LMFDB - Embedded newform 84.2.o.a.31.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [84,2,Mod(19,84)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(84, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 0, 5]))

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

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

chi := DirichletCharacter("84.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 84 = 2^{2} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	84.o (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:	$0.670743376979$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.562828176.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{7} + x^{6} + 2x^{5} - 6x^{4} + 4x^{3} + 4x^{2} - 16x + 16 $ x^8 - 2x^7 + x^6 + 2x^5 - 6x^4 + 4x^3 + 4x^2 - 16x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			31.1
Root			$-1.33790 - 0.458297i$ of defining polynomial
Character	$\chi$	$=$	84.31
Dual form			84.2.o.a.19.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.06584 - 0.929502i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(0.272050 + 1.98141i) q^{4} +(2.12403 - 1.22631i) q^{5} +(1.33790 - 0.458297i) q^{6} +(2.63169 + 0.272415i) q^{7} +(1.55176 - 2.36475i) q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(-1.06584 - 0.929502i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(0.272050 + 1.98141i) q^{4} +(2.12403 - 1.22631i) q^{5} +(1.33790 - 0.458297i) q^{6} +(2.63169 + 0.272415i) q^{7} +(1.55176 - 2.36475i) q^{8} +(-0.500000 - 0.866025i) q^{9} +(-3.40374 - 0.667235i) q^{10} +(-1.09586 - 0.632697i) q^{11} +(-1.85198 - 0.755103i) q^{12} +2.99744i q^{13} +(-2.55176 - 2.73651i) q^{14} +2.45262i q^{15} +(-3.85198 + 1.07809i) q^{16} +(1.58759 + 0.916595i) q^{17} +(-0.272050 + 1.38780i) q^{18} +(-2.07993 - 3.60254i) q^{19} +(3.00766 + 3.87495i) q^{20} +(-1.55176 + 2.14290i) q^{21} +(0.579927 + 1.69296i) q^{22} +(-5.83564 + 3.36921i) q^{23} +(1.27205 + 2.52624i) q^{24} +(0.507662 - 0.879296i) q^{25} +(2.78613 - 3.19481i) q^{26} +1.00000 q^{27} +(0.176187 + 5.28857i) q^{28} -9.42323 q^{29} +(2.27971 - 2.61411i) q^{30} +(4.71989 - 8.17509i) q^{31} +(5.10769 + 2.43135i) q^{32} +(1.09586 - 0.632697i) q^{33} +(-0.840146 - 2.45262i) q^{34} +(5.92385 - 2.64865i) q^{35} +(1.57993 - 1.22631i) q^{36} +(-3.75572 - 6.50509i) q^{37} +(-1.13169 + 5.77304i) q^{38} +(-2.59586 - 1.49872i) q^{39} +(0.396078 - 6.92573i) q^{40} -1.08966i q^{41} +(3.64577 - 0.841635i) q^{42} +6.27176i q^{43} +(0.955503 - 2.34348i) q^{44} +(-2.12403 - 1.22631i) q^{45} +(9.35158 + 1.83319i) q^{46} +(3.67579 + 6.36666i) q^{47} +(0.992338 - 3.87495i) q^{48} +(6.85158 + 1.43382i) q^{49} +(-1.35840 + 0.465320i) q^{50} +(-1.58759 + 0.916595i) q^{51} +(-5.93917 + 0.815456i) q^{52} +(0.0358262 - 0.0620528i) q^{53} +(-1.06584 - 0.929502i) q^{54} -3.10353 q^{55} +(4.72795 - 5.80056i) q^{56} +4.15985 q^{57} +(10.0437 + 8.75892i) q^{58} +(1.68345 - 2.91583i) q^{59} +(-4.85964 + 0.667235i) q^{60} +(-9.61496 + 5.55120i) q^{61} +(-12.6294 + 4.32623i) q^{62} +(-1.07993 - 2.41532i) q^{63} +(-3.18406 - 7.33906i) q^{64} +(3.67579 + 6.36666i) q^{65} +(-1.75611 - 0.344251i) q^{66} +(-2.43151 - 1.40383i) q^{67} +(-1.38425 + 3.39503i) q^{68} -6.73842i q^{69} +(-8.77582 - 2.68318i) q^{70} +2.92285i q^{71} +(-2.82381 - 0.161492i) q^{72} +(7.01910 + 4.05248i) q^{73} +(-2.04349 + 10.4244i) q^{74} +(0.507662 + 0.879296i) q^{75} +(6.57226 - 5.10126i) q^{76} +(-2.71162 - 1.96359i) q^{77} +(1.37372 + 4.01027i) q^{78} +(-1.54471 + 0.891841i) q^{79} +(-6.85964 + 7.01360i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-1.01284 + 1.16141i) q^{82} -5.33626 q^{83} +(-4.66813 - 2.49170i) q^{84} +4.49611 q^{85} +(5.82962 - 6.68473i) q^{86} +(4.71162 - 8.16076i) q^{87} +(-3.19669 + 1.60964i) q^{88} +(7.42323 - 4.28581i) q^{89} +(1.12403 + 3.28134i) q^{90} +(-0.816548 + 7.88834i) q^{91} +(-8.26338 - 10.6462i) q^{92} +(4.71989 + 8.17509i) q^{93} +(2.00000 - 10.2025i) q^{94} +(-8.83564 - 5.10126i) q^{95} +(-4.65946 + 3.20772i) q^{96} -7.10394i q^{97} +(-5.96998 - 7.89679i) q^{98} +1.26539i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + q^{2} - 4 q^{3} - q^{4} - 2 q^{6} + 2 q^{7} + 4 q^{8} - 4 q^{9}+O(q^{10}) $ 8 * q + q^2 - 4 * q^3 - q^4 - 2 * q^6 + 2 * q^7 + 4 * q^8 - 4 * q^9	$ 8 q + q^{2} - 4 q^{3} - q^{4} - 2 q^{6} + 2 q^{7} + 4 q^{8} - 4 q^{9} - 5 q^{10} + 6 q^{11} - q^{12} - 12 q^{14} - 17 q^{16} + q^{18} - 6 q^{19} + 22 q^{20} - 4 q^{21} - 6 q^{22} + 7 q^{24} + 2 q^{25} + 18 q^{26} + 8 q^{27} + 13 q^{28} - 16 q^{29} + 13 q^{30} + 6 q^{31} - 9 q^{32} - 6 q^{33} - 28 q^{34} - 12 q^{35} + 2 q^{36} + 6 q^{37} + 10 q^{38} - 6 q^{39} - 17 q^{40} + 9 q^{42} - 23 q^{44} + 24 q^{46} + 4 q^{47} + 10 q^{48} + 4 q^{49} + 2 q^{50} + 16 q^{52} - 4 q^{53} + q^{54} - 8 q^{55} + 41 q^{56} + 12 q^{57} + 37 q^{58} - 14 q^{59} - 23 q^{60} + 12 q^{61} - 48 q^{62} + 2 q^{63} + 2 q^{64} + 4 q^{65} - 15 q^{66} + 42 q^{67} - 26 q^{68} + 3 q^{70} - 11 q^{72} - 18 q^{73} - 10 q^{74} + 2 q^{75} + 44 q^{76} + 8 q^{77} - 6 q^{78} - 6 q^{79} - 39 q^{80} - 4 q^{81} - 10 q^{82} + 4 q^{83} - 14 q^{84} - 32 q^{85} + 36 q^{86} + 8 q^{87} - 37 q^{88} - 8 q^{90} - 34 q^{91} - 28 q^{92} + 6 q^{93} + 16 q^{94} - 24 q^{95} + 21 q^{96} - 53 q^{98}+O(q^{100}) $ 8 * q + q^2 - 4 * q^3 - q^4 - 2 * q^6 + 2 * q^7 + 4 * q^8 - 4 * q^9 - 5 * q^10 + 6 * q^11 - q^12 - 12 * q^14 - 17 * q^16 + q^18 - 6 * q^19 + 22 * q^20 - 4 * q^21 - 6 * q^22 + 7 * q^24 + 2 * q^25 + 18 * q^26 + 8 * q^27 + 13 * q^28 - 16 * q^29 + 13 * q^30 + 6 * q^31 - 9 * q^32 - 6 * q^33 - 28 * q^34 - 12 * q^35 + 2 * q^36 + 6 * q^37 + 10 * q^38 - 6 * q^39 - 17 * q^40 + 9 * q^42 - 23 * q^44 + 24 * q^46 + 4 * q^47 + 10 * q^48 + 4 * q^49 + 2 * q^50 + 16 * q^52 - 4 * q^53 + q^54 - 8 * q^55 + 41 * q^56 + 12 * q^57 + 37 * q^58 - 14 * q^59 - 23 * q^60 + 12 * q^61 - 48 * q^62 + 2 * q^63 + 2 * q^64 + 4 * q^65 - 15 * q^66 + 42 * q^67 - 26 * q^68 + 3 * q^70 - 11 * q^72 - 18 * q^73 - 10 * q^74 + 2 * q^75 + 44 * q^76 + 8 * q^77 - 6 * q^78 - 6 * q^79 - 39 * q^80 - 4 * q^81 - 10 * q^82 + 4 * q^83 - 14 * q^84 - 32 * q^85 + 36 * q^86 + 8 * q^87 - 37 * q^88 - 8 * q^90 - 34 * q^91 - 28 * q^92 + 6 * q^93 + 16 * q^94 - 24 * q^95 + 21 * q^96 - 53 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/84\mathbb{Z}\right)^\times$.

$n$	$29$	$43$	$73$
$\chi(n)$	$1$	$-1$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−1.06584	−	0.929502i	−0.753666	−	0.657257i
$2$	−1.06584	−	0.929502i	−0.753666	−	0.657257i
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$4$	0.272050	+	1.98141i	0.136025	+	0.990705i
$5$	2.12403	−	1.22631i	0.949894	−	0.548422i	0.0568460	−	0.998383i	$-0.481896\pi$
$5$	2.12403	−	1.22631i	0.949894	−	0.548422i	0.893048	+	0.449961i	$0.148562\pi$
$6$	1.33790	−	0.458297i	0.546193	−	0.187099i
$7$	2.63169	+	0.272415i	0.994685	+	0.102963i
$7$	2.63169	+	0.272415i	0.994685	+	0.102963i
$8$	1.55176	−	2.36475i	0.548631	−	0.836065i
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$	−3.40374	−	0.667235i	−1.07636	−	0.210998i
$11$	−1.09586	−	0.632697i	−0.330415	−	0.190765i	0.325610	−	0.945504i	$-0.394430\pi$
$11$	−1.09586	−	0.632697i	−0.330415	−	0.190765i	−0.656025	+	0.754739i	$0.727764\pi$
$12$	−1.85198	−	0.755103i	−0.534620	−	0.217979i
$13$			2.99744i			0.831342i	0.909515	+	0.415671i	$0.136453\pi$
$13$			2.99744i			0.831342i	−0.909515	+	0.415671i	$0.863547\pi$
$14$	−2.55176	−	2.73651i	−0.681987	−	0.731364i
$15$			2.45262i			0.633263i
$16$	−3.85198	+	1.07809i	−0.962994	+	0.269522i
$17$	1.58759	+	0.916595i	0.385047	+	0.222307i	0.680012	−	0.733201i	$-0.261975\pi$
$17$	1.58759	+	0.916595i	0.385047	+	0.222307i	−0.294965	+	0.955508i	$0.595308\pi$
$18$	−0.272050	+	1.38780i	−0.0641229	+	0.327108i
$19$	−2.07993	−	3.60254i	−0.477168	−	0.826479i	0.522490	−	0.852646i	$-0.325003\pi$
$19$	−2.07993	−	3.60254i	−0.477168	−	0.826479i	−0.999658	+	0.0261665i	$0.991670\pi$
$20$	3.00766	+	3.87495i	0.672534	+	0.866466i
$21$	−1.55176	+	2.14290i	−0.338622	+	0.467620i
$22$	0.579927	+	1.69296i	0.123641	+	0.360941i
$23$	−5.83564	+	3.36921i	−1.21682	+	0.702529i	−0.964236	−	0.265047i	$-0.914613\pi$
$23$	−5.83564	+	3.36921i	−1.21682	+	0.702529i	−0.252580	+	0.967576i	$0.581279\pi$
$24$	1.27205	+	2.52624i	0.259656	+	0.515667i
$25$	0.507662	−	0.879296i	0.101532	−	0.175859i
$26$	2.78613	−	3.19481i	0.546406	−	0.626554i
$27$	1.00000			0.192450
$28$	0.176187	+	5.28857i	0.0332962	+	0.999446i
$29$	−9.42323			−1.74985			−0.874925	−	0.484258i	$-0.839090\pi$
$29$	−9.42323			−1.74985			−0.874925	+	0.484258i	$0.839090\pi$
$30$	2.27971	−	2.61411i	0.416217	−	0.477269i
$31$	4.71989	−	8.17509i	0.847717	−	1.46829i	−0.0355228	−	0.999369i	$-0.511310\pi$
$31$	4.71989	−	8.17509i	0.847717	−	1.46829i	0.883240	−	0.468921i	$-0.155357\pi$
$32$	5.10769	+	2.43135i	0.902921	+	0.429806i
$33$	1.09586	−	0.632697i	0.190765	−	0.110138i
$34$	−0.840146	−	2.45262i	−0.144084	−	0.420620i
$35$	5.92385	−	2.64865i	1.00131	−	0.447703i
$36$	1.57993	−	1.22631i	0.263321	−	0.204385i
$37$	−3.75572	−	6.50509i	−0.617436	−	1.06943i	−0.989952	−	0.141405i	$-0.954838\pi$
$37$	−3.75572	−	6.50509i	−0.617436	−	1.06943i	0.372516	−	0.928026i	$-0.378495\pi$
$38$	−1.13169	+	5.77304i	−0.183584	+	0.936512i
$39$	−2.59586	−	1.49872i	−0.415671	−	0.239988i
$40$	0.396078	−	6.92573i	0.0626254	−	1.09505i
$41$		−	1.08966i		−	0.170176i	−0.996373	−	0.0850880i	$-0.972883\pi$
$41$		−	1.08966i		−	0.170176i	0.996373	−	0.0850880i	$-0.0271171\pi$
$42$	3.64577	−	0.841635i	0.562555	−	0.129867i
$43$			6.27176i			0.956435i	0.878241	+	0.478218i	$0.158717\pi$
$43$			6.27176i			0.956435i	−0.878241	+	0.478218i	$0.841283\pi$
$44$	0.955503	−	2.34348i	0.144047	−	0.353293i
$45$	−2.12403	−	1.22631i	−0.316631	−	0.182807i
$46$	9.35158	+	1.83319i	1.37882	+	0.270289i
