LMFDB - Embedded newform 430.2.q.a.271.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [430,2,Mod(31,430)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(430, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([0, 34]))

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

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

chi := DirichletCharacter("430.31");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 430 = 2 \cdot 5 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	430.q (of order $21$, degree $12$, 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:	$3.43356728692$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$3$ over $\Q(\zeta_{21})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label			271.2
Character	$\chi$	$=$	430.271
Dual form			430.2.q.a.311.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.222521 + 0.974928i) q^{2} +(-0.387472 + 0.359522i) q^{3} +(-0.900969 - 0.433884i) q^{4} +(-0.988831 - 0.149042i) q^{5} +(-0.264287 - 0.457759i) q^{6} +(1.56569 - 2.71185i) q^{7} +(0.623490 - 0.781831i) q^{8} +(-0.203311 + 2.71300i) q^{9} +O(q^{10})$	\(q+(-0.222521 + 0.974928i) q^{2} +(-0.387472 + 0.359522i) q^{3} +(-0.900969 - 0.433884i) q^{4} +(-0.988831 - 0.149042i) q^{5} +(-0.264287 - 0.457759i) q^{6} +(1.56569 - 2.71185i) q^{7} +(0.623490 - 0.781831i) q^{8} +(-0.203311 + 2.71300i) q^{9} +(0.365341 - 0.930874i) q^{10} +(2.80692 - 1.35174i) q^{11} +(0.505091 - 0.155800i) q^{12} +(1.80896 + 4.60914i) q^{13} +(2.29546 + 2.12987i) q^{14} +(0.436728 - 0.297756i) q^{15} +(0.623490 + 0.781831i) q^{16} +(1.40891 - 0.212358i) q^{17} +(-2.59974 - 0.801914i) q^{18} +(0.0862086 + 1.15037i) q^{19} +(0.826239 + 0.563320i) q^{20} +(0.368308 + 1.61366i) q^{21} +(0.693253 + 3.03734i) q^{22} +(5.44500 + 3.71234i) q^{23} +(0.0395004 + 0.527096i) q^{24} +(0.955573 + 0.294755i) q^{25} +(-4.89611 + 0.737971i) q^{26} +(-1.88529 - 2.36408i) q^{27} +(-2.58726 + 1.76396i) q^{28} +(3.77916 + 3.50655i) q^{29} +(0.193110 + 0.492036i) q^{30} +(-4.98045 + 1.53627i) q^{31} +(-0.900969 + 0.433884i) q^{32} +(-0.601624 + 1.53291i) q^{33} +(-0.106477 + 1.42084i) q^{34} +(-1.95238 + 2.44821i) q^{35} +(1.36030 - 2.35612i) q^{36} +(-3.66600 - 6.34969i) q^{37} +(-1.14071 - 0.171935i) q^{38} +(-2.35801 - 1.13556i) q^{39} +(-0.733052 + 0.680173i) q^{40} +(-0.974368 + 4.26899i) q^{41} -1.65516 q^{42} +(4.90797 - 4.34877i) q^{43} -3.11545 q^{44} +(0.605393 - 2.65240i) q^{45} +(-4.83089 + 4.48241i) q^{46} +(8.11767 + 3.90926i) q^{47} +(-0.522670 - 0.0787799i) q^{48} +(-1.40275 - 2.42963i) q^{49} +(-0.500000 + 0.866025i) q^{50} +(-0.469564 + 0.588815i) q^{51} +(0.370020 - 4.93757i) q^{52} +(2.87956 - 7.33700i) q^{53} +(2.72432 - 1.31196i) q^{54} +(-2.97704 + 0.918295i) q^{55} +(-1.14402 - 2.91491i) q^{56} +(-0.446988 - 0.414744i) q^{57} +(-4.25958 + 2.90413i) q^{58} +(8.09178 + 10.1468i) q^{59} +(-0.522670 + 0.0787799i) q^{60} +(-7.55480 - 2.33035i) q^{61} +(-0.389494 - 5.19743i) q^{62} +(7.03893 + 4.79906i) q^{63} +(-0.222521 - 0.974928i) q^{64} +(-1.10179 - 4.82728i) q^{65} +(-1.36061 - 0.927645i) q^{66} +(-1.00727 - 13.4410i) q^{67} +(-1.36152 - 0.419973i) q^{68} +(-3.44445 + 0.519168i) q^{69} +(-1.95238 - 2.44821i) q^{70} +(-3.14388 + 2.14346i) q^{71} +(1.99435 + 1.85048i) q^{72} +(-0.259796 - 0.661948i) q^{73} +(7.00625 - 2.16114i) q^{74} +(-0.476229 + 0.229340i) q^{75} +(0.421457 - 1.07386i) q^{76} +(0.729039 - 9.72835i) q^{77} +(1.63179 - 2.04620i) q^{78} +(-2.20948 + 3.82694i) q^{79} +(-0.500000 - 0.866025i) q^{80} +(-6.49023 - 0.978245i) q^{81} +(-3.94514 - 1.89988i) q^{82} +(-3.15563 + 2.92800i) q^{83} +(0.368308 - 1.61366i) q^{84} -1.42482 q^{85} +(3.14761 + 5.75261i) q^{86} -2.72500 q^{87} +(0.693253 - 3.03734i) q^{88} +(-1.50564 + 1.39703i) q^{89} +(2.45118 + 1.18043i) q^{90} +(15.3316 + 2.31086i) q^{91} +(-3.29505 - 5.70720i) q^{92} +(1.37747 - 2.38584i) q^{93} +(-5.61760 + 7.04425i) q^{94} +(0.0862086 - 1.15037i) q^{95} +(0.193110 - 0.492036i) q^{96} +(16.3074 - 7.85324i) q^{97} +(2.68085 - 0.826933i) q^{98} +(3.09660 + 7.89001i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 6 q^{2} + 5 q^{3} - 6 q^{4} + 3 q^{5} + 5 q^{6} + q^{7} - 6 q^{8} + 12 q^{9}+O(q^{10}) $ 36 * q - 6 * q^2 + 5 * q^3 - 6 * q^4 + 3 * q^5 + 5 * q^6 + q^7 - 6 * q^8 + 12 * q^9	\( 36 q - 6 q^{2} + 5 q^{3} - 6 q^{4} + 3 q^{5} + 5 q^{6} + q^{7} - 6 q^{8} + 12 q^{9} + 3 q^{10} + 9 q^{11} - 16 q^{12} + 21 q^{13} - 6 q^{14} + 5 q^{15} - 6 q^{16} - 37 q^{17} + 19 q^{18} + 7 q^{19} + 3 q^{20} - 8 q^{21} + 16 q^{22} + 13 q^{23} + 5 q^{24} + 3 q^{25} - 21 q^{26} - 28 q^{27} - 6 q^{28} + 4 q^{29} - 2 q^{30} + 13 q^{31} - 6 q^{32} - 54 q^{33} - 23 q^{34} - 2 q^{35} - 9 q^{36} + 17 q^{37} + 28 q^{38} + 8 q^{39} + 3 q^{40} + 10 q^{41} - 50 q^{42} + 14 q^{43} - 26 q^{44} + 4 q^{45} - 8 q^{46} + 13 q^{47} - 2 q^{48} + 5 q^{49} - 18 q^{50} + 17 q^{51} - 7 q^{52} - 71 q^{53} + 7 q^{54} - 29 q^{55} + q^{56} - 70 q^{57} + 25 q^{58} + 8 q^{59} - 2 q^{60} + 25 q^{61} - 15 q^{62} + 88 q^{63} - 6 q^{64} + 7 q^{65} + 44 q^{66} + 26 q^{67} - 9 q^{68} + 78 q^{69} - 2 q^{70} - 60 q^{71} - 23 q^{72} + 7 q^{73} + 17 q^{74} - 10 q^{75} - 35 q^{76} - 5 q^{77} + 57 q^{78} + 52 q^{79} - 18 q^{80} + q^{81} - 4 q^{82} - 101 q^{83} - 8 q^{84} - 24 q^{85} + 49 q^{86} - 18 q^{87} + 16 q^{88} + 14 q^{89} - 3 q^{90} + 35 q^{91} + 6 q^{92} + 28 q^{93} - 15 q^{94} + 7 q^{95} - 2 q^{96} + 11 q^{97} + 12 q^{98} + 78 q^{99}+O(q^{100}) \) 36 * q - 6 * q^2 + 5 * q^3 - 6 * q^4 + 3 * q^5 + 5 * q^6 + q^7 - 6 * q^8 + 12 * q^9 + 3 * q^10 + 9 * q^11 - 16 * q^12 + 21 * q^13 - 6 * q^14 + 5 * q^15 - 6 * q^16 - 37 * q^17 + 19 * q^18 + 7 * q^19 + 3 * q^20 - 8 * q^21 + 16 * q^22 + 13 * q^23 + 5 * q^24 + 3 * q^25 - 21 * q^26 - 28 * q^27 - 6 * q^28 + 4 * q^29 - 2 * q^30 + 13 * q^31 - 6 * q^32 - 54 * q^33 - 23 * q^34 - 2 * q^35 - 9 * q^36 + 17 * q^37 + 28 * q^38 + 8 * q^39 + 3 * q^40 + 10 * q^41 - 50 * q^42 + 14 * q^43 - 26 * q^44 + 4 * q^45 - 8 * q^46 + 13 * q^47 - 2 * q^48 + 5 * q^49 - 18 * q^50 + 17 * q^51 - 7 * q^52 - 71 * q^53 + 7 * q^54 - 29 * q^55 + q^56 - 70 * q^57 + 25 * q^58 + 8 * q^59 - 2 * q^60 + 25 * q^61 - 15 * q^62 + 88 * q^63 - 6 * q^64 + 7 * q^65 + 44 * q^66 + 26 * q^67 - 9 * q^68 + 78 * q^69 - 2 * q^70 - 60 * q^71 - 23 * q^72 + 7 * q^73 + 17 * q^74 - 10 * q^75 - 35 * q^76 - 5 * q^77 + 57 * q^78 + 52 * q^79 - 18 * q^80 + q^81 - 4 * q^82 - 101 * q^83 - 8 * q^84 - 24 * q^85 + 49 * q^86 - 18 * q^87 + 16 * q^88 + 14 * q^89 - 3 * q^90 + 35 * q^91 + 6 * q^92 + 28 * q^93 - 15 * q^94 + 7 * q^95 - 2 * q^96 + 11 * q^97 + 12 * q^98 + 78 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/430\mathbb{Z}\right)^\times$.

$n$	$87$	$261$
$\chi(n)$	$1$	$e\left(\frac{16}{21}\right)$

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 $

$2$	−0.222521	+	0.974928i	−0.157346	+	0.689378i
$2$	−0.222521	+	0.974928i	−0.157346	+	0.689378i
$3$	−0.387472	+	0.359522i	−0.223707	+	0.207570i	−0.784062	−	0.620683i	$-0.786855\pi$
$3$	−0.387472	+	0.359522i	−0.223707	+	0.207570i	0.560354	+	0.828253i	$0.310665\pi$
$4$	−0.900969	−	0.433884i	−0.450484	−	0.216942i
$5$	−0.988831	−	0.149042i	−0.442219	−	0.0666537i
$5$	−0.988831	−	0.149042i	−0.442219	−	0.0666537i
$6$	−0.264287	−	0.457759i	−0.107895	−	0.186879i
$7$	1.56569	−	2.71185i	0.591774	−	1.02498i	−0.402220	−	0.915543i	$-0.631761\pi$
$7$	1.56569	−	2.71185i	0.591774	−	1.02498i	0.993994	−	0.109439i	$-0.0349054\pi$
$8$	0.623490	−	0.781831i	0.220437	−	0.276419i
$9$	−0.203311	+	2.71300i	−0.0677705	+	0.904334i
$10$	0.365341	−	0.930874i	0.115531	−	0.294368i
$11$	2.80692	−	1.35174i	0.846319	−	0.407566i	0.0401091	−	0.999195i	$-0.487229\pi$
$11$	2.80692	−	1.35174i	0.846319	−	0.407566i	0.806210	+	0.591629i	$0.201515\pi$
$12$	0.505091	−	0.155800i	0.145807	−	0.0449756i
$13$	1.80896	+	4.60914i	0.501714	+	1.27835i	0.927602	+	0.373571i	$0.121867\pi$
$13$	1.80896	+	4.60914i	0.501714	+	1.27835i	−0.425888	+	0.904776i	$0.640038\pi$
$14$	2.29546	+	2.12987i	0.613487	+	0.569233i
$15$	0.436728	−	0.297756i	0.112763	−	0.0768804i
$16$	0.623490	+	0.781831i	0.155872	+	0.195458i
$17$	1.40891	−	0.212358i	0.341710	−	0.0515045i	0.0240543	−	0.999711i	$-0.492343\pi$
$17$	1.40891	−	0.212358i	0.341710	−	0.0515045i	0.317655	+	0.948206i	$0.397104\pi$
$18$	−2.59974	−	0.801914i	−0.612765	−	0.189013i
$19$	0.0862086	+	1.15037i	0.0197776	+	0.263914i	0.998323	+	0.0578840i	$0.0184354\pi$
$19$	0.0862086	+	1.15037i	0.0197776	+	0.263914i	−0.978546	+	0.206030i	$0.933946\pi$
$20$	0.826239	+	0.563320i	0.184753	+	0.125962i
$21$	0.368308	+	1.61366i	0.0803714	+	0.352130i
$22$	0.693253	+	3.03734i	0.147802	+	0.647563i
$23$	5.44500	+	3.71234i	1.13536	+	0.774076i	0.976986	−	0.213303i	$-0.0684221\pi$
$23$	5.44500	+	3.71234i	1.13536	+	0.774076i	0.158375	+	0.987379i	$0.449374\pi$
$24$	0.0395004	+	0.527096i	0.00806298	+	0.107593i
$25$	0.955573	+	0.294755i	0.191115	+	0.0589510i
$26$	−4.89611	+	0.737971i	−0.960207	+	0.144728i
$27$	−1.88529	−	2.36408i	−0.362824	−	0.454967i
$28$	−2.58726	+	1.76396i	−0.488946	+	0.333358i
$29$	3.77916	+	3.50655i	0.701773	+	0.651150i	0.948076	−	0.318043i	$-0.103026\pi$
$29$	3.77916	+	3.50655i	0.701773	+	0.651150i	−0.246304	+	0.969193i	$0.579216\pi$
$30$	0.193110	+	0.492036i	0.0352569	+	0.0898330i
$31$	−4.98045	+	1.53627i	−0.894515	+	0.275921i	−0.707733	−	0.706480i	$-0.750282\pi$
$31$	−4.98045	+	1.53627i	−0.894515	+	0.275921i	−0.186782	+	0.982401i	$0.559806\pi$
$32$	−0.900969	+	0.433884i	−0.159270	+	0.0767005i
$33$	−0.601624	+	1.53291i	−0.104729	+	0.266846i
$34$	−0.106477	+	1.42084i	−0.0182606	+	0.243671i
$35$	−1.95238	+	2.44821i	−0.330012	+	0.413822i
$36$	1.36030	−	2.35612i	0.226717	−	0.392686i
$37$	−3.66600	−	6.34969i	−0.602686	−	1.04388i	−0.992413	−	0.122952i	$-0.960764\pi$
$37$	−3.66600	−	6.34969i	−0.602686	−	1.04388i	0.389727	−	0.920931i	$-0.372570\pi$
$38$	−1.14071	−	0.171935i	−0.185048	−	0.0278916i
$39$	−2.35801	−	1.13556i	−0.377583	−	0.181835i
$40$	−0.733052	+	0.680173i	−0.115906	+	0.107545i
$41$	−0.974368	+	4.26899i	−0.152171	+	0.666704i	0.840081	+	0.542461i	$0.182507\pi$
