LMFDB - Embedded newform 357.2.d.b.188.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [357,2,Mod(188,357)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(357, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1, 0]))

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

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

chi := DirichletCharacter("357.188");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 357 = 3 \cdot 7 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	357.d (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:	$2.85065935216$
Analytic rank:	$0$
Dimension:	$22$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			188.7
Character	$\chi$	$=$	357.188
Dual form			357.2.d.b.188.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.22862i q^{2} +(0.136369 - 1.72667i) q^{3} +0.490482 q^{4} -3.00418 q^{5} +(-2.12143 - 0.167546i) q^{6} +(0.249788 - 2.63393i) q^{7} -3.05987i q^{8} +(-2.96281 - 0.470928i) q^{9} +O(q^{10})$	\(q-1.22862i q^{2} +(0.136369 - 1.72667i) q^{3} +0.490482 q^{4} -3.00418 q^{5} +(-2.12143 - 0.167546i) q^{6} +(0.249788 - 2.63393i) q^{7} -3.05987i q^{8} +(-2.96281 - 0.470928i) q^{9} +3.69101i q^{10} +2.71004i q^{11} +(0.0668864 - 0.846903i) q^{12} +2.99346i q^{13} +(-3.23612 - 0.306895i) q^{14} +(-0.409677 + 5.18725i) q^{15} -2.77846 q^{16} +1.00000 q^{17} +(-0.578594 + 3.64018i) q^{18} -6.46312i q^{19} -1.47350 q^{20} +(-4.51388 - 0.790488i) q^{21} +3.32962 q^{22} -0.531589i q^{23} +(-5.28339 - 0.417270i) q^{24} +4.02512 q^{25} +3.67784 q^{26} +(-1.21717 + 5.05158i) q^{27} +(0.122516 - 1.29190i) q^{28} -8.12374i q^{29} +(6.37318 + 0.503339i) q^{30} +4.76164i q^{31} -2.70605i q^{32} +(4.67936 + 0.369565i) q^{33} -1.22862i q^{34} +(-0.750409 + 7.91282i) q^{35} +(-1.45320 - 0.230982i) q^{36} +0.597131 q^{37} -7.94075 q^{38} +(5.16873 + 0.408214i) q^{39} +9.19240i q^{40} -4.72816 q^{41} +(-0.971213 + 5.54587i) q^{42} +8.79033 q^{43} +1.32923i q^{44} +(8.90082 + 1.41476i) q^{45} -0.653123 q^{46} +5.20995 q^{47} +(-0.378895 + 4.79750i) q^{48} +(-6.87521 - 1.31585i) q^{49} -4.94536i q^{50} +(0.136369 - 1.72667i) q^{51} +1.46824i q^{52} -1.86825i q^{53} +(6.20650 + 1.49545i) q^{54} -8.14147i q^{55} +(-8.05949 - 0.764318i) q^{56} +(-11.1597 - 0.881367i) q^{57} -9.98102 q^{58} +14.9324 q^{59} +(-0.200939 + 2.54425i) q^{60} -8.34042i q^{61} +5.85027 q^{62} +(-1.98047 + 7.68621i) q^{63} -8.88164 q^{64} -8.99290i q^{65} +(0.454056 - 5.74918i) q^{66} +6.91945 q^{67} +0.490482 q^{68} +(-0.917881 - 0.0724921i) q^{69} +(9.72189 + 0.921971i) q^{70} -13.5527i q^{71} +(-1.44098 + 9.06580i) q^{72} -4.26626i q^{73} -0.733650i q^{74} +(0.548901 - 6.95008i) q^{75} -3.17004i q^{76} +(7.13807 + 0.676936i) q^{77} +(0.501542 - 6.35043i) q^{78} -14.5621 q^{79} +8.34702 q^{80} +(8.55645 + 2.79054i) q^{81} +5.80913i q^{82} -3.09582 q^{83} +(-2.21398 - 0.387720i) q^{84} -3.00418 q^{85} -10.8000i q^{86} +(-14.0270 - 1.10782i) q^{87} +8.29237 q^{88} +9.36351 q^{89} +(1.73820 - 10.9358i) q^{90} +(7.88457 + 0.747730i) q^{91} -0.260735i q^{92} +(8.22181 + 0.649339i) q^{93} -6.40108i q^{94} +19.4164i q^{95} +(-4.67246 - 0.369020i) q^{96} +5.63662i q^{97} +(-1.61668 + 8.44705i) q^{98} +(1.27624 - 8.02933i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q - 24 q^{4} + 5 q^{6} - 2 q^{7} - 4 q^{9}+O(q^{10}) $ 22 * q - 24 * q^4 + 5 * q^6 - 2 * q^7 - 4 * q^9	$ 22 q - 24 q^{4} + 5 q^{6} - 2 q^{7} - 4 q^{9} - 8 q^{14} - 4 q^{15} + 20 q^{16} + 22 q^{17} + 8 q^{18} - 30 q^{20} - 4 q^{21} - 12 q^{22} - 44 q^{24} + 14 q^{25} - 24 q^{26} + 6 q^{27} + 8 q^{28} + 5 q^{30} + 28 q^{33} + 10 q^{35} - 3 q^{36} - 16 q^{37} + 88 q^{38} - 14 q^{39} - 16 q^{41} + 19 q^{42} - 24 q^{43} - 46 q^{45} + 4 q^{46} - 16 q^{47} + 25 q^{48} + 6 q^{49} + 36 q^{54} - 40 q^{56} - 6 q^{57} + 24 q^{58} + 24 q^{59} - 21 q^{60} - 20 q^{62} - 6 q^{63} - 20 q^{64} - 116 q^{66} + 8 q^{67} - 24 q^{68} + 6 q^{69} + 4 q^{70} - 7 q^{72} + 54 q^{75} + 6 q^{77} + 2 q^{78} + 16 q^{79} + 128 q^{80} - 4 q^{81} + 8 q^{83} + 42 q^{84} - 48 q^{87} + 32 q^{88} - 100 q^{89} + 47 q^{90} + 18 q^{91} + 20 q^{93} + 88 q^{96} - 8 q^{98} + 18 q^{99}+O(q^{100}) $ 22 * q - 24 * q^4 + 5 * q^6 - 2 * q^7 - 4 * q^9 - 8 * q^14 - 4 * q^15 + 20 * q^16 + 22 * q^17 + 8 * q^18 - 30 * q^20 - 4 * q^21 - 12 * q^22 - 44 * q^24 + 14 * q^25 - 24 * q^26 + 6 * q^27 + 8 * q^28 + 5 * q^30 + 28 * q^33 + 10 * q^35 - 3 * q^36 - 16 * q^37 + 88 * q^38 - 14 * q^39 - 16 * q^41 + 19 * q^42 - 24 * q^43 - 46 * q^45 + 4 * q^46 - 16 * q^47 + 25 * q^48 + 6 * q^49 + 36 * q^54 - 40 * q^56 - 6 * q^57 + 24 * q^58 + 24 * q^59 - 21 * q^60 - 20 * q^62 - 6 * q^63 - 20 * q^64 - 116 * q^66 + 8 * q^67 - 24 * q^68 + 6 * q^69 + 4 * q^70 - 7 * q^72 + 54 * q^75 + 6 * q^77 + 2 * q^78 + 16 * q^79 + 128 * q^80 - 4 * q^81 + 8 * q^83 + 42 * q^84 - 48 * q^87 + 32 * q^88 - 100 * q^89 + 47 * q^90 + 18 * q^91 + 20 * q^93 + 88 * q^96 - 8 * q^98 + 18 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/357\mathbb{Z}\right)^\times$.

$n$	$52$	$190$	$239$
$\chi(n)$	$-1$	$1$	$-1$

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 $

$2$		−	1.22862i		−	0.868769i	−0.900728	−	0.434384i	$-0.856966\pi$
$2$		−	1.22862i		−	0.868769i	0.900728	−	0.434384i	$-0.143034\pi$
$3$	0.136369	−	1.72667i	0.0787325	−	0.996896i
$3$	0.136369	−	1.72667i	0.0787325	−	0.996896i
$4$	0.490482			0.245241
$5$	−3.00418			−1.34351			−0.671756	−	0.740772i	$-0.734460\pi$
$5$	−3.00418			−1.34351			−0.671756	+	0.740772i	$0.734460\pi$
$6$	−2.12143	−	0.167546i	−0.866072	−	0.0684003i
$7$	0.249788	−	2.63393i	0.0944109	−	0.995533i
$7$	0.249788	−	2.63393i	0.0944109	−	0.995533i
$8$		−	3.05987i		−	1.08183i
$9$	−2.96281	−	0.470928i	−0.987602	−	0.156976i
$10$			3.69101i			1.16720i
$11$			2.71004i			0.817109i	0.912734	+	0.408554i	$0.133967\pi$
$11$			2.71004i			0.817109i	−0.912734	+	0.408554i	$0.866033\pi$
$12$	0.0668864	−	0.846903i	0.0193084	−	0.244480i
$13$			2.99346i			0.830236i	0.909768	+	0.415118i	$0.136260\pi$
$13$			2.99346i			0.830236i	−0.909768	+	0.415118i	$0.863740\pi$
$14$	−3.23612	−	0.306895i	−0.864888	−	0.0820213i
$15$	−0.409677	+	5.18725i	−0.105778	+	1.33934i
$16$	−2.77846			−0.694616
$17$	1.00000			0.242536
$17$	1.00000			0.242536
$18$	−0.578594	+	3.64018i	−0.136376	+	0.857998i
$19$		−	6.46312i		−	1.48274i	−0.671096	−	0.741371i	$-0.734176\pi$
$19$		−	6.46312i		−	1.48274i	0.671096	−	0.741371i	$-0.265824\pi$
$20$	−1.47350			−0.329484
$21$	−4.51388	−	0.790488i	−0.985010	−	0.172499i
$22$	3.32962			0.709878
$23$		−	0.531589i		−	0.110844i	−0.998463	−	0.0554220i	$-0.982350\pi$
$23$		−	0.531589i		−	0.110844i	0.998463	−	0.0554220i	$-0.0176504\pi$
$24$	−5.28339	−	0.417270i	−1.07847	−	0.0851749i
$25$	4.02512			0.805025
$26$	3.67784			0.721283
$27$	−1.21717	+	5.05158i	−0.234245	+	0.972178i
$28$	0.122516	−	1.29190i	0.0231534	−	0.244146i
$29$		−	8.12374i		−	1.50854i	−0.656564	−	0.754270i	$-0.727991\pi$
$29$		−	8.12374i		−	1.50854i	0.656564	−	0.754270i	$-0.272009\pi$
$30$	6.37318	+	0.503339i	1.16358	+	0.0918966i
$31$			4.76164i			0.855217i	0.903964	+	0.427608i	$0.140644\pi$
$31$			4.76164i			0.855217i	−0.903964	+	0.427608i	$0.859356\pi$
$32$		−	2.70605i		−	0.478366i
$33$	4.67936	+	0.369565i	0.814572	+	0.0643330i
$34$		−	1.22862i		−	0.210707i
$35$	−0.750409	+	7.91282i	−0.126842	+	1.33751i
$36$	−1.45320	−	0.230982i	−0.242201	−	0.0384970i
$37$	0.597131			0.0981678			0.0490839	−	0.998795i	$-0.484370\pi$
$37$	0.597131			0.0981678			0.0490839	+	0.998795i	$0.484370\pi$
$38$	−7.94075			−1.28816
$39$	5.16873	+	0.408214i	0.827659	+	0.0653666i
$40$			9.19240i			1.45345i
$41$	−4.72816			−0.738414			−0.369207	−	0.929347i	$-0.620371\pi$
$41$	−4.72816			−0.738414			−0.369207	+	0.929347i	$0.620371\pi$
$42$	−0.971213	+	5.54587i	−0.149861	+	0.855746i
$43$	8.79033			1.34051			0.670256	−	0.742130i	$-0.266184\pi$
$43$	8.79033			1.34051			0.670256	+	0.742130i	$0.266184\pi$
$44$			1.32923i			0.200389i
$45$	8.90082	+	1.41476i	1.32686	+	0.210899i
$46$	−0.653123			−0.0962977
