LMFDB - Embedded newform 418.2.q.b.109.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [418,2,Mod(21,418)]

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([9, 1]))

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

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

chi := DirichletCharacter("418.21");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 418 = 2 \cdot 11 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	418.q (of order $18$, 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:	$60$
Relative dimension:	$10$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			109.7
Character	$\chi$	$=$	418.109
Dual form			418.2.q.b.395.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.939693 + 0.342020i) q^{2} +(1.58017 + 0.278627i) q^{3} +(0.766044 - 0.642788i) q^{4} +(-2.47390 - 2.07585i) q^{5} +(-1.58017 + 0.278627i) q^{6} +(-2.13981 + 1.23542i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(-0.399773 - 0.145505i) q^{9} +O(q^{10})$	\(q+(-0.939693 + 0.342020i) q^{2} +(1.58017 + 0.278627i) q^{3} +(0.766044 - 0.642788i) q^{4} +(-2.47390 - 2.07585i) q^{5} +(-1.58017 + 0.278627i) q^{6} +(-2.13981 + 1.23542i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(-0.399773 - 0.145505i) q^{9} +(3.03469 + 1.10454i) q^{10} +(2.53993 - 2.13278i) q^{11} +(1.38958 - 0.802273i) q^{12} +(-0.218926 - 1.24159i) q^{13} +(1.58823 - 1.89278i) q^{14} +(-3.33079 - 3.96949i) q^{15} +(0.173648 - 0.984808i) q^{16} +(-1.59563 - 4.38395i) q^{17} +0.425429 q^{18} +(-0.141589 - 4.35660i) q^{19} -3.22944 q^{20} +(-3.72549 + 1.35597i) q^{21} +(-1.65730 + 2.87287i) q^{22} +(3.21415 - 2.69699i) q^{23} +(-1.03138 + 1.22915i) q^{24} +(0.942791 + 5.34683i) q^{25} +(0.630374 + 1.09184i) q^{26} +(-4.75990 - 2.74813i) q^{27} +(-0.845078 + 2.32183i) q^{28} +(-6.33730 - 2.30659i) q^{29} +(4.48757 + 2.59090i) q^{30} +(-4.00542 + 2.31253i) q^{31} +(0.173648 + 0.984808i) q^{32} +(4.60777 - 2.66247i) q^{33} +(2.99880 + 3.57383i) q^{34} +(7.85823 + 1.38562i) q^{35} +(-0.399773 + 0.145505i) q^{36} +6.72668i q^{37} +(1.62309 + 4.04544i) q^{38} -2.02293i q^{39} +(3.03469 - 1.10454i) q^{40} +(-0.0992381 + 0.562807i) q^{41} +(3.03705 - 2.54839i) q^{42} +(2.64227 - 3.14893i) q^{43} +(0.574773 - 3.26644i) q^{44} +(0.686950 + 1.18983i) q^{45} +(-2.09789 + 3.63364i) q^{46} +(9.37418 + 3.41192i) q^{47} +(0.548787 - 1.50778i) q^{48} +(-0.447467 + 0.775035i) q^{49} +(-2.71466 - 4.70192i) q^{50} +(-1.29988 - 7.37198i) q^{51} +(-0.965788 - 0.810393i) q^{52} +(-3.89576 - 4.64279i) q^{53} +(5.41276 + 0.954416i) q^{54} +(-10.7109 + 0.00378177i) q^{55} -2.47084i q^{56} +(0.990129 - 6.92362i) q^{57} +6.74401 q^{58} +(-1.91054 - 5.24918i) q^{59} +(-5.10307 - 0.899809i) q^{60} +(-1.16401 - 1.38721i) q^{61} +(2.97293 - 3.54300i) q^{62} +(1.03520 - 0.182534i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(-2.03576 + 3.52603i) q^{65} +(-3.41927 + 4.07785i) q^{66} +(-1.77098 + 4.86573i) q^{67} +(-4.04027 - 2.33265i) q^{68} +(5.83035 - 3.36616i) q^{69} +(-7.85823 + 1.38562i) q^{70} +(2.50094 - 2.98050i) q^{71} +(0.325898 - 0.273461i) q^{72} +(15.7116 + 2.77038i) q^{73} +(-2.30066 - 6.32101i) q^{74} +8.71159i q^{75} +(-2.90883 - 3.24634i) q^{76} +(-2.80009 + 7.70164i) q^{77} +(0.691882 + 1.90093i) q^{78} +(-2.25135 + 12.7680i) q^{79} +(-2.47390 + 2.07585i) q^{80} +(-5.77806 - 4.84837i) q^{81} +(-0.0992381 - 0.562807i) q^{82} +(6.86178 - 3.96165i) q^{83} +(-1.98229 + 3.43343i) q^{84} +(-5.15300 + 14.1577i) q^{85} +(-1.40592 + 3.86274i) q^{86} +(-9.37133 - 5.41054i) q^{87} +(0.577079 + 3.26603i) q^{88} +(9.27201 - 1.63490i) q^{89} +(-1.05247 - 0.883126i) q^{90} +(2.00235 + 2.38631i) q^{91} +(0.728588 - 4.13203i) q^{92} +(-6.97358 + 2.53818i) q^{93} -9.97580 q^{94} +(-8.69336 + 11.0717i) q^{95} +1.60455i q^{96} +(2.80742 + 7.71332i) q^{97} +(0.155404 - 0.881338i) q^{98} +(-1.32573 + 0.483055i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q - 3 q^{3} + 3 q^{6} + 18 q^{7} - 30 q^{8} - 3 q^{9}+O(q^{10}) $ 60 * q - 3 * q^3 + 3 * q^6 + 18 * q^7 - 30 * q^8 - 3 * q^9	$ 60 q - 3 q^{3} + 3 q^{6} + 18 q^{7} - 30 q^{8} - 3 q^{9} + 3 q^{11} - 6 q^{13} - 12 q^{14} + 24 q^{15} + 6 q^{17} - 60 q^{18} + 30 q^{19} - 12 q^{20} - 12 q^{21} + 12 q^{22} - 3 q^{24} - 12 q^{25} + 6 q^{26} + 9 q^{27} - 6 q^{28} + 3 q^{29} - 9 q^{31} + 9 q^{33} - 6 q^{34} + 24 q^{35} - 3 q^{36} + 6 q^{38} - 15 q^{41} + 6 q^{42} + 3 q^{43} - 12 q^{44} - 48 q^{45} - 3 q^{46} + 54 q^{47} - 6 q^{48} + 6 q^{49} - 36 q^{50} + 45 q^{51} + 3 q^{52} + 24 q^{53} + 27 q^{54} - 48 q^{55} - 30 q^{57} + 24 q^{58} - 39 q^{59} + 12 q^{60} - 54 q^{61} + 66 q^{63} - 30 q^{64} - 30 q^{66} + 9 q^{67} + 27 q^{68} + 54 q^{69} - 24 q^{70} - 33 q^{71} + 6 q^{72} - 12 q^{74} + 18 q^{77} - 36 q^{79} - 93 q^{81} - 15 q^{82} + 36 q^{83} - 24 q^{84} + 60 q^{85} - 3 q^{86} - 54 q^{87} + 3 q^{88} - 3 q^{89} + 24 q^{90} - 12 q^{91} - 102 q^{93} + 12 q^{94} - 24 q^{95} - 6 q^{97} + 18 q^{98} + 75 q^{99}+O(q^{100}) $ 60 * q - 3 * q^3 + 3 * q^6 + 18 * q^7 - 30 * q^8 - 3 * q^9 + 3 * q^11 - 6 * q^13 - 12 * q^14 + 24 * q^15 + 6 * q^17 - 60 * q^18 + 30 * q^19 - 12 * q^20 - 12 * q^21 + 12 * q^22 - 3 * q^24 - 12 * q^25 + 6 * q^26 + 9 * q^27 - 6 * q^28 + 3 * q^29 - 9 * q^31 + 9 * q^33 - 6 * q^34 + 24 * q^35 - 3 * q^36 + 6 * q^38 - 15 * q^41 + 6 * q^42 + 3 * q^43 - 12 * q^44 - 48 * q^45 - 3 * q^46 + 54 * q^47 - 6 * q^48 + 6 * q^49 - 36 * q^50 + 45 * q^51 + 3 * q^52 + 24 * q^53 + 27 * q^54 - 48 * q^55 - 30 * q^57 + 24 * q^58 - 39 * q^59 + 12 * q^60 - 54 * q^61 + 66 * q^63 - 30 * q^64 - 30 * q^66 + 9 * q^67 + 27 * q^68 + 54 * q^69 - 24 * q^70 - 33 * q^71 + 6 * q^72 - 12 * q^74 + 18 * q^77 - 36 * q^79 - 93 * q^81 - 15 * q^82 + 36 * q^83 - 24 * q^84 + 60 * q^85 - 3 * q^86 - 54 * q^87 + 3 * q^88 - 3 * q^89 + 24 * q^90 - 12 * q^91 - 102 * q^93 + 12 * q^94 - 24 * q^95 - 6 * q^97 + 18 * q^98 + 75 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$287$	$343$
$\chi(n)$	$e\left(\frac{7}{18}\right)$	$-1$

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 $

$2$	−0.939693	+	0.342020i	−0.664463	+	0.241845i
$2$	−0.939693	+	0.342020i	−0.664463	+	0.241845i
$3$	1.58017	+	0.278627i	0.912312	+	0.160865i	0.610053	−	0.792361i	$-0.291148\pi$
$3$	1.58017	+	0.278627i	0.912312	+	0.160865i	0.302259	+	0.953226i	$0.402259\pi$
$4$	0.766044	−	0.642788i	0.383022	−	0.321394i
$5$	−2.47390	−	2.07585i	−1.10636	−	0.928347i	−0.108525	−	0.994094i	$-0.534613\pi$
$5$	−2.47390	−	2.07585i	−1.10636	−	0.928347i	−0.997836	+	0.0657467i	$0.979057\pi$
$6$	−1.58017	+	0.278627i	−0.645102	+	0.113749i
$7$	−2.13981	+	1.23542i	−0.808773	+	0.466945i	−0.846530	−	0.532341i	$-0.821312\pi$
$7$	−2.13981	+	1.23542i	−0.808773	+	0.466945i	0.0377564	+	0.999287i	$0.487979\pi$
$8$	−0.500000	+	0.866025i	−0.176777	+	0.306186i
$9$	−0.399773	−	0.145505i	−0.133258	−	0.0485018i
$10$	3.03469	+	1.10454i	0.959652	+	0.349285i
$11$	2.53993	−	2.13278i	0.765817	−	0.643058i
$11$	2.53993	−	2.13278i	0.765817	−	0.643058i
$12$	1.38958	−	0.802273i	0.401137	−	0.231596i
$13$	−0.218926	−	1.24159i	−0.0607193	−	0.344356i	−0.999999	−	0.00120442i	$-0.999617\pi$
$13$	−0.218926	−	1.24159i	−0.0607193	−	0.344356i	0.939280	−	0.343152i	$-0.111494\pi$
$14$	1.58823	−	1.89278i	0.424472	−	0.505866i
$15$	−3.33079	−	3.96949i	−0.860007	−	1.02492i
$16$	0.173648	−	0.984808i	0.0434120	−	0.246202i
$17$	−1.59563	−	4.38395i	−0.386997	−	1.06327i	−0.968346	−	0.249611i	$-0.919697\pi$
$17$	−1.59563	−	4.38395i	−0.386997	−	1.06327i	0.581349	−	0.813654i	$-0.302525\pi$
$18$	0.425429			0.100275
$19$	−0.141589	−	4.35660i	−0.0324828	−	0.999472i
$19$	−0.141589	−	4.35660i	−0.0324828	−	0.999472i
$20$	−3.22944			−0.722126
$21$	−3.72549	+	1.35597i	−0.812969	+	0.295896i
$22$	−1.65730	+	2.87287i	−0.353337	+	0.612497i
$23$	3.21415	−	2.69699i	0.670196	−	0.562361i	−0.242927	−	0.970044i	$-0.578108\pi$
$23$	3.21415	−	2.69699i	0.670196	−	0.562361i	0.913123	+	0.407683i	$0.133663\pi$
$24$	−1.03138	+	1.22915i	−0.210530	+	0.250900i
$25$	0.942791	+	5.34683i	0.188558	+	1.06937i
$26$	0.630374	+	1.09184i	0.123626	+	0.214127i
$27$	−4.75990	−	2.74813i	−0.916044	−	0.528878i
$28$	−0.845078	+	2.32183i	−0.159705	+	0.438785i
$29$	−6.33730	−	2.30659i	−1.17681	−	0.428323i	−0.321734	−	0.946830i	$-0.604266\pi$
$29$	−6.33730	−	2.30659i	−1.17681	−	0.428323i	−0.855073	+	0.518508i	$0.826488\pi$
$30$	4.48757	+	2.59090i	0.819314	+	0.473031i
$31$	−4.00542	+	2.31253i	−0.719395	+	0.415343i	−0.814530	−	0.580122i	$-0.803005\pi$
$31$	−4.00542	+	2.31253i	−0.719395	+	0.415343i	0.0951351	+	0.995464i	$0.469672\pi$
$32$	0.173648	+	0.984808i	0.0306970	+	0.174091i
$33$	4.60777	−	2.66247i	0.802110	−	0.463476i
$34$	2.99880	+	3.57383i	0.514290	+	0.612907i
$35$	7.85823	+	1.38562i	1.32828	+	0.234212i
$36$	−0.399773	+	0.145505i	−0.0666288	+	0.0242509i
$37$			6.72668i			1.10586i	0.833228	+	0.552929i	$0.186490\pi$
$37$			6.72668i			1.10586i	−0.833228	+	0.552929i	$0.813510\pi$
$38$	1.62309	+	4.04544i	0.263301	+	0.656257i
$39$		−	2.02293i		−	0.323928i
$40$	3.03469	−	1.10454i	0.479826	−	0.174642i
$41$	−0.0992381	+	0.562807i	−0.0154984	+	0.0878957i	−0.991576	−	0.129527i	$-0.958654\pi$
$41$	−0.0992381	+	0.562807i	−0.0154984	+	0.0878957i	0.976077	+	0.217423i	$0.0697651\pi$
$42$	3.03705	−	2.54839i	0.468627	−	0.393224i
$43$	2.64227	−	3.14893i	0.402942	−	0.480208i	−0.525972	−	0.850502i	$-0.676299\pi$
$43$	2.64227	−	3.14893i	0.402942	−	0.480208i	0.928915	+	0.370294i	$0.120743\pi$
$44$	0.574773	−	3.26644i	0.0866502	−	0.492435i
$45$	0.686950	+	1.18983i	0.102404	+	0.177370i
$46$	−2.09789	+	3.63364i	−0.309316	+	0.535752i
$47$	9.37418	+	3.41192i	1.36737	+	0.497680i	0.918324	−	0.395831i	$-0.129543\pi$
$47$	9.37418	+	3.41192i	1.36737	+	0.497680i	0.449042	+	0.893511i	$0.351765\pi$
