LMFDB - Embedded newform 357.2.d.b.188.4

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			188.4
Character	$\chi$	$=$	357.188
Dual form			357.2.d.b.188.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.04055i q^{2} +(-1.36093 + 1.07138i) q^{3} -2.16383 q^{4} -0.263720 q^{5} +(2.18621 + 2.77705i) q^{6} +(2.64172 - 0.145918i) q^{7} +0.334296i q^{8} +(0.704276 - 2.91616i) q^{9} +O(q^{10})$	\(q-2.04055i q^{2} +(-1.36093 + 1.07138i) q^{3} -2.16383 q^{4} -0.263720 q^{5} +(2.18621 + 2.77705i) q^{6} +(2.64172 - 0.145918i) q^{7} +0.334296i q^{8} +(0.704276 - 2.91616i) q^{9} +0.538133i q^{10} -0.0699270i q^{11} +(2.94482 - 2.31829i) q^{12} -2.55799i q^{13} +(-0.297752 - 5.39056i) q^{14} +(0.358905 - 0.282545i) q^{15} -3.64551 q^{16} +1.00000 q^{17} +(-5.95056 - 1.43711i) q^{18} -4.91225i q^{19} +0.570645 q^{20} +(-3.43888 + 3.02888i) q^{21} -0.142689 q^{22} -4.81972i q^{23} +(-0.358159 - 0.454954i) q^{24} -4.93045 q^{25} -5.21969 q^{26} +(2.16585 + 4.72325i) q^{27} +(-5.71623 + 0.315741i) q^{28} +3.01905i q^{29} +(-0.576547 - 0.732363i) q^{30} -8.46024i q^{31} +8.10742i q^{32} +(0.0749186 + 0.0951660i) q^{33} -2.04055i q^{34} +(-0.696676 + 0.0384814i) q^{35} +(-1.52393 + 6.31007i) q^{36} +4.18192 q^{37} -10.0237 q^{38} +(2.74059 + 3.48125i) q^{39} -0.0881606i q^{40} +4.46193 q^{41} +(6.18058 + 7.01718i) q^{42} +5.69089 q^{43} +0.151310i q^{44} +(-0.185732 + 0.769050i) q^{45} -9.83487 q^{46} -4.94892 q^{47} +(4.96129 - 3.90574i) q^{48} +(6.95742 - 0.770949i) q^{49} +10.0608i q^{50} +(-1.36093 + 1.07138i) q^{51} +5.53505i q^{52} +3.10008i q^{53} +(9.63800 - 4.41952i) q^{54} +0.0184412i q^{55} +(0.0487797 + 0.883118i) q^{56} +(5.26290 + 6.68524i) q^{57} +6.16051 q^{58} +11.6634 q^{59} +(-0.776609 + 0.611379i) q^{60} +11.7332i q^{61} -17.2635 q^{62} +(1.43498 - 7.80646i) q^{63} +9.25254 q^{64} +0.674593i q^{65} +(0.194191 - 0.152875i) q^{66} -3.76912 q^{67} -2.16383 q^{68} +(5.16377 + 6.55932i) q^{69} +(0.0785231 + 1.42160i) q^{70} -1.85798i q^{71} +(0.974861 + 0.235437i) q^{72} -0.743764i q^{73} -8.53341i q^{74} +(6.71001 - 5.28240i) q^{75} +10.6293i q^{76} +(-0.0102036 - 0.184728i) q^{77} +(7.10365 - 5.59229i) q^{78} +1.79458 q^{79} +0.961393 q^{80} +(-8.00799 - 4.10756i) q^{81} -9.10476i q^{82} -15.3397 q^{83} +(7.44113 - 6.55398i) q^{84} -0.263720 q^{85} -11.6125i q^{86} +(-3.23456 - 4.10872i) q^{87} +0.0233763 q^{88} -10.1857 q^{89} +(1.56928 + 0.378994i) q^{90} +(-0.373256 - 6.75750i) q^{91} +10.4290i q^{92} +(9.06416 + 11.5138i) q^{93} +10.0985i q^{94} +1.29546i q^{95} +(-8.68615 - 11.0336i) q^{96} +1.94032i q^{97} +(-1.57316 - 14.1969i) q^{98} +(-0.203918 - 0.0492479i) 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 $

$2$		−	2.04055i		−	1.44288i	−0.692475	−	0.721442i	$-0.743480\pi$
$2$		−	2.04055i		−	1.44288i	0.692475	−	0.721442i	$-0.256520\pi$
$3$	−1.36093	+	1.07138i	−0.785735	+	0.618563i
$3$	−1.36093	+	1.07138i	−0.785735	+	0.618563i
$4$	−2.16383			−1.08191
$5$	−0.263720			−0.117939			−0.0589696	−	0.998260i	$-0.518782\pi$
$5$	−0.263720			−0.117939			−0.0589696	+	0.998260i	$0.518782\pi$
$6$	2.18621	+	2.77705i	0.892515	+	1.13372i
$7$	2.64172	−	0.145918i	0.998478	−	0.0551517i
$7$	2.64172	−	0.145918i	0.998478	−	0.0551517i
$8$			0.334296i			0.118192i
$9$	0.704276	−	2.91616i	0.234759	−	0.972054i
$10$			0.538133i			0.170173i
$11$		−	0.0699270i		−	0.0210838i	−0.999944	−	0.0105419i	$-0.996644\pi$
$11$		−	0.0699270i		−	0.0210838i	0.999944	−	0.0105419i	$-0.00335565\pi$
$12$	2.94482	−	2.31829i	0.850097	−	0.669232i
$13$		−	2.55799i		−	0.709459i	−0.934969	−	0.354729i	$-0.884573\pi$
$13$		−	2.55799i		−	0.709459i	0.934969	−	0.354729i	$-0.115427\pi$
$14$	−0.297752	−	5.39056i	−0.0795775	−	1.44069i
$15$	0.358905	−	0.282545i	0.0926689	−	0.0729529i
$16$	−3.64551			−0.911377
$17$	1.00000			0.242536
$17$	1.00000			0.242536
$18$	−5.95056	−	1.43711i	−1.40256	−	0.338729i
$19$		−	4.91225i		−	1.12695i	−0.826134	−	0.563473i	$-0.809465\pi$
$19$		−	4.91225i		−	1.12695i	0.826134	−	0.563473i	$-0.190535\pi$
$20$	0.570645			0.127600
$21$	−3.43888	+	3.02888i	−0.750424	+	0.660957i
$22$	−0.142689			−0.0304215
$23$		−	4.81972i		−	1.00498i	−0.864583	−	0.502491i	$-0.832417\pi$
$23$		−	4.81972i		−	1.00498i	0.864583	−	0.502491i	$-0.167583\pi$
$24$	−0.358159	−	0.454954i	−0.0731089	−	0.0928672i
$25$	−4.93045			−0.986090
$26$	−5.21969			−1.02367
$27$	2.16585	+	4.72325i	0.416819	+	0.908990i
$28$	−5.71623	+	0.315741i	−1.08027	+	0.0596694i
$29$			3.01905i			0.560623i	0.959909	+	0.280312i	$0.0904378\pi$
$29$			3.01905i			0.560623i	−0.959909	+	0.280312i	$0.909562\pi$
$30$	−0.576547	−	0.732363i	−0.105263	−	0.133711i
$31$		−	8.46024i		−	1.51950i	−0.650213	−	0.759752i	$-0.725320\pi$
$31$		−	8.46024i		−	1.51950i	0.650213	−	0.759752i	$-0.274680\pi$
$32$			8.10742i			1.43320i
$33$	0.0749186	+	0.0951660i	0.0130417	+	0.0165663i
$34$		−	2.04055i		−	0.349951i
$35$	−0.696676	+	0.0384814i	−0.117760	+	0.00650455i
$36$	−1.52393	+	6.31007i	−0.253988	+	1.05168i
$37$	4.18192			0.687504			0.343752	−	0.939060i	$-0.388302\pi$
$37$	4.18192			0.687504			0.343752	+	0.939060i	$0.388302\pi$
$38$	−10.0237			−1.62605
$39$	2.74059	+	3.48125i	0.438845	+	0.557446i
$40$		−	0.0881606i		−	0.0139394i
$41$	4.46193			0.696836			0.348418	−	0.937339i	$-0.386719\pi$
$41$	4.46193			0.696836			0.348418	+	0.937339i	$0.386719\pi$
$42$	6.18058	+	7.01718i	0.953683	+	1.08277i
$43$	5.69089			0.867853			0.433927	−	0.900948i	$-0.357128\pi$
$43$	5.69089			0.867853			0.433927	+	0.900948i	$0.357128\pi$
$44$			0.151310i			0.0228108i
$45$	−0.185732	+	0.769050i	−0.0276872	+	0.114643i
$46$	−9.83487			−1.45007
$47$	−4.94892			−0.721874			−0.360937	−	0.932590i	$-0.617543\pi$
$47$	−4.94892			−0.721874			−0.360937	+	0.932590i	$0.617543\pi$
$48$	4.96129	−	3.90574i	0.716101	−	0.563744i
$49$	6.95742	−	0.770949i	0.993917	−	0.110136i
$50$			10.0608i			1.42281i
$51$	−1.36093	+	1.07138i	−0.190569	+	0.150024i
$52$			5.53505i			0.767573i
$53$			3.10008i			0.425829i	0.977071	+	0.212914i	$0.0682955\pi$
$53$			3.10008i			0.425829i	−0.977071	+	0.212914i	$0.931704\pi$
$54$	9.63800	−	4.41952i	1.31157	−	0.601421i
$55$			0.0184412i			0.00248661i
$56$	0.0487797	+	0.883118i	0.00651846	+	0.118012i
$57$	5.26290	+	6.68524i	0.697088	+	0.885481i
$58$	6.16051			0.808914
$59$	11.6634			1.51844			0.759221	−	0.650833i	$-0.225580\pi$
$59$	11.6634			1.51844			0.759221	+	0.650833i	$0.225580\pi$
$60$	−0.776609	+	0.611379i	−0.100260	+	0.0789287i
$61$			11.7332i			1.50228i	0.660143	+	0.751140i	$0.270496\pi$
$61$			11.7332i			1.50228i	−0.660143	+	0.751140i	$0.729504\pi$
$62$	−17.2635			−2.19247
$63$	1.43498	−	7.80646i	0.180791	−	0.983522i
$64$	9.25254			1.15657
$65$			0.674593i			0.0836730i
$66$	0.194191	−	0.152875i	0.0239032	−	0.0188176i
$67$	−3.76912			−0.460471			−0.230235	−	0.973135i	$-0.573950\pi$
$67$	−3.76912			−0.460471			−0.230235	+	0.973135i	$0.573950\pi$
$68$	−2.16383			−0.262403
$69$	5.16377	+	6.55932i	0.621645	+	0.789649i
$70$	0.0785231	+	1.42160i	0.00938530	+	0.169914i
$71$		−	1.85798i		−	0.220502i	−0.993904	−	0.110251i	$-0.964835\pi$
$71$		−	1.85798i		−	0.220502i	0.993904	−	0.110251i	$-0.0351654\pi$
$72$	0.974861	+	0.235437i	0.114888	+	0.0277465i
$73$		−	0.743764i		−	0.0870510i	−0.999052	−	0.0435255i	$-0.986141\pi$
$73$		−	0.743764i		−	0.0870510i	0.999052	−	0.0435255i	$-0.0138590\pi$
$74$		−	8.53341i		−	0.991988i
$75$	6.71001	−	5.28240i	0.774806	−	0.609959i
$76$			10.6293i			1.21926i
$77$	−0.0102036	−	0.184728i	−0.00116281	−	0.0210517i
$78$	7.10365	−	5.59229i	0.804330	−	0.633202i
