LMFDB - Embedded newform 279.2.h.c.253.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [279,2,Mod(118,279)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(279, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2]))

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

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

chi := DirichletCharacter("279.118");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 279 = 3^{2} \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	279.h (of order $3$, degree $2$, 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:	$2.22782621639$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{2}, \sqrt{-3})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 2x^{2} + 4 $ x^4 + 2*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 31)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			253.1
Root			$0.707107 + 1.22474i$ of defining polynomial
Character	$\chi$	$=$	279.253
Dual form			279.2.h.c.118.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.414214 q^{2} -1.82843 q^{4} +(0.500000 + 0.866025i) q^{5} +(0.207107 - 0.358719i) q^{7} +1.58579 q^{8} +O(q^{10})$	\(q-0.414214 q^{2} -1.82843 q^{4} +(0.500000 + 0.866025i) q^{5} +(0.207107 - 0.358719i) q^{7} +1.58579 q^{8} +(-0.207107 - 0.358719i) q^{10} +(1.62132 + 2.80821i) q^{11} +(1.91421 + 3.31552i) q^{13} +(-0.0857864 + 0.148586i) q^{14} +3.00000 q^{16} +(-2.91421 + 5.04757i) q^{17} +(-2.20711 + 3.82282i) q^{19} +(-0.914214 - 1.58346i) q^{20} +(-0.671573 - 1.16320i) q^{22} +4.00000 q^{23} +(2.00000 - 3.46410i) q^{25} +(-0.792893 - 1.37333i) q^{26} +(-0.378680 + 0.655892i) q^{28} +6.82843 q^{29} +(-5.00000 + 2.44949i) q^{31} -4.41421 q^{32} +(1.20711 - 2.09077i) q^{34} +0.414214 q^{35} +(-0.500000 + 0.866025i) q^{37} +(0.914214 - 1.58346i) q^{38} +(0.792893 + 1.37333i) q^{40} +(-3.74264 - 6.48244i) q^{41} +(5.44975 - 9.43924i) q^{43} +(-2.96447 - 5.13461i) q^{44} -1.65685 q^{46} -9.65685 q^{47} +(3.41421 + 5.91359i) q^{49} +(-0.828427 + 1.43488i) q^{50} +(-3.50000 - 6.06218i) q^{52} +(2.91421 + 5.04757i) q^{53} +(-1.62132 + 2.80821i) q^{55} +(0.328427 - 0.568852i) q^{56} -2.82843 q^{58} +(2.03553 - 3.52565i) q^{59} -2.82843 q^{61} +(2.07107 - 1.01461i) q^{62} -4.17157 q^{64} +(-1.91421 + 3.31552i) q^{65} +(-1.62132 - 2.80821i) q^{67} +(5.32843 - 9.22911i) q^{68} -0.171573 q^{70} +(0.0355339 + 0.0615465i) q^{71} +(0.914214 + 1.58346i) q^{73} +(0.207107 - 0.358719i) q^{74} +(4.03553 - 6.98975i) q^{76} +1.34315 q^{77} +(3.37868 - 5.85204i) q^{79} +(1.50000 + 2.59808i) q^{80} +(1.55025 + 2.68512i) q^{82} +(-5.03553 - 8.72180i) q^{83} -5.82843 q^{85} +(-2.25736 + 3.90986i) q^{86} +(2.57107 + 4.45322i) q^{88} -4.48528 q^{89} +1.58579 q^{91} -7.31371 q^{92} +4.00000 q^{94} -4.41421 q^{95} +5.17157 q^{97} +(-1.41421 - 2.44949i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{2} + 4 q^{4} + 2 q^{5} - 2 q^{7} + 12 q^{8}+O(q^{10}) $ 4 * q + 4 * q^2 + 4 * q^4 + 2 * q^5 - 2 * q^7 + 12 * q^8	$ 4 q + 4 q^{2} + 4 q^{4} + 2 q^{5} - 2 q^{7} + 12 q^{8} + 2 q^{10} - 2 q^{11} + 2 q^{13} - 6 q^{14} + 12 q^{16} - 6 q^{17} - 6 q^{19} + 2 q^{20} - 14 q^{22} + 16 q^{23} + 8 q^{25} - 6 q^{26} - 10 q^{28} + 16 q^{29} - 20 q^{31} - 12 q^{32} + 2 q^{34} - 4 q^{35} - 2 q^{37} - 2 q^{38} + 6 q^{40} + 2 q^{41} + 2 q^{43} - 26 q^{44} + 16 q^{46} - 16 q^{47} + 8 q^{49} + 8 q^{50} - 14 q^{52} + 6 q^{53} + 2 q^{55} - 10 q^{56} - 6 q^{59} - 20 q^{62} - 28 q^{64} - 2 q^{65} + 2 q^{67} + 10 q^{68} - 12 q^{70} - 14 q^{71} - 2 q^{73} - 2 q^{74} + 2 q^{76} + 28 q^{77} + 22 q^{79} + 6 q^{80} + 26 q^{82} - 6 q^{83} - 12 q^{85} - 26 q^{86} - 18 q^{88} + 16 q^{89} + 12 q^{91} + 16 q^{92} + 16 q^{94} - 12 q^{95} + 32 q^{97}+O(q^{100}) $ 4 * q + 4 * q^2 + 4 * q^4 + 2 * q^5 - 2 * q^7 + 12 * q^8 + 2 * q^10 - 2 * q^11 + 2 * q^13 - 6 * q^14 + 12 * q^16 - 6 * q^17 - 6 * q^19 + 2 * q^20 - 14 * q^22 + 16 * q^23 + 8 * q^25 - 6 * q^26 - 10 * q^28 + 16 * q^29 - 20 * q^31 - 12 * q^32 + 2 * q^34 - 4 * q^35 - 2 * q^37 - 2 * q^38 + 6 * q^40 + 2 * q^41 + 2 * q^43 - 26 * q^44 + 16 * q^46 - 16 * q^47 + 8 * q^49 + 8 * q^50 - 14 * q^52 + 6 * q^53 + 2 * q^55 - 10 * q^56 - 6 * q^59 - 20 * q^62 - 28 * q^64 - 2 * q^65 + 2 * q^67 + 10 * q^68 - 12 * q^70 - 14 * q^71 - 2 * q^73 - 2 * q^74 + 2 * q^76 + 28 * q^77 + 22 * q^79 + 6 * q^80 + 26 * q^82 - 6 * q^83 - 12 * q^85 - 26 * q^86 - 18 * q^88 + 16 * q^89 + 12 * q^91 + 16 * q^92 + 16 * q^94 - 12 * q^95 + 32 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/279\mathbb{Z}\right)^\times$.

$n$	$127$	$218$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

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 $

$2$	−0.414214			−0.292893			−0.146447	−	0.989219i	$-0.546784\pi$
$2$	−0.414214			−0.292893			−0.146447	+	0.989219i	$0.546784\pi$
$3$		0			0
$3$		0			0
$4$	−1.82843			−0.914214
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i	0.955901	−	0.293691i	$-0.0948835\pi$
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i	−0.732294	+	0.680989i	$0.761550\pi$
$6$		0			0
$7$	0.207107	−	0.358719i	0.0782790	−	0.135583i	−0.824228	−	0.566257i	$-0.808391\pi$
$7$	0.207107	−	0.358719i	0.0782790	−	0.135583i	0.902507	+	0.430674i	$0.141724\pi$
$8$	1.58579			0.560660
$9$		0			0
$10$	−0.207107	−	0.358719i	−0.0654929	−	0.113437i
$11$	1.62132	+	2.80821i	0.488846	+	0.846707i	0.999918	−	0.0128314i	$-0.00408449\pi$
$11$	1.62132	+	2.80821i	0.488846	+	0.846707i	−0.511071	+	0.859538i	$0.670751\pi$
$12$		0			0
$13$	1.91421	+	3.31552i	0.530907	+	0.919558i	0.999349	+	0.0360643i	$0.0114821\pi$
$13$	1.91421	+	3.31552i	0.530907	+	0.919558i	−0.468442	+	0.883494i	$0.655185\pi$
$14$	−0.0857864	+	0.148586i	−0.0229274	+	0.0397114i
$15$		0			0
$16$	3.00000			0.750000
$17$	−2.91421	+	5.04757i	−0.706801	+	1.22421i	0.259237	+	0.965814i	$0.416529\pi$
$17$	−2.91421	+	5.04757i	−0.706801	+	1.22421i	−0.966038	+	0.258401i	$0.916804\pi$
$18$		0			0
$19$	−2.20711	+	3.82282i	−0.506345	+	0.877015i	0.493628	+	0.869673i	$0.335670\pi$
$19$	−2.20711	+	3.82282i	−0.506345	+	0.877015i	−0.999973	+	0.00734216i	$0.997663\pi$
$20$	−0.914214	−	1.58346i	−0.204424	−	0.354073i
$21$		0			0
$22$	−0.671573	−	1.16320i	−0.143180	−	0.247995i
$23$	4.00000			0.834058			0.417029	−	0.908893i	$-0.363071\pi$
$23$	4.00000			0.834058			0.417029	+	0.908893i	$0.363071\pi$
$24$		0			0
$25$	2.00000	−	3.46410i	0.400000	−	0.692820i
$26$	−0.792893	−	1.37333i	−0.155499	−	0.269332i
$27$		0			0
$28$	−0.378680	+	0.655892i	−0.0715637	+	0.123952i
$29$	6.82843			1.26801			0.634004	−	0.773330i	$-0.281410\pi$
$29$	6.82843			1.26801			0.634004	+	0.773330i	$0.281410\pi$
$30$		0			0
$31$	−5.00000	+	2.44949i	−0.898027	+	0.439941i
$31$	−5.00000	+	2.44949i	−0.898027	+	0.439941i
$32$	−4.41421			−0.780330
$33$		0			0
$34$	1.20711	−	2.09077i	0.207017	−	0.358564i
$35$	0.414214			0.0700149
$36$		0			0
$37$	−0.500000	+	0.866025i	−0.0821995	+	0.142374i	−0.904194	−	0.427121i	$-0.859528\pi$
$37$	−0.500000	+	0.866025i	−0.0821995	+	0.142374i	0.821995	+	0.569495i	$0.192861\pi$
$38$	0.914214	−	1.58346i	0.148305	−	0.256872i
$39$		0			0
$40$	0.792893	+	1.37333i	0.125367	+	0.217143i
$41$	−3.74264	−	6.48244i	−0.584502	−	1.01239i	−0.994937	−	0.100498i	$-0.967956\pi$
$41$	−3.74264	−	6.48244i	−0.584502	−	1.01239i	0.410435	−	0.911890i	$-0.365377\pi$
$42$		0			0
$43$	5.44975	−	9.43924i	0.831079	−	1.43947i	−0.0661049	−	0.997813i	$-0.521057\pi$
$43$	5.44975	−	9.43924i	0.831079	−	1.43947i	0.897184	−	0.441658i	$-0.145609\pi$
$44$	−2.96447	−	5.13461i	−0.446910	−	0.774071i
$45$		0			0
$46$	−1.65685			−0.244290
$47$	−9.65685			−1.40860			−0.704298	−	0.709904i	$-0.748738\pi$
$47$	−9.65685			−1.40860			−0.704298	+	0.709904i	$0.748738\pi$
$48$		0			0
$49$	3.41421	+	5.91359i	0.487745	+	0.844799i
$50$	−0.828427	+	1.43488i	−0.117157	+	0.202922i
