LMFDB - Embedded newform 23.25.b.c.22.31

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [23,25,Mod(22,23)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(23, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1])) N = Newforms(chi, 25, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("23.22"); S:= CuspForms(chi, 25); N := Newforms(S);

Level:	$ N $	$=$	$ 23 $
Weight:	$ k $	$=$	$ 25 $
Character orbit:	$[\chi]$	$=$	23.b (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [44] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$83.9424450193$
Analytic rank:	$0$
Dimension:	$44$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			22.31
Character	$\chi$	$=$	23.22
Dual form			23.25.b.c.22.32

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+2985.73 q^{2} +115484. q^{3} -7.86263e6 q^{4} -1.34313e8i q^{5} +3.44805e8 q^{6} -1.30902e10i q^{7} -7.35679e10 q^{8} -2.69093e11 q^{9} -4.01021e11i q^{10} -2.85381e12i q^{11} -9.08011e11 q^{12} -2.36167e13 q^{13} -3.90839e13i q^{14} -1.55110e13i q^{15} -8.77409e13 q^{16} +4.84231e14i q^{17} -8.03439e14 q^{18} +1.60859e15i q^{19} +1.05605e15i q^{20} -1.51172e15i q^{21} -8.52070e15i q^{22} +(4.19846e15 - 2.15087e16i) q^{23} -8.49594e15 q^{24} +4.15647e16 q^{25} -7.05129e16 q^{26} -6.36922e16 q^{27} +1.02924e17i q^{28} -9.26708e16 q^{29} -4.63117e16i q^{30} +4.37102e17 q^{31} +9.72295e17 q^{32} -3.29570e17i q^{33} +1.44578e18i q^{34} -1.75819e18 q^{35} +2.11578e18 q^{36} +1.54887e18i q^{37} +4.80280e18i q^{38} -2.72735e18 q^{39} +9.88111e18i q^{40} -7.65489e18 q^{41} -4.51358e18i q^{42} +2.83655e19i q^{43} +2.24385e19i q^{44} +3.61426e19i q^{45} +(1.25355e19 - 6.42191e19i) q^{46} +4.11080e19 q^{47} -1.01327e19 q^{48} +2.02266e19 q^{49} +1.24101e20 q^{50} +5.59211e19i q^{51} +1.85689e20 q^{52} +3.21206e20i q^{53} -1.90168e20 q^{54} -3.83303e20 q^{55} +9.63023e20i q^{56} +1.85766e20i q^{57} -2.76690e20 q^{58} -5.45183e20 q^{59} +1.21957e20i q^{60} +2.60916e20i q^{61} +1.30507e21 q^{62} +3.52249e21i q^{63} +4.37506e21 q^{64} +3.17202e21i q^{65} -9.84008e20i q^{66} -1.94453e21i q^{67} -3.80733e21i q^{68} +(4.84856e20 - 2.48392e21i) q^{69} -5.24947e21 q^{70} -1.51878e22 q^{71} +1.97966e22 q^{72} -1.69139e21 q^{73} +4.62451e21i q^{74} +4.80008e21 q^{75} -1.26477e22i q^{76} -3.73571e22 q^{77} -8.14314e21 q^{78} -2.50834e22i q^{79} +1.17847e22i q^{80} +6.86443e22 q^{81} -2.28554e22 q^{82} +2.83163e22i q^{83} +1.18861e22i q^{84} +6.50384e22 q^{85} +8.46918e22i q^{86} -1.07020e22 q^{87} +2.09949e23i q^{88} +7.63947e22i q^{89} +1.07912e23i q^{90} +3.09148e23i q^{91} +(-3.30109e22 + 1.69115e23i) q^{92} +5.04785e22 q^{93} +1.22738e23 q^{94} +2.16053e23 q^{95} +1.12285e23 q^{96} +7.48901e23i q^{97} +6.03912e22 q^{98} +7.67940e23i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q - 4232 q^{2} - 434562 q^{3} + 317760360 q^{4} - 8460029520 q^{6} - 198307023760 q^{8} + 4220041988298 q^{9} - 67439597688792 q^{12} + 5771152551358 q^{13} + 18\!\cdots\!92 q^{16} + 18\!\cdots\!68 q^{18}+ \cdots - 20\!\cdots\!92 q^{98}+O(q^{100}) $ 44 * q - 4232 * q^2 - 434562 * q^3 + 317760360 * q^4 - 8460029520 * q^6 - 198307023760 * q^8 + 4220041988298 * q^9 - 67439597688792 * q^12 + 5771152551358 * q^13 + 1801550792530192 * q^16 + 1842830558165568 * q^18 - 117204213263210644 * q^23 - 186493005437450784 * q^24 - 689533084157602612 * q^25 - 548650296251047576 * q^26 + 824037505793640630 * q^27 - 1583078054945709602 * q^29 - 77249813729122274 * q^31 - 2838716832733708512 * q^32 + 3418569899175948192 * q^35 + 71181245116739335248 * q^36 + 47106572467817156310 * q^39 - 9150679195666184738 * q^41 - 153049487518536134480 * q^46 + 22735751396127769438 * q^47 - 1317482931964495330032 * q^48 - 1842110772006482246836 * q^49 + 284936617115007894520 * q^50 + 207129175371045152568 * q^52 - 381774025126375304544 * q^54 - 5430040696094013021792 * q^55 - 2168901871328366220760 * q^58 + 16048018791948427185304 * q^59 + 14054450375064171442400 * q^62 + 20310379126091866412192 * q^64 + 24476879859710435470878 * q^69 - 118028399895318845638416 * q^70 - 68204988047209908888578 * q^71 - 106777935582637627887744 * q^72 - 7319375899831086678722 * q^73 + 12913295383070041819998 * q^75 + 111116199573084838704480 * q^77 - 422583593213386075404144 * q^78 - 331350288185757013618680 * q^81 + 1000764218021118649437320 * q^82 - 113385735487939722862944 * q^85 - 248828610584854760185290 * q^87 - 4238455111972177116774696 * q^92 + 4492289396741153284965270 * q^93 - 1602622056539190351258592 * q^94 - 1668692394291208047471936 * q^95 - 12092663288748189077973504 * q^96 - 2067304853876486831513192 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/23\mathbb{Z}\right)^\times$.

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

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 $

$2$	2985.73			0.728938			0.364469	−	0.931216i	$-0.381251\pi$
$2$	2985.73			0.728938			0.364469	+	0.931216i	$0.381251\pi$
$3$	115484.			0.217304			0.108652	−	0.994080i	$-0.465347\pi$
$3$	115484.			0.217304			0.108652	+	0.994080i	$0.465347\pi$
$4$	−7.86263e6			−0.468649
$5$		−	1.34313e8i		−	0.550145i	−0.961424	−	0.275072i	$-0.911298\pi$
$5$		−	1.34313e8i		−	0.550145i	0.961424	−	0.275072i	$-0.0887018\pi$
$6$	3.44805e8			0.158401
$7$		−	1.30902e10i		−	0.945739i	−0.881132	−	0.472870i	$-0.843218\pi$
$7$		−	1.30902e10i		−	0.945739i	0.881132	−	0.472870i	$-0.156782\pi$
$8$	−7.35679e10			−1.07055
$9$	−2.69093e11			−0.952779
$10$		−	4.01021e11i		−	0.401021i
$11$		−	2.85381e12i		−	0.909312i	−0.890667	−	0.454656i	$-0.849762\pi$
$11$		−	2.85381e12i		−	0.909312i	0.890667	−	0.454656i	$-0.150238\pi$
$12$	−9.08011e11			−0.101839
$13$	−2.36167e13			−1.01367			−0.506837	−	0.862042i	$-0.669185\pi$
$13$	−2.36167e13			−1.01367			−0.506837	+	0.862042i	$0.669185\pi$
$14$		−	3.90839e13i		−	0.689385i
$15$		−	1.55110e13i		−	0.119549i
$16$	−8.77409e13			−0.311718
$17$			4.84231e14i			0.831124i	0.909565	+	0.415562i	$0.136415\pi$
$17$			4.84231e14i			0.831124i	−0.909565	+	0.415562i	$0.863585\pi$
$18$	−8.03439e14			−0.694517
$19$			1.60859e15i			0.726776i	0.931638	+	0.363388i	$0.118380\pi$
$19$			1.60859e15i			0.726776i	−0.931638	+	0.363388i	$0.881620\pi$
$20$			1.05605e15i			0.257825i
$21$		−	1.51172e15i		−	0.205513i
$22$		−	8.52070e15i		−	0.662832i
$23$	4.19846e15	−	2.15087e16i	0.191582	−	0.981477i
$23$	4.19846e15	−	2.15087e16i	0.191582	−	0.981477i
$24$	−8.49594e15			−0.232636
$25$	4.15647e16			0.697341
$26$	−7.05129e16			−0.738905
$27$	−6.36922e16			−0.424347
$28$			1.02924e17i			0.443220i
$29$	−9.26708e16			−0.261919			−0.130959	−	0.991388i	$-0.541806\pi$
$29$	−9.26708e16			−0.261919			−0.130959	+	0.991388i	$0.541806\pi$
$30$		−	4.63117e16i		−	0.0871436i
$31$	4.37102e17			0.554936			0.277468	−	0.960735i	$-0.410505\pi$
$31$	4.37102e17			0.554936			0.277468	+	0.960735i	$0.410505\pi$
$32$	9.72295e17			0.843331
$33$		−	3.29570e17i		−	0.197597i
$34$			1.44578e18i			0.605838i
$35$	−1.75819e18			−0.520294
$36$	2.11578e18			0.446519
$37$			1.54887e18i			0.235285i	0.993056	+	0.117643i	$0.0375337\pi$
$37$			1.54887e18i			0.235285i	−0.993056	+	0.117643i	$0.962466\pi$
$38$			4.80280e18i			0.529775i
$39$	−2.72735e18			−0.220275
$40$			9.88111e18i			0.588960i
$41$	−7.65489e18			−0.339260			−0.169630	−	0.985508i	$-0.554257\pi$
$41$	−7.65489e18			−0.339260			−0.169630	+	0.985508i	$0.554257\pi$
$42$		−	4.51358e18i		−	0.149806i
