LMFDB - Embedded newform 189.2.bd.a.185.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [189,2,Mod(47,189)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(189, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([7, 15]))

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

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

chi := DirichletCharacter("189.47");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 189 = 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	189.bd (of order $18$, degree $6$, 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:	$1.50917259820$
Analytic rank:	$0$
Dimension:	$132$
Relative dimension:	$22$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			185.9
Character	$\chi$	$=$	189.185
Dual form			189.2.bd.a.47.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.877614 + 0.154747i) q^{2} +(-0.824649 - 1.52314i) q^{3} +(-1.13313 + 0.412424i) q^{4} +(-1.30288 + 0.474210i) q^{5} +(0.959425 + 1.20912i) q^{6} +(1.81190 + 1.92796i) q^{7} +(2.47415 - 1.42845i) q^{8} +(-1.63991 + 2.51211i) q^{9} +O(q^{10})$	\(q+(-0.877614 + 0.154747i) q^{2} +(-0.824649 - 1.52314i) q^{3} +(-1.13313 + 0.412424i) q^{4} +(-1.30288 + 0.474210i) q^{5} +(0.959425 + 1.20912i) q^{6} +(1.81190 + 1.92796i) q^{7} +(2.47415 - 1.42845i) q^{8} +(-1.63991 + 2.51211i) q^{9} +(1.07004 - 0.617790i) q^{10} +(-0.197926 + 0.543796i) q^{11} +(1.56261 + 1.38580i) q^{12} +(1.85992 + 5.11010i) q^{13} +(-1.88849 - 1.41162i) q^{14} +(1.79671 + 1.59341i) q^{15} +(-0.102835 + 0.0862885i) q^{16} +(1.15616 + 2.00253i) q^{17} +(1.05047 - 2.45844i) q^{18} +(2.96522 + 1.71197i) q^{19} +(1.28075 - 1.07468i) q^{20} +(1.44237 - 4.34966i) q^{21} +(0.0895514 - 0.507871i) q^{22} +(-6.58928 - 1.16187i) q^{23} +(-4.21603 - 2.59050i) q^{24} +(-2.35760 + 1.97826i) q^{25} +(-2.42307 - 4.19688i) q^{26} +(5.17864 + 0.426201i) q^{27} +(-2.84824 - 1.43735i) q^{28} +(-0.224543 + 0.616928i) q^{29} +(-1.82339 - 1.12037i) q^{30} +(0.595291 + 1.63555i) q^{31} +(-3.59586 + 4.28538i) q^{32} +(0.991496 - 0.146972i) q^{33} +(-1.32455 - 1.57853i) q^{34} +(-3.27494 - 1.65268i) q^{35} +(0.822168 - 3.52287i) q^{36} -1.08507 q^{37} +(-2.86724 - 1.04359i) q^{38} +(6.24961 - 7.04696i) q^{39} +(-2.54613 + 3.03436i) q^{40} +(-1.37400 + 0.500093i) q^{41} +(-0.592745 + 4.04053i) q^{42} +(-0.681623 - 3.86568i) q^{43} -0.697818i q^{44} +(0.945338 - 4.05064i) q^{45} +5.96264 q^{46} +(5.79174 + 2.10802i) q^{47} +(0.216232 + 0.0854738i) q^{48} +(-0.434042 + 6.98653i) q^{49} +(1.76293 - 2.10098i) q^{50} +(2.09670 - 3.41237i) q^{51} +(-4.21505 - 5.02331i) q^{52} +(-8.16395 - 4.71346i) q^{53} +(-4.61081 + 0.427340i) q^{54} -0.802359i q^{55} +(7.23690 + 2.18184i) q^{56} +(0.162305 - 5.92822i) q^{57} +(0.101595 - 0.576172i) q^{58} +(3.88097 + 3.25652i) q^{59} +(-2.69305 - 1.06453i) q^{60} +(4.62542 - 12.7082i) q^{61} +(-0.775532 - 1.34326i) q^{62} +(-7.81459 + 1.39002i) q^{63} +(2.62687 - 4.54987i) q^{64} +(-4.84652 - 5.77585i) q^{65} +(-0.847408 + 0.282416i) q^{66} +(-1.43047 + 8.11262i) q^{67} +(-2.13596 - 1.79229i) q^{68} +(3.66415 + 10.9945i) q^{69} +(3.12988 + 0.943626i) q^{70} +(13.6154 + 7.86086i) q^{71} +(-0.468953 + 8.55786i) q^{72} +2.39174i q^{73} +(0.952276 - 0.167912i) q^{74} +(4.95736 + 1.95958i) q^{75} +(-4.06603 - 0.716950i) q^{76} +(-1.40704 + 0.603711i) q^{77} +(-4.39425 + 7.15162i) q^{78} +(-0.465552 - 2.64028i) q^{79} +(0.0930623 - 0.161189i) q^{80} +(-3.62140 - 8.23926i) q^{81} +(1.12845 - 0.651511i) q^{82} +(11.2771 + 4.10455i) q^{83} +(0.159521 + 5.52358i) q^{84} +(-2.45595 - 2.06079i) q^{85} +(1.19640 + 3.28709i) q^{86} +(1.12484 - 0.166738i) q^{87} +(0.287088 + 1.62816i) q^{88} +(-5.91604 + 10.2469i) q^{89} +(-0.202817 + 3.70119i) q^{90} +(-6.48206 + 12.8448i) q^{91} +(7.94566 - 1.40103i) q^{92} +(2.00026 - 2.25547i) q^{93} +(-5.40912 - 0.953774i) q^{94} +(-4.67516 - 0.824357i) q^{95} +(9.49256 + 1.94307i) q^{96} +(-18.3532 + 3.23616i) q^{97} +(-0.700224 - 6.19865i) q^{98} +(-1.04150 - 1.38899i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 132 q - 3 q^{2} - 9 q^{3} - 3 q^{4} - 9 q^{5} + 18 q^{6} - 6 q^{7} - 18 q^{8} - 15 q^{9}+O(q^{10}) $ 132 * q - 3 * q^2 - 9 * q^3 - 3 * q^4 - 9 * q^5 + 18 * q^6 - 6 * q^7 - 18 * q^8 - 15 * q^9	\( 132 q - 3 q^{2} - 9 q^{3} - 3 q^{4} - 9 q^{5} + 18 q^{6} - 6 q^{7} - 18 q^{8} - 15 q^{9} - 9 q^{10} + 9 q^{11} - 9 q^{12} - 42 q^{14} - 24 q^{15} - 15 q^{16} - 9 q^{17} - 3 q^{18} - 9 q^{19} - 18 q^{20} + 15 q^{21} - 12 q^{22} + 30 q^{23} - 36 q^{24} - 3 q^{25} - 12 q^{28} + 6 q^{29} - 3 q^{30} - 9 q^{31} - 51 q^{32} - 9 q^{33} + 18 q^{34} - 9 q^{35} - 6 q^{37} - 9 q^{38} - 9 q^{39} - 9 q^{40} + 27 q^{42} - 12 q^{43} - 63 q^{45} - 6 q^{46} + 45 q^{47} + 30 q^{49} - 9 q^{50} + 33 q^{51} - 9 q^{52} + 45 q^{53} + 117 q^{54} - 51 q^{56} - 3 q^{58} - 9 q^{59} - 15 q^{60} - 63 q^{61} + 99 q^{62} - 33 q^{63} + 18 q^{64} - 102 q^{65} + 63 q^{66} - 3 q^{67} + 144 q^{68} - 108 q^{69} - 15 q^{70} + 18 q^{71} + 15 q^{72} - 33 q^{74} - 9 q^{75} - 36 q^{76} - 57 q^{77} + 66 q^{78} - 21 q^{79} - 72 q^{80} + 57 q^{81} - 18 q^{82} + 90 q^{83} + 51 q^{84} + 9 q^{85} - 33 q^{86} - 9 q^{87} + 45 q^{88} - 9 q^{89} - 81 q^{90} - 21 q^{91} + 150 q^{92} - 87 q^{93} - 9 q^{94} + 27 q^{95} - 9 q^{96} - 180 q^{98} + 96 q^{99}+O(q^{100}) \) 132 * q - 3 * q^2 - 9 * q^3 - 3 * q^4 - 9 * q^5 + 18 * q^6 - 6 * q^7 - 18 * q^8 - 15 * q^9 - 9 * q^10 + 9 * q^11 - 9 * q^12 - 42 * q^14 - 24 * q^15 - 15 * q^16 - 9 * q^17 - 3 * q^18 - 9 * q^19 - 18 * q^20 + 15 * q^21 - 12 * q^22 + 30 * q^23 - 36 * q^24 - 3 * q^25 - 12 * q^28 + 6 * q^29 - 3 * q^30 - 9 * q^31 - 51 * q^32 - 9 * q^33 + 18 * q^34 - 9 * q^35 - 6 * q^37 - 9 * q^38 - 9 * q^39 - 9 * q^40 + 27 * q^42 - 12 * q^43 - 63 * q^45 - 6 * q^46 + 45 * q^47 + 30 * q^49 - 9 * q^50 + 33 * q^51 - 9 * q^52 + 45 * q^53 + 117 * q^54 - 51 * q^56 - 3 * q^58 - 9 * q^59 - 15 * q^60 - 63 * q^61 + 99 * q^62 - 33 * q^63 + 18 * q^64 - 102 * q^65 + 63 * q^66 - 3 * q^67 + 144 * q^68 - 108 * q^69 - 15 * q^70 + 18 * q^71 + 15 * q^72 - 33 * q^74 - 9 * q^75 - 36 * q^76 - 57 * q^77 + 66 * q^78 - 21 * q^79 - 72 * q^80 + 57 * q^81 - 18 * q^82 + 90 * q^83 + 51 * q^84 + 9 * q^85 - 33 * q^86 - 9 * q^87 + 45 * q^88 - 9 * q^89 - 81 * q^90 - 21 * q^91 + 150 * q^92 - 87 * q^93 - 9 * q^94 + 27 * q^95 - 9 * q^96 - 180 * q^98 + 96 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/189\mathbb{Z}\right)^\times$.

$n$	$29$	$136$
$\chi(n)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−0.877614	+	0.154747i	−0.620567	+	0.109423i	−0.475087	−	0.879939i	$-0.657584\pi$
$2$	−0.877614	+	0.154747i	−0.620567	+	0.109423i	−0.145480	+	0.989361i	$0.546472\pi$
$3$	−0.824649	−	1.52314i	−0.476111	−	0.879385i
$3$	−0.824649	−	1.52314i	−0.476111	−	0.879385i
$4$	−1.13313	+	0.412424i	−0.566563	+	0.206212i
$5$	−1.30288	+	0.474210i	−0.582666	+	0.212073i	−0.616501	−	0.787354i	$-0.711450\pi$
$5$	−1.30288	+	0.474210i	−0.582666	+	0.212073i	0.0338349	+	0.999427i	$0.489228\pi$
$6$	0.959425	+	1.20912i	0.391684	+	0.493620i
$7$	1.81190	+	1.92796i	0.684834	+	0.728700i
$7$	1.81190	+	1.92796i	0.684834	+	0.728700i
$8$	2.47415	−	1.42845i	0.874743	−	0.505033i
$9$	−1.63991	+	2.51211i	−0.546636	+	0.837370i
$10$	1.07004	−	0.617790i	0.338377	−	0.195362i
$11$	−0.197926	+	0.543796i	−0.0596768	+	0.163961i	−0.965948	−	0.258736i	$-0.916694\pi$
$11$	−0.197926	+	0.543796i	−0.0596768	+	0.163961i	0.906271	+	0.422696i	$0.138916\pi$
$12$	1.56261	+	1.38580i	0.451086	+	0.400047i
$13$	1.85992	+	5.11010i	0.515850	+	1.41729i	0.875053	+	0.484027i	$0.160826\pi$
$13$	1.85992	+	5.11010i	0.515850	+	1.41729i	−0.359203	+	0.933260i	$0.616951\pi$
$14$	−1.88849	−	1.41162i	−0.504721	−	0.377271i
$15$	1.79671	+	1.59341i	0.463907	+	0.411417i
$16$	−0.102835	+	0.0862885i	−0.0257086	+	0.0215721i
$17$	1.15616	+	2.00253i	0.280410	+	0.485684i	0.971486	−	0.237098i	$-0.0761963\pi$
$17$	1.15616	+	2.00253i	0.280410	+	0.485684i	−0.691076	+	0.722782i	$0.742863\pi$
$18$	1.05047	−	2.45844i	0.247597	−	0.579459i
$19$	2.96522	+	1.71197i	0.680269	+	0.392753i	0.799956	−	0.600058i	$-0.204856\pi$
$19$	2.96522	+	1.71197i	0.680269	+	0.392753i	−0.119688	+	0.992812i	$0.538189\pi$
$20$	1.28075	−	1.07468i	0.286385	−	0.240305i
$21$	1.44237	−	4.34966i	0.314751	−	0.949174i
$22$	0.0895514	−	0.507871i	0.0190924	−	0.108279i
$23$	−6.58928	−	1.16187i	−1.37396	−	0.242266i	−0.562559	−	0.826757i	$-0.690183\pi$
$23$	−6.58928	−	1.16187i	−1.37396	−	0.242266i	−0.811400	+	0.584491i	$0.801294\pi$
$24$	−4.21603	−	2.59050i	−0.860594	−	0.528784i
$25$	−2.35760	+	1.97826i	−0.471520	+	0.395652i
$26$	−2.42307	−	4.19688i	−0.475203	−	0.823076i
$27$	5.17864	+	0.426201i	0.996630	+	0.0820224i
$28$	−2.84824	−	1.43735i	−0.538268	−	0.271633i
$29$	−0.224543	+	0.616928i	−0.0416967	+	0.114561i	−0.958794	−	0.284104i	$-0.908304\pi$
$29$	−0.224543	+	0.616928i	−0.0416967	+	0.114561i	0.917097	+	0.398664i	$0.130526\pi$
$30$	−1.82339	−	1.12037i	−0.332904	−	0.204550i
$31$	0.595291	+	1.63555i	0.106917	+	0.293753i	0.981602	−	0.190940i	$-0.0611535\pi$
$31$	0.595291	+	1.63555i	0.106917	+	0.293753i	−0.874684	+	0.484693i	$0.838931\pi$
$32$	−3.59586	+	4.28538i	−0.635665	+	0.757556i
$33$	0.991496	−	0.146972i	0.172597	−	0.0255846i
$34$	−1.32455	−	1.57853i	−0.227158	−	0.270716i
$35$	−3.27494	−	1.65268i	−0.553566	−	0.279354i
$36$	0.822168	−	3.52287i	0.137028	−	0.587145i
$37$	−1.08507			−0.178385			−0.0891925	−	0.996014i	$-0.528429\pi$
$37$	−1.08507			−0.178385			−0.0891925	+	0.996014i	$0.528429\pi$
$38$	−2.86724	−	1.04359i	−0.465128	−	0.169293i
$39$	6.24961	−	7.04696i	1.00074	−	1.12842i
$40$	−2.54613	+	3.03436i	−0.402579	+	0.479775i
$41$	−1.37400	+	0.500093i	−0.214582	+	0.0781015i	−0.447074	−	0.894497i	$-0.647534\pi$
$41$	−1.37400	+	0.500093i	−0.214582	+	0.0781015i	0.232492	+	0.972598i	$0.425312\pi$
$42$	−0.592745	+	4.04053i	−0.0914626	+	0.623467i
$43$	−0.681623	−	3.86568i	−0.103947	−	0.589510i	−0.991636	−	0.129067i	$-0.958802\pi$
$43$	−0.681623	−	3.86568i	−0.103947	−	0.589510i	0.887689	−	0.460443i	$-0.152309\pi$