$51$		0			0
$52$	−3.50000	−	6.06218i	−0.485363	−	0.840673i
$53$	2.91421	+	5.04757i	0.400298	+	0.693337i	0.993762	−	0.111524i	$-0.0355733\pi$
$53$	2.91421	+	5.04757i	0.400298	+	0.693337i	−0.593464	+	0.804861i	$0.702240\pi$
$54$		0			0
$55$	−1.62132	+	2.80821i	−0.218619	+	0.378659i
$56$	0.328427	−	0.568852i	0.0438879	−	0.0760161i
$57$		0			0
$58$	−2.82843			−0.371391
$59$	2.03553	−	3.52565i	0.265004	−	0.459000i	−0.702561	−	0.711624i	$-0.747960\pi$
$59$	2.03553	−	3.52565i	0.265004	−	0.459000i	0.967565	+	0.252624i	$0.0812934\pi$
$60$		0			0
$61$	−2.82843			−0.362143			−0.181071	−	0.983470i	$-0.557957\pi$
$61$	−2.82843			−0.362143			−0.181071	+	0.983470i	$0.557957\pi$
$62$	2.07107	−	1.01461i	0.263026	−	0.128856i
$63$		0			0
$64$	−4.17157			−0.521447
$65$	−1.91421	+	3.31552i	−0.237429	+	0.411239i
$66$		0			0
$67$	−1.62132	−	2.80821i	−0.198076	−	0.343077i	0.749829	−	0.661632i	$-0.230136\pi$
$67$	−1.62132	−	2.80821i	−0.198076	−	0.343077i	−0.947904	+	0.318555i	$0.896803\pi$
$68$	5.32843	−	9.22911i	0.646167	−	1.11919i
$69$		0			0
$70$	−0.171573			−0.0205069
$71$	0.0355339	+	0.0615465i	0.00421710	+	0.00730423i	0.868126	−	0.496343i	$-0.165324\pi$
$71$	0.0355339	+	0.0615465i	0.00421710	+	0.00730423i	−0.863909	+	0.503648i	$0.831991\pi$
$72$		0			0
$73$	0.914214	+	1.58346i	0.107001	+	0.185330i	0.914554	−	0.404464i	$-0.132542\pi$
$73$	0.914214	+	1.58346i	0.107001	+	0.185330i	−0.807553	+	0.589795i	$0.799209\pi$
$74$	0.207107	−	0.358719i	0.0240757	−	0.0417003i
$75$		0			0
$76$	4.03553	−	6.98975i	0.462907	−	0.801779i
$77$	1.34315			0.153066
$78$		0			0
$79$	3.37868	−	5.85204i	0.380131	−	0.658406i	−0.610950	−	0.791670i	$-0.709212\pi$
$79$	3.37868	−	5.85204i	0.380131	−	0.658406i	0.991081	+	0.133263i	$0.0425455\pi$
$80$	1.50000	+	2.59808i	0.167705	+	0.290474i
$81$		0			0
$82$	1.55025	+	2.68512i	0.171197	+	0.296521i
$83$	−5.03553	−	8.72180i	−0.552722	−	0.957342i	−0.998077	−	0.0619880i	$-0.980256\pi$
$83$	−5.03553	−	8.72180i	−0.552722	−	0.957342i	0.445355	−	0.895354i	$-0.353077\pi$
$84$		0			0
$85$	−5.82843			−0.632182
$86$	−2.25736	+	3.90986i	−0.243417	+	0.421611i
$87$		0			0
$88$	2.57107	+	4.45322i	0.274077	+	0.474715i
$89$	−4.48528			−0.475439			−0.237719	−	0.971334i	$-0.576400\pi$
$89$	−4.48528			−0.475439			−0.237719	+	0.971334i	$0.576400\pi$
$90$		0			0
$91$	1.58579			0.166236
$92$	−7.31371			−0.762507
$93$		0			0
$94$	4.00000			0.412568
$95$	−4.41421			−0.452889
$96$		0			0
$97$	5.17157			0.525094			0.262547	−	0.964919i	$-0.415438\pi$
$97$	5.17157			0.525094			0.262547	+	0.964919i	$0.415438\pi$
$98$	−1.41421	−	2.44949i	−0.142857	−	0.247436i
$99$		0			0
$100$	−3.65685	+	6.33386i	−0.365685	+	0.633386i
$101$	8.48528			0.844317			0.422159	−	0.906522i	$-0.361273\pi$
$101$	8.48528			0.844317			0.422159	+	0.906522i	$0.361273\pi$
$102$		0			0
$103$	−1.03553	−	1.79360i	−0.102034	−	0.176728i	0.810488	−	0.585755i	$-0.199202\pi$
$103$	−1.03553	−	1.79360i	−0.102034	−	0.176728i	−0.912523	+	0.409026i	$0.865868\pi$
$104$	3.03553	+	5.25770i	0.297659	+	0.515560i
$105$		0			0
$106$	−1.20711	−	2.09077i	−0.117245	−	0.203074i
$107$	6.20711	−	10.7510i	0.600064	−	1.03934i	−0.392747	−	0.919646i	$-0.628475\pi$
$107$	6.20711	−	10.7510i	0.600064	−	1.03934i	0.992811	−	0.119694i	$-0.0381914\pi$
$108$		0			0
$109$	−10.8284			−1.03718			−0.518588	−	0.855024i	$-0.673542\pi$
$109$	−10.8284			−1.03718			−0.518588	+	0.855024i	$0.673542\pi$
$110$	0.671573	−	1.16320i	0.0640320	−	0.110907i
$111$		0			0
$112$	0.621320	−	1.07616i	0.0587093	−	0.101687i
$113$	8.32843	+	14.4253i	0.783473	+	1.35701i	0.929907	+	0.367794i	$0.119887\pi$
$113$	8.32843	+	14.4253i	0.783473	+	1.35701i	−0.146435	+	0.989220i	$0.546780\pi$
$114$		0			0
$115$	2.00000	+	3.46410i	0.186501	+	0.323029i
$116$	−12.4853			−1.15923
$117$		0			0
$118$	−0.843146	+	1.46037i	−0.0776179	+	0.134438i
$119$	1.20711	+	2.09077i	0.110655	+	0.191661i
$120$		0			0
$121$	0.242641	−	0.420266i	0.0220582	−	0.0382060i
$122$	1.17157			0.106069
$123$		0			0
$124$	9.14214	−	4.47871i	0.820988	−	0.402200i
$125$	9.00000			0.804984
$126$		0			0
$127$	−4.44975	+	7.70719i	−0.394851	+	0.683902i	−0.993082	−	0.117421i	$-0.962537\pi$
$127$	−4.44975	+	7.70719i	−0.394851	+	0.683902i	0.598231	+	0.801324i	$0.295871\pi$
$128$	10.5563			0.933058
$129$		0			0
$130$	0.792893	−	1.37333i	0.0695413	−	0.120449i
$131$	−6.62132	+	11.4685i	−0.578507	+	1.00200i	0.417143	+	0.908841i	$0.363031\pi$
$131$	−6.62132	+	11.4685i	−0.578507	+	1.00200i	−0.995651	+	0.0931636i	$0.970302\pi$
$132$		0			0
$133$	0.914214	+	1.58346i	0.0792724	+	0.137304i
$134$	0.671573	+	1.16320i	0.0580151	+	0.100485i
$135$		0			0
$136$	−4.62132	+	8.00436i	−0.396275	+	0.686368i
$137$	4.74264	+	8.21449i	0.405191	+	0.701812i	0.994344	−	0.106210i	$-0.0338716\pi$
$137$	4.74264	+	8.21449i	0.405191	+	0.701812i	−0.589153	+	0.808022i	$0.700538\pi$
$138$		0			0
$139$		0			0			−	1.00000i	$-0.5\pi$
$139$		0			0				1.00000i	$0.5\pi$
$140$	−0.757359			−0.0640085
$141$		0			0
$142$	−0.0147186	−	0.0254934i	−0.00123516	−	0.00213936i
$143$	−6.20711	+	10.7510i	−0.519064	+	0.899046i
$144$		0			0
$145$	3.41421	+	5.91359i	0.283535	+	0.491097i
$146$	−0.378680	−	0.655892i	−0.0313398	−	0.0542820i
$147$		0			0
$148$	0.914214	−	1.58346i	0.0751479	−	0.130160i
$149$	0.500000	−	0.866025i	0.0409616	−	0.0709476i	−0.844818	−	0.535054i	$-0.820291\pi$
$149$	0.500000	−	0.866025i	0.0409616	−	0.0709476i	0.885779	+	0.464107i	$0.153625\pi$
$150$		0			0
$151$	5.31371			0.432423			0.216212	−	0.976346i	$-0.430630\pi$
$151$	5.31371			0.432423			0.216212	+	0.976346i	$0.430630\pi$
$152$	−3.50000	+	6.06218i	−0.283887	+	0.491708i
$153$		0			0
$154$	−0.556349			−0.0448319
$155$	−4.62132	−	3.10538i	−0.371193	−	0.249430i
$156$		0			0
$157$	9.17157			0.731971			0.365986	−	0.930621i	$-0.380732\pi$
$157$	9.17157			0.731971			0.365986	+	0.930621i	$0.380732\pi$
$158$	−1.39949	+	2.42400i	−0.111338	+	0.192843i
$159$		0			0
$160$	−2.20711	−	3.82282i	−0.174487	−	0.302221i
$161$	0.828427	−	1.43488i	0.0652892	−	0.113084i
$162$		0			0
$163$	20.9706			1.64254			0.821271	−	0.570539i	$-0.193266\pi$
$163$	20.9706			1.64254			0.821271	+	0.570539i	$0.193266\pi$
$164$	6.84315	+	11.8527i	0.534360	+	0.925539i
$165$		0			0
$166$	2.08579	+	3.61269i	0.161888	+	0.280399i
$167$	11.2782	−	19.5344i	0.872731	−	1.51162i	0.0135714	−	0.999908i	$-0.495680\pi$
$167$	11.2782	−	19.5344i	0.872731	−	1.51162i	0.859160	−	0.511707i	$-0.170987\pi$
$168$		0			0
$169$	−0.828427	+	1.43488i	−0.0637252	+	0.110375i
$170$	2.41421			0.185162
$171$		0			0
$172$	−9.96447	+	17.2590i	−0.759783	+	1.31598i
$173$	4.15685	+	7.19988i	0.316040	+	0.547397i	0.979658	−	0.200674i	$-0.0643134\pi$
$173$	4.15685	+	7.19988i	0.316040	+	0.547397i	−0.663618	+	0.748071i	$0.730980\pi$
$174$		0			0
$175$	−0.828427	−	1.43488i	−0.0626232	−	0.108467i
$176$	4.86396	+	8.42463i	0.366635	+	0.635030i
$177$		0			0
$178$	1.85786			0.139253
$179$	−7.62132	+	13.2005i	−0.569644	+	0.986653i	0.426957	+	0.904272i	$0.359586\pi$
$179$	−7.62132	+	13.2005i	−0.569644	+	0.986653i	−0.996601	+	0.0823807i	$0.973748\pi$
$180$		0			0
$181$	−6.15685	−	10.6640i	−0.457635	−	0.792648i	0.541200	−	0.840894i	$-0.317970\pi$
$181$	−6.15685	−	10.6640i	−0.457635	−	0.792648i	−0.998835	+	0.0482461i	$0.984637\pi$
$182$	−0.656854			−0.0486893
$183$		0			0
$184$	6.34315			0.467623
$185$	−1.00000			−0.0735215
$186$		0			0
$187$	−18.8995			−1.38207
$188$	17.6569			1.28776
$189$		0			0
$190$	1.82843			0.132648
$191$	−10.4497	−	18.0995i	−0.756117	−	1.30963i	−0.944817	−	0.327599i	$-0.893761\pi$
$191$	−10.4497	−	18.0995i	−0.756117	−	1.30963i	0.188700	−	0.982035i	$-0.439573\pi$
$192$		0			0
$193$	−3.57107	+	6.18527i	−0.257051	+	0.445226i	−0.965451	−	0.260586i	$-0.916084\pi$
$193$	−3.57107	+	6.18527i	−0.257051	+	0.445226i	0.708400	+	0.705812i	$0.249418\pi$