$41$	−0.974368	+	4.26899i	−0.152171	+	0.666704i	−0.992252	+	0.124243i	$0.960350\pi$
$42$	−1.65516			−0.255397
$43$	4.90797	−	4.34877i	0.748458	−	0.663182i
$43$	4.90797	−	4.34877i	0.748458	−	0.663182i
$44$	−3.11545			−0.469672
$45$	0.605393	−	2.65240i	0.0902466	−	0.395396i
$46$	−4.83089	+	4.48241i	−0.712276	+	0.660895i
$47$	8.11767	+	3.90926i	1.18408	+	0.570225i	0.919098	−	0.394028i	$-0.128919\pi$
$47$	8.11767	+	3.90926i	1.18408	+	0.570225i	0.264985	+	0.964253i	$0.414633\pi$
$48$	−0.522670	−	0.0787799i	−0.0754410	−	0.0113709i
$49$	−1.40275	−	2.42963i	−0.200392	−	0.347090i
$50$	−0.500000	+	0.866025i	−0.0707107	+	0.122474i
$51$	−0.469564	+	0.588815i	−0.0657522	+	0.0824506i
$52$	0.370020	−	4.93757i	0.0513125	−	0.684718i
$53$	2.87956	−	7.33700i	0.395538	−	1.00781i	−0.584921	−	0.811090i	$-0.698875\pi$
$53$	2.87956	−	7.33700i	0.395538	−	1.00781i	0.980459	−	0.196724i	$-0.0630302\pi$
$54$	2.72432	−	1.31196i	0.370733	−	0.178536i
$55$	−2.97704	+	0.918295i	−0.401424	+	0.123823i
$56$	−1.14402	−	2.91491i	−0.152876	−	0.389522i
$57$	−0.446988	−	0.414744i	−0.0592050	−	0.0549342i
$58$	−4.25958	+	2.90413i	−0.559310	+	0.381331i
$59$	8.09178	+	10.1468i	1.05346	+	1.32100i	0.945063	+	0.326889i	$0.106000\pi$
$59$	8.09178	+	10.1468i	1.05346	+	1.32100i	0.108397	+	0.994108i	$0.465428\pi$
$60$	−0.522670	+	0.0787799i	−0.0674765	+	0.0101704i
$61$	−7.55480	−	2.33035i	−0.967293	−	0.298370i	−0.229433	−	0.973324i	$-0.573687\pi$
$61$	−7.55480	−	2.33035i	−0.967293	−	0.298370i	−0.737860	+	0.674954i	$0.764163\pi$
$62$	−0.389494	−	5.19743i	−0.0494657	−	0.660074i
$63$	7.03893	+	4.79906i	0.886821	+	0.604625i
$64$	−0.222521	−	0.974928i	−0.0278151	−	0.121866i
$65$	−1.10179	−	4.82728i	−0.136661	−	0.598750i
$66$	−1.36061	−	0.927645i	−0.167479	−	0.114185i
$67$	−1.00727	−	13.4410i	−0.123057	−	1.64208i	−0.627484	−	0.778630i	$-0.715915\pi$
$67$	−1.00727	−	13.4410i	−0.123057	−	1.64208i	0.504426	−	0.863455i	$-0.331704\pi$
$68$	−1.36152	−	0.419973i	−0.165108	−	0.0509292i
$69$	−3.44445	+	0.519168i	−0.414663	+	0.0625005i
$70$	−1.95238	−	2.44821i	−0.233354	−	0.292617i
$71$	−3.14388	+	2.14346i	−0.373110	+	0.254382i	−0.735328	−	0.677711i	$-0.762972\pi$
$71$	−3.14388	+	2.14346i	−0.373110	+	0.254382i	0.362218	+	0.932093i	$0.382020\pi$
$72$	1.99435	+	1.85048i	0.235036	+	0.218082i
$73$	−0.259796	−	0.661948i	−0.0304068	−	0.0774752i	0.914864	−	0.403762i	$-0.132298\pi$
$73$	−0.259796	−	0.661948i	−0.0304068	−	0.0774752i	−0.945271	+	0.326287i	$0.894202\pi$
$74$	7.00625	−	2.16114i	0.814460	−	0.251228i
$75$	−0.476229	+	0.229340i	−0.0549902	+	0.0264819i
$76$	0.421457	−	1.07386i	0.0483445	−	0.123180i
$77$	0.729039	−	9.72835i	0.0830817	−	1.10865i
$78$	1.63179	−	2.04620i	0.184764	−	0.231687i
$79$	−2.20948	+	3.82694i	−0.248586	+	0.430564i	−0.963134	−	0.269023i	$-0.913299\pi$
$79$	−2.20948	+	3.82694i	−0.248586	+	0.430564i	0.714548	+	0.699587i	$0.246633\pi$
$80$	−0.500000	−	0.866025i	−0.0559017	−	0.0968246i
$81$	−6.49023	−	0.978245i	−0.721137	−	0.108694i
$82$	−3.94514	−	1.89988i	−0.435667	−	0.209806i
$83$	−3.15563	+	2.92800i	−0.346375	+	0.321389i	−0.834105	−	0.551605i	$-0.814016\pi$
$83$	−3.15563	+	2.92800i	−0.346375	+	0.321389i	0.487730	+	0.872995i	$0.337825\pi$
$84$	0.368308	−	1.61366i	0.0401857	−	0.176065i
$85$	−1.42482			−0.154543
$86$	3.14761	+	5.75261i	0.339416	+	0.620320i
$87$	−2.72500			−0.292151
$88$	0.693253	−	3.03734i	0.0739010	−	0.323781i
$89$	−1.50564	+	1.39703i	−0.159597	+	0.148085i	−0.755929	−	0.654653i	$-0.772815\pi$
$89$	−1.50564	+	1.39703i	−0.159597	+	0.148085i	0.596332	+	0.802738i	$0.296624\pi$
$90$	2.45118	+	1.18043i	0.258378	+	0.124428i
$91$	15.3316	+	2.31086i	1.60718	+	0.242244i
$92$	−3.29505	−	5.70720i	−0.343533	−	0.595017i
$93$	1.37747	−	2.38584i	0.142836	−	0.247400i
$94$	−5.61760	+	7.04425i	−0.579411	+	0.726559i
$95$	0.0862086	−	1.15037i	0.00884482	−	0.118026i
$96$	0.193110	−	0.492036i	0.0197092	−	0.0502182i
$97$	16.3074	−	7.85324i	1.65577	−	0.797376i	0.656702	−	0.754150i	$-0.271951\pi$
$97$	16.3074	−	7.85324i	1.65577	−	0.797376i	0.999065	−	0.0432254i	$-0.0137633\pi$
$98$	2.68085	−	0.826933i	0.270807	−	0.0835329i
$99$	3.09660	+	7.89001i	0.311220	+	0.792976i
$100$	−0.733052	−	0.680173i	−0.0733052	−	0.0680173i
$101$	3.38924	−	2.31074i	0.337242	−	0.229928i	−0.382843	−	0.923813i	$-0.625055\pi$
$101$	3.38924	−	2.31074i	0.337242	−	0.229928i	0.720085	+	0.693886i	$0.244103\pi$
$102$	−0.469564	−	0.588815i	−0.0464938	−	0.0583014i
$103$	−5.67229	+	0.854960i	−0.558907	+	0.0842417i	−0.422420	−	0.906400i	$-0.638819\pi$
$103$	−5.67229	+	0.854960i	−0.558907	+	0.0842417i	−0.136487	+	0.990642i	$0.543581\pi$
$104$	4.73144	+	1.45946i	0.463956	+	0.143111i
$105$	−0.123690	−	1.65053i	−0.0120710	−	0.161076i
$106$	6.51228	+	4.44000i	0.632529	+	0.431251i
$107$	−0.194976	−	0.854247i	−0.0188491	−	0.0825832i	0.964629	−	0.263613i	$-0.0849141\pi$
$107$	−0.194976	−	0.854247i	−0.0188491	−	0.0825832i	−0.983478	+	0.181030i	$0.942057\pi$
$108$	0.672851	+	2.94795i	0.0647451	+	0.283667i
$109$	−16.7008	−	11.3864i	−1.59964	−	1.09062i	−0.941128	−	0.338051i	$-0.890232\pi$
$109$	−16.7008	−	11.3864i	−1.59964	−	1.09062i	−0.658515	−	0.752568i	$-0.728815\pi$
$110$	−0.232818	−	3.10674i	−0.0221983	−	0.296216i
$111$	3.70332	+	1.14232i	0.351504	+	0.108425i
$112$	3.09640	−	0.466707i	0.292582	−	0.0440997i
$113$	−6.64048	−	8.32689i	−0.624683	−	0.783328i	0.364312	−	0.931277i	$-0.381304\pi$
$113$	−6.64048	−	8.32689i	−0.624683	−	0.783328i	−0.988995	+	0.147949i	$0.952733\pi$
$114$	0.503810	−	0.343492i	0.0471861	−	0.0321709i
$115$	−4.83089	−	4.48241i	−0.450483	−	0.417987i
$116$	−1.88347	−	4.79901i	−0.174876	−	0.445577i
$117$	−12.8724	+	3.97061i	−1.19005	+	0.367083i
$118$	−11.6930	+	5.63103i	−1.07642	+	0.518379i
$119$	1.63002	−	4.15322i	0.149424	−	0.380725i
$120$	0.0395004	−	0.527096i	0.00360588	−	0.0481171i
$121$	−0.806780	+	1.01167i	−0.0733436	+	0.0919700i
$122$	3.95302	−	6.84683i	0.357890	−	0.619883i
$123$	−1.15725	−	2.00442i	−0.104346	−	0.180732i
$124$	5.15379	+	0.776809i	0.462824	+	0.0697595i
$125$	−0.900969	−	0.433884i	−0.0805851	−	0.0388077i
$126$	−6.24505	+	5.79456i	−0.556353	+	0.516220i
$127$	0.631204	−	2.76549i	0.0560103	−	0.245397i	−0.939171	−	0.343450i	$-0.888404\pi$
$127$	0.631204	−	2.76549i	0.0560103	−	0.245397i	0.995181	+	0.0980530i	$0.0312615\pi$
$128$	1.00000			0.0883883
$129$	−0.338224	+	3.44955i	−0.0297790	+	0.303716i
$130$	4.95142			0.434268
$131$	3.47876	−	15.2415i	0.303941	−	1.33165i	−0.560182	−	0.828370i	$-0.689269\pi$
$131$	3.47876	−	15.2415i	0.303941	−	1.33165i	0.864122	−	0.503282i	$-0.167874\pi$
$132$	1.20715	−	1.12007i	0.105069	−	0.0974897i
$133$	3.25461	+	1.56734i	0.282211	+	0.135906i
$134$	13.3282	+	2.00890i	1.15138	+	0.173543i
$135$	1.51188	+	2.61866i	0.130122	+	0.225378i
$136$	0.712410	−	1.23393i	0.0610886	−	0.105809i
$137$	−4.82405	+	6.04917i	−0.412147	+	0.516815i	−0.943966	−	0.330042i	$-0.892937\pi$
$137$	−4.82405	+	6.04917i	−0.412147	+	0.516815i	0.531820	+	0.846858i	$0.321508\pi$
$138$	0.260312	−	3.47362i	0.0221592	−	0.295694i
$139$	4.70166	−	11.9796i	0.398790	−	1.01610i	−0.580613	−	0.814180i	$-0.697187\pi$
$139$	4.70166	−	11.9796i	0.398790	−	1.01610i	0.979402	−	0.201919i	$-0.0647179\pi$
$140$	2.82127	−	1.35865i	0.238441	−	0.114827i
$141$	−4.55084	+	1.40375i	−0.383249	+	0.118217i
$142$	−1.39014	−	3.54203i	−0.116658	−	0.297240i
$143$	11.3080	+	10.4923i	0.945621	+	0.877408i
$144$	−2.24787	+	1.53257i	−0.187323	+	0.127714i
$145$	−3.21433	−	4.03064i	−0.266935	−	0.334726i
$146$	0.703162	−	0.105985i	0.0581941	−	0.00877135i
$147$	1.41703	+	0.437096i	0.116875	+	0.0360510i
$148$	0.547920	+	7.31149i	0.0450388	+	0.601001i
$149$	−3.00743	−	2.05043i	−0.246379	−	0.167978i	0.433834	−	0.900993i	$-0.357160\pi$
$149$	−3.00743	−	2.05043i	−0.246379	−	0.167978i	−0.680213	+	0.733015i	$0.738113\pi$
$150$	−0.117619	−	0.515322i	−0.00960353	−	0.0420758i
$151$	−1.12274	−	4.91904i	−0.0913671	−	0.400306i	0.908477	−	0.417934i	$-0.137246\pi$
$151$	−1.12274	−	4.91904i	−0.0913671	−	0.400306i	−0.999845	+	0.0176282i	$0.994388\pi$
$152$	0.953149	+	0.649846i	0.0773106	+	0.0527095i
$153$	0.289682	+	3.86554i	0.0234194	+	0.312510i
$154$	9.32222	+	2.87552i	0.751206	+	0.231716i
$155$	5.15379	−	0.776809i	0.413962	−	0.0623948i
$156$	1.63179	+	2.04620i	0.130648	+	0.163827i
$157$	−11.4723	+	7.82166i	−0.915587	+	0.624237i	−0.926741	−	0.375701i	$-0.877402\pi$
$157$	−11.4723	+	7.82166i	−0.915587	+	0.624237i	0.0111538	+	0.999938i	$0.496450\pi$
$158$	−3.23933	−	3.00566i	−0.257707	−	0.239117i
$159$	1.52206	+	3.87815i	0.120707	+	0.307557i
$160$	0.955573	−	0.294755i	0.0755447	−	0.0233024i
$161$	18.5925	−	8.95366i	1.46529	−	0.705647i
$162$	2.39793	−	6.10983i	0.188399	−	0.480034i
$163$	−0.888215	+	11.8524i	−0.0695703	+	0.928352i	0.847800	+	0.530316i	$0.177927\pi$
$163$	−0.888215	+	11.8524i	−0.0695703	+	0.928352i	−0.917370	+	0.398035i	$0.869692\pi$
$164$	2.73012	−	3.42346i	0.213186	−	0.267327i
$165$	0.823373	−	1.42612i	0.0640995	−	0.111024i
$166$	−2.15239	−	3.72805i	−0.167058	−	0.289353i
$167$	−5.11321	−	0.770692i	−0.395672	−	0.0596379i	−0.0518070	−	0.998657i	$-0.516498\pi$
$167$	−5.11321	−	0.770692i	−0.395672	−	0.0596379i	−0.343865	+	0.939019i	$0.611736\pi$
$168$	1.49125	+	0.718148i	0.115052	+	0.0554063i
$169$	−8.44222	+	7.83323i	−0.649401	+	0.602556i
$170$	0.317052	−	1.38910i	0.0243168	−	0.106539i
$171$	−3.13849			−0.240007
$172$	−6.30879	+	1.78862i	−0.481041	+	0.136381i
$173$	−25.1803			−1.91442			−0.957211	−	0.289392i	$-0.906547\pi$
$173$	−25.1803			−1.91442			−0.957211	+	0.289392i	$0.906547\pi$
$174$	0.606370	−	2.65668i	0.0459688	−	0.201402i
$175$	2.29546	−	2.12987i	0.173520	−	0.161003i
$176$	2.80692	+	1.35174i	0.211580	+	0.101891i
$177$	−6.78332	−	1.02242i	−0.509866	−	0.0768499i
$178$	−1.02697	−	1.77876i	−0.0769744	−	0.133324i
$179$	−11.2108	+	19.4176i	−0.837933	+	1.45134i	0.0536865	+	0.998558i	$0.482903\pi$
$179$	−11.2108	+	19.4176i	−0.837933	+	1.45134i	−0.891620	+	0.452785i	$0.850431\pi$
$180$	−1.69627	+	2.12706i	−0.126433	+	0.158542i
$181$	−1.61092	+	21.4962i	−0.119739	+	1.59780i	0.536933	+	0.843625i	$0.319583\pi$
$181$	−1.61092	+	21.4962i	−0.119739	+	1.59780i	−0.656671	+	0.754177i	$0.728036\pi$
