LMFDB - Embedded newform 418.2.j.c.199.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [418,2,Mod(23,418)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(418, base_ring=CyclotomicField(18))

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

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

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

chi := DirichletCharacter("418.23");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 418 = 2 \cdot 11 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	418.j (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:	$3.33774680449$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$5$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			199.5
Character	$\chi$	$=$	418.199
Dual form			418.2.j.c.397.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.173648 - 0.984808i) q^{2} +(1.56977 - 1.31719i) q^{3} +(-0.939693 + 0.342020i) q^{4} +(1.25616 + 0.457206i) q^{5} +(-1.56977 - 1.31719i) q^{6} +(1.39952 - 2.42403i) q^{7} +(0.500000 + 0.866025i) q^{8} +(0.208231 - 1.18093i) q^{9} +O(q^{10})$	\(q+(-0.173648 - 0.984808i) q^{2} +(1.56977 - 1.31719i) q^{3} +(-0.939693 + 0.342020i) q^{4} +(1.25616 + 0.457206i) q^{5} +(-1.56977 - 1.31719i) q^{6} +(1.39952 - 2.42403i) q^{7} +(0.500000 + 0.866025i) q^{8} +(0.208231 - 1.18093i) q^{9} +(0.232130 - 1.31647i) q^{10} +(-0.500000 - 0.866025i) q^{11} +(-1.02459 + 1.77464i) q^{12} +(-0.500512 - 0.419979i) q^{13} +(-2.63023 - 0.957325i) q^{14} +(2.57411 - 0.936899i) q^{15} +(0.766044 - 0.642788i) q^{16} +(-0.176083 - 0.998615i) q^{17} -1.19915 q^{18} +(3.24767 + 2.90735i) q^{19} -1.33678 q^{20} +(-0.995999 - 5.64859i) q^{21} +(-0.766044 + 0.642788i) q^{22} +(-1.25897 + 0.458229i) q^{23} +(1.92560 + 0.700862i) q^{24} +(-2.46131 - 2.06529i) q^{25} +(-0.326686 + 0.565836i) q^{26} +(1.84513 + 3.19586i) q^{27} +(-0.486047 + 2.75651i) q^{28} +(1.03631 - 5.87719i) q^{29} +(-1.36965 - 2.37231i) q^{30} +(-1.83033 + 3.17022i) q^{31} +(-0.766044 - 0.642788i) q^{32} +(-1.92560 - 0.700862i) q^{33} +(-0.952867 + 0.346815i) q^{34} +(2.86630 - 2.40511i) q^{35} +(0.208231 + 1.18093i) q^{36} +1.07334 q^{37} +(2.29923 - 3.70318i) q^{38} -1.33888 q^{39} +(0.232130 + 1.31647i) q^{40} +(-3.75916 + 3.15431i) q^{41} +(-5.38982 + 1.96174i) q^{42} +(-3.16935 - 1.15355i) q^{43} +(0.766044 + 0.642788i) q^{44} +(0.801502 - 1.38824i) q^{45} +(0.669885 + 1.16028i) q^{46} +(-2.09930 + 11.9057i) q^{47} +(0.355837 - 2.01805i) q^{48} +(-0.417290 - 0.722767i) q^{49} +(-1.60651 + 2.78255i) q^{50} +(-1.59177 - 1.33566i) q^{51} +(0.613969 + 0.223466i) q^{52} +(-6.69105 + 2.43534i) q^{53} +(2.82691 - 2.37206i) q^{54} +(-0.232130 - 1.31647i) q^{55} +2.79903 q^{56} +(8.92760 + 0.286060i) q^{57} -5.96786 q^{58} +(0.167728 + 0.951230i) q^{59} +(-2.09843 + 1.76079i) q^{60} +(1.23846 - 0.450762i) q^{61} +(3.43989 + 1.25202i) q^{62} +(-2.57120 - 2.15750i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(-0.436707 - 0.756399i) q^{65} +(-0.355837 + 2.01805i) q^{66} +(0.133983 - 0.759853i) q^{67} +(0.507010 + 0.878167i) q^{68} +(-1.37272 + 2.37762i) q^{69} +(-2.86630 - 2.40511i) q^{70} +(6.55116 + 2.38443i) q^{71} +(1.12684 - 0.410134i) q^{72} +(6.09391 - 5.11340i) q^{73} +(-0.186383 - 1.05703i) q^{74} -6.58406 q^{75} +(-4.04618 - 1.62125i) q^{76} -2.79903 q^{77} +(0.232494 + 1.31854i) q^{78} +(13.0200 - 10.9251i) q^{79} +(1.25616 - 0.457206i) q^{80} +(10.4865 + 3.81677i) q^{81} +(3.75916 + 3.15431i) q^{82} +(-2.77995 + 4.81501i) q^{83} +(2.86786 + 4.96729i) q^{84} +(0.235384 - 1.33493i) q^{85} +(-0.585672 + 3.32151i) q^{86} +(-6.11462 - 10.5908i) q^{87} +(0.500000 - 0.866025i) q^{88} +(5.38404 + 4.51775i) q^{89} +(-1.50633 - 0.548260i) q^{90} +(-1.71852 + 0.625489i) q^{91} +(1.02632 - 0.861188i) q^{92} +(1.30260 + 7.38739i) q^{93} +12.0894 q^{94} +(2.75034 + 5.13696i) q^{95} -2.04918 q^{96} +(0.359987 + 2.04159i) q^{97} +(-0.639325 + 0.536457i) q^{98} +(-1.12684 + 0.410134i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q - 12 q^{7} + 15 q^{8}+O(q^{10}) $ 30 * q - 12 * q^7 + 15 * q^8	$ 30 q - 12 q^{7} + 15 q^{8} - 15 q^{11} + 3 q^{12} - 3 q^{13} + 9 q^{14} + 27 q^{15} - 36 q^{18} - 9 q^{19} + 18 q^{20} - 27 q^{21} - 3 q^{23} - 12 q^{25} + 3 q^{27} + 9 q^{28} + 3 q^{29} + 9 q^{30} + 30 q^{31} - 9 q^{34} + 15 q^{35} + 18 q^{37} + 6 q^{38} - 6 q^{41} - 45 q^{42} + 39 q^{43} - 18 q^{45} + 21 q^{46} + 45 q^{47} - 33 q^{49} + 36 q^{50} - 36 q^{51} + 6 q^{52} - 24 q^{53} + 45 q^{54} - 24 q^{56} - 24 q^{57} - 30 q^{58} + 3 q^{59} - 9 q^{60} - 27 q^{61} + 15 q^{62} - 93 q^{63} - 15 q^{64} + 18 q^{65} - 9 q^{67} - 21 q^{68} + 48 q^{69} - 15 q^{70} + 39 q^{73} + 3 q^{74} - 42 q^{75} - 15 q^{76} + 24 q^{77} + 6 q^{78} + 21 q^{79} + 84 q^{81} + 6 q^{82} - 36 q^{83} - 27 q^{84} + 63 q^{85} + 6 q^{86} - 21 q^{87} + 15 q^{88} + 54 q^{89} + 12 q^{90} + 3 q^{91} - 3 q^{92} + 51 q^{93} - 78 q^{94} + 6 q^{95} + 6 q^{96} - 18 q^{97} + 3 q^{98}+O(q^{100}) $ 30 * q - 12 * q^7 + 15 * q^8 - 15 * q^11 + 3 * q^12 - 3 * q^13 + 9 * q^14 + 27 * q^15 - 36 * q^18 - 9 * q^19 + 18 * q^20 - 27 * q^21 - 3 * q^23 - 12 * q^25 + 3 * q^27 + 9 * q^28 + 3 * q^29 + 9 * q^30 + 30 * q^31 - 9 * q^34 + 15 * q^35 + 18 * q^37 + 6 * q^38 - 6 * q^41 - 45 * q^42 + 39 * q^43 - 18 * q^45 + 21 * q^46 + 45 * q^47 - 33 * q^49 + 36 * q^50 - 36 * q^51 + 6 * q^52 - 24 * q^53 + 45 * q^54 - 24 * q^56 - 24 * q^57 - 30 * q^58 + 3 * q^59 - 9 * q^60 - 27 * q^61 + 15 * q^62 - 93 * q^63 - 15 * q^64 + 18 * q^65 - 9 * q^67 - 21 * q^68 + 48 * q^69 - 15 * q^70 + 39 * q^73 + 3 * q^74 - 42 * q^75 - 15 * q^76 + 24 * q^77 + 6 * q^78 + 21 * q^79 + 84 * q^81 + 6 * q^82 - 36 * q^83 - 27 * q^84 + 63 * q^85 + 6 * q^86 - 21 * q^87 + 15 * q^88 + 54 * q^89 + 12 * q^90 + 3 * q^91 - 3 * q^92 + 51 * q^93 - 78 * q^94 + 6 * q^95 + 6 * q^96 - 18 * q^97 + 3 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/418\mathbb{Z}\right)^\times$.

$n$	$287$	$343$
$\chi(n)$	$e\left(\frac{4}{9}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.173648	−	0.984808i	−0.122788	−	0.696364i
$2$	−0.173648	−	0.984808i	−0.122788	−	0.696364i
$3$	1.56977	−	1.31719i	0.906305	−	0.760480i	−0.0651078	−	0.997878i	$-0.520739\pi$
$3$	1.56977	−	1.31719i	0.906305	−	0.760480i	0.971412	+	0.237398i	$0.0762947\pi$
$4$	−0.939693	+	0.342020i	−0.469846	+	0.171010i
$5$	1.25616	+	0.457206i	0.561773	+	0.204469i	0.607270	−	0.794496i	$-0.292265\pi$
$5$	1.25616	+	0.457206i	0.561773	+	0.204469i	−0.0454964	+	0.998965i	$0.514487\pi$
$6$	−1.56977	−	1.31719i	−0.640854	−	0.537740i
$7$	1.39952	−	2.42403i	0.528967	−	0.916198i	−0.470462	−	0.882420i	$-0.655913\pi$
$7$	1.39952	−	2.42403i	0.528967	−	0.916198i	0.999429	−	0.0337780i	$-0.0107539\pi$
$8$	0.500000	+	0.866025i	0.176777	+	0.306186i
$9$	0.208231	−	1.18093i	0.0694102	−	0.393645i
$10$	0.232130	−	1.31647i	0.0734058	−	0.416305i
$11$	−0.500000	−	0.866025i	−0.150756	−	0.261116i
$11$	−0.500000	−	0.866025i	−0.150756	−	0.261116i
$12$	−1.02459	+	1.77464i	−0.295774	+	0.512296i
$13$	−0.500512	−	0.419979i	−0.138817	−	0.116481i	0.570735	−	0.821134i	$-0.306658\pi$
$13$	−0.500512	−	0.419979i	−0.138817	−	0.116481i	−0.709552	+	0.704653i	$0.751103\pi$
$14$	−2.63023	−	0.957325i	−0.702958	−	0.255856i
$15$	2.57411	−	0.936899i	0.664632	−	0.241906i
$16$	0.766044	−	0.642788i	0.191511	−	0.160697i
$17$	−0.176083	−	0.998615i	−0.0427063	−	0.242200i	0.955981	−	0.293430i	$-0.0947968\pi$
$17$	−0.176083	−	0.998615i	−0.0427063	−	0.242200i	−0.998687	+	0.0512305i	$0.983686\pi$
$18$	−1.19915			−0.282643
$19$	3.24767	+	2.90735i	0.745066	+	0.666991i
$19$	3.24767	+	2.90735i	0.745066	+	0.666991i
$20$	−1.33678			−0.298913
$21$	−0.995999	−	5.64859i	−0.217345	−	1.23262i
$22$	−0.766044	+	0.642788i	−0.163321	+	0.137043i
$23$	−1.25897	+	0.458229i	−0.262514	+	0.0955473i	−0.469924	−	0.882707i	$-0.655719\pi$
$23$	−1.25897	+	0.458229i	−0.262514	+	0.0955473i	0.207410	+	0.978254i	$0.433497\pi$
$24$	1.92560	+	0.700862i	0.393062	+	0.143063i
$25$	−2.46131	−	2.06529i	−0.492263	−	0.413057i
$26$	−0.326686	+	0.565836i	−0.0640684	+	0.110970i
$27$	1.84513	+	3.19586i	0.355096	+	0.615044i
$28$	−0.486047	+	2.75651i	−0.0918542	+	0.520931i
$29$	1.03631	−	5.87719i	0.192438	−	1.09137i	−0.723583	−	0.690237i	$-0.757506\pi$
$29$	1.03631	−	5.87719i	0.192438	−	1.09137i	0.916021	−	0.401131i	$-0.131383\pi$
$30$	−1.36965	−	2.37231i	−0.250064	−	0.433123i
$31$	−1.83033	+	3.17022i	−0.328736	+	0.569388i	−0.982261	−	0.187517i	$-0.939956\pi$
$31$	−1.83033	+	3.17022i	−0.328736	+	0.569388i	0.653525	+	0.756905i	$0.273289\pi$
$32$	−0.766044	−	0.642788i	−0.135419	−	0.113630i
$33$	−1.92560	−	0.700862i	−0.335204	−	0.122004i
$34$	−0.952867	+	0.346815i	−0.163415	+	0.0594783i
$35$	2.86630	−	2.40511i	0.484494	−	0.406538i
$36$	0.208231	+	1.18093i	0.0347051	+	0.196822i
$37$	1.07334			0.176456			0.0882279	−	0.996100i	$-0.471880\pi$
$37$	1.07334			0.176456			0.0882279	+	0.996100i	$0.471880\pi$
$38$	2.29923	−	3.70318i	0.372984	−	0.600735i
$39$	−1.33888			−0.214392
$40$	0.232130	+	1.31647i	0.0367029	+	0.208153i
$41$	−3.75916	+	3.15431i	−0.587081	+	0.492620i	−0.887264	−	0.461262i	$-0.847397\pi$
$41$	−3.75916	+	3.15431i	−0.587081	+	0.492620i	0.300183	+	0.953882i	$0.402952\pi$
$42$	−5.38982	+	1.96174i	−0.831668	+	0.302702i
$43$	−3.16935	−	1.15355i	−0.483321	−	0.175915i	0.0888560	−	0.996044i	$-0.471679\pi$
$43$	−3.16935	−	1.15355i	−0.483321	−	0.175915i	−0.572177	+	0.820130i	$0.693901\pi$
$44$	0.766044	+	0.642788i	0.115486	+	0.0969039i
$45$	0.801502	−	1.38824i	0.119481	−	0.206947i
$46$	0.669885	+	1.16028i	0.0987692	+	0.171073i
$47$	−2.09930	+	11.9057i	−0.306214	+	1.73662i	0.311523	+	0.950239i	$0.399161\pi$
$47$	−2.09930	+	11.9057i	−0.306214	+	1.73662i	−0.617736	+	0.786385i	$0.711950\pi$
$48$	0.355837	−	2.01805i	0.0513606	−	0.291281i