$47$	5.20995			0.759950			0.379975	−	0.924997i	$-0.375933\pi$
$47$	5.20995			0.759950			0.379975	+	0.924997i	$0.375933\pi$
$48$	−0.378895	+	4.79750i	−0.0546888	+	0.692460i
$49$	−6.87521	−	1.31585i	−0.982173	−	0.187978i
$50$		−	4.94536i		−	0.699380i
$51$	0.136369	−	1.72667i	0.0190954	−	0.241783i
$52$			1.46824i			0.203608i
$53$		−	1.86825i		−	0.256624i	−0.991734	−	0.128312i	$-0.959044\pi$
$53$		−	1.86825i		−	0.256624i	0.991734	−	0.128312i	$-0.0409558\pi$
$54$	6.20650	+	1.49545i	0.844597	+	0.203505i
$55$		−	8.14147i		−	1.09780i
$56$	−8.05949	−	0.764318i	−1.07699	−	0.102136i
$57$	−11.1597	−	0.881367i	−1.47814	−	0.116740i
$58$	−9.98102			−1.31057
$59$	14.9324			1.94404			0.972019	−	0.234902i	$-0.0754770\pi$
$59$	14.9324			1.94404			0.972019	+	0.234902i	$0.0754770\pi$
$60$	−0.200939	+	2.54425i	−0.0259411	+	0.328461i
$61$		−	8.34042i		−	1.06788i	−0.845522	−	0.533941i	$-0.820711\pi$
$61$		−	8.34042i		−	1.06788i	0.845522	−	0.533941i	$-0.179289\pi$
$62$	5.85027			0.742985
$63$	−1.98047	+	7.68621i	−0.249515	+	0.968371i
$64$	−8.88164			−1.11021
$65$		−	8.99290i		−	1.11543i
$66$	0.454056	−	5.74918i	0.0558905	−	0.707675i
$67$	6.91945			0.845346			0.422673	−	0.906282i	$-0.361092\pi$
$67$	6.91945			0.845346			0.422673	+	0.906282i	$0.361092\pi$
$68$	0.490482			0.0594797
$69$	−0.917881	−	0.0724921i	−0.110500	−	0.00872702i
$70$	9.72189	+	0.921971i	1.16199	+	0.110197i
$71$		−	13.5527i		−	1.60840i	−0.594356	−	0.804202i	$-0.702593\pi$
$71$		−	13.5527i		−	1.60840i	0.594356	−	0.804202i	$-0.297407\pi$
$72$	−1.44098	+	9.06580i	−0.169821	+	1.06841i
$73$		−	4.26626i		−	0.499327i	−0.968333	−	0.249664i	$-0.919680\pi$
$73$		−	4.26626i		−	0.499327i	0.968333	−	0.249664i	$-0.0803201\pi$
$74$		−	0.733650i		−	0.0852851i
$75$	0.548901	−	6.95008i	0.0633816	−	0.802526i
$76$		−	3.17004i		−	0.363629i
$77$	7.13807	+	0.676936i	0.813459	+	0.0771440i
$78$	0.501542	−	6.35043i	0.0567884	−	0.719044i
$79$	−14.5621			−1.63837			−0.819183	−	0.573533i	$-0.805572\pi$
$79$	−14.5621			−1.63837			−0.819183	+	0.573533i	$0.805572\pi$
$80$	8.34702			0.933225
$81$	8.55645	+	2.79054i	0.950717	+	0.310060i
$82$			5.80913i			0.641511i
$83$	−3.09582			−0.339810			−0.169905	−	0.985460i	$-0.554346\pi$
$83$	−3.09582			−0.339810			−0.169905	+	0.985460i	$0.554346\pi$
$84$	−2.21398	−	0.387720i	−0.241565	−	0.0423037i
$85$	−3.00418			−0.325850
$86$		−	10.8000i		−	1.16460i
$87$	−14.0270	−	1.10782i	−1.50386	−	0.118771i
$88$	8.29237			0.883970
$89$	9.36351			0.992530			0.496265	−	0.868171i	$-0.334704\pi$
$89$	9.36351			0.992530			0.496265	+	0.868171i	$0.334704\pi$
$90$	1.73820	−	10.9358i	0.183223	−	1.15273i
$91$	7.88457	+	0.747730i	0.826528	+	0.0783834i
$92$		−	0.260735i		−	0.0271835i
$93$	8.22181	+	0.649339i	0.852562	+	0.0673333i
$94$		−	6.40108i		−	0.660221i
$95$			19.4164i			1.99208i
$96$	−4.67246	−	0.369020i	−0.476881	−	0.0376629i
$97$			5.63662i			0.572312i	0.958183	+	0.286156i	$0.0923776\pi$
$97$			5.63662i			0.572312i	−0.958183	+	0.286156i	$0.907622\pi$
$98$	−1.61668	+	8.44705i	−0.163310	+	0.853281i
$99$	1.27624	−	8.02933i	0.128267	−	0.806978i
$100$	1.97425			0.197425
$101$	10.4805			1.04285			0.521424	−	0.853298i	$-0.325401\pi$
$101$	10.4805			1.04285			0.521424	+	0.853298i	$0.325401\pi$
$102$	−2.12143	−	0.167546i	−0.210053	−	0.0165895i
$103$			9.10806i			0.897444i	0.893671	+	0.448722i	$0.148121\pi$
$103$			9.10806i			0.897444i	−0.893671	+	0.448722i	$0.851879\pi$
$104$	9.15959			0.898171
$105$	13.5605	+	2.37477i	1.32337	+	0.231754i
$106$	−2.29538			−0.222947
$107$			3.78210i			0.365629i	0.983147	+	0.182815i	$0.0585208\pi$
$107$			3.78210i			0.365629i	−0.983147	+	0.182815i	$0.941479\pi$
$108$	−0.597002	+	2.47771i	−0.0574465	+	0.238418i
$109$	1.21102			0.115994			0.0579972	−	0.998317i	$-0.481529\pi$
$109$	1.21102			0.115994			0.0579972	+	0.998317i	$0.481529\pi$
$110$	−10.0028			−0.953730
$111$	0.0814300	−	1.03105i	0.00772899	−	0.0978630i
$112$	−0.694026	+	7.31829i	−0.0655793	+	0.691513i
$113$			12.7701i			1.20131i	0.799508	+	0.600656i	$0.205094\pi$
$113$			12.7701i			1.20131i	−0.799508	+	0.600656i	$0.794906\pi$
$114$	−1.08287	+	13.7111i	−0.101420	+	1.28416i
$115$			1.59699i			0.148920i
$116$		−	3.98455i		−	0.369956i
$117$	1.40971	−	8.86904i	0.130327	−	0.819943i
$118$		−	18.3464i		−	1.68892i
$119$	0.249788	−	2.63393i	0.0228980	−	0.241452i
$120$	15.8723	+	1.25356i	1.44893	+	0.114433i
$121$	3.65567			0.332334
$122$	−10.2472			−0.927742
$123$	−0.644772	+	8.16399i	−0.0581372	+	0.736122i
$124$			2.33550i			0.209734i
$125$	2.92871			0.261952
$126$	9.44346	+	2.43325i	0.841290	+	0.216771i
$127$	3.20497			0.284395			0.142198	−	0.989838i	$-0.454583\pi$
$127$	3.20497			0.284395			0.142198	+	0.989838i	$0.454583\pi$
$128$			5.50011i			0.486146i
$129$	1.19873	−	15.1780i	0.105542	−	1.33635i
$130$	−11.0489			−0.969053
$131$	−16.4029			−1.43313			−0.716563	−	0.697522i	$-0.754286\pi$
$131$	−16.4029			−1.43313			−0.716563	+	0.697522i	$0.754286\pi$
$132$	2.29514	+	0.181265i	0.199766	+	0.0157771i
$133$	−17.0234	−	1.61441i	−1.47612	−	0.139987i
$134$		−	8.50141i		−	0.734410i
$135$	3.65662	−	15.1759i	0.314711	−	1.30613i
$136$		−	3.05987i		−	0.262381i
$137$		−	2.68829i		−	0.229676i	−0.993384	−	0.114838i	$-0.963365\pi$
$137$		−	2.68829i		−	0.229676i	0.993384	−	0.114838i	$-0.0366349\pi$
$138$	−0.0890655	+	1.12773i	−0.00758176	+	0.0959988i
$139$			5.43082i			0.460636i	0.973115	+	0.230318i	$0.0739767\pi$
$139$			5.43082i			0.460636i	−0.973115	+	0.230318i	$0.926023\pi$
$140$	−0.368062	+	3.88110i	−0.0311069	+	0.328013i
$141$	0.710475	−	8.99589i	0.0598327	−	0.757591i
$142$	−16.6511			−1.39733
$143$	−8.11240			−0.678393
$144$	8.23205	+	1.30846i	0.686004	+	0.109038i
$145$			24.4052i			2.02674i
$146$	−5.24163			−0.433800
$147$	−3.20961	+	11.6918i	−0.264724	+	0.964324i
$148$	0.292882			0.0240748
$149$		−	10.6857i		−	0.875407i	−0.899119	−	0.437704i	$-0.855792\pi$
$149$		−	10.6857i		−	0.875407i	0.899119	−	0.437704i	$-0.144208\pi$
$150$	−8.53903	−	0.674393i	−0.697209	−	0.0550639i
$151$	−24.1137			−1.96235			−0.981175	−	0.193123i	$-0.938138\pi$
$151$	−24.1137			−1.96235			−0.981175	+	0.193123i	$0.938138\pi$
$152$	−19.7763			−1.60407
$153$	−2.96281	−	0.470928i	−0.239529	−	0.0380723i
$154$	0.831700	−	8.77001i	0.0670203	−	0.706708i
$155$		−	14.3049i		−	1.14899i
$156$	2.53517	+	0.200222i	0.202976	+	0.0160306i
$157$			8.02899i			0.640783i	0.947285	+	0.320391i	$0.103814\pi$
$157$			8.02899i			0.640783i	−0.947285	+	0.320391i	$0.896186\pi$
$158$			17.8914i			1.42336i
$159$	−3.22586	−	0.254771i	−0.255827	−	0.0202046i
$160$			8.12946i			0.642690i
$161$	−1.40017	−	0.132784i	−0.110349	−	0.0104649i
$162$	3.42853	−	10.5127i	0.269370	−	0.825953i
$163$	20.1216			1.57605			0.788024	−	0.615645i	$-0.211104\pi$
$163$	20.1216			1.57605			0.788024	+	0.615645i	$0.211104\pi$
$164$	−2.31908			−0.181089
$165$	−14.0577	−	1.11024i	−1.09439	−	0.0864321i
$166$			3.80360i			0.295216i
$167$	10.7807			0.834236			0.417118	−	0.908852i	$-0.363040\pi$
$167$	10.7807			0.834236			0.417118	+	0.908852i	$0.363040\pi$
$168$	−2.41879	+	13.8119i	−0.186614	+	1.06561i
$169$	4.03920			0.310708
$170$			3.69101i			0.283088i
$171$	−3.04367	+	19.1490i	−0.232755	+	1.46436i
$172$	4.31150			0.328749
$173$	−6.17862			−0.469752			−0.234876	−	0.972025i	$-0.575468\pi$
$173$	−6.17862			−0.469752			−0.234876	+	0.972025i	$0.575468\pi$
$174$	−1.36110	+	17.2340i	−0.103185	+	1.30650i
$175$	1.00543	−	10.6019i	0.0760031	−	0.801429i
$176$		−	7.52975i		−	0.567577i
$177$	2.03632	−	25.7835i	0.153059	−	1.93800i
$178$		−	11.5042i		−	0.862279i
$179$			21.8189i			1.63082i	0.578883	+	0.815411i	$0.303489\pi$
$179$			21.8189i			1.63082i	−0.578883	+	0.815411i	$0.696511\pi$
$180$	4.36569	+	0.693912i	0.325399	+	0.0517212i
$181$			9.03021i			0.671211i	0.942003	+	0.335605i	$0.108941\pi$
$181$			9.03021i			0.671211i	−0.942003	+	0.335605i	$0.891059\pi$
$182$	0.918679	−	9.68718i	0.0680970	−	0.718061i
$183$	−14.4012	−	1.13737i	−1.06457	−	0.0840770i
$184$	−1.62659			−0.119914
$185$	−1.79389			−0.131890
