LMFDB - Embedded newform 945.2.bs.a.16.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [945,2,Mod(16,945)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(945, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([4, 0, 6]))

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

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

chi := DirichletCharacter("945.16");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 945 = 3^{3} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	945.bs (of order $9$, degree $6$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$7.54586299101$
Analytic rank:	$0$
Dimension:	$276$
Relative dimension:	$46$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			16.19
Character	$\chi$	$=$	945.16
Dual form			945.2.bs.a.886.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.736718 + 0.268143i) q^{2} +(1.69896 - 0.336949i) q^{3} +(-1.06124 + 0.890484i) q^{4} +(-0.766044 + 0.642788i) q^{5} +(-1.16130 + 0.703801i) q^{6} +(1.87165 + 1.87001i) q^{7} +(1.32705 - 2.29852i) q^{8} +(2.77293 - 1.14493i) q^{9} +O(q^{10})$	\(q+(-0.736718 + 0.268143i) q^{2} +(1.69896 - 0.336949i) q^{3} +(-1.06124 + 0.890484i) q^{4} +(-0.766044 + 0.642788i) q^{5} +(-1.16130 + 0.703801i) q^{6} +(1.87165 + 1.87001i) q^{7} +(1.32705 - 2.29852i) q^{8} +(2.77293 - 1.14493i) q^{9} +(0.391999 - 0.678963i) q^{10} +(-4.50539 - 3.78047i) q^{11} +(-1.50295 + 1.87048i) q^{12} +(1.90995 - 1.60264i) q^{13} +(-1.88031 - 0.875801i) q^{14} +(-1.08489 + 1.35019i) q^{15} +(0.119796 - 0.679397i) q^{16} +(3.55730 - 6.16143i) q^{17} +(-1.73586 + 1.58703i) q^{18} +(2.94921 + 5.10817i) q^{19} +(0.240563 - 1.36430i) q^{20} +(3.80995 + 2.54643i) q^{21} +(4.33291 + 1.57705i) q^{22} +(8.36859 + 3.04592i) q^{23} +(1.48013 - 4.35225i) q^{24} +(0.173648 - 0.984808i) q^{25} +(-0.977356 + 1.69283i) q^{26} +(4.32532 - 2.87952i) q^{27} +(-3.65147 - 0.317856i) q^{28} +(0.957073 + 0.803080i) q^{29} +(0.437215 - 1.28561i) q^{30} +(-2.02940 + 1.70287i) q^{31} +(1.01568 + 5.76022i) q^{32} +(-8.92831 - 4.90478i) q^{33} +(-0.968581 + 5.49310i) q^{34} +(-2.63578 - 0.229441i) q^{35} +(-1.92320 + 3.68429i) q^{36} -0.982650 q^{37} +(-3.54245 - 2.97247i) q^{38} +(2.70492 - 3.36637i) q^{39} +(0.460881 + 2.61378i) q^{40} +(-5.47266 + 4.59211i) q^{41} +(-3.48966 - 0.854384i) q^{42} +(1.63493 - 0.595067i) q^{43} +8.14774 q^{44} +(-1.38824 + 2.65947i) q^{45} -6.98203 q^{46} +(5.54799 + 4.65532i) q^{47} +(-0.0253934 - 1.19463i) q^{48} +(0.00611490 + 7.00000i) q^{49} +(0.136140 + 0.772088i) q^{50} +(3.96763 - 11.6666i) q^{51} +(-0.599786 + 3.40156i) q^{52} +(1.11625 + 1.93340i) q^{53} +(-2.41441 + 3.28120i) q^{54} +5.88137 q^{55} +(6.78204 - 1.82042i) q^{56} +(6.73178 + 7.68485i) q^{57} +(-0.920433 - 0.335010i) q^{58} +(0.752151 + 4.26566i) q^{59} +(-0.0509926 - 2.39895i) q^{60} +(-0.587618 - 0.493070i) q^{61} +(1.03848 - 1.79871i) q^{62} +(7.33097 + 3.04252i) q^{63} +(-1.60296 - 2.77640i) q^{64} +(-0.432950 + 2.45538i) q^{65} +(7.89282 + 1.21938i) q^{66} +(6.96571 + 2.53531i) q^{67} +(1.71151 + 9.70645i) q^{68} +(15.2442 + 2.35511i) q^{69} +(2.00335 - 0.537734i) q^{70} +(-5.31779 - 9.21068i) q^{71} +(1.04819 - 7.89302i) q^{72} -14.3614 q^{73} +(0.723936 - 0.263491i) q^{74} +(-0.0368086 - 1.73166i) q^{75} +(-7.67855 - 2.79476i) q^{76} +(-1.36297 - 15.5008i) q^{77} +(-1.09009 + 3.20537i) q^{78} +(9.05526 - 3.29584i) q^{79} +(0.344939 + 0.597452i) q^{80} +(6.37829 - 6.34960i) q^{81} +(2.80046 - 4.85055i) q^{82} +(3.66164 + 3.07248i) q^{83} +(-6.31081 + 0.690336i) q^{84} +(1.23544 + 7.00651i) q^{85} +(-1.04492 + 0.876793i) q^{86} +(1.89663 + 1.04192i) q^{87} +(-14.6684 + 5.33886i) q^{88} +(-8.02786 - 13.9047i) q^{89} +(0.309625 - 2.33153i) q^{90} +(6.57170 + 0.572057i) q^{91} +(-11.5934 + 4.21965i) q^{92} +(-2.87409 + 3.57692i) q^{93} +(-5.33560 - 1.94200i) q^{94} +(-5.54269 - 2.01738i) q^{95} +(3.66650 + 9.44414i) q^{96} +(0.795243 - 0.289445i) q^{97} +(-1.88151 - 5.15538i) q^{98} +(-16.8215 - 5.32465i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 276 q - 6 q^{3} + 6 q^{9}+O(q^{10}) $ 276 * q - 6 * q^3 + 6 * q^9	$ 276 q - 6 q^{3} + 6 q^{9} + 6 q^{11} + 42 q^{12} + 3 q^{13} + 36 q^{14} - 24 q^{17} + 42 q^{22} + 9 q^{23} + 60 q^{24} - 24 q^{27} - 12 q^{31} - 78 q^{33} - 60 q^{34} + 18 q^{36} - 96 q^{37} - 60 q^{38} - 30 q^{39} + 48 q^{41} - 63 q^{42} - 15 q^{43} + 6 q^{45} - 120 q^{46} + 27 q^{47} - 66 q^{48} + 18 q^{49} - 48 q^{51} + 102 q^{52} - 75 q^{54} - 33 q^{56} - 12 q^{57} - 30 q^{59} - 12 q^{61} - 81 q^{62} - 162 q^{63} - 54 q^{64} - 3 q^{65} + 54 q^{66} - 18 q^{67} - 57 q^{68} + 90 q^{69} + 9 q^{70} + 12 q^{71} - 147 q^{72} + 36 q^{73} - 78 q^{74} - 108 q^{76} - 45 q^{77} + 102 q^{78} - 9 q^{79} + 102 q^{80} + 6 q^{81} - 42 q^{83} + 21 q^{84} + 18 q^{85} + 3 q^{86} - 30 q^{87} + 84 q^{88} + 30 q^{90} + 18 q^{91} - 24 q^{92} - 12 q^{93} + 156 q^{94} + 168 q^{96} + 45 q^{97} - 24 q^{98} - 102 q^{99}+O(q^{100}) $ 276 * q - 6 * q^3 + 6 * q^9 + 6 * q^11 + 42 * q^12 + 3 * q^13 + 36 * q^14 - 24 * q^17 + 42 * q^22 + 9 * q^23 + 60 * q^24 - 24 * q^27 - 12 * q^31 - 78 * q^33 - 60 * q^34 + 18 * q^36 - 96 * q^37 - 60 * q^38 - 30 * q^39 + 48 * q^41 - 63 * q^42 - 15 * q^43 + 6 * q^45 - 120 * q^46 + 27 * q^47 - 66 * q^48 + 18 * q^49 - 48 * q^51 + 102 * q^52 - 75 * q^54 - 33 * q^56 - 12 * q^57 - 30 * q^59 - 12 * q^61 - 81 * q^62 - 162 * q^63 - 54 * q^64 - 3 * q^65 + 54 * q^66 - 18 * q^67 - 57 * q^68 + 90 * q^69 + 9 * q^70 + 12 * q^71 - 147 * q^72 + 36 * q^73 - 78 * q^74 - 108 * q^76 - 45 * q^77 + 102 * q^78 - 9 * q^79 + 102 * q^80 + 6 * q^81 - 42 * q^83 + 21 * q^84 + 18 * q^85 + 3 * q^86 - 30 * q^87 + 84 * q^88 + 30 * q^90 + 18 * q^91 - 24 * q^92 - 12 * q^93 + 156 * q^94 + 168 * q^96 + 45 * q^97 - 24 * q^98 - 102 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/945\mathbb{Z}\right)^\times$.

$n$	$136$	$596$	$757$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{9}\right)$	$1$

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 $

$2$	−0.736718	+	0.268143i	−0.520938	+	0.189606i	−0.589088	−	0.808069i	$-0.700513\pi$
$2$	−0.736718	+	0.268143i	−0.520938	+	0.189606i	0.0681496	+	0.997675i	$0.478290\pi$
$3$	1.69896	−	0.336949i	0.980895	−	0.194538i
$3$	1.69896	−	0.336949i	0.980895	−	0.194538i
$4$	−1.06124	+	0.890484i	−0.530618	+	0.445242i
$5$	−0.766044	+	0.642788i	−0.342585	+	0.287463i
$5$	−0.766044	+	0.642788i	−0.342585	+	0.287463i
$6$	−1.16130	+	0.703801i	−0.474100	+	0.287325i
$7$	1.87165	+	1.87001i	0.707416	+	0.706798i
$7$	1.87165	+	1.87001i	0.707416	+	0.706798i
$8$	1.32705	−	2.29852i	0.469184	−	0.812651i
$9$	2.77293	−	1.14493i	0.924310	−	0.381642i
$10$	0.391999	−	0.678963i	0.123961	−	0.214707i
$11$	−4.50539	−	3.78047i	−1.35843	−	1.13986i	−0.976465	−	0.215677i	$-0.930804\pi$
$11$	−4.50539	−	3.78047i	−1.35843	−	1.13986i	−0.381962	−	0.924178i	$-0.624751\pi$
$12$	−1.50295	+	1.87048i	−0.433865	+	0.539961i
$13$	1.90995	−	1.60264i	0.529725	−	0.444492i	−0.338282	−	0.941045i	$-0.609846\pi$
$13$	1.90995	−	1.60264i	0.529725	−	0.444492i	0.868006	+	0.496553i	$0.165401\pi$
$14$	−1.88031	−	0.875801i	−0.502533	−	0.234068i
$15$	−1.08489	+	1.35019i	−0.280118	+	0.348617i
$16$	0.119796	−	0.679397i	0.0299490	−	0.169849i
$17$	3.55730	−	6.16143i	0.862772	−	1.49437i	−0.00647039	−	0.999979i	$-0.502060\pi$
$17$	3.55730	−	6.16143i	0.862772	−	1.49437i	0.869242	−	0.494386i	$-0.164607\pi$
$18$	−1.73586	+	1.58703i	−0.409147	+	0.374066i
$19$	2.94921	+	5.10817i	0.676594	+	1.17190i	0.976000	+	0.217770i	$0.0698782\pi$
$19$	2.94921	+	5.10817i	0.676594	+	1.17190i	−0.299406	+	0.954126i	$0.596788\pi$
$20$	0.240563	−	1.36430i	0.0537915	−	0.305067i
$21$	3.80995	+	2.54643i	0.831399	+	0.555676i
$22$	4.33291	+	1.57705i	0.923779	+	0.336228i
$23$	8.36859	+	3.04592i	1.74497	+	0.635118i	0.999506	−	0.0314263i	$-0.0100050\pi$
$23$	8.36859	+	3.04592i	1.74497	+	0.635118i	0.745466	+	0.666544i	$0.232227\pi$
$24$	1.48013	−	4.35225i	0.302129	−	0.888399i
$25$	0.173648	−	0.984808i	0.0347296	−	0.196962i
$26$	−0.977356	+	1.69283i	−0.191675	+	0.331991i
$27$	4.32532	−	2.87952i	0.832408	−	0.554164i
$28$	−3.65147	−	0.317856i	−0.690064	−	0.0600691i
$29$	0.957073	+	0.803080i	0.177724	+	0.149128i	0.727310	−	0.686309i	$-0.240770\pi$
$29$	0.957073	+	0.803080i	0.177724	+	0.149128i	−0.549586	+	0.835437i	$0.685215\pi$
$30$	0.437215	−	1.28561i	0.0798242	−	0.234720i
$31$	−2.02940	+	1.70287i	−0.364492	+	0.305845i	−0.806578	−	0.591128i	$-0.798683\pi$
$31$	−2.02940	+	1.70287i	−0.364492	+	0.305845i	0.442086	+	0.896972i	$0.354238\pi$
$32$	1.01568	+	5.76022i	0.179549	+	1.01827i
$33$	−8.92831	−	4.90478i	−1.55422	−	0.853813i
$34$	−0.968581	+	5.49310i	−0.166110	+	0.942058i
$35$	−2.63578	−	0.229441i	−0.445529	−	0.0387826i
$36$	−1.92320	+	3.68429i	−0.320533	+	0.614048i
$37$	−0.982650			−0.161547			−0.0807733	−	0.996732i	$-0.525739\pi$
$37$	−0.982650			−0.161547			−0.0807733	+	0.996732i	$0.525739\pi$
$38$	−3.54245	−	2.97247i	−0.574662	−	0.482199i
$39$	2.70492	−	3.36637i	0.433134	−	0.539051i
$40$	0.460881	+	2.61378i	0.0728716	+	0.413276i
$41$	−5.47266	+	4.59211i	−0.854687	+	0.717167i	−0.960817	−	0.277185i	$-0.910598\pi$
$41$	−5.47266	+	4.59211i	−0.854687	+	0.717167i	0.106130	+	0.994352i	$0.466154\pi$
$42$	−3.48966	−	0.854384i	−0.538467	−	0.131834i
$43$	1.63493	−	0.595067i	0.249325	−	0.0907469i	−0.214335	−	0.976760i	$-0.568758\pi$
$43$	1.63493	−	0.595067i	0.249325	−	0.0907469i	0.463660	+	0.886013i	$0.346536\pi$
$44$	8.14774			1.22832
$45$	−1.38824	+	2.65947i	−0.206947	+	0.396450i
$46$	−6.98203			−1.02944
$47$	5.54799	+	4.65532i	0.809258	+	0.679048i	0.950431	−	0.310937i	$-0.100643\pi$
$47$	5.54799	+	4.65532i	0.809258	+	0.679048i	−0.141172	+	0.989985i	$0.545087\pi$
$48$	−0.0253934	−	1.19463i	−0.00366522	−	0.172430i
$49$	0.00611490	+	7.00000i	0.000873557	+	1.00000i