$194$	−2.14214			−0.153796
$195$		0			0
$196$	−6.24264	−	10.8126i	−0.445903	−	0.772326i
$197$	−6.74264	−	11.6786i	−0.480393	−	0.832066i	0.519354	−	0.854559i	$-0.326173\pi$
$197$	−6.74264	−	11.6786i	−0.480393	−	0.832066i	−0.999747	+	0.0224938i	$0.992839\pi$
$198$		0			0
$199$	−9.20711	−	15.9472i	−0.652674	−	1.13047i	−0.982471	−	0.186413i	$-0.940314\pi$
$199$	−9.20711	−	15.9472i	−0.652674	−	1.13047i	0.329797	−	0.944052i	$-0.393020\pi$
$200$	3.17157	−	5.49333i	0.224264	−	0.388437i
$201$		0			0
$202$	−3.51472			−0.247295
$203$	1.41421	−	2.44949i	0.0992583	−	0.171920i
$204$		0			0
$205$	3.74264	−	6.48244i	0.261397	−	0.452754i
$206$	0.428932	+	0.742932i	0.0298851	+	0.0517625i
$207$		0			0
$208$	5.74264	+	9.94655i	0.398180	+	0.689669i
$209$	−14.3137			−0.990100
$210$		0			0
$211$	−5.20711	+	9.01897i	−0.358472	+	0.620892i	−0.987706	−	0.156324i	$-0.950035\pi$
$211$	−5.20711	+	9.01897i	−0.358472	+	0.620892i	0.629234	+	0.777216i	$0.283369\pi$
$212$	−5.32843	−	9.22911i	−0.365958	−	0.633858i
$213$		0			0
$214$	−2.57107	+	4.45322i	−0.175755	+	0.304416i
$215$	10.8995			0.743339
$216$		0			0
$217$	−0.156854	+	2.30090i	−0.0106480	+	0.156195i
$218$	4.48528			0.303782
$219$		0			0
$220$	2.96447	−	5.13461i	0.199864	−	0.346175i
$221$	−22.3137			−1.50098
$222$		0			0
$223$	11.8640	−	20.5490i	0.794470	−	1.37606i	−0.128706	−	0.991683i	$-0.541082\pi$
$223$	11.8640	−	20.5490i	0.794470	−	1.37606i	0.923175	−	0.384379i	$-0.125584\pi$
$224$	−0.914214	+	1.58346i	−0.0610835	+	0.105800i
$225$		0			0
$226$	−3.44975	−	5.97514i	−0.229474	−	0.397460i
$227$	−9.20711	−	15.9472i	−0.611097	−	1.05845i	−0.991056	−	0.133448i	$-0.957395\pi$
$227$	−9.20711	−	15.9472i	−0.611097	−	1.05845i	0.379959	−	0.925003i	$-0.375938\pi$
$228$		0			0
$229$	2.74264	−	4.75039i	0.181239	−	0.313915i	−0.761064	−	0.648677i	$-0.775323\pi$
$229$	2.74264	−	4.75039i	0.181239	−	0.313915i	0.942303	+	0.334762i	$0.108656\pi$
$230$	−0.828427	−	1.43488i	−0.0546249	−	0.0946130i
$231$		0			0
$232$	10.8284			0.710921
$233$	9.17157			0.600850			0.300425	−	0.953805i	$-0.402872\pi$
$233$	9.17157			0.600850			0.300425	+	0.953805i	$0.402872\pi$
$234$		0			0
$235$	−4.82843	−	8.36308i	−0.314972	−	0.545547i
$236$	−3.72183	+	6.44639i	−0.242270	+	0.419624i
$237$		0			0
$238$	−0.500000	−	0.866025i	−0.0324102	−	0.0561361i
$239$	−10.6213	−	18.3967i	−0.687036	−	1.18998i	−0.972792	−	0.231679i	$-0.925578\pi$
$239$	−10.6213	−	18.3967i	−0.687036	−	1.18998i	0.285756	−	0.958302i	$-0.407755\pi$
$240$		0			0
$241$	−6.67157	+	11.5555i	−0.429754	+	0.744355i	−0.996851	−	0.0792954i	$-0.974733\pi$
$241$	−6.67157	+	11.5555i	−0.429754	+	0.744355i	0.567097	+	0.823651i	$0.308066\pi$
$242$	−0.100505	+	0.174080i	−0.00646071	+	0.0111903i
$243$		0			0
$244$	5.17157			0.331076
$245$	−3.41421	+	5.91359i	−0.218126	+	0.377805i
$246$		0			0
$247$	−16.8995			−1.07529
$248$	−7.92893	+	3.88437i	−0.503488	+	0.246658i
$249$		0			0
$250$	−3.72792			−0.235774
$251$	3.20711	−	5.55487i	0.202431	−	0.350620i	−0.746880	−	0.664958i	$-0.768449\pi$
$251$	3.20711	−	5.55487i	0.202431	−	0.350620i	0.949311	+	0.314338i	$0.101783\pi$
$252$		0			0
$253$	6.48528	+	11.2328i	0.407726	+	0.706202i
$254$	1.84315	−	3.19242i	0.115649	−	0.200310i
$255$		0			0
$256$	3.97056			0.248160
$257$	11.1569	+	19.3242i	0.695945	+	1.20541i	0.969861	+	0.243659i	$0.0783478\pi$
$257$	11.1569	+	19.3242i	0.695945	+	1.20541i	−0.273915	+	0.961754i	$0.588319\pi$
$258$		0			0
$259$	0.207107	+	0.358719i	0.0128690	+	0.0222897i
$260$	3.50000	−	6.06218i	0.217061	−	0.375960i
$261$		0			0
$262$	2.74264	−	4.75039i	0.169441	−	0.293480i
$263$	23.3137			1.43758			0.718792	−	0.695225i	$-0.244695\pi$
$263$	23.3137			1.43758			0.718792	+	0.695225i	$0.244695\pi$
$264$		0			0
$265$	−2.91421	+	5.04757i	−0.179019	+	0.310070i
$266$	−0.378680	−	0.655892i	−0.0232183	−	0.0402153i
$267$		0			0
$268$	2.96447	+	5.13461i	0.181084	+	0.313646i
$269$	−13.0858	−	22.6652i	−0.797854	−	1.38192i	−0.921011	−	0.389537i	$-0.872635\pi$
$269$	−13.0858	−	22.6652i	−0.797854	−	1.38192i	0.123156	−	0.992387i	$-0.460698\pi$
$270$		0			0
$271$	−0.686292			−0.0416892			−0.0208446	−	0.999783i	$-0.506636\pi$
$271$	−0.686292			−0.0416892			−0.0208446	+	0.999783i	$0.506636\pi$
$272$	−8.74264	+	15.1427i	−0.530100	+	0.918161i
$273$		0			0
$274$	−1.96447	−	3.40256i	−0.118678	−	0.205556i
$275$	12.9706			0.782154
$276$		0			0
$277$	14.1421			0.849719			0.424859	−	0.905259i	$-0.360324\pi$
$277$	14.1421			0.849719			0.424859	+	0.905259i	$0.360324\pi$
$278$		0			0
$279$		0			0
$280$	0.656854			0.0392545
$281$	−2.00000			−0.119310			−0.0596550	−	0.998219i	$-0.519000\pi$
$281$	−2.00000			−0.119310			−0.0596550	+	0.998219i	$0.519000\pi$
$282$		0			0
$283$	−13.6569			−0.811816			−0.405908	−	0.913914i	$-0.633045\pi$
$283$	−13.6569			−0.811816			−0.405908	+	0.913914i	$0.633045\pi$
$284$	−0.0649712	−	0.112533i	−0.00385533	−	0.00667763i
$285$		0			0
$286$	2.57107	−	4.45322i	0.152030	−	0.263324i
$287$	−3.10051			−0.183017
$288$		0			0
$289$	−8.48528	−	14.6969i	−0.499134	−	0.864526i
$290$	−1.41421	−	2.44949i	−0.0830455	−	0.143839i
$291$		0			0
$292$	−1.67157	−	2.89525i	−0.0978214	−	0.169432i
$293$	7.39949	−	12.8163i	0.432283	−	0.748736i	−0.564786	−	0.825237i	$-0.691041\pi$
$293$	7.39949	−	12.8163i	0.432283	−	0.748736i	0.997070	+	0.0765008i	$0.0243748\pi$
$294$		0			0
$295$	4.07107			0.237027
$296$	−0.792893	+	1.37333i	−0.0460860	+	0.0798233i
$297$		0			0
$298$	−0.207107	+	0.358719i	−0.0119974	+	0.0207801i
$299$	7.65685	+	13.2621i	0.442807	+	0.766965i
$300$		0			0
$301$	−2.25736	−	3.90986i	−0.130112	−	0.225361i
$302$	−2.20101			−0.126654
$303$		0			0
$304$	−6.62132	+	11.4685i	−0.379759	+	0.657761i
$305$	−1.41421	−	2.44949i	−0.0809776	−	0.140257i
$306$		0			0
$307$	5.62132	−	9.73641i	0.320826	−	0.555686i	−0.659833	−	0.751412i	$-0.729373\pi$
$307$	5.62132	−	9.73641i	0.320826	−	0.555686i	0.980659	+	0.195726i	$0.0627063\pi$
$308$	−2.45584			−0.139935
$309$		0			0
$310$	1.91421	+	1.28629i	0.108720	+	0.0730564i
$311$	−11.3137			−0.641542			−0.320771	−	0.947157i	$-0.603942\pi$
$311$	−11.3137			−0.641542			−0.320771	+	0.947157i	$0.603942\pi$
$312$		0			0
$313$	0.914214	−	1.58346i	0.0516744	−	0.0895027i	−0.839031	−	0.544083i	$-0.816878\pi$
$313$	0.914214	−	1.58346i	0.0516744	−	0.0895027i	0.890706	+	0.454581i	$0.150211\pi$
$314$	−3.79899			−0.214389
$315$		0			0
$316$	−6.17767	+	10.7000i	−0.347521	+	0.601924i
$317$	−3.91421	+	6.77962i	−0.219844	+	0.380781i	−0.954760	−	0.297377i	$-0.903888\pi$
$317$	−3.91421	+	6.77962i	−0.219844	+	0.380781i	0.734916	+	0.678158i	$0.237222\pi$
$318$		0			0
$319$	11.0711	+	19.1757i	0.619861	+	1.07363i
$320$	−2.08579	−	3.61269i	−0.116599	−	0.201955i
$321$		0			0
$322$	−0.343146	+	0.594346i	−0.0191228	+	0.0331216i
$323$	−12.8640	−	22.2810i	−0.715770	−	1.23975i
$324$		0			0
$325$	15.3137			0.849452
$326$	−8.68629			−0.481089
$327$		0			0
$328$	−5.93503	−	10.2798i	−0.327707	−	0.567605i
$329$	−2.00000	+	3.46410i	−0.110264	+	0.190982i
$330$		0			0
$331$	−4.62132	−	8.00436i	−0.254011	−	0.439960i	0.710616	−	0.703580i	$-0.248417\pi$
$331$	−4.62132	−	8.00436i	−0.254011	−	0.439960i	−0.964626	+	0.263621i	$0.915083\pi$
$332$	9.20711	+	15.9472i	0.505306	+	0.875215i
$333$		0			0
$334$	−4.67157	+	8.09140i	−0.255617	+	0.442742i
$335$	1.62132	−	2.80821i	0.0885822	−	0.153429i
$336$		0			0
$337$	9.31371			0.507350			0.253675	−	0.967290i	$-0.418361\pi$
$337$	9.31371			0.507350			0.253675	+	0.967290i	$0.418361\pi$
$338$	0.343146	−	0.594346i	0.0186647	−	0.0323282i
$339$		0			0
$340$	10.6569			0.577949
$341$	−14.9853	−	10.0696i	−0.811498	−	0.545301i
$342$		0			0
$343$	5.72792			0.309279
$344$	8.64214	−	14.9686i	0.465953	−	0.807054i
$345$		0			0
$346$	−1.72183	−	2.98229i	−0.0925659	−	0.160329i
$347$	−4.27817	+	7.41002i	−0.229664	+	0.397790i	−0.957709	−	0.287740i	$-0.907096\pi$
