LMFDB - Embedded newform 324.2.p.a.11.11

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			11.11
Character	$\chi$	$=$	324.11
Dual form			324.2.p.a.59.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.18334 - 0.774405i) q^{2} +(-1.00564 + 1.41021i) q^{3} +(0.800594 + 1.83277i) q^{4} +(-0.0544195 + 0.465589i) q^{5} +(2.28209 - 0.889987i) q^{6} +(-1.91763 - 3.81831i) q^{7} +(0.471930 - 2.78878i) q^{8} +(-0.977379 - 2.83632i) q^{9} +O(q^{10})$	\(q+(-1.18334 - 0.774405i) q^{2} +(-1.00564 + 1.41021i) q^{3} +(0.800594 + 1.83277i) q^{4} +(-0.0544195 + 0.465589i) q^{5} +(2.28209 - 0.889987i) q^{6} +(-1.91763 - 3.81831i) q^{7} +(0.471930 - 2.78878i) q^{8} +(-0.977379 - 2.83632i) q^{9} +(0.424951 - 0.508808i) q^{10} +(-1.09526 + 2.53910i) q^{11} +(-3.38970 - 0.714101i) q^{12} +(5.82606 - 1.38080i) q^{13} +(-0.687710 + 6.00339i) q^{14} +(-0.601851 - 0.544957i) q^{15} +(-2.71810 + 2.93461i) q^{16} +(2.98567 - 0.526453i) q^{17} +(-1.03989 + 4.11323i) q^{18} +(7.32660 + 1.29188i) q^{19} +(-0.896885 + 0.273009i) q^{20} +(7.31307 + 1.13559i) q^{21} +(3.26236 - 2.15645i) q^{22} +(-0.566827 - 0.284671i) q^{23} +(3.45817 + 3.47002i) q^{24} +(4.65141 + 1.10241i) q^{25} +(-7.96351 - 2.87777i) q^{26} +(4.98270 + 1.47401i) q^{27} +(5.46285 - 6.57150i) q^{28} +(-6.28669 + 1.88211i) q^{29} +(0.290178 + 1.11095i) q^{30} +(-2.91826 - 4.43700i) q^{31} +(5.48902 - 1.36774i) q^{32} +(-2.47922 - 4.09796i) q^{33} +(-3.94075 - 1.68914i) q^{34} +(1.88212 - 0.685036i) q^{35} +(4.41585 - 4.06206i) q^{36} +(-2.98790 - 1.08751i) q^{37} +(-7.66943 - 7.20249i) q^{38} +(-3.91169 + 9.60455i) q^{39} +(1.27274 + 0.371489i) q^{40} +(8.26630 - 7.79885i) q^{41} +(-7.77445 - 7.00706i) q^{42} +(4.56266 - 3.39677i) q^{43} +(-5.53044 + 0.0254270i) q^{44} +(1.37375 - 0.300705i) q^{45} +(0.450299 + 0.775817i) q^{46} +(0.597073 + 0.392701i) q^{47} +(-1.40499 - 6.78425i) q^{48} +(-6.72211 + 9.02936i) q^{49} +(-4.65050 - 4.90660i) q^{50} +(-2.26009 + 4.73983i) q^{51} +(7.19500 + 9.57237i) q^{52} +(3.18889 - 1.84111i) q^{53} +(-4.75476 - 5.60288i) q^{54} +(-1.12257 - 0.648117i) q^{55} +(-11.5534 + 3.54587i) q^{56} +(-9.18973 + 9.03288i) q^{57} +(8.89682 + 2.64126i) q^{58} +(1.27603 + 2.95816i) q^{59} +(0.516943 - 1.53934i) q^{60} +(0.334705 - 5.74666i) q^{61} +(0.0172650 + 7.51039i) q^{62} +(-8.95572 + 9.17096i) q^{63} +(-7.55456 - 2.63222i) q^{64} +(0.325834 + 2.78769i) q^{65} +(-0.239715 + 6.76921i) q^{66} +(-0.618183 - 0.185072i) q^{67} +(3.35518 + 5.05056i) q^{68} +(0.971469 - 0.513068i) q^{69} +(-2.75769 - 0.646892i) q^{70} +(6.02886 - 5.05881i) q^{71} +(-8.37113 + 1.38715i) q^{72} +(1.12442 + 0.943504i) q^{73} +(2.69354 + 3.60074i) q^{74} +(-6.23227 + 5.45084i) q^{75} +(3.49792 + 14.4622i) q^{76} +(11.7954 - 0.687003i) q^{77} +(12.0667 - 8.33622i) q^{78} +(-3.18709 - 3.00686i) q^{79} +(-1.21840 - 1.42522i) q^{80} +(-7.08946 + 5.54433i) q^{81} +(-15.8213 + 2.82724i) q^{82} +(9.78501 - 10.3715i) q^{83} +(3.77353 + 14.3123i) q^{84} +(0.0826323 + 1.41874i) q^{85} +(-8.02966 + 0.486199i) q^{86} +(3.66797 - 10.7583i) q^{87} +(6.56409 + 4.25271i) q^{88} +(-11.2165 + 13.3673i) q^{89} +(-1.85848 - 0.708000i) q^{90} +(-16.4446 - 19.5979i) q^{91} +(0.0679386 - 1.26677i) q^{92} +(9.19181 + 0.346663i) q^{93} +(-0.402432 - 0.927076i) q^{94} +(-1.00019 + 3.34088i) q^{95} +(-3.59117 + 9.11611i) q^{96} +(-6.61046 + 0.772651i) q^{97} +(14.9469 - 5.47919i) q^{98} +(8.27219 + 0.624850i) 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 $

$2$	−1.18334	−	0.774405i	−0.836749	−	0.547587i
$2$	−1.18334	−	0.774405i	−0.836749	−	0.547587i
$3$	−1.00564	+	1.41021i	−0.580606	+	0.814185i
$3$	−1.00564	+	1.41021i	−0.580606	+	0.814185i
$4$	0.800594	+	1.83277i	0.400297	+	0.916385i
$5$	−0.0544195	+	0.465589i	−0.0243371	+	0.208218i	−0.999936	−	0.0113446i	$-0.996389\pi$
$5$	−0.0544195	+	0.465589i	−0.0243371	+	0.208218i	0.975599	+	0.219562i	$0.0704629\pi$
$6$	2.28209	−	0.889987i	0.931658	−	0.363336i
$7$	−1.91763	−	3.81831i	−0.724796	−	1.44319i	−0.889543	−	0.456851i	$-0.848977\pi$
$7$	−1.91763	−	3.81831i	−0.724796	−	1.44319i	0.164747	−	0.986336i	$-0.447319\pi$
$8$	0.471930	−	2.78878i	0.166852	−	0.985982i
$9$	−0.977379	−	2.83632i	−0.325793	−	0.945441i
$10$	0.424951	−	0.508808i	0.134381	−	0.160899i
$11$	−1.09526	+	2.53910i	−0.330233	+	0.765567i	0.669508	+	0.742805i	$0.266505\pi$
$11$	−1.09526	+	2.53910i	−0.330233	+	0.765567i	−0.999741	+	0.0227616i	$0.992754\pi$
$12$	−3.38970	−	0.714101i	−0.978522	−	0.206143i
$13$	5.82606	−	1.38080i	1.61586	−	0.382965i	0.679406	−	0.733763i	$-0.262238\pi$
$13$	5.82606	−	1.38080i	1.61586	−	0.382965i	0.936451	+	0.350797i	$0.114089\pi$
$14$	−0.687710	+	6.00339i	−0.183798	+	1.60447i
$15$	−0.601851	−	0.544957i	−0.155397	−	0.140707i
$16$	−2.71810	+	2.93461i	−0.679524	+	0.733653i
$17$	2.98567	−	0.526453i	0.724130	−	0.127684i	0.200579	−	0.979678i	$-0.435718\pi$
$17$	2.98567	−	0.526453i	0.724130	−	0.127684i	0.523552	+	0.851994i	$0.324607\pi$
$18$	−1.03989	+	4.11323i	−0.245104	+	0.969497i
$19$	7.32660	+	1.29188i	1.68084	+	0.296377i	0.930939	−	0.365176i	$-0.118991\pi$
$19$	7.32660	+	1.29188i	1.68084	+	0.296377i	0.749899	+	0.661553i	$0.230102\pi$
$20$	−0.896885	+	0.273009i	−0.200550	+	0.0610467i
$21$	7.31307	+	1.13559i	1.59584	+	0.247806i
$22$	3.26236	−	2.15645i	0.695537	−	0.459756i
$23$	−0.566827	−	0.284671i	−0.118192	−	0.0593580i	0.388721	−	0.921356i	$-0.372917\pi$
$23$	−0.566827	−	0.284671i	−0.118192	−	0.0593580i	−0.506913	+	0.861997i	$0.669213\pi$
$24$	3.45817	+	3.47002i	0.705896	+	0.708316i
$25$	4.65141	+	1.10241i	0.930283	+	0.220481i
$26$	−7.96351	−	2.87777i	−1.56177	−	0.564377i
$27$	4.98270	+	1.47401i	0.958921	+	0.283673i
$28$	5.46285	−	6.57150i	1.03238	−	1.24190i
$29$	−6.28669	+	1.88211i	−1.16741	+	0.349499i	−0.811122	−	0.584877i	$-0.801143\pi$
$29$	−6.28669	+	1.88211i	−1.16741	+	0.349499i	−0.356287	+	0.934377i	$0.615957\pi$
$30$	0.290178	+	1.11095i	0.0529790	+	0.202830i
$31$	−2.91826	−	4.43700i	−0.524135	−	0.796908i	0.472286	−	0.881445i	$-0.343429\pi$
$31$	−2.91826	−	4.43700i	−0.524135	−	0.796908i	−0.996420	+	0.0845377i	$0.973059\pi$
$32$	5.48902	−	1.36774i	0.970330	−	0.241785i
$33$	−2.47922	−	4.09796i	−0.431577	−	0.713364i
$34$	−3.94075	−	1.68914i	−0.675833	−	0.289685i
$35$	1.88212	−	0.685036i	0.318136	−	0.115792i
$36$	4.41585	−	4.06206i	0.735974	−	0.677009i
$37$	−2.98790	−	1.08751i	−0.491208	−	0.178785i	0.0845274	−	0.996421i	$-0.473062\pi$
$37$	−2.98790	−	1.08751i	−0.491208	−	0.178785i	−0.575735	+	0.817636i	$0.695284\pi$
$38$	−7.66943	−	7.20249i	−1.24415	−	1.16840i
$39$	−3.91169	+	9.60455i	−0.626372	+	1.53796i
$40$	1.27274	+	0.371489i	0.201238	+	0.0587376i
$41$	8.26630	−	7.79885i	1.29098	−	1.21798i	0.329165	−	0.944272i	$-0.393233\pi$
$41$	8.26630	−	7.79885i	1.29098	−	1.21798i	0.961814	−	0.273703i	$-0.0882486\pi$
$42$	−7.77445	−	7.00706i	−1.19962	−	1.08121i
$43$	4.56266	−	3.39677i	0.695799	−	0.518003i	−0.190168	−	0.981752i	$-0.560903\pi$
$43$	4.56266	−	3.39677i	0.695799	−	0.518003i	0.885967	+	0.463748i	$0.153496\pi$
$44$	−5.53044	+	0.0254270i	−0.833746	+	0.00383327i
$45$	1.37375	−	0.300705i	0.204786	−	0.0448265i
$46$	0.450299	+	0.775817i	0.0663930	+	0.114388i
$47$	0.597073	+	0.392701i	0.0870921	+	0.0572814i	0.592308	−	0.805712i	$-0.298217\pi$
$47$	0.597073	+	0.392701i	0.0870921	+	0.0572814i	−0.505216	+	0.862993i	$0.668587\pi$
$48$	−1.40499	−	6.78425i	−0.202793	−	0.979222i
$49$	−6.72211	+	9.02936i	−0.960302	+	1.28991i
$50$	−4.65050	−	4.90660i	−0.657680	−	0.693898i
$51$	−2.26009	+	4.73983i	−0.316476	+	0.663710i
$52$	7.19500	+	9.57237i	0.997767	+	1.32745i
$53$	3.18889	−	1.84111i	0.438028	−	0.252895i	−0.264733	−	0.964322i	$-0.585284\pi$
$53$	3.18889	−	1.84111i	0.438028	−	0.252895i	0.702761	+	0.711426i	$0.251950\pi$
$54$	−4.75476	−	5.60288i	−0.647040	−	0.762456i
$55$	−1.12257	−	0.648117i	−0.151368	−	0.0873921i
$56$	−11.5534	+	3.54587i	−1.54389	+	0.473836i
$57$	−9.18973	+	9.03288i	−1.21721	+	1.19643i
$58$	8.89682	+	2.64126i	1.16821	+	0.346815i
$59$	1.27603	+	2.95816i	0.166125	+	0.385120i	0.980860	−	0.194712i	$-0.0623773\pi$
$59$	1.27603	+	2.95816i	0.166125	+	0.385120i	−0.814736	+	0.579832i	$0.803118\pi$
$60$	0.516943	−	1.53934i	0.0667370	−	0.198728i
$61$	0.334705	−	5.74666i	0.0428545	−	0.735784i	−0.906622	−	0.421945i	$-0.861348\pi$
$61$	0.334705	−	5.74666i	0.0428545	−	0.735784i	0.949476	−	0.313839i	$-0.101615\pi$
$62$	0.0172650	+	7.51039i	0.00219266	+	0.953821i
$63$	−8.95572	+	9.17096i	−1.12832	+	1.15543i
$64$	−7.55456	−	2.63222i	−0.944321	−	0.329027i
$65$	0.325834	+	2.78769i	0.0404147	+	0.345770i
$66$	−0.239715	+	6.76921i	−0.0295068	+	0.833232i
$67$	−0.618183	−	0.185072i	−0.0755231	−	0.0226101i	0.248819	−	0.968550i	$-0.419958\pi$
$67$	−0.618183	−	0.185072i	−0.0755231	−	0.0226101i	−0.324342	+	0.945940i	$0.605143\pi$
$68$	3.35518	+	5.05056i	0.406875	+	0.612471i
$69$	0.971469	−	0.513068i	0.116951	−	0.0617661i
$70$	−2.75769	−	0.646892i	−0.329606	−	0.0773183i
$71$	6.02886	−	5.05881i	0.715494	−	0.600371i	−0.210641	−	0.977564i	$-0.567555\pi$
$71$	6.02886	−	5.05881i	0.715494	−	0.600371i	0.926135	+	0.377193i	$0.123111\pi$
$72$	−8.37113	+	1.38715i	−0.986547	+	0.163477i
$73$	1.12442	+	0.943504i	0.131604	+	0.110429i	0.706214	−	0.707999i	$-0.250402\pi$
$73$	1.12442	+	0.943504i	0.131604	+	0.110429i	−0.574610	+	0.818427i	$0.694846\pi$
$74$	2.69354	+	3.60074i	0.313117	+	0.418577i
$75$	−6.23227	+	5.45084i	−0.719640	+	0.629409i
$76$	3.49792	+	14.4622i	0.401239	+	1.65893i