$182$	−5.66451	+	14.4329i	−0.419882	+	1.06984i
$183$	3.76508	−	1.81317i	0.278323	−	0.134033i
$184$	6.29733	−	1.94247i	0.464245	−	0.143201i
$185$	2.67868	+	6.82516i	0.196940	+	0.501796i
$186$	2.01951	+	1.87383i	0.148077	+	0.137396i
$187$	3.66764	−	2.50055i	0.268204	−	0.182858i
$188$	−5.61760	−	7.04425i	−0.409706	−	0.513755i
$189$	−9.36278	+	1.41121i	−0.681042	+	0.102651i
$190$	1.10235	+	0.340029i	0.0799728	+	0.0246683i
$191$	−0.122270	−	1.63157i	−0.00884711	−	0.118057i	0.991032	−	0.133627i	$-0.0426625\pi$
$191$	−0.122270	−	1.63157i	−0.00884711	−	0.118057i	−0.999879	+	0.0155708i	$0.995043\pi$
$192$	0.436728	+	0.297756i	0.0315182	+	0.0214887i
$193$	1.78119	+	7.80391i	0.128213	+	0.561738i	0.997700	+	0.0677823i	$0.0215923\pi$
$193$	1.78119	+	7.80391i	0.128213	+	0.561738i	−0.869487	+	0.493956i	$0.835551\pi$
$194$	4.02760	+	17.6461i	0.289165	+	1.26691i
$195$	2.16242	+	1.47432i	0.154854	+	0.105578i
$196$	0.209655	+	2.79765i	0.0149753	+	0.199832i
$197$	3.40178	+	1.04931i	0.242367	+	0.0747602i	0.413559	−	0.910477i	$-0.364286\pi$
$197$	3.40178	+	1.04931i	0.242367	+	0.0747602i	−0.171192	+	0.985238i	$0.554762\pi$
$198$	−8.38125	+	1.26327i	−0.595630	+	0.0897767i
$199$	−0.128041	−	0.160559i	−0.00907660	−	0.0113817i	0.777272	−	0.629164i	$-0.216603\pi$
$199$	−0.128041	−	0.160559i	−0.00907660	−	0.0113817i	−0.786349	+	0.617782i	$0.788031\pi$
$200$	0.826239	−	0.563320i	0.0584239	−	0.0398327i
$201$	5.22263	+	4.84590i	0.368376	+	0.341803i
$202$	1.49863	+	3.81845i	0.105443	+	0.268665i
$203$	15.4262	−	4.75836i	1.08271	−	0.333971i
$204$	0.678540	−	0.326768i	0.0475073	−	0.0228783i
$205$	1.59974	−	4.07608i	0.111731	−	0.284686i
$206$	0.428679	−	5.72032i	0.0298675	−	0.398554i
$207$	−11.1786	+	14.0175i	−0.776967	+	0.974286i
$208$	−2.47571	+	4.28805i	−0.171660	+	0.297323i
$209$	1.79699	+	3.11248i	0.124300	+	0.215295i
$210$	1.63668	+	0.246689i	0.112941	+	0.0170232i
$211$	−13.9990	−	6.74156i	−0.963731	−	0.464108i	−0.115251	−	0.993336i	$-0.536767\pi$
$211$	−13.9990	−	6.74156i	−0.963731	−	0.464108i	−0.848480	+	0.529228i	$0.822482\pi$
$212$	−5.77780	+	5.36101i	−0.396821	+	0.368196i
$213$	0.447546	−	1.96083i	0.0306653	−	0.134354i
$214$	0.876216			0.0598969
$215$	−5.50130	+	3.56871i	−0.375186	+	0.243384i
$216$	−3.02377			−0.205741
$217$	−3.63170	+	15.9115i	−0.246536	+	1.08015i
$218$	14.8172	−	13.7483i	1.00355	−	0.931154i
$219$	0.338648	+	0.163084i	0.0228837	+	0.0110202i
$220$	3.08065	+	0.464334i	0.207698	+	0.0313054i
$221$	3.52744	+	6.10970i	0.237281	+	0.410983i
$222$	−1.93775	+	3.35628i	−0.130053	+	0.225259i
$223$	−6.00881	+	7.53481i	−0.402379	+	0.504568i	−0.941199	−	0.337853i	$-0.890299\pi$
$223$	−6.00881	+	7.53481i	−0.402379	+	0.504568i	0.538819	+	0.842421i	$0.318871\pi$
$224$	−0.234008	+	3.12262i	−0.0156353	+	0.208639i
$225$	−0.993950	+	2.53254i	−0.0662633	+	0.168836i
$226$	9.59577	−	4.62108i	0.638301	−	0.307389i
$227$	20.9125	−	6.45064i	1.38801	−	0.428144i	0.491387	−	0.870941i	$-0.336490\pi$
$227$	20.9125	−	6.45064i	1.38801	−	0.428144i	0.896622	+	0.442797i	$0.146014\pi$
$228$	0.222771	+	0.567612i	0.0147534	+	0.0375910i
$229$	−9.08909	−	8.43344i	−0.600624	−	0.557297i	0.320164	−	0.947362i	$-0.396262\pi$
$229$	−9.08909	−	8.43344i	−0.600624	−	0.557297i	−0.920787	+	0.390065i	$0.872453\pi$
$230$	5.44500	−	3.71234i	0.359033	−	0.244784i
$231$	3.21507	+	4.03157i	0.211536	+	0.265258i
$232$	5.09780	−	0.768370i	0.334687	−	0.0504460i
$233$	4.94824	+	1.52633i	0.324170	+	0.0999933i	0.452569	−	0.891729i	$-0.350508\pi$
$233$	4.94824	+	1.52633i	0.324170	+	0.0999933i	−0.128399	+	0.991723i	$0.540984\pi$
$234$	−1.00668	−	13.4332i	−0.0658087	−	0.878156i
$235$	−7.44435	−	5.07547i	−0.485616	−	0.331087i
$236$	−2.88792	−	12.6528i	−0.187988	−	0.823628i
$237$	−0.519753	−	2.27719i	−0.0337616	−	0.147919i
$238$	3.68638	+	2.51333i	0.238953	+	0.162915i
$239$	−0.525935	−	7.01812i	−0.0340199	−	0.453964i	−0.988038	−	0.154214i	$-0.950716\pi$
$239$	−0.525935	−	7.01812i	−0.0340199	−	0.453964i	0.954018	−	0.299751i	$-0.0969034\pi$
$240$	0.505091	+	0.155800i	0.0326035	+	0.0100568i
$241$	28.1499	−	4.24292i	1.81330	−	0.273310i	0.847158	−	0.531340i	$-0.178311\pi$
$241$	28.1499	−	4.24292i	1.81330	−	0.273310i	0.966137	+	0.258030i	$0.0830734\pi$
$242$	−0.806780	−	1.01167i	−0.0518618	−	0.0650326i
$243$	10.3615	−	7.06438i	0.664693	−	0.453180i
$244$	5.79554	+	5.37747i	0.371021	+	0.344257i
$245$	1.02496	+	2.61156i	0.0654824	+	0.166846i
$246$	2.21168	−	0.682212i	0.141011	−	0.0434963i
$247$	−5.14629	+	2.47832i	−0.327451	+	0.157692i
$248$	−1.90416	+	4.85172i	−0.120914	+	0.308084i
$249$	0.170041	−	2.26903i	0.0107759	−	0.143794i
$250$	0.623490	−	0.781831i	0.0394330	−	0.0494474i
$251$	−6.20003	+	10.7388i	−0.391343	+	0.677825i	−0.992627	−	0.121210i	$-0.961323\pi$
$251$	−6.20003	+	10.7388i	−0.391343	+	0.677825i	0.601284	+	0.799035i	$0.294656\pi$
$252$	−4.25962	−	7.37788i	−0.268331	−	0.464763i
$253$	20.3018	+	3.06001i	1.27636	+	0.192381i
$254$	2.55569	+	1.23076i	0.160358	+	0.0772246i
$255$	0.552078	−	0.512254i	0.0345725	−	0.0320786i
$256$	−0.222521	+	0.974928i	−0.0139076	+	0.0609330i
$257$	−4.85256			−0.302694			−0.151347	−	0.988481i	$-0.548361\pi$
$257$	−4.85256			−0.302694			−0.151347	+	0.988481i	$0.548361\pi$
$258$	−3.28780	−	1.09734i	−0.204690	−	0.0683175i
$259$	−22.9592			−1.42662
$260$	−1.10179	+	4.82728i	−0.0683304	+	0.299375i
$261$	−10.2816	+	9.53995i	−0.636417	+	0.590508i
$262$	14.0852	+	6.78308i	0.870188	+	0.419060i
$263$	25.1531	+	3.79122i	1.55101	+	0.233777i	0.867974	−	0.496610i	$-0.165422\pi$
$263$	25.1531	+	3.79122i	1.55101	+	0.233777i	0.683034	+	0.730387i	$0.260660\pi$
$264$	0.823373	+	1.42612i	0.0506751	+	0.0877718i
$265$	−3.94092	+	6.82587i	−0.242089	+	0.419310i
$266$	−2.25226	+	2.82425i	−0.138095	+	0.173166i
$267$	0.0811311	−	1.08262i	0.00496514	−	0.0662552i
$268$	−4.92433	+	12.5470i	−0.300801	+	0.766430i
$269$	0.188388	−	0.0907231i	0.0114862	−	0.00553149i	−0.428132	−	0.903716i	$-0.640828\pi$
$269$	0.188388	−	0.0907231i	0.0114862	−	0.00553149i	0.439618	+	0.898185i	$0.355114\pi$
$270$	−2.88943	+	0.891271i	−0.175845	+	0.0542410i
$271$	0.970351	+	2.47241i	0.0589446	+	0.150188i	0.957312	−	0.289056i	$-0.0933414\pi$
$271$	0.970351	+	2.47241i	0.0589446	+	0.150188i	−0.898368	+	0.439245i	$0.855246\pi$
$272$	1.04447	+	0.969123i	0.0633301	+	0.0587617i
$273$	−6.77136	+	4.61663i	−0.409821	+	0.279411i
$274$	−4.82405	−	6.04917i	−0.291432	−	0.365444i
$275$	3.08065	−	0.464334i	0.185770	−	0.0280004i
$276$	3.32860	+	1.02674i	0.200358	+	0.0618024i
$277$	−1.42116	−	18.9641i	−0.0853893	−	1.13944i	−0.861129	−	0.508387i	$-0.830242\pi$
$277$	−1.42116	−	18.9641i	−0.0853893	−	1.13944i	0.775739	−	0.631053i	$-0.217377\pi$
$278$	10.6331	+	7.24950i	0.637729	+	0.434796i
$279$	−3.15531	−	13.8243i	−0.188903	−	0.827640i
$280$	0.696796	+	3.05286i	0.0416415	+	0.182443i
$281$	8.09950	+	5.52215i	0.483176	+	0.329424i	0.780290	−	0.625418i	$-0.215072\pi$
$281$	8.09950	+	5.52215i	0.483176	+	0.329424i	−0.297114	+	0.954842i	$0.596024\pi$
$282$	−0.355896	−	4.74910i	−0.0211933	−	0.282805i
$283$	−23.0159	−	7.09946i	−1.36815	−	0.422019i	−0.478271	−	0.878212i	$-0.658736\pi$
$283$	−23.0159	−	7.09946i	−1.36815	−	0.422019i	−0.889881	+	0.456193i	$0.849213\pi$
$284$	3.76256	−	0.567114i	0.223267	−	0.0336520i
$285$	0.380181	+	0.476732i	0.0225200	+	0.0282392i
$286$	−12.7455	+	8.68971i	−0.753655	+	0.513834i
$287$	10.0513	+	9.32623i	0.593309	+	0.550510i
$288$	−0.993950	−	2.53254i	−0.0585691	−	0.149232i
$289$	−14.3048	+	4.41245i	−0.841460	+	0.259556i
$290$	4.64484	−	2.23684i	0.272754	−	0.131352i
$291$	−3.49526	+	8.90578i	−0.204896	+	0.522066i
$292$	−0.0531409	+	0.709116i	−0.00310983	+	0.0414979i
$293$	3.85272	−	4.83116i	0.225079	−	0.282240i	−0.656451	−	0.754369i	$-0.727943\pi$
$293$	3.85272	−	4.83116i	0.225079	−	0.282240i	0.881529	+	0.472129i	$0.156514\pi$
$294$	−0.741455	+	1.28424i	−0.0432426	+	0.0748983i
$295$	−6.48910	−	11.2395i	−0.377810	−	0.654386i
$296$	−7.25010	−	1.09278i	−0.421403	−	0.0635164i
$297$	−8.48748	−	4.08735i	−0.492493	−	0.237172i
$298$	2.66824	−	2.47577i	0.154567	−	0.143417i
$299$	−7.26094	+	31.8123i	−0.419911	+	1.83975i
$300$	0.528574			0.0305172
$301$	−4.10887	−	20.1185i	−0.236831	−	1.15961i
$302$	5.04554			0.290338
$303$	−0.482473	+	2.11385i	−0.0277174	+	0.121438i
$304$	−0.845648	+	0.784647i	−0.0485013	+	0.0450026i
$305$	7.12310	+	3.43030i	0.407867	+	0.196419i
$306$	−3.83308	−	0.577744i	−0.219123	−	0.0330274i
$307$	3.72920	+	6.45916i	0.212837	+	0.368644i	0.952601	−	0.304222i	$-0.0983965\pi$
$307$	3.72920	+	6.45916i	0.212837	+	0.368644i	−0.739765	+	0.672866i	$0.765063\pi$
$308$	−4.87782	+	8.44863i	−0.277939	+	0.481405i
$309$	1.89048	−	2.37058i	0.107546	−	0.134858i
$310$	−0.389494	+	5.19743i	−0.0221217	+	0.295194i
$311$	4.90586	−	12.4999i	0.278186	−	0.708805i	−0.721677	−	0.692230i	$-0.756628\pi$
$311$	4.90586	−	12.4999i	0.278186	−	0.708805i	0.999863	−	0.0165755i	$-0.00527638\pi$
$312$	−2.35801	+	1.13556i	−0.133496	+	0.0642882i
$313$	−14.8208	+	4.57160i	−0.837720	+	0.258402i	−0.683790	−	0.729679i	$-0.739669\pi$
$313$	−14.8208	+	4.57160i	−0.837720	+	0.258402i	−0.153930	+	0.988082i	$0.549193\pi$
$314$	−5.07274	−	12.9251i	−0.286271	−	0.729407i
$315$	−6.24505	−	5.79456i	−0.351868	−	0.326486i
$316$	3.65112	−	2.48929i	0.205392	−	0.140034i
$317$	−17.8294	−	22.3574i	−1.00140	−	1.25572i	−0.966592	−	0.256322i	$-0.917489\pi$
$317$	−17.8294	−	22.3574i	−1.00140	−	1.25572i	−0.0348083	−	0.999394i	$-0.511082\pi$
$318$	−4.11960	+	0.620930i	−0.231016	+	0.0348200i
$319$	15.3478	+	4.73416i	0.859310	+	0.265062i
$320$	0.0747301	+	0.997204i	0.00417754	+	0.0557454i
$321$	0.382668	+	0.260899i	0.0213585	+	0.0145620i
$322$	4.59196	+	20.1187i	0.255900	+	1.12117i
$323$	0.365751	+	1.60246i	0.0203509	+	0.0891633i
$324$	5.42305	+	3.69738i	0.301281	+	0.205410i
$325$	0.370020	+	4.93757i	0.0205250	+	0.273887i
$326$	−11.3576	−	3.50335i	−0.629039	−	0.194033i
$327$	10.5647	−	1.59238i	0.584231	−	0.0880587i
$328$	2.73012	+	3.42346i	0.150746	+	0.189029i
$329$	23.3110	−	15.8932i	1.28518	−	0.876221i
$330$	1.20715	+	1.12007i	0.0664514	+	0.0616579i
$331$	−2.13244	−	5.43338i	−0.117210	−	0.298646i	0.860214	−	0.509933i	$-0.170330\pi$