$48$	0.548787	−	1.50778i	0.0792106	−	0.217629i
$49$	−0.447467	+	0.775035i	−0.0639238	+	0.110719i
$50$	−2.71466	−	4.70192i	−0.383911	−	0.664953i
$51$	−1.29988	−	7.37198i	−0.182019	−	1.03228i
$52$	−0.965788	−	0.810393i	−0.133931	−	0.112381i
$53$	−3.89576	−	4.64279i	−0.535124	−	0.637736i	0.428963	−	0.903322i	$-0.358879\pi$
$53$	−3.89576	−	4.64279i	−0.535124	−	0.637736i	−0.964087	+	0.265586i	$0.914435\pi$
$54$	5.41276	+	0.954416i	0.736584	+	0.129880i
$55$	−10.7109	+	0.00378177i	−1.44425	+	0.000509933i
$56$		−	2.47084i		−	0.330180i
$57$	0.990129	−	6.92362i	0.131146	−	0.917056i
$58$	6.74401			0.885532
$59$	−1.91054	−	5.24918i	−0.248732	−	0.683385i	−0.999734	−	0.0230845i	$-0.992651\pi$
$59$	−1.91054	−	5.24918i	−0.248732	−	0.683385i	0.751002	−	0.660300i	$-0.229571\pi$
$60$	−5.10307	−	0.899809i	−0.658804	−	0.116165i
$61$	−1.16401	−	1.38721i	−0.149036	−	0.177614i	0.686361	−	0.727261i	$-0.259207\pi$
$61$	−1.16401	−	1.38721i	−0.149036	−	0.177614i	−0.835397	+	0.549646i	$0.814762\pi$
$62$	2.97293	−	3.54300i	0.377563	−	0.449962i
$63$	1.03520	−	0.182534i	0.130423	−	0.0229971i
$64$	−0.500000	−	0.866025i	−0.0625000	−	0.108253i
$65$	−2.03576	+	3.52603i	−0.252505	+	0.437351i
$66$	−3.41927	+	4.07785i	−0.420883	+	0.501949i
$67$	−1.77098	+	4.86573i	−0.216360	+	0.594443i	−0.999629	−	0.0272394i	$-0.991328\pi$
$67$	−1.77098	+	4.86573i	−0.216360	+	0.594443i	0.783269	+	0.621682i	$0.213551\pi$
$68$	−4.04027	−	2.33265i	−0.489955	−	0.282876i
$69$	5.83035	−	3.36616i	0.701892	−	0.405238i
$70$	−7.85823	+	1.38562i	−0.939238	+	0.165613i
$71$	2.50094	−	2.98050i	0.296806	−	0.353720i	−0.596945	−	0.802282i	$-0.703619\pi$
$71$	2.50094	−	2.98050i	0.296806	−	0.353720i	0.893752	+	0.448562i	$0.148064\pi$
$72$	0.325898	−	0.273461i	0.0384074	−	0.0322276i
$73$	15.7116	+	2.77038i	1.83890	+	0.324248i	0.981656	−	0.190661i	$-0.0610630\pi$
$73$	15.7116	+	2.77038i	1.83890	+	0.324248i	0.857245	+	0.514909i	$0.172174\pi$
$74$	−2.30066	−	6.32101i	−0.267446	−	0.734802i
$75$			8.71159i			1.00593i
$76$	−2.90883	−	3.24634i	−0.333666	−	0.372380i
$77$	−2.80009	+	7.70164i	−0.319100	+	0.877683i
$78$	0.691882	+	1.90093i	0.0783402	+	0.215238i
$79$	−2.25135	+	12.7680i	−0.253297	+	1.43652i	0.547111	+	0.837060i	$0.315728\pi$
$79$	−2.25135	+	12.7680i	−0.253297	+	1.43652i	−0.800408	+	0.599456i	$0.795384\pi$
$80$	−2.47390	+	2.07585i	−0.276590	+	0.232087i
$81$	−5.77806	−	4.84837i	−0.642007	−	0.538708i
$82$	−0.0992381	−	0.562807i	−0.0109590	−	0.0621517i
$83$	6.86178	−	3.96165i	0.753178	−	0.434848i	−0.0736628	−	0.997283i	$-0.523469\pi$
$83$	6.86178	−	3.96165i	0.753178	−	0.434848i	0.826841	+	0.562435i	$0.190136\pi$
$84$	−1.98229	+	3.43343i	−0.216286	+	0.374618i
$85$	−5.15300	+	14.1577i	−0.558921	+	1.53562i
$86$	−1.40592	+	3.86274i	−0.151604	+	0.416530i
$87$	−9.37133	−	5.41054i	−1.00471	−	0.580071i
$88$	0.577079	+	3.26603i	0.0615168	+	0.348160i
$89$	9.27201	−	1.63490i	0.982831	−	0.173300i	0.340931	−	0.940088i	$-0.389258\pi$
$89$	9.27201	−	1.63490i	0.982831	−	0.173300i	0.641900	+	0.766789i	$0.278147\pi$
$90$	−1.05247	−	0.883126i	−0.110940	−	0.0930896i
$91$	2.00235	+	2.38631i	0.209904	+	0.250153i
$92$	0.728588	−	4.13203i	0.0759605	−	0.430794i
$93$	−6.97358	+	2.53818i	−0.723126	+	0.263197i
$94$	−9.97580			−1.02893
$95$	−8.69336	+	11.0717i	−0.891919	+	1.13593i
$96$			1.60455i			0.163763i
$97$	2.80742	+	7.71332i	0.285050	+	0.783169i	0.996740	+	0.0806753i	$0.0257077\pi$
$97$	2.80742	+	7.71332i	0.285050	+	0.783169i	−0.711690	+	0.702493i	$0.752070\pi$
$98$	0.155404	−	0.881338i	0.0156981	−	0.0890286i
$99$	−1.32573	+	0.483055i	−0.133240	+	0.0485488i
$100$	4.15910	+	3.48990i	0.415910	+	0.348990i
$101$	7.80438	−	1.37612i	0.776564	−	0.136929i	0.228701	−	0.973497i	$-0.426552\pi$
$101$	7.80438	−	1.37612i	0.776564	−	0.136929i	0.547864	+	0.836568i	$0.315441\pi$
$102$	3.74285	+	6.48281i	0.370598	+	0.641894i
$103$	5.52624	+	3.19058i	0.544517	+	0.314377i	0.746907	−	0.664928i	$-0.231538\pi$
$103$	5.52624	+	3.19058i	0.544517	+	0.314377i	−0.202391	+	0.979305i	$0.564871\pi$
$104$	1.18471	+	0.431201i	0.116171	+	0.0422827i
$105$	12.0313	+	4.37902i	1.17413	+	0.427349i
$106$	5.24875	+	3.03037i	0.509804	+	0.294335i
$107$	4.89556	+	8.47935i	0.473271	+	0.819730i	0.999532	−	0.0305934i	$-0.00973970\pi$
$107$	4.89556	+	8.47935i	0.473271	+	0.819730i	−0.526261	+	0.850323i	$0.676406\pi$
$108$	−5.41276	+	0.954416i	−0.520843	+	0.0918387i
$109$	−7.40352	−	6.21229i	−0.709128	−	0.595029i	0.215226	−	0.976564i	$-0.430951\pi$
$109$	−7.40352	−	6.21229i	−0.709128	−	0.595029i	−0.924354	+	0.381535i	$0.875396\pi$
$110$	10.0636	−	3.66688i	0.959528	−	0.349624i
$111$	−1.87423	+	10.6293i	−0.177894	+	1.00889i
$112$	0.845078	+	2.32183i	0.0798524	+	0.219393i
$113$		−	1.30770i		−	0.123019i	−0.998107	−	0.0615093i	$-0.980409\pi$
$113$		−	1.30770i		−	0.123019i	0.998107	−	0.0615093i	$-0.0195914\pi$
$114$	1.43760	+	6.84472i	0.134644	+	0.641067i
$115$	−13.5500			−1.26354
$116$	−6.33730	+	2.30659i	−0.588403	+	0.214161i
$117$	−0.0931377	+	0.528210i	−0.00861058	+	0.0488330i
$118$	3.59065	+	4.27917i	0.330546	+	0.393929i
$119$	8.83038	+	7.40957i	0.809480	+	0.679234i
$120$	5.10307	−	0.899809i	0.465845	−	0.0821410i
$121$	1.90248	−	10.8342i	0.172953	−	0.984930i
$122$	1.56826	+	0.905438i	0.141984	+	0.0819745i
$123$	−0.313626	+	0.861681i	−0.0282787	+	0.0776951i
$124$	−1.58186	+	4.34614i	−0.142056	+	0.390295i
$125$	0.693224	−	1.20070i	0.0620039	−	0.107394i
$126$	−0.910339	+	0.525584i	−0.0810994	+	0.0468228i
$127$	−2.52866	−	14.3407i	−0.224382	−	1.27254i	−0.863862	−	0.503728i	$-0.831961\pi$
$127$	−2.52866	−	14.3407i	−0.224382	−	1.27254i	0.639480	−	0.768808i	$-0.279150\pi$
$128$	0.766044	+	0.642788i	0.0677094	+	0.0568149i
$129$	5.05261	−	4.23964i	0.444858	−	0.373280i
$130$	0.707011	−	4.00966i	0.0620090	−	0.351670i
$131$	−6.06207	−	16.6554i	−0.529646	−	1.45519i	−0.859489	−	0.511154i	$-0.829218\pi$
$131$	−6.06207	−	16.6554i	−0.529646	−	1.45519i	0.329844	−	0.944036i	$-0.393004\pi$
$132$	1.81836	−	5.00139i	0.158268	−	0.435315i
$133$	5.68521	+	9.14738i	0.492970	+	0.793179i
$134$		−	5.17800i		−	0.447311i
$135$	6.07081	+	16.6794i	0.522493	+	1.43554i
$136$	4.59443	+	0.810122i	0.393969	+	0.0694674i
$137$	−3.01500	+	2.52989i	−0.257589	+	0.216143i	−0.762432	−	0.647068i	$-0.775995\pi$
$137$	−3.01500	+	2.52989i	−0.257589	+	0.216143i	0.504843	+	0.863211i	$0.331550\pi$
$138$	−4.32745	+	5.15725i	−0.368377	+	0.439014i
$139$	−7.33914	+	1.29409i	−0.622498	+	0.109763i	−0.475996	−	0.879447i	$-0.657912\pi$
$139$	−7.33914	+	1.29409i	−0.622498	+	0.109763i	−0.146502	+	0.989210i	$0.546801\pi$
$140$	6.91041	−	3.98973i	0.584036	−	0.337193i
$141$	13.8622	+	8.00332i	1.16740	+	0.674001i
$142$	−1.33072	+	3.65612i	−0.111672	+	0.306815i
$143$	−3.20411	−	2.68664i	−0.267941	−	0.224668i
$144$	−0.212715	+	0.368432i	−0.0177262	+	0.0307027i
$145$	10.8897	+	18.8615i	0.904341	+	1.56636i
$146$	−15.7116	+	2.77038i	−1.30030	+	0.229278i
$147$	−0.923019	+	1.10001i	−0.0761294	+	0.0907274i
$148$	4.32382	+	5.15293i	0.355416	+	0.423568i
$149$	15.7797	+	2.78239i	1.29273	+	0.227942i	0.777375	−	0.629037i	$-0.216551\pi$
$149$	15.7797	+	2.78239i	1.29273	+	0.227942i	0.515351	+	0.856979i	$0.327662\pi$
$150$	−2.97954	−	8.18622i	−0.243278	−	0.668402i
$151$	−18.5447			−1.50915			−0.754574	−	0.656215i	$-0.772156\pi$
$151$	−18.5447			−1.50915			−0.754574	+	0.656215i	$0.772156\pi$
$152$	3.84372	+	2.05568i	0.311767	+	0.166738i
$153$			1.98476i			0.160458i
$154$	−0.00289342	−	8.19486i	−0.000233159	−	0.660361i
$155$	14.7095	+	2.59368i	1.18149	+	0.208329i
$156$	−1.30031	−	1.54965i	−0.104108	−	0.124072i
$157$	−16.5562	−	13.8923i	−1.32133	−	1.10873i	−0.986021	−	0.166620i	$-0.946715\pi$
$157$	−16.5562	−	13.8923i	−1.32133	−	1.10873i	−0.335310	−	0.942108i	$-0.608841\pi$
$158$	−2.25135	−	12.7680i	−0.179108	−	1.01577i
$159$	−4.86237	−	8.42187i	−0.385611	−	0.667897i
$160$	1.61472	−	2.79678i	0.127655	−	0.221105i
$161$	−3.54575	+	9.74188i	−0.279445	+	0.767768i
$162$	7.08784	+	2.57976i	0.556873	+	0.202685i
$163$	6.00784	−	10.4059i	0.470571	−	0.815052i	−0.528863	−	0.848707i	$-0.677381\pi$
$163$	6.00784	−	10.4059i	0.470571	−	0.815052i	0.999434	+	0.0336550i	$0.0107147\pi$
$164$	0.285745	+	0.494924i	0.0223129	+	0.0386471i
$165$	−16.9260	−	2.97835i	−1.31769	−	0.231865i
$166$	−5.09300	+	6.06960i	−0.395294	+	0.471092i
$167$	−10.6302	+	8.91979i	−0.822589	+	0.690234i	−0.953577	−	0.301150i	$-0.902629\pi$
$167$	−10.6302	+	8.91979i	−0.822589	+	0.690234i	0.130988	+	0.991384i	$0.458185\pi$
$168$	0.688443	−	3.90435i	0.0531145	−	0.301227i
$169$	10.7224	−	3.90263i	0.824798	−	0.300202i
$170$		−	15.0664i		−	1.15554i
$171$	−0.577305	+	1.76225i	−0.0441476	+	0.134763i
$172$		−	4.11064i		−	0.313433i
$173$	10.2507	−	3.73096i	0.779349	−	0.283660i	0.0784479	−	0.996918i	$-0.475004\pi$
$173$	10.2507	−	3.73096i	0.779349	−	0.283660i	0.700901	+	0.713258i	$0.252781\pi$
$174$	10.6567	+	1.87906i	0.807881	+	0.142451i
$175$	−8.62299	−	10.2765i	−0.651837	−	0.776829i
$176$	−1.65933	−	2.87170i	−0.125076	−	0.216462i
$177$	−1.55642	−	8.82692i	−0.116988	−	0.663472i
$178$	−8.15367	+	4.70752i	−0.611143	+	0.352844i
$179$	−22.6991	−	13.1054i	−1.69661	−	0.979540i	−0.948931	−	0.315483i	$-0.897834\pi$
$179$	−22.6991	−	13.1054i	−1.69661	−	0.979540i	−0.747682	−	0.664057i	$-0.768833\pi$
$180$	1.29104	+	0.469901i	0.0962287	+	0.0350244i
$181$	4.61187	−	12.6710i	0.342798	−	0.941829i	−0.641781	−	0.766888i	$-0.721804\pi$
$181$	4.61187	−	12.6710i	0.342798	−	0.941829i	0.984579	−	0.174941i	$-0.0559736\pi$
$182$	−2.69776	−	1.55755i	−0.199972	−	0.115454i
$183$	−1.45282	−	2.51635i	−0.107395	−	0.186014i
$184$	0.728588	+	4.13203i	0.0537122	+	0.304617i
$185$	13.9636	−	16.6411i	1.02662	−	1.22348i
$186$	5.68491	−	4.77021i	0.416838	−	0.349769i
$187$	−13.4028	−	7.73180i	−0.980110	−	0.565406i
$188$	9.37418	−	3.41192i	0.683683	−	0.248840i
