LMFDB - Embedded newform 1155.2.c.e.694.11

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			694.11
Root			$0.332438i$ of defining polynomial
Character	$\chi$	$=$	1155.694
Dual form			1155.2.c.e.694.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.332438i q^{2} -1.00000i q^{3} +1.88948 q^{4} +(-0.370655 + 2.20513i) q^{5} +0.332438 q^{6} +1.00000i q^{7} +1.29301i q^{8} -1.00000 q^{9} +O(q^{10})$	\(q+0.332438i q^{2} -1.00000i q^{3} +1.88948 q^{4} +(-0.370655 + 2.20513i) q^{5} +0.332438 q^{6} +1.00000i q^{7} +1.29301i q^{8} -1.00000 q^{9} +(-0.733071 - 0.123220i) q^{10} -1.00000 q^{11} -1.88948i q^{12} +5.50702i q^{13} -0.332438 q^{14} +(2.20513 + 0.370655i) q^{15} +3.34912 q^{16} -6.85571i q^{17} -0.332438i q^{18} +3.55629 q^{19} +(-0.700347 + 4.16657i) q^{20} +1.00000 q^{21} -0.332438i q^{22} +8.38198i q^{23} +1.29301 q^{24} +(-4.72523 - 1.63469i) q^{25} -1.83074 q^{26} +1.00000i q^{27} +1.88948i q^{28} -8.24013 q^{29} +(-0.123220 + 0.733071i) q^{30} +0.582000 q^{31} +3.69940i q^{32} +1.00000i q^{33} +2.27910 q^{34} +(-2.20513 - 0.370655i) q^{35} -1.88948 q^{36} +9.80818i q^{37} +1.18225i q^{38} +5.50702 q^{39} +(-2.85127 - 0.479262i) q^{40} +6.19751 q^{41} +0.332438i q^{42} +3.22504i q^{43} -1.88948 q^{44} +(0.370655 - 2.20513i) q^{45} -2.78649 q^{46} +6.73820i q^{47} -3.34912i q^{48} -1.00000 q^{49} +(0.543433 - 1.57085i) q^{50} -6.85571 q^{51} +10.4054i q^{52} -14.0460i q^{53} -0.332438 q^{54} +(0.370655 - 2.20513i) q^{55} -1.29301 q^{56} -3.55629i q^{57} -2.73933i q^{58} -2.05642 q^{59} +(4.16657 + 0.700347i) q^{60} +11.2070 q^{61} +0.193479i q^{62} -1.00000i q^{63} +5.46842 q^{64} +(-12.1437 - 2.04120i) q^{65} -0.332438 q^{66} -1.52881i q^{67} -12.9538i q^{68} +8.38198 q^{69} +(0.123220 - 0.733071i) q^{70} -2.12361 q^{71} -1.29301i q^{72} -1.03179i q^{73} -3.26062 q^{74} +(-1.63469 + 4.72523i) q^{75} +6.71955 q^{76} -1.00000i q^{77} +1.83074i q^{78} +1.77494 q^{79} +(-1.24137 + 7.38526i) q^{80} +1.00000 q^{81} +2.06029i q^{82} -4.43704i q^{83} +1.88948 q^{84} +(15.1177 + 2.54110i) q^{85} -1.07213 q^{86} +8.24013i q^{87} -1.29301i q^{88} -2.23530 q^{89} +(0.733071 + 0.123220i) q^{90} -5.50702 q^{91} +15.8376i q^{92} -0.582000i q^{93} -2.24004 q^{94} +(-1.31816 + 7.84209i) q^{95} +3.69940 q^{96} +11.2496i q^{97} -0.332438i q^{98} +1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$			0.332438i			0.235069i	0.993069	+	0.117535i	$0.0374991\pi$
$2$			0.332438i			0.235069i	−0.993069	+	0.117535i	$0.962501\pi$
$3$		−	1.00000i		−	0.577350i
$3$		−	1.00000i		−	0.577350i
$4$	1.88948			0.944742
$5$	−0.370655	+	2.20513i	−0.165762	+	0.986166i
$5$	−0.370655	+	2.20513i	−0.165762	+	0.986166i
$6$	0.332438			0.135717
$7$			1.00000i			0.377964i
$7$			1.00000i			0.377964i
$8$			1.29301i			0.457149i
$9$	−1.00000			−0.333333
$10$	−0.733071	−	0.123220i	−0.231817	−	0.0389656i
$11$	−1.00000			−0.301511
$11$	−1.00000			−0.301511
$12$		−	1.88948i		−	0.545447i
$13$			5.50702i			1.52737i	0.645587	+	0.763686i	$0.276613\pi$
$13$			5.50702i			1.52737i	−0.645587	+	0.763686i	$0.723387\pi$
$14$	−0.332438			−0.0888479
$15$	2.20513	+	0.370655i	0.569363	+	0.0957027i
$16$	3.34912			0.837281
$17$		−	6.85571i		−	1.66275i	−0.555710	−	0.831376i	$-0.687553\pi$
$17$		−	6.85571i		−	1.66275i	0.555710	−	0.831376i	$-0.312447\pi$
$18$		−	0.332438i		−	0.0783565i
$19$	3.55629			0.815868			0.407934	−	0.913011i	$-0.366249\pi$
$19$	3.55629			0.815868			0.407934	+	0.913011i	$0.366249\pi$
$20$	−0.700347	+	4.16657i	−0.156602	+	0.931673i
$21$	1.00000			0.218218
$22$		−	0.332438i		−	0.0708761i
$23$			8.38198i			1.74776i	0.486138	+	0.873882i	$0.338405\pi$
$23$			8.38198i			1.74776i	−0.486138	+	0.873882i	$0.661595\pi$
$24$	1.29301			0.263935
$25$	−4.72523	−	1.63469i	−0.945046	−	0.326938i
$26$	−1.83074			−0.359039
$27$			1.00000i			0.192450i
$28$			1.88948i			0.357079i
$29$	−8.24013			−1.53015			−0.765077	−	0.643939i	$-0.777299\pi$
$29$	−8.24013			−1.53015			−0.765077	+	0.643939i	$0.777299\pi$
$30$	−0.123220	+	0.733071i	−0.0224968	+	0.133840i
$31$	0.582000			0.104530			0.0522651	−	0.998633i	$-0.483356\pi$
$31$	0.582000			0.104530			0.0522651	+	0.998633i	$0.483356\pi$
$32$			3.69940i			0.653968i
$33$			1.00000i			0.174078i
$34$	2.27910			0.390862
$35$	−2.20513	−	0.370655i	−0.372736	−	0.0626521i
$36$	−1.88948			−0.314914
$37$			9.80818i			1.61246i	0.591605	+	0.806228i	$0.298494\pi$
$37$			9.80818i			1.61246i	−0.591605	+	0.806228i	$0.701506\pi$
$38$			1.18225i			0.191786i
$39$	5.50702			0.881829
$40$	−2.85127	−	0.479262i	−0.450825	−	0.0757780i
$41$	6.19751			0.967888			0.483944	−	0.875099i	$-0.339204\pi$
$41$	6.19751			0.967888			0.483944	+	0.875099i	$0.339204\pi$
$42$			0.332438i			0.0512963i
$43$			3.22504i			0.491815i	0.969293	+	0.245907i	$0.0790859\pi$
$43$			3.22504i			0.491815i	−0.969293	+	0.245907i	$0.920914\pi$
$44$	−1.88948			−0.284851
$45$	0.370655	−	2.20513i	0.0552540	−	0.328722i
$46$	−2.78649			−0.410846
$47$			6.73820i			0.982867i	0.870915	+	0.491434i	$0.163527\pi$
$47$			6.73820i			0.982867i	−0.870915	+	0.491434i	$0.836473\pi$
$48$		−	3.34912i		−	0.483404i
$49$	−1.00000			−0.142857
$50$	0.543433	−	1.57085i	0.0768530	−	0.222151i
$51$	−6.85571			−0.959991
$52$			10.4054i			1.44297i
$53$		−	14.0460i		−	1.92937i	−0.263407	−	0.964685i	$-0.584846\pi$
$53$		−	14.0460i		−	1.92937i	0.263407	−	0.964685i	$-0.415154\pi$
$54$	−0.332438			−0.0452391
$55$	0.370655	−	2.20513i	0.0499791	−	0.297340i
$56$	−1.29301			−0.172786
$57$		−	3.55629i		−	0.471042i
$58$		−	2.73933i		−	0.359692i
$59$	−2.05642			−0.267723			−0.133861	−	0.991000i	$-0.542738\pi$
$59$	−2.05642			−0.267723			−0.133861	+	0.991000i	$0.542738\pi$
$60$	4.16657	+	0.700347i	0.537901	+	0.0904144i
$61$	11.2070			1.43491			0.717454	−	0.696605i	$-0.245307\pi$
$61$	11.2070			1.43491			0.717454	+	0.696605i	$0.245307\pi$
$62$			0.193479i			0.0245719i
$63$		−	1.00000i		−	0.125988i
$64$	5.46842			0.683553
$65$	−12.1437	−	2.04120i	−1.50624	−	0.253180i
$66$	−0.332438			−0.0409203
$67$		−	1.52881i		−	0.186774i	−0.995630	−	0.0933868i	$-0.970231\pi$
$67$		−	1.52881i		−	0.186774i	0.995630	−	0.0933868i	$-0.0297693\pi$
$68$		−	12.9538i		−	1.57087i
$69$	8.38198			1.00907
$70$	0.123220	−	0.733071i	0.0147276	−	0.0876187i
$71$	−2.12361			−0.252026			−0.126013	−	0.992029i	$-0.540218\pi$
$71$	−2.12361			−0.252026			−0.126013	+	0.992029i	$0.540218\pi$
$72$		−	1.29301i		−	0.152383i
$73$		−	1.03179i		−	0.120762i	−0.998175	−	0.0603809i	$-0.980768\pi$
$73$		−	1.03179i		−	0.120762i	0.998175	−	0.0603809i	$-0.0192315\pi$
$74$	−3.26062			−0.379039
$75$	−1.63469	+	4.72523i	−0.188758	+	0.545623i
$76$	6.71955			0.770785
$77$		−	1.00000i		−	0.113961i
$78$			1.83074i			0.207291i
$79$	1.77494			0.199697			0.0998483	−	0.995003i	$-0.468164\pi$
$79$	1.77494			0.199697			0.0998483	+	0.995003i	$0.468164\pi$
$80$	−1.24137	+	7.38526i	−0.138789	+	0.825697i
