LMFDB - Embedded newform 357.2.d.b.188.17

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			188.17
Character	$\chi$	$=$	357.188
Dual form			357.2.d.b.188.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.84940i q^{2} +(-1.59187 + 0.682594i) q^{3} -1.42026 q^{4} -2.40027 q^{5} +(-1.26239 - 2.94401i) q^{6} +(-1.26533 - 2.32356i) q^{7} +1.07216i q^{8} +(2.06813 - 2.17321i) q^{9} +O(q^{10})$	\(q+1.84940i q^{2} +(-1.59187 + 0.682594i) q^{3} -1.42026 q^{4} -2.40027 q^{5} +(-1.26239 - 2.94401i) q^{6} +(-1.26533 - 2.32356i) q^{7} +1.07216i q^{8} +(2.06813 - 2.17321i) q^{9} -4.43904i q^{10} -3.68075i q^{11} +(2.26088 - 0.969462i) q^{12} +2.24417i q^{13} +(4.29718 - 2.34010i) q^{14} +(3.82093 - 1.63841i) q^{15} -4.82338 q^{16} +1.00000 q^{17} +(4.01912 + 3.82479i) q^{18} -4.04170i q^{19} +3.40901 q^{20} +(3.60030 + 2.83511i) q^{21} +6.80717 q^{22} -0.471982i q^{23} +(-0.731852 - 1.70675i) q^{24} +0.761284 q^{25} -4.15036 q^{26} +(-1.80879 + 4.87117i) q^{27} +(1.79710 + 3.30007i) q^{28} -1.76445i q^{29} +(3.03006 + 7.06640i) q^{30} -5.78300i q^{31} -6.77601i q^{32} +(2.51246 + 5.85930i) q^{33} +1.84940i q^{34} +(3.03714 + 5.57717i) q^{35} +(-2.93729 + 3.08653i) q^{36} -11.0340 q^{37} +7.47470 q^{38} +(-1.53186 - 3.57244i) q^{39} -2.57348i q^{40} -7.07450 q^{41} +(-5.24324 + 6.65837i) q^{42} +3.80862 q^{43} +5.22764i q^{44} +(-4.96407 + 5.21628i) q^{45} +0.872881 q^{46} +9.80340 q^{47} +(7.67822 - 3.29241i) q^{48} +(-3.79787 + 5.88015i) q^{49} +1.40791i q^{50} +(-1.59187 + 0.682594i) q^{51} -3.18732i q^{52} -13.4223i q^{53} +(-9.00872 - 3.34516i) q^{54} +8.83480i q^{55} +(2.49124 - 1.35664i) q^{56} +(2.75884 + 6.43388i) q^{57} +3.26316 q^{58} -8.69788 q^{59} +(-5.42672 + 2.32697i) q^{60} -4.34312i q^{61} +10.6950 q^{62} +(-7.66645 - 2.05560i) q^{63} +2.88476 q^{64} -5.38662i q^{65} +(-10.8362 + 4.64653i) q^{66} -12.7593 q^{67} -1.42026 q^{68} +(0.322172 + 0.751336i) q^{69} +(-10.3144 + 5.61686i) q^{70} +4.79041i q^{71} +(2.33003 + 2.21738i) q^{72} +4.36271i q^{73} -20.4063i q^{74} +(-1.21187 + 0.519648i) q^{75} +5.74028i q^{76} +(-8.55246 + 4.65738i) q^{77} +(6.60686 - 2.83301i) q^{78} +13.7946 q^{79} +11.5774 q^{80} +(-0.445665 - 8.98896i) q^{81} -13.0835i q^{82} -7.25354 q^{83} +(-5.11337 - 4.02660i) q^{84} -2.40027 q^{85} +7.04364i q^{86} +(1.20440 + 2.80878i) q^{87} +3.94637 q^{88} -10.5542 q^{89} +(-9.64696 - 9.18052i) q^{90} +(5.21448 - 2.83963i) q^{91} +0.670338i q^{92} +(3.94744 + 9.20581i) q^{93} +18.1304i q^{94} +9.70116i q^{95} +(4.62526 + 10.7866i) q^{96} +0.875014i q^{97} +(-10.8747 - 7.02376i) q^{98} +(-7.99904 - 7.61228i) 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 $

$2$			1.84940i			1.30772i	0.756616	+	0.653860i	$0.226851\pi$
$2$			1.84940i			1.30772i	−0.756616	+	0.653860i	$0.773149\pi$
$3$	−1.59187	+	0.682594i	−0.919069	+	0.394096i
$3$	−1.59187	+	0.682594i	−0.919069	+	0.394096i
$4$	−1.42026			−0.710131
$5$	−2.40027			−1.07343			−0.536716	−	0.843763i	$-0.680335\pi$
$5$	−2.40027			−1.07343			−0.536716	+	0.843763i	$0.680335\pi$
$6$	−1.26239	−	2.94401i	−0.515367	−	1.20189i
$7$	−1.26533	−	2.32356i	−0.478251	−	0.878223i
$7$	−1.26533	−	2.32356i	−0.478251	−	0.878223i
$8$			1.07216i			0.379067i
$9$	2.06813	−	2.17321i	0.689377	−	0.724403i
$10$		−	4.43904i		−	1.40375i
$11$		−	3.68075i		−	1.10979i	−0.831921	−	0.554895i	$-0.812759\pi$
$11$		−	3.68075i		−	1.10979i	0.831921	−	0.554895i	$-0.187241\pi$
$12$	2.26088	−	0.969462i	0.652660	−	0.279860i
$13$			2.24417i			0.622422i	0.950341	+	0.311211i	$0.100735\pi$
$13$			2.24417i			0.622422i	−0.950341	+	0.311211i	$0.899265\pi$
$14$	4.29718	−	2.34010i	1.14847	−	0.625418i
$15$	3.82093	−	1.63841i	0.986559	−	0.423035i
$16$	−4.82338			−1.20584
$17$	1.00000			0.242536
$17$	1.00000			0.242536
$18$	4.01912	+	3.82479i	0.947316	+	0.901512i
$19$		−	4.04170i		−	0.927230i	−0.886037	−	0.463615i	$-0.846552\pi$
$19$		−	4.04170i		−	0.927230i	0.886037	−	0.463615i	$-0.153448\pi$
$20$	3.40901			0.762278
$21$	3.60030	+	2.83511i	0.785650	+	0.618672i
$22$	6.80717			1.45129
$23$		−	0.471982i		−	0.0984150i	−0.998789	−	0.0492075i	$-0.984330\pi$
$23$		−	0.471982i		−	0.0984150i	0.998789	−	0.0492075i	$-0.0156696\pi$
$24$	−0.731852	−	1.70675i	−0.149389	−	0.348389i
$25$	0.761284			0.152257
$26$	−4.15036			−0.813954
$27$	−1.80879	+	4.87117i	−0.348101	+	0.937457i
$28$	1.79710	+	3.30007i	0.339621	+	0.623654i
$29$		−	1.76445i		−	0.327650i	−0.986489	−	0.163825i	$-0.947617\pi$
$29$		−	1.76445i		−	0.327650i	0.986489	−	0.163825i	$-0.0523833\pi$
$30$	3.03006	+	7.06640i	0.553211	+	1.29014i
$31$		−	5.78300i		−	1.03866i	−0.854575	−	0.519328i	$-0.826182\pi$
$31$		−	5.78300i		−	1.03866i	0.854575	−	0.519328i	$-0.173818\pi$
$32$		−	6.77601i		−	1.19784i
$33$	2.51246	+	5.85930i	0.437363	+	1.01997i
$34$			1.84940i			0.317169i
$35$	3.03714	+	5.57717i	0.513370	+	0.942713i
$36$	−2.93729	+	3.08653i	−0.489548	+	0.514421i
$37$	−11.0340			−1.81398			−0.906992	−	0.421148i	$-0.861627\pi$
$37$	−11.0340			−1.81398			−0.906992	+	0.421148i	$0.861627\pi$
$38$	7.47470			1.21256
$39$	−1.53186	−	3.57244i	−0.245294	−	0.572049i
$40$		−	2.57348i		−	0.406903i
$41$	−7.07450			−1.10485			−0.552425	−	0.833562i	$-0.686298\pi$
$41$	−7.07450			−1.10485			−0.552425	+	0.833562i	$0.686298\pi$
$42$	−5.24324	+	6.65837i	−0.809049	+	1.02741i
$43$	3.80862			0.580809			0.290405	−	0.956904i	$-0.406210\pi$
$43$	3.80862			0.580809			0.290405	+	0.956904i	$0.406210\pi$
$44$			5.22764i			0.788096i
$45$	−4.96407	+	5.21628i	−0.740000	+	0.777597i
$46$	0.872881			0.128699
$47$	9.80340			1.42997			0.714987	−	0.699138i	$-0.246433\pi$
$47$	9.80340			1.42997			0.714987	+	0.699138i	$0.246433\pi$
$48$	7.67822	−	3.29241i	1.10826	−	0.475218i
$49$	−3.79787	+	5.88015i	−0.542553	+	0.840022i
$50$			1.40791i			0.199109i
$51$	−1.59187	+	0.682594i	−0.222907	+	0.0955823i
$52$		−	3.18732i		−	0.442001i
$53$		−	13.4223i		−	1.84369i	−0.387558	−	0.921845i	$-0.626681\pi$
$53$		−	13.4223i		−	1.84369i	0.387558	−	0.921845i	$-0.373319\pi$
$54$	−9.00872	−	3.34516i	−1.22593	−	0.455219i
$55$			8.83480i			1.19128i
$56$	2.49124	−	1.35664i	0.332906	−	0.181289i
$57$	2.75884	+	6.43388i	0.365417	+	0.852188i
$58$	3.26316			0.428475
$59$	−8.69788			−1.13237			−0.566184	−	0.824279i	$-0.691581\pi$
$59$	−8.69788			−1.13237			−0.566184	+	0.824279i	$0.691581\pi$
$60$	−5.42672	+	2.32697i	−0.700586	+	0.300410i
$61$		−	4.34312i		−	0.556080i	−0.960570	−	0.278040i	$-0.910315\pi$
$61$		−	4.34312i		−	0.556080i	0.960570	−	0.278040i	$-0.0896847\pi$
$62$	10.6950			1.35827
$63$	−7.66645	−	2.05560i	−0.965882	−	0.258981i
$64$	2.88476			0.360594
$65$		−	5.38662i		−	0.668128i
$66$	−10.8362	+	4.64653i	−1.33384	+	0.571949i
$67$	−12.7593			−1.55880			−0.779399	−	0.626528i	$-0.784476\pi$
$67$	−12.7593			−1.55880			−0.779399	+	0.626528i	$0.784476\pi$
$68$	−1.42026			−0.172232
$69$	0.322172	+	0.751336i	0.0387849	+	0.0904502i
$70$	−10.3144	+	5.61686i	−1.23280	+	0.671344i
$71$			4.79041i			0.568517i	0.958748	+	0.284259i	$0.0917475\pi$
$71$			4.79041i			0.568517i	−0.958748	+	0.284259i	$0.908253\pi$
$72$	2.33003	+	2.21738i	0.274597	+	0.261320i
$73$			4.36271i			0.510617i	0.966860	+	0.255308i	$0.0821770\pi$
$73$			4.36271i			0.510617i	−0.966860	+	0.255308i	$0.917823\pi$
$74$		−	20.4063i		−	2.37218i
$75$	−1.21187	+	0.519648i	−0.139935	+	0.0600038i
$76$			5.74028i			0.658455i
$77$	−8.55246	+	4.65738i	−0.974643	+	0.530757i
$78$	6.60686	−	2.83301i	0.748080	−	0.320776i