$47$	3.67579	+	6.36666i	0.536169	+	0.928672i	0.999106	+	0.0422808i	$0.0134624\pi$
$47$	3.67579	+	6.36666i	0.536169	+	0.928672i	−0.462937	+	0.886391i	$0.653204\pi$
$48$	0.992338	−	3.87495i	0.143232	−	0.559301i
$49$	6.85158	+	1.43382i	0.978797	+	0.204832i
$50$	−1.35840	+	0.465320i	−0.192106	+	0.0658063i
$51$	−1.58759	+	0.916595i	−0.222307	+	0.128349i
$52$	−5.93917	+	0.815456i	−0.823615	+	0.113083i
$53$	0.0358262	−	0.0620528i	0.00492111	−	0.00852361i	−0.863554	−	0.504256i	$-0.831767\pi$
$53$	0.0358262	−	0.0620528i	0.00492111	−	0.00852361i	0.868475	+	0.495732i	$0.165100\pi$
$54$	−1.06584	−	0.929502i	−0.145043	−	0.126489i
$55$	−3.10353			−0.418479
$56$	4.72795	−	5.80056i	0.631799	−	0.775132i
$57$	4.15985			0.550986
$58$	10.0437	+	8.75892i	1.31880	+	1.15010i
$59$	1.68345	−	2.91583i	0.219167	−	0.379608i	−0.735387	−	0.677648i	$-0.762999\pi$
$59$	1.68345	−	2.91583i	0.219167	−	0.379608i	0.954553	+	0.298040i	$0.0963328\pi$
$60$	−4.85964	+	0.667235i	−0.627377	+	0.0861397i
$61$	−9.61496	+	5.55120i	−1.23107	+	0.710758i	−0.967253	−	0.253815i	$-0.918315\pi$
$61$	−9.61496	+	5.55120i	−1.23107	+	0.710758i	−0.263817	+	0.964573i	$0.584981\pi$
$62$	−12.6294	+	4.32623i	−1.60394	+	0.549432i
$63$	−1.07993	−	2.41532i	−0.136058	−	0.304301i
$64$	−3.18406	−	7.33906i	−0.398008	−	0.917382i
$65$	3.67579	+	6.36666i	0.455926	+	0.789686i
$66$	−1.75611	−	0.344251i	−0.216163	−	0.0423744i
$67$	−2.43151	−	1.40383i	−0.297056	−	0.171505i	0.344064	−	0.938946i	$-0.388196\pi$
$67$	−2.43151	−	1.40383i	−0.297056	−	0.171505i	−0.641120	+	0.767441i	$0.721530\pi$
$68$	−1.38425	+	3.39503i	−0.167865	+	0.411707i
$69$		−	6.73842i		−	0.811211i
$70$	−8.77582	−	2.68318i	−1.04891	−	0.320702i
$71$			2.92285i			0.346878i	0.984845	+	0.173439i	$0.0554880\pi$
$71$			2.92285i			0.346878i	−0.984845	+	0.173439i	$0.944512\pi$
$72$	−2.82381	−	0.161492i	−0.332790	−	0.0190320i
$73$	7.01910	+	4.05248i	0.821523	+	0.474307i	0.850941	−	0.525261i	$-0.176032\pi$
$73$	7.01910	+	4.05248i	0.821523	+	0.474307i	−0.0294183	+	0.999567i	$0.509365\pi$
$74$	−2.04349	+	10.4244i	−0.237551	+	1.21181i
$75$	0.507662	+	0.879296i	0.0586198	+	0.101532i
$76$	6.57226	−	5.10126i	0.753890	−	0.585155i
$77$	−2.71162	−	1.96359i	−0.309017	−	0.223772i
$78$	1.37372	+	4.01027i	0.155543	+	0.454073i
$79$	−1.54471	+	0.891841i	−0.173794	+	0.100340i	−0.584374	−	0.811485i	$-0.698660\pi$
$79$	−1.54471	+	0.891841i	−0.173794	+	0.100340i	0.410580	+	0.911825i	$0.365326\pi$
$80$	−6.85964	+	7.01360i	−0.766931	+	0.784144i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	−1.01284	+	1.16141i	−0.111849	+	0.128256i
$83$	−5.33626			−0.585730			−0.292865	−	0.956154i	$-0.594609\pi$
$83$	−5.33626			−0.585730			−0.292865	+	0.956154i	$0.594609\pi$
$84$	−4.66813	−	2.49170i	−0.509335	−	0.271867i
$85$	4.49611			0.487672
$86$	5.82962	−	6.68473i	0.628624	−	0.720833i
$87$	4.71162	−	8.16076i	0.505138	−	0.874925i
$88$	−3.19669	+	1.60964i	−0.340768	+	0.171589i
$89$	7.42323	−	4.28581i	0.786861	−	0.454294i	−0.0519952	−	0.998647i	$-0.516558\pi$
$89$	7.42323	−	4.28581i	0.786861	−	0.454294i	0.838856	+	0.544353i	$0.183225\pi$
$90$	1.12403	+	3.28134i	0.118483	+	0.345884i
$91$	−0.816548	+	7.88834i	−0.0855974	+	0.826923i
$92$	−8.26338	−	10.6462i	−0.861517	−	1.10994i
$93$	4.71989	+	8.17509i	0.489430	+	0.847717i
$94$	2.00000	−	10.2025i	0.206284	−	1.05231i
$95$	−8.83564	−	5.10126i	−0.906518	−	0.523378i
$96$	−4.65946	+	3.20772i	−0.475554	+	0.327386i
$97$		−	7.10394i		−	0.721296i	−0.932702	−	0.360648i	$-0.882556\pi$
$97$		−	7.10394i		−	0.721296i	0.932702	−	0.360648i	$-0.117444\pi$
$98$	−5.96998	−	7.89679i	−0.603059	−	0.797696i
$99$			1.26539i			0.127177i
$100$	1.88036	+	0.766674i	0.188036	+	0.0766674i
$101$	0.808273	+	0.466657i	0.0804262	+	0.0464341i	0.539674	−	0.841874i	$-0.318548\pi$
$101$	0.808273	+	0.466657i	0.0804262	+	0.0464341i	−0.459248	+	0.888308i	$0.651881\pi$
$102$	2.54410	+	0.498720i	0.251904	+	0.0493806i
$103$	2.06460	+	3.57600i	0.203431	+	0.352353i	0.949632	−	0.313368i	$-0.101457\pi$
$103$	2.06460	+	3.57600i	0.203431	+	0.352353i	−0.746200	+	0.665721i	$0.768124\pi$
$104$	7.08820	+	4.65132i	0.695055	+	0.456100i
$105$	−0.668128	+	6.45452i	−0.0652026	+	0.629897i
$106$	−0.0958634	+	0.0328381i	−0.00931108	+	0.00318952i
$107$	11.9878	−	6.92118i	1.15891	−	0.669096i	0.207866	−	0.978157i	$-0.433348\pi$
$107$	11.9878	−	6.92118i	1.15891	−	0.669096i	0.951042	+	0.309062i	$0.100015\pi$
$108$	0.272050	+	1.98141i	0.0261781	+	0.190661i
$109$	0.492338	−	0.852754i	0.0471574	−	0.0816791i	−0.841483	−	0.540283i	$-0.818317\pi$
$109$	0.492338	−	0.852754i	0.0471574	−	0.0816791i	0.888641	+	0.458604i	$0.151650\pi$
$110$	3.30788	+	2.88473i	0.315394	+	0.275049i
$111$	7.51143			0.712954
$112$	−10.4309	+	1.78786i	−0.985627	+	0.168936i
$113$	5.03187			0.473359			0.236679	−	0.971588i	$-0.423941\pi$
$113$	5.03187			0.473359			0.236679	+	0.971588i	$0.423941\pi$
$114$	−4.43376	−	3.86659i	−0.415260	−	0.362140i
$115$	−8.26338	+	14.3126i	−0.770564	+	1.33466i
$116$	−2.56359	−	18.6713i	−0.238024	−	1.73359i
$117$	2.59586	−	1.49872i	0.239988	−	0.138557i
$118$	−4.50457	+	1.54304i	−0.414679	+	0.142049i
$119$	3.92835	+	2.84468i	0.360111	+	0.260771i
$120$	5.79982	+	3.80588i	0.529449	+	0.347428i
$121$	−4.69939	−	8.13958i	−0.427217	−	0.739962i
$122$	15.4079	+	3.02041i	1.39497	+	0.273455i
$123$	0.943672	+	0.544829i	0.0850880	+	0.0491256i
$124$	17.4823	+	7.12801i	1.56995	+	0.640114i
$125$			9.77288i			0.874113i
$126$	−1.09401	+	3.57815i	−0.0974621	+	0.318767i
$127$			6.38337i			0.566433i	0.959056	+	0.283216i	$0.0914015\pi$
$127$			6.38337i			0.566433i	−0.959056	+	0.283216i	$0.908599\pi$
$128$	−3.42795	+	10.7819i	−0.302991	+	0.952993i
$129$	−5.43151	−	3.13588i	−0.478218	−	0.276099i
$130$	2.00000	−	10.2025i	0.175412	−	0.894820i
$131$	−1.93601	−	3.35327i	−0.169150	−	0.292976i	0.768971	−	0.639283i	$-0.220769\pi$
$131$	−1.93601	−	3.35327i	−0.169150	−	0.292976i	−0.938121	+	0.346307i	$0.887436\pi$
$132$	1.55176	+	1.99923i	0.135064	+	0.174011i
$133$	−4.49234	−	10.0474i	−0.389535	−	0.871217i
$134$	1.28674	+	3.75636i	0.111158	+	0.324500i
$135$	2.12403	−	1.22631i	0.182807	−	0.105544i
$136$	4.63108	−	2.33191i	0.397112	−	0.199960i
$137$	7.35158	−	12.7333i	0.628088	−	1.08788i	−0.359847	−	0.933011i	$-0.617171\pi$
$137$	7.35158	−	12.7333i	0.628088	−	1.08788i	0.987935	−	0.154869i	$-0.0494955\pi$
$138$	−6.26338	+	7.18211i	−0.533174	+	0.611382i
$139$	2.01655			0.171041			0.0855207	−	0.996336i	$-0.472745\pi$
$139$	2.01655			0.171041			0.0855207	+	0.996336i	$0.472745\pi$
$140$	6.85964	+	11.0170i	0.579745	+	0.931107i
$141$	−7.35158			−0.619115
$142$	2.71679	−	3.11530i	0.227988	−	0.261430i
$143$	1.89647	−	3.28479i	0.158591	−	0.274688i
$144$	2.85964	+	2.79687i	0.238303	+	0.233072i
$145$	−20.0152	+	11.5558i	−1.66217	+	0.959656i
$146$	−3.71448	−	10.8436i	−0.307413	−	0.897421i
$147$	−4.66752	+	5.21673i	−0.384970	+	0.430269i
$148$	11.8675	−	9.21133i	0.975504	−	0.757167i
$149$	0.248055	+	0.429644i	0.0203215	+	0.0351978i	0.876007	−	0.482298i	$-0.160198\pi$
$149$	0.248055	+	0.429644i	0.0203215	+	0.0351978i	−0.855686	+	0.517496i	$0.826864\pi$
$150$	0.276219	−	1.40907i	0.0225532	−	0.115050i
$151$	−11.4636	−	6.61849i	−0.932891	−	0.538605i	−0.0451665	−	0.998979i	$-0.514382\pi$
$151$	−11.4636	−	6.61849i	−0.932891	−	0.538605i	−0.887725	+	0.460374i	$0.847715\pi$
$152$	−11.7466	−	0.671783i	−0.952779	−	0.0544888i
$153$		−	1.83319i		−	0.148205i
$154$	1.06500	+	4.61334i	0.0858201	+	0.371753i
$155$		−	23.1522i		−	1.85963i
$156$	2.26338	−	5.55120i	0.181215	−	0.444452i
$157$	4.38345	+	2.53079i	0.349838	+	0.201979i	0.664614	−	0.747187i	$-0.268596\pi$
$157$	4.38345	+	2.53079i	0.349838	+	0.201979i	−0.314776	+	0.949166i	$0.601929\pi$
$158$	2.47539	+	0.485251i	0.196932	+	0.0386045i
$159$	0.0358262	+	0.0620528i	0.00284120	+	0.00492111i
$160$	13.8305	−	1.09935i	1.09339	−	0.0869115i
$161$	−16.2754	+	7.27700i	−1.28268	+	0.573508i
$162$	1.33790	−	0.458297i	0.105115	−	0.0360072i
$163$	10.4232	−	6.01786i	0.816411	−	0.471355i	−0.0327665	−	0.999463i	$-0.510432\pi$
$163$	10.4232	−	6.01786i	0.816411	−	0.471355i	0.849177	+	0.528108i	$0.177098\pi$
$164$	2.15906	−	0.296442i	0.168594	−	0.0231482i
$165$	1.55176	−	2.68773i	0.120805	−	0.209240i
$166$	5.68762	+	4.96006i	0.441445	+	0.384976i
$167$	−7.46424			−0.577600			−0.288800	−	0.957389i	$-0.593256\pi$
$167$	−7.46424			−0.577600			−0.288800	+	0.957389i	$0.593256\pi$
$168$	2.65946	+	6.99480i	0.205182	+	0.539661i
$169$	4.01532			0.308871
$170$	−4.79216	−	4.17915i	−0.367542	−	0.320526i
$171$	−2.07993	+	3.60254i	−0.159056	+	0.275493i
$172$	−12.4269	+	1.70624i	−0.947545	+	0.130099i
$173$	3.77932	−	2.18199i	0.287336	−	0.165894i	−0.349404	−	0.936972i	$-0.613616\pi$
$173$	3.77932	−	2.18199i	0.287336	−	0.165894i	0.636740	+	0.771079i	$0.280283\pi$
$174$	−12.6073	+	4.31864i	−0.955757	+	0.327396i
$175$	1.57554	−	2.17574i	0.119100	−	0.164471i
$176$	4.90334	+	1.25570i	0.369603	+	0.0946518i
$177$	1.68345	+	2.91583i	0.126536	+	0.219167i
$178$	−11.8957	−	2.33191i	−0.891619	−	0.174784i
$179$	21.2754	+	12.2834i	1.59020	+	0.918102i	0.993272	+	0.115808i	$0.0369457\pi$
$179$	21.2754	+	12.2834i	1.59020	+	0.918102i	0.596928	+	0.802295i	$0.296388\pi$
$180$	1.85198	−	4.54219i	0.138038	−	0.338555i
$181$			11.7182i			0.871011i	0.900186	+	0.435505i	$0.143430\pi$
$181$			11.7182i			0.871011i	−0.900186	+	0.435505i	$0.856570\pi$
$182$	8.20255	−	7.64877i	0.608013	−	0.566964i
$183$		−	11.1024i		−	0.820713i
$184$	−1.08820	+	19.0280i	−0.0802233	+	1.40277i
$185$	−15.9545	−	9.21133i	−1.17300	−	0.677231i
$186$	2.56810	−	13.1005i	0.188302	−	0.960577i
$187$	−1.15985	−	2.00893i	−0.0848169	−	0.146907i
$188$	−11.6150	+	9.01530i	−0.847108	+	0.657508i
$189$	2.63169	+	0.272415i	0.191427	+	0.0198152i
$190$	4.67579	+	13.6499i	0.339217	+	0.990268i