$81$	1.00000			0.111111
$82$			2.06029i			0.227521i
$83$		−	4.43704i		−	0.487028i	−0.969897	−	0.243514i	$-0.921700\pi$
$83$		−	4.43704i		−	0.487028i	0.969897	−	0.243514i	$-0.0783002\pi$
$84$	1.88948			0.206160
$85$	15.1177	+	2.54110i	1.63975	+	0.275621i
$86$	−1.07213			−0.115611
$87$			8.24013i			0.883434i
$88$		−	1.29301i		−	0.137836i
$89$	−2.23530			−0.236942			−0.118471	−	0.992958i	$-0.537799\pi$
$89$	−2.23530			−0.236942			−0.118471	+	0.992958i	$0.537799\pi$
$90$	0.733071	+	0.123220i	0.0772725	+	0.0129885i
$91$	−5.50702			−0.577293
$92$			15.8376i			1.65119i
$93$		−	0.582000i		−	0.0603506i
$94$	−2.24004			−0.231042
$95$	−1.31816	+	7.84209i	−0.135240	+	0.804581i
$96$	3.69940			0.377569
$97$			11.2496i			1.14223i	0.820871	+	0.571114i	$0.193489\pi$
$97$			11.2496i			1.14223i	−0.820871	+	0.571114i	$0.806511\pi$
$98$		−	0.332438i		−	0.0335813i
$99$	1.00000			0.100504
$100$	−8.92825	−	3.08872i	−0.892825	−	0.308872i
$101$	15.7132			1.56352			0.781762	−	0.623576i	$-0.214321\pi$
$101$	15.7132			1.56352			0.781762	+	0.623576i	$0.214321\pi$
$102$		−	2.27910i		−	0.225664i
$103$		−	9.00401i		−	0.887192i	−0.896227	−	0.443596i	$-0.853703\pi$
$103$		−	9.00401i		−	0.887192i	0.896227	−	0.443596i	$-0.146297\pi$
$104$	−7.12065			−0.698237
$105$	−0.370655	+	2.20513i	−0.0361722	+	0.215199i
$106$	4.66944			0.453536
$107$		−	7.11539i		−	0.687871i	−0.938993	−	0.343935i	$-0.888240\pi$
$107$		−	7.11539i		−	0.687871i	0.938993	−	0.343935i	$-0.111760\pi$
$108$			1.88948i			0.181816i
$109$	1.84137			0.176372			0.0881858	−	0.996104i	$-0.471893\pi$
$109$	1.84137			0.176372			0.0881858	+	0.996104i	$0.471893\pi$
$110$	0.733071	+	0.123220i	0.0698956	+	0.0117486i
$111$	9.80818			0.930952
$112$			3.34912i			0.316462i
$113$			17.2295i			1.62082i	0.585866	+	0.810408i	$0.300754\pi$
$113$			17.2295i			1.62082i	−0.585866	+	0.810408i	$0.699246\pi$
$114$	1.18225			0.110727
$115$	−18.4834	−	3.10682i	−1.72359	−	0.289713i
$116$	−15.5696			−1.44560
$117$		−	5.50702i		−	0.509124i
$118$		−	0.683632i		−	0.0629334i
$119$	6.85571			0.628462
$120$	−0.479262	+	2.85127i	−0.0437504	+	0.260284i
$121$	1.00000			0.0909091
$122$			3.72563i			0.337303i
$123$		−	6.19751i		−	0.558810i
$124$	1.09968			0.0987542
$125$	5.35614	−	9.81386i	0.479067	−	0.877778i
$126$	0.332438			0.0296160
$127$		−	21.8825i		−	1.94176i	−0.239562	−	0.970881i	$-0.577004\pi$
$127$		−	21.8825i		−	1.94176i	0.239562	−	0.970881i	$-0.422996\pi$
$128$			9.21672i			0.814651i
$129$	3.22504			0.283949
$130$	0.678575	−	4.03704i	0.0595149	−	0.354072i
$131$	−2.60035			−0.227193			−0.113597	−	0.993527i	$-0.536237\pi$
$131$	−2.60035			−0.227193			−0.113597	+	0.993527i	$0.536237\pi$
$132$			1.88948i			0.164459i
$133$			3.55629i			0.308369i
$134$	0.508234			0.0439048
$135$	−2.20513	−	0.370655i	−0.189788	−	0.0319009i
$136$	8.86452			0.760126
$137$			16.2047i			1.38446i	0.721678	+	0.692229i	$0.243371\pi$
$137$			16.2047i			1.38446i	−0.721678	+	0.692229i	$0.756629\pi$
$138$			2.78649i			0.237202i
$139$	6.94911			0.589416			0.294708	−	0.955587i	$-0.404778\pi$
$139$	6.94911			0.589416			0.294708	+	0.955587i	$0.404778\pi$
$140$	−4.16657	−	0.700347i	−0.352139	−	0.0591901i
$141$	6.73820			0.567459
$142$		−	0.705968i		−	0.0592435i
$143$		−	5.50702i		−	0.460520i
$144$	−3.34912			−0.279094
$145$	3.05424	−	18.1706i	0.253641	−	1.50898i
$146$	0.343006			0.0283874
$147$			1.00000i			0.0824786i
$148$			18.5324i			1.52336i
$149$	1.33816			0.109626			0.0548130	−	0.998497i	$-0.482544\pi$
$149$	1.33816			0.109626			0.0548130	+	0.998497i	$0.482544\pi$
$150$	−1.57085	−	0.543433i	−0.128259	−	0.0443711i
$151$	7.67483			0.624569			0.312284	−	0.949989i	$-0.398906\pi$
$151$	7.67483			0.624569			0.312284	+	0.949989i	$0.398906\pi$
$152$			4.59833i			0.372974i
$153$			6.85571i			0.554251i
$154$	0.332438			0.0267886
$155$	−0.215721	+	1.28339i	−0.0173271	+	0.103084i
$156$	10.4054			0.833101
$157$		−	14.3690i		−	1.14677i	−0.819287	−	0.573384i	$-0.805630\pi$
$157$		−	14.3690i		−	1.14677i	0.819287	−	0.573384i	$-0.194370\pi$
$158$			0.590059i			0.0469426i
$159$	−14.0460			−1.11392
$160$	−8.15768	−	1.37120i	−0.644921	−	0.108403i
$161$	−8.38198			−0.660593
$162$			0.332438i			0.0261188i
$163$		−	12.5382i		−	0.982070i	−0.871140	−	0.491035i	$-0.836619\pi$
$163$		−	12.5382i		−	0.982070i	0.871140	−	0.491035i	$-0.163381\pi$
$164$	11.7101			0.914405
$165$	−2.20513	−	0.370655i	−0.171669	−	0.0288555i
$166$	1.47504			0.114485
$167$		−	4.04140i		−	0.312733i	−0.987699	−	0.156366i	$-0.950022\pi$
$167$		−	4.04140i		−	0.312733i	0.987699	−	0.156366i	$-0.0499780\pi$
$168$			1.29301i			0.0997582i
$169$	−17.3273			−1.33287
$170$	−0.844760	+	5.02572i	−0.0647901	+	0.385455i
$171$	−3.55629			−0.271956
$172$			6.09367i			0.464638i
$173$		−	15.8667i		−	1.20632i	−0.797620	−	0.603161i	$-0.793908\pi$
$173$		−	15.8667i		−	1.20632i	0.797620	−	0.603161i	$-0.206092\pi$
$174$	−2.73933			−0.207668
$175$	1.63469	−	4.72523i	0.123571	−	0.357194i
$176$	−3.34912			−0.252450
$177$			2.05642i			0.154570i
$178$		−	0.743101i		−	0.0556978i
$179$	0.737568			0.0551285			0.0275642	−	0.999620i	$-0.491225\pi$
$179$	0.737568			0.0551285			0.0275642	+	0.999620i	$0.491225\pi$
$180$	0.700347	−	4.16657i	0.0522008	−	0.310558i
$181$	16.1942			1.20370			0.601852	−	0.798608i	$-0.294430\pi$
$181$	16.1942			1.20370			0.601852	+	0.798608i	$0.294430\pi$
$182$		−	1.83074i		−	0.135704i
$183$		−	11.2070i		−	0.828445i
$184$	−10.8380			−0.798989
$185$	−21.6284	−	3.63545i	−1.59015	−	0.267284i
$186$	0.193479			0.0141866
$187$			6.85571i			0.501339i
$188$			12.7317i			0.928557i
$189$	−1.00000			−0.0727393
$190$	−2.60701	−	0.438205i	−0.189132	−	0.0317908i
$191$	−14.0663			−1.01780			−0.508901	−	0.860825i	$-0.669948\pi$
$191$	−14.0663			−1.01780			−0.508901	+	0.860825i	$0.669948\pi$
$192$		−	5.46842i		−	0.394649i
$193$		−	1.40939i		−	0.101450i	−0.998713	−	0.0507249i	$-0.983847\pi$
$193$		−	1.40939i		−	0.101450i	0.998713	−	0.0507249i	$-0.0161532\pi$
$194$	−3.73981			−0.268503
$195$	−2.04120	+	12.1437i	−0.146174	+	0.869630i
$196$	−1.88948			−0.134963
$197$			2.36583i			0.168558i	0.996442	+	0.0842791i	$0.0268587\pi$
$197$			2.36583i			0.168558i	−0.996442	+	0.0842791i	$0.973141\pi$
$198$			0.332438i			0.0236254i
$199$	−7.68972			−0.545110			−0.272555	−	0.962140i	$-0.587869\pi$
$199$	−7.68972			−0.545110			−0.272555	+	0.962140i	$0.587869\pi$
$200$	2.11367	−	6.10979i	0.149459	−	0.432027i
$201$	−1.52881			−0.107834
$202$			5.22368i			0.367537i
$203$		−	8.24013i		−	0.578344i
$204$	−12.9538			−0.906944
$205$	−2.29714	+	13.6663i	−0.160439	+	0.954498i
$206$	2.99328			0.208552
$207$		−	8.38198i		−	0.582588i
$208$			18.4437i			1.27884i
$209$	−3.55629			−0.245994
$210$	−0.733071	−	0.123220i	−0.0505867	−	0.00850298i
$211$	−24.9194			−1.71552			−0.857762	−	0.514047i	$-0.828146\pi$
$211$	−24.9194			−1.71552			−0.857762	+	0.514047i	$0.828146\pi$