$49$	−0.417290	−	0.722767i	−0.0596128	−	0.103252i
$50$	−1.60651	+	2.78255i	−0.227195	+	0.393513i
$51$	−1.59177	−	1.33566i	−0.222893	−	0.187029i
$52$	0.613969	+	0.223466i	0.0851421	+	0.0309892i
$53$	−6.69105	+	2.43534i	−0.919086	+	0.334520i	−0.757875	−	0.652400i	$-0.773762\pi$
$53$	−6.69105	+	2.43534i	−0.919086	+	0.334520i	−0.161211	+	0.986920i	$0.551540\pi$
$54$	2.82691	−	2.37206i	0.384693	−	0.322796i
$55$	−0.232130	−	1.31647i	−0.0313004	−	0.177513i
$56$	2.79903			0.374036
$57$	8.92760	+	0.286060i	1.18249	+	0.0378896i
$58$	−5.96786			−0.783618
$59$	0.167728	+	0.951230i	0.0218363	+	0.123840i	0.993777	−	0.111385i	$-0.0355286\pi$
$59$	0.167728	+	0.951230i	0.0218363	+	0.123840i	−0.971941	+	0.235224i	$0.924417\pi$
$60$	−2.09843	+	1.76079i	−0.270907	+	0.227318i
$61$	1.23846	−	0.450762i	0.158568	−	0.0577142i	−0.261516	−	0.965199i	$-0.584223\pi$
$61$	1.23846	−	0.450762i	0.158568	−	0.0577142i	0.420085	+	0.907485i	$0.362000\pi$
$62$	3.43989	+	1.25202i	0.436866	+	0.159006i
$63$	−2.57120	−	2.15750i	−0.323941	−	0.271819i
$64$	−0.500000	+	0.866025i	−0.0625000	+	0.108253i
$65$	−0.436707	−	0.756399i	−0.0541669	−	0.0938198i
$66$	−0.355837	+	2.01805i	−0.0438005	+	0.248405i
$67$	0.133983	−	0.759853i	0.0163686	−	0.0928308i	−0.975529	−	0.219871i	$-0.929436\pi$
$67$	0.133983	−	0.759853i	0.0163686	−	0.0928308i	0.991898	+	0.127040i	$0.0405476\pi$
$68$	0.507010	+	0.878167i	0.0614840	+	0.106493i
$69$	−1.37272	+	2.37762i	−0.165256	+	0.286232i
$70$	−2.86630	−	2.40511i	−0.342589	−	0.287466i
$71$	6.55116	+	2.38443i	0.777479	+	0.282979i	0.700121	−	0.714024i	$-0.253129\pi$
$71$	6.55116	+	2.38443i	0.777479	+	0.282979i	0.0773580	+	0.997003i	$0.475352\pi$
$72$	1.12684	−	0.410134i	0.132799	−	0.0483348i
$73$	6.09391	−	5.11340i	0.713239	−	0.598478i	−0.212267	−	0.977212i	$-0.568085\pi$
$73$	6.09391	−	5.11340i	0.713239	−	0.598478i	0.925506	+	0.378733i	$0.123640\pi$
$74$	−0.186383	−	1.05703i	−0.0216666	−	0.122877i
$75$	−6.58406			−0.760262
$76$	−4.04618	−	1.62125i	−0.464129	−	0.185970i
$77$	−2.79903			−0.318979
$78$	0.232494	+	1.31854i	0.0263247	+	0.149295i
$79$	13.0200	−	10.9251i	1.46487	−	1.22917i	0.544123	−	0.839005i	$-0.316862\pi$
$79$	13.0200	−	10.9251i	1.46487	−	1.22917i	0.920745	−	0.390165i	$-0.127582\pi$
$80$	1.25616	−	0.457206i	0.140443	−	0.0511172i
$81$	10.4865	+	3.81677i	1.16517	+	0.424086i
$82$	3.75916	+	3.15431i	0.415129	+	0.348335i
$83$	−2.77995	+	4.81501i	−0.305139	+	0.528516i	−0.977292	−	0.211896i	$-0.932036\pi$
$83$	−2.77995	+	4.81501i	−0.305139	+	0.528516i	0.672153	+	0.740412i	$0.265369\pi$
$84$	2.86786	+	4.96729i	0.312910	+	0.541976i
$85$	0.235384	−	1.33493i	0.0255310	−	0.144793i
$86$	−0.585672	+	3.32151i	−0.0631547	+	0.358168i
$87$	−6.11462	−	10.5908i	−0.655556	−	1.13546i
$88$	0.500000	−	0.866025i	0.0533002	−	0.0923186i
$89$	5.38404	+	4.51775i	0.570708	+	0.478881i	0.881881	−	0.471473i	$-0.156277\pi$
$89$	5.38404	+	4.51775i	0.570708	+	0.478881i	−0.311173	+	0.950353i	$0.600722\pi$
$90$	−1.50633	−	0.548260i	−0.158781	−	0.0577917i
$91$	−1.71852	+	0.625489i	−0.180150	+	0.0655691i
$92$	1.02632	−	0.861188i	0.107002	−	0.0897851i
$93$	1.30260	+	7.38739i	0.135073	+	0.766036i
$94$	12.0894			1.24692
$95$	2.75034	+	5.13696i	0.282179	+	0.527040i
$96$	−2.04918			−0.209144
$97$	0.359987	+	2.04159i	0.0365512	+	0.207292i	0.997614	−	0.0690378i	$-0.0219929\pi$
$97$	0.359987	+	2.04159i	0.0365512	+	0.207292i	−0.961063	+	0.276330i	$0.910882\pi$
$98$	−0.639325	+	0.536457i	−0.0645816	+	0.0541904i
$99$	−1.12684	+	0.410134i	−0.113251	+	0.0412201i
$100$	3.01925	+	1.09892i	0.301925	+	0.109892i
$101$	3.19901	+	2.68429i	0.318313	+	0.267097i	0.787918	−	0.615780i	$-0.211159\pi$
$101$	3.19901	+	2.68429i	0.318313	+	0.267097i	−0.469605	+	0.882877i	$0.655604\pi$
$102$	−1.03896	+	1.79953i	−0.102872	+	0.178180i
$103$	5.27819	+	9.14210i	0.520076	+	0.900798i	0.999728	+	0.0233387i	$0.00742961\pi$
$103$	5.27819	+	9.14210i	0.520076	+	0.900798i	−0.479652	+	0.877459i	$0.659237\pi$
$104$	0.113457	−	0.643445i	0.0111254	−	0.0630950i
$105$	1.33143	−	7.55093i	0.129935	−	0.736895i
$106$	3.56023	+	6.16651i	0.345800	+	0.598944i
$107$	−7.82923	+	13.5606i	−0.756880	+	1.31095i	0.187554	+	0.982254i	$0.439944\pi$
$107$	−7.82923	+	13.5606i	−0.756880	+	1.31095i	−0.944434	+	0.328700i	$0.893389\pi$
$108$	−2.82691	−	2.37206i	−0.272019	−	0.228251i
$109$	7.90799	+	2.87827i	0.757448	+	0.275689i	0.691737	−	0.722150i	$-0.256846\pi$
$109$	7.90799	+	2.87827i	0.757448	+	0.275689i	0.0657119	+	0.997839i	$0.479068\pi$
$110$	−1.25616	+	0.457206i	−0.119770	+	0.0435929i
$111$	1.68489	−	1.41379i	0.159923	−	0.134191i
$112$	−0.486047	−	2.75651i	−0.0459271	−	0.260466i
$113$	−9.01508			−0.848068			−0.424034	−	0.905646i	$-0.639386\pi$
$113$	−9.01508			−0.848068			−0.424034	+	0.905646i	$0.639386\pi$
$114$	−1.26855	−	8.84165i	−0.118810	−	0.828096i
$115$	−1.79098			−0.167010
$116$	1.03631	+	5.87719i	0.0962188	+	0.545684i
$117$	−0.600190	+	0.503619i	−0.0554876	+	0.0465596i
$118$	0.907653	−	0.330359i	0.0835562	−	0.0304120i
$119$	−2.66710	−	0.970747i	−0.244493	−	0.0889882i
$120$	2.09843	+	1.76079i	0.191560	+	0.160738i
$121$	−0.500000	+	0.866025i	−0.0454545	+	0.0787296i
$122$	−0.658970	−	1.14137i	−0.0596603	−	0.103335i
$123$	−1.74617	+	9.90304i	−0.157447	+	0.892927i
$124$	0.635666	−	3.60504i	0.0570845	−	0.323742i
$125$	−5.48950	−	9.50810i	−0.490996	−	0.850430i
$126$	−1.67823	+	2.90679i	−0.149509	+	0.258957i
$127$	5.91246	+	4.96114i	0.524646	+	0.440230i	0.866248	−	0.499614i	$-0.166525\pi$
$127$	5.91246	+	4.96114i	0.524646	+	0.440230i	−0.341602	+	0.939845i	$0.610969\pi$
$128$	0.939693	+	0.342020i	0.0830579	+	0.0302306i
$129$	−6.49458	+	2.36383i	−0.571816	+	0.208124i
$130$	−0.669075	+	0.561420i	−0.0586817	+	0.0492398i
$131$	−0.492806	−	2.79484i	−0.0430567	−	0.244186i	0.955682	−	0.294402i	$-0.0951204\pi$
$131$	−0.492806	−	2.79484i	−0.0430567	−	0.244186i	−0.998738	+	0.0502153i	$0.984009\pi$
$132$	2.04918			0.178359
$133$	11.5927	−	3.80357i	1.00521	−	0.329811i
$134$	−0.771575			−0.0666539
$135$	0.856620	+	4.85813i	0.0737261	+	0.418122i
$136$	0.776784	−	0.651799i	0.0666087	−	0.0558913i
$137$	−20.7339	+	7.54652i	−1.77142	+	0.644742i	−0.771451	+	0.636289i	$0.780469\pi$
$137$	−20.7339	+	7.54652i	−1.77142	+	0.644742i	−0.999964	+	0.00845396i	$0.997309\pi$
$138$	2.57987	+	0.938995i	0.219613	+	0.0799325i
$139$	−4.22551	−	3.54562i	−0.358403	−	0.300736i	0.445751	−	0.895157i	$-0.352937\pi$
$139$	−4.22551	−	3.54562i	−0.358403	−	0.300736i	−0.804154	+	0.594421i	$0.797381\pi$
$140$	−1.87085	+	3.24040i	−0.158115	+	0.273864i
$141$	12.3867	+	21.4543i	1.04314	+	1.80678i
$142$	1.21060	−	6.86568i	0.101592	−	0.576155i
$143$	−0.113457	+	0.643445i	−0.00948773	+	0.0538076i
$144$	−0.599576	−	1.03850i	−0.0499647	−	0.0865414i
$145$	3.98886	−	6.90891i	0.331257	−	0.573754i
$146$	−6.09391	−	5.11340i	−0.504336	−	0.423188i
$147$	−1.60707	−	0.584925i	−0.132549	−	0.0482438i
$148$	−1.00861	+	0.367103i	−0.0829071	+	0.0301757i
$149$	12.8522	−	10.7843i	1.05290	−	0.883485i	0.0595008	−	0.998228i	$-0.481049\pi$
$149$	12.8522	−	10.7843i	1.05290	−	0.883485i	0.993395	+	0.114744i	$0.0366047\pi$
$150$	1.14331	+	6.48403i	0.0933509	+	0.529419i
$151$	−8.90544			−0.724714			−0.362357	−	0.932039i	$-0.618028\pi$
$151$	−8.90544			−0.724714			−0.362357	+	0.932039i	$0.618028\pi$
$152$	−0.894003	+	4.26623i	−0.0725132	+	0.346037i
$153$	−1.21596			−0.0983049
$154$	0.486047	+	2.75651i	0.0391668	+	0.222126i
$155$	−3.74863	+	3.14548i	−0.301097	+	0.252651i
$156$	1.25813	−	0.457923i	0.100731	−	0.0366632i
$157$	−4.09793	−	1.49153i	−0.327051	−	0.119037i	0.173276	−	0.984873i	$-0.444565\pi$
$157$	−4.09793	−	1.49153i	−0.327051	−	0.119037i	−0.500327	+	0.865837i	$0.666787\pi$
$158$	−13.0200	−	10.9251i	−1.03582	−	0.869155i
$159$	−7.29557	+	12.6363i	−0.578576	+	1.00212i
$160$	−0.668391	−	1.15769i	−0.0528409	−	0.0915231i
$161$	−0.651191	+	3.69309i	−0.0513211	+	0.291056i
$162$	1.93783	−	10.9900i	0.152250	−	0.863452i
$163$	−6.77356	−	11.7321i	−0.530546	−	0.918933i	−0.999365	−	0.0356383i	$-0.988654\pi$
$163$	−6.77356	−	11.7321i	−0.530546	−	0.918933i	0.468819	−	0.883294i	$-0.344680\pi$
$164$	2.45361	−	4.24978i	0.191595	−	0.331852i
$165$	−2.09843	−	1.76079i	−0.163363	−	0.137078i
$166$	5.22459	+	1.90159i	0.405507	+	0.147592i
$167$	−12.7230	+	4.63081i	−0.984539	+	0.358343i	−0.783603	−	0.621262i	$-0.786620\pi$
$167$	−12.7230	+	4.63081i	−0.984539	+	0.358343i	−0.200935	+	0.979604i	$0.564398\pi$
$168$	4.39382	−	3.68686i	0.338991	−	0.284447i
$169$	−2.18330	−	12.3821i	−0.167946	−	0.952469i
$170$	−1.35552			−0.103964
$171$	4.10965	−	3.22988i	0.314273	−	0.246995i
$172$	3.37275			0.257170
$173$	0.308505	+	1.74962i	0.0234552	+	0.133021i	0.994287	−	0.106741i	$-0.0340416\pi$
$173$	0.308505	+	1.74962i	0.0234552	+	0.133021i	−0.970832	+	0.239762i	$0.922931\pi$
$174$	−9.36814	+	7.86080i	−0.710197	+	0.595926i
$175$	−8.45097	+	3.07590i	−0.638833	+	0.232516i
$176$	−0.939693	−	0.342020i	−0.0708320	−	0.0257807i
$177$	1.51624	+	1.27228i	0.113968	+	0.0956304i
$178$	3.51419	−	6.08675i	0.263399	−	0.456221i
$179$	7.96465	+	13.7952i	0.595306	+	1.03110i	0.993504	+	0.113801i	$0.0363025\pi$
$179$	7.96465	+	13.7952i	0.595306	+	1.03110i	−0.398198	+	0.917300i	$0.630364\pi$
$180$	−0.278359	+	1.57865i	−0.0207476	+	0.117666i
$181$	0.183362	−	1.03990i	0.0136292	−	0.0772951i	−0.977235	−	0.212162i	$-0.931950\pi$
$181$	0.183362	−	1.03990i	0.0136292	−	0.0772951i	0.990864	+	0.134867i	$0.0430607\pi$
$182$	0.914404	+	1.58379i	0.0677801	+	0.117399i
$183$	1.35035	−	2.33888i	0.0998208	−	0.172895i
$184$	−1.02632	−	0.861188i	−0.0756616	−	0.0634876i
$185$	1.34829	+	0.490737i	0.0991281	+	0.0360797i
$186$	7.04896	−	2.56561i	0.516855	−	0.188120i
$187$	−0.776784	+	0.651799i	−0.0568041	+	0.0476643i
