LMFDB - Embedded newform 483.2.h.a.160.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [483,2,Mod(160,483)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(483, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("483.160");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 483 = 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	483.h (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$3.85677441763$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.0.342102016.5
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + x^{6} + 4x^{4} + 4x^{2} + 16 $ x^8 + x^6 + 4x^4 + 4x^2 + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{23}]$
Coefficient ring index:	$ 2^{3} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			160.1
Root			$-0.599676 - 1.28078i$ of defining polynomial
Character	$\chi$	$=$	483.160
Dual form			483.2.h.a.160.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -1.00000i q^{3} -1.00000 q^{4} -3.33513 q^{5} +1.00000i q^{6} +(-2.60399 + 0.468213i) q^{7} +3.00000 q^{8} -1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.00000i q^{3} -1.00000 q^{4} -3.33513 q^{5} +1.00000i q^{6} +(-2.60399 + 0.468213i) q^{7} +3.00000 q^{8} -1.00000 q^{9} +3.33513 q^{10} -4.27156i q^{11} +1.00000i q^{12} +3.12311i q^{13} +(2.60399 - 0.468213i) q^{14} +3.33513i q^{15} -1.00000 q^{16} +3.33513 q^{17} +1.00000 q^{18} -1.46228 q^{19} +3.33513 q^{20} +(0.468213 + 2.60399i) q^{21} +4.27156i q^{22} +(1.56155 + 4.53448i) q^{23} -3.00000i q^{24} +6.12311 q^{25} -3.12311i q^{26} +1.00000i q^{27} +(2.60399 - 0.468213i) q^{28} +8.24621 q^{29} -3.33513i q^{30} +10.2462i q^{31} -5.00000 q^{32} -4.27156 q^{33} -3.33513 q^{34} +(8.68466 - 1.56155i) q^{35} +1.00000 q^{36} -1.87285i q^{37} +1.46228 q^{38} +3.12311 q^{39} -10.0054 q^{40} -11.1231i q^{41} +(-0.468213 - 2.60399i) q^{42} -0.936426i q^{43} +4.27156i q^{44} +3.33513 q^{45} +(-1.56155 - 4.53448i) q^{46} -7.12311i q^{47} +1.00000i q^{48} +(6.56155 - 2.43845i) q^{49} -6.12311 q^{50} -3.33513i q^{51} -3.12311i q^{52} +10.0054i q^{53} -1.00000i q^{54} +14.2462i q^{55} +(-7.81198 + 1.40464i) q^{56} +1.46228i q^{57} -8.24621 q^{58} +7.12311i q^{59} -3.33513i q^{60} +1.87285 q^{61} -10.2462i q^{62} +(2.60399 - 0.468213i) q^{63} +7.00000 q^{64} -10.4160i q^{65} +4.27156 q^{66} +4.68213i q^{67} -3.33513 q^{68} +(4.53448 - 1.56155i) q^{69} +(-8.68466 + 1.56155i) q^{70} -11.1231 q^{71} -3.00000 q^{72} +6.24621i q^{73} +1.87285i q^{74} -6.12311i q^{75} +1.46228 q^{76} +(2.00000 + 11.1231i) q^{77} -3.12311 q^{78} +16.1498i q^{79} +3.33513 q^{80} +1.00000 q^{81} +11.1231i q^{82} +17.0862 q^{83} +(-0.468213 - 2.60399i) q^{84} -11.1231 q^{85} +0.936426i q^{86} -8.24621i q^{87} -12.8147i q^{88} -10.0054 q^{89} -3.33513 q^{90} +(-1.46228 - 8.13254i) q^{91} +(-1.56155 - 4.53448i) q^{92} +10.2462 q^{93} +7.12311i q^{94} +4.87689 q^{95} +5.00000i q^{96} -1.87285 q^{97} +(-6.56155 + 2.43845i) q^{98} +4.27156i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{2} - 8 q^{4} + 24 q^{8} - 8 q^{9}+O(q^{10}) $ 8 * q - 8 * q^2 - 8 * q^4 + 24 * q^8 - 8 * q^9	$ 8 q - 8 q^{2} - 8 q^{4} + 24 q^{8} - 8 q^{9} - 8 q^{16} + 8 q^{18} - 4 q^{23} + 16 q^{25} - 40 q^{32} + 20 q^{35} + 8 q^{36} - 8 q^{39} + 4 q^{46} + 36 q^{49} - 16 q^{50} + 56 q^{64} - 20 q^{70} - 56 q^{71} - 24 q^{72} + 16 q^{77} + 8 q^{78} + 8 q^{81} - 56 q^{85} + 4 q^{92} + 16 q^{93} + 72 q^{95} - 36 q^{98}+O(q^{100}) $ 8 * q - 8 * q^2 - 8 * q^4 + 24 * q^8 - 8 * q^9 - 8 * q^16 + 8 * q^18 - 4 * q^23 + 16 * q^25 - 40 * q^32 + 20 * q^35 + 8 * q^36 - 8 * q^39 + 4 * q^46 + 36 * q^49 - 16 * q^50 + 56 * q^64 - 20 * q^70 - 56 * q^71 - 24 * q^72 + 16 * q^77 + 8 * q^78 + 8 * q^81 - 56 * q^85 + 4 * q^92 + 16 * q^93 + 72 * q^95 - 36 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/483\mathbb{Z}\right)^\times$.

$n$	$323$	$346$	$442$
$\chi(n)$	$1$	$-1$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.00000			−0.707107			−0.353553	−	0.935414i	$-0.615027\pi$
$2$	−1.00000			−0.707107			−0.353553	+	0.935414i	$0.615027\pi$
$3$		−	1.00000i		−	0.577350i
$3$		−	1.00000i		−	0.577350i
$4$	−1.00000			−0.500000
$5$	−3.33513			−1.49152			−0.745758	−	0.666217i	$-0.767913\pi$
$5$	−3.33513			−1.49152			−0.745758	+	0.666217i	$0.767913\pi$
$6$			1.00000i			0.408248i
$7$	−2.60399	+	0.468213i	−0.984217	+	0.176968i
$7$	−2.60399	+	0.468213i	−0.984217	+	0.176968i
$8$	3.00000			1.06066
$9$	−1.00000			−0.333333
$10$	3.33513			1.05466
$11$		−	4.27156i		−	1.28792i	−0.765058	−	0.643962i	$-0.777290\pi$
$11$		−	4.27156i		−	1.28792i	0.765058	−	0.643962i	$-0.222710\pi$
$12$			1.00000i			0.288675i
$13$			3.12311i			0.866194i	0.901347	+	0.433097i	$0.142579\pi$
$13$			3.12311i			0.866194i	−0.901347	+	0.433097i	$0.857421\pi$
$14$	2.60399	−	0.468213i	0.695946	−	0.125135i
$15$			3.33513i			0.861127i
$16$	−1.00000			−0.250000
$17$	3.33513			0.808888			0.404444	−	0.914563i	$-0.367465\pi$
$17$	3.33513			0.808888			0.404444	+	0.914563i	$0.367465\pi$
$18$	1.00000			0.235702
$19$	−1.46228			−0.335470			−0.167735	−	0.985832i	$-0.553645\pi$
$19$	−1.46228			−0.335470			−0.167735	+	0.985832i	$0.553645\pi$
$20$	3.33513			0.745758
$21$	0.468213	+	2.60399i	0.102172	+	0.568238i
$22$			4.27156i			0.910699i
$23$	1.56155	+	4.53448i	0.325606	+	0.945505i
$23$	1.56155	+	4.53448i	0.325606	+	0.945505i
$24$		−	3.00000i		−	0.612372i
$25$	6.12311			1.22462
$26$		−	3.12311i		−	0.612491i
$27$			1.00000i			0.192450i
$28$	2.60399	−	0.468213i	0.492108	−	0.0884840i
$29$	8.24621			1.53128			0.765641	−	0.643268i	$-0.222422\pi$
$29$	8.24621			1.53128			0.765641	+	0.643268i	$0.222422\pi$
$30$		−	3.33513i		−	0.608909i
$31$			10.2462i			1.84027i	0.391597	+	0.920137i	$0.371923\pi$
$31$			10.2462i			1.84027i	−0.391597	+	0.920137i	$0.628077\pi$
$32$	−5.00000			−0.883883
$33$	−4.27156			−0.743583
$34$	−3.33513			−0.571970
$35$	8.68466	−	1.56155i	1.46798	−	0.263951i
$36$	1.00000			0.166667
$37$		−	1.87285i		−	0.307895i	−0.988079	−	0.153948i	$-0.950801\pi$
$37$		−	1.87285i		−	0.307895i	0.988079	−	0.153948i	$-0.0491987\pi$
$38$	1.46228			0.237213
$39$	3.12311			0.500097
$40$	−10.0054			−1.58199
$41$		−	11.1231i		−	1.73714i	−0.495569	−	0.868569i	$-0.665040\pi$
$41$		−	11.1231i		−	1.73714i	0.495569	−	0.868569i	$-0.334960\pi$
$42$	−0.468213	−	2.60399i	−0.0722469	−	0.401805i
$43$		−	0.936426i		−	0.142804i	−0.997448	−	0.0714018i	$-0.977253\pi$
$43$		−	0.936426i		−	0.142804i	0.997448	−	0.0714018i	$-0.0227473\pi$
$44$			4.27156i			0.643962i
$45$	3.33513			0.497172
$46$	−1.56155	−	4.53448i	−0.230238	−	0.668573i
$47$		−	7.12311i		−	1.03901i	−0.854467	−	0.519506i	$-0.826116\pi$
$47$		−	7.12311i		−	1.03901i	0.854467	−	0.519506i	$-0.173884\pi$
$48$			1.00000i			0.144338i
$49$	6.56155	−	2.43845i	0.937365	−	0.348350i
$50$	−6.12311			−0.865938
$51$		−	3.33513i		−	0.467012i
$52$		−	3.12311i		−	0.433097i
$53$			10.0054i			1.37435i	0.726493	+	0.687173i	$0.241149\pi$
$53$			10.0054i			1.37435i	−0.726493	+	0.687173i	$0.758851\pi$
$54$		−	1.00000i		−	0.136083i
$55$			14.2462i			1.92096i
$56$	−7.81198	+	1.40464i	−1.04392	+	0.187703i