$212$		−	26.5397i		−	1.82276i
$213$			2.12361i			0.145507i
$214$	2.36543			0.161697
$215$	−7.11166	−	1.19538i	−0.485011	−	0.0815242i
$216$	−1.29301			−0.0879784
$217$			0.582000i			0.0395087i
$218$			0.612143i			0.0414596i
$219$	−1.03179			−0.0697218
$220$	0.700347	−	4.16657i	0.0472174	−	0.280910i
$221$	37.7545			2.53964
$222$			3.26062i			0.218838i
$223$		−	12.7387i		−	0.853047i	−0.904477	−	0.426523i	$-0.859738\pi$
$223$		−	12.7387i		−	0.853047i	0.904477	−	0.426523i	$-0.140262\pi$
$224$	−3.69940			−0.247177
$225$	4.72523	+	1.63469i	0.315015	+	0.108979i
$226$	−5.72775			−0.381004
$227$		−	19.9513i		−	1.32421i	−0.749409	−	0.662107i	$-0.769662\pi$
$227$		−	19.9513i		−	1.32421i	0.749409	−	0.662107i	$-0.230338\pi$
$228$		−	6.71955i		−	0.445013i
$229$	3.18850			0.210702			0.105351	−	0.994435i	$-0.466403\pi$
$229$	3.18850			0.210702			0.105351	+	0.994435i	$0.466403\pi$
$230$	1.03283	−	6.14459i	0.0681026	−	0.405162i
$231$	−1.00000			−0.0657952
$232$		−	10.6546i		−	0.699509i
$233$			7.68450i			0.503428i	0.967802	+	0.251714i	$0.0809943\pi$
$233$			7.68450i			0.503428i	−0.967802	+	0.251714i	$0.919006\pi$
$234$	1.83074			0.119680
$235$	−14.8586	−	2.49755i	−0.969270	−	0.162922i
$236$	−3.88557			−0.252929
$237$		−	1.77494i		−	0.115295i
$238$			2.27910i			0.147732i
$239$	−11.5466			−0.746887			−0.373444	−	0.927653i	$-0.621823\pi$
$239$	−11.5466			−0.746887			−0.373444	+	0.927653i	$0.621823\pi$
$240$	7.38526	+	1.24137i	0.476717	+	0.0801300i
$241$	2.94329			0.189594			0.0947969	−	0.995497i	$-0.469780\pi$
$241$	2.94329			0.189594			0.0947969	+	0.995497i	$0.469780\pi$
$242$			0.332438i			0.0213699i
$243$		−	1.00000i		−	0.0641500i
$244$	21.1754			1.35562
$245$	0.370655	−	2.20513i	0.0236803	−	0.140881i
$246$	2.06029			0.131359
$247$			19.5845i			1.24613i
$248$			0.752534i			0.0477859i
$249$	−4.43704			−0.281186
$250$	3.26250	+	1.78058i	0.206339	+	0.112614i
$251$	19.3563			1.22176			0.610879	−	0.791724i	$-0.290816\pi$
$251$	19.3563			1.22176			0.610879	+	0.791724i	$0.290816\pi$
$252$		−	1.88948i		−	0.119026i
$253$		−	8.38198i		−	0.526971i
$254$	7.27460			0.456449
$255$	2.54110	−	15.1177i	0.159130	−	0.946710i
$256$	7.87285			0.492053
$257$		−	11.3301i		−	0.706755i	−0.935481	−	0.353378i	$-0.885033\pi$
$257$		−	11.3301i		−	0.706755i	0.935481	−	0.353378i	$-0.114967\pi$
$258$			1.07213i			0.0667478i
$259$	−9.80818			−0.609451
$260$	−22.9454	−	3.85683i	−1.42301	−	0.239190i
$261$	8.24013			0.510051
$262$		−	0.864455i		−	0.0534062i
$263$		−	3.36193i		−	0.207306i	−0.994614	−	0.103653i	$-0.966947\pi$
$263$		−	3.36193i		−	0.207306i	0.994614	−	0.103653i	$-0.0330531\pi$
$264$	−1.29301			−0.0795795
$265$	30.9734	+	5.20623i	1.90268	+	0.319816i
$266$	−1.18225			−0.0724882
$267$			2.23530i			0.136798i
$268$		−	2.88866i		−	0.176453i
$269$	6.35047			0.387195			0.193598	−	0.981081i	$-0.437984\pi$
$269$	6.35047			0.387195			0.193598	+	0.981081i	$0.437984\pi$
$270$	0.123220	−	0.733071i	0.00749893	−	0.0446133i
$271$	14.2641			0.866485			0.433242	−	0.901277i	$-0.357369\pi$
$271$	14.2641			0.866485			0.433242	+	0.901277i	$0.357369\pi$
$272$		−	22.9606i		−	1.39219i
$273$			5.50702i			0.333300i
$274$	−5.38705			−0.325443
$275$	4.72523	+	1.63469i	0.284942	+	0.0985754i
$276$	15.8376			0.953313
$277$		−	24.0288i		−	1.44375i	−0.692024	−	0.721875i	$-0.743281\pi$
$277$		−	24.0288i		−	1.44375i	0.692024	−	0.721875i	$-0.256719\pi$
$278$			2.31015i			0.138554i
$279$	−0.582000			−0.0348434
$280$	0.479262	−	2.85127i	0.0286414	−	0.170396i
$281$	11.6299			0.693779			0.346890	−	0.937906i	$-0.387238\pi$
$281$	11.6299			0.693779			0.346890	+	0.937906i	$0.387238\pi$
$282$			2.24004i			0.133392i
$283$		−	7.02079i		−	0.417343i	−0.977986	−	0.208671i	$-0.933086\pi$
$283$		−	7.02079i		−	0.417343i	0.977986	−	0.208671i	$-0.0669139\pi$
$284$	−4.01252			−0.238099
$285$	7.84209	+	1.31816i	0.464525	+	0.0780808i
$286$	1.83074			0.108254
$287$			6.19751i			0.365827i
$288$		−	3.69940i		−	0.217989i
$289$	−30.0007			−1.76475
$290$	6.04060	+	1.01535i	0.354716	+	0.0596233i
$291$	11.2496			0.659466
$292$		−	1.94955i		−	0.114089i
$293$		−	12.3870i		−	0.723657i	−0.932245	−	0.361829i	$-0.882153\pi$
$293$		−	12.3870i		−	0.723657i	0.932245	−	0.361829i	$-0.117847\pi$
$294$	−0.332438			−0.0193882
$295$	0.762221	−	4.53467i	0.0443782	−	0.264019i
$296$	−12.6821			−0.737133
$297$		−	1.00000i		−	0.0580259i
$298$			0.444854i			0.0257697i
$299$	−46.1597			−2.66949
$300$	−3.08872	+	8.92825i	−0.178327	+	0.515473i
$301$	−3.22504			−0.185888
$302$			2.55141i			0.146817i
$303$		−	15.7132i		−	0.902701i
$304$	11.9104			0.683111
$305$	−4.15393	+	24.7129i	−0.237853	+	1.41506i
$306$	−2.27910			−0.130287
$307$		−	8.76620i		−	0.500314i	−0.968205	−	0.250157i	$-0.919518\pi$
$307$		−	8.76620i		−	0.500314i	0.968205	−	0.250157i	$-0.0804822\pi$
$308$		−	1.88948i		−	0.107663i
$309$	−9.00401			−0.512220
$310$	−0.426647	−	0.0717140i	−0.0242319	−	0.00407308i
$311$	−13.6554			−0.774328			−0.387164	−	0.922011i	$-0.626545\pi$
$311$	−13.6554			−0.774328			−0.387164	+	0.922011i	$0.626545\pi$
$312$			7.12065i			0.403128i
$313$		−	20.7806i		−	1.17459i	−0.809373	−	0.587295i	$-0.800193\pi$
$313$		−	20.7806i		−	1.17459i	0.809373	−	0.587295i	$-0.199807\pi$
$314$	4.77679			0.269570
$315$	2.20513	+	0.370655i	0.124245	+	0.0208840i
$316$	3.35373			0.188662
$317$			10.4361i			0.586148i	0.956090	+	0.293074i	$0.0946783\pi$
$317$			10.4361i			0.586148i	−0.956090	+	0.293074i	$0.905322\pi$
$318$		−	4.66944i		−	0.261849i
$319$	8.24013			0.461359
$320$	−2.02690	+	12.0586i	−0.113307	+	0.674096i
$321$	−7.11539			−0.397142
$322$		−	2.78649i		−	0.155285i
$323$		−	24.3809i		−	1.35659i
$324$	1.88948			0.104971
$325$	9.00226	−	26.0219i	0.499356	−	1.44344i
$326$	4.16819			0.230854
$327$		−	1.84137i		−	0.101828i
$328$			8.01346i			0.442469i
$329$	−6.73820			−0.371489
$330$	0.123220	−	0.733071i	0.00678303	−	0.0403542i
$331$	−6.63873			−0.364897			−0.182449	−	0.983215i	$-0.558402\pi$
$331$	−6.63873			−0.364897			−0.182449	+	0.983215i	$0.558402\pi$
$332$		−	8.38371i		−	0.460116i
$333$		−	9.80818i		−	0.537485i
$334$	1.34351			0.0735139
$335$	3.37123	+	0.566660i	0.184190	+	0.0309600i
$336$	3.34912			0.182710
$337$		−	16.2216i		−	0.883644i	−0.897103	−	0.441822i	$-0.854332\pi$
$337$		−	16.2216i		−	0.883644i	0.897103	−	0.441822i	$-0.145668\pi$
$338$		−	5.76025i		−	0.313316i
$339$	17.2295			0.935778
$340$	28.5648	+	4.80137i	1.54914	+	0.260391i
$341$	−0.582000			−0.0315171
$342$		−	1.18225i		−	0.0639285i
$343$		−	1.00000i		−	0.0539949i
$344$	−4.17003			−0.224833
$345$	−3.10682	+	18.4834i	−0.167266	+	0.995112i
$346$	5.27469			0.283569
$347$			26.5268i			1.42403i	0.702162	+	0.712017i	$0.252218\pi$
$347$			26.5268i			1.42403i	−0.702162	+	0.712017i	$0.747782\pi$
$348$			15.5696i			0.834618i
$349$	−29.4038			−1.57395			−0.786975	−	0.616985i	$-0.788354\pi$
