LMFDB - Embedded newform 1155.2.c.e.694.15

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			694.15
Root			$1.76011i$ of defining polynomial
Character	$\chi$	$=$	1155.694
Dual form			1155.2.c.e.694.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.76011i q^{2} +1.00000i q^{3} -1.09799 q^{4} +(2.22415 + 0.230563i) q^{5} -1.76011 q^{6} -1.00000i q^{7} +1.58764i q^{8} -1.00000 q^{9} +O(q^{10})$	\(q+1.76011i q^{2} +1.00000i q^{3} -1.09799 q^{4} +(2.22415 + 0.230563i) q^{5} -1.76011 q^{6} -1.00000i q^{7} +1.58764i q^{8} -1.00000 q^{9} +(-0.405817 + 3.91475i) q^{10} -1.00000 q^{11} -1.09799i q^{12} +4.21462i q^{13} +1.76011 q^{14} +(-0.230563 + 2.22415i) q^{15} -4.99040 q^{16} +1.43361i q^{17} -1.76011i q^{18} +6.78233 q^{19} +(-2.44209 - 0.253156i) q^{20} +1.00000 q^{21} -1.76011i q^{22} -2.64270i q^{23} -1.58764 q^{24} +(4.89368 + 1.02561i) q^{25} -7.41820 q^{26} -1.00000i q^{27} +1.09799i q^{28} -8.97759 q^{29} +(-3.91475 - 0.405817i) q^{30} -0.288914 q^{31} -5.60837i q^{32} -1.00000i q^{33} -2.52331 q^{34} +(0.230563 - 2.22415i) q^{35} +1.09799 q^{36} +10.7089i q^{37} +11.9377i q^{38} -4.21462 q^{39} +(-0.366052 + 3.53115i) q^{40} +1.62215 q^{41} +1.76011i q^{42} +8.21640i q^{43} +1.09799 q^{44} +(-2.22415 - 0.230563i) q^{45} +4.65144 q^{46} +3.94493i q^{47} -4.99040i q^{48} -1.00000 q^{49} +(-1.80519 + 8.61342i) q^{50} -1.43361 q^{51} -4.62760i q^{52} -5.94827i q^{53} +1.76011 q^{54} +(-2.22415 - 0.230563i) q^{55} +1.58764 q^{56} +6.78233i q^{57} -15.8015i q^{58} -6.45500 q^{59} +(0.253156 - 2.44209i) q^{60} +4.07606 q^{61} -0.508520i q^{62} +1.00000i q^{63} -0.109452 q^{64} +(-0.971738 + 9.37395i) q^{65} +1.76011 q^{66} -12.3695i q^{67} -1.57408i q^{68} +2.64270 q^{69} +(3.91475 + 0.405817i) q^{70} +15.0283 q^{71} -1.58764i q^{72} -8.54550i q^{73} -18.8488 q^{74} +(-1.02561 + 4.89368i) q^{75} -7.44692 q^{76} +1.00000i q^{77} -7.41820i q^{78} +0.690394 q^{79} +(-11.0994 - 1.15060i) q^{80} +1.00000 q^{81} +2.85516i q^{82} +8.67547i q^{83} -1.09799 q^{84} +(-0.330537 + 3.18856i) q^{85} -14.4618 q^{86} -8.97759i q^{87} -1.58764i q^{88} -16.3392 q^{89} +(0.405817 - 3.91475i) q^{90} +4.21462 q^{91} +2.90165i q^{92} -0.288914i q^{93} -6.94351 q^{94} +(15.0849 + 1.56376i) q^{95} +5.60837 q^{96} -15.4515i q^{97} -1.76011i q^{98} +1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$			1.76011i			1.24459i	0.782784	+	0.622293i	$0.213799\pi$
$2$			1.76011i			1.24459i	−0.782784	+	0.622293i	$0.786201\pi$
$3$			1.00000i			0.577350i
$3$			1.00000i			0.577350i
$4$	−1.09799			−0.548994
$5$	2.22415	+	0.230563i	0.994670	+	0.103111i
$5$	2.22415	+	0.230563i	0.994670	+	0.103111i
$6$	−1.76011			−0.718562
$7$		−	1.00000i		−	0.377964i
$7$		−	1.00000i		−	0.377964i
$8$			1.58764i			0.561316i
$9$	−1.00000			−0.333333
$10$	−0.405817	+	3.91475i	−0.128331	+	1.23795i
$11$	−1.00000			−0.301511
$11$	−1.00000			−0.301511
$12$		−	1.09799i		−	0.316962i
$13$			4.21462i			1.16893i	0.811420	+	0.584463i	$0.198695\pi$
$13$			4.21462i			1.16893i	−0.811420	+	0.584463i	$0.801305\pi$
$14$	1.76011			0.470409
$15$	−0.230563	+	2.22415i	−0.0595312	+	0.574273i
$16$	−4.99040			−1.24760
$17$			1.43361i			0.347701i	0.984772	+	0.173850i	$0.0556209\pi$
$17$			1.43361i			0.347701i	−0.984772	+	0.173850i	$0.944379\pi$
$18$		−	1.76011i		−	0.414862i
$19$	6.78233			1.55597			0.777987	−	0.628281i	$-0.216241\pi$
$19$	6.78233			1.55597			0.777987	+	0.628281i	$0.216241\pi$
$20$	−2.44209	−	0.253156i	−0.546067	−	0.0566073i
$21$	1.00000			0.218218
$22$		−	1.76011i		−	0.375257i
$23$		−	2.64270i		−	0.551041i	−0.961295	−	0.275521i	$-0.911150\pi$
$23$		−	2.64270i		−	0.551041i	0.961295	−	0.275521i	$-0.0888502\pi$
$24$	−1.58764			−0.324076
$25$	4.89368	+	1.02561i	0.978736	+	0.205123i
$26$	−7.41820			−1.45483
$27$		−	1.00000i		−	0.192450i
$28$			1.09799i			0.207500i
$29$	−8.97759			−1.66710			−0.833548	−	0.552447i	$-0.813694\pi$
$29$	−8.97759			−1.66710			−0.833548	+	0.552447i	$0.813694\pi$
$30$	−3.91475	−	0.405817i	−0.714732	−	0.0740917i
$31$	−0.288914			−0.0518904			−0.0259452	−	0.999663i	$-0.508260\pi$
$31$	−0.288914			−0.0518904			−0.0259452	+	0.999663i	$0.508260\pi$
$32$		−	5.60837i		−	0.991429i
$33$		−	1.00000i		−	0.174078i
$34$	−2.52331			−0.432744
$35$	0.230563	−	2.22415i	0.0389723	−	0.375950i
$36$	1.09799			0.182998
$37$			10.7089i			1.76053i	0.474481	+	0.880266i	$0.342636\pi$
$37$			10.7089i			1.76053i	−0.474481	+	0.880266i	$0.657364\pi$
$38$			11.9377i			1.93654i
$39$	−4.21462			−0.674880
$40$	−0.366052	+	3.53115i	−0.0578779	+	0.558324i
$41$	1.62215			0.253337			0.126669	−	0.991945i	$-0.459571\pi$
$41$	1.62215			0.253337			0.126669	+	0.991945i	$0.459571\pi$
$42$			1.76011i			0.271591i
$43$			8.21640i			1.25299i	0.779426	+	0.626494i	$0.215511\pi$
$43$			8.21640i			1.25299i	−0.779426	+	0.626494i	$0.784489\pi$
$44$	1.09799			0.165528
$45$	−2.22415	−	0.230563i	−0.331557	−	0.0343704i
$46$	4.65144			0.685818
$47$			3.94493i			0.575427i	0.957717	+	0.287714i	$0.0928951\pi$
$47$			3.94493i			0.575427i	−0.957717	+	0.287714i	$0.907105\pi$
$48$		−	4.99040i		−	0.720302i
$49$	−1.00000			−0.142857
$50$	−1.80519	+	8.61342i	−0.255293	+	1.21812i
$51$	−1.43361			−0.200745
$52$		−	4.62760i		−	0.641733i
$53$		−	5.94827i		−	0.817057i	−0.912746	−	0.408529i	$-0.866042\pi$
$53$		−	5.94827i		−	0.817057i	0.912746	−	0.408529i	$-0.133958\pi$
$54$	1.76011			0.239521
$55$	−2.22415	−	0.230563i	−0.299904	−	0.0310892i
$56$	1.58764			0.212158
$57$			6.78233i			0.898342i
$58$		−	15.8015i		−	2.07484i
$59$	−6.45500			−0.840369			−0.420185	−	0.907439i	$-0.638035\pi$
$59$	−6.45500			−0.840369			−0.420185	+	0.907439i	$0.638035\pi$
$60$	0.253156	−	2.44209i	0.0326823	−	0.315272i
$61$	4.07606			0.521886			0.260943	−	0.965354i	$-0.415966\pi$
$61$	4.07606			0.521886			0.260943	+	0.965354i	$0.415966\pi$
$62$		−	0.508520i		−	0.0645821i
$63$			1.00000i			0.125988i
$64$	−0.109452			−0.0136816
$65$	−0.971738	+	9.37395i	−0.120529	+	1.16270i
$66$	1.76011			0.216655
$67$		−	12.3695i		−	1.51117i	−0.655050	−	0.755585i	$-0.727352\pi$
$67$		−	12.3695i		−	1.51117i	0.655050	−	0.755585i	$-0.272648\pi$
$68$		−	1.57408i		−	0.190886i
$69$	2.64270			0.318144
$70$	3.91475	+	0.405817i	0.467902	+	0.0485044i
$71$	15.0283			1.78353			0.891767	−	0.452494i	$-0.149466\pi$
$71$	15.0283			1.78353			0.891767	+	0.452494i	$0.149466\pi$
$72$		−	1.58764i		−	0.187105i
$73$		−	8.54550i		−	1.00018i	−0.865975	−	0.500088i	$-0.833301\pi$
$73$		−	8.54550i		−	1.00018i	0.865975	−	0.500088i	$-0.166699\pi$
$74$	−18.8488			−2.19113
$75$	−1.02561	+	4.89368i	−0.118428	+	0.565074i
$76$	−7.44692			−0.854220
$77$			1.00000i			0.113961i
$78$		−	7.41820i		−	0.839946i
$79$	0.690394			0.0776754			0.0388377	−	0.999246i	$-0.487634\pi$
$79$	0.690394			0.0776754			0.0388377	+	0.999246i	$0.487634\pi$
$80$	−11.0994	−	1.15060i	−1.24095	−	0.128641i
