LMFDB - Embedded newform 231.2.y.a.130.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [231,2,Mod(4,231)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(231, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([0, 20, 6]))

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

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

chi := DirichletCharacter("231.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 231 = 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	231.y (of order $15$, degree $8$, 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:	$1.84454428669$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$8$ over $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			130.1
Character	$\chi$	$=$	231.130
Dual form			231.2.y.a.16.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.26770 + 0.482014i) q^{2} +(0.104528 + 0.994522i) q^{3} +(3.08302 - 1.37265i) q^{4} +(-0.445594 + 0.494882i) q^{5} +(-0.716412 - 2.20489i) q^{6} +(2.34578 - 1.22364i) q^{7} +(-2.57853 + 1.87341i) q^{8} +(-0.978148 + 0.207912i) q^{9} +O(q^{10})$	\(q+(-2.26770 + 0.482014i) q^{2} +(0.104528 + 0.994522i) q^{3} +(3.08302 - 1.37265i) q^{4} +(-0.445594 + 0.494882i) q^{5} +(-0.716412 - 2.20489i) q^{6} +(2.34578 - 1.22364i) q^{7} +(-2.57853 + 1.87341i) q^{8} +(-0.978148 + 0.207912i) q^{9} +(0.771931 - 1.33702i) q^{10} +(3.22918 - 0.756589i) q^{11} +(1.68739 + 2.92265i) q^{12} +(0.731897 - 2.25255i) q^{13} +(-4.72971 + 3.90555i) q^{14} +(-0.538748 - 0.391423i) q^{15} +(0.427970 - 0.475309i) q^{16} +(-2.20729 - 0.469175i) q^{17} +(2.11793 - 0.942961i) q^{18} +(4.27152 + 1.90180i) q^{19} +(-0.694474 + 2.13737i) q^{20} +(1.46214 + 2.20503i) q^{21} +(-6.95810 + 3.27222i) q^{22} +(3.11153 + 5.38932i) q^{23} +(-2.13268 - 2.36858i) q^{24} +(0.476288 + 4.53158i) q^{25} +(-0.573961 + 5.46088i) q^{26} +(-0.309017 - 0.951057i) q^{27} +(5.55246 - 6.99245i) q^{28} +(2.47656 + 1.79933i) q^{29} +(1.41039 + 0.627945i) q^{30} +(0.825857 + 0.917207i) q^{31} +(2.44584 - 4.23631i) q^{32} +(1.08999 + 3.13240i) q^{33} +5.23162 q^{34} +(-0.439707 + 1.70613i) q^{35} +(-2.73026 + 1.98365i) q^{36} +(-0.608071 + 5.78541i) q^{37} +(-10.6032 - 2.25378i) q^{38} +(2.31671 + 0.492432i) q^{39} +(0.221859 - 2.11085i) q^{40} +(7.64687 - 5.55577i) q^{41} +(-4.37855 - 4.29556i) q^{42} -10.0978 q^{43} +(8.91707 - 6.76510i) q^{44} +(0.332965 - 0.576711i) q^{45} +(-9.65373 - 10.7216i) q^{46} +(-7.21068 - 3.21040i) q^{47} +(0.517440 + 0.375942i) q^{48} +(4.00539 - 5.74080i) q^{49} +(-3.26436 - 10.0467i) q^{50} +(0.235880 - 2.24425i) q^{51} +(-0.835503 - 7.94928i) q^{52} +(-0.497021 - 0.551997i) q^{53} +(1.15918 + 2.00776i) q^{54} +(-1.06448 + 1.93519i) q^{55} +(-3.75628 + 7.54982i) q^{56} +(-1.44489 + 4.44691i) q^{57} +(-6.48339 - 2.88659i) q^{58} +(1.40388 - 0.625048i) q^{59} +(-2.19826 - 0.467254i) q^{60} +(7.65446 - 8.50114i) q^{61} +(-2.31490 - 1.68187i) q^{62} +(-2.04011 + 1.68462i) q^{63} +(-3.89974 + 12.0022i) q^{64} +(0.788616 + 1.36592i) q^{65} +(-3.98161 - 6.57794i) q^{66} +(3.83114 - 6.63573i) q^{67} +(-7.44914 + 1.58336i) q^{68} +(-5.03456 + 3.65782i) q^{69} +(0.174741 - 4.08093i) q^{70} +(-0.166693 - 0.513029i) q^{71} +(2.13268 - 2.36858i) q^{72} +(-5.74046 + 2.55582i) q^{73} +(-1.40973 - 13.4127i) q^{74} +(-4.45697 + 0.947358i) q^{75} +15.7797 q^{76} +(6.64915 - 5.72615i) q^{77} -5.49096 q^{78} +(-2.56750 + 0.545738i) q^{79} +(0.0445210 + 0.423589i) q^{80} +(0.913545 - 0.406737i) q^{81} +(-14.6628 + 16.2847i) q^{82} +(-0.860119 - 2.64718i) q^{83} +(7.53453 + 4.79113i) q^{84} +(1.21574 - 0.883289i) q^{85} +(22.8986 - 4.86726i) q^{86} +(-1.53060 + 2.65108i) q^{87} +(-6.90912 + 8.00046i) q^{88} +(-0.887017 - 1.53636i) q^{89} +(-0.477080 + 1.46830i) q^{90} +(-1.03944 - 6.17957i) q^{91} +(16.9905 + 12.3443i) q^{92} +(-0.825857 + 0.917207i) q^{93} +(17.8991 + 3.80457i) q^{94} +(-2.84453 + 1.26647i) q^{95} +(4.46877 + 1.98962i) q^{96} +(-3.55675 + 10.9466i) q^{97} +(-6.31586 + 14.9491i) q^{98} +(-3.00131 + 1.41144i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q - 8 q^{3} + 10 q^{4} - q^{7} + 8 q^{8} + 8 q^{9}+O(q^{10}) $ 64 * q - 8 * q^3 + 10 * q^4 - q^7 + 8 * q^8 + 8 * q^9	\( 64 q - 8 q^{3} + 10 q^{4} - q^{7} + 8 q^{8} + 8 q^{9} - 22 q^{10} - 13 q^{11} + 30 q^{12} - 8 q^{13} - 26 q^{14} + 4 q^{17} - 5 q^{18} + 10 q^{19} + 24 q^{20} + 2 q^{21} - 38 q^{22} - 8 q^{23} + 14 q^{24} - 2 q^{25} + 4 q^{26} + 16 q^{27} - 67 q^{28} + 2 q^{29} - 3 q^{30} + 25 q^{31} + 72 q^{32} - 12 q^{33} - 56 q^{34} + 19 q^{35} - 20 q^{36} - 12 q^{37} - 37 q^{38} - 4 q^{39} - 9 q^{40} + 20 q^{41} + 9 q^{42} - 100 q^{43} - 5 q^{44} - 33 q^{46} - 18 q^{47} + 10 q^{48} + 29 q^{49} - 46 q^{50} + 6 q^{51} + 26 q^{52} - 49 q^{53} - 10 q^{54} - 24 q^{55} - 48 q^{56} + 20 q^{57} - 40 q^{58} + q^{59} + 12 q^{60} + 3 q^{61} + 4 q^{62} - 7 q^{63} - 24 q^{64} + 82 q^{65} + 11 q^{66} + 76 q^{67} - 39 q^{68} - 16 q^{69} + 59 q^{70} + 70 q^{71} - 14 q^{72} - 3 q^{73} + 32 q^{74} - 28 q^{75} + 104 q^{76} + 38 q^{77} - 12 q^{78} - 15 q^{79} - 83 q^{80} + 8 q^{81} + 42 q^{82} + 68 q^{83} + 27 q^{84} + 62 q^{85} - 47 q^{86} - 54 q^{87} - 64 q^{88} + 82 q^{89} - 16 q^{90} - 10 q^{91} + 190 q^{92} - 25 q^{93} - 6 q^{94} - 53 q^{95} + 8 q^{96} - 32 q^{97} - 152 q^{98} + 16 q^{99}+O(q^{100}) \) 64 * q - 8 * q^3 + 10 * q^4 - q^7 + 8 * q^8 + 8 * q^9 - 22 * q^10 - 13 * q^11 + 30 * q^12 - 8 * q^13 - 26 * q^14 + 4 * q^17 - 5 * q^18 + 10 * q^19 + 24 * q^20 + 2 * q^21 - 38 * q^22 - 8 * q^23 + 14 * q^24 - 2 * q^25 + 4 * q^26 + 16 * q^27 - 67 * q^28 + 2 * q^29 - 3 * q^30 + 25 * q^31 + 72 * q^32 - 12 * q^33 - 56 * q^34 + 19 * q^35 - 20 * q^36 - 12 * q^37 - 37 * q^38 - 4 * q^39 - 9 * q^40 + 20 * q^41 + 9 * q^42 - 100 * q^43 - 5 * q^44 - 33 * q^46 - 18 * q^47 + 10 * q^48 + 29 * q^49 - 46 * q^50 + 6 * q^51 + 26 * q^52 - 49 * q^53 - 10 * q^54 - 24 * q^55 - 48 * q^56 + 20 * q^57 - 40 * q^58 + q^59 + 12 * q^60 + 3 * q^61 + 4 * q^62 - 7 * q^63 - 24 * q^64 + 82 * q^65 + 11 * q^66 + 76 * q^67 - 39 * q^68 - 16 * q^69 + 59 * q^70 + 70 * q^71 - 14 * q^72 - 3 * q^73 + 32 * q^74 - 28 * q^75 + 104 * q^76 + 38 * q^77 - 12 * q^78 - 15 * q^79 - 83 * q^80 + 8 * q^81 + 42 * q^82 + 68 * q^83 + 27 * q^84 + 62 * q^85 - 47 * q^86 - 54 * q^87 - 64 * q^88 + 82 * q^89 - 16 * q^90 - 10 * q^91 + 190 * q^92 - 25 * q^93 - 6 * q^94 - 53 * q^95 + 8 * q^96 - 32 * q^97 - 152 * q^98 + 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/231\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$211$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{3}{5}\right)$

Coefficient data

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

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

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

$2$	−2.26770	+	0.482014i	−1.60350	+	0.340835i	−0.920853	−	0.389910i	$-0.872506\pi$
$2$	−2.26770	+	0.482014i	−1.60350	+	0.340835i	−0.682650	+	0.730745i	$0.739173\pi$
$3$	0.104528	+	0.994522i	0.0603495	+	0.574187i
$3$	0.104528	+	0.994522i	0.0603495	+	0.574187i
$4$	3.08302	−	1.37265i	1.54151	−	0.686324i
$5$	−0.445594	+	0.494882i	−0.199275	+	0.221318i	−0.834497	−	0.551012i	$-0.814242\pi$
$5$	−0.445594	+	0.494882i	−0.199275	+	0.221318i	0.635222	+	0.772330i	$0.280909\pi$
$6$	−0.716412	−	2.20489i	−0.292474	−	0.900142i
$7$	2.34578	−	1.22364i	0.886622	−	0.462494i
$7$	2.34578	−	1.22364i	0.886622	−	0.462494i
$8$	−2.57853	+	1.87341i	−0.911648	+	0.662351i
$9$	−0.978148	+	0.207912i	−0.326049	+	0.0693039i
$10$	0.771931	−	1.33702i	0.244106	−	0.422804i
$11$	3.22918	−	0.756589i	0.973633	−	0.228120i
$11$	3.22918	−	0.756589i	0.973633	−	0.228120i
$12$	1.68739	+	2.92265i	0.487108	+	0.843696i
$13$	0.731897	−	2.25255i	0.202992	−	0.624744i	−0.796798	−	0.604246i	$-0.793475\pi$
$13$	0.731897	−	2.25255i	0.202992	−	0.624744i	0.999790	−	0.0204988i	$-0.00652542\pi$
$14$	−4.72971	+	3.90555i	−1.26407	+	1.04380i
$15$	−0.538748	−	0.391423i	−0.139104	−	0.101065i
$16$	0.427970	−	0.475309i	0.106993	−	0.118827i
$17$	−2.20729	−	0.469175i	−0.535348	−	0.113792i	−0.0676985	−	0.997706i	$-0.521566\pi$
$17$	−2.20729	−	0.469175i	−0.535348	−	0.113792i	−0.467649	+	0.883914i	$0.654899\pi$
$18$	2.11793	−	0.942961i	0.499200	−	0.222258i
$19$	4.27152	+	1.90180i	0.979954	+	0.436304i	0.833262	−	0.552878i	$-0.186471\pi$
$19$	4.27152	+	1.90180i	0.979954	+	0.436304i	0.146692	+	0.989182i	$0.453137\pi$
$20$	−0.694474	+	2.13737i	−0.155289	+	0.477931i
$21$	1.46214	+	2.20503i	0.319065	+	0.481176i
$22$	−6.95810	+	3.27222i	−1.48347	+	0.697640i
$23$	3.11153	+	5.38932i	0.648798	+	1.12375i	0.983410	+	0.181396i	$0.0580615\pi$
$23$	3.11153	+	5.38932i	0.648798	+	1.12375i	−0.334612	+	0.942356i	$0.608605\pi$
$24$	−2.13268	−	2.36858i	−0.435331	−	0.483484i
$25$	0.476288	+	4.53158i	0.0952576	+	0.906315i
$26$	−0.573961	+	5.46088i	−0.112563	+	1.07097i
$27$	−0.309017	−	0.951057i	−0.0594703	−	0.183031i
$28$	5.55246	−	6.99245i	1.04932	−	1.32145i
$29$	2.47656	+	1.79933i	0.459886	+	0.334127i	0.793487	−	0.608588i	$-0.208264\pi$
$29$	2.47656	+	1.79933i	0.459886	+	0.334127i	−0.333601	+	0.942715i	$0.608264\pi$
$30$	1.41039	+	0.627945i	0.257500	+	0.114647i
$31$	0.825857	+	0.917207i	0.148328	+	0.164735i	0.812730	−	0.582640i	$-0.197980\pi$
$31$	0.825857	+	0.917207i	0.148328	+	0.164735i	−0.664402	+	0.747375i	$0.731314\pi$
$32$	2.44584	−	4.23631i	0.432367	−	0.748881i
$33$	1.08999	+	3.13240i	0.189742	+	0.545281i
$34$	5.23162			0.897216
$35$	−0.439707	+	1.70613i	−0.0743240	+	0.288389i
$36$	−2.73026	+	1.98365i	−0.455043	+	0.330608i
$37$	−0.608071	+	5.78541i	−0.0999663	+	0.951116i	0.823469	+	0.567362i	$0.192036\pi$
$37$	−0.608071	+	5.78541i	−0.0999663	+	0.951116i	−0.923435	+	0.383754i	$0.874631\pi$
$38$	−10.6032	−	2.25378i	−1.72007	−	0.365612i
$39$	2.31671	+	0.492432i	0.370971	+	0.0788523i
$40$	0.221859	−	2.11085i	0.0350790	−	0.333754i
$41$	7.64687	−	5.55577i	1.19424	−	0.867666i	0.200534	−	0.979687i	$-0.435732\pi$
$41$	7.64687	−	5.55577i	1.19424	−	0.867666i	0.993706	+	0.112021i	$0.0357323\pi$
$42$	−4.37855	−	4.29556i	−0.675624	−	0.662819i
