LMFDB - Embedded newform 418.2.j.d.177.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("418.23");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 418 = 2 \cdot 11 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	418.j (of order $9$, degree $6$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.33774680449$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$5$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			177.4
Character	$\chi$	$=$	418.177
Dual form			418.2.j.d.111.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.766044 - 0.642788i) q^{2} +(1.64633 + 0.599214i) q^{3} +(0.173648 - 0.984808i) q^{4} +(0.477535 + 2.70824i) q^{5} +(1.64633 - 0.599214i) q^{6} +(-1.91741 + 3.32106i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(0.0532024 + 0.0446421i) q^{9} +O(q^{10})$	\(q+(0.766044 - 0.642788i) q^{2} +(1.64633 + 0.599214i) q^{3} +(0.173648 - 0.984808i) q^{4} +(0.477535 + 2.70824i) q^{5} +(1.64633 - 0.599214i) q^{6} +(-1.91741 + 3.32106i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(0.0532024 + 0.0446421i) q^{9} +(2.10664 + 1.76768i) q^{10} +(0.500000 + 0.866025i) q^{11} +(0.875992 - 1.51726i) q^{12} +(2.81802 - 1.02567i) q^{13} +(0.665911 + 3.77657i) q^{14} +(-0.836635 + 4.74479i) q^{15} +(-0.939693 - 0.342020i) q^{16} +(5.31902 - 4.46319i) q^{17} +0.0694508 q^{18} +(-2.84692 + 3.30077i) q^{19} +2.75002 q^{20} +(-5.14671 + 4.31861i) q^{21} +(0.939693 + 0.342020i) q^{22} +(0.183844 - 1.04263i) q^{23} +(-0.304229 - 1.72537i) q^{24} +(-2.40805 + 0.876459i) q^{25} +(1.49944 - 2.59710i) q^{26} +(-2.56714 - 4.44641i) q^{27} +(2.93765 + 2.46498i) q^{28} +(-5.34139 - 4.48196i) q^{29} +(2.40899 + 4.17250i) q^{30} +(2.70296 - 4.68167i) q^{31} +(-0.939693 + 0.342020i) q^{32} +(0.304229 + 1.72537i) q^{33} +(1.20572 - 6.83800i) q^{34} +(-9.90985 - 3.60689i) q^{35} +(0.0532024 - 0.0446421i) q^{36} +5.74381 q^{37} +(-0.0591724 + 4.35850i) q^{38} +5.25398 q^{39} +(2.10664 - 1.76768i) q^{40} +(-5.91848 - 2.15415i) q^{41} +(-1.16667 + 6.61649i) q^{42} +(-0.915209 - 5.19041i) q^{43} +(0.939693 - 0.342020i) q^{44} +(-0.0954954 + 0.165403i) q^{45} +(-0.529359 - 0.916876i) q^{46} +(7.47868 + 6.27536i) q^{47} +(-1.34210 - 1.12615i) q^{48} +(-3.85295 - 6.67350i) q^{49} +(-1.28130 + 2.21927i) q^{50} +(11.4313 - 4.16064i) q^{51} +(-0.520748 - 2.95331i) q^{52} +(-1.31309 + 7.44691i) q^{53} +(-4.82464 - 1.75603i) q^{54} +(-2.10664 + 1.76768i) q^{55} +3.83483 q^{56} +(-6.66482 + 3.72823i) q^{57} -6.97269 q^{58} +(0.760935 - 0.638501i) q^{59} +(4.52743 + 1.64785i) q^{60} +(1.09411 - 6.20503i) q^{61} +(-0.938729 - 5.32380i) q^{62} +(-0.250270 + 0.0910908i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(4.12347 + 7.14206i) q^{65} +(1.34210 + 1.12615i) q^{66} +(1.52853 + 1.28259i) q^{67} +(-3.47174 - 6.01324i) q^{68} +(0.927428 - 1.60635i) q^{69} +(-9.90985 + 3.60689i) q^{70} +(2.32103 + 13.1632i) q^{71} +(0.0120600 - 0.0683957i) q^{72} +(-8.03632 - 2.92498i) q^{73} +(4.40002 - 3.69205i) q^{74} -4.48963 q^{75} +(2.75626 + 3.37684i) q^{76} -3.83483 q^{77} +(4.02478 - 3.37719i) q^{78} +(-9.03521 - 3.28855i) q^{79} +(0.477535 - 2.70824i) q^{80} +(-1.59818 - 9.06371i) q^{81} +(-5.91848 + 2.15415i) q^{82} +(4.93156 - 8.54171i) q^{83} +(3.35928 + 5.81844i) q^{84} +(14.6274 + 12.2738i) q^{85} +(-4.03742 - 3.38780i) q^{86} +(-6.10803 - 10.5794i) q^{87} +(0.500000 - 0.866025i) q^{88} +(-12.3935 + 4.51086i) q^{89} +(0.0331652 + 0.188089i) q^{90} +(-1.99698 + 11.3254i) q^{91} +(-0.994869 - 0.362103i) q^{92} +(7.25528 - 6.08791i) q^{93} +9.76272 q^{94} +(-10.2988 - 6.13390i) q^{95} -1.75198 q^{96} +(-4.67128 + 3.91967i) q^{97} +(-7.24118 - 2.63557i) q^{98} +(-0.0120600 + 0.0683957i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q - 15 q^{8}+O(q^{10}) $ 30 * q - 15 * q^8	$ 30 q - 15 q^{8} + 15 q^{11} - 3 q^{12} - 21 q^{13} - 9 q^{14} + 3 q^{15} + 6 q^{17} + 60 q^{18} - 9 q^{19} + 18 q^{20} - 39 q^{21} + 15 q^{23} + 24 q^{25} - 3 q^{27} + 9 q^{28} - 3 q^{29} - 21 q^{30} - 18 q^{31} + 15 q^{34} + 51 q^{35} - 18 q^{37} - 6 q^{38} - 6 q^{41} + 51 q^{42} + 39 q^{43} - 54 q^{45} - 21 q^{46} - 3 q^{47} - 33 q^{49} - 24 q^{50} - 48 q^{51} - 12 q^{52} - 24 q^{53} - 9 q^{54} - 6 q^{57} - 18 q^{58} + 21 q^{59} + 3 q^{60} + 63 q^{61} - 27 q^{62} + 57 q^{63} - 15 q^{64} - 6 q^{65} - 45 q^{67} - 21 q^{68} + 42 q^{69} + 51 q^{70} - 48 q^{71} + 87 q^{73} + 9 q^{74} + 42 q^{75} - 9 q^{76} - 36 q^{78} - 57 q^{79} + 36 q^{81} - 6 q^{82} - 30 q^{83} + 9 q^{84} + 81 q^{85} - 24 q^{86} - 9 q^{87} + 15 q^{88} - 6 q^{89} - 114 q^{90} - 51 q^{91} - 3 q^{92} + 33 q^{93} + 78 q^{94} - 132 q^{95} + 6 q^{96} - 66 q^{97} + 9 q^{98}+O(q^{100}) $ 30 * q - 15 * q^8 + 15 * q^11 - 3 * q^12 - 21 * q^13 - 9 * q^14 + 3 * q^15 + 6 * q^17 + 60 * q^18 - 9 * q^19 + 18 * q^20 - 39 * q^21 + 15 * q^23 + 24 * q^25 - 3 * q^27 + 9 * q^28 - 3 * q^29 - 21 * q^30 - 18 * q^31 + 15 * q^34 + 51 * q^35 - 18 * q^37 - 6 * q^38 - 6 * q^41 + 51 * q^42 + 39 * q^43 - 54 * q^45 - 21 * q^46 - 3 * q^47 - 33 * q^49 - 24 * q^50 - 48 * q^51 - 12 * q^52 - 24 * q^53 - 9 * q^54 - 6 * q^57 - 18 * q^58 + 21 * q^59 + 3 * q^60 + 63 * q^61 - 27 * q^62 + 57 * q^63 - 15 * q^64 - 6 * q^65 - 45 * q^67 - 21 * q^68 + 42 * q^69 + 51 * q^70 - 48 * q^71 + 87 * q^73 + 9 * q^74 + 42 * q^75 - 9 * q^76 - 36 * q^78 - 57 * q^79 + 36 * q^81 - 6 * q^82 - 30 * q^83 + 9 * q^84 + 81 * q^85 - 24 * q^86 - 9 * q^87 + 15 * q^88 - 6 * q^89 - 114 * q^90 - 51 * q^91 - 3 * q^92 + 33 * q^93 + 78 * q^94 - 132 * q^95 + 6 * q^96 - 66 * q^97 + 9 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$287$	$343$
$\chi(n)$	$e\left(\frac{7}{9}\right)$	$1$

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 $

$2$	0.766044	−	0.642788i	0.541675	−	0.454519i
$2$	0.766044	−	0.642788i	0.541675	−	0.454519i
$3$	1.64633	+	0.599214i	0.950507	+	0.345956i	0.770307	−	0.637673i	$-0.220103\pi$
$3$	1.64633	+	0.599214i	0.950507	+	0.345956i	0.180201	+	0.983630i	$0.442325\pi$
$4$	0.173648	−	0.984808i	0.0868241	−	0.492404i
$5$	0.477535	+	2.70824i	0.213560	+	1.21116i	0.883387	+	0.468644i	$0.155257\pi$
$5$	0.477535	+	2.70824i	0.213560	+	1.21116i	−0.669827	+	0.742517i	$0.733632\pi$
$6$	1.64633	−	0.599214i	0.672110	−	0.244628i
$7$	−1.91741	+	3.32106i	−0.724714	+	1.25524i	0.234377	+	0.972146i	$0.424695\pi$
$7$	−1.91741	+	3.32106i	−0.724714	+	1.25524i	−0.959092	+	0.283096i	$0.908638\pi$
$8$	−0.500000	−	0.866025i	−0.176777	−	0.306186i
$9$	0.0532024	+	0.0446421i	0.0177341	+	0.0148807i
$10$	2.10664	+	1.76768i	0.666177	+	0.558989i
$11$	0.500000	+	0.866025i	0.150756	+	0.261116i
$11$	0.500000	+	0.866025i	0.150756	+	0.261116i
$12$	0.875992	−	1.51726i	0.252877	−	0.437996i
$13$	2.81802	−	1.02567i	0.781577	−	0.284471i	0.0797470	−	0.996815i	$-0.474589\pi$
$13$	2.81802	−	1.02567i	0.781577	−	0.284471i	0.701830	+	0.712344i	$0.252367\pi$
$14$	0.665911	+	3.77657i	0.177972	+	1.00933i
$15$	−0.836635	+	4.74479i	−0.216018	+	1.22510i
$16$	−0.939693	−	0.342020i	−0.234923	−	0.0855050i
$17$	5.31902	−	4.46319i	1.29005	−	1.08248i	0.298278	−	0.954479i	$-0.403588\pi$
$17$	5.31902	−	4.46319i	1.29005	−	1.08248i	0.991774	−	0.128003i	$-0.0408568\pi$
$18$	0.0694508			0.0163697
$19$	−2.84692	+	3.30077i	−0.653127	+	0.757248i
$19$	−2.84692	+	3.30077i	−0.653127	+	0.757248i
$20$	2.75002			0.614923
$21$	−5.14671	+	4.31861i	−1.12311	+	0.942397i
$22$	0.939693	+	0.342020i	0.200343	+	0.0729189i
$23$	0.183844	−	1.04263i	0.0383342	−	0.217404i	−0.959623	−	0.281289i	$-0.909238\pi$
$23$	0.183844	−	1.04263i	0.0383342	−	0.217404i	0.997957	+	0.0638851i	$0.0203491\pi$
$24$	−0.304229	−	1.72537i	−0.0621005	−	0.352189i
$25$	−2.40805	+	0.876459i	−0.481610	+	0.175292i
$26$	1.49944	−	2.59710i	0.294063	−	0.509333i
$27$	−2.56714	−	4.44641i	−0.494046	−	0.855713i
$28$	2.93765	+	2.46498i	0.555163	+	0.465837i
$29$	−5.34139	−	4.48196i	−0.991872	−	0.832279i	−0.00603405	−	0.999982i	$-0.501921\pi$
$29$	−5.34139	−	4.48196i	−0.991872	−	0.832279i	−0.985838	+	0.167703i	$0.946365\pi$
$30$	2.40899	+	4.17250i	0.439820	+	0.761791i
$31$	2.70296	−	4.68167i	0.485466	−	0.840853i	−0.514394	−	0.857554i	$-0.671983\pi$
$31$	2.70296	−	4.68167i	0.485466	−	0.840853i	0.999861	+	0.0167014i	$0.00531646\pi$
$32$	−0.939693	+	0.342020i	−0.166116	+	0.0604612i
$33$	0.304229	+	1.72537i	0.0529595	+	0.300348i
$34$	1.20572	−	6.83800i	0.206780	−	1.17271i
$35$	−9.90985	−	3.60689i	−1.67507	−	0.609676i
$36$	0.0532024	−	0.0446421i	0.00886707	−	0.00744035i
$37$	5.74381			0.944277			0.472139	−	0.881524i	$-0.343482\pi$
$37$	5.74381			0.944277			0.472139	+	0.881524i	$0.343482\pi$
$38$	−0.0591724	+	4.35850i	−0.00959902	+	0.707042i
$39$	5.25398			0.841309
$40$	2.10664	−	1.76768i	0.333088	−	0.279494i
$41$	−5.91848	−	2.15415i	−0.924311	−	0.336422i	−0.164359	−	0.986401i	$-0.552556\pi$
$41$	−5.91848	−	2.15415i	−0.924311	−	0.336422i	−0.759952	+	0.649979i	$0.774778\pi$
$42$	−1.16667	+	6.61649i	−0.180020	+	1.02095i
$43$	−0.915209	−	5.19041i	−0.139568	−	0.791530i	−0.971569	−	0.236756i	$-0.923916\pi$
$43$	−0.915209	−	5.19041i	−0.139568	−	0.791530i	0.832001	−	0.554774i	$-0.187195\pi$
$44$	0.939693	−	0.342020i	0.141664	−	0.0515615i
$45$	−0.0954954	+	0.165403i	−0.0142356	+	0.0246568i
$46$	−0.529359	−	0.916876i	−0.0780497	−	0.135186i
$47$	7.47868	+	6.27536i	1.09088	+	0.915355i	0.996778	−	0.0802082i	$-0.0255585\pi$
$47$	7.47868	+	6.27536i	1.09088	+	0.915355i	0.0940990	+	0.995563i	$0.470003\pi$
$48$	−1.34210	−	1.12615i	−0.193715	−	0.162546i
$49$	−3.85295	−	6.67350i	−0.550421	−	0.953358i
$50$	−1.28130	+	2.21927i	−0.181203	+	0.313853i
$51$	11.4313	−	4.16064i	1.60070	−	0.582606i
$52$	−0.520748	−	2.95331i	−0.0722148	−	0.409551i
$53$	−1.31309	+	7.44691i	−0.180367	+	1.02291i	0.751398	+	0.659849i	$0.229380\pi$