$43$			2.83655e19i			0.709854i	0.934894	+	0.354927i	$0.115494\pi$
$43$			2.83655e19i			0.709854i	−0.934894	+	0.354927i	$0.884506\pi$
$44$			2.24385e19i			0.426148i
$45$			3.61426e19i			0.524166i
$46$	1.25355e19	−	6.42191e19i	0.139652	−	0.715435i
$47$	4.11080e19			0.353796			0.176898	−	0.984229i	$-0.443394\pi$
$47$	4.11080e19			0.353796			0.176898	+	0.984229i	$0.443394\pi$
$48$	−1.01327e19			−0.0677376
$49$	2.02266e19			0.105577
$50$	1.24101e20			0.508318
$51$			5.59211e19i			0.180607i
$52$	1.85689e20			0.475058
$53$			3.21206e20i			0.653843i	0.945051	+	0.326922i	$0.106011\pi$
$53$			3.21206e20i			0.653843i	−0.945051	+	0.326922i	$0.893989\pi$
$54$	−1.90168e20			−0.309323
$55$	−3.83303e20			−0.500253
$56$			9.63023e20i			1.01247i
$57$			1.85766e20i			0.157932i
$58$	−2.76690e20			−0.190923
$59$	−5.45183e20			−0.306421			−0.153210	−	0.988194i	$-0.548961\pi$
$59$	−5.45183e20			−0.306421			−0.153210	+	0.988194i	$0.548961\pi$
$60$			1.21957e20i			0.0560265i
$61$			2.60916e20i			0.0982977i	0.998791	+	0.0491488i	$0.0156509\pi$
$61$			2.60916e20i			0.0982977i	−0.998791	+	0.0491488i	$0.984349\pi$
$62$	1.30507e21			0.404514
$63$			3.52249e21i			0.901080i
$64$	4.37506e21			0.926454
$65$			3.17202e21i			0.557667i
$66$		−	9.84008e20i		−	0.144036i
$67$		−	1.94453e21i		−	0.237638i	−0.992916	−	0.118819i	$-0.962089\pi$
$67$		−	1.94453e21i		−	0.237638i	0.992916	−	0.118819i	$-0.0379109\pi$
$68$		−	3.80733e21i		−	0.389506i
$69$	4.84856e20	−	2.48392e21i	0.0416316	−	0.213279i
$70$	−5.24947e21			−0.379262
$71$	−1.51878e22			−0.925542			−0.462771	−	0.886478i	$-0.653145\pi$
$71$	−1.51878e22			−0.925542			−0.462771	+	0.886478i	$0.653145\pi$
$72$	1.97966e22			1.02000
$73$	−1.69139e21			−0.0738532			−0.0369266	−	0.999318i	$-0.511757\pi$
$73$	−1.69139e21			−0.0738532			−0.0369266	+	0.999318i	$0.511757\pi$
$74$			4.62451e21i			0.171508i
$75$	4.80008e21			0.151535
$76$		−	1.26477e22i		−	0.340603i
$77$	−3.73571e22			−0.859972
$78$	−8.14314e21			−0.160567
$79$		−	2.50834e22i		−	0.424484i	−0.977217	−	0.212242i	$-0.931924\pi$
$79$		−	2.50834e22i		−	0.424484i	0.977217	−	0.212242i	$-0.0680765\pi$
$80$			1.17847e22i			0.171490i
$81$	6.86443e22			0.860567
$82$	−2.28554e22			−0.247300
$83$			2.83163e22i			0.264911i	0.991189	+	0.132455i	$0.0422862\pi$
$83$			2.83163e22i			0.264911i	−0.991189	+	0.132455i	$0.957714\pi$
$84$			1.18861e22i			0.0963136i
$85$	6.50384e22			0.457239
$86$			8.46918e22i			0.517440i
$87$	−1.07020e22			−0.0569160
$88$			2.09949e23i			0.973467i
$89$			7.63947e22i			0.309302i	0.987969	+	0.154651i	$0.0494253\pi$
$89$			7.63947e22i			0.309302i	−0.987969	+	0.154651i	$0.950575\pi$
$90$			1.07912e23i			0.382085i
$91$			3.09148e23i			0.958671i
$92$	−3.30109e22	+	1.69115e23i	−0.0897850	+	0.459968i
$93$	5.04785e22			0.120590
$94$	1.22738e23			0.257895
$95$	2.16053e23			0.399832
$96$	1.12285e23			0.183259
$97$			7.48901e23i			1.07935i	0.841873	+	0.539676i	$0.181453\pi$
$97$			7.48901e23i			1.07935i	−0.841873	+	0.539676i	$0.818547\pi$
$98$	6.03912e22			0.0769592
$99$			7.67940e23i			0.866373i
$100$	−3.26808e23			−0.326808
$101$	−1.93222e23			−0.171475			−0.0857374	−	0.996318i	$-0.527325\pi$
$101$	−1.93222e23			−0.171475			−0.0857374	+	0.996318i	$0.527325\pi$
$102$			1.66965e23i			0.131651i
$103$			2.55738e24i			1.79369i	0.442340	+	0.896847i	$0.354148\pi$
$103$			2.55738e24i			1.79369i	−0.442340	+	0.896847i	$0.645852\pi$
$104$	1.73743e24			1.08519
$105$	−2.03043e23			−0.113062
$106$			9.59036e23i			0.476611i
$107$			2.19255e24i			0.973519i	0.873536	+	0.486759i	$0.161821\pi$
$107$			2.19255e24i			0.973519i	−0.873536	+	0.486759i	$0.838179\pi$
$108$	5.00788e23			0.198870
$109$			2.96807e24i			1.05525i	0.849477	+	0.527625i	$0.176917\pi$
$109$			2.96807e24i			1.05525i	−0.849477	+	0.527625i	$0.823083\pi$
$110$	−1.14444e24			−0.364653
$111$			1.78870e23i			0.0511284i
$112$			1.14855e24i			0.294804i
$113$		−	1.68978e24i		−	0.389843i	−0.980819	−	0.194922i	$-0.937555\pi$
$113$		−	1.68978e24i		−	0.389843i	0.980819	−	0.194922i	$-0.0624452\pi$
$114$			5.54648e23i			0.115122i
$115$	−2.88889e24	−	5.63906e23i	−0.539954	−	0.105398i
$116$	7.28636e23			0.122748
$117$	6.35507e24			0.965807
$118$	−1.62777e24			−0.223362
$119$	6.33871e24			0.786027
$120$			1.14111e24i			0.127983i
$121$	1.70551e24			0.173153
$122$			7.79026e23i			0.0716529i
$123$	−8.84020e23			−0.0737226
$124$	−3.43678e24			−0.260070
$125$		−	1.35883e25i		−	0.933783i
$126$			1.05172e25i			0.656832i
$127$	−1.96652e25			−1.11700			−0.558500	−	0.829505i	$-0.688623\pi$
$127$	−1.96652e25			−1.11700			−0.558500	+	0.829505i	$0.688623\pi$
$128$	−3.24966e24			−0.168003
$129$			3.27577e24i			0.154254i
$130$			9.47078e24i			0.406505i
$131$	−1.01177e25			−0.396119			−0.198059	−	0.980190i	$-0.563464\pi$
$131$	−1.01177e25			−0.396119			−0.198059	+	0.980190i	$0.563464\pi$
$132$			2.59129e24i			0.0926038i
$133$	2.10568e25			0.687341
$134$		−	5.80583e24i		−	0.173224i
$135$			8.55467e24i			0.233452i
$136$		−	3.56239e25i		−	0.889763i
$137$		−	4.40953e25i		−	1.00866i	−0.863511	−	0.504330i	$-0.831739\pi$
$137$		−	4.40953e25i		−	1.00866i	0.863511	−	0.504330i	$-0.168261\pi$
$138$	1.44765e24	−	7.41630e24i	0.0303469	−	0.155467i
$139$	3.89274e25			0.748303			0.374151	−	0.927368i	$-0.377934\pi$
$139$	3.89274e25			0.748303			0.374151	+	0.927368i	$0.377934\pi$
$140$	1.38240e25			0.243835
$141$	4.74733e24			0.0768813
$142$	−4.53468e25			−0.674662
$143$			6.73974e25i			0.921745i
$144$	2.36104e25			0.296999
$145$			1.24469e25i			0.144093i
$146$	−5.05003e24			−0.0538344
$147$	2.33586e24			0.0229424
$148$		−	1.21782e25i		−	0.110266i
$149$			1.36859e25i			0.114298i	0.998366	+	0.0571488i	$0.0182010\pi$
$149$			1.36859e25i			0.114298i	−0.998366	+	0.0571488i	$0.981799\pi$
$150$	1.43317e25			0.110460
$151$	−1.31507e26			−0.935890			−0.467945	−	0.883758i	$-0.655005\pi$
$151$	−1.31507e26			−0.935890			−0.467945	+	0.883758i	$0.655005\pi$
$152$		−	1.18340e26i		−	0.778054i
$153$		−	1.30303e26i		−	0.791877i
$154$	−1.11538e26			−0.626866
$155$		−	5.87084e25i		−	0.305295i
$156$	2.14442e25			0.103232
$157$		−	4.16986e26i		−	1.85920i	−0.368574	−	0.929598i	$-0.620154\pi$
$157$		−	4.16986e26i		−	1.85920i	0.368574	−	0.929598i	$-0.379846\pi$
$158$		−	7.48922e25i		−	0.309422i
$159$			3.70943e25i			0.142083i
$160$		−	1.30592e26i		−	0.463954i
$161$	−2.81554e26	−	5.49588e25i	−0.928221	−	0.181187i
$162$	2.04953e26			0.627300
$163$	2.03376e26			0.578161			0.289080	−	0.957305i	$-0.406650\pi$
$163$	2.03376e26			0.578161			0.289080	+	0.957305i	$0.406650\pi$
$164$	6.01876e25			0.158994
$165$	−4.42655e25			−0.108707
$166$			8.45449e25i			0.193104i
$167$	−1.85599e26			−0.394437			−0.197219	−	0.980360i	$-0.563191\pi$
$167$	−1.85599e26			−0.394437			−0.197219	+	0.980360i	$0.563191\pi$
$168$			1.11214e26i			0.220013i
$169$	1.49454e25			0.0275339
$170$	1.94187e26			0.333299
$171$		−	4.32859e26i		−	0.692457i
$172$		−	2.23028e26i		−	0.332673i
$173$	4.88942e26			0.680306			0.340153	−	0.940370i	$-0.389521\pi$
$173$	4.88942e26			0.680306			0.340153	+	0.940370i	$0.389521\pi$
$174$	−3.19533e25			−0.0414883
$175$		−	5.44093e26i		−	0.659502i
$176$			2.50396e26i			0.283449i
$177$	−6.29601e25			−0.0665865
$178$			2.28094e26i			0.225462i
$179$	−1.82848e27			−1.68987			−0.844937	−	0.534866i	$-0.820362\pi$
$179$	−1.82848e27			−1.68987			−0.844937	+	0.534866i	$0.820362\pi$
$180$		−	2.84176e26i		−	0.245650i
$181$		−	3.57441e26i		−	0.289109i	−0.989497	−	0.144555i	$-0.953825\pi$