$50$	0.136140	+	0.772088i	0.0192531	+	0.109190i
$51$	3.96763	−	11.6666i	0.555579	−	1.63366i
$52$	−0.599786	+	3.40156i	−0.0831754	+	0.471711i
$53$	1.11625	+	1.93340i	0.153329	+	0.265573i	0.932449	−	0.361301i	$-0.117667\pi$
$53$	1.11625	+	1.93340i	0.153329	+	0.265573i	−0.779120	+	0.626874i	$0.784334\pi$
$54$	−2.41441	+	3.28120i	−0.328560	+	0.446514i
$55$	5.88137			0.793044
$56$	6.78204	−	1.82042i	0.906288	−	0.243263i
$57$	6.73178	+	7.68485i	0.891646	+	1.01788i
$58$	−0.920433	−	0.335010i	−0.120859	−	0.0439890i
$59$	0.752151	+	4.26566i	0.0979218	+	0.555342i	0.993813	+	0.111068i	$0.0354272\pi$
$59$	0.752151	+	4.26566i	0.0979218	+	0.555342i	−0.895891	+	0.444274i	$0.853462\pi$
$60$	−0.0509926	−	2.39895i	−0.00658312	−	0.309703i
$61$	−0.587618	−	0.493070i	−0.0752368	−	0.0631312i	0.604394	−	0.796686i	$-0.293415\pi$
$61$	−0.587618	−	0.493070i	−0.0752368	−	0.0631312i	−0.679630	+	0.733555i	$0.737860\pi$
$62$	1.03848	−	1.79871i	0.131888	−	0.228436i
$63$	7.33097	+	3.04252i	0.923615	+	0.383321i
$64$	−1.60296	−	2.77640i	−0.200369	−	0.347050i
$65$	−0.432950	+	2.45538i	−0.0537009	+	0.304553i
$66$	7.89282	+	1.21938i	0.971540	+	0.150095i
$67$	6.96571	+	2.53531i	0.850997	+	0.309738i	0.730447	−	0.682969i	$-0.239312\pi$
$67$	6.96571	+	2.53531i	0.850997	+	0.309738i	0.120550	+	0.992707i	$0.461534\pi$
$68$	1.71151	+	9.70645i	0.207551	+	1.17708i
$69$	15.2442	+	2.35511i	1.83519	+	0.283521i
$70$	2.00335	−	0.537734i	0.239446	−	0.0642715i
$71$	−5.31779	−	9.21068i	−0.631105	−	1.09311i	−0.987326	−	0.158705i	$-0.949268\pi$
$71$	−5.31779	−	9.21068i	−0.631105	−	1.09311i	0.356221	−	0.934402i	$-0.384065\pi$
$72$	1.04819	−	7.89302i	0.123530	−	0.930202i
$73$	−14.3614			−1.68088			−0.840439	−	0.541906i	$-0.817703\pi$
$73$	−14.3614			−1.68088			−0.840439	+	0.541906i	$0.817703\pi$
$74$	0.723936	−	0.263491i	0.0841558	−	0.0306302i
$75$	−0.0368086	−	1.73166i	−0.00425029	−	0.199955i
$76$	−7.67855	−	2.79476i	−0.880790	−	0.320581i
$77$	−1.36297	−	15.5008i	−0.155325	−	1.76648i
$78$	−1.09009	+	3.20537i	−0.123429	+	0.362937i
$79$	9.05526	−	3.29584i	1.01880	−	0.370811i	0.221992	−	0.975049i	$-0.428744\pi$
$79$	9.05526	−	3.29584i	1.01880	−	0.370811i	0.796805	+	0.604237i	$0.206522\pi$
$80$	0.344939	+	0.597452i	0.0385653	+	0.0667971i
$81$	6.37829	−	6.34960i	0.708699	−	0.705511i
$82$	2.80046	−	4.85055i	0.309260	−	0.535653i
$83$	3.66164	+	3.07248i	0.401918	+	0.337249i	0.821234	−	0.570591i	$-0.193286\pi$
$83$	3.66164	+	3.07248i	0.401918	+	0.337249i	−0.419317	+	0.907840i	$0.637730\pi$
$84$	−6.31081	+	0.690336i	−0.688566	+	0.0753219i
$85$	1.23544	+	7.00651i	0.134002	+	0.759963i
$86$	−1.04492	+	0.876793i	−0.112677	+	0.0945471i
$87$	1.89663	+	1.04192i	0.203340	+	0.111705i
$88$	−14.6684	+	5.33886i	−1.56366	+	0.569124i
$89$	−8.02786	−	13.9047i	−0.850951	−	1.47389i	−0.880351	−	0.474323i	$-0.842693\pi$
$89$	−8.02786	−	13.9047i	−0.850951	−	1.47389i	0.0294001	−	0.999568i	$-0.490640\pi$
$90$	0.309625	−	2.33153i	0.0326374	−	0.245764i
$91$	6.57170	+	0.572057i	0.688901	+	0.0599678i
$92$	−11.5934	+	4.21965i	−1.20870	+	0.439929i
$93$	−2.87409	+	3.57692i	−0.298030	+	0.370909i
$94$	−5.33560	−	1.94200i	−0.550325	−	0.200302i
$95$	−5.54269	−	2.01738i	−0.568668	−	0.206978i
$96$	3.66650	+	9.44414i	0.374211	+	0.963889i
$97$	0.795243	−	0.289445i	0.0807447	−	0.0293887i	−0.301332	−	0.953519i	$-0.597431\pi$
$97$	0.795243	−	0.289445i	0.0807447	−	0.0293887i	0.382077	+	0.924131i	$0.375209\pi$
$98$	−1.88151	−	5.15538i	−0.190061	−	0.520772i
$99$	−16.8215	−	5.32465i	−1.69062	−	0.535148i
$100$	0.692673	+	1.19975i	0.0692673	+	0.119975i
$101$	12.3705	−	4.50251i	1.23091	−	0.448016i	0.357004	−	0.934103i	$-0.383798\pi$
$101$	12.3705	−	4.50251i	1.23091	−	0.448016i	0.873911	+	0.486087i	$0.161576\pi$
$102$	0.205312	+	9.65891i	0.0203289	+	0.956375i
$103$	4.14506	−	3.47812i	0.408425	−	0.342710i	−0.415314	−	0.909678i	$-0.636328\pi$
$103$	4.14506	−	3.47812i	0.408425	−	0.342710i	0.823739	+	0.566969i	$0.191884\pi$
$104$	−1.14910	−	6.51685i	−0.112678	−	0.639029i
$105$	−4.55540	+	0.498313i	−0.444562	+	0.0486304i
$106$	−1.34079	−	1.12506i	−0.130229	−	0.109275i
$107$	8.55833	−	14.8235i	0.827365	−	1.43304i	−0.0727338	−	0.997351i	$-0.523172\pi$
$107$	8.55833	−	14.8235i	0.827365	−	1.43304i	0.900099	−	0.435686i	$-0.143494\pi$
$108$	−2.02602	+	6.90748i	−0.194954	+	0.664672i
$109$	2.43881	+	4.22415i	0.233596	+	0.404600i	0.958864	−	0.283867i	$-0.0916173\pi$
$109$	2.43881	+	4.22415i	0.233596	+	0.404600i	−0.725268	+	0.688467i	$0.758284\pi$
$110$	−4.33291	+	1.57705i	−0.413127	+	0.150366i
$111$	−1.66948	+	0.331103i	−0.158460	+	0.0314269i
$112$	1.49470	−	1.04757i	0.141235	−	0.0989861i
$113$	−6.13017	−	2.23120i	−0.576678	−	0.209894i	0.0371820	−	0.999309i	$-0.488162\pi$
$113$	−6.13017	−	2.23120i	−0.576678	−	0.209894i	−0.613860	+	0.789415i	$0.710384\pi$
$114$	−7.02006	−	3.85649i	−0.657489	−	0.361193i
$115$	−8.36859	+	3.04592i	−0.780375	+	0.284033i
$116$	−1.73081			−0.160702
$117$	3.46126	−	6.63075i	0.319993	−	0.613013i
$118$	−1.69793	−	2.94090i	−0.156307	−	0.270732i
$119$	18.1799	−	4.87981i	1.66655	−	0.447332i
$120$	1.66373	+	4.28542i	0.151877	+	0.391204i
$121$	4.09645	+	23.2321i	0.372405	+	2.11201i
$122$	0.565122	+	0.205688i	0.0511637	+	0.0186221i
$123$	−7.75053	+	9.64582i	−0.698842	+	0.869734i
$124$	0.637299	−	3.61430i	0.0572311	−	0.324574i
$125$	0.500000	+	0.866025i	0.0447214	+	0.0774597i
$126$	−6.21668	−	0.275726i	−0.553826	−	0.0245637i
$127$	0.132812	−	0.230037i	0.0117851	−	0.0204125i	−0.860073	−	0.510172i	$-0.829582\pi$
$127$	0.132812	−	0.230037i	0.0117851	−	0.0204125i	0.871858	+	0.489759i	$0.162915\pi$
$128$	−7.03591	−	5.90383i	−0.621892	−	0.521829i
$129$	2.57718	−	1.56189i	0.226908	−	0.137516i
$130$	−0.339432	−	1.92502i	−0.0297702	−	0.168835i
$131$	4.39565	+	1.59989i	0.384050	+	0.139783i	0.526828	−	0.849972i	$-0.323381\pi$
$131$	4.39565	+	1.59989i	0.384050	+	0.139783i	−0.142778	+	0.989755i	$0.545603\pi$
$132$	13.8427	−	2.74537i	1.20485	−	0.238954i
$133$	−4.03248	+	15.0757i	−0.349660	+	1.30723i
$134$	−5.81159			−0.502045
$135$	−1.46247	+	4.98610i	−0.125869	+	0.429135i
$136$	−9.44145	−	16.3531i	−0.809598	−	1.40226i
$137$	2.28672	−	12.9687i	0.195368	−	1.10799i	−0.716526	−	0.697561i	$-0.754269\pi$
$137$	2.28672	−	12.9687i	0.195368	−	1.10799i	0.911894	−	0.410426i	$-0.134620\pi$
$138$	−11.8622	+	2.35259i	−1.00978	+	0.200266i
$139$	−0.815234	−	4.62342i	−0.0691473	−	0.392154i	−0.999664	−	0.0259053i	$-0.991753\pi$
$139$	−0.815234	−	4.62342i	−0.0691473	−	0.392154i	0.930517	−	0.366248i	$-0.119358\pi$
$140$	3.00150	−	2.10363i	0.253673	−	0.177789i
$141$	10.9944	+	6.03981i	0.925898	+	0.508644i
$142$	6.38749	+	5.35974i	0.536026	+	0.449779i
$143$	−14.6638			−1.22625
$144$	−0.445673	−	2.02108i	−0.0371394	−	0.168423i
$145$	−1.24937			−0.103755
$146$	10.5803	−	3.85092i	0.875633	−	0.318704i
$147$	2.36903	+	11.8907i	0.195394	+	0.980725i
$148$	1.04282	−	0.875034i	0.0857197	−	0.0719273i
$149$	0.393995	+	2.23446i	0.0322774	+	0.183054i	0.996684	−	0.0813696i	$-0.0259294\pi$
$149$	0.393995	+	2.23446i	0.0322774	+	0.183054i	−0.964407	+	0.264424i	$0.914818\pi$
$150$	0.491450	+	1.26587i	0.0401268	+	0.103358i
$151$	−11.7821	−	9.88639i	−0.958817	−	0.804543i	0.0219432	−	0.999759i	$-0.493015\pi$
$151$	−11.7821	−	9.88639i	−0.958817	−	0.804543i	−0.980760	+	0.195216i	$0.937459\pi$
$152$	15.6550			1.26979
$153$	2.80978	−	21.1580i	0.227157	−	1.71053i
$154$	5.16057	+	11.0543i	0.415850	+	0.890778i
$155$	0.460028	−	2.60895i	0.0369504	−	0.209556i
$156$	0.127138	+	5.98121i	0.0101792	+	0.478880i
$157$	1.15269	+	6.53722i	0.0919946	+	0.521727i	0.995627	+	0.0934183i	$0.0297794\pi$
$157$	1.15269	+	6.53722i	0.0919946	+	0.521727i	−0.903632	+	0.428309i	$0.859109\pi$
$158$	−5.78741	+	4.85621i	−0.460422	+	0.386340i
$159$	2.54792	+	2.90865i	0.202063	+	0.230671i
$160$	−4.48065	−	3.75971i	−0.354227	−	0.297231i
$161$	9.96713	+	21.3502i	0.785520	+	1.68263i
$162$	−2.99640	+	6.38816i	−0.235419	+	0.501901i
$163$	−8.12179	+	14.0673i	−0.636147	+	1.10184i	0.350123	+	0.936704i	$0.386140\pi$
$163$	−8.12179	+	14.0673i	−0.636147	+	1.10184i	−0.986271	+	0.165136i	$0.947194\pi$
$164$	1.71859	−	9.74664i	0.134200	−	0.761084i
$165$	9.99221	−	1.98172i	0.777893	−	0.154277i
$166$	−3.52146	−	1.28171i	−0.273318	−	0.0994798i
$167$	−21.1255	−	7.68906i	−1.63474	−	0.594997i	−0.648633	−	0.761102i	$-0.724659\pi$
$167$	−21.1255	−	7.68906i	−1.63474	−	0.594997i	−0.986108	+	0.166105i	$0.946881\pi$
$168$	10.9090	−	5.37802i	0.841650	−	0.414923i
$169$	−1.17797	+	6.68059i	−0.0906129	+	0.513892i
$170$	−2.78892	−	4.83055i	−0.213900	−	0.370486i
$171$	14.0264	+	10.7880i	1.07263	+	0.824979i
$172$	−1.20516	+	2.08739i	−0.0918922	+	0.159162i
$173$	−3.13368	+	17.7720i	−0.238249	+	1.35118i	0.597413	+	0.801933i	$0.296195\pi$
$173$	−3.13368	+	17.7720i	−0.238249	+	1.35118i	−0.835662	+	0.549244i	$0.814916\pi$
$174$	−1.67666	−	0.259030i	−0.127107	−	0.0196370i
$175$	2.16661	−	1.51849i	0.163780	−	0.114787i
$176$	−3.10817	+	2.60806i	−0.234287	+	0.196590i
$177$	2.71519	+	6.99375i	0.204086	+	0.525683i
$178$	9.64270	+	8.09119i	0.722751	+	0.606460i
$179$	−4.67388	+	8.09539i	−0.349342	+	0.605078i	−0.986133	−	0.165959i	$-0.946928\pi$
$179$	−4.67388	+	8.09539i	−0.349342	+	0.605078i	0.636791	+	0.771037i	$0.280262\pi$
$180$	−0.894958	−	4.05854i	−0.0667062	−	0.302505i
$181$	3.76804	−	6.52644i	0.280076	−	0.485107i	−0.691327	−	0.722542i	$-0.742974\pi$
$181$	3.76804	−	6.52644i	0.280076	−	0.485107i	0.971403	+	0.237435i	$0.0763068\pi$
$182$	−4.99488	+	1.34071i	−0.370245	+	0.0993802i
$183$	−1.16448	−	0.639709i	−0.0860808	−	0.0472887i
$184$	18.1067	−	15.1933i	1.33484	−	1.12007i
$185$	0.752754	−	0.631635i	0.0553436	−	0.0464388i
$186$	1.15827	−	3.40585i	0.0849285	−	0.249729i
$187$	−39.3201	+	14.3114i	−2.87537	+	1.04655i
$188$	−10.0332			−0.731748
$189$	13.4802	+	2.69895i	0.980540	+	0.196320i
