LMFDB - Embedded newform 1110.2.e.d.739.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1110,2,Mod(739,1110)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1110, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1110.739");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1110 = 2 \cdot 3 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1110.e (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:	$8.86339462436$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 2 x^{15} + 2 x^{14} + 8 x^{13} + 138 x^{12} - 220 x^{11} + 196 x^{10} + 744 x^{9} + 4241 x^{8} + \cdots + 64 $ x^16 - 2x^15 + 2x^14 + 8x^13 + 138x^12 - 220x^11 + 196x^10 + 744x^9 + 4241x^8 - 3018x^7 + 658x^6 - 1584x^5 + 16372x^4 - 18840x^3 + 10952x^2 - 1184*x + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			739.12
Root			$0.0603067 + 0.0603067i$ of defining polynomial
Character	$\chi$	$=$	1110.739
Dual form			1110.2.e.d.739.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +1.00000i q^{3} +1.00000 q^{4} +(0.0603067 + 2.23525i) q^{5} +1.00000i q^{6} +3.18244i q^{7} +1.00000 q^{8} -1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.00000i q^{3} +1.00000 q^{4} +(0.0603067 + 2.23525i) q^{5} +1.00000i q^{6} +3.18244i q^{7} +1.00000 q^{8} -1.00000 q^{9} +(0.0603067 + 2.23525i) q^{10} +2.65476 q^{11} +1.00000i q^{12} +0.269602 q^{13} +3.18244i q^{14} +(-2.23525 + 0.0603067i) q^{15} +1.00000 q^{16} -1.00678 q^{17} -1.00000 q^{18} -0.921428i q^{19} +(0.0603067 + 2.23525i) q^{20} -3.18244 q^{21} +2.65476 q^{22} -2.37657 q^{23} +1.00000i q^{24} +(-4.99273 + 0.269602i) q^{25} +0.269602 q^{26} -1.00000i q^{27} +3.18244i q^{28} -1.10656i q^{29} +(-2.23525 + 0.0603067i) q^{30} -3.57707i q^{31} +1.00000 q^{32} +2.65476i q^{33} -1.00678 q^{34} +(-7.11357 + 0.191923i) q^{35} -1.00000 q^{36} +(2.36505 + 5.60415i) q^{37} -0.921428i q^{38} +0.269602i q^{39} +(0.0603067 + 2.23525i) q^{40} +4.25889 q^{41} -3.18244 q^{42} -6.87448 q^{43} +2.65476 q^{44} +(-0.0603067 - 2.23525i) q^{45} -2.37657 q^{46} +3.07130i q^{47} +1.00000i q^{48} -3.12795 q^{49} +(-4.99273 + 0.269602i) q^{50} -1.00678i q^{51} +0.269602 q^{52} +3.55039i q^{53} -1.00000i q^{54} +(0.160100 + 5.93406i) q^{55} +3.18244i q^{56} +0.921428 q^{57} -1.10656i q^{58} +3.24508i q^{59} +(-2.23525 + 0.0603067i) q^{60} -2.85126i q^{61} -3.57707i q^{62} -3.18244i q^{63} +1.00000 q^{64} +(0.0162588 + 0.602628i) q^{65} +2.65476i q^{66} -4.14002i q^{67} -1.00678 q^{68} -2.37657i q^{69} +(-7.11357 + 0.191923i) q^{70} +10.9926 q^{71} -1.00000 q^{72} +2.97265i q^{73} +(2.36505 + 5.60415i) q^{74} +(-0.269602 - 4.99273i) q^{75} -0.921428i q^{76} +8.44862i q^{77} +0.269602i q^{78} -10.1431i q^{79} +(0.0603067 + 2.23525i) q^{80} +1.00000 q^{81} +4.25889 q^{82} +9.43016i q^{83} -3.18244 q^{84} +(-0.0607156 - 2.25041i) q^{85} -6.87448 q^{86} +1.10656 q^{87} +2.65476 q^{88} -12.2141i q^{89} +(-0.0603067 - 2.23525i) q^{90} +0.857992i q^{91} -2.37657 q^{92} +3.57707 q^{93} +3.07130i q^{94} +(2.05963 - 0.0555683i) q^{95} +1.00000i q^{96} +10.5793 q^{97} -3.12795 q^{98} -2.65476 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 16 q^{2} + 16 q^{4} + 2 q^{5} + 16 q^{8} - 16 q^{9}+O(q^{10}) $ 16 * q + 16 * q^2 + 16 * q^4 + 2 * q^5 + 16 * q^8 - 16 * q^9	$ 16 q + 16 q^{2} + 16 q^{4} + 2 q^{5} + 16 q^{8} - 16 q^{9} + 2 q^{10} + 2 q^{11} - 6 q^{15} + 16 q^{16} + 38 q^{17} - 16 q^{18} + 2 q^{20} + 6 q^{21} + 2 q^{22} + 20 q^{23} - 4 q^{25} - 6 q^{30} + 16 q^{32} + 38 q^{34} + 10 q^{35} - 16 q^{36} + 4 q^{37} + 2 q^{40} - 6 q^{41} + 6 q^{42} + 2 q^{43} + 2 q^{44} - 2 q^{45} + 20 q^{46} - 18 q^{49} - 4 q^{50} - 20 q^{55} - 16 q^{57} - 6 q^{60} + 16 q^{64} + 12 q^{65} + 38 q^{68} + 10 q^{70} - 24 q^{71} - 16 q^{72} + 4 q^{74} + 2 q^{80} + 16 q^{81} - 6 q^{82} + 6 q^{84} + 2 q^{86} - 2 q^{87} + 2 q^{88} - 2 q^{90} + 20 q^{92} - 22 q^{93} - 16 q^{95} - 38 q^{97} - 18 q^{98} - 2 q^{99}+O(q^{100}) $ 16 * q + 16 * q^2 + 16 * q^4 + 2 * q^5 + 16 * q^8 - 16 * q^9 + 2 * q^10 + 2 * q^11 - 6 * q^15 + 16 * q^16 + 38 * q^17 - 16 * q^18 + 2 * q^20 + 6 * q^21 + 2 * q^22 + 20 * q^23 - 4 * q^25 - 6 * q^30 + 16 * q^32 + 38 * q^34 + 10 * q^35 - 16 * q^36 + 4 * q^37 + 2 * q^40 - 6 * q^41 + 6 * q^42 + 2 * q^43 + 2 * q^44 - 2 * q^45 + 20 * q^46 - 18 * q^49 - 4 * q^50 - 20 * q^55 - 16 * q^57 - 6 * q^60 + 16 * q^64 + 12 * q^65 + 38 * q^68 + 10 * q^70 - 24 * q^71 - 16 * q^72 + 4 * q^74 + 2 * q^80 + 16 * q^81 - 6 * q^82 + 6 * q^84 + 2 * q^86 - 2 * q^87 + 2 * q^88 - 2 * q^90 + 20 * q^92 - 22 * q^93 - 16 * q^95 - 38 * q^97 - 18 * q^98 - 2 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times$.

$n$	$371$	$631$	$667$
$\chi(n)$	$1$	$-1$	$-1$

Coefficient data

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

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

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

$2$	1.00000			0.707107
$2$	1.00000			0.707107
$3$			1.00000i			0.577350i
$3$			1.00000i			0.577350i
$4$	1.00000			0.500000
$5$	0.0603067	+	2.23525i	0.0269700	+	0.999636i
$5$	0.0603067	+	2.23525i	0.0269700	+	0.999636i
$6$			1.00000i			0.408248i
$7$			3.18244i			1.20285i	0.798929	+	0.601425i	$0.205400\pi$
$7$			3.18244i			1.20285i	−0.798929	+	0.601425i	$0.794600\pi$
$8$	1.00000			0.353553
$9$	−1.00000			−0.333333
$10$	0.0603067	+	2.23525i	0.0190706	+	0.706850i
$11$	2.65476			0.800440			0.400220	−	0.916419i	$-0.368934\pi$
$11$	2.65476			0.800440			0.400220	+	0.916419i	$0.368934\pi$
$12$			1.00000i			0.288675i
$13$	0.269602			0.0747740			0.0373870	−	0.999301i	$-0.488097\pi$
$13$	0.269602			0.0747740			0.0373870	+	0.999301i	$0.488097\pi$
$14$			3.18244i			0.850544i
$15$	−2.23525	+	0.0603067i	−0.577140	+	0.0155711i
$16$	1.00000			0.250000
$17$	−1.00678			−0.244180			−0.122090	−	0.992519i	$-0.538960\pi$
$17$	−1.00678			−0.244180			−0.122090	+	0.992519i	$0.538960\pi$
$18$	−1.00000			−0.235702
$19$		−	0.921428i		−	0.211390i	−0.994399	−	0.105695i	$-0.966293\pi$
$19$		−	0.921428i		−	0.211390i	0.994399	−	0.105695i	$-0.0337067\pi$
$20$	0.0603067	+	2.23525i	0.0134850	+	0.499818i
$21$	−3.18244			−0.694466
$22$	2.65476			0.565996
$23$	−2.37657			−0.495549			−0.247775	−	0.968818i	$-0.579699\pi$
$23$	−2.37657			−0.495549			−0.247775	+	0.968818i	$0.579699\pi$
$24$			1.00000i			0.204124i
$25$	−4.99273	+	0.269602i	−0.998545	+	0.0539203i
$26$	0.269602			0.0528732
$27$		−	1.00000i		−	0.192450i
$28$			3.18244i			0.601425i
$29$		−	1.10656i		−	0.205483i	−0.994708	−	0.102741i	$-0.967239\pi$
$29$		−	1.10656i		−	0.205483i	0.994708	−	0.102741i	$-0.0327614\pi$
$30$	−2.23525	+	0.0603067i	−0.408100	+	0.0110104i
$31$		−	3.57707i		−	0.642460i	−0.947001	−	0.321230i	$-0.895904\pi$
$31$		−	3.57707i		−	0.642460i	0.947001	−	0.321230i	$-0.104096\pi$
$32$	1.00000			0.176777
$33$			2.65476i			0.462134i
$34$	−1.00678			−0.172661
$35$	−7.11357	+	0.191923i	−1.20241	+	0.0324408i
$36$	−1.00000			−0.166667
$37$	2.36505	+	5.60415i	0.388812	+	0.921317i
$37$	2.36505	+	5.60415i	0.388812	+	0.921317i
$38$		−	0.921428i		−	0.149475i
$39$			0.269602i			0.0431708i
$40$	0.0603067	+	2.23525i	0.00953532	+	0.353425i
$41$	4.25889			0.665127			0.332563	−	0.943081i	$-0.392086\pi$
$41$	4.25889			0.665127			0.332563	+	0.943081i	$0.392086\pi$
$42$	−3.18244			−0.491062
$43$	−6.87448			−1.04835			−0.524175	−	0.851611i	$-0.675626\pi$
$43$	−6.87448			−1.04835			−0.524175	+	0.851611i	$0.675626\pi$
$44$	2.65476			0.400220
$45$	−0.0603067	−	2.23525i	−0.00898999	−	0.333212i
$46$	−2.37657			−0.350406
