LMFDB - Embedded newform 950.2.l.h.301.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [950,2,Mod(101,950)]

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([0, 14]))

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

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

chi := DirichletCharacter("950.101");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 950 = 2 \cdot 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	950.l (of order $9$, degree $6$, 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:	$12$
Relative dimension:	$2$ over $\Q(\zeta_{9})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 12x^{10} + 105x^{8} + 394x^{6} + 1077x^{4} + 1443x^{2} + 1369 $ x^12 + 12x^10 + 105x^8 + 394x^6 + 1077x^4 + 1443*x^2 + 1369
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 190)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			301.2
Root			$-1.36120 + 2.35767i$ of defining polynomial
Character	$\chi$	$=$	950.301
Dual form			950.2.l.h.101.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.766044 + 0.642788i) q^{2} +(2.55822 - 0.931116i) q^{3} +(0.173648 + 0.984808i) q^{4} +(2.55822 + 0.931116i) q^{6} +(1.33394 + 2.31045i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(3.37939 - 2.83564i) q^{9} +O(q^{10})$	\(q+(0.766044 + 0.642788i) q^{2} +(2.55822 - 0.931116i) q^{3} +(0.173648 + 0.984808i) q^{4} +(2.55822 + 0.931116i) q^{6} +(1.33394 + 2.31045i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(3.37939 - 2.83564i) q^{9} +(2.46306 - 4.26615i) q^{11} +(1.36120 + 2.35767i) q^{12} +(-4.24577 - 1.54534i) q^{13} +(-0.463273 + 2.62735i) q^{14} +(-0.939693 + 0.342020i) q^{16} +(3.76005 + 3.15506i) q^{17} +4.41147 q^{18} +(-0.628373 - 4.31337i) q^{19} +(5.56382 + 4.66860i) q^{21} +(4.62905 - 1.68484i) q^{22} +(0.542723 + 3.07794i) q^{23} +(-0.472740 + 2.68104i) q^{24} +(-2.25913 - 3.91293i) q^{26} +(1.92130 - 3.32779i) q^{27} +(-2.04372 + 1.71488i) q^{28} +(0.227157 - 0.190607i) q^{29} +(3.13596 + 5.43165i) q^{31} +(-0.939693 - 0.342020i) q^{32} +(2.32878 - 13.2072i) q^{33} +(0.852334 + 4.83382i) q^{34} +(3.37939 + 2.83564i) q^{36} -8.79946 q^{37} +(2.29122 - 3.70814i) q^{38} -12.3005 q^{39} +(-7.15482 + 2.60414i) q^{41} +(1.26122 + 7.15271i) q^{42} +(-0.528937 + 2.99975i) q^{43} +(4.62905 + 1.68484i) q^{44} +(-1.56271 + 2.70669i) q^{46} +(1.73024 - 1.45184i) q^{47} +(-2.08548 + 1.74993i) q^{48} +(-0.0587989 + 0.101843i) q^{49} +(12.5568 + 4.57029i) q^{51} +(0.784587 - 4.44962i) q^{52} +(2.29471 + 13.0140i) q^{53} +(3.61086 - 1.31425i) q^{54} -2.66788 q^{56} +(-5.62377 - 10.4495i) q^{57} +0.296532 q^{58} +(-9.63183 - 8.08206i) q^{59} +(-0.806491 - 4.57384i) q^{61} +(-1.08911 + 6.17664i) q^{62} +(11.0595 + 4.02534i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(10.2733 - 8.62036i) q^{66} +(7.47864 - 6.27533i) q^{67} +(-2.45420 + 4.25079i) q^{68} +(4.25432 + 7.36870i) q^{69} +(0.702893 - 3.98630i) q^{71} +(0.766044 + 4.34445i) q^{72} +(-4.45766 + 1.62245i) q^{73} +(-6.74078 - 5.65618i) q^{74} +(4.13872 - 1.36784i) q^{76} +13.1423 q^{77} +(-9.42274 - 7.90662i) q^{78} +(-0.708572 + 0.257899i) q^{79} +(-0.481582 + 2.73119i) q^{81} +(-7.15482 - 2.60414i) q^{82} +(-5.52668 - 9.57249i) q^{83} +(-3.63152 + 6.28999i) q^{84} +(-2.33339 + 1.95795i) q^{86} +(0.403640 - 0.699125i) q^{87} +(2.46306 + 4.26615i) q^{88} +(-7.44939 - 2.71136i) q^{89} +(-2.09319 - 11.8711i) q^{91} +(-2.93693 + 1.06896i) q^{92} +(13.0800 + 10.9754i) q^{93} +2.25866 q^{94} -2.72240 q^{96} +(-5.45292 - 4.57554i) q^{97} +(-0.110506 + 0.0402208i) q^{98} +(-3.77363 - 21.4013i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 6 q^{7} - 6 q^{8} + 18 q^{9}+O(q^{10}) $ 12 * q - 6 * q^7 - 6 * q^8 + 18 * q^9	$ 12 q - 6 q^{7} - 6 q^{8} + 18 q^{9} + 6 q^{11} - 6 q^{13} + 18 q^{17} + 12 q^{18} + 12 q^{21} + 6 q^{22} + 30 q^{23} - 6 q^{29} + 6 q^{31} + 24 q^{33} + 18 q^{36} - 36 q^{37} - 18 q^{38} - 36 q^{39} - 6 q^{41} + 30 q^{42} + 6 q^{44} - 12 q^{46} + 6 q^{47} - 18 q^{49} + 12 q^{52} + 12 q^{53} + 12 q^{56} + 18 q^{57} + 36 q^{58} - 24 q^{59} - 30 q^{61} + 6 q^{62} - 18 q^{63} - 6 q^{64} + 24 q^{66} - 12 q^{67} - 12 q^{68} + 6 q^{69} - 42 q^{71} - 6 q^{73} + 6 q^{74} + 18 q^{76} + 24 q^{77} - 48 q^{78} + 60 q^{79} + 18 q^{81} - 6 q^{82} - 24 q^{83} - 24 q^{84} - 36 q^{86} - 54 q^{87} + 6 q^{88} - 12 q^{89} + 24 q^{91} - 24 q^{92} - 6 q^{93} + 60 q^{94} - 30 q^{97} - 36 q^{98} - 12 q^{99}+O(q^{100}) $ 12 * q - 6 * q^7 - 6 * q^8 + 18 * q^9 + 6 * q^11 - 6 * q^13 + 18 * q^17 + 12 * q^18 + 12 * q^21 + 6 * q^22 + 30 * q^23 - 6 * q^29 + 6 * q^31 + 24 * q^33 + 18 * q^36 - 36 * q^37 - 18 * q^38 - 36 * q^39 - 6 * q^41 + 30 * q^42 + 6 * q^44 - 12 * q^46 + 6 * q^47 - 18 * q^49 + 12 * q^52 + 12 * q^53 + 12 * q^56 + 18 * q^57 + 36 * q^58 - 24 * q^59 - 30 * q^61 + 6 * q^62 - 18 * q^63 - 6 * q^64 + 24 * q^66 - 12 * q^67 - 12 * q^68 + 6 * q^69 - 42 * q^71 - 6 * q^73 + 6 * q^74 + 18 * q^76 + 24 * q^77 - 48 * q^78 + 60 * q^79 + 18 * q^81 - 6 * q^82 - 24 * q^83 - 24 * q^84 - 36 * q^86 - 54 * q^87 + 6 * q^88 - 12 * q^89 + 24 * q^91 - 24 * q^92 - 6 * q^93 + 60 * q^94 - 30 * q^97 - 36 * q^98 - 12 * 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 $

$2$	0.766044	+	0.642788i	0.541675	+	0.454519i
$2$	0.766044	+	0.642788i	0.541675	+	0.454519i
$3$	2.55822	−	0.931116i	1.47699	−	0.537580i	0.527001	−	0.849865i	$-0.323316\pi$
$3$	2.55822	−	0.931116i	1.47699	−	0.537580i	0.949989	+	0.312284i	$0.101094\pi$
$4$	0.173648	+	0.984808i	0.0868241	+	0.492404i
$5$		0			0
$5$		0			0
$6$	2.55822	+	0.931116i	1.04439	+	0.380127i
$7$	1.33394	+	2.31045i	0.504182	+	0.873270i	0.999988	+	0.00483621i	$0.00153942\pi$
$7$	1.33394	+	2.31045i	0.504182	+	0.873270i	−0.495806	+	0.868433i	$0.665127\pi$
$8$	−0.500000	+	0.866025i	−0.176777	+	0.306186i
$9$	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	$-0.0997609\pi$
$12$	1.36120	+	2.35767i	0.392945	+	0.680601i
$13$	−4.24577	−	1.54534i	−1.17757	−	0.428599i	−0.322224	−	0.946663i	$-0.604431\pi$
$13$	−4.24577	−	1.54534i	−1.17757	−	0.428599i	−0.855342	+	0.518064i	$0.826653\pi$
$14$	−0.463273	+	2.62735i	−0.123815	+	0.702189i
$15$		0			0
$16$	−0.939693	+	0.342020i	−0.234923	+	0.0855050i
$17$	3.76005	+	3.15506i	0.911946	+	0.765213i	0.972488	−	0.232952i	$-0.0748386\pi$
$17$	3.76005	+	3.15506i	0.911946	+	0.765213i	−0.0605425	+	0.998166i	$0.519283\pi$
$18$	4.41147			1.03979
$19$	−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
$22$	4.62905	−	1.68484i	0.986916	−	0.359208i
$23$	0.542723	+	3.07794i	0.113166	+	0.641794i	0.987642	+	0.156726i	$0.0500940\pi$
$23$	0.542723	+	3.07794i	0.113166	+	0.641794i	−0.874477	+	0.485068i	$0.838795\pi$
$24$	−0.472740	+	2.68104i	−0.0964977	+	0.547266i
$25$		0			0
$26$	−2.25913	−	3.91293i	−0.443052	−	0.767388i
$27$	1.92130	−	3.32779i	0.369754	−	0.640433i
$28$	−2.04372	+	1.71488i	−0.386226	+	0.324082i
$29$	0.227157	−	0.190607i	0.0421820	−	0.0353949i	−0.621453	−	0.783451i	$-0.713457\pi$
$29$	0.227157	−	0.190607i	0.0421820	−	0.0353949i	0.663635	+	0.748057i	$0.269013\pi$
$30$		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	$0.642890\pi$
$32$	−0.939693	−	0.342020i	−0.166116	−	0.0604612i
$33$	2.32878	−	13.2072i	0.405388	−	2.29907i
$34$	0.852334	+	4.83382i	0.146174	+	0.828994i
$35$		0			0
$36$	3.37939	+	2.83564i	0.563231	+	0.472607i
$37$	−8.79946			−1.44662			−0.723311	−	0.690522i	$-0.757381\pi$
$37$	−8.79946			−1.44662			−0.723311	+	0.690522i	$0.757381\pi$
$38$	2.29122	−	3.70814i	0.371685	−	0.601540i
$39$	−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	$0.591560\pi$
$42$	1.26122	+	7.15271i	0.194610	+	1.10369i
$43$	−0.528937	+	2.99975i	−0.0806621	+	0.457458i	0.917547	+	0.397628i	$0.130167\pi$
$43$	−0.528937	+	2.99975i	−0.0806621	+	0.457458i	−0.998209	+	0.0598292i	$0.980944\pi$
$44$	4.62905	+	1.68484i	0.697855	+	0.253998i
$45$		0			0
$46$	−1.56271	+	2.70669i	−0.230409	+	0.399080i
$47$	1.73024	−	1.45184i	0.252381	−	0.211773i	−0.507816	−	0.861466i	$-0.669547\pi$