$57$			1.46228i			0.193684i
$58$	−8.24621			−1.08278
$59$			7.12311i			0.927349i	0.886006	+	0.463675i	$0.153469\pi$
$59$			7.12311i			0.927349i	−0.886006	+	0.463675i	$0.846531\pi$
$60$		−	3.33513i		−	0.430564i
$61$	1.87285			0.239794			0.119897	−	0.992786i	$-0.461744\pi$
$61$	1.87285			0.239794			0.119897	+	0.992786i	$0.461744\pi$
$62$		−	10.2462i		−	1.30127i
$63$	2.60399	−	0.468213i	0.328072	−	0.0589893i
$64$	7.00000			0.875000
$65$		−	10.4160i		−	1.29194i
$66$	4.27156			0.525792
$67$			4.68213i			0.572013i	0.958228	+	0.286007i	$0.0923280\pi$
$67$			4.68213i			0.572013i	−0.958228	+	0.286007i	$0.907672\pi$
$68$	−3.33513			−0.404444
$69$	4.53448	−	1.56155i	0.545888	−	0.187989i
$70$	−8.68466	+	1.56155i	−1.03802	+	0.186641i
$71$	−11.1231			−1.32007			−0.660035	−	0.751235i	$-0.729459\pi$
$71$	−11.1231			−1.32007			−0.660035	+	0.751235i	$0.729459\pi$
$72$	−3.00000			−0.353553
$73$			6.24621i			0.731064i	0.930799	+	0.365532i	$0.119113\pi$
$73$			6.24621i			0.731064i	−0.930799	+	0.365532i	$0.880887\pi$
$74$			1.87285i			0.217715i
$75$		−	6.12311i		−	0.707035i
$76$	1.46228			0.167735
$77$	2.00000	+	11.1231i	0.227921	+	1.26760i
$78$	−3.12311			−0.353622
$79$			16.1498i			1.81700i	0.417890	+	0.908498i	$0.362770\pi$
$79$			16.1498i			1.81700i	−0.417890	+	0.908498i	$0.637230\pi$
$80$	3.33513			0.372879
$81$	1.00000			0.111111
$82$			11.1231i			1.22834i
$83$	17.0862			1.87546			0.937729	−	0.347368i	$-0.112925\pi$
$83$	17.0862			1.87546			0.937729	+	0.347368i	$0.112925\pi$
$84$	−0.468213	−	2.60399i	−0.0510862	−	0.284119i
$85$	−11.1231			−1.20647
$86$			0.936426i			0.100977i
$87$		−	8.24621i		−	0.884087i
$88$		−	12.8147i		−	1.36605i
$89$	−10.0054			−1.06057			−0.530285	−	0.847819i	$-0.677915\pi$
$89$	−10.0054			−1.06057			−0.530285	+	0.847819i	$0.677915\pi$
$90$	−3.33513			−0.351554
$91$	−1.46228	−	8.13254i	−0.153289	−	0.852522i
$92$	−1.56155	−	4.53448i	−0.162803	−	0.472753i
$93$	10.2462			1.06248
$94$			7.12311i			0.734692i
$95$	4.87689			0.500359
$96$			5.00000i			0.510310i
$97$	−1.87285			−0.190159			−0.0950797	−	0.995470i	$-0.530311\pi$
$97$	−1.87285			−0.190159			−0.0950797	+	0.995470i	$0.530311\pi$
$98$	−6.56155	+	2.43845i	−0.662817	+	0.246320i
$99$			4.27156i			0.429308i
$100$	−6.12311			−0.612311
$101$		−	3.12311i		−	0.310761i	−0.987855	−	0.155380i	$-0.950340\pi$
$101$		−	3.12311i		−	0.310761i	0.987855	−	0.155380i	$-0.0496603\pi$
$102$			3.33513i			0.330227i
$103$	5.20798			0.513158			0.256579	−	0.966523i	$-0.417405\pi$
$103$	5.20798			0.513158			0.256579	+	0.966523i	$0.417405\pi$
$104$			9.36932i			0.918737i
$105$	−1.56155	−	8.68466i	−0.152392	−	0.847536i
$106$		−	10.0054i		−	0.971810i
$107$		−	9.06897i		−	0.876730i	−0.898797	−	0.438365i	$-0.855558\pi$
$107$		−	9.06897i		−	0.876730i	0.898797	−	0.438365i	$-0.144442\pi$
$108$		−	1.00000i		−	0.0962250i
$109$		−	12.2888i		−	1.17706i	−0.808477	−	0.588528i	$-0.799708\pi$
$109$		−	12.2888i		−	1.17706i	0.808477	−	0.588528i	$-0.200292\pi$
$110$		−	14.2462i		−	1.35832i
$111$	−1.87285			−0.177763
$112$	2.60399	−	0.468213i	0.246054	−	0.0442420i
$113$			8.95369i			0.842292i	0.906993	+	0.421146i	$0.138372\pi$
$113$			8.95369i			0.842292i	−0.906993	+	0.421146i	$0.861628\pi$
$114$		−	1.46228i		−	0.136955i
$115$	−5.20798	−	15.1231i	−0.485647	−	1.41024i
$116$	−8.24621			−0.765641
$117$		−	3.12311i		−	0.288731i
$118$		−	7.12311i		−	0.655735i
$119$	−8.68466	+	1.56155i	−0.796121	+	0.143147i
$120$			10.0054i			0.913364i
$121$	−7.24621			−0.658746
$122$	−1.87285			−0.169560
$123$	−11.1231			−1.00294
$124$		−	10.2462i		−	0.920137i
$125$	−3.74571			−0.335026
$126$	−2.60399	+	0.468213i	−0.231982	+	0.0417117i
$127$	−6.24621			−0.554262			−0.277131	−	0.960832i	$-0.589384\pi$
$127$	−6.24621			−0.554262			−0.277131	+	0.960832i	$0.589384\pi$
$128$	3.00000			0.265165
$129$	−0.936426			−0.0824477
$130$			10.4160i			0.913541i
$131$			12.0000i			1.04844i	0.851581	+	0.524222i	$0.175644\pi$
$131$			12.0000i			1.04844i	−0.851581	+	0.524222i	$0.824356\pi$
$132$	4.27156			0.371791
$133$	3.80776	−	0.684658i	0.330175	−	0.0593674i
$134$		−	4.68213i		−	0.404475i
$135$		−	3.33513i		−	0.287042i
$136$	10.0054			0.857956
$137$			14.8028i			1.26469i	0.774687	+	0.632345i	$0.217907\pi$
$137$			14.8028i			1.26469i	−0.774687	+	0.632345i	$0.782093\pi$
$138$	−4.53448	+	1.56155i	−0.386001	+	0.132928i
$139$			12.0000i			1.01783i	0.860818	+	0.508913i	$0.169953\pi$
$139$			12.0000i			1.01783i	−0.860818	+	0.508913i	$0.830047\pi$
$140$	−8.68466	+	1.56155i	−0.733988	+	0.131975i
$141$	−7.12311			−0.599874
$142$	11.1231			0.933430
$143$	13.3405			1.11559
$144$	1.00000			0.0833333
$145$	−27.5022			−2.28393
$146$		−	6.24621i		−	0.516940i
$147$	−2.43845	−	6.56155i	−0.201120	−	0.541188i
$148$			1.87285i			0.153948i
$149$			0.410574i			0.0336355i	0.999859	+	0.0168177i	$0.00535351\pi$
$149$			0.410574i			0.0336355i	−0.999859	+	0.0168177i	$0.994646\pi$
$150$			6.12311i			0.499949i
$151$	−20.4924			−1.66765			−0.833825	−	0.552029i	$-0.813854\pi$
$151$	−20.4924			−1.66765			−0.833825	+	0.552029i	$0.813854\pi$
$152$	−4.38684			−0.355820
$153$	−3.33513			−0.269629
$154$	−2.00000	−	11.1231i	−0.161165	−	0.896325i
$155$		−	34.1725i		−	2.74480i
$156$	−3.12311			−0.250049
$157$	15.2134			1.21416			0.607080	−	0.794641i	$-0.292341\pi$
$157$	15.2134			1.21416			0.607080	+	0.794641i	$0.292341\pi$
$158$		−	16.1498i		−	1.28481i
$159$	10.0054			0.793480
$160$	16.6757			1.31833
$161$	−6.18938	−	11.0766i	−0.487791	−	0.872960i
$162$	−1.00000			−0.0785674
$163$	12.0000			0.939913			0.469956	−	0.882690i	$-0.344270\pi$
$163$	12.0000			0.939913			0.469956	+	0.882690i	$0.344270\pi$
$164$			11.1231i			0.868569i
$165$	14.2462			1.10907
$166$	−17.0862			−1.32615
$167$		−	5.75379i		−	0.445242i	−0.974905	−	0.222621i	$-0.928539\pi$
$167$		−	5.75379i		−	0.445242i	0.974905	−	0.222621i	$-0.0714612\pi$
$168$	1.40464	+	7.81198i	0.108370	+	0.602707i
$169$	3.24621			0.249709
$170$	11.1231			0.853103
$171$	1.46228			0.111823
$172$			0.936426i			0.0714018i
$173$			3.12311i			0.237445i	0.992927	+	0.118723i	$0.0378799\pi$
$173$			3.12311i			0.237445i	−0.992927	+	0.118723i	$0.962120\pi$
$174$			8.24621i			0.625144i
$175$	−15.9445	+	2.86692i	−1.20529	+	0.216719i
$176$			4.27156i			0.321981i
$177$	7.12311			0.535405
$178$	10.0054			0.749936
$179$	−4.00000			−0.298974			−0.149487	−	0.988764i	$-0.547762\pi$
$179$	−4.00000			−0.298974			−0.149487	+	0.988764i	$0.547762\pi$
$180$	−3.33513			−0.248586
$181$	12.2888			0.913421			0.456710	−	0.889615i	$-0.349028\pi$
$181$	12.2888			0.913421			0.456710	+	0.889615i	$0.349028\pi$
$182$	1.46228	+	8.13254i	0.108391	+	0.602824i
$183$		−	1.87285i		−	0.138445i
$184$	4.68466	+	13.6035i	0.345358	+	1.00286i
$185$			6.24621i			0.459231i
$186$	−10.2462			−0.751289
$187$		−	14.2462i		−	1.04179i
$188$			7.12311i			0.519506i
$189$	−0.468213	−	2.60399i	−0.0340575	−	0.189413i
$190$	−4.87689			−0.353807
$191$		−	3.45041i		−	0.249663i	−0.992178	−	0.124832i	$-0.960161\pi$
$191$		−	3.45041i		−	0.249663i	0.992178	−	0.124832i	$-0.0398390\pi$
$192$		−	7.00000i		−	0.505181i
