LMFDB - Embedded newform 720.2.cf.a.11.76

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [720,2,Mod(11,720)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(720, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 3, 2, 0]))

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

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

chi := DirichletCharacter("720.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 720 = 2^{4} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	720.cf (of order $12$, degree $4$, 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:	$5.74922894553$
Analytic rank:	$0$
Dimension:	$384$
Relative dimension:	$96$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			11.76
Character	$\chi$	$=$	720.11
Dual form			720.2.cf.a.131.76

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.09740 + 0.892027i) q^{2} +(-0.894914 - 1.48295i) q^{3} +(0.408576 + 1.95782i) q^{4} +(0.965926 + 0.258819i) q^{5} +(0.340749 - 2.42567i) q^{6} +(-1.19019 + 2.06148i) q^{7} +(-1.29806 + 2.51298i) q^{8} +(-1.39826 + 2.65422i) q^{9} +O(q^{10})$	\(q+(1.09740 + 0.892027i) q^{2} +(-0.894914 - 1.48295i) q^{3} +(0.408576 + 1.95782i) q^{4} +(0.965926 + 0.258819i) q^{5} +(0.340749 - 2.42567i) q^{6} +(-1.19019 + 2.06148i) q^{7} +(-1.29806 + 2.51298i) q^{8} +(-1.39826 + 2.65422i) q^{9} +(0.829134 + 1.14566i) q^{10} +(1.55731 - 0.417280i) q^{11} +(2.53770 - 2.35798i) q^{12} +(0.895760 + 0.240018i) q^{13} +(-3.14501 + 1.20058i) q^{14} +(-0.480606 - 1.66404i) q^{15} +(-3.66613 + 1.59984i) q^{16} +4.74153i q^{17} +(-3.90208 + 1.66546i) q^{18} +(-0.0735050 - 0.0735050i) q^{19} +(-0.112068 + 1.99686i) q^{20} +(4.12218 - 0.0798499i) q^{21} +(2.08122 + 0.931238i) q^{22} +(-4.51696 + 2.60787i) q^{23} +(4.88826 - 0.323945i) q^{24} +(0.866025 + 0.500000i) q^{25} +(0.768905 + 1.06244i) q^{26} +(5.18738 - 0.301753i) q^{27} +(-4.52229 - 1.48792i) q^{28} +(0.403219 - 0.108042i) q^{29} +(0.956949 - 2.25483i) q^{30} +(1.53992 - 0.889074i) q^{31} +(-5.45031 - 1.51463i) q^{32} +(-2.01246 - 1.93598i) q^{33} +(-4.22957 + 5.20336i) q^{34} +(-1.68319 + 1.68319i) q^{35} +(-5.76778 - 1.65309i) q^{36} +(6.28521 + 6.28521i) q^{37} +(-0.0150960 - 0.146233i) q^{38} +(-0.445694 - 1.54316i) q^{39} +(-1.90423 + 2.09139i) q^{40} +(3.22696 + 5.58926i) q^{41} +(4.59491 + 3.58947i) q^{42} +(0.408072 + 1.52295i) q^{43} +(1.45324 + 2.87844i) q^{44} +(-2.03758 + 2.20188i) q^{45} +(-7.28321 - 1.16737i) q^{46} +(3.77316 - 6.53530i) q^{47} +(5.65334 + 4.00496i) q^{48} +(0.666877 + 1.15506i) q^{49} +(0.504363 + 1.32122i) q^{50} +(7.03144 - 4.24326i) q^{51} +(-0.103927 + 1.85180i) q^{52} +(0.108443 - 0.108443i) q^{53} +(5.96181 + 4.29614i) q^{54} +1.61224 q^{55} +(-3.63550 - 5.66684i) q^{56} +(-0.0432233 + 0.174784i) q^{57} +(0.538870 + 0.241117i) q^{58} +(2.01928 - 7.53605i) q^{59} +(3.06152 - 1.62083i) q^{60} +(-1.53772 - 5.73887i) q^{61} +(2.48299 + 0.397981i) q^{62} +(-3.80741 - 6.04151i) q^{63} +(-4.63009 - 6.52398i) q^{64} +(0.803117 + 0.463680i) q^{65} +(-0.481532 - 3.91971i) q^{66} +(-3.03263 + 11.3179i) q^{67} +(-9.28307 + 1.93727i) q^{68} +(7.90962 + 4.36459i) q^{69} +(-3.34858 + 0.345682i) q^{70} -15.8467i q^{71} +(-4.85496 - 6.95912i) q^{72} +2.08269i q^{73} +(1.29082 + 12.5040i) q^{74} +(-0.0335449 - 1.73173i) q^{75} +(0.113877 - 0.173942i) q^{76} +(-0.993287 + 3.70700i) q^{77} +(0.887435 - 2.09104i) q^{78} +(-10.3996 - 6.00420i) q^{79} +(-3.95528 + 0.596459i) q^{80} +(-5.08974 - 7.42257i) q^{81} +(-1.44450 + 9.01220i) q^{82} +(0.701005 + 2.61619i) q^{83} +(1.84055 + 8.03787i) q^{84} +(-1.22720 + 4.57997i) q^{85} +(-0.910690 + 2.03529i) q^{86} +(-0.521067 - 0.501264i) q^{87} +(-0.972864 + 4.45513i) q^{88} +3.82213 q^{89} +(-4.20018 + 0.598773i) q^{90} +(-1.56092 + 1.56092i) q^{91} +(-6.95126 - 7.77789i) q^{92} +(-2.69654 - 1.48798i) q^{93} +(9.97033 - 3.80608i) q^{94} +(-0.0519759 - 0.0900248i) q^{95} +(2.63145 + 9.43798i) q^{96} +(-1.49815 + 2.59487i) q^{97} +(-0.298518 + 1.86244i) q^{98} +(-1.06997 + 4.71690i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 384 q - 12 q^{6}+O(q^{10}) $ 384 * q - 12 * q^6	$ 384 q - 12 q^{6} + 24 q^{12} + 20 q^{18} - 24 q^{24} + 24 q^{27} - 12 q^{36} + 48 q^{39} - 80 q^{42} + 24 q^{46} - 40 q^{48} - 192 q^{49} + 40 q^{51} + 12 q^{54} - 36 q^{58} + 72 q^{59} - 28 q^{60} + 72 q^{64} - 72 q^{66} - 156 q^{68} - 112 q^{72} - 168 q^{74} + 12 q^{76} - 116 q^{78} + 72 q^{82} - 120 q^{83} - 116 q^{84} - 36 q^{90} + 48 q^{93} + 20 q^{96} - 32 q^{99}+O(q^{100}) $ 384 * q - 12 * q^6 + 24 * q^12 + 20 * q^18 - 24 * q^24 + 24 * q^27 - 12 * q^36 + 48 * q^39 - 80 * q^42 + 24 * q^46 - 40 * q^48 - 192 * q^49 + 40 * q^51 + 12 * q^54 - 36 * q^58 + 72 * q^59 - 28 * q^60 + 72 * q^64 - 72 * q^66 - 156 * q^68 - 112 * q^72 - 168 * q^74 + 12 * q^76 - 116 * q^78 + 72 * q^82 - 120 * q^83 - 116 * q^84 - 36 * q^90 + 48 * q^93 + 20 * q^96 - 32 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/720\mathbb{Z}\right)^\times$.

$n$	$181$	$271$	$577$	$641$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$	$1$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	1.09740	+	0.892027i	0.775979	+	0.630758i
$2$	1.09740	+	0.892027i	0.775979	+	0.630758i
$3$	−0.894914	−	1.48295i	−0.516679	−	0.856179i
$3$	−0.894914	−	1.48295i	−0.516679	−	0.856179i
$4$	0.408576	+	1.95782i	0.204288	+	0.978911i
$5$	0.965926	+	0.258819i	0.431975	+	0.115747i
$5$	0.965926	+	0.258819i	0.431975	+	0.115747i
$6$	0.340749	−	2.42567i	0.139110	−	0.990277i
$7$	−1.19019	+	2.06148i	−0.449851	+	0.779165i	−0.998376	−	0.0569694i	$-0.981856\pi$
$7$	−1.19019	+	2.06148i	−0.449851	+	0.779165i	0.548525	+	0.836134i	$0.315190\pi$
$8$	−1.29806	+	2.51298i	−0.458933	+	0.888471i
$9$	−1.39826	+	2.65422i	−0.466086	+	0.884739i
$10$	0.829134	+	1.14566i	0.262195	+	0.362290i
$11$	1.55731	−	0.417280i	0.469546	−	0.125815i	−0.0162846	−	0.999867i	$-0.505184\pi$
$11$	1.55731	−	0.417280i	0.469546	−	0.125815i	0.485831	+	0.874053i	$0.338517\pi$
$12$	2.53770	−	2.35798i	0.732572	−	0.680689i
$13$	0.895760	+	0.240018i	0.248439	+	0.0665691i	0.380889	−	0.924621i	$-0.375618\pi$
$13$	0.895760	+	0.240018i	0.248439	+	0.0665691i	−0.132450	+	0.991190i	$0.542284\pi$
$14$	−3.14501	+	1.20058i	−0.840540	+	0.320869i
$15$	−0.480606	−	1.66404i	−0.124092	−	0.429652i
$16$	−3.66613	+	1.59984i	−0.916533	+	0.399959i
$17$			4.74153i			1.14999i	0.818157	+	0.574995i	$0.194996\pi$
$17$			4.74153i			1.14999i	−0.818157	+	0.574995i	$0.805004\pi$
$18$	−3.90208	+	1.66546i	−0.919730	+	0.392552i
$19$	−0.0735050	−	0.0735050i	−0.0168632	−	0.0168632i	0.698625	−	0.715488i	$-0.253796\pi$
$19$	−0.0735050	−	0.0735050i	−0.0168632	−	0.0168632i	−0.715488	+	0.698625i	$0.753796\pi$
$20$	−0.112068	+	1.99686i	−0.0250591	+	0.446511i
$21$	4.12218	−	0.0798499i	0.899533	−	0.0174247i
$22$	2.08122	+	0.931238i	0.443717	+	0.198541i
$23$	−4.51696	+	2.60787i	−0.941852	+	0.543778i	−0.890540	−	0.454904i	$-0.849673\pi$
$23$	−4.51696	+	2.60787i	−0.941852	+	0.543778i	−0.0513114	+	0.998683i	$0.516340\pi$
$24$	4.88826	−	0.323945i	0.997811	−	0.0661250i
$25$	0.866025	+	0.500000i	0.173205	+	0.100000i
$26$	0.768905	+	1.06244i	0.150795	+	0.208361i
$27$	5.18738	−	0.301753i	0.998312	−	0.0580724i
$28$	−4.52229	−	1.48792i	−0.854632	−	0.281190i
$29$	0.403219	−	0.108042i	0.0748759	−	0.0200629i	−0.221187	−	0.975232i	$-0.570993\pi$
$29$	0.403219	−	0.108042i	0.0748759	−	0.0200629i	0.296063	+	0.955169i	$0.404326\pi$
$30$	0.956949	−	2.25483i	0.174714	−	0.411673i
$31$	1.53992	−	0.889074i	0.276578	−	0.159682i	−0.355295	−	0.934754i	$-0.615620\pi$
$31$	1.53992	−	0.889074i	0.276578	−	0.159682i	0.631873	+	0.775072i	$0.282286\pi$
$32$	−5.45031	−	1.51463i	−0.963488	−	0.267751i
$33$	−2.01246	−	1.93598i	−0.350324	−	0.337010i
$34$	−4.22957	+	5.20336i	−0.725366	+	0.892369i
$35$	−1.68319	+	1.68319i	−0.284511	+	0.284511i
$36$	−5.76778	−	1.65309i	−0.961297	−	0.275515i
$37$	6.28521	+	6.28521i	1.03328	+	1.03328i	0.999427	+	0.0338558i	$0.0107787\pi$
$37$	6.28521	+	6.28521i	1.03328	+	1.03328i	0.0338558	+	0.999427i	$0.489221\pi$
$38$	−0.0150960	−	0.146233i	−0.00244889	−	0.0237221i
$39$	−0.445694	−	1.54316i	−0.0713682	−	0.247103i
$40$	−1.90423	+	2.09139i	−0.301086	+	0.330677i
$41$	3.22696	+	5.58926i	0.503967	+	0.872896i	0.999989	+	0.00458661i	$0.00145997\pi$
$41$	3.22696	+	5.58926i	0.503967	+	0.872896i	−0.496023	+	0.868310i	$0.665207\pi$
$42$	4.59491	+	3.58947i	0.709010	+	0.553867i
$43$	0.408072	+	1.52295i	0.0622304	+	0.232247i	0.990035	−	0.140818i	$-0.0449734\pi$
$43$	0.408072	+	1.52295i	0.0622304	+	0.232247i	−0.927805	+	0.373065i	$0.878307\pi$
$44$	1.45324	+	2.87844i	0.219084	+	0.433942i
$45$	−2.03758	+	2.20188i	−0.303744	+	0.328237i
$46$	−7.28321	−	1.16737i	−1.07385	−	0.172120i
$47$	3.77316	−	6.53530i	0.550372	−	0.953272i	−0.447876	−	0.894096i	$-0.647819\pi$
$47$	3.77316	−	6.53530i	0.550372	−	0.953272i	0.998248	−	0.0591760i	$-0.0188473\pi$
$48$	5.65334	+	4.00496i	0.815990	+	0.578066i
$49$	0.666877	+	1.15506i	0.0952681	+	0.165009i
$50$	0.504363	+	1.32122i	0.0713277	+	0.186848i
$51$	7.03144	−	4.24326i	0.984598	−	0.594175i
$52$	−0.103927	+	1.85180i	−0.0144121	+	0.256799i
$53$	0.108443	−	0.108443i	0.0148958	−	0.0148958i	−0.699620	−	0.714515i	$-0.746647\pi$
$53$	0.108443	−	0.108443i	0.0148958	−	0.0148958i	0.714515	+	0.699620i	$0.246647\pi$
$54$	5.96181	+	4.29614i	0.811299	+	0.584631i
$55$	1.61224			0.217395
$56$	−3.63550	−	5.66684i	−0.485814	−	0.757264i
$57$	−0.0432233	+	0.174784i	−0.00572507	+	0.0231508i
$58$	0.538870	+	0.241117i	0.0707571	+	0.0316602i
$59$	2.01928	−	7.53605i	0.262888	−	0.981110i	−0.700643	−	0.713512i	$-0.747103\pi$