$47$	1.73024	−	1.45184i	0.252381	−	0.211773i	0.760197	+	0.649693i	$0.225103\pi$
$48$	−2.08548	+	1.74993i	−0.301013	+	0.252580i
$49$	−0.0587989	+	0.101843i	−0.00839985	+	0.0145490i
$50$		0			0
$51$	12.5568	+	4.57029i	1.75830	+	0.639968i
$52$	0.784587	−	4.44962i	0.108803	−	0.617051i
$53$	2.29471	+	13.0140i	0.315203	+	1.78761i	0.571077	+	0.820896i	$0.306526\pi$
$53$	2.29471	+	13.0140i	0.315203	+	1.78761i	−0.255874	+	0.966710i	$0.582363\pi$
$54$	3.61086	−	1.31425i	0.491376	−	0.178846i
$55$		0			0
$56$	−2.66788			−0.356511
$57$	−5.62377	−	10.4495i	−0.744886	−	1.38407i
$58$	0.296532			0.0389366
$59$	−9.63183	−	8.08206i	−1.25396	−	1.05220i	−0.996299	−	0.0859593i	$-0.972605\pi$
$59$	−9.63183	−	8.08206i	−1.25396	−	1.05220i	−0.257659	−	0.966236i	$-0.582951\pi$
$60$		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	$-0.151651\pi$
$62$	−1.08911	+	6.17664i	−0.138317	+	0.784434i
$63$	11.0595	+	4.02534i	1.39337	+	0.507145i
$64$	−0.500000	−	0.866025i	−0.0625000	−	0.108253i
$65$		0			0
$66$	10.2733	−	8.62036i	1.26456	−	1.06109i
$67$	7.47864	−	6.27533i	0.913662	−	0.766653i	−0.0591504	−	0.998249i	$-0.518839\pi$
$67$	7.47864	−	6.27533i	0.913662	−	0.766653i	0.972812	+	0.231596i	$0.0743947\pi$
$68$	−2.45420	+	4.25079i	−0.297615	+	0.515485i
$69$	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	$-0.0216551\pi$
$72$	0.766044	+	4.34445i	0.0902792	+	0.511999i
$73$	−4.45766	+	1.62245i	−0.521729	+	0.189894i	−0.589442	−	0.807811i	$-0.700652\pi$
$73$	−4.45766	+	1.62245i	−0.521729	+	0.189894i	0.0677123	+	0.997705i	$0.478430\pi$
$74$	−6.74078	−	5.65618i	−0.783599	−	0.657518i
$75$		0			0
$76$	4.13872	−	1.36784i	0.474744	−	0.156901i
$77$	13.1423			1.49771
$78$	−9.42274	−	7.90662i	−1.06692	−	0.895248i
$79$	−0.708572	+	0.257899i	−0.0797206	+	0.0290159i	−0.381573	−	0.924339i	$-0.624617\pi$
$79$	−0.708572	+	0.257899i	−0.0797206	+	0.0290159i	0.301852	+	0.953355i	$0.402395\pi$
$80$		0			0
$81$	−0.481582	+	2.73119i	−0.0535091	+	0.303465i
$82$	−7.15482	−	2.60414i	−0.790118	−	0.287579i
$83$	−5.52668	−	9.57249i	−0.606632	−	1.05072i	−0.991791	−	0.127868i	$-0.959187\pi$
$83$	−5.52668	−	9.57249i	−0.606632	−	1.05072i	0.385159	−	0.922850i	$-0.374147\pi$
$84$	−3.63152	+	6.28999i	−0.396232	+	0.686294i
$85$		0			0
$86$	−2.33339	+	1.95795i	−0.251616	+	0.211131i
$87$	0.403640	−	0.699125i	0.0432747	−	0.0749541i
$88$	2.46306	+	4.26615i	0.262564	+	0.454773i
$89$	−7.44939	−	2.71136i	−0.789634	−	0.287403i	−0.0844501	−	0.996428i	$-0.526913\pi$
$89$	−7.44939	−	2.71136i	−0.789634	−	0.287403i	−0.705184	+	0.709024i	$0.749136\pi$
$90$		0			0
$91$	−2.09319	−	11.8711i	−0.219426	−	1.24442i
$92$	−2.93693	+	1.06896i	−0.306196	+	0.111446i
$93$	13.0800	+	10.9754i	1.35633	+	1.13810i
$94$	2.25866			0.232963
$95$		0			0
$96$	−2.72240			−0.277854
$97$	−5.45292	−	4.57554i	−0.553660	−	0.464576i	0.322518	−	0.946563i	$-0.395471\pi$
$97$	−5.45292	−	4.57554i	−0.553660	−	0.464576i	−0.876178	+	0.481987i	$0.839915\pi$
$98$	−0.110506	+	0.0402208i	−0.0111628	+	0.00406292i
$99$	−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	$0.508485\pi$
$102$	6.68131	+	11.5724i	0.661548	+	1.14584i
$103$	4.02870	−	6.97792i	0.396960	−	0.687555i	−0.596389	−	0.802695i	$-0.703399\pi$
$103$	4.02870	−	6.97792i	0.396960	−	0.687555i	0.993349	+	0.115141i	$0.0367319\pi$
$104$	3.46119	−	2.90428i	0.339397	−	0.284788i
$105$		0			0
$106$	−6.60737	+	11.4443i	−0.641764	+	1.11157i
$107$	−3.04424	−	5.27279i	−0.294298	−	0.509739i	0.680523	−	0.732727i	$-0.261753\pi$
$107$	−3.04424	−	5.27279i	−0.294298	−	0.509739i	−0.974821	+	0.222987i	$0.928419\pi$
$108$	3.61086	+	1.31425i	0.347455	+	0.126463i
$109$	1.52473	−	8.64718i	0.146043	−	0.828250i	−0.820481	−	0.571673i	$-0.806294\pi$
$109$	1.52473	−	8.64718i	0.146043	−	0.828250i	0.966524	−	0.256576i	$-0.0825945\pi$
$110$		0			0
$111$	−22.5110	+	8.19332i	−2.13665	+	0.777676i
$112$	−2.04372	−	1.71488i	−0.193113	−	0.162041i
$113$	−20.1754			−1.89794			−0.948971	−	0.315364i	$-0.897873\pi$
$113$	−20.1754			−1.89794			−0.948971	+	0.315364i	$0.897873\pi$
$114$	2.40873	−	11.6196i	0.225598	−	1.08828i
$115$		0			0
$116$	0.227157	+	0.190607i	0.0210910	+	0.0176974i
$117$	−18.7301	+	6.81721i	−1.73160	+	0.630251i
$118$	−2.18336	−	12.3824i	−0.200994	−	1.13990i
$119$	−2.27393	+	12.8961i	−0.208450	+	1.18218i
$120$		0			0
$121$	−6.63337	−	11.4893i	−0.603034	−	1.04449i
$122$	2.32220	−	4.02216i	0.210242	−	0.364150i
$123$	−15.8789	+	13.3239i	−1.43175	+	1.20138i
$124$	−4.80457	+	4.03152i	−0.431463	+	0.362041i
$125$		0			0
$126$	5.88465	+	10.1925i	0.524246	+	0.908021i
$127$	6.02301	+	2.19220i	0.534456	+	0.194526i	0.595127	−	0.803632i	$-0.297102\pi$
$127$	6.02301	+	2.19220i	0.534456	+	0.194526i	−0.0606709	+	0.998158i	$0.519324\pi$
$128$	0.173648	−	0.984808i	0.0153485	−	0.0870455i
$129$	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	$0.514923\pi$
$132$	13.4109			1.16727
$133$	9.12763	−	7.20561i	0.791466	−	0.624805i
$134$	9.76267			0.843367
$135$		0			0
$136$	−4.61238	+	1.67877i	−0.395509	+	0.143953i
$137$	2.46370	+	13.9723i	0.210488	+	1.19374i	0.888567	+	0.458747i	$0.151701\pi$
$137$	2.46370	+	13.9723i	0.210488	+	1.19374i	−0.678079	+	0.734989i	$0.737187\pi$
$138$	−1.47751	+	8.37938i	−0.125774	+	0.713300i
$139$	18.8253	+	6.85185i	1.59674	+	0.581167i	0.978757	−	0.205023i	$-0.0657269\pi$
$139$	18.8253	+	6.85185i	1.59674	+	0.581167i	0.617985	+	0.786190i	$0.287949\pi$
$140$		0			0
$141$	3.07450	−	5.32518i	0.258919	−	0.448461i
$142$	3.10079	−	2.60188i	0.260213	−	0.218345i
$143$	−17.0503	+	14.3069i	−1.42581	+	1.19640i
$144$	−2.20574	+	3.82045i	−0.183811	+	0.318371i
$145$		0			0
$146$	−4.45766	−	1.62245i	−0.368918	−	0.134275i
$147$	−0.0555932	+	0.315285i	−0.00458525	+	0.0260043i
$148$	−1.52801	−	8.66578i	−0.125602	−	0.712322i
$149$	4.21077	−	1.53259i	0.344959	−	0.125555i	−0.163730	−	0.986505i	$-0.552353\pi$
$149$	4.21077	−	1.53259i	0.344959	−	0.125555i	0.508689	+	0.860950i	$0.330130\pi$
$150$		0			0
$151$	−13.9346			−1.13398			−0.566990	−	0.823724i	$-0.691892\pi$
$151$	−13.9346			−1.13398			−0.566990	+	0.823724i	$0.691892\pi$
$152$	4.04967	+	1.61250i	0.328472	+	0.130791i
$153$	21.6533			1.75056
$154$	10.0676	+	8.44773i	0.811271	+	0.680737i
$155$		0			0
$156$	−2.13596	−	12.1136i	−0.171014	−	0.969868i
$157$	−1.24825	+	7.07915i	−0.0996209	+	0.564978i	0.893612	+	0.448840i	$0.148163\pi$
$157$	−1.24825	+	7.07915i	−0.0996209	+	0.564978i	−0.993233	+	0.116138i	$0.962948\pi$
$158$	−0.708572	−	0.257899i	−0.0563710	−	0.0205174i
$159$	17.9879	+	31.1560i	1.42653	+	2.47083i
$160$		0			0
$161$	−6.38747	+	5.35972i	−0.503403	+	0.422405i
$162$	−2.12449	+	1.78265i	−0.166915	+	0.140059i
$163$	−0.799136	+	1.38414i	−0.0625932	+	0.108415i	−0.895624	−	0.444812i	$-0.853270\pi$
$163$	−0.799136	+	1.38414i	−0.0625932	+	0.108415i	0.833031	+	0.553227i	$0.186604\pi$
$164$	−3.80700	−	6.59392i	−0.297277	−	0.514899i
$165$		0			0
$166$	1.91940	−	10.8854i	0.148974	−	0.844874i
$167$	−1.45895	−	8.27409i	−0.112897	−	0.640268i	−0.987770	−	0.155917i	$-0.950167\pi$
$167$	−1.45895	−	8.27409i	−0.112897	−	0.640268i	0.874874	−	0.484351i	$-0.160944\pi$
$168$	−6.82503	+	2.48411i	−0.526563	+	0.191653i
$169$	5.67996	+	4.76605i	0.436920	+	0.366619i
$170$		0			0
$171$	−14.3547	−	12.7947i	−1.09773	−	0.978435i
$172$	−3.04603			−0.232257
$173$	−6.60745	−	5.54431i	−0.502355	−	0.421526i	0.356075	−	0.934458i	$-0.384115\pi$
$173$	−6.60745	−	5.54431i	−0.502355	−	0.421526i	−0.858429	+	0.512932i	$0.828559\pi$
$174$	0.758595	−	0.276106i	0.0575089	−	0.0209315i
$175$		0			0
$176$	−0.855413	+	4.85129i	−0.0644792	+	0.365680i
$177$	−32.1657	−	11.7074i	−2.41772	−	0.879979i
$178$	−3.96374	−	6.86540i	−0.297095	−	0.514583i
$179$	−2.68184	+	4.64508i	−0.200450	+	0.347189i	−0.948673	−	0.316257i	$-0.897574\pi$
$179$	−2.68184	+	4.64508i	−0.200450	+	0.347189i	0.748224	+	0.663447i	$0.230907\pi$
$180$		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	$0.989636\pi$
$182$	6.02709	−	10.4392i	0.446758	−	0.773807i
$183$	−6.32195	−	10.9499i	−0.467332	−	0.809443i
$184$	−2.93693	−	1.06896i	−0.216514	−	0.0788045i
