LMFDB - Embedded newform 668.2.b.b.667.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [668,2,Mod(667,668)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(668, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1]))

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

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

chi := DirichletCharacter("668.667");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 668 = 2^{2} \cdot 167 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	668.b (of order $2$, degree $1$, 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:	$5.33400685502$
Analytic rank:	$0$
Dimension:	$60$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			667.15
Character	$\chi$	$=$	668.667
Dual form			668.2.b.b.667.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.12623 + 0.855338i) q^{2} -0.530251i q^{3} +(0.536794 - 1.92662i) q^{4} -0.936151i q^{5} +(0.453544 + 0.597186i) q^{6} -2.10467i q^{7} +(1.04335 + 2.62896i) q^{8} +2.71883 q^{9} +O(q^{10})$	\(q+(-1.12623 + 0.855338i) q^{2} -0.530251i q^{3} +(0.536794 - 1.92662i) q^{4} -0.936151i q^{5} +(0.453544 + 0.597186i) q^{6} -2.10467i q^{7} +(1.04335 + 2.62896i) q^{8} +2.71883 q^{9} +(0.800726 + 1.05432i) q^{10} +3.33803i q^{11} +(-1.02159 - 0.284636i) q^{12} +6.89163i q^{13} +(1.80021 + 2.37035i) q^{14} -0.496396 q^{15} +(-3.42370 - 2.06839i) q^{16} -4.43066i q^{17} +(-3.06204 + 2.32552i) q^{18} -2.41662i q^{19} +(-1.80360 - 0.502520i) q^{20} -1.11601 q^{21} +(-2.85514 - 3.75940i) q^{22} +4.70781 q^{23} +(1.39401 - 0.553240i) q^{24} +4.12362 q^{25} +(-5.89467 - 7.76157i) q^{26} -3.03242i q^{27} +(-4.05490 - 1.12977i) q^{28} +5.19782 q^{29} +(0.559056 - 0.424586i) q^{30} -7.62802i q^{31} +(5.62506 - 0.598937i) q^{32} +1.77000 q^{33} +(3.78971 + 4.98995i) q^{34} -1.97029 q^{35} +(1.45945 - 5.23815i) q^{36} -10.0279i q^{37} +(2.06702 + 2.72167i) q^{38} +3.65430 q^{39} +(2.46110 - 0.976738i) q^{40} +10.7614i q^{41} +(1.25688 - 0.954562i) q^{42} -5.34823 q^{43} +(6.43111 + 1.79183i) q^{44} -2.54524i q^{45} +(-5.30208 + 4.02677i) q^{46} -8.05982i q^{47} +(-1.09677 + 1.81542i) q^{48} +2.57036 q^{49} +(-4.64415 + 3.52709i) q^{50} -2.34936 q^{51} +(13.2775 + 3.69938i) q^{52} +4.37764i q^{53} +(2.59374 + 3.41521i) q^{54} +3.12490 q^{55} +(5.53309 - 2.19592i) q^{56} -1.28141 q^{57} +(-5.85394 + 4.44589i) q^{58} -3.05853 q^{59} +(-0.266462 + 0.956364i) q^{60} +4.51224 q^{61} +(6.52453 + 8.59091i) q^{62} -5.72225i q^{63} +(-5.82282 + 5.48587i) q^{64} +6.45161 q^{65} +(-1.99342 + 1.51394i) q^{66} -11.1425 q^{67} +(-8.53619 - 2.37835i) q^{68} -2.49632i q^{69} +(2.21900 - 1.68526i) q^{70} +12.3919 q^{71} +(2.83671 + 7.14769i) q^{72} -5.90507i q^{73} +(8.57720 + 11.2937i) q^{74} -2.18656i q^{75} +(-4.65589 - 1.29722i) q^{76} +7.02546 q^{77} +(-4.11558 + 3.12566i) q^{78} -17.0408 q^{79} +(-1.93633 + 3.20511i) q^{80} +6.54856 q^{81} +(-9.20466 - 12.1199i) q^{82} +8.34783 q^{83} +(-0.599065 + 2.15011i) q^{84} -4.14777 q^{85} +(6.02334 - 4.57454i) q^{86} -2.75615i q^{87} +(-8.77554 + 3.48275i) q^{88} +8.03271 q^{89} +(2.17704 + 2.86653i) q^{90} +14.5046 q^{91} +(2.52712 - 9.07014i) q^{92} -4.04477 q^{93} +(6.89387 + 9.07722i) q^{94} -2.26232 q^{95} +(-0.317587 - 2.98269i) q^{96} -6.12006 q^{97} +(-2.89482 + 2.19852i) q^{98} +9.07555i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q - 2 q^{2} + 2 q^{4} - 8 q^{6} - 8 q^{8} - 16 q^{9}+O(q^{10}) $ 60 * q - 2 * q^2 + 2 * q^4 - 8 * q^6 - 8 * q^8 - 16 * q^9	$ 60 q - 2 q^{2} + 2 q^{4} - 8 q^{6} - 8 q^{8} - 16 q^{9} + 18 q^{12} + 10 q^{14} + 10 q^{16} - 20 q^{18} + 20 q^{22} + 10 q^{24} - 188 q^{25} + 4 q^{29} + 18 q^{32} + 8 q^{33} + 30 q^{36} - 36 q^{38} + 14 q^{42} + 28 q^{44} - 28 q^{48} + 72 q^{49} - 40 q^{50} - 74 q^{54} + 50 q^{56} + 8 q^{57} - 22 q^{58} + 36 q^{61} + 104 q^{62} + 8 q^{64} + 24 q^{65} + 24 q^{66} + 90 q^{72} - 36 q^{76} - 84 q^{81} - 110 q^{84} - 16 q^{85} - 20 q^{88} + 28 q^{89} + 72 q^{93} + 90 q^{94} + 2 q^{96} - 4 q^{97} - 114 q^{98}+O(q^{100}) $ 60 * q - 2 * q^2 + 2 * q^4 - 8 * q^6 - 8 * q^8 - 16 * q^9 + 18 * q^12 + 10 * q^14 + 10 * q^16 - 20 * q^18 + 20 * q^22 + 10 * q^24 - 188 * q^25 + 4 * q^29 + 18 * q^32 + 8 * q^33 + 30 * q^36 - 36 * q^38 + 14 * q^42 + 28 * q^44 - 28 * q^48 + 72 * q^49 - 40 * q^50 - 74 * q^54 + 50 * q^56 + 8 * q^57 - 22 * q^58 + 36 * q^61 + 104 * q^62 + 8 * q^64 + 24 * q^65 + 24 * q^66 + 90 * q^72 - 36 * q^76 - 84 * q^81 - 110 * q^84 - 16 * q^85 - 20 * q^88 + 28 * q^89 + 72 * q^93 + 90 * q^94 + 2 * q^96 - 4 * q^97 - 114 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/668\mathbb{Z}\right)^\times$.

$n$	$5$	$335$
$\chi(n)$	$-1$	$-1$

Coefficient data

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

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

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

$2$	−1.12623	+	0.855338i	−0.796366	+	0.604815i
$2$	−1.12623	+	0.855338i	−0.796366	+	0.604815i
$3$		−	0.530251i		−	0.306141i	−0.988215	−	0.153070i	$-0.951084\pi$
$3$		−	0.530251i		−	0.306141i	0.988215	−	0.153070i	$-0.0489161\pi$
$4$	0.536794	−	1.92662i	0.268397	−	0.963308i
$5$		−	0.936151i		−	0.418660i	−0.977845	−	0.209330i	$-0.932872\pi$
$5$		−	0.936151i		−	0.418660i	0.977845	−	0.209330i	$-0.0671282\pi$
$6$	0.453544	+	0.597186i	0.185159	+	0.243800i
$7$		−	2.10467i		−	0.795491i	−0.917496	−	0.397746i	$-0.869793\pi$
$7$		−	2.10467i		−	0.795491i	0.917496	−	0.397746i	$-0.130207\pi$
$8$	1.04335	+	2.62896i	0.368882	+	0.929476i
$9$	2.71883			0.906278
$10$	0.800726	+	1.05432i	0.253212	+	0.333406i
$11$			3.33803i			1.00645i	0.864154	+	0.503227i	$0.167854\pi$
$11$			3.33803i			1.00645i	−0.864154	+	0.503227i	$0.832146\pi$
$12$	−1.02159	−	0.284636i	−0.294908	−	0.0821673i
$13$			6.89163i			1.91139i	0.294352	+	0.955697i	$0.404896\pi$
$13$			6.89163i			1.91139i	−0.294352	+	0.955697i	$0.595104\pi$
$14$	1.80021	+	2.37035i	0.481125	+	0.633502i
$15$	−0.496396			−0.128169
$16$	−3.42370	−	2.06839i	−0.855926	−	0.517098i
$17$		−	4.43066i		−	1.07459i	−0.843393	−	0.537297i	$-0.819446\pi$
$17$		−	4.43066i		−	1.07459i	0.843393	−	0.537297i	$-0.180554\pi$
$18$	−3.06204	+	2.32552i	−0.721729	+	0.548131i
$19$		−	2.41662i		−	0.554410i	−0.960811	−	0.277205i	$-0.910592\pi$
$19$		−	2.41662i		−	0.554410i	0.960811	−	0.277205i	$-0.0894081\pi$
$20$	−1.80360	−	0.502520i	−0.403298	−	0.112367i
$21$	−1.11601			−0.243532
$22$	−2.85514	−	3.75940i	−0.608719	−	0.801506i
$23$	4.70781			0.981646			0.490823	−	0.871259i	$-0.336696\pi$
$23$	4.70781			0.981646			0.490823	+	0.871259i	$0.336696\pi$
$24$	1.39401	−	0.553240i	0.284551	−	0.112930i
$25$	4.12362			0.824724
$26$	−5.89467	−	7.76157i	−1.15604	−	1.52217i
$27$		−	3.03242i		−	0.583589i
$28$	−4.05490	−	1.12977i	−0.766303	−	0.213507i
$29$	5.19782			0.965211			0.482605	−	0.875838i	$-0.339691\pi$
$29$	5.19782			0.965211			0.482605	+	0.875838i	$0.339691\pi$
$30$	0.559056	−	0.424586i	0.102069	−	0.0775184i
$31$		−	7.62802i		−	1.37003i	−0.728528	−	0.685016i	$-0.759795\pi$
$31$		−	7.62802i		−	1.37003i	0.728528	−	0.685016i	$-0.240205\pi$
$32$	5.62506	−	0.598937i	0.994379	−	0.105878i
$33$	1.77000			0.308117
$34$	3.78971	+	4.98995i	0.649930	+	0.855769i
$35$	−1.97029			−0.333040
$36$	1.45945	−	5.23815i	0.243242	−	0.873025i
$37$		−	10.0279i		−	1.64857i	−0.566176	−	0.824285i	$-0.691578\pi$
$37$		−	10.0279i		−	1.64857i	0.566176	−	0.824285i	$-0.308422\pi$
$38$	2.06702	+	2.72167i	0.335316	+	0.441513i
$39$	3.65430			0.585156
$40$	2.46110	−	0.976738i	0.389134	−	0.154436i
$41$			10.7614i			1.68065i	0.542081	+	0.840326i	$0.317637\pi$
$41$			10.7614i			1.68065i	−0.542081	+	0.840326i	$0.682363\pi$
$42$	1.25688	−	0.954562i	0.193941	−	0.147292i
$43$	−5.34823			−0.815597			−0.407799	−	0.913072i	$-0.633703\pi$
$43$	−5.34823			−0.815597			−0.407799	+	0.913072i	$0.633703\pi$
$44$	6.43111	+	1.79183i	0.969526	+	0.270129i
$45$		−	2.54524i		−	0.379422i
$46$	−5.30208	+	4.02677i	−0.781749	+	0.593714i
$47$		−	8.05982i		−	1.17565i	−0.808990	−	0.587823i	$-0.799985\pi$
$47$		−	8.05982i		−	1.17565i	0.808990	−	0.587823i	$-0.200015\pi$
$48$	−1.09677	+	1.81542i	−0.158305	+	0.262034i
