LMFDB - Embedded newform 63.2.i.b.38.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [63,2,Mod(5,63)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(63, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([5, 5]))

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

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

chi := DirichletCharacter("63.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 63 = 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	63.i (of order $6$, degree $2$, 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:	$0.503057532734$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{6})$
Coefficient field:	10.0.288778218147.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - x^{9} + 7x^{8} - 4x^{7} + 34x^{6} - 19x^{5} + 64x^{4} - x^{3} + 64x^{2} - 21x + 9 $ x^10 - x^9 + 7x^8 - 4x^7 + 34x^6 - 19x^5 + 64x^4 - x^3 + 64x^2 - 21*x + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			38.2
Root			$0.187540 + 0.324828i$ of defining polynomial
Character	$\chi$	$=$	63.38
Dual form			63.2.i.b.5.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.718167i q^{2} +(-0.271473 + 1.71064i) q^{3} +1.48424 q^{4} +(-0.723774 + 1.25361i) q^{5} +(1.22853 + 0.194963i) q^{6} +(0.182786 - 2.63943i) q^{7} -2.50226i q^{8} +(-2.85261 - 0.928786i) q^{9} +O(q^{10})$	\(q-0.718167i q^{2} +(-0.271473 + 1.71064i) q^{3} +1.48424 q^{4} +(-0.723774 + 1.25361i) q^{5} +(1.22853 + 0.194963i) q^{6} +(0.182786 - 2.63943i) q^{7} -2.50226i q^{8} +(-2.85261 - 0.928786i) q^{9} +(0.900304 + 0.519791i) q^{10} +(-1.55933 + 0.900281i) q^{11} +(-0.402930 + 2.53900i) q^{12} +(-1.88867 + 1.09042i) q^{13} +(-1.89555 - 0.131271i) q^{14} +(-1.94800 - 1.57844i) q^{15} +1.17143 q^{16} +(1.95230 - 3.38149i) q^{17} +(-0.667023 + 2.04865i) q^{18} +(-3.47456 + 2.00604i) q^{19} +(-1.07425 + 1.86066i) q^{20} +(4.46550 + 1.02922i) q^{21} +(0.646552 + 1.11986i) q^{22} +(-4.91522 - 2.83781i) q^{23} +(4.28048 + 0.679296i) q^{24} +(1.45230 + 2.51546i) q^{25} +(0.783106 + 1.35638i) q^{26} +(2.36323 - 4.62765i) q^{27} +(0.271298 - 3.91754i) q^{28} +(8.49418 + 4.90412i) q^{29} +(-1.13358 + 1.39899i) q^{30} -2.83050i q^{31} -5.84581i q^{32} +(-1.11674 - 2.91186i) q^{33} +(-2.42847 - 1.40208i) q^{34} +(3.17653 + 2.13949i) q^{35} +(-4.23394 - 1.37854i) q^{36} +(-0.411767 - 0.713202i) q^{37} +(1.44067 + 2.49531i) q^{38} +(-1.35261 - 3.52686i) q^{39} +(3.13687 + 1.81107i) q^{40} +(5.90617 + 10.2298i) q^{41} +(0.739148 - 3.20698i) q^{42} +(-3.76766 + 6.52578i) q^{43} +(-2.31442 + 1.33623i) q^{44} +(3.22898 - 2.90383i) q^{45} +(-2.03802 + 3.52995i) q^{46} +2.33839 q^{47} +(-0.318012 + 2.00390i) q^{48} +(-6.93318 - 0.964903i) q^{49} +(1.80652 - 1.04299i) q^{50} +(5.25452 + 4.25767i) q^{51} +(-2.80323 + 1.61845i) q^{52} +(0.996713 + 0.575453i) q^{53} +(-3.32343 - 1.69719i) q^{54} -2.60640i q^{55} +(-6.60455 - 0.457379i) q^{56} +(-2.48837 - 6.48831i) q^{57} +(3.52198 - 6.10024i) q^{58} -9.79110 q^{59} +(-2.89130 - 2.34278i) q^{60} -2.35536i q^{61} -2.03277 q^{62} +(-2.97288 + 7.35948i) q^{63} -1.85540 q^{64} -3.15688i q^{65} +(-2.09120 + 0.802008i) q^{66} -0.312805 q^{67} +(2.89768 - 5.01893i) q^{68} +(6.18882 - 7.63781i) q^{69} +(1.53651 - 2.28128i) q^{70} -1.94933i q^{71} +(-2.32407 + 7.13797i) q^{72} +(2.42847 + 1.40208i) q^{73} +(-0.512198 + 0.295717i) q^{74} +(-4.69732 + 1.80149i) q^{75} +(-5.15706 + 2.97743i) q^{76} +(2.09120 + 4.28031i) q^{77} +(-2.53287 + 0.971396i) q^{78} +12.4317 q^{79} +(-0.847852 + 1.46852i) q^{80} +(7.27471 + 5.29892i) q^{81} +(7.34669 - 4.24162i) q^{82} +(3.60916 - 6.25124i) q^{83} +(6.62786 + 1.52760i) q^{84} +(2.82605 + 4.89486i) q^{85} +(4.68660 + 2.70581i) q^{86} +(-10.6951 + 13.1992i) q^{87} +(2.25274 + 3.90186i) q^{88} +(-5.28999 - 9.16253i) q^{89} +(-2.08544 - 2.31895i) q^{90} +(2.53287 + 5.18433i) q^{91} +(-7.29536 - 4.21198i) q^{92} +(4.84198 + 0.768404i) q^{93} -1.67935i q^{94} -5.80767i q^{95} +(10.0001 + 1.58698i) q^{96} +(-13.4322 - 7.75510i) q^{97} +(-0.692961 + 4.97918i) q^{98} +(5.28433 - 1.11986i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 3 q^{3} - 8 q^{4} + 12 q^{6} - 6 q^{7} + 3 q^{9}+O(q^{10}) $ 10 * q - 3 * q^3 - 8 * q^4 + 12 * q^6 - 6 * q^7 + 3 * q^9	$ 10 q - 3 q^{3} - 8 q^{4} + 12 q^{6} - 6 q^{7} + 3 q^{9} - 15 q^{10} - 12 q^{11} - 12 q^{12} - 6 q^{13} + 12 q^{14} - 3 q^{15} + 12 q^{16} + 12 q^{17} + 24 q^{18} + 3 q^{19} + 3 q^{20} - 9 q^{21} + 5 q^{22} - 15 q^{23} + 7 q^{25} - 3 q^{26} - 27 q^{27} + 2 q^{28} - 15 q^{29} + 6 q^{30} - 3 q^{34} + 15 q^{35} - 18 q^{36} + 6 q^{37} + 18 q^{38} + 18 q^{39} + 15 q^{40} + 9 q^{41} - 12 q^{42} + 3 q^{43} - 24 q^{44} + 30 q^{45} - 13 q^{46} + 30 q^{47} + 15 q^{48} + 4 q^{49} + 3 q^{50} + 21 q^{51} - 12 q^{52} + 9 q^{53} + 9 q^{54} - 30 q^{56} - 36 q^{57} + 8 q^{58} - 36 q^{59} - 48 q^{60} - 12 q^{62} - 15 q^{63} + 6 q^{64} - 39 q^{66} + 20 q^{67} - 27 q^{68} + 3 q^{69} + 6 q^{70} - 30 q^{72} + 3 q^{73} - 30 q^{74} + 6 q^{75} - 9 q^{76} + 39 q^{77} + 24 q^{78} - 40 q^{79} + 30 q^{80} + 15 q^{81} + 9 q^{82} + 15 q^{83} + 93 q^{84} + 18 q^{85} + 54 q^{86} + 6 q^{87} - 8 q^{88} - 24 q^{89} - 24 q^{90} - 24 q^{91} + 39 q^{92} + 36 q^{93} + 33 q^{96} - 6 q^{97} - 45 q^{98} + 21 q^{99}+O(q^{100}) $ 10 * q - 3 * q^3 - 8 * q^4 + 12 * q^6 - 6 * q^7 + 3 * q^9 - 15 * q^10 - 12 * q^11 - 12 * q^12 - 6 * q^13 + 12 * q^14 - 3 * q^15 + 12 * q^16 + 12 * q^17 + 24 * q^18 + 3 * q^19 + 3 * q^20 - 9 * q^21 + 5 * q^22 - 15 * q^23 + 7 * q^25 - 3 * q^26 - 27 * q^27 + 2 * q^28 - 15 * q^29 + 6 * q^30 - 3 * q^34 + 15 * q^35 - 18 * q^36 + 6 * q^37 + 18 * q^38 + 18 * q^39 + 15 * q^40 + 9 * q^41 - 12 * q^42 + 3 * q^43 - 24 * q^44 + 30 * q^45 - 13 * q^46 + 30 * q^47 + 15 * q^48 + 4 * q^49 + 3 * q^50 + 21 * q^51 - 12 * q^52 + 9 * q^53 + 9 * q^54 - 30 * q^56 - 36 * q^57 + 8 * q^58 - 36 * q^59 - 48 * q^60 - 12 * q^62 - 15 * q^63 + 6 * q^64 - 39 * q^66 + 20 * q^67 - 27 * q^68 + 3 * q^69 + 6 * q^70 - 30 * q^72 + 3 * q^73 - 30 * q^74 + 6 * q^75 - 9 * q^76 + 39 * q^77 + 24 * q^78 - 40 * q^79 + 30 * q^80 + 15 * q^81 + 9 * q^82 + 15 * q^83 + 93 * q^84 + 18 * q^85 + 54 * q^86 + 6 * q^87 - 8 * q^88 - 24 * q^89 - 24 * q^90 - 24 * q^91 + 39 * q^92 + 36 * q^93 + 33 * q^96 - 6 * q^97 - 45 * q^98 + 21 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/63\mathbb{Z}\right)^\times$.

$n$	$10$	$29$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$		−	0.718167i		−	0.507821i	−0.967228	−	0.253910i	$-0.918283\pi$
$2$		−	0.718167i		−	0.507821i	0.967228	−	0.253910i	$-0.0817168\pi$
$3$	−0.271473	+	1.71064i	−0.156735	+	0.987641i
$3$	−0.271473	+	1.71064i	−0.156735	+	0.987641i
$4$	1.48424			0.742118
$5$	−0.723774	+	1.25361i	−0.323682	+	0.560633i	−0.981245	−	0.192766i	$-0.938254\pi$
$5$	−0.723774	+	1.25361i	−0.323682	+	0.560633i	0.657563	+	0.753400i	$0.271587\pi$
$6$	1.22853	+	0.194963i	0.501544	+	0.0795931i
$7$	0.182786	−	2.63943i	0.0690867	−	0.997611i
$7$	0.182786	−	2.63943i	0.0690867	−	0.997611i
$8$		−	2.50226i		−	0.884683i
$9$	−2.85261	−	0.928786i	−0.950868	−	0.309595i
$10$	0.900304	+	0.519791i	0.284701	+	0.164372i
$11$	−1.55933	+	0.900281i	−0.470156	+	0.271445i	−0.716305	−	0.697787i	$-0.754168\pi$
$11$	−1.55933	+	0.900281i	−0.470156	+	0.271445i	0.246149	+	0.969232i	$0.420835\pi$
$12$	−0.402930	+	2.53900i	−0.116316	+	0.732946i
$13$	−1.88867	+	1.09042i	−0.523823	+	0.302429i	−0.738497	−	0.674256i	$-0.764464\pi$
$13$	−1.88867	+	1.09042i	−0.523823	+	0.302429i	0.214675	+	0.976686i	$0.431131\pi$
$14$	−1.89555	−	0.131271i	−0.506607	−	0.0350837i
$15$	−1.94800	−	1.57844i	−0.502972	−	0.407552i
$16$	1.17143			0.292858
$17$	1.95230	−	3.38149i	0.473503	−	0.820131i	−0.526037	−	0.850462i	$-0.676323\pi$
$17$	1.95230	−	3.38149i	0.473503	−	0.820131i	0.999540	+	0.0303308i	$0.00965608\pi$
$18$	−0.667023	+	2.04865i	−0.157219	+	0.482870i
$19$	−3.47456	+	2.00604i	−0.797118	+	0.460216i	−0.842462	−	0.538755i	$-0.818895\pi$
$19$	−3.47456	+	2.00604i	−0.797118	+	0.460216i	0.0453446	+	0.998971i	$0.485561\pi$
$20$	−1.07425	+	1.86066i	−0.240210	+	0.416056i
$21$	4.46550	+	1.02922i	0.974453	+	0.224593i
$22$	0.646552	+	1.11986i	0.137845	+	0.238755i
$23$	−4.91522	−	2.83781i	−1.02490	−	0.591723i	−0.109377	−	0.994000i	$-0.534886\pi$
$23$	−4.91522	−	2.83781i	−1.02490	−	0.591723i	−0.915518	+	0.402277i	$0.868219\pi$
$24$	4.28048	+	0.679296i	0.873749	+	0.138661i
$25$	1.45230	+	2.51546i	0.290460	+	0.503092i
$26$	0.783106	+	1.35638i	0.153580	+	0.266008i
$27$	2.36323	−	4.62765i	0.454803	−	0.890592i
$28$	0.271298	−	3.91754i	0.0512705	−	0.740345i
$29$	8.49418	+	4.90412i	1.57733	+	0.910672i	0.995230	+	0.0975551i	$0.0311022\pi$
$29$	8.49418	+	4.90412i	1.57733	+	0.910672i	0.582100	+	0.813117i	$0.302231\pi$
$30$	−1.13358	+	1.39899i	−0.206963	+	0.255419i
$31$		−	2.83050i		−	0.508374i	−0.967155	−	0.254187i	$-0.918192\pi$
$31$		−	2.83050i		−	0.508374i	0.967155	−	0.254187i	$-0.0818078\pi$
$32$		−	5.84581i		−	1.03340i
$33$	−1.11674	−	2.91186i	−0.194400	−	0.506890i
$34$	−2.42847	−	1.40208i	−0.416479	−	0.240454i
$35$	3.17653	+	2.13949i	0.536931	+	0.361641i
$36$	−4.23394	−	1.37854i	−0.705657	−	0.229756i
$37$	−0.411767	−	0.713202i	−0.0676941	−	0.117250i	0.830192	−	0.557478i	$-0.188231\pi$
$37$	−0.411767	−	0.713202i	−0.0676941	−	0.117250i	−0.897886	+	0.440228i	$0.854898\pi$
$38$	1.44067	+	2.49531i	0.233707	+	0.404793i
$39$	−1.35261	−	3.52686i	−0.216590	−	0.564750i
$40$	3.13687	+	1.81107i	0.495983	+	0.286356i
$41$	5.90617	+	10.2298i	0.922389	+	1.59762i	0.795708	+	0.605681i	$0.207099\pi$
$41$	5.90617	+	10.2298i	0.922389	+	1.59762i	0.126681	+	0.991943i	$0.459567\pi$
$42$	0.739148	−	3.20698i	0.114053	−	0.494847i
$43$	−3.76766	+	6.52578i	−0.574563	+	0.995172i	0.421526	+	0.906816i	$0.361494\pi$
$43$	−3.76766	+	6.52578i	−0.574563	+	0.995172i	−0.996089	+	0.0883555i	$0.971839\pi$
