LMFDB - Embedded newform 230.2.j.a.119.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [230,2,Mod(9,230)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(230, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([11, 10]))

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

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

chi := DirichletCharacter("230.9");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 230 = 2 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	230.j (of order $22$, degree $10$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$1.83655924649$
Analytic rank:	$0$
Dimension:	$120$
Relative dimension:	$12$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			119.4
Character	$\chi$	$=$	230.119
Dual form			230.2.j.a.29.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.909632 + 0.415415i) q^{2} +(0.192005 + 0.653908i) q^{3} +(0.654861 - 0.755750i) q^{4} +(2.23607 - 0.00163718i) q^{5} +(-0.446297 - 0.515054i) q^{6} +(-0.838442 + 0.120550i) q^{7} +(-0.281733 + 0.959493i) q^{8} +(2.13303 - 1.37082i) q^{9} +O(q^{10})$	\(q+(-0.909632 + 0.415415i) q^{2} +(0.192005 + 0.653908i) q^{3} +(0.654861 - 0.755750i) q^{4} +(2.23607 - 0.00163718i) q^{5} +(-0.446297 - 0.515054i) q^{6} +(-0.838442 + 0.120550i) q^{7} +(-0.281733 + 0.959493i) q^{8} +(2.13303 - 1.37082i) q^{9} +(-2.03332 + 0.930385i) q^{10} +(0.0655354 - 0.143502i) q^{11} +(0.619927 + 0.283111i) q^{12} +(2.33610 + 0.335881i) q^{13} +(0.712596 - 0.457958i) q^{14} +(0.430406 + 1.46187i) q^{15} +(-0.142315 - 0.989821i) q^{16} +(-1.02083 + 0.884550i) q^{17} +(-1.37082 + 2.13303i) q^{18} +(-1.86520 + 2.15256i) q^{19} +(1.46308 - 1.69098i) q^{20} +(-0.239813 - 0.525118i) q^{21} +0.157759i q^{22} +(3.82181 + 2.89719i) q^{23} -0.681514 q^{24} +(4.99999 - 0.00732171i) q^{25} +(-2.26452 + 0.664924i) q^{26} +(2.85110 + 2.47049i) q^{27} +(-0.457958 + 0.712596i) q^{28} +(5.24884 + 6.05748i) q^{29} +(-0.998792 - 1.15096i) q^{30} +(-8.15854 - 2.39556i) q^{31} +(0.540641 + 0.841254i) q^{32} +(0.106420 + 0.0153010i) q^{33} +(0.561120 - 1.22868i) q^{34} +(-1.87462 + 0.270930i) q^{35} +(0.360845 - 2.50973i) q^{36} +(-5.32167 - 8.28068i) q^{37} +(0.802442 - 2.73287i) q^{38} +(0.228907 + 1.59209i) q^{39} +(-0.628402 + 2.14595i) q^{40} +(-4.40840 - 2.83311i) q^{41} +(0.436284 + 0.378042i) q^{42} +(-0.846481 - 2.88285i) q^{43} +(-0.0655354 - 0.143502i) q^{44} +(4.76736 - 3.06873i) q^{45} +(-4.67998 - 1.04774i) q^{46} -5.12942i q^{47} +(0.619927 - 0.283111i) q^{48} +(-6.02800 + 1.76998i) q^{49} +(-4.54511 + 2.08373i) q^{50} +(-0.774417 - 0.497688i) q^{51} +(1.78366 - 1.54555i) q^{52} +(2.24070 - 0.322165i) q^{53} +(-3.61973 - 1.06285i) q^{54} +(0.146307 - 0.320989i) q^{55} +(0.120550 - 0.838442i) q^{56} +(-1.76570 - 0.806368i) q^{57} +(-7.29088 - 3.32963i) q^{58} +(1.21457 - 8.44754i) q^{59} +(1.38666 + 0.632040i) q^{60} +(-7.90952 - 2.32245i) q^{61} +(8.41642 - 1.21010i) q^{62} +(-1.62317 + 1.40649i) q^{63} +(-0.841254 - 0.540641i) q^{64} +(5.22423 + 0.747227i) q^{65} +(-0.103160 + 0.0302904i) q^{66} +(-9.98767 + 4.56122i) q^{67} +1.35075i q^{68} +(-1.16069 + 3.05539i) q^{69} +(1.59266 - 1.02519i) q^{70} +(-2.29577 - 5.02704i) q^{71} +(0.714344 + 2.43283i) q^{72} +(-0.325011 - 0.281624i) q^{73} +(8.28068 + 5.32167i) q^{74} +(0.964810 + 3.26813i) q^{75} +(0.405347 + 2.81925i) q^{76} +(-0.0376485 + 0.128219i) q^{77} +(-0.869598 - 1.35312i) q^{78} +(-0.416071 + 2.89384i) q^{79} +(-0.319846 - 2.21307i) q^{80} +(2.09185 - 4.58052i) q^{81} +(5.18694 + 0.745770i) q^{82} +(4.37858 + 6.81320i) q^{83} +(-0.553902 - 0.162640i) q^{84} +(-2.28119 + 1.97958i) q^{85} +(1.96756 + 2.27069i) q^{86} +(-2.95323 + 4.59532i) q^{87} +(0.119226 + 0.103310i) q^{88} +(5.58913 - 1.64112i) q^{89} +(-3.06174 + 4.77185i) q^{90} -1.99918 q^{91} +(4.69231 - 0.991076i) q^{92} -5.79489i q^{93} +(2.13084 + 4.66589i) q^{94} +(-4.16719 + 4.81631i) q^{95} +(-0.446297 + 0.515054i) q^{96} +(3.23796 - 5.03836i) q^{97} +(4.74798 - 4.11415i) q^{98} +(-0.0569265 - 0.395932i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 120 q + 12 q^{4} - 4 q^{6} + 8 q^{9}+O(q^{10}) $ 120 * q + 12 * q^4 - 4 * q^6 + 8 * q^9	$ 120 q + 12 q^{4} - 4 q^{6} + 8 q^{9} + 8 q^{11} - 6 q^{15} - 12 q^{16} - 16 q^{19} - 22 q^{20} + 4 q^{24} - 52 q^{25} - 4 q^{26} - 8 q^{29} - 44 q^{30} + 12 q^{31} + 16 q^{35} - 8 q^{36} - 36 q^{39} - 28 q^{41} - 8 q^{44} + 16 q^{45} - 4 q^{46} - 58 q^{49} + 12 q^{50} - 24 q^{51} - 6 q^{54} - 36 q^{55} + 22 q^{56} - 102 q^{59} - 38 q^{60} + 72 q^{61} + 12 q^{64} - 138 q^{65} + 80 q^{66} - 212 q^{69} - 108 q^{70} + 176 q^{71} - 88 q^{74} - 100 q^{75} + 16 q^{76} - 104 q^{79} - 22 q^{80} - 28 q^{81} - 22 q^{84} + 2 q^{85} + 62 q^{86} + 48 q^{89} + 24 q^{90} - 56 q^{91} + 24 q^{94} + 18 q^{95} - 4 q^{96} + 188 q^{99}+O(q^{100}) $ 120 * q + 12 * q^4 - 4 * q^6 + 8 * q^9 + 8 * q^11 - 6 * q^15 - 12 * q^16 - 16 * q^19 - 22 * q^20 + 4 * q^24 - 52 * q^25 - 4 * q^26 - 8 * q^29 - 44 * q^30 + 12 * q^31 + 16 * q^35 - 8 * q^36 - 36 * q^39 - 28 * q^41 - 8 * q^44 + 16 * q^45 - 4 * q^46 - 58 * q^49 + 12 * q^50 - 24 * q^51 - 6 * q^54 - 36 * q^55 + 22 * q^56 - 102 * q^59 - 38 * q^60 + 72 * q^61 + 12 * q^64 - 138 * q^65 + 80 * q^66 - 212 * q^69 - 108 * q^70 + 176 * q^71 - 88 * q^74 - 100 * q^75 + 16 * q^76 - 104 * q^79 - 22 * q^80 - 28 * q^81 - 22 * q^84 + 2 * q^85 + 62 * q^86 + 48 * q^89 + 24 * q^90 - 56 * q^91 + 24 * q^94 + 18 * q^95 - 4 * q^96 + 188 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/230\mathbb{Z}\right)^\times$.

$n$	$47$	$51$
$\chi(n)$	$-1$	$e\left(\frac{2}{11}\right)$

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 $

$2$	−0.909632	+	0.415415i	−0.643207	+	0.293743i
$2$	−0.909632	+	0.415415i	−0.643207	+	0.293743i
$3$	0.192005	+	0.653908i	0.110854	+	0.377534i	0.996168	−	0.0874597i	$-0.0278749\pi$
$3$	0.192005	+	0.653908i	0.110854	+	0.377534i	−0.885314	+	0.464993i	$0.846057\pi$
$4$	0.654861	−	0.755750i	0.327430	−	0.377875i
$5$	2.23607	−	0.00163718i	1.00000	−	0.000732171i
$5$	2.23607	−	0.00163718i	1.00000	−	0.000732171i
$6$	−0.446297	−	0.515054i	−0.182200	−	0.210270i
$7$	−0.838442	+	0.120550i	−0.316901	+	0.0455636i	−0.298930	−	0.954275i	$-0.596630\pi$
$7$	−0.838442	+	0.120550i	−0.316901	+	0.0455636i	−0.0179712	+	0.999839i	$0.505721\pi$
$8$	−0.281733	+	0.959493i	−0.0996075	+	0.339232i
$9$	2.13303	−	1.37082i	0.711010	−	0.456939i
$10$	−2.03332	+	0.930385i	−0.642992	+	0.294214i
$11$	0.0655354	−	0.143502i	0.0197597	−	0.0432676i	−0.899495	−	0.436931i	$-0.856065\pi$
$11$	0.0655354	−	0.143502i	0.0197597	−	0.0432676i	0.919255	+	0.393664i	$0.128793\pi$
$12$	0.619927	+	0.283111i	0.178957	+	0.0817271i
$13$	2.33610	+	0.335881i	0.647918	+	0.0931566i	0.458436	−	0.888728i	$-0.348410\pi$
$13$	2.33610	+	0.335881i	0.647918	+	0.0931566i	0.189482	+	0.981884i	$0.439319\pi$
$14$	0.712596	−	0.457958i	0.190449	−	0.122394i
$15$	0.430406	+	1.46187i	0.111130	+	0.377452i
$16$	−0.142315	−	0.989821i	−0.0355787	−	0.247455i
$17$	−1.02083	+	0.884550i	−0.247586	+	0.214535i	−0.769809	−	0.638274i	$-0.779649\pi$
$17$	−1.02083	+	0.884550i	−0.247586	+	0.214535i	0.522222	+	0.852809i	$0.325103\pi$
$18$	−1.37082	+	2.13303i	−0.323104	+	0.502760i
$19$	−1.86520	+	2.15256i	−0.427906	+	0.493830i	−0.928229	−	0.372009i	$-0.878669\pi$
$19$	−1.86520	+	2.15256i	−0.427906	+	0.493830i	0.500323	+	0.865839i	$0.333215\pi$
$20$	1.46308	−	1.69098i	0.327154	−	0.378114i
$21$	−0.239813	−	0.525118i	−0.0523315	−	0.114590i
$22$			0.157759i			0.0336343i
$23$	3.82181	+	2.89719i	0.796903	+	0.604107i
$23$	3.82181	+	2.89719i	0.796903	+	0.604107i
$24$	−0.681514			−0.139113
$25$	4.99999	−	0.00732171i	0.999999	−	0.00146434i
$26$	−2.26452	+	0.664924i	−0.444110	+	0.130402i
$27$	2.85110	+	2.47049i	0.548694	+	0.475446i
$28$	−0.457958	+	0.712596i	−0.0865458	+	0.134668i
$29$	5.24884	+	6.05748i	0.974685	+	1.12485i	0.992157	+	0.124999i	$0.0398926\pi$
$29$	5.24884	+	6.05748i	0.974685	+	1.12485i	−0.0174724	+	0.999847i	$0.505562\pi$
$30$	−0.998792	−	1.15096i	−0.182354	−	0.210136i
$31$	−8.15854	−	2.39556i	−1.46532	−	0.430256i	−0.550743	−	0.834675i	$-0.685656\pi$
$31$	−8.15854	−	2.39556i	−1.46532	−	0.430256i	−0.914574	+	0.404419i	$0.867474\pi$
$32$	0.540641	+	0.841254i	0.0955727	+	0.148714i
$33$	0.106420	+	0.0153010i	0.0185254	+	0.00266355i
$34$	0.561120	−	1.22868i	0.0962312	−	0.210717i
$35$	−1.87462	+	0.270930i	−0.316868	+	0.0457956i
$36$	0.360845	−	2.50973i	0.0601408	−	0.418289i
$37$	−5.32167	−	8.28068i	−0.874877	−	1.36133i	−0.931806	−	0.362957i	$-0.881767\pi$
$37$	−5.32167	−	8.28068i	−0.874877	−	1.36133i	0.0569291	−	0.998378i	$-0.481869\pi$
$38$	0.802442	−	2.73287i	0.130173	−	0.443329i
$39$	0.228907	+	1.59209i	0.0366545	+	0.254938i
$40$	−0.628402	+	2.14595i	−0.0993591	+	0.339305i
$41$	−4.40840	−	2.83311i	−0.688477	−	0.442457i	0.149067	−	0.988827i	$-0.452373\pi$
$41$	−4.40840	−	2.83311i	−0.688477	−	0.442457i	−0.837544	+	0.546370i	$0.816009\pi$
$42$	0.436284	+	0.378042i	0.0673200	+	0.0583331i
$43$	−0.846481	−	2.88285i	−0.129087	−	0.439630i	0.869431	−	0.494055i	$-0.164486\pi$
$43$	−0.846481	−	2.88285i	−0.129087	−	0.439630i	−0.998518	+	0.0544244i	$0.982668\pi$
$44$	−0.0655354	−	0.143502i	−0.00987983	−	0.0216338i
$45$	4.76736	−	3.06873i	0.710676	−	0.457459i
$46$	−4.67998	−	1.04774i	−0.690026	−	0.154481i
$47$		−	5.12942i		−	0.748203i	−0.927388	−	0.374102i	$-0.877951\pi$
$47$		−	5.12942i		−	0.748203i	0.927388	−	0.374102i	$-0.122049\pi$
$48$	0.619927	−	0.283111i	0.0894787	−	0.0408636i
$49$	−6.02800	+	1.76998i	−0.861142	+	0.252854i
$50$	−4.54511	+	2.08373i	−0.642776	+	0.294684i
$51$	−0.774417	−	0.497688i	−0.108440	−	0.0696902i
$52$	1.78366	−	1.54555i	0.247350	−	0.214330i
$53$	2.24070	−	0.322165i	0.307784	−	0.0442527i	0.0133079	−	0.999911i	$-0.495764\pi$
$53$	2.24070	−	0.322165i	0.307784	−	0.0442527i	0.294476	+	0.955659i	$0.404855\pi$