$49$	2.57036			0.367194
$50$	−4.64415	+	3.52709i	−0.656782	+	0.498806i
$51$	−2.34936			−0.328977
$52$	13.2775	+	3.69938i	1.84126	+	0.513012i
$53$			4.37764i			0.601315i	0.953732	+	0.300657i	$0.0972061\pi$
$53$			4.37764i			0.601315i	−0.953732	+	0.300657i	$0.902794\pi$
$54$	2.59374	+	3.41521i	0.352964	+	0.464751i
$55$	3.12490			0.421362
$56$	5.53309	−	2.19592i	0.739390	−	0.293442i
$57$	−1.28141			−0.169727
$58$	−5.85394	+	4.44589i	−0.768661	+	0.583774i
$59$	−3.05853			−0.398187			−0.199094	−	0.979980i	$-0.563800\pi$
$59$	−3.05853			−0.398187			−0.199094	+	0.979980i	$0.563800\pi$
$60$	−0.266462	+	0.956364i	−0.0344001	+	0.123466i
$61$	4.51224			0.577733			0.288867	−	0.957369i	$-0.406722\pi$
$61$	4.51224			0.577733			0.288867	+	0.957369i	$0.406722\pi$
$62$	6.52453	+	8.59091i	0.828616	+	1.09105i
$63$		−	5.72225i		−	0.720936i
$64$	−5.82282	+	5.48587i	−0.727853	+	0.685733i
$65$	6.45161			0.800224
$66$	−1.99342	+	1.51394i	−0.245374	+	0.186354i
$67$	−11.1425			−1.36127			−0.680635	−	0.732623i	$-0.738296\pi$
$67$	−11.1425			−1.36127			−0.680635	+	0.732623i	$0.738296\pi$
$68$	−8.53619	−	2.37835i	−1.03516	−	0.288418i
$69$		−	2.49632i		−	0.300522i
$70$	2.21900	−	1.68526i	0.265222	−	0.201428i
$71$	12.3919			1.47065			0.735324	−	0.677716i	$-0.237030\pi$
$71$	12.3919			1.47065			0.735324	+	0.677716i	$0.237030\pi$
$72$	2.83671	+	7.14769i	0.334309	+	0.842364i
$73$		−	5.90507i		−	0.691137i	−0.938394	−	0.345568i	$-0.887686\pi$
$73$		−	5.90507i		−	0.691137i	0.938394	−	0.345568i	$-0.112314\pi$
$74$	8.57720	+	11.2937i	0.997080	+	1.31286i
$75$		−	2.18656i		−	0.252482i
$76$	−4.65589	−	1.29722i	−0.534068	−	0.148802i
$77$	7.02546			0.800625
$78$	−4.11558	+	3.12566i	−0.465998	+	0.353911i
$79$	−17.0408			−1.91724			−0.958618	−	0.284695i	$-0.908108\pi$
$79$	−17.0408			−1.91724			−0.958618	+	0.284695i	$0.908108\pi$
$80$	−1.93633	+	3.20511i	−0.216488	+	0.358342i
$81$	6.54856			0.727617
$82$	−9.20466	−	12.1199i	−1.01648	−	1.33841i
$83$	8.34783			0.916294			0.458147	−	0.888877i	$-0.348513\pi$
$83$	8.34783			0.916294			0.458147	+	0.888877i	$0.348513\pi$
$84$	−0.599065	+	2.15011i	−0.0653633	+	0.234597i
$85$	−4.14777			−0.449889
$86$	6.02334	−	4.57454i	0.649514	−	0.493286i
$87$		−	2.75615i		−	0.295490i
$88$	−8.77554	+	3.48275i	−0.935476	+	0.371262i
$89$	8.03271			0.851466			0.425733	−	0.904849i	$-0.360016\pi$
$89$	8.03271			0.851466			0.425733	+	0.904849i	$0.360016\pi$
$90$	2.17704	+	2.86653i	0.229480	+	0.302159i
$91$	14.5046			1.52050
$92$	2.52712	−	9.07014i	0.263471	−	0.945628i
$93$	−4.04477			−0.419423
$94$	6.89387	+	9.07722i	0.711048	+	0.936244i
$95$	−2.26232			−0.232109
$96$	−0.317587	−	2.98269i	−0.0324136	−	0.304420i
$97$	−6.12006			−0.621397			−0.310699	−	0.950508i	$-0.600563\pi$
$97$	−6.12006			−0.621397			−0.310699	+	0.950508i	$0.600563\pi$
$98$	−2.89482	+	2.19852i	−0.292421	+	0.222084i
$99$			9.07555i			0.912127i
$100$	2.21353	−	7.94464i	0.221353	−	0.794464i
$101$			2.64561i			0.263248i	0.991300	+	0.131624i	$0.0420191\pi$
$101$			2.64561i			0.263248i	−0.991300	+	0.131624i	$0.957981\pi$
$102$	2.64593	−	2.00950i	0.261986	−	0.198970i
$103$	12.9582			1.27681			0.638406	−	0.769700i	$-0.279594\pi$
$103$	12.9582			1.27681			0.638406	+	0.769700i	$0.279594\pi$
$104$	−18.1178	+	7.19041i	−1.77660	+	0.705078i
$105$			1.04475i			0.101957i
$106$	−3.74436	−	4.93023i	−0.363684	−	0.478867i
$107$			11.4267i			1.10466i	0.833625	+	0.552332i	$0.186262\pi$
$107$			11.4267i			1.10466i	−0.833625	+	0.552332i	$0.813738\pi$
$108$	−5.84231	−	1.62778i	−0.562177	−	0.156634i
$109$		−	0.424653i		−	0.0406744i	−0.999793	−	0.0203372i	$-0.993526\pi$
$109$		−	0.424653i		−	0.0406744i	0.999793	−	0.0203372i	$-0.00647397\pi$
$110$	−3.51936	+	2.67285i	−0.335558	+	0.254846i
$111$	−5.31728			−0.504694
$112$	−4.35329	+	7.20577i	−0.411347	+	0.680882i
$113$			5.61502i			0.528217i	0.964493	+	0.264109i	$0.0850777\pi$
$113$			5.61502i			0.528217i	−0.964493	+	0.264109i	$0.914922\pi$
$114$	1.44317	−	1.09604i	0.135165	−	0.102654i
$115$		−	4.40722i		−	0.410976i
$116$	2.79016	−	10.0142i	0.259060	−	0.929795i
$117$			18.7372i			1.73225i
$118$	3.44462	−	2.61608i	0.317103	−	0.240830i
$119$	−9.32509			−0.854829
$120$	−0.517917	−	1.30500i	−0.0472791	−	0.119130i
$121$	−0.142453			−0.0129503
$122$	−5.08183	+	3.85949i	−0.460087	+	0.349422i
$123$	5.70626			0.514516
$124$	−14.6963	−	4.09467i	−1.31976	−	0.367712i
$125$		−	8.54109i		−	0.763938i
$126$	4.89446	+	6.44458i	0.436033	+	0.574129i
$127$			3.92348i			0.348152i	0.984732	+	0.174076i	$0.0556939\pi$
$127$			3.92348i			0.348152i	−0.984732	+	0.174076i	$0.944306\pi$
$128$	1.86557	−	11.1588i	0.164895	−	0.986311i
$129$			2.83591i			0.249688i
$130$	−7.26600	+	5.51831i	−0.637271	+	0.483987i
$131$	5.37496			0.469612			0.234806	−	0.972042i	$-0.424555\pi$
$131$	5.37496			0.469612			0.234806	+	0.972042i	$0.424555\pi$
$132$	0.950123	−	3.41010i	0.0826976	−	0.296811i
$133$	−5.08618			−0.441028
$134$	12.5490	−	9.53058i	1.08407	−	0.823316i
$135$	−2.83880			−0.244325
$136$	11.6480	−	4.62275i	0.998809	−	0.396398i
$137$	−12.3438			−1.05460			−0.527302	−	0.849678i	$-0.676796\pi$
$137$	−12.3438			−1.05460			−0.527302	+	0.849678i	$0.676796\pi$
$138$	2.13520	+	2.81144i	0.181760	+	0.239325i
$139$	18.9620			1.60834			0.804169	−	0.594401i	$-0.202611\pi$
$139$	18.9620			1.60834			0.804169	+	0.594401i	$0.202611\pi$
$140$	−1.05764	+	3.79600i	−0.0893869	+	0.320820i
$141$	−4.27373			−0.359913
$142$	−13.9561	+	10.5993i	−1.17117	+	0.889470i
$143$	−23.0045			−1.92373
$144$	−9.30848	−	5.62361i	−0.775707	−	0.468634i
$145$		−	4.86594i		−	0.404095i
$146$	5.05083	+	6.65048i	0.418010	+	0.550398i
$147$		−	1.36294i		−	0.112413i
$148$	−19.3198	−	5.38289i	−1.58808	−	0.442471i
$149$		−	13.6477i		−	1.11807i	−0.829145	−	0.559033i	$-0.811172\pi$
$149$		−	13.6477i		−	1.11807i	0.829145	−	0.559033i	$-0.188828\pi$
$150$	1.87024	+	2.46257i	0.152705	+	0.201068i
$151$	−16.7916			−1.36648			−0.683241	−	0.730193i	$-0.739430\pi$
$151$	−16.7916			−1.36648			−0.683241	+	0.730193i	$0.739430\pi$
$152$	6.35318	−	2.52139i	0.515311	−	0.204512i
$153$		−	12.0462i		−	0.973880i
$154$	−7.91229	+	6.00914i	−0.637591	+	0.484231i
$155$	−7.14098			−0.573577
$156$	1.96160	−	7.04043i	0.157054	−	0.563686i
$157$	−11.6625			−0.930766			−0.465383	−	0.885109i	$-0.654083\pi$
$157$	−11.6625			−0.930766			−0.465383	+	0.885109i	$0.654083\pi$
$158$	19.1918	−	14.5756i	1.52682	−	1.15957i
$159$	2.32125			0.184087
$160$	−0.560695	−	5.26591i	−0.0443269	−	0.416306i
$161$		−	9.90839i		−	0.780891i
$162$	−7.37519	+	5.60123i	−0.579449	+	0.440074i
$163$	5.76751			0.451747			0.225873	−	0.974157i	$-0.427476\pi$
$163$	5.76751			0.451747			0.225873	+	0.974157i	$0.427476\pi$
$164$	20.7331	+	5.77667i	1.61899	+	0.451082i
$165$		−	1.65698i		−	0.128996i
$166$	−9.40159	+	7.14022i	−0.729705	+	0.554188i
$167$	−0.874423	−	12.8932i	−0.0676649	−	0.997708i
$167$	−0.874423	−	12.8932i	−0.0676649	−	0.997708i
$168$	−1.16439	−	2.93393i	−0.0898346	−	0.226358i
$169$	−34.4946			−2.65343
$170$	4.67135	−	3.54774i	0.358276	−	0.272100i
$171$		−	6.57038i		−	0.502449i
$172$	−2.87090	+	10.3040i	−0.218904	+	0.785672i
$173$	−14.9428			−1.13608			−0.568040	−	0.823001i	$-0.692298\pi$
$173$	−14.9428			−1.13608			−0.568040	+	0.823001i	$0.692298\pi$
$174$	2.35744	+	3.10406i	0.178717	+	0.235318i
$175$		−	8.67887i		−	0.656061i
$176$	6.90436	−	11.4284i	0.520436	−	0.861451i
$177$			1.62179i			0.121901i
$178$	−9.04669	+	6.87068i	−0.678078	+	0.514980i
$179$			23.4182i			1.75036i	0.483801	+	0.875178i	$0.339256\pi$
$179$			23.4182i			1.75036i	−0.483801	+	0.875178i	$0.660744\pi$
$180$	−4.90370	−	1.36627i	−0.365500	−	0.101836i
$181$	−10.8267			−0.804744			−0.402372	−	0.915476i	$-0.631814\pi$
$181$	−10.8267			−0.804744			−0.402372	+	0.915476i	$0.631814\pi$
$182$	−16.3356	+	12.4064i	−1.21087	+	0.919620i
$183$		−	2.39262i		−	0.176868i
$184$	4.91191	+	12.3766i	0.362111	+	0.912417i
$185$	−9.38759			−0.690189
$186$	4.55534	−	3.45964i	0.334014	−	0.253673i
$187$	14.7897			1.08153
$188$	−15.5282	−	4.32646i	−1.13251	−	0.315540i
$189$	−6.38225			−0.464240
