LMFDB - Embedded newform 618.2.i.b.169.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [618,2,Mod(13,618)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(618, base_ring=CyclotomicField(34))

chi = DirichletCharacter(H, H._module([0, 24]))

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

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

chi := DirichletCharacter("618.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 618 = 2 \cdot 3 \cdot 103 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	618.i (of order $17$, degree $16$, 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:	$4.93475484492$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$2$ over $\Q(\zeta_{17})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{17}]$

Embedding invariants

Embedding label			169.2
Character	$\chi$	$=$	618.169
Dual form			618.2.i.b.373.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.932472 + 0.361242i) q^{2} +(-0.982973 - 0.183750i) q^{3} +(0.739009 + 0.673696i) q^{4} +(1.12572 + 3.95648i) q^{5} +(-0.850217 - 0.526432i) q^{6} +(0.724947 - 1.45589i) q^{7} +(0.445738 + 0.895163i) q^{8} +(0.932472 + 0.361242i) q^{9} +O(q^{10})$	\(q+(0.932472 + 0.361242i) q^{2} +(-0.982973 - 0.183750i) q^{3} +(0.739009 + 0.673696i) q^{4} +(1.12572 + 3.95648i) q^{5} +(-0.850217 - 0.526432i) q^{6} +(0.724947 - 1.45589i) q^{7} +(0.445738 + 0.895163i) q^{8} +(0.932472 + 0.361242i) q^{9} +(-0.379547 + 4.09597i) q^{10} +(0.0697120 + 0.0270066i) q^{11} +(-0.602635 - 0.798017i) q^{12} +(-1.33598 + 2.68301i) q^{13} +(1.20192 - 1.09570i) q^{14} +(-0.379547 - 4.09597i) q^{15} +(0.0922684 + 0.995734i) q^{16} +(1.38942 - 0.860295i) q^{17} +(0.739009 + 0.673696i) q^{18} +(-3.03883 + 0.568057i) q^{19} +(-1.83355 + 3.68227i) q^{20} +(-0.980122 + 1.29789i) q^{21} +(0.0552486 + 0.0503657i) q^{22} +(2.08283 - 0.806893i) q^{23} +(-0.273663 - 0.961826i) q^{24} +(-10.1354 + 6.27559i) q^{25} +(-2.21498 + 2.01922i) q^{26} +(-0.850217 - 0.526432i) q^{27} +(1.51657 - 0.587522i) q^{28} +(2.06191 + 7.24687i) q^{29} +(1.12572 - 3.95648i) q^{30} +(-0.204989 - 2.21218i) q^{31} +(-0.273663 + 0.961826i) q^{32} +(-0.0635626 - 0.0393563i) q^{33} +(1.60637 - 0.300283i) q^{34} +(6.57628 + 1.22932i) q^{35} +(0.445738 + 0.895163i) q^{36} +(-0.327363 - 0.433499i) q^{37} +(-3.03883 - 0.568057i) q^{38} +(1.80624 - 2.39184i) q^{39} +(-3.03992 + 2.77126i) q^{40} +(1.70318 - 5.98606i) q^{41} +(-1.38279 + 0.856187i) q^{42} +(-1.61092 + 2.13320i) q^{43} +(0.0333236 + 0.0669227i) q^{44} +(-0.379547 + 4.09597i) q^{45} +2.23367 q^{46} +7.95677 q^{47} +(0.0922684 - 0.995734i) q^{48} +(2.62438 + 3.47524i) q^{49} +(-11.7180 + 2.19048i) q^{50} +(-1.52385 + 0.590341i) q^{51} +(-2.79484 + 1.08273i) q^{52} +(-8.27136 + 1.54618i) q^{53} +(-0.602635 - 0.798017i) q^{54} +(-0.0283751 + 0.306216i) q^{55} +1.62639 q^{56} +3.09147 q^{57} +(-0.695196 + 7.50235i) q^{58} +(-0.0621278 - 0.124770i) q^{59} +(2.47895 - 3.28265i) q^{60} +(9.77978 - 6.05539i) q^{61} +(0.607985 - 2.13685i) q^{62} +(1.20192 - 1.09570i) q^{63} +(-0.602635 + 0.798017i) q^{64} +(-12.1192 - 2.26548i) q^{65} +(-0.0450532 - 0.0596601i) q^{66} +(1.81171 + 3.63841i) q^{67} +(1.60637 + 0.300283i) q^{68} +(-2.19563 + 0.410435i) q^{69} +(5.68812 + 3.52194i) q^{70} +(2.65396 - 9.32769i) q^{71} +(0.0922684 + 0.995734i) q^{72} +(0.813866 - 2.86044i) q^{73} +(-0.148659 - 0.522483i) q^{74} +(11.1160 - 4.30636i) q^{75} +(-2.62842 - 1.62745i) q^{76} +(0.0898560 - 0.0819146i) q^{77} +(2.54830 - 1.57784i) q^{78} +(-0.602675 - 2.11818i) q^{79} +(-3.83574 + 1.48597i) q^{80} +(0.739009 + 0.673696i) q^{81} +(3.75059 - 4.96658i) q^{82} +(3.96908 - 7.97099i) q^{83} +(-1.59870 + 0.298849i) q^{84} +(4.96784 + 4.52879i) q^{85} +(-2.27274 + 1.40722i) q^{86} +(-0.695196 - 7.50235i) q^{87} +(0.00689802 + 0.0744415i) q^{88} +(5.71629 - 5.21109i) q^{89} +(-1.83355 + 3.68227i) q^{90} +(2.93766 + 3.89008i) q^{91} +(2.08283 + 0.806893i) q^{92} +(-0.204989 + 2.21218i) q^{93} +(7.41947 + 2.87432i) q^{94} +(-5.66837 - 11.3836i) q^{95} +(0.445738 - 0.895163i) q^{96} +(1.01759 + 0.630068i) q^{97} +(1.19176 + 4.18860i) q^{98} +(0.0552486 + 0.0503657i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 2 q^{2} - 2 q^{3} - 2 q^{4} + q^{5} - 2 q^{6} + 6 q^{7} - 2 q^{8} - 2 q^{9}+O(q^{10}) $ 32 * q - 2 * q^2 - 2 * q^3 - 2 * q^4 + q^5 - 2 * q^6 + 6 * q^7 - 2 * q^8 - 2 * q^9	\( 32 q - 2 q^{2} - 2 q^{3} - 2 q^{4} + q^{5} - 2 q^{6} + 6 q^{7} - 2 q^{8} - 2 q^{9} + q^{10} + 5 q^{11} - 2 q^{12} - 14 q^{13} + 6 q^{14} + q^{15} - 2 q^{16} + 32 q^{17} - 2 q^{18} - 3 q^{19} + q^{20} - 11 q^{21} - 12 q^{22} - 15 q^{23} - 2 q^{24} - 15 q^{25} - 31 q^{26} - 2 q^{27} + 6 q^{28} + 7 q^{29} + q^{30} + 6 q^{31} - 2 q^{32} + 5 q^{33} - 2 q^{34} + 41 q^{35} - 2 q^{36} - 13 q^{37} - 3 q^{38} - 14 q^{39} - 16 q^{40} - 5 q^{41} - 11 q^{42} - 3 q^{43} - 12 q^{44} + q^{45} - 66 q^{46} - 14 q^{47} - 2 q^{48} - 6 q^{49} - 15 q^{50} - 2 q^{51} + 20 q^{52} - 6 q^{53} - 2 q^{54} + 11 q^{55} + 6 q^{56} + 14 q^{57} + 24 q^{58} - 43 q^{59} + 18 q^{60} + 48 q^{61} + 6 q^{62} + 6 q^{63} - 2 q^{64} - 84 q^{65} + 5 q^{66} + 7 q^{67} - 2 q^{68} + 19 q^{69} - 10 q^{70} - 59 q^{71} - 2 q^{72} - 9 q^{73} + 21 q^{74} + 19 q^{75} - 3 q^{76} - 33 q^{77} + 20 q^{78} + 33 q^{79} + q^{80} - 2 q^{81} + 46 q^{82} + 71 q^{83} - 11 q^{84} + 42 q^{85} - 20 q^{86} + 24 q^{87} - 12 q^{88} - q^{89} + q^{90} + 50 q^{91} - 15 q^{92} + 6 q^{93} + 20 q^{94} - 5 q^{95} - 2 q^{96} - 61 q^{97} - 57 q^{98} - 12 q^{99}+O(q^{100}) \) 32 * q - 2 * q^2 - 2 * q^3 - 2 * q^4 + q^5 - 2 * q^6 + 6 * q^7 - 2 * q^8 - 2 * q^9 + q^10 + 5 * q^11 - 2 * q^12 - 14 * q^13 + 6 * q^14 + q^15 - 2 * q^16 + 32 * q^17 - 2 * q^18 - 3 * q^19 + q^20 - 11 * q^21 - 12 * q^22 - 15 * q^23 - 2 * q^24 - 15 * q^25 - 31 * q^26 - 2 * q^27 + 6 * q^28 + 7 * q^29 + q^30 + 6 * q^31 - 2 * q^32 + 5 * q^33 - 2 * q^34 + 41 * q^35 - 2 * q^36 - 13 * q^37 - 3 * q^38 - 14 * q^39 - 16 * q^40 - 5 * q^41 - 11 * q^42 - 3 * q^43 - 12 * q^44 + q^45 - 66 * q^46 - 14 * q^47 - 2 * q^48 - 6 * q^49 - 15 * q^50 - 2 * q^51 + 20 * q^52 - 6 * q^53 - 2 * q^54 + 11 * q^55 + 6 * q^56 + 14 * q^57 + 24 * q^58 - 43 * q^59 + 18 * q^60 + 48 * q^61 + 6 * q^62 + 6 * q^63 - 2 * q^64 - 84 * q^65 + 5 * q^66 + 7 * q^67 - 2 * q^68 + 19 * q^69 - 10 * q^70 - 59 * q^71 - 2 * q^72 - 9 * q^73 + 21 * q^74 + 19 * q^75 - 3 * q^76 - 33 * q^77 + 20 * q^78 + 33 * q^79 + q^80 - 2 * q^81 + 46 * q^82 + 71 * q^83 - 11 * q^84 + 42 * q^85 - 20 * q^86 + 24 * q^87 - 12 * q^88 - q^89 + q^90 + 50 * q^91 - 15 * q^92 + 6 * q^93 + 20 * q^94 - 5 * q^95 - 2 * q^96 - 61 * q^97 - 57 * q^98 - 12 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/618\mathbb{Z}\right)^\times$.

$n$	$211$	$413$
$\chi(n)$	$e\left(\frac{7}{17}\right)$	$1$

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 $

$2$	0.932472	+	0.361242i	0.659357	+	0.255436i
$2$	0.932472	+	0.361242i	0.659357	+	0.255436i
$3$	−0.982973	−	0.183750i	−0.567520	−	0.106088i
$3$	−0.982973	−	0.183750i	−0.567520	−	0.106088i
$4$	0.739009	+	0.673696i	0.369504	+	0.336848i
$5$	1.12572	+	3.95648i	0.503436	+	1.76939i	0.629105	+	0.777321i	$0.283422\pi$
$5$	1.12572	+	3.95648i	0.503436	+	1.76939i	−0.125669	+	0.992072i	$0.540108\pi$
$6$	−0.850217	−	0.526432i	−0.347100	−	0.214915i
$7$	0.724947	−	1.45589i	0.274004	−	0.550274i	−0.714829	−	0.699299i	$-0.753496\pi$
$7$	0.724947	−	1.45589i	0.274004	−	0.550274i	0.988834	+	0.149024i	$0.0476133\pi$
$8$	0.445738	+	0.895163i	0.157592	+	0.316488i
$9$	0.932472	+	0.361242i	0.310824	+	0.120414i
$10$	−0.379547	+	4.09597i	−0.120023	+	1.29526i
$11$	0.0697120	+	0.0270066i	0.0210190	+	0.00814279i	0.371728	−	0.928342i	$-0.378765\pi$
$11$	0.0697120	+	0.0270066i	0.0210190	+	0.00814279i	−0.350709	+	0.936484i	$0.614059\pi$
$12$	−0.602635	−	0.798017i	−0.173966	−	0.230368i
$13$	−1.33598	+	2.68301i	−0.370535	+	0.744134i	−0.999444	−	0.0333446i	$-0.989384\pi$
$13$	−1.33598	+	2.68301i	−0.370535	+	0.744134i	0.628909	+	0.777479i	$0.283502\pi$
$14$	1.20192	−	1.09570i	0.321227	−	0.292837i
$15$	−0.379547	−	4.09597i	−0.0979987	−	1.05757i
$16$	0.0922684	+	0.995734i	0.0230671	+	0.248934i
$17$	1.38942	−	0.860295i	0.336985	−	0.208652i	−0.347499	−	0.937680i	$-0.612969\pi$
$17$	1.38942	−	0.860295i	0.336985	−	0.208652i	0.684484	+	0.729028i	$0.260028\pi$
$18$	0.739009	+	0.673696i	0.174186	+	0.158792i
$19$	−3.03883	+	0.568057i	−0.697156	+	0.130321i	−0.520386	−	0.853931i	$-0.674212\pi$
$19$	−3.03883	+	0.568057i	−0.697156	+	0.130321i	−0.176770	+	0.984252i	$0.556565\pi$
$20$	−1.83355	+	3.68227i	−0.409994	+	0.823380i
$21$	−0.980122	+	1.29789i	−0.213880	+	0.283223i
$22$	0.0552486	+	0.0503657i	0.0117790	+	0.0107380i
$23$	2.08283	−	0.806893i	0.434300	−	0.168249i	−0.134160	−	0.990960i	$-0.542834\pi$
$23$	2.08283	−	0.806893i	0.434300	−	0.168249i	0.568460	+	0.822711i	$0.307539\pi$
$24$	−0.273663	−	0.961826i	−0.0558612	−	0.196332i
$25$	−10.1354	+	6.27559i	−2.02709	+	1.25512i
$26$	−2.21498	+	2.01922i	−0.434394	+	0.396002i
$27$	−0.850217	−	0.526432i	−0.163624	−	0.101312i
$28$	1.51657	−	0.587522i	0.286604	−	0.111031i
$29$	2.06191	+	7.24687i	0.382888	+	1.34571i	0.878739	+	0.477303i	$0.158385\pi$
$29$	2.06191	+	7.24687i	0.382888	+	1.34571i	−0.495851	+	0.868407i	$0.665144\pi$
$30$	1.12572	−	3.95648i	0.205527	−	0.722352i
$31$	−0.204989	−	2.21218i	−0.0368170	−	0.397319i	−0.994124	−	0.108246i	$-0.965477\pi$
$31$	−0.204989	−	2.21218i	−0.0368170	−	0.397319i	0.957307	−	0.289073i	$-0.0933470\pi$
$32$	−0.273663	+	0.961826i	−0.0483772	+	0.170028i
$33$	−0.0635626	−	0.0393563i	−0.0110648	−	0.00685105i
$34$	1.60637	−	0.300283i	0.275491	−	0.0514982i
$35$	6.57628	+	1.22932i	1.11159	+	0.207793i
$36$	0.445738	+	0.895163i	0.0742897	+	0.149194i
$37$	−0.327363	−	0.433499i	−0.0538182	−	0.0712668i	0.770312	−	0.637667i	$-0.220100\pi$
$37$	−0.327363	−	0.433499i	−0.0538182	−	0.0712668i	−0.824130	+	0.566400i	$0.808336\pi$
$38$	−3.03883	−	0.568057i	−0.492964	−	0.0921509i
$39$	1.80624	−	2.39184i	0.289229	−	0.383002i
$40$	−3.03992	+	2.77126i	−0.480654	+	0.438174i
$41$	1.70318	−	5.98606i	0.265992	−	0.934866i	−0.707608	−	0.706605i	$-0.750226\pi$