$181$		−	3.57441e26i		−	0.289109i	0.989497	−	0.144555i	$-0.0461749\pi$
$182$			9.23032e26i			0.698812i
$183$			3.01317e25i			0.0213605i
$184$	−3.08872e26	+	1.58235e27i	−0.205099	+	1.05072i
$185$	2.08033e26			0.129441
$186$	1.50715e26			0.0879025
$187$	1.38190e27			0.755751
$188$	−3.23218e26			−0.165806
$189$			8.33747e26i			0.401322i
$190$	6.45077e26			0.291453
$191$			2.40710e27i			1.02116i	0.859830	+	0.510580i	$0.170569\pi$
$191$			2.40710e27i			1.02116i	−0.859830	+	0.510580i	$0.829431\pi$
$192$	5.05250e26			0.201322
$193$	3.16791e27			1.18600			0.593002	−	0.805201i	$-0.297943\pi$
$193$	3.16791e27			1.18600			0.593002	+	0.805201i	$0.297943\pi$
$194$			2.23602e27i			0.786781i
$195$			3.66318e26i			0.121183i
$196$	−1.59034e26			−0.0494787
$197$	4.40882e26			0.129041			0.0645205	−	0.997916i	$-0.479448\pi$
$197$	4.40882e26			0.129041			0.0645205	+	0.997916i	$0.479448\pi$
$198$			2.29286e27i			0.631532i
$199$			1.59204e26i			0.0412779i	0.999787	+	0.0206389i	$0.00657004\pi$
$199$			1.59204e26i			0.0412779i	−0.999787	+	0.0206389i	$0.993430\pi$
$200$	−3.05783e27			−0.746541
$201$		−	2.24562e26i		−	0.0516398i
$202$	−5.76909e26			−0.124995
$203$			1.21308e27i			0.247707i
$204$		−	4.39687e26i		−	0.0846412i
$205$			1.02815e27i			0.186642i
$206$			7.63564e27i			1.30749i
$207$	−1.12977e27	+	5.78784e27i	−0.182536	+	0.935130i
$208$	2.07215e27			0.315980
$209$	4.59059e27			0.660866
$210$	−6.06232e26			−0.0824151
$211$	−3.68492e27			−0.473193			−0.236597	−	0.971608i	$-0.576032\pi$
$211$	−3.68492e27			−0.473193			−0.236597	+	0.971608i	$0.576032\pi$
$212$		−	2.52553e27i		−	0.306423i
$213$	−1.75396e27			−0.201124
$214$			6.54636e27i			0.709635i
$215$	3.80985e27			0.390523
$216$	4.68570e27			0.454286
$217$		−	5.72178e27i		−	0.524825i
$218$			8.86184e27i			0.769212i
$219$	−1.95329e26			−0.0160486
$220$	3.01377e27			0.234443
$221$		−	1.14359e28i		−	0.842488i
$222$			5.34058e26i			0.0372695i
$223$	−6.04925e27			−0.399984			−0.199992	−	0.979798i	$-0.564092\pi$
$223$	−6.04925e27			−0.399984			−0.199992	+	0.979798i	$0.564092\pi$
$224$		−	1.27276e28i		−	0.797571i
$225$	−1.11848e28			−0.664411
$226$		−	5.04524e27i		−	0.284171i
$227$		−	3.28463e28i		−	1.75459i	−0.479950	−	0.877296i	$-0.659345\pi$
$227$		−	3.28463e28i		−	1.75459i	0.479950	−	0.877296i	$-0.340655\pi$
$228$		−	1.46061e27i		−	0.0740145i
$229$		−	2.60730e28i		−	1.25362i	−0.779173	−	0.626809i	$-0.784361\pi$
$229$		−	2.60730e28i		−	1.25362i	0.779173	−	0.626809i	$-0.215639\pi$
$230$	−8.62545e27	−	1.68367e27i	−0.393593	−	0.0768287i
$231$	−4.31416e27			−0.186875
$232$	6.81760e27			0.280398
$233$	−3.05909e28			−1.19487			−0.597435	−	0.801917i	$-0.703813\pi$
$233$	−3.05909e28			−1.19487			−0.597435	+	0.801917i	$0.703813\pi$
$234$	1.89745e28			0.704013
$235$		−	5.52133e27i		−	0.194639i
$236$	4.28658e27			0.143604
$237$		−	2.89674e27i		−	0.0922421i
$238$	1.89257e28			0.572965
$239$	−4.19745e27			−0.120840			−0.0604200	−	0.998173i	$-0.519244\pi$
$239$	−4.19745e27			−0.120840			−0.0604200	+	0.998173i	$0.519244\pi$
$240$			1.36095e27i			0.0372655i
$241$			2.57487e28i			0.670736i	0.942087	+	0.335368i	$0.108861\pi$
$241$			2.57487e28i			0.670736i	−0.942087	+	0.335368i	$0.891139\pi$
$242$	5.09218e27			0.126217
$243$	2.59159e28			0.611352
$244$		−	2.05149e27i		−	0.0460672i
$245$		−	2.71669e27i		−	0.0580827i
$246$	−2.63945e27			−0.0537392
$247$		−	3.79894e28i		−	0.736714i
$248$	−3.21567e28			−0.594089
$249$			3.27009e27i			0.0575662i
$250$		−	4.05711e28i		−	0.680670i
$251$			2.64645e28i			0.423232i	0.977353	+	0.211616i	$0.0678726\pi$
$251$			2.64645e28i			0.423232i	−0.977353	+	0.211616i	$0.932127\pi$
$252$		−	2.76961e28i		−	0.422291i
$253$	−6.13817e28	−	1.19816e28i	−0.892468	−	0.174208i
$254$	−5.87148e28			−0.814223
$255$	7.51092e27			0.0993598
$256$	−8.31039e28			−1.04892
$257$	1.48091e29			1.78374			0.891870	−	0.452291i	$-0.149393\pi$
$257$	1.48091e29			1.78374			0.891870	+	0.452291i	$0.149393\pi$
$258$			9.78057e27i			0.112442i
$259$	2.02751e28			0.222518
$260$		−	2.49404e28i		−	0.261350i
$261$	2.49370e28			0.249551
$262$	−3.02087e28			−0.288746
$263$			1.17020e29i			1.06854i	0.845314	+	0.534270i	$0.179413\pi$
$263$			1.17020e29i			1.06854i	−0.845314	+	0.534270i	$0.820587\pi$
$264$			2.42458e28i			0.211538i
$265$	4.31421e28			0.359709
$266$	6.28699e28			0.501029
$267$			8.82239e27i			0.0672126i
$268$			1.52891e28i			0.111369i
$269$	1.66884e29			1.16248			0.581241	−	0.813731i	$-0.302567\pi$
$269$	1.66884e29			1.16248			0.581241	+	0.813731i	$0.302567\pi$
$270$			2.55419e28i			0.170172i
$271$	−2.33169e29			−1.48607			−0.743034	−	0.669254i	$-0.766614\pi$
$271$	−2.33169e29			−1.48607			−0.743034	+	0.669254i	$0.766614\pi$
$272$		−	4.24869e28i		−	0.259076i
$273$			3.57017e28i			0.208323i
$274$		−	1.31657e29i		−	0.735251i
$275$		−	1.18618e29i		−	0.634100i
$276$	−3.81224e27	+	1.95301e28i	−0.0195106	+	0.0999530i
$277$	−1.54534e29			−0.757296			−0.378648	−	0.925541i	$-0.623611\pi$
$277$	−1.54534e29			−0.757296			−0.378648	+	0.925541i	$0.623611\pi$
$278$	1.16227e29			0.545466
$279$	−1.17621e29			−0.528731
$280$	1.29346e29			0.557003
$281$			1.18571e29i			0.489218i	0.969622	+	0.244609i	$0.0786596\pi$
$281$			1.18571e29i			0.489218i	−0.969622	+	0.244609i	$0.921340\pi$
$282$	1.41743e28			0.0560417
$283$		−	1.19638e29i		−	0.453346i	−0.973971	−	0.226673i	$-0.927215\pi$
$283$		−	1.19638e29i		−	0.453346i	0.973971	−	0.226673i	$-0.0727849\pi$
$284$	1.19416e29			0.433755
$285$	2.49508e28			0.0868852
$286$			2.01230e29i			0.671895i
$287$			1.00204e29i			0.320852i
$288$	−2.61638e29			−0.803508
$289$	1.04969e29			0.309233
$290$			3.71630e28i			0.105035i
$291$			8.64863e28i			0.234548i
$292$	1.32988e28			0.0346113
$293$			6.10198e29i			1.52426i	0.647424	+	0.762130i	$0.275846\pi$
$293$			6.10198e29i			1.52426i	−0.647424	+	0.762130i	$0.724154\pi$
$294$	6.97423e27			0.0167236
$295$			7.32251e28i			0.168576i
$296$		−	1.13947e29i		−	0.251886i
$297$			1.81765e29i			0.385864i
$298$			4.08623e28i			0.0833159i
$299$	−9.91535e28	+	5.07963e29i	−0.194202	+	0.994897i
$300$	−3.77412e28			−0.0710168
$301$	3.71312e29			0.671337
$302$	−3.92644e29			−0.682206
$303$	−2.23141e28			−0.0372622
$304$		−	1.41139e29i		−	0.226549i
$305$	3.50444e28			0.0540780
$306$		−	3.89050e29i		−	0.577230i
$307$	1.06953e30			1.52593			0.762964	−	0.646441i	$-0.223743\pi$
$307$	1.06953e30			1.52593			0.762964	+	0.646441i	$0.223743\pi$
$308$	2.93725e29			0.403025
$309$			2.95337e29i			0.389777i
$310$		−	1.75287e29i		−	0.222541i
$311$	1.13222e29			0.138295			0.0691476	−	0.997606i	$-0.477972\pi$
$311$	1.13222e29			0.138295			0.0691476	+	0.997606i	$0.477972\pi$
$312$	2.00646e29			0.235817
$313$			1.65370e30i			1.87036i	0.354171	+	0.935181i	$0.384763\pi$
$313$			1.65370e30i			1.87036i	−0.354171	+	0.935181i	$0.615237\pi$
$314$		−	1.24501e30i		−	1.35524i
$315$	4.73116e29			0.495725
$316$			1.97222e29i			0.198934i
$317$	−1.64424e30			−1.59682			−0.798409	−	0.602116i	$-0.794325\pi$
$317$	−1.64424e30			−1.59682			−0.798409	+	0.602116i	$0.794325\pi$
$318$			1.10754e29i			0.103570i
$319$			2.64465e29i			0.238166i
$320$		−	5.87626e29i		−	0.509684i
$321$			2.53205e29i			0.211550i
$322$	−8.40645e29	−	1.64092e29i	−0.676615	−	0.132074i
$323$	−7.78927e29			−0.604041
$324$	−5.39725e29			−0.403304
$325$	−9.81620e29			−0.706876
$326$	6.07226e29			0.421443
$327$			3.42765e29i			0.229310i
$328$	5.63155e29			0.363197
$329$		−	5.38115e29i		−	0.334599i
