * q^39 - 11 * q^40 - 24 * q^41 - 38 * q^42 + 21 * q^43 + 41 * q^44 + 6 * q^45 + 48 * q^46 - 8 * q^47 - 26 * q^48 - 23 * q^49 + 2 * q^50 + 26 * q^51 - 27 * q^52 + 26 * q^53 + 11 * q^54 - q^55 - 48 * q^56 + 62 * q^57 + 52 * q^58 + 10 * q^59 - 18 * q^60 - 40 * q^61 - 28 * q^62 + 26 * q^63 + 9 * q^64 + 5 * q^65 - 2 * q^66 - 26 * q^67 - 8 * q^68 + 64 * q^69 - 6 * q^70 - 7 * q^71 - 127 * q^72 - 51 * q^73 - q^74 + 43 * q^76 - 39 * q^77 - 31 * q^78 + 31 * q^79 + 24 * q^80 + 34 * q^81 + 58 * q^82 + 6 * q^83 + 113 * q^84 - 7 * q^85 - 22 * q^86 + 4 * q^87 - 28 * q^88 + 13 * q^89 + 18 * q^90 + 54 * q^91 - 2 * q^92 - 72 * q^93 - 10 * q^94 - 2 * q^95 + 101 * q^96 - 39 * q^97 - 220 * q^98 - 170 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$32$	$96$
$\chi(n)$	$1$	$e\left(\frac{3}{5}\right)$

Coefficient data

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

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

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

$2$	0.420591	+	1.29445i	0.297403	+	0.915311i	0.982404	+	0.186769i	$0.0598016\pi$
$2$	0.420591	+	1.29445i	0.297403	+	0.915311i	−0.685001	+	0.728542i	$0.740198\pi$
$3$	−0.973089	+	2.99486i	−0.561813	+	1.72908i	0.115422	+	0.993317i	$0.463178\pi$
$3$	−0.973089	+	2.99486i	−0.561813	+	1.72908i	−0.677235	+	0.735767i	$0.736822\pi$
$4$	0.119342	−	0.0867070i	0.0596710	−	0.0433535i
$5$	−1.00000			−0.447214
$5$	−1.00000			−0.447214
$6$	−4.28595			−1.74973
$7$	−0.741309	+	0.538593i	−0.280189	+	0.203569i	−0.719000	−	0.695010i	$-0.755400\pi$
$7$	−0.741309	+	0.538593i	−0.280189	+	0.203569i	0.438811	+	0.898579i	$0.355400\pi$
$8$	2.36467	+	1.71804i	0.836038	+	0.607417i
$9$	−5.59523	−	4.06517i	−1.86508	−	1.35506i
$10$	−0.420591	−	1.29445i	−0.133002	−	0.409340i
$11$	4.53839	−	3.29733i	1.36838	−	0.994183i	0.370513	−	0.928827i	$-0.379182\pi$
$11$	4.53839	−	3.29733i	1.36838	−	0.994183i	0.997862	−	0.0653556i	$-0.0208182\pi$
$12$	0.143545	+	0.441786i	0.0414379	+	0.127533i
$13$	−0.592172	+	1.82252i	−0.164239	+	0.505476i	−0.998979	−	0.0451681i	$-0.985618\pi$
$13$	−0.592172	+	1.82252i	−0.164239	+	0.505476i	0.834740	+	0.550644i	$0.185618\pi$
$14$	−1.00897	−	0.733057i	−0.269658	−	0.195918i
$15$	0.973089	−	2.99486i	0.251250	−	0.773270i
$16$	−1.13817	+	3.50294i	−0.284544	+	0.875735i
$17$	−1.86192	−	1.35276i	−0.451581	−	0.328093i	0.338639	−	0.940917i	$-0.390034\pi$
$17$	−1.86192	−	1.35276i	−0.451581	−	0.328093i	−0.790220	+	0.612824i	$0.790034\pi$
$18$	2.90884	−	8.95250i	0.685621	−	2.11012i
$19$	1.97142	+	6.06741i	0.452275	+	1.39196i	0.874305	+	0.485377i	$0.161317\pi$
$19$	1.97142	+	6.06741i	0.452275	+	1.39196i	−0.422031	+	0.906582i	$0.638683\pi$
$20$	−0.119342	+	0.0867070i	−0.0266857	+	0.0193883i
$21$	−0.891650	−	2.74422i	−0.194574	−	0.598837i
$22$	6.17702	+	4.48787i	1.31694	+	0.956816i
$23$	−2.98754	−	2.17057i	−0.622944	−	0.452596i	0.231004	−	0.972953i	$-0.425799\pi$
$23$	−2.98754	−	2.17057i	−0.622944	−	0.452596i	−0.853949	+	0.520357i	$0.825799\pi$
$24$	−7.44631	+	5.41006i	−1.51997	+	1.10432i
$25$	1.00000			0.200000
$26$	−2.60821			−0.511512
$27$	9.97655	−	7.24839i	1.91999	−	1.39495i
$28$	−0.0417696	+	0.128554i	−0.00789371	+	0.0242943i
$29$	0.643286	+	1.97983i	0.119455	+	0.367645i	0.992850	−	0.119367i	$-0.0380866\pi$
$29$	0.643286	+	1.97983i	0.119455	+	0.367645i	−0.873395	+	0.487012i	$0.838087\pi$
$30$	4.28595			0.782505
$31$	5.54716	+	0.478553i	0.996299	+	0.0859507i
$31$	5.54716	+	0.478553i	0.996299	+	0.0859507i
$32$	0.832724			0.147206
$33$	5.45879	+	16.8004i	0.950253	+	2.92458i
$34$	0.967971	−	2.97911i	0.166006	−	0.510913i
$35$	0.741309	−	0.538593i	0.125304	−	0.0910388i
$36$	−1.02023			−0.170038
$37$	8.06343			1.32562			0.662810	−	0.748788i	$-0.269364\pi$
$37$	8.06343			1.32562			0.662810	+	0.748788i	$0.269364\pi$
$38$	−7.02476	+	5.10379i	−1.13957	+	0.827944i
$39$	−4.88195	−	3.54694i	−0.781738	−	0.567966i
$40$	−2.36467	−	1.71804i	−0.373888	−	0.271645i
$41$	−0.782302	−	2.40768i	−0.122175	−	0.376016i	0.871201	−	0.490927i	$-0.163342\pi$
$41$	−0.782302	−	2.40768i	−0.122175	−	0.376016i	−0.993376	+	0.114911i	$0.963342\pi$
$42$	3.17722	−	2.30838i	0.490255	−	0.356191i
$43$	−2.94598	−	9.06681i	−0.449258	−	1.38268i	−0.877746	−	0.479127i	$-0.840953\pi$
$43$	−2.94598	−	9.06681i	−0.449258	−	1.38268i	0.428487	−	0.903548i	$-0.359047\pi$
$44$	0.255718	−	0.787020i	0.0385510	−	0.118648i
$45$	5.59523	+	4.06517i	0.834088	+	0.606000i
$46$	1.55316	−	4.78013i	0.229001	−	0.704791i
$47$	1.28959	−	3.96894i	0.188106	−	0.578929i	−0.811883	−	0.583821i	$-0.801557\pi$
$47$	1.28959	−	3.96894i	0.188106	−	0.578929i	0.999988	+	0.00489158i	$0.00155705\pi$
$48$	−9.38327	−	6.81735i	−1.35436	−	0.983999i
$49$	−1.90366	+	5.85887i	−0.271952	+	0.836981i
$50$	0.420591	+	1.29445i	0.0594805	+	0.183062i
$51$	5.86314	−	4.25982i	0.821004	−	0.596494i
$52$	0.0873542	+	0.268848i	0.0121138	+	0.0372826i
$53$	−6.25519	−	4.54466i	−0.859217	−	0.624258i	0.0684548	−	0.997654i	$-0.478193\pi$
$53$	−6.25519	−	4.54466i	−0.859217	−	0.624258i	−0.927672	+	0.373396i	$0.878193\pi$
$54$	13.5787	+	9.86549i	1.84782	+	1.34252i
$55$	−4.53839	+	3.29733i	−0.611956	+	0.444612i
$56$	−2.67828			−0.357900
$57$	−20.0894			−2.66091
$58$	−2.29222	+	1.66540i	−0.300983	+	0.218677i
$59$	3.04742	−	9.37899i	0.396740	−	1.22104i	−0.530858	−	0.847461i	$-0.678130\pi$
$59$	3.04742	−	9.37899i	0.396740	−	1.22104i	0.927598	−	0.373580i	$-0.121870\pi$
$60$	−0.143545	−	0.441786i	−0.0185316	−	0.0570344i
$61$	−6.81609			−0.872711			−0.436355	−	0.899774i	$-0.643731\pi$
$61$	−6.81609			−0.872711			−0.436355	+	0.899774i	$0.643731\pi$
$62$	1.71362	+	7.38177i	0.217630	+	0.937486i
$63$	6.33727			0.798421
$64$	2.62658	+	8.08380i	0.328323	+	1.01047i
$65$	0.592172	−	1.82252i	0.0734499	−	0.226056i
$66$	−19.4513	+	14.1322i	−2.39429	+	1.73956i
$67$	0.414188			0.0506011			0.0253006	−	0.999680i	$-0.491946\pi$
$67$	0.414188			0.0506011			0.0253006	+	0.999680i	$0.491946\pi$
$68$	−0.339499			−0.0411703
$69$	9.40770	−	6.83509i	1.13255	−	0.822849i
$70$	1.00897	+	0.733057i	0.120595	+	0.0876171i
$71$	4.68617	+	3.40470i	0.556146	+	0.404064i	0.830046	−	0.557694i	$-0.188314\pi$
$71$	4.68617	+	3.40470i	0.556146	+	0.404064i	−0.273901	+	0.961758i	$0.588314\pi$
$72$	−6.24678	−	19.2256i	−0.736190	−	2.26576i
$73$	5.11470	−	3.71605i	0.598631	−	0.434931i	−0.246762	−	0.969076i	$-0.579367\pi$
$73$	5.11470	−	3.71605i	0.598631	−	0.434931i	0.845393	+	0.534145i	$0.179367\pi$
$74$	3.39140	+	10.4377i	0.394243	+	1.21335i
$75$	−0.973089	+	2.99486i	−0.112363	+	0.345817i
$76$	0.761360	+	0.553160i	0.0873340	+	0.0634518i
$77$	−1.58843	+	4.88869i	−0.181018	+	0.557117i
$78$	2.53802	−	7.81123i	0.287374	−	0.884448i
$79$	−8.59071	−	6.24151i	−0.966530	−	0.702225i	−0.0118721	−	0.999930i	$-0.503779\pi$
$79$	−8.59071	−	6.24151i	−0.966530	−	0.702225i	−0.954658	+	0.297704i	$0.903779\pi$
$80$	1.13817	−	3.50294i	0.127252	−	0.391641i
$81$	5.58827	+	17.1989i	0.620919	+	1.91099i
$82$	2.78758	−	2.02529i	0.307836	−	0.223656i
$83$	−3.10371	−	9.55223i	−0.340676	−	1.04849i	−0.963858	−	0.266416i	$-0.914160\pi$
$83$	−3.10371	−	9.55223i	−0.340676	−	1.04849i	0.623182	−	0.782077i	$-0.285840\pi$
$84$	−0.344354	−	0.250188i	−0.0375721	−	0.0272977i
$85$	1.86192	+	1.35276i	0.201953	+	0.146728i
$86$	10.4974	−	7.62683i	1.13197	−	0.822422i
$87$	−6.55529			−0.702800
$88$	16.3967			1.74790
$89$	1.86543	−	1.35532i	0.197735	−	0.143663i	−0.484512	−	0.874785i	$-0.661003\pi$
$89$	1.86543	−	1.35532i	0.197735	−	0.143663i	0.682247	+	0.731122i	$0.261003\pi$
$90$	−2.90884	+	8.95250i	−0.306619	+	0.943676i
$91$	−0.542612	−	1.66999i	−0.0568812	−	0.175062i
$92$	−0.544743			−0.0567933
$93$	−6.83108	+	16.1473i	−0.708350	+	1.67440i
$94$	5.67996			0.585843
$95$	−1.97142	−	6.06741i	−0.202263	−	0.622503i
$96$	−0.810314	+	2.49389i	−0.0827024	+	0.254532i
$97$	−9.18599	+	6.67401i	−0.932696	+	0.677643i	−0.946651	−	0.322260i	$-0.895558\pi$
$97$	−9.18599	+	6.67401i	−0.932696	+	0.677643i	0.0139556	+	0.999903i	$0.495558\pi$
$98$	−8.38465			−0.846977
$99$	−38.7976			−3.89930
$100$	0.119342	−	0.0867070i	0.0119342	−	0.00867070i
$101$	−3.83286	−	2.78473i	−0.381383	−	0.277091i	0.380532	−	0.924768i	$-0.375741\pi$
$101$	−3.83286	−	2.78473i	−0.381383	−	0.277091i	−0.761915	+	0.647676i	$0.775741\pi$
$102$	7.98009	+	5.79787i	0.790147	+	0.574075i
$103$	0.381335	+	1.17363i	0.0375740	+	0.115641i	0.968084	−	0.250625i	$-0.0806361\pi$
$103$	0.381335	+	1.17363i	0.0375740	+	0.115641i	−0.930510	+	0.366266i	$0.880636\pi$
$104$	−4.53144	+	3.29229i	−0.444345	+	0.322835i
$105$	0.891650	+	2.74422i	0.0870161	+	0.267808i
$106$	3.25194	−	10.0085i	0.315857	−	0.972107i
$107$	10.3951	+	7.55250i	1.00493	+	0.730127i	0.963140	−	0.268999i	$-0.0866928\pi$
$107$	10.3951	+	7.55250i	1.00493	+	0.730127i	0.0417936	+	0.999126i	$0.486693\pi$
$108$	0.562135	−	1.73007i	0.0540915	−	0.166476i
$109$	0.325129	−	1.00064i	0.0311417	−	0.0958444i	−0.934278	−	0.356547i	$-0.883954\pi$