$193$	25.6155			1.84385			0.921923	−	0.387373i	$-0.126617\pi$
$193$	25.6155			1.84385			0.921923	+	0.387373i	$0.126617\pi$
$194$	1.87285			0.134463
$195$	−10.4160			−0.745903
$196$	−6.56155	+	2.43845i	−0.468682	+	0.174175i
$197$	18.4924			1.31753			0.658765	−	0.752349i	$-0.271079\pi$
$197$	18.4924			1.31753			0.658765	+	0.752349i	$0.271079\pi$
$198$		−	4.27156i		−	0.303566i
$199$	5.20798			0.369184			0.184592	−	0.982815i	$-0.440904\pi$
$199$	5.20798			0.369184			0.184592	+	0.982815i	$0.440904\pi$
$200$	18.3693			1.29891
$201$	4.68213			0.330252
$202$			3.12311i			0.219741i
$203$	−21.4731	+	3.86098i	−1.50711	+	0.270988i
$204$			3.33513i			0.233506i
$205$			37.0970i			2.59097i
$206$	−5.20798			−0.362857
$207$	−1.56155	−	4.53448i	−0.108535	−	0.315168i
$208$		−	3.12311i		−	0.216548i
$209$			6.24621i			0.432059i
$210$	1.56155	+	8.68466i	0.107757	+	0.599298i
$211$	−10.2462			−0.705378			−0.352689	−	0.935741i	$-0.614733\pi$
$211$	−10.2462			−0.705378			−0.352689	+	0.935741i	$0.614733\pi$
$212$		−	10.0054i		−	0.687173i
$213$			11.1231i			0.762143i
$214$			9.06897i			0.619942i
$215$			3.12311i			0.212994i
$216$			3.00000i			0.204124i
$217$	−4.79741	−	26.6811i	−0.325669	−	1.81123i
$218$			12.2888i			0.832304i
$219$	6.24621			0.422080
$220$		−	14.2462i		−	0.960479i
$221$			10.4160i			0.700654i
$222$	1.87285			0.125698
$223$			4.00000i			0.267860i	0.990991	+	0.133930i	$0.0427597\pi$
$223$			4.00000i			0.267860i	−0.990991	+	0.133930i	$0.957240\pi$
$224$	13.0200	−	2.34107i	0.869933	−	0.156419i
$225$	−6.12311			−0.408207
$226$		−	8.95369i		−	0.595591i
$227$	6.67026			0.442721			0.221360	−	0.975192i	$-0.428950\pi$
$227$	6.67026			0.442721			0.221360	+	0.975192i	$0.428950\pi$
$228$		−	1.46228i		−	0.0968418i
$229$	12.2888			0.812068			0.406034	−	0.913858i	$-0.366911\pi$
$229$	12.2888			0.812068			0.406034	+	0.913858i	$0.366911\pi$
$230$	5.20798	+	15.1231i	0.343404	+	0.997188i
$231$	11.1231	−	2.00000i	0.731847	−	0.131590i
$232$	24.7386			1.62417
$233$	−3.75379			−0.245919			−0.122959	−	0.992412i	$-0.539239\pi$
$233$	−3.75379			−0.245919			−0.122959	+	0.992412i	$0.539239\pi$
$234$			3.12311i			0.204164i
$235$			23.7565i			1.54970i
$236$		−	7.12311i		−	0.463675i
$237$	16.1498			1.04904
$238$	8.68466	−	1.56155i	0.562943	−	0.101220i
$239$	−1.36932			−0.0885737			−0.0442869	−	0.999019i	$-0.514102\pi$
$239$	−1.36932			−0.0885737			−0.0442869	+	0.999019i	$0.514102\pi$
$240$		−	3.33513i		−	0.215282i
$241$	11.4677			0.738698			0.369349	−	0.929291i	$-0.379581\pi$
$241$	11.4677			0.738698			0.369349	+	0.929291i	$0.379581\pi$
$242$	7.24621			0.465804
$243$		−	1.00000i		−	0.0641500i
$244$	−1.87285			−0.119897
$245$	−21.8836	+	8.13254i	−1.39809	+	0.519569i
$246$	11.1231			0.709183
$247$		−	4.56685i		−	0.290582i
$248$			30.7386i			1.95191i
$249$		−	17.0862i		−	1.08280i
$250$	3.74571			0.236899
$251$	−0.821147			−0.0518303			−0.0259152	−	0.999664i	$-0.508250\pi$
$251$	−0.821147			−0.0518303			−0.0259152	+	0.999664i	$0.508250\pi$
$252$	−2.60399	+	0.468213i	−0.164036	+	0.0294947i
$253$	19.3693	−	6.67026i	1.21774	−	0.419356i
$254$	6.24621			0.391922
$255$			11.1231i			0.696556i
$256$	−17.0000			−1.06250
$257$			17.3693i			1.08347i	0.840550	+	0.541734i	$0.182232\pi$
$257$			17.3693i			1.08347i	−0.840550	+	0.541734i	$0.817768\pi$
$258$	0.936426			0.0582994
$259$	0.876894	+	4.87689i	0.0544876	+	0.303035i
$260$			10.4160i			0.645971i
$261$	−8.24621			−0.510428
$262$		−	12.0000i		−	0.741362i
$263$			20.5366i			1.26634i	0.774011	+	0.633172i	$0.218247\pi$
$263$			20.5366i			1.26634i	−0.774011	+	0.633172i	$0.781753\pi$
$264$	−12.8147			−0.788689
$265$		−	33.3693i		−	2.04986i
$266$	−3.80776	+	0.684658i	−0.233469	+	0.0419791i
$267$			10.0054i			0.612320i
$268$		−	4.68213i		−	0.286007i
$269$		−	6.63068i		−	0.404280i	−0.979357	−	0.202140i	$-0.935210\pi$
$269$		−	6.63068i		−	0.404280i	0.979357	−	0.202140i	$-0.0647896\pi$
$270$			3.33513i			0.202970i
$271$			16.4924i			1.00184i	0.865493	+	0.500922i	$0.167006\pi$
$271$			16.4924i			1.00184i	−0.865493	+	0.500922i	$0.832994\pi$
$272$	−3.33513			−0.202222
$273$	−8.13254	+	1.46228i	−0.492204	+	0.0885012i
$274$		−	14.8028i		−	0.894270i
$275$		−	26.1552i		−	1.57722i
$276$	−4.53448	+	1.56155i	−0.272944	+	0.0939944i
$277$	16.2462			0.976140			0.488070	−	0.872804i	$-0.337701\pi$
$277$	16.2462			0.976140			0.488070	+	0.872804i	$0.337701\pi$
$278$		−	12.0000i		−	0.719712i
$279$		−	10.2462i		−	0.613425i
$280$	26.0540	−	4.68466i	1.55702	−	0.279962i
$281$			22.2942i			1.32996i	0.746860	+	0.664981i	$0.231560\pi$
$281$			22.2942i			1.32996i	−0.746860	+	0.664981i	$0.768440\pi$
$282$	7.12311			0.424175
$283$	−19.3697			−1.15141			−0.575703	−	0.817659i	$-0.695272\pi$
$283$	−19.3697			−1.15141			−0.575703	+	0.817659i	$0.695272\pi$
$284$	11.1231			0.660035
$285$		−	4.87689i		−	0.288882i
$286$	−13.3405			−0.788842
$287$	5.20798	+	28.9645i	0.307418	+	1.70972i
$288$	5.00000			0.294628
$289$	−5.87689			−0.345700
$290$	27.5022			1.61498
$291$			1.87285i			0.109789i
$292$		−	6.24621i		−	0.365532i
$293$	−9.18425			−0.536550			−0.268275	−	0.963342i	$-0.586454\pi$
$293$	−9.18425			−0.536550			−0.268275	+	0.963342i	$0.586454\pi$
$294$	2.43845	+	6.56155i	0.142213	+	0.382678i
$295$		−	23.7565i		−	1.38316i
$296$		−	5.61856i		−	0.326572i
$297$	4.27156			0.247861
$298$		−	0.410574i		−	0.0237839i
$299$	−14.1617	+	4.87689i	−0.818991	+	0.282038i
$300$			6.12311i			0.353518i
$301$	0.438447	+	2.43845i	0.0252717	+	0.140550i
$302$	20.4924			1.17921
$303$	−3.12311			−0.179418
$304$	1.46228			0.0838675
$305$	−6.24621			−0.357657
$306$	3.33513			0.190657
$307$			2.24621i			0.128198i	0.997944	+	0.0640990i	$0.0204174\pi$
$307$			2.24621i			0.128198i	−0.997944	+	0.0640990i	$0.979583\pi$
$308$	−2.00000	−	11.1231i	−0.113961	−	0.633798i
$309$		−	5.20798i		−	0.296272i
$310$			34.1725i			1.94087i
$311$			2.63068i			0.149172i	0.997215	+	0.0745862i	$0.0237636\pi$
$311$			2.63068i			0.149172i	−0.997215	+	0.0745862i	$0.976236\pi$
$312$	9.36932			0.530433
$313$	14.3922			0.813497			0.406749	−	0.913540i	$-0.366663\pi$
$313$	14.3922			0.813497			0.406749	+	0.913540i	$0.366663\pi$
$314$	−15.2134			−0.858541
$315$	−8.68466	+	1.56155i	−0.489325	+	0.0879835i
$316$		−	16.1498i		−	0.908498i
$317$	−14.0000			−0.786318			−0.393159	−	0.919470i	$-0.628618\pi$
$317$	−14.0000			−0.786318			−0.393159	+	0.919470i	$0.628618\pi$
$318$	−10.0054			−0.561075
$319$		−	35.2242i		−	1.97218i
$320$	−23.3459			−1.30508
$321$	−9.06897			−0.506181
$322$	6.18938	+	11.0766i	0.344921	+	0.617276i
$323$	−4.87689			−0.271358
$324$	−1.00000			−0.0555556
$325$			19.1231i			1.06076i
$326$	−12.0000			−0.664619
$327$	−12.2888			−0.679573
$328$		−	33.3693i		−	1.84251i
$329$	3.33513	+	18.5485i	0.183872	+	1.02261i
$330$	−14.2462			−0.784228
$331$	−16.4924			−0.906506			−0.453253	−	0.891382i	$-0.649737\pi$
$331$	−16.4924			−0.906506			−0.453253	+	0.891382i	$0.649737\pi$
$332$	−17.0862			−0.937729
$333$			1.87285i			0.102632i
$334$			5.75379i			0.314833i
$335$		−	15.6155i		−	0.853167i
$336$	−0.468213	−	2.60399i	−0.0255431	−	0.142059i