$190$	2.54789	−	1.93505i	0.184844	−	0.140383i
$191$		−	12.8768i		−	0.931730i	−0.884856	−	0.465865i	$-0.845743\pi$
$191$		−	12.8768i		−	0.931730i	0.884856	−	0.465865i	$-0.154257\pi$
$192$	2.90889	+	3.08756i	0.209931	+	0.222825i
$193$			24.5004i			1.76358i	0.471644	+	0.881789i	$0.343661\pi$
$193$			24.5004i			1.76358i	−0.471644	+	0.881789i	$0.656339\pi$
$194$	6.89260	−	5.23472i	0.494860	−	0.375831i
$195$		−	3.42097i		−	0.244981i
$196$	1.37975	−	4.95209i	0.0985537	−	0.353721i
$197$			8.59912i			0.612662i	0.951925	+	0.306331i	$0.0991015\pi$
$197$			8.59912i			0.612662i	−0.951925	+	0.306331i	$0.900899\pi$
$198$	−7.76266	−	10.2212i	−0.551668	−	0.726387i
$199$			15.4755i			1.09703i	0.836142	+	0.548513i	$0.184806\pi$
$199$			15.4755i			1.09703i	−0.836142	+	0.548513i	$0.815194\pi$
$200$	4.30240	+	10.8408i	0.304225	+	0.766562i
$201$			5.90831i			0.416740i
$202$	−2.26289	−	2.97957i	−0.159216	−	0.209642i
$203$		−	10.9397i		−	0.767816i
$204$	−1.26112	+	4.52633i	−0.0882964	+	0.316906i
$205$	10.0743			0.703621
$206$	−14.5940	+	11.0837i	−1.01681	+	0.772235i
$207$	12.7997			0.889644
$208$	14.2546	−	23.5949i	0.988378	−	1.63601i
$209$	8.06674			0.557988
$210$	−0.893614	−	1.17663i	−0.0616652	−	0.0811952i
$211$			21.0200i			1.44707i	0.690285	+	0.723537i	$0.257485\pi$
$211$			21.0200i			1.44707i	−0.690285	+	0.723537i	$0.742515\pi$
$212$	8.43403	+	2.34989i	0.579252	+	0.161391i
$213$		−	6.57082i		−	0.450225i
$214$	−9.77371	−	12.8691i	−0.668117	−	0.879716i
$215$			5.00675i			0.341458i
$216$	7.97210	−	3.16389i	0.542433	−	0.215275i
$217$	−16.0545			−1.08985
$218$	0.363222	+	0.478257i	0.0246005	+	0.0323917i
$219$	−3.13117			−0.211585
$220$	1.67743	−	6.02049i	0.113092	−	0.405901i
$221$	30.5345			2.05397
$222$	5.98849	−	4.54808i	0.401921	−	0.305247i
$223$		−	1.69278i		−	0.113357i	−0.998392	−	0.0566786i	$-0.981949\pi$
$223$		−	1.69278i		−	0.113357i	0.998392	−	0.0566786i	$-0.0180510\pi$
$224$	−1.26057	−	11.8389i	−0.0842251	−	0.791020i
$225$	11.2114			0.747429
$226$	−4.80274	−	6.32382i	−0.319474	−	0.420654i
$227$	−2.87132			−0.190576			−0.0952882	−	0.995450i	$-0.530377\pi$
$227$	−2.87132			−0.190576			−0.0952882	+	0.995450i	$0.530377\pi$
$228$	−0.687855	+	2.46879i	−0.0455543	+	0.163500i
$229$	23.3491			1.54295			0.771475	−	0.636259i	$-0.219519\pi$
$229$	23.3491			1.54295			0.771475	+	0.636259i	$0.219519\pi$
$230$	3.76966	+	4.96355i	0.248564	+	0.327287i
$231$		−	3.72526i		−	0.245104i
$232$	5.42317	+	13.6648i	0.356048	+	0.897140i
$233$	−22.2295			−1.45630			−0.728152	−	0.685416i	$-0.759620\pi$
$233$	−22.2295			−1.45630			−0.728152	+	0.685416i	$0.759620\pi$
$234$	−16.0266	−	21.1024i	−1.04769	−	1.37951i
$235$	−7.54521			−0.492195
$236$	−1.64180	+	5.89262i	−0.106872	+	0.383577i
$237$			9.03589i			0.586944i
$238$	10.5022	−	7.97610i	0.680757	−	0.517014i
$239$			13.4005i			0.866808i	0.901200	+	0.433404i	$0.142688\pi$
$239$			13.4005i			0.866808i	−0.901200	+	0.433404i	$0.857312\pi$
$240$	1.69951	+	1.02674i	0.109703	+	0.0662758i
$241$		−	13.1889i		−	0.849573i	−0.905294	−	0.424786i	$-0.860349\pi$
$241$		−	13.1889i		−	0.849573i	0.905294	−	0.424786i	$-0.139651\pi$
$242$	0.160435	−	0.121846i	0.0103132	−	0.00783253i
$243$		−	12.5696i		−	0.806343i
$244$	2.42214	−	8.69336i	0.155062	−	0.556535i
$245$		−	2.40624i		−	0.153729i
$246$	−6.42657	+	4.88078i	−0.409743	+	0.311187i
$247$	16.6544			1.05970
$248$	20.0537	−	7.95872i	1.27341	−	0.505379i
$249$		−	4.42645i		−	0.280515i
$250$	7.30552	+	9.61924i	0.462042	+	0.608374i
$251$			23.9674i			1.51281i	0.654103	+	0.756406i	$0.273046\pi$
$251$			23.9674i			1.51281i	−0.654103	+	0.756406i	$0.726954\pi$
$252$	−11.0246	−	3.07167i	−0.694484	−	0.193497i
$253$			15.7148i			0.987982i
$254$	−3.35590	−	4.41874i	−0.210568	−	0.277257i
$255$			2.19936i			0.137729i
$256$	7.44351	+	14.1631i	0.465219	+	0.885195i
$257$		−	7.51271i		−	0.468630i	−0.972161	−	0.234315i	$-0.924715\pi$
$257$		−	7.51271i		−	0.468630i	0.972161	−	0.234315i	$-0.0752847\pi$
$258$	−2.42566	−	3.19389i	−0.151015	−	0.198843i
$259$	−21.1053			−1.31142
$260$	3.46318	−	12.4298i	0.214778	−	0.770862i
$261$	14.1320			0.874749
$262$	−6.05344	+	4.59740i	−0.373983	+	0.284029i
$263$			20.9672i			1.29289i	0.762959	+	0.646447i	$0.223746\pi$
$263$			20.9672i			1.29289i	−0.762959	+	0.646447i	$0.776254\pi$
$264$	1.84673	+	4.65324i	0.113659	+	0.286387i
$265$	4.09813			0.251746
$266$	5.72822	−	4.35041i	0.351220	−	0.266741i
$267$		−	4.25936i		−	0.260668i
$268$	−5.98121	+	21.4673i	−0.365360	+	1.31132i
$269$			1.05355i			0.0642361i	0.999484	+	0.0321180i	$0.0102252\pi$
$269$			1.05355i			0.0642361i	−0.999484	+	0.0321180i	$0.989775\pi$
$270$	3.19715	−	2.42814i	0.194572	−	0.147772i
$271$	−15.2363			−0.925542			−0.462771	−	0.886478i	$-0.653145\pi$
$271$	−15.2363			−0.925542			−0.462771	+	0.886478i	$0.653145\pi$
$272$	−9.16434	+	15.1693i	−0.555670	+	0.919772i
$273$		−	7.69110i		−	0.465486i
$274$	13.9020	−	10.5581i	0.839851	−	0.637841i
$275$			13.7648i			0.830047i
$276$	−4.80946	−	1.34001i	−0.289495	−	0.0806592i
$277$		−	14.1378i		−	0.849456i	−0.905321	−	0.424728i	$-0.860370\pi$
$277$		−	14.1378i		−	0.849456i	0.905321	−	0.424728i	$-0.139630\pi$
$278$	−21.3556	+	16.2189i	−1.28083	+	0.972748i
$279$		−	20.7393i		−	1.24163i
$280$	−2.05571	−	5.17981i	−0.122852	−	0.309553i
$281$	11.7073			0.698396			0.349198	−	0.937049i	$-0.386454\pi$
$281$	11.7073			0.698396			0.349198	+	0.937049i	$0.386454\pi$
$282$	4.81321	−	3.65548i	0.286622	−	0.217681i
$283$			12.7233i			0.756324i	0.925739	+	0.378162i	$0.123444\pi$
$283$			12.7233i			0.756324i	−0.925739	+	0.378162i	$0.876556\pi$
$284$	6.65189	−	23.8744i	0.394717	−	1.41669i
$285$			1.19960i			0.0710580i
$286$	25.9084	−	19.6766i	1.53199	−	1.16350i
$287$	22.6493			1.33694
$288$	15.2936	−	1.62841i	0.901184	−	0.0959549i
$289$	−2.63076			−0.154751
$290$	4.16203	+	5.48018i	0.244403	+	0.321807i
$291$			3.24517i			0.190235i
$292$	−11.3768	−	3.16981i	−0.665778	−	0.185499i
$293$	−2.08396			−0.121746			−0.0608731	−	0.998146i	$-0.519388\pi$
$293$	−2.08396			−0.121746			−0.0608731	+	0.998146i	$0.519388\pi$
$294$	1.16577	+	1.53498i	0.0679891	+	0.0895219i
$295$			2.86325i			0.166705i
$296$	26.3628	−	10.4626i	1.53231	−	0.608127i
$297$	10.1223			0.587356
$298$	11.6734	+	15.3705i	0.676223	+	0.890390i
$299$			32.4445i			1.87631i
$300$	−4.21266	−	1.17373i	−0.243218	−	0.0677653i
$301$			11.2563i			0.648800i
$302$	18.9112	−	14.3625i	1.08822	−	0.826469i
$303$	1.40284			0.0805909
$304$	−4.99851	+	8.27378i	−0.286684	+	0.474534i
$305$		−	4.22414i		−	0.241874i
$306$	10.3036	+	13.5668i	0.589017	+	0.775565i
$307$	−29.1765			−1.66519			−0.832597	−	0.553880i	$-0.813147\pi$
$307$	−29.1765			−1.66519			−0.832597	+	0.553880i	$0.813147\pi$
$308$	3.77122	−	13.5354i	0.214885	−	0.771249i
$309$		−	6.87112i		−	0.390884i
$310$	8.04239	−	6.10795i	0.456777	−	0.346908i
$311$			11.9635i			0.678388i	0.940716	+	0.339194i	$0.110154\pi$
$311$			11.9635i			0.678388i	−0.940716	+	0.339194i	$0.889846\pi$
$312$	3.81273	+	9.60699i	0.215853	+	0.543889i
$313$		−	10.0478i		−	0.567936i	−0.958834	−	0.283968i	$-0.908349\pi$
$313$		−	10.0478i		−	0.567936i	0.958834	−	0.283968i	$-0.0916509\pi$
$314$	13.1346	−	9.97535i	0.741230	−	0.562941i
$315$	−5.35689			−0.301827
$316$	−9.14738	+	32.8310i	−0.514580	+	1.84689i
$317$	−0.817925			−0.0459393			−0.0229696	−	0.999736i	$-0.507312\pi$
$317$	−0.817925			−0.0459393			−0.0229696	+	0.999736i	$0.507312\pi$
$318$	−2.61426	+	1.98545i	−0.146601	+	0.111339i
$319$			17.3505i			0.971440i
$320$	5.13560	+	5.45104i	0.287089	+	0.304723i
$321$	6.05904			0.338182
$322$	8.47502	+	11.1591i	0.472295	+	0.621875i
$323$	−10.7072			−0.595765
$324$	3.51522	−	12.6166i	0.195290	−	0.700920i
$325$			28.4185i			1.57637i
$326$	−6.49555	+	4.93317i	−0.359755	+	0.273223i
$327$	−0.225173			−0.0124521
$328$	−28.2913	+	11.2280i	−1.56213	+	0.619962i
$329$	−16.9633			−0.935215
$330$	1.41728	+	1.86615i	0.0780188	+	0.102728i
$331$	0.588558			0.0323501			0.0161750	−	0.999869i	$-0.494851\pi$
$331$	0.588558			0.0323501			0.0161750	+	0.999869i	$0.494851\pi$
$332$	4.48106	−	16.0831i	0.245930	−	0.882673i
$333$		−	27.2641i		−	1.49406i