$54$	−3.61973	−	1.06285i	−0.492583	−	0.144635i
$55$	0.146307	−	0.320989i	0.0197280	−	0.0432821i
$56$	0.120550	−	0.838442i	0.0161091	−	0.112042i
$57$	−1.76570	−	0.806368i	−0.233873	−	0.106806i
$58$	−7.29088	−	3.32963i	−0.957339	−	0.437202i
$59$	1.21457	−	8.44754i	0.158124	−	1.09978i	−0.743963	−	0.668221i	$-0.767056\pi$
$59$	1.21457	−	8.44754i	0.158124	−	1.09978i	0.902087	−	0.431555i	$-0.142035\pi$
$60$	1.38666	+	0.632040i	0.179017	+	0.0815961i
$61$	−7.90952	−	2.32245i	−1.01271	−	0.297359i	−0.267049	−	0.963683i	$-0.586048\pi$
$61$	−7.90952	−	2.32245i	−1.01271	−	0.297359i	−0.745662	+	0.666324i	$0.767867\pi$
$62$	8.41642	−	1.21010i	1.06889	−	0.153683i
$63$	−1.62317	+	1.40649i	−0.204500	+	0.177201i
$64$	−0.841254	−	0.540641i	−0.105157	−	0.0675801i
$65$	5.22423	+	0.747227i	0.647986	+	0.0926821i
$66$	−0.103160	+	0.0302904i	−0.0126981	+	0.00372849i
$67$	−9.98767	+	4.56122i	−1.22019	+	0.557241i	−0.918218	−	0.396076i	$-0.870372\pi$
$67$	−9.98767	+	4.56122i	−1.22019	+	0.557241i	−0.301971	+	0.953317i	$0.597644\pi$
$68$			1.35075i			0.163802i
$69$	−1.16069	+	3.05539i	−0.139731	+	0.367825i
$70$	1.59266	−	1.02519i	0.190360	−	0.122534i
$71$	−2.29577	−	5.02704i	−0.272458	−	0.596599i	0.723101	−	0.690742i	$-0.242716\pi$
$71$	−2.29577	−	5.02704i	−0.272458	−	0.596599i	−0.995559	+	0.0941431i	$0.969989\pi$
$72$	0.714344	+	2.43283i	0.0841862	+	0.286712i
$73$	−0.325011	−	0.281624i	−0.0380397	−	0.0329616i	0.635633	−	0.771991i	$-0.280739\pi$
$73$	−0.325011	−	0.281624i	−0.0380397	−	0.0329616i	−0.673673	+	0.739029i	$0.735284\pi$
$74$	8.28068	+	5.32167i	0.962609	+	0.618631i
$75$	0.964810	+	3.26813i	0.111407	+	0.377371i
$76$	0.405347	+	2.81925i	0.0464965	+	0.323390i
$77$	−0.0376485	+	0.128219i	−0.00429044	+	0.0146119i
$78$	−0.869598	−	1.35312i	−0.0984625	−	0.153211i
$79$	−0.416071	+	2.89384i	−0.0468117	+	0.325582i	0.952937	+	0.303168i	$0.0980444\pi$
$79$	−0.416071	+	2.89384i	−0.0468117	+	0.325582i	−0.999749	+	0.0224143i	$0.992865\pi$
$80$	−0.319846	−	2.21307i	−0.0357599	−	0.247429i
$81$	2.09185	−	4.58052i	0.232428	−	0.508947i
$82$	5.18694	+	0.745770i	0.572802	+	0.0823565i
$83$	4.37858	+	6.81320i	0.480611	+	0.747846i	0.993890	−	0.110376i	$-0.0352056\pi$
$83$	4.37858	+	6.81320i	0.480611	+	0.747846i	−0.513279	+	0.858222i	$0.671569\pi$
$84$	−0.553902	−	0.162640i	−0.0604356	−	0.0177455i
$85$	−2.28119	+	1.97958i	−0.247429	+	0.214716i
$86$	1.96756	+	2.27069i	0.212168	+	0.244855i
$87$	−2.95323	+	4.59532i	−0.316620	+	0.492670i
$88$	0.119226	+	0.103310i	0.0127096	+	0.0110129i
$89$	5.58913	−	1.64112i	0.592446	−	0.173958i	0.0282533	−	0.999601i	$-0.491005\pi$
$89$	5.58913	−	1.64112i	0.592446	−	0.173958i	0.564193	+	0.825643i	$0.309187\pi$
$90$	−3.06174	+	4.77185i	−0.322736	+	0.502997i
$91$	−1.99918			−0.209571
$92$	4.69231	−	0.991076i	0.489207	−	0.103327i
$93$		−	5.79489i		−	0.600902i
$94$	2.13084	+	4.66589i	0.219779	+	0.481249i
$95$	−4.16719	+	4.81631i	−0.427545	+	0.494143i
$96$	−0.446297	+	0.515054i	−0.0455499	+	0.0525674i
$97$	3.23796	−	5.03836i	0.328765	−	0.511568i	−0.637043	−	0.770829i	$-0.719842\pi$
$97$	3.23796	−	5.03836i	0.328765	−	0.511568i	0.965807	+	0.259260i	$0.0834788\pi$
$98$	4.74798	−	4.11415i	0.479619	−	0.415592i
$99$	−0.0569265	−	0.395932i	−0.00572133	−	0.0397927i
$100$	3.26877	−	3.78354i	0.326877	−	0.378354i
$101$	1.28915	−	0.828487i	0.128275	−	0.0824376i	−0.474930	−	0.880024i	$-0.657526\pi$
$101$	1.28915	−	0.828487i	0.128275	−	0.0824376i	0.603205	+	0.797586i	$0.293890\pi$
$102$	0.911181	+	0.131008i	0.0902204	+	0.0129717i
$103$	−6.55682	−	2.99440i	−0.646063	−	0.295047i	0.0653068	−	0.997865i	$-0.479197\pi$
$103$	−6.55682	−	2.99440i	−0.646063	−	0.295047i	−0.711369	+	0.702818i	$0.751925\pi$
$104$	−0.980431	+	2.14684i	−0.0961392	+	0.210515i
$105$	−0.537098	−	1.17381i	−0.0524154	−	0.114552i
$106$	−1.90438	+	1.22387i	−0.184970	+	0.118873i
$107$	−3.12112	+	10.6296i	−0.301730	+	1.02760i	0.659467	+	0.751734i	$0.270782\pi$
$107$	−3.12112	+	10.6296i	−0.301730	+	1.02760i	−0.961197	+	0.275864i	$0.911036\pi$
$108$	3.73415	−	0.536889i	0.359318	−	0.0516622i
$109$	0.652738	+	0.753300i	0.0625210	+	0.0721531i	0.786148	−	0.618038i	$-0.212072\pi$
$109$	0.652738	+	0.753300i	0.0625210	+	0.0721531i	−0.723628	+	0.690191i	$0.757527\pi$
$110$	0.000258280		0.352759i	2.46261e−5		0.0336343i
$111$	4.39301	−	5.06981i	0.416966	−	0.481205i
$112$	0.238646	+	0.812752i	0.0225499	+	0.0767979i
$113$	−11.5161	+	5.25925i	−1.08335	+	0.494748i	−0.875404	−	0.483392i	$-0.839404\pi$
$113$	−11.5161	+	5.25925i	−1.08335	+	0.494748i	−0.207944	+	0.978141i	$0.566677\pi$
$114$	1.94111			0.181802
$115$	8.55058	+	6.47206i	0.797346	+	0.603523i
$116$	8.01520			0.744192
$117$	5.44341	−	2.48592i	0.503243	−	0.229824i
$118$	2.40442	+	8.18871i	0.221345	+	0.753831i
$119$	0.749271	−	0.864704i	0.0686855	−	0.0792673i
$120$	−1.52391	+	0.00111576i	−0.139113	+	0.000101855i
$121$	7.18717	+	8.29444i	0.653379	+	0.754040i
$122$	8.15954	−	1.17316i	0.738730	−	0.106213i
$123$	1.00616	−	3.42666i	0.0907222	−	0.308971i
$124$	−7.15315	+	4.59705i	−0.642372	+	0.412828i
$125$	11.1803	−	0.0245577i	0.999998	−	0.00219651i
$126$	0.892214	−	1.95368i	0.0794847	−	0.174047i
$127$	−5.83410	−	2.66434i	−0.517693	−	0.236422i	0.139395	−	0.990237i	$-0.455484\pi$
$127$	−5.83410	−	2.66434i	−0.517693	−	0.236422i	−0.657087	+	0.753815i	$0.728212\pi$
$128$	0.989821	+	0.142315i	0.0874887	+	0.0125790i
$129$	1.72259	−	1.10704i	0.151665	−	0.0974695i
$130$	−5.06254	+	1.49052i	−0.444014	+	0.130727i
$131$	1.11243	+	7.73713i	0.0971936	+	0.675997i	0.978921	+	0.204238i	$0.0654716\pi$
$131$	1.11243	+	7.73713i	0.0971936	+	0.675997i	−0.881728	+	0.471759i	$0.843619\pi$
$132$	0.0812543	−	0.0704072i	0.00707228	−	0.00612816i
$133$	1.30437	−	2.02964i	0.113103	−	0.175992i
$134$	7.19031	−	8.29806i	0.621148	−	0.716843i
$135$	6.37930	+	5.51952i	0.549042	+	0.475045i
$136$	−0.561120	−	1.22868i	−0.0481156	−	0.105359i
$137$			10.5092i			0.897863i	0.893566	+	0.448931i	$0.148195\pi$
$137$			10.5092i			0.897863i	−0.893566	+	0.448931i	$0.851805\pi$
$138$	−0.213452	−	3.26145i	−0.0181703	−	0.277633i
$139$	6.93930			0.588584			0.294292	−	0.955716i	$-0.404916\pi$
$139$	6.93930			0.588584			0.294292	+	0.955716i	$0.404916\pi$
$140$	−1.02286	+	1.59416i	−0.0864472	+	0.134731i
$141$	3.35417	−	0.984873i	0.282472	−	0.0829412i
$142$	4.17661	+	3.61905i	0.350493	+	0.303704i
$143$	0.201297	−	0.313224i	0.0168333	−	0.0261931i
$144$	−1.66043	−	1.91623i	−0.138369	−	0.159686i
$145$	11.7467	+	13.5363i	0.975508	+	1.12413i
$146$	0.412631	+	0.121160i	0.0341496	+	0.0100272i
$147$	−2.31481	−	3.60191i	−0.190922	−	0.297080i
$148$	−9.74307	−	1.40084i	−0.800875	−	0.115149i
$149$	4.86908	−	10.6618i	0.398891	−	0.873449i	−0.598491	−	0.801130i	$-0.704233\pi$
$149$	4.86908	−	10.6618i	0.398891	−	0.873449i	0.997382	−	0.0723190i	$-0.0230400\pi$
$150$	−2.23525	−	2.57200i	−0.182507	−	0.210003i
$151$	−0.142151	+	0.988679i	−0.0115681	+	0.0804576i	−0.994788	−	0.101968i	$-0.967486\pi$
$151$	−0.142151	+	0.988679i	−0.0115681	+	0.0804576i	0.983220	+	0.182426i	$0.0583950\pi$
$152$	−1.53987	−	2.39609i	−0.124900	−	0.194349i
$153$	−0.964897	+	3.28614i	−0.0780073	+	0.265668i
$154$	−0.0190178	−	0.132272i	−0.00153250	−	0.0106588i
$155$	−18.2470	−	5.34329i	−1.46563	−	0.429183i
$156$	1.35312	+	0.869598i	0.108336	+	0.0696235i
$157$	−11.6398	−	10.0859i	−0.928958	−	0.804946i	0.0521041	−	0.998642i	$-0.483407\pi$
$157$	−11.6398	−	10.0859i	−0.928958	−	0.804946i	−0.981062	+	0.193695i	$0.937953\pi$
$158$	−0.823673	−	2.80517i	−0.0655279	−	0.223167i
$159$	0.640891	+	1.40336i	0.0508260	+	0.111293i
$160$	1.21029	+	1.88021i	0.0956816	+	0.148644i
$161$	−3.55363	−	1.96841i	−0.280065	−	0.155133i
$162$			5.03558i			0.395632i
$163$	15.1132	−	6.90196i	1.18376	−	0.540603i	0.276432	−	0.961034i	$-0.410848\pi$
$163$	15.1132	−	6.90196i	1.18376	−	0.540603i	0.907325	+	0.420430i	$0.138121\pi$
$164$	−5.02801	+	1.47636i	−0.392622	+	0.115284i
$165$	0.237988	+	0.0340397i	0.0185274	+	0.00264999i
$166$	−6.81320	−	4.37858i	−0.528807	−	0.339843i
$167$	−11.1305	+	9.64460i	−0.861301	+	0.746322i	−0.968790	−	0.247884i	$-0.920265\pi$
$167$	−11.1305	+	9.64460i	−0.861301	+	0.746322i	0.107488	+	0.994206i	$0.465719\pi$
$168$	0.571410	−	0.0821563i	0.0440852	−	0.00633850i
$169$	−7.12885	−	2.09322i	−0.548373	−	0.161017i
$170$	1.25269	−	2.74833i	0.0960769	−	0.210787i
$171$	−1.02777	+	7.14831i	−0.0785957	+	0.546645i
$172$	−2.73304	−	1.24814i	−0.208392	−	0.0951696i
$173$	−18.3348	−	8.37321i	−1.39397	−	0.636603i	−0.430050	−	0.902805i	$-0.641504\pi$
$173$	−18.3348	−	8.37321i	−1.39397	−	0.636603i	−0.963917	+	0.266202i	$0.914231\pi$
$174$	0.777390	−	5.40687i	0.0589338	−	0.409893i
$175$	−4.19133	+	0.608887i	−0.316834	+	0.0460276i
$176$	−0.151369	−	0.0444458i	−0.0114098	−	0.00335023i
$177$	5.75711	−	0.827748i	0.432731	−	0.0622174i
$178$	−4.40231	+	3.81462i	−0.329967	+	0.285918i
$179$	−3.08803	−	1.98456i	−0.230810	−	0.148333i	0.420124	−	0.907467i	$-0.361986\pi$
$179$	−3.08803	−	1.98456i	−0.230810	−	0.148333i	−0.650935	+	0.759134i	$0.725623\pi$
$180$	0.802765	−	5.61252i	0.0598345	−	0.418332i
$181$	18.3680	−	5.39332i	1.36528	−	0.400883i	0.484659	−	0.874703i	$-0.338944\pi$
$181$	18.3680	−	5.39332i	1.36528	−	0.400883i	0.880621	+	0.473821i	$0.157125\pi$
$182$	1.81852	−	0.830488i	0.134797	−	0.0615599i
$183$		−	5.61802i		−	0.415296i
$184$	−3.85657	+	2.85077i	−0.284310	+	0.210162i
$185$	−11.9132	−	18.5074i	−0.875873	−	1.36069i
$186$	2.40728	+	5.27122i	0.176511	+	0.386504i
$187$	0.0600349	+	0.204460i	0.00439019	+	0.0149516i
$188$	−3.87656	−	3.35906i	−0.282727	−	0.244984i
$189$	−2.68830	−	1.72767i	−0.195545	−	0.125669i
$190$	1.78984	−	6.11218i	0.129849	−	0.443424i
$191$	3.32960	+	23.1579i	0.240922	+	1.67565i	0.647527	+	0.762043i	$0.275803\pi$
$191$	3.32960	+	23.1579i	0.240922	+	1.67565i	−0.406605	+	0.913604i	$0.633287\pi$