$337$		−	6.67026i		−	0.363352i	−0.983358	−	0.181676i	$-0.941848\pi$
$337$		−	6.67026i		−	0.363352i	0.983358	−	0.181676i	$-0.0581523\pi$
$338$	−3.24621			−0.176571
$339$	8.95369			0.486298
$340$	11.1231			0.603235
$341$	43.7673			2.37013
$342$	−1.46228			−0.0790710
$343$	−15.9445	+	9.42190i	−0.860923	+	0.508735i
$344$		−	2.80928i		−	0.151466i
$345$	−15.1231	+	5.20798i	−0.814201	+	0.280388i
$346$		−	3.12311i		−	0.167899i
$347$	−16.4924			−0.885360			−0.442680	−	0.896680i	$-0.645972\pi$
$347$	−16.4924			−0.885360			−0.442680	+	0.896680i	$0.645972\pi$
$348$			8.24621i			0.442043i
$349$		−	9.36932i		−	0.501528i	−0.968048	−	0.250764i	$-0.919318\pi$
$349$		−	9.36932i		−	0.501528i	0.968048	−	0.250764i	$-0.0806818\pi$
$350$	15.9445	−	2.86692i	0.852270	−	0.153243i
$351$	−3.12311			−0.166699
$352$			21.3578i			1.13837i
$353$		−	17.3693i		−	0.924475i	−0.886756	−	0.462238i	$-0.847047\pi$
$353$		−	17.3693i		−	0.924475i	0.886756	−	0.462238i	$-0.152953\pi$
$354$	−7.12311			−0.378589
$355$	37.0970			1.96891
$356$	10.0054			0.530285
$357$	1.56155	+	8.68466i	0.0826461	+	0.459641i
$358$	4.00000			0.211407
$359$		−	25.3341i		−	1.33708i	−0.743676	−	0.668540i	$-0.766919\pi$
$359$		−	25.3341i		−	1.33708i	0.743676	−	0.668540i	$-0.233081\pi$
$360$	10.0054			0.527331
$361$	−16.8617			−0.887460
$362$	−12.2888			−0.645886
$363$			7.24621i			0.380327i
$364$	1.46228	+	8.13254i	0.0766443	+	0.426261i
$365$		−	20.8319i		−	1.09039i
$366$			1.87285i			0.0978956i
$367$	12.6994			0.662903			0.331452	−	0.943472i	$-0.392462\pi$
$367$	12.6994			0.662903			0.331452	+	0.943472i	$0.392462\pi$
$368$	−1.56155	−	4.53448i	−0.0814016	−	0.236376i
$369$			11.1231i			0.579046i
$370$		−	6.24621i		−	0.324725i
$371$	−4.68466	−	26.0540i	−0.243215	−	1.35266i
$372$	−10.2462			−0.531241
$373$		−	15.2134i		−	0.787719i	−0.919171	−	0.393860i	$-0.871140\pi$
$373$		−	15.2134i		−	0.787719i	0.919171	−	0.393860i	$-0.128860\pi$
$374$			14.2462i			0.736654i
$375$			3.74571i			0.193427i
$376$		−	21.3693i		−	1.10204i
$377$			25.7538i			1.32639i
$378$	0.468213	+	2.60399i	0.0240823	+	0.133935i
$379$			21.7684i			1.11817i	0.829112	+	0.559083i	$0.188847\pi$
$379$			21.7684i			1.11817i	−0.829112	+	0.559083i	$0.811153\pi$
$380$	−4.87689			−0.250179
$381$			6.24621i			0.320003i
$382$			3.45041i			0.176538i
$383$	16.2651			0.831107			0.415554	−	0.909569i	$-0.363588\pi$
$383$	16.2651			0.831107			0.415554	+	0.909569i	$0.363588\pi$
$384$		−	3.00000i		−	0.153093i
$385$	−6.67026	−	37.0970i	−0.339948	−	1.89064i
$386$	−25.6155			−1.30380
$387$			0.936426i			0.0476012i
$388$	1.87285			0.0950797
$389$			14.5722i			0.738842i	0.929262	+	0.369421i	$0.120444\pi$
$389$			14.5722i			0.738842i	−0.929262	+	0.369421i	$0.879556\pi$
$390$	10.4160			0.527433
$391$	5.20798	+	15.1231i	0.263379	+	0.764808i
$392$	19.6847	−	7.31534i	0.994225	−	0.369481i
$393$	12.0000			0.605320
$394$	−18.4924			−0.931635
$395$		−	53.8617i		−	2.71008i
$396$		−	4.27156i		−	0.214654i
$397$			20.4924i			1.02849i	0.857645	+	0.514243i	$0.171927\pi$
$397$			20.4924i			1.02849i	−0.857645	+	0.514243i	$0.828073\pi$
$398$	−5.20798			−0.261053
$399$	−0.684658	−	3.80776i	−0.0342758	−	0.190627i
$400$	−6.12311			−0.306155
$401$		−	11.8782i		−	0.593171i	−0.955006	−	0.296586i	$-0.904152\pi$
$401$		−	11.8782i		−	0.593171i	0.955006	−	0.296586i	$-0.0958480\pi$
$402$	−4.68213			−0.233524
$403$	−32.0000			−1.59403
$404$			3.12311i			0.155380i
$405$	−3.33513			−0.165724
$406$	21.4731	−	3.86098i	1.06569	−	0.191617i
$407$	−8.00000			−0.396545
$408$		−	10.0054i		−	0.495341i
$409$		−	1.36932i		−	0.0677084i	−0.999427	−	0.0338542i	$-0.989222\pi$
$409$		−	1.36932i		−	0.0677084i	0.999427	−	0.0338542i	$-0.0107782\pi$
$410$		−	37.0970i		−	1.83209i
$411$	14.8028			0.730169
$412$	−5.20798			−0.256579
$413$	−3.33513	−	18.5485i	−0.164111	−	0.912713i
$414$	1.56155	+	4.53448i	0.0767461	+	0.222858i
$415$	−56.9848			−2.79728
$416$		−	15.6155i		−	0.765614i
$417$	12.0000			0.587643
$418$		−	6.24621i		−	0.305512i
$419$	−9.59482			−0.468738			−0.234369	−	0.972148i	$-0.575302\pi$
$419$	−9.59482			−0.468738			−0.234369	+	0.972148i	$0.575302\pi$
$420$	1.56155	+	8.68466i	0.0761960	+	0.423768i
$421$			25.6294i			1.24910i	0.780986	+	0.624549i	$0.214717\pi$
$421$			25.6294i			1.24910i	−0.780986	+	0.624549i	$0.785283\pi$
$422$	10.2462			0.498778
$423$			7.12311i			0.346337i
$424$			30.0162i			1.45771i
$425$	20.4214			0.990582
$426$		−	11.1231i		−	0.538916i
$427$	−4.87689	+	0.876894i	−0.236009	+	0.0424359i
$428$			9.06897i			0.438365i
$429$		−	13.3405i		−	0.644087i
$430$		−	3.12311i		−	0.150610i
$431$		−	28.8492i		−	1.38962i	−0.719195	−	0.694809i	$-0.755489\pi$
$431$		−	28.8492i		−	1.38962i	0.719195	−	0.694809i	$-0.244511\pi$
$432$		−	1.00000i		−	0.0481125i
$433$	−18.1379			−0.871654			−0.435827	−	0.900031i	$-0.643544\pi$
$433$	−18.1379			−0.871654			−0.435827	+	0.900031i	$0.643544\pi$
$434$	4.79741	+	26.6811i	0.230283	+	1.28073i
$435$			27.5022i			1.31863i
$436$			12.2888i			0.588528i
$437$	−2.28343	−	6.63068i	−0.109231	−	0.317189i
$438$	−6.24621			−0.298456
$439$		−	21.7538i		−	1.03825i	−0.854698	−	0.519126i	$-0.826258\pi$
$439$		−	21.7538i		−	1.03825i	0.854698	−	0.519126i	$-0.173742\pi$
$440$			42.7386i			2.03748i
$441$	−6.56155	+	2.43845i	−0.312455	+	0.116117i
$442$		−	10.4160i		−	0.495437i
$443$	29.3693			1.39538			0.697689	−	0.716401i	$-0.254212\pi$
$443$	29.3693			1.39538			0.697689	+	0.716401i	$0.254212\pi$
$444$	1.87285			0.0888817
$445$	33.3693			1.58186
$446$		−	4.00000i		−	0.189405i
$447$	0.410574			0.0194195
$448$	−18.2279	+	3.27749i	−0.861190	+	0.154847i
$449$	1.50758			0.0711470			0.0355735	−	0.999367i	$-0.488674\pi$
$449$	1.50758			0.0711470			0.0355735	+	0.999367i	$0.488674\pi$
$450$	6.12311			0.288646
$451$	−47.5130			−2.23730
$452$		−	8.95369i		−	0.421146i
$453$			20.4924i			0.962818i
$454$	−6.67026			−0.313051
$455$	4.87689	+	27.1231i	0.228632	+	1.27155i
$456$			4.38684i			0.205433i
$457$			29.6056i			1.38489i	0.721470	+	0.692446i	$0.243467\pi$
$457$			29.6056i			1.38489i	−0.721470	+	0.692446i	$0.756533\pi$
$458$	−12.2888			−0.574219
$459$			3.33513i			0.155671i
$460$	5.20798	+	15.1231i	0.242824	+	0.705118i
$461$		−	9.36932i		−	0.436373i	−0.975907	−	0.218186i	$-0.929986\pi$
$461$		−	9.36932i		−	0.436373i	0.975907	−	0.218186i	$-0.0700140\pi$
$462$	−11.1231	+	2.00000i	−0.517494	+	0.0930484i
$463$	8.00000			0.371792			0.185896	−	0.982569i	$-0.440481\pi$
$463$	8.00000			0.371792			0.185896	+	0.982569i	$0.440481\pi$
$464$	−8.24621			−0.382821
$465$	−34.1725			−1.58471
$466$	3.75379			0.173891
$467$	6.67026			0.308663			0.154332	−	0.988019i	$-0.450678\pi$
$467$	6.67026			0.308663			0.154332	+	0.988019i	$0.450678\pi$
$468$			3.12311i			0.144366i
$469$	−2.19224	−	12.1922i	−0.101228	−	0.562985i
$470$		−	23.7565i		−	1.09581i
$471$		−	15.2134i		−	0.700996i
$472$			21.3693i			0.983603i
$473$	−4.00000			−0.183920
$474$	−16.1498			−0.741785
$475$	−8.95369			−0.410823
$476$	8.68466	−	1.56155i	0.398061	−	0.0715737i
$477$		−	10.0054i		−	0.458116i
$478$	1.36932			0.0626311