$191$	−13.7628	+	7.94594i	−0.995839	+	0.574948i	−0.907014	−	0.421099i	$-0.861644\pi$
$191$	−13.7628	+	7.94594i	−0.995839	+	0.574948i	−0.0888244	+	0.996047i	$0.528311\pi$
$192$	7.94784	+	0.912047i	0.573586	+	0.0658213i
$193$	−9.86690	+	17.0900i	−0.710235	+	1.23016i	0.254533	+	0.967064i	$0.418078\pi$
$193$	−9.86690	+	17.0900i	−0.710235	+	1.23016i	−0.964769	+	0.263100i	$0.915255\pi$
$194$	−6.60313	+	7.57170i	−0.474077	+	0.543616i
$195$	−7.35158			−0.526458
$196$	−0.977014	+	13.9659i	−0.0697867	+	0.997562i
$197$	0.998775			0.0711598			0.0355799	−	0.999367i	$-0.488672\pi$
$197$	0.998775			0.0711598			0.0355799	+	0.999367i	$0.488672\pi$
$198$	1.17619	−	1.34871i	0.0835880	−	0.0958489i
$199$	−1.35158	+	2.34101i	−0.0958110	+	0.165950i	−0.909947	−	0.414725i	$-0.863878\pi$
$199$	−1.35158	+	2.34101i	−0.0958110	+	0.165950i	0.814136	+	0.580675i	$0.197211\pi$
$200$	−1.29154	−	2.56495i	−0.0913259	−	0.181370i
$201$	2.43151	−	1.40383i	0.171505	−	0.0990186i
$202$	−0.427735	−	1.24868i	−0.0300953	−	0.0878565i
$203$	−24.7990	−	2.56703i	−1.74055	−	0.180170i
$204$	−2.24806	−	2.89631i	−0.157395	−	0.202782i
$205$	−1.33626	−	2.31446i	−0.0933282	−	0.161649i
$206$	1.12335	−	5.73051i	0.0782676	−	0.399264i
$207$	5.83564	+	3.36921i	0.405605	+	0.234176i
$208$	−3.23151	−	11.5461i	−0.224065	−	0.800577i
$209$			5.26385i			0.364108i
$210$	6.71162	−	6.25849i	0.463146	−	0.431877i
$211$		−	18.1798i		−	1.25155i	−0.780004	−	0.625774i	$-0.784783\pi$
$211$		−	18.1798i		−	1.25155i	0.780004	−	0.625774i	$-0.215217\pi$
$212$	0.132699	+	0.0541049i	0.00911378	+	0.00371594i
$213$	−2.53126	−	1.46142i	−0.173439	−	0.100135i
$214$	−19.2104	−	3.76582i	−1.31320	−	0.257426i
$215$	7.69111	+	13.3214i	0.524530	+	0.908512i
$216$	1.55176	−	2.36475i	0.105584	−	0.160901i
$217$	14.6483	−	20.2285i	0.994392	−	1.37320i
$218$	−1.31739	+	0.451274i	−0.0892251	+	0.0305642i
$219$	−7.01910	+	4.05248i	−0.474307	+	0.273841i
$220$	−0.844315	−	6.14936i	−0.0569237	−	0.414590i
$221$	−2.74744	+	4.75871i	−0.184813	+	0.320106i
$222$	−8.00602	−	6.98190i	−0.537329	−	0.468594i
$223$	11.5996			0.776769			0.388385	−	0.921497i	$-0.373033\pi$
$223$	11.5996			0.776769			0.388385	+	0.921497i	$0.373033\pi$
$224$	12.7795	+	7.78997i	0.853868	+	0.520489i
$225$	−1.01532			−0.0676883
$226$	−5.36320	−	4.67714i	−0.356754	−	0.311119i
$227$	−5.08054	+	8.79975i	−0.337207	+	0.584060i	−0.983906	−	0.178685i	$-0.942816\pi$
$227$	−5.08054	+	8.79975i	−0.337207	+	0.584060i	0.646699	+	0.762745i	$0.276149\pi$
$228$	1.13169	+	8.24238i	0.0749480	+	0.545865i
$229$	20.0025	−	11.5485i	1.32181	−	0.763145i	0.337789	−	0.941222i	$-0.390321\pi$
$229$	20.0025	−	11.5485i	1.32181	−	0.763145i	0.984017	+	0.178077i	$0.0569876\pi$
$230$	22.1111	−	7.57417i	1.45796	−	0.499426i
$231$	3.05633	−	1.36653i	0.201092	−	0.0899113i
$232$	−14.6226	+	22.2836i	−0.960022	+	1.46299i
$233$	3.42774	+	5.93701i	0.224558	+	0.388947i	0.956187	−	0.292757i	$-0.0945727\pi$
$233$	3.42774	+	5.93701i	0.224558	+	0.388947i	−0.731628	+	0.681704i	$0.761239\pi$
$234$	−4.15985	−	0.815456i	−0.271938	−	0.0533080i
$235$	15.6150	+	9.01530i	1.01861	+	0.588093i
$236$	6.23543	+	2.54236i	0.405892	+	0.165494i
$237$		−	1.78368i		−	0.115863i
$238$	−1.54288	−	6.68339i	−0.100010	−	0.433220i
$239$			22.2257i			1.43766i	0.695184	+	0.718832i	$0.255323\pi$
$239$			22.2257i			1.43766i	−0.695184	+	0.718832i	$0.744677\pi$
$240$	−2.64413	−	9.44742i	−0.170678	−	0.609828i
$241$	13.3605	+	7.71367i	0.860623	+	0.496881i	0.864221	−	0.503112i	$-0.167812\pi$
$241$	13.3605	+	7.71367i	0.860623	+	0.496881i	−0.00359762	+	0.999994i	$0.501145\pi$
$242$	−2.55694	+	13.0436i	−0.164366	+	0.838476i
$243$	−0.500000	−	0.866025i	−0.0320750	−	0.0555556i
$244$	−13.6150	−	17.5410i	−0.871608	−	1.12295i
$245$	16.3113	−	5.35667i	1.04209	−	0.342225i
$246$	−0.499388	−	1.45785i	−0.0318398	−	0.0929490i
$247$	10.7984	−	6.23447i	0.687087	−	0.396690i
$248$	−12.0079	−	23.8472i	−0.762501	−	1.51430i
$249$	2.66813	−	4.62133i	0.169086	−	0.292865i
$250$	9.08392	−	10.4164i	0.574517	−	0.658789i
$251$	22.2954			1.40727			0.703636	−	0.710561i	$-0.251559\pi$
$251$	22.2954			1.40727			0.703636	+	0.710561i	$0.251559\pi$
$252$	4.49194	−	2.79687i	0.282966	−	0.176186i
$253$	8.52676			0.536073
$254$	5.93336	−	6.80369i	0.372292	−	0.426901i
$255$	−2.24806	+	3.89375i	−0.140779	+	0.243836i
$256$	13.6755	−	8.30553i	0.854716	−	0.519096i
$257$	2.48529	−	1.43488i	0.155028	−	0.0895055i	−0.420479	−	0.907302i	$-0.638138\pi$
$257$	2.48529	−	1.43488i	0.155028	−	0.0895055i	0.575507	+	0.817797i	$0.304805\pi$
$258$	2.87433	+	8.39096i	0.178948	+	0.522399i
$259$	−8.11180	−	18.1425i	−0.504043	−	1.12732i
$260$	−11.6150	+	9.01530i	−0.720329	+	0.559105i
$261$	4.71162	+	8.16076i	0.291642	+	0.505138i
$262$	−1.05338	+	5.37359i	−0.0650783	+	0.331981i
$263$	8.98186	+	5.18568i	0.553845	+	0.319763i	0.750672	−	0.660676i	$-0.229730\pi$
$263$	8.98186	+	5.18568i	0.553845	+	0.319763i	−0.196826	+	0.980438i	$0.563063\pi$
$264$	0.204351	−	3.57324i	0.0125769	−	0.219917i
$265$		−	0.175736i		−	0.0107954i
$266$	−4.55092	+	14.8846i	−0.279035	+	0.912632i
$267$			8.57161i			0.524574i
$268$	2.12007	−	5.19973i	0.129504	−	0.317624i
$269$	4.48011	+	2.58659i	0.273157	+	0.157707i	0.630322	−	0.776334i	$-0.282923\pi$
$269$	4.48011	+	2.58659i	0.273157	+	0.157707i	−0.357164	+	0.934042i	$0.616256\pi$
$270$	−3.40374	−	0.667235i	−0.207145	−	0.0406066i
$271$	−12.1195	−	20.9916i	−0.736209	−	1.27515i	−0.954191	−	0.299198i	$-0.903281\pi$
$271$	−12.1195	−	20.9916i	−0.736209	−	1.27515i	0.217982	−	0.975953i	$-0.430053\pi$
$272$	−7.10353	−	1.81914i	−0.430714	−	0.110302i
$273$	−6.42323	−	4.65132i	−0.388752	−	0.281511i
$274$	−19.6713	+	6.73842i	−1.18839	+	0.407083i
$275$	−1.11266	+	0.642393i	−0.0670957	+	0.0387377i
$276$	13.3516	−	1.83319i	0.803671	−	0.110345i
$277$	1.50766	−	2.61135i	0.0905866	−	0.156901i	−0.817171	−	0.576395i	$-0.804459\pi$
$277$	1.50766	−	2.61135i	0.0905866	−	0.156901i	0.907758	+	0.419494i	$0.137792\pi$
$278$	−2.14933	−	1.87439i	−0.128908	−	0.112418i
$279$	−9.43978			−0.565145
$280$	2.92902	−	18.1185i	0.175043	−	1.08279i
$281$	−6.91922			−0.412766			−0.206383	−	0.978471i	$-0.566169\pi$
$281$	−6.91922			−0.412766			−0.206383	+	0.978471i	$0.566169\pi$
$282$	7.83564	+	6.83331i	0.466606	+	0.406918i
$283$	−10.2870	+	17.8176i	−0.611497	+	1.05914i	0.379491	+	0.925195i	$0.376099\pi$
$283$	−10.2870	+	17.8176i	−0.611497	+	1.05914i	−0.990988	+	0.133949i	$0.957234\pi$
$284$	−5.79136	+	0.795162i	−0.343654	+	0.0471842i
$285$	8.83564	−	5.10126i	0.523378	−	0.302173i
$286$	−5.07457	+	1.73830i	−0.300066	+	0.102788i
$287$	0.296839	−	2.86764i	0.0175218	−	0.169272i
$288$	−0.448237	−	5.63907i	−0.0264126	−	0.332285i
$289$	−6.81971	−	11.8121i	−0.401159	−	0.694828i
$290$	32.0742	+	6.28751i	1.88346	+	0.369215i
$291$	6.15219	+	3.55197i	0.360648	+	0.208220i
$292$	−6.12007	+	15.0102i	−0.358150	+	0.878405i
$293$		−	28.3113i		−	1.65396i	−0.562229	−	0.826982i	$-0.690056\pi$
$293$		−	28.3113i		−	1.65396i	0.562229	−	0.826982i	$-0.309944\pi$
$294$	9.82381	−	1.22176i	0.572936	−	0.0712545i
$295$		−	8.25772i		−	0.480783i
$296$	−21.2109	−	1.21304i	−1.23286	−	0.0705063i
$297$	−1.09586	−	0.632697i	−0.0635884	−	0.0367128i
$298$	0.134967	−	0.688502i	0.00781843	−	0.0398838i
$299$	−10.0990	−	17.4920i	−0.584042	−	1.01159i
$300$	−1.60414	+	1.24510i	−0.0926149	+	0.0718859i
$301$	−1.70852	+	16.5053i	−0.0984775	+	0.951352i
$302$	6.06647	+	17.7097i	0.349086	+	1.01908i
$303$	−0.808273	+	0.466657i	−0.0464341	+	0.0268087i
$304$	11.8957	+	11.6346i	0.682264	+	0.667288i
$305$	−13.6150	+	23.5818i	−0.779590	+	1.35029i
$306$	−1.70395	+	1.95390i	−0.0974086	+	0.111697i
$307$	−8.65596			−0.494022			−0.247011	−	0.969013i	$-0.579448\pi$
$307$	−8.65596			−0.494022			−0.247011	+	0.969013i	$0.579448\pi$
$308$	3.15298	−	5.90702i	0.179658	−	0.336584i
$309$	−4.12921			−0.234902
$310$	−21.5200	+	24.6766i	−1.22225	+	1.40154i
$311$	−4.67129	+	8.09091i	−0.264884	+	0.458793i	−0.967533	−	0.252743i	$-0.918667\pi$
$311$	−4.67129	+	8.09091i	−0.264884	+	0.458793i	0.702649	+	0.711537i	$0.252000\pi$
$312$	−7.57226	+	3.81290i	−0.428695	+	0.215863i
$313$	−6.38734	+	3.68773i	−0.361034	+	0.208443i	−0.669534	−	0.742781i	$-0.733506\pi$
$313$	−6.38734	+	3.68773i	−0.361034	+	0.208443i	0.308500	+	0.951224i	$0.400173\pi$
$314$	−2.31971	−	6.77186i	−0.130909	−	0.382158i
$315$	−5.25572	−	3.80588i	−0.296126	−	0.214437i
$316$	−2.18734	−	2.81809i	−0.123048	−	0.158530i
$317$	1.81514	+	3.14392i	0.101949	+	0.176580i	0.912487	−	0.409105i	$-0.134159\pi$
$317$	1.81514	+	3.14392i	0.101949	+	0.176580i	−0.810539	+	0.585685i	$0.800826\pi$
$318$	0.0194931	−	0.0994392i	0.00109312	−	0.00557627i
$319$	10.3266	+	5.96205i	0.578177	+	0.333811i
$320$	−15.7630	−	11.6837i	−0.881178	−	0.653139i
$321$			13.8424i			0.772605i
$322$	24.1111	+	7.37189i	1.34366	+	0.410820i
$323$		−	7.62580i		−	0.424311i
$324$	−1.85198	−	0.755103i	−0.102888	−	0.0419502i
$325$	2.63564	+	1.52169i	0.146199	+	0.0844081i
$326$	−16.7032	−	3.27432i	−0.925103	−	0.181348i
$327$	0.492338	+	0.852754i	0.0272264	+	0.0471574i
$328$	−2.57677	−	1.69089i	−0.142278	−	0.0933638i
$329$	7.93917	+	17.7564i	0.437701	+	0.978942i
$330$	−4.15219	+	1.42234i	−0.228571	+	0.0782971i
$331$	−0.544164	+	0.314173i	−0.0299100	+	0.0172685i	−0.514880	−	0.857262i	$-0.672164\pi$
$331$	−0.544164	+	0.314173i	−0.0299100	+	0.0172685i	0.484970	+	0.874531i	$0.338830\pi$
$332$	−1.45173	−	10.5733i	−0.0796741	−	0.580286i
$333$	−3.75572	+	6.50509i	−0.205812	+	0.356477i
$334$	7.95572	+	6.93803i	0.435318	+	0.379632i
$335$	−6.88612			−0.376229
$336$	3.66712	−	9.92735i	0.200058	−	0.541581i
$337$	−22.3119			−1.21541			−0.607704	−	0.794164i	$-0.707909\pi$
$337$	−22.3119			−1.21541			−0.607704	+	0.794164i	$0.707909\pi$
$338$	−4.27971	−	3.73225i	−0.232786	−	0.203008i