$81$	1.00000			0.111111
$82$			2.85516i			0.315300i
$83$			8.67547i			0.952256i	0.879376	+	0.476128i	$0.157960\pi$
$83$			8.67547i			0.952256i	−0.879376	+	0.476128i	$0.842040\pi$
$84$	−1.09799			−0.119800
$85$	−0.330537	+	3.18856i	−0.0358518	+	0.345848i
$86$	−14.4618			−1.55945
$87$		−	8.97759i		−	0.962499i
$88$		−	1.58764i		−	0.169243i
$89$	−16.3392			−1.73195			−0.865975	−	0.500087i	$-0.833302\pi$
$89$	−16.3392			−1.73195			−0.865975	+	0.500087i	$0.833302\pi$
$90$	0.405817	−	3.91475i	0.0427769	−	0.412651i
$91$	4.21462			0.441813
$92$			2.90165i			0.302518i
$93$		−	0.288914i		−	0.0299589i
$94$	−6.94351			−0.716168
$95$	15.0849	+	1.56376i	1.54768	+	0.160438i
$96$	5.60837			0.572402
$97$		−	15.4515i		−	1.56886i	−0.620217	−	0.784430i	$-0.712956\pi$
$97$		−	15.4515i		−	1.56886i	0.620217	−	0.784430i	$-0.287044\pi$
$98$		−	1.76011i		−	0.177798i
$99$	1.00000			0.100504
$100$	−5.37320	−	1.12611i	−0.537320	−	0.112611i
$101$	6.16833			0.613772			0.306886	−	0.951746i	$-0.400713\pi$
$101$	6.16833			0.613772			0.306886	+	0.951746i	$0.400713\pi$
$102$		−	2.52331i		−	0.249845i
$103$		−	8.41237i		−	0.828896i	−0.910073	−	0.414448i	$-0.863975\pi$
$103$		−	8.41237i		−	0.828896i	0.910073	−	0.414448i	$-0.136025\pi$
$104$	−6.69131			−0.656137
$105$	2.22415	+	0.230563i	0.217055	+	0.0225007i
$106$	10.4696			1.01690
$107$		−	6.91382i		−	0.668384i	−0.942505	−	0.334192i	$-0.891537\pi$
$107$		−	6.91382i		−	0.668384i	0.942505	−	0.334192i	$-0.108463\pi$
$108$			1.09799i			0.105654i
$109$	12.2807			1.17628			0.588141	−	0.808759i	$-0.299860\pi$
$109$	12.2807			1.17628			0.588141	+	0.808759i	$0.299860\pi$
$110$	0.405817	−	3.91475i	0.0386931	−	0.373257i
$111$	−10.7089			−1.01644
$112$			4.99040i			0.471548i
$113$		−	9.86801i		−	0.928304i	−0.885755	−	0.464152i	$-0.846359\pi$
$113$		−	9.86801i		−	0.928304i	0.885755	−	0.464152i	$-0.153641\pi$
$114$	−11.9377			−1.11806
$115$	0.609310	−	5.87776i	0.0568184	−	0.548104i
$116$	9.85728			0.915226
$117$		−	4.21462i		−	0.389642i
$118$		−	11.3615i		−	1.04591i
$119$	1.43361			0.131419
$120$	−3.53115	−	0.366052i	−0.322349	−	0.0334158i
$121$	1.00000			0.0909091
$122$			7.17432i			0.649532i
$123$			1.62215i			0.146264i
$124$	0.317224			0.0284875
$125$	10.6478	+	3.40942i	0.952369	+	0.304948i
$126$	−1.76011			−0.156803
$127$			11.9392i			1.05943i	0.848176	+	0.529715i	$0.177701\pi$
$127$			11.9392i			1.05943i	−0.848176	+	0.529715i	$0.822299\pi$
$128$		−	11.4094i		−	1.00846i
$129$	−8.21640			−0.723413
$130$	−16.4992	−	1.71037i	−1.44707	−	0.150009i
$131$	−3.51910			−0.307465			−0.153733	−	0.988112i	$-0.549129\pi$
$131$	−3.51910			−0.307465			−0.153733	+	0.988112i	$0.549129\pi$
$132$			1.09799i			0.0955675i
$133$		−	6.78233i		−	0.588103i
$134$	21.7716			1.88078
$135$	0.230563	−	2.22415i	0.0198437	−	0.191424i
$136$	−2.27605			−0.195170
$137$			8.26959i			0.706518i	0.935525	+	0.353259i	$0.114927\pi$
$137$			8.26959i			0.706518i	−0.935525	+	0.353259i	$0.885073\pi$
$138$			4.65144i			0.395957i
$139$	15.6717			1.32926			0.664628	−	0.747174i	$-0.268590\pi$
$139$	15.6717			1.32926			0.664628	+	0.747174i	$0.268590\pi$
$140$	−0.253156	+	2.44209i	−0.0213956	+	0.206394i
$141$	−3.94493			−0.332223
$142$			26.4515i			2.21976i
$143$		−	4.21462i		−	0.352445i
$144$	4.99040			0.415867
$145$	−19.9675	−	2.06990i	−1.65821	−	0.171896i
$146$	15.0410			1.24480
$147$		−	1.00000i		−	0.0824786i
$148$		−	11.7582i		−	0.966521i
$149$	−11.8212			−0.968428			−0.484214	−	0.874950i	$-0.660894\pi$
$149$	−11.8212			−0.968428			−0.484214	+	0.874950i	$0.660894\pi$
$150$	−8.61342	−	1.80519i	−0.703283	−	0.147394i
$151$	16.7850			1.36594			0.682972	−	0.730445i	$-0.260687\pi$
$151$	16.7850			1.36594			0.682972	+	0.730445i	$0.260687\pi$
$152$			10.7679i			0.873393i
$153$		−	1.43361i		−	0.115900i
$154$	−1.76011			−0.141834
$155$	−0.642587	−	0.0666129i	−0.0516138	−	0.00535048i
$156$	4.62760			0.370505
$157$		−	6.22134i		−	0.496517i	−0.968694	−	0.248258i	$-0.920142\pi$
$157$		−	6.22134i		−	0.496517i	0.968694	−	0.248258i	$-0.0798582\pi$
$158$			1.21517i			0.0966737i
$159$	5.94827			0.471728
$160$	1.29308	−	12.4738i	0.102227	−	0.986144i
$161$	−2.64270			−0.208274
$162$			1.76011i			0.138287i
$163$			7.54879i			0.591267i	0.955301	+	0.295633i	$0.0955307\pi$
$163$			7.54879i			0.591267i	−0.955301	+	0.295633i	$0.904469\pi$
$164$	−1.78110			−0.139081
$165$	0.230563	−	2.22415i	0.0179493	−	0.173150i
$166$	−15.2698			−1.18516
$167$		−	8.21780i		−	0.635913i	−0.948105	−	0.317956i	$-0.897003\pi$
$167$		−	8.21780i		−	0.635913i	0.948105	−	0.317956i	$-0.102997\pi$
$168$			1.58764i			0.122489i
$169$	−4.76305			−0.366388
$170$	−5.61221	−	0.581782i	−0.430437	−	0.0446206i
$171$	−6.78233			−0.518658
$172$		−	9.02150i		−	0.687883i
$173$			14.7464i			1.12115i	0.828104	+	0.560575i	$0.189420\pi$
$173$			14.7464i			1.12115i	−0.828104	+	0.560575i	$0.810580\pi$
$174$	15.8015			1.19791
$175$	1.02561	−	4.89368i	0.0775292	−	0.369928i
$176$	4.99040			0.376165
$177$		−	6.45500i		−	0.485188i
$178$		−	28.7588i		−	2.15556i
$179$	0.455241			0.0340263			0.0170132	−	0.999855i	$-0.494584\pi$
$179$	0.455241			0.0340263			0.0170132	+	0.999855i	$0.494584\pi$
$180$	2.44209	+	0.253156i	0.182022	+	0.0188691i
$181$	8.07223			0.600004			0.300002	−	0.953939i	$-0.403013\pi$
$181$	8.07223			0.600004			0.300002	+	0.953939i	$0.403013\pi$
$182$			7.41820i			0.549874i
$183$			4.07606i			0.301311i
$184$	4.19566			0.309308
$185$	−2.46908	+	23.8182i	−0.181530	+	1.75115i
$186$	0.508520			0.0372865
$187$		−	1.43361i		−	0.104836i
$188$		−	4.33148i		−	0.315906i
$189$	−1.00000			−0.0727393
$190$	−2.75238	+	26.5511i	−0.199679	+	1.92622i
$191$	15.5526			1.12535			0.562673	−	0.826679i	$-0.309773\pi$
$191$	15.5526			1.12535			0.562673	+	0.826679i	$0.309773\pi$
$192$		−	0.109452i		−	0.00789905i
$193$		−	19.9679i		−	1.43732i	−0.695363	−	0.718659i	$-0.744756\pi$
$193$		−	19.9679i		−	1.43732i	0.695363	−	0.718659i	$-0.255244\pi$
$194$	27.1963			1.95258
$195$	−9.37395	−	0.971738i	−0.671283	−	0.0695876i
$196$	1.09799			0.0784277
$197$		−	15.0465i		−	1.07202i	−0.844213	−	0.536008i	$-0.819932\pi$
$197$		−	15.0465i		−	1.07202i	0.844213	−	0.536008i	$-0.180068\pi$
$198$			1.76011i			0.125086i
$199$	6.25560			0.443448			0.221724	−	0.975109i	$-0.428832\pi$
$199$	6.25560			0.443448			0.221724	+	0.975109i	$0.428832\pi$
$200$	−1.62831	+	7.76941i	−0.115139	+	0.549380i
$201$	12.3695			0.872475
$202$			10.8569i			0.763891i
$203$			8.97759i			0.630103i
$204$	1.57408			0.110208
$205$	3.60791	+	0.374008i	0.251987	+	0.0261219i
$206$	14.8067			1.03163
$207$			2.64270i			0.183680i
$208$		−	21.0326i		−	1.45835i
$209$	−6.78233			−0.469144
$210$	−0.405817	+	3.91475i	−0.0280040	+	0.270143i
$211$	15.7435			1.08383			0.541913	−	0.840435i	$-0.317700\pi$
$211$	15.7435			1.08383			0.541913	+	0.840435i	$0.317700\pi$
$212$			6.53112i			0.448559i