$43$	−10.0978			−1.53989			−0.769947	−	0.638108i	$-0.779717\pi$
$43$	−10.0978			−1.53989			−0.769947	+	0.638108i	$0.779717\pi$
$44$	8.91707	−	6.76510i	1.34430	−	1.01988i
$45$	0.332965	−	0.576711i	0.0496354	−	0.0859711i
$46$	−9.65373	−	10.7216i	−1.42336	−	1.58081i
$47$	−7.21068	−	3.21040i	−1.05179	−	0.468285i	−0.193309	−	0.981138i	$-0.561922\pi$
$47$	−7.21068	−	3.21040i	−1.05179	−	0.468285i	−0.858477	+	0.512852i	$0.828589\pi$
$48$	0.517440	+	0.375942i	0.0746861	+	0.0542626i
$49$	4.00539	−	5.74080i	0.572199	−	0.820115i
$50$	−3.26436	−	10.0467i	−0.461650	−	1.42081i
$51$	0.235880	−	2.24425i	0.0330298	−	0.314257i
$52$	−0.835503	−	7.94928i	−0.115863	−	1.10237i
$53$	−0.497021	−	0.551997i	−0.0682710	−	0.0758227i	0.708042	−	0.706171i	$-0.249579\pi$
$53$	−0.497021	−	0.551997i	−0.0682710	−	0.0758227i	−0.776313	+	0.630348i	$0.782912\pi$
$54$	1.15918	+	2.00776i	0.157744	+	0.273221i
$55$	−1.06448	+	1.93519i	−0.143534	+	0.260941i
$56$	−3.75628	+	7.54982i	−0.501954	+	1.00889i
$57$	−1.44489	+	4.44691i	−0.191380	+	0.589008i
$58$	−6.48339	−	2.88659i	−0.851311	−	0.379028i
$59$	1.40388	−	0.625048i	0.182770	−	0.0813743i	−0.313312	−	0.949650i	$-0.601438\pi$
$59$	1.40388	−	0.625048i	0.182770	−	0.0813743i	0.496081	+	0.868276i	$0.334772\pi$
$60$	−2.19826	−	0.467254i	−0.283794	−	0.0603222i
$61$	7.65446	−	8.50114i	0.980053	−	1.08846i	−0.0160152	−	0.999872i	$-0.505098\pi$
$61$	7.65446	−	8.50114i	0.980053	−	1.08846i	0.996068	−	0.0885876i	$-0.0282353\pi$
$62$	−2.31490	−	1.68187i	−0.293992	−	0.213598i
$63$	−2.04011	+	1.68462i	−0.257030	+	0.212242i
$64$	−3.89974	+	12.0022i	−0.487468	+	1.50027i
$65$	0.788616	+	1.36592i	0.0978158	+	0.169422i
$66$	−3.98161	−	6.57794i	−0.490103	−	0.809689i
$67$	3.83114	−	6.63573i	0.468049	−	0.810684i	−0.531285	−	0.847193i	$-0.678291\pi$
$67$	3.83114	−	6.63573i	0.468049	−	0.810684i	0.999333	+	0.0365095i	$0.0116239\pi$
$68$	−7.44914	+	1.58336i	−0.903341	+	0.192011i
$69$	−5.03456	+	3.65782i	−0.606090	+	0.440350i
$70$	0.174741	−	4.08093i	0.0208856	−	0.487765i
$71$	−0.166693	−	0.513029i	−0.0197829	−	0.0608854i	0.940678	−	0.339301i	$-0.110191\pi$
$71$	−0.166693	−	0.513029i	−0.0197829	−	0.0608854i	−0.960461	+	0.278416i	$0.910191\pi$
$72$	2.13268	−	2.36858i	0.251339	−	0.279140i
$73$	−5.74046	+	2.55582i	−0.671871	+	0.299136i	−0.714173	−	0.699969i	$-0.753197\pi$
$73$	−5.74046	+	2.55582i	−0.671871	+	0.299136i	0.0423029	+	0.999105i	$0.486531\pi$
$74$	−1.40973	−	13.4127i	−0.163877	−	1.55919i
$75$	−4.45697	+	0.947358i	−0.514646	+	0.109391i
$76$	15.7797			1.81005
$77$	6.64915	−	5.72615i	0.757741	−	0.652556i
$78$	−5.49096			−0.621729
$79$	−2.56750	+	0.545738i	−0.288866	+	0.0614003i	−0.350066	−	0.936725i	$-0.613841\pi$
$79$	−2.56750	+	0.545738i	−0.288866	+	0.0614003i	0.0611997	+	0.998126i	$0.480507\pi$
$80$	0.0445210	+	0.423589i	0.00497760	+	0.0473587i
$81$	0.913545	−	0.406737i	0.101505	−	0.0451930i
$82$	−14.6628	+	16.2847i	−1.61924	+	1.79834i
$83$	−0.860119	−	2.64718i	−0.0944104	−	0.290565i	0.892689	−	0.450673i	$-0.148816\pi$
$83$	−0.860119	−	2.64718i	−0.0944104	−	0.290565i	−0.987100	+	0.160108i	$0.948816\pi$
$84$	7.53453	+	4.79113i	0.822085	+	0.522755i
$85$	1.21574	−	0.883289i	0.131866	−	0.0958061i
$86$	22.8986	−	4.86726i	2.46922	−	0.524850i
$87$	−1.53060	+	2.65108i	−0.164097	+	0.284225i
$88$	−6.90912	+	8.00046i	−0.736515	+	0.852852i
$89$	−0.887017	−	1.53636i	−0.0940236	−	0.162854i	0.815177	−	0.579212i	$-0.196640\pi$
$89$	−0.887017	−	1.53636i	−0.0940236	−	0.162854i	−0.909201	+	0.416358i	$0.863306\pi$
$90$	−0.477080	+	1.46830i	−0.0502886	+	0.154772i
$91$	−1.03944	−	6.17957i	−0.108963	−	0.647795i
$92$	16.9905	+	12.3443i	1.77139	+	1.28699i
$93$	−0.825857	+	0.917207i	−0.0856374	+	0.0951099i
$94$	17.8991	+	3.80457i	1.84615	+	0.392411i
$95$	−2.84453	+	1.26647i	−0.291843	+	0.129937i
$96$	4.46877	+	1.98962i	0.456091	+	0.203065i
$97$	−3.55675	+	10.9466i	−0.361134	+	1.11146i	0.591233	+	0.806501i	$0.298641\pi$
$97$	−3.55675	+	10.9466i	−0.361134	+	1.11146i	−0.952367	+	0.304954i	$0.901359\pi$
$98$	−6.31586	+	14.9491i	−0.637999	+	1.51008i
$99$	−3.00131	+	1.41144i	−0.301643	+	0.141855i
$100$	7.68866	+	13.3172i	0.768866	+	1.33172i
$101$	9.61837	+	10.6823i	0.957063	+	1.06293i	0.997965	+	0.0637632i	$0.0203102\pi$
$101$	9.61837	+	10.6823i	0.957063	+	1.06293i	−0.0409019	+	0.999163i	$0.513023\pi$
$102$	0.546853	+	5.20296i	0.0541466	+	0.515170i
$103$	0.485501	−	4.61923i	0.0478378	−	0.455147i	−0.944215	−	0.329328i	$-0.893178\pi$
$103$	0.485501	−	4.61923i	0.0478378	−	0.455147i	0.992053	−	0.125818i	$-0.0401556\pi$
$104$	2.33273	+	7.17940i	0.228743	+	0.703999i
$105$	−1.74275	−	0.258958i	−0.170075	−	0.0252717i
$106$	1.39316	+	1.01219i	0.135316	+	0.0983127i
$107$	−2.93096	−	1.30495i	−0.283347	−	0.126154i	0.260143	−	0.965570i	$-0.416230\pi$
$107$	−2.93096	−	1.30495i	−0.283347	−	0.126154i	−0.543489	+	0.839416i	$0.682897\pi$
$108$	−2.25817	−	2.50795i	−0.217293	−	0.241328i
$109$	−8.94252	+	15.4889i	−0.856538	+	1.48357i	0.0186726	+	0.999826i	$0.494056\pi$
$109$	−8.94252	+	15.4889i	−0.856538	+	1.48357i	−0.875211	+	0.483742i	$0.839277\pi$
$110$	1.48112	−	4.90152i	0.141220	−	0.467341i
$111$	−5.81728			−0.552152
$112$	0.422316	−	1.63865i	0.0399051	−	0.154838i
$113$	15.3170	−	11.1284i	1.44090	−	1.04688i	0.453048	−	0.891486i	$-0.350337\pi$
$113$	15.3170	−	11.1284i	1.44090	−	1.04688i	0.987853	−	0.155390i	$-0.0496635\pi$
$114$	1.13310	−	10.7807i	0.106124	−	1.00971i
$115$	−4.05356	−	0.861610i	−0.377996	−	0.0803455i
$116$	10.1051	+	2.14791i	0.938237	+	0.199429i
$117$	−0.247572	+	2.35549i	−0.0228881	+	0.217766i
$118$	−2.88229	+	2.09411i	−0.265337	+	0.192778i
$119$	−5.75194	+	1.60036i	−0.527279	+	0.146705i
$120$	2.12247			0.193754
$121$	9.85515	−	4.88632i	0.895922	−	0.444211i
$122$	−13.2603	+	22.9676i	−1.20053	+	2.07938i
$123$	6.32465	+	7.02424i	0.570275	+	0.633354i
$124$	3.80513	+	1.69415i	0.341711	+	0.152140i
$125$	−5.14857	−	3.74065i	−0.460502	−	0.334574i
$126$	3.81434	−	4.80357i	0.339809	−	0.427936i
$127$	−0.746289	−	2.29684i	−0.0662225	−	0.203812i	0.912470	−	0.409144i	$-0.134173\pi$
$127$	−0.746289	−	2.29684i	−0.0662225	−	0.203812i	−0.978692	+	0.205332i	$0.934173\pi$
$128$	2.03558	−	19.3673i	0.179922	−	1.71184i
$129$	−1.05550	−	10.0424i	−0.0929319	−	0.884188i
$130$	−2.44674	−	2.71737i	−0.214593	−	0.238330i
$131$	−10.2463	−	17.7472i	−0.895226	−	1.55058i	−0.833525	−	0.552482i	$-0.813681\pi$
$131$	−10.2463	−	17.7472i	−0.895226	−	1.55058i	−0.0617012	−	0.998095i	$-0.519653\pi$
$132$	7.66013	+	8.16108i	0.666728	+	0.710331i
$133$	12.3472	−	0.765602i	1.07064	−	0.0663861i
$134$	−5.48935	+	16.8945i	−0.474208	+	1.45946i
$135$	0.608356	+	0.270858i	0.0523590	+	0.0233117i
$136$	6.57053	−	2.92539i	0.563418	−	0.250850i
$137$	−2.76689	−	0.588121i	−0.236392	−	0.0502466i	0.0881923	−	0.996103i	$-0.471891\pi$
$137$	−2.76689	−	0.588121i	−0.236392	−	0.0502466i	−0.324584	+	0.945857i	$0.605224\pi$
$138$	9.65373	−	10.7216i	0.821780	−	0.912679i
$139$	−18.4609	−	13.4126i	−1.56583	−	1.13764i	−0.931015	−	0.364982i	$-0.881075\pi$
$139$	−18.4609	−	13.4126i	−1.56583	−	1.13764i	−0.634818	−	0.772662i	$-0.718925\pi$
$140$	0.986296	+	5.86360i	0.0833573	+	0.495565i
$141$	2.43909	−	7.50676i	0.205409	−	0.632183i
$142$	0.625297	+	1.08305i	0.0524738	+	0.0908872i
$143$	0.659171	−	7.82762i	0.0551226	−	0.654578i
$144$	−0.319796	+	0.553902i	−0.0266496	+	0.0461585i
$145$	−1.99399	+	0.423837i	−0.165592	+	0.0351977i
$146$	11.7857	−	8.56280i	0.975390	−	0.708663i
$147$	6.12803	+	3.38337i	0.505432	+	0.279056i
$148$	6.06664	+	18.6712i	0.498675	+	1.53476i
$149$	−14.6482	+	16.2685i	−1.20003	+	1.33277i	−0.271080	+	0.962557i	$0.587381\pi$
$149$	−14.6482	+	16.2685i	−1.20003	+	1.33277i	−0.928948	+	0.370209i	$0.879286\pi$
$150$	9.65041	−	4.29664i	0.787952	−	0.350819i
$151$	−0.612465	−	5.82722i	−0.0498417	−	0.474212i	−0.990765	−	0.135592i	$-0.956706\pi$
$151$	−0.612465	−	5.82722i	−0.0498417	−	0.474212i	0.940923	−	0.338620i	$-0.109960\pi$
$152$	−14.5771	+	3.09846i	−1.18236	+	0.251318i
$153$	2.25661			0.182436
$154$	−12.3182	+	16.1902i	−0.992626	+	1.30464i
$155$	−0.821906			−0.0660170
$156$	7.81840	−	1.66185i	0.625973	−	0.133055i
$157$	−1.20543	−	11.4689i	−0.0962035	−	0.915315i	−0.931065	−	0.364854i	$-0.881119\pi$
$157$	−1.20543	−	11.4689i	−0.0962035	−	0.915315i	0.834861	−	0.550461i	$-0.185548\pi$
$158$	5.55925	−	2.47514i	0.442270	−	0.196911i
$159$	0.497021	−	0.551997i	0.0394163	−	0.0437762i
$160$	1.00663	+	3.09807i	0.0795807	+	0.244924i
$161$	13.8936	+	8.83478i	1.09497	+	0.696278i
$162$	−1.87559	+	1.36270i	−0.147360	+	0.107064i
$163$	−14.8749	+	3.16175i	−1.16509	+	0.247647i	−0.749563	−	0.661934i	$-0.769736\pi$
$163$	−14.8749	+	3.16175i	−1.16509	+	0.247647i	−0.415527	+	0.909581i	$0.636403\pi$
$164$	15.9493	−	27.6250i	1.24543	−	2.15715i
$165$	−2.03586	−	0.856364i	−0.158491	−	0.0666678i
$166$	3.22646	+	5.58840i	0.250422	+	0.433744i
$167$	−2.83845	+	8.73585i	−0.219646	+	0.676000i	0.779145	+	0.626843i	$0.215653\pi$
$167$	−2.83845	+	8.73585i	−0.219646	+	0.676000i	−0.998791	+	0.0491567i	$0.984347\pi$
$168$	−7.90110	−	2.94653i	−0.609583	−	0.227330i
$169$	5.97892	+	4.34394i	0.459917	+	0.334149i
$170$	−2.33118	+	2.58903i	−0.178793	+	0.198570i
$171$	−4.57359	−	0.972146i	−0.349751	−	0.0743418i
$172$	−31.1316	+	13.8607i	−2.37376	+	1.05687i
$173$	−17.0767	−	7.60304i	−1.29832	−	0.578048i	−0.362978	−	0.931798i	$-0.618240\pi$
$173$	−17.0767	−	7.60304i	−1.29832	−	0.578048i	−0.935340	+	0.353749i	$0.884907\pi$
$174$	2.19308	−	6.74960i	0.166257	−	0.511686i
$175$	6.66230	+	10.0473i	0.503623	+	0.759504i
$176$	1.02238	−	1.85865i	0.0770646	−	0.140101i
$177$	0.768370	+	1.33086i	0.0577542	+	0.100033i
$178$	2.75203	+	3.05644i	0.206273	+	0.229090i
$179$	1.18598	+	11.2839i	0.0886446	+	0.843397i	0.945013	+	0.327032i	$0.106049\pi$
$179$	1.18598	+	11.2839i	0.0886446	+	0.843397i	−0.856369	+	0.516365i	$0.827285\pi$
$180$	0.234914	−	2.23505i	0.0175094	−	0.166591i
$181$	−7.29178	−	22.4418i	−0.541994	−	1.66808i	−0.728033	−	0.685543i	$-0.759565\pi$
$181$	−7.29178	−	22.4418i	−0.541994	−	1.66808i	0.186039	−	0.982542i	$-0.440435\pi$