$79$	1.79458			0.201906			0.100953	−	0.994891i	$-0.467811\pi$
$79$	1.79458			0.201906			0.100953	+	0.994891i	$0.467811\pi$
$80$	0.961393			0.107487
$81$	−8.00799	−	4.10756i	−0.889777	−	0.456396i
$82$		−	9.10476i		−	1.00545i
$83$	−15.3397			−1.68375			−0.841874	−	0.539674i	$-0.818547\pi$
$83$	−15.3397			−1.68375			−0.841874	+	0.539674i	$0.818547\pi$
$84$	7.44113	−	6.55398i	0.811894	−	0.715098i
$85$	−0.263720			−0.0286045
$86$		−	11.6125i		−	1.25221i
$87$	−3.23456	−	4.10872i	−0.346781	−	0.440501i
$88$	0.0233763			0.00249193
$89$	−10.1857			−1.07968			−0.539842	−	0.841766i	$-0.681516\pi$
$89$	−10.1857			−1.07968			−0.539842	+	0.841766i	$0.681516\pi$
$90$	1.56928	+	0.378994i	0.165417	+	0.0399495i
$91$	−0.373256	−	6.75750i	−0.0391278	−	0.708379i
$92$			10.4290i			1.08730i
$93$	9.06416	+	11.5138i	0.939909	+	1.19393i
$94$			10.0985i			1.04158i
$95$			1.29546i			0.132911i
$96$	−8.68615	−	11.0336i	−0.886526	−	1.12612i
$97$			1.94032i			0.197010i	0.995137	+	0.0985050i	$0.0314060\pi$
$97$			1.94032i			0.197010i	−0.995137	+	0.0985050i	$0.968594\pi$
$98$	−1.57316	−	14.1969i	−0.158913	−	1.43411i
$99$	−0.203918	−	0.0492479i	−0.0204946	−	0.00494960i
$100$	10.6686			1.06686
$101$	13.5054			1.34384			0.671920	−	0.740624i	$-0.265470\pi$
$101$	13.5054			1.34384			0.671920	+	0.740624i	$0.265470\pi$
$102$	2.18621	+	2.77705i	0.216467	+	0.274968i
$103$			14.7537i			1.45373i	0.686782	+	0.726864i	$0.259023\pi$
$103$			14.7537i			1.45373i	−0.686782	+	0.726864i	$0.740977\pi$
$104$	0.855126			0.0838520
$105$	0.906900	−	0.798777i	0.0885044	−	0.0779527i
$106$	6.32585			0.614421
$107$			14.3152i			1.38390i	0.721944	+	0.691951i	$0.243249\pi$
$107$			14.3152i			1.38390i	−0.721944	+	0.691951i	$0.756751\pi$
$108$	−4.68653	−	10.2203i	−0.450962	−	0.983448i
$109$	11.2228			1.07495			0.537473	−	0.843281i	$-0.319379\pi$
$109$	11.2228			1.07495			0.537473	+	0.843281i	$0.319379\pi$
$110$	0.0376300			0.00358788
$111$	−5.69132	+	4.48044i	−0.540196	+	0.425265i
$112$	−9.63043	+	0.531944i	−0.909990	+	0.0502640i
$113$		−	4.87908i		−	0.458985i	−0.973310	−	0.229493i	$-0.926293\pi$
$113$		−	4.87908i		−	0.458985i	0.973310	−	0.229493i	$-0.0737067\pi$
$114$	13.6415	−	10.7392i	1.27765	−	1.00582i
$115$			1.27106i			0.118527i
$116$		−	6.53270i		−	0.606546i
$117$	−7.45951	−	1.80153i	−0.689632	−	0.166552i
$118$		−	23.7996i		−	2.19093i
$119$	2.64172	−	0.145918i	0.242166	−	0.0133763i
$120$	0.0944538	+	0.119981i	0.00862241	+	0.0109527i
$121$	10.9951			0.999555
$122$	23.9421			2.16762
$123$	−6.07238	+	4.78043i	−0.547528	+	0.431037i
$124$			18.3065i			1.64397i
$125$	2.61886			0.234238
$126$	−15.9294	−	2.92815i	−1.41911	−	0.260860i
$127$	−2.52437			−0.224002			−0.112001	−	0.993708i	$-0.535726\pi$
$127$	−2.52437			−0.224002			−0.112001	+	0.993708i	$0.535726\pi$
$128$		−	2.66540i		−	0.235590i
$129$	−7.74492	+	6.09713i	−0.681903	+	0.536822i
$130$	1.37654			0.120730
$131$	9.11623			0.796488			0.398244	−	0.917279i	$-0.369620\pi$
$131$	9.11623			0.796488			0.398244	+	0.917279i	$0.369620\pi$
$132$	−0.162111	−	0.205923i	−0.0141099	−	0.0179233i
$133$	−0.716784	−	12.9768i	−0.0621530	−	1.12523i
$134$			7.69106i			0.664406i
$135$	−0.571179	−	1.24562i	−0.0491593	−	0.107206i
$136$			0.334296i			0.0286657i
$137$			8.23044i			0.703174i	0.936155	+	0.351587i	$0.114358\pi$
$137$			8.23044i			0.703174i	−0.936155	+	0.351587i	$0.885642\pi$
$138$	13.3846	−	10.5369i	1.13937	−	0.896961i
$139$		−	2.88762i		−	0.244925i	−0.992473	−	0.122462i	$-0.960921\pi$
$139$		−	2.88762i		−	0.244925i	0.992473	−	0.122462i	$-0.0390791\pi$
$140$	1.50749	−	0.0832671i	0.127406	−	0.00703736i
$141$	6.73515	−	5.30219i	0.567202	−	0.446525i
$142$	−3.79129			−0.318158
$143$	−0.178873			−0.0149581
$144$	−2.56744	+	10.6309i	−0.213954	+	0.885907i
$145$		−	0.796184i		−	0.0661194i
$146$	−1.51768			−0.125604
$147$	−8.64259	+	8.50327i	−0.712829	+	0.701338i
$148$	−9.04896			−0.743820
$149$			19.0355i			1.55945i	0.626125	+	0.779723i	$0.284640\pi$
$149$			19.0355i			1.55945i	−0.626125	+	0.779723i	$0.715360\pi$
$150$	−10.7790	−	13.6921i	−0.880101	−	1.11795i
$151$	−23.0925			−1.87924			−0.939622	−	0.342214i	$-0.888823\pi$
$151$	−23.0925			−1.87924			−0.939622	+	0.342214i	$0.888823\pi$
$152$	1.64214			0.133196
$153$	0.704276	−	2.91616i	0.0569373	−	0.235758i
$154$	−0.376946	+	0.0208209i	−0.0303752	+	0.00167779i
$155$			2.23113i			0.179209i
$156$	−5.93016	−	7.53283i	−0.474792	−	0.603109i
$157$			10.3071i			0.822595i	0.911501	+	0.411297i	$0.134924\pi$
$157$			10.3071i			0.822595i	−0.911501	+	0.411297i	$0.865076\pi$
$158$		−	3.66193i		−	0.291327i
$159$	−3.32137	−	4.21900i	−0.263402	−	0.334588i
$160$		−	2.13809i		−	0.169031i
$161$	−0.703283	−	12.7324i	−0.0554264	−	1.00345i
$162$	−8.38167	+	16.3407i	−0.658526	+	1.28384i
$163$	−17.6751			−1.38442			−0.692209	−	0.721697i	$-0.743362\pi$
$163$	−17.6751			−1.38442			−0.692209	+	0.721697i	$0.743362\pi$
$164$	−9.65484			−0.753916
$165$	−0.0197576	−	0.0250972i	−0.00153812	−	0.00195381i
$166$			31.3013i			2.42945i
$167$	19.9231			1.54169			0.770846	−	0.637021i	$-0.219834\pi$
$167$	19.9231			1.54169			0.770846	+	0.637021i	$0.219834\pi$
$168$	−1.01254	−	1.14960i	−0.0781195	−	0.0886938i
$169$	6.45669			0.496669
$170$			0.538133i			0.0412729i
$171$	−14.3249	−	3.45958i	−1.09545	−	0.264560i
$172$	−12.3141			−0.938942
$173$	1.33440			0.101452			0.0507261	−	0.998713i	$-0.483846\pi$
$173$	1.33440			0.101452			0.0507261	+	0.998713i	$0.483846\pi$
$174$	−8.38403	+	6.60026i	−0.635592	+	0.500365i
$175$	−13.0249	+	0.719440i	−0.984590	+	0.0543846i
$176$			0.254919i			0.0192153i
$177$	−15.8731	+	12.4959i	−1.19309	+	0.939252i
$178$			20.7844i			1.55786i
$179$		−	13.3395i		−	0.997042i	−0.866878	−	0.498521i	$-0.833877\pi$
$179$		−	13.3395i		−	0.997042i	0.866878	−	0.498521i	$-0.166123\pi$
$180$	0.401891	−	1.66409i	0.0299552	−	0.124034i
$181$			6.08181i			0.452057i	0.974121	+	0.226029i	$0.0725743\pi$
$181$			6.08181i			0.452057i	−0.974121	+	0.226029i	$0.927426\pi$
$182$	−13.7890	+	0.761646i	−1.02211	+	0.0564569i
$183$	−12.5707	−	15.9681i	−0.929256	−	1.18039i
$184$	1.61121			0.118780
$185$	−1.10286			−0.0810837
$186$	23.4945	−	18.4958i	1.72270	−	1.35618i
$187$		−	0.0699270i		−	0.00511357i
$188$	10.7086			0.781006
$189$	6.41080	+	12.1615i	0.466317	+	0.884618i
$190$	2.64344			0.191775
$191$		−	3.57812i		−	0.258904i	−0.991586	−	0.129452i	$-0.958678\pi$
$191$		−	3.57812i		−	0.258904i	0.991586	−	0.129452i	$-0.0413218\pi$
$192$	−12.5921	+	9.91302i	−0.908755	+	0.715410i
$193$	−13.2192			−0.951535			−0.475768	−	0.879571i	$-0.657830\pi$
$193$	−13.2192			−0.951535			−0.475768	+	0.879571i	$0.657830\pi$
$194$	3.95932			0.284262
$195$	−0.722748	−	0.918076i	−0.0517570	−	0.0657448i
$196$	−15.0546	+	1.66820i	−1.07533	+	0.119157i
$197$			5.74504i			0.409317i	0.978833	+	0.204658i	$0.0656084\pi$
$197$			5.74504i			0.409317i	−0.978833	+	0.204658i	$0.934392\pi$
$198$	−0.100493	+	0.416105i	−0.00714170	+	0.0295713i
$199$		−	25.0797i		−	1.77785i	−0.458052	−	0.888926i	$-0.651453\pi$
$199$		−	25.0797i		−	1.77785i	0.458052	−	0.888926i	$-0.348547\pi$
$200$		−	1.64823i		−	0.116548i
$201$	5.12952	−	4.03817i	0.361808	−	0.284830i
$202$		−	27.5584i		−	1.93900i
$203$	0.440532	+	7.97549i	0.0309193	+	0.559770i
$204$	2.94482	−	2.31829i	0.206179	−	0.162313i
$205$	−1.17670			−0.0821843
$206$	30.1056			2.09756
$207$	−14.0551	−	3.39441i	−0.976896	−	0.235928i
$208$			9.32517i			0.646584i
$209$	−0.343499			−0.0237603
$210$	−1.62994	−	1.85057i	−0.112477	−	0.127702i