$186$	0.797794	−	10.1015i	0.0584971	−	0.740679i
$187$			2.71004i			0.198178i
$188$	2.55539			0.186371
$189$	13.0015	+	4.46778i	0.945720	+	0.324983i
$190$	23.8555			1.73066
$191$			20.8478i			1.50849i	0.656591	+	0.754247i	$0.271998\pi$
$191$			20.8478i			1.50849i	−0.656591	+	0.754247i	$0.728002\pi$
$192$	−1.21118	+	15.3357i	−0.0874092	+	1.10676i
$193$	9.78332			0.704218			0.352109	−	0.935959i	$-0.385465\pi$
$193$	9.78332			0.704218			0.352109	+	0.935959i	$0.385465\pi$
$194$	6.92529			0.497207
$195$	−15.5278	−	1.22635i	−1.11197	−	0.0878208i
$196$	−3.37217	−	0.645400i	−0.240869	−	0.0461000i
$197$			13.1357i			0.935878i	0.883761	+	0.467939i	$0.155003\pi$
$197$			13.1357i			0.935878i	−0.883761	+	0.467939i	$0.844997\pi$
$198$	−9.86504	−	1.56802i	−0.701078	−	0.111434i
$199$		−	3.64836i		−	0.258625i	−0.991604	−	0.129313i	$-0.958723\pi$
$199$		−	3.64836i		−	0.258625i	0.991604	−	0.129313i	$-0.0412771\pi$
$200$		−	12.3163i		−	0.870897i
$201$	0.943597	−	11.9476i	0.0665562	−	0.842722i
$202$		−	12.8766i		−	0.905993i
$203$	−21.3974	−	2.02921i	−1.50180	−	0.142423i
$204$	0.0668864	−	0.846903i	0.00468298	−	0.0592950i
$205$	14.2043			0.992068
$206$	11.1904			0.779671
$207$	−0.250340	+	1.57500i	−0.0173999	+	0.109470i
$208$		−	8.31722i		−	0.576695i
$209$	17.5153			1.21156
$210$	2.91770	−	16.6608i	0.201341	−	1.14970i
$211$	−11.7832			−0.811191			−0.405595	−	0.914053i	$-0.632936\pi$
$211$	−11.7832			−0.811191			−0.405595	+	0.914053i	$0.632936\pi$
$212$		−	0.916342i		−	0.0629346i
$213$	−23.4010	−	1.84816i	−1.60341	−	0.126634i
$214$	4.64678			0.317647
$215$	−26.4078			−1.80100
$216$	15.4572	+	3.72439i	1.05173	+	0.253413i
$217$	12.5419	+	1.18940i	0.851397	+	0.0807418i
$218$		−	1.48789i		−	0.100772i
$219$	−7.36643	−	0.581784i	−0.497777	−	0.0393133i
$220$		−	3.99324i		−	0.269224i
$221$			2.99346i			0.201362i
$222$	−1.26677	−	0.100047i	−0.0850203	−	0.00671471i
$223$		−	3.55814i		−	0.238271i	−0.992878	−	0.119135i	$-0.961988\pi$
$223$		−	3.55814i		−	0.238271i	0.992878	−	0.119135i	$-0.0380122\pi$
$224$	−7.12755	−	0.675937i	−0.476229	−	0.0451630i
$225$	−11.9257	−	1.89555i	−0.795044	−	0.126370i
$226$	15.6897			1.04366
$227$	7.93223			0.526481			0.263240	−	0.964730i	$-0.415209\pi$
$227$	7.93223			0.526481			0.263240	+	0.964730i	$0.415209\pi$
$228$	−5.47363	−	0.432295i	−0.362500	−	0.0286294i
$229$		−	0.974888i		−	0.0644224i	−0.999481	−	0.0322112i	$-0.989745\pi$
$229$		−	0.974888i		−	0.0644224i	0.999481	−	0.0322112i	$-0.0102549\pi$
$230$	1.96210			0.129377
$231$	2.14226	−	12.2328i	0.140950	−	0.804860i
$232$	−24.8576			−1.63198
$233$			19.3740i			1.26924i	0.772826	+	0.634618i	$0.218843\pi$
$233$			19.3740i			1.26924i	−0.772826	+	0.634618i	$0.781157\pi$
$234$	−10.8967	−	1.73200i	−0.712341	−	0.113224i
$235$	−15.6517			−1.02100
$236$	7.32409			0.476758
$237$	−1.98582	+	25.1440i	−0.128993	+	1.63328i
$238$	−3.23612	−	0.306895i	−0.209766	−	0.0198931i
$239$			18.0965i			1.17057i	0.810829	+	0.585283i	$0.199017\pi$
$239$			18.0965i			1.17057i	−0.810829	+	0.585283i	$0.800983\pi$
$240$	1.13827	−	14.4126i	0.0734751	−	0.930328i
$241$		−	3.49419i		−	0.225081i	−0.993647	−	0.112540i	$-0.964101\pi$
$241$		−	3.49419i		−	0.225081i	0.993647	−	0.112540i	$-0.0358988\pi$
$242$		−	4.49144i		−	0.288721i
$243$	5.98519	−	14.3937i	0.383950	−	0.923354i
$244$		−	4.09083i		−	0.261888i
$245$	20.6544	+	3.95305i	1.31956	+	0.252551i
$246$	10.0305	+	0.792183i	0.639520	+	0.0505078i
$247$	19.3471			1.23103
$248$	14.5700			0.925196
$249$	−0.422172	+	5.34547i	−0.0267541	+	0.338755i
$250$		−	3.59828i		−	0.227575i
$251$	−23.3779			−1.47560			−0.737799	−	0.675020i	$-0.764135\pi$
$251$	−23.3779			−1.47560			−0.737799	+	0.675020i	$0.764135\pi$
$252$	−0.971384	+	3.76995i	−0.0611914	+	0.237484i
$253$	1.44063			0.0905715
$254$		−	3.93770i		−	0.247073i
$255$	−0.409677	+	5.18725i	−0.0256549	+	0.324838i
$256$	−11.0057			−0.687857
$257$	−15.4048			−0.960925			−0.480463	−	0.877015i	$-0.659531\pi$
$257$	−15.4048			−0.960925			−0.480463	+	0.877015i	$0.659531\pi$
$258$	−18.6481	−	1.47278i	−1.16098	−	0.0916915i
$259$	0.149156	−	1.57280i	0.00926811	−	0.0977293i
$260$		−	4.41086i		−	0.273550i
$261$	−3.82570	+	24.0691i	−0.236805	+	1.48984i
$262$			20.1530i			1.24506i
$263$		−	13.4618i		−	0.830093i	−0.909800	−	0.415046i	$-0.863765\pi$
$263$		−	13.4618i		−	0.830093i	0.909800	−	0.415046i	$-0.136235\pi$
$264$	1.13082	−	14.3182i	0.0695971	−	0.881226i
$265$			5.61256i			0.344777i
$266$	−1.98350	+	20.9154i	−0.121616	+	1.28241i
$267$	1.27689	−	16.1677i	0.0781444	−	0.989449i
$268$	3.39387			0.207313
$269$	6.99859			0.426711			0.213356	−	0.976975i	$-0.431561\pi$
$269$	6.99859			0.426711			0.213356	+	0.976975i	$0.431561\pi$
$270$	−18.6455	−	4.49261i	−1.13473	−	0.273411i
$271$			0.552213i			0.0335446i	0.999859	+	0.0167723i	$0.00533903\pi$
$271$			0.552213i			0.0335446i	−0.999859	+	0.0167723i	$0.994661\pi$
$272$	−2.77846			−0.168469
$273$	2.36629	−	13.5121i	0.143215	−	0.817791i
$274$	−3.30290			−0.199536
$275$			10.9083i			0.657793i
$276$	−0.450204	−	0.0355560i	−0.0270991	−	0.00214022i
$277$	16.0296			0.963125			0.481563	−	0.876412i	$-0.340069\pi$
$277$	16.0296			0.963125			0.481563	+	0.876412i	$0.340069\pi$
$278$	6.67244			0.400186
$279$	2.24239	−	14.1078i	0.134249	−	0.844614i
$280$	24.2122	+	2.29615i	1.44695	+	0.137221i
$281$			5.67454i			0.338515i	0.985572	+	0.169257i	$0.0541369\pi$
$281$			5.67454i			0.338515i	−0.985572	+	0.169257i	$0.945863\pi$
$282$	−11.0526	−	0.872906i	−0.658171	−	0.0519808i
$283$		−	20.6342i		−	1.22657i	−0.789860	−	0.613287i	$-0.789847\pi$
$283$		−	20.6342i		−	1.22657i	0.789860	−	0.613287i	$-0.210153\pi$
$284$		−	6.64734i		−	0.394447i
$285$	33.5258	+	2.64779i	1.98590	+	0.156842i
$286$			9.96709i			0.589367i
$287$	−1.18104	+	12.4537i	−0.0697144	+	0.735116i
$288$	−1.27435	+	8.01749i	−0.0750920	+	0.472435i
$289$	1.00000			0.0588235
$290$	29.9848			1.76077
$291$	9.73261	+	0.768658i	0.570536	+	0.0450596i
$292$		−	2.09252i		−	0.122456i
$293$	6.67620			0.390028			0.195014	−	0.980800i	$-0.437525\pi$
$293$	6.67620			0.390028			0.195014	+	0.980800i	$0.437525\pi$
$294$	14.3648	+	3.94340i	0.837775	+	0.229984i
$295$	−44.8598			−2.61184
$296$		−	1.82714i		−	0.106200i
$297$	−13.6900	−	3.29859i	−0.794375	−	0.191404i
$298$	−13.1287			−0.760526
$299$	1.59129			0.0920266
$300$	0.269226	−	3.40889i	0.0155438	−	0.196812i
$301$	2.19572	−	23.1531i	0.126559	−	1.33453i
$302$			29.6267i			1.70483i
$303$	1.42921	−	18.0964i	0.0821060	−	1.03961i
$304$			17.9575i			1.02994i
$305$			25.0562i			1.43471i
$306$	−0.578594	+	3.64018i	−0.0330760	+	0.208095i
$307$		−	27.0663i		−	1.54476i	−0.635163	−	0.772378i	$-0.719067\pi$
$307$		−	27.0663i		−	1.54476i	0.635163	−	0.772378i	$-0.280933\pi$
$308$	3.50110	+	0.332025i	0.199493	+	0.0189189i
$309$	15.7266	+	1.24205i	0.894658	+	0.0706580i
$310$	−17.5753			−0.998210
$311$	−6.71135			−0.380566			−0.190283	−	0.981729i	$-0.560940\pi$
$311$	−6.71135			−0.380566			−0.190283	+	0.981729i	$0.560940\pi$
$312$	1.24908	−	15.8156i	0.0707153	−	0.895383i
$313$			1.29308i			0.0730890i	0.999332	+	0.0365445i	$0.0116351\pi$
$313$			1.29308i			0.0730890i	−0.999332	+	0.0365445i	$0.988365\pi$
$314$	9.86461			0.556692
$315$	5.94969	−	23.0908i	0.335227	−	1.30102i
$316$	−7.14245			−0.401794
$317$		−	29.8814i		−	1.67831i	−0.543894	−	0.839154i	$-0.683051\pi$
$317$		−	29.8814i		−	1.67831i	0.543894	−	0.839154i	$-0.316949\pi$
$318$	−0.313017	+	3.96337i	−0.0175531	+	0.222254i
$319$	22.0157			1.23264
$320$	26.6821			1.49157
$321$	6.53045	+	0.515760i	0.364494	+	0.0287869i
$322$	−0.163142	+	1.72028i	−0.00909156	+	0.0958676i
$323$		−	6.46312i		−	0.359618i
$324$	4.19679	+	1.36871i	0.233155	+	0.0760394i
$325$			12.0490i			0.668361i
$326$		−	24.7219i		−	1.36922i
$327$	0.165145	−	2.09103i	0.00913253	−	0.115634i
$328$			14.4675i			0.798836i
$329$	1.30138	−	13.7227i	0.0717476	−	0.756556i
$330$	−1.36407	+	17.2716i	−0.0750895	+	0.950769i
$331$	18.1791			0.999214			0.499607	−	0.866252i	$-0.333478\pi$
$331$	18.1791			0.999214			0.499607	+	0.866252i	$0.333478\pi$
