LMFDB - Embedded newform 798.2.cj.b.241.13

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [798,2,Mod(241,798)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(798, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([0, 3, 5])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("798.241"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 798 = 2 \cdot 3 \cdot 7 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	798.cj (of order $18$, degree $6$, minimal)

Newform invariants

comment:select newform

sage:traces = [84] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$6.37206208130$
Analytic rank:	$0$
Dimension:	$84$
Relative dimension:	$14$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			241.13
Character	$\chi$	$=$	798.241
Dual form			798.2.cj.b.649.13

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.342020 - 0.939693i) q^{2} +(-0.766044 + 0.642788i) q^{3} +(-0.766044 - 0.642788i) q^{4} +(0.494314 + 0.589100i) q^{5} +(0.342020 + 0.939693i) q^{6} +(1.48242 - 2.19145i) q^{7} +(-0.866025 + 0.500000i) q^{8} +(0.173648 - 0.984808i) q^{9} +(0.722638 - 0.263019i) q^{10} +1.35983 q^{11} +1.00000 q^{12} +(-2.33175 + 0.848687i) q^{13} +(-1.55227 - 2.14254i) q^{14} +(-0.757332 - 0.133538i) q^{15} +(0.173648 + 0.984808i) q^{16} +(1.46565 - 0.258434i) q^{17} +(-0.866025 - 0.500000i) q^{18} +(2.96477 - 3.19533i) q^{19} -0.769015i q^{20} +(0.273038 + 2.63163i) q^{21} +(0.465088 - 1.27782i) q^{22} +(0.508204 - 0.184971i) q^{23} +(0.342020 - 0.939693i) q^{24} +(0.765548 - 4.34164i) q^{25} +2.48139i q^{26} +(0.500000 + 0.866025i) q^{27} +(-2.54423 + 0.725867i) q^{28} +(2.80329 - 3.34083i) q^{29} +(-0.384508 + 0.665987i) q^{30} +(0.867561 + 1.50266i) q^{31} +(0.984808 + 0.173648i) q^{32} +(-1.04169 + 0.874080i) q^{33} +(0.258434 - 1.46565i) q^{34} +(2.02376 - 0.209971i) q^{35} +(-0.766044 + 0.642788i) q^{36} +(1.65762 - 0.957026i) q^{37} +(-1.98861 - 3.87884i) q^{38} +(1.24070 - 2.14895i) q^{39} +(-0.722638 - 0.263019i) q^{40} +(-5.37537 - 1.95647i) q^{41} +(2.56630 + 0.643497i) q^{42} +(-0.928358 - 5.26498i) q^{43} +(-1.04169 - 0.874080i) q^{44} +(0.665987 - 0.384508i) q^{45} -0.540820i q^{46} +(10.8123 + 1.90650i) q^{47} +(-0.766044 - 0.642788i) q^{48} +(-2.60488 - 6.49728i) q^{49} +(-3.81797 - 2.20431i) q^{50} +(-0.956637 + 1.14008i) q^{51} +(2.33175 + 0.848687i) q^{52} +(7.28695 - 8.68425i) q^{53} +(0.984808 - 0.173648i) q^{54} +(0.672181 + 0.801074i) q^{55} +(-0.188087 + 2.63906i) q^{56} +(-0.217232 + 4.35348i) q^{57} +(-2.18057 - 3.77686i) q^{58} +(-0.0929914 - 0.527381i) q^{59} +(0.494314 + 0.589100i) q^{60} +(-0.0497788 - 0.136766i) q^{61} +(1.70876 - 0.301301i) q^{62} +(-1.90074 - 1.84044i) q^{63} +(0.500000 - 0.866025i) q^{64} +(-1.65258 - 0.954115i) q^{65} +(0.465088 + 1.27782i) q^{66} +(-1.64694 - 4.52493i) q^{67} +(-1.28887 - 0.744132i) q^{68} +(-0.270410 + 0.468364i) q^{69} +(0.494859 - 1.97353i) q^{70} +(-1.28219 + 0.226084i) q^{71} +(0.342020 + 0.939693i) q^{72} +(0.0210860 + 0.0251293i) q^{73} +(-0.332372 - 1.88497i) q^{74} +(2.20431 + 3.81797i) q^{75} +(-4.32507 + 0.542042i) q^{76} +(2.01583 - 2.97999i) q^{77} +(-1.59501 - 1.90086i) q^{78} +(-15.7957 + 2.78520i) q^{79} +(-0.494314 + 0.589100i) q^{80} +(-0.939693 - 0.342020i) q^{81} +(-3.67697 + 4.38204i) q^{82} +(9.95997 + 5.75039i) q^{83} +(1.48242 - 2.19145i) q^{84} +(0.876736 + 0.735669i) q^{85} +(-5.26498 - 0.928358i) q^{86} +4.36115i q^{87} +(-1.17764 + 0.679913i) q^{88} +(3.64339 + 3.05717i) q^{89} +(-0.133538 - 0.757332i) q^{90} +(-1.59677 + 6.36801i) q^{91} +(-0.508204 - 0.184971i) q^{92} +(-1.63048 - 0.593447i) q^{93} +(5.48954 - 9.50816i) q^{94} +(3.34789 + 0.167055i) q^{95} +(-0.866025 + 0.500000i) q^{96} +(-10.4929 + 8.80463i) q^{97} +(-6.99636 + 0.225590i) q^{98} +(0.236131 - 1.33917i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 84 q + 12 q^{7} - 12 q^{10} - 12 q^{11} + 84 q^{12} + 24 q^{13} + 6 q^{14} + 6 q^{19} - 6 q^{21} + 12 q^{22} - 42 q^{23} - 30 q^{25} + 42 q^{27} + 6 q^{28} + 6 q^{31} + 12 q^{33} - 30 q^{34} - 42 q^{35}+ \cdots + 6 q^{99}+O(q^{100}) $ 84 * q + 12 * q^7 - 12 * q^10 - 12 * q^11 + 84 * q^12 + 24 * q^13 + 6 * q^14 + 6 * q^19 - 6 * q^21 + 12 * q^22 - 42 * q^23 - 30 * q^25 + 42 * q^27 + 6 * q^28 + 6 * q^31 + 12 * q^33 - 30 * q^34 - 42 * q^35 - 18 * q^37 + 12 * q^38 + 12 * q^40 + 36 * q^41 + 18 * q^42 + 12 * q^43 + 12 * q^44 - 18 * q^45 + 18 * q^47 - 24 * q^49 + 18 * q^51 - 24 * q^52 + 60 * q^53 - 30 * q^55 - 18 * q^56 + 6 * q^57 + 48 * q^59 - 12 * q^62 - 6 * q^63 + 42 * q^64 + 108 * q^65 + 12 * q^66 + 42 * q^67 + 6 * q^69 + 18 * q^70 + 42 * q^71 - 48 * q^73 - 18 * q^74 - 48 * q^75 + 18 * q^76 - 96 * q^77 - 12 * q^78 - 60 * q^79 - 6 * q^82 + 54 * q^83 + 12 * q^84 - 24 * q^85 - 12 * q^86 - 24 * q^89 + 6 * q^90 + 24 * q^91 + 42 * q^92 - 36 * q^93 + 18 * q^94 - 12 * q^95 - 78 * q^97 + 24 * q^98 + 6 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/798\mathbb{Z}\right)^\times$.

$n$	$115$	$211$	$533$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{18}\right)$	$1$

Coefficient data

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

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

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

$2$	0.342020	−	0.939693i	0.241845	−	0.664463i
$2$	0.342020	−	0.939693i	0.241845	−	0.664463i
$3$	−0.766044	+	0.642788i	−0.442276	+	0.371114i
$3$	−0.766044	+	0.642788i	−0.442276	+	0.371114i
$4$	−0.766044	−	0.642788i	−0.383022	−	0.321394i
$5$	0.494314	+	0.589100i	0.221064	+	0.263453i	0.865166	−	0.501486i	$-0.167213\pi$
$5$	0.494314	+	0.589100i	0.221064	+	0.263453i	−0.644102	+	0.764940i	$0.722769\pi$
$6$	0.342020	+	0.939693i	0.139629	+	0.383628i
$7$	1.48242	−	2.19145i	0.560301	−	0.828289i
$7$	1.48242	−	2.19145i	0.560301	−	0.828289i
$8$	−0.866025	+	0.500000i	−0.306186	+	0.176777i
$9$	0.173648	−	0.984808i	0.0578827	−	0.328269i
$10$	0.722638	−	0.263019i	0.228518	−	0.0831738i
$11$	1.35983			0.410003			0.205002	−	0.978762i	$-0.434280\pi$
$11$	1.35983			0.410003			0.205002	+	0.978762i	$0.434280\pi$
$12$	1.00000			0.288675
$13$	−2.33175	+	0.848687i	−0.646711	+	0.235383i	−0.644488	−	0.764614i	$-0.722930\pi$
$13$	−2.33175	+	0.848687i	−0.646711	+	0.235383i	−0.00222223	+	0.999998i	$0.500707\pi$
$14$	−1.55227	−	2.14254i	−0.414862	−	0.572617i
$15$	−0.757332	−	0.133538i	−0.195542	−	0.0344794i
$16$	0.173648	+	0.984808i	0.0434120	+	0.246202i
$17$	1.46565	−	0.258434i	0.355473	−	0.0626795i	0.00693991	−	0.999976i	$-0.497791\pi$
$17$	1.46565	−	0.258434i	0.355473	−	0.0626795i	0.348533	+	0.937296i	$0.386680\pi$
$18$	−0.866025	−	0.500000i	−0.204124	−	0.117851i
$19$	2.96477	−	3.19533i	0.680166	−	0.733058i
$19$	2.96477	−	3.19533i	0.680166	−	0.733058i
$20$		−	0.769015i		−	0.171957i
$21$	0.273038	+	2.63163i	0.0595818	+	0.574268i
$22$	0.465088	−	1.27782i	0.0991571	−	0.272432i
$23$	0.508204	−	0.184971i	0.105968	−	0.0385692i	−0.288492	−	0.957482i	$-0.593154\pi$
$23$	0.508204	−	0.184971i	0.105968	−	0.0385692i	0.394460	+	0.918913i	$0.370932\pi$
$24$	0.342020	−	0.939693i	0.0698146	−	0.191814i
$25$	0.765548	−	4.34164i	0.153110	−	0.868328i
$26$			2.48139i			0.486642i
$27$	0.500000	+	0.866025i	0.0962250	+	0.166667i
$28$	−2.54423	+	0.725867i	−0.480815	+	0.137176i
$29$	2.80329	−	3.34083i	0.520558	−	0.620377i	−0.440155	−	0.897922i	$-0.645076\pi$
$29$	2.80329	−	3.34083i	0.520558	−	0.620377i	0.960713	+	0.277545i	$0.0895208\pi$
$30$	−0.384508	+	0.665987i	−0.0702012	+	0.121592i
$31$	0.867561	+	1.50266i	0.155819	+	0.269886i	0.933357	−	0.358950i	$-0.116865\pi$
$31$	0.867561	+	1.50266i	0.155819	+	0.269886i	−0.777538	+	0.628836i	$0.783532\pi$
$32$	0.984808	+	0.173648i	0.174091	+	0.0306970i
$33$	−1.04169	+	0.874080i	−0.181335	+	0.152158i
$34$	0.258434	−	1.46565i	0.0443211	−	0.251358i
$35$	2.02376	−	0.209971i	0.342078	−	0.0354915i
$36$	−0.766044	+	0.642788i	−0.127674	+	0.107131i
$37$	1.65762	−	0.957026i	0.272511	−	0.157334i	−0.357517	−	0.933906i	$-0.616377\pi$
$37$	1.65762	−	0.957026i	0.272511	−	0.157334i	0.630028	+	0.776572i	$0.283043\pi$
$38$	−1.98861	−	3.87884i	−0.322596	−	0.629231i
$39$	1.24070	−	2.14895i	0.198671	−	0.344108i
$40$	−0.722638	−	0.263019i	−0.114259	−	0.0415869i
$41$	−5.37537	−	1.95647i	−0.839492	−	0.305550i	−0.113743	−	0.993510i	$-0.536284\pi$
$41$	−5.37537	−	1.95647i	−0.839492	−	0.305550i	−0.725748	+	0.687960i	$0.758506\pi$
$42$	2.56630	+	0.643497i	0.395989	+	0.0992937i
$43$	−0.928358	−	5.26498i	−0.141573	−	0.802902i	−0.970055	−	0.242886i	$-0.921906\pi$
$43$	−0.928358	−	5.26498i	−0.141573	−	0.802902i	0.828482	−	0.560016i	$-0.189205\pi$
$44$	−1.04169	−	0.874080i	−0.157040	−	0.131772i
$45$	0.665987	−	0.384508i	0.0992795	−	0.0573190i
$46$		−	0.540820i		−	0.0797395i
$47$	10.8123	+	1.90650i	1.57713	+	0.278091i	0.892586	−	0.450877i	$-0.148889\pi$
$47$	10.8123	+	1.90650i	1.57713	+	0.278091i	0.684547	+	0.728968i	$0.260000\pi$
$48$	−0.766044	−	0.642788i	−0.110569	−	0.0927784i
$49$	−2.60488	−	6.49728i	−0.372126	−	0.928182i
$50$	−3.81797	−	2.20431i	−0.539943	−	0.311736i
$51$	−0.956637	+	1.14008i	−0.133956	+	0.159643i
$52$	2.33175	+	0.848687i	0.323355	+	0.117692i
$53$	7.28695	−	8.68425i	1.00094	−	1.19287i	0.0197550	−	0.999805i	$-0.493711\pi$
$53$	7.28695	−	8.68425i	1.00094	−	1.19287i	0.981185	−	0.193069i	$-0.0618442\pi$
$54$	0.984808	−	0.173648i	0.134015	−	0.0236305i
$55$	0.672181	+	0.801074i	0.0906368	+	0.108017i
$56$	−0.188087	+	2.63906i	−0.0251342	+	0.352659i
$57$	−0.217232	+	4.35348i	−0.0287731	+	0.576633i
$58$	−2.18057	−	3.77686i	−0.286323	−	0.495927i
$59$	−0.0929914	−	0.527381i	−0.0121065	−	0.0686591i	0.978156	−	0.207872i	$-0.0666538\pi$