$213$			15.0283i			1.02972i
$214$	12.1691			0.831862
$215$	−1.89440	+	18.2745i	−0.129197	+	1.24631i
$216$	1.58764			0.108025
$217$			0.288914i			0.0196127i
$218$			21.6154i			1.46398i
$219$	8.54550			0.577452
$220$	2.44209	+	0.253156i	0.164646	+	0.0170678i
$221$	−6.04212			−0.406437
$222$		−	18.8488i		−	1.26505i
$223$		−	10.0023i		−	0.669802i	−0.942253	−	0.334901i	$-0.891297\pi$
$223$		−	10.0023i		−	0.669802i	0.942253	−	0.334901i	$-0.108703\pi$
$224$	−5.60837			−0.374725
$225$	−4.89368	−	1.02561i	−0.326245	−	0.0683743i
$226$	17.3688			1.15535
$227$			15.8599i			1.05266i	0.850280	+	0.526330i	$0.176432\pi$
$227$			15.8599i			1.05266i	−0.850280	+	0.526330i	$0.823568\pi$
$228$		−	7.44692i		−	0.493184i
$229$	−23.1722			−1.53126			−0.765632	−	0.643279i	$-0.777573\pi$
$229$	−23.1722			−1.53126			−0.765632	+	0.643279i	$0.777573\pi$
$230$	10.3455	+	1.07245i	0.682162	+	0.0707154i
$231$	−1.00000			−0.0657952
$232$		−	14.2532i		−	0.935768i
$233$			18.5186i			1.21319i	0.795010	+	0.606597i	$0.207466\pi$
$233$			18.5186i			1.21319i	−0.795010	+	0.606597i	$0.792534\pi$
$234$	7.41820			0.484943
$235$	−0.909556	+	8.77411i	−0.0593329	+	0.572360i
$236$	7.08751			0.461358
$237$			0.690394i			0.0448459i
$238$			2.52331i			0.163562i
$239$	28.1822			1.82295			0.911477	−	0.411351i	$-0.134943\pi$
$239$	28.1822			1.82295			0.911477	+	0.411351i	$0.134943\pi$
$240$	1.15060	−	11.0994i	0.0742711	−	0.716463i
$241$	−7.08108			−0.456132			−0.228066	−	0.973646i	$-0.573240\pi$
$241$	−7.08108			−0.456132			−0.228066	+	0.973646i	$0.573240\pi$
$242$			1.76011i			0.113144i
$243$			1.00000i			0.0641500i
$244$	−4.47547			−0.286512
$245$	−2.22415	−	0.230563i	−0.142096	−	0.0147302i
$246$	−2.85516			−0.182039
$247$			28.5850i			1.81882i
$248$		−	0.458691i		−	0.0291269i
$249$	−8.67547			−0.549785
$250$	−6.00096	+	18.7413i	−0.379534	+	1.18530i
$251$	−8.74303			−0.551855			−0.275927	−	0.961178i	$-0.588985\pi$
$251$	−8.74303			−0.551855			−0.275927	+	0.961178i	$0.588985\pi$
$252$		−	1.09799i		−	0.0691667i
$253$			2.64270i			0.166145i
$254$	−21.0142			−1.31855
$255$	−3.18856	−	0.330537i	−0.199675	−	0.0206991i
$256$	19.8629			1.24143
$257$		−	20.9626i		−	1.30761i	−0.756662	−	0.653806i	$-0.773171\pi$
$257$		−	20.9626i		−	1.30761i	0.756662	−	0.653806i	$-0.226829\pi$
$258$		−	14.4618i		−	0.900350i
$259$	10.7089			0.665419
$260$	1.06696	−	10.2925i	0.0661698	−	0.638313i
$261$	8.97759			0.555699
$262$		−	6.19401i		−	0.382667i
$263$		−	6.30742i		−	0.388932i	−0.980909	−	0.194466i	$-0.937703\pi$
$263$		−	6.30742i		−	0.388932i	0.980909	−	0.194466i	$-0.0622974\pi$
$264$	1.58764			0.0977126
$265$	1.37145	−	13.2298i	0.0842476	−	0.812702i
$266$	11.9377			0.731944
$267$		−	16.3392i		−	0.999942i
$268$			13.5815i			0.829623i
$269$	−24.8014			−1.51217			−0.756083	−	0.654476i	$-0.772889\pi$
$269$	−24.8014			−1.51217			−0.756083	+	0.654476i	$0.772889\pi$
$270$	3.91475	+	0.405817i	0.238244	+	0.0246972i
$271$	9.73698			0.591479			0.295740	−	0.955269i	$-0.404434\pi$
$271$	9.73698			0.591479			0.295740	+	0.955269i	$0.404434\pi$
$272$		−	7.15427i		−	0.433791i
$273$			4.21462i			0.255081i
$274$	−14.5554			−0.879323
$275$	−4.89368	−	1.02561i	−0.295100	−	0.0618469i
$276$	−2.90165			−0.174659
$277$			0.787221i			0.0472995i	0.999720	+	0.0236498i	$0.00752866\pi$
$277$			0.787221i			0.0472995i	−0.999720	+	0.0236498i	$0.992471\pi$
$278$			27.5839i			1.65437i
$279$	0.288914			0.0172968
$280$	3.53115	+	0.366052i	0.211027	+	0.0218758i
$281$	12.4309			0.741565			0.370782	−	0.928720i	$-0.379090\pi$
$281$	12.4309			0.741565			0.370782	+	0.928720i	$0.379090\pi$
$282$		−	6.94351i		−	0.413480i
$283$			2.09042i			0.124263i	0.998068	+	0.0621314i	$0.0197898\pi$
$283$			2.09042i			0.124263i	−0.998068	+	0.0621314i	$0.980210\pi$
$284$	−16.5009			−0.979149
$285$	−1.56376	+	15.0849i	−0.0926290	+	0.893554i
$286$	7.41820			0.438647
$287$		−	1.62215i		−	0.0957525i
$288$			5.60837i			0.330476i
$289$	14.9448			0.879104
$290$	3.64326	−	35.1450i	0.213939	−	2.06379i
$291$	15.4515			0.905782
$292$			9.38286i			0.549090i
$293$		−	10.4989i		−	0.613353i	−0.951814	−	0.306676i	$-0.900783\pi$
$293$		−	10.4989i		−	0.613353i	0.951814	−	0.306676i	$-0.0992169\pi$
$294$	1.76011			0.102652
$295$	−14.3569	−	1.48829i	−0.835890	−	0.0866514i
$296$	−17.0019			−0.988215
$297$			1.00000i			0.0580259i
$298$		−	20.8066i		−	1.20529i
$299$	11.1380			0.644126
$300$	1.12611	−	5.37320i	0.0650161	−	0.310222i
$301$	8.21640			0.473585
$302$			29.5434i			1.70003i
$303$			6.16833i			0.354361i
$304$	−33.8465			−1.94123
$305$	9.06577	+	0.939791i	0.519105	+	0.0538123i
$306$	2.52331			0.144248
$307$			26.9278i			1.53685i	0.639939	+	0.768426i	$0.278960\pi$
$307$			26.9278i			1.53685i	−0.639939	+	0.768426i	$0.721040\pi$
$308$		−	1.09799i		−	0.0625636i
$309$	8.41237			0.478563
$310$	0.117246	−	1.13102i	0.00665913	−	0.0642378i
$311$	15.0673			0.854391			0.427195	−	0.904159i	$-0.359502\pi$
$311$	15.0673			0.854391			0.427195	+	0.904159i	$0.359502\pi$
$312$		−	6.69131i		−	0.378821i
$313$			23.5904i			1.33341i	0.745322	+	0.666704i	$0.232296\pi$
$313$			23.5904i			1.33341i	−0.745322	+	0.666704i	$0.767704\pi$
$314$	10.9502			0.617958
$315$	−0.230563	+	2.22415i	−0.0129908	+	0.125317i
$316$	−0.758044			−0.0426433
$317$			24.0122i			1.34866i	0.738430	+	0.674330i	$0.235568\pi$
$317$			24.0122i			1.34866i	−0.738430	+	0.674330i	$0.764432\pi$
$318$			10.4696i			0.587106i
$319$	8.97759			0.502649
$320$	−0.243439	−	0.0252357i	−0.0136086	−	0.00141072i
$321$	6.91382			0.385892
$322$		−	4.65144i		−	0.259215i
$323$			9.72320i			0.541013i
$324$	−1.09799			−0.0609993
$325$	−4.32258	+	20.6250i	−0.239774	+	1.14407i
$326$	−13.2867			−0.735882
$327$			12.2807i			0.679126i
$328$			2.57539i			0.142202i
$329$	3.94493			0.217491
$330$	3.91475	+	0.405817i	0.215500	+	0.0223395i
$331$	−21.5409			−1.18400			−0.591998	−	0.805940i	$-0.701661\pi$
$331$	−21.5409			−1.18400			−0.591998	+	0.805940i	$0.701661\pi$
$332$		−	9.52555i		−	0.522783i
$333$		−	10.7089i		−	0.586844i
$334$	14.4642			0.791448
$335$	2.85195	−	27.5115i	0.155818	−	1.50312i
$336$	−4.99040			−0.272249
$337$			1.35270i			0.0736864i	0.999321	+	0.0368432i	$0.0117302\pi$
$337$			1.35270i			0.0736864i	−0.999321	+	0.0368432i	$0.988270\pi$
$338$		−	8.38349i		−	0.456002i
$339$	9.86801			0.535957
$340$	0.362926	−	3.50100i	0.0196824	−	0.189868i
$341$	0.288914			0.0156455
$342$		−	11.9377i		−	0.645514i
$343$			1.00000i			0.0539949i
$344$	−13.0447			−0.703323
$345$	5.87776	+	0.609310i	0.316448	+	0.0328041i
$346$	−25.9553			−1.39537
$347$			6.68647i			0.358948i	0.983763	+	0.179474i	$0.0574396\pi$
$347$			6.68647i			0.358948i	−0.983763	+	0.179474i	$0.942560\pi$
$348$			9.85728i			0.528406i
$349$	−4.60906			−0.246718			−0.123359	−	0.992362i	$-0.539367\pi$
$349$	−4.60906			−0.246718			−0.123359	+	0.992362i	$0.539367\pi$