$189$	13.5804			0.987829
$190$	4.38234	−	13.3773i	0.317928	−	0.970491i
$191$	−23.8428			−1.72520			−0.862601	−	0.505884i	$-0.831166\pi$
$191$	−23.8428			−1.72520			−0.862601	+	0.505884i	$0.831166\pi$
$192$	−0.548787	−	1.50778i	−0.0396053	−	0.108815i
$193$	−0.678568	+	3.84835i	−0.0488444	+	0.277010i	−0.999441	−	0.0334171i	$-0.989361\pi$
$193$	−0.678568	+	3.84835i	−0.0488444	+	0.277010i	0.950597	+	0.310427i	$0.100472\pi$
$194$	−5.27622	−	6.28795i	−0.378810	−	0.451449i
$195$	−4.19929	+	5.00452i	−0.300717	+	0.358381i
$196$	0.155404	+	0.881338i	0.0111003	+	0.0629527i
$197$	−13.6838	+	7.90035i	−0.974931	+	0.562877i	−0.900736	−	0.434367i	$-0.856972\pi$
$197$	−13.6838	+	7.90035i	−0.974931	+	0.562877i	−0.0741949	+	0.997244i	$0.523639\pi$
$198$	1.08056	−	0.907348i	0.0767920	−	0.0644824i
$199$	13.1762	+	4.79575i	0.934037	+	0.339962i	0.763809	−	0.645443i	$-0.223327\pi$
$199$	13.1762	+	4.79575i	0.934037	+	0.339962i	0.170229	+	0.985405i	$0.445549\pi$
$200$	−5.10189	−	1.85694i	−0.360758	−	0.131305i
$201$	−4.15417	+	7.19523i	−0.293013	+	0.507513i
$202$	−6.86305	+	3.96239i	−0.482883	+	0.278792i
$203$	16.4102	−	2.89357i	1.15177	−	0.203089i
$204$	−5.73438	−	4.81172i	−0.401487	−	0.336888i
$205$	1.41381	−	1.18632i	0.0987445	−	0.0828565i
$206$	−6.28421	−	1.10808i	−0.437842	−	0.0772033i
$207$	−1.67735	+	0.610507i	−0.116584	+	0.0424332i
$208$	−1.26075			−0.0874171
$209$	−9.65130	−	10.7635i	−0.667595	−	0.744525i
$210$	−12.8034			−0.883519
$211$	19.6318	−	7.14538i	1.35151	−	0.491909i	0.438090	−	0.898931i	$-0.355655\pi$
$211$	19.6318	−	7.14538i	1.35151	−	0.491909i	0.913418	+	0.407023i	$0.133433\pi$
$212$	−5.96866	−	1.05244i	−0.409929	−	0.0722816i
$213$	4.78235	−	4.01287i	0.327681	−	0.274957i
$214$	−7.50043	−	6.29361i	−0.512719	−	0.430222i
$215$	−13.0734	+	2.30519i	−0.891599	+	0.157213i
$216$	4.75990	−	2.74813i	0.323870	−	0.186987i
$217$	5.71390	−	9.89677i	0.387885	−	0.671836i
$218$	9.08176	+	3.30549i	0.615094	+	0.223876i
$219$	24.0551	+	8.75533i	1.62549	+	0.591630i
$220$	−8.20256	+	6.88770i	−0.553017	+	0.464369i
$221$	−5.09376	+	2.94089i	−0.342644	+	0.197825i
$222$	−1.87423	−	10.6293i	−0.125790	−	0.713391i
$223$	3.55212	−	4.23325i	0.237868	−	0.283480i	−0.633884	−	0.773429i	$-0.718540\pi$
$223$	3.55212	−	4.23325i	0.237868	−	0.283480i	0.871751	+	0.489949i	$0.162985\pi$
$224$	−1.58823	−	1.89278i	−0.106118	−	0.126466i
$225$	0.401091	−	2.27470i	0.0267394	−	0.151647i
$226$	0.447261	+	1.22884i	0.0297514	+	0.0817412i
$227$	12.5215			0.831078			0.415539	−	0.909575i	$-0.363593\pi$
$227$	12.5215			0.831078			0.415539	+	0.909575i	$0.363593\pi$
$228$	−3.69193	−	5.94024i	−0.244504	−	0.393402i
$229$	15.8068			1.04454			0.522271	−	0.852779i	$-0.325085\pi$
$229$	15.8068			1.04454			0.522271	+	0.852779i	$0.325085\pi$
$230$	12.7328	−	4.63438i	0.839579	−	0.305582i
$231$	−6.57050	+	11.3897i	−0.432307	+	0.749389i
$232$	5.16621	−	4.33497i	0.339178	−	0.284605i
$233$	11.8922	−	14.1726i	0.779086	−	0.928479i	−0.219805	−	0.975544i	$-0.570542\pi$
$233$	11.8922	−	14.1726i	0.779086	−	0.928479i	0.998892	+	0.0470647i	$0.0149867\pi$
$234$	−0.0931377	−	0.528210i	−0.00608860	−	0.0345302i
$235$	−16.1081	−	27.9001i	−1.05078	−	1.82000i
$236$	−4.83767	−	2.79303i	−0.314905	−	0.181811i
$237$	−7.11503	+	19.5484i	−0.462171	+	1.26980i
$238$	−10.8321	−	3.94255i	−0.702138	−	0.255557i
$239$	−15.1171	−	8.72788i	−0.977846	−	0.564560i	−0.0762272	−	0.997090i	$-0.524287\pi$
$239$	−15.1171	−	8.72788i	−0.977846	−	0.564560i	−0.901619	+	0.432531i	$0.857621\pi$
$240$	−4.48757	+	2.59090i	−0.289671	+	0.167242i
$241$	3.43343	+	19.4720i	0.221167	+	1.25430i	0.869879	+	0.493266i	$0.164197\pi$
$241$	3.43343	+	19.4720i	0.221167	+	1.25430i	−0.648712	+	0.761034i	$0.724692\pi$
$242$	1.91778	+	10.8315i	0.123280	+	0.696277i
$243$	2.81935	+	3.35997i	0.180861	+	0.215542i
$244$	−1.78336	−	0.314455i	−0.114168	−	0.0201309i
$245$	2.71584	−	0.988486i	0.173509	−	0.0631521i
$246$		−	0.916982i		−	0.0584646i
$247$	−5.37813	+	1.12957i	−0.342202	+	0.0718729i
$248$		−	4.62506i		−	0.293692i
$249$	11.9466	−	4.34821i	0.757085	−	0.275557i
$250$	−0.240754	+	1.36539i	−0.0152266	+	0.0863546i
$251$	−4.13492	+	3.46961i	−0.260994	+	0.219000i	−0.763889	−	0.645348i	$-0.776713\pi$
$251$	−4.13492	+	3.46961i	−0.260994	+	0.219000i	0.502895	+	0.864347i	$0.332268\pi$
$252$	0.675678	−	0.805242i	0.0425637	−	0.0507255i
$253$	2.41161	−	13.7052i	0.151617	−	0.861641i
$254$	7.28099	+	12.6110i	0.456850	+	0.791287i
$255$	−12.0873	+	20.9359i	−0.756938	+	1.31106i
$256$	−0.939693	−	0.342020i	−0.0587308	−	0.0213763i
$257$	7.10605	−	19.5237i	0.443263	−	1.21786i	−0.494070	−	0.869422i	$-0.664491\pi$
$257$	7.10605	−	19.5237i	0.443263	−	1.21786i	0.937333	−	0.348434i	$-0.113286\pi$
$258$	−3.29786	+	5.71206i	−0.205316	+	0.355617i
$259$	−8.31028	−	14.3938i	−0.516376	−	0.894389i
$260$	0.707011	+	4.00966i	0.0438470	+	0.248668i
$261$	2.19786	+	1.84422i	0.136044	+	0.114154i
$262$	11.3930	+	13.5776i	0.703860	+	0.838827i
$263$	8.09809	+	1.42791i	0.499350	+	0.0880488i	0.417650	−	0.908608i	$-0.362854\pi$
$263$	8.09809	+	1.42791i	0.499350	+	0.0880488i	0.0817000	+	0.996657i	$0.473965\pi$
$264$	0.00187897	+	5.32168i	0.000115642	+	0.327527i
$265$			19.5728i			1.20235i
$266$	−8.47094	−	6.65127i	−0.519387	−	0.407816i
$267$	15.1069			0.924526
$268$	1.77098	+	4.86573i	0.108180	+	0.297222i
$269$	15.3360	+	2.70415i	0.935051	+	0.164875i	0.620358	−	0.784319i	$-0.286987\pi$
$269$	15.3360	+	2.70415i	0.935051	+	0.164875i	0.314693	+	0.949193i	$0.398098\pi$
$270$	−11.4094	−	13.5972i	−0.694354	−	0.827499i
$271$	10.6922	−	12.7424i	0.649503	−	0.774047i	−0.336336	−	0.941742i	$-0.609188\pi$
$271$	10.6922	−	12.7424i	0.649503	−	0.774047i	0.985839	+	0.167695i	$0.0536323\pi$
$272$	−4.59443	+	0.810122i	−0.278578	+	0.0491209i
$273$	2.49917	+	4.32869i	0.151257	+	0.261984i
$274$	1.96790	−	3.40851i	0.118885	−	0.205915i
$275$	13.7982	+	11.5698i	0.832066	+	0.697686i
$276$	2.30259	−	6.32630i	0.138599	−	0.380799i
$277$	19.5912	+	11.3110i	1.17712	+	0.679613i	0.955347	−	0.295485i	$-0.0954812\pi$
$277$	19.5912	+	11.3110i	1.17712	+	0.679613i	0.221776	+	0.975098i	$0.428815\pi$
$278$	6.45394	−	3.72618i	0.387081	−	0.223482i
$279$	1.93774	−	0.341676i	0.116010	−	0.0204556i
$280$	−5.12909	+	6.11262i	−0.306522	+	0.365299i
$281$	−10.6802	+	8.96172i	−0.637125	+	0.534611i	−0.903134	−	0.429359i	$-0.858739\pi$
$281$	−10.6802	+	8.96172i	−0.637125	+	0.534611i	0.266009	+	0.963971i	$0.414295\pi$
$282$	−15.7635	−	2.77952i	−0.938700	−	0.165518i
$283$	0.177309	+	0.487153i	0.0105399	+	0.0289582i	0.944851	−	0.327500i	$-0.106206\pi$
$283$	0.177309	+	0.487153i	0.0105399	+	0.0289582i	−0.934311	+	0.356459i	$0.883984\pi$
$284$		−	3.89076i		−	0.230874i
$285$	−16.8219	+	15.0730i	−0.996441	+	0.892846i
$286$	3.92976	+	1.42874i	0.232372	+	0.0844834i
$287$	−0.482953	−	1.32690i	−0.0285078	−	0.0783246i
$288$	0.0738750	−	0.418966i	0.00435313	−	0.0246878i
$289$	−3.65027	+	3.06294i	−0.214722	+	0.180173i
$290$	−16.6840	−	13.9995i	−0.979718	−	0.822081i
$291$	2.28706	+	12.9706i	0.134070	+	0.760348i
$292$	13.8165	−	7.97698i	0.808551	−	0.466817i
$293$	−4.78145	+	8.28172i	−0.279335	+	0.483823i	−0.971220	−	0.238185i	$-0.923447\pi$
$293$	−4.78145	+	8.28172i	−0.279335	+	0.483823i	0.691884	+	0.722008i	$0.256781\pi$
$294$	0.491128	−	1.34936i	0.0286432	−	0.0786965i
$295$	−6.17000	+	16.9519i	−0.359231	+	0.986979i
$296$	−5.82547	−	3.36334i	−0.338599	−	0.195490i
$297$	−17.9510	+	3.17178i	−1.04162	+	0.184045i
$298$	−15.7797	+	2.78239i	−0.914095	+	0.161180i
$299$	−4.05223	−	3.40022i	−0.234346	−	0.196640i
$300$	5.59970	+	6.67347i	0.323299	+	0.385293i
$301$	−1.76370	+	10.0024i	−0.101658	+	0.576531i
$302$	17.4263	−	6.34267i	1.00277	−	0.364979i
$303$	12.7157			0.730496
$304$	−4.31500	−	0.617077i	−0.247482	−	0.0353918i
$305$			5.84812i			0.334863i
$306$	−0.678827	−	1.86506i	−0.0388060	−	0.106618i
$307$	5.11471	−	29.0069i	0.291912	−	1.65551i	−0.387584	−	0.921834i	$-0.626690\pi$
$307$	5.11471	−	29.0069i	0.291912	−	1.65551i	0.679496	−	0.733679i	$-0.262199\pi$
$308$	2.80553	+	7.69966i	0.159860	+	0.438729i
$309$	7.84342	+	6.58141i	0.446197	+	0.374403i
$310$	−14.7095	+	2.59368i	−0.835441	+	0.147311i
$311$	−12.7514	−	22.0860i	−0.723064	−	1.25238i	−0.959766	−	0.280801i	$-0.909400\pi$
$311$	−12.7514	−	22.0860i	−0.723064	−	1.25238i	0.236703	−	0.971582i	$-0.423933\pi$
$312$	1.75191	+	1.01146i	0.0991822	+	0.0572629i
$313$	−4.35958	−	1.58676i	−0.246418	−	0.0896888i	0.215859	−	0.976425i	$-0.430745\pi$
$313$	−4.35958	−	1.58676i	−0.246418	−	0.0896888i	−0.462276	+	0.886736i	$0.652967\pi$
$314$	20.3092	+	7.39195i	1.14612	+	0.417152i
$315$	−2.93989	−	1.69735i	−0.165644	−	0.0956346i
$316$	6.48250	+	11.2280i	0.364669	+	0.631626i
$317$	22.1231	−	3.90091i	1.24256	−	0.219097i	0.486547	−	0.873654i	$-0.338256\pi$
$317$	22.1231	−	3.90091i	1.24256	−	0.219097i	0.756012	+	0.654557i	$0.227145\pi$
$318$	7.44958	+	6.25094i	0.417752	+	0.350535i
$319$	−21.0157	+	7.65751i	−1.17666	+	0.428738i
$320$	−0.560787	+	3.18038i	−0.0313490	+	0.177789i
$321$	5.37324	+	14.7629i	0.299905	+	0.823982i
$322$		−	10.3671i		−	0.577735i
$323$	−18.8732	+	7.57224i	−1.05013	+	0.421331i
$324$	−7.54272			−0.419040
$325$	6.43219	−	2.34113i	0.356794	−	0.129862i
$326$	−2.08650	+	11.8331i	−0.115561	+	0.655377i
$327$	−9.96791	−	11.8793i	−0.551226	−	0.656926i
$328$	−0.437786	−	0.367346i	−0.0241727	−	0.0202833i
$329$	−24.2742	+	4.28019i	−1.33828	+	0.235975i
$330$	16.9239	−	2.99031i	0.931631	−	0.164611i
$331$	3.48980	+	2.01484i	0.191817	+	0.110746i	0.592833	−	0.805326i	$-0.298009\pi$
$331$	3.48980	+	2.01484i	0.191817	+	0.110746i	−0.401016	+	0.916071i	$0.631343\pi$
$332$	2.70993	−	7.44547i	0.148727	−	0.408623i
$333$	0.978767	−	2.68914i	0.0536361	−	0.147364i
$334$	6.93836	−	12.0176i	0.379650	−	0.657574i