$59$	−0.0929914	−	0.527381i	−0.0121065	−	0.0686591i	−0.990262	+	0.139213i	$0.955543\pi$
$60$	0.494314	+	0.589100i	0.0638156	+	0.0760525i
$61$	−0.0497788	−	0.136766i	−0.00637352	−	0.0175111i	0.936465	−	0.350761i	$-0.114077\pi$
$61$	−0.0497788	−	0.136766i	−0.00637352	−	0.0175111i	−0.942839	+	0.333250i	$0.891855\pi$
$62$	1.70876	−	0.301301i	0.217013	−	0.0382652i
$63$	−1.90074	−	1.84044i	−0.239470	−	0.231873i
$64$	0.500000	−	0.866025i	0.0625000	−	0.108253i
$65$	−1.65258	−	0.954115i	−0.204977	−	0.118343i
$66$	0.465088	+	1.27782i	0.0572484	+	0.157289i
$67$	−1.64694	−	4.52493i	−0.201206	−	0.552808i	0.797519	−	0.603294i	$-0.206145\pi$
$67$	−1.64694	−	4.52493i	−0.201206	−	0.552808i	−0.998725	+	0.0504856i	$0.983923\pi$
$68$	−1.28887	−	0.744132i	−0.156299	−	0.0902392i
$69$	−0.270410	+	0.468364i	−0.0325535	+	0.0563844i
$70$	0.494859	−	1.97353i	0.0591470	−	0.235882i
$71$	−1.28219	+	0.226084i	−0.152168	+	0.0268313i	−0.249213	−	0.968449i	$-0.580172\pi$
$71$	−1.28219	+	0.226084i	−0.152168	+	0.0268313i	0.0970453	+	0.995280i	$0.469061\pi$
$72$	0.342020	+	0.939693i	0.0403075	+	0.110744i
$73$	0.0210860	+	0.0251293i	0.00246793	+	0.00294116i	0.767277	−	0.641316i	$-0.221611\pi$
$73$	0.0210860	+	0.0251293i	0.00246793	+	0.00294116i	−0.764809	+	0.644257i	$0.777167\pi$
$74$	−0.332372	−	1.88497i	−0.0386374	−	0.219124i
$75$	2.20431	+	3.81797i	0.254532	+	0.440862i
$76$	−4.32507	+	0.542042i	−0.496119	+	0.0621765i
$77$	2.01583	−	2.97999i	0.229725	−	0.339601i
$78$	−1.59501	−	1.90086i	−0.180599	−	0.215230i
$79$	−15.7957	+	2.78520i	−1.77715	+	0.313360i	−0.963443	−	0.267915i	$-0.913665\pi$
$79$	−15.7957	+	2.78520i	−1.77715	+	0.313360i	−0.813708	+	0.581274i	$0.802554\pi$
$80$	−0.494314	+	0.589100i	−0.0552659	+	0.0658634i
$81$	−0.939693	−	0.342020i	−0.104410	−	0.0380022i
$82$	−3.67697	+	4.38204i	−0.406053	+	0.483916i
$83$	9.95997	+	5.75039i	1.09325	+	0.631187i	0.934439	−	0.356122i	$-0.115901\pi$
$83$	9.95997	+	5.75039i	1.09325	+	0.631187i	0.158809	+	0.987309i	$0.449235\pi$
$84$	1.48242	−	2.19145i	0.161745	−	0.239106i
$85$	0.876736	+	0.735669i	0.0950954	+	0.0797945i
$86$	−5.26498	−	0.928358i	−0.567737	−	0.100107i
$87$			4.36115i			0.467564i
$88$	−1.17764	+	0.679913i	−0.125537	+	0.0724790i
$89$	3.64339	+	3.05717i	0.386198	+	0.324059i	0.815130	−	0.579278i	$-0.196665\pi$
$89$	3.64339	+	3.05717i	0.386198	+	0.324059i	−0.428932	+	0.903337i	$0.641110\pi$
$90$	−0.133538	−	0.757332i	−0.0140762	−	0.0798298i
$91$	−1.59677	+	6.36801i	−0.167387	+	0.667549i
$92$	−0.508204	−	0.184971i	−0.0529840	−	0.0192846i
$93$	−1.63048	−	0.593447i	−0.169073	−	0.0615376i
$94$	5.48954	−	9.50816i	0.566203	−	0.980692i
$95$	3.34789	+	0.167055i	0.343487	+	0.0171395i
$96$	−0.866025	+	0.500000i	−0.0883883	+	0.0510310i
$97$	−10.4929	+	8.80463i	−1.06540	+	0.893974i	−0.994628	−	0.103518i	$-0.966990\pi$
$97$	−10.4929	+	8.80463i	−1.06540	+	0.893974i	−0.0707696	+	0.997493i	$0.522545\pi$
$98$	−6.99636	+	0.225590i	−0.706739	+	0.0227880i
$99$	0.236131	−	1.33917i	0.0237321	−	0.134591i
$100$	−3.37720	+	2.83380i	−0.337720	+	0.283380i
$101$	4.84125	+	0.853643i	0.481722	+	0.0849407i	0.409236	−	0.912429i	$-0.365795\pi$
$101$	4.84125	+	0.853643i	0.481722	+	0.0849407i	0.0724867	+	0.997369i	$0.476906\pi$
$102$	0.744132	+	1.28887i	0.0736800	+	0.127618i
$103$	−5.73645	+	9.93583i	−0.565230	+	0.979006i	0.431799	+	0.901970i	$0.357879\pi$
$103$	−5.73645	+	9.93583i	−0.565230	+	0.979006i	−0.997028	+	0.0770364i	$0.975454\pi$
$104$	1.59501	−	1.90086i	0.156404	−	0.186395i
$105$	−1.41532	+	1.46169i	−0.138121	+	0.142647i
$106$	−5.66824	−	9.81769i	−0.550549	−	0.953578i
$107$			18.6882i			1.80666i	0.428950	+	0.903328i	$0.358884\pi$
$107$			18.6882i			1.80666i	−0.428950	+	0.903328i	$0.641116\pi$
$108$	0.173648	−	0.984808i	0.0167093	−	0.0947632i
$109$	2.75220	−	7.56160i	0.263613	−	0.724270i	−0.735304	−	0.677737i	$-0.762961\pi$
$109$	2.75220	−	7.56160i	0.263613	−	0.724270i	0.998917	−	0.0465323i	$-0.0148171\pi$
$110$	0.982662	−	0.357660i	0.0936932	−	0.0341015i
$111$	−0.654644	+	1.79862i	−0.0621361	+	0.170717i
$112$	2.41557	+	1.07935i	0.228250	+	0.101989i
$113$		−	2.66777i		−	0.250962i	−0.992096	−	0.125481i	$-0.959953\pi$
$113$		−	2.66777i		−	0.250962i	0.992096	−	0.125481i	$-0.0400474\pi$
$114$	4.01664	+	1.69311i	0.376193	+	0.158574i
$115$	0.360179	+	0.207949i	0.0335869	+	0.0193914i
$116$	−4.29489	+	0.757305i	−0.398771	+	0.0703140i
$117$	0.430890	+	2.44370i	0.0398358	+	0.225920i
$118$	−0.527381	−	0.0929914i	−0.0485493	−	0.00856056i
$119$	1.60636	−	3.59501i	0.147255	−	0.329554i
$120$	0.722638	−	0.263019i	0.0659675	−	0.0240102i
$121$	−9.15087			−0.831897
$122$	−0.145543			−0.0131769
$123$	5.37537	−	1.95647i	0.484681	−	0.176409i
$124$	0.301301	−	1.70876i	0.0270576	−	0.153451i
$125$	6.26601	−	3.61768i	0.560449	−	0.323576i
$126$	−2.37953	+	1.15664i	−0.211986	+	0.103042i
$127$	1.11781	+	3.07115i	0.0991893	+	0.272520i	0.979356	−	0.202145i	$-0.0647913\pi$
$127$	1.11781	+	3.07115i	0.0991893	+	0.272520i	−0.880166	+	0.474665i	$0.842569\pi$
$128$	−0.642788	−	0.766044i	−0.0568149	−	0.0677094i
$129$	4.09543	+	3.43647i	0.360582	+	0.302564i
$130$	−1.46179	+	1.22659i	−0.128207	+	0.107579i
$131$	−5.87064	+	16.1294i	−0.512920	+	1.40924i	0.365260	+	0.930906i	$0.380980\pi$
$131$	−5.87064	+	16.1294i	−0.512920	+	1.40924i	−0.878180	+	0.478331i	$0.841242\pi$
$132$	1.35983			0.118358
$133$	−2.60736	−	11.2340i	−0.226087	−	0.974107i
$134$	−4.81533			−0.415981
$135$	−0.263019	+	0.722638i	−0.0226370	+	0.0621948i
$136$	−1.14008	+	0.956637i	−0.0977607	+	0.0820310i
$137$	2.58406	+	2.16828i	0.220771	+	0.185249i	0.746465	−	0.665425i	$-0.231750\pi$
$137$	2.58406	+	2.16828i	0.220771	+	0.185249i	−0.525693	+	0.850674i	$0.676194\pi$
$138$	0.347632	+	0.414292i	0.0295924	+	0.0352669i
$139$	5.76337	+	15.8347i	0.488843	+	1.34308i	0.901729	+	0.432302i	$0.142298\pi$
$139$	5.76337	+	15.8347i	0.488843	+	1.34308i	−0.412887	+	0.910782i	$0.635479\pi$
$140$	−1.68526	−	1.14000i	−0.142430	−	0.0963477i
$141$	−9.50816	+	5.48954i	−0.800732	+	0.462303i
$142$	−0.226084	+	1.28219i	−0.0189726	+	0.107599i
$143$	−3.17077	+	1.15407i	−0.265153	+	0.0965079i
$144$	1.00000			0.0833333
$145$	3.35379			0.278517
$146$	0.0308256	−	0.0112196i	0.00255115	−	0.000928541i
$147$	6.17182	+	3.30282i	0.509043	+	0.272412i
$148$	−1.88497	−	0.332372i	−0.154944	−	0.0273208i
$149$	1.77057	+	10.0414i	0.145051	+	0.822624i	0.967326	+	0.253535i	$0.0815932\pi$
$149$	1.77057	+	10.0414i	0.145051	+	0.822624i	−0.822275	+	0.569090i	$0.807296\pi$
$150$	4.34164	−	0.765548i	0.354493	−	0.0625067i
$151$	8.33072	+	4.80974i	0.677944	+	0.391411i	0.799080	−	0.601225i	$-0.205320\pi$
$151$	8.33072	+	4.80974i	0.677944	+	0.391411i	−0.121136	+	0.992636i	$0.538654\pi$
$152$	−0.969906	+	4.24962i	−0.0786698	+	0.344690i
$153$		−	1.48826i		−	0.120319i
$154$	−2.11082	−	2.91348i	−0.170095	−	0.234775i
$155$	−0.456370	+	1.25387i	−0.0366565	+	0.100713i
$156$	−2.33175	+	0.848687i	−0.186689	+	0.0679493i
$157$	4.54839	−	12.4966i	0.363001	−	0.997337i	−0.614962	−	0.788557i	$-0.710828\pi$
$157$	4.54839	−	12.4966i	0.363001	−	0.997337i	0.977963	−	0.208780i	$-0.0669493\pi$
$158$	−2.78520	+	15.7957i	−0.221579	+	1.25664i
$159$			11.3365i			0.899042i
$160$	0.384508	+	0.665987i	0.0303980	+	0.0526509i
$161$	0.348016	−	1.38791i	0.0274275	−	0.109382i
$162$	−0.642788	+	0.766044i	−0.0505022	+	0.0601861i
$163$	7.10595	−	12.3079i	0.556581	−	0.964027i	−0.441198	−	0.897410i	$-0.645446\pi$
$163$	7.10595	−	12.3079i	0.556581	−	0.964027i	0.997779	−	0.0666167i	$-0.0212205\pi$
$164$	2.86017	+	4.95397i	0.223342	+	0.386840i
$165$	−1.02984	−	0.181589i	−0.0801730	−	0.0141367i
$166$	8.81011	−	7.39256i	0.683797	−	0.573774i
$167$	−2.34642	+	13.3072i	−0.181571	+	1.02974i	0.748711	+	0.662897i	$0.230673\pi$
$167$	−2.34642	+	13.3072i	−0.181571	+	1.02974i	−0.930282	+	0.366845i	$0.880438\pi$
$168$	−1.55227	−	2.14254i	−0.119760	−	0.165300i
$169$	−5.24180	+	4.39839i	−0.403215	+	0.338338i
$170$	0.991164	−	0.572249i	0.0760188	−	0.0438895i
$171$	−2.63196	−	3.47460i	−0.201271	−	0.265709i
$172$	−2.67310	+	4.62995i	−0.203822	+	0.353030i
$173$	−3.52483	−	1.28293i	−0.267988	−	0.0975396i	0.204531	−	0.978860i	$-0.434433\pi$
$173$	−3.52483	−	1.28293i	−0.267988	−	0.0975396i	−0.472519	+	0.881320i	$0.656655\pi$
$174$	4.09814	+	1.49160i	0.310679	+	0.113078i
$175$	−8.37961	−	8.11378i	−0.633439	−	0.613344i
$176$	0.236131	+	1.33917i	0.0177991	+	0.100944i
$177$	0.410229	+	0.344223i	0.0308347	+	0.0258734i
$178$	4.11891	−	2.37805i	0.308725	−	0.178243i
$179$			19.4629i			1.45473i	0.686252	+	0.727364i	$0.259255\pi$
$179$			19.4629i			1.45473i	−0.686252	+	0.727364i	$0.740745\pi$
$180$	−0.757332	−	0.133538i	−0.0564482	−	0.00995334i
$181$	−1.49306	−	1.25282i	−0.110978	−	0.0931216i	0.585610	−	0.810593i	$-0.300855\pi$
$181$	−1.49306	−	1.25282i	−0.110978	−	0.0931216i	−0.696588	+	0.717471i	$0.745299\pi$
$182$	5.43785	+	3.67846i	0.403080	+	0.272666i
$183$	0.126044	+	0.0727717i	0.00931746	+	0.00537944i
$184$	−0.347632	+	0.414292i	−0.0256278	+	0.0305420i
$185$	1.38317	+	0.503431i	0.101692	+	0.0370130i
$186$	−1.11531	+	1.32918i	−0.0817789	+	0.0974602i
$187$	1.99303	−	0.351426i	0.145745	−	0.0256988i
$188$	−7.05722	−	8.41046i	−0.514700	−	0.613396i
$189$	2.63906	+	0.188087i	0.191963	+	0.0136813i
$190$	1.30203	−	3.08886i	0.0944590	−	0.224089i
$191$	−1.40959	−	2.44148i	−0.101994	−	0.176659i	0.810512	−	0.585722i	$-0.199189\pi$
$191$	−1.40959	−	2.44148i	−0.101994	−	0.176659i	−0.912506	+	0.409063i	$0.865856\pi$
$192$	0.173648	+	0.984808i	0.0125320	+	0.0710724i
$193$	−7.31455	−	8.71714i	−0.526513	−	0.627474i	0.435595	−	0.900143i	$-0.356538\pi$
$193$	−7.31455	−	8.71714i	−0.526513	−	0.627474i	−0.962108	+	0.272669i	$0.912094\pi$