$47$			3.07130i			0.447995i	0.974590	+	0.223997i	$0.0719107\pi$
$47$			3.07130i			0.447995i	−0.974590	+	0.223997i	$0.928089\pi$
$48$			1.00000i			0.144338i
$49$	−3.12795			−0.446851
$50$	−4.99273	+	0.269602i	−0.706078	+	0.0381274i
$51$		−	1.00678i		−	0.140977i
$52$	0.269602			0.0373870
$53$			3.55039i			0.487684i	0.969815	+	0.243842i	$0.0784078\pi$
$53$			3.55039i			0.487684i	−0.969815	+	0.243842i	$0.921592\pi$
$54$		−	1.00000i		−	0.136083i
$55$	0.160100	+	5.93406i	0.0215878	+	0.800149i
$56$			3.18244i			0.425272i
$57$	0.921428			0.122046
$58$		−	1.10656i		−	0.145298i
$59$			3.24508i			0.422473i	0.977435	+	0.211236i	$0.0677490\pi$
$59$			3.24508i			0.422473i	−0.977435	+	0.211236i	$0.932251\pi$
$60$	−2.23525	+	0.0603067i	−0.288570	+	0.00778556i
$61$		−	2.85126i		−	0.365066i	−0.983200	−	0.182533i	$-0.941570\pi$
$61$		−	2.85126i		−	0.365066i	0.983200	−	0.182533i	$-0.0584297\pi$
$62$		−	3.57707i		−	0.454288i
$63$		−	3.18244i		−	0.400950i
$64$	1.00000			0.125000
$65$	0.0162588	+	0.602628i	0.00201665	+	0.0747468i
$66$			2.65476i			0.326778i
$67$		−	4.14002i		−	0.505783i	−0.967495	−	0.252892i	$-0.918618\pi$
$67$		−	4.14002i		−	0.505783i	0.967495	−	0.252892i	$-0.0813816\pi$
$68$	−1.00678			−0.122090
$69$		−	2.37657i		−	0.286106i
$70$	−7.11357	+	0.191923i	−0.850235	+	0.0229391i
$71$	10.9926			1.30458			0.652290	−	0.757970i	$-0.273808\pi$
$71$	10.9926			1.30458			0.652290	+	0.757970i	$0.273808\pi$
$72$	−1.00000			−0.117851
$73$			2.97265i			0.347923i	0.984752	+	0.173961i	$0.0556568\pi$
$73$			2.97265i			0.347923i	−0.984752	+	0.173961i	$0.944343\pi$
$74$	2.36505	+	5.60415i	0.274932	+	0.651470i
$75$	−0.269602	−	4.99273i	−0.0311309	−	0.576510i
$76$		−	0.921428i		−	0.105695i
$77$			8.44862i			0.962810i
$78$			0.269602i			0.0305264i
$79$		−	10.1431i		−	1.14118i	−0.821234	−	0.570592i	$-0.806714\pi$
$79$		−	10.1431i		−	1.14118i	0.821234	−	0.570592i	$-0.193286\pi$
$80$	0.0603067	+	2.23525i	0.00674249	+	0.249909i
$81$	1.00000			0.111111
$82$	4.25889			0.470316
$83$			9.43016i			1.03509i	0.855655	+	0.517547i	$0.173155\pi$
$83$			9.43016i			1.03509i	−0.855655	+	0.517547i	$0.826845\pi$
$84$	−3.18244			−0.347233
$85$	−0.0607156	−	2.25041i	−0.00658553	−	0.244091i
$86$	−6.87448			−0.741295
$87$	1.10656			0.118636
$88$	2.65476			0.282998
$89$		−	12.2141i		−	1.29469i	−0.762196	−	0.647347i	$-0.775879\pi$
$89$		−	12.2141i		−	1.29469i	0.762196	−	0.647347i	$-0.224121\pi$
$90$	−0.0603067	−	2.23525i	−0.00635688	−	0.235617i
$91$			0.857992i			0.0899420i
$92$	−2.37657			−0.247775
$93$	3.57707			0.370925
$94$			3.07130i			0.316780i
$95$	2.05963	−	0.0555683i	0.211313	−	0.00570119i
$96$			1.00000i			0.102062i
$97$	10.5793			1.07417			0.537084	−	0.843529i	$-0.319526\pi$
$97$	10.5793			1.07417			0.537084	+	0.843529i	$0.319526\pi$
$98$	−3.12795			−0.315971
$99$	−2.65476			−0.266813
$100$	−4.99273	+	0.269602i	−0.499273	+	0.0269602i
$101$	18.2540			1.81634			0.908171	−	0.418599i	$-0.137479\pi$
$101$	18.2540			1.81634			0.908171	+	0.418599i	$0.137479\pi$
$102$		−	1.00678i		−	0.0996861i
$103$	−1.52241			−0.150007			−0.0750035	−	0.997183i	$-0.523897\pi$
$103$	−1.52241			−0.150007			−0.0750035	+	0.997183i	$0.523897\pi$
$104$	0.269602			0.0264366
$105$	−0.191923	−	7.11357i	−0.0187297	−	0.694214i
$106$			3.55039i			0.344845i
$107$			8.18691i			0.791459i	0.918367	+	0.395729i	$0.129508\pi$
$107$			8.18691i			0.791459i	−0.918367	+	0.395729i	$0.870492\pi$
$108$		−	1.00000i		−	0.0962250i
$109$		−	11.5302i		−	1.10439i	−0.833714	−	0.552197i	$-0.813790\pi$
$109$		−	11.5302i		−	1.10439i	0.833714	−	0.552197i	$-0.186210\pi$
$110$	0.160100	+	5.93406i	0.0152649	+	0.565791i
$111$	−5.60415	+	2.36505i	−0.531923	+	0.224481i
$112$			3.18244i			0.300713i
$113$	8.93042			0.840103			0.420051	−	0.907500i	$-0.362012\pi$
$113$	8.93042			0.840103			0.420051	+	0.907500i	$0.362012\pi$
$114$	0.921428			0.0862997
$115$	−0.143323	−	5.31224i	−0.0133650	−	0.495369i
$116$		−	1.10656i		−	0.102741i
$117$	−0.269602			−0.0249247
$118$			3.24508i			0.298733i
$119$		−	3.20402i		−	0.293712i
$120$	−2.23525	+	0.0603067i	−0.204050	+	0.00550522i
$121$	−3.95226			−0.359296
$122$		−	2.85126i		−	0.258141i
$123$			4.25889i			0.384011i
$124$		−	3.57707i		−	0.321230i
$125$	−0.903723	−	11.1438i	−0.0808314	−	0.996728i
$126$		−	3.18244i		−	0.283515i
$127$			3.22594i			0.286256i	0.989704	+	0.143128i	$0.0457160\pi$
$127$			3.22594i			0.286256i	−0.989704	+	0.143128i	$0.954284\pi$
$128$	1.00000			0.0883883
$129$		−	6.87448i		−	0.605265i
$130$	0.0162588	+	0.602628i	0.00142599	+	0.0528540i
$131$			17.3542i			1.51624i	0.652114	+	0.758121i	$0.273883\pi$
$131$			17.3542i			1.51624i	−0.652114	+	0.758121i	$0.726117\pi$
$132$			2.65476i			0.231067i
$133$	2.93239			0.254271
$134$		−	4.14002i		−	0.357643i
$135$	2.23525	−	0.0603067i	0.192380	−	0.00519037i
$136$	−1.00678			−0.0863307
$137$		−	2.63659i		−	0.225259i	−0.993637	−	0.112629i	$-0.964073\pi$
$137$		−	2.63659i		−	0.225259i	0.993637	−	0.112629i	$-0.0359273\pi$
$138$		−	2.37657i		−	0.202307i
$139$	−1.15632			−0.0980777			−0.0490389	−	0.998797i	$-0.515616\pi$
$139$	−1.15632			−0.0980777			−0.0490389	+	0.998797i	$0.515616\pi$
$140$	−7.11357	+	0.191923i	−0.601207	+	0.0162204i
$141$	−3.07130			−0.258650
$142$	10.9926			0.922477
$143$	0.715727			0.0598521
$144$	−1.00000			−0.0833333
$145$	2.47344	−	0.0667329i	0.205408	−	0.00554186i
$146$			2.97265i			0.246019i
$147$		−	3.12795i		−	0.257989i
$148$	2.36505	+	5.60415i	0.194406	+	0.460659i
$149$	0.905691			0.0741971			0.0370985	−	0.999312i	$-0.488188\pi$
$149$	0.905691			0.0741971			0.0370985	+	0.999312i	$0.488188\pi$
$150$	−0.269602	−	4.99273i	−0.0220129	−	0.407654i
$151$	8.60991			0.700664			0.350332	−	0.936626i	$-0.386069\pi$
$151$	8.60991			0.700664			0.350332	+	0.936626i	$0.386069\pi$
$152$		−	0.921428i		−	0.0747377i
$153$	1.00678			0.0813934
$154$			8.44862i			0.680809i
$155$	7.99566	−	0.215721i	0.642227	−	0.0173271i
$156$			0.269602i			0.0215854i
$157$			4.84051i			0.386315i	0.981168	+	0.193157i	$0.0618728\pi$
$157$			4.84051i			0.386315i	−0.981168	+	0.193157i	$0.938127\pi$
$158$		−	10.1431i		−	0.806939i
$159$	−3.55039			−0.281564
$160$	0.0603067	+	2.23525i	0.00476766	+	0.176712i
$161$		−	7.56331i		−	0.596072i
$162$	1.00000			0.0785674
$163$	−16.2160			−1.27013			−0.635066	−	0.772458i	$-0.719027\pi$
$163$	−16.2160			−1.27013			−0.635066	+	0.772458i	$0.719027\pi$
$164$	4.25889			0.332563
$165$	−5.93406	+	0.160100i	−0.461966	+	0.0124637i
$166$			9.43016i			0.731922i
$167$	11.3881			0.881239			0.440619	−	0.897694i	$-0.354759\pi$
$167$	11.3881			0.881239			0.440619	+	0.897694i	$0.354759\pi$
$168$	−3.18244			−0.245531
$169$	−12.9273			−0.994409
$170$	−0.0607156	−	2.25041i	−0.00465667	−	0.172599i
$171$			0.921428i			0.0704634i
$172$	−6.87448			−0.524175
$173$		−	21.3699i		−	1.62472i	−0.583155	−	0.812361i	$-0.698182\pi$
$173$		−	21.3699i		−	1.62472i	0.583155	−	0.812361i	$-0.301818\pi$
$174$	1.10656			0.0838880
$175$	−0.857992	−	15.8891i	−0.0648581	−	1.20110i
$176$	2.65476			0.200110
$177$	−3.24508			−0.243915
$178$		−	12.2141i		−	0.915487i
$179$		−	1.95979i		−	0.146482i	−0.997314	−	0.0732408i	$-0.976666\pi$
$179$		−	1.95979i		−	0.146482i	0.997314	−	0.0732408i	$-0.0233342\pi$
$180$	−0.0603067	−	2.23525i	−0.00449499	−	0.166606i
$181$	6.56630			0.488069			0.244035	−	0.969766i	$-0.421529\pi$
$181$	6.56630			0.488069			0.244035	+	0.969766i	$0.421529\pi$
$182$			0.857992i			0.0635986i
$183$	2.85126			0.210771
$184$	−2.37657			−0.175203
