LMFDB - Embedded newform 950.2.u.e.149.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [950,2,Mod(99,950)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(950, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 2]))

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

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

chi := DirichletCharacter("950.99");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 950 = 2 \cdot 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	950.u (of order $18$, degree $6$, not 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:	$7.58578819202$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$4$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 190)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			149.4
Character	$\chi$	$=$	950.149
Dual form			950.2.u.e.899.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.642788 - 0.766044i) q^{2} +(0.931116 + 2.55822i) q^{3} +(-0.173648 - 0.984808i) q^{4} +(2.55822 + 0.931116i) q^{6} +(2.31045 - 1.33394i) q^{7} +(-0.866025 - 0.500000i) q^{8} +(-3.37939 + 2.83564i) q^{9} +O(q^{10})$	\(q+(0.642788 - 0.766044i) q^{2} +(0.931116 + 2.55822i) q^{3} +(-0.173648 - 0.984808i) q^{4} +(2.55822 + 0.931116i) q^{6} +(2.31045 - 1.33394i) q^{7} +(-0.866025 - 0.500000i) q^{8} +(-3.37939 + 2.83564i) q^{9} +(2.46306 - 4.26615i) q^{11} +(2.35767 - 1.36120i) q^{12} +(1.54534 - 4.24577i) q^{13} +(0.463273 - 2.62735i) q^{14} +(-0.939693 + 0.342020i) q^{16} +(3.15506 - 3.76005i) q^{17} +4.41147i q^{18} +(0.628373 + 4.31337i) q^{19} +(5.56382 + 4.66860i) q^{21} +(-1.68484 - 4.62905i) q^{22} +(-3.07794 + 0.542723i) q^{23} +(0.472740 - 2.68104i) q^{24} +(-2.25913 - 3.91293i) q^{26} +(-3.32779 - 1.92130i) q^{27} +(-1.71488 - 2.04372i) q^{28} +(-0.227157 + 0.190607i) q^{29} +(3.13596 + 5.43165i) q^{31} +(-0.342020 + 0.939693i) q^{32} +(13.2072 + 2.32878i) q^{33} +(-0.852334 - 4.83382i) q^{34} +(3.37939 + 2.83564i) q^{36} +8.79946i q^{37} +(3.70814 + 2.29122i) q^{38} +12.3005 q^{39} +(-7.15482 + 2.60414i) q^{41} +(7.15271 - 1.26122i) q^{42} +(-2.99975 - 0.528937i) q^{43} +(-4.62905 - 1.68484i) q^{44} +(-1.56271 + 2.70669i) q^{46} +(-1.45184 - 1.73024i) q^{47} +(-1.74993 - 2.08548i) q^{48} +(0.0587989 - 0.101843i) q^{49} +(12.5568 + 4.57029i) q^{51} +(-4.44962 - 0.784587i) q^{52} +(-13.0140 + 2.29471i) q^{53} +(-3.61086 + 1.31425i) q^{54} -2.66788 q^{56} +(-10.4495 + 5.62377i) q^{57} +0.296532i q^{58} +(9.63183 + 8.08206i) q^{59} +(-0.806491 - 4.57384i) q^{61} +(6.17664 + 1.08911i) q^{62} +(-4.02534 + 11.0595i) q^{63} +(0.500000 + 0.866025i) q^{64} +(10.2733 - 8.62036i) q^{66} +(-6.27533 - 7.47864i) q^{67} +(-4.25079 - 2.45420i) q^{68} +(-4.25432 - 7.36870i) q^{69} +(0.702893 - 3.98630i) q^{71} +(4.34445 - 0.766044i) q^{72} +(-1.62245 - 4.45766i) q^{73} +(6.74078 + 5.65618i) q^{74} +(4.13872 - 1.36784i) q^{76} -13.1423i q^{77} +(7.90662 - 9.42274i) q^{78} +(0.708572 - 0.257899i) q^{79} +(-0.481582 + 2.73119i) q^{81} +(-2.60414 + 7.15482i) q^{82} +(9.57249 - 5.52668i) q^{83} +(3.63152 - 6.28999i) q^{84} +(-2.33339 + 1.95795i) q^{86} +(-0.699125 - 0.403640i) q^{87} +(-4.26615 + 2.46306i) q^{88} +(7.44939 + 2.71136i) q^{89} +(-2.09319 - 11.8711i) q^{91} +(1.06896 + 2.93693i) q^{92} +(-10.9754 + 13.0800i) q^{93} -2.25866 q^{94} -2.72240 q^{96} +(-4.57554 + 5.45292i) q^{97} +(-0.0402208 - 0.110506i) q^{98} +(3.77363 + 21.4013i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 36 q^{9}+O(q^{10}) $ 24 * q - 36 * q^9	$ 24 q - 36 q^{9} + 12 q^{11} + 24 q^{21} + 12 q^{29} + 12 q^{31} + 36 q^{36} + 72 q^{39} - 12 q^{41} - 12 q^{44} - 24 q^{46} + 36 q^{49} + 24 q^{56} + 48 q^{59} - 60 q^{61} + 12 q^{64} + 48 q^{66} - 12 q^{69} - 84 q^{71} - 12 q^{74} + 36 q^{76} - 120 q^{79} + 36 q^{81} + 48 q^{84} - 72 q^{86} + 24 q^{89} + 48 q^{91} - 120 q^{94} + 24 q^{99}+O(q^{100}) $ 24 * q - 36 * q^9 + 12 * q^11 + 24 * q^21 + 12 * q^29 + 12 * q^31 + 36 * q^36 + 72 * q^39 - 12 * q^41 - 12 * q^44 - 24 * q^46 + 36 * q^49 + 24 * q^56 + 48 * q^59 - 60 * q^61 + 12 * q^64 + 48 * q^66 - 12 * q^69 - 84 * q^71 - 12 * q^74 + 36 * q^76 - 120 * q^79 + 36 * q^81 + 48 * q^84 - 72 * q^86 + 24 * q^89 + 48 * q^91 - 120 * q^94 + 24 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/950\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$-1$	$e\left(\frac{2}{9}\right)$

Coefficient data

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

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

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

$2$	0.642788	−	0.766044i	0.454519	−	0.541675i
$2$	0.642788	−	0.766044i	0.454519	−	0.541675i
$3$	0.931116	+	2.55822i	0.537580	+	1.47699i	0.849865	+	0.527001i	$0.176684\pi$
$3$	0.931116	+	2.55822i	0.537580	+	1.47699i	−0.312284	+	0.949989i	$0.601094\pi$
$4$	−0.173648	−	0.984808i	−0.0868241	−	0.492404i
$5$		0			0
$5$		0			0
$6$	2.55822	+	0.931116i	1.04439	+	0.380127i
$7$	2.31045	−	1.33394i	0.873270	−	0.504182i	0.00483621	−	0.999988i	$-0.498461\pi$
$7$	2.31045	−	1.33394i	0.873270	−	0.504182i	0.868433	+	0.495806i	$0.165127\pi$
$8$	−0.866025	−	0.500000i	−0.306186	−	0.176777i
$9$	−3.37939	+	2.83564i	−1.12646	+	0.945214i
$10$		0			0
$11$	2.46306	−	4.26615i	0.742642	−	1.28629i	−0.208646	−	0.977991i	$-0.566906\pi$
$11$	2.46306	−	4.26615i	0.742642	−	1.28629i	0.951288	−	0.308302i	$-0.0997609\pi$
$12$	2.35767	−	1.36120i	0.680601	−	0.392945i
$13$	1.54534	−	4.24577i	0.428599	−	1.17757i	−0.518064	−	0.855342i	$-0.673347\pi$
$13$	1.54534	−	4.24577i	0.428599	−	1.17757i	0.946663	−	0.322224i	$-0.104431\pi$
$14$	0.463273	−	2.62735i	0.123815	−	0.702189i
$15$		0			0
$16$	−0.939693	+	0.342020i	−0.234923	+	0.0855050i
$17$	3.15506	−	3.76005i	0.765213	−	0.911946i	−0.232952	−	0.972488i	$-0.574839\pi$
$17$	3.15506	−	3.76005i	0.765213	−	0.911946i	0.998166	+	0.0605425i	$0.0192831\pi$
$18$			4.41147i			1.03979i
$19$	0.628373	+	4.31337i	0.144159	+	0.989555i
$19$	0.628373	+	4.31337i	0.144159	+	0.989555i
$20$		0			0
$21$	5.56382	+	4.66860i	1.21412	+	1.01877i
$22$	−1.68484	−	4.62905i	−0.359208	−	0.986916i
$23$	−3.07794	+	0.542723i	−0.641794	+	0.113166i	−0.485068	−	0.874477i	$-0.661205\pi$
$23$	−3.07794	+	0.542723i	−0.641794	+	0.113166i	−0.156726	+	0.987642i	$0.550094\pi$
$24$	0.472740	−	2.68104i	0.0964977	−	0.547266i
$25$		0			0
$26$	−2.25913	−	3.91293i	−0.443052	−	0.767388i
$27$	−3.32779	−	1.92130i	−0.640433	−	0.369754i
$28$	−1.71488	−	2.04372i	−0.324082	−	0.386226i
$29$	−0.227157	+	0.190607i	−0.0421820	+	0.0353949i	−0.663635	−	0.748057i	$-0.730987\pi$
$29$	−0.227157	+	0.190607i	−0.0421820	+	0.0353949i	0.621453	+	0.783451i	$0.286543\pi$
$30$		0			0
$31$	3.13596	+	5.43165i	0.563235	+	0.975552i	0.997211	+	0.0746280i	$0.0237769\pi$
$31$	3.13596	+	5.43165i	0.563235	+	0.975552i	−0.433976	+	0.900924i	$0.642890\pi$
$32$	−0.342020	+	0.939693i	−0.0604612	+	0.166116i
$33$	13.2072	+	2.32878i	2.29907	+	0.405388i
$34$	−0.852334	−	4.83382i	−0.146174	−	0.828994i
$35$		0			0
$36$	3.37939	+	2.83564i	0.563231	+	0.472607i
$37$			8.79946i			1.44662i	0.690522	+	0.723311i	$0.257381\pi$
$37$			8.79946i			1.44662i	−0.690522	+	0.723311i	$0.742619\pi$
$38$	3.70814	+	2.29122i	0.601540	+	0.371685i
$39$	12.3005			1.96966
$40$		0			0
$41$	−7.15482	+	2.60414i	−1.11740	+	0.406699i	−0.833701	−	0.552216i	$-0.813782\pi$
$41$	−7.15482	+	2.60414i	−1.11740	+	0.406699i	−0.283694	+	0.958915i	$0.591560\pi$
$42$	7.15271	−	1.26122i	1.10369	−	0.194610i
$43$	−2.99975	−	0.528937i	−0.457458	−	0.0806621i	−0.0598292	−	0.998209i	$-0.519056\pi$
$43$	−2.99975	−	0.528937i	−0.457458	−	0.0806621i	−0.397628	+	0.917547i	$0.630167\pi$
$44$	−4.62905	−	1.68484i	−0.697855	−	0.253998i
$45$		0			0
$46$	−1.56271	+	2.70669i	−0.230409	+	0.399080i
$47$	−1.45184	−	1.73024i	−0.211773	−	0.252381i	0.649693	−	0.760197i	$-0.274897\pi$
$47$	−1.45184	−	1.73024i	−0.211773	−	0.252381i	−0.861466	+	0.507816i	$0.830453\pi$
$48$	−1.74993	−	2.08548i	−0.252580	−	0.301013i
$49$	0.0587989	−	0.101843i	0.00839985	−	0.0145490i
$50$		0			0
$51$	12.5568	+	4.57029i	1.75830	+	0.639968i
$52$	−4.44962	−	0.784587i	−0.617051	−	0.108803i
$53$	−13.0140	+	2.29471i	−1.78761	+	0.315203i	−0.966710	−	0.255874i	$-0.917637\pi$
$53$	−13.0140	+	2.29471i	−1.78761	+	0.315203i	−0.820896	+	0.571077i	$0.806526\pi$
$54$	−3.61086	+	1.31425i	−0.491376	+	0.178846i
$55$		0			0
$56$	−2.66788			−0.356511
$57$	−10.4495	+	5.62377i	−1.38407	+	0.744886i
$58$			0.296532i			0.0389366i
$59$	9.63183	+	8.08206i	1.25396	+	1.05220i	0.996299	+	0.0859593i	$0.0273955\pi$