$190$	4.62435			0.335485
$191$	−6.82395	+	2.48371i	−0.493764	+	0.179715i	−0.576887	−	0.816824i	$-0.695733\pi$
$191$	−6.82395	+	2.48371i	−0.493764	+	0.179715i	0.0831233	+	0.996539i	$0.473510\pi$
$192$	−3.65886	−	4.17688i	−0.264056	−	0.301440i
$193$	3.58841	−	3.01103i	0.258299	−	0.216739i	−0.504437	−	0.863448i	$-0.668300\pi$
$193$	3.58841	−	3.01103i	0.258299	−	0.216739i	0.762736	+	0.646710i	$0.223855\pi$
$194$	−0.508257	+	0.426478i	−0.0364907	+	0.0306194i
$195$	0.0917734	+	4.31748i	0.00657203	+	0.309181i
$196$	−6.23987	−	7.42321i	−0.445705	−	0.530229i
$197$	1.84232	−	3.19099i	0.131260	−	0.227349i	−0.792903	−	0.609348i	$-0.791431\pi$
$197$	1.84232	−	3.19099i	0.131260	−	0.227349i	0.924162	+	0.382000i	$0.124764\pi$
$198$	13.8205	−	0.587808i	0.982177	−	0.0417737i
$199$	9.16783	−	15.8791i	0.649890	−	1.12564i	−0.333259	−	0.942835i	$-0.608148\pi$
$199$	9.16783	−	15.8791i	0.649890	−	1.12564i	0.983149	−	0.182807i	$-0.0585184\pi$
$200$	−2.03316	−	1.70603i	−0.143766	−	0.120634i
$201$	12.6887	+	1.96031i	0.894995	+	0.138269i
$202$	−7.90627	+	6.63415i	−0.556284	+	0.466777i
$203$	0.289534	+	3.29282i	0.0203213	+	0.231111i
$204$	6.17836	+	15.9142i	0.432572	+	1.11422i
$205$	1.24055	−	7.03552i	0.0866439	−	0.491382i
$206$	−2.12111	+	3.67386i	−0.147785	+	0.255970i
$207$	26.6929	−	1.13529i	1.85528	−	0.0789083i
$208$	−0.860023	−	1.48960i	−0.0596318	−	0.103285i
$209$	6.02399	−	34.1637i	0.416688	−	2.36315i
$210$	3.22242	−	1.58862i	0.222368	−	0.109625i
$211$	5.36542	+	1.95285i	0.369370	+	0.134440i	0.520035	−	0.854145i	$-0.325919\pi$
$211$	5.36542	+	1.95285i	0.369370	+	0.134440i	−0.150664	+	0.988585i	$0.548141\pi$
$212$	−2.90627	−	1.05780i	−0.199603	−	0.0726497i
$213$	−12.1382	−	13.8568i	−0.831698	−	0.949449i
$214$	−2.33026	+	13.2156i	−0.159293	+	0.903397i
$215$	−0.869930	+	1.50676i	−0.0593288	+	0.102760i
$216$	−0.878715	−	13.7631i	−0.0597890	−	0.936462i
$217$	−6.98271	−	0.607835i	−0.474017	−	0.0412625i
$218$	−2.92939	−	2.45805i	−0.198404	−	0.166480i
$219$	−24.3995	+	4.83907i	−1.64876	+	0.326994i
$220$	−6.24153	+	5.23726i	−0.420804	+	0.353096i
$221$	−3.08027	−	17.4691i	−0.207201	−	1.17510i
$222$	1.14115	−	0.691590i	0.0765893	−	0.0464165i
$223$	2.58036	−	14.6339i	0.172794	−	0.979961i	−0.767866	−	0.640610i	$-0.778681\pi$
$223$	2.58036	−	14.6339i	0.172794	−	0.979961i	0.940660	−	0.339351i	$-0.110207\pi$
$224$	−8.87067	+	12.6804i	−0.592697	+	0.847246i
$225$	−0.646017	−	2.92962i	−0.0430678	−	0.195308i
$226$	5.11449			0.340211
$227$	−15.5128	−	13.0168i	−1.02962	−	0.863953i	−0.0388134	−	0.999246i	$-0.512358\pi$
$227$	−15.5128	−	13.0168i	−1.02962	−	0.863953i	−0.990806	+	0.135294i	$0.956802\pi$
$228$	−13.9872	−	2.16091i	−0.926328	−	0.143110i
$229$	2.00033	+	11.3444i	0.132185	+	0.749660i	0.976778	+	0.214252i	$0.0687313\pi$
$229$	2.00033	+	11.3444i	0.132185	+	0.749660i	−0.844593	+	0.535409i	$0.820158\pi$
$230$	5.34854	−	4.48796i	0.352673	−	0.295927i
$231$	−7.53862	−	25.8761i	−0.496005	−	1.70252i
$232$	3.11598	−	1.13413i	0.204574	−	0.0744590i
$233$	−21.8988			−1.43464			−0.717318	−	0.696746i	$-0.754630\pi$
$233$	−21.8988			−1.43464			−0.717318	+	0.696746i	$0.754630\pi$
$234$	−0.771976	+	5.81310i	−0.0504657	+	0.380014i
$235$	−7.24239			−0.472442
$236$	−4.59671	−	3.85710i	−0.299221	−	0.251076i
$237$	14.2740	−	8.65067i	0.927195	−	0.561921i
$238$	−12.0850	+	8.46987i	−0.783354	+	0.549020i
$239$	2.67991	+	15.1985i	0.173349	+	0.983110i	0.940033	+	0.341085i	$0.110794\pi$
$239$	2.67991	+	15.1985i	0.173349	+	0.983110i	−0.766684	+	0.642025i	$0.778095\pi$
$240$	0.787348	+	0.898820i	0.0508231	+	0.0580186i
$241$	−0.397760	+	2.25581i	−0.0256220	+	0.145309i	−0.994935	−	0.100520i	$-0.967949\pi$
$241$	−0.397760	+	2.25581i	−0.0256220	+	0.145309i	0.969313	+	0.245830i	$0.0790604\pi$
$242$	−9.24747	−	16.0171i	−0.594450	−	1.02962i
$243$	8.69697	−	12.9369i	0.557911	−	0.829901i
$244$	1.06267			0.0680307
$245$	−4.50420	−	5.35838i	−0.287763	−	0.342334i
$246$	3.12349	−	9.18450i	0.199147	−	0.585582i
$247$	13.8194	+	5.02984i	0.879306	+	0.320041i
$248$	1.22096	+	6.92443i	0.0775313	+	0.439702i
$249$	7.25626	+	3.98624i	0.459847	+	0.252618i
$250$	−0.600578	−	0.503944i	−0.0379839	−	0.0318722i
$251$	−10.3916	+	17.9987i	−0.655909	+	1.13607i	0.325756	+	0.945454i	$0.394381\pi$
$251$	−10.3916	+	17.9987i	−0.655909	+	1.13607i	−0.981665	+	0.190614i	$0.938952\pi$
$252$	−10.4892	+	3.29927i	−0.660758	+	0.207835i
$253$	−26.1888	−	45.3603i	−1.64647	−	2.85178i
$254$	−0.0361620	+	0.205085i	−0.00226900	+	0.0128682i
$255$	4.45980	+	11.4875i	0.279283	+	0.719376i
$256$	12.7917	+	4.65579i	0.799480	+	0.290987i
$257$	2.12532	+	12.0533i	0.132574	+	0.751864i	0.976519	+	0.215433i	$0.0691164\pi$
$257$	2.12532	+	12.0533i	0.132574	+	0.751864i	−0.843945	+	0.536430i	$0.819772\pi$
$258$	−1.47985	+	1.84172i	−0.0921312	+	0.114661i
$259$	−1.83917	−	1.83757i	−0.114281	−	0.114181i
$260$	−1.72702	−	2.99128i	−0.107105	−	0.185511i
$261$	3.57336	+	1.13111i	0.221186	+	0.0700138i
$262$	−3.66735			−0.226570
$263$	−16.2201	+	5.90364i	−1.00017	+	0.364034i	−0.789652	−	0.613555i	$-0.789739\pi$
$263$	−16.2201	+	5.90364i	−1.00017	+	0.364034i	−0.210523	+	0.977589i	$0.567517\pi$
$264$	−23.1221	+	14.0130i	−1.42307	+	0.862441i
$265$	−2.09786	−	0.763560i	−0.128871	−	0.0469051i
$266$	−1.07166	−	12.1878i	−0.0657078	−	0.747285i
$267$	−18.3242	−	20.9185i	−1.12142	−	1.28019i
$268$	−9.64993	+	3.51229i	−0.589463	+	0.214547i
$269$	1.03135	+	1.78635i	0.0628825	+	0.108916i	0.895753	−	0.444553i	$-0.146637\pi$
$269$	1.03135	+	1.78635i	0.0628825	+	0.108916i	−0.832870	+	0.553468i	$0.813304\pi$
$270$	−0.259564	−	4.06550i	−0.0157966	−	0.247418i
$271$	0.324406	−	0.561887i	0.0197062	−	0.0341322i	−0.856004	−	0.516969i	$-0.827060\pi$
$271$	0.324406	−	0.561887i	0.0197062	−	0.0341322i	0.875710	+	0.482837i	$0.160394\pi$
$272$	−3.75990	−	3.15493i	−0.227978	−	0.191296i
$273$	11.3578	−	1.24242i	0.687406	−	0.0751950i
$274$	1.79279	+	10.1674i	0.108306	+	0.614235i
$275$	−4.50539	+	3.78047i	−0.271685	+	0.227971i
$276$	−18.2749	+	11.0754i	−1.10002	+	0.666661i
$277$	−13.1482	+	4.78554i	−0.789996	+	0.287535i	−0.705335	−	0.708875i	$-0.749203\pi$
$277$	−13.1482	+	4.78554i	−0.789996	+	0.287535i	−0.0846619	+	0.996410i	$0.526981\pi$
$278$	1.84034	+	3.18756i	0.110376	+	0.191177i
$279$	−3.67773	+	7.04546i	−0.220180	+	0.421801i
$280$	−4.02520	+	5.75393i	−0.240552	+	0.343863i
$281$	−9.58789	+	3.48971i	−0.571965	+	0.208178i	−0.611779	−	0.791029i	$-0.709546\pi$
$281$	−9.58789	+	3.48971i	−0.571965	+	0.208178i	0.0398136	+	0.999207i	$0.487324\pi$
$282$	−9.71932	−	1.50155i	−0.578777	−	0.0894163i
$283$	−8.65549	−	3.15034i	−0.514516	−	0.187268i	0.0716957	−	0.997427i	$-0.477159\pi$
$283$	−8.65549	−	3.15034i	−0.514516	−	0.187268i	−0.586211	+	0.810158i	$0.699381\pi$
$284$	13.8454	+	5.03931i	0.821573	+	0.299028i
$285$	−10.0966	−	1.55984i	−0.598069	−	0.0923967i
$286$	10.8031	−	3.93200i	0.638799	−	0.232504i
$287$	−18.8302	−	1.63914i	−1.11151	−	0.0967554i
$288$	9.41143	+	14.8098i	0.554574	+	0.872676i
$289$	−16.8088	−	29.1136i	−0.988751	−	1.71257i
$290$	0.920433	−	0.335010i	0.0540497	−	0.0196725i
$291$	1.25356	−	0.759712i	0.0734849	−	0.0445351i
$292$	15.2409	−	12.7886i	0.891905	−	0.748397i
$293$	1.17575	+	6.66803i	0.0686882	+	0.389550i	0.999698	+	0.0245571i	$0.00781755\pi$
$293$	1.17575	+	6.66803i	0.0686882	+	0.389550i	−0.931010	+	0.364993i	$0.881071\pi$
$294$	−4.93371	−	8.12482i	−0.287740	−	0.473849i
$295$	−3.31810	−	2.78421i	−0.193187	−	0.162103i
$296$	−1.30403	+	2.25864i	−0.0757951	+	0.131281i
$297$	−30.3732	−	3.37838i	−1.76243	−	0.196034i
$298$	−0.889419	−	1.54052i	−0.0515226	−	0.0892398i
$299$	20.8651	−	7.59427i	1.20666	−	0.439188i
$300$	1.58108	+	1.80492i	0.0912835	+	0.104207i
$301$	4.17280	+	1.94359i	0.240516	+	0.112027i
$302$	11.3311	+	4.12418i	0.652030	+	0.237320i
$303$	19.4999	−	11.8178i	1.12024	−	0.678916i
$304$	3.82378	−	1.39174i	0.219309	−	0.0798219i
$305$	0.767081			0.0439229
$306$	3.60338	+	16.3409i	0.205991	+	0.934149i
$307$	14.5757	+	25.2458i	0.831879	+	1.44086i	0.896547	+	0.442949i	$0.146068\pi$
$307$	14.5757	+	25.2458i	0.831879	+	1.44086i	−0.0646679	+	0.997907i	$0.520599\pi$
$308$	15.2497	+	15.2364i	0.868931	+	0.868172i
$309$	5.87035	−	7.30587i	0.333953	−	0.415616i
$310$	0.360661	+	2.04541i	0.0204842	+	0.116172i
$311$	6.03351	+	2.19602i	0.342129	+	0.124525i	0.507370	−	0.861728i	$-0.330618\pi$
$311$	6.03351	+	2.19602i	0.342129	+	0.124525i	−0.165241	+	0.986253i	$0.552840\pi$
$312$	−4.14811	−	10.6847i	−0.234841	−	0.604901i
$313$	3.10766	−	17.6244i	0.175655	−	0.996190i	−0.761730	−	0.647895i	$-0.775650\pi$
$313$	3.10766	−	17.6244i	0.175655	−	0.996190i	0.937385	−	0.348295i	$-0.113239\pi$
$314$	−2.60212	−	4.50700i	−0.146846	−	0.254345i
$315$	−7.57154	+	2.38155i	−0.426608	+	0.134185i
$316$	−6.67488	+	11.5612i	−0.375491	+	0.650370i
$317$	12.5440	+	10.5257i	0.704543	+	0.591182i	0.923062	−	0.384651i	$-0.125678\pi$
$317$	12.5440	+	10.5257i	0.704543	+	0.591182i	−0.218519	+	0.975833i	$0.570123\pi$
$318$	−2.65703	−	1.45965i	−0.148999	−	0.0818530i
$319$	−1.27597	−	7.23638i	−0.0714405	−	0.405159i
$320$	3.01257	+	1.09649i	0.168408	+	0.0612954i
$321$	9.54551	−	28.0682i	0.532778	−	1.56661i
$322$	−13.0679	−	13.0565i	−0.728245	−	0.727609i
$323$	41.9648			2.33499
$324$	−1.11467	+	12.4182i	−0.0619258	+	0.689900i
$325$	−1.24663	−	2.15923i	−0.0691506	−	0.119772i
$326$	2.21140	−	12.5415i	0.122478	−	0.694607i
$327$	5.56677	+	6.35491i	0.307843	+	0.351427i
$328$	3.29256	+	18.6730i	0.181801	+	1.03105i
$329$	1.67838	+	19.0879i	0.0925320	+	1.05235i
$330$	−6.83005	+	4.13931i	−0.375982	+	0.227862i
$331$	−0.776677	−	0.651709i	−0.0426900	−	0.0358212i	0.621193	−	0.783658i	$-0.286648\pi$
$331$	−0.776677	−	0.651709i	−0.0426900	−	0.0358212i	−0.663883	+	0.747836i	$0.731093\pi$
$332$	−6.62187			−0.363422
$333$	−2.72482	+	1.12506i	−0.149319	+	0.0616530i