$349$	−29.4038			−1.57395			−0.786975	+	0.616985i	$0.788354\pi$
$350$	1.57085	+	0.543433i	0.0839653	+	0.0290477i
$351$	−5.50702			−0.293943
$352$		−	3.69940i		−	0.197179i
$353$			2.61496i			0.139180i	0.997576	+	0.0695901i	$0.0221691\pi$
$353$			2.61496i			0.139180i	−0.997576	+	0.0695901i	$0.977831\pi$
$354$	−0.683632			−0.0363346
$355$	0.787125	−	4.68283i	0.0417763	−	0.248539i
$356$	−4.22357			−0.223849
$357$		−	6.85571i		−	0.362842i
$358$			0.245196i			0.0129590i
$359$	1.18009			0.0622826			0.0311413	−	0.999515i	$-0.490086\pi$
$359$	1.18009			0.0622826			0.0311413	+	0.999515i	$0.490086\pi$
$360$	2.85127	+	0.479262i	0.150275	+	0.0252593i
$361$	−6.35282			−0.334359
$362$			5.38356i			0.282954i
$363$		−	1.00000i		−	0.0524864i
$364$	−10.4054			−0.545393
$365$	2.27523	+	0.382438i	0.119091	+	0.0200177i
$366$	3.72563			0.194742
$367$			9.34246i			0.487673i	0.969816	+	0.243836i	$0.0784059\pi$
$367$			9.34246i			0.487673i	−0.969816	+	0.243836i	$0.921594\pi$
$368$			28.0723i			1.46337i
$369$	−6.19751			−0.322629
$370$	1.20856	−	7.19009i	0.0628302	−	0.373795i
$371$	14.0460			0.729233
$372$		−	1.09968i		−	0.0570158i
$373$			14.1464i			0.732473i	0.930522	+	0.366236i	$0.119354\pi$
$373$			14.1464i			0.732473i	−0.930522	+	0.366236i	$0.880646\pi$
$374$	−2.27910			−0.117849
$375$	−9.81386	−	5.35614i	−0.506785	−	0.276590i
$376$	−8.71258			−0.449317
$377$		−	45.3786i		−	2.33711i
$378$		−	0.332438i		−	0.0170988i
$379$	6.99655			0.359389			0.179694	−	0.983723i	$-0.442489\pi$
$379$	6.99655			0.359389			0.179694	+	0.983723i	$0.442489\pi$
$380$	−2.49064	+	14.8175i	−0.127767	+	0.760122i
$381$	−21.8825			−1.12108
$382$		−	4.67617i		−	0.239254i
$383$		−	0.0280405i		−	0.00143280i	−1.00000		0.000716402i	$-0.999772\pi$
$383$		−	0.0280405i		−	0.00143280i	1.00000		0.000716402i	$-0.000228038\pi$
$384$	9.21672			0.470339
$385$	2.20513	+	0.370655i	0.112384	+	0.0188903i
$386$	0.468534			0.0238478
$387$		−	3.22504i		−	0.163938i
$388$			21.2560i			1.07911i
$389$	29.0572			1.47326			0.736630	−	0.676296i	$-0.236416\pi$
$389$	29.0572			1.47326			0.736630	+	0.676296i	$0.236416\pi$
$390$	−4.03704	−	0.678575i	−0.204423	−	0.0343610i
$391$	57.4644			2.90610
$392$		−	1.29301i		−	0.0653071i
$393$			2.60035i			0.131170i
$394$	−0.786492			−0.0396229
$395$	−0.657891	+	3.91398i	−0.0331021	+	0.196934i
$396$	1.88948			0.0949502
$397$			34.6718i			1.74013i	0.492941	+	0.870063i	$0.335922\pi$
$397$			34.6718i			1.74013i	−0.492941	+	0.870063i	$0.664078\pi$
$398$		−	2.55636i		−	0.128139i
$399$	3.55629			0.178037
$400$	−15.8254	−	5.47477i	−0.791269	−	0.273738i
$401$	35.3446			1.76502			0.882512	−	0.470291i	$-0.155851\pi$
$401$	35.3446			1.76502			0.882512	+	0.470291i	$0.155851\pi$
$402$		−	0.508234i		−	0.0253484i
$403$			3.20509i			0.159657i
$404$	29.6899			1.47713
$405$	−0.370655	+	2.20513i	−0.0184180	+	0.109574i
$406$	2.73933			0.135951
$407$		−	9.80818i		−	0.486174i
$408$		−	8.86452i		−	0.438859i
$409$	13.5552			0.670261			0.335131	−	0.942172i	$-0.391220\pi$
$409$	13.5552			0.670261			0.335131	+	0.942172i	$0.391220\pi$
$410$	−4.54321	−	0.763656i	−0.224373	−	0.0377143i
$411$	16.2047			0.799317
$412$		−	17.0129i		−	0.838168i
$413$		−	2.05642i		−	0.101190i
$414$	2.78649			0.136949
$415$	9.78426	+	1.64461i	0.480290	+	0.0807307i
$416$	−20.3727			−0.998853
$417$		−	6.94911i		−	0.340299i
$418$		−	1.18225i		−	0.0578255i
$419$	−17.6316			−0.861361			−0.430680	−	0.902505i	$-0.641726\pi$
$419$	−17.6316			−0.861361			−0.430680	+	0.902505i	$0.641726\pi$
$420$	−0.700347	+	4.16657i	−0.0341734	+	0.203308i
$421$	10.1093			0.492697			0.246349	−	0.969181i	$-0.420769\pi$
$421$	10.1093			0.492697			0.246349	+	0.969181i	$0.420769\pi$
$422$		−	8.28417i		−	0.403267i
$423$		−	6.73820i		−	0.327622i
$424$	18.1617			0.882010
$425$	−11.2069	+	32.3948i	−0.543616	+	1.57138i
$426$	−0.705968			−0.0342042
$427$			11.2070i			0.542345i
$428$		−	13.4444i		−	0.649861i
$429$	−5.50702			−0.265881
$430$	0.397390	−	2.36419i	0.0191638	−	0.114011i
$431$	27.4527			1.32235			0.661175	−	0.750232i	$-0.270058\pi$
$431$	27.4527			1.32235			0.661175	+	0.750232i	$0.270058\pi$
$432$			3.34912i			0.161135i
$433$			35.3493i			1.69878i	0.527767	+	0.849389i	$0.323029\pi$
$433$			35.3493i			1.69878i	−0.527767	+	0.849389i	$0.676971\pi$
$434$	−0.193479			−0.00928729
$435$	−18.1706	−	3.05424i	−0.871213	−	0.146440i
$436$	3.47925			0.166626
$437$			29.8087i			1.42595i
$438$		−	0.343006i		−	0.0163895i
$439$	−17.0486			−0.813687			−0.406844	−	0.913498i	$-0.633371\pi$
$439$	−17.0486			−0.813687			−0.406844	+	0.913498i	$0.633371\pi$
$440$	2.85127	+	0.479262i	0.135929	+	0.0228479i
$441$	1.00000			0.0476190
$442$			12.5510i			0.596992i
$443$		−	29.6424i		−	1.40835i	−0.710026	−	0.704176i	$-0.751317\pi$
$443$		−	29.6424i		−	1.40835i	0.710026	−	0.704176i	$-0.248683\pi$
$444$	18.5324			0.879510
$445$	0.828527	−	4.92915i	0.0392759	−	0.233664i
$446$	4.23483			0.200525
$447$		−	1.33816i		−	0.0632926i
$448$			5.46842i			0.258359i
$449$	−5.74336			−0.271046			−0.135523	−	0.990774i	$-0.543271\pi$
$449$	−5.74336			−0.271046			−0.135523	+	0.990774i	$0.543271\pi$
$450$	−0.543433	+	1.57085i	−0.0256177	+	0.0740504i
$451$	−6.19751			−0.291829
$452$			32.5549i			1.53125i
$453$		−	7.67483i		−	0.360595i
$454$	6.63258			0.311282
$455$	2.04120	−	12.1437i	0.0956932	−	0.569306i
$456$	4.59833			0.215336
$457$		−	36.8697i		−	1.72469i	−0.506320	−	0.862346i	$-0.668995\pi$
$457$		−	36.8697i		−	1.72469i	0.506320	−	0.862346i	$-0.331005\pi$
$458$			1.05998i			0.0495296i
$459$	6.85571			0.319997
$460$	−34.9241	−	5.87030i	−1.62834	−	0.273704i
$461$	19.6725			0.916238			0.458119	−	0.888891i	$-0.348523\pi$
$461$	19.6725			0.916238			0.458119	+	0.888891i	$0.348523\pi$
$462$		−	0.332438i		−	0.0154664i
$463$			35.9987i			1.67300i	0.547967	+	0.836500i	$0.315402\pi$
$463$			35.9987i			1.67300i	−0.547967	+	0.836500i	$0.684598\pi$
$464$	−27.5972			−1.28117
$465$	1.28339	+	0.215721i	0.0595157	+	0.0100038i
$466$	−2.55462			−0.118341
$467$			11.9968i			0.555144i	0.960705	+	0.277572i	$0.0895297\pi$
$467$			11.9968i			0.555144i	−0.960705	+	0.277572i	$0.910470\pi$
$468$		−	10.4054i		−	0.480991i
$469$	1.52881			0.0705938
$470$	0.830281	−	4.93958i	0.0382980	−	0.227846i
$471$	−14.3690			−0.662086
$472$		−	2.65898i		−	0.122389i
$473$		−	3.22504i		−	0.148288i
$474$	0.590059			0.0271023
$475$	−16.8043	−	5.81342i	−0.771033	−	0.266738i
$476$	12.9538			0.593734
$477$			14.0460i			0.643123i
$478$		−	3.83853i		−	0.175570i
$479$	7.45562			0.340656			0.170328	−	0.985387i	$-0.445517\pi$
$479$	7.45562			0.340656			0.170328	+	0.985387i	$0.445517\pi$
$480$	−1.37120	+	8.15768i	−0.0625866	+	0.372345i
$481$	−54.0139			−2.46282
$482$			0.978462i			0.0445677i
$483$			8.38198i			0.381393i
$484$	1.88948			0.0858857
$485$	−24.8070	−	4.16974i	−1.12643	−	0.189338i
$486$	0.332438			0.0150797