$331$	−2.13244	−	5.43338i	−0.117210	−	0.298646i	−0.977424	+	0.211287i	$0.932234\pi$
$332$	4.11353	−	1.26886i	0.225760	−	0.0696376i
$333$	17.9721	−	8.65489i	0.984863	−	0.474285i
$334$	1.88916	−	4.81351i	0.103370	−	0.263384i
$335$	−1.00727	+	13.4410i	−0.0550329	+	0.734362i
$336$	−1.03198	+	1.29406i	−0.0562989	+	0.0705966i
$337$	−6.31933	+	10.9454i	−0.344236	+	0.596234i	−0.985215	−	0.171325i	$-0.945195\pi$
$337$	−6.31933	+	10.9454i	−0.344236	+	0.596234i	0.640979	+	0.767559i	$0.278529\pi$
$338$	−5.75827	−	9.97361i	−0.313209	−	0.542493i
$339$	5.56670	+	0.839045i	0.302342	+	0.0455707i
$340$	1.28372	+	0.618206i	0.0696194	+	0.0335269i
$341$	−11.9031	+	11.0445i	−0.644589	+	0.598091i
$342$	0.698381	−	3.05981i	0.0377641	−	0.165455i
$343$	13.1346			0.709200
$344$	−0.339938	−	6.54862i	−0.0183282	−	0.353078i
$345$	3.48336			0.187538
$346$	5.60314	−	24.5490i	0.301227	−	1.31976i
$347$	22.2032	−	20.6016i	1.19193	−	1.10595i	0.199918	−	0.979813i	$-0.435932\pi$
$347$	22.2032	−	20.6016i	1.19193	−	1.10595i	0.992013	−	0.126138i	$-0.0402582\pi$
$348$	2.45514	+	1.18233i	0.131609	+	0.0633797i
$349$	13.6546	+	2.05811i	0.730917	+	0.110168i	0.503948	−	0.863734i	$-0.331880\pi$
$349$	13.6546	+	2.05811i	0.730917	+	0.110168i	0.226969	+	0.973902i	$0.427118\pi$
$350$	1.56569	+	2.71185i	0.0836894	+	0.144954i
$351$	7.48596	−	12.9661i	0.399571	−	0.692078i
$352$	−1.94245	+	2.43576i	−0.103533	+	0.129826i
$353$	1.36494	−	18.2138i	0.0726482	−	0.969423i	−0.835152	−	0.550020i	$-0.814620\pi$
$353$	1.36494	−	18.2138i	0.0726482	−	0.969423i	0.907800	−	0.419403i	$-0.137761\pi$
$354$	2.50622	−	6.38574i	0.133204	−	0.339398i
$355$	3.42824	−	1.65095i	0.181952	−	0.0876234i
$356$	1.96268	−	0.605407i	0.104022	−	0.0320865i
$357$	0.861586	+	2.19529i	0.0456000	+	0.116187i
$358$	−16.4362	−	15.2505i	−0.868679	−	0.806016i
$359$	4.51448	−	3.07792i	0.238265	−	0.162446i	−0.438301	−	0.898828i	$-0.644420\pi$
$359$	4.51448	−	3.07792i	0.238265	−	0.162446i	0.676566	+	0.736382i	$0.263467\pi$
$360$	−1.69627	−	2.12706i	−0.0894014	−	0.112106i
$361$	17.4719	−	2.63346i	0.919571	−	0.138603i
$362$	−20.5988	−	6.35389i	−1.08265	−	0.333953i
$363$	−0.0511125	−	0.682049i	−0.00268271	−	0.0357983i
$364$	−12.8106	−	8.73413i	−0.671458	−	0.457793i
$365$	0.158236	+	0.693275i	0.00828243	+	0.0362877i
$366$	0.929899	+	4.07415i	0.0486066	+	0.212959i
$367$	19.8672	+	13.5452i	1.03706	+	0.707055i	0.957104	−	0.289743i	$-0.0935699\pi$
$367$	19.8672	+	13.5452i	1.03706	+	0.707055i	0.0799552	+	0.996798i	$0.474522\pi$
$368$	0.492479	+	6.57168i	0.0256723	+	0.342572i
$369$	−11.3837	−	3.51140i	−0.592610	−	0.182796i
$370$	−7.25010	+	1.09278i	−0.376915	+	0.0568108i
$371$	−15.3883	−	19.2964i	−0.798923	−	1.00182i
$372$	−2.27623	+	1.55191i	−0.118017	+	0.0804627i
$373$	−24.8474	−	23.0550i	−1.28655	−	1.19375i	−0.969432	−	0.245359i	$-0.921094\pi$
$373$	−24.8474	−	23.0550i	−1.28655	−	1.19375i	−0.317119	−	0.948386i	$-0.602715\pi$
$374$	1.62173	+	4.13211i	0.0838578	+	0.213666i
$375$	0.505091	−	0.155800i	0.0260828	−	0.00804547i
$376$	8.11767	−	3.90926i	0.418637	−	0.201605i
$377$	−9.32586	+	23.7619i	−0.480306	+	1.22380i
$378$	0.707585	−	9.44206i	0.0363942	−	0.485647i
$379$	14.5920	−	18.2978i	0.749542	−	0.939896i	−0.250056	−	0.968231i	$-0.580449\pi$
$379$	14.5920	−	18.2978i	0.749542	−	0.939896i	0.999598	+	0.0283353i	$0.00902060\pi$
$380$	−0.576800	+	0.999047i	−0.0295892	+	0.0512500i
$381$	0.749678	+	1.29848i	0.0384072	+	0.0665232i
$382$	1.61787	+	0.243855i	0.0827776	+	0.0124767i
$383$	−25.9273	−	12.4859i	−1.32482	−	0.638002i	−0.368314	−	0.929701i	$-0.620065\pi$
$383$	−25.9273	−	12.4859i	−1.32482	−	0.638002i	−0.956510	+	0.291700i	$0.905779\pi$
$384$	−0.387472	+	0.359522i	−0.0197731	+	0.0183468i
$385$	−2.17083	+	9.51104i	−0.110636	+	0.484727i
$386$	−8.00461			−0.407424
$387$	10.8004	+	14.1995i	0.549014	+	0.721801i
$388$	−18.0999			−0.918882
$389$	6.87171	−	30.1069i	0.348410	−	1.52648i	−0.432382	−	0.901691i	$-0.642327\pi$
$389$	6.87171	−	30.1069i	0.348410	−	1.52648i	0.780791	−	0.624792i	$-0.214816\pi$
$390$	−1.91854	+	1.78014i	−0.0971489	+	0.0901410i
$391$	8.45984	+	4.07404i	0.427832	+	0.206033i
$392$	−2.77416	−	0.418137i	−0.140116	−	0.0211191i
$393$	4.13171	+	7.15633i	0.208417	+	0.360989i
$394$	−1.77997	+	3.08300i	−0.0896735	+	0.155319i
$395$	2.75518	−	3.45489i	0.138628	−	0.173834i
$396$	0.633406	−	8.45222i	0.0318299	−	0.424740i
$397$	−4.02577	+	10.2575i	−0.202048	+	0.514809i	−0.995601	−	0.0936914i	$-0.970133\pi$
$397$	−4.02577	+	10.2575i	−0.202048	+	0.514809i	0.793554	+	0.608500i	$0.208229\pi$
$398$	0.185025	−	0.0891033i	0.00927446	−	0.00446634i
$399$	−1.82457	+	0.562804i	−0.0913425	+	0.0281754i
$400$	0.365341	+	0.930874i	0.0182671	+	0.0465437i
$401$	21.1221	+	19.5984i	1.05479	+	0.978697i	0.999804	−	0.0197899i	$-0.00629974\pi$
$401$	21.1221	+	19.5984i	1.05479	+	0.978697i	0.0549809	+	0.998487i	$0.482490\pi$
$402$	−5.88654	+	4.01338i	−0.293594	+	0.200169i
$403$	−16.0903	−	20.1766i	−0.801514	−	1.00507i
$404$	−4.05619	+	0.611373i	−0.201803	+	0.0304169i
$405$	6.27194	+	1.93464i	0.311655	+	0.0961330i
$406$	1.20640	+	16.0983i	0.0598726	+	0.798944i
$407$	−18.8733	−	12.8676i	−0.935516	−	0.637824i
$408$	0.167586	+	0.734240i	0.00829672	+	0.0363503i
$409$	7.36093	+	32.2503i	0.363974	+	1.59468i	0.743001	+	0.669290i	$0.233402\pi$
$409$	7.36093	+	32.2503i	0.363974	+	1.59468i	−0.379027	+	0.925386i	$0.623741\pi$
$410$	3.61791	+	2.46665i	0.178676	+	0.121819i
$411$	−0.305622	−	4.07824i	−0.0150752	−	0.201165i
$412$	5.48151	+	1.69082i	0.270055	+	0.0833008i
$413$	40.1857	−	6.05702i	1.97741	−	0.298046i
$414$	−11.1786	−	14.0175i	−0.549399	−	0.688924i
$415$	3.55678	−	2.42497i	0.174595	−	0.119037i
$416$	−3.62965	−	3.36782i	−0.177958	−	0.165121i
$417$	2.48518	+	6.33212i	0.121700	+	0.310085i
$418$	−3.43431	+	1.05934i	−0.167978	+	0.0518142i
$419$	−4.54036	+	2.18652i	−0.221811	+	0.106819i	−0.541489	−	0.840708i	$-0.682139\pi$
$419$	−4.54036	+	2.18652i	−0.221811	+	0.106819i	0.319678	+	0.947526i	$0.396425\pi$
$420$	−0.604699	+	1.54075i	−0.0295063	+	0.0751808i
$421$	2.06053	−	27.4959i	0.100424	−	1.34007i	−0.688348	−	0.725381i	$-0.741664\pi$
$421$	2.06053	−	27.4959i	0.100424	−	1.34007i	0.788772	−	0.614686i	$-0.210717\pi$
$422$	9.68761	−	12.1479i	0.471585	−	0.591349i
$423$	−12.2563	+	21.2285i	−0.595919	+	1.03216i
$424$	−3.94092	−	6.82587i	−0.191388	−	0.331494i
$425$	1.40891	+	0.212358i	0.0683420	+	0.0103009i
$426$	1.81208	+	0.872650i	0.0877954	+	0.0422800i
$427$	−18.1480	+	16.8389i	−0.878243	+	0.814890i
$428$	−0.194976	+	0.854247i	−0.00942454	+	0.0412916i
$429$	−8.15373			−0.393666
$430$	−2.25508	−	6.15749i	−0.108749	−	0.296940i
$431$	−37.7001			−1.81595			−0.907976	−	0.419022i	$-0.862373\pi$
$431$	−37.7001			−1.81595			−0.907976	+	0.419022i	$0.862373\pi$
$432$	0.672851	−	2.94795i	0.0323726	−	0.141833i
$433$	2.49722	−	2.31708i	0.120009	−	0.111352i	−0.617886	−	0.786268i	$-0.712011\pi$
$433$	2.49722	−	2.31708i	0.120009	−	0.111352i	0.737895	+	0.674916i	$0.235820\pi$
$434$	−14.7045	−	7.08130i	−0.705837	−	0.339913i
$435$	2.69457	+	0.406140i	0.129195	+	0.0194729i
$436$	10.1065	+	17.5050i	0.484014	+	0.838336i
$437$	−3.80117	+	6.58382i	−0.181835	+	0.314947i
$438$	−0.234352	+	0.293868i	−0.0111978	+	0.0140416i
$439$	1.51808	−	20.2573i	0.0724539	−	0.966830i	−0.835969	−	0.548777i	$-0.815094\pi$
$439$	1.51808	−	20.2573i	0.0724539	−	0.966830i	0.908423	−	0.418053i	$-0.137287\pi$
$440$	−1.13820	+	2.90009i	−0.0542616	+	0.138256i
$441$	6.87678	−	3.31168i	0.327466	−	0.157699i
$442$	−6.74145	+	2.07946i	−0.320658	+	0.0989099i
$443$	0.823425	+	2.09805i	0.0391221	+	0.0996815i	0.949100	−	0.314976i	$-0.101997\pi$
$443$	0.823425	+	2.09805i	0.0391221	+	0.0996815i	−0.909977	+	0.414658i	$0.863901\pi$
$444$	−2.84094	−	2.63601i	−0.134825	−	0.125099i
$445$	1.69704	−	1.15702i	0.0804473	−	0.0548481i
$446$	−6.00881	−	7.53481i	−0.284525	−	0.356783i
$447$	1.90247	−	0.286752i	0.0899839	−	0.0135629i
$448$	−2.99225	−	0.922988i	−0.141371	−	0.0436071i
$449$	−2.39719	−	31.9882i	−0.113130	−	1.50962i	−0.708239	−	0.705973i	$-0.750510\pi$
$449$	−2.39719	−	31.9882i	−0.113130	−	1.50962i	0.595109	−	0.803645i	$-0.297109\pi$
$450$	−2.24787	−	1.53257i	−0.105966	−	0.0722462i
$451$	3.03559	+	13.2998i	0.142941	+	0.626264i
$452$	2.36996	+	10.3835i	0.111473	+	0.488397i
$453$	2.20353	+	1.50234i	0.103531	+	0.0705862i
$454$	1.63545	+	21.8235i	0.0767554	+	1.02423i
$455$	−14.8159	−	4.57010i	−0.694580	−	0.214250i
$456$	−0.602952	+	0.0908804i	−0.0282358	+	0.00425587i
$457$	−16.2612	−	20.3909i	−0.760668	−	0.953848i	0.239185	−	0.970974i	$-0.423120\pi$
$457$	−16.2612	−	20.3909i	−0.760668	−	0.953848i	−0.999853	+	0.0171261i	$0.994548\pi$
$458$	10.2445	−	6.98459i	0.478694	−	0.326368i
$459$	−3.15822	−	2.93040i	−0.147413	−	0.136779i
$460$	2.40764	+	6.13456i	0.112257	+	0.286025i
$461$	−6.72743	+	2.07514i	−0.313328	+	0.0966487i	−0.447431	−	0.894319i	$-0.647661\pi$
$461$	−6.72743	+	2.07514i	−0.313328	+	0.0966487i	0.134103	+	0.990967i	$0.457185\pi$
$462$	−4.64591	+	2.23735i	−0.216147	+	0.104091i
$463$	2.16683	−	5.52098i	0.100701	−	0.256582i	−0.871641	−	0.490146i	$-0.836944\pi$
$463$	2.16683	−	5.52098i	0.100701	−	0.256582i	0.972341	+	0.233564i	$0.0750388\pi$
$464$	−0.385262	+	5.14097i	−0.0178853	+	0.238663i
$465$	−1.71767	+	2.15389i	−0.0796551	+	0.0998843i
$466$	−2.58915	+	4.48454i	−0.119940	+	0.207742i
$467$	15.5201	+	26.8817i	0.718186	+	1.24394i	0.961718	+	0.274042i	$0.0883608\pi$
$467$	15.5201	+	26.8817i	0.718186	+	1.24394i	−0.243531	+	0.969893i	$0.578306\pi$
$468$	13.3204	+	2.00773i	0.615736	+	0.0928073i
$469$	−38.0271	−	18.3129i	−1.75593	−	0.845611i
$470$	6.60475	−	6.12831i	0.304654	−	0.282678i
$471$	1.63313	−	7.15521i	0.0752506	−	0.329695i
$472$	12.9782			0.597370
$473$	7.89787	−	18.8410i	0.363145	−	0.866309i
$474$	2.33575			0.107285
$475$	−0.256700	+	1.12468i	−0.0117782	+	0.0516037i
$476$	−3.27061	+	3.03469i	−0.149908	+	0.139095i
$477$	19.3198	+	9.30395i	0.884595	+	0.425998i
$478$	6.95919	+	1.04893i	0.318306	+	0.0479769i
$479$	−10.9895	−	19.0343i	−0.502122	−	0.869700i	−0.999997	−	0.00245152i	$-0.999220\pi$
