LMFDB - Embedded newform 1155.2.c.e.694.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1155,2,Mod(694,1155)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1155, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1155.694");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1155 = 3 \cdot 5 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1155.c (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:	$9.22272143346$
Analytic rank:	$0$
Dimension:	$20$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 33 x^{18} + 456 x^{16} + 3426 x^{14} + 15194 x^{12} + 40320 x^{10} + 61593 x^{8} + 48545 x^{6} + \cdots + 100 $ x^20 + 33x^18 + 456x^16 + 3426x^14 + 15194x^12 + 40320x^10 + 61593x^8 + 48545x^6 + 15624x^4 + 2116*x^2 + 100
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			694.18
Root			$2.51027i$ of defining polynomial
Character	$\chi$	$=$	1155.694
Dual form			1155.2.c.e.694.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.51027i q^{2} +1.00000i q^{3} -4.30144 q^{4} +(-1.80593 + 1.31856i) q^{5} -2.51027 q^{6} -1.00000i q^{7} -5.77723i q^{8} -1.00000 q^{9} +O(q^{10})$	\(q+2.51027i q^{2} +1.00000i q^{3} -4.30144 q^{4} +(-1.80593 + 1.31856i) q^{5} -2.51027 q^{6} -1.00000i q^{7} -5.77723i q^{8} -1.00000 q^{9} +(-3.30994 - 4.53337i) q^{10} -1.00000 q^{11} -4.30144i q^{12} -7.07998i q^{13} +2.51027 q^{14} +(-1.31856 - 1.80593i) q^{15} +5.89951 q^{16} +0.968488i q^{17} -2.51027i q^{18} +2.31494 q^{19} +(7.76811 - 5.67172i) q^{20} +1.00000 q^{21} -2.51027i q^{22} +5.12905i q^{23} +5.77723 q^{24} +(1.52278 - 4.76247i) q^{25} +17.7726 q^{26} -1.00000i q^{27} +4.30144i q^{28} -6.98999 q^{29} +(4.53337 - 3.30994i) q^{30} +6.96479 q^{31} +3.25488i q^{32} -1.00000i q^{33} -2.43116 q^{34} +(1.31856 + 1.80593i) q^{35} +4.30144 q^{36} +4.39198i q^{37} +5.81112i q^{38} +7.07998 q^{39} +(7.61764 + 10.4333i) q^{40} -8.89382 q^{41} +2.51027i q^{42} -12.7301i q^{43} +4.30144 q^{44} +(1.80593 - 1.31856i) q^{45} -12.8753 q^{46} -7.09593i q^{47} +5.89951i q^{48} -1.00000 q^{49} +(11.9551 + 3.82260i) q^{50} -0.968488 q^{51} +30.4541i q^{52} -5.21281i q^{53} +2.51027 q^{54} +(1.80593 - 1.31856i) q^{55} -5.77723 q^{56} +2.31494i q^{57} -17.5467i q^{58} -8.48666 q^{59} +(5.67172 + 7.76811i) q^{60} -1.53492 q^{61} +17.4835i q^{62} +1.00000i q^{63} +3.62839 q^{64} +(9.33540 + 12.7860i) q^{65} +2.51027 q^{66} +3.70876i q^{67} -4.16589i q^{68} -5.12905 q^{69} +(-4.53337 + 3.30994i) q^{70} +11.7199 q^{71} +5.77723i q^{72} -1.94702i q^{73} -11.0251 q^{74} +(4.76247 + 1.52278i) q^{75} -9.95758 q^{76} +1.00000i q^{77} +17.7726i q^{78} -13.1925 q^{79} +(-10.6541 + 7.77887i) q^{80} +1.00000 q^{81} -22.3259i q^{82} +8.06703i q^{83} -4.30144 q^{84} +(-1.27701 - 1.74902i) q^{85} +31.9559 q^{86} -6.98999i q^{87} +5.77723i q^{88} +12.6271 q^{89} +(3.30994 + 4.53337i) q^{90} -7.07998 q^{91} -22.0623i q^{92} +6.96479i q^{93} +17.8127 q^{94} +(-4.18063 + 3.05240i) q^{95} -3.25488 q^{96} +4.07780i q^{97} -2.51027i q^{98} +1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 26 q^{4} - 2 q^{5} + 6 q^{6} - 20 q^{9}+O(q^{10}) $ 20 * q - 26 * q^4 - 2 * q^5 + 6 * q^6 - 20 * q^9	$ 20 q - 26 q^{4} - 2 q^{5} + 6 q^{6} - 20 q^{9} - 2 q^{10} - 20 q^{11} - 6 q^{14} + 2 q^{15} + 38 q^{16} + 2 q^{19} + 4 q^{20} + 20 q^{21} - 18 q^{24} + 12 q^{25} + 20 q^{26} - 38 q^{29} + 6 q^{30} + 20 q^{31} - 32 q^{34} - 2 q^{35} + 26 q^{36} + 2 q^{40} + 12 q^{41} + 26 q^{44} + 2 q^{45} + 8 q^{46} - 20 q^{49} - 6 q^{50} + 26 q^{51} - 6 q^{54} + 2 q^{55} + 18 q^{56} - 22 q^{59} + 16 q^{60} + 34 q^{61} - 26 q^{64} - 28 q^{65} - 6 q^{66} - 26 q^{69} - 6 q^{70} + 72 q^{71} - 72 q^{74} - 8 q^{75} + 44 q^{76} + 4 q^{79} - 8 q^{80} + 20 q^{81} - 26 q^{84} - 16 q^{85} + 52 q^{86} + 6 q^{89} + 2 q^{90} + 16 q^{94} + 14 q^{95} + 62 q^{96} + 20 q^{99}+O(q^{100}) $ 20 * q - 26 * q^4 - 2 * q^5 + 6 * q^6 - 20 * q^9 - 2 * q^10 - 20 * q^11 - 6 * q^14 + 2 * q^15 + 38 * q^16 + 2 * q^19 + 4 * q^20 + 20 * q^21 - 18 * q^24 + 12 * q^25 + 20 * q^26 - 38 * q^29 + 6 * q^30 + 20 * q^31 - 32 * q^34 - 2 * q^35 + 26 * q^36 + 2 * q^40 + 12 * q^41 + 26 * q^44 + 2 * q^45 + 8 * q^46 - 20 * q^49 - 6 * q^50 + 26 * q^51 - 6 * q^54 + 2 * q^55 + 18 * q^56 - 22 * q^59 + 16 * q^60 + 34 * q^61 - 26 * q^64 - 28 * q^65 - 6 * q^66 - 26 * q^69 - 6 * q^70 + 72 * q^71 - 72 * q^74 - 8 * q^75 + 44 * q^76 + 4 * q^79 - 8 * q^80 + 20 * q^81 - 26 * q^84 - 16 * q^85 + 52 * q^86 + 6 * q^89 + 2 * q^90 + 16 * q^94 + 14 * q^95 + 62 * q^96 + 20 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1155\mathbb{Z}\right)^\times$.

$n$	$211$	$232$	$386$	$661$
$\chi(n)$	$1$	$-1$	$1$	$1$

Coefficient data

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

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

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

$2$			2.51027i			1.77503i	0.460782	+	0.887513i	$0.347569\pi$
$2$			2.51027i			1.77503i	−0.460782	+	0.887513i	$0.652431\pi$
$3$			1.00000i			0.577350i
$3$			1.00000i			0.577350i
$4$	−4.30144			−2.15072
$5$	−1.80593	+	1.31856i	−0.807638	+	0.589679i
$5$	−1.80593	+	1.31856i	−0.807638	+	0.589679i
$6$	−2.51027			−1.02481
$7$		−	1.00000i		−	0.377964i
$7$		−	1.00000i		−	0.377964i
$8$		−	5.77723i		−	2.04256i
$9$	−1.00000			−0.333333
$10$	−3.30994	−	4.53337i	−1.04670	−	1.43358i
$11$	−1.00000			−0.301511
$11$	−1.00000			−0.301511
$12$		−	4.30144i		−	1.24172i
$13$		−	7.07998i		−	1.96363i	−0.189831	−	0.981817i	$-0.560794\pi$
$13$		−	7.07998i		−	1.96363i	0.189831	−	0.981817i	$-0.439206\pi$
$14$	2.51027			0.670897
$15$	−1.31856	−	1.80593i	−0.340451	−	0.466290i
$16$	5.89951			1.47488
$17$			0.968488i			0.234893i	0.993079	+	0.117446i	$0.0374708\pi$
$17$			0.968488i			0.234893i	−0.993079	+	0.117446i	$0.962529\pi$
$18$		−	2.51027i		−	0.591676i
$19$	2.31494			0.531084			0.265542	−	0.964099i	$-0.414449\pi$
$19$	2.31494			0.531084			0.265542	+	0.964099i	$0.414449\pi$
$20$	7.76811	−	5.67172i	1.73700	−	1.26823i
$21$	1.00000			0.218218
$22$		−	2.51027i		−	0.535191i
$23$			5.12905i			1.06948i	0.845016	+	0.534741i	$0.179591\pi$
$23$			5.12905i			1.06948i	−0.845016	+	0.534741i	$0.820409\pi$
$24$	5.77723			1.17927
$25$	1.52278	−	4.76247i	0.304557	−	0.952494i
$26$	17.7726			3.48550
$27$		−	1.00000i		−	0.192450i
$28$			4.30144i			0.812896i
$29$	−6.98999			−1.29801			−0.649004	−	0.760785i	$-0.724814\pi$
$29$	−6.98999			−1.29801			−0.649004	+	0.760785i	$0.724814\pi$
$30$	4.53337	−	3.30994i	0.827677	−	0.604310i
$31$	6.96479			1.25091			0.625457	−	0.780259i	$-0.284913\pi$
$31$	6.96479			1.25091			0.625457	+	0.780259i	$0.284913\pi$
$32$			3.25488i			0.575387i
$33$		−	1.00000i		−	0.174078i
$34$	−2.43116			−0.416941
$35$	1.31856	+	1.80593i	0.222878	+	0.305258i
$36$	4.30144			0.716907
$37$			4.39198i			0.722038i	0.932559	+	0.361019i	$0.117571\pi$
$37$			4.39198i			0.722038i	−0.932559	+	0.361019i	$0.882429\pi$
$38$			5.81112i			0.942688i
$39$	7.07998			1.13370
$40$	7.61764	+	10.4333i	1.20445	+	1.64965i
$41$	−8.89382			−1.38898			−0.694490	−	0.719502i	$-0.744370\pi$
$41$	−8.89382			−1.38898			−0.694490	+	0.719502i	$0.744370\pi$
$42$			2.51027i			0.387343i
$43$		−	12.7301i		−	1.94132i	−0.240453	−	0.970661i	$-0.577296\pi$
$43$		−	12.7301i		−	1.94132i	0.240453	−	0.970661i	$-0.422704\pi$