$44$		−	0.697818i		−	0.105200i
$45$	0.945338	−	4.05064i	0.140923	−	0.603834i
$46$	5.96264			0.879143
$47$	5.79174	+	2.10802i	0.844812	+	0.307486i	0.727923	−	0.685659i	$-0.240486\pi$
$47$	5.79174	+	2.10802i	0.844812	+	0.307486i	0.116889	+	0.993145i	$0.462708\pi$
$48$	0.216232	+	0.0854738i	0.0312104	+	0.0123371i
$49$	−0.434042	+	6.98653i	−0.0620060	+	0.998076i
$50$	1.76293	−	2.10098i	0.249316	−	0.297124i
$51$	2.09670	−	3.41237i	0.293597	−	0.477828i
$52$	−4.21505	−	5.02331i	−0.584523	−	0.696607i
$53$	−8.16395	−	4.71346i	−1.12141	−	0.647444i	−0.179646	−	0.983731i	$-0.557495\pi$
$53$	−8.16395	−	4.71346i	−1.12141	−	0.647444i	−0.941759	+	0.336288i	$0.890829\pi$
$54$	−4.61081	+	0.427340i	−0.627451	+	0.0581536i
$55$		−	0.802359i		−	0.108190i
$56$	7.23690	+	2.18184i	0.967071	+	0.291561i
$57$	0.162305	−	5.92822i	0.0214979	−	0.785212i
$58$	0.101595	−	0.576172i	0.0133400	−	0.0756551i
$59$	3.88097	+	3.25652i	0.505259	+	0.423963i	0.859457	−	0.511207i	$-0.170802\pi$
$59$	3.88097	+	3.25652i	0.505259	+	0.423963i	−0.354198	+	0.935171i	$0.615246\pi$
$60$	−2.69305	−	1.06453i	−0.347672	−	0.137430i
$61$	4.62542	−	12.7082i	0.592225	−	1.62712i	−0.174141	−	0.984721i	$-0.555715\pi$
$61$	4.62542	−	12.7082i	0.592225	−	1.62712i	0.766366	−	0.642404i	$-0.222063\pi$
$62$	−0.775532	−	1.34326i	−0.0984927	−	0.170594i
$63$	−7.81459	+	1.39002i	−0.984546	+	0.175126i
$64$	2.62687	−	4.54987i	0.328359	−	0.568734i
$65$	−4.84652	−	5.77585i	−0.601136	−	0.716407i
$66$	−0.847408	+	0.282416i	−0.104309	+	0.0347630i
$67$	−1.43047	+	8.11262i	−0.174760	+	0.991114i	0.763660	+	0.645619i	$0.223400\pi$
$67$	−1.43047	+	8.11262i	−0.174760	+	0.991114i	−0.938420	+	0.345496i	$0.887711\pi$
$68$	−2.13596	−	1.79229i	−0.259024	−	0.217347i
$69$	3.66415	+	10.9945i	0.441112	+	1.32359i
$70$	3.12988	+	0.943626i	0.374093	+	0.112785i
$71$	13.6154	+	7.86086i	1.61585	+	0.932913i	0.987977	+	0.154599i	$0.0494085\pi$
$71$	13.6154	+	7.86086i	1.61585	+	0.932913i	0.627875	+	0.778314i	$0.283925\pi$
$72$	−0.468953	+	8.55786i	−0.0552666	+	1.00855i
$73$			2.39174i			0.279932i	0.990156	+	0.139966i	$0.0446994\pi$
$73$			2.39174i			0.279932i	−0.990156	+	0.139966i	$0.955301\pi$
$74$	0.952276	−	0.167912i	0.110700	−	0.0195194i
$75$	4.95736	+	1.95958i	0.572427	+	0.226273i
$76$	−4.06603	−	0.716950i	−0.466405	−	0.0822398i
$77$	−1.40704	+	0.603711i	−0.160347	+	0.0687993i
$78$	−4.39425	+	7.15162i	−0.497551	+	0.809762i
$79$	−0.465552	−	2.64028i	−0.0523787	−	0.297054i	0.947354	−	0.320189i	$-0.103746\pi$
$79$	−0.465552	−	2.64028i	−0.0523787	−	0.297054i	−0.999732	+	0.0231347i	$0.992635\pi$
$80$	0.0930623	−	0.161189i	0.0104047	−	0.0180214i
$81$	−3.62140	−	8.23926i	−0.402378	−	0.915474i
$82$	1.12845	−	0.651511i	0.124616	−	0.0719473i
$83$	11.2771	+	4.10455i	1.23783	+	0.450532i	0.876271	−	0.481818i	$-0.160023\pi$
$83$	11.2771	+	4.10455i	1.23783	+	0.450532i	0.361556	+	0.932350i	$0.382246\pi$
$84$	0.159521	+	5.52358i	0.0174052	+	0.602672i
$85$	−2.45595	−	2.06079i	−0.266386	−	0.223524i
$86$	1.19640	+	3.28709i	0.129012	+	0.354456i
$87$	1.12484	−	0.166738i	0.120595	−	0.0178762i
$88$	0.287088	+	1.62816i	0.0306037	+	0.173562i
$89$	−5.91604	+	10.2469i	−0.627099	+	1.08617i	0.361032	+	0.932553i	$0.382424\pi$
$89$	−5.91604	+	10.2469i	−0.627099	+	1.08617i	−0.988131	+	0.153613i	$0.950909\pi$
$90$	−0.202817	+	3.70119i	−0.0213788	+	0.390139i
$91$	−6.48206	+	12.8448i	−0.679505	+	1.34651i
$92$	7.94566	−	1.40103i	0.828392	−	0.146068i
$93$	2.00026	−	2.25547i	0.207418	−	0.233881i
$94$	−5.40912	−	0.953774i	−0.557908	−	0.0983743i
$95$	−4.67516	−	0.824357i	−0.479661	−	0.0845773i
$96$	9.49256	+	1.94307i	0.968830	+	0.198313i
$97$	−18.3532	+	3.23616i	−1.86348	+	0.328582i	−0.987974	−	0.154618i	$-0.950585\pi$
$97$	−18.3532	+	3.23616i	−1.86348	+	0.328582i	−0.875510	+	0.483201i	$0.839474\pi$
$98$	−0.700224	−	6.19865i	−0.0707333	−	0.626158i
$99$	−1.04150	−	1.38899i	−0.104674	−	0.139598i
$100$	1.85557	−	3.21395i	0.185557	−	0.321395i
$101$	2.11473	+	11.9933i	0.210424	+	1.19337i	0.888673	+	0.458542i	$0.151628\pi$
$101$	2.11473	+	11.9933i	0.210424	+	1.19337i	−0.678249	+	0.734832i	$0.737261\pi$
$102$	−1.31204	+	3.31921i	−0.129911	+	0.328650i
$103$	−4.39540	−	12.0763i	−0.433092	−	1.18991i	−0.943905	−	0.330218i	$-0.892878\pi$
$103$	−4.39540	−	12.0763i	−0.433092	−	1.18991i	0.510813	−	0.859692i	$-0.329345\pi$
$104$	11.9012	+	9.98633i	1.16701	+	0.979241i
$105$	0.183419	+	6.35107i	0.0178999	+	0.619801i
$106$	7.89420	+	2.87325i	0.766752	+	0.279075i
$107$	8.97631	−	5.18247i	0.867772	−	0.501009i	0.00116512	−	0.999999i	$-0.499629\pi$
$107$	8.97631	−	5.18247i	0.867772	−	0.501009i	0.866607	+	0.498991i	$0.166296\pi$
$108$	−6.04383	+	1.65286i	−0.581568	+	0.159046i
$109$	8.42552	−	14.5934i	0.807019	−	1.39780i	−0.107901	−	0.994162i	$-0.534413\pi$
$109$	8.42552	−	14.5934i	0.807019	−	1.39780i	0.914920	−	0.403636i	$-0.132254\pi$
$110$	0.124163	+	0.704162i	0.0118384	+	0.0671392i
$111$	0.894805	+	1.65272i	0.0849311	+	0.156869i
$112$	−0.352686	−	0.0419147i	−0.0333257	−	0.00396057i
$113$	−20.0144	−	3.52907i	−1.88279	−	0.331987i	−0.890409	−	0.455162i	$-0.849581\pi$
$113$	−20.0144	−	3.52907i	−1.88279	−	0.331987i	−0.992385	+	0.123174i	$0.960693\pi$
$114$	0.774934	+	5.22781i	0.0725792	+	0.489629i
$115$	9.13601	−	1.61092i	0.851937	−	0.150220i
$116$		−	0.791664i		−	0.0735041i
$117$	−15.8872	−	3.70776i	−1.46878	−	0.342783i
$118$	−3.90993	−	2.25740i	−0.359939	−	0.207811i
$119$	−1.76594	+	5.85740i	−0.161884	+	0.536947i
$120$	6.72142	+	1.37583i	0.613579	+	0.125596i
$121$	8.16995	+	6.85540i	0.742723	+	0.623218i
$122$	−2.09277	+	11.8687i	−0.189471	+	1.07454i
$123$	1.89478	+	1.68039i	0.170846	+	0.151515i
$124$	−1.34908	−	1.60777i	−0.121151	−	0.144382i
$125$	5.59980	−	9.69914i	0.500861	−	0.867517i
$126$	6.64310	−	2.42918i	0.591814	−	0.216409i
$127$	−0.987545	−	1.71048i	−0.0876305	−	0.151780i	0.818879	−	0.573967i	$-0.194596\pi$
$127$	−0.987545	−	1.71048i	−0.0876305	−	0.151780i	−0.906509	+	0.422186i	$0.861263\pi$
$128$	2.22534	−	6.11406i	0.196694	−	0.540412i
$129$	−5.32587	+	4.22603i	−0.468916	+	0.372081i
$130$	5.14717	+	4.31899i	0.451437	+	0.378800i
$131$	−0.387413	+	2.19713i	−0.0338484	+	0.191964i	−0.997043	−	0.0768396i	$-0.975517\pi$
$131$	−0.387413	+	2.19713i	−0.0338484	+	0.191964i	0.963195	+	0.268803i	$0.0866282\pi$
$132$	−1.06287	+	0.575455i	−0.0925113	+	0.0500869i
$133$	2.07207	+	8.81874i	0.179672	+	0.764682i
$134$		−	7.34111i		−	0.634176i
$135$	−6.94926	+	1.90047i	−0.598097	+	0.163567i
$136$	5.72102	+	3.30303i	0.490573	+	0.283233i
$137$	−0.857163	−	1.02153i	−0.0732323	−	0.0872749i	0.728184	−	0.685381i	$-0.240364\pi$
$137$	−0.857163	−	1.02153i	−0.0732323	−	0.0872749i	−0.801417	+	0.598106i	$0.795920\pi$
$138$	−4.91708	−	9.08193i	−0.418570	−	0.773106i
$139$	9.79765	−	11.6764i	0.831026	−	0.990378i	−0.168963	−	0.985622i	$-0.554042\pi$
$139$	9.79765	−	11.6764i	0.831026	−	0.990378i	0.999989	−	0.00475527i	$-0.00151366\pi$
$140$	4.39252	+	0.522026i	0.371236	+	0.0441192i
$141$	−1.56534	−	10.5600i	−0.131825	−	0.889313i
$142$	−13.1655	−	4.79186i	−1.10483	−	0.402124i
$143$	−3.14698			−0.263164
$144$	−0.0481268	−	0.399837i	−0.00401057	−	0.0333198i
$145$		−	0.910264i		−	0.0755933i
$146$	−0.370115	−	2.09903i	−0.0306310	−	0.173717i
$147$	10.9994	−	5.10033i	0.907215	−	0.420668i
$148$	1.22952	−	0.447510i	0.101066	−	0.0367851i
$149$	12.8138	−	15.2708i	1.04974	−	1.25104i	0.0826605	−	0.996578i	$-0.473658\pi$
$149$	12.8138	−	15.2708i	1.04974	−	1.25104i	0.967084	−	0.254459i	$-0.0818973\pi$
$150$	−4.65389	−	0.952621i	−0.379989	−	0.0777812i
$151$	2.71476	+	0.988092i	0.220924	+	0.0804098i	0.450111	−	0.892973i	$-0.351384\pi$
$151$	2.71476	+	0.988092i	0.220924	+	0.0804098i	−0.229187	+	0.973382i	$0.573607\pi$
$152$	9.78186			0.793414
$153$	−6.92656	−	0.379561i	−0.559980	−	0.0306857i
$154$	1.14141	−	0.747561i	0.0919777	−	0.0602401i
$155$	−1.55119	−	1.84863i	−0.124594	−	0.148486i
$156$	−4.17526	+	10.5626i	−0.334288	+	0.845683i
$157$	5.22143	−	6.22265i	0.416715	−	0.496622i	−0.516326	−	0.856392i	$-0.672701\pi$
$157$	5.22143	−	6.22265i	0.416715	−	0.496622i	0.933041	+	0.359771i	$0.117145\pi$
$158$	0.817150	+	2.24510i	0.0650090	+	0.178611i
$159$	−0.446865	+	16.3218i	−0.0354387	+	1.29440i
$160$	2.65281	−	7.28853i	0.209723	−	0.576209i
$161$	−9.69908	−	14.8090i	−0.764394	−	1.16712i
$162$	4.45319	+	6.67049i	0.349876	+	0.524084i
$163$	0.518631	+	0.898295i	0.0406223	+	0.0703599i	0.885622	−	0.464407i	$-0.153733\pi$
$163$	0.518631	+	0.898295i	0.0406223	+	0.0703599i	−0.844999	+	0.534767i	$0.820399\pi$
$164$	1.35066	−	1.13334i	0.105469	−	0.0884987i
$165$	−1.22210	+	0.661664i	−0.0951407	+	0.0515105i
$166$	−10.5322	−	1.85710i	−0.817454	−	0.144139i
$167$	2.43922	−	13.8335i	0.188753	−	1.07047i	−0.732286	−	0.680998i	$-0.761546\pi$
$167$	2.43922	−	13.8335i	0.188753	−	1.07047i	0.921038	−	0.389472i	$-0.127342\pi$
$168$	−2.64464	−	12.8221i	−0.204039	−	0.989243i
$169$	−12.6952	+	10.6526i	−0.976556	+	0.819428i
$170$	2.47428	+	1.42853i	0.189769	+	0.109563i
$171$	−9.16336	+	4.64149i	−0.700739	+	0.354943i
$172$	2.36666	+	4.09918i	0.180456	+	0.312559i
$173$	−4.48578	+	3.76401i	−0.341047	+	0.286173i	−0.797183	−	0.603737i	$-0.793678\pi$
$173$	−4.48578	+	3.76401i	−0.341047	+	0.286173i	0.456136	+	0.889910i	$0.349233\pi$
$174$	−0.961371	+	0.320397i	−0.0728813	+	0.0242892i
$175$	−8.08574	−	0.960943i	−0.611224	−	0.0726405i
$176$	−0.0265697	−	0.0729997i	−0.00200277	−	0.00550256i
$177$	1.75970	−	8.59675i	0.132267	−	0.646171i
$178$	3.60632	−	9.90829i	0.270305	−	0.742658i
$179$	7.35936	−	4.24893i	0.550064	−	0.317580i	−0.199084	−	0.979983i	$-0.563797\pi$
$179$	7.35936	−	4.24893i	0.550064	−	0.317580i	0.749148	+	0.662403i	$0.230463\pi$
$180$	0.599394	+	4.97976i	0.0446762	+	0.371169i
$181$	−5.00733	+	2.89098i	−0.372192	+	0.214885i	−0.674416	−	0.738352i	$-0.735604\pi$
$181$	−5.00733	+	2.89098i	−0.372192	+	0.214885i	0.302224	+	0.953237i	$0.402271\pi$
$182$	3.70105	−	12.2759i	0.274340	−	0.909950i
$183$	−23.1708	+	3.43468i	−1.71283	+	0.253898i
$184$	−17.9625	+	6.53782i	−1.32421	+	0.481975i