$334$	12.0129	+	13.7728i	0.657315	+	0.753616i
$335$			10.4310i			0.569908i
$336$	3.82087	+	2.30834i	0.208446	+	0.125930i
$337$	−5.73381			−0.312341			−0.156170	−	0.987730i	$-0.549915\pi$
$337$	−5.73381			−0.312341			−0.156170	+	0.987730i	$0.549915\pi$
$338$	38.8489	−	29.5045i	2.11310	−	1.60483i
$339$	2.97737			0.161709
$340$	−2.22650	+	7.99116i	−0.120749	+	0.433382i
$341$	25.4626			1.37887
$342$	5.61989	+	7.39977i	0.303889	+	0.400133i
$343$		−	20.1425i		−	1.08759i
$344$	−5.58010	−	14.0603i	−0.300859	−	0.758078i
$345$	−2.33694			−0.125816
$346$	16.8290	−	12.7811i	0.904735	−	0.687118i
$347$	−15.9665			−0.857129			−0.428565	−	0.903511i	$-0.640981\pi$
$347$	−15.9665			−0.857129			−0.428565	+	0.903511i	$0.640981\pi$
$348$	−5.31005	−	1.47948i	−0.284648	−	0.0793087i
$349$		−	19.0416i		−	1.01927i	−0.860390	−	0.509636i	$-0.829780\pi$
$349$		−	19.0416i		−	1.01927i	0.860390	−	0.509636i	$-0.170220\pi$
$350$	7.42337	+	9.77441i	0.396796	+	0.522464i
$351$	20.8983			1.11547
$352$	1.99927	+	18.7766i	0.106561	+	1.00080i
$353$	−1.70344			−0.0906650			−0.0453325	−	0.998972i	$-0.514435\pi$
$353$	−1.70344			−0.0906650			−0.0453325	+	0.998972i	$0.514435\pi$
$354$	−1.38718	−	1.82651i	−0.0737278	−	0.0970781i
$355$		−	11.6007i		−	0.615701i
$356$	4.31191	−	15.4760i	0.228531	−	0.820224i
$357$			4.94464i			0.261698i
$358$	−20.0305	−	26.3743i	−1.05864	−	1.39392i
$359$		−	25.8030i		−	1.36183i	−0.732362	−	0.680916i	$-0.761582\pi$
$359$		−	25.8030i		−	1.36183i	0.732362	−	0.680916i	$-0.238418\pi$
$360$	6.69132	−	2.65559i	0.352664	−	0.139962i
$361$	13.1600			0.692630
$362$	12.1934	−	9.26050i	0.640870	−	0.486721i
$363$			0.0755360i			0.00396461i
$364$	7.78599	−	27.9448i	0.408097	−	1.46471i
$365$	−5.52804			−0.289351
$366$	2.04650	+	2.69465i	0.106972	+	0.140851i
$367$			5.31412i			0.277395i	0.990335	+	0.138698i	$0.0442916\pi$
$367$			5.31412i			0.277395i	−0.990335	+	0.138698i	$0.955708\pi$
$368$	−16.1181	−	9.73759i	−0.840216	−	0.507607i
$369$			29.2585i			1.52314i
$370$	10.5726	−	8.02956i	0.549643	−	0.417437i
$371$	9.21349			0.478341
$372$	−2.17121	+	7.79271i	−0.112572	+	0.404033i
$373$		−	17.3441i		−	0.898043i	−0.893521	−	0.449021i	$-0.851773\pi$
$373$		−	17.3441i		−	0.898043i	0.893521	−	0.449021i	$-0.148227\pi$
$374$	−16.6566	+	12.6502i	−0.861293	+	0.654125i
$375$	−4.52893			−0.233873
$376$	21.1889	−	8.40925i	1.09273	−	0.433674i
$377$			35.8214i			1.84490i
$378$	7.18789	−	5.45898i	0.369705	−	0.280780i
$379$	24.9394			1.28105			0.640525	−	0.767937i	$-0.278717\pi$
$379$	24.9394			1.28105			0.640525	+	0.767937i	$0.278717\pi$
$380$	−1.21440	+	4.35862i	−0.0622974	+	0.223593i
$381$	2.08043			0.106584
$382$	11.0140	+	14.5022i	0.563525	+	0.741998i
$383$		−	27.6843i		−	1.41460i	−0.706913	−	0.707301i	$-0.749913\pi$
$383$		−	27.6843i		−	1.41460i	0.706913	−	0.707301i	$-0.250087\pi$
$384$	−5.91699	−	0.989224i	−0.301950	−	0.0504811i
$385$		−	6.57689i		−	0.335190i
$386$	−20.9561	−	27.5931i	−1.06664	−	1.40445i
$387$	−14.5409			−0.739158
$388$	−3.28521	+	11.7910i	−0.166781	+	0.598597i
$389$			13.5887i			0.688974i	0.938791	+	0.344487i	$0.111947\pi$
$389$			13.5887i			0.688974i	−0.938791	+	0.344487i	$0.888053\pi$
$390$	2.92609	+	3.85281i	0.148168	+	0.195095i
$391$		−	20.8587i		−	1.05487i
$392$	2.68179	+	6.75736i	0.135451	+	0.341298i
$393$		−	2.85008i		−	0.143767i
$394$	−7.35516	−	9.68460i	−0.370547	−	0.487903i
$395$			15.9527i			0.802670i
$396$	17.4851	+	4.87170i	0.878660	+	0.244812i
$397$	2.74383			0.137709			0.0688544	−	0.997627i	$-0.478066\pi$
$397$	2.74383			0.137709			0.0688544	+	0.997627i	$0.478066\pi$
$398$	−13.2367	−	17.4289i	−0.663498	−	0.873634i
$399$			2.69696i			0.135017i
$400$	−14.1181	−	8.52926i	−0.705903	−	0.426463i
$401$			29.3274i			1.46454i	0.681015	+	0.732269i	$0.261539\pi$
$401$			29.3274i			1.46454i	−0.681015	+	0.732269i	$0.738461\pi$
$402$	−5.05360	−	6.65412i	−0.252051	−	0.331878i
$403$	52.5695			2.61867
$404$	5.09707	+	1.42015i	0.253589	+	0.0706549i
$405$		−	6.13044i		−	0.304624i
$406$	9.35714	+	12.3206i	0.464387	+	0.611463i
$407$	33.4733			1.65921
$408$	−2.45122	−	6.17638i	−0.121353	−	0.305776i
$409$	−15.4848			−0.765672			−0.382836	−	0.923816i	$-0.625053\pi$
$409$	−15.4848			−0.765672			−0.382836	+	0.923816i	$0.625053\pi$
$410$	−11.3460	+	8.61695i	−0.560340	+	0.425561i
$411$			6.54534i			0.322858i
$412$	6.95590	−	24.9655i	0.342692	−	1.22996i
$413$			6.43721i			0.316754i
$414$	−14.4155	+	10.9481i	−0.708482	+	0.538070i
$415$		−	7.81483i		−	0.383615i
$416$	4.12765	+	38.7658i	0.202375	+	1.90065i
$417$		−	10.0546i		−	0.492378i
$418$	−9.08502	+	6.89979i	−0.444363	+	0.337480i
$419$		−	3.03311i		−	0.148177i	−0.997252	−	0.0740887i	$-0.976395\pi$
$419$		−	3.03311i		−	0.148177i	0.997252	−	0.0740887i	$-0.0236048\pi$
$420$	2.01283	+	0.560815i	0.0982162	+	0.0273650i
$421$	−36.1037			−1.75958			−0.879792	−	0.475358i	$-0.842318\pi$
$421$	−36.1037			−1.75958			−0.879792	+	0.475358i	$0.842318\pi$
$422$	−17.9792	−	23.6734i	−0.875213	−	1.15240i
$423$		−	21.9133i		−	1.06546i
$424$	−11.5086	+	4.56743i	−0.558908	+	0.221814i
$425$		−	18.2704i		−	0.886243i
$426$	5.62027	+	7.40026i	0.272303	+	0.358544i
$427$		−	9.49679i		−	0.459582i
$428$	22.0149	+	6.13380i	1.06413	+	0.296488i
$429$			12.1982i			0.588933i
$430$	−4.28246	−	5.63876i	−0.206519	−	0.271925i
$431$			29.7984i			1.43534i	0.696385	+	0.717668i	$0.254791\pi$
$431$			29.7984i			1.43534i	−0.696385	+	0.717668i	$0.745209\pi$
$432$	−6.27223	+	10.3821i	−0.301773	+	0.499509i
$433$	−17.1154			−0.822515			−0.411258	−	0.911519i	$-0.634910\pi$
$433$	−17.1154			−0.822515			−0.411258	+	0.911519i	$0.634910\pi$
$434$	18.0810	−	13.7320i	0.867918	−	0.659157i
$435$	−2.58017			−0.123710
$436$	−0.818143	−	0.227951i	−0.0391819	−	0.0109169i
$437$		−	11.3770i		−	0.544234i
$438$	3.52643	−	2.67821i	0.168499	−	0.127970i
$439$	−16.8059			−0.802100			−0.401050	−	0.916056i	$-0.631355\pi$
$439$	−16.8059			−0.802100			−0.401050	+	0.916056i	$0.631355\pi$
$440$	3.26038	+	8.21523i	0.155433	+	0.391646i
$441$	6.98837			0.332780
$442$	−34.3889	+	26.1173i	−1.63571	+	1.24227i
$443$	−17.3705			−0.825299			−0.412649	−	0.910890i	$-0.635397\pi$
$443$	−17.3705			−0.825299			−0.412649	+	0.910890i	$0.635397\pi$
$444$	−2.85429	+	10.2444i	−0.135458	+	0.486176i
$445$		−	7.51983i		−	0.356474i
$446$	1.44790	+	1.90646i	0.0685601	+	0.0902737i
$447$	−7.23673			−0.342286
$448$	11.5459	+	12.2551i	0.545495	+	0.579000i
$449$	−6.27530			−0.296150			−0.148075	−	0.988976i	$-0.547308\pi$
$449$	−6.27530			−0.296150			−0.148075	+	0.988976i	$0.547308\pi$
$450$	−12.6267	+	9.58957i	−0.595227	+	0.452057i
$451$	−35.9220			−1.69150
$452$	10.8180	+	3.01411i	0.508836	+	0.141772i
$453$			8.90378i			0.418336i
$454$	3.23377	−	2.45595i	0.151769	−	0.115264i
$455$		−	13.5785i		−	0.636571i
$456$	−1.33697	−	3.36878i	−0.0626093	−	0.157758i
$457$		−	9.39098i		−	0.439291i	−0.975580	−	0.219646i	$-0.929510\pi$
$457$		−	9.39098i		−	0.439291i	0.975580	−	0.219646i	$-0.0704901\pi$
$458$	−26.2965	+	19.9714i	−1.22875	+	0.933200i
$459$	−13.4356			−0.627121
$460$	−8.49103	−	2.36577i	−0.395896	−	0.110305i
$461$	−5.07816			−0.236514			−0.118257	−	0.992983i	$-0.537731\pi$
$461$	−5.07816			−0.236514			−0.118257	+	0.992983i	$0.537731\pi$
$462$	3.18636	+	4.19550i	0.148243	+	0.195193i
$463$	−7.34383			−0.341297			−0.170648	−	0.985332i	$-0.554586\pi$
$463$	−7.34383			−0.341297			−0.170648	+	0.985332i	$0.554586\pi$
$464$	−17.7958	−	10.7511i	−0.826149	−	0.499108i
$465$			3.78651i			0.175595i
$466$	25.0356	−	19.0137i	1.15975	−	0.880795i
$467$			13.2055i			0.611076i	0.952180	+	0.305538i	$0.0988363\pi$
$467$			13.2055i			0.611076i	−0.952180	+	0.305538i	$0.901164\pi$
$468$	36.0994	+	10.0580i	1.66870	+	0.464932i
$469$			23.4512i			1.08288i
$470$	8.49765	−	6.45370i	0.391967	−	0.297687i
$471$			6.18404i			0.284945i
$472$	−3.19113	−	8.04075i	−0.146884	−	0.370106i
$473$		−	17.8526i		−	0.820861i
$474$	−7.72874	−	10.1765i	−0.354993	−	0.467422i
$475$		−	9.96521i		−	0.457235i
$476$	−5.00565	+	17.9659i	−0.229434	+	0.823464i
$477$			11.9021i			0.544958i
$478$	−11.4620	−	15.0921i	−0.524259	−	0.690296i