$335$	14.4817	−	8.36103i	0.791221	−	0.456812i
$336$	0.688443	+	3.90435i	0.0375576	+	0.213000i
$337$	7.85040	+	6.58727i	0.427638	+	0.358831i	0.831060	−	0.556183i	$-0.187735\pi$
$337$	7.85040	+	6.58727i	0.427638	+	0.358831i	−0.403421	+	0.915014i	$0.632179\pi$
$338$	−8.74096	+	7.33454i	−0.475446	+	0.398946i
$339$	0.364361	−	2.06640i	0.0197894	−	0.112231i
$340$	5.15300	+	14.1577i	0.279460	+	0.767811i
$341$	−5.24136	+	14.4164i	−0.283836	+	0.780689i
$342$	−0.0602362	−	1.85342i	−0.00325720	−	0.100222i
$343$		−	19.5071i		−	1.05329i
$344$	1.40592	+	3.86274i	0.0758022	+	0.208265i
$345$	−21.4113	−	3.77539i	−1.15275	−	0.203260i
$346$	−8.35648	+	7.01192i	−0.449247	+	0.376963i
$347$	−6.60754	+	7.87457i	−0.354712	+	0.422729i	−0.913664	−	0.406471i	$-0.866759\pi$
$347$	−6.60754	+	7.87457i	−0.354712	+	0.422729i	0.558952	+	0.829200i	$0.311204\pi$
$348$	−10.6567	+	1.87906i	−0.571258	+	0.100728i
$349$	12.1514	−	7.01564i	0.650452	−	0.375539i	−0.138177	−	0.990407i	$-0.544124\pi$
$349$	12.1514	−	7.01564i	0.650452	−	0.375539i	0.788629	+	0.614869i	$0.210791\pi$
$350$	11.6177	+	6.70749i	0.620993	+	0.358531i
$351$	−2.36999	+	6.51150i	−0.126501	+	0.347558i
$352$	2.54143	+	2.13099i	0.135459	+	0.113582i
$353$	−10.0454	+	17.3992i	−0.534665	+	0.926066i	0.464515	+	0.885565i	$0.346229\pi$
$353$	−10.0454	+	17.3992i	−0.534665	+	0.926066i	−0.999180	+	0.0405009i	$0.987105\pi$
$354$	4.48155	+	7.76226i	0.238191	+	0.412560i
$355$	−12.3741	+	2.18189i	−0.656750	+	0.115803i
$356$	6.05187	−	7.21234i	0.320749	−	0.382253i
$357$	11.8890	+	14.1688i	0.629233	+	0.749890i
$358$	25.8125	+	4.55144i	1.36423	+	0.240551i
$359$	5.82455	+	16.0028i	0.307408	+	0.844597i	0.993160	+	0.116761i	$0.0372513\pi$
$359$	5.82455	+	16.0028i	0.307408	+	0.844597i	−0.685752	+	0.727835i	$0.740526\pi$
$360$	−1.37390			−0.0724109
$361$	−18.9599	+	1.23370i	−0.997890	+	0.0649314i
$362$			13.4842i			0.708715i
$363$	6.02495	−	16.5898i	0.316228	−	0.870741i
$364$	3.06778	+	0.540933i	0.160796	+	0.0283526i
$365$	−33.1180	−	39.4685i	−1.73347	−	2.06587i
$366$	2.22585	+	1.86771i	0.116347	+	0.0976266i
$367$	4.41344	+	25.0299i	0.230380	+	1.30655i	0.852129	+	0.523332i	$0.175311\pi$
$367$	4.41344	+	25.0299i	0.230380	+	1.30655i	−0.621749	+	0.783216i	$0.713578\pi$
$368$	−2.09789	−	3.63364i	−0.109360	−	0.189417i
$369$	0.121564	−	0.210555i	0.00632837	−	0.0109611i
$370$	−7.42985	+	20.4133i	−0.386260	+	1.06124i
$371$	14.0720	+	5.12179i	0.730583	+	0.265910i
$372$	−3.71056	+	6.42689i	−0.192384	+	0.333218i
$373$	8.65774	+	14.9957i	0.448281	+	0.776446i	0.998274	−	0.0587236i	$-0.0187031\pi$
$373$	8.65774	+	14.9957i	0.448281	+	0.776446i	−0.549993	+	0.835169i	$0.685370\pi$
$374$	15.2390	+	2.68149i	0.787987	+	0.138657i
$375$	1.42996	−	1.70416i	0.0738428	−	0.0880024i
$376$	−7.64190	+	6.41232i	−0.394101	+	0.330690i
$377$	−1.47644	+	8.37332i	−0.0760407	+	0.431248i
$378$	−12.7614	+	4.64477i	−0.656376	+	0.238901i
$379$			21.3493i			1.09664i	0.836269	+	0.548320i	$0.184732\pi$
$379$			21.3493i			1.09664i	−0.836269	+	0.548320i	$0.815268\pi$
$380$	0.457255	+	14.0694i	0.0234567	+	0.721745i
$381$		−	23.3654i		−	1.19704i
$382$	22.4049	−	8.15471i	1.14633	−	0.417231i
$383$	0.180277	+	0.0317877i	0.00921171	+	0.00162427i	0.178252	−	0.983985i	$-0.442956\pi$
$383$	0.180277	+	0.0317877i	0.00921171	+	0.00162427i	−0.169040	+	0.985609i	$0.554067\pi$
$384$	1.03138	+	1.22915i	0.0526325	+	0.0627250i
$385$	22.9146	−	13.2405i	1.16783	−	0.674799i
$386$	−0.678568	−	3.84835i	−0.0345382	−	0.195876i
$387$	−1.51449	+	0.874393i	−0.0769860	+	0.0444479i
$388$	7.10863	+	4.10417i	0.360886	+	0.208358i
$389$	−29.7244	−	10.8188i	−1.50709	−	0.548534i	−0.549201	−	0.835690i	$-0.685068\pi$
$389$	−29.7244	−	10.8188i	−1.50709	−	0.548534i	−0.957884	+	0.287156i	$0.907290\pi$
$390$	2.23440	−	6.13895i	0.113143	−	0.310858i
$391$	−16.9521	−	9.78728i	−0.857303	−	0.494964i
$392$	−0.447467	−	0.775035i	−0.0226005	−	0.0391452i
$393$	−4.93847	−	28.0074i	−0.249113	−	1.41279i
$394$	10.1565	−	12.1040i	0.511677	−	0.609793i
$395$	32.0741	−	26.9134i	1.61382	−	1.35416i
$396$	−0.705063	+	1.22220i	−0.0354307	+	0.0614179i
$397$	18.1512	−	6.60650i	0.910983	−	0.331571i	0.156337	−	0.987704i	$-0.450031\pi$
$397$	18.1512	−	6.60650i	0.910983	−	0.331571i	0.754645	+	0.656133i	$0.227809\pi$
$398$	−14.0218			−0.702851
$399$	6.43490	+	16.0385i	0.322148	+	0.802928i
$400$	5.42931			0.271466
$401$	−2.91130	−	7.99874i	−0.145384	−	0.399438i	0.845532	−	0.533925i	$-0.179284\pi$
$401$	−2.91130	−	7.99874i	−0.145384	−	0.399438i	−0.990915	+	0.134487i	$0.957061\pi$
$402$	1.44273	−	8.18212i	0.0719567	−	0.408087i
$403$	3.74812	+	4.46683i	0.186707	+	0.222509i
$404$	5.09394	−	6.07073i	0.253433	−	0.302030i
$405$	4.22986	+	23.9887i	0.210184	+	1.19201i
$406$	−14.4309	+	8.33170i	−0.716195	+	0.413495i
$407$	14.3465	+	17.0853i	0.711131	+	0.846886i
$408$	7.03426	+	2.56026i	0.348248	+	0.126752i
$409$	−6.55719	−	2.38662i	−0.324232	−	0.118011i	0.174776	−	0.984608i	$-0.444080\pi$
$409$	−6.55719	−	2.38662i	−0.324232	−	0.118011i	−0.499008	+	0.866597i	$0.666302\pi$
$410$	−0.922797	+	1.59833i	−0.0455737	+	0.0789359i
$411$	−5.46911	+	3.15759i	−0.269771	+	0.155753i
$412$	6.28421	−	1.10808i	0.309601	−	0.0545910i
$413$	10.5732	+	8.87193i	0.520271	+	0.436559i
$414$	1.36739	−	1.14738i	0.0672036	−	0.0563905i
$415$	−25.1991	−	4.44329i	−1.23698	−	0.218112i
$416$	1.18471	−	0.431201i	0.0580854	−	0.0211414i
$417$	−11.9577			−0.585569
$418$	12.7506	+	6.81342i	0.623651	+	0.333255i
$419$	−4.56395			−0.222963			−0.111482	−	0.993766i	$-0.535560\pi$
$419$	−4.56395			−0.222963			−0.111482	+	0.993766i	$0.535560\pi$
$420$	12.0313	−	4.37902i	0.587066	−	0.213674i
$421$	−22.5656	−	3.97892i	−1.09978	−	0.193921i	−0.405833	−	0.913947i	$-0.633018\pi$
$421$	−22.5656	−	3.97892i	−1.09978	−	0.193921i	−0.693947	+	0.720027i	$0.744130\pi$
$422$	−16.0040	+	13.4289i	−0.779061	+	0.653710i
$423$	−3.25109	−	2.72799i	−0.158073	−	0.132639i
$424$	5.96866	−	1.05244i	0.289864	−	0.0511108i
$425$	21.9359	−	12.6647i	1.06405	−	0.614329i
$426$	−3.12146	+	5.40652i	−0.151235	+	0.261947i
$427$	4.20455	+	1.53033i	0.203472	+	0.0740579i
$428$	9.20064	+	3.34876i	0.444730	+	0.161868i
$429$	−4.31446	−	5.13809i	−0.208304	−	0.248070i
$430$	11.4966	−	6.63754i	0.554414	−	0.320091i
$431$	−2.18981	−	12.4190i	−0.105479	−	0.598203i	−0.991028	−	0.133656i	$-0.957328\pi$
$431$	−2.18981	−	12.4190i	−0.105479	−	0.598203i	0.885549	−	0.464547i	$-0.153783\pi$
$432$	−3.53293	+	4.21038i	−0.169978	+	0.202572i
$433$	−3.13406	−	3.73503i	−0.150614	−	0.179494i	0.685462	−	0.728108i	$-0.259600\pi$
$433$	−3.13406	−	3.73503i	−0.150614	−	0.179494i	−0.836076	+	0.548614i	$0.815156\pi$
$434$	−1.98442	+	11.2542i	−0.0952551	+	0.540218i
$435$	11.9523	+	32.8386i	0.573067	+	1.57449i
$436$	−9.66460			−0.462851
$437$	−12.2048	−	13.6209i	−0.583834	−	0.651575i
$438$	−25.5989			−1.22316
$439$	37.0940	−	13.5011i	1.77040	−	0.644373i	0.770423	−	0.637533i	$-0.220045\pi$
$439$	37.0940	−	13.5011i	1.77040	−	0.644373i	0.999977	−	0.00684024i	$-0.00217733\pi$
$440$	5.35215	−	9.27776i	0.255154	−	0.442300i
$441$	0.291657	−	0.244729i	0.0138884	−	0.0116538i
$442$	3.78073	−	4.50570i	0.179831	−	0.214314i
$443$	−0.533510	−	3.02569i	−0.0253478	−	0.143755i	0.969507	−	0.245062i	$-0.0788085\pi$
$443$	−0.533510	−	3.02569i	−0.0253478	−	0.143755i	−0.994855	+	0.101308i	$0.967697\pi$
$444$	5.39663	+	9.34724i	0.256113	+	0.443601i
$445$	−26.3318	−	15.2027i	−1.24825	−	0.720676i
$446$	−1.89004	+	5.19285i	−0.0894962	+	0.245889i
$447$	24.1594	+	8.79331i	1.14270	+	0.415909i
$448$	2.13981	+	1.23542i	0.101097	+	0.0583682i
$449$	−17.9021	+	10.3358i	−0.844854	+	0.487777i	−0.858911	−	0.512124i	$-0.828859\pi$
$449$	−17.9021	+	10.3358i	−0.844854	+	0.487777i	0.0140572	+	0.999901i	$0.495525\pi$
$450$	0.401091	+	2.27470i	0.0189076	+	0.107230i
$451$	0.948287	+	1.64114i	0.0446531	+	0.0772784i
$452$	−0.840576	−	1.00176i	−0.0395374	−	0.0471188i
$453$	−29.3038	−	5.16705i	−1.37681	−	0.242769i
$454$	−11.7663	+	4.28259i	−0.552221	+	0.200992i
$455$		−	10.0601i		−	0.471623i
$456$	5.50096	+	4.31929i	0.257606	+	0.202269i
$457$		−	36.7121i		−	1.71732i	−0.512545	−	0.858660i	$-0.671297\pi$
$457$		−	36.7121i		−	1.71732i	0.512545	−	0.858660i	$-0.328703\pi$
$458$	−14.8535	+	5.40624i	−0.694060	+	0.252617i
$459$	−4.45264	+	25.2522i	−0.207832	+	1.17867i
$460$	−10.3799	+	8.70978i	−0.483966	+	0.406096i
$461$	−18.9255	+	22.5545i	−0.881446	+	1.05047i	0.116909	+	0.993143i	$0.462701\pi$
$461$	−18.9255	+	22.5545i	−0.881446	+	1.05047i	−0.998356	+	0.0573243i	$0.981743\pi$
$462$	2.27873	−	12.9501i	0.106016	−	0.602492i
$463$	0.650543	+	1.12677i	0.0302333	+	0.0523656i	0.880746	−	0.473589i	$-0.157042\pi$
$463$	0.650543	+	1.12677i	0.0302333	+	0.0523656i	−0.850513	+	0.525954i	$0.823708\pi$
$464$	−3.37201	+	5.84049i	−0.156541	+	0.271138i
$465$	22.5208	+	8.19690i	1.04438	+	0.380122i
$466$	−6.32773	+	17.3853i	−0.293126	+	0.805358i
$467$	−11.6213	+	20.1287i	−0.537770	+	0.931445i	0.461254	+	0.887268i	$0.347400\pi$
$467$	−11.6213	+	20.1287i	−0.537770	+	0.931445i	−0.999024	+	0.0441768i	$0.985934\pi$
$468$	0.268179	+	0.464500i	0.0123966	+	0.0214715i
$469$	−2.22166	−	12.5997i	−0.102587	−	0.581798i
$470$	24.6791	+	20.7082i	1.13836	+	0.955200i
$471$	−22.2909	−	26.5652i	−1.02711	−	1.22406i
$472$	5.50119	+	0.970009i	0.253213	+	0.0446483i
$473$	−0.00481367	−	13.6335i	−0.000221333	−	0.626867i
$474$		−	20.8030i		−	0.955511i
$475$	23.1605	−	4.86441i	1.06268	−	0.223195i
$476$	11.5272			0.528350
$477$	0.881869	+	2.42292i	0.0403780	+	0.110938i
$478$	17.1906	+	3.03116i	0.786279	+	0.138642i
$479$	−12.8005	−	15.2550i	−0.584868	−	0.697019i	0.389743	−	0.920924i	$-0.372564\pi$
$479$	−12.8005	−	15.2550i	−0.584868	−	0.697019i	−0.974611	+	0.223905i	$0.928120\pi$
$480$	3.33079	−	3.96949i	0.152029	−	0.181181i