$479$	−5.84912			−0.267253			−0.133626	−	0.991032i	$-0.542662\pi$
$479$	−5.84912			−0.267253			−0.133626	+	0.991032i	$0.542662\pi$
$480$		−	16.6757i		−	0.761136i
$481$	5.84912			0.266697
$482$	−11.4677			−0.522338
$483$	−11.0766	+	6.18938i	−0.504004	+	0.281626i
$484$	7.24621			0.329373
$485$	6.24621			0.283626
$486$			1.00000i			0.0453609i
$487$	−14.2462			−0.645557			−0.322779	−	0.946474i	$-0.604617\pi$
$487$	−14.2462			−0.645557			−0.322779	+	0.946474i	$0.604617\pi$
$488$	5.61856			0.254340
$489$		−	12.0000i		−	0.542659i
$490$	21.8836	−	8.13254i	0.988602	−	0.367391i
$491$	−32.4924			−1.46636			−0.733181	−	0.680033i	$-0.761965\pi$
$491$	−32.4924			−1.46636			−0.733181	+	0.680033i	$0.761965\pi$
$492$	11.1231			0.501468
$493$	27.5022			1.23864
$494$			4.56685i			0.205472i
$495$		−	14.2462i		−	0.640320i
$496$		−	10.2462i		−	0.460068i
$497$	28.9645	−	5.20798i	1.29923	−	0.233610i
$498$			17.0862i			0.765652i
$499$	5.75379			0.257575			0.128787	−	0.991672i	$-0.458891\pi$
$499$	5.75379			0.257575			0.128787	+	0.991672i	$0.458891\pi$
$500$	3.74571			0.167513
$501$	−5.75379			−0.257060
$502$	0.821147			0.0366496
$503$	−34.1725			−1.52368			−0.761838	−	0.647768i	$-0.775703\pi$
$503$	−34.1725			−1.52368			−0.761838	+	0.647768i	$0.775703\pi$
$504$	7.81198	−	1.40464i	0.347973	−	0.0625676i
$505$			10.4160i			0.463505i
$506$	−19.3693	+	6.67026i	−0.861071	+	0.296529i
$507$		−	3.24621i		−	0.144169i
$508$	6.24621			0.277131
$509$			15.6155i			0.692146i	0.938208	+	0.346073i	$0.112485\pi$
$509$			15.6155i			0.692146i	−0.938208	+	0.346073i	$0.887515\pi$
$510$		−	11.1231i		−	0.492539i
$511$	−2.92456	−	16.2651i	−0.129375	−	0.719525i
$512$	11.0000			0.486136
$513$		−	1.46228i		−	0.0645612i
$514$		−	17.3693i		−	0.766128i
$515$	−17.3693			−0.765384
$516$	0.936426			0.0412239
$517$	−30.4268			−1.33817
$518$	−0.876894	−	4.87689i	−0.0385285	−	0.214278i
$519$	3.12311			0.137089
$520$		−	31.2479i		−	1.37031i
$521$	3.33513			0.146115			0.0730574	−	0.997328i	$-0.476724\pi$
$521$	3.33513			0.146115			0.0730574	+	0.997328i	$0.476724\pi$
$522$	8.24621			0.360927
$523$	11.8782			0.519400			0.259700	−	0.965689i	$-0.416376\pi$
$523$	11.8782			0.519400			0.259700	+	0.965689i	$0.416376\pi$
$524$		−	12.0000i		−	0.524222i
$525$	2.86692	+	15.9445i	0.125123	+	0.695876i
$526$		−	20.5366i		−	0.895440i
$527$			34.1725i			1.48858i
$528$	4.27156			0.185896
$529$	−18.1231	+	14.1617i	−0.787961	+	0.615725i
$530$			33.3693i			1.44947i
$531$		−	7.12311i		−	0.309116i
$532$	−3.80776	+	0.684658i	−0.165088	+	0.0296837i
$533$	34.7386			1.50470
$534$		−	10.0054i		−	0.432976i
$535$			30.2462i			1.30766i
$536$			14.0464i			0.606712i
$537$			4.00000i			0.172613i
$538$			6.63068i			0.285869i
$539$	−10.4160	−	28.0281i	−0.448648	−	1.20725i
$540$			3.33513i			0.143521i
$541$	22.8769			0.983555			0.491777	−	0.870721i	$-0.336347\pi$
$541$	22.8769			0.983555			0.491777	+	0.870721i	$0.336347\pi$
$542$		−	16.4924i		−	0.708410i
$543$		−	12.2888i		−	0.527364i
$544$	−16.6757			−0.714963
$545$			40.9848i			1.75560i
$546$	8.13254	−	1.46228i	0.348041	−	0.0625798i
$547$	20.0000			0.855138			0.427569	−	0.903983i	$-0.359370\pi$
$547$	20.0000			0.855138			0.427569	+	0.903983i	$0.359370\pi$
$548$		−	14.8028i		−	0.632345i
$549$	−1.87285			−0.0799314
$550$			26.1552i			1.11526i
$551$	−12.0583			−0.513699
$552$	13.6035	−	4.68466i	0.579001	−	0.199392i
$553$	−7.56155	−	42.0540i	−0.321550	−	1.78832i
$554$	−16.2462			−0.690235
$555$	6.24621			0.265137
$556$		−	12.0000i		−	0.508913i
$557$			15.8545i			0.671777i	0.941902	+	0.335889i	$0.109037\pi$
$557$			15.8545i			0.671777i	−0.941902	+	0.335889i	$0.890963\pi$
$558$			10.2462i			0.433757i
$559$	2.92456			0.123696
$560$	−8.68466	+	1.56155i	−0.366994	+	0.0659877i
$561$	−14.2462			−0.601476
$562$		−	22.2942i		−	0.940425i
$563$	0.821147			0.0346072			0.0173036	−	0.999850i	$-0.494492\pi$
$563$	0.821147			0.0346072			0.0173036	+	0.999850i	$0.494492\pi$
$564$	7.12311			0.299937
$565$		−	29.8617i		−	1.25629i
$566$	19.3697			0.814168
$567$	−2.60399	+	0.468213i	−0.109357	+	0.0196631i
$568$	−33.3693			−1.40015
$569$			0.641132i			0.0268777i	0.999910	+	0.0134388i	$0.00427784\pi$
$569$			0.641132i			0.0268777i	−0.999910	+	0.0134388i	$0.995722\pi$
$570$			4.87689i			0.204271i
$571$		−	24.6929i		−	1.03337i	−0.856177	−	0.516683i	$-0.827166\pi$
$571$		−	24.6929i		−	1.03337i	0.856177	−	0.516683i	$-0.172834\pi$
$572$	−13.3405			−0.557796
$573$	−3.45041			−0.144143
$574$	−5.20798	−	28.9645i	−0.217377	−	1.20895i
$575$	9.56155	+	27.7651i	0.398744	+	1.15789i
$576$	−7.00000			−0.291667
$577$			27.1231i			1.12915i	0.825382	+	0.564575i	$0.190960\pi$
$577$			27.1231i			1.12915i	−0.825382	+	0.564575i	$0.809040\pi$
$578$	5.87689			0.244447
$579$		−	25.6155i		−	1.06455i
$580$	27.5022			1.14197
$581$	−44.4924	+	8.00000i	−1.84586	+	0.331896i
$582$		−	1.87285i		−	0.0776322i
$583$	42.7386			1.77005
$584$			18.7386i			0.775410i
$585$			10.4160i			0.430647i
$586$	9.18425			0.379398
$587$		−	32.4924i		−	1.34111i	−0.741862	−	0.670553i	$-0.766057\pi$
$587$		−	32.4924i		−	1.34111i	0.741862	−	0.670553i	$-0.233943\pi$
$588$	2.43845	+	6.56155i	0.100560	+	0.270594i
$589$		−	14.9828i		−	0.617356i
$590$			23.7565i			0.978040i
$591$		−	18.4924i		−	0.760677i
$592$			1.87285i			0.0769738i
$593$		−	17.3693i		−	0.713272i	−0.934243	−	0.356636i	$-0.883924\pi$
$593$		−	17.3693i		−	0.713272i	0.934243	−	0.356636i	$-0.116076\pi$
$594$	−4.27156			−0.175264
$595$	28.9645	−	5.20798i	1.18743	−	0.213507i
$596$		−	0.410574i		−	0.0168177i
$597$		−	5.20798i		−	0.213149i
$598$	14.1617	−	4.87689i	0.579114	−	0.199431i
$599$	−14.6307			−0.597794			−0.298897	−	0.954285i	$-0.596619\pi$
$599$	−14.6307			−0.597794			−0.298897	+	0.954285i	$0.596619\pi$
$600$		−	18.3693i		−	0.749924i
$601$			33.3693i			1.36116i	0.732672	+	0.680581i	$0.238273\pi$
$601$			33.3693i			1.36116i	−0.732672	+	0.680581i	$0.761727\pi$
$602$	−0.438447	−	2.43845i	−0.0178698	−	0.0993837i
$603$		−	4.68213i		−	0.190671i
$604$	20.4924			0.833825
$605$	24.1671			0.982531
$606$	3.12311			0.126867
$607$			22.7386i			0.922933i	0.887158	+	0.461466i	$0.152676\pi$
$607$			22.7386i			0.922933i	−0.887158	+	0.461466i	$0.847324\pi$
$608$	7.31140			0.296516
$609$	3.86098	+	21.4731i	0.156455	+	0.870133i
$610$	6.24621			0.252902
$611$	22.2462			0.899985
$612$	3.33513			0.134815
$613$			41.8944i			1.69210i	0.533103	+	0.846050i	$0.321026\pi$
$613$			41.8944i			1.69210i	−0.533103	+	0.846050i	$0.678974\pi$
$614$		−	2.24621i		−	0.0906497i
$615$	37.0970			1.49590
$616$	6.00000	+	33.3693i	0.241747	+	1.34449i
$617$		−	11.0571i		−	0.445142i	−0.974916	−	0.222571i	$-0.928555\pi$
$617$		−	11.0571i		−	0.445142i	0.974916	−	0.222571i	$-0.0714449\pi$
$618$			5.20798i			0.209496i
$619$	−29.7856			−1.19719			−0.598593	−	0.801053i	$-0.704273\pi$
$619$	−29.7856			−1.19719			−0.598593	+	0.801053i	$0.704273\pi$
$620$			34.1725i			1.37240i
$621$	−4.53448	+	1.56155i	−0.181963	+	0.0626630i
$622$		−	2.63068i		−	0.105481i
$623$	26.0540	−	4.68466i	1.04383	−	0.187687i
$624$	−3.12311			−0.125024
$625$	−18.1231			−0.724924
$626$	−14.3922			−0.575229