$44$	−2.31442	+	1.33623i	−0.348912	+	0.201444i
$45$	3.22898	−	2.90383i	0.481348	−	0.432878i
$46$	−2.03802	+	3.52995i	−0.300489	+	0.520463i
$47$	2.33839			0.341089			0.170545	−	0.985350i	$-0.445447\pi$
$47$	2.33839			0.341089			0.170545	+	0.985350i	$0.445447\pi$
$48$	−0.318012	+	2.00390i	−0.0459010	+	0.289238i
$49$	−6.93318	−	0.964903i	−0.990454	−	0.137843i
$50$	1.80652	−	1.04299i	0.255480	−	0.147502i
$51$	5.25452	+	4.25767i	0.735780	+	0.596194i
$52$	−2.80323	+	1.61845i	−0.388738	+	0.224438i
$53$	0.996713	+	0.575453i	0.136909	+	0.0790445i	0.566890	−	0.823793i	$-0.308146\pi$
$53$	0.996713	+	0.575453i	0.136909	+	0.0790445i	−0.429981	+	0.902838i	$0.641480\pi$
$54$	−3.32343	−	1.69719i	−0.452261	−	0.230958i
$55$		−	2.60640i		−	0.351447i
$56$	−6.60455	−	0.457379i	−0.882570	−	0.0611199i
$57$	−2.48837	−	6.48831i	−0.329592	−	0.859398i
$58$	3.52198	−	6.10024i	0.462458	−	0.801001i
$59$	−9.79110			−1.27469			−0.637346	−	0.770577i	$-0.719968\pi$
$59$	−9.79110			−1.27469			−0.637346	+	0.770577i	$0.719968\pi$
$60$	−2.89130	−	2.34278i	−0.373265	−	0.302452i
$61$		−	2.35536i		−	0.301573i	−0.988566	−	0.150786i	$-0.951819\pi$
$61$		−	2.35536i		−	0.301573i	0.988566	−	0.150786i	$-0.0481806\pi$
$62$	−2.03277			−0.258163
$63$	−2.97288	+	7.35948i	−0.374548	+	0.927208i
$64$	−1.85540			−0.231925
$65$		−	3.15688i		−	0.391563i
$66$	−2.09120	+	0.802008i	−0.257409	+	0.0987204i
$67$	−0.312805			−0.0382152			−0.0191076	−	0.999817i	$-0.506083\pi$
$67$	−0.312805			−0.0382152			−0.0191076	+	0.999817i	$0.506083\pi$
$68$	2.89768	−	5.01893i	0.351395	−	0.608634i
$69$	6.18882	−	7.63781i	0.745047	−	0.919484i
$70$	1.53651	−	2.28128i	0.183649	−	0.272665i
$71$		−	1.94933i		−	0.231343i	−0.993288	−	0.115671i	$-0.963098\pi$
$71$		−	1.94933i		−	0.231343i	0.993288	−	0.115671i	$-0.0369019\pi$
$72$	−2.32407	+	7.13797i	−0.273894	+	0.841218i
$73$	2.42847	+	1.40208i	0.284231	+	0.164101i	0.635337	−	0.772235i	$-0.280861\pi$
$73$	2.42847	+	1.40208i	0.284231	+	0.164101i	−0.351106	+	0.936336i	$0.614194\pi$
$74$	−0.512198	+	0.295717i	−0.0595418	+	0.0343765i
$75$	−4.69732	+	1.80149i	−0.542399	+	0.208018i
$76$	−5.15706	+	2.97743i	−0.591556	+	0.341535i
$77$	2.09120	+	4.28031i	0.238315	+	0.487786i
$78$	−2.53287	+	0.971396i	−0.286792	+	0.109989i
$79$	12.4317			1.39867			0.699336	−	0.714793i	$-0.253479\pi$
$79$	12.4317			1.39867			0.699336	+	0.714793i	$0.253479\pi$
$80$	−0.847852	+	1.46852i	−0.0947927	+	0.164186i
$81$	7.27471	+	5.29892i	0.808302	+	0.588769i
$82$	7.34669	−	4.24162i	0.811306	−	0.468408i
$83$	3.60916	−	6.25124i	0.396157	−	0.686163i	−0.597092	−	0.802173i	$-0.703677\pi$
$83$	3.60916	−	6.25124i	0.396157	−	0.686163i	0.993248	+	0.116010i	$0.0370104\pi$
$84$	6.62786	+	1.52760i	0.723159	+	0.166675i
$85$	2.82605	+	4.89486i	0.306528	+	0.530923i
$86$	4.68660	+	2.70581i	0.505369	+	0.291775i
$87$	−10.6951	+	13.1992i	−1.14664	+	1.41510i
$88$	2.25274	+	3.90186i	0.240143	+	0.415939i
$89$	−5.28999	−	9.16253i	−0.560737	−	0.971226i	−0.997432	−	0.0716161i	$-0.977184\pi$
$89$	−5.28999	−	9.16253i	−0.560737	−	0.971226i	0.436695	−	0.899610i	$-0.356149\pi$
$90$	−2.08544	−	2.31895i	−0.219824	−	0.244438i
$91$	2.53287	+	5.18433i	0.265517	+	0.543465i
$92$	−7.29536	−	4.21198i	−0.760593	−	0.439129i
$93$	4.84198	+	0.768404i	0.502090	+	0.0796798i
$94$		−	1.67935i		−	0.173212i
$95$		−	5.80767i		−	0.595854i
$96$	10.0001	+	1.58698i	1.02063	+	0.161970i
$97$	−13.4322	−	7.75510i	−1.36384	−	0.787411i	−0.373704	−	0.927548i	$-0.621912\pi$
$97$	−13.4322	−	7.75510i	−1.36384	−	0.787411i	−0.990132	+	0.140137i	$0.955246\pi$
$98$	−0.692961	+	4.97918i	−0.0699997	+	0.502973i
$99$	5.28433	−	1.11986i	0.531095	−	0.112550i
$100$	2.15556	+	3.73354i	0.215556	+	0.373354i
$101$	−1.97309	−	3.41749i	−0.196330	−	0.340053i	0.751006	−	0.660295i	$-0.229569\pi$
$101$	−1.97309	−	3.41749i	−0.196330	−	0.340053i	−0.947336	+	0.320242i	$0.896236\pi$
$102$	3.05772	−	3.77362i	0.302759	−	0.373644i
$103$	3.59853	+	2.07761i	0.354573	+	0.204713i	0.666698	−	0.745328i	$-0.267707\pi$
$103$	3.59853	+	2.07761i	0.354573	+	0.204713i	−0.312124	+	0.950041i	$0.601041\pi$
$104$	2.72853	+	4.72595i	0.267554	+	0.463417i
$105$	−4.52225	+	4.85310i	−0.441327	+	0.473614i
$106$	0.413271	−	0.715806i	0.0401404	−	0.0695253i
$107$	−4.91092	+	2.83532i	−0.474757	+	0.274101i	−0.718229	−	0.695807i	$-0.755047\pi$
$107$	−4.91092	+	2.83532i	−0.474757	+	0.274101i	0.243472	+	0.969908i	$0.421714\pi$
$108$	3.50759	−	6.86853i	0.337518	−	0.660925i
$109$	5.99916	−	10.3908i	0.574615	−	0.995262i	−0.421468	−	0.906843i	$-0.638485\pi$
$109$	5.99916	−	10.3908i	0.574615	−	0.995262i	0.996083	−	0.0884193i	$-0.0281815\pi$
$110$	−1.87183			−0.178472
$111$	1.33182	−	0.510772i	0.126411	−	0.0484804i
$112$	0.214122	−	3.09191i	0.0202326	−	0.292158i
$113$	6.27800	−	3.62461i	0.590585	−	0.340974i	−0.174744	−	0.984614i	$-0.555910\pi$
$113$	6.27800	−	3.62461i	0.590585	−	0.340974i	0.765329	+	0.643640i	$0.222576\pi$
$114$	−4.65969	+	1.78706i	−0.436420	+	0.167374i
$115$	7.11502	−	4.10786i	0.663479	−	0.383060i
$116$	12.6074	+	7.27887i	1.17057	+	0.675826i
$117$	6.40040	−	1.35638i	0.591717	−	0.125397i
$118$			7.03164i			0.647315i
$119$	−8.56834	−	5.77105i	−0.785458	−	0.529032i
$120$	−3.94968	+	4.87441i	−0.360554	+	0.444971i
$121$	−3.87899	+	6.71861i	−0.352635	+	0.610782i
$122$	−1.69154			−0.153145
$123$	−19.1029	+	7.32625i	−1.72245	+	0.660586i
$124$		−	4.20114i		−	0.377273i
$125$	−11.4423			−1.02343
$126$	5.28533	+	2.13502i	0.470855	+	0.190203i
$127$	−0.881336			−0.0782059			−0.0391030	−	0.999235i	$-0.512450\pi$
$127$	−0.881336			−0.0782059			−0.0391030	+	0.999235i	$0.512450\pi$
$128$		−	10.3591i		−	0.915626i
$129$	−10.1405	−	8.21669i	−0.892818	−	0.723439i
$130$	−2.26717			−0.198844
$131$	−1.48721	+	2.57592i	−0.129938	+	0.225059i	−0.923652	−	0.383232i	$-0.874811\pi$
$131$	−1.48721	+	2.57592i	−0.129938	+	0.225059i	0.793714	+	0.608291i	$0.208144\pi$
$132$	−1.65751	−	4.32189i	−0.144268	−	0.376173i
$133$	4.65969	+	9.53752i	0.404046	+	0.827008i
$134$			0.224646i			0.0194065i
$135$	4.09085	+	6.31195i	0.352084	+	0.543246i
$136$	−8.46137	−	4.88517i	−0.725556	−	0.418900i
$137$	−10.3045	+	5.94930i	−0.880372	+	0.508283i	−0.870781	−	0.491671i	$-0.836386\pi$
$137$	−10.3045	+	5.94930i	−0.880372	+	0.508283i	−0.00959114	+	0.999954i	$0.503053\pi$
$138$	−5.48522	−	4.44461i	−0.466933	−	0.378350i
$139$	10.4143	−	6.01268i	0.883327	−	0.509989i	0.0115731	−	0.999933i	$-0.496316\pi$
$139$	10.4143	−	6.01268i	0.883327	−	0.509989i	0.871754	+	0.489944i	$0.162983\pi$
$140$	4.71472	+	3.17552i	0.398467	+	0.268380i
$141$	−0.634809	+	4.00015i	−0.0534606	+	0.336874i
$142$	−1.39994			−0.117481
$143$	1.96338	−	3.40067i	0.164186	−	0.284378i
$144$	−3.34163	−	1.08801i	−0.278469	−	0.0906674i
$145$	−12.2957	+	7.09895i	−1.02111	+	0.589536i
$146$	1.00693	−	1.74405i	0.0833338	−	0.144338i
$147$	3.53277	−	11.5983i	0.291378	−	0.956608i
$148$	−0.611160	−	1.05856i	−0.0502370	−	0.0870131i
$149$	6.13061	+	3.53951i	0.502239	+	0.289968i	0.729638	−	0.683834i	$-0.239689\pi$
$149$	6.13061	+	3.53951i	0.502239	+	0.289968i	−0.227399	+	0.973802i	$0.573022\pi$
$150$	1.29377	+	3.37346i	0.105636	+	0.275442i
$151$	−7.79093	−	13.4943i	−0.634017	−	1.09815i	−0.986723	−	0.162415i	$-0.948072\pi$
$151$	−7.79093	−	13.4943i	−0.634017	−	1.09815i	0.352706	−	0.935734i	$-0.385262\pi$
$152$	5.01963	+	8.69425i	0.407146	+	0.705197i
$153$	−8.70982	+	7.83277i	−0.704147	+	0.633242i
$154$	3.07397	−	1.50183i	0.247708	−	0.121021i
$155$	3.54836	+	2.04865i	0.285011	+	0.164551i
$156$	−2.00759	−	5.23470i	−0.160736	−	0.419111i
$157$			2.08628i			0.166503i	0.996529	+	0.0832517i	$0.0265305\pi$
$157$			2.08628i			0.166503i	−0.996529	+	0.0832517i	$0.973469\pi$
$158$		−	8.92801i		−	0.710274i
$159$	−1.25498	+	1.54880i	−0.0995260	+	0.122828i
$160$	7.32839	+	4.23105i	0.579360	+	0.334494i
$161$	−8.38862	+	12.4547i	−0.661116	+	0.981566i
$162$	3.80551	−	5.22446i	0.298989	−	0.410472i
$163$	−5.58983	−	9.68188i	−0.437830	−	0.758343i	0.559692	−	0.828700i	$-0.310919\pi$
$163$	−5.58983	−	9.68188i	−0.437830	−	0.758343i	−0.997522	+	0.0703575i	$0.977586\pi$
$164$	8.76616	+	15.1834i	0.684522	+	1.18563i
$165$	4.45862	+	0.707566i	0.347103	+	0.0550839i
$166$	−4.48944	−	2.59198i	−0.348448	−	0.201176i
$167$	−0.960750	−	1.66407i	−0.0743450	−	0.128769i	0.826456	−	0.563001i	$-0.190353\pi$
$167$	−0.960750	−	1.66407i	−0.0743450	−	0.128769i	−0.900801	+	0.434232i	$0.857020\pi$
$168$	2.57537	−	11.1739i	0.198694	−	0.862082i
$169$	−4.12195	+	7.13943i	−0.317073	+	0.549187i
$170$	3.51533	−	2.02958i	0.269613	−	0.155661i
$171$	11.7747	−	2.49531i	0.900435	−	0.190821i
$172$	−5.59210	+	9.68580i	−0.426393	+	0.738535i
$173$	15.2258			1.15760			0.578798	−	0.815471i	$-0.303522\pi$
$173$	15.2258			1.15760			0.578798	+	0.815471i	$0.303522\pi$
$174$	9.47922	+	7.68089i	0.718618	+	0.582287i
$175$	6.90484	−	3.37346i	0.521957	−	0.255009i
$176$	−1.82665	+	1.05462i	−0.137689	+	0.0794948i
$177$	2.65802	−	16.7491i	0.199789	−	1.25894i
$178$	−6.58022	+	3.79909i	−0.493208	+	0.284754i
$179$	0.299401	+	0.172859i	0.0223783	+	0.0129201i	0.511147	−	0.859493i	$-0.329221\pi$
$179$	0.299401	+	0.172859i	0.0223783	+	0.0129201i	−0.488769	+	0.872413i	$0.662554\pi$
$180$	4.79257	−	4.30998i	0.357217	−	0.321247i
$181$		−	3.27661i		−	0.243548i	−0.992558	−	0.121774i	$-0.961142\pi$
$181$		−	3.27661i		−	0.243548i	0.992558	−	0.121774i	$-0.0388583\pi$
$182$	3.72321	−	1.81903i	0.275983	−	0.134835i
$183$	4.02918	+	0.639415i	0.297846	+	0.0472669i
$184$	−7.10094	+	12.2992i	−0.523488	+	0.906708i
$185$	1.19211			0.0876454
$186$	0.551842	−	3.47735i	0.0404630	−	0.254972i
$187$			7.03048i			0.514120i
$188$	3.47073			0.253129
$189$	−11.7824	−	7.08344i	−0.857043	−	0.515244i
$190$	−4.17087			−0.302587
$191$			7.39120i			0.534808i	0.963584	+	0.267404i	$0.0861659\pi$
