LMFDB - Embedded newform 324.2.p.a.11.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [324,2,Mod(11,324)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(324, base_ring=CyclotomicField(54))

chi = DirichletCharacter(H, H._module([27, 13]))

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

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

chi := DirichletCharacter("324.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 324 = 2^{2} \cdot 3^{4} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	324.p (of order $54$, degree $18$, 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:	$2.58715302549$
Analytic rank:	$0$
Dimension:	$936$
Relative dimension:	$52$ over $\Q(\zeta_{54})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{54}]$

Embedding invariants

Embedding label			11.19
Character	$\chi$	$=$	324.11
Dual form			324.2.p.a.59.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.607055 + 1.27730i) q^{2} +(-1.65046 + 0.525329i) q^{3} +(-1.26297 - 1.55078i) q^{4} +(-0.0392046 + 0.335417i) q^{5} +(0.330922 - 2.42703i) q^{6} +(-0.385340 - 0.767275i) q^{7} +(2.74749 - 0.671779i) q^{8} +(2.44806 - 1.73407i) q^{9} +O(q^{10})$	\(q+(-0.607055 + 1.27730i) q^{2} +(-1.65046 + 0.525329i) q^{3} +(-1.26297 - 1.55078i) q^{4} +(-0.0392046 + 0.335417i) q^{5} +(0.330922 - 2.42703i) q^{6} +(-0.385340 - 0.767275i) q^{7} +(2.74749 - 0.671779i) q^{8} +(2.44806 - 1.73407i) q^{9} +(-0.404627 - 0.253692i) q^{10} +(2.00131 - 4.63956i) q^{11} +(2.89915 + 1.89603i) q^{12} +(-6.16365 + 1.46081i) q^{13} +(1.21396 - 0.0264153i) q^{14} +(-0.111498 - 0.574189i) q^{15} +(-0.809817 + 3.91717i) q^{16} +(5.08597 - 0.896794i) q^{17} +(0.728816 + 4.17957i) q^{18} +(6.01443 + 1.06051i) q^{19} +(0.569671 - 0.362824i) q^{20} +(1.03906 + 1.06393i) q^{21} +(4.71118 + 5.37273i) q^{22} +(3.13383 + 1.57387i) q^{23} +(-4.18173 + 2.55208i) q^{24} +(4.75426 + 1.12678i) q^{25} +(1.87578 - 8.75959i) q^{26} +(-3.12948 + 4.14806i) q^{27} +(-0.703200 + 1.56662i) q^{28} +(2.92162 - 0.874674i) q^{29} +(0.801095 + 0.206148i) q^{30} +(-3.20948 - 4.87978i) q^{31} +(-4.51178 - 3.41231i) q^{32} +(-0.865797 + 8.70877i) q^{33} +(-1.94199 + 7.04070i) q^{34} +(0.272464 - 0.0991689i) q^{35} +(-5.78098 - 1.60632i) q^{36} +(-8.27851 - 3.01313i) q^{37} +(-5.00566 + 7.03842i) q^{38} +(9.40547 - 5.64895i) q^{39} +(0.117612 + 0.947892i) q^{40} +(1.71579 - 1.61877i) q^{41} +(-1.98972 + 0.681325i) q^{42} +(5.97906 - 4.45124i) q^{43} +(-9.72251 + 2.75603i) q^{44} +(0.485662 + 0.889104i) q^{45} +(-3.91270 + 3.04740i) q^{46} +(-0.678332 - 0.446146i) q^{47} +(-0.721226 - 6.89056i) q^{48} +(3.73989 - 5.02354i) q^{49} +(-4.32532 + 5.38858i) q^{50} +(-7.92310 + 4.15193i) q^{51} +(10.0499 + 7.71348i) q^{52} +(9.56115 - 5.52013i) q^{53} +(-3.39853 - 6.51536i) q^{54} +(1.47773 + 0.853165i) q^{55} +(-1.57416 - 1.84922i) q^{56} +(-10.4837 + 1.40922i) q^{57} +(-0.656363 + 4.26274i) q^{58} +(-3.29294 - 7.63389i) q^{59} +(-0.749620 + 0.898092i) q^{60} +(-0.421617 + 7.23888i) q^{61} +(8.18125 - 1.13716i) q^{62} +(-2.27385 - 1.21013i) q^{63} +(7.09743 - 3.69142i) q^{64} +(-0.248337 - 2.12466i) q^{65} +(-10.5981 - 6.39258i) q^{66} +(-7.97426 - 2.38734i) q^{67} +(-7.81416 - 6.75459i) q^{68} +(-5.99907 - 0.951323i) q^{69} +(-0.0387327 + 0.408218i) q^{70} +(2.23902 - 1.87876i) q^{71} +(5.56111 - 6.40890i) q^{72} +(-4.15461 - 3.48613i) q^{73} +(8.87417 - 8.74497i) q^{74} +(-8.43866 + 0.637838i) q^{75} +(-5.95143 - 10.6664i) q^{76} +(-4.33100 + 0.252252i) q^{77} +(1.50575 + 15.4428i) q^{78} +(9.10965 + 8.59452i) q^{79} +(-1.28214 - 0.425197i) q^{80} +(2.98599 - 8.49022i) q^{81} +(1.02606 + 3.17425i) q^{82} +(-2.47994 + 2.62859i) q^{83} +(0.337615 - 2.95506i) q^{84} +(0.101406 + 1.74108i) q^{85} +(2.05594 + 10.3392i) q^{86} +(-4.36253 + 2.97843i) q^{87} +(2.38182 - 14.0916i) q^{88} +(-0.960590 + 1.14479i) q^{89} +(-1.43047 + 0.0805986i) q^{90} +(3.49594 + 4.16630i) q^{91} +(-1.51721 - 6.84762i) q^{92} +(7.86062 + 6.36787i) q^{93} +(0.981645 - 0.595596i) q^{94} +(-0.591505 + 1.97576i) q^{95} +(9.23911 + 3.26173i) q^{96} +(-8.48223 + 0.991430i) q^{97} +(4.14623 + 7.82650i) q^{98} +(-3.14600 - 14.8283i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 936 q - 18 q^{2} - 18 q^{4} - 36 q^{5} - 18 q^{6} - 18 q^{8} - 36 q^{9}+O(q^{10}) $ 936 * q - 18 * q^2 - 18 * q^4 - 36 * q^5 - 18 * q^6 - 18 * q^8 - 36 * q^9	$ 936 q - 18 q^{2} - 18 q^{4} - 36 q^{5} - 18 q^{6} - 18 q^{8} - 36 q^{9} - 18 q^{10} - 18 q^{12} - 36 q^{13} - 18 q^{14} - 18 q^{16} - 36 q^{17} - 18 q^{18} - 18 q^{20} - 36 q^{21} - 18 q^{22} - 18 q^{24} - 36 q^{25} - 27 q^{26} - 9 q^{28} - 36 q^{29} - 18 q^{30} - 18 q^{32} - 36 q^{33} - 18 q^{34} - 18 q^{36} - 36 q^{37} - 18 q^{38} - 18 q^{40} - 36 q^{41} - 63 q^{42} - 90 q^{44} - 36 q^{45} - 18 q^{46} - 117 q^{48} - 36 q^{49} - 135 q^{50} - 18 q^{52} - 54 q^{53} - 144 q^{54} - 144 q^{56} - 36 q^{57} - 18 q^{58} - 135 q^{60} - 36 q^{61} - 117 q^{62} - 18 q^{64} - 36 q^{65} - 90 q^{66} - 63 q^{68} - 36 q^{69} - 18 q^{70} - 18 q^{72} - 36 q^{73} - 18 q^{74} - 18 q^{76} - 36 q^{77} + 9 q^{78} - 36 q^{81} - 36 q^{82} - 45 q^{84} - 36 q^{85} - 18 q^{86} - 18 q^{88} - 54 q^{89} + 45 q^{90} + 72 q^{92} - 144 q^{93} - 18 q^{94} + 99 q^{96} - 36 q^{97} + 153 q^{98}+O(q^{100}) $ 936 * q - 18 * q^2 - 18 * q^4 - 36 * q^5 - 18 * q^6 - 18 * q^8 - 36 * q^9 - 18 * q^10 - 18 * q^12 - 36 * q^13 - 18 * q^14 - 18 * q^16 - 36 * q^17 - 18 * q^18 - 18 * q^20 - 36 * q^21 - 18 * q^22 - 18 * q^24 - 36 * q^25 - 27 * q^26 - 9 * q^28 - 36 * q^29 - 18 * q^30 - 18 * q^32 - 36 * q^33 - 18 * q^34 - 18 * q^36 - 36 * q^37 - 18 * q^38 - 18 * q^40 - 36 * q^41 - 63 * q^42 - 90 * q^44 - 36 * q^45 - 18 * q^46 - 117 * q^48 - 36 * q^49 - 135 * q^50 - 18 * q^52 - 54 * q^53 - 144 * q^54 - 144 * q^56 - 36 * q^57 - 18 * q^58 - 135 * q^60 - 36 * q^61 - 117 * q^62 - 18 * q^64 - 36 * q^65 - 90 * q^66 - 63 * q^68 - 36 * q^69 - 18 * q^70 - 18 * q^72 - 36 * q^73 - 18 * q^74 - 18 * q^76 - 36 * q^77 + 9 * q^78 - 36 * q^81 - 36 * q^82 - 45 * q^84 - 36 * q^85 - 18 * q^86 - 18 * q^88 - 54 * q^89 + 45 * q^90 + 72 * q^92 - 144 * q^93 - 18 * q^94 + 99 * q^96 - 36 * q^97 + 153 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/324\mathbb{Z}\right)^\times$.

$n$	$163$	$245$
$\chi(n)$	$-1$	$e\left(\frac{13}{54}\right)$

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 $

$2$	−0.607055	+	1.27730i	−0.429252	+	0.903185i
$2$	−0.607055	+	1.27730i	−0.429252	+	0.903185i
$3$	−1.65046	+	0.525329i	−0.952896	+	0.303299i
$3$	−1.65046	+	0.525329i	−0.952896	+	0.303299i
$4$	−1.26297	−	1.55078i	−0.631485	−	0.775388i
$5$	−0.0392046	+	0.335417i	−0.0175328	+	0.150003i	−0.999169	−	0.0407599i	$-0.987022\pi$
$5$	−0.0392046	+	0.335417i	−0.0175328	+	0.150003i	0.981636	+	0.190763i	$0.0610962\pi$
$6$	0.330922	−	2.42703i	0.135098	−	0.990832i
$7$	−0.385340	−	0.767275i	−0.145645	−	0.290003i	0.808968	−	0.587853i	$-0.200027\pi$
$7$	−0.385340	−	0.767275i	−0.145645	−	0.290003i	−0.954613	+	0.297850i	$0.903730\pi$
$8$	2.74749	−	0.671779i	0.971385	−	0.237510i
$9$	2.44806	−	1.73407i	0.816020	−	0.578024i
$10$	−0.404627	−	0.253692i	−0.127954	−	0.0802246i
$11$	2.00131	−	4.63956i	0.603418	−	1.39888i	−0.293190	−	0.956054i	$-0.594717\pi$
$11$	2.00131	−	4.63956i	0.603418	−	1.39888i	0.896608	−	0.442825i	$-0.146024\pi$
$12$	2.89915	+	1.89603i	0.836913	+	0.547336i
$13$	−6.16365	+	1.46081i	−1.70949	+	0.405156i	−0.964952	−	0.262426i	$-0.915477\pi$
$13$	−6.16365	+	1.46081i	−1.70949	+	0.405156i	−0.744536	+	0.667582i	$0.767329\pi$
$14$	1.21396	−	0.0264153i	0.324444	−	0.00705979i
$15$	−0.111498	−	0.574189i	−0.0287887	−	0.148255i
$16$	−0.809817	+	3.91717i	−0.202454	+	0.979292i
$17$	5.08597	−	0.896794i	1.23353	−	0.217505i	0.481389	−	0.876507i	$-0.340132\pi$
$17$	5.08597	−	0.896794i	1.23353	−	0.217505i	0.752141	+	0.659002i	$0.229021\pi$
$18$	0.728816	+	4.17957i	0.171783	+	0.985135i
$19$	6.01443	+	1.06051i	1.37980	+	0.243297i	0.813819	−	0.581119i	$-0.197385\pi$
$19$	6.01443	+	1.06051i	1.37980	+	0.243297i	0.565985	+	0.824415i	$0.308496\pi$
$20$	0.569671	−	0.362824i	0.127382	−	0.0811298i
$21$	1.03906	+	1.06393i	0.226742	+	0.232168i
$22$	4.71118	+	5.37273i	1.00443	+	1.14547i
$23$	3.13383	+	1.57387i	0.653449	+	0.328174i	0.744452	−	0.667676i	$-0.232711\pi$
$23$	3.13383	+	1.57387i	0.653449	+	0.328174i	−0.0910028	+	0.995851i	$0.529007\pi$
$24$	−4.18173	+	2.55208i	−0.853592	+	0.520942i
$25$	4.75426	+	1.12678i	0.950851	+	0.225356i
$26$	1.87578	−	8.75959i	0.367871	−	1.71790i
$27$	−3.12948	+	4.14806i	−0.602268	+	0.798294i
$28$	−0.703200	+	1.56662i	−0.132892	+	0.296064i
$29$	2.92162	−	0.874674i	0.542530	−	0.162423i	−0.00379985	−	0.999993i	$-0.501210\pi$
$29$	2.92162	−	0.874674i	0.542530	−	0.162423i	0.546330	+	0.837570i	$0.316024\pi$
$30$	0.801095	+	0.206148i	0.146259	+	0.0376372i
$31$	−3.20948	−	4.87978i	−0.576440	−	0.876434i	0.423121	−	0.906073i	$-0.360935\pi$
$31$	−3.20948	−	4.87978i	−0.576440	−	0.876434i	−0.999561	+	0.0296390i	$0.990564\pi$
$32$	−4.51178	−	3.41231i	−0.797577	−	0.603217i
$33$	−0.865797	+	8.70877i	−0.150716	+	1.51600i
$34$	−1.94199	+	7.04070i	−0.333049	+	1.20747i
$35$	0.272464	−	0.0991689i	0.0460549	−	0.0167626i
$36$	−5.78098	−	1.60632i	−0.963497	−	0.267719i
$37$	−8.27851	−	3.01313i	−1.36098	−	0.495356i	−0.444622	−	0.895718i	$-0.646662\pi$
$37$	−8.27851	−	3.01313i	−1.36098	−	0.495356i	−0.916357	+	0.400362i	$0.868884\pi$
$38$	−5.00566	+	7.03842i	−0.812026	+	1.14178i
$39$	9.40547	−	5.64895i	1.50608	−	0.904557i
$40$	0.117612	+	0.947892i	0.0185960	+	0.149875i
$41$	1.71579	−	1.61877i	0.267962	−	0.252809i	−0.540519	−	0.841332i	$-0.681772\pi$
$41$	1.71579	−	1.61877i	0.267962	−	0.252809i	0.808480	+	0.588523i	$0.200290\pi$
$42$	−1.98972	+	0.681325i	−0.307020	+	0.105131i
$43$	5.97906	−	4.45124i	0.911798	−	0.678808i	−0.0354293	−	0.999372i	$-0.511280\pi$
$43$	5.97906	−	4.45124i	0.911798	−	0.678808i	0.947227	+	0.320564i	$0.103872\pi$
$44$	−9.72251	+	2.75603i	−1.46572	+	0.415488i
$45$	0.485662	+	0.889104i	0.0723982	+	0.132540i
$46$	−3.91270	+	3.04740i	−0.576897	+	0.449315i
$47$	−0.678332	−	0.446146i	−0.0989449	−	0.0650771i	0.499072	−	0.866560i	$-0.333674\pi$