$185$	1.41372	−	0.514552i	0.103939	−	0.0378306i
$186$	−1.40643	+	2.28896i	−0.103125	+	0.167835i
$187$	−1.31780	+	0.232364i	−0.0963670	+	0.0169921i
$188$	−7.43216			−0.542046
$189$	8.56148	+	10.7564i	0.622756	+	0.782416i
$190$	4.23056			0.306917
$191$	−23.4234	+	4.13019i	−1.69486	+	0.298850i	−0.935895	−	0.352280i	$-0.885406\pi$
$191$	−23.4234	+	4.13019i	−1.69486	+	0.298850i	−0.758966	+	0.651130i	$0.774295\pi$
$192$	−9.09634	−	0.249043i	−0.656472	−	0.0179731i
$193$	17.7806	−	6.47160i	1.27987	−	0.465836i	0.389483	−	0.921034i	$-0.372654\pi$
$193$	17.7806	−	6.47160i	1.27987	−	0.465836i	0.890390	+	0.455198i	$0.150431\pi$
$194$	15.6062	−	5.68020i	1.12046	−	0.407815i
$195$	−4.80076	+	12.1450i	−0.343789	+	0.869720i
$196$	−2.38959	−	8.09562i	−0.170685	−	0.578259i
$197$	−9.22224	+	5.32447i	−0.657058	+	0.379352i	−0.791155	−	0.611616i	$-0.790520\pi$
$197$	−9.22224	+	5.32447i	−0.657058	+	0.379352i	0.134097	+	0.990968i	$0.457187\pi$
$198$	1.12897	+	1.05783i	0.0802326	+	0.0751764i
$199$	8.68386	−	5.01363i	0.615582	−	0.355407i	−0.159565	−	0.987187i	$-0.551009\pi$
$199$	8.68386	−	5.01363i	0.615582	−	0.355407i	0.775147	+	0.631781i	$0.217676\pi$
$200$	−3.00720	+	8.26223i	−0.212641	+	0.584228i
$201$	13.5363	−	4.51125i	0.954776	−	0.318199i
$202$	−3.71184	−	10.1982i	−0.261164	−	0.717543i
$203$	−1.59626	+	0.684901i	−0.112036	+	0.0480706i
$204$	−0.968482	+	4.73138i	−0.0678073	+	0.331263i
$205$	1.55300	−	1.30312i	0.108466	−	0.0910141i
$206$	5.72624	+	9.91813i	0.398966	+	0.691029i
$207$	13.7246	−	14.6476i	0.953923	−	1.01808i
$208$	−0.632207	−	0.365005i	−0.0438357	−	0.0253085i
$209$	−1.51786	+	1.27363i	−0.104992	+	0.0880990i
$210$	−1.14378	−	5.54541i	−0.0789284	−	0.382670i
$211$	−1.04018	+	5.89915i	−0.0716089	+	0.406114i	0.927842	+	0.372974i	$0.121662\pi$
$211$	−1.04018	+	5.89915i	−0.0716089	+	0.406114i	−0.999451	+	0.0331403i	$0.989449\pi$
$212$	11.1947	+	1.97393i	0.768857	+	0.135570i
$213$	0.745257	−	27.2206i	0.0510642	−	1.86513i
$214$	−7.07576	+	5.93727i	−0.483689	+	0.405863i
$215$	2.72121	+	4.71328i	0.185585	+	0.321443i
$216$	13.4215	−	6.34295i	0.913220	−	0.431583i
$217$	−2.07466	+	4.11115i	−0.140837	+	0.279083i
$218$	−5.13607	+	14.1112i	−0.347858	+	0.955733i
$219$	3.64296	−	1.97235i	0.246168	−	0.133279i
$220$	0.330912	+	0.909173i	0.0223101	+	0.0612964i
$221$	−8.08274	+	9.63264i	−0.543704	+	0.647961i
$222$	−1.04105	−	1.31198i	−0.0698705	−	0.0880544i
$223$	−3.68146	−	4.38739i	−0.246528	−	0.293801i	0.628563	−	0.777759i	$-0.283643\pi$
$223$	−3.68146	−	4.38739i	−0.246528	−	0.293801i	−0.875092	+	0.483957i	$0.839199\pi$
$224$	−14.7774	+	0.832010i	−0.987355	+	0.0555910i
$225$	−1.10336	−	9.16672i	−0.0735575	−	0.611115i
$226$	18.1110			1.20473
$227$	16.6154	+	6.04749i	1.10280	+	0.401386i	0.828348	−	0.560214i	$-0.189281\pi$
$227$	16.6154	+	6.04749i	1.10280	+	0.401386i	0.274452	+	0.961601i	$0.411504\pi$
$228$	2.26103	+	6.78436i	0.149740	+	0.449305i
$229$	8.82135	−	10.5129i	0.582932	−	0.694711i	−0.391299	−	0.920263i	$-0.627974\pi$
$229$	8.82135	−	10.5129i	0.582932	−	0.694711i	0.974231	+	0.225553i	$0.0724188\pi$
$230$	−7.76861	+	2.82754i	−0.512247	+	0.186443i
$231$	2.07985	+	1.64526i	0.136844	+	0.108250i
$232$	0.325697	+	1.84712i	0.0213831	+	0.121269i
$233$			9.14606i			0.599178i	0.954068	+	0.299589i	$0.0968496\pi$
$233$			9.14606i			0.599178i	−0.954068	+	0.299589i	$0.903150\pi$
$234$	14.5166	+	0.795481i	0.948982	+	0.0520022i
$235$	−8.54558			−0.557452
$236$	−5.74069	−	2.08944i	−0.373687	−	0.136011i
$237$	−3.63759	+	2.88640i	−0.236287	+	0.187492i
$238$	0.643400	−	5.41381i	0.0417054	−	0.350925i
$239$	1.62286	−	1.93405i	0.104974	−	0.125103i	−0.710999	−	0.703193i	$-0.751757\pi$
$239$	1.62286	−	1.93405i	0.104974	−	0.125103i	0.815973	+	0.578089i	$0.196202\pi$
$240$	−0.322257	−	0.00882287i	−0.0208016	−	0.000569514i
$241$	4.62353	+	5.51011i	0.297828	+	0.354938i	0.894118	−	0.447832i	$-0.147804\pi$
$241$	4.62353	+	5.51011i	0.297828	+	0.354938i	−0.596290	+	0.802769i	$0.703359\pi$
$242$	−8.23092	−	4.75212i	−0.529103	−	0.305478i
$243$	−9.56317	+	12.3104i	−0.613477	+	0.789712i
$244$			16.3077i			1.04399i
$245$	−2.74758	−	9.30844i	−0.175536	−	0.594694i
$246$	−1.92292	−	1.18152i	−0.122601	−	0.0753309i
$247$	−3.23326	+	18.3367i	−0.205727	+	1.16674i
$248$	3.80914	+	3.19625i	0.241880	+	0.202962i
$249$	−3.04789	−	20.5615i	−0.193152	−	1.30303i
$250$	−3.41355	+	9.37865i	−0.215892	+	0.593158i
$251$	0.469593	+	0.813359i	0.0296405	+	0.0513388i	0.880465	−	0.474111i	$-0.157230\pi$
$251$	0.469593	+	0.813359i	0.0296405	+	0.0513388i	−0.850825	+	0.525450i	$0.823897\pi$
$252$	8.28163	−	4.79799i	0.521694	−	0.302245i
$253$	1.93601	−	3.35326i	0.121716	−	0.210818i
$254$	1.13138	+	1.34832i	0.0709888	+	0.0846012i
$255$	−1.11357	+	5.44019i	−0.0697346	+	0.340678i
$256$	−2.83146	+	16.0580i	−0.176966	+	1.00363i
$257$	15.0111	+	12.5958i	0.936364	+	0.785703i	0.976949	−	0.213473i	$-0.0684777\pi$
$257$	15.0111	+	12.5958i	0.936364	+	0.785703i	−0.0405849	+	0.999176i	$0.512922\pi$
$258$	4.02009	−	4.53299i	0.250280	−	0.282212i
$259$	−1.96604	−	2.09198i	−0.122164	−	0.129989i
$260$	7.87381	+	4.54595i	0.488313	+	0.281928i
$261$	−1.18156	−	1.57578i	−0.0731368	−	0.0975386i
$262$		−	1.98818i		−	0.122830i
$263$	−11.7453	+	2.07102i	−0.724247	+	0.127704i	−0.523606	−	0.851961i	$-0.675414\pi$
$263$	−11.7453	+	2.07102i	−0.724247	+	0.127704i	−0.200641	+	0.979665i	$0.564302\pi$
$264$	2.24316	−	1.77993i	0.138057	−	0.109547i
$265$	12.8718	+	2.26965i	0.790710	+	0.139423i
$266$	−3.18316	−	7.41881i	−0.195172	−	0.454876i
$267$	20.4861	+	0.560876i	1.25373	+	0.0343251i
$268$	−1.72493	−	9.78258i	−0.105367	−	0.597566i
$269$	8.21836	−	14.2346i	0.501082	−	0.867900i	−0.498917	−	0.866650i	$-0.666269\pi$
$269$	8.21836	−	14.2346i	0.501082	−	0.867900i	0.999999	−	0.00125014i	$-0.000397931\pi$
$270$	5.80468	−	2.74326i	0.353261	−	0.166950i
$271$	−12.7971	+	7.38840i	−0.777367	+	0.448813i	−0.835496	−	0.549496i	$-0.814820\pi$
$271$	−12.7971	+	7.38840i	−0.777367	+	0.448813i	0.0581291	+	0.998309i	$0.481487\pi$
$272$	−0.291688	−	0.106166i	−0.0176862	−	0.00643725i
$273$	24.9099	−	0.719399i	1.50762	−	0.0435400i
$274$	0.910336	+	0.763863i	0.0549954	+	0.0461466i
$275$	−0.609141	−	1.67360i	−0.0367326	−	0.100922i
$276$	−8.68635	−	10.9470i	−0.522857	−	0.658931i
$277$	4.81322	+	27.2971i	0.289199	+	1.64013i	0.689890	+	0.723914i	$0.257659\pi$
$277$	4.81322	+	27.2971i	0.289199	+	1.64013i	−0.400692	+	0.916213i	$0.631230\pi$
$278$	−6.79167	+	11.7635i	−0.407337	+	0.705529i
$279$	−5.08490	−	1.18671i	−0.304425	−	0.0710467i
$280$	−10.4635	+	0.589124i	−0.625311	+	0.0352069i
$281$	6.13171	−	1.08119i	0.365787	−	0.0644981i	0.0122663	−	0.999925i	$-0.496095\pi$
$281$	6.13171	−	1.08119i	0.365787	−	0.0644981i	0.353521	+	0.935427i	$0.384984\pi$
$282$	3.00789	+	9.02538i	0.179118	+	0.537453i
$283$	5.40960	+	0.953859i	0.321567	+	0.0567010i	0.332102	−	0.943243i	$-0.392242\pi$
$283$	5.40960	+	0.953859i	0.321567	+	0.0567010i	−0.0105345	+	0.999945i	$0.503353\pi$
$284$	−18.6700	−	3.29202i	−1.10786	−	0.195345i
$285$	2.59976	+	7.80073i	0.153996	+	0.462075i
$286$	2.76183	−	0.486986i	0.163311	−	0.0287961i
$287$	−3.45370	−	1.74289i	−0.203865	−	0.102879i
$288$	−4.86847	−	16.0608i	−0.286877	−	0.946394i
$289$	5.82659	−	10.0920i	0.342741	−	0.593644i
$290$	0.140861	+	0.798861i	0.00827162	+	0.0469107i
$291$	20.0641	+	25.2858i	1.17618	+	1.48228i
$292$	−0.986412	−	2.71015i	−0.0577254	−	0.158599i
$293$	−17.8320	−	14.9629i	−1.04176	−	0.874140i	−0.0495561	−	0.998771i	$-0.515781\pi$
$293$	−17.8320	−	14.9629i	−1.04176	−	0.874140i	−0.992203	+	0.124632i	$0.960225\pi$
$294$	−8.86396	+	6.17824i	−0.516957	+	0.360323i
$295$	−6.60071	−	2.40246i	−0.384308	−	0.139877i
$296$	−2.68463	+	1.54997i	−0.156041	+	0.0900904i
$297$	−1.25675	+	2.73177i	−0.0729242	+	0.158513i
$298$	−8.88242	+	15.3848i	−0.514545	+	0.891218i
$299$	−6.31830	−	35.8329i	−0.365397	−	2.07227i
$300$	−6.42549	−	0.175920i	−0.370976	−	0.0101567i
$301$	6.21783	−	8.31836i	0.358390	−	0.479462i
$302$	−2.53542	−	0.447062i	−0.145897	−	0.0257255i
$303$	16.5235	−	13.1113i	0.949250	−	0.753222i
$304$	−0.452651	+	0.0798145i	−0.0259613	+	0.00457768i
$305$			18.7507i			1.07366i
$306$	6.13759	−	0.738757i	0.350863	−	0.0422319i
$307$	−15.1010	−	8.71859i	−0.861862	−	0.497596i	0.00277334	−	0.999996i	$-0.499117\pi$
$307$	−15.1010	−	8.71859i	−0.861862	−	0.497596i	−0.864635	+	0.502400i	$0.832451\pi$
$308$	1.34536	−	1.26438i	0.0766592	−	0.0720445i
$309$	−14.7692	+	16.6535i	−0.840189	+	0.947384i
$310$	1.64741	+	1.38234i	0.0935668	+	0.0785118i
$311$	0.262128	−	1.48660i	0.0148639	−	0.0842975i	−0.976473	−	0.215638i	$-0.930817\pi$
$311$	0.262128	−	1.48660i	0.0148639	−	0.0842975i	0.991337	+	0.131340i	$0.0419281\pi$
$312$	5.39623	−	26.3625i	0.305501	−	1.49248i
$313$	18.7170	+	22.3060i	1.05794	+	1.26081i	0.964190	+	0.265214i	$0.0854426\pi$
$313$	18.7170	+	22.3060i	1.05794	+	1.26081i	0.0937550	+	0.995595i	$0.470113\pi$
$314$	−3.61946	+	6.26909i	−0.204258	+	0.353785i
$315$	9.52232	−	5.51678i	0.536522	−	0.310835i
$316$	1.61644	+	2.79976i	0.0909320	+	0.157499i
$317$	−10.3980	+	28.5684i	−0.584013	+	1.60456i	0.197246	+	0.980354i	$0.436800\pi$
$317$	−10.3980	+	28.5684i	−0.584013	+	1.60456i	−0.781259	+	0.624207i	$0.785422\pi$
$318$	−2.13357	−	14.3934i	−0.119645	−	0.807141i
$319$	−0.291040	−	0.244212i	−0.0162951	−	0.0136732i
$320$	−1.26490	+	7.17363i	−0.0707103	+	0.401018i
$321$	−15.2959	−	9.39845i	−0.853736	−	0.524570i
$322$	10.8037	+	11.4957i	0.602067	+	0.640631i
$323$			7.91725i			0.440527i
$324$	7.50157	+	7.84257i	0.416754	+	0.435698i
$325$	−14.4941	−	8.36816i	−0.803987	−	0.464182i
$326$	−0.594166	−	0.708100i	−0.0329078	−	0.0392180i
$327$	−29.1759	−	0.798790i	−1.61343	−	0.0441732i
$328$	−2.68511	+	3.19999i	−0.148260	+	0.176690i
$329$	6.42987	+	14.9857i	0.354490	+	0.826191i
$330$	0.970146	−	0.769803i	0.0534048	−	0.0423763i
$331$	26.5955	+	9.67996i	1.46182	+	0.532059i	0.945866	−	0.324558i	$-0.105215\pi$
$331$	26.5955	+	9.67996i	1.46182	+	0.532059i	0.515954	+	0.856617i	$0.327438\pi$
$332$	−14.4712			−0.794212