$77$	11.7954	−	0.687003i	1.34421	−	0.0782912i
$78$	12.0667	−	8.33622i	1.36628	−	0.943891i
$79$	−3.18709	−	3.00686i	−0.358575	−	0.338298i	0.485781	−	0.874081i	$-0.338535\pi$
$79$	−3.18709	−	3.00686i	−0.358575	−	0.338298i	−0.844356	+	0.535782i	$0.820017\pi$
$80$	−1.21840	−	1.42522i	−0.136222	−	0.159344i
$81$	−7.08946	+	5.54433i	−0.787718	+	0.616036i
$82$	−15.8213	+	2.82724i	−1.74717	+	0.312217i
$83$	9.78501	−	10.3715i	1.07404	−	1.13842i	0.0841734	−	0.996451i	$-0.473175\pi$
$83$	9.78501	−	10.3715i	1.07404	−	1.13842i	0.989871	−	0.141970i	$-0.0453435\pi$
$84$	3.77353	+	14.3123i	0.411725	+	1.56160i
$85$	0.0826323	+	1.41874i	0.00896273	+	0.153884i
$86$	−8.02966	+	0.486199i	−0.865861	+	0.0524281i
$87$	3.66797	−	10.7583i	0.393248	−	1.15341i
$88$	6.56409	+	4.25271i	0.699735	+	0.453341i
$89$	−11.2165	+	13.3673i	−1.18894	+	1.41693i	−0.303089	+	0.952962i	$0.598018\pi$
$89$	−11.2165	+	13.3673i	−1.18894	+	1.41693i	−0.885854	+	0.463965i	$0.846426\pi$
$90$	−1.85848	−	0.708000i	−0.195901	−	0.0746298i
$91$	−16.4446	−	19.5979i	−1.72386	−	2.05441i
$92$	0.0679386	−	1.26677i	0.00708309	−	0.132070i
$93$	9.19181	+	0.346663i	0.953146	+	0.0359473i
$94$	−0.402432	−	0.927076i	−0.0415077	−	0.0956206i
$95$	−1.00019	+	3.34088i	−0.102618	+	0.342767i
$96$	−3.59117	+	9.11611i	−0.366522	+	0.930409i
$97$	−6.61046	+	0.772651i	−0.671190	+	0.0784509i	−0.444860	−	0.895600i	$-0.646747\pi$
$97$	−6.61046	+	0.772651i	−0.671190	+	0.0784509i	−0.226330	+	0.974051i	$0.572673\pi$
$98$	14.9469	−	5.47919i	1.50987	−	0.553481i
$99$	8.27219	+	0.624850i	0.831386	+	0.0627998i
$100$	1.70344	+	9.40755i	0.170344	+	0.940755i
$101$	−17.5045	−	1.01952i	−1.74177	−	0.101446i	−0.842457	−	0.538763i	$-0.818892\pi$
$101$	−17.5045	−	1.01952i	−1.74177	−	0.101446i	−0.899308	+	0.437317i	$0.855929\pi$
$102$	6.34501	−	3.85862i	0.628250	−	0.382060i
$103$	−3.09433	+	1.33476i	−0.304893	+	0.131518i	−0.543029	−	0.839714i	$-0.682723\pi$
$103$	−3.09433	+	1.33476i	−0.304893	+	0.131518i	0.238136	+	0.971232i	$0.423463\pi$
$104$	−1.10126	−	16.8992i	−0.107987	−	1.65710i
$105$	−0.926690	+	3.34308i	−0.0904357	+	0.326251i
$106$	−5.19931	−	0.290834i	−0.505001	−	0.0282483i
$107$	−0.273062	+	0.472958i	−0.0263979	+	0.0457226i	−0.878923	−	0.476964i	$-0.841737\pi$
$107$	−0.273062	+	0.472958i	−0.0263979	+	0.0457226i	0.852525	+	0.522687i	$0.175070\pi$
$108$	1.28760	+	10.3122i	0.123899	+	0.992295i
$109$	3.43891	+	5.95636i	0.329388	+	0.570516i	0.982390	−	0.186839i	$-0.0598244\pi$
$109$	3.43891	+	5.95636i	0.329388	+	0.570516i	−0.653003	+	0.757355i	$0.726491\pi$
$110$	0.826481	+	1.63627i	0.0788018	+	0.156012i
$111$	4.53836	−	3.11993i	0.430763	−	0.296130i
$112$	16.4176	+	4.75105i	1.55132	+	0.448932i
$113$	−0.433437	−	0.322682i	−0.0407743	−	0.0303553i	0.576579	−	0.817042i	$-0.304387\pi$
$113$	−0.433437	−	0.322682i	−0.0407743	−	0.0303553i	−0.617353	+	0.786686i	$0.711795\pi$
$114$	17.8697	−	3.57240i	1.67365	−	0.334586i
$115$	0.163386	−	0.248416i	0.0152358	−	0.0231650i
$116$	−8.48257	−	10.0153i	−0.787586	−	0.929893i
$117$	−9.61066	−	15.1750i	−0.888506	−	1.40293i
$118$	0.780840	−	4.48868i	0.0718822	−	0.413216i
$119$	−7.73557	−	10.3907i	−0.709118	−	0.952511i
$120$	−1.80380	+	1.42125i	−0.164663	+	0.129741i
$121$	2.30123	+	2.43917i	0.209203	+	0.221742i
$122$	−4.84631	+	6.54106i	−0.438764	+	0.592200i
$123$	2.68509	+	19.5000i	0.242107	+	1.75826i
$124$	5.79565	−	8.90073i	0.520465	−	0.799309i
$125$	−1.56802	+	4.30810i	−0.140248	+	0.385328i
$126$	17.6997	−	3.91702i	1.57682	−	0.348956i
$127$	1.18587	+	3.25816i	0.105229	+	0.289115i	0.981122	−	0.193391i	$-0.0619487\pi$
$127$	1.18587	+	3.25816i	0.105229	+	0.289115i	−0.875892	+	0.482507i	$0.839726\pi$
$128$	6.90123	+	8.96510i	0.609988	+	0.792410i
$129$	0.201772	+	9.85024i	0.0177650	+	0.867265i
$130$	1.77323	−	3.55111i	0.155522	−	0.311453i
$131$	5.01118	−	3.29590i	0.437829	−	0.287964i	−0.311396	−	0.950280i	$-0.600797\pi$
$131$	5.01118	−	3.29590i	0.437829	−	0.287964i	0.749225	+	0.662316i	$0.230426\pi$
$132$	5.52577	−	7.82465i	0.480957	−	0.681049i
$133$	−9.11691	−	30.4526i	−0.790537	−	2.64058i
$134$	0.588202	+	0.697728i	0.0508129	+	0.0602745i
$135$	−0.957438	+	2.23967i	−0.0824031	+	0.192760i
$136$	−0.0591365	−	8.57481i	−0.00507091	−	0.735284i
$137$	1.78174	−	7.51773i	0.152224	−	0.642283i	−0.842411	−	0.538836i	$-0.818864\pi$
$137$	1.78174	−	7.51773i	0.152224	−	0.642283i	0.994635	−	0.103448i	$-0.0329874\pi$
$138$	−1.54690	−	0.145176i	−0.131681	−	0.0123582i
$139$	−8.01954	+	15.9682i	−0.680209	+	1.35441i	0.242969	+	0.970034i	$0.421879\pi$
$139$	−8.01954	+	15.9682i	−0.680209	+	1.35441i	−0.923178	+	0.384373i	$0.874418\pi$
$140$	2.76233	+	2.90106i	0.233459	+	0.245184i
$141$	−1.15423	+	0.447082i	−0.0972038	+	0.0376511i
$142$	−11.0518	+	1.31753i	−0.927444	+	0.110564i
$143$	−2.87506	+	16.3053i	−0.240424	+	1.36351i
$144$	10.9801	+	4.84117i	0.915010	+	0.403431i
$145$	−0.534171	−	3.02943i	−0.0443605	−	0.251581i
$146$	−0.599924	−	1.98725i	−0.0496501	−	0.164466i
$147$	−5.97327	−	18.5599i	−0.492667	−	1.53079i
$148$	−0.398946	−	6.34679i	−0.0327931	−	0.521703i
$149$	0.473918	+	1.99962i	0.0388249	+	0.163815i	0.989004	−	0.147890i	$-0.0472481\pi$
$149$	0.473918	+	1.99962i	0.0388249	+	0.163815i	−0.950179	+	0.311705i	$0.899100\pi$
$150$	11.5961	−	1.62391i	0.946814	−	0.132592i
$151$	8.58724	+	3.70418i	0.698820	+	0.301441i	0.715692	−	0.698416i	$-0.246112\pi$
$151$	8.58724	+	3.70418i	0.698820	+	0.301441i	−0.0168719	+	0.999858i	$0.505371\pi$
$152$	7.06040	−	19.8226i	0.572674	−	1.60782i
$153$	−4.41132	−	7.95377i	−0.356634	−	0.643024i
$154$	−14.4900	−	8.32144i	−1.16764	−	0.670561i
$155$	2.22462	−	1.11725i	0.178686	−	0.0897395i
$156$	−20.7346	+	0.520107i	−1.66010	+	0.0416419i
$157$	1.75114	+	0.204679i	0.139756	+	0.0163351i	0.185683	−	0.982610i	$-0.440550\pi$
$157$	1.75114	+	0.204679i	0.139756	+	0.0163351i	−0.0459273	+	0.998945i	$0.514624\pi$
$158$	1.44288	+	6.02624i	0.114790	+	0.479422i
$159$	−0.610528	+	6.34849i	−0.0484180	+	0.503468i
$160$	0.338095	+	2.63005i	0.0267287	+	0.207924i
$161$			2.71022i			0.213595i
$162$	12.6828	−	1.07072i	0.996455	−	0.0841237i
$163$			1.71941i			0.134674i	0.997730	+	0.0673371i	$0.0214503\pi$
$163$			1.71941i			0.134674i	−0.997730	+	0.0673371i	$0.978550\pi$
$164$	20.9115	+	8.90651i	1.63291	+	0.695482i
$165$	2.04288	−	0.931289i	0.159038	−	0.0725007i
$166$	−19.6108	+	4.69547i	−1.52209	+	0.364439i
$167$	17.0444	+	1.99220i	1.31893	+	0.154161i	0.746277	−	0.665636i	$-0.231840\pi$
$167$	17.0444	+	1.99220i	1.31893	+	0.154161i	0.572655	+	0.819797i	$0.305914\pi$
$168$	6.61816	−	19.8586i	0.510602	−	1.53212i
$169$	20.4191	−	10.2549i	1.57070	−	0.788835i
$170$	1.00090	−	1.74285i	0.0767654	−	0.133670i
$171$	−3.49669	−	22.0433i	−0.267398	−	1.68569i
$172$	9.87835	+	5.64287i	0.753217	+	0.430265i
$173$	2.33941	+	1.00912i	0.177862	+	0.0767223i	0.483149	−	0.875538i	$-0.339493\pi$
$173$	2.33941	+	1.00912i	0.177862	+	0.0767223i	−0.305287	+	0.952261i	$0.598752\pi$
$174$	−12.6717	+	9.89021i	−0.960641	+	0.749775i
$175$	−4.71036	−	19.8746i	−0.356070	−	1.50238i
$176$	−4.47424	−	10.1157i	−0.337259	−	0.762498i
$177$	−5.45485	−	1.17538i	−0.410012	−	0.0883470i
$178$	23.6246	−	7.13195i	1.77074	−	0.534562i
$179$	−2.52971	−	14.3467i	−0.189079	−	1.07232i	−0.920601	−	0.390504i	$-0.872301\pi$
$179$	−2.52971	−	14.3467i	−0.189079	−	1.07232i	0.731522	−	0.681818i	$-0.238810\pi$
$180$	1.65094	+	2.27702i	0.123054	+	0.169719i
$181$	−1.71890	+	9.74838i	−0.127765	+	0.724591i	0.851862	+	0.523766i	$0.175473\pi$
$181$	−1.71890	+	9.74838i	−0.127765	+	0.724591i	−0.979627	+	0.200825i	$0.935638\pi$
$182$	4.28285	+	35.9257i	0.317466	+	2.66299i
$183$	7.76740	+	6.25107i	0.574182	+	0.462092i
$184$	−1.06139	+	1.44641i	−0.0782465	+	0.106631i
$185$	0.668931	−	1.33195i	0.0491808	−	0.0979270i
$186$	−10.6086	−	7.52840i	−0.777859	−	0.552009i
$187$	−1.93336	+	8.15750i	−0.141382	+	0.596536i
$188$	−0.241718	+	1.40869i	−0.0176291	+	0.102739i
$189$	−3.92674	−	21.8521i	−0.285628	−	1.58951i
$190$	3.77076	−	3.17885i	0.273560	−	0.230618i
$191$	3.41905	+	11.4204i	0.247394	+	0.826352i	0.988005	+	0.154419i	$0.0493506\pi$
$191$	3.41905	+	11.4204i	0.247394	+	0.826352i	−0.740612	+	0.671933i	$0.765464\pi$
$192$	11.3091	−	8.00646i	0.816167	−	0.577816i
$193$	−9.44575	+	6.21257i	−0.679920	+	0.447191i	−0.841922	−	0.539600i	$-0.818575\pi$
$193$	−9.44575	+	6.21257i	−0.679920	+	0.447191i	0.162001	+	0.986791i	$0.448205\pi$
$194$	8.42077	+	4.20486i	0.604576	+	0.301891i
$195$	−4.25889	−	2.34391i	−0.304986	−	0.167851i
$196$	−21.9304	−	5.09123i	−1.56646	−	0.363660i
$197$	−1.83879	−	5.05205i	−0.131009	−	0.359943i	0.856793	−	0.515660i	$-0.172453\pi$
$197$	−1.83879	−	5.05205i	−0.131009	−	0.359943i	−0.987802	+	0.155717i	$0.950231\pi$
$198$	−9.30494	−	7.14543i	−0.661273	−	0.507804i
$199$	−1.83701	+	5.04713i	−0.130222	+	0.357782i	−0.987619	−	0.156875i	$-0.949858\pi$
$199$	−1.83701	+	5.04713i	−0.130222	+	0.357782i	0.857397	+	0.514656i	$0.172080\pi$
$200$	5.26950	−	12.4515i	0.372610	−	0.880454i
$201$	0.882660	−	0.685652i	0.0622580	−	0.0483622i
$202$	19.9243	+	14.7620i	1.40187	+	1.03865i
$203$	19.2420	+	20.3954i	1.35053	+	1.43147i
$204$	−10.4964	−	0.347548i	−0.734898	−	0.0243332i
$205$	3.18121	+	4.27310i	0.222185	+	0.298447i
$206$	4.69529	+	0.816782i	0.327136	+	0.0569079i
$207$	−0.253415	+	1.88594i	−0.0176135	+	0.131082i
$208$	−11.7837	+	20.8504i	−0.817051	+	1.44571i
$209$	−11.3047	+	17.1880i	−0.781965	+	1.18892i
$210$	3.68549	−	3.23837i	0.254323	−	0.223469i