$59$	9.63183	+	8.08206i	1.25396	+	1.05220i	0.257659	+	0.966236i	$0.417049\pi$
$60$		0			0
$61$	−0.806491	−	4.57384i	−0.103261	−	0.585620i	−0.991901	−	0.127015i	$-0.959460\pi$
$61$	−0.806491	−	4.57384i	−0.103261	−	0.585620i	0.888640	−	0.458605i	$-0.151651\pi$
$62$	6.17664	+	1.08911i	0.784434	+	0.138317i
$63$	−4.02534	+	11.0595i	−0.507145	+	1.39337i
$64$	0.500000	+	0.866025i	0.0625000	+	0.108253i
$65$		0			0
$66$	10.2733	−	8.62036i	1.26456	−	1.06109i
$67$	−6.27533	−	7.47864i	−0.766653	−	0.913662i	0.231596	−	0.972812i	$-0.425605\pi$
$67$	−6.27533	−	7.47864i	−0.766653	−	0.913662i	−0.998249	+	0.0591504i	$0.981161\pi$
$68$	−4.25079	−	2.45420i	−0.515485	−	0.297615i
$69$	−4.25432	−	7.36870i	−0.512160	−	0.887088i
$70$		0			0
$71$	0.702893	−	3.98630i	0.0834180	−	0.473087i	−0.914269	−	0.405108i	$-0.867234\pi$
$71$	0.702893	−	3.98630i	0.0834180	−	0.473087i	0.997687	−	0.0679789i	$-0.0216551\pi$
$72$	4.34445	−	0.766044i	0.511999	−	0.0902792i
$73$	−1.62245	−	4.45766i	−0.189894	−	0.521729i	0.807811	−	0.589442i	$-0.200652\pi$
$73$	−1.62245	−	4.45766i	−0.189894	−	0.521729i	−0.997705	+	0.0677123i	$0.978430\pi$
$74$	6.74078	+	5.65618i	0.783599	+	0.657518i
$75$		0			0
$76$	4.13872	−	1.36784i	0.474744	−	0.156901i
$77$		−	13.1423i		−	1.49771i
$78$	7.90662	−	9.42274i	0.895248	−	1.06692i
$79$	0.708572	−	0.257899i	0.0797206	−	0.0290159i	−0.301852	−	0.953355i	$-0.597605\pi$
$79$	0.708572	−	0.257899i	0.0797206	−	0.0290159i	0.381573	+	0.924339i	$0.375383\pi$
$80$		0			0
$81$	−0.481582	+	2.73119i	−0.0535091	+	0.303465i
$82$	−2.60414	+	7.15482i	−0.287579	+	0.790118i
$83$	9.57249	−	5.52668i	1.05072	−	0.606632i	0.127868	−	0.991791i	$-0.459187\pi$
$83$	9.57249	−	5.52668i	1.05072	−	0.606632i	0.922850	+	0.385159i	$0.125853\pi$
$84$	3.63152	−	6.28999i	0.396232	−	0.686294i
$85$		0			0
$86$	−2.33339	+	1.95795i	−0.251616	+	0.211131i
$87$	−0.699125	−	0.403640i	−0.0749541	−	0.0432747i
$88$	−4.26615	+	2.46306i	−0.454773	+	0.262564i
$89$	7.44939	+	2.71136i	0.789634	+	0.287403i	0.705184	−	0.709024i	$-0.250864\pi$
$89$	7.44939	+	2.71136i	0.789634	+	0.287403i	0.0844501	+	0.996428i	$0.473087\pi$
$90$		0			0
$91$	−2.09319	−	11.8711i	−0.219426	−	1.24442i
$92$	1.06896	+	2.93693i	0.111446	+	0.306196i
$93$	−10.9754	+	13.0800i	−1.13810	+	1.35633i
$94$	−2.25866			−0.232963
$95$		0			0
$96$	−2.72240			−0.277854
$97$	−4.57554	+	5.45292i	−0.464576	+	0.553660i	−0.946563	−	0.322518i	$-0.895471\pi$
$97$	−4.57554	+	5.45292i	−0.464576	+	0.553660i	0.481987	+	0.876178i	$0.339915\pi$
$98$	−0.0402208	−	0.110506i	−0.00406292	−	0.0111628i
$99$	3.77363	+	21.4013i	0.379264	+	2.15092i
$100$		0			0
$101$	5.98456	+	2.17820i	0.595486	+	0.216739i	0.622141	−	0.782906i	$-0.286263\pi$
$101$	5.98456	+	2.17820i	0.595486	+	0.216739i	−0.0266547	+	0.999645i	$0.508485\pi$
$102$	11.5724	−	6.68131i	1.14584	−	0.661548i
$103$	6.97792	+	4.02870i	0.687555	+	0.396960i	0.802695	−	0.596389i	$-0.203399\pi$
$103$	6.97792	+	4.02870i	0.687555	+	0.396960i	−0.115141	+	0.993349i	$0.536732\pi$
$104$	−3.46119	+	2.90428i	−0.339397	+	0.284788i
$105$		0			0
$106$	−6.60737	+	11.4443i	−0.641764	+	1.11157i
$107$	−5.27279	+	3.04424i	−0.509739	+	0.294298i	−0.732727	−	0.680523i	$-0.761753\pi$
$107$	−5.27279	+	3.04424i	−0.509739	+	0.294298i	0.222987	+	0.974821i	$0.428419\pi$
$108$	−1.31425	+	3.61086i	−0.126463	+	0.347455i
$109$	−1.52473	+	8.64718i	−0.146043	+	0.828250i	0.820481	+	0.571673i	$0.193706\pi$
$109$	−1.52473	+	8.64718i	−0.146043	+	0.828250i	−0.966524	+	0.256576i	$0.917406\pi$
$110$		0			0
$111$	−22.5110	+	8.19332i	−2.13665	+	0.777676i
$112$	−1.71488	+	2.04372i	−0.162041	+	0.193113i
$113$		−	20.1754i		−	1.89794i	−0.315364	−	0.948971i	$-0.602127\pi$
$113$		−	20.1754i		−	1.89794i	0.315364	−	0.948971i	$-0.397873\pi$
$114$	−2.40873	+	11.6196i	−0.225598	+	1.08828i
$115$		0			0
$116$	0.227157	+	0.190607i	0.0210910	+	0.0176974i
$117$	6.81721	+	18.7301i	0.630251	+	1.73160i
$118$	12.3824	−	2.18336i	1.13990	−	0.200994i
$119$	2.27393	−	12.8961i	0.208450	−	1.18218i
$120$		0			0
$121$	−6.63337	−	11.4893i	−0.603034	−	1.04449i
$122$	−4.02216	−	2.32220i	−0.364150	−	0.210242i
$123$	−13.3239	−	15.8789i	−1.20138	−	1.43175i
$124$	4.80457	−	4.03152i	0.431463	−	0.362041i
$125$		0			0
$126$	5.88465	+	10.1925i	0.524246	+	0.908021i
$127$	2.19220	−	6.02301i	0.194526	−	0.534456i	−0.803632	−	0.595127i	$-0.797102\pi$
$127$	2.19220	−	6.02301i	0.194526	−	0.534456i	0.998158	+	0.0606709i	$0.0193240\pi$
$128$	0.984808	+	0.173648i	0.0870455	+	0.0153485i
$129$	−1.43998	−	8.16653i	−0.126783	−	0.719023i
$130$		0			0
$131$	10.6297	+	8.91940i	0.928723	+	0.779291i	0.975588	−	0.219610i	$-0.0704785\pi$
$131$	10.6297	+	8.91940i	0.928723	+	0.779291i	−0.0468646	+	0.998901i	$0.514923\pi$
$132$		−	13.4109i		−	1.16727i
$133$	7.20561	+	9.12763i	0.624805	+	0.791466i
$134$	−9.76267			−0.843367
$135$		0			0
$136$	−4.61238	+	1.67877i	−0.395509	+	0.143953i
$137$	13.9723	−	2.46370i	1.19374	−	0.210488i	0.458747	−	0.888567i	$-0.348299\pi$
$137$	13.9723	−	2.46370i	1.19374	−	0.210488i	0.734989	+	0.678079i	$0.237187\pi$
$138$	−8.37938	−	1.47751i	−0.713300	−	0.125774i
$139$	−18.8253	−	6.85185i	−1.59674	−	0.581167i	−0.617985	−	0.786190i	$-0.712051\pi$
$139$	−18.8253	−	6.85185i	−1.59674	−	0.581167i	−0.978757	+	0.205023i	$0.934273\pi$
$140$		0			0
$141$	3.07450	−	5.32518i	0.258919	−	0.448461i
$142$	−2.60188	−	3.10079i	−0.218345	−	0.260213i
$143$	−14.3069	−	17.0503i	−1.19640	−	1.42581i
$144$	2.20574	−	3.82045i	0.183811	−	0.318371i
$145$		0			0
$146$	−4.45766	−	1.62245i	−0.368918	−	0.134275i
$147$	0.315285	+	0.0555932i	0.0260043	+	0.00458525i
$148$	8.66578	−	1.52801i	0.712322	−	0.125602i
$149$	−4.21077	+	1.53259i	−0.344959	+	0.125555i	−0.508689	−	0.860950i	$-0.669870\pi$
$149$	−4.21077	+	1.53259i	−0.344959	+	0.125555i	0.163730	+	0.986505i	$0.447647\pi$
$150$		0			0
$151$	−13.9346			−1.13398			−0.566990	−	0.823724i	$-0.691892\pi$
$151$	−13.9346			−1.13398			−0.566990	+	0.823724i	$0.691892\pi$
$152$	1.61250	−	4.04967i	0.130791	−	0.328472i
$153$			21.6533i			1.75056i
$154$	−10.0676	−	8.44773i	−0.811271	−	0.680737i
$155$		0			0
$156$	−2.13596	−	12.1136i	−0.171014	−	0.969868i
$157$	7.07915	+	1.24825i	0.564978	+	0.0996209i	0.448840	−	0.893612i	$-0.351837\pi$
$157$	7.07915	+	1.24825i	0.564978	+	0.0996209i	0.116138	+	0.993233i	$0.462948\pi$
$158$	0.257899	−	0.708572i	0.0205174	−	0.0563710i
$159$	−17.9879	−	31.1560i	−1.42653	−	2.47083i
$160$		0			0
$161$	−6.38747	+	5.35972i	−0.503403	+	0.422405i
$162$	1.78265	+	2.12449i	0.140059	+	0.166915i
$163$	−1.38414	−	0.799136i	−0.108415	−	0.0625932i	0.444812	−	0.895624i	$-0.353270\pi$
$163$	−1.38414	−	0.799136i	−0.108415	−	0.0625932i	−0.553227	+	0.833031i	$0.686604\pi$
$164$	3.80700	+	6.59392i	0.297277	+	0.514899i
$165$		0			0
$166$	1.91940	−	10.8854i	0.148974	−	0.844874i
$167$	−8.27409	+	1.45895i	−0.640268	+	0.112897i	−0.484351	−	0.874874i	$-0.660944\pi$
$167$	−8.27409	+	1.45895i	−0.640268	+	0.112897i	−0.155917	+	0.987770i	$0.549833\pi$
$168$	−2.48411	−	6.82503i	−0.191653	−	0.526563i
$169$	−5.67996	−	4.76605i	−0.436920	−	0.366619i
$170$		0			0
$171$	−14.3547	−	12.7947i	−1.09773	−	0.978435i
$172$			3.04603i			0.232257i
$173$	5.54431	−	6.60745i	0.421526	−	0.502355i	−0.512932	−	0.858429i	$-0.671441\pi$
$173$	5.54431	−	6.60745i	0.421526	−	0.502355i	0.934458	+	0.356075i	$0.115885\pi$
$174$	−0.758595	+	0.276106i	−0.0575089	+	0.0209315i
$175$		0			0
$176$	−0.855413	+	4.85129i	−0.0644792	+	0.365680i
$177$	−11.7074	+	32.1657i	−0.879979	+	2.41772i
$178$	6.86540	−	3.96374i	0.514583	−	0.297095i
$179$	2.68184	−	4.64508i	0.200450	−	0.347189i	−0.748224	−	0.663447i	$-0.769093\pi$
$179$	2.68184	−	4.64508i	0.200450	−	0.347189i	0.948673	+	0.316257i	$0.102426\pi$
$180$		0			0
$181$	−16.2127	+	13.6041i	−1.20508	+	1.01119i	−0.205614	+	0.978633i	$0.565919\pi$
$181$	−16.2127	+	13.6041i	−1.20508	+	1.01119i	−0.999470	+	0.0325524i	$0.989636\pi$
$182$	−10.4392	−	6.02709i	−0.773807	−	0.446758i
$183$	10.9499	−	6.32195i	0.809443	−	0.467332i
$184$	2.93693	+	1.06896i	0.216514	+	0.0788045i
$185$		0			0
$186$	2.96499	+	16.8153i	0.217404	+	1.23296i
$187$	−8.26984	−	22.7212i	−0.604750	−	1.66154i
$188$	−1.45184	+	1.73024i	−0.105886	+	0.126190i
$189$	−10.2516			−0.745695
$190$		0			0
$191$	−14.9062			−1.07858			−0.539288	−	0.842121i	$-0.681307\pi$
$191$	−14.9062			−1.07858			−0.539288	+	0.842121i	$0.681307\pi$
$192$	−1.74993	+	2.08548i	−0.126290	+	0.150507i
$193$	7.86461	+	21.6078i	0.566107	+	1.55537i	0.810530	+	0.585697i	$0.199179\pi$
$193$	7.86461	+	21.6078i	0.566107	+	1.55537i	−0.244423	+	0.969669i	$0.578598\pi$