$109$	0.325129	−	1.00064i	0.0311417	−	0.0958444i	0.965419	+	0.260702i	$0.0839541\pi$
$110$	−6.17702	−	4.48787i	−0.588956	−	0.427901i
$111$	−7.84643	+	24.1488i	−0.744750	+	2.29211i
$112$	−1.04292	−	3.20978i	−0.0985466	−	0.303295i
$113$	−9.95912	+	7.23572i	−0.936875	+	0.680680i	−0.947666	−	0.319262i	$-0.896565\pi$
$113$	−9.95912	+	7.23572i	−0.936875	+	0.680680i	0.0107913	+	0.999942i	$0.496565\pi$
$114$	−8.44941	−	26.0046i	−0.791360	−	2.43556i
$115$	2.98754	+	2.17057i	0.278589	+	0.202407i
$116$	0.248436	+	0.180499i	0.0230667	+	0.0167589i
$117$	10.7222	−	7.79013i	0.991267	−	0.720198i
$118$	13.4223			1.23562
$119$	2.10884			0.193317
$120$	7.44631	−	5.41006i	0.679752	−	0.493869i
$121$	6.32538	−	19.4675i	0.575034	−	1.76977i
$122$	−2.86678	−	8.82306i	−0.259546	−	0.798802i
$123$	7.97190			0.718802
$124$	0.703503	−	0.423866i	0.0631765	−	0.0380643i
$125$	−1.00000			−0.0894427
$126$	2.66540	+	8.20325i	0.237453	+	0.730804i
$127$	−0.142802	+	0.439500i	−0.0126716	+	0.0389993i	−0.957192	−	0.289452i	$-0.906527\pi$
$127$	−0.142802	+	0.439500i	−0.0126716	+	0.0389993i	0.944521	+	0.328452i	$0.106527\pi$
$128$	−8.01194	+	5.82101i	−0.708162	+	0.514510i
$129$	30.0205			2.64316
$130$	2.60821			0.228755
$131$	3.15547	−	2.29258i	0.275694	−	0.200304i	−0.441343	−	0.897339i	$-0.645498\pi$
$131$	3.15547	−	2.29258i	0.275694	−	0.200304i	0.717037	+	0.697035i	$0.245498\pi$
$132$	2.10818	+	1.53168i	0.183493	+	0.133316i
$133$	−4.72929	−	3.43603i	−0.410082	−	0.297942i
$134$	0.174204	+	0.536144i	0.0150489	+	0.0463158i
$135$	−9.97655	+	7.24839i	−0.858645	+	0.623842i
$136$	−2.07873	−	6.39768i	−0.178250	−	0.548596i
$137$	3.52887	−	10.8607i	0.301491	−	0.927895i	−0.679472	−	0.733702i	$-0.737791\pi$
$137$	3.52887	−	10.8607i	0.301491	−	0.927895i	0.980963	−	0.194193i	$-0.0622089\pi$
$138$	12.8044	+	9.30298i	1.08999	+	0.791922i
$139$	−2.91380	+	8.96774i	−0.247145	+	0.760634i	0.748131	+	0.663551i	$0.230951\pi$
$139$	−2.91380	+	8.96774i	−0.247145	+	0.760634i	−0.995276	+	0.0970833i	$0.969049\pi$
$140$	0.0417696	−	0.128554i	0.00353017	−	0.0108648i
$141$	10.6315	+	7.72426i	0.895337	+	0.650500i
$142$	−2.43624	+	7.49797i	−0.204445	+	0.629216i
$143$	3.32194	+	10.2239i	0.277795	+	0.854964i
$144$	20.6084	−	14.9729i	1.71737	−	1.24774i
$145$	−0.643286	−	1.97983i	−0.0534220	−	0.164416i
$146$	6.96142	+	5.05777i	0.576131	+	0.418584i
$147$	−15.6941	−	11.4024i	−1.29442	−	0.940454i
$148$	0.962306	−	0.699156i	0.0791010	−	0.0574703i
$149$	−16.3472			−1.33922			−0.669608	−	0.742715i	$-0.733538\pi$
$149$	−16.3472			−1.33922			−0.669608	+	0.742715i	$0.733538\pi$
$150$	−4.28595			−0.349947
$151$	−2.41419	+	1.75402i	−0.196464	+	0.142740i	−0.681668	−	0.731661i	$-0.738745\pi$
$151$	−2.41419	+	1.75402i	−0.196464	+	0.142740i	0.485204	+	0.874401i	$0.338745\pi$
$152$	−5.76226	+	17.7344i	−0.467381	+	1.43845i
$153$	4.91864	+	15.1380i	0.397649	+	1.22384i
$154$	−6.99621			−0.563771
$155$	−5.54716	−	0.478553i	−0.445559	−	0.0384383i
$156$	−0.890167			−0.0712704
$157$	−2.56540	−	7.89548i	−0.204741	−	0.630128i	−0.999724	−	0.0234963i	$-0.992520\pi$
$157$	−2.56540	−	7.89548i	−0.204741	−	0.630128i	0.794983	−	0.606632i	$-0.207480\pi$
$158$	4.46613	−	13.7453i	0.355306	−	1.09352i
$159$	19.6975	−	14.3111i	1.56211	−	1.13494i
$160$	−0.832724			−0.0658326
$161$	3.38374			0.266676
$162$	−19.9127	+	14.4674i	−1.56449	+	1.13667i
$163$	18.4867	+	13.4314i	1.44799	+	1.05203i	0.986295	+	0.164992i	$0.0527597\pi$
$163$	18.4867	+	13.4314i	1.44799	+	1.05203i	0.461698	+	0.887037i	$0.347240\pi$
$164$	−0.302124	−	0.219506i	−0.0235919	−	0.0171405i
$165$	−5.45879	−	16.8004i	−0.424966	−	1.30791i
$166$	11.0594	−	8.03516i	0.858379	−	0.623649i
$167$	4.62307	+	14.2283i	0.357744	+	1.10102i	0.954401	+	0.298526i	$0.0964951\pi$
$167$	4.62307	+	14.2283i	0.357744	+	1.10102i	−0.596657	+	0.802496i	$0.703505\pi$
$168$	2.60620	−	8.02106i	0.201073	−	0.618838i
$169$	7.54632	+	5.48272i	0.580486	+	0.421748i
$170$	−0.967971	+	2.97911i	−0.0742400	+	0.228487i
$171$	13.6345	−	41.9627i	1.04266	−	3.20897i
$172$	−1.13774	−	0.826613i	−0.0867515	−	0.0630287i
$173$	−0.833317	+	2.56469i	−0.0633560	+	0.194990i	−0.977724	−	0.209894i	$-0.932688\pi$
$173$	−0.833317	+	2.56469i	−0.0633560	+	0.194990i	0.914368	+	0.404884i	$0.132688\pi$
$174$	−2.75709	−	8.48546i	−0.209015	−	0.643281i
$175$	−0.741309	+	0.538593i	−0.0560377	+	0.0407138i
$176$	6.38488	+	19.6506i	0.481278	+	1.48122i
$177$	25.1234	+	18.2532i	1.88839	+	1.37199i
$178$	2.53896	+	1.84467i	0.190303	+	0.138264i
$179$	19.7892	−	14.3777i	1.47911	−	1.07464i	0.501271	−	0.865290i	$-0.332866\pi$
$179$	19.7892	−	14.3777i	1.47911	−	1.07464i	0.977841	−	0.209348i	$-0.0671342\pi$
$180$	1.02023			0.0760431
$181$	−18.9958			−1.41194			−0.705972	−	0.708239i	$-0.749490\pi$
$181$	−18.9958			−1.41194			−0.705972	+	0.708239i	$0.749490\pi$
$182$	1.93349	−	1.40476i	0.143320	−	0.104128i
$183$	6.63266	−	20.4132i	0.490301	−	1.50899i
$184$	−3.33543	−	10.2654i	−0.245891	−	0.756775i
$185$	−8.06343			−0.592835
$186$	−23.7749	−	2.05106i	−1.74326	−	0.150391i
$187$	−12.9106			−0.944117
$188$	−0.190233	−	0.585477i	−0.0138742	−	0.0427003i
$189$	−3.49178	+	10.7466i	−0.253990	+	0.781700i
$190$	7.02476	−	5.10379i	0.509630	−	0.370268i
$191$	−22.8593			−1.65404			−0.827021	−	0.562171i	$-0.809966\pi$
$191$	−22.8593			−1.65404			−0.827021	+	0.562171i	$0.809966\pi$
$192$	−26.7657			−1.93165
$193$	10.3326	−	7.50709i	0.743759	−	0.540372i	−0.150127	−	0.988667i	$-0.547968\pi$
$193$	10.3326	−	7.50709i	0.743759	−	0.540372i	0.893886	+	0.448294i	$0.147968\pi$
$194$	−12.5027	−	9.08373i	−0.897640	−	0.652174i
$195$	4.88195	+	3.54694i	0.349604	+	0.254002i
$196$	0.280818	+	0.864270i	0.0200585	+	0.0617336i
$197$	−14.8306	+	10.7751i	−1.05664	+	0.767693i	−0.973464	−	0.228842i	$-0.926506\pi$
$197$	−14.8306	+	10.7751i	−1.05664	+	0.767693i	−0.0831754	+	0.996535i	$0.526506\pi$
$198$	−16.3179	−	50.2213i	−1.15966	−	3.56907i
$199$	−7.21304	+	22.1995i	−0.511319	+	1.57368i	0.278562	+	0.960418i	$0.410142\pi$
$199$	−7.21304	+	22.1995i	−0.511319	+	1.57368i	−0.789881	+	0.613260i	$0.789858\pi$
$200$	2.36467	+	1.71804i	0.167208	+	0.121483i
$201$	−0.403042	+	1.24043i	−0.0284284	+	0.0874935i
$202$	1.99262	−	6.13265i	0.140200	−	0.431492i
$203$	−1.54320	−	1.12120i	−0.108311	−	0.0786926i
$204$	0.330363	−	1.01675i	0.0231300	−	0.0711868i
$205$	0.782302	+	2.40768i	0.0546383	+	0.168159i
$206$	−1.35881	+	0.987234i	−0.0946729	+	0.0687839i
$207$	7.89221	+	24.2897i	0.548546	+	1.68825i
$208$	−5.71018	−	4.14869i	−0.395930	−	0.287660i
$209$	28.9533	+	21.0358i	2.00274	+	1.45508i
$210$	−3.17722	+	2.30838i	−0.219249	+	0.159294i
$211$	−4.87701			−0.335747			−0.167874	−	0.985809i	$-0.553690\pi$
$211$	−4.87701			−0.335747			−0.167874	+	0.985809i	$0.553690\pi$
$212$	−1.14056			−0.0783341
$213$	−14.7567	+	10.7213i	−1.01111	+	0.734614i
$214$	−5.40420	+	16.6324i	−0.369424	+	1.13697i
$215$	2.94598	+	9.06681i	0.200914	+	0.618351i
$216$	36.0443			2.45250
$217$	−4.36991	+	2.63290i	−0.296649	+	0.178733i
$218$	1.43203			0.0969891
$219$	6.15199	+	18.9339i	0.415713	+	1.27943i
$220$	−0.255718	+	0.787020i	−0.0172405	+	0.0530609i
$221$	3.56801	−	2.59231i	0.240010	−	0.174378i
$222$	−34.5595			−2.31948
$223$	−10.8420			−0.726032			−0.363016	−	0.931783i	$-0.618253\pi$
$223$	−10.8420			−0.726032			−0.363016	+	0.931783i	$0.618253\pi$
$224$	−0.617306	+	0.448499i	−0.0412455	+	0.0299666i
$225$	−5.59523	−	4.06517i	−0.373016	−	0.271012i
$226$	−13.5550	−	9.84826i	−0.901663	−	0.655096i
$227$	−1.70815	−	5.25714i	−0.113374	−	0.348929i	0.878231	−	0.478238i	$-0.158724\pi$
$227$	−1.70815	−	5.25714i	−0.113374	−	0.348929i	−0.991604	+	0.129309i	$0.958724\pi$
$228$	−2.39751	+	1.74189i	−0.158779	+	0.115360i
$229$	−3.15229	−	9.70174i	−0.208309	−	0.641109i	−0.999561	−	0.0296192i	$-0.990571\pi$
$229$	−3.15229	−	9.70174i	−0.208309	−	0.641109i	0.791252	−	0.611490i	$-0.209429\pi$
$230$	−1.55316	+	4.78013i	−0.102412	+	0.315192i
$231$	−13.0952	−	9.51425i	−0.861604	−	0.625992i
$232$	−1.88026	+	5.78684i	−0.123445	+	0.379924i
$233$	−2.79870	+	8.61352i	−0.183349	+	0.564290i	−0.999916	−	0.0129605i	$-0.995874\pi$
$233$	−2.79870	+	8.61352i	−0.183349	+	0.564290i	0.816567	+	0.577251i	$0.195874\pi$
$234$	14.5936	+	10.6028i	0.954010	+	0.693129i
$235$	−1.28959	+	3.96894i	−0.0841233	+	0.258905i
$236$	−0.449540	−	1.38354i	−0.0292625	−	0.0900608i
$237$	27.0520	−	19.6544i	1.75722	−	1.27669i
$238$	0.886960	+	2.72978i	0.0574931	+	0.176946i
$239$	−9.64391	−	7.00671i	−0.623813	−	0.453226i	0.230439	−	0.973087i	$-0.425984\pi$
$239$	−9.64391	−	7.00671i	−0.623813	−	0.453226i	−0.854251	+	0.519860i	$0.825984\pi$
$240$	9.38327	+	6.81735i	0.605688	+	0.440058i
$241$	−14.1964	+	10.3143i	−0.914473	+	0.664404i	−0.942142	−	0.335213i	$-0.891192\pi$
$241$	−14.1964	+	10.3143i	−0.914473	+	0.664404i	0.0276690	+	0.999617i	$0.491192\pi$
$242$	27.8600			1.79091
$243$	−19.9512			−1.27987