$334$	17.6253			0.964414
$335$	−6.96571	+	2.53531i	−0.380578	+	0.138519i
$336$	2.18645	−	2.28342i	0.119281	−	0.124571i
$337$	−16.1793	+	13.5761i	−0.881345	+	0.739536i	−0.966455	−	0.256835i	$-0.917320\pi$
$337$	−16.1793	+	13.5761i	−0.881345	+	0.739536i	0.0851101	+	0.996372i	$0.472876\pi$
$338$	−0.923525	−	5.23757i	−0.0502331	−	0.284886i
$339$	−11.1667	−	1.72517i	−0.606493	−	0.0936981i
$340$	−7.55028	−	6.33543i	−0.409471	−	0.343587i
$341$	15.5809			0.843754
$342$	−13.2262	−	4.18661i	−0.715193	−	0.226386i
$343$	−13.0786	+	13.1129i	−0.706180	+	0.708033i
$344$	0.801868	−	4.54762i	0.0432338	−	0.245191i
$345$	−13.1916	+	7.99468i	−0.710211	+	0.430419i
$346$	−2.45680	−	13.9332i	−0.132078	−	0.749053i
$347$	−14.1058	+	11.8362i	−0.757238	+	0.635398i	−0.937406	−	0.348237i	$-0.886780\pi$
$347$	−14.1058	+	11.8362i	−0.757238	+	0.635398i	0.180168	+	0.983636i	$0.442336\pi$
$348$	−2.94058	+	0.583195i	−0.157632	+	0.0312625i
$349$	11.7183	+	9.83284i	0.627267	+	0.526340i	0.900078	−	0.435728i	$-0.143509\pi$
$349$	11.7183	+	9.83284i	0.627267	+	0.526340i	−0.272811	+	0.962068i	$0.587953\pi$
$350$	−1.18901	+	1.69966i	−0.0635551	+	0.0908505i
$351$	3.64631	−	12.4316i	0.194626	−	0.663552i
$352$	17.2003	−	29.7918i	0.916779	−	1.58791i
$353$	2.73947	−	15.5363i	0.145807	−	0.826914i	−0.820908	−	0.571060i	$-0.806532\pi$
$353$	2.73947	−	15.5363i	0.145807	−	0.826914i	0.966715	−	0.255854i	$-0.0823566\pi$
$354$	−3.87565	−	4.42436i	−0.205989	−	0.235152i
$355$	9.99417	+	3.63758i	0.530436	+	0.193063i
$356$	20.9013	+	7.60746i	1.10777	+	0.403195i
$357$	29.2427	−	14.4163i	1.54769	−	0.762992i
$358$	1.27260	−	7.21729i	0.0672591	−	0.381445i
$359$	−13.9473	−	24.1575i	−0.736111	−	1.27498i	−0.954234	−	0.299060i	$-0.903327\pi$
$359$	−13.9473	−	24.1575i	−0.736111	−	1.27498i	0.218123	−	0.975921i	$-0.430007\pi$
$360$	4.27058	+	6.72017i	0.225079	+	0.354184i
$361$	−7.89563	+	13.6756i	−0.415560	+	0.719770i
$362$	−1.02596	+	5.81852i	−0.0539234	+	0.305815i
$363$	14.7877	+	38.0902i	0.776155	+	1.99921i
$364$	−7.48354	+	5.24490i	−0.392244	+	0.274908i
$365$	11.0015	−	9.23135i	0.575844	−	0.483191i
$366$	1.02943	+	0.159038i	0.0538090	+	0.00831304i
$367$	−6.84210	−	5.74120i	−0.357155	−	0.299688i	0.446501	−	0.894783i	$-0.352670\pi$
$367$	−6.84210	−	5.74120i	−0.357155	−	0.299688i	−0.803655	+	0.595095i	$0.797114\pi$
$368$	3.07191	−	5.32071i	0.160134	−	0.277361i
$369$	−9.91770	+	18.9994i	−0.516295	+	0.989069i
$370$	−0.385198	+	0.667183i	−0.0200255	+	0.0346852i
$371$	−1.52626	+	5.70604i	−0.0792394	+	0.296243i
$372$	−0.135090	−	6.35529i	−0.00700407	−	0.329506i
$373$	−9.99646	+	8.38803i	−0.517597	+	0.434316i	−0.863793	−	0.503847i	$-0.831918\pi$
$373$	−9.99646	+	8.38803i	−0.517597	+	0.434316i	0.346196	+	0.938162i	$0.387473\pi$
$374$	25.1303	−	21.0869i	1.29946	−	1.09038i
$375$	1.14129	+	1.30287i	0.0589358	+	0.0672798i
$376$	18.0628	−	6.57434i	0.931520	−	0.339046i
$377$	3.11501			0.160431
$378$	−10.6548	+	1.62626i	−0.548024	+	0.0836456i
$379$	−1.94550			−0.0999337			−0.0499668	−	0.998751i	$-0.515912\pi$
$379$	−1.94550			−0.0999337			−0.0499668	+	0.998751i	$0.515912\pi$
$380$	7.67855	−	2.79476i	0.393901	−	0.143368i
$381$	0.148131	−	0.435574i	0.00758899	−	0.0223151i
$382$	4.36133	−	3.65959i	0.223145	−	0.187241i
$383$	−13.3176	+	11.1748i	−0.680497	+	0.571005i	−0.916151	−	0.400832i	$-0.868721\pi$
$383$	−13.3176	+	11.1748i	−0.680497	+	0.571005i	0.235655	+	0.971837i	$0.424277\pi$
$384$	−13.9430	−	7.65962i	−0.711526	−	0.390879i
$385$	11.0078	+	10.9982i	0.561012	+	0.560522i
$386$	−1.83625	+	3.18049i	−0.0934629	+	0.161882i
$387$	3.85225	−	3.52196i	0.195821	−	0.179031i
$388$	−0.586196	+	1.01532i	−0.0297596	+	0.0515451i
$389$	−16.3109	−	13.6865i	−0.826997	−	0.693932i	0.127603	−	0.991825i	$-0.459272\pi$
$389$	−16.3109	−	13.6865i	−0.826997	−	0.693932i	−0.954599	+	0.297893i	$0.903716\pi$
$390$	−1.22531	−	3.15615i	−0.0620462	−	0.159818i
$391$	48.5368	−	40.7272i	2.45461	−	2.05966i
$392$	16.0978	+	9.27531i	0.813060	+	0.468474i
$393$	8.00712	+	1.23703i	0.403906	+	0.0624001i
$394$	−0.501626	+	2.84486i	−0.0252716	+	0.143322i
$395$	−4.81820	+	8.34537i	−0.242430	+	0.419901i
$396$	22.5931	−	9.32855i	1.13535	−	0.468777i
$397$	10.5351	+	18.2473i	0.528741	+	0.915806i	0.999438	+	0.0335113i	$0.0106690\pi$
$397$	10.5351	+	18.2473i	0.528741	+	0.915806i	−0.470698	+	0.882295i	$0.655998\pi$
$398$	−2.49621	+	14.1567i	−0.125124	+	0.709613i
$399$	−1.77126	+	26.9718i	−0.0886740	+	1.35028i
$400$	−0.648273	−	0.235952i	−0.0324137	−	0.0117976i
$401$	−16.1136	−	5.86489i	−0.804677	−	0.292879i	−0.0932540	−	0.995642i	$-0.529727\pi$
$401$	−16.1136	−	5.86489i	−0.804677	−	0.292879i	−0.711423	+	0.702764i	$0.751949\pi$
$402$	−9.87366	+	1.95821i	−0.492453	+	0.0976666i
$403$	−1.14697	+	6.50479i	−0.0571347	+	0.324027i
$404$	−9.11866	+	15.7940i	−0.453670	+	0.785780i
$405$	−0.804611	+	8.96396i	−0.0399815	+	0.445423i
$406$	−1.09625	−	2.34824i	−0.0544060	−	0.116541i
$407$	4.42722	+	3.71488i	0.219449	+	0.184140i
$408$	−21.5508	−	24.6019i	−1.06692	−	1.21798i
$409$	6.12666	−	5.14087i	0.302944	−	0.254200i	−0.478625	−	0.878020i	$-0.658865\pi$
$409$	6.12666	−	5.14087i	0.302944	−	0.254200i	0.781568	+	0.623820i	$0.214420\pi$
$410$	0.972591	+	5.51584i	0.0480329	+	0.272408i
$411$	−0.484722	−	22.8037i	−0.0239096	−	1.12483i
$412$	−1.30169	+	7.38222i	−0.0641294	+	0.363696i
$413$	−6.56908	+	9.39034i	−0.323243	+	0.462069i
$414$	−19.3607	+	7.99390i	−0.951526	+	0.392879i
$415$	−4.77994			−0.234638
$416$	11.1714	+	9.37395i	0.547725	+	0.459596i
$417$	−2.94291	−	7.58032i	−0.144115	−	0.371210i
$418$	4.72279	+	26.7843i	0.230999	+	1.31006i
$419$	−2.27174	+	1.90621i	−0.110982	+	0.0931246i	−0.696590	−	0.717470i	$-0.745300\pi$
$419$	−2.27174	+	1.90621i	−0.110982	+	0.0931246i	0.585608	+	0.810594i	$0.300856\pi$
$420$	4.39062	−	4.58534i	0.214240	−	0.223742i
$421$	−5.00487	+	1.82162i	−0.243922	+	0.0887805i	−0.461088	−	0.887354i	$-0.652541\pi$
$421$	−5.00487	+	1.82162i	−0.243922	+	0.0887805i	0.217166	+	0.976135i	$0.430319\pi$
$422$	−4.47644			−0.217910
$423$	20.7142	+	6.55684i	1.00716	+	0.318804i
$424$	5.92529			0.287758
$425$	−5.45010	−	4.57318i	−0.264369	−	0.221832i
$426$	12.6580	+	6.95373i	0.613284	+	0.336909i
$427$	−0.177766	−	2.02171i	−0.00860271	−	0.0978372i
$428$	4.11763	+	23.3523i	0.199033	+	1.12877i
$429$	−24.9132	+	4.94095i	−1.20282	+	0.238551i
$430$	0.236864	−	1.34333i	0.0114226	−	0.0647809i
$431$	−9.89766	−	17.1433i	−0.476754	−	0.825761i	0.522892	−	0.852399i	$-0.324853\pi$
$431$	−9.89766	−	17.1433i	−0.476754	−	0.825761i	−0.999645	+	0.0266378i	$0.991520\pi$
$432$	−1.43818	−	3.28356i	−0.0691945	−	0.157980i
$433$	34.3742			1.65192			0.825959	−	0.563731i	$-0.190634\pi$
$433$	34.3742			1.65192			0.825959	+	0.563731i	$0.190634\pi$
$434$	5.30727	−	1.42456i	0.254757	−	0.0683813i
$435$	−2.12263	+	0.420974i	−0.101772	+	0.0201842i
$436$	−6.34970	−	2.31110i	−0.304095	−	0.110682i
$437$	9.12162	+	51.7313i	0.436346	+	2.47464i
$438$	16.6780	−	10.1076i	0.796904	−	0.482959i
$439$	−22.7357	−	19.0775i	−1.08512	−	0.910520i	−0.0887801	−	0.996051i	$-0.528297\pi$
$439$	−22.7357	−	19.0775i	−1.08512	−	0.910520i	−0.996335	+	0.0855312i	$0.972741\pi$
$440$	7.80489	−	13.5185i	0.372084	−	0.644468i
$441$	8.03143	+	19.4035i	0.382449	+	0.923977i
$442$	6.95350	+	12.0438i	0.330744	+	0.572866i
$443$	3.82129	−	21.6716i	0.181555	−	1.02965i	−0.748747	−	0.662856i	$-0.769344\pi$
$443$	3.82129	−	21.6716i	0.181555	−	1.02965i	0.930302	−	0.366794i	$-0.119545\pi$
$444$	1.47688	−	1.83803i	0.0700894	−	0.0872289i
$445$	15.0874	+	5.49138i	0.715213	+	0.260316i
$446$	2.02300	+	11.4730i	0.0957917	+	0.543262i
$447$	1.42228	+	3.66350i	0.0672716	+	0.173278i
$448$	2.19174	−	8.19398i	0.103550	−	0.387129i
$449$	0.219693	+	0.380519i	0.0103680	+	0.0179578i	0.871163	−	0.490994i	$-0.163366\pi$
$449$	0.219693	+	0.380519i	0.0103680	+	0.0179578i	−0.860795	+	0.508952i	$0.830033\pi$
$450$	1.26149	+	1.98508i	0.0594672	+	0.0935774i
$451$	42.0168			1.97850
$452$	8.49241	−	3.09099i	0.399449	−	0.145388i
$453$	−23.3486	−	12.8266i	−1.09701	−	0.602646i
$454$	14.9189	+	5.43003i	0.700178	+	0.254844i
$455$	−5.40192	+	3.78598i	−0.253246	+	0.177490i
$456$	26.5972	−	5.27494i	1.24553	−	0.247022i
$457$	−0.159472	+	0.0580430i	−0.00745978	+	0.00271514i	−0.345747	−	0.938328i	$-0.612375\pi$
$457$	−0.159472	+	0.0580430i	−0.00745978	+	0.00271514i	0.338288	+	0.941043i	$0.390152\pi$
$458$	−4.51561	−	7.82126i	−0.211000	−	0.365463i
$459$	−2.35549	−	36.8934i	−0.109945	−	1.72204i
$460$	6.16872	−	10.6845i	0.287618	−	0.498169i
$461$	26.5505	+	22.2785i	1.23658	+	1.03761i	0.997783	+	0.0665448i	$0.0211975\pi$
$461$	26.5505	+	22.2785i	1.23658	+	1.03761i	0.238797	+	0.971069i	$0.423247\pi$
$462$	12.4923	+	17.0419i	0.581196	+	0.792861i
$463$	−6.15690	−	34.9175i	−0.286135	−	1.62275i	−0.701201	−	0.712963i	$-0.747353\pi$
$463$	−6.15690	−	34.9175i	−0.286135	−	1.62275i	0.415066	−	0.909791i	$-0.363758\pi$
$464$	0.660263	−	0.554027i	0.0306520	−	0.0257201i
$465$	−0.0975132	−	4.58751i	−0.00452207	−	0.212741i
$466$	16.1332	−	5.87200i	0.747356	−	0.272015i
$467$	17.9584	+	31.1048i	0.831014	+	1.43936i	0.897235	+	0.441553i	$0.145572\pi$
$467$	17.9584	+	31.1048i	0.831014	+	1.43936i	−0.0662218	+	0.997805i	$0.521094\pi$
$468$	2.23136	+	10.1190i	0.103145	+	0.467751i
$469$	8.29629	+	17.7712i	0.383087	+	0.820596i
$470$	5.33560	−	1.94200i	0.246113	−	0.0895777i
$471$	4.16108	+	10.7181i	0.191733	+	0.493863i
$472$	10.8029	+	3.93192i	0.497242	+	0.180981i
$473$	−9.61566	−	3.49981i	−0.442128	−	0.160922i
$474$	−8.19628	+	10.2006i	−0.376468	+	0.468528i
$475$	5.54269	−	2.01738i	0.254316	−	0.0925635i
$476$	−14.9478	+	21.3676i	−0.685133	+	0.979381i
$477$	5.30889	+	4.08317i	0.243077	+	0.186955i
$478$	−6.04971	−	10.4784i	−0.276707	−	0.479271i
$479$	−5.12955	+	1.86700i	−0.234375	+	0.0853055i	−0.456538	−	0.889704i	$-0.650911\pi$