$487$			25.2921i			1.14609i	0.819523	+	0.573046i	$0.194239\pi$
$487$			25.2921i			1.14609i	−0.819523	+	0.573046i	$0.805761\pi$
$488$			14.4908i			0.655968i
$489$	−12.5382			−0.566998
$490$	0.733071	+	0.123220i	0.0331168	+	0.00556651i
$491$	−22.2420			−1.00377			−0.501883	−	0.864936i	$-0.667359\pi$
$491$	−22.2420			−1.00377			−0.501883	+	0.864936i	$0.667359\pi$
$492$		−	11.7101i		−	0.527932i
$493$			56.4919i			2.54427i
$494$	−6.51065			−0.292928
$495$	−0.370655	+	2.20513i	−0.0166597	+	0.0991134i
$496$	1.94919			0.0875212
$497$		−	2.12361i		−	0.0952567i
$498$		−	1.47504i		−	0.0660981i
$499$	11.9546			0.535163			0.267582	−	0.963535i	$-0.413776\pi$
$499$	11.9546			0.535163			0.267582	+	0.963535i	$0.413776\pi$
$500$	10.1203	−	18.5431i	0.452595	−	0.829274i
$501$	−4.04140			−0.180556
$502$			6.43477i			0.287198i
$503$		−	1.86300i		−	0.0830672i	−0.999137	−	0.0415336i	$-0.986776\pi$
$503$		−	1.86300i		−	0.0830672i	0.999137	−	0.0415336i	$-0.0132244\pi$
$504$	1.29301			0.0575954
$505$	−5.82419	+	34.6498i	−0.259173	+	1.54189i
$506$	2.78649			0.123875
$507$			17.3273i			0.769531i
$508$		−	41.3467i		−	1.83447i
$509$	−3.50365			−0.155297			−0.0776483	−	0.996981i	$-0.524741\pi$
$509$	−3.50365			−0.155297			−0.0776483	+	0.996981i	$0.524741\pi$
$510$	5.02572	+	0.844760i	0.222543	+	0.0374066i
$511$	1.03179			0.0456436
$512$			21.0507i			0.930317i
$513$			3.55629i			0.157014i
$514$	3.76658			0.166137
$515$	19.8551	+	3.33738i	0.874918	+	0.147063i
$516$	6.09367			0.268259
$517$		−	6.73820i		−	0.296346i
$518$		−	3.26062i		−	0.143263i
$519$	−15.8667			−0.696470
$520$	2.63931	−	15.7020i	0.115741	−	0.688578i
$521$	−30.0815			−1.31789			−0.658947	−	0.752190i	$-0.728998\pi$
$521$	−30.0815			−1.31789			−0.658947	+	0.752190i	$0.728998\pi$
$522$			2.73933i			0.119897i
$523$			15.9803i			0.698771i	0.936979	+	0.349386i	$0.113610\pi$
$523$			15.9803i			0.698771i	−0.936979	+	0.349386i	$0.886390\pi$
$524$	−4.91331			−0.214639
$525$	−4.72523	−	1.63469i	−0.206226	−	0.0713436i
$526$	1.11763			0.0487312
$527$		−	3.99002i		−	0.173808i
$528$			3.34912i			0.145752i
$529$	−47.2576			−2.05468
$530$	−1.73075	+	10.2967i	−0.0751790	+	0.447261i
$531$	2.05642			0.0892409
$532$			6.71955i			0.291329i
$533$			34.1298i			1.47833i
$534$	−0.743101			−0.0321571
$535$	15.6904	+	2.63735i	0.678355	+	0.114023i
$536$	1.97677			0.0853834
$537$		−	0.737568i		−	0.0318284i
$538$			2.11114i			0.0910177i
$539$	1.00000			0.0430730
$540$	−4.16657	−	0.700347i	−0.179300	−	0.0301381i
$541$	11.8502			0.509479			0.254740	−	0.967010i	$-0.418010\pi$
$541$	11.8502			0.509479			0.254740	+	0.967010i	$0.418010\pi$
$542$			4.74195i			0.203684i
$543$		−	16.1942i		−	0.694958i
$544$	25.3620			1.08739
$545$	−0.682514	+	4.06047i	−0.0292357	+	0.173932i
$546$	−1.83074			−0.0783486
$547$		−	6.76118i		−	0.289087i	−0.989498	−	0.144544i	$-0.953829\pi$
$547$		−	6.76118i		−	0.289087i	0.989498	−	0.144544i	$-0.0461714\pi$
$548$			30.6185i			1.30796i
$549$	−11.2070			−0.478303
$550$	−0.543433	+	1.57085i	−0.0231721	+	0.0669812i
$551$	−29.3043			−1.24840
$552$			10.8380i			0.461297i
$553$			1.77494i			0.0754782i
$554$	7.98809			0.339381
$555$	−3.63545	+	21.6284i	−0.154316	+	0.918073i
$556$	13.1302			0.556846
$557$			3.53109i			0.149617i	0.997198	+	0.0748086i	$0.0238346\pi$
$557$			3.53109i			0.149617i	−0.997198	+	0.0748086i	$0.976165\pi$
$558$		−	0.193479i		−	0.00819062i
$559$	−17.7604			−0.751184
$560$	−7.38526	−	1.24137i	−0.312084	−	0.0524574i
$561$	6.85571			0.289448
$562$			3.86621i			0.163086i
$563$		−	41.0193i		−	1.72876i	−0.502842	−	0.864379i	$-0.667712\pi$
$563$		−	41.0193i		−	1.72876i	0.502842	−	0.864379i	$-0.332288\pi$
$564$	12.7317			0.536102
$565$	−37.9934	−	6.38620i	−1.59839	−	0.268670i
$566$	2.33398			0.0981045
$567$			1.00000i			0.0419961i
$568$		−	2.74585i		−	0.115213i
$569$	−27.9208			−1.17050			−0.585250	−	0.810853i	$-0.699004\pi$
$569$	−27.9208			−1.17050			−0.585250	+	0.810853i	$0.699004\pi$
$570$	−0.438205	+	2.60701i	−0.0183544	+	0.109196i
$571$	25.8993			1.08385			0.541927	−	0.840426i	$-0.317695\pi$
$571$	25.8993			1.08385			0.541927	+	0.840426i	$0.317695\pi$
$572$		−	10.4054i		−	0.435073i
$573$			14.0663i			0.587628i
$574$	−2.06029			−0.0859948
$575$	13.7019	−	39.6068i	0.571410	−	1.65172i
$576$	−5.46842			−0.227851
$577$		−	15.3525i		−	0.639132i	−0.947564	−	0.319566i	$-0.896463\pi$
$577$		−	15.3525i		−	0.639132i	0.947564	−	0.319566i	$-0.103537\pi$
$578$		−	9.97338i		−	0.414838i
$579$	−1.40939			−0.0585721
$580$	5.77095	−	34.3330i	0.239626	−	1.42560i
$581$	4.43704			0.184079
$582$			3.73981i			0.155020i
$583$			14.0460i			0.581727i
$584$	1.33412			0.0552061
$585$	12.1437	+	2.04120i	0.502081	+	0.0843934i
$586$	4.11792			0.170110
$587$		−	13.4591i		−	0.555518i	−0.960651	−	0.277759i	$-0.910408\pi$
$587$		−	13.4591i		−	0.555518i	0.960651	−	0.277759i	$-0.0895916\pi$
$588$			1.88948i			0.0779210i
$589$	2.06976			0.0852829
$590$	1.50750	+	0.253392i	0.0620628	+	0.0104320i
$591$	2.36583			0.0973172
$592$			32.8488i			1.35008i
$593$			15.3775i			0.631479i	0.948846	+	0.315740i	$0.102253\pi$
$593$			15.3775i			0.631479i	−0.948846	+	0.315740i	$0.897747\pi$
$594$	0.332438			0.0136401
$595$	−2.54110	+	15.1177i	−0.104175	+	0.619767i
$596$	2.52843			0.103568
$597$			7.68972i			0.314719i
$598$		−	15.3453i		−	0.627515i
$599$	0.728071			0.0297482			0.0148741	−	0.999889i	$-0.495265\pi$
$599$	0.728071			0.0297482			0.0148741	+	0.999889i	$0.495265\pi$
$600$	−6.10979	−	2.11367i	−0.249431	−	0.0862904i
$601$	11.3171			0.461636			0.230818	−	0.972997i	$-0.425860\pi$
$601$	11.3171			0.461636			0.230818	+	0.972997i	$0.425860\pi$
$602$		−	1.07213i		−	0.0436967i
$603$			1.52881i			0.0622579i
$604$	14.5015			0.590056
$605$	−0.370655	+	2.20513i	−0.0150693	+	0.0896514i
$606$	5.22368			0.212197
$607$		−	25.4779i		−	1.03411i	−0.855951	−	0.517057i	$-0.827027\pi$
$607$		−	25.4779i		−	1.03411i	0.855951	−	0.517057i	$-0.172973\pi$
$608$			13.1561i			0.533552i
$609$	−8.24013			−0.333907
$610$	−8.21552	−	1.38093i	−0.332637	−	0.0559120i
$611$	−37.1074			−1.50120
$612$			12.9538i			0.523624i
$613$			2.51148i			0.101438i	0.998713	+	0.0507189i	$0.0161513\pi$
$613$			2.51148i			0.101438i	−0.998713	+	0.0507189i	$0.983849\pi$
$614$	2.91422			0.117608
$615$	13.6663	+	2.29714i	0.551080	+	0.0926295i
$616$	1.29301			0.0520970
$617$			16.4368i			0.661722i	0.943680	+	0.330861i	$0.107339\pi$
$617$			16.4368i			0.661722i	−0.943680	+	0.330861i	$0.892661\pi$
$618$		−	2.99328i		−	0.120407i
$619$	−46.1846			−1.85632			−0.928158	−	0.372187i	$-0.878608\pi$
$619$	−46.1846			−1.85632			−0.928158	+	0.372187i	$0.878608\pi$
$620$	−0.407602	+	2.42494i	−0.0163697	+	0.0973880i
$621$	−8.38198			−0.336357
$622$		−	4.53958i		−	0.182021i
$623$		−	2.23530i		−	0.0895556i
$624$	18.4437			0.738338
$625$	19.6556	+	15.4486i	0.786224	+	0.617942i
$626$	6.90827			0.276110
$627$			3.55629i			0.142024i