$47$	−0.678332	−	0.446146i	−0.0989449	−	0.0650771i	−0.598017	+	0.801483i	$0.704045\pi$
$48$	−0.721226	−	6.89056i	−0.104100	−	0.994567i
$49$	3.73989	−	5.02354i	0.534269	−	0.717648i
$50$	−4.32532	+	5.38858i	−0.611693	+	0.762060i
$51$	−7.92310	+	4.15193i	−1.10946	+	0.581387i
$52$	10.0499	+	7.71348i	1.39367	+	1.06967i
$53$	9.56115	−	5.52013i	1.31332	−	0.758248i	0.330679	−	0.943743i	$-0.392722\pi$
$53$	9.56115	−	5.52013i	1.31332	−	0.758248i	0.982645	+	0.185495i	$0.0593889\pi$
$54$	−3.39853	−	6.51536i	−0.462482	−	0.886629i
$55$	1.47773	+	0.853165i	0.199256	+	0.115041i
$56$	−1.57416	−	1.84922i	−0.210356	−	0.247112i
$57$	−10.4837	+	1.40922i	−1.38860	+	0.186656i
$58$	−0.656363	+	4.26274i	−0.0861846	+	0.559726i
$59$	−3.29294	−	7.63389i	−0.428704	−	0.993848i	−0.986484	−	0.163859i	$-0.947606\pi$
$59$	−3.29294	−	7.63389i	−0.428704	−	0.993848i	0.557779	−	0.829989i	$-0.311654\pi$
$60$	−0.749620	+	0.898092i	−0.0967755	+	0.115943i
$61$	−0.421617	+	7.23888i	−0.0539825	+	0.926843i	0.857237	+	0.514922i	$0.172179\pi$
$61$	−0.421617	+	7.23888i	−0.0539825	+	0.926843i	−0.911219	+	0.411921i	$0.864858\pi$
$62$	8.18125	−	1.13716i	1.03902	−	0.144420i
$63$	−2.27385	−	1.21013i	−0.286478	−	0.152462i
$64$	7.09743	−	3.69142i	0.887178	−	0.461427i
$65$	−0.248337	−	2.12466i	−0.0308025	−	0.263532i
$66$	−10.5981	−	6.39258i	−1.30453	−	0.786872i
$67$	−7.97426	−	2.38734i	−0.974211	−	0.291659i	−0.240144	−	0.970737i	$-0.577195\pi$
$67$	−7.97426	−	2.38734i	−0.974211	−	0.291659i	−0.734066	+	0.679078i	$0.762380\pi$
$68$	−7.81416	−	6.75459i	−0.947606	−	0.819114i
$69$	−5.99907	−	0.951323i	−0.722203	−	0.114526i
$70$	−0.0387327	+	0.408218i	−0.00462944	+	0.0487914i
$71$	2.23902	−	1.87876i	0.265723	−	0.222968i	−0.500185	−	0.865919i	$-0.666735\pi$
$71$	2.23902	−	1.87876i	0.265723	−	0.222968i	0.765907	+	0.642951i	$0.222290\pi$
$72$	5.56111	−	6.40890i	0.655383	−	0.755296i
$73$	−4.15461	−	3.48613i	−0.486260	−	0.408021i	0.366424	−	0.930448i	$-0.380582\pi$
$73$	−4.15461	−	3.48613i	−0.486260	−	0.408021i	−0.852684	+	0.522427i	$0.825027\pi$
$74$	8.87417	−	8.74497i	1.03160	−	1.01658i
$75$	−8.43866	+	0.637838i	−0.974412	+	0.0736512i
$76$	−5.95143	−	10.6664i	−0.682676	−	1.22352i
$77$	−4.33100	+	0.252252i	−0.493563	+	0.0287468i
$78$	1.50575	+	15.4428i	0.170493	+	1.74855i
$79$	9.10965	+	8.59452i	1.02492	+	0.966959i	0.999465	−	0.0327174i	$-0.0104161\pi$
$79$	9.10965	+	8.59452i	1.02492	+	0.966959i	0.0254516	+	0.999676i	$0.491898\pi$
$80$	−1.28214	−	0.425197i	−0.143347	−	0.0475385i
$81$	2.98599	−	8.49022i	0.331777	−	0.943358i
$82$	1.02606	+	3.17425i	0.113310	+	0.350538i
$83$	−2.47994	+	2.62859i	−0.272209	+	0.288525i	−0.849029	−	0.528347i	$-0.822812\pi$
$83$	−2.47994	+	2.62859i	−0.272209	+	0.288525i	0.576819	+	0.816872i	$0.304294\pi$
$84$	0.337615	−	2.95506i	0.0368368	−	0.322424i
$85$	0.101406	+	1.74108i	0.0109991	+	0.188847i
$86$	2.05594	+	10.3392i	0.221698	+	1.11490i
$87$	−4.36253	+	2.97843i	−0.467712	+	0.319321i
$88$	2.38182	−	14.0916i	0.253903	−	1.50217i
$89$	−0.960590	+	1.14479i	−0.101822	+	0.121347i	−0.814549	−	0.580095i	$-0.803016\pi$
$89$	−0.960590	+	1.14479i	−0.101822	+	0.121347i	0.712727	+	0.701442i	$0.247460\pi$
$90$	−1.43047	+	0.0805986i	−0.150785	+	0.00849583i
$91$	3.49594	+	4.16630i	0.366474	+	0.436747i
$92$	−1.51721	−	6.84762i	−0.158180	−	0.713914i
$93$	7.86062	+	6.36787i	0.815108	+	0.660317i
$94$	0.981645	−	0.595596i	0.101249	−	0.0614310i
$95$	−0.591505	+	1.97576i	−0.0606871	+	0.202709i
$96$	9.23911	+	3.26173i	0.942963	+	0.332899i
$97$	−8.48223	+	0.991430i	−0.861240	+	0.100665i	−0.535235	−	0.844703i	$-0.679777\pi$
$97$	−8.48223	+	0.991430i	−0.861240	+	0.100665i	−0.326005	+	0.945368i	$0.605703\pi$
$98$	4.14623	+	7.82650i	0.418832	+	0.790596i
$99$	−3.14600	−	14.8283i	−0.316185	−	1.49030i
$100$	−4.25710	−	8.79588i	−0.425710	−	0.879588i
$101$	1.65595	+	0.0964483i	0.164774	+	0.00959697i	0.140333	−	0.990104i	$-0.455183\pi$
$101$	1.65595	+	0.0964483i	0.164774	+	0.00959697i	0.0244403	+	0.999701i	$0.492220\pi$
$102$	−0.493491	−	12.6406i	−0.0488629	−	1.25161i
$103$	3.06312	−	1.32130i	0.301818	−	0.130192i	−0.239785	−	0.970826i	$-0.577077\pi$
$103$	3.06312	−	1.32130i	0.301818	−	0.130192i	0.541603	+	0.840634i	$0.317818\pi$
$104$	−15.9532	+	8.15418i	−1.56434	+	0.799583i
$105$	−0.397596	+	0.306808i	−0.0388014	+	0.0299414i
$106$	1.24670	+	15.5634i	0.121090	+	1.51165i
$107$	−2.18532	+	3.78509i	−0.211263	+	0.365918i	−0.952110	−	0.305755i	$-0.901091\pi$
$107$	−2.18532	+	3.78509i	−0.211263	+	0.365918i	0.740847	+	0.671674i	$0.234424\pi$
$108$	10.3851	−	0.385749i	0.999311	−	0.0371187i
$109$	−3.64122	−	6.30678i	−0.348766	−	0.604080i	0.637265	−	0.770645i	$-0.280066\pi$
$109$	−3.64122	−	6.30678i	−0.348766	−	0.604080i	−0.986030	+	0.166565i	$0.946732\pi$
$110$	−1.98680	+	1.36957i	−0.189434	+	0.130584i
$111$	15.2463	+	0.624126i	1.44711	+	0.0592394i
$112$	3.31760	−	0.888089i	0.313484	−	0.0839165i
$113$	15.5107	+	11.5473i	1.45912	+	1.08628i	0.977753	+	0.209759i	$0.0672678\pi$
$113$	15.5107	+	11.5473i	1.45912	+	1.08628i	0.481369	+	0.876518i	$0.340140\pi$
$114$	4.56419	−	14.2463i	0.427475	−	1.33429i
$115$	−0.650763	+	0.989437i	−0.0606840	+	0.0922655i
$116$	−5.04634	−	3.42609i	−0.468541	−	0.318104i
$117$	−12.5558	+	14.2644i	−1.16079	+	1.31874i
$118$	11.7497	+	0.428132i	1.08165	+	0.0394127i
$119$	−2.64792	−	3.55677i	−0.242734	−	0.326049i
$120$	−0.692069	−	1.50268i	−0.0631769	−	0.137175i
$121$	−9.97159	−	10.5693i	−0.906509	−	0.960843i
$122$	−8.99024	−	4.93292i	−0.813938	−	0.446606i
$123$	−1.98147	+	3.57307i	−0.178663	+	0.322173i
$124$	−3.51397	+	11.1402i	−0.315564	+	1.00042i
$125$	−1.14183	+	3.13716i	−0.102129	+	0.280596i
$126$	2.92604	−	2.16976i	0.260672	−	0.193297i
$127$	−0.159290	−	0.437645i	−0.0141347	−	0.0388347i	0.932425	−	0.361364i	$-0.117689\pi$
$127$	−0.159290	−	0.437645i	−0.0141347	−	0.0388347i	−0.946559	+	0.322530i	$0.895467\pi$
$128$	0.406505	+	11.3064i	0.0359303	+	0.999354i
$129$	−7.52985	+	10.4876i	−0.662966	+	0.923380i
$130$	2.86458	+	0.972586i	0.251240	+	0.0853014i
$131$	−5.95479	+	3.91653i	−0.520272	+	0.342189i	−0.782330	−	0.622864i	$-0.785969\pi$
$131$	−5.95479	+	3.91653i	−0.520272	+	0.342189i	0.262058	+	0.965052i	$0.415599\pi$
$132$	14.5988	−	9.65625i	1.27066	−	0.840468i
$133$	−1.50390	−	5.02337i	−0.130405	−	0.435582i
$134$	7.89014	−	8.73624i	0.681605	−	0.754696i
$135$	−1.26864	−	1.21230i	−0.109187	−	0.104338i
$136$	13.3712	−	5.88059i	1.14657	−	0.504256i
$137$	−0.294559	+	1.24284i	−0.0251658	+	0.106183i	−0.984178	−	0.177181i	$-0.943302\pi$
$137$	−0.294559	+	1.24284i	−0.0251658	+	0.106183i	0.959012	+	0.283364i	$0.0914504\pi$
$138$	4.85689	−	7.08508i	0.413446	−	0.603122i
$139$	−3.68950	+	7.34639i	−0.312939	+	0.623113i	−0.994033	−	0.109084i	$-0.965208\pi$
$139$	−3.68950	+	7.34639i	−0.312939	+	0.623113i	0.681094	+	0.732196i	$0.261505\pi$
$140$	−0.497903	−	0.297284i	−0.0420805	−	0.0251251i
$141$	1.35394	+	0.380001i	0.114022	+	0.0320018i
$142$	1.04053	+	4.00040i	0.0873190	+	0.335706i
$143$	−5.55785	+	31.5201i	−0.464771	+	2.63585i
$144$	4.81016	+	10.9937i	0.400847	+	0.916145i
$145$	0.178840	+	1.01425i	0.0148518	+	0.0842289i
$146$	6.97490	−	3.19039i	0.577247	−	0.264039i
$147$	−3.53354	+	10.2558i	−0.291441	+	0.845887i
$148$	5.78281	+	16.6436i	0.475344	+	1.36810i
$149$	−0.925260	−	3.90398i	−0.0758002	−	0.319826i	0.921915	−	0.387393i	$-0.126624\pi$
$149$	−0.925260	−	3.90398i	−0.0758002	−	0.319826i	−0.997715	+	0.0675671i	$0.978476\pi$
$150$	4.30802	−	11.1659i	0.351748	−	0.911689i
$151$	−16.6142	−	7.16668i	−1.35205	−	0.583217i	−0.407987	−	0.912988i	$-0.633769\pi$
$151$	−16.6142	−	7.16668i	−1.35205	−	0.583217i	−0.944061	+	0.329771i	$0.893028\pi$
$152$	17.2370	−	1.12664i	1.39811	−	0.0913822i
$153$	10.8957	−	11.0148i	0.880862	−	0.890498i
$154$	2.30695	−	5.68510i	0.185900	−	0.458119i
$155$	1.76259	−	0.885205i	0.141574	−	0.0711014i
$156$	−20.6391	−	7.45133i	−1.65245	−	0.596584i
$157$	−3.76205	−	0.439720i	−0.300244	−	0.0350935i	−0.0353628	−	0.999375i	$-0.511259\pi$
$157$	−3.76205	−	0.439720i	−0.300244	−	0.0350935i	−0.264881	+	0.964281i	$0.585333\pi$
$158$	−16.5078	+	6.41838i	−1.31329	+	0.510619i
$159$	−12.8804	+	14.1335i	−1.02149	+	1.12086i
$160$	1.32143	−	1.37955i	0.104468	−	0.109063i
$161$		−	3.01099i		−	0.237299i
$162$	9.03186	+	8.96803i	0.709610	+	0.704595i
$163$			23.2953i			1.82463i	0.409494	+	0.912313i	$0.365705\pi$
$163$			23.2953i			1.82463i	−0.409494	+	0.912313i	$0.634295\pi$
$164$	−4.67734	−	0.616358i	−0.365239	−	0.0481295i
$165$	−2.88712	−	0.631827i	−0.224762	−	0.0491877i
$166$	−1.85202	−	4.76332i	−0.143745	−	0.369705i
$167$	14.9975	+	1.75296i	1.16054	+	0.135648i	0.674491	−	0.738283i	$-0.264363\pi$
$167$	14.9975	+	1.75296i	1.16054	+	0.135648i	0.486050	+	0.873931i	$0.338437\pi$
$168$	3.56954	+	2.22512i	0.275396	+	0.171672i
$169$	24.2393	−	12.1735i	1.86457	−	0.936420i
$170$	−2.28543	−	0.927405i	−0.175285	−	0.0711287i
$171$	16.5627	−	7.83326i	1.26658	−	0.599024i
$172$	−14.4542	−	3.65040i	−1.10213	−	0.278340i
$173$	−10.7265	−	4.62697i	−0.815523	−	0.351782i	−0.0528793	−	0.998601i	$-0.516840\pi$
$173$	−10.7265	−	4.62697i	−0.815523	−	0.351782i	−0.762644	+	0.646819i	$0.776099\pi$
$174$	−1.15604	−	7.38031i	−0.0876390	−	0.559500i
$175$	−0.967456	−	4.08202i	−0.0731328	−	0.308571i
$176$	16.5532	+	11.5967i	1.24775	+	0.874131i
$177$	9.44518	+	10.8696i	0.709943	+	0.817008i
$178$	−0.879101	−	1.92191i	−0.0658914	−	0.144053i
$179$	3.13282	+	17.7671i	0.234158	+	1.32797i	0.844380	+	0.535744i	$0.179969\pi$
$179$	3.13282	+	17.7671i	0.234158	+	1.32797i	−0.610222	+	0.792230i	$0.708920\pi$
$180$	0.765427	−	1.87606i	0.0570515	−	0.139834i
$181$	0.156285	−	0.886335i	0.0116166	−	0.0658807i	−0.978448	−	0.206491i	$-0.933795\pi$
$181$	0.156285	−	0.886335i	0.0116166	−	0.0658807i	0.990065	+	0.140611i	$0.0449066\pi$
$182$	−7.44383	+	1.93618i	−0.551773	+	0.143519i
$183$	−3.10693	−	12.1690i	−0.229671	−	0.899558i
$184$	9.66747	+	2.21895i	0.712695	+	0.163583i
$185$	1.33521	−	2.65862i	0.0981667	−	0.195466i
$186$	−12.9055	+	6.17469i	−0.946275	+	0.452751i
$187$	6.01788	−	25.3914i	0.440071	−	1.85681i