$182$	5.33578	+	13.5124i	0.395514	+	1.00160i
$183$	9.25468	+	6.72392i	0.684125	+	0.497046i
$184$	−18.1196	−	8.06736i	−1.33579	−	0.594734i
$185$	−2.59214	−	2.87887i	−0.190578	−	0.211658i
$186$	1.43069	−	2.47802i	0.104903	−	0.181697i
$187$	−7.48271	+	0.154967i	−0.547190	+	0.0113323i
$188$	−26.6374			−1.94273
$189$	−1.88864	−	1.85285i	−0.137378	−	0.134775i
$190$	5.84008	−	4.24306i	0.423684	−	0.307824i
$191$	−1.12007	+	10.6568i	−0.0810458	+	0.771099i	0.876224	+	0.481903i	$0.160054\pi$
$191$	−1.12007	+	10.6568i	−0.0810458	+	0.771099i	−0.957270	+	0.289195i	$0.906612\pi$
$192$	−12.3441	−	2.62381i	−0.890856	−	0.189357i
$193$	21.4551	+	4.56043i	1.54437	+	0.328267i	0.899810	−	0.436283i	$-0.143705\pi$
$193$	21.4551	+	4.56043i	1.54437	+	0.328267i	0.644565	+	0.764550i	$0.277039\pi$
$194$	2.78924	−	26.5379i	0.200256	−	1.90531i
$195$	−1.27601	+	0.927074i	−0.0913768	+	0.0663891i
$196$	4.46859	−	23.1970i	0.319185	−	1.65693i
$197$	−9.48266			−0.675612			−0.337806	−	0.941216i	$-0.609685\pi$
$197$	−9.48266			−0.675612			−0.337806	+	0.941216i	$0.609685\pi$
$198$	6.12572	−	4.64739i	0.435336	−	0.330275i
$199$	−0.609238	+	1.05523i	−0.0431878	+	0.0748034i	−0.886811	−	0.462132i	$-0.847085\pi$
$199$	−0.609238	+	1.05523i	−0.0431878	+	0.0748034i	0.843624	+	0.536935i	$0.180418\pi$
$200$	−9.71763	−	10.7925i	−0.687140	−	0.763146i
$201$	6.99985	+	3.11653i	0.493731	+	0.219823i
$202$	−26.9605	−	19.5880i	−1.89694	−	1.37821i
$203$	8.01121	+	1.19040i	0.562277	+	0.0835498i
$204$	−2.35334	−	7.24283i	−0.164767	−	0.507099i
$205$	−0.657943	+	6.25991i	−0.0459527	+	0.437211i
$206$	1.12557	+	10.7090i	0.0784218	+	0.746134i
$207$	−4.16404	−	4.62463i	−0.289421	−	0.321434i
$208$	−0.757426	−	1.31190i	−0.0525180	−	0.0909639i
$209$	15.2324	+	2.90947i	1.05365	+	0.201252i
$210$	4.07684	−	0.252790i	0.281329	−	0.0174441i
$211$	4.63626	−	14.2689i	0.319173	−	0.982315i	−0.654829	−	0.755777i	$-0.727259\pi$
$211$	4.63626	−	14.2689i	0.319173	−	0.982315i	0.974002	−	0.226538i	$-0.0727406\pi$
$212$	−2.29002	−	1.01958i	−0.157279	−	0.0700253i
$213$	0.492795	−	0.219406i	0.0337657	−	0.0150335i
$214$	7.27553	+	1.54646i	0.497345	+	0.105714i
$215$	4.49950	−	4.99720i	0.306863	−	0.340806i
$216$	2.57853	+	1.87341i	0.175447	+	0.127469i
$217$	3.05962	+	1.14101i	0.207700	+	0.0774570i
$218$	12.8131	−	39.4345i	0.867810	−	2.67084i
$219$	−3.14186	−	5.44186i	−0.212307	−	0.367727i
$220$	−0.625467	+	7.42738i	−0.0421689	+	0.500754i
$221$	−2.67235	+	4.62865i	−0.179762	+	0.311357i
$222$	13.1918	−	2.80401i	0.885377	−	0.188193i
$223$	9.42019	−	6.84417i	0.630823	−	0.458320i	−0.225862	−	0.974159i	$-0.572520\pi$
$223$	9.42019	−	6.84417i	0.630823	−	0.458320i	0.856685	+	0.515840i	$0.172520\pi$
$224$	0.553662	−	12.9303i	0.0369931	−	0.863942i
$225$	−1.40805	−	4.33353i	−0.0938699	−	0.288902i
$226$	−29.3702	+	32.6189i	−1.95368	+	2.16978i
$227$	−23.1899	+	10.3248i	−1.53917	+	0.685282i	−0.988746	−	0.149604i	$-0.952200\pi$
$227$	−23.1899	+	10.3248i	−1.53917	+	0.685282i	−0.550423	+	0.834886i	$0.685533\pi$
$228$	1.64943	+	15.6932i	0.109236	+	1.03931i
$229$	6.17209	−	1.31192i	0.407863	−	0.0866940i	0.000588804	−	1.00000i	$-0.499813\pi$
$229$	6.17209	−	1.31192i	0.407863	−	0.0866940i	0.407274	+	0.913306i	$0.366479\pi$
$230$	9.60754			0.633502
$231$	6.38981	+	6.01418i	0.420419	+	0.395704i
$232$	−9.75677			−0.640563
$233$	−3.40456	+	0.723661i	−0.223040	+	0.0474086i	−0.318076	−	0.948065i	$-0.603037\pi$
$233$	−3.40456	+	0.723661i	−0.223040	+	0.0474086i	0.0950361	+	0.995474i	$0.469703\pi$
$234$	−0.573961	−	5.46088i	−0.0375210	−	0.356989i
$235$	4.80180	−	2.13790i	0.313235	−	0.139461i
$236$	3.47022	−	3.85407i	0.225892	−	0.250878i
$237$	−0.811125	−	2.49639i	−0.0526882	−	0.162158i
$238$	12.2722	−	6.40164i	0.795492	−	0.414957i
$239$	−3.28440	+	2.38626i	−0.212450	+	0.154354i	−0.688922	−	0.724836i	$-0.741916\pi$
$239$	−3.28440	+	2.38626i	−0.212450	+	0.154354i	0.476471	+	0.879190i	$0.341916\pi$
$240$	−0.416615	+	0.0885543i	−0.0268924	+	0.00571615i
$241$	7.39874	−	12.8150i	0.476595	−	0.825487i	−0.523045	−	0.852305i	$-0.675204\pi$
$241$	7.39874	−	12.8150i	0.476595	−	0.825487i	0.999640	+	0.0268181i	$0.00853748\pi$
$242$	−19.9932	+	15.8310i	−1.28521	+	1.01766i
$243$	0.500000	+	0.866025i	0.0320750	+	0.0555556i
$244$	11.9298	−	36.7160i	0.763725	−	2.35050i
$245$	1.05624	+	4.54026i	0.0674809	+	0.290067i
$246$	−17.7282	−	12.8803i	−1.13031	−	0.821216i
$247$	7.41022	−	8.22988i	0.471501	−	0.523655i
$248$	−3.84780	−	0.817876i	−0.244336	−	0.0519351i
$249$	2.54277	−	1.13211i	0.161141	−	0.0717447i
$250$	13.4784	+	6.00098i	0.852451	+	0.379535i
$251$	−5.91290	+	18.1980i	−0.373219	+	1.14865i	0.571453	+	0.820635i	$0.306380\pi$
$251$	−5.91290	+	18.1980i	−0.373219	+	1.14865i	−0.944672	+	0.328016i	$0.893620\pi$
$252$	−3.97731	+	7.99407i	−0.250547	+	0.503579i
$253$	14.1252	+	15.0489i	0.888042	+	0.946118i
$254$	2.79947	+	4.84882i	0.175654	+	0.304242i
$255$	1.00553	+	1.11675i	0.0629687	+	0.0699338i
$256$	2.08094	+	19.7988i	0.130059	+	1.23743i
$257$	−0.172266	+	1.63900i	−0.0107456	+	0.102238i	−0.998580	−	0.0532714i	$-0.983035\pi$
$257$	−0.172266	+	1.63900i	−0.0107456	+	0.102238i	0.987834	+	0.155509i	$0.0497018\pi$
$258$	7.23415	+	22.2644i	0.450379	+	1.38612i
$259$	5.65288	+	14.3154i	0.351253	+	0.889515i
$260$	4.30625	+	3.12867i	0.267062	+	0.194032i
$261$	−2.79654	−	1.24510i	−0.173102	−	0.0770699i
$262$	31.7899	+	35.3063i	1.96399	+	2.18123i
$263$	−9.05745	+	15.6880i	−0.558506	+	0.967361i	0.439115	+	0.898431i	$0.355292\pi$
$263$	−9.05745	+	15.6880i	−0.558506	+	0.967361i	−0.997621	+	0.0689303i	$0.978041\pi$
$264$	−8.67883	−	6.03500i	−0.534145	−	0.371428i
$265$	0.494643			0.0303857
$266$	−27.6306	+	7.68767i	−1.69414	+	0.471361i
$267$	1.43522	−	1.04275i	0.0878343	−	0.0638153i
$268$	2.70295	−	25.7169i	0.165109	−	1.57091i
$269$	−18.1618	−	3.86041i	−1.10735	−	0.235374i	−0.382275	−	0.924048i	$-0.624859\pi$
$269$	−18.1618	−	3.86041i	−1.10735	−	0.235374i	−0.725070	+	0.688675i	$0.758193\pi$
$270$	−1.51012	−	0.320987i	−0.0919033	−	0.0195346i
$271$	−0.0921717	+	0.876955i	−0.00559903	+	0.0532712i	−0.996965	−	0.0778554i	$-0.975193\pi$
$271$	−0.0921717	+	0.876955i	−0.00559903	+	0.0532712i	0.991366	+	0.131127i	$0.0418594\pi$
$272$	−1.16766	+	0.848354i	−0.0707997	+	0.0514390i
$273$	6.03706	−	1.67969i	0.365380	−	0.101660i
$274$	6.55796			0.396181
$275$	4.96656	+	14.2729i	0.299495	+	0.860688i
$276$	−10.5007	+	18.1878i	−0.632070	+	1.09478i
$277$	−3.53076	−	3.92131i	−0.212143	−	0.235608i	0.627677	−	0.778474i	$-0.284006\pi$
$277$	−3.53076	−	3.92131i	−0.212143	−	0.235608i	−0.839820	+	0.542866i	$0.817339\pi$
$278$	48.3288	+	21.5173i	2.89857	+	1.29052i
$279$	−0.998508	−	0.725459i	−0.0597791	−	0.0434321i
$280$	−2.06249	−	5.22306i	−0.123257	−	0.312138i
$281$	−6.41504	−	19.7435i	−0.382689	−	1.17780i	−0.938143	−	0.346248i	$-0.887455\pi$
$281$	−6.41504	−	19.7435i	−0.382689	−	1.17780i	0.555454	−	0.831547i	$-0.312545\pi$
$282$	−1.91276	+	18.1987i	−0.113903	+	1.08372i
$283$	−1.78507	−	16.9838i	−0.106112	−	1.00958i	−0.909945	−	0.414730i	$-0.863876\pi$
$283$	−1.78507	−	16.9838i	−0.106112	−	1.00958i	0.803833	−	0.594855i	$-0.202790\pi$
$284$	−1.21813	−	1.35287i	−0.0722825	−	0.0802779i
$285$	−1.55686	−	2.69657i	−0.0922206	−	0.159731i
$286$	2.27822	+	18.0684i	0.134714	+	1.06841i
$287$	11.1396	−	22.3897i	0.657550	−	1.32162i
$288$	−1.51161	+	4.65226i	−0.0890725	+	0.274137i
$289$	−10.8782	−	4.84331i	−0.639897	−	0.284900i
$290$	4.31748	−	1.92227i	0.253531	−	0.112879i
$291$	−11.2584	−	2.39304i	−0.659978	−	0.140283i
$292$	−14.1897	+	15.7593i	−0.830390	+	0.922241i
$293$	7.43882	+	5.40462i	0.434581	+	0.315741i	0.783478	−	0.621420i	$-0.213444\pi$
$293$	7.43882	+	5.40462i	0.434581	+	0.315741i	−0.348897	+	0.937161i	$0.613444\pi$
$294$	−15.5273	−	4.71866i	−0.905573	−	0.275198i
$295$	−0.316235	+	0.973273i	−0.0184119	+	0.0566661i
$296$	−9.27053	−	16.0570i	−0.538838	−	0.933296i
$297$	−1.71743	−	2.83733i	−0.0996553	−	0.164639i
$298$	25.3761	−	43.9526i	1.47000	−	2.54611i
$299$	14.4170	−	3.06443i	0.833758	−	0.177221i
$300$	−12.4405	+	9.03857i	−0.718254	+	0.521842i
$301$	−23.6871	+	12.3561i	−1.36530	+	0.712191i
$302$	4.19768	+	12.9191i	0.241550	+	0.743413i
$303$	−9.61837	+	10.6823i	−0.552561	+	0.613681i
$304$	2.73203	−	1.21638i	0.156693	−	0.0697640i
$305$	0.796281	+	7.57610i	0.0455949	+	0.433807i
$306$	−5.11730	+	1.08772i	−0.292537	+	0.0621806i
$307$	−6.01942			−0.343546			−0.171773	−	0.985137i	$-0.554950\pi$
$307$	−6.01942			−0.343546			−0.171773	+	0.985137i	$0.554950\pi$
$308$	12.6394	−	26.7808i	0.720199	−	1.52598i
$309$	4.64468			0.264227
$310$	1.86383	−	0.396170i	0.105859	−	0.0225009i
$311$	2.24963	+	21.4038i	0.127565	+	1.21370i	0.851696	+	0.524036i	$0.175574\pi$
$311$	2.24963	+	21.4038i	0.127565	+	1.21370i	−0.724131	+	0.689662i	$0.757759\pi$
$312$	−6.89624	+	3.07040i	−0.390423	+	0.173827i
$313$	−11.0332	+	12.2536i	−0.623635	+	0.692617i	−0.969339	−	0.245727i	$-0.920973\pi$
$313$	−11.0332	+	12.2536i	−0.623635	+	0.692617i	0.345704	+	0.938344i	$0.387640\pi$
$314$	8.26169	+	25.4269i	0.466234	+	1.43492i
$315$	0.0753729	−	1.76027i	0.00424678	−	0.0991800i
$316$	−7.16653	+	5.20679i	−0.403149	+	0.292905i
$317$	30.8089	−	6.54863i	1.73040	−	0.367808i	0.768213	−	0.640195i	$-0.221146\pi$
$317$	30.8089	−	6.54863i	1.73040	−	0.367808i	0.962188	+	0.272387i	$0.0878130\pi$
$318$	−0.861022	+	1.49133i	−0.0482837	+	0.0836298i
$319$	9.35860	+	3.93660i	0.523981	+	0.220408i
$320$	−4.20196	−	7.27800i	−0.234896	−	0.406853i
$321$	0.991430	−	3.05131i	0.0553362	−	0.170307i
$322$	−35.7649	−	13.3377i	−1.99310	−	0.743281i
$323$	−8.53623	−	6.20193i	−0.474968	−	0.345085i
$324$	2.25817	−	2.50795i	0.125454	−	0.139331i
$325$	10.5562	+	2.24379i	0.585552	+	0.124463i
$326$	32.2077	−	14.3398i	1.78382	−	0.794207i
$327$	−16.3388	−	7.27450i	−0.903538	−	0.402281i
$328$	−9.30942	+	28.6514i	−0.514027	+	1.58201i
$329$	−20.8431	+	1.29240i	−1.14912	+	0.0712524i
$330$	5.02949	+	0.960661i	0.276864	+	0.0528826i
$331$	2.99413	+	5.18599i	0.164572	+	0.285048i	0.936503	−	0.350659i	$-0.114042\pi$
$331$	2.99413	+	5.18599i	0.164572	+	0.285048i	−0.771931	+	0.635706i	$0.780709\pi$