$479$	31.2786			1.42916			0.714578	−	0.699556i	$-0.246619\pi$
$479$	31.2786			1.42916			0.714578	+	0.699556i	$0.246619\pi$
$480$	−2.79225	+	0.297310i	−0.127448	+	0.0135703i
$481$	69.1083			3.15107
$482$	11.2810	+	14.8538i	0.513835	+	0.676571i
$483$	−5.25394			−0.239063
$484$	−0.0764680	+	0.274453i	−0.00347582	+	0.0124751i
$485$			5.72930i			0.260154i
$486$	10.7513	+	14.1563i	0.487688	+	0.642144i
$487$	6.91426			0.313315			0.156658	−	0.987653i	$-0.449928\pi$
$487$	6.91426			0.313315			0.156658	+	0.987653i	$0.449928\pi$
$488$	4.70787	+	11.8625i	0.213115	+	0.536989i
$489$		−	3.05823i		−	0.138298i
$490$	2.05815	+	2.70999i	0.0929778	+	0.122425i
$491$		−	11.7020i		−	0.528102i	−0.964509	−	0.264051i	$-0.914941\pi$
$491$		−	11.7020i		−	0.528102i	0.964509	−	0.264051i	$-0.0850587\pi$
$492$	3.06309	−	10.9938i	0.138095	−	0.495638i
$493$		−	23.0298i		−	1.03721i
$494$	−18.7567	+	14.2452i	−0.843906	+	0.640920i
$495$	8.49609			0.381871
$496$	−15.7777	+	26.1161i	−0.708441	+	1.17265i
$497$		−	26.0809i		−	1.16989i
$498$	3.78611	+	4.98521i	0.169660	+	0.223392i
$499$	3.31627			0.148457			0.0742284	−	0.997241i	$-0.476351\pi$
$499$	3.31627			0.148457			0.0742284	+	0.997241i	$0.476351\pi$
$500$	−16.4554	−	4.58480i	−0.735908	−	0.205039i
$501$	−6.83665	+	0.463664i	−0.305439	+	0.0207150i
$502$	−20.5003	−	26.9929i	−0.914971	−	1.20475i
$503$		−	5.24182i		−	0.233721i	−0.993148	−	0.116861i	$-0.962717\pi$
$503$		−	5.24182i		−	0.233721i	0.993148	−	0.116861i	$-0.0372831\pi$
$504$	15.0436	−	5.97034i	0.670093	−	0.265940i
$505$	2.47669			0.110211
$506$	−13.4415	−	17.6985i	−0.597546	−	0.786795i
$507$			18.2908i			0.812323i
$508$	7.55904	+	2.10610i	0.335378	+	0.0934430i
$509$	−20.1587			−0.893519			−0.446760	−	0.894654i	$-0.647422\pi$
$509$	−20.1587			−0.893519			−0.446760	+	0.894654i	$0.647422\pi$
$510$	−1.88120	−	2.47699i	−0.0833008	−	0.109683i
$511$	−12.4282			−0.549793
$512$	−20.4974	−	9.58424i	−0.905864	−	0.423568i
$513$	−7.32820			−0.323548
$514$	6.42591	+	8.46105i	0.283435	+	0.373201i
$515$		−	12.1309i		−	0.534550i
$516$	5.46370	+	1.52230i	0.240526	+	0.0670154i
$517$	26.9039			1.18323
$518$	23.7695	−	18.0522i	1.04437	−	0.793168i
$519$			7.92344i			0.347800i
$520$	6.73132	+	16.9610i	0.295188	+	0.743789i
$521$		−	20.4665i		−	0.896652i	−0.893870	−	0.448326i	$-0.852020\pi$
$521$		−	20.4665i		−	0.896652i	0.893870	−	0.448326i	$-0.147980\pi$
$522$	−15.9159	+	12.0876i	−0.696620	+	0.529061i
$523$			30.7422i			1.34426i	0.740432	+	0.672131i	$0.234621\pi$
$523$			30.7422i			1.34426i	−0.740432	+	0.672131i	$0.765379\pi$
$524$	2.88524	−	10.3555i	0.126042	−	0.452381i
$525$	−4.60198			−0.200847
$526$	−17.9341	−	23.6139i	−0.781962	−	1.02962i
$527$	−33.7972			−1.47223
$528$	−6.05994	−	3.66105i	−0.263725	−	0.159327i
$529$	−0.836538			−0.0363712
$530$	−4.61544	+	3.50529i	−0.200482	+	0.152260i
$531$	−8.31564			−0.360868
$532$	−2.73023	+	9.79913i	−0.118371	+	0.424846i
$533$	−74.1638			−3.21239
$534$	3.64319	+	4.79702i	0.157656	+	0.207587i
$535$	10.6971			0.462478
$536$	−11.6255	−	29.2931i	−0.502147	−	1.26527i
$537$	12.4175			0.535856
$538$	−0.901141	−	1.18654i	−0.0388509	−	0.0511554i
$539$			8.57993i			0.369564i
$540$	−1.52385	+	5.46929i	−0.0655762	+	0.235361i
$541$		−	25.8472i		−	1.11126i	−0.831430	−	0.555629i	$-0.812477\pi$
$541$		−	25.8472i		−	1.11126i	0.831430	−	0.555629i	$-0.187523\pi$
$542$	17.1597	−	13.0322i	0.737070	−	0.559782i
$543$			5.74088i			0.246365i
$544$	−2.65369	−	24.9227i	−0.113776	−	1.06855i
$545$	−0.397539			−0.0170287
$546$	6.57849	+	8.66195i	0.281533	+	0.370697i
$547$	−0.178361			−0.00762618			−0.00381309	−	0.999993i	$-0.501214\pi$
$547$	−0.178361			−0.00762618			−0.00381309	+	0.999993i	$0.501214\pi$
$548$	−6.62609	+	23.7818i	−0.283053	+	1.01591i
$549$	12.2680			0.523587
$550$	−11.7735	−	15.5023i	−0.502025	−	0.661021i
$551$		−	12.5611i		−	0.535122i
$552$	6.56272	−	2.60455i	0.279328	−	0.110857i
$553$			35.8652i			1.52514i
$554$	12.0926	+	15.9224i	0.513764	+	0.676478i
$555$			4.97778i			0.211295i
$556$	10.1787	−	36.5326i	0.431673	−	1.54933i
$557$	28.0070			1.18669			0.593346	−	0.804947i	$-0.297806\pi$
$557$	28.0070			1.18669			0.593346	+	0.804947i	$0.297806\pi$
$558$	17.7391	+	23.3573i	0.750957	+	0.988791i
$559$		−	36.8580i		−	1.55893i
$560$	6.74570	+	4.07534i	0.285058	+	0.172214i
$561$		−	7.84225i		−	0.331100i
$562$	−13.1851	+	10.0137i	−0.556179	+	0.422401i
$563$			3.48356i			0.146814i	0.997302	+	0.0734072i	$0.0233873\pi$
$563$			3.48356i			0.146814i	−0.997302	+	0.0734072i	$0.976613\pi$
$564$	−2.29411	+	8.23384i	−0.0965996	+	0.346707i
$565$	5.25651			0.221143
$566$	−10.8828	−	14.3294i	−0.457436	−	0.602311i
$567$		−	13.7826i		−	0.578813i
$568$	12.9291	+	32.5777i	0.542495	+	1.36693i
$569$			19.4658i			0.816048i	0.912971	+	0.408024i	$0.133782\pi$
$569$			19.4658i			0.816048i	−0.912971	+	0.408024i	$0.866218\pi$
$570$	−1.02606	−	1.35102i	−0.0429770	−	0.0565882i
$571$	−13.1095			−0.548615			−0.274307	−	0.961642i	$-0.588449\pi$
$571$	−13.1095			−0.548615			−0.274307	+	0.961642i	$0.588449\pi$
$572$	−12.3487	+	44.3208i	−0.516323	+	1.85315i
$573$	−6.82793			−0.285241
$574$	−25.5083	+	19.3728i	−1.06470	+	0.808604i
$575$	19.4132			0.809587
$576$	−15.8313	+	14.9152i	−0.659637	+	0.621465i
$577$	−32.7272			−1.36245			−0.681226	−	0.732073i	$-0.738553\pi$
$577$	−32.7272			−1.36245			−0.681226	+	0.732073i	$0.738553\pi$
$578$	2.96284	−	2.25019i	0.123238	−	0.0935955i
$579$	12.9914			0.539903
$580$	−9.37481	−	2.61201i	−0.389268	−	0.108458i
$581$		−	17.5694i		−	0.728903i
$582$	−2.77572	−	3.65481i	−0.115057	−	0.151497i
$583$	−14.6127			−0.605196
$584$	15.5242	−	6.16109i	0.642395	−	0.254948i
$585$	17.5408			0.725225
$586$	2.34702	−	1.78249i	0.0969545	−	0.0736339i
$587$	−44.1672			−1.82297			−0.911487	−	0.411330i	$-0.865065\pi$
$587$	−44.1672			−1.82297			−0.911487	+	0.411330i	$0.865065\pi$
$588$	−2.62585	−	0.731615i	−0.108288	−	0.0301713i
$589$	−18.4340			−0.759559
$590$	−2.44905	−	3.22468i	−0.100826	−	0.132758i
$591$	4.55970			0.187561
$592$	−20.7415	+	34.3324i	−0.852472	+	1.41105i
$593$			30.3842i			1.24773i	0.781532	+	0.623866i	$0.214439\pi$
$593$			30.3842i			1.24773i	−0.781532	+	0.623866i	$0.785561\pi$
$594$	−11.4001	+	8.65800i	−0.467750	+	0.355242i
$595$			8.72969i			0.357883i
$596$	−26.2940	−	7.32602i	−1.07704	−	0.300086i
$597$	8.20588			0.335844
$598$	−27.7510	−	36.5400i	−1.13482	−	1.49423i
$599$		−	11.2027i		−	0.457728i	−0.973458	−	0.228864i	$-0.926499\pi$
$599$		−	11.2027i		−	0.457728i	0.973458	−	0.228864i	$-0.0735011\pi$
$600$	5.74836	−	2.28135i	0.234676	−	0.0931358i
$601$	13.3368			0.544021			0.272011	−	0.962294i	$-0.412311\pi$
$601$	13.3368			0.544021			0.272011	+	0.962294i	$0.412311\pi$
$602$	−9.62791	−	12.6772i	−0.392404	−	0.516682i
$603$	−30.2945			−1.23369
$604$	−9.01363	+	32.3510i	−0.366760	+	1.31634i
$605$			0.133358i			0.00542176i
$606$	−1.57992	+	1.19990i	−0.0641798	+	0.0487426i
$607$	29.7367			1.20697			0.603487	−	0.797372i	$-0.293777\pi$
$607$	29.7367			1.20697			0.603487	+	0.797372i	$0.293777\pi$
$608$	−1.44740	−	13.5936i	−0.0586998	−	0.551294i
$609$	−5.80079			−0.235060
$610$	3.61307	+	4.75736i	0.146289	+	0.192620i
$611$	55.5453			2.24712
$612$	−23.2085	−	6.46634i	−0.938147	−	0.261386i
$613$	13.0821			0.528380			0.264190	−	0.964471i	$-0.414895\pi$
$613$	13.0821			0.528380			0.264190	+	0.964471i	$0.414895\pi$
$614$	32.8595	−	24.9558i	1.32610	−	1.00713i
$615$		−	5.34192i		−	0.215407i
$616$	7.33005	+	18.4696i	0.295336	+	0.744163i
$617$	−15.7303			−0.633276			−0.316638	−	0.948546i	$-0.602554\pi$
$617$	−15.7303			−0.633276			−0.316638	+	0.948546i	$0.602554\pi$
$618$	5.87713	+	7.73847i	0.236413	+	0.311287i
$619$	46.8494			1.88304			0.941518	−	0.336964i	$-0.109400\pi$
$619$	46.8494			1.88304			0.941518	+	0.336964i	$0.109400\pi$
$620$	−3.83323	+	13.7579i	−0.153946	+	0.552532i
$621$		−	14.2761i		−	0.572878i
$622$	−10.2328	−	13.4737i	−0.410300	−	0.540245i
$623$		−	16.9062i		−	0.677333i
$624$	−12.5112	−	7.55852i	−0.500850	−	0.302583i
$625$	12.6224			0.504894
$626$	8.59427	+	11.3162i	0.343496	+	0.452284i
$627$		−	4.27740i		−	0.170823i
$628$	−6.26034	+	22.4691i	−0.249815	+	0.896615i