$194$	1.23608	+	7.01014i	0.0887451	+	0.503299i
$195$		0			0
$196$	−0.110506	−	0.0402208i	−0.00789328	−	0.00287292i
$197$	−12.3336	+	7.12078i	−0.878729	+	0.507335i	−0.870239	−	0.492629i	$-0.836036\pi$
$197$	−12.3336	+	7.12078i	−0.878729	+	0.507335i	−0.00849002	+	0.999964i	$0.502702\pi$
$198$	18.8200	+	10.8657i	1.33748	+	0.772195i
$199$	−0.828568	+	0.695251i	−0.0587356	+	0.0492850i	−0.671683	−	0.740839i	$-0.734428\pi$
$199$	−0.828568	+	0.695251i	−0.0587356	+	0.0492850i	0.612947	+	0.790124i	$0.289984\pi$
$200$		0			0
$201$	13.2890	−	23.0172i	0.937331	−	1.62351i
$202$	5.51540	−	3.18432i	0.388062	−	0.224048i
$203$	−0.270577	+	0.743403i	−0.0189908	+	0.0521767i
$204$	2.32040	−	13.1596i	0.162460	−	0.921357i
$205$		0			0
$206$	7.57148	−	2.75579i	0.527530	−	0.192005i
$207$	8.86256	−	10.5620i	0.615991	−	0.734109i
$208$			4.51826i			0.313285i
$209$	19.9492	+	7.94337i	1.37992	+	0.549454i
$210$		0			0
$211$	19.4619	+	16.3305i	1.33981	+	1.12424i	0.981674	+	0.190566i	$0.0610323\pi$
$211$	19.4619	+	16.3305i	1.33981	+	1.12424i	0.358137	+	0.933669i	$0.383412\pi$
$212$	4.51971	+	12.4178i	0.310415	+	0.852857i
$213$	10.8523	−	1.91356i	0.743589	−	0.131115i
$214$	−1.05725	+	5.99599i	−0.0722725	+	0.409877i
$215$		0			0
$216$	1.92130	+	3.32779i	0.130728	+	0.226427i
$217$	14.4910	+	8.36638i	0.983713	+	0.567947i
$218$	5.64405	+	6.72631i	0.382263	+	0.455563i
$219$	9.89298	−	8.30120i	0.668506	−	0.560943i
$220$		0			0
$221$	−11.0887	−	19.2062i	−0.745907	−	1.29195i
$222$	−8.19332	+	22.5110i	−0.549900	+	1.51084i
$223$	−26.6797	−	4.70436i	−1.78661	−	0.315027i	−0.820207	−	0.572067i	$-0.806142\pi$
$223$	−26.6797	−	4.70436i	−1.78661	−	0.315027i	−0.966401	+	0.257040i	$0.917253\pi$
$224$	0.463273	+	2.62735i	0.0309537	+	0.175547i
$225$		0			0
$226$	−15.4552	−	12.9685i	−1.02807	−	0.862651i
$227$		−	2.74631i		−	0.182279i	−0.995838	−	0.0911394i	$-0.970949\pi$
$227$		−	2.74631i		−	0.182279i	0.995838	−	0.0911394i	$-0.0290509\pi$
$228$	7.35286	+	9.31416i	0.486955	+	0.616845i
$229$	−18.3269			−1.21107			−0.605537	−	0.795817i	$-0.707042\pi$
$229$	−18.3269			−1.21107			−0.605537	+	0.795817i	$0.707042\pi$
$230$		0			0
$231$	33.6210	−	12.2370i	2.21210	−	0.805138i
$232$	0.292027	−	0.0514923i	0.0191725	−	0.00338063i
$233$	5.65161	+	0.996532i	0.370250	+	0.0652850i	0.355677	−	0.934609i	$-0.384250\pi$
$233$	5.65161	+	0.996532i	0.370250	+	0.0652850i	0.0145723	+	0.999894i	$0.495361\pi$
$234$	18.7301	+	6.81721i	1.22443	+	0.445655i
$235$		0			0
$236$	6.28673	−	10.8889i	0.409231	−	0.708809i
$237$	1.31953	+	1.57255i	0.0857124	+	0.102148i
$238$	−8.41732	−	10.0314i	−0.545614	−	0.650237i
$239$	−3.55176	+	6.15182i	−0.229744	+	0.397928i	−0.957732	−	0.287661i	$-0.907122\pi$
$239$	−3.55176	+	6.15182i	−0.229744	+	0.397928i	0.727988	+	0.685590i	$0.240456\pi$
$240$		0			0
$241$	13.4258	+	4.88658i	0.864829	+	0.314772i	0.736071	−	0.676904i	$-0.236679\pi$
$241$	13.4258	+	4.88658i	0.864829	+	0.314772i	0.128758	+	0.991676i	$0.458901\pi$
$242$	−13.0652	−	2.30375i	−0.839863	−	0.148090i
$243$	−18.7881	+	3.31284i	−1.20525	+	0.212519i
$244$	−4.36430	+	1.58848i	−0.279396	+	0.101692i
$245$		0			0
$246$	−20.7284			−1.32159
$247$	19.2846	+	3.99767i	1.22705	+	0.254366i
$248$		−	6.27192i		−	0.398268i
$249$	23.0516	+	19.3426i	1.46083	+	1.22579i
$250$		0			0
$251$	1.01488	+	5.75569i	0.0640589	+	0.363296i	0.999940	+	0.0109793i	$0.00349489\pi$
$251$	1.01488	+	5.75569i	0.0640589	+	0.363296i	−0.935881	+	0.352317i	$0.885394\pi$
$252$	11.5905	+	2.04372i	0.730132	+	0.128742i
$253$	−5.26581	+	14.4677i	−0.331059	+	0.909577i
$254$	−3.20478	−	5.55084i	−0.201086	−	0.348291i
$255$		0			0
$256$	0.766044	−	0.642788i	0.0478778	−	0.0401742i
$257$	−11.6659	−	13.9029i	−0.727700	−	0.867239i	0.267655	−	0.963515i	$-0.413751\pi$
$257$	−11.6659	−	13.9029i	−0.727700	−	0.867239i	−0.995355	+	0.0962757i	$0.969307\pi$
$258$	−7.18152	−	4.14625i	−0.447102	−	0.258135i
$259$	11.7380	+	20.3307i	0.729362	+	1.26329i
$260$		0			0
$261$	0.227157	−	1.28827i	0.0140607	−	0.0797419i
$262$	13.6653	−	2.40956i	0.844245	−	0.148863i
$263$	−4.72850	−	12.9914i	−0.291572	−	0.801087i	−0.995837	−	0.0911502i	$-0.970946\pi$
$263$	−4.72850	−	12.9914i	−0.291572	−	0.801087i	0.704265	−	0.709937i	$-0.251277\pi$
$264$	−10.2733	−	8.62036i	−0.632281	−	0.530547i
$265$		0			0
$266$	11.6238	+	0.347310i	0.712704	+	0.0212950i
$267$			21.5818i			1.32078i
$268$	−6.27533	+	7.47864i	−0.383327	+	0.456831i
$269$	−6.31020	+	2.29673i	−0.384740	+	0.140034i	−0.527147	−	0.849774i	$-0.676738\pi$
$269$	−6.31020	+	2.29673i	−0.384740	+	0.140034i	0.142407	+	0.989808i	$0.454516\pi$
$270$		0			0
$271$	−0.0177021	+	0.100393i	−0.00107532	+	0.00609847i	−0.985341	−	0.170598i	$-0.945430\pi$
$271$	−0.0177021	+	0.100393i	−0.00107532	+	0.00609847i	0.984265	+	0.176697i	$0.0565411\pi$
$272$	−1.67877	+	4.61238i	−0.101790	+	0.279667i
$273$	28.4198	−	16.4082i	1.72004	−	0.993068i
$274$	7.09393	−	12.2870i	0.428560	−	0.742288i
$275$		0			0
$276$	−6.51800	+	5.46925i	−0.392338	+	0.329210i
$277$	9.56705	+	5.52354i	0.574829	+	0.331877i	0.759076	−	0.651003i	$-0.225651\pi$
$277$	9.56705	+	5.52354i	0.574829	+	0.331877i	−0.184247	+	0.982880i	$0.558985\pi$
$278$	−17.3495	+	10.0167i	−1.04055	+	0.600764i
$279$	−25.9998	−	9.46316i	−1.55657	−	0.566545i
$280$		0			0
$281$	4.20063	+	23.8230i	0.250589	+	1.42116i	0.807147	+	0.590350i	$0.201010\pi$
$281$	4.20063	+	23.8230i	0.250589	+	1.42116i	−0.556559	+	0.830808i	$0.687879\pi$
$282$	−2.10308	−	5.77816i	−0.125236	−	0.344084i
$283$	4.77703	−	5.69304i	0.283965	−	0.338416i	−0.605141	−	0.796119i	$-0.706883\pi$
$283$	4.77703	−	5.69304i	0.283965	−	0.338416i	0.889105	+	0.457703i	$0.151328\pi$
$284$	−4.04780			−0.240193
$285$		0			0
$286$	−22.2575			−1.31612
$287$	−13.0571	+	15.5609i	−0.770737	+	0.918529i
$288$	−1.50881	−	4.14543i	−0.0889077	−	0.244272i
$289$	−1.23157	−	6.98459i	−0.0724454	−	0.410858i
$290$		0			0
$291$	−18.2101	−	6.62795i	−1.06750	−	0.388537i
$292$	−4.10820	+	2.37187i	−0.240414	+	0.138803i
$293$	2.25716	+	1.30317i	0.131865	+	0.0761322i	0.564481	−	0.825446i	$-0.309076\pi$
$293$	2.25716	+	1.30317i	0.131865	+	0.0761322i	−0.432616	+	0.901578i	$0.642410\pi$
$294$	0.245248	−	0.205788i	0.0143032	−	0.0120018i
$295$		0			0
$296$	4.39973	−	7.62056i	0.255729	−	0.442936i
$297$	−16.3931	+	9.46457i	−0.951225	+	0.549190i
$298$	−1.53259	+	4.21077i	−0.0887807	+	0.243923i
$299$	−2.45216	+	13.9069i	−0.141812	+	0.804257i
$300$		0			0
$301$	−7.63636	+	2.77941i	−0.440152	+	0.160202i
$302$	−8.95698	+	10.6745i	−0.515416	+	0.614249i
$303$			17.3380i			0.996041i
$304$	−2.06574	−	3.83832i	−0.118478	−	0.220143i
$305$		0			0
$306$	16.5874	+	13.9184i	0.948236	+	0.795665i
$307$	2.96206	+	8.13819i	0.169054	+	0.464471i	0.995070	−	0.0991751i	$-0.0316204\pi$
$307$	2.96206	+	8.13819i	0.169054	+	0.464471i	−0.826016	+	0.563646i	$0.809398\pi$
$308$	−12.9427	+	2.28214i	−0.737477	+	0.130037i
$309$	−3.80906	+	21.6022i	−0.216690	+	1.22891i
$310$		0			0
$311$	−13.7098	−	23.7461i	−0.777414	−	1.34652i	−0.933428	−	0.358765i	$-0.883198\pi$
$311$	−13.7098	−	23.7461i	−0.777414	−	1.34652i	0.156014	−	0.987755i	$-0.450135\pi$
$312$	−10.6526	−	6.15026i	−0.603082	−	0.348190i
$313$	17.1355	+	20.4213i	0.968557	+	1.15428i	0.987997	+	0.154470i	$0.0493671\pi$
$313$	17.1355	+	20.4213i	0.968557	+	1.15428i	−0.0194404	+	0.999811i	$0.506188\pi$
$314$	5.50660	−	4.62059i	0.310756	−	0.260755i
$315$		0			0
$316$	−0.377023	−	0.653023i	−0.0212092	−	0.0367354i
$317$	7.23957	−	19.8906i	0.406615	−	1.11717i	−0.552343	−	0.833617i	$-0.686266\pi$
$317$	7.23957	−	19.8906i	0.406615	−	1.11717i	0.958958	−	0.283548i	$-0.0915116\pi$
$318$	−35.4293	−	6.24714i	−1.98677	−	0.350322i
$319$	0.253658	+	1.43856i	0.0142021	+	0.0805441i
$320$		0			0
$321$	−12.6974	−	10.6544i	−0.708701	−	0.594671i
$322$			8.33825i			0.464672i
$323$	18.2010	+	11.2462i	1.01273	+	0.625755i
$324$	2.77332			0.154073
$325$		0			0
$326$	−1.50188	+	0.546641i	−0.0831817	+	0.0302757i
$327$	−23.5411	+	4.15093i	−1.30183	+	0.229547i
$328$	7.49833	+	1.32216i	0.414026	+	0.0730039i
$329$	−5.66245	−	2.06096i	−0.312181	−	0.113624i
$330$		0			0
$331$	1.38851	−	2.40497i	0.0763195	−	0.132189i	−0.825340	−	0.564636i	$-0.809016\pi$
$331$	1.38851	−	2.40497i	0.0763195	−	0.132189i	0.901659	+	0.432447i	$0.142350\pi$
$332$	−7.10497	−	8.46737i	−0.389936	−	0.464707i
$333$	−24.9521	−	29.7368i	−1.36737	−	1.62956i
$334$	−4.20086	+	7.27611i	−0.229861	+	0.398131i
$335$		0			0
$336$	−6.82503	−	2.48411i	−0.372336	−	0.135519i
$337$	2.21538	+	0.390631i	0.120679	+	0.0212791i	0.233662	−	0.972318i	$-0.424929\pi$