$332$	−1.51844			−0.0833353
$333$	−1.76918	−	0.281206i	−0.0969507	−	0.0154100i
$334$		−	13.2454i		−	0.724758i
$335$	−20.7873			−1.13573
$336$	12.5417	+	2.19634i	0.684203	+	0.119820i
$337$	24.1849			1.31743			0.658717	−	0.752391i	$-0.271099\pi$
$337$	24.1849			1.31743			0.658717	+	0.752391i	$0.271099\pi$
$338$		−	4.96266i		−	0.269933i
$339$	22.0498	+	1.74144i	1.19758	+	0.0945822i
$340$	−1.47350			−0.0799117
$341$	−12.9043			−0.698805
$342$	23.5269	+	3.73952i	1.27219	+	0.202210i
$343$	−5.18320	+	17.7802i	−0.279867	+	0.960039i
$344$		−	26.8972i		−	1.45020i
$345$	2.75748	+	0.217779i	0.148458	+	0.0117249i
$346$			7.59120i			0.408106i
$347$			2.13217i			0.114461i	0.998361	+	0.0572305i	$0.0182270\pi$
$347$			2.13217i			0.114461i	−0.998361	+	0.0572305i	$0.981773\pi$
$348$	−6.88002	−	0.543367i	−0.368808	−	0.0291276i
$349$		−	17.7147i		−	0.948244i	−0.880459	−	0.474122i	$-0.842766\pi$
$349$		−	17.7147i		−	0.948244i	0.880459	−	0.474122i	$-0.157234\pi$
$350$	−13.0258	−	1.23529i	−0.696256	−	0.0660291i
$351$	−15.1217	−	3.64356i	−0.807137	−	0.194479i
$352$	7.33350			0.390877
$353$	−7.42870			−0.395390			−0.197695	−	0.980264i	$-0.563345\pi$
$353$	−7.42870			−0.395390			−0.197695	+	0.980264i	$0.563345\pi$
$354$	−31.6782	−	2.50187i	−1.68368	−	0.132973i
$355$			40.7147i			2.16091i
$356$	4.59263			0.243409
$357$	−4.51388	−	0.790488i	−0.238900	−	0.0418371i
$358$	26.8072			1.41681
$359$			11.9387i			0.630100i	0.949075	+	0.315050i	$0.102021\pi$
$359$			11.9387i			0.630100i	−0.949075	+	0.315050i	$0.897979\pi$
$360$	4.32897	−	27.2353i	0.228156	−	1.43543i
$361$	−22.7719			−1.19852
$362$	11.0947			0.583127
$363$	0.498519	−	6.31215i	0.0261654	−	0.331302i
$364$	3.86724	+	0.366748i	0.202699	+	0.0192228i
$365$			12.8166i			0.670853i
$366$	−1.39740	+	17.6937i	−0.0730434	+	0.924862i
$367$			26.5938i			1.38819i	0.719885	+	0.694094i	$0.244195\pi$
$367$			26.5938i			1.38819i	−0.719885	+	0.694094i	$0.755805\pi$
$368$			1.47700i			0.0769939i
$369$	14.0086	+	2.22662i	0.729259	+	0.115913i
$370$			2.20402i			0.114582i
$371$	−4.92084	−	0.466666i	−0.255477	−	0.0242281i
$372$	4.03265	+	0.318489i	0.209083	+	0.0165129i
$373$	−6.11354			−0.316547			−0.158274	−	0.987395i	$-0.550593\pi$
$373$	−6.11354			−0.316547			−0.158274	+	0.987395i	$0.550593\pi$
$374$	3.32962			0.172171
$375$	0.399384	−	5.05693i	0.0206241	−	0.261139i
$376$		−	15.9418i		−	0.822134i
$377$	24.3181			1.25244
$378$	5.48922	−	15.9740i	0.282335	−	0.821612i
$379$	20.6838			1.06246			0.531229	−	0.847228i	$-0.321730\pi$
$379$	20.6838			1.06246			0.531229	+	0.847228i	$0.321730\pi$
$380$			9.52340i			0.488540i
$381$	0.437057	−	5.53394i	0.0223911	−	0.283512i
$382$	25.6141			1.31053
$383$	−20.8998			−1.06793			−0.533964	−	0.845507i	$-0.679298\pi$
$383$	−20.8998			−1.06793			−0.533964	+	0.845507i	$0.679298\pi$
$384$	9.49690	+	0.750042i	0.484636	+	0.0382754i
$385$	−21.4441	−	2.03364i	−1.09289	−	0.103644i
$386$		−	12.0200i		−	0.611803i
$387$	−26.0441	−	4.13962i	−1.32389	−	0.210429i
$388$			2.76466i			0.140354i
$389$		−	9.80791i		−	0.497281i	−0.968596	−	0.248640i	$-0.920016\pi$
$389$		−	9.80791i		−	0.497281i	0.968596	−	0.248640i	$-0.0799837\pi$
$390$	−1.50672	+	19.0778i	−0.0762959	+	0.966044i
$391$		−	0.531589i		−	0.0268836i
$392$	−4.02632	+	21.0372i	−0.203360	+	1.06254i
$393$	−2.23684	+	28.3224i	−0.112834	+	1.42868i
$394$	16.1388			0.813062
$395$	43.7473			2.20116
$396$	0.625971	−	3.93824i	0.0314562	−	0.197904i
$397$			1.04327i			0.0523603i	0.999657	+	0.0261801i	$0.00833435\pi$
$397$			1.04327i			0.0523603i	−0.999657	+	0.0261801i	$0.991666\pi$
$398$	−4.48246			−0.224686
$399$	−5.10902	+	29.1738i	−0.255771	+	1.46051i
$400$	−11.1837			−0.559183
$401$		−	25.1455i		−	1.25571i	−0.778332	−	0.627853i	$-0.783934\pi$
$401$		−	25.1455i		−	1.25571i	0.778332	−	0.627853i	$-0.216066\pi$
$402$	−14.6792	−	1.15933i	−0.732130	−	0.0578219i
$403$	−14.2538			−0.710032
$404$	5.14049			0.255749
$405$	−25.7052	−	8.38330i	−1.27730	−	0.416569i
$406$	−2.49314	+	26.2894i	−0.123732	+	1.30472i
$407$			1.61825i			0.0802137i
$408$	−5.28339	−	0.417270i	−0.261567	−	0.0206579i
$409$		−	29.0276i		−	1.43532i	−0.696393	−	0.717660i	$-0.745213\pi$
$409$		−	29.0276i		−	1.43532i	0.696393	−	0.717660i	$-0.254787\pi$
$410$		−	17.4517i		−	0.861878i
$411$	−4.64180	−	0.366599i	−0.228963	−	0.0180830i
$412$			4.46734i			0.220090i
$413$	3.72994	−	39.3311i	0.183538	−	1.93535i
$414$	1.93508	+	0.307574i	0.0951039	+	0.0151164i
$415$	9.30040			0.456539
$416$	8.10044			0.397157
$417$	9.37726	+	0.740594i	0.459206	+	0.0362670i
$418$		−	21.5198i		−	1.05257i
$419$	32.3595			1.58087			0.790433	−	0.612548i	$-0.209855\pi$
$419$	32.3595			1.58087			0.790433	+	0.612548i	$0.209855\pi$
$420$	6.65120	+	1.16478i	0.324545	+	0.0568356i
$421$	−5.90023			−0.287559			−0.143780	−	0.989610i	$-0.545926\pi$
$421$	−5.90023			−0.287559			−0.143780	+	0.989610i	$0.545926\pi$
$422$			14.4772i			0.704737i
$423$	−15.4361	−	2.45352i	−0.750528	−	0.119294i
$424$	−5.71659			−0.277622
$425$	4.02512			0.195247
$426$	−2.27069	+	28.7511i	−0.110015	+	1.39299i
$427$	−21.9681	−	2.08334i	−1.06311	−	0.100820i
$428$			1.85505i			0.0896673i
$429$	−1.10628	+	14.0075i	−0.0534116	+	0.676287i
$430$			32.4452i			1.56465i
$431$			19.1252i			0.921231i	0.887600	+	0.460615i	$0.152371\pi$
$431$			19.1252i			0.921231i	−0.887600	+	0.460615i	$0.847629\pi$
$432$	3.38187	−	14.0356i	0.162710	−	0.675290i
$433$			18.0455i			0.867213i	0.901102	+	0.433606i	$0.142759\pi$
$433$			18.0455i			0.867213i	−0.901102	+	0.433606i	$0.857241\pi$
$434$	1.46133	−	15.4092i	0.0701459	−	0.739667i
$435$	42.1398	+	3.32811i	2.02045	+	0.159570i
$436$	0.593982			0.0284466
$437$	−3.43572			−0.164353
$438$	−0.714794	+	9.05058i	−0.0341542	+	0.432453i
$439$		−	28.8969i		−	1.37917i	−0.724203	−	0.689587i	$-0.757792\pi$
$439$		−	28.8969i		−	1.37917i	0.724203	−	0.689587i	$-0.242208\pi$
$440$	−24.9118			−1.18762
$441$	19.7503	+	7.13634i	0.940488	+	0.339826i
$442$	3.67784			0.174937
$443$		−	30.4478i		−	1.44662i	−0.690525	−	0.723309i	$-0.742620\pi$
$443$		−	30.4478i		−	1.44662i	0.690525	−	0.723309i	$-0.257380\pi$
$444$	0.0399399	−	0.505712i	0.00189547	−	0.0240000i
$445$	−28.1297			−1.33348
$446$	−4.37162			−0.207002
$447$	−18.4507	−	1.45720i	−0.872690	−	0.0689230i
$448$	−2.21853	+	23.3937i	−0.104816	+	1.10525i
$449$			19.0952i			0.901157i	0.892737	+	0.450579i	$0.148782\pi$
$449$			19.0952i			0.901157i	−0.892737	+	0.450579i	$0.851218\pi$
$450$	−2.32891	+	14.6522i	−0.109786	+	0.690710i
$451$		−	12.8135i		−	0.603364i
$452$			6.26351i			0.294611i
$453$	−3.28836	+	41.6366i	−0.154501	+	1.95626i
$454$		−	9.74574i		−	0.457390i
$455$	−23.6867	−	2.24632i	−1.11045	−	0.105309i
$456$	−2.69687	+	34.1472i	−0.126292	+	1.59909i
$457$	−28.2748			−1.32264			−0.661319	−	0.750104i	$-0.730003\pi$
$457$	−28.2748			−1.32264			−0.661319	+	0.750104i	$0.730003\pi$
$458$	−1.19777			−0.0559682
$459$	−1.21717	+	5.05158i	−0.0568128	+	0.235788i
$460$			0.783295i			0.0365213i
$461$	−20.6354			−0.961085			−0.480542	−	0.876972i	$-0.659560\pi$
$461$	−20.6354			−0.961085			−0.480542	+	0.876972i	$0.659560\pi$
$462$	−15.0295	−	2.63203i	−0.699237	−	0.122453i
$463$	−10.8622			−0.504809			−0.252404	−	0.967622i	$-0.581221\pi$
$463$	−10.8622			−0.504809			−0.252404	+	0.967622i	$0.581221\pi$
$464$			22.5715i			1.04786i
$465$	−24.6998	−	1.95073i	−1.14543	−	0.0904631i
$466$	23.8034			1.10267
$467$	34.9145			1.61565			0.807825	−	0.589422i	$-0.200645\pi$
$467$	34.9145			1.61565			0.807825	+	0.589422i	$0.200645\pi$
$468$	0.691435	−	4.35011i	0.0319616	−	0.201084i
$469$	1.72840	−	18.2254i	0.0798099	−	0.841570i
$470$			19.2300i			0.887014i
$471$	13.8634	+	1.09490i	0.638794	+	0.0504504i
$472$		−	45.6913i		−	2.10311i
$473$			23.8222i			1.09534i
$474$	30.8925	+	2.43982i	1.41894	+	0.112065i
$475$		−	26.0149i		−	1.19364i
$476$	0.122516	−	1.29190i	0.00561553	−	0.0592140i
$477$	−0.879811	+	5.53526i	−0.0402838	+	0.253442i
$478$	22.2338			1.01695
$479$	−19.0616			−0.870945			−0.435473	−	0.900202i	$-0.643419\pi$