$628$		−	27.1499i		−	1.08340i
$629$	67.2420			2.68112
$630$	−0.123220	+	0.733071i	−0.00490920	+	0.0292062i
$631$	−28.4586			−1.13292			−0.566459	−	0.824090i	$-0.691687\pi$
$631$	−28.4586			−1.13292			−0.566459	+	0.824090i	$0.691687\pi$
$632$			2.29502i			0.0912912i
$633$			24.9194i			0.990458i
$634$	−3.46935			−0.137785
$635$	48.2539	+	8.11088i	1.91490	+	0.321870i
$636$	−26.5397			−1.05237
$637$		−	5.50702i		−	0.218196i
$638$			2.73933i			0.108451i
$639$	2.12361			0.0840085
$640$	−20.3241	−	3.41622i	−0.803381	−	0.135038i
$641$	37.0419			1.46307			0.731533	−	0.681806i	$-0.238805\pi$
$641$	37.0419			1.46307			0.731533	+	0.681806i	$0.238805\pi$
$642$		−	2.36543i		−	0.0933560i
$643$			36.6680i			1.44604i	0.690825	+	0.723022i	$0.257248\pi$
$643$			36.6680i			1.44604i	−0.690825	+	0.723022i	$0.742752\pi$
$644$	−15.8376			−0.624090
$645$	−1.19538	+	7.11166i	−0.0470680	+	0.280021i
$646$	8.10513			0.318892
$647$			12.8196i			0.503992i	0.967728	+	0.251996i	$0.0810869\pi$
$647$			12.8196i			0.503992i	−0.967728	+	0.251996i	$0.918913\pi$
$648$			1.29301i			0.0507944i
$649$	2.05642			0.0807214
$650$	8.65069	+	2.99270i	0.339308	+	0.117383i
$651$	0.582000			0.0228104
$652$		−	23.6908i		−	0.927803i
$653$			14.5397i			0.568981i	0.958679	+	0.284490i	$0.0918243\pi$
$653$			14.5397i			0.568981i	−0.958679	+	0.284490i	$0.908176\pi$
$654$	0.612143			0.0239367
$655$	0.963832	−	5.73411i	0.0376600	−	0.224050i
$656$	20.7562			0.810394
$657$			1.03179i			0.0402539i
$658$		−	2.24004i		−	0.0873257i
$659$	15.8977			0.619285			0.309642	−	0.950853i	$-0.399791\pi$
$659$	15.8977			0.619285			0.309642	+	0.950853i	$0.399791\pi$
$660$	−4.16657	−	0.700347i	−0.162183	−	0.0272610i
$661$	−3.04949			−0.118611			−0.0593057	−	0.998240i	$-0.518889\pi$
$661$	−3.04949			−0.118611			−0.0593057	+	0.998240i	$0.518889\pi$
$662$		−	2.20697i		−	0.0857762i
$663$		−	37.7545i		−	1.46626i
$664$	5.73715			0.222644
$665$	−7.84209	−	1.31816i	−0.304103	−	0.0511159i
$666$	3.26062			0.126346
$667$		−	69.0686i		−	2.67435i
$668$		−	7.63616i		−	0.295452i
$669$	−12.7387			−0.492507
$670$	−0.188380	+	1.12072i	−0.00727774	+	0.0432974i
$671$	−11.2070			−0.432641
$672$			3.69940i			0.142708i
$673$			21.2732i			0.820023i	0.912080	+	0.410012i	$0.134475\pi$
$673$			21.2732i			0.820023i	−0.912080	+	0.410012i	$0.865525\pi$
$674$	5.39266			0.207718
$675$	1.63469	−	4.72523i	0.0629192	−	0.181874i
$676$	−32.7396			−1.25922
$677$			8.51680i			0.327327i	0.986516	+	0.163664i	$0.0523312\pi$
$677$			8.51680i			0.327327i	−0.986516	+	0.163664i	$0.947669\pi$
$678$			5.72775i			0.219973i
$679$	−11.2496			−0.431722
$680$	−3.28568	+	19.5475i	−0.126000	+	0.749611i
$681$	−19.9513			−0.764536
$682$		−	0.193479i		−	0.00740870i
$683$		−	17.2169i		−	0.658785i	−0.944193	−	0.329393i	$-0.893156\pi$
$683$		−	17.2169i		−	0.658785i	0.944193	−	0.329393i	$-0.106844\pi$
$684$	−6.71955			−0.256928
$685$	−35.7334	−	6.00634i	−1.36530	−	0.229490i
$686$	0.332438			0.0126926
$687$		−	3.18850i		−	0.121649i
$688$			10.8011i			0.411787i
$689$	77.3517			2.94687
$690$	−6.14459	−	1.03283i	−0.233920	−	0.0393191i
$691$	41.7563			1.58848			0.794242	−	0.607602i	$-0.207868\pi$
$691$	41.7563			1.58848			0.794242	+	0.607602i	$0.207868\pi$
$692$		−	29.9799i		−	1.13966i
$693$			1.00000i			0.0379869i
$694$	−8.81853			−0.334747
$695$	−2.57572	+	15.3237i	−0.0977028	+	0.581262i
$696$	−10.6546			−0.403861
$697$		−	42.4883i		−	1.60936i
$698$		−	9.77495i		−	0.369987i
$699$	7.68450			0.290655
$700$	3.08872	−	8.92825i	0.116743	−	0.337456i
$701$	−8.05791			−0.304343			−0.152172	−	0.988354i	$-0.548627\pi$
$701$	−8.05791			−0.304343			−0.152172	+	0.988354i	$0.548627\pi$
$702$		−	1.83074i		−	0.0690970i
$703$			34.8807i			1.31555i
$704$	−5.46842			−0.206099
$705$	−2.49755	+	14.8586i	−0.0940631	+	0.559608i
$706$	−0.869313			−0.0327170
$707$			15.7132i			0.590957i
$708$			3.88557i			0.146029i
$709$	13.4079			0.503543			0.251771	−	0.967787i	$-0.418987\pi$
$709$	13.4079			0.503543			0.251771	+	0.967787i	$0.418987\pi$
$710$	1.55675	+	0.261670i	0.0584239	+	0.00982032i
$711$	−1.77494			−0.0665655
$712$		−	2.89028i		−	0.108318i
$713$			4.87831i			0.182694i
$714$	2.27910			0.0852931
$715$	12.1437	+	2.04120i	0.454149	+	0.0763367i
$716$	1.39362			0.0520822
$717$			11.5466i			0.431215i
$718$			0.392306i			0.0146407i
$719$	27.1797			1.01363			0.506815	−	0.862055i	$-0.330823\pi$
$719$	27.1797			1.01363			0.506815	+	0.862055i	$0.330823\pi$
$720$	1.24137	−	7.38526i	0.0462631	−	0.275232i
$721$	9.00401			0.335327
$722$		−	2.11192i		−	0.0785975i
$723$		−	2.94329i		−	0.109462i
$724$	30.5986			1.13719
$725$	38.9365	+	13.4700i	1.44607	+	0.500265i
$726$	0.332438			0.0123379
$727$			18.7437i			0.695165i	0.937649	+	0.347582i	$0.112997\pi$
$727$			18.7437i			0.695165i	−0.937649	+	0.347582i	$0.887003\pi$
$728$		−	7.12065i		−	0.263909i
$729$	−1.00000			−0.0370370
$730$	−0.127137	+	0.756374i	−0.00470555	+	0.0279947i
$731$	22.1100			0.817766
$732$		−	21.1754i		−	0.782667i
$733$			15.1358i			0.559053i	0.960138	+	0.279526i	$0.0901774\pi$
$733$			15.1358i			0.559053i	−0.960138	+	0.279526i	$0.909823\pi$
$734$	−3.10579			−0.114637
$735$	−2.20513	−	0.370655i	−0.0813376	−	0.0136718i
$736$	−31.0083			−1.14298
$737$			1.52881i			0.0563144i
$738$		−	2.06029i		−	0.0758403i
$739$	−48.3650			−1.77914			−0.889568	−	0.456804i	$-0.848994\pi$
$739$	−48.3650			−1.77914			−0.889568	+	0.456804i	$0.848994\pi$
$740$	−40.8665	−	6.86913i	−1.50228	−	0.252514i
$741$	19.5845			0.719456
$742$			4.66944i			0.171420i
$743$			4.53993i			0.166554i	0.996526	+	0.0832770i	$0.0265386\pi$
$743$			4.53993i			0.166554i	−0.996526	+	0.0832770i	$0.973461\pi$
$744$	0.752534			0.0275892
$745$	−0.495994	+	2.95081i	−0.0181718	+	0.108109i
$746$	−4.70280			−0.172182
$747$			4.43704i			0.162343i
$748$			12.9538i			0.473636i
$749$	7.11539			0.259991
$750$	1.78058	−	3.26250i	0.0650178	−	0.119130i
$751$	−25.3018			−0.923277			−0.461639	−	0.887068i	$-0.652738\pi$
$751$	−25.3018			−0.923277			−0.461639	+	0.887068i	$0.652738\pi$
$752$			22.5671i			0.822936i
$753$		−	19.3563i		−	0.705382i
$754$	15.0856			0.549384
$755$	−2.84471	+	16.9240i	−0.103530	+	0.615928i
$756$	−1.88948			−0.0687199
$757$		−	5.94684i		−	0.216142i	−0.994143	−	0.108071i	$-0.965533\pi$
$757$		−	5.94684i		−	0.216142i	0.994143	−	0.108071i	$-0.0344673\pi$
$758$			2.32592i			0.0844812i
$759$	−8.38198			−0.304247
$760$	−10.1399	−	1.70439i	−0.367814	−	0.0618249i
$761$	23.3343			0.845867			0.422934	−	0.906161i	$-0.361000\pi$
$761$	23.3343			0.845867			0.422934	+	0.906161i	$0.361000\pi$
$762$		−	7.27460i		−	0.263531i
$763$			1.84137i			0.0666622i
$764$	−26.5780			−0.961560
$765$	−15.1177	−	2.54110i	−0.546583	−	0.0918737i
$766$	0.00932174			0.000336808
$767$		−	11.3247i		−	0.408912i
$768$		−	7.87285i		−	0.284087i
$769$	36.2453			1.30704			0.653520	−	0.756909i	$-0.273292\pi$