$337$	2.21538	+	0.390631i	0.120679	+	0.0212791i	−0.112982	+	0.993597i	$0.536040\pi$
$338$	−7.30202	+	1.28754i	−0.397177	+	0.0700331i
$339$	51.6131	−	18.7856i	2.80324	−	1.02030i
$340$		0			0
$341$	30.8963			1.67313
$342$	−19.0283	+	2.77205i	−1.02893	+	0.149895i
$343$			18.3614i			0.991425i
$344$	2.33339	+	1.95795i	0.125808	+	0.105565i
$345$		0			0
$346$	−1.49779	−	8.49437i	−0.0805215	−	0.456660i
$347$	−19.8767	−	3.50481i	−1.06704	−	0.188148i	−0.387561	−	0.921844i	$-0.626683\pi$
$347$	−19.8767	−	3.50481i	−1.06704	−	0.188148i	−0.679478	+	0.733696i	$0.737794\pi$
$348$	−0.276106	+	0.758595i	−0.0148008	+	0.0406650i
$349$	11.1094	+	19.2421i	0.594673	+	1.03000i	0.993593	+	0.113018i	$0.0360517\pi$
$349$	11.1094	+	19.2421i	0.594673	+	1.03000i	−0.398920	+	0.916986i	$0.630615\pi$
$350$		0			0
$351$	−13.3000	+	11.1600i	−0.709899	+	0.595676i
$352$	3.16645	+	3.77363i	0.168773	+	0.201135i
$353$	2.66564	+	1.53901i	0.141878	+	0.0819130i	0.569259	−	0.822159i	$-0.307230\pi$
$353$	2.66564	+	1.53901i	0.141878	+	0.0819130i	−0.427381	+	0.904072i	$0.640564\pi$
$354$	17.1150	+	29.6441i	0.909652	+	1.57556i
$355$		0			0
$356$	1.37659	−	7.80704i	0.0729592	−	0.413772i
$357$	35.1083	−	6.19054i	1.85813	−	0.327638i
$358$	−1.83448	−	5.04021i	−0.0969555	−	0.266383i
$359$	−15.6987	−	13.1727i	−0.828543	−	0.695230i	0.126413	−	0.991978i	$-0.459654\pi$
$359$	−15.6987	−	13.1727i	−0.828543	−	0.695230i	−0.954956	+	0.296747i	$0.904098\pi$
$360$		0			0
$361$	−18.2103	+	5.42081i	−0.958437	+	0.285306i
$362$			21.1642i			1.11237i
$363$	23.2158	−	27.6676i	1.21852	−	1.45217i
$364$	−11.3272	+	4.12277i	−0.593708	+	0.216092i
$365$		0			0
$366$	2.19559	−	12.4518i	0.114765	−	0.650867i
$367$	1.26399	−	3.47279i	0.0659798	−	0.181278i	−0.902321	−	0.431064i	$-0.858138\pi$
$367$	1.26399	−	3.47279i	0.0659798	−	0.181278i	0.968301	+	0.249786i	$0.0803604\pi$
$368$	2.70669	−	1.56271i	0.141096	−	0.0814618i
$369$	16.7945	−	29.0889i	0.874286	−	1.51431i
$370$		0			0
$371$	−27.0072	+	22.6617i	−1.40214	+	1.17654i
$372$	14.7871	+	8.53735i	0.766677	+	0.442641i
$373$	4.81387	−	2.77929i	0.249253	−	0.143906i	−0.370169	−	0.928964i	$-0.620700\pi$
$373$	4.81387	−	2.77929i	0.249253	−	0.143906i	0.619422	+	0.785058i	$0.287367\pi$
$374$	−22.7212	−	8.26984i	−1.17488	−	0.427623i
$375$		0			0
$376$	0.392213	+	2.22435i	0.0202268	+	0.114712i
$377$	0.458242	+	1.25901i	0.0236006	+	0.0648422i
$378$	−6.58961	+	7.85319i	−0.338933	+	0.403924i
$379$	−6.50034			−0.333900			−0.166950	−	0.985965i	$-0.553392\pi$
$379$	−6.50034			−0.333900			−0.166950	+	0.985965i	$0.553392\pi$
$380$		0			0
$381$	17.4494			0.893959
$382$	−9.58154	+	11.4188i	−0.490234	+	0.584238i
$383$	−1.83600	−	5.04437i	−0.0938152	−	0.257755i	0.883905	−	0.467666i	$-0.154905\pi$
$383$	−1.83600	−	5.04437i	−0.0938152	−	0.257755i	−0.977721	+	0.209911i	$0.932683\pi$
$384$	0.472740	+	2.68104i	0.0241244	+	0.136816i
$385$		0			0
$386$	21.6078	+	7.86461i	1.09981	+	0.400298i
$387$	11.6372	−	6.71873i	0.591551	−	0.341532i
$388$	6.16461	+	3.55914i	0.312961	+	0.180688i
$389$	−6.23034	+	5.22788i	−0.315891	+	0.265064i	−0.786922	−	0.617053i	$-0.788326\pi$
$389$	−6.23034	+	5.22788i	−0.315891	+	0.265064i	0.471031	+	0.882117i	$0.343882\pi$
$390$		0			0
$391$	−7.67039	+	13.2855i	−0.387908	+	0.671877i
$392$	−0.101843	+	0.0587989i	−0.00514384	+	0.00296979i
$393$	−12.9203	+	35.4982i	−0.651742	+	1.79065i
$394$	−2.47302	+	14.0252i	−0.124589	+	0.706579i
$395$		0			0
$396$	20.4209	−	7.43261i	1.02619	−	0.373503i
$397$	12.3067	−	14.6665i	0.617654	−	0.736091i	−0.363012	−	0.931785i	$-0.618251\pi$
$397$	12.3067	−	14.6665i	0.617654	−	0.736091i	0.980665	+	0.195694i	$0.0626959\pi$
$398$			1.08162i			0.0542167i
$399$	−16.6412	+	26.9324i	−0.833104	+	1.34831i
$400$		0			0
$401$	−14.4187	−	12.0987i	−0.720035	−	0.604181i	0.207360	−	0.978265i	$-0.433513\pi$
$401$	−14.4187	−	12.0987i	−0.720035	−	0.604181i	−0.927395	+	0.374084i	$0.877957\pi$
$402$	−9.09019	−	24.9751i	−0.453377	−	1.24564i
$403$	27.9077	−	4.92087i	1.39018	−	0.245126i
$404$	1.10590	−	6.27188i	0.0550207	−	0.312038i
$405$		0			0
$406$	0.395557	+	0.685124i	0.0196311	+	0.0340021i
$407$	37.5398	+	21.6736i	1.86078	+	1.07432i
$408$	−8.58933	−	10.2364i	−0.425235	−	0.506776i
$409$	−17.0844	+	14.3355i	−0.844769	+	0.708845i	−0.958631	−	0.284651i	$-0.908122\pi$
$409$	−17.0844	+	14.3355i	−0.844769	+	0.708845i	0.113862	+	0.993497i	$0.463678\pi$
$410$		0			0
$411$	19.3125	+	33.4503i	0.952617	+	1.64998i
$412$	2.75579	−	7.57148i	0.135768	−	0.373020i
$413$	33.0349	+	5.82494i	1.62554	+	0.286627i
$414$	−2.39421	−	13.5782i	−0.117669	−	0.667334i
$415$		0			0
$416$	3.46119	+	2.90428i	0.169699	+	0.142394i
$417$		−	54.5392i		−	2.67080i
$418$	18.9081	−	10.1761i	0.924825	−	0.497729i
$419$	6.32056			0.308780			0.154390	−	0.988010i	$-0.450659\pi$
$419$	6.32056			0.308780			0.154390	+	0.988010i	$0.450659\pi$
$420$		0			0
$421$	26.4030	−	9.60989i	1.28680	−	0.468358i	0.394126	−	0.919056i	$-0.371047\pi$
$421$	26.4030	−	9.60989i	1.28680	−	0.468358i	0.892676	+	0.450699i	$0.148825\pi$
$422$	25.0197	−	4.41165i	1.21794	−	0.214756i
$423$	9.81266	+	1.73024i	0.477108	+	0.0841270i
$424$	12.4178	+	4.51971i	0.603061	+	0.219496i
$425$		0			0
$426$	5.50987	−	9.54337i	0.266954	−	0.462378i
$427$	−7.96459	−	9.49183i	−0.385433	−	0.459342i
$428$	3.91360	+	4.66405i	0.189171	+	0.225445i
$429$	30.2970	−	52.4759i	1.46275	−	2.53356i
$430$		0			0
$431$	32.4448	+	11.8089i	1.56281	+	0.568817i	0.971378	−	0.237538i	$-0.0763405\pi$
$431$	32.4448	+	11.8089i	1.56281	+	0.568817i	0.591432	+	0.806355i	$0.298563\pi$
$432$	3.78422	+	0.667261i	0.182068	+	0.0321036i
$433$	−9.45404	+	1.66700i	−0.454332	+	0.0801110i	−0.396131	−	0.918194i	$-0.629647\pi$
$433$	−9.45404	+	1.66700i	−0.454332	+	0.0801110i	−0.0582009	+	0.998305i	$0.518536\pi$
$434$	15.7237	−	5.72294i	0.754759	−	0.274710i
$435$		0			0
$436$	8.78058			0.420513
$437$	−4.27506	−	12.9352i	−0.204504	−	0.618776i
$438$		−	12.9144i		−	0.617072i
$439$	−7.13348	−	5.98570i	−0.340462	−	0.285682i	0.456484	−	0.889731i	$-0.349108\pi$
$439$	−7.13348	−	5.98570i	−0.340462	−	0.285682i	−0.796947	+	0.604050i	$0.793553\pi$
$440$		0			0
$441$	0.0900852	+	0.510899i	0.00428977	+	0.0243285i
$442$	−21.8405	−	3.85106i	−1.03885	−	0.183176i
$443$	11.4563	−	31.4760i	0.544307	−	1.49547i	−0.296980	−	0.954884i	$-0.595979\pi$
$443$	11.4563	−	31.4760i	0.544307	−	1.49547i	0.841287	−	0.540588i	$-0.181798\pi$
$444$	11.9778	+	20.7462i	0.568443	+	0.984572i
$445$		0			0
$446$	−20.7532	+	17.4140i	−0.982690	+	0.824575i
$447$	−7.84143	−	9.34505i	−0.370887	−	0.442006i
$448$	2.31045	+	1.33394i	0.109159	+	0.0630228i
$449$	1.10835	+	1.91973i	0.0523064	+	0.0905974i	0.890993	−	0.454017i	$-0.150009\pi$
$449$	1.10835	+	1.91973i	0.0523064	+	0.0905974i	−0.838687	+	0.544614i	$0.816676\pi$
$450$		0			0
$451$	−6.51312	+	36.9377i	−0.306691	+	1.73933i
$452$	−19.8689	+	3.50342i	−0.934554	+	0.164787i
$453$	−12.9747	−	35.6478i	−0.609606	−	1.67488i
$454$	−2.10379	−	1.76529i	−0.0987359	−	0.0828493i
$455$		0			0
$456$	11.8614	+	0.354408i	0.555460	+	0.0165967i
$457$		−	14.3375i		−	0.670680i	−0.942097	−	0.335340i	$-0.891149\pi$
$457$		−	14.3375i		−	0.670680i	0.942097	−	0.335340i	$-0.108851\pi$
$458$	−11.7803	+	14.0392i	−0.550457	+	0.656009i
$459$	−17.7235	+	6.45084i	−0.827264	+	0.301099i
$460$		0			0
$461$	1.67669	−	9.50899i	0.0780913	−	0.442878i	−0.920543	−	0.390640i	$-0.872254\pi$
$461$	1.67669	−	9.50899i	0.0780913	−	0.442878i	0.998635	−	0.0522375i	$-0.0166353\pi$
$462$	12.2370	−	33.6210i	0.569319	−	1.56419i
$463$	−26.7649	+	15.4527i	−1.24387	+	0.718148i	−0.969880	−	0.243585i	$-0.921677\pi$
$463$	−26.7649	+	15.4527i	−1.24387	+	0.718148i	−0.273989	+	0.961733i	$0.588343\pi$
$464$	0.148266	−	0.256804i	0.00688308	−	0.0119218i
$465$		0			0
$466$	4.39618	−	3.68883i	0.203649	−	0.170882i
$467$	−5.41613	−	3.12701i	−0.250629	−	0.144701i	0.369423	−	0.929261i	$-0.379555\pi$
$467$	−5.41613	−	3.12701i	−0.250629	−	0.144701i	−0.620052	+	0.784561i	$0.712889\pi$
$468$	17.2618	−	9.96609i	0.797926	−	0.460683i
$469$	−24.4749	−	8.90814i	−1.13015	−	0.411340i
$470$		0			0
$471$	3.39823	+	19.2723i	0.156582	+	0.888021i
$472$	−4.30038	−	11.8152i	−0.197941	−	0.543838i
$473$	−9.64510	+	11.4946i	−0.443482	+	0.528522i
$474$	2.05282			0.0942891
$475$		0			0
$476$	−13.0950			−0.600209
$477$	37.4722	−	44.6577i	1.71574	−	2.04473i
$478$	2.42955	+	6.67512i	0.111125	+	0.305313i
$479$	−5.92188	−	33.5846i	−0.270578	−	1.53452i	−0.752668	−	0.658400i	$-0.771234\pi$
$479$	−5.92188	−	33.5846i	−0.270578	−	1.53452i	0.482091	−	0.876121i	$-0.339878\pi$