$188$	−2.09930	−	11.9057i	−0.153107	−	0.868312i
$189$	10.3292			0.751337
$190$	4.58132	−	3.60058i	0.332364	−	0.261214i
$191$	−7.70674			−0.557640			−0.278820	−	0.960343i	$-0.589943\pi$
$191$	−7.70674			−0.557640			−0.278820	+	0.960343i	$0.589943\pi$
$192$	0.355837	+	2.01805i	0.0256803	+	0.145640i
$193$	2.20345	−	1.84892i	0.158608	−	0.133088i	−0.560030	−	0.828472i	$-0.689210\pi$
$193$	2.20345	−	1.84892i	0.158608	−	0.133088i	0.718638	+	0.695385i	$0.244766\pi$
$194$	1.94806	−	0.709037i	0.139863	−	0.0509059i
$195$	−1.68185	−	0.612143i	−0.120440	−	0.0438365i
$196$	0.639325	+	0.536457i	0.0456661	+	0.0383184i
$197$	11.0627	−	19.1611i	0.788182	−	1.36517i	−0.138898	−	0.990307i	$-0.544356\pi$
$197$	11.0627	−	19.1611i	0.788182	−	1.36517i	0.927080	−	0.374864i	$-0.122311\pi$
$198$	0.599576	+	1.03850i	0.0426100	+	0.0738028i
$199$	4.72090	−	26.7736i	0.334656	−	1.89793i	−0.0959484	−	0.995386i	$-0.530588\pi$
$199$	4.72090	−	26.7736i	0.334656	−	1.89793i	0.430604	−	0.902541i	$-0.358301\pi$
$200$	0.557934	−	3.16420i	0.0394519	−	0.223743i
$201$	−0.790550	−	1.36927i	−0.0557611	−	0.0965810i
$202$	2.08800	−	3.61653i	0.146912	−	0.254458i
$203$	−12.7962	−	10.7373i	−0.898116	−	0.753609i
$204$	1.95260	+	0.710688i	0.136709	+	0.0497581i
$205$	−6.16428	+	2.24361i	−0.430532	+	0.156701i
$206$	8.08666	−	6.78551i	0.563424	−	0.472769i
$207$	0.278981	+	1.58218i	0.0193906	+	0.109969i
$208$	−0.653372			−0.0453032
$209$	0.894003	−	4.26623i	0.0618395	−	0.295102i
$210$	−7.66742			−0.529102
$211$	0.735305	+	4.17012i	0.0506205	+	0.287083i	0.999601	−	0.0282523i	$-0.00899417\pi$
$211$	0.735305	+	4.17012i	0.0506205	+	0.287083i	−0.948980	+	0.315335i	$0.897883\pi$
$212$	5.45459	−	4.57695i	0.374623	−	0.314346i
$213$	13.4245	−	4.88613i	0.919833	−	0.334792i
$214$	14.7141	+	5.35551i	1.00584	+	0.366095i
$215$	−3.45381	−	2.89809i	−0.235548	−	0.197648i
$216$	−1.84513	+	3.19586i	−0.125545	+	0.217451i
$217$	5.12314	+	8.87354i	0.347782	+	0.602375i
$218$	1.46134	−	8.28766i	0.0989743	−	0.561311i
$219$	2.83070	−	16.0537i	0.191281	−	1.08481i
$220$	0.668391	+	1.15769i	0.0450629	+	0.0780512i
$221$	−0.331266	+	0.573769i	−0.0222834	+	0.0385959i
$222$	−1.68489	−	1.41379i	−0.113082	−	0.0948874i
$223$	−0.207614	−	0.0755654i	−0.0139029	−	0.00506024i	0.335059	−	0.942197i	$-0.391244\pi$
$223$	−0.207614	−	0.0755654i	−0.0139029	−	0.00506024i	−0.348962	+	0.937137i	$0.613466\pi$
$224$	−2.63023	+	0.957325i	−0.175740	+	0.0639640i
$225$	−2.95149	+	2.47659i	−0.196766	+	0.165106i
$226$	1.56545	+	8.87812i	0.104132	+	0.590564i
$227$	−23.3689			−1.55105			−0.775524	−	0.631318i	$-0.782514\pi$
$227$	−23.3689			−1.55105			−0.775524	+	0.631318i	$0.782514\pi$
$228$	−8.48704	+	2.78461i	−0.562068	+	0.184415i
$229$	−6.05487			−0.400117			−0.200058	−	0.979784i	$-0.564113\pi$
$229$	−6.05487			−0.400117			−0.200058	+	0.979784i	$0.564113\pi$
$230$	0.311001	+	1.76377i	0.0205068	+	0.116300i
$231$	−4.39382	+	3.68686i	−0.289092	+	0.242577i
$232$	5.60795	−	2.04113i	0.368180	−	0.134007i
$233$	−19.9415	−	7.25813i	−1.30641	−	0.475496i	−0.407334	−	0.913279i	$-0.633541\pi$
$233$	−19.9415	−	7.25813i	−1.30641	−	0.475496i	−0.899080	+	0.437783i	$0.855764\pi$
$234$	0.600190	+	0.503619i	0.0392356	+	0.0329226i
$235$	−8.08041	+	13.9957i	−0.527108	+	0.912978i
$236$	−0.482952	−	0.836498i	−0.0314375	−	0.0544514i
$237$	6.04796	−	34.2997i	0.392857	−	2.22801i
$238$	−0.492861	+	2.79515i	−0.0319474	+	0.181183i
$239$	−9.40890	−	16.2967i	−0.608611	−	1.05414i	−0.991470	−	0.130338i	$-0.958394\pi$
$239$	−9.40890	−	16.2967i	−0.608611	−	1.05414i	0.382859	−	0.923807i	$-0.374940\pi$
$240$	1.36965	−	2.37231i	0.0884108	−	0.153132i
$241$	1.04495	+	0.876817i	0.0673111	+	0.0564808i	0.675823	−	0.737064i	$-0.263789\pi$
$241$	1.04495	+	0.876817i	0.0673111	+	0.0564808i	−0.608511	+	0.793545i	$0.708233\pi$
$242$	0.939693	+	0.342020i	0.0604057	+	0.0219859i
$243$	11.0856	−	4.03483i	0.711141	−	0.258834i
$244$	−1.00960	+	0.847155i	−0.0646331	+	0.0542336i
$245$	−0.193731	−	1.09870i	−0.0123770	−	0.0701934i
$246$	10.0558			0.641135
$247$	−0.404470	−	2.81911i	−0.0257358	−	0.179376i
$248$	−3.66065			−0.232452
$249$	1.97842	+	11.2201i	0.125377	+	0.711048i
$250$	−8.41041	+	7.05717i	−0.531921	+	0.446335i
$251$	−19.0702	+	6.94098i	−1.20370	+	0.438111i	−0.864514	−	0.502609i	$-0.832374\pi$
$251$	−19.0702	+	6.94098i	−1.20370	+	0.438111i	−0.339186	+	0.940720i	$0.610151\pi$
$252$	3.15405	+	1.14798i	0.198686	+	0.0723159i
$253$	1.02632	+	0.861188i	0.0645244	+	0.0541424i
$254$	3.85908	−	6.68413i	0.242140	−	0.419400i
$255$	−1.38886	−	2.40557i	−0.0869736	−	0.150643i
$256$	0.173648	−	0.984808i	0.0108530	−	0.0615505i
$257$	1.54753	−	8.77649i	0.0965324	−	0.547463i	−0.897735	−	0.440537i	$-0.854788\pi$
$257$	1.54753	−	8.77649i	0.0965324	−	0.547463i	0.994267	−	0.106926i	$-0.0341007\pi$
$258$	3.45569	+	5.98544i	0.215142	+	0.372637i
$259$	1.50215	−	2.60181i	0.0933393	−	0.161668i
$260$	0.669075	+	0.561420i	0.0414942	+	0.0348178i
$261$	−6.72479	−	2.44762i	−0.416254	−	0.151504i
$262$	−2.66681	+	0.970638i	−0.164756	+	0.0599662i
$263$	8.89360	−	7.46262i	0.548403	−	0.460165i	−0.325997	−	0.945371i	$-0.605700\pi$
$263$	8.89360	−	7.46262i	0.548403	−	0.460165i	0.874400	+	0.485206i	$0.161255\pi$
$264$	−0.355837	−	2.01805i	−0.0219003	−	0.124202i
$265$	−9.51851			−0.584717
$266$	−5.75883	−	10.7561i	−0.353097	−	0.659496i
$267$	14.4024			0.881414
$268$	0.133983	+	0.759853i	0.00818429	+	0.0464154i
$269$	−4.51199	+	3.78601i	−0.275101	+	0.230837i	−0.769891	−	0.638176i	$-0.779689\pi$
$269$	−4.51199	+	3.78601i	−0.275101	+	0.230837i	0.494790	+	0.869013i	$0.335245\pi$
$270$	4.63558	−	1.68721i	0.282112	−	0.102680i
$271$	−21.5429	−	7.84097i	−1.30864	−	0.476305i	−0.408838	−	0.912607i	$-0.634066\pi$
$271$	−21.5429	−	7.84097i	−1.30864	−	0.476305i	−0.899800	+	0.436302i	$0.856288\pi$
$272$	−0.776784	−	0.651799i	−0.0470995	−	0.0395211i
$273$	−1.87378	+	3.24548i	−0.113406	+	0.196426i
$274$	11.0323	+	19.1085i	0.666484	+	1.15438i
$275$	−0.557934	+	3.16420i	−0.0336447	+	0.190809i
$276$	0.476740	−	2.70373i	0.0286964	−	0.162745i
$277$	−8.92613	−	15.4605i	−0.536319	−	0.928932i	−0.999098	−	0.0424582i	$-0.986481\pi$
$277$	−8.92613	−	15.4605i	−0.536319	−	0.928932i	0.462779	−	0.886474i	$-0.346852\pi$
$278$	−2.75800	+	4.77700i	−0.165414	+	0.286506i
$279$	3.36269	+	2.82163i	0.201319	+	0.168927i
$280$	3.51604	+	1.27973i	0.210124	+	0.0764788i
$281$	−10.6241	+	3.86687i	−0.633783	+	0.230678i	−0.638877	−	0.769309i	$-0.720601\pi$
$281$	−10.6241	+	3.86687i	−0.633783	+	0.230678i	0.00509410	+	0.999987i	$0.498378\pi$
$282$	18.9775	−	15.9240i	1.13009	−	0.948259i
$283$	5.21774	+	29.5913i	0.310162	+	1.75902i	0.598150	+	0.801384i	$0.295903\pi$
$283$	5.21774	+	29.5913i	0.310162	+	1.75902i	−0.287988	+	0.957634i	$0.592986\pi$
$284$	−6.97159			−0.413688
$285$	11.0837	+	4.44109i	0.656544	+	0.263068i
$286$	0.653372			0.0386347
$287$	2.38514	+	13.5268i	0.140791	+	0.798463i
$288$	−0.918604	+	0.770801i	−0.0541293	+	0.0454199i
$289$	15.0085	−	5.46266i	0.882856	−	0.321333i
$290$	−7.49661	−	2.72854i	−0.440216	−	0.160225i
$291$	3.25426	+	2.73065i	0.190768	+	0.160073i
$292$	−3.97752	+	6.88927i	−0.232767	+	0.403164i
$293$	−4.87568	−	8.44492i	−0.284840	−	0.493358i	0.687730	−	0.725966i	$-0.258607\pi$
$293$	−4.87568	−	8.44492i	−0.284840	−	0.493358i	−0.972570	+	0.232609i	$0.925274\pi$
$294$	−0.296974	+	1.68422i	−0.0173199	+	0.0982260i
$295$	−0.224215	+	1.27159i	−0.0130543	+	0.0740346i
$296$	0.536669	+	0.929538i	0.0311933	+	0.0540283i
$297$	1.84513	−	3.19586i	0.107065	−	0.185443i
$298$	−12.8522	−	10.7843i	−0.744510	−	0.624718i
$299$	0.822577	+	0.299394i	0.0475709	+	0.0173144i
$300$	6.18699	−	2.25188i	0.357206	−	0.130012i
$301$	−7.23180	+	6.06820i	−0.416834	+	0.349765i
$302$	1.54641	+	8.77015i	0.0889861	+	0.504665i
$303$	8.55741			0.491610
$304$	4.35666	+	0.139597i	0.249872	+	0.00800645i
$305$	1.76180			0.100880
$306$	0.211150	+	1.19749i	0.0120706	+	0.0684560i
$307$	0.908318	−	0.762170i	0.0518405	−	0.0434993i	−0.616499	−	0.787355i	$-0.711450\pi$
$307$	0.908318	−	0.762170i	0.0518405	−	0.0434993i	0.668340	+	0.743856i	$0.267005\pi$
$308$	2.63023	−	0.957325i	0.149871	−	0.0545487i
$309$	20.3274	+	7.39857i	1.15639	+	0.420890i
$310$	3.74863	+	3.14548i	0.212908	+	0.178651i
$311$	−1.96938	+	3.41107i	−0.111674	+	0.193424i	−0.916445	−	0.400160i	$-0.868954\pi$
$311$	−1.96938	+	3.41107i	−0.111674	+	0.193424i	0.804772	+	0.593585i	$0.202288\pi$
$312$	−0.669439	−	1.15950i	−0.0378995	−	0.0656439i
$313$	3.41924	−	19.3915i	0.193267	−	1.09607i	−0.721599	−	0.692312i	$-0.756592\pi$
$313$	3.41924	−	19.3915i	0.193267	−	1.09607i	0.914866	−	0.403759i	$-0.132296\pi$
$314$	−0.757267	+	4.29468i	−0.0427351	+	0.242363i
$315$	−2.24343	−	3.88574i	−0.126403	−	0.218936i
$316$	−8.49822	+	14.7194i	−0.478062	+	0.828028i
$317$	17.7824	+	14.9212i	0.998760	+	0.838060i	0.986812	−	0.161869i	$-0.0517522\pi$
$317$	17.7824	+	14.9212i	0.998760	+	0.838060i	0.0119482	+	0.999929i	$0.496197\pi$
$318$	13.7112	+	4.99046i	0.768885	+	0.279851i
$319$	−5.60795	+	2.04113i	−0.313985	+	0.114281i
$320$	−1.02403	+	0.859266i	−0.0572452	+	0.0480344i
$321$	5.57186	+	31.5996i	0.310991	+	1.76372i
$322$	3.75006			0.208983
$323$	2.33146	−	3.75510i	0.129726	−	0.208939i
$324$	−11.1595			−0.619972
$325$	0.364539	+	2.06740i	0.0202210	+	0.114679i
$326$	−10.3777	+	8.70792i	−0.574767	+	0.482287i
$327$	16.2049	−	5.89811i	0.896135	−	0.326166i
$328$	−4.61129	−	1.67837i	−0.254616	−	0.0926725i
$329$	25.9218	+	21.7510i	1.42911	+	1.19917i
$330$	−1.36965	+	2.37231i	−0.0753970	+	0.130591i
$331$	15.8043	+	27.3739i	0.868683	+	1.50460i	0.863343	+	0.504617i	$0.168366\pi$
$331$	15.8043	+	27.3739i	0.868683	+	1.50460i	0.00533984	+	0.999986i	$0.498300\pi$
$332$	0.965465	−	5.47542i	0.0529868	−	0.300503i
$333$	0.223502	−	1.26754i	0.0122478	−	0.0694609i