$185$		0			0
$186$	2.96499	+	16.8153i	0.217404	+	1.23296i
$187$	22.7212	−	8.26984i	1.66154	−	0.604750i
$188$	1.73024	+	1.45184i	0.126190	+	0.105886i
$189$	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	$0.681307\pi$
$192$	−2.08548	−	1.74993i	−0.150507	−	0.126290i
$193$	21.6078	−	7.86461i	1.55537	−	0.566107i	0.585697	−	0.810530i	$-0.300821\pi$
$193$	21.6078	−	7.86461i	1.55537	−	0.566107i	0.969669	+	0.244423i	$0.0785985\pi$
$194$	−1.23608	−	7.01014i	−0.0887451	−	0.503299i
$195$		0			0
$196$	−0.110506	−	0.0402208i	−0.00789328	−	0.00287292i
$197$	−7.12078	−	12.3336i	−0.507335	−	0.878729i	−0.999964	−	0.00849002i	$-0.997298\pi$
$197$	−7.12078	−	12.3336i	−0.507335	−	0.878729i	0.492629	−	0.870239i	$-0.336036\pi$
$198$	10.8657	−	18.8200i	0.772195	−	1.33748i
$199$	0.828568	−	0.695251i	0.0587356	−	0.0492850i	−0.612947	−	0.790124i	$-0.710016\pi$
$199$	0.828568	−	0.695251i	0.0587356	−	0.0492850i	0.671683	+	0.740839i	$0.265572\pi$
$200$		0			0
$201$	13.2890	−	23.0172i	0.937331	−	1.62351i
$202$	3.18432	+	5.51540i	0.224048	+	0.388062i
$203$	0.743403	+	0.270577i	0.0521767	+	0.0189908i
$204$	−2.32040	+	13.1596i	−0.162460	+	0.921357i
$205$		0			0
$206$	7.57148	−	2.75579i	0.527530	−	0.192005i
$207$	10.5620	+	8.86256i	0.734109	+	0.615991i
$208$	4.51826			0.313285
$209$	−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	$0.383412\pi$
$212$	−12.4178	+	4.51971i	−0.852857	+	0.310415i
$213$	−1.91356	−	10.8523i	−0.131115	−	0.743589i
$214$	1.05725	−	5.99599i	0.0722725	−	0.409877i
$215$		0			0
$216$	1.92130	+	3.32779i	0.130728	+	0.226427i
$217$	−8.36638	+	14.4910i	−0.567947	+	0.983713i
$218$	6.72631	−	5.64405i	0.455563	−	0.382263i
$219$	−9.89298	+	8.30120i	−0.668506	+	0.560943i
$220$		0			0
$221$	−11.0887	−	19.2062i	−0.745907	−	1.29195i
$222$	−22.5110	−	8.19332i	−1.51084	−	0.549900i
$223$	−4.70436	+	26.6797i	−0.315027	+	1.78661i	0.257040	+	0.966401i	$0.417253\pi$
$223$	−4.70436	+	26.6797i	−0.315027	+	1.78661i	−0.572067	+	0.820207i	$0.693858\pi$
$224$	−0.463273	−	2.62735i	−0.0309537	−	0.175547i
$225$		0			0
$226$	−15.4552	−	12.9685i	−1.02807	−	0.862651i
$227$	2.74631			0.182279			0.0911394	−	0.995838i	$-0.470949\pi$
$227$	2.74631			0.182279			0.0911394	+	0.995838i	$0.470949\pi$
$228$	9.31416	−	7.35286i	0.616845	−	0.486955i
$229$	18.3269			1.21107			0.605537	−	0.795817i	$-0.292958\pi$
$229$	18.3269			1.21107			0.605537	+	0.795817i	$0.292958\pi$
$230$		0			0
$231$	33.6210	−	12.2370i	2.21210	−	0.805138i
$232$	0.0514923	+	0.292027i	0.00338063	+	0.0191725i
$233$	0.996532	−	5.65161i	0.0652850	−	0.370250i	−0.934609	−	0.355677i	$-0.884250\pi$
$233$	0.996532	−	5.65161i	0.0652850	−	0.370250i	0.999894	−	0.0145723i	$-0.00463866\pi$
$234$	−18.7301	−	6.81721i	−1.22443	−	0.445655i
$235$		0			0
$236$	6.28673	−	10.8889i	0.409231	−	0.708809i
$237$	−1.57255	+	1.31953i	−0.102148	+	0.0857124i
$238$	−10.0314	+	8.41732i	−0.650237	+	0.545614i
$239$	3.55176	−	6.15182i	0.229744	−	0.397928i	−0.727988	−	0.685590i	$-0.759544\pi$
$239$	3.55176	−	6.15182i	0.229744	−	0.397928i	0.957732	+	0.287661i	$0.0928777\pi$
$240$		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	$0.458901\pi$
$242$	2.30375	−	13.0652i	0.148090	−	0.839863i
$243$	3.31284	+	18.7881i	0.212519	+	1.20525i
$244$	4.36430	−	1.58848i	0.279396	−	0.101692i
$245$		0			0
$246$	−20.7284			−1.32159
$247$	−3.99767	+	19.2846i	−0.254366	+	1.22705i
$248$	−6.27192			−0.398268
$249$	−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	$0.885394\pi$
$252$	−2.04372	+	11.5905i	−0.128742	+	0.730132i
$253$	14.4677	+	5.26581i	0.909577	+	0.331059i
$254$	3.20478	+	5.55084i	0.201086	+	0.348291i
$255$		0			0
$256$	0.766044	−	0.642788i	0.0478778	−	0.0401742i
$257$	13.9029	−	11.6659i	0.867239	−	0.727700i	−0.0962757	−	0.995355i	$-0.530693\pi$
$257$	13.9029	−	11.6659i	0.867239	−	0.727700i	0.963515	+	0.267655i	$0.0862486\pi$
$258$	−4.14625	+	7.18152i	−0.258135	+	0.447102i
$259$	−11.7380	−	20.3307i	−0.729362	−	1.26329i
$260$		0			0
$261$	0.227157	−	1.28827i	0.0140607	−	0.0797419i
$262$	2.40956	+	13.6653i	0.148863	+	0.844245i
$263$	−12.9914	+	4.72850i	−0.801087	+	0.291572i	−0.709937	−	0.704265i	$-0.751277\pi$
$263$	−12.9914	+	4.72850i	−0.801087	+	0.291572i	−0.0911502	+	0.995837i	$0.529054\pi$
$264$	10.2733	+	8.62036i	0.632281	+	0.530547i
$265$		0			0
$266$	11.6238	+	0.347310i	0.712704	+	0.0212950i
$267$	−21.5818			−1.32078
$268$	7.47864	+	6.27533i	0.456831	+	0.383327i
$269$	6.31020	−	2.29673i	0.384740	−	0.140034i	−0.142407	−	0.989808i	$-0.545484\pi$
$269$	6.31020	−	2.29673i	0.384740	−	0.140034i	0.527147	+	0.849774i	$0.323262\pi$
$270$		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	$0.0565411\pi$
$272$	−4.61238	−	1.67877i	−0.279667	−	0.101790i
$273$	−16.4082	−	28.4198i	−0.993068	−	1.72004i
$274$	−7.09393	+	12.2870i	−0.428560	+	0.742288i
$275$		0			0
$276$	−6.51800	+	5.46925i	−0.392338	+	0.329210i
$277$	−5.52354	+	9.56705i	−0.331877	+	0.574829i	−0.982880	−	0.184247i	$-0.941015\pi$
$277$	−5.52354	+	9.56705i	−0.331877	+	0.574829i	0.651003	+	0.759076i	$0.274349\pi$
$278$	10.0167	+	17.3495i	0.600764	+	1.04055i
$279$	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	$0.687879\pi$
$282$	5.77816	−	2.10308i	0.344084	−	0.125236i
$283$	−5.69304	−	4.77703i	−0.338416	−	0.283965i	0.457703	−	0.889105i	$-0.348672\pi$
$283$	−5.69304	−	4.77703i	−0.338416	−	0.283965i	−0.796119	+	0.605141i	$0.793117\pi$
$284$	4.04780			0.240193
$285$		0			0
$286$	−22.2575			−1.31612
$287$	−15.5609	−	13.0571i	−0.918529	−	0.770737i
$288$	−4.14543	+	1.50881i	−0.244272	+	0.0889077i
$289$	1.23157	+	6.98459i	0.0724454	+	0.410858i
$290$		0			0
$291$	−18.2101	−	6.62795i	−1.06750	−	0.388537i
$292$	−2.37187	−	4.10820i	−0.138803	−	0.240414i
$293$	1.30317	−	2.25716i	0.0761322	−	0.131865i	−0.825446	−	0.564481i	$-0.809076\pi$
$293$	1.30317	−	2.25716i	0.0761322	−	0.131865i	0.901578	+	0.432616i	$0.142410\pi$
$294$	−0.245248	+	0.205788i	−0.0143032	+	0.0120018i
$295$		0			0
$296$	4.39973	−	7.62056i	0.255729	−	0.442936i
$297$	−9.46457	−	16.3931i	−0.549190	−	0.951225i
$298$	4.21077	+	1.53259i	0.243923	+	0.0887807i
$299$	2.45216	−	13.9069i	0.141812	−	0.804257i
$300$		0			0
$301$	−7.63636	+	2.77941i	−0.440152	+	0.160202i
$302$	−10.6745	−	8.95698i	−0.614249	−	0.515416i
$303$	17.3380			0.996041
$304$	2.06574	+	3.83832i	0.118478	+	0.220143i
$305$		0			0
$306$	16.5874	+	13.9184i	0.948236	+	0.795665i
$307$	−8.13819	+	2.96206i	−0.464471	+	0.169054i	−0.563646	−	0.826016i	$-0.690602\pi$
$307$	−8.13819	+	2.96206i	−0.464471	+	0.169054i	0.0991751	+	0.995070i	$0.468380\pi$
$308$	2.28214	+	12.9427i	0.130037	+	0.737477i
$309$	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	$-0.450135\pi$
$312$	6.15026	−	10.6526i	0.348190	−	0.603082i
$313$	20.4213	−	17.1355i	1.15428	−	0.968557i	0.154470	−	0.987997i	$-0.450633\pi$
$313$	20.4213	−	17.1355i	1.15428	−	0.968557i	0.999811	+	0.0194404i	$0.00618845\pi$
$314$	−5.50660	+	4.62059i	−0.310756	+	0.260755i
$315$		0			0
$316$	−0.377023	−	0.653023i	−0.0212092	−	0.0367354i
$317$	19.8906	+	7.23957i	1.11717	+	0.406615i	0.833617	−	0.552343i	$-0.186266\pi$
$317$	19.8906	+	7.23957i	1.11717	+	0.406615i	0.283548	+	0.958958i	$0.408488\pi$
$318$	−6.24714	+	35.4293i	−0.350322	+	1.98677i
$319$	−0.253658	−	1.43856i	−0.0142021	−	0.0805441i
$320$		0			0
$321$	−12.6974	−	10.6544i	−0.708701	−	0.594671i
$322$	−8.33825			−0.464672
$323$	11.2462	−	18.2010i	0.625755	−	1.01273i
$324$	−2.77332			−0.154073
$325$		0			0
$326$	−1.50188	+	0.546641i	−0.0831817	+	0.0302757i
$327$	−4.15093	−	23.5411i	−0.229547	−	1.30183i
$328$	1.32216	−	7.49833i	0.0730039	−	0.414026i
$329$	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	$0.142350\pi$
$332$	8.46737	−	7.10497i	0.464707	−	0.389936i
$333$	−29.7368	+	24.9521i	−1.62956	+	1.36737i
$334$	4.20086	−	7.27611i	0.229861	−	0.398131i
$335$		0			0
$336$	−6.82503	−	2.48411i	−0.372336	−	0.135519i
$337$	−0.390631	+	2.21538i	−0.0212791	+	0.120679i	−0.993597	−	0.112982i	$-0.963960\pi$