$629$	−44.4300			−1.77154
$630$	6.03310	−	4.58195i	0.240365	−	0.182549i
$631$		−	36.4544i		−	1.45123i	−0.688103	−	0.725613i	$-0.741556\pi$
$631$		−	36.4544i		−	1.45123i	0.688103	−	0.725613i	$-0.258444\pi$
$632$	−17.7796	−	44.7994i	−0.707233	−	1.78203i
$633$	11.1459			0.443009
$634$	0.921173	−	0.699603i	0.0365845	−	0.0277848i
$635$	3.67297			0.145757
$636$	1.24603	−	4.47216i	0.0494084	−	0.177333i
$637$			17.7139i			0.701852i
$638$	−14.8405	−	19.5407i	−0.587542	−	0.773622i
$639$	33.6915			1.33281
$640$	−10.4464	−	1.74646i	−0.412929	−	0.0690349i
$641$			17.7237i			0.700044i	0.936741	+	0.350022i	$0.113826\pi$
$641$			17.7237i			0.700044i	−0.936741	+	0.350022i	$0.886174\pi$
$642$	−6.82388	+	5.18252i	−0.269317	+	0.204538i
$643$	−1.39018			−0.0548233			−0.0274116	−	0.999624i	$-0.508726\pi$
$643$	−1.39018			−0.0548233			−0.0274116	+	0.999624i	$0.508726\pi$
$644$	−19.0897	−	5.31876i	−0.752239	−	0.209589i
$645$	2.65484			0.104534
$646$	12.0588	−	9.15828i	0.474447	−	0.360328i
$647$	−23.2995			−0.915999			−0.457999	−	0.888953i	$-0.651434\pi$
$647$	−23.2995			−0.915999			−0.457999	+	0.888953i	$0.651434\pi$
$648$	6.83246	+	17.2159i	0.268405	+	0.676303i
$649$		−	10.2095i		−	0.400757i
$650$	−24.3074	−	32.0058i	−0.953414	−	1.25537i
$651$			8.51290i			0.333647i
$652$	3.09597	−	11.1118i	0.121247	−	0.435171i
$653$	−18.2743			−0.715128			−0.357564	−	0.933889i	$-0.616393\pi$
$653$	−18.2743			−0.715128			−0.357564	+	0.933889i	$0.616393\pi$
$654$	0.253597	−	0.192599i	0.00991641	−	0.00753121i
$655$		−	5.03177i		−	0.196608i
$656$	22.2588	−	36.8439i	0.869062	−	1.43851i
$657$		−	16.0549i		−	0.626362i
$658$	19.1046	−	14.5093i	0.744774	−	0.565633i
$659$	−18.0351			−0.702547			−0.351273	−	0.936273i	$-0.614251\pi$
$659$	−18.0351			−0.702547			−0.351273	+	0.936273i	$0.614251\pi$
$660$	−3.19237	−	0.889459i	−0.124263	−	0.0346221i
$661$		−	0.469633i		−	0.0182666i	−0.999958	−	0.00913331i	$-0.997093\pi$
$661$		−	0.469633i		−	0.0182666i	0.999958	−	0.00913331i	$-0.00290726\pi$
$662$	−0.662852	+	0.503416i	−0.0257625	+	0.0195658i
$663$		−	16.1910i		−	0.628804i
$664$	8.70975	+	21.9461i	0.338004	+	0.851673i
$665$			4.76144i			0.184641i
$666$	23.3200	+	30.7056i	0.903631	+	1.18982i
$667$	24.4703			0.947495
$668$	−25.3097	−	5.23633i	−0.979262	−	0.202600i
$669$	−0.897600			−0.0347032
$670$	−8.92206	−	11.7478i	−0.344689	−	0.453856i
$671$			15.0620i			0.581462i
$672$	−6.27759	+	0.668417i	−0.242163	+	0.0257847i
$673$			28.9111i			1.11444i	0.830365	+	0.557220i	$0.188132\pi$
$673$			28.9111i			1.11444i	−0.830365	+	0.557220i	$0.811868\pi$
$674$	6.45760	−	4.90435i	0.248738	−	0.188908i
$675$		−	12.5045i		−	0.481300i
$676$	−18.5165	+	66.4578i	−0.712172	+	2.55607i
$677$	24.2201			0.930855			0.465427	−	0.885086i	$-0.345901\pi$
$677$	24.2201			0.930855			0.465427	+	0.885086i	$0.345901\pi$
$678$	−3.35321	+	2.54666i	−0.128779	+	0.0978039i
$679$			12.8807i			0.494316i
$680$	−4.32759	−	10.9043i	−0.165956	−	0.418161i
$681$			1.52252i			0.0583432i
$682$	−28.6767	+	21.7791i	−1.09809	+	0.833964i
$683$	−10.4026			−0.398043			−0.199022	−	0.979995i	$-0.563776\pi$
$683$	−10.4026			−0.398043			−0.199022	+	0.979995i	$0.563776\pi$
$684$	−12.6586	−	3.52694i	−0.484014	−	0.134856i
$685$			11.5557i			0.441520i
$686$	17.2286	+	22.6851i	0.657791	+	0.866120i
$687$		−	12.3809i		−	0.472360i
$688$	18.3108	+	11.0622i	0.698091	+	0.421744i
$689$	−30.1691			−1.14935
$690$	2.63193	−	1.99887i	0.100196	−	0.0760957i
$691$	−10.3385			−0.393295			−0.196648	−	0.980474i	$-0.563005\pi$
$691$	−10.3385			−0.393295			−0.196648	+	0.980474i	$0.563005\pi$
$692$	−8.02120	+	28.7890i	−0.304920	+	1.09439i
$693$	19.1011			0.725589
$694$	17.9820	−	13.6568i	0.682588	−	0.518405i
$695$		−	17.7513i		−	0.673346i
$696$	7.24580	−	2.87564i	0.274651	−	0.109001i
$697$	47.6802			1.80602
$698$	16.2870	+	21.4452i	0.616472	+	0.811714i
$699$			11.7872i			0.445834i
$700$	−16.7209	−	4.65876i	−0.631989	−	0.176085i
$701$	−13.8542			−0.523265			−0.261633	−	0.965168i	$-0.584261\pi$
$701$	−13.8542			−0.523265			−0.261633	+	0.965168i	$0.584261\pi$
$702$	−23.5363	+	17.8751i	−0.888322	+	0.674653i
$703$	−24.2335			−0.913983
$704$	−18.3120	−	19.4368i	−0.690159	−	0.732551i
$705$			4.00086i			0.150681i
$706$	1.91847	−	1.45702i	0.0722025	−	0.0548356i
$707$	5.56814			0.209411
$708$	3.12457	+	0.870568i	0.117429	+	0.0327179i
$709$			33.7616i			1.26794i	0.773356	+	0.633971i	$0.218576\pi$
$709$			33.7616i			1.26794i	−0.773356	+	0.633971i	$0.781424\pi$
$710$	9.92251	+	13.0651i	0.372385	+	0.490323i
$711$	−46.3310			−1.73755
$712$	8.38097	+	21.1176i	0.314090	+	0.791417i
$713$		−	35.9112i		−	1.34489i
$714$	−4.22934	−	5.56881i	−0.158279	−	0.208407i
$715$			21.5357i			0.805388i
$716$	45.1178	+	12.5707i	1.68613	+	0.469790i
$717$	7.10565			0.265365
$718$	22.0703	+	29.0602i	0.823657	+	1.08452i
$719$	−26.4453			−0.986243			−0.493122	−	0.869960i	$-0.664144\pi$
$719$	−26.4453			−0.986243			−0.493122	+	0.869960i	$0.664144\pi$
$720$	−5.26455	+	8.71415i	−0.196198	+	0.324757i
$721$		−	27.2728i		−	1.01569i
$722$	−14.8212	+	11.2562i	−0.551587	+	0.418913i
$723$	−6.99344			−0.260089
$724$	−5.81172	+	20.8589i	−0.215991	+	0.775216i
$725$	21.4338			0.796032
$726$	−0.0646088	−	0.0850710i	−0.00239786	−	0.00315728i
$727$	11.3078			0.419382			0.209691	−	0.977768i	$-0.432754\pi$
$727$	11.3078			0.419382			0.209691	+	0.977768i	$0.432754\pi$
$728$	15.1335	+	38.1320i	0.560883	+	1.41327i
$729$	12.9806			0.480763
$730$	6.22585	−	4.72834i	0.230429	−	0.175004i
$731$			23.6962i			0.876435i
$732$	−4.60967	−	1.28435i	−0.170378	−	0.0474708i
$733$	16.6230			0.613985			0.306992	−	0.951712i	$-0.400677\pi$
$733$	16.6230			0.613985			0.306992	+	0.951712i	$0.400677\pi$
$734$	−4.54537	−	5.98493i	−0.167773	−	0.220908i
$735$	−1.27591			−0.0470628
$736$	26.4817	−	2.81968i	0.976128	−	0.103935i
$737$		−	37.1939i		−	1.37006i
$738$	−25.0259	−	32.9519i	−0.921217	−	1.21297i
$739$	−9.56489			−0.351850			−0.175925	−	0.984404i	$-0.556292\pi$
$739$	−9.56489			−0.351850			−0.175925	+	0.984404i	$0.556292\pi$
$740$	−5.03920	+	18.0863i	−0.185245	+	0.664865i
$741$		−	8.83103i		−	0.324416i
$742$	−10.3765	+	7.88065i	−0.380934	+	0.289308i
$743$			21.2701i			0.780324i	0.920746	+	0.390162i	$0.127581\pi$
$743$			21.2701i			0.780324i	−0.920746	+	0.390162i	$0.872419\pi$
$744$	−4.22012	−	10.6335i	−0.154717	−	0.389844i
$745$	−12.7763			−0.468089
$746$	14.8351	+	19.5335i	0.543150	+	0.715170i
$747$	22.6964			0.830417
$748$	7.93901	−	28.4941i	0.290279	−	1.04185i
$749$	24.0495			0.878750
$750$	5.10062	−	3.87376i	0.186248	−	0.141450i
$751$	−15.7821			−0.575896			−0.287948	−	0.957646i	$-0.592973\pi$
$751$	−15.7821			−0.575896			−0.287948	+	0.957646i	$0.592973\pi$
$752$	−16.6709	+	27.5944i	−0.607924	+	1.00627i
$753$	12.7088			0.463133
$754$	−30.6394	−	40.3432i	−1.11582	−	1.46921i
$755$			15.7195i			0.572091i
$756$	−3.42595	+	12.2961i	−0.124601	+	0.447207i
$757$	25.5352			0.928092			0.464046	−	0.885811i	$-0.346397\pi$
$757$	25.5352			0.928092			0.464046	+	0.885811i	$0.346397\pi$
$758$	−28.0875	+	21.3316i	−1.02018	+	0.774799i
$759$	8.33280			0.302462
$760$	−2.36040	−	5.94754i	−0.0856207	−	0.215740i
$761$	36.2141			1.31276			0.656380	−	0.754431i	$-0.272087\pi$
$761$	36.2141			1.31276			0.656380	+	0.754431i	$0.272087\pi$
$762$	−2.34305	+	1.77947i	−0.0848796	+	0.0644634i
$763$	−0.893754			−0.0323561
$764$	−24.8086	−	6.91217i	−0.897544	−	0.250074i
$765$	−11.2771			−0.407724
$766$	23.6794	+	31.1789i	0.855572	+	1.12654i
$767$		−	21.0783i		−	0.761093i
$768$	7.51002	−	3.94693i	0.270994	−	0.142423i
$769$		−	52.3354i		−	1.88726i	−0.330997	−	0.943632i	$-0.607385\pi$
$769$		−	52.3354i		−	1.88726i	0.330997	−	0.943632i	$-0.392615\pi$
$770$	5.62547	+	7.40710i	0.202728	+	0.266933i
$771$	−3.98363			−0.143467
$772$	47.2029	+	13.1517i	1.69887	+	0.473339i
$773$		−	31.0143i		−	1.11551i	−0.830006	−	0.557754i	$-0.811663\pi$
$773$		−	31.0143i		−	1.11551i	0.830006	−	0.557754i	$-0.188337\pi$
$774$	16.3765	−	12.4374i	0.588640	−	0.447054i
$775$		−	31.4550i		−	1.12990i
$776$	−6.38539	−	16.0894i	−0.229222	−	0.577574i
$777$			11.1911i			0.401480i