$244$	−0.813446	+	0.591003i	−0.0520755	+	0.0378351i
$245$	1.90366	−	5.85887i	0.121620	−	0.374309i
$246$	3.35291	+	10.3192i	0.213774	+	0.657928i
$247$	−12.2254			−0.777882
$248$	12.2951	+	10.6618i	0.780737	+	0.677028i
$249$	31.6278			2.00433
$250$	−0.420591	−	1.29445i	−0.0266005	−	0.0818679i
$251$	7.48819	−	23.0463i	0.472650	−	1.45467i	−0.376450	−	0.926437i	$-0.622855\pi$
$251$	7.48819	−	23.0463i	0.472650	−	1.45467i	0.849100	−	0.528231i	$-0.177145\pi$
$252$	0.756303	−	0.549486i	0.0476426	−	0.0346144i
$253$	−20.7157			−1.30238
$254$	−0.628970			−0.0394651
$255$	−5.86314	+	4.25982i	−0.367164	+	0.266760i
$256$	2.84824	+	2.06937i	0.178015	+	0.129336i
$257$	−4.46143	−	3.24142i	−0.278296	−	0.202194i	0.439878	−	0.898058i	$-0.355022\pi$
$257$	−4.46143	−	3.24142i	−0.278296	−	0.202194i	−0.718174	+	0.695864i	$0.755022\pi$
$258$	12.6264	+	38.8599i	0.786082	+	2.41931i
$259$	−5.97750	+	4.34290i	−0.371423	+	0.269855i
$260$	−0.0873542	−	0.268848i	−0.00541747	−	0.0166733i
$261$	4.44902	−	13.6927i	0.275387	−	0.847555i
$262$	4.29478	+	3.12034i	0.265332	+	0.192775i
$263$	−2.44499	+	7.52489i	−0.150764	+	0.464005i	−0.997707	−	0.0676792i	$-0.978441\pi$
$263$	−2.44499	+	7.52489i	−0.150764	+	0.464005i	0.846943	+	0.531684i	$0.178441\pi$
$264$	−15.9555	+	49.1059i	−0.981992	+	3.02226i
$265$	6.25519	+	4.54466i	0.384254	+	0.279177i
$266$	2.45866	−	7.56697i	0.150750	−	0.463961i
$267$	2.24375	+	6.90555i	0.137315	+	0.422613i
$268$	0.0494300	−	0.0359130i	0.00301942	−	0.00219374i
$269$	0.166570	+	0.512649i	0.0101559	+	0.0312568i	0.956006	−	0.293347i	$-0.0947691\pi$
$269$	0.166570	+	0.512649i	0.0101559	+	0.0312568i	−0.945850	+	0.324604i	$0.894769\pi$
$270$	−13.5787	−	9.86549i	−0.826372	−	0.600395i
$271$	10.5152	+	7.63975i	0.638754	+	0.464082i	0.859422	−	0.511267i	$-0.170824\pi$
$271$	10.5152	+	7.63975i	0.638754	+	0.464082i	−0.220668	+	0.975349i	$0.570824\pi$
$272$	6.85783	−	4.98250i	0.415817	−	0.302109i
$273$	5.52939			0.334654
$274$	15.5428			0.938977
$275$	4.53839	−	3.29733i	0.273675	−	0.198837i
$276$	0.530083	−	1.63143i	0.0319072	−	0.0982004i
$277$	−0.394056	−	1.21278i	−0.0236765	−	0.0728689i	0.938520	−	0.345225i	$-0.112197\pi$
$277$	−0.394056	−	1.21278i	−0.0236765	−	0.0728689i	−0.962197	+	0.272356i	$0.912197\pi$
$278$	−12.8338			−0.769718
$279$	−29.0923	−	25.2278i	−1.74171	−	1.51035i
$280$	2.67828			0.160058
$281$	3.36754	+	10.3642i	0.200891	+	0.618278i	0.999857	+	0.0169022i	$0.00538040\pi$
$281$	3.36754	+	10.3642i	0.200891	+	0.618278i	−0.798967	+	0.601375i	$0.794620\pi$
$282$	−5.52711	+	17.0107i	−0.329135	+	1.01297i
$283$	8.36935	−	6.08069i	0.497506	−	0.361460i	−0.310557	−	0.950555i	$-0.600516\pi$
$283$	8.36935	−	6.08069i	0.497506	−	0.361460i	0.808064	+	0.589095i	$0.200516\pi$
$284$	0.854468			0.0507034
$285$	20.0894			1.18999
$286$	−11.8371	+	8.60014i	−0.699941	+	0.508537i
$287$	1.87668	+	1.36349i	0.110777	+	0.0804843i
$288$	−4.65928	−	3.38517i	−0.274551	−	0.199473i
$289$	−3.61652	−	11.1305i	−0.212736	−	0.654736i
$290$	2.29222	−	1.66540i	0.134604	−	0.0977954i
$291$	−11.0489	−	34.0052i	−0.647701	−	1.99342i
$292$	0.288191	−	0.886962i	0.0168651	−	0.0519055i
$293$	−15.5304	−	11.2835i	−0.907297	−	0.659190i	0.0330331	−	0.999454i	$-0.489483\pi$
$293$	−15.5304	−	11.2835i	−0.907297	−	0.659190i	−0.940330	+	0.340265i	$0.889483\pi$
$294$	8.15901	−	25.1108i	0.475843	−	1.46449i
$295$	−3.04742	+	9.37899i	−0.177428	+	0.546066i
$296$	19.0674	+	13.8533i	1.10827	+	0.805204i
$297$	21.3771	−	65.7920i	1.24043	−	3.81764i
$298$	−6.87549	−	21.1606i	−0.398286	−	1.22580i
$299$	5.72504	−	4.15949i	0.331088	−	0.240549i
$300$	0.143545	+	0.441786i	0.00828758	+	0.0255065i
$301$	7.06720	+	5.13462i	0.407347	+	0.295955i
$302$	−3.28586	−	2.38732i	−0.189080	−	0.137375i
$303$	12.0696	−	8.76907i	0.693380	−	0.503770i
$304$	−23.4976			−1.34768
$305$	6.81609			0.390288
$306$	−17.5266	+	12.7338i	−1.00193	+	0.727945i
$307$	−2.95997	+	9.10984i	−0.168934	+	0.519926i	−0.999305	−	0.0372856i	$-0.988129\pi$
$307$	−2.95997	+	9.10984i	−0.168934	+	0.519926i	0.830370	+	0.557212i	$0.188129\pi$
$308$	0.234317	+	0.721154i	0.0133515	+	0.0410915i
$309$	−3.88593			−0.221063
$310$	−1.71362	−	7.38177i	−0.0973273	−	0.419256i
$311$	0.0597943			0.00339063			0.00169531	−	0.999999i	$-0.499460\pi$
$311$	0.0597943			0.00339063			0.00169531	+	0.999999i	$0.499460\pi$
$312$	−5.45044	−	16.7747i	−0.308570	−	0.949682i
$313$	3.00795	−	9.25752i	0.170019	−	0.523266i	−0.829352	−	0.558727i	$-0.811290\pi$
$313$	3.00795	−	9.25752i	0.170019	−	0.523266i	0.999371	+	0.0354611i	$0.0112900\pi$
$314$	9.14129	−	6.64153i	0.515873	−	0.374804i
$315$	−6.33727			−0.357065
$316$	−1.56642			−0.0881178
$317$	5.30371	−	3.85337i	0.297886	−	0.216427i	−0.428795	−	0.903402i	$-0.641062\pi$
$317$	5.30371	−	3.85337i	0.297886	−	0.216427i	0.726681	+	0.686975i	$0.241062\pi$
$318$	26.8095	+	19.4782i	1.50340	+	1.09228i
$319$	9.44763	+	6.86411i	0.528966	+	0.384316i
$320$	−2.62658	−	8.08380i	−0.146831	−	0.451898i
$321$	−32.7340	+	23.7827i	−1.82704	+	1.32742i
$322$	1.42317	+	4.38007i	0.0793102	+	0.244092i
$323$	4.53713	−	13.9639i	0.252453	−	0.776970i
$324$	2.15818	+	1.56801i	0.119899	+	0.0871117i
$325$	−0.592172	+	1.82252i	−0.0328478	+	0.101095i
$326$	−9.61086	+	29.5792i	−0.532297	+	1.63824i
$327$	2.68041	+	1.94743i	0.148227	+	0.107693i
$328$	2.28659	−	7.03739i	0.126256	−	0.388575i
$329$	1.18166	+	3.63677i	0.0651470	+	0.200502i
$330$	19.4513	−	14.1322i	1.07076	−	0.777953i
$331$	−3.02132	−	9.29868i	−0.166067	−	0.511101i	0.833046	−	0.553203i	$-0.186595\pi$
$331$	−3.02132	−	9.29868i	−0.166067	−	0.511101i	−0.999113	+	0.0421017i	$0.986595\pi$
$332$	−1.19865	−	0.870869i	−0.0657844	−	0.0477951i
$333$	−45.1168	−	32.7792i	−2.47238	−	1.79629i
$334$	−16.4734	+	11.9686i	−0.901384	+	0.654894i
$335$	−0.414188			−0.0226295
$336$	10.6277			0.579788
$337$	−4.87501	+	3.54190i	−0.265559	+	0.192940i	−0.712594	−	0.701577i	$-0.752480\pi$
$337$	−4.87501	+	3.54190i	−0.265559	+	0.192940i	0.447035	+	0.894516i	$0.352480\pi$
$338$	−3.92317	+	12.0743i	−0.213392	+	0.656754i
$339$	−11.9789	−	36.8672i	−0.650603	−	2.00235i
$340$	0.339499			0.0184119
$341$	26.7531	−	16.1190i	1.44876	−	0.872891i
$342$	60.0530			3.24729
$343$	−3.72643	−	11.4688i	−0.201208	−	0.619255i
$344$	8.61081	−	26.5013i	0.464264	−	1.42886i
$345$	−9.40770	+	6.83509i	−0.506494	+	0.367989i
$346$	−3.67033			−0.197318
$347$	19.0290			1.02153			0.510765	−	0.859720i	$-0.329362\pi$
$347$	19.0290			1.02153			0.510765	+	0.859720i	$0.329362\pi$
$348$	−0.782321	+	0.568389i	−0.0419368	+	0.0304689i
$349$	−14.0832	−	10.2321i	−0.753859	−	0.547710i	0.143162	−	0.989699i	$-0.454273\pi$
$349$	−14.0832	−	10.2321i	−0.753859	−	0.547710i	−0.897021	+	0.441989i	$0.854273\pi$
$350$	−1.00897	−	0.733057i	−0.0539315	−	0.0391836i
$351$	7.30248	+	22.4747i	0.389778	+	1.19961i
$352$	3.77922	−	2.74577i	0.201433	−	0.146350i
$353$	3.68802	+	11.3506i	0.196293	+	0.604129i	0.999959	+	0.00904788i	$0.00288007\pi$
$353$	3.68802	+	11.3506i	0.196293	+	0.604129i	−0.803666	+	0.595081i	$0.797120\pi$
$354$	−13.0611	+	40.1979i	−0.694190	+	2.13650i
$355$	−4.68617	−	3.40470i	−0.248716	−	0.180703i
$356$	0.105109	−	0.323492i	0.00557076	−	0.0171450i
$357$	−2.05209	+	6.31569i	−0.108608	+	0.334262i
$358$	26.9343	+	19.5689i	1.42352	+	1.03425i
$359$	−9.86202	+	30.3522i	−0.520497	+	1.60193i	0.252554	+	0.967583i	$0.418729\pi$
$359$	−9.86202	+	30.3522i	−0.520497	+	1.60193i	−0.773052	+	0.634343i	$0.781271\pi$
$360$	6.24678	+	19.2256i	0.329234	+	1.01328i
$361$	−17.5556	+	12.7549i	−0.923978	+	0.671310i
$362$	−7.98945	−	24.5890i	−0.419916	−	1.29237i
$363$	52.1473	+	37.8872i	2.73702	+	1.98856i
$364$	−0.209556	−	0.152252i	−0.0109837	−	0.00798015i
$365$	−5.11470	+	3.71605i	−0.267716	+	0.194507i
$366$	29.2135			1.52701
$367$	16.2510			0.848293			0.424147	−	0.905593i	$-0.360574\pi$
$367$	16.2510			0.848293			0.424147	+	0.905593i	$0.360574\pi$
$368$	11.0037	−	7.99467i	0.573609	−	0.416751i
$369$	−5.41047	+	16.6517i	−0.281658	+	0.866853i
$370$	−3.39140	−	10.4377i	−0.176311	−	0.542628i
$371$	7.08476			0.367822
$372$	0.584849	+	2.51935i	0.0303230	+	0.130622i
$373$	21.1742			1.09636			0.548180	−	0.836360i	$-0.315321\pi$
$373$	21.1742			1.09636			0.548180	+	0.836360i	$0.315321\pi$
$374$	−5.43008	−	16.7121i	−0.280783	−	0.864160i
$375$	0.973089	−	2.99486i	0.0502501	−	0.154654i
$376$	9.86823	−	7.16969i	0.508915	−	0.369748i
$377$	−3.98921			−0.205455
$378$	−15.3795			−0.791036
$379$	5.43943	−	3.95198i	0.279405	−	0.203000i	−0.439253	−	0.898363i	$-0.644757\pi$
$379$	5.43943	−	3.95198i	0.279405	−	0.203000i	0.718658	+	0.695364i	$0.244757\pi$
$380$	−0.761360	−	0.553160i	−0.0390569	−	0.0283765i
$381$	−1.17728	−	0.855345i	−0.0603140	−	0.0438207i
$382$	−9.61442	−	29.5901i	−0.491916	−	1.51396i
$383$	14.9958	−	10.8951i	0.766251	−	0.556714i	−0.134571	−	0.990904i	$-0.542965\pi$
$383$	14.9958	−	10.8951i	0.766251	−	0.556714i	0.900821	+	0.434190i	$0.142965\pi$