$185$	−12.3841	+	5.62446i	−0.910496	+	0.413519i
$186$	3.57707			0.262283
$187$	−2.67276			−0.195452
$188$			3.07130i			0.223997i
$189$	3.18244			0.231489
$190$	2.05963	−	0.0555683i	0.149421	−	0.00403135i
$191$			5.01873i			0.363142i	0.983378	+	0.181571i	$0.0581183\pi$
$191$			5.01873i			0.363142i	−0.983378	+	0.181571i	$0.941882\pi$
$192$			1.00000i			0.0721688i
$193$	−13.8051			−0.993712			−0.496856	−	0.867833i	$-0.665512\pi$
$193$	−13.8051			−0.993712			−0.496856	+	0.867833i	$0.665512\pi$
$194$	10.5793			0.759551
$195$	−0.602628	+	0.0162588i	−0.0431551	+	0.00116431i
$196$	−3.12795			−0.223425
$197$		−	13.7617i		−	0.980479i	−0.871588	−	0.490240i	$-0.836909\pi$
$197$		−	13.7617i		−	0.980479i	0.871588	−	0.490240i	$-0.163091\pi$
$198$	−2.65476			−0.188665
$199$		−	3.38359i		−	0.239856i	−0.992783	−	0.119928i	$-0.961734\pi$
$199$		−	3.38359i		−	0.239856i	0.992783	−	0.119928i	$-0.0382664\pi$
$200$	−4.99273	+	0.269602i	−0.353039	+	0.0190637i
$201$	4.14002			0.292014
$202$	18.2540			1.28435
$203$	3.52156			0.247165
$204$		−	1.00678i		−	0.0704887i
$205$	0.256839	+	9.51970i	0.0179384	+	0.664885i
$206$	−1.52241			−0.106071
$207$	2.37657			0.165183
$208$	0.269602			0.0186935
$209$		−	2.44617i		−	0.169205i
$210$	−0.191923	−	7.11357i	−0.0132439	−	0.490883i
$211$	−0.976050			−0.0671941			−0.0335970	−	0.999435i	$-0.510696\pi$
$211$	−0.976050			−0.0671941			−0.0335970	+	0.999435i	$0.510696\pi$
$212$			3.55039i			0.243842i
$213$			10.9926i			0.753199i
$214$			8.18691i			0.559646i
$215$	−0.414577	−	15.3662i	−0.0282739	−	1.04797i
$216$		−	1.00000i		−	0.0680414i
$217$	11.3838			0.772784
$218$		−	11.5302i		−	0.780925i
$219$	−2.97265			−0.200873
$220$	0.160100	+	5.93406i	0.0107939	+	0.400074i
$221$	−0.271430			−0.0182583
$222$	−5.60415	+	2.36505i	−0.376126	+	0.158732i
$223$		−	19.4559i		−	1.30286i	−0.758707	−	0.651432i	$-0.774169\pi$
$223$		−	19.4559i		−	1.30286i	0.758707	−	0.651432i	$-0.225831\pi$
$224$			3.18244i			0.212636i
$225$	4.99273	−	0.269602i	0.332848	−	0.0179734i
$226$	8.93042			0.594042
$227$	20.5781			1.36582			0.682909	−	0.730504i	$-0.260715\pi$
$227$	20.5781			1.36582			0.682909	+	0.730504i	$0.260715\pi$
$228$	0.921428			0.0610231
$229$	16.8837			1.11571			0.557853	−	0.829940i	$-0.311625\pi$
$229$	16.8837			1.11571			0.557853	+	0.829940i	$0.311625\pi$
$230$	−0.143323	−	5.31224i	−0.00945045	−	0.350279i
$231$	−8.44862			−0.555878
$232$		−	1.10656i		−	0.0726491i
$233$		−	21.3887i		−	1.40122i	−0.713544	−	0.700611i	$-0.752911\pi$
$233$		−	21.3887i		−	1.40122i	0.713544	−	0.700611i	$-0.247089\pi$
$234$	−0.269602			−0.0176244
$235$	−6.86513	+	0.185220i	−0.447832	+	0.0120824i
$236$			3.24508i			0.211236i
$237$	10.1431			0.658863
$238$		−	3.20402i		−	0.207686i
$239$			22.4598i			1.45280i	0.687271	+	0.726401i	$0.258809\pi$
$239$			22.4598i			1.45280i	−0.687271	+	0.726401i	$0.741191\pi$
$240$	−2.23525	+	0.0603067i	−0.144285	+	0.00389278i
$241$		−	7.62427i		−	0.491123i	−0.969381	−	0.245561i	$-0.921028\pi$
$241$		−	7.62427i		−	0.491123i	0.969381	−	0.245561i	$-0.0789723\pi$
$242$	−3.95226			−0.254061
$243$			1.00000i			0.0641500i
$244$		−	2.85126i		−	0.182533i
$245$	−0.188636	−	6.99177i	−0.0120515	−	0.446688i
$246$			4.25889i			0.271537i
$247$		−	0.248419i		−	0.0158065i
$248$		−	3.57707i		−	0.227144i
$249$	−9.43016			−0.597612
$250$	−0.903723	−	11.1438i	−0.0571565	−	0.704793i
$251$			4.40440i			0.278003i	0.990292	+	0.139001i	$0.0443893\pi$
$251$			4.40440i			0.278003i	−0.990292	+	0.139001i	$0.955611\pi$
$252$		−	3.18244i		−	0.200475i
$253$	−6.30922			−0.396657
$254$			3.22594i			0.202413i
$255$	2.25041	−	0.0607156i	0.140926	−	0.00380216i
$256$	1.00000			0.0625000
$257$	28.8644			1.80051			0.900255	−	0.435363i	$-0.143380\pi$
$257$	28.8644			1.80051			0.900255	+	0.435363i	$0.143380\pi$
$258$		−	6.87448i		−	0.427987i
$259$	−17.8349	+	7.52665i	−1.10821	+	0.467683i
$260$	0.0162588	+	0.602628i	0.00100833	+	0.0373734i
$261$			1.10656i			0.0684943i
$262$			17.3542i			1.07215i
$263$		−	2.55084i		−	0.157291i	−0.996903	−	0.0786456i	$-0.974940\pi$
$263$		−	2.55084i		−	0.157291i	0.996903	−	0.0786456i	$-0.0250596\pi$
$264$			2.65476i			0.163389i
$265$	−7.93603	+	0.214112i	−0.487507	+	0.0131528i
$266$	2.93239			0.179797
$267$	12.2141			0.747492
$268$		−	4.14002i		−	0.252892i
$269$	24.0583			1.46686			0.733431	−	0.679764i	$-0.237918\pi$
$269$	24.0583			1.46686			0.733431	+	0.679764i	$0.237918\pi$
$270$	2.23525	−	0.0603067i	0.136033	−	0.00367015i
$271$	−8.19198			−0.497627			−0.248814	−	0.968551i	$-0.580041\pi$
$271$	−8.19198			−0.497627			−0.248814	+	0.968551i	$0.580041\pi$
$272$	−1.00678			−0.0610450
$273$	−0.857992			−0.0519280
$274$		−	2.63659i		−	0.159282i
$275$	−13.2545	+	0.715727i	−0.799275	+	0.0431600i
$276$		−	2.37657i		−	0.143053i
$277$	7.49799			0.450510			0.225255	−	0.974300i	$-0.427678\pi$
$277$	7.49799			0.450510			0.225255	+	0.974300i	$0.427678\pi$
$278$	−1.15632			−0.0693514
$279$			3.57707i			0.214153i
$280$	−7.11357	+	0.191923i	−0.425117	+	0.0114696i
$281$			17.1365i			1.02228i	0.859498	+	0.511139i	$0.170776\pi$
$281$			17.1365i			1.02228i	−0.859498	+	0.511139i	$0.829224\pi$
$282$	−3.07130			−0.182893
$283$	−6.95405			−0.413375			−0.206688	−	0.978407i	$-0.566268\pi$
$283$	−6.95405			−0.413375			−0.206688	+	0.978407i	$0.566268\pi$
$284$	10.9926			0.652290
$285$	0.0555683	+	2.05963i	0.00329158	+	0.122002i
$286$	0.715727			0.0423218
$287$			13.5537i			0.800048i
$288$	−1.00000			−0.0589256
$289$	−15.9864			−0.940376
$290$	2.47344	−	0.0667329i	0.145245	−	0.00391869i
$291$			10.5793i			0.620171i
$292$			2.97265i			0.173961i
$293$		−	19.8208i		−	1.15794i	−0.815349	−	0.578970i	$-0.803455\pi$
$293$		−	19.8208i		−	1.15794i	0.815349	−	0.578970i	$-0.196545\pi$
$294$		−	3.12795i		−	0.182426i
$295$	−7.25357	+	0.195700i	−0.422319	+	0.0113941i
$296$	2.36505	+	5.60415i	0.137466	+	0.325735i
$297$		−	2.65476i		−	0.154045i
$298$	0.905691			0.0524653
$299$	−0.640727			−0.0370542
$300$	−0.269602	−	4.99273i	−0.0155655	−	0.288255i
$301$		−	21.8777i		−	1.26101i
$302$	8.60991			0.495445
$303$			18.2540i			1.04867i
$304$		−	0.921428i		−	0.0528475i
$305$	6.37329	−	0.171950i	0.364933	−	0.00984582i
$306$	1.00678			0.0575538
$307$		−	27.9359i		−	1.59439i	−0.603725	−	0.797193i	$-0.706317\pi$
$307$		−	27.9359i		−	1.59439i	0.603725	−	0.797193i	$-0.293683\pi$
$308$			8.44862i			0.481405i
$309$		−	1.52241i		−	0.0866066i
$310$	7.99566	−	0.215721i	0.454123	−	0.0122521i
$311$			19.8697i			1.12671i	0.826216	+	0.563353i	$0.190489\pi$
$311$			19.8697i			1.12671i	−0.826216	+	0.563353i	$0.809511\pi$
$312$			0.269602i			0.0152632i
$313$	−5.86017			−0.331236			−0.165618	−	0.986190i	$-0.552962\pi$
$313$	−5.86017			−0.331236			−0.165618	+	0.986190i	$0.552962\pi$
$314$			4.84051i			0.273166i
$315$	7.11357	−	0.191923i	0.400804	−	0.0108136i
$316$		−	10.1431i		−	0.570592i
$317$			12.2579i			0.688474i	0.938883	+	0.344237i	$0.111862\pi$
$317$			12.2579i			0.688474i	−0.938883	+	0.344237i	$0.888138\pi$
$318$	−3.55039			−0.199096
$319$		−	2.93765i		−	0.164477i
$320$	0.0603067	+	2.23525i	0.00337125	+	0.124955i
$321$	−8.18691			−0.456949
$322$		−	7.56331i		−	0.421487i
$323$			0.927676i			0.0516173i
$324$	1.00000			0.0555556
$325$	−1.34605	+	0.0726850i	−0.0746652	+	0.00403184i
$326$	−16.2160			−0.898119
$327$	11.5302			0.637622
$328$	4.25889			0.235158
$329$	−9.77424			−0.538871
$330$	−5.93406	+	0.160100i	−0.326659	+	0.00881320i
$331$		−	14.7826i		−	0.812526i	−0.913756	−	0.406263i	$-0.866832\pi$