$79$	13.7946			1.55201			0.776006	−	0.630725i	$-0.217242\pi$
$79$	13.7946			1.55201			0.776006	+	0.630725i	$0.217242\pi$
$80$	11.5774			1.29439
$81$	−0.445665	−	8.98896i	−0.0495183	−	0.998773i
$82$		−	13.0835i		−	1.44484i
$83$	−7.25354			−0.796179			−0.398090	−	0.917347i	$-0.630327\pi$
$83$	−7.25354			−0.796179			−0.398090	+	0.917347i	$0.630327\pi$
$84$	−5.11337	−	4.02660i	−0.557914	−	0.439338i
$85$	−2.40027			−0.260346
$86$			7.04364i			0.759536i
$87$	1.20440	+	2.80878i	0.129126	+	0.301133i
$88$	3.94637			0.420685
$89$	−10.5542			−1.11874			−0.559372	−	0.828917i	$-0.688958\pi$
$89$	−10.5542			−1.11874			−0.559372	+	0.828917i	$0.688958\pi$
$90$	−9.64696	−	9.18052i	−1.01688	−	0.967712i
$91$	5.21448	−	2.83963i	0.546626	−	0.297674i
$92$			0.670338i			0.0698876i
$93$	3.94744	+	9.20581i	0.409330	+	0.954598i
$94$			18.1304i			1.87000i
$95$			9.70116i			0.995318i
$96$	4.62526	+	10.7866i	0.472064	+	1.10090i
$97$			0.875014i			0.0888442i	0.999013	+	0.0444221i	$0.0141446\pi$
$97$			0.875014i			0.0888442i	−0.999013	+	0.0444221i	$0.985855\pi$
$98$	−10.8747	−	7.02376i	−1.09851	−	0.709507i
$99$	−7.99904	−	7.61228i	−0.803934	−	0.765063i
$100$	−1.08122			−0.108122
$101$	1.19341			0.118748			0.0593742	−	0.998236i	$-0.481089\pi$
$101$	1.19341			0.118748			0.0593742	+	0.998236i	$0.481089\pi$
$102$	−1.26239	−	2.94401i	−0.124995	−	0.291500i
$103$			4.05164i			0.399220i	0.979875	+	0.199610i	$0.0639675\pi$
$103$			4.05164i			0.399220i	−0.979875	+	0.199610i	$0.936033\pi$
$104$	−2.40612			−0.235940
$105$	−8.64168	−	6.80502i	−0.843342	−	0.664102i
$106$	24.8231			2.41103
$107$			2.31674i			0.223968i	0.993710	+	0.111984i	$0.0357205\pi$
$107$			2.31674i			0.223968i	−0.993710	+	0.111984i	$0.964279\pi$
$108$	2.56895	−	6.91834i	0.247198	−	0.665717i
$109$	−15.7891			−1.51232			−0.756159	−	0.654388i	$-0.772926\pi$
$109$	−15.7891			−1.51232			−0.756159	+	0.654388i	$0.772926\pi$
$110$	−16.3390			−1.55787
$111$	17.5648	−	7.53176i	1.66718	−	0.714883i
$112$	6.10318	+	11.2074i	0.576696	+	1.05900i
$113$		−	0.745374i		−	0.0701189i	−0.999385	−	0.0350594i	$-0.988838\pi$
$113$		−	0.745374i		−	0.0701189i	0.999385	−	0.0350594i	$-0.0111620\pi$
$114$	−11.8988	+	5.10218i	−1.11442	+	0.477863i
$115$			1.13288i			0.105642i
$116$			2.50598i			0.232675i
$117$	4.87706	+	4.64125i	0.450884	+	0.429083i
$118$		−	16.0858i		−	1.48082i
$119$	−1.26533	−	2.32356i	−0.115993	−	0.213000i
$120$	1.75664	+	4.09666i	0.160359	+	0.373972i
$121$	−2.54795			−0.231632
$122$	8.03215			0.727196
$123$	11.2617	−	4.82901i	1.01543	−	0.435417i
$124$			8.21337i			0.737583i
$125$	10.1741			0.909995
$126$	3.80162	−	14.1783i	0.338675	−	1.26310i
$127$	0.00820814			0.000728355			0.000364177	−	1.00000i	$-0.499884\pi$
$127$	0.00820814			0.000728355			0.000364177		1.00000i	$0.499884\pi$
$128$		−	8.21696i		−	0.726284i
$129$	−6.06285	+	2.59974i	−0.533804	+	0.228894i
$130$	9.96199			0.873724
$131$	3.26903			0.285617			0.142808	−	0.989750i	$-0.454387\pi$
$131$	3.26903			0.285617			0.142808	+	0.989750i	$0.454387\pi$
$132$	−3.56835	−	8.32174i	−0.310585	−	0.724315i
$133$	−9.39114	+	5.11409i	−0.814315	+	0.443448i
$134$		−	23.5970i		−	2.03847i
$135$	4.34158	−	11.6921i	0.373663	−	1.00630i
$136$			1.07216i			0.0919373i
$137$			4.75427i			0.406185i	0.979160	+	0.203092i	$0.0650992\pi$
$137$			4.75427i			0.406185i	−0.979160	+	0.203092i	$0.934901\pi$
$138$	−1.38952	+	0.595823i	−0.118284	+	0.0507198i
$139$		−	0.184168i		−	0.0156209i	−0.999969	−	0.00781047i	$-0.997514\pi$
$139$		−	0.184168i		−	0.0156209i	0.999969	−	0.00781047i	$-0.00248618\pi$
$140$	−4.31353	−	7.92104i	−0.364560	−	0.669450i
$141$	−15.6058	+	6.69174i	−1.31424	+	0.563546i
$142$	−8.85937			−0.743461
$143$	8.26025			0.690757
$144$	−9.97538	+	10.4822i	−0.831282	+	0.873517i
$145$			4.23515i			0.351710i
$146$	−8.06838			−0.667744
$147$	2.03198	−	11.9529i	0.167595	−	0.985856i
$148$	15.6712			1.28817
$149$			14.6746i			1.20219i	0.799177	+	0.601096i	$0.205269\pi$
$149$			14.6746i			1.20219i	−0.799177	+	0.601096i	$0.794731\pi$
$150$	−0.961034	−	2.24122i	−0.0784681	−	0.182995i
$151$	14.2407			1.15889			0.579445	−	0.815011i	$-0.303269\pi$
$151$	14.2407			1.15889			0.579445	+	0.815011i	$0.303269\pi$
$152$	4.33337			0.351482
$153$	2.06813	−	2.17321i	0.167199	−	0.175693i
$154$	−8.61333	−	15.8169i	−0.694082	−	1.27456i
$155$			13.8807i			1.11493i
$156$	2.17564	+	5.07381i	0.174191	+	0.406230i
$157$			12.6334i			1.00825i	0.863630	+	0.504126i	$0.168185\pi$
$157$			12.6334i			1.00825i	−0.863630	+	0.504126i	$0.831815\pi$
$158$			25.5116i			2.02960i
$159$	9.16196	+	21.3666i	0.726591	+	1.69448i
$160$			16.2642i			1.28580i
$161$	−1.09668	+	0.597214i	−0.0864304	+	0.0470670i
$162$	16.6241	−	0.824211i	1.30612	−	0.0647561i
$163$	12.1532			0.951915			0.475958	−	0.879468i	$-0.342102\pi$
$163$	12.1532			0.951915			0.475958	+	0.879468i	$0.342102\pi$
$164$	10.0476			0.784589
$165$	−6.03058	−	14.0639i	−0.469480	−	1.09487i
$166$		−	13.4147i		−	1.04118i
$167$	6.22625			0.481802			0.240901	−	0.970550i	$-0.422557\pi$
$167$	6.22625			0.481802			0.240901	+	0.970550i	$0.422557\pi$
$168$	−3.03970	+	3.86011i	−0.234518	+	0.297814i
$169$	7.96368			0.612591
$170$		−	4.43904i		−	0.340459i
$171$	−8.78346	−	8.35877i	−0.671688	−	0.639211i
$172$	−5.40924			−0.412451
$173$	12.1737			0.925548			0.462774	−	0.886476i	$-0.346854\pi$
$173$	12.1737			0.925548			0.462774	+	0.886476i	$0.346854\pi$
$174$	−5.19455	+	2.22742i	−0.393798	+	0.168860i
$175$	−0.963277	−	1.76889i	−0.0728169	−	0.133715i
$176$			17.7537i			1.33823i
$177$	13.8459	−	5.93712i	1.04072	−	0.446261i
$178$		−	19.5189i		−	1.46300i
$179$			23.2813i			1.74012i	0.492942	+	0.870062i	$0.335922\pi$
$179$			23.2813i			1.74012i	−0.492942	+	0.870062i	$0.664078\pi$
$180$	7.05028	−	7.40849i	0.525497	−	0.552196i
$181$		−	5.15359i		−	0.383063i	−0.981486	−	0.191532i	$-0.938655\pi$
$181$		−	5.15359i		−	0.383063i	0.981486	−	0.191532i	$-0.0613455\pi$
$182$	5.25159	+	9.64363i	0.389274	+	0.714833i
$183$	2.96459	+	6.91371i	0.219149	+	0.511076i
$184$	0.506042			0.0373059
$185$	26.4846			1.94719
$186$	−17.0252	+	7.30037i	−1.24835	+	0.535289i
$187$		−	3.68075i		−	0.269163i
$188$	−13.9234			−1.01547
$189$	13.6072	−	1.96082i	0.989776	−	0.142628i
$190$	−17.9413			−1.30160
$191$		−	15.5871i		−	1.12784i	−0.825829	−	0.563921i	$-0.809292\pi$
$191$		−	15.5871i		−	1.12784i	0.825829	−	0.563921i	$-0.190708\pi$
$192$	−4.59217	+	1.96912i	−0.331411	+	0.142109i
$193$	−3.46178			−0.249184			−0.124592	−	0.992208i	$-0.539762\pi$
$193$	−3.46178			−0.249184			−0.124592	+	0.992208i	$0.539762\pi$
$194$	−1.61825			−0.116183
$195$	3.67687	+	8.57482i	0.263306	+	0.614056i
$196$	5.39397	−	8.35136i	0.385284	−	0.596526i
$197$			26.7125i			1.90318i	0.307364	+	0.951592i	$0.400553\pi$
$197$			26.7125i			1.90318i	−0.307364	+	0.951592i	$0.599447\pi$
$198$	14.0781	−	14.7934i	1.00049	−	1.05132i
$199$		−	20.4627i		−	1.45057i	−0.688451	−	0.725283i	$-0.741709\pi$
$199$		−	20.4627i		−	1.45057i	0.688451	−	0.725283i	$-0.258291\pi$
$200$			0.816221i			0.0577156i
$201$	20.3112	−	8.70943i	1.43264	−	0.614316i
$202$			2.20708i			0.155290i
$203$	−4.09981	+	2.23261i	−0.287750	+	0.156699i
$204$	2.26088	−	0.969462i	0.158293	−	0.0678759i
$205$	16.9807			1.18598
$206$	−7.49308			−0.522068
$207$	−1.02571	−	0.976121i	−0.0712921	−	0.0678451i
$208$		−	10.8245i		−	0.750544i
$209$	−14.8765			−1.02903
$210$	12.5852	−	15.9819i	0.868460	−	1.10285i
$211$	−15.3721			−1.05826			−0.529131	−	0.848540i	$-0.677482\pi$