$337$	−0.390631	+	2.21538i	−0.0212791	+	0.120679i	0.972318	+	0.233662i	$0.0750708\pi$
$338$	1.28754	+	7.30202i	0.0700331	+	0.397177i
$339$	−51.6131	+	18.7856i	−2.80324	+	1.02030i
$340$		0			0
$341$	30.8963			1.67313
$342$	−2.77205	−	19.0283i	−0.149895	−	1.02893i
$343$	18.3614			0.991425
$344$	−2.33339	−	1.95795i	−0.125808	−	0.105565i
$345$		0			0
$346$	−1.49779	−	8.49437i	−0.0805215	−	0.456660i
$347$	3.50481	−	19.8767i	0.188148	−	1.06704i	−0.733696	−	0.679478i	$-0.762206\pi$
$347$	3.50481	−	19.8767i	0.188148	−	1.06704i	0.921844	−	0.387561i	$-0.126683\pi$
$348$	0.758595	+	0.276106i	0.0406650	+	0.0148008i
$349$	−11.1094	−	19.2421i	−0.594673	−	1.03000i	−0.993593	−	0.113018i	$-0.963948\pi$
$349$	−11.1094	−	19.2421i	−0.594673	−	1.03000i	0.398920	−	0.916986i	$-0.369385\pi$
$350$		0			0
$351$	−13.3000	+	11.1600i	−0.709899	+	0.595676i
$352$	−3.77363	+	3.16645i	−0.201135	+	0.168773i
$353$	1.53901	−	2.66564i	0.0819130	−	0.141878i	−0.822159	−	0.569259i	$-0.807230\pi$
$353$	1.53901	−	2.66564i	0.0819130	−	0.141878i	0.904072	+	0.427381i	$0.140564\pi$
$354$	−17.1150	−	29.6441i	−0.909652	−	1.57556i
$355$		0			0
$356$	1.37659	−	7.80704i	0.0729592	−	0.413772i
$357$	6.19054	+	35.1083i	0.327638	+	1.85813i
$358$	−5.04021	+	1.83448i	−0.266383	+	0.0969555i
$359$	15.6987	+	13.1727i	0.828543	+	0.695230i	0.954956	−	0.296747i	$-0.0959020\pi$
$359$	15.6987	+	13.1727i	0.828543	+	0.695230i	−0.126413	+	0.991978i	$0.540346\pi$
$360$		0			0
$361$	−18.2103	+	5.42081i	−0.958437	+	0.285306i
$362$	−21.1642			−1.11237
$363$	−27.6676	−	23.2158i	−1.45217	−	1.21852i
$364$	11.3272	−	4.12277i	0.593708	−	0.216092i
$365$		0			0
$366$	2.19559	−	12.4518i	0.114765	−	0.650867i
$367$	3.47279	+	1.26399i	0.181278	+	0.0659798i	0.431064	−	0.902321i	$-0.358138\pi$
$367$	3.47279	+	1.26399i	0.181278	+	0.0659798i	−0.249786	+	0.968301i	$0.580360\pi$
$368$	−1.56271	−	2.70669i	−0.0814618	−	0.141096i
$369$	−16.7945	+	29.0889i	−0.874286	+	1.51431i
$370$		0			0
$371$	−27.0072	+	22.6617i	−1.40214	+	1.17654i
$372$	−8.53735	+	14.7871i	−0.442641	+	0.766677i
$373$	−2.77929	−	4.81387i	−0.143906	−	0.249253i	0.785058	−	0.619422i	$-0.212633\pi$
$373$	−2.77929	−	4.81387i	−0.143906	−	0.249253i	−0.928964	+	0.370169i	$0.879300\pi$
$374$	22.7212	+	8.26984i	1.17488	+	0.427623i
$375$		0			0
$376$	0.392213	+	2.22435i	0.0202268	+	0.114712i
$377$	−1.25901	+	0.458242i	−0.0648422	+	0.0236006i
$378$	7.85319	+	6.58961i	0.403924	+	0.338933i
$379$	6.50034			0.333900			0.166950	−	0.985965i	$-0.446608\pi$
$379$	6.50034			0.333900			0.166950	+	0.985965i	$0.446608\pi$
$380$		0			0
$381$	17.4494			0.893959
$382$	−11.4188	−	9.58154i	−0.584238	−	0.490234i
$383$	−5.04437	+	1.83600i	−0.257755	+	0.0938152i	−0.467666	−	0.883905i	$-0.654905\pi$
$383$	−5.04437	+	1.83600i	−0.257755	+	0.0938152i	0.209911	+	0.977721i	$0.432683\pi$
$384$	−0.472740	−	2.68104i	−0.0241244	−	0.136816i
$385$		0			0
$386$	21.6078	+	7.86461i	1.09981	+	0.400298i
$387$	6.71873	+	11.6372i	0.341532	+	0.591551i
$388$	3.55914	−	6.16461i	0.180688	−	0.312961i
$389$	6.23034	−	5.22788i	0.315891	−	0.265064i	−0.471031	−	0.882117i	$-0.656118\pi$
$389$	6.23034	−	5.22788i	0.315891	−	0.265064i	0.786922	+	0.617053i	$0.211674\pi$
$390$		0			0
$391$	−7.67039	+	13.2855i	−0.387908	+	0.671877i
$392$	−0.0587989	−	0.101843i	−0.00296979	−	0.00514384i
$393$	35.4982	+	12.9203i	1.79065	+	0.651742i
$394$	2.47302	−	14.0252i	0.124589	−	0.706579i
$395$		0			0
$396$	20.4209	−	7.43261i	1.02619	−	0.373503i
$397$	14.6665	+	12.3067i	0.736091	+	0.617654i	0.931785	−	0.363012i	$-0.118251\pi$
$397$	14.6665	+	12.3067i	0.736091	+	0.617654i	−0.195694	+	0.980665i	$0.562696\pi$
$398$	1.08162			0.0542167
$399$	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	$0.877957\pi$
$402$	24.9751	−	9.09019i	1.24564	−	0.453377i
$403$	−4.92087	−	27.9077i	−0.245126	−	1.39018i
$404$	−1.10590	+	6.27188i	−0.0550207	+	0.312038i
$405$		0			0
$406$	0.395557	+	0.685124i	0.0196311	+	0.0340021i
$407$	−21.6736	+	37.5398i	−1.07432	+	1.86078i
$408$	−10.2364	+	8.58933i	−0.506776	+	0.425235i
$409$	17.0844	−	14.3355i	0.844769	−	0.708845i	−0.113862	−	0.993497i	$-0.536322\pi$
$409$	17.0844	−	14.3355i	0.844769	−	0.708845i	0.958631	+	0.284651i	$0.0918779\pi$
$410$		0			0
$411$	19.3125	+	33.4503i	0.952617	+	1.64998i
$412$	7.57148	+	2.75579i	0.373020	+	0.135768i
$413$	5.82494	−	33.0349i	0.286627	−	1.62554i
$414$	2.39421	+	13.5782i	0.117669	+	0.667334i
$415$		0			0
$416$	3.46119	+	2.90428i	0.169699	+	0.142394i
$417$	54.5392			2.67080
$418$	−10.1761	−	18.9081i	−0.497729	−	0.924825i
$419$	−6.32056			−0.308780			−0.154390	−	0.988010i	$-0.549341\pi$
$419$	−6.32056			−0.308780			−0.154390	+	0.988010i	$0.549341\pi$
$420$		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	$0.148825\pi$
$422$	4.41165	+	25.0197i	0.214756	+	1.21794i
$423$	1.73024	−	9.81266i	0.0841270	−	0.477108i
$424$	−12.4178	−	4.51971i	−0.603061	−	0.219496i
$425$		0			0
$426$	5.50987	−	9.54337i	0.266954	−	0.462378i
$427$	9.49183	−	7.96459i	0.459342	−	0.385433i
$428$	4.66405	−	3.91360i	0.225445	−	0.189171i
$429$	−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	$0.298563\pi$
$432$	−0.667261	+	3.78422i	−0.0321036	+	0.182068i
$433$	1.66700	+	9.45404i	0.0801110	+	0.454332i	0.998305	+	0.0582009i	$0.0185364\pi$
$433$	1.66700	+	9.45404i	0.0801110	+	0.454332i	−0.918194	+	0.396131i	$0.870353\pi$
$434$	−15.7237	+	5.72294i	−0.754759	+	0.274710i
$435$		0			0
$436$	8.78058			0.420513
$437$	12.9352	−	4.27506i	0.618776	−	0.204504i
$438$	−12.9144			−0.617072
$439$	7.13348	+	5.98570i	0.340462	+	0.285682i	0.796947	−	0.604050i	$-0.206447\pi$
$439$	7.13348	+	5.98570i	0.340462	+	0.285682i	−0.456484	+	0.889731i	$0.650892\pi$
$440$		0			0
$441$	0.0900852	+	0.510899i	0.00428977	+	0.0243285i
$442$	3.85106	−	21.8405i	0.183176	−	1.03885i
$443$	−31.4760	−	11.4563i	−1.49547	−	0.544307i	−0.540588	−	0.841287i	$-0.681798\pi$
$443$	−31.4760	−	11.4563i	−1.49547	−	0.544307i	−0.954884	+	0.296980i	$0.904021\pi$
$444$	−11.9778	−	20.7462i	−0.568443	−	0.984572i
$445$		0			0
$446$	−20.7532	+	17.4140i	−0.982690	+	0.824575i
$447$	9.34505	−	7.84143i	0.442006	−	0.370887i
$448$	1.33394	−	2.31045i	0.0630228	−	0.109159i
$449$	−1.10835	−	1.91973i	−0.0523064	−	0.0905974i	0.838687	−	0.544614i	$-0.183324\pi$
$449$	−1.10835	−	1.91973i	−0.0523064	−	0.0905974i	−0.890993	+	0.454017i	$0.849991\pi$
$450$		0			0
$451$	−6.51312	+	36.9377i	−0.306691	+	1.73933i
$452$	−3.50342	−	19.8689i	−0.164787	−	0.934554i
$453$	−35.6478	+	12.9747i	−1.67488	+	0.609606i
$454$	2.10379	+	1.76529i	0.0987359	+	0.0828493i
$455$		0			0
$456$	11.8614	+	0.354408i	0.555460	+	0.0165967i
$457$	14.3375			0.670680			0.335340	−	0.942097i	$-0.391149\pi$
$457$	14.3375			0.670680			0.335340	+	0.942097i	$0.391149\pi$
$458$	14.0392	+	11.7803i	0.656009	+	0.550457i
$459$	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	$-0.0166353\pi$
$462$	33.6210	+	12.2370i	1.56419	+	0.569319i
$463$	15.4527	+	26.7649i	0.718148	+	1.24387i	0.961733	+	0.273989i	$0.0883433\pi$
$463$	15.4527	+	26.7649i	0.718148	+	1.24387i	−0.243585	+	0.969880i	$0.578323\pi$
$464$	−0.148266	+	0.256804i	−0.00688308	+	0.0119218i
$465$		0			0
$466$	4.39618	−	3.68883i	0.203649	−	0.170882i
$467$	3.12701	−	5.41613i	0.144701	−	0.250629i	−0.784561	−	0.620052i	$-0.787111\pi$
$467$	3.12701	−	5.41613i	0.144701	−	0.250629i	0.929261	+	0.369423i	$0.120445\pi$
$468$	−9.96609	−	17.2618i	−0.460683	−	0.797926i
$469$	24.4749	+	8.90814i	1.13015	+	0.411340i
$470$		0			0
$471$	3.39823	+	19.2723i	0.156582	+	0.888021i
$472$	11.8152	−	4.30038i	0.543838	−	0.197941i
$473$	11.4946	+	9.64510i	0.528522	+	0.443482i
$474$	−2.05282			−0.0942891
$475$		0			0
$476$	−13.0950			−0.600209
$477$	44.6577	+	37.4722i	2.04473	+	1.71574i
$478$	6.67512	−	2.42955i	0.305313	−	0.111125i
$479$	5.92188	+	33.5846i	0.270578	+	1.53452i	0.752668	+	0.658400i	$0.228766\pi$
$479$	5.92188	+	33.5846i	0.270578	+	1.53452i	−0.482091	+	0.876121i	$0.660122\pi$
$480$		0			0
$481$	37.3605	+	13.5981i	1.70349	+	0.620021i
$482$	7.14370	+	12.3732i	0.325387	+	0.563586i