$188$	0.164840	+	1.61541i	0.0120222	+	0.117816i
$189$	4.38861	+	0.802757i	0.319225	+	0.0583920i
$190$	−2.16456	−	1.95492i	−0.157034	−	0.141825i
$191$	−0.420241	−	1.40370i	−0.0304075	−	0.101568i	0.941439	−	0.337184i	$-0.109474\pi$
$191$	−0.420241	−	1.40370i	−0.0304075	−	0.101568i	−0.971846	+	0.235616i	$0.924289\pi$
$192$	−9.77484	+	9.82103i	−0.705438	+	0.708772i
$193$	7.24844	−	4.76737i	0.521754	−	0.343163i	−0.261157	−	0.965296i	$-0.584104\pi$
$193$	7.24844	−	4.76737i	0.521754	−	0.343163i	0.782911	+	0.622133i	$0.213734\pi$
$194$	3.88283	−	11.4362i	0.278771	−	0.821069i
$195$	1.52602	+	3.37622i	0.109280	+	0.241776i
$196$	−12.5137	+	0.544847i	−0.893839	+	0.0389176i
$197$	0.0403513	+	0.110864i	0.00287491	+	0.00789875i	0.941122	−	0.338068i	$-0.109773\pi$
$197$	0.0403513	+	0.110864i	0.00287491	+	0.00789875i	−0.938247	+	0.345966i	$0.887551\pi$
$198$	20.8500	+	4.98324i	1.48174	+	0.354143i
$199$	0.814376	−	2.23748i	0.0577296	−	0.158611i	−0.907475	−	0.420105i	$-0.861993\pi$
$199$	0.814376	−	2.23748i	0.0577296	−	0.158611i	0.965205	+	0.261495i	$0.0842154\pi$
$200$	13.8192	−	0.0979927i	0.977167	−	0.00692913i
$201$	14.4154	−	0.248894i	1.01678	−	0.0175556i
$202$	−1.12845	+	2.05659i	−0.0793973	+	0.144701i
$203$	−1.79693	−	1.90464i	−0.126120	−	0.133679i
$204$	16.4454	+	7.04320i	1.15141	+	0.493123i
$205$	0.475695	+	0.638969i	0.0332240	+	0.0446275i
$206$	−0.171789	+	4.71462i	−0.0119691	+	0.328483i
$207$	10.4010	−	1.58136i	0.722920	−	0.109912i
$208$	−0.730814	−	25.3270i	−0.0506728	−	1.75611i
$209$	16.9570	−	25.7819i	1.17294	−	1.78337i
$210$	−0.150522	−	0.694097i	−0.0103870	−	0.0478972i
$211$	−3.23366	−	2.40737i	−0.222614	−	0.165730i	0.480074	−	0.877228i	$-0.340610\pi$
$211$	−3.23366	−	2.40737i	−0.222614	−	0.165730i	−0.702688	+	0.711498i	$0.748017\pi$
$212$	−20.6359	−	7.85545i	−1.41728	−	0.539514i
$213$	−2.70845	+	4.27705i	−0.185580	+	0.293058i
$214$	−3.50807	−	5.08906i	−0.239807	−	0.347881i
$215$	1.25862	+	2.17999i	0.0858369	+	0.148674i
$216$	−5.81163	+	13.4991i	−0.395432	+	0.918495i
$217$	−2.50739	+	4.34293i	−0.170213	+	0.294817i
$218$	10.2660	−	0.822356i	0.695304	−	0.0556970i
$219$	8.68840	+	3.57120i	0.587107	+	0.241319i
$220$	−0.543253	−	3.36914i	−0.0366261	−	0.227148i
$221$	−30.0381	+	12.9572i	−2.02058	+	0.871594i
$222$	−10.0525	+	19.0951i	−0.674680	+	1.28158i
$223$	0.393193	+	0.0229009i	0.0263302	+	0.00153356i	0.0713049	−	0.997455i	$-0.477284\pi$
$223$	0.393193	+	0.0229009i	0.0263302	+	0.00153356i	−0.0449747	+	0.998988i	$0.514321\pi$
$224$	−0.879612	+	4.77667i	−0.0587716	+	0.319155i
$225$	13.5926	−	5.48580i	0.906175	−	0.365720i
$226$	−24.1651	+	12.8019i	−1.60744	+	0.851570i
$227$	1.59426	−	0.186343i	0.105815	−	0.0123680i	−0.0630206	−	0.998012i	$-0.520073\pi$
$227$	1.59426	−	0.186343i	0.105815	−	0.0123680i	0.168836	+	0.985644i	$0.445999\pi$
$228$	15.4260	+	14.4781i	1.02161	+	0.958834i
$229$	−4.95295	+	16.5440i	−0.327300	+	1.09326i	0.623078	+	0.782160i	$0.285882\pi$
$229$	−4.95295	+	16.5440i	−0.327300	+	1.09326i	−0.950378	+	0.311098i	$0.899303\pi$
$230$	−0.868755	−	1.43186i	−0.0572840	−	0.0944140i
$231$	7.01565	−	2.69153i	0.461596	−	0.177090i
$232$	7.43953	−	4.36584i	0.488429	−	0.286632i
$233$	−8.02263	−	9.56100i	−0.525580	−	0.626362i	0.436311	−	0.899796i	$-0.356285\pi$
$233$	−8.02263	−	9.56100i	−0.525580	−	0.626362i	−0.961891	+	0.273434i	$0.911840\pi$
$234$	−10.5977	−	24.6967i	−0.692795	−	1.61448i
$235$	0.176239	−	0.210033i	0.0114965	−	0.0137010i
$236$	−7.67958	+	14.7480i	−0.499898	+	0.960012i
$237$	−19.5501	−	9.39937i	−1.26992	−	0.610555i
$238$	6.15048	−	1.22302i	0.398676	−	0.0792766i
$239$	0.303626	+	5.21306i	0.0196399	+	0.337205i	0.993788	+	0.111293i	$0.0354991\pi$
$239$	0.303626	+	5.21306i	0.0196399	+	0.337205i	−0.974148	+	0.225912i	$0.927464\pi$
$240$	2.33949	+	0.0282305i	0.151013	+	0.00182227i
$241$	−7.48261	+	7.93110i	−0.481997	+	0.510887i	−0.922043	−	0.387088i	$-0.873481\pi$
$241$	−7.48261	+	7.93110i	−0.481997	+	0.510887i	0.440046	+	0.897975i	$0.354962\pi$
$242$	19.5534	−	6.32055i	1.25694	−	0.406300i
$243$	−0.468121	+	15.5814i	−0.0300300	+	0.999549i
$244$	11.7584	−	8.48865i	0.752753	−	0.543430i
$245$	1.53836	+	1.45137i	0.0982822	+	0.0927244i
$246$	−3.36101	−	4.69997i	−0.214290	−	0.299659i
$247$	−38.6200	+	2.24936i	−2.45733	+	0.143123i
$248$	−12.0962	−	11.2511i	−0.768107	−	0.714445i
$249$	2.71219	−	5.64117i	0.171878	−	0.357495i
$250$	−3.31392	−	3.36288i	−0.209591	−	0.212687i
$251$	−12.8004	−	10.7408i	−0.807954	−	0.677954i	0.142165	−	0.989843i	$-0.454594\pi$
$251$	−12.8004	−	10.7408i	−0.807954	−	0.677954i	−0.950118	+	0.311889i	$0.899038\pi$
$252$	0.995158	+	5.05458i	0.0626890	+	0.318409i
$253$	13.5738	−	11.3898i	0.853379	−	0.716070i
$254$	0.655699	+	0.0622143i	0.0411422	+	0.00390367i
$255$	−1.08201	−	2.82032i	−0.0677579	−	0.176615i
$256$	−14.6884	−	6.34438i	−0.918025	−	0.396524i
$257$	−1.50761	−	0.451349i	−0.0940422	−	0.0281544i	0.239436	−	0.970912i	$-0.423037\pi$
$257$	−1.50761	−	0.451349i	−0.0940422	−	0.0281544i	−0.333479	+	0.942758i	$0.608223\pi$
$258$	−8.82471	−	15.9844i	−0.549403	−	0.995144i
$259$	0.878141	+	7.51298i	0.0545650	+	0.466834i
$260$	−2.98123	+	3.06850i	−0.184888	+	0.190300i
$261$	5.63554	−	7.20754i	0.348831	−	0.446136i
$262$	−1.38768	−	9.98357i	−0.0857312	−	0.616787i
$263$	1.44098	−	24.7406i	0.0888544	−	1.52557i	−0.599605	−	0.800296i	$-0.704675\pi$
$263$	1.44098	−	24.7406i	0.0888544	−	1.52557i	0.688459	−	0.725275i	$-0.258288\pi$
$264$	3.47160	+	24.5089i	0.213662	+	1.50842i
$265$	1.47670	+	3.42339i	0.0907132	+	0.210297i
$266$	7.32928	+	1.12854i	0.449387	+	0.0691951i
$267$	0.984030	−	2.39405i	0.0602217	−	0.146514i
$268$	6.36902	+	15.3814i	0.389050	+	0.939570i
$269$	9.66412	+	5.57958i	0.589232	+	0.340193i	0.764794	−	0.644275i	$-0.222841\pi$
$269$	9.66412	+	5.57958i	0.589232	+	0.340193i	−0.175562	+	0.984468i	$0.556174\pi$
$270$	2.31860	−	0.884493i	0.141106	−	0.0538285i
$271$	7.35446	−	4.24610i	0.446752	−	0.257932i	−0.259706	−	0.965688i	$-0.583626\pi$
$271$	7.35446	−	4.24610i	0.446752	−	0.257932i	0.706457	+	0.707756i	$0.250292\pi$
$272$	−0.605815	+	20.6488i	−0.0367330	+	1.25202i
$273$	−7.95861	−	5.03981i	−0.481677	−	0.305023i
$274$	−1.40866	−	1.13071i	−0.0851004	−	0.0683087i
$275$	14.7425	−	19.8026i	0.889006	−	1.19414i
$276$	6.10135	+	10.5047i	0.367258	+	0.632309i
$277$	13.4996	+	8.87881i	0.811111	+	0.533476i	0.885983	−	0.463717i	$-0.153485\pi$
$277$	13.4996	+	8.87881i	0.811111	+	0.533476i	−0.0748726	+	0.997193i	$0.523855\pi$
$278$	−7.14379	−	9.17224i	−0.428456	−	0.550114i
$279$	−16.3189	−	6.38052i	−0.976986	−	0.381992i
$280$	0.681974	−	0.455501i	0.0407557	−	0.0272214i
$281$	−20.4239	+	15.2050i	−1.21839	+	0.907056i	−0.997666	−	0.0682805i	$-0.978249\pi$
$281$	−20.4239	+	15.2050i	−1.21839	+	0.907056i	−0.220722	+	0.975337i	$0.570841\pi$
$282$	−1.30729	+	1.49869i	−0.0778477	+	0.0892460i
$283$	−0.647561	+	0.610943i	−0.0384935	+	0.0363168i	−0.705248	−	0.708961i	$-0.749164\pi$
$283$	−0.647561	+	0.610943i	−0.0384935	+	0.0363168i	0.666755	+	0.745277i	$0.267683\pi$
$284$	−5.74135	−	1.09940i	−0.340687	−	0.0652376i
$285$	−0.0616678	−	3.57166i	−0.00365289	−	0.211567i
$286$	−36.8866	−	26.2335i	−2.18115	−	1.55122i
$287$	−1.90320	−	0.692709i	−0.112342	−	0.0408893i
$288$	−16.9623	−	0.529797i	−0.999513	−	0.0312186i
$289$	9.08811	−	3.30780i	0.534595	−	0.194577i
$290$	−1.40406	−	0.387274i	−0.0824495	−	0.0227415i
$291$	13.4788	−	6.09228i	0.790140	−	0.357136i
$292$	−0.159067	+	10.8457i	−0.00930871	+	0.634699i
$293$	17.3744	+	26.4165i	1.01502	+	1.54327i	0.827857	+	0.560940i	$0.189560\pi$
$293$	17.3744	+	26.4165i	1.01502	+	1.54327i	0.187167	+	0.982328i	$0.440070\pi$
$294$	−10.9547	−	10.7392i	−0.638890	−	0.626324i
$295$	2.68964	−	0.805224i	0.156597	−	0.0468820i
$296$	−24.7693	−	2.71722i	−1.43969	−	0.157935i
$297$	12.9821	+	22.8209i	0.753298	+	1.32420i
$298$	5.54822	+	1.18810i	0.321400	+	0.0688246i
$299$	−21.6150	−	5.12284i	−1.25002	−	0.296261i
$300$	11.6469	+	12.2809i	0.672435	+	0.709038i
$301$	−5.71930	−	2.87234i	−0.329655	−	0.165559i
$302$	19.2397	−	16.8707i	1.10712	−	0.970802i
$303$	−2.78376	+	0.710735i	−0.159923	+	0.0408307i
$304$	−9.02476	+	22.7007i	−0.517606	+	1.30197i
$305$	−2.41151	−	0.425215i	−0.138083	−	0.0243477i
$306$	7.45495	+	20.6036i	0.426171	+	1.17783i
$307$	22.0341	−	3.88521i	1.25755	−	0.221741i	0.495130	−	0.868819i	$-0.335120\pi$
$307$	22.0341	−	3.88521i	1.25755	−	0.221741i	0.762424	+	0.647078i	$0.224009\pi$
$308$	5.86111	+	6.39783i	0.333968	+	0.364550i
$309$	−4.36145	+	3.78991i	−0.248114	+	0.215600i
$310$	0.0606813	+	2.78871i	0.00344647	+	0.158388i
$311$	19.8844	−	4.71270i	1.12754	−	0.267233i	0.375808	−	0.926698i	$-0.377365\pi$
$311$	19.8844	−	4.71270i	1.12754	−	0.267233i	0.751735	+	0.659465i	$0.229217\pi$
$312$	22.0466	−	21.8389i	1.24814	−	1.23638i
$313$	−5.43003	+	12.5882i	−0.306923	+	0.711528i	−0.999956	−	0.00937793i	$-0.997015\pi$
$313$	−5.43003	+	12.5882i	−0.306923	+	0.711528i	0.693033	+	0.720906i	$0.256274\pi$
$314$	2.84542	−	4.53831i	0.160576	−	0.256112i
$315$	0.495043	−	0.715244i	0.0278925	−	0.0402994i
$316$	1.82296	−	24.9817i	0.102550	−	1.40533i
$317$	−13.6261	−	27.1319i	−0.765320	−	1.52388i	−0.849596	−	0.527434i	$-0.823154\pi$
$317$	−13.6261	−	27.1319i	−0.765320	−	1.52388i	0.0842760	−	0.996442i	$-0.473142\pi$
$318$	−10.2335	−	25.0319i	−0.573869	−	1.40372i
$319$	1.78896	−	15.3055i	0.100162	−	0.856943i
$320$	0.959912	+	2.52532i	0.0536607	+	0.141170i
$321$	1.61838	−	7.39517i	0.0903292	−	0.412758i
$322$	3.84592	+	1.82783i	0.214325	+	0.101861i
$323$	31.5403			1.75495
$324$	−16.9377	+	6.09228i	−0.940981	+	0.338460i
$325$	−30.9496			−1.71677
$326$	−29.7549	−	14.1415i	−1.64797	−	0.783225i
$327$	9.32283	+	8.49627i	0.515554	+	0.469845i
$328$	3.62667	−	5.60018i	0.200249	−	0.309218i
$329$	−0.0809282	+	0.692385i	−0.00446172	+	0.0381724i
$330$	2.55967	−	3.30416i	0.140905	−	0.181888i
$331$	−12.5011	−	24.8918i	−0.687125	−	1.36818i	−0.918542	−	0.395324i	$-0.870632\pi$
$331$	−12.5011	−	24.8918i	−0.687125	−	1.36818i	0.231416	−	0.972855i	$-0.425664\pi$
$332$	7.20845	+	0.526015i	0.395615	+	0.0288688i
$333$	−25.4913	+	6.97920i	−1.39691	+	0.382458i