$479$	−5.12955	+	1.86700i	−0.234375	+	0.0853055i	0.222163	+	0.975010i	$0.428688\pi$
$480$	−8.87928	−	4.87785i	−0.405282	−	0.222642i
$481$	−1.87681	+	1.57483i	−0.0855752	+	0.0718062i
$482$	−0.311843	−	1.76855i	−0.0142041	−	0.0805552i
$483$	24.1277	+	32.9148i	1.09785	+	1.49767i
$484$	−25.0351	−	21.0070i	−1.13796	−	0.954862i
$485$	−0.423140	+	0.732900i	−0.0192138	+	0.0332793i
$486$	−2.93828	+	11.8629i	−0.133283	+	0.538110i
$487$	−5.34422	−	9.25646i	−0.242170	−	0.419450i	0.719162	−	0.694842i	$-0.244526\pi$
$487$	−5.34422	−	9.25646i	−0.242170	−	0.419450i	−0.961332	+	0.275392i	$0.911192\pi$
$488$	−1.91313	+	0.696324i	−0.0866035	+	0.0315211i
$489$	−9.05861	+	26.6365i	−0.409645	+	1.20454i
$490$	4.75513	+	2.73984i	0.214815	+	0.123773i
$491$	−18.3349	−	6.67337i	−0.827444	−	0.301165i	−0.106634	−	0.994298i	$-0.534007\pi$
$491$	−18.3349	−	6.67337i	−0.827444	−	0.301165i	−0.720809	+	0.693133i	$0.756230\pi$
$492$	−0.364294	−	17.1382i	−0.0164237	−	0.772651i
$493$	8.35271	−	3.04014i	0.376187	−	0.136921i
$494$	−11.5297			−0.518746
$495$	16.3086	−	6.73373i	0.733019	−	0.302659i
$496$	0.913811	+	1.58277i	0.0410313	+	0.0710684i
$497$	7.27106	−	27.1835i	0.326152	−	1.21934i
$498$	−6.41469	−	0.991017i	−0.287449	−	0.0444085i
$499$	0.677002	+	3.83947i	0.0303068	+	0.171878i	0.996204	−	0.0870466i	$-0.0277429\pi$
$499$	0.677002	+	3.83947i	0.0303068	+	0.171878i	−0.965897	+	0.258925i	$0.916632\pi$
$500$	−1.30180	−	0.473816i	−0.0582183	−	0.0211897i
$501$	−38.4822	−	5.94518i	−1.71926	−	0.265611i
$502$	2.82941	−	16.0464i	0.126283	−	0.716185i
$503$	7.94005	+	13.7526i	0.354029	+	0.613196i	0.986951	−	0.161019i	$-0.0514780\pi$
$503$	7.94005	+	13.7526i	0.354029	+	0.613196i	−0.632922	+	0.774215i	$0.718145\pi$
$504$	16.7219	−	12.8128i	0.744852	−	0.570728i
$505$	−6.58223	+	11.4007i	−0.292905	+	0.507327i
$506$	31.4568	+	26.3954i	1.39842	+	1.17342i
$507$	0.249696	+	11.7470i	0.0110894	+	0.521701i
$508$	0.0638992	+	0.362390i	0.00283507	+	0.0160785i
$509$	−21.7437	−	7.91405i	−0.963771	−	0.350784i	−0.188261	−	0.982119i	$-0.560285\pi$
$509$	−21.7437	−	7.91405i	−0.963771	−	0.350784i	−0.775510	+	0.631335i	$0.782507\pi$
$510$	−6.36591	−	7.26718i	−0.281887	−	0.321796i
$511$	−26.8795	−	26.8560i	−1.18908	−	1.18804i
$512$	7.69717			0.340170
$513$	27.4653	+	13.6022i	1.21262	+	0.600551i
$514$	−4.79777	−	8.30998i	−0.211621	−	0.366537i
$515$	−0.939610	+	5.32879i	−0.0414042	+	0.234815i
$516$	−1.34417	+	3.95247i	−0.0591736	+	0.173998i
$517$	−7.39658	−	41.9481i	−0.325301	−	1.84487i
$518$	1.84768	+	0.860606i	0.0811825	+	0.0378129i
$519$	0.664252	+	31.2497i	0.0291574	+	1.37171i
$520$	5.06921	+	4.25357i	0.222299	+	0.186531i
$521$	−5.69700			−0.249590			−0.124795	−	0.992183i	$-0.539827\pi$
$521$	−5.69700			−0.249590			−0.124795	+	0.992183i	$0.539827\pi$
$522$	−2.93586	+	0.124867i	−0.128499	+	0.00546528i
$523$	24.2364			1.05978			0.529892	−	0.848065i	$-0.322233\pi$
$523$	24.2364			1.05978			0.529892	+	0.848065i	$0.322233\pi$
$524$	−6.08950	+	2.21640i	−0.266021	+	0.0968238i
$525$	3.16933	−	3.30989i	0.138321	−	0.144455i
$526$	10.3666	−	8.69863i	0.452006	−	0.379278i
$527$	3.27292	+	18.5616i	0.142571	+	0.808558i
$528$	−4.40187	+	5.47829i	−0.191567	+	0.238412i
$529$	43.1367	+	36.1960i	1.87551	+	1.57374i
$530$	1.75028			0.0760272
$531$	6.96953	+	10.9672i	0.302452	+	0.475937i
$532$	−9.14529	−	19.5898i	−0.396498	−	0.849325i
$533$	−3.09302	+	17.5414i	−0.133974	+	0.759802i
$534$	19.1089	+	10.4975i	0.826922	+	0.454272i
$535$	2.97228	+	16.8566i	0.128503	+	0.728775i
$536$	15.0713	−	12.6464i	0.650983	−	0.546240i
$537$	−5.21300	+	15.3286i	−0.224957	+	0.661478i
$538$	−1.23881	−	1.03949i	−0.0534089	−	0.0448154i
$539$	26.4357	−	31.5608i	1.13867	−	1.35942i
$540$	−2.88802	−	6.59374i	−0.124280	−	0.283749i
$541$	−5.22682	+	9.05312i	−0.224719	+	0.389224i	−0.956235	−	0.292600i	$-0.905480\pi$
$541$	−5.22682	+	9.05312i	−0.224719	+	0.389224i	0.731516	+	0.681824i	$0.238813\pi$
$542$	−0.0883291	+	0.500939i	−0.00379406	+	0.0215172i
$543$	4.20268	−	12.3578i	0.180354	−	0.530324i
$544$	39.1042	+	14.2328i	1.67658	+	0.610225i
$545$	−4.58347	−	1.66825i	−0.196334	−	0.0714599i
$546$	−8.03435	+	3.96084i	−0.343838	+	0.169508i
$547$	−3.23470	+	18.3449i	−0.138306	+	0.784370i	0.834195	+	0.551470i	$0.185933\pi$
$547$	−3.23470	+	18.3449i	−0.138306	+	0.784370i	−0.972501	+	0.232901i	$0.925178\pi$
$548$	9.12162	+	15.7991i	0.389656	+	0.674904i
$549$	−2.19395	−	0.694471i	−0.0936356	−	0.0296393i
$550$	2.30549	−	3.99323i	0.0983065	−	0.170272i
$551$	−1.27967	+	7.25734i	−0.0545156	+	0.309173i
$552$	25.6432	−	31.9138i	1.09145	−	1.35834i
$553$	23.1115	+	10.7648i	0.982801	+	0.457765i
$554$	8.40327	−	7.05118i	0.357021	−	0.299576i
$555$	1.06607	−	1.32676i	0.0452521	−	0.0563179i
$556$	4.98224	+	4.18060i	0.211294	+	0.177297i
$557$	−4.60265	+	7.97203i	−0.195021	+	0.337786i	−0.946907	−	0.321507i	$-0.895811\pi$
$557$	−4.60265	+	7.97203i	−0.195021	+	0.337786i	0.751887	+	0.659292i	$0.229144\pi$
$558$	0.820258	−	6.17667i	0.0347243	−	0.261479i
$559$	2.16896	−	3.75676i	0.0917374	−	0.158894i
$560$	−0.471638	+	1.76326i	−0.0199303	+	0.0745112i
$561$	−61.9811	+	37.5633i	−2.61685	+	1.58592i
$562$	6.12782	−	5.14185i	0.258487	−	0.216896i
$563$	21.3341	−	17.9015i	0.899126	−	0.754456i	−0.0708932	−	0.997484i	$-0.522585\pi$
$563$	21.3341	−	17.9015i	0.899126	−	0.754456i	0.970019	+	0.243027i	$0.0781405\pi$
$564$	−17.0460	+	3.38068i	−0.717768	+	0.142352i
$565$	6.13017	−	2.23120i	0.257898	−	0.0938673i
$566$	7.22140			0.303538
$567$	23.8117	+	0.0432784i	0.999998	+	0.00181752i
$568$	−28.2279			−1.18442
$569$	−29.5738	+	10.7640i	−1.23980	+	0.451249i	−0.876942	−	0.480597i	$-0.840420\pi$
$569$	−29.5738	+	10.7640i	−1.23980	+	0.451249i	−0.362855	+	0.931846i	$0.618198\pi$
$570$	7.85658	−	1.55817i	0.329076	−	0.0652645i
$571$	−29.2685	+	24.5592i	−1.22485	+	1.02777i	−0.226294	+	0.974059i	$0.572661\pi$
$571$	−29.2685	+	24.5592i	−1.22485	+	1.02777i	−0.998556	+	0.0537128i	$0.982894\pi$
$572$	15.5618	−	13.0579i	0.650670	−	0.545977i
$573$	−10.7567	+	6.51905i	−0.449369	+	0.272337i
$574$	14.3121	−	3.84160i	0.597374	−	0.160345i
$575$	4.45283	−	7.71253i	0.185696	−	0.321635i
$576$	−7.62366	−	5.86350i	−0.317652	−	0.244313i
$577$	1.65407	−	2.86493i	0.0688599	−	0.119269i	−0.829540	−	0.558448i	$-0.811397\pi$
$577$	1.65407	−	2.86493i	0.0688599	−	0.119269i	0.898400	+	0.439179i	$0.144731\pi$
$578$	20.1899	+	16.9414i	0.839791	+	0.704668i
$579$	5.08200	−	6.32473i	0.211201	−	0.262847i
$580$	1.32588	−	1.11254i	0.0550541	−	0.0461959i
$581$	1.10772	+	12.5979i	0.0459559	+	0.522650i
$582$	−0.719807	+	0.895826i	−0.0298370	+	0.0371332i
$583$	2.28003	−	12.9307i	0.0944291	−	0.535534i
$584$	−19.0584	+	33.0101i	−0.788641	+	1.36597i
$585$	1.61069	+	7.30430i	0.0665938	+	0.301996i
$586$	−2.65418	−	4.59718i	−0.109643	−	0.189908i
$587$	−2.27178	+	12.8839i	−0.0937666	+	0.531777i	0.901352	+	0.433088i	$0.142576\pi$
$587$	−2.27178	+	12.8839i	−0.0937666	+	0.531777i	−0.995118	+	0.0986888i	$0.968535\pi$
$588$	−13.1025	−	10.5092i	−0.540339	−	0.433393i
$589$	−14.6837	−	5.34443i	−0.605031	−	0.220213i
$590$	3.19107	+	1.16145i	0.131374	+	0.0478163i
$591$	2.05482	−	6.04213i	0.0845242	−	0.248540i
$592$	−0.117718	+	0.667610i	−0.00483816	+	0.0274386i
$593$	4.38348	−	7.59241i	0.180008	−	0.311783i	−0.761875	−	0.647724i	$-0.775721\pi$
$593$	4.38348	−	7.59241i	0.180008	−	0.311783i	0.941883	+	0.335941i	$0.109054\pi$
$594$	23.2824	−	5.65545i	0.955286	−	0.232046i
$595$	−10.7900	+	15.4240i	−0.442345	+	0.632322i
$596$	−2.40787	−	2.02044i	−0.0986303	−	0.0827606i
$597$	10.2253	−	30.0671i	0.418494	−	1.23057i
$598$	−13.3353	+	11.1897i	−0.545322	+	0.457579i
$599$	−0.390211	−	2.21300i	−0.0159436	−	0.0904206i	0.975798	−	0.218675i	$-0.0701736\pi$
$599$	−0.390211	−	2.21300i	−0.0159436	−	0.0904206i	−0.991741	+	0.128255i	$0.959062\pi$
$600$	−4.02911	−	2.21340i	−0.164488	−	0.0903616i
$601$	−3.26093	+	18.4937i	−0.133016	+	0.754373i	0.843204	+	0.537593i	$0.180666\pi$
$601$	−3.26093	+	18.4937i	−0.133016	+	0.754373i	−0.976221	+	0.216779i	$0.930445\pi$
$602$	−3.59534	−	0.312969i	−0.146535	−	0.0127557i
$603$	22.2182	−	0.944977i	0.904795	−	0.0384824i
$604$	21.3073			0.866982
$605$	−18.0714	−	15.1637i	−0.734706	−	0.616492i
$606$	−11.1971	+	13.9352i	−0.454850	+	0.566078i
$607$	−2.89256	−	16.4045i	−0.117405	−	0.665839i	−0.985531	−	0.169495i	$-0.945786\pi$
$607$	−2.89256	−	16.4045i	−0.117405	−	0.665839i	0.868126	−	0.496344i	$-0.165325\pi$
$608$	−26.4287	+	22.1763i	−1.07183	+	0.899369i
$609$	1.60142	+	5.49681i	0.0648927	+	0.222742i
$610$	−0.565122	+	0.205688i	−0.0228811	+	0.00832805i
$611$	18.0572			0.730515
$612$	15.8591	+	24.9558i	0.641064	+	1.00878i
$613$	−12.9322			−0.522327			−0.261163	−	0.965295i	$-0.584106\pi$
$613$	−12.9322			−0.522327			−0.261163	+	0.965295i	$0.584106\pi$
$614$	−17.5077	−	14.6907i	−0.706552	−	0.592868i
$615$	−0.262963	−	12.3711i	−0.0106037	−	0.498850i
$616$	−37.4378	−	17.4376i	−1.50841	−	0.702582i
$617$	6.73487	+	38.1954i	0.271136	+	1.53769i	0.750975	+	0.660331i	$0.229584\pi$
$617$	6.73487	+	38.1954i	0.271136	+	1.53769i	−0.479839	+	0.877356i	$0.659305\pi$
$618$	−2.36577	+	6.95645i	−0.0951653	+	0.279830i
$619$	−3.22743	+	18.3037i	−0.129721	+	0.735686i	0.848670	+	0.528923i	$0.177404\pi$
$619$	−3.22743	+	18.3037i	−0.129721	+	0.735686i	−0.978391	+	0.206763i	$0.933707\pi$
$620$	1.83503	+	3.17836i	0.0736965	+	0.127646i
$621$	44.9676	−	10.9230i	1.80449	−	0.438323i
$622$	−5.03384			−0.201839
$623$	10.9766	−	41.0368i	0.439767	−	1.64410i
$624$	−1.96306	−	2.24099i	−0.0785855	−	0.0897115i
$625$	−0.939693	−	0.342020i	−0.0375877	−	0.0136808i
$626$	2.43640	+	13.8175i	0.0973781	+	0.552259i
$627$	−1.27692	−	60.0726i	−0.0509952	−	2.39907i
$628$	−7.04457	−	5.91109i	−0.281109	−	0.235878i
$629$	−3.49558	+	6.05453i	−0.139378	+	0.241410i
$630$	4.93949	−	3.78479i	0.196794	−	0.150790i