$333$	1.77942	−	2.72583i	0.0975117	−	0.149374i
$334$			12.5180i			0.684952i
$335$	−1.98335	−	11.2481i	−0.108362	−	0.614550i
$336$	0.227000	+	0.571756i	0.0123839	+	0.0311918i
$337$	7.63576	−	2.77919i	0.415946	−	0.151392i	−0.125565	−	0.992085i	$-0.540074\pi$
$337$	7.63576	−	2.77919i	0.415946	−	0.151392i	0.541512	+	0.840693i	$0.317852\pi$
$338$	9.49306	−	11.3134i	0.516355	−	0.615367i
$339$	11.1296	+	33.3949i	0.604475	+	1.81376i
$340$	3.63282	+	1.32224i	0.197017	+	0.0717085i
$341$	−1.00723			−0.0545445
$342$	7.32363	−	5.49144i	0.396017	−	0.296943i
$343$	−14.2562	+	11.8221i	−0.769761	+	0.638332i
$344$	−7.20836	−	8.59059i	−0.388649	−	0.463174i
$345$	−9.98766	−	12.5870i	−0.537718	−	0.677660i
$346$	3.35431	−	3.99751i	0.180329	−	0.214908i
$347$	−4.70885	−	12.9375i	−0.252784	−	0.694519i	−0.999566	−	0.0294501i	$-0.990624\pi$
$347$	−4.70885	−	12.9375i	−0.252784	−	0.694519i	0.746782	−	0.665069i	$-0.231598\pi$
$348$	−1.20581	+	0.652845i	−0.0646384	+	0.0349961i
$349$	−0.460133	+	1.26420i	−0.0246303	+	0.0676713i	−0.951398	−	0.307963i	$-0.900353\pi$
$349$	−0.460133	+	1.26420i	−0.0246303	+	0.0676713i	0.926768	+	0.375634i	$0.122575\pi$
$350$	7.24486	−	0.407907i	0.387254	−	0.0218036i
$351$	7.45396	+	27.2561i	0.397863	+	1.45482i
$352$	−1.61866	−	2.80360i	−0.0862749	−	0.149432i
$353$	−12.0674	+	10.1257i	−0.642281	+	0.538938i	−0.904718	−	0.426011i	$-0.859918\pi$
$353$	−12.0674	+	10.1257i	−0.642281	+	0.538938i	0.262436	+	0.964949i	$0.415474\pi$
$354$	−0.214015	+	7.81694i	−0.0113748	+	0.415466i
$355$	−21.4669	−	3.78520i	−1.13935	−	0.200898i
$356$	2.47755	−	14.0509i	0.131310	−	0.744697i
$357$	10.3779	−	2.14052i	0.549258	−	0.113289i
$358$	−5.80117	+	4.86776i	−0.306601	+	0.257269i
$359$	25.9575	+	14.9866i	1.36999	+	0.790962i	0.990926	−	0.134411i	$-0.0429141\pi$
$359$	25.9575	+	14.9866i	1.36999	+	0.790962i	0.379060	+	0.925372i	$0.376247\pi$
$360$	−3.44723	−	11.3722i	−0.181685	−	0.599370i
$361$	−3.63831	−	6.30173i	−0.191490	−	0.331670i
$362$	3.94713	−	3.31204i	0.207457	−	0.174077i
$363$	3.70439	−	18.0973i	0.194430	−	0.949860i
$364$	2.04747	−	17.2282i	0.107316	−	0.903002i
$365$	−1.13419	−	3.11616i	−0.0593661	−	0.163107i
$366$	19.8035	−	6.59993i	1.03515	−	0.344984i
$367$	1.63420	−	4.48993i	0.0853046	−	0.234372i	−0.889705	−	0.456536i	$-0.849090\pi$
$367$	1.63420	−	4.48993i	0.0853046	−	0.234372i	0.975009	+	0.222164i	$0.0713120\pi$
$368$	0.777862	−	0.449099i	0.0405488	−	0.0234109i
$369$	0.996937	−	4.27174i	0.0518985	−	0.222378i
$370$	−1.16108	+	0.670348i	−0.0603615	+	0.0348497i
$371$	−5.70491	−	24.2801i	−0.296184	−	1.26056i
$372$	−1.33634	+	3.38068i	−0.0692861	+	0.175280i
$373$	−12.9963	+	4.73027i	−0.672923	+	0.244924i	−0.655806	−	0.754929i	$-0.727671\pi$
$373$	−12.9963	+	4.73027i	−0.672923	+	0.244924i	−0.0171173	+	0.999853i	$0.505449\pi$
$374$	1.12056	−	0.407851i	0.0579429	−	0.0210895i
$375$	−19.3910	−	0.530895i	−1.00135	−	0.0274153i
$376$	17.3408	−	3.05765i	0.894284	−	0.157686i
$377$	−3.57020			−0.183875
$378$	−9.17821	−	8.11514i	−0.472076	−	0.417398i
$379$	−8.84194			−0.454180			−0.227090	−	0.973874i	$-0.572921\pi$
$379$	−8.84194			−0.454180			−0.227090	+	0.973874i	$0.572921\pi$
$380$	5.63753	−	0.994048i	0.289199	−	0.0509936i
$381$	−1.79092	+	2.91471i	−0.0917516	+	0.149325i
$382$	19.9176	−	7.24942i	1.01907	−	0.370913i
$383$	28.2722	−	10.2902i	1.44464	−	0.525807i	0.503552	−	0.863965i	$-0.332026\pi$
$383$	28.2722	−	10.2902i	1.44464	−	0.525807i	0.941089	+	0.338158i	$0.109804\pi$
$384$	−11.1477	+	1.65246i	−0.568878	+	0.0843265i
$385$	1.54691	−	1.45379i	0.0788380	−	0.0740922i
$386$	−14.6030	+	8.43106i	−0.743274	+	0.429130i
$387$	10.8288	+	4.62704i	0.550459	+	0.235206i
$388$	19.4618	−	11.2363i	0.988023	−	0.570435i
$389$	3.38182	−	9.29147i	0.171465	−	0.471096i	−0.823959	−	0.566649i	$-0.808240\pi$
$389$	3.38182	−	9.29147i	0.171465	−	0.471096i	0.995424	+	0.0955526i	$0.0304618\pi$
$390$	2.33381	−	11.4015i	0.118177	−	0.577338i
$391$	−5.29159	−	14.5385i	−0.267607	−	0.735244i
$392$	8.90602	+	17.9057i	0.449822	+	0.904375i
$393$	3.66601	−	1.22177i	0.184926	−	0.0616303i
$394$	7.26963	−	6.09994i	0.366239	−	0.307311i
$395$	1.85860	+	3.21920i	0.0935165	+	0.161975i
$396$	1.75300	+	1.14436i	0.0880914	+	0.0575061i
$397$	9.95052	+	5.74493i	0.499402	+	0.288330i	0.728467	−	0.685081i	$-0.240233\pi$
$397$	9.95052	+	5.74493i	0.499402	+	0.288330i	−0.229064	+	0.973411i	$0.573567\pi$
$398$	−6.84523	+	5.74383i	−0.343121	+	0.287912i
$399$	11.7234	−	10.4284i	0.586906	−	0.522074i
$400$	0.0717417	−	0.406867i	0.00358709	−	0.0203434i
$401$	−16.2345	−	2.86258i	−0.810713	−	0.142951i	−0.247100	−	0.968990i	$-0.579478\pi$
$401$	−16.2345	−	2.86258i	−0.810713	−	0.142951i	−0.563612	+	0.826039i	$0.690589\pi$
$402$	−11.1815	+	6.05384i	−0.557685	+	0.301938i
$403$	−7.25062	+	6.08400i	−0.361179	+	0.303065i
$404$	−7.34256	−	12.7177i	−0.365306	−	0.632729i
$405$	8.62539	+	9.01747i	0.428599	+	0.448082i
$406$	1.29492	−	0.848096i	0.0642656	−	0.0420903i
$407$	0.214764	−	0.590059i	0.0106454	−	0.0292481i
$408$	0.313147	−	11.4377i	0.0155031	−	0.566253i
$409$	3.12161	+	8.57657i	0.154354	+	0.424084i	0.992633	−	0.121157i	$-0.0386604\pi$
$409$	3.12161	+	8.57657i	0.154354	+	0.424084i	−0.838279	+	0.545241i	$0.816438\pi$
$410$	−1.16128	+	1.38396i	−0.0573516	+	0.0683490i
$411$	−0.849070	+	2.14798i	−0.0418815	+	0.105952i
$412$	9.96108	+	11.8712i	0.490747	+	0.584850i
$413$	0.753493	+	13.3828i	0.0370770	+	0.658526i
$414$	−9.77819	+	14.9788i	−0.480572	+	0.736169i
$415$	−16.6392			−0.816786
$416$	−28.5868	−	10.4047i	−1.40158	−	0.510134i
$417$	−25.8644	−	5.29427i	−1.26658	−	0.259262i
$418$	1.13500	−	1.35264i	0.0555147	−	0.0661599i
$419$	27.5287	−	10.0196i	1.34487	−	0.489492i	0.433525	−	0.901142i	$-0.357270\pi$
$419$	27.5287	−	10.0196i	1.34487	−	0.489492i	0.911342	+	0.411650i	$0.135047\pi$
$420$	−2.82717	−	7.12092i	−0.137952	−	0.347465i
$421$	2.05835	+	11.6735i	0.100318	+	0.568930i	0.992988	+	0.118219i	$0.0377184\pi$
$421$	2.05835	+	11.6735i	0.100318	+	0.568930i	−0.892670	+	0.450711i	$0.851171\pi$
$422$		−	5.33814i		−	0.259857i
$423$	−14.7935	+	11.0925i	−0.719285	+	0.539337i
$424$	−26.9318			−1.30792
$425$	−6.68728	−	2.43397i	−0.324381	−	0.118065i
$426$	3.55826	+	24.0045i	0.172398	+	1.16302i
$427$	32.8818	−	14.1084i	1.59126	−	0.682756i
$428$	−8.03390	+	9.57443i	−0.388333	+	0.462798i
$429$	2.59515	+	4.79329i	0.125295	+	0.231422i
$430$	−3.11754	−	3.71534i	−0.150341	−	0.179170i
$431$	10.4044	+	6.00699i	0.501163	+	0.289347i	0.729194	−	0.684307i	$-0.239895\pi$
$431$	10.4044	+	6.00699i	0.501163	+	0.289347i	−0.228031	+	0.973654i	$0.573229\pi$
$432$	−0.569320	+	0.403029i	−0.0273914	+	0.0193907i
$433$			1.86378i			0.0895673i	0.998997	+	0.0447837i	$0.0142599\pi$
$433$			1.86378i			0.0895673i	−0.998997	+	0.0447837i	$0.985740\pi$
$434$	1.18456	−	3.92905i	0.0568609	−	0.188600i
$435$	−1.38646	+	0.750648i	−0.0664756	+	0.0359908i
$436$	−3.52849	+	20.0111i	−0.168984	+	0.958356i
$437$	−17.5496	−	14.7259i	−0.839511	−	0.704433i
$438$	−2.89190	+	2.29470i	−0.138180	+	0.109645i
$439$	8.93164	−	24.5395i	0.426284	−	1.17121i	−0.521767	−	0.853088i	$-0.674727\pi$
$439$	8.93164	−	24.5395i	0.426284	−	1.17121i	0.948051	−	0.318118i	$-0.103051\pi$
$440$	−1.14613	−	1.98515i	−0.0546396	−	0.0946385i
$441$	−16.8391	−	12.5476i	−0.801864	−	0.597506i
$442$	5.60291	−	9.70452i	0.266503	−	0.461597i
$443$	−5.03219	−	5.99713i	−0.239086	−	0.284932i	0.633137	−	0.774040i	$-0.281767\pi$
$443$	−5.03219	−	5.99713i	−0.239086	−	0.284932i	−0.872223	+	0.489108i	$0.837323\pi$
$444$	−1.69555	−	1.50370i	−0.0804671	−	0.0713624i
$445$	2.84872	−	16.1559i	0.135042	−	0.765863i
$446$	3.90983	+	3.28074i	0.185136	+	0.155348i
$447$	−33.8265	−	6.92406i	−1.59994	−	0.327497i
$448$	13.5316	−	3.17942i	0.639308	−	0.150213i
$449$	2.53492	+	1.46354i	0.119630	+	0.0690687i	0.558621	−	0.829423i	$-0.311331\pi$
$449$	2.53492	+	1.46354i	0.119630	+	0.0690687i	−0.438991	+	0.898492i	$0.644664\pi$
$450$	2.38685	+	7.87410i	0.112517	+	0.371189i
$451$		−	0.846154i		−	0.0398438i
$452$	24.1343	−	4.25552i	1.13518	−	0.200163i
$453$	−0.733722	−	4.94979i	−0.0344733	−	0.232561i
$454$	−15.5177	−	2.73619i	−0.728282	−	0.128416i
$455$	2.35420	−	19.8091i	0.110367	−	0.928667i
$456$	−8.06660	−	14.8991i	−0.377753	−	0.697716i
$457$	−4.27552	−	24.2477i	−0.200001	−	1.13426i	−0.905115	−	0.425166i	$-0.860216\pi$
$457$	−4.27552	−	24.2477i	−0.200001	−	1.13426i	0.705115	−	0.709093i	$-0.250895\pi$
$458$	−6.11491	+	10.5913i	−0.285731	+	0.494900i
$459$	5.13386	+	10.8631i	0.239628	+	0.507047i
$460$	−9.68786	+	5.59329i	−0.451699	+	0.260788i
$461$	35.5416	+	12.9361i	1.65534	+	0.602493i	0.989620	−	0.143711i	$-0.0459036\pi$
$461$	35.5416	+	12.9361i	1.65534	+	0.602493i	0.665717	+	0.746204i	$0.268126\pi$
$462$	−2.07990	−	1.12206i	−0.0967659	−	0.0522028i
$463$	−8.27501	−	6.94356i	−0.384572	−	0.322695i	0.429922	−	0.902866i	$-0.358541\pi$
$463$	−8.27501	−	6.94356i	−0.384572	−	0.322695i	−0.814494	+	0.580171i	$0.802986\pi$
$464$	−0.0301429	−	0.0828171i	−0.00139935	−	0.00384469i
$465$	−1.53654	+	3.88714i	−0.0712553	+	0.180262i
$466$	−1.41533	−	8.02671i	−0.0655637	−	0.371830i
$467$	−14.5184	+	25.1467i	−0.671833	+	1.16365i	0.305550	+	0.952176i	$0.401160\pi$
$467$	−14.5184	+	25.1467i	−0.671833	+	1.16365i	−0.977384	+	0.211473i	$0.932174\pi$
$468$	19.5314	−	2.35092i	0.902840	−	0.108671i
$469$	−18.2327	+	11.9414i	−0.841906	+	0.551401i
$470$	7.49973	−	1.32240i	0.345937	−	0.0609979i
$471$	−13.7838	−	2.82146i	−0.635124	−	0.130006i
$472$	14.2539	+	2.51334i	0.656088	+	0.115686i
$473$	2.23705	+	0.394452i	0.102860	+	0.0181369i
$474$	2.74574	−	3.09606i	0.126116	−	0.142207i
$475$	−10.3775	+	1.82984i	−0.476154	+	0.0839588i
$476$	−0.414699	−	7.36549i	−0.0190077	−	0.337597i
$477$	25.2289	−	12.7791i	1.15515	−	0.585115i
$478$	−1.12496	+	1.94848i	−0.0514543	+	0.0891215i
$479$	−2.36831	−	13.4313i	−0.108211	−	0.613694i	−0.989889	−	0.141843i	$-0.954697\pi$
$479$	−2.36831	−	13.4313i	−0.108211	−	0.613694i	0.881678	−	0.471851i	$-0.156414\pi$
$480$	−13.2891	+	1.96988i	−0.606561	+	0.0899123i