$339$	−2.51594	+	4.35773i	−0.136647	+	0.236679i
$340$	1.22317	+	8.90864i	0.0663356	+	0.483139i
$341$	−10.3447	+	5.97252i	−0.560198	+	0.323430i
$342$	5.56545	−	1.90645i	0.300945	−	0.103089i
$343$	17.6406	+	5.63984i	0.952505	+	0.304523i
$344$	14.8311	+	9.73229i	0.799642	+	0.524730i
$345$	−8.26338	−	14.3126i	−0.444885	−	0.770564i
$346$	−6.05633	−	1.18722i	−0.325590	−	0.0638254i
$347$	−5.97104	−	3.44738i	−0.320542	−	0.185065i	0.331092	−	0.943598i	$-0.392583\pi$
$347$	−5.97104	−	3.44738i	−0.320542	−	0.185065i	−0.651634	+	0.758533i	$0.725916\pi$
$348$	17.4516	+	7.11551i	0.935505	+	0.381431i
$349$			13.4768i			0.721399i	0.932682	+	0.360699i	$0.117462\pi$
$349$			13.4768i			0.721399i	−0.932682	+	0.360699i	$0.882538\pi$
$350$	−3.70164	+	0.854532i	−0.197861	+	0.0456766i
$351$			2.99744i			0.159992i
$352$	−4.05903	−	5.89605i	−0.216347	−	0.314260i
$353$	−24.7550	−	14.2923i	−1.31758	−	0.760702i	−0.334237	−	0.942489i	$-0.608479\pi$
$353$	−24.7550	−	14.2923i	−1.31758	−	0.760702i	−0.983338	+	0.181787i	$0.941812\pi$
$354$	0.915968	−	4.67259i	0.0486831	−	0.248345i
$355$	3.58431	+	6.20821i	0.190236	+	0.329498i
$356$	10.5114	+	13.5425i	0.557105	+	0.717752i
$357$	−4.42774	+	1.97971i	−0.234341	+	0.104777i
$358$	−11.2589	−	32.8677i	−0.595050	−	1.73711i
$359$	6.00000	−	3.46410i	0.316668	−	0.182828i	−0.333238	−	0.942843i	$-0.608141\pi$
$359$	6.00000	−	3.46410i	0.316668	−	0.182828i	0.649906	+	0.760014i	$0.274808\pi$
$360$	−6.19590	+	3.11985i	−0.326552	+	0.164431i
$361$	0.847808	−	1.46845i	0.0446215	−	0.0772867i
$362$	10.8921	−	12.4898i	0.572478	−	0.656451i
$363$	9.39878			0.493308
$364$	−15.8522	+	0.528111i	−0.830881	+	0.0276805i
$365$	19.8783			1.04048
$366$	−10.3197	+	11.8334i	−0.539420	+	0.618544i
$367$	6.47184	−	11.2095i	0.337827	−	0.585134i	−0.646197	−	0.763171i	$-0.723641\pi$
$367$	6.47184	−	11.2095i	0.337827	−	0.585134i	0.984024	+	0.178037i	$0.0569748\pi$
$368$	18.8465	−	19.2695i	0.982440	−	1.00449i
$369$	−0.943672	+	0.544829i	−0.0491256	+	0.0283627i
$370$	8.44306	+	24.6476i	0.438934	+	1.28137i
$371$	0.111188	−	0.153544i	0.00577257	−	0.00797162i
$372$	−14.9142	+	11.5761i	−0.773263	+	0.600192i
$373$	−1.53954	−	2.66655i	−0.0797141	−	0.138069i	0.823412	−	0.567443i	$-0.192067\pi$
$373$	−1.53954	−	2.66655i	−0.0797141	−	0.138069i	−0.903127	+	0.429374i	$0.858734\pi$
$374$	−0.631077	+	3.21929i	−0.0326322	+	0.166466i
$375$	−8.46356	−	4.88644i	−0.437056	−	0.252335i
$376$	20.7595	+	1.18722i	1.07059	+	0.0612263i
$377$		−	28.2456i		−	1.45472i
$378$	−2.55176	−	2.73651i	−0.131249	−	0.140751i
$379$		−	5.21020i		−	0.267630i	−0.991006	−	0.133815i	$-0.957277\pi$
$379$		−	5.21020i		−	0.267630i	0.991006	−	0.133815i	$-0.0427228\pi$
$380$	7.70395	−	18.8948i	0.395205	−	0.969285i
$381$	−5.52816	−	3.19169i	−0.283216	−	0.163515i
$382$	22.0547	+	4.32339i	1.12842	+	0.221204i
$383$	−19.4353	−	33.6629i	−0.993096	−	1.72009i	−0.598134	−	0.801396i	$-0.704091\pi$
$383$	−19.4353	−	33.6629i	−0.993096	−	1.72009i	−0.394963	−	0.918697i	$-0.629242\pi$
$384$	−7.62342	−	8.35964i	−0.389031	−	0.426601i
$385$	−8.16752	−	0.845446i	−0.416255	−	0.0430879i
$386$	26.4018	−	9.04395i	1.34381	−	0.460325i
$387$	5.43151	−	3.13588i	0.276099	−	0.159406i
$388$	14.0758	−	1.93263i	0.714592	−	0.0981144i
$389$	1.86752	−	3.23463i	0.0946869	−	0.164002i	−0.814791	−	0.579755i	$-0.803148\pi$
$389$	1.86752	−	3.23463i	0.0946869	−	0.164002i	0.909478	+	0.415752i	$0.136482\pi$
$390$	7.83564	+	6.83331i	0.396773	+	0.346018i
$391$	−12.3528			−0.624708
$392$	14.0227	−	13.9773i	0.708251	−	0.705961i
$393$	3.87202			0.195318
$394$	−1.06454	−	0.928364i	−0.0536307	−	0.0467703i
$395$	−2.18734	+	3.78859i	−0.110057	+	0.190625i
$396$	−2.50727	+	0.344251i	−0.125995	+	0.0172993i
$397$	−5.81082	+	3.35488i	−0.291637	+	0.168377i	−0.638680	−	0.769473i	$-0.720519\pi$
$397$	−5.81082	+	3.35488i	−0.291637	+	0.168377i	0.347043	+	0.937849i	$0.387186\pi$
$398$	3.61655	−	1.23885i	0.181281	−	0.0620980i
$399$	10.9474	+	1.13320i	0.548058	+	0.0567312i
$400$	−1.00754	+	3.93433i	−0.0503772	+	0.196717i
$401$	−2.92385	−	5.06425i	−0.146010	−	0.252897i	0.783739	−	0.621090i	$-0.213310\pi$
$401$	−2.92385	−	5.06425i	−0.146010	−	0.252897i	−0.929749	+	0.368193i	$0.879976\pi$
$402$	−3.89647	−	0.763826i	−0.194338	−	0.0380962i
$403$	24.5044	+	14.1476i	1.22065	+	0.704743i
$404$	−0.704748	+	1.72848i	−0.0350625	+	0.0859949i
$405$			2.45262i			0.121871i
$406$	24.0459	+	25.7868i	1.19338	+	1.27978i
$407$			9.50492i			0.471142i
$408$	−0.296046	+	5.17659i	−0.0146564	+	0.256279i
$409$	−26.7299	−	15.4325i	−1.32171	−	0.763089i	−0.337708	−	0.941251i	$-0.609652\pi$
$409$	−26.7299	−	15.4325i	−1.32171	−	0.763089i	−0.984001	+	0.178162i	$0.942985\pi$
$410$	−0.727058	+	3.70891i	−0.0359068	+	0.183170i
$411$	7.35158	+	12.7333i	0.362627	+	0.628088i
$412$	−6.52384	+	5.06368i	−0.321407	+	0.249469i
$413$	5.22464	−	7.21495i	0.257088	−	0.355024i
$414$	−3.08820	−	9.01530i	−0.151777	−	0.443078i
$415$	−11.3344	+	6.54389i	−0.556382	+	0.321227i
$416$	−7.28783	+	15.3100i	−0.357315	+	0.750636i
$417$	−1.00827	+	1.74638i	−0.0493754	+	0.0855207i
$418$	4.89277	−	5.61045i	0.239313	−	0.274416i
$419$	29.0866			1.42097			0.710487	−	0.703710i	$-0.248475\pi$
$419$	29.0866			1.42097			0.710487	+	0.703710i	$0.248475\pi$
$420$	−12.9708	+	0.432119i	−0.632912	+	0.0210852i
$421$	13.8642			0.675702			0.337851	−	0.941200i	$-0.390300\pi$
$421$	13.8642			0.675702			0.337851	+	0.941200i	$0.390300\pi$
$422$	−16.8982	+	19.3768i	−0.822590	+	0.943250i
$423$	3.67579	−	6.36666i	0.178723	−	0.309557i
$424$	−0.0911455	−	0.181011i	−0.00442642	−	0.00879068i
$425$	1.61192	−	0.930641i	0.0781895	−	0.0451427i
$426$	1.33953	+	3.91046i	0.0649006	+	0.189463i
$427$	−26.8158	+	11.9898i	−1.29771	+	0.580226i
$428$	16.9750	+	21.8699i	0.820517	+	1.05712i
$429$	1.89647	+	3.28479i	0.0915627	+	0.158591i
$430$	4.18474	−	21.3475i	0.201806	−	1.02947i
$431$	−27.6258	−	15.9498i	−1.33069	−	0.768273i	−0.345282	−	0.938499i	$-0.612217\pi$
$431$	−27.6258	−	15.9498i	−1.33069	−	0.768273i	−0.985405	+	0.170226i	$0.945550\pi$
$432$	−3.85198	+	1.07809i	−0.185328	+	0.0518695i
$433$			9.82239i			0.472034i	0.971749	+	0.236017i	$0.0758421\pi$
$433$			9.82239i			0.472034i	−0.971749	+	0.236017i	$0.924158\pi$
$434$	−34.4153	+	7.94485i	−1.65199	+	0.381365i
$435$		−	23.1116i		−	1.10811i
$436$	1.82360	+	0.743532i	0.0873345	+	0.0356087i
$437$	24.2754	+	14.0154i	1.16125	+	0.670449i
$438$	11.2481	+	2.20496i	0.537453	+	0.105357i
$439$	8.51989	+	14.7569i	0.406632	+	0.704308i	0.994510	−	0.104642i	$-0.0333697\pi$
$439$	8.51989	+	14.7569i	0.406632	+	0.704308i	−0.587878	+	0.808950i	$0.700036\pi$
$440$	−4.81594	+	7.33906i	−0.229591	+	0.349876i
$441$	−2.18406	−	6.65055i	−0.104003	−	0.316693i
$442$	7.35158	−	2.51829i	0.349679	−	0.119783i
$443$	7.30000	−	4.21466i	0.346833	−	0.200244i	−0.316456	−	0.948607i	$-0.602493\pi$
$443$	7.30000	−	4.21466i	0.346833	−	0.200244i	0.663290	+	0.748363i	$0.269160\pi$
$444$	2.04349	+	14.8832i	0.0969797	+	0.706327i
$445$	10.5114	−	18.2063i	0.498290	−	0.863063i
$446$	−12.3634	−	10.7819i	−0.585425	−	0.510537i
$447$	−0.496110			−0.0234652
$448$	−6.38020	−	20.1815i	−0.301436	−	0.953486i
$449$	9.64064			0.454970			0.227485	−	0.973782i	$-0.426950\pi$
$449$	9.64064			0.454970			0.227485	+	0.973782i	$0.426950\pi$
$450$	1.08218	+	0.943746i	0.0510144	+	0.0444886i
$451$	−0.689424	+	1.19412i	−0.0324637	+	0.0562288i
$452$	1.36892	+	9.97021i	0.0643887	+	0.468959i
$453$	11.4636	−	6.61849i	0.538605	−	0.310964i
$454$	13.5945	−	4.65680i	0.638020	−	0.218554i
$455$	7.93917	+	17.7564i	0.372194	+	0.832433i
$456$	6.45511	−	9.83701i	0.302288	−	0.460660i
$457$	14.5229	+	25.1543i	0.679351	+	1.17667i	0.975177	+	0.221429i	$0.0710720\pi$
$457$	14.5229	+	25.1543i	0.679351	+	1.17667i	−0.295825	+	0.955242i	$0.595595\pi$
$458$	−32.0539	−	6.28353i	−1.49778	−	0.293610i
$459$	1.58759	+	0.916595i	0.0741023	+	0.0427830i
$460$	−30.6072	−	12.4794i	−1.42707	−	0.581855i
$461$			23.9796i			1.11684i	0.829559	+	0.558420i	$0.188592\pi$
$461$			23.9796i			1.11684i	−0.829559	+	0.558420i	$0.811408\pi$
$462$	−4.52777	−	1.38435i	−0.210651	−	0.0644059i
$463$			28.4975i			1.32439i	0.749331	+	0.662196i	$0.230375\pi$
$463$			28.4975i			1.32439i	−0.749331	+	0.662196i	$0.769625\pi$
$464$	36.2981	−	10.1591i	1.68510	−	0.471623i
$465$	20.0504	+	11.5761i	0.929813	+	0.536828i
$466$	1.86503	−	9.51402i	0.0863960	−	0.440729i
$467$	9.29075	+	16.0921i	0.429925	+	0.744651i	0.996866	−	0.0791067i	$-0.0252068\pi$
$467$	9.29075	+	16.0921i	0.429925	+	0.744651i	−0.566942	+	0.823758i	$0.691873\pi$
$468$	3.67579	+	4.73574i	0.169913	+	0.218910i
$469$	−6.01655	−	4.35683i	−0.277818	−	0.201180i
$470$	−8.26338	−	24.1231i	−0.381161	−	1.11271i
$471$	−4.38345	+	2.53079i	−0.201979	+	0.116613i
$472$	−4.28287	−	8.50561i	−0.197135	−	0.391502i
$473$	3.96813	−	6.87300i	0.182455	−	0.316021i
$474$	−1.65794	+	1.90113i	−0.0761515	+	0.0873217i
$475$	−4.22360			−0.193792
$476$	−4.56776	+	8.55757i	−0.209363	+	0.392235i
$477$	−0.0716524			−0.00328074
$478$	20.6589	−	23.6892i	0.944915	−	1.08352i
$479$	14.1707	−	24.5443i	0.647475	−	1.12146i	−0.336249	−	0.941773i	$-0.609158\pi$
$479$	14.1707	−	24.5443i	0.647475	−	1.12146i	0.983724	−	0.179686i	$-0.0575082\pi$
$480$	−5.96316	+	12.5272i	−0.272180	+	0.571786i
$481$	19.4987	−	11.2576i	0.889062	−	0.513300i
$482$	−7.07031	−	20.6402i	−0.322044	−	0.940134i
$483$	1.83564	−	17.7334i	0.0835247	−	0.806899i
$484$	14.8494	−	11.5258i	0.674972	−	0.523900i
$485$	−8.71162	−	15.0890i	−0.395574	−	0.685154i
$486$	−0.272050	+	1.38780i	−0.0123405	+	0.0629519i
$487$	−35.9498	−	20.7556i	−1.62904	−	0.940528i	−0.984379	−	0.176060i	$-0.943665\pi$
$487$	−35.9498	−	20.7556i	−1.62904	−	0.940528i	−0.644662	−	0.764468i	$-0.723002\pi$
$488$	−1.79295	+	31.3511i	−0.0811630	+	1.41920i
$489$			12.0357i			0.544274i