$53$	−1.31309	+	7.44691i	−0.180367	+	1.02291i	−0.931765	+	0.363062i	$0.881731\pi$
$54$	−4.82464	−	1.75603i	−0.656551	−	0.238965i
$55$	−2.10664	+	1.76768i	−0.284059	+	0.238354i
$56$	3.83483			0.512450
$57$	−6.66482	+	3.72823i	−0.882777	+	0.493816i
$58$	−6.97269			−0.915559
$59$	0.760935	−	0.638501i	0.0990653	−	0.0831257i	−0.591910	−	0.806004i	$-0.701626\pi$
$59$	0.760935	−	0.638501i	0.0990653	−	0.0831257i	0.690975	+	0.722879i	$0.257181\pi$
$60$	4.52743	+	1.64785i	0.584488	+	0.212736i
$61$	1.09411	−	6.20503i	0.140087	−	0.794473i	−0.831094	−	0.556131i	$-0.812285\pi$
$61$	1.09411	−	6.20503i	0.140087	−	0.794473i	0.971181	−	0.238341i	$-0.0766037\pi$
$62$	−0.938729	−	5.32380i	−0.119219	−	0.676123i
$63$	−0.250270	+	0.0910908i	−0.0315311	+	0.0114764i
$64$	−0.500000	+	0.866025i	−0.0625000	+	0.108253i
$65$	4.12347	+	7.14206i	0.511454	+	0.885864i
$66$	1.34210	+	1.12615i	0.165201	+	0.138620i
$67$	1.52853	+	1.28259i	0.186739	+	0.156693i	0.731365	−	0.681986i	$-0.238884\pi$
$67$	1.52853	+	1.28259i	0.186739	+	0.156693i	−0.544625	+	0.838679i	$0.683328\pi$
$68$	−3.47174	−	6.01324i	−0.421011	−	0.729212i
$69$	0.927428	−	1.60635i	0.111649	−	0.193382i
$70$	−9.90985	+	3.60689i	−1.18445	+	0.431106i
$71$	2.32103	+	13.1632i	0.275455	+	1.56218i	0.737512	+	0.675334i	$0.236001\pi$
$71$	2.32103	+	13.1632i	0.275455	+	1.56218i	−0.462056	+	0.886851i	$0.652888\pi$
$72$	0.0120600	−	0.0683957i	0.00142129	−	0.00806051i
$73$	−8.03632	−	2.92498i	−0.940580	−	0.342343i	−0.174185	−	0.984713i	$-0.555729\pi$
$73$	−8.03632	−	2.92498i	−0.940580	−	0.342343i	−0.766395	+	0.642370i	$0.777951\pi$
$74$	4.40002	−	3.69205i	0.511492	−	0.429192i
$75$	−4.48963			−0.518418
$76$	2.75626	+	3.37684i	0.316165	+	0.387350i
$77$	−3.83483			−0.437019
$78$	4.02478	−	3.37719i	0.455716	−	0.382391i
$79$	−9.03521	−	3.28855i	−1.01654	−	0.369991i	−0.220600	−	0.975364i	$-0.570801\pi$
$79$	−9.03521	−	3.28855i	−1.01654	−	0.369991i	−0.795941	+	0.605374i	$0.793024\pi$
$80$	0.477535	−	2.70824i	0.0533901	−	0.302790i
$81$	−1.59818	−	9.06371i	−0.177575	−	1.00708i
$82$	−5.91848	+	2.15415i	−0.653587	+	0.237886i
$83$	4.93156	−	8.54171i	0.541309	−	0.937575i	−0.457520	−	0.889199i	$-0.651262\pi$
$83$	4.93156	−	8.54171i	0.541309	−	0.937575i	0.998829	−	0.0483754i	$-0.0154044\pi$
$84$	3.35928	+	5.81844i	0.366527	+	0.634844i
$85$	14.6274	+	12.2738i	1.58656	+	1.33129i
$86$	−4.03742	−	3.38780i	−0.435367	−	0.365316i
$87$	−6.10803	−	10.5794i	−0.654849	−	1.13423i
$88$	0.500000	−	0.866025i	0.0533002	−	0.0923186i
$89$	−12.3935	+	4.51086i	−1.31371	+	0.478150i	−0.901436	−	0.432912i	$-0.857486\pi$
$89$	−12.3935	+	4.51086i	−1.31371	+	0.478150i	−0.412270	+	0.911062i	$0.635264\pi$
$90$	0.0331652	+	0.188089i	0.00349592	+	0.0198264i
$91$	−1.99698	+	11.3254i	−0.209340	+	1.18723i
$92$	−0.994869	−	0.362103i	−0.103722	−	0.0377518i
$93$	7.25528	−	6.08791i	0.752338	−	0.631286i
$94$	9.76272			1.00695
$95$	−10.2988	−	6.13390i	−1.05663	−	0.629324i
$96$	−1.75198			−0.178811
$97$	−4.67128	+	3.91967i	−0.474296	+	0.397982i	−0.848359	−	0.529422i	$-0.822409\pi$
$97$	−4.67128	+	3.91967i	−0.474296	+	0.397982i	0.374063	+	0.927403i	$0.377965\pi$
$98$	−7.24118	−	2.63557i	−0.731469	−	0.266233i
$99$	−0.0120600	+	0.0683957i	−0.00121208	+	0.00687402i
$100$	0.444990	+	2.52366i	0.0444990	+	0.252366i
$101$	16.8080	−	6.11760i	1.67245	−	0.608724i	0.680209	−	0.733018i	$-0.261889\pi$
$101$	16.8080	−	6.11760i	1.67245	−	0.608724i	0.992245	+	0.124294i	$0.0396667\pi$
$102$	6.08244	−	10.5351i	0.602252	−	1.04313i
$103$	−0.817615	−	1.41615i	−0.0805620	−	0.139537i	0.822929	−	0.568144i	$-0.192338\pi$
$103$	−0.817615	−	1.41615i	−0.0805620	−	0.139537i	−0.903491	+	0.428606i	$0.859005\pi$
$104$	−2.29727	−	1.92764i	−0.225266	−	0.189020i
$105$	−14.1536	−	11.8762i	−1.38125	−	1.15900i
$106$	3.78089	+	6.54870i	0.367233	+	0.636066i
$107$	−3.34627	+	5.79590i	−0.323496	+	0.560311i	−0.981207	−	0.192959i	$-0.938191\pi$
$107$	−3.34627	+	5.79590i	−0.323496	+	0.560311i	0.657711	+	0.753270i	$0.271525\pi$
$108$	−4.82464	+	1.75603i	−0.464251	+	0.168974i
$109$	0.459503	+	2.60597i	0.0440124	+	0.249607i	0.998874	−	0.0474446i	$-0.0151078\pi$
$109$	0.459503	+	2.60597i	0.0440124	+	0.249607i	−0.954861	+	0.297052i	$0.903997\pi$
$110$	−0.477535	+	2.70824i	−0.0455312	+	0.258220i
$111$	9.45620	+	3.44177i	0.897543	+	0.326679i
$112$	2.93765	−	2.46498i	0.277582	−	0.232919i
$113$	8.01087			0.753599			0.376800	−	0.926295i	$-0.377025\pi$
$113$	8.01087			0.753599			0.376800	+	0.926295i	$0.377025\pi$
$114$	−2.70909	+	7.14006i	−0.253730	+	0.668727i
$115$	2.91149			0.271498
$116$	−5.34139	+	4.48196i	−0.495936	+	0.416140i
$117$	0.195713	+	0.0712339i	0.0180937	+	0.00658557i
$118$	0.172490	−	0.978240i	0.0158790	−	0.0900543i
$119$	4.62374	+	26.2226i	0.423858	+	2.40382i
$120$	4.52743	−	1.64785i	0.413296	−	0.150427i
$121$	−0.500000	+	0.866025i	−0.0454545	+	0.0787296i
$122$	−3.15038	−	5.45661i	−0.285222	−	0.494019i
$123$	−8.45296	−	7.09287i	−0.762177	−	0.639543i
$124$	−4.14118	−	3.47486i	−0.371889	−	0.312052i
$125$	3.35145	+	5.80489i	0.299763	+	0.519205i
$126$	−0.133166	+	0.230650i	−0.0118634	+	0.0205479i
$127$	−19.5379	+	7.11122i	−1.73371	+	0.631019i	−0.998884	−	0.0472376i	$-0.984958\pi$
$127$	−19.5379	+	7.11122i	−1.73371	+	0.631019i	−0.734826	+	0.678256i	$0.762736\pi$
$128$	0.173648	+	0.984808i	0.0153485	+	0.0870455i
$129$	1.60343	−	9.09352i	0.141174	−	0.800640i
$130$	7.74959	+	2.82062i	0.679684	+	0.247385i
$131$	−5.12377	+	4.29935i	−0.447665	+	0.375636i	−0.838569	−	0.544796i	$-0.816607\pi$
$131$	−5.12377	+	4.29935i	−0.447665	+	0.375636i	0.390903	+	0.920432i	$0.372163\pi$
$132$	1.75198			0.152491
$133$	−5.50332	−	15.7837i	−0.477199	−	1.36862i
$134$	1.99535			0.172372
$135$	10.8161	−	9.07574i	0.930897	−	0.781116i
$136$	−6.52474	−	2.37481i	−0.559492	−	0.203639i
$137$	2.84751	−	16.1490i	0.243279	−	1.37970i	−0.581177	−	0.813777i	$-0.697407\pi$
$137$	2.84751	−	16.1490i	0.243279	−	1.37970i	0.824456	−	0.565927i	$-0.191481\pi$
$138$	−0.322092	−	1.82668i	−0.0274183	−	0.155497i
$139$	−12.4003	+	4.51334i	−1.05178	+	0.382817i	−0.809334	−	0.587348i	$-0.800172\pi$
$139$	−12.4003	+	4.51334i	−1.05178	+	0.382817i	−0.242446	+	0.970165i	$0.577950\pi$
$140$	−5.27292	+	9.13297i	−0.445643	+	0.771876i
$141$	8.55207	+	14.8126i	0.720214	+	1.24745i
$142$	10.2392	+	8.59167i	0.859251	+	0.720997i
$143$	2.29727	+	1.92764i	0.192107	+	0.161197i
$144$	−0.0347254	−	0.0601462i	−0.00289378	−	0.00501218i
$145$	9.58751	−	16.6061i	0.796200	−	1.37906i
$146$	−8.03632	+	2.92498i	−0.665091	+	0.242073i
$147$	−2.34436	−	13.2955i	−0.193359	−	1.09660i
$148$	0.997403	−	5.65655i	0.0819860	−	0.464966i
$149$	−9.79758	−	3.56603i	−0.802649	−	0.292140i	−0.0920650	−	0.995753i	$-0.529347\pi$
$149$	−9.79758	−	3.56603i	−0.802649	−	0.292140i	−0.710584	+	0.703613i	$0.751569\pi$
$150$	−3.43925	+	2.88588i	−0.280814	+	0.235631i
$151$	0.887856			0.0722527			0.0361264	−	0.999347i	$-0.488498\pi$
$151$	0.887856			0.0722527			0.0361264	+	0.999347i	$0.488498\pi$
$152$	4.28201	+	0.815119i	0.347317	+	0.0661148i
$153$	0.482231			0.0389860
$154$	−2.93765	+	2.46498i	−0.236722	+	0.198634i
$155$	13.9698	+	5.08460i	1.12208	+	0.408405i
$156$	0.912343	−	5.17416i	0.0730459	−	0.414264i
$157$	−1.33541	−	7.57349i	−0.106577	−	0.604430i	−0.990579	−	0.136946i	$-0.956271\pi$
$157$	−1.33541	−	7.57349i	−0.106577	−	0.604430i	0.884001	−	0.467485i	$-0.154840\pi$
$158$	−9.03521	+	3.28855i	−0.718803	+	0.261623i
$159$	−6.62407	+	11.4732i	−0.525323	+	0.909886i
$160$	−1.37501	−	2.38158i	−0.108704	−	0.188281i
$161$	3.11014	+	2.60972i	0.245113	+	0.205674i
$162$	−7.05031	−	5.91591i	−0.553925	−	0.464798i
$163$	−0.488622	−	0.846318i	−0.0382718	−	0.0662887i	0.846255	−	0.532778i	$-0.178852\pi$
$163$	−0.488622	−	0.846318i	−0.0382718	−	0.0662887i	−0.884527	+	0.466489i	$0.845519\pi$
$164$	−3.14916	+	5.45450i	−0.245908	+	0.425925i
$165$	−4.52743	+	1.64785i	−0.352460	+	0.128285i
$166$	−1.71271	−	9.71328i	−0.132932	−	0.753896i
$167$	−2.50710	+	14.2185i	−0.194005	+	1.10026i	0.719823	+	0.694157i	$0.244223\pi$
$167$	−2.50710	+	14.2185i	−0.194005	+	1.10026i	−0.913828	+	0.406100i	$0.866888\pi$
$168$	6.31338	+	2.29788i	0.487088	+	0.177285i
$169$	−3.06937	+	2.57551i	−0.236105	+	0.198116i
$170$	19.0947			1.46450
$171$	−0.298816	+	0.0485164i	−0.0228510	+	0.00371014i
$172$	−5.27048			−0.401870
$173$	−15.8905	+	13.3338i	−1.20814	+	1.01375i	−0.208776	+	0.977963i	$0.566948\pi$
$173$	−15.8905	+	13.3338i	−1.20814	+	1.01375i	−0.999360	+	0.0357828i	$0.988608\pi$
$174$	−11.4793	−	4.17814i	−0.870246	−	0.316744i
$175$	1.70646	−	9.67781i	0.128996	−	0.731574i
$176$	−0.173648	−	0.984808i	−0.0130892	−	0.0742327i
$177$	1.63535	−	0.595218i	0.122920	−	0.0447393i
$178$	−6.59443	+	11.4219i	−0.494274	+	0.856107i
$179$	9.76518	+	16.9138i	0.729884	+	1.26420i	0.956932	+	0.290312i	$0.0937591\pi$
$179$	9.76518	+	16.9138i	0.729884	+	1.26420i	−0.227048	+	0.973883i	$0.572908\pi$
$180$	0.146308	+	0.122767i	0.0109051	+	0.00915048i
$181$	0.401744	+	0.337103i	0.0298614	+	0.0250567i	0.657596	−	0.753371i	$-0.271573\pi$
$181$	0.401744	+	0.337103i	0.0298614	+	0.0250567i	−0.627735	+	0.778427i	$0.716018\pi$
$182$	5.75007	+	9.95942i	0.426224	+	0.738241i
$183$	5.51941	−	9.55990i	0.408007	−	0.706688i
$184$	−0.994869	+	0.362103i	−0.0733427	+	0.0266946i
$185$	2.74288	+	15.5556i	0.201660	+	1.14367i
$186$	1.64464	−	9.32721i	0.120591	−	0.683904i
$187$	6.52474	+	2.37481i	0.477137	+	0.173664i
$188$	7.47868	−	6.27536i	0.545439	−	0.457677i
$189$	19.6891			1.43217
$190$	−11.8321	+	1.92108i	−0.858391	+	0.139370i
$191$	19.6960			1.42515			0.712576	−	0.701595i	$-0.247528\pi$
$191$	19.6960			1.42515			0.712576	+	0.701595i	$0.247528\pi$