$211$	−2.06643	−	1.53840i	−0.142259	−	0.105908i	0.523677	−	0.851917i	$-0.324560\pi$
$211$	−2.06643	−	1.53840i	−0.142259	−	0.105908i	−0.665935	+	0.746009i	$0.731967\pi$
$212$	5.92733	+	4.37053i	0.407091	+	0.300169i
$213$	1.07113	+	13.5893i	0.0733924	+	0.931123i
$214$	0.689387	−	0.348210i	0.0471255	−	0.0238031i
$215$	1.33320	+	2.30917i	0.0909236	+	0.157484i
$216$	6.46217	−	13.2000i	0.439695	−	0.898147i
$217$	−11.3457	+	19.6513i	−0.770197	+	1.33402i
$218$	0.543234	−	9.71152i	0.0367924	−	0.657747i
$219$	−2.46130	+	0.636849i	−0.166319	+	0.0430342i
$220$	0.289125	−	2.57629i	0.0194928	−	0.173694i
$221$	16.6677	−	7.18976i	1.12119	−	0.483635i
$222$	−7.78652	+	0.177407i	−0.522597	+	0.0119068i
$223$	−8.74007	−	0.509051i	−0.585278	−	0.0340886i	−0.237048	−	0.971498i	$-0.576180\pi$
$223$	−8.74007	−	0.509051i	−0.585278	−	0.0340886i	−0.348230	+	0.937409i	$0.613217\pi$
$224$	−15.7484	−	18.3360i	−1.05223	−	1.22512i
$225$	−1.41942	−	14.2704i	−0.0946278	−	0.951359i
$226$	0.263017	+	0.717498i	0.0174957	+	0.0477273i
$227$	2.23649	−	0.261408i	0.148441	−	0.0173502i	−0.0415479	−	0.999137i	$-0.513229\pi$
$227$	2.23649	−	0.261408i	0.148441	−	0.0173502i	0.189989	+	0.981786i	$0.439155\pi$
$228$	−23.9124	−	9.61101i	−1.58364	−	0.636505i
$229$	0.134999	−	0.450928i	0.00892098	−	0.0297982i	−0.953413	−	0.301668i	$-0.902457\pi$
$229$	0.134999	−	0.450928i	0.00892098	−	0.0297982i	0.962334	+	0.271869i	$0.0876419\pi$
$230$	−0.385716	+	0.167435i	−0.0254334	+	0.0110403i
$231$	−10.8931	+	17.3248i	−0.716712	+	1.13989i
$232$	2.28191	+	18.4204i	0.149815	+	1.20936i
$233$	−6.62380	−	7.89394i	−0.433939	−	0.517149i	0.504115	−	0.863636i	$-0.331819\pi$
$233$	−6.62380	−	7.89394i	−0.433939	−	0.517149i	−0.938055	+	0.346488i	$0.887374\pi$
$234$	−0.378907	+	25.3998i	−0.0247699	+	1.66043i
$235$	−0.215330	+	0.256620i	−0.0140466	+	0.0167400i
$236$	−4.40006	+	4.70695i	−0.286419	+	0.306397i
$237$	7.44536	−	1.47064i	0.483628	−	0.0955284i
$238$	1.10723	+	18.2862i	0.0717712	+	1.18532i
$239$	−1.33463	−	22.9148i	−0.0863302	−	1.48223i	−0.712019	−	0.702160i	$-0.752219\pi$
$239$	−1.33463	−	22.9148i	−0.0863302	−	1.48223i	0.625689	−	0.780073i	$-0.284818\pi$
$240$	3.23513	−	0.284952i	0.208827	−	0.0183936i
$241$	−4.65448	+	4.93346i	−0.299821	+	0.317792i	−0.859717	−	0.510771i	$-0.829360\pi$
$241$	−4.65448	+	4.93346i	−0.299821	+	0.317792i	0.559895	+	0.828563i	$0.310841\pi$
$242$	−0.834244	−	4.66845i	−0.0536272	−	0.300100i
$243$	−0.689220	−	15.5732i	−0.0442135	−	0.999022i
$244$	10.8003	−	3.98730i	0.691416	−	0.255261i
$245$	−3.83815	−	3.62111i	−0.245211	−	0.231344i
$246$	11.9235	−	25.1546i	0.760217	−	1.60380i
$247$	44.4690	−	2.59003i	2.82950	−	0.164799i
$248$	−13.7510	+	6.04442i	−0.873190	+	0.383821i
$249$	4.78580	+	24.2289i	0.303288	+	1.53544i
$250$	5.19171	−	3.88367i	0.328353	−	0.245625i
$251$	17.9443	+	15.0570i	1.13263	+	0.950391i	0.999173	−	0.0406636i	$-0.0129472\pi$
$251$	17.9443	+	15.0570i	1.13263	+	0.950391i	0.133459	+	0.991054i	$0.457392\pi$
$252$	−23.9782	−	9.07157i	−1.51048	−	0.571455i
$253$	1.34363	−	1.12744i	0.0844734	−	0.0708816i
$254$	1.11984	−	4.77387i	0.0702652	−	0.299539i
$255$	−2.08382	−	1.31021i	−0.130494	−	0.0820487i
$256$	−1.22389	−	15.9531i	−0.0764933	−	0.997070i
$257$	−3.79756	−	1.13691i	−0.236885	−	0.0709187i	0.166160	−	0.986099i	$-0.446863\pi$
$257$	−3.79756	−	1.13691i	−0.236885	−	0.0709187i	−0.403045	+	0.915180i	$0.632048\pi$
$258$	7.38930	−	11.8124i	0.460038	−	0.735411i
$259$	1.57724	+	13.4942i	0.0980052	+	0.838488i
$260$	−4.84833	+	2.82899i	−0.300681	+	0.175446i
$261$	11.4828	+	15.9915i	0.710765	+	0.989852i
$262$	−8.48230	+	0.0194992i	−0.524038	+	0.00120467i
$263$	−0.726793	+	12.4785i	−0.0448160	+	0.769460i	0.898788	+	0.438384i	$0.144449\pi$
$263$	−0.726793	+	12.4785i	−0.0448160	+	0.769460i	−0.943604	+	0.331077i	$0.892588\pi$
$264$	−12.5983	+	4.98005i	−0.775373	+	0.306501i
$265$	0.683660	+	1.58490i	0.0419969	+	0.0973598i
$266$	−12.7942	+	43.0960i	−0.784464	+	2.64239i
$267$	−7.57092	−	29.2602i	−0.463333	−	1.79070i
$268$	−0.155720	−	1.28116i	−0.00951209	−	0.0782591i
$269$	13.7973	+	7.96585i	0.841233	+	0.485686i	0.857683	−	0.514178i	$-0.171903\pi$
$269$	13.7973	+	7.96585i	0.841233	+	0.485686i	−0.0164499	+	0.999865i	$0.505236\pi$
$270$	2.86739	−	1.90885i	0.174504	−	0.116169i
$271$	−5.09165	+	2.93967i	−0.309296	+	0.178572i	−0.646611	−	0.762820i	$-0.723814\pi$
$271$	−5.09165	+	2.93967i	−0.309296	+	0.178572i	0.337316	+	0.941392i	$0.390481\pi$
$272$	−6.57039	+	10.1927i	−0.398389	+	0.618024i
$273$	44.1744	−	3.48188i	2.67355	−	0.210733i
$274$	−7.93017	+	7.51626i	−0.479079	+	0.454074i
$275$	−7.89362	+	10.6030i	−0.476003	+	0.639383i
$276$	1.71809	+	1.36972i	0.103417	+	0.0824475i
$277$	−12.3902	−	8.14914i	−0.744453	−	0.489635i	0.119733	−	0.992806i	$-0.461796\pi$
$277$	−12.3902	−	8.14914i	−0.744453	−	0.489635i	−0.864187	+	0.503171i	$0.832166\pi$
$278$	21.8557	−	12.6855i	1.31082	−	0.760825i
$279$	−9.73251	+	12.6137i	−0.582670	+	0.755165i
$280$	−1.02218	−	5.57210i	−0.0610871	−	0.332997i
$281$	−2.92434	+	2.17709i	−0.174451	+	0.129874i	−0.680843	−	0.732429i	$-0.738386\pi$
$281$	−2.92434	+	2.17709i	−0.174451	+	0.129874i	0.506392	+	0.862304i	$0.330979\pi$
$282$	1.71207	+	0.364791i	0.101952	+	0.0217230i
$283$	−15.1235	+	14.2683i	−0.898999	+	0.848162i	−0.989021	−	0.147778i	$-0.952788\pi$
$283$	−15.1235	+	14.2683i	−0.898999	+	0.848162i	0.0900213	+	0.995940i	$0.471306\pi$
$284$	14.0983	+	6.99946i	0.836581	+	0.415341i
$285$	−3.70550	−	4.77020i	−0.219495	−	0.282562i
$286$	16.0291	−	17.0682i	0.947818	−	1.00927i
$287$	−45.6302	−	16.6080i	−2.69346	−	0.980341i
$288$	−9.24420	−	14.2318i	−0.544720	−	0.838618i
$289$	−7.33773	+	2.67072i	−0.431631	+	0.157101i
$290$	−1.71390	+	3.99852i	−0.100644	+	0.234801i
$291$	5.55813	−	10.0991i	0.325824	−	0.592022i
$292$	−0.829019	+	2.81618i	−0.0485147	+	0.164804i
$293$	2.28238	+	3.47020i	0.133338	+	0.202731i	0.895985	−	0.444084i	$-0.146471\pi$
$293$	2.28238	+	3.47020i	0.133338	+	0.202731i	−0.762647	+	0.646815i	$0.776101\pi$
$294$	−7.30443	+	26.5884i	−0.426003	+	1.55067i
$295$	−1.44673	+	0.433122i	−0.0842318	+	0.0252173i
$296$	−4.44290	+	7.81937i	−0.258238	+	0.454492i
$297$	−9.20001	+	11.0371i	−0.533838	+	0.640440i
$298$	0.987707	−	2.73324i	0.0572163	−	0.158332i
$299$	−3.69544	−	0.875835i	−0.213713	−	0.0506509i
$300$	−14.9797	−	7.05840i	−0.864851	−	0.407517i
$301$	−21.7194	−	10.9079i	−1.25189	−	0.628722i
$302$	−7.29311	−	11.0333i	−0.419671	−	0.634895i
$303$	19.0410	−	23.6598i	1.09388	−	1.35922i
$304$	−23.7056	+	17.9893i	−1.35961	+	1.03176i
$305$	2.65736	+	0.468565i	0.152160	+	0.0268299i
$306$	−0.939339	+	12.8282i	−0.0536984	+	0.733338i
$307$	−25.0611	+	4.41895i	−1.43031	+	0.252203i	−0.834539	−	0.550949i	$-0.814266\pi$
$307$	−25.0611	+	4.41895i	−1.43031	+	0.252203i	−0.595774	+	0.803152i	$0.703155\pi$
$308$	10.7024	+	21.0682i	0.609828	+	1.20047i
$309$	1.22948	−	5.70594i	0.0699428	−	0.324599i
$310$	−3.49769	−	0.400673i	−0.198656	−	0.0227567i
$311$	−30.7952	+	7.29861i	−1.74624	+	0.413866i	−0.974915	−	0.222578i	$-0.928553\pi$
$311$	−30.7952	+	7.29861i	−1.74624	+	0.413866i	−0.771323	+	0.636444i	$0.780405\pi$
$312$	24.9389	+	15.4415i	1.41189	+	0.874204i
$313$	8.29213	−	19.2233i	0.468699	−	1.08657i	−0.505897	−	0.862594i	$-0.668838\pi$
$313$	8.29213	−	19.2233i	0.468699	−	1.08657i	0.974596	−	0.223972i	$-0.0719023\pi$
$314$	−1.91369	−	1.59829i	−0.107996	−	0.0901969i
$315$	−3.78253	−	4.66876i	−0.213121	−	0.263055i
$316$	2.95932	−	8.24847i	0.166475	−	0.464013i
$317$	−3.36461	−	6.69949i	−0.188975	−	0.376281i	0.779115	−	0.626880i	$-0.215669\pi$
$317$	−3.36461	−	6.69949i	−0.188975	−	0.376281i	−0.968091	+	0.250600i	$0.919372\pi$
$318$	5.63877	−	7.03964i	0.316206	−	0.394763i
$319$	2.10669	−	18.0239i	0.117952	−	1.00915i
$320$	1.63665	−	3.37407i	0.0914912	−	0.188617i
$321$	−0.392367	−	0.860700i	−0.0218998	−	0.0480396i
$322$	2.09881	−	3.20711i	0.116962	−	0.178725i
$323$	22.5549			1.25499
$324$	−15.8373	−	8.55460i	−0.879848	−	0.475255i
$325$	28.6216			1.58764
$326$	1.33152	−	2.03464i	0.0737458	−	0.112688i
$327$	−11.8580	−	1.14037i	−0.655750	−	0.0630628i
$328$	−17.8481	−	26.7334i	−0.985499	−	1.47610i
$329$	0.354492	−	3.03287i	0.0195438	−	0.167207i
$330$	−3.13862	−	0.479985i	−0.172775	−	0.0264223i
$331$	11.9976	+	23.8891i	0.659446	+	1.31307i	0.935977	+	0.352060i	$0.114519\pi$
$331$	11.9976	+	23.8891i	0.659446	+	1.31307i	−0.276531	+	0.961005i	$0.589185\pi$
$332$	26.8424	+	9.63031i	1.47317	+	0.528532i
$333$	−0.164209	+	9.53756i	−0.00899862	+	0.522655i
$334$	−18.6265	−	15.5567i	−1.01920	−	0.851224i
$335$	0.119809	−	0.277748i	0.00654584	−	0.0151750i
$336$	−23.2101	+	18.3744i	−1.26622	+	1.00240i
$337$	−23.6696	+	5.60979i	−1.28936	+	0.305585i	−0.817419	−	0.576043i	$-0.804596\pi$
$337$	−23.6696	+	5.60979i	−1.28936	+	0.305585i	−0.471945	+	0.881628i	$0.656448\pi$
$338$	−32.1042	−	3.67765i	−1.74624	−	0.200038i
$339$	0.890930	−	0.286735i	0.0483887	−	0.0155733i
$340$	−2.53407	+	1.28728i	−0.137429	+	0.0698127i
$341$	14.4622	−	2.55008i	0.783173	−	0.138095i
$342$	−12.9326	+	28.7926i	−0.699317	+	1.55692i
$343$	17.9123	+	3.15841i	0.967171	+	0.170538i
$344$	−7.31959	−	14.3273i	−0.394646	−	0.772476i
$345$	0.186012	+	0.480226i	0.0100145	+	0.0258545i
$346$	−1.98685	−	3.00579i	−0.106814	−	0.161592i
$347$	−17.3113	−	8.69407i	−0.929320	−	0.466722i	−0.0813023	−	0.996689i	$-0.525908\pi$
$347$	−17.3113	−	8.69407i	−0.929320	−	0.466722i	−0.848018	+	0.529967i	$0.822204\pi$
$348$	22.6540	−	1.89046i	1.21438	−	0.101339i
