LMFDB - Embedded newform 1155.2.c.f.694.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1155,2,Mod(694,1155)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1155, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1, 0, 0]))

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

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

chi := DirichletCharacter("1155.694");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1155 = 3 \cdot 5 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1155.c (of order $2$, degree $1$, 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:	$9.22272143346$
Analytic rank:	$0$
Dimension:	$20$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 33 x^{18} + 456 x^{16} + 3426 x^{14} + 15210 x^{12} + 40640 x^{10} + 63865 x^{8} + 55281 x^{6} + \cdots + 4 $ x^20 + 33x^18 + 456x^16 + 3426x^14 + 15210x^12 + 40640x^10 + 63865x^8 + 55281x^6 + 22984x^4 + 3428*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			694.3
Root			$-2.32980i$ of defining polynomial
Character	$\chi$	$=$	1155.694
Dual form			1155.2.c.f.694.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.32980i q^{2} -1.00000i q^{3} -3.42795 q^{4} +(1.29334 + 1.82408i) q^{5} -2.32980 q^{6} -1.00000i q^{7} +3.32682i q^{8} -1.00000 q^{9} +O(q^{10})$	\(q-2.32980i q^{2} -1.00000i q^{3} -3.42795 q^{4} +(1.29334 + 1.82408i) q^{5} -2.32980 q^{6} -1.00000i q^{7} +3.32682i q^{8} -1.00000 q^{9} +(4.24974 - 3.01322i) q^{10} +1.00000 q^{11} +3.42795i q^{12} -0.502672i q^{13} -2.32980 q^{14} +(1.82408 - 1.29334i) q^{15} +0.894923 q^{16} -4.71613i q^{17} +2.32980i q^{18} -5.19890 q^{19} +(-4.43350 - 6.25285i) q^{20} -1.00000 q^{21} -2.32980i q^{22} -8.45438i q^{23} +3.32682 q^{24} +(-1.65455 + 4.71831i) q^{25} -1.17112 q^{26} +1.00000i q^{27} +3.42795i q^{28} -6.83657 q^{29} +(-3.01322 - 4.24974i) q^{30} -3.74688 q^{31} +4.56866i q^{32} -1.00000i q^{33} -10.9876 q^{34} +(1.82408 - 1.29334i) q^{35} +3.42795 q^{36} -10.6116i q^{37} +12.1124i q^{38} -0.502672 q^{39} +(-6.06840 + 4.30271i) q^{40} +4.41258 q^{41} +2.32980i q^{42} -2.08689i q^{43} -3.42795 q^{44} +(-1.29334 - 1.82408i) q^{45} -19.6970 q^{46} +3.12029i q^{47} -0.894923i q^{48} -1.00000 q^{49} +(10.9927 + 3.85476i) q^{50} -4.71613 q^{51} +1.72313i q^{52} +6.43526i q^{53} +2.32980 q^{54} +(1.29334 + 1.82408i) q^{55} +3.32682 q^{56} +5.19890i q^{57} +15.9278i q^{58} -9.33062 q^{59} +(-6.25285 + 4.43350i) q^{60} +14.8948 q^{61} +8.72946i q^{62} +1.00000i q^{63} +12.4339 q^{64} +(0.916914 - 0.650125i) q^{65} -2.32980 q^{66} -8.31898i q^{67} +16.1666i q^{68} -8.45438 q^{69} +(-3.01322 - 4.24974i) q^{70} -13.6447 q^{71} -3.32682i q^{72} -1.67769i q^{73} -24.7229 q^{74} +(4.71831 + 1.65455i) q^{75} +17.8216 q^{76} -1.00000i q^{77} +1.17112i q^{78} +11.0211 q^{79} +(1.15744 + 1.63241i) q^{80} +1.00000 q^{81} -10.2804i q^{82} -5.93207i q^{83} +3.42795 q^{84} +(8.60260 - 6.09955i) q^{85} -4.86202 q^{86} +6.83657i q^{87} +3.32682i q^{88} +4.63463 q^{89} +(-4.24974 + 3.01322i) q^{90} -0.502672 q^{91} +28.9812i q^{92} +3.74688i q^{93} +7.26963 q^{94} +(-6.72395 - 9.48322i) q^{95} +4.56866 q^{96} -6.94873i q^{97} +2.32980i q^{98} -1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 26 q^{4} - 2 q^{5} + 6 q^{6} - 20 q^{9}+O(q^{10}) $ 20 * q - 26 * q^4 - 2 * q^5 + 6 * q^6 - 20 * q^9	$ 20 q - 26 q^{4} - 2 q^{5} + 6 q^{6} - 20 q^{9} + 2 q^{10} + 20 q^{11} + 6 q^{14} - 2 q^{15} + 38 q^{16} - 34 q^{19} + 4 q^{20} - 20 q^{21} - 18 q^{24} - 4 q^{25} + 28 q^{26} - 10 q^{29} - 6 q^{30} + 12 q^{31} - 32 q^{34} - 2 q^{35} + 26 q^{36} - 2 q^{40} + 52 q^{41} - 26 q^{44} + 2 q^{45} + 40 q^{46} - 20 q^{49} + 6 q^{50} + 6 q^{51} - 6 q^{54} - 2 q^{55} - 18 q^{56} - 14 q^{59} - 28 q^{60} + 78 q^{61} - 26 q^{64} - 4 q^{65} + 6 q^{66} - 18 q^{69} - 6 q^{70} - 8 q^{74} - 8 q^{75} + 84 q^{76} - 52 q^{79} - 40 q^{80} + 20 q^{81} + 26 q^{84} - 24 q^{85} + 4 q^{86} - 10 q^{89} - 2 q^{90} - 96 q^{94} - 30 q^{95} + 62 q^{96} - 20 q^{99}+O(q^{100}) $ 20 * q - 26 * q^4 - 2 * q^5 + 6 * q^6 - 20 * q^9 + 2 * q^10 + 20 * q^11 + 6 * q^14 - 2 * q^15 + 38 * q^16 - 34 * q^19 + 4 * q^20 - 20 * q^21 - 18 * q^24 - 4 * q^25 + 28 * q^26 - 10 * q^29 - 6 * q^30 + 12 * q^31 - 32 * q^34 - 2 * q^35 + 26 * q^36 - 2 * q^40 + 52 * q^41 - 26 * q^44 + 2 * q^45 + 40 * q^46 - 20 * q^49 + 6 * q^50 + 6 * q^51 - 6 * q^54 - 2 * q^55 - 18 * q^56 - 14 * q^59 - 28 * q^60 + 78 * q^61 - 26 * q^64 - 4 * q^65 + 6 * q^66 - 18 * q^69 - 6 * q^70 - 8 * q^74 - 8 * q^75 + 84 * q^76 - 52 * q^79 - 40 * q^80 + 20 * q^81 + 26 * q^84 - 24 * q^85 + 4 * q^86 - 10 * q^89 - 2 * q^90 - 96 * q^94 - 30 * q^95 + 62 * q^96 - 20 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1155\mathbb{Z}\right)^\times$.