$211$	−15.3721			−1.05826			−0.529131	+	0.848540i	$0.677482\pi$
$212$			19.0631i			1.30926i
$213$	−3.26991	−	7.62574i	−0.224050	−	0.522507i
$214$	−4.28457			−0.292887
$215$	−9.14171			−0.623459
$216$	−5.22269	−	1.93932i	−0.355359	−	0.131954i
$217$	−13.4371	+	7.31741i	−0.912173	+	0.496738i
$218$		−	29.2002i		−	1.97769i
$219$	−2.97796	−	6.94489i	−0.201232	−	0.469292i
$220$		−	12.5477i		−	0.845968i
$221$			2.24417i			0.150959i
$222$	13.9292	+	32.4843i	0.934867	+	2.18020i
$223$		−	22.0243i		−	1.47486i	−0.675426	−	0.737428i	$-0.736040\pi$
$223$		−	22.0243i		−	1.47486i	0.675426	−	0.737428i	$-0.263960\pi$
$224$	−15.7445	+	8.57390i	−1.05197	+	0.572868i
$225$	1.57444	−	1.65443i	0.104962	−	0.110295i
$226$	1.37849			0.0916958
$227$	−9.19208			−0.610100			−0.305050	−	0.952336i	$-0.598673\pi$
$227$	−9.19208			−0.610100			−0.305050	+	0.952336i	$0.598673\pi$
$228$	−3.91828	−	9.13780i	−0.259494	−	0.605166i
$229$		−	21.8189i		−	1.44183i	−0.693021	−	0.720917i	$-0.743721\pi$
$229$		−	21.8189i		−	1.44183i	0.693021	−	0.720917i	$-0.256279\pi$
$230$	−2.09515			−0.138150
$231$	10.4353	−	13.2518i	0.686595	−	0.871905i
$232$	1.89178			0.124201
$233$		−	13.5354i		−	0.886733i	−0.896340	−	0.443366i	$-0.853784\pi$
$233$		−	13.5354i		−	0.886733i	0.896340	−	0.443366i	$-0.146216\pi$
$234$	−8.58350	+	9.01961i	−0.561121	+	0.589630i
$235$	−23.5308			−1.53498
$236$	12.3533			0.804129
$237$	−21.9593	+	9.41610i	−1.42641	+	0.611642i
$238$	4.29718	−	2.34010i	0.278545	−	0.151686i
$239$		−	12.0568i		−	0.779889i	−0.920838	−	0.389945i	$-0.872494\pi$
$239$		−	12.0568i		−	0.779889i	0.920838	−	0.389945i	$-0.127506\pi$
$240$	−18.4298	+	7.90266i	−1.18964	+	0.510115i
$241$			6.51847i			0.419892i	0.977713	+	0.209946i	$0.0673288\pi$
$241$			6.51847i			0.419892i	−0.977713	+	0.209946i	$0.932671\pi$
$242$		−	4.71217i		−	0.302910i
$243$	6.84525	+	14.0051i	0.439123	+	0.898427i
$244$			6.16837i			0.394890i
$245$	9.11590	−	14.1139i	0.582394	−	0.901706i
$246$	8.93074	+	20.8274i	0.569403	+	1.32790i
$247$	9.07028			0.577128
$248$	6.20032			0.393721
$249$	11.5467	−	4.95122i	0.731744	−	0.313771i
$250$			18.8158i			1.19002i
$251$	17.4818			1.10344			0.551720	−	0.834029i	$-0.313972\pi$
$251$	17.4818			1.10344			0.551720	+	0.834029i	$0.313972\pi$
$252$	10.8884	+	2.91949i	0.685903	+	0.183911i
$253$	−1.73725			−0.109220
$254$			0.0151801i			0.000952484i
$255$	3.82093	−	1.63841i	0.239276	−	0.102601i
$256$	20.9659			1.31037
$257$	−30.4942			−1.90218			−0.951089	−	0.308918i	$-0.900033\pi$
$257$	−30.4942			−1.90218			−0.951089	+	0.308918i	$0.900033\pi$
$258$	−4.80795	−	11.2126i	−0.299330	−	0.698066i
$259$	13.9617	+	25.6382i	0.867539	+	1.59308i
$260$			7.65041i			0.474458i
$261$	−3.83452	−	3.64911i	−0.237351	−	0.225874i
$262$			6.04573i			0.373506i
$263$		−	10.9726i		−	0.676599i	−0.941039	−	0.338299i	$-0.890148\pi$
$263$		−	10.9726i		−	0.676599i	0.941039	−	0.338299i	$-0.109852\pi$
$264$	−6.28213	+	2.69377i	−0.386638	+	0.165790i
$265$			32.2170i			1.97908i
$266$	−9.45798	−	17.3679i	−0.579906	−	1.06490i
$267$	16.8010	−	7.20424i	1.02820	−	0.440892i
$268$	18.1216			1.10695
$269$	−12.5199			−0.763351			−0.381675	−	0.924296i	$-0.624653\pi$
$269$	−12.5199			−0.763351			−0.381675	+	0.924296i	$0.624653\pi$
$270$	21.6233	+	8.02929i	1.31595	+	0.488647i
$271$		−	20.9605i		−	1.27326i	−0.771170	−	0.636629i	$-0.780328\pi$
$271$		−	20.9605i		−	1.27326i	0.771170	−	0.636629i	$-0.219672\pi$
$272$	−4.82338			−0.292460
$273$	−6.36248	+	8.07970i	−0.385075	+	0.489006i
$274$	−8.79253			−0.531176
$275$		−	2.80210i		−	0.168973i
$276$	−0.457569	−	1.06709i	−0.0275424	−	0.0642315i
$277$	−19.4964			−1.17143			−0.585713	−	0.810518i	$-0.699186\pi$
$277$	−19.4964			−1.17143			−0.585713	+	0.810518i	$0.699186\pi$
$278$	0.340600			0.0204278
$279$	−12.5677	−	11.9600i	−0.752406	−	0.716026i
$280$	−5.97964	+	3.25631i	−0.357352	+	0.194602i
$281$			5.80477i			0.346284i	0.984897	+	0.173142i	$0.0553919\pi$
$281$			5.80477i			0.346284i	−0.984897	+	0.173142i	$0.944608\pi$
$282$	−12.3757	−	28.8613i	−0.736961	−	1.71866i
$283$		−	19.2180i		−	1.14239i	−0.820814	−	0.571195i	$-0.806480\pi$
$283$		−	19.2180i		−	1.14239i	0.820814	−	0.571195i	$-0.193520\pi$
$284$		−	6.80364i		−	0.403722i
$285$	−6.62195	−	15.4430i	−0.392251	−	0.914767i
$286$			15.2765i			0.903317i
$287$	8.95159	+	16.4380i	0.528395	+	0.970306i
$288$	−14.7257	−	14.0137i	−0.867719	−	0.825764i
$289$	1.00000			0.0588235
$290$	−7.83247			−0.459938
$291$	−0.597279	−	1.39291i	−0.0350131	−	0.0816540i
$292$		−	6.19620i		−	0.362605i
$293$	5.45107			0.318455			0.159227	−	0.987242i	$-0.449100\pi$
$293$	5.45107			0.318455			0.159227	+	0.987242i	$0.449100\pi$
$294$	22.1056	+	3.75793i	1.28922	+	0.219167i
$295$	20.8772			1.21552
$296$		−	11.8303i		−	0.687622i
$297$	17.9296	+	6.65771i	1.04038	+	0.386319i
$298$	−27.1392			−1.57213
$299$	1.05921			0.0612557
$300$	1.72117	−	0.738036i	0.0993719	−	0.0426105i
$301$	−4.81917	−	8.84956i	−0.277772	−	0.510080i
$302$			26.3367i			1.51550i
$303$	−1.89975	+	0.814611i	−0.109138	+	0.0467982i
$304$			19.4947i			1.11810i
$305$			10.4247i			0.596914i
$306$	4.01912	+	3.82479i	0.229758	+	0.218649i
$307$		−	9.64181i		−	0.550287i	−0.961403	−	0.275143i	$-0.911275\pi$
$307$		−	9.64181i		−	0.550287i	0.961403	−	0.275143i	$-0.0887254\pi$
$308$	12.1467	−	6.61470i	0.692124	−	0.376907i
$309$	−2.76562	−	6.44970i	−0.157331	−	0.366911i
$310$	−25.6710			−1.45801
$311$	−19.0177			−1.07839			−0.539197	−	0.842180i	$-0.681272\pi$
$311$	−19.0177			−1.07839			−0.539197	+	0.842180i	$0.681272\pi$
$312$	3.83025	−	1.64240i	0.216845	−	0.0929828i
$313$			27.2218i			1.53867i	0.638846	+	0.769334i	$0.279412\pi$
$313$			27.2218i			1.53867i	−0.638846	+	0.769334i	$0.720588\pi$
$314$	−23.3641			−1.31851
$315$	18.4015	+	4.93399i	1.03681	+	0.277999i
$316$	−19.5919			−1.10213
$317$		−	7.06573i		−	0.396851i	−0.980116	−	0.198425i	$-0.936417\pi$
$317$		−	7.06573i		−	0.396851i	0.980116	−	0.198425i	$-0.0635828\pi$
$318$	−39.5152	+	16.9441i	−2.21590	+	0.950177i
$319$	−6.49451			−0.363623
$320$	−6.92419			−0.387074
$321$	−1.58139	−	3.68796i	−0.0882648	−	0.205842i
$322$	−1.10448	−	2.02819i	−0.0615505	−	0.113027i
$323$		−	4.04170i		−	0.224886i
$324$	0.632961	+	12.7667i	0.0351645	+	0.709260i
$325$			1.70845i			0.0947680i
$326$			22.4761i			1.24484i
$327$	25.1342	−	10.7775i	1.38992	−	0.595998i
$328$		−	7.58502i		−	0.418813i
$329$	−12.4046	−	22.7788i	−0.683886	−	1.25584i
$330$	26.0097	−	11.1529i	1.43179	−	0.613948i
$331$	−17.5535			−0.964830			−0.482415	−	0.875943i	$-0.660240\pi$
$331$	−17.5535			−0.964830			−0.482415	+	0.875943i	$0.660240\pi$
$332$	10.3019			0.565392
$333$	−22.8198	+	23.9792i	−1.25052	+	1.31405i
$334$			11.5148i			0.630062i
$335$	30.6258			1.67326
$336$	−17.3656	−	13.6748i	−0.947371	−	0.746022i
$337$	1.88673			0.102777			0.0513885	−	0.998679i	$-0.483635\pi$
$337$	1.88673			0.102777			0.0513885	+	0.998679i	$0.483635\pi$
$338$			14.7280i			0.801097i
$339$	0.508787	+	1.18654i	0.0276335	+	0.0644441i
$340$	3.40901			0.184880
$341$	−21.2858			−1.15269
$342$	15.4587	−	16.2441i	0.835909	−	0.878379i
$343$	18.4685	+	1.38424i	0.997203	+	0.0747417i
$344$			4.08346i			0.220166i
$345$	−0.773299	−	1.80341i	−0.0416330	−	0.0970922i
$346$			22.5140i			1.21036i
$347$			20.2703i			1.08816i	0.839032	+	0.544082i	$0.183122\pi$
$347$			20.2703i			1.08816i	−0.839032	+	0.544082i	$0.816878\pi$
$348$	−1.71057	−	3.98921i	−0.0916961	−	0.213844i
$349$		−	19.7718i		−	1.05836i	−0.848509	−	0.529180i	$-0.822499\pi$