$194$	4.68484	+	12.8715i	0.336352	+	0.924120i
$195$	1.87924	−	0.331361i	0.134575	−	0.0237292i
$196$	−2.18091	+	6.65159i	−0.155779	+	0.475113i
$197$	3.33286	−	5.77268i	0.237456	−	0.411286i	−0.722527	−	0.691342i	$-0.757020\pi$
$197$	3.33286	−	5.77268i	0.237456	−	0.411286i	0.959984	+	0.280056i	$0.0903530\pi$
$198$	−1.17764	−	0.679913i	−0.0836915	−	0.0483193i
$199$	−5.04137	−	13.8510i	−0.357373	−	0.981874i	−0.979937	−	0.199306i	$-0.936131\pi$
$199$	−5.04137	−	13.8510i	−0.357373	−	0.981874i	0.622564	−	0.782569i	$-0.286091\pi$
$200$	1.50784	+	4.14274i	0.106620	+	0.292936i
$201$	4.17020	+	2.40766i	0.294143	+	0.169824i
$202$	2.45797	−	4.25732i	0.172942	−	0.299544i
$203$	−3.16561	−	11.0958i	−0.222182	−	0.778770i
$204$	1.46565	−	0.258434i	0.102616	−	0.0180940i
$205$	−1.50456	−	4.13374i	−0.105083	−	0.288713i
$206$	7.37464	+	8.78876i	0.513816	+	0.612342i
$207$	−0.0939124	−	0.532604i	−0.00652736	−	0.0370185i
$208$	−1.24070	−	2.14895i	−0.0860269	−	0.149003i
$209$	4.03158	−	4.34509i	0.278870	−	0.300556i
$210$	0.889474	+	1.82990i	0.0613796	+	0.126275i
$211$	−2.46159	−	2.93360i	−0.169463	−	0.201958i	0.674629	−	0.738157i	$-0.264304\pi$
$211$	−2.46159	−	2.93360i	−0.169463	−	0.201958i	−0.844091	+	0.536200i	$0.819859\pi$
$212$	−11.1643	+	1.96856i	−0.766765	+	0.135201i
$213$	0.836889	−	0.997366i	0.0573427	−	0.0683384i
$214$	17.5612	+	6.39174i	1.20046	+	0.436931i
$215$	2.64270	−	3.14945i	0.180231	−	0.214790i
$216$	−0.866025	−	0.500000i	−0.0589256	−	0.0340207i
$217$	4.57909	+	0.326354i	0.310849	+	0.0221543i
$218$	−6.16427	−	5.17244i	−0.417497	−	0.350322i
$219$	−0.0323056	−	0.00569634i	−0.00218301	−	0.000384923i
$220$		−	1.04573i		−	0.0705029i
$221$	−3.19821	+	1.84648i	−0.215135	+	0.124208i
$222$	1.46625	+	1.23033i	0.0984082	+	0.0825742i
$223$	3.18122	+	18.0416i	0.213030	+	1.20815i	0.884292	+	0.466934i	$0.154641\pi$
$223$	3.18122	+	18.0416i	0.213030	+	1.20815i	−0.671262	+	0.741220i	$0.734247\pi$
$224$	1.84044	−	1.90074i	0.122969	−	0.126998i
$225$	−4.14274	−	1.50784i	−0.276183	−	0.100522i
$226$	−2.50688	−	0.912429i	−0.166755	−	0.0606939i
$227$	12.7576	−	22.0968i	0.846753	−	1.46662i	−0.0373375	−	0.999303i	$-0.511888\pi$
$227$	12.7576	−	22.0968i	0.846753	−	1.46662i	0.884090	−	0.467316i	$-0.154779\pi$
$228$	2.96477	−	3.19533i	0.196347	−	0.211616i
$229$	−3.31739	+	1.91530i	−0.219220	+	0.126566i	−0.605589	−	0.795778i	$-0.707062\pi$
$229$	−3.31739	+	1.91530i	−0.219220	+	0.126566i	0.386369	+	0.922344i	$0.373729\pi$
$230$	0.318597	−	0.267335i	0.0210077	−	0.0176275i
$231$	0.371284	+	3.57855i	0.0244287	+	0.235452i
$232$	−0.757305	+	4.29489i	−0.0497195	+	0.281973i
$233$	−5.07411	+	4.25769i	−0.332416	+	0.278930i	−0.793684	−	0.608331i	$-0.791839\pi$
$233$	−5.07411	+	4.25769i	−0.332416	+	0.278930i	0.461267	+	0.887261i	$0.347395\pi$
$234$	2.44370	+	0.430890i	0.159749	+	0.0281681i
$235$	4.22154	+	7.31192i	0.275383	+	0.476977i
$236$	−0.267758	+	0.463771i	−0.0174296	+	0.0301889i
$237$	10.3099	−	12.2868i	0.669699	−	0.798116i
$238$	−2.82880	−	2.73905i	−0.183364	−	0.177547i
$239$	−9.42895	−	16.3314i	−0.609908	−	1.05639i	−0.991255	−	0.131960i	$-0.957873\pi$
$239$	−9.42895	−	16.3314i	−0.609908	−	1.05639i	0.381347	−	0.924432i	$-0.375460\pi$
$240$		−	0.769015i		−	0.0496397i
$241$	0.838561	−	4.75571i	0.0540164	−	0.306342i	−0.945815	−	0.324706i	$-0.894735\pi$
$241$	0.838561	−	4.75571i	0.0540164	−	0.306342i	0.999831	+	0.0183637i	$0.00584568\pi$
$242$	−3.12978	+	8.59901i	−0.201190	+	0.552765i
$243$	0.939693	−	0.342020i	0.0602813	−	0.0219406i
$244$	−0.0497788	+	0.136766i	−0.00318676	+	0.00875555i
$245$	2.53992	−	4.74623i	0.162269	−	0.303225i
$246$		−	5.72035i		−	0.364716i
$247$	−4.20127	+	9.96686i	−0.267321	+	0.634176i
$248$	−1.50266	−	0.867561i	−0.0954190	−	0.0550902i
$249$	−11.3261	+	1.99709i	−0.717760	+	0.126560i
$250$	−1.25641	−	7.12545i	−0.0794623	−	0.450653i
$251$	6.67499	+	1.17698i	0.421322	+	0.0742904i	0.380290	−	0.924867i	$-0.375824\pi$
$251$	6.67499	+	1.17698i	0.421322	+	0.0742904i	0.0410320	+	0.999158i	$0.486935\pi$
$252$	0.273038	+	2.63163i	0.0171998	+	0.165777i
$253$	0.691070	−	0.251529i	0.0434472	−	0.0158135i
$254$	3.26825			0.205068
$255$	−1.14450			−0.0716712
$256$	−0.939693	+	0.342020i	−0.0587308	+	0.0213763i
$257$	−0.0197422	+	0.111964i	−0.00123149	+	0.00698411i	−0.985417	−	0.170155i	$-0.945573\pi$
$257$	−0.0197422	+	0.111964i	−0.00123149	+	0.00698411i	0.984186	+	0.177139i	$0.0566843\pi$
$258$	4.62995	−	2.67310i	0.288248	−	0.166420i
$259$	0.360008	−	5.05129i	0.0223698	−	0.313872i
$260$	0.652653	+	1.79315i	0.0404758	+	0.111206i
$261$	−2.80329	−	3.34083i	−0.173519	−	0.206792i
$262$	13.1488	+	11.0332i	0.812339	+	0.681633i
$263$	−16.5459	+	13.8836i	−1.02026	+	0.856102i	−0.989661	−	0.143429i	$-0.954187\pi$
$263$	−16.5459	+	13.8836i	−1.02026	+	0.856102i	−0.0306026	+	0.999532i	$0.509743\pi$
$264$	0.465088	−	1.27782i	0.0286242	−	0.0786443i
$265$	8.71793			0.535538
$266$	−11.4482	−	1.39212i	−0.701936	−	0.0853564i
$267$	−4.75610			−0.291069
$268$	−1.64694	+	4.52493i	−0.100603	+	0.276404i
$269$	−9.67615	+	8.11925i	−0.589965	+	0.495039i	−0.888202	−	0.459452i	$-0.848046\pi$
$269$	−9.67615	+	8.11925i	−0.589965	+	0.495039i	0.298237	+	0.954492i	$0.403601\pi$
$270$	0.589100	+	0.494314i	0.0358515	+	0.0300830i
$271$	18.7229	+	22.3131i	1.13733	+	1.35542i	0.925783	+	0.378054i	$0.123407\pi$
$271$	18.7229	+	22.3131i	1.13733	+	1.35542i	0.211550	+	0.977367i	$0.432149\pi$
$272$	0.509016	+	1.39851i	0.0308636	+	0.0847971i
$273$	−2.87008	−	5.90456i	−0.173705	−	0.357360i
$274$	2.92132	−	1.68663i	0.176484	−	0.101893i
$275$	1.04101	−	5.90387i	0.0627754	−	0.356017i
$276$	0.508204	−	0.184971i	0.0305903	−	0.0111340i
$277$	−1.11233			−0.0668334			−0.0334167	−	0.999442i	$-0.510639\pi$
$277$	−1.11233			−0.0668334			−0.0334167	+	0.999442i	$0.510639\pi$
$278$	16.8510			1.01065
$279$	1.63048	−	0.593447i	0.0976144	−	0.0355287i
$280$	−1.64764	+	1.19372i	−0.0984655	+	0.0713384i
$281$	16.2394	+	2.86345i	0.968762	+	0.170819i	0.635573	−	0.772041i	$-0.280764\pi$
$281$	16.2394	+	2.86345i	0.968762	+	0.170819i	0.333189	+	0.942860i	$0.391875\pi$
$282$	1.90650	+	10.8123i	0.113530	+	0.643862i
$283$	1.81020	−	0.319187i	0.107605	−	0.0189737i	−0.119586	−	0.992824i	$-0.538157\pi$
$283$	1.81020	−	0.319187i	0.107605	−	0.0189737i	0.227191	+	0.973850i	$0.427046\pi$
$284$	1.12754	+	0.650984i	0.0669071	+	0.0386288i
$285$	−2.67202	+	2.02401i	−0.158277	+	0.119892i
$286$			3.37427i			0.199525i
$287$	−12.2560	+	8.87953i	−0.723452	+	0.524142i
$288$	0.342020	−	0.939693i	0.0201537	−	0.0553719i
$289$	−13.8934	+	5.05679i	−0.817260	+	0.297458i
$290$	1.14706	−	3.15153i	0.0673579	−	0.185064i
$291$	2.37856	−	13.4895i	0.139434	−	0.790767i
$292$		−	0.0328039i		−	0.00191971i
$293$	2.67129	+	4.62682i	0.156059	+	0.270302i	0.933444	−	0.358723i	$-0.116788\pi$
$293$	2.67129	+	4.62682i	0.156059	+	0.270302i	−0.777385	+	0.629025i	$0.783454\pi$
$294$	5.21452	−	4.66999i	0.304117	−	0.272359i
$295$	0.264713	−	0.315473i	0.0154122	−	0.0183675i
$296$	−0.957026	+	1.65762i	−0.0556260	+	0.0963470i
$297$	0.679913	+	1.17764i	0.0394526	+	0.0683338i
$298$	10.0414	+	1.77057i	0.581683	+	0.102566i
$299$	−1.02802	+	0.862613i	−0.0594521	+	0.0498862i
$300$	0.765548	−	4.34164i	0.0441989	−	0.250665i
$301$	−12.9141	−	5.77045i	−0.744359	−	0.332603i
$302$	7.36895	−	6.18329i	0.424036	−	0.355808i
$303$	−4.25732	+	2.45797i	−0.244577	+	0.141207i
$304$	3.66161	+	2.36487i	0.210008	+	0.135635i
$305$	0.0559625	−	0.0969300i	0.00320441	−	0.00555019i
$306$	−1.39851	−	0.509016i	−0.0799475	−	0.0290985i
$307$	5.71493	+	2.08007i	0.326169	+	0.118716i	0.499914	−	0.866075i	$-0.333365\pi$
$307$	5.71493	+	2.08007i	0.326169	+	0.118716i	−0.173746	+	0.984791i	$0.555587\pi$
$308$	−3.45971	+	0.987053i	−0.197135	+	0.0562426i
$309$	−1.99225	−	11.2986i	−0.113335	−	0.642755i
$310$	1.02216	+	0.857694i	0.0580548	+	0.0487138i
$311$	−18.4835	+	10.6714i	−1.04810	+	0.605121i	−0.922117	−	0.386911i	$-0.873542\pi$
$311$	−18.4835	+	10.6714i	−1.04810	+	0.605121i	−0.125984	+	0.992032i	$0.540209\pi$
$312$			2.48139i			0.140481i
$313$	2.40383	+	0.423860i	0.135872	+	0.0239580i	0.241171	−	0.970483i	$-0.422469\pi$
$313$	2.40383	+	0.423860i	0.135872	+	0.0239580i	−0.105298	+	0.994441i	$0.533580\pi$
$314$	−10.1873	−	8.54818i	−0.574904	−	0.482402i
$315$	0.144642	−	2.02948i	0.00814963	−	0.114348i
$316$	13.8905	+	8.01967i	0.781400	+	0.451141i
$317$	−1.86023	+	2.21694i	−0.104481	+	0.124516i	−0.815751	−	0.578403i	$-0.803676\pi$
$317$	−1.86023	+	2.21694i	−0.104481	+	0.124516i	0.711270	+	0.702919i	$0.248120\pi$
$318$	10.6528	+	3.87731i	0.597380	+	0.217429i
$319$	3.81199	−	4.54295i	0.213430	−	0.254356i
$320$	0.757332	−	0.133538i	0.0423362	−	0.00746501i
$321$	−12.0125	−	14.3160i	−0.670475	−	0.799041i
$322$	−1.18518	−	0.801720i	−0.0660474	−	0.0446781i
$323$	3.51955	−	5.44944i	0.195833	−	0.303215i
$324$	0.500000	+	0.866025i	0.0277778	+	0.0481125i
$325$	1.89963	+	10.7733i	0.105372	+	0.597596i
$326$	−9.13524	−	10.8869i	−0.505954	−	0.602972i
$327$	2.75220	+	7.56160i	0.152197	+	0.418157i
$328$	5.63344	−	0.993328i	0.311055	−	0.0548474i
$329$	20.2063	−	20.8683i	1.11401	−	1.15051i
$330$	−0.522864	+	0.905626i	−0.0287827	+	0.0498531i
$331$	−9.80760	−	5.66242i	−0.539074	−	0.311235i	0.205629	−	0.978630i	$-0.434076\pi$
$331$	−9.80760	−	5.66242i	−0.539074	−	0.311235i	−0.744704	+	0.667395i	$0.767409\pi$
$332$	−3.93350	−	10.8072i	−0.215879	−	0.593122i
$333$	−0.654644	−	1.79862i	−0.0358743	−	0.0985638i
$334$	11.7021	+	6.75624i	0.640313	+	0.369685i
$335$	1.85153	−	3.20695i	0.101160	−	0.175214i
$336$	−2.54423	+	0.725867i	−0.138799	+	0.0395993i
$337$	9.26562	−	1.63378i	0.504730	−	0.0889976i	0.0845154	−	0.996422i	$-0.473066\pi$