$n$	$211$	$232$	$386$	$661$
$\chi(n)$	$1$	$-1$	$1$	$1$

Coefficient data

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

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

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

$2$		−	2.32980i		−	1.64741i	−0.567016	−	0.823707i	$-0.691902\pi$
$2$		−	2.32980i		−	1.64741i	0.567016	−	0.823707i	$-0.308098\pi$
$3$		−	1.00000i		−	0.577350i
$3$		−	1.00000i		−	0.577350i
$4$	−3.42795			−1.71397
$5$	1.29334	+	1.82408i	0.578399	+	0.815754i
$5$	1.29334	+	1.82408i	0.578399	+	0.815754i
$6$	−2.32980			−0.951135
$7$		−	1.00000i		−	0.377964i
$7$		−	1.00000i		−	0.377964i
$8$			3.32682i			1.17621i
$9$	−1.00000			−0.333333
$10$	4.24974	−	3.01322i	1.34388	−	0.952862i
$11$	1.00000			0.301511
$11$	1.00000			0.301511
$12$			3.42795i			0.989563i
$13$		−	0.502672i		−	0.139416i	−0.997567	−	0.0697080i	$-0.977793\pi$
$13$		−	0.502672i		−	0.139416i	0.997567	−	0.0697080i	$-0.0222068\pi$
$14$	−2.32980			−0.622664
$15$	1.82408	−	1.29334i	0.470976	−	0.333939i
$16$	0.894923			0.223731
$17$		−	4.71613i		−	1.14383i	−0.820313	−	0.571914i	$-0.806201\pi$
$17$		−	4.71613i		−	1.14383i	0.820313	−	0.571914i	$-0.193799\pi$
$18$			2.32980i			0.549138i
$19$	−5.19890			−1.19271			−0.596355	−	0.802721i	$-0.703385\pi$
$19$	−5.19890			−1.19271			−0.596355	+	0.802721i	$0.703385\pi$
$20$	−4.43350	−	6.25285i	−0.991360	−	1.39818i
$21$	−1.00000			−0.218218
$22$		−	2.32980i		−	0.496714i
$23$		−	8.45438i		−	1.76286i	−0.472315	−	0.881430i	$-0.656582\pi$
$23$		−	8.45438i		−	1.76286i	0.472315	−	0.881430i	$-0.343418\pi$
$24$	3.32682			0.679085
$25$	−1.65455	+	4.71831i	−0.330909	+	0.943663i
$26$	−1.17112			−0.229676
$27$			1.00000i			0.192450i
$28$			3.42795i			0.647821i
$29$	−6.83657			−1.26952			−0.634759	−	0.772710i	$-0.718901\pi$
$29$	−6.83657			−1.26952			−0.634759	+	0.772710i	$0.718901\pi$
$30$	−3.01322	−	4.24974i	−0.550135	−	0.775892i
$31$	−3.74688			−0.672960			−0.336480	−	0.941691i	$-0.609236\pi$
$31$	−3.74688			−0.672960			−0.336480	+	0.941691i	$0.609236\pi$
$32$			4.56866i			0.807632i
$33$		−	1.00000i		−	0.174078i
$34$	−10.9876			−1.88436
$35$	1.82408	−	1.29334i	0.308326	−	0.218614i
$36$	3.42795			0.571324
$37$		−	10.6116i		−	1.74454i	−0.489022	−	0.872271i	$-0.662646\pi$
$37$		−	10.6116i		−	1.74454i	0.489022	−	0.872271i	$-0.337354\pi$
$38$			12.1124i			1.96489i
$39$	−0.502672			−0.0804919
$40$	−6.06840	+	4.30271i	−0.959498	+	0.680318i
$41$	4.41258			0.689130			0.344565	−	0.938763i	$-0.388026\pi$
$41$	4.41258			0.689130			0.344565	+	0.938763i	$0.388026\pi$
$42$			2.32980i			0.359495i
$43$		−	2.08689i		−	0.318247i	−0.987259	−	0.159124i	$-0.949133\pi$
$43$		−	2.08689i		−	0.318247i	0.987259	−	0.159124i	$-0.0508669\pi$
$44$	−3.42795			−0.516782
$45$	−1.29334	−	1.82408i	−0.192800	−	0.271918i
$46$	−19.6970			−2.90416
$47$			3.12029i			0.455141i	0.973762	+	0.227570i	$0.0730782\pi$
$47$			3.12029i			0.455141i	−0.973762	+	0.227570i	$0.926922\pi$
$48$		−	0.894923i		−	0.129171i
$49$	−1.00000			−0.142857
$50$	10.9927	+	3.85476i	1.55460	+	0.545145i
$51$	−4.71613			−0.660390
$52$			1.72313i			0.238955i
$53$			6.43526i			0.883951i	0.897027	+	0.441975i	$0.145722\pi$
$53$			6.43526i			0.883951i	−0.897027	+	0.441975i	$0.854278\pi$
$54$	2.32980			0.317045
$55$	1.29334	+	1.82408i	0.174394	+	0.245959i
$56$	3.32682			0.444565
$57$			5.19890i			0.688612i
$58$			15.9278i			2.09142i
$59$	−9.33062			−1.21474			−0.607372	−	0.794418i	$-0.707776\pi$
$59$	−9.33062			−1.21474			−0.607372	+	0.794418i	$0.707776\pi$
$60$	−6.25285	+	4.43350i	−0.807240	+	0.572362i
$61$	14.8948			1.90709			0.953543	−	0.301258i	$-0.0974066\pi$
$61$	14.8948			1.90709			0.953543	+	0.301258i	$0.0974066\pi$
$62$			8.72946i			1.10864i
$63$			1.00000i			0.125988i
$64$	12.4339			1.55424
$65$	0.916914	−	0.650125i	0.113729	−	0.0806381i
$66$	−2.32980			−0.286778
$67$		−	8.31898i		−	1.01633i	−0.861261	−	0.508163i	$-0.830325\pi$
$67$		−	8.31898i		−	1.01633i	0.861261	−	0.508163i	$-0.169675\pi$
$68$			16.1666i			1.96049i
$69$	−8.45438			−1.01779
$70$	−3.01322	−	4.24974i	−0.360148	−	0.507941i
$71$	−13.6447			−1.61933			−0.809664	−	0.586894i	$-0.800351\pi$
$71$	−13.6447			−1.61933			−0.809664	+	0.586894i	$0.800351\pi$
$72$		−	3.32682i		−	0.392070i
$73$		−	1.67769i		−	0.196358i	−0.995169	−	0.0981792i	$-0.968698\pi$
$73$		−	1.67769i		−	0.196358i	0.995169	−	0.0981792i	$-0.0313018\pi$
$74$	−24.7229			−2.87398
$75$	4.71831	+	1.65455i	0.544824	+	0.191051i
$76$	17.8216			2.04427
$77$		−	1.00000i		−	0.113961i
$78$			1.17112i			0.132604i
$79$	11.0211			1.23997			0.619987	−	0.784612i	$-0.287138\pi$
$79$	11.0211			1.23997			0.619987	+	0.784612i	$0.287138\pi$
$80$	1.15744	+	1.63241i	0.129406	+	0.182509i
$81$	1.00000			0.111111
$82$		−	10.2804i		−	1.13528i
$83$		−	5.93207i		−	0.651130i	−0.945520	−	0.325565i	$-0.894446\pi$
$83$		−	5.93207i		−	0.651130i	0.945520	−	0.325565i	$-0.105554\pi$
$84$	3.42795			0.374020
$85$	8.60260	−	6.09955i	0.933083	−	0.661589i
$86$	−4.86202			−0.524285
$87$			6.83657i			0.732957i
$88$			3.32682i			0.354640i
$89$	4.63463			0.491270			0.245635	−	0.969362i	$-0.421004\pi$
$89$	4.63463			0.491270			0.245635	+	0.969362i	$0.421004\pi$
$90$	−4.24974	+	3.01322i	−0.447962	+	0.317621i
$91$	−0.502672			−0.0526943
$92$			28.9812i			3.02149i
$93$			3.74688i			0.388533i
$94$	7.26963			0.749805
$95$	−6.72395	−	9.48322i	−0.689862	−	0.972958i
$96$	4.56866			0.466287
$97$		−	6.94873i		−	0.705536i	−0.935711	−	0.352768i	$-0.885240\pi$
$97$		−	6.94873i		−	0.705536i	0.935711	−	0.352768i	$-0.114760\pi$
$98$			2.32980i			0.235345i
$99$	−1.00000			−0.100504
$100$	5.67170	−	16.1741i	0.567170	−	1.61741i
$101$	10.4435			1.03917			0.519583	−	0.854420i	$-0.326087\pi$
$101$	10.4435			1.03917			0.519583	+	0.854420i	$0.326087\pi$
$102$			10.9876i			1.08794i
$103$		−	2.04502i		−	0.201502i	−0.994912	−	0.100751i	$-0.967876\pi$
$103$		−	2.04502i		−	0.201502i	0.994912	−	0.100751i	$-0.0321245\pi$
$104$	1.67230			0.163982
$105$	−1.29334	−	1.82408i	−0.126217	−	0.178012i
$106$	14.9928			1.45623
$107$			9.20478i			0.889860i	0.895565	+	0.444930i	$0.146771\pi$
$107$			9.20478i			0.889860i	−0.895565	+	0.444930i	$0.853229\pi$
$108$		−	3.42795i		−	0.329854i
$109$	−9.14803			−0.876222			−0.438111	−	0.898921i	$-0.644352\pi$
$109$	−9.14803			−0.876222			−0.438111	+	0.898921i	$0.644352\pi$
$110$	4.24974	−	3.01322i	0.405196	−	0.287299i
$111$	−10.6116			−1.00721
$112$		−	0.894923i		−	0.0845623i
$113$			15.0844i			1.41903i	0.704693	+	0.709513i	$0.251085\pi$
$113$			15.0844i			1.41903i	−0.704693	+	0.709513i	$0.748915\pi$
$114$	12.1124			1.13443
$115$	15.4215	−	10.9344i	1.43806	−	1.01964i
$116$	23.4354			2.17592
$117$			0.502672i			0.0464720i
$118$			21.7384i			2.00119i
$119$	−4.71613			−0.432327
$120$	4.30271	+	6.06840i	0.392782	+	0.553966i
$121$	1.00000			0.0909091
$122$		−	34.7019i		−	3.14176i
$123$		−	4.41258i		−	0.397869i
$124$	12.8441			1.15343
$125$	−10.7465	+	3.08435i	−0.961194	+	0.275873i
$126$	2.32980			0.207555
$127$		−	8.21728i		−	0.729166i	−0.931171	−	0.364583i	$-0.881212\pi$
$127$		−	8.21728i		−	0.729166i	0.931171	−	0.364583i	$-0.118788\pi$
$128$		−	19.8311i		−	1.75284i
$129$	−2.08689			−0.183740
$130$	−1.51466	−	2.13622i	−0.132844	−	0.187359i
$131$	20.6729			1.80620			0.903100	−	0.429431i	$-0.141286\pi$
$131$	20.6729			1.80620			0.903100	+	0.429431i	$0.141286\pi$
$132$			3.42795i			0.298364i
$133$			5.19890i			0.450802i
$134$	−19.3815			−1.67431
$135$	−1.82408	+	1.29334i	−0.156992	+	0.111313i
$136$	15.6897			1.34538
$137$			17.2798i			1.47631i	0.674629	+	0.738157i	$0.264304\pi$
$137$			17.2798i			1.47631i	−0.674629	+	0.738157i	$0.735696\pi$
$138$			19.6970i			1.67672i
$139$	16.1272			1.36789			0.683946	−	0.729533i	$-0.260262\pi$
$139$	16.1272			1.36789			0.683946	+	0.729533i	$0.260262\pi$
$140$	−6.25285	+	4.43350i	−0.528463	+	0.374699i
$141$	3.12029			0.262776
$142$			31.7894i			2.66770i
$143$		−	0.502672i		−	0.0420355i
$144$	−0.894923			−0.0745769
$145$	−8.84200	−	12.4705i	−0.734288	−	1.03561i
$146$	−3.90867			−0.323484
$147$			1.00000i			0.0824786i
$148$			36.3761i			2.99010i
$149$	5.44786			0.446306			0.223153	−	0.974783i	$-0.428365\pi$
$149$	5.44786			0.446306			0.223153	+	0.974783i	$0.428365\pi$
$150$	3.85476	−	10.9927i	0.314740	−	0.897550i