$490$	−22.3643	−	9.45197i	−1.01032	−	0.426996i
$491$			1.72728i			0.0779509i	0.999240	+	0.0389755i	$0.0124094\pi$
$491$			1.72728i			0.0779509i	−0.999240	+	0.0389755i	$0.987591\pi$
$492$	−0.822804	+	2.01802i	−0.0370949	+	0.0909795i
$493$	−14.9602	−	8.63729i	−0.673774	−	0.389004i
$494$	−17.3044	−	3.39218i	−0.778561	−	0.152621i
$495$	1.55176	+	2.68773i	0.0697465	+	0.120805i
$496$	−9.36745	+	36.5787i	−0.420611	+	1.64243i
$497$	−0.796226	+	7.69203i	−0.0357156	+	0.345035i
$498$	−7.13935	+	2.44559i	−0.319922	+	0.109590i
$499$	−36.6216	+	21.1435i	−1.63941	+	0.946514i	−0.658373	+	0.752691i	$0.728755\pi$
$499$	−36.6216	+	21.1435i	−1.63941	+	0.946514i	−0.981037	+	0.193822i	$0.937911\pi$
$500$	−19.3641	+	2.65872i	−0.865988	+	0.118901i
$501$	3.73212	−	6.46422i	0.166739	−	0.288800i
$502$	−23.7634	−	20.7236i	−1.06061	−	0.924940i
$503$	4.23770			0.188950			0.0944748	−	0.995527i	$-0.469883\pi$
$503$	4.23770			0.188950			0.0944748	+	0.995527i	$0.469883\pi$
$504$	−7.38741	−	1.19424i	−0.329061	−	0.0531959i
$505$	2.28906			0.101862
$506$	−9.08820	−	7.92564i	−0.404020	−	0.352338i
$507$	−2.00766	+	3.47737i	−0.0891634	+	0.154436i
$508$	−12.6481	+	1.73660i	−0.561168	+	0.0770491i
$509$	−36.1788	+	20.8878i	−1.60360	+	0.925836i	−0.612836	+	0.790210i	$0.709971\pi$
$509$	−36.1788	+	20.8878i	−1.60360	+	0.925836i	−0.990760	+	0.135626i	$0.956695\pi$
$510$	6.01532	−	2.06056i	0.266363	−	0.0912429i
$511$	17.3681	+	12.5770i	0.768321	+	0.556372i
$512$	−22.2959	−	3.85896i	−0.985350	−	0.170544i
$513$	−2.07993	−	3.60254i	−0.0918310	−	0.159056i
$514$	−3.98266	−	0.780720i	−0.175668	−	0.0344361i
$515$	8.77055	+	5.06368i	0.386476	+	0.223132i
$516$	4.73583	−	11.6152i	0.208483	−	0.511329i
$517$		−	9.30265i		−	0.409130i
$518$	−8.21758	+	26.8770i	−0.361060	+	1.18091i
$519$			4.36398i			0.191557i
$520$	20.7595	+	1.18722i	0.910364	+	0.0520631i
$521$	30.2681	+	17.4753i	1.32607	+	0.765607i	0.984689	−	0.174318i	$-0.0557721\pi$
$521$	30.2681	+	17.4753i	1.32607	+	0.765607i	0.341381	+	0.939925i	$0.389105\pi$
$522$	2.56359	−	13.0776i	0.112205	−	0.572389i
$523$	6.13503	+	10.6262i	0.268266	+	0.464651i	0.968414	−	0.249347i	$-0.0802160\pi$
$523$	6.13503	+	10.6262i	0.268266	+	0.464651i	−0.700148	+	0.713998i	$0.746883\pi$
$524$	6.11751	−	4.74829i	0.267245	−	0.207430i
$525$	1.09648	+	2.45233i	0.0478541	+	0.107028i
$526$	−4.75317	−	13.8758i	−0.207248	−	0.605014i
$527$	14.9865	−	8.65246i	0.652822	−	0.376907i
$528$	−3.53914	+	3.61857i	−0.154021	+	0.157478i
$529$	11.2032	−	19.4044i	0.487094	−	0.843671i
$530$	−0.163347	+	0.187307i	−0.00709534	+	0.00813610i
$531$	−3.36690			−0.146111
$532$	18.6858	−	11.6346i	0.810133	−	0.504422i
$533$	3.26619			0.141474
$534$	7.96733	−	9.13601i	0.344780	−	0.395354i
$535$	16.9750	−	29.4016i	0.733893	−	1.27114i
$536$	−7.09283	+	3.57149i	−0.306364	+	0.154265i
$537$	−21.2754	+	12.2834i	−0.918102	+	0.530067i
$538$	−2.37086	−	6.92118i	−0.102215	−	0.298393i
$539$	−6.60122	−	5.90625i	−0.284335	−	0.254400i
$540$	3.00766	+	3.87495i	0.129429	+	0.166751i
$541$	0.467883	+	0.810397i	0.0201158	+	0.0348417i	0.875908	−	0.482478i	$-0.160263\pi$
$541$	0.467883	+	0.810397i	0.0201158	+	0.0348417i	−0.855792	+	0.517320i	$0.826930\pi$
$542$	−6.59424	+	33.6390i	−0.283247	+	1.44492i
$543$	−10.1483	−	5.85912i	−0.435505	−	0.251439i
$544$	5.88036	+	8.54167i	0.252118	+	0.366221i
$545$		−	2.41503i		−	0.103449i
$546$	2.52275	+	10.9280i	0.107964	+	0.467675i
$547$		−	7.13048i		−	0.304877i	−0.988313	−	0.152439i	$-0.951287\pi$
$547$		−	7.13048i		−	0.304877i	0.988313	−	0.152439i	$-0.0487127\pi$
$548$	27.2299	+	11.1024i	1.16320	+	0.474271i
$549$	9.61496	+	5.55120i	0.410356	+	0.236919i
$550$	1.78302	+	0.349526i	0.0760284	+	0.0149038i
$551$	19.5996	+	33.9476i	0.834973	+	1.44621i
$552$	−15.9347	−	10.4564i	−0.678224	−	0.445055i
$553$	−4.30816	+	1.92625i	−0.183201	+	0.0819123i
$554$	−4.03419	+	1.38192i	−0.171396	+	0.0587120i
$555$	15.9545	−	9.21133i	0.677231	−	0.390999i
$556$	0.548603	+	3.99561i	0.0232659	+	0.169452i
$557$	−4.97622	+	8.61907i	−0.210849	+	0.365202i	−0.951981	−	0.306159i	$-0.900956\pi$
$557$	−4.97622	+	8.61907i	−0.210849	+	0.365202i	0.741131	+	0.671360i	$0.234290\pi$
$558$	10.0613	+	8.77430i	0.425931	+	0.371446i
$559$	−18.7993			−0.795124
$560$	−19.9630	+	16.5889i	−0.843593	+	0.701011i
$561$	2.31971			0.0979381
$562$	7.37481	+	6.43143i	0.311088	+	0.271293i
$563$	0.844531	−	1.46277i	0.0355927	−	0.0616484i	−0.847680	−	0.530507i	$-0.822001\pi$
$563$	0.844531	−	1.46277i	0.0355927	−	0.0616484i	0.883273	+	0.468859i	$0.155335\pi$
$564$	−2.00000	−	14.5665i	−0.0842152	−	0.613360i
$565$	10.6878	−	6.17063i	0.449641	−	0.259600i
$566$	27.5258	−	9.42899i	1.15700	−	0.396330i
$567$	−1.55176	+	2.14290i	−0.0651679	+	0.0899935i
$568$	6.91180	+	4.53557i	0.290013	+	0.190308i
$569$	6.96935	+	12.0713i	0.292170	+	0.506054i	0.974323	−	0.225156i	$-0.0722892\pi$
$569$	6.96935	+	12.0713i	0.292170	+	0.506054i	−0.682152	+	0.731210i	$0.738956\pi$
$570$	−14.1591	−	2.77560i	−0.593058	−	0.116257i
$571$	−16.1591	−	9.32947i	−0.676238	−	0.390426i	0.122198	−	0.992506i	$-0.461006\pi$
$571$	−16.1591	−	9.32947i	−0.676238	−	0.390426i	−0.798436	+	0.602079i	$0.794339\pi$
$572$	7.02446	+	2.86407i	0.293707	+	0.119753i
$573$		−	15.8919i		−	0.663893i
$574$	−2.98186	+	2.78055i	−0.124461	+	0.116058i
$575$			6.84168i			0.285318i
$576$	−4.76378	+	6.42701i	−0.198491	+	0.267792i
$577$	29.4591	+	17.0082i	1.22640	+	0.708062i	0.966275	−	0.257513i	$-0.0829031\pi$
$577$	29.4591	+	17.0082i	1.22640	+	0.708062i	0.260125	+	0.965575i	$0.416236\pi$
$578$	−3.71061	+	18.9288i	−0.154341	+	0.787333i
$579$	−9.86690	−	17.0900i	−0.410055	−	0.710235i
$580$	−28.3419	−	36.5146i	−1.17683	−	1.51619i
$581$	−14.0434	−	1.45367i	−0.582617	−	0.0603086i
$582$	−3.25572	−	9.50433i	−0.134954	−	0.393967i
$583$	−0.0785213	+	0.0453343i	−0.00325202	+	0.00187755i
$584$	20.4751	−	10.3099i	0.847264	−	0.426627i
$585$	3.67579	−	6.36666i	0.151975	−	0.263229i
$586$	−26.3154	+	30.1755i	−1.08708	+	1.24654i
$587$	−41.9153			−1.73003			−0.865015	−	0.501746i	$-0.832691\pi$
$587$	−41.9153			−1.73003			−0.865015	+	0.501746i	$0.832691\pi$
$588$	−11.6063	−	7.82905i	−0.478635	−	0.322865i
$589$	−39.2681			−1.61801
$590$	−7.67557	+	8.80145i	−0.315998	+	0.362350i
$591$	−0.499388	+	0.864965i	−0.0205421	+	0.0355799i
$592$	21.4800	+	21.0085i	0.882822	+	0.863443i
$593$	21.1354	−	12.2025i	0.867927	−	0.501098i	0.00126806	−	0.999999i	$-0.499596\pi$
$593$	21.1354	−	12.2025i	0.867927	−	0.501098i	0.866659	+	0.498901i	$0.166263\pi$
$594$	0.579927	+	1.69296i	0.0237947	+	0.0694632i
$595$	11.8324	+	1.22481i	0.485080	+	0.0502121i
$596$	−0.783818	+	0.608384i	−0.0321064	+	0.0249204i
$597$	−1.35158	−	2.34101i	−0.0553165	−	0.0958110i
$598$	−5.49489	+	28.0308i	−0.224703	+	1.14627i
$599$	−18.0000	−	10.3923i	−0.735460	−	0.424618i	0.0849563	−	0.996385i	$-0.472925\pi$
$599$	−18.0000	−	10.3923i	−0.735460	−	0.424618i	−0.820416	+	0.571767i	$0.806258\pi$
$600$	2.86709	+	0.163967i	0.117048	+	0.00669391i
$601$		−	10.6623i		−	0.434924i	−0.976069	−	0.217462i	$-0.930222\pi$
$601$		−	10.6623i		−	0.434924i	0.976069	−	0.217462i	$-0.0697778\pi$
$602$	17.1628	−	16.0041i	0.699502	−	0.652277i
$603$			2.80766i			0.114337i
$604$	9.99528	−	24.5146i	0.406702	−	0.997484i
$605$	−19.9633	−	11.5258i	−0.811622	−	0.468590i
$606$	1.29525	+	0.253908i	0.0526160	+	0.0103143i
$607$	20.0215	+	34.6782i	0.812646	+	1.40754i	0.911006	+	0.412393i	$0.135307\pi$
$607$	20.0215	+	34.6782i	0.812646	+	1.40754i	−0.0983597	+	0.995151i	$0.531360\pi$
$608$	−1.86460	−	23.4577i	−0.0756196	−	0.951335i
$609$	14.6226	−	20.1931i	0.592539	−	0.818265i
$610$	36.4308	−	12.4794i	1.47504	−	0.505276i
$611$	−19.0837	+	11.0180i	−0.772044	+	0.445740i
$612$	3.63230	−	0.498720i	0.146827	−	0.0201596i
$613$	−11.2481	+	19.4822i	−0.454305	+	0.786879i	−0.998648	−	0.0519838i	$-0.983446\pi$
$613$	−11.2481	+	19.4822i	−0.454305	+	0.786879i	0.544343	+	0.838863i	$0.316779\pi$
$614$	9.22591	+	8.04574i	0.372328	+	0.324700i
$615$	2.67251			0.107766
$616$	−8.85118	+	3.36526i	−0.356624	+	0.135590i
$617$	−18.0820			−0.727954			−0.363977	−	0.931408i	$-0.618581\pi$
$617$	−18.0820			−0.727954			−0.363977	+	0.931408i	$0.618581\pi$
$618$	4.40109	+	3.83811i	0.177038	+	0.154391i
$619$	16.0465	−	27.7933i	0.644962	−	1.11711i	−0.339348	−	0.940661i	$-0.610207\pi$
$619$	16.0465	−	27.7933i	0.644962	−	1.11711i	0.984310	−	0.176446i	$-0.0564601\pi$
$620$	45.8739	−	6.29855i	1.84234	−	0.252956i
$621$	−5.83564	+	3.36921i	−0.234176	+	0.135202i
$622$	12.4994	−	4.28168i	0.501180	−	0.171680i
$623$	20.7032	−	9.25671i	0.829455	−	0.370862i
$624$	11.6150	+	2.97448i	0.464971	+	0.119074i
$625$	14.5229	+	25.1543i	0.580915	+	1.00617i
$626$	10.2357	+	2.00650i	0.409100	+	0.0801958i
$627$	−4.55863	−	2.63193i	−0.182054	−	0.105109i
$628$	−3.82201	+	9.37392i	−0.152515	+	0.374060i
$629$		−	13.7699i		−	0.549041i
$630$	2.06421	+	8.94168i	0.0822399	+	0.356245i
$631$			2.95509i			0.117640i	0.998269	+	0.0588201i	$0.0187338\pi$
$631$			2.95509i			0.117640i	−0.998269	+	0.0588201i	$0.981266\pi$
$632$	−0.288050	+	5.03678i	−0.0114580	+	0.200352i
$633$	15.7442	+	9.08990i	0.625774	+	0.361291i
$634$	0.987620	−	5.03811i	0.0392234	−	0.200089i
$635$	7.82798	+	13.5585i	0.310644	+	0.538051i
$636$	−0.113206	+	0.0878679i	−0.00448889	+	0.00348419i
$637$	−4.29780	+	20.5372i	−0.170285	+	0.813715i
$638$	−5.46479	−	15.9532i	−0.216353	−	0.631593i
$639$	2.53126	−	1.46142i	0.100135	−	0.0578130i
$640$	5.94085	+	27.1048i	0.234833	+	1.07141i
$641$	20.7459	−	35.9329i	0.819412	−	1.41926i	−0.0867040	−	0.996234i	$-0.527633\pi$
$641$	20.7459	−	35.9329i	0.819412	−	1.41926i	0.906116	−	0.423029i	$-0.139033\pi$
$642$	12.8665	−	14.7538i	0.507801	−	0.582286i
$643$	16.7686			0.661290			0.330645	−	0.943755i	$-0.392734\pi$