$211$	9.23991			0.636101			0.318051	−	0.948074i	$-0.396972\pi$
$211$	9.23991			0.636101			0.318051	+	0.948074i	$0.396972\pi$
$212$		−	6.70803i		−	0.460710i
$213$	1.99061	+	2.52859i	0.136394	+	0.173256i
$214$	29.2108			1.99681
$215$	−1.50080			−0.102354
$216$	−1.57896	+	0.724037i	−0.107435	+	0.0492644i
$217$	−1.23450	−	22.3496i	−0.0838032	−	1.51719i
$218$		−	22.9006i		−	1.55102i
$219$	0.796856	+	1.01221i	0.0538466	+	0.0683990i
$220$		−	0.0399035i		−	0.00269029i
$221$		−	2.55799i		−	0.172069i
$222$	9.14255	+	11.6134i	0.613608	+	0.779440i
$223$		−	0.171537i		−	0.0114870i	−0.999984	−	0.00574348i	$-0.998172\pi$
$223$		−	0.171537i		−	0.0114870i	0.999984	−	0.00574348i	$-0.00182822\pi$
$224$	1.18302	+	21.4176i	0.0790435	+	1.43102i
$225$	−3.47240	+	14.3780i	−0.231493	+	0.958533i
$226$	−9.95598			−0.662262
$227$	−15.5636			−1.03299			−0.516497	−	0.856289i	$-0.672764\pi$
$227$	−15.5636			−1.03299			−0.516497	+	0.856289i	$0.672764\pi$
$228$	−11.3880	−	14.4657i	−0.754189	−	0.958014i
$229$		−	5.43842i		−	0.359381i	−0.983723	−	0.179690i	$-0.942490\pi$
$229$		−	5.43842i		−	0.359381i	0.983723	−	0.179690i	$-0.0575096\pi$
$230$	2.59365			0.171020
$231$	0.211801	+	0.240470i	0.0139355	+	0.0158218i
$232$	−1.00926			−0.0662609
$233$			19.5563i			1.28118i	0.767884	+	0.640589i	$0.221310\pi$
$233$			19.5563i			1.28118i	−0.767884	+	0.640589i	$0.778690\pi$
$234$	−3.67610	+	15.2215i	−0.240314	+	0.995059i
$235$	1.30513			0.0851373
$236$	−25.2375			−1.64282
$237$	−2.44231	+	1.92269i	−0.158645	+	0.124892i
$238$	−0.297752	−	5.39056i	−0.0193004	−	0.349418i
$239$		−	16.2502i		−	1.05114i	−0.850750	−	0.525570i	$-0.823852\pi$
$239$		−	16.2502i		−	1.05114i	0.850750	−	0.525570i	$-0.176148\pi$
$240$	−1.30839	+	1.03002i	−0.0844563	+	0.0664876i
$241$			7.07456i			0.455712i	0.973695	+	0.227856i	$0.0731716\pi$
$241$			7.07456i			0.455712i	−0.973695	+	0.227856i	$0.926828\pi$
$242$		−	22.4360i		−	1.44224i
$243$	15.2991	−	2.98951i	0.981438	−	0.191777i
$244$		−	25.3886i		−	1.62534i
$245$	−1.83481	+	0.203315i	−0.117222	+	0.0129893i
$246$	9.75469	+	12.3910i	0.621936	+	0.790020i
$247$	−12.5655			−0.799522
$248$	2.82822			0.179592
$249$	20.8763	−	16.4347i	1.32298	−	1.04150i
$250$		−	5.34390i		−	0.337978i
$251$	30.5110			1.92584			0.962918	−	0.269796i	$-0.0869563\pi$
$251$	30.5110			1.92584			0.962918	+	0.269796i	$0.0869563\pi$
$252$	−3.10505	+	16.8918i	−0.195600	+	1.06409i
$253$	−0.337029			−0.0211888
$254$			5.15110i			0.323209i
$255$	0.358905	−	0.282545i	0.0224755	−	0.0176937i
$256$	13.0662			0.816638
$257$	17.2123			1.07367			0.536837	−	0.843686i	$-0.319619\pi$
$257$	17.2123			1.07367			0.536837	+	0.843686i	$0.319619\pi$
$258$	12.4415	+	15.8039i	0.774572	+	0.983906i
$259$	11.0475	−	0.610217i	0.686458	−	0.0379170i
$260$		−	1.45970i		−	0.0905269i
$261$	8.80403	+	2.12624i	0.544956	+	0.131611i
$262$		−	18.6021i		−	1.14924i
$263$		−	29.9817i		−	1.84875i	−0.381481	−	0.924377i	$-0.624586\pi$
$263$		−	29.9817i		−	1.84875i	0.381481	−	0.924377i	$-0.375414\pi$
$264$	−0.0318136	+	0.0250450i	−0.00195799	+	0.00154141i
$265$		−	0.817553i		−	0.0502219i
$266$	−26.4798	+	1.46263i	−1.62358	+	0.0896796i
$267$	13.8621	−	10.9128i	0.848345	−	0.667853i
$268$	8.15572			0.498190
$269$	−12.1771			−0.742449			−0.371224	−	0.928543i	$-0.621062\pi$
$269$	−12.1771			−0.742449			−0.371224	+	0.928543i	$0.621062\pi$
$270$	−2.54174	+	1.16552i	−0.154685	+	0.0709311i
$271$			17.1394i			1.04114i	0.853818	+	0.520572i	$0.174281\pi$
$271$			17.1394i			1.04114i	−0.853818	+	0.520572i	$0.825719\pi$
$272$	−3.64551			−0.221041
$273$	7.74785	+	8.79661i	0.468921	+	0.532395i
$274$	16.7946			1.01460
$275$			0.344772i			0.0207905i
$276$	−11.1735	−	14.1932i	−0.672566	−	0.854332i
$277$	16.2642			0.977221			0.488610	−	0.872502i	$-0.337504\pi$
$277$	16.2642			0.977221			0.488610	+	0.872502i	$0.337504\pi$
$278$	−5.89232			−0.353398
$279$	−24.6714	−	5.95834i	−1.47704	−	0.356717i
$280$	−0.0128642	−	0.232896i	−0.000768782	−	0.0139182i
$281$		−	13.6572i		−	0.814722i	−0.913267	−	0.407361i	$-0.866449\pi$
$281$		−	13.6572i		−	0.814722i	0.913267	−	0.407361i	$-0.133551\pi$
$282$	−10.8194	−	13.7434i	−0.644284	−	0.818406i
$283$		−	18.1000i		−	1.07593i	−0.842966	−	0.537966i	$-0.819193\pi$
$283$		−	18.1000i		−	1.07593i	0.842966	−	0.537966i	$-0.180807\pi$
$284$			4.02035i			0.238564i
$285$	−1.38793	−	1.76303i	−0.0822140	−	0.104433i
$286$			0.364998i			0.0215828i
$287$	11.7872	−	0.651074i	0.695775	−	0.0384317i
$288$	23.6425	+	5.70986i	1.39315	+	0.336457i
$289$	1.00000			0.0588235
$290$	−1.62465			−0.0954027
$291$	−2.07883	−	2.64065i	−0.121863	−	0.154798i
$292$			1.60938i			0.0941816i
$293$	−12.6336			−0.738063			−0.369031	−	0.929417i	$-0.620311\pi$
$293$	−12.6336			−0.738063			−0.369031	+	0.929417i	$0.620311\pi$
$294$	17.3513	+	17.6356i	1.01195	+	1.02853i
$295$	−3.07587			−0.179084
$296$			1.39800i			0.0812571i
$297$	0.330283	−	0.151452i	0.0191649	−	0.00878812i
$298$	38.8427			2.25010
$299$	−12.3288			−0.712993
$300$	−14.5193	+	11.4302i	−0.838273	+	0.659923i
$301$	15.0338	−	0.830402i	0.866532	−	0.0478636i
$302$			47.1214i			2.71153i
$303$	−18.3800	+	14.4695i	−1.05590	+	0.831250i
$304$			17.9076i			1.02707i
$305$		−	3.09428i		−	0.177178i
$306$	−5.95056	−	1.43711i	−0.340171	−	0.0821539i
$307$			13.1848i			0.752494i	0.926519	+	0.376247i	$0.122786\pi$
$307$			13.1848i			0.752494i	−0.926519	+	0.376247i	$0.877214\pi$
$308$	0.0220788	+	0.399719i	0.00125806	+	0.0227761i
$309$	−15.8069	−	20.0788i	−0.899223	−	1.14224i
$310$	4.55273			0.258578
$311$	24.8306			1.40801			0.704006	−	0.710194i	$-0.251393\pi$
$311$	24.8306			1.40801			0.704006	+	0.710194i	$0.251393\pi$
$312$	−1.16377	+	0.916167i	−0.0658854	+	0.0518678i
$313$		−	23.8362i		−	1.34730i	−0.739051	−	0.673650i	$-0.764726\pi$
$313$		−	23.8362i		−	1.34730i	0.739051	−	0.673650i	$-0.235274\pi$
$314$	21.0321			1.18691
$315$	−0.378434	+	2.05872i	−0.0213223	+	0.115996i
$316$	−3.88317			−0.218445
$317$			9.37106i			0.526331i	0.964751	+	0.263166i	$0.0847666\pi$
$317$			9.37106i			0.526331i	−0.964751	+	0.263166i	$0.915233\pi$
$318$	−8.60906	+	6.77741i	−0.482772	+	0.380058i
$319$	0.211113			0.0118201
$320$	−2.44008			−0.136405
$321$	−15.3371	−	19.4820i	−0.856031	−	1.08738i
$322$	−25.9810	+	1.43508i	−1.44786	+	0.0799739i
$323$		−	4.91225i		−	0.273325i
$324$	17.3279	+	8.88806i	0.962661	+	0.493781i
$325$			12.6120i			0.699590i
$326$			36.0668i			1.99755i
$327$	−15.2734	+	12.0239i	−0.844623	+	0.664923i
$328$			1.49160i			0.0823601i
$329$	−13.0737	+	0.722135i	−0.720776	+	0.0398126i
$330$	−0.0512119	+	0.0403162i	−0.00281912	+	0.00221933i
$331$	−14.4983			−0.796899			−0.398449	−	0.917190i	$-0.630452\pi$
$331$	−14.4983			−0.796899			−0.398449	+	0.917190i	$0.630452\pi$
$332$	33.1924			1.82167
$333$	2.94523	−	12.1952i	0.161397	−	0.668291i
$334$		−	40.6539i		−	2.22448i
$335$	0.993992			0.0543076
$336$	12.5364	−	11.0418i	0.683919	−	0.602380i
$337$	4.74715			0.258594			0.129297	−	0.991606i	$-0.458728\pi$
$337$	4.74715			0.258594			0.129297	+	0.991606i	$0.458728\pi$
$338$		−	13.1752i		−	0.716635i
$339$	5.22736	+	6.64010i	0.283911	+	0.360641i
$340$	0.570645			0.0309475
$341$	−0.591599			−0.0320369
$342$	−7.05942	+	29.2306i	−0.381730	+	1.58061i
$343$	18.2671	−	3.05184i	0.986330	−	0.164784i
$344$			1.90244i			0.102573i
$345$	−1.36179	−	1.72982i	−0.0733163	−	0.0931306i
$346$		−	2.72290i		−	0.146384i
$347$		−	10.1697i		−	0.545937i	−0.962023	−	0.272968i	$-0.911995\pi$
$347$		−	10.1697i		−	0.545937i	0.962023	−	0.272968i	$-0.0880054\pi$
$348$	6.99902	+	8.89056i	0.375187	+	0.476584i