$151$	2.55941			0.208282			0.104141	−	0.994563i	$-0.466791\pi$
$151$	2.55941			0.208282			0.104141	+	0.994563i	$0.466791\pi$
$152$		−	17.2958i		−	1.40288i
$153$			4.71613i			0.381276i
$154$	−2.32980			−0.187740
$155$	−4.84599	−	6.83461i	−0.389239	−	0.548969i
$156$	1.72313			0.137961
$157$		−	3.64395i		−	0.290819i	−0.989372	−	0.145410i	$-0.953550\pi$
$157$		−	3.64395i		−	0.290819i	0.989372	−	0.145410i	$-0.0464500\pi$
$158$		−	25.6770i		−	2.04275i
$159$	6.43526			0.510349
$160$	−8.33360	+	5.90882i	−0.658829	+	0.467134i
$161$	−8.45438			−0.666298
$162$		−	2.32980i		−	0.183046i
$163$		−	18.8621i		−	1.47740i	−0.674036	−	0.738698i	$-0.735441\pi$
$163$		−	18.8621i		−	1.47740i	0.674036	−	0.738698i	$-0.264559\pi$
$164$	−15.1261			−1.18115
$165$	1.82408	−	1.29334i	0.142005	−	0.100686i
$166$	−13.8205			−1.07268
$167$		−	10.8689i		−	0.841062i	−0.907278	−	0.420531i	$-0.861844\pi$
$167$		−	10.8689i		−	0.841062i	0.907278	−	0.420531i	$-0.138156\pi$
$168$		−	3.32682i		−	0.256670i
$169$	12.7473			0.980563
$170$	−14.2107	−	20.0423i	−1.08991	−	1.53717i
$171$	5.19890			0.397570
$172$			7.15374i			0.545467i
$173$			4.64430i			0.353100i	0.984292	+	0.176550i	$0.0564937\pi$
$173$			4.64430i			0.353100i	−0.984292	+	0.176550i	$0.943506\pi$
$174$	15.9278			1.20748
$175$	4.71831	+	1.65455i	0.356671	+	0.125072i
$176$	0.894923			0.0674574
$177$			9.33062i			0.701332i
$178$		−	10.7977i		−	0.809325i
$179$	−18.7959			−1.40487			−0.702434	−	0.711748i	$-0.747904\pi$
$179$	−18.7959			−1.40487			−0.702434	+	0.711748i	$0.747904\pi$
$180$	4.43350	+	6.25285i	0.330453	+	0.466060i
$181$	9.99140			0.742655			0.371328	−	0.928502i	$-0.378903\pi$
$181$	9.99140			0.742655			0.371328	+	0.928502i	$0.378903\pi$
$182$			1.17112i			0.0868094i
$183$		−	14.8948i		−	1.10106i
$184$	28.1262			2.07349
$185$	19.3565	−	13.7245i	1.42312	−	1.00904i
$186$	8.72946			0.640075
$187$		−	4.71613i		−	0.344877i
$188$		−	10.6962i		−	0.780099i
$189$	1.00000			0.0727393
$190$	−22.0940	+	15.6654i	−1.60287	+	1.13649i
$191$	3.75850			0.271956			0.135978	−	0.990712i	$-0.456582\pi$
$191$	3.75850			0.271956			0.135978	+	0.990712i	$0.456582\pi$
$192$		−	12.4339i		−	0.897338i
$193$		−	7.19543i		−	0.517938i	−0.965886	−	0.258969i	$-0.916617\pi$
$193$		−	7.19543i		−	0.517938i	0.965886	−	0.258969i	$-0.0833828\pi$
$194$	−16.1891			−1.16231
$195$	−0.650125	−	0.916914i	−0.0465564	−	0.0656616i
$196$	3.42795			0.244853
$197$			4.89259i			0.348583i	0.984694	+	0.174291i	$0.0557634\pi$
$197$			4.89259i			0.348583i	−0.984694	+	0.174291i	$0.944237\pi$
$198$			2.32980i			0.165571i
$199$	−24.5120			−1.73761			−0.868804	−	0.495156i	$-0.835111\pi$
$199$	−24.5120			−1.73761			−0.868804	+	0.495156i	$0.835111\pi$
$200$	−15.6970	−	5.50438i	−1.10994	−	0.389219i
$201$	−8.31898			−0.586776
$202$		−	24.3312i		−	1.71194i
$203$			6.83657i			0.479833i
$204$	16.1666			1.13189
$205$	5.70697	+	8.04891i	0.398592	+	0.562160i
$206$	−4.76447			−0.331957
$207$			8.45438i			0.587620i
$208$		−	0.449853i		−	0.0311917i
$209$	−5.19890			−0.359616
$210$	−4.24974	+	3.01322i	−0.293260	+	0.207932i
$211$	7.61523			0.524254			0.262127	−	0.965033i	$-0.415576\pi$
$211$	7.61523			0.524254			0.262127	+	0.965033i	$0.415576\pi$
$212$		−	22.0597i		−	1.51507i
$213$			13.6447i			0.934919i
$214$	21.4453			1.46597
$215$	3.80665	−	2.69905i	0.259612	−	0.184074i
$216$	−3.32682			−0.226362
$217$			3.74688i			0.254355i
$218$			21.3130i			1.44350i
$219$	−1.67769			−0.113368
$220$	−4.43350	−	6.25285i	−0.298906	−	0.421567i
$221$	−2.37066			−0.159468
$222$			24.7229i			1.65930i
$223$			19.0382i			1.27489i	0.770495	+	0.637446i	$0.220009\pi$
$223$			19.0382i			1.27489i	−0.770495	+	0.637446i	$0.779991\pi$
$224$	4.56866			0.305256
$225$	1.65455	−	4.71831i	0.110303	−	0.314554i
$226$	35.1437			2.33772
$227$			11.4181i			0.757846i	0.925428	+	0.378923i	$0.123706\pi$
$227$			11.4181i			0.757846i	−0.925428	+	0.378923i	$0.876294\pi$
$228$		−	17.8216i		−	1.18026i
$229$	−10.4889			−0.693127			−0.346564	−	0.938026i	$-0.612652\pi$
$229$	−10.4889			−0.693127			−0.346564	+	0.938026i	$0.612652\pi$
$230$	−25.4749	−	35.9289i	−1.67976	−	2.36908i
$231$	−1.00000			−0.0657952
$232$		−	22.7440i		−	1.49322i
$233$			6.53550i			0.428155i	0.976817	+	0.214078i	$0.0686745\pi$
$233$			6.53550i			0.428155i	−0.976817	+	0.214078i	$0.931325\pi$
$234$	1.17112			0.0765587
$235$	−5.69166	+	4.03559i	−0.371283	+	0.263253i
$236$	31.9849			2.08204
$237$		−	11.0211i		−	0.715900i
$238$			10.9876i			0.712221i
$239$	−10.7986			−0.698503			−0.349252	−	0.937029i	$-0.613564\pi$
$239$	−10.7986			−0.698503			−0.349252	+	0.937029i	$0.613564\pi$
$240$	1.63241	−	1.15744i	0.105372	−	0.0747124i
$241$	−17.6856			−1.13923			−0.569614	−	0.821912i	$-0.692907\pi$
$241$	−17.6856			−1.13923			−0.569614	+	0.821912i	$0.692907\pi$
$242$		−	2.32980i		−	0.149765i
$243$		−	1.00000i		−	0.0641500i
$244$	−51.0586			−3.26869
$245$	−1.29334	−	1.82408i	−0.0826284	−	0.116536i
$246$	−10.2804			−0.655455
$247$			2.61334i			0.166283i
$248$		−	12.4652i		−	0.791541i
$249$	−5.93207			−0.375930
$250$	7.18590	+	25.0371i	0.454477	+	1.58348i
$251$	15.4676			0.976304			0.488152	−	0.872759i	$-0.337671\pi$
$251$	15.4676			0.976304			0.488152	+	0.872759i	$0.337671\pi$
$252$		−	3.42795i		−	0.215940i
$253$		−	8.45438i		−	0.531522i
$254$	−19.1446			−1.20124
$255$	−6.09955	−	8.60260i	−0.381969	−	0.538716i
$256$	−21.3346			−1.33341
$257$		−	16.1456i		−	1.00714i	−0.863956	−	0.503568i	$-0.832020\pi$
$257$		−	16.1456i		−	1.00714i	0.863956	−	0.503568i	$-0.167980\pi$
$258$			4.86202i			0.302696i
$259$	−10.6116			−0.659375
$260$	−3.14313	+	2.22859i	−0.194929	+	0.138212i
$261$	6.83657			0.423173
$262$		−	48.1636i		−	2.97556i
$263$		−	28.5409i		−	1.75991i	−0.475059	−	0.879954i	$-0.657573\pi$
$263$		−	28.5409i		−	1.75991i	0.475059	−	0.879954i	$-0.342427\pi$
$264$	3.32682			0.204752
$265$	−11.7384	+	8.32297i	−0.721086	+	0.511276i
$266$	12.1124			0.742658
$267$		−	4.63463i		−	0.283635i
$268$			28.5170i			1.74195i
$269$	4.36108			0.265900			0.132950	−	0.991123i	$-0.457555\pi$
$269$	4.36108			0.265900			0.132950	+	0.991123i	$0.457555\pi$
$270$	3.01322	+	4.24974i	0.183378	+	0.258631i
$271$	10.8089			0.656592			0.328296	−	0.944575i	$-0.393526\pi$
$271$	10.8089			0.656592			0.328296	+	0.944575i	$0.393526\pi$
$272$		−	4.22057i		−	0.255910i
$273$			0.502672i			0.0304231i
$274$	40.2584			2.43210
$275$	−1.65455	+	4.71831i	−0.0997729	+	0.284525i
$276$	28.9812			1.74446
$277$			9.03117i			0.542630i	0.962491	+	0.271315i	$0.0874586\pi$
$277$			9.03117i			0.542630i	−0.962491	+	0.271315i	$0.912541\pi$
$278$		−	37.5731i		−	2.25348i
$279$	3.74688			0.224320
$280$	4.30271	+	6.06840i	0.257136	+	0.362656i
$281$	−30.3762			−1.81209			−0.906046	−	0.423179i	$-0.860914\pi$
$281$	−30.3762			−1.81209			−0.906046	+	0.423179i	$0.860914\pi$
$282$		−	7.26963i		−	0.432900i
$283$		−	17.4504i		−	1.03732i	−0.854981	−	0.518659i	$-0.826431\pi$
$283$		−	17.4504i		−	1.03732i	0.854981	−	0.518659i	$-0.173569\pi$
$284$	46.7733			2.77548
$285$	−9.48322	+	6.72395i	−0.561738	+	0.398292i
$286$	−1.17112			−0.0692499
$287$		−	4.41258i		−	0.260467i
$288$		−	4.56866i		−	0.269211i
$289$	−5.24185			−0.308344
$290$	−29.0536	+	20.6000i	−1.70609	+	1.20968i
$291$	−6.94873			−0.407341
$292$			5.75102i			0.336553i
$293$		−	19.9039i		−	1.16280i	−0.813619	−	0.581399i	$-0.802506\pi$
$293$		−	19.9039i		−	1.16280i	0.813619	−	0.581399i	$-0.197494\pi$
$294$	2.32980			0.135876
$295$	−12.0677	−	17.0198i	−0.702606	−	0.990932i
$296$	35.3030			2.05195
$297$			1.00000i			0.0580259i
$298$		−	12.6924i		−	0.735250i
$299$	−4.24978			−0.245771
$300$	−16.1741	−	5.67170i	−0.933813	−	0.327456i
$301$	−2.08689			−0.120286
$302$		−	5.96291i		−	0.343127i
$303$		−	10.4435i		−	0.599963i
$304$	−4.65262			−0.266846
$305$	19.2640	+	27.1694i	1.10306	+	1.55571i
$306$	10.9876			0.628120
$307$		−	8.54297i		−	0.487573i	−0.969829	−	0.243786i	$-0.921610\pi$
$307$		−	8.54297i		−	0.487573i	0.969829	−	0.243786i	$-0.0783896\pi$
$308$			3.42795i			0.195325i
$309$	−2.04502			−0.116337
$310$	−15.9233	+	11.2902i	−0.904380	+	0.641238i
$311$	−9.58210			−0.543351			−0.271675	−	0.962389i	$-0.587578\pi$
$311$	−9.58210			−0.543351			−0.271675	+	0.962389i	$0.587578\pi$
$312$		−	1.67230i		−	0.0946753i