$334$	6.76979	+	11.7256i	0.370426	+	0.641597i
$335$	0.515714	−	0.893242i	0.0281764	−	0.0488030i
$336$	−4.39382	−	3.68686i	−0.239703	−	0.201134i
$337$	−29.8695	−	10.8716i	−1.62710	−	0.592215i	−0.642382	−	0.766385i	$-0.722054\pi$
$337$	−29.8695	−	10.8716i	−1.62710	−	0.592215i	−0.984716	+	0.174170i	$0.944276\pi$
$338$	−11.8149	+	4.30026i	−0.642643	+	0.233903i
$339$	−14.1516	+	11.8746i	−0.768608	+	0.644938i
$340$	0.235384	+	1.33493i	0.0127655	+	0.0723967i
$341$	3.66065			0.198235
$342$	−3.89445	−	3.48635i	−0.210588	−	0.188520i
$343$	17.2572			0.931802
$344$	−0.585672	−	3.32151i	−0.0315773	−	0.179084i
$345$	−2.81142	+	2.35906i	−0.151362	+	0.127008i
$346$	1.66947	−	0.607636i	0.0897510	−	0.0326667i
$347$	−14.2788	−	5.19706i	−0.766526	−	0.278993i	−0.0709837	−	0.997477i	$-0.522614\pi$
$347$	−14.2788	−	5.19706i	−0.766526	−	0.278993i	−0.695543	+	0.718485i	$0.744836\pi$
$348$	9.36814	+	7.86080i	0.502185	+	0.421383i
$349$	−0.327028	+	0.566429i	−0.0175054	+	0.0303202i	−0.874645	−	0.484763i	$-0.838906\pi$
$349$	−0.327028	+	0.566429i	−0.0175054	+	0.0303202i	0.857140	+	0.515083i	$0.172239\pi$
$350$	4.49667	+	7.78846i	0.240357	+	0.416311i
$351$	0.418686	−	2.37449i	0.0223478	−	0.126741i
$352$	−0.173648	+	0.984808i	−0.00925548	+	0.0524904i
$353$	8.26784	+	14.3203i	0.440053	+	0.762194i	0.997693	−	0.0678889i	$-0.0216263\pi$
$353$	8.26784	+	14.3203i	0.440053	+	0.762194i	−0.557640	+	0.830083i	$0.688293\pi$
$354$	0.989658	−	1.71414i	0.0525997	−	0.0911054i
$355$	7.13915	+	5.99046i	0.378907	+	0.317940i
$356$	−6.60451	−	2.40384i	−0.350038	−	0.127404i
$357$	−5.46539	+	1.98924i	−0.289259	+	0.105282i
$358$	12.2026	−	10.2392i	0.644925	−	0.541156i
$359$	−2.24028	−	12.7052i	−0.118237	−	0.670557i	−0.985096	−	0.172003i	$-0.944976\pi$
$359$	−2.24028	−	12.7052i	−0.118237	−	0.670557i	0.866859	−	0.498553i	$-0.166135\pi$
$360$	1.60300			0.0844858
$361$	2.09467	+	18.8842i	0.110246	+	0.993904i
$362$	−1.05594			−0.0554991
$363$	0.355837	+	2.01805i	0.0186766	+	0.105920i
$364$	1.40095	−	1.17554i	0.0734296	−	0.0616148i
$365$	9.99283	−	3.63709i	0.523049	−	0.190374i
$366$	−2.53783	−	0.923694i	−0.132654	−	0.0482823i
$367$	14.5457	+	12.2053i	0.759281	+	0.637113i	0.937940	−	0.346799i	$-0.112731\pi$
$367$	14.5457	+	12.2053i	0.759281	+	0.637113i	−0.178658	+	0.983911i	$0.557176\pi$
$368$	−0.669885	+	1.16028i	−0.0349202	+	0.0604836i
$369$	2.94226	+	5.09614i	0.153168	+	0.265295i
$370$	0.249154	−	1.41302i	0.0129529	−	0.0734594i
$371$	−3.46088	+	19.6276i	−0.179680	+	1.01902i
$372$	−3.75067	−	6.49636i	−0.194463	−	0.336821i
$373$	2.92130	−	5.05985i	0.151259	−	0.261989i	−0.780431	−	0.625242i	$-0.785000\pi$
$373$	2.92130	−	5.05985i	0.151259	−	0.261989i	0.931691	+	0.363253i	$0.118334\pi$
$374$	0.776784	+	0.651799i	0.0401666	+	0.0337037i
$375$	−21.1412	−	7.69477i	−1.09173	−	0.397356i
$376$	−11.3603	+	4.13480i	−0.585862	+	0.213236i
$377$	−2.98698	+	2.50638i	−0.153837	+	0.129085i
$378$	−1.79364	−	10.1722i	−0.0922550	−	0.523204i
$379$	−14.2608			−0.732529			−0.366265	−	0.930511i	$-0.619363\pi$
$379$	−14.2608			−0.732529			−0.366265	+	0.930511i	$0.619363\pi$
$380$	−4.34142	−	3.88649i	−0.222710	−	0.199373i
$381$	15.8159			0.810275
$382$	1.33826	+	7.58965i	0.0684714	+	0.388320i
$383$	11.2994	−	9.48134i	0.577373	−	0.484474i	−0.306710	−	0.951803i	$-0.599228\pi$
$383$	11.2994	−	9.48134i	0.577373	−	0.484474i	0.884083	+	0.467329i	$0.154784\pi$
$384$	1.92560	−	0.700862i	0.0982655	−	0.0357657i
$385$	−3.51604	−	1.27973i	−0.179194	−	0.0652213i
$386$	−2.20345	−	1.84892i	−0.112153	−	0.0941073i
$387$	−2.02222	+	3.50259i	−0.102795	+	0.178047i
$388$	−1.03654	−	1.79534i	−0.0526224	−	0.0911448i
$389$	1.09435	−	6.20639i	0.0554860	−	0.314677i	−0.944415	−	0.328756i	$-0.893371\pi$
$389$	1.09435	−	6.20639i	0.0554860	−	0.314677i	0.999901	+	0.0140794i	$0.00448176\pi$
$390$	−0.310793	+	1.76260i	−0.0157376	+	0.0892525i
$391$	0.679277	+	1.17654i	0.0343525	+	0.0595003i
$392$	0.417290	−	0.722767i	0.0210763	−	0.0365052i
$393$	−4.45493	−	3.73813i	−0.224721	−	0.188564i
$394$	−20.7910	−	7.56730i	−1.04744	−	0.381235i
$395$	21.3503	−	7.77088i	1.07425	−	0.390995i
$396$	0.918604	−	0.770801i	0.0461616	−	0.0387342i
$397$	−1.54902	−	8.78495i	−0.0777433	−	0.440904i	−0.998688	−	0.0512105i	$-0.983692\pi$
$397$	−1.54902	−	8.78495i	−0.0777433	−	0.440904i	0.920945	−	0.389693i	$-0.127419\pi$
$398$	−27.1866			−1.36274
$399$	13.1877	−	21.2405i	0.660213	−	1.06335i
$400$	−3.21302			−0.160651
$401$	−4.67780	−	26.5291i	−0.233598	−	1.32480i	−0.845546	−	0.533903i	$-0.820725\pi$
$401$	−4.67780	−	26.5291i	−0.233598	−	1.32480i	0.611948	−	0.790898i	$-0.290386\pi$
$402$	−1.21119	+	1.01631i	−0.0604088	+	0.0506890i
$403$	2.24753	−	0.818032i	0.111957	−	0.0407491i
$404$	−3.92417	−	1.42828i	−0.195235	−	0.0710596i
$405$	11.4277	+	9.58898i	0.567847	+	0.476480i
$406$	−8.35211	+	14.4663i	−0.414508	+	0.717950i
$407$	−0.536669	−	0.929538i	−0.0266017	−	0.0460755i
$408$	0.360826	−	2.04634i	0.0178635	−	0.101309i
$409$	3.02110	−	17.1335i	0.149384	−	0.847197i	−0.814358	−	0.580362i	$-0.802911\pi$
$409$	3.02110	−	17.1335i	0.149384	−	0.847197i	0.963742	−	0.266835i	$-0.0859779\pi$
$410$	3.27995	+	5.68103i	0.161985	+	0.280566i
$411$	−22.6071	+	39.1567i	−1.11513	+	1.93146i
$412$	−8.08666	−	6.78551i	−0.398401	−	0.334298i
$413$	2.54055	+	0.924685i	0.125012	+	0.0455008i
$414$	1.50970	−	0.549486i	0.0741977	−	0.0270058i
$415$	−5.69352	+	4.77743i	−0.279484	+	0.234515i
$416$	0.113457	+	0.643445i	0.00556268	+	0.0315475i
$417$	−11.3033			−0.553525
$418$	−4.35666	−	0.139597i	−0.213091	−	0.00682793i
$419$	16.0677			0.784959			0.392479	−	0.919761i	$-0.371617\pi$
$419$	16.0677			0.784959			0.392479	+	0.919761i	$0.371617\pi$
$420$	1.33143	+	7.55093i	0.0649673	+	0.368448i
$421$	10.6043	−	8.89808i	0.516823	−	0.433666i	−0.346700	−	0.937976i	$-0.612698\pi$
$421$	10.6043	−	8.89808i	0.516823	−	0.433666i	0.863522	+	0.504310i	$0.168253\pi$
$422$	3.97908	−	1.44827i	0.193699	−	0.0705006i
$423$	13.6227	+	4.95826i	0.662359	+	0.241079i
$424$	−5.45459	−	4.57695i	−0.264899	−	0.222276i
$425$	−1.62903	+	2.82156i	−0.0790196	+	0.136866i
$426$	−7.14304	−	12.3721i	−0.346081	−	0.599430i
$427$	0.640580	−	3.63291i	0.0309999	−	0.175809i
$428$	2.71906	−	15.4206i	0.131431	−	0.745381i
$429$	0.669439	+	1.15950i	0.0323208	+	0.0559813i
$430$	−2.25432	+	3.90459i	−0.108713	+	0.188296i
$431$	29.2955	+	24.5818i	1.41111	+	1.18406i	0.955904	+	0.293680i	$0.0948800\pi$
$431$	29.2955	+	24.5818i	1.41111	+	1.18406i	0.455209	+	0.890384i	$0.349564\pi$
$432$	3.46772	+	1.26215i	0.166841	+	0.0607250i
$433$	2.19729	−	0.799747i	0.105595	−	0.0384334i	−0.288682	−	0.957425i	$-0.593217\pi$
$433$	2.19729	−	0.799747i	0.105595	−	0.0384334i	0.394277	+	0.918992i	$0.370995\pi$
$434$	7.84911	−	6.58618i	0.376769	−	0.316147i
$435$	−2.83877	−	16.0995i	−0.136109	−	0.771910i
$436$	−8.41551			−0.403030
$437$	−5.42095	−	2.17210i	−0.259319	−	0.103905i
$438$	−16.3013			−0.778908
$439$	−3.61000	−	20.4733i	−0.172296	−	0.977139i	−0.941219	−	0.337797i	$-0.890318\pi$
$439$	−3.61000	−	20.4733i	−0.172296	−	0.977139i	0.768923	−	0.639341i	$-0.220793\pi$
$440$	1.02403	−	0.859266i	0.0488189	−	0.0409639i
$441$	−0.940433	+	0.342290i	−0.0447825	+	0.0162995i
$442$	0.622576	+	0.226599i	0.0296129	+	0.0107782i
$443$	18.3782	+	15.4212i	0.873177	+	0.732682i	0.964765	−	0.263115i	$-0.0847498\pi$
$443$	18.3782	+	15.4212i	0.873177	+	0.732682i	−0.0915878	+	0.995797i	$0.529194\pi$
$444$	−1.09973	+	1.90479i	−0.0521910	+	0.0903975i
$445$	4.69770	+	8.13665i	0.222692	+	0.385714i
$446$	−0.0383656	+	0.217582i	−0.00181666	+	0.0103028i
$447$	5.97002	−	33.8577i	0.282372	−	1.60141i
$448$	1.39952	+	2.42403i	0.0661209	+	0.114525i
$449$	11.8897	−	20.5936i	0.561111	−	0.971872i	−0.436289	−	0.899806i	$-0.643708\pi$
$449$	11.8897	−	20.5936i	0.561111	−	0.971872i	0.997400	−	0.0720656i	$-0.0229591\pi$
$450$	2.95149	+	2.47659i	0.139135	+	0.116748i
$451$	4.61129	+	1.67837i	0.217137	+	0.0790314i
$452$	8.47141	−	3.08334i	0.398461	−	0.145028i
$453$	−13.9795	+	11.7302i	−0.656812	+	0.551131i
$454$	4.05797	+	23.0139i	0.190450	+	1.08009i
$455$	−2.44472			−0.114610
$456$	4.21607	+	7.87456i	0.197435	+	0.368760i
$457$	−11.4201			−0.534209			−0.267104	−	0.963668i	$-0.586067\pi$
$457$	−11.4201			−0.534209			−0.267104	+	0.963668i	$0.586067\pi$
$458$	1.05142	+	5.96288i	0.0491295	+	0.278627i
$459$	2.86654	−	2.40531i	0.133799	−	0.112270i
$460$	1.68297	−	0.612551i	0.0784689	−	0.0285604i
$461$	17.7306	+	6.45341i	0.825796	+	0.300565i	0.720132	−	0.693837i	$-0.244081\pi$
$461$	17.7306	+	6.45341i	0.825796	+	0.300565i	0.105664	+	0.994402i	$0.466303\pi$
$462$	4.39382	+	3.68686i	0.204419	+	0.171528i
$463$	5.28665	−	9.15675i	0.245692	−	0.425550i	−0.716634	−	0.697449i	$-0.754318\pi$
$463$	5.28665	−	9.15675i	0.245692	−	0.425550i	0.962326	+	0.271899i	$0.0876516\pi$
$464$	−2.98393	−	5.16832i	−0.138525	−	0.239933i
$465$	−1.74129	+	9.87532i	−0.0807502	+	0.457957i
$466$	−3.68505	+	20.8990i	−0.170707	+	0.968125i
$467$	−13.8570	−	24.0010i	−0.641224	−	1.11063i	−0.985160	−	0.171639i	$-0.945094\pi$
$467$	−13.8570	−	24.0010i	−0.641224	−	1.11063i	0.343936	−	0.938993i	$-0.388240\pi$
$468$	0.391746	−	0.678524i	0.0181085	−	0.0313648i
$469$	−1.65440	−	1.38820i	−0.0763930	−	0.0641013i
$470$	15.1862	+	5.52733i	0.700488	+	0.254957i
$471$	−8.39742	+	3.05641i	−0.386933	+	0.140832i
$472$	−0.739926	+	0.620871i	−0.0340578	+	0.0285779i
$473$	0.585672	+	3.32151i	0.0269292	+	0.152723i
$474$	−34.8288			−1.59974
$475$	−1.98902	−	13.8633i	−0.0912624	−	0.636090i
$476$	2.83827			0.130092
$477$	1.48270	+	8.40881i	0.0678882	+	0.385013i
$478$	−14.4153	+	12.0958i	−0.659339	+	0.553251i
$479$	−2.78893	+	1.01509i	−0.127429	+	0.0463805i	−0.404948	−	0.914340i	$-0.632710\pi$
$479$	−2.78893	+	1.01509i	−0.127429	+	0.0463805i	0.277518	+	0.960720i	$0.410488\pi$
