LMFDB - Embedded newform 342.2.bf.a.257.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [342,2,Mod(155,342)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(342, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([3, 13]))

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

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

chi := DirichletCharacter("342.155");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 342 = 2 \cdot 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	342.bf (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:	$2.73088374913$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$2$ over $\Q(\zeta_{18})$
Coefficient field:	12.0.1952986685049.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 6 x^{11} + 27 x^{10} - 80 x^{9} + 186 x^{8} - 330 x^{7} + 463 x^{6} - 504 x^{5} + 420 x^{4} + \cdots + 3 $ x^12 - 6x^11 + 27x^10 - 80x^9 + 186x^8 - 330x^7 + 463x^6 - 504x^5 + 420x^4 - 258x^3 + 108x^2 - 27*x + 3
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			257.2
Root			$0.500000 + 1.68614i$ of defining polynomial
Character	$\chi$	$=$	342.257
Dual form			342.2.bf.a.173.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.766044 - 0.642788i) q^{2} +(-0.210069 + 1.71926i) q^{3} +(0.173648 - 0.984808i) q^{4} +(0.649762 + 0.774356i) q^{5} +(0.944200 + 1.45206i) q^{6} +2.88840 q^{7} +(-0.500000 - 0.866025i) q^{8} +(-2.91174 - 0.722330i) q^{9} +O(q^{10})$	\(q+(0.766044 - 0.642788i) q^{2} +(-0.210069 + 1.71926i) q^{3} +(0.173648 - 0.984808i) q^{4} +(0.649762 + 0.774356i) q^{5} +(0.944200 + 1.45206i) q^{6} +2.88840 q^{7} +(-0.500000 - 0.866025i) q^{8} +(-2.91174 - 0.722330i) q^{9} +(0.995493 + 0.175532i) q^{10} +(0.354477 + 0.204658i) q^{11} +(1.65667 + 0.505425i) q^{12} +(1.10505 + 3.03609i) q^{13} +(2.21264 - 1.85663i) q^{14} +(-1.46782 + 0.954444i) q^{15} +(-0.939693 - 0.342020i) q^{16} +(1.64303 - 0.289711i) q^{17} +(-2.69483 + 1.31830i) q^{18} +(0.598294 + 4.31764i) q^{19} +(0.875422 - 0.505425i) q^{20} +(-0.606764 + 4.96592i) q^{21} +(0.403097 - 0.0710768i) q^{22} +(-0.732021 - 0.129075i) q^{23} +(1.59396 - 0.677707i) q^{24} +(0.690804 - 3.91774i) q^{25} +(2.79807 + 1.61547i) q^{26} +(1.85354 - 4.85432i) q^{27} +(0.501565 - 2.84452i) q^{28} +(-5.00832 + 1.82288i) q^{29} +(-0.510909 + 1.67464i) q^{30} +(4.11334 - 2.37484i) q^{31} +(-0.939693 + 0.342020i) q^{32} +(-0.426325 + 0.566448i) q^{33} +(1.07241 - 1.27805i) q^{34} +(1.87677 + 2.23665i) q^{35} +(-1.21697 + 2.74207i) q^{36} -0.635980i q^{37} +(3.23365 + 2.92293i) q^{38} +(-5.45197 + 1.26208i) q^{39} +(0.345731 - 0.949888i) q^{40} +(-0.485725 - 2.75468i) q^{41} +(2.72723 + 4.19414i) q^{42} +(-0.859287 - 4.87326i) q^{43} +(0.263103 - 0.313554i) q^{44} +(-1.33260 - 2.72407i) q^{45} +(-0.643729 + 0.371657i) q^{46} +(-4.56352 - 12.5382i) q^{47} +(0.785424 - 1.54373i) q^{48} +1.34285 q^{49} +(-1.98909 - 3.44521i) q^{50} +(0.152939 + 2.88567i) q^{51} +(3.18185 - 0.561046i) q^{52} +(-11.6345 + 4.23461i) q^{53} +(-1.70040 - 4.91006i) q^{54} +(0.0718480 + 0.407470i) q^{55} +(-1.44420 - 2.50143i) q^{56} +(-7.54885 + 0.121621i) q^{57} +(-2.66487 + 4.61569i) q^{58} +(-6.37472 - 2.32021i) q^{59} +(0.685060 + 1.61126i) q^{60} +(3.61301 + 3.03168i) q^{61} +(1.62449 - 4.46324i) q^{62} +(-8.41027 - 2.08638i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(-1.63300 + 2.82843i) q^{65} +(0.0375216 + 0.707961i) q^{66} +(3.57361 - 4.25886i) q^{67} -1.66838i q^{68} +(0.375690 - 1.23142i) q^{69} +(2.87538 + 0.507007i) q^{70} +(2.24554 + 0.817311i) q^{71} +(0.830315 + 2.88281i) q^{72} +(-6.53990 + 5.48763i) q^{73} +(-0.408800 - 0.487189i) q^{74} +(6.59052 + 2.01067i) q^{75} +(4.35594 + 0.160547i) q^{76} +(1.02387 + 0.591133i) q^{77} +(-3.36521 + 4.47127i) q^{78} +(4.10023 - 11.2653i) q^{79} +(-0.345731 - 0.949888i) q^{80} +(7.95648 + 4.20647i) q^{81} +(-2.14276 - 1.79799i) q^{82} -12.4849i q^{83} +(4.78512 + 1.45987i) q^{84} +(1.29192 + 1.08405i) q^{85} +(-3.79072 - 3.18079i) q^{86} +(-2.08192 - 8.99355i) q^{87} -0.409315i q^{88} +(5.14599 + 4.31800i) q^{89} +(-2.77183 - 1.23018i) q^{90} +(3.19181 + 8.76943i) q^{91} +(-0.254228 + 0.698487i) q^{92} +(3.21889 + 7.57080i) q^{93} +(-11.5552 - 6.67142i) q^{94} +(-2.95465 + 3.26873i) q^{95} +(-0.390623 - 1.68743i) q^{96} +(10.7196 + 12.7751i) q^{97} +(1.02868 - 0.863167i) q^{98} +(-0.884316 - 0.851960i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 6 q^{3} + 3 q^{6} + 18 q^{7} - 6 q^{8}+O(q^{10}) $ 12 * q - 6 * q^3 + 3 * q^6 + 18 * q^7 - 6 * q^8	$ 12 q - 6 q^{3} + 3 q^{6} + 18 q^{7} - 6 q^{8} + 9 q^{10} + 9 q^{11} + 3 q^{12} - 3 q^{13} - 3 q^{14} - 9 q^{15} + 9 q^{18} + 15 q^{19} + 9 q^{20} + 3 q^{21} + 9 q^{22} + 18 q^{23} + 3 q^{24} + 18 q^{26} - 9 q^{27} - 3 q^{28} - 27 q^{29} - 27 q^{30} + 36 q^{31} - 9 q^{34} - 18 q^{35} - 9 q^{36} - 9 q^{38} + 9 q^{40} - 36 q^{41} + 30 q^{42} + 21 q^{43} - 18 q^{44} + 9 q^{45} - 27 q^{46} + 3 q^{48} - 6 q^{49} - 3 q^{50} - 27 q^{51} + 12 q^{52} - 9 q^{55} - 9 q^{56} - 57 q^{57} + 9 q^{58} - 36 q^{59} + 6 q^{61} - 6 q^{62} - 18 q^{63} - 6 q^{64} - 27 q^{65} + 9 q^{66} - 33 q^{67} + 9 q^{69} - 18 q^{70} + 9 q^{71} - 9 q^{72} - 24 q^{73} + 42 q^{74} + 24 q^{75} + 9 q^{76} + 27 q^{77} + 9 q^{78} - 30 q^{79} - 9 q^{80} + 36 q^{81} - 6 q^{84} + 54 q^{85} + 12 q^{86} - 27 q^{87} + 9 q^{89} - 9 q^{90} + 6 q^{91} - 18 q^{93} - 36 q^{94} + 54 q^{95} + 3 q^{96} - 18 q^{97} - 6 q^{98} + 72 q^{99}+O(q^{100}) $ 12 * q - 6 * q^3 + 3 * q^6 + 18 * q^7 - 6 * q^8 + 9 * q^10 + 9 * q^11 + 3 * q^12 - 3 * q^13 - 3 * q^14 - 9 * q^15 + 9 * q^18 + 15 * q^19 + 9 * q^20 + 3 * q^21 + 9 * q^22 + 18 * q^23 + 3 * q^24 + 18 * q^26 - 9 * q^27 - 3 * q^28 - 27 * q^29 - 27 * q^30 + 36 * q^31 - 9 * q^34 - 18 * q^35 - 9 * q^36 - 9 * q^38 + 9 * q^40 - 36 * q^41 + 30 * q^42 + 21 * q^43 - 18 * q^44 + 9 * q^45 - 27 * q^46 + 3 * q^48 - 6 * q^49 - 3 * q^50 - 27 * q^51 + 12 * q^52 - 9 * q^55 - 9 * q^56 - 57 * q^57 + 9 * q^58 - 36 * q^59 + 6 * q^61 - 6 * q^62 - 18 * q^63 - 6 * q^64 - 27 * q^65 + 9 * q^66 - 33 * q^67 + 9 * q^69 - 18 * q^70 + 9 * q^71 - 9 * q^72 - 24 * q^73 + 42 * q^74 + 24 * q^75 + 9 * q^76 + 27 * q^77 + 9 * q^78 - 30 * q^79 - 9 * q^80 + 36 * q^81 - 6 * q^84 + 54 * q^85 + 12 * q^86 - 27 * q^87 + 9 * q^89 - 9 * q^90 + 6 * q^91 - 18 * q^93 - 36 * q^94 + 54 * q^95 + 3 * q^96 - 18 * q^97 - 6 * q^98 + 72 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/342\mathbb{Z}\right)^\times$.

$n$	$191$	$325$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{17}{18}\right)$

Coefficient data

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

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

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

$2$	0.766044	−	0.642788i	0.541675	−	0.454519i
$2$	0.766044	−	0.642788i	0.541675	−	0.454519i
$3$	−0.210069	+	1.71926i	−0.121284	+	0.992618i
$3$	−0.210069	+	1.71926i	−0.121284	+	0.992618i
$4$	0.173648	−	0.984808i	0.0868241	−	0.492404i
$5$	0.649762	+	0.774356i	0.290582	+	0.346303i	0.891510	−	0.453001i	$-0.149647\pi$
$5$	0.649762	+	0.774356i	0.290582	+	0.346303i	−0.600928	+	0.799303i	$0.705202\pi$
$6$	0.944200	+	1.45206i	0.385468	+	0.592802i
$7$	2.88840			1.09171			0.545856	−	0.837879i	$-0.316205\pi$
$7$	2.88840			1.09171			0.545856	+	0.837879i	$0.316205\pi$
$8$	−0.500000	−	0.866025i	−0.176777	−	0.306186i
$9$	−2.91174	−	0.722330i	−0.970581	−	0.240777i
$10$	0.995493	+	0.175532i	0.314803	+	0.0555082i
$11$	0.354477	+	0.204658i	0.106879	+	0.0617066i	0.552487	−	0.833522i	$-0.313679\pi$
$11$	0.354477	+	0.204658i	0.106879	+	0.0617066i	−0.445608	+	0.895228i	$0.647012\pi$
$12$	1.65667	+	0.505425i	0.478239	+	0.145904i
$13$	1.10505	+	3.03609i	0.306484	+	0.842059i	0.993335	+	0.115261i	$0.0367703\pi$
$13$	1.10505	+	3.03609i	0.306484	+	0.842059i	−0.686851	+	0.726798i	$0.741007\pi$
$14$	2.21264	−	1.85663i	0.591353	−	0.496204i
$15$	−1.46782	+	0.954444i	−0.378989	+	0.246436i
$16$	−0.939693	−	0.342020i	−0.234923	−	0.0855050i
$17$	1.64303	−	0.289711i	0.398494	−	0.0702652i	0.0291898	−	0.999574i	$-0.490707\pi$
$17$	1.64303	−	0.289711i	0.398494	−	0.0702652i	0.369304	+	0.929309i	$0.379596\pi$
$18$	−2.69483	+	1.31830i	−0.635177	+	0.310725i
$19$	0.598294	+	4.31764i	0.137258	+	0.990535i
$19$	0.598294	+	4.31764i	0.137258	+	0.990535i
$20$	0.875422	−	0.505425i	0.195750	−	0.113016i
$21$	−0.606764	+	4.96592i	−0.132407	+	1.08365i
$22$	0.403097	−	0.0710768i	0.0859405	−	0.0151536i
$23$	−0.732021	−	0.129075i	−0.152637	−	0.0269140i	0.0968075	−	0.995303i	$-0.469137\pi$
$23$	−0.732021	−	0.129075i	−0.152637	−	0.0269140i	−0.249444	+	0.968389i	$0.580248\pi$
$24$	1.59396	−	0.677707i	0.325366	−	0.138336i
$25$	0.690804	−	3.91774i	0.138161	−	0.783549i
$26$	2.79807	+	1.61547i	0.548747	+	0.316819i
$27$	1.85354	−	4.85432i	0.356715	−	0.934213i
$28$	0.501565	−	2.84452i	0.0947869	−	0.537563i
$29$	−5.00832	+	1.82288i	−0.930021	+	0.338500i	−0.762218	−	0.647321i	$-0.775890\pi$
$29$	−5.00832	+	1.82288i	−0.930021	+	0.338500i	−0.167803	+	0.985821i	$0.553667\pi$
$30$	−0.510909	+	1.67464i	−0.0932788	+	0.305746i
$31$	4.11334	−	2.37484i	0.738778	−	0.426534i	−0.0828470	−	0.996562i	$-0.526401\pi$
$31$	4.11334	−	2.37484i	0.738778	−	0.426534i	0.821625	+	0.570029i	$0.193068\pi$
$32$	−0.939693	+	0.342020i	−0.166116	+	0.0604612i
$33$	−0.426325	+	0.566448i	−0.0742137	+	0.0986060i
$34$	1.07241	−	1.27805i	0.183917	−	0.219184i
$35$	1.87677	+	2.23665i	0.317232	+	0.378063i
$36$	−1.21697	+	2.74207i	−0.202829	+	0.457012i
$37$		−	0.635980i		−	0.104554i	−0.998633	−	0.0522772i	$-0.983352\pi$
$37$		−	0.635980i		−	0.104554i	0.998633	−	0.0522772i	$-0.0166479\pi$
$38$	3.23365	+	2.92293i	0.524567	+	0.474162i
$39$	−5.45197	+	1.26208i	−0.873014	+	0.202094i
$40$	0.345731	−	0.949888i	0.0546649	−	0.150191i
$41$	−0.485725	−	2.75468i	−0.0758575	−	0.430209i	−0.998958	−	0.0456494i	$-0.985464\pi$
$41$	−0.485725	−	2.75468i	−0.0758575	−	0.430209i	0.923100	−	0.384560i	$-0.125647\pi$