$330$	−1.32165e29			−0.0792407
$331$	2.67835e30			1.54857			0.774286	−	0.632836i	$-0.218109\pi$
$331$	2.67835e30			1.54857			0.774286	+	0.632836i	$0.218109\pi$
$332$		−	2.22641e29i		−	0.124150i
$333$		−	4.16790e29i		−	0.224175i
$334$	−5.54149e29			−0.287520
$335$	−2.61175e29			−0.130735
$336$			1.32639e29i			0.0640622i
$337$		−	3.26029e30i		−	1.51949i	−0.650222	−	0.759745i	$-0.725324\pi$
$337$		−	3.26029e30i		−	1.51949i	0.650222	−	0.759745i	$-0.274676\pi$
$338$	4.46230e28			0.0200705
$339$		−	1.95144e29i		−	0.0847145i
$340$	−5.11373e29			−0.214285
$341$		−	1.24741e30i		−	0.504610i
$342$		−	1.29240e30i		−	0.504758i
$343$		−	2.77262e30i		−	1.04559i
$344$		−	2.08679e30i		−	0.759938i
$345$	−3.33622e29	−	6.51223e28i	−0.117334	−	0.0229034i
$346$	1.45985e30			0.495901
$347$	2.59376e30			0.851092			0.425546	−	0.904937i	$-0.360082\pi$
$347$	2.59376e30			0.851092			0.425546	+	0.904937i	$0.360082\pi$
$348$	8.41461e28			0.0266737
$349$	−3.21703e30			−0.985258			−0.492629	−	0.870239i	$-0.663964\pi$
$349$	−3.21703e30			−0.985258			−0.492629	+	0.870239i	$0.663964\pi$
$350$		−	1.62451e30i		−	0.480736i
$351$	1.50420e30			0.430149
$352$		−	2.77474e30i		−	0.766851i
$353$	−5.16242e30			−1.37898			−0.689488	−	0.724297i	$-0.742164\pi$
$353$	−5.16242e30			−1.37898			−0.689488	+	0.724297i	$0.742164\pi$
$354$	−1.87982e29			−0.0485375
$355$			2.03992e30i			0.509182i
$356$		−	6.00663e29i		−	0.144954i
$357$	7.32021e29			0.170807
$358$	−5.45935e30			−1.23181
$359$			6.72582e30i			1.46761i	0.679358	+	0.733807i	$0.262258\pi$
$359$			6.72582e30i			1.46761i	−0.679358	+	0.733807i	$0.737742\pi$
$360$		−	2.65894e30i		−	0.561149i
$361$	2.31122e30			0.471796
$362$		−	1.06722e30i		−	0.210743i
$363$	1.96959e29			0.0376268
$364$		−	2.43072e30i		−	0.449281i
$365$			2.27175e29i			0.0406300i
$366$			8.99652e28i			0.0155705i
$367$		−	3.27926e30i		−	0.549266i	−0.961549	−	0.274633i	$-0.911444\pi$
$367$		−	3.27926e30i		−	0.549266i	0.961549	−	0.274633i	$-0.0885563\pi$
$368$	−3.68376e29	+	1.88719e30i	−0.0597197	+	0.305944i
$369$	2.05988e30			0.323240
$370$	6.21130e29			0.0943544
$371$	4.20467e30			0.618365
$372$	−3.96894e29			−0.0565144
$373$			2.96291e30i			0.408519i	0.978917	+	0.204260i	$0.0654787\pi$
$373$			2.96291e30i			0.408519i	−0.978917	+	0.204260i	$0.934521\pi$
$374$	4.12599e30			0.550895
$375$		−	1.56924e30i		−	0.202915i
$376$	−3.02423e30			−0.378758
$377$	2.18857e30			0.265500
$378$			2.48934e30i			0.292538i
$379$			1.52919e31i			1.74096i	0.492200	+	0.870482i	$0.336193\pi$
$379$			1.52919e31i			1.74096i	−0.492200	+	0.870482i	$0.663807\pi$
$380$	−1.69875e30			−0.187381
$381$	−2.27102e30			−0.242728
$382$			7.18696e30i			0.744363i
$383$			1.49575e31i			1.50133i	0.660685	+	0.750663i	$0.270266\pi$
$383$			1.49575e31i			1.50133i	−0.660685	+	0.750663i	$0.729734\pi$
$384$	−3.75285e29			−0.0365078
$385$			5.01753e30i			0.473109i
$386$	9.45854e30			0.864523
$387$		−	7.63296e30i		−	0.676334i
$388$		−	5.88833e30i		−	0.505838i
$389$			1.46964e31i			1.22410i	0.790820	+	0.612049i	$0.209654\pi$
$389$			1.46964e31i			1.22410i	−0.790820	+	0.612049i	$0.790346\pi$
$390$			1.09373e30i			0.0883352i
$391$	1.04152e31	+	2.03302e30i	0.815729	+	0.159229i
$392$	−1.48803e30			−0.113026
$393$	−1.16843e30			−0.0860782
$394$	1.31636e30			0.0940629
$395$	−3.36902e30			−0.233528
$396$		−	6.03803e30i		−	0.406025i
$397$	−1.22870e31			−0.801606			−0.400803	−	0.916164i	$-0.631269\pi$
$397$	−1.22870e31			−0.801606			−0.400803	+	0.916164i	$0.631269\pi$
$398$			4.75340e29i			0.0300890i
$399$	2.43173e30			0.149362
$400$	−3.64693e30			−0.217374
$401$			2.37793e31i			1.37552i	0.725938	+	0.687760i	$0.241406\pi$
$401$			2.37793e31i			1.37552i	−0.725938	+	0.687760i	$0.758594\pi$
$402$		−	6.70483e29i		−	0.0376422i
$403$	−1.03229e31			−0.562524
$404$	1.51923e30			0.0803616
$405$		−	9.21981e30i		−	0.473436i
$406$			3.62194e30i			0.180563i
$407$	4.42018e30			0.213948
$408$		−	4.11400e30i		−	0.193349i
$409$	2.27082e31			1.03634			0.518170	−	0.855277i	$-0.326613\pi$
$409$	2.27082e31			1.03634			0.518170	+	0.855277i	$0.326613\pi$
$410$			3.06978e30i			0.136051i
$411$		−	5.09231e30i		−	0.219186i
$412$		−	2.01077e31i		−	0.840614i
$413$			7.13659e30i			0.289794i
$414$	−3.37320e30	+	1.72809e31i	−0.133057	+	0.681652i
$415$	3.80324e30			0.145739
$416$	−2.29623e31			−0.854862
$417$	4.49550e30			0.162609
$418$	1.37063e31			0.481730
$419$		−	1.22238e31i		−	0.417483i	−0.977971	−	0.208741i	$-0.933063\pi$
$419$		−	1.22238e31i		−	0.417483i	0.977971	−	0.208741i	$-0.0669367\pi$
$420$	1.59645e30			0.0529864
$421$		−	6.74716e30i		−	0.217638i	−0.994062	−	0.108819i	$-0.965293\pi$
$421$		−	6.74716e30i		−	0.217638i	0.994062	−	0.108819i	$-0.0347070\pi$
$422$	−1.10022e31			−0.344929
$423$	−1.10619e31			−0.337089
$424$		−	2.36305e31i		−	0.699975i
$425$			2.01269e31i			0.579577i
$426$	−5.23684e30			−0.146607
$427$	3.41546e30			0.0929640
$428$		−	1.72392e31i		−	0.456239i
$429$			7.78334e30i			0.200299i
$430$	1.13752e31			0.284667
$431$		−	4.02874e30i		−	0.0980488i	−0.998798	−	0.0490244i	$-0.984389\pi$
$431$		−	4.02874e30i		−	0.0980488i	0.998798	−	0.0490244i	$-0.0156112\pi$
$432$	5.58841e30			0.132277
$433$		−	2.83639e31i		−	0.652997i	−0.945198	−	0.326498i	$-0.894131\pi$
$433$		−	2.83639e31i		−	0.652997i	0.945198	−	0.326498i	$-0.105869\pi$
$434$		−	1.70837e31i		−	0.382565i
$435$			1.43742e30i			0.0313121i
$436$		−	2.33368e31i		−	0.494543i
$437$	3.45986e31	+	6.75357e30i	0.713314	+	0.139238i
$438$	−5.83199e29			−0.0116984
$439$	−6.10803e31			−1.19214			−0.596070	−	0.802933i	$-0.703272\pi$
$439$	−6.10803e31			−1.19214			−0.596070	+	0.802933i	$0.703272\pi$
$440$	2.81988e31			0.535548
$441$	−5.44284e30			−0.100592
$442$		−	3.41446e31i		−	0.614122i
$443$	−6.08809e31			−1.06570			−0.532851	−	0.846209i	$-0.678880\pi$
$443$	−6.08809e31			−1.06570			−0.532851	+	0.846209i	$0.678880\pi$
$444$		−	1.40639e30i		−	0.0239613i
$445$	1.02608e31			0.170161
$446$	−1.80614e31			−0.291564
$447$			1.58050e30i			0.0248374i
$448$		−	5.72706e31i		−	0.876184i
$449$	5.76703e31			0.859005			0.429503	−	0.903066i	$-0.358689\pi$
$449$	5.76703e31			0.859005			0.429503	+	0.903066i	$0.358689\pi$
$450$	−3.33947e31			−0.484315
$451$			2.18456e31i			0.308493i
$452$			1.32862e31i			0.182700i
$453$	−1.51870e31			−0.203373
$454$		−	9.80702e31i		−	1.27899i
$455$	4.15225e31			0.527408
$456$		−	1.36664e31i		−	0.169074i
$457$			9.01138e31i			1.08592i	0.839759	+	0.542959i	$0.182696\pi$
$457$			9.01138e31i			1.08592i	−0.839759	+	0.542959i	$0.817304\pi$
$458$		−	7.78469e31i		−	0.913810i
$459$		−	3.08418e31i		−	0.352685i
$460$	2.27143e31	+	4.43379e30i	0.253049	+	0.0493947i
$461$	2.91525e31			0.316420			0.158210	−	0.987405i	$-0.449428\pi$
$461$	2.91525e31			0.316420			0.158210	+	0.987405i	$0.449428\pi$
$462$	−1.28809e31			−0.136221
$463$	−8.11738e30			−0.0836458			−0.0418229	−	0.999125i	$-0.513317\pi$
$463$	−8.11738e30			−0.0836458			−0.0418229	+	0.999125i	$0.513317\pi$
$464$	8.13101e30			0.0816449
$465$		−	6.77990e30i		−	0.0663419i
$466$	−9.13360e31			−0.870986
$467$			2.10293e32i			1.95444i	0.212240	+	0.977218i	$0.431924\pi$
$467$			2.10293e32i			1.95444i	−0.212240	+	0.977218i	$0.568076\pi$
$468$	−4.99676e31			−0.452625
$469$	−2.54543e31			−0.224744
$470$		−	1.64852e31i		−	0.141880i
$471$		−	4.81553e31i		−	0.404011i
$472$	4.01080e31			0.328040
$473$	8.09498e31			0.645479
$474$		−	8.64888e30i		−	0.0672388i
$475$			6.68604e31i			0.506811i