$334$	−11.3433	+	18.0921i	−0.620680	+	0.989956i
$335$	1.11338	−	2.58111i	0.0608305	−	0.141021i
$336$	−5.00904	+	3.20859i	−0.273265	+	0.175043i
$337$	−9.10801	+	2.15864i	−0.496145	+	0.117589i	−0.471068	−	0.882097i	$-0.656131\pi$
$337$	−9.10801	+	2.15864i	−0.496145	+	0.117589i	−0.0250772	+	0.999686i	$0.507983\pi$
$338$	0.834498	+	38.3508i	0.0453907	+	2.08601i
$339$	−31.6659	−	10.9102i	−1.71986	−	0.592558i
$340$	2.57195	−	2.35619i	0.139484	−	0.127782i
$341$	−29.0632	+	5.12462i	−1.57386	+	0.277514i
$342$	−0.0490526	+	25.9106i	−0.00265246	+	1.40109i
$343$	−11.2145	−	1.97741i	−0.605525	−	0.106770i
$344$	13.4372	−	16.2464i	0.724483	−	0.875945i
$345$	0.554281	−	1.97489i	0.0298415	−	0.106325i
$346$	12.4216	−	10.8921i	0.667790	−	0.585565i
$347$	10.8054	+	5.42667i	0.580064	+	0.291319i	0.714536	−	0.699598i	$-0.246638\pi$
$347$	10.8054	+	5.42667i	0.580064	+	0.291319i	−0.134473	+	0.990917i	$0.542934\pi$
$348$	10.1286	+	3.00365i	0.542951	+	0.161012i
$349$	1.73157	+	0.410390i	0.0926889	+	0.0219677i	0.276699	−	0.960957i	$-0.410760\pi$
$349$	1.73157	+	0.410390i	0.0926889	+	0.0219677i	−0.184010	+	0.982924i	$0.558908\pi$
$350$	5.80124	+	1.24228i	0.310089	+	0.0664027i
$351$	13.2295	−	30.1387i	0.706136	−	1.60869i
$352$	−24.8611	+	14.1036i	−1.32510	+	0.751722i
$353$	5.16991	−	1.54777i	0.275166	−	0.0823794i	−0.146247	−	0.989248i	$-0.546719\pi$
$353$	5.16991	−	1.54777i	0.275166	−	0.0823794i	0.421413	+	0.906869i	$0.361534\pi$
$354$	−19.6174	+	5.46586i	−1.04265	+	0.290507i
$355$	0.542388	+	0.824661i	0.0287870	+	0.0437685i
$356$	2.98851	+	0.0438304i	0.158390	+	0.00232301i
$357$	6.23876	+	4.47929i	0.330190	+	0.237069i
$358$	−24.5956	−	6.78406i	−1.29992	−	0.358549i
$359$	−16.1140	+	5.86502i	−0.850466	+	0.309544i	−0.730230	−	0.683201i	$-0.760587\pi$
$359$	−16.1140	+	5.86502i	−0.850466	+	0.309544i	−0.120235	+	0.992745i	$0.538365\pi$
$360$	1.93163	+	2.11655i	0.101806	+	0.111552i
$361$	17.1945	+	6.25828i	0.904973	+	0.329383i
$362$	1.03724	+	0.737675i	0.0545160	+	0.0387714i
$363$	22.0101	+	12.2058i	1.15523	+	0.640640i
$364$	2.04574	−	10.6833i	0.107226	−	0.559959i
$365$	1.33219	−	1.25685i	0.0697299	−	0.0657868i
$366$	17.4295	+	3.41878i	0.911053	+	0.178702i
$367$	−12.4994	+	9.30542i	−0.652461	+	0.485739i	−0.871769	−	0.489916i	$-0.837027\pi$
$367$	−12.4994	+	9.30542i	−0.652461	+	0.485739i	0.219309	+	0.975656i	$0.429620\pi$
$368$	−8.70294	+	11.0012i	−0.453672	+	0.573477i
$369$	1.39331	−	6.93814i	0.0725326	−	0.361185i
$370$	2.58530	+	3.31939i	0.134404	+	0.172567i
$371$	−7.91975	−	5.20890i	−0.411173	−	0.270433i
$372$	−0.0525821	−	20.2325i	−0.00272625	−	1.04901i
$373$	10.8174	−	14.5303i	0.560104	−	0.752350i	−0.428393	−	0.903593i	$-0.640920\pi$
$373$	10.8174	−	14.5303i	0.560104	−	0.752350i	0.988497	+	0.151242i	$0.0483274\pi$
$374$	28.7792	+	23.1006i	1.48814	+	1.19450i
$375$	0.236514	−	5.77760i	0.0122135	−	0.298354i
$376$	−2.16342	−	0.770093i	−0.111570	−	0.0397145i
$377$	−16.7301	+	9.65911i	−0.861643	+	0.497470i
$378$	−3.68949	+	5.11824i	−0.189767	+	0.263254i
$379$	3.86387	+	2.23081i	0.198474	+	0.114589i	0.595943	−	0.803027i	$-0.296778\pi$
$379$	3.86387	+	2.23081i	0.198474	+	0.114589i	−0.397470	+	0.917615i	$0.630112\pi$
$380$	3.81102	−	1.57804i	0.195501	−	0.0809516i
$381$	0.492809	+	0.638637i	0.0252474	+	0.0327184i
$382$	2.04805	+	0.315352i	0.104787	+	0.0161348i
$383$	−1.94148	−	4.50086i	−0.0992051	−	0.229983i	0.861385	−	0.507953i	$-0.169598\pi$
$383$	−1.94148	−	4.50086i	−0.0992051	−	0.229983i	−0.960590	+	0.277970i	$0.910338\pi$
$384$	−6.61050	−	18.4473i	−0.337341	−	0.941383i
$385$	0.0851856	−	1.46258i	0.00434146	−	0.0745400i
$386$	1.68915	+	12.1525i	0.0859754	+	0.618544i
$387$	6.91832	−	21.2650i	0.351678	−	1.08096i
$388$	12.2503	+	11.9019i	0.621914	+	0.604227i
$389$	2.81892	+	24.1174i	0.142925	+	1.22280i	0.854221	+	0.519909i	$0.174034\pi$
$389$	2.81892	+	24.1174i	0.142925	+	1.22280i	−0.711296	+	0.702892i	$0.751892\pi$
$390$	−5.23881	−	0.100374i	−0.265277	−	0.00508262i
$391$	17.3500	+	5.19425i	0.877428	+	0.262685i
$392$	6.90060	−	16.3145i	0.348533	−	0.824007i
$393$	7.77070	−	9.59231i	0.391980	−	0.483868i
$394$	−0.166102	−	0.0157601i	−0.00836809	−	0.000793984i
$395$	−3.23989	+	2.71859i	−0.163016	+	0.136787i
$396$	−19.0221	+	23.6065i	−0.955898	+	1.18627i
$397$	25.3139	+	21.2408i	1.27047	+	1.06605i	0.994484	+	0.104884i	$0.0334473\pi$
$397$	25.3139	+	21.2408i	1.27047	+	1.06605i	0.275981	+	0.961163i	$0.410997\pi$
$398$	2.36355	+	2.39847i	0.118474	+	0.120224i
$399$	5.12105	+	7.50085i	0.256373	+	0.375512i
$400$	−8.26386	+	17.7107i	−0.413193	+	0.885537i
$401$	−4.25726	+	0.247957i	−0.212597	+	0.0123824i	−0.164113	−	0.986442i	$-0.552476\pi$
$401$	−4.25726	+	0.247957i	−0.212597	+	0.0123824i	−0.0484844	+	0.998824i	$0.515439\pi$
$402$	−8.43300	+	18.5638i	−0.420600	+	0.925877i
$403$	26.9105	+	25.3888i	1.34051	+	1.26471i
$404$	−1.94185	−	2.68983i	−0.0966106	−	0.133824i
$405$	2.73070	+	1.33441i	0.135690	+	0.0663073i
$406$	3.52362	−	1.13899i	0.174874	−	0.0565274i
$407$	−30.5475	+	32.3784i	−1.51418	+	1.60494i
$408$	−18.9795	+	16.7300i	−0.939624	+	0.828257i
$409$	1.55623	+	26.7195i	0.0769508	+	1.32119i	0.786961	+	0.617002i	$0.211653\pi$
$409$	1.55623	+	26.7195i	0.0769508	+	1.32119i	−0.710010	+	0.704191i	$0.751310\pi$
$410$	−1.10492	+	0.219714i	−0.0545683	+	0.0108509i
$411$	−0.166741	−	2.20600i	−0.00822474	−	0.108814i
$412$	−5.91767	−	3.08146i	−0.291543	−	0.151812i
$413$	−4.58840	+	5.46824i	−0.225780	+	0.269074i
$414$	−4.29412	+	14.2451i	−0.211044	+	0.700110i
$415$	−0.784447	−	0.934868i	−0.0385070	−	0.0458909i
$416$	32.7937	+	14.4414i	1.60785	+	0.708049i
$417$	2.23011	−	14.0632i	0.109209	−	0.688675i
$418$	22.6372	+	37.3101i	1.10722	+	1.82490i
$419$	4.31206	−	14.4033i	0.210658	−	0.703646i	−0.785718	−	0.618585i	$-0.787706\pi$
$419$	4.31206	−	14.4033i	0.210658	−	0.703646i	0.996376	−	0.0850610i	$-0.0271085\pi$
$420$	0.977942	+	0.229094i	0.0477187	+	0.0111786i
$421$	5.52689	−	0.646001i	0.269364	−	0.0314842i	0.0196614	−	0.999807i	$-0.493741\pi$
$421$	5.52689	−	0.646001i	0.269364	−	0.0314842i	0.249703	+	0.968323i	$0.419667\pi$
$422$	5.03793	−	2.66894i	0.245243	−	0.129922i
$423$	−2.43425	+	0.0840838i	−0.118357	+	0.00408830i
$424$	22.5609	−	21.5895i	1.09565	−	1.04848i
$425$	25.1905	+	1.46718i	1.22192	+	0.0711687i
$426$	−3.81888	−	6.05590i	−0.185025	−	0.293409i
$427$	5.71668	−	2.46593i	0.276649	−	0.119335i
$428$	8.62983	−	1.39150i	0.417138	−	0.0672609i
$429$	−7.38539	−	54.9425i	−0.356570	−	2.65265i
$430$	−3.54854	+	0.284254i	−0.171126	+	0.0137079i
$431$	−2.57942	+	4.46768i	−0.124246	+	0.215201i	−0.921438	−	0.388525i	$-0.872985\pi$
$431$	−2.57942	+	4.46768i	−0.124246	+	0.215201i	0.797192	+	0.603726i	$0.206318\pi$
$432$	−13.7143	−	15.6179i	−0.659831	−	0.751414i
$433$	9.37834	+	16.2438i	0.450694	+	0.780625i	0.998429	−	0.0560265i	$-0.0178431\pi$
$433$	9.37834	+	16.2438i	0.450694	+	0.780625i	−0.547735	+	0.836652i	$0.684510\pi$
$434$	−4.02508	−	5.83908i	−0.193210	−	0.280285i
$435$	−0.827983	−	1.58003i	−0.0396988	−	0.0757568i
$436$	−5.18165	+	13.6120i	−0.248156	+	0.651896i
$437$	17.1791	+	12.7894i	0.821788	+	0.611798i
$438$	−9.83581	+	8.92974i	−0.469973	+	0.426679i
$439$	2.27794	−	3.46345i	0.108720	−	0.165301i	−0.777029	−	0.629464i	$-0.783274\pi$
$439$	2.27794	−	3.46345i	0.108720	−	0.165301i	0.885750	+	0.464163i	$0.153645\pi$
$440$	4.63318	+	1.35136i	0.220878	+	0.0644235i
$441$	0.444292	−	18.7832i	0.0211568	−	0.894436i
$442$	1.68463	−	46.2332i	0.0801295	−	2.19909i
$443$	−16.9099	−	22.7140i	−0.803415	−	1.07917i	−0.995212	−	0.0977391i	$-0.968839\pi$
$443$	−16.9099	−	22.7140i	−0.803415	−	1.07917i	0.191797	−	0.981435i	$-0.438568\pi$
$444$	−18.2877	−	24.4318i	−0.867895	−	1.15948i
$445$	−0.346321	−	0.367079i	−0.0164172	−	0.0174012i
$446$	−0.267941	+	0.488322i	−0.0126874	+	0.0231227i
$447$	3.57798	+	5.95731i	0.169233	+	0.281771i
$448$	−5.56725	−	4.02323i	−0.263028	−	0.190080i
$449$	−3.27102	+	8.98705i	−0.154369	+	0.424125i	−0.992636	−	0.121135i	$-0.961347\pi$
$449$	−3.27102	+	8.98705i	−0.154369	+	0.424125i	0.838267	+	0.545260i	$0.183569\pi$
$450$	−1.24448	+	20.6920i	−0.0586654	+	0.975429i
$451$	−4.07653	−	11.2002i	−0.191956	−	0.527395i
$452$	−1.68227	−	38.6375i	−0.0791273	−	1.81735i
$453$	31.1861	+	3.10042i	1.46525	+	0.145670i
$454$	−0.729790	+	2.14946i	−0.0342507	+	0.100879i
$455$	−1.53451	+	1.00926i	−0.0719388	+	0.0473149i
$456$	−27.8572	+	10.9146i	−1.30453	+	0.511121i
$457$	−7.60544	−	25.4040i	−0.355768	−	1.18835i	−0.929350	−	0.369199i	$-0.879632\pi$
$457$	−7.60544	−	25.4040i	−0.355768	−	1.18835i	0.573583	−	0.819148i	$-0.305553\pi$
$458$	−18.1249	−	16.3695i	−0.846919	−	0.764896i
$459$	−12.1965	+	23.9034i	−0.569283	+	1.11572i
$460$	2.35629	−	0.240441i	0.109863	−	0.0112106i
$461$	−2.72964	+	11.5173i	−0.127132	+	0.536413i	0.871785	+	0.489889i	$0.162963\pi$
$461$	−2.72964	+	11.5173i	−0.127132	+	0.536413i	−0.998917	+	0.0465241i	$0.985186\pi$
$462$	−0.820998	+	10.5950i	−0.0381963	+	0.492922i
$463$	−7.97799	+	15.8855i	−0.370769	+	0.738261i	−0.999216	−	0.0395908i	$-0.987395\pi$
$463$	−7.97799	+	15.8855i	−0.370769	+	0.738261i	0.628447	+	0.777852i	$0.283691\pi$
$464$	1.06027	+	12.1528i	0.0492218	+	0.564179i
$465$	−2.44406	+	2.38694i	−0.113341	+	0.110691i
$466$	17.0824	−	4.44322i	0.791327	−	0.205828i
$467$	6.09134	−	34.5457i	0.281873	−	1.59858i	−0.434371	−	0.900734i	$-0.643029\pi$
$467$	6.09134	−	34.5457i	0.281873	−	1.59858i	0.716244	−	0.697850i	$-0.245860\pi$
$468$	37.9785	+	1.45584i	1.75555	+	0.0672963i
$469$	1.24106	+	7.03839i	0.0573067	+	0.325002i
$470$	0.161288	+	0.352610i	0.00743965	+	0.0162647i
$471$	6.44012	−	1.25057i	0.296745	−	0.0576232i
$472$	−14.1756	−	18.7619i	−0.652486	−	0.863588i
$473$	−8.68585	−	36.6485i	−0.399376	−	1.68510i
$474$	23.8738	−	19.2653i	1.09656	−	0.884886i
$475$	27.3992	+	11.8188i	1.25716	+	0.542286i
$476$	−2.17152	+	8.59842i	−0.0995314	+	0.394108i
$477$	13.8340	−	30.0933i	0.633413	−	1.37788i
$478$	−6.84294	−	2.77679i	−0.312989	−	0.127008i
$479$	5.90292	−	2.96456i	0.269711	−	0.135454i	−0.308804	−	0.951126i	$-0.599929\pi$
$479$	5.90292	−	2.96456i	0.269711	−	0.135454i	0.578515	+	0.815672i	$0.303632\pi$
$480$	−1.45625	+	2.97108i	−0.0664686	+	0.135611i