$191$			7.39120i			0.534808i	−0.963584	+	0.267404i	$0.913834\pi$
$192$	0.503691	−	3.17393i	0.0363507	−	0.229059i
$193$	13.0285			0.937812			0.468906	−	0.883248i	$-0.344648\pi$
$193$	13.0285			0.937812			0.468906	+	0.883248i	$0.344648\pi$
$194$	−5.56945	+	9.64658i	−0.399863	+	0.692584i
$195$	5.40030	+	0.857007i	0.386724	+	0.0613716i
$196$	−10.2905	−	1.43214i	−0.735034	−	0.102296i
$197$			4.03035i			0.287151i	0.989639	+	0.143575i	$0.0458599\pi$
$197$			4.03035i			0.287151i	−0.989639	+	0.143575i	$0.954140\pi$
$198$	−0.804246	−	3.79503i	−0.0571553	−	0.269701i
$199$	14.2096	+	8.20390i	1.00729	+	0.581559i	0.910397	−	0.413736i	$-0.135776\pi$
$199$	14.2096	+	8.20390i	1.00729	+	0.581559i	0.0968925	+	0.995295i	$0.469110\pi$
$200$	6.29434	−	3.63404i	0.445077	−	0.256965i
$201$	0.0849180	−	0.535098i	0.00598965	−	0.0377429i
$202$	−2.45433	+	1.41701i	−0.172686	+	0.0997003i
$203$	14.4967	−	21.5234i	1.01747	−	1.51065i
$204$	7.79895	+	6.31940i	0.546036	+	0.442446i
$205$	−17.0989			−1.19424
$206$	1.49207	−	2.58434i	0.103957	−	0.180060i
$207$	11.3855	+	12.6603i	0.791346	+	0.879954i
$208$	−2.21245	+	1.27736i	−0.153406	+	0.0885688i
$209$	3.61199	−	6.25615i	0.249847	−	0.432747i
$210$	3.48533	+	3.24773i	0.240511	+	0.224115i
$211$	−6.00827	−	10.4066i	−0.413627	−	0.716422i	0.581657	−	0.813434i	$-0.302405\pi$
$211$	−6.00827	−	10.4066i	−0.413627	−	0.716422i	−0.995283	+	0.0970121i	$0.969071\pi$
$212$	1.47936	+	0.854108i	0.101603	+	0.0586604i
$213$	3.33461	+	0.529189i	0.228483	+	0.0362594i
$214$	2.03623	+	3.52686i	0.139194	+	0.241091i
$215$	−5.45387	−	9.44638i	−0.371951	−	0.644238i
$216$	−11.5796	−	5.91341i	−0.787892	−	0.402357i
$217$	−7.47092	−	0.517377i	−0.507159	−	0.0351219i
$218$	−7.46236	−	4.30839i	−0.505415	−	0.291801i
$219$	−3.05772	+	3.77362i	−0.206622	+	0.254998i
$220$		−	3.86851i		−	0.260815i
$221$			8.51535i			0.572804i
$222$	−0.366820	−	0.956467i	−0.0246193	−	0.0641939i
$223$	22.7932	+	13.1597i	1.52635	+	0.881237i	0.999511	+	0.0312693i	$0.00995496\pi$
$223$	22.7932	+	13.1597i	1.52635	+	0.881237i	0.526836	+	0.849967i	$0.323378\pi$
$224$	−15.4296	−	1.06853i	−1.03093	−	0.0713944i
$225$	−1.80652	−	8.52449i	−0.120435	−	0.568300i
$226$	−2.60307	−	4.50865i	−0.173154	−	0.299911i
$227$	5.40410	+	9.36018i	0.358683	+	0.621257i	0.987741	−	0.156101i	$-0.0498926\pi$
$227$	5.40410	+	9.36018i	0.358683	+	0.621257i	−0.629058	+	0.777358i	$0.716559\pi$
$228$	−3.69332	−	9.63019i	−0.244596	−	0.637775i
$229$	−8.39777	−	4.84846i	−0.554941	−	0.320395i	0.196172	−	0.980570i	$-0.437149\pi$
$229$	−8.39777	−	4.84846i	−0.554941	−	0.320395i	−0.751112	+	0.660174i	$0.770482\pi$
$230$	−2.95013	−	5.10977i	−0.194526	−	0.336928i
$231$	−7.88978	+	2.41532i	−0.519110	+	0.158916i
$232$	12.2714	−	21.2547i	0.805657	−	1.39544i
$233$	1.92897	−	1.11369i	0.126371	−	0.0729605i	−0.435482	−	0.900198i	$-0.643422\pi$
$233$	1.92897	−	1.11369i	0.126371	−	0.0729605i	0.561853	+	0.827237i	$0.310089\pi$
$234$	−0.974107	−	4.59655i	−0.0636793	−	0.300486i
$235$	−1.69247	+	2.93144i	−0.110404	+	0.191226i
$236$	−14.5323			−0.945973
$237$	−3.37486	+	21.2661i	−0.219220	+	1.38138i
$238$	−4.14458	+	6.15350i	−0.268653	+	0.398872i
$239$	−15.9697	+	9.22008i	−1.03299	+	0.596398i	−0.917840	−	0.396950i	$-0.870068\pi$
$239$	−15.9697	+	9.22008i	−1.03299	+	0.596398i	−0.115151	+	0.993348i	$0.536735\pi$
$240$	−2.28195	−	1.84904i	−0.147299	−	0.119355i
$241$	5.60475	−	3.23591i	0.361034	−	0.208443i	−0.308500	−	0.951224i	$-0.599827\pi$
$241$	5.60475	−	3.23591i	0.361034	−	0.208443i	0.669534	+	0.742781i	$0.266494\pi$
$242$	4.82508	+	2.78576i	0.310168	+	0.179075i
$243$	−11.0394	+	11.0059i	−0.708181	+	0.706031i
$244$		−	3.49591i		−	0.223803i
$245$	6.22767	−	7.99316i	0.397871	−	0.510664i
$246$	5.26147	+	13.7191i	0.335459	+	0.874695i
$247$	4.37486	−	7.57748i	0.278366	−	0.482143i
$248$	−7.08266			−0.449750
$249$	9.71387	+	7.87102i	0.615591	+	0.498806i
$250$			8.21748i			0.519719i
$251$	−0.416679			−0.0263005			−0.0131503	−	0.999914i	$-0.504186\pi$
$251$	−0.416679			−0.0263005			−0.0131503	+	0.999914i	$0.504186\pi$
$252$	−4.41246	+	10.9232i	−0.277959	+	0.688098i
$253$	10.2193			0.642481
$254$			0.632946i			0.0397146i
$255$	−9.14057	+	3.50555i	−0.572404	+	0.219526i
$256$	−11.1504			−0.696899
$257$	−10.5642	+	18.2977i	−0.658976	+	1.14138i	0.321906	+	0.946772i	$0.395677\pi$
$257$	−10.5642	+	18.2977i	−0.658976	+	1.14138i	−0.980881	+	0.194607i	$0.937657\pi$
$258$	−5.90095	+	7.28254i	−0.367377	+	0.453391i
$259$	−1.95771	+	0.956467i	−0.121646	+	0.0594320i
$260$		−	4.68556i		−	0.290586i
$261$	−19.6757	−	21.8788i	−1.21789	−	1.35426i
$262$	1.84994	+	1.06806i	0.114290	+	0.0659851i
$263$	−19.2653	+	11.1228i	−1.18795	+	0.685862i	−0.957840	−	0.287304i	$-0.907241\pi$
$263$	−19.2653	+	11.1228i	−1.18795	+	0.685862i	−0.230108	+	0.973165i	$0.573908\pi$
$264$	−7.28625	+	2.79439i	−0.448437	+	0.171983i
$265$	−1.44279	+	0.832996i	−0.0886299	+	0.0511705i
$266$	6.84953	−	3.34643i	0.419972	−	0.205183i
$267$	17.1099	−	6.56191i	1.04711	−	0.401582i
$268$	−0.464277			−0.0283602
$269$	14.5164	−	25.1432i	0.885083	−	1.53301i	0.0394642	−	0.999221i	$-0.487435\pi$
$269$	14.5164	−	25.1432i	0.885083	−	1.53301i	0.845619	−	0.533788i	$-0.179232\pi$
$270$	4.53303	−	2.93791i	0.275871	−	0.178795i
$271$	20.8174	−	12.0189i	1.26456	−	0.730097i	0.290610	−	0.956842i	$-0.406142\pi$
$271$	20.8174	−	12.0189i	1.26456	−	0.730097i	0.973954	+	0.226745i	$0.0728084\pi$
$272$	2.28699	−	3.96118i	0.138669	−	0.240182i
$273$	−9.55614	+	2.92544i	−0.578364	+	0.177056i
$274$	4.27259	+	7.40034i	0.258117	+	0.447071i
$275$	−4.52924	−	2.61496i	−0.273124	−	0.157688i
$276$	9.18568	−	11.3363i	0.552913	−	0.682366i
$277$	−4.03243	−	6.98437i	−0.242285	−	0.419650i	0.719080	−	0.694928i	$-0.244564\pi$
$277$	−4.03243	−	6.98437i	−0.242285	−	0.419650i	−0.961365	+	0.275278i	$0.911230\pi$
$278$	−4.31811	−	7.47918i	−0.258983	−	0.448572i
$279$	−2.62893	+	8.07431i	−0.157390	+	0.483396i
$280$	5.35358	−	7.94851i	0.319937	−	0.475014i
$281$	−12.0876	−	6.97879i	−0.721087	−	0.416320i	0.0940658	−	0.995566i	$-0.470014\pi$
$281$	−12.0876	−	6.97879i	−0.721087	−	0.416320i	−0.815153	+	0.579246i	$0.803347\pi$
$282$	2.87278	+	0.455899i	0.171071	+	0.0271484i
$283$			15.5375i			0.923609i	0.886982	+	0.461805i	$0.152798\pi$
$283$			15.5375i			0.923609i	−0.886982	+	0.461805i	$0.847202\pi$
$284$		−	2.89326i		−	0.171684i
$285$	9.93485	+	1.57662i	0.588490	+	0.0933911i
$286$	−2.44225	−	1.41003i	−0.144413	−	0.0833769i
$287$	28.0804	−	13.7191i	1.65753	−	0.809810i
$288$	−5.42950	+	16.6758i	−0.319937	+	0.982630i
$289$	0.877036	+	1.51907i	0.0515904	+	0.0893571i
$290$	5.09823	+	8.83039i	0.299378	+	0.518539i
$291$	16.9127	−	20.8725i	0.991440	−	1.22357i
$292$	3.60442	+	2.08102i	0.210933	+	0.121782i
$293$	−6.73712	−	11.6690i	−0.393587	−	0.681712i	0.599333	−	0.800500i	$-0.295433\pi$
$293$	−6.73712	−	11.6690i	−0.393587	−	0.681712i	−0.992920	+	0.118788i	$0.962099\pi$
$294$	−8.32948	−	2.53712i	−0.485785	−	0.147968i
$295$	7.08655	−	12.2743i	0.412595	−	0.714635i
$296$	−1.78462	+	1.03035i	−0.103729	+	0.0598879i
$297$	0.481132	+	9.34361i	0.0279181	+	0.542171i
$298$	2.54196	−	4.40280i	0.147252	−	0.255047i
$299$	12.3776			0.715818
$300$	−6.97193	+	2.67384i	−0.402525	+	0.154374i
$301$	16.5357	+	11.1373i	0.953099	+	0.641943i
$302$	−9.69114	+	5.59518i	−0.557663	+	0.321967i
$303$	6.38175	−	2.44750i	0.366622	−	0.140605i
$304$	−4.07020	+	2.34993i	−0.233442	+	0.134778i
$305$	2.95271	+	1.70475i	0.169072	+	0.0976136i
$306$	5.62524	+	6.25510i	0.321573	+	0.357580i
$307$			8.62791i			0.492421i	0.969216	+	0.246210i	$0.0791854\pi$
$307$			8.62791i			0.492421i	−0.969216	+	0.246210i	$0.920815\pi$
$308$	3.10384	+	6.35299i	0.176858	+	0.361995i
$309$	−4.53095	+	5.59178i	−0.257757	+	0.318106i
$310$	1.47127	−	2.54831i	0.0835625	−	0.144734i
$311$	−16.2440			−0.921113			−0.460556	−	0.887630i	$-0.652350\pi$
$311$	−16.2440			−0.921113			−0.460556	+	0.887630i	$0.652350\pi$
$312$	−8.82513	+	3.38457i	−0.499625	+	0.191614i
$313$		−	6.77692i		−	0.383054i	−0.981487	−	0.191527i	$-0.938656\pi$
$313$		−	6.77692i		−	0.383054i	0.981487	−	0.191527i	$-0.0613440\pi$
$314$	1.49830			0.0845538
$315$	−7.07425	−	9.05345i	−0.398589	−	0.510104i
$316$	18.4515			1.03798
$317$			21.9676i			1.23382i	0.787033	+	0.616911i	$0.211616\pi$
$317$			21.9676i			1.23382i	−0.787033	+	0.616911i	$0.788384\pi$
$318$	1.11230	+	0.901281i	0.0623746	+	0.0505413i
$319$	−17.6603			−0.988789
$320$	1.34289	−	2.32596i	0.0750699	−	0.130025i
$321$	−3.51705	−	9.17056i	−0.196302	−	0.511850i
$322$	8.94453	+	6.02443i	0.498459	+	0.335728i
$323$			15.6655i			0.871654i
$324$	10.7974	+	7.86485i	0.599855	+	0.436936i
$325$	−5.48584	−	3.16725i	−0.304299	−	0.175687i
$326$	−6.95320	+	4.01443i	−0.385102	+	0.222339i
$327$	16.1464	+	13.0833i	0.892900	+	0.723505i
$328$	25.5976	−	14.7788i	1.41339	−	0.816022i
$329$	0.427426	−	6.17202i	0.0235648	−	0.340274i
$330$	0.508150	−	3.20203i	0.0279728	−	0.176266i
$331$	−14.6036			−0.802685			−0.401342	−	0.915928i	$-0.631456\pi$
$331$	−14.6036			−0.802685			−0.401342	+	0.915928i	$0.631456\pi$
$332$	5.35684	−	9.27833i	0.293995	−	0.509214i
$333$	0.512198	+	2.41693i	0.0280683	+	0.132447i
$334$	−1.19508	+	0.689978i	−0.0653917	+	0.0377539i
$335$	0.226400	−	0.392137i	0.0123696	−	0.0214247i
$336$	5.23103	+	1.20566i	0.285376	+	0.0657739i
$337$	−16.2629	−	28.1681i	−0.885894	−	1.53441i	−0.844685	−	0.535263i	$-0.820212\pi$
$337$	−16.2629	−	28.1681i	−0.885894	−	1.53441i	−0.0412090	−	0.999151i	$-0.513121\pi$
$338$	5.12730	+	2.96025i	0.278888	+	0.161016i
$339$	4.49610	+	11.7234i	0.244195	+	0.636728i
$340$	4.19453	+	7.26514i	0.227480	+	0.394007i
$341$	2.54825	+	4.41370i	0.137995	+	0.239015i
$342$	−1.79205	−	8.45621i	−0.0969029	−	0.457259i
$343$	−3.81408	+	18.1233i	−0.205941	+	0.978564i