$631$	−7.69055	−	13.3204i	−0.306156	−	0.530278i	0.671362	−	0.741130i	$-0.265710\pi$
$631$	−7.69055	−	13.3204i	−0.306156	−	0.530278i	−0.977518	+	0.210852i	$0.932376\pi$
$632$	4.44123	−	25.1875i	0.176663	−	1.00190i
$633$	9.77364	+	1.50995i	0.388467	+	0.0600150i
$634$	−12.0638	−	4.39087i	−0.479115	−	0.174384i
$635$	0.0461250	+	0.261588i	0.00183042	+	0.0103808i
$636$	−5.29406	−	0.817888i	−0.209923	−	0.0324314i
$637$	11.2301	+	13.3598i	0.444954	+	0.529336i
$638$	2.88041	+	4.98902i	0.114037	+	0.197517i
$639$	−25.2914	−	19.4521i	−1.00051	−	0.769513i
$640$	9.18472			0.363058
$641$	−34.8090	+	12.6695i	−1.37487	+	0.500413i	−0.920620	−	0.390459i	$-0.872316\pi$
$641$	−34.8090	+	12.6695i	−1.37487	+	0.500413i	−0.454254	+	0.890872i	$0.650094\pi$
$642$	0.493950	+	23.2379i	0.0194947	+	0.917126i
$643$	−34.0335	−	12.3872i	−1.34215	−	0.488502i	−0.431660	−	0.902036i	$-0.642072\pi$
$643$	−34.0335	−	12.3872i	−1.34215	−	0.488502i	−0.910489	+	0.413534i	$0.864294\pi$
$644$	−29.5895	−	13.7821i	−1.16599	−	0.543091i
$645$	−0.970275	+	2.85305i	−0.0382045	+	0.112339i
$646$	−30.9162	+	11.2526i	−1.21638	+	0.442727i
$647$	−9.43531	−	16.3424i	−0.370940	−	0.642487i	0.618770	−	0.785572i	$-0.287631\pi$
$647$	−9.43531	−	16.3424i	−0.370940	−	0.642487i	−0.989710	+	0.143085i	$0.954298\pi$
$648$	−6.13037	−	23.0869i	−0.240824	−	0.906939i
$649$	12.7375	−	22.0620i	0.499990	−	0.866008i
$650$	1.49740	+	1.25647i	0.0587327	+	0.0492826i
$651$	−12.0682	+	1.32013i	−0.472988	+	0.0517400i
$652$	−3.90760	−	22.1611i	−0.153033	−	0.867896i
$653$	−8.27619	+	6.94455i	−0.323872	+	0.271761i	−0.790198	−	0.612852i	$-0.790022\pi$
$653$	−8.27619	+	6.94455i	−0.323872	+	0.271761i	0.466325	+	0.884613i	$0.345578\pi$
$654$	−5.80516	−	3.18908i	−0.227000	−	0.124703i
$655$	−4.39565	+	1.59989i	−0.171752	+	0.0625128i
$656$	2.46426	+	4.26823i	0.0962133	+	0.166646i
$657$	−39.8232	+	16.4428i	−1.55365	+	0.641493i
$658$	−6.35479	−	13.6124i	−0.247735	−	0.530665i
$659$	40.2027	−	14.6326i	1.56608	−	0.570005i	0.593958	−	0.804496i	$-0.297565\pi$
$659$	40.2027	−	14.6326i	1.56608	−	0.570005i	0.972118	+	0.234491i	$0.0753423\pi$
$660$	−8.83942	+	11.0010i	−0.344074	+	0.428212i
$661$	−8.19858	−	2.98404i	−0.318888	−	0.116066i	0.177617	−	0.984100i	$-0.443161\pi$
$661$	−8.19858	−	2.98404i	−0.318888	−	0.116066i	−0.496505	+	0.868034i	$0.665383\pi$
$662$	0.746943	+	0.271865i	0.0290308	+	0.0105663i
$663$	−11.1194	−	28.6414i	−0.431843	−	1.11234i
$664$	11.9214	−	4.33902i	0.462639	−	0.168387i
$665$	−6.60144	−	14.1407i	−0.255993	−	0.548353i
$666$	1.70575	−	1.55949i	0.0660963	−	0.0604292i
$667$	5.56324	+	9.63581i	0.215409	+	0.373100i
$668$	29.2661	−	10.6520i	1.13234	−	0.412139i
$669$	−0.546964	−	25.7319i	−0.0211469	−	0.994854i
$670$	4.45194	−	3.73562i	0.171993	−	0.144320i
$671$	0.783412	+	4.44295i	0.0302433	+	0.171518i
$672$	−10.7983	+	24.5325i	−0.416552	+	0.946361i
$673$	−5.43849	−	4.56344i	−0.209638	−	0.175908i	0.531923	−	0.846793i	$-0.321470\pi$
$673$	−5.43849	−	4.56344i	−0.209638	−	0.175908i	−0.741561	+	0.670886i	$0.765914\pi$
$674$	8.27927	−	14.3401i	0.318906	−	0.552361i
$675$	−2.08469	−	4.75963i	−0.0802397	−	0.183198i
$676$	−4.69885	−	8.13865i	−0.180725	−	0.313025i
$677$	−4.61457	+	1.67957i	−0.177352	+	0.0645510i	−0.429170	−	0.903224i	$-0.641194\pi$
$677$	−4.61457	+	1.67957i	−0.177352	+	0.0645510i	0.251818	+	0.967775i	$0.418972\pi$
$678$	8.68931	−	1.72332i	0.333711	−	0.0661837i
$679$	2.02968	+	0.945376i	0.0778919	+	0.0362802i
$680$	17.7441	+	6.45833i	0.680456	+	0.247666i
$681$	−30.7416	−	16.8879i	−1.17802	−	0.647148i
$682$	−11.4787	+	4.17792i	−0.439543	+	0.159981i
$683$	−14.0531			−0.537726			−0.268863	−	0.963178i	$-0.586648\pi$
$683$	−14.0531			−0.537726			−0.268863	+	0.963178i	$0.586648\pi$
$684$	−24.4919	+	1.04168i	−0.936471	+	0.0398297i
$685$	6.58436	+	11.4044i	0.251575	+	0.435741i
$686$	6.11911	−	13.1675i	0.233629	−	0.502737i
$687$	7.22097	+	18.5997i	0.275497	+	0.709623i
$688$	−0.208428	−	1.18206i	−0.00794626	−	0.0450655i
$689$	5.23052	+	1.90375i	0.199267	+	0.0725273i
$690$	7.57475	−	9.42705i	0.288366	−	0.358882i
$691$	4.27507	−	24.2451i	0.162631	−	0.922328i	−0.788842	−	0.614596i	$-0.789319\pi$
$691$	4.27507	−	24.2451i	0.162631	−	0.922328i	0.951473	−	0.307731i	$-0.0995698\pi$
$692$	−12.5001	−	21.6507i	−0.475181	−	0.823038i
$693$	−21.5267	−	41.4223i	−0.817733	−	1.57350i
$694$	7.21819	−	12.5023i	0.273999	−	0.474580i
$695$	3.59639	+	3.01773i	0.136419	+	0.114469i
$696$	4.91179	−	2.97676i	0.186181	−	0.112834i
$697$	8.82603	+	50.0549i	0.334310	+	1.89597i
$698$	−11.2697	−	4.10183i	−0.426564	−	0.155257i
$699$	−37.2051	+	7.37876i	−1.40723	+	0.279090i
$700$	−0.947098	+	3.54080i	−0.0357970	+	0.133830i
$701$	0.442332			0.0167066			0.00835332	−	0.999965i	$-0.497341\pi$
$701$	0.442332			0.0167066			0.00835332	+	0.999965i	$0.497341\pi$
$702$	0.647162	+	10.1363i	0.0244255	+	0.382572i
$703$	−2.89804	−	5.01955i	−0.109302	−	0.189316i
$704$	−3.27416	+	18.5687i	−0.123400	+	0.699834i
$705$	−12.3045	+	2.44032i	−0.463416	+	0.0919076i
$706$	2.14774	+	12.1804i	0.0808313	+	0.458417i
$707$	31.5730	+	14.7059i	1.18742	+	0.553074i
$708$	−9.10928	−	5.00420i	−0.342348	−	0.188069i
$709$	37.8626	+	31.7705i	1.42196	+	1.19317i	0.950280	+	0.311397i	$0.100797\pi$
$709$	37.8626	+	31.7705i	1.42196	+	1.19317i	0.471681	+	0.881769i	$0.343647\pi$
$710$	−8.33828			−0.312930
$711$	21.3361	−	19.5067i	0.800167	−	0.731560i
$712$	−42.6136			−1.59701
$713$	−22.1700	+	8.06924i	−0.830275	+	0.302195i
$714$	−17.6780	+	18.4620i	−0.661583	+	0.690923i
$715$	11.2331	−	9.42570i	0.420095	−	0.352501i
$716$	−2.24872	−	12.7531i	−0.0840387	−	0.476607i
$717$	9.67417	+	24.9187i	0.361289	+	0.930604i
$718$	16.7529	+	14.0573i	0.625212	+	0.524615i
$719$	−22.9671			−0.856527			−0.428263	−	0.903654i	$-0.640874\pi$
$719$	−22.9671			−0.856527			−0.428263	+	0.903654i	$0.640874\pi$
$720$	1.64053	+	1.26176i	0.0611389	+	0.0470231i
$721$	14.2622	+	1.24151i	0.531153	+	0.0462361i
$722$	2.14982	−	12.1922i	0.0800081	−	0.453748i
$723$	0.0843140	+	3.96655i	0.00313567	+	0.147518i
$724$	1.81290	+	10.2815i	0.0673760	+	0.382108i
$725$	0.957073	−	0.803080i	0.0355448	−	0.0298256i
$726$	−21.1080	−	24.0965i	−0.783392	−	0.894303i
$727$	−17.0632	−	14.3178i	−0.632841	−	0.531017i	0.268969	−	0.963149i	$-0.413317\pi$
$727$	−17.0632	−	14.3178i	−0.632841	−	0.531017i	−0.901810	+	0.432132i	$0.857761\pi$
$728$	10.0359	−	14.3461i	0.371954	−	0.531700i
$729$	10.4167	−	24.9097i	0.385805	−	0.922580i
$730$	−5.62967	+	9.75087i	−0.208363	+	0.360896i
$731$	2.14949	−	12.1904i	0.0795017	−	0.450877i
$732$	1.80544	−	0.358067i	0.0667309	−	0.0132345i
$733$	10.7329	+	3.90644i	0.396428	+	0.144288i	0.532538	−	0.846406i	$-0.321238\pi$
$733$	10.7329	+	3.90644i	0.396428	+	0.144288i	−0.136111	+	0.990694i	$0.543460\pi$
$734$	6.58016	+	2.39498i	0.242878	+	0.0884004i
$735$	−9.45795	−	7.58599i	−0.348862	−	0.279813i
$736$	−9.04532	+	51.2986i	−0.333415	+	1.89089i
$737$	−21.7986	−	37.7563i	−0.802961	−	1.39077i
$738$	2.21198	−	16.6566i	0.0814241	−	0.613136i
$739$	24.9506	−	43.2158i	0.917824	−	1.58972i	0.115111	−	0.993353i	$-0.463278\pi$
$739$	24.9506	−	43.2158i	0.917824	−	1.58972i	0.802713	−	0.596365i	$-0.203389\pi$
$740$	−0.236389	+	1.34063i	−0.00868984	+	0.0492825i
$741$	25.1734	+	3.88908i	0.924767	+	0.142869i
$742$	−0.405615	−	4.61300i	−0.0148906	−	0.169349i
$743$	31.8866	−	26.7560i	1.16981	−	0.981583i	0.169813	−	0.985476i	$-0.445684\pi$
$743$	31.8866	−	26.7560i	1.16981	−	0.981583i	0.999992	+	0.00389284i	$0.00123913\pi$
$744$	4.40755	+	11.3529i	0.161589	+	0.416219i
$745$	−1.73810	−	1.45844i	−0.0636791	−	0.0534331i
$746$	5.11538	−	8.86009i	0.187287	−	0.324391i
$747$	13.6712	+	4.32748i	0.500205	+	0.158334i
$748$	28.9839	−	50.2017i	1.05976	−	1.83555i
$749$	43.7382	−	11.7401i	1.59816	−	0.428974i
$750$	−1.19016	−	0.653818i	−0.0434585	−	0.0238740i
$751$	−15.0097	+	12.5946i	−0.547710	+	0.459584i	−0.874165	−	0.485629i	$-0.838590\pi$
$751$	−15.0097	+	12.5946i	−0.547710	+	0.459584i	0.326454	+	0.945213i	$0.394146\pi$
$752$	3.82744	−	3.21160i	0.139572	−	0.117115i
$753$	−11.5902	+	34.0805i	−0.422370	+	1.24196i
$754$	−2.29488	+	0.835268i	−0.0835746	+	0.0304187i
$755$	15.3805			0.559753
$756$	−16.7091	+	9.13966i	−0.607702	+	0.332406i
$757$	−16.0784			−0.584381			−0.292190	−	0.956360i	$-0.594384\pi$
$757$	−16.0784			−0.584381			−0.292190	+	0.956360i	$0.594384\pi$
$758$	1.43328	−	0.521673i	0.0520593	−	0.0189480i
$759$	−59.7778	−	68.2410i	−2.16980	−	2.47699i
$760$	−11.9924	+	10.0628i	−0.435011	+	0.365018i
$761$	9.74967	−	8.18095i	0.353425	−	0.296559i	−0.448738	−	0.893663i	$-0.648127\pi$
$761$	9.74967	−	8.18095i	0.353425	−	0.296559i	0.802164	+	0.597104i	$0.203682\pi$
$762$	0.00766533	+	0.360615i	0.000277685	+	0.0130637i
$763$	−3.33461	+	12.4667i	−0.120721	+	0.451326i
$764$	5.03012	−	8.71242i	0.181983	−	0.315204i
$765$	11.4477	+	18.0141i	0.413893	+	0.651301i
$766$	6.81486	−	11.8037i	0.246231	−	0.426484i
$767$	8.27288	+	6.94177i	0.298716	+	0.250653i
$768$	23.3013	+	3.59986i	0.840814	+	0.129899i
$769$	−24.5305	+	20.5835i	−0.884591	+	0.742260i	−0.967118	−	0.254329i	$-0.918145\pi$
$769$	−24.5305	+	20.5835i	−0.884591	+	0.742260i	0.0825270	+	0.996589i	$0.473701\pi$
$770$	−11.0588	−	5.15091i	−0.398530	−	0.185626i
$771$	7.67218	+	19.7619i	0.276307	+	0.711709i
$772$	−1.12688	+	6.39083i	−0.0405572	+	0.230011i
$773$	−14.2882	+	24.7479i	−0.513911	+	0.890121i	0.485958	+	0.873982i	$0.338471\pi$
$773$	−14.2882	+	24.7479i	−0.513911	+	0.890121i	−0.999870	+	0.0161388i	$0.994863\pi$
$774$	−1.89363	+	3.62764i	−0.0680652	+	0.130393i
$775$	1.32460	+	2.29427i	0.0475810	+	0.0824127i
$776$	0.390034	−	2.21199i	0.0140014	−	0.0794060i
$777$	−3.74385	−	2.50225i	−0.134310	−	0.0897676i
$778$	15.6865	+	5.70941i	0.562388	+	0.204692i
$779$	−39.5973	−	14.4122i	−1.41872	−	0.516372i
$780$	−3.94204	−	4.50015i	−0.141148	−	0.161131i