$349$	17.6586	+	4.18517i	0.945245	+	0.224027i	0.674208	−	0.738542i	$-0.264485\pi$
$349$	17.6586	+	4.18517i	0.945245	+	0.224027i	0.271037	+	0.962569i	$0.412633\pi$
$350$	−9.81700	+	27.1661i	−0.524740	+	1.45209i
$351$	31.0648	+	1.70755i	1.65812	+	0.0911420i
$352$	−2.53907	+	15.4352i	−0.135333	+	0.822698i
$353$	6.05926	−	1.81402i	0.322502	−	0.0965507i	−0.121460	−	0.992596i	$-0.538758\pi$
$353$	6.05926	−	1.81402i	0.322502	−	0.0965507i	0.443962	+	0.896046i	$0.353573\pi$
$354$	5.54473	+	5.61514i	0.294699	+	0.298441i
$355$	2.02724	+	3.08227i	0.107595	+	0.163590i
$356$	−33.4790	−	9.85545i	−1.77438	−	0.522338i
$357$	22.4322	−	0.459501i	1.18724	−	0.0243194i
$358$	−8.11664	+	18.9361i	−0.428978	+	1.00080i
$359$	2.54468	−	0.926186i	0.134303	−	0.0488822i	−0.273994	−	0.961731i	$-0.588345\pi$
$359$	2.54468	−	0.926186i	0.134303	−	0.0488822i	0.408297	+	0.912849i	$0.366123\pi$
$360$	−0.190287	−	3.97299i	−0.0100290	−	0.209395i
$361$	34.1560	+	12.4318i	1.79768	+	0.654303i
$362$	9.58324	−	10.2045i	0.503684	−	0.536338i
$363$	−5.75394	+	0.792300i	−0.302004	+	0.0415850i
$364$	22.7530	−	45.8290i	1.19258	−	2.40209i
$365$	−0.500475	+	0.472174i	−0.0261961	+	0.0247147i
$366$	−4.35062	−	13.4123i	−0.227411	−	0.701070i
$367$	14.9057	−	11.0969i	0.778072	−	0.579253i	−0.133185	−	0.991091i	$-0.542521\pi$
$367$	14.9057	−	11.0969i	0.778072	−	0.579253i	0.911257	+	0.411838i	$0.135113\pi$
$368$	2.37609	−	0.889653i	0.123862	−	0.0463764i
$369$	−30.1994	−	15.8235i	−1.57212	−	0.823737i
$370$	−1.82304	+	1.05813i	−0.0947755	+	0.0550096i
$371$	−13.1450	−	8.64563i	−0.682456	−	0.448859i
$372$	6.72355	+	17.1240i	0.348600	+	0.887838i
$373$	2.54215	−	3.41470i	0.131628	−	0.176807i	−0.731423	−	0.681924i	$-0.761143\pi$
$373$	2.54215	−	3.41470i	0.131628	−	0.176807i	0.863051	+	0.505117i	$0.168551\pi$
$374$	8.60504	−	8.15590i	0.444956	−	0.421732i
$375$	−4.49845	−	6.54362i	−0.232299	−	0.337911i
$376$	1.37693	−	1.47978i	0.0710099	−	0.0763137i
$377$	−34.0278	+	19.6460i	−1.75252	+	1.01182i
$378$	−12.2757	+	28.8994i	−0.631394	+	1.48643i
$379$	18.2776	+	10.5526i	0.938857	+	0.542049i	0.889602	−	0.456737i	$-0.150982\pi$
$379$	18.2776	+	10.5526i	0.938857	+	0.542049i	0.0492553	+	0.998786i	$0.484315\pi$
$380$	−6.92381	+	0.841563i	−0.355184	+	0.0431713i
$381$	−5.78725	−	1.60421i	−0.296490	−	0.0821860i
$382$	4.79812	−	16.1620i	0.245493	−	0.826919i
$383$	−7.02759	−	16.2918i	−0.359093	−	0.832471i	−0.998002	−	0.0631884i	$-0.979873\pi$
$383$	−7.02759	−	16.2918i	−0.359093	−	0.832471i	0.638909	−	0.769283i	$-0.279386\pi$
$384$	−19.5828	+	0.716517i	−0.999331	+	0.0365646i
$385$	−0.322038	+	5.52918i	−0.0164126	+	0.281793i
$386$	15.9886	−	0.0367548i	0.813798	−	0.00187077i
$387$	−14.0938	−	9.62124i	−0.716428	−	0.489075i
$388$	−6.70839	−	11.4969i	−0.340567	−	0.583665i
$389$	−3.03504	−	25.9665i	−0.153883	−	1.31655i	−0.820712	−	0.571342i	$-0.806423\pi$
$389$	−3.03504	−	25.9665i	−0.153883	−	1.31655i	0.666830	−	0.745210i	$-0.267651\pi$
$390$	3.22459	+	6.07176i	0.163283	+	0.307455i
$391$	−1.84222	−	0.551525i	−0.0931652	−	0.0278918i
$392$	22.0085	+	23.0077i	1.11160	+	1.16206i
$393$	−0.391524	+	10.3813i	−0.0197498	+	0.523667i
$394$	−1.73641	+	7.40227i	−0.0874789	+	0.372921i
$395$	1.57340	−	1.32024i	0.0791663	−	0.0664284i
$396$	5.47746	+	15.6613i	0.275253	+	0.787009i
$397$	19.8598	+	16.6644i	0.996736	+	0.836361i	0.986529	−	0.163587i	$-0.0523065\pi$
$397$	19.8598	+	16.6644i	0.996736	+	0.836361i	0.0102070	+	0.999948i	$0.496751\pi$
$398$	6.08233	−	4.54989i	0.304880	−	0.228066i
$399$	52.1129	+	17.7676i	2.60891	+	0.889492i
$400$	−15.8781	+	10.6536i	−0.793906	+	0.532682i
$401$	27.8719	−	1.62335i	1.39186	−	0.0810664i	0.654240	−	0.756287i	$-0.272989\pi$
$401$	27.8719	−	1.62335i	1.39186	−	0.0810664i	0.737616	+	0.675221i	$0.235952\pi$
$402$	−1.57546	+	0.127825i	−0.0785768	+	0.00637532i
$403$	−23.1285	−	21.8207i	−1.15211	−	1.08696i
$404$	−12.1455	−	32.8980i	−0.604260	−	1.63674i
$405$	−2.19557	−	3.60249i	−0.109099	−	0.179009i
$406$	−6.97563	−	39.0358i	−0.346195	−	1.93731i
$407$	6.03382	−	6.39547i	0.299085	−	0.317012i
$408$	12.1517	+	8.53977i	0.601601	+	0.422782i
$409$	0.299265	+	5.13819i	0.0147977	+	0.254067i	0.997592	+	0.0693613i	$0.0220961\pi$
$409$	0.299265	+	5.13819i	0.0147977	+	0.254067i	−0.982794	+	0.184706i	$0.940867\pi$
$410$	−0.455343	−	7.52008i	−0.0224878	−	0.371390i
$411$	8.80979	+	10.0727i	0.434555	+	0.496852i
$412$	−4.92361	−	4.60259i	−0.242569	−	0.226753i
$413$	8.84825	−	10.5449i	0.435394	−	0.518882i
$414$	1.76035	−	2.03546i	0.0865167	−	0.100037i
$415$	4.29636	+	5.12020i	0.210900	+	0.251341i
$416$	30.0907	−	15.5478i	1.47532	−	0.762292i
$417$	−14.4538	−	27.3675i	−0.707804	−	1.34019i
$418$	26.6878	−	11.5849i	1.30535	−	0.566634i
$419$	−7.38587	+	24.6705i	−0.360823	+	1.20523i	0.564301	+	0.825569i	$0.309146\pi$
$419$	−7.38587	+	24.6705i	−0.360823	+	1.20523i	−0.925124	+	0.379665i	$0.876039\pi$
$420$	−6.86901	+	0.978041i	−0.335173	+	0.0477235i
$421$	27.7978	−	3.24910i	1.35478	−	0.158352i	0.592488	−	0.805580i	$-0.298146\pi$
$421$	27.7978	−	3.24910i	1.35478	−	0.158352i	0.762296	+	0.647228i	$0.224072\pi$
$422$	1.25394	+	3.42070i	0.0610411	+	0.166517i
$423$	0.530261	−	2.07731i	0.0257822	−	0.101002i
$424$	−3.62950	−	9.76198i	−0.176264	−	0.474084i
$425$	14.4679	+	0.842661i	0.701798	+	0.0408751i
$426$	9.25610	−	16.9103i	0.448460	−	0.819305i
$427$	−22.5844	+	9.74195i	−1.09293	+	0.471446i
$428$	−1.08544	−	0.121813i	−0.0524665	−	0.00588807i
$429$	−20.1026	−	20.4516i	−0.970561	−	0.987415i
$430$	0.210602	−	3.76498i	0.0101561	−	0.181563i
$431$	−1.02829	+	1.78105i	−0.0495308	+	0.0857899i	−0.889728	−	0.456491i	$-0.849106\pi$
$431$	−1.02829	+	1.78105i	−0.0495308	+	0.0857899i	0.840197	+	0.542281i	$0.182439\pi$
$432$	−17.8691	+	10.6158i	−0.859728	+	0.510752i
$433$	−15.1416	−	26.2260i	−0.727658	−	1.26034i	−0.957871	−	0.287200i	$-0.907276\pi$
$433$	−15.1416	−	26.2260i	−0.727658	−	1.26034i	0.230213	−	0.973140i	$-0.426058\pi$
$434$	28.6439	−	14.4681i	1.37495	−	0.694490i
$435$	4.80932	+	2.29323i	0.230589	+	0.109952i
$436$	−8.16348	+	11.0714i	−0.390960	+	0.530222i
$437$	−3.78515	−	2.81794i	−0.181069	−	0.134801i
$438$	3.40574	+	1.15244i	0.162733	+	0.0550655i
$439$	12.0685	−	18.3493i	0.575999	−	0.875764i	−0.423548	−	0.905874i	$-0.639215\pi$
$439$	12.0685	−	18.3493i	0.575999	−	0.875764i	0.999547	+	0.0301101i	$0.00958580\pi$
$440$	−2.33723	+	2.82474i	−0.111423	+	0.134664i
$441$	32.1802	+	10.2410i	1.53239	+	0.487665i
$442$	−25.2914	−	4.39963i	−1.20299	−	0.209269i
$443$	1.85619	+	2.49330i	0.0881905	+	0.118460i	0.844029	−	0.536298i	$-0.180178\pi$
$443$	1.85619	+	2.49330i	0.0881905	+	0.118460i	−0.755838	+	0.654759i	$0.772770\pi$
$444$	9.35150	+	5.81999i	0.443803	+	0.276204i
$445$	−5.61325	−	5.94970i	−0.266094	−	0.282043i
$446$	9.94827	+	7.37073i	0.471064	+	0.349014i
$447$	−3.29647	−	1.34257i	−0.155918	−	0.0635014i
$448$	4.43623	+	33.8933i	0.209592	+	1.60131i
$449$	−0.456846	+	1.25517i	−0.0215599	+	0.0592353i	−0.950006	−	0.312233i	$-0.898923\pi$
$449$	−0.456846	+	1.25517i	−0.0215599	+	0.0592353i	0.928446	+	0.371468i	$0.121145\pi$
$450$	−9.37140	+	17.9859i	−0.441772	+	0.847865i
$451$	10.7483	+	29.5307i	0.506118	+	1.39055i
$452$	0.244395	−	1.05273i	0.0114954	−	0.0495161i
$453$	−13.8593	+	8.38474i	−0.651168	+	0.393950i
$454$	−2.84896	−	1.42261i	−0.133708	−	0.0667664i
$455$	10.0194	−	6.58989i	0.469719	−	0.308939i
$456$	20.8538	+	29.8910i	0.976567	+	1.39978i
$457$	3.11792	+	10.4146i	0.145850	+	0.487173i	0.999429	−	0.0337906i	$-0.0107579\pi$
$457$	3.11792	+	10.4146i	0.145850	+	0.487173i	−0.853579	+	0.520964i	$0.825573\pi$
$458$	−0.508951	+	0.429058i	−0.0237817	+	0.0200486i
$459$	15.6527	+	1.77774i	0.730604	+	0.0829778i
$460$	0.586096	+	0.100568i	0.0273269	+	0.00468903i
$461$	−4.69402	+	19.8056i	−0.218623	+	0.922441i	0.747480	+	0.664284i	$0.231263\pi$
$461$	−4.69402	+	19.8056i	−0.218623	+	0.922441i	−0.966103	+	0.258157i	$0.916885\pi$
$462$	26.3067	−	12.0655i	1.22390	−	0.561339i
$463$	−13.0575	+	25.9997i	−0.606835	+	1.20831i	0.355049	+	0.934848i	$0.384464\pi$
$463$	−13.0575	+	25.9997i	−0.606835	+	1.20831i	−0.961883	+	0.273460i	$0.911832\pi$
$464$	11.5646	−	23.5648i	0.536872	−	1.09397i
$465$	−0.661616	+	4.26073i	−0.0306817	+	0.197587i
$466$	1.72511	+	14.4707i	0.0799144	+	0.670343i
$467$	−2.29577	+	13.0200i	−0.106236	+	0.602492i	0.884484	+	0.466570i	$0.154511\pi$
$467$	−2.29577	+	13.0200i	−0.106236	+	0.602492i	−0.990720	+	0.135921i	$0.956601\pi$
$468$	20.1181	−	29.7632i	0.929959	−	1.37580i
$469$	0.478784	+	2.71532i	0.0221082	+	0.125382i
$470$	0.453536	−	0.136917i	0.0209201	−	0.00631549i
$471$	−2.04965	+	2.26364i	−0.0944430	+	0.104303i
$472$	8.85186	−	2.16251i	0.407440	−	0.0995376i
$473$	3.62744	+	15.3054i	0.166790	+	0.703743i
$474$	−9.94928	−	4.02545i	−0.456985	−	0.184895i
$475$	32.6549	+	14.0859i	1.49831	+	0.646307i
$476$	12.8507	−	22.4962i	0.589009	−	1.03111i
$477$	−8.33873	−	7.24526i	−0.381804	−	0.331738i
$478$	−16.1660	+	28.1495i	−0.739415	+	1.28753i
$479$	−19.1827	+	9.63393i	−0.876482	+	0.440186i	−0.829367	−	0.558704i	$-0.811299\pi$
$479$	−19.1827	+	9.63393i	−0.876482	+	0.440186i	−0.0471144	+	0.998890i	$0.515003\pi$
$480$	−4.04893	−	2.16810i	−0.184807	−	0.0989599i
$481$	−18.9093	−	2.21018i	−0.862191	−	0.100776i
$482$	9.32833	−	2.23352i	0.424894	−	0.101734i
$483$	−3.82197	−	2.72550i	−0.173906	−	0.124015i
$484$	−2.62808	+	6.17042i	−0.119458	+	0.280473i
$485$		−	3.11980i		−	0.141663i
$486$	−11.2444	+	18.9622i	−0.510056	+	0.860141i
$487$			24.6005i			1.11475i	0.830260	+	0.557377i	$0.188192\pi$