$479$	−19.0616			−0.870945			−0.435473	+	0.900202i	$0.643419\pi$
$480$	14.0369	+	1.10860i	0.640695	+	0.0506006i
$481$			1.78749i			0.0815024i
$482$	−4.29305			−0.195543
$483$	−0.420215	+	2.39953i	−0.0191204	+	0.109182i
$484$	1.79304			0.0815018
$485$		−	16.9334i		−	0.768908i
$486$	−17.6844	−	7.35355i	−0.802181	−	0.333564i
$487$	−7.03914			−0.318974			−0.159487	−	0.987200i	$-0.550984\pi$
$487$	−7.03914			−0.318974			−0.159487	+	0.987200i	$0.550984\pi$
$488$	−25.5206			−1.15526
$489$	2.74396	−	34.7435i	0.124086	−	1.57115i
$490$	4.85682	−	25.3765i	0.219409	−	1.14639i
$491$			23.6946i			1.06932i	0.845067	+	0.534660i	$0.179560\pi$
$491$			23.6946i			1.06932i	−0.845067	+	0.534660i	$0.820440\pi$
$492$	−0.316249	+	4.00429i	−0.0142576	+	0.180527i
$493$		−	8.12374i		−	0.365875i
$494$		−	23.7703i		−	1.06948i
$495$	−3.83405	+	24.1216i	−0.172328	+	1.08419i
$496$		−	13.2301i		−	0.594047i
$497$	−35.6968	−	3.38529i	−1.60122	−	0.151851i
$498$	6.56757	+	0.518691i	0.294300	+	0.0232431i
$499$	2.86089			0.128071			0.0640355	−	0.997948i	$-0.479603\pi$
$499$	2.86089			0.128071			0.0640355	+	0.997948i	$0.479603\pi$
$500$	1.43648			0.0642413
$501$	1.47015	−	18.6148i	0.0656815	−	0.831646i
$502$			28.7226i			1.28195i
$503$	−41.9710			−1.87140			−0.935698	−	0.352802i	$-0.885229\pi$
$503$	−41.9710			−1.87140			−0.935698	+	0.352802i	$0.885229\pi$
$504$	23.5188	+	6.05997i	1.04761	+	0.269932i
$505$	−31.4853			−1.40108
$506$		−	1.76999i		−	0.0786857i
$507$	0.550821	−	6.97439i	0.0244628	−	0.309743i
$508$	1.57198			0.0697453
$509$	32.6383			1.44667			0.723334	−	0.690498i	$-0.242609\pi$
$509$	32.6383			1.44667			0.723334	+	0.690498i	$0.242609\pi$
$510$	6.37318	+	0.503339i	0.282209	+	0.0222882i
$511$	−11.2370	−	1.06566i	−0.497097	−	0.0471420i
$512$			24.5221i			1.08373i
$513$	32.6490	+	7.86674i	1.44149	+	0.347325i
$514$			18.9267i			0.834822i
$515$		−	27.3623i		−	1.20573i
$516$	0.587953	−	7.44455i	0.0258832	−	0.327728i
$517$			14.1192i			0.620962i
$518$	−1.93239	−	0.183257i	−0.0849041	−	0.00805184i
$519$	−0.842570	+	10.6685i	−0.0369847	+	0.468294i
$520$	−27.5171			−1.20670
$521$	10.0633			0.440880			0.220440	−	0.975401i	$-0.429251\pi$
$521$	10.0633			0.440880			0.220440	+	0.975401i	$0.429251\pi$
$522$	29.5718	+	4.70035i	1.29432	+	0.205729i
$523$			13.4622i			0.588663i	0.955703	+	0.294331i	$0.0950969\pi$
$523$			13.4622i			0.588663i	−0.955703	+	0.294331i	$0.904903\pi$
$524$	−8.04532			−0.351461
$525$	−18.1689	−	3.18181i	−0.792957	−	0.138866i
$526$	−16.5395			−0.721158
$527$			4.76164i			0.207420i
$528$	−13.0014	−	1.02682i	−0.565815	−	0.0446867i
$529$	22.7174			0.987714
$530$	6.89573			0.299531
$531$	−44.2419	−	7.03211i	−1.91994	−	0.305168i
$532$	−8.34969	−	0.791839i	−0.362005	−	0.0343306i
$533$		−	14.1535i		−	0.613058i
$534$	−19.8641	−	1.56882i	−0.859602	−	0.0678894i
$535$		−	11.3621i		−	0.491228i
$536$		−	21.1726i		−	0.914517i
$537$	37.6741	+	2.97542i	1.62576	+	0.128399i
$538$		−	8.59863i		−	0.370713i
$539$	3.56601	−	18.6321i	0.153599	−	0.802542i
$540$	1.79350	−	7.44350i	0.0771801	−	0.320317i
$541$	−16.5318			−0.710756			−0.355378	−	0.934723i	$-0.615648\pi$
$541$	−16.5318			−0.710756			−0.355378	+	0.934723i	$0.615648\pi$
$542$	0.678462			0.0291425
$543$	15.5922	+	1.23144i	0.669127	+	0.0528461i
$544$		−	2.70605i		−	0.116021i
$545$	−3.63812			−0.155840
$546$	−16.6013	−	2.90729i	−0.710471	−	0.124420i
$547$	25.6085			1.09494			0.547470	−	0.836825i	$-0.315591\pi$
$547$	25.6085			1.09494			0.547470	+	0.836825i	$0.315591\pi$
$548$		−	1.31856i		−	0.0563261i
$549$	−3.92774	+	24.7111i	−0.167632	+	1.05464i
$550$	13.4021			0.571470
$551$	−52.5047			−2.23678
$552$	−0.221816	+	2.80859i	−0.00944112	+	0.119542i
$553$	−3.63744	+	38.3556i	−0.154680	+	1.63105i
$554$		−	19.6944i		−	0.836733i
$555$	−0.244631	+	3.09747i	−0.0103840	+	0.131480i
$556$			2.66372i			0.112967i
$557$		−	33.6261i		−	1.42478i	−0.701782	−	0.712392i	$-0.747612\pi$
$557$		−	33.6261i		−	1.42478i	0.701782	−	0.712392i	$-0.252388\pi$
$558$	−17.3332	−	2.75506i	−0.733774	−	0.116631i
$559$			26.3135i			1.11294i
$560$	2.08498	−	21.9855i	0.0881066	−	0.929056i
$561$	4.67936	+	0.369565i	0.197563	+	0.0156030i
$562$	6.97188			0.294091
$563$	20.5940			0.867933			0.433967	−	0.900929i	$-0.357114\pi$
$563$	20.5940			0.867933			0.433967	+	0.900929i	$0.357114\pi$
$564$	0.348475	−	4.41232i	0.0146734	−	0.185792i
$565$		−	38.3638i		−	1.61398i
$566$	−25.3517			−1.06561
$567$	9.48740	−	21.8401i	0.398433	−	0.917197i
$568$	−41.4693			−1.74001
$569$		−	21.0258i		−	0.881447i	−0.897643	−	0.440723i	$-0.854722\pi$
$569$		−	21.0258i		−	0.881447i	0.897643	−	0.440723i	$-0.145278\pi$
$570$	3.25314	−	41.1906i	0.136259	−	1.72529i
$571$	−5.89096			−0.246529			−0.123264	−	0.992374i	$-0.539336\pi$
$571$	−5.89096			−0.246529			−0.123264	+	0.992374i	$0.539336\pi$
$572$	−3.97899			−0.166370
$573$	35.9974	+	2.84299i	1.50381	+	0.118767i
$574$	15.3009	+	1.45105i	0.638646	+	0.0605657i
$575$		−	2.13971i		−	0.0892321i
$576$	26.3146	+	4.18262i	1.09644	+	0.174276i
$577$		−	30.9745i		−	1.28948i	−0.764400	−	0.644742i	$-0.776965\pi$
$577$		−	30.9745i		−	1.28948i	0.764400	−	0.644742i	$-0.223035\pi$
$578$		−	1.22862i		−	0.0511040i
$579$	1.33414	−	16.8926i	0.0554449	−	0.702032i
$580$			11.9703i			0.497040i
$581$	−0.773297	+	8.15417i	−0.0320818	+	0.338292i
$582$	0.944392	−	11.9577i	0.0391463	−	0.495663i
$583$	5.06303			0.209689
$584$	−13.0542			−0.540186
$585$	−4.23501	+	26.6442i	−0.175096	+	1.10160i
$586$		−	8.20254i		−	0.338844i
$587$	41.3358			1.70611			0.853056	−	0.521820i	$-0.174747\pi$
$587$	41.3358			1.70611			0.853056	+	0.521820i	$0.174747\pi$
$588$	−1.57425	+	5.73462i	−0.0649211	+	0.236492i
$589$	30.7751			1.26807
$590$			55.1158i			2.26908i
$591$	22.6810	+	1.79130i	0.932973	+	0.0736840i
$592$	−1.65911			−0.0681889
$593$	8.76929			0.360111			0.180056	−	0.983656i	$-0.442372\pi$
$593$	8.76929			0.360111			0.180056	+	0.983656i	$0.442372\pi$
$594$	−4.05273	+	16.8199i	−0.166286	+	0.690128i
$595$	−0.750409	+	7.91282i	−0.0307638	+	0.324394i
$596$		−	5.24115i		−	0.214686i
$597$	−6.29953	−	0.497522i	−0.257822	−	0.0203622i
$598$		−	1.95510i		−	0.0799499i
$599$		−	27.7297i		−	1.13301i	−0.824060	−	0.566503i	$-0.808296\pi$
$599$		−	27.7297i		−	1.13301i	0.824060	−	0.566503i	$-0.191704\pi$
$600$	−21.2663	−	1.67956i	−0.868193	−	0.0685679i
$601$			23.8020i			0.970904i	0.874263	+	0.485452i	$0.161345\pi$
$601$			23.8020i			0.970904i	−0.874263	+	0.485452i	$0.838655\pi$
$602$	−28.4465	−	2.69771i	−1.15939	−	0.109951i
$603$	−20.5010	−	3.25857i	−0.834866	−	0.132699i
$604$	−11.8274			−0.481248
$605$	−10.9823			−0.446494
$606$	−22.2337	−	1.75596i	−0.903181	−	0.0713311i
$607$		−	9.23563i		−	0.374863i	−0.982278	−	0.187431i	$-0.939984\pi$
$607$		−	9.23563i		−	0.374863i	0.982278	−	0.187431i	$-0.0600162\pi$
$608$	−17.4895			−0.709293
$609$	−6.42172	+	36.6696i	−0.260221	+	1.48593i
$610$	30.7846			1.24643
$611$			15.5958i			0.630938i
$612$	−1.45320	−	0.230982i	−0.0587423	−	0.00933689i
$613$	1.11970			0.0452241			0.0226120	−	0.999744i	$-0.492802\pi$
$613$	1.11970			0.0452241			0.0226120	+	0.999744i	$0.492802\pi$
$614$	−33.2543			−1.34204
$615$	1.93702	−	24.5261i	0.0781080	−	0.988989i
$616$	2.07133	−	21.8416i	0.0834564	−	0.880021i
$617$			21.5270i			0.866646i	0.901239	+	0.433323i	$0.142659\pi$
$617$			21.5270i			0.866646i	−0.901239	+	0.433323i	$0.857341\pi$
$618$	1.52602	−	19.3221i	0.0613854	−	0.777251i
$619$			37.0861i			1.49062i	0.666721	+	0.745308i	$0.267697\pi$
$619$			37.0861i			1.49062i	−0.666721	+	0.745308i	$0.732303\pi$
$620$		−	7.01628i		−	0.281780i
$621$	2.68536	+	0.647036i	0.107760	+	0.0259647i
$622$			8.24573i			0.330623i
$623$	2.33889	−	24.6629i	0.0937057	−	0.988097i
$624$	−14.3611	−	1.13421i	−0.574905	−	0.0454046i
$625$	−28.9240			−1.15696
$626$	1.58871			0.0634975
$627$	2.38854	−	30.2433i	0.0953892	−	1.20780i
$628$			3.93807i			0.157146i
$629$	0.597131			0.0238092
$630$	−28.3699	−	7.30993i	−1.13028	−	0.291235i
$631$	12.9917			0.517189			0.258595	−	0.965986i	$-0.416741\pi$