$192$	0.192005	−	0.653908i	0.0138567	−	0.0471917i
$193$	3.74555	+	5.82819i	0.269611	+	0.419522i	0.949488	−	0.313804i	$-0.101603\pi$
$193$	3.74555	+	5.82819i	0.269611	+	0.419522i	−0.679877	+	0.733326i	$0.737967\pi$
$194$	−0.852340	+	5.92815i	−0.0611944	+	0.425617i
$195$	0.514459	+	3.55964i	0.0368412	+	0.254911i
$196$	−2.60984	+	5.71475i	−0.186417	+	0.408196i
$197$	0.961948	+	0.138307i	0.0685360	+	0.00985398i	0.176498	−	0.984301i	$-0.443523\pi$
$197$	0.961948	+	0.138307i	0.0685360	+	0.00985398i	−0.107962	+	0.994155i	$0.534432\pi$
$198$	0.216258	+	0.336505i	0.0153688	+	0.0239143i
$199$	−24.9595	−	7.32878i	−1.76933	−	0.519523i	−0.775594	−	0.631233i	$-0.782549\pi$
$199$	−24.9595	−	7.32878i	−1.76933	−	0.519523i	−0.993741	+	0.111709i	$0.964367\pi$
$200$	−1.40164	+	4.79952i	−0.0991106	+	0.339377i
$201$	−4.90029	−	5.65524i	−0.345640	−	0.398890i
$202$	−0.828487	+	1.28915i	−0.0582922	+	0.0907044i
$203$	−5.13108	−	4.44610i	−0.360131	−	0.312055i
$204$	−0.883262	+	0.259349i	−0.0618407	+	0.0181581i
$205$	−9.86213	−	6.32781i	−0.688801	−	0.441953i
$206$	7.20821			0.502220
$207$	12.1236	+	0.940801i	0.842646	+	0.0653902i
$208$		−	2.36012i		−	0.163645i
$209$	0.186660	+	0.408729i	0.0129116	+	0.0282724i
$210$	0.976178	+	0.844613i	0.0673627	+	0.0582838i
$211$	−0.242799	+	0.280204i	−0.0167149	+	0.0192901i	−0.764045	−	0.645162i	$-0.776790\pi$
$211$	−0.242799	+	0.280204i	−0.0167149	+	0.0192901i	0.747331	+	0.664452i	$0.231335\pi$
$212$	1.22387	−	1.90438i	0.0840559	−	0.130794i
$213$	2.84642	−	2.46644i	0.195033	−	0.168997i
$214$	−1.57661	−	10.9655i	−0.107775	−	0.749589i
$215$	−1.89751	−	6.44486i	−0.129409	−	0.439536i
$216$	−3.17367	+	2.03959i	−0.215941	+	0.138777i
$217$	7.12925	+	1.02503i	0.483965	+	0.0695837i
$218$	−0.906684	−	0.414069i	−0.0614084	−	0.0280443i
$219$	0.121752	−	0.266600i	0.00822726	−	0.0180152i
$220$	−0.146776	−	0.320774i	−0.00989567	−	0.0216266i
$221$	−2.68185	+	1.72352i	−0.180401	+	0.115937i
$222$	−1.88995	+	6.43658i	−0.126845	+	0.431995i
$223$	28.5755	−	4.10853i	1.91356	−	0.275128i	0.920313	−	0.391183i	$-0.127934\pi$
$223$	28.5755	−	4.10853i	1.91356	−	0.275128i	0.993243	+	0.116055i	$0.0370250\pi$
$224$	−0.554709	−	0.640169i	−0.0370631	−	0.0427731i
$225$	10.6551	−	6.86969i	0.710341	−	0.457979i
$226$	8.29069	−	9.56796i	0.551488	−	0.636451i
$227$	−7.35169	−	25.0376i	−0.487949	−	1.66180i	−0.723798	−	0.690012i	$-0.757605\pi$
$227$	−7.35169	−	25.0376i	−0.487949	−	1.66180i	0.235849	−	0.971790i	$-0.424213\pi$
$228$	−1.76570	+	0.806368i	−0.116936	+	0.0534030i
$229$	−1.92024			−0.126893			−0.0634464	−	0.997985i	$-0.520209\pi$
$229$	−1.92024			−0.126893			−0.0634464	+	0.997985i	$0.520209\pi$
$230$	−10.4665	−	2.33516i	−0.690139	−	0.153976i
$231$	−0.0910720			−0.00599209
$232$	−7.29088	+	3.32963i	−0.478670	+	0.218601i
$233$	6.15875	+	20.9748i	0.403473	+	1.37410i	0.871503	+	0.490390i	$0.163146\pi$
$233$	6.15875	+	20.9748i	0.403473	+	1.37410i	−0.468030	+	0.883713i	$0.655036\pi$
$234$	−3.91881	+	4.52255i	−0.256181	+	0.295648i
$235$	−0.00839781	−	11.4697i	−0.000547813	−	0.748203i
$236$	−5.58885	−	6.44988i	−0.363803	−	0.419851i
$237$	−1.97219	+	0.283558i	−0.128108	+	0.0184191i
$238$	−0.322349	+	1.09782i	−0.0208948	+	0.0711612i
$239$	9.65214	−	6.20306i	0.624345	−	0.401242i	−0.189867	−	0.981810i	$-0.560806\pi$
$239$	9.65214	−	6.20306i	0.624345	−	0.401242i	0.814212	+	0.580568i	$0.197169\pi$
$240$	1.38573	−	0.634070i	0.0894488	−	0.0409291i
$241$	−7.16563	+	15.6905i	−0.461579	+	1.01072i	0.525546	+	0.850765i	$0.323861\pi$
$241$	−7.16563	+	15.6905i	−0.461579	+	1.01072i	−0.987125	+	0.159952i	$0.948866\pi$
$242$	−9.98331	−	4.55923i	−0.641752	−	0.293078i
$243$	14.5993	+	2.09907i	0.936547	+	0.134655i
$244$	−6.93482	+	4.45674i	−0.443957	+	0.285314i
$245$	−13.4761	+	3.96766i	−0.860957	+	0.253485i
$246$	0.508252	+	3.53497i	0.0324050	+	0.225382i
$247$	−5.08030	+	4.40210i	−0.323252	+	0.280099i
$248$	4.59705	−	7.15315i	0.291913	−	0.454226i
$249$	−3.61449	+	4.17135i	−0.229059	+	0.264349i
$250$	−10.1598	+	4.66681i	−0.642560	+	0.295155i
$251$	−1.85426	−	4.06026i	−0.117040	−	0.256281i	0.842041	−	0.539413i	$-0.181354\pi$
$251$	−1.85426	−	4.06026i	−0.117040	−	0.256281i	−0.959081	+	0.283132i	$0.908627\pi$
$252$			2.14776i			0.135296i
$253$	0.666219	−	0.358571i	0.0418848	−	0.0225432i
$254$	6.41369			0.402431
$255$	−1.73246	−	1.11159i	−0.108491	−	0.0696108i
$256$	−0.959493	+	0.281733i	−0.0599683	+	0.0176083i
$257$	11.9204	+	10.3291i	0.743573	+	0.644310i	0.941926	−	0.335821i	$-0.109014\pi$
$257$	11.9204	+	10.3291i	0.743573	+	0.644310i	−0.198353	+	0.980131i	$0.563559\pi$
$258$	−1.10704	+	1.72259i	−0.0689213	+	0.107244i
$259$	5.46015	+	6.30135i	0.339277	+	0.391547i
$260$	3.98586	−	3.45888i	0.247193	−	0.214511i
$261$	19.4996	+	5.72561i	1.20700	+	0.354406i
$262$	−4.22603	−	6.57582i	−0.261085	−	0.406256i
$263$	−4.57476	−	0.657751i	−0.282092	−	0.0405586i	−0.000183226	−	1.00000i	$-0.500058\pi$
$263$	−4.57476	−	0.657751i	−0.282092	−	0.0405586i	−0.281908	+	0.959441i	$0.590967\pi$
$264$	−0.0446633	+	0.0977989i	−0.00274883	+	0.00601911i
$265$	5.00984	−	0.724050i	0.307752	−	0.0444780i
$266$	−0.343355	+	2.38808i	−0.0210524	+	0.146423i
$267$	2.14628	+	3.33967i	0.131350	+	0.204385i
$268$	−3.09340	+	10.5351i	−0.188959	+	0.643536i
$269$	1.66055	+	11.5494i	0.101245	+	0.704176i	0.975707	+	0.219081i	$0.0703060\pi$
$269$	1.66055	+	11.5494i	0.101245	+	0.704176i	−0.874461	+	0.485095i	$0.838785\pi$
$270$	−8.09570	−	2.37068i	−0.492689	−	0.144275i
$271$	23.8621	+	15.3353i	1.44952	+	0.931550i	0.999253	+	0.0386569i	$0.0123079\pi$
$271$	23.8621	+	15.3353i	1.44952	+	0.931550i	0.450268	+	0.892893i	$0.351328\pi$
$272$	1.02083	+	0.884550i	0.0618966	+	0.0536337i
$273$	−0.383851	−	1.30728i	−0.0232317	−	0.0791200i
$274$	−4.36568	−	9.55952i	−0.263741	−	0.577511i
$275$	0.326626	−	0.717992i	0.0196963	−	0.0432965i
$276$	1.54902	+	2.87805i	0.0932399	+	0.173238i
$277$		−	27.9347i		−	1.67843i	−0.543797	−	0.839217i	$-0.683014\pi$
$277$		−	27.9347i		−	1.67843i	0.543797	−	0.839217i	$-0.316986\pi$
$278$	−6.31221	+	2.88269i	−0.378581	+	0.172892i
$279$	−20.6863	+	6.07405i	−1.23846	+	0.363644i
$280$	0.268185	−	1.87501i	0.0160271	−	0.112053i
$281$	−2.62086	−	1.68433i	−0.156348	−	0.100479i	0.460128	−	0.887853i	$-0.347804\pi$
$281$	−2.62086	−	1.68433i	−0.156348	−	0.100479i	−0.616475	+	0.787374i	$0.711440\pi$
$282$	−2.64193	+	2.28924i	−0.157325	+	0.136322i
$283$	−0.729777	+	0.104926i	−0.0433807	+	0.00623721i	−0.163971	−	0.986465i	$-0.552430\pi$
$283$	−0.729777	+	0.104926i	−0.0433807	+	0.00623721i	0.120590	+	0.992702i	$0.461521\pi$
$284$	−5.30259	−	1.55698i	−0.314651	−	0.0923898i
$285$	−3.94954	−	1.80020i	−0.233951	−	0.106635i
$286$	−0.0529882	+	0.368541i	−0.00313326	+	0.0217923i
$287$	4.03772	+	1.84397i	0.238339	+	0.108846i
$288$	2.30641	+	1.05330i	0.135906	+	0.0620664i
$289$	−2.15970	+	15.0210i	−0.127041	+	0.883590i
$290$	−16.3083	−	7.43335i	−0.957659	−	0.436501i
$291$	3.91633	+	1.14994i	0.229579	+	0.0674105i
$292$	−0.425674	+	0.0612027i	−0.0249107	+	0.00358162i
$293$	−10.2257	+	8.86058i	−0.597389	+	0.517640i	−0.900238	−	0.435398i	$-0.856608\pi$
$293$	−10.2257	+	8.86058i	−0.597389	+	0.517640i	0.302849	+	0.953039i	$0.402062\pi$
$294$	3.60191	+	2.31481i	0.210068	+	0.135002i
$295$	2.70204	−	18.8913i	0.157319	−	1.09989i
$296$	9.44454	−	2.77317i	0.548953	−	0.161187i
$297$	0.541370	−	0.247235i	0.0314135	−	0.0143460i
$298$			11.7210i			0.678979i
$299$	7.95504	+	8.05181i	0.460052	+	0.465648i
$300$	3.10170	+	1.41101i	0.179077	+	0.0814650i
$301$	1.05725	+	2.31506i	0.0609390	+	0.133438i
$302$	−0.281407	−	0.958386i	−0.0161932	−	0.0551489i
$303$	0.789277	+	0.683912i	0.0453428	+	0.0392897i
$304$	2.39609	+	1.53987i	0.137425	+	0.0883178i
$305$	−17.6900	−	5.18020i	−1.01293	−	0.296617i
$306$	−0.487409	−	3.39001i	−0.0278633	−	0.193794i
$307$	−3.95317	+	13.4633i	−0.225619	+	0.768389i	0.766407	+	0.642356i	$0.222043\pi$
$307$	−3.95317	+	13.4633i	−0.225619	+	0.768389i	−0.992026	+	0.126033i	$0.959775\pi$
$308$	0.0722469	+	0.112418i	0.00411665	+	0.00640563i
$309$	0.699121	−	4.86249i	0.0397716	−	0.276618i
$310$	18.8177	−	2.71964i	1.06877	−	0.154465i
$311$	9.54217	−	20.8944i	0.541087	−	1.18481i	−0.419735	−	0.907647i	$-0.637877\pi$
$311$	9.54217	−	20.8944i	0.541087	−	1.18481i	0.960822	−	0.277168i	$-0.0893958\pi$
$312$	−1.59209	−	0.228907i	−0.0901341	−	0.0129593i
$313$	10.0294	+	15.6060i	0.566893	+	0.882102i	0.999813	−	0.0193299i	$-0.00615327\pi$
$313$	10.0294	+	15.6060i	0.566893	+	0.882102i	−0.432920	+	0.901432i	$0.642517\pi$
$314$	14.7778	+	4.33915i	0.833959	+	0.244873i
$315$	−3.62722	+	3.14766i	−0.204371	+	0.177350i
$316$	1.91455	+	2.20951i	0.107702	+	0.124295i
$317$	2.94533	−	4.58303i	0.165426	−	0.257409i	−0.748637	−	0.662980i	$-0.769291\pi$
$317$	2.94533	−	4.58303i	0.165426	−	0.257409i	0.914063	+	0.405572i	$0.132928\pi$
$318$	−1.16595	−	1.01030i	−0.0653832	−	0.0566549i
$319$	1.21325	−	0.356242i	0.0679289	−	0.0199457i
$320$	−1.88198	−	1.20753i	−0.105206	−	0.0675031i
$321$	−7.55002			−0.421401
$322$	4.05020	+	0.314299i	0.225709	+	0.0175152i
$323$		−	3.84724i		−	0.214066i
$324$	−2.09185	−	4.58052i	−0.116214	−	0.254473i
$325$	11.6830	+	1.66230i	0.648054	+	0.0922077i
$326$	−10.8803	+	12.5565i	−0.602602	+	0.695440i
$327$	−0.367260	+	0.571467i	−0.0203095	+	0.0316022i
$328$	3.96034	−	3.43165i	0.218673	−	0.189481i
$329$	0.618351	+	4.30073i	0.0340908	+	0.237107i
$330$	−0.230622	+	0.0679003i	−0.0126953	+	0.00373779i
$331$	18.6460	−	11.9831i	1.02488	−	0.658649i	0.0836763	−	0.996493i	$-0.473334\pi$
$331$	18.6460	−	11.9831i	1.02488	−	0.658649i	0.941202	+	0.337844i	$0.109697\pi$
$332$	8.01643	+	1.15259i	0.439959	+	0.0632565i
$333$	−22.7026	−	10.3679i	−1.24409	−	0.568158i
$334$	6.11812	−	13.3968i	0.334768	−	0.733040i
$335$	−22.3256	+	10.2155i	−1.21978	+	0.558135i