$643$	16.7686			0.661290			0.330645	+	0.943755i	$0.392734\pi$
$644$	−18.8465	−	30.2686i	−0.742655	−	1.19275i
$645$	−15.3822			−0.605675
$646$	−7.08820	+	8.12792i	−0.278882	+	0.319789i
$647$	9.31180	−	16.1285i	0.366085	−	0.634077i	−0.622865	−	0.782329i	$-0.714031\pi$
$647$	9.31180	−	16.1285i	0.366085	−	0.634077i	0.988950	+	0.148252i	$0.0473647\pi$
$648$	1.27205	+	2.52624i	0.0499709	+	0.0992401i
$649$	−3.68967	+	2.13023i	−0.144832	+	0.0836189i
$650$	−1.39477	−	4.07172i	−0.0547075	−	0.159706i
$651$	10.1943	+	22.8001i	0.399545	+	0.893605i
$652$	14.7595	+	19.0155i	0.578026	+	0.744706i
$653$	−12.8305	−	22.2230i	−0.502095	−	0.869654i	−0.999997	−	0.00242072i	$-0.999229\pi$
$653$	−12.8305	−	22.2230i	−0.502095	−	0.869654i	0.497902	−	0.867233i	$-0.334104\pi$
$654$	0.267881	−	1.36653i	0.0104750	−	0.0534357i
$655$	−8.22428	−	4.74829i	−0.321349	−	0.185531i
$656$	1.17475	+	4.19734i	0.0458661	+	0.163879i
$657$		−	8.10495i		−	0.316204i
$658$	8.04270	−	26.3050i	0.313537	−	1.02548i
$659$			27.7044i			1.07921i	0.841919	+	0.539604i	$0.181426\pi$
$659$			27.7044i			1.07921i	−0.841919	+	0.539604i	$0.818574\pi$
$660$	5.74766	+	2.34348i	0.223727	+	0.0912199i
$661$	−29.5472	−	17.0591i	−1.14925	−	0.663522i	−0.200548	−	0.979684i	$-0.564272\pi$
$661$	−29.5472	−	17.0591i	−1.14925	−	0.663522i	−0.948705	+	0.316162i	$0.897606\pi$
$662$	0.872019	+	0.170942i	0.0338920	+	0.00664385i
$663$	−2.74744	−	4.75871i	−0.106702	−	0.184813i
$664$	−8.28060	+	12.6189i	−0.321350	+	0.489708i
$665$	−21.8630	−	15.8319i	−0.847811	−	0.613935i
$666$	10.0495	−	3.44247i	0.389411	−	0.133393i
$667$	54.9906	−	31.7489i	2.12925	−	1.22932i
$668$	−2.03065	−	14.7897i	−0.0785681	−	0.572231i
$669$	−5.79982	+	10.0456i	−0.224234	+	0.388385i
$670$	7.33953	+	6.40066i	0.283551	+	0.247279i
$671$	14.0489			0.542352
$672$	−13.1361	+	7.17242i	−0.506735	+	0.276682i
$673$	−17.7032			−0.682407			−0.341203	−	0.939990i	$-0.610834\pi$
$673$	−17.7032			−0.682407			−0.341203	+	0.939990i	$0.610834\pi$
$674$	23.7811	+	20.7390i	0.916012	+	0.798836i
$675$	0.507662	−	0.879296i	0.0195399	−	0.0338441i
$676$	1.09237	+	7.95601i	0.0420142	+	0.306000i
$677$	−35.5808	+	20.5426i	−1.36748	+	0.789516i	−0.990606	−	0.136747i	$-0.956335\pi$
$677$	−35.5808	+	20.5426i	−1.36748	+	0.789516i	−0.376876	+	0.926264i	$0.623002\pi$
$678$	6.73212	−	2.30609i	0.258545	−	0.0885650i
$679$	1.93522	−	18.6954i	0.0742668	−	0.717462i
$680$	6.97690	−	10.6322i	0.267552	−	0.407725i
$681$	−5.08054	−	8.79975i	−0.194687	−	0.337207i
$682$	16.5773	+	3.24965i	0.634779	+	0.124436i
$683$	−18.3842	−	10.6141i	−0.703450	−	0.406137i	0.105181	−	0.994453i	$-0.466458\pi$
$683$	−18.3842	−	10.6141i	−0.703450	−	0.406137i	−0.808631	+	0.588316i	$0.799791\pi$
$684$	−7.70395	−	3.14112i	−0.294568	−	0.120104i
$685$		−	36.0612i		−	1.37783i
$686$	−13.5599	−	22.4082i	−0.517721	−	0.855550i
$687$			23.0970i			0.881204i
$688$	−6.76151	−	24.1587i	−0.257780	−	0.921042i
$689$	0.186000	+	0.107387i	0.00708603	+	0.00409112i
$690$	−4.49611	+	22.9358i	−0.171164	+	0.873152i
$691$	−19.4878	−	33.7539i	−0.741352	−	1.28406i	−0.951880	−	0.306472i	$-0.900851\pi$
$691$	−19.4878	−	33.7539i	−0.741352	−	1.28406i	0.210528	−	0.977588i	$-0.432482\pi$
$692$	5.35158	+	6.89477i	0.203437	+	0.262100i
$693$	−0.344712	+	3.33012i	−0.0130945	+	0.126501i
$694$	3.15985	+	9.22447i	0.119946	+	0.350156i
$695$	4.28321	−	2.47291i	0.162471	−	0.0938028i
$696$	−11.9868	−	23.8053i	−0.454359	−	0.902339i
$697$	0.998775	−	1.72993i	0.0378313	−	0.0655257i
$698$	12.5268	−	14.3642i	0.474145	−	0.543694i
$699$	−6.85547			−0.259298
$700$	4.73966	+	2.52989i	0.179142	+	0.0956207i
$701$	4.28115			0.161697			0.0808485	−	0.996726i	$-0.474237\pi$
$701$	4.28115			0.161697			0.0808485	+	0.996726i	$0.474237\pi$
$702$	2.78613	−	3.19481i	0.105156	−	0.120580i
$703$	−15.6232	+	27.0602i	−0.589241	+	1.02060i
$704$	−1.15410	+	10.0572i	−0.0434967	+	0.379043i
$705$	−15.6150	+	9.01530i	−0.588093	+	0.339536i
$706$	13.1002	+	38.2432i	0.493034	+	1.43930i
$707$	2.00000	+	1.44828i	0.0752177	+	0.0544682i
$708$	−5.31946	+	4.12886i	−0.199918	+	0.155172i
$709$	21.8796	+	37.8965i	0.821704	+	1.42323i	0.904412	+	0.426660i	$0.140310\pi$
$709$	21.8796	+	37.8965i	0.821704	+	1.42323i	−0.0827080	+	0.996574i	$0.526357\pi$
$710$	1.95023	−	9.94861i	0.0731907	−	0.373365i
$711$	1.54471	+	0.891841i	0.0579313	+	0.0334466i
$712$	1.38425	−	24.2046i	0.0518768	−	0.907107i
$713$			63.6092i			2.38218i
$714$	6.55942	+	2.00553i	0.245480	+	0.0750549i
$715$		−	9.30265i		−	0.347899i
$716$	−18.5504	+	45.4971i	−0.693262	+	1.70030i
$717$	−19.2481	−	11.1129i	−0.718832	−	0.415018i
$718$	−9.61496	−	1.88482i	−0.358827	−	0.0703409i
$719$	−20.7657	−	35.9672i	−0.774429	−	1.34135i	−0.935115	−	0.354345i	$-0.884704\pi$
$719$	−20.7657	−	35.9672i	−0.774429	−	1.34135i	0.160685	−	0.987006i	$-0.448630\pi$
$720$	9.50377	+	2.43382i	0.354185	+	0.0907033i
$721$	4.45924	+	9.97334i	0.166071	+	0.371427i
$722$	−2.26856	+	0.777097i	−0.0844270	+	0.0289205i
$723$	−13.3605	+	7.71367i	−0.496881	+	0.286874i
$724$	−23.2187	+	3.18795i	−0.862915	+	0.118479i
$725$	−4.78382	+	8.28582i	−0.177667	+	0.307727i
$726$	−10.0176	−	8.73619i	−0.371789	−	0.324230i
$727$	−7.19963			−0.267020			−0.133510	−	0.991047i	$-0.542625\pi$
$727$	−7.19963			−0.267020			−0.133510	+	0.991047i	$0.542625\pi$
$728$	17.3869	+	14.1718i	0.644400	+	0.525241i
$729$	1.00000			0.0370370
$730$	−21.1872	−	18.4770i	−0.784174	−	0.683863i
$731$	−5.74867	+	9.95698i	−0.212622	+	0.368272i
$732$	21.9984	−	3.02041i	0.813085	−	0.111638i
$733$	20.9219	−	12.0793i	0.772768	−	0.446158i	−0.0610934	−	0.998132i	$-0.519459\pi$
$733$	20.9219	−	12.0793i	0.772768	−	0.446158i	0.833861	+	0.551974i	$0.186125\pi$
$734$	−17.3173	+	5.93205i	−0.639192	+	0.218956i
$735$	−3.51661	+	16.8043i	−0.129712	+	0.619836i
$736$	−37.9984	+	3.02041i	−1.40064	+	0.111334i
$737$	1.77640	+	3.07682i	0.0654345	+	0.113336i
$738$	1.51223	+	0.296442i	0.0556659	+	0.0109122i
$739$	8.16690	+	4.71516i	0.300424	+	0.173450i	0.642634	−	0.766174i	$-0.277842\pi$
$739$	8.16690	+	4.71516i	0.300424	+	0.173450i	−0.342209	+	0.939624i	$0.611175\pi$
$740$	13.9110	−	34.1184i	0.511379	−	1.25422i
$741$			12.4689i			0.458058i
$742$	−0.261228	+	0.0603051i	−0.00958999	+	0.00221387i
$743$		−	2.32851i		−	0.0854248i	−0.999087	−	0.0427124i	$-0.986400\pi$
$743$		−	2.32851i		−	0.0854248i	0.999087	−	0.0427124i	$-0.0135999\pi$
$744$	26.6562	+	1.52445i	0.977263	+	0.0558890i
$745$	1.05375	+	0.608384i	0.0386065	+	0.0222895i
$746$	−0.837662	+	4.27313i	−0.0306690	+	0.156451i
$747$	2.66813	+	4.62133i	0.0976217	+	0.169086i
$748$	3.66497	−	2.84468i	0.134005	−	0.104012i
$749$	33.4337	−	14.9487i	1.22164	−	0.546215i
$750$	4.47889	+	13.0751i	0.163546	+	0.477435i
$751$	−26.9834	+	15.5789i	−0.984638	+	0.568481i	−0.903667	−	0.428235i	$-0.859135\pi$
$751$	−26.9834	+	15.5789i	−0.984638	+	0.568481i	−0.0809709	+	0.996716i	$0.525802\pi$
$752$	−21.0229	−	20.5614i	−0.766625	−	0.749797i
$753$	−11.1477	+	19.3084i	−0.406244	+	0.703636i
$754$	−26.2544	+	30.1054i	−0.956128	+	1.09638i
$755$	−32.4652			−1.18153
$756$	0.176187	+	5.28857i	0.00640786	+	0.192343i
$757$	−0.559856			−0.0203483			−0.0101742	−	0.999948i	$-0.503239\pi$
$757$	−0.559856			−0.0203483			−0.0101742	+	0.999948i	$0.503239\pi$
$758$	−4.84289	+	5.55326i	−0.175902	+	0.201704i
$759$	−4.26338	+	7.38439i	−0.154751	+	0.268036i
$760$	−25.7740	+	12.9781i	−0.934922	+	0.470766i
$761$	39.6196	−	22.8744i	1.43621	−	0.829196i	0.438625	−	0.898670i	$-0.355466\pi$
$761$	39.6196	−	22.8744i	1.43621	−	0.829196i	0.997584	+	0.0694744i	$0.0221322\pi$
$762$	2.92548	+	8.54029i	0.105979	+	0.309382i
$763$	1.52798	−	2.11006i	0.0553167	−	0.0763895i
$764$	−19.4883	−	25.1080i	−0.705063	−	0.908376i
$765$	−2.24806	−	3.89375i	−0.0812786	−	0.140779i
$766$	−10.5747	+	53.9446i	−0.382081	+	1.94910i
$767$	8.74002	+	5.04606i	0.315584	+	0.182203i
$768$	0.355074	+	15.9961i	0.0128126	+	0.577208i
$769$		−	8.33377i		−	0.300524i	−0.988646	−	0.150262i	$-0.951988\pi$
$769$		−	8.33377i		−	0.300524i	0.988646	−	0.150262i	$-0.0480117\pi$
$770$	7.91946	+	8.49284i	0.285398	+	0.306061i
$771$			2.86976i			0.103352i
$772$	−36.5466	−	14.9011i	−1.31534	−	0.536301i
$773$	26.5674	+	15.3387i	0.955563	+	0.551695i	0.894805	−	0.446458i	$-0.147315\pi$
$773$	26.5674	+	15.3387i	0.955563	+	0.551695i	0.0607584	+	0.998153i	$0.480648\pi$
$774$	−8.70395	−	1.70624i	−0.312857	−	0.0613294i
$775$	−4.79222	−	8.30037i	−0.172142	−	0.298158i
$776$	−16.7990	−	11.0236i	−0.603050	−	0.395725i
$777$	19.7678	+	2.04622i	0.709165	+	0.0734079i
$778$	−4.99708	+	1.71176i	−0.179154	+	0.0613695i
$779$	−3.92554	+	2.26641i	−0.140647	+	0.0812025i
$780$	−2.00000	−	14.5665i	−0.0716115	−	0.521564i
$781$	1.84928	−	3.20304i	0.0661723	−	0.114614i
$782$	13.1662	+	11.4820i	0.470821	+	0.410594i
$783$	−9.42323			−0.336759
$784$	−27.9379	+	1.86355i	−0.997783	+	0.0665555i
$785$	12.4141			0.443078
$786$	−4.12697	−	3.59905i	−0.147204	−	0.128374i
$787$	11.0792	−	19.1897i	0.394931	−	0.684040i	−0.598162	−	0.801375i	$-0.704102\pi$
$787$	11.0792	−	19.1897i	0.394931	−	0.684040i	0.993092	+	0.117335i	$0.0374353\pi$
$788$	0.271717	+	1.97898i	0.00967952	+	0.0704984i
$789$	−8.98186	+	5.18568i	−0.319763	+	0.184615i
$790$	5.85287	−	2.00491i	0.208236	−	0.0713314i
$791$	13.2423	+	1.37076i	0.470843	+	0.0487385i
$792$	2.99234	+	1.96359i	0.106328	+	0.0697732i
$793$	−16.6394	−	28.8203i	−0.590883	−	1.02344i
$794$	9.31180	+	1.82539i	0.330463	+	0.0647807i
$795$	0.152192	+	0.0878679i	0.00539768	+	0.00311635i
$796$	−5.00619	−	2.04116i	−0.177440	−	0.0723472i
$797$			24.1705i			0.856164i	0.903740	+	0.428082i	$0.140811\pi$
$797$			24.1705i			0.856164i	−0.903740	+	0.428082i	$0.859189\pi$
$798$	−10.6150	−	11.3835i	−0.375766	−	0.402971i
$799$			13.4768i			0.476776i
$800$	4.73086	−	3.25687i	0.167261	−	0.115148i