$313$			0.783593i			0.0442913i	0.999755	+	0.0221456i	$0.00704975\pi$
$313$			0.783593i			0.0442913i	−0.999755	+	0.0221456i	$0.992950\pi$
$314$	−8.48966			−0.479099
$315$	−1.82408	+	1.29334i	−0.102775	+	0.0728714i
$316$	−37.7799			−2.12528
$317$			23.4582i			1.31755i	0.752342	+	0.658773i	$0.228924\pi$
$317$			23.4582i			1.31755i	−0.752342	+	0.658773i	$0.771076\pi$
$318$		−	14.9928i		−	0.840757i
$319$	−6.83657			−0.382774
$320$	16.0812	+	22.6804i	0.898968	+	1.26787i
$321$	9.20478			0.513761
$322$			19.6970i			1.09767i
$323$			24.5187i			1.36426i
$324$	−3.42795			−0.190441
$325$	2.37176	+	0.831694i	0.131562	+	0.0461341i
$326$	−43.9449			−2.43388
$327$			9.14803i			0.505887i
$328$			14.6799i			0.810561i
$329$	3.12029			0.172027
$330$	−3.01322	−	4.24974i	−0.165872	−	0.233940i
$331$	10.5485			0.579799			0.289899	−	0.957057i	$-0.406378\pi$
$331$	10.5485			0.579799			0.289899	+	0.957057i	$0.406378\pi$
$332$			20.3348i			1.11602i
$333$			10.6116i			0.581514i
$334$	−25.3223			−1.38558
$335$	15.1745	−	10.7593i	0.829072	−	0.587842i
$336$	−0.894923			−0.0488220
$337$			4.56724i			0.248794i	0.992233	+	0.124397i	$0.0396996\pi$
$337$			4.56724i			0.248794i	−0.992233	+	0.124397i	$0.960300\pi$
$338$		−	29.6986i		−	1.61539i
$339$	15.0844			0.819275
$340$	−29.4892	+	20.9089i	−1.59928	+	1.13395i
$341$	−3.74688			−0.202905
$342$		−	12.1124i		−	0.654963i
$343$			1.00000i			0.0539949i
$344$	6.94270			0.374325
$345$	−10.9344	−	15.4215i	−0.588687	−	0.830264i
$346$	10.8203			0.581702
$347$			17.9689i			0.964619i	0.876001	+	0.482309i	$0.160202\pi$
$347$			17.9689i			0.964619i	−0.876001	+	0.482309i	$0.839798\pi$
$348$		−	23.4354i		−	1.25627i
$349$	32.8127			1.75642			0.878211	−	0.478274i	$-0.158737\pi$
$349$	32.8127			1.75642			0.878211	+	0.478274i	$0.158737\pi$
$350$	3.85476	−	10.9927i	0.206045	−	0.587585i
$351$	0.502672			0.0268306
$352$			4.56866i			0.243510i
$353$		−	14.1536i		−	0.753322i	−0.926351	−	0.376661i	$-0.877072\pi$
$353$		−	14.1536i		−	0.753322i	0.926351	−	0.376661i	$-0.122928\pi$
$354$	21.7384			1.15538
$355$	−17.6472	−	24.8890i	−0.936617	−	1.32097i
$356$	−15.8873			−0.842023
$357$			4.71613i			0.249604i
$358$			43.7905i			2.31440i
$359$	31.9939			1.68858			0.844288	−	0.535890i	$-0.180024\pi$
$359$	31.9939			1.68858			0.844288	+	0.535890i	$0.180024\pi$
$360$	6.06840	−	4.30271i	0.319833	−	0.226773i
$361$	8.02860			0.422558
$362$		−	23.2779i		−	1.22346i
$363$		−	1.00000i		−	0.0524864i
$364$	1.72313			0.0903167
$365$	3.06024	−	2.16982i	0.160180	−	0.113573i
$366$	−34.7019			−1.81390
$367$			1.40078i			0.0731202i	0.999331	+	0.0365601i	$0.0116400\pi$
$367$			1.40078i			0.0731202i	−0.999331	+	0.0365601i	$0.988360\pi$
$368$		−	7.56602i		−	0.394406i
$369$	−4.41258			−0.229710
$370$	−31.9752	−	45.0967i	−1.66231	−	2.34446i
$371$	6.43526			0.334102
$372$		−	12.8441i		−	0.665936i
$373$			30.5899i			1.58388i	0.610597	+	0.791942i	$0.290930\pi$
$373$			30.5899i			1.58388i	−0.610597	+	0.791942i	$0.709070\pi$
$374$	−10.9876			−0.568156
$375$	3.08435	+	10.7465i	0.159275	+	0.554946i
$376$	−10.3806			−0.535341
$377$			3.43655i			0.176991i
$378$		−	2.32980i		−	0.119832i
$379$	0.405321			0.0208200			0.0104100	−	0.999946i	$-0.496686\pi$
$379$	0.405321			0.0208200			0.0104100	+	0.999946i	$0.496686\pi$
$380$	23.0493	+	32.5080i	1.18241	+	1.66762i
$381$	−8.21728			−0.420984
$382$		−	8.75654i		−	0.448023i
$383$		−	17.4994i		−	0.894177i	−0.894490	−	0.447088i	$-0.852461\pi$
$383$		−	17.4994i		−	0.894177i	0.894490	−	0.447088i	$-0.147539\pi$
$384$	−19.8311			−1.01200
$385$	1.82408	−	1.29334i	0.0929638	−	0.0659147i
$386$	−16.7639			−0.853259
$387$			2.08689i			0.106082i
$388$			23.8199i			1.20927i
$389$	18.4639			0.936157			0.468079	−	0.883687i	$-0.344946\pi$
$389$	18.4639			0.936157			0.468079	+	0.883687i	$0.344946\pi$
$390$	−2.13622	+	1.51466i	−0.108172	+	0.0766977i
$391$	−39.8719			−2.01641
$392$		−	3.32682i		−	0.168030i
$393$		−	20.6729i		−	1.04281i
$394$	11.3987			0.574260
$395$	14.2541	+	20.1035i	0.717200	+	1.01151i
$396$	3.42795			0.172261
$397$		−	30.7021i		−	1.54090i	−0.637503	−	0.770448i	$-0.720033\pi$
$397$		−	30.7021i		−	1.54090i	0.637503	−	0.770448i	$-0.279967\pi$
$398$			57.1079i			2.86256i
$399$	5.19890			0.260271
$400$	−1.48069	+	4.22253i	−0.0740346	+	0.211126i
$401$	22.1714			1.10719			0.553594	−	0.832787i	$-0.313256\pi$
$401$	22.1714			1.10719			0.553594	+	0.832787i	$0.313256\pi$
$402$			19.3815i			0.966663i
$403$			1.88345i			0.0938214i
$404$	−35.7997			−1.78110
$405$	1.29334	+	1.82408i	0.0642665	+	0.0906393i
$406$	15.9278			0.790483
$407$		−	10.6116i		−	0.525999i
$408$		−	15.6897i		−	0.776757i
$409$	15.0454			0.743945			0.371973	−	0.928244i	$-0.378682\pi$
$409$	15.0454			0.743945			0.371973	+	0.928244i	$0.378682\pi$
$410$	18.7523	−	13.2961i	0.926111	−	0.656646i
$411$	17.2798			0.852350
$412$			7.01021i			0.345368i
$413$			9.33062i			0.459130i
$414$	19.6970			0.968053
$415$	10.8206	−	7.67219i	0.531162	−	0.376613i
$416$	2.29654			0.112597
$417$		−	16.1272i		−	0.789753i
$418$			12.1124i			0.592436i
$419$	−20.1252			−0.983179			−0.491589	−	0.870827i	$-0.663584\pi$
$419$	−20.1252			−0.983179			−0.491589	+	0.870827i	$0.663584\pi$
$420$	4.43350	+	6.25285i	0.216333	+	0.305108i
$421$	5.87543			0.286351			0.143176	−	0.989697i	$-0.454269\pi$
$421$	5.87543			0.286351			0.143176	+	0.989697i	$0.454269\pi$
$422$		−	17.7419i		−	0.863664i
$423$		−	3.12029i		−	0.151714i
$424$	−21.4090			−1.03971
$425$	22.2522	+	7.80305i	1.07939	+	0.378504i
$426$	31.7894			1.54020
$427$		−	14.8948i		−	0.720810i
$428$		−	31.5535i		−	1.52520i
$429$	−0.502672			−0.0242692
$430$	−6.28824	−	8.86872i	−0.303246	−	0.427688i
$431$	15.0602			0.725427			0.362713	−	0.931901i	$-0.381850\pi$
$431$	15.0602			0.725427			0.362713	+	0.931901i	$0.381850\pi$
$432$			0.894923i			0.0430570i
$433$		−	11.6048i		−	0.557691i	−0.960336	−	0.278846i	$-0.910048\pi$
$433$		−	11.6048i		−	0.557691i	0.960336	−	0.278846i	$-0.0899518\pi$
$434$	8.72946			0.419028
$435$	−12.4705	+	8.84200i	−0.597913	+	0.423941i
$436$	31.3589			1.50182
$437$			43.9535i			2.10258i
$438$			3.90867i			0.186763i
$439$	30.7688			1.46851			0.734257	−	0.678872i	$-0.237531\pi$
$439$	30.7688			1.46851			0.734257	+	0.678872i	$0.237531\pi$
$440$	−6.06840	+	4.30271i	−0.289299	+	0.205124i
$441$	1.00000			0.0476190
$442$			5.52316i			0.262710i
$443$		−	30.3108i		−	1.44011i	−0.693916	−	0.720056i	$-0.744116\pi$
$443$		−	30.3108i		−	1.44011i	0.693916	−	0.720056i	$-0.255884\pi$
$444$	36.3761			1.72633
$445$	5.99415	+	8.45395i	0.284150	+	0.400755i
$446$	44.3551			2.10028
$447$		−	5.44786i		−	0.257675i
$448$		−	12.4339i		−	0.587446i
$449$	15.8570			0.748337			0.374169	−	0.927361i	$-0.377928\pi$
$449$	15.8570			0.748337			0.374169	+	0.927361i	$0.377928\pi$
$450$	−10.9927	−	3.85476i	−0.518201	−	0.181715i
$451$	4.41258			0.207780
$452$		−	51.7087i		−	2.43217i
$453$		−	2.55941i		−	0.120252i
$454$	26.6018			1.24849
$455$	−0.650125	−	0.916914i	−0.0304783	−	0.0429856i
$456$	−17.2958			−0.809951
$457$			16.2624i			0.760725i	0.924838	+	0.380362i	$0.124201\pi$
$457$			16.2624i			0.760725i	−0.924838	+	0.380362i	$0.875799\pi$
$458$			24.4370i			1.14187i
$459$	4.71613			0.220130
$460$	−52.8640	+	37.4825i	−2.46480	+	1.74763i
$461$	2.53215			0.117934			0.0589670	−	0.998260i	$-0.481219\pi$
$461$	2.53215			0.117934			0.0589670	+	0.998260i	$0.481219\pi$
$462$			2.32980i			0.108392i
$463$		−	31.2078i		−	1.45035i	−0.688564	−	0.725175i	$-0.741759\pi$
$463$		−	31.2078i		−	1.45035i	0.688564	−	0.725175i	$-0.258241\pi$
$464$	−6.11820			−0.284030
$465$	−6.83461	+	4.84599i	−0.316948	+	0.224727i
$466$	15.2264			0.705349
$467$		−	34.5799i		−	1.60017i	−0.599889	−	0.800083i	$-0.704789\pi$
$467$		−	34.5799i		−	1.60017i	0.599889	−	0.800083i	$-0.295211\pi$
$468$		−	1.72313i		−	0.0796518i
$469$	−8.31898			−0.384135
$470$	9.40210	+	13.2604i	0.433687	+	0.611657i
$471$	−3.64395			−0.167904
$472$		−	31.0413i		−	1.42879i
$473$		−	2.08689i		−	0.0959552i
$474$	−25.6770			−1.17938
$475$	8.60183	−	24.5301i	0.394679	−	1.12552i
$476$	16.1666			0.740996
$477$		−	6.43526i		−	0.294650i
$478$			25.1585i			1.15072i
$479$	13.0340			0.595538			0.297769	−	0.954638i	$-0.403757\pi$
$479$	13.0340			0.595538			0.297769	+	0.954638i	$0.403757\pi$
