LMFDB - Embedded newform 1045.2.f.b.626.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1045,2,Mod(626,1045)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1045, 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("1045.626");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1045 = 5 \cdot 11 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1045.f (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:	$8.34436701122$
Analytic rank:	$0$
Dimension:	$40$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			626.6
Character	$\chi$	$=$	1045.626
Dual form			1045.2.f.b.626.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.34872 q^{2} -1.68631i q^{3} +3.51646 q^{4} +1.00000 q^{5} +3.96066i q^{6} +0.129031i q^{7} -3.56174 q^{8} +0.156361 q^{9} +O(q^{10})$	\(q-2.34872 q^{2} -1.68631i q^{3} +3.51646 q^{4} +1.00000 q^{5} +3.96066i q^{6} +0.129031i q^{7} -3.56174 q^{8} +0.156361 q^{9} -2.34872 q^{10} +(2.08709 - 2.57761i) q^{11} -5.92985i q^{12} -0.796203 q^{13} -0.303057i q^{14} -1.68631i q^{15} +1.33259 q^{16} -0.145494i q^{17} -0.367247 q^{18} +(-4.34664 + 0.326663i) q^{19} +3.51646 q^{20} +0.217586 q^{21} +(-4.90198 + 6.05406i) q^{22} -5.91791 q^{23} +6.00620i q^{24} +1.00000 q^{25} +1.87005 q^{26} -5.32260i q^{27} +0.453733i q^{28} +9.53862 q^{29} +3.96066i q^{30} -1.20563i q^{31} +3.99361 q^{32} +(-4.34664 - 3.51948i) q^{33} +0.341724i q^{34} +0.129031i q^{35} +0.549837 q^{36} -10.6070i q^{37} +(10.2090 - 0.767239i) q^{38} +1.34265i q^{39} -3.56174 q^{40} +2.99763 q^{41} -0.511048 q^{42} -5.01980i q^{43} +(7.33918 - 9.06406i) q^{44} +0.156361 q^{45} +13.8995 q^{46} -4.18420 q^{47} -2.24716i q^{48} +6.98335 q^{49} -2.34872 q^{50} -0.245348 q^{51} -2.79982 q^{52} +11.5975i q^{53} +12.5013i q^{54} +(2.08709 - 2.57761i) q^{55} -0.459575i q^{56} +(0.550855 + 7.32978i) q^{57} -22.4035 q^{58} +14.0728i q^{59} -5.92985i q^{60} -8.51426i q^{61} +2.83169i q^{62} +0.0201754i q^{63} -12.0450 q^{64} -0.796203 q^{65} +(10.2090 + 8.26626i) q^{66} -7.38401i q^{67} -0.511624i q^{68} +9.97942i q^{69} -0.303057i q^{70} -8.32061i q^{71} -0.556917 q^{72} -14.6894i q^{73} +24.9129i q^{74} -1.68631i q^{75} +(-15.2848 + 1.14870i) q^{76} +(0.332591 + 0.269299i) q^{77} -3.15349i q^{78} +2.27930 q^{79} +1.33259 q^{80} -8.50647 q^{81} -7.04059 q^{82} +10.5103i q^{83} +0.765134 q^{84} -0.145494i q^{85} +11.7901i q^{86} -16.0851i q^{87} +(-7.43368 + 9.18077i) q^{88} -6.38464i q^{89} -0.367247 q^{90} -0.102735i q^{91} -20.8101 q^{92} -2.03307 q^{93} +9.82749 q^{94} +(-4.34664 + 0.326663i) q^{95} -6.73446i q^{96} -0.618546i q^{97} -16.4019 q^{98} +(0.326339 - 0.403036i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 40 q^{4} + 40 q^{5} - 28 q^{9}+O(q^{10}) $ 40 * q + 40 * q^4 + 40 * q^5 - 28 * q^9	$ 40 q + 40 q^{4} + 40 q^{5} - 28 q^{9} - 4 q^{11} + 48 q^{16} + 40 q^{20} + 24 q^{23} + 40 q^{25} - 24 q^{26} + 24 q^{36} - 28 q^{38} - 60 q^{42} - 48 q^{44} - 28 q^{45} - 36 q^{49} - 4 q^{55} - 36 q^{58} - 40 q^{64} - 28 q^{66} + 8 q^{77} + 48 q^{80} + 80 q^{81} + 8 q^{82} + 4 q^{92} + 56 q^{93} - 16 q^{99}+O(q^{100}) $ 40 * q + 40 * q^4 + 40 * q^5 - 28 * q^9 - 4 * q^11 + 48 * q^16 + 40 * q^20 + 24 * q^23 + 40 * q^25 - 24 * q^26 + 24 * q^36 - 28 * q^38 - 60 * q^42 - 48 * q^44 - 28 * q^45 - 36 * q^49 - 4 * q^55 - 36 * q^58 - 40 * q^64 - 28 * q^66 + 8 * q^77 + 48 * q^80 + 80 * q^81 + 8 * q^82 + 4 * q^92 + 56 * q^93 - 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1045\mathbb{Z}\right)^\times$.

$n$	$496$	$761$	$837$
$\chi(n)$	$-1$	$-1$	$1$

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 $

$2$	−2.34872			−1.66079			−0.830396	−	0.557173i	$-0.811886\pi$
$2$	−2.34872			−1.66079			−0.830396	+	0.557173i	$0.811886\pi$
$3$		−	1.68631i		−	0.973591i	−0.873516	−	0.486796i	$-0.838166\pi$
$3$		−	1.68631i		−	0.973591i	0.873516	−	0.486796i	$-0.161834\pi$
$4$	3.51646			1.75823
$5$	1.00000			0.447214
$5$	1.00000			0.447214
$6$			3.96066i			1.61693i
$7$			0.129031i			0.0487691i	0.999703	+	0.0243846i	$0.00776262\pi$
$7$			0.129031i			0.0487691i	−0.999703	+	0.0243846i	$0.992237\pi$
$8$	−3.56174			−1.25927
$9$	0.156361			0.0521202
$10$	−2.34872			−0.742729
$11$	2.08709	−	2.57761i	0.629281	−	0.777177i
$11$	2.08709	−	2.57761i	0.629281	−	0.777177i
$12$		−	5.92985i		−	1.71180i
$13$	−0.796203			−0.220827			−0.110414	−	0.993886i	$-0.535218\pi$
$13$	−0.796203			−0.220827			−0.110414	+	0.993886i	$0.535218\pi$
$14$		−	0.303057i		−	0.0809954i
$15$		−	1.68631i		−	0.435403i
$16$	1.33259			0.333148
$17$		−	0.145494i		−	0.0352875i	−0.999844	−	0.0176437i	$-0.994384\pi$
$17$		−	0.145494i		−	0.0352875i	0.999844	−	0.0176437i	$-0.00561647\pi$
$18$	−0.367247			−0.0865609
$19$	−4.34664	+	0.326663i	−0.997188	+	0.0749417i
$19$	−4.34664	+	0.326663i	−0.997188	+	0.0749417i
$20$	3.51646			0.786305
$21$	0.217586			0.0474812
$22$	−4.90198	+	6.05406i	−1.04511	+	1.29073i
$23$	−5.91791			−1.23397			−0.616984	−	0.786975i	$-0.711646\pi$
$23$	−5.91791			−1.23397			−0.616984	+	0.786975i	$0.711646\pi$
$24$			6.00620i			1.22601i
$25$	1.00000			0.200000
$26$	1.87005			0.366748
$27$		−	5.32260i		−	1.02433i
$28$			0.453733i			0.0857475i
$29$	9.53862			1.77128			0.885639	−	0.464375i	$-0.153721\pi$
$29$	9.53862			1.77128			0.885639	+	0.464375i	$0.153721\pi$
$30$			3.96066i			0.723114i
$31$		−	1.20563i		−	0.216538i	−0.994122	−	0.108269i	$-0.965469\pi$
$31$		−	1.20563i		−	0.216538i	0.994122	−	0.108269i	$-0.0345308\pi$
$32$	3.99361			0.705977
$33$	−4.34664	−	3.51948i	−0.756653	−	0.612663i
$34$			0.341724i			0.0586052i
$35$			0.129031i			0.0218102i
$36$	0.549837			0.0916395
$37$		−	10.6070i		−	1.74378i	−0.489698	−	0.871892i	$-0.662893\pi$
$37$		−	10.6070i		−	1.74378i	0.489698	−	0.871892i	$-0.337107\pi$
$38$	10.2090	−	0.767239i	1.65612	−	0.124463i
$39$			1.34265i			0.214995i
$40$	−3.56174			−0.563161
$41$	2.99763			0.468152			0.234076	−	0.972218i	$-0.424794\pi$
$41$	2.99763			0.468152			0.234076	+	0.972218i	$0.424794\pi$
$42$	−0.511048			−0.0788564
$43$		−	5.01980i		−	0.765512i	−0.923850	−	0.382756i	$-0.874975\pi$
$43$		−	5.01980i		−	0.765512i	0.923850	−	0.382756i	$-0.125025\pi$
$44$	7.33918	−	9.06406i	1.10642	−	1.36646i
$45$	0.156361			0.0233089
$46$	13.8995			2.04937
$47$	−4.18420			−0.610328			−0.305164	−	0.952300i	$-0.598711\pi$
$47$	−4.18420			−0.610328			−0.305164	+	0.952300i	$0.598711\pi$
$48$		−	2.24716i		−	0.324350i
$49$	6.98335			0.997622
$50$	−2.34872			−0.332159
$51$	−0.245348			−0.0343556
$52$	−2.79982			−0.388265
$53$			11.5975i			1.59304i	0.604613	+	0.796520i	$0.293328\pi$
$53$			11.5975i			1.59304i	−0.604613	+	0.796520i	$0.706672\pi$
$54$			12.5013i			1.70121i
$55$	2.08709	−	2.57761i	0.281423	−	0.347564i
$56$		−	0.459575i		−	0.0614133i