$336$	−0.485644	+	0.312104i	−0.0264940	+	0.0170267i
$337$	−6.81020	+	23.1934i	−0.370975	+	1.26343i	0.536707	+	0.843769i	$0.319668\pi$
$337$	−6.81020	+	23.1934i	−0.370975	+	1.26343i	−0.907683	+	0.419658i	$0.862150\pi$
$338$	7.35419	−	1.05737i	0.400015	−	0.0575135i
$339$	−5.65021	−	6.52070i	−0.306878	−	0.354156i
$340$	0.00221142	+	3.02036i	0.000119931	+	0.163802i
$341$	−0.878443	+	1.01378i	−0.0475703	+	0.0548991i
$342$	−2.03462	−	6.92929i	−0.110020	−	0.374693i
$343$	10.2344	−	4.67388i	0.552604	−	0.252366i
$344$	3.00455			0.161995
$345$	−2.59038	+	6.83395i	−0.139461	+	0.367928i
$346$	20.1563			1.08361
$347$	20.7095	−	9.45771i	1.11174	−	0.507716i	0.227047	−	0.973884i	$-0.427093\pi$
$347$	20.7095	−	9.45771i	1.11174	−	0.507716i	0.884696	+	0.466168i	$0.154366\pi$
$348$	1.53895	+	5.24120i	0.0824966	+	0.280958i
$349$	21.9046	−	25.2793i	1.17253	−	1.35317i	0.249528	−	0.968368i	$-0.419725\pi$
$349$	21.9046	−	25.2793i	1.17253	−	1.35317i	0.922999	−	0.384801i	$-0.125730\pi$
$350$	3.55962	−	2.29500i	0.190270	−	0.122673i
$351$	5.83067	+	6.72895i	0.311218	+	0.359165i
$352$	0.156153	−	0.0224514i	0.00832299	−	0.00119666i
$353$	−9.09561	+	30.9768i	−0.484110	+	1.64873i	0.248914	+	0.968526i	$0.419926\pi$
$353$	−9.09561	+	30.9768i	−0.484110	+	1.64873i	−0.733024	+	0.680203i	$0.761892\pi$
$354$	−4.89300	+	3.14454i	−0.260060	+	0.167130i
$355$	−5.14173	−	11.2370i	−0.272895	−	0.596400i
$356$	2.41983	−	5.29868i	0.128251	−	0.280830i
$357$	0.709300	+	0.323927i	0.0375401	+	0.0171440i
$358$	3.63339	+	0.522402i	0.192031	+	0.0276098i
$359$	27.6221	−	17.7516i	1.45784	−	0.936895i	0.459012	−	0.888430i	$-0.348203\pi$
$359$	27.6221	−	17.7516i	1.45784	−	0.936895i	0.998825	−	0.0484650i	$-0.0154329\pi$
$360$	1.60130	+	5.43881i	0.0843961	+	0.286650i
$361$	1.54946	+	10.7767i	0.0815504	+	0.567196i
$362$	−14.4676	+	12.5363i	−0.760402	+	0.658892i
$363$	−4.04382	+	6.29231i	−0.212246	+	0.330261i
$364$	−1.30918	+	1.51088i	−0.0686198	+	0.0791915i
$365$	−0.727208	−	0.629198i	−0.0380638	−	0.0329337i
$366$	2.33381	+	5.11033i	0.121990	+	0.267121i
$367$		−	10.7767i		−	0.562537i	−0.959629	−	0.281269i	$-0.909245\pi$
$367$		−	10.7767i		−	0.562537i	0.959629	−	0.281269i	$-0.0907552\pi$
$368$	2.32380	−	4.19523i	0.121137	−	0.218691i
$369$	−13.2869			−0.691690
$370$	18.5249	+	11.8861i	0.963062	+	0.617926i
$371$	−1.83986	+	0.540233i	−0.0955210	+	0.0280475i
$372$	−4.37949	−	3.79485i	−0.227066	−	0.196754i
$373$	−15.4129	+	23.9830i	−0.798050	+	1.24179i	0.168598	+	0.985685i	$0.446076\pi$
$373$	−15.4129	+	23.9830i	−0.798050	+	1.24179i	−0.966649	+	0.256106i	$0.917560\pi$
$374$	−0.139546	−	0.161044i	−0.00721573	−	0.00832740i
$375$	2.16273	+	7.30618i	0.111683	+	0.377289i
$376$	4.92164	+	1.44513i	0.253814	+	0.0745266i
$377$	10.2272	+	15.9139i	0.526729	+	0.819606i
$378$	3.16306	+	0.454780i	0.162690	+	0.0233913i
$379$	−5.60508	+	12.2734i	−0.287914	+	0.630443i	−0.997225	−	0.0744526i	$-0.976279\pi$
$379$	−5.60508	+	12.2734i	−0.287914	+	0.630443i	0.709311	+	0.704896i	$0.249006\pi$
$380$	0.910998	+	6.30336i	0.0467332	+	0.323356i
$381$	0.622061	−	4.32653i	0.0318691	−	0.221655i
$382$	−12.6489	−	19.6820i	−0.647172	−	1.00702i
$383$	10.5663	−	35.9854i	0.539911	−	1.83877i	−0.00456073	−	0.999990i	$-0.501452\pi$
$383$	10.5663	−	35.9854i	0.539911	−	1.83877i	0.544472	−	0.838779i	$-0.316730\pi$
$384$	0.0969895	+	0.674577i	0.00494947	+	0.0344244i
$385$	−0.0839746	+	0.286768i	−0.00427974	+	0.0146150i
$386$	−5.82819	−	3.74555i	−0.296647	−	0.190643i
$387$	−5.75743	−	4.98884i	−0.292666	−	0.253597i
$388$	−1.68733	−	5.74651i	−0.0856611	−	0.291735i
$389$	−2.93825	−	6.43387i	−0.148975	−	0.326210i	0.820402	−	0.571787i	$-0.193750\pi$
$389$	−2.93825	−	6.43387i	−0.148975	−	0.326210i	−0.969377	+	0.245577i	$0.921023\pi$
$390$	−1.94669	−	3.02424i	−0.0985747	−	0.153139i
$391$	−6.46412	+	0.423058i	−0.326904	+	0.0213950i
$392$		−	6.28248i		−	0.317313i
$393$	−4.84578	+	2.21299i	−0.244437	+	0.111631i
$394$	−0.932474	+	0.273799i	−0.0469773	+	0.0137938i
$395$	−0.925626	+	6.47150i	−0.0465733	+	0.325617i
$396$	−0.336505	−	0.216258i	−0.0169100	−	0.0108674i
$397$	10.7817	−	9.34236i	0.541116	−	0.468880i	−0.340900	−	0.940100i	$-0.610732\pi$
$397$	10.7817	−	9.34236i	0.541116	−	0.468880i	0.882016	+	0.471220i	$0.156186\pi$
$398$	25.7485	−	3.70207i	1.29065	−	0.185568i
$399$	1.57764	+	0.463238i	0.0789810	+	0.0231909i
$400$	−0.718821	−	4.94806i	−0.0359410	−	0.247403i
$401$	−2.31363	+	16.0916i	−0.115537	+	0.803577i	0.846838	+	0.531851i	$0.178504\pi$
$401$	−2.31363	+	16.0916i	−0.115537	+	0.803577i	−0.962375	+	0.271726i	$0.912406\pi$
$402$	6.80673	+	3.10853i	0.339489	+	0.155039i
$403$	−18.2546	−	8.33658i	−0.909324	−	0.415275i
$404$	0.218086	−	1.51682i	0.0108502	−	0.0754646i
$405$	4.67003	−	10.2458i	0.232056	−	0.509117i
$406$	6.51437	+	1.91279i	0.323303	+	0.0949302i
$407$	−1.53706	+	0.220995i	−0.0761890	+	0.0109543i
$408$	0.695706	−	0.602833i	0.0344426	−	0.0298447i
$409$	−30.4398	−	19.5625i	−1.50515	−	0.967302i	−0.994183	−	0.107702i	$-0.965651\pi$
$409$	−30.4398	−	19.5625i	−1.50515	−	0.967302i	−0.510968	−	0.859600i	$-0.670713\pi$
$410$	11.5996	+	1.65910i	0.572862	+	0.0819371i
$411$	−6.87205	+	2.01782i	−0.338973	+	0.0995316i
$412$	−6.55682	+	2.99440i	−0.323031	+	0.147523i
$413$			7.22919i			0.355725i
$414$	−11.4188	+	4.18053i	−0.561204	+	0.205462i
$415$	9.80195	+	15.2276i	0.481159	+	0.747494i
$416$	0.980431	+	2.14684i	0.0480696	+	0.105258i
$417$	1.33238	+	4.53766i	0.0652468	+	0.222210i
$418$	−0.339585	−	0.294252i	−0.0166096	−	0.0143923i
$419$	19.8526	+	12.7585i	0.969864	+	0.623294i	0.926711	−	0.375775i	$-0.122623\pi$
$419$	19.8526	+	12.7585i	0.969864	+	0.623294i	0.0431532	+	0.999068i	$0.486260\pi$
$420$	−1.23883	−	0.362768i	−0.0604486	−	0.0177012i
$421$	−2.62284	−	18.2422i	−0.127829	−	0.889072i	−0.948298	−	0.317381i	$-0.897197\pi$
$421$	−2.62284	−	18.2422i	−0.127829	−	0.889072i	0.820469	−	0.571691i	$-0.193712\pi$
$422$	0.104456	−	0.355745i	0.00508485	−	0.0173174i
$423$	−7.03149	−	10.9412i	−0.341883	−	0.531980i
$424$	−0.322165	+	2.24070i	−0.0156457	+	0.108818i
$425$	−5.09764	+	4.43022i	−0.247272	+	0.214897i
$426$	−1.56460	+	3.42599i	−0.0758050	+	0.165990i
$427$	6.91165	+	0.993745i	0.334478	+	0.0480907i
$428$	5.98938	+	9.31966i	0.289508	+	0.450483i
$429$	0.243470	+	0.0714892i	0.0117548	+	0.00345153i
$430$	4.40333	+	5.07420i	0.212347	+	0.244699i
$431$	−10.5778	−	12.2074i	−0.509515	−	0.588011i	0.441460	−	0.897281i	$-0.354461\pi$
$431$	−10.5778	−	12.2074i	−0.509515	−	0.588011i	−0.950974	+	0.309270i	$0.899915\pi$
$432$	2.03959	−	3.17367i	0.0981299	−	0.152693i
$433$	−14.7923	−	12.8176i	−0.710871	−	0.615973i	0.222480	−	0.974937i	$-0.428585\pi$
$433$	−14.7923	−	12.8176i	−0.710871	−	0.615973i	−0.933352	+	0.358964i	$0.883130\pi$
$434$	−6.91081	+	2.02920i	−0.331729	+	0.0974046i
$435$	−6.59610	+	10.2803i	−0.316259	+	0.492901i
$436$	0.996759			0.0477361
$437$	−13.3648	+	2.82282i	−0.639326	+	0.135034i
$438$			0.293086i			0.0140042i
$439$	2.87649	+	6.29864i	0.137288	+	0.300618i	0.965771	−	0.259395i	$-0.0835233\pi$
$439$	2.87649	+	6.29864i	0.137288	+	0.300618i	−0.828484	+	0.560013i	$0.810796\pi$
$440$	0.266767	+	0.230813i	0.0127176	+	0.0110036i
$441$	−10.4316	+	12.0387i	−0.496742	+	0.573271i
$442$	1.72352	−	2.68185i	0.0819796	−	0.127563i
$443$	16.1098	−	13.9592i	0.765398	−	0.663221i	−0.181993	−	0.983300i	$-0.558255\pi$
$443$	16.1098	−	13.9592i	0.765398	−	0.663221i	0.947391	+	0.320079i	$0.103709\pi$
$444$	−0.954693	−	6.64003i	−0.0453077	−	0.315122i
$445$	12.4950	−	3.67880i	0.592319	−	0.174392i
$446$	−24.2864	+	15.6079i	−1.15000	+	0.739057i
$447$	7.90672	+	1.13681i	0.373975	+	0.0537695i
$448$	0.770517	+	0.351883i	0.0364035	+	0.0166249i
$449$	2.15138	−	4.71086i	0.101530	−	0.222319i	−0.852050	−	0.523461i	$-0.824641\pi$
$449$	2.15138	−	4.71086i	0.101530	−	0.222319i	0.953579	+	0.301142i	$0.0973678\pi$
$450$	−6.83846	+	10.6752i	−0.322368	+	0.503233i
$451$	−0.695465	+	0.446948i	−0.0327482	+	0.0210460i
$452$	−3.56680	+	12.1474i	−0.167768	+	0.571366i
$453$	−0.673798	+	0.0968776i	−0.0316578	+	0.00455170i
$454$	17.0883	+	19.7210i	0.801994	+	0.925551i
$455$	−4.47030	+	0.00327302i	−0.209571	+	0.000153442i
$456$	1.27116	−	1.46700i	0.0595275	−	0.0686984i
$457$	8.23241	+	28.0370i	0.385096	+	1.31152i	0.892982	+	0.450092i	$0.148609\pi$
$457$	8.23241	+	28.0370i	0.385096	+	1.31152i	−0.507886	+	0.861424i	$0.669573\pi$
$458$	1.74671	−	0.797695i	0.0816184	−	0.0372739i
$459$	−5.09575			−0.237849
$460$	10.4907	−	2.22380i	0.489131	−	0.103685i
$461$	−19.3274			−0.900165			−0.450082	−	0.892987i	$-0.648605\pi$
$461$	−19.3274			−0.900165			−0.450082	+	0.892987i	$0.648605\pi$
$462$	0.0828420	−	0.0378327i	0.00385416	−	0.00176013i
$463$	9.18540	+	31.2826i	0.426882	+	1.45383i	0.839719	+	0.543021i	$0.182720\pi$
$463$	9.18540	+	31.2826i	0.426882	+	1.45383i	−0.412837	+	0.910805i	$0.635462\pi$
$464$	5.24884	−	6.05748i	0.243671	−	0.281211i
$465$	−0.00948730	−	12.9578i	−0.000439963	−	0.600902i
$466$	−14.3154	−	16.5209i	−0.663149	−	0.765315i
$467$	−0.134260	+	0.0193037i	−0.00621283	+	0.000893271i	−0.145421	−	0.989370i	$-0.546454\pi$
$467$	−0.134260	+	0.0193037i	−0.00621283	+	0.000893271i	0.139208	+	0.990263i	$0.455544\pi$
$468$	1.68594	−	5.74179i	0.0779326	−	0.265414i
$469$	7.82423	−	5.02833i	0.361290	−	0.232187i
$470$	4.77234	+	10.4297i	0.220132	+	0.481088i
$471$	4.36038	−	9.54790i	0.200916	−	0.439944i
$472$	7.76317	+	3.54532i	0.357329	+	0.163187i
$473$	−0.469171	−	0.0674565i	−0.0215725	−	0.00310165i
$474$	1.67617	−	1.07721i	0.0769892	−	0.0494780i
$475$	−9.31023	+	10.7764i	−0.427183	+	0.494456i
$476$	−0.162832	−	1.13252i	−0.00746340	−	0.0519091i
$477$	4.33786	−	3.75878i	0.198617	−	0.172103i
$478$	−6.20306	+	9.65214i	−0.283721	+	0.441479i
$479$	−25.2392	+	29.1276i	−1.15321	+	1.33087i	−0.218342	+	0.975872i	$0.570065\pi$