$344$	16.3292	+	9.42767i	0.880412	+	0.508306i
$345$	5.09555	+	13.2864i	0.274335	+	0.715318i
$346$		−	10.9347i		−	0.587851i
$347$		−	3.18703i		−	0.171089i	−0.996334	−	0.0855444i	$-0.972737\pi$
$347$		−	3.18703i		−	0.171089i	0.996334	−	0.0855444i	$-0.0272630\pi$
$348$	−15.8741	+	19.5907i	−0.850942	+	1.05017i
$349$	6.48224	+	3.74252i	0.346986	+	0.200333i	0.663357	−	0.748303i	$-0.269131\pi$
$349$	6.48224	+	3.74252i	0.346986	+	0.200333i	−0.316371	+	0.948636i	$0.602464\pi$
$350$	−2.42270	−	4.95883i	−0.129499	−	0.265060i
$351$	0.582750	+	11.3170i	0.0311049	+	0.604058i
$352$	5.26287	+	9.11556i	0.280512	+	0.485861i
$353$	−5.69040	−	9.85606i	−0.302869	−	0.524585i	0.673915	−	0.738809i	$-0.264611\pi$
$353$	−5.69040	−	9.85606i	−0.302869	−	0.524585i	−0.976785	+	0.214223i	$0.931278\pi$
$354$	−12.0286	−	1.90890i	−0.639315	−	0.101457i
$355$	2.44370	+	1.41087i	0.129698	+	0.0748814i
$356$	−7.85159	−	13.5994i	−0.416134	−	0.720764i
$357$	12.1983	−	13.0907i	0.645602	−	0.692833i
$358$	0.124142	−	0.215020i	0.00656109	−	0.0113641i
$359$	4.77569	−	2.75725i	0.252051	−	0.145522i	−0.368652	−	0.929568i	$-0.620181\pi$
$359$	4.77569	−	2.75725i	0.252051	−	0.145522i	0.620703	+	0.784046i	$0.286847\pi$
$360$	−7.26616	−	8.07976i	−0.382960	−	0.425841i
$361$	−1.45164	+	2.51432i	−0.0764022	+	0.132332i
$362$	−2.35315			−0.123679
$363$	−10.4401	−	8.45949i	−0.547963	−	0.444008i
$364$	3.75939	+	7.69477i	0.197045	+	0.403315i
$365$	−3.51533	+	2.02958i	−0.184001	+	0.106233i
$366$	0.459207	−	2.89362i	0.0240031	−	0.151252i
$367$	−18.2753	+	10.5512i	−0.953962	+	0.550770i	−0.894309	−	0.447449i	$-0.852333\pi$
$367$	−18.2753	+	10.5512i	−0.953962	+	0.550770i	−0.0596526	+	0.998219i	$0.518999\pi$
$368$	−5.75785	−	3.32430i	−0.300149	−	0.173291i
$369$	−7.34669	−	34.6671i	−0.382454	−	1.80470i
$370$		−	0.856131i		−	0.0445081i
$371$	1.70105	−	2.52557i	0.0883143	−	0.131121i
$372$	7.18665	+	1.14049i	0.372611	+	0.0591318i
$373$	−7.68498	+	13.3108i	−0.397913	+	0.689206i	−0.993468	−	0.114109i	$-0.963599\pi$
$373$	−7.68498	+	13.3108i	−0.397913	+	0.689206i	0.595555	+	0.803314i	$0.296932\pi$
$374$	5.04906			0.261080
$375$	3.10627	−	19.5737i	0.160407	−	1.01078i
$376$		−	5.85127i		−	0.301756i
$377$	−21.3903			−1.10166
$378$	−5.08709	+	8.46172i	−0.261652	+	0.435224i
$379$	−32.3630			−1.66238			−0.831188	−	0.555991i	$-0.812339\pi$
$379$	−32.3630			−1.66238			−0.831188	+	0.555991i	$0.812339\pi$
$380$		−	8.61995i		−	0.442194i
$381$	0.239259	−	1.50765i	0.0122576	−	0.0772394i
$382$	5.30811			0.271587
$383$	9.91730	−	17.1773i	0.506750	−	0.877718i	−0.493219	−	0.869905i	$-0.664180\pi$
$383$	9.91730	−	17.1773i	0.506750	−	0.877718i	0.999969	−	0.00781236i	$-0.00248678\pi$
$384$	17.7208	+	2.81222i	0.904310	+	0.143510i
$385$	−6.87941	−	0.476414i	−0.350607	−	0.0242803i
$386$		−	9.35663i		−	0.476240i
$387$	16.8087	−	15.1161i	0.854434	−	0.768395i
$388$	−19.9366	−	11.5104i	−1.01213	−	0.584352i
$389$	4.41918	−	2.55141i	0.224061	−	0.129362i	−0.383768	−	0.923429i	$-0.625374\pi$
$389$	4.41918	−	2.55141i	0.224061	−	0.129362i	0.607829	+	0.794068i	$0.292040\pi$
$390$	0.615474	−	3.87832i	0.0311657	−	0.196386i
$391$	−19.1920	+	11.0805i	−0.970581	+	0.560365i
$392$	−2.41444	+	17.3486i	−0.121948	+	0.876238i
$393$	−4.00274	−	3.24337i	−0.201912	−	0.163607i
$394$	2.89446			0.145821
$395$	−8.99772	+	15.5845i	−0.452724	+	0.784141i
$396$	7.84319	−	1.66214i	0.394135	−	0.0835256i
$397$	−11.5288	+	6.65615i	−0.578613	+	0.334062i	−0.760582	−	0.649242i	$-0.775086\pi$
$397$	−11.5288	+	6.65615i	−0.578613	+	0.334062i	0.181969	+	0.983304i	$0.441753\pi$
$398$	5.89177	−	10.2048i	0.295328	−	0.511522i
$399$	−17.5803	+	5.38189i	−0.880115	+	0.269432i
$400$	1.70127	+	2.94669i	0.0850636	+	0.147334i
$401$	14.1750	+	8.18392i	0.707864	+	0.408685i	0.810270	−	0.586057i	$-0.199321\pi$
$401$	14.1750	+	8.18392i	0.707864	+	0.408685i	−0.102406	+	0.994743i	$0.532654\pi$
$402$	−0.384289	−	0.0609852i	−0.0191666	−	0.00304167i
$403$	3.08645	+	5.34589i	0.153747	+	0.266298i
$404$	−2.92853	−	5.07237i	−0.145700	−	0.252360i
$405$	−11.9080	+	5.28446i	−0.591716	+	0.262587i
$406$	−15.4574	−	10.4110i	−0.767137	−	0.516692i
$407$	1.28416	+	0.741412i	0.0636536	+	0.0367504i
$408$	10.6538	−	13.1482i	0.527443	−	0.650933i
$409$			4.33710i			0.214456i	0.994234	+	0.107228i	$0.0341975\pi$
$409$			4.33710i			0.214456i	−0.994234	+	0.107228i	$0.965803\pi$
$410$			12.2799i			0.606460i
$411$	−7.37975	−	19.2424i	−0.364016	−	0.949157i
$412$	5.34107	+	3.08367i	0.263135	+	0.151921i
$413$	−1.78968	+	25.8429i	−0.0880644	+	1.27165i
$414$	9.09223	−	8.17667i	0.446859	−	0.401862i
$415$	5.22443	+	9.04898i	0.256457	+	0.444197i
$416$	6.37441	+	11.0408i	0.312531	+	0.541320i
$417$	7.45837	+	19.4474i	0.365238	+	0.952343i
$418$	−4.49296	−	2.59401i	−0.219758	−	0.126877i
$419$	9.41294	+	16.3037i	0.459852	+	0.796487i	0.998953	−	0.0457540i	$-0.0145690\pi$
$419$	9.41294	+	16.3037i	0.459852	+	0.796487i	−0.539100	+	0.842241i	$0.681236\pi$
$420$	−6.71210	+	7.20314i	−0.327517	+	0.351477i
$421$	0.913453	−	1.58215i	0.0445190	−	0.0771092i	−0.842907	−	0.538059i	$-0.819158\pi$
$421$	0.913453	−	1.58215i	0.0445190	−	0.0771092i	0.887426	+	0.460950i	$0.152491\pi$
$422$	−7.47370	+	4.31494i	−0.363814	+	0.210048i
$423$	−6.67051	−	2.17186i	−0.324331	−	0.105600i
$424$	1.43993	−	2.49404i	0.0699294	−	0.121121i
$425$	11.3413			0.550135
$426$	0.380046	−	2.39480i	0.0184133	−	0.116029i
$427$	−6.21680	−	0.430527i	−0.300852	−	0.0208347i
$428$	−7.28897	+	4.20829i	−0.352326	+	0.203415i
$429$	5.28433	+	4.28182i	0.255130	+	0.206728i
$430$	−6.78407	+	3.91679i	−0.327157	+	0.188884i
$431$	12.4526	+	7.18954i	0.599823	+	0.346308i	0.768972	−	0.639283i	$-0.220769\pi$
$431$	12.4526	+	7.18954i	0.599823	+	0.346308i	−0.169149	+	0.985590i	$0.554102\pi$
$432$	2.76836	−	5.42098i	0.133193	−	0.260817i
$433$		−	2.22130i		−	0.106749i	−0.998575	−	0.0533745i	$-0.983002\pi$
$433$		−	2.22130i		−	0.106749i	0.998575	−	0.0533745i	$-0.0169977\pi$
$434$	−0.371563	+	5.36536i	−0.0178356	+	0.257546i
$435$	−8.80582	−	22.9608i	−0.422207	−	1.10089i
$436$	8.90417	−	15.4225i	0.426432	−	0.738602i
$437$	22.7710			1.08928
$438$	2.71009	+	2.19595i	0.129493	+	0.104927i
$439$		−	10.0448i		−	0.479413i	−0.970845	−	0.239706i	$-0.922949\pi$
$439$		−	10.0448i		−	0.479413i	0.970845	−	0.239706i	$-0.0770512\pi$
$440$	−6.52190			−0.310919
$441$	18.8814	+	9.19193i	0.899116	+	0.437711i
$442$	6.11544			0.290882
$443$			13.8934i			0.660097i	0.943964	+	0.330049i	$0.107065\pi$
$443$			13.8934i			0.660097i	−0.943964	+	0.330049i	$0.892935\pi$
$444$	1.97673	−	0.758107i	0.0938116	−	0.0359782i
$445$	15.3150			0.726002
$446$	9.45084	−	16.3693i	0.447510	−	0.775110i
$447$	−7.71913	+	9.52640i	−0.365102	+	0.450583i
$448$	−0.339142	+	4.89720i	−0.0160230	+	0.231371i
$449$			10.5630i			0.498498i	0.968439	+	0.249249i	$0.0801837\pi$
$449$			10.5630i			0.498498i	−0.968439	+	0.249249i	$0.919816\pi$
$450$	−6.12201	+	1.29738i	−0.288594	+	0.0611592i
$451$	−18.4194	−	10.6344i	−0.867334	−	0.500755i
$452$	9.31804	−	5.37977i	0.438284	−	0.253043i
$453$	25.1989	−	9.66417i	1.18395	−	0.454063i
$454$	6.72217	−	3.88105i	0.315487	−	0.182147i
$455$	−8.33237	−	0.577035i	−0.390628	−	0.0270518i
$456$	−16.2355	+	6.22655i	−0.760295	+	0.291585i
$457$	5.11307			0.239179			0.119590	−	0.992823i	$-0.461842\pi$
$457$	5.11307			0.239179			0.119590	+	0.992823i	$0.461842\pi$
$458$	−3.48200	+	6.03100i	−0.162703	+	0.281810i
$459$	−11.0346	−	17.0258i	−0.515051	−	0.794696i
$460$	10.5604	−	6.09704i	0.492380	−	0.284276i
$461$	4.16691	−	7.21730i	0.194072	−	0.336143i	−0.752524	−	0.658565i	$-0.771164\pi$
$461$	4.16691	−	7.21730i	0.194072	−	0.336143i	0.946596	+	0.322422i	$0.104497\pi$
$462$	1.73460	+	5.66618i	0.0807009	+	0.263615i
$463$	10.0143	+	17.3452i	0.465403	+	0.806102i	0.999220	−	0.0394986i	$-0.0125761\pi$
$463$	10.0143	+	17.3452i	0.465403	+	0.806102i	−0.533817	+	0.845600i	$0.679243\pi$
$464$	9.95036	+	5.74484i	0.461934	+	0.266698i
$465$	−4.46779	+	5.51383i	−0.207189	+	0.255698i
$466$	−0.799817	−	1.38532i	−0.0370508	−	0.0641739i
$467$	10.3896	+	17.9953i	0.480773	+	0.832723i	0.999757	−	0.0220611i	$-0.00702284\pi$
$467$	10.3896	+	17.9953i	0.480773	+	0.832723i	−0.518984	+	0.854784i	$0.673690\pi$
$468$	9.49971	−	2.01319i	0.439124	−	0.0930597i
$469$	−0.0571765	+	0.825627i	−0.00264016	+	0.0381239i
$470$	2.10526	+	1.21547i	0.0971085	+	0.0560656i
$471$	−3.56888	−	0.566368i	−0.164445	−	0.0260969i
$472$			24.4999i			1.12770i
$473$		−	13.5678i		−	0.623848i
$474$	15.2726	+	2.42371i	0.701496	+	0.111325i
$475$	−10.0922	−	5.82674i	−0.463062	−	0.267349i
$476$	−12.7174	−	8.56561i	−0.582903	−	0.392604i
$477$	−2.30876	−	2.56727i	−0.105711	−	0.117547i
$478$	6.62156	+	11.4689i	0.302863	+	0.524574i
$479$	−16.0308	−	27.7662i	−0.732468	−	1.26867i	−0.955825	−	0.293935i	$-0.905035\pi$
$479$	−16.0308	−	27.7662i	−0.732468	−	1.26867i	0.223357	−	0.974737i	$-0.428298\pi$
$480$	−9.22727	+	11.3876i	−0.421165	+	0.519773i
$481$	1.55538	+	0.898002i	0.0709194	+	0.0409454i
$482$	−2.32392	−	4.02515i	−0.105852	−	0.183340i
$483$	−19.0282	−	17.7311i	−0.865815	−	0.806791i
$484$	−5.75734	+	9.97200i	−0.261697	+	0.453273i
$485$	19.4438	−	11.2259i	0.882897	−	0.509741i
$486$	7.90410	+	7.92816i	0.358537	+	0.359629i
$487$	11.8375	−	20.5032i	0.536408	−	0.929087i	−0.462685	−	0.886523i	$-0.653114\pi$
$487$	11.8375	−	20.5032i	0.536408	−	0.929087i	0.999094	−	0.0425641i	$-0.0135527\pi$
$488$	−5.89373			−0.266796
$489$	18.0797	−	6.93385i	0.817594	−	0.313560i
$490$	−5.74042	−	4.47251i	−0.259326	−	0.202047i
$491$	15.4664	−	8.92951i	0.697987	−	0.402983i	−0.108610	−	0.994084i	$-0.534640\pi$
$491$	15.4664	−	8.92951i	0.697987	−	0.402983i	0.806597	+	0.591101i	$0.201307\pi$
$492$	−28.3532	+	10.8739i	−1.27826	+	0.490233i
$493$	33.1664	−	19.1486i	1.49374	−	0.862411i