$59$	2.01928	−	7.53605i	0.262888	−	0.981110i	0.963531	−	0.267598i	$-0.0862299\pi$
$60$	3.06152	−	1.62083i	0.395241	−	0.209248i
$61$	−1.53772	−	5.73887i	−0.196885	−	0.734787i	−0.991771	−	0.128027i	$-0.959136\pi$
$61$	−1.53772	−	5.73887i	−0.196885	−	0.734787i	0.794885	−	0.606760i	$-0.207531\pi$
$62$	2.48299	+	0.397981i	0.315340	+	0.0505436i
$63$	−3.80741	−	6.04151i	−0.479688	−	0.761159i
$64$	−4.63009	−	6.52398i	−0.578761	−	0.815497i
$65$	0.803117	+	0.463680i	0.0996144	+	0.0575124i
$66$	−0.481532	−	3.91971i	−0.0592725	−	0.482483i
$67$	−3.03263	+	11.3179i	−0.370495	+	1.38271i	0.489322	+	0.872103i	$0.337244\pi$
$67$	−3.03263	+	11.3179i	−0.370495	+	1.38271i	−0.859817	+	0.510603i	$0.829422\pi$
$68$	−9.28307	+	1.93727i	−1.12574	+	0.234929i
$69$	7.90962	+	4.36459i	0.952206	+	0.525435i
$70$	−3.34858	+	0.345682i	−0.400232	+	0.0413169i
$71$		−	15.8467i		−	1.88066i	−0.340267	−	0.940329i	$-0.610517\pi$
$71$		−	15.8467i		−	1.88066i	0.340267	−	0.940329i	$-0.389483\pi$
$72$	−4.85496	−	6.95912i	−0.572163	−	0.820140i
$73$			2.08269i			0.243760i	0.992545	+	0.121880i	$0.0388923\pi$
$73$			2.08269i			0.243760i	−0.992545	+	0.121880i	$0.961108\pi$
$74$	1.29082	+	12.5040i	0.150054	+	1.45356i
$75$	−0.0335449	−	1.73173i	−0.00387343	−	0.199962i
$76$	0.113877	−	0.173942i	0.0130626	−	0.0199525i
$77$	−0.993287	+	3.70700i	−0.113196	+	0.422452i
$78$	0.887435	−	2.09104i	0.100482	−	0.236763i
$79$	−10.3996	−	6.00420i	−1.17004	−	0.675525i	−0.216354	−	0.976315i	$-0.569416\pi$
$79$	−10.3996	−	6.00420i	−1.17004	−	0.675525i	−0.953690	+	0.300790i	$0.902750\pi$
$80$	−3.95528	+	0.596459i	−0.442214	+	0.0666862i
$81$	−5.08974	−	7.42257i	−0.565527	−	0.824730i
$82$	−1.44450	+	9.01220i	−0.159519	+	0.995231i
$83$	0.701005	+	2.61619i	0.0769453	+	0.287164i	0.993667	−	0.112362i	$-0.0358416\pi$
$83$	0.701005	+	2.61619i	0.0769453	+	0.287164i	−0.916722	+	0.399526i	$0.869175\pi$
$84$	1.84055	+	8.03787i	0.200821	+	0.877003i
$85$	−1.22720	+	4.57997i	−0.133108	+	0.496767i
$86$	−0.910690	+	2.03529i	−0.0982023	+	0.219471i
$87$	−0.521067	−	0.501264i	−0.0558643	−	0.0537411i
$88$	−0.972864	+	4.45513i	−0.103708	+	0.474919i
$89$	3.82213			0.405145			0.202572	−	0.979267i	$-0.435070\pi$
$89$	3.82213			0.405145			0.202572	+	0.979267i	$0.435070\pi$
$90$	−4.20018	+	0.598773i	−0.442737	+	0.0631162i
$91$	−1.56092	+	1.56092i	−0.163629	+	0.163629i
$92$	−6.95126	−	7.77789i	−0.724719	−	0.810902i
$93$	−2.69654	−	1.48798i	−0.279619	−	0.154296i
$94$	9.97033	−	3.80608i	1.02836	−	0.392568i
$95$	−0.0519759	−	0.0900248i	−0.00533261	−	0.00923635i
$96$	2.63145	+	9.43798i	0.268571	+	0.963260i
$97$	−1.49815	+	2.59487i	−0.152114	+	0.263469i	−0.932004	−	0.362447i	$-0.881941\pi$
$97$	−1.49815	+	2.59487i	−0.152114	+	0.263469i	0.779891	+	0.625916i	$0.215275\pi$
$98$	−0.298518	+	1.86244i	−0.0301549	+	0.188135i
$99$	−1.06997	+	4.71690i	−0.107536	+	0.474066i
$100$	−0.625074	+	1.89981i	−0.0625074	+	0.189981i
$101$	−3.43952	−	12.8365i	−0.342245	−	1.27727i	−0.895798	−	0.444461i	$-0.853395\pi$
$101$	−3.43952	−	12.8365i	−0.342245	−	1.27727i	0.553554	−	0.832814i	$-0.313271\pi$
$102$	11.5014	+	1.61567i	1.13881	+	0.159975i
$103$	−0.105796	−	0.183244i	−0.0104244	−	0.0180555i	0.860766	−	0.509001i	$-0.169985\pi$
$103$	−0.105796	−	0.183244i	−0.0104244	−	0.0180555i	−0.871191	+	0.490945i	$0.836652\pi$
$104$	−1.76591	+	1.93947i	−0.173162	+	0.190180i
$105$	4.00239	+	0.989769i	0.390593	+	0.0965916i
$106$	0.215739	−	0.0222713i	0.0209545	−	0.00216318i
$107$	−13.0000	−	13.0000i	−1.25676	−	1.25676i	−0.952630	−	0.304132i	$-0.901634\pi$
$107$	−13.0000	−	13.0000i	−1.25676	−	1.25676i	−0.304132	−	0.952630i	$-0.598366\pi$
$108$	2.71022	+	10.0327i	0.260791	+	0.965395i
$109$	4.67500	−	4.67500i	0.447784	−	0.447784i	−0.446833	−	0.894617i	$-0.647448\pi$
$109$	4.67500	−	4.67500i	0.447784	−	0.447784i	0.894617	+	0.446833i	$0.147448\pi$
$110$	1.76928	+	1.43817i	0.168694	+	0.137124i
$111$	3.69591	−	14.9454i	0.350800	−	1.41855i
$112$	1.06538	−	9.46176i	0.100669	−	0.894052i
$113$	14.8809	−	8.59147i	1.39987	−	0.808217i	0.405494	−	0.914098i	$-0.367099\pi$
$113$	14.8809	−	8.59147i	1.39987	−	0.808217i	0.994379	+	0.105880i	$0.0337661\pi$
$114$	−0.203346	+	0.153252i	−0.0190451	+	0.0143534i
$115$	−5.03802	+	1.34993i	−0.469797	+	0.125882i
$116$	0.376273	+	0.745288i	0.0349361	+	0.0691982i
$117$	−1.88957	+	2.04194i	−0.174690	+	0.188777i
$118$	8.93831	−	6.46881i	0.822838	−	0.595502i
$119$	−9.77456	−	5.64334i	−0.896032	−	0.517324i
$120$	4.80554	+	0.952267i	0.438684	+	0.0869297i
$121$	−7.27519	+	4.20033i	−0.661381	+	0.381849i
$122$	3.43172	−	7.66953i	0.310694	−	0.694366i
$123$	5.40072	−	9.78732i	0.486967	−	0.882493i
$124$	2.36982	+	2.65164i	0.212816	+	0.238124i
$125$	0.707107	+	0.707107i	0.0632456	+	0.0632456i
$126$	1.21094	−	10.0263i	0.107879	−	0.893211i
$127$		−	1.49759i		−	0.132890i	−0.997790	−	0.0664449i	$-0.978834\pi$
$127$		−	1.49759i		−	0.132890i	0.997790	−	0.0664449i	$-0.0211657\pi$
$128$	0.738503	−	11.2896i	0.0652750	−	0.997867i
$129$	1.89326	−	1.96805i	0.166692	−	0.173278i
$130$	0.467726	+	1.22524i	0.0410223	+	0.107461i
$131$	18.4745	+	4.95024i	1.61413	+	0.432504i	0.949269	−	0.314464i	$-0.101825\pi$
$131$	18.4745	+	4.95024i	1.61413	+	0.432504i	0.664859	+	0.746969i	$0.268492\pi$
$132$	2.96805	−	4.73103i	0.258336	−	0.411783i
$133$	0.239014	−	0.0640436i	0.0207251	−	0.00555328i
$134$	−13.4239	+	9.71512i	−1.15965	+	0.839259i
$135$	5.08873	+	1.05112i	0.437968	+	0.0904662i
$136$	−11.9154	−	6.15479i	−1.02173	−	0.527768i
$137$	8.42582	−	14.5939i	0.719866	−	1.24684i	−0.241186	−	0.970479i	$-0.577537\pi$
$137$	8.42582	−	14.5939i	0.719866	−	1.24684i	0.961053	−	0.276366i	$-0.0891301\pi$
$138$	4.78669	+	11.8453i	0.407470	+	1.00834i
$139$	10.1013	+	2.70662i	0.856777	+	0.229573i	0.660361	−	0.750948i	$-0.270403\pi$
$139$	10.1013	+	2.70662i	0.856777	+	0.229573i	0.196416	+	0.980521i	$0.437070\pi$
$140$	−3.98309	−	2.60767i	−0.336633	−	0.220389i
$141$	−13.0682	+	0.253141i	−1.10054	+	0.0213183i
$142$	14.1357	−	17.3902i	1.18624	−	1.45935i
$143$	1.49513			0.125029
$144$	0.879885	−	11.9677i	0.0733238	−	0.997308i
$145$	0.417443			0.0346668
$146$	−1.85781	+	2.28554i	−0.153754	+	0.189153i
$147$	1.11610	−	2.02263i	0.0920545	−	0.166823i
$148$	−9.73734	+	14.8733i	−0.800404	+	1.22258i
$149$	11.6267	+	3.11535i	0.952492	+	0.255220i	0.701420	−	0.712749i	$-0.252550\pi$
$149$	11.6267	+	3.11535i	0.952492	+	0.255220i	0.251073	+	0.967968i	$0.419217\pi$
$150$	1.50793	−	1.93032i	0.123122	−	0.157610i
$151$	1.49389	−	2.58750i	0.121571	−	0.210568i	−0.798816	−	0.601575i	$-0.794540\pi$
$151$	1.49389	−	2.58750i	0.121571	−	0.210568i	0.920387	+	0.391008i	$0.127873\pi$
$152$	0.280130	−	0.0893024i	0.0227215	−	0.00724338i
$153$	−12.5851	−	6.62989i	−1.01744	−	0.535995i
$154$	−4.39678	+	3.18202i	−0.354302	+	0.256415i
$155$	1.71756	−	0.460218i	0.137958	−	0.0369656i
$156$	2.83913	−	1.50309i	0.227312	−	0.120343i
$157$	−4.72457	−	1.26594i	−0.377062	−	0.101033i	0.0653104	−	0.997865i	$-0.479196\pi$
$157$	−4.72457	−	1.26594i	−0.377062	−	0.101033i	−0.442372	+	0.896832i	$0.645863\pi$
$158$	−6.05660	−	15.8657i	−0.481837	−	1.26221i
$159$	−0.257862	−	0.0637680i	−0.0204498	−	0.00505713i
$160$	−4.87258	−	2.87366i	−0.385212	−	0.227183i
$161$		−	12.4155i		−	0.978477i
$162$	1.03564	−	12.6857i	0.0813677	−	0.996684i
$163$	10.9610	+	10.9610i	0.858535	+	0.858535i	0.991166	−	0.132630i	$-0.0423423\pi$
$163$	10.9610	+	10.9610i	0.858535	+	0.858535i	−0.132630	+	0.991166i	$0.542342\pi$
$164$	−9.62432	+	8.60145i	−0.751533	+	0.671661i
$165$	−1.44282	−	2.39087i	−0.112323	−	0.186129i
$166$	−1.56443	+	3.49632i	−0.121423	+	0.271367i
$167$	−6.92842	+	4.00012i	−0.536137	+	0.309539i	−0.743512	−	0.668723i	$-0.766841\pi$
$167$	−6.92842	+	4.00012i	−0.536137	+	0.309539i	0.207375	+	0.978262i	$0.433508\pi$
$168$	−5.15017	+	10.4626i	−0.397344	+	0.807206i
$169$	−10.5136	−	6.07000i	−0.808735	−	0.466923i
$170$	−5.43218	+	3.93136i	−0.416629	+	0.301522i
$171$	0.297877	−	0.0923192i	0.0227792	−	0.00705983i
$172$	−2.81493	+	1.42117i	−0.214636	+	0.108363i
$173$	−8.28528	+	2.22003i	−0.629918	+	0.168786i	−0.559632	−	0.828741i	$-0.689058\pi$
$173$	−8.28528	+	2.22003i	−0.629918	+	0.168786i	−0.0702855	+	0.997527i	$0.522391\pi$
$174$	−0.124679	−	1.01489i	−0.00945186	−	0.0769389i
$175$	−2.06148	+	1.19019i	−0.155833	+	0.0899702i
$176$	−5.04172	+	4.02124i	−0.380034	+	0.303113i
$177$	−12.9826	+	3.74963i	−0.975834	+	0.281840i
$178$	4.19441	+	3.40944i	0.314384	+	0.255549i
$179$	−1.95671	+	1.95671i	−0.146252	+	0.146252i	−0.776441	−	0.630190i	$-0.782977\pi$
$179$	−1.95671	+	1.95671i	−0.146252	+	0.146252i	0.630190	+	0.776441i	$0.282977\pi$
$180$	−5.14340	−	3.08958i	−0.383366	−	0.230283i
$181$	17.2336	+	17.2336i	1.28097	+	1.28097i	0.940119	+	0.340847i	$0.110714\pi$
$181$	17.2336	+	17.2336i	1.28097	+	1.28097i	0.340847	+	0.940119i	$0.389286\pi$
$182$	−3.10534	+	0.320572i	−0.230183	+	0.0237624i
$183$	−7.13430	+	7.41615i	−0.527383	+	0.548218i
$184$	−0.690230	−	14.7362i	−0.0508844	−	1.08637i
$185$	4.44432	+	7.69778i	0.326753	+	0.565952i
$186$	−1.63188	−	4.03830i	−0.119655	−	0.296102i
$187$	1.97854	+	7.38403i	0.144685	+	0.539974i
$188$	14.3366	+	4.71701i	1.04560	+	0.344023i
$189$	−5.55193	+	11.0528i	−0.403844	+	0.803974i
$190$	0.0232662	−	0.145157i	0.00168791	−	0.0105308i
$191$	8.46674	−	14.6648i	0.612632	−	1.06111i	−0.378163	−	0.925739i	$-0.623444\pi$
$191$	8.46674	−	14.6648i	0.612632	−	1.06111i	0.990795	−	0.135371i	$-0.0432225\pi$
$192$	−5.53118	+	12.7046i	−0.399178	+	0.916873i
$193$	5.98505	+	10.3664i	0.430814	+	0.746191i	0.996944	−	0.0781250i	$-0.0248933\pi$
$193$	5.98505	+	10.3664i	0.430814	+	0.746191i	−0.566130	+	0.824316i	$0.691560\pi$
$194$	−3.95876	+	1.51122i	−0.284222	+	0.108499i