$481$	−2.01816	−	5.54484i	−0.0920200	−	0.252823i
$482$	−4.91035	−	4.12027i	−0.223660	−	0.187673i
$483$	−14.5579	+	26.9853i	−0.662407	+	1.22787i
$484$	−12.0849	−	4.39855i	−0.549314	−	0.199934i
$485$	22.3774	−	12.9196i	1.01610	−	0.586648i
$486$	6.48777	−	12.2837i	0.294291	−	0.557198i
$487$	16.0866	−	27.8628i	0.728954	−	1.26259i	−0.228371	−	0.973574i	$-0.573340\pi$
$487$	16.0866	−	27.8628i	0.728954	−	1.26259i	0.957325	−	0.289012i	$-0.0933267\pi$
$488$	−6.70911	−	38.0493i	−0.303707	−	1.72241i
$489$	0.940540	−	1.53072i	0.0425327	−	0.0692218i
$490$	3.85176	+	7.74404i	0.174005	+	0.349840i
$491$	24.2362	+	4.27350i	1.09377	+	0.192860i	0.691295	−	0.722573i	$-0.257041\pi$
$491$	24.2362	+	4.27350i	1.09377	+	0.192860i	0.402470	+	0.915433i	$0.368152\pi$
$492$	−2.84005	−	1.12264i	−0.128039	−	0.0506123i
$493$	−1.49502	+	0.263613i	−0.0673324	+	0.0118725i
$494$		−	16.5929i		−	0.746550i
$495$	2.01561	+	1.31580i	0.0905951	+	0.0591406i
$496$	−0.202346	−	0.116824i	−0.00908558	−	0.00524556i
$497$	9.51435	+	40.4930i	0.426777	+	1.81636i
$498$	5.85670	+	17.5734i	0.262445	+	0.787483i
$499$	−20.0623	−	16.8343i	−0.898114	−	0.753607i	0.0717071	−	0.997426i	$-0.477155\pi$
$499$	−20.0623	−	16.8343i	−0.898114	−	0.753607i	−0.969821	+	0.243819i	$0.921600\pi$
$500$	−2.34512	+	13.2998i	−0.104877	+	0.594786i
$501$	−23.0819	+	7.69252i	−1.03122	+	0.343676i
$502$	−0.537987	−	0.641148i	−0.0240115	−	0.0286158i
$503$	−3.69643	+	6.40240i	−0.164815	+	0.285469i	−0.936590	−	0.350428i	$-0.886036\pi$
$503$	−3.69643	+	6.40240i	−0.164815	+	0.285469i	0.771774	+	0.635897i	$0.219370\pi$
$504$	−17.3489	+	14.6019i	−0.772781	+	0.650418i
$505$	−8.44256	−	14.6229i	−0.375689	−	0.650713i
$506$	−1.18016	+	3.24246i	−0.0524645	+	0.144145i
$507$	26.6945	+	10.5520i	1.18554	+	0.468630i
$508$	1.82445	+	1.53090i	0.0809471	+	0.0679227i
$509$	−2.79269	+	15.8381i	−0.123784	+	0.702013i	0.858239	+	0.513251i	$0.171559\pi$
$509$	−2.79269	+	15.8381i	−0.123784	+	0.702013i	−0.982023	+	0.188763i	$0.939552\pi$
$510$	0.135433	−	4.94671i	0.00599707	−	0.219044i
$511$	−4.61118	+	4.33360i	−0.203987	+	0.191707i
$512$		−	1.51799i		−	0.0670865i
$513$	14.6262	+	10.1295i	0.645762	+	0.447227i
$514$	−15.1231	−	8.73131i	−0.667050	−	0.385122i
$515$	11.4534	+	13.6496i	0.504696	+	0.601473i
$516$	4.29196	−	6.98514i	0.188943	−	0.307504i
$517$	−2.29267	+	2.73229i	−0.100831	+	0.120166i
$518$	2.04916	+	1.53171i	0.0900348	+	0.0672994i
$519$	9.43231	+	3.72848i	0.414032	+	0.163662i
$520$	−20.2415	−	7.36731i	−0.887649	−	0.323078i
$521$	16.9295			0.741693			0.370847	−	0.928694i	$-0.379068\pi$
$521$	16.9295			0.741693			0.370847	+	0.928694i	$0.379068\pi$
$522$	1.28080	+	1.20009i	0.0560592	+	0.0525264i
$523$			10.0732i			0.440472i	0.975447	+	0.220236i	$0.0706827\pi$
$523$			10.0732i			0.440472i	−0.975447	+	0.220236i	$0.929317\pi$
$524$	−0.467160	−	2.64940i	−0.0204080	−	0.115739i
$525$	5.20425	+	13.1082i	0.227132	+	0.572087i
$526$	9.98737	−	3.63511i	0.435470	−	0.158498i
$527$	−2.58698	+	3.08304i	−0.112691	+	0.134299i
$528$	−0.0892781	+	0.100669i	−0.00388533	+	0.00438104i
$529$	20.4557	+	7.44528i	0.889380	+	0.323708i
$530$	−11.6477			−0.505944
$531$	−14.5452	+	4.40903i	−0.631207	+	0.191336i
$532$	−5.98498	−	9.13817i	−0.259482	−	0.396190i
$533$	−5.11105	−	6.09112i	−0.221384	−	0.263836i
$534$	−18.0657	+	2.67793i	−0.781778	+	0.115885i
$535$	−9.23747	+	11.0088i	−0.399371	+	0.475952i
$536$	8.04927	+	22.1152i	0.347675	+	0.955230i
$537$	−12.5406	−	7.70546i	−0.541167	−	0.332515i
$538$	−5.00978	+	13.7643i	−0.215987	+	0.593420i
$539$	−3.71334	−	1.61884i	−0.159945	−	0.0697285i
$540$	7.09058	−	5.01951i	0.305130	−	0.216006i
$541$	9.39785	+	16.2776i	0.404045	+	0.699827i	0.994210	−	0.107456i	$-0.0342705\pi$
$541$	9.39785	+	16.2776i	0.404045	+	0.699827i	−0.590165	+	0.807283i	$0.700937\pi$
$542$	10.0876	−	8.46448i	0.433298	−	0.363580i
$543$	8.53266	+	5.24282i	0.366172	+	0.224991i
$544$	−12.7390	−	2.24623i	−0.546179	−	0.0963062i
$545$	−4.05710	+	23.0090i	−0.173787	+	0.985595i
$546$	−21.7500	+	4.48609i	−0.930813	+	0.191987i
$547$	−9.76636	+	8.19495i	−0.417579	+	0.350391i	−0.827241	−	0.561847i	$-0.810091\pi$
$547$	−9.76636	+	8.19495i	−0.417579	+	0.350391i	0.409662	+	0.912237i	$0.365647\pi$
$548$	1.39257	+	0.804003i	0.0594878	+	0.0343453i
$549$	24.3393	+	32.4599i	1.03877	+	1.38536i
$550$	0.793576	+	1.37451i	0.0338382	+	0.0586095i
$551$	−1.72198	+	1.44492i	−0.0733590	+	0.0615555i
$552$	24.7708	+	21.9680i	1.05431	+	0.935021i
$553$	4.24681	−	5.68148i	0.180593	−	0.241601i
$554$	−8.44831	−	23.2115i	−0.358934	−	0.986164i
$555$	−1.94956	−	1.72897i	−0.0827542	−	0.0733907i
$556$	−6.28634	+	17.2716i	−0.266600	+	0.732478i
$557$	23.6502	−	13.6544i	1.00209	−	0.578557i	0.0932236	−	0.995645i	$-0.470283\pi$
$557$	23.6502	−	13.6544i	1.00209	−	0.578557i	0.908866	+	0.417089i	$0.136950\pi$
$558$	4.64622	+	0.254603i	0.196690	+	0.0107782i
$559$	18.4862	−	10.6730i	0.781884	−	0.451421i
$560$	0.479384	−	0.112637i	0.0202577	−	0.00475980i
$561$	1.44064	+	1.81557i	0.0608240	+	0.0766536i
$562$	−5.21397	+	1.89773i	−0.219938	+	0.0800508i
$563$	22.1420	−	8.05901i	0.933172	−	0.339647i	0.169706	−	0.985495i	$-0.445718\pi$
$563$	22.1420	−	8.05901i	0.933172	−	0.339647i	0.763466	+	0.645848i	$0.223496\pi$
$564$	6.12892	+	11.3202i	0.258074	+	0.476667i
$565$	27.7498	−	4.89305i	1.16744	−	0.205852i
$566$	−4.89515			−0.205759
$567$	9.32334	−	21.9106i	0.391544	−	0.920160i
$568$	44.9154			1.88461
$569$	−13.0318	+	2.29786i	−0.546321	+	0.0963312i	−0.439995	−	0.898000i	$-0.645020\pi$
$569$	−13.0318	+	2.29786i	−0.546321	+	0.0963312i	−0.106326	+	0.994331i	$0.533909\pi$
$570$	−3.48872	−	6.44373i	−0.146127	−	0.269898i
$571$	−6.22715	+	2.26650i	−0.260598	+	0.0948499i	−0.469015	−	0.883190i	$-0.655391\pi$
$571$	−6.22715	+	2.26650i	−0.260598	+	0.0948499i	0.208417	+	0.978040i	$0.433169\pi$
$572$	3.56592	−	1.29789i	0.149099	−	0.0542675i
$573$	25.6070	+	32.2712i	1.06975	+	1.34815i
$574$	3.30072	+	0.995132i	0.137770	+	0.0415360i
$575$	17.8334	−	10.2961i	0.743703	−	0.429377i
$576$	7.12196	+	14.0604i	0.296748	+	0.585849i
$577$	−1.30013	+	0.750628i	−0.0541249	+	0.0312490i	−0.526818	−	0.849978i	$-0.676615\pi$
$577$	−1.30013	+	0.750628i	−0.0541249	+	0.0312490i	0.472693	+	0.881227i	$0.343282\pi$
$578$	−3.55180	+	9.75849i	−0.147735	+	0.405900i
$579$	−24.5199	−	21.7455i	−1.01901	−	0.903712i
$580$	0.375415	+	1.03144i	0.0155882	+	0.0428283i
$581$	12.5197	+	29.1789i	0.519403	+	1.21054i
$582$	−21.5214	−	19.0863i	−0.892091	−	0.791152i
$583$	4.17902	−	3.50661i	0.173077	−	0.145229i
$584$	3.41649	+	5.91753i	0.141375	+	0.244869i
$585$	22.4574	−	2.70311i	0.928500	−	0.111760i
$586$	17.9651	+	10.3722i	0.742132	+	0.428470i
$587$	2.83790	−	2.38128i	0.117133	−	0.0982861i	−0.582340	−	0.812945i	$-0.697863\pi$
$587$	2.83790	−	2.38128i	0.117133	−	0.0982861i	0.699473	+	0.714659i	$0.253418\pi$
$588$	−10.3602	+	10.3157i	−0.427247	+	0.425413i
$589$	−1.03484	+	5.86889i	−0.0426400	+	0.241823i
$590$	6.16466	+	1.08700i	0.253795	+	0.0447509i
$591$	15.7150	+	9.65595i	0.646429	+	0.397193i
$592$	0.111583	−	0.0936294i	0.00458604	−	0.00384814i
$593$	13.5970	+	23.5507i	0.558362	+	0.967112i	0.997633	+	0.0687572i	$0.0219034\pi$
$593$	13.5970	+	23.5507i	0.558362	+	0.967112i	−0.439271	+	0.898355i	$0.644763\pi$
$594$	0.680210	−	2.59192i	0.0279094	−	0.106348i
$595$	−0.476825	−	8.46892i	−0.0195479	−	0.347192i
$596$	−8.22153	+	22.5885i	−0.336767	+	0.925260i
$597$	−14.7976	−	9.09225i	−0.605625	−	0.372121i
$598$	11.0901	+	30.4697i	0.453506	+	1.24600i
$599$	1.35106	−	1.61014i	0.0552030	−	0.0657884i	−0.737736	−	0.675089i	$-0.764105\pi$
$599$	1.35106	−	1.61014i	0.0552030	−	0.0657884i	0.792939	+	0.609301i	$0.208550\pi$
$600$	15.0644	−	2.23304i	0.615002	−	0.0911636i
$601$	6.40627	+	7.63469i	0.261317	+	0.311426i	0.880710	−	0.473655i	$-0.157066\pi$
$601$	6.40627	+	7.63469i	0.261317	+	0.311426i	−0.619393	+	0.785081i	$0.712621\pi$
$602$	−4.16961	+	8.26250i	−0.169941	+	0.336754i
$603$	−18.0340	−	16.8975i	−0.734399	−	0.688118i
$604$	−3.48367			−0.141749
$605$	−13.8954	−	5.05750i	−0.564927	−	0.205617i
$606$	−12.4723	+	14.0636i	−0.506653	+	0.571294i
$607$	−14.5869	+	17.3839i	−0.592062	+	0.705592i	−0.976001	−	0.217766i	$-0.930123\pi$
$607$	−14.5869	+	17.3839i	−0.592062	+	0.705592i	0.383939	+	0.923359i	$0.374567\pi$
$608$	−17.9990	+	6.55109i	−0.729955	+	0.265682i
$609$	2.35956	+	1.86653i	0.0956140	+	0.0756354i
$610$	−2.90162	−	16.4559i	−0.117483	−	0.666281i
$611$			33.5171i			1.35596i
$612$	8.00520	−	2.42659i	0.323591	−	0.0980891i
$613$	−28.6005			−1.15516			−0.577581	−	0.816334i	$-0.696003\pi$
$613$	−28.6005			−1.15516			−0.577581	+	0.816334i	$0.696003\pi$
$614$	14.6021	+	5.31472i	0.589291	+	0.214485i
$615$	−3.26552	−	1.29082i	−0.131678	−	0.0520509i
$616$	−2.61884	+	3.50355i	−0.105516	+	0.141162i
$617$	0.142287	−	0.169571i	0.00572826	−	0.00682668i	−0.763173	−	0.646195i	$-0.776359\pi$
$617$	0.142287	−	0.169571i	0.00572826	−	0.00682668i	0.768901	+	0.639368i	$0.220804\pi$
$618$	10.3846	−	16.9008i	0.417728	−	0.679851i
$619$	−15.3662	−	18.3127i	−0.617619	−	0.736050i	0.363040	−	0.931774i	$-0.381739\pi$
$619$	−15.3662	−	18.3127i	−0.617619	−	0.736050i	−0.980659	+	0.195724i	$0.937294\pi$
$620$	2.52011	+	1.45498i	0.101210	+	0.0584336i
$621$	−33.6283	−	8.82526i	−1.34946	−	0.354145i
$622$			1.34523i			0.0539387i
$623$	−30.4748	+	7.16044i	−1.22095	+	0.286877i
$624$	−0.0346047	+	1.26394i	−0.00138530	+	0.0505981i
$625$	−0.0243202	+	0.137927i	−0.000972809	+	0.00551707i
$626$	−19.8781	−	16.6797i	−0.794487	−	0.666653i
$627$	3.19162	+	1.26161i	0.127461	+	0.0503837i
$628$	−3.35016	+	9.20448i	−0.133686	+	0.367299i
$629$	−1.25452	−	2.17289i	−0.0500209	−	0.0866388i
$630$	−7.50322	+	6.31515i	−0.298935	+	0.251602i
$631$	8.84858	−	15.3262i	0.352256	−	0.610126i	−0.634388	−	0.773015i	$-0.718748\pi$
$631$	8.84858	−	15.3262i	0.352256	−	0.610126i	0.986644	+	0.162889i	$0.0520812\pi$
$632$	−4.92335	−	5.86742i	−0.195840	−	0.233393i
$633$	9.84301	−	3.28039i	0.391225	−	0.130384i
$634$	4.70460	−	26.6811i	0.186844	−	1.05964i
$635$	2.09778	+	1.76025i	0.0832478	+	0.0698532i