$331$		−	14.7826i		−	0.812526i	0.913756	−	0.406263i	$-0.133168\pi$
$332$			9.43016i			0.517547i
$333$	−2.36505	−	5.60415i	−0.129604	−	0.307106i
$334$	11.3881			0.623130
$335$	9.25399	−	0.249671i	0.505599	−	0.0136410i
$336$	−3.18244			−0.173617
$337$		−	12.4555i		−	0.678494i	−0.940697	−	0.339247i	$-0.889828\pi$
$337$		−	12.4555i		−	0.678494i	0.940697	−	0.339247i	$-0.110172\pi$
$338$	−12.9273			−0.703153
$339$			8.93042i			0.485034i
$340$	−0.0607156	−	2.25041i	−0.00329277	−	0.122046i
$341$		−	9.49625i		−	0.514251i
$342$			0.921428i			0.0498251i
$343$			12.3226i			0.665356i
$344$	−6.87448			−0.370647
$345$	5.31224	−	0.143323i	0.286002	−	0.00771626i
$346$		−	21.3699i		−	1.14885i
$347$	−3.46810			−0.186177			−0.0930887	−	0.995658i	$-0.529674\pi$
$347$	−3.46810			−0.186177			−0.0930887	+	0.995658i	$0.529674\pi$
$348$	1.10656			0.0593178
$349$	−0.800607			−0.0428555			−0.0214278	−	0.999770i	$-0.506821\pi$
$349$	−0.800607			−0.0428555			−0.0214278	+	0.999770i	$0.506821\pi$
$350$	−0.857992	−	15.8891i	−0.0458616	−	0.849307i
$351$		−	0.269602i		−	0.0143903i
$352$	2.65476			0.141499
$353$	10.6676			0.567779			0.283890	−	0.958857i	$-0.408375\pi$
$353$	10.6676			0.567779			0.283890	+	0.958857i	$0.408375\pi$
$354$	−3.24508			−0.172474
$355$	0.662926	+	24.5712i	0.0351845	+	1.30411i
$356$		−	12.2141i		−	0.647347i
$357$	3.20402			0.169575
$358$		−	1.95979i		−	0.103578i
$359$	−22.0101			−1.16165			−0.580825	−	0.814029i	$-0.697270\pi$
$359$	−22.0101			−1.16165			−0.580825	+	0.814029i	$0.697270\pi$
$360$	−0.0603067	−	2.23525i	−0.00317844	−	0.117808i
$361$	18.1510			0.955314
$362$	6.56630			0.345117
$363$		−	3.95226i		−	0.207440i
$364$			0.857992i			0.0449710i
$365$	−6.64464	+	0.179271i	−0.347796	+	0.00938346i
$366$	2.85126			0.149038
$367$			10.3033i			0.537826i	0.963164	+	0.268913i	$0.0866644\pi$
$367$			10.3033i			0.537826i	−0.963164	+	0.268913i	$0.913336\pi$
$368$	−2.37657			−0.123887
$369$	−4.25889			−0.221709
$370$	−12.3841	+	5.62446i	−0.643818	+	0.292402i
$371$	−11.2989			−0.586611
$372$	3.57707			0.185462
$373$			12.7176i			0.658495i	0.944244	+	0.329247i	$0.106795\pi$
$373$			12.7176i			0.658495i	−0.944244	+	0.329247i	$0.893205\pi$
$374$	−2.67276			−0.138205
$375$	11.1438	−	0.903723i	0.575461	−	0.0466680i
$376$			3.07130i			0.158390i
$377$		−	0.298330i		−	0.0153648i
$378$	3.18244			0.163687
$379$	−14.4925			−0.744430			−0.372215	−	0.928146i	$-0.621402\pi$
$379$	−14.4925			−0.744430			−0.372215	+	0.928146i	$0.621402\pi$
$380$	2.05963	−	0.0555683i	0.105657	−	0.00285059i
$381$	−3.22594			−0.165270
$382$			5.01873i			0.256781i
$383$	−3.52883			−0.180315			−0.0901574	−	0.995928i	$-0.528737\pi$
$383$	−3.52883			−0.180315			−0.0901574	+	0.995928i	$0.528737\pi$
$384$			1.00000i			0.0510310i
$385$	−18.8848	+	0.509508i	−0.962460	+	0.0259669i
$386$	−13.8051			−0.702660
$387$	6.87448			0.349450
$388$	10.5793			0.537084
$389$			15.5504i			0.788438i	0.919017	+	0.394219i	$0.128985\pi$
$389$			15.5504i			0.788438i	−0.919017	+	0.394219i	$0.871015\pi$
$390$	−0.602628	+	0.0162588i	−0.0305153	+	0.000823295i
$391$	2.39269			0.121003
$392$	−3.12795			−0.157986
$393$	−17.3542			−0.875403
$394$		−	13.7617i		−	0.693304i
$395$	22.6723	−	0.611695i	1.14077	−	0.0307777i
$396$	−2.65476			−0.133407
$397$		−	24.1917i		−	1.21415i	−0.794646	−	0.607073i	$-0.792343\pi$
$397$		−	24.1917i		−	1.21415i	0.794646	−	0.607073i	$-0.207657\pi$
$398$		−	3.38359i		−	0.169604i
$399$			2.93239i			0.146803i
$400$	−4.99273	+	0.269602i	−0.249636	+	0.0134801i
$401$		−	1.68192i		−	0.0839913i	−0.999118	−	0.0419956i	$-0.986628\pi$
$401$		−	1.68192i		−	0.0839913i	0.999118	−	0.0419956i	$-0.0133716\pi$
$402$	4.14002			0.206485
$403$		−	0.964383i		−	0.0480393i
$404$	18.2540			0.908171
$405$	0.0603067	+	2.23525i	0.00299666	+	0.111071i
$406$	3.52156			0.174772
$407$	6.27864	+	14.8777i	0.311221	+	0.737459i
$408$		−	1.00678i		−	0.0498431i
$409$			24.1471i			1.19400i	0.802242	+	0.596999i	$0.203640\pi$
$409$			24.1471i			1.19400i	−0.802242	+	0.596999i	$0.796360\pi$
$410$	0.256839	+	9.51970i	0.0126844	+	0.470145i
$411$	2.63659			0.130053
$412$	−1.52241			−0.0750035
$413$	−10.3273			−0.508172
$414$	2.37657			0.116802
$415$	−21.0788	+	0.568702i	−1.03472	+	0.0279165i
$416$	0.269602			0.0132183
$417$		−	1.15632i		−	0.0566252i
$418$		−	2.44617i		−	0.119646i
$419$	−34.4448			−1.68274			−0.841369	−	0.540461i	$-0.818250\pi$
$419$	−34.4448			−1.68274			−0.841369	+	0.540461i	$0.818250\pi$
$420$	−0.191923	−	7.11357i	−0.00936487	−	0.347107i
$421$		−	28.1779i		−	1.37331i	−0.726986	−	0.686653i	$-0.759079\pi$
$421$		−	28.1779i		−	1.37331i	0.726986	−	0.686653i	$-0.240921\pi$
$422$	−0.976050			−0.0475134
$423$		−	3.07130i		−	0.149332i
$424$			3.55039i			0.172422i
$425$	5.02658	−	0.271430i	0.243825	−	0.0131663i
$426$			10.9926i			0.532592i
$427$	9.07397			0.439120
$428$			8.18691i			0.395729i
$429$			0.715727i			0.0345556i
$430$	−0.414577	−	15.3662i	−0.0199927	−	0.741025i
$431$			10.9928i			0.529504i	0.964317	+	0.264752i	$0.0852901\pi$
$431$			10.9928i			0.529504i	−0.964317	+	0.264752i	$0.914710\pi$
$432$		−	1.00000i		−	0.0481125i
$433$			5.86609i			0.281906i	0.990016	+	0.140953i	$0.0450167\pi$
$433$			5.86609i			0.281906i	−0.990016	+	0.140953i	$0.954983\pi$
$434$	11.3838			0.546441
$435$	0.0667329	+	2.47344i	0.00319960	+	0.118592i
$436$		−	11.5302i		−	0.552197i
$437$			2.18984i			0.104754i
$438$	−2.97265			−0.142039
$439$			29.2804i			1.39748i	0.715377	+	0.698739i	$0.246255\pi$
$439$			29.2804i			1.39748i	−0.715377	+	0.698739i	$0.753745\pi$
$440$	0.160100	+	5.93406i	0.00763245	+	0.282895i
$441$	3.12795			0.148950
$442$	−0.271430			−0.0129106
$443$			13.5480i			0.643683i	0.946794	+	0.321841i	$0.104302\pi$
$443$			13.5480i			0.643683i	−0.946794	+	0.321841i	$0.895698\pi$
$444$	−5.60415	+	2.36505i	−0.265961	+	0.112240i
$445$	27.3017	−	0.736593i	1.29422	−	0.0349178i
$446$		−	19.4559i		−	0.921263i
$447$			0.905691i			0.0428377i
$448$			3.18244i			0.150356i
$449$			1.52836i			0.0721280i	0.999349	+	0.0360640i	$0.0114820\pi$
$449$			1.52836i			0.0721280i	−0.999349	+	0.0360640i	$0.988518\pi$
$450$	4.99273	−	0.269602i	0.235359	−	0.0127091i
$451$	11.3063			0.532394
$452$	8.93042			0.420051
$453$			8.60991i			0.404529i
$454$	20.5781			0.965779
$455$	−1.91783	+	0.0517426i	−0.0899093	+	0.00242573i
$456$	0.921428			0.0431498
$457$	−36.6818			−1.71590			−0.857952	−	0.513730i	$-0.828263\pi$
$457$	−36.6818			−1.71590			−0.857952	+	0.513730i	$0.828263\pi$
$458$	16.8837			0.788924
$459$			1.00678i			0.0469925i
$460$	−0.143323	−	5.31224i	−0.00668248	−	0.247685i
$461$			4.98730i			0.232282i	0.993233	+	0.116141i	$0.0370524\pi$
$461$			4.98730i			0.232282i	−0.993233	+	0.116141i	$0.962948\pi$
$462$	−8.44862			−0.393065
$463$	−33.2211			−1.54391			−0.771957	−	0.635675i	$-0.780722\pi$
$463$	−33.2211			−1.54391			−0.771957	+	0.635675i	$0.780722\pi$
$464$		−	1.10656i		−	0.0513707i
$465$	0.215721	+	7.99566i	0.0100038	+	0.370790i
$466$		−	21.3887i		−	0.990813i
$467$	−29.1945			−1.35096			−0.675481	−	0.737377i	$-0.736064\pi$
$467$	−29.1945			−1.35096			−0.675481	+	0.737377i	$0.736064\pi$
$468$	−0.269602			−0.0124623
$469$	13.1754			0.608382
$470$	−6.86513	+	0.185220i	−0.316665	+	0.00854355i
$471$	−4.84051			−0.223039
$472$			3.24508i			0.149367i
$473$	−18.2501			−0.839140
$474$	10.1431			0.465886
$475$	0.248419	+	4.60044i	0.0113982	+	0.211083i
$476$		−	3.20402i		−	0.146856i
$477$		−	3.55039i		−	0.162561i
$478$			22.4598i			1.02729i