$332$	−6.28540	−	6.98065i	−0.344956	−	0.383113i
$333$	−0.608071	−	5.78541i	−0.0333221	−	0.317039i
$334$	2.22594	−	21.1784i	0.121798	−	1.15883i
$335$	1.57677	+	4.85280i	0.0861482	+	0.265137i
$336$	1.67382	+	0.248716i	0.0913145	+	0.0135686i
$337$	10.0904	+	7.33111i	0.549659	+	0.399351i	0.827660	−	0.561230i	$-0.189672\pi$
$337$	10.0904	+	7.33111i	0.549659	+	0.399351i	−0.278001	+	0.960581i	$0.589672\pi$
$338$	−15.6522	−	6.96882i	−0.851368	−	0.379054i
$339$	12.6685	+	14.0698i	0.688061	+	0.764169i
$340$	2.53571	−	4.39198i	0.137518	−	0.238189i
$341$	3.36079	+	2.33699i	0.181997	+	0.126555i
$342$	10.8401			0.586165
$343$	2.37108	−	18.3679i	0.128026	−	0.991771i
$344$	26.0374	−	18.9172i	1.40384	−	1.01995i
$345$	0.433178	−	4.12141i	0.0233215	−	0.221889i
$346$	42.3896	+	9.01018i	2.27888	+	0.484390i
$347$	7.42537	+	1.57831i	0.398615	+	0.0847282i	0.402857	−	0.915263i	$-0.368017\pi$
$347$	7.42537	+	1.57831i	0.398615	+	0.0847282i	−0.00424253	+	0.999991i	$0.501350\pi$
$348$	−1.07987	+	10.2743i	−0.0578872	+	0.550760i
$349$	−22.9446	+	16.6703i	−1.22820	+	0.892338i	−0.996754	−	0.0805099i	$-0.974345\pi$
$349$	−22.9446	+	16.6703i	−1.22820	+	0.892338i	−0.231444	+	0.972848i	$0.574345\pi$
$350$	−19.9510	−	19.5729i	−1.06643	−	1.04621i
$351$	−2.36847			−0.126420
$352$	4.69289	−	15.5303i	0.250132	−	0.827767i
$353$	16.7999	−	29.0983i	0.894168	−	1.54874i	0.0593376	−	0.998238i	$-0.481101\pi$
$353$	16.7999	−	29.0983i	0.894168	−	1.54874i	0.834831	−	0.550507i	$-0.185566\pi$
$354$	−2.38392	−	2.64761i	−0.126704	−	0.140719i
$355$	0.328166	+	0.146109i	0.0174173	+	0.00775466i
$356$	−4.84357	−	3.51906i	−0.256709	−	0.186510i
$357$	−2.19283	−	5.55314i	−0.116057	−	0.293904i
$358$	−8.12844	−	25.0168i	−0.429601	−	1.32218i
$359$	2.34354	−	22.2973i	0.123687	−	1.17681i	−0.739938	−	0.672675i	$-0.765145\pi$
$359$	2.34354	−	22.2973i	0.123687	−	1.17681i	0.863626	−	0.504133i	$-0.168188\pi$
$360$	0.221859	+	2.11085i	0.0116930	+	0.111251i
$361$	1.91555	+	2.12744i	0.100819	+	0.111970i
$362$	27.3528	+	47.3764i	1.43763	+	2.49005i
$363$	5.88969	+	9.29040i	0.309129	+	0.487619i
$364$	−11.6870	−	17.6249i	−0.612565	−	0.923797i
$365$	1.29309	−	3.97971i	0.0676832	−	0.208307i
$366$	−24.2278	−	10.7869i	−1.26641	−	0.563841i
$367$	−30.2687	+	13.4765i	−1.58001	+	0.703467i	−0.994257	−	0.107020i	$-0.965869\pi$
$367$	−30.2687	+	13.4765i	−1.58001	+	0.703467i	−0.585757	+	0.810487i	$0.699203\pi$
$368$	3.89324	+	0.827533i	0.202949	+	0.0431381i
$369$	−6.32465	+	7.02424i	−0.329248	+	0.365667i
$370$	7.26584	+	5.27894i	0.377733	+	0.274439i
$371$	−1.84135	−	0.686690i	−0.0955982	−	0.0356511i
$372$	−1.28713	+	3.96138i	−0.0667345	+	0.205388i
$373$	−13.8041	−	23.9094i	−0.714749	−	1.23798i	−0.963056	−	0.269301i	$-0.913207\pi$
$373$	−13.8041	−	23.9094i	−0.714749	−	1.23798i	0.248307	−	0.968681i	$-0.420126\pi$
$374$	16.8938	−	3.95819i	0.873559	−	0.204673i
$375$	3.18199	−	5.51137i	0.164317	−	0.284606i
$376$	24.6074	−	5.23046i	1.26903	−	0.269740i
$377$	5.86566	−	4.26165i	0.302097	−	0.219486i
$378$	5.17596	+	3.29134i	0.266223	+	0.169288i
$379$	−0.606379	−	1.86624i	−0.0311476	−	0.0958625i	0.934274	−	0.356556i	$-0.116049\pi$
$379$	−0.606379	−	1.86624i	−0.0311476	−	0.0958625i	−0.965422	+	0.260693i	$0.916049\pi$
$380$	−7.03132	+	7.80907i	−0.360699	+	0.400597i
$381$	2.20625	−	0.982286i	0.113030	−	0.0503241i
$382$	−2.59673	−	24.7063i	−0.132860	−	1.26408i
$383$	−35.2819	+	7.49940i	−1.80282	+	0.383201i	−0.982135	−	0.188179i	$-0.939741\pi$
$383$	−35.2819	+	7.49940i	−1.80282	+	0.383201i	−0.820685	+	0.571380i	$0.806408\pi$
$384$	19.4739			0.993775
$385$	−0.129048	+	5.84208i	−0.00657689	+	0.297740i
$386$	−50.8519			−2.58829
$387$	9.87710	−	2.09944i	0.502081	−	0.106721i
$388$	4.06024	+	38.6306i	0.206127	+	1.96117i
$389$	−9.56993	+	4.26081i	−0.485215	+	0.216032i	−0.634739	−	0.772726i	$-0.718892\pi$
$389$	−9.56993	+	4.26081i	−0.485215	+	0.216032i	0.149524	+	0.988758i	$0.452226\pi$
$390$	2.44674	−	2.71737i	0.123895	−	0.137600i
$391$	−4.33952	−	13.3557i	−0.219459	−	0.675426i
$392$	0.426868	+	22.3066i	0.0215601	+	1.12665i
$393$	16.5789	−	12.0453i	0.836295	−	0.607604i
$394$	21.5038	−	4.57077i	1.08335	−	0.230272i
$395$	0.873984	−	1.51378i	0.0439749	−	0.0761667i
$396$	−7.31567	+	8.47123i	−0.367626	+	0.425695i
$397$	7.71571	+	13.3640i	0.387241	+	0.670720i	0.992077	−	0.125629i	$-0.0400950\pi$
$397$	7.71571	+	13.3640i	0.387241	+	0.670720i	−0.604837	+	0.796350i	$0.706762\pi$
$398$	0.872931	−	2.68661i	0.0437561	−	0.134667i
$399$	2.05204	+	12.1995i	0.102731	+	0.610740i
$400$	2.35774	+	1.71300i	0.117887	+	0.0856498i
$401$	7.67290	−	8.52162i	0.383167	−	0.425550i	−0.520450	−	0.853892i	$-0.674236\pi$
$401$	7.67290	−	8.52162i	0.383167	−	0.425550i	0.903616	+	0.428343i	$0.140902\pi$
$402$	−17.3757	−	3.69333i	−0.866623	−	0.184206i
$403$	2.67050	−	1.18898i	0.133027	−	0.0592274i
$404$	44.3166	+	19.7310i	2.20483	+	0.981655i
$405$	−0.205783	+	0.633336i	−0.0102255	+	0.0314707i
$406$	−18.7408	+	1.16204i	−0.930089	+	0.0576713i
$407$	2.41361	+	19.1422i	0.119638	+	0.948842i
$408$	3.59617	+	6.22875i	0.178037	+	0.308369i
$409$	17.4273	+	19.3550i	0.861724	+	0.957041i	0.999441	−	0.0334306i	$-0.0106433\pi$
$409$	17.4273	+	19.3550i	0.861724	+	0.957041i	−0.137717	+	0.990472i	$0.543977\pi$
$410$	−1.52535	−	14.5127i	−0.0753315	−	0.716732i
$411$	0.295681	−	2.81321i	0.0145848	−	0.138766i
$412$	−4.84377	−	14.9076i	−0.238636	−	0.734445i
$413$	2.52836	−	3.18408i	0.124413	−	0.156678i
$414$	11.6719	+	8.48014i	0.573643	+	0.416776i
$415$	1.69330	+	0.753907i	0.0831209	+	0.0370078i
$416$	−7.75240	−	8.60991i	−0.380093	−	0.422136i
$417$	11.4095	−	19.7618i	0.558724	−	0.967738i
$418$	−35.9448	+	0.744417i	−1.75812	+	0.0364106i
$419$	−10.3958			−0.507868			−0.253934	−	0.967222i	$-0.581725\pi$
$419$	−10.3958			−0.507868			−0.253934	+	0.967222i	$0.581725\pi$
$420$	−5.72838	+	1.59381i	−0.279516	+	0.0777698i
$421$	−19.0189	+	13.8181i	−0.926926	+	0.673451i	−0.945238	−	0.326381i	$-0.894171\pi$
$421$	−19.0189	+	13.8181i	−0.926926	+	0.673451i	0.0183120	+	0.999832i	$0.494171\pi$
$422$	−3.63580	+	34.5924i	−0.176988	+	1.68393i
$423$	7.72059	+	1.64106i	0.375388	+	0.0797912i
$424$	2.31570	+	0.492217i	0.112460	+	0.0239042i
$425$	1.07479	−	10.2260i	0.0521352	−	0.496033i
$426$	−1.01175	+	0.735081i	−0.0490195	+	0.0356148i
$427$	7.55333	−	29.3082i	0.365531	−	1.41832i
$428$	−10.8274			−0.523364
$429$	7.85364	−	0.162649i	0.379177	−	0.00785276i
$430$	−7.79477	+	13.5009i	−0.375897	+	0.651073i
$431$	14.0767	+	15.6338i	0.678052	+	0.753053i	0.979722	−	0.200359i	$-0.0642109\pi$
$431$	14.0767	+	15.6338i	0.678052	+	0.753053i	−0.301671	+	0.953412i	$0.597544\pi$
$432$	−0.584296	−	0.260145i	−0.0281119	−	0.0125162i
$433$	25.6199	+	18.6140i	1.23121	+	0.894530i	0.996981	−	0.0776503i	$-0.0247418\pi$
$433$	25.6199	+	18.6140i	1.23121	+	0.894530i	0.234234	+	0.972180i	$0.424742\pi$
$434$	−7.48826	−	1.11270i	−0.359448	−	0.0534111i
$435$	−0.629944	−	1.93877i	−0.0302035	−	0.0929568i
$436$	−6.30914	+	60.0275i	−0.302153	+	2.87479i
$437$	3.04152	+	28.9381i	0.145496	+	1.38430i
$438$	9.74784	+	10.8261i	0.465770	+	0.517290i
$439$	3.65718	+	6.33442i	0.174548	+	0.302326i	0.940005	−	0.341162i	$-0.110820\pi$
$439$	3.65718	+	6.33442i	0.174548	+	0.302326i	−0.765457	+	0.643487i	$0.777487\pi$
$440$	−0.880622	−	6.98415i	−0.0419820	−	0.332956i
$441$	−2.72428	+	6.44812i	−0.129728	+	0.307053i
$442$	3.82901	−	11.7845i	0.182127	−	0.560531i
$443$	3.97024	+	1.76766i	0.188632	+	0.0839842i	0.498879	−	0.866672i	$-0.333745\pi$
$443$	3.97024	+	1.76766i	0.188632	+	0.0839842i	−0.310247	+	0.950656i	$0.600412\pi$
$444$	−17.9348	+	7.98508i	−0.851147	+	0.378955i
$445$	1.15557	+	0.245623i	0.0547790	+	0.0116436i
$446$	−18.0632	+	20.0612i	−0.855315	+	0.949924i
$447$	−17.7105	−	12.8674i	−0.837679	−	0.608609i
$448$	5.53844	+	32.9264i	0.261667	+	1.55563i
$449$	−4.30506	+	13.2496i	−0.203168	+	0.625288i	0.796615	+	0.604487i	$0.206622\pi$
$449$	−4.30506	+	13.2496i	−0.203168	+	0.625288i	−0.999784	+	0.0208012i	$0.993378\pi$
$450$	5.28184	+	9.14842i	0.248988	+	0.431261i
$451$	20.4896	−	23.7261i	0.964819	−	1.11722i
$452$	31.9471	−	55.3340i	1.50267	−	2.60269i
$453$	5.73128	−	1.21822i	0.269279	−	0.0572370i
$454$	47.6110	−	34.5914i	2.23449	−	1.62345i
$455$	3.52133	+	2.23917i	0.165082	+	0.104974i
$456$	−4.60521	−	14.1734i	−0.215659	−	0.663729i
$457$	−0.935580	+	1.03907i	−0.0437646	+	0.0486055i	−0.764630	−	0.644470i	$-0.777078\pi$
$457$	−0.935580	+	1.03907i	−0.0437646	+	0.0486055i	0.720865	+	0.693075i	$0.243745\pi$
$458$	−13.3641	+	5.95006i	−0.624462	+	0.278028i
$459$	0.235880	+	2.24425i	0.0110099	+	0.104752i
$460$	−13.6799	+	2.90775i	−0.637827	+	0.135574i
$461$	3.24931			0.151335			0.0756677	−	0.997133i	$-0.475891\pi$
$461$	3.24931			0.151335			0.0756677	+	0.997133i	$0.475891\pi$
$462$	−17.3891	−	10.5583i	−0.809012	−	0.491219i
$463$	−2.27361			−0.105664			−0.0528318	−	0.998603i	$-0.516825\pi$
$463$	−2.27361			−0.105664			−0.0528318	+	0.998603i	$0.516825\pi$
$464$	1.91513	−	0.407074i	0.0889077	−	0.0188979i
$465$	−0.0859125	−	0.817403i	−0.00398410	−	0.0379062i
$466$	7.37168	−	3.28208i	0.341487	−	0.152040i
$467$	10.9302	−	12.1392i	0.505788	−	0.561735i	−0.435130	−	0.900367i	$-0.643298\pi$
$467$	10.9302	−	12.1392i	0.505788	−	0.561735i	0.940919	+	0.338633i	$0.109964\pi$
$468$	2.46999	+	7.60186i	0.114175	+	0.351396i
$469$	0.867253	−	20.2539i	0.0400460	−	0.935240i
$470$	−9.85853	+	7.16264i	−0.454740	+	0.330388i
$471$	11.2800	−	2.39765i	0.519757	−	0.110478i
$472$	−2.44898	+	4.24175i	−0.112723	+	0.195242i
$473$	−32.6074	+	7.63985i	−1.49929	+	0.351281i
$474$	3.04268	+	5.27007i	0.139755	+	0.242062i
$475$	−6.58370	+	20.2625i	−0.302081	+	0.929709i
$476$	−15.5366	+	12.8293i	−0.712118	+	0.588031i
$477$	0.600926	+	0.436599i	0.0275145	+	0.0199905i
$478$	6.29782	−	6.99444i	0.288056	−	0.319918i
$479$	−9.29740	−	1.97622i	−0.424809	−	0.0902959i	−0.00945387	−	0.999955i	$-0.503009\pi$
$479$	−9.29740	−	1.97622i	−0.424809	−	0.0902959i	−0.415355	+	0.909659i	$0.636343\pi$
$480$	−2.97588	+	1.32495i	−0.135830	+	0.0604753i