$494$	−5.44189	−	3.14188i	−0.244842	−	0.141360i
$495$	−2.42079	+	7.43503i	−0.108806	+	0.334180i
$496$		−	3.31574i		−	0.148881i
$497$	−5.14511	−	0.356310i	−0.230790	−	0.0159827i
$498$	5.65271	−	6.97617i	0.253304	−	0.312610i
$499$	11.5602	−	20.0229i	0.517506	−	0.896346i	−0.482288	−	0.876013i	$-0.660194\pi$
$499$	11.5602	−	20.0229i	0.517506	−	0.896346i	0.999793	−	0.0203330i	$-0.00647265\pi$
$500$	−16.9831			−0.759506
$501$	3.10744	−	1.19175i	0.138830	−	0.0532436i
$502$			0.299245i			0.0133560i
$503$	13.9995			0.624206			0.312103	−	0.950048i	$-0.398967\pi$
$503$	13.9995			0.624206			0.312103	+	0.950048i	$0.398967\pi$
$504$	18.4154	+	7.43893i	0.820285	+	0.331356i
$505$	5.71228			0.254193
$506$		−	7.33915i		−	0.326265i
$507$	−11.0940	−	8.98935i	−0.492703	−	0.399231i
$508$	−1.30811			−0.0580381
$509$	−6.79171	+	11.7636i	−0.301037	+	0.521411i	−0.976371	−	0.216100i	$-0.930666\pi$
$509$	−6.79171	+	11.7636i	−0.301037	+	0.521411i	0.675334	+	0.737512i	$0.263999\pi$
$510$	2.51757	+	6.56445i	0.111480	+	0.290679i
$511$	4.14458	−	6.15350i	0.183345	−	0.272215i
$512$		−	12.7104i		−	0.561727i
$513$	1.07208	+	20.8198i	0.0473333	+	0.919214i
$514$	13.1408	+	7.58684i	0.579616	+	0.334641i
$515$	−5.20904	+	3.00744i	−0.229538	+	0.132524i
$516$	−15.0508	−	12.1955i	−0.662577	−	0.536878i
$517$	−3.64633	+	2.10521i	−0.160365	+	0.0925870i
$518$	0.686903	+	1.40596i	0.0301808	+	0.0617745i
$519$	−4.13339	+	26.0459i	−0.181435	+	1.14329i
$520$	−7.89935			−0.346409
$521$	−15.9477	+	27.6222i	−0.698682	+	1.21015i	0.270242	+	0.962792i	$0.412896\pi$
$521$	−15.9477	+	27.6222i	−0.698682	+	1.21015i	−0.968924	+	0.247360i	$0.920437\pi$
$522$	−15.7126	+	14.1304i	−0.687723	+	0.618472i
$523$	−1.20531	+	0.695886i	−0.0527046	+	0.0304290i	−0.526121	−	0.850410i	$-0.676354\pi$
$523$	−1.20531	+	0.695886i	−0.0527046	+	0.0304290i	0.473416	+	0.880839i	$0.343021\pi$
$524$	−2.20737	+	3.82327i	−0.0964293	+	0.167020i
$525$	3.89631	+	12.7275i	0.170049	+	0.555475i
$526$	7.98803	+	13.8357i	0.348295	+	0.603264i
$527$	−9.57131	−	5.52600i	−0.416933	−	0.240716i
$528$	−1.30819	−	3.41105i	−0.0569316	−	0.148447i
$529$	4.60628	+	7.97832i	0.200273	+	0.346883i
$530$	0.598230	+	1.03616i	0.0259854	+	0.0450081i
$531$	27.9301	+	9.09384i	1.21207	+	0.394639i
$532$	6.91608	+	14.1559i	0.299850	+	0.613738i
$533$	−22.3096	−	12.8805i	−0.966337	−	0.557915i
$534$	−4.71254	−	12.2878i	−0.203932	−	0.531744i
$535$		−	8.20854i		−	0.354886i
$536$			0.782720i			0.0338084i
$537$	−0.376979	+	0.465242i	−0.0162679	+	0.0200767i
$538$	−18.0570	−	10.4252i	−0.778493	−	0.449463i
$539$	11.6798	−	4.73720i	0.503085	−	0.204046i
$540$	6.07178	+	9.36842i	0.261288	+	0.403153i
$541$	12.9736	+	22.4709i	0.557779	+	0.966101i	0.997682	+	0.0680555i	$0.0216795\pi$
$541$	12.9736	+	22.4709i	0.557779	+	0.966101i	−0.439903	+	0.898045i	$0.644987\pi$
$542$	−8.63158	−	14.9503i	−0.370758	−	0.642172i
$543$	5.60511	+	0.889509i	0.240538	+	0.0381725i
$544$	−19.7675	−	11.4128i	−0.847525	−	0.489319i
$545$	8.68407	+	15.0413i	0.371985	+	0.644296i
$546$	2.10096	+	6.86290i	0.0899126	+	0.293705i
$547$	−9.32438	+	16.1503i	−0.398682	+	0.690537i	−0.993564	−	0.113276i	$-0.963865\pi$
$547$	−9.32438	+	16.1503i	−0.398682	+	0.690537i	0.594882	+	0.803813i	$0.297199\pi$
$548$	−15.2943	+	8.83017i	−0.653340	+	0.377206i
$549$	−2.18762	+	6.71891i	−0.0933655	+	0.286756i
$550$	−1.87798	+	3.25275i	−0.0800772	+	0.138698i
$551$	−39.3514			−1.67642
$552$	−19.1118	−	15.4861i	−0.813453	−	0.659131i
$553$	2.27234	−	32.8125i	0.0966296	−	1.39533i
$554$	−5.01594	+	2.89595i	−0.213107	+	0.123037i
$555$	−0.323624	+	2.03927i	−0.0137371	+	0.0865621i
$556$	15.4572	−	8.92424i	0.655533	−	0.378472i
$557$	−36.3567	−	20.9905i	−1.54048	−	0.889398i	−0.998808	−	0.0488092i	$-0.984457\pi$
$557$	−36.3567	−	20.9905i	−1.54048	−	0.889398i	−0.541674	−	0.840589i	$-0.682209\pi$
$558$	5.79870	+	1.88801i	0.245479	+	0.0799259i
$559$		−	16.4334i		−	0.695058i
$560$	3.72109	+	2.50627i	0.157245	+	0.105909i
$561$	−12.0266	−	1.90858i	−0.507765	−	0.0805804i
$562$	−5.01193	+	8.68092i	−0.211416	+	0.366183i
$563$	38.6011			1.62684			0.813422	−	0.581675i	$-0.197602\pi$
$563$	38.6011			1.62684			0.813422	+	0.581675i	$0.197602\pi$
$564$	−0.942207	+	5.93718i	−0.0396741	+	0.250000i
$565$			10.4936i			0.441468i
$566$	11.1585			0.469028
$567$	15.3158	−	18.2325i	0.643205	−	0.765694i
$568$	−4.87773			−0.204665
$569$		−	35.1560i		−	1.47382i	−0.675993	−	0.736908i	$-0.736285\pi$
$569$		−	35.1560i		−	1.47382i	0.675993	−	0.736908i	$-0.263715\pi$
$570$	1.13228	−	7.13488i	0.0474259	−	0.298847i
$571$	−35.3532			−1.47948			−0.739742	−	0.672891i	$-0.765052\pi$
$571$	−35.3532			−1.47948			−0.739742	+	0.672891i	$0.765052\pi$
$572$	2.91411	−	5.04739i	0.121845	−	0.211042i
$573$	−12.6437	−	2.00651i	−0.528198	−	0.0838230i
$574$	−9.85257	−	20.1664i	−0.411238	−	0.841729i
$575$		−	16.4854i		−	0.687489i
$576$	5.29273	+	1.72327i	0.220530	+	0.0718029i
$577$	23.2557	+	13.4267i	0.968147	+	0.558960i	0.898671	−	0.438624i	$-0.144534\pi$
$577$	23.2557	+	13.4267i	0.968147	+	0.558960i	0.0694761	+	0.997584i	$0.477867\pi$
$578$	1.09095	−	0.629858i	0.0453774	−	0.0261986i
$579$	−3.53688	+	22.2871i	−0.146988	+	0.926221i
$580$	−18.2498	+	10.5365i	−0.757781	+	0.437505i
$581$	−15.8400	−	10.6688i	−0.657155	−	0.442615i
$582$	−14.9899	−	12.1461i	−0.621352	−	0.503473i
$583$	−2.07228			−0.0858249
$584$	3.50837	−	6.07667i	0.145177	−	0.251454i
$585$	−2.93207	+	9.00534i	−0.121226	+	0.372325i
$586$	−8.38031	+	4.83837i	−0.346187	+	0.199871i
$587$	−15.6788	+	27.1565i	−0.647134	+	1.12087i	0.336671	+	0.941622i	$0.390699\pi$
$587$	−15.6788	+	27.1565i	−0.647134	+	1.12087i	−0.983804	+	0.179246i	$0.942634\pi$
$588$	5.24347	−	17.2146i	0.216237	−	0.709916i
$589$	5.67809	+	9.83474i	0.233962	+	0.405234i
$590$	−8.81496	−	5.08932i	−0.362906	−	0.209524i
$591$	−6.89450	−	1.09413i	−0.283602	−	0.0450065i
$592$	−0.482357	−	0.835467i	−0.0198248	−	0.0343375i
$593$	4.56131	+	7.90043i	0.187311	+	0.324432i	0.944353	−	0.328935i	$-0.106690\pi$
$593$	4.56131	+	7.90043i	0.187311	+	0.324432i	−0.757042	+	0.653366i	$0.773356\pi$
$594$	6.71027	−	0.345533i	0.275326	−	0.0141774i
$595$	13.4362	−	6.56445i	0.550831	−	0.269116i
$596$	9.09927	+	5.25347i	0.372721	+	0.215190i
$597$	−17.8915	+	22.0804i	−0.732248	+	0.903690i
$598$		−	8.88921i		−	0.363507i
$599$		−	1.28537i		−	0.0525186i	−0.999655	−	0.0262593i	$-0.991640\pi$
$599$		−	1.28537i		−	0.0525186i	0.999655	−	0.0262593i	$-0.00835956\pi$
$600$	4.50781	+	11.7539i	0.184030	+	0.479852i
$601$	16.7126	+	9.64903i	0.681721	+	0.393592i	0.800503	−	0.599328i	$-0.204566\pi$
$601$	16.7126	+	9.64903i	0.681721	+	0.393592i	−0.118782	+	0.992920i	$0.537899\pi$
$602$	7.99843	−	11.8754i	0.325992	−	0.484003i
$603$	0.892309	+	0.290529i	0.0363376	+	0.0118312i
$604$	−11.5636	−	20.0287i	−0.470515	−	0.814956i
$605$	−5.61502	−	9.72551i	−0.228283	−	0.395398i
$606$	−1.75771	−	4.58316i	−0.0714022	−	0.186178i
$607$	33.7319	+	19.4751i	1.36913	+	0.790470i	0.990817	−	0.135206i	$-0.0431697\pi$
$607$	33.7319	+	19.4751i	1.36913	+	0.790470i	0.378317	+	0.925676i	$0.376503\pi$
$608$	11.7269	+	20.3116i	0.475589	+	0.823744i
$609$	32.8834	+	30.6417i	1.33250	+	1.24166i
$610$	1.22429	−	2.12054i	0.0495702	−	0.0858581i
$611$	−4.41645	+	2.54984i	−0.178670	+	0.103155i
$612$	−12.9274	+	11.6257i	−0.522561	+	0.469941i
$613$	−3.65018	+	6.32229i	−0.147429	+	0.255355i	−0.930277	−	0.366859i	$-0.880433\pi$
$613$	−3.65018	+	6.32229i	−0.147429	+	0.255355i	0.782847	+	0.622214i	$0.213767\pi$
$614$	6.19628			0.250061
$615$	4.64189	−	29.2502i	0.187179	−	1.17948i
$616$	10.7105	−	5.23274i	0.431536	−	0.210833i
$617$	38.3641	−	22.1495i	1.54448	−	0.891706i	0.545932	−	0.837829i	$-0.316176\pi$
$617$	38.3641	−	22.1495i	1.54448	−	0.891706i	0.998548	−	0.0538763i	$-0.0171577\pi$
$618$	4.01583	+	3.25398i	0.161541	+	0.130894i
$619$	−0.408449	+	0.235818i	−0.0164169	+	0.00947832i	−0.508186	−	0.861247i	$-0.669684\pi$
$619$	−0.408449	+	0.235818i	−0.0164169	+	0.00947832i	0.491769	+	0.870726i	$0.336350\pi$
$620$	5.26660	+	3.04068i	0.211512	+	0.122116i
$621$	−24.7482	+	16.0396i	−0.993110	+	0.643646i
$622$			11.6659i			0.467760i
$623$	−25.1508	+	12.2878i	−1.00764	+	0.492299i
$624$	−1.58448	−	4.13148i	−0.0634302	−	0.165391i
$625$	1.02013	−	1.76692i	0.0408052	−	0.0706768i
$626$	−4.86696			−0.194523
$627$	9.72149	+	7.87720i	0.388239	+	0.314585i
$628$			3.09653i			0.123565i
$629$	−3.21558			−0.128213
$630$	−6.50189	+	5.08049i	−0.259041	+	0.202412i
$631$	10.2247			0.407038			0.203519	−	0.979071i	$-0.434762\pi$
$631$	10.2247			0.407038			0.203519	+	0.979071i	$0.434762\pi$
$632$		−	31.1073i		−	1.23738i
$633$	19.4331	−	7.45290i	0.772398	−	0.296226i
$634$	15.7764			0.626560
$635$	0.637888	−	1.10485i	0.0253138	−	0.0438448i
$636$	−1.86268	+	2.29879i	−0.0738601	+	0.0911529i
$637$	14.1466	−	5.73772i	0.560510	−	0.227337i
$638$			12.6831i			0.502127i
$639$	−1.81051	+	5.56066i	−0.0716226	+	0.219976i
$640$	12.9863	+	7.49767i	0.513330	+	0.296371i
$641$	43.4584	−	25.0907i	1.71651	−	0.991025i	0.791414	−	0.611280i	$-0.209345\pi$
$641$	43.4584	−	25.0907i	1.71651	−	0.991025i	0.925091	−	0.379745i	$-0.123988\pi$
$642$	−6.58599	+	2.52583i	−0.259928	+	0.0996864i
$643$	−9.18633	+	5.30373i	−0.362274	+	0.209159i	−0.670078	−	0.742291i	$-0.733739\pi$
$643$	−9.18633	+	5.30373i	−0.362274	+	0.209159i	0.307804	+	0.951450i	$0.400406\pi$
$644$	−12.4507	+	18.4857i	−0.490626	+	0.728438i
$645$	17.6400	−	6.76520i	0.694573	−	0.266379i
$646$	11.2505			0.442644
$647$	−14.9203	+	25.8427i	−0.586577	+	1.01598i	0.408100	+	0.912937i	$0.366191\pi$
$647$	−14.9203	+	25.8427i	−0.586577	+	1.01598i	−0.994677	+	0.103044i	$0.967142\pi$
$648$	13.2593	−	18.2032i	0.520874	−	0.715091i
$649$	15.2676	−	8.81474i	0.599305	−	0.346009i
$650$	−2.27461	+	3.93975i	−0.0892177	+	0.154530i