$41$	1.70318	−	5.98606i	0.265992	−	0.934866i	0.973600	−	0.228261i	$-0.0733038\pi$
$42$	−1.38279	+	0.856187i	−0.213369	+	0.132112i
$43$	−1.61092	+	2.13320i	−0.245663	+	0.325310i	−0.904096	−	0.427329i	$-0.859455\pi$
$43$	−1.61092	+	2.13320i	−0.245663	+	0.325310i	0.658434	+	0.752639i	$0.271219\pi$
$44$	0.0333236	+	0.0669227i	0.00502372	+	0.0100890i
$45$	−0.379547	+	4.09597i	−0.0565795	+	0.610591i
$46$	2.23367			0.329336
$47$	7.95677			1.16061			0.580307	−	0.814398i	$-0.302933\pi$
$47$	7.95677			1.16061			0.580307	+	0.814398i	$0.302933\pi$
$48$	0.0922684	−	0.995734i	0.0133178	−	0.143722i
$49$	2.62438	+	3.47524i	0.374911	+	0.496462i
$50$	−11.7180	+	2.19048i	−1.65718	+	0.309780i
$51$	−1.52385	+	0.590341i	−0.213381	+	0.0826643i
$52$	−2.79484	+	1.08273i	−0.387574	+	0.150147i
$53$	−8.27136	+	1.54618i	−1.13616	+	0.212385i	−0.718036	−	0.696006i	$-0.754959\pi$
$53$	−8.27136	+	1.54618i	−1.13616	+	0.212385i	−0.418122	+	0.908391i	$0.637312\pi$
$54$	−0.602635	−	0.798017i	−0.0820082	−	0.108596i
$55$	−0.0283751	+	0.306216i	−0.00382610	+	0.0412902i
$56$	1.62639			0.217336
$57$	3.09147			0.409476
$58$	−0.695196	+	7.50235i	−0.0912836	+	0.985107i
$59$	−0.0621278	−	0.124770i	−0.00808835	−	0.0162436i	0.891082	−	0.453842i	$-0.149947\pi$
$59$	−0.0621278	−	0.124770i	−0.00808835	−	0.0162436i	−0.899171	+	0.437598i	$0.855829\pi$
$60$	2.47895	−	3.28265i	0.320031	−	0.423789i
$61$	9.77978	−	6.05539i	1.25217	−	0.775313i	0.269922	−	0.962882i	$-0.413002\pi$
$61$	9.77978	−	6.05539i	1.25217	−	0.775313i	0.982251	+	0.187570i	$0.0600610\pi$
$62$	0.607985	−	2.13685i	0.0772142	−	0.271380i
$63$	1.20192	−	1.09570i	0.151428	−	0.138045i
$64$	−0.602635	+	0.798017i	−0.0753293	+	0.0997522i
$65$	−12.1192	−	2.26548i	−1.50321	−	0.280998i
$66$	−0.0450532	−	0.0596601i	−0.00554566	−	0.00734365i
$67$	1.81171	+	3.63841i	0.221336	+	0.444503i	0.977802	−	0.209530i	$-0.0671934\pi$
$67$	1.81171	+	3.63841i	0.221336	+	0.444503i	−0.756466	+	0.654033i	$0.773076\pi$
$68$	1.60637	+	0.300283i	0.194801	+	0.0364147i
$69$	−2.19563	+	0.410435i	−0.264323	+	0.0494106i
$70$	5.68812	+	3.52194i	0.679860	+	0.420952i
$71$	2.65396	−	9.32769i	0.314967	−	1.10699i	−0.629123	−	0.777306i	$-0.716586\pi$
$71$	2.65396	−	9.32769i	0.314967	−	1.10699i	0.944090	−	0.329688i	$-0.106943\pi$
$72$	0.0922684	+	0.995734i	0.0108739	+	0.117348i
$73$	0.813866	−	2.86044i	0.0952558	−	0.334789i	−0.899519	−	0.436881i	$-0.856083\pi$
$73$	0.813866	−	2.86044i	0.0952558	−	0.334789i	0.994775	+	0.102092i	$0.0325536\pi$
$74$	−0.148659	−	0.522483i	−0.0172813	−	0.0607374i
$75$	11.1160	−	4.30636i	1.28356	−	0.497256i
$76$	−2.62842	−	1.62745i	−0.301501	−	0.186681i
$77$	0.0898560	−	0.0819146i	0.0102400	−	0.00933503i
$78$	2.54830	−	1.57784i	0.288538	−	0.178655i
$79$	−0.602675	−	2.11818i	−0.0678062	−	0.238314i	0.920513	−	0.390712i	$-0.127771\pi$
$79$	−0.602675	−	2.11818i	−0.0678062	−	0.238314i	−0.988319	+	0.152398i	$0.951301\pi$
$80$	−3.83574	+	1.48597i	−0.428848	+	0.166137i
$81$	0.739009	+	0.673696i	0.0821121	+	0.0748551i
$82$	3.75059	−	4.96658i	0.414183	−	0.548467i
$83$	3.96908	−	7.97099i	0.435663	−	0.874930i	−0.563156	−	0.826351i	$-0.690413\pi$
$83$	3.96908	−	7.97099i	0.435663	−	0.874930i	0.998819	−	0.0485791i	$-0.0154693\pi$
$84$	−1.59870	+	0.298849i	−0.174433	+	0.0326071i
$85$	4.96784	+	4.52879i	0.538838	+	0.491216i
$86$	−2.27274	+	1.40722i	−0.245075	+	0.151744i
$87$	−0.695196	−	7.50235i	−0.0745328	−	0.804337i
$88$	0.00689802	+	0.0744415i	0.000735331	+	0.00793549i
$89$	5.71629	−	5.21109i	0.605926	−	0.552374i	−0.311518	−	0.950240i	$-0.600837\pi$
$89$	5.71629	−	5.21109i	0.605926	−	0.552374i	0.917443	+	0.397866i	$0.130249\pi$
$90$	−1.83355	+	3.68227i	−0.193273	+	0.388145i
$91$	2.93766	+	3.89008i	0.307950	+	0.407792i
$92$	2.08283	+	0.806893i	0.217150	+	0.0841244i
$93$	−0.204989	+	2.21218i	−0.0212563	+	0.229392i
$94$	7.41947	+	2.87432i	0.765260	+	0.296463i
$95$	−5.66837	−	11.3836i	−0.581563	−	1.16794i
$96$	0.445738	−	0.895163i	0.0454930	−	0.0913622i
$97$	1.01759	+	0.630068i	0.103321	+	0.0639737i	0.577120	−	0.816659i	$-0.304176\pi$
$97$	1.01759	+	0.630068i	0.103321	+	0.0639737i	−0.473799	+	0.880633i	$0.657118\pi$
$98$	1.19176	+	4.18860i	0.120386	+	0.423112i
$99$	0.0552486	+	0.0503657i	0.00555269	+	0.00506195i
$100$	−11.7180	−	2.19048i	−1.17180	−	0.219048i
$101$	15.5060	+	6.00704i	1.54290	+	0.597723i	0.974372	−	0.224941i	$-0.0722191\pi$
$101$	15.5060	+	6.00704i	1.54290	+	0.597723i	0.568528	+	0.822664i	$0.307513\pi$
$102$	−1.63420			−0.161810
$103$	8.93998	+	4.80383i	0.880882	+	0.473335i
$103$	8.93998	+	4.80383i	0.880882	+	0.473335i
$104$	−2.99723			−0.293903
$105$	−6.23842	−	2.41678i	−0.608808	−	0.235853i
$106$	−8.27136	−	1.54618i	−0.803385	−	0.150179i
$107$	−12.5291	−	11.4217i	−1.21123	−	1.10418i	−0.991700	−	0.128575i	$-0.958960\pi$
$107$	−12.5291	−	11.4217i	−1.21123	−	1.10418i	−0.219529	−	0.975606i	$-0.570452\pi$
$108$	−0.273663	−	0.961826i	−0.0263332	−	0.0925517i
$109$	−15.6946	−	9.71770i	−1.50327	−	0.930787i	−0.997684	−	0.0680122i	$-0.978334\pi$
$109$	−15.6946	−	9.71770i	−1.50327	−	0.930787i	−0.505588	−	0.862775i	$-0.668725\pi$
$110$	−0.137077	+	0.275288i	−0.0130698	+	0.0262476i
$111$	0.242134	+	0.486271i	0.0229823	+	0.0461548i
$112$	1.51657	+	0.587522i	0.143302	+	0.0555156i
$113$	0.966599	−	10.4313i	0.0909300	−	0.981291i	−0.820995	−	0.570935i	$-0.806581\pi$
$113$	0.966599	−	10.4313i	0.0909300	−	0.981291i	0.911925	−	0.410356i	$-0.134596\pi$
$114$	2.88271	+	1.11677i	0.269991	+	0.104595i
$115$	5.53713	+	7.33235i	0.516340	+	0.683745i
$116$	−3.35841	+	6.74460i	−0.311821	+	0.626221i
$117$	−2.21498	+	2.01922i	−0.204775	+	0.186677i
$118$	−0.0128605	−	0.138787i	−0.00118391	−	0.0127764i
$119$	−0.245236	−	2.64652i	−0.0224807	−	0.242606i
$120$	3.49738	−	2.16549i	0.319266	−	0.197681i
$121$	−8.12497	−	7.40689i	−0.738633	−	0.673353i
$122$	11.3068	−	2.11361i	1.02367	−	0.191358i
$123$	−2.77412	+	5.57118i	−0.250134	+	0.502336i
$124$	1.33885	−	1.77292i	0.120232	−	0.159213i
$125$	−21.0393	−	19.1798i	−1.88181	−	1.71550i
$126$	1.51657	−	0.587522i	0.135107	−	0.0523406i
$127$	−5.29320	−	18.6037i	−0.469696	−	1.65081i	−0.728624	−	0.684914i	$-0.759840\pi$
$127$	−5.29320	−	18.6037i	−0.469696	−	1.65081i	0.258928	−	0.965897i	$-0.416631\pi$
$128$	−0.850217	+	0.526432i	−0.0751493	+	0.0465305i
$129$	1.97546	−	1.80087i	0.173930	−	0.158558i
$130$	−10.4825	−	6.49047i	−0.919373	−	0.569252i
$131$	−8.33954	+	3.23075i	−0.728629	+	0.282272i	−0.696844	−	0.717222i	$-0.745413\pi$
$131$	−8.33954	+	3.23075i	−0.728629	+	0.282272i	−0.0317845	+	0.999495i	$0.510119\pi$
$132$	−0.0204591	−	0.0719064i	−0.00178074	−	0.00625865i
$133$	−1.37597	+	4.83602i	−0.119311	+	0.419336i
$134$	0.375027	+	4.04718i	0.0323974	+	0.349623i
$135$	1.12572	−	3.95648i	0.0968862	−	0.340520i
$136$	1.38942	+	0.860295i	0.119142	+	0.0737697i
$137$	3.17939	−	0.594330i	0.271633	−	0.0507771i	−0.0461705	−	0.998934i	$-0.514702\pi$
$137$	3.17939	−	0.594330i	0.271633	−	0.0507771i	0.317804	+	0.948157i	$0.397055\pi$
$138$	−2.19563	−	0.410435i	−0.186905	−	0.0349385i
$139$	8.21056	+	16.4890i	0.696411	+	1.39858i	0.907052	+	0.421018i	$0.138327\pi$
$139$	8.21056	+	16.4890i	0.696411	+	1.39858i	−0.210642	+	0.977563i	$0.567555\pi$
$140$	4.03174	+	5.33889i	0.340745	+	0.451219i
$141$	−7.82129	−	1.46205i	−0.658671	−	0.123127i
$142$	5.84429	−	7.73909i	0.490442	−	0.649450i
$143$	−0.165593	+	0.150958i	−0.0138476	+	0.0126237i
$144$	−0.273663	+	0.961826i	−0.0228052	+	0.0801521i
$145$	−26.3510	+	16.3158i	−2.18833	+	1.35496i
$146$	1.79222	−	2.37328i	0.148325	−	0.196414i
$147$	−1.94112	−	3.89829i	−0.160101	−	0.321526i
$148$	0.0501220	−	0.540903i	0.00412000	−	0.0444619i
$149$	9.52423			0.780255			0.390127	−	0.920761i	$-0.372431\pi$
$149$	9.52423			0.780255			0.390127	+	0.920761i	$0.372431\pi$
$150$	11.9210			0.973345
$151$	−0.145106	+	1.56595i	−0.0118086	+	0.127435i	−0.999598	−	0.0283618i	$-0.990971\pi$
$151$	−0.145106	+	1.56595i	−0.0118086	+	0.127435i	0.987789	+	0.155797i	$0.0497945\pi$
$152$	−1.86303	−	2.46705i	−0.151112	−	0.200104i
$153$	1.60637	−	0.300283i	0.129868	−	0.0242765i
$154$	0.113379	−	0.0439233i	0.00913636	−	0.00353944i
$155$	8.52169	−	3.30132i	0.684479	−	0.265168i
$156$	2.94620	−	0.550740i	0.235885	−	0.0440945i
$157$	−8.69727	−	11.5170i	−0.694117	−	0.919160i	0.305335	−	0.952245i	$-0.401232\pi$
$157$	−8.69727	−	11.5170i	−0.694117	−	0.919160i	−0.999453	+	0.0330849i	$0.989467\pi$
$158$	0.203198	−	2.19286i	0.0161656	−	0.174454i
$159$	8.41463			0.667324
$160$	−4.11351			−0.325202
$161$	0.335195	−	3.61732i	0.0264170	−	0.285085i
$162$	0.445738	+	0.895163i	0.0350205	+	0.0703307i
$163$	3.70473	−	4.90586i	0.290177	−	0.384256i	−0.629455	−	0.777037i	$-0.716722\pi$
$163$	3.70473	−	4.90586i	0.290177	−	0.384256i	0.919632	+	0.392780i	$0.128487\pi$
$164$	5.29145	−	3.27633i	0.413193	−	0.255838i
$165$	0.0841590	−	0.295788i	0.00655177	−	0.0230271i
$166$	6.58051	−	5.99893i	0.510747	−	0.465607i
$167$	13.1190	−	17.3723i	1.01518	−	1.34431i	0.0774293	−	0.996998i	$-0.475329\pi$
$167$	13.1190	−	17.3723i	1.01518	−	1.34431i	0.937749	−	0.347315i	$-0.112907\pi$
$168$	−1.59870	−	0.298849i	−0.123343	−	0.0230567i
$169$	2.42053	+	3.20531i	0.186195	+	0.246562i
$170$	2.99639	+	6.01756i	0.229812	+	0.461526i
$171$	−3.03883	−	0.568057i	−0.232385	−	0.0434404i
$172$	−2.62761	+	0.491185i	−0.200353	+	0.0374525i
$173$	16.1964	+	10.0284i	1.23139	+	0.762446i	0.978739	−	0.205111i	$-0.0657556\pi$
$173$	16.1964	+	10.0284i	1.23139	+	0.762446i	0.252653	+	0.967557i	$0.418697\pi$
$174$	2.06191	−	7.24687i	0.156313	−	0.549384i
$175$	1.78892	+	19.3055i	0.135230	+	1.45936i
$176$	−0.0204591	+	0.0719064i	−0.00154217	+	0.00542015i
$177$	0.0381436	+	0.134061i	0.00286705	+	0.0100766i
$178$	7.21274	−	2.79423i	0.540618	−	0.209437i
$179$	18.5026	+	11.4563i	1.38295	+	0.856285i	0.997782	−	0.0665629i	$-0.0212033\pi$
$179$	18.5026	+	11.4563i	1.38295	+	0.856285i	0.385165	+	0.922848i	$0.374144\pi$
$180$	−3.03992	+	2.77126i	−0.226582	+	0.206557i
$181$	−3.69425	+	2.28738i	−0.274592	+	0.170020i	−0.656819	−	0.754048i	$-0.728098\pi$
$181$	−3.69425	+	2.28738i	−0.274592	+	0.170020i	0.382227	+	0.924068i	$0.375157\pi$