$480$	−2.57411	−	0.936899i	−0.117491	−	0.0427634i
$481$	−0.537218	−	0.450780i	−0.0244950	−	0.0205538i
$482$	0.682043	−	1.18133i	0.0310662	−	0.0538082i
$483$	3.84228	+	6.65503i	0.174830	+	0.302814i
$484$	0.173648	−	0.984808i	0.00789310	−	0.0447640i
$485$	−0.481224	+	2.72916i	−0.0218513	+	0.123925i
$486$	−5.89852	−	10.2165i	−0.267562	−	0.463432i
$487$	6.49241	−	11.2452i	0.294199	−	0.509568i	−0.680599	−	0.732656i	$-0.738280\pi$
$487$	6.49241	−	11.2452i	0.294199	−	0.509568i	0.974798	+	0.223088i	$0.0716137\pi$
$488$	1.00960	+	0.847155i	0.0457025	+	0.0383489i
$489$	−26.0864	−	9.49466i	−1.17967	−	0.429363i
$490$	−1.04837	+	0.381575i	−0.0473604	+	0.0172378i
$491$	−12.9211	+	10.8421i	−0.583121	+	0.489297i	−0.885970	−	0.463742i	$-0.846507\pi$
$491$	−12.9211	+	10.8421i	−0.583121	+	0.489297i	0.302849	+	0.953038i	$0.402062\pi$
$492$	−1.74617	−	9.90304i	−0.0787236	−	0.446464i
$493$	−6.05153			−0.272547
$494$	−2.70605	+	0.887859i	−0.121751	+	0.0399467i
$495$	−1.60300			−0.0720497
$496$	0.635666	+	3.60504i	0.0285422	+	0.161871i
$497$	14.9484	−	12.5432i	0.670526	−	0.562638i
$498$	10.7061	−	3.89672i	0.479754	−	0.174616i
$499$	24.5873	+	8.94903i	1.10068	+	0.400614i	0.827566	−	0.561369i	$-0.189725\pi$
$499$	24.5873	+	8.94903i	1.10068	+	0.400614i	0.273111	+	0.961982i	$0.411947\pi$
$500$	8.41041	+	7.05717i	0.376125	+	0.315606i
$501$	−13.8725	+	24.0279i	−0.619779	+	1.07349i
$502$	10.1470	+	17.5752i	0.452884	+	0.784419i
$503$	−0.424327	+	2.40648i	−0.0189198	+	0.107300i	−0.992805	−	0.119740i	$-0.961794\pi$
$503$	−0.424327	+	2.40648i	−0.0189198	+	0.107300i	0.973885	+	0.227040i	$0.0729049\pi$
$504$	0.582844	−	3.30547i	0.0259620	−	0.147238i
$505$	2.79121	+	4.83451i	0.124207	+	0.215133i
$506$	0.669885	−	1.16028i	0.0297800	−	0.0515805i
$507$	−19.7368	−	16.5612i	−0.876543	−	0.735507i
$508$	−7.25271	−	2.63977i	−0.321787	−	0.117121i
$509$	−40.6549	+	14.7972i	−1.80200	+	0.655873i	−0.803863	+	0.594815i	$0.797225\pi$
$509$	−40.6549	+	14.7972i	−1.80200	+	0.655873i	−0.998134	+	0.0610587i	$0.980552\pi$
$510$	−2.12785	+	1.78548i	−0.0942229	+	0.0790624i
$511$	−3.86652	−	21.9281i	−0.171045	−	0.970044i
$512$	−1.00000			−0.0441942
$513$	−3.29911	+	15.7435i	−0.145659	+	0.695094i
$514$	−8.91189			−0.393086
$515$	2.45045	+	13.8972i	0.107980	+	0.612383i
$516$	5.29443	−	4.44255i	0.233074	−	0.195573i
$517$	11.3603	−	4.13480i	0.499625	−	0.181848i
$518$	−2.82313	−	1.02753i	−0.124041	−	0.0451472i
$519$	2.78886	+	2.34013i	0.122417	+	0.102720i
$520$	0.436707	−	0.756399i	0.0191509	−	0.0331703i
$521$	15.6080	+	27.0339i	0.683800	+	1.18438i	0.973812	+	0.227353i	$0.0730071\pi$
$521$	15.6080	+	27.0339i	0.683800	+	1.18438i	−0.290013	+	0.957023i	$0.593660\pi$
$522$	−1.24269	+	7.04765i	−0.0543911	+	0.308467i
$523$	−7.13844	+	40.4841i	−0.312142	+	1.77025i	0.275673	+	0.961252i	$0.411099\pi$
$523$	−7.13844	+	40.4841i	−0.312142	+	1.77025i	−0.587815	+	0.808995i	$0.700012\pi$
$524$	1.41898	+	2.45774i	0.0619884	+	0.107367i
$525$	−9.21450	+	15.9600i	−0.402154	+	0.696550i
$526$	−8.89360	−	7.46262i	−0.387780	−	0.325386i
$527$	3.48812	+	1.26957i	0.151945	+	0.0553033i
$528$	−1.92560	+	0.700862i	−0.0838011	+	0.0305011i
$529$	−16.2440	+	13.6303i	−0.706260	+	0.592623i
$530$	1.65287	+	9.37390i	0.0717961	+	0.407176i
$531$	1.15827			0.0502645
$532$	−9.59264	+	7.53911i	−0.415894	+	0.326862i
$533$	3.20624			0.138878
$534$	−2.50095	−	14.1836i	−0.108227	−	0.613785i
$535$	−16.0348	+	13.4548i	−0.693244	+	0.581701i
$536$	0.725044	−	0.263894i	0.0313171	−	0.0113985i
$537$	30.6735	+	11.1642i	1.32366	+	0.481773i
$538$	4.51199	+	3.78601i	0.194526	+	0.163226i
$539$	−0.417290	+	0.722767i	−0.0179739	+	0.0311318i
$540$	−2.46654	−	4.27217i	−0.106143	−	0.183845i
$541$	0.735386	−	4.17058i	0.0316167	−	0.179307i	−0.964910	−	0.262581i	$-0.915426\pi$
$541$	0.735386	−	4.17058i	0.0316167	−	0.179307i	0.996527	+	0.0832735i	$0.0265375\pi$
$542$	−3.98097	+	22.5772i	−0.170997	+	0.969773i
$543$	−1.08191	−	1.87392i	−0.0464292	−	0.0804177i
$544$	−0.507010	+	0.878167i	−0.0217379	+	0.0376511i
$545$	8.61777	+	7.23117i	0.369145	+	0.309749i
$546$	3.52156	+	1.28174i	0.150709	+	0.0548535i
$547$	37.5004	−	13.6490i	1.60340	−	0.583591i	0.623283	−	0.781997i	$-0.285799\pi$
$547$	37.5004	−	13.6490i	1.60340	−	0.583591i	0.980120	+	0.198406i	$0.0635763\pi$
$548$	16.9024	−	14.1828i	0.722036	−	0.605860i
$549$	−0.274436	−	1.55640i	−0.0117126	−	0.0664256i
$550$	3.21302			0.137003
$551$	20.4526	−	16.0743i	0.871311	−	0.684786i
$552$	−2.74544			−0.116854
$553$	−8.26107	−	46.8508i	−0.351296	−	1.99230i
$554$	−13.6756	+	11.4752i	−0.581021	+	0.487535i
$555$	2.76289	−	1.00561i	0.117278	−	0.0426857i
$556$	5.18335	+	1.88659i	0.219823	+	0.0800090i
$557$	17.8432	+	14.9723i	0.756042	+	0.634395i	0.937093	−	0.349079i	$-0.113505\pi$
$557$	17.8432	+	14.9723i	0.756042	+	0.634395i	−0.181051	+	0.983474i	$0.557950\pi$
$558$	2.19484	−	3.80158i	0.0929150	−	0.160934i
$559$	1.10183	+	1.90843i	0.0466025	+	0.0807178i
$560$	0.649738	−	3.68485i	0.0274564	−	0.155713i
$561$	−0.360826	+	2.04634i	−0.0152341	+	0.0863967i
$562$	5.65299	+	9.79126i	0.238457	+	0.413019i
$563$	1.05197	−	1.82207i	0.0443354	−	0.0767912i	−0.843006	−	0.537904i	$-0.819216\pi$
$563$	1.05197	−	1.82207i	0.0443354	−	0.0767912i	0.887342	+	0.461113i	$0.152550\pi$
$564$	−18.9775	−	15.9240i	−0.799095	−	0.670521i
$565$	−11.3244	−	4.12175i	−0.476422	−	0.173403i
$566$	28.2357	−	10.2769i	1.18683	−	0.431972i
$567$	23.9280	−	20.0780i	1.00488	−	0.843195i
$568$	1.21060	+	6.86568i	0.0507958	+	0.288078i
$569$	−16.1211			−0.675833			−0.337917	−	0.941176i	$-0.609722\pi$
$569$	−16.1211			−0.675833			−0.337917	+	0.941176i	$0.609722\pi$
$570$	2.44895	−	11.6865i	0.102575	−	0.489495i
$571$	−46.7743			−1.95744			−0.978722	−	0.205191i	$-0.934219\pi$
$571$	−46.7743			−1.95744			−0.978722	+	0.205191i	$0.934219\pi$
$572$	−0.113457	−	0.643445i	−0.00474387	−	0.0269038i
$573$	−12.0978	+	10.1512i	−0.505392	+	0.424074i
$574$	12.9071	−	4.69781i	0.538734	−	0.196083i
$575$	4.04510	+	1.47230i	0.168692	+	0.0613990i
$576$	0.918604	+	0.770801i	0.0382752	+	0.0321167i
$577$	−3.07074	+	5.31868i	−0.127837	+	0.221420i	−0.922838	−	0.385188i	$-0.874137\pi$
$577$	−3.07074	+	5.31868i	−0.127837	+	0.221420i	0.795002	+	0.606607i	$0.207470\pi$
$578$	−7.98588	−	13.8320i	−0.332169	−	0.575333i
$579$	1.02353	−	5.80473i	0.0425365	−	0.241236i
$580$	−1.38532	+	7.85652i	−0.0575221	+	0.326224i
$581$	7.78116	+	13.4774i	0.322817	+	0.559135i
$582$	2.12406	−	3.67899i	0.0880453	−	0.152499i
$583$	5.45459	+	4.57695i	0.225906	+	0.189558i
$584$	7.47529	+	2.72078i	0.309330	+	0.112587i
$585$	−0.984195	+	0.358218i	−0.0406914	+	0.0148105i
$586$	−7.46997	+	6.26805i	−0.308582	+	0.258931i
$587$	−4.45410	−	25.2605i	−0.183840	−	1.04261i	−0.927436	−	0.373981i	$-0.877992\pi$
$587$	−4.45410	−	25.2605i	−0.183840	−	1.04261i	0.743596	−	0.668629i	$-0.233119\pi$
$588$	1.71021			0.0705277
$589$	−15.1612	+	4.97442i	−0.624707	+	0.204967i
$590$	1.29120			0.0531580
$591$	−7.87301	−	44.6500i	−0.323852	−	1.83666i
$592$	0.822225	−	0.689928i	0.0337932	−	0.0283559i
$593$	−23.7019	+	8.62680i	−0.973321	+	0.354260i	−0.779240	−	0.626725i	$-0.784395\pi$
$593$	−23.7019	+	8.62680i	−0.973321	+	0.354260i	−0.194081	+	0.980985i	$0.562173\pi$
$594$	−3.46772	−	1.26215i	−0.142282	−	0.0517865i
$595$	−2.90649	−	2.43883i	−0.119154	−	0.0999824i
$596$	−8.38870	+	14.5297i	−0.343614	+	0.595158i
$597$	−27.8551	−	48.2465i	−1.14004	−	1.97460i
$598$	0.152006	−	0.862070i	0.00621599	−	0.0352526i
$599$	2.79663	−	15.8605i	0.114267	−	0.648042i	−0.872843	−	0.488001i	$-0.837726\pi$
$599$	2.79663	−	15.8605i	0.114267	−	0.648042i	0.987110	−	0.160041i	$-0.0511626\pi$
$600$	−3.29203	−	5.70196i	−0.134397	−	0.232782i
$601$	8.08259	−	13.9995i	0.329696	−	0.571050i	−0.652756	−	0.757569i	$-0.726387\pi$
$601$	8.08259	−	13.9995i	0.329696	−	0.571050i	0.982451	+	0.186519i	$0.0597204\pi$
$602$	7.23180	+	6.06820i	0.294746	+	0.247321i
$603$	−0.869438	−	0.316450i	−0.0354063	−	0.0128868i
$604$	8.36838	−	3.04584i	0.340504	−	0.123933i
$605$	−1.02403	+	0.859266i	−0.0416329	+	0.0349341i
$606$	−1.48598	−	8.42740i	−0.0603638	−	0.342340i
$607$	−3.97454			−0.161322			−0.0806608	−	0.996742i	$-0.525703\pi$
$607$	−3.97454			−0.161322			−0.0806608	+	0.996742i	$0.525703\pi$
$608$	−0.619050	−	4.31472i	−0.0251058	−	0.174985i
$609$	−34.2300			−1.38707
$610$	−0.305933	−	1.73503i	−0.0123869	−	0.0702494i
$611$	6.05087	−	5.07728i	0.244792	−	0.205405i
$612$	1.14263	−	0.415884i	0.0461882	−	0.0168111i
$613$	4.76323	+	1.73367i	0.192385	+	0.0700225i	0.436416	−	0.899745i	$-0.356248\pi$
$613$	4.76323	+	1.73367i	0.192385	+	0.0700225i	−0.244031	+	0.969767i	$0.578470\pi$
$614$	−0.908318	−	0.762170i	−0.0366568	−	0.0307587i
$615$	−6.72121	+	11.6415i	−0.271025	+	0.469430i
$616$	−1.39952	−	2.42403i	−0.0563881	−	0.0976671i
$617$	5.59789	−	31.7472i	0.225363	−	1.27810i	−0.636628	−	0.771171i	$-0.719671\pi$
$617$	5.59789	−	31.7472i	0.225363	−	1.27810i	0.861991	−	0.506924i	$-0.169218\pi$
$618$	3.75635	−	21.3033i	0.151103	−	0.856946i
$619$	−5.96578	−	10.3330i	−0.239785	−	0.415320i	0.720868	−	0.693073i	$-0.243744\pi$
$619$	−5.96578	−	10.3330i	−0.239785	−	0.415320i	−0.960652	+	0.277753i	$0.910410\pi$
$620$	2.44675	−	4.23789i	0.0982637	−	0.170198i
$621$	−3.78741	−	3.17801i	−0.151983	−	0.127529i
$622$	3.70123	+	1.34714i	0.148406	+	0.0540153i
$623$	18.4862	−	6.72844i	0.740635	−	0.269569i
$624$	−1.02564	+	0.860614i	−0.0410585	+	0.0344522i
$625$	0.241120	+	1.36746i	0.00964479	+	0.0546983i
$626$	−19.6906			−0.786995
$627$	−4.21607	−	7.87456i	−0.168373	−	0.314480i
$628$	4.36093			0.174020
$629$	−0.188996	−	1.07185i	−0.00753577	−	0.0427375i
$630$	−3.43714	+	2.88410i	−0.136939	+	0.114905i
$631$	41.0638	−	14.9460i	1.63472	−	0.594990i	0.648618	−	0.761114i	$-0.275347\pi$