$42$	2.72723	+	4.19414i	0.420820	+	0.647170i
$43$	−0.859287	−	4.87326i	−0.131040	−	0.743165i	−0.977536	−	0.210770i	$-0.932403\pi$
$43$	−0.859287	−	4.87326i	−0.131040	−	0.743165i	0.846496	−	0.532396i	$-0.178708\pi$
$44$	0.263103	−	0.313554i	0.0396642	−	0.0472700i
$45$	−1.33260	−	2.72407i	−0.198652	−	0.406080i
$46$	−0.643729	+	0.371657i	−0.0949126	+	0.0547978i
$47$	−4.56352	−	12.5382i	−0.665658	−	1.82888i	−0.549213	−	0.835682i	$-0.685072\pi$
$47$	−4.56352	−	12.5382i	−0.665658	−	1.82888i	−0.116445	−	0.993197i	$-0.537150\pi$
$48$	0.785424	−	1.54373i	0.113366	−	0.222819i
$49$	1.34285			0.191836
$50$	−1.98909	−	3.44521i	−0.281300	−	0.487226i
$51$	0.152939	+	2.88567i	0.0214157	+	0.404074i
$52$	3.18185	−	0.561046i	0.441243	−	0.0778031i
$53$	−11.6345	+	4.23461i	−1.59812	+	0.581669i	−0.979042	−	0.203659i	$-0.934716\pi$
$53$	−11.6345	+	4.23461i	−1.59812	+	0.581669i	−0.619080	+	0.785328i	$0.712494\pi$
$54$	−1.70040	−	4.91006i	−0.231395	−	0.668174i
$55$	0.0718480	+	0.407470i	0.00968799	+	0.0549433i
$56$	−1.44420	−	2.50143i	−0.192989	−	0.334267i
$57$	−7.54885	+	0.121621i	−0.999870	+	0.0161091i
$58$	−2.66487	+	4.61569i	−0.349915	+	0.606070i
$59$	−6.37472	−	2.32021i	−0.829918	−	0.302066i	−0.108093	−	0.994141i	$-0.534474\pi$
$59$	−6.37472	−	2.32021i	−0.829918	−	0.302066i	−0.721825	+	0.692075i	$0.756697\pi$
$60$	0.685060	+	1.61126i	0.0884409	+	0.208012i
$61$	3.61301	+	3.03168i	0.462599	+	0.388166i	0.844086	−	0.536208i	$-0.180144\pi$
$61$	3.61301	+	3.03168i	0.462599	+	0.388166i	−0.381487	+	0.924374i	$0.624588\pi$
$62$	1.62449	−	4.46324i	0.206310	−	0.566832i
$63$	−8.41027	−	2.08638i	−1.05959	−	0.262859i
$64$	−0.500000	+	0.866025i	−0.0625000	+	0.108253i
$65$	−1.63300	+	2.82843i	−0.202548	+	0.350824i
$66$	0.0375216	+	0.707961i	0.00461859	+	0.0871440i
$67$	3.57361	−	4.25886i	0.436586	−	0.520303i	−0.502225	−	0.864737i	$-0.667485\pi$
$67$	3.57361	−	4.25886i	0.436586	−	0.520303i	0.938810	+	0.344435i	$0.111929\pi$
$68$		−	1.66838i		−	0.202321i
$69$	0.375690	−	1.23142i	0.0452277	−	0.148246i
$70$	2.87538	+	0.507007i	0.343674	+	0.0605990i
$71$	2.24554	+	0.817311i	0.266497	+	0.0969969i	0.471813	−	0.881699i	$-0.343600\pi$
$71$	2.24554	+	0.817311i	0.266497	+	0.0969969i	−0.205316	+	0.978696i	$0.565822\pi$
$72$	0.830315	+	2.88281i	0.0978536	+	0.339742i
$73$	−6.53990	+	5.48763i	−0.765438	+	0.642278i	−0.939536	−	0.342450i	$-0.888743\pi$
$73$	−6.53990	+	5.48763i	−0.765438	+	0.642278i	0.174099	+	0.984728i	$0.444299\pi$
$74$	−0.408800	−	0.487189i	−0.0475220	−	0.0566346i
$75$	6.59052	+	2.01067i	0.761008	+	0.232173i
$76$	4.35594	+	0.160547i	0.499661	+	0.0184160i
$77$	1.02387	+	0.591133i	0.116681	+	0.0673658i
$78$	−3.36521	+	4.47127i	−0.381035	+	0.506271i
$79$	4.10023	−	11.2653i	0.461312	−	1.26744i	−0.463188	−	0.886260i	$-0.653294\pi$
$79$	4.10023	−	11.2653i	0.461312	−	1.26744i	0.924499	−	0.381184i	$-0.124483\pi$
$80$	−0.345731	−	0.949888i	−0.0386539	−	0.106201i
$81$	7.95648	+	4.20647i	0.884053	+	0.467386i
$82$	−2.14276	−	1.79799i	−0.236629	−	0.198555i
$83$		−	12.4849i		−	1.37040i	−0.728357	−	0.685198i	$-0.759716\pi$
$83$		−	12.4849i		−	1.37040i	0.728357	−	0.685198i	$-0.240284\pi$
$84$	4.78512	+	1.45987i	0.522099	+	0.159285i
$85$	1.29192	+	1.08405i	0.140128	+	0.117582i
$86$	−3.79072	−	3.18079i	−0.408764	−	0.342994i
$87$	−2.08192	−	8.99355i	−0.223205	−	0.964210i
$88$		−	0.409315i		−	0.0436331i
$89$	5.14599	+	4.31800i	0.545473	+	0.457707i	0.873405	−	0.486995i	$-0.161907\pi$
$89$	5.14599	+	4.31800i	0.545473	+	0.457707i	−0.327931	+	0.944702i	$0.606351\pi$
$90$	−2.77183	−	1.23018i	−0.292176	−	0.129672i
$91$	3.19181	+	8.76943i	0.334593	+	0.919286i
$92$	−0.254228	+	0.698487i	−0.0265051	+	0.0728223i
$93$	3.21889	+	7.57080i	0.333783	+	0.785056i
$94$	−11.5552	−	6.67142i	−1.19183	−	0.688104i
$95$	−2.95465	+	3.26873i	−0.303140	+	0.335365i
$96$	−0.390623	−	1.68743i	−0.0398677	−	0.172222i
$97$	10.7196	+	12.7751i	1.08841	+	1.29712i	0.951876	+	0.306482i	$0.0991519\pi$
$97$	10.7196	+	12.7751i	1.08841	+	1.29712i	0.136534	+	0.990635i	$0.456404\pi$
$98$	1.02868	−	0.863167i	0.103913	−	0.0871930i
$99$	−0.884316	−	0.851960i	−0.0888771	−	0.0856252i
$100$	−3.73827	−	1.36062i	−0.373827	−	0.136062i
$101$	−10.9014	−	1.92221i	−1.08473	−	0.191267i	−0.397425	−	0.917635i	$-0.630096\pi$
$101$	−10.9014	−	1.92221i	−1.08473	−	0.191267i	−0.687307	+	0.726367i	$0.741207\pi$
$102$	1.97203	+	2.11224i	0.195260	+	0.209143i
$103$		−	5.43050i		−	0.535083i	−0.963546	−	0.267541i	$-0.913789\pi$
$103$		−	5.43050i		−	0.535083i	0.963546	−	0.267541i	$-0.0862112\pi$
$104$	2.07681	−	2.47504i	0.203648	−	0.242698i
$105$	−4.23964	+	2.75682i	−0.413747	+	0.269038i
$106$	−6.19059	+	10.7224i	−0.601283	+	1.04145i
$107$	−2.09564	+	3.62976i	−0.202593	+	0.350902i	−0.949363	−	0.314181i	$-0.898270\pi$
$107$	−2.09564	+	3.62976i	−0.202593	+	0.350902i	0.746770	+	0.665082i	$0.231604\pi$
$108$	−4.45870	−	2.66833i	−0.429039	−	0.256760i
$109$	−3.79855	+	10.4364i	−0.363835	+	0.999628i	0.613826	+	0.789441i	$0.289629\pi$
$109$	−3.79855	+	10.4364i	−0.363835	+	0.999628i	−0.977661	+	0.210187i	$0.932593\pi$
$110$	0.316956	+	0.265957i	0.0302205	+	0.0253580i
$111$	1.09342	+	0.133600i	0.103783	+	0.0126807i
$112$	−2.71421	−	0.987891i	−0.256468	−	0.0933469i
$113$	−0.996386	+	1.72579i	−0.0937321	+	0.162349i	−0.909079	−	0.416624i	$-0.863213\pi$
$113$	−0.996386	+	1.72579i	−0.0937321	+	0.162349i	0.815347	+	0.578973i	$0.196546\pi$
$114$	−5.70458	+	4.94548i	−0.534283	+	0.463186i
$115$	−0.375690	−	0.650713i	−0.0350332	−	0.0606793i
$116$	0.925500	+	5.24877i	0.0859305	+	0.487336i
$117$	−1.02455	−	9.63851i	−0.0947198	−	0.891080i
$118$	−6.37472	+	2.32021i	−0.586841	+	0.213593i
$119$	4.74573	−	0.836800i	0.435040	−	0.0767094i
$120$	1.56048	+	0.793946i	0.142452	+	0.0724770i
$121$	−5.41623	−	9.38119i	−0.492385	−	0.852835i
$122$	4.71645			0.427007
$123$	4.83807	−	0.256415i	0.436234	−	0.0231202i
$124$	−1.62449	−	4.46324i	−0.145883	−	0.400810i
$125$	7.85970	−	4.53780i	0.702993	−	0.405873i
$126$	−7.78374	+	3.80776i	−0.693431	+	0.339222i
$127$	−5.20894	+	6.20777i	−0.462219	+	0.550851i	−0.945927	−	0.324378i	$-0.894845\pi$
$127$	−5.20894	+	6.20777i	−0.462219	+	0.550851i	0.483709	+	0.875229i	$0.339289\pi$
$128$	0.173648	+	0.984808i	0.0153485	+	0.0870455i
$129$	8.55893	−	0.453620i	0.753572	−	0.0399390i
$130$	0.567134	+	3.21637i	0.0497409	+	0.282095i
$131$	−3.26123	+	8.96015i	−0.284935	+	0.782852i	0.711821	+	0.702361i	$0.247871\pi$
$131$	−3.26123	+	8.96015i	−0.284935	+	0.782852i	−0.996755	+	0.0804904i	$0.974351\pi$
$132$	0.483812	+	0.518211i	0.0421104	+	0.0451045i
$133$	1.72811	+	12.4711i	0.149846	+	1.08138i
$134$		−	5.55955i		−	0.480272i
$135$	4.96333	−	1.71885i	0.427175	−	0.147935i
$136$	−1.07241	−	1.27805i	−0.0919586	−	0.109592i
$137$	−1.98575	+	2.36652i	−0.169654	+	0.202185i	−0.844172	−	0.536073i	$-0.819907\pi$
$137$	−1.98575	+	2.36652i	−0.169654	+	0.202185i	0.674518	+	0.738259i	$0.264352\pi$
$138$	−0.503749	−	1.18481i	−0.0428820	−	0.100858i
$139$	3.70785	−	1.34955i	0.314496	−	0.114467i	−0.179950	−	0.983676i	$-0.557593\pi$
$139$	3.70785	−	1.34955i	0.314496	−	0.114467i	0.494445	+	0.869209i	$0.335371\pi$
$140$	2.52857	−	1.45987i	0.213703	−	0.123381i
$141$	22.5151	−	5.21201i	1.89611	−	0.438931i
$142$	2.24554	−	0.817311i	0.188442	−	0.0685872i
$143$	−0.229645	+	1.30238i	−0.0192039	+	0.108910i
$144$	2.48909	+	1.67464i	0.207424	+	0.139554i
$145$	−4.66577	−	2.69378i	−0.387471	−	0.223707i
$146$	−1.48248	+	8.40753i	−0.122691	+	0.695813i
$147$	−0.282091	+	2.30871i	−0.0232665	+	0.190419i
$148$	−0.626318	−	0.110437i	−0.0514830	−	0.00907785i
$149$	9.51954	−	1.67855i	0.779871	−	0.137512i	0.230479	−	0.973077i	$-0.425971\pi$
$149$	9.51954	−	1.67855i	0.779871	−	0.137512i	0.549392	+	0.835565i	$0.314860\pi$
$150$	6.34107	−	2.69604i	0.517746	−	0.220131i
$151$	−2.94612	+	1.70094i	−0.239752	+	0.138421i	−0.615063	−	0.788478i	$-0.710869\pi$
$151$	−2.94612	+	1.70094i	−0.239752	+	0.138421i	0.375311	+	0.926899i	$0.377536\pi$
$152$	3.44004	−	2.67696i	0.279024	−	0.217130i
$153$	−4.99335	−	0.343247i	−0.403688	−	0.0277499i
$154$	1.16430	−	0.205298i	0.0938223	−	0.0165434i
$155$	4.51166	+	1.64211i	0.362385	+	0.131898i
$156$	0.296178	+	5.58830i	0.0237132	+	0.447422i
$157$	8.30407	−	6.96794i	0.662737	−	0.556102i	−0.248169	−	0.968717i	$-0.579829\pi$
$157$	8.30407	−	6.96794i	0.662737	−	0.556102i	0.910906	+	0.412614i	$0.135384\pi$
$158$	−4.10023	−	11.2653i	−0.326197	−	0.896218i
$159$	−4.83637	−	20.8923i	−0.383549	−	1.65687i
$160$	−0.875422	−	0.505425i	−0.0692082	−	0.0399574i
$161$	−2.11437	−	0.372820i	−0.166636	−	0.0293824i
$162$	8.79889	−	1.89198i	0.691306	−	0.148648i
$163$	8.49553	+	14.7147i	0.665422	+	1.15254i	0.979171	+	0.203038i	$0.0650815\pi$
$163$	8.49553	+	14.7147i	0.665422	+	1.15254i	−0.313749	+	0.949506i	$0.601585\pi$
$164$	−2.79718			−0.218423
$165$	−0.715643	+	0.0379287i	−0.0557127	+	0.00295275i
$166$	−8.02514	−	9.56399i	−0.622872	−	0.742310i
$167$	−3.84286	+	21.7939i	−0.297369	+	1.68646i	0.360045	+	0.932935i	$0.382761\pi$
$167$	−3.84286	+	21.7939i	−0.297369	+	1.68646i	−0.657414	+	0.753530i	$0.728350\pi$
$168$	4.60400	−	1.95749i	0.355206	−	0.151023i
$169$	1.96188	−	1.64621i	0.150914	−	0.126632i
$170$	1.68648			0.129347
$171$	1.37668	−	13.0040i	0.105278	−	0.994443i
$172$	−4.94844			−0.377315
$173$	9.84564	−	8.26147i	0.748550	−	0.628108i	−0.186569	−	0.982442i	$-0.559737\pi$
$173$	9.84564	−	8.26147i	0.748550	−	0.628108i	0.935119	+	0.354334i	$0.115292\pi$
$174$	−7.37578	−	5.55123i	−0.559157	−	0.420838i
$175$	1.99532	−	11.3160i	0.150832	−	0.855410i
$176$	−0.263103	−	0.313554i	−0.0198321	−	0.0236350i
$177$	5.32819	−	10.4724i	0.400491	−	0.787156i
$178$	6.71761			0.503506
$179$	1.30430	+	2.25911i	0.0974878	+	0.168854i	0.910644	−	0.413191i	$-0.135586\pi$
$179$	1.30430	+	2.25911i	0.0974878	+	0.168854i	−0.813156	+	0.582045i	$0.802253\pi$
$180$	−2.91409	+	0.839324i	−0.217203	+	0.0625595i
$181$	8.59253	+	1.51510i	0.638678	+	0.112616i	0.483604	−	0.875287i	$-0.339327\pi$