$481$	12.5869	+	5.60404i	0.573912	+	0.255522i
$482$	−10.6011	+	32.6268i	−0.482867	+	1.48611i
$483$	−7.33411	+	14.7410i	−0.333714	+	0.670737i
$484$	23.6764	−	28.5922i	1.07620	−	1.29965i
$485$	−3.83239	−	6.63789i	−0.174020	−	0.301411i
$486$	−1.55128	−	1.72288i	−0.0703677	−	0.0781512i
$487$	−1.76711	−	16.8129i	−0.0800753	−	0.761865i	−0.958713	−	0.284376i	$-0.908214\pi$
$487$	−1.76711	−	16.8129i	−0.0800753	−	0.761865i	0.878638	−	0.477489i	$-0.158453\pi$
$488$	−3.81112	+	36.2604i	−0.172521	+	1.64143i
$489$	−4.69928	−	14.4629i	−0.212509	−	0.654034i
$490$	−4.58371	−	9.78681i	−0.207071	−	0.442123i
$491$	−10.1961	−	7.40787i	−0.460142	−	0.334313i	0.333445	−	0.942770i	$-0.391789\pi$
$491$	−10.1961	−	7.40787i	−0.460142	−	0.334313i	−0.793587	+	0.608457i	$0.791789\pi$
$492$	29.1408	+	12.9743i	1.31377	+	0.584928i
$493$	−4.62230	−	5.13359i	−0.208178	−	0.231205i
$494$	−12.8372	+	22.2347i	−0.577573	+	1.00039i
$495$	0.638867	−	2.11422i	0.0287149	−	0.0950271i
$496$	0.789399			0.0354451
$497$	−1.01879	−	0.999482i	−0.0456990	−	0.0448329i
$498$	−5.22053	+	3.79294i	−0.233937	+	0.169966i
$499$	−0.814083	+	7.74548i	−0.0364434	+	0.346735i	0.961073	+	0.276296i	$0.0891069\pi$
$499$	−0.814083	+	7.74548i	−0.0364434	+	0.346735i	−0.997516	+	0.0704397i	$0.977560\pi$
$500$	−21.0077	−	4.46533i	−0.939493	−	0.199695i
$501$	−8.98469	−	1.90975i	−0.401406	−	0.0853215i
$502$	4.63696	−	44.1177i	0.206958	−	1.96907i
$503$	20.3473	−	14.7831i	0.907239	−	0.659148i	−0.0330759	−	0.999453i	$-0.510530\pi$
$503$	20.3473	−	14.7831i	0.907239	−	0.659148i	0.940315	+	0.340305i	$0.110530\pi$
$504$	2.10450	−	8.16581i	0.0937420	−	0.363734i
$505$	−9.57235			−0.425964
$506$	−39.2854	−	27.3179i	−1.74645	−	1.21443i
$507$	−3.69518	+	6.40024i	−0.164109	+	0.284244i
$508$	−5.45358	−	6.05681i	−0.241963	−	0.268728i
$509$	−0.332923	−	0.148227i	−0.0147566	−	0.00657005i	0.399345	−	0.916801i	$-0.369238\pi$
$509$	−0.332923	−	0.148227i	−0.0147566	−	0.00657005i	−0.414102	+	0.910231i	$0.635904\pi$
$510$	−2.81853	−	2.04778i	−0.124806	−	0.0906772i
$511$	−10.3385	+	13.0197i	−0.457347	+	0.575957i
$512$	−2.22669	−	6.85306i	−0.0984069	−	0.302865i
$513$	0.488750	−	4.65015i	0.0215788	−	0.205309i
$514$	−0.399373	−	3.79978i	−0.0176156	−	0.167601i
$515$	2.06964	+	2.29857i	0.0911992	+	0.101287i
$516$	−17.0389	−	29.5122i	−0.750094	−	1.29920i
$517$	−25.7135	−	4.91143i	−1.13088	−	0.216004i
$518$	−19.7192	−	29.7382i	−0.866413	−	1.30662i
$519$	5.77639	−	17.7779i	0.253555	−	0.780363i
$520$	−4.59241	−	2.04467i	−0.201390	−	0.0896647i
$521$	37.7772	−	16.8195i	1.65505	−	0.736876i	0.655223	−	0.755436i	$-0.272575\pi$
$521$	37.7772	−	16.8195i	1.65505	−	0.736876i	0.999828	+	0.0185595i	$0.00590801\pi$
$522$	6.94187	+	1.47554i	0.303837	+	0.0645826i
$523$	20.9579	−	23.2761i	0.916425	−	1.01779i	−0.0833484	−	0.996520i	$-0.526561\pi$
$523$	20.9579	−	23.2761i	0.916425	−	1.01779i	0.999774	−	0.0212730i	$-0.00677191\pi$
$524$	−55.9502	−	40.6502i	−2.44420	−	1.77581i
$525$	−9.29585	+	7.67604i	−0.405704	+	0.335010i
$526$	12.9777	−	39.9413i	0.565856	−	1.74153i
$527$	−1.39258	−	2.41202i	−0.0606617	−	0.105069i
$528$	1.95534	+	0.822494i	0.0850952	+	0.0357945i
$529$	−7.86321	+	13.6195i	−0.341879	+	0.592151i
$530$	−1.12170	+	0.238425i	−0.0487235	+	0.0103565i
$531$	−1.24325	+	0.903273i	−0.0539524	+	0.0391987i
$532$	37.0157	−	19.3087i	1.60483	−	0.837139i
$533$	−6.91793	−	21.2912i	−0.299649	−	0.922224i
$534$	−2.75203	+	3.05644i	−0.119092	+	0.132265i
$535$	1.95181	−	0.869002i	0.0843842	−	0.0375702i
$536$	2.55274	+	24.2877i	0.110262	+	1.04907i
$537$	−11.0981	+	2.35897i	−0.478918	+	0.101797i
$538$	43.0463			1.85586
$539$	8.59068	−	21.5685i	0.370027	−	0.929021i
$540$	2.24737			0.0967112
$541$	−11.6042	+	2.46654i	−0.498902	+	0.106045i	−0.450488	−	0.892782i	$-0.648750\pi$
$541$	−11.6042	+	2.46654i	−0.498902	+	0.106045i	−0.0484139	+	0.998827i	$0.515417\pi$
$542$	−0.213687	−	2.03310i	−0.00917864	−	0.0873289i
$543$	21.5567	−	9.59764i	0.925084	−	0.411874i
$544$	−7.38625	+	8.20327i	−0.316683	+	0.351712i
$545$	−3.68044	−	11.3272i	−0.157653	−	0.485206i
$546$	−12.8806	+	6.71898i	−0.551239	+	0.287546i
$547$	28.4903	−	20.6994i	1.21816	−	0.885044i	0.222212	−	0.974998i	$-0.428672\pi$
$547$	28.4903	−	20.6994i	1.21816	−	0.885044i	0.995946	+	0.0899548i	$0.0286723\pi$
$548$	−9.33767	+	1.98478i	−0.398885	+	0.0847857i
$549$	−5.71971	+	9.90682i	−0.244111	+	0.422813i
$550$	−18.1424	−	29.9727i	−0.773594	−	1.27804i
$551$	7.15672	+	12.3958i	0.304886	+	0.528079i
$552$	6.12915	−	18.8636i	0.260874	−	0.802888i
$553$	−5.35500	+	4.42188i	−0.227718	+	0.188038i
$554$	9.89681	+	7.19046i	0.420475	+	0.305493i
$555$	2.59214	−	2.87887i	0.110030	−	0.122201i
$556$	−75.3260	−	16.0110i	−3.19454	−	0.679020i
$557$	−10.9234	+	4.86343i	−0.462841	+	0.206070i	−0.624890	−	0.780713i	$-0.714856\pi$
$557$	−10.9234	+	4.86343i	−0.462841	+	0.206070i	0.162049	+	0.986783i	$0.448190\pi$
$558$	2.61399	+	1.16382i	0.110659	+	0.0492686i
$559$	−7.39052	+	22.7457i	−0.312586	+	0.962040i
$560$	0.622759	+	0.939170i	0.0263164	+	0.0396872i
$561$	−0.936275	−	7.42553i	−0.0395296	−	0.313506i
$562$	24.0640	+	41.6800i	1.01508	+	1.75817i
$563$	2.19085	+	2.43319i	0.0923334	+	0.102547i	0.787541	−	0.616263i	$-0.211354\pi$
$563$	2.19085	+	2.43319i	0.0923334	+	0.102547i	−0.695207	+	0.718809i	$0.744687\pi$
$564$	−2.78437	−	26.4915i	−0.117243	−	1.11549i
$565$	−1.31789	+	12.5389i	−0.0554440	+	0.527514i
$566$	12.2344	+	37.6538i	0.514252	+	1.58271i
$567$	1.64528	−	2.07197i	0.0690952	−	0.0870146i
$568$	1.39094	+	1.01058i	0.0583625	+	0.0424028i
$569$	−30.7793	−	13.7038i	−1.29034	−	0.574495i	−0.357204	−	0.934026i	$-0.616270\pi$
$569$	−30.7793	−	13.7038i	−1.29034	−	0.574495i	−0.933133	+	0.359531i	$0.882937\pi$
$570$	4.83027	+	5.36456i	0.202318	+	0.224697i
$571$	−1.94633	+	3.37114i	−0.0814514	+	0.141078i	−0.903874	−	0.427800i	$-0.859289\pi$
$571$	−1.94633	+	3.37114i	−0.0814514	+	0.141078i	0.822422	+	0.568878i	$0.192622\pi$
$572$	−8.71233	−	25.0375i	−0.364281	−	1.04687i
$573$	−10.7155			−0.447646
$574$	−14.4691	+	56.1424i	−0.603928	+	2.34334i
$575$	−22.9402	+	16.6670i	−0.956671	+	0.695062i
$576$	1.31913	−	12.5507i	0.0549638	−	0.522946i
$577$	13.1974	+	2.80519i	0.549414	+	0.116781i	0.474251	−	0.880390i	$-0.342719\pi$
$577$	13.1974	+	2.80519i	0.549414	+	0.116781i	0.0751628	+	0.997171i	$0.476052\pi$
$578$	27.0031	+	5.73969i	1.12318	+	0.238739i
$579$	−2.29278	+	21.8143i	−0.0952845	+	0.906571i
$580$	−5.56574	+	4.04375i	−0.231105	+	0.167907i
$581$	−5.25685	−	5.15722i	−0.218091	−	0.213957i
$582$	26.6841			1.10609
$583$	−2.02260	−	1.40646i	−0.0837676	−	0.0582495i
$584$	10.0139	−	17.3445i	0.414376	−	0.717721i
$585$	−1.05537	−	1.17211i	−0.0436344	−	0.0484609i
$586$	−19.4741	−	8.67042i	−0.804467	−	0.358172i
$587$	19.2994	+	14.0219i	0.796573	+	0.578744i	0.909907	−	0.414813i	$-0.136153\pi$
$587$	19.2994	+	14.0219i	0.796573	+	0.578744i	−0.113334	+	0.993557i	$0.536153\pi$
$588$	23.5370	+	2.01936i	0.970650	+	0.0832772i
$589$	1.78332	+	5.48849i	0.0734803	+	0.226149i
$590$	0.247995	−	2.35952i	0.0102098	−	0.0971397i
$591$	−0.991208	−	9.43072i	−0.0407729	−	0.387928i
$592$	2.48962	+	2.76501i	0.102323	+	0.113641i
$593$	9.26394	+	16.0456i	0.380424	+	0.658914i	0.991123	−	0.132949i	$-0.0424446\pi$
$593$	9.26394	+	16.0456i	0.380424	+	0.658914i	−0.610698	+	0.791863i	$0.709111\pi$
$594$	5.26224	+	5.60638i	0.215912	+	0.230032i
$595$	1.77104	−	3.55964i	0.0726054	−	0.145931i
$596$	−22.8298	+	70.2628i	−0.935144	+	2.87808i
$597$	−1.11313	−	0.495599i	−0.0455575	−	0.0202835i
$598$	−31.2163	+	13.8984i	−1.27653	+	0.568348i
$599$	10.3020	+	2.18977i	0.420930	+	0.0894714i	0.413507	−	0.910501i	$-0.364304\pi$
$599$	10.3020	+	2.18977i	0.420930	+	0.0894714i	0.00742304	+	0.999972i	$0.497637\pi$
$600$	9.71763	−	10.7925i	0.396721	−	0.440603i
$601$	30.7873	+	22.3682i	1.25584	+	0.912420i	0.998546	−	0.0539137i	$-0.0171696\pi$
$601$	30.7873	+	22.3682i	1.25584	+	0.912420i	0.257293	+	0.966334i	$0.417170\pi$
$602$	47.7594	−	39.4373i	1.94653	−	1.60734i
$603$	−2.36778	+	7.28727i	−0.0964233	+	0.296760i
$604$	−9.88696	−	17.1247i	−0.402295	−	0.696795i
$605$	−1.97324	+	7.05444i	−0.0802236	+	0.286804i
$606$	16.6625	−	28.8603i	0.676869	−	1.17237i
$607$	2.13823	−	0.454495i	0.0867882	−	0.0184474i	−0.164313	−	0.986408i	$-0.552541\pi$
$607$	2.13823	−	0.454495i	0.0867882	−	0.0184474i	0.251101	+	0.967961i	$0.419207\pi$
$608$	18.5041	−	13.4440i	0.750439	−	0.545226i
$609$	−0.346481	+	8.09176i	−0.0140401	+	0.327895i
$610$	−5.45751	−	16.7965i	−0.220968	−	0.680070i
$611$	−12.5091	+	13.8927i	−0.506063	+	0.562039i
$612$	6.95716	−	3.09753i	0.281226	−	0.125210i
$613$	4.88272	+	46.4559i	0.197211	+	1.87634i	0.428625	+	0.903482i	$0.358998\pi$
$613$	4.88272	+	46.4559i	0.197211	+	1.87634i	−0.231414	+	0.972855i	$0.574335\pi$
$614$	13.6502	−	2.90144i	0.550878	−	0.117093i
$615$	−6.29439			−0.253814
$616$	−6.41758	+	27.2216i	−0.258572	+	1.09679i
$617$	38.7372			1.55950			0.779750	−	0.626091i	$-0.215346\pi$
$617$	38.7372			1.55950			0.779750	+	0.626091i	$0.215346\pi$
$618$	−10.5327	+	2.23880i	−0.423688	+	0.0900577i
$619$	−3.22898	−	30.7217i	−0.129784	−	1.23481i	−0.844562	−	0.535457i	$-0.820139\pi$
$619$	−3.22898	−	30.7217i	−0.129784	−	1.23481i	0.714779	−	0.699351i	$-0.246527\pi$
$620$	−2.53395	+	1.12819i	−0.101766	+	0.0453091i
$621$	4.16404	−	4.62463i	0.167097	−	0.185580i
$622$	−15.4184	−	47.4530i	−0.618221	−	1.90269i
$623$	−3.96071	−	2.51857i	−0.158682	−	0.100904i
$624$	1.22554	−	0.890408i	0.0490609	−	0.0356448i
$625$	−18.1395	+	3.85567i	−0.725580	+	0.154227i
$626$	19.1136	−	33.1057i	0.763932	−	1.32317i
$627$	−1.30132	+	15.4531i	−0.0519695	+	0.617135i
$628$	−19.4591	−	33.7041i	−0.776501	−	1.34494i
$629$	4.05656	−	12.4848i	0.161746	−	0.497802i
$630$	0.677551	+	4.02809i	0.0269943	+	0.160483i
$631$	16.3412	+	11.8726i	0.650532	+	0.472639i	0.863452	−	0.504430i	$-0.168297\pi$
$631$	16.3412	+	11.8726i	0.650532	+	0.472639i	−0.212920	+	0.977070i	$0.568297\pi$
$632$	5.59797	−	6.21718i	0.222675	−	0.247306i
$633$	14.6754	+	3.11935i	0.583295	+	0.123983i
$634$	−66.7087	+	29.7006i	−2.64934	+	1.17956i