$651$	2.91320	−	12.6396i	0.114177	−	0.495386i
$652$	−8.29664	−	14.3702i	−0.324921	−	0.562780i
$653$	−30.5327	−	17.6281i	−1.19484	−	0.689839i	−0.235437	−	0.971890i	$-0.575652\pi$
$653$	−30.5327	−	17.6281i	−1.19484	−	0.689839i	−0.959400	+	0.282050i	$0.908986\pi$
$654$	9.39595	−	11.5958i	0.367411	−	0.453433i
$655$	−2.15280	−	3.72877i	−0.0841170	−	0.145695i
$656$	6.91868	+	11.9835i	0.270129	+	0.467877i
$657$	−5.62524	−	6.25510i	−0.219461	−	0.244035i
$658$	−4.43254	−	0.306963i	−0.172798	−	0.0119667i
$659$	29.3751	+	16.9597i	1.14429	+	0.660656i	0.947489	−	0.319787i	$-0.103611\pi$
$659$	29.3751	+	16.9597i	1.14429	+	0.660656i	0.196801	+	0.980443i	$0.436945\pi$
$660$	6.61765	+	1.05020i	0.257592	+	0.0408788i
$661$		−	15.7674i		−	0.613281i	−0.951825	−	0.306641i	$-0.900795\pi$
$661$		−	15.7674i		−	0.613281i	0.951825	−	0.306641i	$-0.0992050\pi$
$662$			10.4878i			0.407620i
$663$	−14.5667	−	2.31168i	−0.565725	−	0.0897783i
$664$	−15.6423	−	9.03106i	−0.607037	−	0.350473i
$665$	−15.3289	−	1.06156i	−0.594430	−	0.0411656i
$666$	1.73576	−	0.367843i	0.0672592	−	0.0142536i
$667$	−27.8339	−	48.2097i	−1.07773	−	1.86669i
$668$	−1.42598	−	2.46987i	−0.0551728	−	0.0955621i
$669$	−28.6992	+	35.4186i	−1.10958	+	1.36936i
$670$	−0.281619	−	0.162593i	−0.0108799	−	0.00628152i
$671$	2.12048	+	3.67279i	0.0818604	+	0.141786i
$672$	6.01659	−	26.1045i	0.232095	−	1.00700i
$673$	−7.35627	+	12.7414i	−0.283563	+	0.491146i	−0.972260	−	0.233904i	$-0.924850\pi$
$673$	−7.35627	+	12.7414i	−0.283563	+	0.491146i	0.688696	+	0.725050i	$0.258183\pi$
$674$	−20.2294	+	11.6794i	−0.779207	+	0.449875i
$675$	15.0728	−	0.776146i	0.580152	−	0.0298739i
$676$	−6.11795	+	10.5966i	−0.235306	+	0.407562i
$677$	3.98434			0.153131			0.0765654	−	0.997065i	$-0.475605\pi$
$677$	3.98434			0.153131			0.0765654	+	0.997065i	$0.475605\pi$
$678$	8.41936	−	3.22895i	0.323344	−	0.124007i
$679$	−22.9243	+	34.0359i	−0.879753	+	1.30618i
$680$	12.2482	−	7.07152i	0.469698	−	0.271181i
$681$	−17.4790	+	6.70347i	−0.669797	+	0.256877i
$682$	3.16977	−	1.83007i	0.121377	−	0.0700769i
$683$	19.2812	+	11.1320i	0.737774	+	0.425954i	0.821259	−	0.570555i	$-0.193272\pi$
$683$	19.2812	+	11.1320i	0.737774	+	0.425954i	−0.0834856	+	0.996509i	$0.526605\pi$
$684$	17.4765	−	3.70363i	0.668229	−	0.141612i
$685$		−	17.2238i		−	0.658088i
$686$	13.0155	+	2.73915i	0.496935	+	0.104581i
$687$	10.5737	−	13.0494i	0.403414	−	0.497865i
$688$	−4.41356	+	7.64450i	−0.168265	+	0.291444i
$689$	−2.50995			−0.0956215
$690$	9.54188	−	3.65946i	0.363253	−	0.139313i
$691$			48.3823i			1.84055i	0.391271	+	0.920275i	$0.372035\pi$
$691$			48.3823i			1.84055i	−0.391271	+	0.920275i	$0.627965\pi$
$692$	22.5987			0.859073
$693$	−1.98989	−	14.1523i	−0.0755897	−	0.537602i
$694$	−2.28882			−0.0868824
$695$			17.4073i			0.660297i
$696$	33.0278	+	26.7620i	1.25192	+	1.01441i
$697$	46.1225			1.74701
$698$	2.68775	−	4.65533i	0.101733	−	0.176207i
$699$	1.38147	+	3.60212i	0.0522520	+	0.136245i
$700$	10.2484	−	5.00701i	0.387354	−	0.189247i
$701$		−	23.3129i		−	0.880514i	−0.897872	−	0.440257i	$-0.854887\pi$
$701$		−	23.3129i		−	0.880514i	0.897872	−	0.440257i	$-0.145113\pi$
$702$	8.12751	−	0.418511i	0.306753	−	0.0157957i
$703$	2.86142	+	1.65204i	0.107920	+	0.0623079i
$704$	2.89319	−	1.67038i	0.109041	−	0.0629549i
$705$	−4.55519	−	3.69101i	−0.171558	−	0.139012i
$706$	−7.07830	+	4.08666i	−0.266395	+	0.153803i
$707$	−9.38088	+	4.58316i	−0.352804	+	0.172367i
$708$	3.94512	−	24.8596i	0.148267	−	0.934281i
$709$	17.6777			0.663899			0.331949	−	0.943297i	$-0.392294\pi$
$709$	17.6777			0.663899			0.331949	+	0.943297i	$0.392294\pi$
$710$	1.01324	−	1.75499i	0.0380263	−	0.0658635i
$711$	−35.4626	−	11.5464i	−1.32995	−	0.433022i
$712$	−22.9270	+	13.2369i	−0.859227	+	0.496075i
$713$	−8.03242	+	13.9126i	−0.300817	+	0.521030i
$714$	−9.40130	−	8.76040i	−0.351835	−	0.327850i
$715$	2.84208	+	4.92263i	0.106288	+	0.184096i
$716$	0.444382	+	0.256564i	0.0166073	+	0.00958824i
$717$	−11.4370	−	29.8214i	−0.427121	−	1.11370i
$718$	−1.98016	−	3.42974i	−0.0738990	−	0.127997i
$719$	−15.2102	−	26.3449i	−0.567246	−	0.982498i	−0.996837	−	0.0794749i	$-0.974676\pi$
$719$	−15.2102	−	26.3449i	−0.567246	−	0.982498i	0.429591	−	0.903024i	$-0.358658\pi$
$720$	3.78253	−	3.40164i	0.140967	−	0.126772i
$721$	6.14147	−	9.11830i	0.228720	−	0.339583i
$722$	1.80570	+	1.04252i	0.0672011	+	0.0387986i
$723$	4.01395	+	10.4662i	0.149280	+	0.389242i
$724$		−	4.86326i		−	0.180742i
$725$			28.4890i			1.05806i
$726$	−6.07532	+	7.49773i	−0.225476	+	0.278267i
$727$	−38.5219	−	22.2406i	−1.42870	−	0.824859i	−0.431680	−	0.902027i	$-0.642079\pi$
$727$	−38.5219	−	22.2406i	−1.42870	−	0.824859i	−0.997018	+	0.0771674i	$0.975412\pi$
$728$	12.9725	−	6.33792i	0.480795	−	0.234899i
$729$	−15.8303	−	21.8724i	−0.586308	−	0.810088i
$730$	1.45757	+	2.52459i	0.0539472	+	0.0934393i
$731$	14.7112	+	25.4806i	0.544114	+	0.942433i
$732$	5.98026	+	0.949044i	0.221037	+	0.0350777i
$733$	−39.2270	−	22.6477i	−1.44888	−	0.836512i	−0.450466	−	0.892794i	$-0.648742\pi$
$733$	−39.2270	−	22.6477i	−1.44888	−	0.836512i	−0.998415	+	0.0562818i	$0.982075\pi$
$734$	7.57755	+	13.1247i	0.279692	+	0.484442i
$735$	11.9828	+	12.8233i	0.441992	+	0.472993i
$736$	−16.5893	+	28.7335i	−0.611489	+	1.05913i
$737$	0.487767	−	0.281612i	0.0179671	−	0.0103733i
$738$	−24.8968	+	5.27615i	−0.916463	+	0.194218i
$739$	−10.3086	+	17.8550i	−0.379208	+	0.656808i	−0.990947	−	0.134252i	$-0.957137\pi$
$739$	−10.3086	+	17.8550i	−0.379208	+	0.656808i	0.611739	+	0.791060i	$0.290470\pi$
$740$	1.76937			0.0650432
$741$	11.7747	+	9.54090i	0.432555	+	0.350494i
$742$	−1.81378	−	1.22164i	−0.0665860	−	0.0448478i
$743$	7.69885	−	4.44493i	0.282443	−	0.163069i	−0.352086	−	0.935968i	$-0.614527\pi$
$743$	7.69885	−	4.44493i	0.282443	−	0.163069i	0.634529	+	0.772899i	$0.281194\pi$
$744$	1.92275	−	12.1159i	0.0704914	−	0.444191i
$745$	−8.87435	+	5.12361i	−0.325131	+	0.187714i
$746$	9.55935	+	5.51909i	0.349993	+	0.202068i
$747$	−16.1016	+	14.4802i	−0.589126	+	0.529803i
$748$			10.4349i			0.381538i
$749$	6.58599	+	13.4803i	0.240647	+	0.492559i
$750$	−14.0572	−	2.23082i	−0.513295	−	0.0814580i
$751$	12.5008	−	21.6521i	0.456162	−	0.790095i	−0.542592	−	0.839996i	$-0.682557\pi$
$751$	12.5008	−	21.6521i	0.456162	−	0.790095i	0.998754	+	0.0499007i	$0.0158905\pi$
$752$	2.73927			0.0998907
$753$	0.113117	−	0.712789i	0.00412221	−	0.0259755i
$754$			15.3618i			0.559443i
$755$	22.5555			0.820878
$756$	−17.4879	−	10.5135i	−0.636028	−	0.382372i
$757$	−27.1262			−0.985919			−0.492959	−	0.870052i	$-0.664085\pi$
$757$	−27.1262			−0.985919			−0.492959	+	0.870052i	$0.664085\pi$
$758$			23.2420i			0.844189i
$759$	−2.77426	+	17.4816i	−0.100699	+	0.634541i
$760$	−14.5323			−0.527142
$761$	−1.58366	+	2.74298i	−0.0574075	+	0.0994328i	−0.893301	−	0.449459i	$-0.851617\pi$
$761$	−1.58366	+	2.74298i	−0.0574075	+	0.0994328i	0.835893	+	0.548892i	$0.184950\pi$
$762$	−1.08275	−	0.171828i	−0.0392237	−	0.00622465i
$763$	−26.3293	−	17.7337i	−0.953186	−	0.642002i
$764$			10.9703i			0.396891i
$765$	−3.51533	−	16.5879i	−0.127097	−	0.599737i
$766$	−12.3361	−	7.12228i	−0.445723	−	0.257338i
$767$	18.4922	−	10.6765i	0.667713	−	0.385504i
$768$	3.02702	−	19.0743i	0.109228	−	0.688286i
$769$	−2.48873	+	1.43687i	−0.0897460	+	0.0518149i	−0.544201	−	0.838955i	$-0.683167\pi$
$769$	−2.48873	+	1.43687i	−0.0897460	+	0.0518149i	0.454455	+	0.890770i	$0.349834\pi$
$770$	−0.342145	+	4.94056i	−0.0123300	+	0.178046i
$771$	−28.4330	−	23.0389i	−1.02399	−	0.829725i
$772$	19.3374			0.695967
$773$	−6.15679	+	10.6639i	−0.221444	+	0.383553i	−0.955247	−	0.295810i	$-0.904410\pi$
$773$	−6.15679	+	10.6639i	−0.221444	+	0.383553i	0.733802	+	0.679363i	$0.237744\pi$
$774$	−10.8559	−	12.0714i	−0.390207	−	0.433899i
$775$	7.12002	−	4.11075i	0.255759	−	0.147662i
$776$	−19.4053	+	33.6110i	−0.696610	+	1.20656i
$777$	−1.10471	−	3.60860i	−0.0396312	−	0.129458i
$778$	−1.83234	−	3.17371i	−0.0656926	−	0.113783i
$779$	−41.0426	−	23.6960i	−1.47051	−	0.848997i
$780$	8.01533	+	1.27200i	0.286995	+	0.0455450i
$781$	1.75494	+	3.03965i	0.0627968	+	0.108767i
$782$	7.95765	+	13.7831i	0.284565	+	0.492881i
$783$	42.7682	−	27.7186i	1.52841	−	0.990581i
$784$	−8.12174	−	1.13032i	−0.290062	−	0.0403685i
$785$	−2.61539	−	1.51000i	−0.0933473	−	0.0538941i
$786$	−2.32928	+	2.87464i	−0.0830827	+	0.102535i
$787$		−	3.81570i		−	0.136015i	−0.997685	−	0.0680076i	$-0.978336\pi$
$787$		−	3.81570i		−	0.136015i	0.997685	−	0.0680076i	$-0.0216642\pi$
$788$			5.98200i			0.213100i
$789$	−13.7972	−	35.9755i	−0.491192	−	1.28076i
$790$	11.1923	+	6.46186i	0.398203	+	0.229903i
$791$	−8.41936	−	17.2329i	−0.299358	−	0.612730i
$792$	−2.80218	−	13.2228i	−0.0995713	−	0.469851i
$793$	2.56834	+	4.44849i	0.0912044	+	0.157971i
$794$	4.78022	+	8.27959i	0.169644	+	0.293832i
$795$	−1.03328	−	2.69424i	−0.0366467	−	0.0955547i
$796$	21.0904	+	12.1765i	0.747528	+	0.431585i
$797$	−24.5682	−	42.5535i	−0.870252	−	1.50732i	−0.861736	−	0.507357i	$-0.830623\pi$
$797$	−24.5682	−	42.5535i	−0.870252	−	1.50732i	−0.00851609	−	0.999964i	$-0.502711\pi$
$798$	3.86510	+	12.6256i	0.136823	+	0.446940i
$799$	4.56524	−	7.90724i	0.161507	−	0.279738i
$800$	14.7049	−	8.48988i	0.519897	−	0.300162i
$801$	6.58022	+	31.0503i	0.232501	+	1.09711i
$802$	5.87742	−	10.1800i	0.207539	−	0.359468i
$803$	−5.04906			−0.178177
$804$	0.126038	−	0.794212i	0.00444503	−	0.0280097i
$805$	−9.54188	−	19.5305i	−0.336307	−	0.688359i
$806$	3.83924	−	2.21659i	0.135231	−	0.0780759i
$807$	39.0703	+	31.6581i	1.37534	+	1.11442i
$808$	−8.55146	+	4.93719i	−0.300839	+	0.173690i
$809$	−39.4929	−	22.8012i	−1.38850	−	0.801648i	−0.395350	−	0.918531i	$-0.629377\pi$
$809$	−39.4929	−	22.8012i	−1.38850	−	0.801648i	−0.993146	+	0.116882i	$0.962710\pi$
$810$	3.79512	+	8.55196i	0.133347	+	0.300485i