$481$	55.4274	+	6.47854i	2.52727	+	0.295396i
$482$	−5.58801	−	14.3721i	−0.254527	−	0.654632i
$483$	1.58176	+	4.96952i	0.0719724	+	0.226121i
$484$	−3.79677	+	28.8124i	−0.172580	+	1.30965i
$485$		−	2.88395i		−	0.130954i
$486$	−19.6179	−	10.0567i	−0.889887	−	0.456181i
$487$			27.7401i			1.25702i	0.777801	+	0.628511i	$0.216335\pi$
$487$			27.7401i			1.25702i	−0.777801	+	0.628511i	$0.783665\pi$
$488$	3.70454	+	20.1720i	0.167697	+	0.913143i
$489$	−12.2377	−	38.4480i	−0.553406	−	1.73868i
$490$	−2.78769	+	1.08388i	−0.125935	+	0.0489647i
$491$	9.88252	+	1.15510i	0.445992	+	0.0521290i	0.336125	−	0.941817i	$-0.390883\pi$
$491$	9.88252	+	1.15510i	0.445992	+	0.0521290i	0.109867	+	0.993946i	$0.464958\pi$
$492$	8.04356	−	1.43986i	0.362632	−	0.0649140i
$493$	14.0749	−	7.06866i	0.633900	−	0.318356i
$494$	20.5713	−	50.6946i	0.925549	−	2.28086i
$495$	5.09701	−	0.473882i	0.229094	−	0.0212994i
$496$	21.7140	−	8.62035i	0.974988	−	0.387065i
$497$	−2.30431	−	0.993983i	−0.103362	−	0.0445862i
$498$	5.55900	+	6.88876i	0.249105	+	0.308693i
$499$	3.97764	+	16.7830i	0.178064	+	0.751309i	0.986640	+	0.162918i	$0.0520905\pi$
$499$	3.97764	+	16.7830i	0.178064	+	0.751309i	−0.808576	+	0.588392i	$0.799761\pi$
$500$	6.30713	−	2.19141i	0.282063	−	0.0980027i
$501$	−25.6737	+	4.98542i	−1.14702	+	0.222732i
$502$	21.4897	−	9.82964i	0.959134	−	0.438718i
$503$	3.82290	+	21.6808i	0.170455	+	0.966697i	0.943260	+	0.332054i	$0.107742\pi$
$503$	3.82290	+	21.6808i	0.170455	+	0.966697i	−0.772805	+	0.634643i	$0.781147\pi$
$504$	−7.06031	−	1.79730i	−0.314491	−	0.0800580i
$505$	−0.0972714	+	0.551654i	−0.00432852	+	0.0245483i
$506$	6.30808	+	24.2520i	0.280428	+	1.07813i
$507$	−33.6111	+	32.8255i	−1.49272	+	1.45783i
$508$	−0.477511	+	0.799755i	−0.0211861	+	0.0354834i
$509$	14.3327	−	28.5387i	0.635286	−	1.26496i	−0.313665	−	0.949534i	$-0.601557\pi$
$509$	14.3327	−	28.5387i	0.635286	−	1.26496i	0.948951	−	0.315424i	$-0.102147\pi$
$510$	4.25922	+	0.330045i	0.188601	+	0.0146146i
$511$	−1.07388	+	4.53107i	−0.0475059	+	0.200443i
$512$	17.0203	−	14.9100i	0.752198	−	0.658937i
$513$	−23.2210	+	21.6294i	−1.02523	+	0.954959i
$514$	1.49171	−	1.65167i	0.0657965	−	0.0728522i
$515$	0.323099	+	1.07922i	0.0142374	+	0.0475563i
$516$	25.7739	−	1.56838i	1.13463	−	0.0690440i
$517$	−3.42747	+	2.25428i	−0.150740	+	0.0991433i
$518$	−10.1294	−	3.43914i	−0.445059	−	0.151107i
$519$	20.1344	+	2.00170i	0.883804	+	0.0878649i
$520$	−2.10961	−	5.67066i	−0.0925125	−	0.248675i
$521$	−0.865017	−	2.37661i	−0.0378971	−	0.104121i	0.919301	−	0.393556i	$-0.128755\pi$
$521$	−0.865017	−	2.37661i	−0.0378971	−	0.104121i	−0.957198	+	0.289434i	$0.906533\pi$
$522$	5.78508	+	11.5736i	0.253206	+	0.506564i
$523$	−2.76105	+	7.58593i	−0.120732	+	0.331710i	−0.985306	−	0.170796i	$-0.945366\pi$
$523$	−2.76105	+	7.58593i	−0.120732	+	0.331710i	0.864574	+	0.502506i	$0.167588\pi$
$524$	13.5944	+	4.28810i	0.593873	+	0.187326i
$525$	3.74115	+	6.22899i	0.163277	+	0.271855i
$526$	30.7263	+	16.8595i	1.33973	+	0.735107i
$527$	−20.6995	−	21.9402i	−0.901684	−	0.955729i
$528$	−33.4126	−	10.4440i	−1.45409	−	0.454516i
$529$	−6.39082	−	8.58435i	−0.277862	−	0.373233i
$530$	−5.26912	−	0.191994i	−0.228876	−	0.00833968i
$531$	−21.2990	−	12.9780i	−0.924299	−	0.563199i
$532$	−5.89075	+	8.67658i	−0.255397	+	0.376177i
$533$	−8.21082	+	12.4839i	−0.355650	+	0.540740i
$534$	2.46056	+	2.71022i	0.106479	+	0.117283i
$535$	−1.18391	−	0.881387i	−0.0511848	−	0.0381057i
$536$	−23.5130	−	1.20225i	−1.01561	−	0.0519291i
$537$	−14.5042	−	27.6782i	−0.625901	−	1.19440i
$538$	−12.9934	+	8.95683i	−0.560186	+	0.386156i
$539$	−15.8223	−	27.4051i	−0.681516	−	1.18042i
$540$	−0.277759	+	3.49848i	−0.0119528	+	0.150550i
$541$	−9.88296	+	17.1178i	−0.424902	+	0.735951i	−0.996411	−	0.0846441i	$-0.973025\pi$
$541$	−9.88296	+	17.1178i	−0.424902	+	0.735951i	0.571510	+	0.820595i	$0.306358\pi$
$542$	0.958967	+	11.9714i	0.0411911	+	0.514217i
$543$	0.207675	+	1.54496i	0.00891217	+	0.0663008i
$544$	−26.0069	−	13.3088i	−1.11504	−	0.570609i
$545$	2.25815	−	0.974072i	0.0967286	−	0.0417247i
$546$	11.2686	−	7.10605i	0.482253	−	0.304111i
$547$	7.06323	+	0.411386i	0.302002	+	0.0175896i	0.208477	−	0.978027i	$-0.433149\pi$
$547$	7.06323	+	0.411386i	0.302002	+	0.0175896i	0.0935250	+	0.995617i	$0.470186\pi$
$548$	2.29939	−	1.11287i	0.0982249	−	0.0475396i
$549$	11.5206	+	18.4523i	0.491687	+	0.787526i
$550$	16.3443	+	30.8518i	0.696923	+	1.31553i
$551$	18.4994	−	2.16227i	0.788103	−	0.0921160i
$552$	−17.1215	+	1.41630i	−0.728739	+	0.0602817i
$553$	3.08404	−	10.3014i	0.131147	−	0.438061i
$554$	−19.5358	+	11.8530i	−0.829998	+	0.503587i
$555$	−0.807067	+	5.08939i	−0.0342581	+	0.216032i
$556$	16.0523	−	3.55668i	0.680771	−	0.150837i
$557$	−18.7833	−	22.3850i	−0.795872	−	0.948483i	0.203661	−	0.979041i	$-0.434716\pi$
$557$	−18.7833	−	22.3850i	−0.795872	−	0.948483i	−0.999533	+	0.0305583i	$0.990271\pi$
$558$	18.0563	−	16.9707i	0.764383	−	0.718428i
$559$	−30.3504	+	36.1702i	−1.28368	+	1.52983i
$560$	0.167815	+	1.14760i	0.00709147	+	0.0484948i
$561$	3.40655	+	45.0690i	0.143825	+	1.90281i
$562$	−7.02290	−	35.3177i	−0.296243	−	1.48979i
$563$	0.299442	+	5.14123i	0.0126200	+	0.216677i	0.998722	+	0.0505370i	$0.0160933\pi$
$563$	0.299442	+	5.14123i	0.0126200	+	0.216677i	−0.986102	+	0.166140i	$0.946870\pi$
$564$	−1.12068	−	2.57958i	−0.0471893	−	0.108620i
$565$	−4.48124	+	4.74984i	−0.188527	+	0.199827i
$566$	−0.387249	−	1.19800i	−0.0162773	−	0.0503558i
$567$	−7.66496	+	0.980542i	−0.321898	+	0.0411789i
$568$	4.88958	−	6.66601i	0.205162	−	0.279699i
$569$	18.3035	+	17.2685i	0.767323	+	0.723932i	0.966678	−	0.255995i	$-0.0824032\pi$
$569$	18.3035	+	17.2685i	0.767323	+	0.723932i	−0.199355	+	0.979927i	$0.563885\pi$
$570$	4.59950	+	2.08942i	0.192652	+	0.0875164i
$571$	15.6550	−	0.911799i	0.655140	−	0.0381576i	0.272645	−	0.962115i	$-0.412102\pi$
$571$	15.6550	−	0.911799i	0.655140	−	0.0381576i	0.382496	+	0.923957i	$0.375065\pi$
$572$	55.9001	−	31.1900i	2.33730	−	1.30412i
$573$	1.43100	+	2.09599i	0.0597807	+	0.0875614i
$574$	2.04014	−	2.01044i	0.0851539	−	0.0839141i
$575$	13.1256	+	11.0137i	0.547377	+	0.459304i
$576$	10.9737	−	21.3442i	0.457239	−	0.889344i
$577$	−28.7730	+	24.1434i	−1.19784	+	1.00510i	−0.198148	+	0.980172i	$0.563493\pi$
$577$	−28.7730	+	24.1434i	−1.19784	+	1.00510i	−0.999689	+	0.0249325i	$0.992063\pi$
$578$	−1.29194	+	13.6162i	−0.0537376	+	0.566360i
$579$	−9.45885	+	11.6762i	−0.393096	+	0.485246i
$580$	1.34701	−	1.55831i	0.0559314	−	0.0647052i
$581$	2.97247	+	0.889899i	0.123319	+	0.0369193i
$582$	−0.400719	+	20.9147i	−0.0166103	+	0.866944i
$583$	−6.47615	−	55.4070i	−0.268215	−	2.29472i
$584$	−13.7567	−	6.78714i	−0.569255	−	0.280854i
$585$	−4.29226	−	4.77067i	−0.177463	−	0.197243i
$586$	−44.2889	+	6.15599i	−1.82956	+	0.254302i
$587$	−1.00219	+	17.2069i	−0.0413646	+	0.710203i	0.912335	+	0.409444i	$0.134277\pi$
$587$	−1.00219	+	17.2069i	−0.0413646	+	0.710203i	−0.953700	+	0.300759i	$0.902760\pi$
$588$	20.3673	−	7.47308i	0.839932	−	0.308185i
$589$	−14.1282	−	32.7527i	−0.582140	−	1.34955i
$590$	−0.604247	+	3.92428i	−0.0248764	+	0.161560i
$591$	−0.124838	−	0.161780i	−0.00513517	−	0.00665473i
$592$	18.5070	−	29.9882i	0.760634	−	1.23251i
$593$	38.3141	+	22.1207i	1.57337	+	0.908387i	0.995751	+	0.0920829i	$0.0293525\pi$
$593$	38.3141	+	22.1207i	1.57337	+	0.908387i	0.577622	+	0.816305i	$0.303981\pi$
$594$	−37.0299	+	2.72842i	−1.51936	+	0.111949i
$595$	1.29681	−	0.748715i	0.0531641	−	0.0306943i
$596$	−4.88562	+	6.36548i	−0.200123	+	0.260740i
$597$	−0.168686	+	4.12069i	−0.00690386	+	0.168649i
$598$	19.6648	−	24.4988i	0.804155	−	1.00183i
$599$	−19.7070	+	26.4711i	−0.805206	+	1.08158i	0.189806	+	0.981822i	$0.439214\pi$
$599$	−19.7070	+	26.4711i	−0.805206	+	1.08158i	−0.995012	+	0.0997577i	$0.968193\pi$
$600$	−22.7567	+	7.42137i	−0.929037	+	0.302976i
$601$	−1.63266	−	1.07382i	−0.0665975	−	0.0438019i	0.515774	−	0.856725i	$-0.327505\pi$
$601$	−1.63266	−	1.07382i	−0.0665975	−	0.0438019i	−0.582371	+	0.812923i	$0.697875\pi$
$602$	7.14075	−	5.56157i	0.291035	−	0.226673i
$603$	−23.6613	+	7.98359i	−0.963561	+	0.325117i
$604$	9.86935	+	34.8163i	0.401578	+	1.41665i
$605$	3.93605	−	2.93028i	0.160023	−	0.119133i
$606$	0.782074	−	3.98714i	0.0317696	−	0.161966i
$607$	−10.6253	+	10.0245i	−0.431268	+	0.406880i	−0.871027	−	0.491236i	$-0.836545\pi$
$607$	−10.6253	+	10.0245i	−0.431268	+	0.406880i	0.439759	+	0.898116i	$0.355064\pi$
$608$	−23.5170	−	25.3079i	−0.953739	−	1.02637i
$609$	3.96633	+	2.19955i	0.160724	+	0.0891304i
$610$	2.00705	−	2.82209i	0.0812629	−	0.114263i
$611$	4.83273	+	1.75897i	0.195511	+	0.0711604i
$612$	−30.8425	−	2.98533i	−1.24673	−	0.120675i
$613$	33.8276	−	12.3122i	1.36628	−	0.497286i	0.448292	−	0.893887i	$-0.352033\pi$
$613$	33.8276	−	12.3122i	1.36628	−	0.497286i	0.917991	+	0.396601i	$0.129810\pi$
$614$	−8.41335	+	30.5026i	−0.339535	+	1.23099i
$615$	−1.12079	−	0.804699i	−0.0451944	−	0.0324486i
$616$	−11.7299	+	3.60254i	−0.472613	+	0.145150i
$617$	−21.0628	−	32.0245i	−0.847957	−	1.28926i	−0.955481	−	0.295054i	$-0.904662\pi$
$617$	−21.0628	−	32.0245i	−0.847957	−	1.28926i	0.107524	−	0.994203i	$-0.465708\pi$
$618$	−2.19319	−	7.87155i	−0.0882231	−	0.316640i
$619$	19.5948	−	5.86630i	0.787582	−	0.235787i	0.132339	−	0.991205i	$-0.457751\pi$
$619$	19.5948	−	5.86630i	0.787582	−	0.235787i	0.655243	+	0.755418i	$0.272566\pi$
$620$	−3.59885	−	1.61539i	−0.144533	−	0.0648758i
$621$	−16.3357	+	8.07392i	−0.655531	+	0.323995i
$622$	−6.05143	+	28.2592i	−0.242640	+	1.13309i
$623$	1.24852	+	0.295905i	0.0500209	+	0.0118552i
$624$	14.5112	+	41.4174i	0.580912	+	1.65802i
$625$	20.8238	+	10.4581i	0.832951	+	0.418324i
$626$	−12.7826	−	14.5775i	−0.510894	−	0.582634i
$627$	−14.4430	+	51.4600i	−0.576796	+	2.05512i
$628$	4.06944	+	6.38945i	0.162388	+	0.254967i
$629$	−44.8064	−	7.90059i	−1.78655	−	0.315017i
$630$	0.613060	+	1.06651i	0.0244249	+	0.0424907i
$631$	22.7125	−	4.00484i	0.904172	−	0.159430i	0.297816	−	0.954623i	$-0.403742\pi$
$631$	22.7125	−	4.00484i	0.904172	−	0.159430i	0.606356	+	0.795193i	$0.292631\pi$
$632$	30.8023	+	17.4937i	1.22525	+	0.695862i