$781$	−10.8620	+	61.6015i	−0.388673	+	2.20427i
$782$	−24.8372	+	43.0193i	−0.888176	+	1.53837i
$783$	6.45213	+	0.717665i	0.230580	+	0.0256472i
$784$	4.75651	+	0.834417i	0.169875	+	0.0298006i
$785$	−5.08506	−	4.26687i	−0.181493	−	0.152291i
$786$	−6.23069	+	1.23571i	−0.222241	+	0.0440764i
$787$	37.2823	−	31.2835i	1.32897	−	1.11514i	0.344651	−	0.938731i	$-0.387997\pi$
$787$	37.2823	−	31.2835i	1.32897	−	1.11514i	0.984317	−	0.176407i	$-0.0564473\pi$
$788$	0.886387	+	5.02695i	0.0315762	+	0.179078i
$789$	−25.5681	+	15.4954i	−0.910248	+	0.551651i
$790$	1.31190	−	7.44015i	0.0466753	−	0.264709i
$791$	−7.30114	−	15.6395i	−0.259599	−	0.556077i
$792$	−34.5619	+	31.5985i	−1.22810	+	1.12280i
$793$	−1.91253			−0.0679161
$794$	−12.6543	−	10.6182i	−0.449083	−	0.376826i
$795$	−3.82147	−	0.590385i	−0.135534	−	0.0209388i
$796$	4.41088	+	25.0153i	0.156339	+	0.886645i
$797$	−11.4588	+	9.61503i	−0.405890	+	0.340582i	−0.822765	−	0.568382i	$-0.807570\pi$
$797$	−11.4588	+	9.61503i	−0.405890	+	0.340582i	0.416875	+	0.908964i	$0.363125\pi$
$798$	−5.92739	−	20.3456i	−0.209827	−	0.720225i
$799$	48.4193	−	17.6232i	1.71295	−	0.623463i
$800$	5.84908			0.206796
$801$	−38.1805	−	29.3653i	−1.34904	−	1.03757i
$802$	13.4438			0.474718
$803$	64.7038	+	54.2930i	2.28335	+	1.91596i
$804$	−15.2114	+	9.21877i	−0.536464	+	0.325121i
$805$	−21.3589	−	9.94848i	−0.752804	−	0.350638i
$806$	−0.899223	−	5.09975i	−0.0316738	−	0.179631i
$807$	2.35413	+	2.68742i	0.0828693	+	0.0946018i
$808$	6.06724	−	34.4090i	0.213445	−	1.21051i
$809$	1.63854	+	2.83804i	0.0576081	+	0.0997801i	0.893391	−	0.449280i	$-0.148319\pi$
$809$	1.63854	+	2.83804i	0.0576081	+	0.0997801i	−0.835783	+	0.549060i	$0.814986\pi$
$810$	−1.81085	−	6.81966i	−0.0636269	−	0.239618i
$811$	−15.9558			−0.560282			−0.280141	−	0.959959i	$-0.590381\pi$
$811$	−15.9558			−0.560282			−0.280141	+	0.959959i	$0.590381\pi$
$812$	−3.23946	−	3.23664i	−0.113683	−	0.113584i
$813$	0.361825	−	1.06393i	0.0126898	−	0.0373137i
$814$	−4.25773	−	1.54969i	−0.149233	−	0.0543165i
$815$	−2.82067	−	15.9968i	−0.0988037	−	0.560343i
$816$	−7.45098	−	4.09321i	−0.260836	−	0.143291i
$817$	7.86147	+	6.59655i	0.275038	+	0.230784i
$818$	−3.13512	+	5.43019i	−0.109617	+	0.189862i
$819$	18.8778	−	5.93783i	0.659645	−	0.207485i
$820$	4.94850	+	8.57105i	0.172809	+	0.299314i
$821$	3.28293	−	18.6184i	0.114575	−	0.649788i	−0.872385	−	0.488820i	$-0.837427\pi$
$821$	3.28293	−	18.6184i	0.114575	−	0.649788i	0.986960	−	0.160968i	$-0.0514615\pi$
$822$	6.47177	+	16.6699i	0.225729	+	0.581431i
$823$	−37.4615	−	13.6349i	−1.30582	−	0.475281i	−0.406935	−	0.913457i	$-0.633403\pi$
$823$	−37.4615	−	13.6349i	−1.30582	−	0.475281i	−0.898889	+	0.438176i	$0.855625\pi$
$824$	−2.49382	−	14.1432i	−0.0868765	−	0.492701i
$825$	−6.38065	+	7.94096i	−0.222146	+	0.276469i
$826$	2.32160	−	8.67948i	0.0807787	−	0.301998i
$827$	−27.1764	−	47.0708i	−0.945014	−	1.63681i	−0.755723	−	0.654892i	$-0.772714\pi$
$827$	−27.1764	−	47.0708i	−0.945014	−	1.63681i	−0.189292	−	0.981921i	$-0.560619\pi$
$828$	−27.3165	+	24.9744i	−0.949314	+	0.867920i
$829$	1.72012			0.0597421			0.0298711	−	0.999554i	$-0.490490\pi$
$829$	1.72012			0.0597421			0.0298711	+	0.999554i	$0.490490\pi$
$830$	3.52146	−	1.28171i	0.122232	−	0.0444887i
$831$	−20.7257	+	12.5607i	−0.718967	+	0.435726i
$832$	−7.51113	−	2.73383i	−0.260401	−	0.0947784i
$833$	43.1517	+	24.8634i	1.49512	+	0.861466i
$834$	4.20070	+	4.79543i	0.145458	+	0.166052i
$835$	21.1255	−	7.68906i	0.731078	−	0.266091i
$836$	24.0294	+	41.6201i	0.831073	+	1.43946i
$837$	−3.87436	+	13.2092i	−0.133918	+	0.456576i
$838$	1.16249	−	2.01349i	0.0401575	−	0.0695549i
$839$	35.3266	+	29.6425i	1.21961	+	1.02337i	0.998845	+	0.0480459i	$0.0152994\pi$
$839$	35.3266	+	29.6425i	1.21961	+	1.02337i	0.220764	+	0.975327i	$0.429145\pi$
$840$	−4.89988	+	11.1320i	−0.169062	+	0.384090i
$841$	−4.76475	−	27.0222i	−0.164302	−	0.931800i
$842$	3.19872	−	2.68404i	0.110235	−	0.0924983i
$843$	−15.1136	+	9.15950i	−0.520540	+	0.315470i
$844$	−7.43296	+	2.70538i	−0.255853	+	0.0931229i
$845$	−3.39182	−	5.87481i	−0.116682	−	0.202100i
$846$	−17.0187	+	0.723834i	−0.585114	+	0.0248859i
$847$	−35.7772	+	51.1427i	−1.22932	+	1.75728i
$848$	1.44727	−	0.526763i	0.0496994	−	0.0180891i
$849$	−15.7668	−	2.43585i	−0.541117	−	0.0835980i
$850$	5.24145	+	1.90773i	0.179780	+	0.0654347i
$851$	−8.22340	−	2.99307i	−0.281894	−	0.102601i
$852$	25.2208	+	3.89640i	0.864049	+	0.133488i
$853$	18.1008	−	6.58816i	0.619761	−	0.225574i	−0.0130079	−	0.999915i	$-0.504141\pi$
$853$	18.1008	−	6.58816i	0.619761	−	0.225574i	0.632769	+	0.774341i	$0.281918\pi$
$854$	0.673070	+	1.44176i	0.0230320	+	0.0493360i
$855$	−17.6793	+	0.751929i	−0.604618	+	0.0257154i
$856$	−22.7147	−	39.3430i	−0.776373	−	1.34472i
$857$	1.47668	−	0.537467i	0.0504424	−	0.0183595i	−0.316676	−	0.948534i	$-0.602567\pi$
$857$	1.47668	−	0.537467i	0.0504424	−	0.0183595i	0.367118	+	0.930174i	$0.380344\pi$
$858$	17.0291	−	10.3204i	0.581364	−	0.352332i
$859$	−3.11729	+	2.61572i	−0.106361	+	0.0892472i	−0.694417	−	0.719573i	$-0.744338\pi$
$859$	−3.11729	+	2.61572i	−0.106361	+	0.0892472i	0.588056	+	0.808820i	$0.299893\pi$
$860$	−0.418546	−	2.37369i	−0.0142723	−	0.0809422i
$861$	−32.5440	+	3.55998i	−1.10910	+	0.121324i
$862$	11.8886	+	9.97574i	0.404928	+	0.339775i
$863$	−17.9703	+	31.1254i	−0.611715	+	1.05952i	0.379236	+	0.925300i	$0.376187\pi$
$863$	−17.9703	+	31.1254i	−0.611715	+	1.05952i	−0.990951	+	0.134222i	$0.957147\pi$
$864$	20.9798	+	21.9901i	0.713747	+	0.748118i
$865$	−9.02306	−	15.6284i	−0.306793	−	0.531381i
$866$	−25.3241	+	9.21720i	−0.860547	+	0.313213i
$867$	−38.3672	−	43.7992i	−1.30302	−	1.48750i
$868$	7.95158	−	5.57293i	0.269894	−	0.189158i
$869$	−53.2573	−	19.3841i	−1.80663	−	0.657560i
$870$	1.45090	−	0.879308i	0.0491900	−	0.0298113i
$871$	17.3673	−	6.32120i	0.588470	−	0.214186i
$872$	12.9457			0.438398
$873$	1.87376	−	1.71311i	0.0634172	−	0.0579798i
$874$	−20.5914	−	35.6654i	−0.696516	−	1.20640i
$875$	−0.683655	+	2.55590i	−0.0231117	+	0.0864051i
$876$	21.5845	−	26.8627i	0.729274	−	0.907608i
$877$	−6.65194	−	37.7250i	−0.224620	−	1.27388i	−0.863410	−	0.504503i	$-0.831676\pi$
$877$	−6.65194	−	37.7250i	−0.224620	−	1.27388i	0.638790	−	0.769381i	$-0.279435\pi$
$878$	21.8653	+	7.95832i	0.737918	+	0.268580i
$879$	4.24434	+	10.9325i	0.143158	+	0.368745i
$880$	0.704565	−	3.99579i	0.0237509	−	0.134698i
$881$	−1.87415	−	3.24611i	−0.0631416	−	0.109364i	0.832727	−	0.553684i	$-0.186779\pi$
$881$	−1.87415	−	3.24611i	−0.0631416	−	0.109364i	−0.895868	+	0.444320i	$0.853445\pi$
$882$	−11.1198	−	12.1413i	−0.374424	−	0.408820i
$883$	1.46178	−	2.53188i	0.0491929	−	0.0852046i	−0.840380	−	0.541997i	$-0.817668\pi$
$883$	1.46178	−	2.53188i	0.0491929	−	0.0852046i	0.889573	+	0.456792i	$0.151002\pi$
$884$	18.8248	+	15.7959i	0.633147	+	0.531273i
$885$	−6.57545	−	3.61224i	−0.221031	−	0.121424i
$886$	2.99589	+	16.9905i	0.100649	+	0.570807i
$887$	−19.7106	−	7.17406i	−0.661817	−	0.240882i	−0.0107961	−	0.999942i	$-0.503437\pi$
$887$	−19.7106	−	7.17406i	−0.661817	−	0.240882i	−0.651020	+	0.759060i	$0.725659\pi$
$888$	−1.45445	+	4.27674i	−0.0488080	+	0.143518i
$889$	0.678748	−	0.182188i	0.0227645	−	0.00611038i
$890$	−12.5877			−0.421939
$891$	−52.7412	+	4.49447i	−1.76690	+	0.150571i
$892$	10.2929	+	17.8278i	0.344632	+	0.596921i
$893$	−7.41801	+	42.0696i	−0.248234	+	1.40781i
$894$	−2.03016	−	2.31759i	−0.0678988	−	0.0775118i
$895$	−1.62322	−	9.20574i	−0.0542583	−	0.307714i
$896$	−2.12850	−	24.2071i	−0.0711082	−	0.808702i
$897$	32.8901	−	19.9328i	1.09817	−	0.665538i
$898$	−0.263885	−	0.221426i	−0.00880597	−	0.00738909i
$899$	−3.30983			−0.110389
$900$	3.29435	+	2.53375i	0.109812	+	0.0844584i
$901$	15.8833			0.529151
$902$	−30.9545	+	11.2665i	−1.03067	+	0.375135i
$903$	7.74431	+	1.89606i	0.257715	+	0.0630970i
$904$	−13.2635	+	11.1294i	−0.441138	+	0.370159i
$905$	1.30863	+	7.42160i	0.0435003	+	0.246702i
$906$	20.6407	+	3.18881i	0.685741	+	0.105941i
$907$	3.12967	+	2.62611i	0.103919	+	0.0871984i	0.693267	−	0.720681i	$-0.256171\pi$
$907$	3.12967	+	2.62611i	0.103919	+	0.0871984i	−0.589348	+	0.807879i	$0.700615\pi$
$908$	28.0539			0.931003
$909$	29.1476	−	26.6485i	0.966765	−	0.883874i
$910$	2.96451	−	4.23769i	0.0982724	−	0.140478i
$911$	−2.36509	+	13.4131i	−0.0783590	+	0.444396i	0.920234	+	0.391368i	$0.127998\pi$
$911$	−2.36509	+	13.4131i	−0.0783590	+	0.444396i	−0.998593	+	0.0530274i	$0.983113\pi$
$912$	6.02751	−	3.65293i	0.199591	−	0.120961i
$913$	−4.88170	−	27.6855i	−0.161561	−	0.916256i
$914$	0.101922	−	0.0855227i	0.00337128	−	0.00282884i
$915$	1.30324	−	0.258467i	0.0430838	−	0.00854466i
$916$	−12.2248	−	10.2579i	−0.403920	−	0.338929i
$917$	5.23530	+	11.2143i	0.172885	+	0.370330i
$918$	11.6281	+	26.5484i	0.383783	+	0.876229i
$919$	−9.17952	+	15.8994i	−0.302804	+	0.524472i	−0.976770	−	0.214290i	$-0.931256\pi$
$919$	−9.17952	+	15.8994i	−0.302804	+	0.524472i	0.673966	+	0.738763i	$0.264590\pi$
$920$	−4.10445	+	23.2775i	−0.135320	+	0.767436i
$921$	33.2701	+	37.9804i	1.09629	+	1.25150i
$922$	−25.5341	−	9.29364i	−0.840920	−	0.306070i
$923$	−24.9181	−	9.06944i	−0.820189	−	0.298524i
$924$	31.0425	+	20.7476i	1.02122	+	0.682546i
$925$	−0.170635	+	0.967722i	−0.00561046	+	0.0318185i
$926$	13.8988	+	24.0734i	0.456743	+	0.791101i
$927$	7.51179	−	14.3904i	0.246719	−	0.472642i
$928$	−3.65383	+	6.32862i	−0.119943	+	0.207747i
$929$	−9.89434	+	56.1136i	−0.324623	+	1.84103i	0.187691	+	0.982228i	$0.439900\pi$
$929$	−9.89434	+	56.1136i	−0.324623	+	1.84103i	−0.512313	+	0.858799i	$0.671211\pi$
$930$	1.30195	+	3.35355i	0.0426926	+	0.109967i
$931$	−35.7392	+	20.6757i	−1.17130	+	0.677618i
$932$	23.2398	−	19.5005i	0.761244	−	0.638760i
$933$	10.9906	+	1.69796i	0.359818	+	0.0555888i
$934$	−21.5708	−	18.1000i	−0.705817	−	0.592251i
$935$	20.9218	−	36.2376i	0.684216	−	1.18510i
$936$	−10.6477	−	16.7551i	−0.348030	−	0.547659i