$811$			39.1391i			1.37436i	0.726488	+	0.687180i	$0.241151\pi$
$811$			39.1391i			1.37436i	−0.726488	+	0.687180i	$0.758849\pi$
$812$	21.5165	−	31.9458i	0.755082	−	1.12108i
$813$	14.9087	+	38.8739i	0.522872	+	1.36337i
$814$	0.532458	−	0.922243i	0.0186626	−	0.0323246i
$815$	16.1831			0.566870
$816$	6.15531	+	4.98757i	0.215479	+	0.174600i
$817$		−	30.2322i		−	1.05769i
$818$	3.11476			0.108905
$819$	−2.41016	−	17.1413i	−0.0842179	−	0.598967i
$820$	−25.3789			−0.886269
$821$			11.8906i			0.414985i	0.978237	+	0.207492i	$0.0665302\pi$
$821$			11.8906i			0.414985i	−0.978237	+	0.207492i	$0.933470\pi$
$822$	−13.8192	+	5.29989i	−0.482001	+	0.184855i
$823$	3.02389			0.105406			0.0527031	−	0.998610i	$-0.483216\pi$
$823$	3.02389			0.105406			0.0527031	+	0.998610i	$0.483216\pi$
$824$	5.19873	−	9.00446i	0.181106	−	0.313685i
$825$	5.70283	−	7.03803i	0.198547	−	0.245033i
$826$	18.5595	+	1.28529i	0.645768	+	0.0447209i
$827$			15.2436i			0.530071i	0.964239	+	0.265035i	$0.0853836\pi$
$827$			15.2436i			0.530071i	−0.964239	+	0.265035i	$0.914616\pi$
$828$	16.8987	+	18.7909i	0.587272	+	0.653030i
$829$	−29.7306	−	17.1649i	−1.03259	−	0.596163i	−0.114861	−	0.993382i	$-0.536642\pi$
$829$	−29.7306	−	17.1649i	−1.03259	−	0.596163i	−0.917724	+	0.397218i	$0.869976\pi$
$830$	6.49868	−	3.75201i	0.225572	−	0.130234i
$831$	13.0425	−	5.00198i	0.452438	−	0.173517i
$832$	3.50424	−	2.02317i	0.121488	−	0.0701409i
$833$	−16.7985	+	21.5607i	−0.582032	+	0.747033i
$834$	13.9665	−	5.35635i	0.483619	−	0.185475i
$835$	2.78146			0.0962565
$836$	5.36105	−	9.28561i	0.185416	−	0.321150i
$837$	−13.0986	−	6.68912i	−0.452753	−	0.231210i
$838$	11.7088	−	6.76006i	0.404473	−	0.233522i
$839$	6.16024	−	10.6698i	0.212675	−	0.368364i	−0.739876	−	0.672744i	$-0.765116\pi$
$839$	6.16024	−	10.6698i	0.212675	−	0.368364i	0.952551	+	0.304379i	$0.0984491\pi$
$840$	12.1437	+	11.3159i	0.418998	+	0.390435i
$841$	33.6008	+	58.1983i	1.15865	+	2.00684i
$842$	−1.13625	−	0.656012i	−0.0391576	−	0.0226077i
$843$	15.2197	−	18.7831i	0.524194	−	0.646923i
$844$	−8.91770	−	15.4459i	−0.306960	−	0.531670i
$845$	−5.96672	−	10.3347i	−0.205262	−	0.355523i
$846$	−1.55976	+	4.79054i	−0.0536257	+	0.164702i
$847$	17.0243	+	11.4664i	0.584961	+	0.393990i
$848$	1.16758	+	0.674104i	0.0400949	+	0.0231488i
$849$	−26.5792	−	4.21801i	−0.912194	−	0.144762i
$850$		−	8.14496i		−	0.279370i
$851$			4.67406i			0.160225i
$852$	4.94934	+	0.785442i	0.169562	+	0.0269088i
$853$	3.92537	+	2.26631i	0.134402	+	0.0775971i	0.565693	−	0.824616i	$-0.308609\pi$
$853$	3.92537	+	2.26631i	0.134402	+	0.0775971i	−0.431291	+	0.902213i	$0.641942\pi$
$854$	−0.309190	+	4.46470i	−0.0105803	+	0.152779i
$855$	−5.39408	+	16.5670i	−0.184474	+	0.566579i
$856$	7.09472	+	12.2884i	0.242493	+	0.420010i
$857$	−16.1307	−	27.9392i	−0.551014	−	0.954384i	−0.998202	−	0.0599442i	$-0.980908\pi$
$857$	−16.1307	−	27.9392i	−0.551014	−	0.954384i	0.447188	−	0.894440i	$-0.352426\pi$
$858$	3.07506	−	3.79503i	0.104981	−	0.129560i
$859$	15.2711	+	8.81675i	0.521042	+	0.300824i	0.737361	−	0.675499i	$-0.236072\pi$
$859$	15.2711	+	8.81675i	0.521042	+	0.300824i	−0.216319	+	0.976323i	$0.569405\pi$
$860$	−8.09483	−	14.0207i	−0.276032	−	0.478101i
$861$	15.8454	+	51.7599i	0.540009	+	1.76397i
$862$	5.16329	−	8.94307i	0.175862	−	0.304602i
$863$	26.4091	−	15.2473i	0.898975	−	0.519023i	0.0221074	−	0.999756i	$-0.492962\pi$
$863$	26.4091	−	15.2473i	0.898975	−	0.519023i	0.876867	+	0.480732i	$0.159629\pi$
$864$	−27.0524	−	13.8150i	−0.920340	−	0.469995i
$865$	−11.0200	+	19.0873i	−0.374693	+	0.648987i
$866$	−1.59526			−0.0542093
$867$	−2.83668	+	1.08791i	−0.0963388	+	0.0369474i
$868$	−11.0886	−	0.767911i	−0.376372	−	0.0260646i
$869$	−19.3851	+	11.1920i	−0.657594	+	0.379662i
$870$	−16.4897	+	6.32405i	−0.559053	+	0.214405i
$871$	0.590785	−	0.341090i	0.0200180	−	0.0115574i
$872$	−26.0006	−	15.0115i	−0.880492	−	0.508352i
$873$	31.1140	+	34.5979i	1.05305	+	1.17096i
$874$		−	16.3533i		−	0.553160i
$875$	−2.09150	+	30.2011i	−0.0707055	+	1.02098i
$876$	−4.53838	+	5.60095i	−0.153338	+	0.189239i
$877$	−4.40363	+	7.62730i	−0.148700	+	0.257556i	−0.930747	−	0.365663i	$-0.880842\pi$
$877$	−4.40363	+	7.62730i	−0.148700	+	0.257556i	0.782047	+	0.623219i	$0.214176\pi$
$878$	−7.21385			−0.243456
$879$	21.7905	−	8.35699i	0.734975	−	0.281874i
$880$		−	3.05322i		−	0.102924i
$881$	38.6776			1.30308			0.651540	−	0.758614i	$-0.274123\pi$
$881$	38.6776			1.30308			0.651540	+	0.758614i	$0.274123\pi$
$882$	6.60133	−	13.5600i	0.222279	−	0.456589i
$883$	37.4489			1.26026			0.630128	−	0.776491i	$-0.283002\pi$
$883$	37.4489			1.26026			0.630128	+	0.776491i	$0.283002\pi$
$884$			12.6388i			0.425089i
$885$	19.0731	+	15.4547i	0.641135	+	0.519503i
$886$	9.97781			0.335211
$887$	13.7025	−	23.7335i	0.460086	−	0.796892i	−0.538879	−	0.842383i	$-0.681152\pi$
$887$	13.7025	−	23.7335i	0.460086	−	0.796892i	0.998965	+	0.0454915i	$0.0144854\pi$
$888$	−1.27809	−	3.33256i	−0.0428898	−	0.111833i
$889$	−0.161096	+	2.32622i	−0.00540299	+	0.0780191i
$890$		−	10.9987i		−	0.368679i
$891$	−16.1142	−	1.71349i	−0.539846	−	0.0574040i
$892$	33.8305	+	19.5321i	1.13273	+	0.653982i
$893$	−8.12487	+	4.69090i	−0.271888	+	0.156975i
$894$	6.84155	+	5.54362i	0.228816	+	0.185406i
$895$	−0.433397	+	0.250222i	−0.0144869	+	0.00836400i
$896$	−27.3422	−	1.89351i	−0.913439	−	0.0632576i
$897$	−3.36019	+	21.1737i	−0.112194	+	0.706971i
$898$	7.58598			0.253147
$899$	13.8811	−	24.0428i	0.462962	−	0.801873i
$900$	−2.68130	−	12.6524i	−0.0893768	−	0.421745i
$901$	3.89177	−	2.24691i	0.129654	−	0.0748556i
$902$	−7.63729	+	13.2282i	−0.254294	+	0.440450i
$903$	−23.5409	+	25.2631i	−0.783393	+	0.840705i
$904$	−9.06971	−	15.7092i	−0.301654	−	0.522480i
$905$	4.10760	+	2.37152i	0.136541	+	0.0788321i
$906$	−6.94049	−	18.0970i	−0.230582	−	0.601234i
$907$	11.8216	+	20.4757i	0.392531	+	0.679883i	0.992783	−	0.119928i	$-0.0382663\pi$
$907$	11.8216	+	20.4757i	0.392531	+	0.679883i	−0.600252	+	0.799811i	$0.704933\pi$
$908$	8.02097	+	13.8927i	0.266185	+	0.461046i
$909$	2.45433	+	11.5813i	0.0814049	+	0.384128i
$910$	−0.414407	+	5.98403i	−0.0137375	+	0.198369i
$911$	−3.92249	−	2.26465i	−0.129958	−	0.0750313i	0.433612	−	0.901100i	$-0.357239\pi$
$911$	−3.92249	−	2.26465i	−0.129958	−	0.0750313i	−0.563570	+	0.826069i	$0.690572\pi$
$912$	−2.91495	−	7.60061i	−0.0965237	−	0.251681i
$913$			12.9970i			0.430139i
$914$		−	3.67204i		−	0.121460i
$915$	−3.71780	+	4.58824i	−0.122907	+	0.151683i
$916$	−12.4643	−	7.19626i	−0.411832	−	0.237771i
$917$	6.52711	+	4.39622i	0.215544	+	0.145176i
$918$	−12.2274	+	7.92469i	−0.403563	+	0.261554i
$919$	16.9149	+	29.2975i	0.557971	+	0.966434i	0.997666	+	0.0682866i	$0.0217532\pi$
$919$	16.9149	+	29.2975i	0.557971	+	0.966434i	−0.439695	+	0.898147i	$0.644913\pi$
$920$	−10.2789	−	17.8037i	−0.338887	−	0.586969i
$921$	−14.7593	−	2.34224i	−0.486335	−	0.0771795i
$922$	−5.18323	−	2.99254i	−0.170700	−	0.0985540i
$923$	2.12559	+	3.68164i	0.0699648	+	0.121183i
$924$	−11.7103	+	3.58490i	−0.385241	+	0.117935i
$925$	1.19602	−	2.07157i	0.0393249	−	0.0681127i
$926$	12.4568	−	7.19192i	0.409355	−	0.236341i
$927$	−8.33552	−	9.26886i	−0.273774	−	0.304429i
$928$	28.6685	−	49.6554i	0.941091	−	1.63002i
$929$	32.9164			1.07995			0.539976	−	0.841680i	$-0.318433\pi$
$929$	32.9164			1.07995			0.539976	+	0.841680i	$0.318433\pi$
$930$	3.95985	+	3.20861i	0.129849	+	0.105215i
$931$	26.0253	−	10.5556i	0.852946	−	0.345946i
$932$	2.86305	−	1.65298i	0.0937824	−	0.0541453i
$933$	4.40980	−	27.7877i	0.144370	−	0.909729i
$934$	12.9236	−	7.46146i	0.422874	−	0.244146i
$935$	−8.81350	−	5.08848i	−0.288232	−	0.166411i
$936$	−3.39402	−	16.0155i	−0.110937	−	0.523482i
$937$		−	38.1057i		−	1.24486i	−0.782676	−	0.622430i	$-0.786146\pi$
$937$		−	38.1057i		−	1.24486i	0.782676	−	0.622430i	$-0.213854\pi$
$938$	0.592938	+	0.0410622i	0.0193601	+	0.00134073i
$939$	11.5929	+	1.83975i	0.378320	+	0.0600379i
$940$	−2.51202	+	4.35095i	−0.0819331	+	0.141912i
$941$	−19.8771			−0.647975			−0.323987	−	0.946061i	$-0.605024\pi$
$941$	−19.8771			−0.647975			−0.323987	+	0.946061i	$0.605024\pi$
$942$	−0.406747	+	2.56305i	−0.0132525	+	0.0835088i
$943$		−	67.0423i		−	2.18320i
$944$	−11.4696			−0.373304
$945$	17.4077	−	9.64376i	0.566272	−	0.313712i
$946$	−9.74394			−0.316803
$947$			20.7495i			0.674267i	0.941457	+	0.337134i	$0.109457\pi$
$947$			20.7495i			0.674267i	−0.941457	+	0.337134i	$0.890543\pi$
$948$	−5.00908	+	31.5640i	−0.162687	+	1.02515i
$949$	−6.11544			−0.198516
$950$	−4.18457	+	7.24789i	−0.135765	+	0.235152i
$951$	−37.5787	−	5.96359i	−1.21857	−	0.193383i
$952$	−14.4407	+	21.4402i	−0.468025	+	0.694882i
$953$			12.8345i			0.415751i	0.978155	+	0.207876i	$0.0666549\pi$
$953$			12.8345i			0.415751i	−0.978155	+	0.207876i	$0.933345\pi$
$954$	−1.84373	+	1.65807i	−0.0596930	+	0.0536821i
$955$	−9.26571	−	5.34956i	−0.299831	−	0.173108i
$956$	−23.7027	+	13.6848i	−0.766602	+	0.442598i
$957$	4.79430	−	30.2105i	0.154978	−	0.976568i
$958$	−19.9408	+	11.5128i	−0.644258	+	0.371962i
$959$	13.8192	+	28.2854i	0.446247	+	0.913384i
$960$	3.61433	+	2.92864i	0.116652	+	0.0945215i
$961$	22.9882			0.741556
$962$	0.644915	−	1.11703i	0.0207929	−	0.0360143i
$963$	16.6423	−	3.52686i	0.536292	−	0.113652i
$964$	8.31878	−	4.80285i	0.267930	−	0.154689i
$965$	−9.42969	+	16.3327i	−0.303552	+	0.525768i
$966$	−12.7339	+	13.6654i	−0.409705	+	0.439678i
$967$	−17.8941	−	30.9936i	−0.575437	−	0.996685i	−0.995994	−	0.0894195i	$-0.971499\pi$
$967$	−17.8941	−	30.9936i	−0.575437	−	0.996685i	0.420557	−	0.907266i	$-0.361835\pi$
$968$	16.8117	+	9.70625i	0.540349	+	0.311971i
$969$	−26.7982	−	4.25277i	−0.860881	−	0.136619i
$970$	−8.06205	−	13.9639i	−0.258857	−	0.448353i
$971$	−14.5129	−	25.1370i	−0.465740	−	0.806686i	0.533494	−	0.845804i	$-0.320879\pi$