$479$	−10.9895	−	19.0343i	−0.502122	−	0.869700i	0.497875	−	0.867249i	$-0.334114\pi$
$480$	−0.264287	+	0.457759i	−0.0120630	+	0.0208937i
$481$	22.6350	−	28.3834i	1.03207	−	1.29417i
$482$	−2.12741	+	28.3883i	−0.0969007	+	1.29305i
$483$	−3.98503	+	10.1537i	−0.181325	+	0.462009i
$484$	1.16583	−	0.561434i	0.0529923	−	0.0255197i
$485$	−17.2957	+	5.33503i	−0.785359	+	0.242251i
$486$	4.58160	+	11.6737i	0.207826	+	0.529531i
$487$	26.6866	+	24.7615i	1.20928	+	1.12205i	0.989200	+	0.146570i	$0.0468233\pi$
$487$	26.6866	+	24.7615i	1.20928	+	1.12205i	0.220083	+	0.975481i	$0.429367\pi$
$488$	−6.53228	+	4.45363i	−0.295702	+	0.201606i
$489$	−3.91704	−	4.91181i	−0.177134	−	0.222120i
$490$	−2.77416	+	0.418137i	−0.125324	+	0.0188895i
$491$	−4.23335	−	1.30582i	−0.191048	−	0.0589306i	0.197755	−	0.980252i	$-0.436635\pi$
$491$	−4.23335	−	1.30582i	−0.191048	−	0.0589306i	−0.388803	+	0.921321i	$0.627111\pi$
$492$	0.172963	+	2.30803i	0.00779778	+	0.104054i
$493$	6.06913	+	4.13786i	0.273340	+	0.186360i
$494$	−1.27103	−	5.56874i	−0.0571863	−	0.250550i
$495$	−1.88607	−	8.26341i	−0.0847725	−	0.371413i
$496$	−4.30636	−	2.93603i	−0.193361	−	0.131831i
$497$	0.890412	+	11.8817i	0.0399405	+	0.532968i
$498$	2.17431	+	0.670685i	0.0974331	+	0.0300541i
$499$	1.00714	−	0.151801i	0.0450856	−	0.00679556i	−0.126461	−	0.991972i	$-0.540362\pi$
$499$	1.00714	−	0.151801i	0.0450856	−	0.00679556i	0.171546	+	0.985176i	$0.445124\pi$
$500$	0.623490	+	0.781831i	0.0278833	+	0.0349646i
$501$	2.25831	−	1.53969i	0.100894	−	0.0687881i
$502$	−9.08989	−	8.43418i	−0.405702	−	0.376436i
$503$	−8.38507	−	21.3648i	−0.373872	−	0.952610i	−0.986723	−	0.162412i	$-0.948073\pi$
$503$	−8.38507	−	21.3648i	−0.373872	−	0.952610i	0.612851	−	0.790198i	$-0.290022\pi$
$504$	8.14076	−	2.51109i	0.362618	−	0.111853i
$505$	−3.69578	+	1.77979i	−0.164460	+	0.0791998i
$506$	−7.50087	+	19.1119i	−0.333454	+	0.849628i
$507$	0.454908	−	6.07032i	0.0202032	−	0.269592i
$508$	−1.76859	+	2.21775i	−0.0784687	+	0.0983966i
$509$	−2.83063	+	4.90280i	−0.125465	+	0.217313i	−0.921915	−	0.387393i	$-0.873376\pi$
$509$	−2.83063	+	4.90280i	−0.125465	+	0.217313i	0.796449	+	0.604705i	$0.206709\pi$
$510$	0.376561	+	0.652223i	0.0166744	+	0.0288809i
$511$	−2.20186	−	0.331877i	−0.0974046	−	0.0146814i
$512$	−0.900969	−	0.433884i	−0.0398176	−	0.0191751i
$513$	2.55704	−	2.37259i	0.112896	−	0.104752i
$514$	1.07980	−	4.73089i	0.0476277	−	0.208671i
$515$	5.73636			0.252774
$516$	1.80143	−	2.96119i	0.0793037	−	0.130359i
$517$	28.0700			1.23452
$518$	5.10890	−	22.3836i	0.224472	−	0.983477i
$519$	9.75666	−	9.05286i	0.428270	−	0.397376i
$520$	−4.46107	−	2.14834i	−0.195631	−	0.0942109i
$521$	−22.4999	−	3.39132i	−0.985739	−	0.148576i	−0.363661	−	0.931531i	$-0.618473\pi$
$521$	−22.4999	−	3.39132i	−0.985739	−	0.148576i	−0.622078	+	0.782955i	$0.713711\pi$
$522$	−7.01289	−	12.1467i	−0.306946	−	0.531646i
$523$	−5.14050	+	8.90361i	−0.224778	+	0.389328i	−0.956253	−	0.292541i	$-0.905499\pi$
$523$	−5.14050	+	8.90361i	−0.224778	+	0.389328i	0.731474	+	0.681869i	$0.238833\pi$
$524$	−9.74727	+	12.2227i	−0.425812	+	0.533951i
$525$	−0.123690	+	1.65053i	−0.00539829	+	0.0720352i
$526$	−9.29326	+	23.6788i	−0.405206	+	1.03245i
$527$	−6.69074	+	3.22209i	−0.291453	+	0.140357i
$528$	−1.57359	+	0.485387i	−0.0684815	+	0.0211238i
$529$	7.46373	+	19.0173i	0.324510	+	0.826839i
$530$	−5.77780	−	5.36101i	−0.250971	−	0.232867i
$531$	−29.1734	+	19.8901i	−1.26602	+	0.863155i
$532$	−2.25226	−	2.82425i	−0.0976480	−	0.122447i
$533$	−21.4390	+	3.23140i	−0.928625	+	0.139968i
$534$	1.03742	+	0.320003i	0.0448937	+	0.0138479i
$535$	0.0654797	+	0.873766i	0.00283093	+	0.0377762i
$536$	−11.1366	−	7.59284i	−0.481030	−	0.327961i
$537$	−2.63720	−	11.5543i	−0.113803	−	0.498606i
$538$	0.0465281	+	0.203853i	0.00200597	+	0.00878873i
$539$	−7.22163	−	4.92363i	−0.311058	−	0.212076i
$540$	−0.225966	−	3.01531i	−0.00972404	−	0.129758i
$541$	28.8693	+	8.90502i	1.24119	+	0.382856i	0.844729	−	0.535195i	$-0.179762\pi$
$541$	28.8693	+	8.90502i	1.24119	+	0.382856i	0.396462	+	0.918051i	$0.370238\pi$
$542$	−2.62635	+	0.395858i	−0.112811	+	0.0170036i
$543$	−7.10417	−	8.90835i	−0.304869	−	0.382294i
$544$	−1.17724	+	0.802629i	−0.0504738	+	0.0344125i
$545$	14.8172	+	13.7483i	0.634698	+	0.588914i
$546$	−2.99412	−	7.62888i	−0.128136	−	0.326486i
$547$	17.1174	−	5.28002i	0.731887	−	0.225757i	0.0936589	−	0.995604i	$-0.470144\pi$
$547$	17.1174	−	5.28002i	0.731887	−	0.225757i	0.638229	+	0.769847i	$0.279667\pi$
$548$	6.97096	−	3.35704i	0.297785	−	0.143405i
$549$	7.85821	−	20.0224i	0.335380	−	0.854535i
$550$	−0.232818	+	3.10674i	−0.00992739	+	0.132472i
$551$	−3.70805	+	4.64974i	−0.157968	+	0.198086i
$552$	−1.74168	+	3.01668i	−0.0741308	+	0.128398i
$553$	6.91871	+	11.9836i	0.294214	+	0.509593i
$554$	18.8048	+	2.83437i	0.798941	+	0.120421i
$555$	−3.49171	−	1.68152i	−0.148215	−	0.0713764i
$556$	−9.43382	+	8.75330i	−0.400083	+	0.371223i
$557$	−0.357487	+	1.56625i	−0.0151472	+	0.0663642i	−0.981937	−	0.189210i	$-0.939407\pi$
$557$	−0.357487	+	1.56625i	−0.0151472	+	0.0663642i	0.966789	+	0.255574i	$0.0822645\pi$
$558$	14.1798			0.600280
$559$	28.9224	+	14.7548i	1.22329	+	0.624062i
$560$	−3.13137			−0.132325
$561$	−0.522104	+	2.28749i	−0.0220433	+	0.0965778i
$562$	−7.18600	+	6.66764i	−0.303123	+	0.281257i
$563$	12.7791	+	6.15411i	0.538577	+	0.259365i	0.683339	−	0.730102i	$-0.260527\pi$
$563$	12.7791	+	6.15411i	0.538577	+	0.259365i	−0.144762	+	0.989467i	$0.546242\pi$
$564$	4.70922	+	0.709801i	0.198294	+	0.0298880i
$565$	5.32525	+	9.22360i	0.224035	+	0.388040i
$566$	12.0430	−	20.8590i	0.506204	−	0.876771i
$567$	−12.8145	+	16.0689i	−0.538159	+	0.674831i
$568$	−0.284352	+	3.79442i	−0.0119312	+	0.159210i
$569$	−11.9617	+	30.4778i	−0.501459	+	1.27770i	0.426322	+	0.904571i	$0.359809\pi$
$569$	−11.9617	+	30.4778i	−0.501459	+	1.27770i	−0.927781	+	0.373125i	$0.878286\pi$
$570$	−0.549377	+	0.264566i	−0.0230109	+	0.0110815i
$571$	10.0304	−	3.09398i	0.419761	−	0.129479i	−0.0776772	−	0.996979i	$-0.524750\pi$
$571$	10.0304	−	3.09398i	0.419761	−	0.129479i	0.497438	+	0.867499i	$0.334274\pi$
$572$	−5.63571	−	14.3596i	−0.235641	−	0.600403i
$573$	0.633962	+	0.588231i	0.0264841	+	0.0245737i
$574$	−11.3290	+	7.72400i	−0.472864	+	0.322393i
$575$	4.10886	+	5.15235i	0.171351	+	0.214868i
$576$	2.69022	−	0.405486i	0.112093	−	0.0168952i
$577$	30.8990	+	9.53109i	1.28634	+	0.396784i	0.861165	−	0.508325i	$-0.169735\pi$
$577$	30.8990	+	9.53109i	1.28634	+	0.396784i	0.425178	+	0.905110i	$0.360211\pi$
$578$	−1.11870	−	14.9280i	−0.0465318	−	0.620924i
$579$	−3.49584	−	2.38342i	−0.145282	−	0.0990516i
$580$	1.14718	+	5.02613i	0.0476341	+	0.208699i
$581$	2.99956	+	13.1419i	0.124443	+	0.545218i
$582$	−7.90473	−	5.38935i	−0.327661	−	0.223396i
$583$	−1.83503	−	24.4868i	−0.0759993	−	1.01414i
$584$	−0.679512	−	0.209602i	−0.0281184	−	0.00867338i
$585$	13.3204	−	2.00773i	0.550731	−	0.0830094i
$586$	3.85272	+	4.83116i	0.159155	+	0.199574i
$587$	−24.7761	+	16.8920i	−1.02262	+	0.697209i	−0.953807	−	0.300421i	$-0.902873\pi$
$587$	−24.7761	+	16.8920i	−1.02262	+	0.697209i	−0.0688110	+	0.997630i	$0.521921\pi$
$588$	−1.08705	−	1.00864i	−0.0448292	−	0.0415954i
$589$	−2.19664	−	5.59694i	−0.0905109	−	0.230618i
$590$	12.4016	−	3.82539i	0.510567	−	0.157489i
$591$	−1.69534	+	0.816435i	−0.0697371	+	0.0335836i
$592$	2.67868	−	6.82516i	0.110093	−	0.280512i
$593$	−2.42214	+	32.3213i	−0.0994656	+	1.32728i	0.694579	+	0.719416i	$0.255591\pi$
$593$	−2.42214	+	32.3213i	−0.0994656	+	1.32728i	−0.794045	+	0.607859i	$0.792028\pi$
$594$	5.87352	−	7.36516i	0.240993	−	0.302196i
$595$	−2.23082	+	3.86389i	−0.0914547	+	0.158404i
$596$	1.81995	+	3.15225i	0.0745482	+	0.129121i
$597$	0.107337	+	0.0161784i	0.00439300	+	0.000662138i
$598$	−29.3989	−	14.1578i	−1.20221	−	0.578955i
$599$	−15.5929	+	14.4681i	−0.637108	+	0.591150i	−0.931147	−	0.364643i	$-0.881191\pi$
$599$	−15.5929	+	14.4681i	−0.637108	+	0.591150i	0.294039	+	0.955793i	$0.405000\pi$
$600$	−0.117619	+	0.515322i	−0.00480177	+	0.0210379i
$601$	−8.53929			−0.348325			−0.174162	−	0.984717i	$-0.555722\pi$
$601$	−8.53929			−0.348325			−0.174162	+	0.984717i	$0.555722\pi$
$602$	20.5284	+	0.470932i	0.836674	+	0.0191938i
$603$	36.6704			1.49333
$604$	−1.12274	+	4.91904i	−0.0456836	+	0.200153i
$605$	0.948550	−	0.880126i	0.0385641	−	0.0357822i
$606$	−1.95349	−	0.940753i	−0.0793553	−	0.0382155i
$607$	21.2824	+	3.20781i	0.863826	+	0.130201i	0.565986	−	0.824415i	$-0.308496\pi$
$607$	21.2824	+	3.20781i	0.863826	+	0.130201i	0.297840	+	0.954616i	$0.403734\pi$
$608$	−0.576800	−	0.999047i	−0.0233923	−	0.0405167i
$609$	−4.26650	+	7.38979i	−0.172887	+	0.299449i
$610$	−4.92934	+	6.18119i	−0.199583	+	0.250269i
$611$	−3.33385	+	44.4872i	−0.134873	+	1.79976i
$612$	1.41620	−	3.60842i	0.0572465	−	0.145862i
$613$	−41.1087	+	19.7969i	−1.66036	+	0.799589i	−0.661602	+	0.749855i	$0.730123\pi$
$613$	−41.1087	+	19.7969i	−1.66036	+	0.799589i	−0.998762	+	0.0497342i	$0.984163\pi$
$614$	−7.12704	+	2.19840i	−0.287624	+	0.0887203i
$615$	0.845584	+	2.15451i	0.0340972	+	0.0868783i
$616$	−7.15138	−	6.63552i	−0.288137	−	0.267353i
$617$	10.9294	−	7.45151i	0.440000	−	0.299987i	−0.322984	−	0.946404i	$-0.604686\pi$
$617$	10.9294	−	7.45151i	0.440000	−	0.299987i	0.762984	+	0.646418i	$0.223734\pi$
$618$	1.89048	+	2.37058i	0.0760462	+	0.0953589i
$619$	41.8993	−	6.31531i	1.68408	−	0.253834i	0.763899	−	0.645336i	$-0.223283\pi$
$619$	41.8993	−	6.31531i	1.68408	−	0.253834i	0.920177	+	0.391502i	$0.128045\pi$
$620$	−4.98045	−	1.53627i	−0.200020	−	0.0616979i
$621$	−1.48914	−	19.8712i	−0.0597572	−	0.797405i
$622$	11.0949	+	7.56435i	0.444864	+	0.303303i
$623$	1.43117	+	6.27037i	0.0573387	+	0.251217i
$624$	−0.582380	−	2.55157i	−0.0233139	−	0.102145i
$625$	0.826239	+	0.563320i	0.0330496	+	0.0225328i
$626$	−1.15905	−	15.4665i	−0.0463250	−	0.618164i
$627$	−1.81529	−	0.559942i	−0.0724956	−	0.0223619i
$628$	13.7299	−	2.06944i	0.547881	−	0.0825798i
$629$	−6.51345	−	8.16761i	−0.259708	−	0.325664i
$630$	7.03893	−	4.79906i	0.280438	−	0.191199i
$631$	−4.80368	−	4.45717i	−0.191232	−	0.177437i	0.578746	−	0.815508i	$-0.303542\pi$