$349$		−	19.7718i		−	1.05836i	0.848509	−	0.529180i	$-0.177501\pi$
$350$	3.27138	−	1.78148i	0.174862	−	0.0952241i
$351$	−10.9318	−	4.05924i	−0.583494	−	0.216666i
$352$	−24.9408			−1.32935
$353$	22.5769			1.20165			0.600823	−	0.799382i	$-0.294840\pi$
$353$	22.5769			1.20165			0.600823	+	0.799382i	$0.294840\pi$
$354$	10.9801	+	25.6066i	0.583584	+	1.36098i
$355$		−	11.4983i		−	0.610265i
$356$	14.9897			0.794455
$357$	3.60030	+	2.83511i	0.190548	+	0.150050i
$358$	−43.0563			−2.27560
$359$			12.3863i			0.653723i	0.945072	+	0.326861i	$0.105991\pi$
$359$			12.3863i			0.653723i	−0.945072	+	0.326861i	$0.894009\pi$
$360$	−5.59271	−	5.32229i	−0.294762	−	0.280510i
$361$	2.66466			0.140245
$362$	9.53103			0.500940
$363$	4.05602	−	1.73922i	0.212886	−	0.0912852i
$364$	−7.40592	+	4.03301i	−0.388176	+	0.211387i
$365$		−	10.4717i		−	0.548113i
$366$	−12.7862	+	5.48269i	−0.668344	+	0.286585i
$367$		−	29.8154i		−	1.55635i	−0.628046	−	0.778176i	$-0.716145\pi$
$367$		−	29.8154i		−	1.55635i	0.628046	−	0.778176i	$-0.283855\pi$
$368$			2.27655i			0.118673i
$369$	−14.6310	+	15.3743i	−0.761659	+	0.800357i
$370$			48.9806i			2.54638i
$371$	−31.1875	+	16.9836i	−1.61917	+	0.881746i
$372$	−5.60640	−	13.0747i	−0.290678	−	0.677890i
$373$	30.7866			1.59407			0.797034	−	0.603934i	$-0.206401\pi$
$373$	30.7866			1.59407			0.797034	+	0.603934i	$0.206401\pi$
$374$	6.80717			0.351990
$375$	−16.1958	+	6.94474i	−0.836348	+	0.358625i
$376$			10.5109i			0.542056i
$377$	3.95973			0.203937
$378$	3.62633	+	25.1650i	0.186518	+	1.29435i
$379$	−6.70310			−0.344315			−0.172158	−	0.985069i	$-0.555074\pi$
$379$	−6.70310			−0.344315			−0.172158	+	0.985069i	$0.555074\pi$
$380$		−	13.7782i		−	0.706807i
$381$	−0.0130663	+	0.00560283i	−0.000669408	+	0.000287041i
$382$	28.8267			1.47490
$383$	−23.8439			−1.21837			−0.609183	−	0.793030i	$-0.708503\pi$
$383$	−23.8439			−1.21837			−0.609183	+	0.793030i	$0.708503\pi$
$384$	5.60885	+	13.0804i	0.286225	+	0.667505i
$385$	20.5282	−	11.1790i	1.04621	−	0.569732i
$386$		−	6.40220i		−	0.325863i
$387$	7.87673	−	8.27692i	0.400396	−	0.420740i
$388$		−	1.24275i		−	0.0630910i
$389$		−	35.9558i		−	1.82303i	−0.411266	−	0.911515i	$-0.634913\pi$
$389$		−	35.9558i		−	1.82303i	0.411266	−	0.911515i	$-0.365087\pi$
$390$	−15.8582	+	6.79999i	−0.803013	+	0.344331i
$391$		−	0.471982i		−	0.0238691i
$392$	−6.30449	−	4.07194i	−0.318425	−	0.205664i
$393$	−5.20389	+	2.23142i	−0.262501	+	0.112560i
$394$	−49.4019			−2.48883
$395$	−33.1107			−1.66598
$396$	11.3607	+	10.8114i	0.570899	+	0.543295i
$397$			5.63741i			0.282933i	0.989943	+	0.141467i	$0.0451818\pi$
$397$			5.63741i			0.282933i	−0.989943	+	0.141467i	$0.954818\pi$
$398$	37.8437			1.89693
$399$	11.4587	−	14.5513i	0.573651	−	0.728478i
$400$	−3.67196			−0.183598
$401$		−	6.93880i		−	0.346507i	−0.984877	−	0.173254i	$-0.944572\pi$
$401$		−	6.93880i		−	0.346507i	0.984877	−	0.173254i	$-0.0554281\pi$
$402$	16.1072	+	37.5635i	0.803353	+	1.87350i
$403$	12.9781			0.646483
$404$	−1.69495			−0.0843269
$405$	1.06972	+	21.5759i	0.0531546	+	1.07212i
$406$	−4.12899	−	7.58216i	−0.204918	−	0.376296i
$407$			40.6136i			2.01314i
$408$	−0.731852	−	1.70675i	−0.0362321	−	0.0844967i
$409$			32.2586i			1.59509i	0.603261	+	0.797544i	$0.293868\pi$
$409$			32.2586i			1.59509i	−0.603261	+	0.797544i	$0.706132\pi$
$410$			31.4040i			1.55093i
$411$	−3.24524	−	7.56821i	−0.160076	−	0.373312i
$412$		−	5.75439i		−	0.283498i
$413$	11.0057	+	20.2100i	0.541555	+	0.994471i
$414$	1.80523	−	1.89695i	0.0887223	−	0.0932301i
$415$	17.4104			0.854644
$416$	15.2065			0.745562
$417$	0.125712	+	0.293173i	0.00615615	+	0.0143567i
$418$		−	27.5125i		−	1.34568i
$419$	27.2583			1.33166			0.665828	−	0.746105i	$-0.268078\pi$
$419$	27.2583			1.33166			0.665828	+	0.746105i	$0.268078\pi$
$420$	12.2735	+	9.66492i	0.598883	+	0.471600i
$421$	−13.7243			−0.668879			−0.334440	−	0.942417i	$-0.608547\pi$
$421$	−13.7243			−0.668879			−0.334440	+	0.942417i	$0.608547\pi$
$422$		−	28.4292i		−	1.38391i
$423$	20.2747	−	21.3048i	0.985791	−	1.03588i
$424$	14.3909			0.698883
$425$	0.761284			0.0369277
$426$	14.1030	−	6.04735i	0.683293	−	0.292995i
$427$	−10.0915	+	5.49549i	−0.488362	+	0.265945i
$428$		−	3.29038i		−	0.159047i
$429$	−13.1493	+	5.63840i	−0.634854	+	0.272224i
$430$		−	16.9066i		−	0.815310i
$431$		−	23.0788i		−	1.11167i	−0.831294	−	0.555833i	$-0.812399\pi$
$431$		−	23.0788i		−	1.11167i	0.831294	−	0.555833i	$-0.187601\pi$
$432$	8.72447	−	23.4955i	0.419756	−	1.13043i
$433$			3.56077i			0.171120i	0.996333	+	0.0855598i	$0.0272679\pi$
$433$			3.56077i			0.171120i	−0.996333	+	0.0855598i	$0.972732\pi$
$434$	−13.5328	−	24.8506i	−0.649594	−	1.19287i
$435$	−2.89089	−	6.74183i	−0.138607	−	0.323246i
$436$	22.4246			1.07394
$437$	−1.90761			−0.0912533
$438$	12.8438	−	5.50742i	0.613703	−	0.263155i
$439$			17.1346i			0.817791i	0.912581	+	0.408896i	$0.134086\pi$
$439$			17.1346i			0.817791i	−0.912581	+	0.408896i	$0.865914\pi$
$440$	−9.47235			−0.451576
$441$	4.92430	+	20.4145i	0.234490	+	0.972118i
$442$	−4.15036			−0.197413
$443$			4.64002i			0.220454i	0.993906	+	0.110227i	$0.0351578\pi$
$443$			4.64002i			0.220454i	−0.993906	+	0.110227i	$0.964842\pi$
$444$	−24.9466	+	10.6971i	−1.18391	+	0.507661i
$445$	25.3329			1.20090
$446$	40.7316			1.92870
$447$	−10.0168	−	23.3602i	−0.473779	−	1.10490i
$448$	−3.65017	−	6.70291i	−0.172455	−	0.316683i
$449$			2.49810i			0.117893i	0.998261	+	0.0589464i	$0.0187741\pi$
$449$			2.49810i			0.117893i	−0.998261	+	0.0589464i	$0.981226\pi$
$450$	3.05969	+	2.91175i	0.144235	+	0.137261i
$451$			26.0395i			1.22615i
$452$			1.05863i			0.0497936i
$453$	−22.6694	+	9.72061i	−1.06510	+	0.456714i
$454$		−	16.9998i		−	0.797840i
$455$	−12.5161	+	6.81586i	−0.586765	+	0.319532i
$456$	−6.89818	+	2.95793i	−0.323037	+	0.138518i
$457$	27.4450			1.28382			0.641912	−	0.766778i	$-0.278141\pi$
$457$	27.4450			1.28382			0.641912	+	0.766778i	$0.278141\pi$
$458$	40.3518			1.88552
$459$	−1.80879	+	4.87117i	−0.0844270	+	0.227367i
$460$		−	1.60899i		−	0.0750196i
$461$	−19.1085			−0.889971			−0.444985	−	0.895538i	$-0.646791\pi$
$461$	−19.1085			−0.889971			−0.444985	+	0.895538i	$0.646791\pi$
$462$	24.5078	+	19.2991i	1.14021	+	0.897874i
$463$	0.367529			0.0170805			0.00854025	−	0.999964i	$-0.497282\pi$
$463$	0.367529			0.0170805			0.00854025	+	0.999964i	$0.497282\pi$
$464$			8.51061i			0.395095i
$465$	−9.47491	−	22.0964i	−0.439388	−	1.02470i
$466$	25.0323			1.15960
$467$	−8.48587			−0.392679			−0.196340	−	0.980536i	$-0.562905\pi$
$467$	−8.48587			−0.392679			−0.196340	+	0.980536i	$0.562905\pi$
$468$	−6.92670	−	6.59179i	−0.320187	−	0.304706i
$469$	16.1448	+	29.6470i	0.745496	+	1.36897i
$470$		−	43.5177i		−	2.00732i
$471$	−8.62345	−	20.1107i	−0.397348	−	0.926653i
$472$		−	9.32555i		−	0.429243i
$473$		−	14.0186i		−	0.644576i
$474$	−17.4141	−	40.6114i	−0.799856	−	1.86534i
$475$		−	3.07688i		−	0.141177i
$476$	1.79710	+	3.30007i	0.0823701	+	0.151258i
$477$	−29.1694	−	27.7590i	−1.33557	−	1.27100i
$478$	22.2978			1.01988
$479$	9.42080			0.430447			0.215224	−	0.976565i	$-0.430952\pi$
$479$	9.42080			0.430447			0.215224	+	0.976565i	$0.430952\pi$
$480$	−11.1019	−	25.8906i	−0.506728	−	1.18174i
$481$		−	24.7623i		−	1.12906i
$482$	−12.0552			−0.549101
$483$	1.33812	−	1.69928i	0.0608866	−	0.0773197i
$484$	3.61876			0.164489
$485$		−	2.10027i		−	0.0953682i
$486$	−25.9009	+	12.6596i	−1.17489	+	0.574250i
$487$	−29.3693			−1.33085			−0.665424	−	0.746465i	$-0.731749\pi$