$480$		0			0
$481$	37.3605	+	13.5981i	1.70349	+	0.620021i
$482$	12.3732	−	7.14370i	0.563586	−	0.325387i
$483$	−19.6588	−	11.3500i	−0.894508	−	0.516444i
$484$	−10.1629	+	8.52770i	−0.461951	+	0.387623i
$485$		0			0
$486$	−9.53894	+	16.5219i	−0.432695	+	0.749450i
$487$	−14.4281	+	8.33010i	−0.653802	+	0.377473i	−0.789911	−	0.613221i	$-0.789873\pi$
$487$	−14.4281	+	8.33010i	−0.653802	+	0.377473i	0.136109	+	0.990694i	$0.456540\pi$
$488$	−1.58848	+	4.36430i	−0.0719069	+	0.197563i
$489$	0.755567	−	4.28504i	0.0341679	−	0.193776i
$490$		0			0
$491$	24.6572	−	8.97450i	1.11277	−	0.405013i	0.280758	−	0.959779i	$-0.409414\pi$
$491$	24.6572	−	8.97450i	1.11277	−	0.405013i	0.832007	+	0.554765i	$0.187192\pi$
$492$	−13.3239	+	15.8789i	−0.600690	+	0.715874i
$493$			1.45550i			0.0655523i
$494$	15.4583	−	12.2032i	0.695503	−	0.549049i
$495$		0			0
$496$	−4.80457	−	4.03152i	−0.215732	−	0.181020i
$497$	−3.69349	−	10.1478i	−0.165676	−	0.455191i
$498$	29.6345	−	5.22537i	1.32796	−	0.234154i
$499$	3.75717	−	21.3080i	0.168194	−	0.953877i	−0.777515	−	0.628864i	$-0.783520\pi$
$499$	3.75717	−	21.3080i	0.168194	−	0.953877i	0.945710	−	0.325013i	$-0.105369\pi$
$500$		0			0
$501$	−11.4364	−	19.8085i	−0.510943	−	0.884979i
$502$	5.06147	+	2.92224i	0.225904	+	0.130426i
$503$	−22.2971	−	26.5727i	−0.994179	−	1.18482i	−0.982761	−	0.184882i	$-0.940810\pi$
$503$	−22.2971	−	26.5727i	−0.994179	−	1.18482i	−0.0114181	−	0.999935i	$-0.503635\pi$
$504$	9.01580	−	7.56516i	0.401596	−	0.336979i
$505$		0			0
$506$	7.69811	+	13.3335i	0.342223	+	0.592747i
$507$	6.90391	−	18.9683i	0.306614	−	0.842414i
$508$	−6.31218	−	1.11301i	−0.280058	−	0.0493817i
$509$	−5.08253	−	28.8245i	−0.225279	−	1.27762i	−0.862151	−	0.506652i	$-0.830883\pi$
$509$	−5.08253	−	28.8245i	−0.225279	−	1.27762i	0.636871	−	0.770970i	$-0.280228\pi$
$510$		0			0
$511$	−9.69486	−	8.13495i	−0.428875	−	0.359869i
$512$		−	1.00000i		−	0.0441942i
$513$	6.19618	−	15.5613i	0.273568	−	0.687047i
$514$	−18.1490			−0.800516
$515$		0			0
$516$	−7.79241	+	2.83621i	−0.343042	+	0.124857i
$517$	−10.9574	+	1.93209i	−0.481907	+	0.0849733i
$518$	23.1193	+	4.07655i	1.01580	+	0.179113i
$519$	22.0657	+	8.03126i	0.968577	+	0.352533i
$520$		0			0
$521$	4.30030	−	7.44834i	0.188400	−	0.326318i	−0.756317	−	0.654205i	$-0.773003\pi$
$521$	4.30030	−	7.44834i	0.188400	−	0.326318i	0.944717	+	0.327887i	$0.106337\pi$
$522$	−0.840859	−	1.00210i	−0.0368034	−	0.0438606i
$523$	−10.4413	−	12.4434i	−0.456566	−	0.544114i	0.487824	−	0.872942i	$-0.337791\pi$
$523$	−10.4413	−	12.4434i	−0.456566	−	0.544114i	−0.944390	+	0.328828i	$0.893346\pi$
$524$	6.93806	−	12.0171i	0.303090	−	0.524968i
$525$		0			0
$526$	−12.9914	−	4.72850i	−0.566454	−	0.206172i
$527$	30.3174	+	5.34577i	1.32065	+	0.232866i
$528$	−13.2072	+	2.32878i	−0.574768	+	0.101347i
$529$	−12.4338	+	4.52553i	−0.540600	+	0.196762i
$530$		0			0
$531$	−55.4675			−2.40708
$532$	7.73772	−	8.68113i	0.335473	−	0.376375i
$533$			34.4020i			1.49012i
$534$	16.5326	+	13.8725i	0.715436	+	0.600322i
$535$		0			0
$536$	1.69527	+	9.61436i	0.0732245	+	0.415277i
$537$	14.3802	+	2.53562i	0.620553	+	0.109420i
$538$	−2.29673	+	6.31020i	−0.0990189	+	0.272052i
$539$	−0.289651	−	0.501691i	−0.0124762	−	0.0216093i
$540$		0			0
$541$	20.1240	−	16.8860i	0.865198	−	0.725987i	−0.0978834	−	0.995198i	$-0.531207\pi$
$541$	20.1240	−	16.8860i	0.865198	−	0.725987i	0.963081	+	0.269211i	$0.0867628\pi$
$542$	0.0655272	+	0.0780922i	0.00281463	+	0.00335435i
$543$	−49.8983	−	28.8088i	−2.14134	−	1.23630i
$544$	2.45420	+	4.25079i	0.105223	+	0.182251i
$545$		0			0
$546$	5.69850	−	32.3178i	0.243873	−	1.38307i
$547$	32.4802	−	5.72713i	1.38875	−	0.244874i	0.571239	−	0.820784i	$-0.306463\pi$
$547$	32.4802	−	5.72713i	1.38875	−	0.244874i	0.817513	+	0.575910i	$0.195352\pi$
$548$	−4.85253	−	13.3322i	−0.207290	−	0.569525i
$549$	15.6952	+	13.1698i	0.669855	+	0.562075i
$550$		0			0
$551$	−0.964898	−	0.860039i	−0.0411061	−	0.0366389i
$552$			8.50864i			0.362152i
$553$	1.29310	−	1.54106i	0.0549882	−	0.0655324i
$554$	10.3809	−	3.77832i	0.441041	−	0.160526i
$555$		0			0
$556$	−3.47878	+	19.7291i	−0.147533	+	0.836701i
$557$	3.41346	−	9.37840i	0.144633	−	0.397376i	−0.846131	−	0.532975i	$-0.821074\pi$
$557$	3.41346	−	9.37840i	0.144633	−	0.397376i	0.990764	+	0.135600i	$0.0432961\pi$
$558$	−23.9616	+	13.8342i	−1.01437	+	0.585649i
$559$	−6.88137	+	11.9189i	−0.291051	+	0.504115i
$560$		0			0
$561$	50.4257	−	42.3121i	2.12897	−	1.78642i
$562$	20.9496	+	12.0952i	0.883704	+	0.510207i
$563$	8.85537	−	5.11265i	0.373209	−	0.215472i	−0.301650	−	0.953419i	$-0.597538\pi$
$563$	8.85537	−	5.11265i	0.373209	−	0.215472i	0.674860	+	0.737946i	$0.264204\pi$
$564$	−5.77816	−	2.10308i	−0.243304	−	0.0885556i
$565$		0			0
$566$	−1.29051	−	7.31883i	−0.0542440	−	0.307633i
$567$	2.53057	+	6.95268i	0.106274	+	0.291985i
$568$	−2.60188	+	3.10079i	−0.109172	+	0.130106i
$569$	−4.84333			−0.203043			−0.101521	−	0.994833i	$-0.532371\pi$
$569$	−4.84333			−0.203043			−0.101521	+	0.994833i	$0.532371\pi$
$570$		0			0
$571$	20.7617			0.868850			0.434425	−	0.900708i	$-0.356952\pi$
$571$	20.7617			0.868850			0.434425	+	0.900708i	$0.356952\pi$
$572$	−14.3069	+	17.0503i	−0.598200	+	0.712907i
$573$	−13.8794	−	38.1334i	−0.579822	−	1.59305i
$574$	3.52736	+	20.0047i	0.147229	+	0.834978i
$575$		0			0
$576$	−4.14543	−	1.50881i	−0.172726	−	0.0628672i
$577$	−36.8802	+	21.2928i	−1.53534	+	0.886430i	−0.536239	+	0.844066i	$0.680155\pi$
$577$	−36.8802	+	21.2928i	−1.53534	+	0.886430i	−0.999102	+	0.0423635i	$0.986511\pi$
$578$	−6.14214	−	3.54617i	−0.255480	−	0.147501i
$579$	−47.9548	+	40.2388i	−1.99293	+	1.67227i
$580$		0			0
$581$	14.7445	−	25.5383i	0.611707	−	1.05951i
$582$	−16.7826	+	9.68941i	−0.695659	+	0.401639i
$583$	−22.2647	+	61.1716i	−0.922108	+	2.53347i
$584$	−0.823742	+	4.67167i	−0.0340867	+	0.193315i
$585$		0			0
$586$	2.44916	−	0.891423i	0.101174	−	0.0368243i
$587$	17.2989	−	20.6160i	0.714000	−	0.850912i	−0.280033	−	0.959990i	$-0.590345\pi$
$587$	17.2989	−	20.6160i	0.714000	−	0.850912i	0.994033	+	0.109078i	$0.0347899\pi$
$588$		−	0.320149i		−	0.0132027i
$589$	−21.4581	+	16.9397i	−0.884167	+	0.697987i
$590$		0			0
$591$	−29.7005	−	24.9217i	−1.22172	−	1.02514i
$592$	−3.00959	−	8.26879i	−0.123693	−	0.339845i
$593$	−20.4496	+	3.60581i	−0.839763	+	0.148073i	−0.576955	−	0.816776i	$-0.695759\pi$
$593$	−20.4496	+	3.60581i	−0.839763	+	0.148073i	−0.262807	+	0.964848i	$0.584648\pi$
$594$	−3.28701	+	18.6416i	−0.134868	+	0.764873i
$595$		0			0
$596$	2.24050	+	3.88066i	0.0917745	+	0.158958i
$597$	−2.55010	−	1.47230i	−0.104369	−	0.0602573i
$598$	9.07709	+	10.8177i	0.371190	+	0.442367i
$599$	22.6279	−	18.9871i	0.924550	−	0.775790i	−0.0502805	−	0.998735i	$-0.516012\pi$
$599$	22.6279	−	18.9871i	0.924550	−	0.775790i	0.974831	+	0.222945i	$0.0715671\pi$
$600$		0			0
$601$	11.5040	+	19.9255i	0.469257	+	0.812777i	0.999382	−	0.0351423i	$-0.0111884\pi$
$601$	11.5040	+	19.9255i	0.469257	+	0.812777i	−0.530125	+	0.847919i	$0.677855\pi$
$602$	−2.77941	+	7.63636i	−0.113280	+	0.311235i
$603$	42.4135	+	7.47864i	1.72721	+	0.304554i
$604$	2.41972	+	13.7229i	0.0984568	+	0.558376i
$605$		0			0
$606$	13.2817	+	11.1446i	0.539531	+	0.452720i
$607$		−	6.16015i		−	0.250033i	−0.992155	−	0.125016i	$-0.960102\pi$
$607$		−	6.16015i		−	0.250033i	0.992155	−	0.125016i	$-0.0398983\pi$
$608$	−4.26816	−	0.884781i	−0.173097	−	0.0358826i
$609$	−2.15373			−0.0872735
$610$		0			0
$611$	−9.58977	+	3.49039i	−0.387961	+	0.141206i
$612$	21.3243	−	3.76005i	0.861983	−	0.151991i
$613$	35.1256	+	6.19360i	1.41871	+	0.250157i	0.829809	−	0.558048i	$-0.188449\pi$
$613$	35.1256	+	6.19360i	1.41871	+	0.250157i	0.588902	+	0.808205i	$0.299561\pi$
$614$	8.13819	+	2.96206i	0.328431	+	0.119539i
$615$		0			0
$616$	−6.57117	+	11.3816i	−0.264760	+	0.458578i
$617$	4.72973	+	5.63668i	0.190412	+	0.226924i	0.852801	−	0.522236i	$-0.174902\pi$
$617$	4.72973	+	5.63668i	0.190412	+	0.226924i	−0.662389	+	0.749160i	$0.730457\pi$
$618$	14.0999	+	16.8036i	0.567180	+	0.675939i
$619$	12.7001	−	21.9972i	0.510459	−	0.884141i	−0.489468	−	0.872021i	$-0.662809\pi$
$619$	12.7001	−	21.9972i	0.510459	−	0.884141i	0.999927	−	0.0121194i	$-0.00385781\pi$
$620$		0			0
$621$	11.2855	+	4.10757i	0.452870	+	0.164831i
$622$	−27.0031	−	4.76138i	−1.08273	−	0.190914i
$623$	20.8283	−	3.67259i	0.834467	−	0.147139i
$624$	−11.5587	+	4.20702i	−0.462719	+	0.168416i
$625$		0			0
$626$	26.6581			1.06547
$627$	−1.74586	+	58.4307i	−0.0697229	+	2.33350i
$628$		−	7.18836i		−	0.286847i