$633$	6.60170	+	2.27454i	0.262394	+	0.0904050i
$634$	42.9272	−	0.934080i	1.70486	−	0.0370970i
$635$	0.153038	−	0.0362708i	0.00607314	−	0.00143936i
$636$	38.1855	+	2.12449i	1.51415	+	0.0842416i
$637$	−15.7129	+	36.4266i	−0.622568	+	1.44327i
$638$	18.4637	+	11.5763i	0.730983	+	0.458310i
$639$	2.22335	−	8.48194i	0.0879544	−	0.335540i
$640$	−3.80830	−	0.306915i	−0.150536	−	0.0121319i
$641$	9.17478	+	18.2685i	0.362382	+	0.721562i	0.998758	−	0.0498168i	$-0.0158637\pi$
$641$	9.17478	+	18.2685i	0.362382	+	0.721562i	−0.636376	+	0.771379i	$0.719567\pi$
$642$	8.46337	+	6.55642i	0.334023	+	0.258761i
$643$	−2.66304	+	22.7838i	−0.105020	+	0.898505i	0.833320	+	0.552791i	$0.186437\pi$
$643$	−2.66304	+	22.7838i	−0.105020	+	0.898505i	−0.938340	+	0.345714i	$0.887637\pi$
$644$	−4.66937	+	3.80278i	−0.183999	+	0.149851i
$645$	−3.22251	−	2.93680i	−0.126886	−	0.115636i
$646$	−19.1467	+	40.2862i	−0.753315	+	1.58504i
$647$	−39.6461			−1.55865			−0.779324	−	0.626621i	$-0.784437\pi$
$647$	−39.6461			−1.55865			−0.779324	+	0.626621i	$0.784437\pi$
$648$	2.50044	−	25.3327i	0.0982267	−	0.995164i
$649$	−42.0081			−1.64896
$650$	18.7881	−	39.5318i	0.736929	−	1.55056i
$651$	1.85689	−	8.48505i	0.0727774	−	0.332555i
$652$	36.1257	−	29.4212i	1.41479	−	1.15222i
$653$	−3.21990	+	27.5480i	−0.126004	+	1.07804i	0.771253	+	0.636529i	$0.219630\pi$
$653$	−3.21990	+	27.5480i	−0.126004	+	1.07804i	−0.897257	+	0.441508i	$0.854444\pi$
$654$	−16.5117	+	6.75031i	−0.645659	+	0.263958i
$655$	−1.08021	−	2.15088i	−0.0422075	−	0.0840420i
$656$	4.95150	+	8.03195i	0.193324	+	0.313595i
$657$	−16.2159	−	1.32987i	−0.632644	−	0.0518832i
$658$	−0.835253	−	0.523685i	−0.0325615	−	0.0204154i
$659$	5.74016	−	13.3072i	0.223605	−	0.518374i	−0.769074	−	0.639160i	$-0.779282\pi$
$659$	5.74016	−	13.3072i	0.223605	−	0.518374i	0.992679	+	0.120786i	$0.0385415\pi$
$660$	2.66653	+	5.27526i	0.103794	+	0.205339i
$661$	−22.8619	+	5.41836i	−0.889223	+	0.210750i	−0.649745	−	0.760152i	$-0.725124\pi$
$661$	−22.8619	+	5.41836i	−0.889223	+	0.210750i	−0.239478	+	0.970902i	$0.576976\pi$
$662$	39.3831	−	0.856962i	1.53067	−	0.0333068i
$663$	42.7700	−	37.1652i	1.66105	−	1.44338i
$664$	−5.04780	+	8.88800i	−0.195893	+	0.344921i
$665$	1.74388	−	0.307494i	0.0676250	−	0.0119241i
$666$	6.56009	−	36.7967i	0.254199	−	1.42584i
$667$	10.5325	+	1.85716i	0.407819	+	0.0719095i
$668$	−16.2229	−	25.4717i	−0.627684	−	0.985529i
$669$	−0.660982	+	0.168759i	−0.0255550	+	0.00652458i
$670$	2.62095	+	2.98899i	0.101256	+	0.115475i
$671$	32.7414	+	16.4433i	1.26397	+	0.634788i
$672$	−1.05756	−	8.34581i	−0.0407961	−	0.321947i
$673$	−30.1685	−	7.15007i	−1.16291	−	0.275615i	−0.396542	−	0.918017i	$-0.629790\pi$
$673$	−30.1685	−	7.15007i	−1.16291	−	0.275615i	−0.766368	+	0.642402i	$0.777938\pi$
$674$	2.77184	−	12.9440i	0.106767	−	0.498586i
$675$	−19.5523	+	16.1947i	−0.752568	+	0.623334i
$676$	−49.4919	−	22.2151i	−1.90353	−	0.854427i
$677$	−22.3235	+	6.68322i	−0.857962	+	0.256857i	−0.685423	−	0.728146i	$-0.740382\pi$
$677$	−22.3235	+	6.68322i	−0.857962	+	0.256857i	−0.172540	+	0.985003i	$0.555197\pi$
$678$	33.1584	−	33.8237i	1.27344	−	1.29899i
$679$	4.02924	+	6.12617i	0.154628	+	0.235101i
$680$	1.44823	+	4.71548i	0.0555373	+	0.180830i
$681$	−2.53338	+	1.14506i	−0.0970794	+	0.0438789i
$682$	11.0973	−	40.2332i	0.424937	−	1.54061i
$683$	−33.2711	+	12.1097i	−1.27308	+	0.463364i	−0.888138	−	0.459576i	$-0.848001\pi$
$683$	−33.2711	+	12.1097i	−1.27308	+	0.463364i	−0.384944	+	0.922940i	$0.625779\pi$
$684$	−33.0658	−	15.7918i	−1.26430	−	0.603816i
$685$	−0.405322	−	0.147525i	−0.0154865	−	0.00563664i
$686$	9.33354	−	13.1238i	0.356356	−	0.501069i
$687$	−0.516374	−	29.9072i	−0.0197009	−	1.14103i
$688$	12.5943	+	27.0257i	0.480154	+	1.03034i
$689$	−50.8677	+	47.9912i	−1.93790	+	1.82832i
$690$	2.18605	+	1.90685i	0.0832213	+	0.0725925i
$691$	−25.5778	+	19.0420i	−0.973026	+	0.724391i	−0.961290	−	0.275540i	$-0.911143\pi$
$691$	−25.5778	+	19.0420i	−0.973026	+	0.724391i	−0.0117364	+	0.999931i	$0.503736\pi$
$692$	6.37188	+	22.4782i	0.242222	+	0.854492i
$693$	−10.1651	+	8.12779i	−0.386141	+	0.308749i
$694$	−13.4909	+	10.5074i	−0.512109	+	0.398855i
$695$	−2.31946	−	1.52553i	−0.0879821	−	0.0578667i
$696$	−9.98517	+	11.1139i	−0.378487	+	0.421270i
$697$	7.27477	−	9.77171i	0.275552	−	0.370130i
$698$	−1.57535	+	1.96260i	−0.0596278	+	0.0742855i
$699$	18.2637	+	11.5656i	0.690797	+	0.437450i
$700$	−5.10843	+	6.65577i	−0.193080	+	0.251564i
$701$	42.2293	−	24.3811i	1.59498	−	0.920861i	0.602544	−	0.798086i	$-0.294154\pi$
$701$	42.2293	−	24.3811i	1.59498	−	0.920861i	0.992434	−	0.122776i	$-0.0391795\pi$
$702$	30.4651	+	35.1938i	1.14983	+	1.32830i
$703$	−46.5950	−	26.9017i	−1.75737	−	1.01462i
$704$	−2.92239	−	40.3166i	−0.110142	−	1.51949i
$705$	−0.180539	+	0.439235i	−0.00679950	+	0.0165426i
$706$	−1.16146	+	7.54308i	−0.0437120	+	0.283887i
$707$	−0.564103	−	1.30774i	−0.0212153	−	0.0491825i
$708$	4.92733	−	28.3753i	0.185180	−	1.06641i
$709$	−2.67913	+	45.9988i	−0.100617	+	1.72752i	0.450228	+	0.892914i	$0.351343\pi$
$709$	−2.67913	+	45.9988i	−0.100617	+	1.72752i	−0.550845	+	0.834608i	$0.685694\pi$
$710$	−1.38260	+	0.192176i	−0.0518879	+	0.00721223i
$711$	37.2045	+	5.24310i	1.39528	+	0.196632i
$712$	−1.87017	+	3.79060i	−0.0700876	+	0.142059i
$713$	−2.37784	−	20.3437i	−0.0890508	−	0.761878i
$714$	−9.50865	+	5.24957i	−0.355852	+	0.196460i
$715$	−10.3545	−	3.09993i	−0.387236	−	0.115931i
$716$	23.5961	−	27.2976i	0.881829	−	1.02016i
$717$	−3.23969	−	8.44446i	−0.120989	−	0.315364i
$718$	2.29072	−	24.1428i	0.0854889	−	0.901000i
$719$	38.1126	−	31.9803i	1.42136	−	1.19266i	0.470755	−	0.882264i	$-0.343981\pi$
$719$	38.1126	−	31.9803i	1.42136	−	1.19266i	0.950606	−	0.310400i	$-0.100463\pi$
$720$	−3.87607	+	1.18241i	−0.144453	+	0.0440657i
$721$	−2.19415	−	1.84111i	−0.0817143	−	0.0685664i
$722$	−18.4317	+	18.1633i	−0.685956	+	0.675969i
$723$	8.18334	−	17.0208i	0.304342	−	0.633011i
$724$	−1.57189	+	0.877051i	−0.0584188	+	0.0325953i
$725$	14.8757	−	0.866410i	0.552469	−	0.0321776i
$726$	−28.9518	+	20.7038i	−1.07450	+	0.768390i
$727$	−34.2737	−	32.3355i	−1.27114	−	1.19926i	−0.969295	−	0.245901i	$-0.920916\pi$
$727$	−34.2737	−	32.3355i	−1.27114	−	1.19926i	−0.301844	−	0.953357i	$-0.597602\pi$
$728$	12.4039	+	9.09838i	0.459720	+	0.337209i
$729$	−7.41275	−	25.9625i	−0.274546	−	0.961574i
$730$	0.796664	+	2.46458i	0.0294859	+	0.0912181i
$731$	26.4175	−	28.0009i	0.977086	−	1.03565i
$732$	−14.9474	+	20.1872i	−0.552473	+	0.746141i
$733$	−1.33069	−	22.8471i	−0.0491502	−	0.843876i	−0.929333	−	0.369242i	$-0.879617\pi$
$733$	−1.33069	−	22.8471i	−0.0491502	−	0.843876i	0.880183	−	0.474634i	$-0.157420\pi$
$734$	−4.29799	−	21.6143i	−0.158642	−	0.797797i
$735$	−3.30145	−	1.58728i	−0.121776	−	0.0585479i
$736$	−8.76862	−	17.7946i	−0.323216	−	0.655916i
$737$	−27.0351	+	32.2192i	−0.995852	+	1.18681i
$738$	8.01625	+	5.99149i	0.295082	+	0.220550i
$739$	2.10050	+	2.50328i	0.0772682	+	0.0920846i	0.803294	−	0.595583i	$-0.203079\pi$
$739$	2.10050	+	2.50328i	0.0772682	+	0.0920846i	−0.726025	+	0.687668i	$0.758635\pi$
$740$	−5.80926	+	1.28715i	−0.213553	+	0.0473164i
$741$	62.5592	−	24.0007i	2.29817	−	0.881687i
$742$	11.4610	−	6.95378i	0.420748	−	0.255281i
$743$	−9.95470	+	33.2510i	−0.365202	+	1.21986i	0.556133	+	0.831093i	$0.312284\pi$
$743$	−9.95470	+	33.2510i	−0.365202	+	1.21986i	−0.921336	+	0.388768i	$0.872901\pi$
$744$	25.8748	+	12.2151i	0.948616	+	0.447826i
$745$	1.34573	−	0.157294i	0.0493039	−	0.00576280i
$746$	11.9927	+	22.6377i	0.439085	+	0.828826i
$747$	−1.51289	+	10.7353i	−0.0553539	+	0.392785i
$748$	−46.9768	+	22.7362i	−1.71764	+	0.831318i
$749$	3.74630	+	0.218197i	0.136887	+	0.00797274i
$750$	7.23613	+	3.80942i	0.264226	+	0.139100i
$751$	−8.17229	+	3.52518i	−0.298211	+	0.128636i	−0.539928	−	0.841711i	$-0.681549\pi$
$751$	−8.17229	+	3.52518i	−0.298211	+	0.128636i	0.241717	+	0.970347i	$0.422289\pi$
$752$	2.29695	−	2.29584i	0.0837613	−	0.0837208i
$753$	26.7690	+	11.0029i	0.975518	+	0.400968i
$754$	−2.18148	−	27.2329i	−0.0794446	−	0.991762i
$755$	3.05518	−	5.29173i	0.111189	−	0.192586i
$756$	−4.29779	−	7.81962i	−0.156309	−	0.284397i
$757$	0.824521	+	1.42811i	0.0299677	+	0.0519056i	0.880620	−	0.473823i	$-0.157126\pi$
$757$	0.824521	+	1.42811i	0.0299677	+	0.0519056i	−0.850653	+	0.525728i	$0.823793\pi$
$758$	−5.19498	+	3.58108i	−0.188690	+	0.130071i
$759$	−16.4197	+	25.9291i	−0.595998	+	0.941168i
$760$	−0.297878	+	5.82576i	−0.0108052	+	0.211322i
$761$	−2.32628	−	1.73185i	−0.0843276	−	0.0627796i	0.554169	−	0.832404i	$-0.313036\pi$
$761$	−2.32628	−	1.73185i	−0.0843276	−	0.0627796i	−0.638497	+	0.769624i	$0.720443\pi$
$762$	−1.11489	+	0.241775i	−0.0403882	+	0.00875859i
$763$	−3.43593	+	5.22407i	−0.124389	+	0.189124i
$764$	−1.64608	+	2.42453i	−0.0595530	+	0.0877165i
$765$	3.26741	+	4.08642i	0.118133	+	0.147745i
$766$	6.92752	+	0.252422i	0.250301	+	0.00912037i
$767$	31.4482	+	42.2423i	1.13553	+	1.52528i
$768$	27.5755	+	2.75493i	0.995047	+	0.0994101i
$769$	−5.41300	−	5.73744i	−0.195198	−	0.206897i	0.622381	−	0.782715i	$-0.286166\pi$
$769$	−5.41300	−	5.73744i	−0.195198	−	0.206897i	−0.817579	+	0.575817i	$0.804684\pi$
$770$	1.81644	+	0.996674i	0.0654598	+	0.0359176i
$771$	2.72536	−	0.0470558i	0.0981516	−	0.00169467i
$772$	−16.5477	−	5.21967i	−0.595564	−	0.187860i
$773$	17.9818	−	49.4046i	0.646761	−	1.77696i	0.0173994	−	0.999849i	$-0.494461\pi$
$773$	17.9818	−	49.4046i	0.646761	−	1.77696i	0.629362	−	0.777113i	$-0.283316\pi$
$774$	22.9619	+	21.7458i	0.825349	+	0.781635i
$775$	−9.76026	−	26.8161i	−0.350599	−	0.963263i
$776$	−22.6388	+	8.42213i	−0.812687	+	0.302337i
$777$	−5.39612	−	11.9386i	−0.193585	−	0.428294i
$778$	−32.5163	−	11.0400i	−1.16577	−	0.395803i
$779$	12.0362	−	7.91634i	0.431242	−	0.283632i
$780$	3.30845	−	6.63057i	0.118461	−	0.237413i
$781$	−4.23565	−	14.1480i	−0.151563	−	0.506257i
$782$	−17.1670	+	19.0079i	−0.613891	+	0.679721i
$783$	−5.51493	+	14.8563i	−0.197088	+	0.530921i
$784$	16.6494	+	18.7179i	0.594622	+	0.668497i
$785$	0.294979	−	1.24462i	0.0105283	−	0.0444222i
$786$	7.53497	+	15.7485i	0.268764	+	0.561732i