$480$	5.90882	+	8.33360i	0.269700	+	0.380375i
$481$	−5.33417			−0.243217
$482$			41.2038i			1.87678i
$483$			8.45438i			0.384688i
$484$	−3.42795			−0.155816
$485$	12.6750	−	8.98706i	0.575544	−	0.408081i
$486$	−2.32980			−0.105682
$487$			30.4396i			1.37935i	0.724119	+	0.689675i	$0.242247\pi$
$487$			30.4396i			1.37935i	−0.724119	+	0.689675i	$0.757753\pi$
$488$			49.5524i			2.24313i
$489$	−18.8621			−0.852975
$490$	−4.24974	+	3.01322i	−0.191984	+	0.136123i
$491$	−6.52901			−0.294650			−0.147325	−	0.989088i	$-0.547066\pi$
$491$	−6.52901			−0.294650			−0.147325	+	0.989088i	$0.547066\pi$
$492$			15.1261i			0.681937i
$493$			32.2421i			1.45211i
$494$	6.08855			0.273937
$495$	−1.29334	−	1.82408i	−0.0581313	−	0.0819864i
$496$	−3.35317			−0.150562
$497$			13.6447i			0.612048i
$498$			13.8205i			0.619312i
$499$	11.5379			0.516509			0.258254	−	0.966077i	$-0.416853\pi$
$499$	11.5379			0.516509			0.258254	+	0.966077i	$0.416853\pi$
$500$	36.8383	−	10.5730i	1.64746	−	0.472838i
$501$	−10.8689			−0.485587
$502$		−	36.0363i		−	1.60838i
$503$		−	1.01447i		−	0.0452330i	−0.999744	−	0.0226165i	$-0.992800\pi$
$503$		−	1.01447i		−	0.0452330i	0.999744	−	0.0226165i	$-0.00719967\pi$
$504$	−3.32682			−0.148188
$505$	13.5070	+	19.0498i	0.601053	+	0.847704i
$506$	−19.6970			−0.875637
$507$		−	12.7473i		−	0.566128i
$508$			28.1684i			1.24977i
$509$	25.6895			1.13867			0.569333	−	0.822107i	$-0.307201\pi$
$509$	25.6895			1.13867			0.569333	+	0.822107i	$0.307201\pi$
$510$	−20.0423	+	14.2107i	−0.887488	+	0.629261i
$511$	−1.67769			−0.0742165
$512$			10.0431i			0.443846i
$513$		−	5.19890i		−	0.229537i
$514$	−37.6160			−1.65917
$515$	3.73028	−	2.64490i	0.164376	−	0.116548i
$516$	7.15374			0.314926
$517$			3.12029i			0.137230i
$518$			24.7229i			1.08626i
$519$	4.64430			0.203862
$520$	2.16285	+	3.05041i	0.0948473	+	0.133769i
$521$	−0.758188			−0.0332168			−0.0166084	−	0.999862i	$-0.505287\pi$
$521$	−0.758188			−0.0332168			−0.0166084	+	0.999862i	$0.505287\pi$
$522$		−	15.9278i		−	0.697141i
$523$		−	16.8030i		−	0.734743i	−0.930074	−	0.367372i	$-0.880258\pi$
$523$		−	16.8030i		−	0.734743i	0.930074	−	0.367372i	$-0.119742\pi$
$524$	−70.8656			−3.09578
$525$	1.65455	−	4.71831i	0.0722104	−	0.205924i
$526$	−66.4945			−2.89930
$527$			17.6708i			0.769750i
$528$		−	0.894923i		−	0.0389465i
$529$	−48.4765			−2.10767
$530$	19.3908	+	27.3482i	0.842284	+	1.18793i
$531$	9.33062			0.404914
$532$		−	17.8216i		−	0.772663i
$533$		−	2.21808i		−	0.0960758i
$534$	−10.7977			−0.467264
$535$	−16.7903	+	11.9049i	−0.725907	+	0.514694i
$536$	27.6758			1.19541
$537$			18.7959i			0.811101i
$538$		−	10.1604i		−	0.438047i
$539$	−1.00000			−0.0430730
$540$	6.25285	−	4.43350i	0.269080	−	0.190787i
$541$	31.2607			1.34400			0.672000	−	0.740551i	$-0.265435\pi$
$541$	31.2607			1.34400			0.672000	+	0.740551i	$0.265435\pi$
$542$		−	25.1825i		−	1.08168i
$543$		−	9.99140i		−	0.428772i
$544$	21.5464			0.923793
$545$	−11.8315	−	16.6867i	−0.506806	−	0.714782i
$546$	1.17112			0.0501194
$547$		−	12.6978i		−	0.542919i	−0.962450	−	0.271459i	$-0.912494\pi$
$547$		−	12.6978i		−	0.542919i	0.962450	−	0.271459i	$-0.0875062\pi$
$548$		−	59.2343i		−	2.53036i
$549$	−14.8948			−0.635695
$550$	10.9927	+	3.85476i	0.468730	+	0.164367i
$551$	35.5426			1.51417
$552$		−	28.1262i		−	1.19713i
$553$		−	11.0211i		−	0.468666i
$554$	21.0408			0.893937
$555$	−13.7245	−	19.3565i	−0.582571	−	0.821638i
$556$	−55.2832			−2.34453
$557$			38.8708i			1.64701i	0.567310	+	0.823505i	$0.307984\pi$
$557$			38.8708i			1.64701i	−0.567310	+	0.823505i	$0.692016\pi$
$558$		−	8.72946i		−	0.369548i
$559$	−1.04902			−0.0443688
$560$	1.63241	−	1.15744i	0.0689820	−	0.0489107i
$561$	−4.71613			−0.199115
$562$			70.7703i			2.98527i
$563$			14.4642i			0.609595i	0.952417	+	0.304798i	$0.0985888\pi$
$563$			14.4642i			0.609595i	−0.952417	+	0.304798i	$0.901411\pi$
$564$	−10.6962			−0.450391
$565$	−27.5153	+	19.5093i	−1.15758	+	0.820763i
$566$	−40.6558			−1.70889
$567$		−	1.00000i		−	0.0419961i
$568$		−	45.3935i		−	1.90467i
$569$	−45.5262			−1.90856			−0.954278	−	0.298921i	$-0.903373\pi$
$569$	−45.5262			−1.90856			−0.954278	+	0.298921i	$0.903373\pi$
$570$	15.6654	+	22.0940i	0.656152	+	0.925415i
$571$	27.9409			1.16929			0.584646	−	0.811289i	$-0.301234\pi$
$571$	27.9409			1.16929			0.584646	+	0.811289i	$0.301234\pi$
$572$			1.72313i			0.0720478i
$573$		−	3.75850i		−	0.157014i
$574$	−10.2804			−0.429096
$575$	39.8904	+	13.9882i	1.66354	+	0.583347i
$576$	−12.4339			−0.518078
$577$		−	12.2137i		−	0.508462i	−0.967144	−	0.254231i	$-0.918178\pi$
$577$		−	12.2137i		−	0.508462i	0.967144	−	0.254231i	$-0.0818224\pi$
$578$			12.2124i			0.507970i
$579$	−7.19543			−0.299032
$580$	30.3099	+	42.7480i	1.25855	+	1.77502i
$581$	−5.93207			−0.246104
$582$			16.1891i			0.671060i
$583$			6.43526i			0.266521i
$584$	5.58137			0.230959
$585$	−0.916914	+	0.650125i	−0.0379097	+	0.0268794i
$586$	−46.3720			−1.91561
$587$			24.3211i			1.00384i	0.864914	+	0.501920i	$0.167373\pi$
$587$			24.3211i			1.00384i	−0.864914	+	0.501920i	$0.832627\pi$
$588$		−	3.42795i		−	0.141366i
$589$	19.4797			0.802646
$590$	−39.6527	+	28.1152i	−1.63247	+	1.15748i
$591$	4.89259			0.201254
$592$		−	9.49660i		−	0.390308i
$593$		−	31.8814i		−	1.30921i	−0.755970	−	0.654606i	$-0.772834\pi$
$593$		−	31.8814i		−	1.30921i	0.755970	−	0.654606i	$-0.227166\pi$
$594$	2.32980			0.0955927
$595$	−6.09955	−	8.60260i	−0.250057	−	0.352672i
$596$	−18.6750			−0.764956
$597$			24.5120i			1.00321i
$598$			9.90111i			0.404887i
$599$	−13.2913			−0.543069			−0.271535	−	0.962429i	$-0.587531\pi$
$599$	−13.2913			−0.543069			−0.271535	+	0.962429i	$0.587531\pi$
$600$	−5.50438	+	15.6970i	−0.224716	+	0.640827i
$601$	17.2111			0.702056			0.351028	−	0.936365i	$-0.385832\pi$
$601$	17.2111			0.702056			0.351028	+	0.936365i	$0.385832\pi$
$602$			4.86202i			0.198161i
$603$			8.31898i			0.338775i
$604$	−8.77354			−0.356990
$605$	1.29334	+	1.82408i	0.0525817	+	0.0741595i
$606$	−24.3312			−0.988387
$607$			30.0763i			1.22076i	0.792108	+	0.610380i	$0.208983\pi$
$607$			30.0763i			1.22076i	−0.792108	+	0.610380i	$0.791017\pi$
$608$		−	23.7520i		−	0.963271i
$609$	6.83657			0.277032
$610$	63.2990	−	44.8813i	2.56290	−	1.81719i
$611$	1.56848			0.0634540
$612$		−	16.1666i		−	0.653497i
$613$		−	33.1534i		−	1.33905i	−0.742789	−	0.669526i	$-0.766497\pi$
$613$		−	33.1534i		−	1.33905i	0.742789	−	0.669526i	$-0.233503\pi$
$614$	−19.9034			−0.803234
$615$	8.04891	−	5.70697i	0.324563	−	0.230127i
$616$	3.32682			0.134041
$617$			20.4211i			0.822122i	0.911608	+	0.411061i	$0.134842\pi$
$617$			20.4211i			0.822122i	−0.911608	+	0.411061i	$0.865158\pi$
$618$			4.76447i			0.191655i
$619$	5.17686			0.208076			0.104038	−	0.994573i	$-0.466824\pi$
$619$	5.17686			0.208076			0.104038	+	0.994573i	$0.466824\pi$
$620$	16.6118	+	23.4287i	0.667145	+	0.940919i
$621$	8.45438			0.339262
$622$			22.3243i			0.895124i
$623$		−	4.63463i		−	0.185683i
$624$	−0.449853			−0.0180085
$625$	−19.5249	−	15.6133i	−0.780998	−	0.624534i
$626$	1.82561			0.0729661
$627$			5.19890i			0.207624i
$628$			12.4913i			0.498456i
$629$	−50.0458			−1.99546
$630$	3.01322	+	4.24974i	0.120049	+	0.169314i
$631$	−12.3700			−0.492443			−0.246222	−	0.969214i	$-0.579189\pi$
$631$	−12.3700			−0.492443			−0.246222	+	0.969214i	$0.579189\pi$
$632$			36.6654i			1.45847i
$633$		−	7.61523i		−	0.302678i
$634$	54.6529			2.17054
$635$	14.9890	−	10.6277i	0.594820	−	0.421749i
$636$	−22.0597			−0.874725
$637$			0.502672i			0.0199166i
$638$			15.9278i			0.630588i
$639$	13.6447			0.539776
$640$	36.1735	−	25.6483i	1.42988	−	1.01384i
$641$	−24.6379			−0.973137			−0.486569	−	0.873642i	$-0.661752\pi$
$641$	−24.6379			−0.973137			−0.486569	+	0.873642i	$0.661752\pi$
$642$		−	21.4453i		−	0.846377i
$643$			0.396623i			0.0156413i	0.999969	+	0.00782064i	$0.00248941\pi$
$643$			0.396623i			0.0156413i	−0.999969	+	0.00782064i	$0.997511\pi$
$644$	28.9812			1.14202
$645$	−2.69905	−	3.80665i	−0.106275	−	0.149887i
$646$	57.1235			2.24749
$647$			32.2192i			1.26667i	0.773880	+	0.633333i	$0.218314\pi$
$647$			32.2192i			1.26667i	−0.773880	+	0.633333i	$0.781686\pi$
$648$			3.32682i			0.130690i
$649$	−9.33062			−0.366259
$650$	1.93768	−	5.52572i	0.0760019	−	0.216737i