$487$	−29.3693			−1.33085			−0.665424	+	0.746465i	$0.731749\pi$
$488$	4.65654			0.210792
$489$	−19.3464	+	8.29573i	−0.874876	+	0.375146i
$490$	26.1022	+	16.8589i	1.17918	+	0.761608i
$491$		−	16.9299i		−	0.764035i	−0.924155	−	0.382017i	$-0.875229\pi$
$491$		−	16.9299i		−	0.764035i	0.924155	−	0.382017i	$-0.124771\pi$
$492$	−15.9946	+	6.85846i	−0.721092	+	0.309203i
$493$		−	1.76445i		−	0.0794668i
$494$			16.7745i			0.754722i
$495$	19.1998	+	18.2715i	0.862969	+	0.821244i
$496$			27.8936i			1.25246i
$497$	11.1308	−	6.06146i	0.499285	−	0.271894i
$498$	9.15676	+	21.3545i	0.410324	+	0.956916i
$499$	−3.70233			−0.165739			−0.0828696	−	0.996560i	$-0.526409\pi$
$499$	−3.70233			−0.165739			−0.0828696	+	0.996560i	$0.526409\pi$
$500$	−14.4498			−0.646216
$501$	−9.91141	+	4.25000i	−0.442809	+	0.189876i
$502$			32.3307i			1.44299i
$503$	0.974087			0.0434324			0.0217162	−	0.999764i	$-0.493087\pi$
$503$	0.974087			0.0434324			0.0217162	+	0.999764i	$0.493087\pi$
$504$	2.20394	−	8.21969i	0.0981713	−	0.366134i
$505$	−2.86449			−0.127468
$506$		−	3.21286i		−	0.142829i
$507$	−12.6772	+	5.43596i	−0.563014	+	0.241419i
$508$	−0.0116577			−0.000517227
$509$	4.40350			0.195182			0.0975908	−	0.995227i	$-0.468886\pi$
$509$	4.40350			0.195182			0.0975908	+	0.995227i	$0.468886\pi$
$510$	3.03006	+	7.06640i	0.134173	+	0.312906i
$511$	10.1370	−	5.52028i	0.448436	−	0.244203i
$512$			22.3403i			0.987313i
$513$	19.6878	+	7.31058i	0.869238	+	0.322770i
$514$		−	56.3959i		−	2.48751i
$515$		−	9.72502i		−	0.428535i
$516$	8.61083	−	3.69231i	0.379071	−	0.162545i
$517$		−	36.0839i		−	1.58697i
$518$	−47.4153	+	25.8207i	−2.08331	+	1.13450i
$519$	−19.3790	+	8.30968i	−0.850643	+	0.364755i
$520$	5.77534			0.253265
$521$	28.5477			1.25070			0.625350	−	0.780345i	$-0.284956\pi$
$521$	28.5477			1.25070			0.625350	+	0.780345i	$0.284956\pi$
$522$	6.74865	−	7.09154i	0.295381	−	0.310388i
$523$		−	45.1385i		−	1.97377i	−0.161430	−	0.986884i	$-0.551610\pi$
$523$		−	45.1385i		−	1.97377i	0.161430	−	0.986884i	$-0.448390\pi$
$524$	−4.64288			−0.202825
$525$	2.74085	+	2.15832i	0.119620	+	0.0941970i
$526$	20.2927			0.884802
$527$		−	5.78300i		−	0.251911i
$528$	−12.1185	−	28.2616i	−0.527392	−	1.22993i
$529$	22.7772			0.990314
$530$	−59.5820			−2.58808
$531$	−17.9884	+	18.9023i	−0.780628	+	0.820290i
$532$	13.3379	−	7.26335i	0.578270	−	0.314906i
$533$		−	15.8764i		−	0.687683i
$534$	13.3235	+	31.0717i	0.576564	+	1.34460i
$535$		−	5.56080i		−	0.240414i
$536$		−	13.6801i		−	0.590889i
$537$	−15.8917	−	37.0609i	−0.685776	−	1.59930i
$538$		−	23.1542i		−	0.998249i
$539$	21.6434	+	13.9790i	0.932247	+	0.602119i
$540$	−6.16618	+	16.6059i	−0.265350	+	0.714603i
$541$	30.4587			1.30952			0.654761	−	0.755836i	$-0.272769\pi$
$541$	30.4587			1.30952			0.654761	+	0.755836i	$0.272769\pi$
$542$	38.7642			1.66507
$543$	3.51781	+	8.20387i	0.150964	+	0.352062i
$544$		−	6.77601i		−	0.290519i
$545$	37.8980			1.62337
$546$	−14.9426	−	11.7667i	−0.639482	−	0.503570i
$547$	8.33798			0.356506			0.178253	−	0.983985i	$-0.442955\pi$
$547$	8.33798			0.356506			0.178253	+	0.983985i	$0.442955\pi$
$548$		−	6.75232i		−	0.288445i
$549$	−9.43851	−	8.98215i	−0.402826	−	0.383349i
$550$	5.18219			0.220969
$551$	−7.13138			−0.303807
$552$	−0.805555	+	0.345421i	−0.0342867	+	0.0147021i
$553$	−17.4547	−	32.0526i	−0.742251	−	1.36301i
$554$		−	36.0566i		−	1.53190i
$555$	−42.1602	+	18.0782i	−1.78960	+	0.767379i
$556$			0.261567i			0.0110929i
$557$		−	8.06570i		−	0.341755i	−0.985292	−	0.170877i	$-0.945340\pi$
$557$		−	8.06570i		−	0.341755i	0.985292	−	0.170877i	$-0.0546602\pi$
$558$	22.1188	−	23.2426i	0.936362	−	0.983936i
$559$			8.54721i			0.361508i
$560$	−14.6493	−	26.9008i	−0.619044	−	1.13677i
$561$	2.51246	+	5.85930i	0.106076	+	0.247380i
$562$	−10.7353			−0.452842
$563$	34.2145			1.44197			0.720984	−	0.692952i	$-0.243690\pi$
$563$	34.2145			1.44197			0.720984	+	0.692952i	$0.243690\pi$
$564$	22.1643	−	9.50403i	0.933286	−	0.400192i
$565$			1.78910i			0.0752678i
$566$	35.5416			1.49393
$567$	−20.3225	+	12.4095i	−0.853464	+	0.521152i
$568$	−5.13611			−0.215506
$569$		−	4.53799i		−	0.190243i	−0.995466	−	0.0951213i	$-0.969676\pi$
$569$		−	4.53799i		−	0.190243i	0.995466	−	0.0951213i	$-0.0303239\pi$
$570$	28.5603	−	12.2466i	1.19626	−	0.512954i
$571$	2.87144			0.120166			0.0600830	−	0.998193i	$-0.480863\pi$
$571$	2.87144			0.120166			0.0600830	+	0.998193i	$0.480863\pi$
$572$	−11.7317			−0.490528
$573$	10.6396	+	24.8127i	0.444478	+	1.03656i
$574$	−30.4004	+	16.5550i	−1.26889	+	0.690993i
$575$		−	0.359312i		−	0.0149844i
$576$	5.96605	−	6.26917i	0.248586	−	0.261216i
$577$			29.6322i			1.23360i	0.787118	+	0.616802i	$0.211572\pi$
$577$			29.6322i			1.23360i	−0.787118	+	0.616802i	$0.788428\pi$
$578$			1.84940i			0.0769247i
$579$	5.51072	−	2.36299i	0.229018	−	0.0982024i
$580$		−	6.01503i		−	0.249760i
$581$	9.17813	+	16.8540i	0.380773	+	0.699223i
$582$	2.57605	−	1.10461i	0.106781	−	0.0457874i
$583$	−49.4041			−2.04611
$584$	−4.67754			−0.193558
$585$	−11.7062	−	11.1402i	−0.483994	−	0.460592i
$586$			10.0812i			0.416449i
$587$	−8.84010			−0.364870			−0.182435	−	0.983218i	$-0.558398\pi$
$587$	−8.84010			−0.364870			−0.182435	+	0.983218i	$0.558398\pi$
$588$	−2.88594	+	16.9762i	−0.119014	+	0.700087i
$589$	−23.3731			−0.963073
$590$			38.6102i			1.58956i
$591$	−18.2338	−	42.5229i	−0.750037	−	1.74916i
$592$	53.2213			2.18738
$593$	−25.2047			−1.03503			−0.517517	−	0.855673i	$-0.673144\pi$
$593$	−25.2047			−1.03503			−0.517517	+	0.855673i	$0.673144\pi$
$594$	−12.3127	+	33.1589i	−0.505197	+	1.36052i
$595$	3.03714	+	5.57717i	0.124510	+	0.228642i
$596$		−	20.8418i		−	0.853714i
$597$	13.9677	+	32.5741i	0.571662	+	1.33317i
$598$			1.95890i			0.0801053i
$599$		−	15.7154i		−	0.642114i	−0.947060	−	0.321057i	$-0.895962\pi$
$599$		−	15.7154i		−	0.642114i	0.947060	−	0.321057i	$-0.104038\pi$
$600$	−0.557148	−	1.29932i	−0.0227455	−	0.0530446i
$601$			0.412843i			0.0168402i	0.999965	+	0.00842012i	$0.00268024\pi$
$601$			0.412843i			0.0168402i	−0.999965	+	0.00842012i	$0.997320\pi$
$602$	16.3663	−	8.91255i	0.667042	−	0.363248i
$603$	−26.3879	+	27.7286i	−1.07460	+	1.12920i
$604$	−20.2255			−0.822965
$605$	6.11577			0.248641
$606$	−1.50654	−	3.51339i	−0.0611989	−	0.142722i
$607$			9.47160i			0.384440i	0.981352	+	0.192220i	$0.0615688\pi$
$607$			9.47160i			0.384440i	−0.981352	+	0.192220i	$0.938431\pi$
$608$	−27.3866			−1.11067
$609$	5.00241	−	6.35255i	0.202708	−	0.257418i
$610$	−19.2793			−0.780596
$611$			22.0005i			0.890047i
$612$	−2.93729	+	3.08653i	−0.118733	+	0.124765i
$613$	24.8720			1.00457			0.502285	−	0.864702i	$-0.332493\pi$
$613$	24.8720			1.00457			0.502285	+	0.864702i	$0.332493\pi$
$614$	17.8315			0.719621
$615$	−27.0311	+	11.5909i	−1.09000	+	0.467391i
$616$	−4.99347	−	9.16963i	−0.201193	−	0.369455i
$617$		−	42.4565i		−	1.70923i	−0.519259	−	0.854617i	$-0.673792\pi$
$617$		−	42.4565i		−	1.70923i	0.519259	−	0.854617i	$-0.326208\pi$
$618$	11.9280	−	5.11473i	0.479816	−	0.205745i
$619$			15.9541i			0.641251i	0.947206	+	0.320625i	$0.103893\pi$
$619$			15.9541i			0.641251i	−0.947206	+	0.320625i	$0.896107\pi$
$620$		−	19.7143i		−	0.791745i
$621$	2.29910	+	0.853715i	0.0922598	+	0.0342584i
$622$		−	35.1712i		−	1.41024i
$623$	13.3546	+	24.5233i	0.535040	+	0.982507i
$624$	7.38874	+	17.2313i	0.295786	+	0.689802i
$625$	−28.2269			−1.12907
$626$	−50.3439			−2.01215
$627$	23.6815	−	10.1546i	0.945750	−	0.405536i