$350$	8.61342	+	1.80519i	0.460407	+	0.0964917i
$351$	4.21462			0.224960
$352$			5.60837i			0.298927i
$353$		−	17.5120i		−	0.932071i	−0.884766	−	0.466036i	$-0.845682\pi$
$353$		−	17.5120i		−	0.932071i	0.884766	−	0.466036i	$-0.154318\pi$
$354$	11.3615			0.603857
$355$	33.4253	+	3.46498i	1.77403	+	0.183902i
$356$	17.9402			0.950830
$357$			1.43361i			0.0758746i
$358$			0.801274i			0.0423487i
$359$	−21.3097			−1.12469			−0.562343	−	0.826904i	$-0.690100\pi$
$359$	−21.3097			−1.12469			−0.562343	+	0.826904i	$0.690100\pi$
$360$	0.366052	−	3.53115i	0.0192926	−	0.186108i
$361$	27.0000			1.42105
$362$			14.2080i			0.746756i
$363$			1.00000i			0.0524864i
$364$	−4.62760			−0.242552
$365$	1.97028	−	19.0065i	0.103129	−	0.994844i
$366$	−7.17432			−0.375008
$367$		−	19.0886i		−	0.996414i	−0.867058	−	0.498207i	$-0.833992\pi$
$367$		−	19.0886i		−	0.996414i	0.867058	−	0.498207i	$-0.166008\pi$
$368$			13.1881i			0.687479i
$369$	−1.62215			−0.0844458
$370$	−41.9226	−	4.34585i	−2.17945	−	0.225930i
$371$	−5.94827			−0.308819
$372$			0.317224i			0.0164473i
$373$			17.0590i			0.883282i	0.897192	+	0.441641i	$0.145603\pi$
$373$			17.0590i			0.883282i	−0.897192	+	0.441641i	$0.854397\pi$
$374$	2.52331			0.130477
$375$	−3.40942	+	10.6478i	−0.176062	+	0.549850i
$376$	−6.26313			−0.322996
$377$		−	37.8372i		−	1.94871i
$378$		−	1.76011i		−	0.0905303i
$379$	−33.8078			−1.73659			−0.868295	−	0.496048i	$-0.834784\pi$
$379$	−33.8078			−1.73659			−0.868295	+	0.496048i	$0.834784\pi$
$380$	−16.5631	−	1.71699i	−0.849667	−	0.0880795i
$381$	−11.9392			−0.611662
$382$			27.3743i			1.40059i
$383$		−	12.6409i		−	0.645920i	−0.946413	−	0.322960i	$-0.895322\pi$
$383$		−	12.6409i		−	0.645920i	0.946413	−	0.322960i	$-0.104678\pi$
$384$	11.4094			0.582233
$385$	−0.230563	+	2.22415i	−0.0117506	+	0.113353i
$386$	35.1456			1.78887
$387$		−	8.21640i		−	0.417663i
$388$			16.9655i			0.861294i
$389$	−2.90831			−0.147457			−0.0737285	−	0.997278i	$-0.523490\pi$
$389$	−2.90831			−0.147457			−0.0737285	+	0.997278i	$0.523490\pi$
$390$	1.71037	−	16.4992i	0.0866077	−	0.835469i
$391$	3.78859			0.191597
$392$		−	1.58764i		−	0.0801880i
$393$		−	3.51910i		−	0.177515i
$394$	26.4834			1.33422
$395$	1.53554	+	0.159180i	0.0772614	+	0.00800920i
$396$	−1.09799			−0.0551759
$397$		−	11.6301i		−	0.583700i	−0.956464	−	0.291850i	$-0.905729\pi$
$397$		−	11.6301i		−	0.583700i	0.956464	−	0.291850i	$-0.0942708\pi$
$398$			11.0106i			0.551909i
$399$	6.78233			0.339541
$400$	−24.4214	−	5.11823i	−1.22107	−	0.255911i
$401$	22.4120			1.11920			0.559602	−	0.828761i	$-0.310954\pi$
$401$	22.4120			1.11920			0.559602	+	0.828761i	$0.310954\pi$
$402$			21.7716i			1.08587i
$403$		−	1.21766i		−	0.0606561i
$404$	−6.77275			−0.336957
$405$	2.22415	+	0.230563i	0.110519	+	0.0114568i
$406$	−15.8015			−0.784218
$407$		−	10.7089i		−	0.530820i
$408$		−	2.27605i		−	0.112681i
$409$	12.4627			0.616239			0.308120	−	0.951348i	$-0.400300\pi$
$409$	12.4627			0.616239			0.308120	+	0.951348i	$0.400300\pi$
$410$	−0.658296	+	6.35031i	−0.0325109	+	0.313619i
$411$	−8.26959			−0.407909
$412$			9.23668i			0.455058i
$413$			6.45500i			0.317630i
$414$	−4.65144			−0.228606
$415$	−2.00024	+	19.2955i	−0.0981881	+	0.947180i
$416$	23.6372			1.15891
$417$			15.6717i			0.767447i
$418$		−	11.9377i		−	0.583890i
$419$	7.16999			0.350277			0.175139	−	0.984544i	$-0.443963\pi$
$419$	7.16999			0.350277			0.175139	+	0.984544i	$0.443963\pi$
$420$	−2.44209	−	0.253156i	−0.119162	−	0.0123527i
$421$	26.8929			1.31068			0.655341	−	0.755334i	$-0.272525\pi$
$421$	26.8929			1.31068			0.655341	+	0.755334i	$0.272525\pi$
$422$			27.7103i			1.34891i
$423$		−	3.94493i		−	0.191809i
$424$	9.44371			0.458627
$425$	−1.47033	+	7.01562i	−0.0713214	+	0.340307i
$426$	−26.4515			−1.28158
$427$		−	4.07606i		−	0.197255i
$428$			7.59129i			0.366939i
$429$	4.21462			0.203484
$430$	−32.1651	−	3.33435i	−1.55114	−	0.160797i
$431$	8.06019			0.388246			0.194123	−	0.980977i	$-0.437814\pi$
$431$	8.06019			0.388246			0.194123	+	0.980977i	$0.437814\pi$
$432$			4.99040i			0.240101i
$433$		−	14.4948i		−	0.696576i	−0.937388	−	0.348288i	$-0.886763\pi$
$433$		−	14.4948i		−	0.696576i	0.937388	−	0.348288i	$-0.113237\pi$
$434$	−0.508520			−0.0244097
$435$	2.06990	−	19.9675i	0.0992443	−	0.957368i
$436$	−13.4841			−0.645771
$437$		−	17.9237i		−	0.857405i
$438$			15.0410i			0.718688i
$439$	−4.28674			−0.204595			−0.102298	−	0.994754i	$-0.532619\pi$
$439$	−4.28674			−0.204595			−0.102298	+	0.994754i	$0.532619\pi$
$440$	0.366052	−	3.53115i	0.0174508	−	0.168341i
$441$	1.00000			0.0476190
$442$		−	10.6348i		−	0.505845i
$443$			4.83452i			0.229695i	0.993383	+	0.114848i	$0.0366380\pi$
$443$			4.83452i			0.229695i	−0.993383	+	0.114848i	$0.963362\pi$
$444$	11.7582			0.558021
$445$	−36.3408	−	3.76722i	−1.72272	−	0.178583i
$446$	17.6051			0.833626
$447$		−	11.8212i		−	0.559122i
$448$			0.109452i			0.00517114i
$449$	−35.7884			−1.68896			−0.844479	−	0.535588i	$-0.820090\pi$
$449$	−35.7884			−1.68896			−0.844479	+	0.535588i	$0.820090\pi$
$450$	1.80519	−	8.61342i	0.0850977	−	0.406040i
$451$	−1.62215			−0.0763841
$452$			10.8350i			0.509633i
$453$			16.7850i			0.788628i
$454$	−27.9152			−1.31013
$455$	9.37395	+	0.971738i	0.439458	+	0.0455558i
$456$	−10.7679			−0.504254
$457$		−	15.6563i		−	0.732370i	−0.930542	−	0.366185i	$-0.880664\pi$
$457$		−	15.6563i		−	0.732370i	0.930542	−	0.366185i	$-0.119336\pi$
$458$		−	40.7856i		−	1.90579i
$459$	1.43361			0.0669151
$460$	−0.669014	+	6.45371i	−0.0311930	+	0.300906i
$461$	−38.1784			−1.77815			−0.889073	−	0.457766i	$-0.848650\pi$
$461$	−38.1784			−1.77815			−0.889073	+	0.457766i	$0.848650\pi$
$462$		−	1.76011i		−	0.0818877i
$463$		−	13.4364i		−	0.624442i	−0.950010	−	0.312221i	$-0.898927\pi$
$463$		−	13.4364i		−	0.624442i	0.950010	−	0.312221i	$-0.101073\pi$
$464$	44.8017			2.07987
$465$	0.0666129	−	0.642587i	0.00308910	−	0.0297993i
$466$	−32.5948			−1.50992
$467$		−	37.5213i		−	1.73628i	−0.496321	−	0.868139i	$-0.665316\pi$
$467$		−	37.5213i		−	1.73628i	0.496321	−	0.868139i	$-0.334684\pi$
$468$			4.62760i			0.213911i
$469$	−12.3695			−0.571169
$470$	−15.4434	−	1.60092i	−0.712351	−	0.0738449i
$471$	6.22134			0.286664
$472$		−	10.2482i		−	0.471713i
$473$		−	8.21640i		−	0.377790i
$474$	−1.21517			−0.0558146
$475$	33.1906	+	6.95606i	1.52289	+	0.319166i
$476$	−1.57408			−0.0721480
$477$			5.94827i			0.272352i
$478$			49.6037i			2.26882i
$479$	19.6828			0.899329			0.449665	−	0.893198i	$-0.351544\pi$
$479$	19.6828			0.899329			0.449665	+	0.893198i	$0.351544\pi$
$480$	12.4738	+	1.29308i	0.569351	+	0.0590209i
$481$	−45.1340			−2.05793
$482$		−	12.4635i		−	0.567696i
$483$		−	2.64270i		−	0.120247i
$484$	−1.09799			−0.0499085
$485$	3.56254	−	34.3664i	0.161767	−	1.56050i
$486$	−1.76011			−0.0798402
$487$			24.5893i			1.11425i	0.830430	+	0.557123i	$0.188095\pi$