$182$	1.33402	+	4.68860i	0.0988842	+	0.347542i
$183$	−10.7259	+	4.15525i	−0.792884	+	0.307165i
$184$	1.65070	+	1.50481i	0.121691	+	0.110936i
$185$	1.34661	−	1.78320i	0.0990049	−	0.131104i
$186$	−0.990278	+	1.98875i	−0.0726107	+	0.145822i
$187$	0.120093	−	0.0224493i	0.00878208	−	0.00164166i
$188$	5.88012	+	5.36044i	0.428852	+	0.390950i
$189$	−1.38279	+	0.856187i	−0.100583	+	0.0622784i
$190$	−1.17336	−	12.6626i	−0.0851244	−	0.918639i
$191$	1.48839	+	16.0623i	0.107696	+	1.16223i	0.862423	+	0.506189i	$0.168946\pi$
$191$	1.48839	+	16.0623i	0.107696	+	1.16223i	−0.754726	+	0.656040i	$0.772230\pi$
$192$	0.739009	−	0.673696i	0.0533334	−	0.0486198i
$193$	−2.89943	+	5.82284i	−0.208705	+	0.419137i	−0.974639	−	0.223783i	$-0.928159\pi$
$193$	−2.89943	+	5.82284i	−0.208705	+	0.419137i	0.765934	+	0.642920i	$0.222277\pi$
$194$	0.721272	+	0.955118i	0.0517843	+	0.0685735i
$195$	11.4966	+	4.45381i	0.823289	+	0.318944i
$196$	−0.401814	+	4.33626i	−0.0287010	+	0.309733i
$197$	−10.7481	−	4.16385i	−0.765772	−	0.296662i	−0.0535027	−	0.998568i	$-0.517039\pi$
$197$	−10.7481	−	4.16385i	−0.765772	−	0.296662i	−0.712270	+	0.701906i	$0.752333\pi$
$198$	0.0333236	+	0.0669227i	0.00236820	+	0.00475599i
$199$	−6.59402	+	13.2426i	−0.467437	+	0.938741i	0.528521	+	0.848920i	$0.322747\pi$
$199$	−6.59402	+	13.2426i	−0.467437	+	0.938741i	−0.995958	+	0.0898203i	$0.971371\pi$
$200$	−10.1354	−	6.27559i	−0.716683	−	0.443752i
$201$	−1.11231	−	3.90936i	−0.0784563	−	0.275745i
$202$	12.2889	+	11.2028i	0.864642	+	0.788226i
$203$	12.0454	+	2.25168i	0.845423	+	0.158037i
$204$	−1.52385	−	0.590341i	−0.106691	−	0.0413321i
$205$	25.6011			1.78806
$206$	6.60094	+	7.70893i	0.459909	+	0.537106i
$207$	2.23367			0.155250
$208$	−2.79484	−	1.08273i	−0.193787	−	0.0750735i
$209$	−0.227184	−	0.0424681i	−0.0157147	−	0.00293758i
$210$	−4.94412	−	4.50716i	−0.341176	−	0.311023i
$211$	3.53671	+	12.4303i	0.243477	+	0.855734i	0.983155	+	0.182773i	$0.0585074\pi$
$211$	3.53671	+	12.4303i	0.243477	+	0.855734i	−0.739678	+	0.672961i	$0.765022\pi$
$212$	−7.15426	−	4.42973i	−0.491357	−	0.304235i
$213$	−4.32273	+	8.68121i	−0.296188	+	0.594826i
$214$	−7.55698	−	15.1765i	−0.516585	−	1.03744i
$215$	−10.2534	−	3.97219i	−0.699276	−	0.270901i
$216$	0.0922684	−	0.995734i	0.00627807	−	0.0677511i
$217$	−3.36929	−	1.30527i	−0.228723	−	0.0886076i
$218$	−11.1244	−	14.7310i	−0.753437	−	0.997712i
$219$	−1.32561	+	2.66219i	−0.0895766	+	0.179894i
$220$	−0.227266	+	0.207180i	−0.0153223	+	0.0139681i
$221$	0.451938	+	4.87718i	0.0304006	+	0.328075i
$222$	0.0501220	+	0.540903i	0.00336397	+	0.0363030i
$223$	12.7257	−	7.87942i	0.852176	−	0.527645i	−0.0294649	−	0.999566i	$-0.509380\pi$
$223$	12.7257	−	7.87942i	0.852176	−	0.527645i	0.881641	+	0.471921i	$0.156439\pi$
$224$	1.20192	+	1.09570i	0.0803067	+	0.0732092i
$225$	−11.7180	+	2.19048i	−0.781201	+	0.146032i
$226$	4.66953	−	9.37769i	0.310613	−	0.623795i
$227$	−14.3489	+	19.0010i	−0.952367	+	1.26114i	0.0129120	+	0.999917i	$0.495890\pi$
$227$	−14.3489	+	19.0010i	−0.952367	+	1.26114i	−0.965279	+	0.261221i	$0.915875\pi$
$228$	2.28463	+	2.08271i	0.151303	+	0.137931i
$229$	3.93872	−	1.52587i	0.260278	−	0.100832i	−0.227567	−	0.973762i	$-0.573077\pi$
$229$	3.93872	−	1.52587i	0.260278	−	0.100832i	0.487845	+	0.872930i	$0.337783\pi$
$230$	2.51447	+	8.83746i	0.165799	+	0.582725i
$231$	−0.103378	+	0.0640088i	−0.00680176	+	0.00421147i
$232$	−5.56806	+	5.07596i	−0.365561	+	0.333253i
$233$	7.52312	+	4.65812i	0.492856	+	0.305163i	0.750263	−	0.661140i	$-0.229927\pi$
$233$	7.52312	+	4.65812i	0.492856	+	0.305163i	−0.257407	+	0.966303i	$0.582868\pi$
$234$	−2.79484	+	1.08273i	−0.182704	+	0.0707800i
$235$	8.95707	+	31.4808i	0.584295	+	2.05358i
$236$	0.0381436	−	0.134061i	0.00248294	−	0.00872663i
$237$	0.203198	+	2.19286i	0.0131991	+	0.142441i
$238$	0.727356	−	2.55639i	0.0471475	−	0.165706i
$239$	3.55898	+	2.20363i	0.230211	+	0.142541i	0.636691	−	0.771119i	$-0.280303\pi$
$239$	3.55898	+	2.20363i	0.230211	+	0.142541i	−0.406480	+	0.913660i	$0.633244\pi$
$240$	4.04347	−	0.755856i	0.261005	−	0.0487903i
$241$	9.80820	+	1.83347i	0.631802	+	0.118104i	0.489903	−	0.871777i	$-0.337032\pi$
$241$	9.80820	+	1.83347i	0.631802	+	0.118104i	0.141899	+	0.989881i	$0.454679\pi$
$242$	−4.90063	−	9.84179i	−0.315024	−	0.632654i
$243$	−0.602635	−	0.798017i	−0.0386590	−	0.0511928i
$244$	11.3068	+	2.11361i	0.723846	+	0.135310i
$245$	−10.7954	+	14.2954i	−0.689693	+	0.913302i
$246$	−4.59933	+	4.19284i	−0.293243	+	0.267326i
$247$	2.53572	−	8.91215i	0.161344	−	0.567066i
$248$	1.88889	−	1.16955i	0.119945	−	0.0742666i
$249$	−5.36616	+	7.10595i	−0.340067	+	0.450321i
$250$	−12.6900	−	25.4849i	−0.802586	−	1.61181i
$251$	2.04925	−	22.1149i	0.129348	−	1.39588i	−0.645512	−	0.763750i	$-0.723356\pi$
$251$	2.04925	−	22.1149i	0.129348	−	1.39588i	0.774860	−	0.632133i	$-0.217820\pi$
$252$	1.62639			0.102453
$253$	0.166990			0.0104985
$254$	1.78466	−	19.2595i	0.111980	−	1.20845i
$255$	−4.05109	−	5.36451i	−0.253689	−	0.335939i
$256$	−0.982973	+	0.183750i	−0.0614358	+	0.0114843i
$257$	−5.55344	+	2.15141i	−0.346414	+	0.134202i	−0.528162	−	0.849144i	$-0.677119\pi$
$257$	−5.55344	+	2.15141i	−0.346414	+	0.134202i	0.181748	+	0.983345i	$0.441825\pi$
$258$	2.49261	−	0.965644i	0.155183	−	0.0601183i
$259$	−0.868447	+	0.162341i	−0.0539627	+	0.0100874i
$260$	−7.42998	−	9.83889i	−0.460788	−	0.610182i
$261$	−0.695196	+	7.50235i	−0.0430315	+	0.464384i
$262$	−8.94347			−0.552529
$263$	−11.0783			−0.683115			−0.341557	−	0.939861i	$-0.610954\pi$
$263$	−11.0783			−0.683115			−0.341557	+	0.939861i	$0.610954\pi$
$264$	0.00689802	−	0.0744415i	0.000424544	−	0.00458156i
$265$	−15.4287	−	30.9849i	−0.947775	−	1.90339i
$266$	−3.03002	+	4.01239i	−0.185782	+	0.246016i
$267$	−6.57649	+	4.07199i	−0.402475	+	0.249202i
$268$	−1.11231	+	3.90936i	−0.0679451	+	0.238802i
$269$	8.20740	−	7.48204i	0.500414	−	0.456188i	−0.383701	−	0.923458i	$-0.625351\pi$
$269$	8.20740	−	7.48204i	0.500414	−	0.456188i	0.884115	+	0.467270i	$0.154762\pi$
$270$	2.47895	−	3.28265i	0.150864	−	0.199776i
$271$	−8.60746	−	1.60901i	−0.522866	−	0.0977406i	−0.0843014	−	0.996440i	$-0.526866\pi$
$271$	−8.60746	−	1.60901i	−0.522866	−	0.0977406i	−0.438564	+	0.898700i	$0.644513\pi$
$272$	0.984825	+	1.30412i	0.0597138	+	0.0790739i
$273$	−2.17283	−	4.36364i	−0.131506	−	0.264100i
$274$	3.17939	+	0.594330i	0.192074	+	0.0359048i
$275$	−0.876043	+	0.163761i	−0.0528274	+	0.00987515i
$276$	−1.89910	−	1.17587i	−0.114312	−	0.0707793i
$277$	−4.96993	+	17.4675i	−0.298614	+	1.04952i	0.656755	+	0.754104i	$0.271929\pi$
$277$	−4.96993	+	17.4675i	−0.298614	+	1.04952i	−0.955369	+	0.295416i	$0.904542\pi$
$278$	1.69960	+	18.3416i	0.101935	+	1.10005i
$279$	0.607985	−	2.13685i	0.0363991	−	0.127930i
$280$	1.83086	+	6.43480i	0.109415	+	0.384553i
$281$	−25.4959	+	9.87717i	−1.52096	+	0.589222i	−0.969524	−	0.244996i	$-0.921213\pi$
$281$	−25.4959	+	9.87717i	−1.52096	+	0.589222i	−0.551434	+	0.834218i	$0.685919\pi$
$282$	−6.76498	−	4.18870i	−0.402849	−	0.249433i
$283$	−9.98426	+	9.10186i	−0.593503	+	0.541049i	−0.913746	−	0.406286i	$-0.866824\pi$
$283$	−9.98426	+	9.10186i	−0.593503	+	0.541049i	0.320243	+	0.947335i	$0.396235\pi$
$284$	8.24532	−	5.10529i	0.489270	−	0.302943i
$285$	3.48012	+	12.2314i	0.206145	+	0.724523i
$286$	−0.208943	+	0.0809450i	−0.0123551	+	0.00478638i
$287$	−7.48033	−	6.81922i	−0.441550	−	0.402526i
$288$	−0.602635	+	0.798017i	−0.0355106	+	0.0470236i
$289$	−6.38716	+	12.8271i	−0.375715	+	0.754538i
$290$	−30.4655	+	5.69499i	−1.78900	+	0.334422i
$291$	−0.884493	−	0.806322i	−0.0518499	−	0.0472674i
$292$	2.52852	−	1.56559i	0.147971	−	0.0916195i
$293$	−3.02335	−	32.6271i	−0.176626	−	1.90610i	−0.376731	−	0.926323i	$-0.622952\pi$
$293$	−3.02335	−	32.6271i	−0.176626	−	1.90610i	0.200106	−	0.979774i	$-0.435872\pi$
$294$	−0.401814	−	4.33626i	−0.0234343	−	0.252896i
$295$	0.423710	−	0.386263i	0.0246694	−	0.0224891i
$296$	0.242134	−	0.486271i	0.0140738	−	0.0282639i
$297$	−0.0450532	−	0.0596601i	−0.00261425	−	0.00346183i
$298$	8.88108	+	3.44055i	0.514467	+	0.199306i
$299$	−0.617720	+	6.66626i	−0.0357237	+	0.385520i
$300$	11.1160	+	4.30636i	0.641782	+	0.248628i
$301$	1.93787	+	3.89177i	0.111697	+	0.224318i
$302$	−0.700992	+	1.40778i	−0.0403376	+	0.0810088i
$303$	−14.1381	−	8.75397i	−0.812215	−	0.502902i
$304$	−0.846022	−	2.97346i	−0.0485227	−	0.170539i
$305$	34.9673	+	31.8769i	2.00222	+	1.82527i
$306$	1.60637	+	0.300283i	0.0918303	+	0.0171661i
$307$	−4.15256	−	1.60871i	−0.236999	−	0.0918139i	0.239813	−	0.970819i	$-0.422914\pi$
$307$	−4.15256	−	1.60871i	−0.236999	−	0.0918139i	−0.476812	+	0.879005i	$0.658208\pi$
$308$	0.121590			0.00692823
$309$	−7.90506	−	6.36475i	−0.449703	−	0.362078i
$310$	9.13882			0.519050
$311$	8.75906	+	3.39328i	0.496681	+	0.192415i	0.596535	−	0.802587i	$-0.296544\pi$
$311$	8.75906	+	3.39328i	0.496681	+	0.192415i	−0.0998544	+	0.995002i	$0.531838\pi$
$312$	2.94620	+	0.550740i	0.166796	+	0.0311795i
$313$	−3.55591	−	3.24164i	−0.200992	−	0.183228i	0.566942	−	0.823758i	$-0.308127\pi$
$313$	−3.55591	−	3.24164i	−0.200992	−	0.183228i	−0.767933	+	0.640530i	$0.778715\pi$
$314$	−3.94952	−	13.8811i	−0.222885	−	0.783358i
$315$	5.68812	+	3.52194i	0.320489	+	0.198439i
$316$	0.981628	−	1.97138i	0.0552209	−	0.110899i
$317$	−3.04421	−	6.11360i	−0.170980	−	0.343374i	0.793055	−	0.609150i	$-0.208489\pi$
$317$	−3.04421	−	6.11360i	−0.170980	−	0.343374i	−0.964035	+	0.265776i	$0.914372\pi$
$318$	7.84641	+	3.03972i	0.440005	+	0.170459i
$319$	−0.0519731	+	0.560879i	−0.00290993	+	0.0314032i
$320$	−3.83574	−	1.48597i	−0.214424	−	0.0830684i
$321$	10.2170	+	13.5295i	0.570256	+	0.755141i
$322$	1.61929	−	3.25197i	0.0902394	−	0.181225i
$323$	−3.73353	+	3.40357i	−0.207739	+	0.189379i
$324$	0.0922684	+	0.995734i	0.00512602	+	0.0553186i
$325$	−3.29675	−	35.5776i	−0.182871	−	1.97349i
$326$	5.22676	−	3.23627i	0.289483	−	0.179240i
$327$	13.6418	+	12.4361i	0.754392	+	0.687719i
$328$	6.11768	−	1.14359i	0.337792	−	0.0631443i
$329$	5.76823	−	11.5842i	0.318013	−	0.638656i
$330$	0.185327	−	0.245413i	0.0102019	−	0.0135095i