$181$	8.59253	+	1.51510i	0.638678	+	0.112616i	0.155074	+	0.987903i	$0.450439\pi$
$182$	8.08195	+	4.66612i	0.599074	+	0.345876i
$183$	−5.97124	+	5.57486i	−0.441406	+	0.412105i
$184$	0.254228	+	0.698487i	0.0187420	+	0.0514931i
$185$	0.492475	−	0.413236i	0.0362075	−	0.0303817i
$186$	7.33223	+	3.73051i	0.537625	+	0.273534i
$187$	0.641709	+	0.233563i	0.0469264	+	0.0170798i
$188$	−13.1401	+	2.31696i	−0.958343	+	0.168982i
$189$	5.35377	−	14.0212i	0.389430	−	1.01989i
$190$	−0.162289	+	4.40320i	−0.0117736	+	0.319442i
$191$	18.6993	−	10.7961i	1.35304	−	0.781176i	0.364362	−	0.931257i	$-0.381287\pi$
$191$	18.6993	−	10.7961i	1.35304	−	0.781176i	0.988674	+	0.150082i	$0.0479536\pi$
$192$	−1.38389	−	1.04156i	−0.0998738	−	0.0751680i
$193$	−26.9236	+	4.74735i	−1.93800	+	0.341722i	−0.999988	−	0.00487592i	$-0.998448\pi$
$193$	−26.9236	+	4.74735i	−1.93800	+	0.341722i	−0.938014	+	0.346598i	$0.887337\pi$
$194$	16.4234	+	2.89589i	1.17913	+	0.207912i
$195$	−4.51978	−	3.40172i	−0.323668	−	0.243602i
$196$	0.233183	−	1.32245i	0.0166560	−	0.0944606i
$197$	3.11357	+	1.79762i	0.221833	+	0.128075i	0.606799	−	0.794856i	$-0.292453\pi$
$197$	3.11357	+	1.79762i	0.221833	+	0.128075i	−0.384966	+	0.922931i	$0.625787\pi$
$198$	−1.22505	−	0.0842113i	−0.0870608	−	0.00598464i
$199$	1.74096	−	9.87350i	0.123414	−	0.699914i	−0.858824	−	0.512271i	$-0.828804\pi$
$199$	1.74096	−	9.87350i	0.123414	−	0.699914i	0.982237	−	0.187642i	$-0.0600846\pi$
$200$	−3.73827	+	1.36062i	−0.264335	+	0.0962102i
$201$	6.57140	+	7.03864i	0.463511	+	0.496467i
$202$	−9.58655	+	5.53479i	−0.674507	+	0.389427i
$203$	−14.4660	+	5.26520i	−1.01532	+	0.369545i
$204$	2.86838	+	0.350475i	0.200827	+	0.0245382i
$205$	1.81750	−	2.16601i	0.126940	−	0.151281i
$206$	−3.49066	−	4.16000i	−0.243206	−	0.289841i
$207$	2.03822	+	0.904594i	0.141666	+	0.0628736i
$208$		−	3.23094i		−	0.224025i
$209$	−0.671557	+	1.65295i	−0.0464526	+	0.114337i
$210$	−1.47571	+	4.83703i	−0.101834	+	0.333787i
$211$	4.08704	−	11.2291i	0.281364	−	0.773040i	−0.715837	−	0.698268i	$-0.753955\pi$
$211$	4.08704	−	11.2291i	0.281364	−	0.773040i	0.997201	−	0.0747729i	$-0.0238232\pi$
$212$	2.14997	+	12.1931i	0.147660	+	0.837424i
$213$	−1.87689	+	3.68899i	−0.128603	+	0.252765i
$214$	0.727808	+	4.12761i	0.0497520	+	0.282157i
$215$	3.21531	−	3.83185i	0.219282	−	0.261330i
$216$	−5.13073	+	0.821942i	−0.349102	+	0.0559261i
$217$	11.8810	−	6.85948i	0.806533	−	0.465652i
$218$	3.79855	+	10.4364i	0.257270	+	0.706844i
$219$	−8.06085	−	12.3966i	−0.544702	−	0.837685i
$220$	0.413756			0.0278954
$221$	2.69521	+	4.66824i	0.181300	+	0.314020i
$222$	0.923483	−	0.600492i	0.0619801	−	0.0403024i
$223$	13.1570	−	2.31994i	0.881061	−	0.155355i	0.285225	−	0.958461i	$-0.407932\pi$
$223$	13.1570	−	2.31994i	0.881061	−	0.155355i	0.595836	+	0.803106i	$0.296821\pi$
$224$	−2.71421	+	0.987891i	−0.181351	+	0.0660062i
$225$	−4.84135	+	10.9085i	−0.322756	+	0.727231i
$226$	0.346041	+	1.96250i	0.0230183	+	0.130543i
$227$	13.0470	+	22.5981i	0.865961	+	1.49989i	0.866090	+	0.499888i	$0.166626\pi$
$227$	13.0470	+	22.5981i	0.865961	+	1.49989i	−0.000129184		1.00000i	$0.500041\pi$
$228$	−1.19107	+	7.45529i	−0.0788806	+	0.493739i
$229$	−13.6371	+	23.6201i	−0.901163	+	1.56086i	−0.0751761	+	0.997170i	$0.523952\pi$
$229$	−13.6371	+	23.6201i	−0.901163	+	1.56086i	−0.825987	+	0.563690i	$0.809381\pi$
$230$	−0.706065	−	0.256987i	−0.0465566	−	0.0169452i
$231$	−1.23140	+	1.63613i	−0.0810200	+	0.107649i
$232$	4.08282	+	3.42589i	0.268050	+	0.224921i
$233$	0.0878820	−	0.241454i	0.00575734	−	0.0158182i	−0.936781	−	0.349917i	$-0.886210\pi$
$233$	0.0878820	−	0.241454i	0.00575734	−	0.0158182i	0.942538	+	0.334099i	$0.108432\pi$
$234$	−6.98036	−	6.72496i	−0.456321	−	0.439624i
$235$	6.74381	−	11.6806i	0.439917	−	0.761959i
$236$	−3.39192	+	5.87498i	−0.220795	+	0.382428i
$237$	18.5067	+	9.41587i	1.20214	+	0.611627i
$238$	3.09756	−	3.69152i	0.200785	−	0.239286i
$239$			21.2469i			1.37435i	0.726493	+	0.687174i	$0.241149\pi$
$239$			21.2469i			1.37435i	−0.726493	+	0.687174i	$0.758851\pi$
$240$	1.70574	−	0.394861i	0.110105	−	0.0254882i
$241$	−8.41901	−	1.48450i	−0.542316	−	0.0956250i	−0.104222	−	0.994554i	$-0.533235\pi$
$241$	−8.41901	−	1.48450i	−0.542316	−	0.0956250i	−0.438094	+	0.898929i	$0.644346\pi$
$242$	−10.1792	−	3.70492i	−0.654343	−	0.238161i
$243$	−8.90345	+	12.7956i	−0.571157	+	0.820841i
$244$	3.61301	−	3.03168i	0.231299	−	0.194083i
$245$	0.872533	+	1.03984i	0.0557441	+	0.0664332i
$246$	3.54135	−	3.30628i	0.225788	−	0.210800i
$247$	−12.4476	+	6.58766i	−0.792022	+	0.419163i
$248$	−4.11334	−	2.37484i	−0.261197	−	0.150802i
$249$	21.4649	+	2.62270i	1.36028	+	0.166207i
$250$	3.10404	−	8.52827i	0.196317	−	0.539375i
$251$	2.31121	+	6.34999i	0.145882	+	0.400808i	0.991015	−	0.133748i	$-0.0427012\pi$
$251$	2.31121	+	6.34999i	0.145882	+	0.400808i	−0.845133	+	0.534556i	$0.820479\pi$
$252$	−3.51511	+	7.92021i	−0.221431	+	0.498926i
$253$	−0.233069	−	0.195568i	−0.0146529	−	0.0122953i
$254$			8.10367i			0.508470i
$255$	−2.13516	+	1.99342i	−0.133709	+	0.124833i
$256$	0.766044	+	0.642788i	0.0478778	+	0.0401742i
$257$	−15.1571	−	12.7183i	−0.945473	−	0.793346i	0.0330565	−	0.999453i	$-0.489476\pi$
$257$	−15.1571	−	12.7183i	−0.945473	−	0.793346i	−0.978529	+	0.206108i	$0.933920\pi$
$258$	6.26494	−	5.84907i	0.390038	−	0.364147i
$259$		−	1.83696i		−	0.114143i
$260$	2.50190	+	2.09934i	0.155161	+	0.130195i
$261$	15.8996	−	1.69010i	0.984163	−	0.104614i
$262$	3.26123	+	8.96015i	0.201479	+	0.553560i
$263$	−0.862304	+	2.36916i	−0.0531720	+	0.146089i	−0.963435	−	0.267941i	$-0.913657\pi$
$263$	−0.862304	+	2.36916i	−0.0531720	+	0.146089i	0.910263	+	0.414030i	$0.135879\pi$
$264$	0.703721	+	0.0859846i	0.0433110	+	0.00529198i
$265$	−10.8388	−	6.25776i	−0.665819	−	0.384411i
$266$	9.34006	+	8.44259i	0.572676	+	0.517648i
$267$	−8.50479	+	7.94023i	−0.520485	+	0.485934i
$268$	−3.57361	−	4.25886i	−0.218293	−	0.260151i
$269$	3.73531	−	3.13429i	0.227746	−	0.191101i	−0.521773	−	0.853084i	$-0.674729\pi$
$269$	3.73531	−	3.13429i	0.227746	−	0.191101i	0.749519	+	0.661983i	$0.230285\pi$
$270$	2.69728	−	4.50708i	0.164151	−	0.274292i
$271$	−20.5325	−	7.47322i	−1.24726	−	0.453966i	−0.367786	−	0.929910i	$-0.619884\pi$
$271$	−20.5325	−	7.47322i	−1.24726	−	0.453966i	−0.879475	+	0.475944i	$0.842106\pi$
$272$	−1.64303	−	0.289711i	−0.0996234	−	0.0175663i
$273$	−15.7475	+	3.64538i	−0.953080	+	0.220628i
$274$			3.08927i			0.186630i
$275$	1.04667	−	1.24737i	0.0631166	−	0.0752194i
$276$	−1.14748	−	0.583816i	−0.0690701	−	0.0351416i
$277$	−6.10759	+	10.5787i	−0.366970	+	0.635610i	−0.989090	−	0.147312i	$-0.952938\pi$
$277$	−6.10759	+	10.5787i	−0.366970	+	0.635610i	0.622121	+	0.782921i	$0.286271\pi$
$278$	1.97290	−	3.41717i	0.118327	−	0.204948i
$279$	−13.6924	+	3.94373i	−0.819743	+	0.236105i
$280$	0.998609	−	2.74366i	0.0596783	−	0.163965i
$281$	4.01609	+	3.36990i	0.239580	+	0.201031i	0.754670	−	0.656105i	$-0.227797\pi$
$281$	4.01609	+	3.36990i	0.239580	+	0.201031i	−0.515090	+	0.857136i	$0.672242\pi$
$282$	13.8973	−	18.4651i	0.827574	−	1.09958i
$283$	−9.58679	−	3.48931i	−0.569875	−	0.207418i	0.0409799	−	0.999160i	$-0.486952\pi$
$283$	−9.58679	−	3.48931i	−0.569875	−	0.207418i	−0.610855	+	0.791742i	$0.709174\pi$
$284$	1.19483	−	2.06950i	0.0709000	−	0.122802i
$285$	−4.99914	−	5.76648i	−0.296123	−	0.341577i
$286$	0.661236	+	1.14529i	0.0390997	+	0.0677226i
$287$	−1.40297	−	7.95663i	−0.0828146	−	0.469665i
$288$	2.98319	−	0.317107i	0.175786	−	0.0186857i
$289$	−13.3592	+	4.86233i	−0.785833	+	0.286020i
$290$	−5.30572	+	0.935541i	−0.311563	+	0.0549369i
$291$	−24.2157	+	15.7462i	−1.41955	+	0.923057i
$292$	4.26862	+	7.39346i	0.249802	+	0.432670i
$293$	10.0670			0.588120			0.294060	−	0.955787i	$-0.404993\pi$
$293$	10.0670			0.588120			0.294060	+	0.955787i	$0.404993\pi$
$294$	1.26792	+	1.94990i	0.0739465	+	0.113721i
$295$	−2.34538	−	6.44389i	−0.136554	−	0.375178i
$296$	−0.550775	+	0.317990i	−0.0320131	+	0.0184828i
$297$	1.65051	−	1.34140i	0.0957724	−	0.0778361i
$298$	6.21344	−	7.40488i	0.359935	−	0.428953i
$299$	−0.417033	−	2.36511i	−0.0241177	−	0.136778i
$300$	3.12456	−	6.14125i	0.180396	−	0.354565i
$301$	−2.48196	−	14.0759i	−0.143058	−	0.811322i
$302$	−1.16351	+	3.19672i	−0.0669526	+	0.183951i
$303$	5.59485	−	18.3386i	0.321416	−	1.05353i
$304$	0.914509	−	4.26189i	0.0524507	−	0.244436i
$305$			4.76762i			0.272993i
$306$	−4.04576	+	2.94672i	−0.231281	+	0.168453i
$307$	−20.4172	−	24.3323i	−1.16527	−	1.38872i	−0.906194	−	0.422863i	$-0.861025\pi$
$307$	−20.4172	−	24.3323i	−1.16527	−	1.38872i	−0.259080	−	0.965856i	$-0.583419\pi$
$308$	0.759946	−	0.905668i	0.0433019	−	0.0516052i
$309$	9.33646	+	1.14078i	0.531133	+	0.0648968i
$310$	4.51166	−	1.64211i	0.256245	−	0.0932656i
$311$	20.9854	−	12.1159i	1.18997	−	0.687030i	0.231671	−	0.972794i	$-0.425581\pi$
$311$	20.9854	−	12.1159i	1.18997	−	0.687030i	0.958300	+	0.285764i	$0.0922474\pi$
$312$	3.81898	+	4.09051i	0.216207	+	0.231579i
$313$	−27.8806	+	10.1477i	−1.57590	+	0.573582i	−0.974308	−	0.225220i	$-0.927690\pi$
$313$	−27.8806	+	10.1477i	−1.57590	+	0.573582i	−0.601595	+	0.798801i	$0.705468\pi$
$314$	1.88238	−	10.6755i	0.106229	−	0.602454i
$315$	−3.84908	−	7.86819i	−0.216871	−	0.443322i
$316$	−10.3821	−	5.99413i	−0.584041	−	0.337196i
$317$	−4.86907	+	27.6139i	−0.273474	+	1.55095i	0.470292	+	0.882511i	$0.344149\pi$
$317$	−4.86907	+	27.6139i	−0.273474	+	1.55095i	−0.743767	+	0.668439i	$0.766963\pi$
$318$	−17.1342	−	12.8957i	−0.960839	−	0.723156i
$319$	−2.14840	−	0.378821i	−0.120287	−	0.0212099i
$320$	−0.995493	+	0.175532i	−0.0556498	+	0.00981255i
$321$	−5.80028	−	4.36546i	−0.323740	−	0.243656i
$322$	−1.85935	+	1.07349i	−0.103617	+	0.0598235i
$323$	2.23388	+	6.92069i	0.124297	+	0.385078i
$324$	5.52420	−	7.10516i	0.306900	−	0.394731i
$325$	12.6580	−	2.23194i	0.702138	−	0.123806i
$326$	15.9664	+	5.81129i	0.884296	+	0.321857i
$327$	−17.1450	−	8.72308i	−0.948121	−	0.482387i
$328$	−2.14276	+	1.79799i	−0.118314	+	0.0992775i