$487$			24.5893i			1.11425i	−0.830430	+	0.557123i	$0.811905\pi$
$488$			6.47133i			0.292943i
$489$	−7.54879			−0.341368
$490$	0.405817	−	3.91475i	0.0183329	−	0.176850i
$491$	32.0804			1.44777			0.723883	−	0.689922i	$-0.242355\pi$
$491$	32.0804			1.44777			0.723883	+	0.689922i	$0.242355\pi$
$492$		−	1.78110i		−	0.0802982i
$493$		−	12.8703i		−	0.579651i
$494$	−50.3127			−2.26368
$495$	2.22415	+	0.230563i	0.0999681	+	0.0103631i
$496$	1.44179			0.0647385
$497$		−	15.0283i		−	0.674113i
$498$		−	15.2698i		−	0.684255i
$499$	42.5393			1.90432			0.952161	−	0.305597i	$-0.0988559\pi$
$499$	42.5393			1.90432			0.952161	+	0.305597i	$0.0988559\pi$
$500$	−11.6912	−	3.74350i	−0.522845	−	0.167415i
$501$	8.21780			0.367144
$502$		−	15.3887i		−	0.686831i
$503$		−	25.6136i		−	1.14205i	−0.820931	−	0.571027i	$-0.806545\pi$
$503$		−	25.6136i		−	1.14205i	0.820931	−	0.571027i	$-0.193455\pi$
$504$	−1.58764			−0.0707192
$505$	13.7193	+	1.42219i	0.610500	+	0.0632866i
$506$	−4.65144			−0.206782
$507$		−	4.76305i		−	0.211534i
$508$		−	13.1091i		−	0.581620i
$509$	−32.8590			−1.45645			−0.728226	−	0.685337i	$-0.759655\pi$
$509$	−32.8590			−1.45645			−0.728226	+	0.685337i	$0.759655\pi$
$510$	0.581782	−	5.61221i	0.0257617	−	0.248513i
$511$	−8.54550			−0.378031
$512$			12.1421i			0.536608i
$513$		−	6.78233i		−	0.299447i
$514$	36.8965			1.62744
$515$	1.93958	−	18.7104i	0.0854683	−	0.824477i
$516$	9.02150			0.397149
$517$		−	3.94493i		−	0.173498i
$518$			18.8488i			0.828170i
$519$	−14.7464			−0.647296
$520$	−14.8825	−	1.54277i	−0.652640	−	0.0676550i
$521$	32.2802			1.41422			0.707111	−	0.707103i	$-0.249998\pi$
$521$	32.2802			1.41422			0.707111	+	0.707103i	$0.249998\pi$
$522$			15.8015i			0.691615i
$523$		−	17.5863i		−	0.768996i	−0.923126	−	0.384498i	$-0.874375\pi$
$523$		−	17.5863i		−	0.768996i	0.923126	−	0.384498i	$-0.125625\pi$
$524$	3.86393			0.168797
$525$	4.89368	+	1.02561i	0.213578	+	0.0447615i
$526$	11.1018			0.484060
$527$		−	0.414189i		−	0.0180423i
$528$			4.99040i			0.217179i
$529$	16.0161			0.696354
$530$	23.2860	+	2.41391i	1.01148	+	0.104853i
$531$	6.45500			0.280123
$532$			7.44692i			0.322865i
$533$			6.83675i			0.296133i
$534$	28.7588			1.24451
$535$	1.59407	−	15.3774i	0.0689178	−	0.664822i
$536$	19.6383			0.848244
$537$			0.455241i			0.0196451i
$538$		−	43.6531i		−	1.88202i
$539$	1.00000			0.0430730
$540$	−0.253156	+	2.44209i	−0.0108941	+	0.105091i
$541$	−30.5935			−1.31532			−0.657659	−	0.753316i	$-0.728453\pi$
$541$	−30.5935			−1.31532			−0.657659	+	0.753316i	$0.728453\pi$
$542$			17.1382i			0.736147i
$543$			8.07223i			0.346412i
$544$	8.04020			0.344721
$545$	27.3142	+	2.83149i	1.17001	+	0.121288i
$546$	−7.41820			−0.317470
$547$			42.4854i			1.81655i	0.418378	+	0.908273i	$0.362599\pi$
$547$			42.4854i			1.81655i	−0.418378	+	0.908273i	$0.637401\pi$
$548$		−	9.07990i		−	0.387874i
$549$	−4.07606			−0.173962
$550$	1.80519	−	8.61342i	0.0769738	−	0.367277i
$551$	−60.8890			−2.59396
$552$			4.19566i			0.178579i
$553$		−	0.690394i		−	0.0293586i
$554$	−1.38560			−0.0588683
$555$	−23.8182	−	2.46908i	−1.01103	−	0.104807i
$556$	−17.2073			−0.729753
$557$		−	29.1333i		−	1.23442i	−0.786799	−	0.617209i	$-0.788263\pi$
$557$		−	29.1333i		−	1.23442i	0.786799	−	0.617209i	$-0.211737\pi$
$558$			0.508520i			0.0215274i
$559$	−34.6290			−1.46465
$560$	−1.15060	+	11.0994i	−0.0486218	+	0.469035i
$561$	1.43361			0.0605270
$562$			21.8797i			0.922941i
$563$			37.5476i			1.58244i	0.611531	+	0.791221i	$0.290554\pi$
$563$			37.5476i			1.58244i	−0.611531	+	0.791221i	$0.709446\pi$
$564$	4.33148			0.182388
$565$	2.27520	−	21.9479i	0.0957185	−	0.923356i
$566$	−3.67938			−0.154656
$567$		−	1.00000i		−	0.0419961i
$568$			23.8596i			1.00113i
$569$	−0.484384			−0.0203064			−0.0101532	−	0.999948i	$-0.503232\pi$
$569$	−0.484384			−0.0203064			−0.0101532	+	0.999948i	$0.503232\pi$
$570$	−26.5511	−	2.75238i	−1.11210	−	0.115285i
$571$	7.23540			0.302792			0.151396	−	0.988473i	$-0.451623\pi$
$571$	7.23540			0.302792			0.151396	+	0.988473i	$0.451623\pi$
$572$			4.62760i			0.193490i
$573$			15.5526i			0.649719i
$574$	2.85516			0.119172
$575$	2.71039	−	12.9325i	0.113031	−	0.539324i
$576$	0.109452			0.00456052
$577$		−	23.8497i		−	0.992878i	−0.868072	−	0.496439i	$-0.834641\pi$
$577$		−	23.8497i		−	0.992878i	0.868072	−	0.496439i	$-0.165359\pi$
$578$			26.3044i			1.09412i
$579$	19.9679			0.829836
$580$	21.9241	+	2.27273i	0.910347	+	0.0943699i
$581$	8.67547			0.359919
$582$			27.1963i			1.12732i
$583$			5.94827i			0.246352i
$584$	13.5672			0.561415
$585$	0.971738	−	9.37395i	0.0401764	−	0.387565i
$586$	18.4792			0.763370
$587$		−	25.6673i		−	1.05940i	−0.848184	−	0.529701i	$-0.822304\pi$
$587$		−	25.6673i		−	1.05940i	0.848184	−	0.529701i	$-0.177696\pi$
$588$			1.09799i			0.0452802i
$589$	−1.95951			−0.0807401
$590$	2.61955	−	25.2697i	0.107845	−	1.04034i
$591$	15.0465			0.618929
$592$		−	53.4417i		−	2.19644i
$593$			25.8664i			1.06221i	0.847308	+	0.531103i	$0.178222\pi$
$593$			25.8664i			1.06221i	−0.847308	+	0.531103i	$0.821778\pi$
$594$	−1.76011			−0.0722182
$595$	3.18856	+	0.330537i	0.130718	+	0.0135507i
$596$	12.9795			0.531661
$597$			6.25560i			0.256025i
$598$			19.6041i			0.801670i
$599$	−23.1007			−0.943870			−0.471935	−	0.881633i	$-0.656444\pi$
$599$	−23.1007			−0.943870			−0.471935	+	0.881633i	$0.656444\pi$
$600$	−7.76941	−	1.62831i	−0.317185	−	0.0664754i
$601$	−25.3840			−1.03544			−0.517718	−	0.855551i	$-0.673218\pi$
$601$	−25.3840			−1.03544			−0.517718	+	0.855551i	$0.673218\pi$
$602$			14.4618i			0.589417i
$603$			12.3695i			0.503724i
$604$	−18.4297			−0.749895
$605$	2.22415	+	0.230563i	0.0904245	+	0.00937373i
$606$	−10.8569			−0.441033
$607$		−	25.9728i		−	1.05420i	−0.849802	−	0.527102i	$-0.823278\pi$
$607$		−	25.9728i		−	1.05420i	0.849802	−	0.527102i	$-0.176722\pi$
$608$		−	38.0378i		−	1.54264i
$609$	−8.97759			−0.363790
$610$	−1.65414	+	15.9568i	−0.0669740	+	0.646070i
$611$	−16.6264			−0.672632
$612$			1.57408i			0.0636285i
$613$		−	18.6868i		−	0.754753i	−0.926060	−	0.377377i	$-0.876826\pi$
$613$		−	18.6868i		−	0.754753i	0.926060	−	0.377377i	$-0.123174\pi$
$614$	−47.3959			−1.91274
$615$	−0.374008	+	3.60791i	−0.0150815	+	0.145485i
$616$	−1.58764			−0.0639679
$617$		−	12.4067i		−	0.499476i	−0.968313	−	0.249738i	$-0.919656\pi$
$617$		−	12.4067i		−	0.499476i	0.968313	−	0.249738i	$-0.0803445\pi$
$618$			14.8067i			0.595613i
$619$	3.23070			0.129853			0.0649265	−	0.997890i	$-0.479319\pi$
$619$	3.23070			0.129853			0.0649265	+	0.997890i	$0.479319\pi$
$620$	0.705553	+	0.0731401i	0.0283357	+	0.00293738i
$621$	−2.64270			−0.106048
$622$			26.5202i			1.06336i
$623$			16.3392i			0.654616i
$624$	21.0326			0.841980
$625$	22.8962	+	10.0381i	0.915849	+	0.401522i
$626$	−41.5217			−1.65954
$627$		−	6.78233i		−	0.270860i
$628$			6.83095i			0.272585i