$195$	−0.0311082	−	1.60593i	−0.00222770	−	0.115003i
$196$	−1.98894	+	1.77756i	−0.142067	+	0.126968i
$197$	−10.8234	+	10.8234i	−0.771133	+	0.771133i	−0.978305	−	0.207171i	$-0.933574\pi$
$197$	−10.8234	+	10.8234i	−0.771133	+	0.771133i	0.207171	+	0.978305i	$0.433574\pi$
$198$	−5.38179	+	4.22189i	−0.382467	+	0.300037i
$199$	−3.68884			−0.261495			−0.130748	−	0.991416i	$-0.541738\pi$
$199$	−3.68884			−0.261495			−0.130748	+	0.991416i	$0.541738\pi$
$200$	−2.38064	+	1.52727i	−0.168337	+	0.107994i
$201$	19.4978	−	5.63135i	1.37527	−	0.397205i
$202$	7.67593	−	17.1549i	0.540077	−	1.20701i
$203$	−0.257183	+	0.959818i	−0.0180507	+	0.0673660i
$204$	11.1804	+	12.0326i	0.782786	+	0.842451i
$205$	1.67040	+	6.23401i	0.116666	+	0.435402i
$206$	0.0473580	−	0.295464i	0.00329959	−	0.0205860i
$207$	−0.605971	−	15.6355i	−0.0421179	−	1.08674i
$208$	−3.66796	+	0.553132i	−0.254328	+	0.0383528i
$209$	−0.145142	−	0.0837978i	−0.0100397	−	0.00579641i
$210$	3.50932	+	4.65641i	0.242166	+	0.321323i
$211$	−0.419650	+	1.56615i	−0.0288899	+	0.107818i	−0.978865	−	0.204506i	$-0.934441\pi$
$211$	−0.419650	+	1.56615i	−0.0288899	+	0.107818i	0.949975	+	0.312325i	$0.101108\pi$
$212$	0.256619	+	0.168005i	0.0176247	+	0.0115386i
$213$	−23.4998	+	14.1814i	−1.61018	+	0.971696i
$214$	−2.66987	−	25.8626i	−0.182508	−	1.76793i
$215$			1.57667i			0.107528i
$216$	−5.97523	+	13.4275i	−0.406563	+	0.913623i
$217$			4.23268i			0.287333i
$218$	9.30058	−	0.960122i	0.629915	−	0.0650276i
$219$	3.08851	−	1.86382i	0.208702	−	0.125946i
$220$	0.658724	+	3.15649i	0.0444112	+	0.212810i
$221$	−1.13805	+	4.24728i	−0.0765538	+	0.285703i
$222$	17.3876	−	13.1042i	1.16698	−	0.879496i
$223$	18.9530	+	10.9425i	1.26919	+	0.732767i	0.974835	−	0.222930i	$-0.0715620\pi$
$223$	18.9530	+	10.9425i	1.26919	+	0.732767i	0.294355	+	0.955696i	$0.404895\pi$
$224$	9.60930	−	9.43299i	0.642048	−	0.630268i
$225$	−2.53804	+	1.59949i	−0.169202	+	0.106633i
$226$	23.9941	+	3.84585i	1.59606	+	0.255822i
$227$	−3.44733	−	12.8656i	−0.228807	−	0.853921i	−0.980843	−	0.194799i	$-0.937595\pi$
$227$	−3.44733	−	12.8656i	−0.228807	−	0.853921i	0.752036	−	0.659122i	$-0.229072\pi$
$228$	−0.359857	−	0.0132108i	−0.0238321	−	0.000874907i
$229$	1.43830	−	5.36780i	0.0950454	−	0.354714i	−0.901981	−	0.431776i	$-0.857887\pi$
$229$	1.43830	−	5.36780i	0.0950454	−	0.354714i	0.997026	+	0.0770616i	$0.0245538\pi$
$230$	−6.73290	−	3.01263i	−0.443954	−	0.198647i
$231$	6.38619	−	1.84445i	0.420180	−	0.121356i
$232$	−0.251895	+	1.15353i	−0.0165377	+	0.0757326i
$233$	9.36458			0.613494			0.306747	−	0.951791i	$-0.400760\pi$
$233$	9.36458			0.613494			0.306747	+	0.951791i	$0.400760\pi$
$234$	−3.89507	+	0.555277i	−0.254629	+	0.0362996i
$235$	5.33605	−	5.33605i	0.348086	−	0.348086i
$236$	15.5793	+	0.874339i	1.01412	+	0.0569147i
$237$	0.402821	+	20.7953i	0.0261660	+	1.35080i
$238$	−5.69259	−	14.9122i	−0.368996	−	0.966613i
$239$	9.06641	+	15.7035i	0.586457	+	1.01577i	0.994692	+	0.102897i	$0.0328112\pi$
$239$	9.06641	+	15.7035i	0.586457	+	1.01577i	−0.408235	+	0.912877i	$0.633855\pi$
$240$	4.42415	+	5.33169i	0.285578	+	0.344159i
$241$	3.88499	−	6.72901i	0.250254	−	0.433453i	−0.713341	−	0.700817i	$-0.752819\pi$
$241$	3.88499	−	6.72901i	0.250254	−	0.433453i	0.963596	+	0.267363i	$0.0861524\pi$
$242$	−11.7306	−	1.88022i	−0.754072	−	0.120865i
$243$	−6.45239	+	14.1904i	−0.413921	+	0.910313i
$244$	10.6074	−	5.35535i	0.679069	−	0.342841i
$245$	0.345201	+	1.28831i	0.0220541	+	0.0823069i
$246$	14.6573	−	5.92302i	0.934516	−	0.377638i
$247$	−0.0482003	−	0.0834853i	−0.00306691	−	0.00531205i
$248$	0.235313	+	5.02385i	0.0149424	+	0.319015i
$249$	3.25232	−	3.38081i	0.206108	−	0.214250i
$250$	0.145221	+	1.40674i	0.00918458	+	0.0889699i
$251$	7.85438	+	7.85438i	0.495764	+	0.495764i	0.910116	−	0.414353i	$-0.135992\pi$
$251$	7.85438	+	7.85438i	0.495764	+	0.495764i	−0.414353	+	0.910116i	$0.635992\pi$
$252$	10.2726	−	9.92264i	0.647112	−	0.625068i
$253$	−5.94609	+	5.94609i	−0.373828	+	0.373828i
$254$	1.33589	−	1.64346i	0.0838214	−	0.103120i
$255$	7.89008	−	2.27881i	0.494096	−	0.142704i
$256$	10.8810	−	11.7304i	0.680065	−	0.733152i
$257$	−24.5542	+	14.1764i	−1.53165	+	0.884299i	−0.532364	+	0.846515i	$0.678696\pi$
$257$	−24.5542	+	14.1764i	−1.53165	+	0.884299i	−0.999286	+	0.0377834i	$0.987970\pi$
$258$	3.83322	−	0.470907i	0.238646	−	0.0293174i
$259$	−20.4374	+	5.47619i	−1.26992	+	0.340274i
$260$	−0.579668	+	1.76181i	−0.0359495	+	0.109263i
$261$	−0.277037	+	1.22130i	−0.0171482	+	0.0755967i
$262$	15.8582	+	21.9122i	0.979725	+	1.35374i
$263$	−24.5266	−	14.1605i	−1.51238	−	0.873172i	−0.999895	−	0.0144738i	$-0.995393\pi$
$263$	−24.5266	−	14.1605i	−1.51238	−	0.873172i	−0.512482	−	0.858698i	$-0.671274\pi$
$264$	7.47735	−	2.54425i	0.460199	−	0.156588i
$265$	0.132815	−	0.0766807i	0.00815876	−	0.00471046i
$266$	0.319423	+	0.142925i	0.0195851	+	0.00876332i
$267$	−3.42048	−	5.66801i	−0.209330	−	0.346877i
$268$	−23.3976	−	1.31312i	−1.42923	−	0.0802115i
$269$	5.67765	+	5.67765i	0.346172	+	0.346172i	0.858682	−	0.512509i	$-0.171284\pi$
$269$	5.67765	+	5.67765i	0.346172	+	0.346172i	−0.512509	+	0.858682i	$0.671284\pi$
$270$	4.64674	+	5.69278i	0.282792	+	0.346452i
$271$			13.2573i			0.805321i	0.915349	+	0.402661i	$0.131915\pi$
$271$			13.2573i			0.805321i	−0.915349	+	0.402661i	$0.868085\pi$
$272$	−7.58568	−	17.3831i	−0.459949	−	1.05400i
$273$	3.71165	+	0.917872i	0.224639	+	0.0555521i
$274$	22.2647	−	8.49934i	1.34506	−	0.513464i
$275$	1.55731	+	0.417280i	0.0939092	+	0.0251629i
$276$	−5.31342	+	17.2689i	−0.319830	+	1.03947i
$277$	0.158885	−	0.0425732i	0.00954649	−	0.00255797i	−0.254043	−	0.967193i	$-0.581760\pi$
$277$	0.158885	−	0.0425732i	0.00954649	−	0.00255797i	0.263589	+	0.964635i	$0.415094\pi$
$278$	8.67074	+	11.9808i	0.520037	+	0.718563i
$279$	0.206587	+	5.33044i	0.0123681	+	0.319125i
$280$	−2.04493	−	6.41469i	−0.122208	−	0.383351i
$281$	10.5940	−	18.3494i	0.631985	−	1.09463i	−0.355160	−	0.934805i	$-0.615574\pi$
$281$	10.5940	−	18.3494i	0.631985	−	1.09463i	0.987145	−	0.159825i	$-0.0510930\pi$
$282$	−14.5668	−	11.3793i	−0.867441	−	0.677630i
$283$	21.7642	+	5.83170i	1.29375	+	0.346658i	0.839082	−	0.544004i	$-0.183093\pi$
$283$	21.7642	+	5.83170i	1.29375	+	0.346658i	0.454664	+	0.890663i	$0.349759\pi$
$284$	31.0250	−	6.47458i	1.84100	−	0.384196i
$285$	−0.0869881	+	0.157642i	−0.00515273	+	0.00933790i
$286$	1.64076	+	1.33370i	0.0970199	+	0.0788631i
$287$	−15.3628			−0.906840
$288$	11.6411	−	12.3485i	0.685958	−	0.727641i
$289$	−5.48212			−0.322478
$290$	0.458102	+	0.372371i	0.0269007	+	0.0218664i
$291$	5.18876	−	0.100510i	0.304170	−	0.00589202i
$292$	−4.07753	+	0.850935i	−0.238619	+	0.0497972i
$293$	−15.9940	−	4.28559i	−0.934381	−	0.250367i	−0.240659	−	0.970610i	$-0.577364\pi$
$293$	−15.9940	−	4.28559i	−0.934381	−	0.250367i	−0.693722	+	0.720243i	$0.744030\pi$
$294$	3.02905	−	1.22404i	0.176658	−	0.0713873i
$295$	3.90095	−	6.75664i	0.227122	−	0.393387i
$296$	−23.9532	+	7.63601i	−1.39225	+	0.443834i
$297$	7.95244	−	2.63451i	0.461447	−	0.152870i
$298$	9.98012	+	13.7901i	0.578133	+	0.798838i
$299$	−4.67205	+	1.25187i	−0.270192	+	0.0723976i
$300$	3.37670	−	0.773216i	0.194954	−	0.0446417i
$301$	−3.62520	−	0.971370i	−0.208953	−	0.0559888i
$302$	3.94752	−	1.50693i	0.227154	−	0.0867140i
$303$	−15.9577	+	16.5881i	−0.916746	+	0.952963i
$304$	0.387075	+	0.151883i	0.0222003	+	0.00871108i
$305$		−	5.94131i		−	0.340199i
$306$	−7.89681	−	18.5019i	−0.451431	−	1.05768i
$307$	16.2316	+	16.2316i	0.926386	+	0.926386i	0.997470	−	0.0710844i	$-0.0226460\pi$
$307$	16.2316	+	16.2316i	0.926386	+	0.926386i	−0.0710844	+	0.997470i	$0.522646\pi$
$308$	−7.66348	−	0.430090i	−0.436667	−	0.0245066i
$309$	−0.177062	+	0.320877i	−0.0100727	+	0.0182540i
$310$	2.29538	+	1.02706i	0.130369	+	0.0583334i
$311$	−15.7087	+	9.06945i	−0.890761	+	0.514281i	−0.874191	−	0.485582i	$-0.838608\pi$
$311$	−15.7087	+	9.06945i	−0.890761	+	0.514281i	−0.0165697	+	0.999863i	$0.505275\pi$
$312$	4.45646	+	0.883094i	0.252297	+	0.0499953i
$313$	−16.1335	−	9.31466i	−0.911918	−	0.526496i	−0.0308701	−	0.999523i	$-0.509828\pi$
$313$	−16.1335	−	9.31466i	−0.911918	−	0.526496i	−0.881048	+	0.473027i	$0.843161\pi$
$314$	−4.05549	−	5.60369i	−0.228864	−	0.316235i
$315$	−2.11402	−	6.82108i	−0.119111	−	0.384324i
$316$	7.50614	−	22.8137i	0.422253	−	1.28337i
$317$	−9.78783	+	2.62264i	−0.549740	+	0.147302i	−0.522988	−	0.852340i	$-0.675183\pi$
$317$	−9.78783	+	2.62264i	−0.549740	+	0.147302i	−0.0267512	+	0.999642i	$0.508516\pi$
$318$	−0.226095	−	0.299999i	−0.0126788	−	0.0168231i
$319$	0.582853	−	0.336510i	0.0326335	−	0.0188410i
$320$	−2.78379	−	7.50003i	−0.155619	−	0.419265i
$321$	−7.64445	+	30.9123i	−0.426671	+	1.72536i
$322$	11.0749	−	13.6248i	0.617182	−	0.759278i
$323$	0.348526	−	0.348526i	0.0193925	−	0.0193925i
$324$	12.4525	−	12.9975i	0.691806	−	0.722083i
$325$	0.655742	+	0.655742i	0.0363740	+	0.0363740i
$326$	2.25111	+	21.8062i	0.124677	+	1.20773i
$327$	−11.1165	−	2.74905i	−0.614744	−	0.152023i
$328$	−18.2345	+	0.854086i	−1.00683	+	0.0471590i
$329$	8.98158	+	15.5566i	0.495171	+	0.857661i
$330$	0.549371	−	3.91078i	0.0302419	−	0.215281i
$331$	9.38602	+	35.0291i	0.515902	+	1.92537i	0.336991	+	0.941508i	$0.390591\pi$
$331$	9.38602	+	35.0291i	0.515902	+	1.92537i	0.178911	+	0.983865i	$0.442743\pi$
$332$	−4.83561	+	2.44135i	−0.265389	+	0.133987i
$333$	−25.4707	+	7.89397i	−1.39578	+	0.432587i
$334$	−11.1715	−	1.79060i	−0.611275	−	0.0979771i
$335$	−5.85860	+	10.1474i	−0.320089	+	0.554411i
$336$	−14.9847	+	6.88756i	−0.817483	+	0.375747i
$337$	−0.903216	−	1.56442i	−0.0492013	−	0.0852192i	0.840376	−	0.542004i	$-0.182334\pi$