$479$	−25.2392	+	29.1276i	−1.15321	+	1.33087i	−0.934866	+	0.355001i	$0.884481\pi$
$480$	−0.997106	+	1.15243i	−0.0455114	+	0.0526008i
$481$	−9.65064	−	21.1320i	−0.440031	−	0.963534i
$482$		−	17.2493i		−	0.785686i
$483$	0.604846	−	2.70169i	0.0275215	−	0.122931i
$484$	10.9751			0.498869
$485$	7.23205	−	11.2714i	0.328390	−	0.511809i
$486$	−14.1520	+	4.15540i	−0.641947	+	0.188493i
$487$	−3.33150	−	2.88676i	−0.150965	−	0.130811i	0.576104	−	0.817376i	$-0.304572\pi$
$487$	−3.33150	−	2.88676i	−0.150965	−	0.130811i	−0.727069	+	0.686565i	$0.759118\pi$
$488$	4.45674	−	6.93482i	0.201747	−	0.313925i
$489$	7.41505	+	8.55742i	0.335320	+	0.386980i
$490$	10.6101	−	9.20729i	0.479314	−	0.415943i
$491$	−2.94594	−	0.865007i	−0.132949	−	0.0390372i	0.214581	−	0.976706i	$-0.431161\pi$
$491$	−2.94594	−	0.865007i	−0.132949	−	0.0390372i	−0.347530	+	0.937669i	$0.612979\pi$
$492$	−1.93080	−	3.00439i	−0.0870473	−	0.135448i
$493$	−10.7163	−	1.54077i	−0.482637	−	0.0693928i
$494$	2.79250	−	6.11473i	0.125641	−	0.275115i
$495$	−0.127940	−	0.885238i	−0.00575046	−	0.0397885i
$496$	−1.21010	+	8.41642i	−0.0543350	+	0.377909i
$497$	2.53088	+	3.93812i	0.113525	+	0.176649i
$498$	1.55502	−	5.29591i	0.0696821	−	0.237315i
$499$	−2.86829	−	19.9494i	−0.128402	−	0.893056i	−0.947580	−	0.319517i	$-0.896479\pi$
$499$	−2.86829	−	19.9494i	−0.128402	−	0.893056i	0.819178	−	0.573539i	$-0.194430\pi$
$500$	7.30299	−	8.46560i	0.326600	−	0.378593i
$501$	−8.44378	−	5.42649i	−0.377240	−	0.242438i
$502$	3.37338	+	2.92305i	0.150562	+	0.130462i
$503$	−8.17978	−	27.8578i	−0.364719	−	1.24212i	−0.913737	−	0.406307i	$-0.866816\pi$
$503$	−8.17978	−	27.8578i	−0.364719	−	1.24212i	0.549018	−	0.835810i	$-0.315002\pi$
$504$	−0.892214	−	1.95368i	−0.0397424	−	0.0870236i
$505$	2.88127	−	1.85466i	0.128215	−	0.0825315i
$506$	−0.457058	+	0.602925i	−0.0203187	+	0.0268033i
$507$		−	5.06352i		−	0.224879i
$508$	−5.83410	+	2.66434i	−0.258846	+	0.118211i
$509$	−20.6803	+	6.07230i	−0.916640	+	0.269150i	−0.705833	−	0.708378i	$-0.749427\pi$
$509$	−20.6803	+	6.07230i	−0.916640	+	0.269150i	−0.210807	+	0.977528i	$0.567609\pi$
$510$	2.03768	+	0.291451i	0.0902299	+	0.0129057i
$511$	0.306453	+	0.196945i	0.0135567	+	0.00871235i
$512$	0.755750	−	0.654861i	0.0333997	−	0.0289410i
$513$	−10.6357	+	1.52919i	−0.469579	+	0.0675153i
$514$	−15.1340	−	4.44375i	−0.667533	−	0.196005i
$515$	−14.6664	−	6.68494i	−0.646279	−	0.294574i
$516$	0.291410	−	2.02680i	0.0128286	−	0.0892250i
$517$	−0.736085	−	0.336159i	−0.0323730	−	0.0147842i
$518$	−7.58440	−	3.46368i	−0.333239	−	0.152185i
$519$	1.95495	−	13.5969i	0.0858126	−	0.596839i
$520$	−2.18880	+	4.80210i	−0.0959850	+	0.210586i
$521$	−12.4496	−	3.65553i	−0.545427	−	0.160152i	−0.00260018	−	0.999997i	$-0.500828\pi$
$521$	−12.4496	−	3.65553i	−0.545427	−	0.160152i	−0.542826	+	0.839845i	$0.682646\pi$
$522$	−20.1160	+	2.89224i	−0.880453	+	0.126590i
$523$	33.2436	−	28.8058i	1.45364	−	1.25959i	0.547371	−	0.836890i	$-0.315629\pi$
$523$	33.2436	−	28.8058i	1.45364	−	1.25959i	0.906271	−	0.422698i	$-0.138917\pi$
$524$	6.57582	+	4.22603i	0.287266	+	0.184615i
$525$	−1.20291	−	2.62383i	−0.0524993	−	0.114513i
$526$	4.43458	−	1.30211i	0.193357	−	0.0567748i
$527$	10.4474	−	4.77119i	0.455098	−	0.207836i
$528$		−	0.107515i		−	0.00467898i
$529$	6.21254	+	22.1451i	0.270110	+	0.962829i
$530$	−4.25633	+	2.73978i	−0.184883	+	0.119008i
$531$	−8.98930	−	19.6838i	−0.390102	−	0.854205i
$532$	−0.679720	−	2.31491i	−0.0294696	−	0.100364i
$533$	−9.34690	−	8.09913i	−0.404859	−	0.350812i
$534$	−3.33967	−	2.14628i	−0.144522	−	0.0928785i
$535$	−6.96163	+	23.7735i	−0.300978	+	1.02782i
$536$	−1.56260	−	10.8681i	−0.0674942	−	0.469432i
$537$	0.704801	−	2.40033i	0.0304144	−	0.103582i
$538$	−6.30826	−	9.81584i	−0.271968	−	0.423191i
$539$	−0.141051	+	0.981029i	−0.00607548	+	0.0422559i
$540$	8.34892	−	1.20663i	0.359280	−	0.0519253i
$541$	11.0401	−	24.1744i	0.474650	−	1.03934i	−0.509250	−	0.860619i	$-0.670077\pi$
$541$	11.0401	−	24.1744i	0.474650	−	1.03934i	0.983900	−	0.178720i	$-0.0571956\pi$
$542$	−28.0762	−	4.03675i	−1.20598	−	0.173393i
$543$	7.05347	+	10.9754i	0.302693	+	0.471000i
$544$	−1.29603	−	0.380549i	−0.0555668	−	0.0163159i
$545$	1.46080	+	1.68336i	0.0625738	+	0.0721073i
$546$	0.892226	+	1.02968i	0.0381837	+	0.0440664i
$547$	−2.15783	+	3.35764i	−0.0922620	+	0.143562i	−0.884317	−	0.466888i	$-0.845375\pi$
$547$	−2.15783	+	3.35764i	−0.0922620	+	0.143562i	0.792055	+	0.610450i	$0.209012\pi$
$548$	7.94233	+	6.88207i	0.339280	+	0.293987i
$549$	−20.0549	+	5.88865i	−0.855923	+	0.251322i
$550$	0.00115506	+	0.788793i	4.92521e−5	+	0.0336343i
$551$	−22.8292			−0.972556
$552$	−2.60462	−	1.97448i	−0.110860	−	0.0840393i
$553$		−	2.47648i		−	0.105310i
$554$	11.6045	+	25.4103i	0.493028	+	1.07958i
$555$	9.81477	−	11.3436i	0.416614	−	0.481510i
$556$	4.54427	−	5.24437i	0.192720	−	0.222411i
$557$	16.0950	−	25.0443i	0.681968	−	1.06116i	−0.311849	−	0.950132i	$-0.600948\pi$
$557$	16.0950	−	25.0443i	0.681968	−	1.06116i	0.993817	−	0.111031i	$-0.0354153\pi$
$558$	16.2937	−	14.1185i	0.689766	−	0.597686i
$559$	−1.00917	−	7.01895i	−0.0426834	−	0.296870i
$560$	0.534958	+	1.81698i	0.0226061	+	0.0767813i
$561$	−0.122171	+	0.0785146i	−0.00515807	+	0.00331489i
$562$	3.08372	+	0.443371i	0.130079	+	0.0187025i
$563$	−30.2254	−	13.8035i	−1.27385	−	0.581747i	−0.340339	−	0.940303i	$-0.610542\pi$
$563$	−30.2254	−	13.8035i	−1.27385	−	0.581747i	−0.933508	+	0.358556i	$0.883269\pi$
$564$	1.45220	−	3.17987i	0.0611485	−	0.133896i
$565$	−25.7423	+	11.7789i	−1.08299	+	0.495542i
$566$	0.620241	−	0.398604i	0.0260707	−	0.0167546i
$567$	−1.20172	+	4.09268i	−0.0504674	+	0.171876i
$568$	5.47020	−	0.786496i	0.229524	−	0.0330006i
$569$	9.00955	+	10.3976i	0.377700	+	0.435889i	0.912492	−	0.409095i	$-0.134155\pi$
$569$	9.00955	+	10.3976i	0.377700	+	0.435889i	−0.534792	+	0.844984i	$0.679610\pi$
$570$	4.34046	−	0.00317796i	0.181802	−	0.000133110i
$571$	−27.6480	+	31.9075i	−1.15703	+	1.33529i	−0.224386	+	0.974500i	$0.572038\pi$
$571$	−27.6480	+	31.9075i	−1.15703	+	1.33529i	−0.932648	+	0.360788i	$0.882508\pi$
$572$	−0.104898	−	0.357249i	−0.00438599	−	0.0149373i
$573$	−14.5038	+	6.62368i	−0.605906	+	0.276708i
$574$	−4.43885			−0.185274
$575$	19.1303	+	14.4580i	0.797787	+	0.602939i
$576$	−2.53554			−0.105647
$577$	−11.6030	+	5.29891i	−0.483039	+	0.220597i	−0.642024	−	0.766684i	$-0.721905\pi$
$577$	−11.6030	+	5.29891i	−0.483039	+	0.220597i	0.158985	+	0.987281i	$0.449178\pi$
$578$	−4.27543	−	14.5608i	−0.177834	−	0.605648i
$579$	−3.09193	+	3.56828i	−0.128496	+	0.148293i
$580$	17.9225	−	0.0131224i	0.744192	−	0.000544876i
$581$	−4.49251	−	5.18464i	−0.186381	−	0.215095i
$582$	−4.04012	+	0.580881i	−0.167468	+	0.0240783i
$583$	0.100614	−	0.342660i	0.00416700	−	0.0141915i
$584$	0.361782	−	0.232503i	0.0149707	−	0.00962106i
$585$	12.1678	−	5.56760i	0.503075	−	0.230192i
$586$	5.62076	−	12.3078i	0.232192	−	0.508429i
$587$	10.2048	+	4.66037i	0.421197	+	0.192354i	0.614727	−	0.788740i	$-0.289266\pi$
$587$	10.2048	+	4.66037i	0.421197	+	0.192354i	−0.193530	+	0.981094i	$0.561994\pi$
$588$	−4.23802	−	0.609335i	−0.174773	−	0.0251285i
$589$	20.3739	−	13.0935i	0.839492	−	0.539509i
$590$	5.38985	+	18.3066i	0.221897	+	0.753669i
$591$	0.0942583	+	0.655581i	0.00387727	+	0.0269670i
$592$	−7.43904	+	6.44596i	−0.305743	+	0.264928i
$593$	−3.28292	+	5.10832i	−0.134813	+	0.209774i	−0.902096	−	0.431535i	$-0.857972\pi$
$593$	−3.28292	+	5.10832i	−0.134813	+	0.209774i	0.767283	+	0.641309i	$0.221608\pi$
$594$	−0.389742	+	0.449786i	−0.0159913	+	0.0184550i
$595$	1.67400	−	1.93476i	0.0686275	−	0.0793176i
$596$	−4.86908	−	10.6618i	−0.199445	−	0.436724i
$597$		−	17.7284i		−	0.725575i
$598$	−10.5810	−	4.01955i	−0.432689	−	0.164371i
$599$	34.6374			1.41524			0.707622	−	0.706591i	$-0.249768\pi$
$599$	34.6374			1.41524			0.707622	+	0.706591i	$0.249768\pi$
$600$	−3.40756	+	0.00498984i	−0.139113	+	0.000203710i
$601$	26.2051	−	7.69450i	1.06893	−	0.313865i	0.300486	−	0.953786i	$-0.402851\pi$
$601$	26.2051	−	7.69450i	1.06893	−	0.313865i	0.768441	+	0.639921i	$0.221033\pi$
$602$	−1.92342	−	1.66665i	−0.0783928	−	0.0679277i
$603$	−15.0514	+	23.4205i	−0.612942	+	0.953756i
$604$	0.654105	+	0.754877i	0.0266152	+	0.0307155i
$605$	16.0846	+	18.5352i	0.653931	+	0.753561i
$606$	−1.00206	−	0.294231i	−0.0407059	−	0.0119523i
$607$	13.7892	+	21.4564i	0.559686	+	0.870889i	0.999632	−	0.0271355i	$-0.00863857\pi$
$607$	13.7892	+	21.4564i	0.559686	+	0.870889i	−0.439945	+	0.898025i	$0.645002\pi$
$608$	−2.81925	−	0.405347i	−0.114336	−	0.0164390i
$609$	1.92215	−	4.20892i	0.0778894	−	0.170554i
$610$	18.2434	−	2.63663i	0.738652	−	0.106754i
$611$	1.72287	−	11.9829i	0.0697000	−	0.484774i
$612$	1.85162	+	2.88118i	0.0748474	+	0.116465i
$613$	7.87930	−	26.8344i	0.318242	−	1.08383i	−0.632683	−	0.774411i	$-0.718046\pi$
$613$	7.87930	−	26.8344i	0.318242	−	1.08383i	0.950925	−	0.309422i	$-0.100135\pi$
$614$	−1.99691	−	13.8888i	−0.0805888	−	0.560507i
$615$	2.24423	−	7.66389i	0.0904959	−	0.309038i
$616$	−0.112418	−	0.0722469i	−0.00452946	−	0.00291091i
$617$	12.3085	+	10.6654i	0.495523	+	0.429373i	0.866431	−	0.499296i	$-0.166408\pi$
$617$	12.3085	+	10.6654i	0.495523	+	0.429373i	−0.370908	+	0.928670i	$0.620954\pi$
$618$	1.38401	+	4.71350i	0.0556730	+	0.189605i
$619$	2.39946	+	5.25407i	0.0964423	+	0.211179i	0.951704	−	0.307017i	$-0.0993309\pi$
$619$	2.39946	+	5.25407i	0.0964423	+	0.211179i	−0.855262	+	0.518196i	$0.826604\pi$
$620$	−15.9874	+	10.2910i	−0.642070	+	0.413298i
$621$	3.73888	+	17.7020i	0.150036	+	0.710355i
$622$			22.9702i			0.921021i
$623$	−4.48833	+	2.04975i	−0.179821	+	0.0821215i
$624$	1.54330	−	0.453155i	0.0617816	−	0.0181407i
$625$	24.9999	−	0.0732170i	0.999996	−	0.00292868i
$626$	−15.6060	−	10.0294i	−0.623740	−	0.400854i
$627$	−0.231432	+	0.200537i	−0.00924249	+	0.00800866i
$628$	−15.2449	+	2.19189i	−0.608338	+	0.0874658i