$629$	−15.3524			−0.612139
$630$	−3.91475	−	0.405817i	−0.155967	−	0.0161681i
$631$	−15.6686			−0.623758			−0.311879	−	0.950122i	$-0.600958\pi$
$631$	−15.6686			−0.623758			−0.311879	+	0.950122i	$0.600958\pi$
$632$			1.09610i			0.0436005i
$633$			15.7435i			0.625747i
$634$	−42.2641			−1.67852
$635$	−2.75273	+	26.5545i	−0.109239	+	1.05378i
$636$	−6.53112			−0.258976
$637$		−	4.21462i		−	0.166989i
$638$			15.8015i			0.625589i
$639$	−15.0283			−0.594512
$640$	2.63059	−	25.3762i	0.103983	−	1.00308i
$641$	−40.4745			−1.59865			−0.799323	−	0.600901i	$-0.794809\pi$
$641$	−40.4745			−1.59865			−0.799323	+	0.600901i	$0.794809\pi$
$642$			12.1691i			0.480276i
$643$			27.5878i			1.08796i	0.839099	+	0.543979i	$0.183083\pi$
$643$			27.5878i			1.08796i	−0.839099	+	0.543979i	$0.816917\pi$
$644$	2.90165			0.114341
$645$	−18.2745	−	1.89440i	−0.719557	−	0.0745919i
$646$	−17.1139			−0.673338
$647$		−	12.5975i		−	0.495257i	−0.968855	−	0.247628i	$-0.920349\pi$
$647$		−	12.5975i		−	0.495257i	0.968855	−	0.247628i	$-0.0796512\pi$
$648$			1.58764i			0.0623684i
$649$	6.45500			0.253381
$650$	−36.3023	−	7.60822i	−1.42389	−	0.298419i
$651$	−0.288914			−0.0113234
$652$		−	8.28848i		−	0.324602i
$653$		−	27.9716i		−	1.09461i	−0.836932	−	0.547307i	$-0.815653\pi$
$653$		−	27.9716i		−	1.09461i	0.836932	−	0.547307i	$-0.184347\pi$
$654$	−21.6154			−0.845231
$655$	−7.82701	−	0.811376i	−0.305827	−	0.0317031i
$656$	−8.09518			−0.316064
$657$			8.54550i			0.333392i
$658$			6.94351i			0.270686i
$659$	−25.4690			−0.992130			−0.496065	−	0.868285i	$-0.665222\pi$
$659$	−25.4690			−0.992130			−0.496065	+	0.868285i	$0.665222\pi$
$660$	−0.253156	+	2.44209i	−0.00985407	+	0.0950581i
$661$	34.5066			1.34215			0.671075	−	0.741390i	$-0.265833\pi$
$661$	34.5066			1.34215			0.671075	+	0.741390i	$0.265833\pi$
$662$		−	37.9144i		−	1.47358i
$663$		−	6.04212i		−	0.234656i
$664$	−13.7735			−0.534517
$665$	1.56376	−	15.0849i	0.0606399	−	0.584968i
$666$	18.8488			0.730378
$667$			23.7251i			0.918639i
$668$			9.02304i			0.349112i
$669$	10.0023			0.386711
$670$	48.4233	+	5.01974i	1.87076	+	0.193929i
$671$	−4.07606			−0.157355
$672$		−	5.60837i		−	0.216347i
$673$			38.8076i			1.49592i	0.663743	+	0.747961i	$0.268967\pi$
$673$			38.8076i			1.49592i	−0.663743	+	0.747961i	$0.731033\pi$
$674$	−2.38091			−0.0917090
$675$	1.02561	−	4.89368i	0.0394759	−	0.188358i
$676$	5.22977			0.201145
$677$		−	24.9110i		−	0.957407i	−0.877977	−	0.478704i	$-0.841107\pi$
$677$		−	24.9110i		−	0.957407i	0.877977	−	0.478704i	$-0.158893\pi$
$678$			17.3688i			0.667044i
$679$	−15.4515			−0.592973
$680$	−5.06229	−	0.524775i	−0.194130	−	0.0201242i
$681$	−15.8599			−0.607754
$682$			0.508520i			0.0194722i
$683$			2.62542i			0.100459i	0.998738	+	0.0502295i	$0.0159953\pi$
$683$			2.62542i			0.100459i	−0.998738	+	0.0502295i	$0.984005\pi$
$684$	7.44692			0.284740
$685$	−1.90666	+	18.3928i	−0.0728499	+	0.702753i
$686$	−1.76011			−0.0672013
$687$		−	23.1722i		−	0.884075i
$688$		−	41.0031i		−	1.56323i
$689$	25.0697			0.955079
$690$	−1.07245	+	10.3455i	−0.0408276	+	0.393847i
$691$	−20.8124			−0.791741			−0.395871	−	0.918306i	$-0.629557\pi$
$691$	−20.8124			−0.791741			−0.395871	+	0.918306i	$0.629557\pi$
$692$		−	16.1914i		−	0.615504i
$693$		−	1.00000i		−	0.0379869i
$694$	−11.7689			−0.446742
$695$	34.8562	+	3.61332i	1.32217	+	0.137061i
$696$	14.2532			0.540266
$697$			2.32553i			0.0880856i
$698$		−	8.11246i		−	0.307061i
$699$	−18.5186			−0.700437
$700$	−1.12611	+	5.37320i	−0.0425630	+	0.203088i
$701$	3.23339			0.122124			0.0610618	−	0.998134i	$-0.480551\pi$
$701$	3.23339			0.122124			0.0610618	+	0.998134i	$0.480551\pi$
$702$			7.41820i			0.279982i
$703$			72.6313i			2.73934i
$704$	0.109452			0.00412514
$705$	−8.77411	−	0.909556i	−0.330452	−	0.0342559i
$706$	30.8231			1.16004
$707$		−	6.16833i		−	0.231984i
$708$			7.08751i			0.266365i
$709$	−2.02814			−0.0761684			−0.0380842	−	0.999275i	$-0.512126\pi$
$709$	−2.02814			−0.0761684			−0.0380842	+	0.999275i	$0.512126\pi$
$710$	−6.09875	+	58.8321i	−0.228882	+	2.20793i
$711$	−0.690394			−0.0258918
$712$		−	25.9408i		−	0.972172i
$713$			0.763512i			0.0285938i
$714$	−2.52331			−0.0944324
$715$	0.971738	−	9.37395i	0.0363409	−	0.350566i
$716$	−0.499849			−0.0186802
$717$			28.1822i			1.05248i
$718$		−	37.5075i		−	1.39977i
$719$	−24.9232			−0.929477			−0.464739	−	0.885448i	$-0.653852\pi$
$719$	−24.9232			−0.929477			−0.464739	+	0.885448i	$0.653852\pi$
$720$	11.0994	+	1.15060i	0.413650	+	0.0428804i
$721$	−8.41237			−0.313293
$722$			47.5230i			1.76862i
$723$		−	7.08108i		−	0.263348i
$724$	−8.86321			−0.329398
$725$	−43.9335	−	9.20755i	−1.63165	−	0.341960i
$726$	−1.76011			−0.0653238
$727$		−	2.18158i		−	0.0809104i	−0.999181	−	0.0404552i	$-0.987119\pi$
$727$		−	2.18158i		−	0.0809104i	0.999181	−	0.0404552i	$-0.0128808\pi$
$728$			6.69131i			0.247996i
$729$	−1.00000			−0.0370370
$730$	33.4535	+	3.46791i	1.23817	+	0.128353i
$731$	−11.7791			−0.435665
$732$		−	4.47547i		−	0.165418i
$733$		−	17.1410i		−	0.633118i	−0.948573	−	0.316559i	$-0.897473\pi$
$733$		−	17.1410i		−	0.633118i	0.948573	−	0.316559i	$-0.102527\pi$
$734$	33.5980			1.24012
$735$	0.230563	−	2.22415i	0.00850446	−	0.0820390i
$736$	−14.8212			−0.546318
$737$			12.3695i			0.455635i
$738$		−	2.85516i		−	0.105100i
$739$	0.235487			0.00866254			0.00433127	−	0.999991i	$-0.498621\pi$
$739$	0.235487			0.00866254			0.00433127	+	0.999991i	$0.498621\pi$
$740$	2.71102	−	26.1521i	0.0996590	−	0.961369i
$741$	−28.5850			−1.05010
$742$		−	10.4696i		−	0.384351i
$743$		−	18.2853i		−	0.670823i	−0.942072	−	0.335412i	$-0.891125\pi$
$743$		−	18.2853i		−	0.670823i	0.942072	−	0.335412i	$-0.108875\pi$
$744$	0.458691			0.0168164
$745$	−26.2921	−	2.72553i	−0.963266	−	0.0998557i
$746$	−30.0257			−1.09932
$747$		−	8.67547i		−	0.317419i
$748$			1.57408i			0.0575542i
$749$	−6.91382			−0.252626
$750$	−18.7413	−	6.00096i	−0.684336	−	0.219124i
$751$	40.5425			1.47942			0.739708	−	0.672928i	$-0.234963\pi$
$751$	40.5425			1.47942			0.739708	+	0.672928i	$0.234963\pi$
$752$		−	19.6868i		−	0.717903i
$753$		−	8.74303i		−	0.318614i
$754$	66.5976			2.42534
$755$	37.3323	+	3.87001i	1.35866	+	0.140844i
$756$	1.09799			0.0399334
$757$			16.5593i			0.601857i	0.953647	+	0.300928i	$0.0972965\pi$
$757$			16.5593i			0.601857i	−0.953647	+	0.300928i	$0.902703\pi$
$758$		−	59.5055i		−	2.16134i
$759$	−2.64270			−0.0959239
$760$	−2.48269	+	23.9494i	−0.0900565	+	0.868738i
$761$	−37.4981			−1.35930			−0.679652	−	0.733534i	$-0.737869\pi$
$761$	−37.4981			−1.35930			−0.679652	+	0.733534i	$0.737869\pi$
$762$		−	21.0142i		−	0.761266i
$763$		−	12.2807i		−	0.444593i
$764$	−17.0766			−0.617808
$765$	0.330537	−	3.18856i	0.0119506	−	0.115283i
$766$	22.2494			0.803902
$767$		−	27.2054i		−	0.982330i
$768$			19.8629i			0.716739i