$384$	−9.63679	−	29.6590i	−0.491776	−	1.51353i
$385$	1.58843	−	4.88869i	0.0809539	−	0.249150i
$386$	14.0633	+	10.2176i	0.715805	+	0.520062i
$387$	−20.3747	+	62.7068i	−1.03570	+	3.18757i
$388$	−0.517590	+	1.59298i	−0.0262767	+	0.0808713i
$389$	2.34427	+	1.70321i	0.118859	+	0.0863562i	0.645627	−	0.763653i	$-0.276596\pi$
$389$	2.34427	+	1.70321i	0.118859	+	0.0863562i	−0.526768	+	0.850009i	$0.676596\pi$
$390$	−2.53802	+	7.81123i	−0.128518	+	0.395537i
$391$	2.62628	+	8.08285i	0.132817	+	0.408767i
$392$	−14.5673	+	10.5838i	−0.735759	+	0.534560i
$393$	3.79541	+	11.6811i	0.191453	+	0.589232i
$394$	−20.1854	−	14.6655i	−1.01693	−	0.738839i
$395$	8.59071	+	6.24151i	0.432245	+	0.314045i
$396$	−4.63018	+	3.36402i	−0.232675	+	0.169048i
$397$	−21.8732			−1.09778			−0.548891	−	0.835894i	$-0.684950\pi$
$397$	−21.8732			−1.09778			−0.548891	+	0.835894i	$0.684950\pi$
$398$	−31.7697			−1.59247
$399$	14.8925	−	10.8200i	0.745555	−	0.541678i
$400$	−1.13817	+	3.50294i	−0.0569087	+	0.175147i
$401$	−1.69586	−	5.21933i	−0.0846874	−	0.260641i	0.899742	−	0.436423i	$-0.143755\pi$
$401$	−1.69586	−	5.21933i	−0.0846874	−	0.260641i	−0.984429	+	0.175782i	$0.943755\pi$
$402$	−1.77519			−0.0885385
$403$	−4.15705	+	9.82641i	−0.207077	+	0.489489i
$404$	−0.698877			−0.0347704
$405$	−5.58827	−	17.1989i	−0.277683	−	0.854621i
$406$	0.802275	−	2.46915i	0.0398162	−	0.122542i
$407$	36.5950	−	26.5878i	1.81394	−	1.31791i
$408$	21.1829			1.04871
$409$	20.9396			1.03540			0.517698	−	0.855563i	$-0.326789\pi$
$409$	20.9396			1.03540			0.517698	+	0.855563i	$0.326789\pi$
$410$	−2.78758	+	2.02529i	−0.137669	+	0.100022i
$411$	29.0925	+	21.1369i	1.43503	+	1.04261i
$412$	0.147271	+	0.106999i	0.00725553	+	0.00527145i
$413$	2.79238	+	8.59406i	0.137404	+	0.422886i
$414$	−28.1223	+	20.4321i	−1.38214	+	1.00418i
$415$	3.10371	+	9.55223i	0.152355	+	0.468900i
$416$	−0.493116	+	1.51765i	−0.0241770	+	0.0744091i
$417$	−24.0218	−	17.4528i	−1.17635	−	0.854669i
$418$	−15.0522	+	46.3259i	−0.736228	+	2.26588i
$419$	0.278033	−	0.855696i	0.0135828	−	0.0418035i	−0.944035	−	0.329844i	$-0.893004\pi$
$419$	0.278033	−	0.855696i	0.0135828	−	0.0418035i	0.957618	+	0.288041i	$0.0930038\pi$
$420$	0.344354	+	0.250188i	0.0168028	+	0.0122079i
$421$	−7.08975	+	21.8200i	−0.345533	+	1.06344i	0.615765	+	0.787930i	$0.288847\pi$
$421$	−7.08975	+	21.8200i	−0.345533	+	1.06344i	−0.961298	+	0.275512i	$0.911153\pi$
$422$	−2.05122	−	6.31302i	−0.0998521	−	0.307313i
$423$	−23.3500	+	16.9647i	−1.13531	+	0.824854i
$424$	−6.98360	−	21.4933i	−0.339153	−	1.04381i
$425$	−1.86192	−	1.35276i	−0.0903162	−	0.0656186i
$426$	−20.0847	−	14.5924i	−0.973107	−	0.707004i
$427$	5.05283	−	3.67110i	0.244524	−	0.177657i
$428$	1.89543			0.0916190
$429$	−33.8516			−1.63437
$430$	−10.4974	+	7.62683i	−0.506231	+	0.367798i
$431$	−10.6468	+	32.7676i	−0.512840	+	1.57836i	0.274337	+	0.961634i	$0.411542\pi$
$431$	−10.6468	+	32.7676i	−0.512840	+	1.57836i	−0.787177	+	0.616727i	$0.788458\pi$
$432$	14.0356	+	43.1972i	0.675289	+	2.07833i
$433$	0.131862			0.00633687			0.00316844	−	0.999995i	$-0.498991\pi$
$433$	0.131862			0.00633687			0.00316844	+	0.999995i	$0.498991\pi$
$434$	−5.24609	−	4.54923i	−0.251821	−	0.218370i
$435$	6.55529			0.314302
$436$	−0.0479614	−	0.147610i	−0.00229693	−	0.00706924i
$437$	7.28005	−	22.4057i	0.348252	−	1.07181i
$438$	−21.9214	+	15.9268i	−1.04744	+	0.761013i
$439$	27.8217			1.32786			0.663929	−	0.747795i	$-0.268888\pi$
$439$	27.8217			1.32786			0.663929	+	0.747795i	$0.268888\pi$
$440$	−16.3967			−0.781684
$441$	34.4688	−	25.0430i	1.64137	−	1.19252i
$442$	4.85627	+	3.52829i	0.230989	+	0.167824i
$443$	−18.9099	−	13.7389i	−0.898437	−	0.652753i	0.0396273	−	0.999215i	$-0.487383\pi$
$443$	−18.9099	−	13.7389i	−0.898437	−	0.652753i	−0.938064	+	0.346462i	$0.887383\pi$
$444$	1.15747	+	3.56231i	0.0549309	+	0.169060i
$445$	−1.86543	+	1.35532i	−0.0884299	+	0.0642481i
$446$	−4.56003	−	14.0343i	−0.215924	−	0.664545i
$447$	15.9073	−	48.9576i	0.752389	−	2.31562i
$448$	−6.30099	−	4.57794i	−0.297694	−	0.216287i
$449$	−1.68488	+	5.18553i	−0.0795145	+	0.244721i	−0.982910	−	0.184089i	$-0.941067\pi$
$449$	−1.68488	+	5.18553i	−0.0795145	+	0.244721i	0.903395	+	0.428809i	$0.141067\pi$
$450$	2.90884	−	8.95250i	0.137124	−	0.422025i
$451$	−11.4893	−	8.34746i	−0.541010	−	0.393067i
$452$	−0.561153	+	1.72705i	−0.0263944	+	0.0812337i
$453$	−2.90380	−	8.93699i	−0.136433	−	0.419896i
$454$	6.08665	−	4.42221i	0.285661	−	0.207545i
$455$	0.542612	+	1.66999i	0.0254381	+	0.0782903i
$456$	−47.5049	−	34.5143i	−2.22462	−	1.61628i
$457$	−26.8169	−	19.4836i	−1.25444	−	0.911404i	−0.255969	−	0.966685i	$-0.582394\pi$
$457$	−26.8169	−	19.4836i	−1.25444	−	0.911404i	−0.998471	+	0.0552814i	$0.982394\pi$
$458$	11.2325	−	8.16093i	0.524863	−	0.381335i
$459$	−28.3808			−1.32470
$460$	0.544743			0.0253988
$461$	5.65240	−	4.10671i	0.263259	−	0.191269i	−0.448324	−	0.893871i	$-0.647979\pi$
$461$	5.65240	−	4.10671i	0.263259	−	0.191269i	0.711582	+	0.702603i	$0.247979\pi$
$462$	6.80794	−	20.9527i	0.316734	−	0.974807i
$463$	−6.10820	−	18.7991i	−0.283872	−	0.873668i	−0.986734	−	0.162342i	$-0.948095\pi$
$463$	−6.10820	−	18.7991i	−0.283872	−	0.873668i	0.702863	−	0.711326i	$-0.251905\pi$
$464$	−7.66740			−0.355950
$465$	6.83108	−	16.1473i	0.316784	−	0.748813i
$466$	−12.3268			−0.571029
$467$	5.16887	+	15.9082i	0.239187	+	0.736142i	0.996538	+	0.0831341i	$0.0264930\pi$
$467$	5.16887	+	15.9082i	0.239187	+	0.736142i	−0.757351	+	0.653007i	$0.773507\pi$
$468$	0.604149	−	1.85938i	0.0279268	−	0.0859499i
$469$	−0.307041	+	0.223079i	−0.0141779	+	0.0103008i
$470$	−5.67996			−0.261997
$471$	26.1422			1.20457
$472$	23.3196	−	16.9427i	1.07337	−	0.779850i
$473$	−43.2663	−	31.4348i	−1.98939	−	1.44537i
$474$	36.8194	+	26.7508i	1.69117	+	1.22871i
$475$	1.97142	+	6.06741i	0.0904549	+	0.278392i
$476$	0.251674	−	0.182852i	0.0115354	−	0.00838099i
$477$	16.5244	+	50.8569i	0.756601	+	2.32858i
$478$	5.01366	−	15.4305i	0.229320	−	0.705773i
$479$	−3.37161	−	2.44962i	−0.154053	−	0.111926i	0.508089	−	0.861305i	$-0.330352\pi$
$479$	−3.37161	−	2.44962i	−0.154053	−	0.111926i	−0.662141	+	0.749379i	$0.730352\pi$
$480$	0.810314	−	2.49389i	0.0369856	−	0.113830i
$481$	−4.77494	+	14.6957i	−0.217718	+	0.670068i
$482$	−19.3222	−	14.0384i	−0.880103	−	0.639432i
$483$	−3.29268	+	10.1338i	−0.149822	+	0.461106i
$484$	−0.933087	−	2.87175i	−0.0424130	−	0.130534i
$485$	9.18599	−	6.67401i	0.417114	−	0.303051i
$486$	−8.39127	−	25.8257i	−0.380636	−	1.17148i
$487$	−5.26178	−	3.82291i	−0.238434	−	0.173232i	0.462151	−	0.886801i	$-0.347078\pi$
$487$	−5.26178	−	3.82291i	−0.238434	−	0.173232i	−0.700585	+	0.713569i	$0.747078\pi$
$488$	−16.1178	−	11.7103i	−0.729620	−	0.530100i
$489$	−58.2144	+	42.2952i	−2.63255	+	1.91266i
$490$	8.38465			0.378780
$491$	25.5391			1.15256			0.576282	−	0.817251i	$-0.304503\pi$
$491$	25.5391			1.15256			0.576282	+	0.817251i	$0.304503\pi$
$492$	0.951383	−	0.691220i	0.0428917	−	0.0311626i
$493$	1.48049	−	4.55649i	0.0666780	−	0.205214i
$494$	−5.14188	−	15.8251i	−0.231344	−	0.712004i
$495$	38.7976			1.74382
$496$	−7.98998	+	18.8867i	−0.358761	+	0.848038i
$497$	−5.30765			−0.238081
$498$	13.3023	+	40.9404i	0.596092	+	1.83458i
$499$	2.83976	−	8.73989i	0.127125	−	0.391251i	−0.867157	−	0.498035i	$-0.834055\pi$
$499$	2.83976	−	8.73989i	0.127125	−	0.391251i	0.994282	+	0.106783i	$0.0340552\pi$
$500$	−0.119342	+	0.0867070i	−0.00533714	+	0.00387766i
$501$	−47.1106			−2.10474
$502$	32.9816			1.47204
$503$	20.1892	−	14.6683i	0.900193	−	0.654029i	−0.0383223	−	0.999265i	$-0.512201\pi$
$503$	20.1892	−	14.6683i	0.900193	−	0.654029i	0.938516	+	0.345237i	$0.112201\pi$
$504$	14.9856	+	10.8877i	0.667511	+	0.484975i
$505$	3.83286	+	2.78473i	0.170560	+	0.123919i
$506$	−8.71283	−	26.8153i	−0.387333	−	1.19209i
$507$	−23.7632	+	17.2650i	−1.05536	+	0.766765i
$508$	0.0210654	+	0.0648328i	0.000934628	+	0.00287649i
$509$	−2.71759	+	8.36389i	−0.120455	+	0.370723i	−0.993046	−	0.117729i	$-0.962438\pi$
$509$	−2.71759	+	8.36389i	−0.120455	+	0.370723i	0.872590	+	0.488453i	$0.162438\pi$
$510$	−7.98009	−	5.79787i	−0.353364	−	0.256734i
$511$	−1.79014	+	5.50949i	−0.0791912	+	0.243725i
$512$	−7.60132	+	23.3945i	−0.335934	+	1.03390i
$513$	63.6469	+	46.2422i	2.81008	+	2.04164i
$514$	2.31940	−	7.13839i	0.102305	−	0.314861i
$515$	−0.381335	−	1.17363i	−0.0168036	−	0.0517162i
$516$	3.58271	−	2.60299i	0.157720	−	0.114590i
$517$	−7.23426	−	22.2648i	−0.318163	−	0.979204i
$518$	−8.13573	−	5.91096i	−0.357464	−	0.259712i
$519$	−6.86999	−	4.99134i	−0.301559	−	0.219095i
$520$	4.53144	−	3.29229i	0.198717	−	0.144376i
$521$	21.3783			0.936602			0.468301	−	0.883569i	$-0.344866\pi$
$521$	21.3783			0.936602			0.468301	+	0.883569i	$0.344866\pi$
$522$	19.5956			0.857678
$523$	−32.4578	+	23.5819i	−1.41928	+	1.03117i	−0.427389	+	0.904068i	$0.640567\pi$