$337$	−0.903216	−	1.56442i	−0.0492013	−	0.0852192i	−0.889577	+	0.456785i	$0.849001\pi$
$338$	−6.12297	−	16.0396i	−0.333046	−	0.872439i
$339$	−26.0578	−	14.3789i	−1.41526	−	0.780954i
$340$	−9.46816	−	0.531372i	−0.513483	−	0.0288177i
$341$	2.02714	−	2.02714i	0.109776	−	0.109776i
$342$	0.409242	+	0.164403i	0.0221293	+	0.00888991i
$343$	−19.8376			−1.07113
$344$	−4.35683	−	0.951398i	−0.234904	−	0.0512959i
$345$	6.51047	+	6.26303i	0.350512	+	0.337190i
$346$	−11.0726	−	4.95442i	−0.595266	−	0.266352i
$347$	8.84233	−	33.0000i	0.474681	−	1.77154i	−0.147924	−	0.988999i	$-0.547259\pi$
$347$	8.84233	−	33.0000i	0.474681	−	1.77154i	0.622605	−	0.782536i	$-0.286074\pi$
$348$	0.768490	−	1.22496i	0.0411954	−	0.0656648i
$349$	−8.90898	−	33.2488i	−0.476887	−	1.77977i	−0.614105	−	0.789224i	$-0.710483\pi$
$349$	−8.90898	−	33.2488i	−0.476887	−	1.77977i	0.137219	−	0.990541i	$-0.456184\pi$
$350$	−3.32395	−	0.532773i	−0.177673	−	0.0284779i
$351$	4.71908	+	0.974768i	0.251886	+	0.0520293i
$352$	−9.11984	−	0.0844364i	−0.486089	−	0.00450048i
$353$	26.1540	+	15.1000i	1.39204	+	0.803693i	0.993541	−	0.113477i	$-0.0361989\pi$
$353$	26.1540	+	15.1000i	1.39204	+	0.803693i	0.398496	+	0.917170i	$0.369532\pi$
$354$	−17.5919	−	7.46601i	−0.935000	−	0.396814i
$355$	4.10143	−	15.3067i	0.217681	−	0.812398i
$356$	1.56163	+	7.48305i	0.0827662	+	0.396601i
$357$	0.378611	+	19.5454i	0.0200382	+	1.03445i
$358$	−3.89274	+	0.401857i	−0.205738	+	0.0212388i
$359$		−	13.0585i		−	0.689204i	−0.938749	−	0.344602i	$-0.888014\pi$
$359$		−	13.0585i		−	0.689204i	0.938749	−	0.344602i	$-0.111986\pi$
$360$	−2.88838	−	7.97855i	−0.152231	−	0.420507i
$361$		−	18.9892i		−	0.999431i
$362$	3.53933	+	34.2851i	0.186023	+	1.80198i
$363$	12.7395	+	7.02978i	0.668652	+	0.368968i
$364$	−3.69376	−	2.41825i	−0.193606	−	0.126751i
$365$	−0.539039	+	2.01172i	−0.0282146	+	0.105298i
$366$	−14.4446	+	1.77450i	−0.755031	+	0.0927548i
$367$	−16.4968	−	9.52445i	−0.861127	−	0.497172i	0.00326228	−	0.999995i	$-0.498962\pi$
$367$	−16.4968	−	9.52445i	−0.861127	−	0.497172i	−0.864390	+	0.502823i	$0.832295\pi$
$368$	12.3876	−	16.7872i	0.645749	−	0.875093i
$369$	−19.3472	+	0.749825i	−1.00718	+	0.0390343i
$370$	−1.98943	+	12.4120i	−0.103426	+	0.645269i
$371$	0.0944844	+	0.352621i	0.00490539	+	0.0183072i
$372$	1.81145	−	5.88731i	0.0939192	−	0.305243i
$373$	2.54597	−	9.50168i	0.131825	−	0.491978i	−0.868166	−	0.496275i	$-0.834701\pi$
$373$	2.54597	−	9.50168i	0.131825	−	0.491978i	0.999991	+	0.00429643i	$0.00136760\pi$
$374$	−4.41550	+	9.86815i	−0.228320	+	0.510270i
$375$	0.415802	−	1.68140i	0.0214719	−	0.0868272i
$376$	11.5253	+	17.9651i	0.594370	+	0.926477i
$377$	0.387120			0.0199377
$378$	−15.9521	+	7.17689i	−0.820488	+	0.369139i
$379$	−2.84829	+	2.84829i	−0.146307	+	0.146307i	−0.776466	−	0.630159i	$-0.782990\pi$
$379$	−2.84829	+	2.84829i	−0.146307	+	0.146307i	0.630159	+	0.776466i	$0.282990\pi$
$380$	0.155016	−	0.138541i	0.00795218	−	0.00710702i
$381$	−2.22085	+	1.34022i	−0.113778	+	0.0686614i
$382$	22.3728	−	8.54063i	1.14469	−	0.436976i
$383$	15.6203	+	27.0551i	0.798158	+	1.38245i	0.920815	+	0.390000i	$0.127525\pi$
$383$	15.6203	+	27.0551i	0.798158	+	1.38245i	−0.122657	+	0.992449i	$0.539142\pi$
$384$	−17.4027	+	9.00804i	−0.888080	+	0.459690i
$385$	−1.91888	+	3.32360i	−0.0977954	+	0.169387i
$386$	−2.67912	+	16.7149i	−0.136364	+	0.850768i
$387$	−4.61282	−	1.04636i	−0.234483	−	0.0531895i
$388$	−5.69239	−	1.87290i	−0.288987	−	0.0950823i
$389$	−0.352262	−	1.31466i	−0.0178604	−	0.0666558i	0.956421	−	0.291993i	$-0.0943183\pi$
$389$	−0.352262	−	1.31466i	−0.0178604	−	0.0666558i	−0.974281	+	0.225337i	$0.927652\pi$
$390$	1.39840	−	1.79010i	0.0708106	−	0.0906452i
$391$	−12.3653	−	21.4173i	−0.625340	−	1.08312i
$392$	−3.76829	+	0.176504i	−0.190328	+	0.00891478i
$393$	−9.19219	−	31.8268i	−0.463684	−	1.60545i
$394$	−21.5323	+	2.22283i	−1.08478	+	0.111985i
$395$	−8.49122	−	8.49122i	−0.427240	−	0.427240i
$396$	−9.67202	−	0.167598i	−0.486037	−	0.00842213i
$397$	−24.2703	+	24.2703i	−1.21809	+	1.21809i	−0.249790	+	0.968300i	$0.580362\pi$
$397$	−24.2703	+	24.2703i	−1.21809	+	1.21809i	−0.968300	+	0.249790i	$0.919638\pi$
$398$	−4.04814	−	3.29055i	−0.202915	−	0.164940i
$399$	−0.308870	−	0.297131i	−0.0154628	−	0.0148752i
$400$	−3.97488	−	0.447566i	−0.198744	−	0.0223783i
$401$	19.9488	−	11.5175i	0.996198	−	0.575155i	0.0890768	−	0.996025i	$-0.471608\pi$
$401$	19.9488	−	11.5175i	0.996198	−	0.575155i	0.907121	+	0.420870i	$0.138275\pi$
$402$	26.4203	+	11.2128i	1.31772	+	0.559241i
$403$	1.59279	−	0.426788i	0.0793427	−	0.0212598i
$404$	23.7262	−	11.9786i	1.18042	−	0.595959i
$405$	−2.99521	−	8.48697i	−0.148833	−	0.421721i
$406$	−1.13842	+	0.823891i	−0.0564986	+	0.0408890i
$407$	12.4107	+	7.16532i	0.615176	+	0.355172i
$408$	1.53600	+	23.1778i	0.0760431	+	1.14747i
$409$	−2.65411	+	1.53235i	−0.131237	+	0.0757699i	−0.564181	−	0.825651i	$-0.690808\pi$
$409$	−2.65411	+	1.53235i	−0.131237	+	0.0757699i	0.432944	+	0.901421i	$0.357475\pi$
$410$	−3.72781	+	8.33125i	−0.184103	+	0.411451i
$411$	−29.1824	+	0.565287i	−1.43946	+	0.0278835i
$412$	0.315533	−	0.281998i	0.0155452	−	0.0138931i
$413$	13.1321	+	13.1321i	0.646186	+	0.646186i
$414$	13.2823	−	17.6989i	0.652788	−	0.869855i
$415$			2.70848i			0.132954i
$416$	−4.51864	−	2.66492i	−0.221544	−	0.130658i
$417$	−5.02598	−	17.4018i	−0.246123	−	0.852170i
$418$	−0.0845290	−	0.221430i	−0.00413445	−	0.0108305i
$419$	−10.2660	−	2.75078i	−0.501529	−	0.134384i	−0.000819224	−	1.00000i	$-0.500261\pi$
$419$	−10.2660	−	2.75078i	−0.501529	−	0.134384i	−0.500709	+	0.865616i	$0.666927\pi$
$420$	−0.302514	+	8.24035i	−0.0147612	+	0.402088i
$421$	31.8906	−	8.54505i	1.55425	−	0.416460i	0.623414	−	0.781892i	$-0.285745\pi$
$421$	31.8906	−	8.54505i	1.55425	−	0.416460i	0.930838	+	0.365432i	$0.119079\pi$
$422$	−1.85758	+	1.34436i	−0.0904254	+	0.0654424i
$423$	12.0703	+	19.1528i	0.586876	+	0.931242i
$424$	0.131749	+	0.413280i	0.00639830	+	0.0200706i
$425$	−2.37077	+	4.10629i	−0.114999	+	0.199184i
$426$	−38.4389	−	5.39975i	−1.86237	−	0.261619i
$427$	13.6607	+	3.66038i	0.661089	+	0.177138i
$428$	20.1403	−	30.7633i	0.973516	−	1.48700i
$429$	−1.33801	−	2.21720i	−0.0645998	−	0.107047i
$430$	−1.40643	+	1.73024i	−0.0678242	+	0.0834395i
$431$	−21.0436			−1.01363			−0.506817	−	0.862054i	$-0.669178\pi$
$431$	−21.0436			−1.01363			−0.506817	+	0.862054i	$0.669178\pi$
$432$	−18.5349	+	9.40524i	−0.891760	+	0.452510i
$433$	28.8515			1.38652			0.693258	−	0.720690i	$-0.256175\pi$
$433$	28.8515			1.38652			0.693258	+	0.720690i	$0.256175\pi$
$434$	−3.77567	+	4.64495i	−0.181238	+	0.222965i
$435$	−0.373576	−	0.619046i	−0.0179116	−	0.0296810i
$436$	11.0629	+	7.24273i	0.529817	+	0.346864i
$437$	0.523710	+	0.140328i	0.0250525	+	0.00671279i
$438$	5.05192	+	0.709674i	0.241390	+	0.0339095i
$439$	−16.1095	+	27.9025i	−0.768865	+	1.33171i	0.169313	+	0.985562i	$0.445845\pi$
$439$	−16.1095	+	27.9025i	−0.768865	+	1.33171i	−0.938179	+	0.346151i	$0.887488\pi$
$440$	−2.09279	+	4.05153i	−0.0997697	+	0.193149i
$441$	−3.99826	+	0.154957i	−0.190393	+	0.00737891i
$442$	−5.03759	+	3.64579i	−0.239613	+	0.173412i
$443$	4.78988	−	1.28344i	0.227574	−	0.0609783i	−0.143230	−	0.989689i	$-0.545749\pi$
$443$	4.78988	−	1.28344i	0.227574	−	0.0609783i	0.370804	+	0.928711i	$0.379082\pi$
$444$	30.7704	+	1.12962i	1.46030	+	0.0536094i
$445$	3.69189	+	0.989240i	0.175013	+	0.0468945i
$446$	11.0380	+	28.9150i	0.522666	+	1.36916i
$447$	−5.78495	−	20.0297i	−0.273619	−	0.947371i
$448$	18.9597	−	1.78002i	0.895763	−	0.0840980i
$449$			17.1037i			0.807172i	0.914942	+	0.403586i	$0.132236\pi$
$449$			17.1037i			0.807172i	−0.914942	+	0.403586i	$0.867764\pi$
$450$	−4.21203	−	0.508715i	−0.198557	−	0.0239811i
$451$	7.35766	+	7.35766i	0.346459	+	0.346459i
$452$	22.9005	+	25.6238i	1.07715	+	1.20524i
$453$	−5.17402	+	0.100225i	−0.243097	+	0.00470898i
$454$	7.69337	−	17.1938i	0.361068	−	0.806947i
$455$	−1.91173	+	1.10374i	−0.0896232	+	0.0517440i
$456$	−0.383123	−	0.335500i	−0.0179414	−	0.0157112i
$457$	−22.8955	−	13.2187i	−1.07101	−	0.618347i	−0.142551	−	0.989787i	$-0.545531\pi$
$457$	−22.8955	−	13.2187i	−1.07101	−	0.618347i	−0.928457	+	0.371441i	$0.878864\pi$
$458$	6.36661	−	4.60763i	0.297492	−	0.215300i
$459$	1.43077	+	24.5961i	0.0667827	+	1.14805i
$460$	−4.70134	−	9.31199i	−0.219201	−	0.434174i
$461$	28.2274	−	7.56351i	1.31468	−	0.352268i	0.467698	−	0.883888i	$-0.345083\pi$
$461$	28.2274	−	7.56351i	1.31468	−	0.352268i	0.846983	+	0.531620i	$0.178417\pi$
$462$	8.65350	+	3.67255i	0.402597	+	0.170862i
$463$	10.8554	−	6.26737i	0.504493	−	0.291269i	−0.226074	−	0.974110i	$-0.572589\pi$
$463$	10.8554	−	6.26737i	0.504493	−	0.291269i	0.730567	+	0.682841i	$0.239256\pi$
$464$	−1.30540	+	1.04118i	−0.0606019	+	0.0483357i
$465$	−2.21955	−	2.13519i	−0.102929	−	0.0990171i
$466$	10.2767	+	8.35345i	0.476058	+	0.386966i
$467$	−1.86839	+	1.86839i	−0.0864590	+	0.0864590i	−0.749014	−	0.662555i	$-0.769472\pi$
$467$	−1.86839	+	1.86839i	−0.0864590	+	0.0864590i	0.662555	+	0.749014i	$0.269472\pi$
$468$	−4.76978	−	2.86515i	−0.220483	−	0.132441i
$469$	−19.7222	−	19.7222i	−0.910688	−	0.910688i
$470$	10.6157	−	1.09588i	0.489665	−	0.0505494i
$471$	2.35075	+	8.13919i	0.108317	+	0.375034i
$472$	16.3168	+	14.8566i	0.751040	+	0.683832i
$473$	1.27099	+	2.20142i	0.0584401	+	0.101221i
$474$	−18.1079	+	23.1801i	−0.831722	+	1.06470i
$475$	−0.0269047	−	0.100410i	−0.00123447	−	0.00460711i
$476$	7.05501	−	21.4426i	0.323366	−	0.982819i
$477$	0.136200	+	0.439462i	0.00623616	+	0.0201216i
$478$	−4.05845	+	25.3205i	−0.185629	+	1.15813i
$479$	−15.4111	+	26.6928i	−0.704151	+	1.21963i	0.262846	+	0.964838i	$0.415339\pi$