$629$	33.0864	+	27.7628i	1.31924	+	1.10697i
$630$		0			0
$631$	2.25203	+	12.7719i	0.0896518	+	0.508440i	0.996256	+	0.0864575i	$0.0275547\pi$
$631$	2.25203	+	12.7719i	0.0896518	+	0.508440i	−0.906604	+	0.421983i	$0.861334\pi$
$632$	−0.742591	−	0.130939i	−0.0295387	−	0.00520847i
$633$	−23.6556	+	64.9934i	−0.940228	+	2.58325i
$634$	−10.5835	−	18.3312i	−0.420326	−	0.728027i
$635$		0			0
$636$	−27.5591	+	23.1248i	−1.09279	+	0.916958i
$637$	−0.341537	−	0.407028i	−0.0135322	−	0.0161270i
$638$	1.26505	+	0.730378i	0.0500839	+	0.0289159i
$639$	8.92838	+	15.4644i	0.353201	+	0.611763i
$640$		0			0
$641$	−3.39110	+	19.2319i	−0.133941	+	0.759615i	0.841651	+	0.540022i	$0.181584\pi$
$641$	−3.39110	+	19.2319i	−0.133941	+	0.759615i	−0.975592	+	0.219593i	$0.929527\pi$
$642$	−16.3235	+	2.87827i	−0.644237	+	0.113596i
$643$	0.816169	+	2.24241i	0.0321866	+	0.0884319i	0.954745	−	0.297425i	$-0.0961279\pi$
$643$	0.816169	+	2.24241i	0.0321866	+	0.0884319i	−0.922558	+	0.385857i	$0.873906\pi$
$644$	6.38747	+	5.35972i	0.251702	+	0.211203i
$645$		0			0
$646$	20.3145	−	6.71387i	0.799263	−	0.264154i
$647$			30.5353i			1.20047i	0.799825	+	0.600234i	$0.204926\pi$
$647$			30.5353i			1.20047i	−0.799825	+	0.600234i	$0.795074\pi$
$648$	1.78265	−	2.12449i	0.0700293	−	0.0834577i
$649$	58.2031	−	21.1842i	2.28467	−	0.831553i
$650$		0			0
$651$	−7.91025	+	44.8612i	−0.310027	+	1.75825i
$652$	−0.546641	+	1.50188i	−0.0214081	+	0.0588183i
$653$	−8.66524	+	5.00288i	−0.339097	+	0.195778i	−0.659873	−	0.751377i	$-0.729390\pi$
$653$	−8.66524	+	5.00288i	−0.339097	+	0.195778i	0.320776	+	0.947155i	$0.396056\pi$
$654$	−11.9521	+	20.7017i	−0.467365	+	0.809500i
$655$		0			0
$656$	5.83266	−	4.89419i	0.227727	−	0.191086i
$657$	18.1232	+	10.4634i	0.707054	+	0.408218i
$658$	−5.21854	+	3.01292i	−0.203440	+	0.117456i
$659$	30.0120	+	10.9235i	1.16910	+	0.425518i	0.852340	−	0.522988i	$-0.175183\pi$
$659$	30.0120	+	10.9235i	1.16910	+	0.425518i	0.316761	+	0.948505i	$0.397405\pi$
$660$		0			0
$661$	−3.03844	−	17.2319i	−0.118182	−	0.670242i	−0.985126	−	0.171836i	$-0.945030\pi$
$661$	−3.03844	−	17.2319i	−0.118182	−	0.670242i	0.866944	−	0.498406i	$-0.166081\pi$
$662$	−0.949797	−	2.60955i	−0.0369149	−	0.101423i
$663$	38.8088	−	46.2505i	1.50721	−	1.79622i
$664$	−11.0534			−0.428954
$665$		0			0
$666$	−38.8186			−1.50419
$667$	0.595727	−	0.709960i	0.0230667	−	0.0274898i
$668$	2.87356	+	7.89504i	0.111181	+	0.305468i
$669$	−12.8072	−	72.6330i	−0.495153	−	2.80815i
$670$		0			0
$671$	−21.4991	−	7.82504i	−0.829964	−	0.302082i
$672$	−6.28999	+	3.63152i	−0.242641	+	0.140089i
$673$	−3.99652	−	2.30739i	−0.154055	−	0.0889435i	0.420991	−	0.907065i	$-0.361682\pi$
$673$	−3.99652	−	2.30739i	−0.154055	−	0.0889435i	−0.575046	+	0.818121i	$0.695016\pi$
$674$	1.72326	−	1.44599i	0.0663775	−	0.0556973i
$675$		0			0
$676$	−3.70733	+	6.42128i	−0.142590	+	0.246972i
$677$	−16.5817	+	9.57347i	−0.637288	+	0.367938i	−0.783569	−	0.621305i	$-0.786603\pi$
$677$	−16.5817	+	9.57347i	−0.637288	+	0.367938i	0.146281	+	0.989243i	$0.453270\pi$
$678$	18.7856	−	51.6131i	0.721458	−	1.98219i
$679$	−3.29771	+	18.7022i	−0.126554	+	0.717726i
$680$		0			0
$681$	7.02566	−	2.55713i	0.269224	−	0.0979895i
$682$	19.8598	−	23.6679i	0.760470	−	0.906293i
$683$		−	2.23430i		−	0.0854930i	−0.999086	−	0.0427465i	$-0.986389\pi$
$683$		−	2.23430i		−	0.0854930i	0.999086	−	0.0427465i	$-0.0136108\pi$
$684$	−10.1076	+	16.3584i	−0.386476	+	0.625478i
$685$		0			0
$686$	14.0657	+	11.8025i	0.537030	+	0.450622i
$687$	−17.0645	−	46.8842i	−0.651050	−	1.78875i
$688$	2.99975	−	0.528937i	0.114364	−	0.0201655i
$689$	−10.3681	+	58.8005i	−0.394994	+	2.24012i
$690$		0			0
$691$	−25.8951	−	44.8516i	−0.985095	−	1.70623i	−0.641513	−	0.767112i	$-0.721693\pi$
$691$	−25.8951	−	44.8516i	−0.985095	−	1.70623i	−0.343582	−	0.939123i	$-0.611640\pi$
$692$	−7.46982	−	4.31270i	−0.283960	−	0.163944i
$693$	37.2669	+	44.4130i	1.41565	+	1.68711i
$694$	−15.4614	+	12.9736i	−0.586905	+	0.492472i
$695$		0			0
$696$	0.403640	+	0.699125i	0.0152999	+	0.0265003i
$697$	−12.7822	+	35.1187i	−0.484159	+	1.33022i
$698$	21.8813	+	3.85826i	0.828218	+	0.146037i
$699$	2.71296	+	15.3860i	0.102614	+	0.581951i
$700$		0			0
$701$	17.0304	+	14.2902i	0.643230	+	0.539734i	0.905008	−	0.425394i	$-0.139864\pi$
$701$	17.0304	+	14.2902i	0.643230	+	0.539734i	−0.261778	+	0.965128i	$0.584309\pi$
$702$			17.3619i			0.655281i
$703$	−37.9553	+	5.52934i	−1.43151	+	0.208543i
$704$	4.92613			0.185660
$705$		0			0
$706$	2.89239	−	1.05274i	0.108856	−	0.0396205i
$707$	16.7326	−	2.95042i	0.629296	−	0.110962i
$708$	33.7100	+	5.94398i	1.26690	+	0.223388i
$709$	−18.2309	−	6.63549i	−0.684674	−	0.249201i	−0.0238211	−	0.999716i	$-0.507583\pi$
$709$	−18.2309	−	6.63549i	−0.684674	−	0.249201i	−0.660853	+	0.750515i	$0.729805\pi$
$710$		0			0
$711$	−1.66323	+	2.88080i	−0.0623759	+	0.108038i
$712$	−5.09568	−	6.07280i	−0.190969	−	0.227588i
$713$	−12.6002	−	15.0163i	−0.471880	−	0.562365i
$714$	17.8250	−	30.8737i	0.667082	−	1.15542i
$715$		0			0
$716$	−5.04021	−	1.83448i	−0.188361	−	0.0685579i
$717$	−19.0448	−	3.35812i	−0.711242	−	0.125411i
$718$	−20.1818	+	3.55860i	−0.753178	+	0.132806i
$719$	20.3444	−	7.40475i	0.758718	−	0.276151i	0.0664483	−	0.997790i	$-0.478833\pi$
$719$	20.3444	−	7.40475i	0.758718	−	0.276151i	0.692269	+	0.721639i	$0.256611\pi$
$720$		0			0
$721$	21.4962			0.800561
$722$	−7.55277	+	17.4343i	−0.281085	+	0.648838i
$723$			38.8960i			1.44656i
$724$	16.2127	+	13.6041i	0.602542	+	0.505593i
$725$		0			0
$726$	−6.27173	−	35.5687i	−0.232766	−	1.32008i
$727$	−39.8864	−	7.03305i	−1.47931	−	0.260841i	−0.625005	−	0.780621i	$-0.714903\pi$
$727$	−39.8864	−	7.03305i	−1.47931	−	0.260841i	−0.854300	+	0.519780i	$0.826014\pi$
$728$	−4.12277	+	11.3272i	−0.152800	+	0.419815i
$729$	−21.8089	−	37.7741i	−0.807736	−	1.39904i
$730$		0			0
$731$	−11.4532	+	9.61038i	−0.423612	+	0.355453i
$732$	−8.12735	−	9.68580i	−0.300395	−	0.357997i
$733$	39.8449	+	23.0045i	1.47170	+	0.849689i	0.999494	−	0.0317969i	$-0.0101230\pi$
$733$	39.8449	+	23.0045i	1.47170	+	0.849689i	0.472210	+	0.881486i	$0.343456\pi$
$734$	−1.84783	−	3.20054i	−0.0682047	−	0.118134i
$735$		0			0
$736$	0.542723	−	3.07794i	0.0200050	−	0.113454i
$737$	−47.3616	+	8.35112i	−1.74459	+	0.307618i
$738$	−11.4881	−	31.5633i	−0.422883	−	1.16186i
$739$	−8.81246	−	7.39453i	−0.324172	−	0.272012i	0.466148	−	0.884707i	$-0.345641\pi$
$739$	−8.81246	−	7.39453i	−0.324172	−	0.272012i	−0.790320	+	0.612694i	$0.790086\pi$
$740$		0			0
$741$	7.72931	+	53.0567i	0.283943	+	1.94909i
$742$			35.2554i			1.29426i
$743$	−1.06807	+	1.27288i	−0.0391837	+	0.0466974i	−0.785280	−	0.619140i	$-0.787481\pi$
$743$	−1.06807	+	1.27288i	−0.0391837	+	0.0466974i	0.746097	+	0.665838i	$0.231926\pi$
$744$	16.0450	−	5.83989i	0.588237	−	0.214101i
$745$		0			0
$746$	0.965237	−	5.47413i	0.0353398	−	0.200422i
$747$	−16.6775	+	45.8209i	−0.610196	+	1.67650i
$748$	−20.9400	+	12.0897i	−0.765641	+	0.442043i
$749$	−8.12169	+	14.0672i	−0.296760	+	0.514003i
$750$		0			0
$751$	25.5865	−	21.4696i	0.933665	−	0.783438i	−0.0428066	−	0.999083i	$-0.513630\pi$
$751$	25.5865	−	21.4696i	0.933665	−	0.783438i	0.976472	+	0.215645i	$0.0691855\pi$
$752$	1.95606	+	1.12933i	0.0713302	+	0.0411825i
$753$	−13.7794	+	7.95551i	−0.502148	+	0.289915i
$754$	1.25901	+	0.458242i	0.0458504	+	0.0166882i
$755$		0			0
$756$	1.78017	+	10.0959i	0.0647443	+	0.367183i
$757$	17.1760	+	47.1908i	0.624273	+	1.71518i	0.696277	+	0.717773i	$0.254838\pi$
$757$	17.1760	+	47.1908i	0.624273	+	1.71518i	−0.0720041	+	0.997404i	$0.522939\pi$
$758$	−4.17834	+	4.97955i	−0.151764	+	0.180865i
$759$	−41.9147			−1.52141
$760$		0			0
$761$	−5.39530			−0.195579			−0.0977897	−	0.995207i	$-0.531177\pi$
$761$	−5.39530			−0.195579			−0.0977897	+	0.995207i	$0.531177\pi$
$762$	11.2163	−	13.3670i	0.406322	−	0.484236i
$763$	8.01201	+	22.0128i	0.290054	+	0.796917i
$764$	2.58844	+	14.6798i	0.0936464	+	0.531095i
$765$		0			0
$766$	−5.04437	−	1.83600i	−0.182260	−	0.0663374i
$767$	49.1990	−	28.4051i	1.77647	−	1.02565i
$768$	2.35767	+	1.36120i	0.0850751	+	0.0491181i
$769$	−17.8525	+	14.9800i	−0.643779	+	0.540194i	−0.905176	−	0.425037i	$-0.860261\pi$
$769$	−17.8525	+	14.9800i	−0.643779	+	0.540194i	0.261397	+	0.965231i	$0.415817\pi$
$770$		0			0
$771$	24.7044	−	42.7892i	0.889706	−	1.54102i
$772$	19.9139	−	11.4973i	0.716717	−	0.413797i
$773$	11.6443	−	31.9923i	0.418815	−	1.15068i	−0.533562	−	0.845761i	$-0.679147\pi$
$773$	11.6443	−	31.9923i	0.418815	−	1.15068i	0.952377	−	0.304923i	$-0.0986308\pi$
$774$	2.33339	−	13.2333i	0.0838720	−	0.475662i