$631$	−4.80368	−	4.45717i	−0.191232	−	0.177437i	−0.769978	+	0.638071i	$0.779733\pi$
$632$	1.61443	+	4.11350i	0.0642185	+	0.163626i
$633$	7.84796	−	2.42078i	0.311928	−	0.0962172i
$634$	25.7643	−	12.4074i	1.02323	−	0.492761i
$635$	−1.03633	+	2.64052i	−0.0411254	+	0.104786i
$636$	0.311336	−	4.15449i	0.0123453	−	0.164736i
$637$	8.66100	−	10.8606i	0.343161	−	0.430311i
$638$	−8.03067	+	13.9095i	−0.317937	+	0.550683i
$639$	−5.17603	−	8.96516i	−0.204761	−	0.354656i
$640$	−0.988831	−	0.149042i	−0.0390870	−	0.00589141i
$641$	−5.14351	−	2.47698i	−0.203156	−	0.0978350i	0.329539	−	0.944142i	$-0.393107\pi$
$641$	−5.14351	−	2.47698i	−0.203156	−	0.0978350i	−0.532696	+	0.846307i	$0.678821\pi$
$642$	−0.339509	+	0.315019i	−0.0133994	+	0.0124328i
$643$	8.77039	−	38.4256i	0.345870	−	1.51536i	−0.440585	−	0.897711i	$-0.645229\pi$
$643$	8.77039	−	38.4256i	0.345870	−	1.51536i	0.786456	−	0.617647i	$-0.211914\pi$
$644$	−20.6361			−0.813175
$645$	0.848575	−	3.36061i	0.0334126	−	0.132324i
$646$	−1.64367			−0.0646694
$647$	2.42545	−	10.6266i	0.0953544	−	0.417775i	−0.904610	−	0.426241i	$-0.859838\pi$
$647$	2.42545	−	10.6266i	0.0953544	−	0.417775i	0.999964	+	0.00846576i	$0.00269477\pi$
$648$	−4.81142	+	4.46434i	−0.189010	+	0.175376i
$649$	36.4288	+	17.5432i	1.42996	+	0.688631i
$650$	−4.89611	−	0.737971i	−0.192041	−	0.0289456i
$651$	−4.31336	−	7.47095i	−0.169054	−	0.292810i
$652$	5.94282	−	10.2933i	0.232739	−	0.403115i
$653$	−8.39066	+	10.5216i	−0.328352	+	0.411740i	−0.918416	−	0.395616i	$-0.870531\pi$
$653$	−8.39066	+	10.5216i	−0.328352	+	0.411740i	0.590064	+	0.807357i	$0.299103\pi$
$654$	−0.798421	+	10.6542i	−0.0312207	+	0.416612i
$655$	−5.71153	+	14.5527i	−0.223168	+	0.568622i
$656$	−3.94514	+	1.89988i	−0.154032	+	0.0741778i
$657$	1.84869	−	0.570244i	0.0721241	−	0.0222473i
$658$	10.3075	+	26.2632i	0.401829	+	1.02384i
$659$	7.40794	+	6.87356i	0.288572	+	0.267756i	0.811153	−	0.584834i	$-0.198840\pi$
$659$	7.40794	+	6.87356i	0.288572	+	0.267756i	−0.522581	+	0.852590i	$0.675031\pi$
$660$	−1.36061	+	0.927645i	−0.0529615	+	0.0361085i
$661$	3.91701	+	4.91177i	0.152354	+	0.191046i	0.852151	−	0.523296i	$-0.175298\pi$
$661$	3.91701	+	4.91177i	0.152354	+	0.191046i	−0.699797	+	0.714342i	$0.746726\pi$
$662$	5.77167	−	0.869939i	0.224322	−	0.0338111i
$663$	−3.56335	−	1.09915i	−0.138389	−	0.0426874i
$664$	0.321697	+	4.29275i	0.0124843	+	0.166591i
$665$	−2.98466	−	2.03491i	−0.115740	−	0.0789104i
$666$	4.43873	+	19.4474i	0.171997	+	0.753570i
$667$	7.56004	+	33.1227i	0.292726	+	1.28252i
$668$	4.27245	+	2.91291i	0.165306	+	0.112704i
$669$	−0.380680	−	5.07982i	−0.0147179	−	0.196397i
$670$	−12.8799	−	3.97293i	−0.497594	−	0.153487i
$671$	−24.3558	+	3.67104i	−0.940244	+	0.141719i
$672$	−1.03198	−	1.29406i	−0.0398094	−	0.0499194i
$673$	−11.7672	+	8.02274i	−0.453592	+	0.309254i	−0.768479	−	0.639876i	$-0.778986\pi$
$673$	−11.7672	+	8.02274i	−0.453592	+	0.309254i	0.314887	+	0.949129i	$0.398034\pi$
$674$	−9.26479	−	8.59647i	−0.356867	−	0.331124i
$675$	−1.10471	−	2.81474i	−0.0425201	−	0.108340i
$676$	11.0049	−	3.39456i	0.423265	−	0.130560i
$677$	7.38222	−	3.55509i	0.283722	−	0.136633i	−0.286611	−	0.958047i	$-0.592529\pi$
$677$	7.38222	−	3.55509i	0.283722	−	0.136633i	0.570333	+	0.821414i	$0.306814\pi$
$678$	−2.05672	+	5.24042i	−0.0789877	+	0.201257i
$679$	4.23551	−	56.5189i	0.162544	−	2.16900i
$680$	−0.888360	+	1.11397i	−0.0340671	+	0.0427188i
$681$	−5.78385	+	10.0179i	−0.221638	+	0.383888i
$682$	−8.11887	−	14.0623i	−0.310888	−	0.538473i
$683$	11.8333	+	1.78358i	0.452789	+	0.0682469i	0.371478	−	0.928442i	$-0.378851\pi$
$683$	11.8333	+	1.78358i	0.452789	+	0.0682469i	0.0813111	+	0.996689i	$0.474089\pi$
$684$	2.82769	+	1.36174i	0.108119	+	0.0520675i
$685$	5.67175	−	5.26262i	0.216707	−	0.201074i
$686$	−2.92272	+	12.8053i	−0.111590	+	0.488907i
$687$	6.55377			0.250042
$688$	6.46008	+	1.12579i	0.246288	+	0.0429203i
$689$	39.0263			1.48678
$690$	−0.775120	+	3.39602i	−0.0295083	+	0.129284i
$691$	−22.4945	+	20.8719i	−0.855733	+	0.794004i	−0.980156	−	0.198225i	$-0.936482\pi$
$691$	−22.4945	+	20.8719i	−0.855733	+	0.794004i	0.124424	+	0.992229i	$0.460292\pi$
$692$	22.6866	+	10.9253i	0.862417	+	0.415318i
$693$	26.2448	+	3.95577i	0.996958	+	0.150267i
$694$	15.1444	+	26.2308i	0.574872	+	0.995708i
$695$	−6.43462	+	11.1451i	−0.244079	+	0.422757i
$696$	−1.69901	+	2.13049i	−0.0644008	+	0.0807561i
$697$	−0.466238	+	6.22151i	−0.0176600	+	0.235657i
$698$	−5.04495	+	12.8543i	−0.190954	+	0.486543i
$699$	−2.46606	+	1.18759i	−0.0932748	+	0.0449188i
$700$	−2.99225	+	0.922988i	−0.113097	+	0.0348857i
$701$	6.90713	+	17.5991i	0.260879	+	0.664708i	0.999960	−	0.00890764i	$-0.00283543\pi$
$701$	6.90713	+	17.5991i	0.260879	+	0.664708i	−0.739082	+	0.673616i	$0.764740\pi$
$702$	10.9752	+	10.1835i	0.414232	+	0.384351i
$703$	6.98848	−	4.76466i	0.263575	−	0.179703i
$704$	−1.94245	−	2.43576i	−0.0732089	−	0.0918010i
$705$	4.70922	−	0.709801i	0.177360	−	0.0267327i
$706$	17.4534	+	5.38367i	0.656868	+	0.202617i
$707$	−0.959902	−	12.8090i	−0.0361008	−	0.481732i
$708$	5.66795	+	3.86434i	0.213015	+	0.145231i
$709$	−4.18021	−	18.3147i	−0.156991	−	0.687823i	−0.990751	−	0.135695i	$-0.956673\pi$
$709$	−4.18021	−	18.3147i	−0.156991	−	0.687823i	0.833759	−	0.552128i	$-0.186184\pi$
$710$	0.846704	+	3.70965i	0.0317763	+	0.139221i
$711$	−9.93327	−	6.77239i	−0.372527	−	0.253984i
$712$	0.153491	+	2.04819i	0.00575230	+	0.0767591i
$713$	−32.8217	−	10.1242i	−1.22918	−	0.379152i
$714$	−2.33197	+	0.351487i	−0.0872717	+	0.0131541i
$715$	−9.61789	−	12.0604i	−0.359689	−	0.451035i
$716$	18.5256	−	12.6305i	0.692333	−	0.472025i
$717$	2.72695	+	2.53024i	0.101840	+	0.0944935i
$718$	1.99618	+	5.08619i	0.0744969	+	0.189815i
$719$	19.7752	−	6.09985i	0.737492	−	0.227486i	0.0968210	−	0.995302i	$-0.469133\pi$
$719$	19.7752	−	6.09985i	0.737492	−	0.227486i	0.640671	+	0.767816i	$0.278656\pi$
$720$	2.45118	−	1.18043i	0.0913502	−	0.0439920i
$721$	−6.56250	+	16.7210i	−0.244400	+	0.622722i
$722$	−1.32042	+	17.6198i	−0.0491410	+	0.655741i
$723$	−9.38189	+	11.7645i	−0.348916	+	0.437527i
$724$	10.7783	−	18.6685i	0.400571	−	0.693809i
$725$	2.57769	+	4.46469i	0.0957330	+	0.165814i
$726$	0.676322	+	0.101939i	0.0251007	+	0.00378332i
$727$	−14.7402	−	7.09848i	−0.546682	−	0.263268i	0.140093	−	0.990138i	$-0.455260\pi$
$727$	−14.7402	−	7.09848i	−0.546682	−	0.263268i	−0.686775	+	0.726870i	$0.740974\pi$
$728$	11.3658	−	10.5459i	0.421244	−	0.390857i
$729$	2.90657	−	12.7345i	0.107651	−	0.471648i
$730$	−0.711104			−0.0263191
$731$	5.99137	−	7.16926i	0.221599	−	0.265165i
$732$	−4.17893			−0.154458
$733$	−5.94167	+	26.0322i	−0.219461	+	0.961520i	0.738417	+	0.674344i	$0.235574\pi$
$733$	−5.94167	+	26.0322i	−0.219461	+	0.961520i	−0.957878	+	0.287176i	$0.907284\pi$
$734$	−17.6265	+	16.3550i	−0.650606	+	0.603674i
$735$	−1.33606	−	0.643411i	−0.0492812	−	0.0237326i
$736$	−6.51650	−	0.982204i	−0.240201	−	0.0362045i
$737$	−20.9961	−	36.3664i	−0.773403	−	1.33957i
$738$	5.95646	−	10.3169i	0.219260	−	0.379770i
$739$	7.93947	−	9.95578i	0.292058	−	0.366229i	−0.614056	−	0.789262i	$-0.710463\pi$
$739$	7.93947	−	9.95578i	0.292058	−	0.366229i	0.906114	+	0.423033i	$0.139035\pi$
$740$	0.547920	−	7.31149i	0.0201420	−	0.268776i
$741$	1.10303	−	2.81049i	0.0405210	−	0.103246i
$742$	22.2368	−	10.7087i	0.816338	−	0.393128i
$743$	2.39125	−	0.737602i	0.0877264	−	0.0270600i	−0.250581	−	0.968096i	$-0.580622\pi$
$743$	2.39125	−	0.737602i	0.0877264	−	0.0270600i	0.338308	+	0.941036i	$0.390146\pi$
$744$	−1.00649	−	2.56449i	−0.0368997	−	0.0940189i
$745$	2.66824	+	2.47577i	0.0977568	+	0.0907051i
$746$	28.0061	−	19.0942i	1.02538	−	0.699089i
$747$	−7.30209	−	9.15653i	−0.267169	−	0.335020i
$748$	−4.38937	+	0.661592i	−0.160491	+	0.0241902i
$749$	−2.62186	−	0.808737i	−0.0958007	−	0.0295506i
$750$	0.0395004	+	0.527096i	0.00144235	+	0.0192468i
$751$	−21.7377	−	14.8205i	−0.793218	−	0.540807i	0.0975683	−	0.995229i	$-0.468894\pi$
$751$	−21.7377	−	14.8205i	−0.793218	−	0.540807i	−0.890787	+	0.454422i	$0.849846\pi$
$752$	2.00490	+	8.78403i	0.0731111	+	0.320321i
$753$	−1.45848	−	6.39002i	−0.0531500	−	0.232865i
$754$	−21.0909	−	14.3796i	−0.768087	−	0.523673i
$755$	0.377054	+	5.03143i	0.0137224	+	0.183113i
$756$	9.04788	+	2.79090i	0.329068	+	0.101504i
$757$	6.54418	−	0.986376i	0.237852	−	0.0358505i	−0.0290343	−	0.999578i	$-0.509243\pi$
$757$	6.54418	−	0.986376i	0.237852	−	0.0358505i	0.266887	+	0.963728i	$0.414005\pi$
$758$	14.5920	+	18.2978i	0.530006	+	0.664607i
$759$	−8.96653	+	6.11328i	−0.325465	+	0.221898i
$760$	−0.845648	−	0.784647i	−0.0306749	−	0.0284621i
$761$	16.9154	+	43.0998i	0.613184	+	1.56237i	0.812832	+	0.582499i	$0.197925\pi$
$761$	16.9154	+	43.0998i	0.613184	+	1.56237i	−0.199648	+	0.979868i	$0.563980\pi$
$762$	−1.43274	+	0.441943i	−0.0519028	+	0.0160099i
$763$	−57.0263	+	27.4624i	−2.06449	+	0.994206i
$764$	−0.597752	+	1.52305i	−0.0216259	+	0.0551019i
$765$	0.289682	−	3.86554i	0.0104735	−	0.139759i
$766$	17.9423	−	22.4989i	0.648280	−	0.812918i
$767$	−32.1303	+	55.6512i	−1.16016	+	2.00945i
$768$	−0.264287	−	0.457759i	−0.00953664	−	0.0165179i
$769$	7.16894	+	1.08054i	0.258519	+	0.0389654i	0.277023	−	0.960863i	$-0.410652\pi$
$769$	7.16894	+	1.08054i	0.258519	+	0.0389654i	−0.0185041	+	0.999829i	$0.505890\pi$
$770$	−8.78952	−	4.23281i	−0.316752	−	0.152540i
$771$	1.88023	−	1.74460i	0.0677148	−	0.0628302i
$772$	1.78119	−	7.80391i	0.0641065	−	0.280869i
$773$	29.2069			1.05050			0.525250	−	0.850948i	$-0.323972\pi$
$773$	29.2069			1.05050			0.525250	+	0.850948i	$0.323972\pi$
$774$	−16.2468	+	7.36991i	−0.583979	+	0.264906i
$775$	−5.21200			−0.187221
$776$	4.02760	−	17.6461i	0.144582	−	0.633457i
$777$	8.89605	−	8.25433i	0.319144	−	0.296122i
$778$	27.8230	+	13.3988i	0.997503	+	0.480372i
$779$	−4.99493	−	0.752864i	−0.178962	−	0.0269742i
$780$	−1.30860	−	2.26655i	−0.0468552	−	0.0811556i
$781$	−5.92723	+	10.2663i	−0.212093	+	0.367356i
$782$	−5.85439	+	7.34117i	−0.209353	+	0.262520i
$783$	1.16494	−	15.5451i	0.0416317	−	0.555536i
$784$	1.02496	−	2.61156i	0.0366058	−	0.0932700i
$785$	12.5099	−	6.02445i	0.446497	−	0.215022i
$786$	−7.89630	+	2.43568i	−0.281652	+	0.0868780i