$479$	−15.4111	+	26.6928i	−0.704151	+	1.21963i	−0.966997	+	0.254788i	$0.917994\pi$
$480$	0.0990567	+	9.79746i	0.00452130	+	0.447191i
$481$	4.12148	+	7.13861i	0.187923	+	0.325493i
$482$	10.2659	−	3.91890i	0.467597	−	0.178501i
$483$	−18.4115	+	11.1108i	−0.837752	+	0.505558i
$484$	−11.1960	−	12.5274i	−0.508908	−	0.569426i
$485$	−2.11870	+	2.11870i	−0.0962051	+	0.0962051i
$486$	−19.7390	+	9.81682i	−0.895381	+	0.445300i
$487$	23.4292			1.06168			0.530839	−	0.847473i	$-0.321877\pi$
$487$	23.4292			1.06168			0.530839	+	0.847473i	$0.321877\pi$
$488$	16.4177	+	3.58512i	0.743194	+	0.162291i
$489$	6.44545	−	26.0638i	0.291473	−	1.17865i
$490$	−0.770381	+	1.72172i	−0.0348023	+	0.0777793i
$491$	2.97647	−	11.1083i	0.134326	−	0.501313i	−0.865673	−	0.500609i	$-0.833109\pi$
$491$	2.97647	−	11.1083i	0.134326	−	0.501313i	1.00000		0.000703543i	$-0.000223945\pi$
$492$	21.3684	+	6.57479i	0.963363	+	0.296414i
$493$	0.512286	+	1.91188i	0.0230722	+	0.0861066i
$494$	0.0215762	−	0.134613i	0.000970757	−	0.00605652i
$495$	−2.25434	+	4.27925i	−0.101325	+	0.192338i
$496$	−4.22318	+	5.72308i	−0.189626	+	0.256974i
$497$	32.6676	+	18.8607i	1.46534	+	0.846016i
$498$	6.58488	−	0.808945i	0.295075	−	0.0362497i
$499$	3.16760	−	11.8216i	0.141801	−	0.529209i	−0.858076	−	0.513523i	$-0.828340\pi$
$499$	3.16760	−	11.8216i	0.141801	−	0.529209i	0.999877	−	0.0156862i	$-0.00499329\pi$
$500$	−1.09548	+	1.67330i	−0.0489915	+	0.0748321i
$501$	12.1323	+	6.69470i	0.542031	+	0.299097i
$502$	1.61308	+	15.6257i	0.0719953	+	0.697410i
$503$			10.1706i			0.453487i	0.973955	+	0.226743i	$0.0728079\pi$
$503$			10.1706i			0.453487i	−0.973955	+	0.226743i	$0.927192\pi$
$504$	20.1244	−	1.72569i	0.896412	−	0.0768682i
$505$		−	13.2893i		−	0.591365i
$506$	−11.8293	+	1.22117i	−0.525877	+	0.0542876i
$507$	0.407235	+	21.0232i	0.0180860	+	0.933671i
$508$	2.93202	−	0.611880i	0.130087	−	0.0271478i
$509$	9.18175	−	34.2668i	0.406974	−	1.51885i	−0.393412	−	0.919362i	$-0.628705\pi$
$509$	9.18175	−	34.2668i	0.406974	−	1.51885i	0.800386	−	0.599485i	$-0.204628\pi$
$510$	10.6913	+	4.53740i	0.473420	+	0.200920i
$511$	−4.29341	−	2.47880i	−0.189929	−	0.109656i
$512$	22.4047	−	3.16679i	0.990158	−	0.139954i
$513$	−0.403479	−	0.359118i	−0.0178140	−	0.0158554i
$514$	−39.5915	−	6.34585i	−1.74631	−	0.279904i
$515$	−0.0547639	−	0.204382i	−0.00241319	−	0.00900614i
$516$	4.62664	+	2.90256i	0.203676	+	0.127778i
$517$	3.14892	−	11.7519i	0.138490	−	0.516850i
$518$	−27.3130	−	12.2212i	−1.20006	−	0.536967i
$519$	10.7068	+	10.2999i	0.469976	+	0.452115i
$520$	−2.20771	+	1.41633i	−0.0968144	+	0.0621101i
$521$	14.9053			0.653013			0.326506	−	0.945195i	$-0.394129\pi$
$521$	14.9053			0.653013			0.326506	+	0.945195i	$0.394129\pi$
$522$	−1.39346	+	1.09313i	−0.0609899	+	0.0478452i
$523$	−19.2646	+	19.2646i	−0.842381	+	0.842381i	−0.989168	−	0.146787i	$-0.953107\pi$
$523$	−19.2646	+	19.2646i	−0.842381	+	0.842381i	0.146787	+	0.989168i	$0.453107\pi$
$524$	−2.14343	+	38.1924i	−0.0936364	+	1.66844i
$525$	3.60984	+	1.99194i	0.157546	+	0.0869353i
$526$	−14.2840	−	37.4181i	−0.622814	−	1.63151i
$527$	4.21557	+	7.30158i	0.183633	+	0.318062i
$528$	10.4752	+	3.87793i	0.455874	+	0.168765i
$529$	2.10196	−	3.64071i	0.0913897	−	0.158292i
$530$	0.214152	+	0.0343250i	0.00930219	+	0.00149098i
$531$	17.1788	+	15.8969i	0.745498	+	0.689869i
$532$	0.223041	+	0.441780i	0.00967006	+	0.0191536i
$533$	1.54906	+	5.78117i	0.0670972	+	0.250410i
$534$	1.30239	−	9.27124i	0.0563598	−	0.401206i
$535$	−9.19242	−	15.9217i	−0.397423	−	0.688357i
$536$	−24.5052	−	22.3123i	−1.05846	−	0.963744i
$537$	4.65279	+	1.15061i	0.200783	+	0.0496525i
$538$	1.16604	+	11.2953i	0.0502715	+	0.486974i
$539$	1.52052	+	1.52052i	0.0654934	+	0.0654934i
$540$	0.0212204	+	10.3923i	0.000913182	+	0.447213i
$541$	−0.122976	+	0.122976i	−0.00528717	+	0.00528717i	−0.709745	−	0.704458i	$-0.751190\pi$
$541$	−0.122976	+	0.122976i	−0.00528717	+	0.00528717i	0.704458	+	0.709745i	$0.251190\pi$
$542$	−11.8258	+	14.5485i	−0.507963	+	0.624913i
$543$	10.1339	−	40.9792i	0.434889	−	1.75858i
$544$	7.18165	−	25.8428i	0.307911	−	1.10800i
$545$	5.72568	−	3.30573i	0.245261	−	0.141602i
$546$	3.25440	+	4.31816i	0.139275	+	0.184800i
$547$	−19.7333	+	5.28753i	−0.843737	+	0.226079i	−0.654698	−	0.755891i	$-0.727204\pi$
$547$	−19.7333	+	5.28753i	−0.843737	+	0.226079i	−0.189039	+	0.981970i	$0.560537\pi$
$548$	32.0149	+	10.5335i	1.36761	+	0.449969i
$549$	17.3823	+	3.94297i	0.741860	+	0.168282i
$550$	1.33677	+	1.84708i	0.0569999	+	0.0787599i
$551$	−0.0375803	−	0.0216970i	−0.00160097	−	0.000924322i
$552$	−21.2353	+	14.2112i	−0.903833	+	0.604868i
$553$	24.7550	−	14.2923i	1.05269	−	0.607772i
$554$	0.212337	+	0.0950101i	0.00902134	+	0.00403659i
$555$	7.43812	−	13.4795i	0.315730	−	0.572174i
$556$	−1.17196	+	20.8823i	−0.0497021	+	0.885608i
$557$	12.7434	+	12.7434i	0.539956	+	0.539956i	0.923516	−	0.383560i	$-0.125302\pi$
$557$	12.7434	+	12.7434i	0.539956	+	0.539956i	−0.383560	+	0.923516i	$0.625302\pi$
$558$	−4.52819	+	6.03391i	−0.191693	+	0.255436i
$559$			1.46214i			0.0618419i
$560$	3.47796	−	8.86362i	0.146971	−	0.374556i
$561$	9.17949	−	9.54214i	0.387558	−	0.402870i
$562$	27.9940	−	10.6865i	1.18085	−	0.450781i
$563$	25.4689	+	6.82436i	1.07338	+	0.287613i	0.751883	−	0.659297i	$-0.229146\pi$
$563$	25.4689	+	6.82436i	1.07338	+	0.287613i	0.321502	+	0.946909i	$0.395812\pi$
$564$	−5.83493	−	25.4817i	−0.245695	−	1.07297i
$565$	16.5974	−	4.44727i	0.698259	−	0.187098i
$566$	18.6820	+	25.8139i	0.785263	+	1.08504i
$567$	21.3592	−	1.65809i	0.897003	−	0.0696334i
$568$	39.8224	+	20.5700i	1.67091	+	0.863096i
$569$	−10.0531	+	17.4124i	−0.421446	+	0.729966i	−0.996081	−	0.0884440i	$-0.971811\pi$
$569$	−10.0531	+	17.4124i	−0.421446	+	0.729966i	0.574635	+	0.818410i	$0.305144\pi$
$570$	−0.236082	+	0.0954005i	−0.00988837	+	0.00399589i
$571$	−18.8332	−	5.04634i	−0.788145	−	0.211183i	−0.157772	−	0.987476i	$-0.550431\pi$
$571$	−18.8332	−	5.04634i	−0.788145	−	0.211183i	−0.630372	+	0.776293i	$0.717098\pi$
$572$	0.610874	+	2.92720i	0.0255419	+	0.122392i
$573$	−29.3242	+	0.568032i	−1.22503	+	0.0237299i
$574$	−16.8592	−	13.7041i	−0.703689	−	0.571997i
$575$	−5.21574			−0.217511
$576$	23.7901	−	3.16705i	0.991255	−	0.131961i
$577$	−9.40639			−0.391593			−0.195797	−	0.980645i	$-0.562729\pi$
$577$	−9.40639			−0.391593			−0.195797	+	0.980645i	$0.562729\pi$
$578$	−6.01608	−	4.89020i	−0.250236	−	0.203406i
$579$	10.0167	−	18.1526i	0.416281	−	0.754395i
$580$	0.170557	+	0.817280i	0.00708200	+	0.0339357i
$581$	−6.22754	−	1.66866i	−0.258362	−	0.0692278i
$582$	5.78380	+	4.51821i	0.239746	+	0.187286i
$583$	0.123628	−	0.214130i	0.00512015	−	0.00886836i
$584$	−5.23374	−	2.70345i	−0.216574	−	0.111870i
$585$	−2.35367	+	1.48330i	−0.0973123	+	0.0613270i
$586$	−13.7290	−	18.9701i	−0.567139	−	0.783648i
$587$	6.16972	−	1.65317i	0.254652	−	0.0682337i	−0.129235	−	0.991614i	$-0.541252\pi$
$587$	6.16972	−	1.65317i	0.254652	−	0.0682337i	0.383886	+	0.923380i	$0.374585\pi$
$588$	4.41595	+	1.35873i	0.182111	+	0.0560332i
$589$	−0.178543	−	0.0478405i	−0.00735674	−	0.00197123i
$590$	10.3080	−	3.93499i	0.424374	−	0.162001i
$591$	25.7365	+	6.36449i	1.05866	+	0.261800i
$592$	−33.0977	−	12.9871i	−1.36031	−	0.533767i
$593$		−	19.0737i		−	0.783262i	−0.920122	−	0.391631i	$-0.871911\pi$
$593$		−	19.0737i		−	0.783262i	0.920122	−	0.391631i	$-0.128089\pi$
$594$	11.0771	+	4.20268i	0.454498	+	0.172438i
$595$	−7.98089	−	7.98089i	−0.327185	−	0.327185i
$596$	−1.34894	+	24.0358i	−0.0552545	+	0.984543i
$597$	3.30120	+	5.47036i	0.135109	+	0.223887i
$598$	−6.24382	−	2.79379i	−0.255329	−	0.114247i
$599$	−11.0582	+	6.38448i	−0.451827	+	0.260863i	−0.708602	−	0.705609i	$-0.750674\pi$
$599$	−11.0582	+	6.38448i	−0.451827	+	0.260863i	0.256774	+	0.966471i	$0.417340\pi$
$600$	4.39533	+	2.16358i	0.179438	+	0.0883279i
$601$	−25.2868	−	14.5993i	−1.03147	−	0.595520i	−0.114065	−	0.993473i	$-0.536387\pi$
$601$	−25.2868	−	14.5993i	−1.03147	−	0.595520i	−0.917406	+	0.397953i	$0.869721\pi$
$602$	−3.11181	−	4.29976i	−0.126828	−	0.175245i
$603$	−25.7999	−	23.8747i	−1.05065	−	0.972252i
$604$	5.67623	+	1.86759i	0.230962	+	0.0759910i
$605$	−8.11442	+	2.17425i	−0.329898	+	0.0883959i
$606$	−32.3090	+	3.96913i	−1.31247	+	0.161235i
$607$	−13.0592	+	7.53975i	−0.530058	+	0.306029i	−0.741040	−	0.671461i	$-0.765667\pi$
$607$	−13.0592	+	7.53975i	−0.530058	+	0.306029i	0.210982	+	0.977490i	$0.432334\pi$
$608$	0.289292	+	0.511958i	0.0117324	+	0.0207626i
$609$	1.65351	−	0.477567i	0.0670038	−	0.0193520i
$610$	5.29981	−	6.52000i	0.214583	−	0.263987i
$611$	4.94844	−	4.94844i	0.200192	−	0.200192i
$612$	7.83819	−	27.3481i	0.316840	−	1.10548i
$613$	−19.4783	−	19.4783i	−0.786721	−	0.786721i	0.194234	−	0.980955i	$-0.437778\pi$
$613$	−19.4783	−	19.4783i	−0.786721	−	0.786721i	−0.980955	+	0.194234i	$0.937778\pi$
$614$	3.33354	+	32.2916i	0.134531	+	1.30318i
$615$	7.74984	−	8.05601i	0.312504	−	0.324850i
$616$	−8.02625	−	7.30801i	−0.323387	−	0.294448i
$617$	12.3469	+	21.3854i	0.497067	+	0.860945i	0.999994	−	0.00338356i	$-0.00107702\pi$
$617$	12.3469	+	21.3854i	0.497067	+	0.860945i	−0.502927	+	0.864329i	$0.667744\pi$
$618$	−0.480539	+	0.194186i	−0.0193301	+	0.00781130i
$619$	7.71282	+	28.7846i	0.310004	+	1.15695i	0.928551	+	0.371204i	$0.121055\pi$
$619$	7.71282	+	28.7846i	0.310004	+	1.15695i	−0.618547	+	0.785748i	$0.712278\pi$
$620$	1.60278	+	3.17464i	0.0643691	+	0.127497i
$621$	−22.6443	+	14.8910i	−0.908684	+	0.597556i
$622$	−25.3290	−	4.05981i	−1.01560	−	0.162783i
$623$	−4.54908	+	7.87923i	−0.182255	+	0.315675i
$624$	4.10278	+	4.94439i	0.164243	+	0.197934i
$625$	0.500000	+	0.866025i	0.0200000	+	0.0346410i
$626$	−9.39595	−	24.6134i	−0.375538	−	0.983750i