$769$	−0.466341			−0.0168167			−0.00840835	−	0.999965i	$-0.502676\pi$
$769$	−0.466341			−0.0168167			−0.00840835	+	0.999965i	$0.502676\pi$
$770$	−3.91475	−	0.405817i	−0.141078	−	0.0146246i
$771$	20.9626			0.754950
$772$			21.9245i			0.789078i
$773$			15.0027i			0.539608i	0.962915	+	0.269804i	$0.0869590\pi$
$773$			15.0027i			0.539608i	−0.962915	+	0.269804i	$0.913041\pi$
$774$	14.4618			0.519817
$775$	−1.41385	−	0.296314i	−0.0507870	−	0.0106439i
$776$	24.5314			0.880626
$777$			10.7089i			0.384180i
$778$		−	5.11894i		−	0.183523i
$779$	11.0020			0.394186
$780$	10.2925	+	1.06696i	0.368530	+	0.0382031i
$781$	−15.0283			−0.537756
$782$			6.66834i			0.238459i
$783$			8.97759i			0.320833i
$784$	4.99040			0.178229
$785$	1.43441	−	13.8372i	0.0511964	−	0.493870i
$786$	6.19401			0.220933
$787$		−	32.4641i		−	1.15722i	−0.815604	−	0.578610i	$-0.803595\pi$
$787$		−	32.4641i		−	1.15722i	0.815604	−	0.578610i	$-0.196405\pi$
$788$			16.5208i			0.588530i
$789$	6.30742			0.224550
$790$	−0.280174	+	2.70272i	−0.00996813	+	0.0961584i
$791$	−9.86801			−0.350866
$792$			1.58764i			0.0564144i
$793$			17.1791i			0.610047i
$794$	20.4703			0.726465
$795$	13.2298	+	1.37145i	0.469214	+	0.0486404i
$796$	−6.86857			−0.243450
$797$			13.9482i			0.494072i	0.969006	+	0.247036i	$0.0794566\pi$
$797$			13.9482i			0.494072i	−0.969006	+	0.247036i	$0.920543\pi$
$798$			11.9377i			0.422588i
$799$	−5.65548			−0.200077
$800$	5.75202	−	27.4456i	0.203365	−	0.970347i
$801$	16.3392			0.577317
$802$			39.4477i			1.39295i
$803$			8.54550i			0.301564i
$804$	−13.5815			−0.478983
$805$	−5.87776	−	0.609310i	−0.207164	−	0.0214753i
$806$	2.14322			0.0754917
$807$		−	24.8014i		−	0.873049i
$808$			9.79309i			0.344520i
$809$	−27.3872			−0.962883			−0.481442	−	0.876478i	$-0.659887\pi$
$809$	−27.3872			−0.962883			−0.481442	+	0.876478i	$0.659887\pi$
$810$	−0.405817	+	3.91475i	−0.0142590	+	0.137550i
$811$	−17.7628			−0.623736			−0.311868	−	0.950125i	$-0.600955\pi$
$811$	−17.7628			−0.623736			−0.311868	+	0.950125i	$0.600955\pi$
$812$		−	9.85728i		−	0.345923i
$813$			9.73698i			0.341491i
$814$	18.8488			0.660651
$815$	−1.74047	+	16.7896i	−0.0609662	+	0.588115i
$816$	7.15427			0.250450
$817$			55.7263i			1.94962i
$818$			21.9357i			0.766963i
$819$	−4.21462			−0.147271
$820$	−3.96143	−	0.410657i	−0.138339	−	0.0143408i
$821$	23.0623			0.804879			0.402440	−	0.915447i	$-0.368162\pi$
$821$	23.0623			0.804879			0.402440	+	0.915447i	$0.368162\pi$
$822$		−	14.5554i		−	0.507677i
$823$		−	36.9625i		−	1.28843i	−0.764844	−	0.644216i	$-0.777184\pi$
$823$		−	36.9625i		−	1.28843i	0.764844	−	0.644216i	$-0.222816\pi$
$824$	13.3558			0.465272
$825$	1.02561	−	4.89368i	0.0357073	−	0.170376i
$826$	−11.3615			−0.395318
$827$		−	1.32975i		−	0.0462398i	−0.999733	−	0.0231199i	$-0.992640\pi$
$827$		−	1.32975i		−	0.0462398i	0.999733	−	0.0231199i	$-0.00735995\pi$
$828$		−	2.90165i		−	0.100839i
$829$	−26.1935			−0.909738			−0.454869	−	0.890558i	$-0.650314\pi$
$829$	−26.1935			−0.909738			−0.454869	+	0.890558i	$0.650314\pi$
$830$	−33.9623	−	3.52065i	−1.17885	−	0.122204i
$831$	−0.787221			−0.0273084
$832$		−	0.461301i		−	0.0159927i
$833$		−	1.43361i		−	0.0496716i
$834$	−27.5839			−0.955153
$835$	1.89472	−	18.2776i	0.0655696	−	0.632523i
$836$	7.44692			0.257557
$837$			0.288914i			0.00998632i
$838$			12.6200i			0.435950i
$839$	−14.9850			−0.517340			−0.258670	−	0.965966i	$-0.583284\pi$
$839$	−14.9850			−0.517340			−0.258670	+	0.965966i	$0.583284\pi$
$840$	−0.366052	+	3.53115i	−0.0126300	+	0.121836i
$841$	51.5971			1.77921
$842$			47.3345i			1.63126i
$843$			12.4309i			0.428143i
$844$	−17.2861			−0.595014
$845$	−10.5937	−	1.09818i	−0.364436	−	0.0377787i
$846$	6.94351			0.238723
$847$		−	1.00000i		−	0.0343604i
$848$			29.6842i			1.01936i
$849$	−2.09042			−0.0717432
$850$	−12.3483	−	2.58794i	−0.423542	−	0.0887656i
$851$	28.3004			0.970125
$852$		−	16.5009i		−	0.565312i
$853$			2.04939i			0.0701697i	0.999384	+	0.0350849i	$0.0111702\pi$
$853$			2.04939i			0.0701697i	−0.999384	+	0.0350849i	$0.988830\pi$
$854$	7.17432			0.245500
$855$	−15.0849	−	1.56376i	−0.515893	−	0.0534794i
$856$	10.9767			0.375175
$857$		−	2.00984i		−	0.0686550i	−0.999411	−	0.0343275i	$-0.989071\pi$
$857$		−	2.00984i		−	0.0686550i	0.999411	−	0.0343275i	$-0.0109289\pi$
$858$			7.41820i			0.253253i
$859$	−40.9339			−1.39665			−0.698323	−	0.715782i	$-0.746070\pi$
$859$	−40.9339			−1.39665			−0.698323	+	0.715782i	$0.746070\pi$
$860$	2.08003	−	20.0652i	0.0709283	−	0.684216i
$861$	1.62215			0.0552827
$862$			14.1868i			0.483205i
$863$			48.3974i			1.64747i	0.566978	+	0.823733i	$0.308112\pi$
$863$			48.3974i			1.64747i	−0.566978	+	0.823733i	$0.691888\pi$
$864$	−5.60837			−0.190801
$865$	−3.39998	+	32.7982i	−0.115603	+	1.11517i
$866$	25.5125			0.866949
$867$			14.9448i			0.507551i
$868$		−	0.317224i		−	0.0107673i
$869$	−0.690394			−0.0234200
$870$	35.1450	+	3.64326i	1.19153	+	0.123518i
$871$	52.1326			1.76645
$872$			19.4974i			0.660265i
$873$			15.4515i			0.522953i
$874$	31.5476			1.06711
$875$	3.40942	−	10.6478i	0.115260	−	0.359962i
$876$	−9.38286			−0.317017
$877$			0.951733i			0.0321377i	0.999871	+	0.0160689i	$0.00511510\pi$
$877$			0.951733i			0.0321377i	−0.999871	+	0.0160689i	$0.994885\pi$
$878$		−	7.54514i		−	0.254636i
$879$	10.4989			0.354119
$880$	11.0994	+	1.15060i	0.374160	+	0.0387868i
$881$	−37.9056			−1.27707			−0.638535	−	0.769593i	$-0.720459\pi$
$881$	−37.9056			−1.27707			−0.638535	+	0.769593i	$0.720459\pi$
$882$			1.76011i			0.0592660i
$883$		−	41.8084i		−	1.40696i	−0.710713	−	0.703482i	$-0.751628\pi$
$883$		−	41.8084i		−	1.40696i	0.710713	−	0.703482i	$-0.248372\pi$
$884$	6.63417			0.223131
$885$	1.48829	−	14.3569i	0.0500282	−	0.482601i
$886$	−8.50929			−0.285875
$887$			23.7956i			0.798979i	0.916738	+	0.399490i	$0.130813\pi$
$887$			23.7956i			0.798979i	−0.916738	+	0.399490i	$0.869187\pi$
$888$		−	17.0019i		−	0.570546i
$889$	11.9392			0.400427
$890$	6.63072	−	63.9638i	0.222262	−	2.14407i
$891$	−1.00000			−0.0335013
$892$			10.9824i			0.367717i
$893$			26.7558i			0.895350i
$894$	20.8066			0.695876
$895$	1.01252	+	0.104962i	0.0338449	+	0.00350849i
$896$	−11.4094			−0.381161
$897$			11.1380i			0.371887i
$898$		−	62.9915i		−	2.10205i
$899$	2.59375			0.0865063
$900$	5.37320	+	1.12611i	0.179107	+	0.0375371i
$901$	8.52748			0.284091
$902$		−	2.85516i		−	0.0950665i
$903$			8.21640i			0.273425i
$904$	15.6669			0.521072
$905$	17.9538	+	1.86116i	0.596806	+	0.0618670i
$906$	−29.5434			−0.981515
$907$		−	43.3339i		−	1.43888i	−0.694556	−	0.719439i	$-0.744399\pi$
$907$		−	43.3339i		−	1.43888i	0.694556	−	0.719439i	$-0.255601\pi$
$908$		−	17.4140i		−	0.577904i
$909$	−6.16833			−0.204591
$910$	−1.71037	+	16.4992i	−0.0566981	+	0.546943i
$911$	3.13409			0.103837			0.0519185	−	0.998651i	$-0.483466\pi$
$911$	3.13409			0.103837			0.0519185	+	0.998651i	$0.483466\pi$