$57$	0.550855	+	7.32978i	0.0729626	+	0.970853i
$58$	−22.4035			−2.94172
$59$			14.0728i			1.83213i	0.401033	+	0.916064i	$0.368651\pi$
$59$			14.0728i			1.83213i	−0.401033	+	0.916064i	$0.631349\pi$
$60$		−	5.92985i		−	0.765540i
$61$		−	8.51426i		−	1.09014i	−0.838391	−	0.545070i	$-0.816503\pi$
$61$		−	8.51426i		−	1.09014i	0.838391	−	0.545070i	$-0.183497\pi$
$62$			2.83169i			0.359625i
$63$			0.0201754i			0.00254186i
$64$	−12.0450			−1.50563
$65$	−0.796203			−0.0987569
$66$	10.2090	+	8.26626i	1.25664	+	1.01751i
$67$		−	7.38401i		−	0.902100i	−0.892499	−	0.451050i	$-0.851050\pi$
$67$		−	7.38401i		−	0.902100i	0.892499	−	0.451050i	$-0.148950\pi$
$68$		−	0.511624i		−	0.0620436i
$69$			9.97942i			1.20138i
$70$		−	0.303057i		−	0.0362223i
$71$		−	8.32061i		−	0.987475i	−0.869611	−	0.493737i	$-0.835630\pi$
$71$		−	8.32061i		−	0.987475i	0.869611	−	0.493737i	$-0.164370\pi$
$72$	−0.556917			−0.0656332
$73$		−	14.6894i		−	1.71926i	−0.510915	−	0.859631i	$-0.670693\pi$
$73$		−	14.6894i		−	1.71926i	0.510915	−	0.859631i	$-0.329307\pi$
$74$			24.9129i			2.89606i
$75$		−	1.68631i		−	0.194718i
$76$	−15.2848	+	1.14870i	−1.75329	+	0.131765i
$77$	0.332591	+	0.269299i	0.0379023	+	0.0306895i
$78$		−	3.15349i		−	0.357063i
$79$	2.27930			0.256442			0.128221	−	0.991746i	$-0.459073\pi$
$79$	2.27930			0.256442			0.128221	+	0.991746i	$0.459073\pi$
$80$	1.33259			0.148988
$81$	−8.50647			−0.945163
$82$	−7.04059			−0.777503
$83$			10.5103i			1.15365i	0.816867	+	0.576826i	$0.195709\pi$
$83$			10.5103i			1.15365i	−0.816867	+	0.576826i	$0.804291\pi$
$84$	0.765134			0.0834830
$85$		−	0.145494i		−	0.0157810i
$86$			11.7901i			1.27136i
$87$		−	16.0851i		−	1.72450i
$88$	−7.43368	+	9.18077i	−0.792433	+	0.978673i
$89$		−	6.38464i		−	0.676770i	−0.941008	−	0.338385i	$-0.890119\pi$
$89$		−	6.38464i		−	0.676770i	0.941008	−	0.338385i	$-0.109881\pi$
$90$	−0.367247			−0.0387112
$91$		−	0.102735i		−	0.0107695i
$92$	−20.8101			−2.16960
$93$	−2.03307			−0.210820
$94$	9.82749			1.01363
$95$	−4.34664	+	0.326663i	−0.445956	+	0.0335149i
$96$		−	6.73446i		−	0.687333i
$97$		−	0.618546i		−	0.0628038i	−0.999507	−	0.0314019i	$-0.990003\pi$
$97$		−	0.618546i		−	0.0628038i	0.999507	−	0.0314019i	$-0.00999718\pi$
$98$	−16.4019			−1.65684
$99$	0.326339	−	0.403036i	0.0327983	−	0.0405067i
$100$	3.51646			0.351646
$101$		−	12.6138i		−	1.25512i	−0.778567	−	0.627562i	$-0.784053\pi$
$101$		−	12.6138i		−	1.25512i	0.778567	−	0.627562i	$-0.215947\pi$
$102$	0.576252			0.0570575
$103$			8.03929i			0.792135i	0.918221	+	0.396067i	$0.129625\pi$
$103$			8.03929i			0.792135i	−0.918221	+	0.396067i	$0.870375\pi$
$104$	2.83587			0.278080
$105$	0.217586			0.0212342
$106$		−	27.2392i		−	2.64571i
$107$	−11.1360			−1.07656			−0.538278	−	0.842767i	$-0.680925\pi$
$107$	−11.1360			−1.07656			−0.538278	+	0.842767i	$0.680925\pi$
$108$		−	18.7167i		−	1.80102i
$109$	−13.5130			−1.29431			−0.647155	−	0.762359i	$-0.724041\pi$
$109$	−13.5130			−1.29431			−0.647155	+	0.762359i	$0.724041\pi$
$110$	−4.90198	+	6.05406i	−0.467386	+	0.577232i
$111$	−17.8867			−1.69773
$112$			0.171946i			0.0162473i
$113$		−	14.1362i		−	1.32982i	−0.746924	−	0.664909i	$-0.768470\pi$
$113$		−	14.1362i		−	1.32982i	0.746924	−	0.664909i	$-0.231530\pi$
$114$	−1.29380	−	17.2156i	−0.121176	−	1.61239i
$115$	−5.91791			−0.551848
$116$	33.5422			3.11432
$117$	−0.124495			−0.0115096
$118$		−	33.0531i		−	3.04278i
$119$	0.0187732			0.00172094
$120$			6.00620i			0.548288i
$121$	−2.28811	−	10.7594i	−0.208010	−	0.978127i
$122$			19.9976i			1.81050i
$123$		−	5.05494i		−	0.455788i
$124$		−	4.23956i		−	0.380724i
$125$	1.00000			0.0894427
$126$		−	0.0473862i		−	0.00422150i
$127$	−2.91498			−0.258663			−0.129331	−	0.991601i	$-0.541283\pi$
$127$	−2.91498			−0.258663			−0.129331	+	0.991601i	$0.541283\pi$
$128$	20.3031			1.79456
$129$	−8.46493			−0.745296
$130$	1.87005			0.164015
$131$		−	0.455257i		−	0.0397759i	−0.999802	−	0.0198880i	$-0.993669\pi$
$131$		−	0.455257i		−	0.0397759i	0.999802	−	0.0198880i	$-0.00633096\pi$
$132$	−15.2848	−	12.3761i	−1.33037	−	1.07720i
$133$	−0.0421497	−	0.560852i	−0.00365484	−	0.0486320i
$134$			17.3429i			1.49820i
$135$		−	5.32260i		−	0.458097i
$136$			0.518212i			0.0444363i
$137$	17.6638			1.50912			0.754558	−	0.656233i	$-0.227851\pi$
$137$	17.6638			1.50912			0.754558	+	0.656233i	$0.227851\pi$
$138$		−	23.4388i		−	1.99524i
$139$			20.0954i			1.70447i	0.523159	+	0.852235i	$0.324753\pi$
$139$			20.0954i			1.70447i	−0.523159	+	0.852235i	$0.675247\pi$
$140$			0.453733i			0.0383474i
$141$			7.05585i			0.594210i
$142$			19.5427i			1.63999i
$143$	−1.66175	+	2.05230i	−0.138962	+	0.171622i
$144$	0.208365			0.0173637
$145$	9.53862			0.792139
$146$			34.5012i			2.85534i
$147$		−	11.7761i		−	0.971276i
$148$		−	37.2992i		−	3.06598i
$149$		−	17.6142i		−	1.44301i	−0.692409	−	0.721505i	$-0.743450\pi$
$149$		−	17.6142i		−	1.44301i	0.692409	−	0.721505i	$-0.256550\pi$
$150$			3.96066i			0.323387i
$151$	−15.3631			−1.25023			−0.625116	−	0.780532i	$-0.714948\pi$
$151$	−15.3631			−1.25023			−0.625116	+	0.780532i	$0.714948\pi$
$152$	15.4816	−	1.16349i	1.25572	−	0.0943715i
$153$		−	0.0227495i		−	0.00183919i
$154$	−0.781162	−	0.632508i	−0.0629478	−	0.0509689i
$155$		−	1.20563i		−	0.0968388i
$156$			4.72136i			0.378012i
$157$	−16.1914			−1.29222			−0.646108	−	0.763246i	$-0.723604\pi$
$157$	−16.1914			−1.29222			−0.646108	+	0.763246i	$0.723604\pi$
$158$	−5.35343			−0.425896
$159$	19.5570			1.55097
$160$	3.99361			0.315722
$161$		−	0.763593i		−	0.0601796i
$162$	19.9793			1.56972
$163$	−8.67546			−0.679514			−0.339757	−	0.940513i	$-0.610345\pi$
$163$	−8.67546			−0.679514			−0.339757	+	0.940513i	$0.610345\pi$
$164$	10.5411			0.823119
$165$	−4.34664	−	3.51948i	−0.338386	−	0.273991i
$166$		−	24.6856i		−	1.91598i
$167$	19.0328			1.47281			0.736403	−	0.676544i	$-0.236523\pi$
$167$	19.0328			1.47281			0.736403	+	0.676544i	$0.236523\pi$
$168$	−0.774986			−0.0597915
$169$	−12.3661			−0.951235
$170$			0.341724i			0.0262090i
$171$	−0.679644	+	0.0510773i	−0.0519737	+	0.00390598i
$172$		−	17.6519i		−	1.34595i
$173$	6.12997			0.466053			0.233026	−	0.972470i	$-0.425137\pi$
$173$	6.12997			0.466053			0.233026	+	0.972470i	$0.425137\pi$
$174$			37.7792i			2.86404i
$175$			0.129031i			0.00975383i
$176$	2.78124	−	3.43490i	0.209644	−	0.258915i
$177$	23.7312			1.78374
$178$			14.9957i			1.12397i
$179$		−	14.8330i		−	1.10867i	−0.832292	−	0.554337i	$-0.812972\pi$
$179$		−	14.8330i		−	1.10867i	0.832292	−	0.554337i	$-0.187028\pi$
$180$	0.549837			0.0409824
$181$			14.7873i			1.09913i	0.835450	+	0.549566i	$0.185207\pi$
$181$			14.7873i			1.09913i	−0.835450	+	0.549566i	$0.814793\pi$
$182$			0.241295i			0.0178860i
$183$	−14.3577			−1.06135