$479$		−	33.9326i		−	1.55042i	−0.631705	−	0.775209i	$-0.717645\pi$
$479$		−	33.9326i		−	1.55042i	0.631705	−	0.775209i	$-0.282355\pi$
$480$	−2.23525	+	0.0603067i	−0.102025	+	0.00275261i
$481$	0.637622	+	1.51089i	0.0290731	+	0.0688906i
$482$		−	7.62427i		−	0.347276i
$483$	7.56331			0.344142
$484$	−3.95226			−0.179648
$485$	0.638004	+	23.6475i	0.0289702	+	1.07378i
$486$			1.00000i			0.0453609i
$487$	−26.5071			−1.20115			−0.600576	−	0.799567i	$-0.705062\pi$
$487$	−26.5071			−1.20115			−0.600576	+	0.799567i	$0.705062\pi$
$488$		−	2.85126i		−	0.129070i
$489$		−	16.2160i		−	0.733311i
$490$	−0.188636	−	6.99177i	−0.00852173	−	0.315856i
$491$	18.7959			0.848247			0.424124	−	0.905604i	$-0.360582\pi$
$491$	18.7959			0.848247			0.424124	+	0.905604i	$0.360582\pi$
$492$			4.25889i			0.192006i
$493$			1.11406i			0.0501748i
$494$		−	0.248419i		−	0.0111769i
$495$	−0.160100	−	5.93406i	−0.00719594	−	0.266716i
$496$		−	3.57707i		−	0.160615i
$497$			34.9833i			1.56922i
$498$	−9.43016			−0.422576
$499$			12.2075i			0.546481i	0.961946	+	0.273241i	$0.0880955\pi$
$499$			12.2075i			0.546481i	−0.961946	+	0.273241i	$0.911904\pi$
$500$	−0.903723	−	11.1438i	−0.0404157	−	0.498364i
$501$			11.3881i			0.508783i
$502$			4.40440i			0.196578i
$503$	4.34121			0.193565			0.0967825	−	0.995306i	$-0.469145\pi$
$503$	4.34121			0.193565			0.0967825	+	0.995306i	$0.469145\pi$
$504$		−	3.18244i		−	0.141757i
$505$	1.10084	+	40.8024i	0.0489867	+	1.81568i
$506$	−6.30922			−0.280479
$507$		−	12.9273i		−	0.574122i
$508$			3.22594i			0.143128i
$509$	21.3590			0.946722			0.473361	−	0.880869i	$-0.343041\pi$
$509$	21.3590			0.946722			0.473361	+	0.880869i	$0.343041\pi$
$510$	2.25041	−	0.0607156i	0.0996499	−	0.00268853i
$511$	−9.46030			−0.418499
$512$	1.00000			0.0441942
$513$	−0.921428			−0.0406821
$514$	28.8644			1.27315
$515$	−0.0918112	−	3.40296i	−0.00404568	−	0.149952i
$516$		−	6.87448i		−	0.302632i
$517$			8.15355i			0.358593i
$518$	−17.8349	+	7.52665i	−0.783621	+	0.330702i
$519$	21.3699			0.938034
$520$	0.0162588	+	0.602628i	0.000712994	+	0.0264270i
$521$	−6.52576			−0.285899			−0.142949	−	0.989730i	$-0.545659\pi$
$521$	−6.52576			−0.285899			−0.142949	+	0.989730i	$0.545659\pi$
$522$			1.10656i			0.0484328i
$523$	−2.72424			−0.119123			−0.0595614	−	0.998225i	$-0.518970\pi$
$523$	−2.72424			−0.119123			−0.0595614	+	0.998225i	$0.518970\pi$
$524$			17.3542i			0.758121i
$525$	15.8891	−	0.857992i	0.693456	−	0.0374458i
$526$		−	2.55084i		−	0.111222i
$527$			3.60132i			0.156876i
$528$			2.65476i			0.115534i
$529$	−17.3519			−0.754431
$530$	−7.93603	+	0.214112i	−0.344719	+	0.00930045i
$531$		−	3.24508i		−	0.140824i
$532$	2.93239			0.127135
$533$	1.14820			0.0497342
$534$	12.2141			0.528556
$535$	−18.2998	+	0.493725i	−0.791171	+	0.0213456i
$536$		−	4.14002i		−	0.178821i
$537$	1.95979			0.0845712
$538$	24.0583			1.03723
$539$	−8.30396			−0.357677
$540$	2.23525	−	0.0603067i	0.0961900	−	0.00259519i
$541$		−	16.8353i		−	0.723806i	−0.932216	−	0.361903i	$-0.882127\pi$
$541$		−	16.8353i		−	0.723806i	0.932216	−	0.361903i	$-0.117873\pi$
$542$	−8.19198			−0.351876
$543$			6.56630i			0.281787i
$544$	−1.00678			−0.0431654
$545$	25.7730	−	0.695349i	1.10399	−	0.0297855i
$546$	−0.857992			−0.0367187
$547$	18.7381			0.801184			0.400592	−	0.916257i	$-0.368804\pi$
$547$	18.7381			0.801184			0.400592	+	0.916257i	$0.368804\pi$
$548$		−	2.63659i		−	0.112629i
$549$			2.85126i			0.121689i
$550$	−13.2545	+	0.715727i	−0.565173	+	0.0305187i
$551$	−1.01961			−0.0434370
$552$		−	2.37657i		−	0.101154i
$553$	32.2797			1.37267
$554$	7.49799			0.318559
$555$	−5.62446	−	12.3841i	−0.238745	−	0.525675i
$556$	−1.15632			−0.0490389
$557$	−17.3425			−0.734826			−0.367413	−	0.930058i	$-0.619756\pi$
$557$	−17.3425			−0.734826			−0.367413	+	0.930058i	$0.619756\pi$
$558$			3.57707i			0.151429i
$559$	−1.85337			−0.0783893
$560$	−7.11357	+	0.191923i	−0.300603	+	0.00811021i
$561$		−	2.67276i		−	0.112844i
$562$			17.1365i			0.722860i
$563$	−2.40611			−0.101406			−0.0507028	−	0.998714i	$-0.516146\pi$
$563$	−2.40611			−0.101406			−0.0507028	+	0.998714i	$0.516146\pi$
$564$	−3.07130			−0.129325
$565$	0.538564	+	19.9618i	0.0226575	+	0.839797i
$566$	−6.95405			−0.292300
$567$			3.18244i			0.133650i
$568$	10.9926			0.461239
$569$		−	32.0856i		−	1.34510i	−0.740052	−	0.672550i	$-0.765199\pi$
$569$		−	32.0856i		−	1.34510i	0.740052	−	0.672550i	$-0.234801\pi$
$570$	0.0555683	+	2.05963i	0.00232750	+	0.0862683i
$571$	31.0992			1.30146			0.650731	−	0.759309i	$-0.274463\pi$
$571$	31.0992			1.30146			0.650731	+	0.759309i	$0.274463\pi$
$572$	0.715727			0.0299260
$573$	−5.01873			−0.209660
$574$			13.5537i			0.565720i
$575$	11.8656	−	0.640727i	0.494829	−	0.0267202i
$576$	−1.00000			−0.0416667
$577$	34.7582			1.44700			0.723502	−	0.690323i	$-0.242531\pi$
$577$	34.7582			1.44700			0.723502	+	0.690323i	$0.242531\pi$
$578$	−15.9864			−0.664946
$579$		−	13.8051i		−	0.573720i
$580$	2.47344	−	0.0667329i	0.102704	−	0.00277093i
$581$	−30.0110			−1.24506
$582$			10.5793i			0.438527i
$583$			9.42543i			0.390362i
$584$			2.97265i			0.123009i
$585$	−0.0162588	−	0.602628i	−0.000672218	−	0.0249156i
$586$		−	19.8208i		−	0.818788i
$587$	32.6137			1.34611			0.673056	−	0.739591i	$-0.264981\pi$
$587$	32.6137			1.34611			0.673056	+	0.739591i	$0.264981\pi$
$588$		−	3.12795i		−	0.128995i
$589$	−3.29601			−0.135810
$590$	−7.25357	+	0.195700i	−0.298625	+	0.00805683i
$591$	13.7617			0.566080
$592$	2.36505	+	5.60415i	0.0972031	+	0.230329i
$593$		−	15.1515i		−	0.622197i	−0.950378	−	0.311098i	$-0.899303\pi$
$593$		−	15.1515i		−	0.622197i	0.950378	−	0.311098i	$-0.100697\pi$
$594$		−	2.65476i		−	0.108926i
$595$	7.16181	−	0.193224i	0.293606	−	0.00792141i
$596$	0.905691			0.0370985
$597$	3.38359			0.138481
$598$	−0.640727			−0.0262013
$599$	−14.1826			−0.579485			−0.289743	−	0.957105i	$-0.593570\pi$
$599$	−14.1826			−0.579485			−0.289743	+	0.957105i	$0.593570\pi$
$600$	−0.269602	−	4.99273i	−0.0110064	−	0.203827i
$601$	−40.6657			−1.65879			−0.829395	−	0.558663i	$-0.811315\pi$
$601$	−40.6657			−1.65879			−0.829395	+	0.558663i	$0.811315\pi$
$602$		−	21.8777i		−	0.891667i
$603$			4.14002i			0.168594i
$604$	8.60991			0.350332
$605$	−0.238348	−	8.83430i	−0.00969021	−	0.359165i
$606$			18.2540i			0.741519i
$607$	−13.0571			−0.529973			−0.264987	−	0.964252i	$-0.585368\pi$
$607$	−13.0571			−0.529973			−0.264987	+	0.964252i	$0.585368\pi$
$608$		−	0.921428i		−	0.0373689i
$609$			3.52156i			0.142701i
$610$	6.37329	−	0.171950i	0.258047	−	0.00696205i
$611$			0.828027i			0.0334984i
$612$	1.00678			0.0406967
$613$		−	9.82165i		−	0.396693i	−0.980132	−	0.198346i	$-0.936443\pi$
$613$		−	9.82165i		−	0.396693i	0.980132	−	0.198346i	$-0.0635571\pi$
$614$		−	27.9359i		−	1.12740i
$615$	−9.51970	+	0.256839i	−0.383871	+	0.0103568i
$616$			8.44862i			0.340405i
$617$			11.4558i			0.461194i	0.973049	+	0.230597i	$0.0740679\pi$
$617$			11.4558i			0.461194i	−0.973049	+	0.230597i	$0.925932\pi$
$618$		−	1.52241i		−	0.0612401i
$619$	−9.75342			−0.392023			−0.196011	−	0.980602i	$-0.562799\pi$
$619$	−9.75342			−0.392023			−0.196011	+	0.980602i	$0.562799\pi$
$620$	7.99566	−	0.215721i	0.321113	−	0.00866357i
$621$			2.37657i			0.0953685i
$622$			19.8697i			0.796701i
$623$	38.8707			1.55732
$624$			0.269602i			0.0107927i
$625$	24.8546	−	2.69209i	0.994185	−	0.107684i
$626$	−5.86017			−0.234220
$627$	2.44617			0.0976906
$628$			4.84051i			0.193157i
$629$	−2.38109	−	5.64215i	−0.0949402	−	0.224967i
$630$	7.11357	−	0.191923i	0.283412	−	0.00764638i