$337$	9.26562	−	1.63378i	0.504730	−	0.0889976i	0.420215	+	0.907425i	$0.361955\pi$
$338$	2.34033	+	6.43002i	0.127297	+	0.349747i
$339$	1.71481	+	2.04363i	0.0931355	+	0.110995i
$340$	−0.198740	−	1.12711i	−0.0107782	−	0.0611261i
$341$	1.17973	+	2.04336i	0.0638861	+	0.110654i
$342$	−4.16523	+	1.28485i	−0.225230	+	0.0694766i
$343$	−18.1000	−	3.92321i	−0.977306	−	0.211833i
$344$	3.43647	+	4.09543i	0.185282	+	0.220811i
$345$	−0.409580	+	0.0722201i	−0.0220511	+	0.00388820i
$346$	−2.41113	+	2.87347i	−0.129623	+	0.154479i
$347$	9.84909	+	3.58478i	0.528727	+	0.192441i	0.592570	−	0.805519i	$-0.298113\pi$
$347$	9.84909	+	3.58478i	0.528727	+	0.192441i	−0.0638429	+	0.997960i	$0.520336\pi$
$348$	2.80329	−	3.34083i	0.150272	−	0.179087i
$349$	−12.5648	−	7.25431i	−0.672580	−	0.388314i	0.124473	−	0.992223i	$-0.460276\pi$
$349$	−12.5648	−	7.25431i	−0.672580	−	0.388314i	−0.797054	+	0.603909i	$0.793609\pi$
$350$	−10.4905	+	5.09918i	−0.560738	+	0.272563i
$351$	−1.90086	−	1.59501i	−0.101460	−	0.0851353i
$352$	1.33917	+	0.236131i	0.0713779	+	0.0125858i
$353$		−	11.7898i		−	0.627506i	−0.949505	−	0.313753i	$-0.898414\pi$
$353$		−	11.7898i		−	0.627506i	0.949505	−	0.313753i	$-0.101586\pi$
$354$	0.463771	−	0.267758i	0.0246491	−	0.0142312i
$355$	−0.766990	−	0.643581i	−0.0407076	−	0.0341577i
$356$	−0.825889	−	4.68385i	−0.0437720	−	0.248243i
$357$	1.08028	+	3.78649i	0.0571746	+	0.200402i
$358$	18.2892	+	6.65671i	0.966613	+	0.351818i
$359$	−12.2764	−	4.46825i	−0.647925	−	0.235825i	−0.00291043	−	0.999996i	$-0.500926\pi$
$359$	−12.2764	−	4.46825i	−0.647925	−	0.235825i	−0.645014	+	0.764170i	$0.723149\pi$
$360$	−0.384508	+	0.665987i	−0.0202653	+	0.0351006i
$361$	−1.42023	−	18.9468i	−0.0747489	−	0.997202i
$362$	−1.68792	+	0.974523i	−0.0887153	+	0.0512198i
$363$	7.00997	−	5.88207i	0.367928	−	0.308728i
$364$	5.31647	−	3.85180i	0.278659	−	0.201889i
$365$	−0.00438058	+	0.0248435i	−0.000229290	+	0.00130037i
$366$	0.111493	−	0.0935535i	0.00582782	−	0.00489012i
$367$	−18.9329	−	3.33838i	−0.988290	−	0.174262i	−0.343939	−	0.938992i	$-0.611761\pi$
$367$	−18.9329	−	3.33838i	−0.988290	−	0.174262i	−0.644351	+	0.764730i	$0.722872\pi$
$368$	0.270410	+	0.468364i	0.0140961	+	0.0244151i
$369$	−2.86017	+	4.95397i	−0.148895	+	0.257893i
$370$	0.946141	−	1.12757i	0.0491876	−	0.0586194i
$371$	−8.22878	−	28.8427i	−0.427217	−	1.49744i
$372$	0.867561	+	1.50266i	0.0449809	+	0.0779093i
$373$		−	26.8201i		−	1.38869i	−0.719642	−	0.694345i	$-0.755694\pi$
$373$		−	26.8201i		−	1.38869i	0.719642	−	0.694345i	$-0.244306\pi$
$374$	0.351426	−	1.99303i	0.0181718	−	0.103057i
$375$	−2.47464	+	6.79902i	−0.127790	+	0.351100i
$376$	−10.3170	+	3.75507i	−0.532056	+	0.193653i
$377$	−3.70125	+	10.1691i	−0.190624	+	0.523735i
$378$	1.07935	−	2.41557i	0.0555160	−	0.124244i
$379$			25.4003i			1.30473i	0.757906	+	0.652364i	$0.226223\pi$
$379$			25.4003i			1.30473i	−0.757906	+	0.652364i	$0.773777\pi$
$380$	−2.45726	−	2.27996i	−0.126055	−	0.116959i
$381$	−2.83039	−	1.63412i	−0.145005	−	0.0837187i
$382$	−2.77635	+	0.489545i	−0.142050	+	0.0250473i
$383$	−3.99130	−	22.6358i	−0.203946	−	1.15663i	−0.899090	−	0.437764i	$-0.855771\pi$
$383$	−3.99130	−	22.6358i	−0.203946	−	1.15663i	0.695144	−	0.718870i	$-0.255340\pi$
$384$	0.984808	+	0.173648i	0.0502558	+	0.00886145i
$385$	2.75196	−	0.285523i	0.140253	−	0.0145516i
$386$	−10.6932	+	3.89199i	−0.544268	+	0.198097i
$387$	−5.34620			−0.271763
$388$	13.6976			0.695389
$389$	2.12414	−	0.773124i	0.107698	−	0.0391990i	−0.287609	−	0.957748i	$-0.592860\pi$
$389$	2.12414	−	0.773124i	0.107698	−	0.0391990i	0.395307	+	0.918549i	$0.370638\pi$
$390$	0.331361	−	1.87924i	0.0167791	−	0.0951590i
$391$	0.697049	−	0.402441i	0.0352513	−	0.0203523i
$392$	5.50453	+	4.32436i	0.278021	+	0.218413i
$393$	−5.87064	−	16.1294i	−0.296135	−	0.813623i
$394$	−4.28464	−	5.10623i	−0.215857	−	0.257248i
$395$	−9.44877	−	7.92846i	−0.475419	−	0.398924i
$396$	−1.04169	+	0.874080i	−0.0523468	+	0.0439241i
$397$	3.68053	−	10.1122i	0.184721	−	0.507516i	−0.812421	−	0.583071i	$-0.801851\pi$
$397$	3.68053	−	10.1122i	0.184721	−	0.507516i	0.997142	+	0.0755555i	$0.0240730\pi$
$398$	−14.7400			−0.738848
$399$	9.21840	+	6.92973i	0.461497	+	0.346920i
$400$	4.40862			0.220431
$401$	−8.84224	+	24.2939i	−0.441561	+	1.21318i	0.496905	+	0.867805i	$0.334470\pi$
$401$	−8.84224	+	24.2939i	−0.441561	+	1.21318i	−0.938466	+	0.345373i	$0.887752\pi$
$402$	3.68876	−	3.09523i	0.183978	−	0.154376i
$403$	−3.29822	−	2.76754i	−0.164296	−	0.137861i
$404$	−3.15990	−	3.76582i	−0.157211	−	0.187357i
$405$	−0.263019	−	0.722638i	−0.0130695	−	0.0359082i
$406$	−11.5093	−	0.820274i	−0.571198	−	0.0407095i
$407$	2.25407	−	1.30139i	0.111730	−	0.0645074i
$408$	0.258434	−	1.46565i	0.0127944	−	0.0725607i
$409$	1.67489	−	0.609610i	0.0828180	−	0.0301433i	−0.300279	−	0.953851i	$-0.597080\pi$
$409$	1.67489	−	0.609610i	0.0828180	−	0.0301433i	0.383097	+	0.923708i	$0.374858\pi$
$410$	−4.39904			−0.217253
$411$	−3.37325			−0.166390
$412$	10.7810	−	3.92397i	0.531142	−	0.193320i
$413$	−1.29358	−	0.578012i	−0.0636529	−	0.0284421i
$414$	−0.532604	−	0.0939124i	−0.0261760	−	0.00461554i
$415$	1.53579	+	8.70991i	0.0753891	+	0.427553i
$416$	−2.44370	+	0.430890i	−0.119812	+	0.0211261i
$417$	−14.5934	−	8.42548i	−0.714640	−	0.412598i
$418$	−2.70417	−	5.27455i	−0.132265	−	0.257987i
$419$		−	12.0202i		−	0.587225i	−0.955924	−	0.293613i	$-0.905142\pi$
$419$		−	12.0202i		−	0.587225i	0.955924	−	0.293613i	$-0.0948576\pi$
$420$	2.02376	−	0.209971i	0.0987494	−	0.0102455i
$421$	−5.36679	+	14.7451i	−0.261562	+	0.718634i	0.737501	+	0.675346i	$0.236006\pi$
$421$	−5.36679	+	14.7451i	−0.261562	+	0.718634i	−0.999063	+	0.0432885i	$0.986217\pi$
$422$	−3.59860	+	1.30978i	−0.175177	+	0.0637592i
$423$	3.75507	−	10.3170i	0.182578	−	0.501628i
$424$	−1.96856	+	11.1643i	−0.0956018	+	0.542184i
$425$		−	6.56118i		−	0.318264i
$426$	−0.650984	−	1.12754i	−0.0315403	−	0.0546294i
$427$	−0.373508	−	0.0936567i	−0.0180753	−	0.00453236i
$428$	12.0125	−	14.3160i	0.580648	−	0.691990i
$429$	1.68713	−	2.92220i	0.0814555	−	0.141085i
$430$	−2.05565	−	3.56050i	−0.0991325	−	0.171702i
$431$	−3.41719	−	0.602542i	−0.164600	−	0.0290234i	0.0907407	−	0.995875i	$-0.471077\pi$
$431$	−3.41719	−	0.602542i	−0.164600	−	0.0290234i	−0.255341	+	0.966851i	$0.582188\pi$
$432$	−0.766044	+	0.642788i	−0.0368563	+	0.0309261i
$433$	−4.30345	+	24.4061i	−0.206810	+	1.17288i	0.687755	+	0.725943i	$0.258596\pi$
$433$	−4.30345	+	24.4061i	−0.206810	+	1.17288i	−0.894565	+	0.446937i	$0.852515\pi$
$434$	1.87281	−	4.19131i	0.0898978	−	0.201190i
$435$	−2.56915	+	2.15577i	−0.123181	+	0.103361i
$436$	−6.96880	+	4.02344i	−0.333745	+	0.192688i
$437$	0.915668	−	2.17228i	0.0438023	−	0.103914i
$438$	−0.0164020	+	0.0284090i	−0.000783716	+	0.00135744i
$439$	10.3921	+	3.78240i	0.495986	+	0.180524i	0.577888	−	0.816116i	$-0.303877\pi$
$439$	10.3921	+	3.78240i	0.495986	+	0.180524i	−0.0819016	+	0.996640i	$0.526099\pi$
$440$	−0.982662	−	0.357660i	−0.0468466	−	0.0170508i
$441$	−6.85090	+	1.43707i	−0.326233	+	0.0684318i
$442$	0.641277	+	3.63686i	0.0305025	+	0.172988i
$443$	25.4861	+	21.3854i	1.21088	+	1.01605i	0.999251	+	0.0387011i	$0.0123220\pi$
$443$	25.4861	+	21.3854i	1.21088	+	1.01605i	0.211631	+	0.977350i	$0.432122\pi$
$444$	1.65762	−	0.957026i	0.0786670	−	0.0454184i
$445$			3.65752i			0.173383i
$446$	18.0416	+	3.18122i	0.854294	+	0.150635i
$447$	−7.81083	−	6.55406i	−0.369440	−	0.309997i
$448$	−1.15664	−	2.37953i	−0.0546461	−	0.112422i
$449$	−9.17258	−	5.29579i	−0.432881	−	0.249924i	0.267692	−	0.963504i	$-0.413739\pi$
$449$	−9.17258	−	5.29579i	−0.432881	−	0.249924i	−0.700573	+	0.713581i	$0.747072\pi$
$450$	−2.83380	+	3.37720i	−0.133587	+	0.159203i
$451$	−7.30957	−	2.66047i	−0.344194	−	0.125276i
$452$	−1.71481	+	2.04363i	−0.0806577	+	0.0961241i
$453$	−9.47334	+	1.67041i	−0.445096	+	0.0784825i
$454$	−16.4009	−	19.5458i	−0.769731	−	0.917330i
$455$	−4.54070	+	2.20714i	−0.212871	+	0.103472i
$456$	−1.98861	−	3.87884i	−0.0931253	−	0.181643i
$457$	4.84312	+	8.38853i	0.226551	+	0.392399i	0.956784	−	0.290800i	$-0.0939215\pi$
$457$	4.84312	+	8.38853i	0.226551	+	0.392399i	−0.730232	+	0.683199i	$0.760588\pi$
$458$	0.665176	+	3.77240i	0.0310816	+	0.176273i
$459$	0.956637	+	1.14008i	0.0446520	+	0.0532142i
$460$	−0.142246	−	0.390817i	−0.00663224	−	0.0182219i
$461$	7.70609	−	1.35879i	0.358908	−	0.0632852i	0.00871326	−	0.999962i	$-0.497226\pi$
$461$	7.70609	−	1.35879i	0.358908	−	0.0632852i	0.350195	+	0.936677i	$0.386115\pi$
$462$	3.48973	+	0.875044i	0.162357	+	0.0407107i
$463$	10.4459	−	18.0928i	0.485462	−	0.840845i	−0.514398	−	0.857551i	$-0.671985\pi$
$463$	10.4459	−	18.0928i	0.485462	−	0.840845i	0.999860	+	0.0167062i	$0.00531801\pi$
$464$	3.77686	+	2.18057i	0.175337	+	0.101231i
$465$	−0.456370	−	1.25387i	−0.0211636	−	0.0581466i
$466$	2.26547	+	6.22432i	0.104946	+	0.288336i
$467$	1.76643	+	1.01985i	0.0817408	+	0.0471931i	0.540313	−	0.841464i	$-0.318306\pi$
$467$	1.76643	+	1.01985i	0.0817408	+	0.0471931i	−0.458573	+	0.888657i	$0.651639\pi$
$468$	1.24070	−	2.14895i	0.0573513	−	0.0993353i
$469$	−12.3576	−	3.09865i	−0.570621	−	0.143082i
$470$	8.31481	−	1.46613i	0.383534	−	0.0676273i
$471$	4.54839	+	12.4966i	0.209579	+	0.575813i
$472$	0.344223	+	0.410229i	0.0158442	+	0.0188823i
$473$	−1.26241	−	7.15946i	−0.0580455	−	0.329192i
$474$	−8.01967	−	13.8905i	−0.368355	−	0.638010i
$475$	−11.6033	−	15.3182i	−0.532395	−	0.702845i
$476$	−3.54137	+	1.72139i	−0.162319	+	0.0788996i
$477$	−7.28695	−	8.68425i	−0.333647	−	0.397625i
$478$	−18.5714	+	3.27464i	−0.849436	+	0.149779i
$479$	10.1317	−	12.0744i	0.462927	−	0.551695i	−0.483192	−	0.875515i	$-0.660523\pi$