$184$	21.0781			1.55389
$185$		−	10.6070i		−	0.779844i
$186$	4.77510			0.350127
$187$	−0.375026	−	0.303659i	−0.0274246	−	0.0222058i
$188$	−14.7136			−1.07310
$189$	0.686781			0.0499559
$190$	10.2090	−	0.767239i	0.740640	−	0.0556614i
$191$	−18.8378			−1.36306			−0.681529	−	0.731791i	$-0.738684\pi$
$191$	−18.8378			−1.36306			−0.681529	+	0.731791i	$0.738684\pi$
$192$			20.3116i			1.46587i
$193$	10.0791			0.725512			0.362756	−	0.931884i	$-0.381836\pi$
$193$	10.0791			0.725512			0.362756	+	0.931884i	$0.381836\pi$
$194$			1.45279i			0.104304i
$195$			1.34265i			0.0961488i
$196$	24.5567			1.75405
$197$			25.8968i			1.84507i	0.385915	+	0.922534i	$0.373886\pi$
$197$			25.8968i			1.84507i	−0.385915	+	0.922534i	$0.626114\pi$
$198$	−0.766477	+	0.946618i	−0.0544712	+	0.0672732i
$199$	17.6307			1.24981			0.624903	−	0.780702i	$-0.285138\pi$
$199$	17.6307			1.24981			0.624903	+	0.780702i	$0.285138\pi$
$200$	−3.56174			−0.251853
$201$	−12.4517			−0.878277
$202$			29.6263i			2.08450i
$203$			1.23078i			0.0863837i
$204$	−0.862757			−0.0604051
$205$	2.99763			0.209364
$206$		−	18.8820i		−	1.31557i
$207$	−0.925328			−0.0643147
$208$	−1.06101			−0.0735680
$209$	−8.22982	+	11.8857i	−0.569269	+	0.822151i
$210$	−0.511048			−0.0352657
$211$	−3.39456			−0.233691			−0.116845	−	0.993150i	$-0.537278\pi$
$211$	−3.39456			−0.233691			−0.116845	+	0.993150i	$0.537278\pi$
$212$			40.7822i			2.80093i
$213$	−14.0311			−0.961397
$214$	26.1552			1.78794
$215$		−	5.01980i		−	0.342347i
$216$			18.9577i			1.28991i
$217$	0.155564			0.0105604
$218$	31.7382			2.14958
$219$	−24.7708			−1.67386
$220$	7.33918	−	9.06406i	0.494807	−	0.611099i
$221$			0.115843i			0.00779243i
$222$	42.0108			2.81958
$223$		−	11.2166i		−	0.751119i	−0.926798	−	0.375560i	$-0.877451\pi$
$223$		−	11.2166i		−	0.751119i	0.926798	−	0.375560i	$-0.122549\pi$
$224$			0.515299i			0.0344299i
$225$	0.156361			0.0104240
$226$			33.2018i			2.20855i
$227$	4.37388			0.290304			0.145152	−	0.989409i	$-0.453633\pi$
$227$	4.37388			0.290304			0.145152	+	0.989409i	$0.453633\pi$
$228$	1.93706	+	25.7749i	0.128285	+	1.70699i
$229$	−1.61561			−0.106762			−0.0533812	−	0.998574i	$-0.517000\pi$
$229$	−1.61561			−0.106762			−0.0533812	+	0.998574i	$0.517000\pi$
$230$	13.8995			0.916504
$231$	0.454122	−	0.560852i	0.0298790	−	0.0369013i
$232$	−33.9741			−2.23051
$233$		−	0.431825i		−	0.0282898i	−0.999900	−	0.0141449i	$-0.995497\pi$
$233$		−	0.431825i		−	0.0282898i	0.999900	−	0.0141449i	$-0.00450261\pi$
$234$	0.292403			0.0191150
$235$	−4.18420			−0.272947
$236$			49.4866i			3.22130i
$237$		−	3.84361i		−	0.249669i
$238$	−0.0440930			−0.00285812
$239$		−	11.0267i		−	0.713256i	−0.934246	−	0.356628i	$-0.883926\pi$
$239$		−	11.0267i		−	0.713256i	0.934246	−	0.356628i	$-0.116074\pi$
$240$		−	2.24716i		−	0.145054i
$241$	7.70870			0.496561			0.248280	−	0.968688i	$-0.420135\pi$
$241$	7.70870			0.496561			0.248280	+	0.968688i	$0.420135\pi$
$242$	5.37411	+	25.2708i	0.345461	+	1.62447i
$243$		−	1.62326i		−	0.104132i
$244$		−	29.9401i		−	1.91672i
$245$	6.98335			0.446150
$246$			11.8726i			0.756970i
$247$	3.46081	−	0.260090i	0.220206	−	0.0165492i
$248$			4.29415i			0.272679i
$249$	17.7236			1.12319
$250$	−2.34872			−0.148546
$251$	20.0974			1.26854			0.634269	−	0.773112i	$-0.281301\pi$
$251$	20.0974			1.26854			0.634269	+	0.773112i	$0.281301\pi$
$252$			0.0709460i			0.00446918i
$253$	−12.3512	+	15.2540i	−0.776514	+	0.959013i
$254$	6.84646			0.429585
$255$	−0.245348			−0.0153643
$256$	−23.5962			−1.47476
$257$			9.22758i			0.575601i	0.957690	+	0.287800i	$0.0929240\pi$
$257$			9.22758i			0.575601i	−0.957690	+	0.287800i	$0.907076\pi$
$258$	19.8817			1.23778
$259$	1.36864			0.0850428
$260$	−2.79982			−0.173637
$261$	1.49147			0.0923194
$262$			1.06927i			0.0660596i
$263$			14.3325i			0.883778i	0.897070	+	0.441889i	$0.145691\pi$
$263$			14.3325i			0.883778i	−0.897070	+	0.441889i	$0.854309\pi$
$264$	15.4816	+	12.5355i	0.952828	+	0.771506i
$265$			11.5975i			0.712429i
$266$	0.0989977	+	1.31728i	0.00606994	+	0.0807677i
$267$	−10.7665			−0.658897
$268$		−	25.9656i		−	1.58610i
$269$			9.42055i			0.574381i	0.957873	+	0.287191i	$0.0927213\pi$
$269$			9.42055i			0.574381i	−0.957873	+	0.287191i	$0.907279\pi$
$270$			12.5013i			0.760803i
$271$			9.46149i			0.574745i	0.957819	+	0.287372i	$0.0927817\pi$
$271$			9.46149i			0.574745i	−0.957819	+	0.287372i	$0.907218\pi$
$272$		−	0.193884i		−	0.0117559i
$273$	−0.173243			−0.0104851
$274$	−41.4871			−2.50633
$275$	2.08709	−	2.57761i	0.125856	−	0.155435i
$276$			35.0923i			2.11231i
$277$			0.101601i			0.00610463i	0.999995	+	0.00305232i	$0.000971584\pi$
$277$			0.101601i			0.00610463i	−0.999995	+	0.00305232i	$0.999028\pi$
$278$		−	47.1984i		−	2.83077i
$279$		−	0.188514i		−	0.0112860i
$280$		−	0.459575i		−	0.0274649i
$281$	1.14794			0.0684803			0.0342402	−	0.999414i	$-0.489099\pi$
$281$	1.14794			0.0684803			0.0342402	+	0.999414i	$0.489099\pi$
$282$		−	16.5722i		−	0.986859i
$283$		−	8.31728i		−	0.494411i	−0.968963	−	0.247206i	$-0.920488\pi$
$283$		−	8.31728i		−	0.494411i	0.968963	−	0.247206i	$-0.0795123\pi$
$284$		−	29.2591i		−	1.73621i
$285$	0.550855	+	7.32978i	0.0326299	+	0.434179i
$286$	3.90297	−	4.82027i	0.230788	−	0.285028i
$287$			0.386788i			0.0228314i
$288$	0.624443			0.0367957
$289$	16.9788			0.998755
$290$	−22.4035			−1.31558
$291$	−1.04306			−0.0611453
$292$		−	51.6547i		−	3.02286i
$293$	10.0086			0.584708			0.292354	−	0.956310i	$-0.405561\pi$
$293$	10.0086			0.584708			0.292354	+	0.956310i	$0.405561\pi$
$294$			27.6587i			1.61309i
$295$			14.0728i			0.819352i
$296$			37.7795i			2.19589i
$297$	−13.7196	−	11.1087i	−0.796090	−	0.644595i
$298$			41.3707i			2.39654i
$299$	4.71186			0.272494
$300$		−	5.92985i		−	0.342360i
$301$	0.647710			0.0373334
$302$	36.0836			2.07638
$303$	−21.2708			−1.22198
$304$	−5.79230	+	0.435309i	−0.332211	+	0.0249667i
$305$		−	8.51426i		−	0.487525i
$306$			0.0534322i			0.00305452i
$307$	21.2327			1.21181			0.605907	−	0.795535i	$-0.292810\pi$
$307$	21.2327			1.21181			0.605907	+	0.795535i	$0.292810\pi$
$308$	1.16954	+	0.946982i	0.0666410	+	0.0539593i
$309$	13.5567			0.771215
$310$			2.83169i			0.160829i
$311$	−14.4055			−0.816863			−0.408432	−	0.912789i	$-0.633924\pi$
$311$	−14.4055			−0.816863			−0.408432	+	0.912789i	$0.633924\pi$
$312$		−	4.78216i		−	0.270736i
$313$	14.2598			0.806011			0.403006	−	0.915197i	$-0.367965\pi$
$313$	14.2598			0.806011			0.403006	+	0.915197i	$0.367965\pi$
$314$	38.0290			2.14610
$315$			0.0201754i			0.00113675i
$316$	8.01508			0.450884
$317$			19.0771i			1.07148i	0.844383	+	0.535739i	$0.179967\pi$
$317$			19.0771i			1.07148i	−0.844383	+	0.535739i	$0.820033\pi$
$318$	−45.9338			−2.57584