$631$	41.0638	−	14.9460i	1.63472	−	0.594990i	0.986105	+	0.166124i	$0.0531251\pi$
$632$	15.9714	+	5.81313i	0.635310	+	0.231234i
$633$	6.64710	+	5.57758i	0.264198	+	0.221689i
$634$	11.6067	−	20.1033i	0.460959	−	0.798405i
$635$	5.15875	+	8.93522i	0.204719	+	0.354583i
$636$	2.53373	−	14.3695i	0.100469	−	0.569787i
$637$	−0.0946887	+	0.537006i	−0.00375170	+	0.0212770i
$638$	2.98393	+	5.16832i	0.118135	+	0.204616i
$639$	4.18000	−	7.23998i	0.165358	−	0.286409i
$640$	1.02403	+	0.859266i	0.0404785	+	0.0339655i
$641$	−40.0421	−	14.5741i	−1.58157	−	0.575644i	−0.606025	−	0.795446i	$-0.707237\pi$
$641$	−40.0421	−	14.5741i	−1.58157	−	0.575644i	−0.975545	+	0.219802i	$0.929459\pi$
$642$	30.1520	−	10.9744i	1.19000	−	0.433126i
$643$	23.1009	−	19.3840i	0.911012	−	0.764430i	−0.0612993	−	0.998119i	$-0.519524\pi$
$643$	23.1009	−	19.3840i	0.911012	−	0.764430i	0.972311	+	0.233690i	$0.0750800\pi$
$644$	−0.651191	−	3.69309i	−0.0256605	−	0.145528i
$645$	−9.23901			−0.363786
$646$	−4.10291	−	1.64397i	−0.161427	−	0.0646813i
$647$	49.3061			1.93842			0.969212	−	0.246229i	$-0.0791915\pi$
$647$	49.3061			1.93842			0.969212	+	0.246229i	$0.0791915\pi$
$648$	1.93783	+	10.9900i	0.0761250	+	0.431726i
$649$	0.739926	−	0.620871i	0.0290446	−	0.0243713i
$650$	1.97269	−	0.718001i	0.0773753	−	0.0281623i
$651$	19.7303	+	7.18123i	0.773290	+	0.281455i
$652$	10.3777	+	8.70792i	0.406422	+	0.341028i
$653$	4.44987	−	7.70740i	0.174137	−	0.301614i	−0.765725	−	0.643168i	$-0.777620\pi$
$653$	4.44987	−	7.70740i	0.174137	−	0.301614i	0.939862	+	0.341554i	$0.110953\pi$
$654$	−8.62246	−	14.9345i	−0.337165	−	0.583987i
$655$	0.658774	−	3.73609i	0.0257404	−	0.145981i
$656$	−0.852131	+	4.83268i	−0.0332701	+	0.188684i
$657$	−4.76965	−	8.26128i	−0.186082	−	0.322303i
$658$	16.9193	−	29.3050i	0.659581	−	1.14243i
$659$	18.6742	+	15.6695i	0.727442	+	0.610397i	0.929433	−	0.368991i	$-0.120297\pi$
$659$	18.6742	+	15.6695i	0.727442	+	0.610397i	−0.201991	+	0.979387i	$0.564741\pi$
$660$	2.57411	+	0.936899i	0.100197	+	0.0364687i
$661$	−8.72241	+	3.17470i	−0.339262	+	0.123481i	−0.506032	−	0.862514i	$-0.668888\pi$
$661$	−8.72241	+	3.17470i	−0.339262	+	0.123481i	0.166770	+	0.985996i	$0.446666\pi$
$662$	24.2136	−	20.3176i	0.941088	−	0.789667i
$663$	0.235753	+	1.33702i	0.00915590	+	0.0519257i
$664$	−5.55989			−0.215766
$665$	16.3013	+	0.522330i	0.632137	+	0.0202551i
$666$	−1.28710			−0.0498740
$667$	1.38842	+	7.87409i	0.0537596	+	0.304886i
$668$	10.3719	−	8.70307i	0.401302	−	0.336732i
$669$	−0.425440	+	0.154847i	−0.0164485	+	0.00598675i
$670$	−0.969224	−	0.352769i	−0.0374444	−	0.0136287i
$671$	−1.00960	−	0.847155i	−0.0389752	−	0.0327041i
$672$	−2.86786	+	4.96729i	−0.110630	+	0.191617i
$673$	−21.0606	−	36.4780i	−0.811825	−	1.40612i	−0.911586	−	0.411110i	$-0.865141\pi$
$673$	−21.0606	−	36.4780i	−0.811825	−	1.40612i	0.0997608	−	0.995011i	$-0.468192\pi$
$674$	−5.51967	+	31.3036i	−0.212610	+	1.20577i
$675$	2.05893	−	11.6768i	0.0792481	−	0.449438i
$676$	6.28655	+	10.8886i	0.241790	+	0.418793i
$677$	−3.14228	+	5.44258i	−0.120767	+	0.209175i	−0.920071	−	0.391753i	$-0.871869\pi$
$677$	−3.14228	+	5.44258i	−0.120767	+	0.209175i	0.799303	+	0.600928i	$0.205202\pi$
$678$	14.1516	+	11.8746i	0.543488	+	0.456040i
$679$	5.45269	+	1.98462i	0.209255	+	0.0761626i
$680$	1.27377	−	0.463616i	0.0488470	−	0.0177789i
$681$	−36.6837	+	30.7813i	−1.40572	+	1.17954i
$682$	−0.635666	−	3.60504i	−0.0243409	−	0.138044i
$683$	−12.0687			−0.461797			−0.230898	−	0.972978i	$-0.574166\pi$
$683$	−12.0687			−0.461797			−0.230898	+	0.972978i	$0.574166\pi$
$684$	−2.75712	+	4.44068i	−0.105421	+	0.169794i
$685$	−29.4955			−1.12696
$686$	−2.99668	−	16.9950i	−0.114414	−	0.648873i
$687$	−9.50472	+	7.97541i	−0.362628	+	0.304281i
$688$	−3.16935	+	1.15355i	−0.120830	+	0.0439787i
$689$	4.37174	+	1.59118i	0.166550	+	0.0606193i
$690$	2.81142	+	2.35906i	0.107029	+	0.0898079i
$691$	8.54641	−	14.8028i	0.325121	−	0.563125i	−0.656416	−	0.754399i	$-0.727928\pi$
$691$	8.54641	−	14.8028i	0.325121	−	0.563125i	0.981537	+	0.191274i	$0.0612618\pi$
$692$	−0.888304	−	1.53859i	−0.0337683	−	0.0584883i
$693$	−0.582844	+	3.30547i	−0.0221404	+	0.125565i
$694$	−2.63862	+	14.9643i	−0.100161	+	0.568039i
$695$	−3.68685	−	6.38581i	−0.139850	−	0.242227i
$696$	6.11462	−	10.5908i	0.231774	−	0.401444i
$697$	3.81186	+	3.19853i	0.144384	+	0.121153i
$698$	0.614611	+	0.223700i	0.0232634	+	0.00846717i
$699$	−40.8639	+	14.8732i	−1.54561	+	0.562558i
$700$	6.88929	−	5.78080i	0.260391	−	0.218494i
$701$	−0.817821	−	4.63809i	−0.0308887	−	0.175178i	0.965461	−	0.260549i	$-0.0839036\pi$
$701$	−0.817821	−	4.63809i	−0.0308887	−	0.175178i	−0.996349	+	0.0853708i	$0.972793\pi$
$702$	−2.41112			−0.0910017
$703$	3.48584	+	3.12057i	0.131471	+	0.117694i
$704$	1.00000			0.0376889
$705$	5.75062	+	32.6134i	0.216581	+	1.22829i
$706$	12.6671	−	10.6289i	0.476732	−	0.400025i
$707$	10.9839	−	3.99780i	0.413091	−	0.150353i
$708$	−1.85995	−	0.676966i	−0.0699011	−	0.0254419i
$709$	−22.5830	−	18.9494i	−0.848124	−	0.711661i	0.111252	−	0.993792i	$-0.464514\pi$
$709$	−22.5830	−	18.9494i	−0.848124	−	0.711661i	−0.959376	+	0.282132i	$0.908958\pi$
$710$	4.65975	−	8.07092i	0.174877	−	0.302896i
$711$	−10.1907	−	17.6508i	−0.382180	−	0.661955i
$712$	−1.22046	+	6.92159i	−0.0457388	+	0.259398i
$713$	0.851646	−	4.82993i	0.0318944	−	0.180882i
$714$	2.90807	+	5.03693i	0.108832	+	0.188502i
$715$	−0.436707	+	0.756399i	−0.0163319	+	0.0282877i
$716$	−12.2026	−	10.2392i	−0.456031	−	0.382655i
$717$	−36.2356	−	13.1887i	−1.35324	−	0.492540i
$718$	−12.1232	+	4.41248i	−0.452434	+	0.164672i
$719$	36.2479	−	30.4156i	1.35182	−	1.13431i	0.373402	−	0.927669i	$-0.378191\pi$
$719$	36.2479	−	30.4156i	1.35182	−	1.13431i	0.978417	−	0.206641i	$-0.0662534\pi$
$720$	−0.278359	−	1.57865i	−0.0103738	−	0.0588329i
$721$	29.5477			1.10041
$722$	18.2336	−	5.34205i	0.678583	−	0.198811i
$723$	2.79526			0.103957
$724$	0.183362	+	1.03990i	0.00681461	+	0.0386476i
$725$	−14.6888	+	12.3253i	−0.545527	+	0.457752i
$726$	1.92560	−	0.700862i	0.0714658	−	0.0260114i
$727$	−20.8024	−	7.57147i	−0.771520	−	0.280810i	−0.0738878	−	0.997267i	$-0.523541\pi$
$727$	−20.8024	−	7.57147i	−0.771520	−	0.280810i	−0.697632	+	0.716456i	$0.745763\pi$
$728$	−1.40095	−	1.17554i	−0.0519226	−	0.0435682i
$729$	−4.65208	+	8.05764i	−0.172299	+	0.298431i
$730$	−5.31707	−	9.20944i	−0.196794	−	0.340857i
$731$	−0.593883	+	3.36808i	−0.0219656	+	0.124573i
$732$	−0.468972	+	2.65967i	−0.0173337	+	0.0983043i
$733$	12.2176	+	21.1615i	0.451267	+	0.781618i	0.998465	−	0.0553856i	$-0.0176388\pi$
$733$	12.2176	+	21.1615i	0.451267	+	0.781618i	−0.547198	+	0.837003i	$0.684305\pi$
$734$	9.49406	−	16.4442i	0.350432	−	0.606966i
$735$	−1.75131	−	1.46952i	−0.0645980	−	0.0542042i
$736$	1.25897	+	0.458229i	0.0464064	+	0.0168905i
$737$	−0.725044	+	0.263894i	−0.0267073	+	0.00972067i
$738$	4.50780	−	3.78249i	0.165934	−	0.139236i
$739$	6.94786	+	39.4033i	0.255581	+	1.44947i	0.794577	+	0.607164i	$0.207693\pi$
$739$	6.94786	+	39.4033i	0.255581	+	1.44947i	−0.538996	+	0.842309i	$0.681196\pi$
$740$	−1.43482			−0.0527450
$741$	−4.34823	−	3.89258i	−0.159736	−	0.142998i
$742$	19.9304			0.731669
$743$	−5.33194	−	30.2389i	−0.195610	−	1.10936i	−0.911547	−	0.411195i	$-0.865112\pi$
$743$	−5.33194	−	30.2389i	−0.195610	−	1.10936i	0.715937	−	0.698164i	$-0.246000\pi$
$744$	−5.74637	+	4.82177i	−0.210672	+	0.176775i
$745$	21.0752	−	7.67073i	0.772134	−	0.281034i
$746$	−5.49026	−	1.99829i	−0.201013	−	0.0731626i
$747$	5.10734	+	4.28557i	0.186868	+	0.156801i
$748$	0.507010	−	0.878167i	0.0185381	−	0.0321090i
$749$	21.9143	+	37.9566i	0.800729	+	1.38690i
$750$	−3.90674	+	22.1562i	−0.142654	+	0.809030i
$751$	−8.58303	+	48.6768i	−0.313199	+	1.77624i	0.268946	+	0.963155i	$0.413325\pi$
$751$	−8.58303	+	48.6768i	−0.313199	+	1.77624i	−0.582145	+	0.813085i	$0.697786\pi$
$752$	6.04468	+	10.4697i	0.220427	+	0.381790i
$753$	−20.7931	+	36.0148i	−0.757744	+	1.31245i
$754$	2.98698	+	2.50638i	0.108780	+	0.0912769i
$755$	−11.1867	−	4.07162i	−0.407125	−	0.148181i
$756$	−9.70625	+	3.53279i	−0.353013	+	0.128486i
$757$	−17.0667	+	14.3207i	−0.620300	+	0.520494i	−0.897898	−	0.440204i	$-0.854906\pi$
$757$	−17.0667	+	14.3207i	−0.620300	+	0.520494i	0.277598	+	0.960697i	$0.410462\pi$
$758$	2.47637	+	14.0442i	0.0899457	+	0.510107i
$759$	2.74544			0.0996530
$760$	−3.07356	+	4.95034i	−0.111490	+	0.179568i
$761$	5.62582			0.203936			0.101968	−	0.994788i	$-0.467486\pi$
$761$	5.62582			0.203936			0.101968	+	0.994788i	$0.467486\pi$
$762$	−2.74641	−	15.5757i	−0.0994919	−	0.564247i
$763$	18.0444	−	15.1410i	0.653251	−	0.548143i
$764$	7.24196	−	2.63586i	0.262005	−	0.0953620i
$765$	−1.52745	−	0.555946i	−0.0552251	−	0.0201003i
$766$	−11.2994	−	9.48134i	−0.408265	−	0.342575i
$767$	0.315547	−	0.546544i	0.0113938	−	0.0197346i
$768$	−1.02459	−	1.77464i	−0.0369718	−	0.0640370i
$769$	0.908084	−	5.15000i	0.0327463	−	0.185714i	−0.964047	−	0.265731i	$-0.914387\pi$
$769$	0.908084	−	5.15000i	0.0327463	−	0.185714i	0.996793	+	0.0800177i	$0.0254977\pi$
$770$	−0.649738	+	3.68485i	−0.0234149	+	0.132793i
$771$	−9.13104	−	15.8154i	−0.328847	−	0.569579i
$772$	−1.43820	+	2.49104i	−0.0517620	+	0.0896544i
$773$	−16.8396	−	14.1301i	−0.605678	−	0.508224i	0.287587	−	0.957754i	$-0.407147\pi$
$773$	−16.8396	−	14.1301i	−0.605678	−	0.508224i	−0.893265	+	0.449530i	$0.851591\pi$
$774$	3.80054	+	1.38328i	0.136607	+	0.0497210i
$775$	11.0524	−	4.02275i	0.397015	−	0.144501i
$776$	−1.58807	+	1.33255i	−0.0570086	+	0.0478359i
$777$	−1.06904	−	6.06285i	−0.0383517	−	0.217503i
$778$	−6.30213			−0.225942
$779$	−21.3791	−	0.685036i	−0.765987	−	0.0245440i
$780$	1.78979			0.0640847
$781$	−1.21060	−	6.86568i	−0.0433188	−	0.245673i
$782$	1.04071	−	0.873262i	0.0372158	−	0.0312278i