$347$	−4.27817	+	7.41002i	−0.229664	+	0.397790i	0.728044	+	0.685530i	$0.240430\pi$
$348$		0			0
$349$	−27.1127			−1.45131			−0.725655	−	0.688059i	$-0.758463\pi$
$349$	−27.1127			−1.45131			−0.725655	+	0.688059i	$0.758463\pi$
$350$	0.343146	+	0.594346i	0.0183419	+	0.0317691i
$351$		0			0
$352$	−7.15685	−	12.3960i	−0.381462	−	0.660711i
$353$	1.50000	−	2.59808i	0.0798369	−	0.138282i	−0.823343	−	0.567545i	$-0.807893\pi$
$353$	1.50000	−	2.59808i	0.0798369	−	0.138282i	0.903179	+	0.429263i	$0.141227\pi$
$354$		0			0
$355$	−0.0355339	+	0.0615465i	−0.00188594	+	0.00326655i
$356$	8.20101			0.434653
$357$		0			0
$358$	3.15685	−	5.46783i	0.166845	−	0.288984i
$359$	3.55025	+	6.14922i	0.187375	+	0.324543i	0.944374	−	0.328873i	$-0.106669\pi$
$359$	3.55025	+	6.14922i	0.187375	+	0.324543i	−0.756999	+	0.653416i	$0.773335\pi$
$360$		0			0
$361$	−0.242641	−	0.420266i	−0.0127706	−	0.0221193i
$362$	2.55025	+	4.41717i	0.134038	+	0.232161i
$363$		0			0
$364$	−2.89949			−0.151975
$365$	−0.914214	+	1.58346i	−0.0478521	+	0.0828823i
$366$		0			0
$367$	12.1066	+	20.9692i	0.631959	+	1.09459i	0.987151	+	0.159792i	$0.0510824\pi$
$367$	12.1066	+	20.9692i	0.631959	+	1.09459i	−0.355191	+	0.934794i	$0.615584\pi$
$368$	12.0000			0.625543
$369$		0			0
$370$	0.414214			0.0215339
$371$	2.41421			0.125340
$372$		0			0
$373$	10.0000			0.517780			0.258890	−	0.965907i	$-0.416643\pi$
$373$	10.0000			0.517780			0.258890	+	0.965907i	$0.416643\pi$
$374$	7.82843			0.404798
$375$		0			0
$376$	−15.3137			−0.789744
$377$	13.0711	+	22.6398i	0.673194	+	1.16601i
$378$		0			0
$379$	−3.69239	+	6.39540i	−0.189665	+	0.328510i	−0.945139	−	0.326669i	$-0.894074\pi$
$379$	−3.69239	+	6.39540i	−0.189665	+	0.328510i	0.755473	+	0.655179i	$0.227407\pi$
$380$	8.07107			0.414037
$381$		0			0
$382$	4.32843	+	7.49706i	0.221462	+	0.383583i
$383$	2.55025	+	4.41717i	0.130312	+	0.225707i	0.923797	−	0.382883i	$-0.125069\pi$
$383$	2.55025	+	4.41717i	0.130312	+	0.225707i	−0.793485	+	0.608590i	$0.791735\pi$
$384$		0			0
$385$	0.671573	+	1.16320i	0.0342265	+	0.0592821i
$386$	1.47918	−	2.56202i	0.0752885	−	0.130404i
$387$		0			0
$388$	−9.45584			−0.480048
$389$	−5.57107	+	9.64937i	−0.282464	+	0.489243i	−0.971991	−	0.235018i	$-0.924485\pi$
$389$	−5.57107	+	9.64937i	−0.282464	+	0.489243i	0.689527	+	0.724260i	$0.257819\pi$
$390$		0			0
$391$	−11.6569	+	20.1903i	−0.589512	+	1.02107i
$392$	5.41421	+	9.37769i	0.273459	+	0.473645i
$393$		0			0
$394$	2.79289	+	4.83743i	0.140704	+	0.243706i
$395$	6.75736			0.340000
$396$		0			0
$397$	16.7426	−	28.9991i	0.840289	−	1.45542i	−0.0493613	−	0.998781i	$-0.515719\pi$
$397$	16.7426	−	28.9991i	0.840289	−	1.45542i	0.889650	−	0.456642i	$-0.150948\pi$
$398$	3.81371	+	6.60554i	0.191164	+	0.331106i
$399$		0			0
$400$	6.00000	−	10.3923i	0.300000	−	0.519615i
$401$	26.8284			1.33975			0.669874	−	0.742475i	$-0.266348\pi$
$401$	26.8284			1.33975			0.669874	+	0.742475i	$0.266348\pi$
$402$		0			0
$403$	−17.6924	−	11.8887i	−0.881321	−	0.592220i
$404$	−15.5147			−0.771886
$405$		0			0
$406$	−0.585786	+	1.01461i	−0.0290721	+	0.0503543i
$407$	−3.24264			−0.160732
$408$		0			0
$409$	−10.3284	+	17.8894i	−0.510708	+	0.884572i	0.489215	+	0.872163i	$0.337283\pi$
$409$	−10.3284	+	17.8894i	−0.510708	+	0.884572i	−0.999923	+	0.0124088i	$0.996050\pi$
$410$	−1.55025	+	2.68512i	−0.0765615	+	0.132608i
$411$		0			0
$412$	1.89340	+	3.27946i	0.0932810	+	0.161567i
$413$	−0.843146	−	1.46037i	−0.0414885	−	0.0718602i
$414$		0			0
$415$	5.03553	−	8.72180i	0.247185	−	0.428136i
$416$	−8.44975	−	14.6354i	−0.414283	−	0.717559i
$417$		0			0
$418$	5.92893			0.289994
$419$	−28.0000			−1.36789			−0.683945	−	0.729534i	$-0.739737\pi$
$419$	−28.0000			−1.36789			−0.683945	+	0.729534i	$0.739737\pi$
$420$		0			0
$421$	15.5711	+	26.9699i	0.758887	+	1.31443i	0.943418	+	0.331605i	$0.107590\pi$
$421$	15.5711	+	26.9699i	0.758887	+	1.31443i	−0.184531	+	0.982827i	$0.559077\pi$
$422$	2.15685	−	3.73578i	0.104994	−	0.181855i
$423$		0			0
$424$	4.62132	+	8.00436i	0.224431	+	0.388726i
$425$	11.6569	+	20.1903i	0.565440	+	0.979372i
$426$		0			0
$427$	−0.585786	+	1.01461i	−0.0283482	+	0.0491005i
$428$	−11.3492	+	19.6575i	−0.548586	+	0.950179i
$429$		0			0
$430$	−4.51472			−0.217719
$431$	−8.37868	+	14.5123i	−0.403587	+	0.699033i	−0.994156	−	0.107954i	$-0.965570\pi$
$431$	−8.37868	+	14.5123i	−0.403587	+	0.699033i	0.590569	+	0.806987i	$0.298903\pi$
$432$		0			0
$433$	27.1127			1.30295			0.651477	−	0.758669i	$-0.274150\pi$
$433$	27.1127			1.30295			0.651477	+	0.758669i	$0.274150\pi$
$434$	0.0649712	−	0.953065i	0.00311872	−	0.0457486i
$435$		0			0
$436$	19.7990			0.948200
$437$	−8.82843	+	15.2913i	−0.422321	+	0.731481i
$438$		0			0
$439$	−1.03553	−	1.79360i	−0.0494233	−	0.0856037i	0.840255	−	0.542191i	$-0.182405\pi$
$439$	−1.03553	−	1.79360i	−0.0494233	−	0.0856037i	−0.889679	+	0.456587i	$0.849072\pi$
$440$	−2.57107	+	4.45322i	−0.122571	+	0.212299i
$441$		0			0
$442$	9.24264			0.439628
$443$	−2.37868	−	4.11999i	−0.113014	−	0.195747i	0.803970	−	0.594670i	$-0.202717\pi$
$443$	−2.37868	−	4.11999i	−0.113014	−	0.195747i	−0.916984	+	0.398923i	$0.869384\pi$
$444$		0			0
$445$	−2.24264	−	3.88437i	−0.106311	−	0.184137i
$446$	−4.91421	+	8.51167i	−0.232695	+	0.403039i
$447$		0			0
$448$	−0.863961	+	1.49642i	−0.0408183	+	0.0706994i
$449$	40.6274			1.91733			0.958663	−	0.284543i	$-0.0918420\pi$
$449$	40.6274			1.91733			0.958663	+	0.284543i	$0.0918420\pi$
$450$		0			0
$451$	12.1360	−	21.0202i	0.571464	−	0.989804i
$452$	−15.2279	−	26.3755i	−0.716261	−	1.24060i
$453$		0			0
$454$	3.81371	+	6.60554i	0.178986	+	0.310013i
$455$	0.792893	+	1.37333i	0.0371714	+	0.0643828i
$456$		0			0
$457$	−31.1127			−1.45539			−0.727695	−	0.685901i	$-0.759409\pi$
$457$	−31.1127			−1.45539			−0.727695	+	0.685901i	$0.759409\pi$
$458$	−1.13604	+	1.96768i	−0.0530836	+	0.0919435i
$459$		0			0
$460$	−3.65685	−	6.33386i	−0.170502	−	0.295318i
$461$	2.14214			0.0997692			0.0498846	−	0.998755i	$-0.484115\pi$
$461$	2.14214			0.0997692			0.0498846	+	0.998755i	$0.484115\pi$
$462$		0			0
$463$	−8.97056			−0.416897			−0.208449	−	0.978033i	$-0.566841\pi$
$463$	−8.97056			−0.416897			−0.208449	+	0.978033i	$0.566841\pi$
$464$	20.4853			0.951005
$465$		0			0
$466$	−3.79899			−0.175985
$467$	8.00000			0.370196			0.185098	−	0.982720i	$-0.440740\pi$
$467$	8.00000			0.370196			0.185098	+	0.982720i	$0.440740\pi$
$468$		0			0
$469$	−1.34315			−0.0620207
$470$	2.00000	+	3.46410i	0.0922531	+	0.159787i
$471$		0			0
$472$	3.22792	−	5.59093i	0.148577	−	0.257343i
$473$	35.3431			1.62508
$474$		0			0
$475$	8.82843	+	15.2913i	0.405076	+	0.701612i
$476$	−2.20711	−	3.82282i	−0.101163	−	0.175219i
$477$		0			0
$478$	4.39949	+	7.62015i	0.201228	+	0.348537i
$479$	−7.86396	+	13.6208i	−0.359314	+	0.622349i	−0.987846	−	0.155434i	$-0.950322\pi$
$479$	−7.86396	+	13.6208i	−0.359314	+	0.622349i	0.628533	+	0.777783i	$0.283656\pi$
$480$		0			0
$481$	−3.82843			−0.174561
$482$	2.76346	−	4.78645i	0.125872	−	0.218017i
$483$		0			0
$484$	−0.443651	+	0.768426i	−0.0201659	+	0.0349284i
$485$	2.58579	+	4.47871i	0.117415	+	0.203368i
$486$		0			0
$487$	−9.69239	−	16.7877i	−0.439204	−	0.760724i	0.558424	−	0.829556i	$-0.311406\pi$
$487$	−9.69239	−	16.7877i	−0.439204	−	0.760724i	−0.997628	+	0.0688318i	$0.978073\pi$
$488$	−4.48528			−0.203039
$489$		0			0
$490$	1.41421	−	2.44949i	0.0638877	−	0.110657i
$491$	0.792893	+	1.37333i	0.0357828	+	0.0619776i	0.883362	−	0.468691i	$-0.155274\pi$
$491$	0.792893	+	1.37333i	0.0357828	+	0.0619776i	−0.847579	+	0.530669i	$0.821941\pi$
$492$		0			0
$493$	−19.8995	+	34.4669i	−0.896228	+	1.55231i
$494$	7.00000			0.314945
$495$		0			0
$496$	−15.0000	+	7.34847i	−0.673520	+	0.329956i
$497$	0.0294373			0.00132044
$498$		0			0
$499$	1.10660	−	1.91669i	0.0495383	−	0.0858028i	−0.840193	−	0.542288i	$-0.817558\pi$