$635$	1.46921	+	0.654133i	0.0583037	+	0.0259585i
$636$	0.774625	−	2.38405i	0.0307159	−	0.0945338i
$637$	−9.99990	−	13.2240i	−0.396211	−	0.523955i
$638$	−23.1200	−	4.41605i	−0.915328	−	0.174833i
$639$	0.269716	+	0.467161i	0.0106698	+	0.0184806i
$640$	8.67746	+	9.63729i	0.343007	+	0.380948i
$641$	−2.27154	−	21.6122i	−0.0897203	−	0.853632i	−0.943137	−	0.332403i	$-0.892141\pi$
$641$	−2.27154	−	21.6122i	−0.0897203	−	0.853632i	0.853417	−	0.521229i	$-0.174526\pi$
$642$	−0.777490	+	7.39732i	−0.0306851	+	0.291949i
$643$	−0.387035	−	1.19117i	−0.0152632	−	0.0469751i	0.943135	−	0.332410i	$-0.107862\pi$
$643$	−0.387035	−	1.19117i	−0.0152632	−	0.0469751i	−0.958398	+	0.285435i	$0.907862\pi$
$644$	54.9612	+	8.16679i	2.16577	+	0.321817i
$645$	5.44015	+	3.95250i	0.214206	+	0.155629i
$646$	22.3470	+	9.94952i	0.879230	+	0.391459i
$647$	−3.72893	−	4.14140i	−0.146599	−	0.162815i	0.665373	−	0.746511i	$-0.268273\pi$
$647$	−3.72893	−	4.14140i	−0.146599	−	0.162815i	−0.811972	+	0.583696i	$0.801606\pi$
$648$	−1.59362	+	2.76023i	−0.0626033	+	0.108432i
$649$	4.06047	−	3.08055i	0.159388	−	0.120922i
$650$	−25.0198			−0.981356
$651$	−0.814946	+	3.16212i	−0.0319403	+	0.123933i
$652$	−41.5195	+	30.1657i	−1.62603	+	1.18138i
$653$	−1.41614	+	13.4737i	−0.0554178	+	0.527265i	0.931234	+	0.364421i	$0.118733\pi$
$653$	−1.41614	+	13.4737i	−0.0554178	+	0.527265i	−0.986652	+	0.162843i	$0.947933\pi$
$654$	40.5578	+	8.62083i	1.58594	+	0.337101i
$655$	13.3484	+	2.83730i	0.521567	+	0.110862i
$656$	0.631921	−	6.01233i	0.0246724	−	0.234742i
$657$	5.08364	−	3.69348i	0.198332	−	0.144096i
$658$	46.6428	−	12.9774i	1.81833	−	0.505913i
$659$	27.0530			1.05384			0.526918	−	0.849916i	$-0.323348\pi$
$659$	27.0530			1.05384			0.526918	+	0.849916i	$0.323348\pi$
$660$	−7.45207	+	0.154332i	−0.290071	+	0.00600738i
$661$	−20.5116	+	35.5271i	−0.797808	+	1.38184i	0.123232	+	0.992378i	$0.460674\pi$
$661$	−20.5116	+	35.5271i	−0.797808	+	1.38184i	−0.921041	+	0.389467i	$0.872659\pi$
$662$	−9.28949	−	10.3170i	−0.361046	−	0.400983i
$663$	−4.88263	−	2.17389i	−0.189626	−	0.0844268i
$664$	7.17709	+	5.21446i	0.278525	+	0.202360i
$665$	−5.12295	+	6.45155i	−0.198659	+	0.250180i
$666$	4.16757	+	12.8265i	0.161490	+	0.497015i
$667$	−1.99127	+	18.9457i	−0.0771022	+	0.733579i
$668$	3.24025	+	30.8290i	0.125369	+	1.19281i
$669$	7.79136	+	8.65318i	0.301231	+	0.334551i
$670$	−5.91475	−	10.2447i	−0.228507	−	0.395786i
$671$	18.2857	−	33.2429i	0.705912	−	1.28333i
$672$	12.9173	−	0.800955i	0.498297	−	0.0308975i
$673$	−4.57799	+	14.0896i	−0.176468	+	0.543114i	−0.999697	−	0.0245954i	$-0.992170\pi$
$673$	−4.57799	+	14.0896i	−0.176468	+	0.543114i	0.823229	+	0.567709i	$0.192170\pi$
$674$	−26.4157	−	11.7610i	−1.01749	−	0.453017i
$675$	4.16261	−	1.85331i	0.160219	−	0.0713340i
$676$	24.3958	+	5.18549i	0.938301	+	0.199442i
$677$	5.55616	−	6.17074i	0.213540	−	0.237161i	−0.626853	−	0.779138i	$-0.715657\pi$
$677$	5.55616	−	6.17074i	0.213540	−	0.237161i	0.840393	+	0.541977i	$0.182324\pi$
$678$	−35.5103	−	25.7997i	−1.36376	−	0.990832i
$679$	5.05132	+	30.0305i	0.193852	+	1.15246i
$680$	−1.48006	+	4.55517i	−0.0567579	+	0.174683i
$681$	−12.6923	−	21.9836i	−0.486368	−	0.842415i
$682$	−8.74770	−	3.67963i	−0.334967	−	0.140900i
$683$	7.35810	−	12.7446i	0.281550	−	0.487659i	−0.690217	−	0.723603i	$-0.742485\pi$
$683$	7.35810	−	12.7446i	0.281550	−	0.487659i	0.971767	+	0.235944i	$0.0758181\pi$
$684$	−15.4349	+	3.28078i	−0.590166	+	0.125444i
$685$	1.52396	−	1.10722i	0.0582275	−	0.0423048i
$686$	3.47667	+	42.7956i	0.132740	+	1.63394i
$687$	1.94989	+	6.00115i	0.0743930	+	0.228958i
$688$	−4.32154	+	4.79955i	−0.164757	+	0.182981i
$689$	−1.60717	+	0.715558i	−0.0612282	+	0.0272606i
$690$	1.00426	+	9.55491i	0.0382316	+	0.363749i
$691$	−11.1121	+	2.36194i	−0.422723	+	0.0898526i	−0.414361	−	0.910112i	$-0.635995\pi$
$691$	−11.1121	+	2.36194i	−0.422723	+	0.0898526i	−0.00836182	+	0.999965i	$0.502662\pi$
$692$	−63.0841			−2.39810
$693$	−5.31331	+	6.98346i	−0.201836	+	0.265280i
$694$	−17.5992			−0.668058
$695$	14.8637	−	3.15938i	0.563813	−	0.119842i
$696$	−1.01986	−	9.70332i	−0.0386577	−	0.367803i
$697$	−19.4855	+	8.67551i	−0.738067	+	0.328608i
$698$	43.9962	−	48.8627i	1.66528	−	1.84948i
$699$	−1.07557	−	3.31026i	−0.0406818	−	0.125206i
$700$	34.3314	+	21.8310i	1.29760	+	0.825133i
$701$	−7.04684	+	5.11983i	−0.266156	+	0.193373i	−0.712856	−	0.701310i	$-0.752599\pi$
$701$	−7.04684	+	5.11983i	−0.266156	+	0.193373i	0.446701	+	0.894683i	$0.352599\pi$
$702$	5.37097	−	1.14163i	0.202714	−	0.0430882i
$703$	−13.6001	+	23.5561i	−0.512938	+	0.888434i
$704$	−3.51224	+	41.7076i	−0.132372	+	1.57192i
$705$	2.62811	+	4.55203i	0.0989805	+	0.171439i
$706$	−24.0713	+	74.0838i	−0.905935	+	2.78818i
$707$	35.6339	+	13.2888i	1.34015	+	0.499779i
$708$	4.19569	+	3.04835i	0.157684	+	0.114564i
$709$	12.0939	−	13.4317i	0.454197	−	0.504437i	−0.471936	−	0.881633i	$-0.656445\pi$
$709$	12.0939	−	13.4317i	0.454197	−	0.504437i	0.926134	+	0.377195i	$0.123112\pi$
$710$	−0.814608	−	0.173150i	−0.0305717	−	0.00649822i
$711$	2.39792	−	1.06762i	0.0899292	−	0.0400391i
$712$	5.16543	+	2.29980i	0.193583	+	0.0861886i
$713$	−2.37345	+	7.30473i	−0.0888864	+	0.273564i
$714$	7.64937	+	11.5359i	0.286271	+	0.431719i
$715$	3.58002	+	3.81415i	0.133885	+	0.142641i
$716$	19.1452	+	33.1605i	0.715490	+	1.23927i
$717$	−2.71650	−	3.01698i	−0.101450	−	0.112671i
$718$	5.43317	+	51.6932i	0.202764	+	1.92917i
$719$	0.778833	−	7.41010i	0.0290456	−	0.276350i	−0.970354	−	0.241690i	$-0.922298\pi$
$719$	0.778833	−	7.41010i	0.0290456	−	0.276350i	0.999399	−	0.0346604i	$-0.0110350\pi$
$720$	−0.131617	−	0.405076i	−0.00490509	−	0.0150963i
$721$	−4.51342	−	11.4298i	−0.168088	−	0.425668i
$722$	−5.36935	−	3.90106i	−0.199826	−	0.145182i
$723$	13.5182	+	6.01868i	0.502746	+	0.223837i
$724$	−53.2853	−	59.1794i	−1.98033	−	2.19938i
$725$	−6.97424	+	12.0797i	−0.259017	+	0.448630i
$726$	−17.8341	−	18.2289i	−0.661887	−	0.676537i
$727$	−18.3923			−0.682133			−0.341066	−	0.940039i	$-0.610788\pi$
$727$	−18.3923			−0.682133			−0.341066	+	0.940039i	$0.610788\pi$
$728$	14.2571	+	13.9869i	0.528404	+	0.518389i
$729$	−0.809017	+	0.587785i	−0.0299636	+	0.0217698i
$730$	−1.01405	+	9.64805i	−0.0375317	+	0.357090i
$731$	22.2887	+	4.73762i	0.824378	+	0.175227i
$732$	37.7619	+	8.02654i	1.39572	+	0.296669i
$733$	0.208874	−	1.98731i	0.00771495	−	0.0734029i	−0.989987	−	0.141159i	$-0.954917\pi$
$733$	0.208874	−	1.98731i	0.00771495	−	0.0734029i	0.997702	+	0.0677558i	$0.0215839\pi$
$734$	62.1444	−	45.1505i	2.29379	−	1.66654i
$735$	−4.40498	+	1.52504i	−0.162480	+	0.0562521i
$736$	30.4412			1.12208
$737$	7.35091	−	24.3265i	0.270774	−	0.896080i
$738$	10.9566	−	18.9774i	0.403318	−	0.698568i
$739$	−25.2545	−	28.0480i	−0.929002	−	1.03176i	−0.999414	−	0.0342430i	$-0.989098\pi$
$739$	−25.2545	−	28.0480i	−0.929002	−	1.03176i	0.0704118	−	0.997518i	$-0.477569\pi$
$740$	−11.9433	−	5.31749i	−0.439044	−	0.195475i
$741$	8.95938	+	6.50937i	0.329131	+	0.239128i
$742$	4.50662	+	0.669647i	0.165443	+	0.0245835i
$743$	−3.83076	−	11.7899i	−0.140537	−	0.432528i	0.855873	−	0.517186i	$-0.173020\pi$
$743$	−3.83076	−	11.7899i	−0.140537	−	0.432528i	−0.996410	+	0.0846575i	$0.973020\pi$
$744$	0.411190	−	3.91221i	0.0150750	−	0.143429i
$745$	−1.52383	−	14.4983i	−0.0558288	−	0.531175i
$746$	42.8282	+	47.5655i	1.56805	+	1.74150i
$747$	1.39170	+	2.41050i	0.0509197	+	0.0881955i
$748$	−22.8566	+	10.7489i	−0.835721	+	0.393019i
$749$	−8.47218	+	0.525328i	−0.309567	+	0.0191951i
$750$	−4.55923	+	14.0319i	−0.166479	+	0.512371i
$751$	15.0629	+	6.70643i	0.549653	+	0.244721i	0.662722	−	0.748866i	$-0.269401\pi$
$751$	15.0629	+	6.70643i	0.549653	+	0.244721i	−0.113069	+	0.993587i	$0.536068\pi$
$752$	−4.61189	+	2.05335i	−0.168178	+	0.0748778i
$753$	−18.7164	−	3.97830i	−0.682064	−	0.144977i
$754$	−11.2474	+	12.4915i	−0.409605	+	0.454912i
$755$	3.15669	+	2.29347i	0.114884	+	0.0834680i
$756$	−8.36602	−	3.11991i	−0.304269	−	0.113470i
$757$	−12.7398	+	39.2092i	−0.463037	+	1.42508i	0.398397	+	0.917213i	$0.369567\pi$
$757$	−12.7398	+	39.2092i	−0.463037	+	1.42508i	−0.861434	+	0.507869i	$0.830433\pi$
$758$	2.27464	+	3.93979i	0.0826186	+	0.143100i
$759$	−13.4900	+	15.6208i	−0.489656	+	0.567000i
$760$	4.96209	−	8.59459i	0.179994	−	0.311759i
$761$	−7.25970	+	1.54310i	−0.263164	+	0.0559372i	−0.337604	−	0.941288i	$-0.609616\pi$
$761$	−7.25970	+	1.54310i	−0.263164	+	0.0559372i	0.0744400	+	0.997225i	$0.476283\pi$
$762$	−4.52963	+	3.29097i	−0.164091	+	0.119219i
$763$	−2.02431	+	47.2760i	−0.0732850	+	1.71151i
$764$	11.1748	+	34.3926i	0.404291	+	1.24428i
$765$	−1.00553	+	1.11675i	−0.0363550	+	0.0403763i
$766$	76.3938	−	34.0127i	2.76022	−	1.22893i
$767$	−0.380454	−	3.61978i	−0.0137374	−	0.130703i
$768$	−19.4729	+	4.13908i	−0.702666	+	0.149356i
$769$	35.1512			1.26759			0.633793	−	0.773503i	$-0.281497\pi$
$769$	35.1512			1.26759			0.633793	+	0.773503i	$0.281497\pi$
$770$	−2.52332	−	13.3103i	−0.0909342	−	0.479669i
$771$	−1.64803			−0.0593522
$772$	72.4064	−	15.3905i	2.60596	−	0.553915i
$773$	−4.95910	−	47.1827i	−0.178366	−	1.69704i	−0.607918	−	0.794000i	$-0.707995\pi$
$773$	−4.95910	−	47.1827i	−0.178366	−	1.69704i	0.429551	−	0.903042i	$-0.358672\pi$
$774$	−21.3863	+	9.52179i	−0.768714	+	0.342254i
$775$	−3.76305	+	4.17929i	−0.135173	+	0.150124i
$776$	−11.3362	−	34.8893i	−0.406947	−	1.25245i
$777$	−13.6461	+	7.11828i	−0.489550	+	0.255367i
$778$	19.6479	−	14.2751i	0.704412	−	0.511786i
$779$	43.2297	−	9.18876i	1.54887	−	0.329222i
$780$	−2.66141	+	4.60969i	−0.0952937	+	0.165054i
$781$	−0.926435	−	1.53054i	−0.0331504	−	0.0547672i
$782$	16.2783	+	28.1949i	0.582112	+	1.00825i
$783$	0.945962	−	2.91137i	0.0338059	−	0.104044i
$784$	−1.01447	−	4.36069i	−0.0362310	−	0.155739i
$785$	6.21286	+	4.51391i	0.221747	+	0.161108i
$786$	−31.7899	+	35.3063i	−1.13391	+	1.25933i
$787$	−16.7047	−	3.55069i	−0.595457	−	0.126568i	−0.0996821	−	0.995019i	$-0.531783\pi$
$787$	−16.7047	−	3.55069i	−0.595457	−	0.126568i	−0.495775	+	0.868451i	$0.665116\pi$
$788$	−29.2352	+	13.0164i	−1.04146	+	0.463688i