$912$		−	33.8465i		−	1.12077i
$913$		−	8.67547i		−	0.287116i
$914$	27.5568			0.911497
$915$	−0.939791	+	9.06577i	−0.0310685	+	0.299705i
$916$	25.4428			0.840654
$917$			3.51910i			0.116211i
$918$			2.52331i			0.0832815i
$919$	19.9236			0.657219			0.328610	−	0.944466i	$-0.393420\pi$
$919$	19.9236			0.657219			0.328610	+	0.944466i	$0.393420\pi$
$920$	9.33177	+	0.967365i	0.307660	+	0.0318931i
$921$	−26.9278			−0.887302
$922$		−	67.1982i		−	2.21305i
$923$			63.3388i			2.08482i
$924$	1.09799			0.0361211
$925$	−10.9832	+	52.4059i	−0.361125	+	1.72310i
$926$	23.6495			0.777171
$927$			8.41237i			0.276299i
$928$			50.3496i			1.65281i
$929$	36.3569			1.19283			0.596415	−	0.802676i	$-0.296591\pi$
$929$	36.3569			1.19283			0.596415	+	0.802676i	$0.296591\pi$
$930$	1.13102	+	0.117246i	0.0370877	+	0.00384465i
$931$	−6.78233			−0.222282
$932$		−	20.3332i		−	0.666035i
$933$			15.0673i			0.493283i
$934$	66.0416			2.16095
$935$	0.330537	−	3.18856i	0.0108097	−	0.104277i
$936$	6.69131			0.218712
$937$			33.4114i			1.09150i	0.837947	+	0.545752i	$0.183756\pi$
$937$			33.4114i			1.09150i	−0.837947	+	0.545752i	$0.816244\pi$
$938$		−	21.7716i		−	0.710869i
$939$	−23.5904			−0.769844
$940$	0.998681	−	9.63387i	0.0325734	−	0.314222i
$941$	53.7688			1.75281			0.876406	−	0.481572i	$-0.159934\pi$
$941$	53.7688			1.75281			0.876406	+	0.481572i	$0.159934\pi$
$942$			10.9502i			0.356778i
$943$		−	4.28686i		−	0.139599i
$944$	32.2130			1.04844
$945$	−2.22415	−	0.230563i	−0.0723516	−	0.00750023i
$946$	14.4618			0.470192
$947$			22.0800i			0.717504i	0.933433	+	0.358752i	$0.116798\pi$
$947$			22.0800i			0.717504i	−0.933433	+	0.358752i	$0.883202\pi$
$948$		−	0.758044i		−	0.0246201i
$949$	36.0161			1.16913
$950$	−12.2434	+	58.4191i	−0.397229	+	1.89536i
$951$	−24.0122			−0.778649
$952$			2.27605i			0.0737674i
$953$		−	14.4516i		−	0.468134i	−0.972221	−	0.234067i	$-0.924797\pi$
$953$		−	14.4516i		−	0.468134i	0.972221	−	0.234067i	$-0.0752035\pi$
$954$	−10.4696			−0.338966
$955$	34.5913	+	3.58586i	1.11935	+	0.116036i
$956$	−30.9437			−1.00079
$957$			8.97759i			0.290204i
$958$			34.6439i			1.11929i
$959$	8.26959			0.267039
$960$	0.0252357	−	0.243439i	0.000814479	−	0.00785694i
$961$	−30.9165			−0.997307
$962$		−	79.4408i		−	2.56127i
$963$			6.91382i			0.222795i
$964$	7.77493			0.250414
$965$	4.60386	−	44.4115i	0.148203	−	1.42966i
$966$	4.65144			0.149658
$967$		−	42.3008i		−	1.36030i	−0.733072	−	0.680152i	$-0.761914\pi$
$967$		−	42.3008i		−	1.36030i	0.733072	−	0.680152i	$-0.238086\pi$
$968$			1.58764i			0.0510287i
$969$	−9.72320			−0.312354
$970$	60.4886	+	6.27047i	1.94217	+	0.201333i
$971$	−30.0533			−0.964457			−0.482229	−	0.876045i	$-0.660173\pi$
$971$	−30.0533			−0.964457			−0.482229	+	0.876045i	$0.660173\pi$
$972$		−	1.09799i		−	0.0352180i
$973$		−	15.6717i		−	0.502412i
$974$	−43.2798			−1.38677
$975$	−20.6250	−	4.32258i	−0.660529	−	0.138433i
$976$	−20.3412			−0.651105
$977$		−	11.9074i		−	0.380952i	−0.981692	−	0.190476i	$-0.938997\pi$
$977$		−	11.9074i		−	0.380952i	0.981692	−	0.190476i	$-0.0610031\pi$
$978$		−	13.2867i		−	0.424862i
$979$	16.3392			0.522203
$980$	2.44209	+	0.253156i	0.0780096	+	0.00808676i
$981$	−12.2807			−0.392094
$982$			56.4650i			1.80187i
$983$		−	23.1043i		−	0.736913i	−0.929645	−	0.368456i	$-0.879886\pi$
$983$		−	23.1043i		−	0.736913i	0.929645	−	0.368456i	$-0.120114\pi$
$984$	−2.57539			−0.0821005
$985$	3.46916	−	33.4656i	0.110537	−	1.06630i
$986$	22.6532			0.721425
$987$			3.94493i			0.125568i
$988$		−	31.3859i		−	0.998520i
$989$	21.7135			0.690448
$990$	−0.405817	+	3.91475i	−0.0128977	+	0.124419i
$991$	20.8358			0.661871			0.330936	−	0.943653i	$-0.392636\pi$
$991$	20.8358			0.661871			0.330936	+	0.943653i	$0.392636\pi$
$992$			1.62033i			0.0514457i
$993$		−	21.5409i		−	0.683580i
$994$	26.4515			0.838991
$995$	13.9134	+	1.44231i	0.441084	+	0.0457244i
$996$	9.52555			0.301829
$997$			53.0422i			1.67986i	0.542693	+	0.839931i	$0.317405\pi$
$997$			53.0422i			1.67986i	−0.542693	+	0.839931i	$0.682595\pi$
$998$			74.8739i			2.37009i
$999$	10.7089			0.338815

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1155.2.c.e.694.15	yes	20
5.2	odd	4		5775.2.a.cp.1.3		10
5.3	odd	4		5775.2.a.cm.1.8		10
5.4	even	2	inner	1155.2.c.e.694.6	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1155.2.c.e.694.6	✓	20	5.4	even	2	inner
1155.2.c.e.694.15	yes	20	1.1	even	1	trivial
5775.2.a.cm.1.8		10	5.3	odd	4
5775.2.a.cp.1.3		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)

\(f(q)\)	\(=\)	\(q+1.76011i q^{2} +1.00000i q^{3} -1.09799 q^{4} +(2.22415 + 0.230563i) q^{5} -1.76011 q^{6} -1.00000i q^{7} +1.58764i q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q+1.76011i q^{2} +1.00000i q^{3} -1.09799 q^{4} +(2.22415 + 0.230563i) q^{5} -1.76011 q^{6} -1.00000i q^{7} +1.58764i q^{8} -1.00000 q^{9} +(-0.405817 + 3.91475i) q^{10} -1.00000 q^{11} -1.09799i q^{12} +4.21462i q^{13} +1.76011 q^{14} +(-0.230563 + 2.22415i) q^{15} -4.99040 q^{16} +1.43361i q^{17} -1.76011i q^{18} +6.78233 q^{19} +(-2.44209 - 0.253156i) q^{20} +1.00000 q^{21} -1.76011i q^{22} -2.64270i q^{23} -1.58764 q^{24} +(4.89368 + 1.02561i) q^{25} -7.41820 q^{26} -1.00000i q^{27} +1.09799i q^{28} -8.97759 q^{29} +(-3.91475 - 0.405817i) q^{30} -0.288914 q^{31} -5.60837i q^{32} -1.00000i q^{33} -2.52331 q^{34} +(0.230563 - 2.22415i) q^{35} +1.09799 q^{36} +10.7089i q^{37} +11.9377i q^{38} -4.21462 q^{39} +(-0.366052 + 3.53115i) q^{40} +1.62215 q^{41} +1.76011i q^{42} +8.21640i q^{43} +1.09799 q^{44} +(-2.22415 - 0.230563i) q^{45} +4.65144 q^{46} +3.94493i q^{47} -4.99040i q^{48} -1.00000 q^{49} +(-1.80519 + 8.61342i) q^{50} -1.43361 q^{51} -4.62760i q^{52} -5.94827i q^{53} +1.76011 q^{54} +(-2.22415 - 0.230563i) q^{55} +1.58764 q^{56} +6.78233i q^{57} -15.8015i q^{58} -6.45500 q^{59} +(0.253156 - 2.44209i) q^{60} +4.07606 q^{61} -0.508520i q^{62} +1.00000i q^{63} -0.109452 q^{64} +(-0.971738 + 9.37395i) q^{65} +1.76011 q^{66} -12.3695i q^{67} -1.57408i q^{68} +2.64270 q^{69} +(3.91475 + 0.405817i) q^{70} +15.0283 q^{71} -1.58764i q^{72} -8.54550i q^{73} -18.8488 q^{74} +(-1.02561 + 4.89368i) q^{75} -7.44692 q^{76} +1.00000i q^{77} -7.41820i q^{78} +0.690394 q^{79} +(-11.0994 - 1.15060i) q^{80} +1.00000 q^{81} +2.85516i q^{82} +8.67547i q^{83} -1.09799 q^{84} +(-0.330537 + 3.18856i) q^{85} -14.4618 q^{86} -8.97759i q^{87} -1.58764i q^{88} -16.3392 q^{89} +(0.405817 - 3.91475i) q^{90} +4.21462 q^{91} +2.90165i q^{92} -0.288914i q^{93} -6.94351 q^{94} +(15.0849 + 1.56376i) q^{95} +5.60837 q^{96} -15.4515i q^{97} -1.76011i q^{98} +1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 26 q^{4} - 2 q^{5} + 6 q^{6} - 20 q^{9}+O(q^{10}) \) 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

Introduction

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