$192$	−1.34210	+	1.12615i	−0.0968576	+	0.0812732i
$193$	0.524395	+	0.190864i	0.0377468	+	0.0137387i	0.360825	−	0.932634i	$-0.382495\pi$
$193$	0.524395	+	0.190864i	0.0377468	+	0.0137387i	−0.323078	+	0.946372i	$0.604718\pi$
$194$	−1.05889	+	6.00528i	−0.0760240	+	0.431154i
$195$	2.50896	+	14.2290i	0.179670	+	1.01896i
$196$	−7.24118	+	2.63557i	−0.517227	+	0.188255i
$197$	13.6174	−	23.5861i	0.970202	−	1.68044i	0.275265	−	0.961368i	$-0.411234\pi$
$197$	13.6174	−	23.5861i	0.970202	−	1.68044i	0.694937	−	0.719071i	$-0.255432\pi$
$198$	0.0347254	+	0.0601462i	0.00246783	+	0.00427440i
$199$	−7.40057	−	6.20982i	−0.524613	−	0.440202i	0.341624	−	0.939837i	$-0.389023\pi$
$199$	−7.40057	−	6.20982i	−0.524613	−	0.440202i	−0.866236	+	0.499635i	$0.833468\pi$
$200$	1.96306	+	1.64720i	0.138809	+	0.116475i
$201$	1.74791	+	3.02747i	0.123288	+	0.213542i
$202$	8.94333	−	15.4903i	0.629250	−	1.08989i
$203$	25.1265	−	9.14530i	1.76354	−	0.641874i
$204$	−2.11241	−	11.9801i	−0.147898	−	0.838773i
$205$	3.00767	−	17.0573i	0.210065	−	1.19134i
$206$	−1.53661	−	0.559281i	−0.107061	−	0.0389670i
$207$	0.0563263	−	0.0472634i	0.00391495	−	0.00328503i
$208$	−2.99887			−0.207934
$209$	−4.28201	−	0.815119i	−0.296193	−	0.0563829i
$210$	−18.4762			−1.27498
$211$	12.8148	−	10.7529i	0.882205	−	0.740258i	−0.0844260	−	0.996430i	$-0.526906\pi$
$211$	12.8148	−	10.7529i	0.882205	−	0.740258i	0.966631	+	0.256172i	$0.0824612\pi$
$212$	7.10576	+	2.58628i	0.488025	+	0.177627i
$213$	−4.06641	+	23.0617i	−0.278626	+	1.58016i
$214$	1.16215	+	6.59086i	0.0794426	+	0.450542i
$215$	13.6198	−	4.95721i	0.928864	−	0.338079i
$216$	−2.56714	+	4.44641i	−0.174672	+	0.302540i
$217$	10.3654	+	17.9534i	0.703649	+	1.21876i
$218$	2.02709	+	1.70093i	0.137292	+	0.115201i
$219$	−11.4777	−	9.63095i	−0.775593	−	0.650800i
$220$	1.37501	+	2.38158i	0.0927031	+	0.160566i
$221$	10.4113	−	18.0329i	0.700341	−	1.21303i
$222$	9.45620	−	3.44177i	0.634658	−	0.230997i
$223$	−1.70832	−	9.68837i	−0.114398	−	0.648781i	−0.987047	−	0.160433i	$-0.948711\pi$
$223$	−1.70832	−	9.68837i	−0.114398	−	0.648781i	0.872649	−	0.488348i	$-0.162400\pi$
$224$	0.665911	−	3.77657i	0.0444930	−	0.252333i
$225$	−0.167241	−	0.0608708i	−0.0111494	−	0.00405805i
$226$	6.13668	−	5.14929i	0.408206	−	0.342525i
$227$	0.864686			0.0573913			0.0286956	−	0.999588i	$-0.490865\pi$
$227$	0.864686			0.0573913			0.0286956	+	0.999588i	$0.490865\pi$
$228$	2.51426	+	7.21097i	0.166511	+	0.477558i
$229$	8.33952			0.551091			0.275545	−	0.961288i	$-0.411142\pi$
$229$	8.33952			0.551091			0.275545	+	0.961288i	$0.411142\pi$
$230$	2.23033	−	1.87147i	0.147064	−	0.123401i
$231$	−6.31338	−	2.29788i	−0.415390	−	0.151190i
$232$	−1.21080	+	6.86676i	−0.0794926	+	0.450825i
$233$	3.44822	+	19.5558i	0.225901	+	1.28115i	0.860956	+	0.508679i	$0.169866\pi$
$233$	3.44822	+	19.5558i	0.225901	+	1.28115i	−0.635056	+	0.772466i	$0.719023\pi$
$234$	0.195713	−	0.0712339i	0.0127942	−	0.00465670i
$235$	−13.4238	+	23.2507i	−0.875674	+	1.51671i
$236$	−0.496665	−	0.860249i	−0.0323302	−	0.0559975i
$237$	−12.9044	−	10.8281i	−0.838229	−	0.703358i
$238$	20.3975	+	17.1156i	1.32218	+	1.10944i
$239$	7.88224	+	13.6524i	0.509860	+	0.883103i	0.999935	+	0.0114229i	$0.00363609\pi$
$239$	7.88224	+	13.6524i	0.509860	+	0.883103i	−0.490075	+	0.871680i	$0.663031\pi$
$240$	2.40899	−	4.17250i	0.155500	−	0.269334i
$241$	20.7523	−	7.55322i	1.33677	−	0.486546i	0.427978	−	0.903789i	$-0.359226\pi$
$241$	20.7523	−	7.55322i	1.33677	−	0.486546i	0.908795	+	0.417243i	$0.137004\pi$
$242$	0.173648	+	0.984808i	0.0111625	+	0.0633058i
$243$	0.125306	−	0.710647i	0.00803840	−	0.0455880i
$244$	−5.92077	−	2.15498i	−0.379039	−	0.137959i
$245$	16.2335	−	13.6215i	1.03712	−	0.870248i
$246$	−11.0346			−0.703537
$247$	−4.63715	+	12.2216i	−0.295055	+	0.777643i
$248$	−5.40593			−0.343277
$249$	13.2373	−	11.1074i	0.838878	−	0.703902i
$250$	6.29867	+	2.29253i	0.398363	+	0.144992i
$251$	1.36076	−	7.71724i	0.0858903	−	0.487108i	−0.911271	−	0.411808i	$-0.864897\pi$
$251$	1.36076	−	7.71724i	0.0858903	−	0.487108i	0.997161	−	0.0753001i	$-0.0239915\pi$
$252$	0.0462480	+	0.262286i	0.00291335	+	0.0165224i
$253$	0.994869	−	0.362103i	0.0625469	−	0.0227652i
$254$	−10.3959	+	18.0062i	−0.652297	+	1.12981i
$255$	16.7268	+	28.9717i	1.04747	+	1.81428i
$256$	0.766044	+	0.642788i	0.0478778	+	0.0401742i
$257$	−15.6971	−	13.1715i	−0.979161	−	0.821614i	0.00480162	−	0.999988i	$-0.498472\pi$
$257$	−15.6971	−	13.1715i	−0.979161	−	0.821614i	−0.983963	+	0.178375i	$0.942916\pi$
$258$	−4.61690	−	7.99671i	−0.287436	−	0.497853i
$259$	−11.0133	+	19.0755i	−0.684331	+	1.18530i
$260$	7.74959	−	2.82062i	0.480609	−	0.174928i
$261$	−0.0840907	−	0.476902i	−0.00520508	−	0.0295195i
$262$	−1.16146	+	6.58699i	−0.0717554	+	0.406945i
$263$	25.1972	+	9.17102i	1.55372	+	0.565509i	0.969288	−	0.245930i	$-0.0790933\pi$
$263$	25.1972	+	9.17102i	1.55372	+	0.565509i	0.584437	+	0.811439i	$0.301316\pi$
$264$	1.34210	−	1.12615i	0.0826004	−	0.0693100i
$265$	−20.7950			−1.27743
$266$	−14.3614	−	8.55356i	−0.880552	−	0.524452i
$267$	−23.1067			−1.41411
$268$	1.52853	−	1.28259i	0.0933697	−	0.0783465i
$269$	−10.3002	−	3.74895i	−0.628011	−	0.228577i	0.00835415	−	0.999965i	$-0.497341\pi$
$269$	−10.3002	−	3.74895i	−0.628011	−	0.228577i	−0.636366	+	0.771388i	$0.719563\pi$
$270$	2.45180	−	13.9048i	0.149212	−	0.846222i
$271$	0.323056	+	1.83214i	0.0196242	+	0.111295i	0.993046	−	0.117723i	$-0.0375596\pi$
$271$	0.323056	+	1.83214i	0.0196242	+	0.111295i	−0.973422	+	0.229018i	$0.926449\pi$
$272$	−6.52474	+	2.37481i	−0.395621	+	0.143994i
$273$	−10.0740	+	17.4488i	−0.609709	+	1.05605i
$274$	−8.19907	−	14.2012i	−0.495324	−	0.857927i
$275$	−1.96306	−	1.64720i	−0.118377	−	0.0993302i
$276$	−1.42090	−	1.19228i	−0.0855283	−	0.0717667i
$277$	−9.38844	−	16.2613i	−0.564097	−	0.977044i	−0.997133	−	0.0756677i	$-0.975891\pi$
$277$	−9.38844	−	16.2613i	−0.564097	−	0.977044i	0.433036	−	0.901376i	$-0.357442\pi$
$278$	−6.59806	+	11.4282i	−0.395726	+	0.685417i
$279$	0.352804	−	0.128410i	0.0211218	−	0.00768771i
$280$	1.83127	+	10.3856i	0.109439	+	0.620660i
$281$	2.20716	−	12.5174i	0.131668	−	0.746727i	−0.845454	−	0.534048i	$-0.820670\pi$
$281$	2.20716	−	12.5174i	0.131668	−	0.746727i	0.977122	−	0.212679i	$-0.0682187\pi$
$282$	16.0726	+	5.84996i	0.957111	+	0.348360i
$283$	−8.38601	+	7.03670i	−0.498497	+	0.418288i	−0.857060	−	0.515217i	$-0.827711\pi$
$283$	−8.38601	+	7.03670i	−0.498497	+	0.418288i	0.358563	+	0.933506i	$0.383267\pi$
$284$	13.3663			0.793142
$285$	−13.2796	−	16.2696i	−0.786617	−	0.963726i
$286$	2.99887			0.177327
$287$	18.5022	−	15.5252i	1.09215	−	0.916424i
$288$	−0.0652624	−	0.0237536i	−0.00384562	−	0.00139969i
$289$	5.41991	−	30.7378i	0.318818	−	1.80811i
$290$	−3.32971	−	18.8837i	−0.195527	−	1.10889i
$291$	−10.0392	+	3.65396i	−0.588506	+	0.214199i
$292$	−4.27604	+	7.40631i	−0.250236	+	0.433422i
$293$	2.14750	+	3.71957i	0.125458	+	0.217300i	0.921912	−	0.387400i	$-0.126627\pi$
$293$	2.14750	+	3.71957i	0.125458	+	0.217300i	−0.796454	+	0.604699i	$0.793293\pi$
$294$	−10.3421	−	8.67803i	−0.603162	−	0.506113i
$295$	2.09259	+	1.75589i	0.121835	+	0.102232i
$296$	−2.87191	−	4.97429i	−0.166926	−	0.289125i
$297$	2.56714	−	4.44641i	0.148961	−	0.258007i
$298$	−9.79758	+	3.56603i	−0.567558	+	0.206574i
$299$	−0.551325	−	3.12672i	−0.0318840	−	0.180823i
$300$	−0.779616	+	4.42142i	−0.0450111	+	0.255271i
$301$	18.9925	+	6.91270i	1.09471	+	0.398441i
$302$	0.680137	−	0.570703i	0.0391375	−	0.0328403i
$303$	31.3372			1.80027
$304$	3.80416	−	2.12800i	0.218183	−	0.122049i
$305$	17.3272			0.992152
$306$	0.369410	−	0.309972i	0.0211178	−	0.0177199i
$307$	−31.2018	−	11.3565i	−1.78078	−	0.648151i	−0.999719	−	0.0236974i	$-0.992456\pi$
$307$	−31.2018	−	11.3565i	−1.78078	−	0.648151i	−0.781062	−	0.624454i	$-0.785322\pi$
$308$	−0.665911	+	3.77657i	−0.0379438	+	0.215190i
$309$	−0.497484	−	2.82137i	−0.0283009	−	0.160502i
$310$	13.9698	−	5.08460i	0.793433	−	0.288786i
$311$	−14.7118	+	25.4816i	−0.834230	+	1.44493i	0.0604263	+	0.998173i	$0.480754\pi$
$311$	−14.7118	+	25.4816i	−0.834230	+	1.44493i	−0.894656	+	0.446756i	$0.852579\pi$
$312$	−2.62699	−	4.55008i	−0.148724	−	0.257597i
$313$	−6.69206	−	5.61530i	−0.378257	−	0.317396i	0.433761	−	0.901028i	$-0.357186\pi$
$313$	−6.69206	−	5.61530i	−0.378257	−	0.317396i	−0.812018	+	0.583633i	$0.801631\pi$
$314$	−5.89113	−	4.94325i	−0.332456	−	0.278963i
$315$	−0.366208	−	0.634292i	−0.0206335	−	0.0357383i
$316$	−4.80754	+	8.32690i	−0.270445	+	0.468425i
$317$	−2.83658	+	1.03243i	−0.159318	+	0.0579872i	−0.420448	−	0.907317i	$-0.638127\pi$
$317$	−2.83658	+	1.03243i	−0.159318	+	0.0579872i	0.261130	+	0.965304i	$0.415905\pi$
$318$	2.30052	+	13.0469i	0.129006	+	0.731632i
$319$	1.21080	−	6.86676i	0.0677915	−	0.384465i
$320$	−2.58417	−	0.940561i	−0.144460	−	0.0525790i
$321$	−8.98203	+	7.53682i	−0.501328	+	0.420664i
$322$	4.06000			0.226255
$323$	−0.410863	+	30.2632i	−0.0228610	+	1.68389i
$324$	−9.20353			−0.511307
$325$	−5.88697	+	4.93975i	−0.326550	+	0.274008i
$326$	−0.918309	−	0.334237i	−0.0508604	−	0.0185117i
$327$	−0.805043	+	4.56563i	−0.0445190	+	0.252480i
$328$	1.09369	+	6.20263i	0.0603890	+	0.342483i
$329$	−35.1805	+	12.8047i	−1.93957	+	0.705944i
$330$	−2.40899	+	4.17250i	−0.132611	+	0.229689i
$331$	−10.5242	−	18.2284i	−0.578461	−	1.00192i	−0.995656	−	0.0931066i	$-0.970320\pi$
$331$	−10.5242	−	18.2284i	−0.578461	−	1.00192i	0.417195	−	0.908817i	$-0.363013\pi$
$332$	−7.55559	−	6.33989i	−0.414667	−	0.347947i
$333$	0.305585	+	0.256416i	0.0167459	+	0.0140515i
$334$	7.21890	+	12.5035i	0.395001	+	0.684161i
$335$	−2.74363	+	4.75210i	−0.149900	+	0.259635i
$336$	6.31338	−	2.29788i	0.344423	−	0.125360i