$349$			32.7972i			1.75559i	0.479034	+	0.877796i	$0.340987\pi$
$349$			32.7972i			1.75559i	−0.479034	+	0.877796i	$0.659013\pi$
$350$	1.46805	+	26.5779i	0.0784706	+	1.42065i
$351$	12.0820	−	5.54023i	0.644890	−	0.295716i
$352$	0.566928			0.0302173
$353$	−4.18118			−0.222542			−0.111271	−	0.993790i	$-0.535492\pi$
$353$	−4.18118			−0.222542			−0.111271	+	0.993790i	$0.535492\pi$
$354$	25.4985	+	32.3897i	1.35523	+	1.72149i
$355$			0.489987i			0.0260058i
$356$	22.0401			1.16812
$357$	−3.43888	+	3.02888i	−0.182005	+	0.160306i
$358$	−27.2199			−1.43862
$359$		−	22.3402i		−	1.17907i	−0.807743	−	0.589535i	$-0.799311\pi$
$359$		−	22.3402i		−	1.17907i	0.807743	−	0.589535i	$-0.200689\pi$
$360$	−0.257090	−	0.0620894i	−0.0135499	−	0.00327240i
$361$	−5.13016			−0.270009
$362$	12.4102			0.652266
$363$	−14.9636	+	11.7800i	−0.785386	+	0.618288i
$364$	0.807661	+	14.6221i	0.0423329	+	0.766404i
$365$			0.196145i			0.0102667i
$366$	−32.5836	+	25.6512i	−1.70317	+	1.34081i
$367$			13.1145i			0.684573i	0.939596	+	0.342287i	$0.111201\pi$
$367$			13.1145i			0.684573i	−0.939596	+	0.342287i	$0.888799\pi$
$368$			17.5703i			0.915917i
$369$	3.14243	−	13.0117i	0.163588	−	0.677362i
$370$			2.25043i			0.116994i
$371$	0.452356	+	8.18955i	0.0234852	+	0.425180i
$372$	−19.6133	−	24.9139i	−1.01690	−	1.29173i
$373$	−22.3878			−1.15920			−0.579599	−	0.814902i	$-0.696791\pi$
$373$	−22.3878			−1.15920			−0.579599	+	0.814902i	$0.696791\pi$
$374$	−0.142689			−0.00737829
$375$	−3.56409	+	2.80580i	−0.184049	+	0.144891i
$376$		−	1.65440i		−	0.0853194i
$377$	7.72269			0.397739
$378$	24.8161	−	13.0815i	1.27640	−	0.672841i
$379$	−0.390445			−0.0200558			−0.0100279	−	0.999950i	$-0.503192\pi$
$379$	−0.390445			−0.0200558			−0.0100279	+	0.999950i	$0.503192\pi$
$380$		−	2.80315i		−	0.143798i
$381$	3.43550	−	2.70457i	0.176006	−	0.138559i
$382$	−7.30132			−0.373568
$383$	15.6437			0.799357			0.399679	−	0.916655i	$-0.369122\pi$
$383$	15.6437			0.799357			0.399679	+	0.916655i	$0.369122\pi$
$384$	2.85566	+	3.62743i	0.145727	+	0.185111i
$385$	0.00269089	+	0.0487165i	0.000137141	+	0.00248282i
$386$			26.9743i			1.37295i
$387$	4.00796	−	16.5956i	0.203736	−	0.843600i
$388$		−	4.19852i		−	0.213148i
$389$		−	0.971573i		−	0.0492607i	−0.999697	−	0.0246303i	$-0.992159\pi$
$389$		−	0.971573i		−	0.0492607i	0.999697	−	0.0246303i	$-0.00784088\pi$
$390$	−1.87338	+	1.47480i	−0.0948621	+	0.0746794i
$391$		−	4.81972i		−	0.243744i
$392$	0.257725	+	2.32584i	0.0130171	+	0.117473i
$393$	−12.4066	+	9.76697i	−0.625829	+	0.492679i
$394$	11.7230			0.590597
$395$	−0.473267			−0.0238127
$396$	0.441244	+	0.106564i	0.0221734	+	0.00535504i
$397$			14.9684i			0.751242i	0.926773	+	0.375621i	$0.122571\pi$
$397$			14.9684i			0.751242i	−0.926773	+	0.375621i	$0.877429\pi$
$398$	−51.1762			−2.56523
$399$	14.8786	+	16.8926i	0.744863	+	0.845688i
$400$	17.9740			0.898700
$401$			12.3168i			0.615072i	0.951537	+	0.307536i	$0.0995044\pi$
$401$			12.3168i			0.615072i	−0.951537	+	0.307536i	$0.900496\pi$
$402$	−8.24007	−	10.4670i	−0.410977	−	0.522047i
$403$	−21.6412			−1.07802
$404$	−29.2234			−1.45392
$405$	2.11187	+	1.08325i	0.104940	+	0.0538270i
$406$	16.2744	−	0.898927i	0.807683	−	0.0446130i
$407$		−	0.292429i		−	0.0144952i
$408$	−0.358159	−	0.454954i	−0.0177315	−	0.0225236i
$409$		−	25.9892i		−	1.28508i	−0.766252	−	0.642541i	$-0.777880\pi$
$409$		−	25.9892i		−	1.28508i	0.766252	−	0.642541i	$-0.222120\pi$
$410$			2.40111i			0.118582i
$411$	−8.81796	−	11.2011i	−0.434958	−	0.552509i
$412$		−	31.9245i		−	1.57281i
$413$	30.8114	−	1.70189i	1.51613	−	0.0837446i
$414$	−6.92646	+	28.6801i	−0.340417	+	1.40955i
$415$	4.04538			0.198580
$416$	20.7387			1.01680
$417$	3.09375	+	3.92986i	0.151502	+	0.192446i
$418$			0.700925i			0.0342834i
$419$	6.60817			0.322830			0.161415	−	0.986887i	$-0.448394\pi$
$419$	6.60817			0.322830			0.161415	+	0.986887i	$0.448394\pi$
$420$	−1.96238	+	1.72842i	−0.0957541	+	0.0843381i
$421$	5.17503			0.252215			0.126108	−	0.992017i	$-0.459752\pi$
$421$	5.17503			0.252215			0.126108	+	0.992017i	$0.459752\pi$
$422$		−	18.8545i		−	0.917820i
$423$	−3.48541	+	14.4319i	−0.169466	+	0.701701i
$424$	−1.03634			−0.0503293
$425$	−4.93045			−0.239162
$426$	5.15970	−	4.06193i	0.249988	−	0.196801i
$427$	1.71208	+	30.9958i	0.0828533	+	1.49999i
$428$		−	30.9756i		−	1.49726i
$429$	0.243434	−	0.191641i	0.0117531	−	0.00925252i
$430$			3.06246i			0.147685i
$431$			3.36646i			0.162156i	0.996708	+	0.0810782i	$0.0258364\pi$
$431$			3.36646i			0.162156i	−0.996708	+	0.0810782i	$0.974164\pi$
$432$	−7.89564	−	17.2186i	−0.379879	−	0.828432i
$433$		−	10.6945i		−	0.513943i	−0.966419	−	0.256972i	$-0.917275\pi$
$433$		−	10.6945i		−	0.513943i	0.966419	−	0.256972i	$-0.0827247\pi$
$434$	−45.6054	+	2.51905i	−2.18913	+	0.120918i
$435$	0.853018	+	1.08355i	0.0408991	+	0.0519524i
$436$	−24.2841			−1.16300
$437$	−23.6757			−1.13256
$438$	2.06547	−	1.62602i	0.0986918	−	0.0776943i
$439$			30.6677i			1.46369i	0.681471	+	0.731845i	$0.261341\pi$
$439$			30.6677i			1.46369i	−0.681471	+	0.731845i	$0.738659\pi$
$440$	−0.00616481			−0.000293896
$441$	2.65173	−	20.8319i	0.126273	−	0.991996i
$442$	−5.21969			−0.248276
$443$			23.1556i			1.10016i	0.835113	+	0.550079i	$0.185402\pi$
$443$			23.1556i			1.10016i	−0.835113	+	0.550079i	$0.814598\pi$
$444$	12.3150	−	9.69490i	0.584445	−	0.460100i
$445$	2.68618			0.127337
$446$	−0.350029			−0.0165744
$447$	−20.3943	−	25.9060i	−0.964616	−	1.22531i
$448$	24.4427	−	1.35011i	1.15481	−	0.0637866i
$449$		−	4.81523i		−	0.227245i	−0.993524	−	0.113622i	$-0.963755\pi$
$449$		−	4.81523i		−	0.227245i	0.993524	−	0.113622i	$-0.0362454\pi$
$450$	29.3389	+	7.08559i	1.38305	+	0.334018i
$451$		−	0.312009i		−	0.0146919i
$452$			10.5575i			0.496582i
$453$	31.4274	−	24.7410i	1.47659	−	1.16243i
$454$			31.7583i			1.49049i
$455$	0.0984351	+	1.78209i	0.00461471	+	0.0835456i
$456$	−2.23485	+	1.75937i	−0.104656	+	0.0823899i
$457$	15.8885			0.743231			0.371616	−	0.928387i	$-0.378804\pi$
$457$	15.8885			0.743231			0.371616	+	0.928387i	$0.378804\pi$
$458$	−11.0973			−0.518545
$459$	2.16585	+	4.72325i	0.101093	+	0.220462i
$460$		−	2.75035i		−	0.128236i
$461$	−22.1763			−1.03285			−0.516426	−	0.856332i	$-0.672738\pi$
$461$	−22.1763			−1.03285			−0.516426	+	0.856332i	$0.672738\pi$
$462$	0.490691	−	0.432189i	0.0228290	−	0.0201073i
$463$	−12.7987			−0.594806			−0.297403	−	0.954752i	$-0.596120\pi$
$463$	−12.7987			−0.594806			−0.297403	+	0.954752i	$0.596120\pi$
$464$		−	11.0060i		−	0.510939i
$465$	−2.39040	−	3.03642i	−0.110852	−	0.140811i
$466$	39.9056			1.84859
$467$	−8.50881			−0.393741			−0.196870	−	0.980430i	$-0.563078\pi$
$467$	−8.50881			−0.393741			−0.196870	+	0.980430i	$0.563078\pi$
$468$	16.1411	+	3.89820i	0.746122	+	0.180194i
$469$	−9.95697	+	0.549981i	−0.459770	+	0.0253958i
$470$		−	2.66318i		−	0.122843i
$471$	−11.0428	−	14.0272i	−0.508827	−	0.646341i
$472$			3.89902i			0.179467i
$473$		−	0.397947i		−	0.0182976i
$474$	3.92333	+	4.98364i	0.180204	+	0.228906i
$475$			24.2196i			1.11127i
$476$	−5.71623	+	0.315741i	−0.262003	+	0.0144719i
$477$	9.04033	+	2.18331i	0.413928	+	0.0999669i
$478$	−33.1594			−1.51667
$479$	−6.36555			−0.290850			−0.145425	−	0.989369i	$-0.546455\pi$
$479$	−6.36555			−0.290850			−0.145425	+	0.989369i	$0.546455\pi$
$480$	2.29071	+	2.90979i	0.104556	+	0.132813i
$481$		−	10.6973i		−	0.487756i
$482$	14.4360			0.657540
$483$	14.5984	+	16.5744i	0.664249	+	0.754163i
$484$	−23.7915			−1.08143
$485$		−	0.511702i		−	0.0232352i
$486$	−6.10023	−	31.2185i	−0.276712	−	1.41610i