$769$	36.2453			1.30704			0.653520	+	0.756909i	$0.273292\pi$
$770$	−0.123220	+	0.733071i	−0.00444054	+	0.0264180i
$771$	−11.3301			−0.408045
$772$		−	2.66301i		−	0.0958440i
$773$		−	36.7722i		−	1.32261i	−0.750119	−	0.661303i	$-0.770004\pi$
$773$		−	36.7722i		−	1.32261i	0.750119	−	0.661303i	$-0.229996\pi$
$774$	1.07213			0.0385369
$775$	−2.75008	−	0.951388i	−0.0987859	−	0.0341749i
$776$	−14.5459			−0.522169
$777$			9.80818i			0.351867i
$778$			9.65974i			0.346318i
$779$	22.0401			0.789669
$780$	−3.85683	+	22.9454i	−0.138097	+	0.821576i
$781$	2.12361			0.0759886
$782$			19.1034i			0.683135i
$783$		−	8.24013i		−	0.294478i
$784$	−3.34912			−0.119612
$785$	31.6855	+	5.32592i	1.13090	+	0.190090i
$786$	−0.864455			−0.0308341
$787$			53.8452i			1.91937i	0.281071	+	0.959687i	$0.409310\pi$
$787$			53.8452i			1.91937i	−0.281071	+	0.959687i	$0.590690\pi$
$788$			4.47020i			0.159244i
$789$	−3.36193			−0.119688
$790$	−1.30116	−	0.218708i	−0.0462931	−	0.00778129i
$791$	−17.2295			−0.612611
$792$			1.29301i			0.0459452i
$793$			61.7172i			2.19164i
$794$	−11.5262			−0.409050
$795$	5.20623	−	30.9734i	0.184646	−	1.09851i
$796$	−14.5296			−0.514988
$797$			16.1632i			0.572529i	0.958151	+	0.286264i	$0.0924136\pi$
$797$			16.1632i			0.572529i	−0.958151	+	0.286264i	$0.907586\pi$
$798$			1.18225i			0.0418511i
$799$	46.1951			1.63427
$800$	6.04737	−	17.4805i	0.213807	−	0.618030i
$801$	2.23530			0.0789806
$802$			11.7499i			0.414903i
$803$			1.03179i			0.0364110i
$804$	−2.88866			−0.101875
$805$	3.10682	−	18.4834i	0.109501	−	0.651454i
$806$	−1.06549			−0.0375304
$807$		−	6.35047i		−	0.223547i
$808$			20.3174i			0.714764i
$809$	42.7944			1.50457			0.752286	−	0.658837i	$-0.228951\pi$
$809$	42.7944			1.50457			0.752286	+	0.658837i	$0.228951\pi$
$810$	−0.733071	−	0.123220i	−0.0257575	−	0.00432951i
$811$	−41.4027			−1.45384			−0.726922	−	0.686720i	$-0.759050\pi$
$811$	−41.4027			−1.45384			−0.726922	+	0.686720i	$0.759050\pi$
$812$		−	15.5696i		−	0.546386i
$813$		−	14.2641i		−	0.500265i
$814$	3.26062			0.114285
$815$	27.6485	+	4.64736i	0.968483	+	0.162790i
$816$	−22.9606			−0.803782
$817$			11.4692i			0.401256i
$818$			4.50626i			0.157558i
$819$	5.50702			0.192431
$820$	−4.34041	+	25.8223i	−0.151574	+	0.901755i
$821$	42.0113			1.46620			0.733102	−	0.680119i	$-0.238072\pi$
$821$	42.0113			1.46620			0.733102	+	0.680119i	$0.238072\pi$
$822$			5.38705i			0.187895i
$823$			4.54879i			0.158561i	0.996852	+	0.0792804i	$0.0252622\pi$
$823$			4.54879i			0.158561i	−0.996852	+	0.0792804i	$0.974738\pi$
$824$	11.6423			0.405579
$825$	1.63469	−	4.72523i	0.0569125	−	0.164511i
$826$	0.683632			0.0237866
$827$		−	51.8270i		−	1.80220i	−0.433609	−	0.901101i	$-0.642760\pi$
$827$		−	51.8270i		−	1.80220i	0.433609	−	0.901101i	$-0.357240\pi$
$828$		−	15.8376i		−	0.550396i
$829$	−0.130463			−0.00453116			−0.00226558	−	0.999997i	$-0.500721\pi$
$829$	−0.130463			−0.00453116			−0.00226558	+	0.999997i	$0.500721\pi$
$830$	−0.546731	+	3.25266i	−0.0189773	+	0.112902i
$831$	−24.0288			−0.833549
$832$			30.1147i			1.04404i
$833$			6.85571i			0.237536i
$834$	2.31015			0.0799940
$835$	8.91182	+	1.49796i	0.308406	+	0.0518392i
$836$	−6.71955			−0.232401
$837$			0.582000i			0.0201169i
$838$		−	5.86142i		−	0.202480i
$839$	46.9683			1.62153			0.810763	−	0.585375i	$-0.199053\pi$
$839$	46.9683			1.62153			0.810763	+	0.585375i	$0.199053\pi$
$840$	−2.85127	−	0.479262i	−0.0983781	−	0.0165361i
$841$	38.8997			1.34137
$842$			3.36072i			0.115818i
$843$		−	11.6299i		−	0.400554i
$844$	−47.0849			−1.62073
$845$	6.42244	−	38.2090i	0.220939	−	1.31443i
$846$	2.24004			0.0770140
$847$			1.00000i			0.0343604i
$848$		−	47.0418i		−	1.61542i
$849$	−7.02079			−0.240953
$850$	−10.7693	−	3.72562i	−0.369383	−	0.127788i
$851$	−82.2120			−2.81819
$852$			4.01252i			0.137467i
$853$		−	35.5217i		−	1.21624i	−0.793845	−	0.608120i	$-0.791924\pi$
$853$		−	35.5217i		−	1.21624i	0.793845	−	0.608120i	$-0.208076\pi$
$854$	−3.72563			−0.127489
$855$	1.31816	−	7.84209i	0.0450800	−	0.268194i
$856$	9.20030			0.314460
$857$			37.8906i			1.29432i	0.762355	+	0.647160i	$0.224043\pi$
$857$			37.8906i			1.29432i	−0.762355	+	0.647160i	$0.775957\pi$
$858$		−	1.83074i		−	0.0625006i
$859$	47.6594			1.62612			0.813059	−	0.582182i	$-0.197801\pi$
$859$	47.6594			1.62612			0.813059	+	0.582182i	$0.197801\pi$
$860$	−13.4374	−	2.25865i	−0.458210	−	0.0770194i
$861$	6.19751			0.211210
$862$			9.12633i			0.310844i
$863$			12.3002i			0.418703i	0.977840	+	0.209352i	$0.0671353\pi$
$863$			12.3002i			0.418703i	−0.977840	+	0.209352i	$0.932865\pi$
$864$	−3.69940			−0.125856
$865$	34.9882	+	5.88107i	1.18963	+	0.199962i
$866$	−11.7515			−0.399331
$867$			30.0007i			1.01888i
$868$			1.09968i			0.0373256i
$869$	−1.77494			−0.0602108
$870$	1.01535	−	6.04060i	0.0344235	−	0.204795i
$871$	8.41918			0.285273
$872$			2.38092i			0.0806281i
$873$		−	11.2496i		−	0.380743i
$874$	−9.90957			−0.335196
$875$	9.81386	+	5.35614i	0.331769	+	0.181070i
$876$	−1.94955			−0.0658692
$877$		−	26.0524i		−	0.879727i	−0.898065	−	0.439864i	$-0.855027\pi$
$877$		−	26.0524i		−	0.879727i	0.898065	−	0.439864i	$-0.144973\pi$
$878$		−	5.66762i		−	0.191273i
$879$	−12.3870			−0.417804
$880$	1.24137	−	7.38526i	0.0418465	−	0.248957i
$881$	19.1202			0.644176			0.322088	−	0.946710i	$-0.395615\pi$
$881$	19.1202			0.644176			0.322088	+	0.946710i	$0.395615\pi$
$882$			0.332438i			0.0111938i
$883$		−	46.6003i		−	1.56823i	−0.620618	−	0.784113i	$-0.713118\pi$
$883$		−	46.6003i		−	1.56823i	0.620618	−	0.784113i	$-0.286882\pi$
$884$	71.3366			2.39931
$885$	−4.53467	−	0.762221i	−0.152431	−	0.0256218i
$886$	9.85426			0.331060
$887$			43.9801i			1.47671i	0.674413	+	0.738354i	$0.264397\pi$
$887$			43.9801i			1.47671i	−0.674413	+	0.738354i	$0.735603\pi$
$888$			12.6821i			0.425584i
$889$	21.8825			0.733917
$890$	1.63864	+	0.275434i	0.0549272	+	0.00923257i
$891$	−1.00000			−0.0335013
$892$		−	24.0696i		−	0.805909i
$893$			23.9630i			0.801890i
$894$	0.444854			0.0148782
$895$	−0.273383	+	1.62644i	−0.00913820	+	0.0543658i
$896$	−9.21672			−0.307909
$897$			46.1597i			1.54123i
$898$		−	1.90931i		−	0.0637146i
$899$	−4.79575			−0.159947
$900$	8.92825	+	3.08872i	0.297608	+	0.102957i
$901$	−96.2954			−3.20806
$902$		−	2.06029i		−	0.0686001i
$903$			3.22504i			0.107323i
$904$	−22.2780			−0.740955
$905$	−6.00245	+	35.7103i	−0.199528	+	1.18705i
$906$	2.55141			0.0847648
$907$		−	52.4317i		−	1.74097i	−0.492199	−	0.870483i	$-0.663807\pi$
$907$		−	52.4317i		−	1.74097i	0.492199	−	0.870483i	$-0.336193\pi$
$908$		−	37.6977i		−	1.25104i
$909$	−15.7132			−0.521175
$910$	4.03704	+	0.678575i	0.133826	+	0.0224945i
$911$	6.08013			0.201444			0.100722	−	0.994915i	$-0.467885\pi$
$911$	6.08013			0.201444			0.100722	+	0.994915i	$0.467885\pi$
$912$		−	11.9104i		−	0.394394i
$913$			4.43704i			0.146844i
$914$	12.2569			0.405422
