LMFDB - Embedded newform 1110.2.h.g.961.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1110,2,Mod(961,1110)]

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, 0, 1]))

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

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

chi := DirichletCharacter("1110.961");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$8.86339462436$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 20x^{6} + 132x^{4} + 297x^{2} + 64 $ x^8 + 20x^6 + 132x^4 + 297*x^2 + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			961.7
Root			$2.87151i$ of defining polynomial
Character	$\chi$	$=$	1110.961
Dual form			1110.2.h.g.961.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.00000i q^{2} +1.00000 q^{3} -1.00000 q^{4} -1.00000i q^{5} +1.00000i q^{6} +0.374052 q^{7} -1.00000i q^{8} +1.00000 q^{9} +1.00000 q^{10} -6.11707 q^{11} -1.00000 q^{12} -5.44814i q^{13} +0.374052i q^{14} -1.00000i q^{15} +1.00000 q^{16} -2.37405i q^{17} +1.00000i q^{18} -1.70513i q^{19} +1.00000i q^{20} +0.374052 q^{21} -6.11707i q^{22} -5.44814i q^{23} -1.00000i q^{24} -1.00000 q^{25} +5.44814 q^{26} +1.00000 q^{27} -0.374052 q^{28} +4.41194i q^{29} +1.00000 q^{30} -3.07409i q^{31} +1.00000i q^{32} -6.11707 q^{33} +2.37405 q^{34} -0.374052i q^{35} -1.00000 q^{36} +(2.70513 + 5.44814i) q^{37} +1.70513 q^{38} -5.44814i q^{39} -1.00000 q^{40} +3.07409 q^{41} +0.374052i q^{42} -7.82220i q^{43} +6.11707 q^{44} -1.00000i q^{45} +5.44814 q^{46} -13.3874 q^{47} +1.00000 q^{48} -6.86009 q^{49} -1.00000i q^{50} -2.37405i q^{51} +5.44814i q^{52} +2.37405 q^{53} +1.00000i q^{54} +6.11707i q^{55} -0.374052i q^{56} -1.70513i q^{57} -4.41194 q^{58} -10.8963i q^{59} +1.00000i q^{60} +4.07918i q^{61} +3.07409 q^{62} +0.374052 q^{63} -1.00000 q^{64} -5.44814 q^{65} -6.11707i q^{66} +10.1482 q^{67} +2.37405i q^{68} -5.44814i q^{69} +0.374052 q^{70} +4.74810 q^{71} -1.00000i q^{72} +8.19625 q^{73} +(-5.44814 + 2.70513i) q^{74} -1.00000 q^{75} +1.70513i q^{76} -2.28810 q^{77} +5.44814 q^{78} -12.1482i q^{79} -1.00000i q^{80} +1.00000 q^{81} +3.07409i q^{82} +6.78599 q^{83} -0.374052 q^{84} -2.37405 q^{85} +7.82220 q^{86} +4.41194i q^{87} +6.11707i q^{88} -0.551855i q^{89} +1.00000 q^{90} -2.03789i q^{91} +5.44814i q^{92} -3.07409i q^{93} -13.3874i q^{94} -1.70513 q^{95} +1.00000i q^{96} -8.15496i q^{97} -6.86009i q^{98} -6.11707 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 8 q^{3} - 8 q^{4} - 4 q^{7} + 8 q^{9} + 8 q^{10} - 4 q^{11} - 8 q^{12} + 8 q^{16} - 4 q^{21} - 8 q^{25} + 2 q^{26} + 8 q^{27} + 4 q^{28} + 8 q^{30} - 4 q^{33} + 12 q^{34} - 8 q^{36} + 18 q^{37} + 10 q^{38}+ \cdots - 4 q^{99}+O(q^{100}) $ 8 * q + 8 * q^3 - 8 * q^4 - 4 * q^7 + 8 * q^9 + 8 * q^10 - 4 * q^11 - 8 * q^12 + 8 * q^16 - 4 * q^21 - 8 * q^25 + 2 * q^26 + 8 * q^27 + 4 * q^28 + 8 * q^30 - 4 * q^33 + 12 * q^34 - 8 * q^36 + 18 * q^37 + 10 * q^38 - 8 * q^40 - 10 * q^41 + 4 * q^44 + 2 * q^46 + 28 * q^47 + 8 * q^48 + 28 * q^49 + 12 * q^53 + 6 * q^58 - 10 * q^62 - 4 * q^63 - 8 * q^64 - 2 * q^65 + 12 * q^67 - 4 * q^70 + 24 * q^71 + 10 * q^73 - 2 * q^74 - 8 * q^75 - 32 * q^77 + 2 * q^78 + 8 * q^81 + 6 * q^83 + 4 * q^84 - 12 * q^85 + 14 * q^86 + 8 * q^90 - 10 * q^95 - 4 * q^99

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 $

$2$			1.00000i			0.707107i
$2$			1.00000i			0.707107i
$3$	1.00000			0.577350
$3$	1.00000			0.577350
$4$	−1.00000			−0.500000
$5$		−	1.00000i		−	0.447214i
$5$		−	1.00000i		−	0.447214i
$6$			1.00000i			0.408248i
$7$	0.374052			0.141378			0.0706892	−	0.997498i	$-0.477480\pi$
$7$	0.374052			0.141378			0.0706892	+	0.997498i	$0.477480\pi$
$8$		−	1.00000i		−	0.353553i
$9$	1.00000			0.333333
$10$	1.00000			0.316228
$11$	−6.11707			−1.84437			−0.922183	−	0.386754i	$-0.873596\pi$
$11$	−6.11707			−1.84437			−0.922183	+	0.386754i	$0.873596\pi$
$12$	−1.00000			−0.288675
$13$		−	5.44814i		−	1.51104i	−0.655124	−	0.755522i	$-0.727383\pi$
$13$		−	5.44814i		−	1.51104i	0.655124	−	0.755522i	$-0.272617\pi$
$14$			0.374052i			0.0999696i
$15$		−	1.00000i		−	0.258199i
$16$	1.00000			0.250000
$17$		−	2.37405i		−	0.575792i	−0.957662	−	0.287896i	$-0.907044\pi$
$17$		−	2.37405i		−	0.575792i	0.957662	−	0.287896i	$-0.0929558\pi$
$18$			1.00000i			0.235702i
$19$		−	1.70513i		−	0.391183i	−0.980685	−	0.195592i	$-0.937337\pi$
$19$		−	1.70513i		−	0.391183i	0.980685	−	0.195592i	$-0.0626627\pi$
$20$			1.00000i			0.223607i
$21$	0.374052			0.0816248
$22$		−	6.11707i		−	1.30416i
$23$		−	5.44814i		−	1.13602i	−0.823023	−	0.568008i	$-0.807714\pi$
$23$		−	5.44814i		−	1.13602i	0.823023	−	0.568008i	$-0.192286\pi$
$24$		−	1.00000i		−	0.204124i
$25$	−1.00000			−0.200000
$26$	5.44814			1.06847
$27$	1.00000			0.192450
$28$	−0.374052			−0.0706892
$29$			4.41194i			0.819277i	0.912248	+	0.409638i	$0.134345\pi$
$29$			4.41194i			0.819277i	−0.912248	+	0.409638i	$0.865655\pi$
$30$	1.00000			0.182574
$31$		−	3.07409i		−	0.552123i	−0.961140	−	0.276062i	$-0.910971\pi$
$31$		−	3.07409i		−	0.552123i	0.961140	−	0.276062i	$-0.0890294\pi$
$32$			1.00000i			0.176777i
$33$	−6.11707			−1.06484
$34$	2.37405			0.407147
$35$		−	0.374052i		−	0.0632263i
$36$	−1.00000			−0.166667
$37$	2.70513	+	5.44814i	0.444720	+	0.895669i
$37$	2.70513	+	5.44814i	0.444720	+	0.895669i
$38$	1.70513			0.276608
$39$		−	5.44814i		−	0.872401i
$40$	−1.00000			−0.158114
$41$	3.07409			0.480093			0.240046	−	0.970761i	$-0.422837\pi$
$41$	3.07409			0.480093			0.240046	+	0.970761i	$0.422837\pi$
$42$			0.374052i			0.0577175i
$43$		−	7.82220i		−	1.19287i	−0.802660	−	0.596437i	$-0.796583\pi$
$43$		−	7.82220i		−	1.19287i	0.802660	−	0.596437i	$-0.203417\pi$
$44$	6.11707			0.922183
$45$		−	1.00000i		−	0.149071i
$46$	5.44814			0.803285
$47$	−13.3874			−1.95275			−0.976377	−	0.216073i	$-0.930675\pi$
$47$	−13.3874			−1.95275			−0.976377	+	0.216073i	$0.930675\pi$
$48$	1.00000			0.144338
$49$	−6.86009			−0.980012
$50$		−	1.00000i		−	0.141421i
$51$		−	2.37405i		−	0.332434i
$52$			5.44814i			0.755522i
$53$	2.37405			0.326101			0.163051	−	0.986618i	$-0.447867\pi$
$53$	2.37405			0.326101			0.163051	+	0.986618i	$0.447867\pi$
$54$			1.00000i			0.136083i
$55$			6.11707i			0.824825i
$56$		−	0.374052i		−	0.0499848i
$57$		−	1.70513i		−	0.225850i
$58$	−4.41194			−0.579316
$59$		−	10.8963i		−	1.41858i	−0.704919	−	0.709288i	$-0.749017\pi$
$59$		−	10.8963i		−	1.41858i	0.704919	−	0.709288i	$-0.250983\pi$
$60$			1.00000i			0.129099i
$61$			4.07918i			0.522285i	0.965300	+	0.261143i	$0.0840993\pi$
$61$			4.07918i			0.522285i	−0.965300	+	0.261143i	$0.915901\pi$