$44$	4.30144			0.648467
$45$	1.80593	−	1.31856i	0.269213	−	0.196560i
$46$	−12.8753			−1.89836
$47$		−	7.09593i		−	1.03505i	−0.855669	−	0.517524i	$-0.826854\pi$
$47$		−	7.09593i		−	1.03505i	0.855669	−	0.517524i	$-0.173146\pi$
$48$			5.89951i			0.851521i
$49$	−1.00000			−0.142857
$50$	11.9551	+	3.82260i	1.69070	+	0.540597i
$51$	−0.968488			−0.135615
$52$			30.4541i			4.22323i
$53$		−	5.21281i		−	0.716034i	−0.933715	−	0.358017i	$-0.883453\pi$
$53$		−	5.21281i		−	0.716034i	0.933715	−	0.358017i	$-0.116547\pi$
$54$	2.51027			0.341604
$55$	1.80593	−	1.31856i	0.243512	−	0.177795i
$56$	−5.77723			−0.772015
$57$			2.31494i			0.306622i
$58$		−	17.5467i		−	2.30400i
$59$	−8.48666			−1.10487			−0.552435	−	0.833556i	$-0.686301\pi$
$59$	−8.48666			−1.10487			−0.552435	+	0.833556i	$0.686301\pi$
$60$	5.67172	+	7.76811i	0.732216	+	1.00286i
$61$	−1.53492			−0.196527			−0.0982634	−	0.995160i	$-0.531329\pi$
$61$	−1.53492			−0.196527			−0.0982634	+	0.995160i	$0.531329\pi$
$62$			17.4835i			2.22040i
$63$			1.00000i			0.125988i
$64$	3.62839			0.453549
$65$	9.33540	+	12.7860i	1.15791	+	1.58590i
$66$	2.51027			0.308993
$67$			3.70876i			0.453097i	0.974000	+	0.226549i	$0.0727442\pi$
$67$			3.70876i			0.453097i	−0.974000	+	0.226549i	$0.927256\pi$
$68$		−	4.16589i		−	0.505189i
$69$	−5.12905			−0.617465
$70$	−4.53337	+	3.30994i	−0.541842	+	0.395614i
$71$	11.7199			1.39090			0.695449	−	0.718575i	$-0.255206\pi$
$71$	11.7199			1.39090			0.695449	+	0.718575i	$0.255206\pi$
$72$			5.77723i			0.680853i
$73$		−	1.94702i		−	0.227882i	−0.993488	−	0.113941i	$-0.963653\pi$
$73$		−	1.94702i		−	0.227882i	0.993488	−	0.113941i	$-0.0363475\pi$
$74$	−11.0251			−1.28164
$75$	4.76247	+	1.52278i	0.549923	+	0.175836i
$76$	−9.95758			−1.14221
$77$			1.00000i			0.113961i
$78$			17.7726i			2.01236i
$79$	−13.1925			−1.48428			−0.742139	−	0.670246i	$-0.766189\pi$
$79$	−13.1925			−1.48428			−0.742139	+	0.670246i	$0.766189\pi$
$80$	−10.6541	+	7.77887i	−1.19117	+	0.869704i
$81$	1.00000			0.111111
$82$		−	22.3259i		−	2.46548i
$83$			8.06703i			0.885472i	0.896652	+	0.442736i	$0.145992\pi$
$83$			8.06703i			0.885472i	−0.896652	+	0.442736i	$0.854008\pi$
$84$	−4.30144			−0.469326
$85$	−1.27701	−	1.74902i	−0.138511	−	0.189708i
$86$	31.9559			3.44590
$87$		−	6.98999i		−	0.749405i
$88$			5.77723i			0.615855i
$89$	12.6271			1.33847			0.669236	−	0.743050i	$-0.266621\pi$
$89$	12.6271			1.33847			0.669236	+	0.743050i	$0.266621\pi$
$90$	3.30994	+	4.53337i	0.348899	+	0.477859i
$91$	−7.07998			−0.742184
$92$		−	22.0623i		−	2.30016i
$93$			6.96479i			0.722215i
$94$	17.8127			1.83724
$95$	−4.18063	+	3.05240i	−0.428923	+	0.313169i
$96$	−3.25488			−0.332200
$97$			4.07780i			0.414038i	0.978337	+	0.207019i	$0.0663761\pi$
$97$			4.07780i			0.414038i	−0.978337	+	0.207019i	$0.933624\pi$
$98$		−	2.51027i		−	0.253575i
$99$	1.00000			0.100504
$100$	−6.55017	+	20.4855i	−0.655017	+	2.04855i
$101$	−3.88589			−0.386661			−0.193330	−	0.981134i	$-0.561929\pi$
$101$	−3.88589			−0.386661			−0.193330	+	0.981134i	$0.561929\pi$
$102$		−	2.43116i		−	0.240721i
$103$			6.12722i			0.603733i	0.953350	+	0.301866i	$0.0976096\pi$
$103$			6.12722i			0.603733i	−0.953350	+	0.301866i	$0.902390\pi$
$104$	−40.9027			−4.01084
$105$	−1.80593	+	1.31856i	−0.176241	+	0.128679i
$106$	13.0855			1.27098
$107$		−	17.8842i		−	1.72893i	−0.502690	−	0.864467i	$-0.667656\pi$
$107$		−	17.8842i		−	1.72893i	0.502690	−	0.864467i	$-0.332344\pi$
$108$			4.30144i			0.413906i
$109$	−4.81924			−0.461599			−0.230800	−	0.973001i	$-0.574134\pi$
$109$	−4.81924			−0.461599			−0.230800	+	0.973001i	$0.574134\pi$
$110$	3.30994	+	4.53337i	0.315591	+	0.432240i
$111$	−4.39198			−0.416869
$112$		−	5.89951i		−	0.557451i
$113$		−	15.7928i		−	1.48566i	−0.669479	−	0.742831i	$-0.733482\pi$
$113$		−	15.7928i		−	1.48566i	0.669479	−	0.742831i	$-0.266518\pi$
$114$	−5.81112			−0.544261
$115$	−6.76298	−	9.26272i	−0.630651	−	0.863754i
$116$	30.0670			2.79165
$117$			7.07998i			0.654545i
$118$		−	21.3038i		−	1.96117i
$119$	0.968488			0.0887811
$120$	−10.4333	+	7.61764i	−0.952424	+	0.695392i
$121$	1.00000			0.0909091
$122$		−	3.85307i		−	0.348840i
$123$		−	8.89382i		−	0.801928i
$124$	−29.9586			−2.69036
$125$	3.52957	+	10.6086i	0.315694	+	0.948861i
$126$	−2.51027			−0.223632
$127$		−	5.32684i		−	0.472681i	−0.971670	−	0.236340i	$-0.924052\pi$
$127$		−	5.32684i		−	0.472681i	0.971670	−	0.236340i	$-0.0759480\pi$
$128$			15.6180i			1.38045i
$129$	12.7301			1.12082
$130$	−32.0962	+	23.4343i	−2.81502	+	2.05533i
$131$	17.1131			1.49518			0.747588	−	0.664163i	$-0.231212\pi$
$131$	17.1131			1.49518			0.747588	+	0.664163i	$0.231212\pi$
$132$			4.30144i			0.374392i
$133$		−	2.31494i		−	0.200731i
$134$	−9.30998			−0.804260
$135$	1.31856	+	1.80593i	0.113484	+	0.155430i
$136$	5.59518			0.479782
$137$		−	2.36803i		−	0.202315i	−0.994870	−	0.101157i	$-0.967745\pi$
$137$		−	2.36803i		−	0.202315i	0.994870	−	0.101157i	$-0.0322546\pi$
$138$		−	12.8753i		−	1.09602i
$139$	−4.62584			−0.392359			−0.196179	−	0.980568i	$-0.562854\pi$
$139$	−4.62584			−0.392359			−0.196179	+	0.980568i	$0.562854\pi$
$140$	−5.67172	−	7.76811i	−0.479348	−	0.656525i
$141$	7.09593			0.597585
$142$			29.4201i			2.46888i
$143$			7.07998i			0.592058i
$144$	−5.89951			−0.491626
$145$	12.6234	−	9.21673i	1.04832	−	0.765408i
$146$	4.88755			0.404497
$147$		−	1.00000i		−	0.0824786i
$148$		−	18.8919i		−	1.55290i
$149$	−12.5025			−1.02424			−0.512122	−	0.858913i	$-0.671140\pi$
$149$	−12.5025			−1.02424			−0.512122	+	0.858913i	$0.671140\pi$
$150$	−3.82260	+	11.9551i	−0.312114	+	0.976128i
$151$	−14.5167			−1.18135			−0.590677	−	0.806908i	$-0.701139\pi$
$151$	−14.5167			−1.18135			−0.590677	+	0.806908i	$0.701139\pi$
$152$		−	13.3740i		−	1.08477i
$153$		−	0.968488i		−	0.0782976i
$154$	−2.51027			−0.202283
$155$	−12.5779	+	9.18351i	−1.01028	+	0.737638i
$156$	−30.4541			−2.43828
$157$		−	13.5603i		−	1.08223i	−0.840948	−	0.541117i	$-0.818002\pi$
$157$		−	13.5603i		−	1.08223i	0.840948	−	0.541117i	$-0.181998\pi$
$158$		−	33.1168i		−	2.63463i
$159$	5.21281			0.413402
$160$	−4.29177	−	5.87810i	−0.339294	−	0.464704i
$161$	5.12905			0.404226
$162$			2.51027i			0.197225i
$163$		−	16.4125i		−	1.28553i	−0.766064	−	0.642764i	$-0.777787\pi$
$163$		−	16.4125i		−	1.28553i	0.766064	−	0.642764i	$-0.222213\pi$
$164$	38.2562			2.98731
$165$	1.31856	+	1.80593i	0.102650	+	0.140592i
$166$	−20.2504			−1.57174
$167$		−	14.9188i		−	1.15445i	−0.816584	−	0.577226i	$-0.804135\pi$
$167$		−	14.9188i		−	1.15445i	0.816584	−	0.577226i	$-0.195865\pi$
$168$		−	5.77723i		−	0.445723i
$169$	−37.1261			−2.85586
$170$	4.39052	−	3.20564i	0.336737	−	0.245861i
$171$	−2.31494			−0.177028
$172$			54.7578i			4.17524i
$173$		−	6.15172i		−	0.467706i	−0.972272	−	0.233853i	$-0.924866\pi$
$173$		−	6.15172i		−	0.467706i	0.972272	−	0.233853i	$-0.0751335\pi$
$174$	17.5467			1.33021
$175$	−4.76247	−	1.52278i	−0.360009	−	0.115112i
$176$	−5.89951			−0.444692
$177$		−	8.48666i		−	0.637896i
$178$			31.6975i			2.37582i
$179$	0.615080			0.0459732			0.0229866	−	0.999736i	$-0.492682\pi$
$179$	0.615080			0.0459732			0.0229866	+	0.999736i	$0.492682\pi$
$180$	−7.76811	+	5.67172i	−0.579001	+	0.422745i
$181$	16.2500			1.20785			0.603926	−	0.797040i	$-0.293602\pi$
$181$	16.2500			1.20785			0.603926	+	0.797040i	$0.293602\pi$