$331$	−25.3419	−	23.1022i	−1.39292	−	1.26981i	−0.921758	−	0.387765i	$-0.873247\pi$
$331$	−25.3419	−	23.1022i	−1.39292	−	1.26981i	−0.471160	−	0.882048i	$-0.656165\pi$
$332$	8.30321	−	3.21668i	0.455698	−	0.176538i
$333$	−0.148659	−	0.522483i	−0.00814647	−	0.0286319i
$334$	18.5087	−	11.4601i	1.01275	−	0.627069i
$335$	−12.3558	+	11.2638i	−0.675071	+	0.615409i
$336$	−1.38279	−	0.856187i	−0.0754373	−	0.0467088i
$337$	−2.46142	+	0.953560i	−0.134082	+	0.0519437i	−0.427348	−	0.904087i	$-0.640552\pi$
$337$	−2.46142	+	0.953560i	−0.134082	+	0.0519437i	0.293266	+	0.956031i	$0.405258\pi$
$338$	1.09919	+	3.86326i	0.0597881	+	0.210133i
$339$	−2.86688	+	10.0760i	−0.155708	+	0.547255i
$340$	0.620256	+	6.69363i	0.0336381	+	0.363013i
$341$	0.0454532	−	0.159751i	0.00246143	−	0.00865103i
$342$	−2.62842	−	1.62745i	−0.142129	−	0.0880024i
$343$	18.1530	−	3.39339i	0.980170	−	0.183226i
$344$	−2.62761	−	0.491185i	−0.141671	−	0.0264829i
$345$	−4.09554	−	8.22495i	−0.220496	−	0.442816i
$346$	11.4800	+	15.2020i	0.617171	+	0.817267i
$347$	−23.4230	−	4.37852i	−1.25741	−	0.235051i	−0.487456	−	0.873147i	$-0.662075\pi$
$347$	−23.4230	−	4.37852i	−1.25741	−	0.235051i	−0.769957	+	0.638096i	$0.779722\pi$
$348$	4.54055	−	6.01266i	0.243399	−	0.322312i
$349$	11.9977	−	10.9374i	0.642223	−	0.585464i	−0.285662	−	0.958330i	$-0.592213\pi$
$349$	11.9977	−	10.9374i	0.642223	−	0.585464i	0.927885	+	0.372867i	$0.121625\pi$
$350$	−5.30585	+	18.6481i	−0.283609	+	0.996783i
$351$	2.54830	−	1.57784i	0.136018	−	0.0842189i
$352$	−0.0450532	+	0.0596601i	−0.00240134	+	0.00317989i
$353$	5.31151	+	10.6670i	0.282703	+	0.567745i	0.990312	−	0.138860i	$-0.0443437\pi$
$353$	5.31151	+	10.6670i	0.282703	+	0.567745i	−0.707609	+	0.706604i	$0.750226\pi$
$354$	−0.0128605	+	0.138787i	−0.000683530	+	0.00737646i
$355$	39.8925			2.11727
$356$	7.73508			0.409958
$357$	−0.245236	+	2.64652i	−0.0129793	+	0.140068i
$358$	13.1146	+	17.3666i	0.693130	+	0.917853i
$359$	−1.50505	+	0.281343i	−0.0794337	+	0.0148487i	−0.223316	−	0.974746i	$-0.571688\pi$
$359$	−1.50505	+	0.281343i	−0.0794337	+	0.0148487i	0.143883	+	0.989595i	$0.454041\pi$
$360$	−3.83574	+	1.48597i	−0.202161	+	0.0783176i
$361$	−8.80515	+	3.41113i	−0.463429	+	0.179533i
$362$	−4.27109	+	0.798404i	−0.224483	+	0.0419632i
$363$	6.62561	+	8.77373i	0.347754	+	0.460501i
$364$	−0.449779	+	4.85389i	−0.0235748	+	0.254413i
$365$	12.2335			0.640329
$366$	−11.5027			−0.601255
$367$	1.73229	−	18.6943i	0.0904246	−	0.975836i	−0.822787	−	0.568350i	$-0.807582\pi$
$367$	1.73229	−	18.6943i	0.0904246	−	0.975836i	0.913211	−	0.407486i	$-0.133595\pi$
$368$	0.995630	+	1.99950i	0.0519008	+	0.104231i
$369$	3.75059	−	4.96658i	0.195248	−	0.258550i
$370$	1.89985	−	1.17634i	0.0987683	−	0.0611548i
$371$	−3.74522	+	13.1631i	−0.194442	+	0.683393i
$372$	−1.64182	+	1.49672i	−0.0851246	+	0.0776013i
$373$	−12.8259	+	16.9842i	−0.664099	+	0.879410i	−0.998001	−	0.0631984i	$-0.979870\pi$
$373$	−12.8259	+	16.9842i	−0.664099	+	0.879410i	0.333902	+	0.942608i	$0.391635\pi$
$374$	0.120093	+	0.0224493i	0.00620987	+	0.00116083i
$375$	17.1568	+	22.7192i	0.885972	+	1.17322i
$376$	3.54664	+	7.12261i	0.182904	+	0.367320i
$377$	−22.1981	−	4.14955i	−1.14326	−	0.213713i
$378$	−1.59870	+	0.298849i	−0.0822284	+	0.0153711i
$379$	−15.6494	−	9.68968i	−0.803854	−	0.497726i	0.0619673	−	0.998078i	$-0.480263\pi$
$379$	−15.6494	−	9.68968i	−0.803854	−	0.497726i	−0.865822	+	0.500353i	$0.833204\pi$
$380$	3.48012	−	12.2314i	0.178526	−	0.627455i
$381$	1.78466	+	19.2595i	0.0914309	+	0.986696i
$382$	−4.41450	+	15.5153i	−0.225865	+	0.793834i
$383$	6.61630	+	23.2539i	0.338077	+	1.18822i	0.925440	+	0.378895i	$0.123696\pi$
$383$	6.61630	+	23.2539i	0.338077	+	1.18822i	−0.587362	+	0.809324i	$0.699834\pi$
$384$	0.932472	−	0.361242i	0.0475850	−	0.0184345i
$385$	0.425246	+	0.263301i	0.0216725	+	0.0134191i
$386$	−4.80709	+	4.38224i	−0.244674	+	0.223050i
$387$	−2.27274	+	1.40722i	−0.115530	+	0.0715329i
$388$	0.327537	+	1.15117i	0.0166282	+	0.0584420i
$389$	−23.5881	+	9.13810i	−1.19597	+	0.463320i	−0.875164	−	0.483826i	$-0.839247\pi$
$389$	−23.5881	+	9.13810i	−1.19597	+	0.463320i	−0.320802	+	0.947146i	$0.603953\pi$
$390$	9.11136	+	8.30610i	0.461372	+	0.420596i
$391$	2.19977	−	2.91297i	0.111247	−	0.147315i
$392$	−1.94112	+	3.89829i	−0.0980413	+	0.196893i
$393$	8.79119	−	1.64336i	0.443457	−	0.0828965i
$394$	−8.51818	−	7.76534i	−0.429140	−	0.391212i
$395$	7.70211	−	4.76895i	0.387535	−	0.239952i
$396$	0.00689802	+	0.0744415i	0.000346638	+	0.00374082i
$397$	−0.0387059	−	0.417703i	−0.00194259	−	0.0209639i	0.994708	−	0.102745i	$-0.0327626\pi$
$397$	−0.0387059	−	0.417703i	−0.00194259	−	0.0209639i	−0.996650	+	0.0817813i	$0.973939\pi$
$398$	−10.9325	+	9.96629i	−0.547997	+	0.499565i
$399$	2.24115	−	4.50084i	0.112198	−	0.225324i
$400$	−7.18400	−	9.51316i	−0.359200	−	0.475658i
$401$	28.6809	+	11.1110i	1.43225	+	0.554859i	0.947490	−	0.319786i	$-0.103611\pi$
$401$	28.6809	+	11.1110i	1.43225	+	0.554859i	0.484765	+	0.874644i	$0.338905\pi$
$402$	0.375027	−	4.04718i	0.0187046	−	0.201855i
$403$	6.20917	+	2.40545i	0.309301	+	0.119824i
$404$	7.41212	+	14.8855i	0.368767	+	0.740584i
$405$	−1.83355	+	3.68227i	−0.0911099	+	0.182973i
$406$	10.4186	+	6.45093i	0.517067	+	0.320154i
$407$	−0.0111138	−	0.0390610i	−0.000550892	−	0.00193618i
$408$	−1.20769	−	1.10095i	−0.0597895	−	0.0545053i
$409$	−33.6665	−	6.29336i	−1.66470	−	0.311187i	−0.734604	−	0.678497i	$-0.762632\pi$
$409$	−33.6665	−	6.29336i	−1.66470	−	0.311187i	−0.930099	+	0.367310i	$0.880279\pi$
$410$	23.8723	+	9.24817i	1.17897	+	0.456734i
$411$	−3.23446			−0.159544
$412$	3.37041	+	9.57290i	0.166048	+	0.471623i
$413$	−0.226690			−0.0111547
$414$	2.08283	+	0.806893i	0.102366	+	0.0396566i
$415$	36.0051	+	6.73053i	1.76742	+	0.330389i
$416$	−2.21498	−	2.01922i	−0.108598	−	0.0990006i
$417$	−5.04091	−	17.7170i	−0.246854	−	0.867603i
$418$	−0.196502	−	0.121669i	−0.00961122	−	0.00595102i
$419$	−7.70496	+	15.4736i	−0.376412	+	0.755937i	−0.999660	−	0.0260874i	$-0.991695\pi$
$419$	−7.70496	+	15.4736i	−0.376412	+	0.755937i	0.623248	+	0.782024i	$0.285813\pi$
$420$	−2.98208	−	5.98882i	−0.145510	−	0.292224i
$421$	−12.6301	−	4.89294i	−0.615555	−	0.238467i	0.0332194	−	0.999448i	$-0.489424\pi$
$421$	−12.6301	−	4.89294i	−0.615555	−	0.238467i	−0.648774	+	0.760981i	$0.724718\pi$
$422$	−1.19244	+	12.8685i	−0.0580471	+	0.626428i
$423$	7.41947	+	2.87432i	0.360747	+	0.139754i
$424$	−5.07095	−	6.71502i	−0.246267	−	0.326110i
$425$	−8.68356	+	17.4389i	−0.421214	+	0.845912i
$426$	−7.16684	+	6.53343i	−0.347234	+	0.316546i
$427$	−1.72615	−	18.6281i	−0.0835342	−	0.901477i
$428$	−1.56430	−	16.8815i	−0.0756135	−	0.816000i
$429$	0.190512	−	0.117960i	0.00919800	−	0.00569516i
$430$	−8.12609	−	7.40791i	−0.391875	−	0.357241i
$431$	−5.75572	+	1.07593i	−0.277243	+	0.0518257i	−0.320535	−	0.947237i	$-0.603863\pi$
$431$	−5.75572	+	1.07593i	−0.277243	+	0.0518257i	0.0432916	+	0.999062i	$0.486216\pi$
$432$	0.445738	−	0.895163i	0.0214456	−	0.0430686i
$433$	−3.07260	+	4.06878i	−0.147660	+	0.195533i	−0.865836	−	0.500329i	$-0.833213\pi$
$433$	−3.07260	+	4.06878i	−0.147660	+	0.195533i	0.718176	+	0.695861i	$0.244977\pi$
$434$	−2.67025	−	2.43426i	−0.128176	−	0.116848i
$435$	28.9003	−	11.1961i	1.38567	−	0.536810i
$436$	−5.05170	−	17.7549i	−0.241932	−	0.850304i
$437$	−5.87102	+	3.63518i	−0.280849	+	0.173894i
$438$	−2.19779	+	2.00355i	−0.105015	+	0.0957334i
$439$	−34.6601	−	21.4606i	−1.65424	−	1.02426i	−0.948995	−	0.315291i	$-0.897898\pi$
$439$	−34.6601	−	21.4606i	−1.65424	−	1.02426i	−0.705241	−	0.708968i	$-0.749161\pi$
$440$	−0.286761	+	0.111092i	−0.0136708	+	0.00529610i
$441$	1.19176	+	4.18860i	0.0567504	+	0.199457i
$442$	−1.34042	+	4.71110i	−0.0637574	+	0.224084i
$443$	−2.68103	−	28.9330i	−0.127380	−	1.37465i	−0.784157	−	0.620562i	$-0.786904\pi$
$443$	−2.68103	−	28.9330i	−0.127380	−	1.37465i	0.656777	−	0.754085i	$-0.271919\pi$
$444$	−0.148659	+	0.522483i	−0.00705505	+	0.0247959i
$445$	27.0525	+	16.7502i	1.28241	+	0.794036i
$446$	14.7127	−	2.75029i	0.696668	−	0.130230i
$447$	−9.36206	−	1.75007i	−0.442810	−	0.0827756i
$448$	0.724947	+	1.45589i	0.0342505	+	0.0687843i
$449$	21.8047	+	28.8741i	1.02903	+	1.36265i	0.929997	+	0.367567i	$0.119809\pi$
$449$	21.8047	+	28.8741i	1.02903	+	1.36265i	0.0990297	+	0.995084i	$0.468426\pi$
$450$	−11.7180	−	2.19048i	−0.552393	−	0.103260i
$451$	0.280395	−	0.371303i	0.0132033	−	0.0174840i
$452$	7.74182	−	7.05760i	0.364145	−	0.331962i
$453$	0.430377	−	1.51262i	0.0202209	−	0.0710691i
$454$	−20.2438	+	12.5345i	−0.950091	+	0.588271i
$455$	−12.0841	+	16.0019i	−0.566511	+	0.750181i
$456$	1.37799	+	2.76737i	0.0645302	+	0.129594i
$457$	3.69245	−	39.8478i	0.172725	−	1.86400i	−0.264151	−	0.964481i	$-0.585092\pi$
$457$	3.69245	−	39.8478i	0.172725	−	1.86400i	0.436876	−	0.899522i	$-0.356085\pi$
$458$	4.22396			0.197373
$459$	−1.63420			−0.0762779
$460$	−0.847781	+	9.14902i	−0.0395280	+	0.426575i
$461$	2.61490	+	3.46269i	0.121788	+	0.161274i	0.854827	−	0.518913i	$-0.173663\pi$
$461$	2.61490	+	3.46269i	0.121788	+	0.161274i	−0.733039	+	0.680187i	$0.761899\pi$
$462$	−0.119520	+	0.0223421i	−0.00556056	+	0.00103945i
$463$	−14.8015	+	5.73413i	−0.687883	+	0.266487i	−0.679712	−	0.733479i	$-0.737895\pi$
$463$	−14.8015	+	5.73413i	−0.687883	+	0.266487i	−0.00817144	+	0.999967i	$0.502601\pi$
$464$	−7.02571	+	2.72177i	−0.326160	+	0.126355i
$465$	−8.98321	+	1.67925i	−0.416586	+	0.0778735i
$466$	5.33239	+	7.06123i	0.247018	+	0.327105i
$467$	1.52855	−	16.4957i	0.0707330	−	0.763331i	−0.884317	−	0.466887i	$-0.845376\pi$
$467$	1.52855	−	16.4957i	0.0707330	−	0.763331i	0.955050	−	0.296444i	$-0.0958008\pi$
$468$	−2.99723			−0.138547
$469$	6.61052			0.305245
$470$	−3.01997	+	32.5907i	−0.139301	+	1.50329i
$471$	6.43293	+	12.9191i	0.296414	+	0.595279i
$472$	0.0839963	−	0.111229i	0.00386624	−	0.00511973i
$473$	−0.169911	+	0.105204i	−0.00781250	+	0.00483729i
$474$	−0.602675	+	2.11818i	−0.0276818	+	0.0972914i
$475$	27.2350	−	24.8280i	1.24963	−	1.13919i
$476$	1.60171	−	2.12101i	0.0734145	−	0.0972165i
$477$	−8.27136	−	1.54618i	−0.378719	−	0.0707949i
$478$	2.52261	+	3.34048i	0.115381	+	0.152790i