$483$	−11.3500	+	19.6588i	−0.516444	+	0.894508i
$484$	10.1629	−	8.52770i	0.461951	−	0.387623i
$485$		0			0
$486$	−9.53894	+	16.5219i	−0.432695	+	0.749450i
$487$	−8.33010	−	14.4281i	−0.377473	−	0.653802i	0.613221	−	0.789911i	$-0.289873\pi$
$487$	−8.33010	−	14.4281i	−0.377473	−	0.653802i	−0.990694	+	0.136109i	$0.956540\pi$
$488$	4.36430	+	1.58848i	0.197563	+	0.0719069i
$489$	−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	$0.187192\pi$
$492$	−15.8789	−	13.3239i	−0.715874	−	0.600690i
$493$	1.45550			0.0655523
$494$	−15.4583	+	12.2032i	−0.695503	+	0.549049i
$495$		0			0
$496$	−4.80457	−	4.03152i	−0.215732	−	0.181020i
$497$	10.1478	−	3.69349i	0.455191	−	0.165676i
$498$	−5.22537	−	29.6345i	−0.234154	−	1.32796i
$499$	−3.75717	+	21.3080i	−0.168194	+	0.953877i	0.777515	+	0.628864i	$0.216480\pi$
$499$	−3.75717	+	21.3080i	−0.168194	+	0.953877i	−0.945710	+	0.325013i	$0.894631\pi$
$500$		0			0
$501$	−11.4364	−	19.8085i	−0.510943	−	0.884979i
$502$	−2.92224	+	5.06147i	−0.130426	+	0.225904i
$503$	−26.5727	+	22.2971i	−1.18482	+	0.994179i	−0.184882	+	0.982761i	$0.559190\pi$
$503$	−26.5727	+	22.2971i	−1.18482	+	0.994179i	−0.999935	+	0.0114181i	$0.996365\pi$
$504$	−9.01580	+	7.56516i	−0.401596	+	0.336979i
$505$		0			0
$506$	7.69811	+	13.3335i	0.342223	+	0.592747i
$507$	18.9683	+	6.90391i	0.842414	+	0.306614i
$508$	−1.11301	+	6.31218i	−0.0493817	+	0.280058i
$509$	5.08253	+	28.8245i	0.225279	+	1.27762i	0.862151	+	0.506652i	$0.169117\pi$
$509$	5.08253	+	28.8245i	0.225279	+	1.27762i	−0.636871	+	0.770970i	$0.719772\pi$
$510$		0			0
$511$	−9.69486	−	8.13495i	−0.428875	−	0.359869i
$512$	1.00000			0.0441942
$513$	−15.5613	−	6.19618i	−0.687047	−	0.273568i
$514$	18.1490			0.800516
$515$		0			0
$516$	−7.79241	+	2.83621i	−0.343042	+	0.124857i
$517$	−1.93209	−	10.9574i	−0.0849733	−	0.481907i
$518$	4.07655	−	23.1193i	0.179113	−	1.01580i
$519$	−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	$0.106337\pi$
$522$	1.00210	−	0.840859i	0.0438606	−	0.0368034i
$523$	−12.4434	+	10.4413i	−0.544114	+	0.456566i	−0.872942	−	0.487824i	$-0.837791\pi$
$523$	−12.4434	+	10.4413i	−0.544114	+	0.456566i	0.328828	+	0.944390i	$0.393346\pi$
$524$	−6.93806	+	12.0171i	−0.303090	+	0.524968i
$525$		0			0
$526$	−12.9914	−	4.72850i	−0.566454	−	0.206172i
$527$	−5.34577	+	30.3174i	−0.232866	+	1.32065i
$528$	2.32878	+	13.2072i	0.101347	+	0.574768i
$529$	12.4338	−	4.52553i	0.540600	−	0.196762i
$530$		0			0
$531$	−55.4675			−2.40708
$532$	8.68113	+	7.73772i	0.376375	+	0.335473i
$533$	34.4020			1.49012
$534$	−16.5326	−	13.8725i	−0.715436	−	0.600322i
$535$		0			0
$536$	1.69527	+	9.61436i	0.0732245	+	0.415277i
$537$	−2.53562	+	14.3802i	−0.109420	+	0.620553i
$538$	6.31020	+	2.29673i	0.272052	+	0.0990189i
$539$	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	$0.0867628\pi$
$542$	−0.0780922	+	0.0655272i	−0.00335435	+	0.00281463i
$543$	−28.8088	+	49.8983i	−1.23630	+	2.14134i
$544$	−2.45420	−	4.25079i	−0.105223	−	0.182251i
$545$		0			0
$546$	5.69850	−	32.3178i	0.243873	−	1.38307i
$547$	5.72713	+	32.4802i	0.244874	+	1.38875i	0.820784	+	0.571239i	$0.193537\pi$
$547$	5.72713	+	32.4802i	0.244874	+	1.38875i	−0.575910	+	0.817513i	$0.695352\pi$
$548$	−13.3322	+	4.85253i	−0.569525	+	0.207290i
$549$	−15.6952	−	13.1698i	−0.669855	−	0.562075i
$550$		0			0
$551$	−0.964898	−	0.860039i	−0.0411061	−	0.0366389i
$552$	−8.50864			−0.362152
$553$	−1.54106	−	1.29310i	−0.0655324	−	0.0549882i
$554$	−10.3809	+	3.77832i	−0.441041	+	0.160526i
$555$		0			0
$556$	−3.47878	+	19.7291i	−0.147533	+	0.836701i
$557$	9.37840	+	3.41346i	0.397376	+	0.144633i	0.532975	−	0.846131i	$-0.321074\pi$
$557$	9.37840	+	3.41346i	0.397376	+	0.144633i	−0.135600	+	0.990764i	$0.543296\pi$
$558$	13.8342	+	23.9616i	0.585649	+	1.01437i
$559$	6.88137	−	11.9189i	0.291051	−	0.504115i
$560$		0			0
$561$	50.4257	−	42.3121i	2.12897	−	1.78642i
$562$	−12.0952	+	20.9496i	−0.510207	+	0.883704i
$563$	−5.11265	−	8.85537i	−0.215472	−	0.373209i	0.737946	−	0.674860i	$-0.235796\pi$
$563$	−5.11265	−	8.85537i	−0.215472	−	0.373209i	−0.953419	+	0.301650i	$0.902462\pi$
$564$	5.77816	+	2.10308i	0.243304	+	0.0885556i
$565$		0			0
$566$	−1.29051	−	7.31883i	−0.0542440	−	0.307633i
$567$	−6.95268	+	2.53057i	−0.291985	+	0.106274i
$568$	3.10079	+	2.60188i	0.130106	+	0.109172i
$569$	4.84333			0.203043			0.101521	−	0.994833i	$-0.467629\pi$
$569$	4.84333			0.203043			0.101521	+	0.994833i	$0.467629\pi$
$570$		0			0
$571$	20.7617			0.868850			0.434425	−	0.900708i	$-0.356952\pi$
$571$	20.7617			0.868850			0.434425	+	0.900708i	$0.356952\pi$
$572$	−17.0503	−	14.3069i	−0.712907	−	0.598200i
$573$	−38.1334	+	13.8794i	−1.59305	+	0.579822i
$574$	−3.52736	−	20.0047i	−0.147229	−	0.834978i
$575$		0			0
$576$	−4.14543	−	1.50881i	−0.172726	−	0.0628672i
$577$	−21.2928	−	36.8802i	−0.886430	−	1.53534i	−0.844066	−	0.536239i	$-0.819845\pi$
$577$	−21.2928	−	36.8802i	−0.886430	−	1.53534i	−0.0423635	−	0.999102i	$-0.513489\pi$
$578$	−3.54617	+	6.14214i	−0.147501	+	0.255480i
$579$	47.9548	−	40.2388i	1.99293	−	1.67227i
$580$		0			0
$581$	14.7445	−	25.5383i	0.611707	−	1.05951i
$582$	−9.68941	−	16.7826i	−0.401639	−	0.695659i
$583$	61.1716	+	22.2647i	2.53347	+	0.922108i
$584$	0.823742	−	4.67167i	0.0340867	−	0.193315i
$585$		0			0
$586$	2.44916	−	0.891423i	0.101174	−	0.0368243i
$587$	20.6160	+	17.2989i	0.850912	+	0.714000i	0.959990	−	0.280033i	$-0.0903455\pi$
$587$	20.6160	+	17.2989i	0.850912	+	0.714000i	−0.109078	+	0.994033i	$0.534790\pi$
$588$	−0.320149			−0.0132027
$589$	21.4581	−	16.9397i	0.884167	−	0.697987i
$590$		0			0
$591$	−29.7005	−	24.9217i	−1.22172	−	1.02514i
$592$	8.26879	−	3.00959i	0.339845	−	0.123693i
$593$	3.60581	+	20.4496i	0.148073	+	0.839763i	0.964848	+	0.262807i	$0.0846483\pi$
$593$	3.60581	+	20.4496i	0.148073	+	0.839763i	−0.816776	+	0.576955i	$0.804241\pi$
$594$	3.28701	−	18.6416i	0.134868	−	0.764873i
$595$		0			0
$596$	2.24050	+	3.88066i	0.0917745	+	0.158958i
$597$	1.47230	−	2.55010i	0.0602573	−	0.104369i
$598$	10.8177	−	9.07709i	0.442367	−	0.371190i
$599$	−22.6279	+	18.9871i	−0.924550	+	0.775790i	−0.974831	−	0.222945i	$-0.928433\pi$
$599$	−22.6279	+	18.9871i	−0.924550	+	0.775790i	0.0502805	+	0.998735i	$0.483988\pi$
$600$		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	$0.677855\pi$
$602$	−7.63636	−	2.77941i	−0.311235	−	0.113280i
$603$	7.47864	−	42.4135i	0.304554	−	1.72721i
$604$	−2.41972	−	13.7229i	−0.0984568	−	0.558376i
$605$		0			0
$606$	13.2817	+	11.1446i	0.539531	+	0.452720i
$607$	6.16015			0.250033			0.125016	−	0.992155i	$-0.460102\pi$
$607$	6.16015			0.250033			0.125016	+	0.992155i	$0.460102\pi$
$608$	−0.884781	+	4.26816i	−0.0358826	+	0.173097i
$609$	2.15373			0.0872735
$610$		0			0
$611$	−9.58977	+	3.49039i	−0.387961	+	0.141206i
$612$	3.76005	+	21.3243i	0.151991	+	0.861983i
$613$	6.19360	−	35.1256i	0.250157	−	1.41871i	−0.558048	−	0.829809i	$-0.688449\pi$
$613$	6.19360	−	35.1256i	0.250157	−	1.41871i	0.808205	−	0.588902i	$-0.200439\pi$
$614$	−8.13819	−	2.96206i	−0.328431	−	0.119539i
$615$		0			0
$616$	−6.57117	+	11.3816i	−0.264760	+	0.458578i
$617$	−5.63668	+	4.72973i	−0.226924	+	0.190412i	−0.749160	−	0.662389i	$-0.769543\pi$
$617$	−5.63668	+	4.72973i	−0.226924	+	0.190412i	0.522236	+	0.852801i	$0.325098\pi$
$618$	16.8036	−	14.0999i	0.675939	−	0.567180i
$619$	−12.7001	+	21.9972i	−0.510459	+	0.884141i	0.489468	+	0.872021i	$0.337191\pi$
$619$	−12.7001	+	21.9972i	−0.510459	+	0.884141i	−0.999927	+	0.0121194i	$0.996142\pi$
$620$		0			0
$621$	11.2855	+	4.10757i	0.452870	+	0.164831i
$622$	4.76138	−	27.0031i	0.190914	−	1.08273i
$623$	−3.67259	−	20.8283i	−0.147139	−	0.834467i
$624$	11.5587	−	4.20702i	0.462719	−	0.168416i
$625$		0			0
$626$	26.6581			1.06547
$627$	−58.4307	−	1.74586i	−2.33350	−	0.0697229i
$628$	−7.18836			−0.286847
$629$	−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	$0.861334\pi$
$632$	0.130939	−	0.742591i	0.00520847	−	0.0295387i
$633$	64.9934	+	23.6556i	2.58325	+	0.940228i
$634$	10.5835	+	18.3312i	0.420326	+	0.728027i
$635$		0			0