$783$	20.6948	−	7.53231i	0.739573	−	0.269183i
$784$	−0.784248	−	0.285443i	−0.0280089	−	0.0101944i
$785$	−4.46574	−	3.74720i	−0.159389	−	0.133743i
$786$	−2.90775	+	5.03636i	−0.103716	+	0.179641i
$787$	23.4817	+	40.6714i	0.837031	+	1.44978i	0.892366	+	0.451312i	$0.149044\pi$
$787$	23.4817	+	40.6714i	0.837031	+	1.44978i	−0.0553351	+	0.998468i	$0.517623\pi$
$788$	−3.84202	+	21.7892i	−0.136866	+	0.776207i
$789$	4.13119	−	23.4291i	0.147074	−	0.834099i
$790$	−11.3603	−	19.6766i	−0.404180	−	0.700060i
$791$	−12.6168	+	21.8529i	−0.448600	+	0.776998i
$792$	−0.918604	−	0.770801i	−0.0326412	−	0.0273892i
$793$	−0.809174	−	0.294515i	−0.0287346	−	0.0104585i
$794$	−8.38250	+	3.05098i	−0.297484	+	0.108275i
$795$	−14.9418	+	12.5377i	−0.529932	+	0.444666i
$796$	4.72090	+	26.7736i	0.167328	+	0.948964i
$797$	21.7885			0.771790			0.385895	−	0.922543i	$-0.373893\pi$
$797$	21.7885			0.771790			0.385895	+	0.922543i	$0.373893\pi$
$798$	−23.2078	−	9.29902i	−0.821547	−	0.329182i
$799$	12.2588			0.433687
$800$	0.557934	+	3.16420i	0.0197260	+	0.111871i
$801$	6.45629	−	5.41747i	0.228122	−	0.191417i
$802$	−25.3138	+	9.21346i	−0.893861	+	0.325339i
$803$	−7.47529	−	2.72078i	−0.263797	−	0.0960144i
$804$	1.21119	+	1.01631i	0.0427155	+	0.0358425i
$805$	−2.50651	+	4.34140i	−0.0883427	+	0.153014i
$806$	−1.19588	−	2.07133i	−0.0421232	−	0.0729595i
$807$	−2.09587	+	11.8863i	−0.0737783	+	0.418417i
$808$	−0.725156	+	4.11257i	−0.0255109	+	0.144680i
$809$	13.8687	+	24.0212i	0.487596	+	0.844541i	0.999898	−	0.0142641i	$-0.00454055\pi$
$809$	13.8687	+	24.0212i	0.487596	+	0.844541i	−0.512302	+	0.858805i	$0.671207\pi$
$810$	7.45890	−	12.9192i	0.262079	−	0.453934i
$811$	19.9349	+	16.7274i	0.700009	+	0.587378i	0.921776	−	0.387722i	$-0.126738\pi$
$811$	19.9349	+	16.7274i	0.700009	+	0.587378i	−0.221767	+	0.975100i	$0.571182\pi$
$812$	15.6968	+	5.71318i	0.550851	+	0.200493i
$813$	−44.1453	+	16.0676i	−1.54824	+	0.563515i
$814$	−0.822225	+	0.689928i	−0.0288190	+	0.0241820i
$815$	−3.14469	−	17.8344i	−0.110154	−	0.624712i
$816$	−2.07791			−0.0727415
$817$	−6.93922	−	12.9607i	−0.242773	−	0.453439i
$818$	−17.3978			−0.608300
$819$	0.380814	+	2.15970i	0.0133067	+	0.0754661i
$820$	5.02517	−	4.21662i	0.175486	−	0.147251i
$821$	11.3165	−	4.11888i	0.394950	−	0.143750i	−0.136908	−	0.990584i	$-0.543716\pi$
$821$	11.3165	−	4.11888i	0.394950	−	0.143750i	0.531858	+	0.846834i	$0.321494\pi$
$822$	42.4875	+	15.4642i	1.48192	+	0.539376i
$823$	−29.2172	−	24.5161i	−1.01845	−	0.854579i	−0.0290155	−	0.999579i	$-0.509237\pi$
$823$	−29.2172	−	24.5161i	−1.01845	−	0.854579i	−0.989432	+	0.145000i	$0.953682\pi$
$824$	−5.27819	+	9.14210i	−0.183875	+	0.318480i
$825$	3.29203	+	5.70196i	0.114614	+	0.198517i
$826$	0.469475	−	2.66252i	0.0163351	−	0.0926410i
$827$	−8.12397	+	46.0733i	−0.282498	+	1.60213i	0.431589	+	0.902070i	$0.357953\pi$
$827$	−8.12397	+	46.0733i	−0.282498	+	1.60213i	−0.714087	+	0.700057i	$0.753158\pi$
$828$	−0.803295	−	1.39135i	−0.0279164	−	0.0483527i
$829$	−20.9437	+	36.2756i	−0.727405	+	1.25990i	0.230571	+	0.973055i	$0.425941\pi$
$829$	−20.9437	+	36.2756i	−0.727405	+	1.25990i	−0.957976	+	0.286847i	$0.907393\pi$
$830$	5.69352	+	4.77743i	0.197625	+	0.165827i
$831$	−34.3763	−	12.5120i	−1.19250	−	0.434035i
$832$	0.613969	−	0.223466i	0.0212855	−	0.00774730i
$833$	−0.648288	+	0.543978i	−0.0224619	+	0.0188477i
$834$	1.96280	+	11.1316i	0.0679662	+	0.385455i
$835$	−18.0995			−0.626357
$836$	0.619050	+	4.31472i	0.0214103	+	0.149228i
$837$	−13.5088			−0.466932
$838$	−2.79013	−	15.8236i	−0.0963833	−	0.546617i
$839$	32.5505	−	27.3131i	1.12377	−	0.942953i	0.124979	−	0.992159i	$-0.460114\pi$
$839$	32.5505	−	27.3131i	1.12377	−	0.942953i	0.998789	+	0.0492060i	$0.0156691\pi$
$840$	7.20501	−	2.62241i	0.248597	−	0.0904818i
$841$	−6.21639	−	2.26258i	−0.214358	−	0.0780200i
$842$	−10.6043	−	8.89808i	−0.365449	−	0.306648i
$843$	−11.5840	+	20.0641i	−0.398974	+	0.691044i
$844$	−2.11723	−	3.66714i	−0.0728779	−	0.126228i
$845$	2.91859	−	16.5521i	0.100403	−	0.569411i
$846$	2.51738	−	14.2767i	0.0865492	−	0.490845i
$847$	1.39952	+	2.42403i	0.0480879	+	0.0832907i
$848$	−3.56023	+	6.16651i	−0.122259	+	0.211759i
$849$	47.1679	+	39.5786i	1.61880	+	1.35833i
$850$	3.06158	+	1.11432i	0.105011	+	0.0382210i
$851$	−1.35130	+	0.491834i	−0.0463221	+	0.0168599i
$852$	−10.9438	+	9.18291i	−0.374927	+	0.314601i
$853$	6.12227	+	34.7211i	0.209622	+	1.18883i	0.889998	+	0.455964i	$0.150706\pi$
$853$	6.12227	+	34.7211i	0.209622	+	1.18883i	−0.680376	+	0.732864i	$0.738183\pi$
$854$	−3.68896			−0.126233
$855$	6.63912	−	2.17830i	0.227053	−	0.0744964i
$856$	−15.6585			−0.535195
$857$	−1.87869	−	10.6546i	−0.0641749	−	0.363954i	−0.999936	−	0.0113192i	$-0.996397\pi$
$857$	−1.87869	−	10.6546i	−0.0641749	−	0.363954i	0.935761	−	0.352635i	$-0.114714\pi$
$858$	1.02564	−	0.860614i	0.0350148	−	0.0293809i
$859$	−3.51628	+	1.27982i	−0.119974	+	0.0436670i	−0.401310	−	0.915942i	$-0.631445\pi$
$859$	−3.51628	+	1.27982i	−0.119974	+	0.0436670i	0.281336	+	0.959609i	$0.409223\pi$
$860$	4.23673	+	1.54204i	0.144471	+	0.0525832i
$861$	21.5615	+	18.0922i	0.734814	+	0.616582i
$862$	19.1213	−	33.1190i	0.651273	−	1.12804i
$863$	−7.92087	−	13.7194i	−0.269630	−	0.467012i	0.699137	−	0.714988i	$-0.253568\pi$
$863$	−7.92087	−	13.7194i	−0.269630	−	0.467012i	−0.968766	+	0.247976i	$0.920235\pi$
$864$	0.640808	−	3.63420i	0.0218007	−	0.123638i
$865$	−0.412403	+	2.33886i	−0.0140221	+	0.0795235i
$866$	−1.16915	−	2.02503i	−0.0397294	−	0.0688133i
$867$	16.3645	−	28.3442i	0.555769	−	0.962620i
$868$	−7.84911	−	6.58618i	−0.266416	−	0.223550i
$869$	−15.9714	−	5.81313i	−0.541794	−	0.197197i
$870$	−15.3619	+	5.59128i	−0.520818	+	0.189562i
$871$	−0.386182	+	0.324046i	−0.0130853	+	0.0109799i
$872$	1.46134	+	8.28766i	0.0494872	+	0.280656i
$873$	2.48594			0.0841365
$874$	−1.19776	+	5.71578i	−0.0405148	+	0.193339i
$875$	−30.7306			−1.03888
$876$	2.83070	+	16.0537i	0.0956404	+	0.542404i
$877$	5.79807	−	4.86516i	0.195787	−	0.164285i	−0.539624	−	0.841906i	$-0.681434\pi$
$877$	5.79807	−	4.86516i	0.195787	−	0.164285i	0.735411	+	0.677621i	$0.236989\pi$
$878$	−19.5354	+	7.11031i	−0.659289	+	0.239961i
$879$	−18.7772	−	6.83435i	−0.633340	−	0.230517i
$880$	−1.02403	−	0.859266i	−0.0345202	−	0.0289659i
$881$	7.49883	−	12.9883i	0.252642	−	0.437589i	−0.711610	−	0.702574i	$-0.752034\pi$
$881$	7.49883	−	12.9883i	0.252642	−	0.437589i	0.964252	+	0.264986i	$0.0853672\pi$
$882$	0.500394	+	0.866708i	0.0168491	+	0.0291836i
$883$	−4.51281	+	25.5934i	−0.151868	+	0.861288i	0.809725	+	0.586809i	$0.199616\pi$
$883$	−4.51281	+	25.5934i	−0.151868	+	0.861288i	−0.961593	+	0.274478i	$0.911495\pi$
$884$	0.115047	−	0.652466i	0.00386946	−	0.0219448i
$885$	1.32296	+	2.29143i	0.0444707	+	0.0770255i
$886$	11.9955	−	20.7769i	0.402998	−	0.698014i
$887$	30.5725	+	25.6534i	1.02652	+	0.861356i	0.990433	−	0.137992i	$-0.0440648\pi$
$887$	30.5725	+	25.6534i	1.02652	+	0.861356i	0.0360913	+	0.999348i	$0.488509\pi$
$888$	2.06682	+	0.752262i	0.0693580	+	0.0252443i
$889$	20.3006	−	7.38880i	0.680859	−	0.247812i
$890$	7.19729	−	6.03924i	0.241254	−	0.202436i
$891$	−1.93783	−	10.9900i	−0.0649196	−	0.368177i
$892$	0.220939			0.00739757
$893$	−41.4318	+	32.5623i	−1.38646	+	1.08966i
$894$	−34.3800			−1.14984
$895$	3.69766	+	20.9705i	0.123599	+	0.700966i
$896$	2.14418	−	1.79918i	0.0716321	−	0.0601065i
$897$	1.68561	−	0.613512i	0.0562809	−	0.0204846i
$898$	−22.3454	−	8.13305i	−0.745674	−	0.271403i
$899$	16.7352	+	14.0425i	0.558150	+	0.468344i
$900$	1.92645	−	3.33671i	0.0642150	−	0.111224i
$901$	3.61015	+	6.25296i	0.120271	+	0.208316i
$902$	0.852131	−	4.83268i	0.0283729	−	0.160911i
$903$	−3.35926	+	19.0513i	−0.111789	+	0.633988i
$904$	−4.50754	−	7.80729i	−0.149919	−	0.259667i
$905$	0.705781	−	1.22245i	0.0234610	−	0.0406356i
$906$	13.9795	+	11.7302i	0.464436	+	0.389708i
$907$	0.411304	+	0.149702i	0.0136571	+	0.00497078i	0.348840	−	0.937182i	$-0.386576\pi$
$907$	0.411304	+	0.149702i	0.0136571	+	0.00497078i	−0.335183	+	0.942153i	$0.608798\pi$
$908$	21.9596	−	7.99263i	0.728754	−	0.265245i
$909$	3.83610	−	3.21887i	0.127235	−	0.106763i
$910$	0.424521	+	2.40758i	0.0140727	+	0.0798103i
$911$	−9.30003			−0.308124			−0.154062	−	0.988061i	$-0.549236\pi$
$911$	−9.30003			−0.308124			−0.154062	+	0.988061i	$0.549236\pi$
$912$	7.02282	−	5.51942i	0.232549	−	0.182766i
$913$	5.55989			0.184006
$914$	1.98308	+	11.2466i	0.0655943	+	0.372004i
$915$	2.76561	−	2.32062i	0.0914282	−	0.0767174i
$916$	5.68972	−	2.07089i	0.187993	−	0.0684240i
$917$	−7.46448	−	2.71685i	−0.246499	−	0.0897182i
$918$	−2.86654	−	2.40531i	−0.0946099	−	0.0793872i
$919$	−24.5307	+	42.4883i	−0.809192	+	1.40156i	0.104233	+	0.994553i	$0.466761\pi$
$919$	−24.5307	+	42.4883i	−0.809192	+	1.40156i	−0.913425	+	0.407008i	$0.866572\pi$
$920$	−0.895490	−	1.55103i	−0.0295234	−	0.0511361i
$921$	0.421925	−	2.39286i	0.0139029	−	0.0788473i
$922$	3.27648	−	18.5818i	0.107905	−	0.611961i
$923$	−2.27752	−	3.94478i	−0.0749655	−	0.129844i
$924$	2.86786	−	4.96729i	0.0943458	−	0.163412i
$925$	−2.64182	−	2.21675i	−0.0868626	−	0.0728863i
$926$	−9.93566	−	3.61628i	−0.326506	−	0.118838i
$927$	11.8953	−	4.32954i	0.390693	−	0.142201i
$928$	−4.57165	+	3.83607i	−0.150072	+	0.125925i
$929$	4.55669	+	25.8423i	0.149500	+	0.847858i	0.963643	+	0.267193i	$0.0860961\pi$
$929$	4.55669	+	25.8423i	0.149500	+	0.847858i	−0.814143	+	0.580665i	$0.802793\pi$
$930$	10.0277			0.328820
$931$	0.746117	−	3.56051i	0.0244530	−	0.116691i
$932$	21.2214			0.695129
$933$	1.40156	+	7.94864i	0.0458850	+	0.260227i
$934$	−21.2301	+	17.8142i	−0.694670	+	0.582897i
$935$	−1.27377	+	0.463616i	−0.0416569	+	0.0151619i
$936$	−0.736242	−	0.267970i	−0.0240648	−	0.00875888i
$937$	−28.2575	−	23.7108i	−0.923132	−	0.774600i	0.0514396	−	0.998676i	$-0.483619\pi$