$778$	−11.6229	−	15.3040i	−0.416702	−	0.548675i
$779$	26.0062			0.931770
$780$	−6.59091	−	1.83636i	−0.235992	−	0.0657522i
$781$			41.3645i			1.48014i
$782$	17.8412	+	23.4917i	0.638002	+	0.840062i
$783$		−	15.7620i		−	0.563287i
$784$	−8.80014	−	5.31651i	−0.314291	−	0.189875i
$785$			10.9178i			0.389674i
$786$	2.43778	+	3.20985i	0.0869527	+	0.114491i
$787$	12.8312			0.457384			0.228692	−	0.973499i	$-0.426555\pi$
$787$	12.8312			0.457384			0.228692	+	0.973499i	$0.426555\pi$
$788$	16.5672	+	4.61596i	0.590183	+	0.164437i
$789$	11.1179			0.395808
$790$	−13.6450	−	17.9665i	−0.485467	−	0.639219i
$791$	11.8178			0.420192
$792$	−23.8592	+	9.46902i	−0.847801	+	0.336467i
$793$			31.0967i			1.10428i
$794$	−3.09018	+	2.34690i	−0.109667	+	0.0832883i
$795$		−	2.17304i		−	0.0770698i
$796$	29.8153	+	8.30713i	1.05677	+	0.294438i
$797$		−	0.754619i		−	0.0267300i	−0.999911	−	0.0133650i	$-0.995746\pi$
$797$		−	0.754619i		−	0.0267300i	0.999911	−	0.0133650i	$-0.00425434\pi$
$798$	−2.30681	−	3.03740i	−0.0816602	−	0.107523i
$799$	−35.7103			−1.26334
$800$	23.1956	−	2.46979i	0.820088	−	0.0873202i
$801$	21.8396			0.771665
$802$	−25.0848	−	33.0294i	−0.885775	−	1.16631i
$803$	19.7113			0.695597
$804$	11.3831	+	3.17154i	0.401449	+	0.111852i
$805$	−9.27575			−0.326927
$806$	−59.2054	+	44.9647i	−2.08542	+	1.58381i
$807$	0.558646			0.0196653
$808$	−6.95519	+	2.76031i	−0.244683	+	0.0971073i
$809$	−2.44424			−0.0859349			−0.0429674	−	0.999076i	$-0.513681\pi$
$809$	−2.44424			−0.0859349			−0.0429674	+	0.999076i	$0.513681\pi$
$810$	5.24360	+	6.90429i	0.184241	+	0.242592i
$811$	41.2267			1.44767			0.723833	−	0.689975i	$-0.242378\pi$
$811$	41.2267			1.44767			0.723833	+	0.689975i	$0.242378\pi$
$812$	−21.0766	−	5.87236i	−0.739644	−	0.206080i
$813$			8.07909i			0.283346i
$814$	−37.6987	+	28.6310i	−1.32134	+	1.00352i
$815$		−	5.39927i		−	0.189128i
$816$	8.04353	+	4.85941i	0.281580	+	0.170113i
$817$			12.9246i			0.452175i
$818$	17.4394	−	13.2447i	0.609755	−	0.463090i
$819$	39.4356			1.37799
$820$	5.40783	−	19.4094i	0.188850	−	0.677804i
$821$			34.2081i			1.19387i	0.802289	+	0.596936i	$0.203615\pi$
$821$			34.2081i			1.19387i	−0.802289	+	0.596936i	$0.796385\pi$
$822$	−5.59847	−	7.37156i	−0.195269	−	0.257113i
$823$	2.13871			0.0745508			0.0372754	−	0.999305i	$-0.488132\pi$
$823$	2.13871			0.0745508			0.0372754	+	0.999305i	$0.488132\pi$
$824$	13.5200	+	34.0666i	0.470992	+	1.18677i
$825$	7.29879			0.254111
$826$	−5.50599	−	7.24979i	−0.191578	−	0.252252i
$827$	−0.551949			−0.0191931			−0.00959657	−	0.999954i	$-0.503055\pi$
$827$	−0.551949			−0.0191931			−0.00959657	+	0.999954i	$0.503055\pi$
$828$	6.87083	−	24.6602i	0.238778	−	0.857001i
$829$			9.84129i			0.341802i	0.985288	+	0.170901i	$0.0546678\pi$
$829$			9.84129i			0.341802i	−0.985288	+	0.170901i	$0.945332\pi$
$830$	6.68432	+	8.80131i	0.232016	+	0.305498i
$831$	−7.49657			−0.260053
$832$	−37.8066	−	40.1287i	−1.31071	−	1.39121i
$833$		−	11.3884i		−	0.394584i
$834$	8.60012	+	11.3239i	0.297798	+	0.392113i
$835$	−12.0700	+	0.818592i	−0.417700	+	0.0283286i
$836$	4.33018	−	15.5415i	0.149762	−	0.537515i
$837$	−23.1313			−0.799536
$838$	2.59434	+	3.41599i	0.0896199	+	0.118003i
$839$		−	0.997044i		−	0.0344218i	−0.999852	−	0.0172109i	$-0.994521\pi$
$839$		−	0.997044i		−	0.0344218i	0.999852	−	0.0172109i	$-0.00547867\pi$
$840$	−2.74660	+	1.09004i	−0.0947668	+	0.0376101i
$841$	−1.98269			−0.0683687
$842$	40.6611	−	30.8808i	1.40127	−	1.06422i
$843$		−	6.20779i		−	0.213808i
$844$	40.4974	+	11.2834i	1.39398	+	0.388390i
$845$			32.2921i			1.11088i
$846$	18.7433	+	24.6794i	0.644407	+	0.848497i
$847$			0.299817i			0.0103018i
$848$	9.05467	−	14.9877i	0.310939	−	0.514681i
$849$	6.74657			0.231542
$850$	15.6273	+	20.5767i	0.536013	+	0.705774i
$851$		−	47.2092i		−	1.61831i
$852$	−12.6594	−	3.52718i	−0.433706	−	0.120839i
$853$	−25.0967			−0.859295			−0.429648	−	0.902997i	$-0.641362\pi$
$853$	−25.0967			−0.859295			−0.429648	+	0.902997i	$0.641362\pi$
$854$	8.12296	+	10.6956i	0.277962	+	0.365995i
$855$	−6.15087			−0.210355
$856$	−30.0404	+	11.9221i	−1.02676	+	0.407490i
$857$	−27.8488			−0.951296			−0.475648	−	0.879636i	$-0.657786\pi$
$857$	−27.8488			−0.951296			−0.475648	+	0.879636i	$0.657786\pi$
$858$	−10.4335	−	13.7379i	−0.356195	−	0.469006i
$859$		−	18.6137i		−	0.635091i	−0.948243	−	0.317545i	$-0.897141\pi$
$859$		−	18.6137i		−	0.635091i	0.948243	−	0.317545i	$-0.102859\pi$
$860$	9.64609	+	2.68759i	0.328929	+	0.0916462i
$861$		−	12.0098i		−	0.409293i
$862$	−25.4877	−	33.5599i	−0.868114	−	1.14305i
$863$			42.3921i			1.44304i	0.692392	+	0.721522i	$0.256557\pi$
$863$			42.3921i			1.44304i	−0.692392	+	0.721522i	$0.743443\pi$
$864$	−1.81623	−	17.0575i	−0.0617893	−	0.580309i
$865$			13.9887i			0.475631i
$866$	19.2759	−	14.6395i	0.655023	−	0.497470i
$867$			1.39496i			0.0473755i
$868$	−8.61794	+	30.9308i	−0.292512	+	1.04986i
$869$		−	56.8826i		−	1.92961i
$870$	2.90587	−	2.20692i	0.0985183	−	0.0748216i
$871$		−	76.7898i		−	2.60192i
$872$	1.11639	−	0.443063i	0.0378058	−	0.0150040i
$873$	−16.6394			−0.563159
$874$	9.73115	+	12.8131i	0.329161	+	0.433410i
$875$	−17.9762			−0.607706
$876$	−1.68079	+	6.03257i	−0.0567888	+	0.203822i
$877$	14.0020			0.472813			0.236406	−	0.971654i	$-0.424030\pi$
$877$	14.0020			0.472813			0.236406	+	0.971654i	$0.424030\pi$
$878$	18.9273	−	14.3747i	0.638765	−	0.485122i
$879$			1.10502i			0.0372715i
$880$	−10.6987	−	6.46352i	−0.360655	−	0.217885i
$881$		−	5.85546i		−	0.197276i	−0.995123	−	0.0986378i	$-0.968551\pi$
$881$		−	5.85546i		−	0.197276i	0.995123	−	0.0986378i	$-0.0314485\pi$
$882$	−7.87052	+	5.97742i	−0.265014	+	0.201270i
$883$		−	23.1119i		−	0.777778i	−0.921285	−	0.388889i	$-0.872859\pi$
$883$		−	23.1119i		−	0.777778i	0.921285	−	0.388889i	$-0.127141\pi$
$884$	16.3907	−	58.8282i	0.551280	−	1.97861i
$885$	1.51824			0.0510352
$886$	19.5632	−	14.8577i	0.657240	−	0.499153i
$887$	−43.7788			−1.46995			−0.734973	−	0.678096i	$-0.762805\pi$
$887$	−43.7788			−1.46995			−0.734973	+	0.678096i	$0.762805\pi$
$888$	−5.54781	−	13.9789i	−0.186172	−	0.469101i
$889$	8.25763			0.276952
$890$	6.43200	+	8.46907i	0.215601	+	0.283884i
$891$			21.8593i			0.732314i
$892$	−3.26134	−	0.908675i	−0.109198	−	0.0304247i
$893$	−19.4775			−0.651789
$894$	8.15023	−	6.18985i	0.272585	−	0.207020i
$895$	21.9230			0.732804
$896$	−23.4857	−	3.92642i	−0.784602	−	0.131173i
$897$	17.2037			0.574416
$898$	7.06743	−	5.36750i	0.235843	−	0.179116i
$899$		−	39.6490i		−	1.32237i
$900$	6.01823	−	21.6001i	0.200608	−	0.720005i
$901$	19.3958			0.646169
$902$	40.4565	−	30.7254i	1.34705	−	1.02304i
$903$	5.96865			0.198624
$904$	−14.7617	+	5.85846i	−0.490965	+	0.194850i
$905$			10.1354i			0.336914i
$906$	−7.61574	−	10.0277i	−0.253016	−	0.333148i
$907$		−	1.30695i		−	0.0433966i	−0.999765	−	0.0216983i	$-0.993093\pi$
$907$		−	1.30695i		−	0.0433966i	0.999765	−	0.0216983i	$-0.00690732\pi$
$908$	−1.54131	+	5.53194i	−0.0511501	+	0.183584i
$909$			7.19297i			0.238576i
$910$	11.6142	+	15.2926i	0.385008	+	0.506943i
$911$		−	15.3232i		−	0.507679i	−0.967246	−	0.253840i	$-0.918306\pi$
$911$		−	15.3232i		−	0.507679i	0.967246	−	0.253840i	$-0.0816935\pi$
$912$	4.38718	+	2.65047i	0.145274	+	0.0877658i
$913$			27.8653i			0.922208i
$914$	8.03246	+	10.5764i	0.265690	+	0.349837i
$915$	−2.23986			−0.0740474
$916$	12.5336	−	44.9847i	0.414123	−	1.48634i
$917$		−	11.3125i		−	0.373572i
$918$	15.1316	−	11.4920i	0.499418	−	0.379293i
$919$			20.7869i			0.685696i	0.939391	+	0.342848i	$0.111392\pi$
$919$			20.7869i			0.685696i	−0.939391	+	0.342848i	$0.888608\pi$
$920$	11.5864	−	4.59829i	0.381992	−	0.151601i
$921$			15.4709i			0.509784i
$922$	5.71919	−	4.34355i	0.188351	−	0.143047i
$923$			85.4003i			2.81099i
$924$	−7.17715	−	1.99970i	−0.236111	−	0.0657852i
$925$		−	41.3511i		−	1.35961i
$926$	8.27085	−	6.28146i	0.271797	−	0.206421i
$927$	35.2313			1.15715
$928$	29.2380	−	3.11316i	0.959785	−	0.102195i
$929$	−44.2658			−1.45231			−0.726157	−	0.687529i	$-0.758696\pi$
$929$	−44.2658			−1.45231			−0.726157	+	0.687529i	$0.758696\pi$
$930$	−3.23875	−	4.26449i	−0.106203	−	0.139838i