$627$	6.24621			0.249450
$628$	−15.2134			−0.607080
$629$		−	6.24621i		−	0.249053i
$630$	8.68466	−	1.56155i	0.346005	−	0.0622138i
$631$			9.47954i			0.377375i	0.982037	+	0.188687i	$0.0604233\pi$
$631$			9.47954i			0.377375i	−0.982037	+	0.188687i	$0.939577\pi$
$632$			48.4494i			1.92721i
$633$			10.2462i			0.407250i
$634$	14.0000			0.556011
$635$	20.8319			0.826690
$636$	−10.0054			−0.396740
$637$	7.61553	+	20.4924i	0.301738	+	0.811939i
$638$			35.2242i			1.39454i
$639$	11.1231			0.440023
$640$	−10.0054			−0.395498
$641$		−	46.0507i		−	1.81889i	−0.415820	−	0.909447i	$-0.636505\pi$
$641$		−	46.0507i		−	1.81889i	0.415820	−	0.909447i	$-0.363495\pi$
$642$	9.06897			0.357924
$643$	35.6347			1.40530			0.702649	−	0.711537i	$-0.252001\pi$
$643$	35.6347			1.40530			0.702649	+	0.711537i	$0.252001\pi$
$644$	6.18938	+	11.0766i	0.243896	+	0.436480i
$645$	3.12311			0.122972
$646$	4.87689			0.191879
$647$		−	35.6155i		−	1.40019i	−0.714049	−	0.700095i	$-0.753141\pi$
$647$		−	35.6155i		−	1.40019i	0.714049	−	0.700095i	$-0.246859\pi$
$648$	3.00000			0.117851
$649$	30.4268			1.19435
$650$		−	19.1231i		−	0.750070i
$651$	−26.6811	+	4.79741i	−1.04571	+	0.188025i
$652$	−12.0000			−0.469956
$653$	14.0000			0.547862			0.273931	−	0.961749i	$-0.411676\pi$
$653$	14.0000			0.547862			0.273931	+	0.961749i	$0.411676\pi$
$654$	12.2888			0.480531
$655$		−	40.0216i		−	1.56377i
$656$			11.1231i			0.434284i
$657$		−	6.24621i		−	0.243688i
$658$	−3.33513	−	18.5485i	−0.130017	−	0.723096i
$659$			24.2824i			0.945906i	0.881088	+	0.472953i	$0.156812\pi$
$659$			24.2824i			0.945906i	−0.881088	+	0.472953i	$0.843188\pi$
$660$	−14.2462			−0.554533
$661$	−38.1487			−1.48381			−0.741907	−	0.670503i	$-0.766078\pi$
$661$	−38.1487			−1.48381			−0.741907	+	0.670503i	$0.766078\pi$
$662$	16.4924			0.640996
$663$	10.4160			0.404523
$664$	51.2587			1.98922
$665$	−12.6994	+	2.28343i	−0.492461	+	0.0885475i
$666$		−	1.87285i		−	0.0725716i
$667$	12.8769	+	37.3923i	0.498595	+	1.44784i
$668$			5.75379i			0.222621i
$669$	4.00000			0.154649
$670$			15.6155i			0.603280i
$671$		−	8.00000i		−	0.308837i
$672$	−2.34107	−	13.0200i	−0.0903086	−	0.502256i
$673$	−13.1231			−0.505859			−0.252929	−	0.967485i	$-0.581394\pi$
$673$	−13.1231			−0.505859			−0.252929	+	0.967485i	$0.581394\pi$
$674$			6.67026i			0.256929i
$675$			6.12311i			0.235678i
$676$	−3.24621			−0.124854
$677$	−9.18425			−0.352979			−0.176490	−	0.984302i	$-0.556474\pi$
$677$	−9.18425			−0.352979			−0.176490	+	0.984302i	$0.556474\pi$
$678$	−8.95369			−0.343864
$679$	4.87689	−	0.876894i	0.187158	−	0.0336521i
$680$	−33.3693			−1.27965
$681$		−	6.67026i		−	0.255605i
$682$	−43.7673			−1.67594
$683$	7.12311			0.272558			0.136279	−	0.990670i	$-0.456486\pi$
$683$	7.12311			0.272558			0.136279	+	0.990670i	$0.456486\pi$
$684$	−1.46228			−0.0559116
$685$		−	49.3693i		−	1.88630i
$686$	15.9445	−	9.42190i	0.608765	−	0.359730i
$687$		−	12.2888i		−	0.468848i
$688$			0.936426i			0.0357009i
$689$	−31.2479			−1.19045
$690$	15.1231	−	5.20798i	0.575727	−	0.198265i
$691$			2.24621i			0.0854499i	0.999087	+	0.0427250i	$0.0136039\pi$
$691$			2.24621i			0.0854499i	−0.999087	+	0.0427250i	$0.986396\pi$
$692$		−	3.12311i		−	0.118723i
$693$	−2.00000	−	11.1231i	−0.0759737	−	0.422532i
$694$	16.4924			0.626044
$695$		−	40.0216i		−	1.51811i
$696$		−	24.7386i		−	0.937715i
$697$		−	37.0970i		−	1.40515i
$698$			9.36932i			0.354634i
$699$			3.75379i			0.141981i
$700$	15.9445	−	2.86692i	0.602646	−	0.108359i
$701$		−	13.7511i		−	0.519372i	−0.965693	−	0.259686i	$-0.916381\pi$
$701$		−	13.7511i		−	0.519372i	0.965693	−	0.259686i	$-0.0836191\pi$
$702$	3.12311			0.117874
$703$			2.73863i			0.103290i
$704$		−	29.9009i		−	1.12693i
$705$	23.7565			0.894721
$706$			17.3693i			0.653703i
$707$	1.46228	+	8.13254i	0.0549947	+	0.305856i
$708$	−7.12311			−0.267703
$709$			27.7328i			1.04153i	0.853701	+	0.520763i	$0.174352\pi$
$709$			27.7328i			1.04153i	−0.853701	+	0.520763i	$0.825648\pi$
$710$	−37.0970			−1.39223
$711$		−	16.1498i		−	0.605665i
$712$	−30.0162			−1.12490
$713$	−46.4613	+	16.0000i	−1.73999	+	0.599205i
$714$	−1.56155	−	8.68466i	−0.0584396	−	0.325015i
$715$	−44.4924			−1.66392
$716$	4.00000			0.149487
$717$			1.36932i			0.0511381i
$718$			25.3341i			0.945459i
$719$			2.63068i			0.0981079i	0.998796	+	0.0490540i	$0.0156206\pi$
$719$			2.63068i			0.0981079i	−0.998796	+	0.0490540i	$0.984379\pi$
$720$	−3.33513			−0.124293
$721$	−13.5616	+	2.43845i	−0.505059	+	0.0908125i
$722$	16.8617			0.627529
$723$		−	11.4677i		−	0.426487i
$724$	−12.2888			−0.456710
$725$	50.4924			1.87524
$726$		−	7.24621i		−	0.268932i
$727$	−52.7210			−1.95531			−0.977656	−	0.210209i	$-0.932586\pi$
$727$	−52.7210			−1.95531			−0.977656	+	0.210209i	$0.932586\pi$
$728$	−4.38684	−	24.3976i	−0.162587	−	0.904236i
$729$	−1.00000			−0.0370370
$730$			20.8319i			0.771025i
$731$		−	3.12311i		−	0.115512i
$732$			1.87285i			0.0692226i
$733$	−8.54312			−0.315547			−0.157774	−	0.987475i	$-0.550432\pi$
$733$	−8.54312			−0.315547			−0.157774	+	0.987475i	$0.550432\pi$
$734$	−12.6994			−0.468743
$735$	8.13254	+	21.8836i	0.299973	+	0.807190i
$736$	−7.80776	−	22.6724i	−0.287798	−	0.835717i
$737$	20.0000			0.736709
$738$		−	11.1231i		−	0.409447i
$739$	14.7386			0.542169			0.271085	−	0.962555i	$-0.412618\pi$
$739$	14.7386			0.542169			0.271085	+	0.962555i	$0.412618\pi$
$740$		−	6.24621i		−	0.229615i
$741$	−4.56685			−0.167768
$742$	4.68466	+	26.0540i	0.171979	+	0.956472i
$743$			7.19612i			0.264000i	0.991250	+	0.132000i	$0.0421399\pi$
$743$			7.19612i			0.264000i	−0.991250	+	0.132000i	$0.957860\pi$
$744$	30.7386			1.12693
$745$		−	1.36932i		−	0.0501679i
$746$			15.2134i			0.557001i
$747$	−17.0862			−0.625153
$748$			14.2462i			0.520893i
$749$	4.24621	+	23.6155i	0.155153	+	0.862893i
$750$		−	3.74571i		−	0.136774i
$751$		−	3.03984i		−	0.110925i	−0.998461	−	0.0554626i	$-0.982337\pi$
$751$		−	3.03984i		−	0.110925i	0.998461	−	0.0554626i	$-0.0176634\pi$
$752$			7.12311i			0.259753i
$753$			0.821147i			0.0299243i
$754$		−	25.7538i		−	0.937898i
$755$	68.3449			2.48733
$756$	0.468213	+	2.60399i	0.0170287	+	0.0947063i
$757$			12.2888i			0.446645i	0.974745	+	0.223322i	$0.0716903\pi$
$757$			12.2888i			0.446645i	−0.974745	+	0.223322i	$0.928310\pi$
$758$		−	21.7684i		−	0.790663i
$759$	−6.67026	−	19.3693i	−0.242115	−	0.703062i
$760$	14.6307			0.530711
$761$		−	20.8769i		−	0.756787i	−0.925645	−	0.378393i	$-0.876477\pi$
$761$		−	20.8769i		−	0.756787i	0.925645	−	0.378393i	$-0.123523\pi$
$762$		−	6.24621i		−	0.226276i
$763$	5.75379	+	32.0000i	0.208301	+	1.15848i
$764$			3.45041i			0.124832i
$765$	11.1231			0.402157
$766$	−16.2651			−0.587681
$767$	−22.2462			−0.803264
$768$			17.0000i			0.613435i
$769$	−37.3276			−1.34607			−0.673034	−	0.739612i	$-0.735009\pi$
$769$	−37.3276			−1.34607			−0.673034	+	0.739612i	$0.735009\pi$
$770$	6.67026	+	37.0970i	0.240380	+	1.33688i
$771$	17.3693			0.625541
$772$	−25.6155			−0.921923
$773$	14.5722			0.524127			0.262064	−	0.965051i	$-0.415597\pi$
$773$	14.5722			0.524127			0.262064	+	0.965051i	$0.415597\pi$