$631$			32.3818i			1.28910i	0.764562	+	0.644550i	$0.222955\pi$
$631$			32.3818i			1.28910i	−0.764562	+	0.644550i	$0.777045\pi$
$632$		−	10.1431i		−	0.403469i
$633$		−	0.976050i		−	0.0387945i
$634$			12.2579i			0.486824i
$635$	−7.21080	+	0.194546i	−0.286152	+	0.00772031i
$636$	−3.55039			−0.140782
$637$	−0.843301			−0.0334128
$638$		−	2.93765i		−	0.116303i
$639$	−10.9926			−0.434860
$640$	0.0603067	+	2.23525i	0.00238383	+	0.0883562i
$641$	−43.9408			−1.73556			−0.867779	−	0.496951i	$-0.834453\pi$
$641$	−43.9408			−1.73556			−0.867779	+	0.496951i	$0.834453\pi$
$642$	−8.18691			−0.323112
$643$	23.9367			0.943971			0.471986	−	0.881606i	$-0.343537\pi$
$643$	23.9367			0.943971			0.471986	+	0.881606i	$0.343537\pi$
$644$		−	7.56331i		−	0.298036i
$645$	15.3662	−	0.414577i	0.605044	−	0.0163240i
$646$			0.927676i			0.0364989i
$647$	−27.4294			−1.07836			−0.539180	−	0.842191i	$-0.681266\pi$
$647$	−27.4294			−1.07836			−0.539180	+	0.842191i	$0.681266\pi$
$648$	1.00000			0.0392837
$649$			8.61489i			0.338164i
$650$	−1.34605	+	0.0726850i	−0.0527963	+	0.00285094i
$651$			11.3838i			0.446167i
$652$	−16.2160			−0.635066
$653$	27.1544			1.06263			0.531317	−	0.847173i	$-0.321697\pi$
$653$	27.1544			1.06263			0.531317	+	0.847173i	$0.321697\pi$
$654$	11.5302			0.450867
$655$	−38.7910	+	1.04657i	−1.51569	+	0.0408930i
$656$	4.25889			0.166282
$657$		−	2.97265i		−	0.115974i
$658$	−9.77424			−0.381039
$659$	−33.8741			−1.31955			−0.659774	−	0.751464i	$-0.729348\pi$
$659$	−33.8741			−1.31955			−0.659774	+	0.751464i	$0.729348\pi$
$660$	−5.93406	+	0.160100i	−0.230983	+	0.00623187i
$661$		−	15.3175i		−	0.595782i	−0.954600	−	0.297891i	$-0.903717\pi$
$661$		−	15.3175i		−	0.595782i	0.954600	−	0.297891i	$-0.0962832\pi$
$662$		−	14.7826i		−	0.574542i
$663$		−	0.271430i		−	0.0105415i
$664$			9.43016i			0.365961i
$665$	0.176843	+	6.55465i	0.00685768	+	0.254178i
$666$	−2.36505	−	5.60415i	−0.0916439	−	0.217157i
$667$			2.62982i			0.101827i
$668$	11.3881			0.440619
$669$	19.4559			0.752208
$670$	9.25399	−	0.249671i	0.357513	−	0.00964562i
$671$		−	7.56940i		−	0.292213i
$672$	−3.18244			−0.122765
$673$			30.3436i			1.16966i	0.811156	+	0.584830i	$0.198839\pi$
$673$			30.3436i			1.16966i	−0.811156	+	0.584830i	$0.801161\pi$
$674$		−	12.4555i		−	0.479768i
$675$	0.269602	+	4.99273i	0.0103770	+	0.192170i
$676$	−12.9273			−0.497204
$677$		−	0.714295i		−	0.0274526i	−0.999906	−	0.0137263i	$-0.995631\pi$
$677$		−	0.714295i		−	0.0274526i	0.999906	−	0.0137263i	$-0.00436935\pi$
$678$			8.93042i			0.342971i
$679$			33.6681i			1.29206i
$680$	−0.0607156	−	2.25041i	−0.00232834	−	0.0862993i
$681$			20.5781i			0.788555i
$682$		−	9.49625i		−	0.363630i
$683$	−23.0368			−0.881477			−0.440739	−	0.897635i	$-0.645283\pi$
$683$	−23.0368			−0.881477			−0.440739	+	0.897635i	$0.645283\pi$
$684$			0.921428i			0.0352317i
$685$	5.89345	−	0.159004i	0.225177	−	0.00607523i
$686$			12.3226i			0.470478i
$687$			16.8837i			0.644153i
$688$	−6.87448			−0.262087
$689$			0.957191i			0.0364661i
$690$	5.31224	−	0.143323i	0.202234	−	0.00545622i
$691$	3.22545			0.122702			0.0613510	−	0.998116i	$-0.480459\pi$
$691$	3.22545			0.122702			0.0613510	+	0.998116i	$0.480459\pi$
$692$		−	21.3699i		−	0.812361i
$693$		−	8.44862i		−	0.320937i
$694$	−3.46810			−0.131647
$695$	−0.0697338	−	2.58467i	−0.00264515	−	0.0980421i
$696$	1.10656			0.0419440
$697$	−4.28777			−0.162411
$698$	−0.800607			−0.0303034
$699$	21.3887			0.808996
$700$	−0.857992	−	15.8891i	−0.0324290	−	0.600551i
$701$		−	21.5228i		−	0.812906i	−0.913672	−	0.406453i	$-0.866765\pi$
$701$		−	21.5228i		−	0.812906i	0.913672	−	0.406453i	$-0.133235\pi$
$702$		−	0.269602i		−	0.0101755i
$703$	5.16383	−	2.17923i	0.194757	−	0.0821911i
$704$	2.65476			0.100055
$705$	−0.185220	−	6.86513i	−0.00697578	−	0.258556i
$706$	10.6676			0.401481
$707$			58.0924i			2.18479i
$708$	−3.24508			−0.121957
$709$		−	32.9377i		−	1.23700i	−0.785784	−	0.618501i	$-0.787740\pi$
$709$		−	32.9377i		−	1.23700i	0.785784	−	0.618501i	$-0.212260\pi$
$710$	0.662926	+	24.5712i	0.0248792	+	0.922142i
$711$			10.1431i			0.380395i
$712$		−	12.2141i		−	0.457743i
$713$			8.50116i			0.318371i
$714$	3.20402			0.119908
$715$	0.0431631	+	1.59983i	0.00161421	+	0.0598303i
$716$		−	1.95979i		−	0.0732408i
$717$	−22.4598			−0.838776
$718$	−22.0101			−0.821410
$719$	−44.9906			−1.67787			−0.838933	−	0.544235i	$-0.816820\pi$
$719$	−44.9906			−1.67787			−0.838933	+	0.544235i	$0.816820\pi$
$720$	−0.0603067	−	2.23525i	−0.00224750	−	0.0833030i
$721$		−	4.84497i		−	0.180436i
$722$	18.1510			0.675509
$723$	7.62427			0.283550
$724$	6.56630			0.244035
$725$	0.298330	+	5.52475i	0.0110797	+	0.205184i
$726$		−	3.95226i		−	0.146682i
$727$	−28.0318			−1.03964			−0.519820	−	0.854276i	$-0.674001\pi$
$727$	−28.0318			−1.03964			−0.519820	+	0.854276i	$0.674001\pi$
$728$			0.857992i			0.0317993i
$729$	−1.00000			−0.0370370
$730$	−6.64464	+	0.179271i	−0.245929	+	0.00663511i
$731$	6.92110			0.255986
$732$	2.85126			0.105386
$733$			37.8367i			1.39753i	0.715352	+	0.698764i	$0.246266\pi$
$733$			37.8367i			1.39753i	−0.715352	+	0.698764i	$0.753734\pi$
$734$			10.3033i			0.380300i
$735$	6.99177	−	0.188636i	0.257895	−	0.00695796i
$736$	−2.37657			−0.0876016
$737$		−	10.9907i		−	0.404849i
$738$	−4.25889			−0.156772
$739$	14.8836			0.547503			0.273752	−	0.961800i	$-0.411735\pi$
$739$	14.8836			0.547503			0.273752	+	0.961800i	$0.411735\pi$
$740$	−12.3841	+	5.62446i	−0.455248	+	0.206759i
$741$	0.248419			0.00912588
$742$	−11.2989			−0.414797
$743$		−	16.4127i		−	0.602124i	−0.953605	−	0.301062i	$-0.902659\pi$
$743$		−	16.4127i		−	0.602124i	0.953605	−	0.301062i	$-0.0973411\pi$
$744$	3.57707			0.131142
$745$	0.0546192	+	2.02445i	0.00200109	+	0.0741701i
$746$			12.7176i			0.465626i
$747$		−	9.43016i		−	0.345031i
$748$	−2.67276			−0.0977258
$749$	−26.0544			−0.952007
$750$	11.1438	−	0.903723i	0.406912	−	0.0329993i
$751$	14.2078			0.518450			0.259225	−	0.965817i	$-0.416533\pi$
$751$	14.2078			0.518450			0.259225	+	0.965817i	$0.416533\pi$
$752$			3.07130i			0.111999i
$753$	−4.40440			−0.160505
$754$		−	0.298330i		−	0.0108645i
$755$	0.519235	+	19.2453i	0.0188969	+	0.700410i
$756$	3.18244			0.115744
$757$	35.3081			1.28329			0.641646	−	0.767001i	$-0.278252\pi$
$757$	35.3081			1.28329			0.641646	+	0.767001i	$0.278252\pi$
$758$	−14.4925			−0.526392
$759$		−	6.30922i		−	0.229010i
$760$	2.05963	−	0.0555683i	0.0747105	−	0.00201567i
$761$	−17.6375			−0.639357			−0.319679	−	0.947526i	$-0.603575\pi$
$761$	−17.6375			−0.639357			−0.319679	+	0.947526i	$0.603575\pi$
$762$	−3.22594			−0.116863
$763$	36.6943			1.32842
$764$			5.01873i			0.181571i
$765$	0.0607156	+	2.25041i	0.00219518	+	0.0813638i
$766$	−3.52883			−0.127502
$767$			0.874877i			0.0315900i
$768$			1.00000i			0.0360844i
$769$			24.2914i			0.875971i	0.898982	+	0.437985i	$0.144308\pi$
$769$			24.2914i			0.875971i	−0.898982	+	0.437985i	$0.855692\pi$
$770$	−18.8848	+	0.509508i	−0.680562	+	0.0183614i
$771$			28.8644i			1.03952i
$772$	−13.8051			−0.496856
$773$		−	5.16742i		−	0.185859i	−0.995673	−	0.0929296i	$-0.970377\pi$
$773$		−	5.16742i		−	0.185859i	0.995673	−	0.0929296i	$-0.0296232\pi$
$774$	6.87448			0.247098
$775$	0.964383	+	17.8593i	0.0346417	+	0.641526i
$776$	10.5793			0.379775
$777$	−7.52665	−	17.8349i	−0.270017	−	0.639824i
$778$			15.5504i			0.557510i
$779$		−	3.92426i		−	0.140601i
$780$	−0.602628	+	0.0162588i	−0.0215775	+	0.000582157i
$781$	29.1827			1.04424
$782$	2.39269			0.0855623
$783$	−1.10656			−0.0395452