$523$	−32.4578	+	23.5819i	−1.41928	+	1.03117i	−0.991890	+	0.127099i	$0.959433\pi$
$524$	0.177797	−	0.547202i	0.00776709	−	0.0239046i
$525$	−0.891650	−	2.74422i	−0.0389148	−	0.119767i
$526$	−10.7689			−0.469546
$527$	−9.68098	−	8.39501i	−0.421710	−	0.365692i
$528$	−65.0640			−2.83155
$529$	−2.89340	−	8.90497i	−0.125800	−	0.387173i
$530$	−3.25194	+	10.0085i	−0.141255	+	0.434739i
$531$	−55.1783	+	40.0894i	−2.39453	+	1.73973i
$532$	−0.862332			−0.0373868
$533$	4.85129			0.210133
$534$	−7.99515	+	5.80882i	−0.345984	+	0.251372i
$535$	−10.3951	−	7.55250i	−0.449420	−	0.326523i
$536$	0.979419	+	0.711590i	0.0423045	+	0.0307360i
$537$	23.8025	+	73.2566i	1.02715	+	3.16125i
$538$	−0.593539	+	0.431231i	−0.0255893	+	0.0185917i
$539$	10.6791	+	32.8668i	0.459980	+	1.41567i
$540$	−0.562135	+	1.73007i	−0.0241904	+	0.0744505i
$541$	32.6156	+	23.6966i	1.40225	+	1.01880i	0.994393	+	0.105751i	$0.0337248\pi$
$541$	32.6156	+	23.6966i	1.40225	+	1.01880i	0.407860	+	0.913045i	$0.366275\pi$
$542$	−5.46664	+	16.8246i	−0.234812	+	0.722677i
$543$	18.4846	−	56.8897i	0.793249	−	2.44137i
$544$	−1.55046	−	1.12648i	−0.0664755	−	0.0482973i
$545$	−0.325129	+	1.00064i	−0.0139270	+	0.0428629i
$546$	2.32561	+	7.15750i	0.0995270	+	0.306313i
$547$	22.3860	−	16.2644i	0.957157	−	0.695416i	0.00466864	−	0.999989i	$-0.498514\pi$
$547$	22.3860	−	16.2644i	0.957157	−	0.695416i	0.952489	+	0.304573i	$0.0985139\pi$
$548$	−0.520560	−	1.60212i	−0.0222372	−	0.0684391i
$549$	38.1376	+	27.7086i	1.62767	+	1.18257i
$550$	6.17702	+	4.48787i	0.263389	+	0.191363i
$551$	−10.7442	+	7.80615i	−0.457720	+	0.332553i
$552$	33.9891			1.44667
$553$	9.73001			0.413762
$554$	1.40414	−	1.02017i	0.0596563	−	0.0433428i
$555$	7.84643	−	24.1488i	0.333063	−	1.02506i
$556$	0.429828	+	1.32288i	0.0182288	+	0.0561024i
$557$	15.4033			0.652657			0.326329	−	0.945256i	$-0.394188\pi$
$557$	15.4033			0.652657			0.326329	+	0.945256i	$0.394188\pi$
$558$	20.4201	−	48.2689i	0.864450	−	2.04339i
$559$	18.2689			0.772694
$560$	1.04292	+	3.20978i	0.0440714	+	0.135638i
$561$	12.5632	−	38.6654i	0.530417	−	1.63246i
$562$	−11.9996	+	8.71819i	−0.506171	+	0.367755i
$563$	1.02980			0.0434009			0.0217005	−	0.999765i	$-0.493092\pi$
$563$	1.02980			0.0434009			0.0217005	+	0.999765i	$0.493092\pi$
$564$	1.93854			0.0816271
$565$	9.95912	−	7.23572i	0.418983	−	0.304409i
$566$	11.3912	+	8.27619i	0.478808	+	0.347874i
$567$	−13.4058	−	9.73992i	−0.562993	−	0.409038i
$568$	5.23186	+	16.1020i	0.219524	+	0.675625i
$569$	−10.0268	+	7.28492i	−0.420347	+	0.305400i	−0.777777	−	0.628540i	$-0.783653\pi$
$569$	−10.0268	+	7.28492i	−0.420347	+	0.305400i	0.357431	+	0.933940i	$0.383653\pi$
$570$	8.44941	+	26.0046i	0.353907	+	1.08921i
$571$	−1.51723	+	4.66955i	−0.0634941	+	0.195415i	−0.977771	−	0.209675i	$-0.932760\pi$
$571$	−1.51723	+	4.66955i	−0.0634941	+	0.195415i	0.914277	+	0.405089i	$0.132760\pi$
$572$	1.28293	+	0.932103i	0.0536420	+	0.0389732i
$573$	22.2442	−	68.4605i	0.929263	−	2.85998i
$574$	−0.975649	+	3.00274i	−0.0407228	+	0.125332i
$575$	−2.98754	−	2.17057i	−0.124589	−	0.0905191i
$576$	18.1657	−	55.9083i	0.756904	−	2.32951i
$577$	−5.19382	−	15.9849i	−0.216221	−	0.665461i	−0.999065	−	0.0432422i	$-0.986231\pi$
$577$	−5.19382	−	15.9849i	−0.216221	−	0.665461i	0.782843	−	0.622219i	$-0.213769\pi$
$578$	12.8868	−	9.36277i	0.536018	−	0.389440i
$579$	12.4281	+	38.2498i	0.516495	+	1.58961i
$580$	−0.248436	−	0.180499i	−0.0103157	−	0.00749483i
$581$	7.44557	+	5.40952i	0.308894	+	0.224425i
$582$	39.3707	−	28.6045i	1.63197	−	1.18569i
$583$	−43.3738			−1.79636
$584$	18.4789			0.764663
$585$	−10.7222	+	7.79013i	−0.443308	+	0.322082i
$586$	8.07393	−	24.8490i	0.333531	−	1.02650i
$587$	12.5220	+	38.5388i	0.516839	+	1.59067i	0.779911	+	0.625891i	$0.215264\pi$
$587$	12.5220	+	38.5388i	0.516839	+	1.59067i	−0.263072	+	0.964776i	$0.584736\pi$
$588$	−2.86163			−0.118012
$589$	8.03220	+	34.6003i	0.330961	+	1.42568i
$590$	−13.4223			−0.552588
$591$	−17.8384	−	54.9008i	−0.733772	−	2.25832i
$592$	−9.17759	+	28.2457i	−0.377197	+	1.16089i
$593$	−34.5799	+	25.1238i	−1.42003	+	1.03171i	−0.428260	+	0.903656i	$0.640873\pi$
$593$	−34.5799	+	25.1238i	−1.42003	+	1.03171i	−0.991767	+	0.128055i	$0.959127\pi$
$594$	94.1551			3.86323
$595$	−2.10884			−0.0864542
$596$	−1.95091	+	1.41742i	−0.0799124	+	0.0580597i
$597$	−59.4654	−	43.2041i	−2.43376	−	1.76823i
$598$	7.79213	+	5.66131i	0.318644	+	0.231508i
$599$	1.73669	+	5.34499i	0.0709594	+	0.218391i	0.980247	−	0.197778i	$-0.0633726\pi$
$599$	1.73669	+	5.34499i	0.0709594	+	0.218391i	−0.909287	+	0.416169i	$0.863373\pi$
$600$	−7.44631	+	5.41006i	−0.303995	+	0.220865i
$601$	−6.95038	−	21.3911i	−0.283512	−	0.872560i	−0.986841	−	0.161695i	$-0.948304\pi$
$601$	−6.95038	−	21.3911i	−0.283512	−	0.872560i	0.703329	−	0.710864i	$-0.251696\pi$
$602$	−3.67409	+	11.3077i	−0.149745	+	0.460867i
$603$	−2.31748	−	1.68375i	−0.0943750	−	0.0685674i
$604$	−0.136029	+	0.418655i	−0.00553496	+	0.0170348i
$605$	−6.32538	+	19.4675i	−0.257163	+	0.791467i
$606$	16.4274	+	11.9352i	0.667319	+	0.484836i
$607$	−5.44889	+	16.7700i	−0.221164	+	0.680671i	0.777495	+	0.628889i	$0.216490\pi$
$607$	−5.44889	+	16.7700i	−0.221164	+	0.680671i	−0.998658	+	0.0517821i	$0.983510\pi$
$608$	1.64165	+	5.05247i	0.0665776	+	0.204905i
$609$	4.85949	−	3.53063i	0.196917	−	0.143068i
$610$	2.86678	+	8.82306i	0.116073	+	0.357235i
$611$	6.46981	+	4.70059i	0.261740	+	0.190165i
$612$	1.89957	+	1.38012i	0.0767858	+	0.0557881i
$613$	29.7965	−	21.6484i	1.20347	−	0.874372i	0.208848	−	0.977948i	$-0.433029\pi$
$613$	29.7965	−	21.6484i	1.20347	−	0.874372i	0.994621	+	0.103577i	$0.0330287\pi$
$614$	−13.0371			−0.526136
$615$	−7.97190			−0.321458
$616$	−12.1551	+	8.83117i	−0.489741	+	0.355818i
$617$	1.02769	−	3.16290i	0.0413731	−	0.127333i	−0.928237	−	0.371991i	$-0.878675\pi$
$617$	1.02769	−	3.16290i	0.0413731	−	0.127333i	0.969610	+	0.244657i	$0.0786754\pi$
$618$	−1.63438	−	5.03012i	−0.0657446	−	0.202341i
$619$	12.2404			0.491982			0.245991	−	0.969272i	$-0.420887\pi$
$619$	12.2404			0.491982			0.245991	+	0.969272i	$0.420887\pi$
$620$	−0.703503	+	0.423866i	−0.0282534	+	0.0170229i
$621$	−45.5385			−1.82740
$622$	0.0251489	+	0.0774005i	0.00100838	+	0.00310348i
$623$	−0.652899	+	2.00942i	−0.0261578	+	0.0805056i
$624$	17.9812	−	13.0641i	0.719826	−	0.522984i
$625$	1.00000			0.0400000
$626$	13.2485			0.529515
$627$	−91.1735	+	66.2414i	−3.64112	+	2.64543i
$628$	−0.990754	−	0.719825i	−0.0395354	−	0.0287241i
$629$	−15.0134	−	10.9079i	−0.598625	−	0.434926i
$630$	−2.66540	−	8.20325i	−0.106192	−	0.326825i
$631$	30.3909	−	22.0803i	1.20984	−	0.879001i	0.214625	−	0.976696i	$-0.431147\pi$
$631$	30.3909	−	22.0803i	1.20984	−	0.879001i	0.995216	+	0.0976951i	$0.0311470\pi$
$632$	−9.59107	−	29.5183i	−0.381512	−	1.17417i
$633$	4.74576	−	14.6060i	0.188627	−	0.580535i
$634$	7.21867	+	5.24467i	0.286690	+	0.208292i
$635$	0.142802	−	0.439500i	0.00566693	−	0.0174410i
$636$	1.10987	−	3.41582i	0.0440091	−	0.135446i
$637$	−9.55060	−	6.93891i	−0.378408	−	0.274930i
$638$	−4.91162	+	15.1164i	−0.194453	+	0.598465i
$639$	−12.3795	−	38.1002i	−0.489725	−	1.50722i
$640$	8.01194	−	5.82101i	0.316700	−	0.230096i
$641$	2.20975	+	6.80091i	0.0872799	+	0.268620i	0.985165	−	0.171610i	$-0.0548969\pi$
$641$	2.20975	+	6.80091i	0.0872799	+	0.268620i	−0.897885	+	0.440230i	$0.854897\pi$
$642$	−44.5530	−	32.3697i	−1.75837	−	1.27753i
$643$	26.8868	+	19.5344i	1.06031	+	0.770363i	0.974146	−	0.225918i	$-0.0725381\pi$
$643$	26.8868	+	19.5344i	1.06031	+	0.770363i	0.0861670	+	0.996281i	$0.472538\pi$
$644$	0.403823	−	0.293394i	0.0159128	−	0.0115614i
$645$	−30.0205			−1.18206
$646$	19.9837			0.786249
$647$	−13.4503	+	9.77225i	−0.528788	+	0.384187i	−0.819904	−	0.572501i	$-0.805973\pi$
$647$	−13.4503	+	9.77225i	−0.528788	+	0.384187i	0.291117	+	0.956688i	$0.405973\pi$
$648$	−16.3339	+	50.2707i	−0.641657	+	1.97482i
$649$	−17.0953	−	52.6139i	−0.671048	−	2.06527i
$650$	−2.60821			−0.102302
$651$	−3.63287	−	15.6493i	−0.142383	−	0.613345i
$652$	3.37084			0.132012
$653$	10.4095	+	32.0372i	0.407356	+	1.25371i	0.918912	+	0.394462i	$0.129069\pi$
$653$	10.4095	+	32.0372i	0.407356	+	1.25371i	−0.511556	+	0.859250i	$0.670931\pi$
$654$	−1.39349	+	4.28872i	−0.0544897	+	0.167702i
$655$	−3.15547	+	2.29258i	−0.123294	+	0.0895785i
$656$	9.32434			0.364054
$657$	−43.7244			−1.70585
$658$	−4.21061	+	3.05919i	−0.164147	+	0.119260i
$659$	12.4643	+	9.05581i	0.485538	+	0.352764i	0.803466	−	0.595351i	$-0.202987\pi$
$659$	12.4643	+	9.05581i	0.485538	+	0.352764i	−0.317928	+	0.948115i	$0.602987\pi$
$660$	−2.10818	−	1.53168i	−0.0820607	−	0.0596206i
$661$	0.797817	+	2.45543i	0.0310315	+	0.0955050i	0.965373	−	0.260875i	$-0.0840109\pi$
$661$	0.797817	+	2.45543i	0.0310315	+	0.0955050i	−0.934341	+	0.356380i	$0.884011\pi$
$662$	10.7659	−	7.82187i	0.418428	−	0.304006i
$663$	4.29161	+	13.2082i	0.166672	+	0.512965i
$664$	9.07182	−	27.9202i	0.352055	−	1.08351i