$329$	−13.1813	−	36.2152i	−0.726707	−	1.99661i
$330$	−0.523834	+	0.489061i	−0.0288361	+	0.0269219i
$331$	−8.38000	−	4.83819i	−0.460606	−	0.265931i	0.251693	−	0.967807i	$-0.419013\pi$
$331$	−8.38000	−	4.83819i	−0.460606	−	0.265931i	−0.712299	+	0.701876i	$0.752346\pi$
$332$	−12.2952	−	2.16798i	−0.674789	−	0.118983i
$333$	−0.459387	+	1.85181i	−0.0251743	+	0.101479i
$334$	11.0651	+	19.1653i	0.605453	+	1.04868i
$335$	5.61987			0.307046
$336$	2.26862	−	4.45892i	0.123763	−	0.243254i
$337$	15.2216	+	18.1404i	0.829171	+	0.988168i	0.999996	+	0.00286650i	$0.000912435\pi$
$337$	15.2216	+	18.1404i	0.829171	+	0.988168i	−0.170825	+	0.985301i	$0.554643\pi$
$338$	0.444722	−	2.52214i	0.0241897	−	0.137187i
$339$	−2.75778	−	2.07559i	−0.149782	−	0.112730i
$340$	1.29192	−	1.08405i	0.0700641	−	0.0587908i
$341$	1.94411			0.105280
$342$	−7.30423	−	10.8466i	−0.394967	−	0.586516i
$343$	−16.3401			−0.882283
$344$	−3.79072	+	3.18079i	−0.204382	+	0.171497i
$345$	1.19767	−	0.509215i	0.0644803	−	0.0274152i
$346$	2.23183	−	12.6573i	0.119984	−	0.680461i
$347$	−1.20118	−	1.43151i	−0.0644826	−	0.0768474i	0.732839	−	0.680402i	$-0.238195\pi$
$347$	−1.20118	−	1.43151i	−0.0644826	−	0.0768474i	−0.797322	+	0.603555i	$0.793750\pi$
$348$	−9.21844	+	0.488573i	−0.494160	+	0.0261903i
$349$	28.2460			1.51197			0.755987	−	0.654586i	$-0.227157\pi$
$349$	28.2460			1.51197			0.755987	+	0.654586i	$0.227157\pi$
$350$	−5.74529	−	9.95113i	−0.307099	−	0.531910i
$351$	16.7864	+	0.263280i	0.895990	+	0.0140529i
$352$	−0.403097	−	0.0710768i	−0.0214851	−	0.00378841i
$353$	−8.98038	−	5.18482i	−0.477977	−	0.275960i	0.241596	−	0.970377i	$-0.422329\pi$
$353$	−8.98038	−	5.18482i	−0.477977	−	0.275960i	−0.719573	+	0.694417i	$0.755662\pi$
$354$	−2.64992	−	11.4472i	−0.140842	−	0.608414i
$355$	0.826178	+	2.26991i	0.0438490	+	0.120474i
$356$	5.14599	−	4.31800i	0.272737	−	0.228853i
$357$	0.441749	+	8.33495i	0.0233798	+	0.441133i
$358$	2.45128	+	0.892193i	0.129554	+	0.0471538i
$359$	32.3227	−	5.69937i	1.70593	−	0.300801i	0.766169	−	0.642639i	$-0.222161\pi$
$359$	32.3227	−	5.69937i	1.70593	−	0.300801i	0.939759	+	0.341838i	$0.111049\pi$
$360$	−1.69281	+	2.51610i	−0.0892190	+	0.132610i
$361$	−18.2841	+	5.16644i	−0.962320	+	0.271918i
$362$	7.55615	−	4.36254i	0.397142	−	0.229290i
$363$	17.2665	−	7.34123i	0.906258	−	0.385315i
$364$	9.19046	−	1.62053i	0.481711	−	0.0849386i
$365$	−8.49876	−	1.49856i	−0.444845	−	0.0784382i
$366$	−0.990782	+	8.10883i	−0.0517890	+	0.423855i
$367$	4.33320	−	24.5748i	0.226191	−	1.28279i	−0.634204	−	0.773166i	$-0.718672\pi$
$367$	4.33320	−	24.5748i	0.226191	−	1.28279i	0.860395	−	0.509627i	$-0.170217\pi$
$368$	0.643729	+	0.371657i	0.0335567	+	0.0193740i
$369$	−0.575484	+	8.37178i	−0.0299585	+	0.435818i
$370$	0.111635	−	0.633114i	0.00580363	−	0.0329140i
$371$	−33.6051	+	12.2312i	−1.74469	+	0.635015i
$372$	8.01474	−	1.85533i	0.415545	−	0.0961944i
$373$	9.84442	−	5.68368i	0.509725	−	0.294290i	−0.222996	−	0.974819i	$-0.571584\pi$
$373$	9.84442	−	5.68368i	0.509725	−	0.294290i	0.732721	+	0.680530i	$0.238250\pi$
$374$	0.641709	−	0.233563i	0.0331820	−	0.0120773i
$375$	6.15059	+	14.4662i	0.317615	+	0.747029i
$376$	−8.57661	+	10.2212i	−0.442305	+	0.527119i
$377$	−11.0688	−	13.1913i	−0.570074	−	0.679388i
$378$	−4.91143	−	14.1822i	−0.252616	−	0.729454i
$379$			11.9933i			0.616053i	0.951378	+	0.308027i	$0.0996686\pi$
$379$			11.9933i			0.616053i	−0.951378	+	0.308027i	$0.900331\pi$
$380$	2.70600	+	3.47737i	0.138815	+	0.178385i
$381$	−9.57857	−	10.2596i	−0.490725	−	0.525616i
$382$	7.38494	−	20.2900i	0.377846	−	1.03812i
$383$	2.54094	+	14.4104i	0.129836	+	0.736337i	0.978317	+	0.207112i	$0.0664063\pi$
$383$	2.54094	+	14.4104i	0.129836	+	0.736337i	−0.848481	+	0.529225i	$0.822483\pi$
$384$	−1.72962	+	0.0916693i	−0.0882645	+	0.00467798i
$385$	0.207526	+	1.17694i	0.0105765	+	0.0599823i
$386$	−17.5731	+	20.9428i	−0.894448	+	1.06596i
$387$	−1.01808	+	14.8104i	−0.0517518	+	0.752853i
$388$	14.4425	−	8.33837i	0.733206	−	0.423317i
$389$	−8.41292	−	23.1143i	−0.426552	−	1.17194i	−0.947892	−	0.318592i	$-0.896790\pi$
$389$	−8.41292	−	23.1143i	−0.426552	−	1.17194i	0.521340	−	0.853349i	$-0.325432\pi$
$390$	−5.64894	+	0.299391i	−0.286045	+	0.0151603i
$391$	−1.24013			−0.0627160
$392$	−0.671425	−	1.16294i	−0.0339121	−	0.0587374i
$393$	−14.7198	−	7.48916i	−0.742515	−	0.377778i
$394$	3.54062	−	0.624307i	0.178374	−	0.0314521i
$395$	11.3875	−	4.14472i	0.572968	−	0.208543i
$396$	−0.992576	+	0.722940i	−0.0498788	+	0.0363291i
$397$	−5.50422	−	31.2160i	−0.276249	−	1.56668i	−0.734967	−	0.678102i	$-0.762803\pi$
$397$	−5.50422	−	31.2160i	−0.276249	−	1.56668i	0.458719	−	0.888581i	$-0.348309\pi$
$398$	−5.01291	−	8.68261i	−0.251274	−	0.435220i
$399$	−21.8041	+	0.351290i	−1.09157	+	0.0175865i
$400$	−1.98909	+	3.44521i	−0.0994545	+	0.172260i
$401$	−5.47894	−	1.99417i	−0.273605	−	0.0995841i	0.201574	−	0.979473i	$-0.435394\pi$
$401$	−5.47894	−	1.99417i	−0.273605	−	0.0995841i	−0.475179	+	0.879889i	$0.657617\pi$
$402$	9.55834	+	1.16789i	0.476726	+	0.0582491i
$403$	11.7556	+	9.86416i	0.585590	+	0.491369i
$404$	−3.78602	+	10.4020i	−0.188362	+	0.517519i
$405$	1.91251	+	8.89436i	0.0950333	+	0.441964i
$406$	−7.69721	+	13.3320i	−0.382006	+	0.661654i
$407$	0.130158	−	0.225441i	0.00645170	−	0.0111747i
$408$	2.42259	−	1.57528i	0.119936	−	0.0779881i
$409$	−10.1942	+	12.1490i	−0.504072	+	0.600729i	−0.956738	−	0.290951i	$-0.906028\pi$
$409$	−10.1942	+	12.1490i	−0.504072	+	0.600729i	0.452666	+	0.891680i	$0.350473\pi$
$410$		−	2.82753i		−	0.139642i
$411$	−3.65153	−	3.91115i	−0.180117	−	0.192923i
$412$	−5.34800	−	0.942996i	−0.263477	−	0.0464581i
$413$	−18.4127	−	6.70169i	−0.906032	−	0.329769i
$414$	2.14283	−	0.617185i	0.105314	−	0.0303330i
$415$	9.66776	−	8.11222i	0.474572	−	0.398213i
$416$	−2.07681	−	2.47504i	−0.101824	−	0.121349i
$417$	1.54132	+	6.65827i	0.0754789	+	0.326057i
$418$	0.548055	+	1.69790i	0.0268062	+	0.0830472i
$419$	3.64611	+	2.10508i	0.178124	+	0.102840i	0.586411	−	0.810014i	$-0.300540\pi$
$419$	3.64611	+	2.10508i	0.178124	+	0.102840i	−0.408287	+	0.912854i	$0.633874\pi$
$420$	1.97873	+	4.65395i	0.0965520	+	0.227090i
$421$	−9.12007	+	25.0572i	−0.444485	+	1.22121i	0.492028	+	0.870579i	$0.336256\pi$
$421$	−9.12007	+	25.0572i	−0.444485	+	1.22121i	−0.936513	+	0.350633i	$0.885966\pi$
$422$	−4.08704	−	11.2291i	−0.198954	−	0.546622i
$423$	4.23110	+	39.8043i	0.205723	+	1.93535i
$424$	9.48453	+	7.95847i	0.460610	+	0.386497i
$425$		−	6.63711i		−	0.321947i
$426$	0.933454	+	4.03237i	0.0452260	+	0.195369i
$427$	10.4358	+	8.75669i	0.505025	+	0.423766i
$428$	3.21071	+	2.69410i	0.155195	+	0.130224i
$429$	−2.19089	−	0.668410i	−0.105777	−	0.0322711i
$430$		−	5.00213i		−	0.241224i
$431$	2.08107	+	1.74622i	0.100242	+	0.0841126i	0.691531	−	0.722347i	$-0.256937\pi$
$431$	2.08107	+	1.74622i	0.100242	+	0.0841126i	−0.591290	+	0.806459i	$0.701381\pi$
$432$	−3.40203	+	3.92762i	−0.163680	+	0.188967i
$433$	11.9741	+	32.8985i	0.575437	+	1.58100i	0.795786	+	0.605578i	$0.207058\pi$
$433$	11.9741	+	32.8985i	0.575437	+	1.58100i	−0.220349	+	0.975421i	$0.570720\pi$
$434$	4.69216	−	12.8916i	0.225231	−	0.618817i
$435$	5.61146	−	7.45581i	0.269049	−	0.357479i
$436$	9.61826	+	5.55310i	0.460631	+	0.265945i
$437$	0.119337	−	3.23783i	0.00570864	−	0.154887i
$438$	−14.1434	−	4.31493i	−0.675796	−	0.206175i
$439$	−7.72481	−	9.20608i	−0.368685	−	0.439382i	0.549524	−	0.835478i	$-0.314809\pi$
$439$	−7.72481	−	9.20608i	−0.368685	−	0.439382i	−0.918209	+	0.396096i	$0.870365\pi$
$440$	0.316956	−	0.265957i	0.0151103	−	0.0126790i
$441$	−3.91003	−	0.969980i	−0.186192	−	0.0461895i
$442$	5.06534	+	1.84363i	0.240934	+	0.0876927i
$443$	−23.7228	−	4.18297i	−1.12710	−	0.198739i	−0.421147	−	0.906993i	$-0.638372\pi$
$443$	−23.7228	−	4.18297i	−1.12710	−	0.198739i	−0.705958	+	0.708254i	$0.749483\pi$
$444$	0.321440	−	1.05361i	0.0152549	−	0.0500020i
$445$			6.79050i			0.321900i
$446$	8.58765	−	10.2344i	0.406637	−	0.484611i
$447$	0.886111	+	16.7192i	0.0419116	+	0.790792i
$448$	−1.44420	+	2.50143i	−0.0682320	+	0.118181i
$449$	15.8827	−	27.5097i	0.749552	−	1.29826i	−0.198486	−	0.980104i	$-0.563602\pi$
$449$	15.8827	−	27.5097i	0.749552	−	1.29826i	0.948038	−	0.318158i	$-0.103064\pi$
$450$	3.30314	+	11.4683i	0.155712	+	0.540622i
$451$	0.391589	−	1.07588i	0.0184392	−	0.0506612i
$452$	1.52655	+	1.28093i	0.0718030	+	0.0602498i
$453$	−2.30548	−	5.42247i	−0.108321	−	0.254770i
$454$	24.5204	+	8.92468i	1.15080	+	0.418856i
$455$	−4.71674	+	8.16964i	−0.221124	+	0.382999i
$456$	3.87975	+	6.47669i	0.181686	+	0.303299i
$457$	−6.91788	−	11.9821i	−0.323605	−	0.560500i	0.657624	−	0.753346i	$-0.271561\pi$
$457$	−6.91788	−	11.9821i	−0.323605	−	0.560500i	−0.981229	+	0.192846i	$0.938228\pi$
$458$	4.73610	+	26.8598i	0.221304	+	1.25508i
$459$	1.63908	−	8.51278i	0.0765058	−	0.397343i
$460$	−0.706065	+	0.256987i	−0.0329205	+	0.0119821i
$461$	−5.60813	+	0.988865i	−0.261197	+	0.0460560i	−0.302713	−	0.953082i	$-0.597892\pi$
$461$	−5.60813	+	0.988865i	−0.261197	+	0.0460560i	0.0415162	+	0.999138i	$0.486781\pi$
$462$	0.108377	+	2.04487i	0.00504217	+	0.0951362i
$463$	19.8743	+	34.4233i	0.923638	+	1.59979i	0.793737	+	0.608261i	$0.208133\pi$
$463$	19.8743	+	34.4233i	0.923638	+	1.59979i	0.129901	+	0.991527i	$0.458534\pi$
$464$	5.32974			0.247427
$465$	−3.77099	+	7.41179i	−0.174875	+	0.343713i
$466$	−0.0878820	−	0.241454i	−0.00407105	−	0.0111851i
$467$	−34.6575	+	20.0095i	−1.60376	+	0.925931i	−0.613033	+	0.790058i	$0.710051\pi$
$467$	−34.6575	+	20.0095i	−1.60376	+	0.925931i	−0.990726	+	0.135873i	$0.956616\pi$
$468$	−9.66999	−	0.664723i	−0.446995	−	0.0307268i
$469$	10.3220	−	12.3013i	0.476626	−	0.568021i
$470$	−2.34210	−	13.2827i	−0.108033	−	0.612685i
$471$	10.2353	+	15.7406i	0.471618	+	0.725291i
$472$	1.17800	+	6.68078i	0.0542219	+	0.307508i
$473$	0.692752	−	1.90332i	0.0318528	−	0.0875147i
$474$	20.2293	−	4.68289i	0.929165	−	0.215092i
$475$	17.3287	+	0.638683i	0.795097	+	0.0293048i