$479$	1.17766	+	2.36507i	0.0538089	+	0.108063i	0.920436	−	0.390894i	$-0.127834\pi$
$479$	1.17766	+	2.36507i	0.0538089	+	0.108063i	−0.866627	+	0.498957i	$0.833717\pi$
$480$	4.04347	+	0.755856i	0.184558	+	0.0345000i
$481$	1.60044	−	0.299173i	0.0729736	−	0.0136411i
$482$	8.48355	+	5.25279i	0.386415	+	0.239258i
$483$	−0.994169	+	3.49414i	−0.0452363	+	0.158989i
$484$	−1.01444	−	10.9475i	−0.0461107	−	0.497614i
$485$	−1.34733	+	4.73537i	−0.0611791	+	0.215022i
$486$	−0.273663	−	0.961826i	−0.0124136	−	0.0436293i
$487$	−24.2416	+	9.39126i	−1.09849	+	0.425558i	−0.841172	−	0.540768i	$-0.818134\pi$
$487$	−24.2416	+	9.39126i	−1.09849	+	0.425558i	−0.257321	+	0.966326i	$0.582840\pi$
$488$	9.77978	+	6.05539i	0.442710	+	0.274114i
$489$	−4.54310	+	4.14158i	−0.205446	+	0.187289i
$490$	−15.2305	+	9.43034i	−0.688045	+	0.426019i
$491$	3.07528	+	10.8085i	0.138786	+	0.487781i	0.999783	−	0.0208284i	$-0.00663038\pi$
$491$	3.07528	+	10.8085i	0.138786	+	0.487781i	−0.860997	+	0.508609i	$0.830160\pi$
$492$	−5.80338	+	2.24824i	−0.261636	+	0.101359i
$493$	9.09932	+	8.29513i	0.409813	+	0.373594i
$494$	5.58393	−	7.39432i	0.251233	−	0.332686i
$495$	−0.137077	+	0.275288i	−0.00616115	+	0.0123733i
$496$	2.18383	−	0.408228i	0.0980568	−	0.0183300i
$497$	−11.6561	−	10.6259i	−0.522848	−	0.476639i
$498$	−7.57077	+	4.68762i	−0.339254	+	0.210057i
$499$	−4.06971	−	43.9192i	−0.182185	−	1.96609i	−0.249538	−	0.968365i	$-0.580279\pi$
$499$	−4.06971	−	43.9192i	−0.182185	−	1.96609i	0.0673525	−	0.997729i	$-0.478545\pi$
$500$	−2.62684	−	28.3482i	−0.117476	−	1.26777i
$501$	−16.0878	+	14.6659i	−0.718749	+	0.655226i
$502$	9.89971	−	19.8813i	0.441846	−	0.887345i
$503$	−13.7827	−	18.2513i	−0.614542	−	0.813785i	0.379220	−	0.925307i	$-0.376192\pi$
$503$	−13.7827	−	18.2513i	−0.614542	−	0.813785i	−0.993762	+	0.111521i	$0.964428\pi$
$504$	1.51657	+	0.587522i	0.0675533	+	0.0261703i
$505$	−6.31144	+	68.1113i	−0.280855	+	3.03091i
$506$	0.155713	+	0.0603236i	0.00692230	+	0.00268171i
$507$	−1.79035	−	3.59550i	−0.0795121	−	0.159682i
$508$	8.62150	−	17.3143i	0.382517	−	0.768198i
$509$	31.9948	+	19.8103i	1.41814	+	0.878078i	0.999547	−	0.0300946i	$-0.00958087\pi$
$509$	31.9948	+	19.8103i	1.41814	+	0.878078i	0.418597	+	0.908172i	$0.362522\pi$
$510$	−1.83965	−	6.46568i	−0.0814609	−	0.286305i
$511$	−3.57448	−	3.25857i	−0.158126	−	0.144151i
$512$	−0.982973	−	0.183750i	−0.0434417	−	0.00812066i
$513$	2.88271	+	1.11677i	0.127275	+	0.0493065i
$514$	−5.95561			−0.262691
$515$	−8.94238	+	40.7786i	−0.394048	+	1.79692i
$516$	2.67312			0.117678
$517$	0.554682	+	0.214885i	0.0243949	+	0.00945063i
$518$	−0.868447	−	0.162341i	−0.0381574	−	0.00713285i
$519$	−14.0779	−	12.8337i	−0.617953	−	0.563339i
$520$	−3.37404	−	11.8585i	−0.147961	−	0.520030i
$521$	21.7440	+	13.4633i	0.952624	+	0.589840i	0.912377	−	0.409350i	$-0.134245\pi$
$521$	21.7440	+	13.4633i	0.952624	+	0.589840i	0.0402464	+	0.999190i	$0.487186\pi$
$522$	−3.35841	+	6.74460i	−0.146994	+	0.295203i
$523$	−1.22022	−	2.45053i	−0.0533565	−	0.107154i	0.866880	−	0.498516i	$-0.166122\pi$
$523$	−1.22022	−	2.45053i	−0.0533565	−	0.107154i	−0.920237	+	0.391362i	$0.872004\pi$
$524$	−8.33954	−	3.23075i	−0.364314	−	0.141136i
$525$	1.78892	−	19.3055i	0.0780749	−	0.842563i
$526$	−10.3302	−	4.00193i	−0.450417	−	0.174492i
$527$	−2.18794	−	2.89731i	−0.0953083	−	0.126209i
$528$	0.0333236	−	0.0669227i	0.00145022	−	0.00291244i
$529$	−13.3101	+	12.1338i	−0.578700	+	0.527555i
$530$	−3.19375	−	34.4660i	−0.138728	−	1.49711i
$531$	−0.0128605	−	0.138787i	−0.000558100	−	0.00602285i
$532$	−4.27485	+	2.64688i	−0.185338	+	0.114757i
$533$	13.7853	+	12.5669i	0.597106	+	0.544334i
$534$	−7.60337	+	1.42132i	−0.329030	+	0.0615064i
$535$	31.0858	−	62.4286i	1.34395	−	2.69902i
$536$	−2.44942	+	3.24356i	−0.105799	+	0.140100i
$537$	−16.0824	−	14.6611i	−0.694009	−	0.632672i
$538$	10.3560	−	4.01194i	0.446479	−	0.172967i
$539$	0.0890963	+	0.313141i	0.00383765	+	0.0134879i
$540$	3.49738	−	2.16549i	0.150503	−	0.0931877i
$541$	20.7901	−	18.9527i	0.893837	−	0.814840i	−0.0896210	−	0.995976i	$-0.528566\pi$
$541$	20.7901	−	18.9527i	0.893837	−	0.814840i	0.983458	+	0.181136i	$0.0579773\pi$
$542$	−7.44497	−	4.60973i	−0.319789	−	0.198005i
$543$	4.05166	−	1.56962i	0.173873	−	0.0673588i
$544$	0.447220	+	1.57182i	0.0191744	+	0.0673910i
$545$	20.7802	−	73.0349i	0.890127	−	3.12847i
$546$	−0.449779	−	4.85389i	−0.0192488	−	0.207727i
$547$	11.0728	−	38.9168i	0.473438	−	1.66396i	−0.245896	−	0.969296i	$-0.579082\pi$
$547$	11.0728	−	38.9168i	0.473438	−	1.66396i	0.719333	−	0.694665i	$-0.244447\pi$
$548$	2.74999	+	1.70272i	0.117474	+	0.0727367i
$549$	11.3068	−	2.11361i	0.482564	−	0.0902068i
$550$	−0.876043	−	0.163761i	−0.0373546	−	0.00698279i
$551$	−10.3824	−	20.8508i	−0.442307	−	0.888272i
$552$	−1.34608	−	1.78250i	−0.0572931	−	0.0758684i
$553$	−3.52075	−	0.658142i	−0.149717	−	0.0279870i
$554$	−10.9443	+	14.4926i	−0.464979	+	0.615732i
$555$	−1.65135	+	1.50540i	−0.0700958	+	0.0639007i
$556$	−5.04091	+	17.7170i	−0.213782	+	0.751366i
$557$	−1.92306	+	1.19071i	−0.0814829	+	0.0504520i	−0.566569	−	0.824014i	$-0.691729\pi$
$557$	−1.92306	+	1.19071i	−0.0814829	+	0.0504520i	0.485086	+	0.874466i	$0.338788\pi$
$558$	1.33885	−	1.77292i	0.0566779	−	0.0750537i
$559$	−3.57125	−	7.17203i	−0.151048	−	0.303344i
$560$	−0.617294	+	6.66166i	−0.0260854	+	0.281506i
$561$	−0.122173			−0.00515816
$562$	−27.3423			−1.15336
$563$	−0.833696	+	8.99702i	−0.0351361	+	0.379179i	0.959950	+	0.280170i	$0.0903908\pi$
$563$	−0.833696	+	8.99702i	−0.0351361	+	0.379179i	−0.995087	+	0.0990091i	$0.968433\pi$
$564$	−4.79502	−	6.34964i	−0.201907	−	0.267368i
$565$	42.3592	−	7.91831i	1.78207	−	0.333126i
$566$	−12.5980	+	4.88050i	−0.529534	+	0.205143i
$567$	1.51657	−	0.587522i	0.0636899	−	0.0246736i
$568$	9.53278	−	1.78198i	0.399986	−	0.0747704i
$569$	24.5096	+	32.4559i	1.02750	+	1.36062i	0.930890	+	0.365301i	$0.119034\pi$
$569$	24.5096	+	32.4559i	1.02750	+	1.36062i	0.0966054	+	0.995323i	$0.469202\pi$
$570$	−1.17336	+	12.6626i	−0.0491466	+	0.530377i
$571$	40.2401			1.68400			0.841998	−	0.539481i	$-0.181380\pi$
$571$	40.2401			1.68400			0.841998	+	0.539481i	$0.181380\pi$
$572$	−0.224074			−0.00936902
$573$	1.48839	−	16.0623i	0.0621785	−	0.671013i
$574$	−4.51181	−	9.06094i	−0.188319	−	0.378196i
$575$	−16.0467	+	21.2492i	−0.669192	+	0.886153i
$576$	−0.850217	+	0.526432i	−0.0354257	+	0.0219347i
$577$	1.30252	−	4.57789i	0.0542247	−	0.190580i	−0.929981	−	0.367607i	$-0.880177\pi$
$577$	1.30252	−	4.57789i	0.0542247	−	0.190580i	0.984206	+	0.177027i	$0.0566479\pi$
$578$	−10.5895	+	9.65365i	−0.440467	+	0.401539i
$579$	3.92000	−	5.19092i	0.162910	−	0.215727i
$580$	−30.4655	−	5.69499i	−1.26501	−	0.236472i
$581$	−8.72750	−	11.5571i	−0.362078	−	0.479469i
$582$	−0.533488	−	1.07139i	−0.0221138	−	0.0444105i
$583$	−0.618370	−	0.115593i	−0.0256103	−	0.00478739i
$584$	2.92333	−	0.546466i	0.120968	−	0.0226129i
$585$	−10.4825	−	6.49047i	−0.433397	−	0.268348i
$586$	8.96709	−	31.5160i	0.370427	−	1.30192i
$587$	0.295806	+	3.19225i	0.0122092	+	0.131758i	0.999657	−	0.0261870i	$-0.00833655\pi$
$587$	0.295806	+	3.19225i	0.0122092	+	0.131758i	−0.987448	+	0.157945i	$0.949513\pi$
$588$	1.19176	−	4.18860i	0.0491473	−	0.172735i
$589$	1.87957	+	6.60600i	0.0774463	+	0.272196i
$590$	0.534632	−	0.207118i	0.0220105	−	0.00852690i
$591$	9.80002	+	6.06791i	0.403119	+	0.249601i
$592$	0.401444	−	0.365965i	0.0164993	−	0.0150411i
$593$	−12.9847	+	8.03977i	−0.533216	+	0.330154i	−0.766489	−	0.642258i	$-0.777998\pi$
$593$	−12.9847	+	8.03977i	−0.533216	+	0.330154i	0.233272	+	0.972411i	$0.425057\pi$
$594$	−0.0204591	−	0.0719064i	−0.000839449	−	0.00295036i
$595$	10.1948	−	3.94950i	0.417947	−	0.161914i
$596$	7.03849	+	6.41643i	0.288308	+	0.262827i
$597$	8.91506	−	11.8054i	0.364869	−	0.483165i
$598$	−2.98414	+	5.99296i	−0.122030	+	0.245070i
$599$	−32.8142	+	6.13404i	−1.34075	+	0.250630i	−0.804764	−	0.593595i	$-0.797708\pi$
$599$	−32.8142	+	6.13404i	−1.34075	+	0.250630i	−0.535989	+	0.844225i	$0.680061\pi$
$600$	8.80972	+	8.03112i	0.359655	+	0.327869i
$601$	−37.2888	+	23.0882i	−1.52104	+	0.941789i	−0.525171	+	0.850997i	$0.675999\pi$
$601$	−37.2888	+	23.0882i	−1.52104	+	0.941789i	−0.995870	+	0.0907918i	$0.971060\pi$
$602$	0.401142	+	4.32901i	0.0163493	+	0.176437i
$603$	0.375027	+	4.04718i	0.0152723	+	0.164814i
$604$	−1.16221	+	1.05949i	−0.0472895	+	0.0431101i
$605$	20.1588	−	40.4843i	0.819572	−	1.64592i
$606$	−10.0211	−	13.2701i	−0.407081	−	0.539062i
$607$	3.14860	+	1.21978i	0.127798	+	0.0495092i	0.424291	−	0.905526i	$-0.360523\pi$
$607$	3.14860	+	1.21978i	0.127798	+	0.0495092i	−0.296494	+	0.955035i	$0.595817\pi$
$608$	0.285245	−	3.07828i	0.0115682	−	0.124841i
$609$	−11.4266	−	4.42668i	−0.463028	−	0.179378i
$610$	21.0908	+	42.3560i	0.853940	+	1.71494i
$611$	−10.6301	+	21.3481i	−0.430048	+	0.863653i
$612$	1.38942	+	0.860295i	0.0561642	+	0.0347754i
$613$	4.17909	+	14.6880i	0.168792	+	0.593242i	0.999341	+	0.0362964i	$0.0115560\pi$
$613$	4.17909	+	14.6880i	0.168792	+	0.593242i	−0.830549	+	0.556945i	$0.811973\pi$
$614$	−3.29101	−	3.00015i	−0.132814	−	0.121076i
$615$	−25.1652	−	4.70418i	−1.01476	−	0.189691i
$616$	0.113379	+	0.0439233i	0.00456818	+	0.00176972i
$617$	36.0742			1.45229			0.726147	−	0.687540i	$-0.241309\pi$
$617$	36.0742			1.45229			0.726147	+	0.687540i	$0.241309\pi$
$618$	−5.07204	−	8.79059i	−0.204027	−	0.353609i
$619$	8.05371			0.323706			0.161853	−	0.986815i	$-0.448253\pi$
$619$	8.05371			0.323706			0.161853	+	0.986815i	$0.448253\pi$
$620$	8.52169	+	3.30132i	0.342239	+	0.132584i
$621$	−2.19563	−	0.410435i	−0.0881077	−	0.0164702i
$622$	6.94179	+	6.32828i	0.278340	+	0.253741i
$623$	−3.44276	−	12.1000i	−0.137931	−	0.484778i
$624$	2.54830	+	1.57784i	0.102014	+	0.0631642i
$625$	25.6322	−	51.4765i	1.02529	−	2.05906i
$626$	−2.14477	−	4.30728i	−0.0857222	−	0.172153i
$627$	0.215513	+	0.0834900i	0.00860675	+	0.00333427i
$628$	1.33162	−	14.3705i	0.0531376	−	0.573446i
$629$	−0.827783	−	0.320685i	−0.0330059	−	0.0127865i
$630$	4.03174	+	5.33889i	0.160629	+	0.212707i
$631$	−9.10613	+	18.2876i	−0.362509	+	0.728017i	−0.999066	−	0.0432132i	$-0.986241\pi$