$631$	12.9917			0.517189			0.258595	+	0.965986i	$0.416741\pi$
$632$			44.5581i			1.77243i
$633$	−1.60686	+	20.3458i	−0.0638671	+	0.808673i
$634$	−36.7131			−1.45806
$635$	−9.62832			−0.382088
$636$	−1.58222	−	0.124960i	−0.0627393	−	0.00495500i
$637$	3.93894	−	20.5807i	0.156067	−	0.815436i
$638$		−	27.0490i		−	1.07088i
$639$	−6.38233	+	40.1539i	−0.252481	+	1.58846i
$640$		−	16.5233i		−	0.653142i
$641$			11.1485i			0.440337i	0.975462	+	0.220169i	$0.0706608\pi$
$641$			11.1485i			0.440337i	−0.975462	+	0.220169i	$0.929339\pi$
$642$	0.633675	−	8.02348i	0.0250092	−	0.316661i
$643$			27.2848i			1.07601i	0.842942	+	0.538004i	$0.180821\pi$
$643$			27.2848i			1.07601i	−0.842942	+	0.538004i	$0.819179\pi$
$644$	−0.686758	−	0.0651284i	−0.0270621	−	0.00256642i
$645$	−3.60119	+	45.5976i	−0.141797	+	1.79540i
$646$	−7.94075			−0.312425
$647$	−16.1065			−0.633212			−0.316606	−	0.948557i	$-0.602543\pi$
$647$	−16.1065			−0.633212			−0.316606	+	0.948557i	$0.602543\pi$
$648$	8.53868	−	26.1816i	0.335431	−	1.02851i
$649$			40.4675i			1.58849i
$650$	14.8037			0.580651
$651$	3.76402	−	21.4935i	0.147524	−	0.842397i
$652$	9.86929			0.386511
$653$		−	20.6267i		−	0.807185i	−0.914939	−	0.403592i	$-0.867761\pi$
$653$		−	20.6267i		−	0.807185i	0.914939	−	0.403592i	$-0.132239\pi$
$654$	−2.56909	−	0.202901i	−0.100459	−	0.00793405i
$655$	49.2773			1.92542
$656$	13.1370			0.512914
$657$	−2.00910	+	12.6401i	−0.0783825	+	0.493137i
$658$	−16.8600	−	1.59891i	−0.657272	−	0.0623321i
$659$			7.17301i			0.279421i	0.990192	+	0.139710i	$0.0446171\pi$
$659$			7.17301i			0.279421i	−0.990192	+	0.139710i	$0.955383\pi$
$660$	−6.89503	−	0.544553i	−0.268389	−	0.0211967i
$661$		−	11.9548i		−	0.464988i	−0.972598	−	0.232494i	$-0.925311\pi$
$661$		−	11.9548i		−	0.464988i	0.972598	−	0.232494i	$-0.0746886\pi$
$662$		−	22.3353i		−	0.868086i
$663$	5.16873	+	0.408214i	0.200737	+	0.0158537i
$664$			9.47279i			0.367615i
$665$	51.1415	+	4.84998i	1.98318	+	0.188074i
$666$	−0.345497	+	2.17366i	−0.0133877	+	0.0842277i
$667$	−4.31849			−0.167213
$668$	5.28774			0.204589
$669$	−6.14375	−	0.485219i	−0.237531	−	0.0187596i
$670$			25.5398i			0.986689i
$671$	22.6029			0.872575
$672$	−2.13910	+	12.2148i	−0.0825175	+	0.471195i
$673$	37.8475			1.45891			0.729457	−	0.684026i	$-0.239773\pi$
$673$	37.8475			1.45891			0.729457	+	0.684026i	$0.239773\pi$
$674$		−	29.7141i		−	1.14455i
$675$	−4.89928	+	20.3332i	−0.188573	+	0.782627i
$676$	1.98116			0.0761983
$677$	0.00897867			0.000345078			0.000172539	−	1.00000i	$-0.499945\pi$
$677$	0.00897867			0.000345078			0.000172539		1.00000i	$0.499945\pi$
$678$	2.13958	−	27.0910i	0.0821701	−	1.04042i
$679$	14.8465	+	1.40796i	0.569756	+	0.0540325i
$680$			9.19240i			0.352513i
$681$	1.08171	−	13.6964i	0.0414511	−	0.524847i
$682$			15.8545i			0.607100i
$683$			39.4446i			1.50930i	0.656125	+	0.754652i	$0.272194\pi$
$683$			39.4446i			1.50930i	−0.656125	+	0.754652i	$0.727806\pi$
$684$	−1.49286	+	9.39223i	−0.0570811	+	0.359121i
$685$			8.07613i			0.308573i
$686$	21.8451	+	6.36821i	0.834052	+	0.243139i
$687$	−1.68331	−	0.132944i	−0.0642224	−	0.00507214i
$688$	−24.4236			−0.931141
$689$	5.59252			0.213058
$690$	0.267569	−	3.38791i	0.0101862	−	0.128976i
$691$		−	17.9068i		−	0.681207i	−0.940207	−	0.340603i	$-0.889369\pi$
$691$		−	17.9068i		−	0.681207i	0.940207	−	0.340603i	$-0.110631\pi$
$692$	−3.03050			−0.115202
$693$	−20.8299	−	5.36715i	−0.791264	−	0.203881i
$694$	2.61964			0.0994402
$695$		−	16.3152i		−	0.618870i
$696$	−3.38979	+	42.9209i	−0.128490	+	1.62691i
$697$	−4.72816			−0.179092
$698$	−21.7647			−0.823804
$699$	33.4527	+	2.64201i	1.26530	+	0.0999301i
$700$	0.493144	−	5.20005i	0.0186391	−	0.196543i
$701$			24.0877i			0.909782i	0.890547	+	0.454891i	$0.150322\pi$
$701$			24.0877i			0.909782i	−0.890547	+	0.454891i	$0.849678\pi$
$702$	−4.47657	+	18.5789i	−0.168957	+	0.701215i
$703$		−	3.85933i		−	0.145557i
$704$		−	24.0696i		−	0.907158i
$705$	−2.13440	+	27.0253i	−0.0803860	+	1.01783i
$706$			9.12708i			0.343502i
$707$	2.61790	−	27.6049i	0.0984562	−	1.03819i
$708$	0.998777	−	12.6463i	0.0375363	−	0.475278i
$709$	−41.8977			−1.57350			−0.786750	−	0.617272i	$-0.788238\pi$
$709$	−41.8977			−1.57350			−0.786750	+	0.617272i	$0.788238\pi$
$710$	50.0231			1.87733
$711$	43.1447	+	6.85771i	1.61805	+	0.257184i
$712$		−	28.6511i		−	1.07375i
$713$	2.53124			0.0947956
$714$	−0.971213	+	5.54587i	−0.0363467	+	0.207549i
$715$	24.3711			0.911429
$716$			10.7018i			0.399944i
$717$	31.2468	+	2.46780i	1.16693	+	0.0921616i
$718$	14.6682			0.547411
$719$	−34.4704			−1.28553			−0.642764	−	0.766064i	$-0.722212\pi$
$719$	−34.4704			−1.28553			−0.642764	+	0.766064i	$0.722212\pi$
$720$	−24.7306	−	3.93085i	−0.921655	−	0.146494i
$721$	23.9900	+	2.27508i	0.893435	+	0.0847285i
$722$			27.9782i			1.04124i
$723$	−6.03333	−	0.476499i	−0.224382	−	0.0177212i
$724$			4.42916i			0.164608i
$725$		−	32.6990i		−	1.21441i
$726$	−7.75526	−	0.612492i	−0.287825	−	0.0227317i
$727$			33.4482i			1.24053i	0.784394	+	0.620263i	$0.212974\pi$
$727$			33.4482i			1.24053i	−0.784394	+	0.620263i	$0.787026\pi$
$728$	2.28795	−	24.1257i	0.0847972	−	0.894160i
$729$	−24.0370	−	12.2973i	−0.890258	−	0.455456i
$730$	15.7468			0.582816
$731$	8.79033			0.325122
$732$	−7.06353	−	0.557861i	−0.261075	−	0.0206191i
$733$		−	29.8929i		−	1.10412i	−0.833804	−	0.552061i	$-0.813842\pi$
$733$		−	29.8929i		−	1.10412i	0.833804	−	0.552061i	$-0.186158\pi$
$734$	32.6738			1.20601
$735$	9.64225	−	35.1244i	0.355660	−	1.29558i
$736$	−1.43850			−0.0530240
$737$			18.7520i			0.690739i
$738$	2.73568	−	17.2113i	0.100702	−	0.633558i
$739$	−26.1837			−0.963181			−0.481591	−	0.876396i	$-0.659941\pi$
$739$	−26.1837			−0.963181			−0.481591	+	0.876396i	$0.659941\pi$
$740$	−0.879872			−0.0323447
$741$	2.63834	−	33.4061i	0.0969217	−	1.22720i
$742$	−0.573357	+	6.04587i	−0.0210486	+	0.221951i
$743$			16.6076i			0.609273i	0.952469	+	0.304636i	$0.0985350\pi$
$743$			16.6076i			0.609273i	−0.952469	+	0.304636i	$0.901465\pi$
$744$	1.98689	−	25.1576i	0.0728430	−	0.922324i
$745$			32.1018i			1.17612i
$746$			7.51125i			0.275006i
$747$	9.17231	+	1.45791i	0.335597	+	0.0533421i
$748$			1.32923i			0.0486014i
$749$	9.96180	+	0.944723i	0.363996	+	0.0345194i
$750$	−6.21306	−	0.490693i	−0.226869	−	0.0179176i
$751$	−17.3250			−0.632198			−0.316099	−	0.948726i	$-0.602373\pi$
$751$	−17.3250			−0.632198			−0.316099	+	0.948726i	$0.602373\pi$
$752$	−14.4757			−0.527873
$753$	−3.18801	+	40.3660i	−0.116177	+	1.47102i
$754$		−	29.8778i		−	1.08808i
$755$	72.4421			2.63644
$756$	6.37700	+	2.19137i	0.231929	+	0.0796992i
$757$	−22.5070			−0.818032			−0.409016	−	0.912527i	$-0.634128\pi$
$757$	−22.5070			−0.818032			−0.409016	+	0.912527i	$0.634128\pi$
$758$		−	25.4127i		−	0.923030i
$759$	0.196457	−	2.48750i	0.00713092	−	0.0902904i
$760$	59.4116			2.15509
$761$	26.2012			0.949794			0.474897	−	0.880041i	$-0.342485\pi$
$761$	26.2012			0.949794			0.474897	+	0.880041i	$0.342485\pi$
$762$	−6.79913	−	0.536979i	−0.246307	−	0.0194527i
$763$	0.302497	−	3.18974i	0.0109511	−	0.115476i
$764$			10.2255i			0.369945i
$765$	8.90082	+	1.41476i	0.321810	+	0.0511506i
$766$			25.6780i			0.927783i
$767$			44.6996i			1.61401i
$768$	−1.50083	+	19.0033i	−0.0541567	+	0.685722i
$769$			15.7530i			0.568068i	0.958814	+	0.284034i	$0.0916729\pi$
$769$			15.7530i			0.568068i	−0.958814	+	0.284034i	$0.908327\pi$
$770$	−2.49858	+	26.3467i	−0.0900426	+	0.949470i
$771$	−2.10073	+	26.5991i	−0.0756560	+	0.957942i
$772$	4.79854			0.172703
$773$	−26.0768			−0.937918			−0.468959	−	0.883220i	$-0.655371\pi$
$773$	−26.0768			−0.937918			−0.468959	+	0.883220i	$0.655371\pi$
$774$	−5.08603	+	31.9984i	−0.182814	+	1.15016i
$775$			19.1662i			0.688470i
$776$	17.2473			0.619142
$777$	−2.69538	−	0.472025i	−0.0966962	−	0.0169338i
$778$	−12.0502			−0.432022
$779$			30.5586i			1.09488i
$780$	−7.61611	−	0.601503i	−0.272701	−	0.0215373i
$781$	36.7283			1.31424
$782$	−0.653123			−0.0233556
$783$	41.0377	+	9.88800i	1.46657	+	0.353368i
$784$	19.1025	+	3.65604i	0.682233	+	0.130573i