$784$	−3.12795			−0.111713
$785$	−10.8198	+	0.291915i	−0.386174	+	0.0104189i
$786$	−17.3542			−0.619003
$787$			10.2557i			0.365575i	0.983152	+	0.182787i	$0.0585120\pi$
$787$			10.2557i			0.365575i	−0.983152	+	0.182787i	$0.941488\pi$
$788$		−	13.7617i		−	0.490240i
$789$	2.55084			0.0908122
$790$	22.6723	−	0.611695i	0.806645	−	0.0217631i
$791$			28.4206i			1.01052i
$792$	−2.65476			−0.0943327
$793$		−	0.768703i		−	0.0272975i
$794$		−	24.1917i		−	0.858531i
$795$	−0.214112	−	7.93603i	−0.00759378	−	0.281462i
$796$		−	3.38359i		−	0.119928i
$797$	−6.88255			−0.243792			−0.121896	−	0.992543i	$-0.538898\pi$
$797$	−6.88255			−0.243792			−0.121896	+	0.992543i	$0.538898\pi$
$798$			2.93239i			0.103806i
$799$		−	3.09212i		−	0.109391i
$800$	−4.99273	+	0.269602i	−0.176520	+	0.00953185i
$801$			12.2141i			0.431565i
$802$		−	1.68192i		−	0.0593908i
$803$			7.89168i			0.278491i
$804$	4.14002			0.146007
$805$	16.9059	−	0.456118i	0.595855	−	0.0160760i
$806$		−	0.964383i		−	0.0339689i
$807$			24.0583i			0.846893i
$808$	18.2540			0.642174
$809$			20.9032i			0.734918i	0.930040	+	0.367459i	$0.119772\pi$
$809$			20.9032i			0.734918i	−0.930040	+	0.367459i	$0.880228\pi$
$810$	0.0603067	+	2.23525i	0.00211896	+	0.0785388i
$811$	3.09270			0.108599			0.0542996	−	0.998525i	$-0.482707\pi$
$811$	3.09270			0.108599			0.0542996	+	0.998525i	$0.482707\pi$
$812$	3.52156			0.123583
$813$		−	8.19198i		−	0.287305i
$814$	6.27864	+	14.8777i	0.220066	+	0.521462i
$815$	−0.977931	−	36.2468i	−0.0342554	−	1.26967i
$816$		−	1.00678i		−	0.0352444i
$817$			6.33435i			0.221611i
$818$			24.1471i			0.844283i
$819$		−	0.857992i		−	0.0299807i
$820$	0.256839	+	9.51970i	0.00896922	+	0.332442i
$821$	−37.0887			−1.29440			−0.647202	−	0.762319i	$-0.724061\pi$
$821$	−37.0887			−1.29440			−0.647202	+	0.762319i	$0.724061\pi$
$822$	2.63659			0.0919616
$823$		−	37.1918i		−	1.29642i	−0.761460	−	0.648212i	$-0.775517\pi$
$823$		−	37.1918i		−	1.29642i	0.761460	−	0.648212i	$-0.224483\pi$
$824$	−1.52241			−0.0530355
$825$	−0.715727	−	13.2545i	−0.0249184	−	0.461462i
$826$	−10.3273			−0.359332
$827$	−41.3675			−1.43849			−0.719245	−	0.694757i	$-0.755512\pi$
$827$	−41.3675			−1.43849			−0.719245	+	0.694757i	$0.755512\pi$
$828$	2.37657			0.0825916
$829$		−	46.5378i		−	1.61633i	−0.588960	−	0.808163i	$-0.700462\pi$
$829$		−	46.5378i		−	1.61633i	0.588960	−	0.808163i	$-0.299538\pi$
$830$	−21.0788	+	0.568702i	−0.731656	+	0.0197399i
$831$			7.49799i			0.260102i
$832$	0.269602			0.00934675
$833$	3.14916			0.109112
$834$		−	1.15632i		−	0.0400401i
$835$	0.686779	+	25.4553i	0.0237670	+	0.880918i
$836$		−	2.44617i		−	0.0846025i
$837$	−3.57707			−0.123642
$838$	−34.4448			−1.18988
$839$	46.4169			1.60249			0.801244	−	0.598338i	$-0.204172\pi$
$839$	46.4169			1.60249			0.801244	+	0.598338i	$0.204172\pi$
$840$	−0.191923	−	7.11357i	−0.00662196	−	0.245442i
$841$	27.7755			0.957777
$842$		−	28.1779i		−	0.971074i
$843$	−17.1365			−0.590212
$844$	−0.976050			−0.0335970
$845$	−0.779603	−	28.8958i	−0.0268192	−	0.994047i
$846$		−	3.07130i		−	0.105593i
$847$		−	12.5778i		−	0.432180i
$848$			3.55039i			0.121921i
$849$		−	6.95405i		−	0.238662i
$850$	5.02658	−	0.271430i	0.172410	−	0.00930996i
$851$	−5.62072	−	13.3187i	−0.192676	−	0.456558i
$852$			10.9926i			0.376600i
$853$	6.90342			0.236369			0.118184	−	0.992992i	$-0.462293\pi$
$853$	6.90342			0.236369			0.118184	+	0.992992i	$0.462293\pi$
$854$	9.07397			0.310505
$855$	−2.05963	+	0.0555683i	−0.0704378	+	0.00190040i
$856$			8.18691i			0.279823i
$857$	−37.9271			−1.29556			−0.647782	−	0.761826i	$-0.724303\pi$
$857$	−37.9271			−1.29556			−0.647782	+	0.761826i	$0.724303\pi$
$858$			0.715727i			0.0244345i
$859$			17.7397i			0.605269i	0.953107	+	0.302635i	$0.0978662\pi$
$859$			17.7397i			0.605269i	−0.953107	+	0.302635i	$0.902134\pi$
$860$	−0.414577	−	15.3662i	−0.0141370	−	0.523984i
$861$	−13.5537			−0.461908
$862$			10.9928i			0.374416i
$863$		−	27.5156i		−	0.936641i	−0.883559	−	0.468321i	$-0.844859\pi$
$863$		−	27.5156i		−	0.936641i	0.883559	−	0.468321i	$-0.155141\pi$
$864$		−	1.00000i		−	0.0340207i
$865$	47.7671	−	1.28875i	1.62413	−	0.0438187i
$866$			5.86609i			0.199338i
$867$		−	15.9864i		−	0.542926i
$868$	11.3838			0.386392
$869$		−	26.9274i		−	0.913449i
$870$	0.0667329	+	2.47344i	0.00226246	+	0.0838575i
$871$		−	1.11615i		−	0.0378195i
$872$		−	11.5302i		−	0.390462i
$873$	−10.5793			−0.358056
$874$			2.18984i			0.0740725i
$875$	35.4644	−	2.87605i	1.19892	−	0.0972282i
$876$	−2.97265			−0.100437
$877$		−	11.3304i		−	0.382601i	−0.981532	−	0.191300i	$-0.938730\pi$
$877$		−	11.3304i		−	0.382601i	0.981532	−	0.191300i	$-0.0612705\pi$
$878$			29.2804i			0.988165i
$879$	19.8208			0.668537
$880$	0.160100	+	5.93406i	0.00539696	+	0.200037i
$881$	−44.7924			−1.50909			−0.754547	−	0.656246i	$-0.772143\pi$
$881$	−44.7924			−1.50909			−0.754547	+	0.656246i	$0.772143\pi$
$882$	3.12795			0.105324
$883$	9.32426			0.313786			0.156893	−	0.987616i	$-0.449852\pi$
$883$	9.32426			0.313786			0.156893	+	0.987616i	$0.449852\pi$
$884$	−0.271430			−0.00912917
$885$	−0.195700	−	7.25357i	−0.00657837	−	0.243826i
$886$			13.5480i			0.455152i
$887$		−	13.6961i		−	0.459871i	−0.973206	−	0.229936i	$-0.926148\pi$
$887$		−	13.6961i		−	0.459871i	0.973206	−	0.229936i	$-0.0738515\pi$
$888$	−5.60415	+	2.36505i	−0.188063	+	0.0793660i
$889$	−10.2664			−0.344323
$890$	27.3017	−	0.736593i	0.915154	−	0.0246906i
$891$	2.65476			0.0889378
$892$		−	19.4559i		−	0.651432i
$893$	2.82998			0.0947017
$894$			0.905691i			0.0302908i
$895$	4.38063	−	0.118188i	0.146428	−	0.00395061i
$896$			3.18244i			0.106318i
$897$		−	0.640727i		−	0.0213933i
$898$			1.52836i			0.0510022i
$899$	−3.95824			−0.132015
$900$	4.99273	−	0.269602i	0.166424	−	0.00898672i
$901$		−	3.57447i		−	0.119083i
$902$	11.3063			0.376459
$903$	21.8777			0.728043
$904$	8.93042			0.297021
$905$	0.395992	+	14.6774i	0.0131632	+	0.487892i
$906$			8.60991i			0.286045i
$907$	−12.6822			−0.421105			−0.210552	−	0.977583i	$-0.567526\pi$
$907$	−12.6822			−0.421105			−0.210552	+	0.977583i	$0.567526\pi$
$908$	20.5781			0.682909
$909$	−18.2540			−0.605447
$910$	−1.91783	+	0.0517426i	−0.0635755	+	0.00171525i
$911$			19.0976i			0.632732i	0.948637	+	0.316366i	$0.102463\pi$
$911$			19.0976i			0.632732i	−0.948637	+	0.316366i	$0.897537\pi$
$912$	0.921428			0.0305115
$913$			25.0348i			0.828531i
$914$	−36.6818			−1.21333
$915$	0.171950	+	6.37329i	0.00568449	+	0.210694i
$916$	16.8837			0.557853
$917$	−55.2288			−1.82381
$918$			1.00678i			0.0332287i
$919$			15.0813i			0.497487i	0.968569	+	0.248743i	$0.0800175\pi$
$919$			15.0813i			0.497487i	−0.968569	+	0.248743i	$0.919982\pi$
$920$	−0.143323	−	5.31224i	−0.00472522	−	0.175139i
$921$	27.9359			0.920519
$922$			4.98730i			0.164248i
$923$	2.96362			0.0975487
$924$	−8.44862			−0.277939
$925$	−13.3189	−	27.3424i	−0.437924	−	0.899012i
$926$	−33.2211			−1.09171
$927$	1.52241			0.0500023
$928$		−	1.10656i		−	0.0363246i
$929$	31.1888			1.02327			0.511636	−	0.859202i	$-0.329040\pi$
$929$	31.1888			1.02327			0.511636	+	0.859202i	$0.329040\pi$
$930$	0.215721	+	7.99566i	0.00707377	+	0.262188i
$931$			2.88219i			0.0944598i
$932$		−	21.3887i		−	0.700611i
$933$	−19.8697			−0.650504
$934$	−29.1945			−0.955274
$935$	−0.161185	−	5.97430i	−0.00527132	−	0.195380i
$936$	−0.269602			−0.00881220
$937$		−	41.5294i		−	1.35671i	−0.734737	−	0.678353i	$-0.762694\pi$
$937$		−	41.5294i		−	1.35671i	0.734737	−	0.678353i	$-0.237306\pi$
$938$	13.1754			0.430191