$787$	−15.9724	−	40.6971i	−0.569356	−	1.45069i	−0.868114	−	0.496366i	$-0.834668\pi$
$787$	−15.9724	−	40.6971i	−0.569356	−	1.45069i	0.298758	−	0.954329i	$-0.403428\pi$
$788$	−2.60962	−	2.42137i	−0.0929638	−	0.0862578i
$789$	−11.1092	+	7.57410i	−0.395497	+	0.269645i
$790$	2.75518	+	3.45489i	0.0980249	+	0.122919i
$791$	−32.9782	+	4.97066i	−1.17257	+	0.176736i
$792$	8.09936	+	2.49832i	0.287798	+	0.0887740i
$793$	−2.92539	−	39.0367i	−0.103884	−	1.38623i
$794$	−9.10450	−	6.20734i	−0.323107	−	0.220290i
$795$	−0.927052	−	4.06168i	−0.0328792	−	0.144053i
$796$	0.0456974	+	0.200213i	0.00161970	+	0.00709637i
$797$	−37.2388	−	25.3890i	−1.31907	−	0.899323i	−0.320219	−	0.947344i	$-0.603756\pi$
$797$	−37.2388	−	25.3890i	−1.31907	−	0.899323i	−0.998846	+	0.0480203i	$0.984709\pi$
$798$	−0.142689	−	1.90406i	−0.00505114	−	0.0674028i
$799$	12.2672	+	3.78393i	0.433982	+	0.133866i
$800$	−0.988831	+	0.149042i	−0.0349604	+	0.00526944i
$801$	−3.48403	−	4.36883i	−0.123102	−	0.154365i
$802$	−23.8071	+	16.2314i	−0.840659	+	0.573152i
$803$	−1.62401	−	1.50686i	−0.0573101	−	0.0531760i
$804$	−2.60287	−	6.63202i	−0.0917963	−	0.233893i
$805$	−19.7193	+	6.08259i	−0.695013	+	0.214383i
$806$	23.2511	−	11.1972i	0.818986	−	0.394403i
$807$	−0.0403784	+	0.102882i	−0.00142139	+	0.00362163i
$808$	0.306543	−	4.09054i	0.0107842	−	0.143905i
$809$	−20.4558	+	25.6507i	−0.719186	+	0.901831i	−0.998292	−	0.0584296i	$-0.981391\pi$
$809$	−20.4558	+	25.6507i	−0.719186	+	0.901831i	0.279105	+	0.960260i	$0.409962\pi$
$810$	−3.28177	+	5.68420i	−0.115310	+	0.199722i
$811$	−15.8722	−	27.4915i	−0.557349	−	0.965357i	−0.997717	−	0.0675397i	$-0.978485\pi$
$811$	−15.8722	−	27.4915i	−0.557349	−	0.965357i	0.440367	−	0.897818i	$-0.354848\pi$
$812$	−15.9631	−	2.40605i	−0.560195	−	0.0844359i
$813$	−1.26487	−	0.609130i	−0.0443609	−	0.0213631i
$814$	16.7447	−	15.5368i	0.586901	−	0.544565i
$815$	2.64480	−	11.5876i	0.0926434	−	0.405897i
$816$	−0.753123			−0.0263646
$817$	5.42582	+	5.27110i	0.189826	+	0.184412i
$818$	−33.0797			−1.15660
$819$	−9.38645	+	41.1247i	−0.327989	+	1.43701i
$820$	−3.20987	+	2.97832i	−0.112093	+	0.104007i
$821$	28.5372	+	13.7428i	0.995955	+	0.479627i	0.859564	−	0.511028i	$-0.170735\pi$
$821$	28.5372	+	13.7428i	0.995955	+	0.479627i	0.136391	+	0.990655i	$0.456450\pi$
$822$	4.04399	+	0.609534i	0.141050	+	0.0212599i
$823$	−22.6347	−	39.2044i	−0.788996	−	1.36658i	−0.926583	−	0.376091i	$-0.877268\pi$
$823$	−22.6347	−	39.2044i	−0.788996	−	1.36658i	0.137587	−	0.990490i	$-0.456065\pi$
$824$	−2.86818	+	4.96783i	−0.0999178	+	0.173063i
$825$	−1.02673	+	1.28748i	−0.0357461	+	0.0448242i
$826$	−3.03700	+	40.5260i	−0.105671	+	1.41008i
$827$	4.33729	−	11.0512i	0.150822	−	0.384289i	−0.835416	−	0.549618i	$-0.814773\pi$
$827$	4.33729	−	11.0512i	0.150822	−	0.384289i	0.986239	+	0.165329i	$0.0528685\pi$
$828$	16.1536	−	7.77915i	0.561375	−	0.270344i
$829$	−24.4943	+	7.55549i	−0.850722	+	0.262413i	−0.689303	−	0.724473i	$-0.742083\pi$
$829$	−24.4943	+	7.55549i	−0.850722	+	0.262413i	−0.161419	+	0.986886i	$0.551607\pi$
$830$	1.57271	+	4.00721i	0.0545897	+	0.139092i
$831$	7.36866	+	6.83711i	0.255616	+	0.237177i
$832$	4.09105	−	2.78923i	0.141832	−	0.0966993i
$833$	−2.49229	−	3.12523i	−0.0863527	−	0.108283i
$834$	−6.72637	+	1.01384i	−0.232915	+	0.0351063i
$835$	4.94123	+	1.52417i	0.170998	+	0.0527460i
$836$	−0.268579	−	3.58393i	−0.00928898	−	0.123953i
$837$	13.0214	+	8.87786i	0.450086	+	0.306864i
$838$	−1.12138	−	4.91307i	−0.0387373	−	0.169719i
$839$	8.10705	+	35.5193i	0.279887	+	1.22626i	0.897937	+	0.440124i	$0.145066\pi$
$839$	8.10705	+	35.5193i	0.279887	+	1.22626i	−0.618050	+	0.786139i	$0.712077\pi$
$840$	−1.36756	−	0.932386i	−0.0471853	−	0.0321704i
$841$	−0.180999	−	2.41526i	−0.00624134	−	0.0832849i
$842$	26.3480	+	8.12727i	0.908011	+	0.280084i
$843$	−5.12366	+	0.772268i	−0.176468	+	0.0265983i
$844$	9.68761	+	12.1479i	0.333461	+	0.418147i
$845$	9.51541	−	6.48750i	0.327340	−	0.223177i
$846$	−17.9689	−	16.6727i	−0.617785	−	0.573220i
$847$	1.48033	+	3.77182i	0.0508648	+	0.129601i
$848$	7.53167	−	2.32321i	0.258639	−	0.0797795i
$849$	11.4704	−	5.52387i	0.393664	−	0.189579i
$850$	−0.520545	+	1.32633i	−0.0178545	+	0.0454926i
$851$	3.61085	−	48.1835i	0.123778	−	1.65171i
$852$	−1.25400	+	1.57246i	−0.0429612	+	0.0538716i
$853$	−16.6643	+	28.8634i	−0.570575	+	0.988264i	0.425932	+	0.904755i	$0.359946\pi$
$853$	−16.6643	+	28.8634i	−0.570575	+	0.988264i	−0.996507	+	0.0835092i	$0.973387\pi$
$854$	−12.3784	−	21.4400i	−0.423579	−	0.733661i
$855$	3.10344	+	0.467768i	0.106135	+	0.0159973i
$856$	−0.789443	−	0.380176i	−0.0269826	−	0.0129941i
$857$	−37.2349	+	34.5489i	−1.27192	+	1.18017i	−0.297677	+	0.954667i	$0.596212\pi$
$857$	−37.2349	+	34.5489i	−1.27192	+	1.18017i	−0.974243	+	0.225503i	$0.927598\pi$
$858$	1.81437	−	7.94930i	0.0619417	−	0.271384i
$859$	−20.1607			−0.687873			−0.343937	−	0.938993i	$-0.611761\pi$
$859$	−20.1607			−0.687873			−0.343937	+	0.938993i	$0.611761\pi$
$860$	6.50491	−	0.828367i	0.221815	−	0.0282471i
$861$	−7.24758			−0.246997
$862$	8.38907	−	36.7549i	0.285733	−	1.25188i
$863$	−28.9317	+	26.8447i	−0.984848	+	0.913805i	−0.996284	−	0.0861296i	$-0.972550\pi$
$863$	−28.9317	+	26.8447i	−0.984848	+	0.913805i	0.0114363	+	0.999935i	$0.496360\pi$
$864$	2.72432	+	1.31196i	0.0926832	+	0.0446339i
$865$	24.8990	+	3.75293i	0.846593	+	0.127603i
$866$	1.70330	+	2.95021i	0.0578806	+	0.100252i
$867$	3.95635	−	6.85260i	0.134365	−	0.232726i
$868$	10.1758	−	12.7601i	0.345389	−	0.433105i
$869$	−1.02881	+	13.7286i	−0.0349001	+	0.465710i
$870$	−0.995555	+	2.53663i	−0.0337525	+	0.0859999i
$871$	60.1296	−	28.9569i	2.03741	−	0.981167i
$872$	−19.3150	+	5.95789i	−0.654088	+	0.201759i
$873$	17.9904	+	45.8387i	0.608882	+	1.55141i
$874$	−5.57291	−	5.17091i	−0.188507	−	0.174909i
$875$	−2.58726	+	1.76396i	−0.0874654	+	0.0596329i
$876$	−0.234352	−	0.293868i	−0.00791802	−	0.00992888i
$877$	−28.6141	+	4.31288i	−0.966229	+	0.145636i	−0.613157	−	0.789961i	$-0.710101\pi$
$877$	−28.6141	+	4.31288i	−0.966229	+	0.145636i	−0.353071	+	0.935596i	$0.614863\pi$
$878$	19.4116	+	5.98770i	0.655111	+	0.202075i
$879$	0.244084	+	3.25708i	0.00823276	+	0.109859i
$880$	−2.57411	−	1.75500i	−0.0867731	−	0.0591609i
$881$	−7.78153	−	34.0931i	−0.262166	−	1.14863i	−0.918896	−	0.394500i	$-0.870918\pi$
$881$	−7.78153	−	34.0931i	−0.262166	−	1.14863i	0.656730	−	0.754126i	$-0.271939\pi$
$882$	1.69842	+	7.44128i	0.0571889	+	0.250561i
$883$	30.5491	+	20.8280i	1.02806	+	0.700918i	0.955060	−	0.296414i	$-0.0957907\pi$
$883$	30.5491	+	20.8280i	1.02806	+	0.700918i	0.0729989	+	0.997332i	$0.476743\pi$
$884$	−0.527212	−	7.03515i	−0.0177320	−	0.236618i
$885$	6.55518	+	2.02200i	0.220350	+	0.0679689i
$886$	−2.22868	+	0.335919i	−0.0748739	+	0.0112854i
$887$	−5.83627	−	7.31845i	−0.195963	−	0.245729i	0.674136	−	0.738607i	$-0.264516\pi$
$887$	−5.83627	−	7.31845i	−0.195963	−	0.245729i	−0.870098	+	0.492878i	$0.835945\pi$
$888$	3.20209	−	2.18315i	0.107455	−	0.0732616i
$889$	−6.51131	−	6.04161i	−0.218382	−	0.202629i
$890$	0.750386	+	1.91195i	0.0251530	+	0.0640888i
$891$	−19.5399	+	6.02727i	−0.654612	+	0.201921i
$892$	8.68298	−	4.18150i	0.290728	−	0.140007i
$893$	−3.79730	+	9.67536i	−0.127072	+	0.323774i
$894$	−0.143778	+	1.91858i	−0.00480865	+	0.0641670i
$895$	13.9796	−	17.5299i	0.467287	−	0.585959i
$896$	1.56569	−	2.71185i	0.0523059	−	0.0905965i
$897$	−8.62378	−	14.9368i	−0.287940	−	0.498726i
$898$	31.7196	+	4.78097i	1.05850	+	0.159543i
$899$	−24.2089	−	11.6584i	−0.807413	−	0.388829i
$900$	1.99435	−	1.85048i	0.0664783	−	0.0616828i
$901$	2.49895	−	10.9486i	0.0832522	−	0.364752i
$902$	−13.6418			−0.454224
$903$	8.82510	+	6.31813i	0.293681	+	0.210254i
$904$	−10.6505			−0.354230
$905$	4.79677	−	21.0160i	0.159450	−	0.698597i
$906$	−1.95501	+	1.81398i	−0.0649507	+	0.0602655i
$907$	−47.5028	−	22.8761i	−1.57730	−	0.759589i	−0.578864	−	0.815424i	$-0.696504\pi$
$907$	−47.5028	−	22.8761i	−1.57730	−	0.759589i	−0.998440	+	0.0558350i	$0.982218\pi$
$908$	−21.6403	−	3.26175i	−0.718159	−	0.108245i
$909$	5.57998	+	9.66481i	0.185076	+	0.320562i
$910$	7.75237	−	13.4275i	0.256988	−	0.445117i
$911$	12.2453	−	15.3551i	0.405705	−	0.508738i	−0.536443	−	0.843937i	$-0.680232\pi$
$911$	12.2453	−	15.3551i	0.405705	−	0.508738i	0.942147	+	0.335199i	$0.108804\pi$
$912$	0.0455676	−	0.608058i	0.00150890	−	0.0201348i
$913$	−4.89971	+	12.4843i	−0.162157	+	0.413169i
$914$	23.4982	−	11.3161i	0.777250	−	0.374304i
$915$	−3.99327	+	1.23176i	−0.132013	+	0.0407208i
$916$	4.52985	+	11.5419i	0.149671	+	0.381354i
$917$	−35.8858	−	33.2972i	−1.18506	−	1.09957i
$918$	3.55970	−	2.42696i	0.117488	−	0.0801017i
$919$	9.21334	+	11.5532i	0.303920	+	0.381104i	0.910215	−	0.414136i	$-0.135916\pi$
$919$	9.21334	+	11.5532i	0.303920	+	0.381104i	−0.606295	+	0.795240i	$0.707345\pi$
$920$	−6.51650	+	0.982204i	−0.214843	+	0.0323823i
$921$	−3.76717	−	1.16202i	−0.124132	−	0.0382898i
$922$	−0.526115	−	7.02052i	−0.0173267	−	0.231208i
$923$	−15.5667	−	10.6132i	−0.512384	−	0.349337i
$924$	−1.14745	−	5.02729i	−0.0377482	−	0.165386i
$925$	−1.63152	−	7.14816i	−0.0536441	−	0.235030i
$926$	4.90040	+	3.34103i	0.161037	+	0.109793i
$927$	−1.16627	−	15.5628i	−0.0383052	−	0.511148i
$928$	−4.92634	−	1.51958i	−0.161715	−	0.0498825i
$929$	30.3489	−	4.57436i	0.995715	−	0.150080i	0.369084	−	0.929396i	$-0.379672\pi$
$929$	30.3489	−	4.57436i	0.995715	−	0.150080i	0.626631	+	0.779316i	$0.284433\pi$
$930$	−1.71767	−	2.15389i	−0.0563247	−	0.0706289i
$931$	2.67405	−	1.82314i	0.0876385	−	0.0597509i
$932$	−3.79596	−	3.52214i	−0.124341	−	0.115372i
$933$	2.59311	+	6.60713i	0.0848946	+	0.216308i
$934$	−29.6612	+	9.14928i	−0.970545	+	0.299374i
$935$	−3.99936	+	1.92599i	−0.130793	+	0.0629866i
$936$	−4.92146	+	12.5397i	−0.160863	+	0.409872i
$937$	0.417002	−	5.56450i	0.0136229	−	0.181784i	−0.986241	−	0.165311i	$-0.947137\pi$
$937$	0.417002	−	5.56450i	0.0136229	−	0.181784i	0.999864	−	0.0164732i	$-0.00524380\pi$
$938$	26.3156	−	32.9987i	0.859234	−	1.07745i
$939$	4.09905	−	7.09976i	0.133767	−	0.231692i
$940$	4.50497	+	7.80283i	0.146936	+	0.254500i
$941$	−58.6990	−	8.84746i	−1.91353	−	0.288419i	−0.919121	−	0.393976i	$-0.871099\pi$