$789$	−16.5488	−	7.36799i	−0.589152	−	0.262307i
$790$	−1.25226	+	3.85407i	−0.0445536	+	0.137122i
$791$	22.3131	−	44.8475i	0.793362	−	1.59459i
$792$	5.09475	−	9.26212i	0.181034	−	0.329115i
$793$	−13.5469	−	23.4640i	−0.481066	−	0.833231i
$794$	−23.9385	−	26.5864i	−0.849546	−	0.943517i
$795$	0.0517042	+	0.491933i	0.00183376	+	0.0174471i
$796$	−0.429831	+	4.08957i	−0.0152349	+	0.144951i
$797$	13.5605	+	41.7350i	0.480338	+	1.47833i	0.838620	+	0.544716i	$0.183363\pi$
$797$	13.5605	+	41.7350i	0.480338	+	1.47833i	−0.358282	+	0.933613i	$0.616637\pi$
$798$	−10.5337	−	26.6757i	−0.372890	−	0.944310i
$799$	14.4099	+	10.4694i	0.509784	+	0.370380i
$800$	20.3621	+	9.06579i	0.719909	+	0.320524i
$801$	1.18706	+	1.31836i	0.0419427	+	0.0465821i
$802$	−13.2923	+	23.0229i	−0.469367	+	0.812967i
$803$	−16.6033	+	12.5964i	−0.585916	+	0.444516i
$804$	25.8585			0.911960
$805$	−10.5631	+	2.93896i	−0.372299	+	0.103585i
$806$	−5.48277	+	3.98346i	−0.193122	+	0.140311i
$807$	1.94084	−	18.4658i	0.0683208	−	0.650029i
$808$	−44.8135	−	9.52541i	−1.57653	−	0.335103i
$809$	−25.4835	−	5.41668i	−0.895951	−	0.190440i	−0.263150	−	0.964755i	$-0.584761\pi$
$809$	−25.4835	−	5.41668i	−0.895951	−	0.190440i	−0.632801	+	0.774315i	$0.718095\pi$
$810$	0.161377	−	1.53540i	0.00567023	−	0.0539486i
$811$	−5.59661	+	4.06618i	−0.196524	+	0.142783i	−0.681695	−	0.731636i	$-0.738757\pi$
$811$	−5.59661	+	4.06618i	−0.196524	+	0.142783i	0.485172	+	0.874419i	$0.338757\pi$
$812$	26.3327	−	7.32654i	0.924097	−	0.257111i
$813$	−0.881785			−0.0309256
$814$	−14.7001	−	42.2452i	−0.515239	−	1.48069i
$815$	5.06345	−	8.77015i	0.177365	−	0.307205i
$816$	−0.965760	−	1.07259i	−0.0338084	−	0.0375480i
$817$	−43.1328	−	19.2040i	−1.50903	−	0.671861i
$818$	−48.8491	−	35.4910i	−1.70797	−	1.24091i
$819$	2.30153	+	5.82842i	0.0804221	+	0.203661i
$820$	6.56420	+	20.2025i	0.229232	+	0.705503i
$821$	1.44636	−	13.7612i	0.0504782	−	0.480268i	−0.939857	−	0.341569i	$-0.889042\pi$
$821$	1.44636	−	13.7612i	0.0504782	−	0.480268i	0.990335	−	0.138698i	$-0.0442918\pi$
$822$	0.685493	+	6.52203i	0.0239093	+	0.227482i
$823$	−36.1120	−	40.1064i	−1.25879	−	1.39802i	−0.881677	−	0.471854i	$-0.843585\pi$
$823$	−36.1120	−	40.1064i	−1.25879	−	1.39802i	−0.377109	−	0.926169i	$-0.623082\pi$
$824$	7.40185	+	12.8204i	0.257856	+	0.446619i
$825$	−13.6756	+	6.43128i	−0.476122	+	0.223908i
$826$	−4.19879	+	8.43923i	−0.146095	+	0.293638i
$827$	8.88051	−	27.3314i	0.308806	−	0.950406i	−0.669424	−	0.742881i	$-0.733459\pi$
$827$	8.88051	−	27.3314i	0.308806	−	0.950406i	0.978230	−	0.207526i	$-0.0665410\pi$
$828$	−19.1858	−	8.54206i	−0.666752	−	0.296857i
$829$	23.6279	−	10.5198i	0.820632	−	0.365369i	0.0469140	−	0.998899i	$-0.485061\pi$
$829$	23.6279	−	10.5198i	0.820632	−	0.365369i	0.773718	+	0.633530i	$0.218395\pi$
$830$	−4.20329	−	0.893436i	−0.145898	−	0.0310116i
$831$	3.53076	−	3.92131i	0.122481	−	0.136029i
$832$	24.1813	+	17.5687i	0.838334	+	0.609085i
$833$	−11.5345	+	10.7924i	−0.399648	+	0.373935i
$834$	−16.3477	+	50.3132i	−0.566076	+	1.74220i
$835$	−3.05842	−	5.29733i	−0.105841	−	0.183322i
$836$	50.9553	−	11.9387i	1.76233	−	0.412910i
$837$	0.617112	−	1.06887i	0.0213305	−	0.0369455i
$838$	23.5745	−	5.01092i	0.814368	−	0.173099i
$839$	−17.4287	+	12.6627i	−0.601707	+	0.437165i	−0.846484	−	0.532414i	$-0.821285\pi$
$839$	−17.4287	+	12.6627i	−0.601707	+	0.437165i	0.244778	+	0.969579i	$0.421285\pi$
$840$	4.97886	−	2.59715i	0.171787	−	0.0896103i
$841$	−6.06571	−	18.6683i	−0.209163	−	0.643736i
$842$	36.4687	−	40.5026i	1.25679	−	1.39581i
$843$	18.9647	−	8.44365i	0.653180	−	0.290815i
$844$	−5.29256	−	50.3554i	−0.182177	−	1.73330i
$845$	−4.81391	+	1.02323i	−0.165603	+	0.0352001i
$846$	−18.2990			−0.629132
$847$	17.1389	−	23.5214i	0.588900	−	0.808206i
$848$	−0.475079			−0.0163143
$849$	16.7042	−	3.55059i	0.573287	−	0.121856i
$850$	2.49176	+	23.7075i	0.0854666	+	0.813161i
$851$	−33.0715	+	14.7244i	−1.13368	+	0.504745i
$852$	1.21813	−	1.35287i	0.0417323	−	0.0463485i
$853$	10.1868	+	31.3519i	0.348791	+	1.07347i	0.959523	+	0.281631i	$0.0908754\pi$
$853$	10.1868	+	31.3519i	0.348791	+	1.07347i	−0.610732	+	0.791838i	$0.709125\pi$
$854$	−3.00173	+	70.1028i	−0.102717	+	2.39887i
$855$	2.51906	−	1.83020i	0.0861499	−	0.0625916i
$856$	10.0023	−	2.12605i	0.341870	−	0.0726668i
$857$	5.03969	−	8.72900i	0.172153	−	0.298177i	−0.767020	−	0.641624i	$-0.778261\pi$
$857$	5.03969	−	8.72900i	0.172153	−	0.298177i	0.939172	+	0.343447i	$0.111594\pi$
$858$	−17.7313	+	4.15440i	−0.605335	+	0.141829i
$859$	−4.13128	−	7.15559i	−0.140958	−	0.244146i	0.786900	−	0.617081i	$-0.211685\pi$
$859$	−4.13128	−	7.15559i	−0.140958	−	0.244146i	−0.927857	+	0.372935i	$0.878351\pi$
$860$	7.01263	−	21.5827i	0.239129	−	0.735963i
$861$	23.4314	+	8.73821i	0.798541	+	0.297798i
$862$	−39.4574	−	28.6675i	−1.34393	−	0.976419i
$863$	−5.53477	+	6.14699i	−0.188406	+	0.209246i	−0.829946	−	0.557843i	$-0.811629\pi$
$863$	−5.53477	+	6.14699i	−0.188406	+	0.209246i	0.641540	+	0.767089i	$0.278296\pi$
$864$	−4.78478	−	1.01704i	−0.162781	−	0.0346003i
$865$	11.3719	−	5.06309i	0.386655	−	0.172150i
$866$	−67.0704	−	29.8617i	−2.27914	−	1.01474i
$867$	3.67969	−	11.3249i	0.124969	−	0.384614i
$868$	10.9991	−	0.682010i	0.373332	−	0.0231489i
$869$	−7.87799	+	3.70482i	−0.267243	+	0.125678i
$870$	2.36303	+	4.09289i	0.0801144	+	0.138762i
$871$	−12.1433	−	13.4865i	−0.411460	−	0.456973i
$872$	−5.95853	−	56.6916i	−0.201781	−	1.91982i
$873$	1.20311	−	11.4468i	0.0407192	−	0.387417i
$874$	−20.8458	−	64.1568i	−0.705120	−	2.17014i
$875$	−16.6546	−	2.47475i	−0.563030	−	0.0836617i
$876$	−17.1562	−	12.4647i	−0.579653	−	0.421143i
$877$	5.22872	+	2.32797i	0.176561	+	0.0786101i	0.493114	−	0.869965i	$-0.335859\pi$
$877$	5.22872	+	2.32797i	0.176561	+	0.0786101i	−0.316552	+	0.948575i	$0.602525\pi$
$878$	−11.3467	−	12.6017i	−0.382931	−	0.425288i
$879$	−4.59744	+	7.96301i	−0.155068	+	0.268586i
$880$	0.464249	+	1.33416i	0.0156498	+	0.0449745i
$881$	11.5990			0.390779			0.195389	−	0.980726i	$-0.437403\pi$
$881$	11.5990			0.390779			0.195389	+	0.980726i	$0.437403\pi$
$882$	3.06976	−	15.9355i	0.103364	−	0.536577i
$883$	−48.0615	+	34.9187i	−1.61740	+	1.17511i	−0.792201	+	0.610260i	$0.791065\pi$
$883$	−48.0615	+	34.9187i	−1.61740	+	1.17511i	−0.825195	+	0.564847i	$0.808935\pi$
$884$	−1.88540	+	17.9384i	−0.0634129	+	0.603334i
$885$	−1.00100	−	0.212768i	−0.0336481	−	0.00715213i
$886$	−9.85533	−	2.09481i	−0.331096	−	0.0703767i
$887$	2.31315	−	22.0082i	0.0776681	−	0.738962i	−0.884506	−	0.466528i	$-0.845505\pi$
$887$	2.31315	−	22.0082i	0.0776681	−	0.738962i	0.962174	−	0.272434i	$-0.0878287\pi$
$888$	15.0000	−	10.8982i	0.503368	−	0.365718i
$889$	−4.56115	−	4.47470i	−0.152976	−	0.150077i
$890$	−2.73886			−0.0918069
$891$	2.64227	−	2.00460i	0.0885192	−	0.0671567i
$892$	19.6480	−	34.0313i	0.657863	−	1.13945i
$893$	−24.6950	−	27.4266i	−0.826388	−	0.917796i
$894$	46.3644	+	20.6427i	1.55066	+	0.690397i
$895$	−6.11266	−	4.44110i	−0.204324	−	0.148450i
$896$	−18.9236	−	47.9222i	−0.632193	−	1.60097i
$897$	4.55464	+	14.0177i	0.152075	+	0.468038i
$898$	3.37607	−	32.1212i	0.112661	−	1.07190i
$899$	0.394930	+	3.75751i	0.0131717	+	0.125320i
$900$	−10.2894	−	11.4276i	−0.342981	−	0.380919i
$901$	0.838088	+	1.45161i	0.0279208	+	0.0483602i
$902$	−35.0280	+	63.6799i	−1.16630	+	2.12031i
$903$	−14.7644	−	22.2658i	−0.491327	−	0.740960i
$904$	−18.6472	+	57.3900i	−0.620195	+	1.90876i
$905$	14.3552	+	6.39135i	0.477183	+	0.212456i
$906$	−12.4096	+	5.52511i	−0.412281	+	0.183559i
$907$	37.9780	+	8.07247i	1.26104	+	0.268042i	0.789471	−	0.613788i	$-0.210355\pi$
$907$	37.9780	+	8.07247i	1.26104	+	0.268042i	0.471567	+	0.881830i	$0.343688\pi$
$908$	−57.3226	+	63.6632i	−1.90232	+	2.11274i
$909$	−11.6292	−	8.44907i	−0.385715	−	0.280238i
$910$	−9.06461	−	3.38044i	−0.300489	−	0.112060i
$911$	4.95879	−	15.2616i	0.164292	−	0.505639i	−0.834691	−	0.550718i	$-0.814354\pi$
$911$	4.95879	−	15.2616i	0.164292	−	0.505639i	0.998983	+	0.0450791i	$0.0143540\pi$
$912$	1.49529	+	2.58992i	0.0495139	+	0.0857607i
$913$	−4.78030	−	7.89744i	−0.158205	−	0.261367i
$914$	1.62077	−	2.80725i	0.0536102	−	0.0928556i
$915$	−7.45137	+	1.58384i	−0.246335	+	0.0523600i
$916$	17.2279	−	12.5168i	0.569225	−	0.413566i
$917$	−45.7519	−	29.0931i	−1.51086	−	0.960740i
$918$	−1.61666	−	4.97557i	−0.0533577	−	0.164218i
$919$	12.9284	−	14.3585i	0.426469	−	0.473642i	−0.491166	−	0.871066i	$-0.663429\pi$
$919$	12.9284	−	14.3585i	0.426469	−	0.473642i	0.917635	+	0.397424i	$0.130096\pi$
$920$	12.0664	−	5.37229i	0.397816	−	0.177119i
$921$	−0.629201	−	5.98644i	−0.0207329	−	0.197260i
$922$	−7.36844	+	1.56621i	−0.242667	+	0.0515804i
$923$	−1.27763			−0.0420536
$924$	27.9552	+	9.77085i	0.919660	+	0.321437i
$925$	−26.5067			−0.871534
$926$	5.15586	−	1.09591i	0.169432	−	0.0360139i
$927$	0.485501	+	4.61923i	0.0159459	+	0.151716i
$928$	13.6798	−	6.09063i	0.449061	−	0.199935i
$929$	−12.4018	+	13.7736i	−0.406891	+	0.451898i	−0.911408	−	0.411503i	$-0.865004\pi$
$929$	−12.4018	+	13.7736i	−0.406891	+	0.451898i	0.504517	+	0.863402i	$0.331670\pi$
$930$	0.588823	+	1.81221i	0.0193083	+	0.0594247i
$931$	28.0270	−	16.9045i	0.918548	−	0.554023i
$932$	−9.50297	+	6.90431i	−0.311280	+	0.226158i
$933$	−21.0514	+	4.47461i	−0.689192	+	0.146492i
$934$	−18.9351	+	32.7965i	−0.619574	+	1.07313i
$935$	3.25756	−	3.77211i	0.106534	−	0.123361i
$936$	−3.77444	−	6.53752i	−0.123371	−	0.213685i
$937$	6.62264	−	20.3824i	0.216352	−	0.665863i	−0.782703	−	0.622396i	$-0.786159\pi$
$937$	6.62264	−	20.3824i	0.216352	−	0.665863i	0.999055	−	0.0434677i	$-0.0138405\pi$
$938$	7.79601	+	46.3478i	0.254549	+	1.51331i
$939$	−13.3398	−	9.69193i	−0.435328	−	0.316284i
$940$	11.8695	−	13.1824i	0.387139	−	0.429961i
$941$	−46.5410	−	9.89259i	−1.51719	−	0.322489i	−0.627342	−	0.778744i	$-0.715857\pi$
$941$	−46.5410	−	9.89259i	−1.51719	−	0.322489i	−0.889849	+	0.456254i	$0.849191\pi$
$942$	−24.4240	+	10.8743i	−0.795777	+	0.354303i
$943$	53.7353	+	23.9245i	1.74986	+	0.779089i
$944$	0.303728	−	0.934779i	0.00988551	−	0.0304245i
$945$	1.75851	−	0.109038i	0.0572042	−	0.00354701i