$476$		−	4.81894i		−	0.220876i
$477$	36.9354	−	3.92615i	1.69116	−	0.179766i
$478$	13.6573	+	16.2761i	0.624668	+	0.744451i
$479$	13.8573	−	16.5145i	0.633158	−	0.754568i	−0.350115	−	0.936707i	$-0.613858\pi$
$479$	13.8573	−	16.5145i	0.633158	−	0.754568i	0.983273	+	0.182139i	$0.0583020\pi$
$480$	1.05286	−	1.39891i	0.0480562	−	0.0638511i
$481$	1.93089	−	0.702787i	0.0880410	−	0.0320443i
$482$	−7.40355	+	4.27444i	−0.337223	+	0.194696i
$483$	1.08514	−	3.55684i	0.0493756	−	0.161842i
$484$	−10.1792	+	3.70492i	−0.462690	+	0.168405i
$485$	−2.92731	+	16.6016i	−0.132922	+	0.753839i
$486$	1.40444	+	15.5251i	0.0637067	+	0.704231i
$487$	22.4850	+	12.9817i	1.01889	+	0.588258i	0.913783	−	0.406203i	$-0.133147\pi$
$487$	22.4850	+	12.9817i	1.01889	+	0.588258i	0.105109	+	0.994461i	$0.466481\pi$
$488$	0.819003	−	4.64480i	0.0370745	−	0.210260i
$489$	−27.0831	+	11.5150i	−1.22474	+	0.520725i
$490$	1.33680	+	0.235713i	0.0603904	+	0.0106484i
$491$	30.1333	−	5.31331i	1.35990	−	0.239786i	0.554332	−	0.832296i	$-0.312974\pi$
$491$	30.1333	−	5.31331i	1.35990	−	0.239786i	0.805564	+	0.592509i	$0.201863\pi$
$492$	0.587602	−	4.80909i	0.0264911	−	0.216811i
$493$	−7.70072	+	4.44601i	−0.346823	+	0.200238i
$494$	−5.30095	+	13.0476i	−0.238501	+	0.587039i
$495$	0.0851250	−	1.23835i	0.00382608	−	0.0556595i
$496$	−4.67752	+	0.824773i	−0.210027	+	0.0370334i
$497$	6.48602	+	2.36072i	0.290938	+	0.105893i
$498$	18.1289	−	11.7882i	0.812374	−	0.528244i
$499$	20.7504	−	17.4117i	0.928917	−	0.779454i	−0.0467060	−	0.998909i	$-0.514872\pi$
$499$	20.7504	−	17.4117i	0.928917	−	0.779454i	0.975623	+	0.219455i	$0.0704279\pi$
$500$	−3.10404	−	8.52827i	−0.138817	−	0.381396i
$501$	−36.6623	−	11.1851i	−1.63795	−	0.499714i
$502$	5.85219	+	3.37876i	0.261196	+	0.150802i
$503$	8.65303	+	1.52576i	0.385820	+	0.0680304i	0.363194	−	0.931714i	$-0.381686\pi$
$503$	8.65303	+	1.52576i	0.385820	+	0.0680304i	0.0226258	+	0.999744i	$0.492797\pi$
$504$	2.39828	+	8.32670i	0.106828	+	0.370901i
$505$	−5.59485	−	9.69056i	−0.248967	−	0.431224i
$506$	−0.304250			−0.0135256
$507$	2.41814	+	3.71881i	0.107394	+	0.165158i
$508$	5.20894	+	6.20777i	0.231109	+	0.275425i
$509$	5.36922	−	30.4504i	0.237987	−	1.34969i	−0.598245	−	0.801313i	$-0.704135\pi$
$509$	5.36922	−	30.4504i	0.237987	−	1.34969i	0.836232	−	0.548376i	$-0.184754\pi$
$510$	−0.354278	+	2.89951i	−0.0156877	+	0.128392i
$511$	−18.8898	+	15.8505i	−0.835638	+	0.701183i
$512$	1.00000			0.0441942
$513$	22.0682	+	5.09863i	0.974333	+	0.225110i
$514$	−19.7862			−0.872730
$515$	4.20514	−	3.52853i	0.185301	−	0.155486i
$516$	1.03951	−	8.50767i	0.0457621	−	0.374529i
$517$	0.948367	−	5.37846i	0.0417091	−	0.236544i
$518$	−1.18078	−	1.40720i	−0.0518804	−	0.0618286i
$519$	12.1354	+	18.6627i	0.532684	+	0.819203i
$520$	3.26599			0.143223
$521$	−7.92465	−	13.7259i	−0.347185	−	0.601342i	0.638563	−	0.769569i	$-0.279529\pi$
$521$	−7.92465	−	13.7259i	−0.347185	−	0.601342i	−0.985748	+	0.168227i	$0.946196\pi$
$522$	11.0935	−	11.5148i	0.485548	−	0.503988i
$523$	30.5603	+	5.38860i	1.33631	+	0.235627i	0.795722	−	0.605662i	$-0.207092\pi$
$523$	30.5603	+	5.38860i	1.33631	+	0.235627i	0.540586	+	0.841289i	$0.318203\pi$
$524$	8.25771	+	4.76759i	0.360740	+	0.208273i
$525$	19.0361	+	5.80763i	0.830802	+	0.253466i
$526$	0.862304	+	2.36916i	0.0375983	+	0.103300i
$527$	6.07033	−	5.09361i	0.264428	−	0.221881i
$528$	0.594352	−	0.386475i	0.0258658	−	0.0168192i
$529$	−21.0937	−	7.67749i	−0.917119	−	0.333804i
$530$	−12.3254	+	2.17330i	−0.535380	+	0.0944020i
$531$	16.8856	+	11.3605i	0.732772	+	0.493004i
$532$	12.5817	+	0.463723i	0.545486	+	0.0201049i
$533$	7.82671	−	4.51875i	0.339013	−	0.195729i
$534$	−1.41116	+	11.5493i	−0.0610670	+	0.499789i
$535$	−4.17239	+	0.735705i	−0.180388	+	0.0318073i
$536$	−5.47509	−	0.965406i	−0.236488	−	0.0416992i
$537$	−4.15800	+	1.76786i	−0.179431	+	0.0762890i
$538$	0.846725	−	4.80202i	0.0365049	−	0.207030i
$539$	0.476010	+	0.274824i	0.0205032	+	0.0118375i
$540$	−0.830860	−	5.18640i	−0.0357545	−	0.223187i
$541$	−1.03169	+	5.85098i	−0.0443556	+	0.251553i	−0.998921	−	0.0464495i	$-0.985209\pi$
$541$	−1.03169	+	5.85098i	−0.0443556	+	0.251553i	0.954565	+	0.298003i	$0.0963205\pi$
$542$	−20.5325	+	7.47322i	−0.881947	+	0.321002i
$543$	−4.40988	+	14.4546i	−0.189246	+	0.620305i
$544$	−1.44486	+	0.834189i	−0.0619478	+	0.0357656i
$545$	−10.5497	+	3.83976i	−0.451898	+	0.164477i
$546$	−9.72006	+	12.9148i	−0.415980	+	0.552703i
$547$	6.34941	−	7.56693i	0.271481	−	0.323539i	−0.613028	−	0.790061i	$-0.710049\pi$
$547$	6.34941	−	7.56693i	0.271481	−	0.323539i	0.884509	+	0.466522i	$0.154493\pi$
$548$	1.98575	+	2.36652i	0.0848268	+	0.101093i
$549$	−8.33029	−	11.4372i	−0.355528	−	0.488130i
$550$		−	1.62833i		−	0.0694322i
$551$	−10.8670	−	20.5335i	−0.462949	−	0.874757i
$552$	−1.25429	+	0.290355i	−0.0533861	+	0.0123583i
$553$	11.8431	−	32.5386i	0.503620	−	1.38368i
$554$	2.12114	+	12.0296i	0.0901188	+	0.511089i
$555$	0.607007	+	0.933503i	0.0257660	+	0.0396250i
$556$	−0.685183	−	3.88586i	−0.0290582	−	0.164797i
$557$	12.5824	−	14.9951i	0.533133	−	0.635363i	−0.430500	−	0.902590i	$-0.641663\pi$
$557$	12.5824	−	14.9951i	0.533133	−	0.635363i	0.963634	+	0.267227i	$0.0861073\pi$
$558$	−7.95401	+	11.8224i	−0.336720	+	0.500481i
$559$	13.8461	−	7.99404i	0.585627	−	0.338112i
$560$	−0.998609	−	2.74366i	−0.0421990	−	0.115941i
$561$	−0.536360	+	1.05420i	−0.0226451	+	0.0445085i
$562$	5.24263			0.221147
$563$	21.1852	+	36.6939i	0.892851	+	1.54646i	0.836442	+	0.548056i	$0.184632\pi$
$563$	21.1852	+	36.6939i	0.892851	+	1.54646i	0.0564098	+	0.998408i	$0.482035\pi$
$564$	−1.22313	−	23.0781i	−0.0515030	−	0.971763i
$565$	−1.98379	+	0.349796i	−0.0834587	+	0.0147160i
$566$	−9.58679	+	3.48931i	−0.402963	+	0.146666i
$567$	22.9815	+	12.1500i	0.965132	+	0.510251i
$568$	−0.414959	−	2.35335i	−0.0174113	−	0.0987445i
$569$	16.6820	+	28.8941i	0.699345	+	1.21130i	0.968694	+	0.248259i	$0.0798584\pi$
$569$	16.6820	+	28.8941i	0.699345	+	1.21130i	−0.269348	+	0.963043i	$0.586808\pi$
$570$	−7.53618	−	1.20399i	−0.315656	−	0.0504298i
$571$	−3.50609	+	6.07273i	−0.146725	+	0.254136i	−0.930015	−	0.367521i	$-0.880207\pi$
$571$	−3.50609	+	6.07273i	−0.146725	+	0.254136i	0.783290	+	0.621657i	$0.213540\pi$
$572$	1.24272	+	0.452312i	0.0519606	+	0.0189121i
$573$	14.6331	+	34.4170i	0.611308	+	1.43779i
$574$	−6.18916	−	5.19332i	−0.258330	−	0.216765i
$575$	−1.01137	+	2.77871i	−0.0421769	+	0.115880i
$576$	2.08143	−	2.16048i	0.0867261	−	0.0900199i
$577$	14.1788	−	24.5585i	0.590273	−	1.02238i	−0.403923	−	0.914793i	$-0.632354\pi$
$577$	14.1788	−	24.5585i	0.590273	−	1.02238i	0.994195	−	0.107589i	$-0.0343131\pi$
$578$	−7.10826	+	12.3119i	−0.295665	+	0.512106i
$579$	−2.50614	−	47.2860i	−0.104152	−	1.96514i
$580$	−3.46306	+	4.12712i	−0.143796	+	0.171369i
$581$		−	36.0614i		−	1.49608i
$582$	−8.42884	+	27.6278i	−0.349387	+	1.14521i
$583$	−4.99081	−	0.880015i	−0.206698	−	0.0364465i
$584$	8.02238	+	2.91991i	0.331968	+	0.120827i
$585$	6.79792	−	7.05610i	0.281060	−	0.291734i
$586$	7.71177	−	6.47094i	0.318570	−	0.267312i
$587$	−26.0563	−	31.0527i	−1.07546	−	1.28168i	−0.957428	−	0.288672i	$-0.906786\pi$
$587$	−26.0563	−	31.0527i	−1.07546	−	1.28168i	−0.118031	−	0.993010i	$-0.537658\pi$
$588$	2.22465	+	0.678710i	0.0917432	+	0.0279895i
$589$	12.7147	+	16.3391i	0.523900	+	0.673240i
$590$	−5.93872	−	3.42872i	−0.244493	−	0.141158i
$591$	−3.74465	+	4.97542i	−0.154034	+	0.204662i
$592$	−0.217518	+	0.597626i	−0.00893993	+	0.0245623i
$593$	5.25014	+	14.4246i	0.215597	+	0.592349i	0.999596	−	0.0284134i	$-0.00904549\pi$
$593$	5.25014	+	14.4246i	0.215597	+	0.592349i	−0.783999	+	0.620762i	$0.786823\pi$
$594$	0.402128	−	2.08850i	0.0164995	−	0.0856923i
$595$	3.73158	+	3.13116i	0.152980	+	0.128365i
$596$		−	9.66639i		−	0.395951i
$597$	16.6094	+	5.06730i	0.679779	+	0.207391i
$598$	−1.83973	−	1.54372i	−0.0752322	−	0.0631274i
$599$	−4.15643	−	3.48766i	−0.169827	−	0.142502i	0.553913	−	0.832575i	$-0.313134\pi$
$599$	−4.15643	−	3.48766i	−0.169827	−	0.142502i	−0.723740	+	0.690073i	$0.757579\pi$
$600$	−1.55397	−	6.71290i	−0.0634405	−	0.274053i
$601$		−	14.7986i		−	0.603647i	−0.953364	−	0.301824i	$-0.902405\pi$
$601$		−	14.7986i		−	0.603647i	0.953364	−	0.301824i	$-0.0975954\pi$
$602$	−10.9491	−	9.18740i	−0.446253	−	0.374451i
$603$	−13.4817	+	9.81938i	−0.549018	+	0.399876i
$604$	1.16351	+	3.19672i	0.0473426	+	0.130073i
$605$	3.74512	−	10.2896i	0.152261	−	0.418333i
$606$	−7.50194	−	17.6445i	−0.304745	−	0.716759i
$607$	−23.1470	−	13.3639i	−0.939508	−	0.542425i	−0.0497017	−	0.998764i	$-0.515827\pi$
$607$	−23.1470	−	13.3639i	−0.939508	−	0.542425i	−0.889806	+	0.456339i	$0.849160\pi$
$608$	−2.03893	−	3.85263i	−0.0826897	−	0.156245i
$609$	−6.01341	−	25.9770i	−0.243675	−	1.05264i
$610$	3.06457	+	3.65221i	0.124081	+	0.147874i
$611$	33.0241	−	27.7105i	1.33601	−	1.12105i
$612$	−1.20512	+	4.85789i	−0.0487140	+	0.196368i
$613$	7.06454	+	2.57128i	0.285334	+	0.103853i	0.480722	−	0.876873i	$-0.340374\pi$
$613$	7.06454	+	2.57128i	0.285334	+	0.103853i	−0.195388	+	0.980726i	$0.562597\pi$
$614$	−31.2810	−	5.51569i	−1.26240	−	0.222595i
$615$	3.34215	+	3.57978i	0.134768	+	0.144351i
$616$		−	1.18227i		−	0.0476348i
$617$	−14.8960	+	17.7523i	−0.599689	+	0.714682i	−0.977437	−	0.211227i	$-0.932254\pi$
$617$	−14.8960	+	17.7523i	−0.599689	+	0.714682i	0.377748	+	0.925908i	$0.376699\pi$
$618$	7.88542	−	5.12747i	0.317198	−	0.206257i
$619$	2.79412	−	4.83955i	0.112305	−	0.194518i	−0.804394	−	0.594096i	$-0.797510\pi$
$619$	2.79412	−	4.83955i	0.112305	−	0.194518i	0.916699	+	0.399578i	$0.130843\pi$
$620$	2.40061	−	4.15797i	0.0964106	−	0.166988i
$621$	−1.98340	+	3.31422i	−0.0795913	+	0.132995i
$622$	8.28777	−	22.7705i	0.332309	−	0.913012i
$623$	14.8637	+	12.4721i	0.595500	+	0.499684i
$624$	5.55483	+	0.678721i	0.222371	+	0.0271706i
$625$	−10.0705	−	3.66538i	−0.402821	−	0.146615i
$626$	−14.8349	+	25.6949i	−0.592923	+	1.02697i
$627$	−2.70079	−	1.50182i	−0.107859	−	0.0599769i
$628$	−5.42010	−	9.38788i	−0.216285	−	0.374617i