$636$	−6.22514	−	18.6789i	−0.246843	−	0.740668i
$637$	−36.5092	+	10.7764i	−1.44655	+	0.426977i
$638$	0.293212	+	0.169286i	0.0116084	+	0.00670210i
$639$	−42.0754	+	21.3123i	−1.66448	+	0.843103i
$640$			9.02117i			0.356593i
$641$	18.8568	−	3.32497i	0.744800	−	0.131328i	0.211646	−	0.977346i	$-0.432118\pi$
$641$	18.8568	−	3.32497i	0.744800	−	0.131328i	0.533154	+	0.846018i	$0.321007\pi$
$642$	14.8783	+	5.88121i	0.587200	+	0.232113i
$643$	29.5375	+	5.20825i	1.16484	+	0.205393i	0.722447	−	0.691426i	$-0.243017\pi$
$643$	29.5375	+	5.20825i	1.16484	+	0.205393i	0.442396	+	0.896820i	$0.354128\pi$
$644$	17.0979	+	12.7804i	0.673750	+	0.503617i
$645$	4.93494	−	8.03159i	0.194313	−	0.316244i
$646$	−1.22517	−	6.94829i	−0.0482037	−	0.273377i
$647$	−0.0112934	+	0.0195607i	−0.000443989	+	0.000769011i	−0.866247	−	0.499615i	$-0.833475\pi$
$647$	−0.0112934	+	0.0195607i	−0.000443989	+	0.000769011i	0.865803	+	0.500384i	$0.166808\pi$
$648$	−20.7292	−	15.2122i	−0.814322	−	0.597590i
$649$	−2.53903	+	1.46591i	−0.0996655	+	0.0575419i
$650$	14.0152	+	5.10110i	0.549720	+	0.200082i
$651$	7.97272	−	0.230252i	0.312475	−	0.00902430i
$652$	−0.958152	−	0.803985i	−0.0375241	−	0.0314865i
$653$	−10.3106	−	28.3282i	−0.403485	−	1.10857i	−0.960552	−	0.278099i	$-0.910296\pi$
$653$	−10.3106	−	28.3282i	−0.403485	−	1.10857i	0.557067	−	0.830467i	$-0.311927\pi$
$654$	25.7288	−	3.81386i	1.00608	−	0.149134i
$655$	−0.537146	−	3.04631i	−0.0209880	−	0.119029i
$656$	0.0981419	−	0.169987i	0.00383180	−	0.00663687i
$657$	−6.00833	−	3.92224i	−0.234407	−	0.153021i
$658$	−7.96195	−	12.1567i	−0.310389	−	0.473918i
$659$	17.6905	−	3.11932i	0.689126	−	0.121511i	0.181890	−	0.983319i	$-0.441778\pi$
$659$	17.6905	−	3.11932i	0.689126	−	0.121511i	0.507236	+	0.861807i	$0.330667\pi$
$660$	1.11191	−	1.25377i	0.0432811	−	0.0488031i
$661$	−33.7358	−	5.94853i	−1.31217	−	0.231371i	−0.526585	−	0.850123i	$-0.676528\pi$
$661$	−33.7358	−	5.94853i	−1.31217	−	0.231371i	−0.785587	+	0.618752i	$0.787639\pi$
$662$	−24.8385	−	4.37970i	−0.965376	−	0.170222i
$663$	21.3373	+	4.36760i	0.828671	+	0.169624i
$664$	33.7645	−	5.95359i	1.31032	−	0.231044i
$665$	−6.88160	−	10.5072i	−0.266857	−	0.407450i
$666$	−1.13983	+	2.66758i	−0.0441676	+	0.103367i
$667$	2.19637	−	3.80422i	0.0850437	−	0.147300i
$668$	2.94133	+	16.6811i	0.113803	+	0.645411i
$669$	−3.64670	+	9.22542i	−0.140989	+	0.356675i
$670$	3.48123	+	9.56459i	0.134491	+	0.369512i
$671$	5.99520	+	5.03057i	0.231442	+	0.194203i
$672$	13.4534	+	21.8219i	0.518977	+	0.841798i
$673$	−16.8698	−	6.14009i	−0.650282	−	0.236683i	−0.00424668	−	0.999991i	$-0.501352\pi$
$673$	−16.8698	−	6.14009i	−0.650282	−	0.236683i	−0.646035	+	0.763308i	$0.723574\pi$
$674$	−6.27118	+	3.62067i	−0.241557	+	0.139463i
$675$	−13.0523	+	9.23990i	−0.502384	+	0.355644i
$676$	9.99192	−	17.3065i	0.384304	−	0.665635i
$677$	−0.583695	−	3.31030i	−0.0224332	−	0.127225i	0.971535	−	0.236898i	$-0.0761307\pi$
$677$	−0.583695	−	3.31030i	−0.0224332	−	0.127225i	−0.993968	+	0.109673i	$0.965020\pi$
$678$	−14.9352	−	27.5856i	−0.573584	−	1.05942i
$679$	−39.4933	−	29.5206i	−1.51561	−	1.13290i
$680$	−9.02013	−	1.59049i	−0.345906	−	0.0609926i
$681$	−4.49065	−	30.2946i	−0.172082	−	1.16089i
$682$	0.883958	−	0.155866i	0.0338485	−	0.00596840i
$683$		−	40.5379i		−	1.55114i	−0.631262	−	0.775570i	$-0.717463\pi$
$683$		−	40.5379i		−	1.55114i	0.631262	−	0.775570i	$-0.282537\pi$
$684$	8.46897	−	9.03857i	0.323819	−	0.345598i
$685$	1.60120	+	0.924452i	0.0611786	+	0.0353215i
$686$	10.6820	−	12.5813i	0.407840	−	0.480357i
$687$	−23.2871	−	4.76672i	−0.888458	−	0.181862i
$688$	0.403658	+	0.338709i	0.0153893	+	0.0129132i
$689$	8.90192	−	50.4853i	0.339136	−	1.92334i
$690$	10.7131	+	9.50094i	0.407841	+	0.361695i
$691$	−27.0323	−	32.2159i	−1.02836	−	1.22555i	−0.973887	−	0.227034i	$-0.927097\pi$
$691$	−27.0323	−	32.2159i	−1.02836	−	1.22555i	−0.0544707	−	0.998515i	$-0.517347\pi$
$692$	3.53058	−	6.11514i	0.134212	−	0.232463i
$693$	0.790822	−	4.52466i	0.0300408	−	0.171878i
$694$	6.13459	+	10.6254i	0.232866	+	0.403335i
$695$	−7.22811	+	19.8591i	−0.274178	+	0.753297i
$696$	2.54484	−	2.01931i	0.0964618	−	0.0765417i
$697$	−2.59001	−	2.17327i	−0.0981035	−	0.0823186i
$698$	0.208187	−	1.18069i	0.00788000	−	0.0446897i
$699$	13.9307	−	7.54229i	0.526908	−	0.285275i
$700$	9.55847	−	2.24588i	0.361276	−	0.0848864i
$701$		−	33.4343i		−	1.26280i	−0.775459	−	0.631398i	$-0.782481\pi$
$701$		−	33.4343i		−	1.26280i	0.775459	−	0.631398i	$-0.217519\pi$
$702$	−10.7595	−	22.7669i	−0.406091	−	0.859280i
$703$	−3.21749	−	1.85762i	−0.121350	−	0.0700613i
$704$	1.95428	+	2.32902i	0.0736546	+	0.0877782i
$705$	7.04710	+	13.0161i	0.265409	+	0.490215i
$706$	9.02357	−	10.7539i	0.339607	−	0.404727i
$707$	−19.2908	+	25.8077i	−0.725505	+	0.970598i
$708$	1.55154	+	10.4669i	0.0583106	+	0.393371i
$709$	−36.2834	−	13.2061i	−1.36265	−	0.495965i	−0.445779	−	0.895143i	$-0.647073\pi$
$709$	−36.2834	−	13.2061i	−1.36265	−	0.495965i	−0.916873	+	0.399178i	$0.869296\pi$
$710$	19.4254			0.729024
$711$	7.39613	+	3.16030i	0.277377	+	0.118520i
$712$			33.8030i			1.26682i
$713$	−2.02225	−	11.4687i	−0.0757338	−	0.429508i
$714$	−8.77658	+	3.48451i	−0.328455	+	0.130404i
$715$	4.10014	−	1.49233i	0.153336	−	0.0558099i
$716$	−6.58672	+	7.84974i	−0.246157	+	0.293359i
$717$	−4.28412	−	0.876931i	−0.159993	−	0.0327496i
$718$	−25.0998	−	9.13559i	−0.936717	−	0.340937i
$719$	−20.7470			−0.773733			−0.386866	−	0.922136i	$-0.626443\pi$
$719$	−20.7470			−0.773733			−0.386866	+	0.922136i	$0.626443\pi$
$720$	0.252310	+	0.498118i	0.00940304	+	0.0185637i
$721$	15.3185	−	30.3551i	0.570491	−	1.13048i
$722$	4.16820	+	4.96747i	0.155124	+	0.184870i
$723$	4.57988	−	11.5862i	0.170328	−	0.430895i
$724$	4.48162	−	5.34099i	0.166558	−	0.198496i
$725$	−0.691061	−	1.89868i	−0.0256654	−	0.0705150i
$726$	−0.450530	+	16.4557i	−0.0167207	+	0.610727i
$727$	−6.23885	+	17.1411i	−0.231386	+	0.635729i	−0.999992	−	0.00399420i	$-0.998729\pi$
$727$	−6.23885	+	17.1411i	−0.231386	+	0.635729i	0.768606	+	0.639723i	$0.220951\pi$
$728$	2.31064	+	41.0393i	0.0856379	+	1.52102i
$729$	26.6367	+	4.41429i	0.986545	+	0.163492i
$730$	1.47760	+	2.55927i	0.0546883	+	0.0947228i
$731$	6.95306	−	5.83431i	0.257168	−	0.215790i
$732$	24.8389	−	13.4481i	0.918071	−	0.497056i
$733$	26.9117	+	4.74525i	0.994005	+	0.175270i	0.646915	−	0.762562i	$-0.276059\pi$
$733$	26.9117	+	4.74525i	0.994005	+	0.175270i	0.347090	+	0.937832i	$0.387170\pi$
$734$	−0.739395	+	4.19331i	−0.0272916	+	0.154778i
$735$	−11.9123	+	11.8611i	−0.439391	+	0.437504i
$736$	28.6732	−	24.0597i	1.05691	−	0.886851i
$737$	−4.12848	−	2.38358i	−0.152075	−	0.0878003i
$738$	−0.213888	+	3.90321i	−0.00787331	+	0.143679i
$739$	−7.06815	−	12.2424i	−0.260006	−	0.450344i	0.706237	−	0.707975i	$-0.250391\pi$
$739$	−7.06815	−	12.2424i	−0.260006	−	0.450344i	−0.966243	+	0.257632i	$0.917058\pi$
$740$	−1.38971	+	1.16610i	−0.0510867	+	0.0428669i
$741$	30.5957	−	10.1967i	1.12396	−	0.374583i
$742$	8.76398	+	20.4257i	0.321736	+	0.749852i
$743$	3.05230	+	8.38613i	0.111978	+	0.307657i	0.983005	−	0.183578i	$-0.0587679\pi$
$743$	3.05230	+	8.38613i	0.111978	+	0.307657i	−0.871027	+	0.491235i	$0.836546\pi$
$744$	1.72713	−	8.43763i	0.0633196	−	0.309338i
$745$	−9.45321	+	25.9725i	−0.346339	+	0.951558i
$746$	10.6737	−	6.16249i	0.390794	−	0.225625i
$747$	−28.8046	+	21.5984i	−1.05390	+	0.790243i
$748$	1.39740	−	0.806789i	0.0510940	−	0.0294991i
$749$	26.2558	+	7.91582i	0.959365	+	0.289238i
$750$	17.1000	−	2.53478i	0.624403	−	0.0925571i
$751$	3.33799	−	1.21493i	0.121805	−	0.0443333i	−0.280399	−	0.959884i	$-0.590467\pi$
$751$	3.33799	−	1.21493i	0.121805	−	0.0443333i	0.402203	+	0.915550i	$0.368244\pi$
$752$	−0.777489	+	0.282983i	−0.0283521	+	0.0103193i
$753$	0.851610	−	1.38599i	0.0310344	−	0.0505083i
$754$	3.13326	−	0.552478i	0.114106	−	0.0201201i
$755$	−4.00557			−0.145778
$756$	−14.1374	−	8.65743i	−0.514174	−	0.314868i
$757$	−21.6011			−0.785104			−0.392552	−	0.919730i	$-0.628408\pi$
$757$	−21.6011			−0.785104			−0.392552	+	0.919730i	$0.628408\pi$
$758$	7.75981	−	1.36826i	0.281849	−	0.0496976i
$759$	−6.70401	−	0.183545i	−0.243340	−	0.00666226i
$760$	−12.7446	+	4.63865i	−0.462295	+	0.168262i
$761$	−9.49989	+	3.45768i	−0.344371	+	0.125341i	−0.508415	−	0.861112i	$-0.669768\pi$
$761$	−9.49989	+	3.45768i	−0.344371	+	0.125341i	0.164044	+	0.986453i	$0.447546\pi$
$762$	1.12069	−	2.83513i	0.0405984	−	0.102706i
$763$	43.4017	−	10.1978i	1.57125	−	0.369184i
$764$	24.8383	−	14.3404i	0.898618	−	0.518818i
$765$	9.20447	−	2.79012i	0.332788	−	0.100877i
$766$	−23.2197	+	13.4059i	−0.838962	+	0.484375i
$767$	−9.42284	+	25.8890i	−0.340239	+	0.934799i
$768$	26.7935	−	8.92951i	0.966829	−	0.322216i
$769$	12.2720	+	33.7171i	0.442540	+	1.21587i	0.937816	+	0.347133i	$0.112845\pi$
$769$	12.2720	+	33.7171i	0.442540	+	1.21587i	−0.495276	+	0.868736i	$0.664933\pi$
$770$	−1.13262	+	1.51525i	−0.0408169	+	0.0546058i
$771$	6.80627	−	33.2510i	0.245122	−	1.19751i
$772$	−17.4786	+	14.6663i	−0.629067	+	0.527850i
$773$	−17.9180	−	31.0349i	−0.644466	−	1.11625i	−0.984425	−	0.175808i	$-0.943746\pi$
$773$	−17.9180	−	31.0349i	−0.644466	−	1.11625i	0.339958	−	0.940441i	$-0.389587\pi$
$774$	−10.2195	−	2.38503i	−0.367334	−	0.0857283i
$775$	−4.63900	−	2.67833i	−0.166638	−	0.0962084i
$776$	−40.7858	+	34.2233i	−1.46412	+	1.22855i
$777$	−1.56508	+	4.71971i	−0.0561468	+	0.169319i
$778$	−1.53010	+	8.67765i	−0.0548569	+	0.311109i
$779$	−4.93035	−	0.869353i	−0.176648	−	0.0311478i
$780$	0.430983	−	15.7417i	0.0154317	−	0.563644i
$781$	−6.96954	+	5.84814i	−0.249390	+	0.209263i
$782$	6.89376	+	11.9403i	0.246520	+	0.426986i
$783$	−1.42577	+	3.09915i	−0.0509527	+	0.110755i
$784$	−0.558222	−	0.755910i	−0.0199365	−	0.0269968i
$785$	−3.85205	+	10.5834i	−0.137486	+	0.377738i
$786$	−3.02828	+	1.63955i	−0.108015	+	0.0584808i
$787$	−8.11545	−	22.2970i	−0.289285	−	0.794803i	−0.996167	−	0.0874718i	$-0.972121\pi$
$787$	−8.11545	−	22.2970i	−0.289285	−	0.794803i	0.706882	−	0.707331i	$-0.250101\pi$
$788$	8.25402	−	9.83676i	0.294037	−	0.350420i