$651$	3.74688			0.146852
$652$			64.6584i			2.53222i
$653$			12.6707i			0.495842i	0.968780	+	0.247921i	$0.0797474\pi$
$653$			12.6707i			0.495842i	−0.968780	+	0.247921i	$0.920253\pi$
$654$	21.3130			0.833406
$655$	26.7371	+	37.7091i	1.04470	+	1.47341i
$656$	3.94892			0.154179
$657$			1.67769i			0.0654528i
$658$		−	7.26963i		−	0.283400i
$659$	−3.55782			−0.138593			−0.0692964	−	0.997596i	$-0.522075\pi$
$659$	−3.55782			−0.138593			−0.0692964	+	0.997596i	$0.522075\pi$
$660$	−6.25285	+	4.43350i	−0.243392	+	0.172574i
$661$	−3.29870			−0.128305			−0.0641523	−	0.997940i	$-0.520434\pi$
$661$	−3.29870			−0.128305			−0.0641523	+	0.997940i	$0.520434\pi$
$662$		−	24.5759i		−	0.955169i
$663$			2.37066i			0.0920689i
$664$	19.7350			0.765865
$665$	−9.48322	+	6.72395i	−0.367744	+	0.260743i
$666$	24.7229			0.957995
$667$			57.7989i			2.23798i
$668$			37.2580i			1.44156i
$669$	19.0382			0.736059
$670$	−25.0669	−	35.3535i	−0.968419	−	1.36582i
$671$	14.8948			0.575008
$672$		−	4.56866i		−	0.176240i
$673$			16.0904i			0.620241i	0.950697	+	0.310121i	$0.100369\pi$
$673$			16.0904i			0.620241i	−0.950697	+	0.310121i	$0.899631\pi$
$674$	10.6407			0.409866
$675$	−4.71831	−	1.65455i	−0.181608	−	0.0636835i
$676$	−43.6971			−1.68066
$677$			18.7022i			0.718785i	0.933187	+	0.359392i	$0.117016\pi$
$677$			18.7022i			0.718785i	−0.933187	+	0.359392i	$0.882984\pi$
$678$		−	35.1437i		−	1.34968i
$679$	−6.94873			−0.266668
$680$	20.2921	+	28.6193i	0.778167	+	1.09750i
$681$	11.4181			0.437543
$682$			8.72946i			0.334268i
$683$		−	19.3689i		−	0.741129i	−0.928807	−	0.370565i	$-0.879164\pi$
$683$		−	19.3689i		−	0.741129i	0.928807	−	0.370565i	$-0.120836\pi$
$684$	−17.8216			−0.681424
$685$	−31.5198	+	22.3487i	−1.20431	+	0.853898i
$686$	2.32980			0.0889520
$687$			10.4889i			0.400177i
$688$		−	1.86760i		−	0.0712017i
$689$	3.23482			0.123237
$690$	−35.9289	+	25.4749i	−1.36779	+	0.969812i
$691$	−21.6971			−0.825396			−0.412698	−	0.910868i	$-0.635414\pi$
$691$	−21.6971			−0.825396			−0.412698	+	0.910868i	$0.635414\pi$
$692$		−	15.9204i		−	0.605204i
$693$			1.00000i			0.0379869i
$694$	41.8638			1.58913
$695$	20.8579	+	29.4173i	0.791187	+	1.11586i
$696$	−22.7440			−0.862111
$697$		−	20.8103i		−	0.788246i
$698$		−	76.4468i		−	2.89355i
$699$	6.53550			0.247195
$700$	−16.1741	−	5.67170i	−0.611324	−	0.214370i
$701$	5.36661			0.202694			0.101347	−	0.994851i	$-0.467685\pi$
$701$	5.36661			0.202694			0.101347	+	0.994851i	$0.467685\pi$
$702$		−	1.17112i		−	0.0442012i
$703$			55.1689i			2.08073i
$704$	12.4339			0.468620
$705$	4.03559	+	5.69166i	0.151989	+	0.214360i
$706$	−32.9751			−1.24103
$707$		−	10.4435i		−	0.392768i
$708$		−	31.9849i		−	1.20206i
$709$	−46.9307			−1.76252			−0.881260	−	0.472632i	$-0.843304\pi$
$709$	−46.9307			−1.76252			−0.881260	+	0.472632i	$0.843304\pi$
$710$	−57.9864	+	41.1144i	−2.17619	+	1.54300i
$711$	−11.0211			−0.413325
$712$			15.4186i			0.577836i
$713$			31.6775i			1.18633i
$714$	10.9876			0.411201
$715$	0.916914	−	0.650125i	0.0342907	−	0.0243133i
$716$	64.4312			2.40791
$717$			10.7986i			0.403281i
$718$		−	74.5393i		−	2.78178i
$719$	−31.4047			−1.17120			−0.585598	−	0.810602i	$-0.699140\pi$
$719$	−31.4047			−1.17120			−0.585598	+	0.810602i	$0.699140\pi$
$720$	−1.15744	−	1.63241i	−0.0431352	−	0.0608364i
$721$	−2.04502			−0.0761605
$722$		−	18.7050i		−	0.696127i
$723$			17.6856i			0.657734i
$724$	−34.2500			−1.27289
$725$	11.3114	−	32.2571i	0.420096	−	1.19800i
$726$	−2.32980			−0.0864668
$727$		−	13.7995i		−	0.511797i	−0.966704	−	0.255898i	$-0.917629\pi$
$727$		−	13.7995i		−	0.511797i	0.966704	−	0.255898i	$-0.0823712\pi$
$728$		−	1.67230i		−	0.0619796i
$729$	−1.00000			−0.0370370
$730$	−5.05523	−	7.12973i	−0.187103	−	0.263883i
$731$	−9.84202			−0.364020
$732$			51.0586i			1.88718i
$733$		−	42.6854i		−	1.57662i	−0.615277	−	0.788311i	$-0.710956\pi$
$733$		−	42.6854i		−	1.57662i	0.615277	−	0.788311i	$-0.289044\pi$
$734$	3.26353			0.120459
$735$	−1.82408	+	1.29334i	−0.0672823	+	0.0477055i
$736$	38.6252			1.42374
$737$		−	8.31898i		−	0.306434i
$738$			10.2804i			0.378427i
$739$	−9.21242			−0.338884			−0.169442	−	0.985540i	$-0.554197\pi$
$739$	−9.21242			−0.338884			−0.169442	+	0.985540i	$0.554197\pi$
$740$	−66.3530	+	47.0467i	−2.43919	+	1.72947i
$741$	2.61334			0.0960035
$742$		−	14.9928i		−	0.550404i
$743$			29.9090i			1.09726i	0.836066	+	0.548628i	$0.184850\pi$
$743$			29.9090i			1.09726i	−0.836066	+	0.548628i	$0.815150\pi$
$744$	−12.4652			−0.456997
$745$	7.04593	+	9.93733i	0.258143	+	0.364076i
$746$	71.2681			2.60931
$747$			5.93207i			0.217043i
$748$			16.1666i			0.591110i
$749$	9.20478			0.336335
$750$	25.0371	−	7.18590i	0.914225	−	0.262392i
$751$	23.4373			0.855239			0.427619	−	0.903959i	$-0.359352\pi$
$751$	23.4373			0.855239			0.427619	+	0.903959i	$0.359352\pi$
$752$			2.79242i			0.101829i
$753$		−	15.4676i		−	0.563669i
$754$	8.00646			0.291578
$755$	3.31019	+	4.66858i	0.120470	+	0.169907i
$756$	−3.42795			−0.124673
$757$			32.4840i			1.18065i	0.807165	+	0.590325i	$0.201001\pi$
$757$			32.4840i			1.18065i	−0.807165	+	0.590325i	$0.798999\pi$
$758$		−	0.944316i		−	0.0342991i
$759$	−8.45438			−0.306874
$760$	31.5490	−	22.3694i	1.14440	−	0.811422i
$761$	10.1062			0.366349			0.183175	−	0.983080i	$-0.441363\pi$
$761$	10.1062			0.366349			0.183175	+	0.983080i	$0.441363\pi$
$762$			19.1446i			0.693535i
$763$			9.14803i			0.331181i
$764$	−12.8839			−0.466125
$765$	−8.60260	+	6.09955i	−0.311028	+	0.220530i
$766$	−40.7700			−1.47308
$767$			4.69024i			0.169355i
$768$			21.3346i			0.769846i
$769$	−0.636387			−0.0229487			−0.0114744	−	0.999934i	$-0.503652\pi$
$769$	−0.636387			−0.0229487			−0.0114744	+	0.999934i	$0.503652\pi$
$770$	−3.01322	−	4.24974i	−0.108589	−	0.153150i
$771$	−16.1456			−0.581470
$772$			24.6655i			0.887732i
$773$		−	16.8161i		−	0.604834i	−0.953176	−	0.302417i	$-0.902206\pi$
$773$		−	16.8161i		−	0.604834i	0.953176	−	0.302417i	$-0.0977936\pi$
$774$	4.86202			0.174762
$775$	6.19939	−	17.6790i	0.222689	−	0.635047i
$776$	23.1172			0.829858
$777$			10.6116i			0.380690i
$778$		−	43.0171i		−	1.54224i
$779$	−22.9406			−0.821932
$780$	2.22859	+	3.14313i	0.0797965	+	0.112542i
$781$	−13.6447			−0.488246
$782$			92.8934i			3.32186i
$783$		−	6.83657i		−	0.244319i
$784$	−0.894923			−0.0319615
$785$	6.64687	−	4.71287i	0.237237	−	0.168209i
$786$	−48.1636			−1.71794
$787$		−	14.1042i		−	0.502761i	−0.967888	−	0.251381i	$-0.919115\pi$
$787$		−	14.1042i		−	0.502761i	0.967888	−	0.251381i	$-0.0808845\pi$
$788$		−	16.7715i		−	0.597461i
$789$	−28.5409			−1.01608
$790$	46.8369	−	33.2091i	1.66638	−	1.18153i
$791$	15.0844			0.536341
$792$		−	3.32682i		−	0.118213i
$793$		−	7.48720i		−	0.265878i
$794$	−71.5296			−2.53849
$795$	8.32297	+	11.7384i	0.295185	+	0.416319i
$796$	84.0257			2.97821
$797$			4.49223i			0.159123i	0.996830	+	0.0795616i	$0.0253520\pi$
$797$			4.49223i			0.159123i	−0.996830	+	0.0795616i	$0.974648\pi$
$798$		−	12.1124i		−	0.428774i
$799$	14.7157			0.520603
$800$	−21.5564	−	7.55906i	−0.762132	−	0.267253i
$801$	−4.63463			−0.163757
$802$		−	51.6549i		−	1.82400i
$803$		−	1.67769i		−	0.0592043i
$804$	28.5170			1.00572
$805$	−10.9344	−	15.4215i	−0.385386	−	0.543536i
$806$	4.38806			0.154563
$807$		−	4.36108i		−	0.153517i
$808$			34.7436i			1.22228i
$809$	−47.8943			−1.68387			−0.841937	−	0.539576i	$-0.818585\pi$
$809$	−47.8943			−1.68387			−0.841937	+	0.539576i	$0.818585\pi$
$810$	4.24974	−	3.01322i	0.149321	−	0.105874i
$811$	7.63956			0.268261			0.134131	−	0.990964i	$-0.457176\pi$
$811$	7.63956			0.268261			0.134131	+	0.990964i	$0.457176\pi$
$812$		−	23.4354i		−	0.822421i
$813$		−	10.8089i		−	0.379084i
$814$	−24.7229			−0.866539
$815$	34.4061	−	24.3951i	1.20519	−	0.854524i
$816$	−4.22057			−0.147749
$817$			10.8495i			0.379577i
$818$		−	35.0526i		−	1.22559i
$819$	0.502672			0.0175648
$820$	−19.5632	−	27.5912i	−0.683176	−	0.963528i
$821$	−34.4565			−1.20254			−0.601270	−	0.799046i	$-0.705338\pi$
$821$	−34.4565			−1.20254			−0.601270	+	0.799046i	$0.705338\pi$
$822$		−	40.2584i		−	1.40417i
$823$		−	14.4258i		−	0.502853i	−0.967876	−	0.251426i	$-0.919100\pi$
$823$		−	14.4258i		−	0.502853i	0.967876	−	0.251426i	$-0.0808996\pi$
$824$	6.80341			0.237008