$499$	1.10660	−	1.91669i	0.0495383	−	0.0858028i	0.889731	+	0.456485i	$0.150892\pi$
$500$	−16.4558			−0.735928
$501$		0			0
$502$	−1.32843	+	2.30090i	−0.0592906	+	0.102694i
$503$	−6.69239	+	11.5916i	−0.298399	+	0.516842i	−0.975770	−	0.218800i	$-0.929786\pi$
$503$	−6.69239	+	11.5916i	−0.298399	+	0.516842i	0.677371	+	0.735642i	$0.263119\pi$
$504$		0			0
$505$	4.24264	+	7.34847i	0.188795	+	0.327003i
$506$	−2.68629	−	4.65279i	−0.119420	−	0.206842i
$507$		0			0
$508$	8.13604	−	14.0920i	0.360978	−	0.625233i
$509$	−16.3995	−	28.4048i	−0.726895	−	1.25902i	−0.958189	−	0.286135i	$-0.907629\pi$
$509$	−16.3995	−	28.4048i	−0.726895	−	1.25902i	0.231294	−	0.972884i	$-0.425704\pi$
$510$		0			0
$511$	0.757359			0.0335036
$512$	−22.7574			−1.00574
$513$		0			0
$514$	−4.62132	−	8.00436i	−0.203838	−	0.353057i
$515$	1.03553	−	1.79360i	0.0456311	−	0.0790353i
$516$		0			0
$517$	−15.6569	−	27.1185i	−0.688588	−	1.19267i
$518$	−0.0857864	−	0.148586i	−0.00376924	−	0.00652851i
$519$		0			0
$520$	−3.03553	+	5.25770i	−0.133117	+	0.230565i
$521$	−10.2279	+	17.7153i	−0.448093	+	0.776121i	−0.998262	−	0.0589331i	$-0.981230\pi$
$521$	−10.2279	+	17.7153i	−0.448093	+	0.776121i	0.550169	+	0.835054i	$0.314563\pi$
$522$		0			0
$523$	−8.00000			−0.349816			−0.174908	−	0.984585i	$-0.555963\pi$
$523$	−8.00000			−0.349816			−0.174908	+	0.984585i	$0.555963\pi$
$524$	12.1066	−	20.9692i	0.528879	−	0.916046i
$525$		0			0
$526$	−9.65685			−0.421059
$527$	2.20711	−	32.3762i	0.0961431	−	1.41033i
$528$		0			0
$529$	−7.00000			−0.304348
$530$	1.20711	−	2.09077i	0.0524334	−	0.0908173i
$531$		0			0
$532$	−1.67157	−	2.89525i	−0.0724719	−	0.125525i
$533$	14.3284	−	24.8176i	0.620633	−	1.07497i
$534$		0			0
$535$	12.4142			0.536713
$536$	−2.57107	−	4.45322i	−0.111053	−	0.192350i
$537$		0			0
$538$	5.42031	+	9.38825i	0.233686	+	0.404756i
$539$	−11.0711	+	19.1757i	−0.476865	+	0.825954i
$540$		0			0
$541$	15.6421	−	27.0930i	0.672508	−	1.16482i	−0.304683	−	0.952454i	$-0.598550\pi$
$541$	15.6421	−	27.0930i	0.672508	−	1.16482i	0.977191	−	0.212364i	$-0.0681162\pi$
$542$	0.284271			0.0122105
$543$		0			0
$544$	12.8640	−	22.2810i	0.551538	−	0.955291i
$545$	−5.41421	−	9.37769i	−0.231919	−	0.401696i
$546$		0			0
$547$	9.86396	+	17.0849i	0.421753	+	0.730497i	0.996111	−	0.0881071i	$-0.0280818\pi$
$547$	9.86396	+	17.0849i	0.421753	+	0.730497i	−0.574358	+	0.818604i	$0.694748\pi$
$548$	−8.67157	−	15.0196i	−0.370431	−	0.641606i
$549$		0			0
$550$	−5.37258			−0.229088
$551$	−15.0711	+	26.1039i	−0.642049	+	1.11206i
$552$		0			0
$553$	−1.39949	−	2.42400i	−0.0595126	−	0.103079i
$554$	−5.85786			−0.248877
$555$		0			0
$556$		0			0
$557$	−27.5147			−1.16584			−0.582918	−	0.812531i	$-0.698089\pi$
$557$	−27.5147			−1.16584			−0.582918	+	0.812531i	$0.698089\pi$
$558$		0			0
$559$	41.7279			1.76490
$560$	1.24264			0.0525112
$561$		0			0
$562$	0.828427			0.0349451
$563$	6.62132	+	11.4685i	0.279055	+	0.483338i	0.971150	−	0.238468i	$-0.0766454\pi$
$563$	6.62132	+	11.4685i	0.279055	+	0.483338i	−0.692095	+	0.721807i	$0.743312\pi$
$564$		0			0
$565$	−8.32843	+	14.4253i	−0.350380	+	0.606875i
$566$	5.65685			0.237775
$567$		0			0
$568$	0.0563492	+	0.0975997i	0.00236436	+	0.00409519i
$569$	−6.57107	−	11.3814i	−0.275473	−	0.477134i	0.694781	−	0.719221i	$-0.255501\pi$
$569$	−6.57107	−	11.3814i	−0.275473	−	0.477134i	−0.970254	+	0.242087i	$0.922168\pi$
$570$		0			0
$571$	10.5503	+	18.2736i	0.441514	+	0.764725i	0.997802	−	0.0662645i	$-0.0211081\pi$
$571$	10.5503	+	18.2736i	0.441514	+	0.764725i	−0.556288	+	0.830990i	$0.687775\pi$
$572$	11.3492	−	19.6575i	0.474536	−	0.821920i
$573$		0			0
$574$	1.28427			0.0536044
$575$	8.00000	−	13.8564i	0.333623	−	0.577852i
$576$		0			0
$577$	0.0147186	−	0.0254934i	0.000612744	−	0.00106130i	−0.865719	−	0.500531i	$-0.833138\pi$
$577$	0.0147186	−	0.0254934i	0.000612744	−	0.00106130i	0.866332	+	0.499469i	$0.166472\pi$
$578$	3.51472	+	6.08767i	0.146193	+	0.253214i
$579$		0			0
$580$	−6.24264	−	10.8126i	−0.259212	−	0.448968i
$581$	−4.17157			−0.173066
$582$		0			0
$583$	−9.44975	+	16.3674i	−0.391369	+	0.677870i
$584$	1.44975	+	2.51104i	0.0599910	+	0.103907i
$585$		0			0
$586$	−3.06497	+	5.30869i	−0.126613	+	0.219300i
$587$	31.6569			1.30662			0.653309	−	0.757091i	$-0.273380\pi$
$587$	31.6569			1.30662			0.653309	+	0.757091i	$0.273380\pi$
$588$		0			0
$589$	1.67157	−	24.5204i	0.0688760	−	1.01035i
$590$	−1.68629			−0.0694235
$591$		0			0
$592$	−1.50000	+	2.59808i	−0.0616496	+	0.106780i
$593$	1.31371			0.0539475			0.0269738	−	0.999636i	$-0.491413\pi$
$593$	1.31371			0.0539475			0.0269738	+	0.999636i	$0.491413\pi$
$594$		0			0
$595$	−1.20711	+	2.09077i	−0.0494866	+	0.0857132i
$596$	−0.914214	+	1.58346i	−0.0374476	+	0.0648612i
$597$		0			0
$598$	−3.17157	−	5.49333i	−0.129695	−	0.224639i
$599$	7.55025	+	13.0774i	0.308495	+	0.534329i	0.978033	−	0.208449i	$-0.0668414\pi$
$599$	7.55025	+	13.0774i	0.308495	+	0.534329i	−0.669538	+	0.742777i	$0.733508\pi$
$600$		0			0
$601$	3.25736	−	5.64191i	0.132870	−	0.230138i	−0.791911	−	0.610636i	$-0.790914\pi$
$601$	3.25736	−	5.64191i	0.132870	−	0.230138i	0.924782	+	0.380498i	$0.124247\pi$
$602$	0.935029	+	1.61952i	0.0381089	+	0.0660066i
$603$		0			0
$604$	−9.71573			−0.395327
$605$	0.485281			0.0197295
$606$		0			0
$607$	0.792893	+	1.37333i	0.0321825	+	0.0557418i	0.881668	−	0.471870i	$-0.156421\pi$
$607$	0.792893	+	1.37333i	0.0321825	+	0.0557418i	−0.849486	+	0.527612i	$0.823088\pi$
$608$	9.74264	−	16.8747i	0.395116	−	0.684361i
$609$		0			0
$610$	0.585786	+	1.01461i	0.0237178	+	0.0410804i
$611$	−18.4853	−	32.0174i	−0.747834	−	1.29529i
$612$		0			0
$613$	−6.15685	+	10.6640i	−0.248673	+	0.430714i	−0.963158	−	0.268937i	$-0.913328\pi$
$613$	−6.15685	+	10.6640i	−0.248673	+	0.430714i	0.714485	+	0.699651i	$0.246661\pi$
$614$	−2.32843	+	4.03295i	−0.0939677	+	0.162757i
$615$		0			0
$616$	2.12994			0.0858178
$617$	−16.6421	+	28.8250i	−0.669987	+	1.16045i	0.307920	+	0.951412i	$0.400367\pi$
$617$	−16.6421	+	28.8250i	−0.669987	+	1.16045i	−0.977907	+	0.209040i	$0.932966\pi$
$618$		0			0
$619$	−20.3431			−0.817660			−0.408830	−	0.912611i	$-0.634063\pi$
$619$	−20.3431			−0.817660			−0.408830	+	0.912611i	$0.634063\pi$
$620$	8.44975	+	5.67796i	0.339350	+	0.228033i
$621$		0			0
$622$	4.68629			0.187903
$623$	−0.928932	+	1.60896i	−0.0372169	+	0.0644615i
$624$		0			0
$625$	−5.50000	−	9.52628i	−0.220000	−	0.381051i
$626$	−0.378680	+	0.655892i	−0.0151351	+	0.0262147i
$627$		0			0
$628$	−16.7696			−0.669178
$629$	−2.91421	−	5.04757i	−0.116197	−	0.201260i
$630$		0			0
$631$	−25.0061	−	43.3118i	−0.995477	−	1.72422i	−0.580013	−	0.814607i	$-0.696953\pi$
$631$	−25.0061	−	43.3118i	−0.995477	−	1.72422i	−0.415464	−	0.909610i	$-0.636381\pi$
$632$	5.35786	−	9.28009i	0.213124	−	0.369142i
$633$		0			0
$634$	1.62132	−	2.80821i	0.0643909	−	0.111528i
$635$	−8.89949			−0.353166
$636$		0			0
$637$	−13.0711	+	22.6398i	−0.517895	+	0.897020i
$638$	−4.58579	−	7.94282i	−0.181553	−	0.314459i
$639$		0			0
$640$	5.27817	+	9.14207i	0.208638	+	0.361372i
$641$	−6.98528	−	12.0989i	−0.275902	−	0.477876i	0.694460	−	0.719531i	$-0.255643\pi$
$641$	−6.98528	−	12.0989i	−0.275902	−	0.477876i	−0.970362	+	0.241655i	$0.922310\pi$
$642$		0			0
$643$	35.3137			1.39264			0.696318	−	0.717733i	$-0.254820\pi$
$643$	35.3137			1.39264			0.696318	+	0.717733i	$0.254820\pi$
$644$	−1.51472	+	2.62357i	−0.0596883	+	0.103383i
$645$		0			0
$646$	5.32843	+	9.22911i	0.209644	+	0.363114i
$647$	45.3137			1.78147			0.890733	−	0.454527i	$-0.150192\pi$
$647$	45.3137			1.78147			0.890733	+	0.454527i	$0.150192\pi$
$648$		0			0
$649$	13.2010			0.518185
$650$	−6.34315			−0.248799
$651$		0			0
$652$	−38.3431			−1.50163
$653$	6.14214			0.240360			0.120180	−	0.992752i	$-0.461653\pi$
$653$	6.14214			0.240360			0.120180	+	0.992752i	$0.461653\pi$