$636$	−27.5591	+	23.1248i	−1.09279	+	0.916958i
$637$	0.407028	−	0.341537i	0.0161270	−	0.0135322i
$638$	0.730378	−	1.26505i	0.0289159	−	0.0500839i
$639$	−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	$0.929527\pi$
$642$	−2.87827	−	16.3235i	−0.113596	−	0.644237i
$643$	2.24241	−	0.816169i	0.0884319	−	0.0321866i	−0.297425	−	0.954745i	$-0.596128\pi$
$643$	2.24241	−	0.816169i	0.0884319	−	0.0321866i	0.385857	+	0.922558i	$0.373906\pi$
$644$	−6.38747	−	5.35972i	−0.251702	−	0.211203i
$645$		0			0
$646$	20.3145	−	6.71387i	0.799263	−	0.264154i
$647$	−30.5353			−1.20047			−0.600234	−	0.799825i	$-0.704926\pi$
$647$	−30.5353			−1.20047			−0.600234	+	0.799825i	$0.704926\pi$
$648$	−2.12449	−	1.78265i	−0.0834577	−	0.0700293i
$649$	−58.2031	+	21.1842i	−2.28467	+	0.831553i
$650$		0			0
$651$	−7.91025	+	44.8612i	−0.310027	+	1.75825i
$652$	−1.50188	−	0.546641i	−0.0588183	−	0.0214081i
$653$	5.00288	+	8.66524i	0.195778	+	0.339097i	0.947155	−	0.320776i	$-0.103944\pi$
$653$	5.00288	+	8.66524i	0.195778	+	0.339097i	−0.751377	+	0.659873i	$0.770610\pi$
$654$	11.9521	−	20.7017i	0.467365	−	0.809500i
$655$		0			0
$656$	5.83266	−	4.89419i	0.227727	−	0.191086i
$657$	−10.4634	+	18.1232i	−0.408218	+	0.707054i
$658$	3.01292	+	5.21854i	0.117456	+	0.203440i
$659$	−30.0120	−	10.9235i	−1.16910	−	0.425518i	−0.316761	−	0.948505i	$-0.602595\pi$
$659$	−30.0120	−	10.9235i	−1.16910	−	0.425518i	−0.852340	+	0.522988i	$0.824817\pi$
$660$		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	$-0.166081\pi$
$662$	2.60955	−	0.949797i	0.101423	−	0.0369149i
$663$	−46.2505	−	38.8088i	−1.79622	−	1.50721i
$664$	11.0534			0.428954
$665$		0			0
$666$	−38.8186			−1.50419
$667$	0.709960	+	0.595727i	0.0274898	+	0.0230667i
$668$	7.89504	−	2.87356i	0.305468	−	0.111181i
$669$	12.8072	+	72.6330i	0.495153	+	2.80815i
$670$		0			0
$671$	−21.4991	−	7.82504i	−0.829964	−	0.302082i
$672$	−3.63152	−	6.28999i	−0.140089	−	0.242641i
$673$	−2.30739	+	3.99652i	−0.0889435	+	0.154055i	−0.907065	−	0.420991i	$-0.861682\pi$
$673$	−2.30739	+	3.99652i	−0.0889435	+	0.154055i	0.818121	+	0.575046i	$0.195016\pi$
$674$	−1.72326	+	1.44599i	−0.0663775	+	0.0556973i
$675$		0			0
$676$	−3.70733	+	6.42128i	−0.142590	+	0.246972i
$677$	−9.57347	−	16.5817i	−0.367938	−	0.637288i	0.621305	−	0.783569i	$-0.286603\pi$
$677$	−9.57347	−	16.5817i	−0.367938	−	0.637288i	−0.989243	+	0.146281i	$0.953270\pi$
$678$	−51.6131	−	18.7856i	−1.98219	−	0.721458i
$679$	3.29771	−	18.7022i	0.126554	−	0.717726i
$680$		0			0
$681$	7.02566	−	2.55713i	0.269224	−	0.0979895i
$682$	23.6679	+	19.8598i	0.906293	+	0.760470i
$683$	−2.23430			−0.0854930			−0.0427465	−	0.999086i	$-0.513611\pi$
$683$	−2.23430			−0.0854930			−0.0427465	+	0.999086i	$0.513611\pi$
$684$	10.1076	−	16.3584i	0.386476	−	0.625478i
$685$		0			0
$686$	14.0657	+	11.8025i	0.537030	+	0.450622i
$687$	46.8842	−	17.0645i	1.78875	−	0.651050i
$688$	−0.528937	−	2.99975i	−0.0201655	−	0.114364i
$689$	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	$-0.611640\pi$
$692$	4.31270	−	7.46982i	0.163944	−	0.283960i
$693$	44.4130	−	37.2669i	1.68711	−	1.41565i
$694$	15.4614	−	12.9736i	0.586905	−	0.492472i
$695$		0			0
$696$	0.403640	+	0.699125i	0.0152999	+	0.0265003i
$697$	−35.1187	−	12.7822i	−1.33022	−	0.484159i
$698$	3.85826	−	21.8813i	0.146037	−	0.828218i
$699$	−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	$0.584309\pi$
$702$	−17.3619			−0.655281
$703$	5.52934	+	37.9553i	0.208543	+	1.43151i
$704$	−4.92613			−0.185660
$705$		0			0
$706$	2.89239	−	1.05274i	0.108856	−	0.0396205i
$707$	2.95042	+	16.7326i	0.110962	+	0.629296i
$708$	5.94398	−	33.7100i	0.223388	−	1.26690i
$709$	18.2309	+	6.63549i	0.684674	+	0.249201i	0.660853	−	0.750515i	$-0.270195\pi$
$709$	18.2309	+	6.63549i	0.684674	+	0.249201i	0.0238211	+	0.999716i	$0.492417\pi$
$710$		0			0
$711$	−1.66323	+	2.88080i	−0.0623759	+	0.108038i
$712$	6.07280	−	5.09568i	0.227588	−	0.190969i
$713$	−15.0163	+	12.6002i	−0.562365	+	0.471880i
$714$	−17.8250	+	30.8737i	−0.667082	+	1.15542i
$715$		0			0
$716$	−5.04021	−	1.83448i	−0.188361	−	0.0685579i
$717$	3.35812	−	19.0448i	0.125411	−	0.711242i
$718$	3.55860	+	20.1818i	0.132806	+	0.753178i
$719$	−20.3444	+	7.40475i	−0.758718	+	0.276151i	−0.692269	−	0.721639i	$-0.743389\pi$
$719$	−20.3444	+	7.40475i	−0.758718	+	0.276151i	−0.0664483	+	0.997790i	$0.521167\pi$
$720$		0			0
$721$	21.4962			0.800561
$722$	−17.4343	−	7.55277i	−0.648838	−	0.281085i
$723$	38.8960			1.44656
$724$	−16.2127	−	13.6041i	−0.602542	−	0.505593i
$725$		0			0
$726$	−6.27173	−	35.5687i	−0.232766	−	1.32008i
$727$	7.03305	−	39.8864i	0.260841	−	1.47931i	−0.519780	−	0.854300i	$-0.673986\pi$
$727$	7.03305	−	39.8864i	0.260841	−	1.47931i	0.780621	−	0.625005i	$-0.214903\pi$
$728$	11.3272	+	4.12277i	0.419815	+	0.152800i
$729$	21.8089	+	37.7741i	0.807736	+	1.39904i
$730$		0			0
$731$	−11.4532	+	9.61038i	−0.423612	+	0.355453i
$732$	9.68580	−	8.12735i	0.357997	−	0.300395i
$733$	23.0045	−	39.8449i	0.849689	−	1.47170i	−0.0317969	−	0.999494i	$-0.510123\pi$
$733$	23.0045	−	39.8449i	0.849689	−	1.47170i	0.881486	−	0.472210i	$-0.156544\pi$
$734$	1.84783	+	3.20054i	0.0682047	+	0.118134i
$735$		0			0
$736$	0.542723	−	3.07794i	0.0200050	−	0.113454i
$737$	−8.35112	−	47.3616i	−0.307618	−	1.74459i
$738$	−31.5633	+	11.4881i	−1.16186	+	0.422883i
$739$	8.81246	+	7.39453i	0.324172	+	0.272012i	0.790320	−	0.612694i	$-0.209914\pi$
$739$	8.81246	+	7.39453i	0.324172	+	0.272012i	−0.466148	+	0.884707i	$0.654359\pi$
$740$		0			0
$741$	7.72931	+	53.0567i	0.283943	+	1.94909i
$742$	−35.2554			−1.29426
$743$	1.27288	+	1.06807i	0.0466974	+	0.0391837i	0.665838	−	0.746097i	$-0.268074\pi$
$743$	1.27288	+	1.06807i	0.0466974	+	0.0391837i	−0.619140	+	0.785280i	$0.712519\pi$
$744$	−16.0450	+	5.83989i	−0.588237	+	0.214101i
$745$		0			0
$746$	0.965237	−	5.47413i	0.0353398	−	0.200422i
$747$	−45.8209	−	16.6775i	−1.67650	−	0.610196i
$748$	12.0897	+	20.9400i	0.442043	+	0.765641i
$749$	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	$0.0691855\pi$
$752$	−1.12933	+	1.95606i	−0.0411825	+	0.0713302i
$753$	7.95551	+	13.7794i	0.289915	+	0.502148i
$754$	−1.25901	−	0.458242i	−0.0458504	−	0.0166882i
$755$		0			0
$756$	1.78017	+	10.0959i	0.0647443	+	0.367183i
$757$	−47.1908	+	17.1760i	−1.71518	+	0.624273i	−0.997404	−	0.0720041i	$-0.977061\pi$
$757$	−47.1908	+	17.1760i	−1.71518	+	0.624273i	−0.717773	+	0.696277i	$0.754838\pi$
$758$	4.97955	+	4.17834i	0.180865	+	0.151764i
$759$	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	$0.531177\pi$
$762$	13.3670	+	11.2163i	0.484236	+	0.406322i
$763$	22.0128	−	8.01201i	0.796917	−	0.290054i
$764$	−2.58844	−	14.6798i	−0.0936464	−	0.531095i
$765$		0			0
$766$	−5.04437	−	1.83600i	−0.182260	−	0.0663374i
$767$	28.4051	+	49.1990i	1.02565	+	1.77647i
$768$	1.36120	−	2.35767i	0.0491181	−	0.0850751i
$769$	17.8525	−	14.9800i	0.643779	−	0.540194i	−0.261397	−	0.965231i	$-0.584183\pi$
$769$	17.8525	−	14.9800i	0.643779	−	0.540194i	0.905176	+	0.425037i	$0.139739\pi$
$770$		0			0
$771$	24.7044	−	42.7892i	0.889706	−	1.54102i
$772$	11.4973	+	19.9139i	0.413797	+	0.716717i
$773$	−31.9923	−	11.6443i	−1.15068	−	0.418815i	−0.304923	−	0.952377i	$-0.598631\pi$
$773$	−31.9923	−	11.6443i	−1.15068	−	0.418815i	−0.845761	+	0.533562i	$0.820853\pi$
$774$	−2.33339	+	13.2333i	−0.0838720	+	0.475662i
$775$		0			0
$776$	6.68900	−	2.43460i	0.240121	−	0.0873969i
$777$	−48.9586	−	41.0811i	−1.75638	−	1.47378i
$778$	8.13313			0.291587
$779$	15.7285	+	29.2250i	0.563533	+	1.04709i
$780$		0			0
$781$	−15.2749	−	12.8172i	−0.546579	−	0.458635i
$782$	−14.4156	+	5.24686i	−0.515502	+	0.187627i
$783$	−0.197864	−	1.12214i	−0.00707109	−	0.0401021i
$784$	0.0204207	−	0.115811i	0.000729309	−	0.00413612i
$785$		0			0
$786$	18.8882	+	32.7153i	0.673719	+	1.16692i
$787$	5.51431	−	9.55106i	0.196564	−	0.340459i	−0.750848	−	0.660475i	$-0.770355\pi$
$787$	5.51431	−	9.55106i	0.196564	−	0.340459i	0.947412	+	0.320016i	$0.103688\pi$
$788$	10.9097	−	9.15430i	0.388641	−	0.326108i