$665$	4.72929	+	3.43603i	0.183394	+	0.133244i
$666$	23.4552	−	72.1878i	0.908872	−	2.79722i
$667$	2.37552	−	7.31111i	0.0919807	−	0.283087i
$668$	1.78542	+	1.29719i	0.0690801	+	0.0501897i
$669$	10.5502	−	32.4702i	0.407895	−	1.25537i
$670$	−0.174204	−	0.536144i	−0.00673007	−	0.0207130i
$671$	−30.9341	+	22.4749i	−1.19420	+	0.867634i
$672$	−0.742498	−	2.28517i	−0.0286425	−	0.0881525i
$673$	12.0917	+	8.78514i	0.466101	+	0.338642i	0.795920	−	0.605402i	$-0.206988\pi$
$673$	12.0917	+	8.78514i	0.466101	+	0.338642i	−0.329819	+	0.944044i	$0.606988\pi$
$674$	−6.63518	−	4.82074i	−0.255578	−	0.185688i
$675$	9.97655	−	7.24839i	0.383998	−	0.278991i
$676$	1.37598			0.0529224
$677$	9.58212			0.368271			0.184135	−	0.982901i	$-0.441052\pi$
$677$	9.58212			0.368271			0.184135	+	0.982901i	$0.441052\pi$
$678$	42.6843	−	31.0120i	1.63928	−	1.19101i
$679$	3.21509	−	9.89501i	0.123384	−	0.379736i
$680$	2.07873	+	6.39768i	0.0797157	+	0.245340i
$681$	17.4066			0.667022
$682$	32.1172	+	27.8509i	1.22983	+	1.06647i
$683$	−42.9429			−1.64317			−0.821583	−	0.570089i	$-0.806909\pi$
$683$	−42.9429			−1.64317			−0.821583	+	0.570089i	$0.806909\pi$
$684$	−2.01129	−	6.19012i	−0.0769037	−	0.236685i
$685$	−3.52887	+	10.8607i	−0.134831	+	0.414967i
$686$	13.2784	−	9.64731i	0.506971	−	0.368336i
$687$	32.1228			1.22556
$688$	35.1135			1.33869
$689$	11.9869	−	8.70898i	0.456664	−	0.331786i
$690$	−12.8044	−	9.30298i	−0.487457	−	0.354158i
$691$	16.0878	+	11.6885i	0.612010	+	0.444651i	0.850122	−	0.526586i	$-0.176528\pi$
$691$	16.0878	+	11.6885i	0.612010	+	0.444651i	−0.238111	+	0.971238i	$0.576528\pi$
$692$	0.122927	+	0.378329i	0.00467297	+	0.0143819i
$693$	28.7610	−	20.8961i	1.09254	−	0.793777i
$694$	8.00343	+	24.6320i	0.303806	+	0.935019i
$695$	2.91380	−	8.96774i	0.110527	−	0.340166i
$696$	−15.5011	−	11.2622i	−0.587568	−	0.426893i
$697$	−1.80043	+	5.54116i	−0.0681962	+	0.209886i
$698$	7.32158	−	22.5335i	0.277126	−	0.852906i
$699$	−23.0729	−	16.7634i	−0.872697	−	0.634051i
$700$	−0.0417696	+	0.128554i	−0.00157874	+	0.00485887i
$701$	4.81083	+	14.8062i	0.181702	+	0.559223i	0.999876	−	0.0157487i	$-0.00501318\pi$
$701$	4.81083	+	14.8062i	0.181702	+	0.559223i	−0.818174	+	0.574971i	$0.805013\pi$
$702$	−26.0210	+	18.9053i	−0.982098	+	0.713536i
$703$	15.8964	+	48.9241i	0.599544	+	1.84521i
$704$	38.5754	+	28.0267i	1.45387	+	1.05630i
$705$	−10.6315	−	7.72426i	−0.400407	−	0.290913i
$706$	−13.1415	+	9.54788i	−0.494588	+	0.359339i
$707$	4.34117			0.163266
$708$	4.58095			0.172163
$709$	34.1492	−	24.8109i	1.28250	−	0.931792i	0.282876	−	0.959157i	$-0.408712\pi$
$709$	34.1492	−	24.8109i	1.28250	−	0.931792i	0.999626	+	0.0273649i	$0.00871162\pi$
$710$	2.43624	−	7.49797i	0.0914304	−	0.281394i
$711$	22.6942	+	69.8455i	0.851098	+	2.61941i
$712$	6.73962			0.252578
$713$	−15.5336	−	13.4702i	−0.581738	−	0.504463i
$714$	−9.03841			−0.338254
$715$	−3.32194	−	10.2239i	−0.124234	−	0.382351i
$716$	1.11503	−	3.43172i	0.0416708	−	0.128249i
$717$	30.3685	−	22.0640i	1.13413	−	0.823995i
$718$	−43.4371			−1.62106
$719$	−46.3827			−1.72978			−0.864891	−	0.501960i	$-0.832613\pi$
$719$	−46.3827			−1.72978			−0.864891	+	0.501960i	$0.832613\pi$
$720$	−20.6084	+	14.9729i	−0.768030	+	0.558007i
$721$	−0.914795	−	0.664637i	−0.0340687	−	0.0247524i
$722$	−23.8942	−	17.3602i	−0.889251	−	0.646078i
$723$	−17.0755	−	52.5531i	−0.635046	−	1.95447i
$724$	−2.26699	+	1.64707i	−0.0842522	+	0.0612128i
$725$	0.643286	+	1.97983i	0.0238910	+	0.0735290i
$726$	−27.1103	+	83.4369i	−1.00616	+	3.09663i
$727$	12.3763	+	8.99188i	0.459010	+	0.333491i	0.793143	−	0.609036i	$-0.208443\pi$
$727$	12.3763	+	8.99188i	0.459010	+	0.333491i	−0.334133	+	0.942526i	$0.608443\pi$
$728$	1.58600	−	4.88121i	0.0587811	−	0.180910i
$729$	2.64945	−	8.15416i	0.0981277	−	0.302006i
$730$	−6.96142	−	5.05777i	−0.257654	−	0.187196i
$731$	−6.78005	+	20.8668i	−0.250769	+	0.771788i
$732$	−0.978416	−	3.01126i	−0.0361633	−	0.111299i
$733$	6.29770	−	4.57555i	0.232611	−	0.169002i	−0.465374	−	0.885114i	$-0.654080\pi$
$733$	6.29770	−	4.57555i	0.232611	−	0.169002i	0.697985	+	0.716112i	$0.254080\pi$
$734$	6.83501	+	21.0360i	0.252285	+	0.776452i
$735$	15.6941	+	11.4024i	0.578884	+	0.420584i
$736$	−2.48779	−	1.80749i	−0.0917013	−	0.0666249i
$737$	1.87975	−	1.36571i	0.0692413	−	0.0503067i
$738$	−23.8303			−0.877206
$739$	−1.12482			−0.0413773			−0.0206887	−	0.999786i	$-0.506586\pi$
$739$	−1.12482			−0.0413773			−0.0206887	+	0.999786i	$0.506586\pi$
$740$	−0.962306	+	0.699156i	−0.0353751	+	0.0257015i
$741$	11.8964	−	36.6133i	0.437024	−	1.34502i
$742$	2.97978	+	9.17083i	0.109391	+	0.336672i
$743$	−37.3958			−1.37192			−0.685960	−	0.727639i	$-0.740618\pi$
$743$	−37.3958			−1.37192			−0.685960	+	0.727639i	$0.740618\pi$
$744$	−43.8949	+	26.4470i	−1.60927	+	0.969595i
$745$	16.3472			0.598916
$746$	8.90569	+	27.4089i	0.326060	+	1.00351i
$747$	−21.4655	+	66.0640i	−0.785382	+	2.41716i
$748$	−1.54078	+	1.11944i	−0.0563364	+	0.0409308i
$749$	−11.7737			−0.430202
$750$	4.28595			0.156501
$751$	−43.0328	+	31.2652i	−1.57029	+	1.14088i	−0.643412	+	0.765520i	$0.722482\pi$
$751$	−43.0328	+	31.2652i	−1.57029	+	1.14088i	−0.926878	+	0.375362i	$0.877518\pi$
$752$	12.4352	+	9.03469i	0.453464	+	0.329461i
$753$	61.7337	+	44.8522i	2.24970	+	1.63450i
$754$	−1.67782	−	5.16381i	−0.0611028	−	0.188055i
$755$	2.41419	−	1.75402i	0.0878615	−	0.0638351i
$756$	0.515089	+	1.58528i	0.0187336	+	0.0576562i
$757$	−6.64091	+	20.4386i	−0.241368	+	0.742854i	0.754845	+	0.655903i	$0.227712\pi$
$757$	−6.64091	+	20.4386i	−0.241368	+	0.742854i	−0.996213	+	0.0869504i	$0.972288\pi$
$758$	7.40340	+	5.37888i	0.268903	+	0.195370i
$759$	20.1582	−	62.0406i	0.731697	−	2.25193i
$760$	5.76226	−	17.7344i	0.209019	−	0.643294i
$761$	−22.9004	−	16.6381i	−0.830138	−	0.603130i	0.0894604	−	0.995990i	$-0.471486\pi$
$761$	−22.9004	−	16.6381i	−0.830138	−	0.603130i	−0.919598	+	0.392860i	$0.871486\pi$
$762$	0.612044	−	1.88368i	0.0221720	−	0.0682384i
$763$	0.297919	+	0.916900i	0.0107854	+	0.0331940i
$764$	−2.72808	+	1.98206i	−0.0986984	+	0.0717086i
$765$	−4.91864	−	15.1380i	−0.177834	−	0.547317i
$766$	20.4102	+	14.8289i	0.737451	+	0.535790i
$767$	15.2888	+	11.1080i	0.552046	+	0.401085i
$768$	−8.96907	+	6.51641i	−0.323643	+	0.235141i
$769$	−8.29866			−0.299257			−0.149629	−	0.988742i	$-0.547808\pi$
$769$	−8.29866			−0.299257			−0.149629	+	0.988742i	$0.547808\pi$
$770$	6.99621			0.252126
$771$	14.0490	−	10.2072i	0.505961	−	0.367602i
$772$	0.582199	−	1.79182i	0.0209538	−	0.0644891i
$773$	3.97213	+	12.2249i	0.142867	+	0.439701i	0.996731	−	0.0807968i	$-0.0257465\pi$
$773$	3.97213	+	12.2249i	0.142867	+	0.439701i	−0.853863	+	0.520498i	$0.825746\pi$
$774$	−89.7400			−3.22564
$775$	5.54716	+	0.478553i	0.199260	+	0.0171901i
$776$	−33.1881			−1.19138
$777$	−7.18976	−	22.1278i	−0.257931	−	0.793830i
$778$	−1.21874	+	3.75088i	−0.0436938	+	0.134476i
$779$	13.0661	−	9.49308i	0.468142	−	0.340125i
$780$	0.890167			0.0318731
$781$	32.4941			1.16273
$782$	−9.35822	+	6.79914i	−0.334649	+	0.243137i
$783$	20.7683	+	15.0891i	0.742200	+	0.539240i
$784$	−18.3566	−	13.3368i	−0.655592	−	0.476315i
$785$	2.56540	+	7.89548i	0.0915630	+	0.281802i
$786$	−13.5242	+	9.82590i	−0.482392	+	0.350478i
$787$	3.60362	+	11.0908i	0.128455	+	0.395345i	0.994515	−	0.104596i	$-0.0333550\pi$
$787$	3.60362	+	11.0908i	0.128455	+	0.395345i	−0.866059	+	0.499941i	$0.833355\pi$
$788$	−0.835642	+	2.57184i	−0.0297685	+	0.0916181i
$789$	−20.1568	−	14.6448i	−0.717601	−	0.521368i
$790$	−4.46613	+	13.7453i	−0.158898	+	0.489037i
$791$	3.48568	−	10.7278i	0.123937	−	0.381437i
$792$	−91.7436	−	66.6556i	−3.25997	−	2.36850i
$793$	4.03630	−	12.4224i	0.143333	−	0.441134i
$794$	−9.19965	−	28.3136i	−0.326483	−	1.00481i
$795$	−19.6975	+	14.3111i	−0.698598	+	0.507561i
$796$	1.06403	+	3.27475i	0.0377136	+	0.116070i
$797$	−4.31568	−	3.13553i	−0.152869	−	0.111066i	0.508721	−	0.860931i	$-0.330118\pi$
$797$	−4.31568	−	3.13553i	−0.152869	−	0.111066i	−0.661591	+	0.749865i	$0.730118\pi$
$798$	20.2695	+	14.7267i	0.717534	+	0.521319i
$799$	−7.77013	+	5.64533i	−0.274887	+	0.199717i
$800$	0.832724			0.0294412
$801$	−15.9471			−0.563464
$802$	6.04288	−	4.39041i	0.213381	−	0.155031i
$803$	10.9595	−	33.7298i	0.386751	−	1.19030i
$804$	0.0594546	+	0.182983i	0.00209680	+	0.00645330i
$805$	−3.38374			−0.119261
$806$	−14.4682	−	1.24817i	−0.509620	−	0.0439649i
$807$	−1.69740			−0.0597513
$808$	−4.27918	−	13.1700i	−0.150541	−	0.463318i
$809$	−5.06021	+	15.5737i	−0.177908	+	0.547543i	−0.999754	−	0.0221653i	$-0.992944\pi$
$809$	−5.06021	+	15.5737i	−0.177908	+	0.547543i	0.821847	+	0.569709i	$0.192944\pi$
$810$	19.9127	−	14.4674i	0.699660	−	0.508333i
$811$	35.0584			1.23107			0.615534	−	0.788110i	$-0.288940\pi$
$811$	35.0584			1.23107			0.615534	+	0.788110i	$0.288940\pi$
$812$	−0.281384			−0.00987463
$813$	−33.1122	+	24.0574i	−1.16130	+	0.843731i