$627$	0.00562198	+	0.290230i	0.000224520	+	0.0115907i
$628$	0.548149	−	9.76710i	0.0218735	−	0.389750i
$629$	−29.8015	+	29.8015i	−1.18826	+	1.18826i
$630$	3.76467	−	9.37122i	0.149988	−	0.373358i
$631$	−18.7677			−0.747130			−0.373565	−	0.927604i	$-0.621865\pi$
$631$	−18.7677			−0.747130			−0.373565	+	0.927604i	$0.621865\pi$
$632$	28.5877	−	18.3401i	1.13716	−	0.729529i
$633$	2.69807	−	0.779255i	0.107239	−	0.0309726i
$634$	−13.0806	−	5.85292i	−0.519499	−	0.232449i
$635$	0.387606	−	1.44656i	0.0153817	−	0.0574051i
$636$	0.0194901	−	0.530902i	0.000772833	−	0.0210516i
$637$	0.320125	+	1.19472i	0.0126838	+	0.0473367i
$638$	0.939799	+	0.150634i	0.0372070	+	0.00596366i
$639$	42.0606	+	22.1578i	1.66389	+	0.876549i
$640$	3.63530	−	10.7138i	0.143698	−	0.423498i
$641$	−5.48364	−	3.16598i	−0.216591	−	0.125049i	0.387780	−	0.921752i	$-0.373242\pi$
$641$	−5.48364	−	3.16598i	−0.216591	−	0.125049i	−0.604371	+	0.796703i	$0.706575\pi$
$642$	−35.9636	+	27.1041i	−1.41937	+	1.06971i
$643$	9.51762	−	35.5202i	0.375338	−	1.40078i	−0.477512	−	0.878625i	$-0.658461\pi$
$643$	9.51762	−	35.5202i	0.375338	−	1.40078i	0.852850	−	0.522156i	$-0.174872\pi$
$644$	24.3073	−	5.07266i	0.957842	−	0.199891i
$645$	2.33812	−	1.41098i	0.0920632	−	0.0555574i
$646$	0.693367	−	0.0715780i	0.0272802	−	0.00281620i
$647$		−	29.8103i		−	1.17196i	−0.810324	−	0.585982i	$-0.800709\pi$
$647$		−	29.8103i		−	1.17196i	0.810324	−	0.585982i	$-0.199291\pi$
$648$	25.2595	−	3.15547i	0.992287	−	0.123959i
$649$		−	12.5786i		−	0.493751i
$650$	0.134672	+	1.30455i	0.00528227	+	0.0511687i
$651$	6.27684	−	3.78788i	0.246009	−	0.148459i
$652$	−16.9814	+	25.9382i	−0.665041	+	1.01582i
$653$	−2.91625	+	10.8836i	−0.114122	+	0.425907i	−0.999220	−	0.0394970i	$-0.987424\pi$
$653$	−2.91625	+	10.8836i	−0.114122	+	0.425907i	0.885098	+	0.465404i	$0.154091\pi$
$654$	−9.74702	−	12.9330i	−0.381139	−	0.505721i
$655$	16.5638	+	9.56313i	0.647202	+	0.373662i
$656$	−20.7724	−	15.3284i	−0.811025	−	0.598472i
$657$	−5.52790	−	2.91213i	−0.215664	−	0.113613i
$658$	−4.02047	+	25.0836i	−0.156734	+	0.977860i
$659$	8.78218	+	32.7755i	0.342105	+	1.27675i	0.895958	+	0.444139i	$0.146490\pi$
$659$	8.78218	+	32.7755i	0.342105	+	1.27675i	−0.553853	+	0.832614i	$0.686843\pi$
$660$	4.09140	−	3.80164i	0.159258	−	0.147978i
$661$	−4.89380	+	18.2639i	−0.190347	+	0.710384i	0.803076	+	0.595877i	$0.203195\pi$
$661$	−4.89380	+	18.2639i	−0.190347	+	0.710384i	−0.993422	+	0.114507i	$0.963471\pi$
$662$	−20.9467	+	46.8135i	−0.814116	+	1.81946i
$663$	7.31694	−	2.11327i	0.284166	−	0.0820727i
$664$	−7.48436	−	1.63435i	−0.290449	−	0.0634253i
$665$	0.247445			0.00959552
$666$	−34.9932	−	14.0577i	−1.35596	−	0.544724i
$667$	−1.53957	+	1.53957i	−0.0596122	+	0.0596122i
$668$	−10.6623	−	11.9303i	−0.412537	−	0.461595i
$669$	−0.734133	−	37.8990i	−0.0283832	−	1.46526i
$670$	−15.4810	+	5.90972i	−0.598082	+	0.228312i
$671$	−4.78942	−	8.29553i	−0.184894	−	0.320245i
$672$	−22.5881	−	5.80835i	−0.871355	−	0.224062i
$673$	24.0896	−	41.7245i	0.928588	−	1.60836i	0.142900	−	0.989737i	$-0.454357\pi$
$673$	24.0896	−	41.7245i	0.928588	−	1.60836i	0.785687	−	0.618624i	$-0.212309\pi$
$674$	0.404312	−	2.52248i	0.0155735	−	0.0971625i
$675$	4.64328	+	2.33237i	0.178720	+	0.0897728i
$676$	7.58840	−	23.0637i	0.291862	−	0.887066i
$677$	−8.94329	−	33.3768i	−0.343719	−	1.28278i	−0.894102	−	0.447863i	$-0.852185\pi$
$677$	−8.94329	−	33.3768i	−0.343719	−	1.28278i	0.550383	−	0.834912i	$-0.314482\pi$
$678$	−15.7694	−	39.0236i	−0.605622	−	1.49869i
$679$	−3.56617	−	6.17679i	−0.136857	−	0.237043i
$680$	−9.91637	−	9.02899i	−0.380275	−	0.346246i
$681$	−15.9940	+	16.6258i	−0.612890	+	0.637103i
$682$	4.03285	−	0.416321i	0.154426	−	0.0159418i
$683$	−11.1864	−	11.1864i	−0.428036	−	0.428036i	0.459923	−	0.887959i	$-0.347877\pi$
$683$	−11.1864	−	11.1864i	−0.428036	−	0.428036i	−0.887959	+	0.459923i	$0.847877\pi$
$684$	0.302450	+	0.545471i	0.0115645	+	0.0208566i
$685$	11.9159	−	11.9159i	0.455283	−	0.455283i
$686$	−21.7698	−	17.6956i	−0.831173	−	0.675623i
$687$	−9.24731	+	2.67080i	−0.352807	+	0.101897i
$688$	−3.93251	−	4.93047i	−0.149926	−	0.187972i
$689$	0.123167	−	0.0711106i	0.00469229	−	0.00270910i
$690$	1.55779	+	12.6806i	0.0593042	+	0.482741i
$691$	11.2837	−	3.02347i	0.429254	−	0.115018i	−0.0377222	−	0.999288i	$-0.512010\pi$
$691$	11.2837	−	3.02347i	0.429254	−	0.115018i	0.466976	+	0.884270i	$0.345344\pi$
$692$	−7.73159	−	15.3140i	−0.293911	−	0.582153i
$693$	−8.45031	−	7.81974i	−0.321001	−	0.297048i
$694$	39.1405	−	28.3267i	1.48575	−	1.07527i
$695$	9.05654	+	5.22879i	0.343534	+	0.198339i
$696$	1.93604	−	0.658759i	0.0733854	−	0.0249702i
$697$	−26.5017	+	15.3007i	−1.00382	+	0.579557i
$698$	19.8821	−	44.4342i	0.752547	−	1.68186i
$699$	−8.38049	−	13.8872i	−0.316979	−	0.525261i
$700$	−3.17246	−	3.54972i	−0.119908	−	0.134167i
$701$	−8.97633	−	8.97633i	−0.339031	−	0.339031i	0.516971	−	0.856003i	$-0.327059\pi$
$701$	−8.97633	−	8.97633i	−0.339031	−	0.339031i	−0.856003	+	0.516971i	$0.827059\pi$
$702$	4.30920	+	5.27926i	0.162640	+	0.199253i
$703$		−	0.923988i		−	0.0348489i
$704$	−9.93280	−	8.22780i	−0.374356	−	0.310097i
$705$	−12.6884	−	3.13777i	−0.477872	−	0.118175i
$706$	15.2318	+	39.9008i	0.573256	+	1.50169i
$707$	30.5557	+	8.18738i	1.14917	+	0.307918i
$708$	−12.6455	−	23.8857i	−0.475247	−	0.897678i
$709$	7.63771	−	2.04652i	0.286840	−	0.0768586i	−0.112530	−	0.993648i	$-0.535895\pi$
$709$	7.63771	−	2.04652i	0.286840	−	0.0768586i	0.399370	+	0.916790i	$0.369229\pi$
$710$	18.1549	−	13.1390i	0.681343	−	0.493099i
$711$	30.4778	−	19.2073i	1.14301	−	0.720331i
$712$	−4.96135	+	9.60492i	−0.185934	+	0.359959i
$713$	−4.63718	+	8.03182i	−0.173664	+	0.300794i
$714$	−17.0196	+	21.7869i	−0.636942	+	0.815355i
$715$	1.44418	+	0.386968i	0.0540094	+	0.0144718i
$716$	−4.63036	−	3.03143i	−0.173045	−	0.113290i
$717$	15.1738	−	27.4983i	0.566675	−	1.02694i
$718$	11.6486	−	14.3305i	0.434721	−	0.534808i
$719$	−12.4638			−0.464822			−0.232411	−	0.972618i	$-0.574661\pi$
$719$	−12.4638			−0.464822			−0.232411	+	0.972618i	$0.574661\pi$
$720$	3.94737	−	11.3322i	0.147110	−	0.422325i
$721$	0.503670			0.0187577
$722$	16.9389	−	20.8388i	0.630400	−	0.775538i
$723$	−13.4555	+	0.260644i	−0.500415	+	0.00969344i
$724$	−26.6991	+	40.7816i	−0.992265	+	1.51564i
$725$	0.403219	+	0.108042i	0.0149752	+	0.00401259i
$726$	7.70962	+	19.0785i	0.286131	+	0.708069i
$727$	16.2618	−	28.1663i	0.603117	−	1.04463i	−0.389229	−	0.921141i	$-0.627258\pi$
$727$	16.2618	−	28.1663i	0.603117	−	1.04463i	0.992346	−	0.123488i	$-0.0394082\pi$
$728$	−1.89639	−	5.94872i	−0.0702848	−	0.220474i
$729$	26.8179	−	3.13062i	0.993255	−	0.115949i
$730$	−2.38605	+	1.72683i	−0.0883117	+	0.0639127i
$731$	−7.22110	+	1.93489i	−0.267082	+	0.0715644i
$732$	−17.4344	−	10.9376i	−0.644394	−	0.404266i
$733$	16.0844	+	4.30979i	0.594089	+	0.159186i	0.543321	−	0.839525i	$-0.317167\pi$
$733$	16.0844	+	4.30979i	0.594089	+	0.159186i	0.0507678	+	0.998710i	$0.483833\pi$
$734$	−9.60756	−	25.1677i	−0.354622	−	0.928959i
$735$	1.60157	−	1.66484i	0.0590746	−	0.0614085i
$736$	28.5688	−	7.37219i	1.05306	−	0.271743i
$737$			18.8910i			0.695858i
$738$	−21.9005	−	16.4354i	−0.806170	−	0.604996i
$739$	−2.76192	−	2.76192i	−0.101599	−	0.101599i	0.654480	−	0.756079i	$-0.272887\pi$
$739$	−2.76192	−	2.76192i	−0.101599	−	0.101599i	−0.756079	+	0.654480i	$0.772887\pi$
$740$	−13.2550	+	11.8463i	−0.487265	+	0.435479i
$741$	−0.0806692	+	0.146191i	−0.00296346	+	0.00537045i
$742$	−0.210860	+	0.471249i	−0.00774091	+	0.0173001i
$743$	1.07868	−	0.622777i	0.0395730	−	0.0228475i	−0.480083	−	0.877223i	$-0.659393\pi$
$743$	1.07868	−	0.622777i	0.0395730	−	0.0228475i	0.519656	+	0.854376i	$0.326060\pi$
$744$	7.23952	−	4.84487i	0.265414	−	0.177622i
$745$	10.4242	+	6.01840i	0.381912	+	0.220497i
$746$	11.2697	−	8.15607i	0.412613	−	0.298615i
$747$	−7.92411	−	1.79749i	−0.289928	−	0.0657666i
$748$	−13.6482	+	6.89057i	−0.499029	+	0.251944i
$749$	42.2719	−	11.3267i	1.54458	−	0.413869i
$750$	1.95616	−	1.47426i	0.0714287	−	0.0538325i
$751$	−28.6410	+	16.5359i	−1.04512	+	0.603403i	−0.921281	−	0.388899i	$-0.872856\pi$
$751$	−28.6410	+	16.5359i	−1.04512	+	0.603403i	−0.123844	+	0.992302i	$0.539522\pi$
$752$	−3.37748	+	29.9957i	−0.123164	+	1.09383i
$753$	4.61863	−	18.6766i	0.168312	−	0.680613i
$754$	0.424826	+	0.345321i	0.0154712	+	0.0125759i
$755$	2.11268	−	2.11268i	0.0768884	−	0.0768884i
$756$	−23.9078	−	6.35379i	−0.869519	−	0.231085i
$757$	−31.0295	−	31.0295i	−1.12779	−	1.12779i	−0.990536	−	0.137251i	$-0.956173\pi$
$757$	−31.0295	−	31.0295i	−1.12779	−	1.12779i	−0.137251	−	0.990536i	$-0.543827\pi$
$758$	−5.66646	+	0.584963i	−0.205815	+	0.0212468i
$759$	14.1390	+	3.49650i	0.513212	+	0.126915i
$760$	0.293698	−	0.0137565i	0.0106535	−	0.000499002i
$761$	−11.6233	−	20.1322i	−0.421345	−	0.729790i	0.574727	−	0.818345i	$-0.305108\pi$
$761$	−11.6233	−	20.1322i	−0.421345	−	0.729790i	−0.996071	+	0.0885553i	$0.971775\pi$
$762$	−3.63267	−	0.510304i	−0.131598	−	0.0184863i
$763$	4.07325	+	15.2016i	0.147461	+	0.550334i
$764$	32.1704	+	10.5847i	1.16388	+	0.382940i
$765$	−10.4403	−	9.66123i	−0.377470	−	0.349303i
$766$	−6.99218	+	43.6239i	−0.252638	+	1.57620i
$767$	3.61758	−	6.26583i	0.130623	−	0.226246i
$768$	−27.1332	−	5.63828i	−0.979085	−	0.203454i
$769$	4.98500	+	8.63427i	0.179764	+	0.311360i	0.941800	−	0.336175i	$-0.109133\pi$
$769$	4.98500	+	8.63427i	0.179764	+	0.311360i	−0.762036	+	0.647535i	$0.775800\pi$
$770$	−5.07053	+	1.93563i	−0.182729	+	0.0697552i
$771$	42.9967	+	23.7259i	1.54849	+	0.854469i
$772$	−17.8502	+	15.9531i	−0.642444	+	0.574166i
$773$	16.9859	−	16.9859i	0.610942	−	0.610942i	−0.332250	−	0.943191i	$-0.607808\pi$