$774$		−	0.936426i		−	0.0336592i
$775$			62.7386i			2.25364i
$776$	−5.61856			−0.201694
$777$	4.87689	−	0.876894i	0.174958	−	0.0314584i
$778$		−	14.5722i		−	0.522440i
$779$			16.2651i			0.582757i
$780$	10.4160			0.372952
$781$			47.5130i			1.70015i
$782$	−5.20798	−	15.1231i	−0.186237	−	0.540801i
$783$			8.24621i			0.294696i
$784$	−6.56155	+	2.43845i	−0.234341	+	0.0870874i
$785$	−50.7386			−1.81094
$786$	−12.0000			−0.428026
$787$	29.7856			1.06174			0.530872	−	0.847452i	$-0.321865\pi$
$787$	29.7856			1.06174			0.530872	+	0.847452i	$0.321865\pi$
$788$	−18.4924			−0.658765
$789$	20.5366			0.731124
$790$			53.8617i			1.91631i
$791$	−4.19224	−	23.3153i	−0.149059	−	0.828998i
$792$			12.8147i			0.455350i
$793$			5.84912i			0.207708i
$794$		−	20.4924i		−	0.727249i
$795$	−33.3693			−1.18349
$796$	−5.20798			−0.184592
$797$	17.4968			0.619769			0.309884	−	0.950774i	$-0.399710\pi$
$797$	17.4968			0.619769			0.309884	+	0.950774i	$0.399710\pi$
$798$	0.684658	+	3.80776i	0.0242366	+	0.134793i
$799$		−	23.7565i		−	0.840444i
$800$	−30.6155			−1.08242
$801$	10.0054			0.353523
$802$			11.8782i			0.419436i
$803$	26.6811			0.941554
$804$	−4.68213			−0.165126
$805$	20.6424	+	36.9420i	0.727549	+	1.30203i
$806$	32.0000			1.12715
$807$	−6.63068			−0.233411
$808$		−	9.36932i		−	0.329611i
$809$	16.2462			0.571186			0.285593	−	0.958351i	$-0.407809\pi$
$809$	16.2462			0.571186			0.285593	+	0.958351i	$0.407809\pi$
$810$	3.33513			0.117185
$811$		−	13.7538i		−	0.482961i	−0.970406	−	0.241480i	$-0.922367\pi$
$811$		−	13.7538i		−	0.482961i	0.970406	−	0.241480i	$-0.0776330\pi$
$812$	21.4731	−	3.86098i	0.753557	−	0.135494i
$813$	16.4924			0.578415
$814$	8.00000			0.280400
$815$	−40.0216			−1.40189
$816$			3.33513i			0.116753i
$817$			1.36932i			0.0479063i
$818$			1.36932i			0.0478770i
$819$	1.46228	+	8.13254i	0.0510962	+	0.284174i
$820$		−	37.0970i		−	1.29548i
$821$	28.7386			1.00299			0.501493	−	0.865162i	$-0.332784\pi$
$821$	28.7386			1.00299			0.501493	+	0.865162i	$0.332784\pi$
$822$	−14.8028			−0.516307
$823$	9.75379			0.339996			0.169998	−	0.985444i	$-0.445624\pi$
$823$	9.75379			0.339996			0.169998	+	0.985444i	$0.445624\pi$
$824$	15.6240			0.544286
$825$	−26.1552			−0.910607
$826$	3.33513	+	18.5485i	0.116044	+	0.645385i
$827$		−	6.14441i		−	0.213662i	−0.994277	−	0.106831i	$-0.965930\pi$
$827$		−	6.14441i		−	0.213662i	0.994277	−	0.106831i	$-0.0340704\pi$
$828$	1.56155	+	4.53448i	0.0542677	+	0.157584i
$829$			12.8769i			0.447233i	0.974677	+	0.223617i	$0.0717863\pi$
$829$			12.8769i			0.447233i	−0.974677	+	0.223617i	$0.928214\pi$
$830$	56.9848			1.97797
$831$		−	16.2462i		−	0.563575i
$832$			21.8617i			0.757919i
$833$	21.8836	−	8.13254i	0.758223	−	0.281776i
$834$	−12.0000			−0.415526
$835$			19.1896i			0.664085i
$836$		−	6.24621i		−	0.216030i
$837$	−10.2462			−0.354161
$838$	9.59482			0.331448
$839$	44.5884			1.53936			0.769682	−	0.638428i	$-0.220415\pi$
$839$	44.5884			1.53936			0.769682	+	0.638428i	$0.220415\pi$
$840$	−4.68466	−	26.0540i	−0.161636	−	0.898948i
$841$	39.0000			1.34483
$842$		−	25.6294i		−	0.883246i
$843$	22.2942			0.767854
$844$	10.2462			0.352689
$845$	−10.8265			−0.372444
$846$		−	7.12311i		−	0.244897i
$847$	18.8691	−	3.39277i	0.648349	−	0.116577i
$848$		−	10.0054i		−	0.343587i
$849$			19.3697i			0.664765i
$850$	−20.4214			−0.700447
$851$	8.49242	−	2.92456i	0.291116	−	0.100253i
$852$		−	11.1231i		−	0.381071i
$853$		−	8.00000i		−	0.273915i	−0.990577	−	0.136957i	$-0.956268\pi$
$853$		−	8.00000i		−	0.273915i	0.990577	−	0.136957i	$-0.0437323\pi$
$854$	4.87689	−	0.876894i	0.166884	−	0.0300067i
$855$	−4.87689			−0.166786
$856$		−	27.2069i		−	0.929913i
$857$			33.3693i			1.13987i	0.821688	+	0.569937i	$0.193032\pi$
$857$			33.3693i			1.13987i	−0.821688	+	0.569937i	$0.806968\pi$
$858$			13.3405i			0.455438i
$859$			12.0000i			0.409435i	0.978821	+	0.204717i	$0.0656275\pi$
$859$			12.0000i			0.409435i	−0.978821	+	0.204717i	$0.934372\pi$
$860$		−	3.12311i		−	0.106497i
$861$	28.9645	−	5.20798i	0.987107	−	0.177488i
$862$			28.8492i			0.982608i
$863$	−56.0000			−1.90626			−0.953131	−	0.302558i	$-0.902160\pi$
$863$	−56.0000			−1.90626			−0.953131	+	0.302558i	$0.902160\pi$
$864$		−	5.00000i		−	0.170103i
$865$		−	10.4160i		−	0.354154i
$866$	18.1379			0.616352
$867$			5.87689i			0.199590i
$868$	4.79741	+	26.6811i	0.162835	+	0.905614i
$869$	68.9848			2.34015
$870$		−	27.5022i		−	0.932412i
$871$	−14.6228			−0.495474
$872$		−	36.8665i		−	1.24846i
$873$	1.87285			0.0633865
$874$	2.28343	+	6.63068i	0.0772380	+	0.224286i
$875$	9.75379	−	1.75379i	0.329738	−	0.0592889i
$876$	−6.24621			−0.211040
$877$	−7.75379			−0.261827			−0.130913	−	0.991394i	$-0.541791\pi$
$877$	−7.75379			−0.261827			−0.130913	+	0.991394i	$0.541791\pi$
$878$			21.7538i			0.734155i
$879$			9.18425i			0.309777i
$880$		−	14.2462i		−	0.480240i
$881$	−2.51398			−0.0846983			−0.0423492	−	0.999103i	$-0.513484\pi$
$881$	−2.51398			−0.0846983			−0.0423492	+	0.999103i	$0.513484\pi$
$882$	6.56155	−	2.43845i	0.220939	−	0.0821068i
$883$	24.4924			0.824236			0.412118	−	0.911131i	$-0.364789\pi$
$883$	24.4924			0.824236			0.412118	+	0.911131i	$0.364789\pi$
$884$		−	10.4160i		−	0.350327i
$885$	−23.7565			−0.798566
$886$	−29.3693			−0.986681
$887$			49.8617i			1.67419i	0.547055	+	0.837097i	$0.315749\pi$
$887$			49.8617i			1.67419i	−0.547055	+	0.837097i	$0.684251\pi$
$888$	−5.61856			−0.188546
$889$	16.2651	−	2.92456i	0.545513	−	0.0980865i
$890$	−33.3693			−1.11854
$891$		−	4.27156i		−	0.143103i
$892$		−	4.00000i		−	0.133930i
$893$			10.4160i			0.348557i
$894$	−0.410574			−0.0137316
$895$	13.3405			0.445925
$896$	−7.81198	+	1.40464i	−0.260980	+	0.0469257i
$897$	4.87689	+	14.1617i	0.162835	+	0.472845i
$898$	−1.50758			−0.0503085
$899$			84.4924i			2.81798i
$900$	6.12311			0.204104
$901$			33.3693i			1.11169i
$902$	47.5130			1.58201
$903$	2.43845	−	0.438447i	0.0811464	−	0.0145906i
$904$			26.8611i			0.893386i
$905$	−40.9848			−1.36238
$906$		−	20.4924i		−	0.680815i
$907$		−	38.0335i		−	1.26288i	−0.775425	−	0.631440i	$-0.782464\pi$
$907$		−	38.0335i		−	1.26288i	0.775425	−	0.631440i	$-0.217536\pi$
$908$	−6.67026			−0.221360
$909$			3.12311i			0.103587i
$910$	−4.87689	−	27.1231i	−0.161667	−	0.899122i
$911$			15.5087i			0.513825i	0.966435	+	0.256913i	$0.0827053\pi$
$911$			15.5087i			0.513825i	−0.966435	+	0.256913i	$0.917295\pi$
$912$		−	1.46228i		−	0.0484209i
$913$		−	72.9848i		−	2.41545i
$914$		−	29.6056i		−	0.979267i
$915$			6.24621i			0.206493i
$916$	−12.2888			−0.406034
$917$	−5.61856	−	31.2479i	−0.185541	−	1.03190i
$918$		−	3.33513i		−	0.110076i
$919$		−	0.936426i		−	0.0308899i	−0.999881	−	0.0154449i	$-0.995084\pi$
$919$		−	0.936426i		−	0.0308899i	0.999881	−	0.0154449i	$-0.00491647\pi$
$920$	−15.6240	−	45.3693i	−0.515107	−	1.49578i
$921$	2.24621			0.0740152
$922$			9.36932i			0.308562i
$923$		−	34.7386i		−	1.14344i
$924$	−11.1231	+	2.00000i	−0.365923	+	0.0657952i
$925$		−	11.4677i		−	0.377055i
$926$	−8.00000			−0.262896
$927$	−5.20798			−0.171053
$928$	−41.2311			−1.35348
$929$		−	27.1231i		−	0.889880i	−0.895560	−	0.444940i	$-0.853225\pi$