$628$		−	17.9427i		−	0.715991i
$629$	−11.0340			−0.439956
$630$	−9.12489	+	34.0317i	−0.363544	+	1.35586i
$631$	44.8372			1.78494			0.892470	−	0.451107i	$-0.148971\pi$
$631$	44.8372			1.78494			0.892470	+	0.451107i	$0.148971\pi$
$632$			14.7901i			0.588317i
$633$	24.4705	−	10.4929i	0.972616	−	0.417056i
$634$	13.0673			0.518970
$635$	−0.0197017			−0.000781839
$636$	−13.0124	−	30.3461i	−0.515975	−	1.20330i
$637$	−13.1961	−	8.52308i	−0.522848	−	0.337697i
$638$		−	12.0109i		−	0.475516i
$639$	10.4106	+	9.90720i	0.411835	+	0.391923i
$640$			19.7229i			0.779616i
$641$			3.65070i			0.144194i	0.997398	+	0.0720970i	$0.0229691\pi$
$641$			3.65070i			0.144194i	−0.997398	+	0.0720970i	$0.977031\pi$
$642$	6.82050	−	2.92462i	0.269184	−	0.115426i
$643$			18.5739i			0.732482i	0.930520	+	0.366241i	$0.119355\pi$
$643$			18.5739i			0.732482i	−0.930520	+	0.366241i	$0.880645\pi$
$644$	1.55757	−	0.848200i	0.0613769	−	0.0334238i
$645$	14.5525	−	6.24007i	0.573002	−	0.245703i
$646$	7.47470			0.294088
$647$	−30.8700			−1.21362			−0.606812	−	0.794845i	$-0.707552\pi$
$647$	−30.8700			−1.21362			−0.606812	+	0.794845i	$0.707552\pi$
$648$	9.63764	−	0.477826i	0.378602	−	0.0187708i
$649$			32.0147i			1.25669i
$650$	−3.15961			−0.123930
$651$	16.3954	−	20.8205i	0.642588	−	0.816020i
$652$	−17.2608			−0.675985
$653$			9.09910i			0.356075i	0.984024	+	0.178038i	$0.0569749\pi$
$653$			9.09910i			0.356075i	−0.984024	+	0.178038i	$0.943025\pi$
$654$	19.9319	+	46.4831i	0.779398	+	1.81763i
$655$	−7.84655			−0.306590
$656$	34.1230			1.33228
$657$	9.48108	+	9.02266i	0.369892	+	0.352008i
$658$	42.1270	−	22.9409i	1.64228	−	0.894331i
$659$		−	29.1793i		−	1.13667i	−0.822799	−	0.568333i	$-0.807589\pi$
$659$		−	29.1793i		−	1.13667i	0.822799	−	0.568333i	$-0.192411\pi$
$660$	8.56500	+	19.9744i	0.333392	+	0.777503i
$661$			22.6497i			0.880970i	0.897760	+	0.440485i	$0.145193\pi$
$661$			22.6497i			0.880970i	−0.897760	+	0.440485i	$0.854807\pi$
$662$		−	32.4634i		−	1.26173i
$663$	−1.53186	−	3.57244i	−0.0594925	−	0.138742i
$664$		−	7.77698i		−	0.301805i
$665$	22.5412	−	12.2752i	0.874112	−	0.476012i
$666$	−44.3471	−	42.2029i	−1.71842	−	1.63533i
$667$	−0.832788			−0.0322457
$668$	−8.84291			−0.342143
$669$	15.0336	+	35.0599i	0.581234	+	1.35549i
$670$			56.6391i			2.18816i
$671$	−15.9860			−0.617131
$672$	19.2107	−	24.3956i	0.741070	−	0.941083i
$673$	−49.0062			−1.88905			−0.944526	−	0.328437i	$-0.893478\pi$
$673$	−49.0062			−1.88905			−0.944526	+	0.328437i	$0.893478\pi$
$674$			3.48932i			0.134403i
$675$	−1.37700	+	3.70834i	−0.0530008	+	0.142734i
$676$	−11.3105			−0.435020
$677$	26.5776			1.02146			0.510730	−	0.859741i	$-0.329375\pi$
$677$	26.5776			1.02146			0.510730	+	0.859741i	$0.329375\pi$
$678$	−2.19438	+	0.940949i	−0.0842748	+	0.0361369i
$679$	2.03315	−	1.10718i	0.0780251	−	0.0424898i
$680$		−	2.57348i		−	0.0986884i
$681$	14.6326	−	6.27446i	0.560724	−	0.240438i
$682$		−	39.3658i		−	1.50740i
$683$		−	0.785358i		−	0.0300509i	−0.999887	−	0.0150254i	$-0.995217\pi$
$683$		−	0.785358i		−	0.0300509i	0.999887	−	0.0150254i	$-0.00478292\pi$
$684$	12.4748	+	11.8716i	0.476986	+	0.453924i
$685$		−	11.4115i		−	0.436012i
$686$	−2.56000	+	34.1555i	−0.0977412	+	1.30406i
$687$	14.8935	+	34.7330i	0.568221	+	1.32515i
$688$	−18.3704			−0.700366
$689$	30.1219			1.14755
$690$	3.33521	−	1.43013i	0.126969	−	0.0544443i
$691$			49.4704i			1.88194i	0.338484	+	0.940972i	$0.390086\pi$
$691$			49.4704i			1.88194i	−0.338484	+	0.940972i	$0.609914\pi$
$692$	−17.2898			−0.657261
$693$	−7.56616	+	28.2183i	−0.287415	+	1.07193i
$694$	−37.4877			−1.42301
$695$			0.442053i			0.0167680i
$696$	−3.01148	+	1.29132i	−0.114150	+	0.0489472i
$697$	−7.07450			−0.267966
$698$	36.5659			1.38404
$699$	9.23917	+	21.5466i	0.349458	+	0.814969i
$700$	1.36811	+	2.51229i	0.0517096	+	0.0949555i
$701$			2.34555i			0.0885904i	0.999018	+	0.0442952i	$0.0141042\pi$
$701$			2.34555i			0.0885904i	−0.999018	+	0.0442952i	$0.985896\pi$
$702$	7.50713	−	20.2171i	0.283338	−	0.763046i
$703$			44.5963i			1.68198i
$704$		−	10.6181i		−	0.400184i
$705$	37.4581	−	16.0620i	1.41075	−	0.604929i
$706$			41.7535i			1.57142i
$707$	−1.51005	−	2.77295i	−0.0567914	−	0.104288i
$708$	−19.6649	+	8.43226i	−0.739051	+	0.316904i
$709$	−19.1594			−0.719546			−0.359773	−	0.933040i	$-0.617146\pi$
$709$	−19.1594			−0.719546			−0.359773	+	0.933040i	$0.617146\pi$
$710$	21.2648			0.798055
$711$	28.5290	−	29.9785i	1.06992	−	1.12428i
$712$		−	11.3158i		−	0.424079i
$713$	−2.72947			−0.102219
$714$	−5.24324	+	6.65837i	−0.196223	+	0.249183i
$715$	−19.8268			−0.741481
$716$		−	33.0655i		−	1.23572i
$717$	8.22989	+	19.1929i	0.307351	+	0.716772i
$718$	−22.9071			−0.854886
$719$	3.51559			0.131109			0.0655547	−	0.997849i	$-0.479118\pi$
$719$	3.51559			0.131109			0.0655547	+	0.997849i	$0.479118\pi$
$720$	23.9436	−	25.1601i	0.892325	−	0.937662i
$721$	9.41423	−	5.12667i	0.350604	−	0.190927i
$722$			4.92800i			0.183401i
$723$	−4.44947	−	10.3766i	−0.165477	−	0.385910i
$724$			7.31945i			0.272025i
$725$		−	1.34325i		−	0.0498870i
$726$	3.21650	+	7.50119i	0.119376	+	0.278395i
$727$			26.0772i			0.967150i	0.875303	+	0.483575i	$0.160662\pi$
$727$			26.0772i			0.967150i	−0.875303	+	0.483575i	$0.839338\pi$
$728$	3.04454	+	5.59077i	0.112838	+	0.207208i
$729$	−20.4566	−	17.6218i	−0.757651	−	0.652660i
$730$	19.3663			0.716778
$731$	3.80862			0.140867
$732$	−4.21049	−	9.81928i	−0.155624	−	0.362931i
$733$			50.5936i			1.86872i	0.356333	+	0.934359i	$0.384027\pi$
$733$			50.5936i			1.86872i	−0.356333	+	0.934359i	$0.615973\pi$
$734$	55.1405			2.03527
$735$	−4.87729	+	28.6901i	−0.179902	+	1.05825i
$736$	−3.19815			−0.117885
$737$			46.9639i			1.72994i
$738$	−28.4332	−	27.0585i	−1.04664	−	0.996036i
$739$	−14.3208			−0.526800			−0.263400	−	0.964687i	$-0.584844\pi$
$739$	−14.3208			−0.526800			−0.263400	+	0.964687i	$0.584844\pi$
$740$	−37.6151			−1.38276
$741$	−14.4388	+	6.19132i	−0.530421	+	0.227444i
$742$	−31.4094	−	57.6779i	−1.15308	−	2.11742i
$743$			37.0285i			1.35844i	0.733933	+	0.679221i	$0.237682\pi$
$743$			37.0285i			1.35844i	−0.733933	+	0.679221i	$0.762318\pi$
$744$	−9.87013	+	4.23230i	−0.361857	+	0.155164i
$745$		−	35.2230i		−	1.29047i
$746$			56.9365i			2.08459i
$747$	−15.0013	+	15.7634i	−0.548868	+	0.576754i
$748$			5.22764i			0.191141i
$749$	5.38309	−	2.93145i	0.196694	−	0.107113i
$750$	−12.8436	−	29.9525i	−0.468981	−	1.09371i
$751$	11.2929			0.412085			0.206042	−	0.978543i	$-0.433941\pi$
$751$	11.2929			0.412085			0.206042	+	0.978543i	$0.433941\pi$
$752$	−47.2855			−1.72433
$753$	−27.8288	+	11.9330i	−1.01414	+	0.434861i
$754$			7.32311i			0.266692i
$755$	−34.1815			−1.24399
$756$	−19.3258	+	2.78487i	−0.702871	+	0.101285i
$757$	−6.27197			−0.227959			−0.113979	−	0.993483i	$-0.536360\pi$
$757$	−6.27197			−0.227959			−0.113979	+	0.993483i	$0.536360\pi$
$758$		−	12.3967i		−	0.450268i
$759$	2.76548	−	1.18584i	0.100381	−	0.0430431i
$760$	−10.4012			−0.377292
$761$	25.4203			0.921486			0.460743	−	0.887534i	$-0.347583\pi$
$761$	25.4203			0.921486			0.460743	+	0.887534i	$0.347583\pi$
$762$	−0.0103618	−	0.0241648i	−0.000375370	−	0.000875399i
$763$	19.9784	+	36.6868i	0.723267	+	1.32815i
$764$			22.1378i			0.800916i
$765$	−4.96407	+	5.21628i	−0.179476	+	0.188595i
$766$		−	44.0968i		−	1.59328i
$767$		−	19.5196i		−	0.704810i
$768$	−33.3751	+	14.3112i	−1.20432	+	0.516411i
$769$		−	42.4419i		−	1.53049i	−0.643737	−	0.765247i	$-0.722617\pi$
$769$		−	42.4419i		−	1.53049i	0.643737	−	0.765247i	$-0.277383\pi$