$479$	10.1317	−	12.0744i	0.462927	−	0.551695i	0.946119	+	0.323820i	$0.104967\pi$
$480$	−0.722638	−	0.263019i	−0.0329838	−	0.0120051i
$481$	−3.05293	+	3.63834i	−0.139202	+	0.165894i
$482$	−4.18210	−	2.41454i	−0.190490	−	0.109979i
$483$	0.625534	+	1.28690i	0.0284628	+	0.0585559i
$484$	7.00997	+	5.88207i	0.318635	+	0.267367i
$485$	−10.3736	−	1.82915i	−0.471041	−	0.0830573i
$486$		−	1.00000i		−	0.0453609i
$487$	34.7304	−	20.0516i	1.57379	−	0.908626i	0.578088	−	0.815974i	$-0.303799\pi$
$487$	34.7304	−	20.0516i	1.57379	−	0.908626i	0.995699	−	0.0926519i	$-0.0295344\pi$
$488$	0.111493	+	0.0935535i	0.00504704	+	0.00423497i
$489$	2.46787	+	13.9960i	0.111601	+	0.632921i
$490$	−3.59129	−	4.01005i	−0.162238	−	0.181155i
$491$	−0.505809	−	0.184099i	−0.0228268	−	0.00830829i	0.330581	−	0.943777i	$-0.392755\pi$
$491$	−0.505809	−	0.184099i	−0.0228268	−	0.00830829i	−0.353408	+	0.935469i	$0.614977\pi$
$492$	−5.37537	−	1.95647i	−0.242340	−	0.0882047i
$493$	3.24527	−	5.62097i	0.146160	−	0.253156i
$494$	7.92887	+	7.35677i	0.356737	+	0.330997i
$495$	0.905626	−	0.522864i	0.0407049	−	0.0235010i
$496$	−1.32918	+	1.11531i	−0.0596820	+	0.0500791i
$497$	−1.40529	+	3.14500i	−0.0630357	+	0.141073i
$498$	−1.99709	+	11.3261i	−0.0894917	+	0.507533i
$499$	18.8278	−	15.7984i	0.842847	−	0.707233i	−0.115355	−	0.993324i	$-0.536801\pi$
$499$	18.8278	−	15.7984i	0.842847	−	0.707233i	0.958202	+	0.286091i	$0.0923561\pi$
$500$	−7.12545	−	1.25641i	−0.318660	−	0.0561883i
$501$	−6.75624	−	11.7021i	−0.301847	−	0.522814i
$502$	3.38898	−	5.86989i	0.151258	−	0.261986i
$503$	25.3437	−	30.2034i	1.13002	−	1.34670i	0.199739	−	0.979849i	$-0.435991\pi$
$503$	25.3437	−	30.2034i	1.13002	−	1.34670i	0.930279	−	0.366853i	$-0.119565\pi$
$504$	2.56630	+	0.643497i	0.114312	+	0.0286636i
$505$	1.89021	+	3.27395i	0.0841134	+	0.145689i
$506$		−	0.735421i		−	0.0326935i
$507$	1.18822	−	6.73873i	0.0527707	−	0.299277i
$508$	1.11781	−	3.07115i	0.0495946	−	0.136260i
$509$	−29.5506	+	10.7555i	−1.30981	+	0.476731i	−0.900179	−	0.435521i	$-0.856564\pi$
$509$	−29.5506	+	10.7555i	−1.30981	+	0.476731i	−0.409629	+	0.912252i	$0.634342\pi$
$510$	−0.391441	+	1.07548i	−0.0173333	+	0.0476229i
$511$	0.0863277	−	0.00895673i	0.00381891	−	0.000396222i
$512$			1.00000i			0.0441942i
$513$	4.24962	+	0.969906i	0.187625	+	0.0428224i
$514$	0.0984593	+	0.0568455i	0.00434285	+	0.00250735i
$515$	−8.68880	+	1.53207i	−0.382874	+	0.0675111i
$516$	−0.928358	−	5.26498i	−0.0408687	−	0.231778i
$517$	14.7028	+	2.59250i	0.646629	+	0.114018i
$518$	−4.62353	−	2.06594i	−0.203146	−	0.0907722i
$519$	3.52483	−	1.28293i	0.154723	−	0.0563145i
$520$	1.90823			0.0836814
$521$	−24.0972			−1.05572			−0.527859	−	0.849332i	$-0.677005\pi$
$521$	−24.0972			−1.05572			−0.527859	+	0.849332i	$0.677005\pi$
$522$	−4.09814	+	1.49160i	−0.179371	+	0.0652856i
$523$	−6.24863	+	35.4378i	−0.273234	+	1.54959i	0.471283	+	0.881982i	$0.343791\pi$
$523$	−6.24863	+	35.4378i	−0.273234	+	1.54959i	−0.744517	+	0.667603i	$0.767320\pi$
$524$	14.8650	−	8.58230i	0.649380	−	0.374920i
$525$	11.6346	+	0.829202i	0.507775	+	0.0361894i
$526$	7.38733	+	20.2965i	0.322103	+	0.884971i
$527$	1.65988	+	1.97817i	0.0723056	+	0.0861705i
$528$	−1.04169	−	0.874080i	−0.0453336	−	0.0380394i
$529$	−17.3950	+	14.5961i	−0.756303	+	0.634613i
$530$	2.98171	−	8.19218i	0.129517	−	0.355845i
$531$	−0.535516			−0.0232394
$532$	−5.22369	+	10.2817i	−0.226476	+	0.445768i
$533$	14.1944			0.614830
$534$	−1.62668	+	4.46928i	−0.0703935	+	0.193405i
$535$	−11.0092	+	9.23783i	−0.475970	+	0.399386i
$536$	3.68876	+	3.09523i	0.159330	+	0.133694i
$537$	−12.5105	−	14.9095i	−0.539869	−	0.643391i
$538$	4.32016	+	11.8695i	0.186255	+	0.511733i
$539$	−3.54219	−	8.83517i	−0.152573	−	0.380558i
$540$	0.665987	−	0.384508i	0.0286595	−	0.0165466i
$541$	6.02624	−	34.1765i	0.259088	−	1.46936i	−0.526269	−	0.850318i	$-0.676409\pi$
$541$	6.02624	−	34.1765i	0.259088	−	1.46936i	0.785357	−	0.619043i	$-0.212480\pi$
$542$	27.3710	−	9.96223i	1.17569	−	0.427915i
$543$	1.94905			0.0836416
$544$	1.48826			0.0638088
$545$	5.81498	−	2.11648i	0.249087	−	0.0906601i
$546$	−6.53010	+	0.677515i	−0.279462	+	0.0289950i
$547$	40.4676	+	7.13553i	1.73027	+	0.305093i	0.948100	−	0.317971i	$-0.103002\pi$
$547$	40.4676	+	7.13553i	1.73027	+	0.305093i	0.782170	+	0.623065i	$0.214113\pi$
$548$	−0.585759	−	3.32201i	−0.0250224	−	0.141909i
$549$	−0.143332	+	0.0252733i	−0.00611727	+	0.00107864i
$550$	−5.19178	−	2.99748i	−0.221378	−	0.127813i
$551$	−2.36393	−	18.8622i	−0.100707	−	0.803559i
$552$		−	0.540820i		−	0.0230188i
$553$	−17.3121	+	38.7442i	−0.736186	+	1.64757i
$554$	−0.380439	+	1.04525i	−0.0161633	+	0.0444083i
$555$	−1.38317	+	0.503431i	−0.0587121	+	0.0213695i
$556$	5.76337	−	15.8347i	0.244421	−	0.671542i
$557$	3.64995	−	20.6999i	0.154653	−	0.877083i	−0.804449	−	0.594022i	$-0.797539\pi$
$557$	3.64995	−	20.6999i	0.154653	−	0.877083i	0.959102	−	0.283061i	$-0.0913498\pi$
$558$		−	1.73512i		−	0.0734536i
$559$	6.63302	+	11.4887i	0.280547	+	0.485921i
$560$	0.558203	+	1.95655i	0.0235884	+	0.0826795i
$561$	−1.30086	+	1.55031i	−0.0549224	+	0.0654539i
$562$	8.24496	−	14.2807i	0.347793	−	0.602395i
$563$	3.93279	+	6.81179i	0.165747	+	0.287083i	0.936920	−	0.349543i	$-0.113663\pi$
$563$	3.93279	+	6.81179i	0.165747	+	0.287083i	−0.771173	+	0.636626i	$0.780330\pi$
$564$	10.8123	+	1.90650i	0.455279	+	0.0802780i
$565$	1.57158	−	1.31871i	0.0661169	−	0.0554786i
$566$	0.319187	−	1.81020i	0.0134164	−	0.0760884i
$567$	−2.14254	+	1.55227i	−0.0899780	+	0.0651892i
$568$	0.997366	−	0.836889i	0.0418485	−	0.0351151i
$569$	32.4145	−	18.7145i	1.35889	−	0.784554i	0.369414	−	0.929265i	$-0.379558\pi$
$569$	32.4145	−	18.7145i	1.35889	−	0.784554i	0.989474	+	0.144711i	$0.0462252\pi$
$570$	0.988067	+	3.20313i	0.0413856	+	0.134164i
$571$	13.6734	−	23.6830i	0.572214	−	0.991103i	−0.424124	−	0.905604i	$-0.639418\pi$
$571$	13.6734	−	23.6830i	0.572214	−	0.991103i	0.996338	−	0.0854994i	$-0.0272486\pi$
$572$	3.17077	+	1.15407i	0.132577	+	0.0482540i
$573$	2.64916	+	0.964215i	0.110670	+	0.0402807i
$574$	4.15221	+	14.5539i	0.173310	+	0.607468i
$575$	−0.414024	−	2.34804i	−0.0172660	−	0.0979202i
$576$	−0.766044	−	0.642788i	−0.0319185	−	0.0267828i
$577$	−2.28917	+	1.32165i	−0.0952993	+	0.0550211i	−0.546892	−	0.837203i	$-0.684189\pi$
$577$	−2.28917	+	1.32165i	−0.0952993	+	0.0550211i	0.451593	+	0.892224i	$0.350856\pi$
$578$			14.7851i			0.614978i
$579$	11.2065	+	1.97602i	0.465728	+	0.0821204i
$580$	−2.56915	−	2.15577i	−0.106678	−	0.0895136i
$581$	27.3665	−	13.3023i	1.13535	−	0.551871i
$582$	−11.8624	−	6.84878i	−0.491714	−	0.283891i
$583$	9.90899	−	11.8091i	0.410389	−	0.489082i
$584$	−0.0308256	−	0.0112196i	−0.00127557	−	0.000464271i
$585$	−1.22659	+	1.46179i	−0.0507131	+	0.0604376i
$586$	5.26142	−	0.927731i	0.217347	−	0.0383242i
$587$	19.0500	+	22.7029i	0.786277	+	0.937048i	0.999199	−	0.0400213i	$-0.0127426\pi$
$587$	19.0500	+	22.7029i	0.786277	+	0.937048i	−0.212922	+	0.977069i	$0.568298\pi$
$588$	−2.60488	−	6.49728i	−0.107424	−	0.267943i
$589$	7.37361	+	1.68291i	0.303824	+	0.0693429i
$590$	−0.205910	−	0.356647i	−0.00847719	−	0.0146829i
$591$	1.15749	+	6.56445i	0.0476128	+	0.270025i
$592$	1.23033	+	1.46625i	0.0505662	+	0.0602624i
$593$	5.71985	+	15.7152i	0.234886	+	0.645344i	0.999999	+	0.00144806i	$0.000460932\pi$
$593$	5.71985	+	15.7152i	0.234886	+	0.645344i	−0.765113	+	0.643896i	$0.777317\pi$
$594$	1.33917	−	0.236131i	0.0549467	−	0.00968859i
$595$	2.91187	−	0.830753i	0.119375	−	0.0340576i
$596$	5.09816	−	8.83027i	0.208829	−	0.361702i
$597$	12.7652	+	7.36998i	0.522444	+	0.301633i
$598$	0.458987	+	1.26106i	0.0187694	+	0.0515684i
$599$	4.03366	+	11.0824i	0.164811	+	0.452814i	0.994415	−	0.105538i	$-0.0336564\pi$
$599$	4.03366	+	11.0824i	0.164811	+	0.452814i	−0.829605	+	0.558351i	$0.811434\pi$
$600$	−3.81797	−	2.20431i	−0.155868	−	0.0899905i
$601$	7.65140	−	13.2526i	0.312107	−	0.540585i	−0.666711	−	0.745316i	$-0.732299\pi$
$601$	7.65140	−	13.2526i	0.312107	−	0.540585i	0.978818	+	0.204731i	$0.0656319\pi$
$602$	−9.83934	+	10.1617i	−0.401022	+	0.414160i
$603$	−4.74217	+	0.836173i	−0.193116	+	0.0340516i
$604$	−3.29006	−	9.03936i	−0.133871	−	0.367806i
$605$	−4.52340	−	5.39078i	−0.183902	−	0.219166i
$606$	0.853643	+	4.84125i	0.0346769	+	0.196662i
$607$	18.8357	+	32.6244i	0.764519	+	1.32419i	0.940501	+	0.339792i	$0.110357\pi$
$607$	18.8357	+	32.6244i	0.764519	+	1.32419i	−0.175982	+	0.984393i	$0.556310\pi$
$608$	3.47460	−	2.63196i	0.140913	−	0.106740i
$609$	9.55722	+	6.46504i	0.387278	+	0.261976i
$610$	−0.0719440	−	0.0857396i	−0.00291293	−	0.00347149i
$611$	−26.8295	+	4.73077i	−1.08541	+	0.191387i
$612$	−0.956637	+	1.14008i	−0.0386698	+	0.0460848i
$613$	19.5692	+	7.12262i	0.790394	+	0.287680i	0.705500	−	0.708710i	$-0.250722\pi$
$613$	19.5692	+	7.12262i	0.790394	+	0.287680i	0.0848944	+	0.996390i	$0.472945\pi$
$614$	3.90925	−	4.65886i	0.157764	−	0.188016i
$615$	3.80968	+	2.19952i	0.153621	+	0.0886931i
$616$	−0.255765	+	3.58866i	−0.0103051	+	0.144591i
$617$	25.0068	+	20.9832i	1.00673	+	0.844750i	0.987903	−	0.155073i	$-0.0495611\pi$
$617$	25.0068	+	20.9832i	1.00673	+	0.844750i	0.0188310	+	0.999823i	$0.494006\pi$
$618$	−11.2986	−	1.99225i	−0.454497	−	0.0801400i
$619$			0.762693i			0.0306552i	0.999883	+	0.0153276i	$0.00487912\pi$
$619$			0.762693i			0.0306552i	−0.999883	+	0.0153276i	$0.995121\pi$
$620$	1.15557	−	0.667168i	0.0464087	−	0.0267941i
$621$	0.414292	+	0.347632i	0.0166250	+	0.0139500i
$622$	3.70615	+	21.0186i	0.148603	+	0.842769i
$623$	12.1006	−	3.45230i	0.484802	−	0.138313i
$624$	2.33175	+	0.848687i	0.0933446	+	0.0339747i