$814$	49.8079	+	36.1876i	1.74577	+	1.26837i
$815$	−18.4867	−	13.4314i	−0.647562	−	0.470482i
$816$	8.24862	+	25.3867i	0.288760	+	0.888711i
$817$	49.2042	−	35.7490i	1.72144	−	1.25070i
$818$	8.80700	+	27.1051i	0.307929	+	0.947709i
$819$	−3.75276	+	11.5498i	−0.131132	+	0.403582i
$820$	0.302124	+	0.219506i	0.0105506	+	0.00766548i
$821$	−7.94004	+	24.4369i	−0.277109	+	0.852855i	0.711544	+	0.702641i	$0.247996\pi$
$821$	−7.94004	+	24.4369i	−0.277109	+	0.852855i	−0.988654	+	0.150214i	$0.952004\pi$
$822$	−15.1246	+	46.5486i	−0.527530	+	1.62357i
$823$	−5.56297	−	4.04173i	−0.193913	−	0.140886i	0.486592	−	0.873629i	$-0.338240\pi$
$823$	−5.56297	−	4.04173i	−0.193913	−	0.140886i	−0.680505	+	0.732743i	$0.738240\pi$
$824$	−1.11460	+	3.43039i	−0.0388290	+	0.119503i
$825$	5.45879	+	16.8004i	0.190051	+	0.584916i
$826$	−9.95009	+	7.22916i	−0.346208	+	0.251535i
$827$	−10.7633	−	33.1261i	−0.374278	−	1.15191i	−0.943965	−	0.330046i	$-0.892936\pi$
$827$	−10.7633	−	33.1261i	−0.374278	−	1.15191i	0.569687	−	0.821862i	$-0.307064\pi$
$828$	3.04796	+	2.21447i	0.105924	+	0.0769583i
$829$	−9.87637	−	7.17560i	−0.343021	−	0.249219i	0.402915	−	0.915238i	$-0.367997\pi$
$829$	−9.87637	−	7.17560i	−0.343021	−	0.249219i	−0.745935	+	0.666019i	$0.767997\pi$
$830$	−11.0594	+	8.03516i	−0.383879	+	0.278904i
$831$	4.01556			0.139298
$832$	−16.2883			−0.564694
$833$	11.4701	−	8.33352i	0.397416	−	0.288739i
$834$	12.4884	−	38.4353i	0.432438	−	1.33091i
$835$	−4.62307	−	14.2283i	−0.159988	−	0.492392i
$836$	5.27930			0.182588
$837$	58.8103	−	35.4337i	2.03278	−	1.22477i
$838$	1.22459			0.0423028
$839$	−2.12550	−	6.54162i	−0.0733804	−	0.225842i	0.907639	−	0.419752i	$-0.137883\pi$
$839$	−2.12550	−	6.54162i	−0.0733804	−	0.225842i	−0.981019	+	0.193910i	$0.937883\pi$
$840$	−2.60620	+	8.02106i	−0.0899225	+	0.276753i
$841$	19.9556	−	14.4986i	0.688124	−	0.499951i
$842$	−31.2267			−1.07614
$843$	−34.3163			−1.18192
$844$	−0.582032	+	0.422871i	−0.0200344	+	0.0145558i
$845$	−7.54632	−	5.48272i	−0.259601	−	0.188611i
$846$	−31.7807	−	23.0900i	−1.09264	−	0.793852i
$847$	5.79600	+	17.8383i	0.199153	+	0.612930i
$848$	23.0392	−	16.7390i	0.791169	−	0.574818i
$849$	10.0667	+	30.9821i	0.345488	+	1.06330i
$850$	0.967971	−	2.97911i	0.0332011	−	0.102183i
$851$	−24.0898	−	17.5023i	−0.825787	−	0.599970i
$852$	−0.831474	+	2.55901i	−0.0284858	+	0.0876703i
$853$	−6.23773	+	19.1978i	−0.213576	+	0.657319i	0.785676	+	0.618639i	$0.212315\pi$
$853$	−6.23773	+	19.1978i	−0.213576	+	0.657319i	−0.999252	+	0.0386804i	$0.987685\pi$
$854$	6.87721	+	4.99659i	0.235333	+	0.170980i
$855$	−13.6345	+	41.9627i	−0.466290	+	1.43509i
$856$	11.6056	+	35.7184i	0.396671	+	1.22083i
$857$	5.27558	−	3.83293i	0.180210	−	0.130931i	−0.494023	−	0.869449i	$-0.664474\pi$
$857$	5.27558	−	3.83293i	0.180210	−	0.130931i	0.674233	+	0.738518i	$0.264474\pi$
$858$	−14.2377	−	43.8191i	−0.486066	−	1.49596i
$859$	−6.94602	−	5.04658i	−0.236995	−	0.172187i	0.462948	−	0.886385i	$-0.346792\pi$
$859$	−6.94602	−	5.04658i	−0.236995	−	0.172187i	−0.699944	+	0.714198i	$0.746792\pi$
$860$	1.13774	+	0.826613i	0.0387965	+	0.0281873i
$861$	−5.90965	+	4.29361i	−0.201400	+	0.146326i
$862$	−46.8939			−1.59721
$863$	46.4756			1.58205			0.791023	−	0.611786i	$-0.209549\pi$
$863$	46.4756			1.58205			0.791023	+	0.611786i	$0.209549\pi$
$864$	8.30771	−	6.03590i	0.282634	−	0.205346i
$865$	0.833317	−	2.56469i	0.0283336	−	0.0872020i
$866$	0.0554598	+	0.170688i	0.00188460	+	0.00580021i
$867$	36.8535			1.25161
$868$	−0.293222	+	0.693118i	−0.00995261	+	0.0235260i
$869$	−59.5683			−2.02072
$870$	2.75709	+	8.48546i	0.0934742	+	0.287684i
$871$	−0.245270	+	0.754865i	−0.00831067	+	0.0255776i
$872$	2.48797	−	1.80761i	0.0842532	−	0.0612136i
$873$	78.5288			2.65780
$874$	32.0649			1.08461
$875$	0.741309	−	0.538593i	0.0250608	−	0.0182078i
$876$	2.37589	+	1.72619i	0.0802739	+	0.0583224i
$877$	−34.5132	−	25.0753i	−1.16543	−	0.846732i	−0.174972	−	0.984573i	$-0.555984\pi$
$877$	−34.5132	−	25.0753i	−1.16543	−	0.846732i	−0.990454	+	0.137841i	$0.955984\pi$
$878$	11.7016	+	36.0137i	0.394909	+	1.21540i
$879$	48.9050	−	35.5316i	1.64952	−	1.19845i
$880$	−6.38488	−	19.6506i	−0.215234	−	0.662423i
$881$	6.10369	−	18.7852i	0.205639	−	0.632891i	−0.794048	−	0.607855i	$-0.792030\pi$
$881$	6.10369	−	18.7852i	0.205639	−	0.632891i	0.999687	−	0.0250354i	$-0.00796985\pi$
$882$	46.9140	+	34.0851i	1.57968	+	1.14770i
$883$	−1.49764	+	4.60925i	−0.0503995	+	0.155114i	−0.973089	−	0.230431i	$-0.925986\pi$
$883$	−1.49764	+	4.60925i	−0.0503995	+	0.155114i	0.922689	+	0.385545i	$0.125986\pi$
$884$	0.201042	−	0.618743i	0.00676176	−	0.0208106i
$885$	−25.1234	−	18.2532i	−0.844513	−	0.613574i
$886$	9.83086	−	30.2563i	0.330274	−	1.01648i
$887$	−10.8335	−	33.3422i	−0.363754	−	1.11952i	−0.950757	−	0.309936i	$-0.899692\pi$
$887$	−10.8335	−	33.3422i	−0.363754	−	1.11952i	0.587003	−	0.809585i	$-0.300308\pi$
$888$	−60.0428	+	43.6237i	−2.01491	+	1.46391i
$889$	−0.130851	−	0.402718i	−0.00438860	−	0.0135067i
$890$	−2.53896	−	1.84467i	−0.0851063	−	0.0618333i
$891$	82.0722	+	59.6290i	2.74952	+	1.99765i
$892$	−1.29390	+	0.940076i	−0.0433231	+	0.0314761i
$893$	26.6235			0.890921
$894$	70.0634			2.34327
$895$	−19.7892	+	14.3777i	−0.661479	+	0.480593i
$896$	2.80417	−	8.63035i	0.0936807	−	0.288320i
$897$	6.88611	+	21.1933i	0.229920	+	0.707622i
$898$	−7.42104			−0.247643
$899$	2.62095	+	11.2903i	0.0874137	+	0.376552i
$900$	−1.02023			−0.0340075
$901$	5.49880	+	16.9236i	0.183192	+	0.563806i
$902$	5.97304	−	18.3831i	0.198880	−	0.612091i
$903$	−22.2545	+	16.1688i	−0.740583	+	0.538065i
$904$	−35.9813			−1.19672
$905$	18.9958			0.631441
$906$	10.3471	−	7.51763i	0.343760	−	0.249756i
$907$	−17.5796	−	12.7723i	−0.583721	−	0.424098i	0.256343	−	0.966586i	$-0.417483\pi$
$907$	−17.5796	−	12.7723i	−0.583721	−	0.424098i	−0.840064	+	0.542488i	$0.817483\pi$
$908$	−0.659685	−	0.479289i	−0.0218924	−	0.0159058i
$909$	10.1253	+	31.1625i	0.335835	+	1.03359i
$910$	−1.93349	+	1.40476i	−0.0640946	+	0.0465675i
$911$	−1.34474	−	4.13869i	−0.0445533	−	0.137121i	0.926305	−	0.376773i	$-0.122966\pi$
$911$	−1.34474	−	4.13869i	−0.0445533	−	0.137121i	−0.970859	+	0.239653i	$0.922966\pi$
$912$	22.8652	−	70.3720i	0.757144	−	2.33025i
$913$	−45.5827	−	33.1178i	−1.50857	−	1.09604i
$914$	13.9415	−	42.9076i	0.461144	−	1.41926i
$915$	−6.63266	+	20.4132i	−0.219269	+	0.674841i
$916$	−1.21741	−	0.884500i	−0.0402243	−	0.0292247i
$917$	−1.10441	+	3.39902i	−0.0364708	+	0.112246i
$918$	−11.9367	−	36.7374i	−0.393970	−	1.21252i
$919$	33.2493	−	24.1571i	1.09679	−	0.796868i	0.116261	−	0.993219i	$-0.462909\pi$
$919$	33.2493	−	24.1571i	1.09679	−	0.796868i	0.980534	+	0.196351i	$0.0629092\pi$
$920$	3.33543	+	10.2654i	0.109966	+	0.338440i
$921$	−24.4024	−	17.7294i	−0.804086	−	0.584203i
$922$	7.69326	+	5.58948i	0.253364	+	0.184080i
$923$	−8.98014	+	6.52446i	−0.295585	+	0.214755i
$924$	−2.38777			−0.0785517
$925$	8.06343			0.265124
$926$	21.7653	−	15.8135i	0.715254	−	0.519662i
$927$	2.63735	−	8.11692i	0.0866218	−	0.266595i
$928$	0.535679	+	1.64865i	0.0175845	+	0.0541196i
$929$	−19.8163			−0.650152			−0.325076	−	0.945688i	$-0.605390\pi$
$929$	−19.8163			−0.650152			−0.325076	+	0.945688i	$0.605390\pi$
$930$	23.7749	+	2.05106i	0.779609	+	0.0672569i
$931$	−39.3010			−1.28804
$932$	0.412850	+	1.27062i	0.0135233	+	0.0416206i
$933$	−0.0581852	+	0.179076i	−0.00190490	+	0.00586267i
$934$	−18.4183	+	13.3816i	−0.602664	+	0.437861i
$935$	12.9106			0.422222
$936$	38.7382			1.26620
$937$	−34.6362	+	25.1647i	−1.13152	+	0.822094i	−0.985915	−	0.167249i	$-0.946512\pi$
$937$	−34.6362	+	25.1647i	−1.13152	+	0.822094i	−0.145601	+	0.989343i	$0.546512\pi$
$938$	−0.417902	−	0.303623i	−0.0136450	−	0.00991366i
$939$	24.7980	+	18.0168i	0.809251	+	0.587955i
$940$	0.190233	+	0.585477i	0.00620472	+	0.0190962i
$941$	−20.5084	+	14.9002i	−0.668554	+	0.485733i	−0.869541	−	0.493861i	$-0.835585\pi$
$941$	−20.5084	+	14.9002i	−0.668554	+	0.485733i	0.200987	+	0.979594i	$0.435585\pi$
$942$	10.9952	+	33.8397i	0.358242	+	1.10256i
$943$	−2.88888	+	8.89106i	−0.0940749	+	0.289533i
$944$	29.3856	+	21.3499i	0.956419	+	0.694879i
$945$	3.49178	−	10.7466i	0.113588	−	0.349587i
$946$	22.4932	−	69.2270i	0.731318	−	2.25076i
$947$	24.8796	+	18.0761i	0.808480	+	0.587395i	0.913389	−	0.407087i	$-0.133455\pi$
$947$	24.8796	+	18.0761i	0.808480	+	0.587395i	−0.104910	+	0.994482i	$0.533455\pi$
$948$	1.52426	−	4.69120i	0.0495057	−	0.152363i
$949$	3.74378	+	11.5222i	0.121528	+	0.374026i
$950$	−7.02476	+	5.10379i	−0.227913	+	0.165589i
$951$	6.37932	+	19.6335i	0.206864	+	0.636661i
$952$	4.98673	+	3.62307i	0.161621	+	0.117424i
$953$	26.3418	+	19.1384i	0.853294	+	0.619955i	0.926052	−	0.377395i	$-0.123180\pi$
$953$	26.3418	+	19.1384i	0.853294	+	0.619955i	−0.0727581	+	0.997350i	$0.523180\pi$
$954$	−58.8815	+	42.7799i	−1.90636	+	1.38505i
$955$	22.8593			0.739710
$956$	−1.75845			−0.0568725