$487$	−34.6237			−1.56895			−0.784474	−	0.620161i	$-0.787067\pi$
$487$	−34.6237			−1.56895			−0.784474	+	0.620161i	$0.787067\pi$
$488$	−3.92236			−0.177557
$489$	24.0546	−	18.9368i	1.08779	−	0.856350i
$490$	0.414873	+	3.74401i	0.0187420	+	0.169137i
$491$		−	35.8060i		−	1.61590i	−0.589250	−	0.807951i	$-0.700577\pi$
$491$		−	35.8060i		−	1.61590i	0.589250	−	0.807951i	$-0.299423\pi$
$492$	13.1396	−	10.3440i	0.592378	−	0.466345i
$493$			3.01905i			0.135971i
$494$			25.6404i			1.15362i
$495$	0.0537774	+	0.0129877i	0.00241711	+	0.000583752i
$496$			30.8419i			1.38484i
$497$	−0.271112	−	4.90827i	−0.0121610	−	0.220166i
$498$	−33.5357	−	42.5990i	−1.50277	−	1.90891i
$499$	38.3510			1.71683			0.858413	−	0.512960i	$-0.171451\pi$
$499$	38.3510			1.71683			0.858413	+	0.512960i	$0.171451\pi$
$500$	−5.66676			−0.253425
$501$	−27.1139	+	21.3452i	−1.21136	+	0.953635i
$502$		−	62.2590i		−	2.77876i
$503$	36.7027			1.63649			0.818247	−	0.574867i	$-0.194946\pi$
$503$	36.7027			1.63649			0.818247	+	0.574867i	$0.194946\pi$
$504$	2.60967	+	0.479709i	0.116244	+	0.0213679i
$505$	−3.56165			−0.158491
$506$			0.687723i			0.0305730i
$507$	−8.78712	+	6.91759i	−0.390250	+	0.307221i
$508$	5.46231			0.242351
$509$	−35.7492			−1.58455			−0.792277	−	0.610162i	$-0.791104\pi$
$509$	−35.7492			−1.58455			−0.792277	+	0.610162i	$0.791104\pi$
$510$	−0.576547	−	0.732363i	−0.0255299	−	0.0324296i
$511$	−0.108528	−	1.96482i	−0.00480101	−	0.0869185i
$512$		−	31.9930i		−	1.41390i
$513$	23.2018	−	10.6392i	1.02438	−	0.469733i
$514$		−	35.1225i		−	1.54919i
$515$		−	3.89085i		−	0.171451i
$516$	16.7587	−	13.1931i	0.737760	−	0.580795i
$517$			0.346063i			0.0152198i
$518$	−1.24517	−	22.5429i	−0.0547098	−	0.990478i
$519$	−1.81602	+	1.42965i	−0.0797146	+	0.0627547i
$520$	−0.225514			−0.00988944
$521$	23.3412			1.02260			0.511299	−	0.859403i	$-0.329164\pi$
$521$	23.3412			1.02260			0.511299	+	0.859403i	$0.329164\pi$
$522$	4.33869	−	17.9650i	0.189900	−	0.786308i
$523$			23.2872i			1.01828i	0.860684	+	0.509140i	$0.170036\pi$
$523$			23.2872i			1.01828i	−0.860684	+	0.509140i	$0.829964\pi$
$524$	−19.7259			−0.861731
$525$	16.9552	−	14.9338i	0.739986	−	0.651763i
$526$	−61.1791			−2.66754
$527$		−	8.46024i		−	0.368534i
$528$	−0.273116	−	0.346928i	−0.0118859	−	0.0150981i
$529$	−0.229732			−0.00998833
$530$	−1.66825			−0.0724643
$531$	8.21423	−	34.0123i	0.356467	−	1.47601i
$532$	1.55100	+	28.0796i	0.0672442	+	1.21740i
$533$		−	11.4136i		−	0.494376i
$534$	−22.2681	−	28.2862i	−0.963634	−	1.22406i
$535$		−	3.77520i		−	0.163216i
$536$		−	1.26000i		−	0.0544238i
$537$	14.2917	+	18.1542i	0.616734	+	0.783411i
$538$			24.8479i			1.07127i
$539$	−0.0539101	−	0.486511i	−0.00232207	−	0.0209555i
$540$	1.23593	+	2.69530i	0.0531861	+	0.115987i
$541$	24.4210			1.04994			0.524971	−	0.851120i	$-0.324076\pi$
$541$	24.4210			1.04994			0.524971	+	0.851120i	$0.324076\pi$
$542$	34.9737			1.50225
$543$	−6.51595	−	8.27693i	−0.279626	−	0.355197i
$544$			8.10742i			0.347603i
$545$	−2.95967			−0.126778
$546$	17.9499	−	15.8098i	0.768184	−	0.676599i
$547$	2.33031			0.0996370			0.0498185	−	0.998758i	$-0.484136\pi$
$547$	2.33031			0.0996370			0.0498185	+	0.998758i	$0.484136\pi$
$548$		−	17.8093i		−	0.760774i
$549$	34.2159	+	8.26340i	1.46030	+	0.352673i
$550$	0.703523			0.0299983
$551$	14.8303			0.631792
$552$	−2.19275	+	1.72623i	−0.0933298	+	0.0734732i
$553$	4.74079	−	0.261861i	0.201599	−	0.0111355i
$554$		−	33.1878i		−	1.41002i
$555$	1.50091	−	1.18158i	0.0637103	−	0.0501554i
$556$			6.24831i			0.264987i
$557$		−	21.6435i		−	0.917064i	−0.888678	−	0.458532i	$-0.848376\pi$
$557$		−	21.6435i		−	0.917064i	0.888678	−	0.458532i	$-0.151624\pi$
$558$	−12.1583	+	50.3432i	−0.514701	+	2.13120i
$559$		−	14.5572i		−	0.615706i
$560$	2.53974	−	0.140284i	0.107323	−	0.00592809i
$561$	0.0749186	+	0.0951660i	0.00316307	+	0.00401791i
$562$	−27.8682			−1.17555
$563$	−31.6460			−1.33372			−0.666860	−	0.745183i	$-0.732362\pi$
$563$	−31.6460			−1.33372			−0.666860	+	0.745183i	$0.732362\pi$
$564$	−14.5737	+	11.4730i	−0.613663	+	0.483101i
$565$			1.28671i			0.0541323i
$566$	−36.9339			−1.55245
$567$	−21.7543	−	9.68254i	−0.913594	−	0.406629i
$568$	0.621115			0.0260614
$569$		−	25.7517i		−	1.07957i	−0.841804	−	0.539784i	$-0.818506\pi$
$569$		−	25.7517i		−	1.07957i	0.841804	−	0.539784i	$-0.181494\pi$
$570$	−3.59755	+	2.83214i	−0.150685	+	0.118625i
$571$	34.3737			1.43850			0.719248	−	0.694753i	$-0.244486\pi$
$571$	34.3737			1.43850			0.719248	+	0.694753i	$0.244486\pi$
$572$	0.387049			0.0161833
$573$	3.83354	+	4.86958i	0.160148	+	0.203430i
$574$	−1.32855	−	24.0523i	−0.0554524	−	1.00392i
$575$			23.7634i			0.991003i
$576$	6.51634	−	26.9819i	0.271514	−	1.12425i
$577$			31.0442i			1.29239i	0.763173	+	0.646194i	$0.223640\pi$
$577$			31.0442i			1.29239i	−0.763173	+	0.646194i	$0.776360\pi$
$578$		−	2.04055i		−	0.0848755i
$579$	17.9904	−	14.1628i	0.747654	−	0.588585i
$580$			1.72280i			0.0715355i
$581$	−40.5232	+	2.23833i	−1.68119	+	0.0928615i
$582$	−5.38837	+	4.24195i	−0.223355	+	0.175834i
$583$	0.216779			0.00897808
$584$	0.248637			0.0102887
$585$	1.96722	+	0.475100i	0.0813346	+	0.0196430i
$586$			25.7794i			1.06494i
$587$	19.5030			0.804976			0.402488	−	0.915425i	$-0.368146\pi$
$587$	19.5030			0.804976			0.402488	+	0.915425i	$0.368146\pi$
$588$	18.7011	−	18.3996i	0.771219	−	0.758787i
$589$	−41.5588			−1.71240
$590$			6.27644i			0.258397i
$591$	−6.15514	−	7.81861i	−0.253188	−	0.321615i
$592$	−15.2452			−0.626575
$593$	−44.0008			−1.80690			−0.903448	−	0.428698i	$-0.858973\pi$
$593$	−44.0008			−1.80690			−0.903448	+	0.428698i	$0.858973\pi$
$594$	−0.309044	−	0.673957i	−0.0126802	−	0.0276528i
$595$	−0.696676	+	0.0384814i	−0.0285609	+	0.00157758i
$596$		−	41.1894i		−	1.68719i
$597$	26.8699	+	34.1318i	1.09971	+	1.39692i
$598$			25.1575i			1.02877i
$599$			33.6070i			1.37315i	0.727061	+	0.686573i	$0.240886\pi$
$599$			33.6070i			1.37315i	−0.727061	+	0.686573i	$0.759114\pi$
$600$	1.76589	+	2.24313i	0.0720920	+	0.0915754i
$601$			44.3159i			1.80768i	0.427867	+	0.903842i	$0.359265\pi$
$601$			44.3159i			1.80768i	−0.427867	+	0.903842i	$0.640735\pi$
$602$	−1.69447	−	30.6771i	−0.0690616	−	1.25031i
$603$	−2.65450	+	10.9914i	−0.108100	+	0.447603i
$604$	49.9683			2.03318
$605$	−2.89963			−0.117887
$606$	29.5256	+	37.5052i	1.19940	+	1.52354i
$607$		−	27.5348i		−	1.11760i	−0.829302	−	0.558801i	$-0.811262\pi$
$607$		−	27.5348i		−	1.11760i	0.829302	−	0.558801i	$-0.188738\pi$
$608$	39.8256			1.61514
$609$	−9.14434	−	10.3821i	−0.370548	−	0.420705i
$610$	−6.31401			−0.255647
$611$			12.6593i			0.512140i
$612$	−1.52393	+	6.31007i	−0.0616013	+	0.255069i
$613$	−23.3586			−0.943445			−0.471723	−	0.881747i	$-0.656368\pi$
$613$	−23.3586			−0.943445			−0.471723	+	0.881747i	$0.656368\pi$
$614$	26.9041			1.08576
$615$	1.60141	−	1.26070i	0.0645750	−	0.0508362i
$616$	0.0617538	−	0.00341102i	0.00248813	−	0.000137434i
$617$			19.5459i			0.786889i	0.919348	+	0.393444i	$0.128717\pi$
$617$			19.5459i			0.786889i	−0.919348	+	0.393444i	$0.871283\pi$
$618$	−40.9718	+	32.2547i	−1.64813	+	1.29747i
$619$			35.3683i			1.42157i	0.703409	+	0.710786i	$0.251660\pi$
$619$			35.3683i			1.42157i	−0.703409	+	0.710786i	$0.748340\pi$
$620$		−	4.82779i		−	0.193889i
$621$	22.7647	−	10.4388i	0.913518	−	0.418895i
$622$		−	50.6679i		−	2.03160i
$623$	−26.9079	+	1.48628i	−1.07804	+	0.0595464i
$624$	−9.99083	−	12.6909i	−0.399953	−	0.508044i
$625$	23.9616			0.958465
$626$	−48.6388			−1.94400
$627$	0.467479	−	0.368019i	0.0186693	−	0.0146973i