$625$	−15.4852	−	5.63614i	−0.619407	−	0.225446i
$626$	1.22046	−	2.11389i	0.0487792	−	0.0844881i
$627$	−0.295398	+	5.91998i	−0.0117971	+	0.236421i
$628$	−11.5169	+	6.64930i	−0.459575	+	0.265336i
$629$	2.18216	−	1.83105i	0.0870086	−	0.0730089i
$630$	−1.85761	−	0.830040i	−0.0740091	−	0.0330696i
$631$	−5.69327	+	32.2881i	−0.226646	+	1.28537i	0.632869	+	0.774259i	$0.281877\pi$
$631$	−5.69327	+	32.2881i	−0.226646	+	1.28537i	−0.859514	+	0.511112i	$0.829234\pi$
$632$	12.2868	−	10.3099i	0.488744	−	0.410105i
$633$	3.77137	+	0.664994i	0.149898	+	0.0264311i
$634$	1.44700	+	2.50628i	0.0574678	+	0.0995372i
$635$	−1.25667	+	2.17661i	−0.0498693	+	0.0863761i
$636$	7.28695	−	8.68425i	0.288947	−	0.344353i
$637$	11.5881	+	12.9393i	0.459137	+	0.512673i
$638$	−2.96520	−	5.13588i	−0.117393	−	0.203331i
$639$			1.30197i			0.0515051i
$640$	0.133538	−	0.757332i	0.00527856	−	0.0299362i
$641$	−1.95796	+	5.37945i	−0.0773348	+	0.212476i	−0.972335	−	0.233590i	$-0.924953\pi$
$641$	−1.95796	+	5.37945i	−0.0773348	+	0.212476i	0.895001	+	0.446065i	$0.147175\pi$
$642$	−17.5612	+	6.39174i	−0.693084	+	0.252262i
$643$	−15.8210	+	43.4677i	−0.623918	+	1.71420i	0.0732712	+	0.997312i	$0.476656\pi$
$643$	−15.8210	+	43.4677i	−0.623918	+	1.71420i	−0.697189	+	0.716888i	$0.745566\pi$
$644$	−1.15873	+	0.839499i	−0.0456602	+	0.0330809i
$645$			4.11131i			0.161883i
$646$	−3.91704	−	5.17111i	−0.154114	−	0.203455i
$647$	−37.1939	−	21.4739i	−1.46224	−	0.844227i	−0.463130	−	0.886291i	$-0.653274\pi$
$647$	−37.1939	−	21.4739i	−1.46224	−	0.844227i	−0.999115	+	0.0420632i	$0.986607\pi$
$648$	0.984808	−	0.173648i	0.0386869	−	0.00682154i
$649$	−0.126452	−	0.717146i	−0.00496368	−	0.0281504i
$650$	10.7733	+	1.89963i	0.422564	+	0.0745095i
$651$	−3.71756	+	2.69338i	−0.145703	+	0.105562i
$652$	−13.3548	+	4.86076i	−0.523015	+	0.190362i
$653$	−6.19522			−0.242438			−0.121219	−	0.992626i	$-0.538680\pi$
$653$	−6.19522			−0.242438			−0.121219	+	0.992626i	$0.538680\pi$
$654$	8.04688			0.314658
$655$	−12.4038	+	4.51461i	−0.484656	+	0.176400i
$656$	0.993328	−	5.63344i	0.0387829	−	0.219949i
$657$	0.0284090	−	0.0164020i	0.00110834	−	0.000639902i
$658$	−12.6988	−	26.1251i	−0.495053	−	1.01846i
$659$	−7.90639	−	21.7226i	−0.307989	−	0.846194i	−0.993048	−	0.117706i	$-0.962446\pi$
$659$	−7.90639	−	21.7226i	−0.307989	−	0.846194i	0.685059	−	0.728487i	$-0.259776\pi$
$660$	0.672181	+	0.801074i	0.0261646	+	0.0311817i
$661$	−7.63268	−	6.40458i	−0.296877	−	0.249109i	0.482166	−	0.876080i	$-0.339850\pi$
$661$	−7.63268	−	6.40458i	−0.296877	−	0.249109i	−0.779043	+	0.626971i	$0.784295\pi$
$662$	−8.67533	+	7.27947i	−0.337176	+	0.282925i
$663$	1.26307	−	3.47026i	0.0490536	−	0.134774i
$664$	−11.5008			−0.446317
$665$	5.32907	−	7.08909i	0.206652	−	0.274903i
$666$	−1.91405			−0.0741680
$667$	0.806687	−	2.21635i	0.0312350	−	0.0858176i
$668$	10.3512	−	8.68565i	0.400498	−	0.336058i
$669$	−14.0339	−	11.7758i	−0.542581	−	0.455279i
$670$	−2.38028	−	2.83671i	−0.0919583	−	0.109592i
$671$	−0.0676905	−	0.185978i	−0.00261316	−	0.00717960i
$672$	−0.188087	+	2.63906i	−0.00725560	+	0.101804i
$673$	−1.61138	+	0.930330i	−0.0621141	+	0.0358616i	−0.530735	−	0.847538i	$-0.678084\pi$
$673$	−1.61138	+	0.930330i	−0.0621141	+	0.0358616i	0.468621	+	0.883399i	$0.344751\pi$
$674$	1.63378	−	9.26562i	0.0629308	−	0.356898i
$675$	4.14274	−	1.50784i	0.159454	−	0.0580366i
$676$	6.84268			0.263180
$677$	−9.81772			−0.377326			−0.188663	−	0.982042i	$-0.560415\pi$
$677$	−9.81772			−0.377326			−0.188663	+	0.982042i	$0.560415\pi$
$678$	2.50688	−	0.912429i	0.0962761	−	0.0350416i
$679$	3.73996	+	36.0469i	0.143526	+	1.38335i
$680$	−1.12711	−	0.198740i	−0.0432227	−	0.00762133i
$681$	4.43067	+	25.1276i	0.169784	+	0.962892i
$682$	2.32362	−	0.409717i	0.0889760	−	0.0156889i
$683$	−19.5179	−	11.2687i	−0.746833	−	0.431184i	0.0777154	−	0.996976i	$-0.475237\pi$
$683$	−19.5179	−	11.2687i	−0.746833	−	0.431184i	−0.824548	+	0.565791i	$0.808571\pi$
$684$	−0.217232	+	4.35348i	−0.00830608	+	0.166460i
$685$			2.59408i			0.0991148i
$686$	−9.87716	+	15.6666i	−0.377112	+	0.598153i
$687$	1.31014	−	3.59958i	0.0499850	−	0.137333i
$688$	5.02378	−	1.82851i	0.191530	−	0.0697112i
$689$	−9.62113	+	26.4338i	−0.366536	+	1.00705i
$690$	−0.0722201	+	0.409580i	−0.00274937	+	0.0155925i
$691$			5.44185i			0.207018i	0.994629	+	0.103509i	$0.0330070\pi$
$691$			5.44185i			0.207018i	−0.994629	+	0.103509i	$0.966993\pi$
$692$	1.87552	+	3.24850i	0.0712967	+	0.123489i
$693$	−2.58467	−	2.50267i	−0.0981835	−	0.0950687i
$694$	6.73717	−	8.02905i	0.255740	−	0.304779i
$695$	−6.47932	+	11.2225i	−0.245775	+	0.425694i
$696$	−2.18057	−	3.77686i	−0.0826544	−	0.143162i
$697$	−8.38405	−	1.47833i	−0.317569	−	0.0559959i
$698$	−11.1142	+	9.32596i	−0.420681	+	0.352993i
$699$	1.15021	−	6.52316i	0.0435049	−	0.246728i
$700$	1.20372	+	11.6018i	0.0454964	+	0.438508i
$701$	−23.6260	+	19.8246i	−0.892342	+	0.748764i	−0.968678	−	0.248319i	$-0.920122\pi$
$701$	−23.6260	+	19.8246i	−0.892342	+	0.748764i	0.0763368	+	0.997082i	$0.475678\pi$
$702$	−2.14895	+	1.24070i	−0.0811069	+	0.0468271i
$703$	1.85645	−	8.13399i	0.0700174	−	0.306779i
$704$	0.679913	−	1.17764i	0.0256252	−	0.0443841i
$705$	−7.93390	−	2.88770i	−0.298808	−	0.108757i
$706$	−11.0788	−	4.03234i	−0.416955	−	0.151759i
$707$	9.04746	−	9.34389i	0.340265	−	0.351413i
$708$	−0.0929914	−	0.527381i	−0.00349483	−	0.0198202i
$709$	13.9049	+	11.6676i	0.522211	+	0.438187i	0.865402	−	0.501079i	$-0.167063\pi$
$709$	13.9049	+	11.6676i	0.522211	+	0.438187i	−0.343191	+	0.939266i	$0.611508\pi$
$710$	−0.867094	+	0.500617i	−0.0325415	+	0.0187878i
$711$			16.0393i			0.601522i
$712$	−4.68385	−	0.825889i	−0.175535	−	0.0309515i
$713$	0.718847	+	0.603185i	0.0269210	+	0.0225894i
$714$	3.92761	+	0.279923i	0.146987	+	0.0104758i
$715$	−2.24722	−	1.29743i	−0.0840411	−	0.0485212i
$716$	12.5105	−	14.9095i	0.467541	−	0.557193i
$717$	17.7206	+	6.44978i	0.661789	+	0.240871i
$718$	−8.39757	+	10.0078i	−0.313394	+	0.373489i
$719$	−34.4444	+	6.07349i	−1.28456	+	0.226503i	−0.773916	−	0.633289i	$-0.781705\pi$
$719$	−34.4444	+	6.07349i	−1.28456	+	0.226503i	−0.510645	+	0.859791i	$0.670594\pi$
$720$	0.494314	+	0.589100i	0.0184220	+	0.0219545i
$721$	13.2700	+	27.3002i	0.494202	+	1.01671i
$722$	−18.2900	−	5.14562i	−0.680682	−	0.191500i
$723$	2.41454	+	4.18210i	0.0897977	+	0.155534i
$724$	0.338448	+	1.91944i	0.0125783	+	0.0713353i
$725$	−12.3586	−	14.7284i	−0.458988	−	0.547001i
$726$	−3.12978	−	8.59901i	−0.116157	−	0.319139i
$727$	50.5536	−	8.91396i	1.87493	−	0.330600i	0.884270	−	0.466975i	$-0.154656\pi$
$727$	50.5536	−	8.91396i	1.87493	−	0.330600i	0.990657	+	0.136375i	$0.0435452\pi$
$728$	−1.80116	−	6.31324i	−0.0667555	−	0.233984i
$729$	−0.500000	+	0.866025i	−0.0185185	+	0.0320750i
$730$	0.0218470	+	0.0126134i	0.000808593	+	0.000466842i
$731$	−2.72130	−	7.47672i	−0.100651	−	0.276536i
$732$	−0.0497788	−	0.136766i	−0.00183988	−	0.00505502i
$733$	−17.2969	−	9.98637i	−0.638876	−	0.368855i	0.145306	−	0.989387i	$-0.453583\pi$
$733$	−17.2969	−	9.98637i	−0.638876	−	0.368855i	−0.784181	+	0.620532i	$0.786917\pi$
$734$	−9.61249	+	16.6493i	−0.354803	+	0.614538i
$735$	1.10513	+	5.26845i	0.0407632	+	0.194330i
$736$	0.532604	−	0.0939124i	0.0196320	−	0.00346166i
$737$	−2.23955	−	6.15312i	−0.0824950	−	0.226653i
$738$	3.67697	+	4.38204i	0.135351	+	0.161305i
$739$	−0.362184	−	2.05405i	−0.0133231	−	0.0755593i	0.977421	−	0.211300i	$-0.0677697\pi$
$739$	−0.362184	−	2.05405i	−0.0133231	−	0.0755593i	−0.990744	+	0.135741i	$0.956659\pi$
$740$	−0.735967	−	1.27473i	−0.0270547	−	0.0468601i
$741$	−3.18821	−	10.3356i	−0.117122	−	0.379687i
$742$	−29.9176	−	2.13224i	−1.09831	−	0.0782771i
$743$	0.949284	+	1.13131i	0.0348259	+	0.0415038i	0.783176	−	0.621800i	$-0.213598\pi$
$743$	0.949284	+	1.13131i	0.0348259	+	0.0415038i	−0.748350	+	0.663304i	$0.769154\pi$
$744$	1.70876	−	0.301301i	0.0626462	−	0.0110462i
$745$	−5.04018	+	6.00665i	−0.184658	+	0.220067i
$746$	−25.2026	−	9.17300i	−0.922733	−	0.335847i
$747$	7.39256	−	8.81011i	0.270480	−	0.322345i
$748$	−1.75264	−	1.01189i	−0.0640830	−	0.0369984i
$749$	40.9542	+	27.7037i	1.49643	+	1.01227i
$750$	5.54261	+	4.65081i	0.202388	+	0.169823i
$751$	13.2490	+	2.33615i	0.483461	+	0.0852473i	0.410066	−	0.912056i	$-0.365506\pi$
$751$	13.2490	+	2.33615i	0.483461	+	0.0852473i	0.0733950	+	0.997303i	$0.476617\pi$
$752$			10.9791i			0.400366i
$753$	−5.86989	+	3.38898i	−0.213911	+	0.123501i
$754$	8.28992	+	6.95607i	0.301901	+	0.253325i
$755$	1.28457	+	7.28515i	0.0467502	+	0.265134i
$756$	−1.90074	−	1.84044i	−0.0691291	−	0.0669360i
$757$	−2.15360	−	0.783847i	−0.0782740	−	0.0284894i	0.302586	−	0.953122i	$-0.402150\pi$
$757$	−2.15360	−	0.783847i	−0.0782740	−	0.0284894i	−0.380860	+	0.924633i	$0.624372\pi$
$758$	23.8685	+	8.68743i	0.866943	+	0.315542i
$759$	−0.367711	+	0.636893i	−0.0133470	+	0.0231178i
$760$	−2.98289	+	1.52927i	−0.108201	+	0.0554726i
$761$	8.14396	−	4.70192i	0.295218	−	0.170444i	−0.345075	−	0.938575i	$-0.612146\pi$
$761$	8.14396	−	4.70192i	0.295218	−	0.170444i	0.640293	+	0.768131i	$0.278813\pi$
$762$	−2.50362	+	2.10079i	−0.0906967	+	0.0761035i
$763$	−12.4909	−	17.2407i	−0.452202	−	0.624156i
$764$	−0.489545	+	2.77635i	−0.0177111	+	0.100445i
$765$	0.876736	−	0.735669i	0.0316985	−	0.0265982i
$766$	−22.6358	−	3.99130i	−0.817864	−	0.144211i
$767$	0.664414	+	1.15080i	0.0239906	+	0.0415529i
$768$	0.500000	−	0.866025i	0.0180422	−	0.0312500i
$769$	−32.2447	+	38.4277i	−1.16277	+	1.38574i	−0.254650	+	0.967033i	$0.581960\pi$
$769$	−32.2447	+	38.4277i	−1.16277	+	1.38574i	−0.908122	+	0.418705i	$0.862484\pi$
$770$	0.672922	−	2.68365i	0.0242504	−	0.0967121i
$771$	−0.0568455	−	0.0984593i	−0.00204724	−	0.00354593i