$629$	12.7572	+	3.74584i	0.508661	+	0.149356i
$630$	1.99185	−	4.37001i	0.0793573	−	0.174105i
$631$	2.99534	−	20.8330i	0.119242	−	0.829349i	−0.839151	−	0.543899i	$-0.816948\pi$
$631$	2.99534	−	20.8330i	0.119242	−	0.829349i	0.958393	−	0.285451i	$-0.0921433\pi$
$632$	−2.65940	−	1.21451i	−0.105785	−	0.0483105i
$633$	−0.229846	−	0.104967i	−0.00913557	−	0.00417207i
$634$	−0.775311	+	5.39241i	−0.0307915	+	0.214160i
$635$	−13.0498	−	5.94810i	−0.517865	−	0.236043i
$636$	1.48028	+	0.434649i	0.0586969	+	0.0172350i
$637$	−14.6765	+	2.11016i	−0.581505	+	0.0836078i
$638$	−0.955621	+	0.828050i	−0.0378334	+	0.0327828i
$639$	−11.7881	−	7.57574i	−0.466330	−	0.299692i
$640$	2.21354	+	0.316605i	0.0874979	+	0.0125149i
$641$	−11.2921	+	3.31566i	−0.446011	+	0.130961i	−0.497023	−	0.867737i	$-0.665574\pi$
$641$	−11.2921	+	3.31566i	−0.446011	+	0.130961i	0.0510119	+	0.998698i	$0.483755\pi$
$642$	6.86774	−	3.13639i	0.271048	−	0.123783i
$643$			4.81021i			0.189696i	0.995492	+	0.0948481i	$0.0302365\pi$
$643$			4.81021i			0.189696i	−0.995492	+	0.0948481i	$0.969763\pi$
$644$	−3.81476	+	1.39662i	−0.150322	+	0.0550344i
$645$	3.85001	−	2.47824i	0.151594	−	0.0975805i
$646$	1.59820	+	3.49958i	0.0628805	+	0.137689i
$647$	−1.01117	−	3.44371i	−0.0397530	−	0.135386i	0.937226	−	0.348724i	$-0.113385\pi$
$647$	−1.01117	−	3.44371i	−0.0397530	−	0.135386i	−0.976979	+	0.213337i	$0.931567\pi$
$648$	3.80563	+	3.29760i	0.149499	+	0.129542i
$649$	−1.13265	−	0.727907i	−0.0444602	−	0.0285729i
$650$	−11.3177	+	3.34120i	−0.443918	+	0.131053i
$651$	0.698573	+	4.85868i	0.0273792	+	0.190427i
$652$	4.68088	−	15.9416i	0.183317	−	0.624322i
$653$	24.5693	+	38.2306i	0.961472	+	1.49608i	0.865630	+	0.500684i	$0.166918\pi$
$653$	24.5693	+	38.2306i	0.961472	+	1.49608i	0.0958421	+	0.995397i	$0.469446\pi$
$654$	0.0966751	−	0.672390i	0.00378030	−	0.0262925i
$655$	2.50014	+	17.2989i	0.0976886	+	0.675925i
$656$	−2.17689	+	4.76673i	−0.0849933	+	0.186109i
$657$	−1.07931	−	0.155182i	−0.0421080	−	0.00605422i
$658$	−2.34906	−	3.65521i	−0.0915758	−	0.142495i
$659$	47.2679	+	13.8791i	1.84130	+	0.540653i	1.00000		7.77027e-5i	$2.47335e-5\pi$
$659$	47.2679	+	13.8791i	1.84130	+	0.540653i	0.841296	+	0.540575i	$0.181793\pi$
$660$	0.181575	−	0.157568i	0.00706779	−	0.00613334i
$661$	−2.19577	−	2.53405i	−0.0854056	−	0.0985633i	0.711438	−	0.702749i	$-0.248044\pi$
$661$	−2.19577	−	2.53405i	−0.0854056	−	0.0985633i	−0.796844	+	0.604185i	$0.793499\pi$
$662$	−11.9831	+	18.6460i	−0.465735	+	0.724699i
$663$	−1.64195	−	1.42276i	−0.0637682	−	0.0552554i
$664$	−7.77080	+	2.28171i	−0.301566	+	0.0885477i
$665$	2.91334	−	4.54055i	0.112975	−	0.176075i
$666$	24.9580			0.967102
$667$	2.51039	+	38.3575i	0.0972025	+	1.48521i
$668$			14.7277i			0.569833i
$669$	8.17322	+	17.8969i	0.315995	+	0.691933i
$670$	16.0644	−	18.5668i	0.620623	−	0.717298i
$671$	−0.851631	+	0.982834i	−0.0328768	+	0.0379419i
$672$	0.312104	−	0.485644i	0.0120397	−	0.0187341i
$673$	27.4474	−	23.7833i	1.05802	−	0.916778i	0.0613312	−	0.998117i	$-0.480465\pi$
$673$	27.4474	−	23.7833i	1.05802	−	0.916778i	0.996686	+	0.0813400i	$0.0259200\pi$
$674$	−3.44012	−	23.9265i	−0.132508	−	0.921616i
$675$	14.2736	+	12.3316i	0.549390	+	0.474642i
$676$	−6.25036	+	4.01686i	−0.240398	+	0.154495i
$677$	3.27028	+	0.470196i	0.125687	+	0.0180711i	0.204871	−	0.978789i	$-0.434322\pi$
$677$	3.27028	+	0.470196i	0.125687	+	0.0180711i	−0.0791841	+	0.996860i	$0.525232\pi$
$678$	7.84841	+	3.58425i	0.301416	+	0.137652i
$679$	−2.10747	+	4.61471i	−0.0808772	+	0.177096i
$680$	−1.25671	−	2.74649i	−0.0481928	−	0.105323i
$681$	14.9607	−	9.61465i	0.573295	−	0.368434i
$682$	0.377921	−	1.28708i	0.0144714	−	0.0492849i
$683$	35.1573	−	5.05486i	1.34526	−	0.193419i	0.568222	−	0.822875i	$-0.307631\pi$
$683$	35.1573	−	5.05486i	1.34526	−	0.193419i	0.777036	+	0.629456i	$0.216722\pi$
$684$	4.72929	+	5.45789i	0.180829	+	0.208688i
$685$	0.0172055	+	23.4993i	0.000657389	+	0.897862i
$686$	−7.36791	+	8.50303i	−0.281308	+	0.324647i
$687$	−0.368694	−	1.25566i	−0.0140666	−	0.0479063i
$688$	−2.73304	+	1.24814i	−0.104196	+	0.0475848i
$689$	5.34272			0.203541
$690$	−0.482633	−	7.29247i	−0.0183735	−	0.277619i
$691$	−16.3035			−0.620215			−0.310108	−	0.950701i	$-0.600365\pi$
$691$	−16.3035			−0.620215			−0.310108	+	0.950701i	$0.600365\pi$
$692$	−18.3348	+	8.37321i	−0.696984	+	0.318302i
$693$	0.0954591	+	0.325104i	0.00362619	+	0.0123497i
$694$	−14.9091	+	17.2061i	−0.565943	+	0.653133i
$695$	15.5167	−	0.0113609i	0.588584	−	0.000430944i
$696$	−3.57715	−	4.12826i	−0.135592	−	0.156481i
$697$	7.00624	−	1.00734i	0.265380	−	0.0381559i
$698$	−9.42375	+	32.0944i	−0.356694	+	1.21479i
$699$	−12.5331	+	8.05450i	−0.474044	+	0.304649i
$700$	−2.28457	+	3.56633i	−0.0863486	+	0.134795i
$701$	−9.69080	+	21.2199i	−0.366017	+	0.801465i	0.633597	+	0.773663i	$0.281578\pi$
$701$	−9.69080	+	21.2199i	−0.366017	+	0.801465i	−0.999613	+	0.0278012i	$0.991149\pi$
$702$	−8.09907	−	3.69872i	−0.305680	−	0.139599i
$703$	27.7506	+	3.98993i	1.04663	+	0.150483i
$704$	−0.132715	+	0.0852909i	−0.00500189	+	0.00321452i
$705$	7.49853	−	2.20773i	0.282411	−	0.0831480i
$706$	−4.59457	−	31.9559i	−0.172919	−	1.20268i
$707$	−0.981005	+	0.850046i	−0.0368945	+	0.0319693i
$708$	3.14454	−	4.89300i	0.118179	−	0.183890i
$709$	−9.72912	+	11.2280i	−0.365385	+	0.421677i	−0.908437	−	0.418023i	$-0.862723\pi$
$709$	−9.72912	+	11.2280i	−0.365385	+	0.421677i	0.543052	+	0.839699i	$0.317269\pi$
$710$	9.34511	+	8.08561i	0.350716	+	0.303448i
$711$	3.07943	+	6.74301i	0.115488	+	0.252883i
$712$			5.82509i			0.218304i
$713$	−24.2400	−	32.7923i	−0.907796	−	1.22808i
$714$	−0.779766			−0.0291820
$715$	0.449601	−	0.700720i	0.0168141	−	0.0262055i
$716$	−3.52206	+	1.03417i	−0.131626	+	0.0386488i
$717$	5.90948	+	5.12059i	0.220694	+	0.191232i
$718$	−17.7516	+	27.6221i	−0.662485	+	1.03085i
$719$	2.47270	+	2.85364i	0.0922160	+	0.106423i	0.799982	−	0.600024i	$-0.204842\pi$
$719$	2.47270	+	2.85364i	0.0922160	+	0.106423i	−0.707766	+	0.706447i	$0.750297\pi$
$720$	−3.71596	−	4.28211i	−0.138486	−	0.159585i
$721$	5.85849	+	1.72021i	0.218182	+	0.0640639i
$722$	−5.88625	−	9.15918i	−0.219063	−	0.340869i
$723$	−11.6360	−	1.67300i	−0.432748	−	0.0622197i
$724$	7.95246	−	17.4135i	0.295551	−	0.647166i
$725$	26.2885	+	30.2489i	0.976331	+	1.12342i
$726$	1.06447	−	7.40356i	0.0395062	−	0.274772i
$727$	−5.14035	−	7.99854i	−0.190645	−	0.296649i	0.732752	−	0.680496i	$-0.238236\pi$
$727$	−5.14035	−	7.99854i	−0.190645	−	0.296649i	−0.923397	+	0.383846i	$0.874599\pi$
$728$	0.563233	−	1.91820i	0.0208748	−	0.0710931i
$729$	−0.719370	−	5.00333i	−0.0266433	−	0.185308i
$730$	0.922870	+	0.270245i	0.0341570	+	0.0100022i
$731$	3.41413	+	2.19413i	0.126276	+	0.0811528i
$732$	−4.24581	−	3.67902i	−0.156930	−	0.135980i
$733$	3.64380	+	12.4097i	0.134587	+	0.458361i	0.999014	−	0.0443972i	$-0.0141367\pi$
$733$	3.64380	+	12.4097i	0.134587	+	0.458361i	−0.864427	+	0.502758i	$0.832319\pi$
$734$	4.47679	+	9.80280i	0.165241	+	0.361828i
$735$	−5.18196	−	8.05032i	−0.191139	−	0.296941i
$736$	−0.371046	+	4.78146i	−0.0136769	+	0.176247i
$737$			1.73218i			0.0638056i
$738$	12.0862	−	5.51959i	0.444900	−	0.203179i
$739$	12.3471	−	3.62543i	0.454195	−	0.133364i	−0.0466302	−	0.998912i	$-0.514848\pi$
$739$	12.3471	−	3.62543i	0.454195	−	0.133364i	0.500825	+	0.865549i	$0.333030\pi$
$740$	−21.7885	−	3.11643i	−0.800960	−	0.114562i
$741$	−3.85401	−	2.47682i	−0.141581	−	0.0909883i
$742$	1.44918	−	1.25572i	0.0532010	−	0.0460989i
$743$	−40.7993	+	5.86605i	−1.49678	+	0.215204i	−0.841531	−	0.540209i	$-0.818345\pi$
$743$	−40.7993	+	5.86605i	−1.49678	+	0.215204i	−0.655249	+	0.755413i	$0.727436\pi$
$744$	5.56016	+	1.63261i	0.203845	+	0.0598544i
$745$	10.8701	−	23.8485i	0.398251	−	0.873740i
$746$	4.05720	−	28.2184i	0.148545	−	1.03315i
$747$	18.6793	+	8.53054i	0.683439	+	0.312116i
$748$	0.193835	+	0.0885216i	0.00708732	+	0.00323667i
$749$	1.33549	−	9.28852i	0.0487977	−	0.339395i
$750$	−5.00238	−	5.74750i	−0.182661	−	0.209869i
$751$	−10.7184	−	3.14721i	−0.391120	−	0.114843i	0.0802587	−	0.996774i	$-0.474425\pi$
$751$	−10.7184	−	3.14721i	−0.391120	−	0.114843i	−0.471379	+	0.881931i	$0.656244\pi$
$752$	−5.07721	+	0.729993i	−0.185147	+	0.0266201i
$753$	2.29901	−	1.99210i	0.0837805	−	0.0725962i
$754$	−15.9139	−	10.2272i	−0.579549	−	0.372454i
$755$	−0.316240	+	2.21099i	−0.0115091	+	0.0804660i
$756$	−3.06614	+	0.900301i	−0.111515	+	0.0327436i
$757$	35.8431	−	16.3690i	1.30274	−	0.594940i	0.361402	−	0.932410i	$-0.382298\pi$
$757$	35.8431	−	16.3690i	1.30274	−	0.594940i	0.941336	+	0.337470i	$0.109571\pi$
$758$		−	13.4927i		−	0.490078i
$759$	0.362389	+	0.366798i	0.0131539	+	0.0133139i
$760$	−3.44719	−	5.35530i	−0.125043	−	0.194257i
$761$	−11.2013	−	24.5275i	−0.406048	−	0.889122i	−0.996621	−	0.0821373i	$-0.973825\pi$
$761$	−11.2013	−	24.5275i	−0.406048	−	0.889122i	0.590573	−	0.806984i	$-0.298902\pi$
$762$	1.23146	+	4.19396i	0.0446110	+	0.151931i
$763$	−0.638094	−	0.552911i	−0.0231005	−	0.0200167i
$764$	19.6820	+	12.6489i	0.712070	+	0.457619i
$765$	−2.15219	+	7.34960i	−0.0778127	+	0.265725i
$766$	5.33746	+	37.1229i	0.192850	+	1.34130i
$767$	5.67473	−	19.3264i	0.204903	−	0.697835i
$768$	−0.368454	−	0.573326i	−0.0132954	−	0.0206881i
$769$	0.400659	−	2.78665i	0.0144481	−	0.100489i	−0.981321	−	0.192376i	$-0.938381\pi$
$769$	0.400659	−	2.78665i	0.0144481	−	0.100489i	0.995769	+	0.0918868i	$0.0292898\pi$
$770$	−0.0427416	−	0.295737i	−0.00154030	−	0.0106576i
$771$	−4.46549	+	9.77805i	−0.160821	+	0.352148i
$772$	6.85746	+	0.985954i	0.246806	+	0.0354853i
$773$	19.7166	+	30.6796i	0.709156	+	1.10347i	0.989635	+	0.143608i	$0.0458703\pi$
$773$	19.7166	+	30.6796i	0.709156	+	1.10347i	−0.280479	+	0.959860i	$0.590493\pi$
$774$	7.30958	+	2.14629i	0.262737	+	0.0771466i
$775$	−40.8102	−	11.9181i	−1.46595	−	0.428110i
$776$	3.92204	+	4.52627i	0.140793	+	0.162484i