$487$			24.6005i			1.11475i	−0.830260	+	0.557377i	$0.811808\pi$
$488$	−15.8682	−	3.64544i	−0.718319	−	0.165021i
$489$	−2.42472	−	1.72910i	−0.109650	−	0.0781927i
$490$	1.73764	+	7.25730i	0.0784986	+	0.327851i
$491$	−22.3140	−	2.60813i	−1.00702	−	0.117703i	−0.403438	−	0.915007i	$-0.632185\pi$
$491$	−22.3140	−	2.60813i	−1.00702	−	0.117703i	−0.603578	+	0.797304i	$0.706259\pi$
$492$	−33.5894	+	20.5328i	−1.51433	+	0.925689i
$493$	−17.7791	+	8.92900i	−0.800731	+	0.402142i
$494$	−54.6278	−	31.3721i	−2.45782	−	1.41150i
$495$	−0.741091	+	3.81743i	−0.0333096	+	0.171581i
$496$	20.9530	+	3.49623i	0.940816	+	0.156985i
$497$	−30.8773	−	13.3191i	−1.38503	−	0.597445i
$498$	13.0997	−	32.3772i	0.587014	−	1.45086i
$499$	−0.540249	−	2.27949i	−0.0241849	−	0.102044i	0.959614	−	0.281321i	$-0.0907724\pi$
$499$	−0.540249	−	2.27949i	−0.0241849	−	0.102044i	−0.983799	+	0.179277i	$0.942624\pi$
$500$	−9.15110	+	0.575218i	−0.409250	+	0.0257245i
$501$	−19.9499	+	22.0327i	−0.891295	+	0.984347i
$502$	−9.57396	−	31.7137i	−0.427307	−	1.41545i
$503$	−1.38838	−	7.87389i	−0.0619047	−	0.351079i	−0.999989	−	0.00467231i	$-0.998513\pi$
$503$	−1.38838	−	7.87389i	−0.0619047	−	0.351079i	0.938084	−	0.346407i	$-0.112598\pi$
$504$	21.3493	+	29.3036i	0.950973	+	1.30528i
$505$	1.42727	−	8.09442i	0.0635125	−	0.360197i
$506$	−2.46307	+	0.293633i	−0.109497	+	0.0130536i
$507$	−6.07276	+	39.1079i	−0.269701	+	1.73684i
$508$	−5.02206	+	4.78190i	−0.222818	+	0.212163i
$509$	4.40265	−	8.76639i	0.195144	−	0.388563i	−0.774686	−	0.632346i	$-0.782092\pi$
$509$	4.40265	−	8.76639i	0.195144	−	0.388563i	0.969830	+	0.243783i	$0.0783884\pi$
$510$	1.45124	+	3.16415i	0.0642618	+	0.140111i
$511$	1.44637	−	6.10270i	0.0639835	−	0.269967i
$512$	−10.9059	+	19.8258i	−0.481977	+	0.876184i
$513$	34.6020	+	17.2365i	1.52772	+	0.761011i
$514$	3.61337	+	4.28620i	0.159379	+	0.189056i
$515$	−0.453058	−	1.51332i	−0.0199641	−	0.0666848i
$516$	−17.8917	+	8.25584i	−0.787638	+	0.363443i
$517$	−1.65106	+	1.08592i	−0.0726134	+	0.0477586i
$518$	8.58354	−	17.1897i	0.377139	−	0.755270i
$519$	−3.77568	+	2.28425i	−0.165734	+	0.100267i
$520$	7.92801	+	0.406915i	0.347666	+	0.0178444i
$521$	9.93296	+	27.2906i	0.435171	+	1.19562i	0.942599	+	0.333928i	$0.108374\pi$
$521$	9.93296	+	27.2906i	0.435171	+	1.19562i	−0.507428	+	0.861694i	$0.669404\pi$
$522$	−1.20409	−	27.8158i	−0.0527016	−	1.21746i
$523$	8.61494	−	23.6694i	0.376705	−	1.03499i	−0.596008	−	0.802978i	$-0.703247\pi$
$523$	8.61494	−	23.6694i	0.376705	−	1.03499i	0.972713	−	0.232011i	$-0.0745304\pi$
$524$	10.0526	+	6.54566i	0.439148	+	0.285948i
$525$	32.7642	+	13.3441i	1.42995	+	0.582382i
$526$	10.5235	−	14.2036i	0.458846	−	0.619304i
$527$	−11.0488	−	11.7111i	−0.481294	−	0.510142i
$528$	18.7647	+	3.86310i	0.816629	+	0.168120i
$529$	−13.4944	−	18.1261i	−0.586713	−	0.788092i
$530$	0.418353	−	2.40491i	0.0181721	−	0.104463i
$531$	7.14315	−	6.51047i	0.309986	−	0.282530i
$532$	48.5137	−	41.0894i	2.10334	−	1.78145i
$533$	37.3913	−	56.8507i	1.61960	−	2.46248i
$534$	−13.7003	+	40.4878i	−0.592868	+	1.75208i
$535$	−0.205344	−	0.152873i	−0.00887779	−	0.00660927i
$536$	−0.807864	+	1.63664i	−0.0348944	+	0.0706919i
$537$	22.7758	+	10.8602i	0.982849	+	0.468651i
$538$	−10.1581	−	20.1110i	−0.437946	−	0.867046i
$539$	−15.5640	−	26.9576i	−0.670388	−	1.16115i
$540$	−4.87133	+	0.0383055i	−0.209629	+	0.00164841i
$541$	−2.84818	+	4.93319i	−0.122453	+	0.212095i	−0.920734	−	0.390190i	$-0.872409\pi$
$541$	−2.84818	+	4.93319i	−0.122453	+	0.212095i	0.798282	+	0.602284i	$0.205743\pi$
$542$	8.30165	+	0.464370i	0.356586	+	0.0199464i
$543$	−12.0187	−	12.2274i	−0.515770	−	0.524726i
$544$	15.6683	−	6.97333i	0.671773	−	0.298979i
$545$	−2.96036	+	1.27697i	−0.126808	+	0.0546995i
$546$	−54.9697	−	30.0886i	−2.35249	−	1.28767i
$547$	1.69676	+	0.0988250i	0.0725482	+	0.00422545i	0.0943805	−	0.995536i	$-0.469913\pi$
$547$	1.69676	+	0.0988250i	0.0725482	+	0.00422545i	−0.0218323	+	0.999762i	$0.506950\pi$
$548$	15.2047	−	2.75314i	0.649514	−	0.117608i
$549$	−16.6265	+	4.66733i	−0.709602	+	0.199197i
$550$	17.5518	−	6.43408i	0.748413	−	0.274350i
$551$	−48.4915	+	5.66785i	−2.06581	+	0.241458i
$552$	−0.972367	−	2.95134i	−0.0413867	−	0.125618i
$553$	−5.36949	+	17.9353i	−0.228334	+	0.762688i
$554$	8.35107	+	19.2382i	0.354803	+	0.817354i
$555$	1.20563	+	2.28280i	0.0511760	+	0.0968993i
$556$	−35.6865	−	1.91391i	−1.51344	−	0.0811681i
$557$	20.9865	+	25.0108i	0.889227	+	1.05974i	0.997842	+	0.0656558i	$0.0209139\pi$
$557$	20.9865	+	25.0108i	0.889227	+	1.05974i	−0.108615	+	0.994084i	$0.534642\pi$
$558$	21.2850	−	7.38947i	0.901067	−	0.312821i
$559$	21.8921	−	26.0899i	0.925935	−	1.10349i
$560$	−3.10547	+	7.38529i	−0.131230	+	0.312085i
$561$	−9.55952	−	10.9299i	−0.403603	−	0.461463i
$562$	5.14644	−	0.311618i	0.217089	−	0.0131448i
$563$	−1.83167	−	31.4485i	−0.0771955	−	1.32540i	−0.785224	−	0.619212i	$-0.787452\pi$
$563$	−1.83167	−	31.4485i	−0.0771955	−	1.32540i	0.708028	−	0.706184i	$-0.249585\pi$
$564$	−1.74347	−	1.75751i	−0.0734133	−	0.0740045i
$565$	0.173824	−	0.184243i	0.00731284	−	0.00775116i
$566$	28.9457	−	5.17255i	1.21668	−	0.217418i
$567$	34.7649	+	16.4378i	1.45999	+	0.690324i
$568$	−11.2627	−	19.2006i	−0.472573	−	0.805637i
$569$	9.49696	+	8.95992i	0.398133	+	0.375619i	0.859108	−	0.511794i	$-0.171019\pi$
$569$	9.49696	+	8.95992i	0.398133	+	0.375619i	−0.460975	+	0.887413i	$0.652500\pi$
$570$	0.690810	+	8.51434i	0.0289348	+	0.356626i
$571$	23.1867	−	1.35047i	0.970333	−	0.0565155i	0.434350	−	0.900744i	$-0.356978\pi$
$571$	23.1867	−	1.35047i	0.970333	−	0.0565155i	0.535983	+	0.844229i	$0.319941\pi$
$572$	−32.1856	+	7.78458i	−1.34575	+	0.325490i
$573$	−19.5435	−	6.66325i	−0.816442	−	0.278361i
$574$	41.1347	+	54.9892i	1.71693	+	2.29520i
$575$	−2.32272	−	1.94900i	−0.0968643	−	0.0812788i
$576$	−0.0821416	+	23.9999i	−0.00342256	+	0.999994i
$577$	0.419010	−	0.351591i	0.0174436	−	0.0146369i	−0.634024	−	0.773313i	$-0.718598\pi$
$577$	0.419010	−	0.351591i	0.0174436	−	0.0146369i	0.651468	+	0.758676i	$0.274154\pi$
$578$	10.7513	+	2.52200i	0.447193	+	0.104902i
$579$	0.737999	−	19.5681i	0.0306702	−	0.813222i
$580$	5.12460	−	3.40436i	0.212788	−	0.141358i
$581$	−58.3657	−	17.4735i	−2.42142	−	0.724925i
$582$	−14.3980	+	7.64648i	−0.596816	+	0.316957i
$583$	1.18209	+	10.1134i	0.0489570	+	0.418854i
$584$	3.16187	−	2.69050i	0.130839	−	0.111334i
$585$	7.58832	−	3.64880i	0.313738	−	0.150859i
$586$	−0.0135030	−	5.87392i	−0.000557805	−	0.242649i
$587$	1.18129	−	20.2820i	0.0487571	−	0.837127i	−0.881946	−	0.471351i	$-0.843767\pi$
$587$	1.18129	−	20.2820i	0.0487571	−	0.837127i	0.930703	−	0.365776i	$-0.119196\pi$
$588$	29.2338	−	25.8066i	1.20558	−	1.06424i
$589$	−15.6489	−	36.2781i	−0.644800	−	1.49481i
$590$	2.04739	+	0.607822i	0.0842895	+	0.0250236i
$591$	8.97360	+	2.48745i	0.369125	+	0.102320i
$592$	11.3128	−	5.81238i	0.464954	−	0.238887i
$593$	−4.69870	−	2.71280i	−0.192952	−	0.111401i	0.400412	−	0.916335i	$-0.368867\pi$
$593$	−4.69870	−	2.71280i	−0.192952	−	0.111401i	−0.593364	+	0.804934i	$0.702201\pi$
$594$	19.4340	−	5.93618i	0.797385	−	0.243564i
$595$	5.25874	−	3.03614i	0.215587	−	0.124469i
$596$	−3.28543	+	2.46947i	−0.134576	+	0.101153i
$597$	−5.27014	−	7.66615i	−0.215693	−	0.313755i
$598$	3.69472	+	3.89818i	0.151088	+	0.159408i
$599$	−2.01056	+	2.70065i	−0.0821493	+	0.110346i	−0.841298	−	0.540571i	$-0.818208\pi$
$599$	−2.01056	+	2.70065i	−0.0821493	+	0.110346i	0.759149	+	0.650917i	$0.225615\pi$
$600$	12.2600	+	19.9528i	0.500512	+	0.814570i
$601$	−27.0320	−	17.7793i	−1.10266	−	0.725231i	−0.138450	−	0.990369i	$-0.544212\pi$
$601$	−27.0320	−	17.7793i	−1.10266	−	0.725231i	−0.964210	+	0.265139i	$0.914582\pi$
$602$	17.2544	+	29.7274i	0.703236	+	1.21160i
$603$	0.0792757	+	1.93425i	0.00322835	+	0.0787689i
$604$	0.0859944	+	18.7040i	0.00349906	+	0.761055i
$605$	−1.26088	+	0.938690i	−0.0512620	+	0.0381632i
$606$	−40.8542	+	13.2522i	−1.65959	+	0.538332i
$607$	23.6353	−	22.2988i	0.959328	−	0.905080i	−0.0362187	−	0.999344i	$-0.511531\pi$
$607$	23.6353	−	22.2988i	0.959328	−	0.905080i	0.995547	+	0.0942641i	$0.0300498\pi$
$608$	41.9828	−	2.92975i	1.70263	−	0.118817i
$609$	−48.1123	+	6.62491i	−1.94961	+	0.268455i
$610$	−2.78171	−	2.61235i	−0.112628	−	0.105771i
$611$	4.02082	+	1.46346i	0.162665	+	0.0592053i
$612$	11.0458	−	14.4527i	0.446498	−	0.584215i
$613$	−12.4199	+	4.52047i	−0.501635	+	0.182580i	−0.580429	−	0.814311i	$-0.697115\pi$
$613$	−12.4199	+	4.52047i	−0.501635	+	0.182580i	0.0787941	+	0.996891i	$0.474893\pi$
$614$	33.0779	+	14.1783i	1.33492	+	0.572190i
$615$	−9.22512	+	0.188967i	−0.371993	+	0.00761989i
$616$	3.65070	−	33.2189i	0.147091	−	1.33843i
$617$	−22.5998	−	34.3613i	−0.909832	−	1.38333i	−0.923571	−	0.383427i	$-0.874744\pi$
$617$	−22.5998	−	34.3613i	−0.909832	−	1.38333i	0.0137387	−	0.999906i	$-0.495627\pi$
$618$	−5.87360	+	5.79995i	−0.236271	+	0.233308i
$619$	−43.9649	+	13.1622i	−1.76710	+	0.529034i	−0.994394	−	0.105734i	$-0.966281\pi$
$619$	−43.9649	+	13.1622i	−1.76710	+	0.529034i	−0.772703	+	0.634768i	$0.781096\pi$
$620$	3.82868	+	3.18276i	0.153764	+	0.127823i
$621$	−2.40472	−	2.25394i	−0.0964981	−	0.0904475i
$622$	42.0934	+	15.2112i	1.68779	+	0.609915i
$623$	72.5494	+	17.1945i	2.90663	+	0.688884i
$624$	−17.5532	−	37.5854i	−0.702692	−	1.50462i
$625$	19.4385	+	9.76240i	0.777542	+	0.390496i
$626$	−24.6990	+	16.3263i	−0.987172	+	0.652529i
$627$	−12.8702	−	33.2270i	−0.513987	−	1.32696i
$628$	1.02682	+	3.37330i	0.0409746	+	0.134609i