$319$	19.9080	−	24.5868i	1.11463	−	1.37660i
$320$	−12.0450			−0.673338
$321$			18.7787i			1.04813i
$322$			1.79346i			0.0999458i
$323$	0.0475276	+	0.632410i	0.00264450	+	0.0351882i
$324$	−29.9127			−1.66182
$325$	−0.796203			−0.0441654
$326$	20.3762			1.12853
$327$			22.7871i			1.26013i
$328$	−10.6768			−0.589528
$329$		−	0.539891i		−	0.0297652i
$330$	10.2090	+	8.26626i	0.561988	+	0.455042i
$331$		−	27.4266i		−	1.50750i	−0.657160	−	0.753751i	$-0.728243\pi$
$331$		−	27.4266i		−	1.50750i	0.657160	−	0.753751i	$-0.271757\pi$
$332$			36.9590i			2.02839i
$333$		−	1.65852i		−	0.0908864i
$334$	−44.7027			−2.44602
$335$		−	7.38401i		−	0.403432i
$336$	0.289953			0.0158183
$337$	−29.2669			−1.59427			−0.797134	−	0.603802i	$-0.793652\pi$
$337$	−29.2669			−1.59427			−0.797134	+	0.603802i	$0.793652\pi$
$338$	29.0444			1.57980
$339$	−23.8379			−1.29470
$340$		−	0.511624i		−	0.0277467i
$341$	−3.10765	−	2.51626i	−0.168288	−	0.136263i
$342$	1.59629	−	0.119966i	0.0863175	−	0.00648702i
$343$			1.80429i			0.0974223i
$344$			17.8792i			0.963983i
$345$			9.97942i			0.537274i
$346$	−14.3976			−0.774017
$347$			26.2675i			1.41011i	0.709150	+	0.705057i	$0.249079\pi$
$347$			26.2675i			1.41011i	−0.709150	+	0.705057i	$0.750921\pi$
$348$		−	56.5626i		−	3.03207i
$349$			15.5629i			0.833065i	0.909121	+	0.416533i	$0.136755\pi$
$349$			15.5629i			0.833065i	−0.909121	+	0.416533i	$0.863245\pi$
$350$		−	0.303057i		−	0.0161991i
$351$			4.23787i			0.226201i
$352$	8.33502	−	10.2939i	0.444258	−	0.548669i
$353$	14.9258			0.794420			0.397210	−	0.917728i	$-0.369978\pi$
$353$	14.9258			0.794420			0.397210	+	0.917728i	$0.369978\pi$
$354$	−55.7377			−2.96243
$355$		−	8.32061i		−	0.441612i
$356$		−	22.4513i		−	1.18992i
$357$		−	0.0316575i		−	0.00167549i
$358$			34.8386i			1.84128i
$359$			19.6173i			1.03536i	0.855574	+	0.517681i	$0.173205\pi$
$359$			19.6173i			1.03536i	−0.855574	+	0.517681i	$0.826795\pi$
$360$	−0.556917			−0.0293521
$361$	18.7866	−	2.83978i	0.988767	−	0.149462i
$362$		−	34.7312i		−	1.82543i
$363$	−18.1437	+	3.85846i	−0.952296	+	0.202516i
$364$		−	0.361264i		−	0.0189354i
$365$		−	14.6894i		−	0.768877i
$366$	33.7221			1.76268
$367$	1.84887			0.0965104			0.0482552	−	0.998835i	$-0.484634\pi$
$367$	1.84887			0.0965104			0.0482552	+	0.998835i	$0.484634\pi$
$368$	−7.88615			−0.411094
$369$	0.468712			0.0244002
$370$			24.9129i			1.29516i
$371$	−1.49644			−0.0776912
$372$	−7.14922			−0.370670
$373$	7.36037			0.381106			0.190553	−	0.981677i	$-0.438972\pi$
$373$	7.36037			0.381106			0.190553	+	0.981677i	$0.438972\pi$
$374$	0.880830	+	0.713209i	0.0455466	+	0.0368792i
$375$		−	1.68631i		−	0.0870806i
$376$	14.9030			0.768565
$377$	−7.59468			−0.391146
$378$	−1.61305			−0.0829665
$379$			3.05906i			0.157133i	0.996909	+	0.0785666i	$0.0250343\pi$
$379$			3.05906i			0.157133i	−0.996909	+	0.0785666i	$0.974966\pi$
$380$	−15.2848	+	1.14870i	−0.784094	+	0.0589271i
$381$			4.91556i			0.251832i
$382$	44.2447			2.26376
$383$		−	31.3729i		−	1.60308i	−0.597940	−	0.801541i	$-0.704014\pi$
$383$		−	31.3729i		−	1.60308i	0.597940	−	0.801541i	$-0.295986\pi$
$384$		−	34.2374i		−	1.74717i
$385$	0.332591	+	0.269299i	0.0169504	+	0.0137248i
$386$	−23.6730			−1.20492
$387$		−	0.784899i		−	0.0398987i
$388$		−	2.17509i		−	0.110424i
$389$	6.16885			0.312773			0.156386	−	0.987696i	$-0.450015\pi$
$389$	6.16885			0.312773			0.156386	+	0.987696i	$0.450015\pi$
$390$		−	3.15349i		−	0.159683i
$391$			0.861020i			0.0435436i
$392$	−24.8729			−1.25627
$393$	−0.767703			−0.0387255
$394$		−	60.8242i		−	3.06428i
$395$	2.27930			0.114684
$396$	1.14756	−	1.41726i	0.0576670	−	0.0712201i
$397$	27.2188			1.36607			0.683035	−	0.730385i	$-0.260659\pi$
$397$	27.2188			1.36607			0.683035	+	0.730385i	$0.260659\pi$
$398$	−41.4095			−2.07567
$399$	−0.945769	+	0.0710774i	−0.0473477	+	0.00355832i
$400$	1.33259			0.0666296
$401$		−	10.8407i		−	0.541361i	−0.962669	−	0.270680i	$-0.912751\pi$
$401$		−	10.8407i		−	0.541361i	0.962669	−	0.270680i	$-0.0872486\pi$
$402$	29.2456			1.45864
$403$			0.959929i			0.0478175i
$404$		−	44.3561i		−	2.20680i
$405$	−8.50647			−0.422690
$406$		−	2.89075i		−	0.143465i
$407$	−27.3407	−	22.1378i	−1.35523	−	1.09733i
$408$	0.873866			0.0432628
$409$	2.67844			0.132440			0.0662201	−	0.997805i	$-0.478906\pi$
$409$	2.67844			0.132440			0.0662201	+	0.997805i	$0.478906\pi$
$410$	−7.04059			−0.347710
$411$		−	29.7866i		−	1.46926i
$412$			28.2699i			1.39276i
$413$	−1.81583			−0.0893513
$414$	2.17333			0.106813
$415$			10.5103i			0.515929i
$416$	−3.17972			−0.155899
$417$	33.8871			1.65946
$418$	19.3295	−	27.9161i	0.945438	−	1.36542i
$419$	−0.581694			−0.0284176			−0.0142088	−	0.999899i	$-0.504523\pi$
$419$	−0.581694			−0.0284176			−0.0142088	+	0.999899i	$0.504523\pi$
$420$	0.765134			0.0373347
$421$			11.4781i			0.559407i	0.960086	+	0.279704i	$0.0902362\pi$
$421$			11.4781i			0.559407i	−0.960086	+	0.279704i	$0.909764\pi$
$422$	7.97285			0.388112
$423$	−0.654244			−0.0318104
$424$		−	41.3073i		−	2.00606i
$425$		−	0.145494i		−	0.00705750i
$426$	32.9551			1.59668
$427$	1.09860			0.0531652
$428$	−39.1593			−1.89283
$429$	3.46081	+	2.80222i	0.167089	+	0.135293i
$430$			11.7901i			0.568568i
$431$	6.72334			0.323852			0.161926	−	0.986803i	$-0.448229\pi$
$431$	6.72334			0.323852			0.161926	+	0.986803i	$0.448229\pi$
$432$		−	7.09285i		−	0.341255i
$433$			21.9456i			1.05464i	0.849668	+	0.527318i	$0.176802\pi$
$433$			21.9456i			1.05464i	−0.849668	+	0.527318i	$0.823198\pi$
$434$	−0.365376			−0.0175386
$435$		−	16.0851i		−	0.771220i
$436$	−47.5179			−2.27570
$437$	25.7230	−	1.93316i	1.23050	−	0.0924757i
$438$	58.1797			2.77993
$439$	−8.14123			−0.388560			−0.194280	−	0.980946i	$-0.562237\pi$
$439$	−8.14123			−0.388560			−0.194280	+	0.980946i	$0.562237\pi$
$440$	−7.43368	+	9.18077i	−0.354387	+	0.437676i
$441$	1.09192			0.0519963
$442$		−	0.272082i		−	0.0129416i
$443$	−11.3355			−0.538565			−0.269282	−	0.963061i	$-0.586786\pi$
$443$	−11.3355			−0.538565			−0.269282	+	0.963061i	$0.586786\pi$
$444$	−62.8980			−2.98501
$445$		−	6.38464i		−	0.302661i
$446$			26.3446i			1.24745i
$447$	−29.7030			−1.40490
$448$		−	1.55418i		−	0.0734282i
$449$			2.00299i			0.0945269i	0.998882	+	0.0472635i	$0.0150500\pi$
$449$			2.00299i			0.0945269i	−0.998882	+	0.0472635i	$0.984950\pi$
$450$	−0.367247			−0.0173122
$451$	6.25633	−	7.72672i	0.294599	−	0.363837i
$452$		−	49.7093i		−	2.33813i
$453$			25.9070i			1.21721i
$454$	−10.2730			−0.482136
$455$		−	0.102735i		−	0.00481629i
$456$	−1.96200	−	26.1068i	−0.0918793	−	1.22256i
$457$			1.03164i			0.0482579i	0.999709	+	0.0241289i	$0.00768123\pi$
$457$			1.03164i			0.0482579i	−0.999709	+	0.0241289i	$0.992319\pi$
$458$	3.79460			0.177310
$459$	−0.774406			−0.0361462