$825$	4.71831	+	1.65455i	0.164271	+	0.0576039i
$826$	21.7384			0.756377
$827$		−	21.9067i		−	0.761771i	−0.924622	−	0.380885i	$-0.875619\pi$
$827$		−	21.9067i		−	0.761771i	0.924622	−	0.380885i	$-0.124381\pi$
$828$		−	28.9812i		−	1.00716i
$829$	−1.78269			−0.0619155			−0.0309577	−	0.999521i	$-0.509856\pi$
$829$	−1.78269			−0.0619155			−0.0309577	+	0.999521i	$0.509856\pi$
$830$	−17.8746	−	25.2098i	−0.620437	−	0.875043i
$831$	9.03117			0.313288
$832$		−	6.25016i		−	0.216685i
$833$			4.71613i			0.163404i
$834$	−37.5731			−1.30105
$835$	19.8258	−	14.0572i	0.686099	−	0.486469i
$836$	17.8216			0.616372
$837$		−	3.74688i		−	0.129511i
$838$			46.8875i			1.61970i
$839$	56.8859			1.96392			0.981960	−	0.189088i	$-0.0605531\pi$
$839$	56.8859			1.96392			0.981960	+	0.189088i	$0.0605531\pi$
$840$	6.06840	−	4.30271i	0.209380	−	0.148458i
$841$	17.7386			0.611677
$842$		−	13.6886i		−	0.471739i
$843$			30.3762i			1.04621i
$844$	−26.1046			−0.898558
$845$	16.4866	+	23.2522i	0.567157	+	0.799898i
$846$	−7.26963			−0.249935
$847$		−	1.00000i		−	0.0343604i
$848$			5.75906i			0.197767i
$849$	−17.4504			−0.598896
$850$	18.1795	−	51.8430i	0.623552	−	1.77820i
$851$	−89.7148			−3.07538
$852$		−	46.7733i		−	1.60243i
$853$		−	55.5210i		−	1.90100i	−0.310722	−	0.950501i	$-0.600571\pi$
$853$		−	55.5210i		−	1.90100i	0.310722	−	0.950501i	$-0.399429\pi$
$854$	−34.7019			−1.18747
$855$	6.72395	+	9.48322i	0.229954	+	0.324319i
$856$	−30.6227			−1.04666
$857$			32.1644i			1.09872i	0.835587	+	0.549358i	$0.185128\pi$
$857$			32.1644i			1.09872i	−0.835587	+	0.549358i	$0.814872\pi$
$858$			1.17112i			0.0399815i
$859$	−23.1925			−0.791318			−0.395659	−	0.918397i	$-0.629484\pi$
$859$	−23.1925			−0.791318			−0.395659	+	0.918397i	$0.629484\pi$
$860$	−13.0490	+	9.25221i	−0.444967	+	0.315498i
$861$	−4.41258			−0.150380
$862$		−	35.0873i		−	1.19508i
$863$			5.73814i			0.195329i	0.995219	+	0.0976643i	$0.0311371\pi$
$863$			5.73814i			0.195329i	−0.995219	+	0.0976643i	$0.968863\pi$
$864$	−4.56866			−0.155429
$865$	−8.47159	+	6.00666i	−0.288043	+	0.204233i
$866$	−27.0368			−0.918748
$867$			5.24185i			0.178022i
$868$		−	12.8441i		−	0.435957i
$869$	11.0211			0.373866
$870$	20.6000	+	29.0536i	0.698407	+	0.985010i
$871$	−4.18172			−0.141692
$872$		−	30.4339i		−	1.03062i
$873$			6.94873i			0.235179i
$874$	102.403			3.46382
$875$	3.08435	+	10.7465i	0.104270	+	0.363297i
$876$	5.75102			0.194309
$877$		−	19.2523i		−	0.650103i	−0.945696	−	0.325052i	$-0.894618\pi$
$877$		−	19.2523i		−	0.650103i	0.945696	−	0.325052i	$-0.105382\pi$
$878$		−	71.6849i		−	2.41925i
$879$	−19.9039			−0.671342
$880$	1.15744	+	1.63241i	0.0390173	+	0.0550286i
$881$	−7.85046			−0.264489			−0.132244	−	0.991217i	$-0.542218\pi$
$881$	−7.85046			−0.264489			−0.132244	+	0.991217i	$0.542218\pi$
$882$		−	2.32980i		−	0.0784483i
$883$			13.0330i			0.438596i	0.975658	+	0.219298i	$0.0703767\pi$
$883$			13.0330i			0.438596i	−0.975658	+	0.219298i	$0.929623\pi$
$884$	8.12651			0.273324
$885$	−17.0198	+	12.0677i	−0.572115	+	0.405650i
$886$	−70.6180			−2.37246
$887$		−	20.2647i		−	0.680421i	−0.940349	−	0.340210i	$-0.889502\pi$
$887$		−	20.2647i		−	0.680421i	0.940349	−	0.340210i	$-0.110498\pi$
$888$		−	35.3030i		−	1.18469i
$889$	−8.21728			−0.275599
$890$	19.6960	−	13.9651i	0.660210	−	0.468113i
$891$	1.00000			0.0335013
$892$		−	65.2619i		−	2.18513i
$893$		−	16.2221i		−	0.542851i
$894$	−12.6924			−0.424497
$895$	−24.3094	−	34.2852i	−0.812575	−	1.14603i
$896$	−19.8311			−0.662510
$897$			4.24978i			0.141896i
$898$		−	36.9435i		−	1.23282i
$899$	25.6158			0.854335
$900$	−5.67170	+	16.1741i	−0.189057	+	0.539137i
$901$	30.3495			1.01109
$902$		−	10.2804i		−	0.342300i
$903$			2.08689i			0.0694473i
$904$	−50.1833			−1.66907
$905$	12.9223	+	18.2251i	0.429551	+	0.605824i
$906$	−5.96291			−0.198105
$907$			55.8825i			1.85555i	0.373142	+	0.927774i	$0.378280\pi$
$907$			55.8825i			1.85555i	−0.373142	+	0.927774i	$0.621720\pi$
$908$		−	39.1407i		−	1.29893i
$909$	−10.4435			−0.346389
$910$	−2.13622	+	1.51466i	−0.0708151	+	0.0502104i
$911$	−37.0320			−1.22692			−0.613462	−	0.789724i	$-0.710224\pi$
$911$	−37.0320			−1.22692			−0.613462	+	0.789724i	$0.710224\pi$
$912$			4.65262i			0.154064i
$913$		−	5.93207i		−	0.196323i
$914$	37.8882			1.25323
$915$	27.1694	−	19.2640i	0.898191	−	0.636850i
$916$	35.9555			1.18800
$917$		−	20.6729i		−	0.682679i
$918$		−	10.9876i		−	0.362645i
$919$	−29.5443			−0.974576			−0.487288	−	0.873241i	$-0.662014\pi$
$919$	−29.5443			−0.974576			−0.487288	+	0.873241i	$0.662014\pi$
$920$	36.3767	+	51.3045i	1.19931	+	1.69146i
$921$	−8.54297			−0.281500
$922$		−	5.89940i		−	0.194286i
$923$			6.85881i			0.225760i
$924$	3.42795			0.112771
$925$	50.0690	+	17.5575i	1.64626	+	0.577286i
$926$	−72.7078			−2.38933
$927$			2.04502i			0.0671672i
$928$		−	31.2339i		−	1.02530i
$929$	29.3502			0.962949			0.481474	−	0.876460i	$-0.340101\pi$
$929$	29.3502			0.962949			0.481474	+	0.876460i	$0.340101\pi$
$930$	11.2902	+	15.9233i	0.370219	+	0.522144i
$931$	5.19890			0.170387
$932$		−	22.4034i		−	0.733846i
$933$			9.58210i			0.313704i
$934$	−80.5641			−2.63614
$935$	8.60260	−	6.09955i	0.281335	−	0.199477i
$936$	−1.67230			−0.0546608
$937$		−	9.60727i		−	0.313856i	−0.987610	−	0.156928i	$-0.949841\pi$
$937$		−	9.60727i		−	0.313856i	0.987610	−	0.156928i	$-0.0501591\pi$
$938$			19.3815i			0.632829i
$939$	0.783593			0.0255716
$940$	19.5107	−	13.8338i	0.636369	−	0.451209i
$941$	−31.0803			−1.01319			−0.506595	−	0.862184i	$-0.669096\pi$
$941$	−31.0803			−1.01319			−0.506595	+	0.862184i	$0.669096\pi$
$942$			8.48966i			0.276608i
$943$		−	37.3056i		−	1.21484i
$944$	−8.35019			−0.271775
$945$	1.29334	+	1.82408i	0.0420723	+	0.0593374i
$946$	−4.86202			−0.158078
$947$		−	29.6400i		−	0.963171i	−0.876399	−	0.481585i	$-0.840061\pi$
$947$		−	29.6400i		−	0.963171i	0.876399	−	0.481585i	$-0.159939\pi$
$948$			37.7799i			1.22703i
$949$	−0.843326			−0.0273755
$950$	−57.1500	−	20.0405i	−1.85419	−	0.650200i
$951$	23.4582			0.760686
$952$		−	15.6897i		−	0.508507i
$953$		−	10.7221i		−	0.347322i	−0.984805	−	0.173661i	$-0.944440\pi$
$953$		−	10.7221i		−	0.347322i	0.984805	−	0.173661i	$-0.0555598\pi$
$954$	−14.9928			−0.485411
$955$	4.86102	+	6.85581i	0.157299	+	0.221849i
$956$	37.0170			1.19722
$957$			6.83657i			0.220995i
$958$		−	30.3665i		−	0.981098i
$959$	17.2798			0.557994
$960$	22.6804	−	16.0812i	0.732007	−	0.519019i
$961$	−16.9609			−0.547126
$962$			12.4275i			0.400680i
$963$		−	9.20478i		−	0.296620i
$964$	60.6252			1.95261
$965$	13.1250	−	9.30613i	0.422510	−	0.299575i
$966$	19.6970			0.633740
$967$			2.75149i			0.0884820i	0.999021	+	0.0442410i	$0.0140869\pi$
$967$			2.75149i			0.0884820i	−0.999021	+	0.0442410i	$0.985913\pi$
$968$			3.32682i			0.106928i
$969$	24.5187			0.787654
$970$	−20.9380	−	29.5303i	−0.672279	−	0.948159i
$971$	8.28514			0.265883			0.132941	−	0.991124i	$-0.457558\pi$
$971$	8.28514			0.265883			0.132941	+	0.991124i	$0.457558\pi$
$972$			3.42795i			0.109951i
$973$		−	16.1272i		−	0.517014i
$974$	70.9180			2.27236
$975$	0.831694	−	2.37176i	0.0266355	−	0.0759572i
$976$	13.3297			0.426674
$977$		−	10.5691i		−	0.338135i	−0.985604	−	0.169068i	$-0.945924\pi$
$977$		−	10.5691i		−	0.338135i	0.985604	−	0.169068i	$-0.0540757\pi$
$978$			43.9449i			1.40520i
$979$	4.63463			0.148123
$980$	4.43350	+	6.25285i	0.141623	+	0.199740i
$981$	9.14803			0.292074
$982$			15.2113i			0.485411i
$983$			18.6361i			0.594400i	0.954815	+	0.297200i	$0.0960528\pi$
$983$			18.6361i			0.594400i	−0.954815	+	0.297200i	$0.903947\pi$
$984$	14.6799			0.467978
$985$	−8.92448	+	6.32778i	−0.284358	+	0.201620i
$986$	75.1175			2.39223
$987$		−	3.12029i		−	0.0993199i
$988$		−	8.95840i		−	0.285005i
$989$	−17.6433			−0.561025
$990$	−4.24974	+	3.01322i	−0.135065	+	0.0957663i
$991$	50.8956			1.61675			0.808376	−	0.588666i	$-0.200347\pi$
$991$	50.8956			1.61675			0.808376	+	0.588666i	$0.200347\pi$
$992$		−	17.1182i		−	0.543504i
$993$		−	10.5485i		−	0.334747i
$994$	31.7894			1.00830
$995$	−31.7023	−	44.7118i	−1.00503	−	1.41746i
$996$	20.3348			0.644334
$997$			33.2198i			1.05208i	0.850459	+	0.526041i	$0.176324\pi$
$997$			33.2198i			1.05208i	−0.850459	+	0.526041i	$0.823676\pi$
$998$		−	26.8810i		−	0.850904i
$999$	10.6116			0.335737