$62$	3.07409			0.390410
$63$	0.374052			0.0471261
$64$	−1.00000			−0.125000
$65$	−5.44814			−0.675759
$66$		−	6.11707i		−	0.752959i
$67$	10.1482			1.23980			0.619899	−	0.784682i	$-0.287174\pi$
$67$	10.1482			1.23980			0.619899	+	0.784682i	$0.287174\pi$
$68$			2.37405i			0.287896i
$69$		−	5.44814i		−	0.655880i
$70$	0.374052			0.0447077
$71$	4.74810			0.563496			0.281748	−	0.959488i	$-0.409086\pi$
$71$	4.74810			0.563496			0.281748	+	0.959488i	$0.409086\pi$
$72$		−	1.00000i		−	0.117851i
$73$	8.19625			0.959298			0.479649	−	0.877460i	$-0.340764\pi$
$73$	8.19625			0.959298			0.479649	+	0.877460i	$0.340764\pi$
$74$	−5.44814	+	2.70513i	−0.633334	+	0.314465i
$75$	−1.00000			−0.115470
$76$			1.70513i			0.195592i
$77$	−2.28810			−0.260753
$78$	5.44814			0.616881
$79$		−	12.1482i		−	1.36678i	−0.730055	−	0.683389i	$-0.760505\pi$
$79$		−	12.1482i		−	1.36678i	0.730055	−	0.683389i	$-0.239495\pi$
$80$		−	1.00000i		−	0.111803i
$81$	1.00000			0.111111
$82$			3.07409i			0.339477i
$83$	6.78599			0.744859			0.372430	−	0.928060i	$-0.378525\pi$
$83$	6.78599			0.744859			0.372430	+	0.928060i	$0.378525\pi$
$84$	−0.374052			−0.0408124
$85$	−2.37405			−0.257502
$86$	7.82220			0.843489
$87$			4.41194i			0.473010i
$88$			6.11707i			0.652082i
$89$		−	0.551855i		−	0.0584965i	−0.999572	−	0.0292483i	$-0.990689\pi$
$89$		−	0.551855i		−	0.0584965i	0.999572	−	0.0292483i	$-0.00931134\pi$
$90$	1.00000			0.105409
$91$		−	2.03789i		−	0.213629i
$92$			5.44814i			0.568008i
$93$		−	3.07409i		−	0.318769i
$94$		−	13.3874i		−	1.38081i
$95$	−1.70513			−0.174942
$96$			1.00000i			0.102062i
$97$		−	8.15496i		−	0.828010i	−0.910275	−	0.414005i	$-0.864130\pi$
$97$		−	8.15496i		−	0.828010i	0.910275	−	0.414005i	$-0.135870\pi$
$98$		−	6.86009i		−	0.692973i
$99$	−6.11707			−0.614789
$100$	1.00000			0.100000
$101$	3.74302			0.372444			0.186222	−	0.982508i	$-0.440376\pi$
$101$	3.74302			0.372444			0.186222	+	0.982508i	$0.440376\pi$
$102$	2.37405			0.235066
$103$			8.49112i			0.836655i	0.908296	+	0.418327i	$0.137384\pi$
$103$			8.49112i			0.836655i	−0.908296	+	0.418327i	$0.862616\pi$
$104$	−5.44814			−0.534235
$105$		−	0.374052i		−	0.0365037i
$106$			2.37405i			0.230588i
$107$	−17.4481			−1.68678			−0.843388	−	0.537305i	$-0.819442\pi$
$107$	−17.4481			−1.68678			−0.843388	+	0.537305i	$0.819442\pi$
$108$	−1.00000			−0.0962250
$109$			8.62086i			0.825729i	0.910793	+	0.412864i	$0.135472\pi$
$109$			8.62086i			0.825729i	−0.910793	+	0.412864i	$0.864528\pi$
$110$	−6.11707			−0.583240
$111$	2.70513	+	5.44814i	0.256759	+	0.517115i
$112$	0.374052			0.0353446
$113$			18.7185i			1.76089i	0.474151	+	0.880444i	$0.342755\pi$
$113$			18.7185i			1.76089i	−0.474151	+	0.880444i	$0.657245\pi$
$114$	1.70513			0.159700
$115$	−5.44814			−0.508042
$116$		−	4.41194i		−	0.409638i
$117$		−	5.44814i		−	0.503681i
$118$	10.8963			1.00308
$119$		−	0.888018i		−	0.0814045i
$120$	−1.00000			−0.0912871
$121$	26.4185			2.40168
$122$	−4.07918			−0.369312
$123$	3.07409			0.277182
$124$			3.07409i			0.276062i
$125$			1.00000i			0.0894427i
$126$			0.374052i			0.0333232i
$127$	16.1861			1.43628			0.718141	−	0.695898i	$-0.244993\pi$
$127$	16.1861			1.43628			0.718141	+	0.695898i	$0.244993\pi$
$128$		−	1.00000i		−	0.0883883i
$129$		−	7.82220i		−	0.688706i
$130$		−	5.44814i		−	0.477834i
$131$			10.8963i			0.952013i	0.879442	+	0.476007i	$0.157916\pi$
$131$			10.8963i			0.952013i	−0.879442	+	0.476007i	$0.842084\pi$
$132$	6.11707			0.532422
$133$		−	0.637806i		−	0.0553048i
$134$			10.1482i			0.876670i
$135$		−	1.00000i		−	0.0860663i
$136$	−2.37405			−0.203573
$137$	0.332760			0.0284296			0.0142148	−	0.999899i	$-0.495475\pi$
$137$	0.332760			0.0284296			0.0142148	+	0.999899i	$0.495475\pi$
$138$	5.44814			0.463777
$139$	−13.8980			−1.17881			−0.589405	−	0.807837i	$-0.700638\pi$
$139$	−13.8980			−1.17881			−0.589405	+	0.807837i	$0.700638\pi$
$140$			0.374052i			0.0316132i
$141$	−13.3874			−1.12742
$142$			4.74810i			0.398452i
$143$			33.3267i			2.78692i
$144$	1.00000			0.0833333
$145$	4.41194			0.366392
$146$			8.19625i			0.678326i
$147$	−6.86009			−0.565810
$148$	−2.70513	−	5.44814i	−0.222360	−	0.447835i
$149$	−11.9014			−0.974999			−0.487499	−	0.873123i	$-0.662091\pi$
$149$	−11.9014			−0.974999			−0.487499	+	0.873123i	$0.662091\pi$
$150$		−	1.00000i		−	0.0816497i
$151$	18.4304			1.49984			0.749922	−	0.661527i	$-0.230091\pi$
$151$	18.4304			1.49984			0.749922	+	0.661527i	$0.230091\pi$
$152$	−1.70513			−0.138304
$153$		−	2.37405i		−	0.191931i
$154$		−	2.28810i		−	0.184380i
$155$	−3.07409			−0.246917
$156$			5.44814i			0.436201i
$157$	7.98056			0.636918			0.318459	−	0.947937i	$-0.396835\pi$
$157$	7.98056			0.636918			0.318459	+	0.947937i	$0.396835\pi$
$158$	12.1482			0.966458
$159$	2.37405			0.188275
$160$	1.00000			0.0790569
$161$		−	2.03789i		−	0.160608i
$162$			1.00000i			0.0785674i
$163$		−	9.86009i		−	0.772301i	−0.922436	−	0.386151i	$-0.873804\pi$
$163$		−	9.86009i		−	0.772301i	0.922436	−	0.386151i	$-0.126196\pi$
$164$	−3.07409			−0.240046
$165$			6.11707i			0.476213i
$166$			6.78599i			0.526695i
$167$			22.4304i			1.73572i	0.496813	+	0.867858i	$0.334504\pi$
$167$			22.4304i			1.73572i	−0.496813	+	0.867858i	$0.665496\pi$
$168$		−	0.374052i		−	0.0288587i
$169$	−16.6823			−1.28325
$170$		−	2.37405i		−	0.182081i
$171$		−	1.70513i		−	0.130394i
$172$			7.82220i			0.596437i
$173$	−22.7665			−1.73091			−0.865454	−	0.500988i	$-0.832970\pi$
$173$	−22.7665			−1.73091			−0.865454	+	0.500988i	$0.832970\pi$
$174$	−4.41194			−0.334468
$175$	−0.374052			−0.0282757
$176$	−6.11707			−0.461091
$177$		−	10.8963i		−	0.819015i
$178$	0.551855			0.0413633
$179$		−	11.1304i		−	0.831927i	−0.909381	−	0.415964i	$-0.863444\pi$
$179$		−	11.1304i		−	0.831927i	0.909381	−	0.415964i	$-0.136556\pi$
$180$			1.00000i			0.0745356i
$181$	−15.3378			−1.14005			−0.570027	−	0.821626i	$-0.693067\pi$
$181$	−15.3378			−1.14005			−0.570027	+	0.821626i	$0.693067\pi$
$182$	2.03789			0.151058
$183$			4.07918i			0.301542i
$184$	−5.44814			−0.401643
$185$	5.44814	−	2.70513i	0.400556	−	0.198885i
$186$	3.07409			0.225403
$187$			14.5222i			1.06197i
$188$	13.3874			0.976377
$189$	0.374052			0.0272083
$190$		−	1.70513i		−	0.123703i
$191$		−	12.0184i		−	0.869624i	−0.900521	−	0.434812i	$-0.856815\pi$
$191$		−	12.0184i		−	0.869624i	0.900521	−	0.434812i	$-0.143185\pi$
$192$	−1.00000			−0.0721688
$193$		−	17.2291i		−	1.24017i	−0.784533	−	0.620087i	$-0.787097\pi$
$193$		−	17.2291i		−	1.24017i	0.784533	−	0.620087i	$-0.212903\pi$
$194$	8.15496			0.585492
$195$	−5.44814			−0.390150
$196$	6.86009			0.490006