$773$	16.9859	−	16.9859i	0.610942	−	0.610942i	0.943191	+	0.332250i	$0.107808\pi$
$774$	−4.12873	−	5.26304i	−0.148404	−	0.189176i
$775$	1.77815			0.0638729
$776$	−4.57615	−	7.13309i	−0.164274	−	0.256063i
$777$	26.4106	+	25.4069i	0.947477	+	0.911467i
$778$	0.786138	−	1.75693i	0.0281844	−	0.0629891i
$779$	0.173641	−	0.648036i	0.00622133	−	0.0232183i
$780$	3.13142	−	0.717049i	0.112123	−	0.0256745i
$781$	−6.61251	−	24.6782i	−0.236614	−	0.883056i
$782$	5.53514	−	34.5336i	0.197936	−	1.23492i
$783$	2.05905	−	0.682129i	0.0735845	−	0.0243773i
$784$	−4.29277	−	3.16772i	−0.153313	−	0.113133i
$785$	−4.23593	−	2.44562i	−0.151187	−	0.0872878i
$786$	18.3029	−	43.1264i	0.652841	−	1.53827i
$787$	−5.04156	+	18.8154i	−0.179712	+	0.670695i	0.815989	+	0.578068i	$0.196193\pi$
$787$	−5.04156	+	18.8154i	−0.179712	+	0.670695i	−0.995701	+	0.0926270i	$0.970474\pi$
$788$	−25.6124	−	16.7681i	−0.912404	−	0.597338i
$789$	0.950023	+	49.0441i	0.0338217	+	1.74602i
$790$	−1.74387	−	16.8927i	−0.0620442	−	0.601014i
$791$			40.9020i			1.45431i
$792$	−10.4646	−	8.81162i	−0.371842	−	0.313107i
$793$		−	5.50973i		−	0.195656i
$794$	−48.2839	+	4.98447i	−1.71353	+	0.176892i
$795$	−0.232571	−	0.128335i	−0.00824845	−	0.00455156i
$796$	−1.50717	−	7.22210i	−0.0534203	−	0.255981i
$797$	1.57802	−	5.88924i	0.0558963	−	0.208608i	−0.932330	−	0.361610i	$-0.882227\pi$
$797$	1.57802	−	5.88924i	0.0558963	−	0.208608i	0.988226	+	0.153002i	$0.0488940\pi$
$798$	−0.0739050	−	0.601592i	−0.00261621	−	0.0212961i
$799$	30.9873	+	17.8905i	1.09625	+	0.632922i
$800$	−3.96280	−	4.03686i	−0.140106	−	0.142725i
$801$	−5.34433	+	10.1448i	−0.188832	+	0.358448i
$802$	32.1658	+	5.15563i	1.13581	+	0.182052i
$803$	0.869062	+	3.24339i	0.0306685	+	0.114457i
$804$	18.9915	+	35.8725i	0.669779	+	1.26512i
$805$	3.21336	−	11.9924i	0.113256	−	0.422678i
$806$	2.12864	+	0.952458i	0.0749781	+	0.0335489i
$807$	3.33864	−	13.5007i	0.117526	−	0.475245i
$808$	36.7224	+	8.01904i	1.29189	+	0.282109i
$809$	−44.1628			−1.55268			−0.776341	−	0.630314i	$-0.782926\pi$
$809$	−44.1628			−1.55268			−0.776341	+	0.630314i	$0.782926\pi$
$810$	4.28366	−	11.9854i	0.150512	−	0.421125i
$811$	7.12249	−	7.12249i	0.250104	−	0.250104i	−0.570909	−	0.821013i	$-0.693409\pi$
$811$	7.12249	−	7.12249i	0.250104	−	0.250104i	0.821013	+	0.570909i	$0.193409\pi$
$812$	−1.98423	−	0.111359i	−0.0696329	−	0.00390794i
$813$	19.6598	−	11.8641i	0.689500	−	0.416092i
$814$	7.22785	+	18.9339i	0.253336	+	0.663633i
$815$	7.75063	+	13.4245i	0.271493	+	0.470239i
$816$	−18.9896	+	26.8055i	−0.664771	+	0.938380i
$817$	0.0819488	−	0.141939i	0.00286702	−	0.00496583i
$818$	−4.27952	−	0.685935i	−0.149630	−	0.0239831i
$819$	−1.96045	−	6.32559i	−0.0685037	−	0.221034i
$820$	−11.5226	+	5.81741i	−0.402387	+	0.203153i
$821$	−9.37258	−	34.9789i	−0.327105	−	1.22077i	−0.912179	−	0.409793i	$-0.865601\pi$
$821$	−9.37258	−	34.9789i	−0.327105	−	1.22077i	0.585074	−	0.810980i	$-0.301066\pi$
$822$	−32.5290	−	25.4112i	−1.13458	−	0.886316i
$823$	−11.2539	−	19.4923i	−0.392286	−	0.679459i	0.600465	−	0.799651i	$-0.294982\pi$
$823$	−11.2539	−	19.4923i	−0.392286	−	0.679459i	−0.992751	+	0.120192i	$0.961649\pi$
$824$	0.597816	−	0.0280012i	0.0208259	−	0.000975467i
$825$	−0.774854	−	2.68283i	−0.0269769	−	0.0934043i
$826$	2.69698	+	26.1253i	0.0938398	+	0.909014i
$827$	−34.1897	−	34.1897i	−1.18889	−	1.18889i	−0.977374	−	0.211520i	$-0.932159\pi$
$827$	−34.1897	−	34.1897i	−1.18889	−	1.18889i	−0.211520	−	0.977374i	$-0.567841\pi$
$828$	30.3639	−	7.57466i	1.05522	−	0.263238i
$829$	30.0698	−	30.0698i	1.04437	−	1.04437i	0.0453977	−	0.998969i	$-0.485544\pi$
$829$	30.0698	−	30.0698i	1.04437	−	1.04437i	0.998969	−	0.0453977i	$-0.0144555\pi$
$830$	−2.41603	+	2.97228i	−0.0838617	+	0.103169i
$831$	−0.205322	−	0.197519i	−0.00712255	−	0.00685186i
$832$	−2.58158	−	6.95523i	−0.0895000	−	0.241129i
$833$	−5.47678	+	3.16202i	−0.189759	+	0.109557i
$834$	10.0074	−	23.5801i	0.346527	−	0.816511i
$835$	−7.72765	+	2.07062i	−0.267426	+	0.0716566i
$836$	0.104760	−	0.318400i	0.00362319	−	0.0110121i
$837$	7.71988	−	5.07664i	0.266838	−	0.175474i
$838$	−8.81218	−	12.1763i	−0.304412	−	0.420623i
$839$	8.81141	+	5.08727i	0.304204	+	0.175632i	0.644330	−	0.764748i	$-0.277136\pi$
$839$	8.81141	+	5.08727i	0.304204	+	0.175632i	−0.340126	+	0.940380i	$0.610470\pi$
$840$	−7.68260	+	8.77312i	−0.265075	+	0.302701i
$841$	−24.9638	+	14.4129i	−0.860822	+	0.496996i
$842$	42.6192	+	19.0699i	1.46875	+	0.657192i
$843$	−36.6918	+	0.710750i	−1.26373	+	0.0244795i
$844$	−3.23771	−	0.181707i	−0.111447	−	0.00625460i
$845$	−8.58428	−	8.58428i	−0.295308	−	0.295308i
$846$	−3.83893	+	31.7853i	−0.131985	+	1.09280i
$847$		−	19.9968i		−	0.687100i
$848$	−0.224075	+	0.571057i	−0.00769477	+	0.0196102i
$849$	−10.8290	−	37.4940i	−0.371650	−	1.28679i
$850$	−6.26460	+	2.39145i	−0.214874	+	0.0820262i
$851$	−44.7811	−	11.9991i	−1.53508	−	0.411322i
$852$	−37.3662	−	40.2143i	−1.28014	−	1.37772i
$853$	39.8311	−	10.6727i	1.36379	−	0.365427i	0.498585	−	0.866841i	$-0.333853\pi$
$853$	39.8311	−	10.6727i	1.36379	−	0.365427i	0.865208	+	0.501414i	$0.167187\pi$
$854$	11.7261	+	16.2026i	0.401260	+	0.554443i
$855$	0.311621	−	0.0120772i	0.0106572	−	0.000413033i
$856$	49.5436	−	15.7940i	1.69337	−	0.539827i
$857$	5.78679	−	10.0230i	0.197673	−	0.342380i	−0.750101	−	0.661324i	$-0.769995\pi$
$857$	5.78679	−	10.0230i	0.197673	−	0.342380i	0.947773	+	0.318944i	$0.103328\pi$
$858$	0.509464	−	3.62670i	0.0173928	−	0.123813i
$859$	−9.26254	−	2.48189i	−0.316034	−	0.0846810i	0.0973153	−	0.995254i	$-0.468974\pi$
$859$	−9.26254	−	2.48189i	−0.316034	−	0.0846810i	−0.413349	+	0.910573i	$0.635641\pi$
$860$	−3.08684	+	0.644189i	−0.105260	+	0.0219667i
$861$	13.7484	+	22.7823i	0.468545	+	0.776418i
$862$	−23.0932	−	18.7714i	−0.786559	−	0.639358i
$863$	−4.82838			−0.164360			−0.0821800	−	0.996617i	$-0.526188\pi$
$863$	−4.82838			−0.164360			−0.0821800	+	0.996617i	$0.526188\pi$
$864$	−28.7299	−	6.21230i	−0.977411	−	0.211347i
$865$	−8.57755			−0.291645
$866$	31.6617	+	25.7363i	1.07591	+	0.874556i
$867$	4.90603	+	8.12969i	0.166617	+	0.276099i
$868$	−8.28683	+	1.72937i	−0.281273	+	0.0586987i
$869$	−18.7008	−	5.01086i	−0.634381	−	0.169982i
$870$	0.142243	−	1.01258i	0.00482251	−	0.0343297i
$871$	−5.43302	+	9.41027i	−0.184091	+	0.318855i
$872$	5.67974	+	17.8166i	0.192340	+	0.603346i
$873$	−4.79254	−	7.60470i	−0.162203	−	0.257380i
$874$	0.449544	+	0.621160i	0.0152060	+	0.0210110i
$875$	−2.29928	+	0.616090i	−0.0777298	+	0.0208276i
$876$	4.91093	+	5.28524i	0.165925	+	0.178572i
$877$	22.6599	+	6.07169i	0.765169	+	0.205026i	0.620236	−	0.784415i	$-0.287037\pi$
$877$	22.6599	+	6.07169i	0.765169	+	0.205026i	0.144933	+	0.989441i	$0.453703\pi$
$878$	−42.5684	+	16.2501i	−1.43661	+	0.548414i
$879$	7.95798	+	27.5535i	0.268416	+	0.929357i
$880$	−5.91070	+	2.57933i	−0.199250	+	0.0869491i
$881$		−	21.6690i		−	0.730046i	−0.930998	−	0.365023i	$-0.881061\pi$
$881$		−	21.6690i		−	0.730046i	0.930998	−	0.365023i	$-0.118939\pi$
$882$	−4.52592	−	3.39651i	−0.152396	−	0.114366i
$883$	20.3335	+	20.3335i	0.684276	+	0.684276i	0.960961	−	0.276685i	$-0.0892357\pi$
$883$	20.3335	+	20.3335i	0.684276	+	0.684276i	−0.276685	+	0.960961i	$0.589236\pi$
$884$	−8.78039	−	0.492773i	−0.295316	−	0.0165737i
$885$	−13.5107	+	0.261714i	−0.454158	+	0.00879741i
$886$	6.40128	+	2.86425i	0.215055	+	0.0962263i
$887$	−7.89139	+	4.55610i	−0.264967	+	0.152979i	−0.626598	−	0.779342i	$-0.715553\pi$
$887$	−7.89139	+	4.55610i	−0.264967	+	0.152979i	0.361631	+	0.932321i	$0.382220\pi$
$888$	32.7598	+	28.6877i	1.09935	+	0.962695i
$889$	3.08725	+	1.78243i	0.103543	+	0.0597806i
$890$	3.16906	+	4.37886i	0.106227	+	0.146780i
$891$	−11.0236	−	9.43538i	−0.369304	−	0.316097i
$892$	−13.6798	+	41.5775i	−0.458033	+	1.39212i
$893$	−0.757723	+	0.203031i	−0.0253562	+	0.00679418i
$894$	11.5186	−	27.1409i	0.385240	−	0.907728i
$895$	−2.39648	+	1.38361i	−0.0801053	+	0.0462488i
$896$	22.3942	+	14.9592i	0.748139	+	0.499752i
$897$	6.03754	+	5.80808i	0.201588	+	0.193926i
$898$	−15.2569	+	18.7696i	−0.509130	+	0.626349i
$899$	0.524868	−	0.524868i	0.0175053	−	0.0175053i
$900$	−4.16850	−	4.31551i	−0.138950	−	0.143850i
$901$	0.514186	+	0.514186i	0.0171300	+	0.0171300i
$902$	1.51107	+	14.6375i	0.0503131	+	0.487377i
$903$	1.80375	+	6.24527i	0.0600252	+	0.207830i
$904$	2.27392	+	48.5474i	0.0756294	+	1.61466i
$905$	12.1860	+	21.1068i	0.405077	+	0.701614i
$906$	−5.76738	−	4.50538i	−0.191608	−	0.149681i
$907$	7.45941	+	27.8389i	0.247686	+	0.924376i	0.972014	+	0.234921i	$0.0754832\pi$
$907$	7.45941	+	27.8389i	0.247686	+	0.924376i	−0.724329	+	0.689455i	$0.757850\pi$
$908$	23.7801	−	12.0058i	0.789170	−	0.398428i
$909$	38.8801	+	8.81945i	1.28957	+	0.292523i
$910$	−3.08250	−	0.494072i	−0.102184	−	0.0163783i
$911$	21.6633	−	37.5219i	0.717736	−	1.24315i	−0.244159	−	0.969735i	$-0.578512\pi$
$911$	21.6633	−	37.5219i	0.717736	−	1.24315i	0.961895	−	0.273419i	$-0.0881546\pi$
$912$	−0.121164	−	0.709933i	−0.00401215	−	0.0235082i
$913$	2.18336	+	3.78169i	0.0722587	+	0.125156i
$914$	−13.3341	−	34.9297i	−0.441053	−	1.15537i
$915$	−8.81065	+	5.31696i	−0.291271	+	0.175773i
$916$	11.0969	+	0.622778i	0.366650	+	0.0205772i
$917$	−32.1931	+	32.1931i	−1.06311	+	1.06311i
$918$	−20.3703	+	28.2681i	−0.672320	+	0.932987i
$919$	48.3322			1.59433			0.797167	−	0.603759i	$-0.206331\pi$
$919$	48.3322			1.59433			0.797167	+	0.603759i	$0.206331\pi$
$920$	3.14729	−	14.4127i	0.103763	−	0.475173i
$921$	9.54470	−	38.5965i	0.314509	−	1.27180i
$922$	37.7236	+	16.8794i	1.24236	+	0.555894i
$923$	3.80350	−	14.1948i	0.125194	−	0.467229i
$924$	6.22035	+	11.7494i	0.204634	+	0.386527i
$925$	2.30055	+	8.58576i	0.0756415	+	0.282298i