$631$	−9.10613	+	18.2876i	−0.362509	+	0.728017i	0.636557	+	0.771230i	$0.280358\pi$
$632$	1.62748	−	1.48365i	0.0647379	−	0.0590163i
$633$	−1.19244	−	12.8685i	−0.0473952	−	0.511476i
$634$	−0.630155	−	6.80046i	−0.0250267	−	0.270081i
$635$	67.6465	−	41.8849i	2.68447	−	1.66215i
$636$	6.21849	+	5.66890i	0.246579	+	0.224787i
$637$	−12.8302	+	2.39839i	−0.508352	+	0.0950275i
$638$	−0.251076	+	0.504229i	−0.00994020	+	0.0199626i
$639$	5.84429	−	7.73909i	0.231197	−	0.306154i
$640$	−3.03992	−	2.77126i	−0.120164	−	0.109544i
$641$	−2.43253	+	0.942366i	−0.0960790	+	0.0372212i	−0.408801	−	0.912623i	$-0.634053\pi$
$641$	−2.43253	+	0.942366i	−0.0960790	+	0.0372212i	0.312722	+	0.949845i	$0.398759\pi$
$642$	4.63964	+	16.3067i	0.183112	+	0.643572i
$643$	−10.4163	+	6.44947i	−0.410777	+	0.254342i	−0.716229	−	0.697865i	$-0.754133\pi$
$643$	−10.4163	+	6.44947i	−0.410777	+	0.254342i	0.305452	+	0.952207i	$0.401192\pi$
$644$	2.68469	−	2.44742i	0.105792	−	0.0964417i
$645$	9.34893	+	5.78861i	0.368114	+	0.227926i
$646$	−4.71093	+	1.82502i	−0.185349	+	0.0718046i
$647$	−6.16070	−	21.6526i	−0.242202	−	0.851252i	−0.983627	−	0.180216i	$-0.942320\pi$
$647$	−6.16070	−	21.6526i	−0.242202	−	0.851252i	0.741425	−	0.671036i	$-0.234150\pi$
$648$	−0.273663	+	0.961826i	−0.0107505	+	0.0377841i
$649$	−0.000961458	−	0.0103758i	−3.77405e−5	−	0.000407285i
$650$	9.77798	−	34.3660i	0.383524	−	1.34795i
$651$	3.07208	+	1.90215i	0.120404	+	0.0745512i
$652$	6.04288	−	1.12961i	0.236658	−	0.0442390i
$653$	24.0824	+	4.50178i	0.942417	+	0.176168i	0.632469	−	0.774586i	$-0.282041\pi$
$653$	24.0824	+	4.50178i	0.942417	+	0.176168i	0.309947	+	0.950754i	$0.399689\pi$
$654$	8.22813	+	16.5243i	0.321745	+	0.646152i
$655$	−22.1704	−	29.3583i	−0.866268	−	1.14712i
$656$	6.11768	+	1.14359i	0.238855	+	0.0446498i
$657$	1.79222	−	2.37328i	0.0699211	−	0.0925905i
$658$	9.56340	−	8.71819i	0.372820	−	0.339871i
$659$	4.89220	−	17.1943i	0.190573	−	0.669795i	−0.806352	−	0.591436i	$-0.798561\pi$
$659$	4.89220	−	17.1943i	0.190573	−	0.669795i	0.996925	−	0.0783590i	$-0.0249680\pi$
$660$	0.261465	−	0.161893i	0.0101775	−	0.00630166i
$661$	−9.98609	+	13.2237i	−0.388414	+	0.514343i	−0.949650	−	0.313313i	$-0.898561\pi$
$661$	−9.98609	+	13.2237i	−0.388414	+	0.514343i	0.561236	+	0.827656i	$0.310326\pi$
$662$	−15.2852	−	30.6967i	−0.594075	−	1.19306i
$663$	0.451938	−	4.87718i	0.0175518	−	0.189414i
$664$	8.90451			0.345562
$665$	−20.6826			−0.802035
$666$	0.0501220	−	0.540903i	0.00194219	−	0.0209596i
$667$	10.1421	+	13.4303i	0.392702	+	0.520022i
$668$	21.3987	−	4.00012i	0.827942	−	0.154769i
$669$	−13.9569	+	5.40692i	−0.539603	+	0.209044i
$670$	−15.5904	+	6.03977i	−0.602311	+	0.233337i
$671$	0.845303	−	0.158015i	0.0326326	−	0.00610008i
$672$	−0.980122	−	1.29789i	−0.0378090	−	0.0500672i
$673$	1.14205	−	12.3246i	0.0440226	−	0.475080i	−0.944974	−	0.327144i	$-0.893914\pi$
$673$	1.14205	−	12.3246i	0.0440226	−	0.475080i	0.988997	−	0.147935i	$-0.0472628\pi$
$674$	−2.63967			−0.101676
$675$	11.9210			0.458839
$676$	−0.370604	+	3.99945i	−0.0142540	+	0.153825i
$677$	−3.25899	−	6.54494i	−0.125253	−	0.251543i	0.823657	−	0.567088i	$-0.191930\pi$
$677$	−3.25899	−	6.54494i	−0.125253	−	0.251543i	−0.948910	+	0.315546i	$0.897812\pi$
$678$	−6.31317	+	8.35999i	−0.242456	+	0.321064i
$679$	1.65501	−	1.02474i	0.0635135	−	0.0393259i
$680$	−1.83965	+	6.46568i	−0.0705472	+	0.247948i
$681$	17.5960	−	16.0408i	0.674279	−	0.614686i
$682$	0.100093	−	0.132544i	0.00383275	−	0.00507538i
$683$	3.75896	+	0.702671i	0.143833	+	0.0268870i	0.255173	−	0.966895i	$-0.417867\pi$
$683$	3.75896	+	0.702671i	0.143833	+	0.0268870i	−0.111341	+	0.993782i	$0.535515\pi$
$684$	−1.86303	−	2.46705i	−0.0712347	−	0.0943299i
$685$	5.93054	+	11.9101i	0.226594	+	0.455063i
$686$	18.1530	+	3.39339i	0.693085	+	0.129560i
$687$	−4.15204	+	0.776150i	−0.158410	+	0.0296120i
$688$	−2.27274	−	1.40722i	−0.0866472	−	0.0536497i
$689$	6.90195	−	24.2578i	0.262943	−	0.924150i
$690$	−0.847781	−	9.14902i	−0.0322745	−	0.348297i
$691$	−11.1752	+	39.2766i	−0.425123	+	1.49415i	0.393232	+	0.919439i	$0.371357\pi$
$691$	−11.1752	+	39.2766i	−0.425123	+	1.49415i	−0.818355	+	0.574713i	$0.805114\pi$
$692$	5.21322	+	18.3226i	0.198177	+	0.696519i
$693$	0.113379	−	0.0439233i	0.00430692	−	0.00166851i
$694$	−20.2596	−	12.5442i	−0.769044	−	0.476172i
$695$	−55.9958	+	51.0469i	−2.12404	+	1.93632i
$696$	6.40596	−	3.96640i	0.242817	−	0.150346i
$697$	−2.78334	−	9.78242i	−0.105426	−	0.370536i
$698$	15.1386	−	5.86471i	0.573003	−	0.221983i
$699$	−6.53909	−	5.96117i	−0.247331	−	0.225472i
$700$	−11.6840	+	15.4722i	−0.441615	+	0.584792i
$701$	−6.17935	+	12.4098i	−0.233391	+	0.468712i	−0.980637	−	0.195836i	$-0.937258\pi$
$701$	−6.17935	+	12.4098i	−0.233391	+	0.468712i	0.747246	+	0.664548i	$0.231376\pi$
$702$	2.94620	−	0.550740i	0.111197	−	0.0207864i
$703$	1.24105	+	1.13137i	0.0468072	+	0.0426704i
$704$	−0.0635626	+	0.0393563i	−0.00239560	+	0.00148330i
$705$	−3.01997	−	32.5907i	−0.113739	−	1.22744i
$706$	1.09949	+	11.8654i	0.0413798	+	0.446559i
$707$	19.9866	−	18.2202i	0.751672	−	0.685240i
$708$	−0.0621278	+	0.124770i	−0.00233491	+	0.00468913i
$709$	−5.22240	−	6.91558i	−0.196131	−	0.259720i	0.689315	−	0.724462i	$-0.257912\pi$
$709$	−5.22240	−	6.91558i	−0.196131	−	0.259720i	−0.885446	+	0.464742i	$0.846147\pi$
$710$	37.1986	+	14.4108i	1.39604	+	0.540828i
$711$	0.203198	−	2.19286i	0.00762053	−	0.0822386i
$712$	7.21274	+	2.79423i	0.270309	+	0.104718i
$713$	−2.21195	−	4.44219i	−0.0828381	−	0.166361i
$714$	−1.18471	+	2.37921i	−0.0443366	+	0.0890398i
$715$	−0.783673	−	0.485230i	−0.0293077	−	0.0181466i
$716$	5.95550	+	20.9314i	0.222568	+	0.782244i
$717$	−3.09347	−	2.82007i	−0.115528	−	0.105317i
$718$	−1.50505	−	0.281343i	−0.0561681	−	0.0104996i
$719$	−30.2031	−	11.7008i	−1.12639	−	0.436365i	−0.275284	−	0.961363i	$-0.588772\pi$
$719$	−30.2031	−	11.7008i	−1.12639	−	0.436365i	−0.851103	+	0.524998i	$0.824066\pi$
$720$	−4.11351			−0.153302
$721$	13.4748	−	9.53310i	0.501830	−	0.355031i
$722$	−9.44280			−0.351425
$723$	−9.30430	−	3.60451i	−0.346031	−	0.134053i
$724$	−4.27109	−	0.798404i	−0.158734	−	0.0296725i
$725$	−66.3768	−	60.5105i	−2.46517	−	2.24730i
$726$	3.00876	+	10.5747i	0.111666	+	0.392464i
$727$	−29.6440	−	18.3548i	−1.09943	−	0.680741i	−0.148122	−	0.988969i	$-0.547323\pi$
$727$	−29.6440	−	18.3548i	−1.09943	−	0.680741i	−0.951313	+	0.308228i	$0.900264\pi$
$728$	−2.17283	+	4.36364i	−0.0805306	+	0.161727i
$729$	0.445738	+	0.895163i	0.0165088	+	0.0331542i
$730$	11.4074	+	4.41924i	0.422206	+	0.163563i
$731$	−0.403067	+	4.34978i	−0.0149080	+	0.160883i
$732$	−10.7259	−	4.15525i	−0.396442	−	0.153582i
$733$	−26.5367	−	35.1402i	−0.980154	−	1.29793i	−0.954484	−	0.298263i	$-0.903593\pi$
$733$	−26.5367	−	35.1402i	−0.980154	−	1.29793i	−0.0256698	−	0.999670i	$-0.508172\pi$
$734$	8.36848	−	16.8062i	0.308886	−	0.620327i
$735$	13.2384	−	12.0684i	0.488305	−	0.445149i
$736$	0.206097	+	2.22414i	0.00759682	+	0.0819828i
$737$	0.0280371	+	0.302569i	0.00103276	+	0.0111453i
$738$	5.29145	−	3.27633i	0.194781	−	0.120603i
$739$	16.0127	+	14.5975i	0.589037	+	0.536979i	0.912402	−	0.409296i	$-0.134226\pi$
$739$	16.0127	+	14.5975i	0.589037	+	0.536979i	−0.323364	+	0.946275i	$0.604814\pi$
$740$	2.19650	−	0.410596i	0.0807448	−	0.0150938i
$741$	−4.13015	+	8.29446i	−0.151725	+	0.304705i
$742$	−8.24737	+	10.9213i	−0.302770	+	0.400933i
$743$	−27.7085	−	25.2596i	−1.01653	−	0.926686i	−0.0192037	−	0.999816i	$-0.506113\pi$
$743$	−27.7085	−	25.2596i	−1.01653	−	0.926686i	−0.997322	+	0.0731296i	$0.976701\pi$
$744$	−2.07163	+	0.802555i	−0.0759498	+	0.0294231i
$745$	10.7216	+	37.6824i	0.392808	+	1.38058i
$746$	−18.0952	+	11.2041i	−0.662512	+	0.410210i
$747$	6.58051	−	5.99893i	0.240768	−	0.219489i
$748$	0.103874	+	0.0643160i	0.00379801	+	0.00235163i
$749$	−25.7117	+	9.96076i	−0.939484	+	0.363958i
$750$	7.79108	+	27.3828i	0.284490	+	0.999878i
$751$	−2.33140	+	8.19404i	−0.0850742	+	0.299005i	−0.992673	−	0.120835i	$-0.961443\pi$
$751$	−2.33140	+	8.19404i	−0.0850742	+	0.299005i	0.907598	+	0.419839i	$0.137914\pi$
$752$	0.734158	+	7.92283i	0.0267720	+	0.288916i
$753$	−6.07797	+	21.3618i	−0.221493	+	0.778469i
$754$	−19.2002	−	11.8882i	−0.699228	−	0.432944i
$755$	−6.35899	+	1.18870i	−0.231427	+	0.0432612i
$756$	−1.59870	−	0.298849i	−0.0581442	−	0.0108690i
$757$	−13.2203	−	26.5500i	−0.480501	−	0.964975i	−0.994255	−	0.107038i	$-0.965863\pi$
$757$	−13.2203	−	26.5500i	−0.480501	−	0.964975i	0.513754	−	0.857937i	$-0.328254\pi$
$758$	−11.0923	−	14.6886i	−0.402890	−	0.533513i
$759$	−0.164146	−	0.0306843i	−0.00595813	−	0.00111377i
$760$	7.66359	−	10.1482i	0.277988	−	0.368115i
$761$	−8.70395	+	7.93470i	−0.315518	+	0.287633i	−0.815925	−	0.578158i	$-0.803772\pi$
$761$	−8.70395	+	7.93470i	−0.315518	+	0.287633i	0.500407	+	0.865790i	$0.333184\pi$
$762$	−5.29320	+	18.6037i	−0.191753	+	0.673940i
$763$	−25.5257	+	15.8048i	−0.924091	+	0.572173i
$764$	−9.72118	+	12.8729i	−0.351700	+	0.465726i
$765$	2.99639	+	6.01756i	0.108335	+	0.217565i
$766$	−2.23076	+	24.0737i	−0.0806005	+	0.869818i
$767$	0.417760			0.0150844
$768$	1.00000			0.0360844
$769$	−1.57533	+	17.0005i	−0.0568077	+	0.613053i	0.918976	+	0.394314i	$0.129018\pi$
$769$	−1.57533	+	17.0005i	−0.0568077	+	0.613053i	−0.975783	+	0.218739i	$0.929806\pi$
$770$	0.301415	+	0.399138i	0.0108622	+	0.0143839i
$771$	5.85420	−	1.09434i	0.210834	−	0.0394117i
$772$	−6.06552	+	2.34980i	−0.218303	+	0.0845710i
$773$	−27.7568	+	10.7530i	−0.998342	+	0.386760i	−0.804293	−	0.594232i	$-0.797456\pi$
$773$	−27.7568	+	10.7530i	−0.998342	+	0.386760i	−0.194048	+	0.980992i	$0.562162\pi$
$774$	−2.62761	+	0.491185i	−0.0944474	+	0.0176553i
$775$	15.9604	+	21.1350i	0.573314	+	0.759191i
$776$	−0.110433	+	1.19176i	−0.00396430	+	0.0427816i
$777$	0.883490			0.0316950
$778$	−25.2964			−0.906918
$779$	−1.77526	+	19.1582i	−0.0636055	+	0.686412i
$780$	5.49558	+	11.0366i	0.196773	+	0.395174i
$781$	0.436921	−	0.578578i	0.0156343	−	0.0207031i
$782$	3.10351	−	1.92161i	0.110981	−	0.0687167i
$783$	2.06191	−	7.24687i	0.0736867	−	0.258982i
$784$	−3.21827	+	2.93384i	−0.114938	+	0.104780i