$654$		0			0
$655$	−13.2426			−0.517433
$656$	−11.2279	−	19.4473i	−0.438377	−	0.759291i
$657$		0			0
$658$	0.828427	−	1.43488i	0.0322955	−	0.0559374i
$659$	1.65685			0.0645419			0.0322709	−	0.999479i	$-0.489726\pi$
$659$	1.65685			0.0645419			0.0322709	+	0.999479i	$0.489726\pi$
$660$		0			0
$661$	−2.42893	−	4.20703i	−0.0944745	−	0.163635i	0.814915	−	0.579581i	$-0.196784\pi$
$661$	−2.42893	−	4.20703i	−0.0944745	−	0.163635i	−0.909389	+	0.415946i	$0.863450\pi$
$662$	1.91421	+	3.31552i	0.0743980	+	0.128861i
$663$		0			0
$664$	−7.98528	−	13.8309i	−0.309889	−	0.536744i
$665$	−0.914214	+	1.58346i	−0.0354517	+	0.0614041i
$666$		0			0
$667$	27.3137			1.05759
$668$	−20.6213	+	35.7172i	−0.797863	+	1.38194i
$669$		0			0
$670$	−0.671573	+	1.16320i	−0.0259451	+	0.0449383i
$671$	−4.58579	−	7.94282i	−0.177032	−	0.306629i
$672$		0			0
$673$	−4.67157	−	8.09140i	−0.180076	−	0.311901i	0.761830	−	0.647777i	$-0.224301\pi$
$673$	−4.67157	−	8.09140i	−0.180076	−	0.311901i	−0.941906	+	0.335876i	$0.890968\pi$
$674$	−3.85786			−0.148599
$675$		0			0
$676$	1.51472	−	2.62357i	0.0582584	−	0.100907i
$677$	−19.2990	−	33.4268i	−0.741720	−	1.28470i	−0.951711	−	0.306994i	$-0.900677\pi$
$677$	−19.2990	−	33.4268i	−0.741720	−	1.28470i	0.209991	−	0.977703i	$-0.432657\pi$
$678$		0			0
$679$	1.07107	−	1.85514i	0.0411038	−	0.0711939i
$680$	−9.24264			−0.354439
$681$		0			0
$682$	6.20711	+	4.17098i	0.237682	+	0.159715i
$683$	1.37258			0.0525204			0.0262602	−	0.999655i	$-0.491640\pi$
$683$	1.37258			0.0525204			0.0262602	+	0.999655i	$0.491640\pi$
$684$		0			0
$685$	−4.74264	+	8.21449i	−0.181207	+	0.313860i
$686$	−2.37258			−0.0905856
$687$		0			0
$688$	16.3492	−	28.3177i	0.623309	−	1.07960i
$689$	−11.1569	+	19.3242i	−0.425042	+	0.736195i
$690$		0			0
$691$	0.0355339	+	0.0615465i	0.00135177	+	0.00234134i	0.866700	−	0.498829i	$-0.166236\pi$
$691$	0.0355339	+	0.0615465i	0.00135177	+	0.00234134i	−0.865349	+	0.501170i	$0.832903\pi$
$692$	−7.60051	−	13.1645i	−0.288928	−	0.500438i
$693$		0			0
$694$	1.77208	−	3.06933i	0.0672672	−	0.116510i
$695$		0			0
$696$		0			0
$697$	43.6274			1.65251
$698$	11.2304			0.425079
$699$		0			0
$700$	1.51472	+	2.62357i	0.0572510	+	0.0991616i
$701$	−6.74264	+	11.6786i	−0.254666	+	0.441094i	−0.964805	−	0.262967i	$-0.915299\pi$
$701$	−6.74264	+	11.6786i	−0.254666	+	0.441094i	0.710139	+	0.704062i	$0.248632\pi$
$702$		0			0
$703$	−2.20711	−	3.82282i	−0.0832426	−	0.144180i
$704$	−6.76346	−	11.7146i	−0.254907	−	0.441512i
$705$		0			0
$706$	−0.621320	+	1.07616i	−0.0233837	+	0.0405018i
$707$	1.75736	−	3.04384i	0.0660923	−	0.114475i
$708$		0			0
$709$	17.3137			0.650230			0.325115	−	0.945674i	$-0.394597\pi$
$709$	17.3137			0.650230			0.325115	+	0.945674i	$0.394597\pi$
$710$	0.0147186	−	0.0254934i	0.000552380	−	0.000956751i
$711$		0			0
$712$	−7.11270			−0.266560
$713$	−20.0000	+	9.79796i	−0.749006	+	0.366936i
$714$		0			0
$715$	−12.4142			−0.464265
$716$	13.9350	−	24.1362i	0.520776	−	0.902011i
$717$		0			0
$718$	−1.47056	−	2.54709i	−0.0548809	−	0.0950565i
$719$	−4.03553	+	6.98975i	−0.150500	+	0.260674i	−0.931411	−	0.363968i	$-0.881422\pi$
$719$	−4.03553	+	6.98975i	−0.150500	+	0.260674i	0.780911	+	0.624642i	$0.214755\pi$
$720$		0			0
$721$	−0.857864			−0.0319485
$722$	0.100505	+	0.174080i	0.00374041	+	0.00647858i
$723$		0			0
$724$	11.2574	+	19.4983i	0.418376	+	0.724649i
$725$	13.6569	−	23.6544i	0.507203	−	0.878501i
$726$		0			0
$727$	−20.4203	+	35.3690i	−0.757347	+	1.31176i	0.186851	+	0.982388i	$0.440172\pi$
$727$	−20.4203	+	35.3690i	−0.757347	+	1.31176i	−0.944199	+	0.329376i	$0.893162\pi$
$728$	2.51472			0.0932017
$729$		0			0
$730$	0.378680	−	0.655892i	0.0140156	−	0.0242757i
$731$	31.7635	+	55.0159i	1.17481	+	2.03484i
$732$		0			0
$733$	−7.81371	−	13.5337i	−0.288606	−	0.499880i	0.684871	−	0.728664i	$-0.259858\pi$
$733$	−7.81371	−	13.5337i	−0.288606	−	0.499880i	−0.973477	+	0.228784i	$0.926525\pi$
$734$	−5.01472	−	8.68575i	−0.185097	−	0.320597i
$735$		0			0
$736$	−17.6569			−0.650840
$737$	5.25736	−	9.10601i	0.193657	−	0.335424i
$738$		0			0
$739$	−22.9350	−	39.7246i	−0.843679	−	1.46129i	−0.886764	−	0.462223i	$-0.847052\pi$
$739$	−22.9350	−	39.7246i	−0.843679	−	1.46129i	0.0430851	−	0.999071i	$-0.486281\pi$
$740$	1.82843			0.0672143
$741$		0			0
$742$	−1.00000			−0.0367112
$743$	−5.65685			−0.207530			−0.103765	−	0.994602i	$-0.533089\pi$
$743$	−5.65685			−0.207530			−0.103765	+	0.994602i	$0.533089\pi$
$744$		0			0
$745$	1.00000			0.0366372
$746$	−4.14214			−0.151654
$747$		0			0
$748$	34.5563			1.26351
$749$	−2.57107	−	4.45322i	−0.0939448	−	0.162717i
$750$		0			0
$751$	−3.62132	+	6.27231i	−0.132144	+	0.228880i	−0.924503	−	0.381175i	$-0.875519\pi$
$751$	−3.62132	+	6.27231i	−0.132144	+	0.228880i	0.792359	+	0.610055i	$0.208853\pi$
$752$	−28.9706			−1.05645
$753$		0			0
$754$	−5.41421	−	9.37769i	−0.197174	−	0.341515i
$755$	2.65685	+	4.60181i	0.0966928	+	0.167477i
$756$		0			0
$757$	−11.6716	−	20.2158i	−0.424211	−	0.734754i	0.572136	−	0.820159i	$-0.306115\pi$
$757$	−11.6716	−	20.2158i	−0.424211	−	0.734754i	−0.996346	+	0.0854047i	$0.972782\pi$
$758$	1.52944	−	2.64906i	0.0555517	−	0.0962183i
$759$		0			0
$760$	−7.00000			−0.253917
$761$	15.2279	−	26.3755i	0.552012	−	0.956112i	−0.446118	−	0.894974i	$-0.647194\pi$
$761$	15.2279	−	26.3755i	0.552012	−	0.956112i	0.998129	−	0.0611380i	$-0.0194730\pi$
$762$		0			0
$763$	−2.24264	+	3.88437i	−0.0811890	+	0.140624i
$764$	19.1066	+	33.0936i	0.691253	+	1.19728i
$765$		0			0
$766$	−1.05635	−	1.82965i	−0.0381674	−	0.0661080i
$767$	15.5858			0.562770
$768$		0			0
$769$	−18.0563	+	31.2745i	−0.651129	+	1.12779i	0.331721	+	0.943378i	$0.392371\pi$
$769$	−18.0563	+	31.2745i	−0.651129	+	1.12779i	−0.982849	+	0.184410i	$0.940963\pi$
$770$	−0.278175	−	0.481813i	−0.0100247	−	0.0173633i
$771$		0			0
$772$	6.52944	−	11.3093i	0.235000	−	0.407031i
$773$	−18.0000			−0.647415			−0.323708	−	0.946157i	$-0.604929\pi$
$773$	−18.0000			−0.647415			−0.323708	+	0.946157i	$0.604929\pi$
$774$		0			0
$775$	−1.51472	+	22.2195i	−0.0544103	+	0.798148i
$776$	8.20101			0.294399
$777$		0			0
$778$	2.30761	−	3.99690i	0.0827319	−	0.143296i
$779$	33.0416			1.18384
$780$		0			0
$781$	−0.115224	+	0.199573i	−0.00412303	+	0.00714129i
$782$	4.82843	−	8.36308i	0.172664	−	0.299063i
$783$		0			0
$784$	10.2426	+	17.7408i	0.365809	+	0.633599i
$785$	4.58579	+	7.94282i	0.163674	+	0.283491i
$786$		0			0
$787$	−21.2071	+	36.7318i	−0.755952	+	1.30935i	0.188948	+	0.981987i	$0.439492\pi$
$787$	−21.2071	+	36.7318i	−0.755952	+	1.30935i	−0.944900	+	0.327360i	$0.893841\pi$
$788$	12.3284	+	21.3535i	0.439182	+	0.760686i
$789$		0			0
$790$	−2.79899			−0.0995836
$791$	6.89949			0.245318
$792$		0			0
$793$	−5.41421	−	9.37769i	−0.192264	−	0.333012i
$794$	−6.93503	+	12.0118i	−0.246115	+	0.426284i
$795$		0			0
$796$	16.8345	+	29.1583i	0.596684	+	1.03349i
$797$	14.2279	+	24.6435i	0.503979	+	0.872917i	0.999989	+	0.00460050i	$0.00146439\pi$
$797$	14.2279	+	24.6435i	0.503979	+	0.872917i	−0.496011	+	0.868316i	$0.665202\pi$
$798$		0			0
$799$	28.1421	−	48.7436i	0.995597	−	1.72442i
$800$	−8.82843	+	15.2913i	−0.312132	+	0.540629i
$801$		0			0
$802$	−11.1127			−0.392403
$803$	−2.96447	+	5.13461i	−0.104614	+	0.181196i
$804$		0			0
$805$	1.65685			0.0583964
$806$	7.32843	+	4.92447i	0.258133	+	0.173457i
$807$		0			0
$808$	13.4558			0.473375
$809$	−6.01472	+	10.4178i	−0.211466	+	0.366270i	−0.952174	−	0.305558i	$-0.901157\pi$
$809$	−6.01472	+	10.4178i	−0.211466	+	0.366270i	0.740707	+	0.671828i	$0.234491\pi$
$810$		0			0
$811$	6.86396	+	11.8887i	0.241026	+	0.417470i	0.961007	−	0.276524i	$-0.0891827\pi$
$811$	6.86396	+	11.8887i	0.241026	+	0.417470i	−0.719981	+	0.693994i	$0.755849\pi$
$812$	−2.58579	+	4.47871i	−0.0907433	+	0.157172i
$813$		0			0
$814$	1.34315			0.0470772