$628$		−	22.3027i		−	0.889976i
$629$	4.18192			0.166744
$630$	4.20091	+	0.772212i	0.167368	+	0.0307656i
$631$	−28.1923			−1.12232			−0.561158	−	0.827708i	$-0.689644\pi$
$631$	−28.1923			−1.12232			−0.561158	+	0.827708i	$0.689644\pi$
$632$			0.599922i			0.0238636i
$633$	−12.5749	+	9.89948i	−0.499807	+	0.393469i
$634$	19.1221			0.759435
$635$	0.665728			0.0264186
$636$	7.18688	+	9.12918i	0.284978	+	0.361996i
$637$	−1.97208	−	17.7970i	−0.0781366	−	0.705143i
$638$		−	0.430786i		−	0.0170550i
$639$	−5.41817	−	1.30853i	−0.214339	−	0.0517647i
$640$			0.702919i			0.0277853i
$641$			31.3711i			1.23909i	0.784963	+	0.619543i	$0.212682\pi$
$641$			31.3711i			1.23909i	−0.784963	+	0.619543i	$0.787318\pi$
$642$	−39.7540	+	31.2960i	−1.56896	+	1.23515i
$643$			11.8278i			0.466443i	0.972424	+	0.233221i	$0.0749267\pi$
$643$			11.8278i			0.466443i	−0.972424	+	0.233221i	$0.925073\pi$
$644$	1.52178	+	27.5507i	0.0599666	+	1.08565i
$645$	2.04249	−	1.60794i	0.0804230	−	0.0633124i
$646$	−10.0237			−0.394376
$647$	0.632198			0.0248543			0.0124271	−	0.999923i	$-0.496044\pi$
$647$	0.632198			0.0248543			0.0124271	+	0.999923i	$0.496044\pi$
$648$	1.37314	−	2.67704i	0.0539421	−	0.105164i
$649$		−	0.815585i		−	0.0320145i
$650$	25.7354			1.00943
$651$	25.6251	+	29.0937i	1.00433	+	1.14027i
$652$	38.2458			1.49782
$653$			25.6928i			1.00544i	0.864450	+	0.502719i	$0.167667\pi$
$653$			25.6928i			1.00544i	−0.864450	+	0.502719i	$0.832333\pi$
$654$	24.5353	+	31.1661i	0.959406	+	1.21869i
$655$	−2.40413			−0.0939372
$656$	−16.2660			−0.635080
$657$	−2.16894	−	0.523815i	−0.0846182	−	0.0204360i
$658$	1.47355	+	26.6775i	0.0574449	+	1.04000i
$659$			49.7743i			1.93893i	0.245228	+	0.969465i	$0.421137\pi$
$659$			49.7743i			1.93893i	−0.245228	+	0.969465i	$0.578863\pi$
$660$	0.0427519	+	0.0543059i	0.00166412	+	0.00211386i
$661$		−	19.2077i		−	0.747092i	−0.927612	−	0.373546i	$-0.878142\pi$
$661$		−	19.2077i		−	0.747092i	0.927612	−	0.373546i	$-0.121858\pi$
$662$			29.5845i			1.14983i
$663$	2.74059	+	3.48125i	0.106436	+	0.135201i
$664$		−	5.12799i		−	0.199005i
$665$	0.189030	+	3.42224i	0.00733028	+	0.132709i
$666$	−24.8848	−	6.00987i	−0.964266	−	0.232878i
$667$	14.5510			0.563416
$668$	−43.1101			−1.66798
$669$	0.183782	+	0.233450i	0.00710542	+	0.00902571i
$670$		−	2.02829i		−	0.0783595i
$671$	0.820467			0.0316738
$672$	−24.5564	−	27.8804i	−0.947284	−	1.07551i
$673$	−5.11607			−0.197210			−0.0986050	−	0.995127i	$-0.531438\pi$
$673$	−5.11607			−0.197210			−0.0986050	+	0.995127i	$0.531438\pi$
$674$		−	9.68678i		−	0.373121i
$675$	−10.6786	−	23.2877i	−0.411021	−	0.896346i
$676$	−13.9712			−0.537352
$677$	−22.4393			−0.862412			−0.431206	−	0.902253i	$-0.641912\pi$
$677$	−22.4393			−0.862412			−0.431206	+	0.902253i	$0.641912\pi$
$678$	13.5494	−	10.6667i	0.520363	−	0.409651i
$679$	0.283127	+	5.12580i	0.0108654	+	0.196710i
$680$		−	0.0881606i		−	0.00338080i
$681$	21.1810	−	16.6746i	0.811659	−	0.638972i
$682$			1.20719i			0.0462255i
$683$			33.3841i			1.27741i	0.769452	+	0.638704i	$0.220529\pi$
$683$			33.3841i			1.27741i	−0.769452	+	0.638704i	$0.779471\pi$
$684$	30.9966	+	7.48592i	1.18518	+	0.286231i
$685$		−	2.17053i		−	0.0829318i
$686$	−6.22743	−	37.2748i	−0.237764	−	1.42316i
$687$	5.82663	+	7.40132i	0.222300	+	0.282378i
$688$	−20.7462			−0.790941
$689$	7.92997			0.302108
$690$	−3.52979	+	2.77879i	−0.134377	+	0.105787i
$691$		−	48.3913i		−	1.84089i	−0.390870	−	0.920446i	$-0.627826\pi$
$691$		−	48.3913i		−	1.84089i	0.390870	−	0.920446i	$-0.372174\pi$
$692$	−2.88740			−0.109763
$693$	−0.545883	−	0.100344i	−0.0207364	−	0.00381176i
$694$	−20.7517			−0.787723
$695$			0.761524i			0.0288862i
$696$	1.37353	−	1.08130i	0.0520635	−	0.0409866i
$697$	4.46193			0.169008
$698$	66.9241			2.53312
$699$	−20.9523	−	26.6149i	−0.792490	−	1.00667i
$700$	28.1836	−	1.55674i	1.06524	−	0.0588394i
$701$		−	38.3871i		−	1.44986i	−0.688821	−	0.724931i	$-0.741872\pi$
$701$		−	38.3871i		−	1.44986i	0.688821	−	0.724931i	$-0.258128\pi$
$702$	−11.3051	−	24.6539i	−0.426683	−	0.930502i
$703$		−	20.5426i		−	0.774780i
$704$		−	0.647003i		−	0.0243848i
$705$	−1.77619	+	1.39829i	−0.0668953	+	0.0526628i
$706$			8.53189i			0.321102i
$707$	35.6776	−	1.97068i	1.34179	−	0.0741150i
$708$	34.3466	−	27.0391i	1.29082	−	1.01619i
$709$	−10.4756			−0.393419			−0.196710	−	0.980462i	$-0.563026\pi$
$709$	−10.4756			−0.393419			−0.196710	+	0.980462i	$0.563026\pi$
$710$	0.999840			0.0375233
$711$	1.26388	−	5.23329i	0.0473992	−	0.196264i
$712$		−	3.40505i		−	0.127609i
$713$	−40.7760			−1.52707
$714$	6.18058	+	7.01718i	0.231302	+	0.262611i
$715$	0.0471723			0.00176414
$716$			28.8644i			1.07871i
$717$	17.4102	+	22.1155i	0.650197	+	0.825918i
$718$	−45.5862			−1.70126
$719$	18.0470			0.673038			0.336519	−	0.941677i	$-0.390750\pi$
$719$	18.0470			0.673038			0.336519	+	0.941677i	$0.390750\pi$
$720$	0.677086	−	2.80358i	0.0252335	−	0.104483i
$721$	2.15283	+	38.9753i	0.0801755	+	1.45151i
$722$			10.4683i			0.389591i
$723$	−7.57956	−	9.62800i	−0.281887	−	0.358069i
$724$		−	13.1600i		−	0.489087i
$725$		−	14.8853i		−	0.552825i
$726$	24.0376	+	30.5339i	0.892118	+	1.13322i
$727$		−	25.9781i		−	0.963474i	−0.876316	−	0.481737i	$-0.840006\pi$
$727$		−	25.9781i		−	0.963474i	0.876316	−	0.481737i	$-0.159994\pi$
$728$	2.25901	−	0.124778i	0.0837244	−	0.00462458i
$729$	−17.6182	+	20.4597i	−0.652524	+	0.757768i
$730$	0.400244			0.0148137
$731$	5.69089			0.210485
$732$	27.2009	+	34.5522i	1.00537	+	1.27708i
$733$		−	25.8154i		−	0.953514i	−0.879035	−	0.476757i	$-0.841812\pi$
$733$		−	25.8154i		−	0.953514i	0.879035	−	0.476757i	$-0.158188\pi$
$734$	26.7608			0.987759
$735$	2.27923	−	2.24248i	0.0840705	−	0.0827152i
$736$	39.0755			1.44034
$737$			0.263563i			0.00970847i
$738$	−26.5510	−	6.41227i	−0.977354	−	0.236039i
$739$	29.2605			1.07637			0.538183	−	0.842828i	$-0.319111\pi$
$739$	29.2605			1.07637			0.538183	+	0.842828i	$0.319111\pi$
$740$	2.38639			0.0877255
$741$	17.1008	−	13.4624i	0.628212	−	0.494555i
$742$	16.7112	−	0.923054i	0.613486	−	0.0338864i
$743$			34.5360i			1.26700i	0.773742	+	0.633501i	$0.218383\pi$
$743$			34.5360i			1.26700i	−0.773742	+	0.633501i	$0.781617\pi$
$744$	−3.84902	+	3.03011i	−0.141112	+	0.111089i
$745$		−	5.02003i		−	0.183920i
$746$			45.6834i			1.67259i
$747$	−10.8034	+	44.7330i	−0.395274	+	1.63669i
$748$			0.151310i			0.00553244i
$749$	2.08884	+	37.8168i	0.0763246	+	1.38180i
$750$	5.72537	+	7.27269i	0.209061	+	0.265561i
$751$	−33.1209			−1.20860			−0.604300	−	0.796757i	$-0.706547\pi$
$751$	−33.1209			−1.20860			−0.604300	+	0.796757i	$0.706547\pi$
$752$	18.0413			0.657900
$753$	−41.5234	+	32.6889i	−1.51320	+	1.19125i
$754$		−	15.7585i		−	0.573891i
$755$	6.08997			0.221637
$756$	−13.8719	−	26.3153i	−0.504514	−	0.957080i
$757$	3.50807			0.127503			0.0637515	−	0.997966i	$-0.479693\pi$
$757$	3.50807			0.127503			0.0637515	+	0.997966i	$0.479693\pi$
$758$			0.796720i			0.0289382i
$759$	0.458674	−	0.361087i	0.0166488	−	0.0131066i
$760$	−0.433067			−0.0157090
$761$	−33.9797			−1.23176			−0.615881	−	0.787839i	$-0.711200\pi$
$761$	−33.9797			−1.23176			−0.615881	+	0.787839i	$0.711200\pi$
$762$	−5.51880	−	7.01030i	−0.199925	−	0.253956i
$763$	29.6475	−	1.63760i	1.07331	−	0.0592851i
$764$			7.74244i			0.280111i
$765$	−0.185732	+	0.769050i	−0.00671514	+	0.0278051i
$766$		−	31.9217i		−	1.15338i
$767$		−	29.8348i		−	1.07727i
$768$	−17.7822	+	13.9989i	−0.641661	+	0.505143i
$769$		−	51.8342i		−	1.86919i	−0.355717	−	0.934594i	$-0.615763\pi$