$481$	8.35180	−	1.47265i	0.380809	−	0.0671469i
$482$	−9.88618	−	17.1234i	−0.450303	−	0.779948i
$483$	−8.31724	+	14.4059i	−0.378448	+	0.655491i
$484$	−5.50673	−	9.52239i	−0.250306	−	0.432836i
$485$	9.06640	−	24.9097i	0.411684	−	1.13109i
$486$	−3.79850	−	2.19307i	−0.172304	−	0.0994795i
$487$	28.7541	−	16.6012i	1.30297	−	0.752272i	0.322060	−	0.946719i	$-0.395625\pi$
$487$	28.7541	−	16.6012i	1.30297	−	0.752272i	0.980913	+	0.194447i	$0.0622913\pi$
$488$	1.78336	−	0.314455i	0.0807291	−	0.0142347i
$489$	12.3928	−	14.7691i	0.560421	−	0.667883i
$490$	−2.21398	+	1.85775i	−0.100017	+	0.0839244i
$491$	17.1354	+	3.02144i	0.773311	+	0.136356i	0.546360	−	0.837550i	$-0.316013\pi$
$491$	17.1354	+	3.02144i	0.773311	+	0.136356i	0.226951	+	0.973906i	$0.427124\pi$
$492$	0.313626	+	0.861681i	0.0141394	+	0.0388476i
$493$			31.4629i			1.41702i
$494$	4.66745	−	2.90088i	0.209999	−	0.130517i
$495$	4.28246	+	1.55697i	0.192482	+	0.0699808i
$496$	1.58186	+	4.34614i	0.0710278	+	0.195147i
$497$	−1.66936	+	9.46742i	−0.0748811	+	0.424672i
$498$	−9.73896	+	8.17196i	−0.436413	+	0.366194i
$499$	17.7585	+	14.9011i	0.794978	+	0.667066i	0.946972	−	0.321316i	$-0.104125\pi$
$499$	17.7585	+	14.9011i	0.794978	+	0.667066i	−0.151994	+	0.988381i	$0.548569\pi$
$500$	−0.240754	−	1.36539i	−0.0107669	−	0.0610619i
$501$	−19.2828	+	11.1329i	−0.861492	+	0.497383i
$502$	2.69888	−	4.67459i	0.120457	−	0.208637i
$503$	10.0349	−	27.5705i	0.447432	−	1.22931i	−0.487074	−	0.873361i	$-0.661936\pi$
$503$	10.0349	−	27.5705i	0.447432	−	1.22931i	0.934506	−	0.355948i	$-0.115842\pi$
$504$	−0.359521	+	0.987775i	−0.0160143	+	0.0439990i
$505$	−22.1639	−	12.7963i	−0.986278	−	0.569428i
$506$	2.42129	+	13.7035i	0.107640	+	0.609196i
$507$	18.0306	−	3.17927i	0.800765	−	0.141197i
$508$	−11.1551	−	9.36026i	−0.494929	−	0.415294i
$509$	12.1950	+	14.5334i	0.540532	+	0.644181i	0.965307	−	0.261118i	$-0.0840911\pi$
$509$	12.1950	+	14.5334i	0.540532	+	0.644181i	−0.424775	+	0.905299i	$0.639647\pi$
$510$	4.19789	−	23.8074i	0.185886	−	1.05421i
$511$	−37.0424	+	13.4823i	−1.63866	+	0.596424i
$512$	1.00000			0.0441942
$513$	−11.2986	+	21.1261i	−0.498843	+	0.932740i
$514$			20.7767i			0.916421i
$515$	−7.04821	−	19.3648i	−0.310581	−	0.853315i
$516$	1.14533	−	6.49551i	0.0504205	−	0.285949i
$517$	31.0867	−	11.3270i	1.36719	−	0.498163i
$518$	12.7321	+	10.6835i	0.559416	+	0.469406i
$519$	17.2375	−	3.03943i	0.756640	−	0.133416i
$520$	−2.03576	−	3.52603i	−0.0892738	−	0.154627i
$521$	−18.4746	−	10.6663i	−0.809386	−	0.467299i	0.0373565	−	0.999302i	$-0.488106\pi$
$521$	−18.4746	−	10.6663i	−0.809386	−	0.467299i	−0.846743	+	0.532003i	$0.821440\pi$
$522$	−2.69607	−	0.981290i	−0.118004	−	0.0429499i
$523$	7.52533	+	2.73899i	0.329060	+	0.119768i	0.501267	−	0.865293i	$-0.332868\pi$
$523$	7.52533	+	2.73899i	0.329060	+	0.119768i	−0.172207	+	0.985061i	$0.555090\pi$
$524$	−15.3497	−	8.86215i	−0.670555	−	0.387145i
$525$	−10.7625	−	18.6412i	−0.469713	−	0.813568i
$526$	−8.09809	+	1.42791i	−0.353094	+	0.0622599i
$527$	16.5292	+	13.8696i	0.720023	+	0.604171i
$528$	−1.82189	−	5.00010i	−0.0792875	−	0.217601i
$529$	−0.936920	+	5.31354i	−0.0407357	+	0.231023i
$530$	−6.69429	−	18.3924i	−0.290782	−	0.798916i
$531$			2.37647i			0.103130i
$532$	10.2349	+	3.35292i	0.443741	+	0.145368i
$533$	0.720504			0.0312085
$534$	−14.1958	+	5.16686i	−0.614313	+	0.223592i
$535$	5.49073	−	31.1395i	0.237385	−	1.34628i
$536$	−3.32835	−	3.96658i	−0.143763	−	0.171330i
$537$	−32.2170	−	27.0333i	−1.39027	−	1.16657i
$538$	−15.3360	+	2.70415i	−0.661181	+	0.116584i
$539$	0.516448	+	2.92288i	0.0222450	+	0.125898i
$540$	15.3718	+	8.87494i	0.661499	+	0.381917i
$541$	3.01436	−	8.28187i	0.129597	−	0.356066i	−0.857875	−	0.513859i	$-0.828216\pi$
$541$	3.01436	−	8.28187i	0.129597	−	0.356066i	0.987472	+	0.157793i	$0.0504379\pi$
$542$	−5.68918	+	15.6309i	−0.244371	+	0.671405i
$543$	10.8180	−	18.7374i	0.464246	−	0.804098i
$544$	4.04027	−	2.33265i	0.173225	−	0.100012i
$545$	5.41979	+	30.7371i	0.232158	+	1.31663i
$546$	−3.82895	−	3.21287i	−0.163864	−	0.137498i
$547$	−23.8376	+	20.0021i	−1.01922	+	0.855228i	−0.989529	−	0.144331i	$-0.953897\pi$
$547$	−23.8376	+	20.0021i	−1.01922	+	0.855228i	−0.0296913	+	0.999559i	$0.509452\pi$
$548$	−0.683446	+	3.87601i	−0.0291953	+	0.165575i
$549$	0.263492	+	0.723938i	0.0112456	+	0.0308969i
$550$	−16.9232	−	6.15278i	−0.721608	−	0.262356i
$551$	−9.15158	+	27.9357i	−0.389871	+	1.19010i
$552$			6.73231i			0.286546i
$553$	−10.9564	−	30.1026i	−0.465915	−	1.28009i
$554$	−22.2783	−	3.92827i	−0.946516	−	0.166896i
$555$	26.7014	−	22.4052i	1.13341	−	0.951047i
$556$	−4.79029	+	5.70884i	−0.203153	+	0.242109i
$557$	23.0534	−	4.06494i	0.976805	−	0.172237i	0.337613	−	0.941285i	$-0.390380\pi$
$557$	23.0534	−	4.06494i	0.976805	−	0.172237i	0.639191	+	0.769048i	$0.279269\pi$
$558$	−1.70402	+	0.983818i	−0.0721370	+	0.0416483i
$559$	−4.48816	−	2.59124i	−0.189829	−	0.109598i
$560$	2.72913	−	7.49823i	0.115327	−	0.316858i
$561$	−19.0244	−	15.9519i	−0.803212	−	0.673492i
$562$	6.97098	−	12.0741i	0.294053	−	0.509315i
$563$	17.9899	+	31.1595i	0.758185	+	1.31322i	0.943775	+	0.330588i	$0.107247\pi$
$563$	17.9899	+	31.1595i	0.758185	+	1.31322i	−0.185590	+	0.982627i	$0.559420\pi$
$564$	15.7635	−	2.77952i	0.663761	−	0.117039i
$565$	−2.71460	+	3.23513i	−0.114204	+	0.136103i
$566$	−0.333232	−	0.397131i	−0.0140068	−	0.0166927i
$567$	18.3537	+	3.23626i	0.770785	+	0.135910i
$568$	1.33072	+	3.65612i	0.0558358	+	0.153408i
$569$	7.76762			0.325635			0.162818	−	0.986656i	$-0.447942\pi$
$569$	7.76762			0.325635			0.162818	+	0.986656i	$0.447942\pi$
$570$	10.6521	−	19.9174i	0.446168	−	0.834247i
$571$			7.43622i			0.311196i	0.987820	+	0.155598i	$0.0497305\pi$
$571$			7.43622i			0.311196i	−0.987820	+	0.155598i	$0.950270\pi$
$572$	−4.18142	+	0.00147637i	−0.174834	+	6.17301e-5i
$573$	−37.6756	−	6.64323i	−1.57392	−	0.277525i
$574$	0.907655	+	1.08170i	0.0378848	+	0.0451493i
$575$	17.4506	+	14.6428i	0.727741	+	0.610647i
$576$	0.0738750	+	0.418966i	0.00307812	+	0.0174569i
$577$	22.6689	+	39.2638i	0.943721	+	1.63457i	0.758293	+	0.651914i	$0.226034\pi$
$577$	22.6689	+	39.2638i	0.943721	+	1.63457i	0.185428	+	0.982658i	$0.440633\pi$
$578$	2.38254	−	4.12669i	0.0991008	−	0.171648i
$579$	−2.14450	+	5.89198i	−0.0891226	+	0.244862i
$580$	20.4660	+	7.44900i	0.849803	+	0.309303i
$581$	−9.78862	+	16.9544i	−0.406100	+	0.703386i
$582$	−6.58533	−	11.4061i	−0.272971	−	0.472799i
$583$	−19.7970	−	3.48354i	−0.819909	−	0.144274i
$584$	−10.2550	+	12.2214i	−0.424355	+	0.505727i
$585$	1.32690	−	1.11340i	0.0548604	−	0.0460334i
$586$	1.66058	−	9.41762i	0.0685980	−	0.389038i
$587$	11.3961	−	4.14784i	0.470367	−	0.171200i	−0.0959513	−	0.995386i	$-0.530589\pi$
$587$	11.3961	−	4.14784i	0.470367	−	0.171200i	0.566319	+	0.824186i	$0.308367\pi$
$588$			1.43596i			0.0592181i
$589$	10.6419	+	17.1226i	0.438492	+	0.705524i
$590$		−	18.0399i		−	0.742690i
$591$	−23.8240	+	8.67122i	−0.979988	+	0.356686i
$592$	6.62448	+	1.16808i	0.272265	+	0.0480076i
$593$	−17.7705	−	21.1781i	−0.729747	−	0.869679i	0.265792	−	0.964030i	$-0.414367\pi$
$593$	−17.7705	−	21.1781i	−0.729747	−	0.869679i	−0.995539	+	0.0943517i	$0.969922\pi$
$594$	15.7836	−	9.12009i	0.647609	−	0.374202i
$595$	−6.46433	−	36.6610i	−0.265012	−	1.50296i
$596$	13.8765	−	8.01158i	0.568402	−	0.328167i
$597$	19.4844	+	11.2493i	0.797445	+	0.460405i
$598$	4.97079	+	1.80922i	0.203271	+	0.0739845i
$599$	−1.57488	+	4.32694i	−0.0643477	+	0.176794i	−0.967699	−	0.252107i	$-0.918877\pi$
$599$	−1.57488	+	4.32694i	−0.0643477	+	0.176794i	0.903352	+	0.428900i	$0.141099\pi$
$600$	−7.54446	−	4.35580i	−0.308001	−	0.177825i
$601$	10.6273	+	18.4070i	0.433495	+	0.750836i	0.997172	−	0.0751598i	$-0.0239467\pi$
$601$	10.6273	+	18.4070i	0.433495	+	0.750836i	−0.563676	+	0.825996i	$0.690613\pi$
$602$	−1.76370	−	10.0024i	−0.0718831	−	0.407669i
$603$	1.41598	−	1.68750i	0.0576631	−	0.0687202i
$604$	−14.2061	+	11.9203i	−0.578037	+	0.485031i
$605$	−27.1968	+	22.8535i	−1.10571	+	0.929128i
$606$	−11.9488	+	4.34901i	−0.485388	+	0.176667i
$607$	−26.2544			−1.06563			−0.532817	−	0.846231i	$-0.678867\pi$
$607$	−26.2544			−1.06563			−0.532817	+	0.846231i	$0.678867\pi$
$608$	4.26583	−	0.895954i	0.173002	−	0.0363357i
$609$	26.7372			1.08345
$610$	−2.00018	−	5.49544i	−0.0809848	−	0.222504i
$611$	2.18397	−	12.3859i	0.0883538	−	0.501079i
$612$	1.27578	+	1.52041i	0.0515702	+	0.0614590i
$613$	6.76610	−	8.06352i	0.273280	−	0.325682i	−0.611896	−	0.790938i	$-0.709593\pi$
$613$	6.76610	−	8.06352i	0.273280	−	0.325682i	0.885176	+	0.465255i	$0.154038\pi$
$614$	5.11471	+	29.0069i	0.206413	+	1.17062i
$615$	2.56460	−	1.48067i	0.103415	−	0.0597064i
$616$	−5.26977	−	6.27577i	−0.212325	−	0.252858i
$617$	15.3435	+	5.58456i	0.617704	+	0.224826i	0.631871	−	0.775074i	$-0.282287\pi$
$617$	15.3435	+	5.58456i	0.617704	+	0.224826i	−0.0141667	+	0.999900i	$0.504510\pi$
$618$	−9.62138	−	3.50190i	−0.387029	−	0.140867i
$619$	−1.83219	+	3.17345i	−0.0736421	+	0.127552i	−0.900495	−	0.434866i	$-0.856796\pi$
$619$	−1.83219	+	3.17345i	−0.0736421	+	0.127552i	0.826853	+	0.562418i	$0.190129\pi$
$620$	12.9353	−	7.46819i	0.519494	−	0.299930i
$621$	−22.7107	+	4.00451i	−0.911349	+	0.160695i
$622$	19.5362	+	16.3928i	0.783331	+	0.657293i
$623$	−17.8206	+	14.9532i	−0.713966	+	0.599088i
$624$	−1.99220	−	0.351278i	−0.0797516	−	0.0140624i
$625$	21.3020	−	7.75329i	0.852080	−	0.310132i
$626$	4.63936			0.185426
$627$	−12.2517	−	19.6972i	−0.489286	−	0.786632i
$628$	−21.6126			−0.862437
$629$	29.4894	−	10.7333i	1.17582	−	0.427964i
$630$	3.34312	+	0.589482i	0.133193	+	0.0234855i
$631$	−3.58163	+	3.00535i	−0.142583	+	0.119641i	−0.711289	−	0.702899i	$-0.751888\pi$
$631$	−3.58163	+	3.00535i	−0.142583	+	0.119641i	0.568707	+	0.822540i	$0.307444\pi$
$632$	−9.93177	−	8.33374i	−0.395065	−	0.331499i