$931$		−	6.21157i		−	0.203576i
$932$	−11.9327	+	42.8277i	−0.390867	+	1.40287i
$933$	6.34367			0.207682
$934$	−11.2951	−	14.8724i	−0.369588	−	0.486640i
$935$		−	13.8454i		−	0.452792i
$936$	−49.2593	+	19.5495i	−1.61009	+	0.638997i
$937$		−	2.18743i		−	0.0714601i	−0.999361	−	0.0357300i	$-0.988624\pi$
$937$		−	2.18743i		−	0.0714601i	0.999361	−	0.0357300i	$-0.0113756\pi$
$938$	−20.0587	−	26.4115i	−0.654941	−	0.862367i
$939$	−5.32786			−0.173868
$940$	−4.05022	+	14.5367i	−0.132104	+	0.474136i
$941$			18.4445i			0.601273i	0.953739	+	0.300637i	$0.0971991\pi$
$941$			18.4445i			0.601273i	−0.953739	+	0.300637i	$0.902801\pi$
$942$	−5.28944	−	6.96466i	−0.172339	−	0.226921i
$943$			50.6627i			1.64981i
$944$	10.4715	+	6.32625i	0.340819	+	0.205902i
$945$			5.97475i			0.194359i
$946$	15.2700	+	20.1061i	0.496469	+	0.653706i
$947$		−	24.2680i		−	0.788605i	−0.918981	−	0.394303i	$-0.870986\pi$
$947$		−	24.2680i		−	0.788605i	0.918981	−	0.394303i	$-0.129014\pi$
$948$	17.4087	+	4.85041i	0.565408	+	0.157534i
$949$	40.6956			1.32103
$950$	8.52362	+	11.2231i	0.276543	+	0.364126i
$951$			0.433706i			0.0140639i
$952$	−9.72937	−	24.5152i	−0.315331	−	0.794544i
$953$		−	41.2589i		−	1.33651i	−0.743934	−	0.668253i	$-0.767042\pi$
$953$		−	41.2589i		−	1.33651i	0.743934	−	0.668253i	$-0.232958\pi$
$954$	−10.1803	−	13.4045i	−0.329599	−	0.433986i
$955$	−12.0546			−0.390078
$956$	25.8177	+	7.19332i	0.835004	+	0.232649i
$957$	9.20012			0.297398
$958$	−35.2269	+	26.7538i	−1.13813	+	0.864375i
$959$			25.9797i			0.838929i
$960$	2.89042	−	2.72316i	0.0932880	−	0.0878896i
$961$	−27.1866			−0.876988
$962$	−77.8319	+	59.1109i	−2.50940	+	1.90581i
$963$			31.0674i			1.00113i
$964$	−25.4100	−	7.07973i	−0.818401	−	0.228023i
$965$	22.9361			0.738339
$966$	5.91715	−	4.49389i	0.190381	−	0.144589i
$967$			14.2594i			0.458551i	0.973362	+	0.229276i	$0.0736357\pi$
$967$			14.2594i			0.458551i	−0.973362	+	0.229276i	$0.926364\pi$
$968$	−0.148629	−	0.374503i	−0.00477712	−	0.0120370i
$969$			5.67751i			0.182388i
$970$	−4.90049	−	6.45252i	−0.157345	−	0.207178i
$971$	−29.3217			−0.940979			−0.470489	−	0.882406i	$-0.655923\pi$
$971$	−29.3217			−0.940979			−0.470489	+	0.882406i	$0.655923\pi$
$972$	−24.2169	−	6.74731i	−0.776757	−	0.216420i
$973$		−	39.9088i		−	1.27942i
$974$	−7.78706	+	5.91403i	−0.249513	+	0.189498i
$975$	15.0689			0.482592
$976$	−15.4486	−	9.33308i	−0.494497	−	0.298745i
$977$		−	1.36513i		−	0.0436743i	−0.999762	−	0.0218372i	$-0.993048\pi$
$977$		−	1.36513i		−	0.0436743i	0.999762	−	0.0218372i	$-0.00695154\pi$
$978$	2.61582	+	3.44428i	0.0836448	+	0.110136i
$979$			26.8134i			0.856961i
$980$	−4.63591	−	1.29166i	−0.148089	−	0.0412605i
$981$		−	1.15456i		−	0.0368623i
$982$	10.0091	+	13.1791i	0.319404	+	0.420562i
$983$	18.5502			0.591659			0.295829	−	0.955241i	$-0.404404\pi$
$983$	18.5502			0.591659			0.295829	+	0.955241i	$0.404404\pi$
$984$	5.95365	+	15.0015i	0.189796	+	0.478231i
$985$	8.05008			0.256497
$986$	19.6982	+	25.9368i	0.627320	+	0.825997i
$987$			8.99480i			0.286308i
$988$	8.93999	−	32.0867i	0.284419	−	1.02081i
$989$	−25.1784			−0.800628
$990$	−9.56856	+	7.26703i	−0.304109	+	0.230961i
$991$	57.2440			1.81842			0.909208	−	0.416342i	$-0.136688\pi$
$991$	57.2440			1.81842			0.909208	+	0.416342i	$0.136688\pi$
$992$	−4.56870	−	42.9080i	−0.145056	−	1.36233i
$993$		−	0.312084i		−	0.00990368i
$994$	22.3080	+	29.3731i	0.707565	+	0.931658i
$995$	14.4874			0.459280
$996$	−8.52807	−	2.37609i	−0.270222	−	0.0752893i
$997$	−41.0353			−1.29960			−0.649801	−	0.760104i	$-0.725148\pi$
$997$	−41.0353			−1.29960			−0.649801	+	0.760104i	$0.725148\pi$
$998$	−3.73489	+	2.83653i	−0.118226	+	0.0897889i
$999$	−30.4087			−0.962088

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	668.2.b.b.667.15	yes	60
4.3	odd	2	inner	668.2.b.b.667.13	✓	60
167.166	odd	2	inner	668.2.b.b.667.16	yes	60
668.667	even	2	inner	668.2.b.b.667.14	yes	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
668.2.b.b.667.13	✓	60	4.3	odd	2	inner
668.2.b.b.667.14	yes	60	668.667	even	2	inner
668.2.b.b.667.15	yes	60	1.1	even	1	trivial
668.2.b.b.667.16	yes	60	167.166	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 668 = 2^{2} \cdot 167 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	668.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.12623 + 0.855338i) q^{2} -0.530251i q^{3} +(0.536794 - 1.92662i) q^{4} -0.936151i q^{5} +(0.453544 + 0.597186i) q^{6} -2.10467i q^{7} +(1.04335 + 2.62896i) q^{8} +2.71883 q^{9} +O(q^{10})\)	\(q+(-1.12623 + 0.855338i) q^{2} -0.530251i q^{3} +(0.536794 - 1.92662i) q^{4} -0.936151i q^{5} +(0.453544 + 0.597186i) q^{6} -2.10467i q^{7} +(1.04335 + 2.62896i) q^{8} +2.71883 q^{9} +(0.800726 + 1.05432i) q^{10} +3.33803i q^{11} +(-1.02159 - 0.284636i) q^{12} +6.89163i q^{13} +(1.80021 + 2.37035i) q^{14} -0.496396 q^{15} +(-3.42370 - 2.06839i) q^{16} -4.43066i q^{17} +(-3.06204 + 2.32552i) q^{18} -2.41662i q^{19} +(-1.80360 - 0.502520i) q^{20} -1.11601 q^{21} +(-2.85514 - 3.75940i) q^{22} +4.70781 q^{23} +(1.39401 - 0.553240i) q^{24} +4.12362 q^{25} +(-5.89467 - 7.76157i) q^{26} -3.03242i q^{27} +(-4.05490 - 1.12977i) q^{28} +5.19782 q^{29} +(0.559056 - 0.424586i) q^{30} -7.62802i q^{31} +(5.62506 - 0.598937i) q^{32} +1.77000 q^{33} +(3.78971 + 4.98995i) q^{34} -1.97029 q^{35} +(1.45945 - 5.23815i) q^{36} -10.0279i q^{37} +(2.06702 + 2.72167i) q^{38} +3.65430 q^{39} +(2.46110 - 0.976738i) q^{40} +10.7614i q^{41} +(1.25688 - 0.954562i) q^{42} -5.34823 q^{43} +(6.43111 + 1.79183i) q^{44} -2.54524i q^{45} +(-5.30208 + 4.02677i) q^{46} -8.05982i q^{47} +(-1.09677 + 1.81542i) q^{48} +2.57036 q^{49} +(-4.64415 + 3.52709i) q^{50} -2.34936 q^{51} +(13.2775 + 3.69938i) q^{52} +4.37764i q^{53} +(2.59374 + 3.41521i) q^{54} +3.12490 q^{55} +(5.53309 - 2.19592i) q^{56} -1.28141 q^{57} +(-5.85394 + 4.44589i) q^{58} -3.05853 q^{59} +(-0.266462 + 0.956364i) q^{60} +4.51224 q^{61} +(6.52453 + 8.59091i) q^{62} -5.72225i q^{63} +(-5.82282 + 5.48587i) q^{64} +6.45161 q^{65} +(-1.99342 + 1.51394i) q^{66} -11.1425 q^{67} +(-8.53619 - 2.37835i) q^{68} -2.49632i q^{69} +(2.21900 - 1.68526i) q^{70} +12.3919 q^{71} +(2.83671 + 7.14769i) q^{72} -5.90507i q^{73} +(8.57720 + 11.2937i) q^{74} -2.18656i q^{75} +(-4.65589 - 1.29722i) q^{76} +7.02546 q^{77} +(-4.11558 + 3.12566i) q^{78} -17.0408 q^{79} +(-1.93633 + 3.20511i) q^{80} +6.54856 q^{81} +(-9.20466 - 12.1199i) q^{82} +8.34783 q^{83} +(-0.599065 + 2.15011i) q^{84} -4.14777 q^{85} +(6.02334 - 4.57454i) q^{86} -2.75615i q^{87} +(-8.77554 + 3.48275i) q^{88} +8.03271 q^{89} +(2.17704 + 2.86653i) q^{90} +14.5046 q^{91} +(2.52712 - 9.07014i) q^{92} -4.04477 q^{93} +(6.89387 + 9.07722i) q^{94} -2.26232 q^{95} +(-0.317587 - 2.98269i) q^{96} -6.12006 q^{97} +(-2.89482 + 2.19852i) q^{98} +9.07555i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q - 2 q^{2} + 2 q^{4} - 8 q^{6} - 8 q^{8} - 16 q^{9}+O(q^{10}) \) 60 * q - 2 * q^2 + 2 * q^4 - 8 * q^6 - 8 * q^8 - 16 * q^9	\( 60 q - 2 q^{2} + 2 q^{4} - 8 q^{6} - 8 q^{8} - 16 q^{9} + 18 q^{12} + 10 q^{14} + 10 q^{16} - 20 q^{18} + 20 q^{22} + 10 q^{24} - 188 q^{25} + 4 q^{29} + 18 q^{32} + 8 q^{33} + 30 q^{36} - 36 q^{38} + 14 q^{42} + 28 q^{44} - 28 q^{48} + 72 q^{49} - 40 q^{50} - 74 q^{54} + 50 q^{56} + 8 q^{57} - 22 q^{58} + 36 q^{61} + 104 q^{62} + 8 q^{64} + 24 q^{65} + 24 q^{66} + 90 q^{72} - 36 q^{76} - 84 q^{81} - 110 q^{84} - 16 q^{85} - 20 q^{88} + 28 q^{89} + 72 q^{93} + 90 q^{94} + 2 q^{96} - 4 q^{97} - 114 q^{98}+O(q^{100}) \) 60 * q - 2 * q^2 + 2 * q^4 - 8 * q^6 - 8 * q^8 - 16 * q^9 + 18 * q^12 + 10 * q^14 + 10 * q^16 - 20 * q^18 + 20 * q^22 + 10 * q^24 - 188 * q^25 + 4 * q^29 + 18 * q^32 + 8 * q^33 + 30 * q^36 - 36 * q^38 + 14 * q^42 + 28 * q^44 - 28 * q^48 + 72 * q^49 - 40 * q^50 - 74 * q^54 + 50 * q^56 + 8 * q^57 - 22 * q^58 + 36 * q^61 + 104 * q^62 + 8 * q^64 + 24 * q^65 + 24 * q^66 + 90 * q^72 - 36 * q^76 - 84 * q^81 - 110 * q^84 - 16 * q^85 - 20 * q^88 + 28 * q^89 + 72 * q^93 + 90 * q^94 + 2 * q^96 - 4 * q^97 - 114 * q^98

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