$801$	−7.42323	−	4.28581i	−0.262287	−	0.151431i
$802$	−1.59087	+	8.11542i	−0.0561754	+	0.286566i
$803$	−5.12798	−	8.88192i	−0.180963	−	0.313436i
$804$	3.44306	+	4.43590i	0.121427	+	0.156442i
$805$	−25.6456	+	35.4152i	−0.903889	+	1.24822i
$806$	−12.9676	−	37.8560i	−0.456765	−	1.33342i
$807$	−4.48011	+	2.58659i	−0.157707	+	0.0910524i
$808$	2.35777	−	1.18722i	0.0829462	−	0.0417663i
$809$	−7.61046	+	13.1817i	−0.267569	+	0.463444i	−0.968234	−	0.250047i	$-0.919554\pi$
$809$	−7.61046	+	13.1817i	−0.267569	+	0.463444i	0.700664	+	0.713491i	$0.252887\pi$
$810$	2.27971	−	2.61411i	0.0801009	−	0.0918504i
$811$	48.4574			1.70157			0.850785	−	0.525515i	$-0.176127\pi$
$811$	48.4574			1.70157			0.850785	+	0.525515i	$0.176127\pi$
$812$	−1.66025	−	49.8354i	−0.0582634	−	1.74888i
$813$	24.2391			0.850101
$814$	8.83485	−	10.1308i	0.309661	−	0.355083i
$815$	14.7595	−	25.5642i	0.517002	−	0.895474i
$816$	5.12719	−	5.24226i	0.179487	−	0.183516i
$817$	22.5943	−	13.0448i	0.790474	−	0.456380i
$818$	14.1454	+	41.2942i	0.494581	+	1.44382i
$819$	7.23978	−	3.23702i	0.252978	−	0.113111i
$820$	4.22238	−	3.27732i	0.147452	−	0.114449i
$821$	−25.7647	−	44.6257i	−0.899193	−	1.55745i	−0.828528	−	0.559948i	$-0.810821\pi$
$821$	−25.7647	−	44.6257i	−0.899193	−	1.55745i	−0.0706654	−	0.997500i	$-0.522512\pi$
$822$	4.00000	−	20.4050i	0.139516	−	0.711708i
$823$	1.90279	+	1.09858i	0.0663272	+	0.0382941i	0.532797	−	0.846243i	$-0.321141\pi$
$823$	1.90279	+	1.09858i	0.0663272	+	0.0382941i	−0.466470	+	0.884537i	$0.654474\pi$
$824$	11.6601	+	0.666834i	0.406199	+	0.0232303i
$825$		−	1.28479i		−	0.0447305i
$826$	−12.2750	+	2.83370i	−0.427101	+	0.0985971i
$827$		−	10.2864i		−	0.357693i	−0.983877	−	0.178846i	$-0.942763\pi$
$827$		−	10.2864i		−	0.357693i	0.983877	−	0.178846i	$-0.0572365\pi$
$828$	−5.08820	+	12.4794i	−0.176827	+	0.433689i
$829$	0.662548	+	0.382522i	0.0230112	+	0.0132855i	0.511461	−	0.859306i	$-0.329104\pi$
$829$	0.662548	+	0.382522i	0.0230112	+	0.0132855i	−0.488450	+	0.872592i	$0.662438\pi$
$830$	18.1632	+	3.56054i	0.630455	+	0.123588i
$831$	1.50766	+	2.61135i	0.0523002	+	0.0905866i
$832$	21.9984	−	9.54406i	0.762658	−	0.330881i
$833$	9.56326	+	8.55644i	0.331347	+	0.296463i
$834$	2.69793	−	0.924179i	0.0934217	−	0.0320017i
$835$	−15.8542	+	9.15345i	−0.548659	+	0.316768i
$836$	−10.4299	+	1.43203i	−0.360724	+	0.0495279i
$837$	4.71989	−	8.17509i	0.163143	−	0.282572i
$838$	−31.0018	−	27.0361i	−1.07094	−	0.933946i
$839$	−3.50389			−0.120968			−0.0604839	−	0.998169i	$-0.519264\pi$
$839$	−3.50389			−0.120968			−0.0604839	+	0.998169i	$0.519264\pi$
$840$	14.2265	+	11.5958i	0.490862	+	0.400095i
$841$	59.7973			2.06198
$842$	−14.7771	−	12.8868i	−0.509253	−	0.444110i
$843$	3.45961	−	5.99222i	0.119155	−	0.206383i
$844$	36.0216	−	4.94582i	1.23992	−	0.170242i
$845$	8.52866	−	4.92402i	0.293395	−	0.169392i
$846$	−9.83564	+	3.36921i	−0.338156	+	0.115836i
$847$	−10.1500	−	22.7010i	−0.348758	−	0.780017i
$848$	−0.0711034	+	0.277650i	−0.00244170	+	0.00953453i
$849$	−10.2870	−	17.8176i	−0.353048	−	0.611497i
$850$	−2.58309	−	0.506362i	−0.0885991	−	0.0173681i
$851$	43.8341	+	25.3076i	1.50261	+	0.867534i
$852$	2.20705	−	5.41305i	0.0756123	−	0.185448i
$853$		−	25.3974i		−	0.869589i	−0.900530	−	0.434795i	$-0.856821\pi$
$853$		−	25.3974i		−	0.869589i	0.900530	−	0.434795i	$-0.143179\pi$
$854$	39.7260	+	12.1461i	1.35940	+	0.415632i
$855$			10.2025i			0.348919i
$856$	2.23543	−	39.0882i	0.0764055	−	1.33601i
$857$	−25.0609	−	14.4689i	−0.856065	−	0.494249i	0.00662744	−	0.999978i	$-0.497890\pi$
$857$	−25.0609	−	14.4689i	−0.856065	−	0.494249i	−0.862693	+	0.505729i	$0.831224\pi$
$858$	1.03187	−	5.26385i	0.0352276	−	0.179705i
$859$	2.34404	+	4.05999i	0.0799775	+	0.138525i	0.903240	−	0.429136i	$-0.141182\pi$
$859$	2.34404	+	4.05999i	0.0799775	+	0.138525i	−0.823263	+	0.567661i	$0.807848\pi$
$860$	−24.3028	+	18.8633i	−0.828718	+	0.643235i
$861$	2.33503	+	1.69089i	0.0795777	+	0.0576254i
$862$	14.6195	+	42.6782i	0.497941	+	1.45363i
$863$	−37.6419	+	21.7325i	−1.28134	+	0.739784i	−0.977094	−	0.212808i	$-0.931739\pi$
$863$	−37.6419	+	21.7325i	−1.28134	+	0.739784i	−0.304250	+	0.952592i	$0.598406\pi$
$864$	5.10769	+	2.43135i	0.173767	+	0.0827162i
$865$	5.35158	−	9.26921i	0.181959	−	0.315163i
$866$	9.12993	−	10.4691i	0.310248	−	0.355756i
$867$	13.6394			0.463219
$868$	44.0661	+	23.5211i	1.49570	+	0.798359i
$869$	2.25706			0.0765655
$870$	−21.4823	+	24.6333i	−0.728317	+	0.835149i
$871$	4.20791	−	7.28831i	0.142580	−	0.246955i
$872$	−1.25256	−	2.48753i	−0.0424169	−	0.0842383i
$873$	−6.15219	+	3.55197i	−0.208220	+	0.120216i
$874$	−12.8465	−	37.5023i	−0.434538	−	1.26854i
$875$	−2.66227	+	25.7192i	−0.0900013	+	0.869467i
$876$	−9.93917	−	12.8052i	−0.335813	−	0.432649i
$877$	23.0063	+	39.8481i	0.776868	+	1.34558i	0.933738	+	0.357956i	$0.116526\pi$
$877$	23.0063	+	39.8481i	0.776868	+	1.34558i	−0.156870	+	0.987619i	$0.550140\pi$
$878$	4.63568	−	23.6478i	0.156447	−	0.798075i
$879$	24.5183	+	14.1556i	0.826982	+	0.477458i
$880$	11.9547	−	3.34587i	0.402993	−	0.112789i
$881$		−	40.8047i		−	1.37475i	−0.726304	−	0.687373i	$-0.758764\pi$
$881$		−	40.8047i		−	1.37475i	0.726304	−	0.687373i	$-0.241236\pi$
$882$	−3.85383	+	9.11855i	−0.129765	+	0.307038i
$883$			6.06234i			0.204014i	0.994784	+	0.102007i	$0.0325264\pi$
$883$			6.06234i			0.204014i	−0.994784	+	0.102007i	$0.967474\pi$
$884$	−10.1764	−	4.14920i	−0.342269	−	0.139553i
$885$	7.15140	+	4.12886i	0.240392	+	0.138790i
$886$	−11.6982	−	2.29320i	−0.393009	−	0.0770415i
$887$	22.1276	+	38.3262i	0.742973	+	1.28687i	0.951136	+	0.308772i	$0.0999181\pi$
$887$	22.1276	+	38.3262i	0.742973	+	1.28687i	−0.208163	+	0.978094i	$0.566749\pi$
$888$	11.6560	−	17.7626i	0.391149	−	0.596075i
$889$	−1.73892	+	16.7991i	−0.0583216	+	0.563422i
$890$	−28.1264	+	9.63473i	−0.942799	+	0.322957i
$891$	1.09586	−	0.632697i	0.0367128	−	0.0211961i
$892$	3.15568	+	22.9836i	0.105660	+	0.769549i
$893$	15.2908	−	26.4844i	0.511685	−	0.886265i
$894$	0.528777	+	0.461136i	0.0176849	+	0.0154227i
$895$	60.2528			2.01403
$896$	−11.9584	+	27.4408i	−0.399504	+	0.916732i
$897$	20.1980			0.674393
$898$	−10.2754	−	8.96100i	−0.342895	−	0.299032i
$899$	−44.4766	+	77.0358i	−1.48338	+	2.56929i
$900$	−0.276219	−	2.01177i	−0.00920731	−	0.0670591i
$901$	0.113755	−	0.0656762i	0.00378971	−	0.00218799i
$902$	1.84475	−	0.631922i	0.0614236	−	0.0210407i
$903$	−13.4398	−	9.73229i	−0.447248	−	0.323870i
$904$	7.80827	−	11.8991i	0.259699	−	0.395759i
$905$	14.3702	+	24.8899i	0.477681	+	0.827368i
$906$	−18.3703	−	3.60113i	−0.610312	−	0.119639i
$907$	−5.54526	−	3.20156i	−0.184127	−	0.106306i	0.405103	−	0.914271i	$-0.367236\pi$
$907$	−5.54526	−	3.20156i	−0.184127	−	0.106306i	−0.589230	+	0.807965i	$0.700569\pi$
$908$	−18.8181	−	7.67266i	−0.624500	−	0.254626i
$909$		−	0.933313i		−	0.0309561i
$910$	8.04270	−	26.3050i	0.266613	−	0.872004i
$911$		−	48.9687i		−	1.62241i	−0.584765	−	0.811203i	$-0.698813\pi$
$911$		−	48.9687i		−	1.62241i	0.584765	−	0.811203i	$-0.301187\pi$
$912$	−16.0237	+	4.48468i	−0.530596	+	0.148503i
$913$	5.84781	+	3.37623i	0.193534	+	0.111737i
$914$	7.90190	−	40.3097i	0.261372	−	1.33333i
$915$	−13.6150	−	23.5818i	−0.450097	−	0.779590i
$916$	28.3240	+	36.4915i	0.935850	+	1.20571i
$917$	−4.18150	−	9.35216i	−0.138085	−	0.308835i
$918$	−0.840146	−	2.45262i	−0.0277290	−	0.0809484i
$919$	−21.2676	+	12.2789i	−0.701554	+	0.405042i	−0.807926	−	0.589284i	$-0.799410\pi$
$919$	−21.2676	+	12.2789i	−0.701554	+	0.405042i	0.106372	+	0.994326i	$0.466077\pi$
$920$	21.0229	+	41.7506i	0.693103	+	1.37648i
$921$	4.32798	−	7.49628i	0.142612	−	0.247011i
$922$	22.2891	−	25.5585i	0.734051	−	0.841724i
$923$	−8.76108			−0.288374
$924$	3.53914	+	5.68408i	0.116429	+	0.186992i
$925$	−7.62654			−0.250759
$926$	26.4885	−	30.3739i	0.870466	−	0.998149i
$927$	2.06460	−	3.57600i	0.0678105	−	0.117451i
$928$	−48.1310	−	22.9112i	−1.57998	−	0.752096i
$929$	−8.51680	+	4.91718i	−0.279427	+	0.161327i	−0.633164	−	0.774018i	$-0.718244\pi$
$929$	−8.51680	+	4.91718i	−0.279427	+	0.161327i	0.353737	+	0.935345i	$0.384911\pi$
$930$	−10.6106	−	30.9752i	−0.347934	−	1.01572i
$931$	−9.08539	−	27.6653i	−0.297762	−	0.906695i
$932$	−10.8311	+	8.40692i	−0.354786	+	0.275378i
$933$	−4.67129	−	8.09091i	−0.152931	−	0.264884i
$934$	5.05510	−	25.7874i	0.165408	−	0.843790i
$935$	−4.92712	−	2.84468i	−0.161134	−	0.0930308i
$936$	0.484063	−	8.46422i	0.0158221	−	0.276662i
$937$			38.1447i			1.24613i	0.782168	+	0.623067i	$0.214114\pi$
$937$			38.1447i			1.24613i	−0.782168	+	0.623067i	$0.785886\pi$
$938$	2.36303	+	10.2361i	0.0771555	+	0.334220i
$939$		−	7.37547i		−	0.240689i
$940$	−13.6150	+	33.3923i	−0.444071	+	1.08914i
$941$	29.7788	+	17.1928i	0.970760	+	0.560469i	0.899468	−	0.436987i	$-0.143954\pi$
$941$	29.7788	+	17.1928i	0.970760	+	0.560469i	0.0712922	+	0.997455i	$0.477288\pi$
$942$	7.02446	+	1.37700i	0.228869	+	0.0448652i
$943$	3.67129	+	6.35886i	0.119554	+	0.207073i
$944$	−3.34111	+	13.0466i	−0.108744	+	0.424631i
$945$	5.92385	−	2.64865i	0.192703	−	0.0861605i
$946$	−10.6179	+	3.63716i	−0.345217	+	0.118254i
$947$	14.2630	−	8.23476i	0.463486	−	0.267594i	−0.250023	−	0.968240i	$-0.580438\pi$
$947$	14.2630	−	8.23476i	0.463486	−	0.267594i	0.713509	+	0.700646i	$0.247105\pi$
$948$	3.53420	−	0.485251i	0.114786	−	0.0157602i
$949$	−12.1471	+	21.0394i	−0.394311	+	0.682966i
$950$	4.50170	+	3.92585i	0.146055	+	0.127371i
$951$	−3.63028			−0.117720
$952$	12.8228	−	4.87529i	0.415589	−	0.158009i
$953$	−52.4540			−1.69915			−0.849576	−	0.527466i	$-0.823142\pi$
$953$	−52.4540			−1.69915			−0.849576	+	0.527466i	$0.823142\pi$
$954$	0.0763704	+	0.0666011i	0.00247258	+	0.00215629i
$955$	−19.4883	+	33.7548i	−0.630628	+	1.09228i
$956$	−44.0383	+	6.04652i	−1.42430	+	0.195558i
$957$	−10.3266	+	5.96205i	−0.333811	+	0.192726i