$777$	−3.07212	+	4.78032i	−0.110212	+	0.171493i
$778$	5.34546	+	4.63186i	0.191644	+	0.166060i
$779$	14.3210	−	4.20502i	0.513102	−	0.150660i
$780$	3.02709	+	1.94226i	0.108387	+	0.0695442i
$781$	−0.871846			−0.0311971
$782$	5.70422	−	3.07012i	0.203983	−	0.109787i
$783$			30.2377i			1.08061i
$784$	2.60984	+	5.71475i	0.0932085	+	0.204098i
$785$	−26.0439	−	22.5338i	−0.929547	−	0.804266i
$786$	3.48856	−	4.02602i	0.124433	−	0.143603i
$787$	4.26468	−	6.63598i	0.152020	−	0.236547i	−0.756888	−	0.653544i	$-0.773281\pi$
$787$	4.26468	−	6.63598i	0.152020	−	0.236547i	0.908908	+	0.416997i	$0.136918\pi$
$788$	0.734468	−	0.636420i	0.0261643	−	0.0226715i
$789$	−0.448266	−	3.11776i	−0.0159587	−	0.110995i
$790$	−1.84638	−	6.27120i	−0.0656913	−	0.223119i
$791$	9.02162	−	5.79785i	0.320772	−	0.206148i
$792$	0.395932	+	0.0569265i	0.0140688	+	0.00202279i
$793$	−17.6974	−	8.08213i	−0.628453	−	0.287005i
$794$	−5.92639	+	12.9770i	−0.210320	+	0.460536i
$795$	1.43537	+	3.13695i	0.0509074	+	0.111256i
$796$	−21.8837	+	14.0638i	−0.775649	+	0.498479i
$797$	4.15567	−	14.1529i	0.147201	−	0.501322i	−0.852572	−	0.522610i	$-0.824958\pi$
$797$	4.15567	−	14.1529i	0.147201	−	0.501322i	0.999773	+	0.0212879i	$0.00677665\pi$
$798$	−1.62751	+	0.234001i	−0.0576133	+	0.00828354i
$799$	4.53723	+	5.23624i	0.160516	+	0.185245i
$800$	2.70936	+	4.20230i	0.0957904	+	0.148574i
$801$	9.67212	−	11.1622i	0.341748	−	0.394398i
$802$	−4.58015	−	15.5986i	−0.161731	−	0.550805i
$803$	−0.0617135	+	0.0281836i	−0.00217782	+	0.000994578i
$804$	−7.48295			−0.263903
$805$	−7.94937	−	4.39568i	−0.280179	−	0.154927i
$806$	20.0681			0.706868
$807$	−7.23337	+	3.30337i	−0.254627	+	0.116284i
$808$	0.431732	+	1.47034i	0.0151883	+	0.0517265i
$809$	17.1468	−	19.7885i	0.602850	−	0.695726i	−0.369506	−	0.929228i	$-0.620473\pi$
$809$	17.1468	−	19.7885i	0.602850	−	0.695726i	0.972356	+	0.233502i	$0.0750186\pi$
$810$	0.00824417	+	11.2599i	0.000289670	+	0.395632i
$811$	−0.182379	−	0.210476i	−0.00640418	−	0.00739082i	0.752538	−	0.658548i	$-0.228829\pi$
$811$	−0.182379	−	0.210476i	−0.00640418	−	0.00739082i	−0.758943	+	0.651157i	$0.774284\pi$
$812$	−6.72028	+	0.966230i	−0.235836	+	0.0339080i
$813$	−5.44620	+	18.5481i	−0.191007	+	0.650509i
$814$	1.30635	−	0.839540i	0.0457875	−	0.0294259i
$815$	33.7828	−	15.4580i	1.18336	−	0.541470i
$816$	−0.382411	+	0.837363i	−0.0133871	+	0.0293136i
$817$	7.78435	+	3.55499i	0.272340	+	0.124373i
$818$	35.8156	+	5.14950i	1.25226	+	0.180048i
$819$	−4.26431	+	2.74050i	−0.149007	+	0.0957610i
$820$	−11.2406	+	3.30947i	−0.392537	+	0.115572i
$821$	5.39901	+	37.5509i	0.188427	+	1.31054i	0.836083	+	0.548604i	$0.184840\pi$
$821$	5.39901	+	37.5509i	0.188427	+	1.31054i	−0.647656	+	0.761933i	$0.724251\pi$
$822$	5.41281	−	4.69022i	0.188793	−	0.163590i
$823$	21.0808	−	32.8024i	0.734832	−	1.14342i	−0.249718	−	0.968319i	$-0.580338\pi$
$823$	21.0808	−	32.8024i	0.734832	−	1.14342i	0.984550	−	0.175102i	$-0.0560256\pi$
$824$	4.72037	−	5.44760i	0.164442	−	0.189776i
$825$	0.532214	+	0.0757255i	0.0185293	+	0.00263642i
$826$	−3.00312	−	6.57591i	−0.104492	−	0.228805i
$827$			0.449302i			0.0156238i	0.999969	+	0.00781188i	$0.00248662\pi$
$827$			0.449302i			0.0156238i	−0.999969	+	0.00781188i	$0.997513\pi$
$828$	8.65026	−	8.54629i	0.300617	−	0.297004i
$829$	−23.3395			−0.810613			−0.405307	−	0.914181i	$-0.632835\pi$
$829$	−23.3395			−0.810613			−0.405307	+	0.914181i	$0.632835\pi$
$830$	−15.2419	−	9.77964i	−0.529055	−	0.339456i
$831$	18.2667	−	5.36359i	0.633665	−	0.186061i
$832$	−1.78366	−	1.54555i	−0.0618374	−	0.0535824i
$833$	4.58790	−	7.13890i	0.158961	−	0.247348i
$834$	−3.09699	−	3.57411i	−0.107240	−	0.123761i
$835$	−24.8727	+	21.5842i	−0.860755	+	0.746952i
$836$	0.431134	+	0.126592i	0.0149111	+	0.00437829i
$837$	−17.3426	−	26.9856i	−0.599448	−	0.932759i
$838$	−23.3587	−	3.35847i	−0.806912	−	0.116016i
$839$	−4.79977	+	10.5100i	−0.165707	+	0.362847i	−0.974210	−	0.225645i	$-0.927551\pi$
$839$	−4.79977	+	10.5100i	−0.165707	+	0.362847i	0.808503	+	0.588492i	$0.200278\pi$
$840$	1.27758	−	0.184643i	0.0440806	−	0.00637078i
$841$	−5.01565	+	34.8846i	−0.172954	+	1.20292i
$842$	9.96392	+	15.5042i	0.343379	+	0.534308i
$843$	0.598176	−	2.03720i	0.0206023	−	0.0701649i
$844$	0.0527652	+	0.366990i	0.00181625	+	0.0126323i
$845$	−15.9440	−	4.66891i	−0.548491	−	0.160615i
$846$	10.9412	+	7.03149i	0.376167	+	0.241748i
$847$	−7.02592	−	6.08800i	−0.241414	−	0.209186i
$848$	−0.637771	−	2.17205i	−0.0219011	−	0.0745884i
$849$	−0.208732	−	0.457060i	−0.00716368	−	0.0156863i
$850$	2.79660	−	6.14751i	0.0959226	−	0.210858i
$851$	3.65230	−	47.0651i	0.125199	−	1.61337i
$852$		−	3.76635i		−	0.129033i
$853$	−35.3051	+	16.1233i	−1.20882	+	0.552051i	−0.914862	−	0.403767i	$-0.867701\pi$
$853$	−35.3051	+	16.1233i	−1.20882	+	0.552051i	−0.293960	+	0.955818i	$0.594973\pi$
$854$	−6.69988	+	1.96726i	−0.229265	+	0.0673183i
$855$	−2.28647	+	15.9858i	−0.0781955	+	0.546703i
$856$	−9.31966	−	5.98938i	−0.318540	−	0.204713i
$857$	−23.5977	+	20.4475i	−0.806081	+	0.698473i	−0.957005	−	0.290072i	$-0.906321\pi$
$857$	−23.5977	+	20.4475i	−0.806081	+	0.698473i	0.150924	+	0.988545i	$0.451775\pi$
$858$	−0.251166	+	0.0361122i	−0.00857465	+	0.00123285i
$859$	−49.8774	−	14.6453i	−1.70179	−	0.499692i	−0.720704	−	0.693243i	$-0.756181\pi$
$859$	−49.8774	−	14.6453i	−1.70179	−	0.499692i	−0.981090	+	0.193551i	$0.937999\pi$
$860$	−6.11330	−	2.78644i	−0.208462	−	0.0950170i
$861$	−0.430522	+	2.99435i	−0.0146722	+	0.102047i
$862$	14.6931	+	6.71009i	0.500447	+	0.228547i
$863$	33.9973	+	15.5261i	1.15728	+	0.528513i	0.899169	−	0.437601i	$-0.144172\pi$
$863$	33.9973	+	15.5261i	1.15728	+	0.528513i	0.258114	+	0.966115i	$0.416899\pi$
$864$	−0.536889	+	3.73415i	−0.0182653	+	0.127038i
$865$	−41.0115	−	18.6930i	−1.39443	−	0.635583i
$866$	18.7801	+	5.51435i	0.638175	+	0.187385i
$867$	−10.2370	+	1.47186i	−0.347668	+	0.0499871i
$868$	5.44333	−	4.71668i	0.184759	−	0.160094i
$869$	0.388006	+	0.249356i	0.0131622	+	0.00845883i
$870$	1.72944	−	12.0914i	0.0586336	−	0.409936i
$871$	−24.8642	+	7.30080i	−0.842493	+	0.247378i
$872$	−0.906684	+	0.414069i	−0.0307042	+	0.0140221i
$873$		−	15.1856i		−	0.513956i
$874$	10.9844	−	8.11968i	0.371554	−	0.274652i
$875$	−9.37109	+	1.36838i	−0.316801	+	0.0462595i
$876$	−0.121752	−	0.266600i	−0.00411363	−	0.00900759i
$877$	−13.3407	−	45.4343i	−0.450484	−	1.53421i	−0.801591	−	0.597873i	$-0.796013\pi$
$877$	−13.3407	−	45.4343i	−0.450484	−	1.53421i	0.351107	−	0.936335i	$-0.385805\pi$
$878$	−5.23310	−	4.53451i	−0.176609	−	0.153032i
$879$	−7.75737	−	4.98536i	−0.261650	−	0.168152i
$880$	−0.338543	−	0.0991360i	−0.0114123	−	0.00334187i
$881$	−3.80998	−	26.4990i	−0.128361	−	0.892773i	−0.947632	−	0.319366i	$-0.896530\pi$
$881$	−3.80998	−	26.4990i	−0.128361	−	0.892773i	0.819270	−	0.573408i	$-0.194379\pi$
$882$	4.48785	−	15.2842i	0.151114	−	0.514647i
$883$	10.1837	+	15.8462i	0.342710	+	0.533267i	0.969236	−	0.246133i	$-0.0791601\pi$
$883$	10.1837	+	15.8462i	0.342710	+	0.533267i	−0.626526	+	0.779401i	$0.715524\pi$
$884$	−0.453689	+	3.15548i	−0.0152592	+	0.106130i
$885$	12.8719	−	1.86033i	0.432686	−	0.0625342i
$886$	−8.85510	+	19.3900i	−0.297493	+	0.651418i
$887$	−16.3855	−	2.35588i	−0.550172	−	0.0791027i	−0.138377	−	0.990380i	$-0.544189\pi$
$887$	−16.3855	−	2.35588i	−0.550172	−	0.0791027i	−0.411794	+	0.911277i	$0.635098\pi$
$888$	3.62679	+	5.64339i	0.121707	+	0.189380i
$889$	5.21274	+	1.53060i	0.174830	+	0.0513346i
$890$	−9.83761	+	8.53695i	−0.329757	+	0.286159i
$891$	−0.520226	−	0.600373i	−0.0174282	−	0.0201132i
$892$	15.6079	−	24.2864i	0.522592	−	0.813170i
$893$	11.0414	+	9.56740i	0.369485	+	0.320161i
$894$	−7.66445	+	2.25049i	−0.256338	+	0.0752675i
$895$	−6.90830	−	4.43255i	−0.230919	−	0.148164i
$896$	−0.847064			−0.0282984
$897$	−3.73774	+	6.74784i	−0.124799	+	0.225304i
$898$			5.17886i			0.172821i
$899$	−28.3118	−	61.9941i	−0.944250	−	2.06762i
$900$	1.78585	−	12.5513i	0.0595282	−	0.418376i
$901$	−2.00240	+	2.31089i	−0.0667095	+	0.0769868i
$902$	0.446948	−	0.695465i	0.0148817	−	0.0231564i
$903$	−1.31084	+	1.13585i	−0.0436220	+	0.0377986i
$904$	−1.80174	−	12.5314i	−0.0599249	−	0.416787i
$905$	41.0632	−	12.0899i	1.36499	−	0.401882i
$906$	0.572664	−	0.368029i	0.0190255	−	0.0122269i
$907$	−31.8222	−	4.57533i	−1.05664	−	0.151921i	−0.407971	−	0.912995i	$-0.633764\pi$
$907$	−31.8222	−	4.57533i	−1.05664	−	0.151921i	−0.648666	+	0.761073i	$0.724673\pi$
$908$	−23.7365	−	10.8401i	−0.787722	−	0.359741i
$909$	1.61410	−	3.53438i	0.0535362	−	0.117228i
$910$	4.06496	−	1.86001i	0.134752	−	0.0616586i
$911$	−25.3281	+	16.2774i	−0.839156	+	0.539293i	−0.888175	−	0.459505i	$-0.848027\pi$
$911$	−25.3281	+	16.2774i	−0.839156	+	0.539293i	0.0490190	+	0.998798i	$0.484391\pi$
$912$	−0.546875	+	1.86248i	−0.0181088	+	0.0616730i
$913$	1.26466	−	0.181831i	0.0418542	−	0.00601773i
$914$	−19.1355	−	22.0835i	−0.632945	−	0.730457i
$915$	−0.00919773	−	12.5623i	−0.000304068	−	0.415296i
$916$	−1.25749	+	1.45122i	−0.0415486	+	0.0479496i
$917$	−1.86542	−	6.35304i	−0.0616016	−	0.209796i
$918$	4.63525	−	2.11685i	0.152986	−	0.0698665i
$919$	−15.0714			−0.497158			−0.248579	−	0.968612i	$-0.579964\pi$
$919$	−15.0714			−0.497158			−0.248579	+	0.968612i	$0.579964\pi$
$920$	−8.61888	+	6.38083i	−0.284156	+	0.210370i
$921$	−9.56276			−0.315104
$922$	17.5808	−	8.02887i	0.578992	−	0.264417i
$923$	−3.67467	−	12.5148i	−0.120953	−	0.411929i
$924$	−0.0596394	+	0.0688276i	−0.00196199	+	0.00226426i
$925$	−26.6689	−	41.3644i	−0.876869	−	1.36005i
$926$	−21.3506	−	24.6399i	−0.701624	−	0.809717i
$927$	−18.0907	+	2.60105i	−0.594176	+	0.0854296i
$928$	−2.25814	+	7.69052i	−0.0741271	+	0.252454i
$929$	−16.9861	+	10.9163i	−0.557295	+	0.358152i	−0.788769	−	0.614689i	$-0.789281\pi$
$929$	−16.9861	+	10.9163i	−0.557295	+	0.358152i	0.231475	+	0.972841i	$0.425645\pi$