$929$		−	27.1231i		−	0.889880i	0.895560	−	0.444940i	$-0.146775\pi$
$930$	34.1725			1.12056
$931$	−9.59482	+	3.56569i	−0.314458	+	0.116861i
$932$	3.75379			0.122959
$933$	2.63068			0.0861247
$934$	−6.67026			−0.218258
$935$			47.5130i			1.55384i
$936$		−	9.36932i		−	0.306246i
$937$	35.2242			1.15072			0.575362	−	0.817899i	$-0.304861\pi$
$937$	35.2242			1.15072			0.575362	+	0.817899i	$0.304861\pi$
$938$	2.19224	+	12.1922i	0.0715790	+	0.398091i
$939$		−	14.3922i		−	0.469673i
$940$		−	23.7565i		−	0.774852i
$941$	−40.4322			−1.31805			−0.659025	−	0.752121i	$-0.729031\pi$
$941$	−40.4322			−1.31805			−0.659025	+	0.752121i	$0.729031\pi$
$942$			15.2134i			0.495679i
$943$	50.4376	−	17.3693i	1.64247	−	0.565623i
$944$		−	7.12311i		−	0.231837i
$945$	1.56155	+	8.68466i	0.0507973	+	0.282512i
$946$	4.00000			0.130051
$947$	32.4924			1.05586			0.527931	−	0.849287i	$-0.322968\pi$
$947$	32.4924			1.05586			0.527931	+	0.849287i	$0.322968\pi$
$948$	−16.1498			−0.524521
$949$	−19.5076			−0.633243
$950$	8.95369			0.290496
$951$			14.0000i			0.453981i
$952$	−26.0540	+	4.68466i	−0.844414	+	0.151831i
$953$			10.2360i			0.331575i	0.986161	+	0.165788i	$0.0530166\pi$
$953$			10.2360i			0.331575i	−0.986161	+	0.165788i	$0.946983\pi$
$954$			10.0054i			0.323937i
$955$			11.5076i			0.372376i
$956$	1.36932			0.0442869
$957$	−35.2242			−1.13864
$958$	5.84912			0.188976
$959$	−6.93087	−	38.5464i	−0.223809	−	1.24473i
$960$			23.3459i			0.753486i
$961$	−73.9848			−2.38661
$962$	−5.84912			−0.188583
$963$			9.06897i			0.292243i
$964$	−11.4677			−0.369349
$965$	−85.4312			−2.75013
$966$	11.0766	−	6.18938i	0.356385	−	0.199140i
$967$	24.0000			0.771788			0.385894	−	0.922543i	$-0.373893\pi$
$967$	24.0000			0.771788			0.385894	+	0.922543i	$0.373893\pi$
$968$	−21.7386			−0.698706
$969$			4.87689i			0.156668i
$970$	−6.24621			−0.200554
$971$	−6.67026			−0.214059			−0.107029	−	0.994256i	$-0.534134\pi$
$971$	−6.67026			−0.214059			−0.107029	+	0.994256i	$0.534134\pi$
$972$			1.00000i			0.0320750i
$973$	−5.61856	−	31.2479i	−0.180123	−	1.00176i
$974$	14.2462			0.456478
$975$	19.1231			0.612430
$976$	−1.87285			−0.0599486
$977$		−	27.3222i		−	0.874114i	−0.899434	−	0.437057i	$-0.856021\pi$
$977$		−	27.3222i		−	0.874114i	0.899434	−	0.437057i	$-0.143979\pi$
$978$			12.0000i			0.383718i
$979$			42.7386i			1.36593i
$980$	21.8836	−	8.13254i	0.699047	−	0.259785i
$981$			12.2888i			0.392352i
$982$	32.4924			1.03687
$983$	−49.1553			−1.56781			−0.783905	−	0.620881i	$-0.786775\pi$
$983$	−49.1553			−1.56781			−0.783905	+	0.620881i	$0.786775\pi$
$984$	−33.3693			−1.06377
$985$	−61.6747			−1.96512
$986$	−27.5022			−0.875849
$987$	18.5485	−	3.33513i	0.590406	−	0.106158i
$988$			4.56685i			0.145291i
$989$	4.24621	−	1.46228i	0.135022	−	0.0464978i
$990$			14.2462i			0.452774i
$991$	−36.4924			−1.15922			−0.579610	−	0.814894i	$-0.696795\pi$
$991$	−36.4924			−1.15922			−0.579610	+	0.814894i	$0.696795\pi$
$992$		−	51.2311i		−	1.62659i
$993$			16.4924i			0.523371i
$994$	−28.9645	+	5.20798i	−0.918698	+	0.165187i
$995$	−17.3693			−0.550644
$996$			17.0862i			0.541398i
$997$		−	44.8769i		−	1.42127i	−0.703563	−	0.710633i	$-0.748409\pi$
$997$		−	44.8769i		−	1.42127i	0.703563	−	0.710633i	$-0.251591\pi$
$998$	−5.75379			−0.182133
$999$	1.87285			0.0592544

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	483.2.h.a.160.1	✓	8
3.2	odd	2		1449.2.h.d.1126.8		8
7.6	odd	2	inner	483.2.h.a.160.8	yes	8
21.20	even	2		1449.2.h.d.1126.2		8
23.22	odd	2	inner	483.2.h.a.160.4	yes	8
69.68	even	2		1449.2.h.d.1126.1		8
161.160	even	2	inner	483.2.h.a.160.5	yes	8
483.482	odd	2		1449.2.h.d.1126.7		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.2.h.a.160.1	✓	8	1.1	even	1	trivial
483.2.h.a.160.4	yes	8	23.22	odd	2	inner
483.2.h.a.160.5	yes	8	161.160	even	2	inner
483.2.h.a.160.8	yes	8	7.6	odd	2	inner
1449.2.h.d.1126.1		8	69.68	even	2
1449.2.h.d.1126.2		8	21.20	even	2
1449.2.h.d.1126.7		8	483.482	odd	2
1449.2.h.d.1126.8		8	3.2	odd	2

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:	\( N \)	\(=\)	\( 483 = 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	483.h (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.00000i q^{3} -1.00000 q^{4} -3.33513 q^{5} +1.00000i q^{6} +(-2.60399 + 0.468213i) q^{7} +3.00000 q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.00000i q^{3} -1.00000 q^{4} -3.33513 q^{5} +1.00000i q^{6} +(-2.60399 + 0.468213i) q^{7} +3.00000 q^{8} -1.00000 q^{9} +3.33513 q^{10} -4.27156i q^{11} +1.00000i q^{12} +3.12311i q^{13} +(2.60399 - 0.468213i) q^{14} +3.33513i q^{15} -1.00000 q^{16} +3.33513 q^{17} +1.00000 q^{18} -1.46228 q^{19} +3.33513 q^{20} +(0.468213 + 2.60399i) q^{21} +4.27156i q^{22} +(1.56155 + 4.53448i) q^{23} -3.00000i q^{24} +6.12311 q^{25} -3.12311i q^{26} +1.00000i q^{27} +(2.60399 - 0.468213i) q^{28} +8.24621 q^{29} -3.33513i q^{30} +10.2462i q^{31} -5.00000 q^{32} -4.27156 q^{33} -3.33513 q^{34} +(8.68466 - 1.56155i) q^{35} +1.00000 q^{36} -1.87285i q^{37} +1.46228 q^{38} +3.12311 q^{39} -10.0054 q^{40} -11.1231i q^{41} +(-0.468213 - 2.60399i) q^{42} -0.936426i q^{43} +4.27156i q^{44} +3.33513 q^{45} +(-1.56155 - 4.53448i) q^{46} -7.12311i q^{47} +1.00000i q^{48} +(6.56155 - 2.43845i) q^{49} -6.12311 q^{50} -3.33513i q^{51} -3.12311i q^{52} +10.0054i q^{53} -1.00000i q^{54} +14.2462i q^{55} +(-7.81198 + 1.40464i) q^{56} +1.46228i q^{57} -8.24621 q^{58} +7.12311i q^{59} -3.33513i q^{60} +1.87285 q^{61} -10.2462i q^{62} +(2.60399 - 0.468213i) q^{63} +7.00000 q^{64} -10.4160i q^{65} +4.27156 q^{66} +4.68213i q^{67} -3.33513 q^{68} +(4.53448 - 1.56155i) q^{69} +(-8.68466 + 1.56155i) q^{70} -11.1231 q^{71} -3.00000 q^{72} +6.24621i q^{73} +1.87285i q^{74} -6.12311i q^{75} +1.46228 q^{76} +(2.00000 + 11.1231i) q^{77} -3.12311 q^{78} +16.1498i q^{79} +3.33513 q^{80} +1.00000 q^{81} +11.1231i q^{82} +17.0862 q^{83} +(-0.468213 - 2.60399i) q^{84} -11.1231 q^{85} +0.936426i q^{86} -8.24621i q^{87} -12.8147i q^{88} -10.0054 q^{89} -3.33513 q^{90} +(-1.46228 - 8.13254i) q^{91} +(-1.56155 - 4.53448i) q^{92} +10.2462 q^{93} +7.12311i q^{94} +4.87689 q^{95} +5.00000i q^{96} -1.87285 q^{97} +(-6.56155 + 2.43845i) q^{98} +4.27156i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{2} - 8 q^{4} + 24 q^{8} - 8 q^{9}+O(q^{10}) \) 8 * q - 8 * q^2 - 8 * q^4 + 24 * q^8 - 8 * q^9	\( 8 q - 8 q^{2} - 8 q^{4} + 24 q^{8} - 8 q^{9} - 8 q^{16} + 8 q^{18} - 4 q^{23} + 16 q^{25} - 40 q^{32} + 20 q^{35} + 8 q^{36} - 8 q^{39} + 4 q^{46} + 36 q^{49} - 16 q^{50} + 56 q^{64} - 20 q^{70} - 56 q^{71} - 24 q^{72} + 16 q^{77} + 8 q^{78} + 8 q^{81} - 56 q^{85} + 4 q^{92} + 16 q^{93} + 72 q^{95} - 36 q^{98}+O(q^{100}) \) 8 * q - 8 * q^2 - 8 * q^4 + 24 * q^8 - 8 * q^9 - 8 * q^16 + 8 * q^18 - 4 * q^23 + 16 * q^25 - 40 * q^32 + 20 * q^35 + 8 * q^36 - 8 * q^39 + 4 * q^46 + 36 * q^49 - 16 * q^50 + 56 * q^64 - 20 * q^70 - 56 * q^71 - 24 * q^72 + 16 * q^77 + 8 * q^78 + 8 * q^81 - 56 * q^85 + 4 * q^92 + 16 * q^93 + 72 * q^95 - 36 * q^98

Introduction

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