$937$	−28.2575	−	23.7108i	−0.923132	−	0.774600i	−0.974572	+	0.224076i	$0.928063\pi$
$938$	−1.07983	+	1.87032i	−0.0352578	+	0.0610682i
$939$	−20.1748	−	34.9438i	−0.658381	−	1.14035i
$940$	2.80630	−	15.9153i	0.0915314	−	0.519100i
$941$	−3.84030	+	21.7794i	−0.125190	+	0.709989i	0.856005	+	0.516968i	$0.172939\pi$
$941$	−3.84030	+	21.7794i	−0.125190	+	0.709989i	−0.981195	+	0.193020i	$0.938172\pi$
$942$	4.46817	+	7.73910i	0.145581	+	0.252154i
$943$	3.28728	−	5.69374i	0.107049	−	0.185414i
$944$	0.739926	+	0.620871i	0.0240825	+	0.0202076i
$945$	12.9751	+	4.72256i	0.422081	+	0.153625i
$946$	3.16935	−	1.15355i	0.103044	−	0.0375051i
$947$	−15.8060	+	13.2628i	−0.513625	+	0.430983i	−0.862403	−	0.506223i	$-0.831041\pi$
$947$	−15.8060	+	13.2628i	−0.513625	+	0.430983i	0.348778	+	0.937205i	$0.386597\pi$
$948$	6.04796	+	34.2997i	0.196429	+	1.11400i
$949$	−5.19760			−0.168721
$950$	−13.3073	+	4.36613i	−0.431744	+	0.141656i
$951$	47.5683			1.54251
$952$	−0.492861	−	2.79515i	−0.0159737	−	0.0905915i
$953$	5.79466	−	4.86230i	0.187707	−	0.157505i	−0.544091	−	0.839026i	$-0.683126\pi$
$953$	5.79466	−	4.86230i	0.187707	−	0.157505i	0.731799	+	0.681521i	$0.238681\pi$
$954$	8.02359	−	2.92035i	0.259773	−	0.0945498i
$955$	−9.68092	−	3.52357i	−0.313267	−	0.114020i
$956$	14.4153	+	12.0958i	0.466223	+	0.391208i
$957$	−6.11462	+	10.5908i	−0.197658	+	0.342353i
$958$	1.48396	+	2.57029i	0.0479445	+	0.0830423i
$959$	−10.7244	+	60.8211i	−0.346309	+	1.96402i
$960$	−0.475676	+	2.69769i	−0.0153524	+	0.0870677i
$961$	8.79981	+	15.2417i	0.283865	+	0.491668i
$962$	−0.350644	+	0.607334i	−0.0113052	+	0.0195812i
$963$	14.3839	+	12.0695i	0.463515	+	0.388936i
$964$	−1.28182	−	0.466545i	−0.0412847	−	0.0150264i
$965$	3.61323	−	1.31511i	0.116314	−	0.0423348i
$966$	5.88672	−	4.93954i	0.189402	−	0.158927i
$967$	−7.09449	−	40.2349i	−0.228144	−	1.29387i	−0.856584	−	0.516008i	$-0.827417\pi$
$967$	−7.09449	−	40.2349i	−0.228144	−	1.29387i	0.628440	−	0.777858i	$-0.283694\pi$
$968$	−1.00000			−0.0321412
$969$	−1.28633	−	8.96560i	−0.0413229	−	0.288017i
$970$	2.77126			0.0889798
$971$	−1.12021	−	6.35301i	−0.0359492	−	0.203878i	0.961543	−	0.274654i	$-0.0885634\pi$
$971$	−1.12021	−	6.35301i	−0.0359492	−	0.203878i	−0.997492	+	0.0707765i	$0.977452\pi$
$972$	−9.03706	+	7.58299i	−0.289864	+	0.243225i
$973$	−14.5084	+	5.28061i	−0.465117	+	0.169289i
$974$	−12.2017	−	4.44107i	−0.390969	−	0.142301i
$975$	3.29540	+	2.76517i	0.105537	+	0.0885563i
$976$	0.658970	−	1.14137i	0.0210931	−	0.0365343i
$977$	26.8376	+	46.4840i	0.858609	+	1.48716i	0.873256	+	0.487262i	$0.162004\pi$
$977$	26.8376	+	46.4840i	0.858609	+	1.48716i	−0.0146463	+	0.999893i	$0.504662\pi$
$978$	−4.82056	+	27.3388i	−0.154145	+	0.874198i
$979$	1.22046	−	6.92159i	0.0390062	−	0.221215i
$980$	0.557825	+	0.966181i	0.0178191	+	0.0308635i
$981$	5.04574	−	8.73948i	0.161098	−	0.279030i
$982$	12.9211	+	10.8421i	0.412329	+	0.345985i
$983$	10.5454	+	3.83823i	0.336347	+	0.122420i	0.504672	−	0.863311i	$-0.331613\pi$
$983$	10.5454	+	3.83823i	0.336347	+	0.122420i	−0.168325	+	0.985732i	$0.553836\pi$
$984$	−9.44937	+	3.43929i	−0.301235	+	0.109641i
$985$	22.6571	−	19.0115i	0.721914	−	0.605758i
$986$	1.05084	+	5.95959i	0.0334655	+	0.189792i
$987$	69.3413			2.20716
$988$	1.34427	+	2.51076i	0.0427670	+	0.0798780i
$989$	4.51872			0.143687
$990$	0.278359	+	1.57865i	0.00884683	+	0.0501728i
$991$	−32.0261	+	26.8731i	−1.01734	+	0.853651i	−0.989291	−	0.145955i	$-0.953374\pi$
$991$	−32.0261	+	26.8731i	−1.01734	+	0.853651i	−0.0280507	+	0.999607i	$0.508930\pi$
$992$	3.43989	−	1.25202i	0.109217	−	0.0397516i
$993$	60.8656	+	22.1533i	1.93151	+	0.703013i
$994$	−14.9484	−	12.5432i	−0.474134	−	0.397845i
$995$	18.1713	−	31.4735i	0.576068	−	0.997778i
$996$	−5.69662	−	9.86683i	−0.180504	−	0.312643i
$997$	6.47628	−	36.7288i	0.205106	−	1.16321i	−0.692167	−	0.721737i	$-0.743344\pi$
$997$	6.47628	−	36.7288i	0.205106	−	1.16321i	0.897273	−	0.441476i	$-0.145545\pi$
$998$	4.54354	−	25.7677i	0.143823	−	0.815663i
$999$	1.98045	+	3.43024i	0.0626587	+	0.108528i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	418.2.j.c.199.5	✓	30
19.6	even	9		7942.2.a.bz.1.13		15
19.13	odd	18		7942.2.a.cb.1.3		15
19.17	even	9	inner	418.2.j.c.397.5	yes	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
418.2.j.c.199.5	✓	30	1.1	even	1	trivial
418.2.j.c.397.5	yes	30	19.17	even	9	inner
7942.2.a.bz.1.13		15	19.6	even	9
7942.2.a.cb.1.3		15	19.13	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:	\( N \)	\(=\)	\( 418 = 2 \cdot 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	418.j (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.173648 - 0.984808i) q^{2} +(1.56977 - 1.31719i) q^{3} +(-0.939693 + 0.342020i) q^{4} +(1.25616 + 0.457206i) q^{5} +(-1.56977 - 1.31719i) q^{6} +(1.39952 - 2.42403i) q^{7} +(0.500000 + 0.866025i) q^{8} +(0.208231 - 1.18093i) q^{9} +O(q^{10})\)	\(q+(-0.173648 - 0.984808i) q^{2} +(1.56977 - 1.31719i) q^{3} +(-0.939693 + 0.342020i) q^{4} +(1.25616 + 0.457206i) q^{5} +(-1.56977 - 1.31719i) q^{6} +(1.39952 - 2.42403i) q^{7} +(0.500000 + 0.866025i) q^{8} +(0.208231 - 1.18093i) q^{9} +(0.232130 - 1.31647i) q^{10} +(-0.500000 - 0.866025i) q^{11} +(-1.02459 + 1.77464i) q^{12} +(-0.500512 - 0.419979i) q^{13} +(-2.63023 - 0.957325i) q^{14} +(2.57411 - 0.936899i) q^{15} +(0.766044 - 0.642788i) q^{16} +(-0.176083 - 0.998615i) q^{17} -1.19915 q^{18} +(3.24767 + 2.90735i) q^{19} -1.33678 q^{20} +(-0.995999 - 5.64859i) q^{21} +(-0.766044 + 0.642788i) q^{22} +(-1.25897 + 0.458229i) q^{23} +(1.92560 + 0.700862i) q^{24} +(-2.46131 - 2.06529i) q^{25} +(-0.326686 + 0.565836i) q^{26} +(1.84513 + 3.19586i) q^{27} +(-0.486047 + 2.75651i) q^{28} +(1.03631 - 5.87719i) q^{29} +(-1.36965 - 2.37231i) q^{30} +(-1.83033 + 3.17022i) q^{31} +(-0.766044 - 0.642788i) q^{32} +(-1.92560 - 0.700862i) q^{33} +(-0.952867 + 0.346815i) q^{34} +(2.86630 - 2.40511i) q^{35} +(0.208231 + 1.18093i) q^{36} +1.07334 q^{37} +(2.29923 - 3.70318i) q^{38} -1.33888 q^{39} +(0.232130 + 1.31647i) q^{40} +(-3.75916 + 3.15431i) q^{41} +(-5.38982 + 1.96174i) q^{42} +(-3.16935 - 1.15355i) q^{43} +(0.766044 + 0.642788i) q^{44} +(0.801502 - 1.38824i) q^{45} +(0.669885 + 1.16028i) q^{46} +(-2.09930 + 11.9057i) q^{47} +(0.355837 - 2.01805i) q^{48} +(-0.417290 - 0.722767i) q^{49} +(-1.60651 + 2.78255i) q^{50} +(-1.59177 - 1.33566i) q^{51} +(0.613969 + 0.223466i) q^{52} +(-6.69105 + 2.43534i) q^{53} +(2.82691 - 2.37206i) q^{54} +(-0.232130 - 1.31647i) q^{55} +2.79903 q^{56} +(8.92760 + 0.286060i) q^{57} -5.96786 q^{58} +(0.167728 + 0.951230i) q^{59} +(-2.09843 + 1.76079i) q^{60} +(1.23846 - 0.450762i) q^{61} +(3.43989 + 1.25202i) q^{62} +(-2.57120 - 2.15750i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(-0.436707 - 0.756399i) q^{65} +(-0.355837 + 2.01805i) q^{66} +(0.133983 - 0.759853i) q^{67} +(0.507010 + 0.878167i) q^{68} +(-1.37272 + 2.37762i) q^{69} +(-2.86630 - 2.40511i) q^{70} +(6.55116 + 2.38443i) q^{71} +(1.12684 - 0.410134i) q^{72} +(6.09391 - 5.11340i) q^{73} +(-0.186383 - 1.05703i) q^{74} -6.58406 q^{75} +(-4.04618 - 1.62125i) q^{76} -2.79903 q^{77} +(0.232494 + 1.31854i) q^{78} +(13.0200 - 10.9251i) q^{79} +(1.25616 - 0.457206i) q^{80} +(10.4865 + 3.81677i) q^{81} +(3.75916 + 3.15431i) q^{82} +(-2.77995 + 4.81501i) q^{83} +(2.86786 + 4.96729i) q^{84} +(0.235384 - 1.33493i) q^{85} +(-0.585672 + 3.32151i) q^{86} +(-6.11462 - 10.5908i) q^{87} +(0.500000 - 0.866025i) q^{88} +(5.38404 + 4.51775i) q^{89} +(-1.50633 - 0.548260i) q^{90} +(-1.71852 + 0.625489i) q^{91} +(1.02632 - 0.861188i) q^{92} +(1.30260 + 7.38739i) q^{93} +12.0894 q^{94} +(2.75034 + 5.13696i) q^{95} -2.04918 q^{96} +(0.359987 + 2.04159i) q^{97} +(-0.639325 + 0.536457i) q^{98} +(-1.12684 + 0.410134i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q - 12 q^{7} + 15 q^{8}+O(q^{10}) \) 30 * q - 12 * q^7 + 15 * q^8	\( 30 q - 12 q^{7} + 15 q^{8} - 15 q^{11} + 3 q^{12} - 3 q^{13} + 9 q^{14} + 27 q^{15} - 36 q^{18} - 9 q^{19} + 18 q^{20} - 27 q^{21} - 3 q^{23} - 12 q^{25} + 3 q^{27} + 9 q^{28} + 3 q^{29} + 9 q^{30} + 30 q^{31} - 9 q^{34} + 15 q^{35} + 18 q^{37} + 6 q^{38} - 6 q^{41} - 45 q^{42} + 39 q^{43} - 18 q^{45} + 21 q^{46} + 45 q^{47} - 33 q^{49} + 36 q^{50} - 36 q^{51} + 6 q^{52} - 24 q^{53} + 45 q^{54} - 24 q^{56} - 24 q^{57} - 30 q^{58} + 3 q^{59} - 9 q^{60} - 27 q^{61} + 15 q^{62} - 93 q^{63} - 15 q^{64} + 18 q^{65} - 9 q^{67} - 21 q^{68} + 48 q^{69} - 15 q^{70} + 39 q^{73} + 3 q^{74} - 42 q^{75} - 15 q^{76} + 24 q^{77} + 6 q^{78} + 21 q^{79} + 84 q^{81} + 6 q^{82} - 36 q^{83} - 27 q^{84} + 63 q^{85} + 6 q^{86} - 21 q^{87} + 15 q^{88} + 54 q^{89} + 12 q^{90} + 3 q^{91} - 3 q^{92} + 51 q^{93} - 78 q^{94} + 6 q^{95} + 6 q^{96} - 18 q^{97} + 3 q^{98}+O(q^{100}) \) 30 * q - 12 * q^7 + 15 * q^8 - 15 * q^11 + 3 * q^12 - 3 * q^13 + 9 * q^14 + 27 * q^15 - 36 * q^18 - 9 * q^19 + 18 * q^20 - 27 * q^21 - 3 * q^23 - 12 * q^25 + 3 * q^27 + 9 * q^28 + 3 * q^29 + 9 * q^30 + 30 * q^31 - 9 * q^34 + 15 * q^35 + 18 * q^37 + 6 * q^38 - 6 * q^41 - 45 * q^42 + 39 * q^43 - 18 * q^45 + 21 * q^46 + 45 * q^47 - 33 * q^49 + 36 * q^50 - 36 * q^51 + 6 * q^52 - 24 * q^53 + 45 * q^54 - 24 * q^56 - 24 * q^57 - 30 * q^58 + 3 * q^59 - 9 * q^60 - 27 * q^61 + 15 * q^62 - 93 * q^63 - 15 * q^64 + 18 * q^65 - 9 * q^67 - 21 * q^68 + 48 * q^69 - 15 * q^70 + 39 * q^73 + 3 * q^74 - 42 * q^75 - 15 * q^76 + 24 * q^77 + 6 * q^78 + 21 * q^79 + 84 * q^81 + 6 * q^82 - 36 * q^83 - 27 * q^84 + 63 * q^85 + 6 * q^86 - 21 * q^87 + 15 * q^88 + 54 * q^89 + 12 * q^90 + 3 * q^91 - 3 * q^92 + 51 * q^93 - 78 * q^94 + 6 * q^95 + 6 * q^96 - 18 * q^97 + 3 * q^98

Introduction

L-functions

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