$197$	1.88970			0.134636			0.0673179	−	0.997732i	$-0.478556\pi$
$197$	1.88970			0.134636			0.0673179	+	0.997732i	$0.478556\pi$
$198$		−	6.11707i		−	0.434721i
$199$		−	14.1584i		−	1.00366i	−0.864966	−	0.501830i	$-0.832660\pi$
$199$		−	14.1584i		−	1.00366i	0.864966	−	0.501830i	$-0.167340\pi$
$200$			1.00000i			0.0707107i
$201$	10.1482			0.715798
$202$			3.74302i			0.263358i
$203$			1.65029i			0.115828i
$204$			2.37405i			0.166217i
$205$		−	3.07409i		−	0.214704i
$206$	−8.49112			−0.591604
$207$		−	5.44814i		−	0.378672i
$208$		−	5.44814i		−	0.377761i
$209$			10.4304i			0.721485i
$210$	0.374052			0.0258120
$211$	11.1600			0.768289			0.384145	−	0.923273i	$-0.374496\pi$
$211$	11.1600			0.768289			0.384145	+	0.923273i	$0.374496\pi$
$212$	−2.37405			−0.163051
$213$	4.74810			0.325335
$214$		−	17.4481i		−	1.19273i
$215$	−7.82220			−0.533469
$216$		−	1.00000i		−	0.0680414i
$217$		−	1.14987i		−	0.0780583i
$218$	−8.62086			−0.583878
$219$	8.19625			0.553851
$220$		−	6.11707i		−	0.412413i
$221$	−12.9342			−0.870047
$222$	−5.44814	+	2.70513i	−0.365656	+	0.181556i
$223$	−10.5703			−0.707840			−0.353920	−	0.935276i	$-0.615151\pi$
$223$	−10.5703			−0.707840			−0.353920	+	0.935276i	$0.615151\pi$
$224$			0.374052i			0.0249924i
$225$	−1.00000			−0.0666667
$226$	−18.7185			−1.24514
$227$			2.05633i			0.136484i	0.997669	+	0.0682418i	$0.0217389\pi$
$227$			2.05633i			0.136484i	−0.997669	+	0.0682418i	$0.978261\pi$
$228$			1.70513i			0.112925i
$229$	8.08595			0.534335			0.267167	−	0.963650i	$-0.413912\pi$
$229$	8.08595			0.534335			0.267167	+	0.963650i	$0.413912\pi$
$230$		−	5.44814i		−	0.359240i
$231$	−2.28810			−0.150546
$232$	4.41194			0.289658
$233$	22.1253			1.44948			0.724740	−	0.689023i	$-0.241960\pi$
$233$	22.1253			1.44948			0.724740	+	0.689023i	$0.241960\pi$
$234$	5.44814			0.356156
$235$			13.3874i			0.873298i
$236$			10.8963i			0.709288i
$237$		−	12.1482i		−	0.789109i
$238$	0.888018			0.0575617
$239$		−	5.23245i		−	0.338459i	−0.985577	−	0.169230i	$-0.945872\pi$
$239$		−	5.23245i		−	0.338459i	0.985577	−	0.169230i	$-0.0541279\pi$
$240$		−	1.00000i		−	0.0645497i
$241$			2.50379i			0.161283i	0.996743	+	0.0806417i	$0.0256970\pi$
$241$			2.50379i			0.161283i	−0.996743	+	0.0806417i	$0.974303\pi$
$242$			26.4185i			1.69825i
$243$	1.00000			0.0641500
$244$		−	4.07918i		−	0.261143i
$245$			6.86009i			0.438275i
$246$			3.07409i			0.195997i
$247$	−9.28978			−0.591095
$248$	−3.07409			−0.195205
$249$	6.78599			0.430045
$250$	−1.00000			−0.0632456
$251$		−	16.9822i		−	1.07191i	−0.844247	−	0.535955i	$-0.819952\pi$
$251$		−	16.9822i		−	1.07191i	0.844247	−	0.535955i	$-0.180048\pi$
$252$	−0.374052			−0.0235631
$253$			33.3267i			2.09523i
$254$			16.1861i			1.01560i
$255$	−2.37405			−0.148669
$256$	1.00000			0.0625000
$257$			6.70004i			0.417937i	0.977922	+	0.208969i	$0.0670106\pi$
$257$			6.70004i			0.417937i	−0.977922	+	0.208969i	$0.932989\pi$
$258$	7.82220			0.486989
$259$	1.01186	+	2.03789i	0.0628738	+	0.126628i
$260$	5.44814			0.337880
$261$			4.41194i			0.273092i
$262$	−10.8963			−0.673175
$263$	8.15496			0.502856			0.251428	−	0.967876i	$-0.419100\pi$
$263$	8.15496			0.502856			0.251428	+	0.967876i	$0.419100\pi$
$264$			6.11707i			0.376480i
$265$		−	2.37405i		−	0.145837i
$266$	0.637806			0.0391064
$267$		−	0.551855i		−	0.0337730i
$268$	−10.1482			−0.619899
$269$	−5.34952			−0.326166			−0.163083	−	0.986612i	$-0.552144\pi$
$269$	−5.34952			−0.326166			−0.163083	+	0.986612i	$0.552144\pi$
$270$	1.00000			0.0608581
$271$	−27.2888			−1.65768			−0.828838	−	0.559489i	$-0.810997\pi$
$271$	−27.2888			−1.65768			−0.828838	+	0.559489i	$0.810997\pi$
$272$		−	2.37405i		−	0.143948i
$273$		−	2.03789i		−	0.123339i
$274$			0.332760i			0.0201028i
$275$	6.11707			0.368873
$276$			5.44814i			0.327940i
$277$		−	6.78599i		−	0.407731i	−0.978999	−	0.203865i	$-0.934650\pi$
$277$		−	6.78599i		−	0.407731i	0.978999	−	0.203865i	$-0.0653505\pi$
$278$		−	13.8980i		−	0.833545i
$279$		−	3.07409i		−	0.184041i
$280$	−0.374052			−0.0223539
$281$			18.8719i			1.12581i	0.826523	+	0.562903i	$0.190315\pi$
$281$			18.8719i			1.12581i	−0.826523	+	0.562903i	$0.809685\pi$
$282$		−	13.3874i		−	0.797209i
$283$			10.5417i			0.626638i	0.949648	+	0.313319i	$0.101441\pi$
$283$			10.5417i			0.626638i	−0.949648	+	0.313319i	$0.898559\pi$
$284$	−4.74810			−0.281748
$285$	−1.70513			−0.101003
$286$	−33.3267			−1.97065
$287$	1.14987			0.0678747
$288$			1.00000i			0.0589256i
$289$	11.3639			0.668463
$290$			4.41194i			0.259078i
$291$		−	8.15496i		−	0.478052i
$292$	−8.19625			−0.479649
$293$	−8.46000			−0.494239			−0.247119	−	0.968985i	$-0.579484\pi$
$293$	−8.46000			−0.494239			−0.247119	+	0.968985i	$0.579484\pi$
$294$		−	6.86009i		−	0.400088i
$295$	−10.8963			−0.634407
$296$	5.44814	−	2.70513i	0.316667	−	0.157232i
$297$	−6.11707			−0.354948
$298$		−	11.9014i		−	0.689428i
$299$	−29.6823			−1.71657
$300$	1.00000			0.0577350
$301$		−	2.92591i		−	0.168646i
$302$			18.4304i			1.06055i
$303$	3.74302			0.215031
$304$		−	1.70513i		−	0.0977958i
$305$	4.07918			0.233573
$306$	2.37405			0.135716
$307$	−16.4683			−0.939894			−0.469947	−	0.882695i	$-0.655727\pi$
$307$	−16.4683			−0.939894			−0.469947	+	0.882695i	$0.655727\pi$
$308$	2.28810			0.130377
$309$			8.49112i			0.483043i
$310$		−	3.07409i		−	0.174597i
$311$		−	21.0741i		−	1.19500i	−0.801868	−	0.597501i	$-0.796160\pi$
$311$		−	21.0741i		−	1.19500i	0.801868	−	0.597501i	$-0.203840\pi$
$312$	−5.44814			−0.308440
$313$			27.6317i			1.56184i	0.624633	+	0.780919i	$0.285249\pi$
$313$			27.6317i			1.56184i	−0.624633	+	0.780919i	$0.714751\pi$
$314$			7.98056i			0.450369i
$315$		−	0.374052i		−	0.0210754i
$316$			12.1482i			0.683389i
$317$	16.4119			0.921786			0.460893	−	0.887456i	$-0.347529\pi$
$317$	16.4119			0.921786			0.460893	+	0.887456i	$0.347529\pi$
$318$			2.37405i			0.133130i
$319$		−	26.9881i		−	1.51105i
$320$			1.00000i			0.0559017i
$321$	−17.4481			−0.973860
$322$	2.03789			0.113567
$323$	−4.04806			−0.225240
$324$	−1.00000			−0.0555556
$325$			5.44814i			0.302209i
$326$	9.86009			0.546100
$327$			8.62086i			0.476735i
$328$		−	3.07409i		−	0.169738i
$329$	−5.00759			−0.276077
$330$	−6.11707			−0.336734
$331$			32.9594i			1.81161i	0.423693	+	0.905806i	$0.360734\pi$
$331$			32.9594i			1.81161i	−0.423693	+	0.905806i	$0.639266\pi$
$332$	−6.78599			−0.372430
$333$	2.70513	+	5.44814i	0.148240	+	0.298556i
$334$	−22.4304			−1.22734
$335$		−	10.1482i		−	0.554455i
$336$	0.374052			0.0204062
$337$	23.1548			1.26132			0.630660	−	0.776059i	$-0.282784\pi$
$337$	23.1548			1.26132			0.630660	+	0.776059i	$0.282784\pi$