$182$		−	17.7726i		−	1.31740i
$183$		−	1.53492i		−	0.113465i
$184$	29.6317			2.18448
$185$	−5.79111	−	7.93163i	−0.425771	−	0.583145i
$186$	−17.4835			−1.28195
$187$		−	0.968488i		−	0.0708228i
$188$			30.5227i			2.22610i
$189$	−1.00000			−0.0727393
$190$	−7.66233	−	10.4945i	−0.555884	−	0.761351i
$191$	−5.57552			−0.403430			−0.201715	−	0.979444i	$-0.564652\pi$
$191$	−5.57552			−0.403430			−0.201715	+	0.979444i	$0.564652\pi$
$192$			3.62839i			0.261857i
$193$		−	8.78659i		−	0.632473i	−0.948680	−	0.316236i	$-0.897581\pi$
$193$		−	8.78659i		−	0.632473i	0.948680	−	0.316236i	$-0.102419\pi$
$194$	−10.2364			−0.734928
$195$	−12.7860	+	9.33540i	−0.915622	+	0.668522i
$196$	4.30144			0.307246
$197$		−	6.85734i		−	0.488566i	−0.969704	−	0.244283i	$-0.921447\pi$
$197$		−	6.85734i		−	0.488566i	0.969704	−	0.244283i	$-0.0785525\pi$
$198$			2.51027i			0.178397i
$199$	−1.09924			−0.0779231			−0.0389616	−	0.999241i	$-0.512405\pi$
$199$	−1.09924			−0.0779231			−0.0389616	+	0.999241i	$0.512405\pi$
$200$	−27.5139	−	8.79748i	−1.94553	−	0.622076i
$201$	−3.70876			−0.261596
$202$		−	9.75462i		−	0.686333i
$203$			6.98999i			0.490601i
$204$	4.16589			0.291671
$205$	16.0616	−	11.7271i	1.12179	−	0.819053i
$206$	−15.3809			−1.07164
$207$		−	5.12905i		−	0.356494i
$208$		−	41.7684i		−	2.89612i
$209$	−2.31494			−0.160128
$210$	−3.30994	−	4.53337i	−0.228408	−	0.312832i
$211$	2.08794			0.143739			0.0718697	−	0.997414i	$-0.477103\pi$
$211$	2.08794			0.143739			0.0718697	+	0.997414i	$0.477103\pi$
$212$			22.4226i			1.53999i
$213$			11.7199i			0.803035i
$214$	44.8942			3.06890
$215$	16.7854	+	22.9897i	1.14476	+	1.56788i
$216$	−5.77723			−0.393091
$217$		−	6.96479i		−	0.472801i
$218$		−	12.0976i		−	0.819351i
$219$	1.94702			0.131568
$220$	−7.76811	+	5.67172i	−0.523726	+	0.382387i
$221$	6.85687			0.461243
$222$		−	11.0251i		−	0.739953i
$223$			26.4956i			1.77428i	0.461503	+	0.887139i	$0.347310\pi$
$223$			26.4956i			1.77428i	−0.461503	+	0.887139i	$0.652690\pi$
$224$	3.25488			0.217476
$225$	−1.52278	+	4.76247i	−0.101519	+	0.317498i
$226$	39.6442			2.63709
$227$		−	0.210227i		−	0.0139533i	−0.999976	−	0.00697664i	$-0.997779\pi$
$227$		−	0.210227i		−	0.0139533i	0.999976	−	0.00697664i	$-0.00222075\pi$
$228$		−	9.95758i		−	0.659457i
$229$	0.750284			0.0495802			0.0247901	−	0.999693i	$-0.492108\pi$
$229$	0.750284			0.0495802			0.0247901	+	0.999693i	$0.492108\pi$
$230$	23.2519	−	16.9769i	1.53319	−	1.11942i
$231$	−1.00000			−0.0657952
$232$			40.3828i			2.65126i
$233$			14.7110i			0.963751i	0.876240	+	0.481876i	$0.160044\pi$
$233$			14.7110i			0.963751i	−0.876240	+	0.481876i	$0.839956\pi$
$234$	−17.7726			−1.16183
$235$	9.35643	+	12.8148i	0.610346	+	0.835944i
$236$	36.5049			2.37626
$237$		−	13.1925i		−	0.856948i
$238$			2.43116i			0.157589i
$239$	−6.33115			−0.409528			−0.204764	−	0.978811i	$-0.565643\pi$
$239$	−6.33115			−0.409528			−0.204764	+	0.978811i	$0.565643\pi$
$240$	−7.77887	−	10.6541i	−0.502124	−	0.687720i
$241$	23.3713			1.50548			0.752739	−	0.658319i	$-0.228732\pi$
$241$	23.3713			1.50548			0.752739	+	0.658319i	$0.228732\pi$
$242$			2.51027i			0.161366i
$243$			1.00000i			0.0641500i
$244$	6.60238			0.422674
$245$	1.80593	−	1.31856i	0.115377	−	0.0842399i
$246$	22.3259			1.42344
$247$		−	16.3897i		−	1.04285i
$248$		−	40.2372i		−	2.55506i
$249$	−8.06703			−0.511227
$250$	−26.6304	+	8.86016i	−1.68425	+	0.560366i
$251$	4.42902			0.279557			0.139779	−	0.990183i	$-0.455361\pi$
$251$	4.42902			0.279557			0.139779	+	0.990183i	$0.455361\pi$
$252$		−	4.30144i		−	0.270965i
$253$		−	5.12905i		−	0.322461i
$254$	13.3718			0.839021
$255$	1.74902	−	1.27701i	0.109528	−	0.0799696i
$256$	−31.9486			−1.99679
$257$		−	10.4463i		−	0.651625i	−0.945434	−	0.325813i	$-0.894362\pi$
$257$		−	10.4463i		−	0.651625i	0.945434	−	0.325813i	$-0.105638\pi$
$258$			31.9559i			1.98949i
$259$	4.39198			0.272905
$260$	−40.1557	−	54.9981i	−2.49035	−	3.41084i
$261$	6.98999			0.432669
$262$			42.9584i			2.65398i
$263$		−	20.6449i		−	1.27302i	−0.771268	−	0.636511i	$-0.780377\pi$
$263$		−	20.6449i		−	1.27302i	0.771268	−	0.636511i	$-0.219623\pi$
$264$	−5.77723			−0.355564
$265$	6.87341	+	9.41398i	0.422230	+	0.578296i
$266$	5.81112			0.356303
$267$			12.6271i			0.772767i
$268$		−	15.9530i		−	0.974485i
$269$	−16.7639			−1.02212			−0.511058	−	0.859546i	$-0.670746\pi$
$269$	−16.7639			−1.02212			−0.511058	+	0.859546i	$0.670746\pi$
$270$	−4.53337	+	3.30994i	−0.275892	+	0.201437i
$271$	−15.7900			−0.959174			−0.479587	−	0.877494i	$-0.659214\pi$
$271$	−15.7900			−0.959174			−0.479587	+	0.877494i	$0.659214\pi$
$272$			5.71360i			0.346438i
$273$		−	7.07998i		−	0.428500i
$274$	5.94440			0.359114
$275$	−1.52278	+	4.76247i	−0.0918274	+	0.287188i
$276$	22.0623			1.32800
$277$			16.9442i			1.01808i	0.860743	+	0.509040i	$0.170000\pi$
$277$			16.9442i			1.01808i	−0.860743	+	0.509040i	$0.830000\pi$
$278$		−	11.6121i		−	0.696448i
$279$	−6.96479			−0.416971
$280$	10.4333	−	7.61764i	0.623508	−	0.455241i
$281$	−17.6550			−1.05321			−0.526605	−	0.850110i	$-0.676535\pi$
$281$	−17.6550			−1.05321			−0.526605	+	0.850110i	$0.676535\pi$
$282$			17.8127i			1.06073i
$283$			18.7184i			1.11269i	0.830951	+	0.556346i	$0.187797\pi$
$283$			18.7184i			1.11269i	−0.830951	+	0.556346i	$0.812203\pi$
$284$	−50.4125			−2.99143
$285$	−3.05240	−	4.18063i	−0.180808	−	0.247639i
$286$	−17.7726			−1.05092
$287$			8.89382i			0.524985i
$288$		−	3.25488i		−	0.191796i
$289$	16.0620			0.944825
$290$	23.1365	+	31.6882i	1.35862	+	1.86080i
$291$	−4.07780			−0.239045
$292$			8.37501i			0.490110i
$293$		−	16.4342i		−	0.960093i	−0.877243	−	0.480047i	$-0.840620\pi$
$293$		−	16.4342i		−	0.960093i	0.877243	−	0.480047i	$-0.159380\pi$
$294$	2.51027			0.146402
$295$	15.3263	−	11.1902i	0.892334	−	0.651518i
$296$	25.3735			1.47480
$297$			1.00000i			0.0580259i
$298$		−	31.3846i		−	1.81806i
$299$	36.3136			2.10007
$300$	−20.4855	−	6.55017i	−1.18273	−	0.378174i
$301$	−12.7301			−0.733751
$302$		−	36.4408i		−	2.09693i
$303$		−	3.88589i		−	0.223239i
$304$	13.6570			0.783284
$305$	2.77197	−	2.02389i	0.158722	−	0.115888i
$306$	2.43116			0.138980
$307$		−	28.0691i		−	1.60199i	−0.598671	−	0.800995i	$-0.704304\pi$
$307$		−	28.0691i		−	1.60199i	0.598671	−	0.800995i	$-0.295696\pi$
$308$		−	4.30144i		−	0.245097i
$309$	−6.12722			−0.348565
$310$	−23.0531	−	31.5740i	−1.30933	−	1.79328i
$311$	−5.23614			−0.296914			−0.148457	−	0.988919i	$-0.547431\pi$
$311$	−5.23614			−0.296914			−0.148457	+	0.988919i	$0.547431\pi$
$312$		−	40.9027i		−	2.31566i
$313$			5.12312i			0.289576i	0.989463	+	0.144788i	$0.0462500\pi$
$313$			5.12312i			0.289576i	−0.989463	+	0.144788i	$0.953750\pi$
$314$	34.0401			1.92099
$315$	−1.31856	−	1.80593i	−0.0742926	−	0.101753i
$316$	56.7470			3.19227
$317$		−	2.66847i		−	0.149876i	−0.997188	−	0.0749382i	$-0.976124\pi$
$317$		−	2.66847i		−	0.149876i	0.997188	−	0.0749382i	$-0.0238760\pi$
$318$			13.0855i			0.733800i
$319$	6.98999			0.391364
$320$	−6.55264	+	4.78427i	−0.366303	+	0.267449i
$321$	17.8842			0.998200
$322$			12.8753i			0.717512i
$323$			2.24199i			0.124748i
$324$	−4.30144			−0.238969
$325$	−33.7182	−	10.7813i	−1.87035	−	0.598038i
$326$	41.1998			2.28185
$327$		−	4.81924i		−	0.266505i
$328$			51.3816i			2.83708i