$629$	−9.49340	−	1.67394i	−0.378527	−	0.0667444i
$630$	0.860511	+	8.45395i	0.0342836	+	0.336813i
$631$	−20.1639	+	3.55544i	−0.802712	+	0.141540i	−0.559929	−	0.828541i	$-0.689172\pi$
$631$	−20.1639	+	3.55544i	−0.802712	+	0.141540i	−0.242783	+	0.970081i	$0.578060\pi$
$632$	−9.88955	+	7.46905i	−0.393385	+	0.297103i
$633$	4.24754	−	1.36702i	0.168825	−	0.0543341i
$634$	−1.20663	+	10.5334i	−0.0479216	+	0.418333i
$635$	−1.58150	+	0.374822i	−0.0627599	+	0.0148744i
$636$	−12.1241	+	3.96361i	−0.480752	+	0.157167i
$637$	−26.6957	+	61.8875i	−1.05772	+	2.45207i
$638$	−16.4507	+	19.6970i	−0.651291	+	0.779812i
$639$	−20.2409	−	12.1554i	−0.800718	−	0.480861i
$640$	−4.54961	+	2.72526i	−0.179839	+	0.107725i
$641$	−1.51801	−	3.02262i	−0.0599580	−	0.119386i	0.861658	−	0.507490i	$-0.169427\pi$
$641$	−1.51801	−	3.02262i	−0.0599580	−	0.119386i	−0.921616	+	0.388104i	$0.873130\pi$
$642$	−0.202226	+	1.32235i	−0.00798122	+	0.0521891i
$643$	3.96632	−	33.9340i	0.156416	−	1.33823i	−0.655828	−	0.754910i	$-0.727680\pi$
$643$	3.96632	−	33.9340i	0.156416	−	1.33823i	0.812245	−	0.583317i	$-0.198245\pi$
$644$	−4.96721	+	2.16978i	−0.195735	+	0.0855015i
$645$	−4.59714	−	0.442102i	−0.181012	−	0.0174078i
$646$	−26.6901	−	17.4666i	−1.05011	−	0.687215i
$647$	−35.9649			−1.41393			−0.706963	−	0.707250i	$-0.749935\pi$
$647$	−35.9649			−1.41393			−0.706963	+	0.707250i	$0.749935\pi$
$648$	12.1162	+	22.3875i	0.475968	+	0.879463i
$649$	−8.90865			−0.349695
$650$	−33.8691	−	22.1647i	−1.32846	−	0.869371i
$651$	−16.3028	−	35.7620i	−0.638957	−	1.40162i
$652$	−3.15128	+	1.37655i	−0.123413	+	0.0539097i
$653$	−2.03555	+	17.4152i	−0.0796572	+	0.681511i	0.893128	+	0.449802i	$0.148506\pi$
$653$	−2.03555	+	17.4152i	−0.0796572	+	0.681511i	−0.972785	+	0.231708i	$0.925568\pi$
$654$	13.1490	+	10.5324i	0.514166	+	0.411848i
$655$	1.26183	+	2.51251i	0.0493038	+	0.0981718i
$656$	0.417994	+	45.4564i	0.0163199	+	1.77477i
$657$	1.57709	−	4.11139i	0.0615283	−	0.160401i
$658$	−2.76815	+	3.31440i	−0.107914	+	0.129209i
$659$	−10.4635	+	24.2572i	−0.407602	+	0.944927i	0.583536	+	0.812087i	$0.301669\pi$
$659$	−10.4635	+	24.2572i	−0.407602	+	0.944927i	−0.991138	+	0.132840i	$0.957590\pi$
$660$	3.34236	+	2.99855i	0.130101	+	0.116718i
$661$	16.7206	−	3.96286i	0.650357	−	0.154137i	0.107821	−	0.994170i	$-0.465613\pi$
$661$	16.7206	−	3.96286i	0.650357	−	0.154137i	0.542536	+	0.840033i	$0.317464\pi$
$662$	4.30263	−	37.5600i	0.167227	−	1.45981i
$663$	−6.62266	+	30.7353i	−0.257203	+	1.19366i
$664$	−24.3060	−	32.1828i	−0.943255	−	1.24894i
$665$	14.6745	−	2.58751i	0.569054	−	0.100340i
$666$	7.58025	−	11.1590i	0.293729	−	0.432404i
$667$	4.09925	+	0.722808i	0.158724	+	0.0279872i
$668$	9.99437	+	32.8333i	0.386694	+	1.27036i
$669$	9.50722	−	11.8134i	0.367570	−	0.456732i
$670$	−0.356864	+	0.235890i	−0.0137868	+	0.00911322i
$671$	14.2247	+	7.14393i	0.549140	+	0.275788i
$672$	41.6947	−	3.76911i	1.60841	−	0.145397i
$673$	5.90302	+	1.39904i	0.227545	+	0.0539291i	0.342806	−	0.939406i	$-0.388623\pi$
$673$	5.90302	+	1.39904i	0.227545	+	0.0539291i	−0.115262	+	0.993335i	$0.536771\pi$
$674$	32.3534	+	11.6915i	1.24621	+	0.450341i
$675$	21.5516	+	12.3492i	0.829523	+	0.475320i
$676$	35.1422	+	29.2136i	1.35162	+	1.12360i
$677$	−36.0484	+	10.7922i	−1.38545	+	0.414777i	−0.890832	−	0.454333i	$-0.849878\pi$
$677$	−36.0484	+	10.7922i	−1.38545	+	0.414777i	−0.494619	+	0.869110i	$0.664692\pi$
$678$	−1.27632	−	0.350635i	−0.0490169	−	0.0134660i
$679$	15.6266	+	23.7591i	0.599695	+	0.911792i
$680$	3.99555	+	0.439103i	0.153222	+	0.0168388i
$681$	−1.88046	+	3.41680i	−0.0720593	+	0.130932i
$682$	−19.0885	−	8.18200i	−0.730938	−	0.313305i
$683$	1.45165	−	0.528357i	0.0555458	−	0.0202170i	−0.314098	−	0.949391i	$-0.601702\pi$
$683$	1.45165	−	0.528357i	0.0555458	−	0.0202170i	0.369644	+	0.929174i	$0.379480\pi$
$684$	37.6008	−	24.0563i	1.43770	−	0.919817i
$685$	3.40321	+	1.23867i	0.130030	+	0.0473270i
$686$	−18.7504	−	17.6088i	−0.715895	−	0.672308i
$687$	0.500142	+	0.643848i	0.0190816	+	0.0245643i
$688$	−2.43354	+	22.6224i	−0.0927778	+	0.862471i
$689$	16.0365	−	15.1296i	0.610940	−	0.576392i
$690$	0.151774	−	0.712320i	0.00577793	−	0.0271175i
$691$	−12.2420	+	9.11382i	−0.465707	+	0.346706i	−0.804297	−	0.594228i	$-0.797458\pi$
$691$	−12.2420	+	9.11382i	−0.465707	+	0.346706i	0.338590	+	0.940934i	$0.390050\pi$
$692$	0.0234273	+	5.09551i	0.000890574	+	0.193702i
$693$	−13.4771	−	32.7840i	−0.511953	−	1.24536i
$694$	13.7525	+	23.6940i	0.522037	+	0.899413i
$695$	−6.99820	−	4.60279i	−0.265457	−	0.174594i
$696$	−28.2714	−	15.3063i	−1.07162	−	0.580184i
$697$	20.5747	−	27.6366i	0.779321	−	1.04681i
$698$	−17.6552	−	18.6274i	−0.668258	−	0.705058i
$699$	17.7933	−	1.40249i	0.673003	−	0.0530470i
$700$	32.6544	−	24.5445i	1.23422	−	0.927694i
$701$	15.9615	−	9.21540i	0.602859	−	0.348061i	−0.167306	−	0.985905i	$-0.553507\pi$
$701$	15.9615	−	9.21540i	0.602859	−	0.348061i	0.770166	+	0.637844i	$0.220174\pi$
$702$	−35.4379	−	26.0773i	−1.33752	−	0.984226i
$703$	−20.4862	−	11.8277i	−0.772653	−	0.446092i
$704$	14.9577	−	16.2988i	0.563738	−	0.614285i
$705$	−0.145344	−	0.561727i	−0.00547396	−	0.0211559i
$706$	−8.57496	−	2.54571i	−0.322723	−	0.0958091i
$707$	29.6743	+	68.7928i	1.11602	+	2.58722i
$708$	−2.21292	−	10.9385i	−0.0831667	−	0.411094i
$709$	−2.56047	+	43.9615i	−0.0961603	+	1.65101i	0.513313	+	0.858202i	$0.328418\pi$
$709$	−2.56047	+	43.9615i	−0.0961603	+	1.65101i	−0.609473	+	0.792807i	$0.708619\pi$
$710$	−0.0119935	−	5.21728i	−0.000450109	−	0.195801i
$711$	−5.41344	+	11.9784i	−0.203020	+	0.449227i
$712$	31.9849	+	37.5886i	1.19869	+	1.40869i
$713$	0.391062	+	3.34575i	0.0146454	+	0.125299i
$714$	−26.9008	−	16.8279i	−1.00674	−	0.629767i
$715$	−7.43509	−	2.22592i	−0.278056	−	0.0832446i
$716$	24.2689	−	16.1223i	0.906972	−	0.602517i
$717$	33.6568	+	21.1619i	1.25694	+	0.790305i
$718$	−3.72846	−	0.874614i	−0.139145	−	0.0326403i
$719$	−33.4789	+	28.0922i	−1.24855	+	1.04766i	−0.251749	+	0.967793i	$0.581006\pi$
$719$	−33.4789	+	28.0922i	−1.24855	+	1.04766i	−0.996805	+	0.0798687i	$0.974550\pi$
$720$	−2.85153	+	4.84876i	−0.106270	+	0.180703i
$721$	11.0303	+	9.25553i	0.410790	+	0.344694i
$722$	−30.7910	−	41.1616i	−1.14592	−	1.53187i
$723$	−2.27648	−	11.5251i	−0.0846633	−	0.428622i
$724$	−19.2427	+	4.65414i	−0.715149	+	0.172970i
$725$	−31.3168	+	1.82400i	−1.16308	+	0.0677416i
$726$	7.42244	+	3.51832i	0.275473	+	0.130577i
$727$	−21.2637	−	20.0613i	−0.788628	−	0.744032i	0.182341	−	0.983235i	$-0.441632\pi$
$727$	−21.2637	−	20.0613i	−0.788628	−	0.744032i	−0.970970	+	0.239203i	$0.923114\pi$
$728$	−62.4147	+	36.6114i	−2.31324	+	1.35691i
$729$	22.6546	+	14.6891i	0.839059	+	0.544040i
$730$	0.957887	−	0.171173i	0.0354530	−	0.00633539i
$731$	11.8343	−	12.5437i	0.437709	−	0.463944i
$732$	−5.23824	+	19.2404i	−0.193611	+	0.711147i
$733$	2.66586	+	45.7711i	0.0984660	+	1.69060i	0.580356	+	0.814363i	$0.302914\pi$
$733$	2.66586	+	45.7711i	0.0984660	+	1.69060i	−0.481890	+	0.876232i	$0.660049\pi$
$734$	−26.2320	+	1.58836i	−0.968242	+	0.0586273i
$735$	8.96632	−	1.77107i	0.330728	−	0.0653268i
$736$	−3.50068	−	0.787292i	−0.129037	−	0.0290200i
$737$	1.14699	−	1.36693i	0.0422498	−	0.0503514i
$738$	23.4824	+	42.1111i	0.864399	+	1.55013i
$739$	−7.46133	−	8.89207i	−0.274469	−	0.327100i	0.611147	−	0.791517i	$-0.290708\pi$
$739$	−7.46133	−	8.89207i	−0.274469	−	0.327100i	−0.885617	+	0.464417i	$0.846264\pi$
$740$	2.97670	+	0.159645i	0.109426	+	0.00586866i
$741$	−41.0673	+	65.3152i	−1.50865	+	2.39942i
$742$	8.85985	+	20.4103i	0.325255	+	0.749286i
$743$	5.38966	−	18.0027i	0.197728	−	0.660456i	−0.800410	−	0.599453i	$-0.795385\pi$
$743$	5.38966	−	18.0027i	0.197728	−	0.660456i	0.998138	−	0.0610031i	$-0.0194299\pi$
$744$	5.30466	−	25.4703i	0.194478	−	0.933787i
$745$	−0.956790	+	0.111833i	−0.0350541	+	0.00409723i
$746$	−5.65260	+	2.07210i	−0.206956	+	0.0758651i
$747$	−38.9806	−	17.6166i	−1.42623	−	0.644556i
$748$	−16.4987	+	2.98744i	−0.603251	+	0.109232i
$749$	2.32954	+	0.135680i	0.0851194	+	0.00495764i
$750$	0.255794	+	11.2270i	0.00934026	+	0.409951i
$751$	−9.60879	+	4.14483i	−0.350630	+	0.151247i	−0.564108	−	0.825701i	$-0.690780\pi$
$751$	−9.60879	+	4.14483i	−0.350630	+	0.151247i	0.213479	+	0.976948i	$0.431521\pi$
$752$	−2.77533	+	0.684778i	−0.101206	+	0.0249713i
$753$	−39.2790	+	10.1632i	−1.43141	+	0.370368i
$754$	55.4804	+	3.10341i	2.02048	+	0.113020i
$755$	−2.19193	+	3.79654i	−0.0797727	+	0.138170i
$756$	36.9062	−	24.6915i	1.34227	−	0.898021i
$757$	−19.4962	−	33.7685i	−0.708603	−	1.22734i	−0.965375	−	0.260865i	$-0.915992\pi$
$757$	−19.4962	−	33.7685i	−0.708603	−	1.22734i	0.256772	−	0.966472i	$-0.417341\pi$
$758$	−13.4567	−	26.6416i	−0.488768	−	0.967665i
$759$	0.238718	+	3.02860i	0.00866493	+	0.109931i
$760$	8.84495	+	4.36598i	0.320840	+	0.158371i
$761$	−14.3921	−	10.7145i	−0.521713	−	0.388401i	0.303842	−	0.952722i	$-0.401730\pi$
$761$	−14.3921	−	10.7145i	−0.521713	−	0.388401i	−0.825555	+	0.564321i	$0.809138\pi$
$762$	5.60599	+	6.38000i	0.203084	+	0.231123i
$763$	16.1487	−	24.5529i	0.584623	−	0.888876i
$764$	−18.1937	+	15.4095i	−0.658226	+	0.557494i
$765$	3.94325	−	1.62102i	0.142568	−	0.0586081i
$766$	−4.30040	+	24.7209i	−0.155380	+	0.893204i
$767$	11.5188	+	15.4725i	0.415921	+	0.558679i
$768$	23.7280	+	14.3171i	0.856212	+	0.516625i
$769$	−5.15153	−	5.46031i	−0.185769	−	0.196904i	0.627795	−	0.778378i	$-0.283957\pi$
$769$	−5.15153	−	5.46031i	−0.185769	−	0.196904i	−0.813565	+	0.581475i	$0.802476\pi$