$338$		−	16.6823i		−	0.907397i
$339$			18.7185i			1.01665i
$340$	2.37405			0.128751
$341$			18.8044i			1.01832i
$342$	1.70513			0.0922028
$343$	−5.18439			−0.279931
$344$	−7.82220			−0.421745
$345$	−5.44814			−0.293318
$346$		−	22.7665i		−	1.22394i
$347$			5.91405i			0.317483i	0.987320	+	0.158741i	$0.0507436\pi$
$347$			5.91405i			0.317483i	−0.987320	+	0.158741i	$0.949256\pi$
$348$		−	4.41194i		−	0.236505i
$349$	3.17949			0.170194			0.0850970	−	0.996373i	$-0.472880\pi$
$349$	3.17949			0.170194			0.0850970	+	0.996373i	$0.472880\pi$
$350$		−	0.374052i		−	0.0199939i
$351$		−	5.44814i		−	0.290800i
$352$		−	6.11707i		−	0.326041i
$353$			0.102026i			0.00543031i	0.999996	+	0.00271515i	$0.000864261\pi$
$353$			0.102026i			0.00543031i	−0.999996	+	0.00271515i	$0.999136\pi$
$354$	10.8963			0.579131
$355$		−	4.74810i		−	0.252003i
$356$			0.551855i			0.0292483i
$357$		−	0.888018i		−	0.0469989i
$358$	11.1304			0.588261
$359$	−13.5720			−0.716302			−0.358151	−	0.933664i	$-0.616593\pi$
$359$	−13.5720			−0.716302			−0.358151	+	0.933664i	$0.616593\pi$
$360$	−1.00000			−0.0527046
$361$	16.0925			0.846976
$362$		−	15.3378i		−	0.806139i
$363$	26.4185			1.38661
$364$			2.03789i			0.106814i
$365$		−	8.19625i		−	0.429011i
$366$	−4.07918			−0.213222
$367$	36.3284			1.89632			0.948162	−	0.317786i	$-0.102939\pi$
$367$	36.3284			1.89632			0.948162	+	0.317786i	$0.102939\pi$
$368$		−	5.44814i		−	0.284004i
$369$	3.07409			0.160031
$370$	2.70513	+	5.44814i	0.140633	+	0.283236i
$371$	0.888018			0.0461036
$372$			3.07409i			0.159384i
$373$	8.89629			0.460632			0.230316	−	0.973116i	$-0.426024\pi$
$373$	8.89629			0.460632			0.230316	+	0.973116i	$0.426024\pi$
$374$	−14.5222			−0.750927
$375$			1.00000i			0.0516398i
$376$			13.3874i			0.690403i
$377$	24.0369			1.23796
$378$			0.374052i			0.0192392i
$379$	−33.2028			−1.70552			−0.852758	−	0.522307i	$-0.825072\pi$
$379$	−33.2028			−1.70552			−0.852758	+	0.522307i	$0.825072\pi$
$380$	1.70513			0.0874712
$381$	16.1861			0.829238
$382$	12.0184			0.614917
$383$			27.2407i			1.39194i	0.718073	+	0.695968i	$0.245024\pi$
$383$			27.2407i			1.39194i	−0.718073	+	0.695968i	$0.754976\pi$
$384$		−	1.00000i		−	0.0510310i
$385$			2.28810i			0.116612i
$386$	17.2291			0.876936
$387$		−	7.82220i		−	0.397625i
$388$			8.15496i			0.414005i
$389$		−	4.64608i		−	0.235565i	−0.993039	−	0.117783i	$-0.962421\pi$
$389$		−	4.64608i		−	0.235565i	0.993039	−	0.117783i	$-0.0375786\pi$
$390$		−	5.44814i		−	0.275878i
$391$	−12.9342			−0.654110
$392$			6.86009i			0.346487i
$393$			10.8963i			0.549645i
$394$			1.88970i			0.0952018i
$395$	−12.1482			−0.611242
$396$	6.11707			0.307394
$397$	−15.5720			−0.781535			−0.390768	−	0.920489i	$-0.627790\pi$
$397$	−15.5720			−0.781535			−0.390768	+	0.920489i	$0.627790\pi$
$398$	14.1584			0.709694
$399$		−	0.637806i		−	0.0319303i
$400$	−1.00000			−0.0500000
$401$		−	28.6645i		−	1.43144i	−0.698388	−	0.715719i	$-0.746099\pi$
$401$		−	28.6645i		−	1.43144i	0.698388	−	0.715719i	$-0.253901\pi$
$402$			10.1482i			0.506146i
$403$	−16.7481			−0.834282
$404$	−3.74302			−0.186222
$405$		−	1.00000i		−	0.0496904i
$406$	−1.65029			−0.0819027
$407$	−16.5475	−	33.3267i	−0.820227	−	1.65194i
$408$	−2.37405			−0.117533
$409$			16.9822i			0.839718i	0.907589	+	0.419859i	$0.137920\pi$
$409$			16.9822i			0.839718i	−0.907589	+	0.419859i	$0.862080\pi$
$410$	3.07409			0.151819
$411$	0.332760			0.0164139
$412$		−	8.49112i		−	0.418327i
$413$		−	4.07578i		−	0.200556i
$414$	5.44814			0.267762
$415$		−	6.78599i		−	0.333111i
$416$	5.44814			0.267117
$417$	−13.8980			−0.680587
$418$	−10.4304			−0.510167
$419$	28.2949			1.38229			0.691147	−	0.722714i	$-0.257105\pi$
$419$	28.2949			1.38229			0.691147	+	0.722714i	$0.257105\pi$
$420$			0.374052i			0.0182519i
$421$		−	11.3150i		−	0.551459i	−0.961235	−	0.275730i	$-0.911081\pi$
$421$		−	11.3150i		−	0.551459i	0.961235	−	0.275730i	$-0.0889195\pi$
$422$			11.1600i			0.543262i
$423$	−13.3874			−0.650918
$424$		−	2.37405i		−	0.115294i
$425$			2.37405i			0.115158i
$426$			4.74810i			0.230046i
$427$			1.52582i			0.0738398i
$428$	17.4481			0.843388
$429$			33.3267i			1.60903i
$430$		−	7.82220i		−	0.377220i
$431$		−	13.1844i		−	0.635070i	−0.948247	−	0.317535i	$-0.897145\pi$
$431$		−	13.1844i		−	0.635070i	0.948247	−	0.317535i	$-0.102855\pi$
$432$	1.00000			0.0481125
$433$	34.9711			1.68060			0.840301	−	0.542120i	$-0.182378\pi$
$433$	34.9711			1.68060			0.840301	+	0.542120i	$0.182378\pi$
$434$	1.14987			0.0551955
$435$	4.41194			0.211536
$436$		−	8.62086i		−	0.412864i
$437$	−9.28978			−0.444391
$438$			8.19625i			0.391632i
$439$			3.27134i			0.156133i	0.996948	+	0.0780663i	$0.0248746\pi$
$439$			3.27134i			0.156133i	−0.996948	+	0.0780663i	$0.975125\pi$
$440$	6.11707			0.291620
$441$	−6.86009			−0.326671
$442$		−	12.9342i		−	0.615216i
$443$	21.9645			1.04356			0.521782	−	0.853079i	$-0.325267\pi$
$443$	21.9645			1.04356			0.521782	+	0.853079i	$0.325267\pi$
$444$	−2.70513	−	5.44814i	−0.128380	−	0.258558i
$445$	−0.551855			−0.0261604
$446$		−	10.5703i		−	0.500518i
$447$	−11.9014			−0.562916
$448$	−0.374052			−0.0176723
$449$			10.8103i			0.510171i	0.966918	+	0.255086i	$0.0821037\pi$
$449$			10.8103i			0.510171i	−0.966918	+	0.255086i	$0.917896\pi$
$450$		−	1.00000i		−	0.0471405i
$451$	−18.8044			−0.885466
$452$		−	18.7185i		−	0.880444i
$453$	18.4304			0.865935
$454$	−2.05633			−0.0965085
$455$	−2.03789			−0.0955377
$456$	−1.70513			−0.0798499
$457$			2.74133i			0.128234i	0.997942	+	0.0641171i	$0.0204231\pi$
$457$			2.74133i			0.128234i	−0.997942	+	0.0641171i	$0.979577\pi$
$458$			8.08595i			0.377832i
$459$		−	2.37405i		−	0.110811i
$460$	5.44814			0.254021
$461$		−	30.9526i		−	1.44161i	−0.693139	−	0.720804i	$-0.743773\pi$
$461$		−	30.9526i		−	1.44161i	0.693139	−	0.720804i	$-0.256227\pi$
$462$		−	2.28810i		−	0.106452i
$463$		−	15.7430i		−	0.731640i	−0.930686	−	0.365820i	$-0.880789\pi$
$463$		−	15.7430i		−	0.731640i	0.930686	−	0.365820i	$-0.119211\pi$
$464$			4.41194i			0.204819i
$465$	−3.07409			−0.142558
$466$			22.1253i			1.02494i
$467$			17.7007i			0.819092i	0.912289	+	0.409546i	$0.134313\pi$
$467$			17.7007i			0.819092i	−0.912289	+	0.409546i	$0.865687\pi$
$468$			5.44814i			0.251841i
$469$	3.79595			0.175281
$470$	−13.3874			−0.617515
$471$	7.98056			0.367725
$472$	−10.8963			−0.501542
$473$			47.8489i			2.20010i
$474$	12.1482			0.557985
$475$			1.70513i			0.0782366i
$476$			0.888018i			0.0407023i
$477$	2.37405			0.108700
$478$	5.23245			0.239327
$479$			4.47945i			0.204671i	0.994750	+	0.102336i	$0.0326315\pi$