$787$	9.25049	−	18.4192i	0.329744	−	0.656575i	−0.666276	−	0.745705i	$-0.732113\pi$
$787$	9.25049	−	18.4192i	0.329744	−	0.656575i	0.996020	+	0.0891308i	$0.0284089\pi$
$788$	0.120963	−	0.202594i	0.00430914	−	0.00721711i
$789$	10.6187	+	41.5905i	0.378035	+	1.48066i
$790$	−1.50565	−	5.78863i	−0.0535687	−	0.205950i
$791$	2.88305	−	16.3506i	0.102509	−	0.581360i
$792$	−18.6050	−	38.6273i	−0.661099	−	1.37256i
$793$	−7.97594	−	45.2338i	−0.283234	−	1.60630i
$794$	−42.4977	+	19.4389i	−1.50819	+	0.689862i
$795$	−4.23565	−	4.87442i	−0.150223	−	0.172878i
$796$	−4.49836	+	1.56295i	−0.159440	+	0.0553974i
$797$	−12.0865	−	50.9971i	−0.428127	−	1.80641i	−0.576053	−	0.817413i	$-0.695408\pi$
$797$	−12.0865	−	50.9971i	−0.428127	−	1.80641i	0.147925	−	0.988999i	$-0.452740\pi$
$798$	−12.6896	+	1.98767i	−0.449206	+	0.0703628i
$799$	−3.85008	−	1.66076i	−0.136206	−	0.0587535i
$800$	−17.6052	−	21.3068i	−0.622439	−	0.753308i
$801$	−0.366441	+	4.46824i	−0.0129475	+	0.157877i
$802$	2.26767	−	5.58830i	0.0800743	−	0.197330i
$803$	−24.4888	+	12.2987i	−0.864190	+	0.434012i
$804$	−18.5921	−	22.0407i	−0.655694	−	0.777314i
$805$	1.00994	+	0.118045i	0.0355956	+	0.00416052i
$806$	−48.7652	+	18.9603i	−1.71768	+	0.667850i
$807$	−18.8814	−	4.13206i	−0.664656	−	0.145455i
$808$	4.61451	−	0.847444i	0.162338	−	0.0298130i
$809$			36.6852i			1.28978i	0.764275	+	0.644891i	$0.223097\pi$
$809$			36.6852i			1.28978i	−0.764275	+	0.644891i	$0.776903\pi$
$810$	−3.36212	+	2.67785i	−0.118133	+	0.0940901i
$811$		−	15.1839i		−	0.533178i	−0.963810	−	0.266589i	$-0.914103\pi$
$811$		−	15.1839i		−	0.533178i	0.963810	−	0.266589i	$-0.0858967\pi$
$812$	−0.684196	+	5.19214i	−0.0240106	+	0.182208i
$813$	−9.90768	+	10.8715i	−0.347477	+	0.381282i
$814$	−22.8128	−	58.6736i	−0.799590	−	2.05651i
$815$	−7.81362	−	0.913282i	−0.273699	−	0.0319909i
$816$	−9.84755	−	34.3984i	−0.344733	−	1.20419i
$817$	40.6812	−	20.4308i	1.42325	−	0.714785i
$818$	−35.0734	−	14.2324i	−1.22631	−	0.497625i
$819$	15.7829	+	4.13715i	0.551501	+	0.144564i
$820$	0.390110	−	1.54469i	0.0136232	−	0.0539431i
$821$	1.94020	+	0.836922i	0.0677136	+	0.0292088i	0.429667	−	0.902987i	$-0.358631\pi$
$821$	1.94020	+	0.836922i	0.0677136	+	0.0292088i	−0.361954	+	0.932196i	$0.617890\pi$
$822$	2.91894	+	1.12619i	0.101810	+	0.0392803i
$823$	−6.71225	−	28.3212i	−0.233974	−	0.987216i	−0.955538	−	0.294868i	$-0.904724\pi$
$823$	−6.71225	−	28.3212i	−0.233974	−	0.987216i	0.721564	−	0.692348i	$-0.243424\pi$
$824$	7.52828	−	5.68801i	0.262260	−	0.198151i
$825$	−13.9291	+	40.4281i	−0.484948	+	1.40753i
$826$	−4.19915	−	9.18026i	−0.146107	−	0.319422i
$827$	−2.29939	−	13.0405i	−0.0799577	−	0.453463i	−0.998331	−	0.0577481i	$-0.981608\pi$
$827$	−2.29939	−	13.0405i	−0.0799577	−	0.453463i	0.918373	−	0.395715i	$-0.129503\pi$
$828$	−15.5885	−	14.1324i	−0.541737	−	0.491136i
$829$	−3.80157	+	21.5598i	−0.132034	+	0.748802i	0.844845	+	0.535011i	$0.179692\pi$
$829$	−3.80157	+	21.5598i	−0.132034	+	0.748802i	−0.976879	+	0.213791i	$0.931419\pi$
$830$	1.67031	−	0.434455i	0.0579772	−	0.0150802i
$831$	−26.9448	−	7.56244i	−0.934706	−	0.262338i
$832$	−38.3536	+	33.1206i	−1.32967	+	1.14825i
$833$	14.5159	−	28.9035i	0.502945	−	1.00145i
$834$	16.6090	+	11.3856i	0.575123	+	0.394252i
$835$	−1.17594	+	4.96169i	−0.0406952	+	0.171706i
$836$	−61.3981	+	6.26518i	−2.12350	+	0.216686i
$837$	30.2856	+	1.95805i	1.04682	+	0.0676799i
$838$	15.7796	+	14.2513i	0.545097	+	0.492304i
$839$	7.82382	+	26.1334i	0.270108	+	0.902224i	0.980182	+	0.198097i	$0.0634762\pi$
$839$	7.82382	+	26.1334i	0.270108	+	0.902224i	−0.710074	+	0.704127i	$0.751339\pi$
$840$	−0.886285	+	1.11005i	−0.0305797	+	0.0383003i
$841$	−16.4584	+	10.8248i	−0.567530	+	0.373270i
$842$	−2.52999	+	7.45163i	−0.0871892	+	0.256800i
$843$	25.7213	−	35.8246i	0.885888	−	1.23387i
$844$	0.350719	+	8.05512i	0.0120722	+	0.277269i
$845$	3.13289	+	8.60754i	0.107775	+	0.296109i
$846$	1.37032	−	3.16030i	0.0471126	−	0.108653i
$847$	−4.26709	+	11.7237i	−0.146619	+	0.402832i
$848$	13.8805	+	41.9229i	0.476658	+	1.43964i
$849$	0.747831	−	1.34852i	0.0256655	−	0.0462811i
$850$	−17.1660	+	31.2851i	−0.588790	+	1.07307i
$851$	−21.2012	−	22.4719i	−0.726767	−	0.770328i
$852$	10.0534	−	1.20157i	0.344425	−	0.0411652i
$853$	−9.55267	−	12.8315i	−0.327077	−	0.439341i	0.607919	−	0.793999i	$-0.292005\pi$
$853$	−9.55267	−	12.8315i	−0.327077	−	0.439341i	−0.934996	+	0.354658i	$0.884597\pi$
$854$	−0.320608	+	8.79884i	−0.0109710	+	0.301090i
$855$	1.97808	+	5.86250i	0.0676488	+	0.200493i
$856$	−3.46141	+	11.8676i	−0.118309	+	0.405625i
$857$	20.8568	−	31.7112i	0.712454	−	1.08323i	−0.279926	−	0.960022i	$-0.590310\pi$
$857$	20.8568	−	31.7112i	0.712454	−	1.08323i	0.992380	−	0.123213i	$-0.0393198\pi$
$858$	74.6612	+	23.9198i	2.54889	+	0.816608i
$859$	28.8151	+	21.4520i	0.983158	+	0.731934i	0.963455	−	0.267872i	$-0.0863204\pi$
$859$	28.8151	+	21.4520i	0.983158	+	0.731934i	0.0197034	+	0.999806i	$0.493728\pi$
$860$	1.79108	−	4.70509i	0.0610753	−	0.160442i
$861$	3.50507	+	0.143485i	0.119452	+	0.00488994i
$862$	−4.14070	−	6.00680i	−0.141033	−	0.204592i
$863$	19.9202	+	34.5027i	0.678090	+	1.17449i	0.975555	+	0.219754i	$0.0705253\pi$
$863$	19.9202	+	34.5027i	0.678090	+	1.17449i	−0.297466	+	0.954733i	$0.596141\pi$
$864$	28.2740	−	8.03636i	0.961900	−	0.273403i
$865$	1.97250	−	3.41646i	0.0670669	−	0.116163i
$866$	−26.4413	+	2.11806i	−0.898510	+	0.0719747i
$867$	−13.2619	+	10.2337i	−0.450398	+	0.347553i
$868$	9.90167	−	1.59658i	0.336085	−	0.0541915i
$869$	58.1060	−	25.0645i	1.97111	−	0.850254i
$870$	2.52080	−	0.0984125i	0.0854632	−	0.00333650i
$871$	52.6379	+	3.06581i	1.78357	+	0.103881i
$872$	−14.2410	−	14.8817i	−0.482261	−	0.503959i
$873$	−19.0458	+	17.1359i	−0.644602	+	0.579961i
$874$	−26.7644	+	14.1789i	−0.905321	+	0.479610i
$875$	2.84706	−	0.332773i	0.0962480	−	0.0112498i
$876$	−5.43505	−	17.9841i	−0.183633	−	0.607626i
$877$	11.4912	−	38.3833i	0.388031	−	1.29611i	−0.511510	−	0.859277i	$-0.670914\pi$
$877$	11.4912	−	38.3833i	0.388031	−	1.29611i	0.899541	−	0.436836i	$-0.143901\pi$
$878$	3.04101	+	5.01211i	0.102629	+	0.169151i
$879$	−42.5531	−	34.4722i	−1.43528	−	1.16272i
$880$	−4.53868	+	5.09759i	−0.152999	+	0.171840i
$881$	0.395782	+	0.471675i	0.0133342	+	0.0158911i	0.772670	−	0.634807i	$-0.218921\pi$
$881$	0.395782	+	0.471675i	0.0133342	+	0.0158911i	−0.759336	+	0.650699i	$0.774476\pi$
$882$	23.7219	+	11.9699i	0.798759	+	0.403047i
$883$	−9.79556	+	11.6739i	−0.329647	+	0.392858i	−0.905256	−	0.424868i	$-0.860321\pi$
$883$	−9.79556	+	11.6739i	−0.329647	+	0.392858i	0.575609	+	0.817725i	$0.304765\pi$
$884$	58.0309	+	30.2179i	1.95179	+	1.01634i
$885$	−4.01614	+	2.74194i	−0.135001	+	0.0921692i
$886$	39.2777	−	7.81036i	1.31956	−	0.262394i
$887$	−0.584473	−	10.0350i	−0.0196247	−	0.336943i	−0.993802	−	0.111160i	$-0.964543\pi$
$887$	−0.584473	−	10.0350i	−0.0196247	−	0.336943i	0.974178	−	0.225782i	$-0.0724938\pi$
$888$	42.3083	−	8.52734i	1.41977	−	0.286159i
$889$	−0.274413	+	0.290861i	−0.00920353	+	0.00975517i
$890$	0.679105	−	0.219518i	0.0227636	−	0.00735825i
$891$	−33.4150	−	30.8453i	−1.11944	−	1.03335i
$892$	−0.461077	−	0.638678i	−0.0154380	−	0.0213845i
$893$	−3.60664	−	3.40269i	−0.120692	−	0.113867i
$894$	−9.78127	+	0.953725i	−0.327135	+	0.0318973i
$895$	−6.08220	+	0.354248i	−0.203306	+	0.0118412i
$896$	8.51848	−	4.66871i	0.284582	−	0.155971i
$897$	38.3659	−	2.89989i	1.28100	−	0.0968246i
$898$	−9.49344	−	9.63369i	−0.316800	−	0.321480i
$899$	−13.6451	−	11.4496i	−0.455089	−	0.381865i
$900$	−25.6743	−	14.1507i	−0.855810	−	0.471691i
$901$	43.6773	−	36.6496i	1.45510	−	1.22098i
$902$	16.7806	+	1.59218i	0.558733	+	0.0530139i
$903$	10.9484	+	1.73618i	0.364340	+	0.0577765i
$904$	50.3727	+	21.3063i	1.67537	+	0.708637i
$905$	0.291165	+	0.0871690i	0.00967864	+	0.00289759i
$906$	−22.8918	+	37.9517i	−0.760529	+	1.26086i
$907$	4.55876	+	39.0027i	0.151371	+	1.29506i	0.828829	+	0.559502i	$0.189007\pi$
$907$	4.55876	+	39.0027i	0.151371	+	1.29506i	−0.677458	+	0.735561i	$0.736918\pi$
$908$	−2.30248	−	2.23700i	−0.0764105	−	0.0742374i
$909$	4.22112	−	2.63543i	0.140006	−	0.0874117i
$910$	−0.357595	−	2.57269i	−0.0118542	−	0.0852840i
$911$	−0.806792	+	13.8521i	−0.0267302	+	0.458940i	0.958212	+	0.286058i	$0.0923450\pi$
$911$	−0.806792	+	13.8521i	−0.0267302	+	0.458940i	−0.984943	+	0.172882i	$0.944692\pi$
$912$	2.96972	−	42.2076i	0.0983372	−	1.39763i
$913$	7.23235	+	16.7665i	0.239356	+	0.554889i
$914$	37.0653	+	5.70719i	1.22601	+	0.188777i
$915$	4.20349	−	0.565035i	0.138963	−	0.0186795i
$916$	31.9115	−	13.2136i	1.05438	−	0.436591i
$917$	5.29967	+	3.05977i	0.175011	+	0.101042i
$918$	−23.1278	−	30.0892i	−0.763331	−	0.993091i
$919$	30.3485	−	17.5217i	1.00111	−	0.577988i	0.0925301	−	0.995710i	$-0.470505\pi$
$919$	30.3485	−	17.5217i	1.00111	−	0.577988i	0.908575	+	0.417722i	$0.137171\pi$
$920$	−1.12328	+	3.15564i	−0.0370335	+	0.104038i
$921$	−34.3255	+	17.9876i	−1.13106	+	0.592710i
$922$	−13.0539	−	10.4782i	−0.429908	−	0.345080i
$923$	−11.0560	+	14.8508i	−0.363913	+	0.488820i
$924$	−13.0345	−	7.48038i	−0.428804	−	0.246086i
$925$	−35.9630	−	23.6533i	−1.18246	−	0.777714i
$926$	−15.4474	−	19.8336i	−0.507633	−	0.651773i
$927$	5.20748	−	8.54630i	0.171036	−	0.280697i
$928$	−16.1663	−	6.02312i	−0.530686	−	0.197719i
$929$	−20.0356	+	14.9159i	−0.657345	+	0.489375i	−0.873398	−	0.487006i	$-0.838089\pi$
$929$	−20.0356	+	14.9159i	−0.657345	+	0.489375i	0.216053	+	0.976382i	$0.430681\pi$
$930$	−1.56514	−	4.57079i	−0.0513231	−	0.149882i
$931$	27.8208	−	26.2475i	0.911788	−	0.860228i
$932$	−4.69464	+	24.5166i	−0.153778	+	0.803067i
$933$	−30.3428	+	18.2240i	−0.993379	+	0.596627i
$934$	40.4273	+	28.7516i	1.32282	+	0.940780i
$935$	8.28079	+	3.01396i	0.270811	+	0.0985670i
$936$	−24.9145	+	47.6259i	−0.814357	+	1.55670i
$937$	−29.3199	+	10.6716i	−0.957839	+	0.348625i	−0.773186	−	0.634179i	$-0.781338\pi$
$937$	−29.3199	+	10.6716i	−0.957839	+	0.348625i	−0.184653	+	0.982804i	$0.559116\pi$
$938$	−9.74349	−	2.68749i	−0.318136	−	0.0877496i
$939$	2.34911	−	23.6289i	0.0766604	−	0.771101i
$940$	−0.548298	−	0.00804152i	−0.0178835	−	0.000262285i
$941$	14.8550	+	22.5859i	0.484258	+	0.736278i	0.992138	−	0.125150i	$-0.0399412\pi$