$971$	−14.5129	−	25.1370i	−0.465740	−	0.806686i	−0.999235	+	0.0391177i	$0.987545\pi$
$972$	−16.3852	+	16.3354i	−0.525554	+	0.523959i
$973$	−13.9665	−	28.5868i	−0.447744	−	0.916450i
$974$	−14.7247	−	8.50130i	−0.471809	−	0.272399i
$975$	6.90729	−	8.52449i	0.221210	−	0.273002i
$976$		−	2.75914i		−	0.0883180i
$977$		−	8.93090i		−	0.285725i	−0.989743	−	0.142862i	$-0.954369\pi$
$977$		−	8.93090i		−	0.285725i	0.989743	−	0.142862i	$-0.0456306\pi$
$978$	−4.97966	−	12.9843i	−0.159232	−	0.415191i
$979$	16.4977	+	9.52495i	0.527268	+	0.304419i
$980$	9.24334	−	11.8637i	0.295268	−	0.378973i
$981$	−26.7641	+	24.0690i	−0.854512	+	0.768466i
$982$	−6.41288	−	11.1074i	−0.204643	−	0.354452i
$983$	−26.1346	−	45.2665i	−0.833566	−	1.44378i	−0.895193	−	0.445679i	$-0.852962\pi$
$983$	−26.1346	−	45.2665i	−0.833566	−	1.44378i	0.0616269	−	0.998099i	$-0.480371\pi$
$984$	18.3322	+	47.8004i	0.584409	+	1.52382i
$985$	−5.05250	−	2.91707i	−0.160986	−	0.0929454i
$986$	−13.7519	−	23.8190i	−0.437950	−	0.758552i
$987$	10.4421	+	2.40671i	0.332375	+	0.0766063i
$988$	6.49333	−	11.2468i	0.206580	−	0.357807i
$989$	37.0378	−	21.3838i	1.17773	−	0.679964i
$990$	5.33959	+	1.73853i	0.169703	+	0.0552541i
$991$	−21.9151	+	37.9581i	−0.696158	+	1.20578i	0.273631	+	0.961835i	$0.411775\pi$
$991$	−21.9151	+	37.9581i	−0.696158	+	1.20578i	−0.969789	+	0.243946i	$0.921558\pi$
$992$	−16.5466			−0.525355
$993$	3.96447	−	24.9815i	0.125809	−	0.792764i
$994$	−0.255890	+	3.69505i	−0.00811635	+	0.117200i
$995$	−20.5690	+	11.8755i	−0.652082	+	0.376480i
$996$	14.4177	+	11.6825i	0.456842	+	0.370173i
$997$	−38.9689	+	22.4987i	−1.23416	+	0.712542i	−0.967894	−	0.251358i	$-0.919123\pi$
$997$	−38.9689	+	22.4987i	−1.23416	+	0.712542i	−0.266264	+	0.963900i	$0.585789\pi$
$998$	−14.3797	−	8.30215i	−0.455183	−	0.262800i
$999$	−4.27355	+	0.220059i	−0.135209	+	0.00696235i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	63.2.i.b.38.2	yes	10
3.2	odd	2		189.2.i.b.143.4		10
4.3	odd	2		1008.2.ca.b.353.3		10
7.2	even	3		441.2.s.b.362.2		10
7.3	odd	6		441.2.o.c.146.4		10
7.4	even	3		441.2.o.d.146.4		10
7.5	odd	6		63.2.s.b.47.2	yes	10
7.6	odd	2		441.2.i.b.227.2		10
9.2	odd	6		567.2.p.c.80.4		10
9.4	even	3		189.2.s.b.17.4		10
9.5	odd	6		63.2.s.b.59.2	yes	10
9.7	even	3		567.2.p.d.80.2		10
12.11	even	2		3024.2.ca.b.2033.4		10
21.2	odd	6		1323.2.s.b.656.4		10
21.5	even	6		189.2.s.b.89.4		10
21.11	odd	6		1323.2.o.c.440.2		10
21.17	even	6		1323.2.o.d.440.2		10
21.20	even	2		1323.2.i.b.521.4		10
28.19	even	6		1008.2.df.b.929.2		10
36.23	even	6		1008.2.df.b.689.2		10
36.31	odd	6		3024.2.df.b.17.4		10
63.4	even	3		1323.2.o.d.881.2		10
63.5	even	6	inner	63.2.i.b.5.4	✓	10
63.13	odd	6		1323.2.s.b.962.4		10
63.23	odd	6		441.2.i.b.68.4		10
63.31	odd	6		1323.2.o.c.881.2		10
63.32	odd	6		441.2.o.c.293.4		10
63.40	odd	6		189.2.i.b.152.2		10
63.41	even	6		441.2.s.b.374.2		10
63.47	even	6		567.2.p.d.404.2		10
63.58	even	3		1323.2.i.b.1097.2		10
63.59	even	6		441.2.o.d.293.4		10
63.61	odd	6		567.2.p.c.404.4		10
84.47	odd	6		3024.2.df.b.1601.4		10
252.103	even	6		3024.2.ca.b.2609.4		10
252.131	odd	6		1008.2.ca.b.257.3		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.2.i.b.5.4	✓	10	63.5	even	6	inner
63.2.i.b.38.2	yes	10	1.1	even	1	trivial
63.2.s.b.47.2	yes	10	7.5	odd	6
63.2.s.b.59.2	yes	10	9.5	odd	6
189.2.i.b.143.4		10	3.2	odd	2
189.2.i.b.152.2		10	63.40	odd	6
189.2.s.b.17.4		10	9.4	even	3
189.2.s.b.89.4		10	21.5	even	6
441.2.i.b.68.4		10	63.23	odd	6
441.2.i.b.227.2		10	7.6	odd	2
441.2.o.c.146.4		10	7.3	odd	6
441.2.o.c.293.4		10	63.32	odd	6
441.2.o.d.146.4		10	7.4	even	3
441.2.o.d.293.4		10	63.59	even	6
441.2.s.b.362.2		10	7.2	even	3
441.2.s.b.374.2		10	63.41	even	6
567.2.p.c.80.4		10	9.2	odd	6
567.2.p.c.404.4		10	63.61	odd	6
567.2.p.d.80.2		10	9.7	even	3
567.2.p.d.404.2		10	63.47	even	6
1008.2.ca.b.257.3		10	252.131	odd	6
1008.2.ca.b.353.3		10	4.3	odd	2
1008.2.df.b.689.2		10	36.23	even	6
1008.2.df.b.929.2		10	28.19	even	6
1323.2.i.b.521.4		10	21.20	even	2
1323.2.i.b.1097.2		10	63.58	even	3
1323.2.o.c.440.2		10	21.11	odd	6
1323.2.o.c.881.2		10	63.31	odd	6
1323.2.o.d.440.2		10	21.17	even	6
1323.2.o.d.881.2		10	63.4	even	3
1323.2.s.b.656.4		10	21.2	odd	6
1323.2.s.b.962.4		10	63.13	odd	6
3024.2.ca.b.2033.4		10	12.11	even	2
3024.2.ca.b.2609.4		10	252.103	even	6
3024.2.df.b.17.4		10	36.31	odd	6
3024.2.df.b.1601.4		10	84.47	odd	6

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:	\( N \)	\(=\)	\( 63 = 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	63.i (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-0.718167i q^{2} +(-0.271473 + 1.71064i) q^{3} +1.48424 q^{4} +(-0.723774 + 1.25361i) q^{5} +(1.22853 + 0.194963i) q^{6} +(0.182786 - 2.63943i) q^{7} -2.50226i q^{8} +(-2.85261 - 0.928786i) q^{9} +O(q^{10})\)	\(q-0.718167i q^{2} +(-0.271473 + 1.71064i) q^{3} +1.48424 q^{4} +(-0.723774 + 1.25361i) q^{5} +(1.22853 + 0.194963i) q^{6} +(0.182786 - 2.63943i) q^{7} -2.50226i q^{8} +(-2.85261 - 0.928786i) q^{9} +(0.900304 + 0.519791i) q^{10} +(-1.55933 + 0.900281i) q^{11} +(-0.402930 + 2.53900i) q^{12} +(-1.88867 + 1.09042i) q^{13} +(-1.89555 - 0.131271i) q^{14} +(-1.94800 - 1.57844i) q^{15} +1.17143 q^{16} +(1.95230 - 3.38149i) q^{17} +(-0.667023 + 2.04865i) q^{18} +(-3.47456 + 2.00604i) q^{19} +(-1.07425 + 1.86066i) q^{20} +(4.46550 + 1.02922i) q^{21} +(0.646552 + 1.11986i) q^{22} +(-4.91522 - 2.83781i) q^{23} +(4.28048 + 0.679296i) q^{24} +(1.45230 + 2.51546i) q^{25} +(0.783106 + 1.35638i) q^{26} +(2.36323 - 4.62765i) q^{27} +(0.271298 - 3.91754i) q^{28} +(8.49418 + 4.90412i) q^{29} +(-1.13358 + 1.39899i) q^{30} -2.83050i q^{31} -5.84581i q^{32} +(-1.11674 - 2.91186i) q^{33} +(-2.42847 - 1.40208i) q^{34} +(3.17653 + 2.13949i) q^{35} +(-4.23394 - 1.37854i) q^{36} +(-0.411767 - 0.713202i) q^{37} +(1.44067 + 2.49531i) q^{38} +(-1.35261 - 3.52686i) q^{39} +(3.13687 + 1.81107i) q^{40} +(5.90617 + 10.2298i) q^{41} +(0.739148 - 3.20698i) q^{42} +(-3.76766 + 6.52578i) q^{43} +(-2.31442 + 1.33623i) q^{44} +(3.22898 - 2.90383i) q^{45} +(-2.03802 + 3.52995i) q^{46} +2.33839 q^{47} +(-0.318012 + 2.00390i) q^{48} +(-6.93318 - 0.964903i) q^{49} +(1.80652 - 1.04299i) q^{50} +(5.25452 + 4.25767i) q^{51} +(-2.80323 + 1.61845i) q^{52} +(0.996713 + 0.575453i) q^{53} +(-3.32343 - 1.69719i) q^{54} -2.60640i q^{55} +(-6.60455 - 0.457379i) q^{56} +(-2.48837 - 6.48831i) q^{57} +(3.52198 - 6.10024i) q^{58} -9.79110 q^{59} +(-2.89130 - 2.34278i) q^{60} -2.35536i q^{61} -2.03277 q^{62} +(-2.97288 + 7.35948i) q^{63} -1.85540 q^{64} -3.15688i q^{65} +(-2.09120 + 0.802008i) q^{66} -0.312805 q^{67} +(2.89768 - 5.01893i) q^{68} +(6.18882 - 7.63781i) q^{69} +(1.53651 - 2.28128i) q^{70} -1.94933i q^{71} +(-2.32407 + 7.13797i) q^{72} +(2.42847 + 1.40208i) q^{73} +(-0.512198 + 0.295717i) q^{74} +(-4.69732 + 1.80149i) q^{75} +(-5.15706 + 2.97743i) q^{76} +(2.09120 + 4.28031i) q^{77} +(-2.53287 + 0.971396i) q^{78} +12.4317 q^{79} +(-0.847852 + 1.46852i) q^{80} +(7.27471 + 5.29892i) q^{81} +(7.34669 - 4.24162i) q^{82} +(3.60916 - 6.25124i) q^{83} +(6.62786 + 1.52760i) q^{84} +(2.82605 + 4.89486i) q^{85} +(4.68660 + 2.70581i) q^{86} +(-10.6951 + 13.1992i) q^{87} +(2.25274 + 3.90186i) q^{88} +(-5.28999 - 9.16253i) q^{89} +(-2.08544 - 2.31895i) q^{90} +(2.53287 + 5.18433i) q^{91} +(-7.29536 - 4.21198i) q^{92} +(4.84198 + 0.768404i) q^{93} -1.67935i q^{94} -5.80767i q^{95} +(10.0001 + 1.58698i) q^{96} +(-13.4322 - 7.75510i) q^{97} +(-0.692961 + 4.97918i) q^{98} +(5.28433 - 1.11986i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 3 q^{3} - 8 q^{4} + 12 q^{6} - 6 q^{7} + 3 q^{9}+O(q^{10}) \) 10 * q - 3 * q^3 - 8 * q^4 + 12 * q^6 - 6 * q^7 + 3 * q^9	\( 10 q - 3 q^{3} - 8 q^{4} + 12 q^{6} - 6 q^{7} + 3 q^{9} - 15 q^{10} - 12 q^{11} - 12 q^{12} - 6 q^{13} + 12 q^{14} - 3 q^{15} + 12 q^{16} + 12 q^{17} + 24 q^{18} + 3 q^{19} + 3 q^{20} - 9 q^{21} + 5 q^{22} - 15 q^{23} + 7 q^{25} - 3 q^{26} - 27 q^{27} + 2 q^{28} - 15 q^{29} + 6 q^{30} - 3 q^{34} + 15 q^{35} - 18 q^{36} + 6 q^{37} + 18 q^{38} + 18 q^{39} + 15 q^{40} + 9 q^{41} - 12 q^{42} + 3 q^{43} - 24 q^{44} + 30 q^{45} - 13 q^{46} + 30 q^{47} + 15 q^{48} + 4 q^{49} + 3 q^{50} + 21 q^{51} - 12 q^{52} + 9 q^{53} + 9 q^{54} - 30 q^{56} - 36 q^{57} + 8 q^{58} - 36 q^{59} - 48 q^{60} - 12 q^{62} - 15 q^{63} + 6 q^{64} - 39 q^{66} + 20 q^{67} - 27 q^{68} + 3 q^{69} + 6 q^{70} - 30 q^{72} + 3 q^{73} - 30 q^{74} + 6 q^{75} - 9 q^{76} + 39 q^{77} + 24 q^{78} - 40 q^{79} + 30 q^{80} + 15 q^{81} + 9 q^{82} + 15 q^{83} + 93 q^{84} + 18 q^{85} + 54 q^{86} + 6 q^{87} - 8 q^{88} - 24 q^{89} - 24 q^{90} - 24 q^{91} + 39 q^{92} + 36 q^{93} + 33 q^{96} - 6 q^{97} - 45 q^{98} + 21 q^{99}+O(q^{100}) \) 10 * q - 3 * q^3 - 8 * q^4 + 12 * q^6 - 6 * q^7 + 3 * q^9 - 15 * q^10 - 12 * q^11 - 12 * q^12 - 6 * q^13 + 12 * q^14 - 3 * q^15 + 12 * q^16 + 12 * q^17 + 24 * q^18 + 3 * q^19 + 3 * q^20 - 9 * q^21 + 5 * q^22 - 15 * q^23 + 7 * q^25 - 3 * q^26 - 27 * q^27 + 2 * q^28 - 15 * q^29 + 6 * q^30 - 3 * q^34 + 15 * q^35 - 18 * q^36 + 6 * q^37 + 18 * q^38 + 18 * q^39 + 15 * q^40 + 9 * q^41 - 12 * q^42 + 3 * q^43 - 24 * q^44 + 30 * q^45 - 13 * q^46 + 30 * q^47 + 15 * q^48 + 4 * q^49 + 3 * q^50 + 21 * q^51 - 12 * q^52 + 9 * q^53 + 9 * q^54 - 30 * q^56 - 36 * q^57 + 8 * q^58 - 36 * q^59 - 48 * q^60 - 12 * q^62 - 15 * q^63 + 6 * q^64 - 39 * q^66 + 20 * q^67 - 27 * q^68 + 3 * q^69 + 6 * q^70 - 30 * q^72 + 3 * q^73 - 30 * q^74 + 6 * q^75 - 9 * q^76 + 39 * q^77 + 24 * q^78 - 40 * q^79 + 30 * q^80 + 15 * q^81 + 9 * q^82 + 15 * q^83 + 93 * q^84 + 18 * q^85 + 54 * q^86 + 6 * q^87 - 8 * q^88 - 24 * q^89 - 24 * q^90 - 24 * q^91 + 39 * q^92 + 36 * q^93 + 33 * q^96 - 6 * q^97 - 45 * q^98 + 21 * q^99

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