$476$	−4.98389e31			−0.368371
$477$		−	8.64344e31i		−	0.622968i
$478$	−1.25324e31			−0.0880848
$479$			3.03109e31i			0.207765i	0.994590	+	0.103883i	$0.0331266\pi$
$479$			3.03109e31i			0.207765i	−0.994590	+	0.103883i	$0.966873\pi$
$480$		−	1.50813e31i		−	0.100819i
$481$		−	3.65791e31i		−	0.238502i
$482$			7.68788e31i			0.488925i
$483$	−3.25151e31	−	6.34688e30i	−0.201706	−	0.0393727i
$484$	−1.34098e31			−0.0811478
$485$	1.00587e32			0.593800
$486$	7.73779e31			0.445637
$487$	1.46668e32			0.824115			0.412057	−	0.911158i	$-0.364810\pi$
$487$	1.46668e32			0.824115			0.412057	+	0.911158i	$0.364810\pi$
$488$		−	1.91951e31i		−	0.105233i
$489$	2.34868e31			0.125637
$490$		−	8.11130e30i		−	0.0423387i
$491$	−2.30564e31			−0.117440			−0.0587198	−	0.998275i	$-0.518702\pi$
$491$	−2.30564e31			−0.117440			−0.0587198	+	0.998275i	$0.518702\pi$
$492$	6.95073e30			0.0345501
$493$		−	4.48741e31i		−	0.217687i
$494$		−	1.13426e32i		−	0.537019i
$495$	1.03144e32			0.476631
$496$	−3.83517e31			−0.172984
$497$			1.98813e32i			0.875321i
$498$			9.76361e30i			0.0419622i
$499$	−3.72367e32			−1.56230			−0.781151	−	0.624342i	$-0.785367\pi$
$499$	−3.72367e32			−1.56230			−0.781151	+	0.624342i	$0.785367\pi$
$500$			1.06840e32i			0.437617i
$501$	−2.14338e31			−0.0857129
$502$			7.90158e31i			0.308510i
$503$			4.83363e32i			1.84271i	0.388721	+	0.921356i	$0.372917\pi$
$503$			4.83363e32i			1.84271i	−0.388721	+	0.921356i	$0.627083\pi$
$504$		−	2.59143e32i		−	0.964656i
$505$			2.59522e31i			0.0943360i
$506$	−1.83269e32	−	3.57738e31i	−0.650554	−	0.126987i
$507$	1.72596e30			0.00598322
$508$	1.54620e32			0.523481
$509$	−2.84051e32			−0.939254			−0.469627	−	0.882865i	$-0.655612\pi$
$509$	−2.84051e32			−0.939254			−0.469627	+	0.882865i	$0.655612\pi$
$510$	2.24256e31			0.0724272
$511$			2.21407e31i			0.0698459i
$512$	−1.93605e32			−0.596593
$513$		−	1.02454e32i		−	0.308405i
$514$	4.42160e32			1.30024
$515$	3.43489e32			0.986792
$516$		−	2.57562e31i		−	0.0722912i
$517$		−	1.17315e32i		−	0.321711i
$518$	6.05360e31			0.162202
$519$	5.64652e31			0.147833
$520$		−	2.33359e32i		−	0.597013i
$521$			6.74758e32i			1.68692i	0.537189	+	0.843462i	$0.319486\pi$
$521$			6.74758e32i			1.68692i	−0.537189	+	0.843462i	$0.680514\pi$
$522$	7.44553e31			0.181907
$523$			3.29526e32i			0.786809i	0.919366	+	0.393404i	$0.128703\pi$
$523$			3.29526e32i			0.786809i	−0.919366	+	0.393404i	$0.871297\pi$
$524$	7.95516e31			0.185641
$525$		−	6.28342e31i		−	0.143313i
$526$			3.49390e32i			0.778899i
$527$			2.11659e32i			0.461221i
$528$			2.89168e31i			0.0615946i
$529$	−4.44997e32	−	1.80607e32i	−0.926592	−	0.376067i
$530$	1.28811e32			0.262205
$531$	1.46705e32			0.291951
$532$	−1.65562e32			−0.322122
$533$	1.80783e32			0.343899
$534$			2.63413e31i			0.0489938i
$535$	2.94487e32			0.535576
$536$			1.43055e32i			0.254405i
$537$	−2.11161e32			−0.367216
$538$	4.98270e32			0.847378
$539$		−	5.77229e31i		−	0.0960025i
$540$		−	6.72622e31i		−	0.109407i
$541$	2.75924e32			0.438957			0.219479	−	0.975617i	$-0.429564\pi$
$541$	2.75924e32			0.438957			0.219479	+	0.975617i	$0.429564\pi$
$542$	−6.96178e32			−1.08325
$543$		−	4.12789e31i		−	0.0628246i
$544$			4.70815e32i			0.700913i
$545$	3.98649e32			0.580541
$546$			1.06596e32i			0.151855i
$547$	−6.05834e32			−0.844318			−0.422159	−	0.906522i	$-0.638728\pi$
$547$	−6.05834e32			−0.844318			−0.422159	+	0.906522i	$0.638728\pi$
$548$			3.46705e32i			0.472708i
$549$		−	7.02107e31i		−	0.0936560i
$550$		−	3.54161e32i		−	0.462219i
$551$		−	1.49069e32i		−	0.190356i
$552$	−3.56698e31	+	1.82737e32i	−0.0445689	+	0.228327i
$553$	−3.28348e32			−0.401451
$554$	−4.61396e32			−0.552022
$555$	2.40246e31			0.0281280
$556$	−3.06072e32			−0.350692
$557$		−	1.51639e33i		−	1.70038i	−0.526472	−	0.850192i	$-0.676486\pi$
$557$		−	1.51639e33i		−	1.70038i	0.526472	−	0.850192i	$-0.323514\pi$
$558$	−3.51185e32			−0.385412
$559$		−	6.69899e32i		−	0.719561i
$560$	1.54265e32			0.162185
$561$	1.59588e32			0.164228
$562$			3.54021e32i			0.356610i
$563$		−	4.42314e32i		−	0.436144i	−0.975933	−	0.218072i	$-0.930023\pi$
$563$		−	4.42314e32i		−	0.436144i	0.975933	−	0.218072i	$-0.0699768\pi$
$564$	−3.73266e31			−0.0360304
$565$	−2.26960e32			−0.214470
$566$		−	3.57205e32i		−	0.330461i
$567$		−	8.98571e32i		−	0.813872i
$568$	1.11734e33			0.990843
$569$		−	1.85447e33i		−	1.61017i	−0.593158	−	0.805086i	$-0.702119\pi$
$569$		−	1.85447e33i		−	1.61017i	0.593158	−	0.805086i	$-0.297881\pi$
$570$	7.44963e31			0.0633339
$571$		−	1.90142e33i		−	1.58287i	−0.611254	−	0.791435i	$-0.709335\pi$
$571$		−	1.90142e33i		−	1.58287i	0.611254	−	0.791435i	$-0.290665\pi$
$572$		−	5.29921e32i		−	0.431975i
$573$			2.77983e32i			0.221902i
$574$			2.99184e32i			0.233881i
$575$	1.74508e32	−	8.94003e32i	0.133598	−	0.684423i
$576$	−1.17730e33			−0.882706
$577$	−4.93175e32			−0.362152			−0.181076	−	0.983469i	$-0.557958\pi$
$577$	−4.93175e32			−0.362152			−0.181076	+	0.983469i	$0.557958\pi$
$578$	3.13408e32			0.225412
$579$	3.65844e32			0.257723
$580$		−	9.78651e31i		−	0.0675293i
$581$	3.70668e32			0.250537
$582$			2.58225e32i			0.170971i
$583$	9.16662e32			0.594547
$584$	1.24432e32			0.0790639
$585$		−	8.53567e32i		−	0.531334i
$586$			1.82189e33i			1.11109i
$587$	−5.95474e32			−0.355799			−0.177900	−	0.984049i	$-0.556930\pi$
$587$	−5.95474e32			−0.355799			−0.177900	+	0.984049i	$0.556930\pi$
$588$	−1.83660e31			−0.0107519
$589$			7.03116e32i			0.403314i
$590$			2.18630e32i			0.122881i
$591$	5.09150e31			0.0280411
$592$		−	1.35899e32i		−	0.0733427i
$593$	−2.33013e31			−0.0123232			−0.00616162	−	0.999981i	$-0.501961\pi$
$593$	−2.33013e31			−0.0123232			−0.00616162	+	0.999981i	$0.501961\pi$
$594$			5.42702e32i			0.281271i
$595$		−	8.51369e32i		−	0.432429i
$596$		−	1.07607e32i		−	0.0535655i
$597$			1.83856e31i			0.00896985i
$598$	−2.96045e32	+	1.51664e33i	−0.141561	+	0.725218i
$599$	−3.21594e33			−1.50725			−0.753626	−	0.657303i	$-0.771697\pi$
$599$	−3.21594e33			−1.50725			−0.753626	+	0.657303i	$0.771697\pi$
$600$	−3.53132e32			−0.162226
$601$	−1.82129e33			−0.820134			−0.410067	−	0.912055i	$-0.634495\pi$
$601$	−1.82129e33			−0.820134			−0.410067	+	0.912055i	$0.634495\pi$
$602$	1.10864e33			0.489363
$603$			5.23259e32i			0.226417i
$604$	1.03399e33			0.438604
$605$		−	2.29071e32i		−	0.0952590i
$606$	−6.66240e31			−0.0271618
$607$	1.14501e33			0.457662			0.228831	−	0.973466i	$-0.426510\pi$
$607$	1.14501e33			0.457662			0.228831	+	0.973466i	$0.426510\pi$
$608$			1.56402e33i			0.612913i
$609$			1.40092e32i			0.0538277i
$610$	1.04633e32			0.0394195
$611$	−9.70834e32			−0.358633
$612$			1.02453e33i			0.371113i
$613$		−	1.54854e33i		−	0.550042i	−0.961438	−	0.275021i	$-0.911315\pi$
$613$		−	1.54854e33i		−	0.550042i	0.961438	−	0.275021i	$-0.0886848\pi$
$614$	3.19334e33			1.11231
$615$			1.18735e32i			0.0405581i
$616$	2.74828e33			0.920646
$617$			9.99137e32i			0.328249i	0.986440	+	0.164124i	$0.0524799\pi$
$617$			9.99137e32i			0.328249i	−0.986440	+	0.164124i	$0.947520\pi$
$618$			8.81797e32i			0.284123i
$619$			2.53128e33i			0.799931i	0.916530	+	0.399965i	$0.130978\pi$
$619$			2.53128e33i			0.799931i	−0.916530	+	0.399965i	$0.869022\pi$
$620$			4.61603e32i			0.143076i
$621$	−2.67409e32	+	1.36994e33i	−0.0812974	+	0.416487i
$622$	3.38051e32			0.100809
$623$	1.00003e33			0.292519
$624$	2.39300e32			0.0686639
$625$	6.52365e32			0.183625
$626$			4.93751e33i			1.36338i
$627$	5.30142e32			0.143609