$479$			4.47945i			0.204671i	−0.994750	+	0.102336i	$0.967368\pi$
$480$	1.00000			0.0456435
$481$	29.6823	−	14.7379i	1.35340	−	0.671992i
$482$	−2.50379			−0.114045
$483$		−	2.03789i		−	0.0927271i
$484$	−26.4185			−1.20084
$485$	−8.15496			−0.370298
$486$			1.00000i			0.0453609i
$487$		−	7.32518i		−	0.331935i	−0.986131	−	0.165968i	$-0.946925\pi$
$487$		−	7.32518i		−	0.331935i	0.986131	−	0.165968i	$-0.0530747\pi$
$488$	4.07918			0.184656
$489$		−	9.86009i		−	0.445888i
$490$	−6.86009			−0.309907
$491$	32.0015			1.44421			0.722104	−	0.691785i	$-0.243175\pi$
$491$	32.0015			1.44421			0.722104	+	0.691785i	$0.243175\pi$
$492$	−3.07409			−0.138591
$493$	10.4742			0.471733
$494$		−	9.28978i		−	0.417967i
$495$			6.11707i			0.274942i
$496$		−	3.07409i		−	0.138031i
$497$	1.77604			0.0796661
$498$			6.78599i			0.304088i
$499$		−	35.4977i		−	1.58910i	−0.607202	−	0.794548i	$-0.707708\pi$
$499$		−	35.4977i		−	1.58910i	0.607202	−	0.794548i	$-0.292292\pi$
$500$		−	1.00000i		−	0.0447214i
$501$			22.4304i			1.00212i
$502$	16.9822			0.757954
$503$			2.01017i			0.0896292i	0.998995	+	0.0448146i	$0.0142697\pi$
$503$			2.01017i			0.0896292i	−0.998995	+	0.0448146i	$0.985730\pi$
$504$		−	0.374052i		−	0.0166616i
$505$		−	3.74302i		−	0.166562i
$506$	−33.3267			−1.48155
$507$	−16.6823			−0.740886
$508$	−16.1861			−0.718141
$509$	−17.5468			−0.777747			−0.388873	−	0.921291i	$-0.627136\pi$
$509$	−17.5468			−0.777747			−0.388873	+	0.921291i	$0.627136\pi$
$510$		−	2.37405i		−	0.105125i
$511$	3.06582			0.135624
$512$			1.00000i			0.0441942i
$513$		−	1.70513i		−	0.0752832i
$514$	−6.70004			−0.295526
$515$	8.49112			0.374163
$516$			7.82220i			0.344353i
$517$	81.8917			3.60159
$518$	−2.03789	+	1.01186i	−0.0895397	+	0.0444585i
$519$	−22.7665			−0.999341
$520$			5.44814i			0.238917i
$521$	8.55676			0.374878			0.187439	−	0.982276i	$-0.439981\pi$
$521$	8.55676			0.374878			0.187439	+	0.982276i	$0.439981\pi$
$522$	−4.41194			−0.193105
$523$			13.7202i			0.599941i	0.953948	+	0.299971i	$0.0969769\pi$
$523$			13.7202i			0.599941i	−0.953948	+	0.299971i	$0.903023\pi$
$524$		−	10.8963i		−	0.476007i
$525$	−0.374052			−0.0163250
$526$			8.15496i			0.355573i
$527$	−7.29806			−0.317908
$528$	−6.11707			−0.266211
$529$	−6.68228			−0.290534
$530$	2.37405			0.103122
$531$		−	10.8963i		−	0.472859i
$532$			0.637806i			0.0276524i
$533$		−	16.7481i		−	0.725441i
$534$	0.551855			0.0238811
$535$			17.4481i			0.754349i
$536$		−	10.1482i		−	0.438335i
$537$		−	11.1304i		−	0.480313i
$538$		−	5.34952i		−	0.230634i
$539$	41.9636			1.80750
$540$			1.00000i			0.0430331i
$541$		−	21.0430i		−	0.904708i	−0.891838	−	0.452354i	$-0.850584\pi$
$541$		−	21.0430i		−	0.904708i	0.891838	−	0.452354i	$-0.149416\pi$
$542$		−	27.2888i		−	1.17215i
$543$	−15.3378			−0.658210
$544$	2.37405			0.101787
$545$	8.62086			0.369277
$546$	2.03789			0.0872136
$547$		−	29.3461i		−	1.25475i	−0.778718	−	0.627375i	$-0.784129\pi$
$547$		−	29.3461i		−	1.25475i	0.778718	−	0.627375i	$-0.215871\pi$
$548$	−0.332760			−0.0142148
$549$			4.07918i			0.174095i
$550$			6.11707i			0.260833i
$551$	7.52292			0.320487
$552$	−5.44814			−0.231888
$553$		−	4.54405i		−	0.193233i
$554$	6.78599			0.288309
$555$	5.44814	−	2.70513i	0.231261	−	0.114826i
$556$	13.8980			0.589405
$557$		−	19.4370i		−	0.823571i	−0.911281	−	0.411785i	$-0.864905\pi$
$557$		−	19.4370i		−	0.823571i	0.911281	−	0.411785i	$-0.135095\pi$
$558$	3.07409			0.130137
$559$	−42.6165			−1.80248
$560$		−	0.374052i		−	0.0158066i
$561$			14.5222i			0.613129i
$562$	−18.8719			−0.796065
$563$		−	43.2981i		−	1.82480i	−0.409305	−	0.912398i	$-0.634229\pi$
$563$		−	43.2981i		−	1.82480i	0.409305	−	0.912398i	$-0.365771\pi$
$564$	13.3874			0.563712
$565$	18.7185			0.787493
$566$	−10.5417			−0.443100
$567$	0.374052			0.0157087
$568$		−	4.74810i		−	0.199226i
$569$		−	28.9240i		−	1.21256i	−0.795252	−	0.606279i	$-0.792662\pi$
$569$		−	28.9240i		−	1.21256i	0.795252	−	0.606279i	$-0.207338\pi$
$570$		−	1.70513i		−	0.0714200i
$571$	−7.07746			−0.296183			−0.148091	−	0.988974i	$-0.547313\pi$
$571$	−7.07746			−0.296183			−0.148091	+	0.988974i	$0.547313\pi$
$572$		−	33.3267i		−	1.39346i
$573$		−	12.0184i		−	0.502078i
$574$			1.14987i			0.0479947i
$575$			5.44814i			0.227203i
$576$	−1.00000			−0.0416667
$577$		−	2.75060i		−	0.114509i	−0.998360	−	0.0572545i	$-0.981765\pi$
$577$		−	2.75060i		−	0.114509i	0.998360	−	0.0572545i	$-0.0182347\pi$
$578$			11.3639i			0.472675i
$579$		−	17.2291i		−	0.716015i
$580$	−4.41194			−0.183196
$581$	2.53831			0.105307
$582$	8.15496			0.338034
$583$	−14.5222			−0.601450
$584$		−	8.19625i		−	0.339163i
$585$	−5.44814			−0.225253
$586$		−	8.46000i		−	0.349480i
$587$		−	8.64271i		−	0.356723i	−0.983965	−	0.178361i	$-0.942920\pi$
$587$		−	8.64271i		−	0.356723i	0.983965	−	0.178361i	$-0.0570796\pi$
$588$	6.86009			0.282905
$589$	−5.24172			−0.215981
$590$		−	10.8963i		−	0.448593i
$591$	1.88970			0.0777320
$592$	2.70513	+	5.44814i	0.111180	+	0.223917i
$593$	32.7253			1.34387			0.671933	−	0.740612i	$-0.265464\pi$
$593$	32.7253			1.34387			0.671933	+	0.740612i	$0.265464\pi$
$594$		−	6.11707i		−	0.250986i
$595$	−0.888018			−0.0364052
$596$	11.9014			0.487499
$597$		−	14.1584i		−	0.579463i
$598$		−	29.6823i		−	1.21380i
$599$	21.5584			0.880854			0.440427	−	0.897788i	$-0.354827\pi$
$599$	21.5584			0.880854			0.440427	+	0.897788i	$0.354827\pi$
$600$			1.00000i			0.0408248i
$601$	14.5946			0.595328			0.297664	−	0.954671i	$-0.403792\pi$
$601$	14.5946			0.595328			0.297664	+	0.954671i	$0.403792\pi$
$602$	2.92591			0.119251
$603$	10.1482			0.413266
$604$	−18.4304			−0.749922
$605$		−	26.4185i		−	1.07407i
$606$			3.74302i			0.152050i
$607$			19.8188i			0.804420i	0.915547	+	0.402210i	$0.131758\pi$
$607$			19.8188i			0.804420i	−0.915547	+	0.402210i	$0.868242\pi$
$608$	1.70513			0.0691521
$609$			1.65029i			0.0668733i
$610$			4.07918i			0.165161i
$611$			72.9365i			2.95070i
$612$			2.37405i			0.0959654i
$613$	43.4666			1.75560			0.877800	−	0.479028i	$-0.159011\pi$
$613$	43.4666			1.75560			0.877800	+	0.479028i	$0.159011\pi$
$614$		−	16.4683i		−	0.664605i
$615$		−	3.07409i		−	0.123959i
$616$			2.28810i			0.0921902i
$617$	22.8599			0.920305			0.460152	−	0.887840i	$-0.347795\pi$
$617$	22.8599			0.920305			0.460152	+	0.887840i	$0.347795\pi$
$618$	−8.49112			−0.341563
$619$	−6.92591			−0.278376			−0.139188	−	0.990266i	$-0.544449\pi$
$619$	−6.92591			−0.278376			−0.139188	+	0.990266i	$0.544449\pi$
$620$	3.07409			0.123459
$621$		−	5.44814i		−	0.218627i
$622$	21.0741			0.844994
$623$		−	0.206422i		−	0.00827014i
$624$		−	5.44814i		−	0.218100i