$329$	−7.09593			−0.391211
$330$	−4.53337	+	3.30994i	−0.249554	+	0.182206i
$331$	−27.1033			−1.48973			−0.744866	−	0.667215i	$-0.767486\pi$
$331$	−27.1033			−1.48973			−0.744866	+	0.667215i	$0.767486\pi$
$332$		−	34.6999i		−	1.90440i
$333$		−	4.39198i		−	0.240679i
$334$	37.4502			2.04918
$335$	−4.89023	−	6.69777i	−0.267182	−	0.365938i
$336$	5.89951			0.321845
$337$			5.84159i			0.318212i	0.987262	+	0.159106i	$0.0508611\pi$
$337$			5.84159i			0.318212i	−0.987262	+	0.159106i	$0.949139\pi$
$338$		−	93.1965i		−	5.06922i
$339$	15.7928			0.857748
$340$	5.49299	+	7.52332i	0.297899	+	0.408009i
$341$	−6.96479			−0.377165
$342$		−	5.81112i		−	0.314229i
$343$			1.00000i			0.0539949i
$344$	−73.5447			−3.96526
$345$	9.26272	−	6.76298i	0.498688	−	0.364107i
$346$	15.4425			0.830191
$347$		−	22.4877i		−	1.20720i	−0.797286	−	0.603602i	$-0.793732\pi$
$347$		−	22.4877i		−	1.20720i	0.797286	−	0.603602i	$-0.206268\pi$
$348$			30.0670i			1.61176i
$349$	−5.44689			−0.291565			−0.145783	−	0.989317i	$-0.546570\pi$
$349$	−5.44689			−0.291565			−0.145783	+	0.989317i	$0.546570\pi$
$350$	3.82260	−	11.9551i	0.204326	−	0.639026i
$351$	−7.07998			−0.377901
$352$		−	3.25488i		−	0.173486i
$353$			13.4009i			0.713259i	0.934246	+	0.356629i	$0.116074\pi$
$353$			13.4009i			0.713259i	−0.934246	+	0.356629i	$0.883926\pi$
$354$	21.3038			1.13228
$355$	−21.1654	+	15.4534i	−1.12334	+	0.820184i
$356$	−54.3148			−2.87868
$357$			0.968488i			0.0512578i
$358$			1.54402i			0.0816037i
$359$	−22.1829			−1.17077			−0.585385	−	0.810755i	$-0.699057\pi$
$359$	−22.1829			−1.17077			−0.585385	+	0.810755i	$0.699057\pi$
$360$	−7.61764	−	10.4333i	−0.401485	−	0.549883i
$361$	−13.6410			−0.717950
$362$			40.7918i			2.14397i
$363$			1.00000i			0.0524864i
$364$	30.4541			1.59623
$365$	2.56727	+	3.51619i	0.134377	+	0.184046i
$366$	3.85307			0.201403
$367$		−	25.4973i		−	1.33095i	−0.746420	−	0.665475i	$-0.768229\pi$
$367$		−	25.4973i		−	1.33095i	0.746420	−	0.665475i	$-0.231771\pi$
$368$			30.2589i			1.57735i
$369$	8.89382			0.462994
$370$	19.9105	−	14.5372i	1.03510	−	0.755754i
$371$	−5.21281			−0.270635
$372$		−	29.9586i		−	1.55328i
$373$		−	16.7286i		−	0.866175i	−0.901352	−	0.433087i	$-0.857424\pi$
$373$		−	16.7286i		−	0.866175i	0.901352	−	0.433087i	$-0.142576\pi$
$374$	2.43116			0.125712
$375$	−10.6086	+	3.52957i	−0.547825	+	0.182266i
$376$	−40.9948			−2.11415
$377$			49.4890i			2.54881i
$378$		−	2.51027i		−	0.129114i
$379$	−1.43179			−0.0735460			−0.0367730	−	0.999324i	$-0.511708\pi$
$379$	−1.43179			−0.0735460			−0.0367730	+	0.999324i	$0.511708\pi$
$380$	17.9827	−	13.1297i	0.922494	−	0.673539i
$381$	5.32684			0.272902
$382$		−	13.9960i		−	0.716100i
$383$			28.5936i			1.46106i	0.682878	+	0.730532i	$0.260728\pi$
$383$			28.5936i			1.46106i	−0.682878	+	0.730532i	$0.739272\pi$
$384$	−15.6180			−0.797003
$385$	−1.31856	−	1.80593i	−0.0672002	−	0.0920388i
$386$	22.0567			1.12266
$387$			12.7301i			0.647107i
$388$		−	17.5404i		−	0.890479i
$389$	−24.6378			−1.24919			−0.624593	−	0.780951i	$-0.714735\pi$
$389$	−24.6378			−1.24919			−0.624593	+	0.780951i	$0.714735\pi$
$390$	−23.4343	−	32.0962i	−1.18664	−	1.62525i
$391$	−4.96742			−0.251213
$392$			5.77723i			0.291794i
$393$			17.1131i			0.863240i
$394$	17.2138			0.867217
$395$	23.8249	−	17.3952i	1.19876	−	0.875248i
$396$	−4.30144			−0.216156
$397$			21.6591i			1.08704i	0.839397	+	0.543518i	$0.182908\pi$
$397$			21.6591i			1.08704i	−0.839397	+	0.543518i	$0.817092\pi$
$398$		−	2.75939i		−	0.138316i
$399$	2.31494			0.115892
$400$	8.98368	−	28.0962i	0.449184	−	1.40481i
$401$	−23.9481			−1.19591			−0.597955	−	0.801529i	$-0.704020\pi$
$401$	−23.9481			−1.19591			−0.597955	+	0.801529i	$0.704020\pi$
$402$		−	9.30998i		−	0.464340i
$403$		−	49.3106i		−	2.45634i
$404$	16.7149			0.831599
$405$	−1.80593	+	1.31856i	−0.0897375	+	0.0655199i
$406$	−17.5467			−0.870830
$407$		−	4.39198i		−	0.217703i
$408$			5.59518i			0.277002i
$409$	22.9941			1.13699			0.568493	−	0.822688i	$-0.307527\pi$
$409$	22.9941			1.13699			0.568493	+	0.822688i	$0.307527\pi$
$410$	29.4380	+	40.3190i	1.45384	+	1.99121i
$411$	2.36803			0.116807
$412$		−	26.3559i		−	1.29846i
$413$			8.48666i			0.417601i
$414$	12.8753			0.632786
$415$	−10.6369	−	14.5685i	−0.522144	−	0.715140i
$416$	23.0445			1.12985
$417$		−	4.62584i		−	0.226529i
$418$		−	5.81112i		−	0.284231i
$419$	7.90663			0.386264			0.193132	−	0.981173i	$-0.438135\pi$
$419$	7.90663			0.386264			0.193132	+	0.981173i	$0.438135\pi$
$420$	7.76811	−	5.67172i	0.379045	−	0.276752i
$421$	10.6716			0.520100			0.260050	−	0.965595i	$-0.416261\pi$
$421$	10.6716			0.520100			0.260050	+	0.965595i	$0.416261\pi$
$422$			5.24127i			0.255141i
$423$			7.09593i			0.345016i
$424$	−30.1156			−1.46254
$425$	4.61239	+	1.47480i	0.223734	+	0.0715382i
$426$	−29.4201			−1.42541
$427$			1.53492i			0.0742802i
$428$			76.9279i			3.71845i
$429$	−7.07998			−0.341825
$430$	−57.7103	+	42.1359i	−2.78304	+	2.03197i
$431$	−24.0475			−1.15833			−0.579164	−	0.815211i	$-0.696621\pi$
$431$	−24.0475			−1.15833			−0.579164	+	0.815211i	$0.696621\pi$
$432$		−	5.89951i		−	0.283840i
$433$			27.3845i			1.31601i	0.753012	+	0.658007i	$0.228600\pi$
$433$			27.3845i			1.31601i	−0.753012	+	0.658007i	$0.771400\pi$
$434$	17.4835			0.839234
$435$	9.21673	+	12.6234i	0.441909	+	0.605248i
$436$	20.7297			0.992771
$437$			11.8735i			0.567985i
$438$			4.88755i			0.233536i
$439$	−29.9437			−1.42913			−0.714566	−	0.699568i	$-0.753376\pi$
$439$	−29.9437			−1.42913			−0.714566	+	0.699568i	$0.753376\pi$
$440$	−7.61764	−	10.4333i	−0.363157	−	0.497387i
$441$	1.00000			0.0476190
$442$			17.2126i			0.818719i
$443$			15.0629i			0.715661i	0.933787	+	0.357830i	$0.116483\pi$
$443$			15.0629i			0.715661i	−0.933787	+	0.357830i	$0.883517\pi$
$444$	18.8919			0.896568
$445$	−22.8037	+	16.6497i	−1.08100	+	0.789269i
$446$	−66.5111			−3.14939
$447$		−	12.5025i		−	0.591347i
$448$		−	3.62839i		−	0.171426i
$449$	20.2088			0.953713			0.476857	−	0.878981i	$-0.341776\pi$
$449$	20.2088			0.953713			0.476857	+	0.878981i	$0.341776\pi$
$450$	−11.9551	−	3.82260i	−0.563568	−	0.180199i
$451$	8.89382			0.418793
$452$			67.9318i			3.19524i
$453$		−	14.5167i		−	0.682055i
$454$	0.527727			0.0247675
$455$	12.7860	−	9.33540i	0.599416	−	0.437650i
$456$	13.3740			0.626293
$457$			1.04343i			0.0488096i	0.999702	+	0.0244048i	$0.00776906\pi$
$457$			1.04343i			0.0488096i	−0.999702	+	0.0244048i	$0.992231\pi$
$458$			1.88341i			0.0880062i
$459$	0.968488			0.0452051
$460$	29.0906	+	39.8431i	1.35635	+	1.85769i
$461$	−5.75152			−0.267875			−0.133938	−	0.990990i	$-0.542762\pi$
$461$	−5.75152			−0.267875			−0.133938	+	0.990990i	$0.542762\pi$
$462$		−	2.51027i		−	0.116788i
$463$			33.9781i			1.57910i	0.613688	+	0.789549i	$0.289685\pi$
$463$			33.9781i			1.57910i	−0.613688	+	0.789549i	$0.710315\pi$
$464$	−41.2375			−1.91440
$465$	−9.18351	−	12.5779i	−0.425875	−	0.583288i
$466$	−36.9286			−1.71068
$467$		−	1.66641i		−	0.0771123i	−0.999256	−	0.0385561i	$-0.987724\pi$
$467$		−	1.66641i		−	0.0771123i	0.999256	−	0.0385561i	$-0.0122758\pi$
$468$		−	30.4541i		−	1.40774i
$469$	3.70876			0.171255
$470$	−32.1685	+	23.4871i	−1.48382	+	1.08338i
$471$	13.5603			0.624828
$472$			49.0294i			2.25676i
$473$			12.7301i			0.585330i