$815$	10.4853	+	18.1610i	0.367283	+	0.636153i
$816$		0			0
$817$	24.0563	+	41.6668i	0.841625	+	1.45774i
$818$	4.27817	−	7.41002i	0.149583	−	0.259085i
$819$		0			0
$820$	−6.84315	+	11.8527i	−0.238973	+	0.413913i
$821$	−8.48528			−0.296138			−0.148069	−	0.988977i	$-0.547306\pi$
$821$	−8.48528			−0.296138			−0.148069	+	0.988977i	$0.547306\pi$
$822$		0			0
$823$	−18.1066	+	31.3616i	−0.631156	+	1.09320i	0.356159	+	0.934425i	$0.384086\pi$
$823$	−18.1066	+	31.3616i	−0.631156	+	1.09320i	−0.987316	+	0.158770i	$0.949247\pi$
$824$	−1.64214	−	2.84426i	−0.0572065	−	0.0990846i
$825$		0			0
$826$	0.349242	+	0.604906i	0.0121517	+	0.0210474i
$827$	18.4497	+	31.9559i	0.641561	+	1.11122i	0.985084	+	0.172072i	$0.0550460\pi$
$827$	18.4497	+	31.9559i	0.641561	+	1.11122i	−0.343524	+	0.939144i	$0.611621\pi$
$828$		0			0
$829$	38.4264			1.33460			0.667302	−	0.744787i	$-0.267449\pi$
$829$	38.4264			1.33460			0.667302	+	0.744787i	$0.267449\pi$
$830$	−2.08579	+	3.61269i	−0.0723987	+	0.125398i
$831$		0			0
$832$	−7.98528	−	13.8309i	−0.276840	−	0.479501i
$833$	−39.7990			−1.37895
$834$		0			0
$835$	22.5563			0.780595
$836$	26.1716			0.905163
$837$		0			0
$838$	11.5980			0.400646
$839$	14.6274			0.504995			0.252497	−	0.967598i	$-0.418748\pi$
$839$	14.6274			0.504995			0.252497	+	0.967598i	$0.418748\pi$
$840$		0			0
$841$	17.6274			0.607842
$842$	−6.44975	−	11.1713i	−0.222273	−	0.384988i
$843$		0			0
$844$	9.52082	−	16.4905i	0.327720	−	0.567628i
$845$	−1.65685			−0.0569975
$846$		0			0
$847$	−0.100505	−	0.174080i	−0.00345339	−	0.00598146i
$848$	8.74264	+	15.1427i	0.300224	+	0.520002i
$849$		0			0
$850$	−4.82843	−	8.36308i	−0.165614	−	0.286851i
$851$	−2.00000	+	3.46410i	−0.0685591	+	0.118748i
$852$		0			0
$853$	−15.5147			−0.531214			−0.265607	−	0.964081i	$-0.585572\pi$
$853$	−15.5147			−0.531214			−0.265607	+	0.964081i	$0.585572\pi$
$854$	0.242641	−	0.420266i	0.00830299	−	0.0143812i
$855$		0			0
$856$	9.84315	−	17.0488i	0.336432	−	0.582717i
$857$	−9.74264	−	16.8747i	−0.332802	−	0.576430i	0.650258	−	0.759714i	$-0.274661\pi$
$857$	−9.74264	−	16.8747i	−0.332802	−	0.576430i	−0.983060	+	0.183283i	$0.941328\pi$
$858$		0			0
$859$	24.6924	+	42.7685i	0.842493	+	1.45924i	0.887780	+	0.460267i	$0.152246\pi$
$859$	24.6924	+	42.7685i	0.842493	+	1.45924i	−0.0452869	+	0.998974i	$0.514420\pi$
$860$	−19.9289			−0.679571
$861$		0			0
$862$	3.47056	−	6.01119i	0.118208	−	0.204742i
$863$	−1.30761	−	2.26485i	−0.0445116	−	0.0770964i	0.842911	−	0.538053i	$-0.180840\pi$
$863$	−1.30761	−	2.26485i	−0.0445116	−	0.0770964i	−0.887423	+	0.460956i	$0.847507\pi$
$864$		0			0
$865$	−4.15685	+	7.19988i	−0.141337	+	0.244803i
$866$	−11.2304			−0.381626
$867$		0			0
$868$	0.286797	−	4.20703i	0.00973451	−	0.142796i
$869$	21.9117			0.743303
$870$		0			0
$871$	6.20711	−	10.7510i	0.210320	−	0.364285i
$872$	−17.1716			−0.581503
$873$		0			0
$874$	3.65685	−	6.33386i	0.123695	−	0.214246i
$875$	1.86396	−	3.22848i	0.0630134	−	0.109142i
$876$		0			0
$877$	−26.9142	−	46.6168i	−0.908828	−	1.57414i	−0.815694	−	0.578483i	$-0.803645\pi$
$877$	−26.9142	−	46.6168i	−0.908828	−	1.57414i	−0.0931343	−	0.995654i	$-0.529689\pi$
$878$	0.428932	+	0.742932i	0.0144758	+	0.0250728i
$879$		0			0
$880$	−4.86396	+	8.42463i	−0.163964	+	0.283994i
$881$	5.84315	+	10.1206i	0.196861	+	0.340973i	0.947509	−	0.319729i	$-0.103592\pi$
$881$	5.84315	+	10.1206i	0.196861	+	0.340973i	−0.750648	+	0.660702i	$0.770259\pi$
$882$		0			0
$883$	−30.2843			−1.01915			−0.509573	−	0.860427i	$-0.670197\pi$
$883$	−30.2843			−1.01915			−0.509573	+	0.860427i	$0.670197\pi$
$884$	40.7990			1.37222
$885$		0			0
$886$	0.985281	+	1.70656i	0.0331012	+	0.0573329i
$887$	−25.6630	+	44.4495i	−0.861678	+	1.49247i	0.00863117	+	0.999963i	$0.497253\pi$
$887$	−25.6630	+	44.4495i	−0.861678	+	1.49247i	−0.870309	+	0.492507i	$0.836081\pi$
$888$		0			0
$889$	1.84315	+	3.19242i	0.0618171	+	0.107070i
$890$	0.928932	+	1.60896i	0.0311379	+	0.0539324i
$891$		0			0
$892$	−21.6924	+	37.5723i	−0.726315	+	1.25801i
$893$	21.3137	−	36.9164i	0.713236	−	1.23536i
$894$		0			0
$895$	−15.2426			−0.509505
$896$	2.18629	−	3.78677i	0.0730389	−	0.126507i
$897$		0			0
$898$	−16.8284			−0.561572
$899$	−34.1421	+	16.7262i	−1.13870	+	0.557849i
$900$		0			0
$901$	−33.9706			−1.13172
$902$	−5.02691	+	8.70687i	−0.167378	+	0.289907i
$903$		0			0
$904$	13.2071	+	22.8754i	0.439262	+	0.760824i
$905$	6.15685	−	10.6640i	0.204661	−	0.354483i
$906$		0			0
$907$	32.6863			1.08533			0.542665	−	0.839949i	$-0.317415\pi$
$907$	32.6863			1.08533			0.542665	+	0.839949i	$0.317415\pi$
$908$	16.8345	+	29.1583i	0.558673	+	0.967651i
$909$		0			0
$910$	−0.328427	−	0.568852i	−0.0108873	−	0.0188573i
$911$	0.479185	−	0.829972i	0.0158761	−	0.0274982i	−0.857978	−	0.513686i	$-0.828280\pi$
$911$	0.479185	−	0.829972i	0.0158761	−	0.0274982i	0.873854	+	0.486188i	$0.161613\pi$
$912$		0			0
$913$	16.3284	−	28.2817i	0.540392	−	0.935987i
$914$	12.8873			0.426274
$915$		0			0
$916$	−5.01472	+	8.68575i	−0.165691	+	0.286985i
$917$	2.74264	+	4.75039i	0.0905700	+	0.156872i
$918$		0			0
$919$	17.4497	+	30.2238i	0.575614	+	0.996993i	0.995975	+	0.0896356i	$0.0285703\pi$
$919$	17.4497	+	30.2238i	0.575614	+	0.996993i	−0.420361	+	0.907357i	$0.638096\pi$
$920$	3.17157	+	5.49333i	0.104564	+	0.181110i
$921$		0			0
$922$	−0.887302			−0.0292217
$923$	−0.136039	+	0.235626i	−0.00447778	+	0.00775574i
$924$		0			0
$925$	2.00000	+	3.46410i	0.0657596	+	0.113899i
$926$	3.71573			0.122106
$927$		0			0
$928$	−30.1421			−0.989464
$929$	−7.51472			−0.246550			−0.123275	−	0.992373i	$-0.539340\pi$
$929$	−7.51472			−0.246550			−0.123275	+	0.992373i	$0.539340\pi$
$930$		0			0
$931$	−30.1421			−0.987869
$932$	−16.7696			−0.549305
$933$		0			0
$934$	−3.31371			−0.108428
$935$	−9.44975	−	16.3674i	−0.309040	−	0.535273i
$936$		0			0
$937$	−7.84315	+	13.5847i	−0.256224	+	0.443794i	−0.965227	−	0.261412i	$-0.915812\pi$
$937$	−7.84315	+	13.5847i	−0.256224	+	0.443794i	0.709003	+	0.705206i	$0.249145\pi$
$938$	0.556349			0.0181654
$939$		0			0
$940$	8.82843	+	15.2913i	0.287952	+	0.498747i
$941$	−17.5000	−	30.3109i	−0.570484	−	0.988107i	−0.996516	−	0.0833989i	$-0.973422\pi$
$941$	−17.5000	−	30.3109i	−0.570484	−	0.988107i	0.426033	−	0.904708i	$-0.359911\pi$
$942$		0			0
$943$	−14.9706	−	25.9298i	−0.487509	−	0.844390i
$944$	6.10660	−	10.5769i	0.198753	−	0.344250i
$945$		0			0
$946$	−14.6396			−0.475975
$947$	9.55025	−	16.5415i	0.310342	−	0.537527i	−0.668095	−	0.744076i	$-0.732890\pi$
$947$	9.55025	−	16.5415i	0.310342	−	0.537527i	0.978436	+	0.206549i	$0.0662233\pi$
$948$		0			0
$949$	−3.50000	+	6.06218i	−0.113615	+	0.196787i
$950$	−3.65685	−	6.33386i	−0.118644	−	0.205497i
$951$		0			0
$952$	1.91421	+	3.31552i	0.0620400	+	0.107456i
$953$	−3.51472			−0.113853			−0.0569265	−	0.998378i	$-0.518130\pi$
$953$	−3.51472			−0.113853			−0.0569265	+	0.998378i	$0.518130\pi$
$954$		0			0
$955$	10.4497	−	18.0995i	0.338146	−	0.585686i
$956$	19.4203	+	33.6370i	0.628098	+	1.08790i
$957$		0			0
$958$	3.25736	−	5.64191i	0.105241	−	0.182282i
$959$	3.92893			0.126872
$960$		0			0
$961$	19.0000	−	24.4949i	0.612903	−	0.790158i
$962$	1.58579			0.0511278
$963$		0			0
$964$	12.1985	−	21.1284i	0.392887	−	0.680500i
$965$	−7.14214			−0.229913
$966$		0			0
$967$	7.72183	−	13.3746i	0.248317	−	0.430098i	−0.714742	−	0.699388i	$-0.753456\pi$
$967$	7.72183	−	13.3746i	0.248317	−	0.430098i	0.963059	+	0.269290i	$0.0867892\pi$
$968$	0.384776	−	0.666452i	0.0123672	−	0.0214206i
$969$		0			0
$970$	−1.07107	−	1.85514i	−0.0343899	−	0.0595651i
$971$	−0.349242	−	0.604906i	−0.0112077	−	0.0194123i	0.860367	−	0.509675i	$-0.170234\pi$
$971$	−0.349242	−	0.604906i	−0.0112077	−	0.0194123i	−0.871575	+	0.490262i	$0.836901\pi$
$972$		0			0
$973$		0			0
$974$	4.01472	+	6.95370i	0.128640	+	0.222811i
$975$		0			0
$976$	−8.48528			−0.271607