$633$	33.0125	−	5.82099i	1.31213	−	0.231363i
$634$	−19.4548	+	11.2322i	−0.772647	+	0.446088i
$635$	−23.5136	+	40.7267i	−0.933107	+	1.61619i
$636$	−9.13826	−	3.32605i	−0.362356	−	0.131887i
$637$	1.06024	+	0.385896i	0.0420083	+	0.0152898i
$638$	17.1293	−	14.3835i	0.678156	−	0.569449i
$639$	−1.43348	+	0.827622i	−0.0567077	+	0.0327402i
$640$	−0.560787	−	3.18038i	−0.0221671	−	0.125716i
$641$	5.55350	−	6.61840i	0.219350	−	0.261411i	−0.645136	−	0.764068i	$-0.723199\pi$
$641$	5.55350	−	6.61840i	0.219350	−	0.261411i	0.864486	+	0.502656i	$0.167644\pi$
$642$	−10.0984	−	12.0348i	−0.398552	−	0.474975i
$643$	4.19387	−	23.7846i	0.165390	−	0.937974i	−0.783271	−	0.621680i	$-0.786450\pi$
$643$	4.19387	−	23.7846i	0.165390	−	0.937974i	0.948661	−	0.316294i	$-0.102438\pi$
$644$	3.54575	+	9.74188i	0.139722	+	0.383884i
$645$	−21.3005			−0.838706
$646$	15.1452	−	13.5706i	0.595878	−	0.533928i
$647$	25.0224			0.983734			0.491867	−	0.870670i	$-0.336315\pi$
$647$	25.0224			0.983734			0.491867	+	0.870670i	$0.336315\pi$
$648$	7.08784	−	2.57976i	0.278437	−	0.101343i
$649$	−16.0480	−	9.25776i	−0.629939	−	0.363399i
$650$	−5.24357	+	4.39988i	−0.205670	+	0.172577i
$651$	11.7864	−	14.0465i	0.461947	−	0.550527i
$652$	−2.08650	−	11.8331i	−0.0817137	−	0.463422i
$653$	14.5219	+	25.1527i	0.568287	+	0.984302i	0.996736	+	0.0807359i	$0.0257270\pi$
$653$	14.5219	+	25.1527i	0.568287	+	0.984302i	−0.428448	+	0.903566i	$0.640940\pi$
$654$	13.4297	+	7.75365i	0.525144	+	0.303192i
$655$	−19.5771	+	53.7877i	−0.764942	+	2.10166i
$656$	0.537024	+	0.195461i	0.0209673	+	0.00763147i
$657$	−5.87795	−	3.39364i	−0.229321	−	0.132398i
$658$	21.3463	−	12.3243i	0.832167	−	0.480452i
$659$	0.951669	+	5.39718i	0.0370717	+	0.210244i	0.997717	−	0.0675339i	$-0.0215131\pi$
$659$	0.951669	+	5.39718i	0.0370717	+	0.210244i	−0.960645	+	0.277778i	$0.910402\pi$
$660$	−14.8805	+	8.59829i	−0.579224	+	0.334688i
$661$	−8.32173	−	9.91745i	−0.323678	−	0.385744i	0.579528	−	0.814952i	$-0.303237\pi$
$661$	−8.32173	−	9.91745i	−0.323678	−	0.385744i	−0.903205	+	0.429208i	$0.858793\pi$
$662$	−3.96846	−	0.699746i	−0.154238	−	0.0271964i
$663$	−8.86842	+	3.22784i	−0.344421	+	0.125359i
$664$			7.92330i			0.307484i
$665$	4.92394	−	34.4313i	0.190942	−	1.33519i
$666$			2.86172i			0.110890i
$667$	−26.5899	+	9.67791i	−1.02956	+	0.374730i
$668$	−2.40967	+	13.6659i	−0.0932328	+	0.528750i
$669$	6.79245	−	5.69954i	0.262611	−	0.220357i
$670$	−10.7487	+	12.8098i	−0.415260	+	0.494887i
$671$	−5.91512	−	1.04084i	−0.228351	−	0.0401812i
$672$	−1.98229	−	3.43343i	−0.0764686	−	0.132447i
$673$	−23.2550	+	40.2789i	−0.896415	+	1.55264i	−0.0643718	+	0.997926i	$0.520504\pi$
$673$	−23.2550	+	40.2789i	−0.896415	+	1.55264i	−0.832043	+	0.554711i	$0.812829\pi$
$674$	−9.62994	−	3.50501i	−0.370931	−	0.135008i
$675$	10.2062	−	28.0413i	0.392837	−	1.07931i
$676$	5.70526	−	9.88180i	0.219433	−	0.380069i
$677$	−16.2348	−	28.1195i	−0.623953	−	1.08072i	−0.988742	−	0.149629i	$-0.952192\pi$
$677$	−16.2348	−	28.1195i	−0.623953	−	1.08072i	0.364789	−	0.931090i	$-0.381141\pi$
$678$	0.364361	+	2.06640i	0.0139932	+	0.0793595i
$679$	−15.5365	−	13.0367i	−0.596238	−	0.500303i
$680$	−9.68446	−	11.5415i	−0.371382	−	0.442596i
$681$	19.7860	+	3.48881i	0.758202	+	0.133692i
$682$	−0.00541607	−	15.3396i	−0.000207392	−	0.587383i
$683$		−	15.8949i		−	0.608202i	−0.952640	−	0.304101i	$-0.901644\pi$
$683$		−	15.8949i		−	0.608202i	0.952640	−	0.304101i	$-0.0983561\pi$
$684$	0.690512	+	1.72105i	0.0264024	+	0.0658059i
$685$	12.7105			0.485642
$686$	6.67184	+	18.3307i	0.254732	+	0.699870i
$687$	24.9774	+	4.40420i	0.952949	+	0.168031i
$688$	−2.64227	−	3.14893i	−0.100736	−	0.120052i
$689$	−4.91157	+	5.85339i	−0.187116	+	0.222996i
$690$	21.4113	−	3.77539i	0.815115	−	0.143727i
$691$	−7.06967	−	12.2450i	−0.268943	−	0.465823i	0.699646	−	0.714489i	$-0.253341\pi$
$691$	−7.06967	−	12.2450i	−0.268943	−	0.465823i	−0.968589	+	0.248667i	$0.920008\pi$
$692$	5.45430	−	9.44713i	0.207342	−	0.359126i
$693$	2.24003	−	2.67148i	0.0850916	−	0.101481i
$694$	3.51580	−	9.65958i	0.133458	−	0.366673i
$695$	20.8426	+	12.0335i	0.790606	+	0.456457i
$696$	9.37133	−	5.41054i	0.355219	−	0.205086i
$697$	2.62567	−	0.462976i	0.0994543	−	0.0175365i
$698$	−9.01913	+	10.7486i	−0.341379	+	0.406840i
$699$	22.7406	−	19.0817i	0.860130	−	0.721734i
$700$	−13.2112	−	2.32949i	−0.499336	−	0.0880464i
$701$	1.80240	+	4.95204i	0.0680755	+	0.187036i	0.969065	−	0.246804i	$-0.0793805\pi$
$701$	1.80240	+	4.95204i	0.0680755	+	0.187036i	−0.900990	+	0.433840i	$0.857158\pi$
$702$		−	6.92940i		−	0.261533i
$703$	29.3054	−	0.952426i	1.10528	−	0.0359214i
$704$	−3.11701	−	1.13325i	−0.117477	−	0.0427110i
$705$	−17.6799	−	48.5751i	−0.665863	−	1.82944i
$706$	3.48874	−	19.7856i	0.131301	−	0.744643i
$707$	−14.9998	+	12.5863i	−0.564126	+	0.473358i
$708$	−6.86613	−	5.76136i	−0.258045	−	0.216525i
$709$	−3.78018	−	21.4384i	−0.141967	−	0.805138i	−0.969752	−	0.244092i	$-0.921510\pi$
$709$	−3.78018	−	21.4384i	−0.141967	−	0.805138i	0.827785	−	0.561046i	$-0.189601\pi$
$710$	10.8816	−	6.28251i	0.408380	−	0.235778i
$711$	2.75784	−	4.77673i	0.103427	−	0.179141i
$712$	−3.22013	+	8.84725i	−0.120680	+	0.331565i
$713$	−6.63714	+	18.2354i	−0.248563	+	0.682921i
$714$	−16.0180	−	9.24800i	−0.599459	−	0.346098i
$715$	2.34959	+	13.2977i	0.0878695	+	0.497306i
$716$	−25.8125	+	4.55144i	−0.964659	+	0.170095i
$717$	−21.4558	−	18.0036i	−0.801283	−	0.672356i
$718$	−10.9466	−	13.0456i	−0.408523	−	0.486858i
$719$	−0.542811	+	3.07843i	−0.0202434	+	0.114806i	−0.993255	−	0.115950i	$-0.963009\pi$
$719$	−0.542811	+	3.07843i	−0.0202434	+	0.114806i	0.973012	+	0.230756i	$0.0741199\pi$
$720$	1.29104	−	0.469901i	0.0481144	−	0.0175122i
$721$	−15.7668			−0.587187
$722$	17.3945	−	7.64396i	0.647358	−	0.284479i
$723$			31.7257i			1.17989i
$724$	−4.61187	−	12.6710i	−0.171399	−	0.470915i
$725$	6.35819	−	36.0591i	0.236137	−	1.33920i
$726$	0.0124637	+	17.6500i	0.000462570	+	0.655053i
$727$	−20.3045	−	17.0375i	−0.753051	−	0.631885i	0.183257	−	0.983065i	$-0.441336\pi$
$727$	−20.3045	−	17.0375i	−0.753051	−	0.631885i	−0.936308	+	0.351180i	$0.885780\pi$
$728$	−3.06778	+	0.540933i	−0.113700	+	0.0200483i
$729$	14.8330	+	25.6914i	0.549369	+	0.951535i
$730$	44.6197	+	25.7612i	1.65145	+	0.953465i
$731$	−18.0209	−	6.55906i	−0.666526	−	0.242596i
$732$	−2.73040	−	0.993786i	−0.100919	−	0.0367314i
$733$	9.94044	+	5.73912i	0.367159	+	0.211979i	0.672216	−	0.740355i	$-0.265342\pi$
$733$	9.94044	+	5.73912i	0.367159	+	0.211979i	−0.305058	+	0.952334i	$0.598676\pi$
$734$	−12.7080	−	22.0109i	−0.469061	−	0.812437i
$735$	4.56691	−	0.805270i	0.168453	−	0.0297028i
$736$	3.21415	+	2.69699i	0.118475	+	0.0994123i
$737$	5.87937	+	16.1357i	0.216569	+	0.594367i
$738$	−0.0422188	+	0.239435i	−0.00155409	+	0.00881371i
$739$	−8.03464	−	22.0750i	−0.295559	−	0.812042i	−0.995228	−	0.0975748i	$-0.968891\pi$
$739$	−8.03464	−	22.0750i	−0.295559	−	0.812042i	0.699669	−	0.714467i	$-0.253331\pi$
$740$		−	21.7234i		−	0.798569i
$741$	−8.81309	+	0.286425i	−0.323757	+	0.0105221i
$742$	−14.9751			−0.549754
$743$	−45.6457	+	16.6137i	−1.67458	+	0.609497i	−0.992551	−	0.121830i	$-0.961124\pi$
$743$	−45.6457	+	16.6137i	−1.67458	+	0.609497i	−0.682027	+	0.731327i	$0.738902\pi$
$744$	1.28867	−	7.30838i	0.0472448	−	0.267938i
$745$	−33.2616	−	39.6397i	−1.21861	−	1.45229i
$746$	−13.2644	−	11.1302i	−0.485645	−	0.407505i
$747$	−3.31959	+	0.585334i	−0.121458	+	0.0214162i
$748$	−15.2371	+	2.69225i	−0.557122	+	0.0984384i
$749$	−20.9512	−	12.0962i	−0.765538	−	0.441984i
$750$	−0.760866	+	2.09046i	−0.0277829	+	0.0763328i
$751$	6.72580	−	18.4790i	0.245428	−	0.674308i	−0.754412	−	0.656401i	$-0.772078\pi$
$751$	6.72580	−	18.4790i	0.245428	−	0.674308i	0.999840	−	0.0179061i	$-0.00569999\pi$
$752$	4.98790	−	8.63929i	0.181890	−	0.315043i
$753$	−7.50060	+	4.33047i	−0.273337	+	0.157811i
$754$	−1.47644	−	8.37332i	−0.0537689	−	0.304938i
$755$	45.8777	+	38.4960i	1.66966	+	1.40101i
$756$	10.4032	−	8.72931i	0.378360	−	0.317482i
$757$	7.10130	−	40.2735i	0.258101	−	1.46376i	−0.529884	−	0.848070i	$-0.677764\pi$
$757$	7.10130	−	40.2735i	0.258101	−	1.46376i	0.787985	−	0.615694i	$-0.211124\pi$
$758$	−7.30189	−	20.0618i	−0.265216	−	0.728676i
$759$	7.62940	−	20.9847i	0.276930	−	0.761695i
$760$	−5.24170	−	13.0645i	−0.190136	−	0.473900i
$761$			51.0588i			1.85088i	0.378894	+	0.925440i	$0.376305\pi$
$761$			51.0588i			1.85088i	−0.378894	+	0.925440i	$0.623695\pi$
$762$	7.99143	+	21.9563i	0.289499	+	0.795392i
$763$	23.5169	+	4.14667i	0.851370	+	0.150120i
$764$	−18.2646	+	15.3258i	−0.660791	+	0.554469i
$765$	4.12005	−	4.91009i	0.148961	−	0.177525i
$766$	−0.180277	+	0.0317877i	−0.00651366	+	0.00114853i
$767$	−6.09908	+	3.52130i	−0.220225	+	0.127147i
$768$	−1.38958	−	0.802273i	−0.0501421	−	0.0289496i
$769$	−13.6761	+	37.5747i	−0.493172	+	1.35498i	0.404590	+	0.914498i	$0.367414\pi$
$769$	−13.6761	+	37.5747i	−0.493172	+	1.35498i	−0.897762	+	0.440481i	$0.854808\pi$
$770$	−17.0041	+	20.2793i	−0.612786	+	0.730814i
$771$	16.6686	−	28.8709i	0.600305	−	1.03976i
$772$	1.95386	+	3.38418i	0.0703209	+	0.121799i
$773$	−24.4034	+	4.30299i	−0.877731	+	0.154768i	−0.594318	−	0.804230i	$-0.702578\pi$
$773$	−24.4034	+	4.30299i	−0.877731	+	0.154768i	−0.283413	+	0.958998i	$0.591467\pi$
$774$	1.12410	−	1.33965i	0.0404049	−	0.0481527i
$775$	−16.1410	−	19.2361i	−0.579801	−	0.690980i
$776$	−8.08364	−	1.42536i	−0.290186	−	0.0511676i
$777$	−9.12115	−	25.0602i	−0.327220	−	0.899028i
$778$	31.6320			1.13406
$779$	2.46598	+	0.352653i	0.0883528	+	0.0126351i
$780$			6.53293i			0.233917i
$781$	−0.00455619	−	12.9042i	−0.000163033	−	0.461749i
$782$	19.2772	+	3.39909i	0.689350	+	0.121551i
$783$	23.8261	+	28.3949i	0.851476	+	1.01475i
$784$	0.685559	+	0.575252i	0.0244843	+	0.0205447i
$785$	12.1201	+	68.7364i	0.432584	+	2.45331i