$337$	5.70569	+	32.3586i	0.310809	+	1.76268i	0.594816	+	0.803862i	$0.297225\pi$
$337$	5.70569	+	32.3586i	0.310809	+	1.76268i	−0.284008	+	0.958822i	$0.591664\pi$
$338$	−0.695769	+	3.94590i	−0.0378449	+	0.214629i
$339$	13.1885	+	4.80022i	0.716302	+	0.260712i
$340$	14.6274	−	12.2738i	0.793282	−	0.665643i
$341$	5.40593			0.292747
$342$	−0.197721	+	0.229241i	−0.0106915	+	0.0123959i
$343$	2.70700			0.146164
$344$	−4.03742	+	3.38780i	−0.217683	+	0.182658i
$345$	4.79327	+	1.74461i	0.258061	+	0.0939264i
$346$	−3.60209	+	20.4285i	−0.193650	+	1.09824i
$347$	−0.270180	−	1.53226i	−0.0145040	−	0.0822563i	0.976697	−	0.214625i	$-0.0688529\pi$
$347$	−0.270180	−	1.53226i	−0.0145040	−	0.0822563i	−0.991201	+	0.132369i	$0.957742\pi$
$348$	−11.4793	+	4.17814i	−0.615357	+	0.223972i
$349$	3.67516	−	6.36557i	0.196727	−	0.340741i	−0.750738	−	0.660600i	$-0.770302\pi$
$349$	3.67516	−	6.36557i	0.196727	−	0.340741i	0.947465	+	0.319859i	$0.103635\pi$
$350$	−4.91355	−	8.51053i	−0.262641	−	0.454907i
$351$	−11.7948	−	9.89702i	−0.629560	−	0.528264i
$352$	−0.766044	−	0.642788i	−0.0408303	−	0.0342607i
$353$	9.68047	+	16.7671i	0.515240	+	0.892421i	0.999844	+	0.0176874i	$0.00563037\pi$
$353$	9.68047	+	16.7671i	0.515240	+	0.892421i	−0.484604	+	0.874734i	$0.661036\pi$
$354$	0.870150	−	1.50714i	0.0462480	−	0.0801038i
$355$	−34.5407	+	12.5718i	−1.83323	+	0.667242i
$356$	2.29022	+	12.9885i	0.121382	+	0.688389i
$357$	−8.10073	+	45.9415i	−0.428736	+	2.43148i
$358$	18.3525	+	6.67977i	0.969961	+	0.353037i
$359$	−11.4198	+	9.58232i	−0.602712	+	0.505736i	−0.892316	−	0.451411i	$-0.850921\pi$
$359$	−11.4198	+	9.58232i	−0.602712	+	0.505736i	0.289604	+	0.957147i	$0.406476\pi$
$360$	0.190991			0.0100661
$361$	−2.79013	−	18.7940i	−0.146849	−	0.989159i
$362$	0.524440			0.0275639
$363$	−1.34210	+	1.12615i	−0.0704419	+	0.0591078i
$364$	10.8066	+	3.93328i	0.566420	+	0.206160i
$365$	4.08392	−	23.1611i	0.213762	−	1.21231i
$366$	−1.91687	−	10.8711i	−0.100196	−	0.568243i
$367$	25.9010	−	9.42721i	1.35202	−	0.492096i	0.438445	−	0.898758i	$-0.355530\pi$
$367$	25.9010	−	9.42721i	1.35202	−	0.492096i	0.913579	+	0.406662i	$0.133307\pi$
$368$	−0.529359	+	0.916876i	−0.0275947	+	0.0477955i
$369$	−0.218711	−	0.378819i	−0.0113857	−	0.0197205i
$370$	12.1001	+	10.1532i	0.629055	+	0.527840i
$371$	−22.2139	−	18.6397i	−1.15329	−	0.967723i
$372$	−4.73555	−	8.20221i	−0.245527	−	0.425265i
$373$	6.84408	−	11.8543i	0.354373	−	0.613792i	−0.632637	−	0.774448i	$-0.718028\pi$
$373$	6.84408	−	11.8543i	0.354373	−	0.613792i	0.987010	+	0.160656i	$0.0513610\pi$
$374$	6.52474	−	2.37481i	0.337387	−	0.122799i
$375$	2.03922	+	11.5650i	0.105305	+	0.597213i
$376$	1.69528	−	9.61440i	0.0874273	−	0.495825i
$377$	−19.6492	−	7.15171i	−1.01198	−	0.368332i
$378$	15.0827	−	12.6559i	0.775770	−	0.650949i
$379$	−6.31554			−0.324407			−0.162204	−	0.986757i	$-0.551860\pi$
$379$	−6.31554			−0.324407			−0.162204	+	0.986757i	$0.551860\pi$
$380$	−7.82907	+	9.07717i	−0.401623	+	0.465649i
$381$	−36.4269			−1.86621
$382$	15.0880	−	12.6603i	0.771969	−	0.647759i
$383$	−3.76831	−	1.37155i	−0.192552	−	0.0700831i	0.243944	−	0.969789i	$-0.421559\pi$
$383$	−3.76831	−	1.37155i	−0.192552	−	0.0700831i	−0.436496	+	0.899706i	$0.643781\pi$
$384$	−0.304229	+	1.72537i	−0.0155251	+	0.0880473i
$385$	−1.83127	−	10.3856i	−0.0933300	−	0.529300i
$386$	0.524395	−	0.190864i	0.0266910	−	0.00971473i
$387$	0.183020	−	0.316999i	0.00930341	−	0.0161140i
$388$	3.04896	+	5.28095i	0.154787	+	0.268100i
$389$	−13.7033	−	11.4984i	−0.694784	−	0.582993i	0.225501	−	0.974243i	$-0.427598\pi$
$389$	−13.7033	−	11.4984i	−0.694784	−	0.582993i	−0.920284	+	0.391250i	$0.872043\pi$
$390$	11.0682	+	9.28733i	0.560461	+	0.470282i
$391$	−3.67560	−	6.36632i	−0.185883	−	0.321959i
$392$	−3.85295	+	6.67350i	−0.194603	+	0.337063i
$393$	−11.0116	+	4.00790i	−0.555463	+	0.202172i
$394$	−4.72929	−	26.8211i	−0.238258	−	1.35123i
$395$	4.59154	−	26.0399i	0.231025	−	1.31021i
$396$	0.0652624	+	0.0237536i	0.00327956	+	0.00119366i
$397$	−5.71727	+	4.79736i	−0.286942	+	0.240773i	−0.774884	−	0.632103i	$-0.782192\pi$
$397$	−5.71727	+	4.79736i	−0.286942	+	0.240773i	0.487943	+	0.872876i	$0.337748\pi$
$398$	−9.66076			−0.484250
$399$	0.397553	−	29.2828i	0.0199025	−	1.46597i
$400$	2.56259			0.128130
$401$	−13.0144	+	10.9204i	−0.649909	+	0.545338i	−0.907043	−	0.421037i	$-0.861666\pi$
$401$	−13.0144	+	10.9204i	−0.649909	+	0.545338i	0.257134	+	0.966376i	$0.417222\pi$
$402$	3.28500	+	1.19564i	0.163841	+	0.0596333i
$403$	2.81513	−	15.9654i	0.140231	−	0.795292i
$404$	−3.10599	−	17.6149i	−0.154529	−	0.876375i
$405$	23.7835	−	8.65648i	1.18181	−	0.430144i
$406$	13.3695	−	23.1567i	0.663519	−	1.14925i
$407$	2.87191	+	4.97429i	0.142355	+	0.246566i
$408$	−9.31884	−	7.81944i	−0.461351	−	0.387120i
$409$	2.88683	+	2.42234i	0.142744	+	0.119777i	0.711364	−	0.702824i	$-0.248078\pi$
$409$	2.88683	+	2.42234i	0.142744	+	0.119777i	−0.568619	+	0.822601i	$0.692522\pi$
$410$	−8.66024	−	15.0000i	−0.427699	−	0.740796i
$411$	14.3647	−	24.8803i	0.708556	−	1.22726i
$412$	−1.53661	+	0.559281i	−0.0757035	+	0.0275538i
$413$	0.661469	+	3.75138i	0.0325488	+	0.184593i
$414$	0.0127681	−	0.0724117i	0.000627520	−	0.00355884i
$415$	25.4880	+	9.27687i	1.25116	+	0.455384i
$416$	−2.29727	+	1.92764i	−0.112633	+	0.0945102i
$417$	−23.1194			−1.13216
$418$	−3.80416	+	2.12800i	−0.186067	+	0.104084i
$419$	32.5461			1.58998			0.794990	−	0.606622i	$-0.207476\pi$
$419$	32.5461			1.58998			0.794990	+	0.606622i	$0.207476\pi$
$420$	−14.1536	+	11.8762i	−0.690623	+	0.579501i
$421$	−3.73750	−	1.36034i	−0.182154	−	0.0662988i	0.249333	−	0.968418i	$-0.419789\pi$
$421$	−3.73750	−	1.36034i	−0.182154	−	0.0662988i	−0.431487	+	0.902119i	$0.642011\pi$
$422$	2.90487	−	16.4744i	0.141407	−	0.801959i
$423$	0.117738	+	0.667728i	0.00572464	+	0.0324660i
$424$	7.10576	−	2.58628i	0.345086	−	0.125601i
$425$	−8.89667	+	15.4095i	−0.431552	+	0.747470i
$426$	11.7087	+	20.2801i	0.567291	+	0.982576i
$427$	18.5094	+	15.5312i	0.895732	+	0.751609i
$428$	5.12678	+	4.30188i	0.247812	+	0.207939i
$429$	2.62699	+	4.55008i	0.126832	+	0.219680i
$430$	7.24696	−	12.5521i	0.349479	−	0.605316i
$431$	3.93098	−	1.43076i	0.189349	−	0.0689173i	−0.245605	−	0.969370i	$-0.578987\pi$
$431$	3.93098	−	1.43076i	0.189349	−	0.0689173i	0.434954	+	0.900453i	$0.356765\pi$
$432$	0.891558	+	5.05628i	0.0428951	+	0.243270i
$433$	2.38616	−	13.5326i	0.114672	−	0.650335i	−0.872241	−	0.489077i	$-0.837334\pi$
$433$	2.38616	−	13.5326i	0.114672	−	0.650335i	0.986912	−	0.161258i	$-0.0515551\pi$
$434$	19.4806	+	7.09035i	0.935097	+	0.340348i
$435$	25.7348	−	21.5940i	1.23389	−	1.03535i
$436$	2.64617			0.126729
$437$	2.91810	+	3.57512i	0.139592	+	0.171021i
$438$	−14.9831			−0.715920
$439$	20.9985	−	17.6198i	1.00220	−	0.840948i	0.0149152	−	0.999889i	$-0.495252\pi$
$439$	20.9985	−	17.6198i	1.00220	−	0.840948i	0.987288	+	0.158940i	$0.0508077\pi$
$440$	2.58417	+	0.940561i	0.123196	+	0.0448395i
$441$	0.0929332	−	0.527050i	0.00442539	−	0.0250976i
$442$	−3.61581	−	20.5063i	−0.171987	−	0.975384i
$443$	−32.4965	+	11.8278i	−1.54396	+	0.561954i	−0.966990	−	0.254815i	$-0.917986\pi$
$443$	−32.4965	+	11.8278i	−1.54396	+	0.561954i	−0.576965	+	0.816769i	$0.695763\pi$
$444$	5.03154	−	8.71488i	0.238786	−	0.413590i
$445$	−18.1348	−	31.4104i	−0.859672	−	1.48900i
$446$	−7.53621	−	6.32363i	−0.356850	−	0.299433i
$447$	−13.9932	−	11.7417i	−0.661856	−	0.555363i
$448$	−1.91741	−	3.32106i	−0.0905893	−	0.156905i
$449$	−7.00319	+	12.1299i	−0.330501	+	0.572445i	−0.982610	−	0.185680i	$-0.940551\pi$
$449$	−7.00319	+	12.1299i	−0.330501	+	0.572445i	0.652109	+	0.758125i	$0.273884\pi$
$450$	−0.167241	+	0.0608708i	−0.00788382	+	0.00286948i
$451$	−1.09369	−	6.20263i	−0.0514999	−	0.292070i
$452$	1.39107	−	7.88916i	0.0654306	−	0.371075i
$453$	1.46170	+	0.532016i	0.0686768	+	0.0249963i
$454$	0.662388	−	0.555810i	0.0310874	−	0.0260854i
$455$	−31.6256			−1.48263
$456$	6.56115	+	3.90779i	0.307254	+	0.182999i
$457$	−34.1525			−1.59759			−0.798793	−	0.601606i	$-0.794528\pi$
$457$	−34.1525			−1.59759			−0.798793	+	0.601606i	$0.794528\pi$
$458$	6.38844	−	5.36054i	0.298512	−	0.250481i
$459$	−33.4999	−	12.1929i	−1.56364	−	0.569118i
$460$	0.505575	−	2.86726i	0.0235726	−	0.133687i
$461$	6.52554	+	37.0082i	0.303925	+	1.72364i	0.628522	+	0.777792i	$0.283660\pi$
$461$	6.52554	+	37.0082i	0.303925	+	1.72364i	−0.324597	+	0.945852i	$0.605229\pi$
$462$	−6.31338	+	2.29788i	−0.293725	+	0.106907i
$463$	−2.76668	+	4.79202i	−0.128578	+	0.222704i	−0.923126	−	0.384498i	$-0.874375\pi$
$463$	−2.76668	+	4.79202i	−0.128578	+	0.222704i	0.794548	+	0.607202i	$0.207708\pi$
$464$	3.48635	+	6.03853i	0.161850	+	0.280332i
$465$	19.9522	+	16.7418i	0.925259	+	0.776384i
$466$	15.2117	+	12.7642i	0.704670	+	0.591289i
$467$	−6.31076	−	10.9306i	−0.292027	−	0.505806i	0.682262	−	0.731108i	$-0.260997\pi$
$467$	−6.31076	−	10.9306i	−0.292027	−	0.505806i	−0.974289	+	0.225302i	$0.927663\pi$
$468$	0.104137	−	0.180371i	0.00481373	−	0.00833763i
$469$	−7.19037	+	2.61708i	−0.332020	+	0.120846i
$470$	4.66205	+	26.4398i	0.215044	+	1.21958i
$471$	2.33962	−	13.2686i	0.107804	−	0.611387i
$472$	−0.933425	−	0.339739i	−0.0429644	−	0.0156378i
$473$	4.03742	−	3.38780i	0.185641	−	0.155771i
$474$	−16.8455			−0.773738
$475$	3.96253	−	10.4436i	0.181814	−	0.479186i
$476$	26.6271			1.22045
$477$	−0.402305	+	0.337574i	−0.0184203	+	0.0154565i
$478$	14.8138	+	5.39177i	0.677566	+	0.246614i
$479$	−3.84917	+	21.8297i	−0.175873	+	0.997426i	0.761258	+	0.648449i	$0.224582\pi$
$479$	−3.84917	+	21.8297i	−0.175873	+	0.997426i	−0.937131	+	0.348977i	$0.886529\pi$
$480$	−0.836635	−	4.74479i	−0.0381870	−	0.216569i
$481$	16.1862	−	5.89128i	0.738025	−	0.268619i
$482$	11.0421	−	19.1254i	0.502952	−	0.871139i