$785$	35.7763	−	47.3755i	1.27691	−	1.69090i
$786$	8.79119	+	1.64336i	0.313571	+	0.0586167i
$787$	8.04828	+	10.6576i	0.286890	+	0.379904i	0.918526	−	0.395362i	$-0.129381\pi$
$787$	8.04828	+	10.6576i	0.286890	+	0.379904i	−0.631635	+	0.775266i	$0.717616\pi$
$788$	−5.13780	−	10.3181i	−0.183026	−	0.367567i
$789$	10.8896	+	2.03563i	0.387681	+	0.0724702i
$790$	8.90475	−	1.66459i	0.316817	−	0.0592233i
$791$	−14.4860	−	8.96937i	−0.515064	−	0.318914i
$792$	−0.0204591	+	0.0719064i	−0.000726984	+	0.00255508i
$793$	3.18107	+	34.3292i	0.112963	+	1.21907i
$794$	0.114800	−	0.403479i	0.00407408	−	0.0143189i
$795$	9.47249	+	33.2923i	0.335955	+	1.18076i
$796$	−13.7945	+	5.34402i	−0.488933	+	0.189414i
$797$	−35.8013	−	22.1672i	−1.26815	−	0.785203i	−0.283367	−	0.959012i	$-0.591451\pi$
$797$	−35.8013	−	22.1672i	−1.26815	−	0.785203i	−0.984779	+	0.173809i	$0.944393\pi$
$798$	3.71570	−	3.38731i	0.131534	−	0.119910i
$799$	11.0553	−	6.84517i	0.391109	−	0.242165i
$800$	−3.26233	−	11.4659i	−0.115341	−	0.405381i
$801$	7.21274	−	2.79423i	0.254850	−	0.0987293i
$802$	22.7304	+	20.7215i	0.802637	+	0.731700i
$803$	0.133987	−	0.177427i	0.00472830	−	0.00626128i
$804$	1.81171	−	3.63841i	0.0638942	−	0.128317i
$805$	14.6892	−	2.74589i	0.517727	−	0.0967799i
$806$	4.92093	+	4.48602i	0.173332	+	0.158013i
$807$	−9.44248	+	5.84654i	−0.332391	+	0.205808i
$808$	1.53432	+	16.5579i	0.0539771	+	0.582506i
$809$	−3.32548	−	35.8877i	−0.116918	−	1.26174i	−0.828840	−	0.559485i	$-0.810999\pi$
$809$	−3.32548	−	35.8877i	−0.116918	−	1.26174i	0.711923	−	0.702258i	$-0.247825\pi$
$810$	−3.03992	+	2.77126i	−0.106812	+	0.0973720i
$811$	10.0801	−	20.2435i	0.353959	−	0.710846i	−0.644599	−	0.764521i	$-0.722976\pi$
$811$	10.0801	−	20.2435i	0.353959	−	0.710846i	0.998558	+	0.0536746i	$0.0170934\pi$
$812$	7.38472	+	9.77896i	0.259153	+	0.343174i
$813$	8.16525	+	3.16323i	0.286368	+	0.110939i
$814$	0.00374714	−	0.0404381i	0.000131337	−	0.00141735i
$815$	23.5804	+	9.13510i	0.825986	+	0.319989i
$816$	−0.728425	−	1.46288i	−0.0255000	−	0.0512109i
$817$	3.68353	−	7.39753i	0.128870	−	0.258807i
$818$	−29.1197	−	18.0301i	−1.01815	−	0.630409i
$819$	1.33402	+	4.68860i	0.0466145	+	0.163833i
$820$	18.9194	+	17.2473i	0.660694	+	0.602303i
$821$	22.8210	+	4.26598i	0.796457	+	0.148884i	0.566223	−	0.824252i	$-0.308404\pi$
$821$	22.8210	+	4.26598i	0.796457	+	0.148884i	0.230233	+	0.973135i	$0.426051\pi$
$822$	−3.01604	−	1.16842i	−0.105197	−	0.0407534i
$823$	17.6577			0.615508			0.307754	−	0.951466i	$-0.400423\pi$
$823$	17.6577			0.615508			0.307754	+	0.951466i	$0.400423\pi$
$824$	−0.315317	+	10.1440i	−0.0109846	+	0.353383i
$825$	0.891218			0.0310282
$826$	−0.211382	−	0.0818898i	−0.00735492	−	0.00284931i
$827$	43.8872	+	8.20395i	1.52611	+	0.285279i	0.878890	−	0.477025i	$-0.158285\pi$
$827$	43.8872	+	8.20395i	1.52611	+	0.285279i	0.647219	+	0.762304i	$0.275932\pi$
$828$	1.65070	+	1.50481i	0.0573657	+	0.0522958i
$829$	4.67007	+	16.4136i	0.162198	+	0.570068i	0.999720	+	0.0236639i	$0.00753315\pi$
$829$	4.67007	+	16.4136i	0.162198	+	0.570068i	−0.837522	+	0.546404i	$0.815996\pi$
$830$	31.1424	+	19.2826i	1.08097	+	0.669308i
$831$	8.09495	−	16.2569i	0.280811	−	0.563944i
$832$	−1.33598	−	2.68301i	−0.0463169	−	0.0930168i
$833$	6.63610	+	2.57084i	0.229927	+	0.0890743i
$834$	1.69960	−	18.3416i	0.0588522	−	0.635116i
$835$	83.5017	+	32.3487i	2.88969	+	1.11947i
$836$	−0.139281	−	0.184437i	−0.00481712	−	0.00637890i
$837$	−0.990278	+	1.98875i	−0.0342290	+	0.0687411i
$838$	−12.7744	+	11.6454i	−0.441284	+	0.402283i
$839$	4.27659	+	46.1518i	0.147644	+	1.59334i	0.671155	+	0.741317i	$0.265799\pi$
$839$	4.27659	+	46.1518i	0.147644	+	1.59334i	−0.523510	+	0.852019i	$0.675378\pi$
$840$	−0.617294	−	6.66166i	−0.0212987	−	0.229849i
$841$	−23.6094	+	14.6183i	−0.814116	+	0.504079i
$842$	−10.0097	−	9.12506i	−0.344957	−	0.314470i
$843$	26.8767	−	5.02413i	0.925683	−	0.173040i
$844$	−5.76055	+	11.5687i	−0.198286	+	0.398212i
$845$	−9.95690	+	13.1851i	−0.342528	+	0.453580i
$846$	5.88012	+	5.36044i	0.202163	+	0.184296i
$847$	−16.6738	+	6.45945i	−0.572918	+	0.221949i
$848$	−2.30277	−	8.09341i	−0.0790776	−	0.277929i
$849$	11.4867	−	7.11228i	0.394223	−	0.244093i
$850$	−14.3968	+	13.1245i	−0.493808	+	0.450165i
$851$	−1.03163	−	0.638758i	−0.0353638	−	0.0218963i
$852$	−9.04302	+	3.50329i	−0.309809	+	0.120021i
$853$	6.91958	+	24.3198i	0.236922	+	0.832694i	0.985504	+	0.169652i	$0.0542644\pi$
$853$	6.91958	+	24.3198i	0.236922	+	0.832694i	−0.748582	+	0.663042i	$0.769265\pi$
$854$	5.11966	−	17.9938i	0.175191	−	0.615734i
$855$	−1.17336	−	12.6626i	−0.0401280	−	0.433051i
$856$	4.63964	−	16.3067i	0.158580	−	0.557350i
$857$	2.97278	+	1.84067i	0.101548	+	0.0628759i	0.576267	−	0.817262i	$-0.304509\pi$
$857$	2.97278	+	1.84067i	0.101548	+	0.0628759i	−0.474719	+	0.880138i	$0.657450\pi$
$858$	0.220259	−	0.0411736i	0.00751952	−	0.00140564i
$859$	16.7625	+	3.13345i	0.571928	+	0.106912i	0.461766	−	0.887002i	$-0.347216\pi$
$859$	16.7625	+	3.13345i	0.571928	+	0.106912i	0.110162	+	0.993914i	$0.464863\pi$
$860$	−4.90131	−	9.84315i	−0.167133	−	0.335649i
$861$	6.09993	+	8.07762i	0.207885	+	0.275284i
$862$	−5.75572	−	1.07593i	−0.196040	−	0.0366463i
$863$	4.49197	−	5.94833i	0.152908	−	0.202483i	−0.715115	−	0.699007i	$-0.753626\pi$
$863$	4.49197	−	5.94833i	0.152908	−	0.202483i	0.868023	+	0.496524i	$0.165390\pi$
$864$	0.739009	−	0.673696i	0.0251416	−	0.0229196i
$865$	−21.4446	+	75.3701i	−0.729139	+	2.56266i
$866$	−4.33492	+	2.68407i	−0.147307	+	0.0912084i
$867$	8.63539	−	11.4351i	0.293273	−	0.388356i
$868$	−1.61058	−	3.23449i	−0.0546667	−	0.109786i
$869$	0.0151912	−	0.163939i	0.000515325	−	0.00556125i
$870$	30.9932			1.05077
$871$	−12.1823			−0.412782
$872$	1.70323	−	18.3808i	0.0576787	−	0.622453i
$873$	0.721272	+	0.955118i	0.0244114	+	0.0323259i
$874$	−6.78774	+	1.26885i	−0.229599	+	0.0429194i
$875$	−43.1761	+	16.7265i	−1.45962	+	0.565459i
$876$	−2.77315	+	1.07432i	−0.0936959	+	0.0362980i
$877$	21.0241	−	3.93009i	0.709935	−	0.132710i	0.183617	−	0.982998i	$-0.441219\pi$
$877$	21.0241	−	3.93009i	0.709935	−	0.132710i	0.526318	+	0.850288i	$0.323572\pi$
$878$	−24.5671	−	32.5321i	−0.829099	−	1.09791i
$879$	−3.02335	+	32.6271i	−0.101975	+	1.10049i
$880$	−0.307528			−0.0103668
$881$	56.0071			1.88693			0.943464	−	0.331474i	$-0.107546\pi$
$881$	56.0071			1.88693			0.943464	+	0.331474i	$0.107546\pi$
$882$	−0.401814	+	4.33626i	−0.0135298	+	0.146010i
$883$	11.8353	+	23.7686i	0.398291	+	0.799877i	0.999999	+	0.00116053i	$0.000369407\pi$
$883$	11.8353	+	23.7686i	0.398291	+	0.799877i	−0.601708	+	0.798716i	$0.705513\pi$
$884$	−2.95175	+	3.90875i	−0.0992782	+	0.131466i
$885$	−0.487471	+	0.301829i	−0.0163862	+	0.0101459i
$886$	7.95181	−	27.9477i	0.267146	−	0.938921i
$887$	−9.40030	+	8.56951i	−0.315631	+	0.287736i	−0.815971	−	0.578094i	$-0.803797\pi$
$887$	−9.40030	+	8.56951i	−0.315631	+	0.287736i	0.500339	+	0.865829i	$0.333209\pi$
$888$	−0.327363	+	0.433499i	−0.0109856	+	0.0145473i
$889$	−30.9222	−	5.78036i	−1.03710	−	0.193867i
$890$	19.1748	+	25.3916i	0.642742	+	0.851128i
$891$	0.0333236	+	0.0669227i	0.00111638	+	0.00224200i
$892$	14.7127	+	2.75029i	0.492619	+	0.0920864i
$893$	−24.1793	+	4.51989i	−0.809130	+	0.151253i
$894$	−8.09766	−	5.01386i	−0.270826	−	0.167689i
$895$	−24.4980	+	86.1017i	−0.818879	+	2.87806i
$896$	0.150065	+	1.61946i	0.00501331	+	0.0541023i
$897$	1.83212	−	6.43925i	0.0611728	−	0.215000i
$898$	9.90175	+	34.8010i	0.330426	+	1.16133i
$899$	15.6087	−	6.04685i	0.520580	−	0.201674i
$900$	−10.1354	−	6.27559i	−0.337848	−	0.209186i
$901$	−10.1623	+	9.26412i	−0.338554	+	0.308632i
$902$	0.395591	−	0.244940i	0.0131717	−	0.00815559i
$903$	−1.18976	−	4.18159i	−0.0395929	−	0.139155i
$904$	9.76854	−	3.78435i	0.324897	−	0.125866i
$905$	−13.2087	−	12.0413i	−0.439071	−	0.400266i
$906$	0.947736	−	1.25501i	0.0314864	−	0.0416948i
$907$	9.74411	−	19.5688i	0.323548	−	0.649772i	−0.672352	−	0.740231i	$-0.734716\pi$
$907$	9.74411	−	19.5688i	0.323548	−	0.649772i	0.995900	+	0.0904596i	$0.0288336\pi$
$908$	−23.4048	+	4.37511i	−0.776715	+	0.145193i
$909$	12.2889	+	11.2028i	0.407596	+	0.371573i
$910$	−17.0486	+	10.5561i	−0.565157	+	0.349930i
$911$	1.88210	+	20.3111i	0.0623568	+	0.672937i	0.968342	+	0.249628i	$0.0803082\pi$
$911$	1.88210	+	20.3111i	0.0623568	+	0.672937i	−0.905985	+	0.423310i	$0.860868\pi$
$912$	0.285245	+	3.07828i	0.00944541	+	0.101932i
$913$	0.491961	−	0.448482i	0.0162815	−	0.0148426i
$914$	17.8378	−	35.8231i	0.590022	−	1.18492i
$915$	−28.5145	−	37.7594i	−0.942662	−	1.24829i
$916$	3.93872	+	1.52587i	0.130139	+	0.0504162i
$917$	−1.34210	+	14.4836i	−0.0443200	+	0.478290i
$918$	−1.52385	−	0.590341i	−0.0502944	−	0.0194842i
$919$	−6.24826	−	12.5482i	−0.206111	−	0.413927i	0.767854	−	0.640625i	$-0.221325\pi$
$919$	−6.24826	−	12.5482i	−0.206111	−	0.413927i	−0.973965	+	0.226698i	$0.927207\pi$
$920$	−4.09554	+	8.22495i	−0.135026	+	0.271169i
$921$	3.78625	+	2.34435i	0.124761	+	0.0772489i
$922$	1.18746	+	4.17348i	0.0391068	+	0.137446i
$923$	21.4807	+	19.5822i	0.707045	+	0.644557i
$924$	−0.119520	−	0.0223421i	−0.00393191	−	0.000735001i
$925$	6.03843	+	2.33930i	0.198542	+	0.0769157i
$926$	−15.8734			−0.521632
$927$	6.60094	+	7.70893i	0.216803	+	0.253194i
$928$	−7.53450			−0.247332
$929$	29.5057	+	11.4306i	0.968051	+	0.375025i	0.792788	−	0.609497i	$-0.208629\pi$
$929$	29.5057	+	11.4306i	0.968051	+	0.375025i	0.175262	+	0.984522i	$0.443923\pi$
$930$	−8.98321	−	1.67925i	−0.294571	−	0.0550649i
$931$	−9.94918	−	9.06987i	−0.326071	−	0.297253i
$932$	2.42150	+	8.51068i	0.0793188	+	0.278777i
$933$	−7.98641	−	4.94498i	−0.261463	−	0.161891i
$934$	7.38427	−	14.8296i	0.241621	−	0.485240i
$935$	0.224011	+	0.449875i	0.00732595	+	0.0147125i
$936$	−2.79484	−	1.08273i	−0.0913521	−	0.0353900i
$937$	−3.27984	+	35.3951i	−0.107148	+	1.15631i	0.757120	+	0.653276i	$0.226606\pi$
$937$	−3.27984	+	35.3951i	−0.107148	+	1.15631i	−0.864268	+	0.503032i	$0.832218\pi$
$938$	6.16413	+	2.38799i	0.201266	+	0.0779708i
$939$	2.89971	+	3.83984i	0.0946285	+	0.125308i
$940$	−14.5891	+	29.2989i	−0.475845	+	0.955626i