$775$		0			0
$776$	6.68900	−	2.43460i	0.240121	−	0.0873969i
$777$	−41.0811	+	48.9586i	−1.47378	+	1.75638i
$778$			8.13313i			0.291587i
$779$	−15.7285	−	29.2250i	−0.563533	−	1.04709i
$780$		0			0
$781$	−15.2749	−	12.8172i	−0.546579	−	0.458635i
$782$	5.24686	+	14.4156i	0.187627	+	0.515502i
$783$	1.12214	−	0.197864i	0.0401021	−	0.00707109i
$784$	−0.0204207	+	0.115811i	−0.000729309	+	0.00413612i
$785$		0			0
$786$	18.8882	+	32.7153i	0.673719	+	1.16692i
$787$	−9.55106	−	5.51431i	−0.340459	−	0.196564i	0.320016	−	0.947412i	$-0.396312\pi$
$787$	−9.55106	−	5.51431i	−0.340459	−	0.196564i	−0.660475	+	0.750848i	$0.729645\pi$
$788$	9.15430	+	10.9097i	0.326108	+	0.388641i
$789$	28.8322	−	24.1931i	1.02645	−	0.861297i
$790$		0			0
$791$	−26.9128	−	46.6143i	−0.956909	−	1.65741i
$792$	7.43261	−	20.4209i	0.264106	−	0.725626i
$793$	−20.6658	−	3.64393i	−0.733863	−	0.129400i
$794$	−3.32463	−	18.8549i	−0.117987	−	0.669135i
$795$		0			0
$796$	0.828568	+	0.695251i	0.0293678	+	0.0246425i
$797$			20.4220i			0.723384i	0.932298	+	0.361692i	$0.117801\pi$
$797$			20.4220i			0.723384i	−0.932298	+	0.361692i	$0.882199\pi$
$798$	9.93465	+	30.0598i	0.351683	+	1.06410i
$799$	−11.0864			−0.392209
$800$		0			0
$801$	−32.8628	+	11.9611i	−1.16115	+	0.422624i
$802$	−18.5363	+	3.26845i	−0.654540	+	0.115413i
$803$	−23.0133	−	4.05786i	−0.812120	−	0.143199i
$804$	−24.9751	−	9.09019i	−0.880803	−	0.320586i
$805$		0			0
$806$	14.1691	−	24.5416i	0.499085	−	0.864440i
$807$	−11.7511	−	14.0044i	−0.413657	−	0.492977i
$808$	−4.09368	−	4.87866i	−0.144015	−	0.171631i
$809$	3.91082	−	6.77373i	0.137497	−	0.238152i	−0.789052	−	0.614327i	$-0.789428\pi$
$809$	3.91082	−	6.77373i	0.137497	−	0.238152i	0.926549	+	0.376175i	$0.122761\pi$
$810$		0			0
$811$	−23.8262	−	8.67202i	−0.836650	−	0.304516i	−0.112065	−	0.993701i	$-0.535746\pi$
$811$	−23.8262	−	8.67202i	−0.836650	−	0.304516i	−0.724585	+	0.689185i	$0.757969\pi$
$812$	0.779094	+	0.137375i	0.0273409	+	0.00482093i
$813$	−0.273311	+	0.0481922i	−0.00958545	+	0.00169017i
$814$	40.7331	−	14.8256i	1.42769	−	0.519638i
$815$		0			0
$816$	−13.3626			−0.467785
$817$	0.396538	−	13.2714i	0.0138731	−	0.464307i
$818$			22.3021i			0.779774i
$819$	40.7357	+	34.1813i	1.42342	+	1.19439i
$820$		0			0
$821$	4.73099	+	26.8308i	0.165113	+	0.936401i	0.948948	+	0.315432i	$0.102149\pi$
$821$	4.73099	+	26.8308i	0.165113	+	0.936401i	−0.783835	+	0.620969i	$0.786739\pi$
$822$	38.0383	+	6.70717i	1.32674	+	0.233940i
$823$	8.50672	−	23.3720i	0.296526	−	0.814698i	−0.698548	−	0.715563i	$-0.746170\pi$
$823$	8.50672	−	23.3720i	0.296526	−	0.814698i	0.995074	−	0.0991348i	$-0.0316075\pi$
$824$	−4.02870	−	6.97792i	−0.140347	−	0.243087i
$825$		0			0
$826$	25.6966	−	21.5620i	0.894099	−	0.750238i
$827$	−2.82219	−	3.36335i	−0.0981371	−	0.116955i	0.714741	−	0.699390i	$-0.246545\pi$
$827$	−2.82219	−	3.36335i	−0.0981371	−	0.116955i	−0.812878	+	0.582434i	$0.802100\pi$
$828$	−11.9405	−	6.89385i	−0.414961	−	0.239578i
$829$	8.45494	+	14.6444i	0.293652	+	0.508620i	0.974670	−	0.223646i	$-0.0717960\pi$
$829$	8.45494	+	14.6444i	0.293652	+	0.508620i	−0.681018	+	0.732266i	$0.738463\pi$
$830$		0			0
$831$	−5.22240	+	29.6177i	−0.181163	+	1.02743i
$832$	4.44962	−	0.784587i	0.154263	−	0.0272007i
$833$	−0.197420	−	0.542406i	−0.00684019	−	0.0187933i
$834$	−41.7794	−	35.0571i	−1.44670	−	1.21393i
$835$		0			0
$836$	4.35855	−	21.0255i	0.150744	−	0.727182i
$837$		−	24.1005i		−	0.833035i
$838$	4.06278	−	4.84183i	0.140346	−	0.167258i
$839$	−12.5821	+	4.57953i	−0.434384	+	0.158103i	−0.549951	−	0.835197i	$-0.685354\pi$
$839$	−12.5821	+	4.57953i	−0.434384	+	0.158103i	0.115567	+	0.993300i	$0.463131\pi$
$840$		0			0
$841$	−5.02053	+	28.4728i	−0.173122	+	0.981822i
$842$	9.60989	−	26.4030i	0.331179	−	0.909906i
$843$	−57.0331	+	32.9281i	−1.96433	+	1.13410i
$844$	12.7028	−	22.0020i	0.437250	−	0.757339i
$845$		0			0
$846$	7.63289	−	6.40476i	0.262424	−	0.220200i
$847$	−30.6522	−	17.6971i	−1.05322	−	0.608078i
$848$	11.4443	−	6.60737i	0.392999	−	0.226898i
$849$	19.0120	+	6.91981i	0.652491	+	0.237487i
$850$		0			0
$851$	−4.77567	−	27.0842i	−0.163708	−	0.928433i
$852$	−3.76897	−	10.3552i	−0.129123	−	0.354762i
$853$	12.8995	−	15.3731i	0.441672	−	0.526364i	−0.498580	−	0.866844i	$-0.666145\pi$
$853$	12.8995	−	15.3731i	0.441672	−	0.526364i	0.940252	+	0.340480i	$0.110589\pi$
$854$	−12.3907			−0.424001
$855$		0			0
$856$	6.08849			0.208100
$857$	1.13284	−	1.35007i	0.0386972	−	0.0461176i	−0.746349	−	0.665555i	$-0.768195\pi$
$857$	1.13284	−	1.35007i	0.0386972	−	0.0461176i	0.785046	+	0.619438i	$0.212639\pi$
$858$	−20.7243	−	56.9397i	−0.707518	−	1.94389i
$859$	6.40605	+	36.3305i	0.218572	+	1.23958i	0.874600	+	0.484845i	$0.161124\pi$
$859$	6.40605	+	36.3305i	0.218572	+	1.23958i	−0.656028	+	0.754736i	$0.727765\pi$
$860$		0			0
$861$	−51.9658	−	18.9140i	−1.77099	−	0.644588i
$862$	29.9013	−	17.2635i	1.01844	−	0.587998i
$863$	−1.53297	−	0.885059i	−0.0521828	−	0.0301278i	0.473682	−	0.880696i	$-0.342925\pi$
$863$	−1.53297	−	0.885059i	−0.0521828	−	0.0301278i	−0.525864	+	0.850568i	$0.676258\pi$
$864$	2.94360	−	2.46998i	0.100143	−	0.0840303i
$865$		0			0
$866$	−4.79994	+	8.31374i	−0.163109	+	0.282512i
$867$	16.7214	−	9.65410i	0.567888	−	0.327870i
$868$	5.72294	−	15.7237i	0.194249	−	0.533695i
$869$	0.645022	−	3.65810i	0.0218809	−	0.124093i
$870$		0			0
$871$	−41.4501	+	15.0866i	−1.40448	+	0.511190i
$872$	5.64405	−	6.72631i	0.191132	−	0.227782i
$873$		−	31.4021i		−	1.06280i
$874$	−12.6569	−	5.03973i	−0.428127	−	0.170471i
$875$		0			0
$876$	−9.89298	−	8.30120i	−0.334253	−	0.280471i
$877$	−1.69573	−	4.65898i	−0.0572608	−	0.157323i	0.907764	−	0.419481i	$-0.137788\pi$
$877$	−1.69573	−	4.65898i	−0.0572608	−	0.157323i	−0.965025	+	0.262158i	$0.915566\pi$
$878$	−9.17063	+	1.61703i	−0.309494	+	0.0545721i
$879$	−1.23212	+	6.98772i	−0.0415585	+	0.235690i
$880$		0			0
$881$	−5.03459	−	8.72016i	−0.169619	−	0.293790i	0.768667	−	0.639650i	$-0.220921\pi$
$881$	−5.03459	−	8.72016i	−0.169619	−	0.293790i	−0.938286	+	0.345860i	$0.887587\pi$
$882$	0.449277	+	0.259390i	0.0151279	+	0.00873412i
$883$	24.9958	+	29.7888i	0.841174	+	1.00247i	0.999885	+	0.0151474i	$0.00482177\pi$
$883$	24.9958	+	29.7888i	0.841174	+	1.00247i	−0.158711	+	0.987325i	$0.550734\pi$
$884$	−16.9889	+	14.2554i	−0.571398	+	0.479459i
$885$		0			0
$886$	−16.7481	−	29.0085i	−0.562662	−	0.974559i
$887$	1.59686	−	4.38734i	0.0536174	−	0.147313i	−0.909993	−	0.414624i	$-0.863913\pi$
$887$	1.59686	−	4.38734i	0.0536174	−	0.147313i	0.963610	+	0.267312i	$0.0861353\pi$
$888$	23.5917	+	4.15986i	0.791687	+	0.139596i
$889$	−2.96937	−	16.8402i	−0.0995896	−	0.564801i
$890$		0			0
$891$	10.4655	+	8.78159i	0.350607	+	0.294194i
$892$			27.0913i			0.907084i
$893$	6.55085	−	7.34956i	0.219216	−	0.245944i
$894$	−12.1991			−0.407999
$895$		0			0
$896$	2.50699	−	0.912470i	0.0837526	−	0.0304835i
$897$	−37.8602	+	6.67578i	−1.26412	+	0.222898i
$898$	2.18303	+	0.384927i	0.0728487	+	0.0128452i
$899$	−1.74767	−	0.636099i	−0.0582879	−	0.0212151i
$900$		0			0
$901$	−32.4316	+	56.1731i	−1.08045	+	1.87140i
$902$	24.1094	+	28.7325i	0.802755	+	0.956686i
$903$	−14.2207	−	16.9475i	−0.473234	−	0.563979i
$904$	−10.0877	+	17.4724i	−0.335512	+	0.581123i
$905$		0			0
$906$	−35.6478	−	12.9747i	−1.18432	−	0.431056i
$907$	4.17835	+	0.736755i	0.138740	+	0.0244636i	0.242587	−	0.970130i	$-0.422004\pi$
$907$	4.17835	+	0.736755i	0.138740	+	0.0244636i	−0.103847	+	0.994593i	$0.533115\pi$
$908$	−2.70458	+	0.476891i	−0.0897548	+	0.0158262i
$909$	−26.4007	+	9.60908i	−0.875657	+	0.318713i
$910$		0			0
$911$	−12.4362			−0.412030			−0.206015	−	0.978549i	$-0.566050\pi$
$911$	−12.4362			−0.412030			−0.206015	+	0.978549i	$0.566050\pi$
$912$	7.89584	−	8.85854i	0.261457	−	0.293335i
$913$		−	54.4503i		−	1.80204i
$914$	−10.9832	−	9.21596i	−0.363291	−	0.304837i
$915$		0			0
$916$	3.18243	+	18.0485i	0.105150	+	0.596338i
$917$	36.4574	+	6.42843i	1.20393	+	0.212285i
$918$	−6.45084	+	17.7235i	−0.212909	+	0.584964i
$919$	−7.42713	−	12.8642i	−0.244999	−	0.424350i	0.717133	−	0.696937i	$-0.245454\pi$
$919$	−7.42713	−	12.8642i	−0.244999	−	0.424350i	−0.962131	+	0.272587i	$0.912121\pi$
$920$		0			0
$921$	−18.0613	+	15.1552i	−0.595139	+	0.499381i
$922$	−6.20655	−	7.39668i	−0.204402	−	0.243597i
$923$	−15.8387	−	9.14450i	−0.521339	−	0.300995i
$924$	−17.8894	−	30.9853i	−0.588517	−	1.01934i
$925$		0			0
$926$	−5.36667	+	30.4359i	−0.176360	+	1.00019i
$927$	−35.0050	+	6.17233i	−1.14972	+	0.202726i
$928$	−0.101420	−	0.278649i	−0.00332927	−	0.00914711i