$770$	20.6743	+	37.9647i	0.745050	+	1.36815i
$771$	48.5430	−	20.8152i	1.74823	−	0.749640i
$772$	4.91663			0.176953
$773$	21.3535			0.768033			0.384017	−	0.923326i	$-0.374541\pi$
$773$	21.3535			0.768033			0.384017	+	0.923326i	$0.374541\pi$
$774$	15.3073	+	14.5672i	0.550210	+	0.523606i
$775$		−	4.40250i		−	0.158143i
$776$	−0.938158			−0.0336779
$777$	−39.7258	−	31.2827i	−1.42516	−	1.12226i
$778$	66.4965			2.38401
$779$			28.5930i			1.02445i
$780$	−5.22212	−	12.1785i	−0.186982	−	0.436060i
$781$	17.6323			0.630934
$782$	0.872881			0.0312142
$783$	8.59493	+	3.19152i	0.307158	+	0.114055i
$784$	18.3186	−	28.3622i	0.654234	−	1.01294i
$785$		−	30.3234i		−	1.08229i
$786$	−4.12678	−	9.62405i	−0.147197	−	0.343278i
$787$			28.9758i			1.03288i	0.856324	+	0.516438i	$0.172743\pi$
$787$			28.9758i			1.03288i	−0.856324	+	0.516438i	$0.827257\pi$
$788$		−	37.9387i		−	1.35151i
$789$	7.48982	+	17.4670i	0.266645	+	0.621841i
$790$		−	61.2348i		−	2.17864i
$791$	−1.73192	+	0.943145i	−0.0615800	+	0.0335344i
$792$	8.16162	−	8.57629i	0.290010	−	0.304745i
$793$	9.74672			0.346116
$794$	−10.4258			−0.369998
$795$	−21.9912	−	51.2855i	−0.779946	−	1.81891i
$796$			29.0625i			1.03009i
$797$	−19.2694			−0.682558			−0.341279	−	0.939962i	$-0.610860\pi$
$797$	−19.2694			−0.682558			−0.341279	+	0.939962i	$0.610860\pi$
$798$	26.9112	+	21.1916i	0.952645	+	0.750175i
$799$	9.80340			0.346819
$800$		−	5.15847i		−	0.182379i
$801$	−21.8275	+	22.9365i	−0.771237	+	0.810421i
$802$	12.8326			0.453135
$803$	16.0581			0.566677
$804$	−28.8473	+	12.3697i	−1.01737	+	0.436245i
$805$	2.63232	−	1.43347i	0.0927772	−	0.0505233i
$806$			24.0015i			0.845418i
$807$	19.9301	−	8.54599i	0.701572	−	0.300833i
$808$			1.27953i			0.0450136i
$809$			23.0438i			0.810175i	0.914278	+	0.405088i	$0.132759\pi$
$809$			23.0438i			0.810175i	−0.914278	+	0.405088i	$0.867241\pi$
$810$	−39.9024	+	1.97833i	−1.40203	+	0.0695113i
$811$		−	36.3231i		−	1.27548i	−0.770254	−	0.637738i	$-0.779870\pi$
$811$		−	36.3231i		−	1.27548i	0.770254	−	0.637738i	$-0.220130\pi$
$812$	5.82280	−	3.17090i	0.204340	−	0.111277i
$813$	14.3075	+	33.3665i	0.501786	+	1.17021i
$814$	−75.1105			−2.63262
$815$	−29.1710			−1.02182
$816$	7.67822	−	3.29241i	0.268791	−	0.115257i
$817$		−	15.3933i		−	0.538543i
$818$	−59.6590			−2.08593
$819$	4.61312	−	17.2049i	0.161196	−	0.601186i
$820$	−24.1170			−0.842203
$821$		−	24.0043i		−	0.837754i	−0.908043	−	0.418877i	$-0.862424\pi$
$821$		−	24.0043i		−	0.837754i	0.908043	−	0.418877i	$-0.137576\pi$
$822$	13.9966	−	6.00173i	0.488188	−	0.209334i
$823$	−31.1876			−1.08713			−0.543565	−	0.839367i	$-0.682926\pi$
$823$	−31.1876			−1.08713			−0.543565	+	0.839367i	$0.682926\pi$
$824$	−4.34402			−0.151331
$825$	1.91270	+	4.46059i	0.0665915	+	0.155298i
$826$	−37.3764	+	20.3539i	−1.30049	+	0.708202i
$827$		−	31.6994i		−	1.10230i	−0.834407	−	0.551149i	$-0.814190\pi$
$827$		−	31.6994i		−	1.10230i	0.834407	−	0.551149i	$-0.185810\pi$
$828$	1.45678	+	1.38635i	0.0506267	+	0.0481789i
$829$			25.0797i			0.871055i	0.900175	+	0.435528i	$0.143438\pi$
$829$			25.0797i			0.871055i	−0.900175	+	0.435528i	$0.856562\pi$
$830$			32.1988i			1.11764i
$831$	31.0359	−	13.3081i	1.07662	−	0.461654i
$832$			6.47389i			0.224442i
$833$	−3.79787	+	5.88015i	−0.131588	+	0.203735i
$834$	−0.542192	+	0.232491i	−0.0187746	+	0.00805052i
$835$	−14.9447			−0.517182
$836$	21.1285			0.730746
$837$	28.1699	+	10.4602i	0.973696	+	0.361558i
$838$			50.4114i			1.74143i
$839$	16.9068			0.583686			0.291843	−	0.956466i	$-0.405731\pi$
$839$	16.9068			0.583686			0.291843	+	0.956466i	$0.405731\pi$
$840$	7.29610	−	9.26530i	0.251739	−	0.319683i
$841$	25.8867			0.892645
$842$		−	25.3816i		−	0.874707i
$843$	−3.96230	−	9.24047i	−0.136469	−	0.318259i
$844$	21.8325			0.751505
$845$	−19.1150			−0.657575
$846$	39.4011	+	37.4960i	1.35464	+	1.28914i
$847$	3.22401	+	5.92032i	0.110778	+	0.203425i
$848$			64.7407i			2.22320i
$849$	13.1181	+	30.5926i	0.450211	+	1.04994i
$850$			1.40791i			0.0482911i
$851$			5.20786i			0.178523i
$852$	4.64412	+	10.8305i	0.159105	+	0.371048i
$853$		−	40.0627i		−	1.37172i	−0.727733	−	0.685861i	$-0.759426\pi$
$853$		−	40.0627i		−	1.37172i	0.727733	−	0.685861i	$-0.240574\pi$
$854$	−10.1633	−	18.6632i	−0.347782	−	0.638641i
$855$	21.0826	+	20.0633i	0.721011	+	0.686150i
$856$	−2.48393			−0.0848989
$857$	−40.6182			−1.38749			−0.693745	−	0.720221i	$-0.744041\pi$
$857$	−40.6182			−1.38749			−0.693745	+	0.720221i	$0.744041\pi$
$858$	−10.4276	−	24.3182i	−0.355993	−	0.830211i
$859$			23.0956i			0.788012i	0.919108	+	0.394006i	$0.128911\pi$
$859$			23.0956i			0.788012i	−0.919108	+	0.394006i	$0.871089\pi$
$860$	12.9836			0.442738
$861$	−25.4703	−	20.0570i	−0.868025	−	0.683540i
$862$	42.6818			1.45375
$863$		−	23.6742i		−	0.805881i	−0.915226	−	0.402940i	$-0.867988\pi$
$863$		−	23.6742i		−	0.805881i	0.915226	−	0.402940i	$-0.132012\pi$
$864$	33.0071	+	12.2564i	1.12292	+	0.416970i
$865$	−29.2201			−0.993514
$866$	−6.58527			−0.223777
$867$	−1.59187	+	0.682594i	−0.0540629	+	0.0231821i
$868$	19.0843	−	10.3926i	0.647762	−	0.352749i
$869$		−	50.7745i		−	1.72241i
$870$	12.4683	−	5.34639i	0.422715	−	0.181260i
$871$		−	28.6341i		−	0.970230i
$872$		−	16.9285i		−	0.573270i
$873$	1.90159	+	1.80964i	0.0643590	+	0.0612472i
$874$		−	3.52792i		−	0.119334i
$875$	−12.8736	−	23.6400i	−0.435206	−	0.799179i
$876$	4.22948	+	9.86357i	0.142901	+	0.333259i
$877$	−39.6109			−1.33756			−0.668782	−	0.743459i	$-0.733184\pi$
$877$	−39.6109			−1.33756			−0.668782	+	0.743459i	$0.733184\pi$
$878$	−31.6887			−1.06944
$879$	−8.67741	+	3.72086i	−0.292682	+	0.125502i
$880$		−	42.6136i		−	1.43650i
$881$	−4.66307			−0.157103			−0.0785514	−	0.996910i	$-0.525029\pi$
$881$	−4.66307			−0.157103			−0.0785514	+	0.996910i	$0.525029\pi$
$882$	−37.7545	+	9.10698i	−1.27126	+	0.306648i
$883$	−1.86821			−0.0628704			−0.0314352	−	0.999506i	$-0.510008\pi$
$883$	−1.86821			−0.0628704			−0.0314352	+	0.999506i	$0.510008\pi$
$884$		−	3.18732i		−	0.107201i
$885$	−33.2339	+	14.2507i	−1.11715	+	0.479031i
$886$	−8.58124			−0.288292
$887$	20.7966			0.698282			0.349141	−	0.937070i	$-0.386473\pi$
$887$	20.7966			0.698282			0.349141	+	0.937070i	$0.386473\pi$
$888$	8.07528	+	18.8323i	0.270989	+	0.631972i
$889$	−0.0103860	−	0.0190721i	−0.000348336	−	0.000639658i
$890$			46.8506i			1.57044i
$891$	−33.0862	+	1.64038i	−1.10843	+	0.0549549i
$892$			31.2803i			1.04734i
$893$		−	39.6224i		−	1.32591i
$894$	43.2022	−	18.5250i	1.44490	−	0.619570i
$895$		−	55.8813i		−	1.86791i
$896$	−19.0926	+	10.3972i	−0.637839	+	0.347346i
$897$	−1.68613	+	0.723010i	−0.0562982	+	0.0241406i
$898$	−4.61998			−0.154171
$899$	−10.2038			−0.340316
$900$	−2.23611	+	2.34972i	−0.0745370	+	0.0783241i
$901$		−	13.4223i		−	0.447161i
$902$	−48.1573			−1.60346
$903$	13.7122	+	10.7979i	0.456312	+	0.359330i
$904$	0.799163			0.0265798
$905$			12.3700i			0.411193i
$906$	−17.9772	−	41.9247i	−0.597254	−	1.39285i
$907$	−49.7588			−1.65221			−0.826107	−	0.563513i	$-0.809450\pi$
$907$	−49.7588			−1.65221			−0.826107	+	0.563513i	$0.809450\pi$
$908$	13.0552			0.433251
$909$	2.46812	−	2.59352i	0.0818624	−	0.0860216i
$910$	−12.6052	−	23.1473i	−0.417859	−	0.767325i
$911$		−	9.00044i		−	0.298198i	−0.988822	−	0.149099i	$-0.952363\pi$
$911$		−	9.00044i		−	0.298198i	0.988822	−	0.149099i	$-0.0476373\pi$
$912$	−13.3069	−	31.0331i	−0.440637	−	1.02761i
$913$			26.6985i			0.883591i
$914$			50.7567i			1.67888i