$629$	−0.184250	−	1.04494i	−0.00734654	−	0.0416643i
$630$	−8.00614	−	3.55325i	−0.318972	−	0.141565i
$631$	−44.4542	+	16.1800i	−1.76969	+	0.644116i	−0.769710	+	0.638394i	$0.779599\pi$
$631$	−44.4542	+	16.1800i	−1.76969	+	0.644116i	−0.999984	+	0.00572156i	$0.998179\pi$
$632$	−11.8061	+	2.08174i	−0.469623	+	0.0828072i
$633$	18.4472	+	9.38559i	0.733209	+	0.373044i
$634$	14.0199	+	24.2832i	0.556803	+	0.964411i
$635$	−8.19160			−0.325074
$636$	−21.4148	+	1.13497i	−0.849151	+	0.0450046i
$637$	1.48391	+	4.07701i	0.0587946	+	0.161537i
$638$	−1.88927	+	1.09077i	−0.0747970	+	0.0431841i
$639$	−5.94807	−	4.00182i	−0.235302	−	0.158309i
$640$	−0.649762	+	0.774356i	−0.0256841	+	0.0306091i
$641$	−4.86807	−	27.6082i	−0.192277	−	1.09046i	−0.916243	−	0.400622i	$-0.868794\pi$
$641$	−4.86807	−	27.6082i	−0.192277	−	1.09046i	0.723966	−	0.689835i	$-0.242317\pi$
$642$	−7.24934	+	0.384212i	−0.286109	+	0.0151636i
$643$	7.88805	+	44.7354i	0.311074	+	1.76419i	0.593434	+	0.804882i	$0.297772\pi$
$643$	7.88805	+	44.7354i	0.311074	+	1.76419i	−0.282360	+	0.959309i	$0.591117\pi$
$644$	−0.734313	+	2.01751i	−0.0289360	+	0.0795010i
$645$	5.91253	+	6.33292i	0.232806	+	0.249358i
$646$	6.15979	+	3.86565i	0.242354	+	0.152092i
$647$			12.6123i			0.495840i	0.968781	+	0.247920i	$0.0797470\pi$
$647$			12.6123i			0.495840i	−0.968781	+	0.247920i	$0.920253\pi$
$648$	−0.335327	−	8.99375i	−0.0131729	−	0.353308i
$649$	−1.78485	−	2.12710i	−0.0700614	−	0.0834959i
$650$	8.26191	−	9.84616i	0.324059	−	0.386198i
$651$	9.29744	+	21.8675i	0.364395	+	0.857055i
$652$	15.9664	−	5.81129i	0.625292	−	0.227588i
$653$	20.7294	−	11.9681i	0.811205	−	0.468350i	−0.0361690	−	0.999346i	$-0.511515\pi$
$653$	20.7294	−	11.9681i	0.811205	−	0.468350i	0.847374	+	0.530996i	$0.178182\pi$
$654$	−18.7409	+	4.33834i	−0.732828	+	0.169642i
$655$	−9.05736	+	3.29661i	−0.353901	+	0.128809i
$656$	−0.485725	+	2.75468i	−0.0189644	+	0.107552i
$657$	23.0064	−	11.2546i	0.897564	−	0.439084i
$658$	−33.3761	−	19.2697i	−1.30114	−	0.751212i
$659$	−3.09035	+	17.5263i	−0.120383	+	0.682726i	0.863560	+	0.504245i	$0.168229\pi$
$659$	−3.09035	+	17.5263i	−0.120383	+	0.682726i	−0.983943	+	0.178481i	$0.942882\pi$
$660$	−0.0869175	+	0.711357i	−0.00338326	+	0.0276895i
$661$	−7.09558	−	1.25114i	−0.275986	−	0.0486638i	0.0339420	−	0.999424i	$-0.489194\pi$
$661$	−7.09558	−	1.25114i	−0.275986	−	0.0486638i	−0.309928	+	0.950760i	$0.600305\pi$
$662$	−9.52938	+	1.68029i	−0.370370	+	0.0653062i
$663$	−8.59213	+	3.65313i	−0.333691	+	0.141876i
$664$	−10.8122	+	6.24245i	−0.419597	+	0.242254i
$665$	−8.53419	+	9.44141i	−0.330942	+	0.366122i
$666$	0.838409	+	1.71386i	0.0324877	+	0.0664106i
$667$	3.90148	−	0.687937i	0.151066	−	0.0266370i
$668$	20.7955	+	7.56895i	0.804603	+	0.292851i
$669$	1.22470	+	23.1078i	0.0473498	+	0.893399i
$670$	4.30507	−	3.61238i	0.166319	−	0.139559i
$671$	0.660275	+	1.81409i	0.0254896	+	0.0700322i
$672$	−1.12827	−	4.87397i	−0.0435241	−	0.188017i
$673$	−5.12628	−	2.95966i	−0.197604	−	0.114087i	0.397934	−	0.917414i	$-0.369727\pi$
$673$	−5.12628	−	2.95966i	−0.197604	−	0.114087i	−0.595537	+	0.803328i	$0.703061\pi$
$674$	23.3208	+	4.11208i	0.898283	+	0.158392i
$675$	−17.7375	−	10.6151i	−0.682718	−	0.408575i
$676$	−1.28053	−	2.21794i	−0.0492510	−	0.0853053i
$677$	15.1092			0.580692			0.290346	−	0.956922i	$-0.406230\pi$
$677$	15.1092			0.580692			0.290346	+	0.956922i	$0.406230\pi$
$678$	−3.44674	+	0.182676i	−0.132371	+	0.00701563i
$679$	30.9625	+	36.8997i	1.18823	+	1.41608i
$680$	0.292854	−	1.66086i	0.0112304	−	0.0636910i
$681$	−41.5929	+	17.6841i	−1.59384	+	0.677656i
$682$	1.48928	−	1.24965i	0.0570274	−	0.0478517i
$683$	−13.2187			−0.505799			−0.252900	−	0.967493i	$-0.581384\pi$
$683$	−13.2187			−0.505799			−0.252900	+	0.967493i	$0.581384\pi$
$684$	−12.5674	−	3.61390i	−0.480527	−	0.138181i
$685$	−3.12279			−0.119316
$686$	−12.5172	+	10.5032i	−0.477911	+	0.401015i
$687$	−37.7445	−	28.4076i	−1.44004	−	1.08382i
$688$	−0.859287	+	4.87326i	−0.0327600	+	0.185791i
$689$	−25.7133	−	30.6439i	−0.979599	−	1.16744i
$690$	0.590151	−	1.15993i	0.0224667	−	0.0441577i
$691$	6.95655			0.264640			0.132320	−	0.991207i	$-0.457757\pi$
$691$	6.95655			0.264640			0.132320	+	0.991207i	$0.457757\pi$
$692$	−6.42628	−	11.1307i	−0.244291	−	0.423124i
$693$	−2.55426	−	2.46080i	−0.0970283	−	0.0934780i
$694$	−1.84031	−	0.324497i	−0.0698573	−	0.0123177i
$695$	3.45425	+	1.99431i	0.131027	+	0.0756485i
$696$	−6.74769	+	6.29977i	−0.255770	+	0.238792i
$697$	−1.59612	−	4.38531i	−0.0604575	−	0.166106i
$698$	21.6377	−	18.1562i	0.818999	−	0.687222i
$699$	0.396662	+	0.201814i	0.0150031	+	0.00763332i
$700$	−10.7976	−	3.93001i	−0.408111	−	0.148540i
$701$	26.6475	−	4.69868i	1.00646	−	0.177467i	0.353967	−	0.935258i	$-0.384833\pi$
$701$	26.6475	−	4.69868i	1.00646	−	0.177467i	0.652497	+	0.757791i	$0.273722\pi$
$702$	13.0283	−	10.5884i	0.491723	−	0.399633i
$703$	2.74593	−	0.380503i	0.103565	−	0.0143509i
$704$	−0.354477	+	0.204658i	−0.0133599	+	0.00771332i
$705$	18.6654	+	14.0481i	0.702980	+	0.529083i
$706$	−10.2121	+	1.80067i	−0.384338	+	0.0677691i
$707$	−31.4876	−	5.55212i	−1.18421	−	0.208809i
$708$	−9.38810	−	7.06576i	−0.352827	−	0.265548i
$709$	6.05974	−	34.3665i	0.227578	−	1.29066i	−0.630116	−	0.776501i	$-0.716993\pi$
$709$	6.05974	−	34.3665i	0.227578	−	1.29066i	0.857694	−	0.514160i	$-0.171896\pi$
$710$	2.09196	+	1.20779i	0.0785098	+	0.0453276i
$711$	−20.0761	+	29.8399i	−0.752911	+	1.11908i
$712$	1.16650	−	6.61555i	0.0437165	−	0.247928i
$713$	−3.31759	+	1.20750i	−0.124245	+	0.0452213i
$714$	5.69600	+	6.10099i	0.213168	+	0.228324i
$715$	−1.15772	+	0.668410i	−0.0432963	+	0.0249971i
$716$	2.45128	−	0.892193i	0.0916086	−	0.0333428i
$717$	−36.5291	−	4.46332i	−1.36420	−	0.166686i
$718$	21.0972	−	25.1426i	0.787339	−	0.938314i
$719$	16.0206	+	19.0926i	0.597468	+	0.712034i	0.977023	−	0.213135i	$-0.0683673\pi$
$719$	16.0206	+	19.0926i	0.597468	+	0.712034i	−0.379555	+	0.925169i	$0.623923\pi$
$720$	0.320547	+	3.01556i	0.0119461	+	0.112383i
$721$		−	15.6854i		−	0.584156i
$722$	−10.6855	+	15.7105i	−0.397673	+	0.584685i
$723$	4.32082	−	14.1627i	0.160693	−	0.526715i
$724$	2.98416	−	8.19890i	0.110905	−	0.304710i
$725$	3.68181	+	20.8806i	0.136739	+	0.775484i
$726$	8.50807	−	16.7224i	0.315764	−	0.620627i
$727$	−1.35153	−	7.66489i	−0.0501254	−	0.284275i	0.949434	−	0.313968i	$-0.101658\pi$
$727$	−1.35153	−	7.66489i	−0.0501254	−	0.284275i	−0.999559	+	0.0296925i	$0.990547\pi$
$728$	5.99864	−	7.14891i	0.222325	−	0.264956i
$729$	−20.1288	−	17.9954i	−0.745509	−	0.666495i
$730$	−7.47368	+	4.31493i	−0.276613	+	0.159703i
$731$	−2.82367	−	7.75797i	−0.104437	−	0.286939i
$732$	4.45327	+	6.84858i	0.164598	+	0.253131i
$733$	−32.5291			−1.20149			−0.600745	−	0.799441i	$-0.705129\pi$
$733$	−32.5291			−1.20149			−0.600745	+	0.799441i	$0.705129\pi$
$734$	−12.4769	−	21.6107i	−0.460532	−	0.797665i
$735$	−1.97106	+	1.28168i	−0.0727036	+	0.0472753i
$736$	0.732021	−	0.129075i	0.0269827	−	0.00475777i
$737$	2.13837	−	0.778304i	0.0787679	−	0.0286692i
$738$	4.94043	+	6.78307i	0.181860	+	0.249688i
$739$	−3.19256	−	18.1059i	−0.117440	−	0.666036i	−0.985513	−	0.169599i	$-0.945753\pi$
$739$	−3.19256	−	18.1059i	−0.117440	−	0.666036i	0.868073	−	0.496436i	$-0.165358\pi$
$740$	−0.321440	−	0.556751i	−0.0118164	−	0.0204666i
$741$	−8.71108	−	22.7846i	−0.320009	−	0.837013i
$742$	−17.8809	+	30.9706i	−0.656428	+	1.13697i
$743$	−29.2579	−	10.6490i	−1.07337	−	0.390674i	−0.255933	−	0.966695i	$-0.582383\pi$
$743$	−29.2579	−	10.6490i	−1.07337	−	0.390674i	−0.817435	+	0.576020i	$0.804605\pi$
$744$	4.94706	−	6.57304i	0.181368	−	0.240979i
$745$	7.48523	+	6.28085i	0.274238	+	0.230113i
$746$	3.88787	−	10.6818i	0.142345	−	0.391089i
$747$	−9.01822	+	36.3528i	−0.329959	+	1.33008i
$748$	0.341446	−	0.591402i	0.0124845	−	0.0216238i
$749$	−6.05305	+	10.4842i	−0.221174	+	0.383084i
$750$	14.0103	+	7.12819i	0.511584	+	0.260285i
$751$	27.0112	−	32.1907i	0.985652	−	1.17465i	0.00102225	−	0.999999i	$-0.499675\pi$
$751$	27.0112	−	32.1907i	0.985652	−	1.17465i	0.984630	−	0.174655i	$-0.0558809\pi$
$752$			13.3428i			0.486563i
$753$	−11.4028	+	2.63964i	−0.415542	+	0.0961939i
$754$	−16.9584	−	2.99023i	−0.617590	−	0.108898i
$755$	−3.23141	−	1.17614i	−0.117603	−	0.0428040i
$756$	−12.8785	−	7.70719i	−0.468387	−	0.280308i
$757$	18.2124	−	15.2820i	0.661942	−	0.555435i	−0.248726	−	0.968574i	$-0.580012\pi$
$757$	18.2124	−	15.2820i	0.661942	−	0.555435i	0.910668	+	0.413139i	$0.135568\pi$
$758$	7.70913	+	9.18739i	0.280008	+	0.333701i
$759$	0.385194	−	0.359624i	0.0139816	−	0.0130535i
$760$	4.30813	+	0.924431i	0.156272	+	0.0335326i
$761$	23.1365	+	13.3579i	0.838698	+	0.484222i	0.856821	−	0.515613i	$-0.172436\pi$
$761$	23.1365	+	13.3579i	0.838698	+	0.484222i	−0.0181236	+	0.999836i	$0.505769\pi$
$762$	−13.9324	−	1.70233i	−0.504716	−	0.0616690i
$763$	−10.9717	+	30.1446i	−0.397203	+	1.09131i
$764$	−7.38494	−	20.2900i	−0.267178	−	0.734065i
$765$	−2.97869	−	4.08966i	−0.107695	−	0.147862i
$766$	11.2093	+	9.40572i	0.405008	+	0.339842i
$767$		−	21.9182i		−	0.791419i
$768$	−1.26604	+	1.18200i	−0.0456844	+	0.0426519i
$769$	36.0026	+	30.2098i	1.29829	+	1.08939i	0.990438	+	0.137958i	$0.0440541\pi$
$769$	36.0026	+	30.2098i	1.29829	+	1.08939i	0.307850	+	0.951435i	$0.400390\pi$
$770$	0.915495	+	0.768191i	0.0329921	+	0.0276837i
$771$	25.0502	−	23.3873i	0.902160	−	0.842273i
$772$			27.3389i			0.983949i
$773$	12.2551	+	10.2833i	0.440786	+	0.369864i	0.836004	−	0.548724i	$-0.184886\pi$
$773$	12.2551	+	10.2833i	0.440786	+	0.369864i	−0.395217	+	0.918588i	$0.629331\pi$
$774$	8.74002	+	11.9998i	0.314154	+	0.431324i
$775$	−6.46250	−	17.7556i	−0.232140	−	0.637799i
$776$	5.70378	−	15.6710i	0.204754	−	0.562556i
$777$	3.15823	+	0.385890i	0.113301	+	0.0138437i
$778$	−21.3023	−	12.2989i	−0.763723	−	0.440936i
$779$	11.6031	−	3.74530i	0.415726	−	0.134189i
$780$	−4.13489	+	3.86041i	−0.148053	+	0.138225i
$781$	0.628725	+	0.749285i	0.0224976	+	0.0268115i