$958$	−37.9178	+	12.9888i	−1.22507	+	0.419648i
$959$	22.8158	−	31.5074i	0.736761	−	1.01743i
$960$	17.9999	−	7.80929i	0.580944	−	0.252044i
$961$	−29.0547	−	50.3243i	−0.937250	−	1.62336i
$962$	−31.2465	−	6.12524i	−1.00743	−	0.197486i
$963$	−11.9878	−	6.92118i	−0.386303	−	0.223032i
$964$	−11.6492	+	28.5711i	−0.375196	+	0.920213i
$965$			48.3995i			1.55803i
$966$	−18.4398	+	17.1949i	−0.593290	+	0.553235i
$967$		−	16.3573i		−	0.526016i	−0.964794	−	0.263008i	$-0.915285\pi$
$967$		−	16.3573i		−	0.526016i	0.964794	−	0.263008i	$-0.0847146\pi$
$968$	−26.5404	−	1.51783i	−0.853040	−	0.0487848i
$969$	6.60414	+	3.81290i	0.212155	+	0.122488i
$970$	−4.74000	+	24.1800i	−0.152192	+	0.776372i
$971$	−11.6591	−	20.1942i	−0.374159	−	0.648063i	0.616042	−	0.787714i	$-0.288735\pi$
$971$	−11.6591	−	20.1942i	−0.374159	−	0.648063i	−0.990201	+	0.139651i	$0.955402\pi$
$972$	1.57993	−	1.22631i	0.0506762	−	0.0393338i
$973$	5.30693	+	0.549337i	0.170132	+	0.0176109i
$974$	19.0245	+	55.5377i	0.609585	+	1.77954i
$975$	−2.63564	+	1.52169i	−0.0844081	+	0.0487331i
$976$	31.0519	−	31.7489i	0.993948	−	1.01626i
$977$	−19.9922	+	34.6275i	−0.639608	+	1.10783i	0.345911	+	0.938267i	$0.387570\pi$
$977$	−19.9922	+	34.6275i	−0.639608	+	1.10783i	−0.985519	+	0.169566i	$0.945763\pi$
$978$	11.1872	−	12.8282i	0.357728	−	0.410201i
$979$	−10.8465			−0.346655
$980$	15.0512	+	30.8620i	0.480795	+	0.985851i
$981$	−0.984676			−0.0314383
$982$	1.60551	−	1.84101i	0.0512338	−	0.0587490i
$983$	10.7628	−	18.6417i	0.343279	−	0.594577i	−0.641761	−	0.766905i	$-0.721796\pi$
$983$	10.7628	−	18.6417i	0.343279	−	0.594577i	0.985040	+	0.172328i	$0.0551290\pi$
$984$	2.75274	−	1.38610i	0.0877541	−	0.0441873i
$985$	2.12143	−	1.22481i	0.0675943	−	0.0390256i
$986$	7.91689	+	23.1116i	0.252125	+	0.736022i
$987$	−19.3471	−	2.00268i	−0.615824	−	0.0637459i
$988$	15.2908	+	19.7000i	0.486464	+	0.626741i
$989$	−21.1309	−	36.5998i	−0.671923	−	1.16381i
$990$	0.844315	−	4.30707i	0.0268341	−	0.136888i
$991$	9.69666	+	5.59837i	0.308025	+	0.177838i	0.646042	−	0.763302i	$-0.276423\pi$
$991$	9.69666	+	5.59837i	0.308025	+	0.177838i	−0.338018	+	0.941140i	$0.609756\pi$
$992$	43.9843	−	30.2802i	1.39650	−	0.961396i
$993$		−	0.628347i		−	0.0199400i
$994$	7.99841	−	7.45841i	0.253694	−	0.236567i
$995$			6.62982i			0.210179i
$996$	9.88263	+	4.02942i	0.313143	+	0.127677i
$997$	−49.1699	−	28.3883i	−1.55723	−	0.899066i	−0.997521	−	0.0703755i	$-0.977580\pi$
$997$	−49.1699	−	28.3883i	−1.55723	−	0.899066i	−0.559707	−	0.828690i	$-0.689086\pi$
$998$	58.6859	+	11.5042i	1.85767	+	0.364159i
$999$	−3.75572	−	6.50509i	−0.118826	−	0.205812i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	84.2.o.a.31.1	yes	8
3.2	odd	2		252.2.bf.g.199.4		8
4.3	odd	2		84.2.o.b.31.2	yes	8
7.2	even	3		588.2.o.b.19.2		8
7.3	odd	6		588.2.b.a.391.7		8
7.4	even	3		588.2.b.b.391.7		8
7.5	odd	6		84.2.o.b.19.2	yes	8
7.6	odd	2		588.2.o.d.31.1		8
8.3	odd	2		1344.2.bl.i.703.1		8
8.5	even	2		1344.2.bl.j.703.1		8
12.11	even	2		252.2.bf.f.199.3		8
21.5	even	6		252.2.bf.f.19.3		8
21.11	odd	6		1764.2.b.i.1567.2		8
21.17	even	6		1764.2.b.j.1567.2		8
28.3	even	6		588.2.b.b.391.8		8
28.11	odd	6		588.2.b.a.391.8		8
28.19	even	6	inner	84.2.o.a.19.1	✓	8
28.23	odd	6		588.2.o.d.19.1		8
28.27	even	2		588.2.o.b.31.2		8
56.5	odd	6		1344.2.bl.i.1279.1		8
56.19	even	6		1344.2.bl.j.1279.1		8
84.11	even	6		1764.2.b.j.1567.1		8
84.47	odd	6		252.2.bf.g.19.4		8
84.59	odd	6		1764.2.b.i.1567.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
84.2.o.a.19.1	✓	8	28.19	even	6	inner
84.2.o.a.31.1	yes	8	1.1	even	1	trivial
84.2.o.b.19.2	yes	8	7.5	odd	6
84.2.o.b.31.2	yes	8	4.3	odd	2
252.2.bf.f.19.3		8	21.5	even	6
252.2.bf.f.199.3		8	12.11	even	2
252.2.bf.g.19.4		8	84.47	odd	6
252.2.bf.g.199.4		8	3.2	odd	2
588.2.b.a.391.7		8	7.3	odd	6
588.2.b.a.391.8		8	28.11	odd	6
588.2.b.b.391.7		8	7.4	even	3
588.2.b.b.391.8		8	28.3	even	6
588.2.o.b.19.2		8	7.2	even	3
588.2.o.b.31.2		8	28.27	even	2
588.2.o.d.19.1		8	28.23	odd	6
588.2.o.d.31.1		8	7.6	odd	2
1344.2.bl.i.703.1		8	8.3	odd	2
1344.2.bl.i.1279.1		8	56.5	odd	6
1344.2.bl.j.703.1		8	8.5	even	2
1344.2.bl.j.1279.1		8	56.19	even	6
1764.2.b.i.1567.1		8	84.59	odd	6
1764.2.b.i.1567.2		8	21.11	odd	6
1764.2.b.j.1567.1		8	84.11	even	6
1764.2.b.j.1567.2		8	21.17	even	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:	\( N \)	\(=\)	\( 84 = 2^{2} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	84.o (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.06584 - 0.929502i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(0.272050 + 1.98141i) q^{4} +(2.12403 - 1.22631i) q^{5} +(1.33790 - 0.458297i) q^{6} +(2.63169 + 0.272415i) q^{7} +(1.55176 - 2.36475i) q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(-1.06584 - 0.929502i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(0.272050 + 1.98141i) q^{4} +(2.12403 - 1.22631i) q^{5} +(1.33790 - 0.458297i) q^{6} +(2.63169 + 0.272415i) q^{7} +(1.55176 - 2.36475i) q^{8} +(-0.500000 - 0.866025i) q^{9} +(-3.40374 - 0.667235i) q^{10} +(-1.09586 - 0.632697i) q^{11} +(-1.85198 - 0.755103i) q^{12} +2.99744i q^{13} +(-2.55176 - 2.73651i) q^{14} +2.45262i q^{15} +(-3.85198 + 1.07809i) q^{16} +(1.58759 + 0.916595i) q^{17} +(-0.272050 + 1.38780i) q^{18} +(-2.07993 - 3.60254i) q^{19} +(3.00766 + 3.87495i) q^{20} +(-1.55176 + 2.14290i) q^{21} +(0.579927 + 1.69296i) q^{22} +(-5.83564 + 3.36921i) q^{23} +(1.27205 + 2.52624i) q^{24} +(0.507662 - 0.879296i) q^{25} +(2.78613 - 3.19481i) q^{26} +1.00000 q^{27} +(0.176187 + 5.28857i) q^{28} -9.42323 q^{29} +(2.27971 - 2.61411i) q^{30} +(4.71989 - 8.17509i) q^{31} +(5.10769 + 2.43135i) q^{32} +(1.09586 - 0.632697i) q^{33} +(-0.840146 - 2.45262i) q^{34} +(5.92385 - 2.64865i) q^{35} +(1.57993 - 1.22631i) q^{36} +(-3.75572 - 6.50509i) q^{37} +(-1.13169 + 5.77304i) q^{38} +(-2.59586 - 1.49872i) q^{39} +(0.396078 - 6.92573i) q^{40} -1.08966i q^{41} +(3.64577 - 0.841635i) q^{42} +6.27176i q^{43} +(0.955503 - 2.34348i) q^{44} +(-2.12403 - 1.22631i) q^{45} +(9.35158 + 1.83319i) q^{46} +(3.67579 + 6.36666i) q^{47} +(0.992338 - 3.87495i) q^{48} +(6.85158 + 1.43382i) q^{49} +(-1.35840 + 0.465320i) q^{50} +(-1.58759 + 0.916595i) q^{51} +(-5.93917 + 0.815456i) q^{52} +(0.0358262 - 0.0620528i) q^{53} +(-1.06584 - 0.929502i) q^{54} -3.10353 q^{55} +(4.72795 - 5.80056i) q^{56} +4.15985 q^{57} +(10.0437 + 8.75892i) q^{58} +(1.68345 - 2.91583i) q^{59} +(-4.85964 + 0.667235i) q^{60} +(-9.61496 + 5.55120i) q^{61} +(-12.6294 + 4.32623i) q^{62} +(-1.07993 - 2.41532i) q^{63} +(-3.18406 - 7.33906i) q^{64} +(3.67579 + 6.36666i) q^{65} +(-1.75611 - 0.344251i) q^{66} +(-2.43151 - 1.40383i) q^{67} +(-1.38425 + 3.39503i) q^{68} -6.73842i q^{69} +(-8.77582 - 2.68318i) q^{70} +2.92285i q^{71} +(-2.82381 - 0.161492i) q^{72} +(7.01910 + 4.05248i) q^{73} +(-2.04349 + 10.4244i) q^{74} +(0.507662 + 0.879296i) q^{75} +(6.57226 - 5.10126i) q^{76} +(-2.71162 - 1.96359i) q^{77} +(1.37372 + 4.01027i) q^{78} +(-1.54471 + 0.891841i) q^{79} +(-6.85964 + 7.01360i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-1.01284 + 1.16141i) q^{82} -5.33626 q^{83} +(-4.66813 - 2.49170i) q^{84} +4.49611 q^{85} +(5.82962 - 6.68473i) q^{86} +(4.71162 - 8.16076i) q^{87} +(-3.19669 + 1.60964i) q^{88} +(7.42323 - 4.28581i) q^{89} +(1.12403 + 3.28134i) q^{90} +(-0.816548 + 7.88834i) q^{91} +(-8.26338 - 10.6462i) q^{92} +(4.71989 + 8.17509i) q^{93} +(2.00000 - 10.2025i) q^{94} +(-8.83564 - 5.10126i) q^{95} +(-4.65946 + 3.20772i) q^{96} -7.10394i q^{97} +(-5.96998 - 7.89679i) q^{98} +1.26539i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + q^{2} - 4 q^{3} - q^{4} - 2 q^{6} + 2 q^{7} + 4 q^{8} - 4 q^{9}+O(q^{10}) \) 8 * q + q^2 - 4 * q^3 - q^4 - 2 * q^6 + 2 * q^7 + 4 * q^8 - 4 * q^9	\( 8 q + q^{2} - 4 q^{3} - q^{4} - 2 q^{6} + 2 q^{7} + 4 q^{8} - 4 q^{9} - 5 q^{10} + 6 q^{11} - q^{12} - 12 q^{14} - 17 q^{16} + q^{18} - 6 q^{19} + 22 q^{20} - 4 q^{21} - 6 q^{22} + 7 q^{24} + 2 q^{25} + 18 q^{26} + 8 q^{27} + 13 q^{28} - 16 q^{29} + 13 q^{30} + 6 q^{31} - 9 q^{32} - 6 q^{33} - 28 q^{34} - 12 q^{35} + 2 q^{36} + 6 q^{37} + 10 q^{38} - 6 q^{39} - 17 q^{40} + 9 q^{42} - 23 q^{44} + 24 q^{46} + 4 q^{47} + 10 q^{48} + 4 q^{49} + 2 q^{50} + 16 q^{52} - 4 q^{53} + q^{54} - 8 q^{55} + 41 q^{56} + 12 q^{57} + 37 q^{58} - 14 q^{59} - 23 q^{60} + 12 q^{61} - 48 q^{62} + 2 q^{63} + 2 q^{64} + 4 q^{65} - 15 q^{66} + 42 q^{67} - 26 q^{68} + 3 q^{70} - 11 q^{72} - 18 q^{73} - 10 q^{74} + 2 q^{75} + 44 q^{76} + 8 q^{77} - 6 q^{78} - 6 q^{79} - 39 q^{80} - 4 q^{81} - 10 q^{82} + 4 q^{83} - 14 q^{84} - 32 q^{85} + 36 q^{86} + 8 q^{87} - 37 q^{88} - 8 q^{90} - 34 q^{91} - 28 q^{92} + 6 q^{93} + 16 q^{94} - 24 q^{95} + 21 q^{96} - 53 q^{98}+O(q^{100}) \) 8 * q + q^2 - 4 * q^3 - q^4 - 2 * q^6 + 2 * q^7 + 4 * q^8 - 4 * q^9 - 5 * q^10 + 6 * q^11 - q^12 - 12 * q^14 - 17 * q^16 + q^18 - 6 * q^19 + 22 * q^20 - 4 * q^21 - 6 * q^22 + 7 * q^24 + 2 * q^25 + 18 * q^26 + 8 * q^27 + 13 * q^28 - 16 * q^29 + 13 * q^30 + 6 * q^31 - 9 * q^32 - 6 * q^33 - 28 * q^34 - 12 * q^35 + 2 * q^36 + 6 * q^37 + 10 * q^38 - 6 * q^39 - 17 * q^40 + 9 * q^42 - 23 * q^44 + 24 * q^46 + 4 * q^47 + 10 * q^48 + 4 * q^49 + 2 * q^50 + 16 * q^52 - 4 * q^53 + q^54 - 8 * q^55 + 41 * q^56 + 12 * q^57 + 37 * q^58 - 14 * q^59 - 23 * q^60 + 12 * q^61 - 48 * q^62 + 2 * q^63 + 2 * q^64 + 4 * q^65 - 15 * q^66 + 42 * q^67 - 26 * q^68 + 3 * q^70 - 11 * q^72 - 18 * q^73 - 10 * q^74 + 2 * q^75 + 44 * q^76 + 8 * q^77 - 6 * q^78 - 6 * q^79 - 39 * q^80 - 4 * q^81 - 10 * q^82 + 4 * q^83 - 14 * q^84 - 32 * q^85 + 36 * q^86 + 8 * q^87 - 37 * q^88 - 8 * q^90 - 34 * q^91 - 28 * q^92 + 6 * q^93 + 16 * q^94 - 24 * q^95 + 21 * q^96 - 53 * q^98

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