$625$	1.00000			0.0400000
$626$	−27.6317			−1.10439
$627$			10.4304i			0.416549i
$628$	−7.98056			−0.318459
$629$	12.9342	−	6.42211i	0.515719	−	0.256066i
$630$	0.374052			0.0149026
$631$		−	6.95262i		−	0.276780i	−0.990378	−	0.138390i	$-0.955807\pi$
$631$		−	6.95262i		−	0.276780i	0.990378	−	0.138390i	$-0.0441927\pi$
$632$	−12.1482			−0.483229
$633$	11.1600			0.443572
$634$			16.4119i			0.651801i
$635$		−	16.1861i		−	0.642325i
$636$	−2.37405			−0.0941373
$637$			37.3747i			1.48084i
$638$	26.9881			1.06847
$639$	4.74810			0.187832
$640$	−1.00000			−0.0395285
$641$	45.9315			1.81419			0.907093	−	0.420931i	$-0.138297\pi$
$641$	45.9315			1.81419			0.907093	+	0.420931i	$0.138297\pi$
$642$		−	17.4481i		−	0.688623i
$643$		−	8.26276i		−	0.325851i	−0.986638	−	0.162926i	$-0.947907\pi$
$643$		−	8.26276i		−	0.325851i	0.986638	−	0.162926i	$-0.0520931\pi$
$644$			2.03789i			0.0803041i
$645$	−7.82220			−0.307999
$646$		−	4.04806i		−	0.159269i
$647$		−	30.6510i		−	1.20501i	−0.798113	−	0.602507i	$-0.794168\pi$
$647$		−	30.6510i		−	1.20501i	0.798113	−	0.602507i	$-0.205832\pi$
$648$		−	1.00000i		−	0.0392837i
$649$			66.6534i			2.61637i
$650$	−5.44814			−0.213694
$651$		−	1.14987i		−	0.0450670i
$652$			9.86009i			0.386151i
$653$		−	27.9645i		−	1.09433i	−0.837023	−	0.547167i	$-0.815706\pi$
$653$		−	27.9645i		−	1.09433i	0.837023	−	0.547167i	$-0.184294\pi$
$654$	−8.62086			−0.337102
$655$	10.8963			0.425753
$656$	3.07409			0.120023
$657$	8.19625			0.319766
$658$		−	5.00759i		−	0.195216i
$659$	44.6762			1.74034			0.870169	−	0.492754i	$-0.164010\pi$
$659$	44.6762			1.74034			0.870169	+	0.492754i	$0.164010\pi$
$660$		−	6.11707i		−	0.238107i
$661$			1.13483i			0.0441397i	0.999756	+	0.0220698i	$0.00702562\pi$
$661$			1.13483i			0.0441397i	−0.999756	+	0.0220698i	$0.992974\pi$
$662$	−32.9594			−1.28100
$663$	−12.9342			−0.502322
$664$		−	6.78599i		−	0.263348i
$665$	−0.637806			−0.0247331
$666$	−5.44814	+	2.70513i	−0.211111	+	0.104822i
$667$	24.0369			0.930712
$668$		−	22.4304i		−	0.867858i
$669$	−10.5703			−0.408671
$670$	10.1482			0.392059
$671$		−	24.9526i		−	0.963285i
$672$			0.374052i			0.0144294i
$673$	−43.4850			−1.67622			−0.838112	−	0.545497i	$-0.816341\pi$
$673$	−43.4850			−1.67622			−0.838112	+	0.545497i	$0.816341\pi$
$674$			23.1548i			0.891889i
$675$	−1.00000			−0.0384900
$676$	16.6823			0.641626
$677$	5.96548			0.229272			0.114636	−	0.993408i	$-0.463430\pi$
$677$	5.96548			0.229272			0.114636	+	0.993408i	$0.463430\pi$
$678$	−18.7185			−0.718879
$679$		−	3.05038i		−	0.117063i
$680$			2.37405i			0.0910407i
$681$			2.05633i			0.0787989i
$682$	−18.8044			−0.720059
$683$			40.5348i			1.55102i	0.631335	+	0.775510i	$0.282507\pi$
$683$			40.5348i			1.55102i	−0.631335	+	0.775510i	$0.717493\pi$
$684$			1.70513i			0.0651972i
$685$		−	0.332760i		−	0.0127141i
$686$		−	5.18439i		−	0.197941i
$687$	8.08595			0.308498
$688$		−	7.82220i		−	0.298218i
$689$		−	12.9342i		−	0.492753i
$690$		−	5.44814i		−	0.207407i
$691$	−32.4843			−1.23576			−0.617881	−	0.786271i	$-0.712009\pi$
$691$	−32.4843			−1.23576			−0.617881	+	0.786271i	$0.712009\pi$
$692$	22.7665			0.865454
$693$	−2.28810			−0.0869178
$694$	−5.91405			−0.224494
$695$			13.8980i			0.527180i
$696$	4.41194			0.167234
$697$		−	7.29806i		−	0.276434i
$698$			3.17949i			0.120345i
$699$	22.1253			0.836857
$700$	0.374052			0.0141378
$701$		−	24.3823i		−	0.920908i	−0.887684	−	0.460454i	$-0.847687\pi$
$701$		−	24.3823i		−	0.920908i	0.887684	−	0.460454i	$-0.152313\pi$
$702$	5.44814			0.205627
$703$	9.28978	−	4.61259i	0.350371	−	0.173967i
$704$	6.11707			0.230546
$705$			13.3874i			0.504199i
$706$	−0.102026			−0.00383981
$707$	1.40008			0.0526555
$708$			10.8963i			0.409508i
$709$			11.8339i			0.444430i	0.974998	+	0.222215i	$0.0713287\pi$
$709$			11.8339i			0.444430i	−0.974998	+	0.222215i	$0.928671\pi$
$710$	4.74810			0.178193
$711$		−	12.1482i		−	0.455593i
$712$	−0.551855			−0.0206816
$713$	−16.7481			−0.627221
$714$	0.888018			0.0332333
$715$	33.3267			1.24635
$716$			11.1304i			0.415964i
$717$		−	5.23245i		−	0.195410i
$718$		−	13.5720i		−	0.506502i
$719$	21.2990			0.794317			0.397159	−	0.917750i	$-0.369996\pi$
$719$	21.2990			0.794317			0.397159	+	0.917750i	$0.369996\pi$
$720$		−	1.00000i		−	0.0372678i
$721$			3.17612i			0.118285i
$722$			16.0925i			0.598902i
$723$			2.50379i			0.0931171i
$724$	15.3378			0.570027
$725$		−	4.41194i		−	0.163855i
$726$			26.4185i			0.980484i
$727$			16.8836i			0.626179i	0.949724	+	0.313089i	$0.101364\pi$
$727$			16.8836i			0.626179i	−0.949724	+	0.313089i	$0.898636\pi$
$728$	−2.03789			−0.0755292
$729$	1.00000			0.0370370
$730$	8.19625			0.303357
$731$	−18.5703			−0.686847
$732$		−	4.07918i		−	0.150771i
$733$	−20.5111			−0.757593			−0.378797	−	0.925480i	$-0.623662\pi$
$733$	−20.5111			−0.757593			−0.378797	+	0.925480i	$0.623662\pi$
$734$			36.3284i			1.34090i
$735$			6.86009i			0.253038i
$736$	5.44814			0.200821
$737$	−62.0771			−2.28664
$738$			3.07409i			0.113159i
$739$	−4.71849			−0.173572			−0.0867862	−	0.996227i	$-0.527660\pi$
$739$	−4.71849			−0.173572			−0.0867862	+	0.996227i	$0.527660\pi$
$740$	−5.44814	+	2.70513i	−0.200278	+	0.0994425i
$741$	−9.28978			−0.341269
$742$			0.888018i			0.0326002i
$743$	−54.0098			−1.98143			−0.990713	−	0.135968i	$-0.956585\pi$
$743$	−54.0098			−1.98143			−0.990713	+	0.135968i	$0.956585\pi$
$744$	−3.07409			−0.112702
$745$			11.9014i			0.436033i
$746$			8.89629i			0.325716i
$747$	6.78599			0.248286
$748$		−	14.5222i		−	0.530986i
$749$	−6.52651			−0.238474
$750$	−1.00000			−0.0365148
$751$	12.6520			0.461677			0.230839	−	0.972992i	$-0.425853\pi$
$751$	12.6520			0.461677			0.230839	+	0.972992i	$0.425853\pi$
$752$	−13.3874			−0.488189
$753$		−	16.9822i		−	0.618867i
$754$			24.0369i			0.875372i
$755$		−	18.4304i		−	0.670750i
$756$	−0.374052			−0.0136041
$757$		−	10.8618i		−	0.394778i	−0.980325	−	0.197389i	$-0.936754\pi$
$757$		−	10.8618i		−	0.394778i	0.980325	−	0.197389i	$-0.0632462\pi$
$758$		−	33.2028i		−	1.20598i
$759$			33.3267i			1.20968i
$760$			1.70513i			0.0618515i
$761$	37.2358			1.34980			0.674899	−	0.737910i	$-0.264187\pi$
$761$	37.2358			1.34980			0.674899	+	0.737910i	$0.264187\pi$
$762$			16.1861i			0.586360i
$763$			3.22465i			0.116740i
$764$			12.0184i			0.434812i
$765$	−2.37405			−0.0858340
$766$	−27.2407			−0.984247
$767$	−59.3646			−2.14353
$768$	1.00000			0.0360844
$769$			15.9039i			0.573508i	0.958004	+	0.286754i	$0.0925763\pi$
$769$			15.9039i			0.573508i	−0.958004	+	0.286754i	$0.907424\pi$
$770$	−2.28810			−0.0824574
$771$			6.70004i			0.241296i