$789$	−28.8322	+	24.1931i	−1.02645	+	0.861297i
$790$		0			0
$791$	−26.9128	−	46.6143i	−0.956909	−	1.65741i
$792$	20.4209	+	7.43261i	0.725626	+	0.264106i
$793$	−3.64393	+	20.6658i	−0.129400	+	0.733863i
$794$	3.32463	+	18.8549i	0.117987	+	0.669135i
$795$		0			0
$796$	0.828568	+	0.695251i	0.0293678	+	0.0246425i
$797$	−20.4220			−0.723384			−0.361692	−	0.932298i	$-0.617801\pi$
$797$	−20.4220			−0.723384			−0.361692	+	0.932298i	$0.617801\pi$
$798$	30.0598	−	9.93465i	1.06410	−	0.351683i
$799$	11.0864			0.392209
$800$		0			0
$801$	−32.8628	+	11.9611i	−1.16115	+	0.422624i
$802$	−3.26845	−	18.5363i	−0.115413	−	0.654540i
$803$	−4.05786	+	23.0133i	−0.143199	+	0.812120i
$804$	24.9751	+	9.09019i	0.880803	+	0.320586i
$805$		0			0
$806$	14.1691	−	24.5416i	0.499085	−	0.864440i
$807$	14.0044	−	11.7511i	0.492977	−	0.413657i
$808$	−4.87866	+	4.09368i	−0.171631	+	0.144015i
$809$	−3.91082	+	6.77373i	−0.137497	+	0.238152i	−0.926549	−	0.376175i	$-0.877239\pi$
$809$	−3.91082	+	6.77373i	−0.137497	+	0.238152i	0.789052	+	0.614327i	$0.210572\pi$
$810$		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	$0.757969\pi$
$812$	−0.137375	+	0.779094i	−0.00482093	+	0.0273409i
$813$	0.0481922	+	0.273311i	0.00169017	+	0.00958545i
$814$	−40.7331	+	14.8256i	−1.42769	+	0.519638i
$815$		0			0
$816$	−13.3626			−0.467785
$817$	13.2714	+	0.396538i	0.464307	+	0.0138731i
$818$	22.3021			0.779774
$819$	−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	$0.786739\pi$
$822$	−6.70717	+	38.0383i	−0.233940	+	1.32674i
$823$	−23.3720	−	8.50672i	−0.814698	−	0.296526i	−0.0991348	−	0.995074i	$-0.531608\pi$
$823$	−23.3720	−	8.50672i	−0.814698	−	0.296526i	−0.715563	+	0.698548i	$0.753830\pi$
$824$	4.02870	+	6.97792i	0.140347	+	0.243087i
$825$		0			0
$826$	25.6966	−	21.5620i	0.894099	−	0.750238i
$827$	3.36335	−	2.82219i	0.116955	−	0.0981371i	−0.582434	−	0.812878i	$-0.697900\pi$
$827$	3.36335	−	2.82219i	0.116955	−	0.0981371i	0.699390	+	0.714741i	$0.253455\pi$
$828$	−6.89385	+	11.9405i	−0.239578	+	0.414961i
$829$	−8.45494	−	14.6444i	−0.293652	−	0.508620i	0.681018	−	0.732266i	$-0.261537\pi$
$829$	−8.45494	−	14.6444i	−0.293652	−	0.508620i	−0.974670	+	0.223646i	$0.928204\pi$
$830$		0			0
$831$	−5.22240	+	29.6177i	−0.181163	+	1.02743i
$832$	0.784587	+	4.44962i	0.0272007	+	0.154263i
$833$	−0.542406	+	0.197420i	−0.0187933	+	0.00684019i
$834$	41.7794	+	35.0571i	1.44670	+	1.21393i
$835$		0			0
$836$	4.35855	−	21.0255i	0.150744	−	0.727182i
$837$	24.1005			0.833035
$838$	−4.84183	−	4.06278i	−0.167258	−	0.140346i
$839$	12.5821	−	4.57953i	0.434384	−	0.158103i	−0.115567	−	0.993300i	$-0.536869\pi$
$839$	12.5821	−	4.57953i	0.434384	−	0.158103i	0.549951	+	0.835197i	$0.314646\pi$
$840$		0			0
$841$	−5.02053	+	28.4728i	−0.173122	+	0.981822i
$842$	26.4030	+	9.60989i	0.909906	+	0.331179i
$843$	32.9281	+	57.0331i	1.13410	+	1.96433i
$844$	−12.7028	+	22.0020i	−0.437250	+	0.757339i
$845$		0			0
$846$	7.63289	−	6.40476i	0.262424	−	0.220200i
$847$	17.6971	−	30.6522i	0.608078	−	1.05322i
$848$	−6.60737	−	11.4443i	−0.226898	−	0.392999i
$849$	−19.0120	−	6.91981i	−0.652491	−	0.237487i
$850$		0			0
$851$	−4.77567	−	27.0842i	−0.163708	−	0.928433i
$852$	10.3552	−	3.76897i	0.354762	−	0.129123i
$853$	−15.3731	−	12.8995i	−0.526364	−	0.441672i	0.340480	−	0.940252i	$-0.389411\pi$
$853$	−15.3731	−	12.8995i	−0.526364	−	0.441672i	−0.866844	+	0.498580i	$0.833855\pi$
$854$	12.3907			0.424001
$855$		0			0
$856$	6.08849			0.208100
$857$	1.35007	+	1.13284i	0.0461176	+	0.0386972i	0.665555	−	0.746349i	$-0.268195\pi$
$857$	1.35007	+	1.13284i	0.0461176	+	0.0386972i	−0.619438	+	0.785046i	$0.712639\pi$
$858$	−56.9397	+	20.7243i	−1.94389	+	0.707518i
$859$	−6.40605	−	36.3305i	−0.218572	−	1.23958i	−0.874600	−	0.484845i	$-0.838876\pi$
$859$	−6.40605	−	36.3305i	−0.218572	−	1.23958i	0.656028	−	0.754736i	$-0.272235\pi$
$860$		0			0
$861$	−51.9658	−	18.9140i	−1.77099	−	0.644588i
$862$	17.2635	+	29.9013i	0.587998	+	1.01844i
$863$	−0.885059	+	1.53297i	−0.0301278	+	0.0521828i	−0.880696	−	0.473682i	$-0.842925\pi$
$863$	−0.885059	+	1.53297i	−0.0301278	+	0.0521828i	0.850568	+	0.525864i	$0.176258\pi$
$864$	−2.94360	+	2.46998i	−0.100143	+	0.0840303i
$865$		0			0
$866$	−4.79994	+	8.31374i	−0.163109	+	0.282512i
$867$	9.65410	+	16.7214i	0.327870	+	0.567888i
$868$	−15.7237	−	5.72294i	−0.533695	−	0.194249i
$869$	−0.645022	+	3.65810i	−0.0218809	+	0.124093i
$870$		0			0
$871$	−41.4501	+	15.0866i	−1.40448	+	0.511190i
$872$	6.72631	+	5.64405i	0.227782	+	0.191132i
$873$	−31.4021			−1.06280
$874$	12.6569	+	5.03973i	0.428127	+	0.170471i
$875$		0			0
$876$	−9.89298	−	8.30120i	−0.334253	−	0.280471i
$877$	4.65898	−	1.69573i	0.157323	−	0.0572608i	−0.262158	−	0.965025i	$-0.584434\pi$
$877$	4.65898	−	1.69573i	0.157323	−	0.0572608i	0.419481	+	0.907764i	$0.362212\pi$
$878$	1.61703	+	9.17063i	0.0545721	+	0.309494i
$879$	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	$0.887587\pi$
$882$	−0.259390	+	0.449277i	−0.00873412	+	0.0151279i
$883$	29.7888	−	24.9958i	1.00247	−	0.841174i	0.0151474	−	0.999885i	$-0.495178\pi$
$883$	29.7888	−	24.9958i	1.00247	−	0.841174i	0.987325	+	0.158711i	$0.0507338\pi$
$884$	16.9889	−	14.2554i	0.571398	−	0.479459i
$885$		0			0
$886$	−16.7481	−	29.0085i	−0.562662	−	0.974559i
$887$	4.38734	+	1.59686i	0.147313	+	0.0536174i	0.414624	−	0.909993i	$-0.363913\pi$
$887$	4.38734	+	1.59686i	0.147313	+	0.0536174i	−0.267312	+	0.963610i	$0.586135\pi$
$888$	4.15986	−	23.5917i	0.139596	−	0.791687i
$889$	2.96937	+	16.8402i	0.0995896	+	0.564801i
$890$		0			0
$891$	10.4655	+	8.78159i	0.350607	+	0.294194i
$892$	−27.0913			−0.907084
$893$	−7.34956	−	6.55085i	−0.245944	−	0.219216i
$894$	12.1991			0.407999
$895$		0			0
$896$	2.50699	−	0.912470i	0.0837526	−	0.0304835i
$897$	−6.67578	−	37.8602i	−0.222898	−	1.26412i
$898$	0.384927	−	2.18303i	0.0128452	−	0.0728487i
$899$	1.74767	+	0.636099i	0.0582879	+	0.0212151i
$900$		0			0
$901$	−32.4316	+	56.1731i	−1.08045	+	1.87140i
$902$	−28.7325	+	24.1094i	−0.956686	+	0.802755i
$903$	−16.9475	+	14.2207i	−0.563979	+	0.473234i
$904$	10.0877	−	17.4724i	0.335512	−	0.581123i
$905$		0			0
$906$	−35.6478	−	12.9747i	−1.18432	−	0.431056i
$907$	−0.736755	+	4.17835i	−0.0244636	+	0.138740i	−0.994593	−	0.103847i	$-0.966885\pi$
$907$	−0.736755	+	4.17835i	−0.0244636	+	0.138740i	0.970130	+	0.242587i	$0.0779959\pi$
$908$	0.476891	+	2.70458i	0.0158262	+	0.0897548i
$909$	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	$0.566050\pi$
$912$	8.85854	+	7.89584i	0.293335	+	0.261457i
$913$	−54.4503			−1.80204
$914$	10.9832	+	9.21596i	0.363291	+	0.304837i
$915$		0			0
$916$	3.18243	+	18.0485i	0.105150	+	0.596338i
$917$	−6.42843	+	36.4574i	−0.212285	+	1.20393i
$918$	17.7235	+	6.45084i	0.584964	+	0.212909i
$919$	7.42713	+	12.8642i	0.244999	+	0.424350i	0.962131	−	0.272587i	$-0.0878792\pi$
$919$	7.42713	+	12.8642i	0.244999	+	0.424350i	−0.717133	+	0.696937i	$0.754546\pi$
$920$		0			0
$921$	−18.0613	+	15.1552i	−0.595139	+	0.499381i
$922$	7.39668	−	6.20655i	0.243597	−	0.204402i
$923$	−9.14450	+	15.8387i	−0.300995	+	0.521339i
$924$	17.8894	+	30.9853i	0.588517	+	1.01934i
$925$		0			0
$926$	−5.36667	+	30.4359i	−0.176360	+	1.00019i
$927$	−6.17233	−	35.0050i	−0.202726	−	1.14972i
$928$	−0.278649	+	0.101420i	−0.00914711	+	0.00332927i
$929$	−28.1439	−	23.6156i	−0.923372	−	0.774801i	0.0512436	−	0.998686i	$-0.483682\pi$
$929$	−28.1439	−	23.6156i	−0.923372	−	0.774801i	−0.974616	+	0.223885i	$0.928126\pi$
$930$		0			0
$931$	0.476233	+	0.189626i	0.0156079	+	0.00621475i
$932$	5.73880			0.187981
$933$	−57.1832	−	47.9824i	−1.87209	−	1.57087i
$934$	5.87685	−	2.13900i	0.192296	−	0.0699901i
$935$		0			0
$936$	3.46119	−	19.6294i	0.113132	−	0.641606i
$937$	30.9607	+	11.2688i	1.01144	+	0.368135i	0.793987	−	0.607935i	$-0.208002\pi$
$937$	30.9607	+	11.2688i	1.01144	+	0.368135i	0.217456	+	0.976070i	$0.430224\pi$
$938$	13.0228	+	22.5562i	0.425211	+	0.736486i
$939$	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	$0.166728\pi$
$942$	−9.78481	+	16.9478i	−0.318806	+	0.552189i