$957$	−29.7504	+	21.6149i	−0.961695	+	0.698712i
$958$	1.75283	−	5.39465i	0.0566313	−	0.174293i
$959$	3.23353	+	9.95178i	0.104416	+	0.321360i
$960$	26.7657			0.863861
$961$	30.5420	+	5.30923i	0.985225	+	0.171265i
$962$	−21.0311			−0.678071
$963$	−27.4609	−	84.5159i	−0.884915	−	2.72349i
$964$	−0.799908	+	2.46186i	−0.0257633	+	0.0792913i
$965$	−10.3326	+	7.50709i	−0.332619	+	0.241662i
$966$	−14.5026			−0.466613
$967$	−29.4715			−0.947741			−0.473870	−	0.880595i	$-0.657143\pi$
$967$	−29.4715			−0.947741			−0.473870	+	0.880595i	$0.657143\pi$
$968$	48.4033	−	35.1671i	1.55574	−	1.13031i
$969$	37.4048	+	27.1762i	1.20161	+	0.873024i
$970$	12.5027	+	9.08373i	0.401437	+	0.291661i
$971$	−15.8132	−	48.6679i	−0.507468	−	1.56183i	−0.796581	−	0.604532i	$-0.793360\pi$
$971$	−15.8132	−	48.6679i	−0.507468	−	1.56183i	0.289113	−	0.957295i	$-0.406640\pi$
$972$	−2.38101	+	1.72991i	−0.0763710	+	0.0554868i
$973$	−2.66994	−	8.21722i	−0.0855943	−	0.263432i
$974$	2.73549	−	8.41896i	0.0876506	−	0.269761i
$975$	−4.88195	−	3.54694i	−0.156348	−	0.113593i
$976$	7.75790	−	23.8764i	0.248324	−	0.764264i
$977$	0.437149	−	1.34541i	0.0139856	−	0.0430433i	−0.943820	−	0.330460i	$-0.892796\pi$
$977$	0.437149	−	1.34541i	0.0139856	−	0.0430433i	0.957806	+	0.287416i	$0.0927963\pi$
$978$	−79.2333	−	57.5664i	−2.53360	−	1.84077i
$979$	3.99713	−	12.3019i	0.127749	−	0.393170i
$980$	−0.280818	−	0.864270i	−0.00897041	−	0.0276081i
$981$	−5.88697	+	4.27713i	−0.187956	+	0.136558i
$982$	10.7415	+	33.0590i	0.342775	+	1.05495i
$983$	−0.479375	−	0.348286i	−0.0152897	−	0.0111086i	0.580114	−	0.814535i	$-0.303008\pi$
$983$	−0.479375	−	0.348286i	−0.0152897	−	0.0111086i	−0.595404	+	0.803427i	$0.703008\pi$
$984$	18.8509	+	13.6960i	0.600946	+	0.436613i
$985$	14.8306	−	10.7751i	0.472543	−	0.343323i
$986$	6.52081			0.207665
$987$	−12.0415			−0.383285
$988$	−1.45900	+	1.06003i	−0.0464170	+	0.0337239i
$989$	−10.8789	+	33.4819i	−0.345930	+	1.06466i
$990$	16.3179	+	50.2213i	0.518617	+	1.59614i
$991$	−61.1371			−1.94208			−0.971042	−	0.238909i	$-0.923210\pi$
$991$	−61.1371			−1.94208			−0.971042	+	0.238909i	$0.923210\pi$
$992$	4.61925	+	0.398503i	0.146661	+	0.0126525i
$993$	30.7882			0.977036
$994$	−2.23235	−	6.87046i	−0.0708058	−	0.217918i
$995$	7.21304	−	22.1995i	0.228669	−	0.703770i
$996$	3.77452	−	2.74235i	0.119600	−	0.0868947i
$997$	21.4914			0.680640			0.340320	−	0.940310i	$-0.389465\pi$
$997$	21.4914			0.680640			0.340320	+	0.940310i	$0.389465\pi$
$998$	12.5077			0.395924
$999$	80.4452	−	58.4468i	2.54517	−	1.84918i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	155.2.h.b.66.5	✓	24
5.2	odd	4		775.2.bf.c.624.4		48
5.3	odd	4		775.2.bf.c.624.9		48
5.4	even	2		775.2.k.d.376.2		24
31.8	even	5	inner	155.2.h.b.101.5	yes	24
31.15	odd	10		4805.2.a.v.1.9		12
31.16	even	5		4805.2.a.u.1.9		12
155.8	odd	20		775.2.bf.c.349.4		48
155.39	even	10		775.2.k.d.101.2		24
155.132	odd	20		775.2.bf.c.349.9		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
155.2.h.b.66.5	✓	24	1.1	even	1	trivial
155.2.h.b.101.5	yes	24	31.8	even	5	inner
775.2.k.d.101.2		24	155.39	even	10
775.2.k.d.376.2		24	5.4	even	2
775.2.bf.c.349.4		48	155.8	odd	20
775.2.bf.c.349.9		48	155.132	odd	20
775.2.bf.c.624.4		48	5.2	odd	4
775.2.bf.c.624.9		48	5.3	odd	4
4805.2.a.u.1.9		12	31.16	even	5
4805.2.a.v.1.9		12	31.15	odd	10

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(0.420591 + 1.29445i) q^{2} +(-0.973089 + 2.99486i) q^{3} +(0.119342 - 0.0867070i) q^{4} -1.00000 q^{5} -4.28595 q^{6} +(-0.741309 + 0.538593i) q^{7} +(2.36467 + 1.71804i) q^{8} +(-5.59523 - 4.06517i) q^{9} +O(q^{10})\)	\(q+(0.420591 + 1.29445i) q^{2} +(-0.973089 + 2.99486i) q^{3} +(0.119342 - 0.0867070i) q^{4} -1.00000 q^{5} -4.28595 q^{6} +(-0.741309 + 0.538593i) q^{7} +(2.36467 + 1.71804i) q^{8} +(-5.59523 - 4.06517i) q^{9} +(-0.420591 - 1.29445i) q^{10} +(4.53839 - 3.29733i) q^{11} +(0.143545 + 0.441786i) q^{12} +(-0.592172 + 1.82252i) q^{13} +(-1.00897 - 0.733057i) q^{14} +(0.973089 - 2.99486i) q^{15} +(-1.13817 + 3.50294i) q^{16} +(-1.86192 - 1.35276i) q^{17} +(2.90884 - 8.95250i) q^{18} +(1.97142 + 6.06741i) q^{19} +(-0.119342 + 0.0867070i) q^{20} +(-0.891650 - 2.74422i) q^{21} +(6.17702 + 4.48787i) q^{22} +(-2.98754 - 2.17057i) q^{23} +(-7.44631 + 5.41006i) q^{24} +1.00000 q^{25} -2.60821 q^{26} +(9.97655 - 7.24839i) q^{27} +(-0.0417696 + 0.128554i) q^{28} +(0.643286 + 1.97983i) q^{29} +4.28595 q^{30} +(5.54716 + 0.478553i) q^{31} +0.832724 q^{32} +(5.45879 + 16.8004i) q^{33} +(0.967971 - 2.97911i) q^{34} +(0.741309 - 0.538593i) q^{35} -1.02023 q^{36} +8.06343 q^{37} +(-7.02476 + 5.10379i) q^{38} +(-4.88195 - 3.54694i) q^{39} +(-2.36467 - 1.71804i) q^{40} +(-0.782302 - 2.40768i) q^{41} +(3.17722 - 2.30838i) q^{42} +(-2.94598 - 9.06681i) q^{43} +(0.255718 - 0.787020i) q^{44} +(5.59523 + 4.06517i) q^{45} +(1.55316 - 4.78013i) q^{46} +(1.28959 - 3.96894i) q^{47} +(-9.38327 - 6.81735i) q^{48} +(-1.90366 + 5.85887i) q^{49} +(0.420591 + 1.29445i) q^{50} +(5.86314 - 4.25982i) q^{51} +(0.0873542 + 0.268848i) q^{52} +(-6.25519 - 4.54466i) q^{53} +(13.5787 + 9.86549i) q^{54} +(-4.53839 + 3.29733i) q^{55} -2.67828 q^{56} -20.0894 q^{57} +(-2.29222 + 1.66540i) q^{58} +(3.04742 - 9.37899i) q^{59} +(-0.143545 - 0.441786i) q^{60} -6.81609 q^{61} +(1.71362 + 7.38177i) q^{62} +6.33727 q^{63} +(2.62658 + 8.08380i) q^{64} +(0.592172 - 1.82252i) q^{65} +(-19.4513 + 14.1322i) q^{66} +0.414188 q^{67} -0.339499 q^{68} +(9.40770 - 6.83509i) q^{69} +(1.00897 + 0.733057i) q^{70} +(4.68617 + 3.40470i) q^{71} +(-6.24678 - 19.2256i) q^{72} +(5.11470 - 3.71605i) q^{73} +(3.39140 + 10.4377i) q^{74} +(-0.973089 + 2.99486i) q^{75} +(0.761360 + 0.553160i) q^{76} +(-1.58843 + 4.88869i) q^{77} +(2.53802 - 7.81123i) q^{78} +(-8.59071 - 6.24151i) q^{79} +(1.13817 - 3.50294i) q^{80} +(5.58827 + 17.1989i) q^{81} +(2.78758 - 2.02529i) q^{82} +(-3.10371 - 9.55223i) q^{83} +(-0.344354 - 0.250188i) q^{84} +(1.86192 + 1.35276i) q^{85} +(10.4974 - 7.62683i) q^{86} -6.55529 q^{87} +16.3967 q^{88} +(1.86543 - 1.35532i) q^{89} +(-2.90884 + 8.95250i) q^{90} +(-0.542612 - 1.66999i) q^{91} -0.544743 q^{92} +(-6.83108 + 16.1473i) q^{93} +5.67996 q^{94} +(-1.97142 - 6.06741i) q^{95} +(-0.810314 + 2.49389i) q^{96} +(-9.18599 + 6.67401i) q^{97} -8.38465 q^{98} -38.7976 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 2 q^{2} - 6 q^{4} - 24 q^{5} - 16 q^{6} - 9 q^{7} + 11 q^{8} - 6 q^{9}+O(q^{10}) \) 24 * q + 2 * q^2 - 6 * q^4 - 24 * q^5 - 16 * q^6 - 9 * q^7 + 11 * q^8 - 6 * q^9	\( 24 q + 2 q^{2} - 6 q^{4} - 24 q^{5} - 16 q^{6} - 9 q^{7} + 11 q^{8} - 6 q^{9} - 2 q^{10} + q^{11} + 18 q^{12} - 5 q^{13} + 6 q^{14} - 24 q^{16} + 7 q^{17} - 18 q^{18} + 2 q^{19} + 6 q^{20} - 10 q^{21} + 28 q^{22} - 15 q^{23} - 32 q^{24} + 24 q^{25} + 22 q^{26} + 9 q^{27} + 38 q^{28} + 15 q^{29} + 16 q^{30} + 6 q^{31} + 74 q^{32} + 5 q^{33} - 20 q^{34} + 9 q^{35} - 58 q^{36} - 56 q^{37} - 21 q^{38} - 10 q^{39} - 11 q^{40} - 24 q^{41} - 38 q^{42} + 21 q^{43} + 41 q^{44} + 6 q^{45} + 48 q^{46} - 8 q^{47} - 26 q^{48} - 23 q^{49} + 2 q^{50} + 26 q^{51} - 27 q^{52} + 26 q^{53} + 11 q^{54} - q^{55} - 48 q^{56} + 62 q^{57} + 52 q^{58} + 10 q^{59} - 18 q^{60} - 40 q^{61} - 28 q^{62} + 26 q^{63} + 9 q^{64} + 5 q^{65} - 2 q^{66} - 26 q^{67} - 8 q^{68} + 64 q^{69} - 6 q^{70} - 7 q^{71} - 127 q^{72} - 51 q^{73} - q^{74} + 43 q^{76} - 39 q^{77} - 31 q^{78} + 31 q^{79} + 24 q^{80} + 34 q^{81} + 58 q^{82} + 6 q^{83} + 113 q^{84} - 7 q^{85} - 22 q^{86} + 4 q^{87} - 28 q^{88} + 13 q^{89} + 18 q^{90} + 54 q^{91} - 2 q^{92} - 72 q^{93} - 10 q^{94} - 2 q^{95} + 101 q^{96} - 39 q^{97} - 220 q^{98} - 170 q^{99}+O(q^{100}) \) 24 * q + 2 * q^2 - 6 * q^4 - 24 * q^5 - 16 * q^6 - 9 * q^7 + 11 * q^8 - 6 * q^9 - 2 * q^10 + q^11 + 18 * q^12 - 5 * q^13 + 6 * q^14 - 24 * q^16 + 7 * q^17 - 18 * q^18 + 2 * q^19 + 6 * q^20 - 10 * q^21 + 28 * q^22 - 15 * q^23 - 32 * q^24 + 24 * q^25 + 22 * q^26 + 9 * q^27 + 38 * q^28 + 15 * q^29 + 16 * q^30 + 6 * q^31 + 74 * q^32 + 5 * q^33 - 20 * q^34 + 9 * q^35 - 58 * q^36 - 56 * q^37 - 21 * q^38 - 10 * q^39 - 11 * q^40 - 24 * q^41 - 38 * q^42 + 21 * q^43 + 41 * q^44 + 6 * q^45 + 48 * q^46 - 8 * q^47 - 26 * q^48 - 23 * q^49 + 2 * q^50 + 26 * q^51 - 27 * q^52 + 26 * q^53 + 11 * q^54 - q^55 - 48 * q^56 + 62 * q^57 + 52 * q^58 + 10 * q^59 - 18 * q^60 - 40 * q^61 - 28 * q^62 + 26 * q^63 + 9 * q^64 + 5 * q^65 - 2 * q^66 - 26 * q^67 - 8 * q^68 + 64 * q^69 - 6 * q^70 - 7 * q^71 - 127 * q^72 - 51 * q^73 - q^74 + 43 * q^76 - 39 * q^77 - 31 * q^78 + 31 * q^79 + 24 * q^80 + 34 * q^81 + 58 * q^82 + 6 * q^83 + 113 * q^84 - 7 * q^85 - 22 * q^86 + 4 * q^87 - 28 * q^88 + 13 * q^89 + 18 * q^90 + 54 * q^91 - 2 * q^92 - 72 * q^93 - 10 * q^94 - 2 * q^95 + 101 * q^96 - 39 * q^97 - 220 * q^98 - 170 * q^99

Introduction

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