$772$			17.2291i			0.620087i
$773$	−48.1666			−1.73243			−0.866217	−	0.499669i	$-0.833455\pi$
$773$	−48.1666			−1.73243			−0.866217	+	0.499669i	$0.833455\pi$
$774$	7.82220			0.281163
$775$			3.07409i			0.110425i
$776$	−8.15496			−0.292746
$777$	1.01186	+	2.03789i	0.0363002	+	0.0731088i
$778$	4.64608			0.166570
$779$		−	5.24172i		−	0.187804i
$780$	5.44814			0.195075
$781$	−29.0445			−1.03929
$782$		−	12.9342i		−	0.462525i
$783$			4.41194i			0.157670i
$784$	−6.86009			−0.245003
$785$		−	7.98056i		−	0.284838i
$786$	−10.8963			−0.388658
$787$	3.42380			0.122045			0.0610226	−	0.998136i	$-0.480564\pi$
$787$	3.42380			0.122045			0.0610226	+	0.998136i	$0.480564\pi$
$788$	−1.88970			−0.0673179
$789$	8.15496			0.290324
$790$		−	12.1482i		−	0.432213i
$791$			7.00168i			0.248951i
$792$			6.11707i			0.217361i
$793$	22.2240			0.789196
$794$		−	15.5720i		−	0.552629i
$795$		−	2.37405i		−	0.0841989i
$796$			14.1584i			0.501830i
$797$		−	20.5407i		−	0.727588i	−0.931479	−	0.363794i	$-0.881481\pi$
$797$		−	20.5407i		−	0.727588i	0.931479	−	0.363794i	$-0.118519\pi$
$798$	0.637806			0.0225781
$799$			31.7824i			1.12438i
$800$		−	1.00000i		−	0.0353553i
$801$		−	0.551855i		−	0.0194988i
$802$	28.6645			1.01218
$803$	−50.1370			−1.76930
$804$	−10.1482			−0.357899
$805$	−2.03789			−0.0718261
$806$		−	16.7481i		−	0.589927i
$807$	−5.34952			−0.188312
$808$		−	3.74302i		−	0.131679i
$809$		−	21.5476i		−	0.757575i	−0.925484	−	0.378787i	$-0.876341\pi$
$809$		−	21.5476i		−	0.757575i	0.925484	−	0.378787i	$-0.123659\pi$
$810$	1.00000			0.0351364
$811$	0.293372			0.0103017			0.00515084	−	0.999987i	$-0.498360\pi$
$811$	0.293372			0.0103017			0.00515084	+	0.999987i	$0.498360\pi$
$812$		−	1.65029i		−	0.0579140i
$813$	−27.2888			−0.957060
$814$	33.3267	−	16.5475i	1.16810	−	0.579988i
$815$	−9.86009			−0.345384
$816$		−	2.37405i		−	0.0831084i
$817$	−13.3378			−0.466632
$818$	−16.9822			−0.593770
$819$		−	2.03789i		−	0.0712096i
$820$			3.07409i			0.107352i
$821$	−33.7217			−1.17689			−0.588447	−	0.808536i	$-0.700261\pi$
$821$	−33.7217			−1.17689			−0.588447	+	0.808536i	$0.700261\pi$
$822$			0.332760i			0.0116064i
$823$	−35.0570			−1.22201			−0.611005	−	0.791626i	$-0.709235\pi$
$823$	−35.0570			−1.22201			−0.611005	+	0.791626i	$0.709235\pi$
$824$	8.49112			0.295802
$825$	6.11707			0.212969
$826$	4.07578			0.141814
$827$		−	30.8044i		−	1.07118i	−0.844480	−	0.535588i	$-0.820090\pi$
$827$		−	30.8044i		−	1.07118i	0.844480	−	0.535588i	$-0.179910\pi$
$828$			5.44814i			0.189336i
$829$		−	27.6133i		−	0.959049i	−0.877529	−	0.479524i	$-0.840809\pi$
$829$		−	27.6133i		−	0.959049i	0.877529	−	0.479524i	$-0.159191\pi$
$830$	6.78599			0.235545
$831$		−	6.78599i		−	0.235403i
$832$			5.44814i			0.188880i
$833$			16.2862i			0.564283i
$834$		−	13.8980i		−	0.481247i
$835$	22.4304			0.776236
$836$		−	10.4304i		−	0.360742i
$837$		−	3.07409i		−	0.106256i
$838$			28.2949i			0.977430i
$839$	15.1761			0.523938			0.261969	−	0.965076i	$-0.415628\pi$
$839$	15.1761			0.523938			0.261969	+	0.965076i	$0.415628\pi$
$840$	−0.374052			−0.0129060
$841$	9.53478			0.328786
$842$	11.3150			0.389941
$843$			18.8719i			0.649984i
$844$	−11.1600			−0.384145
$845$			16.6823i			0.573888i
$846$		−	13.3874i		−	0.460269i
$847$	9.88190			0.339546
$848$	2.37405			0.0815253
$849$			10.5417i			0.361790i
$850$	−2.37405			−0.0814293
$851$	29.6823	−	14.7379i	1.01750	−	0.505210i
$852$	−4.74810			−0.162667
$853$			27.4380i			0.939458i	0.882811	+	0.469729i	$0.155648\pi$
$853$			27.4380i			0.939458i	−0.882811	+	0.469729i	$0.844352\pi$
$854$	−1.52582			−0.0522126
$855$	−1.70513			−0.0583142
$856$			17.4481i			0.596365i
$857$			0.535780i			0.0183019i	0.999958	+	0.00915095i	$0.00291288\pi$
$857$			0.535780i			0.0183019i	−0.999958	+	0.00915095i	$0.997087\pi$
$858$	−33.3267			−1.13775
$859$		−	55.8649i		−	1.90608i	−0.302837	−	0.953042i	$-0.597934\pi$
$859$		−	55.8649i		−	1.90608i	0.302837	−	0.953042i	$-0.402066\pi$
$860$	7.82220			0.266735
$861$	1.14987			0.0391875
$862$	13.1844			0.449062
$863$	10.5343			0.358591			0.179296	−	0.983795i	$-0.442618\pi$
$863$	10.5343			0.358591			0.179296	+	0.983795i	$0.442618\pi$
$864$			1.00000i			0.0340207i
$865$			22.7665i			0.774086i
$866$			34.9711i			1.18837i
$867$	11.3639			0.385938
$868$			1.14987i			0.0390291i
$869$			74.3113i			2.52084i
$870$			4.41194i			0.149579i
$871$		−	55.2888i		−	1.87339i
$872$	8.62086			0.291939
$873$		−	8.15496i		−	0.276003i
$874$		−	9.28978i		−	0.314232i
$875$			0.374052i			0.0126453i
$876$	−8.19625			−0.276926
$877$	−3.99410			−0.134871			−0.0674356	−	0.997724i	$-0.521482\pi$
$877$	−3.99410			−0.134871			−0.0674356	+	0.997724i	$0.521482\pi$
$878$	−3.27134			−0.110402
$879$	−8.46000			−0.285349
$880$			6.11707i			0.206206i
$881$	−23.9971			−0.808483			−0.404241	−	0.914652i	$-0.632464\pi$
$881$	−23.9971			−0.808483			−0.404241	+	0.914652i	$0.632464\pi$
$882$		−	6.86009i		−	0.230991i
$883$			37.4422i			1.26003i	0.776582	+	0.630016i	$0.216952\pi$
$883$			37.4422i			1.26003i	−0.776582	+	0.630016i	$0.783048\pi$
$884$	12.9342			0.435023
$885$	−10.8963			−0.366275
$886$			21.9645i			0.737911i
$887$	1.33444			0.0448063			0.0224031	−	0.999749i	$-0.492868\pi$
$887$	1.33444			0.0448063			0.0224031	+	0.999749i	$0.492868\pi$
$888$	5.44814	−	2.70513i	0.182828	−	0.0907782i
$889$	6.05443			0.203059
$890$		−	0.551855i		−	0.0184982i
$891$	−6.11707			−0.204930
$892$	10.5703			0.353920
$893$			22.8272i			0.763885i
$894$		−	11.9014i		−	0.398042i
$895$	−11.1304			−0.372049
$896$		−	0.374052i		−	0.0124962i
$897$	−29.6823			−0.991063
$898$	−10.8103			−0.360746
$899$	13.5627			0.452342
$900$	1.00000			0.0333333
$901$		−	5.63612i		−	0.187766i
$902$		−	18.8044i		−	0.626119i
$903$		−	2.92591i		−	0.0973681i
$904$	18.7185			0.622568
$905$			15.3378i			0.509847i
$906$			18.4304i			0.612309i
$907$			18.9342i			0.628699i	0.949307	+	0.314350i	$0.101786\pi$
$907$			18.9342i			0.628699i	−0.949307	+	0.314350i	$0.898214\pi$
$908$		−	2.05633i		−	0.0682418i
$909$	3.74302			0.124148
$910$		−	2.03789i		−	0.0675553i
$911$		−	37.1338i		−	1.23030i	−0.788411	−	0.615149i	$-0.789096\pi$
$911$		−	37.1338i		−	1.23030i	0.788411	−	0.615149i	$-0.210904\pi$
$912$		−	1.70513i		−	0.0564624i
$913$	−41.5104			−1.37379
$914$	−2.74133			−0.0906752
$915$	4.07918			0.134854
$916$	−8.08595			−0.267167
$917$			4.07578i			0.134594i
$918$	2.37405			0.0783554
$919$			27.8548i			0.918846i	0.888218	+	0.459423i	$0.151944\pi$
$919$			27.8548i			0.918846i	−0.888218	+	0.459423i	$0.848056\pi$
$920$			5.44814i			0.179620i
$921$	−16.4683			−0.542648