$941$	14.8550	+	22.5859i	0.484258	+	0.736278i	−0.507880	+	0.861428i	$0.669571\pi$
$942$	−2.31216	+	8.98510i	−0.0753342	+	0.292750i
$943$	7.92473	−	2.37251i	0.258065	−	0.0772595i
$944$	32.5699	−	6.71694i	1.06006	−	0.218618i
$945$	−0.441312	+	1.44054i	−0.0143559	+	0.0468609i
$946$	52.0838	+	11.1532i	1.69339	+	0.362623i
$947$	33.1992	+	7.86836i	1.07883	+	0.255687i	0.731352	−	0.682001i	$-0.238890\pi$
$947$	33.1992	+	7.86836i	1.07883	+	0.255687i	0.347478	+	0.937688i	$0.387038\pi$
$948$	10.1148	+	42.1890i	0.328515	+	1.37023i
$949$	30.7001	+	15.4182i	0.996568	+	0.500495i
$950$	−31.7290	+	27.8222i	−1.02942	+	0.902670i
$951$	36.7426	+	37.6219i	1.19146	+	1.21998i
$952$	−9.66450	−	7.99338i	−0.313228	−	0.259067i
$953$	25.2641	+	4.45473i	0.818383	+	0.144303i	0.567140	−	0.823621i	$-0.308050\pi$
$953$	25.2641	+	4.45473i	0.818383	+	0.144303i	0.251243	+	0.967924i	$0.419161\pi$
$954$	30.0401	+	35.9383i	0.972584	+	1.16355i
$955$	0.487301	−	0.0859243i	0.0157687	−	0.00278044i
$956$	7.70082	−	7.05479i	0.249062	−	0.228168i
$957$	5.08781	+	26.2010i	0.164465	+	0.846957i
$958$	0.203222	+	9.33942i	0.00656581	+	0.301743i
$959$	1.06711	−	0.252909i	0.0344586	−	0.00816685i
$960$	−2.91092	−	3.66368i	−0.0939496	−	0.118245i
$961$	−1.23300	+	2.85843i	−0.0397744	+	0.0922073i
$962$	−41.9225	+	66.8644i	−1.35164	+	2.15580i
$963$	1.21381	+	13.0556i	0.0391146	+	0.420712i
$964$	21.7497	+	1.58712i	0.700510	+	0.0511176i
$965$	1.31489	+	2.61815i	0.0423277	+	0.0842813i
$966$	−7.30776	−	0.996400i	−0.235123	−	0.0320587i
$967$	1.59276	−	13.6269i	0.0512198	−	0.438213i	−0.943160	−	0.332340i	$-0.892162\pi$
$967$	1.59276	−	13.6269i	0.0512198	−	0.438213i	0.994380	−	0.105874i	$-0.0337639\pi$
$968$	−34.4971	−	22.3403i	−1.10878	−	0.718044i
$969$	−52.0561	+	16.5690i	−1.67228	+	0.532273i
$970$	3.68366	+	1.75072i	0.118275	+	0.0562121i
$971$	−26.4923			−0.850177			−0.425088	−	0.905152i	$-0.639757\pi$
$971$	−26.4923			−0.850177			−0.425088	+	0.905152i	$0.639757\pi$
$972$	24.7545	−	18.9529i	0.794002	−	0.607915i
$973$	7.05841			0.226282
$974$	−35.4323	−	16.8397i	−1.13532	−	0.539580i
$975$	51.0811	−	16.2587i	1.63591	−	0.520695i
$976$	−28.0145	−	7.51371i	−0.896721	−	0.240508i
$977$	−1.22136	+	10.4494i	−0.0390747	+	0.334306i	0.959535	+	0.281590i	$0.0908618\pi$
$977$	−1.22136	+	10.4494i	−0.0390747	+	0.334306i	−0.998610	+	0.0527157i	$0.983212\pi$
$978$	56.5384	+	7.70891i	1.80790	+	0.246504i
$979$	3.38887	+	6.74779i	0.108309	+	0.215660i
$980$	0.307846	−	4.21868i	0.00983378	−	0.134761i
$981$	−19.8503	−	9.12523i	−0.633772	−	0.291346i
$982$	−7.47464	+	11.9217i	−0.238525	+	0.380437i
$983$	−14.3798	+	33.3361i	−0.458644	+	1.06326i	0.519338	+	0.854569i	$0.326178\pi$
$983$	−14.3798	+	33.3361i	−0.458644	+	1.06326i	−0.977982	+	0.208687i	$0.933081\pi$
$984$	−3.04375	+	11.1481i	−0.0970313	+	0.355388i
$985$	−0.0387677	+	0.00918812i	−0.00123524	+	0.000292758i
$986$	0.484561	+	22.2688i	0.0154316	+	0.709184i
$987$	−0.230161	−	1.18527i	−0.00732609	−	0.0377276i
$988$	52.2641	+	57.0501i	1.66274	+	1.81501i
$989$	25.7430	−	4.53919i	0.818581	−	0.144338i
$990$	−2.48888	+	6.79806i	−0.0791017	+	0.216057i
$991$	14.5372	+	2.56330i	0.461789	+	0.0814258i	0.399702	−	0.916645i	$-0.369113\pi$
$991$	14.5372	+	2.56330i	0.461789	+	0.0814258i	0.0620863	+	0.998071i	$0.480225\pi$
$992$	−2.17086	+	32.9682i	−0.0689247	+	1.04674i
$993$	33.7091	+	34.5159i	1.06973	+	1.09533i
$994$	2.66845	−	2.33988i	0.0846382	−	0.0742166i
$995$	0.718561	+	0.360875i	0.0227799	+	0.0114405i
$996$	−12.1736	+	2.91863i	−0.385735	+	0.0924804i
$997$	12.1943	+	2.89011i	0.386198	+	0.0915306i	0.419128	−	0.907927i	$-0.362336\pi$
$997$	12.1943	+	2.89011i	0.386198	+	0.0915306i	−0.0329303	+	0.999458i	$0.510484\pi$
$998$	−23.8515	−	5.10756i	−0.755005	−	0.161677i
$999$	38.4061	−	24.9102i	1.21511	−	0.788124i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	324.2.p.a.11.19	✓	936
3.2	odd	2		972.2.p.a.359.34		936
4.3	odd	2	inner	324.2.p.a.11.45	yes	936
12.11	even	2		972.2.p.a.359.8		936
81.22	even	27		972.2.p.a.287.8		936
81.59	odd	54	inner	324.2.p.a.59.45	yes	936
324.59	even	54	inner	324.2.p.a.59.19	yes	936
324.103	odd	54		972.2.p.a.287.34		936

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
324.2.p.a.11.19	✓	936	1.1	even	1	trivial
324.2.p.a.11.45	yes	936	4.3	odd	2	inner
324.2.p.a.59.19	yes	936	324.59	even	54	inner
324.2.p.a.59.45	yes	936	81.59	odd	54	inner
972.2.p.a.287.8		936	81.22	even	27
972.2.p.a.287.34		936	324.103	odd	54
972.2.p.a.359.8		936	12.11	even	2
972.2.p.a.359.34		936	3.2	odd	2

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:	\( N \)	\(=\)	\( 324 = 2^{2} \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	324.p (of order \(54\), degree \(18\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.607055 + 1.27730i) q^{2} +(-1.65046 + 0.525329i) q^{3} +(-1.26297 - 1.55078i) q^{4} +(-0.0392046 + 0.335417i) q^{5} +(0.330922 - 2.42703i) q^{6} +(-0.385340 - 0.767275i) q^{7} +(2.74749 - 0.671779i) q^{8} +(2.44806 - 1.73407i) q^{9} +O(q^{10})\)	\(q+(-0.607055 + 1.27730i) q^{2} +(-1.65046 + 0.525329i) q^{3} +(-1.26297 - 1.55078i) q^{4} +(-0.0392046 + 0.335417i) q^{5} +(0.330922 - 2.42703i) q^{6} +(-0.385340 - 0.767275i) q^{7} +(2.74749 - 0.671779i) q^{8} +(2.44806 - 1.73407i) q^{9} +(-0.404627 - 0.253692i) q^{10} +(2.00131 - 4.63956i) q^{11} +(2.89915 + 1.89603i) q^{12} +(-6.16365 + 1.46081i) q^{13} +(1.21396 - 0.0264153i) q^{14} +(-0.111498 - 0.574189i) q^{15} +(-0.809817 + 3.91717i) q^{16} +(5.08597 - 0.896794i) q^{17} +(0.728816 + 4.17957i) q^{18} +(6.01443 + 1.06051i) q^{19} +(0.569671 - 0.362824i) q^{20} +(1.03906 + 1.06393i) q^{21} +(4.71118 + 5.37273i) q^{22} +(3.13383 + 1.57387i) q^{23} +(-4.18173 + 2.55208i) q^{24} +(4.75426 + 1.12678i) q^{25} +(1.87578 - 8.75959i) q^{26} +(-3.12948 + 4.14806i) q^{27} +(-0.703200 + 1.56662i) q^{28} +(2.92162 - 0.874674i) q^{29} +(0.801095 + 0.206148i) q^{30} +(-3.20948 - 4.87978i) q^{31} +(-4.51178 - 3.41231i) q^{32} +(-0.865797 + 8.70877i) q^{33} +(-1.94199 + 7.04070i) q^{34} +(0.272464 - 0.0991689i) q^{35} +(-5.78098 - 1.60632i) q^{36} +(-8.27851 - 3.01313i) q^{37} +(-5.00566 + 7.03842i) q^{38} +(9.40547 - 5.64895i) q^{39} +(0.117612 + 0.947892i) q^{40} +(1.71579 - 1.61877i) q^{41} +(-1.98972 + 0.681325i) q^{42} +(5.97906 - 4.45124i) q^{43} +(-9.72251 + 2.75603i) q^{44} +(0.485662 + 0.889104i) q^{45} +(-3.91270 + 3.04740i) q^{46} +(-0.678332 - 0.446146i) q^{47} +(-0.721226 - 6.89056i) q^{48} +(3.73989 - 5.02354i) q^{49} +(-4.32532 + 5.38858i) q^{50} +(-7.92310 + 4.15193i) q^{51} +(10.0499 + 7.71348i) q^{52} +(9.56115 - 5.52013i) q^{53} +(-3.39853 - 6.51536i) q^{54} +(1.47773 + 0.853165i) q^{55} +(-1.57416 - 1.84922i) q^{56} +(-10.4837 + 1.40922i) q^{57} +(-0.656363 + 4.26274i) q^{58} +(-3.29294 - 7.63389i) q^{59} +(-0.749620 + 0.898092i) q^{60} +(-0.421617 + 7.23888i) q^{61} +(8.18125 - 1.13716i) q^{62} +(-2.27385 - 1.21013i) q^{63} +(7.09743 - 3.69142i) q^{64} +(-0.248337 - 2.12466i) q^{65} +(-10.5981 - 6.39258i) q^{66} +(-7.97426 - 2.38734i) q^{67} +(-7.81416 - 6.75459i) q^{68} +(-5.99907 - 0.951323i) q^{69} +(-0.0387327 + 0.408218i) q^{70} +(2.23902 - 1.87876i) q^{71} +(5.56111 - 6.40890i) q^{72} +(-4.15461 - 3.48613i) q^{73} +(8.87417 - 8.74497i) q^{74} +(-8.43866 + 0.637838i) q^{75} +(-5.95143 - 10.6664i) q^{76} +(-4.33100 + 0.252252i) q^{77} +(1.50575 + 15.4428i) q^{78} +(9.10965 + 8.59452i) q^{79} +(-1.28214 - 0.425197i) q^{80} +(2.98599 - 8.49022i) q^{81} +(1.02606 + 3.17425i) q^{82} +(-2.47994 + 2.62859i) q^{83} +(0.337615 - 2.95506i) q^{84} +(0.101406 + 1.74108i) q^{85} +(2.05594 + 10.3392i) q^{86} +(-4.36253 + 2.97843i) q^{87} +(2.38182 - 14.0916i) q^{88} +(-0.960590 + 1.14479i) q^{89} +(-1.43047 + 0.0805986i) q^{90} +(3.49594 + 4.16630i) q^{91} +(-1.51721 - 6.84762i) q^{92} +(7.86062 + 6.36787i) q^{93} +(0.981645 - 0.595596i) q^{94} +(-0.591505 + 1.97576i) q^{95} +(9.23911 + 3.26173i) q^{96} +(-8.48223 + 0.991430i) q^{97} +(4.14623 + 7.82650i) q^{98} +(-3.14600 - 14.8283i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 936 q - 18 q^{2} - 18 q^{4} - 36 q^{5} - 18 q^{6} - 18 q^{8} - 36 q^{9}+O(q^{10}) \) 936 * q - 18 * q^2 - 18 * q^4 - 36 * q^5 - 18 * q^6 - 18 * q^8 - 36 * q^9	\( 936 q - 18 q^{2} - 18 q^{4} - 36 q^{5} - 18 q^{6} - 18 q^{8} - 36 q^{9} - 18 q^{10} - 18 q^{12} - 36 q^{13} - 18 q^{14} - 18 q^{16} - 36 q^{17} - 18 q^{18} - 18 q^{20} - 36 q^{21} - 18 q^{22} - 18 q^{24} - 36 q^{25} - 27 q^{26} - 9 q^{28} - 36 q^{29} - 18 q^{30} - 18 q^{32} - 36 q^{33} - 18 q^{34} - 18 q^{36} - 36 q^{37} - 18 q^{38} - 18 q^{40} - 36 q^{41} - 63 q^{42} - 90 q^{44} - 36 q^{45} - 18 q^{46} - 117 q^{48} - 36 q^{49} - 135 q^{50} - 18 q^{52} - 54 q^{53} - 144 q^{54} - 144 q^{56} - 36 q^{57} - 18 q^{58} - 135 q^{60} - 36 q^{61} - 117 q^{62} - 18 q^{64} - 36 q^{65} - 90 q^{66} - 63 q^{68} - 36 q^{69} - 18 q^{70} - 18 q^{72} - 36 q^{73} - 18 q^{74} - 18 q^{76} - 36 q^{77} + 9 q^{78} - 36 q^{81} - 36 q^{82} - 45 q^{84} - 36 q^{85} - 18 q^{86} - 18 q^{88} - 54 q^{89} + 45 q^{90} + 72 q^{92} - 144 q^{93} - 18 q^{94} + 99 q^{96} - 36 q^{97} + 153 q^{98}+O(q^{100}) \) 936 * q - 18 * q^2 - 18 * q^4 - 36 * q^5 - 18 * q^6 - 18 * q^8 - 36 * q^9 - 18 * q^10 - 18 * q^12 - 36 * q^13 - 18 * q^14 - 18 * q^16 - 36 * q^17 - 18 * q^18 - 18 * q^20 - 36 * q^21 - 18 * q^22 - 18 * q^24 - 36 * q^25 - 27 * q^26 - 9 * q^28 - 36 * q^29 - 18 * q^30 - 18 * q^32 - 36 * q^33 - 18 * q^34 - 18 * q^36 - 36 * q^37 - 18 * q^38 - 18 * q^40 - 36 * q^41 - 63 * q^42 - 90 * q^44 - 36 * q^45 - 18 * q^46 - 117 * q^48 - 36 * q^49 - 135 * q^50 - 18 * q^52 - 54 * q^53 - 144 * q^54 - 144 * q^56 - 36 * q^57 - 18 * q^58 - 135 * q^60 - 36 * q^61 - 117 * q^62 - 18 * q^64 - 36 * q^65 - 90 * q^66 - 63 * q^68 - 36 * q^69 - 18 * q^70 - 18 * q^72 - 36 * q^73 - 18 * q^74 - 18 * q^76 - 36 * q^77 + 9 * q^78 - 36 * q^81 - 36 * q^82 - 45 * q^84 - 36 * q^85 - 18 * q^86 - 18 * q^88 - 54 * q^89 + 45 * q^90 + 72 * q^92 - 144 * q^93 - 18 * q^94 + 99 * q^96 - 36 * q^97 + 153 * q^98

Introduction

L-functions

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