$789$	12.8402	+	16.1819i	0.457123	+	0.576091i
$790$	−2.12930	−	2.53760i	−0.0757570	−	0.0902837i
$791$	−29.4601	−	44.9812i	−1.04748	−	1.59935i
$792$	−4.56091	−	1.94883i	−0.162065	−	0.0692488i
$793$	73.5434			2.61160
$794$	−9.62173	−	3.50202i	−0.341462	−	0.124282i
$795$	−7.15774	−	21.4772i	−0.253859	−	0.761719i
$796$	−7.77216	+	9.26250i	−0.275477	+	0.328301i
$797$	−25.1031	+	9.13677i	−0.889196	+	0.323641i	−0.745915	−	0.666041i	$-0.767988\pi$
$797$	−25.1031	+	9.13677i	−0.889196	+	0.323641i	−0.143281	+	0.989682i	$0.545765\pi$
$798$	−8.67489	+	10.9663i	−0.307088	+	0.388203i
$799$	2.47481	+	14.0353i	0.0875523	+	0.496534i
$800$		−	17.2168i		−	0.608705i
$801$	−16.0395	−	31.6657i	−0.566729	−	1.11885i
$802$	14.6906			0.518744
$803$	−1.30062	−	0.473387i	−0.0458979	−	0.0167055i
$804$	−13.4778	+	10.6945i	−0.475324	+	0.377166i
$805$	19.6593	+	14.6950i	0.692900	+	0.517931i
$806$	5.42177	−	6.46141i	0.190974	−	0.227594i
$807$	−28.4586	−	0.779150i	−1.00179	−	0.0274274i
$808$	22.3639	+	26.6523i	0.786760	+	0.937624i
$809$	−17.2909	−	9.98289i	−0.607915	−	0.350980i	0.164234	−	0.986421i	$-0.447485\pi$
$809$	−17.2909	−	9.98289i	−0.607915	−	0.350980i	−0.772149	+	0.635442i	$0.780818\pi$
$810$	−8.96519	−	6.57911i	−0.315005	−	0.231166i
$811$			13.5611i			0.476196i	0.971241	+	0.238098i	$0.0765239\pi$
$811$			13.5611i			0.476196i	−0.971241	+	0.238098i	$0.923476\pi$
$812$	1.52629	−	1.43441i	0.0535624	−	0.0503381i
$813$	21.8067	+	13.3989i	0.764793	+	0.469920i
$814$	−0.0971699	+	0.551078i	−0.00340580	+	0.0193153i
$815$	−1.10169	−	0.924431i	−0.0385906	−	0.0323814i
$816$	0.0788349	+	0.531831i	0.00275977	+	0.0186178i
$817$	4.59677	−	12.6295i	0.160820	−	0.441851i
$818$	−4.06677	−	7.04386i	−0.142191	−	0.246283i
$819$	−21.6377	−	37.3480i	−0.756082	−	1.30505i
$820$	−1.22231	+	2.11710i	−0.0426848	+	0.0739322i
$821$	−21.9000	−	26.0994i	−0.764316	−	0.910876i	0.233797	−	0.972285i	$-0.424885\pi$
$821$	−21.9000	−	26.0994i	−0.764316	−	0.910876i	−0.998113	+	0.0614094i	$0.980440\pi$
$822$	0.412762	−	2.01649i	0.0143967	−	0.0703331i
$823$	1.50208	−	8.51870i	0.0523591	−	0.296943i	−0.947372	−	0.320135i	$-0.896272\pi$
$823$	1.50208	−	8.51870i	0.0523591	−	0.296943i	0.999731	+	0.0231918i	$0.00738284\pi$
$824$	−28.1252	−	23.5999i	−0.979788	−	0.822140i
$825$	−2.04680	+	2.30794i	−0.0712605	+	0.0803522i
$826$	−2.73223	−	11.6284i	−0.0950665	−	0.404603i
$827$	−34.8581	−	20.1253i	−1.21213	−	0.699826i	−0.248911	−	0.968526i	$-0.580073\pi$
$827$	−34.8581	−	20.1253i	−1.21213	−	0.699826i	−0.963224	+	0.268700i	$0.913406\pi$
$828$	−9.51060	+	22.2579i	−0.330516	+	0.773517i
$829$			41.3722i			1.43692i	0.695571	+	0.718458i	$0.255152\pi$
$829$			41.3722i			1.43692i	−0.695571	+	0.718458i	$0.744848\pi$
$830$	14.6028	−	2.57487i	0.506870	−	0.0893749i
$831$	37.6082	−	29.8418i	1.30461	−	1.03520i
$832$	28.1361	+	4.96115i	0.975444	+	0.171997i
$833$	−14.4925	+	7.20836i	−0.502137	+	0.249755i
$834$	23.5182	+	0.643891i	0.814369	+	0.0222961i
$835$	3.38197	+	19.1801i	0.117038	+	0.663755i
$836$	1.19464	−	2.06919i	0.0413176	−	0.0715643i
$837$	2.38573	+	8.72364i	0.0824628	+	0.301533i
$838$	−22.6091	+	13.0534i	−0.781019	+	0.450921i
$839$	25.4475	+	9.26215i	0.878547	+	0.319765i	0.741623	−	0.670817i	$-0.234056\pi$
$839$	25.4475	+	9.26215i	0.878547	+	0.319765i	0.136924	+	0.990582i	$0.456278\pi$
$840$	9.52600	+	15.4515i	0.328678	+	0.533127i
$841$	21.8851	+	18.3638i	0.754659	+	0.633234i
$842$	−3.61287	−	9.92627i	−0.124508	−	0.342082i
$843$	−6.70330	−	8.44785i	−0.230874	−	0.290959i
$844$	−1.25430	−	7.11347i	−0.0431747	−	0.244856i
$845$	11.4888	−	19.8992i	0.395227	−	0.684554i
$846$	11.2665	−	12.0242i	0.387349	−	0.413401i
$847$	1.58620	+	28.1726i	0.0545025	+	0.968022i
$848$	1.24625	−	0.219748i	0.0427965	−	0.00754619i
$849$	−3.00816	−	9.02618i	−0.103240	−	0.309778i
$850$	6.24551	+	1.10125i	0.214219	+	0.0377726i
$851$	7.14986	+	1.26071i	0.245094	+	0.0432167i
$852$	10.3820	+	31.1517i	0.355680	+	1.06724i
$853$	19.5183	−	3.44160i	0.668293	−	0.117838i	0.170800	−	0.985306i	$-0.445365\pi$
$853$	19.5183	−	3.44160i	0.668293	−	0.117838i	0.497494	+	0.867468i	$0.334254\pi$
$854$	−26.6743	+	17.4701i	−0.912775	+	0.597816i
$855$	9.73771	−	10.3927i	0.333023	−	0.355421i
$856$	14.8058	−	25.6444i	0.506052	−	0.876508i
$857$	5.50964	+	31.2467i	0.188206	+	1.06737i	0.921767	+	0.387744i	$0.126746\pi$
$857$	5.50964	+	31.2467i	0.188206	+	1.06737i	−0.733561	+	0.679623i	$0.762143\pi$
$858$	−3.01929	−	3.80507i	−0.103077	−	0.129903i
$859$	−0.898554	−	2.46876i	−0.0306583	−	0.0842329i	0.923419	−	0.383793i	$-0.125382\pi$
$859$	−0.898554	−	2.46876i	−0.0306583	−	0.0842329i	−0.954077	+	0.299560i	$0.903160\pi$
$860$	−5.02734	−	4.21844i	−0.171431	−	0.143848i
$861$	0.193431	+	6.69774i	0.00659211	+	0.228258i
$862$	−10.0606	−	3.66177i	−0.342666	−	0.124720i
$863$	−32.4638	+	18.7430i	−1.10508	+	0.638018i	−0.937551	−	0.347849i	$-0.886912\pi$
$863$	−32.4638	+	18.7430i	−1.10508	+	0.638018i	−0.167529	+	0.985867i	$0.553579\pi$
$864$	−20.4481	+	20.6599i	−0.695659	+	0.702864i
$865$	4.05950	−	7.03126i	0.138027	−	0.239070i
$866$	−0.288414	−	1.63568i	−0.00980070	−	0.0555825i
$867$	−20.1763	−	0.552396i	−0.685225	−	0.0187604i
$868$	0.655317	−	5.51408i	0.0222429	−	0.187160i
$869$	1.52792	+	0.269413i	0.0518310	+	0.00913921i
$870$	1.10062	−	0.873330i	0.0373144	−	0.0296087i
$871$	−44.1169	+	7.77900i	−1.49484	+	0.263581i
$872$		−	48.1417i		−	1.63028i
$873$	21.9680	−	51.4122i	0.743503	−	1.74004i
$874$	17.6806	+	10.2079i	0.598054	+	0.345286i
$875$	28.8458	−	6.77768i	0.975166	−	0.229128i
$876$	−3.31449	+	3.73736i	−0.111986	+	0.126274i
$877$	28.6435	+	24.0348i	0.967223	+	0.811596i	0.982113	−	0.188293i	$-0.0602954\pi$
$877$	28.6435	+	24.0348i	0.967223	+	0.811596i	−0.0148900	+	0.999889i	$0.504740\pi$
$878$	−4.04112	+	22.9183i	−0.136381	+	0.773457i
$879$	−8.08535	+	39.4998i	−0.272712	+	1.33230i
$880$	0.0692343	+	0.0825103i	0.00233389	+	0.00278142i
$881$	−3.30548	+	5.72527i	−0.111365	+	0.192889i	−0.916321	−	0.400445i	$-0.868855\pi$
$881$	−3.30548	+	5.72527i	−0.111365	+	0.192889i	0.804956	+	0.593334i	$0.202189\pi$
$882$	16.7200	+	8.40617i	0.562991	+	0.283051i
$883$	27.7285	+	48.0272i	0.933140	+	1.61625i	0.777918	+	0.628366i	$0.216276\pi$
$883$	27.7285	+	48.0272i	0.933140	+	1.61625i	0.155222	+	0.987880i	$0.450391\pi$
$884$	5.18603	−	14.2485i	0.174425	−	0.479229i
$885$	1.78398	+	12.0350i	0.0599680	+	0.404552i
$886$	5.34436	+	4.48445i	0.179547	+	0.150658i
$887$	4.78039	−	27.1109i	0.160510	−	0.910295i	−0.793065	−	0.609138i	$-0.791516\pi$
$887$	4.78039	−	27.1109i	0.160510	−	0.910295i	0.953574	−	0.301158i	$-0.0973731\pi$
$888$	4.57471	+	2.81089i	0.153517	+	0.0943272i
$889$	1.50840	−	5.00316i	0.0505900	−	0.167801i
$890$			14.6195i			0.490046i
$891$	5.19725	−	0.338541i	0.174114	−	0.0113416i
$892$	5.98101	+	3.45314i	0.200259	+	0.115620i
$893$	13.5649	+	16.1660i	0.453933	+	0.540976i
$894$	30.7581	+	0.842107i	1.02870	+	0.0281643i
$895$	−7.57348	+	9.02572i	−0.253154	+	0.301697i
$896$	15.8197	−	6.78771i	0.528501	−	0.226762i
$897$	−49.3681	+	39.1732i	−1.64835	+	1.30795i
$898$	−2.45116	−	0.892151i	−0.0817964	−	0.0297715i
$899$	−1.14268			−0.0381107
$900$	5.03082	+	9.93199i	0.167694	+	0.331066i
$901$		−	21.7980i		−	0.726198i
$902$	0.130940	+	0.742597i	0.00435982	+	0.0247258i
$903$	−17.7975	−	2.61090i	−0.592265	−	0.0868852i
$904$	−54.5596	+	19.8581i	−1.81463	+	0.660470i
$905$	5.15302	−	6.14113i	0.171292	−	0.204138i
$906$	1.40989	+	4.23046i	0.0468404	+	0.140548i
$907$	−38.0728	−	13.8574i	−1.26419	−	0.460127i	−0.379015	−	0.925390i	$-0.623737\pi$
$907$	−38.0728	−	13.8574i	−1.26419	−	0.460127i	−0.885172	+	0.465264i	$0.845959\pi$
$908$	−21.3214			−0.707576
$909$	−33.5964	−	14.3554i	−1.11432	−	0.476139i
$910$	0.999327	+	17.7491i	0.0331274	+	0.588377i
$911$	−32.6169	−	38.8713i	−1.08064	−	1.28786i	−0.955264	−	0.295753i	$-0.904429\pi$
$911$	−32.6169	−	38.8713i	−1.08064	−	1.28786i	−0.125380	−	0.992109i	$-0.540015\pi$
$912$	0.494847	+	0.623631i	0.0163860	+	0.0206505i
$913$	−4.46407	+	5.32007i	−0.147739	+	0.176069i
$914$	7.50452	+	20.6185i	0.248227	+	0.681999i
$915$	28.5600	−	15.4628i	0.944165	−	0.511184i
$916$	−5.65994	+	15.5505i	−0.187010	+	0.513805i
$917$	−4.93792	+	3.23406i	−0.163064	+	0.106798i
$918$	−6.18658	−	8.73919i	−0.204188	−	0.288436i
$919$	27.9766	+	48.4569i	0.922864	+	1.59845i	0.794962	+	0.606660i	$0.207491\pi$
$919$	27.9766	+	48.4569i	0.922864	+	1.59845i	0.127902	+	0.991787i	$0.459176\pi$
$920$	20.3027	−	17.0360i	0.669360	−	0.561660i
$921$	−0.826575	+	30.1908i	−0.0272366	+	0.994820i
$922$	−33.1936	−	5.85293i	−1.09317	−	0.192756i
$923$	−14.8462	+	84.1968i	−0.488667	+	2.77137i
$924$	−3.03527	−	1.00651i	−0.0998532	−	0.0331118i
$925$	2.55817	−	2.14656i	0.0841121	−	0.0705785i
$926$	8.33677	+	4.81323i	0.273963	+	0.158173i
$927$	37.5450	+	8.76224i	1.23314	+	0.287790i
$928$	−1.83635	−	3.18064i	−0.0602810	−	0.104410i
$929$	−17.5023	+	14.6862i	−0.574232	+	0.481838i	−0.883047	−	0.469284i	$-0.844512\pi$
$929$	−17.5023	+	14.6862i	−0.574232	+	0.481838i	0.308815	+	0.951122i	$0.400067\pi$
$930$	0.746965	−	3.64919i	0.0244940	−	0.119662i
$931$	−13.2478	+	19.9735i	−0.434178	+	0.654607i
$932$	−3.77205	−	10.3636i	−0.123558	−	0.339472i
$933$	−2.48047	+	0.826667i	−0.0812069	+	0.0270639i
$934$	8.85022	−	24.3158i	0.289588	−	0.795636i
$935$	1.60675	−	0.927655i	0.0525462	−	0.0303376i
$936$	−44.6037	+	13.5206i	−1.45792	+	0.441934i
$937$	34.1439	−	19.7130i	1.11543	−	0.643995i	0.175201	−	0.984533i	$-0.443943\pi$
$937$	34.1439	−	19.7130i	1.11543	−	0.643995i	0.940231	+	0.340538i	$0.110609\pi$
$938$	14.1534	−	13.3014i	0.462123	−	0.434305i
$939$	18.5402	−	46.9031i	0.605038	−	1.53063i
$940$	9.68321	−	3.52440i	0.315832	−	0.114953i
$941$	−12.7830	+	4.65265i	−0.416716	+	0.151672i	−0.541864	−	0.840466i	$-0.682281\pi$
$941$	−12.7830	+	4.65265i	−0.416716	+	0.151672i	0.125149	+	0.992138i	$0.460059\pi$
$942$	12.5335	+	0.343147i	0.408363	+	0.0111803i
$943$	9.63468	−	1.69885i	0.313748	−	0.0553223i
$944$	−0.680098			−0.0221353
$945$	−16.2554	−	9.95441i	−0.528788	−	0.323817i