$460$	−20.8101			−0.970276
$461$		−	15.5172i		−	0.722706i	−0.932429	−	0.361353i	$-0.882315\pi$
$461$		−	15.5172i		−	0.722706i	0.932429	−	0.361353i	$-0.117685\pi$
$462$	−1.06660	+	1.31728i	−0.0496229	+	0.0612854i
$463$	14.0549			0.653187			0.326593	−	0.945165i	$-0.394099\pi$
$463$	14.0549			0.653187			0.326593	+	0.945165i	$0.394099\pi$
$464$	12.7111			0.590097
$465$	−2.03307			−0.0942814
$466$			1.01423i			0.0469835i
$467$	20.7907			0.962077			0.481039	−	0.876699i	$-0.340260\pi$
$467$	20.7907			0.962077			0.481039	+	0.876699i	$0.340260\pi$
$468$	−0.437782			−0.0202365
$469$	0.952766			0.0439947
$470$	9.82749			0.453308
$471$			27.3037i			1.25809i
$472$		−	50.1238i		−	2.30714i
$473$	−12.9391	−	10.4768i	−0.594939	−	0.481722i
$474$			9.02754i			0.414649i
$475$	−4.34664	+	0.326663i	−0.199438	+	0.0149883i
$476$	0.0660154			0.00302581
$477$			1.81339i			0.0830296i
$478$			25.8985i			1.18457i
$479$		−	6.95752i		−	0.317897i	−0.987287	−	0.158949i	$-0.949190\pi$
$479$		−	6.95752i		−	0.317897i	0.987287	−	0.158949i	$-0.0508104\pi$
$480$		−	6.73446i		−	0.307385i
$481$			8.44535i			0.385075i
$482$	−18.1055			−0.824684
$483$	−1.28765			−0.0585903
$484$	−8.04604	−	37.8350i	−0.365729	−	1.71977i
$485$		−	0.618546i		−	0.0280867i
$486$			3.81258i			0.172942i
$487$		−	12.4774i		−	0.565407i	−0.959207	−	0.282703i	$-0.908769\pi$
$487$		−	12.4774i		−	0.565407i	0.959207	−	0.282703i	$-0.0912312\pi$
$488$			30.3256i			1.37278i
$489$			14.6295i			0.661569i
$490$	−16.4019			−0.740962
$491$		−	37.4983i		−	1.69227i	−0.532966	−	0.846137i	$-0.678923\pi$
$491$		−	37.4983i		−	1.69227i	0.532966	−	0.846137i	$-0.321077\pi$
$492$		−	17.7755i		−	0.801382i
$493$		−	1.38781i		−	0.0625039i
$494$	−8.12846	+	0.610878i	−0.365717	+	0.0274847i
$495$	0.326339	−	0.403036i	0.0146678	−	0.0181151i
$496$		−	1.60662i		−	0.0721392i
$497$	1.07362			0.0481583
$498$	−41.6276			−1.86538
$499$	−24.3747			−1.09116			−0.545580	−	0.838059i	$-0.683691\pi$
$499$	−24.3747			−1.09116			−0.545580	+	0.838059i	$0.683691\pi$
$500$	3.51646			0.157261
$501$		−	32.0953i		−	1.43391i
$502$	−47.2031			−2.10678
$503$			36.0897i			1.60916i	0.593843	+	0.804581i	$0.297610\pi$
$503$			36.0897i			1.60916i	−0.593843	+	0.804581i	$0.702390\pi$
$504$		−	0.0718595i		−	0.00320088i
$505$		−	12.6138i		−	0.561309i
$506$	29.0095	−	35.8274i	1.28963	−	1.59272i
$507$			20.8530i			0.926114i
$508$	−10.2504			−0.454789
$509$		−	13.1945i		−	0.584836i	−0.956291	−	0.292418i	$-0.905540\pi$
$509$		−	13.1945i		−	0.584836i	0.956291	−	0.292418i	$-0.0944599\pi$
$510$	0.576252			0.0255169
$511$	1.89539			0.0838469
$512$	14.8145			0.654716
$513$	1.73870	+	23.1354i	0.0767654	+	1.02145i
$514$		−	21.6730i		−	0.955953i
$515$			8.03929i			0.354253i
$516$	−29.7666			−1.31040
$517$	−8.73280	+	10.7852i	−0.384068	+	0.474333i
$518$	−3.21453			−0.141239
$519$		−	10.3370i		−	0.453745i
$520$	2.83587			0.124361
$521$			26.1772i			1.14684i	0.819260	+	0.573422i	$0.194385\pi$
$521$			26.1772i			1.14684i	−0.819260	+	0.573422i	$0.805615\pi$
$522$	−3.50303			−0.153323
$523$	28.9608			1.26637			0.633184	−	0.774001i	$-0.281747\pi$
$523$	28.9608			1.26637			0.633184	+	0.774001i	$0.281747\pi$
$524$		−	1.60089i		−	0.0699353i
$525$	0.217586			0.00949624
$526$		−	33.6629i		−	1.46777i
$527$	−0.175412			−0.00764108
$528$	−5.79230	−	4.69003i	−0.252077	−	0.204107i
$529$	12.0216			0.522679
$530$		−	27.2392i		−	1.18320i
$531$			2.20044i			0.0954909i
$532$	−0.148218	−	1.97221i	−0.00642606	−	0.0855063i
$533$	−2.38673			−0.103381
$534$	25.2874			1.09429
$535$	−11.1360			−0.481450
$536$			26.2999i			1.13598i
$537$	−25.0131			−1.07939
$538$		−	22.1262i		−	0.953928i
$539$	14.5749	−	18.0003i	0.627785	−	0.775329i
$540$		−	18.7167i		−	0.805440i
$541$		−	23.1544i		−	0.995484i	−0.867325	−	0.497742i	$-0.834163\pi$
$541$		−	23.1544i		−	0.995484i	0.867325	−	0.497742i	$-0.165837\pi$
$542$		−	22.2223i		−	0.954532i
$543$	24.9360			1.07011
$544$		−	0.581046i		−	0.0249121i
$545$	−13.5130			−0.578833
$546$	0.406898			0.0174136
$547$	−28.1729			−1.20459			−0.602293	−	0.798275i	$-0.705746\pi$
$547$	−28.1729			−1.20459			−0.602293	+	0.798275i	$0.705746\pi$
$548$	62.1140			2.65338
$549$		−	1.33130i		−	0.0568183i
$550$	−4.90198	+	6.05406i	−0.209021	+	0.258146i
$551$	−41.4610	+	3.11592i	−1.76630	+	0.132743i
$552$		−	35.5441i		−	1.51286i
$553$			0.294101i			0.0125064i
$554$		−	0.238633i		−	0.0101385i
$555$	−17.8867			−0.759249
$556$			70.6648i			2.99685i
$557$			30.6687i			1.29947i	0.760160	+	0.649736i	$0.225121\pi$
$557$			30.6687i			1.29947i	−0.760160	+	0.649736i	$0.774879\pi$
$558$			0.442765i			0.0187437i
$559$			3.99678i			0.169046i
$560$			0.171946i			0.00726603i
$561$	−0.512063	+	0.632410i	−0.0216193	+	0.0267004i
$562$	−2.69618			−0.113732
$563$	−33.4227			−1.40860			−0.704299	−	0.709904i	$-0.748738\pi$
$563$	−33.4227			−1.40860			−0.704299	+	0.709904i	$0.748738\pi$
$564$			24.8116i			1.04476i
$565$		−	14.1362i		−	0.594713i
$566$			19.5349i			0.821114i
$567$		−	1.09760i		−	0.0460948i
$568$			29.6359i			1.24349i
$569$	40.9456			1.71653			0.858265	−	0.513207i	$-0.171543\pi$
$569$	40.9456			1.71653			0.858265	+	0.513207i	$0.171543\pi$
$570$	−1.29380	−	17.2156i	−0.0541914	−	0.721081i
$571$			25.8065i			1.07997i	0.841675	+	0.539985i	$0.181570\pi$
$571$			25.8065i			1.07997i	−0.841675	+	0.539985i	$0.818430\pi$
$572$	−5.84348	+	7.21683i	−0.244328	+	0.301751i
$573$			31.7664i			1.32706i
$574$		−	0.908454i		−	0.0379182i
$575$	−5.91791			−0.246794
$576$	−1.88337			−0.0784737
$577$	27.7537			1.15540			0.577701	−	0.816248i	$-0.303950\pi$
$577$	27.7537			1.15540			0.577701	+	0.816248i	$0.303950\pi$
$578$	−39.8784			−1.65872
$579$		−	16.9965i		−	0.706352i
$580$	33.5422			1.39276
$581$	−1.35615			−0.0562626
$582$	2.44985			0.101550
$583$	29.8938	+	24.2050i	1.23807	+	1.00247i
$584$			52.3198i			2.16501i
$585$	−0.124495			−0.00514723
$586$	−23.5073			−0.971079
$587$	29.2726			1.20821			0.604105	−	0.796905i	$-0.293531\pi$
$587$	29.2726			1.20821			0.604105	+	0.796905i	$0.293531\pi$
$588$		−	41.4102i		−	1.70773i
$589$	0.393836	+	5.24045i	0.0162277	+	0.215929i
$590$		−	33.0531i		−	1.36077i
$591$	43.6700			1.79634
$592$		−	14.1348i		−	0.580938i
$593$		−	27.8690i		−	1.14444i	−0.820100	−	0.572220i	$-0.806082\pi$
$593$		−	27.8690i		−	1.14444i	0.820100	−	0.572220i	$-0.193918\pi$
$594$	32.2234	+	26.0913i	1.32214	+	1.07054i
$595$	0.0187732			0.000769628
$596$		−	61.9397i		−	2.53715i
$597$		−	29.7308i		−	1.21680i
$598$	−11.0668			−0.452555
$599$			21.9171i			0.895507i	0.894157	+	0.447753i	$0.147776\pi$
$599$			21.9171i			0.895507i	−0.894157	+	0.447753i	$0.852224\pi$
$600$			6.00620i			0.245202i
$601$	−15.7280			−0.641557			−0.320779	−	0.947154i	$-0.603945\pi$