$474$	33.1168			1.52111
$475$	3.52516	−	11.0248i	0.161745	−	0.505854i
$476$	−4.16589			−0.190943
$477$			5.21281i			0.238678i
$478$		−	15.8929i		−	0.726923i
$479$	−18.5420			−0.847207			−0.423604	−	0.905848i	$-0.639235\pi$
$479$	−18.5420			−0.847207			−0.423604	+	0.905848i	$0.639235\pi$
$480$	5.87810	−	4.29177i	0.268297	−	0.195891i
$481$	31.0952			1.41782
$482$			58.6682i			2.67226i
$483$			5.12905i			0.233380i
$484$	−4.30144			−0.195520
$485$	−5.37683	−	7.36423i	−0.244149	−	0.334392i
$486$	−2.51027			−0.113868
$487$		−	37.2652i		−	1.68865i	−0.535834	−	0.844323i	$-0.680003\pi$
$487$		−	37.2652i		−	1.68865i	0.535834	−	0.844323i	$-0.319997\pi$
$488$			8.86761i			0.401418i
$489$	16.4125			0.742200
$490$	3.30994	+	4.53337i	0.149528	+	0.204797i
$491$	−35.0486			−1.58172			−0.790860	−	0.611997i	$-0.790367\pi$
$491$	−35.0486			−1.58172			−0.790860	+	0.611997i	$0.790367\pi$
$492$			38.2562i			1.72472i
$493$		−	6.76971i		−	0.304893i
$494$	41.1426			1.85109
$495$	−1.80593	+	1.31856i	−0.0811706	+	0.0592650i
$496$	41.0888			1.84494
$497$		−	11.7199i		−	0.525710i
$498$		−	20.2504i		−	0.907442i
$499$	2.04402			0.0915029			0.0457514	−	0.998953i	$-0.485432\pi$
$499$	2.04402			0.0915029			0.0457514	+	0.998953i	$0.485432\pi$
$500$	−15.1822	−	45.6322i	−0.678970	−	2.04073i
$501$	14.9188			0.666523
$502$			11.1180i			0.496222i
$503$			17.0980i			0.762362i	0.924500	+	0.381181i	$0.124483\pi$
$503$			17.0980i			0.762362i	−0.924500	+	0.381181i	$0.875517\pi$
$504$	5.77723			0.257338
$505$	7.01766	−	5.12379i	0.312282	−	0.228006i
$506$	12.8753			0.572377
$507$		−	37.1261i		−	1.64883i
$508$			22.9131i			1.01660i
$509$	7.13352			0.316188			0.158094	−	0.987424i	$-0.449465\pi$
$509$	7.13352			0.316188			0.158094	+	0.987424i	$0.449465\pi$
$510$	3.20564	+	4.39052i	0.141948	+	0.194415i
$511$	−1.94702			−0.0861313
$512$		−	48.9634i		−	2.16390i
$513$		−	2.31494i		−	0.102207i
$514$	26.2231			1.15665
$515$	−8.07912	−	11.0653i	−0.356008	−	0.487597i
$516$	−54.7578			−2.41058
$517$			7.09593i			0.312079i
$518$			11.0251i			0.484413i
$519$	6.15172			0.270030
$520$	73.8675	−	53.9328i	3.23930	−	2.36511i
$521$	22.7712			0.997626			0.498813	−	0.866710i	$-0.333769\pi$
$521$	22.7712			0.997626			0.498813	+	0.866710i	$0.333769\pi$
$522$			17.5467i			0.768000i
$523$			2.46312i			0.107705i	0.998549	+	0.0538524i	$0.0171500\pi$
$523$			2.46312i			0.107705i	−0.998549	+	0.0538524i	$0.982850\pi$
$524$	−73.6108			−3.21570
$525$	1.52278	−	4.76247i	0.0664598	−	0.207851i
$526$	51.8243			2.25965
$527$			6.74531i			0.293830i
$528$		−	5.89951i		−	0.256743i
$529$	−3.30719			−0.143791
$530$	−23.6316	+	17.2541i	−1.02649	+	0.749470i
$531$	8.48666			0.368290
$532$			9.95758i			0.431716i
$533$			62.9681i			2.72745i
$534$	−31.6975			−1.37168
$535$	23.5815	+	32.2977i	1.01952	+	1.39635i
$536$	21.4264			0.925478
$537$			0.615080i			0.0265427i
$538$		−	42.0820i		−	1.81428i
$539$	1.00000			0.0430730
$540$	−5.67172	−	7.76811i	−0.244072	−	0.334286i
$541$	7.81554			0.336016			0.168008	−	0.985786i	$-0.446266\pi$
$541$	7.81554			0.336016			0.168008	+	0.985786i	$0.446266\pi$
$542$		−	39.6371i		−	1.70256i
$543$			16.2500i			0.697354i
$544$	−3.15231			−0.135154
$545$	8.70322	−	6.35447i	0.372805	−	0.272196i
$546$	17.7726			0.760599
$547$			4.74889i			0.203048i	0.994833	+	0.101524i	$0.0323718\pi$
$547$			4.74889i			0.203048i	−0.994833	+	0.101524i	$0.967628\pi$
$548$			10.1860i			0.435123i
$549$	1.53492			0.0655090
$550$	−11.9551	−	3.82260i	−0.509766	−	0.162996i
$551$	−16.1814			−0.689351
$552$			29.6317i			1.26121i
$553$			13.1925i			0.561004i
$554$	−42.5346			−1.80712
$555$	7.93163	−	5.79111i	0.336679	−	0.245819i
$556$	19.8978			0.843854
$557$			38.8508i			1.64616i	0.567926	+	0.823080i	$0.307746\pi$
$557$			38.8508i			1.64616i	−0.567926	+	0.823080i	$0.692254\pi$
$558$		−	17.4835i		−	0.740135i
$559$	−90.1289			−3.81204
$560$	7.77887	+	10.6541i	0.328717	+	0.450219i
$561$	0.968488			0.0408896
$562$		−	44.3188i		−	1.86948i
$563$		−	17.6279i		−	0.742928i	−0.928447	−	0.371464i	$-0.878856\pi$
$563$		−	17.6279i		−	0.742928i	0.928447	−	0.371464i	$-0.121144\pi$
$564$	−30.5227			−1.28524
$565$	20.8238	+	28.5207i	0.876064	+	1.19988i
$566$	−46.9881			−1.97506
$567$		−	1.00000i		−	0.0419961i
$568$		−	67.7086i		−	2.84099i
$569$	23.9251			1.00299			0.501496	−	0.865160i	$-0.332783\pi$
$569$	23.9251			1.00299			0.501496	+	0.865160i	$0.332783\pi$
$570$	10.4945	−	7.66233i	0.439566	−	0.320940i
$571$	32.3332			1.35310			0.676552	−	0.736395i	$-0.263474\pi$
$571$	32.3332			1.35310			0.676552	+	0.736395i	$0.263474\pi$
$572$		−	30.4541i		−	1.27335i
$573$		−	5.57552i		−	0.232921i
$574$	−22.3259			−0.931863
$575$	24.4270	+	7.81044i	1.01867	+	0.325718i
$576$	−3.62839			−0.151183
$577$		−	8.30110i		−	0.345579i	−0.984959	−	0.172790i	$-0.944722\pi$
$577$		−	8.30110i		−	0.345579i	0.984959	−	0.172790i	$-0.0552781\pi$
$578$			40.3200i			1.67709i
$579$	8.78659			0.365158
$580$	−54.2990	+	39.6452i	−2.25464	+	1.64618i
$581$	8.06703			0.334677
$582$		−	10.2364i		−	0.424311i
$583$			5.21281i			0.215892i
$584$	−11.2484			−0.465462
$585$	−9.33540	−	12.7860i	−0.385971	−	0.528635i
$586$	41.2541			1.70419
$587$		−	26.9977i		−	1.11431i	−0.830407	−	0.557157i	$-0.811892\pi$
$587$		−	26.9977i		−	1.11431i	0.830407	−	0.557157i	$-0.188108\pi$
$588$			4.30144i			0.177388i
$589$	16.1231			0.664340
$590$	28.0904	+	38.4732i	1.15646	+	1.58392i
$591$	6.85734			0.282073
$592$			25.9105i			1.06492i
$593$			30.3364i			1.24577i	0.782314	+	0.622884i	$0.214039\pi$
$593$			30.3364i			1.24577i	−0.782314	+	0.622884i	$0.785961\pi$
$594$	−2.51027			−0.102998
$595$	−1.74902	+	1.27701i	−0.0717030	+	0.0523524i
$596$	53.7787			2.20286
$597$		−	1.09924i		−	0.0449889i
$598$			91.1568i			3.72768i
$599$	12.5849			0.514206			0.257103	−	0.966384i	$-0.417232\pi$
$599$	12.5849			0.514206			0.257103	+	0.966384i	$0.417232\pi$
$600$	8.79748	−	27.5139i	0.359155	−	1.12325i
$601$	−4.68653			−0.191168			−0.0955838	−	0.995421i	$-0.530472\pi$
$601$	−4.68653			−0.191168			−0.0955838	+	0.995421i	$0.530472\pi$
$602$		−	31.9559i		−	1.30243i
$603$		−	3.70876i		−	0.151032i
$604$	62.4428			2.54076
$605$	−1.80593	+	1.31856i	−0.0734216	+	0.0536072i
$606$	9.75462			0.396255
$607$			11.4569i			0.465019i	0.972594	+	0.232510i	$0.0746937\pi$
$607$			11.4569i			0.465019i	−0.972594	+	0.232510i	$0.925306\pi$
$608$			7.53486i			0.305579i
$609$	−6.98999			−0.283249
$610$	5.08051	+	6.95838i	0.205704	+	0.281737i
$611$	−50.2391			−2.03246
$612$			4.16589i			0.168396i
$613$		−	11.1635i		−	0.450889i	−0.974256	−	0.225444i	$-0.927617\pi$
$613$		−	11.1635i		−	0.450889i	0.974256	−	0.225444i	$-0.0723834\pi$
$614$	70.4610			2.84357
$615$	11.7271	+	16.0616i	0.472881	+	0.647668i
$616$	5.77723			0.232771
$617$			5.44247i			0.219105i	0.993981	+	0.109553i	$0.0349419\pi$
$617$			5.44247i			0.219105i	−0.993981	+	0.109553i	$0.965058\pi$
$618$		−	15.3809i		−	0.618712i
$619$	−17.3985			−0.699303			−0.349652	−	0.936880i	$-0.613700\pi$
$619$	−17.3985			−0.699303			−0.349652	+	0.936880i	$0.613700\pi$
$620$	54.1033	−	39.5023i	2.17284	−	1.58645i
$621$	5.12905			0.205822
$622$		−	13.1441i		−	0.527031i
$623$		−	12.6271i		−	0.505895i
$624$	41.7684			1.67207
$625$	−20.3623	−	14.5044i	−0.814490	−	0.580177i
$626$	−12.8604			−0.514005