$946$	−2.02431			−0.0658159
$947$	−4.67370	+	0.824099i	−0.151875	+	0.0267796i	−0.249069	−	0.968486i	$-0.580124\pi$
$947$	−4.67370	+	0.824099i	−0.151875	+	0.0267796i	0.0971938	+	0.995265i	$0.469013\pi$
$948$	2.93143	−	4.77089i	0.0952084	−	0.154951i
$949$	−12.2221	+	4.44846i	−0.396745	+	0.144403i
$950$	8.82431	−	3.21179i	0.286298	−	0.104204i
$951$	52.0884	−	7.72122i	1.68908	−	0.250378i
$952$	3.99780	+	17.0146i	0.129570	+	0.551448i
$953$	25.1568	−	14.5243i	0.814909	−	0.470488i	−0.0337488	−	0.999430i	$-0.510745\pi$
$953$	25.1568	−	14.5243i	0.814909	−	0.470488i	0.848658	+	0.528942i	$0.177411\pi$
$954$	−20.1637	+	15.1192i	−0.652824	+	0.489503i
$955$	28.5594	−	16.4888i	0.924159	−	0.533564i
$956$	−1.04126	+	2.86083i	−0.0336766	+	0.0925257i
$957$	−0.131963	+	0.644684i	−0.00426574	+	0.0208397i
$958$	4.15692	+	11.4210i	0.134304	+	0.368997i
$959$	0.416368	−	3.50348i	0.0134452	−	0.113133i
$960$	11.9695	−	3.98910i	0.386315	−	0.128748i
$961$	21.4267	−	17.9792i	0.691185	−	0.579973i
$962$	2.62921	+	4.55392i	0.0847691	+	0.146824i
$963$	−1.70138	+	31.0483i	−0.0548262	+	1.00052i
$964$	−7.51154	−	4.33679i	−0.241930	−	0.139679i
$965$	−20.0971	+	16.8634i	−0.646947	+	0.542853i
$966$	8.60032	−	25.9355i	0.276711	−	0.834460i
$967$	−0.574034	+	3.25551i	−0.0184597	+	0.104690i	−0.992645	−	0.121058i	$-0.961371\pi$
$967$	−0.574034	+	3.25551i	−0.0184597	+	0.104690i	0.974186	+	0.225748i	$0.0724825\pi$
$968$	30.0063	+	5.29091i	0.964438	+	0.170056i
$969$	12.0591	−	6.52895i	0.387393	−	0.209740i
$970$	−17.6394	+	14.8012i	−0.566368	+	0.475239i
$971$	−7.79202	−	13.4962i	−0.250058	−	0.433113i	0.713484	−	0.700672i	$-0.247116\pi$
$971$	−7.79202	−	13.4962i	−0.250058	−	0.433113i	−0.963541	+	0.267559i	$0.913783\pi$
$972$	5.75917	−	17.8933i	0.184725	−	0.573928i
$973$	40.2639	−	2.26698i	1.29080	−	0.0726760i
$974$	−9.80616	+	26.9422i	−0.314209	+	0.863283i
$975$	−0.793352	+	28.9773i	−0.0254076	+	0.928016i
$976$	0.620922	+	1.70597i	0.0198752	+	0.0546067i
$977$	−19.6180	+	23.3798i	−0.627636	+	0.747987i	−0.982363	−	0.186983i	$-0.940129\pi$
$977$	−19.6180	+	23.3798i	−0.627636	+	0.747987i	0.354728	+	0.934970i	$0.384574\pi$
$978$	−0.588556	+	1.48893i	−0.0188200	+	0.0476108i
$979$	−4.40127	−	5.24524i	−0.140665	−	0.167638i
$980$	6.95237	+	9.41446i	0.222085	+	0.300734i
$981$	22.8432	+	45.0977i	0.729328	+	1.43986i
$982$	−21.9314			−0.699858
$983$	−17.7061	−	6.44449i	−0.564737	−	0.205547i	0.0438454	−	0.999038i	$-0.486039\pi$
$983$	−17.7061	−	6.44449i	−0.564737	−	0.205547i	−0.608582	+	0.793491i	$0.708261\pi$
$984$	7.08830	+	1.45093i	0.225967	+	0.0462539i
$985$	9.49057	−	11.3104i	0.302395	−	0.360380i
$986$	1.27126	−	0.462701i	0.0404852	−	0.0147354i
$987$	17.5230	−	22.1516i	0.557763	−	0.705092i
$988$	−3.89881	−	22.1113i	−0.124038	−	0.703453i
$989$			26.2640i			0.835146i
$990$	−1.97255	−	0.842850i	−0.0626917	−	0.0267875i
$991$	−19.3398			−0.614349			−0.307175	−	0.951653i	$-0.599384\pi$
$991$	−19.3398			−0.614349			−0.307175	+	0.951653i	$0.599384\pi$
$992$	−9.14954	−	3.33016i	−0.290498	−	0.105733i
$993$	−7.18799	−	48.4912i	−0.228104	−	1.53882i
$994$	−14.6161	−	34.0649i	−0.463595	−	1.08047i
$995$	−8.93652	+	10.6501i	−0.283307	+	0.337632i
$996$	11.9337	+	22.0417i	0.378133	+	0.698418i
$997$	6.47667	+	7.71859i	0.205118	+	0.244450i	0.858790	−	0.512328i	$-0.171217\pi$
$997$	6.47667	+	7.71859i	0.205118	+	0.244450i	−0.653672	+	0.756778i	$0.726772\pi$
$998$	20.2121	+	11.6694i	0.639801	+	0.369390i
$999$	−5.61921	−	0.462460i	−0.177784	−	0.0146316i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	189.2.bd.a.185.9	yes	132
3.2	odd	2		567.2.bd.a.17.14		132
7.5	odd	6		189.2.ba.a.131.14	yes	132
21.5	even	6		567.2.ba.a.341.9		132
27.7	even	9		567.2.ba.a.143.9		132
27.20	odd	18		189.2.ba.a.101.14	✓	132
189.47	even	18	inner	189.2.bd.a.47.9	yes	132
189.61	odd	18		567.2.bd.a.467.14		132

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
189.2.ba.a.101.14	✓	132	27.20	odd	18
189.2.ba.a.131.14	yes	132	7.5	odd	6
189.2.bd.a.47.9	yes	132	189.47	even	18	inner
189.2.bd.a.185.9	yes	132	1.1	even	1	trivial
567.2.ba.a.143.9		132	27.7	even	9
567.2.ba.a.341.9		132	21.5	even	6
567.2.bd.a.17.14		132	3.2	odd	2
567.2.bd.a.467.14		132	189.61	odd	18

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:	\( N \)	\(=\)	\( 189 = 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	189.bd (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.877614 + 0.154747i) q^{2} +(-0.824649 - 1.52314i) q^{3} +(-1.13313 + 0.412424i) q^{4} +(-1.30288 + 0.474210i) q^{5} +(0.959425 + 1.20912i) q^{6} +(1.81190 + 1.92796i) q^{7} +(2.47415 - 1.42845i) q^{8} +(-1.63991 + 2.51211i) q^{9} +O(q^{10})\)	\(q+(-0.877614 + 0.154747i) q^{2} +(-0.824649 - 1.52314i) q^{3} +(-1.13313 + 0.412424i) q^{4} +(-1.30288 + 0.474210i) q^{5} +(0.959425 + 1.20912i) q^{6} +(1.81190 + 1.92796i) q^{7} +(2.47415 - 1.42845i) q^{8} +(-1.63991 + 2.51211i) q^{9} +(1.07004 - 0.617790i) q^{10} +(-0.197926 + 0.543796i) q^{11} +(1.56261 + 1.38580i) q^{12} +(1.85992 + 5.11010i) q^{13} +(-1.88849 - 1.41162i) q^{14} +(1.79671 + 1.59341i) q^{15} +(-0.102835 + 0.0862885i) q^{16} +(1.15616 + 2.00253i) q^{17} +(1.05047 - 2.45844i) q^{18} +(2.96522 + 1.71197i) q^{19} +(1.28075 - 1.07468i) q^{20} +(1.44237 - 4.34966i) q^{21} +(0.0895514 - 0.507871i) q^{22} +(-6.58928 - 1.16187i) q^{23} +(-4.21603 - 2.59050i) q^{24} +(-2.35760 + 1.97826i) q^{25} +(-2.42307 - 4.19688i) q^{26} +(5.17864 + 0.426201i) q^{27} +(-2.84824 - 1.43735i) q^{28} +(-0.224543 + 0.616928i) q^{29} +(-1.82339 - 1.12037i) q^{30} +(0.595291 + 1.63555i) q^{31} +(-3.59586 + 4.28538i) q^{32} +(0.991496 - 0.146972i) q^{33} +(-1.32455 - 1.57853i) q^{34} +(-3.27494 - 1.65268i) q^{35} +(0.822168 - 3.52287i) q^{36} -1.08507 q^{37} +(-2.86724 - 1.04359i) q^{38} +(6.24961 - 7.04696i) q^{39} +(-2.54613 + 3.03436i) q^{40} +(-1.37400 + 0.500093i) q^{41} +(-0.592745 + 4.04053i) q^{42} +(-0.681623 - 3.86568i) q^{43} -0.697818i q^{44} +(0.945338 - 4.05064i) q^{45} +5.96264 q^{46} +(5.79174 + 2.10802i) q^{47} +(0.216232 + 0.0854738i) q^{48} +(-0.434042 + 6.98653i) q^{49} +(1.76293 - 2.10098i) q^{50} +(2.09670 - 3.41237i) q^{51} +(-4.21505 - 5.02331i) q^{52} +(-8.16395 - 4.71346i) q^{53} +(-4.61081 + 0.427340i) q^{54} -0.802359i q^{55} +(7.23690 + 2.18184i) q^{56} +(0.162305 - 5.92822i) q^{57} +(0.101595 - 0.576172i) q^{58} +(3.88097 + 3.25652i) q^{59} +(-2.69305 - 1.06453i) q^{60} +(4.62542 - 12.7082i) q^{61} +(-0.775532 - 1.34326i) q^{62} +(-7.81459 + 1.39002i) q^{63} +(2.62687 - 4.54987i) q^{64} +(-4.84652 - 5.77585i) q^{65} +(-0.847408 + 0.282416i) q^{66} +(-1.43047 + 8.11262i) q^{67} +(-2.13596 - 1.79229i) q^{68} +(3.66415 + 10.9945i) q^{69} +(3.12988 + 0.943626i) q^{70} +(13.6154 + 7.86086i) q^{71} +(-0.468953 + 8.55786i) q^{72} +2.39174i q^{73} +(0.952276 - 0.167912i) q^{74} +(4.95736 + 1.95958i) q^{75} +(-4.06603 - 0.716950i) q^{76} +(-1.40704 + 0.603711i) q^{77} +(-4.39425 + 7.15162i) q^{78} +(-0.465552 - 2.64028i) q^{79} +(0.0930623 - 0.161189i) q^{80} +(-3.62140 - 8.23926i) q^{81} +(1.12845 - 0.651511i) q^{82} +(11.2771 + 4.10455i) q^{83} +(0.159521 + 5.52358i) q^{84} +(-2.45595 - 2.06079i) q^{85} +(1.19640 + 3.28709i) q^{86} +(1.12484 - 0.166738i) q^{87} +(0.287088 + 1.62816i) q^{88} +(-5.91604 + 10.2469i) q^{89} +(-0.202817 + 3.70119i) q^{90} +(-6.48206 + 12.8448i) q^{91} +(7.94566 - 1.40103i) q^{92} +(2.00026 - 2.25547i) q^{93} +(-5.40912 - 0.953774i) q^{94} +(-4.67516 - 0.824357i) q^{95} +(9.49256 + 1.94307i) q^{96} +(-18.3532 + 3.23616i) q^{97} +(-0.700224 - 6.19865i) q^{98} +(-1.04150 - 1.38899i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 132 q - 3 q^{2} - 9 q^{3} - 3 q^{4} - 9 q^{5} + 18 q^{6} - 6 q^{7} - 18 q^{8} - 15 q^{9}+O(q^{10}) \) 132 * q - 3 * q^2 - 9 * q^3 - 3 * q^4 - 9 * q^5 + 18 * q^6 - 6 * q^7 - 18 * q^8 - 15 * q^9	\( 132 q - 3 q^{2} - 9 q^{3} - 3 q^{4} - 9 q^{5} + 18 q^{6} - 6 q^{7} - 18 q^{8} - 15 q^{9} - 9 q^{10} + 9 q^{11} - 9 q^{12} - 42 q^{14} - 24 q^{15} - 15 q^{16} - 9 q^{17} - 3 q^{18} - 9 q^{19} - 18 q^{20} + 15 q^{21} - 12 q^{22} + 30 q^{23} - 36 q^{24} - 3 q^{25} - 12 q^{28} + 6 q^{29} - 3 q^{30} - 9 q^{31} - 51 q^{32} - 9 q^{33} + 18 q^{34} - 9 q^{35} - 6 q^{37} - 9 q^{38} - 9 q^{39} - 9 q^{40} + 27 q^{42} - 12 q^{43} - 63 q^{45} - 6 q^{46} + 45 q^{47} + 30 q^{49} - 9 q^{50} + 33 q^{51} - 9 q^{52} + 45 q^{53} + 117 q^{54} - 51 q^{56} - 3 q^{58} - 9 q^{59} - 15 q^{60} - 63 q^{61} + 99 q^{62} - 33 q^{63} + 18 q^{64} - 102 q^{65} + 63 q^{66} - 3 q^{67} + 144 q^{68} - 108 q^{69} - 15 q^{70} + 18 q^{71} + 15 q^{72} - 33 q^{74} - 9 q^{75} - 36 q^{76} - 57 q^{77} + 66 q^{78} - 21 q^{79} - 72 q^{80} + 57 q^{81} - 18 q^{82} + 90 q^{83} + 51 q^{84} + 9 q^{85} - 33 q^{86} - 9 q^{87} + 45 q^{88} - 9 q^{89} - 81 q^{90} - 21 q^{91} + 150 q^{92} - 87 q^{93} - 9 q^{94} + 27 q^{95} - 9 q^{96} - 180 q^{98} + 96 q^{99}+O(q^{100}) \) 132 * q - 3 * q^2 - 9 * q^3 - 3 * q^4 - 9 * q^5 + 18 * q^6 - 6 * q^7 - 18 * q^8 - 15 * q^9 - 9 * q^10 + 9 * q^11 - 9 * q^12 - 42 * q^14 - 24 * q^15 - 15 * q^16 - 9 * q^17 - 3 * q^18 - 9 * q^19 - 18 * q^20 + 15 * q^21 - 12 * q^22 + 30 * q^23 - 36 * q^24 - 3 * q^25 - 12 * q^28 + 6 * q^29 - 3 * q^30 - 9 * q^31 - 51 * q^32 - 9 * q^33 + 18 * q^34 - 9 * q^35 - 6 * q^37 - 9 * q^38 - 9 * q^39 - 9 * q^40 + 27 * q^42 - 12 * q^43 - 63 * q^45 - 6 * q^46 + 45 * q^47 + 30 * q^49 - 9 * q^50 + 33 * q^51 - 9 * q^52 + 45 * q^53 + 117 * q^54 - 51 * q^56 - 3 * q^58 - 9 * q^59 - 15 * q^60 - 63 * q^61 + 99 * q^62 - 33 * q^63 + 18 * q^64 - 102 * q^65 + 63 * q^66 - 3 * q^67 + 144 * q^68 - 108 * q^69 - 15 * q^70 + 18 * q^71 + 15 * q^72 - 33 * q^74 - 9 * q^75 - 36 * q^76 - 57 * q^77 + 66 * q^78 - 21 * q^79 - 72 * q^80 + 57 * q^81 - 18 * q^82 + 90 * q^83 + 51 * q^84 + 9 * q^85 - 33 * q^86 - 9 * q^87 + 45 * q^88 - 9 * q^89 - 81 * q^90 - 21 * q^91 + 150 * q^92 - 87 * q^93 - 9 * q^94 + 27 * q^95 - 9 * q^96 - 180 * q^98 + 96 * q^99

Introduction

L-functions

Modular forms

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