$937$	−14.3451	+	24.8464i	−0.468633	+	0.811696i	−0.999357	−	0.0358483i	$-0.988587\pi$
$937$	−14.3451	+	24.8464i	−0.468633	+	0.811696i	0.530724	+	0.847545i	$0.321920\pi$
$938$	−10.8772	−	10.8677i	−0.355154	−	0.354844i
$939$	−0.658737	−	30.9903i	−0.0214971	−	1.01133i
$940$	7.68589	−	6.44923i	0.250686	−	0.210351i
$941$	2.31004	−	1.93835i	0.0753051	−	0.0631885i	−0.604358	−	0.796713i	$-0.706570\pi$
$941$	2.31004	−	1.93835i	0.0753051	−	0.0631885i	0.679663	+	0.733524i	$0.262126\pi$
$942$	−5.93953	−	6.78044i	−0.193520	−	0.220919i
$943$	−59.7857	+	21.7602i	−1.94689	+	0.708610i
$944$	2.98818			0.0972571
$945$	−12.0613	+	6.59738i	−0.392354	+	0.214613i
$946$	8.02247			0.260833
$947$	12.0331	−	4.37968i	0.391022	−	0.142320i	−0.139024	−	0.990289i	$-0.544397\pi$
$947$	12.0331	−	4.37968i	0.391022	−	0.142320i	0.530047	+	0.847969i	$0.322174\pi$
$948$	−7.44481	+	21.8912i	−0.241796	+	0.710992i
$949$	−27.4296	+	23.0162i	−0.890402	+	0.747136i
$950$	−3.54245	+	2.97247i	−0.114932	+	0.0964397i
$951$	24.8584	+	13.6560i	0.806090	+	0.442827i
$952$	12.9094	−	48.2628i	0.418396	−	1.56421i
$953$	−0.522977	+	0.905822i	−0.0169409	+	0.0293425i	−0.874372	−	0.485257i	$-0.838726\pi$
$953$	−0.522977	+	0.905822i	−0.0169409	+	0.0293425i	0.857431	+	0.514599i	$0.172059\pi$
$954$	−5.00602	−	1.58460i	−0.162076	−	0.0513033i
$955$	3.63095	−	6.28899i	0.117495	−	0.203507i
$956$	−16.3780	−	13.7428i	−0.529703	−	0.444474i
$957$	−4.60611	−	11.8644i	−0.148894	−	0.383521i
$958$	3.27840	−	2.75091i	0.105920	−	0.0888778i
$959$	28.5315	−	19.9965i	0.921329	−	0.645722i
$960$	5.48770	+	0.847804i	0.177115	+	0.0273627i
$961$	−4.16439	+	23.6174i	−0.134335	+	0.761852i
$962$	0.960399	−	1.66346i	0.0309645	−	0.0536321i
$963$	6.75990	−	50.9031i	0.217835	−	1.64033i
$964$	−1.58664	−	2.74814i	−0.0511023	−	0.0885118i
$965$	−0.813426	+	4.61317i	−0.0261851	+	0.148503i
$966$	−26.6012	−	17.7792i	−0.855879	−	0.572037i
$967$	28.8840	+	10.5129i	0.928846	+	0.338072i	0.761752	−	0.647869i	$-0.224339\pi$
$967$	28.8840	+	10.5129i	0.928846	+	0.338072i	0.167094	+	0.985941i	$0.446562\pi$
$968$	58.8358	+	21.4145i	1.89105	+	0.688287i
$969$	71.2966	−	14.1400i	2.29038	−	0.454243i
$970$	0.115213	−	0.653403i	0.00369925	−	0.0209795i
$971$	−8.26959	+	14.3233i	−0.265384	+	0.459658i	−0.967664	−	0.252242i	$-0.918832\pi$
$971$	−8.26959	+	14.3233i	−0.265384	+	0.459658i	0.702280	+	0.711900i	$0.252165\pi$
$972$	2.29052	+	21.4736i	0.0734686	+	0.688766i
$973$	7.12003	−	10.1779i	0.228258	−	0.326289i
$974$	6.41924	+	5.38638i	0.205686	+	0.172591i
$975$	−2.84553	−	3.24839i	−0.0911297	−	0.104032i
$976$	−0.405385	+	0.340158i	−0.0129760	+	0.0108882i
$977$	4.04860	+	22.9608i	0.129526	+	0.734580i	0.978516	+	0.206171i	$0.0661002\pi$
$977$	4.04860	+	22.9608i	0.129526	+	0.734580i	−0.848990	+	0.528409i	$0.822789\pi$
$978$	−0.468755	−	22.0526i	−0.0149891	−	0.705164i
$979$	−16.3975	+	92.9950i	−0.524067	+	2.97213i
$980$	9.55157	+	1.67560i	0.305114	+	0.0535250i
$981$	11.5990	+	8.92102i	0.370328	+	0.284826i
$982$	15.2971			0.488149
$983$	15.7394	+	13.2069i	0.502009	+	0.421235i	0.858307	−	0.513137i	$-0.171517\pi$
$983$	15.7394	+	13.2069i	0.502009	+	0.421235i	−0.356298	+	0.934372i	$0.615961\pi$
$984$	11.8858	+	30.6153i	0.378905	+	0.975980i
$985$	0.639830	+	3.62866i	0.0203867	+	0.115619i
$986$	−5.33840	+	4.47945i	−0.170009	+	0.142655i
$987$	9.28315	+	31.8641i	0.295486	+	1.01425i
$988$	−19.1446	+	6.96808i	−0.609072	+	0.221684i
$989$	15.4946			0.492700
$990$	−10.2093	+	9.33391i	−0.324471	+	0.296651i
$991$	24.8977			0.790901			0.395451	−	0.918487i	$-0.370588\pi$
$991$	24.8977			0.790901			0.395451	+	0.918487i	$0.370588\pi$
$992$	−11.8701	−	9.96022i	−0.376877	−	0.316237i
$993$	−1.53914	−	0.845528i	−0.0488430	−	0.0268320i
$994$	1.93234	+	21.9762i	0.0612902	+	0.697043i
$995$	3.18395	+	18.0571i	0.100938	+	0.572448i
$996$	−11.2503	+	2.23123i	−0.356479	+	0.0706993i
$997$	10.1616	−	57.6294i	0.321822	−	1.82514i	−0.209307	−	0.977850i	$-0.567121\pi$
$997$	10.1616	−	57.6294i	0.321822	−	1.82514i	0.531129	−	0.847291i	$-0.321768\pi$
$998$	−1.52829	−	2.64707i	−0.0483771	−	0.0837916i
$999$	−4.25027	+	2.82956i	−0.134473	+	0.0895233i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	945.2.bs.a.16.19	✓	276
7.4	even	3		945.2.bu.a.151.28	yes	276
27.22	even	9		945.2.bu.a.751.28	yes	276
189.130	even	9	inner	945.2.bs.a.886.19	yes	276

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
945.2.bs.a.16.19	✓	276	1.1	even	1	trivial
945.2.bs.a.886.19	yes	276	189.130	even	9	inner
945.2.bu.a.151.28	yes	276	7.4	even	3
945.2.bu.a.751.28	yes	276	27.22	even	9

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:	\( N \)	\(=\)	\( 945 = 3^{3} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	945.bs (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.736718 + 0.268143i) q^{2} +(1.69896 - 0.336949i) q^{3} +(-1.06124 + 0.890484i) q^{4} +(-0.766044 + 0.642788i) q^{5} +(-1.16130 + 0.703801i) q^{6} +(1.87165 + 1.87001i) q^{7} +(1.32705 - 2.29852i) q^{8} +(2.77293 - 1.14493i) q^{9} +O(q^{10})\)	\(q+(-0.736718 + 0.268143i) q^{2} +(1.69896 - 0.336949i) q^{3} +(-1.06124 + 0.890484i) q^{4} +(-0.766044 + 0.642788i) q^{5} +(-1.16130 + 0.703801i) q^{6} +(1.87165 + 1.87001i) q^{7} +(1.32705 - 2.29852i) q^{8} +(2.77293 - 1.14493i) q^{9} +(0.391999 - 0.678963i) q^{10} +(-4.50539 - 3.78047i) q^{11} +(-1.50295 + 1.87048i) q^{12} +(1.90995 - 1.60264i) q^{13} +(-1.88031 - 0.875801i) q^{14} +(-1.08489 + 1.35019i) q^{15} +(0.119796 - 0.679397i) q^{16} +(3.55730 - 6.16143i) q^{17} +(-1.73586 + 1.58703i) q^{18} +(2.94921 + 5.10817i) q^{19} +(0.240563 - 1.36430i) q^{20} +(3.80995 + 2.54643i) q^{21} +(4.33291 + 1.57705i) q^{22} +(8.36859 + 3.04592i) q^{23} +(1.48013 - 4.35225i) q^{24} +(0.173648 - 0.984808i) q^{25} +(-0.977356 + 1.69283i) q^{26} +(4.32532 - 2.87952i) q^{27} +(-3.65147 - 0.317856i) q^{28} +(0.957073 + 0.803080i) q^{29} +(0.437215 - 1.28561i) q^{30} +(-2.02940 + 1.70287i) q^{31} +(1.01568 + 5.76022i) q^{32} +(-8.92831 - 4.90478i) q^{33} +(-0.968581 + 5.49310i) q^{34} +(-2.63578 - 0.229441i) q^{35} +(-1.92320 + 3.68429i) q^{36} -0.982650 q^{37} +(-3.54245 - 2.97247i) q^{38} +(2.70492 - 3.36637i) q^{39} +(0.460881 + 2.61378i) q^{40} +(-5.47266 + 4.59211i) q^{41} +(-3.48966 - 0.854384i) q^{42} +(1.63493 - 0.595067i) q^{43} +8.14774 q^{44} +(-1.38824 + 2.65947i) q^{45} -6.98203 q^{46} +(5.54799 + 4.65532i) q^{47} +(-0.0253934 - 1.19463i) q^{48} +(0.00611490 + 7.00000i) q^{49} +(0.136140 + 0.772088i) q^{50} +(3.96763 - 11.6666i) q^{51} +(-0.599786 + 3.40156i) q^{52} +(1.11625 + 1.93340i) q^{53} +(-2.41441 + 3.28120i) q^{54} +5.88137 q^{55} +(6.78204 - 1.82042i) q^{56} +(6.73178 + 7.68485i) q^{57} +(-0.920433 - 0.335010i) q^{58} +(0.752151 + 4.26566i) q^{59} +(-0.0509926 - 2.39895i) q^{60} +(-0.587618 - 0.493070i) q^{61} +(1.03848 - 1.79871i) q^{62} +(7.33097 + 3.04252i) q^{63} +(-1.60296 - 2.77640i) q^{64} +(-0.432950 + 2.45538i) q^{65} +(7.89282 + 1.21938i) q^{66} +(6.96571 + 2.53531i) q^{67} +(1.71151 + 9.70645i) q^{68} +(15.2442 + 2.35511i) q^{69} +(2.00335 - 0.537734i) q^{70} +(-5.31779 - 9.21068i) q^{71} +(1.04819 - 7.89302i) q^{72} -14.3614 q^{73} +(0.723936 - 0.263491i) q^{74} +(-0.0368086 - 1.73166i) q^{75} +(-7.67855 - 2.79476i) q^{76} +(-1.36297 - 15.5008i) q^{77} +(-1.09009 + 3.20537i) q^{78} +(9.05526 - 3.29584i) q^{79} +(0.344939 + 0.597452i) q^{80} +(6.37829 - 6.34960i) q^{81} +(2.80046 - 4.85055i) q^{82} +(3.66164 + 3.07248i) q^{83} +(-6.31081 + 0.690336i) q^{84} +(1.23544 + 7.00651i) q^{85} +(-1.04492 + 0.876793i) q^{86} +(1.89663 + 1.04192i) q^{87} +(-14.6684 + 5.33886i) q^{88} +(-8.02786 - 13.9047i) q^{89} +(0.309625 - 2.33153i) q^{90} +(6.57170 + 0.572057i) q^{91} +(-11.5934 + 4.21965i) q^{92} +(-2.87409 + 3.57692i) q^{93} +(-5.33560 - 1.94200i) q^{94} +(-5.54269 - 2.01738i) q^{95} +(3.66650 + 9.44414i) q^{96} +(0.795243 - 0.289445i) q^{97} +(-1.88151 - 5.15538i) q^{98} +(-16.8215 - 5.32465i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 276 q - 6 q^{3} + 6 q^{9}+O(q^{10}) \) 276 * q - 6 * q^3 + 6 * q^9	\( 276 q - 6 q^{3} + 6 q^{9} + 6 q^{11} + 42 q^{12} + 3 q^{13} + 36 q^{14} - 24 q^{17} + 42 q^{22} + 9 q^{23} + 60 q^{24} - 24 q^{27} - 12 q^{31} - 78 q^{33} - 60 q^{34} + 18 q^{36} - 96 q^{37} - 60 q^{38} - 30 q^{39} + 48 q^{41} - 63 q^{42} - 15 q^{43} + 6 q^{45} - 120 q^{46} + 27 q^{47} - 66 q^{48} + 18 q^{49} - 48 q^{51} + 102 q^{52} - 75 q^{54} - 33 q^{56} - 12 q^{57} - 30 q^{59} - 12 q^{61} - 81 q^{62} - 162 q^{63} - 54 q^{64} - 3 q^{65} + 54 q^{66} - 18 q^{67} - 57 q^{68} + 90 q^{69} + 9 q^{70} + 12 q^{71} - 147 q^{72} + 36 q^{73} - 78 q^{74} - 108 q^{76} - 45 q^{77} + 102 q^{78} - 9 q^{79} + 102 q^{80} + 6 q^{81} - 42 q^{83} + 21 q^{84} + 18 q^{85} + 3 q^{86} - 30 q^{87} + 84 q^{88} + 30 q^{90} + 18 q^{91} - 24 q^{92} - 12 q^{93} + 156 q^{94} + 168 q^{96} + 45 q^{97} - 24 q^{98} - 102 q^{99}+O(q^{100}) \) 276 * q - 6 * q^3 + 6 * q^9 + 6 * q^11 + 42 * q^12 + 3 * q^13 + 36 * q^14 - 24 * q^17 + 42 * q^22 + 9 * q^23 + 60 * q^24 - 24 * q^27 - 12 * q^31 - 78 * q^33 - 60 * q^34 + 18 * q^36 - 96 * q^37 - 60 * q^38 - 30 * q^39 + 48 * q^41 - 63 * q^42 - 15 * q^43 + 6 * q^45 - 120 * q^46 + 27 * q^47 - 66 * q^48 + 18 * q^49 - 48 * q^51 + 102 * q^52 - 75 * q^54 - 33 * q^56 - 12 * q^57 - 30 * q^59 - 12 * q^61 - 81 * q^62 - 162 * q^63 - 54 * q^64 - 3 * q^65 + 54 * q^66 - 18 * q^67 - 57 * q^68 + 90 * q^69 + 9 * q^70 + 12 * q^71 - 147 * q^72 + 36 * q^73 - 78 * q^74 - 108 * q^76 - 45 * q^77 + 102 * q^78 - 9 * q^79 + 102 * q^80 + 6 * q^81 - 42 * q^83 + 21 * q^84 + 18 * q^85 + 3 * q^86 - 30 * q^87 + 84 * q^88 + 30 * q^90 + 18 * q^91 - 24 * q^92 - 12 * q^93 + 156 * q^94 + 168 * q^96 + 45 * q^97 - 24 * q^98 - 102 * q^99

Introduction

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