$483$	3.55653	+	6.16008i	0.161828	+	0.280294i
$484$	0.766044	+	0.642788i	0.0348202	+	0.0292176i
$485$	−12.8461	−	10.7791i	−0.583311	−	0.489456i
$486$	−0.360805	−	0.624932i	−0.0163664	−	0.0283475i
$487$	−4.28301	+	7.41838i	−0.194082	+	0.336159i	−0.946599	−	0.322413i	$-0.895506\pi$
$487$	−4.28301	+	7.41838i	−0.194082	+	0.336159i	0.752518	+	0.658572i	$0.228839\pi$
$488$	−5.92077	+	2.15498i	−0.268021	+	0.0975516i
$489$	−0.297306	−	1.68611i	−0.0134446	−	0.0762483i
$490$	3.67984	−	20.8694i	0.166238	−	0.942784i
$491$	−20.7613	−	7.55649i	−0.936944	−	0.341020i	−0.171985	−	0.985099i	$-0.555018\pi$
$491$	−20.7613	−	7.55649i	−0.936944	−	0.341020i	−0.764958	+	0.644080i	$0.777240\pi$
$492$	−8.45296	+	7.09287i	−0.381089	+	0.319771i
$493$	−48.4148			−2.18049
$494$	4.30365	+	12.3430i	0.193630	+	0.555338i
$495$	−0.190991			−0.00858440
$496$	−4.14118	+	3.47486i	−0.185944	+	0.156026i
$497$	−48.1661	−	17.5310i	−2.16055	−	0.786374i
$498$	3.00065	−	17.0175i	0.134462	−	0.762573i
$499$	−0.473680	−	2.68637i	−0.0212048	−	0.120259i	0.972368	−	0.233453i	$-0.0750027\pi$
$499$	−0.473680	−	2.68637i	−0.0212048	−	0.120259i	−0.993573	+	0.113195i	$0.963892\pi$
$500$	6.29867	−	2.29253i	0.281685	−	0.102525i
$501$	−12.6474	+	21.9060i	−0.565045	+	0.978686i
$502$	−3.91815	−	6.78643i	−0.174875	−	0.302893i
$503$	5.57685	+	4.67953i	0.248659	+	0.208650i	0.758595	−	0.651563i	$-0.225886\pi$
$503$	5.57685	+	4.67953i	0.248659	+	0.208650i	−0.509935	+	0.860213i	$0.670331\pi$
$504$	0.204022	+	0.171195i	0.00908786	+	0.00762562i
$505$	24.5943	+	42.5986i	1.09443	+	1.89561i
$506$	0.529359	−	0.916876i	0.0235329	−	0.0407601i
$507$	−6.59647	+	2.40092i	−0.292959	+	0.106628i
$508$	3.61046	+	20.4759i	0.160188	+	0.908473i
$509$	−4.19084	+	23.7675i	−0.185756	+	1.05347i	0.739224	+	0.673459i	$0.235192\pi$
$509$	−4.19084	+	23.7675i	−0.185756	+	1.05347i	−0.924980	+	0.380015i	$0.875919\pi$
$510$	31.4361	+	11.4418i	1.39202	+	0.506652i
$511$	25.1230	−	21.0807i	1.11138	−	0.932555i
$512$	1.00000			0.0441942
$513$	21.9850	+	4.18504i	0.970662	+	0.184774i
$514$	−20.4912			−0.903827
$515$	3.44483	−	2.89056i	0.151797	−	0.127373i
$516$	−8.67694	−	3.15815i	−0.381981	−	0.139030i
$517$	−1.69528	+	9.61440i	−0.0745583	+	0.422841i
$518$	3.82487	+	21.6919i	0.168055	+	0.953087i
$519$	−34.1508	+	12.4299i	−1.49905	+	0.545611i
$520$	4.12347	−	7.14206i	0.180826	−	0.313200i
$521$	6.42307	+	11.1251i	0.281400	+	0.487399i	0.971730	−	0.236096i	$-0.0758679\pi$
$521$	6.42307	+	11.1251i	0.281400	+	0.487399i	−0.690330	+	0.723495i	$0.742535\pi$
$522$	−0.370964	−	0.311276i	−0.0162367	−	0.0136242i
$523$	−2.25178	−	1.88947i	−0.0984637	−	0.0826208i	0.592227	−	0.805771i	$-0.298249\pi$
$523$	−2.25178	−	1.88947i	−0.0984637	−	0.0826208i	−0.690691	+	0.723150i	$0.742693\pi$
$524$	3.34430	+	5.79250i	0.146096	+	0.253046i
$525$	8.60847	−	14.9103i	0.375705	−	0.650739i
$526$	25.1972	−	9.17102i	1.09865	−	0.399876i
$527$	−6.51805	−	36.9657i	−0.283931	−	1.61025i
$528$	0.304229	−	1.72537i	0.0132399	−	0.0750870i
$529$	20.5596	+	7.48310i	0.893898	+	0.325352i
$530$	−15.9299	+	13.3668i	−0.691952	+	0.580617i
$531$	0.0689876			0.00299381
$532$	−16.4996	+	2.67890i	−0.715347	+	0.116145i
$533$	−18.8878			−0.818123
$534$	−17.7008	+	14.8527i	−0.765987	+	0.642739i
$535$	−17.2946	−	6.29474i	−0.747713	−	0.272145i
$536$	0.346489	−	1.96504i	0.0149661	−	0.0848767i
$537$	5.94170	+	33.6971i	0.256403	+	1.45414i
$538$	−10.3002	+	3.74895i	−0.444071	+	0.161629i
$539$	3.85295	−	6.67350i	0.165958	−	0.287448i
$540$	−7.05968	−	12.2277i	−0.303800	−	0.526197i
$541$	22.4230	+	18.8151i	0.964041	+	0.808926i	0.981606	−	0.190919i	$-0.0611469\pi$
$541$	22.4230	+	18.8151i	0.964041	+	0.808926i	−0.0175649	+	0.999846i	$0.505591\pi$
$542$	1.42515	+	1.19584i	0.0612155	+	0.0513659i
$543$	0.459405	+	0.795713i	0.0197150	+	0.0341473i
$544$	−3.47174	+	6.01324i	−0.148850	+	0.257815i
$545$	−6.83817	+	2.48889i	−0.292915	+	0.106612i
$546$	3.49868	+	19.8420i	0.149730	+	0.849159i
$547$	−4.97215	+	28.1985i	−0.212594	+	1.20568i	0.672439	+	0.740152i	$0.265247\pi$
$547$	−4.97215	+	28.1985i	−0.212594	+	1.20568i	−0.885033	+	0.465528i	$0.845865\pi$
$548$	−15.4092	−	5.60850i	−0.658249	−	0.239583i
$549$	0.335215	−	0.281279i	0.0143066	−	0.0120047i
$550$	−2.56259			−0.109269
$551$	30.0004	−	4.87093i	1.27806	−	0.207508i
$552$	−1.85486			−0.0789479
$553$	28.2457	−	23.7010i	1.20113	−	1.00787i
$554$	−17.6445	−	6.42207i	−0.749643	−	0.272848i
$555$	−4.80548	+	27.2532i	−0.203981	+	1.15683i
$556$	2.29148	+	12.9956i	0.0971805	+	0.551138i
$557$	−1.49785	+	0.545173i	−0.0634659	+	0.0230997i	−0.373558	−	0.927607i	$-0.621862\pi$
$557$	−1.49785	+	0.545173i	−0.0634659	+	0.0230997i	0.310092	+	0.950707i	$0.399640\pi$
$558$	0.187723	−	0.325146i	0.00794694	−	0.0137645i
$559$	−7.90275	−	13.6880i	−0.334251	−	0.578939i
$560$	8.07858	+	6.77874i	0.341382	+	0.286454i
$561$	9.31884	+	7.81944i	0.393442	+	0.330137i
$562$	−6.35526	−	11.0076i	−0.268080	−	0.464329i
$563$	−17.2045	+	29.7990i	−0.725083	+	1.25588i	0.233857	+	0.972271i	$0.424865\pi$
$563$	−17.2045	+	29.7990i	−0.725083	+	1.25588i	−0.958940	+	0.283609i	$0.908468\pi$
$564$	16.0726	−	5.84996i	0.676780	−	0.246328i
$565$	3.82547	+	21.6953i	0.160939	+	0.912730i
$566$	−1.90095	+	10.7808i	−0.0799031	+	0.453153i
$567$	33.1655	+	12.0712i	1.39282	+	0.506944i
$568$	10.2392	−	8.59167i	0.429625	−	0.360499i
$569$	29.9011			1.25352			0.626760	−	0.779213i	$-0.284381\pi$
$569$	29.9011			1.25352			0.626760	+	0.779213i	$0.284381\pi$
$570$	−20.6307	−	3.92723i	−0.864123	−	0.164494i
$571$	9.80807			0.410455			0.205228	−	0.978714i	$-0.434207\pi$
$571$	9.80807			0.410455			0.205228	+	0.978714i	$0.434207\pi$
$572$	2.29727	−	1.92764i	0.0960536	−	0.0805985i
$573$	32.4260	+	11.8021i	1.35462	+	0.493040i
$574$	4.19411	−	23.7860i	0.175059	−	0.992809i
$575$	0.471119	+	2.67185i	0.0196470	+	0.111424i
$576$	−0.0652624	+	0.0237536i	−0.00271927	+	0.000989732i
$577$	2.05948	−	3.56712i	0.0857373	−	0.148501i	−0.819968	−	0.572410i	$-0.806009\pi$
$577$	2.05948	−	3.56712i	0.0857373	−	0.148501i	0.905705	+	0.423908i	$0.139342\pi$
$578$	−15.6060	−	27.0304i	−0.649125	−	1.12432i
$579$	0.748957	+	0.628450i	0.0311256	+	0.0261175i
$580$	−14.6889	−	12.3255i	−0.609924	−	0.511787i
$581$	18.9117	+	32.7560i	0.784589	+	1.35895i
$582$	−5.34173	+	9.25215i	−0.221422	+	0.383514i
$583$	−7.10576	+	2.58628i	−0.294290	+	0.107113i
$584$	1.48505	+	8.42215i	0.0614519	+	0.348511i
$585$	−0.0994582	+	0.564055i	−0.00411209	+	0.0233208i
$586$	4.03597	+	1.46897i	0.166724	+	0.0606827i
$587$	14.3058	−	12.0040i	0.590463	−	0.495457i	−0.297901	−	0.954597i	$-0.596287\pi$
$587$	14.3058	−	12.0040i	0.590463	−	0.495457i	0.888364	+	0.459140i	$0.151842\pi$
$588$	−13.5006			−0.556756
$589$	7.75799	+	22.2502i	0.319662	+	0.916802i
$590$	2.73168			0.112461
$591$	36.5519	−	30.6707i	1.50354	−	1.26162i
$592$	−5.39742	−	1.96450i	−0.221833	−	0.0807405i
$593$	1.45977	−	8.27876i	0.0599455	−	0.339968i	−0.940054	−	0.341026i	$-0.889226\pi$
$593$	1.45977	−	8.27876i	0.0599455	−	0.339968i	0.999999	+	0.00105792i	$0.000336747\pi$
$594$	−0.891558	−	5.05628i	−0.0365811	−	0.207462i
$595$	−68.8089	+	25.0444i	−2.82089	+	1.02672i
$596$	−5.21318	+	9.02949i	−0.213540	+	0.369862i
$597$	−8.46275	−	14.6579i	−0.346357	−	0.599909i
$598$	−2.43216	−	2.04082i	−0.0994583	−	0.0834554i
$599$	−26.9649	−	22.6262i	−1.10176	−	0.924483i	−0.104214	−	0.994555i	$-0.533233\pi$
$599$	−26.9649	−	22.6262i	−1.10176	−	0.924483i	−0.997542	+	0.0700723i	$0.977677\pi$
$600$	2.24481	+	3.88813i	0.0916441	+	0.158732i
$601$	12.9671	−	22.4597i	0.528939	−	0.916148i	−0.470492	−	0.882404i	$-0.655924\pi$
$601$	12.9671	−	22.4597i	0.528939	−	0.916148i	0.999431	−	0.0337442i	$-0.0107431\pi$
$602$	18.9925	−	6.91270i	0.774076	−	0.281741i
$603$	0.0240640	+	0.136473i	0.000979960	+	0.00555763i
$604$	0.154175	−	0.874368i	0.00627328	−	0.0355775i
$605$	−2.58417	−	0.940561i	−0.105061	−	0.0382393i
$606$	24.0057	−	20.1431i	0.975163	−	0.818259i
$607$	14.6858			0.596079			0.298039	−	0.954554i	$-0.403667\pi$
$607$	14.6858			0.596079			0.298039	+	0.954554i	$0.403667\pi$
$608$	1.54630	−	4.07541i	0.0627107	−	0.165280i
$609$	46.8464			1.89831
$610$	13.2734	−	11.1377i	0.537424	−	0.450952i
$611$	27.5115	+	10.0134i	1.11300	+	0.405098i
$612$	0.0837385	−	0.474905i	0.00338493	−	0.0191969i
$613$	−2.42605	−	13.7588i	−0.0979874	−	0.555714i	−0.993791	−	0.111264i	$-0.964510\pi$
$613$	−2.42605	−	13.7588i	−0.0979874	−	0.555714i	0.895804	−	0.444450i	$-0.146601\pi$
$614$	−31.2018	+	11.3565i	−1.25920	+	0.458312i
$615$	15.1726	−	26.2797i	0.611818	−	1.05970i
$616$	1.91741	+	3.32106i	0.0772548	+	0.133809i
$617$	19.3728	+	16.2558i	0.779922	+	0.654432i	0.943229	−	0.332143i	$-0.107772\pi$
$617$	19.3728	+	16.2558i	0.779922	+	0.654432i	−0.163307	+	0.986575i	$0.552216\pi$
$618$	−2.19464	−	1.84152i	−0.0882813	−	0.0740768i
$619$	9.39255	+	16.2684i	0.377518	+	0.653881i	0.990701	−	0.136061i	$-0.0434442\pi$
$619$	9.39255	+	16.2684i	0.377518	+	0.653881i	−0.613182	+	0.789942i	$0.710111\pi$
$620$	7.43319	−	12.8747i	0.298524	−	0.517059i
$621$	−5.10793	+	1.85914i	−0.204974	+	0.0746045i
$622$	5.10935	+	28.9766i	0.204866	+	1.16186i
$623$	8.78261	−	49.8086i	0.351868	−	1.99554i
$624$	−4.93712	−	1.79697i	−0.197643	−	0.0719362i
$625$	−23.9359	+	20.0846i	−0.957435	+	0.803384i
$626$	−8.73586			−0.349155
$627$	−6.56115	−	3.90779i	−0.262027	−	0.156062i
$628$	−7.69032			−0.306877
$629$	30.5515	−	25.6357i	1.21817	−	1.02216i
$630$	−0.688247	−	0.250501i	−0.0274204	−	0.00998021i
$631$	−2.16061	+	12.2534i	−0.0860126	+	0.487802i	0.911121	+	0.412139i	$0.135218\pi$
$631$	−2.16061	+	12.2534i	−0.0860126	+	0.487802i	−0.997133	+	0.0756625i	$0.975893\pi$
$632$	1.66964	+	9.46900i	0.0664147	+	0.376657i