$770$	4.66290	−	6.29352i	0.168039	−	0.226803i
$771$	5.42226	−	4.21202i	0.195278	−	0.151692i
$772$	−18.9484	−	12.3382i	−0.681969	−	0.444060i
$773$	−11.4641	+	31.4973i	−0.412334	+	1.13288i	0.543612	+	0.839337i	$0.317056\pi$
$773$	−11.4641	+	31.4973i	−0.412334	+	1.13288i	−0.955946	+	0.293542i	$0.905166\pi$
$774$	9.22704	+	22.2995i	0.331659	+	0.801540i
$775$	−8.68266	−	23.8554i	−0.311890	−	0.856911i
$776$	−0.964919	+	18.7997i	−0.0346386	+	0.674871i
$777$	−20.6158	−	11.3460i	−0.739586	−	0.407037i
$778$	−16.5171	+	33.0775i	−0.592165	+	1.18589i
$779$	70.6390	−	46.4600i	2.53091	−	1.66460i
$780$	0.886211	−	9.68210i	0.0317315	−	0.346675i
$781$	6.24165	+	20.8486i	0.223344	+	0.746021i
$782$	1.75287	+	2.07927i	0.0626826	+	0.0743545i
$783$	−34.0989	+	0.111357i	−1.21860	+	0.00397957i
$784$	−8.22632	−	44.2695i	−0.293797	−	1.58105i
$785$	−0.190592	+	0.804171i	−0.00680252	+	0.0287021i
$786$	8.50264	−	11.9814i	0.303279	−	0.427363i
$787$	15.8535	−	31.5668i	0.565115	−	1.12524i	−0.411734	−	0.911304i	$-0.635077\pi$
$787$	15.8535	−	31.5668i	0.565115	−	1.12524i	0.976849	−	0.213932i	$-0.0686271\pi$
$788$	7.78711	−	7.41473i	0.277404	−	0.264139i
$789$	−16.8665	−	13.5738i	−0.600462	−	0.483242i
$790$	−2.88427	+	0.343845i	−0.102618	+	0.0122335i
$791$	−0.400929	+	2.27378i	−0.0142554	+	0.0808464i
$792$	5.64646	−	22.7744i	0.200638	−	0.809253i
$793$	−5.98498	−	33.9425i	−0.212533	−	1.20533i
$794$	−10.5960	−	35.0992i	−0.376037	−	1.24562i
$795$	−2.92256	−	0.629737i	−0.103653	−	0.0223345i
$796$	−10.7209	+	0.673895i	−0.379993	+	0.0238856i
$797$	10.0797	+	42.5297i	0.357042	+	1.50648i	0.794514	+	0.607246i	$0.207726\pi$
$797$	10.0797	+	42.5297i	0.357042	+	1.50648i	−0.437472	+	0.899232i	$0.644126\pi$
$798$	−47.9080	−	61.3816i	−1.69593	−	2.17288i
$799$	1.98940	+	0.858143i	0.0703799	+	0.0303589i
$800$	27.0395	−	0.310807i	0.955990	−	0.0109887i
$801$	48.8766	+	18.7486i	1.72697	+	0.662451i
$802$	−34.2391	−	19.6631i	−1.20902	−	0.694330i
$803$	−3.62719	+	1.82164i	−0.128001	+	0.0642843i
$804$	1.96330	+	1.06878i	0.0692401	+	0.0376931i
$805$	−1.26185	−	0.147489i	−0.0444742	−	0.00519829i
$806$	10.4709	+	43.7321i	0.368823	+	1.54040i
$807$	−25.1086	+	11.4462i	−0.883864	+	0.402927i
$808$	−11.1041	+	48.3351i	−0.390642	+	1.70042i
$809$			10.0912i			0.354789i	0.984140	+	0.177394i	$0.0567668\pi$
$809$			10.0912i			0.354789i	−0.984140	+	0.177394i	$0.943233\pi$
$810$	−0.191677	+	5.96324i	−0.00673484	+	0.209527i
$811$			26.1226i			0.917287i	0.888620	+	0.458644i	$0.151665\pi$
$811$			26.1226i			0.917287i	−0.888620	+	0.458644i	$0.848335\pi$
$812$	−21.9750	+	51.5946i	−0.771170	+	1.81062i
$813$	0.974820	−	10.1365i	0.0341884	−	0.355504i
$814$	−12.0928	+	2.89541i	−0.423851	+	0.101484i
$815$	−0.800535	−	0.0935692i	−0.0280415	−	0.00327759i
$816$	−7.76642	−	19.5158i	−0.271879	−	0.683191i
$817$	37.8170	−	18.9924i	1.32305	−	0.664461i
$818$	3.62490	−	6.31198i	0.126742	−	0.220693i
$819$	−39.5133	+	65.7966i	−1.38071	+	2.29912i
$820$	−5.28476	+	9.25145i	−0.184552	+	0.323075i
$821$	44.1228	+	19.0327i	1.53989	+	0.664246i	0.985757	−	0.168179i	$-0.0537886\pi$
$821$	44.1228	+	19.0327i	1.53989	+	0.664246i	0.554138	+	0.832425i	$0.313048\pi$
$822$	−2.62461	−	18.7418i	−0.0915437	−	0.653697i
$823$	6.10643	+	25.7650i	0.212857	+	0.898113i	0.969658	+	0.244467i	$0.0786131\pi$
$823$	6.10643	+	25.7650i	0.212857	+	0.898113i	−0.756801	+	0.653646i	$0.773239\pi$
$824$	2.26205	+	9.25930i	0.0788022	+	0.322563i
$825$	−7.01427	−	21.7944i	−0.244206	−	0.758784i
$826$	−18.6366	+	5.62613i	−0.648449	+	0.195758i
$827$	3.60540	+	20.4473i	0.125372	+	0.711021i	0.981086	+	0.193572i	$0.0620072\pi$
$827$	3.60540	+	20.4473i	0.125372	+	0.711021i	−0.855714	+	0.517449i	$0.826882\pi$
$828$	−3.65937	+	1.04542i	−0.127172	+	0.0363308i
$829$	3.46065	−	19.6263i	0.120193	−	0.681651i	−0.863854	−	0.503743i	$-0.831956\pi$
$829$	3.46065	−	19.6263i	0.120193	−	0.681651i	0.984047	−	0.177908i	$-0.0569329\pi$
$830$	−1.11895	−	9.38607i	−0.0388394	−	0.325795i
$831$	23.9520	−	9.27763i	0.830887	−	0.321838i
$832$	−47.6479	−	4.90409i	−1.65189	−	0.170019i
$833$	−15.3164	+	30.4975i	−0.530683	+	1.05668i
$834$	−4.08979	+	43.5782i	−0.141618	+	1.50899i
$835$	−1.85509	+	7.82724i	−0.0641980	+	0.270873i
$836$	−40.5522	−	6.95836i	−1.40253	−	0.240660i
$837$	−8.00063	−	26.4098i	−0.276542	−	0.912855i
$838$	27.8450	−	23.4740i	0.961889	−	0.810896i
$839$	−15.5311	−	51.8776i	−0.536194	−	1.79101i	−0.608408	−	0.793624i	$-0.708192\pi$
$839$	−15.5311	−	51.8776i	−0.536194	−	1.79101i	0.0722141	−	0.997389i	$-0.476994\pi$
$840$	8.88578	+	4.16203i	0.306588	+	0.143604i
$841$	11.7510	−	7.72873i	0.405206	−	0.266508i
$842$	−35.4105	−	17.6820i	−1.22033	−	0.609362i
$843$	−0.129321	−	6.31329i	−0.00445406	−	0.217441i
$844$	1.16516	−	5.01891i	0.0401065	−	0.172758i
$845$	3.66335	+	10.0650i	0.126023	+	0.346245i
$846$	−2.23616	+	2.04753i	−0.0768807	+	0.0703956i
$847$	4.90059	−	13.4643i	0.168386	−	0.462637i
$848$	−3.26478	+	14.3625i	−0.112113	+	0.493209i
$849$	−4.91248	−	35.6761i	−0.168596	−	1.22440i
$850$	−16.4679	−	12.2012i	−0.564846	−	0.418497i
$851$	1.38404	+	1.46700i	0.0474443	+	0.0502881i
$852$	−24.0485	+	12.8426i	−0.823889	+	0.439982i
$853$	2.70955	+	3.63956i	0.0927732	+	0.124616i	0.846086	−	0.533046i	$-0.178953\pi$
$853$	2.70955	+	3.63956i	0.0927732	+	0.124616i	−0.753313	+	0.657662i	$0.771545\pi$
$854$	34.2693	+	5.96140i	1.17267	+	0.203995i
$855$	10.4534	−	0.428433i	0.357498	−	0.0146521i
$856$	1.19011	+	0.984714i	0.0406771	+	0.0336568i
$857$	−17.8661	+	27.1641i	−0.610296	+	0.927910i	0.389680	+	0.920950i	$0.372586\pi$
$857$	−17.8661	+	27.1641i	−0.610296	+	0.927910i	−0.999976	+	0.00695930i	$0.997785\pi$
$858$	7.95034	+	39.7688i	0.271420	+	1.35768i
$859$	2.21193	+	1.64672i	0.0754701	+	0.0561854i	0.634232	−	0.773142i	$-0.281316\pi$
$859$	2.21193	+	1.64672i	0.0754701	+	0.0561854i	−0.558762	+	0.829328i	$0.688724\pi$
$860$	−3.16483	+	4.29216i	−0.107920	+	0.146362i
$861$	69.3083	−	47.6464i	2.36202	−	1.62378i
$862$	2.59606	−	1.31127i	0.0884223	−	0.0446622i
$863$	18.7456	+	32.4683i	0.638106	+	1.10523i	0.985848	+	0.167642i	$0.0536153\pi$
$863$	18.7456	+	32.4683i	0.638106	+	1.10523i	−0.347742	+	0.937590i	$0.613051\pi$
$864$	29.3662	+	1.27582i	0.999058	+	0.0434043i
$865$	−0.597146	+	1.03429i	−0.0203036	+	0.0351668i
$866$	−2.39187	+	42.7600i	−0.0812790	+	1.45304i
$867$	3.61284	−	13.0335i	0.122699	−	0.442641i
$868$	−45.0997	−	5.06133i	−1.53078	−	0.171793i
$869$	11.1254	−	4.79903i	0.377403	−	0.162796i
$870$	−3.91518	−	6.43803i	−0.132737	−	0.218270i
$871$	−3.85712	−	0.224652i	−0.130694	−	0.00761203i
$872$	18.2339	−	6.77936i	0.617478	−	0.229578i
$873$	8.65241	+	17.9942i	0.292840	+	0.609012i
$874$	2.29690	+	6.26583i	0.0776939	+	0.211945i
$875$	19.4565	−	2.27414i	0.657751	−	0.0768801i
$876$	−3.13770	−	4.00115i	−0.106013	−	0.135186i
$877$	12.6374	−	42.2117i	0.426733	−	1.42539i	−0.426799	−	0.904347i	$-0.640359\pi$
$877$	12.6374	−	42.2117i	0.426733	−	1.42539i	0.853532	−	0.521041i	$-0.174456\pi$
$878$	−28.4910	+	12.3676i	−0.961523	+	0.417385i
$879$	−7.18896	−	0.271127i	−0.242478	−	0.00914489i
$880$	4.95323	−	1.53267i	0.166973	−	0.0516662i
$881$	−19.1391	−	22.8091i	−0.644814	−	0.768459i	0.340309	−	0.940314i	$-0.389468\pi$
$881$	−19.1391	−	22.8091i	−0.644814	−	0.768459i	−0.985122	+	0.171855i	$0.945024\pi$
$882$	−30.1496	−	37.0391i	−1.01519	−	1.24717i
$883$	−23.8215	+	28.3894i	−0.801658	+	0.955379i	−0.999692	−	0.0248161i	$-0.992100\pi$
$883$	−23.8215	+	28.3894i	−0.801658	+	0.955379i	0.198034	+	0.980195i	$0.436544\pi$
$884$	26.5213	+	24.7920i	0.892007	+	0.833847i
$885$	0.844094	−	2.47575i	0.0283739	−	0.0832215i
$886$	−0.265687	−	4.38787i	−0.00892593	−	0.147413i
$887$	2.20865	+	37.9210i	0.0741591	+	1.27326i	0.806053	+	0.591844i	$0.201600\pi$
$887$	2.20865	+	37.9210i	0.0741591	+	1.27326i	−0.731894	+	0.681419i	$0.761363\pi$
$888$	−6.55899	−	14.1289i	−0.220105	−	0.474134i
$889$	10.1666	−	10.7760i	0.340978	−	0.361415i
$890$	2.03492	+	11.3875i	0.0682106	+	0.381708i
$891$	−6.31279	−	24.0733i	−0.211486	−	0.806486i
$892$	−6.06427	−	16.4261i	−0.203047	−	0.549986i
$893$	3.86720	+	3.64851i	0.129411	+	0.122093i
$894$	2.86116	+	4.14152i	0.0956914	+	0.138513i
$895$	6.81732	−	0.397064i	0.227878	−	0.0132724i
$896$	20.9976	−	43.5428i	0.701480	−	1.45466i
$897$	4.95139	−	4.33057i	0.165322	−	0.144593i
$898$	1.51262	−	1.13152i	0.0504767	−	0.0377592i
$899$	26.6971	+	22.4015i	0.890398	+	0.747133i
$900$	25.0180	−	14.0263i	0.833932	−	0.467542i
$901$	8.55170	−	7.17573i	0.284899	−	0.239058i
$902$	10.1498	−	43.2685i	0.337952	−	1.44068i
$903$	37.2244	−	19.6595i	1.23875	−	0.654228i
$904$	−1.10444	+	1.05648i	−0.0367331	+	0.0351379i
$905$	−4.44519	−	1.33080i	−0.147763	−	0.0442374i
$906$	22.8935	+	0.810717i	0.760586	+	0.0269343i
$907$	4.62820	+	39.5968i	0.153677	+	1.31479i	0.821389	+	0.570369i	$0.193200\pi$
$907$	4.62820	+	39.5968i	0.153677	+	1.31479i	−0.667712	+	0.744420i	$0.732726\pi$
$908$	2.26962	+	3.88969i	0.0753199	+	0.129084i
$909$	14.2169	+	50.6449i	0.471544	+	1.67979i
$910$	−16.9597	+	0.0389871i	−0.562207	+	0.00129241i
$911$	2.88939	−	49.6089i	0.0957298	−	1.64362i	−0.518924	−	0.854820i	$-0.673667\pi$
$911$	2.88939	−	49.6089i	0.0957298	−	1.64362i	0.614654	−	0.788797i	$-0.289296\pi$
$912$	−1.52939	−	51.5205i	−0.0506432	−	1.70602i
$913$	15.6171	+	36.2046i	0.516852	+	1.19820i
$914$	4.37553	−	14.7385i	0.144730	−	0.487507i
$915$	−3.33312	+	3.27623i	−0.110190	+	0.108309i
$916$	0.934527	−	0.113588i	0.0308776	−	0.00375306i
$917$	−22.1944	−	12.8139i	−0.732923	−	0.423153i