$939$		−	5.86017i		−	0.191239i
$940$	−6.86513	+	0.185220i	−0.223916	+	0.00604120i
$941$	−28.2723			−0.921650			−0.460825	−	0.887491i	$-0.652446\pi$
$941$	−28.2723			−0.921650			−0.460825	+	0.887491i	$0.652446\pi$
$942$	−4.84051			−0.157712
$943$	−10.1216			−0.329603
$944$			3.24508i			0.105618i
$945$	0.191923	+	7.11357i	0.00624324	+	0.231405i
$946$	−18.2501			−0.593362
$947$	16.9766			0.551664			0.275832	−	0.961206i	$-0.411047\pi$
$947$	16.9766			0.551664			0.275832	+	0.961206i	$0.411047\pi$
$948$	10.1431			0.329431
$949$			0.801432i			0.0260156i
$950$	0.248419	+	4.60044i	0.00805976	+	0.149258i
$951$	−12.2579			−0.397490
$952$		−	3.20402i		−	0.103843i
$953$		−	16.4263i		−	0.532100i	−0.963959	−	0.266050i	$-0.914281\pi$
$953$		−	16.4263i		−	0.532100i	0.963959	−	0.266050i	$-0.0857187\pi$
$954$		−	3.55039i		−	0.114948i
$955$	−11.2181	+	0.302663i	−0.363010	+	0.00979394i
$956$			22.4598i			0.726401i
$957$	2.93765			0.0949606
$958$		−	33.9326i		−	1.09631i
$959$	8.39080			0.270953
$960$	−2.23525	+	0.0603067i	−0.0721425	+	0.00194639i
$961$	18.2046			0.587245
$962$	0.637622	+	1.51089i	0.0205578	+	0.0487130i
$963$		−	8.18691i		−	0.263820i
$964$		−	7.62427i		−	0.245561i
$965$	−0.832539	−	30.8579i	−0.0268004	−	0.993350i
$966$	7.56331			0.243345
$967$	−43.4629			−1.39767			−0.698837	−	0.715281i	$-0.746299\pi$
$967$	−43.4629			−1.39767			−0.698837	+	0.715281i	$0.746299\pi$
$968$	−3.95226			−0.127030
$969$	−0.927676			−0.0298013
$970$	0.638004	+	23.6475i	0.0204851	+	0.759275i
$971$	−10.5655			−0.339064			−0.169532	−	0.985525i	$-0.554226\pi$
$971$	−10.5655			−0.339064			−0.169532	+	0.985525i	$0.554226\pi$
$972$			1.00000i			0.0320750i
$973$		−	3.67992i		−	0.117973i
$974$	−26.5071			−0.849343
$975$	−0.0726850	−	1.34605i	−0.00232778	−	0.0431080i
$976$		−	2.85126i		−	0.0912665i
$977$	19.5444			0.625280			0.312640	−	0.949872i	$-0.398787\pi$
$977$	19.5444			0.625280			0.312640	+	0.949872i	$0.398787\pi$
$978$		−	16.2160i		−	0.518529i
$979$		−	32.4255i		−	1.03632i
$980$	−0.188636	−	6.99177i	−0.00602577	−	0.223344i
$981$			11.5302i			0.368131i
$982$	18.7959			0.599801
$983$		−	33.0473i		−	1.05405i	−0.849851	−	0.527023i	$-0.823308\pi$
$983$		−	33.0473i		−	1.05405i	0.849851	−	0.527023i	$-0.176692\pi$
$984$			4.25889i			0.135768i
$985$	30.7609	−	0.829922i	0.980123	−	0.0264435i
$986$			1.11406i			0.0354790i
$987$		−	9.77424i		−	0.311117i
$988$		−	0.248419i		−	0.00790325i
$989$	16.3377			0.519509
$990$	−0.160100	−	5.93406i	−0.00508830	−	0.188597i
$991$		−	60.8732i		−	1.93370i	−0.255341	−	0.966851i	$-0.582188\pi$
$991$		−	60.8732i		−	1.93370i	0.255341	−	0.966851i	$-0.417812\pi$
$992$		−	3.57707i		−	0.113572i
$993$	14.7826			0.469112
$994$			34.9833i			1.10960i
$995$	7.56318	−	0.204053i	0.239769	−	0.00646892i
$996$	−9.43016			−0.298806
$997$	56.3795			1.78556			0.892779	−	0.450495i	$-0.148753\pi$
$997$	56.3795			1.78556			0.892779	+	0.450495i	$0.148753\pi$
$998$			12.2075i			0.386421i
$999$	5.60415	−	2.36505i	0.177308	−	0.0748269i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1110.2.e.d.739.12	yes	16
3.2	odd	2		3330.2.e.e.739.9		16
5.4	even	2		1110.2.e.c.739.5	✓	16
15.14	odd	2		3330.2.e.f.739.7		16
37.36	even	2		1110.2.e.c.739.13	yes	16
111.110	odd	2		3330.2.e.f.739.8		16
185.184	even	2	inner	1110.2.e.d.739.4	yes	16
555.554	odd	2		3330.2.e.e.739.10		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1110.2.e.c.739.5	✓	16	5.4	even	2
1110.2.e.c.739.13	yes	16	37.36	even	2
1110.2.e.d.739.4	yes	16	185.184	even	2	inner
1110.2.e.d.739.12	yes	16	1.1	even	1	trivial
3330.2.e.e.739.9		16	3.2	odd	2
3330.2.e.e.739.10		16	555.554	odd	2
3330.2.e.f.739.7		16	15.14	odd	2
3330.2.e.f.739.8		16	111.110	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1110.e (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.00000i q^{3} +1.00000 q^{4} +(0.0603067 + 2.23525i) q^{5} +1.00000i q^{6} +3.18244i q^{7} +1.00000 q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.00000i q^{3} +1.00000 q^{4} +(0.0603067 + 2.23525i) q^{5} +1.00000i q^{6} +3.18244i q^{7} +1.00000 q^{8} -1.00000 q^{9} +(0.0603067 + 2.23525i) q^{10} +2.65476 q^{11} +1.00000i q^{12} +0.269602 q^{13} +3.18244i q^{14} +(-2.23525 + 0.0603067i) q^{15} +1.00000 q^{16} -1.00678 q^{17} -1.00000 q^{18} -0.921428i q^{19} +(0.0603067 + 2.23525i) q^{20} -3.18244 q^{21} +2.65476 q^{22} -2.37657 q^{23} +1.00000i q^{24} +(-4.99273 + 0.269602i) q^{25} +0.269602 q^{26} -1.00000i q^{27} +3.18244i q^{28} -1.10656i q^{29} +(-2.23525 + 0.0603067i) q^{30} -3.57707i q^{31} +1.00000 q^{32} +2.65476i q^{33} -1.00678 q^{34} +(-7.11357 + 0.191923i) q^{35} -1.00000 q^{36} +(2.36505 + 5.60415i) q^{37} -0.921428i q^{38} +0.269602i q^{39} +(0.0603067 + 2.23525i) q^{40} +4.25889 q^{41} -3.18244 q^{42} -6.87448 q^{43} +2.65476 q^{44} +(-0.0603067 - 2.23525i) q^{45} -2.37657 q^{46} +3.07130i q^{47} +1.00000i q^{48} -3.12795 q^{49} +(-4.99273 + 0.269602i) q^{50} -1.00678i q^{51} +0.269602 q^{52} +3.55039i q^{53} -1.00000i q^{54} +(0.160100 + 5.93406i) q^{55} +3.18244i q^{56} +0.921428 q^{57} -1.10656i q^{58} +3.24508i q^{59} +(-2.23525 + 0.0603067i) q^{60} -2.85126i q^{61} -3.57707i q^{62} -3.18244i q^{63} +1.00000 q^{64} +(0.0162588 + 0.602628i) q^{65} +2.65476i q^{66} -4.14002i q^{67} -1.00678 q^{68} -2.37657i q^{69} +(-7.11357 + 0.191923i) q^{70} +10.9926 q^{71} -1.00000 q^{72} +2.97265i q^{73} +(2.36505 + 5.60415i) q^{74} +(-0.269602 - 4.99273i) q^{75} -0.921428i q^{76} +8.44862i q^{77} +0.269602i q^{78} -10.1431i q^{79} +(0.0603067 + 2.23525i) q^{80} +1.00000 q^{81} +4.25889 q^{82} +9.43016i q^{83} -3.18244 q^{84} +(-0.0607156 - 2.25041i) q^{85} -6.87448 q^{86} +1.10656 q^{87} +2.65476 q^{88} -12.2141i q^{89} +(-0.0603067 - 2.23525i) q^{90} +0.857992i q^{91} -2.37657 q^{92} +3.57707 q^{93} +3.07130i q^{94} +(2.05963 - 0.0555683i) q^{95} +1.00000i q^{96} +10.5793 q^{97} -3.12795 q^{98} -2.65476 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 16 q^{2} + 16 q^{4} + 2 q^{5} + 16 q^{8} - 16 q^{9}+O(q^{10}) \) 16 * q + 16 * q^2 + 16 * q^4 + 2 * q^5 + 16 * q^8 - 16 * q^9	\( 16 q + 16 q^{2} + 16 q^{4} + 2 q^{5} + 16 q^{8} - 16 q^{9} + 2 q^{10} + 2 q^{11} - 6 q^{15} + 16 q^{16} + 38 q^{17} - 16 q^{18} + 2 q^{20} + 6 q^{21} + 2 q^{22} + 20 q^{23} - 4 q^{25} - 6 q^{30} + 16 q^{32} + 38 q^{34} + 10 q^{35} - 16 q^{36} + 4 q^{37} + 2 q^{40} - 6 q^{41} + 6 q^{42} + 2 q^{43} + 2 q^{44} - 2 q^{45} + 20 q^{46} - 18 q^{49} - 4 q^{50} - 20 q^{55} - 16 q^{57} - 6 q^{60} + 16 q^{64} + 12 q^{65} + 38 q^{68} + 10 q^{70} - 24 q^{71} - 16 q^{72} + 4 q^{74} + 2 q^{80} + 16 q^{81} - 6 q^{82} + 6 q^{84} + 2 q^{86} - 2 q^{87} + 2 q^{88} - 2 q^{90} + 20 q^{92} - 22 q^{93} - 16 q^{95} - 38 q^{97} - 18 q^{98} - 2 q^{99}+O(q^{100}) \) 16 * q + 16 * q^2 + 16 * q^4 + 2 * q^5 + 16 * q^8 - 16 * q^9 + 2 * q^10 + 2 * q^11 - 6 * q^15 + 16 * q^16 + 38 * q^17 - 16 * q^18 + 2 * q^20 + 6 * q^21 + 2 * q^22 + 20 * q^23 - 4 * q^25 - 6 * q^30 + 16 * q^32 + 38 * q^34 + 10 * q^35 - 16 * q^36 + 4 * q^37 + 2 * q^40 - 6 * q^41 + 6 * q^42 + 2 * q^43 + 2 * q^44 - 2 * q^45 + 20 * q^46 - 18 * q^49 - 4 * q^50 - 20 * q^55 - 16 * q^57 - 6 * q^60 + 16 * q^64 + 12 * q^65 + 38 * q^68 + 10 * q^70 - 24 * q^71 - 16 * q^72 + 4 * q^74 + 2 * q^80 + 16 * q^81 - 6 * q^82 + 6 * q^84 + 2 * q^86 - 2 * q^87 + 2 * q^88 - 2 * q^90 + 20 * q^92 - 22 * q^93 - 16 * q^95 - 38 * q^97 - 18 * q^98 - 2 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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