$633$	27.5406	−	10.0240i	1.09464	−	0.398416i
$634$	−1.50931	+	2.61421i	−0.0599425	+	0.103824i
$635$	−28.5889	−	49.5175i	−1.13452	−	1.96504i
$636$	10.1487	+	8.51574i	0.402421	+	0.337671i
$637$	−17.7025	−	14.8542i	−0.701399	−	0.588544i
$638$	−3.48635	−	6.03853i	−0.138026	−	0.239068i
$639$	−0.464149	+	0.803930i	−0.0183614	+	0.0318030i
$640$	−2.58417	+	0.940561i	−0.102148	+	0.0371789i
$641$	−2.14509	−	12.1654i	−0.0847260	−	0.480505i	−0.997415	−	0.0718512i	$-0.977109\pi$
$641$	−2.14509	−	12.1654i	−0.0847260	−	0.480505i	0.912689	−	0.408654i	$-0.134002\pi$
$642$	−2.03606	+	11.5471i	−0.0803569	+	0.455727i
$643$	−17.7994	−	6.47844i	−0.701938	−	0.255485i	−0.0337000	−	0.999432i	$-0.510729\pi$
$643$	−17.7994	−	6.47844i	−0.701938	−	0.255485i	−0.668238	+	0.743947i	$0.732951\pi$
$644$	3.11014	−	2.60972i	0.122557	−	0.102837i
$645$	25.3931			0.999853
$646$	19.1381	+	23.4470i	0.752977	+	0.922511i
$647$	−8.99197			−0.353511			−0.176755	−	0.984255i	$-0.556560\pi$
$647$	−8.99197			−0.353511			−0.176755	+	0.984255i	$0.556560\pi$
$648$	−7.05031	+	5.91591i	−0.276962	+	0.232399i
$649$	0.933425	+	0.339739i	0.0366402	+	0.0133359i
$650$	−1.33447	+	7.56814i	−0.0523421	+	0.296847i
$651$	6.30691	+	35.7682i	0.247187	+	1.40187i
$652$	−0.918309	+	0.334237i	−0.0359637	+	0.0130897i
$653$	21.1884	−	36.6994i	0.829166	−	1.43616i	−0.0695273	−	0.997580i	$-0.522149\pi$
$653$	21.1884	−	36.6994i	0.829166	−	1.43616i	0.898693	−	0.438578i	$-0.144518\pi$
$654$	2.31803	+	4.01494i	0.0906421	+	0.156997i
$655$	−14.0904	−	11.8233i	−0.550559	−	0.461974i
$656$	4.82479	+	4.04848i	0.188376	+	0.158067i
$657$	−0.296974	−	0.514374i	−0.0115861	−	0.0200677i
$658$	−18.7192	+	32.4226i	−0.729749	+	1.26396i
$659$	27.8452	−	10.1348i	1.08469	−	0.394796i	0.263041	−	0.964785i	$-0.415275\pi$
$659$	27.8452	−	10.1348i	1.08469	−	0.394796i	0.821653	+	0.569988i	$0.193052\pi$
$660$	0.836635	+	4.74479i	0.0325660	+	0.184691i
$661$	−8.54104	+	48.4386i	−0.332208	+	1.88404i	0.121021	+	0.992650i	$0.461383\pi$
$661$	−8.54104	+	48.4386i	−0.332208	+	1.88404i	−0.453229	+	0.891394i	$0.649728\pi$
$662$	−19.7790	−	7.19896i	−0.768732	−	0.279795i
$663$	27.9460	−	23.4495i	1.08533	−	0.910702i
$664$	−9.86312			−0.382763
$665$	40.1180	−	22.4416i	1.55571	−	0.870248i
$666$	0.398912			0.0154575
$667$	−5.65502	+	4.74513i	−0.218963	+	0.183732i
$668$	13.5671	+	4.93802i	0.524927	+	0.191058i
$669$	2.99295	−	16.9739i	0.115714	−	0.656248i
$670$	0.952852	+	5.40389i	0.0368119	+	0.208770i
$671$	5.92077	−	2.15498i	0.228569	−	0.0831923i
$672$	3.35928	−	5.81844i	0.129587	−	0.224451i
$673$	15.7296	+	27.2444i	0.606331	+	1.05020i	0.991840	+	0.127492i	$0.0406927\pi$
$673$	15.7296	+	27.2444i	0.606331	+	1.05020i	−0.385509	+	0.922704i	$0.625974\pi$
$674$	25.1705	+	21.1206i	0.969531	+	0.813533i
$675$	10.0789	+	8.45720i	0.387937	+	0.325518i
$676$	2.00339	+	3.46997i	0.0770534	+	0.133460i
$677$	2.97676	−	5.15590i	0.114406	−	0.198157i	−0.803136	−	0.595796i	$-0.796837\pi$
$677$	2.97676	−	5.15590i	0.114406	−	0.198157i	0.917542	+	0.397638i	$0.130170\pi$
$678$	13.1885	−	4.80022i	0.506502	−	0.184352i
$679$	−4.06067	−	23.0292i	−0.155834	−	0.883779i
$680$	3.31576	−	18.8046i	0.127154	−	0.721124i
$681$	1.42356	+	0.518132i	0.0545508	+	0.0198549i
$682$	4.14118	−	3.47486i	0.158574	−	0.133059i
$683$	8.82659			0.337740			0.168870	−	0.985638i	$-0.445988\pi$
$683$	8.82659			0.337740			0.168870	+	0.985638i	$0.445988\pi$
$684$	−0.00410957	+	0.302701i	−0.000157133	+	0.0115741i
$685$	45.0952			1.72300
$686$	2.07368	−	1.74002i	0.0791734	−	0.0664344i
$687$	13.7296	+	4.99716i	0.523816	+	0.190653i
$688$	−0.915209	+	5.19041i	−0.0348920	+	0.197883i
$689$	3.93779	+	22.3323i	0.150018	+	0.850793i
$690$	4.79327	−	1.74461i	0.182477	−	0.0664160i
$691$	−0.0422598	+	0.0731962i	−0.00160764	+	0.00278451i	−0.866828	−	0.498607i	$-0.833845\pi$
$691$	−0.0422598	+	0.0731962i	−0.00160764	+	0.00278451i	0.865220	+	0.501392i	$0.167178\pi$
$692$	10.3718	+	17.9645i	0.394277	+	0.682908i
$693$	−0.204022	−	0.171195i	−0.00775015	−	0.00650315i
$694$	−1.19189	−	1.00011i	−0.0452435	−	0.0379638i
$695$	−18.1448	−	31.4277i	−0.688271	−	1.19212i
$696$	−6.10803	+	10.5794i	−0.231524	+	0.401012i
$697$	−41.0949	+	14.9573i	−1.55658	+	0.566549i
$698$	−1.27637	−	7.23866i	−0.0483113	−	0.273987i
$699$	−6.04123	+	34.2615i	−0.228500	+	1.29589i
$700$	−9.23446	−	3.36107i	−0.349030	−	0.127036i
$701$	−2.09319	+	1.75639i	−0.0790586	+	0.0663380i	−0.681461	−	0.731855i	$-0.738655\pi$
$701$	−2.09319	+	1.75639i	−0.0790586	+	0.0663380i	0.602402	+	0.798193i	$0.294210\pi$
$702$	−15.3970			−0.581124
$703$	−16.3522	+	18.9590i	−0.616733	+	0.715052i
$704$	−1.00000			−0.0376889
$705$	−36.0322	+	30.2346i	−1.35705	+	1.13870i
$706$	18.1933	+	6.62183i	0.684715	+	0.249216i
$707$	−11.9109	+	67.5502i	−0.447956	+	2.54049i
$708$	−0.302200	−	1.71386i	−0.0113574	−	0.0644108i
$709$	4.94726	−	1.80065i	0.185798	−	0.0676250i	−0.247446	−	0.968902i	$-0.579591\pi$
$709$	4.94726	−	1.80065i	0.185798	−	0.0676250i	0.433244	+	0.901277i	$0.357369\pi$
$710$	−18.3787	+	31.8329i	−0.689742	+	1.19467i
$711$	−0.333887	−	0.578310i	−0.0125218	−	0.0216883i
$712$	10.1033	+	8.47764i	0.378636	+	0.317713i
$713$	−4.38434	−	3.67890i	−0.164195	−	0.137776i
$714$	23.3251	+	40.4003i	0.872921	+	1.51194i
$715$	−4.12347	+	7.14206i	−0.154209	+	0.267098i
$716$	18.3525	−	6.67977i	0.685866	−	0.249635i
$717$	4.79601	+	27.1995i	0.179110	+	1.01579i
$718$	−2.58865	+	14.6810i	−0.0966076	+	0.547889i
$719$	−24.3284	−	8.85480i	−0.907295	−	0.330228i	−0.154123	−	0.988052i	$-0.549255\pi$
$719$	−24.3284	−	8.85480i	−0.907295	−	0.330228i	−0.753172	+	0.657823i	$0.771477\pi$
$720$	0.146308	−	0.122767i	0.00545256	−	0.00457524i
$721$	6.27082			0.233538
$722$	−14.2179	−	12.6036i	−0.529136	−	0.469057i
$723$	38.6911			1.43894
$724$	0.401744	−	0.337103i	0.0149307	−	0.0125283i
$725$	16.7906	+	6.11128i	0.623587	+	0.226967i
$726$	−0.304229	+	1.72537i	−0.0112910	+	0.0640344i
$727$	8.59182	+	48.7266i	0.318653	+	1.80717i	0.550963	+	0.834530i	$0.314260\pi$
$727$	8.59182	+	48.7266i	0.318653	+	1.80717i	−0.232310	+	0.972642i	$0.574628\pi$
$728$	10.8066	−	3.93328i	0.400519	−	0.145777i
$729$	−13.1732	+	22.8166i	−0.487895	+	0.845059i
$730$	−11.7592	−	20.3675i	−0.435227	−	0.753835i
$731$	−28.0338	−	23.5232i	−1.03687	−	0.870035i
$732$	−8.45623	−	7.09562i	−0.312551	−	0.262262i
$733$	−15.6900	−	27.1758i	−0.579522	−	1.00376i	−0.995534	−	0.0944021i	$-0.969906\pi$
$733$	−15.6900	−	27.1758i	−0.579522	−	1.00376i	0.416012	−	0.909359i	$-0.363427\pi$
$734$	13.7817	−	23.8705i	0.508690	−	0.881077i
$735$	34.8879	−	12.6982i	1.28686	−	0.468379i
$736$	0.183844	+	1.04263i	0.00677659	+	0.0384320i
$737$	−0.346489	+	1.96504i	−0.0127631	+	0.0723831i
$738$	−0.411043	−	0.149607i	−0.0151307	−	0.00550713i
$739$	25.3711	−	21.2888i	0.933289	−	0.783123i	−0.0431158	−	0.999070i	$-0.513728\pi$
$739$	25.3711	−	21.2888i	0.933289	−	0.783123i	0.976405	+	0.215947i	$0.0692840\pi$
$740$	15.7956			0.580657
$741$	−14.9576	+	17.3422i	−0.549482	+	0.637080i
$742$	−28.9982			−1.06456
$743$	1.25593	−	1.05385i	0.0460758	−	0.0386622i	−0.619459	−	0.785029i	$-0.712648\pi$
$743$	1.25593	−	1.05385i	0.0460758	−	0.0386622i	0.665535	+	0.746367i	$0.268204\pi$
$744$	−8.89992	−	3.23931i	−0.326287	−	0.118759i
$745$	4.97896	−	28.2371i	0.182415	−	1.03453i
$746$	−2.37692	−	13.4802i	−0.0870254	−	0.493545i
$747$	0.643691	−	0.234284i	0.0235514	−	0.00857201i
$748$	3.47174	−	6.01324i	0.126940	−	0.219866i
$749$	−12.8323	−	22.2263i	−0.468884	−	0.812131i
$750$	8.99596	+	7.54851i	0.328486	+	0.275632i
$751$	−21.5247	−	18.0614i	−0.785448	−	0.659069i	0.159167	−	0.987252i	$-0.449119\pi$
$751$	−21.5247	−	18.0614i	−0.785448	−	0.659069i	−0.944614	+	0.328183i	$0.893564\pi$
$752$	−4.88136	−	8.45476i	−0.178005	−	0.308313i
$753$	6.86453	−	11.8897i	0.250158	−	0.433286i
$754$	−19.6492	+	7.15171i	−0.715580	+	0.260450i
$755$	0.423983	+	2.40453i	0.0154303	+	0.0875097i
$756$	3.41897	−	19.3899i	0.124347	−	0.705205i
$757$	23.4284	+	8.52725i	0.851521	+	0.309928i	0.730660	−	0.682741i	$-0.239212\pi$
$757$	23.4284	+	8.52725i	0.851521	+	0.309928i	0.120861	+	0.992669i	$0.461435\pi$
$758$	−4.83798	+	4.05955i	−0.175724	+	0.147450i
$759$	1.85486			0.0673270
$760$	−0.162725	+	11.9859i	−0.00590266	+	0.434776i
$761$	11.5854			0.419972			0.209986	−	0.977704i	$-0.432658\pi$
$761$	11.5854			0.419972			0.209986	+	0.977704i	$0.432658\pi$
$762$	−27.9047	+	23.4148i	−1.01088	+	0.848228i
$763$	−9.53565	−	3.47069i	−0.345214	−	0.125647i
$764$	3.42017	−	19.3968i	0.123737	−	0.701750i
$765$	0.230282	+	1.30600i	0.00832587	+	0.0472184i
$766$	−3.76831	+	1.37155i	−0.136155	+	0.0495562i
$767$	1.48943	−	2.57978i	0.0537804	−	0.0931503i
$768$	0.875992	+	1.51726i	0.0316097	+	0.0547495i
$769$	3.82479	+	3.20938i	0.137925	+	0.115733i	0.709140	−	0.705067i	$-0.249083\pi$
$769$	3.82479	+	3.20938i	0.137925	+	0.115733i	−0.571215	+	0.820800i	$0.693528\pi$
$770$	−8.07858	−	6.77874i	−0.291132	−	0.244289i
$771$	−17.9501	−	31.0905i	−0.646457	−	1.11970i
$772$	0.279025	−	0.483285i	0.0100423	−	0.0173938i
$773$	4.04198	−	1.47116i	0.145380	−	0.0529140i	−0.268305	−	0.963334i	$-0.586464\pi$
$773$	4.04198	−	1.47116i	0.145380	−	0.0529140i	0.413685	+	0.910420i	$0.364241\pi$
$774$	−0.0635620	−	0.360478i	−0.00228469	−	0.0129571i
$775$	−2.40558	+	13.6427i	−0.0864111	+	0.490062i
$776$	5.73017	+	2.08561i	0.205701	+	0.0748691i
$777$	−29.5618	+	24.8053i	−1.06052	+	0.889884i
$778$	−17.8884			−0.641329
$779$	23.9598	−	13.4028i	0.858448	−	0.480206i
$780$	14.4485			0.517340
$781$	−10.2392	+	8.59167i	−0.366386	+	0.307434i
$782$	−6.90786	−	2.51426i	−0.247025	−	0.0899096i
$783$	−6.21656	+	35.2559i	−0.222162	+	1.25994i
$784$	1.33812	+	7.58883i	0.0477898	+	0.271030i