$941$	−58.6990	−	8.84746i	−1.91353	−	0.288419i	−0.994413	+	0.105557i	$0.966337\pi$
$942$	6.61241	+	3.18437i	0.215444	+	0.103752i
$943$	−21.1534	+	19.6274i	−0.688848	+	0.639158i
$944$	−2.88792	+	12.6528i	−0.0939939	+	0.411814i
$945$	9.46854			0.308012
$946$	16.6112	+	11.8924i	0.540075	+	0.386654i
$947$	2.34350			0.0761535			0.0380768	−	0.999275i	$-0.487877\pi$
$947$	2.34350			0.0761535			0.0380768	+	0.999275i	$0.487877\pi$
$948$	−0.519753	+	2.27719i	−0.0168808	+	0.0739596i
$949$	2.58106	−	2.39487i	0.0837846	−	0.0777408i
$950$	−1.03936	−	0.500528i	−0.0337212	−	0.0162393i
$951$	14.9464	+	2.25280i	0.484669	+	0.0730521i
$952$	−2.23082	−	3.86389i	−0.0723013	−	0.125230i
$953$	13.6104	−	23.5739i	0.440884	−	0.763633i	−0.556871	−	0.830599i	$-0.687998\pi$
$953$	13.6104	−	23.5739i	0.440884	−	0.763633i	0.997755	+	0.0669655i	$0.0213317\pi$
$954$	−13.3697	+	16.7651i	−0.432861	+	0.542791i
$955$	−0.122270	+	1.63157i	−0.00395655	+	0.0527965i
$956$	−2.57120	+	6.55130i	−0.0831584	+	0.211884i
$957$	−7.64887	+	3.68350i	−0.247253	+	0.119071i
$958$	21.0025	−	6.47840i	0.678559	−	0.209308i
$959$	8.85148	+	22.5532i	0.285829	+	0.728281i
$960$	−0.387472	−	0.359522i	−0.0125056	−	0.0116035i
$961$	−3.16863	+	2.16034i	−0.102214	+	0.0696883i
$962$	22.6350	+	28.3834i	0.729782	+	0.915118i
$963$	2.35721	−	0.355293i	0.0759602	−	0.0114492i
$964$	−27.2031	−	8.39105i	−0.876154	−	0.270258i
$965$	−0.598185	−	7.98222i	−0.0192563	−	0.256957i
$966$	−9.01236	−	6.14452i	−0.289968	−	0.197697i
$967$	−7.83381	−	34.3222i	−0.251918	−	1.10373i	−0.929658	−	0.368424i	$-0.879897\pi$
$967$	−7.83381	−	34.3222i	−0.251918	−	1.10373i	0.677740	−	0.735302i	$-0.262960\pi$
$968$	0.287936	+	1.26153i	0.00925463	+	0.0405472i
$969$	−0.717838	−	0.489414i	−0.0230603	−	0.0157222i
$970$	−1.35260	−	18.0493i	−0.0434295	−	0.579527i
$971$	−43.4998	−	13.4179i	−1.39598	−	0.430601i	−0.496676	−	0.867936i	$-0.665446\pi$
$971$	−43.4998	−	13.4179i	−1.39598	−	0.430601i	−0.899299	+	0.437334i	$0.855923\pi$
$972$	−12.4005	+	1.86908i	−0.397748	+	0.0599508i
$973$	−25.1256	−	31.5065i	−0.805491	−	1.01005i
$974$	−30.0790	+	20.5075i	−0.963793	+	0.657103i
$975$	−1.91854	−	1.78014i	−0.0614424	−	0.0570102i
$976$	−2.88840	−	7.35953i	−0.0924555	−	0.235573i
$977$	29.4258	−	9.07667i	0.941416	−	0.290388i	0.214194	−	0.976791i	$-0.431287\pi$
$977$	29.4258	−	9.07667i	0.941416	−	0.290388i	0.727222	+	0.686403i	$0.240811\pi$
$978$	5.66028	−	2.72585i	0.180996	−	0.0871630i
$979$	−2.33779	+	5.95659i	−0.0747161	+	0.190373i
$980$	0.209655	−	2.79765i	0.00669717	−	0.0893676i
$981$	34.2867	−	42.9942i	1.09469	−	1.37270i
$982$	2.21508	−	3.83664i	0.0706862	−	0.122432i
$983$	−1.47300	−	2.55131i	−0.0469814	−	0.0813742i	0.841578	−	0.540135i	$-0.181627\pi$
$983$	−1.47300	−	2.55131i	−0.0469814	−	0.0813742i	−0.888560	+	0.458761i	$0.848293\pi$
$984$	−2.28865	−	0.344959i	−0.0729596	−	0.0109969i
$985$	−3.20739	−	1.54460i	−0.102196	−	0.0492150i
$986$	−5.38462	+	4.99620i	−0.171481	+	0.159111i
$987$	−3.31843	+	14.5390i	−0.105627	+	0.462781i
$988$	5.71195			0.181721
$989$	42.8680	−	5.45902i	1.36312	−	0.173587i
$990$	8.47592			0.269382
$991$	−0.936551	+	4.10330i	−0.0297505	+	0.130346i	−0.987622	−	0.156850i	$-0.949866\pi$
$991$	−0.936551	+	4.10330i	−0.0297505	+	0.130346i	0.957872	+	0.287196i	$0.0927231\pi$
$992$	3.82067	−	3.54506i	0.121306	−	0.112556i
$993$	2.77968	+	1.33862i	0.0882105	+	0.0424800i
$994$	−11.7820	−	1.77585i	−0.373701	−	0.0563264i
$995$	0.102681	+	0.177849i	0.00325521	+	0.00563818i
$996$	−1.13770	+	1.97055i	−0.0360494	+	0.0624393i
$997$	3.93947	−	4.93994i	0.124764	−	0.156449i	−0.715526	−	0.698586i	$-0.753813\pi$
$997$	3.93947	−	4.93994i	0.124764	−	0.156449i	0.840290	+	0.542136i	$0.182384\pi$
$998$	−0.0761135	+	1.01566i	−0.00240933	+	0.0321503i
$999$	−8.09969	+	20.6377i	−0.256263	+	0.652947i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	430.2.q.a.271.2	✓	36
43.10	even	21	inner	430.2.q.a.311.2	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
430.2.q.a.271.2	✓	36	1.1	even	1	trivial
430.2.q.a.311.2	yes	36	43.10	even	21	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:	\( N \)	\(=\)	\( 430 = 2 \cdot 5 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	430.q (of order \(21\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.222521 + 0.974928i) q^{2} +(-0.387472 + 0.359522i) q^{3} +(-0.900969 - 0.433884i) q^{4} +(-0.988831 - 0.149042i) q^{5} +(-0.264287 - 0.457759i) q^{6} +(1.56569 - 2.71185i) q^{7} +(0.623490 - 0.781831i) q^{8} +(-0.203311 + 2.71300i) q^{9} +O(q^{10})\)	\(q+(-0.222521 + 0.974928i) q^{2} +(-0.387472 + 0.359522i) q^{3} +(-0.900969 - 0.433884i) q^{4} +(-0.988831 - 0.149042i) q^{5} +(-0.264287 - 0.457759i) q^{6} +(1.56569 - 2.71185i) q^{7} +(0.623490 - 0.781831i) q^{8} +(-0.203311 + 2.71300i) q^{9} +(0.365341 - 0.930874i) q^{10} +(2.80692 - 1.35174i) q^{11} +(0.505091 - 0.155800i) q^{12} +(1.80896 + 4.60914i) q^{13} +(2.29546 + 2.12987i) q^{14} +(0.436728 - 0.297756i) q^{15} +(0.623490 + 0.781831i) q^{16} +(1.40891 - 0.212358i) q^{17} +(-2.59974 - 0.801914i) q^{18} +(0.0862086 + 1.15037i) q^{19} +(0.826239 + 0.563320i) q^{20} +(0.368308 + 1.61366i) q^{21} +(0.693253 + 3.03734i) q^{22} +(5.44500 + 3.71234i) q^{23} +(0.0395004 + 0.527096i) q^{24} +(0.955573 + 0.294755i) q^{25} +(-4.89611 + 0.737971i) q^{26} +(-1.88529 - 2.36408i) q^{27} +(-2.58726 + 1.76396i) q^{28} +(3.77916 + 3.50655i) q^{29} +(0.193110 + 0.492036i) q^{30} +(-4.98045 + 1.53627i) q^{31} +(-0.900969 + 0.433884i) q^{32} +(-0.601624 + 1.53291i) q^{33} +(-0.106477 + 1.42084i) q^{34} +(-1.95238 + 2.44821i) q^{35} +(1.36030 - 2.35612i) q^{36} +(-3.66600 - 6.34969i) q^{37} +(-1.14071 - 0.171935i) q^{38} +(-2.35801 - 1.13556i) q^{39} +(-0.733052 + 0.680173i) q^{40} +(-0.974368 + 4.26899i) q^{41} -1.65516 q^{42} +(4.90797 - 4.34877i) q^{43} -3.11545 q^{44} +(0.605393 - 2.65240i) q^{45} +(-4.83089 + 4.48241i) q^{46} +(8.11767 + 3.90926i) q^{47} +(-0.522670 - 0.0787799i) q^{48} +(-1.40275 - 2.42963i) q^{49} +(-0.500000 + 0.866025i) q^{50} +(-0.469564 + 0.588815i) q^{51} +(0.370020 - 4.93757i) q^{52} +(2.87956 - 7.33700i) q^{53} +(2.72432 - 1.31196i) q^{54} +(-2.97704 + 0.918295i) q^{55} +(-1.14402 - 2.91491i) q^{56} +(-0.446988 - 0.414744i) q^{57} +(-4.25958 + 2.90413i) q^{58} +(8.09178 + 10.1468i) q^{59} +(-0.522670 + 0.0787799i) q^{60} +(-7.55480 - 2.33035i) q^{61} +(-0.389494 - 5.19743i) q^{62} +(7.03893 + 4.79906i) q^{63} +(-0.222521 - 0.974928i) q^{64} +(-1.10179 - 4.82728i) q^{65} +(-1.36061 - 0.927645i) q^{66} +(-1.00727 - 13.4410i) q^{67} +(-1.36152 - 0.419973i) q^{68} +(-3.44445 + 0.519168i) q^{69} +(-1.95238 - 2.44821i) q^{70} +(-3.14388 + 2.14346i) q^{71} +(1.99435 + 1.85048i) q^{72} +(-0.259796 - 0.661948i) q^{73} +(7.00625 - 2.16114i) q^{74} +(-0.476229 + 0.229340i) q^{75} +(0.421457 - 1.07386i) q^{76} +(0.729039 - 9.72835i) q^{77} +(1.63179 - 2.04620i) q^{78} +(-2.20948 + 3.82694i) q^{79} +(-0.500000 - 0.866025i) q^{80} +(-6.49023 - 0.978245i) q^{81} +(-3.94514 - 1.89988i) q^{82} +(-3.15563 + 2.92800i) q^{83} +(0.368308 - 1.61366i) q^{84} -1.42482 q^{85} +(3.14761 + 5.75261i) q^{86} -2.72500 q^{87} +(0.693253 - 3.03734i) q^{88} +(-1.50564 + 1.39703i) q^{89} +(2.45118 + 1.18043i) q^{90} +(15.3316 + 2.31086i) q^{91} +(-3.29505 - 5.70720i) q^{92} +(1.37747 - 2.38584i) q^{93} +(-5.61760 + 7.04425i) q^{94} +(0.0862086 - 1.15037i) q^{95} +(0.193110 - 0.492036i) q^{96} +(16.3074 - 7.85324i) q^{97} +(2.68085 - 0.826933i) q^{98} +(3.09660 + 7.89001i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 6 q^{2} + 5 q^{3} - 6 q^{4} + 3 q^{5} + 5 q^{6} + q^{7} - 6 q^{8} + 12 q^{9}+O(q^{10}) \) 36 * q - 6 * q^2 + 5 * q^3 - 6 * q^4 + 3 * q^5 + 5 * q^6 + q^7 - 6 * q^8 + 12 * q^9	\( 36 q - 6 q^{2} + 5 q^{3} - 6 q^{4} + 3 q^{5} + 5 q^{6} + q^{7} - 6 q^{8} + 12 q^{9} + 3 q^{10} + 9 q^{11} - 16 q^{12} + 21 q^{13} - 6 q^{14} + 5 q^{15} - 6 q^{16} - 37 q^{17} + 19 q^{18} + 7 q^{19} + 3 q^{20} - 8 q^{21} + 16 q^{22} + 13 q^{23} + 5 q^{24} + 3 q^{25} - 21 q^{26} - 28 q^{27} - 6 q^{28} + 4 q^{29} - 2 q^{30} + 13 q^{31} - 6 q^{32} - 54 q^{33} - 23 q^{34} - 2 q^{35} - 9 q^{36} + 17 q^{37} + 28 q^{38} + 8 q^{39} + 3 q^{40} + 10 q^{41} - 50 q^{42} + 14 q^{43} - 26 q^{44} + 4 q^{45} - 8 q^{46} + 13 q^{47} - 2 q^{48} + 5 q^{49} - 18 q^{50} + 17 q^{51} - 7 q^{52} - 71 q^{53} + 7 q^{54} - 29 q^{55} + q^{56} - 70 q^{57} + 25 q^{58} + 8 q^{59} - 2 q^{60} + 25 q^{61} - 15 q^{62} + 88 q^{63} - 6 q^{64} + 7 q^{65} + 44 q^{66} + 26 q^{67} - 9 q^{68} + 78 q^{69} - 2 q^{70} - 60 q^{71} - 23 q^{72} + 7 q^{73} + 17 q^{74} - 10 q^{75} - 35 q^{76} - 5 q^{77} + 57 q^{78} + 52 q^{79} - 18 q^{80} + q^{81} - 4 q^{82} - 101 q^{83} - 8 q^{84} - 24 q^{85} + 49 q^{86} - 18 q^{87} + 16 q^{88} + 14 q^{89} - 3 q^{90} + 35 q^{91} + 6 q^{92} + 28 q^{93} - 15 q^{94} + 7 q^{95} - 2 q^{96} + 11 q^{97} + 12 q^{98} + 78 q^{99}+O(q^{100}) \) 36 * q - 6 * q^2 + 5 * q^3 - 6 * q^4 + 3 * q^5 + 5 * q^6 + q^7 - 6 * q^8 + 12 * q^9 + 3 * q^10 + 9 * q^11 - 16 * q^12 + 21 * q^13 - 6 * q^14 + 5 * q^15 - 6 * q^16 - 37 * q^17 + 19 * q^18 + 7 * q^19 + 3 * q^20 - 8 * q^21 + 16 * q^22 + 13 * q^23 + 5 * q^24 + 3 * q^25 - 21 * q^26 - 28 * q^27 - 6 * q^28 + 4 * q^29 - 2 * q^30 + 13 * q^31 - 6 * q^32 - 54 * q^33 - 23 * q^34 - 2 * q^35 - 9 * q^36 + 17 * q^37 + 28 * q^38 + 8 * q^39 + 3 * q^40 + 10 * q^41 - 50 * q^42 + 14 * q^43 - 26 * q^44 + 4 * q^45 - 8 * q^46 + 13 * q^47 - 2 * q^48 + 5 * q^49 - 18 * q^50 + 17 * q^51 - 7 * q^52 - 71 * q^53 + 7 * q^54 - 29 * q^55 + q^56 - 70 * q^57 + 25 * q^58 + 8 * q^59 - 2 * q^60 + 25 * q^61 - 15 * q^62 + 88 * q^63 - 6 * q^64 + 7 * q^65 + 44 * q^66 + 26 * q^67 - 9 * q^68 + 78 * q^69 - 2 * q^70 - 60 * q^71 - 23 * q^72 + 7 * q^73 + 17 * q^74 - 10 * q^75 - 35 * q^76 - 5 * q^77 + 57 * q^78 + 52 * q^79 - 18 * q^80 + q^81 - 4 * q^82 - 101 * q^83 - 8 * q^84 - 24 * q^85 + 49 * q^86 - 18 * q^87 + 16 * q^88 + 14 * q^89 - 3 * q^90 + 35 * q^91 + 6 * q^92 + 28 * q^93 - 15 * q^94 + 7 * q^95 - 2 * q^96 + 11 * q^97 + 12 * q^98 + 78 * q^99

Introduction

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