$601$	−15.7280			−0.641557			−0.320779	+	0.947154i	$0.603945\pi$
$602$	−1.52129			−0.0620030
$603$		−	1.15457i		−	0.0470177i
$604$	−54.0238			−2.19820
$605$	−2.28811	−	10.7594i	−0.0930248	−	0.437432i
$606$	49.9591			2.02945
$607$	−4.51503			−0.183260			−0.0916298	−	0.995793i	$-0.529208\pi$
$607$	−4.51503			−0.183260			−0.0916298	+	0.995793i	$0.529208\pi$
$608$	−17.3588	+	1.30456i	−0.703991	+	0.0529071i
$609$	2.07547			0.0841024
$610$			19.9976i			0.809678i
$611$	3.33147			0.134777
$612$		−	0.0799980i		−	0.00323373i
$613$			27.9145i			1.12745i	0.825961	+	0.563727i	$0.190633\pi$
$613$			27.9145i			1.12745i	−0.825961	+	0.563727i	$0.809367\pi$
$614$	−49.8696			−2.01257
$615$		−	5.05494i		−	0.203835i
$616$	−1.18460	−	0.959175i	−0.0477291	−	0.0386463i
$617$	−20.2870			−0.816725			−0.408363	−	0.912820i	$-0.633900\pi$
$617$	−20.2870			−0.816725			−0.408363	+	0.912820i	$0.633900\pi$
$618$	−31.8409			−1.28083
$619$	17.8751			0.718460			0.359230	−	0.933249i	$-0.383039\pi$
$619$	17.8751			0.718460			0.359230	+	0.933249i	$0.383039\pi$
$620$		−	4.23956i		−	0.170265i
$621$			31.4986i			1.26400i
$622$	33.8345			1.35664
$623$	0.823816			0.0330055
$624$			1.78920i			0.0716252i
$625$	1.00000			0.0400000
$626$	−33.4922			−1.33862
$627$	20.0430	+	13.8780i	0.800439	+	0.554235i
$628$	−56.9365			−2.27201
$629$	−1.54326			−0.0615337
$630$		−	0.0473862i		−	0.00188791i
$631$	4.04769			0.161136			0.0805680	−	0.996749i	$-0.474327\pi$
$631$	4.04769			0.161136			0.0805680	+	0.996749i	$0.474327\pi$
$632$	−8.11829			−0.322928
$633$			5.72427i			0.227519i
$634$		−	44.8068i		−	1.77950i
$635$	−2.91498			−0.115677
$636$	68.7714			2.72696
$637$	−5.56017			−0.220302
$638$	−46.7582	+	57.7474i	−1.85117	+	2.28624i
$639$		−	1.30102i		−	0.0514674i
$640$	20.3031			0.802552
$641$		−	13.7278i		−	0.542214i	−0.962549	−	0.271107i	$-0.912610\pi$
$641$		−	13.7278i		−	0.542214i	0.962549	−	0.271107i	$-0.0873897\pi$
$642$		−	44.1058i		−	1.74072i
$643$	29.4705			1.16220			0.581101	−	0.813832i	$-0.302622\pi$
$643$	29.4705			1.16220			0.581101	+	0.813832i	$0.302622\pi$
$644$		−	2.68515i		−	0.105810i
$645$	−8.46493			−0.333306
$646$	−0.111629	−	1.48535i	−0.00439197	−	0.0584404i
$647$	34.9788			1.37516			0.687580	−	0.726109i	$-0.258673\pi$
$647$	34.9788			1.37516			0.687580	+	0.726109i	$0.258673\pi$
$648$	30.2979			1.19021
$649$	36.2742	+	29.3713i	1.42389	+	1.15292i
$650$	1.87005			0.0733496
$651$		−	0.262329i		−	0.0102815i
$652$	−30.5069			−1.19474
$653$	39.1254			1.53109			0.765547	−	0.643380i	$-0.222469\pi$
$653$	39.1254			1.53109			0.765547	+	0.643380i	$0.222469\pi$
$654$		−	53.5204i		−	2.09281i
$655$		−	0.455257i		−	0.0177883i
$656$	3.99462			0.155964
$657$		−	2.29684i		−	0.0896083i
$658$			1.26805i			0.0494338i
$659$	25.1007			0.977786			0.488893	−	0.872344i	$-0.337401\pi$
$659$	25.1007			0.977786			0.488893	+	0.872344i	$0.337401\pi$
$660$	−15.2848	−	12.3761i	−0.594960	−	0.481740i
$661$		−	13.4355i		−	0.522582i	−0.965260	−	0.261291i	$-0.915852\pi$
$661$		−	13.4355i		−	0.522582i	0.965260	−	0.261291i	$-0.0841482\pi$
$662$			64.4172i			2.50365i
$663$	0.195347			0.00758664
$664$		−	37.4349i		−	1.45276i
$665$	−0.0421497	−	0.560852i	−0.00163450	−	0.0217489i
$666$			3.89540i			0.150943i
$667$	−56.4487			−2.18570
$668$	66.9283			2.58953
$669$	−18.9147			−0.731283
$670$			17.3429i			0.670016i
$671$	−21.9464	−	17.7700i	−0.847232	−	0.686005i
$672$	0.868954			0.0335206
$673$	34.0790			1.31365			0.656825	−	0.754043i	$-0.271899\pi$
$673$	34.0790			1.31365			0.656825	+	0.754043i	$0.271899\pi$
$674$	68.7395			2.64775
$675$		−	5.32260i		−	0.204867i
$676$	−43.4848			−1.67249
$677$	−47.1954			−1.81387			−0.906933	−	0.421275i	$-0.861583\pi$
$677$	−47.1954			−1.81387			−0.906933	+	0.421275i	$0.861583\pi$
$678$	55.9885			2.15023
$679$	0.0798116			0.00306289
$680$			0.518212i			0.0198725i
$681$		−	7.37571i		−	0.282638i
$682$	7.29898	+	5.90999i	0.279492	+	0.226305i
$683$		−	8.38767i		−	0.320945i	−0.987040	−	0.160473i	$-0.948698\pi$
$683$		−	8.38767i		−	0.320945i	0.987040	−	0.160473i	$-0.0513018\pi$
$684$	−2.38994	+	0.179611i	−0.0913818	+	0.00686762i
$685$	17.6638			0.674897
$686$		−	4.23775i		−	0.161798i
$687$			2.72441i			0.103943i
$688$		−	6.68934i		−	0.255029i
$689$		−	9.23397i		−	0.351786i
$690$		−	23.4388i		−	0.892301i
$691$	−42.4821			−1.61610			−0.808048	−	0.589117i	$-0.799476\pi$
$691$	−42.4821			−1.61610			−0.808048	+	0.589117i	$0.799476\pi$
$692$	21.5558			0.819429
$693$	0.0520042	+	0.0421078i	0.00197548	+	0.00159954i
$694$		−	61.6950i		−	2.34191i
$695$			20.0954i			0.762262i
$696$			57.2909i			2.17160i
$697$		−	0.436138i		−	0.0165199i
$698$		−	36.5529i		−	1.38355i
$699$	−0.728191			−0.0275427
$700$			0.453733i			0.0171495i
$701$			12.6918i			0.479363i	0.970852	+	0.239681i	$0.0770430\pi$
$701$			12.6918i			0.479363i	−0.970852	+	0.239681i	$0.922957\pi$
$702$		−	9.95356i		−	0.375673i
$703$	3.46493	+	46.1049i	0.130682	+	1.73888i
$704$	−25.1391	+	31.0473i	−0.947464	+	1.17014i
$705$			7.05585i			0.265739i
$706$	−35.0564			−1.31937
$707$	1.62758			0.0612113
$708$	83.4498			3.13623
$709$	−3.09588			−0.116268			−0.0581341	−	0.998309i	$-0.518515\pi$
$709$	−3.09588			−0.116268			−0.0581341	+	0.998309i	$0.518515\pi$
$710$			19.5427i			0.733426i
$711$	0.356393			0.0133658
$712$			22.7404i			0.852234i
$713$			7.13482i			0.267201i
$714$			0.0743544i			0.00278264i
$715$	−1.66175	+	2.05230i	−0.0621459	+	0.0767516i
$716$		−	52.1599i		−	1.94931i
$717$	−18.5944			−0.694420
$718$		−	46.0755i		−	1.71952i
$719$	25.1971			0.939695			0.469847	−	0.882748i	$-0.344309\pi$
$719$	25.1971			0.939695			0.469847	+	0.882748i	$0.344309\pi$
$720$	0.208365			0.00776530
$721$	−1.03732			−0.0386317
$722$	−44.1243	+	6.66983i	−1.64214	+	0.248225i
$723$		−	12.9992i		−	0.483447i
$724$			51.9991i			1.93253i
$725$	9.53862			0.354256
$726$	42.6143	−	9.06241i	1.58157	−	0.336338i
$727$	36.3464			1.34801			0.674006	−	0.738726i	$-0.264572\pi$
$727$	36.3464			1.34801			0.674006	+	0.738726i	$0.264572\pi$
$728$			0.365915i			0.0135617i
$729$	−28.2567			−1.04655
$730$			34.5012i			1.27695i
$731$	−0.730350			−0.0270130
$732$	−50.4883			−1.86610
$733$			32.6507i			1.20598i	0.797748	+	0.602991i	$0.206025\pi$
$733$			32.6507i			1.20598i	−0.797748	+	0.602991i	$0.793975\pi$
$734$	−4.34248			−0.160284
$735$		−	11.7761i		−	0.434368i
$736$	−23.6338			−0.871153
$737$	−19.0331	−	15.4111i	−0.701092	−	0.567675i
$738$	−1.10087			−0.0405236
$739$			13.4790i			0.495833i	0.968781	+	0.247916i	$0.0797458\pi$
$739$			13.4790i			0.495833i	−0.968781	+	0.247916i	$0.920254\pi$
$740$		−	37.2992i		−	1.37115i
$741$	−0.438593	−	5.83600i	−0.0161121	−	0.214391i
$742$	3.51471			0.129029
$743$	3.46818			0.127235			0.0636175	−	0.997974i	$-0.479736\pi$