$922$	30.9526			1.01937
$923$		−	25.8684i		−	0.851467i
$924$	2.28810			0.0752730
$925$	−2.70513	−	5.44814i	−0.0889441	−	0.179134i
$926$	15.7430			0.517348
$927$			8.49112i			0.278885i
$928$	−4.41194			−0.144829
$929$	15.7765			0.517610			0.258805	−	0.965930i	$-0.416671\pi$
$929$	15.7765			0.517610			0.258805	+	0.965930i	$0.416671\pi$
$930$		−	3.07409i		−	0.100803i
$931$			11.6973i			0.383364i
$932$	−22.1253			−0.724740
$933$		−	21.0741i		−	0.689935i
$934$	−17.7007			−0.579185
$935$	14.5222			0.474928
$936$	−5.44814			−0.178078
$937$	19.6546			0.642087			0.321043	−	0.947064i	$-0.395966\pi$
$937$	19.6546			0.642087			0.321043	+	0.947064i	$0.395966\pi$
$938$			3.79595i			0.123942i
$939$			27.6317i			0.901727i
$940$		−	13.3874i		−	0.436649i
$941$	−3.57111			−0.116415			−0.0582075	−	0.998305i	$-0.518539\pi$
$941$	−3.57111			−0.116415			−0.0582075	+	0.998305i	$0.518539\pi$
$942$			7.98056i			0.260021i
$943$		−	16.7481i		−	0.545393i
$944$		−	10.8963i		−	0.354644i
$945$		−	0.374052i		−	0.0121679i
$946$	−47.8489			−1.55570
$947$			12.0462i			0.391448i	0.980659	+	0.195724i	$0.0627056\pi$
$947$			12.0462i			0.391448i	−0.980659	+	0.195724i	$0.937294\pi$
$948$			12.1482i			0.394555i
$949$		−	44.6543i		−	1.44954i
$950$	−1.70513			−0.0553217
$951$	16.4119			0.532194
$952$	−0.888018			−0.0287808
$953$	11.4632			0.371329			0.185665	−	0.982613i	$-0.440556\pi$
$953$	11.4632			0.371329			0.185665	+	0.982613i	$0.440556\pi$
$954$			2.37405i			0.0768628i
$955$	−12.0184			−0.388908
$956$			5.23245i			0.169230i
$957$		−	26.9881i		−	0.872403i
$958$	−4.47945			−0.144724
$959$	0.124470			0.00401933
$960$			1.00000i			0.0322749i
$961$	21.5500			0.695160
$962$	14.7379	+	29.6823i	0.475170	+	0.956995i
$963$	−17.4481			−0.562259
$964$		−	2.50379i		−	0.0806417i
$965$	−17.2291			−0.554623
$966$	2.03789			0.0655680
$967$		−	55.1211i		−	1.77258i	−0.463135	−	0.886288i	$-0.653275\pi$
$967$		−	55.1211i		−	1.77258i	0.463135	−	0.886288i	$-0.346725\pi$
$968$		−	26.4185i		−	0.849124i
$969$	−4.04806			−0.130043
$970$		−	8.15496i		−	0.261840i
$971$	20.6486			0.662644			0.331322	−	0.943518i	$-0.392505\pi$
$971$	20.6486			0.662644			0.331322	+	0.943518i	$0.392505\pi$
$972$	−1.00000			−0.0320750
$973$	−5.19856			−0.166658
$974$	7.32518			0.234714
$975$			5.44814i			0.174480i
$976$			4.07918i			0.130571i
$977$			14.1768i			0.453556i	0.973946	+	0.226778i	$0.0728192\pi$
$977$			14.1768i			0.453556i	−0.973946	+	0.226778i	$0.927181\pi$
$978$	9.86009			0.315291
$979$			3.37574i			0.107889i
$980$		−	6.86009i		−	0.219137i
$981$			8.62086i			0.275243i
$982$			32.0015i			1.02121i
$983$	4.04229			0.128929			0.0644645	−	0.997920i	$-0.479466\pi$
$983$	4.04229			0.128929			0.0644645	+	0.997920i	$0.479466\pi$
$984$		−	3.07409i		−	0.0979985i
$985$		−	1.88970i		−	0.0602109i
$986$			10.4742i			0.333566i
$987$	−5.00759			−0.159393
$988$	9.28978			0.295547
$989$	−42.6165			−1.35512
$990$	−6.11707			−0.194413
$991$		−	16.2147i		−	0.515077i	−0.966268	−	0.257538i	$-0.917089\pi$
$991$		−	16.2147i		−	0.515077i	0.966268	−	0.257538i	$-0.0829114\pi$
$992$	3.07409			0.0976025
$993$			32.9594i			1.04593i
$994$			1.77604i			0.0563325i
$995$	−14.1584			−0.448850
$996$	−6.78599			−0.215022
$997$			41.0722i			1.30077i	0.759605	+	0.650385i	$0.225392\pi$
$997$			41.0722i			1.30077i	−0.759605	+	0.650385i	$0.774608\pi$
$998$	35.4977			1.12366
$999$	2.70513	+	5.44814i	0.0855865	+	0.172372i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1110.2.h.g.961.7	yes	8
3.2	odd	2		3330.2.h.o.2071.3		8
37.36	even	2	inner	1110.2.h.g.961.3	✓	8
111.110	odd	2		3330.2.h.o.2071.7		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1110.2.h.g.961.3	✓	8	37.36	even	2	inner
1110.2.h.g.961.7	yes	8	1.1	even	1	trivial
3330.2.h.o.2071.3		8	3.2	odd	2
3330.2.h.o.2071.7		8	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.h (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} +1.00000 q^{3} -1.00000 q^{4} -1.00000i q^{5} +1.00000i q^{6} +0.374052 q^{7} -1.00000i q^{8} +1.00000 q^{9} +1.00000 q^{10} -6.11707 q^{11} -1.00000 q^{12} -5.44814i q^{13} +0.374052i q^{14} -1.00000i q^{15} +1.00000 q^{16} -2.37405i q^{17} +1.00000i q^{18} -1.70513i q^{19} +1.00000i q^{20} +0.374052 q^{21} -6.11707i q^{22} -5.44814i q^{23} -1.00000i q^{24} -1.00000 q^{25} +5.44814 q^{26} +1.00000 q^{27} -0.374052 q^{28} +4.41194i q^{29} +1.00000 q^{30} -3.07409i q^{31} +1.00000i q^{32} -6.11707 q^{33} +2.37405 q^{34} -0.374052i q^{35} -1.00000 q^{36} +(2.70513 + 5.44814i) q^{37} +1.70513 q^{38} -5.44814i q^{39} -1.00000 q^{40} +3.07409 q^{41} +0.374052i q^{42} -7.82220i q^{43} +6.11707 q^{44} -1.00000i q^{45} +5.44814 q^{46} -13.3874 q^{47} +1.00000 q^{48} -6.86009 q^{49} -1.00000i q^{50} -2.37405i q^{51} +5.44814i q^{52} +2.37405 q^{53} +1.00000i q^{54} +6.11707i q^{55} -0.374052i q^{56} -1.70513i q^{57} -4.41194 q^{58} -10.8963i q^{59} +1.00000i q^{60} +4.07918i q^{61} +3.07409 q^{62} +0.374052 q^{63} -1.00000 q^{64} -5.44814 q^{65} -6.11707i q^{66} +10.1482 q^{67} +2.37405i q^{68} -5.44814i q^{69} +0.374052 q^{70} +4.74810 q^{71} -1.00000i q^{72} +8.19625 q^{73} +(-5.44814 + 2.70513i) q^{74} -1.00000 q^{75} +1.70513i q^{76} -2.28810 q^{77} +5.44814 q^{78} -12.1482i q^{79} -1.00000i q^{80} +1.00000 q^{81} +3.07409i q^{82} +6.78599 q^{83} -0.374052 q^{84} -2.37405 q^{85} +7.82220 q^{86} +4.41194i q^{87} +6.11707i q^{88} -0.551855i q^{89} +1.00000 q^{90} -2.03789i q^{91} +5.44814i q^{92} -3.07409i q^{93} -13.3874i q^{94} -1.70513 q^{95} +1.00000i q^{96} -8.15496i q^{97} -6.86009i q^{98} -6.11707 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 8 q^{3} - 8 q^{4} - 4 q^{7} + 8 q^{9} + 8 q^{10} - 4 q^{11} - 8 q^{12} + 8 q^{16} - 4 q^{21} - 8 q^{25} + 2 q^{26} + 8 q^{27} + 4 q^{28} + 8 q^{30} - 4 q^{33} + 12 q^{34} - 8 q^{36} + 18 q^{37} + 10 q^{38}+ \cdots - 4 q^{99}+O(q^{100}) \) 8 * q + 8 * q^3 - 8 * q^4 - 4 * q^7 + 8 * q^9 + 8 * q^10 - 4 * q^11 - 8 * q^12 + 8 * q^16 - 4 * q^21 - 8 * q^25 + 2 * q^26 + 8 * q^27 + 4 * q^28 + 8 * q^30 - 4 * q^33 + 12 * q^34 - 8 * q^36 + 18 * q^37 + 10 * q^38 - 8 * q^40 - 10 * q^41 + 4 * q^44 + 2 * q^46 + 28 * q^47 + 8 * q^48 + 28 * q^49 + 12 * q^53 + 6 * q^58 - 10 * q^62 - 4 * q^63 - 8 * q^64 - 2 * q^65 + 12 * q^67 - 4 * q^70 + 24 * q^71 + 10 * q^73 - 2 * q^74 - 8 * q^75 - 32 * q^77 + 2 * q^78 + 8 * q^81 + 6 * q^83 + 4 * q^84 - 12 * q^85 + 14 * q^86 + 8 * q^90 - 10 * q^95 - 4 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

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Database

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