$628$			3.27861e33i			0.871311i
$629$	−7.50012e32			−0.195551
$630$	1.41260e33			0.361353
$631$		−	4.56230e32i		−	0.114507i	−0.998360	−	0.0572534i	$-0.981766\pi$
$631$		−	4.56230e32i		−	0.114507i	0.998360	−	0.0572534i	$-0.0182343\pi$
$632$			1.84533e33i			0.454433i
$633$	−4.25551e32			−0.102827
$634$	−4.90927e33			−1.16398
$635$			2.64128e33i			0.614511i
$636$		−	2.91659e32i		−	0.0665871i
$637$	−4.77685e32			−0.107021
$638$			7.89620e32i			0.173608i
$639$	4.08694e33			0.881837
$640$			4.36471e32i			0.0924262i
$641$		−	6.62816e33i		−	1.37752i	−0.724992	−	0.688758i	$-0.758156\pi$
$641$		−	6.62816e33i		−	1.37752i	0.724992	−	0.688758i	$-0.241844\pi$
$642$			7.56002e32i			0.154207i
$643$		−	1.02673e33i		−	0.205554i	−0.994704	−	0.102777i	$-0.967227\pi$
$643$		−	1.02673e33i		−	0.205554i	0.994704	−	0.102777i	$-0.0327728\pi$
$644$	2.21376e33	+	4.32121e32i	0.435010	+	0.0849132i
$645$	4.39978e32			0.0848622
$646$	−2.32567e33			−0.440309
$647$	8.19461e32			0.152292			0.0761460	−	0.997097i	$-0.475739\pi$
$647$	8.19461e32			0.152292			0.0761460	+	0.997097i	$0.475739\pi$
$648$	−5.05002e33			−0.921283
$649$			1.55585e33i			0.278632i
$650$	−2.93085e33			−0.515269
$651$		−	6.60776e32i		−	0.114047i
$652$	−1.59907e33			−0.270955
$653$	7.98811e32			0.132888			0.0664440	−	0.997790i	$-0.478835\pi$
$653$	7.98811e32			0.132888			0.0664440	+	0.997790i	$0.478835\pi$
$654$			1.02340e33i			0.167153i
$655$			1.35893e33i			0.217923i
$656$	6.71647e32			0.105754
$657$	4.55141e32			0.0703658
$658$		−	1.60666e33i		−	0.243902i
$659$		−	5.41677e33i		−	0.807449i	−0.914881	−	0.403725i	$-0.867715\pi$
$659$		−	5.41677e33i		−	0.807449i	0.914881	−	0.403725i	$-0.132285\pi$
$660$	3.48043e32			0.0509455
$661$			8.39803e33i			1.20715i	0.797308	+	0.603573i	$0.206257\pi$
$661$			8.39803e33i			1.20715i	−0.797308	+	0.603573i	$0.793743\pi$
$662$	7.99682e33			1.12881
$663$		−	1.32067e33i		−	0.183076i
$664$		−	2.08317e33i		−	0.283602i
$665$		−	2.82819e33i		−	0.378137i
$666$		−	1.24442e33i		−	0.163409i
$667$	−3.89074e32	+	1.99323e33i	−0.0501790	+	0.257067i
$668$	1.45930e33			0.184853
$669$	−6.98593e32			−0.0869182
$670$	−7.79797e32			−0.0952981
$671$	7.44605e32			0.0893832
$672$		−	1.46984e33i		−	0.173316i
$673$	−4.47278e33			−0.518080			−0.259040	−	0.965867i	$-0.583406\pi$
$673$	−4.47278e33			−0.518080			−0.259040	+	0.965867i	$0.583406\pi$
$674$		−	9.73435e33i		−	1.10761i
$675$	−2.64735e33			−0.295914
$676$	−1.17510e32			−0.0129037
$677$		−	1.38087e32i		−	0.0148966i	−0.999972	−	0.00744832i	$-0.997629\pi$
$677$		−	1.38087e32i		−	0.0148966i	0.999972	−	0.00744832i	$-0.00237090\pi$
$678$		−	5.82646e32i		−	0.0617516i
$679$	9.80330e33			1.02079
$680$	−4.78474e33			−0.489499
$681$		−	3.79323e33i		−	0.381280i
$682$		−	3.72442e33i		−	0.367829i
$683$	−9.96674e33			−0.967174			−0.483587	−	0.875296i	$-0.660666\pi$
$683$	−9.96674e33			−0.967174			−0.483587	+	0.875296i	$0.660666\pi$
$684$			3.40341e33i			0.324520i
$685$	−5.92255e33			−0.554910
$686$		−	8.27829e33i		−	0.762169i
$687$		−	3.01102e33i		−	0.272416i
$688$		−	2.48882e33i		−	0.221275i
$689$		−	7.58582e33i		−	0.662784i
$690$	−9.96104e32	−	1.94438e32i	−0.0855294	−	0.0166952i
$691$	6.39593e33			0.539719			0.269859	−	0.962900i	$-0.413023\pi$
$691$	6.39593e33			0.539719			0.269859	+	0.962900i	$0.413023\pi$
$692$	−3.84438e33			−0.318825
$693$	1.00525e34			0.819363
$694$	7.74428e33			0.620393
$695$		−	5.22844e33i		−	0.411675i
$696$	7.87325e32			0.0609317
$697$		−	3.70674e33i		−	0.281967i
$698$	−9.60518e33			−0.718192
$699$	−3.53276e33			−0.259650
$700$			4.27800e33i			0.309075i
$701$		−	8.55870e33i		−	0.607843i	−0.952697	−	0.303922i	$-0.901704\pi$
$701$		−	8.55870e33i		−	0.607843i	0.952697	−	0.303922i	$-0.0982961\pi$
$702$	4.49112e33			0.313552
$703$	−2.49149e33			−0.171000
$704$		−	1.24856e34i		−	0.842436i
$705$		−	6.37627e32i		−	0.0422958i
$706$	−1.54136e34			−1.00519
$707$			2.52933e33i			0.162170i
$708$	4.95032e32			0.0312057
$709$			2.50283e34i			1.55123i	0.631205	+	0.775616i	$0.282561\pi$
$709$			2.50283e34i			1.55123i	−0.631205	+	0.775616i	$0.717439\pi$
$710$			6.09065e33i			0.371162i
$711$			6.74976e33i			0.404439i
$712$		−	5.62020e33i		−	0.331125i
$713$	1.83516e33	−	9.40150e33i	0.106316	−	0.544657i
$714$	2.18562e33			0.124508
$715$	9.05233e33			0.507093
$716$	1.43767e34			0.791958
$717$	−4.84739e32			−0.0262590
$718$			2.00815e34i			1.06980i
$719$	−3.55940e34			−1.86479			−0.932395	−	0.361440i	$-0.882285\pi$
$719$	−3.55940e34			−1.86479			−0.932395	+	0.361440i	$0.882285\pi$
$720$		−	3.17118e33i		−	0.163392i
$721$	3.34767e34			1.69637
$722$	6.90067e33			0.343910
$723$			2.97358e33i			0.145754i
$724$			2.81043e33i			0.135491i
$725$	−3.85184e33			−0.182647
$726$	5.88067e32			0.0274276
$727$			1.56376e34i			0.717394i	0.933454	+	0.358697i	$0.116779\pi$
$727$			1.56376e34i			0.717394i	−0.933454	+	0.358697i	$0.883221\pi$
$728$		−	2.27434e34i		−	1.02631i
$729$	−1.63943e34			−0.727717
$730$			6.78283e32i			0.0296167i
$731$	−1.37355e34			−0.589977
$732$		−	2.36915e32i		−	0.0100106i
$733$			7.92372e33i			0.329368i	0.986346	+	0.164684i	$0.0526604\pi$
$733$			7.92372e33i			0.329368i	−0.986346	+	0.164684i	$0.947340\pi$
$734$		−	9.79097e33i		−	0.400381i
$735$		−	3.13735e32i		−	0.0126216i
$736$	4.08214e33	−	2.09128e34i	0.161567	−	0.827710i
$737$	−5.54931e33			−0.216087
$738$	6.15024e33			0.235622
$739$	−7.28462e32			−0.0274583			−0.0137291	−	0.999906i	$-0.504370\pi$
$739$	−7.28462e32			−0.0274583			−0.0137291	+	0.999906i	$0.504370\pi$
$740$	−1.63569e33			−0.0606624
$741$		−	4.38718e33i		−	0.160091i
$742$	1.25540e34			0.450750
$743$		−	1.13824e34i		−	0.402132i	−0.979578	−	0.201066i	$-0.935559\pi$
$743$		−	1.13824e34i		−	0.402132i	0.979578	−	0.201066i	$-0.0644405\pi$
$744$	−3.71360e33			−0.129098
$745$	1.83819e33			0.0628803
$746$			8.84645e33i			0.297785i
$747$		−	7.61972e33i		−	0.252402i
$748$	−1.08654e34			−0.354182
$749$	2.87010e34			0.920695
$750$		−	4.68533e33i		−	0.147912i
$751$			2.62152e34i			0.814467i	0.913324	+	0.407233i	$0.133506\pi$
$751$			2.62152e34i			0.814467i	−0.913324	+	0.407233i	$0.866494\pi$
$752$	−3.60686e33			−0.110285
$753$			3.05623e33i			0.0919701i
$754$	6.53449e33			0.193533
$755$			1.76630e34i			0.514875i
$756$		−	6.55544e33i		−	0.188079i
$757$			3.92878e34i			1.10945i	0.832034	+	0.554724i	$0.187176\pi$
$757$			3.92878e34i			1.10945i	−0.832034	+	0.554724i	$0.812824\pi$
$758$			4.56574e34i			1.26906i
$759$	−7.08862e33	−	1.38369e33i	−0.193937	−	0.0378561i
$760$	−1.58946e34			−0.428042
$761$	6.08698e33			0.161356			0.0806782	−	0.996740i	$-0.474291\pi$
$761$	6.08698e33			0.161356			0.0806782	+	0.996740i	$0.474291\pi$
$762$	−6.78064e33			−0.176934
$763$	3.88527e34			0.997992
$764$		−	1.89262e34i		−	0.478566i
$765$	−1.75014e34			−0.435647
$766$			4.46592e34i			1.09437i
$767$	1.28754e34			0.310611
$768$	−9.59719e33			−0.227934
$769$		−	3.09123e34i		−	0.722795i	−0.932412	−	0.361398i	$-0.882300\pi$
$769$		−	3.09123e34i		−	0.722795i	0.932412	−	0.361398i	$-0.117700\pi$
$770$			1.49810e34i			0.344867i
$771$	1.71022e34			0.387614
$772$	−2.49082e34			−0.555820
$773$		−	4.70294e33i		−	0.103327i	−0.998665	−	0.0516637i	$-0.983548\pi$
$773$		−	4.70294e33i		−	0.103327i	0.998665	−	0.0516637i	$-0.0164524\pi$
$774$		−	2.27900e34i		−	0.493006i
$775$	1.81680e34			0.386979
$776$		−	5.50951e34i		−	1.15551i
$777$	2.34146e33			0.0483542
$778$			4.38795e34i			0.892291i
$779$		−	1.23135e34i		−	0.246566i