$743$	3.46818			0.127235			0.0636175	+	0.997974i	$0.479736\pi$
$744$	7.24127			0.265478
$745$		−	17.6142i		−	0.645334i
$746$	−17.2874			−0.632937
$747$			1.64339i			0.0601286i
$748$	−1.31877	−	1.06781i	−0.0482189	−	0.0390429i
$749$		−	1.43689i		−	0.0525027i
$750$			3.96066i			0.144623i
$751$		−	2.32314i		−	0.0847725i	−0.999101	−	0.0423862i	$-0.986504\pi$
$751$		−	2.32314i		−	0.0847725i	0.999101	−	0.0423862i	$-0.0134960\pi$
$752$	−5.57582			−0.203329
$753$		−	33.8905i		−	1.23504i
$754$	17.8377			0.649612
$755$	−15.3631			−0.559121
$756$	2.41504			0.0878341
$757$	−54.4023			−1.97729			−0.988643	−	0.150280i	$-0.951982\pi$
$757$	−54.4023			−1.97729			−0.988643	+	0.150280i	$0.951982\pi$
$758$		−	7.18486i		−	0.260966i
$759$	25.7230	+	20.8280i	0.933686	+	0.756007i
$760$	15.4816	−	1.16349i	0.561577	−	0.0422042i
$761$		−	28.1755i		−	1.02136i	−0.859771	−	0.510680i	$-0.829394\pi$
$761$		−	28.1755i		−	1.02136i	0.859771	−	0.510680i	$-0.170606\pi$
$762$		−	11.5452i		−	0.418240i
$763$		−	1.74360i		−	0.0631224i
$764$	−66.2425			−2.39657
$765$		−	0.0227495i		−	0.000822512i
$766$			73.6861i			2.66239i
$767$		−	11.2048i		−	0.404583i
$768$			39.7905i			1.43582i
$769$		−	18.9947i		−	0.684965i	−0.939524	−	0.342482i	$-0.888732\pi$
$769$		−	18.9947i		−	0.684965i	0.939524	−	0.342482i	$-0.111268\pi$
$770$	−0.781162	−	0.632508i	−0.0281511	−	0.0227940i
$771$	15.5606			0.560400
$772$	35.4429			1.27562
$773$			35.4871i			1.27638i	0.769878	+	0.638192i	$0.220317\pi$
$773$			35.4871i			1.27638i	−0.769878	+	0.638192i	$0.779683\pi$
$774$			1.84350i			0.0662634i
$775$		−	1.20563i		−	0.0433076i
$776$			2.20310i			0.0790867i
$777$		−	2.30794i		−	0.0827970i
$778$	−14.4889			−0.519451
$779$	−13.0296	+	0.979217i	−0.466835	+	0.0350841i
$780$			4.72136i			0.169052i
$781$	−21.4473	−	17.3659i	−0.767443	−	0.621399i
$782$		−	2.02229i		−	0.0723170i
$783$		−	50.7703i		−	1.81438i
$784$	9.30595			0.332355
$785$	−16.1914			−0.577896
$786$	1.80312			0.0643150
$787$	−0.993787			−0.0354247			−0.0177123	−	0.999843i	$-0.505638\pi$
$787$	−0.993787			−0.0354247			−0.0177123	+	0.999843i	$0.505638\pi$
$788$			91.0651i			3.24406i
$789$	24.1690			0.860438
$790$	−5.35343			−0.190467
$791$	1.82400			0.0648541
$792$	−1.16234	+	1.43551i	−0.0413018	+	0.0510087i
$793$			6.77908i			0.240732i
$794$	−63.9291			−2.26876
$795$	19.5570			0.693614
$796$	61.9977			2.19745
$797$			2.17389i			0.0770030i	0.999259	+	0.0385015i	$0.0122584\pi$
$797$			2.17389i			0.0770030i	−0.999259	+	0.0385015i	$0.987742\pi$
$798$	2.22134	−	0.166941i	0.0786347	−	0.00590964i
$799$			0.608775i			0.0215369i
$800$	3.99361			0.141195
$801$		−	0.998306i		−	0.0352734i
$802$			25.4618i			0.899088i
$803$	−37.8634	−	30.6581i	−1.33617	−	1.08190i
$804$	−43.7860			−1.54421
$805$		−	0.763593i		−	0.0269131i
$806$		−	2.25460i		−	0.0794149i
$807$	15.8860			0.559213
$808$			44.9273i			1.58054i
$809$			53.1896i			1.87005i	0.354588	+	0.935023i	$0.384621\pi$
$809$			53.1896i			1.87005i	−0.354588	+	0.935023i	$0.615379\pi$
$810$	19.9793			0.702000
$811$	−15.7548			−0.553224			−0.276612	−	0.960982i	$-0.589212\pi$
$811$	−15.7548			−0.553224			−0.276612	+	0.960982i	$0.589212\pi$
$812$			4.32799i			0.151883i
$813$	15.9550			0.559566
$814$	64.2156	+	51.9954i	2.25076	+	1.82244i
$815$	−8.67546			−0.303888
$816$	−0.326948			−0.0114455
$817$	1.63978	+	21.8193i	0.0573688	+	0.763359i
$818$	−6.29089			−0.219956
$819$		−	0.0160637i		−	0.000561311i
$820$	10.5411			0.368110
$821$			22.6839i			0.791675i	0.918321	+	0.395837i	$0.129546\pi$
$821$			22.6839i			0.791675i	−0.918321	+	0.395837i	$0.870454\pi$
$822$			69.9602i			2.44014i
$823$	−10.2949			−0.358858			−0.179429	−	0.983771i	$-0.557425\pi$
$823$	−10.2949			−0.358858			−0.179429	+	0.983771i	$0.557425\pi$
$824$		−	28.6339i		−	0.997508i
$825$	−4.34664	−	3.51948i	−0.151331	−	0.122533i
$826$	4.26487			0.148394
$827$	19.9919			0.695188			0.347594	−	0.937645i	$-0.386999\pi$
$827$	19.9919			0.695188			0.347594	+	0.937645i	$0.386999\pi$
$828$	−3.25388			−0.113080
$829$			39.8327i			1.38345i	0.722162	+	0.691724i	$0.243148\pi$
$829$			39.8327i			1.38345i	−0.722162	+	0.691724i	$0.756852\pi$
$830$		−	24.6856i		−	0.856851i
$831$	0.171331			0.00594342
$832$	9.59029			0.332484
$833$		−	1.01604i		−	0.0352036i
$834$	−79.5911			−2.75601
$835$	19.0328			0.658659
$836$	−28.9399	+	41.7957i	−1.00091	+	1.44553i
$837$	−6.41710			−0.221807
$838$	1.36623			0.0471958
$839$			49.5790i			1.71166i	0.517258	+	0.855829i	$0.326953\pi$
$839$			49.5790i			1.71166i	−0.517258	+	0.855829i	$0.673047\pi$
$840$	−0.774986			−0.0267396
$841$	61.9853			2.13742
$842$		−	26.9587i		−	0.929059i
$843$		−	1.93578i		−	0.0666719i
$844$	−11.9368			−0.410883
$845$	−12.3661			−0.425405
$846$	1.53663			0.0528305
$847$	1.38830	−	0.295237i	0.0477024	−	0.0101445i
$848$			15.4547i			0.530718i
$849$	−14.0255			−0.481354
$850$			0.341724i			0.0117210i
$851$			62.7714i			2.15177i
$852$	−49.3399			−1.69036
$853$		−	23.3203i		−	0.798470i	−0.916849	−	0.399235i	$-0.869276\pi$
$853$		−	23.3203i		−	0.798470i	0.916849	−	0.399235i	$-0.130724\pi$
$854$	−2.58031			−0.0882963
$855$	−0.679644	+	0.0510773i	−0.0232433	+	0.00174681i
$856$	39.6635			1.35567
$857$	14.6808			0.501487			0.250743	−	0.968054i	$-0.419325\pi$
$857$	14.6808			0.501487			0.250743	+	0.968054i	$0.419325\pi$
$858$	−8.12846	−	6.58162i	−0.277501	−	0.224693i
$859$	27.2095			0.928375			0.464188	−	0.885737i	$-0.346346\pi$
$859$	27.2095			0.928375			0.464188	+	0.885737i	$0.346346\pi$
$860$		−	17.6519i		−	0.601926i
$861$	0.652244			0.0222284
$862$	−15.7912			−0.537851
$863$			24.1514i			0.822124i	0.911607	+	0.411062i	$0.134842\pi$
$863$			24.1514i			0.822124i	−0.911607	+	0.411062i	$0.865158\pi$
$864$		−	21.2564i		−	0.723157i
$865$	6.12997			0.208425
$866$		−	51.5439i		−	1.75153i
$867$		−	28.6316i		−	0.972379i
$868$	0.547035			0.0185676
$869$	4.75711	−	5.87514i	0.161374	−	0.199301i
$870$			37.7792i			1.28084i
$871$			5.87917i			0.199208i
$872$	48.1298			1.62988
$873$		−	0.0967163i		−	0.00327335i
$874$	−60.4160	+	4.54045i	−2.04360	+	0.153583i
$875$			0.129031i			0.00436204i
$876$	−87.1058			−2.94303
$877$	−1.41918			−0.0479222			−0.0239611	−	0.999713i	$-0.507628\pi$
$877$	−1.41918			−0.0479222			−0.0239611	+	0.999713i	$0.507628\pi$
$878$	19.1214			0.645317
$879$		−	16.8776i		−	0.569267i
$880$	2.78124	−	3.43490i	0.0937555	−	0.115790i
$881$	−19.4278			−0.654538			−0.327269	−	0.944931i	$-0.606128\pi$
$881$	−19.4278			−0.654538			−0.327269	+	0.944931i	$0.606128\pi$
$882$	−2.56461			−0.0863550
$883$	12.9524			0.435882			0.217941	−	0.975962i	$-0.430066\pi$
$883$	12.9524			0.435882			0.217941	+	0.975962i	$0.430066\pi$
$884$			0.407357i			0.0137009i
$885$	23.7312			0.797714