$926$	17.5034	+	2.80550i	0.575197	+	0.0921943i
$927$	0.634299	−	0.0245830i	0.0208331	−	0.000807410i
$928$	−2.36131	−	0.0218623i	−0.0775140	−	0.000717666i
$929$	−8.76795	−	5.06218i	−0.287667	−	0.166085i	0.349222	−	0.937040i	$-0.386446\pi$
$929$	−8.76795	−	5.06218i	−0.287667	−	0.166085i	−0.636889	+	0.770955i	$0.719779\pi$
$930$	−0.531083	−	4.32305i	−0.0174149	−	0.141759i
$931$	0.0358842	−	0.133922i	0.00117606	−	0.00438911i
$932$	3.82614	+	18.3342i	0.125329	+	0.600556i
$933$	27.5075	+	15.1788i	0.900554	+	0.496933i
$934$	−3.71704	+	0.383719i	−0.121625	+	0.0125557i
$935$			7.64451i			0.250002i
$936$	−2.67857	−	7.39898i	−0.0875517	−	0.241843i
$937$		−	18.3141i		−	0.598295i	−0.954207	−	0.299147i	$-0.903298\pi$
$937$		−	18.3141i		−	0.598295i	0.954207	−	0.299147i	$-0.0967022\pi$
$938$	−4.05043	−	39.2360i	−0.132251	−	1.28110i
$939$	0.624919	+	32.2609i	0.0203935	+	1.05279i
$940$	12.6272	+	8.26686i	0.411854	+	0.269635i
$941$	6.74370	−	25.1678i	0.219838	−	0.820447i	−0.764569	−	0.644542i	$-0.777048\pi$
$941$	6.74370	−	25.1678i	0.219838	−	0.820447i	0.984407	−	0.175905i	$-0.0562853\pi$
$942$	−4.68066	+	11.0289i	−0.152504	+	0.359341i
$943$	−29.1521	−	16.8310i	−0.949324	−	0.548093i
$944$	4.65351	+	30.8587i	0.151459	+	1.00436i
$945$	−8.22344	+	9.23925i	−0.267508	+	0.300553i
$946$	−0.568940	+	3.54959i	−0.0184978	+	0.115407i
$947$	−6.55213	−	24.4529i	−0.212916	−	0.794612i	−0.986890	−	0.161395i	$-0.948401\pi$
$947$	−6.55213	−	24.4529i	−0.212916	−	0.794612i	0.773974	−	0.633217i	$-0.218266\pi$
$948$	−40.5488	+	9.28509i	−1.31696	+	0.301566i
$949$	−0.499883	+	1.86559i	−0.0162269	+	0.0605595i
$950$	0.0600429	−	0.134189i	0.00194805	−	0.00435368i
$951$	12.6485	+	12.1678i	0.410156	+	0.394568i
$952$	26.8695	−	17.2378i	0.870846	−	0.558681i
$953$	1.17883			0.0381862			0.0190931	−	0.999818i	$-0.493922\pi$
$953$	1.17883			0.0381862			0.0190931	+	0.999818i	$0.493922\pi$
$954$	−0.242547	+	0.603760i	−0.00785274	+	0.0195475i
$955$	11.9738	−	11.9738i	0.387462	−	0.387462i
$956$	−27.0403	+	24.1665i	−0.874546	+	0.781600i
$957$	−1.02063	−	0.563192i	−0.0329923	−	0.0182054i
$958$	−40.7229	+	15.5456i	−1.31570	+	0.502255i
$959$	20.0567	+	34.7392i	0.647665	+	1.12179i
$960$	−8.63089	+	10.8401i	−0.278561	+	0.349863i
$961$	−13.9191	+	24.1086i	−0.449003	+	0.777696i
$962$	−1.84492	+	11.5104i	−0.0594826	+	0.371110i
$963$	52.6824	−	16.3275i	1.69767	−	0.526147i
$964$	14.7615	+	4.85682i	0.475436	+	0.156428i
$965$	3.09809	+	11.5622i	0.0997311	+	0.372202i
$966$	−30.1159	−	4.23057i	−0.968963	−	0.136116i
$967$	−16.3265	−	28.2784i	−0.525025	−	0.909371i	−0.999575	−	0.0291420i	$-0.990722\pi$
$967$	−16.3265	−	28.2784i	−0.525025	−	0.909371i	0.474550	−	0.880229i	$-0.342611\pi$
$968$	−1.11171	−	23.7347i	−0.0357317	−	0.762861i
$969$	−0.828746	−	0.204945i	−0.0266232	−	0.00658377i
$970$	−4.21500	+	0.435125i	−0.135335	+	0.0139710i
$971$	35.8955	+	35.8955i	1.15194	+	1.15194i	0.986163	+	0.165780i	$0.0530141\pi$
$971$	35.8955	+	35.8955i	1.15194	+	1.15194i	0.165780	+	0.986163i	$0.446986\pi$
$972$	−30.4185	−	6.83478i	−0.975674	−	0.219226i
$973$	−17.6021	+	17.6021i	−0.564297	+	0.564297i
$974$	25.7112	+	20.8995i	0.823841	+	0.669663i
$975$	0.385598	−	1.55926i	0.0123490	−	0.0499364i
$976$	14.8188	+	18.5793i	0.474337	+	0.594710i
$977$	−47.8025	+	27.5988i	−1.52934	+	0.882963i	−0.529947	+	0.848031i	$0.677788\pi$
$977$	−47.8025	+	27.5988i	−1.52934	+	0.882963i	−0.999390	+	0.0349325i	$0.988878\pi$
$978$	30.3229	−	22.8529i	0.969619	−	0.730757i
$979$	5.95224	−	1.59490i	0.190234	−	0.0509731i
$980$	−2.38124	+	1.20221i	−0.0760658	+	0.0384033i
$981$	5.87161	+	18.9453i	0.187466	+	0.604878i
$982$	13.1753	−	9.53521i	0.420442	−	0.304281i
$983$	−30.5565	−	17.6418i	−0.974602	−	0.562687i	−0.0739659	−	0.997261i	$-0.523566\pi$
$983$	−30.5565	−	17.6418i	−0.974602	−	0.562687i	−0.900636	+	0.434574i	$0.856899\pi$
$984$	17.5848	+	26.2764i	0.560584	+	0.837661i
$985$	−13.2559	+	7.65328i	−0.422367	+	0.243854i
$986$	−1.14326	+	2.55507i	−0.0364089	+	0.0813699i
$987$	15.0318	−	27.2410i	0.478467	−	0.867090i
$988$	0.143756	−	0.128478i	0.00457349	−	0.00408742i
$989$	−5.81489	−	5.81489i	−0.184903	−	0.184903i
$990$	−6.29111	+	2.68512i	−0.199945	+	0.0853388i
$991$		−	4.19259i		−	0.133182i	−0.997780	−	0.0665910i	$-0.978788\pi$
$991$		−	4.19259i		−	0.133182i	0.997780	−	0.0665910i	$-0.0212123\pi$
$992$	−9.73967	+	2.51333i	−0.309235	+	0.0797982i
$993$	43.5466	−	45.2670i	1.38191	−	1.43650i
$994$	19.0252	+	49.8381i	0.603444	+	1.58077i
$995$	−3.56315	−	0.954743i	−0.112959	−	0.0302674i
$996$	7.94785	+	4.98615i	0.251837	+	0.157992i
$997$	43.8663	−	11.7539i	1.38926	−	0.372251i	0.514784	−	0.857320i	$-0.327872\pi$
$997$	43.8663	−	11.7539i	1.38926	−	0.372251i	0.874476	+	0.485069i	$0.161206\pi$
$998$	14.0213	−	10.1475i	0.443838	−	0.321213i
$999$	34.5004	+	30.7072i	1.09154	+	0.971533i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	720.2.cf.a.11.76	✓	384
9.5	odd	6	inner	720.2.cf.a.491.84	yes	384
16.3	odd	4	inner	720.2.cf.a.371.84	yes	384
144.131	even	12	inner	720.2.cf.a.131.76	yes	384

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
720.2.cf.a.11.76	✓	384	1.1	even	1	trivial
720.2.cf.a.131.76	yes	384	144.131	even	12	inner
720.2.cf.a.371.84	yes	384	16.3	odd	4	inner
720.2.cf.a.491.84	yes	384	9.5	odd	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 720 = 2^{4} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	720.cf (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.09740 + 0.892027i) q^{2} +(-0.894914 - 1.48295i) q^{3} +(0.408576 + 1.95782i) q^{4} +(0.965926 + 0.258819i) q^{5} +(0.340749 - 2.42567i) q^{6} +(-1.19019 + 2.06148i) q^{7} +(-1.29806 + 2.51298i) q^{8} +(-1.39826 + 2.65422i) q^{9} +O(q^{10})\)	\(q+(1.09740 + 0.892027i) q^{2} +(-0.894914 - 1.48295i) q^{3} +(0.408576 + 1.95782i) q^{4} +(0.965926 + 0.258819i) q^{5} +(0.340749 - 2.42567i) q^{6} +(-1.19019 + 2.06148i) q^{7} +(-1.29806 + 2.51298i) q^{8} +(-1.39826 + 2.65422i) q^{9} +(0.829134 + 1.14566i) q^{10} +(1.55731 - 0.417280i) q^{11} +(2.53770 - 2.35798i) q^{12} +(0.895760 + 0.240018i) q^{13} +(-3.14501 + 1.20058i) q^{14} +(-0.480606 - 1.66404i) q^{15} +(-3.66613 + 1.59984i) q^{16} +4.74153i q^{17} +(-3.90208 + 1.66546i) q^{18} +(-0.0735050 - 0.0735050i) q^{19} +(-0.112068 + 1.99686i) q^{20} +(4.12218 - 0.0798499i) q^{21} +(2.08122 + 0.931238i) q^{22} +(-4.51696 + 2.60787i) q^{23} +(4.88826 - 0.323945i) q^{24} +(0.866025 + 0.500000i) q^{25} +(0.768905 + 1.06244i) q^{26} +(5.18738 - 0.301753i) q^{27} +(-4.52229 - 1.48792i) q^{28} +(0.403219 - 0.108042i) q^{29} +(0.956949 - 2.25483i) q^{30} +(1.53992 - 0.889074i) q^{31} +(-5.45031 - 1.51463i) q^{32} +(-2.01246 - 1.93598i) q^{33} +(-4.22957 + 5.20336i) q^{34} +(-1.68319 + 1.68319i) q^{35} +(-5.76778 - 1.65309i) q^{36} +(6.28521 + 6.28521i) q^{37} +(-0.0150960 - 0.146233i) q^{38} +(-0.445694 - 1.54316i) q^{39} +(-1.90423 + 2.09139i) q^{40} +(3.22696 + 5.58926i) q^{41} +(4.59491 + 3.58947i) q^{42} +(0.408072 + 1.52295i) q^{43} +(1.45324 + 2.87844i) q^{44} +(-2.03758 + 2.20188i) q^{45} +(-7.28321 - 1.16737i) q^{46} +(3.77316 - 6.53530i) q^{47} +(5.65334 + 4.00496i) q^{48} +(0.666877 + 1.15506i) q^{49} +(0.504363 + 1.32122i) q^{50} +(7.03144 - 4.24326i) q^{51} +(-0.103927 + 1.85180i) q^{52} +(0.108443 - 0.108443i) q^{53} +(5.96181 + 4.29614i) q^{54} +1.61224 q^{55} +(-3.63550 - 5.66684i) q^{56} +(-0.0432233 + 0.174784i) q^{57} +(0.538870 + 0.241117i) q^{58} +(2.01928 - 7.53605i) q^{59} +(3.06152 - 1.62083i) q^{60} +(-1.53772 - 5.73887i) q^{61} +(2.48299 + 0.397981i) q^{62} +(-3.80741 - 6.04151i) q^{63} +(-4.63009 - 6.52398i) q^{64} +(0.803117 + 0.463680i) q^{65} +(-0.481532 - 3.91971i) q^{66} +(-3.03263 + 11.3179i) q^{67} +(-9.28307 + 1.93727i) q^{68} +(7.90962 + 4.36459i) q^{69} +(-3.34858 + 0.345682i) q^{70} -15.8467i q^{71} +(-4.85496 - 6.95912i) q^{72} +2.08269i q^{73} +(1.29082 + 12.5040i) q^{74} +(-0.0335449 - 1.73173i) q^{75} +(0.113877 - 0.173942i) q^{76} +(-0.993287 + 3.70700i) q^{77} +(0.887435 - 2.09104i) q^{78} +(-10.3996 - 6.00420i) q^{79} +(-3.95528 + 0.596459i) q^{80} +(-5.08974 - 7.42257i) q^{81} +(-1.44450 + 9.01220i) q^{82} +(0.701005 + 2.61619i) q^{83} +(1.84055 + 8.03787i) q^{84} +(-1.22720 + 4.57997i) q^{85} +(-0.910690 + 2.03529i) q^{86} +(-0.521067 - 0.501264i) q^{87} +(-0.972864 + 4.45513i) q^{88} +3.82213 q^{89} +(-4.20018 + 0.598773i) q^{90} +(-1.56092 + 1.56092i) q^{91} +(-6.95126 - 7.77789i) q^{92} +(-2.69654 - 1.48798i) q^{93} +(9.97033 - 3.80608i) q^{94} +(-0.0519759 - 0.0900248i) q^{95} +(2.63145 + 9.43798i) q^{96} +(-1.49815 + 2.59487i) q^{97} +(-0.298518 + 1.86244i) q^{98} +(-1.06997 + 4.71690i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 384 q - 12 q^{6}+O(q^{10}) \) 384 * q - 12 * q^6	\( 384 q - 12 q^{6} + 24 q^{12} + 20 q^{18} - 24 q^{24} + 24 q^{27} - 12 q^{36} + 48 q^{39} - 80 q^{42} + 24 q^{46} - 40 q^{48} - 192 q^{49} + 40 q^{51} + 12 q^{54} - 36 q^{58} + 72 q^{59} - 28 q^{60} + 72 q^{64} - 72 q^{66} - 156 q^{68} - 112 q^{72} - 168 q^{74} + 12 q^{76} - 116 q^{78} + 72 q^{82} - 120 q^{83} - 116 q^{84} - 36 q^{90} + 48 q^{93} + 20 q^{96} - 32 q^{99}+O(q^{100}) \) 384 * q - 12 * q^6 + 24 * q^12 + 20 * q^18 - 24 * q^24 + 24 * q^27 - 12 * q^36 + 48 * q^39 - 80 * q^42 + 24 * q^46 - 40 * q^48 - 192 * q^49 + 40 * q^51 + 12 * q^54 - 36 * q^58 + 72 * q^59 - 28 * q^60 + 72 * q^64 - 72 * q^66 - 156 * q^68 - 112 * q^72 - 168 * q^74 + 12 * q^76 - 116 * q^78 + 72 * q^82 - 120 * q^83 - 116 * q^84 - 36 * q^90 + 48 * q^93 + 20 * q^96 - 32 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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