$915$	24.7129	+	4.15393i	0.816984	+	0.137325i
$916$	6.02462			0.199059
$917$		−	2.60035i		−	0.0858710i
$918$			2.27910i			0.0752215i
$919$	−44.3509			−1.46300			−0.731500	−	0.681841i	$-0.761180\pi$
$919$	−44.3509			−1.46300			−0.731500	+	0.681841i	$0.761180\pi$
$920$	4.01717	−	23.8993i	0.132442	−	0.787936i
$921$	−8.76620			−0.288856
$922$			6.53988i			0.215379i
$923$		−	11.6947i		−	0.384937i
$924$	−1.88948			−0.0621595
$925$	16.0333	−	46.3459i	0.527172	−	1.52384i
$926$	−11.9673			−0.393271
$927$			9.00401i			0.295731i
$928$		−	30.4836i		−	1.00067i
$929$	14.1527			0.464336			0.232168	−	0.972676i	$-0.425418\pi$
$929$	14.1527			0.464336			0.232168	+	0.972676i	$0.425418\pi$
$930$	−0.0717140	+	0.426647i	−0.00235159	+	0.0139903i
$931$	−3.55629			−0.116553
$932$			14.5198i			0.475610i
$933$			13.6554i			0.447058i
$934$	−3.98818			−0.130497
$935$	−15.1177	−	2.54110i	−0.494403	−	0.0831029i
$936$	7.12065			0.232746
$937$		−	4.00932i		−	0.130979i	−0.997853	−	0.0654894i	$-0.979139\pi$
$937$		−	4.00932i		−	0.130979i	0.997853	−	0.0654894i	$-0.0208609\pi$
$938$			0.508234i			0.0165944i
$939$	−20.7806			−0.678150
$940$	−28.0752	−	4.71908i	−0.915711	−	0.153919i
$941$	−11.6092			−0.378449			−0.189224	−	0.981934i	$-0.560597\pi$
$941$	−11.6092			−0.378449			−0.189224	+	0.981934i	$0.560597\pi$
$942$		−	4.77679i		−	0.155636i
$943$			51.9474i			1.69164i
$944$	−6.88719			−0.224159
$945$	0.370655	−	2.20513i	0.0120574	−	0.0717330i
$946$	1.07213			0.0348579
$947$			4.89950i			0.159212i	0.996826	+	0.0796062i	$0.0253663\pi$
$947$			4.89950i			0.159212i	−0.996826	+	0.0796062i	$0.974634\pi$
$948$		−	3.35373i		−	0.108924i
$949$	5.68208			0.184448
$950$	1.93260	−	5.58638i	0.0627019	−	0.181246i
$951$	10.4361			0.338413
$952$			8.86452i			0.287301i
$953$			13.1770i			0.426844i	0.976960	+	0.213422i	$0.0684609\pi$
$953$			13.1770i			0.426844i	−0.976960	+	0.213422i	$0.931539\pi$
$954$	−4.66944			−0.151179
$955$	5.21374	−	31.0181i	0.168713	−	1.00372i
$956$	−21.8171			−0.705616
$957$		−	8.24013i		−	0.266365i
$958$			2.47853i			0.0800778i
$959$	−16.2047			−0.523276
$960$	12.0586	+	2.02690i	0.389190	+	0.0654178i
$961$	−30.6613			−0.989073
$962$		−	17.9563i		−	0.578934i
$963$			7.11539i			0.229290i
$964$	5.56130			0.179117
$965$	3.10789	+	0.522396i	0.100046	+	0.0168165i
$966$	−2.78649			−0.0896539
$967$			1.72537i			0.0554841i	0.999615	+	0.0277420i	$0.00883170\pi$
$967$			1.72537i			0.0554841i	−0.999615	+	0.0277420i	$0.991168\pi$
$968$			1.29301i			0.0415590i
$969$	−24.3809			−0.783226
$970$	1.38618	−	8.24679i	0.0445076	−	0.264788i
$971$	41.2450			1.32362			0.661808	−	0.749674i	$-0.269790\pi$
$971$	41.2450			1.32362			0.661808	+	0.749674i	$0.269790\pi$
$972$		−	1.88948i		−	0.0606053i
$973$			6.94911i			0.222778i
$974$	−8.40805			−0.269411
$975$	−26.0219	−	9.00226i	−0.833369	−	0.288303i
$976$	37.5336			1.20142
$977$			59.1538i			1.89250i	0.323438	+	0.946249i	$0.395161\pi$
$977$			59.1538i			1.89250i	−0.323438	+	0.946249i	$0.604839\pi$
$978$		−	4.16819i		−	0.133284i
$979$	2.23530			0.0714406
$980$	0.700347	−	4.16657i	0.0223718	−	0.133096i
$981$	−1.84137			−0.0587905
$982$		−	7.39408i		−	0.235955i
$983$		−	22.6606i		−	0.722761i	−0.932418	−	0.361381i	$-0.882305\pi$
$983$		−	22.6606i		−	0.722761i	0.932418	−	0.361381i	$-0.117695\pi$
$984$	8.01346			0.255460
$985$	−5.21697	−	0.876906i	−0.166226	−	0.0279406i
$986$	−18.7801			−0.598079
$987$			6.73820i			0.214479i
$988$			37.0047i			1.17728i
$989$	−27.0323			−0.859576
$990$	−0.733071	−	0.123220i	−0.0232985	−	0.00391619i
$991$	57.8514			1.83771			0.918855	−	0.394595i	$-0.129115\pi$
$991$	57.8514			1.83771			0.918855	+	0.394595i	$0.129115\pi$
$992$			2.15305i			0.0683595i
$993$			6.63873i			0.210674i
$994$	0.705968			0.0223919
$995$	2.85023	−	16.9569i	0.0903584	−	0.537568i
$996$	−8.38371			−0.265648
$997$			13.9388i			0.441446i	0.975337	+	0.220723i	$0.0708417\pi$
$997$			13.9388i			0.441446i	−0.975337	+	0.220723i	$0.929158\pi$
$998$			3.97418i			0.125800i
$999$	−9.80818			−0.310317

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1155.2.c.e.694.11	yes	20
5.2	odd	4		5775.2.a.cm.1.6		10
5.3	odd	4		5775.2.a.cp.1.5		10
5.4	even	2	inner	1155.2.c.e.694.10	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1155.2.c.e.694.10	✓	20	5.4	even	2	inner
1155.2.c.e.694.11	yes	20	1.1	even	1	trivial
5775.2.a.cm.1.6		10	5.2	odd	4
5775.2.a.cp.1.5		10	5.3	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)

\(f(q)\)	\(=\)	\(q+0.332438i q^{2} -1.00000i q^{3} +1.88948 q^{4} +(-0.370655 + 2.20513i) q^{5} +0.332438 q^{6} +1.00000i q^{7} +1.29301i q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q+0.332438i q^{2} -1.00000i q^{3} +1.88948 q^{4} +(-0.370655 + 2.20513i) q^{5} +0.332438 q^{6} +1.00000i q^{7} +1.29301i q^{8} -1.00000 q^{9} +(-0.733071 - 0.123220i) q^{10} -1.00000 q^{11} -1.88948i q^{12} +5.50702i q^{13} -0.332438 q^{14} +(2.20513 + 0.370655i) q^{15} +3.34912 q^{16} -6.85571i q^{17} -0.332438i q^{18} +3.55629 q^{19} +(-0.700347 + 4.16657i) q^{20} +1.00000 q^{21} -0.332438i q^{22} +8.38198i q^{23} +1.29301 q^{24} +(-4.72523 - 1.63469i) q^{25} -1.83074 q^{26} +1.00000i q^{27} +1.88948i q^{28} -8.24013 q^{29} +(-0.123220 + 0.733071i) q^{30} +0.582000 q^{31} +3.69940i q^{32} +1.00000i q^{33} +2.27910 q^{34} +(-2.20513 - 0.370655i) q^{35} -1.88948 q^{36} +9.80818i q^{37} +1.18225i q^{38} +5.50702 q^{39} +(-2.85127 - 0.479262i) q^{40} +6.19751 q^{41} +0.332438i q^{42} +3.22504i q^{43} -1.88948 q^{44} +(0.370655 - 2.20513i) q^{45} -2.78649 q^{46} +6.73820i q^{47} -3.34912i q^{48} -1.00000 q^{49} +(0.543433 - 1.57085i) q^{50} -6.85571 q^{51} +10.4054i q^{52} -14.0460i q^{53} -0.332438 q^{54} +(0.370655 - 2.20513i) q^{55} -1.29301 q^{56} -3.55629i q^{57} -2.73933i q^{58} -2.05642 q^{59} +(4.16657 + 0.700347i) q^{60} +11.2070 q^{61} +0.193479i q^{62} -1.00000i q^{63} +5.46842 q^{64} +(-12.1437 - 2.04120i) q^{65} -0.332438 q^{66} -1.52881i q^{67} -12.9538i q^{68} +8.38198 q^{69} +(0.123220 - 0.733071i) q^{70} -2.12361 q^{71} -1.29301i q^{72} -1.03179i q^{73} -3.26062 q^{74} +(-1.63469 + 4.72523i) q^{75} +6.71955 q^{76} -1.00000i q^{77} +1.83074i q^{78} +1.77494 q^{79} +(-1.24137 + 7.38526i) q^{80} +1.00000 q^{81} +2.06029i q^{82} -4.43704i q^{83} +1.88948 q^{84} +(15.1177 + 2.54110i) q^{85} -1.07213 q^{86} +8.24013i q^{87} -1.29301i q^{88} -2.23530 q^{89} +(0.733071 + 0.123220i) q^{90} -5.50702 q^{91} +15.8376i q^{92} -0.582000i q^{93} -2.24004 q^{94} +(-1.31816 + 7.84209i) q^{95} +3.69940 q^{96} +11.2496i q^{97} -0.332438i q^{98} +1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 26 q^{4} - 2 q^{5} + 6 q^{6} - 20 q^{9}+O(q^{10}) \) 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

L-functions

Modular forms

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Database

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