$930$	5.39148	+	11.7829i	0.176794	+	0.386375i
$931$	7.43344	−	16.2770i	0.243621	−	0.533456i
$932$	19.8848	+	9.08108i	0.651348	+	0.297461i
$933$	15.4952	+	2.22787i	0.507289	+	0.0729371i
$934$	0.114109	−	0.0733331i	0.00373375	−	0.00239953i
$935$	0.134577	+	0.457089i	0.00440114	+	0.0149484i
$936$	0.851639	+	5.92328i	0.0278367	+	0.193608i
$937$	23.3580	−	20.2398i	0.763072	−	0.661205i	−0.183747	−	0.982974i	$-0.558823\pi$
$937$	23.3580	−	20.2398i	0.763072	−	0.661205i	0.946818	+	0.321768i	$0.104277\pi$
$938$	−5.02833	+	7.82423i	−0.164181	+	0.255470i
$939$	−8.27919	+	9.55469i	−0.270181	+	0.311806i
$940$	−8.67375	−	7.50473i	−0.282906	−	0.244777i
$941$	18.8924	+	41.3685i	0.615873	+	1.34857i	0.918483	+	0.395460i	$0.129415\pi$
$941$	18.8924	+	41.3685i	0.615873	+	1.34857i	−0.302610	+	0.953114i	$0.597858\pi$
$942$			10.4964i			0.341993i
$943$	−8.64004	−	23.5996i	−0.281358	−	0.768509i
$944$	−8.53441			−0.277771
$945$	−6.01405	−	3.85878i	−0.195637	−	0.125526i
$946$	0.454795	−	0.133540i	0.0147867	−	0.00434176i
$947$	−40.0183	−	34.6761i	−1.30042	−	1.12682i	−0.983994	−	0.178204i	$-0.942971\pi$
$947$	−40.0183	−	34.6761i	−1.30042	−	1.12682i	−0.316427	−	0.948617i	$-0.602483\pi$
$948$	−1.07721	+	1.67617i	−0.0349862	+	0.0544396i
$949$	−0.664667	−	0.767067i	−0.0215760	−	0.0249001i
$950$	3.99219	−	13.6702i	0.129524	−	0.443519i
$951$	3.56239	+	1.04601i	0.115519	+	0.0339193i
$952$	0.618584	+	0.962535i	0.0200484	+	0.0311959i
$953$	−16.7807	−	2.41270i	−0.543581	−	0.0781551i	−0.134946	−	0.990853i	$-0.543086\pi$
$953$	−16.7807	−	2.41270i	−0.543581	−	0.0781551i	−0.408635	+	0.912698i	$0.633995\pi$
$954$	−2.38440	+	5.22112i	−0.0771980	+	0.169040i
$955$	7.48313	+	51.7772i	0.242148	+	1.67547i
$956$	1.63285	−	11.3567i	0.0528102	−	0.367303i
$957$	0.465898	+	0.724952i	0.0150604	+	0.0234344i
$958$	10.8583	−	36.9801i	0.350817	−	1.19477i
$959$	−1.26688	−	8.81137i	−0.0409098	−	0.284534i
$960$	0.428265	−	1.46250i	0.0138222	−	0.0472018i
$961$	34.7442	+	22.3287i	1.12078	+	0.720282i
$962$	17.5571	+	15.2133i	0.566062	+	0.490496i
$963$	7.91372	+	26.9517i	0.255016	+	0.868505i
$964$	7.16563	+	15.6905i	0.230790	+	0.505359i
$965$	8.38484	+	13.0261i	0.269918	+	0.419325i
$966$	0.572134	+	2.70880i	0.0184081	+	0.0871543i
$967$			40.4626i			1.30119i	0.759425	+	0.650595i	$0.225480\pi$
$967$			40.4626i			1.30119i	−0.759425	+	0.650595i	$0.774520\pi$
$968$	−9.98331	+	4.55923i	−0.320876	+	0.146539i
$969$	2.51574	−	0.738689i	0.0808173	−	0.0237301i
$970$	−1.89618	+	13.2571i	−0.0608828	+	0.425661i
$971$	47.5157	+	30.5365i	1.52485	+	0.979963i	0.990923	+	0.134434i	$0.0429215\pi$
$971$	47.5157	+	30.5365i	1.52485	+	0.979963i	0.533929	+	0.845529i	$0.320715\pi$
$972$	11.1469	−	9.65884i	0.357537	−	0.309807i
$973$	−5.81820	+	0.836531i	−0.186523	+	0.0268180i
$974$	4.22964	+	1.24193i	0.135526	+	0.0397941i
$975$	1.15619	+	7.95874i	0.0370278	+	0.254884i
$976$	−1.17316	+	8.15954i	−0.0375521	+	0.261180i
$977$	26.2860	+	12.0044i	0.840964	+	0.384055i	0.788850	−	0.614586i	$-0.210677\pi$
$977$	26.2860	+	12.0044i	0.840964	+	0.384055i	0.0521137	+	0.998641i	$0.483404\pi$
$978$	−10.2998	−	4.70378i	−0.329353	−	0.150410i
$979$	0.130781	−	0.909605i	0.00417979	−	0.0290711i
$980$	−5.82642	+	12.7828i	−0.186118	+	0.408333i
$981$	2.42495	+	0.712029i	0.0774226	+	0.0227333i
$982$	3.03906	−	0.436951i	0.0969803	−	0.0139437i
$983$	−14.2224	+	12.3238i	−0.453624	+	0.393067i	−0.851485	−	0.524378i	$-0.824298\pi$
$983$	−14.2224	+	12.3238i	−0.453624	+	0.393067i	0.397862	+	0.917445i	$0.369752\pi$
$984$	3.00439	+	1.93080i	0.0957764	+	0.0615517i
$985$	2.15121	+	0.307689i	0.0685432	+	0.00980380i
$986$	10.3879	−	3.05017i	0.330819	−	0.0971373i
$987$	−2.69355	+	1.23010i	−0.0857367	+	0.0391546i
$988$			6.72220i			0.213862i
$989$	5.11708	−	13.4701i	0.162714	−	0.428325i
$990$	0.484119	+	0.752093i	0.0153863	+	0.0239031i
$991$	10.8384	+	23.7329i	0.344295	+	0.753900i	0.999999	−	0.00111724i	$-0.000355630\pi$
$991$	10.8384	+	23.7329i	0.344295	+	0.753900i	−0.655705	+	0.755017i	$0.727628\pi$
$992$	−2.39556	−	8.15854i	−0.0760592	−	0.259034i
$993$	11.4159	+	9.89197i	0.362274	+	0.313912i
$994$	−3.93812	−	2.53088i	−0.124910	−	0.0802746i
$995$	−55.8232	−	16.3468i	−1.76971	−	0.518228i
$996$	0.785505	+	5.46331i	0.0248897	+	0.173111i
$997$	3.85370	−	13.1245i	0.122048	−	0.415657i	−0.875691	−	0.482873i	$-0.839593\pi$
$997$	3.85370	−	13.1245i	0.122048	−	0.415657i	0.997738	+	0.0672158i	$0.0214116\pi$
$998$	10.8964	+	16.9551i	0.344918	+	0.536703i
$999$	5.28474	−	36.7562i	0.167202	−	1.16291i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	230.2.j.a.119.4	yes	120
5.4	even	2	inner	230.2.j.a.119.9	yes	120
23.6	even	11	inner	230.2.j.a.29.9	yes	120
115.29	even	22	inner	230.2.j.a.29.4	✓	120

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.2.j.a.29.4	✓	120	115.29	even	22	inner
230.2.j.a.29.9	yes	120	23.6	even	11	inner
230.2.j.a.119.4	yes	120	1.1	even	1	trivial
230.2.j.a.119.9	yes	120	5.4	even	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 230 = 2 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	230.j (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.909632 + 0.415415i) q^{2} +(0.192005 + 0.653908i) q^{3} +(0.654861 - 0.755750i) q^{4} +(2.23607 - 0.00163718i) q^{5} +(-0.446297 - 0.515054i) q^{6} +(-0.838442 + 0.120550i) q^{7} +(-0.281733 + 0.959493i) q^{8} +(2.13303 - 1.37082i) q^{9} +O(q^{10})\)	\(q+(-0.909632 + 0.415415i) q^{2} +(0.192005 + 0.653908i) q^{3} +(0.654861 - 0.755750i) q^{4} +(2.23607 - 0.00163718i) q^{5} +(-0.446297 - 0.515054i) q^{6} +(-0.838442 + 0.120550i) q^{7} +(-0.281733 + 0.959493i) q^{8} +(2.13303 - 1.37082i) q^{9} +(-2.03332 + 0.930385i) q^{10} +(0.0655354 - 0.143502i) q^{11} +(0.619927 + 0.283111i) q^{12} +(2.33610 + 0.335881i) q^{13} +(0.712596 - 0.457958i) q^{14} +(0.430406 + 1.46187i) q^{15} +(-0.142315 - 0.989821i) q^{16} +(-1.02083 + 0.884550i) q^{17} +(-1.37082 + 2.13303i) q^{18} +(-1.86520 + 2.15256i) q^{19} +(1.46308 - 1.69098i) q^{20} +(-0.239813 - 0.525118i) q^{21} +0.157759i q^{22} +(3.82181 + 2.89719i) q^{23} -0.681514 q^{24} +(4.99999 - 0.00732171i) q^{25} +(-2.26452 + 0.664924i) q^{26} +(2.85110 + 2.47049i) q^{27} +(-0.457958 + 0.712596i) q^{28} +(5.24884 + 6.05748i) q^{29} +(-0.998792 - 1.15096i) q^{30} +(-8.15854 - 2.39556i) q^{31} +(0.540641 + 0.841254i) q^{32} +(0.106420 + 0.0153010i) q^{33} +(0.561120 - 1.22868i) q^{34} +(-1.87462 + 0.270930i) q^{35} +(0.360845 - 2.50973i) q^{36} +(-5.32167 - 8.28068i) q^{37} +(0.802442 - 2.73287i) q^{38} +(0.228907 + 1.59209i) q^{39} +(-0.628402 + 2.14595i) q^{40} +(-4.40840 - 2.83311i) q^{41} +(0.436284 + 0.378042i) q^{42} +(-0.846481 - 2.88285i) q^{43} +(-0.0655354 - 0.143502i) q^{44} +(4.76736 - 3.06873i) q^{45} +(-4.67998 - 1.04774i) q^{46} -5.12942i q^{47} +(0.619927 - 0.283111i) q^{48} +(-6.02800 + 1.76998i) q^{49} +(-4.54511 + 2.08373i) q^{50} +(-0.774417 - 0.497688i) q^{51} +(1.78366 - 1.54555i) q^{52} +(2.24070 - 0.322165i) q^{53} +(-3.61973 - 1.06285i) q^{54} +(0.146307 - 0.320989i) q^{55} +(0.120550 - 0.838442i) q^{56} +(-1.76570 - 0.806368i) q^{57} +(-7.29088 - 3.32963i) q^{58} +(1.21457 - 8.44754i) q^{59} +(1.38666 + 0.632040i) q^{60} +(-7.90952 - 2.32245i) q^{61} +(8.41642 - 1.21010i) q^{62} +(-1.62317 + 1.40649i) q^{63} +(-0.841254 - 0.540641i) q^{64} +(5.22423 + 0.747227i) q^{65} +(-0.103160 + 0.0302904i) q^{66} +(-9.98767 + 4.56122i) q^{67} +1.35075i q^{68} +(-1.16069 + 3.05539i) q^{69} +(1.59266 - 1.02519i) q^{70} +(-2.29577 - 5.02704i) q^{71} +(0.714344 + 2.43283i) q^{72} +(-0.325011 - 0.281624i) q^{73} +(8.28068 + 5.32167i) q^{74} +(0.964810 + 3.26813i) q^{75} +(0.405347 + 2.81925i) q^{76} +(-0.0376485 + 0.128219i) q^{77} +(-0.869598 - 1.35312i) q^{78} +(-0.416071 + 2.89384i) q^{79} +(-0.319846 - 2.21307i) q^{80} +(2.09185 - 4.58052i) q^{81} +(5.18694 + 0.745770i) q^{82} +(4.37858 + 6.81320i) q^{83} +(-0.553902 - 0.162640i) q^{84} +(-2.28119 + 1.97958i) q^{85} +(1.96756 + 2.27069i) q^{86} +(-2.95323 + 4.59532i) q^{87} +(0.119226 + 0.103310i) q^{88} +(5.58913 - 1.64112i) q^{89} +(-3.06174 + 4.77185i) q^{90} -1.99918 q^{91} +(4.69231 - 0.991076i) q^{92} -5.79489i q^{93} +(2.13084 + 4.66589i) q^{94} +(-4.16719 + 4.81631i) q^{95} +(-0.446297 + 0.515054i) q^{96} +(3.23796 - 5.03836i) q^{97} +(4.74798 - 4.11415i) q^{98} +(-0.0569265 - 0.395932i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 120 q + 12 q^{4} - 4 q^{6} + 8 q^{9}+O(q^{10}) \) 120 * q + 12 * q^4 - 4 * q^6 + 8 * q^9	\( 120 q + 12 q^{4} - 4 q^{6} + 8 q^{9} + 8 q^{11} - 6 q^{15} - 12 q^{16} - 16 q^{19} - 22 q^{20} + 4 q^{24} - 52 q^{25} - 4 q^{26} - 8 q^{29} - 44 q^{30} + 12 q^{31} + 16 q^{35} - 8 q^{36} - 36 q^{39} - 28 q^{41} - 8 q^{44} + 16 q^{45} - 4 q^{46} - 58 q^{49} + 12 q^{50} - 24 q^{51} - 6 q^{54} - 36 q^{55} + 22 q^{56} - 102 q^{59} - 38 q^{60} + 72 q^{61} + 12 q^{64} - 138 q^{65} + 80 q^{66} - 212 q^{69} - 108 q^{70} + 176 q^{71} - 88 q^{74} - 100 q^{75} + 16 q^{76} - 104 q^{79} - 22 q^{80} - 28 q^{81} - 22 q^{84} + 2 q^{85} + 62 q^{86} + 48 q^{89} + 24 q^{90} - 56 q^{91} + 24 q^{94} + 18 q^{95} - 4 q^{96} + 188 q^{99}+O(q^{100}) \) 120 * q + 12 * q^4 - 4 * q^6 + 8 * q^9 + 8 * q^11 - 6 * q^15 - 12 * q^16 - 16 * q^19 - 22 * q^20 + 4 * q^24 - 52 * q^25 - 4 * q^26 - 8 * q^29 - 44 * q^30 + 12 * q^31 + 16 * q^35 - 8 * q^36 - 36 * q^39 - 28 * q^41 - 8 * q^44 + 16 * q^45 - 4 * q^46 - 58 * q^49 + 12 * q^50 - 24 * q^51 - 6 * q^54 - 36 * q^55 + 22 * q^56 - 102 * q^59 - 38 * q^60 + 72 * q^61 + 12 * q^64 - 138 * q^65 + 80 * q^66 - 212 * q^69 - 108 * q^70 + 176 * q^71 - 88 * q^74 - 100 * q^75 + 16 * q^76 - 104 * q^79 - 22 * q^80 - 28 * q^81 - 22 * q^84 + 2 * q^85 + 62 * q^86 + 48 * q^89 + 24 * q^90 - 56 * q^91 + 24 * q^94 + 18 * q^95 - 4 * q^96 + 188 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more