$627$		−	2.31494i		−	0.0924499i
$628$			58.3290i			2.32758i
$629$	−4.25358			−0.169601
$630$	4.53337	−	3.30994i	0.180614	−	0.131871i
$631$	2.43563			0.0969609			0.0484804	−	0.998824i	$-0.484562\pi$
$631$	2.43563			0.0969609			0.0484804	+	0.998824i	$0.484562\pi$
$632$			76.2164i			3.03173i
$633$			2.08794i			0.0829880i
$634$	6.69858			0.266035
$635$	7.02377	+	9.61991i	0.278730	+	0.381755i
$636$	−22.4226			−0.889113
$637$			7.07998i			0.280519i
$638$			17.5467i			0.694682i
$639$	−11.7199			−0.463633
$640$	−20.5933	−	28.2051i	−0.814022	−	1.11490i
$641$	27.9984			1.10587			0.552935	−	0.833224i	$-0.313508\pi$
$641$	27.9984			1.10587			0.552935	+	0.833224i	$0.313508\pi$
$642$			44.8942i			1.77183i
$643$			35.8238i			1.41275i	0.707836	+	0.706377i	$0.249672\pi$
$643$			35.8238i			1.41275i	−0.707836	+	0.706377i	$0.750328\pi$
$644$	−22.0623			−0.869377
$645$	−22.9897	+	16.7854i	−0.905218	+	0.660926i
$646$	−5.62800			−0.221431
$647$		−	29.4236i		−	1.15676i	−0.815767	−	0.578381i	$-0.803685\pi$
$647$		−	29.4236i		−	1.15676i	0.815767	−	0.578381i	$-0.196315\pi$
$648$		−	5.77723i		−	0.226951i
$649$	8.48666			0.333131
$650$	27.0639	−	84.6417i	1.06153	−	3.31992i
$651$	6.96479			0.272972
$652$			70.5975i			2.76481i
$653$			45.8648i			1.79483i	0.441189	+	0.897414i	$0.354557\pi$
$653$			45.8648i			1.79483i	−0.441189	+	0.897414i	$0.645443\pi$
$654$	12.0976			0.473053
$655$	−30.9050	+	22.5646i	−1.20756	+	0.881674i
$656$	−52.4692			−2.04858
$657$			1.94702i			0.0759606i
$658$		−	17.8127i		−	0.694411i
$659$	−35.0588			−1.36570			−0.682849	−	0.730559i	$-0.739259\pi$
$659$	−35.0588			−1.36570			−0.682849	+	0.730559i	$0.739259\pi$
$660$	−5.67172	−	7.76811i	−0.220771	−	0.302373i
$661$	−37.3084			−1.45113			−0.725564	−	0.688155i	$-0.758421\pi$
$661$	−37.3084			−1.45113			−0.725564	+	0.688155i	$0.758421\pi$
$662$		−	68.0365i		−	2.64431i
$663$			6.85687i			0.266299i
$664$	46.6051			1.80863
$665$	3.05240	+	4.18063i	0.118367	+	0.162118i
$666$	11.0251			0.427212
$667$		−	35.8520i		−	1.38820i
$668$			64.1724i			2.48290i
$669$	−26.4956			−1.02438
$670$	16.8132	−	12.2758i	0.649550	−	0.474255i
$671$	1.53492			0.0592551
$672$			3.25488i			0.125560i
$673$			48.2366i			1.85938i	0.368338	+	0.929692i	$0.379927\pi$
$673$			48.2366i			1.85938i	−0.368338	+	0.929692i	$0.620073\pi$
$674$	−14.6640			−0.564834
$675$	−4.76247	−	1.52278i	−0.183308	−	0.0586120i
$676$	159.696			6.14215
$677$		−	17.9598i		−	0.690251i	−0.938557	−	0.345125i	$-0.887836\pi$
$677$		−	17.9598i		−	0.690251i	0.938557	−	0.345125i	$-0.112164\pi$
$678$			39.6442i			1.52252i
$679$	4.07780			0.156491
$680$	−10.1045	+	7.37759i	−0.387490	+	0.282918i
$681$	0.210227			0.00805593
$682$		−	17.4835i		−	0.669477i
$683$		−	22.0852i		−	0.845067i	−0.906347	−	0.422533i	$-0.861141\pi$
$683$		−	22.0852i		−	0.845067i	0.906347	−	0.422533i	$-0.138859\pi$
$684$	9.95758			0.380738
$685$	3.12240	+	4.27651i	0.119301	+	0.163397i
$686$	−2.51027			−0.0958424
$687$			0.750284i			0.0286251i
$688$		−	75.1013i		−	2.86321i
$689$	−36.9066			−1.40603
$690$	16.9769	+	23.2519i	0.646299	+	0.885185i
$691$	−17.3356			−0.659479			−0.329740	−	0.944072i	$-0.606961\pi$
$691$	−17.3356			−0.659479			−0.329740	+	0.944072i	$0.606961\pi$
$692$			26.4612i			1.00591i
$693$		−	1.00000i		−	0.0379869i
$694$	56.4501			2.14282
$695$	8.35396	−	6.09947i	0.316884	−	0.231366i
$696$	−40.3828			−1.53070
$697$		−	8.61355i		−	0.326262i
$698$		−	13.6732i		−	0.517537i
$699$	−14.7110			−0.556422
$700$	20.4855	+	6.55017i	0.774279	+	0.247573i
$701$	14.7225			0.556061			0.278030	−	0.960572i	$-0.410318\pi$
$701$	14.7225			0.556061			0.278030	+	0.960572i	$0.410318\pi$
$702$		−	17.7726i		−	0.670785i
$703$			10.1672i			0.383463i
$704$	−3.62839			−0.136750
$705$	−12.8148	+	9.35643i	−0.482632	+	0.352384i
$706$	−33.6399			−1.26605
$707$			3.88589i			0.146144i
$708$			36.5049i			1.37194i
$709$	31.1199			1.16873			0.584366	−	0.811490i	$-0.301343\pi$
$709$	31.1199			1.16873			0.584366	+	0.811490i	$0.301343\pi$
$710$	−38.7923	−	53.1307i	−1.45585	−	1.99396i
$711$	13.1925			0.494759
$712$		−	72.9498i		−	2.73391i
$713$			35.7228i			1.33783i
$714$	−2.43116			−0.0909840
$715$	−9.33540	−	12.7860i	−0.349124	−	0.478168i
$716$	−2.64573			−0.0988756
$717$		−	6.33115i		−	0.236441i
$718$		−	55.6851i		−	2.07815i
$719$	−15.9930			−0.596437			−0.298219	−	0.954498i	$-0.596392\pi$
$719$	−15.9930			−0.596437			−0.298219	+	0.954498i	$0.596392\pi$
$720$	10.6541	−	7.77887i	0.397055	−	0.289901i
$721$	6.12722			0.228189
$722$		−	34.2427i		−	1.27438i
$723$			23.3713i			0.869188i
$724$	−69.8984			−2.59775
$725$	−10.6442	+	33.2896i	−0.395317	+	1.23634i
$726$	−2.51027			−0.0931647
$727$			31.0625i			1.15205i	0.817434	+	0.576023i	$0.195396\pi$
$727$			31.0625i			1.15205i	−0.817434	+	0.576023i	$0.804604\pi$
$728$			40.9027i			1.51595i
$729$	−1.00000			−0.0370370
$730$	−8.82659	+	6.44454i	−0.326687	+	0.238523i
$731$	12.3289			0.456002
$732$			6.60238i			0.244031i
$733$		−	22.1438i		−	0.817900i	−0.912557	−	0.408950i	$-0.865895\pi$
$733$		−	22.1438i		−	0.817900i	0.912557	−	0.408950i	$-0.134105\pi$
$734$	64.0051			2.36247
$735$	1.31856	+	1.80593i	0.0486359	+	0.0666128i
$736$	−16.6945			−0.615366
$737$		−	3.70876i		−	0.136614i
$738$			22.3259i			0.821826i
$739$	21.4023			0.787295			0.393648	−	0.919261i	$-0.371213\pi$
$739$	21.4023			0.787295			0.393648	+	0.919261i	$0.371213\pi$
$740$	24.9101	+	34.1174i	0.915713	+	1.25418i
$741$	16.3897			0.602092
$742$		−	13.0855i		−	0.480385i
$743$			7.15327i			0.262428i	0.991354	+	0.131214i	$0.0418875\pi$
$743$			7.15327i			0.262428i	−0.991354	+	0.131214i	$0.958113\pi$
$744$	40.2372			1.47517
$745$	22.5786	−	16.4853i	0.827218	−	0.603975i
$746$	41.9933			1.53748
$747$		−	8.06703i		−	0.295157i
$748$			4.16589i			0.152320i
$749$	−17.8842			−0.653475
$750$	−8.86016	−	26.6304i	−0.323527	−	0.972404i
$751$	−37.6774			−1.37487			−0.687434	−	0.726247i	$-0.741263\pi$
$751$	−37.6774			−1.37487			−0.687434	+	0.726247i	$0.741263\pi$
$752$		−	41.8625i		−	1.52657i
$753$			4.42902i			0.161402i
$754$	−124.231			−4.52421
$755$	26.2162	−	19.1412i	0.954105	−	0.696619i
$756$	4.30144			0.156442
$757$		−	49.1107i		−	1.78496i	−0.451090	−	0.892479i	$-0.648965\pi$
$757$		−	49.1107i		−	1.78496i	0.451090	−	0.892479i	$-0.351035\pi$
$758$		−	3.59417i		−	0.130546i
$759$	5.12905			0.186173
$760$	17.6344	+	24.1525i	0.639667	+	0.876102i
$761$	2.40302			0.0871095			0.0435548	−	0.999051i	$-0.486132\pi$
$761$	2.40302			0.0871095			0.0435548	+	0.999051i	$0.486132\pi$
$762$			13.3718i			0.484409i
$763$			4.81924i			0.174468i
$764$	23.9828			0.867666
$765$	1.27701	+	1.74902i	0.0461705	+	0.0632361i
$766$	−71.7775			−2.59343
$767$			60.0854i			2.16956i
$768$		−	31.9486i		−	1.15284i
$769$	32.8831			1.18579			0.592897	−	0.805278i	$-0.297984\pi$
$769$	32.8831			1.18579			0.592897	+	0.805278i	$0.297984\pi$
$770$	4.53337	−	3.30994i	0.163371	−	0.119282i
$771$	10.4463			0.376216
$772$			37.7950i			1.36027i
$773$		−	28.7871i		−	1.03540i	−0.855562	−	0.517701i	$-0.826788\pi$
$773$		−	28.7871i		−	1.03540i	0.855562	−	0.517701i	$-0.173212\pi$
$774$	−31.9559			−1.14863
$775$	10.6059	−	33.1696i	0.380974	−	1.19149i
$776$	23.5584			0.845696
$777$			4.39198i			0.157562i
$778$		−	61.8474i		−	2.21734i