$769$		−	51.8342i		−	1.86919i	0.355717	−	0.934594i	$-0.384237\pi$
$770$	0.0994082	−	0.00549089i	0.00358242	−	0.000197878i
$771$	−23.4248	+	18.4410i	−0.843622	+	0.664135i
$772$	28.6040			1.02948
$773$	3.89615			0.140135			0.0700674	−	0.997542i	$-0.477679\pi$
$773$	3.89615			0.140135			0.0700674	+	0.997542i	$0.477679\pi$
$774$	−33.8640	−	8.17842i	−1.21722	−	0.293967i
$775$			41.7128i			1.49837i
$776$	−0.648642			−0.0232849
$777$	−14.3811	+	12.6666i	−0.515920	+	0.454410i
$778$	−1.98254			−0.0710774
$779$		−	21.9181i		−	0.785297i
$780$	1.56390	+	1.98656i	0.0559966	+	0.0711302i
$781$	−0.129923			−0.00464901
$782$	−9.83487			−0.351694
$783$	−14.2597	+	6.53882i	−0.509601	+	0.233678i
$784$	−25.3633	+	2.81050i	−0.905833	+	0.100375i
$785$		−	2.71819i		−	0.0970162i
$786$	19.9300	+	25.3162i	0.710878	+	0.902998i
$787$		−	52.5973i		−	1.87489i	−0.348130	−	0.937446i	$-0.613183\pi$
$787$		−	52.5973i		−	1.87489i	0.348130	−	0.937446i	$-0.386817\pi$
$788$		−	12.4313i		−	0.442845i
$789$	32.1219	+	40.8031i	1.14357	+	1.45263i
$790$			0.965724i			0.0343589i
$791$	−0.711944	−	12.8892i	−0.0253138	−	0.458287i
$792$	0.0164634	−	0.0681691i	0.000585001	−	0.00242229i
$793$	30.0134			1.06581
$794$	30.5437			1.08396
$795$	0.875913	+	1.11263i	0.0310654	+	0.0394611i
$796$			54.2681i			1.92348i
$797$	−20.5730			−0.728732			−0.364366	−	0.931256i	$-0.618714\pi$
$797$	−20.5730			−0.728732			−0.364366	+	0.931256i	$0.618714\pi$
$798$	34.4701	−	30.3605i	1.22023	−	1.07475i
$799$	−4.94892			−0.175080
$800$		−	39.9732i		−	1.41327i
$801$	−7.17355	+	29.7032i	−0.253465	+	1.04951i
$802$	25.1330			0.887477
$803$	−0.0520092			−0.00183536
$804$	−11.0994	+	8.73790i	−0.391445	+	0.308162i
$805$	0.185470	+	3.35778i	0.00653695	+	0.118346i
$806$			44.1599i			1.55546i
$807$	16.5722	−	13.0463i	0.583368	−	0.459252i
$808$			4.51481i			0.158830i
$809$			45.7554i			1.60868i	0.594172	+	0.804338i	$0.297480\pi$
$809$			45.7554i			1.60868i	−0.594172	+	0.804338i	$0.702520\pi$
$810$	2.21041	−	4.30936i	0.0776661	−	0.151416i
$811$			26.3778i			0.926251i	0.886293	+	0.463126i	$0.153272\pi$
$811$			26.3778i			0.926251i	−0.886293	+	0.463126i	$0.846728\pi$
$812$	−0.953236	−	17.2576i	−0.0334520	−	0.605623i
$813$	−18.3629	−	23.3256i	−0.644014	−	0.818064i
$814$	−0.596716			−0.0209149
$815$	4.66127			0.163277
$816$	4.96129	−	3.90574i	0.173680	−	0.136728i
$817$		−	27.9551i		−	0.978024i
$818$	−53.0321			−1.85422
$819$	−19.9688	−	3.67067i	−0.697768	−	0.128264i
$820$	2.54617			0.0889163
$821$		−	41.2224i		−	1.43867i	−0.694662	−	0.719336i	$-0.744446\pi$
$821$		−	41.2224i		−	1.43867i	0.694662	−	0.719336i	$-0.255554\pi$
$822$	−22.8563	+	17.9934i	−0.797206	+	0.627594i
$823$	−46.4295			−1.61843			−0.809216	−	0.587511i	$-0.800108\pi$
$823$	−46.4295			−1.61843			−0.809216	+	0.587511i	$0.800108\pi$
$824$	−4.93211			−0.171818
$825$	−0.369383	−	0.469211i	−0.0128603	−	0.0163358i
$826$	−3.47279	−	62.8721i	−0.120834	−	2.18760i
$827$			18.7552i			0.652184i	0.945338	+	0.326092i	$0.105732\pi$
$827$			18.7552i			0.652184i	−0.945338	+	0.326092i	$0.894268\pi$
$828$	30.4128	+	7.34492i	1.05692	+	0.255254i
$829$		−	3.33161i		−	0.115712i	−0.998325	−	0.0578558i	$-0.981574\pi$
$829$		−	3.33161i		−	0.115712i	0.998325	−	0.0578558i	$-0.0184263\pi$
$830$		−	8.25478i		−	0.286528i
$831$	−22.1345	+	17.4252i	−0.767836	+	0.604473i
$832$		−	23.6679i		−	0.820537i
$833$	6.95742	−	0.770949i	0.241060	−	0.0267118i
$834$	8.01906	−	6.31294i	0.277677	−	0.218599i
$835$	−5.25411			−0.181826
$836$	0.743272			0.0257066
$837$	39.9598	−	18.3236i	1.38121	−	0.633358i
$838$		−	13.4843i		−	0.465806i
$839$	−38.3901			−1.32537			−0.662687	−	0.748897i	$-0.730584\pi$
$839$	−38.3901			−1.32537			−0.662687	+	0.748897i	$0.730584\pi$
$840$	0.267028	+	0.303173i	0.00921335	+	0.0104605i
$841$	19.8853			0.685702
$842$		−	10.5599i		−	0.363918i
$843$	14.6321	+	18.5866i	0.503957	+	0.640156i
$844$	−19.9936			−0.688207
$845$	−1.70276			−0.0585767
$846$	29.4489	+	7.11213i	1.01247	+	0.244520i
$847$	29.0461	−	1.60438i	0.998034	−	0.0551272i
$848$		−	11.3014i		−	0.388090i
$849$	19.3920	+	24.6329i	0.665533	+	0.845398i
$850$			10.0608i			0.345083i
$851$		−	20.1557i		−	0.690929i
$852$	−4.30733	−	5.47142i	−0.147567	−	0.187448i
$853$			5.48909i			0.187943i	0.995575	+	0.0939714i	$0.0299562\pi$
$853$			5.48909i			0.187943i	−0.995575	+	0.0939714i	$0.970044\pi$
$854$	63.2484	−	3.49358i	2.16432	−	0.119548i
$855$	3.77776	+	0.912360i	0.129197	+	0.0312020i
$856$	−4.78551			−0.163565
$857$	31.0899			1.06201			0.531006	−	0.847368i	$-0.321814\pi$
$857$	31.0899			1.06201			0.531006	+	0.847368i	$0.321814\pi$
$858$	−0.391052	−	0.496737i	−0.0133503	−	0.0169583i
$859$		−	21.4540i		−	0.732002i	−0.930614	−	0.366001i	$-0.880727\pi$
$859$		−	21.4540i		−	0.732002i	0.930614	−	0.366001i	$-0.119273\pi$
$860$	3.24748			0.110738
$861$	−15.3440	+	13.5147i	−0.522922	+	0.460578i
$862$	6.86941			0.233973
$863$		−	5.20977i		−	0.177343i	−0.996061	−	0.0886713i	$-0.971738\pi$
$863$		−	5.20977i		−	0.177343i	0.996061	−	0.0886713i	$-0.0282621\pi$
$864$	−38.2933	+	17.5595i	−1.30277	+	0.597386i
$865$	−0.351907			−0.0119652
$866$	−21.8225			−0.741560
$867$	−1.36093	+	1.07138i	−0.0462197	+	0.0363861i
$868$	2.67124	+	48.3607i	0.0906678	+	1.64147i
$869$		−	0.125490i		−	0.00425695i
$870$	2.21104	−	1.74062i	0.0749612	−	0.0590126i
$871$			9.64136i			0.326685i
$872$			3.75173i			0.127050i
$873$	5.65829	+	1.36652i	0.191504	+	0.0462498i
$874$			48.3113i			1.63415i
$875$	6.91831	−	0.382138i	0.233881	−	0.0129186i
$876$	−1.72426	−	2.19025i	−0.0582573	−	0.0740018i
$877$	53.7049			1.81349			0.906743	−	0.421684i	$-0.138561\pi$
$877$	53.7049			1.81349			0.906743	+	0.421684i	$0.138561\pi$
$878$	62.5789			2.11193
$879$	17.1935	−	13.5354i	0.579922	−	0.456539i
$880$		−	0.0672274i		−	0.00226623i
$881$	28.3120			0.953855			0.476927	−	0.878943i	$-0.341750\pi$
$881$	28.3120			0.953855			0.476927	+	0.878943i	$0.341750\pi$
$882$	−42.5085	−	5.41098i	−1.43133	−	0.182197i
$883$	34.1170			1.14813			0.574065	−	0.818810i	$-0.305366\pi$
$883$	34.1170			1.14813			0.574065	+	0.818810i	$0.305366\pi$
$884$			5.53505i			0.186164i
$885$	4.18605	−	3.29543i	0.140712	−	0.110775i
$886$	47.2502			1.58740
$887$	−11.0751			−0.371866			−0.185933	−	0.982562i	$-0.559531\pi$
$887$	−11.0751			−0.371866			−0.185933	+	0.982562i	$0.559531\pi$
$888$	−1.49779	−	1.90258i	−0.0502627	−	0.0638466i
$889$	−6.66870	+	0.368351i	−0.223661	+	0.0123541i
$890$		−	5.48127i		−	0.183733i
$891$	−0.287230	+	0.559975i	−0.00962256	+	0.0187599i
$892$			0.371176i			0.0124279i
$893$			24.3103i			0.813514i
$894$	−52.8623	+	41.6154i	−1.76798	+	1.39183i
$895$			3.51790i			0.117590i
$896$	−0.388928	−	7.04124i	−0.0129932	−	0.235231i
$897$	16.7787	−	13.2089i	0.560223	−	0.441031i
$898$	−9.82570			−0.327888
$899$	25.5419			0.851869
$900$	7.51367	−	31.1115i	0.250456	−	1.03705i
$901$			3.10008i			0.103279i
$902$	−0.636669			−0.0211988
$903$	−19.5703	+	17.2371i	−0.651258	+	0.573613i
$904$	1.63106			0.0542481
$905$		−	1.60389i		−	0.0533153i
$906$	−50.4851	−	64.1290i	−1.67725	−	2.13054i
$907$	21.5402			0.715231			0.357616	−	0.933869i	$-0.383590\pi$
$907$	21.5402			0.715231			0.357616	+	0.933869i	$0.383590\pi$
$908$	33.6770			1.11761
$909$	9.51154	−	39.3840i	0.315478	−	1.30628i
$910$	3.63643	−	0.200861i	0.120547	−	0.00665848i
$911$		−	36.5320i		−	1.21036i	−0.796089	−	0.605179i	$-0.793101\pi$
$911$		−	36.5320i		−	1.21036i	0.796089	−	0.605179i	$-0.206899\pi$
$912$	−19.1859	−	24.3711i	−0.635310	−	0.807007i
$913$			1.07266i			0.0354998i
$914$		−	32.4211i		−	1.07240i