$929$	28.1439	+	23.6156i	0.923372	+	0.774801i	0.974616	−	0.223885i	$-0.0718740\pi$
$929$	28.1439	+	23.6156i	0.923372	+	0.774801i	−0.0512436	+	0.998686i	$0.516318\pi$
$930$		0			0
$931$	0.476233	+	0.189626i	0.0156079	+	0.00621475i
$932$		−	5.73880i		−	0.187981i
$933$	47.9824	−	57.1832i	1.57087	−	1.87209i
$934$	−5.87685	+	2.13900i	−0.192296	+	0.0699901i
$935$		0			0
$936$	3.46119	−	19.6294i	0.113132	−	0.641606i
$937$	11.2688	−	30.9607i	0.368135	−	1.01144i	−0.607935	−	0.793987i	$-0.708002\pi$
$937$	11.2688	−	30.9607i	0.368135	−	1.01144i	0.976070	−	0.217456i	$-0.0697759\pi$
$938$	−22.5562	+	13.0228i	−0.736486	+	0.425211i
$939$	−36.2871	+	62.8511i	−1.18418	+	2.05107i
$940$		0			0
$941$	16.0658	−	13.4808i	0.523729	−	0.439461i	−0.342201	−	0.939627i	$-0.611172\pi$
$941$	16.0658	−	13.4808i	0.523729	−	0.439461i	0.865929	+	0.500166i	$0.166728\pi$
$942$	16.9478	+	9.78481i	0.552189	+	0.318806i
$943$	20.6088	−	11.8985i	0.671113	−	0.387467i
$944$	−11.8152	−	4.30038i	−0.384552	−	0.139965i
$945$		0			0
$946$	2.60561	+	14.7772i	0.0847157	+	0.480447i
$947$	20.3826	+	56.0006i	0.662344	+	1.81978i	0.565962	+	0.824431i	$0.308505\pi$
$947$	20.3826	+	56.0006i	0.662344	+	1.81978i	0.0963825	+	0.995344i	$0.469273\pi$
$948$	1.31953	−	1.57255i	0.0428562	−	0.0510740i
$949$	−21.4334			−0.695759
$950$		0			0
$951$	57.6253			1.86863
$952$	−8.41732	+	10.0314i	−0.272807	+	0.325118i
$953$	7.28657	+	20.0197i	0.236035	+	0.648501i	0.999995	+	0.00323722i	$0.00103044\pi$
$953$	7.28657	+	20.0197i	0.236035	+	0.648501i	−0.763960	+	0.645264i	$0.776747\pi$
$954$	−10.1231	−	57.4108i	−0.327747	−	1.85874i
$955$		0			0
$956$	6.67512	+	2.42955i	0.215889	+	0.0785771i
$957$	−3.44398	+	1.98838i	−0.111328	+	0.0642753i
$958$	−29.5338	−	17.0514i	−0.954195	−	0.550905i
$959$	28.9960	−	24.3305i	0.936329	−	0.785673i
$960$		0			0
$961$	−4.16852	+	7.22009i	−0.134468	+	0.232906i
$962$	34.4316	−	19.8791i	1.11012	−	0.640928i
$963$	9.18639	−	25.2394i	0.296027	−	0.813328i
$964$	2.48098	−	14.0703i	0.0799070	−	0.453175i
$965$		0			0
$966$	−21.3311	+	7.76388i	−0.686316	+	0.249799i
$967$	−12.0090	+	14.3118i	−0.386184	+	0.460236i	−0.923756	−	0.382982i	$-0.874897\pi$
$967$	−12.0090	+	14.3118i	−0.386184	+	0.460236i	0.537572	+	0.843218i	$0.319342\pi$
$968$			13.2667i			0.426409i
$969$	−11.8230	+	57.0338i	−0.379810	+	1.83219i
$970$		0			0
$971$	22.3516	+	18.7552i	0.717298	+	0.601884i	0.926636	−	0.375959i	$-0.122687\pi$
$971$	22.3516	+	18.7552i	0.717298	+	0.601884i	−0.209338	+	0.977843i	$0.567131\pi$
$972$	6.52502	+	17.9274i	0.209290	+	0.575020i
$973$	−52.6350	+	9.28097i	−1.68740	+	0.297534i
$974$	−2.89301	+	16.4071i	−0.0926981	+	0.525717i
$975$		0			0
$976$	2.32220	+	4.02216i	0.0743317	+	0.128746i
$977$	45.5001	+	26.2695i	1.45568	+	0.840436i	0.998794	−	0.0490904i	$-0.0156322\pi$
$977$	45.5001	+	26.2695i	1.45568	+	0.840436i	0.456884	+	0.889526i	$0.348966\pi$
$978$	−2.79686	−	3.33317i	−0.0894337	−	0.106583i
$979$	29.9154	−	25.1020i	0.956100	−	0.802263i
$980$		0			0
$981$	−19.3676	−	33.5457i	−0.618361	−	1.07103i
$982$	8.97450	−	24.6572i	0.286388	−	0.786844i
$983$	0.514641	+	0.0907451i	0.0164145	+	0.00289432i	0.181849	−	0.983326i	$-0.441792\pi$
$983$	0.514641	+	0.0907451i	0.0164145	+	0.00289432i	−0.165435	+	0.986221i	$0.552903\pi$
$984$	3.59944	+	20.4135i	0.114746	+	0.650757i
$985$		0			0
$986$	1.11498	+	0.935575i	0.0355080	+	0.0297948i
$987$		−	16.4048i		−	0.522170i
$988$	0.588196	−	19.6858i	0.0187130	−	0.626290i
$989$	9.52011			0.302722
$990$		0			0
$991$	7.87802	−	2.86737i	0.250254	−	0.0910849i	−0.213848	−	0.976867i	$-0.568600\pi$
$991$	7.87802	−	2.86737i	0.250254	−	0.0910849i	0.464101	+	0.885782i	$0.346377\pi$
$992$	−6.17664	+	1.08911i	−0.196109	+	0.0345792i
$993$	7.44532	+	1.31281i	0.236270	+	0.0416608i
$994$	−10.1478	−	3.69349i	−0.321868	−	0.117151i
$995$		0			0
$996$	15.0459	−	26.0602i	0.476746	−	0.825748i
$997$	−9.74442	−	11.6129i	−0.308609	−	0.367786i	0.589340	−	0.807885i	$-0.299388\pi$
$997$	−9.74442	−	11.6129i	−0.308609	−	0.367786i	−0.897949	+	0.440099i	$0.854943\pi$
$998$	−13.9078	−	16.5747i	−0.440244	−	0.524662i
$999$	16.9064	−	29.2828i	0.534895	−	0.926465i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	950.2.u.e.149.4		24
5.2	odd	4		950.2.l.h.301.2		12
5.3	odd	4		190.2.k.b.111.1	yes	12
5.4	even	2	inner	950.2.u.e.149.1		24
19.6	even	9	inner	950.2.u.e.899.1		24
95.33	even	36		3610.2.a.be.1.1		6
95.43	odd	36		3610.2.a.bc.1.6		6
95.44	even	18	inner	950.2.u.e.899.4		24
95.63	odd	36		190.2.k.b.101.1	✓	12
95.82	odd	36		950.2.l.h.101.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
190.2.k.b.101.1	✓	12	95.63	odd	36
190.2.k.b.111.1	yes	12	5.3	odd	4
950.2.l.h.101.2		12	95.82	odd	36
950.2.l.h.301.2		12	5.2	odd	4
950.2.u.e.149.1		24	5.4	even	2	inner
950.2.u.e.149.4		24	1.1	even	1	trivial
950.2.u.e.899.1		24	19.6	even	9	inner
950.2.u.e.899.4		24	95.44	even	18	inner
3610.2.a.bc.1.6		6	95.43	odd	36
3610.2.a.be.1.1		6	95.33	even	36

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:	\( N \)	\(=\)	\( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	950.u (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.642788 - 0.766044i) q^{2} +(0.931116 + 2.55822i) q^{3} +(-0.173648 - 0.984808i) q^{4} +(2.55822 + 0.931116i) q^{6} +(2.31045 - 1.33394i) q^{7} +(-0.866025 - 0.500000i) q^{8} +(-3.37939 + 2.83564i) q^{9} +O(q^{10})\)	\(q+(0.642788 - 0.766044i) q^{2} +(0.931116 + 2.55822i) q^{3} +(-0.173648 - 0.984808i) q^{4} +(2.55822 + 0.931116i) q^{6} +(2.31045 - 1.33394i) q^{7} +(-0.866025 - 0.500000i) q^{8} +(-3.37939 + 2.83564i) q^{9} +(2.46306 - 4.26615i) q^{11} +(2.35767 - 1.36120i) q^{12} +(1.54534 - 4.24577i) q^{13} +(0.463273 - 2.62735i) q^{14} +(-0.939693 + 0.342020i) q^{16} +(3.15506 - 3.76005i) q^{17} +4.41147i q^{18} +(0.628373 + 4.31337i) q^{19} +(5.56382 + 4.66860i) q^{21} +(-1.68484 - 4.62905i) q^{22} +(-3.07794 + 0.542723i) q^{23} +(0.472740 - 2.68104i) q^{24} +(-2.25913 - 3.91293i) q^{26} +(-3.32779 - 1.92130i) q^{27} +(-1.71488 - 2.04372i) q^{28} +(-0.227157 + 0.190607i) q^{29} +(3.13596 + 5.43165i) q^{31} +(-0.342020 + 0.939693i) q^{32} +(13.2072 + 2.32878i) q^{33} +(-0.852334 - 4.83382i) q^{34} +(3.37939 + 2.83564i) q^{36} +8.79946i q^{37} +(3.70814 + 2.29122i) q^{38} +12.3005 q^{39} +(-7.15482 + 2.60414i) q^{41} +(7.15271 - 1.26122i) q^{42} +(-2.99975 - 0.528937i) q^{43} +(-4.62905 - 1.68484i) q^{44} +(-1.56271 + 2.70669i) q^{46} +(-1.45184 - 1.73024i) q^{47} +(-1.74993 - 2.08548i) q^{48} +(0.0587989 - 0.101843i) q^{49} +(12.5568 + 4.57029i) q^{51} +(-4.44962 - 0.784587i) q^{52} +(-13.0140 + 2.29471i) q^{53} +(-3.61086 + 1.31425i) q^{54} -2.66788 q^{56} +(-10.4495 + 5.62377i) q^{57} +0.296532i q^{58} +(9.63183 + 8.08206i) q^{59} +(-0.806491 - 4.57384i) q^{61} +(6.17664 + 1.08911i) q^{62} +(-4.02534 + 11.0595i) q^{63} +(0.500000 + 0.866025i) q^{64} +(10.2733 - 8.62036i) q^{66} +(-6.27533 - 7.47864i) q^{67} +(-4.25079 - 2.45420i) q^{68} +(-4.25432 - 7.36870i) q^{69} +(0.702893 - 3.98630i) q^{71} +(4.34445 - 0.766044i) q^{72} +(-1.62245 - 4.45766i) q^{73} +(6.74078 + 5.65618i) q^{74} +(4.13872 - 1.36784i) q^{76} -13.1423i q^{77} +(7.90662 - 9.42274i) q^{78} +(0.708572 - 0.257899i) q^{79} +(-0.481582 + 2.73119i) q^{81} +(-2.60414 + 7.15482i) q^{82} +(9.57249 - 5.52668i) q^{83} +(3.63152 - 6.28999i) q^{84} +(-2.33339 + 1.95795i) q^{86} +(-0.699125 - 0.403640i) q^{87} +(-4.26615 + 2.46306i) q^{88} +(7.44939 + 2.71136i) q^{89} +(-2.09319 - 11.8711i) q^{91} +(1.06896 + 2.93693i) q^{92} +(-10.9754 + 13.0800i) q^{93} -2.25866 q^{94} -2.72240 q^{96} +(-4.57554 + 5.45292i) q^{97} +(-0.0402208 - 0.110506i) q^{98} +(3.77363 + 21.4013i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 36 q^{9}+O(q^{10}) \) 24 * q - 36 * q^9	\( 24 q - 36 q^{9} + 12 q^{11} + 24 q^{21} + 12 q^{29} + 12 q^{31} + 36 q^{36} + 72 q^{39} - 12 q^{41} - 12 q^{44} - 24 q^{46} + 36 q^{49} + 24 q^{56} + 48 q^{59} - 60 q^{61} + 12 q^{64} + 48 q^{66} - 12 q^{69} - 84 q^{71} - 12 q^{74} + 36 q^{76} - 120 q^{79} + 36 q^{81} + 48 q^{84} - 72 q^{86} + 24 q^{89} + 48 q^{91} - 120 q^{94} + 24 q^{99}+O(q^{100}) \) 24 * q - 36 * q^9 + 12 * q^11 + 24 * q^21 + 12 * q^29 + 12 * q^31 + 36 * q^36 + 72 * q^39 - 12 * q^41 - 12 * q^44 - 24 * q^46 + 36 * q^49 + 24 * q^56 + 48 * q^59 - 60 * q^61 + 12 * q^64 + 48 * q^66 - 12 * q^69 - 84 * q^71 - 12 * q^74 + 36 * q^76 - 120 * q^79 + 36 * q^81 + 48 * q^84 - 72 * q^86 + 24 * q^89 + 48 * q^91 - 120 * q^94 + 24 * q^99

Introduction

L-functions

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