$772$			11.3794i			0.409554i
$773$	−3.38429	+	19.1933i	−0.121725	+	0.690334i	0.861475	+	0.507800i	$0.169541\pi$
$773$	−3.38429	+	19.1933i	−0.121725	+	0.690334i	−0.983200	+	0.182534i	$0.941570\pi$
$774$	−1.82851	+	5.02378i	−0.0657244	+	0.180576i
$775$	7.18817	−	2.61628i	0.258207	−	0.0939795i
$776$	4.68484	−	12.8715i	0.168176	−	0.462060i
$777$	2.97113	+	4.10092i	0.106589	+	0.147120i
$778$		−	2.26046i		−	0.0810416i
$779$	−22.1883	+	11.3756i	−0.794980	+	0.407572i
$780$	−1.65258	−	0.954115i	−0.0591717	−	0.0341628i
$781$	−1.74355	+	0.307436i	−0.0623893	+	0.0110009i
$782$	−0.139766	−	0.792655i	−0.00499804	−	0.0283453i
$783$	4.29489	+	0.757305i	0.153487	+	0.0270639i
$784$	5.94623	−	3.69355i	0.212366	−	0.131912i
$785$	9.61008	−	3.49778i	0.342998	−	0.124841i
$786$	−17.1646			−0.612241
$787$	−7.00844			−0.249824			−0.124912	−	0.992168i	$-0.539865\pi$
$787$	−7.00844			−0.249824			−0.124912	+	0.992168i	$0.539865\pi$
$788$	−6.26372	+	2.27981i	−0.223136	+	0.0812148i
$789$	3.75065	−	21.2710i	0.133527	−	0.757267i
$790$	−10.6820	+	6.16725i	−0.380048	+	0.219421i
$791$	−5.84627	−	3.95474i	−0.207869	−	0.140614i
$792$	0.465088	+	1.27782i	0.0165262	+	0.0454053i
$793$	0.232143	+	0.276657i	0.00824364	+	0.00982439i
$794$	−8.24353	−	6.91714i	−0.292552	−	0.245480i
$795$	−6.67832	+	5.60378i	−0.236856	+	0.198746i
$796$	−5.04137	+	13.8510i	−0.178686	+	0.490937i
$797$	28.9651			1.02600			0.512999	−	0.858389i	$-0.328535\pi$
$797$	28.9651			1.02600			0.512999	+	0.858389i	$0.328535\pi$
$798$	9.66469	−	6.29236i	0.342126	−	0.222747i
$799$	16.3398			0.578059
$800$	1.50784	−	4.14274i	0.0533100	−	0.146468i
$801$	3.64339	−	3.05717i	0.128733	−	0.108020i
$802$	19.8045	+	16.6180i	0.699323	+	0.586801i
$803$	0.0286733	+	0.0341714i	0.00101186	+	0.00120588i
$804$	−1.64694	−	4.52493i	−0.0580831	−	0.159582i
$805$	0.989645	−	0.481045i	0.0348804	−	0.0169546i
$806$	−3.72869	+	2.15276i	−0.131338	+	0.0758278i
$807$	2.19340	−	12.4394i	0.0772115	−	0.437888i
$808$	−4.61947	+	1.68135i	−0.162512	+	0.0591496i
$809$	18.8221			0.661751			0.330876	−	0.943674i	$-0.392656\pi$
$809$	18.8221			0.661751			0.330876	+	0.943674i	$0.392656\pi$
$810$	−0.769015			−0.0270204
$811$	−19.3264	+	7.03425i	−0.678643	+	0.247006i	−0.658265	−	0.752787i	$-0.728709\pi$
$811$	−19.3264	+	7.03425i	−0.678643	+	0.247006i	−0.0203782	+	0.999792i	$0.506487\pi$
$812$	−4.70722	+	10.5347i	−0.165191	+	0.369694i
$813$	−28.6851	−	5.05796i	−1.00603	−	0.177390i
$814$	−0.451968	−	2.56324i	−0.0158415	−	0.0898414i
$815$	10.7631	−	1.89783i	0.377016	−	0.0664781i
$816$	−1.28887	−	0.744132i	−0.0451196	−	0.0260498i
$817$	−19.5757	−	12.6431i	−0.684867	−	0.442325i
$818$		−	1.78238i		−	0.0623195i
$819$	5.99399	+	2.67830i	0.209447	+	0.0935875i
$820$	−1.50456	+	4.13374i	−0.0525415	+	0.144357i
$821$	14.7178	−	5.35685i	0.513655	−	0.186955i	−0.0721704	−	0.997392i	$-0.522993\pi$
$821$	14.7178	−	5.35685i	0.513655	−	0.186955i	0.585826	+	0.810437i	$0.300770\pi$
$822$	−1.15372	+	3.16982i	−0.0402406	+	0.110560i
$823$	−3.61255	+	20.4878i	−0.125926	+	0.714160i	0.854828	+	0.518911i	$0.173663\pi$
$823$	−3.61255	+	20.4878i	−0.125926	+	0.714160i	−0.980754	+	0.195249i	$0.937449\pi$
$824$		−	11.4729i		−	0.399678i
$825$	2.99748	+	5.19178i	0.104359	+	0.180755i
$826$	−0.985584	+	1.01787i	−0.0342928	+	0.0354164i
$827$	−35.9324	+	42.8226i	−1.24949	+	1.48909i	−0.444528	+	0.895765i	$0.646628\pi$
$827$	−35.9324	+	42.8226i	−1.24949	+	1.48909i	−0.804965	+	0.593322i	$0.797816\pi$
$828$	−0.270410	+	0.468364i	−0.00939740	+	0.0162768i
$829$	3.89556	+	6.74732i	0.135299	+	0.234344i	0.925711	−	0.378230i	$-0.123467\pi$
$829$	3.89556	+	6.74732i	0.135299	+	0.234344i	−0.790413	+	0.612574i	$0.790134\pi$
$830$	8.70991	+	1.53579i	0.302325	+	0.0533081i
$831$	0.852094	−	0.714992i	0.0295588	−	0.0248028i
$832$	−0.430890	+	2.44370i	−0.0149384	+	0.0847199i
$833$	−5.49697	−	8.84956i	−0.190459	−	0.306619i
$834$	−12.9086	+	10.8316i	−0.446988	+	0.375067i
$835$	−8.99913	+	5.19565i	−0.311428	+	0.179803i
$836$	−5.88134	+	0.737084i	−0.203410	+	0.0254926i
$837$	−0.867561	+	1.50266i	−0.0299873	+	0.0519395i
$838$	−11.2953	−	4.11115i	−0.390189	−	0.142017i
$839$	−11.7453	−	4.27493i	−0.405492	−	0.147587i	0.131218	−	0.991353i	$-0.458111\pi$
$839$	−11.7453	−	4.27493i	−0.405492	−	0.147587i	−0.536711	+	0.843766i	$0.680333\pi$
$840$	0.494859	−	1.97353i	0.0170743	−	0.0680931i
$841$	1.73308	+	9.82877i	0.0597613	+	0.338923i
$842$	12.0204	+	10.0863i	0.414249	+	0.347596i
$843$	−14.2807	+	8.24496i	−0.491853	+	0.283972i
$844$			3.82955i			0.131818i
$845$	−5.18218	−	0.913759i	−0.178273	−	0.0314343i
$846$	−8.41046	−	7.05722i	−0.289158	−	0.242632i
$847$	−13.5654	+	20.0537i	−0.466113	+	0.689052i
$848$	9.81769	+	5.66824i	0.337141	+	0.194648i
$849$	−1.18152	+	1.40809i	−0.0405498	+	0.0483254i
$850$	−6.16549	−	2.24406i	−0.211475	−	0.0769705i
$851$	0.665386	−	0.792976i	0.0228091	−	0.0271829i
$852$	−1.28219	+	0.226084i	−0.0439271	+	0.00774553i
$853$	−23.9556	−	28.5492i	−0.820226	−	0.977507i	0.179755	−	0.983711i	$-0.442470\pi$
$853$	−23.9556	−	28.5492i	−0.820226	−	0.977507i	−0.999981	+	0.00620441i	$0.998025\pi$
$854$	−0.215756	+	0.318951i	−0.00738301	+	0.0109143i
$855$	0.745873	−	3.26802i	0.0255083	−	0.111764i
$856$	−9.34410	−	16.1845i	−0.319375	−	0.553173i
$857$	7.85303	+	44.5367i	0.268254	+	1.52135i	0.759605	+	0.650385i	$0.225392\pi$
$857$	7.85303	+	44.5367i	0.268254	+	1.52135i	−0.491351	+	0.870962i	$0.663497\pi$
$858$	−2.16894	−	2.58484i	−0.0740463	−	0.0882449i
$859$	−3.35935	−	9.22974i	−0.114620	−	0.314915i	0.869097	−	0.494642i	$-0.164701\pi$
$859$	−3.35935	−	9.22974i	−0.114620	−	0.314915i	−0.983716	+	0.179727i	$0.942479\pi$
$860$	−4.04885	+	0.713921i	−0.138065	+	0.0243445i
$861$	3.68103	−	14.6801i	0.125449	−	0.500298i
$862$	−1.73495	+	3.00502i	−0.0590927	+	0.102352i
$863$	27.0907	+	15.6408i	0.922177	+	0.532419i	0.884329	−	0.466864i	$-0.154616\pi$
$863$	27.0907	+	15.6408i	0.922177	+	0.532419i	0.0378483	+	0.999283i	$0.487950\pi$
$864$	0.342020	+	0.939693i	0.0116358	+	0.0319690i
$865$	−0.986595	−	2.71065i	−0.0335452	−	0.0921648i
$866$	21.4623	+	12.3913i	0.729320	+	0.421073i
$867$	7.39254	−	12.8042i	0.251064	−	0.434855i
$868$	−3.29801	−	3.19338i	−0.111942	−	0.108390i
$869$	−21.4794	+	3.78739i	−0.728637	+	0.128478i
$870$	1.14706	+	3.15153i	0.0388891	+	0.106847i
$871$	7.68050	+	9.15326i	0.260244	+	0.310146i
$872$	1.39733	+	7.92463i	0.0473194	+	0.268362i
$873$	6.84878	+	11.8624i	0.231796	+	0.401483i
$874$	−1.72810	−	1.60341i	−0.0584537	−	0.0542361i
$875$	1.36088	−	19.0946i	0.0460061	−	0.645514i
$876$	0.0210860	+	0.0251293i	0.000712429	+	0.000849040i
$877$	24.7826	−	4.36983i	0.836848	−	0.147559i	0.261229	−	0.965277i	$-0.415872\pi$
$877$	24.7826	−	4.36983i	0.836848	−	0.147559i	0.575619	+	0.817718i	$0.304761\pi$
$878$	7.10859	−	8.47169i	0.239903	−	0.285906i
$879$	−5.02039	−	1.82727i	−0.169334	−	0.0616324i
$880$	−0.672181	+	0.801074i	−0.0226592	+	0.0270042i
$881$	−40.5377	−	23.4044i	−1.36575	−	0.788515i	−0.375367	−	0.926876i	$-0.622483\pi$
$881$	−40.5377	−	23.4044i	−1.36575	−	0.788515i	−0.990382	+	0.138361i	$0.955817\pi$
$882$	−0.992744	+	6.92925i	−0.0334274	+	0.233320i
$883$	17.3642	+	14.5703i	0.584353	+	0.490330i	0.886373	−	0.462971i	$-0.153217\pi$
$883$	17.3642	+	14.5703i	0.584353	+	0.490330i	−0.302021	+	0.953301i	$0.597661\pi$
$884$	3.63686	+	0.641277i	0.122321	+	0.0215685i
$885$			0.411820i			0.0138432i
$886$	28.8125	−	16.6349i	0.967974	−	0.558860i
$887$	−37.0525	−	31.0908i	−1.24410	−	1.04393i	−0.997192	−	0.0748872i	$-0.976140\pi$
$887$	−37.0525	−	31.0908i	−1.24410	−	1.04393i	−0.246910	−	0.969038i	$-0.579415\pi$
$888$	−0.332372	−	1.88497i	−0.0111537	−	0.0632555i
$889$	8.38731	+	2.10311i	0.281301	+	0.0705359i
$890$	3.43694	+	1.25094i	0.115207	+	0.0419318i
$891$	−1.27782	−	0.465088i	−0.0428085	−	0.0155810i
$892$	9.15996	−	15.8655i	0.306698	−	0.531217i
$893$	38.1479	−	28.8964i	1.27657	−	0.966982i
$894$	−8.83027	+	5.09816i	−0.295328	+	0.170508i
$895$	−11.4656	+	9.62079i	−0.383253	+	0.321588i
$896$	−2.63163	+	0.273038i	−0.0879164	+	0.00912157i
$897$	0.233034	−	1.32160i	0.00778077	−	0.0441269i
$898$	−8.11362	+	6.80814i	−0.270755	+	0.227190i
$899$	7.45216	+	1.31402i	0.248543	+	0.0438249i
$900$	2.20431	+	3.81797i	0.0734769	+	0.127266i
$901$	8.43584	−	14.6113i	0.281039	−	0.486773i
$902$	−5.00004	+	5.95882i	−0.166483	+	0.198407i
$903$	13.6020	−	3.88063i	0.452645	−	0.129139i
$904$	1.33388	+	2.31035i	0.0443643	+	0.0768412i
$905$		−	1.49885i		−	0.0498233i
$906$	−1.67041	+	9.47334i	−0.0554955	+	0.314731i
$907$	14.4099	−	39.5908i	0.478473	−	1.31459i	−0.432317	−	0.901722i	$-0.642304\pi$
$907$	14.4099	−	39.5908i	0.478473	−	1.31459i	0.910790	−	0.412871i	$-0.135474\pi$
$908$	−23.9765	+	8.72672i	−0.795687	+	0.289607i
$909$	1.68135	−	4.61947i	0.0557668	−	0.153218i
$910$	0.521020	+	5.02175i	0.0172716	+	0.166469i
$911$		−	4.06372i		−	0.134637i	−0.997732	−	0.0673186i	$-0.978556\pi$
$911$		−	4.06372i		−	0.134637i	0.997732	−	0.0673186i	$-0.0214444\pi$
$912$	−4.32507	+	0.542042i	−0.143217	+	0.0179488i
$913$	13.5438	+	7.81953i	0.448235	+	0.258789i
$914$	9.53908	−	1.68200i	0.315525	−	0.0556355i
$915$	0.0194356	+	0.110225i	0.000642521	+	0.00364392i
$916$	3.77240	+	0.665176i	0.124644	+	0.0219780i
$917$	26.6441	+	36.7758i	0.879866	+	1.21444i
$918$	1.39851	−	0.509016i	0.0461577	−	0.0168000i
$919$	−8.36518			−0.275942			−0.137971	−	0.990436i	$-0.544058\pi$
$919$	−8.36518			−0.275942			−0.137971	+	0.990436i	$0.544058\pi$
$920$	−0.415899			−0.0137118
$921$	−5.71493	+	2.08007i	−0.188313	+	0.0685405i
$922$	1.35879	−	7.70609i	0.0447494	−	0.253786i
$923$	2.79787	−	1.61535i	0.0920929	−	0.0531699i