$915$	−7.11580	−	16.5947i	−0.235241	−	0.548605i
$916$			30.9886i			1.02389i
$917$	−4.13641	−	7.59579i	−0.136596	−	0.250835i
$918$	−9.00872	−	3.34516i	−0.297332	−	0.110407i
$919$	−24.5698			−0.810482			−0.405241	−	0.914210i	$-0.632812\pi$
$919$	−24.5698			−0.810482			−0.405241	+	0.914210i	$0.632812\pi$
$920$	−1.21464			−0.0400454
$921$	6.58144	+	15.3485i	0.216866	+	0.505752i
$922$		−	35.3391i		−	1.16383i
$923$	−10.7505			−0.353858
$924$	−14.8209	+	18.8211i	−0.487573	+	0.619167i
$925$	−8.40003			−0.276191
$926$			0.679706i			0.0223365i
$927$	8.80505	+	8.37932i	0.289196	+	0.275213i
$928$	−11.9559			−0.392472
$929$	−10.9039			−0.357746			−0.178873	−	0.983872i	$-0.557245\pi$
$929$	−10.9039			−0.357746			−0.178873	+	0.983872i	$0.557245\pi$
$930$	40.8650	−	17.5228i	1.34002	−	0.574597i
$931$	23.7658	+	15.3499i	0.778893	+	0.503071i
$932$			19.2238i			0.629697i
$933$	30.2738	−	12.9814i	0.991119	−	0.424991i
$934$		−	15.6937i		−	0.513514i
$935$			8.83480i			0.288929i
$936$	−4.97618	+	5.22900i	−0.162651	+	0.170915i
$937$		−	5.40027i		−	0.176419i	−0.996102	−	0.0882095i	$-0.971885\pi$
$937$		−	5.40027i		−	0.176419i	0.996102	−	0.0882095i	$-0.0281145\pi$
$938$	−54.8291	+	29.8581i	−1.79023	+	0.974900i
$939$	−18.5815	−	43.3338i	−0.606383	−	1.41414i
$940$	33.4199			1.09004
$941$	−10.0196			−0.326631			−0.163315	−	0.986574i	$-0.552219\pi$
$941$	−10.0196			−0.326631			−0.163315	+	0.986574i	$0.552219\pi$
$942$	37.1927	−	15.9482i	1.21180	−	0.519619i
$943$			3.33903i			0.108734i
$944$	41.9532			1.36546
$945$	−32.6609	+	4.70648i	−1.06246	+	0.153102i
$946$	25.9259			0.842924
$947$		−	29.6419i		−	0.963232i	−0.876382	−	0.481616i	$-0.840050\pi$
$947$		−	29.6419i		−	0.963232i	0.876382	−	0.481616i	$-0.159950\pi$
$948$	31.1879	−	13.3733i	1.01294	−	0.434346i
$949$	−9.79069			−0.317819
$950$	5.69037			0.184620
$951$	4.82302	+	11.2478i	0.156397	+	0.364733i
$952$	2.49124	−	1.35664i	0.0807415	−	0.0439691i
$953$			21.4547i			0.694985i	0.937683	+	0.347492i	$0.112967\pi$
$953$			21.4547i			0.694985i	−0.937683	+	0.347492i	$0.887033\pi$
$954$	51.3374	−	53.9457i	1.66211	−	1.74656i
$955$			37.4132i			1.21066i
$956$			17.1238i			0.553824i
$957$	10.3384	−	4.43311i	0.334194	−	0.143302i
$958$			17.4228i			0.562904i
$959$	11.0468	−	6.01573i	0.356721	−	0.194258i
$960$	11.0224	−	4.72641i	0.355748	−	0.152544i
$961$	−2.44304			−0.0788078
$962$	45.7953			1.47650
$963$	5.03476	+	4.79133i	0.162243	+	0.154398i
$964$		−	9.25794i		−	0.298178i
$965$	8.30919			0.267482
$966$	3.14263	+	2.47471i	0.101113	+	0.0796226i
$967$	−20.8634			−0.670922			−0.335461	−	0.942054i	$-0.608892\pi$
$967$	−20.8634			−0.670922			−0.335461	+	0.942054i	$0.608892\pi$
$968$		−	2.73182i		−	0.0878041i
$969$	2.75884	+	6.43388i	0.0886267	+	0.206686i
$970$	3.88422			0.124715
$971$	−33.8655			−1.08680			−0.543398	−	0.839475i	$-0.682863\pi$
$971$	−33.8655			−1.08680			−0.543398	+	0.839475i	$0.682863\pi$
$972$	−9.72205	−	19.8909i	−0.311835	−	0.638001i
$973$	−0.427926	+	0.233034i	−0.0137187	+	0.00747073i
$974$		−	54.3154i		−	1.74038i
$975$	−1.16618	−	2.71965i	−0.0373477	−	0.0870983i
$976$			20.9485i			0.670546i
$977$			15.3738i			0.491852i	0.969289	+	0.245926i	$0.0790920\pi$
$977$			15.3738i			0.491852i	−0.969289	+	0.245926i	$0.920908\pi$
$978$	−15.3421	−	35.7792i	−0.490586	−	1.14409i
$979$			38.8475i			1.24157i
$980$	−12.9470	+	20.0455i	−0.413576	+	0.640330i
$981$	−32.6538	+	34.3129i	−1.04256	+	1.09553i
$982$	31.3100			0.999144
$983$	5.34329			0.170424			0.0852122	−	0.996363i	$-0.472843\pi$
$983$	5.34329			0.170424			0.0852122	+	0.996363i	$0.472843\pi$
$984$	5.17749	+	12.0744i	0.165052	+	0.384918i
$985$		−	64.1171i		−	2.04294i
$986$	3.26316			0.103920
$987$	35.2952	+	27.7937i	1.12346	+	0.884684i
$988$	−12.8822			−0.409837
$989$		−	1.79760i		−	0.0571603i
$990$	−33.7913	+	35.5081i	−1.07396	+	1.12852i
$991$	55.7611			1.77131			0.885655	−	0.464345i	$-0.153710\pi$
$991$	55.7611			1.77131			0.885655	+	0.464345i	$0.153710\pi$
$992$	−39.1856			−1.24414
$993$	27.9430	−	11.9819i	0.886745	−	0.380235i
$994$	11.2100	+	20.5853i	0.355561	+	0.652925i
$995$			49.1161i			1.55708i
$996$	−16.3994	+	7.03203i	−0.519634	+	0.222818i
$997$		−	30.4258i		−	0.963594i	−0.876283	−	0.481797i	$-0.839984\pi$
$997$		−	30.4258i		−	0.963594i	0.876283	−	0.481797i	$-0.160016\pi$
$998$		−	6.84708i		−	0.216741i
$999$	19.9582	−	53.7486i	0.631450	−	1.70053i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	357.2.d.b.188.17	yes	22
3.2	odd	2		357.2.d.a.188.6	✓	22
7.6	odd	2		357.2.d.a.188.17	yes	22
21.20	even	2	inner	357.2.d.b.188.6	yes	22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
357.2.d.a.188.6	✓	22	3.2	odd	2
357.2.d.a.188.17	yes	22	7.6	odd	2
357.2.d.b.188.6	yes	22	21.20	even	2	inner
357.2.d.b.188.17	yes	22	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 357 = 3 \cdot 7 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	357.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.84940i q^{2} +(-1.59187 + 0.682594i) q^{3} -1.42026 q^{4} -2.40027 q^{5} +(-1.26239 - 2.94401i) q^{6} +(-1.26533 - 2.32356i) q^{7} +1.07216i q^{8} +(2.06813 - 2.17321i) q^{9} +O(q^{10})\)	\(q+1.84940i q^{2} +(-1.59187 + 0.682594i) q^{3} -1.42026 q^{4} -2.40027 q^{5} +(-1.26239 - 2.94401i) q^{6} +(-1.26533 - 2.32356i) q^{7} +1.07216i q^{8} +(2.06813 - 2.17321i) q^{9} -4.43904i q^{10} -3.68075i q^{11} +(2.26088 - 0.969462i) q^{12} +2.24417i q^{13} +(4.29718 - 2.34010i) q^{14} +(3.82093 - 1.63841i) q^{15} -4.82338 q^{16} +1.00000 q^{17} +(4.01912 + 3.82479i) q^{18} -4.04170i q^{19} +3.40901 q^{20} +(3.60030 + 2.83511i) q^{21} +6.80717 q^{22} -0.471982i q^{23} +(-0.731852 - 1.70675i) q^{24} +0.761284 q^{25} -4.15036 q^{26} +(-1.80879 + 4.87117i) q^{27} +(1.79710 + 3.30007i) q^{28} -1.76445i q^{29} +(3.03006 + 7.06640i) q^{30} -5.78300i q^{31} -6.77601i q^{32} +(2.51246 + 5.85930i) q^{33} +1.84940i q^{34} +(3.03714 + 5.57717i) q^{35} +(-2.93729 + 3.08653i) q^{36} -11.0340 q^{37} +7.47470 q^{38} +(-1.53186 - 3.57244i) q^{39} -2.57348i q^{40} -7.07450 q^{41} +(-5.24324 + 6.65837i) q^{42} +3.80862 q^{43} +5.22764i q^{44} +(-4.96407 + 5.21628i) q^{45} +0.872881 q^{46} +9.80340 q^{47} +(7.67822 - 3.29241i) q^{48} +(-3.79787 + 5.88015i) q^{49} +1.40791i q^{50} +(-1.59187 + 0.682594i) q^{51} -3.18732i q^{52} -13.4223i q^{53} +(-9.00872 - 3.34516i) q^{54} +8.83480i q^{55} +(2.49124 - 1.35664i) q^{56} +(2.75884 + 6.43388i) q^{57} +3.26316 q^{58} -8.69788 q^{59} +(-5.42672 + 2.32697i) q^{60} -4.34312i q^{61} +10.6950 q^{62} +(-7.66645 - 2.05560i) q^{63} +2.88476 q^{64} -5.38662i q^{65} +(-10.8362 + 4.64653i) q^{66} -12.7593 q^{67} -1.42026 q^{68} +(0.322172 + 0.751336i) q^{69} +(-10.3144 + 5.61686i) q^{70} +4.79041i q^{71} +(2.33003 + 2.21738i) q^{72} +4.36271i q^{73} -20.4063i q^{74} +(-1.21187 + 0.519648i) q^{75} +5.74028i q^{76} +(-8.55246 + 4.65738i) q^{77} +(6.60686 - 2.83301i) q^{78} +13.7946 q^{79} +11.5774 q^{80} +(-0.445665 - 8.98896i) q^{81} -13.0835i q^{82} -7.25354 q^{83} +(-5.11337 - 4.02660i) q^{84} -2.40027 q^{85} +7.04364i q^{86} +(1.20440 + 2.80878i) q^{87} +3.94637 q^{88} -10.5542 q^{89} +(-9.64696 - 9.18052i) q^{90} +(5.21448 - 2.83963i) q^{91} +0.670338i q^{92} +(3.94744 + 9.20581i) q^{93} +18.1304i q^{94} +9.70116i q^{95} +(4.62526 + 10.7866i) q^{96} +0.875014i q^{97} +(-10.8747 - 7.02376i) q^{98} +(-7.99904 - 7.61228i) 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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