$977$	0.485281			0.0155255			0.00776276	−	0.999970i	$-0.497529\pi$
$977$	0.485281			0.0155255			0.00776276	+	0.999970i	$0.497529\pi$
$978$		0			0
$979$	−7.27208	−	12.5956i	−0.232417	−	0.402557i
$980$	6.24264	−	10.8126i	0.199414	−	0.345395i
$981$		0			0
$982$	−0.328427	−	0.568852i	−0.0104805	−	0.0181528i
$983$	−19.4203	−	33.6370i	−0.619412	−	1.07285i	−0.989593	−	0.143893i	$-0.954038\pi$
$983$	−19.4203	−	33.6370i	−0.619412	−	1.07285i	0.370182	−	0.928959i	$-0.379295\pi$
$984$		0			0
$985$	6.74264	−	11.6786i	0.214838	−	0.372111i
$986$	8.24264	−	14.2767i	0.262499	−	0.454662i
$987$		0			0
$988$	30.8995			0.983044
$989$	21.7990	−	37.7570i	0.693168	−	1.20060i
$990$		0			0
$991$	47.9411			1.52290			0.761450	−	0.648224i	$-0.224488\pi$
$991$	47.9411			1.52290			0.761450	+	0.648224i	$0.224488\pi$
$992$	22.0711	−	10.8126i	0.700757	−	0.343299i
$993$		0			0
$994$	−0.0121933			−0.000386748
$995$	9.20711	−	15.9472i	0.291885	−	0.505559i
$996$		0			0
$997$	−16.2990	−	28.2307i	−0.516194	−	0.894075i	−0.999823	−	0.0188015i	$-0.994015\pi$
$997$	−16.2990	−	28.2307i	−0.516194	−	0.894075i	0.483629	−	0.875273i	$-0.339318\pi$
$998$	−0.458369	+	0.793919i	−0.0145094	+	0.0251311i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	279.2.h.c.253.1		4
3.2	odd	2		31.2.c.a.5.2	✓	4
12.11	even	2		496.2.i.h.129.2		4
15.2	even	4		775.2.o.d.749.3		8
15.8	even	4		775.2.o.d.749.2		8
15.14	odd	2		775.2.e.e.501.1		4
31.5	even	3		8649.2.a.l.1.1		2
31.25	even	3	inner	279.2.h.c.118.1		4
31.26	odd	6		8649.2.a.k.1.1		2
93.2	odd	10		961.2.g.o.547.2		16
93.5	odd	6		961.2.a.a.1.2		2
93.8	odd	10		961.2.g.o.816.1		16
93.11	even	30		961.2.d.i.388.1		8
93.14	odd	30		961.2.g.o.732.1		16
93.17	even	30		961.2.g.r.732.1		16
93.20	odd	30		961.2.d.l.388.1		8
93.23	even	10		961.2.g.r.816.1		16
93.26	even	6		961.2.a.c.1.2		2
93.29	even	10		961.2.g.r.547.2		16
93.35	odd	10		961.2.g.o.235.1		16
93.38	odd	30		961.2.g.o.338.1		16
93.41	odd	30		961.2.d.l.531.2		8
93.44	even	30		961.2.d.i.628.2		8
93.47	odd	10		961.2.g.o.846.2		16
93.50	odd	30		961.2.g.o.844.2		16
93.53	even	30		961.2.d.i.374.1		8
93.56	odd	6		31.2.c.a.25.2	yes	4
93.59	odd	30		961.2.g.o.448.2		16
93.65	even	30		961.2.g.r.448.2		16
93.68	even	6		961.2.c.a.521.2		4
93.71	odd	30		961.2.d.l.374.1		8
93.74	even	30		961.2.g.r.844.2		16
93.77	even	10		961.2.g.r.846.2		16
93.80	odd	30		961.2.d.l.628.2		8
93.83	even	30		961.2.d.i.531.2		8
93.86	even	30		961.2.g.r.338.1		16
93.89	even	10		961.2.g.r.235.1		16
93.92	even	2		961.2.c.a.439.2		4
372.335	even	6		496.2.i.h.273.2		4
465.149	odd	6		775.2.e.e.676.1		4
465.242	even	12		775.2.o.d.149.3		8
465.428	even	12		775.2.o.d.149.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
31.2.c.a.5.2	✓	4	3.2	odd	2
31.2.c.a.25.2	yes	4	93.56	odd	6
279.2.h.c.118.1		4	31.25	even	3	inner
279.2.h.c.253.1		4	1.1	even	1	trivial
496.2.i.h.129.2		4	12.11	even	2
496.2.i.h.273.2		4	372.335	even	6
775.2.e.e.501.1		4	15.14	odd	2
775.2.e.e.676.1		4	465.149	odd	6
775.2.o.d.149.2		8	465.428	even	12
775.2.o.d.149.3		8	465.242	even	12
775.2.o.d.749.2		8	15.8	even	4
775.2.o.d.749.3		8	15.2	even	4
961.2.a.a.1.2		2	93.5	odd	6
961.2.a.c.1.2		2	93.26	even	6
961.2.c.a.439.2		4	93.92	even	2
961.2.c.a.521.2		4	93.68	even	6
961.2.d.i.374.1		8	93.53	even	30
961.2.d.i.388.1		8	93.11	even	30
961.2.d.i.531.2		8	93.83	even	30
961.2.d.i.628.2		8	93.44	even	30
961.2.d.l.374.1		8	93.71	odd	30
961.2.d.l.388.1		8	93.20	odd	30
961.2.d.l.531.2		8	93.41	odd	30
961.2.d.l.628.2		8	93.80	odd	30
961.2.g.o.235.1		16	93.35	odd	10
961.2.g.o.338.1		16	93.38	odd	30
961.2.g.o.448.2		16	93.59	odd	30
961.2.g.o.547.2		16	93.2	odd	10
961.2.g.o.732.1		16	93.14	odd	30
961.2.g.o.816.1		16	93.8	odd	10
961.2.g.o.844.2		16	93.50	odd	30
961.2.g.o.846.2		16	93.47	odd	10
961.2.g.r.235.1		16	93.89	even	10
961.2.g.r.338.1		16	93.86	even	30
961.2.g.r.448.2		16	93.65	even	30
961.2.g.r.547.2		16	93.29	even	10
961.2.g.r.732.1		16	93.17	even	30
961.2.g.r.816.1		16	93.23	even	10
961.2.g.r.844.2		16	93.74	even	30
961.2.g.r.846.2		16	93.77	even	10
8649.2.a.k.1.1		2	31.26	odd	6
8649.2.a.l.1.1		2	31.5	even	3

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:	\( N \)	\(=\)	\( 279 = 3^{2} \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	279.h (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-0.414214 q^{2} -1.82843 q^{4} +(0.500000 + 0.866025i) q^{5} +(0.207107 - 0.358719i) q^{7} +1.58579 q^{8} +O(q^{10})\)	\(q-0.414214 q^{2} -1.82843 q^{4} +(0.500000 + 0.866025i) q^{5} +(0.207107 - 0.358719i) q^{7} +1.58579 q^{8} +(-0.207107 - 0.358719i) q^{10} +(1.62132 + 2.80821i) q^{11} +(1.91421 + 3.31552i) q^{13} +(-0.0857864 + 0.148586i) q^{14} +3.00000 q^{16} +(-2.91421 + 5.04757i) q^{17} +(-2.20711 + 3.82282i) q^{19} +(-0.914214 - 1.58346i) q^{20} +(-0.671573 - 1.16320i) q^{22} +4.00000 q^{23} +(2.00000 - 3.46410i) q^{25} +(-0.792893 - 1.37333i) q^{26} +(-0.378680 + 0.655892i) q^{28} +6.82843 q^{29} +(-5.00000 + 2.44949i) q^{31} -4.41421 q^{32} +(1.20711 - 2.09077i) q^{34} +0.414214 q^{35} +(-0.500000 + 0.866025i) q^{37} +(0.914214 - 1.58346i) q^{38} +(0.792893 + 1.37333i) q^{40} +(-3.74264 - 6.48244i) q^{41} +(5.44975 - 9.43924i) q^{43} +(-2.96447 - 5.13461i) q^{44} -1.65685 q^{46} -9.65685 q^{47} +(3.41421 + 5.91359i) q^{49} +(-0.828427 + 1.43488i) q^{50} +(-3.50000 - 6.06218i) q^{52} +(2.91421 + 5.04757i) q^{53} +(-1.62132 + 2.80821i) q^{55} +(0.328427 - 0.568852i) q^{56} -2.82843 q^{58} +(2.03553 - 3.52565i) q^{59} -2.82843 q^{61} +(2.07107 - 1.01461i) q^{62} -4.17157 q^{64} +(-1.91421 + 3.31552i) q^{65} +(-1.62132 - 2.80821i) q^{67} +(5.32843 - 9.22911i) q^{68} -0.171573 q^{70} +(0.0355339 + 0.0615465i) q^{71} +(0.914214 + 1.58346i) q^{73} +(0.207107 - 0.358719i) q^{74} +(4.03553 - 6.98975i) q^{76} +1.34315 q^{77} +(3.37868 - 5.85204i) q^{79} +(1.50000 + 2.59808i) q^{80} +(1.55025 + 2.68512i) q^{82} +(-5.03553 - 8.72180i) q^{83} -5.82843 q^{85} +(-2.25736 + 3.90986i) q^{86} +(2.57107 + 4.45322i) q^{88} -4.48528 q^{89} +1.58579 q^{91} -7.31371 q^{92} +4.00000 q^{94} -4.41421 q^{95} +5.17157 q^{97} +(-1.41421 - 2.44949i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{2} + 4 q^{4} + 2 q^{5} - 2 q^{7} + 12 q^{8}+O(q^{10}) \) 4 * q + 4 * q^2 + 4 * q^4 + 2 * q^5 - 2 * q^7 + 12 * q^8	\( 4 q + 4 q^{2} + 4 q^{4} + 2 q^{5} - 2 q^{7} + 12 q^{8} + 2 q^{10} - 2 q^{11} + 2 q^{13} - 6 q^{14} + 12 q^{16} - 6 q^{17} - 6 q^{19} + 2 q^{20} - 14 q^{22} + 16 q^{23} + 8 q^{25} - 6 q^{26} - 10 q^{28} + 16 q^{29} - 20 q^{31} - 12 q^{32} + 2 q^{34} - 4 q^{35} - 2 q^{37} - 2 q^{38} + 6 q^{40} + 2 q^{41} + 2 q^{43} - 26 q^{44} + 16 q^{46} - 16 q^{47} + 8 q^{49} + 8 q^{50} - 14 q^{52} + 6 q^{53} + 2 q^{55} - 10 q^{56} - 6 q^{59} - 20 q^{62} - 28 q^{64} - 2 q^{65} + 2 q^{67} + 10 q^{68} - 12 q^{70} - 14 q^{71} - 2 q^{73} - 2 q^{74} + 2 q^{76} + 28 q^{77} + 22 q^{79} + 6 q^{80} + 26 q^{82} - 6 q^{83} - 12 q^{85} - 26 q^{86} - 18 q^{88} + 16 q^{89} + 12 q^{91} + 16 q^{92} + 16 q^{94} - 12 q^{95} + 32 q^{97}+O(q^{100}) \) 4 * q + 4 * q^2 + 4 * q^4 + 2 * q^5 - 2 * q^7 + 12 * q^8 + 2 * q^10 - 2 * q^11 + 2 * q^13 - 6 * q^14 + 12 * q^16 - 6 * q^17 - 6 * q^19 + 2 * q^20 - 14 * q^22 + 16 * q^23 + 8 * q^25 - 6 * q^26 - 10 * q^28 + 16 * q^29 - 20 * q^31 - 12 * q^32 + 2 * q^34 - 4 * q^35 - 2 * q^37 - 2 * q^38 + 6 * q^40 + 2 * q^41 + 2 * q^43 - 26 * q^44 + 16 * q^46 - 16 * q^47 + 8 * q^49 + 8 * q^50 - 14 * q^52 + 6 * q^53 + 2 * q^55 - 10 * q^56 - 6 * q^59 - 20 * q^62 - 28 * q^64 - 2 * q^65 + 2 * q^67 + 10 * q^68 - 12 * q^70 - 14 * q^71 - 2 * q^73 - 2 * q^74 + 2 * q^76 + 28 * q^77 + 22 * q^79 + 6 * q^80 + 26 * q^82 - 6 * q^83 - 12 * q^85 - 26 * q^86 - 18 * q^88 + 16 * q^89 + 12 * q^91 + 16 * q^92 + 16 * q^94 - 12 * q^95 + 32 * q^97

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