$779$	−20.5887			−0.737666
$780$	54.9981	−	40.1557i	1.96925	−	1.43780i
$781$	−11.7199			−0.419372
$782$		−	12.4696i		−	0.445911i
$783$			6.98999i			0.249802i
$784$	−5.89951			−0.210697
$785$	17.8802	+	24.4891i	0.638170	+	0.874052i
$786$	−42.9584			−1.53227
$787$			1.37725i			0.0490935i	0.999699	+	0.0245468i	$0.00781426\pi$
$787$			1.37725i			0.0490935i	−0.999699	+	0.0245468i	$0.992186\pi$
$788$			29.4965i			1.05077i
$789$	20.6449			0.734979
$790$	43.6666	+	59.8067i	1.55359	+	2.12783i
$791$	−15.7928			−0.561528
$792$		−	5.77723i		−	0.205285i
$793$			10.8672i			0.385907i
$794$	−54.3700			−1.92952
$795$	−9.41398	+	6.87341i	−0.333879	+	0.243775i
$796$	4.72832			0.167591
$797$			45.8922i			1.62558i	0.582554	+	0.812792i	$0.302053\pi$
$797$			45.8922i			1.62558i	−0.582554	+	0.812792i	$0.697947\pi$
$798$			5.81112i			0.205711i
$799$	6.87232			0.243125
$800$	15.5013	+	4.95648i	0.548053	+	0.175238i
$801$	−12.6271			−0.446158
$802$		−	60.1161i		−	2.12277i
$803$			1.94702i			0.0687090i
$804$	15.9530			0.562619
$805$	−9.26272	+	6.76298i	−0.326468	+	0.238364i
$806$	123.783			4.36006
$807$		−	16.7639i		−	0.590119i
$808$			22.4497i			0.789777i
$809$	−14.2412			−0.500694			−0.250347	−	0.968156i	$-0.580545\pi$
$809$	−14.2412			−0.500694			−0.250347	+	0.968156i	$0.580545\pi$
$810$	−3.30994	−	4.53337i	−0.116300	−	0.159286i
$811$	13.8037			0.484713			0.242357	−	0.970187i	$-0.422080\pi$
$811$	13.8037			0.484713			0.242357	+	0.970187i	$0.422080\pi$
$812$		−	30.0670i		−	1.05515i
$813$		−	15.7900i		−	0.553780i
$814$	11.0251			0.386428
$815$	21.6410	+	29.6399i	0.758049	+	1.03824i
$816$	−5.71360			−0.200016
$817$		−	29.4694i		−	1.03100i
$818$			57.7214i			2.01818i
$819$	7.07998			0.247395
$820$	−69.0882	+	50.4432i	−2.41266	+	1.76155i
$821$	−6.77445			−0.236430			−0.118215	−	0.992988i	$-0.537717\pi$
$821$	−6.77445			−0.236430			−0.118215	+	0.992988i	$0.537717\pi$
$822$			5.94440i			0.207335i
$823$		−	13.5187i		−	0.471232i	−0.971846	−	0.235616i	$-0.924289\pi$
$823$		−	13.5187i		−	0.471232i	0.971846	−	0.235616i	$-0.0757107\pi$
$824$	35.3983			1.23316
$825$	−4.76247	−	1.52278i	−0.165808	−	0.0530166i
$826$	−21.3038			−0.741253
$827$		−	16.2876i		−	0.566374i	−0.959065	−	0.283187i	$-0.908608\pi$
$827$		−	16.2876i		−	0.566374i	0.959065	−	0.283187i	$-0.0913917\pi$
$828$			22.0623i			0.766719i
$829$	−51.5383			−1.79000			−0.895000	−	0.446066i	$-0.852825\pi$
$829$	−51.5383			−1.79000			−0.895000	+	0.446066i	$0.852825\pi$
$830$	36.5709	−	26.7014i	1.26939	−	0.926820i
$831$	−16.9442			−0.587789
$832$		−	25.6890i		−	0.890605i
$833$		−	0.968488i		−	0.0335561i
$834$	11.6121			0.402094
$835$	19.6714	+	26.9424i	0.680757	+	0.932379i
$836$	9.95758			0.344390
$837$		−	6.96479i		−	0.240738i
$838$			19.8477i			0.685629i
$839$	35.1066			1.21201			0.606007	−	0.795460i	$-0.292771\pi$
$839$	35.1066			1.21201			0.606007	+	0.795460i	$0.292771\pi$
$840$	7.61764	+	10.4333i	0.262834	+	0.359983i
$841$	19.8599			0.684824
$842$			26.7885i			0.923191i
$843$		−	17.6550i		−	0.608071i
$844$	−8.98113			−0.309143
$845$	67.0473	−	48.9532i	2.30650	−	1.68404i
$846$	−17.8127			−0.612413
$847$		−	1.00000i		−	0.0343604i
$848$		−	30.7530i		−	1.05606i
$849$	−18.7184			−0.642413
$850$	−3.70214	+	11.5783i	−0.126982	+	0.397134i
$851$	−22.5267			−0.772206
$852$		−	50.4125i		−	1.72710i
$853$		−	49.6915i		−	1.70140i	−0.525648	−	0.850702i	$-0.676177\pi$
$853$		−	49.6915i		−	1.70140i	0.525648	−	0.850702i	$-0.323823\pi$
$854$	−3.85307			−0.131849
$855$	4.18063	−	3.05240i	0.142974	−	0.104390i
$856$	−103.321			−3.53145
$857$			23.5393i			0.804089i	0.915620	+	0.402044i	$0.131700\pi$
$857$			23.5393i			0.804089i	−0.915620	+	0.402044i	$0.868300\pi$
$858$		−	17.7726i		−	0.606748i
$859$	37.5900			1.28255			0.641277	−	0.767309i	$-0.278405\pi$
$859$	37.5900			1.28255			0.641277	+	0.767309i	$0.278405\pi$
$860$	−72.2015	−	98.8888i	−2.46205	−	3.37208i
$861$	−8.89382			−0.303100
$862$		−	60.3657i		−	2.05606i
$863$		−	42.8614i		−	1.45902i	−0.683971	−	0.729510i	$-0.739748\pi$
$863$		−	42.8614i		−	1.45902i	0.683971	−	0.729510i	$-0.260252\pi$
$864$	3.25488			0.110733
$865$	8.11143	+	11.1096i	0.275797	+	0.377737i
$866$	−68.7424			−2.33596
$867$			16.0620i			0.545495i
$868$			29.9586i			1.01686i
$869$	13.1925			0.447527
$870$	−31.6882	+	23.1365i	−1.07433	+	0.784400i
$871$	26.2580			0.889717
$872$			27.8419i			0.942844i
$873$		−	4.07780i		−	0.138013i
$874$	−29.8056			−1.00819
$875$	10.6086	−	3.52957i	0.358636	−	0.119321i
$876$	−8.37501			−0.282965
$877$			29.7136i			1.00336i	0.865054	+	0.501678i	$0.167284\pi$
$877$			29.7136i			1.00336i	−0.865054	+	0.501678i	$0.832716\pi$
$878$		−	75.1666i		−	2.53675i
$879$	16.4342			0.554310
$880$	10.6541	−	7.77887i	0.359150	−	0.262226i
$881$	29.1253			0.981256			0.490628	−	0.871369i	$-0.336767\pi$
$881$	29.1253			0.981256			0.490628	+	0.871369i	$0.336767\pi$
$882$			2.51027i			0.0845251i
$883$		−	28.2491i		−	0.950659i	−0.879808	−	0.475330i	$-0.842329\pi$
$883$		−	28.2491i		−	0.950659i	0.879808	−	0.475330i	$-0.157671\pi$
$884$	−29.4944			−0.992005
$885$	11.1902	+	15.3263i	0.376154	+	0.515189i
$886$	−37.8119			−1.27032
$887$		−	19.2729i		−	0.647122i	−0.946207	−	0.323561i	$-0.895120\pi$
$887$		−	19.2729i		−	0.647122i	0.946207	−	0.323561i	$-0.104880\pi$
$888$			25.3735i			0.851479i
$889$	−5.32684			−0.178656
$890$	−41.7951	−	57.2435i	−1.40097	−	1.91881i
$891$	−1.00000			−0.0335013
$892$		−	113.969i		−	3.81597i
$893$		−	16.4267i		−	0.549697i
$894$	31.3846			1.04966
$895$	−1.11079	+	0.811022i	−0.0371297	+	0.0271095i
$896$	15.6180			0.521761
$897$			36.3136i			1.21248i
$898$			50.7295i			1.69287i
$899$	−48.6838			−1.62370
$900$	6.55017	−	20.4855i	0.218339	−	0.682849i
$901$	5.04854			0.168191
$902$			22.3259i			0.743370i
$903$		−	12.7301i		−	0.423631i
$904$	−91.2387			−3.03455
$905$	−29.3464	+	21.4266i	−0.975507	+	0.712245i
$906$	36.4408			1.21067
$907$			12.9313i			0.429378i	0.976683	+	0.214689i	$0.0688737\pi$
$907$			12.9313i			0.429378i	−0.976683	+	0.214689i	$0.931126\pi$
$908$			0.904281i			0.0300096i
$909$	3.88589			0.128887
$910$	23.4343	+	32.0962i	0.776841	+	1.06398i
$911$	31.3233			1.03779			0.518893	−	0.854839i	$-0.326344\pi$
$911$	31.3233			1.03779			0.518893	+	0.854839i	$0.326344\pi$
$912$			13.6570i			0.452229i
$913$		−	8.06703i		−	0.266980i
$914$	−2.61929			−0.0866384
$915$	2.02389	+	2.77197i	0.0669079	+	0.0916385i
$916$	−3.22730			−0.106633
$917$		−	17.1131i		−	0.565123i
$918$			2.43116i			0.0802403i
$919$	−13.1093			−0.432436			−0.216218	−	0.976345i	$-0.569372\pi$
$919$	−13.1093			−0.432436			−0.216218	+	0.976345i	$0.569372\pi$
$920$	−53.5129	+	39.0713i	−1.76427	+	1.28814i
$921$	28.0691			0.924909
$922$		−	14.4379i		−	0.475485i
$923$		−	82.9768i		−	2.73121i
$924$	4.30144			0.141507
$925$	20.9167	+	6.68805i	0.687737	+	0.219902i
$926$	−85.2942			−2.80294
$927$		−	6.12722i		−	0.201244i
$928$		−	22.7516i		−	0.746857i
$929$	−19.4008			−0.636520			−0.318260	−	0.948003i	$-0.603099\pi$
$929$	−19.4008			−0.636520			−0.318260	+	0.948003i	$0.603099\pi$
$930$	31.5740	−	23.0531i	1.03535	−	0.755940i
$931$	−2.31494			−0.0758692
$932$		−	63.2786i		−	2.07276i
$933$		−	5.23614i		−	0.171424i
$934$	4.18313			0.136876
$935$	1.27701	+	1.74902i	0.0417627	+	0.0571992i
$936$	40.9027			1.33695