$780$		−	2.88023e33i		−	0.0567925i
$781$			4.33432e34i			0.841606i
$782$	3.10969e34	+	6.07006e33i	0.594616	+	0.116068i
$783$	5.90240e33			0.111144
$784$	−1.77470e33			−0.0329103
$785$	−5.60065e34			−1.02283
$786$	−3.48863e33			−0.0627457
$787$			3.63159e34i			0.643280i	0.946862	+	0.321640i	$0.104234\pi$
$787$			3.63159e34i			0.643280i	−0.946862	+	0.321640i	$0.895766\pi$
$788$	−3.46650e33			−0.0604750
$789$			1.35140e34i			0.232198i
$790$	−1.00590e34			−0.170227
$791$	−2.21197e34			−0.368690
$792$		−	5.64957e34i		−	0.927499i
$793$		−	6.16197e33i		−	0.0996417i
$794$	−3.66858e34			−0.584321
$795$	4.98224e33			0.0781662
$796$		−	1.25176e33i		−	0.0193448i
$797$			1.02305e35i			1.55739i	0.627401	+	0.778696i	$0.284119\pi$
$797$			1.02305e35i			1.55739i	−0.627401	+	0.778696i	$0.715881\pi$
$798$	7.26048e33			0.108876
$799$			1.99058e34i			0.294048i
$800$	4.04132e34			0.588089
$801$		−	2.05573e34i		−	0.294697i
$802$			7.09986e34i			1.00267i
$803$			4.82690e33i			0.0671556i
$804$			1.76565e33i			0.0242010i
$805$	−7.38167e33	+	3.78163e34i	−0.0996791	+	0.510656i
$806$	−3.08214e34			−0.410045
$807$	1.92724e34			0.252612
$808$	1.42150e34			0.183573
$809$	1.13639e35			1.44592			0.722962	−	0.690888i	$-0.242780\pi$
$809$	1.13639e35			1.44592			0.722962	+	0.690888i	$0.242780\pi$
$810$		−	2.75279e34i		−	0.345106i
$811$	1.09882e35			1.35730			0.678649	−	0.734463i	$-0.262566\pi$
$811$	1.09882e35			1.35730			0.678649	+	0.734463i	$0.262566\pi$
$812$		−	9.53803e33i		−	0.116088i
$813$	−2.69273e34			−0.322929
$814$	1.31975e34			0.155954
$815$		−	2.73160e34i		−	0.318072i
$816$		−	4.90657e33i		−	0.0562984i
$817$	−4.56284e34			−0.515905
$818$	6.78005e34			0.755428
$819$		−	8.31895e34i		−	0.913401i
$820$		−	8.08396e33i		−	0.0874698i
$821$	2.92607e34			0.312008			0.156004	−	0.987756i	$-0.450139\pi$
$821$	2.92607e34			0.312008			0.156004	+	0.987756i	$0.450139\pi$
$822$		−	1.52043e34i		−	0.159773i
$823$	−1.65767e35			−1.71672			−0.858362	−	0.513044i	$-0.828518\pi$
$823$	−1.65767e35			−1.71672			−0.858362	+	0.513044i	$0.828518\pi$
$824$		−	1.88141e35i		−	1.92025i
$825$		−	1.36985e34i		−	0.137793i
$826$			2.13079e34i			0.211242i
$827$		−	6.77123e34i		−	0.661609i	−0.943699	−	0.330805i	$-0.892680\pi$
$827$		−	6.77123e34i		−	0.661609i	0.943699	−	0.330805i	$-0.107320\pi$
$828$	8.88300e33	−	4.55076e34i	0.0855452	−	0.438248i
$829$	−1.12109e35			−1.06411			−0.532055	−	0.846710i	$-0.678580\pi$
$829$	−1.12109e35			−1.06411			−0.532055	+	0.846710i	$0.678580\pi$
$830$	1.13555e34			0.106235
$831$	−1.78462e34			−0.164564
$832$	−1.03324e35			−0.939122
$833$			9.79436e33i			0.0877477i
$834$	1.34223e34			0.118532
$835$			2.49283e34i			0.216998i
$836$	−3.60942e34			−0.309715
$837$	−2.78400e34			−0.235485
$838$		−	3.64970e34i		−	0.304319i
$839$		−	5.78484e34i		−	0.475497i	−0.971327	−	0.237748i	$-0.923591\pi$
$839$		−	5.78484e34i		−	0.475497i	0.971327	−	0.237748i	$-0.0764094\pi$
$840$	1.49375e34			0.121039
$841$	−1.16597e35			−0.931399
$842$		−	2.01452e34i		−	0.158645i
$843$			1.36931e34i			0.106309i
$844$	2.89732e34			0.221762
$845$		−	2.00736e33i		−	0.0151476i
$846$	−3.30278e34			−0.245717
$847$		−	2.23255e34i		−	0.163757i
$848$		−	2.81829e34i		−	0.203815i
$849$		−	1.38163e34i		−	0.0985140i
$850$			6.00936e34i			0.422475i
$851$	3.33142e34	+	6.50287e33i	0.230927	+	0.0450765i
$852$	1.37907e34			0.0942567
$853$	2.64121e35			1.77998			0.889988	−	0.455984i	$-0.150713\pi$
$853$	2.64121e35			1.77998			0.889988	+	0.455984i	$0.150713\pi$
$854$	1.01976e34			0.0677650
$855$	−5.81384e34			−0.380952
$856$		−	1.61301e35i		−	1.04220i
$857$	1.59956e35			1.01913			0.509566	−	0.860432i	$-0.329806\pi$
$857$	1.59956e35			1.01913			0.509566	+	0.860432i	$0.329806\pi$
$858$			2.32390e34i			0.146006i
$859$	7.71785e34			0.478166			0.239083	−	0.970999i	$-0.423153\pi$
$859$	7.71785e34			0.478166			0.239083	+	0.970999i	$0.423153\pi$
$860$	−2.99555e34			−0.183018
$861$			1.15720e34i			0.0697224i
$862$		−	1.20287e34i		−	0.0714715i
$863$	−9.18991e34			−0.538495			−0.269247	−	0.963071i	$-0.586775\pi$
$863$	−9.18991e34			−0.538495			−0.269247	+	0.963071i	$0.586775\pi$
$864$	−6.19276e34			−0.357865
$865$		−	6.56712e34i		−	0.374267i
$866$		−	8.46869e34i		−	0.475994i
$867$	1.21222e34			0.0671976
$868$			4.49883e34i			0.245959i
$869$	−7.15832e34			−0.385988
$870$			4.29174e33i			0.0228246i
$871$			4.59232e34i			0.240888i
$872$		−	2.18355e35i		−	1.12970i
$873$		−	2.01524e35i		−	1.02838i
$874$	1.03302e35	+	2.01643e34i	0.519962	+	0.101496i
$875$	−1.77875e35			−0.883116
$876$	1.53580e33			0.00752117
$877$	1.46869e35			0.709470			0.354735	−	0.934967i	$-0.384571\pi$
$877$	1.46869e35			0.709470			0.354735	+	0.934967i	$0.384571\pi$
$878$	−1.82369e35			−0.868995
$879$			7.04683e34i			0.331228i
$880$	3.36313e34			0.155938
$881$			1.25849e35i			0.575626i	0.957687	+	0.287813i	$0.0929281\pi$
$881$			1.25849e35i			0.575626i	−0.957687	+	0.287813i	$0.907072\pi$
$882$	−1.62508e34			−0.0733251
$883$	2.90903e35			1.29485			0.647426	−	0.762128i	$-0.275845\pi$
$883$	2.90903e35			1.29485			0.647426	+	0.762128i	$0.275845\pi$
$884$			8.99165e34i			0.394832i
$885$			8.45635e33i			0.0366322i
$886$	−1.81774e35			−0.776831
$887$	−2.47889e35			−1.04514			−0.522570	−	0.852596i	$-0.675027\pi$
$887$	−2.47889e35			−1.04514			−0.522570	+	0.852596i	$0.675027\pi$
$888$		−	1.31591e34i		−	0.0547358i
$889$			2.57422e35i			1.05639i
$890$	3.06359e34			0.124037
$891$		−	1.95898e35i		−	0.782523i
$892$	4.75630e34			0.187452
$893$			6.61258e34i			0.257130i
$894$			4.71896e33i			0.0181049i
$895$			2.45588e35i			0.929675i
$896$			4.25389e34i			0.158887i
$897$	−1.14507e34	+	5.86618e34i	−0.0422009	+	0.216195i
$898$	1.72188e35			0.626161
$899$	−4.05066e34			−0.145348
$900$	8.79418e34			0.311376
$901$	−1.55538e35			−0.543425
$902$			6.52251e34i			0.224872i
$903$	4.28807e34			0.145884
$904$			1.24314e35i			0.417348i
$905$	−4.80089e34			−0.159052
$906$	−4.53442e34			−0.148246
$907$			4.19613e35i			1.35382i	0.736065	+	0.676911i	$0.236682\pi$
$907$			4.19613e35i			1.35382i	−0.736065	+	0.676911i	$0.763318\pi$
$908$			2.58258e35i			0.822289i
$909$	5.19947e34			0.163378
$910$	1.23975e35			0.384448
$911$			4.24501e35i			1.29915i	0.760298	+	0.649574i	$0.225053\pi$
$911$			4.24501e35i			1.29915i	−0.760298	+	0.649574i	$0.774947\pi$
$912$		−	1.62993e34i		−	0.0492301i
$913$	8.08094e34			0.240887
$914$			2.69056e35i			0.791567i
$915$	4.04708e33			0.0117514
$916$			2.05002e35i			0.587507i
$917$			1.32443e35i			0.374625i
$918$		−	9.20851e34i		−	0.257085i
$919$			9.13988e34i			0.251857i	0.992039	+	0.125929i	$0.0401910\pi$
$919$			9.13988e34i			0.251857i	−0.992039	+	0.125929i	$0.959809\pi$
$920$	2.12530e35	+	4.14854e34i	0.578050	+	0.112834i
$921$	1.23514e35			0.331591
$922$	8.70414e34			0.230651
$923$	3.58686e35			0.938197
$924$	3.39206e34			0.0875790
$925$			6.43784e34i			0.164074i
$926$	−2.42363e34			−0.0609726
$927$		−	6.88173e35i		−	1.70899i
$928$	−9.01033e34			−0.220884
$929$	−3.75255e35			−0.908109			−0.454055	−	0.890974i	$-0.650023\pi$
$929$	−3.75255e35			−0.908109			−0.454055	+	0.890974i	$0.650023\pi$
$930$		−	2.02430e34i		−	0.0483591i
$931$			3.25362e34i			0.0767310i
$932$	2.40525e35			0.559975
$933$	1.30754e34			0.0300521
$934$			6.27877e35i			1.42466i
$935$		−	1.85607e35i		−	0.415772i
$936$	−4.67530e35			−1.03395
$937$		−	1.27006e35i		−	0.277301i	−0.990341	−	0.138650i	$-0.955724\pi$