$785$	19.8731	−	7.23322i	0.709302	−	0.258165i
$786$	−5.85916	+	10.1484i	−0.208989	+	0.361980i
$787$	−9.58729	−	16.6057i	−0.341750	−	0.591928i	0.643008	−	0.765860i	$-0.277686\pi$
$787$	−9.58729	−	16.6057i	−0.341750	−	0.591928i	−0.984758	+	0.173931i	$0.944353\pi$
$788$	−20.8631	−	17.5062i	−0.743218	−	0.623634i
$789$	35.9874	+	30.1970i	1.28118	+	1.07504i
$790$	−13.2208	−	22.8991i	−0.470375	−	0.814714i
$791$	−15.3601	+	26.6046i	−0.546144	+	0.945949i
$792$	0.0652624	−	0.0237536i	0.00231900	−	0.000844046i
$793$	−3.28111	−	18.6081i	−0.116516	−	0.660792i
$794$	−1.29600	+	7.34999i	−0.0459933	+	0.260841i
$795$	−34.2355	−	12.4607i	−1.21421	−	0.441935i
$796$	−7.40057	+	6.20982i	−0.262306	+	0.220101i
$797$	−26.0624			−0.923179			−0.461589	−	0.887094i	$-0.652721\pi$
$797$	−26.0624			−0.923179			−0.461589	+	0.887094i	$0.652721\pi$
$798$	−18.5181	−	22.6875i	−0.655533	−	0.803128i
$799$	67.7873			2.39814
$800$	1.96306	−	1.64720i	0.0694047	−	0.0582375i
$801$	−0.860737	−	0.313283i	−0.0304126	−	0.0110693i
$802$	−2.95013	+	16.7310i	−0.104173	+	0.590793i
$803$	−1.48505	−	8.42215i	−0.0524064	−	0.297211i
$804$	3.28500	−	1.19564i	0.115853	−	0.0421671i
$805$	−5.58253	+	9.66923i	−0.196758	+	0.340795i
$806$	−8.10583	−	14.0397i	−0.285516	−	0.494528i
$807$	−14.7110	−	12.3440i	−0.517852	−	0.434529i
$808$	−13.7020	−	11.4973i	−0.482034	−	0.404474i
$809$	−7.01650	−	12.1529i	−0.246687	−	0.427275i	0.715918	−	0.698185i	$-0.246009\pi$
$809$	−7.01650	−	12.1529i	−0.246687	−	0.427275i	−0.962605	+	0.270910i	$0.912675\pi$
$810$	12.6549	−	21.9190i	0.444649	−	0.770155i
$811$	−16.0665	+	5.84774i	−0.564172	+	0.205342i	−0.608332	−	0.793683i	$-0.708161\pi$
$811$	−16.0665	+	5.84774i	−0.564172	+	0.205342i	0.0441601	+	0.999024i	$0.485939\pi$
$812$	−4.64319	−	26.3328i	−0.162944	−	0.924102i
$813$	−0.565989	+	3.20988i	−0.0198501	+	0.112575i
$814$	5.39742	+	1.96450i	0.189179	+	0.0688557i
$815$	2.05870	−	1.72745i	0.0721130	−	0.0605100i
$816$	−12.1649			−0.425856
$817$	19.7379	+	11.7558i	0.690540	+	0.411282i
$818$	3.76849			0.131762
$819$	−0.611835	+	0.513391i	−0.0213793	+	0.0179393i
$820$	−16.2759	−	5.92395i	−0.568380	−	0.206873i
$821$	−6.65253	+	37.7284i	−0.232175	+	1.31673i	0.616307	+	0.787506i	$0.288628\pi$
$821$	−6.65253	+	37.7284i	−0.232175	+	1.31673i	−0.848482	+	0.529224i	$0.822483\pi$
$822$	−4.98879	−	28.2928i	−0.174004	−	0.986826i
$823$	42.6780	−	15.5335i	1.48766	−	0.541464i	0.534828	−	0.844961i	$-0.320376\pi$
$823$	42.6780	−	15.5335i	1.48766	−	0.541464i	0.952833	+	0.303497i	$0.0981541\pi$
$824$	−0.817615	+	1.41615i	−0.0284830	+	0.0493339i
$825$	−2.24481	−	3.88813i	−0.0781544	−	0.135367i
$826$	2.91806	+	2.44854i	0.101532	+	0.0851956i
$827$	−29.2880	−	24.5756i	−1.01844	−	0.854576i	−0.0290129	−	0.999579i	$-0.509236\pi$
$827$	−29.2880	−	24.5756i	−1.01844	−	0.854576i	−0.989431	+	0.145003i	$0.953681\pi$
$828$	−0.0367644	−	0.0636778i	−0.00127765	−	0.00221296i
$829$	4.84349	−	8.38917i	0.168221	−	0.291368i	−0.769573	−	0.638559i	$-0.779531\pi$
$829$	4.84349	−	8.38917i	0.168221	−	0.291368i	0.937795	+	0.347191i	$0.112864\pi$
$830$	25.4880	−	9.27687i	0.884701	−	0.322005i
$831$	−5.71247	−	32.3970i	−0.198163	−	1.12384i
$832$	−0.520748	+	2.95331i	−0.0180537	+	0.102388i
$833$	−50.2790	−	18.3001i	−1.74206	−	0.634060i
$834$	−17.7105	+	14.8609i	−0.613264	+	0.514590i
$835$	−39.7042			−1.37402
$836$	−1.54630	+	4.07541i	−0.0534798	+	0.140951i
$837$	−27.7555			−0.959371
$838$	24.9317	−	20.9202i	0.861253	−	0.722677i
$839$	−16.9717	−	6.17719i	−0.585928	−	0.213260i	0.0320097	−	0.999488i	$-0.489809\pi$
$839$	−16.9717	−	6.17719i	−0.585928	−	0.213260i	−0.617937	+	0.786227i	$0.712031\pi$
$840$	−3.20835	+	18.1955i	−0.110699	+	0.627803i
$841$	3.40671	+	19.3204i	0.117473	+	0.666220i
$842$	−3.73750	+	1.36034i	−0.128803	+	0.0468803i
$843$	11.1343	−	19.2852i	0.383486	−	0.664218i
$844$	−8.36425	−	14.4873i	−0.287909	−	0.498674i
$845$	−8.44082	−	7.08269i	−0.290373	−	0.243652i
$846$	0.519400	+	0.435828i	0.0178573	+	0.0149841i
$847$	−1.91741	−	3.32106i	−0.0658831	−	0.114113i
$848$	3.78089	−	6.54870i	0.129836	−	0.224883i
$849$	−18.0226	+	6.55969i	−0.618534	+	0.225128i
$850$	3.08978	+	17.5230i	0.105979	+	0.601035i
$851$	1.05597	−	5.98869i	0.0361981	−	0.205290i
$852$	22.0052	+	8.00926i	0.753887	+	0.274393i
$853$	−40.0281	+	33.5876i	−1.37054	+	1.15002i	−0.397967	+	0.917400i	$0.630284\pi$
$853$	−40.0281	+	33.5876i	−1.37054	+	1.15002i	−0.972569	+	0.232616i	$0.925271\pi$
$854$	24.1623			0.826817
$855$	−0.274089	−	0.786097i	−0.00937365	−	0.0268839i
$856$	6.69253			0.228746
$857$	7.09993	−	5.95755i	0.242529	−	0.203506i	−0.513418	−	0.858138i	$-0.671621\pi$
$857$	7.09993	−	5.95755i	0.242529	−	0.203506i	0.755947	+	0.654633i	$0.227177\pi$
$858$	4.93712	+	1.79697i	0.168551	+	0.0613474i
$859$	5.27882	−	29.9377i	0.180111	−	1.02146i	−0.751966	−	0.659202i	$-0.770894\pi$
$859$	5.27882	−	29.9377i	0.180111	−	1.02146i	0.932077	−	0.362259i	$-0.117994\pi$
$860$	−2.51684	−	14.2737i	−0.0858236	−	0.486730i
$861$	39.7637	−	14.4728i	1.35514	−	0.493231i
$862$	2.09163	−	3.62281i	0.0712413	−	0.123393i
$863$	−10.4084	−	18.0279i	−0.354307	−	0.613678i	0.632692	−	0.774403i	$-0.281950\pi$
$863$	−10.4084	−	18.0279i	−0.354307	−	0.613678i	−0.986999	+	0.160726i	$0.948617\pi$
$864$	3.93308	+	3.30025i	0.133806	+	0.112277i
$865$	−43.6993	−	36.6680i	−1.48582	−	1.24675i
$866$	−6.87068	−	11.9004i	−0.233475	−	0.404391i
$867$	27.3415	−	47.3569i	0.928566	−	1.60832i
$868$	19.4806	−	7.09035i	0.661214	−	0.240662i
$869$	−1.66964	−	9.46900i	−0.0566387	−	0.321214i
$870$	5.83360	−	33.0840i	0.197777	−	1.12165i
$871$	5.62294	+	2.04658i	0.190526	+	0.0693458i
$872$	2.02709	−	1.70093i	0.0686458	−	0.0576007i
$873$	−0.423505			−0.0143335
$874$	4.53343	+	0.862980i	0.153346	+	0.0291907i
$875$	−25.7045			−0.868970
$876$	−11.4777	+	9.63095i	−0.387796	+	0.325400i
$877$	−36.0540	−	13.1226i	−1.21746	−	0.443118i	−0.348172	−	0.937431i	$-0.613198\pi$
$877$	−36.0540	−	13.1226i	−1.21746	−	0.443118i	−0.869284	+	0.494313i	$0.835420\pi$
$878$	4.75997	−	26.9951i	0.160641	−	0.911042i
$879$	1.30666	+	7.41044i	0.0440726	+	0.249948i
$880$	2.58417	−	0.940561i	0.0871124	−	0.0317063i
$881$	5.96000	−	10.3230i	0.200797	−	0.347791i	−0.747988	−	0.663712i	$-0.768980\pi$
$881$	5.96000	−	10.3230i	0.200797	−	0.347791i	0.948786	+	0.315921i	$0.102313\pi$
$882$	−0.267590	−	0.463480i	−0.00901024	−	0.0156062i
$883$	−6.20502	−	5.20663i	−0.208815	−	0.175217i	0.532382	−	0.846504i	$-0.321297\pi$
$883$	−6.20502	−	5.20663i	−0.208815	−	0.175217i	−0.741197	+	0.671288i	$0.765742\pi$
$884$	−15.9511	−	13.3845i	−0.536492	−	0.450170i
$885$	2.39293	+	4.14467i	0.0804374	+	0.139322i
$886$	−17.2910	+	29.9489i	−0.580903	+	1.00615i
$887$	15.4165	−	5.61113i	0.517634	−	0.188403i	−0.0699746	−	0.997549i	$-0.522292\pi$
$887$	15.4165	−	5.61113i	0.517634	−	0.188403i	0.587608	+	0.809145i	$0.300070\pi$
$888$	−1.74743	−	9.91019i	−0.0586401	−	0.332564i
$889$	13.8455	−	78.5217i	0.464363	−	2.63353i
$890$	−34.0823	−	12.4049i	−1.14244	−	0.415814i
$891$	7.05031	−	5.91591i	0.236194	−	0.198191i
$892$	−9.83783			−0.329395
$893$	−42.0047	+	6.81996i	−1.40563	+	0.228221i
$894$	−18.2668			−0.610934
$895$	−41.1433	+	34.5234i	−1.37527	+	1.15399i
$896$	−3.60356	−	1.31159i	−0.120386	−	0.0438171i
$897$	0.965913	−	5.47797i	0.0322509	−	0.182904i
$898$	2.43218	+	13.7936i	0.0811630	+	0.460298i
$899$	−35.4206	+	12.8921i	−1.18134	+	0.429974i
$900$	−0.0889871	+	0.154130i	−0.00296624	+	0.00513767i
$901$	26.2526	+	45.4708i	0.874601	+	1.51485i
$902$	−4.82479	−	4.04848i	−0.160648	−	0.134800i
$903$	27.1257	+	22.7611i	0.902686	+	0.757443i
$904$	−4.00543	−	6.93762i	−0.133219	−	0.230742i
$905$	−0.721109	+	1.24900i	−0.0239705	+	0.0415181i
$906$	1.46170	−	0.532016i	0.0485618	−	0.0176750i
$907$	−0.532714	−	3.02117i	−0.0176885	−	0.100316i	0.974685	−	0.223581i	$-0.0717747\pi$
$907$	−0.532714	−	3.02117i	−0.0176885	−	0.100316i	−0.992374	+	0.123265i	$0.960664\pi$
$908$	0.150151	−	0.851550i	0.00498294	−	0.0282597i
$909$	1.16733	+	0.424872i	0.0387178	+	0.0140921i
$910$	−24.2266	+	20.3285i	−0.803105	+	0.673885i
$911$	32.5171			1.07734			0.538669	−	0.842517i	$-0.318927\pi$
$911$	32.5171			1.07734			0.538669	+	0.842517i	$0.318927\pi$
$912$	7.53801	−	1.22389i	0.249609	−	0.0405269i
$913$	9.86312			0.326422
$914$	−26.1623	+	21.9528i	−0.865373	+	0.726134i
$915$	28.5262	+	10.3827i	0.943047	+	0.343241i
$916$	1.44814	−	8.21282i	0.0478480	−	0.271359i
$917$	−4.45401	−	25.2599i	−0.147084	−	0.834157i
$918$	−33.4999	+	12.1929i	−1.10566	+	0.402427i
$919$	3.35953	−	5.81888i	0.110821	−	0.191947i	−0.805281	−	0.592894i	$-0.797985\pi$
$919$	3.35953	−	5.81888i	0.110821	−	0.191947i	0.916101	+	0.400947i	$0.131319\pi$
$920$	−1.45575	−	2.52142i	−0.0479945	−	0.0831289i
$921$	−44.5634	−	37.3931i	−1.46841	−	1.23215i
$922$	28.7873	+	24.1554i	0.948058	+	0.795515i
$923$	20.0419	+	34.7135i	0.659686	+	1.14261i
$924$	−3.35928	+	5.81844i	−0.110512	+	0.191413i
$925$	−13.8314	+	5.03422i	−0.454774	+	0.165524i
$926$	0.960857	+	5.44929i	0.0315757	+	0.179075i
$927$	0.0197209	−	0.111843i	0.000647718	−	0.00367339i
$928$	6.55219	+	2.38480i	0.215086	+	0.0782849i
$929$	39.6211	−	33.2460i	1.29993	−	1.09077i	0.309768	−	0.950812i	$-0.399749\pi$
$929$	39.6211	−	33.2460i	1.29993	−	1.09077i	0.990158	−	0.139955i	$-0.0446958\pi$
$930$	26.0457			0.854072
$931$	32.9967	+	6.28122i	1.08142	+	0.205859i
$932$	19.8575			0.650455
$933$	−39.4894	+	33.1355i	−1.29282	+	1.08481i
$934$	−11.8604	−	4.31682i	−0.388083	−	0.141251i
$935$	−3.31576	+	18.8046i	−0.108437	+	0.614977i
$936$	−0.0361664	−	0.205110i	−0.00118214	−	0.00670422i
$937$	31.3187	−	11.3991i	1.02314	−	0.372392i	0.224674	−	0.974434i	$-0.427868\pi$