$782$	−0.949994	+	0.797139i	−0.0339717	+	0.0285056i
$783$	−0.434306	+	27.6907i	−0.0155208	+	0.989586i
$784$	−1.26187	−	0.459282i	−0.0450666	−	0.0164029i
$785$	10.7913	+	1.90280i	0.385159	+	0.0679140i
$786$	−16.0899	+	3.72466i	−0.573909	+	0.132854i
$787$		−	27.8300i		−	0.992033i	−0.868313	−	0.496016i	$-0.834796\pi$
$787$		−	27.8300i		−	0.992033i	0.868313	−	0.496016i	$-0.165204\pi$
$788$	2.31098	−	2.75411i	0.0823251	−	0.0981112i
$789$	−3.89207	−	1.98022i	−0.138561	−	0.0704976i
$790$	6.05917	−	10.4948i	0.215576	−	0.373388i
$791$	−2.87796	+	4.98477i	−0.102328	+	0.177238i
$792$	−0.295660	+	1.19182i	−0.0105058	+	0.0423495i
$793$	−5.21189	+	14.3196i	−0.185080	+	0.508502i
$794$	−24.2817	−	20.3748i	−0.861725	−	0.723073i
$795$	13.0356	−	17.3201i	0.462326	−	0.614281i
$796$	−9.42118	−	3.42903i	−0.333925	−	0.121539i
$797$	−17.8201	+	30.8654i	−0.631222	+	1.09331i	0.356080	+	0.934455i	$0.384113\pi$
$797$	−17.8201	+	30.8654i	−0.631222	+	1.09331i	−0.987302	+	0.158853i	$0.949220\pi$
$798$	−16.4771	+	14.2845i	−0.583283	+	0.505666i
$799$	−11.1304	−	19.2785i	−0.393767	−	0.682024i
$800$	0.690804	+	3.91774i	0.0244236	+	0.138513i
$801$	−11.8648	−	16.2900i	−0.419221	−	0.575578i
$802$	−5.47894	+	1.99417i	−0.193468	+	0.0704166i
$803$	−3.44133	+	0.606800i	−0.121442	+	0.0214135i
$804$	8.07282	−	5.24932i	0.284706	−	0.185129i
$805$	−1.08514	−	1.87952i	−0.0382462	−	0.0662444i
$806$	15.3459			0.540536
$807$	4.60401	+	7.08040i	0.162069	+	0.249242i
$808$	3.78602	+	10.4020i	0.133192	+	0.365941i
$809$	−12.5671	+	7.25562i	−0.441836	+	0.255094i	−0.704376	−	0.709827i	$-0.748773\pi$
$809$	−12.5671	+	7.25562i	−0.441836	+	0.255094i	0.262540	+	0.964921i	$0.415440\pi$
$810$	7.18225	+	5.58413i	0.252358	+	0.196206i
$811$	17.7732	−	21.1813i	0.624102	−	0.743776i	−0.357668	−	0.933849i	$-0.616428\pi$
$811$	17.7732	−	21.1813i	0.624102	−	0.743776i	0.981770	+	0.190073i	$0.0608725\pi$
$812$	2.67321	+	15.1605i	0.0938113	+	0.532031i
$813$	17.1617	−	33.7309i	0.601887	−	1.18300i
$814$	−0.0452034	−	0.256361i	−0.00158438	−	0.00898547i
$815$	−5.87434	+	16.1396i	−0.205769	+	0.565346i
$816$	0.843240	−	2.76395i	0.0295193	−	0.0967575i
$817$	20.5269	−	6.62574i	0.718145	−	0.231805i
$818$			15.8594i			0.554510i
$819$	−2.95931	−	27.8399i	−0.103407	−	0.972803i
$820$	−1.81750	−	2.16601i	−0.0634699	−	0.0756405i
$821$	−12.9991	+	15.4917i	−0.453670	+	0.540663i	−0.943595	−	0.331102i	$-0.892580\pi$
$821$	−12.9991	+	15.4917i	−0.453670	+	0.540663i	0.489925	+	0.871765i	$0.337024\pi$
$822$	−5.31127	−	0.648961i	−0.185252	−	0.0226351i
$823$	−20.0307	+	7.29057i	−0.698226	+	0.254133i	−0.666653	−	0.745368i	$-0.732274\pi$
$823$	−20.0307	+	7.29057i	−0.698226	+	0.254133i	−0.0315726	+	0.999501i	$0.510052\pi$
$824$	−4.70295	+	2.71525i	−0.163835	+	0.0945902i
$825$	1.92469	+	2.06154i	0.0670092	+	0.0717736i
$826$	−18.4127	+	6.70169i	−0.640661	+	0.233182i
$827$	−0.0628802	+	0.356612i	−0.00218656	+	0.0124006i	−0.985882	−	0.167444i	$-0.946449\pi$
$827$	−0.0628802	+	0.356612i	−0.00218656	+	0.0124006i	0.983695	+	0.179845i	$0.0575596\pi$
$828$	1.24478	−	1.85018i	0.0432593	−	0.0642981i
$829$	0.319627	+	0.184537i	0.0111011	+	0.00640922i	0.505540	−	0.862803i	$-0.331293\pi$
$829$	0.319627	+	0.184537i	0.0111011	+	0.00640922i	−0.494439	+	0.869212i	$0.664627\pi$
$830$	2.19150	−	12.4286i	0.0760682	−	0.431404i
$831$	−16.9045	−	12.7228i	−0.586410	−	0.441350i
$832$	−3.18185	−	0.561046i	−0.110311	−	0.0194508i
$833$	2.20634	−	0.389038i	0.0764453	−	0.0134794i
$834$	5.46057	+	4.10979i	0.189084	+	0.142310i
$835$	−19.3732	+	11.1851i	−0.670437	+	0.387077i
$836$	1.51123	+	0.948387i	0.0522668	+	0.0328006i
$837$	−3.90396	−	24.3693i	−0.134941	−	0.842327i
$838$	4.14620	−	0.731087i	0.143228	−	0.0252550i
$839$	43.1578	+	15.7081i	1.48997	+	0.542305i	0.953442	−	0.301576i	$-0.0975128\pi$
$839$	43.1578	+	15.7081i	1.48997	+	0.542305i	0.536529	+	0.843882i	$0.319735\pi$
$840$	4.50730	+	2.29323i	0.155516	+	0.0791240i
$841$	−0.454938	+	0.381738i	−0.0156875	+	0.0131634i
$842$	9.12007	+	25.0572i	0.314298	+	0.863528i
$843$	−6.63740	+	6.19680i	−0.228604	+	0.213429i
$844$	−10.3488	−	5.97486i	−0.356219	−	0.205663i
$845$	2.54951	+	0.449547i	0.0877058	+	0.0154649i
$846$	28.8269	+	27.7721i	0.991089	+	0.954826i
$847$	−15.6442	−	27.0966i	−0.537542	−	0.931051i
$848$	12.3812			0.425171
$849$	8.01293	−	15.7492i	0.275003	−	0.540512i
$850$	−4.26625	−	5.08432i	−0.146331	−	0.174391i
$851$	−0.0820892	+	0.465551i	−0.00281398	+	0.0159589i
$852$	3.30703	+	2.48896i	0.113297	+	0.0852705i
$853$	−9.19247	+	7.71340i	−0.314744	+	0.264102i	−0.786450	−	0.617654i	$-0.788083\pi$
$853$	−9.19247	+	7.71340i	−0.314744	+	0.264102i	0.471705	+	0.881756i	$0.343639\pi$
$854$	13.6230			0.466169
$855$	10.9643	−	7.38348i	0.374970	−	0.252510i
$856$	4.19128			0.143255
$857$	−23.7684	+	19.9440i	−0.811912	+	0.681275i	−0.951063	−	0.308996i	$-0.900007\pi$
$857$	−23.7684	+	19.9440i	−0.811912	+	0.681275i	0.139151	+	0.990271i	$0.455563\pi$
$858$	−2.10797	+	0.896248i	−0.0719648	+	0.0305974i
$859$	0.811614	−	4.60289i	0.0276919	−	0.157049i	−0.967826	−	0.251620i	$-0.919037\pi$
$859$	0.811614	−	4.60289i	0.0276919	−	0.157049i	0.995518	+	0.0945710i	$0.0301479\pi$
$860$	−3.21531	−	3.83185i	−0.109641	−	0.130665i
$861$	13.9743	−	0.740630i	0.476242	−	0.0252406i
$862$	2.71664			0.0925292
$863$	3.20513	+	5.55145i	0.109104	+	0.188973i	0.915407	−	0.402528i	$-0.131869\pi$
$863$	3.20513	+	5.55145i	0.109104	+	0.188973i	−0.806304	+	0.591502i	$0.798535\pi$
$864$	−0.0814873	+	5.19551i	−0.00277225	+	0.176755i
$865$	12.7946	+	2.25604i	0.435031	+	0.0767077i
$866$	30.3194	+	17.5049i	1.03029	+	0.594841i
$867$	−5.55329	−	23.9893i	−0.188600	−	0.814721i
$868$	−4.69216	−	12.8916i	−0.159262	−	0.437570i
$869$	3.75897	−	3.15415i	0.127514	−	0.106997i
$870$	−0.493874	−	9.31846i	−0.0167439	−	0.315925i
$871$	16.8793	+	6.14355i	0.571932	+	0.208166i
$872$	10.9375	−	1.92857i	0.370390	−	0.0653097i
$873$	−21.9849	−	44.9409i	−0.744075	−	1.52102i
$874$	−1.98982	−	2.55703i	−0.0673067	−	0.0864929i
$875$	22.7019	−	13.1070i	0.767466	−	0.443097i
$876$	−13.6080	+	5.78574i	−0.459772	+	0.195482i
$877$	−15.2418	+	2.68755i	−0.514680	+	0.0907520i	−0.424955	−	0.905215i	$-0.639710\pi$
$877$	−15.2418	+	2.68755i	−0.514680	+	0.0907520i	−0.0897252	+	0.995967i	$0.528599\pi$
$878$	−11.8351	−	2.08685i	−0.399415	−	0.0704277i
$879$	−2.11477	+	17.3078i	−0.0713294	+	0.583779i
$880$	0.0718480	−	0.407470i	0.00242200	−	0.0137358i
$881$	−27.8657	−	16.0883i	−0.938818	−	0.542027i	−0.0492285	−	0.998788i	$-0.515676\pi$
$881$	−27.8657	−	16.0883i	−0.938818	−	0.542027i	−0.889590	+	0.456761i	$0.849010\pi$
$882$	−3.61875	+	1.77027i	−0.121850	+	0.0596082i
$883$	−5.63252	+	31.9436i	−0.189549	+	1.07499i	0.730420	+	0.682998i	$0.239324\pi$
$883$	−5.63252	+	31.9436i	−0.189549	+	1.07499i	−0.919970	+	0.391989i	$0.871787\pi$
$884$	5.06534	−	1.84363i	0.170366	−	0.0620081i
$885$	11.5714	−	2.67867i	0.388970	−	0.0900426i
$886$	−20.8615	+	12.0444i	−0.700856	+	0.404639i
$887$	−34.5461	+	12.5737i	−1.15994	+	0.422185i	−0.849077	−	0.528269i	$-0.822841\pi$
$887$	−34.5461	+	12.5737i	−1.15994	+	0.422185i	−0.310866	+	0.950454i	$0.600619\pi$
$888$	−0.431008	−	1.01373i	−0.0144637	−	0.0340185i
$889$	−15.0455	+	17.9305i	−0.504610	+	0.601371i
$890$	4.36485	+	5.20182i	0.146310	+	0.174365i
$891$	1.95951	+	3.11945i	0.0656459	+	0.104506i
$892$		−	13.3600i		−	0.447327i
$893$	51.4050	−	27.2052i	1.72020	−	0.910386i
$894$	11.4257	+	12.2381i	0.382133	+	0.409303i
$895$	−0.901873	+	2.47788i	−0.0301463	+	0.0828263i
$896$	0.501565	+	2.84452i	0.0167561	+	0.0950287i
$897$	4.15386	−	0.220153i	0.138693	−	0.00735069i
$898$	−5.51601	−	31.2828i	−0.184072	−	1.04392i
$899$	−16.2719	+	19.3921i	−0.542697	+	0.646761i
$900$	9.90206	+	6.66203i	0.330069	+	0.222068i
$901$	−17.8890	+	10.3282i	−0.595970	+	0.344084i
$902$	−0.391589	−	1.07588i	−0.0130385	−	0.0358229i
$903$	24.7216	−	1.31023i	0.822684	−	0.0436019i
$904$	1.99277			0.0662786
$905$	4.40988	+	7.63813i	0.146589	+	0.253900i
$906$	−5.25160	−	2.67192i	−0.174473	−	0.0887686i
$907$	−17.7897	+	3.13681i	−0.590698	+	0.104156i	−0.461004	−	0.887398i	$-0.652511\pi$
$907$	−17.7897	+	3.13681i	−0.590698	+	0.104156i	−0.129694	+	0.991554i	$0.541400\pi$
$908$	24.5204	−	8.92468i	0.813737	−	0.296176i
$909$	30.3536	+	13.4714i	1.00677	+	0.446818i
$910$	1.63811	+	9.29017i	0.0543028	+	0.307966i
$911$	5.77103	+	9.99571i	0.191203	+	0.331173i	0.945649	−	0.325189i	$-0.105428\pi$
$911$	5.77103	+	9.99571i	0.191203	+	0.331173i	−0.754446	+	0.656362i	$0.772095\pi$
$912$	7.13520	+	2.46757i	0.236270	+	0.0817095i
$913$	2.55513	−	4.42562i	0.0845625	−	0.146467i
$914$	−13.0014	−	4.73211i	−0.430047	−	0.156524i
$915$	−8.19681	−	1.00153i	−0.270978	−	0.0331096i
$916$	20.8932	+	17.5315i	0.690331	+	0.579256i
$917$	−9.41972	+	25.8805i	−0.311067	+	0.854649i
$918$	−4.21630	−	7.57475i	−0.139159	−	0.250004i
$919$	−9.45387	+	16.3746i	−0.311854	+	0.540147i	−0.978764	−	0.204991i	$-0.934283\pi$
$919$	−9.45387	+	16.3746i	−0.311854	+	0.540147i	0.666910	+	0.745139i	$0.267617\pi$
$920$	−0.375690	+	0.650713i	−0.0123861	+	0.0214534i
$921$	46.1227	−	29.9912i	1.51980	−	0.988242i
$922$	−3.66045	+	4.36235i	−0.120550	+	0.143666i
$923$			7.72083i			0.254134i
$924$	1.39744	+	1.49680i	0.0459725	+	0.0492411i
$925$	−2.49161	−	0.439338i	−0.0819235	−	0.0144453i
$926$	37.3515	+	13.5948i	1.22745	+	0.446754i
$927$	−3.92261	+	15.8122i	−0.128835	+	0.519341i
$928$	4.08282	−	3.42589i	0.134025	−	0.112460i
$929$	34.5210	+	41.1405i	1.13260	+	1.34978i	0.928721	+	0.370780i	$0.120910\pi$
$929$	34.5210	+	41.1405i	1.13260	+	1.34978i	0.203877	+	0.978997i	$0.434646\pi$
$930$	1.87546	+	8.10170i	0.0614988	+	0.265665i
$931$	0.803419	+	5.79795i	0.0263310	+	0.190020i
$932$	−0.222525	−	0.128475i	−0.00728905	−	0.00420833i
$933$	16.4221	+	38.6246i	0.537634	+	1.26451i
$934$	−13.6873	+	37.6056i	−0.447863	+	1.23049i
$935$	0.236097	+	0.648672i	0.00772120	+	0.0212138i
$936$	−7.83492	+	5.70654i	−0.256092	+	0.186524i