$918$	−17.1458	−	14.2252i	−0.565895	−	0.469501i
$919$	17.5510	−	10.1331i	0.578956	−	0.334260i	−0.181763	−	0.983342i	$-0.558180\pi$
$919$	17.5510	−	10.1331i	0.578956	−	0.334260i	0.760718	+	0.649082i	$0.224847\pi$
$920$	−0.615672	−	0.572883i	−0.0202981	−	0.0188874i
$921$	18.9708	−	39.7853i	0.625109	−	1.31097i
$922$	20.8922	−	19.8018i	0.688049	−	0.652137i
$923$	28.1393	−	37.7976i	0.926215	−	1.24412i
$924$	−40.4734	−	6.09436i	−1.33148	−	0.200490i
$925$	−12.6991	−	8.35233i	−0.417544	−	0.274623i
$926$	35.5858	−	20.6547i	1.16942	−	0.678755i
$927$	6.81015	+	7.47194i	0.223675	+	0.245411i
$928$	−31.9335	+	18.9295i	−1.04827	+	0.621391i
$929$	9.55070	−	7.11023i	0.313348	−	0.233279i	−0.428982	−	0.903313i	$-0.641128\pi$
$929$	9.55070	−	7.11023i	0.313348	−	0.233279i	0.742331	+	0.670034i	$0.233720\pi$
$930$	4.08245	−	4.52954i	0.133869	−	0.148530i
$931$	−60.9151	+	57.4704i	−1.99641	+	1.88352i
$932$	9.16480	−	18.4597i	0.300203	−	0.604669i
$933$	20.6763	−	50.7675i	0.676913	−	1.66205i
$934$	12.7994	−	13.6292i	0.418809	−	0.445961i
$935$	−3.69283	−	1.34408i	−0.120768	−	0.0439561i
$936$	−46.8553	+	19.6405i	−1.53151	+	0.641969i
$937$	−15.1903	+	5.52881i	−0.496245	+	0.180618i	−0.578004	−	0.816034i	$-0.696168\pi$
$937$	−15.1903	+	5.52881i	−0.496245	+	0.180618i	0.0817594	+	0.996652i	$0.473946\pi$
$938$	1.53619	−	3.58392i	0.0501584	−	0.117019i
$939$	18.7700	+	31.0253i	0.612536	+	1.01247i
$940$	−0.642717	−	0.189201i	−0.0209631	−	0.00617107i
$941$	9.45986	+	14.3830i	0.308383	+	0.468873i	0.956114	−	0.292996i	$-0.0946523\pi$
$941$	9.45986	+	14.3830i	0.308383	+	0.468873i	−0.647731	+	0.761869i	$0.724282\pi$
$942$	4.17841	−	1.09140i	0.136140	−	0.0355596i
$943$	−6.90567	+	2.06742i	−0.224880	+	0.0673245i
$944$	−12.1494	−	4.29593i	−0.395430	−	0.139821i
$945$	10.3878	−	0.639065i	0.337915	−	0.0207888i
$946$	7.56006	−	20.9206i	0.245799	−	0.680188i
$947$	50.3984	+	11.9446i	1.63773	+	0.388148i	0.943438	−	0.331548i	$-0.107571\pi$
$947$	50.3984	+	11.9446i	1.63773	+	0.388148i	0.694289	+	0.719697i	$0.255719\pi$
$948$	8.65606	+	12.4683i	0.281136	+	0.404950i
$949$	7.85375	+	3.94430i	0.254944	+	0.128037i
$950$	−27.7337	−	41.9566i	−0.899798	−	1.36125i
$951$	12.8313	+	1.99247i	0.416082	+	0.0646102i
$952$	−32.6279	+	16.6691i	−1.05748	+	0.540249i
$953$	17.1965	+	3.03221i	0.557051	+	0.0982230i	0.445084	−	0.895489i	$-0.353174\pi$
$953$	17.1965	+	3.03221i	0.557051	+	0.0982230i	0.111967	+	0.993712i	$0.464285\pi$
$954$	4.25680	+	15.0312i	0.137819	+	0.486652i
$955$	−5.50328	+	0.970377i	−0.178082	+	0.0314006i
$956$	40.9290	−	20.7915i	1.32374	−	0.672445i
$957$	23.2989	+	21.0964i	0.753147	+	0.681951i
$958$	30.1603	+	3.45497i	0.974435	+	0.111625i
$959$	−32.1218	+	7.61300i	−1.03727	+	0.245837i
$960$	3.11228	+	5.70111i	0.100448	+	0.184003i
$961$	1.10777	−	2.56811i	0.0357347	−	0.0828423i
$962$	20.6646	+	17.2589i	0.666254	+	0.556448i
$963$	1.60835	+	0.312234i	0.0518283	+	0.0100616i
$964$	−12.7682	−	4.58089i	−0.411238	−	0.147541i
$965$	−2.37847	−	4.73592i	−0.0765656	−	0.152455i
$966$	2.41206	+	6.18495i	0.0776067	+	0.198998i
$967$	0.876724	−	7.50085i	0.0281935	−	0.241211i	−0.971792	−	0.235839i	$-0.924216\pi$
$967$	0.876724	−	7.50085i	0.0281935	−	0.241211i	0.999986	−	0.00537166i	$-0.00170986\pi$
$968$	7.88831	−	5.26652i	0.253540	−	0.169272i
$969$	−22.6821	+	31.8071i	−0.728654	+	1.02179i
$970$	−2.41599	+	3.69179i	−0.0775727	+	0.118536i
$971$	44.3909			1.42457			0.712286	−	0.701889i	$-0.247660\pi$
$971$	44.3909			1.42457			0.712286	+	0.701889i	$0.247660\pi$
$972$	27.9903	−	13.7310i	0.897791	−	0.440422i
$973$	76.3502			2.44767
$974$	19.0507	−	29.1107i	0.610424	−	0.932768i
$975$	−28.7830	+	40.3624i	−0.921794	+	1.29263i
$976$	15.9544	+	16.6022i	0.510689	+	0.531424i
$977$	1.65269	−	14.1397i	0.0528743	−	0.452369i	−0.940705	−	0.339227i	$-0.889835\pi$
$977$	1.65269	−	14.1397i	0.0528743	−	0.452369i	0.993579	−	0.113142i	$-0.0360914\pi$
$978$	1.53025	+	3.92383i	0.0489320	+	0.125470i
$979$	−21.6558	−	43.1203i	−0.692124	−	1.37813i
$980$	3.56386	−	9.93350i	0.113843	−	0.317314i
$981$	13.5331	−	15.5755i	0.432077	−	0.497287i
$982$	24.3853	+	20.3664i	0.778167	+	0.649917i
$983$	−13.7122	+	31.7884i	−0.437350	+	1.01389i	0.546914	+	0.837189i	$0.315803\pi$
$983$	−13.7122	+	31.7884i	−0.437350	+	1.01389i	−0.984264	+	0.176703i	$0.943457\pi$
$984$	55.6485	+	1.71452i	1.77401	+	0.0546569i
$985$	2.45224	−	0.581192i	0.0781349	−	0.0185183i
$986$	27.9534	+	3.20217i	0.890218	+	0.101978i
$987$	3.92049	+	3.54988i	0.124791	+	0.112994i
$988$	40.3486	+	79.4280i	1.28366	+	2.52694i
$989$	−3.55320	+	0.626526i	−0.112985	+	0.0199224i
$990$	3.83320	−	3.94342i	0.121827	−	0.125330i
$991$	26.8191	+	4.72893i	0.851937	+	0.150220i	0.582532	−	0.812807i	$-0.302062\pi$
$991$	26.8191	+	4.72893i	0.851937	+	0.150220i	0.269405	+	0.963027i	$0.413173\pi$
$992$	−22.0870	−	20.3633i	−0.701263	−	0.646536i
$993$	−45.7539	−	7.10476i	−1.45196	−	0.225463i
$994$	26.2239	+	39.6726i	0.831772	+	1.25834i
$995$	−2.24992	−	1.12995i	−0.0713272	−	0.0358219i
$996$	−40.5745	+	28.1688i	−1.28565	+	0.892562i
$997$	−52.8526	−	12.5263i	−1.67386	−	0.396712i	−0.719291	−	0.694709i	$-0.755533\pi$
$997$	−52.8526	−	12.5263i	−1.67386	−	0.396712i	−0.954567	+	0.297997i	$0.903681\pi$
$998$	−1.12595	+	3.11579i	−0.0356413	+	0.0986285i
$999$	−13.2848	−	9.82292i	−0.420313	−	0.310783i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	324.2.p.a.11.11	✓	936
3.2	odd	2		972.2.p.a.359.42		936
4.3	odd	2	inner	324.2.p.a.11.17	yes	936
12.11	even	2		972.2.p.a.359.36		936
81.22	even	27		972.2.p.a.287.36		936
81.59	odd	54	inner	324.2.p.a.59.17	yes	936
324.59	even	54	inner	324.2.p.a.59.11	yes	936
324.103	odd	54		972.2.p.a.287.42		936

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
324.2.p.a.11.11	✓	936	1.1	even	1	trivial
324.2.p.a.11.17	yes	936	4.3	odd	2	inner
324.2.p.a.59.11	yes	936	324.59	even	54	inner
324.2.p.a.59.17	yes	936	81.59	odd	54	inner
972.2.p.a.287.36		936	81.22	even	27
972.2.p.a.287.42		936	324.103	odd	54
972.2.p.a.359.36		936	12.11	even	2
972.2.p.a.359.42		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)

\(f(q)\)	\(=\)	\(q+(-1.18334 - 0.774405i) q^{2} +(-1.00564 + 1.41021i) q^{3} +(0.800594 + 1.83277i) q^{4} +(-0.0544195 + 0.465589i) q^{5} +(2.28209 - 0.889987i) q^{6} +(-1.91763 - 3.81831i) q^{7} +(0.471930 - 2.78878i) q^{8} +(-0.977379 - 2.83632i) q^{9} +O(q^{10})\)	\(q+(-1.18334 - 0.774405i) q^{2} +(-1.00564 + 1.41021i) q^{3} +(0.800594 + 1.83277i) q^{4} +(-0.0544195 + 0.465589i) q^{5} +(2.28209 - 0.889987i) q^{6} +(-1.91763 - 3.81831i) q^{7} +(0.471930 - 2.78878i) q^{8} +(-0.977379 - 2.83632i) q^{9} +(0.424951 - 0.508808i) q^{10} +(-1.09526 + 2.53910i) q^{11} +(-3.38970 - 0.714101i) q^{12} +(5.82606 - 1.38080i) q^{13} +(-0.687710 + 6.00339i) q^{14} +(-0.601851 - 0.544957i) q^{15} +(-2.71810 + 2.93461i) q^{16} +(2.98567 - 0.526453i) q^{17} +(-1.03989 + 4.11323i) q^{18} +(7.32660 + 1.29188i) q^{19} +(-0.896885 + 0.273009i) q^{20} +(7.31307 + 1.13559i) q^{21} +(3.26236 - 2.15645i) q^{22} +(-0.566827 - 0.284671i) q^{23} +(3.45817 + 3.47002i) q^{24} +(4.65141 + 1.10241i) q^{25} +(-7.96351 - 2.87777i) q^{26} +(4.98270 + 1.47401i) q^{27} +(5.46285 - 6.57150i) q^{28} +(-6.28669 + 1.88211i) q^{29} +(0.290178 + 1.11095i) q^{30} +(-2.91826 - 4.43700i) q^{31} +(5.48902 - 1.36774i) q^{32} +(-2.47922 - 4.09796i) q^{33} +(-3.94075 - 1.68914i) q^{34} +(1.88212 - 0.685036i) q^{35} +(4.41585 - 4.06206i) q^{36} +(-2.98790 - 1.08751i) q^{37} +(-7.66943 - 7.20249i) q^{38} +(-3.91169 + 9.60455i) q^{39} +(1.27274 + 0.371489i) q^{40} +(8.26630 - 7.79885i) q^{41} +(-7.77445 - 7.00706i) q^{42} +(4.56266 - 3.39677i) q^{43} +(-5.53044 + 0.0254270i) q^{44} +(1.37375 - 0.300705i) q^{45} +(0.450299 + 0.775817i) q^{46} +(0.597073 + 0.392701i) q^{47} +(-1.40499 - 6.78425i) q^{48} +(-6.72211 + 9.02936i) q^{49} +(-4.65050 - 4.90660i) q^{50} +(-2.26009 + 4.73983i) q^{51} +(7.19500 + 9.57237i) q^{52} +(3.18889 - 1.84111i) q^{53} +(-4.75476 - 5.60288i) q^{54} +(-1.12257 - 0.648117i) q^{55} +(-11.5534 + 3.54587i) q^{56} +(-9.18973 + 9.03288i) q^{57} +(8.89682 + 2.64126i) q^{58} +(1.27603 + 2.95816i) q^{59} +(0.516943 - 1.53934i) q^{60} +(0.334705 - 5.74666i) q^{61} +(0.0172650 + 7.51039i) q^{62} +(-8.95572 + 9.17096i) q^{63} +(-7.55456 - 2.63222i) q^{64} +(0.325834 + 2.78769i) q^{65} +(-0.239715 + 6.76921i) q^{66} +(-0.618183 - 0.185072i) q^{67} +(3.35518 + 5.05056i) q^{68} +(0.971469 - 0.513068i) q^{69} +(-2.75769 - 0.646892i) q^{70} +(6.02886 - 5.05881i) q^{71} +(-8.37113 + 1.38715i) q^{72} +(1.12442 + 0.943504i) q^{73} +(2.69354 + 3.60074i) q^{74} +(-6.23227 + 5.45084i) q^{75} +(3.49792 + 14.4622i) q^{76} +(11.7954 - 0.687003i) q^{77} +(12.0667 - 8.33622i) q^{78} +(-3.18709 - 3.00686i) q^{79} +(-1.21840 - 1.42522i) q^{80} +(-7.08946 + 5.54433i) q^{81} +(-15.8213 + 2.82724i) q^{82} +(9.78501 - 10.3715i) q^{83} +(3.77353 + 14.3123i) q^{84} +(0.0826323 + 1.41874i) q^{85} +(-8.02966 + 0.486199i) q^{86} +(3.66797 - 10.7583i) q^{87} +(6.56409 + 4.25271i) q^{88} +(-11.2165 + 13.3673i) q^{89} +(-1.85848 - 0.708000i) q^{90} +(-16.4446 - 19.5979i) q^{91} +(0.0679386 - 1.26677i) q^{92} +(9.19181 + 0.346663i) q^{93} +(-0.402432 - 0.927076i) q^{94} +(-1.00019 + 3.34088i) q^{95} +(-3.59117 + 9.11611i) q^{96} +(-6.61046 + 0.772651i) q^{97} +(14.9469 - 5.47919i) q^{98} +(8.27219 + 0.624850i) 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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