$915$	3.31516	+	4.21110i	0.109596	+	0.139215i
$916$			11.7678i			0.388819i
$917$	24.0826	−	1.33022i	0.795276	−	0.0439277i
$918$	9.63800	−	4.41952i	0.318102	−	0.145866i
$919$	−21.7341			−0.716943			−0.358472	−	0.933541i	$-0.616702\pi$
$919$	−21.7341			−0.716943			−0.358472	+	0.933541i	$0.616702\pi$
$920$	−0.424910			−0.0140089
$921$	−14.1259	−	17.9436i	−0.465466	−	0.591261i
$922$			45.2517i			1.49028i
$923$	−4.75269			−0.156437
$924$	−0.458300	−	0.520336i	−0.0150770	−	0.0171178i
$925$	−20.6188			−0.677941
$926$			26.1163i			0.858236i
$927$	43.0242	+	10.3907i	1.41310	+	0.341275i
$928$	−24.4767			−0.803486
$929$	40.3941			1.32529			0.662643	−	0.748935i	$-0.269435\pi$
$929$	40.3941			1.32529			0.662643	+	0.748935i	$0.269435\pi$
$930$	−6.19596	+	4.87772i	−0.203174	+	0.159947i
$931$	−3.78709	−	34.1765i	−0.124117	−	1.12009i
$932$		−	42.3165i		−	1.38612i
$933$	−33.7927	+	26.6031i	−1.10632	+	0.870945i
$934$			17.3626i			0.568122i
$935$			0.0184412i			0.000603090i
$936$	0.602244	−	2.49368i	0.0196850	−	0.0815086i
$937$			23.3671i			0.763370i	0.924292	+	0.381685i	$0.124656\pi$
$937$			23.3671i			0.763370i	−0.924292	+	0.381685i	$0.875344\pi$
$938$	1.12226	+	20.3177i	0.0366431	+	0.663395i
$939$	25.5377	+	32.4394i	0.833390	+	1.05862i
$940$	−2.82407			−0.0921112
$941$	19.1256			0.623475			0.311738	−	0.950168i	$-0.399089\pi$
$941$	19.1256			0.623475			0.311738	+	0.950168i	$0.399089\pi$
$942$	−28.6232	+	22.5334i	−0.932596	+	0.734178i
$943$		−	21.5053i		−	0.700307i
$944$	−42.5189			−1.38387
$945$	−1.69066	−	3.20723i	−0.0549970	−	0.104331i
$946$	−0.812030			−0.0264014
$947$		−	27.5995i		−	0.896862i	−0.893817	−	0.448431i	$-0.851983\pi$
$947$		−	27.5995i		−	0.896862i	0.893817	−	0.448431i	$-0.148017\pi$
$948$	5.28473	−	4.16036i	0.171640	−	0.135122i
$949$	−1.90254			−0.0617591
$950$	49.4212			1.60344
$951$	−10.0400	−	12.7534i	−0.325569	−	0.413557i
$952$	0.0487797	+	0.883118i	0.00158096	+	0.0286220i
$953$		−	9.13563i		−	0.295932i	−0.988992	−	0.147966i	$-0.952727\pi$
$953$		−	9.13563i		−	0.295932i	0.988992	−	0.147966i	$-0.0472726\pi$
$954$	4.45515	−	18.4472i	0.144241	−	0.597250i
$955$			0.943622i			0.0305349i
$956$			35.1627i			1.13724i
$957$	−0.287311	+	0.226183i	−0.00928743	+	0.00731146i
$958$			12.9892i			0.419662i
$959$	1.20097	+	21.7426i	0.0387813	+	0.702104i
$960$	3.32079	−	2.61426i	0.107178	−	0.0843749i
$961$	−40.5756			−1.30889
$962$	−21.8284			−0.703775
$963$	41.7454	+	10.0818i	1.34523	+	0.324883i
$964$		−	15.3081i		−	0.493041i
$965$	3.48616			0.112223
$966$	33.8209	−	29.7887i	1.08817	−	0.958434i
$967$	55.8729			1.79675			0.898376	−	0.439227i	$-0.144747\pi$
$967$	55.8729			1.79675			0.898376	+	0.439227i	$0.144747\pi$
$968$			3.67562i			0.118139i
$969$	5.26290	+	6.68524i	0.169069	+	0.214761i
$970$	−1.04415			−0.0335257
$971$	−35.0764			−1.12565			−0.562827	−	0.826575i	$-0.690286\pi$
$971$	−35.0764			−1.12565			−0.562827	+	0.826575i	$0.690286\pi$
$972$	−33.1046	+	6.46878i	−1.06183	+	0.207486i
$973$	−0.421355	−	7.62830i	−0.0135080	−	0.244552i
$974$			70.6512i			2.26381i
$975$	−13.5123	−	17.1641i	−0.432741	−	0.549692i
$976$		−	42.7734i		−	1.36914i
$977$		−	22.5950i		−	0.722877i	−0.932396	−	0.361438i	$-0.882286\pi$
$977$		−	22.5950i		−	0.722877i	0.932396	−	0.361438i	$-0.117714\pi$
$978$	−38.6413	−	49.0845i	−1.23561	−	1.56955i
$979$			0.712257i			0.0227638i
$980$	3.97021	−	0.439938i	0.126824	−	0.0140533i
$981$	7.90393	−	32.7274i	0.252353	−	1.04491i
$982$	−73.0637			−2.33156
$983$	3.93164			0.125400			0.0626999	−	0.998032i	$-0.480029\pi$
$983$	3.93164			0.125400			0.0626999	+	0.998032i	$0.480029\pi$
$984$	−1.59808	−	2.02997i	−0.0509449	−	0.0647132i
$985$		−	1.51508i		−	0.0482745i
$986$	6.16051			0.196190
$987$	17.0187	−	14.9897i	0.541712	−	0.477128i
$988$	27.1895			0.865014
$989$		−	27.4285i		−	0.872177i
$990$	0.0265019	−	0.109735i	0.000842286	−	0.00348761i
$991$	12.5286			0.397983			0.198991	−	0.980001i	$-0.436233\pi$
$991$	12.5286			0.397983			0.198991	+	0.980001i	$0.436233\pi$
$992$	68.5907			2.17776
$993$	19.7312	−	15.5332i	0.626151	−	0.492933i
$994$	−10.0156	+	0.553217i	−0.317674	+	0.0175470i
$995$			6.61401i			0.209678i
$996$	−45.1726	+	35.5618i	−1.43135	+	1.12682i
$997$			30.3090i			0.959896i	0.877297	+	0.479948i	$0.159345\pi$
$997$			30.3090i			0.959896i	−0.877297	+	0.479948i	$0.840655\pi$
$998$		−	78.2569i		−	2.47718i
$999$	9.05744	+	19.7523i	0.286565	+	0.624934i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	357.2.d.b.188.4	yes	22
3.2	odd	2		357.2.d.a.188.19	yes	22
7.6	odd	2		357.2.d.a.188.4	✓	22
21.20	even	2	inner	357.2.d.b.188.19	yes	22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
357.2.d.a.188.4	✓	22	7.6	odd	2
357.2.d.a.188.19	yes	22	3.2	odd	2
357.2.d.b.188.4	yes	22	1.1	even	1	trivial
357.2.d.b.188.19	yes	22	21.20	even	2	inner

Overview	Random
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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)

\(f(q)\)	\(=\)	\(q-2.04055i q^{2} +(-1.36093 + 1.07138i) q^{3} -2.16383 q^{4} -0.263720 q^{5} +(2.18621 + 2.77705i) q^{6} +(2.64172 - 0.145918i) q^{7} +0.334296i q^{8} +(0.704276 - 2.91616i) q^{9} +O(q^{10})\)	\(q-2.04055i q^{2} +(-1.36093 + 1.07138i) q^{3} -2.16383 q^{4} -0.263720 q^{5} +(2.18621 + 2.77705i) q^{6} +(2.64172 - 0.145918i) q^{7} +0.334296i q^{8} +(0.704276 - 2.91616i) q^{9} +0.538133i q^{10} -0.0699270i q^{11} +(2.94482 - 2.31829i) q^{12} -2.55799i q^{13} +(-0.297752 - 5.39056i) q^{14} +(0.358905 - 0.282545i) q^{15} -3.64551 q^{16} +1.00000 q^{17} +(-5.95056 - 1.43711i) q^{18} -4.91225i q^{19} +0.570645 q^{20} +(-3.43888 + 3.02888i) q^{21} -0.142689 q^{22} -4.81972i q^{23} +(-0.358159 - 0.454954i) q^{24} -4.93045 q^{25} -5.21969 q^{26} +(2.16585 + 4.72325i) q^{27} +(-5.71623 + 0.315741i) q^{28} +3.01905i q^{29} +(-0.576547 - 0.732363i) q^{30} -8.46024i q^{31} +8.10742i q^{32} +(0.0749186 + 0.0951660i) q^{33} -2.04055i q^{34} +(-0.696676 + 0.0384814i) q^{35} +(-1.52393 + 6.31007i) q^{36} +4.18192 q^{37} -10.0237 q^{38} +(2.74059 + 3.48125i) q^{39} -0.0881606i q^{40} +4.46193 q^{41} +(6.18058 + 7.01718i) q^{42} +5.69089 q^{43} +0.151310i q^{44} +(-0.185732 + 0.769050i) q^{45} -9.83487 q^{46} -4.94892 q^{47} +(4.96129 - 3.90574i) q^{48} +(6.95742 - 0.770949i) q^{49} +10.0608i q^{50} +(-1.36093 + 1.07138i) q^{51} +5.53505i q^{52} +3.10008i q^{53} +(9.63800 - 4.41952i) q^{54} +0.0184412i q^{55} +(0.0487797 + 0.883118i) q^{56} +(5.26290 + 6.68524i) q^{57} +6.16051 q^{58} +11.6634 q^{59} +(-0.776609 + 0.611379i) q^{60} +11.7332i q^{61} -17.2635 q^{62} +(1.43498 - 7.80646i) q^{63} +9.25254 q^{64} +0.674593i q^{65} +(0.194191 - 0.152875i) q^{66} -3.76912 q^{67} -2.16383 q^{68} +(5.16377 + 6.55932i) q^{69} +(0.0785231 + 1.42160i) q^{70} -1.85798i q^{71} +(0.974861 + 0.235437i) q^{72} -0.743764i q^{73} -8.53341i q^{74} +(6.71001 - 5.28240i) q^{75} +10.6293i q^{76} +(-0.0102036 - 0.184728i) q^{77} +(7.10365 - 5.59229i) q^{78} +1.79458 q^{79} +0.961393 q^{80} +(-8.00799 - 4.10756i) q^{81} -9.10476i q^{82} -15.3397 q^{83} +(7.44113 - 6.55398i) q^{84} -0.263720 q^{85} -11.6125i q^{86} +(-3.23456 - 4.10872i) q^{87} +0.0233763 q^{88} -10.1857 q^{89} +(1.56928 + 0.378994i) q^{90} +(-0.373256 - 6.75750i) q^{91} +10.4290i q^{92} +(9.06416 + 11.5138i) q^{93} +10.0985i q^{94} +1.29546i q^{95} +(-8.68615 - 11.0336i) q^{96} +1.94032i q^{97} +(-1.57316 - 14.1969i) q^{98} +(-0.203918 - 0.0492479i) 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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