$937$	8.48673	+	7.12121i	0.277249	+	0.232640i	0.770800	−	0.637077i	$-0.219857\pi$
$937$	8.48673	+	7.12121i	0.277249	+	0.232640i	−0.493551	+	0.869717i	$0.664301\pi$
$938$		−	16.0582i		−	0.524319i
$939$	−11.5897	−	50.0658i	−0.378216	−	1.63384i
$940$	−10.3321	−	8.66967i	−0.336996	−	0.282773i
$941$	19.2825	+	16.1799i	0.628590	+	0.527450i	0.900491	−	0.434876i	$-0.143208\pi$
$941$	19.2825	+	16.1799i	0.628590	+	0.527450i	−0.271900	+	0.962325i	$0.587652\pi$
$942$	17.9586	+	5.47891i	0.585123	+	0.178512i
$943$			2.07918i			0.0677075i
$944$	5.19672	+	4.36057i	0.169139	+	0.141924i
$945$	14.3361	−	4.96472i	0.466353	−	0.161502i
$946$	−0.692752	−	1.90332i	−0.0225233	−	0.0618823i
$947$	−16.3443	+	44.9056i	−0.531118	+	1.45923i	0.326624	+	0.945154i	$0.394089\pi$
$947$	−16.3443	+	44.9056i	−0.531118	+	1.45923i	−0.857742	+	0.514080i	$0.828133\pi$
$948$	12.4865	−	16.5905i	0.405542	−	0.538833i
$949$	−23.8878	−	13.7916i	−0.775431	−	0.447695i
$950$	13.6851	−	10.6494i	0.444004	−	0.345513i
$951$	−46.4527	−	14.1721i	−1.50633	−	0.459560i
$952$	−3.09756	−	3.69152i	−0.100392	−	0.119643i
$953$	−33.3210	+	27.9596i	−1.07937	+	0.905701i	−0.995869	−	0.0908070i	$-0.971055\pi$
$953$	−33.3210	+	27.9596i	−1.07937	+	0.905701i	−0.0835034	+	0.996507i	$0.526611\pi$
$954$	25.7705	−	26.7493i	0.834351	−	0.866039i
$955$	20.5101	+	7.46507i	0.663692	+	0.241564i
$956$	20.9241	+	3.68949i	0.676735	+	0.119327i
$957$	1.10261	−	3.61409i	0.0356422	−	0.116827i
$958$		−	21.5582i		−	0.696513i
$959$	−5.73562	+	6.83545i	−0.185213	+	0.220728i
$960$	−0.0926639	−	1.74839i	−0.00299071	−	0.0564290i
$961$	−4.22028	+	7.30975i	−0.136138	+	0.235798i
$962$	1.02741	−	1.77952i	0.0331249	−	0.0573740i
$963$	8.72384	−	9.05517i	0.281122	−	0.291799i
$964$	−2.92389	+	8.03333i	−0.0941722	+	0.258736i
$965$	−21.1701	−	17.7638i	−0.681488	−	0.571837i
$966$	−1.45503	−	3.42222i	−0.0468148	−	0.110108i
$967$	−6.36201	−	2.31558i	−0.204588	−	0.0744641i	0.237693	−	0.971340i	$-0.423609\pi$
$967$	−6.36201	−	2.31558i	−0.204588	−	0.0744641i	−0.442282	+	0.896876i	$0.645831\pi$
$968$	−5.41623	+	9.38119i	−0.174084	+	0.301523i
$969$	−12.3678	+	2.38681i	−0.397310	+	0.0766754i
$970$	8.42884	+	14.5992i	0.270634	+	0.468752i
$971$	2.93638	+	16.6530i	0.0942330	+	0.534422i	0.994980	+	0.100077i	$0.0319089\pi$
$971$	2.93638	+	16.6530i	0.0942330	+	0.534422i	−0.900747	+	0.434345i	$0.856980\pi$
$972$	11.0552	+	10.9901i	0.354595	+	0.352509i
$973$	10.7097	−	3.89803i	0.343339	−	0.124965i
$974$	25.5690	−	4.50850i	0.819283	−	0.144462i
$975$	1.17825	+	22.2313i	0.0377341	+	0.711971i
$976$	−2.35823	−	4.08457i	−0.0754850	−	0.130744i
$977$	−28.6494			−0.916575			−0.458287	−	0.888804i	$-0.651537\pi$
$977$	−28.6494			−0.916575			−0.458287	+	0.888804i	$0.651537\pi$
$978$	−13.3452	+	26.2297i	−0.426732	+	0.838732i
$979$	0.940425	+	2.58380i	0.0300561	+	0.0825785i
$980$	1.17556	−	0.678710i	0.0375519	−	0.0216806i
$981$	18.5989	−	27.6444i	0.593818	−	0.882617i
$982$	19.6681	−	23.4395i	0.627634	−	0.747985i
$983$	−3.11614	−	17.6725i	−0.0993893	−	0.563665i	−0.993314	−	0.115447i	$-0.963170\pi$
$983$	−3.11614	−	17.6725i	−0.0993893	−	0.563665i	0.893924	−	0.448218i	$-0.147941\pi$
$984$	−2.64110	−	4.06168i	−0.0841951	−	0.129482i
$985$	0.631081	+	3.57904i	0.0201079	+	0.114038i
$986$	−3.04125	+	8.35577i	−0.0968531	+	0.266102i
$987$	65.0325	−	15.0544i	2.07001	−	0.479186i
$988$	4.32608	+	13.4024i	0.137631	+	0.426388i
$989$			3.67824i			0.116961i
$990$	−0.730784	−	1.00335i	−0.0232259	−	0.0318884i
$991$	−28.5175	−	33.9859i	−0.905889	−	1.07960i	−0.996490	−	0.0837091i	$-0.973323\pi$
$991$	−28.5175	−	33.9859i	−0.905889	−	1.07960i	0.0906013	−	0.995887i	$-0.471121\pi$
$992$	−3.05303	+	3.63846i	−0.0969339	+	0.115521i
$993$	10.0785	−	13.3911i	0.319832	−	0.424953i
$994$	6.48602	−	2.36072i	0.205724	−	0.0748775i
$995$	8.77681	−	5.06730i	0.278244	−	0.160644i
$996$	6.31018	−	20.6833i	0.199946	−	0.655376i
$997$	−0.671347	+	0.244350i	−0.0212618	+	0.00773866i	−0.352629	−	0.935763i	$-0.614712\pi$
$997$	−0.671347	+	0.244350i	−0.0212618	+	0.00773866i	0.331367	+	0.943502i	$0.392490\pi$
$998$	4.70374	−	26.6762i	0.148894	−	0.844421i
$999$	−3.08725	−	1.17882i	−0.0976762	−	0.0372961i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	342.2.bf.a.257.2	yes	12
9.2	odd	6		342.2.x.a.29.2	✓	12
19.2	odd	18		342.2.x.a.59.2	yes	12
171.2	even	18	inner	342.2.bf.a.173.2	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
342.2.x.a.29.2	✓	12	9.2	odd	6
342.2.x.a.59.2	yes	12	19.2	odd	18
342.2.bf.a.173.2	yes	12	171.2	even	18	inner
342.2.bf.a.257.2	yes	12	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 342 = 2 \cdot 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	342.bf (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.766044 - 0.642788i) q^{2} +(-0.210069 + 1.71926i) q^{3} +(0.173648 - 0.984808i) q^{4} +(0.649762 + 0.774356i) q^{5} +(0.944200 + 1.45206i) q^{6} +2.88840 q^{7} +(-0.500000 - 0.866025i) q^{8} +(-2.91174 - 0.722330i) q^{9} +O(q^{10})\)	\(q+(0.766044 - 0.642788i) q^{2} +(-0.210069 + 1.71926i) q^{3} +(0.173648 - 0.984808i) q^{4} +(0.649762 + 0.774356i) q^{5} +(0.944200 + 1.45206i) q^{6} +2.88840 q^{7} +(-0.500000 - 0.866025i) q^{8} +(-2.91174 - 0.722330i) q^{9} +(0.995493 + 0.175532i) q^{10} +(0.354477 + 0.204658i) q^{11} +(1.65667 + 0.505425i) q^{12} +(1.10505 + 3.03609i) q^{13} +(2.21264 - 1.85663i) q^{14} +(-1.46782 + 0.954444i) q^{15} +(-0.939693 - 0.342020i) q^{16} +(1.64303 - 0.289711i) q^{17} +(-2.69483 + 1.31830i) q^{18} +(0.598294 + 4.31764i) q^{19} +(0.875422 - 0.505425i) q^{20} +(-0.606764 + 4.96592i) q^{21} +(0.403097 - 0.0710768i) q^{22} +(-0.732021 - 0.129075i) q^{23} +(1.59396 - 0.677707i) q^{24} +(0.690804 - 3.91774i) q^{25} +(2.79807 + 1.61547i) q^{26} +(1.85354 - 4.85432i) q^{27} +(0.501565 - 2.84452i) q^{28} +(-5.00832 + 1.82288i) q^{29} +(-0.510909 + 1.67464i) q^{30} +(4.11334 - 2.37484i) q^{31} +(-0.939693 + 0.342020i) q^{32} +(-0.426325 + 0.566448i) q^{33} +(1.07241 - 1.27805i) q^{34} +(1.87677 + 2.23665i) q^{35} +(-1.21697 + 2.74207i) q^{36} -0.635980i q^{37} +(3.23365 + 2.92293i) q^{38} +(-5.45197 + 1.26208i) q^{39} +(0.345731 - 0.949888i) q^{40} +(-0.485725 - 2.75468i) q^{41} +(2.72723 + 4.19414i) q^{42} +(-0.859287 - 4.87326i) q^{43} +(0.263103 - 0.313554i) q^{44} +(-1.33260 - 2.72407i) q^{45} +(-0.643729 + 0.371657i) q^{46} +(-4.56352 - 12.5382i) q^{47} +(0.785424 - 1.54373i) q^{48} +1.34285 q^{49} +(-1.98909 - 3.44521i) q^{50} +(0.152939 + 2.88567i) q^{51} +(3.18185 - 0.561046i) q^{52} +(-11.6345 + 4.23461i) q^{53} +(-1.70040 - 4.91006i) q^{54} +(0.0718480 + 0.407470i) q^{55} +(-1.44420 - 2.50143i) q^{56} +(-7.54885 + 0.121621i) q^{57} +(-2.66487 + 4.61569i) q^{58} +(-6.37472 - 2.32021i) q^{59} +(0.685060 + 1.61126i) q^{60} +(3.61301 + 3.03168i) q^{61} +(1.62449 - 4.46324i) q^{62} +(-8.41027 - 2.08638i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(-1.63300 + 2.82843i) q^{65} +(0.0375216 + 0.707961i) q^{66} +(3.57361 - 4.25886i) q^{67} -1.66838i q^{68} +(0.375690 - 1.23142i) q^{69} +(2.87538 + 0.507007i) q^{70} +(2.24554 + 0.817311i) q^{71} +(0.830315 + 2.88281i) q^{72} +(-6.53990 + 5.48763i) q^{73} +(-0.408800 - 0.487189i) q^{74} +(6.59052 + 2.01067i) q^{75} +(4.35594 + 0.160547i) q^{76} +(1.02387 + 0.591133i) q^{77} +(-3.36521 + 4.47127i) q^{78} +(4.10023 - 11.2653i) q^{79} +(-0.345731 - 0.949888i) q^{80} +(7.95648 + 4.20647i) q^{81} +(-2.14276 - 1.79799i) q^{82} -12.4849i q^{83} +(4.78512 + 1.45987i) q^{84} +(1.29192 + 1.08405i) q^{85} +(-3.79072 - 3.18079i) q^{86} +(-2.08192 - 8.99355i) q^{87} -0.409315i q^{88} +(5.14599 + 4.31800i) q^{89} +(-2.77183 - 1.23018i) q^{90} +(3.19181 + 8.76943i) q^{91} +(-0.254228 + 0.698487i) q^{92} +(3.21889 + 7.57080i) q^{93} +(-11.5552 - 6.67142i) q^{94} +(-2.95465 + 3.26873i) q^{95} +(-0.390623 - 1.68743i) q^{96} +(10.7196 + 12.7751i) q^{97} +(1.02868 - 0.863167i) q^{98} +(-0.884316 - 0.851960i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 6 q^{3} + 3 q^{6} + 18 q^{7} - 6 q^{8}+O(q^{10}) \) 12 * q - 6 * q^3 + 3 * q^6 + 18 * q^7 - 6 * q^8	\( 12 q - 6 q^{3} + 3 q^{6} + 18 q^{7} - 6 q^{8} + 9 q^{10} + 9 q^{11} + 3 q^{12} - 3 q^{13} - 3 q^{14} - 9 q^{15} + 9 q^{18} + 15 q^{19} + 9 q^{20} + 3 q^{21} + 9 q^{22} + 18 q^{23} + 3 q^{24} + 18 q^{26} - 9 q^{27} - 3 q^{28} - 27 q^{29} - 27 q^{30} + 36 q^{31} - 9 q^{34} - 18 q^{35} - 9 q^{36} - 9 q^{38} + 9 q^{40} - 36 q^{41} + 30 q^{42} + 21 q^{43} - 18 q^{44} + 9 q^{45} - 27 q^{46} + 3 q^{48} - 6 q^{49} - 3 q^{50} - 27 q^{51} + 12 q^{52} - 9 q^{55} - 9 q^{56} - 57 q^{57} + 9 q^{58} - 36 q^{59} + 6 q^{61} - 6 q^{62} - 18 q^{63} - 6 q^{64} - 27 q^{65} + 9 q^{66} - 33 q^{67} + 9 q^{69} - 18 q^{70} + 9 q^{71} - 9 q^{72} - 24 q^{73} + 42 q^{74} + 24 q^{75} + 9 q^{76} + 27 q^{77} + 9 q^{78} - 30 q^{79} - 9 q^{80} + 36 q^{81} - 6 q^{84} + 54 q^{85} + 12 q^{86} - 27 q^{87} + 9 q^{89} - 9 q^{90} + 6 q^{91} - 18 q^{93} - 36 q^{94} + 54 q^{95} + 3 q^{96} - 18 q^{97} - 6 q^{98} + 72 q^{99}+O(q^{100}) \) 12 * q - 6 * q^3 + 3 * q^6 + 18 * q^7 - 6 * q^8 + 9 * q^10 + 9 * q^11 + 3 * q^12 - 3 * q^13 - 3 * q^14 - 9 * q^15 + 9 * q^18 + 15 * q^19 + 9 * q^20 + 3 * q^21 + 9 * q^22 + 18 * q^23 + 3 * q^24 + 18 * q^26 - 9 * q^27 - 3 * q^28 - 27 * q^29 - 27 * q^30 + 36 * q^31 - 9 * q^34 - 18 * q^35 - 9 * q^36 - 9 * q^38 + 9 * q^40 - 36 * q^41 + 30 * q^42 + 21 * q^43 - 18 * q^44 + 9 * q^45 - 27 * q^46 + 3 * q^48 - 6 * q^49 - 3 * q^50 - 27 * q^51 + 12 * q^52 - 9 * q^55 - 9 * q^56 - 57 * q^57 + 9 * q^58 - 36 * q^59 + 6 * q^61 - 6 * q^62 - 18 * q^63 - 6 * q^64 - 27 * q^65 + 9 * q^66 - 33 * q^67 + 9 * q^69 - 18 * q^70 + 9 * q^71 - 9 * q^72 - 24 * q^73 + 42 * q^74 + 24 * q^75 + 9 * q^76 + 27 * q^77 + 9 * q^78 - 30 * q^79 - 9 * q^80 + 36 * q^81 - 6 * q^84 + 54 * q^85 + 12 * q^86 - 27 * q^87 + 9 * q^89 - 9 * q^90 + 6 * q^91 - 18 * q^93 - 36 * q^94 + 54 * q^95 + 3 * q^96 - 18 * q^97 - 6 * q^98 + 72 * q^99

Introduction

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