$937$		−	17.3747i		−	0.567608i	−0.958882	−	0.283804i	$-0.908403\pi$
$937$		−	17.3747i		−	0.567608i	0.958882	−	0.283804i	$-0.0915965\pi$
$938$			9.30998i			0.303982i
$939$	−5.12312			−0.167187
$940$	−40.2461	−	55.1220i	−1.31268	−	1.79788i
$941$	22.9140			0.746975			0.373487	−	0.927635i	$-0.378162\pi$
$941$	22.9140			0.746975			0.373487	+	0.927635i	$0.378162\pi$
$942$			34.0401i			1.10909i
$943$		−	45.6169i		−	1.48549i
$944$	−50.0671			−1.62955
$945$	1.80593	−	1.31856i	0.0587470	−	0.0428928i
$946$	−31.9559			−1.03898
$947$		−	25.7109i		−	0.835493i	−0.908564	−	0.417746i	$-0.862820\pi$
$947$		−	25.7109i		−	0.835493i	0.908564	−	0.417746i	$-0.137180\pi$
$948$			56.7470i			1.84306i
$949$	−13.7849			−0.447477
$950$	27.6753	+	8.84909i	0.897905	+	0.287102i
$951$	2.66847			0.0865312
$952$		−	5.59518i		−	0.181341i
$953$			35.0339i			1.13486i	0.823422	+	0.567429i	$0.192062\pi$
$953$			35.0339i			1.13486i	−0.823422	+	0.567429i	$0.807938\pi$
$954$	−13.0855			−0.423660
$955$	10.0690	−	7.35167i	0.325825	−	0.237894i
$956$	27.2331			0.880780
$957$			6.98999i			0.225954i
$958$		−	46.5455i		−	1.50382i
$959$	−2.36803			−0.0764678
$960$	−4.78427	−	6.55264i	−0.154412	−	0.211485i
$961$	17.5083			0.564784
$962$			78.0572i			2.51666i
$963$			17.8842i			0.576311i
$964$	−100.530			−3.23786
$965$	11.5857	+	15.8680i	0.372956	+	0.510809i
$966$	−12.8753			−0.414256
$967$		−	8.81007i		−	0.283313i	−0.989916	−	0.141656i	$-0.954757\pi$
$967$		−	8.81007i		−	0.283313i	0.989916	−	0.141656i	$-0.0452428\pi$
$968$		−	5.77723i		−	0.185687i
$969$	−2.24199			−0.0720232
$970$	18.4862	−	13.4973i	0.593555	−	0.433372i
$971$	−0.734125			−0.0235592			−0.0117796	−	0.999931i	$-0.503750\pi$
$971$	−0.734125			−0.0235592			−0.0117796	+	0.999931i	$0.503750\pi$
$972$		−	4.30144i		−	0.137969i
$973$			4.62584i			0.148298i
$974$	93.5455			2.99739
$975$	10.7813	−	33.7182i	0.345278	−	1.07985i
$976$	−9.05530			−0.289853
$977$			28.2054i			0.902370i	0.892431	+	0.451185i	$0.148998\pi$
$977$			28.2054i			0.902370i	−0.892431	+	0.451185i	$0.851002\pi$
$978$			41.1998i			1.31743i
$979$	−12.6271			−0.403565
$980$	−7.76811	+	5.67172i	−0.248143	+	0.181176i
$981$	4.81924			0.153866
$982$		−	87.9813i		−	2.80760i
$983$		−	46.1964i		−	1.47343i	−0.676201	−	0.736717i	$-0.736375\pi$
$983$		−	46.1964i		−	1.47343i	0.676201	−	0.736717i	$-0.263625\pi$
$984$	−51.3816			−1.63799
$985$	9.04184	+	12.3839i	0.288097	+	0.394584i
$986$	16.9938			0.541193
$987$		−	7.09593i		−	0.225866i
$988$			70.4995i			2.24289i
$989$	65.2933			2.07621
$990$	−3.30994	−	4.53337i	−0.105197	−	0.144080i
$991$	−0.269472			−0.00856005			−0.00428003	−	0.999991i	$-0.501362\pi$
$991$	−0.269472			−0.00856005			−0.00428003	+	0.999991i	$0.501362\pi$
$992$			22.6696i			0.719760i
$993$		−	27.1033i		−	0.860097i
$994$	29.4201			0.933149
$995$	1.98515	−	1.44942i	0.0629336	−	0.0459496i
$996$	34.6999			1.09951
$997$		−	41.6719i		−	1.31976i	−0.751369	−	0.659882i	$-0.770606\pi$
$997$		−	41.6719i		−	1.31976i	0.751369	−	0.659882i	$-0.229394\pi$
$998$			5.13104i			0.162420i
$999$	4.39198			0.138956

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1155.2.c.e.694.18	yes	20
5.2	odd	4		5775.2.a.cp.1.1		10
5.3	odd	4		5775.2.a.cm.1.10		10
5.4	even	2	inner	1155.2.c.e.694.3	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1155.2.c.e.694.3	✓	20	5.4	even	2	inner
1155.2.c.e.694.18	yes	20	1.1	even	1	trivial
5775.2.a.cm.1.10		10	5.3	odd	4
5775.2.a.cp.1.1		10	5.2	odd	4

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:	\( N \)	\(=\)	\( 1155 = 3 \cdot 5 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1155.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+2.51027i q^{2} +1.00000i q^{3} -4.30144 q^{4} +(-1.80593 + 1.31856i) q^{5} -2.51027 q^{6} -1.00000i q^{7} -5.77723i q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q+2.51027i q^{2} +1.00000i q^{3} -4.30144 q^{4} +(-1.80593 + 1.31856i) q^{5} -2.51027 q^{6} -1.00000i q^{7} -5.77723i q^{8} -1.00000 q^{9} +(-3.30994 - 4.53337i) q^{10} -1.00000 q^{11} -4.30144i q^{12} -7.07998i q^{13} +2.51027 q^{14} +(-1.31856 - 1.80593i) q^{15} +5.89951 q^{16} +0.968488i q^{17} -2.51027i q^{18} +2.31494 q^{19} +(7.76811 - 5.67172i) q^{20} +1.00000 q^{21} -2.51027i q^{22} +5.12905i q^{23} +5.77723 q^{24} +(1.52278 - 4.76247i) q^{25} +17.7726 q^{26} -1.00000i q^{27} +4.30144i q^{28} -6.98999 q^{29} +(4.53337 - 3.30994i) q^{30} +6.96479 q^{31} +3.25488i q^{32} -1.00000i q^{33} -2.43116 q^{34} +(1.31856 + 1.80593i) q^{35} +4.30144 q^{36} +4.39198i q^{37} +5.81112i q^{38} +7.07998 q^{39} +(7.61764 + 10.4333i) q^{40} -8.89382 q^{41} +2.51027i q^{42} -12.7301i q^{43} +4.30144 q^{44} +(1.80593 - 1.31856i) q^{45} -12.8753 q^{46} -7.09593i q^{47} +5.89951i q^{48} -1.00000 q^{49} +(11.9551 + 3.82260i) q^{50} -0.968488 q^{51} +30.4541i q^{52} -5.21281i q^{53} +2.51027 q^{54} +(1.80593 - 1.31856i) q^{55} -5.77723 q^{56} +2.31494i q^{57} -17.5467i q^{58} -8.48666 q^{59} +(5.67172 + 7.76811i) q^{60} -1.53492 q^{61} +17.4835i q^{62} +1.00000i q^{63} +3.62839 q^{64} +(9.33540 + 12.7860i) q^{65} +2.51027 q^{66} +3.70876i q^{67} -4.16589i q^{68} -5.12905 q^{69} +(-4.53337 + 3.30994i) q^{70} +11.7199 q^{71} +5.77723i q^{72} -1.94702i q^{73} -11.0251 q^{74} +(4.76247 + 1.52278i) q^{75} -9.95758 q^{76} +1.00000i q^{77} +17.7726i q^{78} -13.1925 q^{79} +(-10.6541 + 7.77887i) q^{80} +1.00000 q^{81} -22.3259i q^{82} +8.06703i q^{83} -4.30144 q^{84} +(-1.27701 - 1.74902i) q^{85} +31.9559 q^{86} -6.98999i q^{87} +5.77723i q^{88} +12.6271 q^{89} +(3.30994 + 4.53337i) q^{90} -7.07998 q^{91} -22.0623i q^{92} +6.96479i q^{93} +17.8127 q^{94} +(-4.18063 + 3.05240i) q^{95} -3.25488 q^{96} +4.07780i q^{97} -2.51027i q^{98} +1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 26 q^{4} - 2 q^{5} + 6 q^{6} - 20 q^{9}+O(q^{10}) \) 20 * q - 26 * q^4 - 2 * q^5 + 6 * q^6 - 20 * q^9	\( 20 q - 26 q^{4} - 2 q^{5} + 6 q^{6} - 20 q^{9} - 2 q^{10} - 20 q^{11} - 6 q^{14} + 2 q^{15} + 38 q^{16} + 2 q^{19} + 4 q^{20} + 20 q^{21} - 18 q^{24} + 12 q^{25} + 20 q^{26} - 38 q^{29} + 6 q^{30} + 20 q^{31} - 32 q^{34} - 2 q^{35} + 26 q^{36} + 2 q^{40} + 12 q^{41} + 26 q^{44} + 2 q^{45} + 8 q^{46} - 20 q^{49} - 6 q^{50} + 26 q^{51} - 6 q^{54} + 2 q^{55} + 18 q^{56} - 22 q^{59} + 16 q^{60} + 34 q^{61} - 26 q^{64} - 28 q^{65} - 6 q^{66} - 26 q^{69} - 6 q^{70} + 72 q^{71} - 72 q^{74} - 8 q^{75} + 44 q^{76} + 4 q^{79} - 8 q^{80} + 20 q^{81} - 26 q^{84} - 16 q^{85} + 52 q^{86} + 6 q^{89} + 2 q^{90} + 16 q^{94} + 14 q^{95} + 62 q^{96} + 20 q^{99}+O(q^{100}) \) 20 * q - 26 * q^4 - 2 * q^5 + 6 * q^6 - 20 * q^9 - 2 * q^10 - 20 * q^11 - 6 * q^14 + 2 * q^15 + 38 * q^16 + 2 * q^19 + 4 * q^20 + 20 * q^21 - 18 * q^24 + 12 * q^25 + 20 * q^26 - 38 * q^29 + 6 * q^30 + 20 * q^31 - 32 * q^34 - 2 * q^35 + 26 * q^36 + 2 * q^40 + 12 * q^41 + 26 * q^44 + 2 * q^45 + 8 * q^46 - 20 * q^49 - 6 * q^50 + 26 * q^51 - 6 * q^54 + 2 * q^55 + 18 * q^56 - 22 * q^59 + 16 * q^60 + 34 * q^61 - 26 * q^64 - 28 * q^65 - 6 * q^66 - 26 * q^69 - 6 * q^70 + 72 * q^71 - 72 * q^74 - 8 * q^75 + 44 * q^76 + 4 * q^79 - 8 * q^80 + 20 * q^81 - 26 * q^84 - 16 * q^85 + 52 * q^86 + 6 * q^89 + 2 * q^90 + 16 * q^94 + 14 * q^95 + 62 * q^96 + 20 * q^99

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