$937$	31.3187	−	11.3991i	1.02314	−	0.372392i	0.798464	+	0.602042i	$0.205646\pi$
$938$	−3.82592	+	6.62668i	−0.124921	+	0.216369i
$939$	−7.65255	−	13.2546i	−0.249731	−	0.432547i
$940$	20.5665	+	17.2573i	0.670805	+	0.562872i
$941$	25.2737	+	21.2071i	0.823898	+	0.691333i	0.953882	−	0.300183i	$-0.0970479\pi$
$941$	25.2737	+	21.2071i	0.823898	+	0.691333i	−0.129983	+	0.991516i	$0.541492\pi$
$942$	−6.73667	−	11.6682i	−0.219492	−	0.380172i
$943$	−3.33407	+	5.77477i	−0.108572	+	0.188052i
$944$	−0.933425	+	0.339739i	−0.0303804	+	0.0110576i
$945$	9.40223	+	53.3227i	0.305854	+	1.73459i
$946$	0.915209	−	5.19041i	0.0297560	−	0.168755i
$947$	−5.76795	−	2.09936i	−0.187433	−	0.0682201i	0.246598	−	0.969118i	$-0.420687\pi$
$947$	−5.76795	−	2.09936i	−0.187433	−	0.0682201i	−0.434032	+	0.900898i	$0.642909\pi$
$948$	−12.9044	+	10.8281i	−0.419115	+	0.351679i
$949$	−25.6466			−0.832523
$950$	−3.67755	−	10.5473i	−0.119316	−	0.342201i
$951$	−5.28859			−0.171494
$952$	20.3975	−	17.1156i	0.661088	−	0.554718i
$953$	11.2830	+	4.10667i	0.365491	+	0.133028i	0.518236	−	0.855238i	$-0.326589\pi$
$953$	11.2830	+	4.10667i	0.365491	+	0.133028i	−0.152744	+	0.988266i	$0.548811\pi$
$954$	−0.0911952	+	0.517194i	−0.00295255	+	0.0167448i
$955$	9.40553	+	53.3414i	0.304356	+	1.72609i
$956$	14.8138	−	5.39177i	0.479112	−	0.174382i
$957$	6.10803	−	10.5794i	0.197444	−	0.341984i
$958$	11.0832	+	19.1968i	0.358084	+	0.620219i
$959$	48.1720	+	40.4211i	1.55555	+	1.30527i
$960$	−3.69079	−	3.09694i	−0.119120	−	0.0999534i
$961$	0.887985	+	1.53804i	0.0286447	+	0.0496141i
$962$	8.61248	−	14.9172i	0.277677	−	0.480951i
$963$	−0.436771	+	0.158971i	−0.0140747	+	0.00512278i
$964$	−3.83487	−	21.7486i	−0.123513	−	0.700476i
$965$	−0.266488	+	1.51133i	−0.00857857	+	0.0486515i
$966$	6.68408	+	2.43281i	0.215057	+	0.0782743i
$967$	−37.0707	+	31.1060i	−1.19211	+	1.00030i	−0.192293	+	0.981338i	$0.561592\pi$
$967$	−37.0707	+	31.1060i	−1.19211	+	1.00030i	−0.999820	+	0.0189644i	$0.993963\pi$
$968$	1.00000			0.0321412
$969$	−18.8105	+	49.5769i	−0.604281	+	1.59264i
$970$	−16.7694			−0.538432
$971$	22.7752	−	19.1106i	0.730890	−	0.613289i	−0.199484	−	0.979901i	$-0.563927\pi$
$971$	22.7752	−	19.1106i	0.730890	−	0.613289i	0.930374	+	0.366612i	$0.119482\pi$
$972$	−0.678091	−	0.246805i	−0.0217498	−	0.00791628i
$973$	8.78744	−	49.8361i	0.281712	−	1.59767i
$974$	1.48747	+	8.43587i	0.0476617	+	0.270303i
$975$	−12.6518	+	4.60489i	−0.405183	+	0.147475i
$976$	−3.15038	+	5.45661i	−0.100841	+	0.174662i
$977$	14.0556	+	24.3450i	0.449679	+	0.778867i	0.998365	−	0.0571618i	$-0.0182051\pi$
$977$	14.0556	+	24.3450i	0.449679	+	0.778867i	−0.548686	+	0.836029i	$0.684872\pi$
$978$	−1.31156	−	1.10053i	−0.0419390	−	0.0351910i
$979$	−10.1033	−	8.47764i	−0.322902	−	0.270947i
$980$	−10.5957	−	18.3522i	−0.338466	−	0.586241i
$981$	−0.0918895	+	0.159157i	−0.00293381	+	0.00508150i
$982$	−20.7613	+	7.55649i	−0.662519	+	0.241137i
$983$	−6.33790	−	35.9440i	−0.202148	−	1.14644i	−0.901866	−	0.432017i	$-0.857802\pi$
$983$	−6.33790	−	35.9440i	−0.202148	−	1.14644i	0.699718	−	0.714419i	$-0.253309\pi$
$984$	−1.91613	+	10.8669i	−0.0610840	+	0.346424i
$985$	70.3796	+	25.6161i	2.24248	+	0.816196i
$986$	−37.0879	+	31.1204i	−1.18112	+	0.991077i
$987$	−65.5914			−2.08780
$988$	11.2307	+	6.68896i	0.357297	+	0.212804i
$989$	−5.57995			−0.177432
$990$	−0.146308	+	0.122767i	−0.00464996	+	0.00390178i
$991$	50.9113	+	18.5302i	1.61725	+	0.588631i	0.982855	−	0.184378i	$-0.0590270\pi$
$991$	50.9113	+	18.5302i	1.61725	+	0.588631i	0.634395	+	0.773009i	$0.281249\pi$
$992$	−0.938729	+	5.32380i	−0.0298047	+	0.169031i
$993$	−6.40352	−	36.3161i	−0.203209	−	1.15246i
$994$	−48.1661	+	17.5310i	−1.52774	+	0.556051i
$995$	13.2836	−	23.0079i	0.421119	−	0.729400i
$996$	−8.64002	−	14.9649i	−0.273769	−	0.474183i
$997$	−43.1670	−	36.2214i	−1.36711	−	1.14714i	−0.973714	−	0.227775i	$-0.926855\pi$
$997$	−43.1670	−	36.2214i	−1.36711	−	1.14714i	−0.393398	−	0.919368i	$-0.628701\pi$
$998$	−2.08963	−	1.75340i	−0.0661460	−	0.0555031i
$999$	−14.7452	−	25.5394i	−0.466516	−	0.808030i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	418.2.j.d.177.4	yes	30
19.4	even	9		7942.2.a.ca.1.4		15
19.15	odd	18		7942.2.a.by.1.12		15
19.16	even	9	inner	418.2.j.d.111.4	✓	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
418.2.j.d.111.4	✓	30	19.16	even	9	inner
418.2.j.d.177.4	yes	30	1.1	even	1	trivial
7942.2.a.by.1.12		15	19.15	odd	18
7942.2.a.ca.1.4		15	19.4	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:	\( N \)	\(=\)	\( 418 = 2 \cdot 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	418.j (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.766044 - 0.642788i) q^{2} +(1.64633 + 0.599214i) q^{3} +(0.173648 - 0.984808i) q^{4} +(0.477535 + 2.70824i) q^{5} +(1.64633 - 0.599214i) q^{6} +(-1.91741 + 3.32106i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(0.0532024 + 0.0446421i) q^{9} +O(q^{10})\)	\(q+(0.766044 - 0.642788i) q^{2} +(1.64633 + 0.599214i) q^{3} +(0.173648 - 0.984808i) q^{4} +(0.477535 + 2.70824i) q^{5} +(1.64633 - 0.599214i) q^{6} +(-1.91741 + 3.32106i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(0.0532024 + 0.0446421i) q^{9} +(2.10664 + 1.76768i) q^{10} +(0.500000 + 0.866025i) q^{11} +(0.875992 - 1.51726i) q^{12} +(2.81802 - 1.02567i) q^{13} +(0.665911 + 3.77657i) q^{14} +(-0.836635 + 4.74479i) q^{15} +(-0.939693 - 0.342020i) q^{16} +(5.31902 - 4.46319i) q^{17} +0.0694508 q^{18} +(-2.84692 + 3.30077i) q^{19} +2.75002 q^{20} +(-5.14671 + 4.31861i) q^{21} +(0.939693 + 0.342020i) q^{22} +(0.183844 - 1.04263i) q^{23} +(-0.304229 - 1.72537i) q^{24} +(-2.40805 + 0.876459i) q^{25} +(1.49944 - 2.59710i) q^{26} +(-2.56714 - 4.44641i) q^{27} +(2.93765 + 2.46498i) q^{28} +(-5.34139 - 4.48196i) q^{29} +(2.40899 + 4.17250i) q^{30} +(2.70296 - 4.68167i) q^{31} +(-0.939693 + 0.342020i) q^{32} +(0.304229 + 1.72537i) q^{33} +(1.20572 - 6.83800i) q^{34} +(-9.90985 - 3.60689i) q^{35} +(0.0532024 - 0.0446421i) q^{36} +5.74381 q^{37} +(-0.0591724 + 4.35850i) q^{38} +5.25398 q^{39} +(2.10664 - 1.76768i) q^{40} +(-5.91848 - 2.15415i) q^{41} +(-1.16667 + 6.61649i) q^{42} +(-0.915209 - 5.19041i) q^{43} +(0.939693 - 0.342020i) q^{44} +(-0.0954954 + 0.165403i) q^{45} +(-0.529359 - 0.916876i) q^{46} +(7.47868 + 6.27536i) q^{47} +(-1.34210 - 1.12615i) q^{48} +(-3.85295 - 6.67350i) q^{49} +(-1.28130 + 2.21927i) q^{50} +(11.4313 - 4.16064i) q^{51} +(-0.520748 - 2.95331i) q^{52} +(-1.31309 + 7.44691i) q^{53} +(-4.82464 - 1.75603i) q^{54} +(-2.10664 + 1.76768i) q^{55} +3.83483 q^{56} +(-6.66482 + 3.72823i) q^{57} -6.97269 q^{58} +(0.760935 - 0.638501i) q^{59} +(4.52743 + 1.64785i) q^{60} +(1.09411 - 6.20503i) q^{61} +(-0.938729 - 5.32380i) q^{62} +(-0.250270 + 0.0910908i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(4.12347 + 7.14206i) q^{65} +(1.34210 + 1.12615i) q^{66} +(1.52853 + 1.28259i) q^{67} +(-3.47174 - 6.01324i) q^{68} +(0.927428 - 1.60635i) q^{69} +(-9.90985 + 3.60689i) q^{70} +(2.32103 + 13.1632i) q^{71} +(0.0120600 - 0.0683957i) q^{72} +(-8.03632 - 2.92498i) q^{73} +(4.40002 - 3.69205i) q^{74} -4.48963 q^{75} +(2.75626 + 3.37684i) q^{76} -3.83483 q^{77} +(4.02478 - 3.37719i) q^{78} +(-9.03521 - 3.28855i) q^{79} +(0.477535 - 2.70824i) q^{80} +(-1.59818 - 9.06371i) q^{81} +(-5.91848 + 2.15415i) q^{82} +(4.93156 - 8.54171i) q^{83} +(3.35928 + 5.81844i) q^{84} +(14.6274 + 12.2738i) q^{85} +(-4.03742 - 3.38780i) q^{86} +(-6.10803 - 10.5794i) q^{87} +(0.500000 - 0.866025i) q^{88} +(-12.3935 + 4.51086i) q^{89} +(0.0331652 + 0.188089i) q^{90} +(-1.99698 + 11.3254i) q^{91} +(-0.994869 - 0.362103i) q^{92} +(7.25528 - 6.08791i) q^{93} +9.76272 q^{94} +(-10.2988 - 6.13390i) q^{95} -1.75198 q^{96} +(-4.67128 + 3.91967i) q^{97} +(-7.24118 - 2.63557i) q^{98} +(-0.0120600 + 0.0683957i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q - 15 q^{8}+O(q^{10}) \) 30 * q - 15 * q^8	\( 30 q - 15 q^{8} + 15 q^{11} - 3 q^{12} - 21 q^{13} - 9 q^{14} + 3 q^{15} + 6 q^{17} + 60 q^{18} - 9 q^{19} + 18 q^{20} - 39 q^{21} + 15 q^{23} + 24 q^{25} - 3 q^{27} + 9 q^{28} - 3 q^{29} - 21 q^{30} - 18 q^{31} + 15 q^{34} + 51 q^{35} - 18 q^{37} - 6 q^{38} - 6 q^{41} + 51 q^{42} + 39 q^{43} - 54 q^{45} - 21 q^{46} - 3 q^{47} - 33 q^{49} - 24 q^{50} - 48 q^{51} - 12 q^{52} - 24 q^{53} - 9 q^{54} - 6 q^{57} - 18 q^{58} + 21 q^{59} + 3 q^{60} + 63 q^{61} - 27 q^{62} + 57 q^{63} - 15 q^{64} - 6 q^{65} - 45 q^{67} - 21 q^{68} + 42 q^{69} + 51 q^{70} - 48 q^{71} + 87 q^{73} + 9 q^{74} + 42 q^{75} - 9 q^{76} - 36 q^{78} - 57 q^{79} + 36 q^{81} - 6 q^{82} - 30 q^{83} + 9 q^{84} + 81 q^{85} - 24 q^{86} - 9 q^{87} + 15 q^{88} - 6 q^{89} - 114 q^{90} - 51 q^{91} - 3 q^{92} + 33 q^{93} + 78 q^{94} - 132 q^{95} + 6 q^{96} - 66 q^{97} + 9 q^{98}+O(q^{100}) \) 30 * q - 15 * q^8 + 15 * q^11 - 3 * q^12 - 21 * q^13 - 9 * q^14 + 3 * q^15 + 6 * q^17 + 60 * q^18 - 9 * q^19 + 18 * q^20 - 39 * q^21 + 15 * q^23 + 24 * q^25 - 3 * q^27 + 9 * q^28 - 3 * q^29 - 21 * q^30 - 18 * q^31 + 15 * q^34 + 51 * q^35 - 18 * q^37 - 6 * q^38 - 6 * q^41 + 51 * q^42 + 39 * q^43 - 54 * q^45 - 21 * q^46 - 3 * q^47 - 33 * q^49 - 24 * q^50 - 48 * q^51 - 12 * q^52 - 24 * q^53 - 9 * q^54 - 6 * q^57 - 18 * q^58 + 21 * q^59 + 3 * q^60 + 63 * q^61 - 27 * q^62 + 57 * q^63 - 15 * q^64 - 6 * q^65 - 45 * q^67 - 21 * q^68 + 42 * q^69 + 51 * q^70 - 48 * q^71 + 87 * q^73 + 9 * q^74 + 42 * q^75 - 9 * q^76 - 36 * q^78 - 57 * q^79 + 36 * q^81 - 6 * q^82 - 30 * q^83 + 9 * q^84 + 81 * q^85 - 24 * q^86 - 9 * q^87 + 15 * q^88 - 6 * q^89 - 114 * q^90 - 51 * q^91 - 3 * q^92 + 33 * q^93 + 78 * q^94 - 132 * q^95 + 6 * q^96 - 66 * q^97 + 9 * q^98

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