$946$	70.2612	−	33.0421i	2.28439	−	1.07429i
$947$	14.2862	+	24.7444i	0.464238	+	0.804083i	0.999167	−	0.0408136i	$-0.0129950\pi$
$947$	14.2862	+	24.7444i	0.464238	+	0.804083i	−0.534929	+	0.844897i	$0.679662\pi$
$948$	−5.92737	−	6.58301i	−0.192512	−	0.213806i
$949$	1.55568	+	14.8013i	0.0504994	+	0.480469i
$950$	5.16300	−	49.1227i	0.167510	−	1.59375i
$951$	9.73317	+	29.9556i	0.315620	+	0.971377i
$952$	11.8334	−	14.9023i	0.383523	−	0.482987i
$953$	23.5945	+	17.1424i	0.764299	+	0.555296i	0.900226	−	0.435423i	$-0.143401\pi$
$953$	23.5945	+	17.1424i	0.764299	+	0.555296i	−0.135927	+	0.990719i	$0.543401\pi$
$954$	−1.57316	−	0.700418i	−0.0509331	−	0.0226769i
$955$	−4.77476	−	5.30290i	−0.154508	−	0.171598i
$956$	−6.85038	+	11.8652i	−0.221557	+	0.383748i
$957$	−2.93680	+	9.71882i	−0.0949332	+	0.314165i
$958$	22.0362			0.711958
$959$	−7.21018	+	2.00609i	−0.232829	+	0.0647800i
$960$	6.79891	−	4.93970i	0.219434	−	0.159428i
$961$	3.08115	−	29.3152i	0.0993920	−	0.945652i
$962$	−31.2444	−	6.64121i	−1.00736	−	0.214121i
$963$	3.13822	+	0.667050i	0.101128	+	0.0214954i
$964$	5.21997	−	49.6647i	0.168124	−	1.59959i
$965$	−11.8171	+	8.58566i	−0.380407	+	0.276382i
$966$	9.52619	−	36.9632i	0.306500	−	1.18927i
$967$	38.0519			1.22367			0.611833	−	0.790987i	$-0.290432\pi$
$967$	38.0519			1.22367			0.611833	+	0.790987i	$0.290432\pi$
$968$	−16.2577	+	31.0623i	−0.522542	+	0.998379i
$969$	5.27568	−	9.13774i	0.169479	−	0.293547i
$970$	11.8902	+	13.2055i	0.381773	+	0.424002i
$971$	−21.9060	−	9.75316i	−0.702996	−	0.312994i	0.0239265	−	0.999714i	$-0.492383\pi$
$971$	−21.9060	−	9.75316i	−0.702996	−	0.312994i	−0.726922	+	0.686720i	$0.759050\pi$
$972$	2.73026	+	1.98365i	0.0875730	+	0.0636255i
$973$	−59.7175	−	8.87354i	−1.91446	−	0.284473i
$974$	12.1113	+	37.2748i	0.388071	+	1.19436i
$975$	−1.12807	+	10.7329i	−0.0361273	+	0.343728i
$976$	−0.764787	−	7.27647i	−0.0244803	−	0.232914i
$977$	14.1617	+	15.7281i	0.453073	+	0.503188i	0.925796	−	0.378023i	$-0.123396\pi$
$977$	14.1617	+	15.7281i	0.453073	+	0.503188i	−0.472724	+	0.881211i	$0.656729\pi$
$978$	17.6278	+	30.5323i	0.563676	+	0.976316i
$979$	−4.02673	−	4.29006i	−0.128695	−	0.137111i
$980$	9.48859	+	12.5479i	0.303102	+	0.400826i
$981$	5.52678	−	17.0097i	0.176457	−	0.543077i
$982$	26.6923	+	11.8842i	0.851785	+	0.379239i
$983$	5.36170	−	2.38718i	0.171012	−	0.0761393i	−0.319445	−	0.947605i	$-0.603497\pi$
$983$	5.36170	−	2.38718i	0.171012	−	0.0761393i	0.490457	+	0.871465i	$0.336830\pi$
$984$	−29.4676	−	6.26353i	−0.939392	−	0.199674i
$985$	4.22541	−	4.69280i	0.134633	−	0.149525i
$986$	12.9564	+	9.41340i	0.412617	+	0.299784i
$987$	−3.46402	−	20.5938i	−0.110261	−	0.655508i
$988$	11.5491	−	35.5445i	0.367426	−	1.13082i
$989$	−31.4195	−	54.4201i	−0.999080	−	1.73046i
$990$	−0.429674	+	5.10235i	−0.0136559	+	0.162163i
$991$	−23.7123	+	41.0708i	−0.753245	+	1.30466i	0.192998	+	0.981199i	$0.438179\pi$
$991$	−23.7123	+	41.0708i	−0.753245	+	1.30466i	−0.946242	+	0.323459i	$0.895154\pi$
$992$	5.90549	−	1.25525i	0.187499	−	0.0398542i
$993$	−4.84460	+	3.51981i	−0.153739	+	0.111698i
$994$	2.79207	+	1.77545i	0.0885592	+	0.0563139i
$995$	−0.250742	−	0.771705i	−0.00794906	−	0.0244647i
$996$	6.28540	−	6.98065i	0.199161	−	0.221190i
$997$	3.84049	−	1.70990i	0.121629	−	0.0541529i	−0.345020	−	0.938595i	$-0.612128\pi$
$997$	3.84049	−	1.70990i	0.121629	−	0.0541529i	0.466649	+	0.884443i	$0.345461\pi$
$998$	−1.88734	−	17.9568i	−0.0597426	−	0.568412i
$999$	5.69016	−	1.20948i	0.180029	−	0.0382663i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	231.2.y.a.130.1	yes	64
3.2	odd	2		693.2.by.d.361.8		64
7.2	even	3	inner	231.2.y.a.163.8	yes	64
11.5	even	5	inner	231.2.y.a.214.8	yes	64
21.2	odd	6		693.2.by.d.163.1		64
33.5	odd	10		693.2.by.d.676.1		64
77.16	even	15	inner	231.2.y.a.16.1	✓	64
231.170	odd	30		693.2.by.d.478.8		64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
231.2.y.a.16.1	✓	64	77.16	even	15	inner
231.2.y.a.130.1	yes	64	1.1	even	1	trivial
231.2.y.a.163.8	yes	64	7.2	even	3	inner
231.2.y.a.214.8	yes	64	11.5	even	5	inner
693.2.by.d.163.1		64	21.2	odd	6
693.2.by.d.361.8		64	3.2	odd	2
693.2.by.d.478.8		64	231.170	odd	30
693.2.by.d.676.1		64	33.5	odd	10

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 231 = 3 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	231.y (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.26770 + 0.482014i) q^{2} +(0.104528 + 0.994522i) q^{3} +(3.08302 - 1.37265i) q^{4} +(-0.445594 + 0.494882i) q^{5} +(-0.716412 - 2.20489i) q^{6} +(2.34578 - 1.22364i) q^{7} +(-2.57853 + 1.87341i) q^{8} +(-0.978148 + 0.207912i) q^{9} +O(q^{10})\)	\(q+(-2.26770 + 0.482014i) q^{2} +(0.104528 + 0.994522i) q^{3} +(3.08302 - 1.37265i) q^{4} +(-0.445594 + 0.494882i) q^{5} +(-0.716412 - 2.20489i) q^{6} +(2.34578 - 1.22364i) q^{7} +(-2.57853 + 1.87341i) q^{8} +(-0.978148 + 0.207912i) q^{9} +(0.771931 - 1.33702i) q^{10} +(3.22918 - 0.756589i) q^{11} +(1.68739 + 2.92265i) q^{12} +(0.731897 - 2.25255i) q^{13} +(-4.72971 + 3.90555i) q^{14} +(-0.538748 - 0.391423i) q^{15} +(0.427970 - 0.475309i) q^{16} +(-2.20729 - 0.469175i) q^{17} +(2.11793 - 0.942961i) q^{18} +(4.27152 + 1.90180i) q^{19} +(-0.694474 + 2.13737i) q^{20} +(1.46214 + 2.20503i) q^{21} +(-6.95810 + 3.27222i) q^{22} +(3.11153 + 5.38932i) q^{23} +(-2.13268 - 2.36858i) q^{24} +(0.476288 + 4.53158i) q^{25} +(-0.573961 + 5.46088i) q^{26} +(-0.309017 - 0.951057i) q^{27} +(5.55246 - 6.99245i) q^{28} +(2.47656 + 1.79933i) q^{29} +(1.41039 + 0.627945i) q^{30} +(0.825857 + 0.917207i) q^{31} +(2.44584 - 4.23631i) q^{32} +(1.08999 + 3.13240i) q^{33} +5.23162 q^{34} +(-0.439707 + 1.70613i) q^{35} +(-2.73026 + 1.98365i) q^{36} +(-0.608071 + 5.78541i) q^{37} +(-10.6032 - 2.25378i) q^{38} +(2.31671 + 0.492432i) q^{39} +(0.221859 - 2.11085i) q^{40} +(7.64687 - 5.55577i) q^{41} +(-4.37855 - 4.29556i) q^{42} -10.0978 q^{43} +(8.91707 - 6.76510i) q^{44} +(0.332965 - 0.576711i) q^{45} +(-9.65373 - 10.7216i) q^{46} +(-7.21068 - 3.21040i) q^{47} +(0.517440 + 0.375942i) q^{48} +(4.00539 - 5.74080i) q^{49} +(-3.26436 - 10.0467i) q^{50} +(0.235880 - 2.24425i) q^{51} +(-0.835503 - 7.94928i) q^{52} +(-0.497021 - 0.551997i) q^{53} +(1.15918 + 2.00776i) q^{54} +(-1.06448 + 1.93519i) q^{55} +(-3.75628 + 7.54982i) q^{56} +(-1.44489 + 4.44691i) q^{57} +(-6.48339 - 2.88659i) q^{58} +(1.40388 - 0.625048i) q^{59} +(-2.19826 - 0.467254i) q^{60} +(7.65446 - 8.50114i) q^{61} +(-2.31490 - 1.68187i) q^{62} +(-2.04011 + 1.68462i) q^{63} +(-3.89974 + 12.0022i) q^{64} +(0.788616 + 1.36592i) q^{65} +(-3.98161 - 6.57794i) q^{66} +(3.83114 - 6.63573i) q^{67} +(-7.44914 + 1.58336i) q^{68} +(-5.03456 + 3.65782i) q^{69} +(0.174741 - 4.08093i) q^{70} +(-0.166693 - 0.513029i) q^{71} +(2.13268 - 2.36858i) q^{72} +(-5.74046 + 2.55582i) q^{73} +(-1.40973 - 13.4127i) q^{74} +(-4.45697 + 0.947358i) q^{75} +15.7797 q^{76} +(6.64915 - 5.72615i) q^{77} -5.49096 q^{78} +(-2.56750 + 0.545738i) q^{79} +(0.0445210 + 0.423589i) q^{80} +(0.913545 - 0.406737i) q^{81} +(-14.6628 + 16.2847i) q^{82} +(-0.860119 - 2.64718i) q^{83} +(7.53453 + 4.79113i) q^{84} +(1.21574 - 0.883289i) q^{85} +(22.8986 - 4.86726i) q^{86} +(-1.53060 + 2.65108i) q^{87} +(-6.90912 + 8.00046i) q^{88} +(-0.887017 - 1.53636i) q^{89} +(-0.477080 + 1.46830i) q^{90} +(-1.03944 - 6.17957i) q^{91} +(16.9905 + 12.3443i) q^{92} +(-0.825857 + 0.917207i) q^{93} +(17.8991 + 3.80457i) q^{94} +(-2.84453 + 1.26647i) q^{95} +(4.46877 + 1.98962i) q^{96} +(-3.55675 + 10.9466i) q^{97} +(-6.31586 + 14.9491i) q^{98} +(-3.00131 + 1.41144i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q - 8 q^{3} + 10 q^{4} - q^{7} + 8 q^{8} + 8 q^{9}+O(q^{10}) \) 64 * q - 8 * q^3 + 10 * q^4 - q^7 + 8 * q^8 + 8 * q^9	\( 64 q - 8 q^{3} + 10 q^{4} - q^{7} + 8 q^{8} + 8 q^{9} - 22 q^{10} - 13 q^{11} + 30 q^{12} - 8 q^{13} - 26 q^{14} + 4 q^{17} - 5 q^{18} + 10 q^{19} + 24 q^{20} + 2 q^{21} - 38 q^{22} - 8 q^{23} + 14 q^{24} - 2 q^{25} + 4 q^{26} + 16 q^{27} - 67 q^{28} + 2 q^{29} - 3 q^{30} + 25 q^{31} + 72 q^{32} - 12 q^{33} - 56 q^{34} + 19 q^{35} - 20 q^{36} - 12 q^{37} - 37 q^{38} - 4 q^{39} - 9 q^{40} + 20 q^{41} + 9 q^{42} - 100 q^{43} - 5 q^{44} - 33 q^{46} - 18 q^{47} + 10 q^{48} + 29 q^{49} - 46 q^{50} + 6 q^{51} + 26 q^{52} - 49 q^{53} - 10 q^{54} - 24 q^{55} - 48 q^{56} + 20 q^{57} - 40 q^{58} + q^{59} + 12 q^{60} + 3 q^{61} + 4 q^{62} - 7 q^{63} - 24 q^{64} + 82 q^{65} + 11 q^{66} + 76 q^{67} - 39 q^{68} - 16 q^{69} + 59 q^{70} + 70 q^{71} - 14 q^{72} - 3 q^{73} + 32 q^{74} - 28 q^{75} + 104 q^{76} + 38 q^{77} - 12 q^{78} - 15 q^{79} - 83 q^{80} + 8 q^{81} + 42 q^{82} + 68 q^{83} + 27 q^{84} + 62 q^{85} - 47 q^{86} - 54 q^{87} - 64 q^{88} + 82 q^{89} - 16 q^{90} - 10 q^{91} + 190 q^{92} - 25 q^{93} - 6 q^{94} - 53 q^{95} + 8 q^{96} - 32 q^{97} - 152 q^{98} + 16 q^{99}+O(q^{100}) \) 64 * q - 8 * q^3 + 10 * q^4 - q^7 + 8 * q^8 + 8 * q^9 - 22 * q^10 - 13 * q^11 + 30 * q^12 - 8 * q^13 - 26 * q^14 + 4 * q^17 - 5 * q^18 + 10 * q^19 + 24 * q^20 + 2 * q^21 - 38 * q^22 - 8 * q^23 + 14 * q^24 - 2 * q^25 + 4 * q^26 + 16 * q^27 - 67 * q^28 + 2 * q^29 - 3 * q^30 + 25 * q^31 + 72 * q^32 - 12 * q^33 - 56 * q^34 + 19 * q^35 - 20 * q^36 - 12 * q^37 - 37 * q^38 - 4 * q^39 - 9 * q^40 + 20 * q^41 + 9 * q^42 - 100 * q^43 - 5 * q^44 - 33 * q^46 - 18 * q^47 + 10 * q^48 + 29 * q^49 - 46 * q^50 + 6 * q^51 + 26 * q^52 - 49 * q^53 - 10 * q^54 - 24 * q^55 - 48 * q^56 + 20 * q^57 - 40 * q^58 + q^59 + 12 * q^60 + 3 * q^61 + 4 * q^62 - 7 * q^63 - 24 * q^64 + 82 * q^65 + 11 * q^66 + 76 * q^67 - 39 * q^68 - 16 * q^69 + 59 * q^70 + 70 * q^71 - 14 * q^72 - 3 * q^73 + 32 * q^74 - 28 * q^75 + 104 * q^76 + 38 * q^77 - 12 * q^78 - 15 * q^79 - 83 * q^80 + 8 * q^81 + 42 * q^82 + 68 * q^83 + 27 * q^84 + 62 * q^85 - 47 * q^86 - 54 * q^87 - 64 * q^88 + 82 * q^89 - 16 * q^90 - 10 * q^91 + 190 * q^92 - 25 * q^93 - 6 * q^94 - 53 * q^95 + 8 * q^96 - 32 * q^97 - 152 * q^98 + 16 * q^99

Introduction

L-functions

Modular forms

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