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1155.2.c.f.694.3	✓	20
5.2	odd	4		5775.2.a.cn.1.10		10
5.3	odd	4		5775.2.a.co.1.1		10
5.4	even	2	inner	1155.2.c.f.694.18	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1155.2.c.f.694.3	✓	20	1.1	even	1	trivial
1155.2.c.f.694.18	yes	20	5.4	even	2	inner
5775.2.a.cn.1.10		10	5.2	odd	4
5775.2.a.co.1.1		10	5.3	odd	4

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:	\( N \)	\(=\)	\( 1155 = 3 \cdot 5 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1155.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-2.32980i q^{2} -1.00000i q^{3} -3.42795 q^{4} +(1.29334 + 1.82408i) q^{5} -2.32980 q^{6} -1.00000i q^{7} +3.32682i q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q-2.32980i q^{2} -1.00000i q^{3} -3.42795 q^{4} +(1.29334 + 1.82408i) q^{5} -2.32980 q^{6} -1.00000i q^{7} +3.32682i q^{8} -1.00000 q^{9} +(4.24974 - 3.01322i) q^{10} +1.00000 q^{11} +3.42795i q^{12} -0.502672i q^{13} -2.32980 q^{14} +(1.82408 - 1.29334i) q^{15} +0.894923 q^{16} -4.71613i q^{17} +2.32980i q^{18} -5.19890 q^{19} +(-4.43350 - 6.25285i) q^{20} -1.00000 q^{21} -2.32980i q^{22} -8.45438i q^{23} +3.32682 q^{24} +(-1.65455 + 4.71831i) q^{25} -1.17112 q^{26} +1.00000i q^{27} +3.42795i q^{28} -6.83657 q^{29} +(-3.01322 - 4.24974i) q^{30} -3.74688 q^{31} +4.56866i q^{32} -1.00000i q^{33} -10.9876 q^{34} +(1.82408 - 1.29334i) q^{35} +3.42795 q^{36} -10.6116i q^{37} +12.1124i q^{38} -0.502672 q^{39} +(-6.06840 + 4.30271i) q^{40} +4.41258 q^{41} +2.32980i q^{42} -2.08689i q^{43} -3.42795 q^{44} +(-1.29334 - 1.82408i) q^{45} -19.6970 q^{46} +3.12029i q^{47} -0.894923i q^{48} -1.00000 q^{49} +(10.9927 + 3.85476i) q^{50} -4.71613 q^{51} +1.72313i q^{52} +6.43526i q^{53} +2.32980 q^{54} +(1.29334 + 1.82408i) q^{55} +3.32682 q^{56} +5.19890i q^{57} +15.9278i q^{58} -9.33062 q^{59} +(-6.25285 + 4.43350i) q^{60} +14.8948 q^{61} +8.72946i q^{62} +1.00000i q^{63} +12.4339 q^{64} +(0.916914 - 0.650125i) q^{65} -2.32980 q^{66} -8.31898i q^{67} +16.1666i q^{68} -8.45438 q^{69} +(-3.01322 - 4.24974i) q^{70} -13.6447 q^{71} -3.32682i q^{72} -1.67769i q^{73} -24.7229 q^{74} +(4.71831 + 1.65455i) q^{75} +17.8216 q^{76} -1.00000i q^{77} +1.17112i q^{78} +11.0211 q^{79} +(1.15744 + 1.63241i) q^{80} +1.00000 q^{81} -10.2804i q^{82} -5.93207i q^{83} +3.42795 q^{84} +(8.60260 - 6.09955i) q^{85} -4.86202 q^{86} +6.83657i q^{87} +3.32682i q^{88} +4.63463 q^{89} +(-4.24974 + 3.01322i) q^{90} -0.502672 q^{91} +28.9812i q^{92} +3.74688i q^{93} +7.26963 q^{94} +(-6.72395 - 9.48322i) q^{95} +4.56866 q^{96} -6.94873i q^{97} +2.32980i q^{98} -1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 26 q^{4} - 2 q^{5} + 6 q^{6} - 20 q^{9}+O(q^{10}) \) 20 * q - 26 * q^4 - 2 * q^5 + 6 * q^6 - 20 * q^9	\( 20 q - 26 q^{4} - 2 q^{5} + 6 q^{6} - 20 q^{9} + 2 q^{10} + 20 q^{11} + 6 q^{14} - 2 q^{15} + 38 q^{16} - 34 q^{19} + 4 q^{20} - 20 q^{21} - 18 q^{24} - 4 q^{25} + 28 q^{26} - 10 q^{29} - 6 q^{30} + 12 q^{31} - 32 q^{34} - 2 q^{35} + 26 q^{36} - 2 q^{40} + 52 q^{41} - 26 q^{44} + 2 q^{45} + 40 q^{46} - 20 q^{49} + 6 q^{50} + 6 q^{51} - 6 q^{54} - 2 q^{55} - 18 q^{56} - 14 q^{59} - 28 q^{60} + 78 q^{61} - 26 q^{64} - 4 q^{65} + 6 q^{66} - 18 q^{69} - 6 q^{70} - 8 q^{74} - 8 q^{75} + 84 q^{76} - 52 q^{79} - 40 q^{80} + 20 q^{81} + 26 q^{84} - 24 q^{85} + 4 q^{86} - 10 q^{89} - 2 q^{90} - 96 q^{94} - 30 q^{95} + 62 q^{96} - 20 q^{99}+O(q^{100}) \) 20 * q - 26 * q^4 - 2 * q^5 + 6 * q^6 - 20 * q^9 + 2 * q^10 + 20 * q^11 + 6 * q^14 - 2 * q^15 + 38 * q^16 - 34 * q^19 + 4 * q^20 - 20 * q^21 - 18 * q^24 - 4 * q^25 + 28 * q^26 - 10 * q^29 - 6 * q^30 + 12 * q^31 - 32 * q^34 - 2 * q^35 + 26 * q^36 - 2 * q^40 + 52 * q^41 - 26 * q^44 + 2 * q^45 + 40 * q^46 - 20 * q^49 + 6 * q^50 + 6 * q^51 - 6 * q^54 - 2 * q^55 - 18 * q^56 - 14 * q^59 - 28 * q^60 + 78 * q^61 - 26 * q^64 - 4 * q^65 + 6 * q^66 - 18 * q^69 - 6 * q^70 - 8 * q^74 - 8 * q^75 + 84 * q^76 - 52 * q^79 - 40 * q^80 + 20 * q^81 + 26 * q^84 - 24 * q^85 + 4 * q^86 - 10 * q^89 - 2 * q^90 - 96 * q^94 - 30 * q^95 + 62 * q^96 - 20 * q^99

Introduction

L-functions

Modular forms

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Database

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