$937$		−	1.27006e35i		−	0.277301i	0.990341	−	0.138650i	$-0.0442764\pi$
$938$	−7.59998e34			−0.163824
$939$			1.90977e35i			0.406437i
$940$			4.34122e34i			0.0912174i
$941$		−	6.73327e35i		−	1.39685i	−0.715682	−	0.698426i	$-0.753884\pi$
$941$		−	6.73327e35i		−	1.39685i	0.715682	−	0.698426i	$-0.246116\pi$
$942$		−	1.43779e35i		−	0.294499i
$943$	−3.21387e34	+	1.64647e35i	−0.0649963	+	0.332976i
$944$	4.78349e34			0.0955170
$945$	1.11983e35			0.220785
$946$	2.41694e35			0.470514
$947$	4.23978e35			0.814974			0.407487	−	0.913211i	$-0.366405\pi$
$947$	4.23978e35			0.814974			0.407487	+	0.913211i	$0.366405\pi$
$948$			2.27760e34i			0.0432292i
$949$	3.99450e34			0.0748630
$950$			1.99627e35i			0.369434i
$951$	−1.89884e35			−0.346995
$952$	−4.66326e35			−0.841484
$953$			2.42884e35i			0.432797i	0.976305	+	0.216399i	$0.0694311\pi$
$953$			2.42884e35i			0.432797i	−0.976305	+	0.216399i	$0.930569\pi$
$954$		−	2.58070e35i		−	0.454105i
$955$	3.23304e35			0.561786
$956$	3.30030e34			0.0566316
$957$			3.05415e34i			0.0517544i
$958$			9.05002e34i			0.151448i
$959$	−5.77218e35			−0.953930
$960$		−	6.78616e34i		−	0.110756i
$961$	−4.29354e35			−0.692046
$962$		−	1.09215e35i		−	0.173853i
$963$		−	5.90000e35i		−	0.927548i
$964$		−	2.02453e35i		−	0.314340i
$965$		−	4.25491e35i		−	0.652473i
$966$	−9.70813e34	−	1.89501e34i	−0.147031	−	0.0287002i
$967$	−6.09546e35			−0.911777			−0.455889	−	0.890037i	$-0.650678\pi$
$967$	−6.09546e35			−0.911777			−0.455889	+	0.890037i	$0.650678\pi$
$968$	−1.25471e35			−0.185369
$969$	−8.99539e34			−0.131261
$970$	3.00325e35			0.432844
$971$		−	1.15097e36i		−	1.63844i	−0.573477	−	0.819222i	$-0.694406\pi$
$971$		−	1.15097e36i		−	1.63844i	0.573477	−	0.819222i	$-0.305594\pi$
$972$	−2.03767e35			−0.286510
$973$		−	5.09569e35i		−	0.707699i
$974$	4.37911e35			0.600728
$975$	−1.13362e35			−0.153607
$976$		−	2.28930e34i		−	0.0306412i
$977$		−	6.38407e35i		−	0.844040i	−0.906587	−	0.422020i	$-0.861321\pi$
$977$		−	6.38407e35i		−	0.844040i	0.906587	−	0.422020i	$-0.138679\pi$
$978$	7.01251e34			0.0915814
$979$	2.18016e35			0.281252
$980$			2.13603e34i			0.0272204i
$981$		−	7.98686e35i		−	1.00542i
$982$	−6.88403e34			−0.0856062
$983$		−	4.07154e35i		−	0.500168i	−0.968224	−	0.250084i	$-0.919542\pi$
$983$		−	4.07154e35i		−	0.500168i	0.968224	−	0.250084i	$-0.0804583\pi$
$984$	6.50355e34			0.0789241
$985$		−	5.92161e34i		−	0.0709913i
$986$		−	1.33982e35i		−	0.158680i
$987$		−	6.21438e34i		−	0.0727096i
$988$			2.98697e35i			0.345261i
$989$	6.10105e35	+	1.19091e35i	0.696705	+	0.135996i
$990$	3.07960e35			0.347434
$991$	3.02452e35			0.337110			0.168555	−	0.985692i	$-0.446090\pi$
$991$	3.02452e35			0.337110			0.168555	+	0.985692i	$0.446090\pi$
$992$	4.24992e35			0.467995
$993$	3.09307e35			0.336511
$994$			5.93601e35i			0.638055i
$995$	2.13831e34			0.0227088
$996$		−	2.57115e34i		−	0.0269784i
$997$	−1.01108e36			−1.04820			−0.524098	−	0.851658i	$-0.675597\pi$
$997$	−1.01108e36			−1.04820			−0.524098	+	0.851658i	$0.675597\pi$
$998$	−1.11179e36			−1.13882
$999$		−	9.86510e34i		−	0.0998425i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	23.25.b.c.22.31	✓	44
23.22	odd	2	inner	23.25.b.c.22.32	yes	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
23.25.b.c.22.31	✓	44	1.1	even	1	trivial
23.25.b.c.22.32	yes	44	23.22	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 23 \)
Weight:	\( k \)	\(=\)	\( 25 \)
Character orbit:	\([\chi]\)	\(=\)	23.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+2985.73 q^{2} +115484. q^{3} -7.86263e6 q^{4} -1.34313e8i q^{5} +3.44805e8 q^{6} -1.30902e10i q^{7} -7.35679e10 q^{8} -2.69093e11 q^{9} -4.01021e11i q^{10} -2.85381e12i q^{11} -9.08011e11 q^{12} -2.36167e13 q^{13} -3.90839e13i q^{14} -1.55110e13i q^{15} -8.77409e13 q^{16} +4.84231e14i q^{17} -8.03439e14 q^{18} +1.60859e15i q^{19} +1.05605e15i q^{20} -1.51172e15i q^{21} -8.52070e15i q^{22} +(4.19846e15 - 2.15087e16i) q^{23} -8.49594e15 q^{24} +4.15647e16 q^{25} -7.05129e16 q^{26} -6.36922e16 q^{27} +1.02924e17i q^{28} -9.26708e16 q^{29} -4.63117e16i q^{30} +4.37102e17 q^{31} +9.72295e17 q^{32} -3.29570e17i q^{33} +1.44578e18i q^{34} -1.75819e18 q^{35} +2.11578e18 q^{36} +1.54887e18i q^{37} +4.80280e18i q^{38} -2.72735e18 q^{39} +9.88111e18i q^{40} -7.65489e18 q^{41} -4.51358e18i q^{42} +2.83655e19i q^{43} +2.24385e19i q^{44} +3.61426e19i q^{45} +(1.25355e19 - 6.42191e19i) q^{46} +4.11080e19 q^{47} -1.01327e19 q^{48} +2.02266e19 q^{49} +1.24101e20 q^{50} +5.59211e19i q^{51} +1.85689e20 q^{52} +3.21206e20i q^{53} -1.90168e20 q^{54} -3.83303e20 q^{55} +9.63023e20i q^{56} +1.85766e20i q^{57} -2.76690e20 q^{58} -5.45183e20 q^{59} +1.21957e20i q^{60} +2.60916e20i q^{61} +1.30507e21 q^{62} +3.52249e21i q^{63} +4.37506e21 q^{64} +3.17202e21i q^{65} -9.84008e20i q^{66} -1.94453e21i q^{67} -3.80733e21i q^{68} +(4.84856e20 - 2.48392e21i) q^{69} -5.24947e21 q^{70} -1.51878e22 q^{71} +1.97966e22 q^{72} -1.69139e21 q^{73} +4.62451e21i q^{74} +4.80008e21 q^{75} -1.26477e22i q^{76} -3.73571e22 q^{77} -8.14314e21 q^{78} -2.50834e22i q^{79} +1.17847e22i q^{80} +6.86443e22 q^{81} -2.28554e22 q^{82} +2.83163e22i q^{83} +1.18861e22i q^{84} +6.50384e22 q^{85} +8.46918e22i q^{86} -1.07020e22 q^{87} +2.09949e23i q^{88} +7.63947e22i q^{89} +1.07912e23i q^{90} +3.09148e23i q^{91} +(-3.30109e22 + 1.69115e23i) q^{92} +5.04785e22 q^{93} +1.22738e23 q^{94} +2.16053e23 q^{95} +1.12285e23 q^{96} +7.48901e23i q^{97} +6.03912e22 q^{98} +7.67940e23i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q - 4232 q^{2} - 434562 q^{3} + 317760360 q^{4} - 8460029520 q^{6} - 198307023760 q^{8} + 4220041988298 q^{9} - 67439597688792 q^{12} + 5771152551358 q^{13} + 18\!\cdots\!92 q^{16} + 18\!\cdots\!68 q^{18}+ \cdots - 20\!\cdots\!92 q^{98}+O(q^{100}) \) 44 * q - 4232 * q^2 - 434562 * q^3 + 317760360 * q^4 - 8460029520 * q^6 - 198307023760 * q^8 + 4220041988298 * q^9 - 67439597688792 * q^12 + 5771152551358 * q^13 + 1801550792530192 * q^16 + 1842830558165568 * q^18 - 117204213263210644 * q^23 - 186493005437450784 * q^24 - 689533084157602612 * q^25 - 548650296251047576 * q^26 + 824037505793640630 * q^27 - 1583078054945709602 * q^29 - 77249813729122274 * q^31 - 2838716832733708512 * q^32 + 3418569899175948192 * q^35 + 71181245116739335248 * q^36 + 47106572467817156310 * q^39 - 9150679195666184738 * q^41 - 153049487518536134480 * q^46 + 22735751396127769438 * q^47 - 1317482931964495330032 * q^48 - 1842110772006482246836 * q^49 + 284936617115007894520 * q^50 + 207129175371045152568 * q^52 - 381774025126375304544 * q^54 - 5430040696094013021792 * q^55 - 2168901871328366220760 * q^58 + 16048018791948427185304 * q^59 + 14054450375064171442400 * q^62 + 20310379126091866412192 * q^64 + 24476879859710435470878 * q^69 - 118028399895318845638416 * q^70 - 68204988047209908888578 * q^71 - 106777935582637627887744 * q^72 - 7319375899831086678722 * q^73 + 12913295383070041819998 * q^75 + 111116199573084838704480 * q^77 - 422583593213386075404144 * q^78 - 331350288185757013618680 * q^81 + 1000764218021118649437320 * q^82 - 113385735487939722862944 * q^85 - 248828610584854760185290 * q^87 - 4238455111972177116774696 * q^92 + 4492289396741153284965270 * q^93 - 1602622056539190351258592 * q^94 - 1668692394291208047471936 * q^95 - 12092663288748189077973504 * q^96 - 2067304853876486831513192 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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