$786$	14.2197	+	24.6293i	0.507201	+	0.878499i
$787$	11.3308	−	19.6255i	0.403900	−	0.699575i	−0.590293	−	0.807189i	$-0.700988\pi$
$787$	11.3308	−	19.6255i	0.403900	−	0.699575i	0.994193	+	0.107614i	$0.0343210\pi$
$788$	−5.40416	+	14.8478i	−0.192515	+	0.528931i
$789$	12.3985	+	4.51269i	0.441399	+	0.160656i
$790$	−20.9349	+	36.2603i	−0.744830	+	1.29008i
$791$	1.61557	+	2.79824i	0.0574429	+	0.0994941i
$792$	0.244525	−	1.38964i	0.00868882	−	0.0493787i
$793$	−1.46752	+	1.74892i	−0.0521132	+	0.0621061i
$794$	−14.7970	+	12.4162i	−0.525126	+	0.440633i
$795$	−5.45351	+	30.9284i	−0.193416	+	1.09692i
$796$	13.1762	−	4.79575i	0.467019	−	0.169981i
$797$			36.9749i			1.30972i	0.755751	+	0.654859i	$0.227272\pi$
$797$			36.9749i			1.30972i	−0.755751	+	0.654859i	$0.772728\pi$
$798$	−11.5323	−	12.8704i	−0.408239	−	0.455606i
$799$		−	46.5402i		−	1.64647i
$800$	−5.10189	+	1.85694i	−0.180379	+	0.0656526i
$801$	−3.94458	−	0.695536i	−0.139375	−	0.0245756i
$802$	5.47146	+	6.52063i	0.193204	+	0.230251i
$803$	45.8149	−	26.4728i	1.61677	−	0.934205i
$804$	1.44273	+	8.18212i	0.0508811	+	0.288561i
$805$	28.9945	−	16.7400i	1.02192	−	0.590007i
$806$	−5.04982	−	2.91552i	−0.177872	−	0.102695i
$807$	23.4800	+	8.54603i	0.826536	+	0.300834i
$808$	−2.71043	+	7.44685i	−0.0953526	+	0.261979i
$809$	−7.31542	−	4.22356i	−0.257196	−	0.148492i	0.365859	−	0.930670i	$-0.380775\pi$
$809$	−7.31542	−	4.22356i	−0.257196	−	0.148492i	−0.623055	+	0.782178i	$0.714109\pi$
$810$	−12.1794	−	21.0953i	−0.427941	−	0.741215i
$811$	−4.49657	−	25.5013i	−0.157896	−	0.895472i	−0.956090	−	0.293072i	$-0.905322\pi$
$811$	−4.49657	−	25.5013i	−0.157896	−	0.895472i	0.798194	−	0.602400i	$-0.205789\pi$
$812$	10.7110	−	12.7649i	0.375883	−	0.447960i
$813$	20.4458	−	17.1561i	0.717066	−	0.601690i
$814$	−19.3248	−	11.1481i	−0.677335	−	0.390741i
$815$	−36.4638	+	13.2718i	−1.27727	+	0.464889i
$816$	−7.48570			−0.262052
$817$	−14.0928	−	11.0655i	−0.493043	−	0.387131i
$818$	6.97802			0.243981
$819$	−0.453265	−	1.24533i	−0.0158384	−	0.0435155i
$820$	0.320484	−	1.81755i	0.0111918	−	0.0634718i
$821$	25.3675	+	30.2318i	0.885332	+	1.05510i	0.998108	+	0.0614773i	$0.0195812\pi$
$821$	25.3675	+	30.2318i	0.885332	+	1.05510i	−0.112776	+	0.993620i	$0.535974\pi$
$822$	4.05932	−	4.83771i	0.141585	−	0.168735i
$823$	0.182364	+	1.03424i	0.00635682	+	0.0360513i	0.987821	−	0.155593i	$-0.0497290\pi$
$823$	0.182364	+	1.03424i	0.00635682	+	0.0360513i	−0.981464	+	0.191645i	$0.938618\pi$
$824$	−5.52624	+	3.19058i	−0.192516	+	0.111149i
$825$	18.5799	+	22.1268i	0.646870	+	0.770357i
$826$	−12.9699	−	4.72066i	−0.451280	−	0.164253i
$827$	10.9159	+	3.97305i	0.379582	+	0.138156i	0.524762	−	0.851249i	$-0.324154\pi$
$827$	10.9159	+	3.97305i	0.379582	+	0.138156i	−0.145181	+	0.989405i	$0.546376\pi$
$828$	−0.892501	+	1.54586i	−0.0310166	+	0.0537223i
$829$	39.2453	−	22.6583i	1.36305	−	0.786955i	0.373017	−	0.927824i	$-0.378323\pi$
$829$	39.2453	−	22.6583i	1.36305	−	0.786955i	0.990028	+	0.140870i	$0.0449898\pi$
$830$	25.1991	−	4.44329i	0.874675	−	0.154229i
$831$	27.8059	+	23.3320i	0.964578	+	0.809377i
$832$	−0.965788	+	0.810393i	−0.0334827	+	0.0280953i
$833$	4.11171	+	0.725006i	0.142462	+	0.0251200i
$834$	11.2365	−	4.08976i	0.389089	−	0.141617i
$835$	44.8141			1.55086
$836$	−14.3120	−	2.04156i	−0.494989	−	0.0706088i
$837$	25.4205			0.878663
$838$	4.28871	−	1.56096i	0.148151	−	0.0539225i
$839$	−19.0211	−	3.35393i	−0.656680	−	0.115790i	−0.164627	−	0.986356i	$-0.552642\pi$
$839$	−19.0211	−	3.35393i	−0.656680	−	0.115790i	−0.492053	+	0.870565i	$0.663753\pi$
$840$	−9.80798	+	8.22987i	−0.338407	+	0.283958i
$841$	12.6257	+	10.5942i	0.435369	+	0.365318i
$842$	22.5656	−	3.97892i	0.777661	−	0.137123i
$843$	−19.3735	+	11.1853i	−0.667257	+	0.385241i
$844$	10.4459	−	18.0927i	0.359561	−	0.622778i
$845$	−34.6273	−	12.6033i	−1.19122	−	0.433567i
$846$	3.98805	+	1.45153i	0.137112	+	0.0499047i
$847$	9.31389	+	25.5336i	0.320029	+	0.877345i
$848$	−5.24875	+	3.03037i	−0.180243	+	0.104063i
$849$	0.144445	+	0.819188i	0.00495734	+	0.0281145i
$850$	−16.2814	+	19.4035i	−0.558449	+	0.665533i
$851$	18.1418	+	21.6205i	0.621892	+	0.741142i
$852$	1.08407	−	6.14807i	0.0371397	−	0.210629i
$853$	−10.9001	−	29.9477i	−0.373212	−	1.02539i	−0.974112	−	0.226067i	$-0.927413\pi$
$853$	−10.9001	−	29.9477i	−0.373212	−	1.02539i	0.600900	−	0.799324i	$-0.294809\pi$
$854$	−4.47439			−0.153110
$855$	5.08636	−	3.16123i	0.173950	−	0.108112i
$856$	−9.79111			−0.334653
$857$	−22.4514	+	8.17165i	−0.766926	+	0.279138i	−0.695710	−	0.718323i	$-0.744910\pi$
$857$	−22.4514	+	8.17165i	−0.766926	+	0.279138i	−0.0712158	+	0.997461i	$0.522688\pi$
$858$	5.81160	+	3.35259i	0.198405	+	0.114456i
$859$	−30.3173	+	25.4393i	−1.03441	+	0.867977i	−0.991370	−	0.131096i	$-0.958150\pi$
$859$	−30.3173	+	25.4393i	−1.03441	+	0.867977i	−0.0430447	+	0.999073i	$0.513706\pi$
$860$	−8.53306	+	10.1693i	−0.290975	+	0.346771i
$861$	−0.393438	−	2.23130i	−0.0134083	−	0.0760424i
$862$	6.30530	+	10.9211i	0.214759	+	0.371974i
$863$	26.3243	+	15.1983i	0.896089	+	0.517357i	0.875929	−	0.482440i	$-0.160249\pi$
$863$	26.3243	+	15.1983i	0.896089	+	0.517357i	0.0201594	+	0.999797i	$0.493583\pi$
$864$	1.87983	−	5.16480i	0.0639532	−	0.175710i
$865$	−33.1042	−	12.0489i	−1.12558	−	0.409676i
$866$	4.22251	+	2.43787i	0.143487	+	0.0828422i
$867$	−6.62147	+	3.82291i	−0.224877	+	0.129833i
$868$	−1.98442	−	11.2542i	−0.0673555	−	0.381992i
$869$	21.5132	+	37.2315i	0.729784	+	1.26299i
$870$	−22.4629	−	26.7703i	−0.761564	−	0.907597i
$871$	6.42897	+	1.13360i	0.217837	+	0.0384106i
$872$	9.08176	−	3.30549i	0.307547	−	0.111938i
$873$		−	3.49207i		−	0.118189i
$874$	16.1274	+	8.62516i	0.545516	+	0.291750i
$875$			3.42570i			0.115810i
$876$	24.0551	−	8.75533i	0.812745	−	0.295815i
$877$	−8.97794	+	50.9165i	−0.303164	+	1.71933i	0.328861	+	0.944378i	$0.393335\pi$
$877$	−8.97794	+	50.9165i	−0.303164	+	1.71933i	−0.632025	+	0.774948i	$0.717776\pi$
$878$	−30.2393	+	25.3738i	−1.02053	+	0.856324i
$879$	−9.86301	+	11.7543i	−0.332671	+	0.396462i
$880$	−1.85620	+	10.5488i	−0.0625724	+	0.355600i
$881$	24.5965	+	42.6024i	0.828678	+	1.43531i	0.899076	+	0.437794i	$0.144240\pi$
$881$	24.5965	+	42.6024i	0.828678	+	1.43531i	−0.0703974	+	0.997519i	$0.522427\pi$
$882$	−0.190365	+	0.329723i	−0.00640994	+	0.0111023i
$883$	18.4232	+	6.70548i	0.619989	+	0.225657i	0.632868	−	0.774260i	$-0.281878\pi$
$883$	18.4232	+	6.70548i	0.619989	+	0.225657i	−0.0128794	+	0.999917i	$0.504100\pi$
$884$	−2.01168	+	5.52706i	−0.0676603	+	0.185895i
$885$	−14.4729	+	25.0678i	−0.486501	+	0.842645i
$886$	1.53618	+	2.66075i	0.0516090	+	0.0893895i
$887$	−2.05800	−	11.6715i	−0.0691010	−	0.391891i	−0.999668	−	0.0257694i	$-0.991796\pi$
$887$	−2.05800	−	11.6715i	−0.0691010	−	0.391891i	0.930567	−	0.366122i	$-0.119315\pi$
$888$	−8.26812	−	6.93778i	−0.277460	−	0.232817i
$889$	23.1277	+	27.5626i	0.775679	+	0.924419i
$890$	29.9434	+	5.27984i	1.00371	+	0.176980i
$891$	−25.0164	+	0.00883273i	−0.838080	+	0.000295908i
$892$		−	5.52612i		−	0.185028i
$893$	13.5371	−	41.3226i	0.453002	−	1.38281i
$894$	−25.7099			−0.859868
$895$	28.9506	+	79.5412i	0.967713	+	2.65877i
$896$	−2.43331	−	0.429057i	−0.0812910	−	0.0143338i
$897$	−5.45582	−	6.50199i	−0.182164	−	0.217095i
$898$	13.2875	−	15.8354i	0.443408	−	0.528433i
$899$	30.7176	−	5.41634i	1.02449	−	0.180645i
$900$	−1.15489	−	2.00034i	−0.0384965	−	0.0666778i
$901$	−14.1376	+	24.4870i	−0.470991	+	0.815781i
$902$	−1.45240	−	1.21784i	−0.0483597	−	0.0405495i
$903$	−5.57390	+	15.3142i	−0.185488	+	0.509623i
$904$	1.13251	+	0.653852i	0.0376666	+	0.0217468i
$905$	−37.7124	+	21.7733i	−1.25360	+	0.723768i
$906$	29.3038	−	5.16705i	0.973554	−	0.171664i
$907$	−14.1554	+	16.8697i	−0.470022	+	0.560150i	−0.948020	−	0.318211i	$-0.896918\pi$
$907$	−14.1554	+	16.8697i	−0.470022	+	0.560150i	0.477998	+	0.878361i	$0.341362\pi$
$908$	9.59199	−	8.04864i	0.318321	−	0.267103i
$909$	−3.32021	−	0.585442i	−0.110124	−	0.0194179i
$910$	3.44075	+	9.45337i	0.114060	+	0.313376i
$911$		−	16.3332i		−	0.541144i	−0.962700	−	0.270572i	$-0.912787\pi$
$911$		−	16.3332i		−	0.541144i	0.962700	−	0.270572i	$-0.0872127\pi$
$912$	−6.64650	−	2.17736i	−0.220088	−	0.0720996i
$913$	8.97910	−	24.6970i	0.297165	−	0.817351i
$914$	12.5563	+	34.4981i	0.415325	+	1.14110i
$915$	−1.62944	+	9.24103i	−0.0538677	+	0.305499i
$916$	12.1087	−	10.1604i	0.400083	−	0.335710i
$917$	33.5481	+	28.1502i	1.10786	+	0.929603i
$918$	−4.45264	−	25.2522i	−0.146959	−	0.833447i
$919$	−23.3316	+	13.4705i	−0.769640	+	0.444352i	−0.832746	−	0.553655i	$-0.813233\pi$
$919$	−23.3316	+	13.4705i	−0.769640	+	0.444352i	0.0631062	+	0.998007i	$0.479899\pi$
$920$	6.77501	−	11.7347i	0.223365	−	0.386880i
$921$	16.1642	−	44.4108i	0.532629	−	1.46339i
$922$	10.0700	−	27.6672i	0.331639	−	0.911170i
$923$	−4.24809	−	2.45264i	−0.139828	−	0.0807295i
$924$	2.28788	+	12.9485i	0.0752657	+	0.425973i
$925$	−35.9664	+	6.34185i	−1.18257	+	0.208519i
$926$	−0.996690	−	0.836322i	−0.0327533	−	0.0274833i
$927$	−1.74499	−	2.07960i	−0.0573131	−	0.0683031i
$928$	1.17109	−	6.64156i	0.0384428	−	0.218020i
$929$	−45.3747	+	16.5150i	−1.48870	+	0.541841i	−0.953106	−	0.302638i	$-0.902133\pi$
$929$	−45.3747	+	16.5150i	−1.48870	+	0.541841i	−0.535590	+	0.844478i	$0.679911\pi$
$930$	−23.9661			−0.785880
$931$	3.43988	+	1.83970i	0.112737	+	0.0602936i
$932$		−	18.5010i		−	0.606022i
$933$	−13.9956	−	38.4525i	−0.458195	−	1.25888i
$934$	4.03604	−	22.8895i	0.132063	−	0.748968i
$935$	17.1071	+	46.9499i	0.559463	+	1.53543i
$936$	−0.410874	−	0.344765i	−0.0134299	−	0.0112690i
$937$	−29.1087	+	5.13265i	−0.950939	+	0.167676i	−0.627538	−	0.778586i	$-0.715937\pi$
$937$	−29.1087	+	5.13265i	−0.950939	+	0.167676i	−0.323401	+	0.946262i	$0.604826\pi$
$938$	6.39701	+	11.0799i	0.208870	+	0.361773i