$941$	31.5469	−	28.7588i	1.02840	−	0.937509i	0.0303239	−	0.999540i	$-0.490346\pi$
$941$	31.5469	−	28.7588i	1.02840	−	0.937509i	0.998074	+	0.0620313i	$0.0197579\pi$
$942$	1.33162	+	14.3705i	0.0433866	+	0.468216i
$943$	−1.28267	−	13.8422i	−0.0417696	−	0.450765i
$944$	0.118505	−	0.0733751i	0.00385700	−	0.00238816i
$945$	−4.94412	−	4.50716i	−0.160832	−	0.146618i
$946$	−0.196441	+	0.0367212i	−0.00638685	+	0.00119391i
$947$	−20.2991	+	40.7662i	−0.659633	+	1.32472i	0.272342	+	0.962200i	$0.412202\pi$
$947$	−20.2991	+	40.7662i	−0.659633	+	1.32472i	−0.931975	+	0.362522i	$0.881916\pi$
$948$	−1.32715	+	1.75744i	−0.0431039	+	0.0570789i
$949$	6.58730	+	6.00511i	0.213833	+	0.194934i
$950$	34.3648	−	13.3130i	1.11494	−	0.431930i
$951$	1.86901	+	6.56888i	0.0606067	+	0.213010i
$952$	2.25975	−	1.39918i	0.0732390	−	0.0453477i
$953$	−12.6475	+	11.5297i	−0.409693	+	0.373484i	−0.852143	−	0.523309i	$-0.824697\pi$
$953$	−12.6475	+	11.5297i	−0.409693	+	0.373484i	0.442451	+	0.896793i	$0.354109\pi$
$954$	−7.15426	−	4.42973i	−0.231628	−	0.143418i
$955$	−61.8748	+	23.9704i	−2.00222	+	0.775665i
$956$	1.14554	+	4.02617i	0.0370496	+	0.130216i
$957$	0.154149	−	0.541779i	0.00498294	−	0.0175132i
$958$	0.243778	+	2.63078i	0.00787611	+	0.0849967i
$959$	1.43961	−	5.05969i	0.0464873	−	0.163386i
$960$	3.49738	+	2.16549i	0.112877	+	0.0698908i
$961$	25.6204	−	4.78929i	0.826466	−	0.154493i
$962$	1.60044	+	0.299173i	0.0516001	+	0.00964573i
$963$	−7.55698	−	15.1765i	−0.243520	−	0.489055i
$964$	6.01315	+	7.96270i	0.193670	+	0.256461i
$965$	−26.3019	−	4.91668i	−0.846688	−	0.158273i
$966$	−2.18926	+	2.89905i	−0.0704384	+	0.0932755i
$967$	−10.1984	+	9.29711i	−0.327960	+	0.298975i	−0.820881	−	0.571099i	$-0.806517\pi$
$967$	−10.1984	+	9.29711i	−0.327960	+	0.298975i	0.492921	+	0.870074i	$0.335929\pi$
$968$	3.00876	−	10.5747i	0.0967053	−	0.339884i
$969$	4.29537	−	2.65958i	0.137987	−	0.0854380i
$970$	−2.96696	+	3.92889i	−0.0952634	+	0.126149i
$971$	−3.32528	−	6.67807i	−0.106713	−	0.214309i	0.835370	−	0.549688i	$-0.185253\pi$
$971$	−3.32528	−	6.67807i	−0.106713	−	0.214309i	−0.942083	+	0.335379i	$0.891136\pi$
$972$	0.0922684	−	0.995734i	0.00295951	−	0.0319382i
$973$	29.9584			0.960423
$974$	−25.9972			−0.833003
$975$	−3.29675	+	35.5776i	−0.105580	+	1.13939i
$976$	6.93192	+	9.17934i	0.221885	+	0.293824i
$977$	24.5095	−	4.58161i	0.784127	−	0.146579i	0.223563	−	0.974690i	$-0.428231\pi$
$977$	24.5095	−	4.58161i	0.784127	−	0.146579i	0.560565	+	0.828111i	$0.310584\pi$
$978$	−5.73243	+	2.22075i	−0.183303	+	0.0710119i
$979$	0.539227	−	0.208898i	0.0172338	−	0.00667640i
$980$	−17.6087	+	3.29163i	−0.562489	+	0.105147i
$981$	−11.1244	−	14.7310i	−0.355174	−	0.470326i
$982$	−1.03686	+	11.1895i	−0.0330877	+	0.357073i
$983$	26.6039			0.848532			0.424266	−	0.905538i	$-0.360532\pi$
$983$	26.6039			0.848532			0.424266	+	0.905538i	$0.360532\pi$
$984$	−6.22365			−0.198403
$985$	4.37485	−	47.2121i	0.139394	−	1.50430i
$986$	5.48832	+	11.0220i	0.174784	+	0.351013i
$987$	−7.79860	+	10.3270i	−0.248232	+	0.328713i
$988$	7.87800	−	4.87785i	0.250633	−	0.155185i
$989$	−1.63400	+	5.74293i	−0.0519583	+	0.182615i
$990$	−0.227266	+	0.207180i	−0.00722298	+	0.00658462i
$991$	−8.79063	+	11.6407i	−0.279244	+	0.369778i	−0.915926	−	0.401348i	$-0.868542\pi$
$991$	−8.79063	+	11.6407i	−0.279244	+	0.369778i	0.636682	+	0.771127i	$0.280306\pi$
$992$	2.18383	+	0.408228i	0.0693366	+	0.0129613i
$993$	20.6654	+	27.3654i	0.655797	+	0.868416i
$994$	−7.03046	−	14.1191i	−0.222993	−	0.447830i
$995$	−59.8170	−	11.1817i	−1.89633	−	0.354485i
$996$	−8.75289	+	1.63620i	−0.277346	+	0.0518450i
$997$	2.59983	+	1.60975i	0.0823374	+	0.0509812i	0.566983	−	0.823729i	$-0.308110\pi$
$997$	2.59983	+	1.60975i	0.0823374	+	0.0509812i	−0.484646	+	0.874710i	$0.661052\pi$
$998$	12.0706	−	42.4236i	0.382087	−	1.34290i
$999$	0.0501220	+	0.540903i	0.00158579	+	0.0171134i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	618.2.i.b.169.2	✓	32
103.64	even	17	inner	618.2.i.b.373.2	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
618.2.i.b.169.2	✓	32	1.1	even	1	trivial
618.2.i.b.373.2	yes	32	103.64	even	17	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 618 = 2 \cdot 3 \cdot 103 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	618.i (of order \(17\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(0.932472 + 0.361242i) q^{2} +(-0.982973 - 0.183750i) q^{3} +(0.739009 + 0.673696i) q^{4} +(1.12572 + 3.95648i) q^{5} +(-0.850217 - 0.526432i) q^{6} +(0.724947 - 1.45589i) q^{7} +(0.445738 + 0.895163i) q^{8} +(0.932472 + 0.361242i) q^{9} +O(q^{10})\)	\(q+(0.932472 + 0.361242i) q^{2} +(-0.982973 - 0.183750i) q^{3} +(0.739009 + 0.673696i) q^{4} +(1.12572 + 3.95648i) q^{5} +(-0.850217 - 0.526432i) q^{6} +(0.724947 - 1.45589i) q^{7} +(0.445738 + 0.895163i) q^{8} +(0.932472 + 0.361242i) q^{9} +(-0.379547 + 4.09597i) q^{10} +(0.0697120 + 0.0270066i) q^{11} +(-0.602635 - 0.798017i) q^{12} +(-1.33598 + 2.68301i) q^{13} +(1.20192 - 1.09570i) q^{14} +(-0.379547 - 4.09597i) q^{15} +(0.0922684 + 0.995734i) q^{16} +(1.38942 - 0.860295i) q^{17} +(0.739009 + 0.673696i) q^{18} +(-3.03883 + 0.568057i) q^{19} +(-1.83355 + 3.68227i) q^{20} +(-0.980122 + 1.29789i) q^{21} +(0.0552486 + 0.0503657i) q^{22} +(2.08283 - 0.806893i) q^{23} +(-0.273663 - 0.961826i) q^{24} +(-10.1354 + 6.27559i) q^{25} +(-2.21498 + 2.01922i) q^{26} +(-0.850217 - 0.526432i) q^{27} +(1.51657 - 0.587522i) q^{28} +(2.06191 + 7.24687i) q^{29} +(1.12572 - 3.95648i) q^{30} +(-0.204989 - 2.21218i) q^{31} +(-0.273663 + 0.961826i) q^{32} +(-0.0635626 - 0.0393563i) q^{33} +(1.60637 - 0.300283i) q^{34} +(6.57628 + 1.22932i) q^{35} +(0.445738 + 0.895163i) q^{36} +(-0.327363 - 0.433499i) q^{37} +(-3.03883 - 0.568057i) q^{38} +(1.80624 - 2.39184i) q^{39} +(-3.03992 + 2.77126i) q^{40} +(1.70318 - 5.98606i) q^{41} +(-1.38279 + 0.856187i) q^{42} +(-1.61092 + 2.13320i) q^{43} +(0.0333236 + 0.0669227i) q^{44} +(-0.379547 + 4.09597i) q^{45} +2.23367 q^{46} +7.95677 q^{47} +(0.0922684 - 0.995734i) q^{48} +(2.62438 + 3.47524i) q^{49} +(-11.7180 + 2.19048i) q^{50} +(-1.52385 + 0.590341i) q^{51} +(-2.79484 + 1.08273i) q^{52} +(-8.27136 + 1.54618i) q^{53} +(-0.602635 - 0.798017i) q^{54} +(-0.0283751 + 0.306216i) q^{55} +1.62639 q^{56} +3.09147 q^{57} +(-0.695196 + 7.50235i) q^{58} +(-0.0621278 - 0.124770i) q^{59} +(2.47895 - 3.28265i) q^{60} +(9.77978 - 6.05539i) q^{61} +(0.607985 - 2.13685i) q^{62} +(1.20192 - 1.09570i) q^{63} +(-0.602635 + 0.798017i) q^{64} +(-12.1192 - 2.26548i) q^{65} +(-0.0450532 - 0.0596601i) q^{66} +(1.81171 + 3.63841i) q^{67} +(1.60637 + 0.300283i) q^{68} +(-2.19563 + 0.410435i) q^{69} +(5.68812 + 3.52194i) q^{70} +(2.65396 - 9.32769i) q^{71} +(0.0922684 + 0.995734i) q^{72} +(0.813866 - 2.86044i) q^{73} +(-0.148659 - 0.522483i) q^{74} +(11.1160 - 4.30636i) q^{75} +(-2.62842 - 1.62745i) q^{76} +(0.0898560 - 0.0819146i) q^{77} +(2.54830 - 1.57784i) q^{78} +(-0.602675 - 2.11818i) q^{79} +(-3.83574 + 1.48597i) q^{80} +(0.739009 + 0.673696i) q^{81} +(3.75059 - 4.96658i) q^{82} +(3.96908 - 7.97099i) q^{83} +(-1.59870 + 0.298849i) q^{84} +(4.96784 + 4.52879i) q^{85} +(-2.27274 + 1.40722i) q^{86} +(-0.695196 - 7.50235i) q^{87} +(0.00689802 + 0.0744415i) q^{88} +(5.71629 - 5.21109i) q^{89} +(-1.83355 + 3.68227i) q^{90} +(2.93766 + 3.89008i) q^{91} +(2.08283 + 0.806893i) q^{92} +(-0.204989 + 2.21218i) q^{93} +(7.41947 + 2.87432i) q^{94} +(-5.66837 - 11.3836i) q^{95} +(0.445738 - 0.895163i) q^{96} +(1.01759 + 0.630068i) q^{97} +(1.19176 + 4.18860i) q^{98} +(0.0552486 + 0.0503657i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 2 q^{2} - 2 q^{3} - 2 q^{4} + q^{5} - 2 q^{6} + 6 q^{7} - 2 q^{8} - 2 q^{9}+O(q^{10}) \) 32 * q - 2 * q^2 - 2 * q^3 - 2 * q^4 + q^5 - 2 * q^6 + 6 * q^7 - 2 * q^8 - 2 * q^9	\( 32 q - 2 q^{2} - 2 q^{3} - 2 q^{4} + q^{5} - 2 q^{6} + 6 q^{7} - 2 q^{8} - 2 q^{9} + q^{10} + 5 q^{11} - 2 q^{12} - 14 q^{13} + 6 q^{14} + q^{15} - 2 q^{16} + 32 q^{17} - 2 q^{18} - 3 q^{19} + q^{20} - 11 q^{21} - 12 q^{22} - 15 q^{23} - 2 q^{24} - 15 q^{25} - 31 q^{26} - 2 q^{27} + 6 q^{28} + 7 q^{29} + q^{30} + 6 q^{31} - 2 q^{32} + 5 q^{33} - 2 q^{34} + 41 q^{35} - 2 q^{36} - 13 q^{37} - 3 q^{38} - 14 q^{39} - 16 q^{40} - 5 q^{41} - 11 q^{42} - 3 q^{43} - 12 q^{44} + q^{45} - 66 q^{46} - 14 q^{47} - 2 q^{48} - 6 q^{49} - 15 q^{50} - 2 q^{51} + 20 q^{52} - 6 q^{53} - 2 q^{54} + 11 q^{55} + 6 q^{56} + 14 q^{57} + 24 q^{58} - 43 q^{59} + 18 q^{60} + 48 q^{61} + 6 q^{62} + 6 q^{63} - 2 q^{64} - 84 q^{65} + 5 q^{66} + 7 q^{67} - 2 q^{68} + 19 q^{69} - 10 q^{70} - 59 q^{71} - 2 q^{72} - 9 q^{73} + 21 q^{74} + 19 q^{75} - 3 q^{76} - 33 q^{77} + 20 q^{78} + 33 q^{79} + q^{80} - 2 q^{81} + 46 q^{82} + 71 q^{83} - 11 q^{84} + 42 q^{85} - 20 q^{86} + 24 q^{87} - 12 q^{88} - q^{89} + q^{90} + 50 q^{91} - 15 q^{92} + 6 q^{93} + 20 q^{94} - 5 q^{95} - 2 q^{96} - 61 q^{97} - 57 q^{98} - 12 q^{99}+O(q^{100}) \) 32 * q - 2 * q^2 - 2 * q^3 - 2 * q^4 + q^5 - 2 * q^6 + 6 * q^7 - 2 * q^8 - 2 * q^9 + q^10 + 5 * q^11 - 2 * q^12 - 14 * q^13 + 6 * q^14 + q^15 - 2 * q^16 + 32 * q^17 - 2 * q^18 - 3 * q^19 + q^20 - 11 * q^21 - 12 * q^22 - 15 * q^23 - 2 * q^24 - 15 * q^25 - 31 * q^26 - 2 * q^27 + 6 * q^28 + 7 * q^29 + q^30 + 6 * q^31 - 2 * q^32 + 5 * q^33 - 2 * q^34 + 41 * q^35 - 2 * q^36 - 13 * q^37 - 3 * q^38 - 14 * q^39 - 16 * q^40 - 5 * q^41 - 11 * q^42 - 3 * q^43 - 12 * q^44 + q^45 - 66 * q^46 - 14 * q^47 - 2 * q^48 - 6 * q^49 - 15 * q^50 - 2 * q^51 + 20 * q^52 - 6 * q^53 - 2 * q^54 + 11 * q^55 + 6 * q^56 + 14 * q^57 + 24 * q^58 - 43 * q^59 + 18 * q^60 + 48 * q^61 + 6 * q^62 + 6 * q^63 - 2 * q^64 - 84 * q^65 + 5 * q^66 + 7 * q^67 - 2 * q^68 + 19 * q^69 - 10 * q^70 - 59 * q^71 - 2 * q^72 - 9 * q^73 + 21 * q^74 + 19 * q^75 - 3 * q^76 - 33 * q^77 + 20 * q^78 + 33 * q^79 + q^80 - 2 * q^81 + 46 * q^82 + 71 * q^83 - 11 * q^84 + 42 * q^85 - 20 * q^86 + 24 * q^87 - 12 * q^88 - q^89 + q^90 + 50 * q^91 - 15 * q^92 + 6 * q^93 + 20 * q^94 - 5 * q^95 - 2 * q^96 - 61 * q^97 - 57 * q^98 - 12 * q^99

Introduction

L-functions

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