$943$	−11.8985	−	20.6088i	−0.387467	−	0.671113i
$944$	11.8152	+	4.30038i	0.384552	+	0.139965i
$945$		0			0
$946$	2.60561	+	14.7772i	0.0847157	+	0.480447i
$947$	−56.0006	+	20.3826i	−1.81978	+	0.662344i	−0.824431	+	0.565962i	$0.808505\pi$
$947$	−56.0006	+	20.3826i	−1.81978	+	0.662344i	−0.995344	+	0.0963825i	$0.969273\pi$
$948$	−1.57255	−	1.31953i	−0.0510740	−	0.0428562i
$949$	21.4334			0.695759
$950$		0			0
$951$	57.6253			1.86863
$952$	−10.0314	−	8.41732i	−0.325118	−	0.272807i
$953$	20.0197	−	7.28657i	0.648501	−	0.236035i	0.00323722	−	0.999995i	$-0.498970\pi$
$953$	20.0197	−	7.28657i	0.648501	−	0.236035i	0.645264	+	0.763960i	$0.276747\pi$
$954$	10.1231	+	57.4108i	0.327747	+	1.85874i
$955$		0			0
$956$	6.67512	+	2.42955i	0.215889	+	0.0785771i
$957$	−1.98838	−	3.44398i	−0.0642753	−	0.111328i
$958$	−17.0514	+	29.5338i	−0.550905	+	0.954195i
$959$	−28.9960	+	24.3305i	−0.936329	+	0.785673i
$960$		0			0
$961$	−4.16852	+	7.22009i	−0.134468	+	0.232906i
$962$	19.8791	+	34.4316i	0.640928	+	1.11012i
$963$	−25.2394	−	9.18639i	−0.813328	−	0.296027i
$964$	−2.48098	+	14.0703i	−0.0799070	+	0.453175i
$965$		0			0
$966$	−21.3311	+	7.76388i	−0.686316	+	0.249799i
$967$	−14.3118	−	12.0090i	−0.460236	−	0.386184i	0.382982	−	0.923756i	$-0.374897\pi$
$967$	−14.3118	−	12.0090i	−0.460236	−	0.386184i	−0.843218	+	0.537572i	$0.819342\pi$
$968$	13.2667			0.426409
$969$	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	$0.567131\pi$
$972$	−17.9274	+	6.52502i	−0.575020	+	0.209290i
$973$	9.28097	+	52.6350i	0.297534	+	1.68740i
$974$	2.89301	−	16.4071i	0.0926981	−	0.525717i
$975$		0			0
$976$	2.32220	+	4.02216i	0.0743317	+	0.128746i
$977$	−26.2695	+	45.5001i	−0.840436	+	1.45568i	0.0490904	+	0.998794i	$0.484368\pi$
$977$	−26.2695	+	45.5001i	−0.840436	+	1.45568i	−0.889526	+	0.456884i	$0.848966\pi$
$978$	−3.33317	+	2.79686i	−0.106583	+	0.0894337i
$979$	−29.9154	+	25.1020i	−0.956100	+	0.802263i
$980$		0			0
$981$	−19.3676	−	33.5457i	−0.618361	−	1.07103i
$982$	24.6572	+	8.97450i	0.786844	+	0.286388i
$983$	0.0907451	−	0.514641i	0.00289432	−	0.0164145i	−0.983326	−	0.181849i	$-0.941792\pi$
$983$	0.0907451	−	0.514641i	0.00289432	−	0.0164145i	0.986221	+	0.165435i	$0.0529028\pi$
$984$	−3.59944	−	20.4135i	−0.114746	−	0.650757i
$985$		0			0
$986$	1.11498	+	0.935575i	0.0355080	+	0.0297948i
$987$	16.4048			0.522170
$988$	−19.6858	−	0.588196i	−0.626290	−	0.0187130i
$989$	−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	$0.346377\pi$
$992$	−1.08911	−	6.17664i	−0.0345792	−	0.196109i
$993$	1.31281	−	7.44532i	0.0416608	−	0.236270i
$994$	10.1478	+	3.69349i	0.321868	+	0.117151i
$995$		0			0
$996$	15.0459	−	26.0602i	0.476746	−	0.825748i
$997$	11.6129	−	9.74442i	0.367786	−	0.308609i	−0.440099	−	0.897949i	$-0.645057\pi$
$997$	11.6129	−	9.74442i	0.367786	−	0.308609i	0.807885	+	0.589340i	$0.200612\pi$
$998$	−16.5747	+	13.9078i	−0.524662	+	0.440244i
$999$	−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.l.h.301.2		12
5.2	odd	4		950.2.u.e.149.1		24
5.3	odd	4		950.2.u.e.149.4		24
5.4	even	2		190.2.k.b.111.1	yes	12
19.6	even	9	inner	950.2.l.h.101.2		12
95.14	odd	18		3610.2.a.be.1.1		6
95.24	even	18		3610.2.a.bc.1.6		6
95.44	even	18		190.2.k.b.101.1	✓	12
95.63	odd	36		950.2.u.e.899.1		24
95.82	odd	36		950.2.u.e.899.4		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
190.2.k.b.101.1	✓	12	95.44	even	18
190.2.k.b.111.1	yes	12	5.4	even	2
950.2.l.h.101.2		12	19.6	even	9	inner
950.2.l.h.301.2		12	1.1	even	1	trivial
950.2.u.e.149.1		24	5.2	odd	4
950.2.u.e.149.4		24	5.3	odd	4
950.2.u.e.899.1		24	95.63	odd	36
950.2.u.e.899.4		24	95.82	odd	36
3610.2.a.bc.1.6		6	95.24	even	18
3610.2.a.be.1.1		6	95.14	odd	18

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.l (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.766044 + 0.642788i) q^{2} +(2.55822 - 0.931116i) q^{3} +(0.173648 + 0.984808i) q^{4} +(2.55822 + 0.931116i) q^{6} +(1.33394 + 2.31045i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(3.37939 - 2.83564i) q^{9} +O(q^{10})\)	\(q+(0.766044 + 0.642788i) q^{2} +(2.55822 - 0.931116i) q^{3} +(0.173648 + 0.984808i) q^{4} +(2.55822 + 0.931116i) q^{6} +(1.33394 + 2.31045i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(3.37939 - 2.83564i) q^{9} +(2.46306 - 4.26615i) q^{11} +(1.36120 + 2.35767i) q^{12} +(-4.24577 - 1.54534i) q^{13} +(-0.463273 + 2.62735i) q^{14} +(-0.939693 + 0.342020i) q^{16} +(3.76005 + 3.15506i) q^{17} +4.41147 q^{18} +(-0.628373 - 4.31337i) q^{19} +(5.56382 + 4.66860i) q^{21} +(4.62905 - 1.68484i) q^{22} +(0.542723 + 3.07794i) q^{23} +(-0.472740 + 2.68104i) q^{24} +(-2.25913 - 3.91293i) q^{26} +(1.92130 - 3.32779i) q^{27} +(-2.04372 + 1.71488i) q^{28} +(0.227157 - 0.190607i) q^{29} +(3.13596 + 5.43165i) q^{31} +(-0.939693 - 0.342020i) q^{32} +(2.32878 - 13.2072i) q^{33} +(0.852334 + 4.83382i) q^{34} +(3.37939 + 2.83564i) q^{36} -8.79946 q^{37} +(2.29122 - 3.70814i) q^{38} -12.3005 q^{39} +(-7.15482 + 2.60414i) q^{41} +(1.26122 + 7.15271i) q^{42} +(-0.528937 + 2.99975i) q^{43} +(4.62905 + 1.68484i) q^{44} +(-1.56271 + 2.70669i) q^{46} +(1.73024 - 1.45184i) q^{47} +(-2.08548 + 1.74993i) q^{48} +(-0.0587989 + 0.101843i) q^{49} +(12.5568 + 4.57029i) q^{51} +(0.784587 - 4.44962i) q^{52} +(2.29471 + 13.0140i) q^{53} +(3.61086 - 1.31425i) q^{54} -2.66788 q^{56} +(-5.62377 - 10.4495i) q^{57} +0.296532 q^{58} +(-9.63183 - 8.08206i) q^{59} +(-0.806491 - 4.57384i) q^{61} +(-1.08911 + 6.17664i) q^{62} +(11.0595 + 4.02534i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(10.2733 - 8.62036i) q^{66} +(7.47864 - 6.27533i) q^{67} +(-2.45420 + 4.25079i) q^{68} +(4.25432 + 7.36870i) q^{69} +(0.702893 - 3.98630i) q^{71} +(0.766044 + 4.34445i) q^{72} +(-4.45766 + 1.62245i) q^{73} +(-6.74078 - 5.65618i) q^{74} +(4.13872 - 1.36784i) q^{76} +13.1423 q^{77} +(-9.42274 - 7.90662i) q^{78} +(-0.708572 + 0.257899i) q^{79} +(-0.481582 + 2.73119i) q^{81} +(-7.15482 - 2.60414i) q^{82} +(-5.52668 - 9.57249i) q^{83} +(-3.63152 + 6.28999i) q^{84} +(-2.33339 + 1.95795i) q^{86} +(0.403640 - 0.699125i) q^{87} +(2.46306 + 4.26615i) q^{88} +(-7.44939 - 2.71136i) q^{89} +(-2.09319 - 11.8711i) q^{91} +(-2.93693 + 1.06896i) q^{92} +(13.0800 + 10.9754i) q^{93} +2.25866 q^{94} -2.72240 q^{96} +(-5.45292 - 4.57554i) q^{97} +(-0.110506 + 0.0402208i) q^{98} +(-3.77363 - 21.4013i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 6 q^{7} - 6 q^{8} + 18 q^{9}+O(q^{10}) \) 12 * q - 6 * q^7 - 6 * q^8 + 18 * q^9	\( 12 q - 6 q^{7} - 6 q^{8} + 18 q^{9} + 6 q^{11} - 6 q^{13} + 18 q^{17} + 12 q^{18} + 12 q^{21} + 6 q^{22} + 30 q^{23} - 6 q^{29} + 6 q^{31} + 24 q^{33} + 18 q^{36} - 36 q^{37} - 18 q^{38} - 36 q^{39} - 6 q^{41} + 30 q^{42} + 6 q^{44} - 12 q^{46} + 6 q^{47} - 18 q^{49} + 12 q^{52} + 12 q^{53} + 12 q^{56} + 18 q^{57} + 36 q^{58} - 24 q^{59} - 30 q^{61} + 6 q^{62} - 18 q^{63} - 6 q^{64} + 24 q^{66} - 12 q^{67} - 12 q^{68} + 6 q^{69} - 42 q^{71} - 6 q^{73} + 6 q^{74} + 18 q^{76} + 24 q^{77} - 48 q^{78} + 60 q^{79} + 18 q^{81} - 6 q^{82} - 24 q^{83} - 24 q^{84} - 36 q^{86} - 54 q^{87} + 6 q^{88} - 12 q^{89} + 24 q^{91} - 24 q^{92} - 6 q^{93} + 60 q^{94} - 30 q^{97} - 36 q^{98} - 12 q^{99}+O(q^{100}) \) 12 * q - 6 * q^7 - 6 * q^8 + 18 * q^9 + 6 * q^11 - 6 * q^13 + 18 * q^17 + 12 * q^18 + 12 * q^21 + 6 * q^22 + 30 * q^23 - 6 * q^29 + 6 * q^31 + 24 * q^33 + 18 * q^36 - 36 * q^37 - 18 * q^38 - 36 * q^39 - 6 * q^41 + 30 * q^42 + 6 * q^44 - 12 * q^46 + 6 * q^47 - 18 * q^49 + 12 * q^52 + 12 * q^53 + 12 * q^56 + 18 * q^57 + 36 * q^58 - 24 * q^59 - 30 * q^61 + 6 * q^62 - 18 * q^63 - 6 * q^64 + 24 * q^66 - 12 * q^67 - 12 * q^68 + 6 * q^69 - 42 * q^71 - 6 * q^73 + 6 * q^74 + 18 * q^76 + 24 * q^77 - 48 * q^78 + 60 * q^79 + 18 * q^81 - 6 * q^82 - 24 * q^83 - 24 * q^84 - 36 * q^86 - 54 * q^87 + 6 * q^88 - 12 * q^89 + 24 * q^91 - 24 * q^92 - 6 * q^93 + 60 * q^94 - 30 * q^97 - 36 * q^98 - 12 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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