$785$		−	24.1206i		−	0.860899i
$786$	34.7976	+	2.74823i	1.24119	+	0.0980263i
$787$			7.72021i			0.275196i	0.990488	+	0.137598i	$0.0439381\pi$
$787$			7.72021i			0.275196i	−0.990488	+	0.137598i	$0.956062\pi$
$788$			6.44281i			0.229516i
$789$	−23.2442	−	1.83577i	−0.827516	−	0.0653553i
$790$		−	53.7489i		−	1.91230i
$791$	33.6356	+	3.18982i	1.19595	+	0.113417i
$792$	−24.5687	−	3.90511i	−0.873010	−	0.138762i
$793$	24.9667			0.886594
$794$	1.28179			0.0454890
$795$	9.69107	+	0.765378i	0.343707	+	0.0271451i
$796$		−	1.78945i		−	0.0634255i
$797$	−2.34879			−0.0831986			−0.0415993	−	0.999134i	$-0.513245\pi$
$797$	−2.34879			−0.0831986			−0.0415993	+	0.999134i	$0.513245\pi$
$798$	35.8436	+	6.27707i	1.26885	+	0.222206i
$799$	5.20995			0.184315
$800$		−	10.8922i		−	0.385096i
$801$	−27.7423	−	4.40954i	−0.980225	−	0.155804i
$802$	−30.8943			−1.09092
$803$	11.5617			0.408005
$804$	0.462817	−	5.86010i	0.0163223	−	0.206670i
$805$	4.20637	+	0.398909i	0.148255	+	0.0140597i
$806$			17.5126i			0.616853i
$807$	0.954388	−	12.0843i	0.0335960	−	0.425387i
$808$		−	32.0689i		−	1.12818i
$809$		−	12.7492i		−	0.448237i	−0.974562	−	0.224118i	$-0.928050\pi$
$809$		−	12.7492i		−	0.448237i	0.974562	−	0.224118i	$-0.0719502\pi$
$810$	−10.2999	+	31.5820i	−0.361902	+	1.10968i
$811$		−	20.3839i		−	0.715774i	−0.933765	−	0.357887i	$-0.883497\pi$
$811$		−	20.3839i		−	0.715774i	0.933765	−	0.357887i	$-0.116503\pi$
$812$	−10.4950	−	0.995292i	−0.368303	−	0.0349279i
$813$	0.953492	+	0.0753046i	0.0334404	+	0.00264105i
$814$	1.98822			0.0696872
$815$	−60.4491			−2.11744
$816$	−0.378895	+	4.79750i	−0.0132640	+	0.167946i
$817$		−	56.8130i		−	1.98763i
$818$	−35.6640			−1.24696
$819$	−23.0083	−	5.92845i	−0.803976	−	0.207157i
$820$	6.96693			0.243296
$821$		−	43.4838i		−	1.51759i	−0.651327	−	0.758797i	$-0.725787\pi$
$821$		−	43.4838i		−	1.51759i	0.651327	−	0.758797i	$-0.274213\pi$
$822$	−0.450412	+	5.70303i	−0.0157099	+	0.198916i
$823$	29.1116			1.01477			0.507383	−	0.861721i	$-0.330613\pi$
$823$	29.1116			1.01477			0.507383	+	0.861721i	$0.330613\pi$
$824$	27.8694			0.970878
$825$	18.8350	+	1.48754i	0.655751	+	0.0517896i
$826$	−48.3231	−	4.58270i	−1.68138	−	0.159452i
$827$		−	2.14743i		−	0.0746735i	−0.999303	−	0.0373367i	$-0.988113\pi$
$827$		−	2.14743i		−	0.0746735i	0.999303	−	0.0373367i	$-0.0118874\pi$
$828$	−0.122787	+	0.772507i	−0.00426716	+	0.0268465i
$829$			1.85870i			0.0645555i	0.999479	+	0.0322777i	$0.0102761\pi$
$829$			1.85870i			0.0645555i	−0.999479	+	0.0322777i	$0.989724\pi$
$830$		−	11.4267i		−	0.396627i
$831$	2.18594	−	27.6779i	0.0758293	−	0.960136i
$832$		−	26.5868i		−	0.921732i
$833$	−6.87521	−	1.31585i	−0.238212	−	0.0455915i
$834$	0.909912	−	11.5211i	0.0315077	−	0.398944i
$835$	−32.3872			−1.12081
$836$	8.59096			0.297124
$837$	−24.0538	−	5.79575i	−0.831422	−	0.200330i
$838$		−	39.7577i		−	1.37341i
$839$	49.1521			1.69692			0.848460	−	0.529260i	$-0.177531\pi$
$839$	49.1521			1.69692			0.848460	+	0.529260i	$0.177531\pi$
$840$	7.26649	−	41.4934i	0.250718	−	1.43166i
$841$	−36.9951			−1.27569
$842$			7.24916i			0.249823i
$843$	9.79808	+	0.773830i	0.337464	+	0.0266521i
$844$	−5.77946			−0.198937
$845$	−12.1345			−0.417440
$846$	−3.01445	+	18.9652i	−0.103639	+	0.652036i
$847$	0.913142	−	9.62879i	0.0313759	−	0.330849i
$848$			5.19086i			0.178255i
$849$	−35.6285	−	2.81386i	−1.22277	−	0.0965713i
$850$		−	4.94536i		−	0.169625i
$851$		−	0.317428i		−	0.0108813i
$852$	−11.4778	−	0.906488i	−0.393222	−	0.0310558i
$853$			20.2533i			0.693460i	0.937965	+	0.346730i	$0.112708\pi$
$853$			20.2533i			0.693460i	−0.937965	+	0.346730i	$0.887292\pi$
$854$	−2.55964	+	26.9906i	−0.0875890	+	0.923598i
$855$	9.14374	−	57.5271i	0.312709	−	1.96738i
$856$	11.5727			0.395548
$857$	14.2258			0.485944			0.242972	−	0.970033i	$-0.421878\pi$
$857$	14.2258			0.485944			0.242972	+	0.970033i	$0.421878\pi$
$858$	17.2099	+	1.35920i	0.587537	+	0.0464023i
$859$			26.1292i			0.891517i	0.895153	+	0.445758i	$0.147066\pi$
$859$			26.1292i			0.891517i	−0.895153	+	0.445758i	$0.852934\pi$
$860$	−12.9525			−0.441678
$861$	21.3423	+	3.73755i	0.727345	+	0.127375i
$862$	23.4977			0.800336
$863$			13.8029i			0.469855i	0.972013	+	0.234927i	$0.0754853\pi$
$863$			13.8029i			0.469855i	−0.972013	+	0.234927i	$0.924515\pi$
$864$	13.6698	+	3.29373i	0.465057	+	0.112055i
$865$	18.5617			0.631117
$866$	22.1712			0.753407
$867$	0.136369	−	1.72667i	0.00463132	−	0.0586409i
$868$	6.15155	+	0.583380i	0.208797	+	0.0198012i
$869$		−	39.4639i		−	1.33872i
$870$	4.08899	−	51.7740i	0.138630	−	1.75530i
$871$			20.7131i			0.701837i
$872$		−	3.70555i		−	0.125486i
$873$	2.65445	−	16.7002i	0.0898394	−	0.565217i
$874$			4.22121i			0.142785i
$875$	0.731556	−	7.71403i	0.0247311	−	0.260782i
$876$	−3.61310	−	0.285354i	−0.122075	−	0.00964123i
$877$	51.3087			1.73257			0.866286	−	0.499548i	$-0.166500\pi$
$877$	51.3087			1.73257			0.866286	+	0.499548i	$0.166500\pi$
$878$	−35.5034			−1.19818
$879$	0.910424	−	11.5276i	0.0307078	−	0.388817i
$880$			22.6208i			0.762546i
$881$	−26.8186			−0.903540			−0.451770	−	0.892134i	$-0.649207\pi$
$881$	−26.8186			−0.903540			−0.451770	+	0.892134i	$0.649207\pi$
$882$	8.76788	−	24.2656i	0.295230	−	0.817067i
$883$	−47.8669			−1.61085			−0.805426	−	0.592697i	$-0.798063\pi$
$883$	−47.8669			−1.61085			−0.805426	+	0.592697i	$0.798063\pi$
$884$			1.46824i			0.0493822i
$885$	−6.11747	+	77.4583i	−0.205637	+	2.60373i
$886$	−37.4089			−1.25678
$887$	−18.6224			−0.625279			−0.312639	−	0.949872i	$-0.601213\pi$
$887$	−18.6224			−0.625279			−0.312639	+	0.949872i	$0.601213\pi$
$888$	−3.15488	−	0.249165i	−0.105871	−	0.00836143i
$889$	0.800562	−	8.44168i	0.0268500	−	0.283125i
$890$			34.5608i			1.15848i
$891$	−7.56248	+	23.1884i	−0.253353	+	0.776839i
$892$		−	1.74520i		−	0.0584337i
$893$		−	33.6726i		−	1.12681i
$894$	−1.79035	+	22.6690i	−0.0598781	+	0.758166i
$895$		−	65.5480i		−	2.19103i
$896$	14.4869	+	1.37386i	0.483974	+	0.0458975i
$897$	0.217002	−	2.74764i	0.00724549	−	0.0917410i
$898$	23.4608			0.782897
$899$	38.6824			1.29013
$900$	−5.84932	−	0.929731i	−0.194977	−	0.0309910i
$901$		−	1.86825i		−	0.0622404i
$902$	−15.7430			−0.524184
$903$	−39.6785	−	6.94865i	−1.32042	−	0.231237i
$904$	39.0749			1.29961
$905$		−	27.1284i		−	0.901779i
$906$	51.1557	+	4.04016i	1.69954	+	0.134225i
$907$	−37.7092			−1.25211			−0.626057	−	0.779777i	$-0.715332\pi$
$907$	−37.7092			−1.25211			−0.626057	+	0.779777i	$0.715332\pi$
$908$	3.89062			0.129115
$909$	−31.0517	−	4.93556i	−1.02992	−	0.163702i
$910$	−2.75988	+	29.1021i	−0.0914892	+	0.964724i
$911$		−	23.8170i		−	0.789094i	−0.918876	−	0.394547i	$-0.870902\pi$
$911$		−	23.8170i		−	0.789094i	0.918876	−	0.394547i	$-0.129098\pi$
$912$	31.0068	+	2.44885i	1.02674	+	0.0810894i
$913$		−	8.38979i		−	0.277662i
$914$			34.7391i			1.14907i
$915$	43.2638	+	3.41688i	1.43026	+	0.112958i
$916$		−	0.478165i		−	0.0157990i
$917$	−4.09724	+	43.2041i	−0.135303	+	1.42672i
$918$	6.20650	+	1.49545i	0.204845	+	0.0493572i
$919$	−49.8121			−1.64315			−0.821575	−	0.570101i	$-0.806904\pi$
$919$	−49.8121			−1.64315			−0.821575	+	0.570101i	$0.806904\pi$
$920$	4.88658			0.161106
$921$	−46.7347	−	3.69100i	−1.53996	−	0.121623i
$922$			25.3531i			0.834960i
$923$	40.5693			1.33536
$924$	1.05074	−	5.99997i	0.0345668	−	0.197385i
$925$	2.40353			0.0790275
$926$			13.3456i			0.438562i
$927$	4.28924	−	26.9854i	0.140877	−	0.886318i
$928$	−21.9832			−0.721634
$929$	−37.3128			−1.22419			−0.612097	−	0.790783i	$-0.709674\pi$
$929$	−37.3128			−1.22419			−0.612097	+	0.790783i	$0.709674\pi$
$930$	−2.39672	+	30.3468i	−0.0785915	+	0.995111i
$931$	−8.50449	+	44.4353i	−0.278723	+	1.45631i
$932$			9.50262i			0.311269i
$933$	−0.915218	+	11.5883i	−0.0299629	+	0.379384i
$934$		−	42.8968i		−	1.40363i
$935$		−	8.14147i		−	0.266254i
$936$	−27.1381	−	4.31351i	−0.887036	−	0.140991i
$937$		−	33.1676i		−	1.08354i	−0.840527	−	0.541769i	$-0.817755\pi$
$937$		−	33.1676i		−	1.08354i	0.840527	−	0.541769i	$-0.182245\pi$
$938$	−22.3921	−	2.12355i	−0.731130	−	0.0693363i