$924$	2.01583	−	2.97999i	0.0663159	−	0.0980344i
$925$	−2.88607	−	7.92942i	−0.0948935	−	0.260718i
$926$	−13.4290	−	16.0040i	−0.441304	−	0.525926i
$927$	8.78876	+	7.37464i	0.288661	+	0.242215i
$928$	3.34083	−	2.80329i	0.109668	−	0.0920225i
$929$	−0.826928	+	2.27197i	−0.0271306	+	0.0745408i	−0.952519	−	0.304481i	$-0.901517\pi$
$929$	−0.826928	+	2.27197i	−0.0271306	+	0.0745408i	0.925388	+	0.379021i	$0.123739\pi$
$930$	−1.33434			−0.0437546
$931$	−28.4838	−	10.9395i	−0.933519	−	0.358528i
$932$	6.62379			0.216969
$933$	7.29969	−	20.0557i	0.238981	−	0.656595i
$934$	1.56250	−	1.31109i	0.0511266	−	0.0429003i
$935$	1.19221	+	1.00038i	0.0389894	+	0.0327160i
$936$	−1.59501	−	1.90086i	−0.0521345	−	0.0621315i
$937$	14.6746	+	40.3181i	0.479398	+	1.31713i	0.910006	+	0.414595i	$0.136077\pi$
$937$	14.6746	+	40.3181i	0.479398	+	1.31713i	−0.430608	+	0.902539i	$0.641701\pi$
$938$	−7.13832	+	10.5525i	−0.233075	+	0.344553i
$939$	−2.11389	+	1.22046i	−0.0689843	+	0.0398281i
$940$	1.46613	−	8.31481i	0.0478197	−	0.271199i
$941$	−31.1419	+	11.3347i	−1.01520	+	0.369501i	−0.795426	−	0.606050i	$-0.792753\pi$
$941$	−31.1419	+	11.3347i	−1.01520	+	0.369501i	−0.219770	+	0.975552i	$0.570531\pi$
$942$	13.2986			0.433292
$943$	−3.09368			−0.100744
$944$	0.503221	−	0.183157i	0.0163784	−	0.00596126i
$945$	1.19372	+	1.64764i	0.0388317	+	0.0535978i
$946$	−7.15946	−	1.26241i	−0.232774	−	0.0410443i
$947$	6.84815	+	38.8378i	0.222535	+	1.26206i	0.867342	+	0.497713i	$0.165827\pi$
$947$	6.84815	+	38.8378i	0.222535	+	1.26206i	−0.644807	+	0.764345i	$0.723062\pi$
$948$	−15.7957	+	2.78520i	−0.513019	+	0.0904591i
$949$	−0.0704940	−	0.0406998i	−0.00228833	−	0.00132117i
$950$	−18.3629	+	5.66440i	−0.595772	+	0.183777i
$951$		−	2.89401i		−	0.0938446i
$952$	0.406353	+	3.91655i	0.0131700	+	0.126936i
$953$	−18.6322	+	51.1915i	−0.603555	+	1.65825i	0.140456	+	0.990087i	$0.455143\pi$
$953$	−18.6322	+	51.1915i	−0.603555	+	1.65825i	−0.744011	+	0.668167i	$0.767079\pi$
$954$	−10.6528	+	3.87731i	−0.344898	+	0.125532i
$955$	0.741496	−	2.03724i	0.0239942	−	0.0659237i
$956$	−3.27464	+	18.5714i	−0.105909	+	0.600642i
$957$			5.93040i			0.191703i
$958$	−7.88103	−	13.6503i	−0.254624	−	0.441022i
$959$	8.58234	−	2.44853i	0.277138	−	0.0790672i
$960$	−0.494314	+	0.589100i	−0.0159539	+	0.0190131i
$961$	13.9947	−	24.2395i	0.451441	−	0.781919i
$962$	2.37476	+	4.11320i	0.0765653	+	0.132615i
$963$	18.4043	+	3.24517i	0.593070	+	0.104574i
$964$	−3.69929	+	3.10407i	−0.119146	+	0.0999754i
$965$	1.51959	−	8.61800i	0.0489172	−	0.277423i
$966$	1.42324	−	0.147664i	0.0457918	−	0.00475103i
$967$	43.8069	−	36.7583i	1.40873	−	1.18207i	0.451672	−	0.892184i	$-0.350828\pi$
$967$	43.8069	−	36.7583i	1.40873	−	1.18207i	0.957062	−	0.289883i	$-0.0936165\pi$
$968$	7.92489	−	4.57544i	0.254716	−	0.147060i
$969$	0.806702	+	6.43684i	0.0259150	+	0.206781i
$970$	−5.26682	+	9.12240i	−0.169107	+	0.292903i
$971$	−19.4828	−	7.09116i	−0.625233	−	0.227566i	0.00992222	−	0.999951i	$-0.496842\pi$
$971$	−19.4828	−	7.09116i	−0.625233	−	0.227566i	−0.635155	+	0.772385i	$0.719064\pi$
$972$	−0.939693	−	0.342020i	−0.0301407	−	0.0109703i
$973$	43.2447	+	10.8435i	1.38636	+	0.347628i
$974$	−6.96386	−	39.4940i	−0.223136	−	1.26547i
$975$	−8.38015	−	7.03178i	−0.268380	−	0.225197i
$976$	0.126044	−	0.0727717i	0.00403458	−	0.00232936i
$977$			48.4926i			1.55142i	0.631091	+	0.775709i	$0.282607\pi$
$977$			48.4926i			1.55142i	−0.631091	+	0.775709i	$0.717393\pi$
$978$	13.9960	+	2.46787i	0.447542	+	0.0789138i
$979$	4.95437	+	4.15721i	0.158342	+	0.132865i
$980$	−4.99650	+	2.00319i	−0.159607	+	0.0639897i
$981$	−6.96880	−	4.02344i	−0.222497	−	0.128459i
$982$	−0.345994	+	0.412339i	−0.0110411	+	0.0131583i
$983$	15.3304	+	5.57983i	0.488965	+	0.177969i	0.574724	−	0.818347i	$-0.305109\pi$
$983$	15.3304	+	5.57983i	0.488965	+	0.177969i	−0.0857590	+	0.996316i	$0.527331\pi$
$984$	−3.67697	+	4.38204i	−0.117218	+	0.139694i
$985$	5.04816	−	0.890127i	0.160848	−	0.0283618i
$986$	−4.17204	−	4.97204i	−0.132865	−	0.158342i
$987$	−2.06502	+	28.9744i	−0.0657303	+	0.922266i
$988$	9.62494	−	4.93453i	0.306210	−	0.156988i
$989$	−1.44567	−	2.50397i	−0.0459695	−	0.0796215i
$990$	−0.181589	−	1.02984i	−0.00577127	−	0.0327305i
$991$	−25.6142	−	30.5258i	−0.813662	−	0.969685i	0.186255	−	0.982501i	$-0.440365\pi$
$991$	−25.6142	−	30.5258i	−0.813662	−	0.969685i	−0.999918	+	0.0128162i	$0.995920\pi$
$992$	0.593447	+	1.63048i	0.0188420	+	0.0517678i
$993$	11.1528	−	1.96654i	0.353923	−	0.0624062i
$994$	2.47470	+	2.39619i	0.0784927	+	0.0760025i
$995$	5.66763	−	9.81662i	0.179676	−	0.311208i
$996$	9.95997	+	5.75039i	0.315594	+	0.182208i
$997$	−12.4670	−	34.2528i	−0.394834	−	1.08480i	−0.964767	−	0.263107i	$-0.915253\pi$
$997$	−12.4670	−	34.2528i	−0.394834	−	1.08480i	0.569932	−	0.821692i	$-0.306969\pi$
$998$	−8.40615	−	23.0957i	−0.266092	−	0.731082i
$999$	1.65762	+	0.957026i	0.0524447	+	0.0302790i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	798.2.cj.b.241.13	yes	84
7.5	odd	6		798.2.ca.b.355.2	✓	84
19.3	odd	18		798.2.ca.b.535.2	yes	84
133.117	even	18	inner	798.2.cj.b.649.13	yes	84

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
798.2.ca.b.355.2	✓	84	7.5	odd	6
798.2.ca.b.535.2	yes	84	19.3	odd	18
798.2.cj.b.241.13	yes	84	1.1	even	1	trivial
798.2.cj.b.649.13	yes	84	133.117	even	18	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 798 = 2 \cdot 3 \cdot 7 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	798.cj (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.342020 - 0.939693i) q^{2} +(-0.766044 + 0.642788i) q^{3} +(-0.766044 - 0.642788i) q^{4} +(0.494314 + 0.589100i) q^{5} +(0.342020 + 0.939693i) q^{6} +(1.48242 - 2.19145i) q^{7} +(-0.866025 + 0.500000i) q^{8} +(0.173648 - 0.984808i) q^{9} +(0.722638 - 0.263019i) q^{10} +1.35983 q^{11} +1.00000 q^{12} +(-2.33175 + 0.848687i) q^{13} +(-1.55227 - 2.14254i) q^{14} +(-0.757332 - 0.133538i) q^{15} +(0.173648 + 0.984808i) q^{16} +(1.46565 - 0.258434i) q^{17} +(-0.866025 - 0.500000i) q^{18} +(2.96477 - 3.19533i) q^{19} -0.769015i q^{20} +(0.273038 + 2.63163i) q^{21} +(0.465088 - 1.27782i) q^{22} +(0.508204 - 0.184971i) q^{23} +(0.342020 - 0.939693i) q^{24} +(0.765548 - 4.34164i) q^{25} +2.48139i q^{26} +(0.500000 + 0.866025i) q^{27} +(-2.54423 + 0.725867i) q^{28} +(2.80329 - 3.34083i) q^{29} +(-0.384508 + 0.665987i) q^{30} +(0.867561 + 1.50266i) q^{31} +(0.984808 + 0.173648i) q^{32} +(-1.04169 + 0.874080i) q^{33} +(0.258434 - 1.46565i) q^{34} +(2.02376 - 0.209971i) q^{35} +(-0.766044 + 0.642788i) q^{36} +(1.65762 - 0.957026i) q^{37} +(-1.98861 - 3.87884i) q^{38} +(1.24070 - 2.14895i) q^{39} +(-0.722638 - 0.263019i) q^{40} +(-5.37537 - 1.95647i) q^{41} +(2.56630 + 0.643497i) q^{42} +(-0.928358 - 5.26498i) q^{43} +(-1.04169 - 0.874080i) q^{44} +(0.665987 - 0.384508i) q^{45} -0.540820i q^{46} +(10.8123 + 1.90650i) q^{47} +(-0.766044 - 0.642788i) q^{48} +(-2.60488 - 6.49728i) q^{49} +(-3.81797 - 2.20431i) q^{50} +(-0.956637 + 1.14008i) q^{51} +(2.33175 + 0.848687i) q^{52} +(7.28695 - 8.68425i) q^{53} +(0.984808 - 0.173648i) q^{54} +(0.672181 + 0.801074i) q^{55} +(-0.188087 + 2.63906i) q^{56} +(-0.217232 + 4.35348i) q^{57} +(-2.18057 - 3.77686i) q^{58} +(-0.0929914 - 0.527381i) q^{59} +(0.494314 + 0.589100i) q^{60} +(-0.0497788 - 0.136766i) q^{61} +(1.70876 - 0.301301i) q^{62} +(-1.90074 - 1.84044i) q^{63} +(0.500000 - 0.866025i) q^{64} +(-1.65258 - 0.954115i) q^{65} +(0.465088 + 1.27782i) q^{66} +(-1.64694 - 4.52493i) q^{67} +(-1.28887 - 0.744132i) q^{68} +(-0.270410 + 0.468364i) q^{69} +(0.494859 - 1.97353i) q^{70} +(-1.28219 + 0.226084i) q^{71} +(0.342020 + 0.939693i) q^{72} +(0.0210860 + 0.0251293i) q^{73} +(-0.332372 - 1.88497i) q^{74} +(2.20431 + 3.81797i) q^{75} +(-4.32507 + 0.542042i) q^{76} +(2.01583 - 2.97999i) q^{77} +(-1.59501 - 1.90086i) q^{78} +(-15.7957 + 2.78520i) q^{79} +(-0.494314 + 0.589100i) q^{80} +(-0.939693 - 0.342020i) q^{81} +(-3.67697 + 4.38204i) q^{82} +(9.95997 + 5.75039i) q^{83} +(1.48242 - 2.19145i) q^{84} +(0.876736 + 0.735669i) q^{85} +(-5.26498 - 0.928358i) q^{86} +4.36115i q^{87} +(-1.17764 + 0.679913i) q^{88} +(3.64339 + 3.05717i) q^{89} +(-0.133538 - 0.757332i) q^{90} +(-1.59677 + 6.36801i) q^{91} +(-0.508204 - 0.184971i) q^{92} +(-1.63048 - 0.593447i) q^{93} +(5.48954 - 9.50816i) q^{94} +(3.34789 + 0.167055i) q^{95} +(-0.866025 + 0.500000i) q^{96} +(-10.4929 + 8.80463i) q^{97} +(-6.99636 + 0.225590i) q^{98} +(0.236131 - 1.33917i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 84 q + 12 q^{7} - 12 q^{10} - 12 q^{11} + 84 q^{12} + 24 q^{13} + 6 q^{14} + 6 q^{19} - 6 q^{21} + 12 q^{22} - 42 q^{23} - 30 q^{25} + 42 q^{27} + 6 q^{28} + 6 q^{31} + 12 q^{33} - 30 q^{34} - 42 q^{35}+ \cdots + 6 q^{99}+O(q^{100}) \) 84 * q + 12 * q^7 - 12 * q^10 - 12 * q^11 + 84 * q^12 + 24 * q^13 + 6 * q^14 + 6 * q^19 - 6 * q^21 + 12 * q^22 - 42 * q^23 - 30 * q^25 + 42 * q^27 + 6 * q^28 + 6 * q^31 + 12 * q^33 - 30 * q^34 - 42 * q^35 - 18 * q^37 + 12 * q^38 + 12 * q^40 + 36 * q^41 + 18 * q^42 + 12 * q^43 + 12 * q^44 - 18 * q^45 + 18 * q^47 - 24 * q^49 + 18 * q^51 - 24 * q^52 + 60 * q^53 - 30 * q^55 - 18 * q^56 + 6 * q^57 + 48 * q^59 - 12 * q^62 - 6 * q^63 + 42 * q^64 + 108 * q^65 + 12 * q^66 + 42 * q^67 + 6 * q^69 + 18 * q^70 + 42 * q^71 - 48 * q^73 - 18 * q^74 - 48 * q^75 + 18 * q^76 - 96 * q^77 - 12 * q^78 - 60 * q^79 - 6 * q^82 + 54 * q^83 + 12 * q^84 - 24 * q^85 - 12 * q^86 - 24 * q^89 + 6 * q^90 + 24 * q^91 + 42 * q^92 - 36 * q^93 + 18 * q^94 - 12 * q^95 - 78 * q^97 + 24 * q^98 + 6 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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