$939$	−6.44676	−	3.72204i	−0.210382	−	0.121464i
$940$	−30.2734	−	11.0186i	−0.987410	−	0.359388i
$941$	37.6023	+	13.6861i	1.22580	+	0.446155i	0.872158	−	0.489225i	$-0.162720\pi$
$941$	37.6023	+	13.6861i	1.22580	+	0.446155i	0.353644	+	0.935380i	$0.384943\pi$
$942$	30.0324	+	17.3392i	0.978509	+	0.564943i
$943$	1.19892	+	2.07659i	0.0390422	+	0.0676230i
$944$	−5.50119	+	0.970009i	−0.179049	+	0.0315711i
$945$	−33.5965	−	28.1908i	−1.09290	−	0.917048i
$946$	4.66744	+	12.8096i	0.151752	+	0.416476i
$947$	6.70726	−	38.0388i	0.217957	−	1.23609i	−0.657745	−	0.753241i	$-0.728490\pi$
$947$	6.70726	−	38.0388i	0.217957	−	1.23609i	0.875702	−	0.482853i	$-0.160399\pi$
$948$	7.11503	+	19.5484i	0.231085	+	0.634902i
$949$		−	20.1139i		−	0.652925i
$950$	−20.1000	+	12.4924i	−0.652131	+	0.405307i
$951$	36.0452			1.16885
$952$	−10.8321	+	3.94255i	−0.351069	+	0.127779i
$953$	−4.55523	+	25.8340i	−0.147558	+	0.836845i	0.817719	+	0.575618i	$0.195238\pi$
$953$	−4.55523	+	25.8340i	−0.147558	+	0.836845i	−0.965277	+	0.261227i	$0.915873\pi$
$954$	−1.65737	−	1.97518i	−0.0536594	−	0.0639488i
$955$	58.9846	+	49.4940i	1.90870	+	1.60159i
$956$	−17.1906	+	3.03116i	−0.555983	+	0.0980348i
$957$	−35.3420	+	6.24462i	−1.14245	+	0.201860i
$958$	17.2460	+	9.95700i	0.557194	+	0.321696i
$959$	3.32606	−	9.13828i	0.107404	−	0.295091i
$960$	−1.77228	+	4.86930i	−0.0572000	+	0.157156i
$961$	−4.80440	+	8.32147i	−0.154981	+	0.268435i
$962$	−7.34445	+	4.24032i	−0.236794	+	0.136713i
$963$	−0.723318	−	4.10214i	−0.0233086	−	0.132190i
$964$	15.1465	+	12.7094i	0.487836	+	0.409343i
$965$	9.66729	−	8.11182i	0.311201	−	0.261129i
$966$	2.88855	−	16.3818i	0.0929375	−	0.527075i
$967$	2.70329	+	7.42723i	0.0869319	+	0.238843i	0.975539	−	0.219825i	$-0.0705487\pi$
$967$	2.70329	+	7.42723i	0.0869319	+	0.238843i	−0.888607	+	0.458669i	$0.848326\pi$
$968$	8.43148	+	7.06471i	0.270998	+	0.227068i
$969$	−31.9327	+	6.70684i	−1.02583	+	0.215455i
$970$			26.5084i			0.851133i
$971$	−9.45239	−	25.9702i	−0.303342	−	0.833424i	−0.993914	−	0.110161i	$-0.964863\pi$
$971$	−9.45239	−	25.9702i	−0.303342	−	0.833424i	0.690572	−	0.723264i	$-0.257359\pi$
$972$	4.31950	+	0.761644i	0.138548	+	0.0244297i
$973$	14.1057	−	11.8360i	0.452206	−	0.379446i
$974$	−21.3421	+	25.4345i	−0.683844	+	0.814974i
$975$	10.8163	−	1.90720i	0.346397	−	0.0610792i
$976$	−1.56826	+	0.905438i	−0.0501989	+	0.0289824i
$977$	−24.2177	−	13.9821i	−0.774794	−	0.447328i	0.0597881	−	0.998211i	$-0.480958\pi$
$977$	−24.2177	−	13.9821i	−0.774794	−	0.447328i	−0.834582	+	0.550884i	$0.814291\pi$
$978$	−6.59406	+	18.1170i	−0.210855	+	0.579319i
$979$	20.0633	−	23.9277i	0.641227	−	0.764733i
$980$	1.44507	−	2.50293i	0.0461611	−	0.0799533i
$981$	2.05580	+	3.56075i	0.0656367	+	0.113686i
$982$	−17.1354	+	3.02144i	−0.546814	+	0.0964180i
$983$	13.4446	−	16.0226i	0.428815	−	0.511042i	−0.507765	−	0.861496i	$-0.669528\pi$
$983$	13.4446	−	16.0226i	0.428815	−	0.511042i	0.936580	+	0.350454i	$0.113973\pi$
$984$	−0.589424	−	0.702449i	−0.0187902	−	0.0223932i
$985$	50.2523	+	8.86083i	1.60117	+	0.282330i
$986$	−10.7609	−	29.5654i	−0.342698	−	0.941556i
$987$	−39.5499			−1.25889
$988$	−3.39381	+	4.32230i	−0.107971	+	0.137511i
$989$		−	17.2473i		−	0.548432i
$990$	−4.55671	+	0.00160887i	−0.144822	+	5.11334e-5i
$991$	−36.4531	−	6.42767i	−1.15797	−	0.204182i	−0.438519	−	0.898722i	$-0.644497\pi$
$991$	−36.4531	−	6.42767i	−1.15797	−	0.204182i	−0.719454	+	0.694540i	$0.755608\pi$
$992$	−2.97293	−	3.54300i	−0.0943907	−	0.112490i
$993$	4.95310	+	4.15614i	0.157182	+	0.131891i
$994$	−1.66936	−	9.46742i	−0.0529489	−	0.300288i
$995$	−22.6414	−	39.2160i	−0.717780	−	1.24323i
$996$	6.35666	−	11.0101i	0.201418	−	0.348867i
$997$	1.26444	−	3.47401i	0.0400451	−	0.110023i	−0.918058	−	0.396445i	$-0.870244\pi$
$997$	1.26444	−	3.47401i	0.0400451	−	0.110023i	0.958104	+	0.286422i	$0.0924660\pi$
$998$	−21.7840	−	7.92872i	−0.689560	−	0.250979i
$999$	18.4858	−	32.0183i	0.584864	−	1.01301i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	418.2.q.b.109.7	yes	60
11.10	odd	2		418.2.q.a.109.7	✓	60
19.15	odd	18		418.2.q.a.395.7	yes	60
209.186	even	18	inner	418.2.q.b.395.7	yes	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
418.2.q.a.109.7	✓	60	11.10	odd	2
418.2.q.a.395.7	yes	60	19.15	odd	18
418.2.q.b.109.7	yes	60	1.1	even	1	trivial
418.2.q.b.395.7	yes	60	209.186	even	18	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 418 = 2 \cdot 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	418.q (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.939693 + 0.342020i) q^{2} +(1.58017 + 0.278627i) q^{3} +(0.766044 - 0.642788i) q^{4} +(-2.47390 - 2.07585i) q^{5} +(-1.58017 + 0.278627i) q^{6} +(-2.13981 + 1.23542i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(-0.399773 - 0.145505i) q^{9} +O(q^{10})\)	\(q+(-0.939693 + 0.342020i) q^{2} +(1.58017 + 0.278627i) q^{3} +(0.766044 - 0.642788i) q^{4} +(-2.47390 - 2.07585i) q^{5} +(-1.58017 + 0.278627i) q^{6} +(-2.13981 + 1.23542i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(-0.399773 - 0.145505i) q^{9} +(3.03469 + 1.10454i) q^{10} +(2.53993 - 2.13278i) q^{11} +(1.38958 - 0.802273i) q^{12} +(-0.218926 - 1.24159i) q^{13} +(1.58823 - 1.89278i) q^{14} +(-3.33079 - 3.96949i) q^{15} +(0.173648 - 0.984808i) q^{16} +(-1.59563 - 4.38395i) q^{17} +0.425429 q^{18} +(-0.141589 - 4.35660i) q^{19} -3.22944 q^{20} +(-3.72549 + 1.35597i) q^{21} +(-1.65730 + 2.87287i) q^{22} +(3.21415 - 2.69699i) q^{23} +(-1.03138 + 1.22915i) q^{24} +(0.942791 + 5.34683i) q^{25} +(0.630374 + 1.09184i) q^{26} +(-4.75990 - 2.74813i) q^{27} +(-0.845078 + 2.32183i) q^{28} +(-6.33730 - 2.30659i) q^{29} +(4.48757 + 2.59090i) q^{30} +(-4.00542 + 2.31253i) q^{31} +(0.173648 + 0.984808i) q^{32} +(4.60777 - 2.66247i) q^{33} +(2.99880 + 3.57383i) q^{34} +(7.85823 + 1.38562i) q^{35} +(-0.399773 + 0.145505i) q^{36} +6.72668i q^{37} +(1.62309 + 4.04544i) q^{38} -2.02293i q^{39} +(3.03469 - 1.10454i) q^{40} +(-0.0992381 + 0.562807i) q^{41} +(3.03705 - 2.54839i) q^{42} +(2.64227 - 3.14893i) q^{43} +(0.574773 - 3.26644i) q^{44} +(0.686950 + 1.18983i) q^{45} +(-2.09789 + 3.63364i) q^{46} +(9.37418 + 3.41192i) q^{47} +(0.548787 - 1.50778i) q^{48} +(-0.447467 + 0.775035i) q^{49} +(-2.71466 - 4.70192i) q^{50} +(-1.29988 - 7.37198i) q^{51} +(-0.965788 - 0.810393i) q^{52} +(-3.89576 - 4.64279i) q^{53} +(5.41276 + 0.954416i) q^{54} +(-10.7109 + 0.00378177i) q^{55} -2.47084i q^{56} +(0.990129 - 6.92362i) q^{57} +6.74401 q^{58} +(-1.91054 - 5.24918i) q^{59} +(-5.10307 - 0.899809i) q^{60} +(-1.16401 - 1.38721i) q^{61} +(2.97293 - 3.54300i) q^{62} +(1.03520 - 0.182534i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(-2.03576 + 3.52603i) q^{65} +(-3.41927 + 4.07785i) q^{66} +(-1.77098 + 4.86573i) q^{67} +(-4.04027 - 2.33265i) q^{68} +(5.83035 - 3.36616i) q^{69} +(-7.85823 + 1.38562i) q^{70} +(2.50094 - 2.98050i) q^{71} +(0.325898 - 0.273461i) q^{72} +(15.7116 + 2.77038i) q^{73} +(-2.30066 - 6.32101i) q^{74} +8.71159i q^{75} +(-2.90883 - 3.24634i) q^{76} +(-2.80009 + 7.70164i) q^{77} +(0.691882 + 1.90093i) q^{78} +(-2.25135 + 12.7680i) q^{79} +(-2.47390 + 2.07585i) q^{80} +(-5.77806 - 4.84837i) q^{81} +(-0.0992381 - 0.562807i) q^{82} +(6.86178 - 3.96165i) q^{83} +(-1.98229 + 3.43343i) q^{84} +(-5.15300 + 14.1577i) q^{85} +(-1.40592 + 3.86274i) q^{86} +(-9.37133 - 5.41054i) q^{87} +(0.577079 + 3.26603i) q^{88} +(9.27201 - 1.63490i) q^{89} +(-1.05247 - 0.883126i) q^{90} +(2.00235 + 2.38631i) q^{91} +(0.728588 - 4.13203i) q^{92} +(-6.97358 + 2.53818i) q^{93} -9.97580 q^{94} +(-8.69336 + 11.0717i) q^{95} +1.60455i q^{96} +(2.80742 + 7.71332i) q^{97} +(0.155404 - 0.881338i) q^{98} +(-1.32573 + 0.483055i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q - 3 q^{3} + 3 q^{6} + 18 q^{7} - 30 q^{8} - 3 q^{9}+O(q^{10}) \) 60 * q - 3 * q^3 + 3 * q^6 + 18 * q^7 - 30 * q^8 - 3 * q^9	\( 60 q - 3 q^{3} + 3 q^{6} + 18 q^{7} - 30 q^{8} - 3 q^{9} + 3 q^{11} - 6 q^{13} - 12 q^{14} + 24 q^{15} + 6 q^{17} - 60 q^{18} + 30 q^{19} - 12 q^{20} - 12 q^{21} + 12 q^{22} - 3 q^{24} - 12 q^{25} + 6 q^{26} + 9 q^{27} - 6 q^{28} + 3 q^{29} - 9 q^{31} + 9 q^{33} - 6 q^{34} + 24 q^{35} - 3 q^{36} + 6 q^{38} - 15 q^{41} + 6 q^{42} + 3 q^{43} - 12 q^{44} - 48 q^{45} - 3 q^{46} + 54 q^{47} - 6 q^{48} + 6 q^{49} - 36 q^{50} + 45 q^{51} + 3 q^{52} + 24 q^{53} + 27 q^{54} - 48 q^{55} - 30 q^{57} + 24 q^{58} - 39 q^{59} + 12 q^{60} - 54 q^{61} + 66 q^{63} - 30 q^{64} - 30 q^{66} + 9 q^{67} + 27 q^{68} + 54 q^{69} - 24 q^{70} - 33 q^{71} + 6 q^{72} - 12 q^{74} + 18 q^{77} - 36 q^{79} - 93 q^{81} - 15 q^{82} + 36 q^{83} - 24 q^{84} + 60 q^{85} - 3 q^{86} - 54 q^{87} + 3 q^{88} - 3 q^{89} + 24 q^{90} - 12 q^{91} - 102 q^{93} + 12 q^{94} - 24 q^{95} - 6 q^{97} + 18 q^{98} + 75 q^{99}+O(q^{100}) \) 60 * q - 3 * q^3 + 3 * q^6 + 18 * q^7 - 30 * q^8 - 3 * q^9 + 3 * q^11 - 6 * q^13 - 12 * q^14 + 24 * q^15 + 6 * q^17 - 60 * q^18 + 30 * q^19 - 12 * q^20 - 12 * q^21 + 12 * q^22 - 3 * q^24 - 12 * q^25 + 6 * q^26 + 9 * q^27 - 6 * q^28 + 3 * q^29 - 9 * q^31 + 9 * q^33 - 6 * q^34 + 24 * q^35 - 3 * q^36 + 6 * q^38 - 15 * q^41 + 6 * q^42 + 3 * q^43 - 12 * q^44 - 48 * q^45 - 3 * q^46 + 54 * q^47 - 6 * q^48 + 6 * q^49 - 36 * q^50 + 45 * q^51 + 3 * q^52 + 24 * q^53 + 27 * q^54 - 48 * q^55 - 30 * q^57 + 24 * q^58 - 39 * q^59 + 12 * q^60 - 54 * q^61 + 66 * q^63 - 30 * q^64 - 30 * q^66 + 9 * q^67 + 27 * q^68 + 54 * q^69 - 24 * q^70 - 33 * q^71 + 6 * q^72 - 12 * q^74 + 18 * q^77 - 36 * q^79 - 93 * q^81 - 15 * q^82 + 36 * q^83 - 24 * q^84 + 60 * q^85 - 3 * q^86 - 54 * q^87 + 3 * q^88 - 3 * q^89 + 24 * q^90 - 12 * q^91 - 102 * q^93 + 12 * q^94 - 24 * q^95 - 6 * q^97 + 18 * q^98 + 75 * q^99

Introduction

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