$939$	2.23272	+	0.176335i	0.0728622	+	0.00575448i
$940$	−7.67686			−0.250392
$941$	−9.76426			−0.318306			−0.159153	−	0.987254i	$-0.550876\pi$
$941$	−9.76426			−0.318306			−0.159153	+	0.987254i	$0.550876\pi$
$942$	1.34522	−	17.0330i	0.0438297	−	0.554964i
$943$			2.51344i			0.0818487i
$944$	−41.4892			−1.35036
$945$	−39.0589	−	13.4220i	−1.27059	−	0.436619i
$946$	29.2685			0.951601
$947$		−	2.17145i		−	0.0705626i	−0.999377	−	0.0352813i	$-0.988767\pi$
$947$		−	2.17145i		−	0.0705626i	0.999377	−	0.0352813i	$-0.0112327\pi$
$948$	−0.974007	+	12.3327i	−0.0316343	+	0.400547i
$949$	12.7709			0.414560
$950$	−31.9625			−1.03700
$951$	−51.5955	−	4.07489i	−1.67310	−	0.132137i
$952$	−8.05949	−	0.764318i	−0.261209	−	0.0247717i
$953$			17.0246i			0.551482i	0.961232	+	0.275741i	$0.0889232\pi$
$953$			17.0246i			0.551482i	−0.961232	+	0.275741i	$0.911077\pi$
$954$	6.80075	+	1.08096i	0.220183	+	0.0349973i
$955$		−	62.6306i		−	2.02668i
$956$			8.87601i			0.287071i
$957$	3.00225	−	38.0139i	0.0970489	−	1.22881i
$958$			23.4195i			0.756650i
$959$	−7.08078	−	0.671503i	−0.228650	−	0.0216840i
$960$	3.63860	−	46.0713i	0.117435	−	1.48694i
$961$	8.32674			0.268605
$962$	2.19615			0.0708067
$963$	1.78110	−	11.2056i	0.0573951	−	0.361096i
$964$		−	1.71384i		−	0.0551991i
$965$	−29.3909			−0.946126
$966$	2.94812	+	0.516286i	0.0948542	+	0.0166112i
$967$	33.3443			1.07228			0.536141	−	0.844129i	$-0.319882\pi$
$967$	33.3443			1.07228			0.536141	+	0.844129i	$0.319882\pi$
$968$		−	11.1859i		−	0.359527i
$969$	−11.1597	−	0.881367i	−0.358501	−	0.0283136i
$970$	−20.8048			−0.668003
$971$	3.29550			0.105758			0.0528789	−	0.998601i	$-0.483160\pi$
$971$	3.29550			0.105758			0.0528789	+	0.998601i	$0.483160\pi$
$972$	2.93563	−	7.05983i	0.0941603	−	0.226444i
$973$	14.3044	+	1.35655i	0.458579	+	0.0434891i
$974$			8.64845i			0.277114i
$975$	20.8048	+	1.64311i	0.666286	+	0.0526217i
$976$			23.1736i			0.741767i
$977$			30.8031i			0.985477i	0.870177	+	0.492739i	$0.164004\pi$
$977$			30.8031i			0.985477i	−0.870177	+	0.492739i	$0.835996\pi$
$978$	−42.6867	−	3.37129i	−1.36497	−	0.107802i
$979$			25.3755i			0.811005i
$980$	10.1306	+	1.93890i	0.323611	+	0.0619359i
$981$	−3.58801	−	0.570303i	−0.114556	−	0.0182084i
$982$	29.1117			0.928992
$983$	36.5124			1.16456			0.582282	−	0.812987i	$-0.302160\pi$
$983$	36.5124			1.16456			0.582282	+	0.812987i	$0.302160\pi$
$984$	24.9807	+	1.97292i	0.796356	+	0.0628943i
$985$		−	39.4620i		−	1.25736i
$986$	−9.98102			−0.317861
$987$	−23.5171	−	4.11841i	−0.748558	−	0.131090i
$988$	9.48940			0.301898
$989$		−	4.67284i		−	0.148588i
$990$	29.6364	+	4.71061i	0.941906	+	0.149713i
$991$	−28.0984			−0.892576			−0.446288	−	0.894889i	$-0.647254\pi$
$991$	−28.0984			−0.892576			−0.446288	+	0.894889i	$0.647254\pi$
$992$	12.8852			0.409106
$993$	2.47906	−	31.3894i	0.0786706	−	0.996113i
$994$	−4.15925	+	43.8580i	−0.131923	+	1.39109i
$995$			10.9603i			0.347466i
$996$	−0.207068	+	2.62185i	−0.00656120	+	0.0830766i
$997$		−	12.8636i		−	0.407394i	−0.979034	−	0.203697i	$-0.934704\pi$
$997$		−	12.8636i		−	0.407394i	0.979034	−	0.203697i	$-0.0652957\pi$
$998$		−	3.51496i		−	0.111264i
$999$	−0.726813	+	3.01646i	−0.0229953	+	0.0954365i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	357.2.d.b.188.7	yes	22
3.2	odd	2		357.2.d.a.188.16	yes	22
7.6	odd	2		357.2.d.a.188.7	✓	22
21.20	even	2	inner	357.2.d.b.188.16	yes	22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
357.2.d.a.188.7	✓	22	7.6	odd	2
357.2.d.a.188.16	yes	22	3.2	odd	2
357.2.d.b.188.7	yes	22	1.1	even	1	trivial
357.2.d.b.188.16	yes	22	21.20	even	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:	\( N \)	\(=\)	\( 357 = 3 \cdot 7 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	357.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.22862i q^{2} +(0.136369 - 1.72667i) q^{3} +0.490482 q^{4} -3.00418 q^{5} +(-2.12143 - 0.167546i) q^{6} +(0.249788 - 2.63393i) q^{7} -3.05987i q^{8} +(-2.96281 - 0.470928i) q^{9} +O(q^{10})\)	\(q-1.22862i q^{2} +(0.136369 - 1.72667i) q^{3} +0.490482 q^{4} -3.00418 q^{5} +(-2.12143 - 0.167546i) q^{6} +(0.249788 - 2.63393i) q^{7} -3.05987i q^{8} +(-2.96281 - 0.470928i) q^{9} +3.69101i q^{10} +2.71004i q^{11} +(0.0668864 - 0.846903i) q^{12} +2.99346i q^{13} +(-3.23612 - 0.306895i) q^{14} +(-0.409677 + 5.18725i) q^{15} -2.77846 q^{16} +1.00000 q^{17} +(-0.578594 + 3.64018i) q^{18} -6.46312i q^{19} -1.47350 q^{20} +(-4.51388 - 0.790488i) q^{21} +3.32962 q^{22} -0.531589i q^{23} +(-5.28339 - 0.417270i) q^{24} +4.02512 q^{25} +3.67784 q^{26} +(-1.21717 + 5.05158i) q^{27} +(0.122516 - 1.29190i) q^{28} -8.12374i q^{29} +(6.37318 + 0.503339i) q^{30} +4.76164i q^{31} -2.70605i q^{32} +(4.67936 + 0.369565i) q^{33} -1.22862i q^{34} +(-0.750409 + 7.91282i) q^{35} +(-1.45320 - 0.230982i) q^{36} +0.597131 q^{37} -7.94075 q^{38} +(5.16873 + 0.408214i) q^{39} +9.19240i q^{40} -4.72816 q^{41} +(-0.971213 + 5.54587i) q^{42} +8.79033 q^{43} +1.32923i q^{44} +(8.90082 + 1.41476i) q^{45} -0.653123 q^{46} +5.20995 q^{47} +(-0.378895 + 4.79750i) q^{48} +(-6.87521 - 1.31585i) q^{49} -4.94536i q^{50} +(0.136369 - 1.72667i) q^{51} +1.46824i q^{52} -1.86825i q^{53} +(6.20650 + 1.49545i) q^{54} -8.14147i q^{55} +(-8.05949 - 0.764318i) q^{56} +(-11.1597 - 0.881367i) q^{57} -9.98102 q^{58} +14.9324 q^{59} +(-0.200939 + 2.54425i) q^{60} -8.34042i q^{61} +5.85027 q^{62} +(-1.98047 + 7.68621i) q^{63} -8.88164 q^{64} -8.99290i q^{65} +(0.454056 - 5.74918i) q^{66} +6.91945 q^{67} +0.490482 q^{68} +(-0.917881 - 0.0724921i) q^{69} +(9.72189 + 0.921971i) q^{70} -13.5527i q^{71} +(-1.44098 + 9.06580i) q^{72} -4.26626i q^{73} -0.733650i q^{74} +(0.548901 - 6.95008i) q^{75} -3.17004i q^{76} +(7.13807 + 0.676936i) q^{77} +(0.501542 - 6.35043i) q^{78} -14.5621 q^{79} +8.34702 q^{80} +(8.55645 + 2.79054i) q^{81} +5.80913i q^{82} -3.09582 q^{83} +(-2.21398 - 0.387720i) q^{84} -3.00418 q^{85} -10.8000i q^{86} +(-14.0270 - 1.10782i) q^{87} +8.29237 q^{88} +9.36351 q^{89} +(1.73820 - 10.9358i) q^{90} +(7.88457 + 0.747730i) q^{91} -0.260735i q^{92} +(8.22181 + 0.649339i) q^{93} -6.40108i q^{94} +19.4164i q^{95} +(-4.67246 - 0.369020i) q^{96} +5.63662i q^{97} +(-1.61668 + 8.44705i) q^{98} +(1.27624 - 8.02933i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q - 24 q^{4} + 5 q^{6} - 2 q^{7} - 4 q^{9}+O(q^{10}) \) 22 * q - 24 * q^4 + 5 * q^6 - 2 * q^7 - 4 * q^9	\( 22 q - 24 q^{4} + 5 q^{6} - 2 q^{7} - 4 q^{9} - 8 q^{14} - 4 q^{15} + 20 q^{16} + 22 q^{17} + 8 q^{18} - 30 q^{20} - 4 q^{21} - 12 q^{22} - 44 q^{24} + 14 q^{25} - 24 q^{26} + 6 q^{27} + 8 q^{28} + 5 q^{30} + 28 q^{33} + 10 q^{35} - 3 q^{36} - 16 q^{37} + 88 q^{38} - 14 q^{39} - 16 q^{41} + 19 q^{42} - 24 q^{43} - 46 q^{45} + 4 q^{46} - 16 q^{47} + 25 q^{48} + 6 q^{49} + 36 q^{54} - 40 q^{56} - 6 q^{57} + 24 q^{58} + 24 q^{59} - 21 q^{60} - 20 q^{62} - 6 q^{63} - 20 q^{64} - 116 q^{66} + 8 q^{67} - 24 q^{68} + 6 q^{69} + 4 q^{70} - 7 q^{72} + 54 q^{75} + 6 q^{77} + 2 q^{78} + 16 q^{79} + 128 q^{80} - 4 q^{81} + 8 q^{83} + 42 q^{84} - 48 q^{87} + 32 q^{88} - 100 q^{89} + 47 q^{90} + 18 q^{91} + 20 q^{93} + 88 q^{96} - 8 q^{98} + 18 q^{99}+O(q^{100}) \) 22 * q - 24 * q^4 + 5 * q^6 - 2 * q^7 - 4 * q^9 - 8 * q^14 - 4 * q^15 + 20 * q^16 + 22 * q^17 + 8 * q^18 - 30 * q^20 - 4 * q^21 - 12 * q^22 - 44 * q^24 + 14 * q^25 - 24 * q^26 + 6 * q^27 + 8 * q^28 + 5 * q^30 + 28 * q^33 + 10 * q^35 - 3 * q^36 - 16 * q^37 + 88 * q^38 - 14 * q^39 - 16 * q^41 + 19 * q^42 - 24 * q^43 - 46 * q^45 + 4 * q^46 - 16 * q^47 + 25 * q^48 + 6 * q^49 + 36 * q^54 - 40 * q^56 - 6 * q^57 + 24 * q^58 + 24 * q^59 - 21 * q^60 - 20 * q^62 - 6 * q^63 - 20 * q^64 - 116 * q^66 + 8 * q^67 - 24 * q^68 + 6 * q^69 + 4 * q^70 - 7 * q^72 + 54 * q^75 + 6 * q^77 + 2 * q^78 + 16 * q^79 + 128 * q^80 - 4 * q^81 + 8 * q^83 + 42 * q^84 - 48 * q^87 + 32 * q^88 - 100 * q^89 + 47 * q^90 + 18 * q^91 + 20 * q^93 + 88 * q^96 - 8 * q^98 + 18 * q^99

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