$886$	26.6238			0.894444
$887$	0.696909			0.0233999			0.0117000	−	0.999932i	$-0.496276\pi$
$887$	0.696909			0.0233999			0.0117000	+	0.999932i	$0.496276\pi$
$888$	63.7079			2.13790
$889$		−	0.376123i		−	0.0126148i
$890$			14.9957i			0.502657i
$891$	−17.7538	+	21.9263i	−0.594774	+	0.734560i
$892$		−	39.4428i		−	1.32064i
$893$	18.1872	−	1.36682i	0.608611	−	0.0457390i
$894$	69.7638			2.33325
$895$		−	14.8330i		−	0.495814i
$896$			2.61973i			0.0875192i
$897$		−	7.94565i		−	0.265297i
$898$		−	4.70445i		−	0.156990i
$899$		−	11.5001i		−	0.383549i
$900$	0.549837			0.0183279
$901$	1.68737			0.0562143
$902$	−14.6943	+	18.1479i	−0.489268	+	0.604258i
$903$		−	1.09224i		−	0.0363474i
$904$			50.3494i			1.67459i
$905$			14.7873i			0.491547i
$906$		−	60.8481i		−	2.02154i
$907$		−	27.8889i		−	0.926035i	−0.886349	−	0.463018i	$-0.846767\pi$
$907$		−	27.8889i		−	0.926035i	0.886349	−	0.463018i	$-0.153233\pi$
$908$	15.3806			0.510423
$909$		−	1.97231i		−	0.0654174i
$910$			0.241295i			0.00799886i
$911$			10.3104i			0.341598i	0.985306	+	0.170799i	$0.0546349\pi$
$911$			10.3104i			0.341598i	−0.985306	+	0.170799i	$0.945365\pi$
$912$	0.734065	+	9.76760i	0.0243073	+	0.323438i
$913$	27.0913	+	21.9359i	0.896593	+	0.725972i
$914$		−	2.42302i		−	0.0801464i
$915$	−14.3577			−0.474650
$916$	−5.68123			−0.187713
$917$	0.0587422			0.00193984
$918$	1.81886			0.0600313
$919$		−	22.0448i		−	0.727192i	−0.931557	−	0.363596i	$-0.881549\pi$
$919$		−	22.0448i		−	0.727192i	0.931557	−	0.363596i	$-0.118451\pi$
$920$	21.0781			0.694923
$921$		−	35.8049i		−	1.17981i
$922$			36.4454i			1.20026i
$923$			6.62490i			0.218061i
$924$	1.59690	−	1.97221i	0.0525343	−	0.0648811i
$925$		−	10.6070i		−	0.348757i
$926$	−33.0110			−1.08481
$927$			1.25703i			0.0412862i
$928$	38.0935			1.25048
$929$	19.6407			0.644392			0.322196	−	0.946673i	$-0.395579\pi$
$929$	19.6407			0.644392			0.322196	+	0.946673i	$0.395579\pi$
$930$	4.77510			0.156582
$931$	−30.3541	+	2.28120i	−0.994816	+	0.0747635i
$932$		−	1.51850i		−	0.0497400i
$933$			24.2922i			0.795291i
$934$	−48.8314			−1.59781
$935$	−0.375026	−	0.303659i	−0.0122647	−	0.00993072i
$936$	0.443419			0.0144936
$937$		−	4.38100i		−	0.143121i	−0.997436	−	0.0715604i	$-0.977202\pi$
$937$		−	4.38100i		−	0.143121i	0.997436	−	0.0715604i	$-0.0227979\pi$
$938$	−2.23778			−0.0730660
$939$		−	24.0464i		−	0.784726i
$940$	−14.7136			−0.479904
$941$	56.2201			1.83272			0.916362	−	0.400352i	$-0.131112\pi$
$941$	56.2201			1.83272			0.916362	+	0.400352i	$0.131112\pi$
$942$		−	64.1287i		−	2.08943i
$943$	−17.7397			−0.577685
$944$			18.7533i			0.610369i
$945$	0.686781			0.0223410
$946$	30.3902	+	24.6070i	0.988070	+	0.800041i
$947$	−12.8639			−0.418020			−0.209010	−	0.977913i	$-0.567024\pi$
$947$	−12.8639			−0.418020			−0.209010	+	0.977913i	$0.567024\pi$
$948$		−	13.5159i		−	0.438976i
$949$			11.6957i			0.379660i
$950$	10.2090	−	0.767239i	0.331224	−	0.0248925i
$951$	32.1700			1.04318
$952$	−0.0668654			−0.00216712
$953$	46.2811			1.49919			0.749596	−	0.661896i	$-0.230248\pi$
$953$	46.2811			1.49919			0.749596	+	0.661896i	$0.230248\pi$
$954$		−	4.25914i		−	0.137895i
$955$	−18.8378			−0.609578
$956$		−	38.7749i		−	1.25407i
$957$	−41.4610	−	33.5710i	−1.34024	−	1.08520i
$958$			16.3412i			0.527961i
$959$			2.27917i			0.0735983i
$960$			20.3116i			0.655556i
$961$	29.5464			0.953111
$962$		−	19.8357i		−	0.639529i
$963$	−1.74123			−0.0561103
$964$	27.1074			0.873069
$965$	10.0791			0.324459
$966$	3.02433			0.0973064
$967$		−	17.5981i		−	0.565916i	−0.959132	−	0.282958i	$-0.908684\pi$
$967$		−	17.5981i		−	0.565916i	0.959132	−	0.282958i	$-0.0913157\pi$
$968$	8.14965	+	38.3222i	0.261940	+	1.23172i
$969$	1.06644	−	0.0801462i	0.0342590	−	0.00257467i
$970$			1.45279i			0.0466462i
$971$			38.0228i			1.22021i	0.792321	+	0.610104i	$0.208872\pi$
$971$			38.0228i			1.22021i	−0.792321	+	0.610104i	$0.791128\pi$
$972$		−	5.70815i		−	0.183089i
$973$	−2.59293			−0.0831256
$974$			29.3060i			0.939024i
$975$			1.34265i			0.0429991i
$976$		−	11.3460i		−	0.363178i
$977$			38.6655i			1.23702i	0.785778	+	0.618509i	$0.212263\pi$
$977$			38.6655i			1.23702i	−0.785778	+	0.618509i	$0.787737\pi$
$978$		−	34.3605i		−	1.09873i
$979$	−16.4571	−	13.3253i	−0.525971	−	0.425879i
$980$	24.5567			0.784435
$981$	−2.11290			−0.0674597
$982$			88.0728i			2.81051i
$983$		−	16.8659i		−	0.537939i	−0.963149	−	0.268969i	$-0.913317\pi$
$983$		−	16.8659i		−	0.537939i	0.963149	−	0.268969i	$-0.0866830\pi$
$984$			18.0044i			0.573959i
$985$			25.8968i			0.825140i
$986$			3.25958i			0.103806i
$987$	−0.910423			−0.0289791
$988$	12.1698	−	0.914599i	0.387173	−	0.0290973i
$989$			29.7067i			0.944618i
$990$	−0.766477	+	0.946618i	−0.0243602	+	0.0300855i
$991$			6.32573i			0.200943i	0.994940	+	0.100472i	$0.0320352\pi$
$991$			6.32573i			0.200943i	−0.994940	+	0.100472i	$0.967965\pi$
$992$		−	4.81482i		−	0.152871i
$993$	−46.2497			−1.46769
$994$	−2.52162			−0.0799809
$995$	17.6307			0.558930
$996$	62.3243			1.97482
$997$			27.6464i			0.875570i	0.899080	+	0.437785i	$0.144237\pi$
$997$			27.6464i			0.875570i	−0.899080	+	0.437785i	$0.855763\pi$
$998$	57.2492			1.81219
$999$	−56.4569			−1.78622

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1045.2.f.b.626.6	yes	40
11.10	odd	2	inner	1045.2.f.b.626.36	yes	40
19.18	odd	2	inner	1045.2.f.b.626.35	yes	40
209.208	even	2	inner	1045.2.f.b.626.5	✓	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1045.2.f.b.626.5	✓	40	209.208	even	2	inner
1045.2.f.b.626.6	yes	40	1.1	even	1	trivial
1045.2.f.b.626.35	yes	40	19.18	odd	2	inner
1045.2.f.b.626.36	yes	40	11.10	odd	2	inner

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:	\( N \)	\(=\)	\( 1045 = 5 \cdot 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1045.f (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-2.34872 q^{2} -1.68631i q^{3} +3.51646 q^{4} +1.00000 q^{5} +3.96066i q^{6} +0.129031i q^{7} -3.56174 q^{8} +0.156361 q^{9} +O(q^{10})\)	\(q-2.34872 q^{2} -1.68631i q^{3} +3.51646 q^{4} +1.00000 q^{5} +3.96066i q^{6} +0.129031i q^{7} -3.56174 q^{8} +0.156361 q^{9} -2.34872 q^{10} +(2.08709 - 2.57761i) q^{11} -5.92985i q^{12} -0.796203 q^{13} -0.303057i q^{14} -1.68631i q^{15} +1.33259 q^{16} -0.145494i q^{17} -0.367247 q^{18} +(-4.34664 + 0.326663i) q^{19} +3.51646 q^{20} +0.217586 q^{21} +(-4.90198 + 6.05406i) q^{22} -5.91791 q^{23} +6.00620i q^{24} +1.00000 q^{25} +1.87005 q^{26} -5.32260i q^{27} +0.453733i q^{28} +9.53862 q^{29} +3.96066i q^{30} -1.20563i q^{31} +3.99361 q^{32} +(-4.34664 - 3.51948i) q^{33} +0.341724i q^{34} +0.129031i q^{35} +0.549837 q^{36} -10.6070i q^{37} +(10.2090 - 0.767239i) q^{38} +1.34265i q^{39} -3.56174 q^{40} +2.99763 q^{41} -0.511048 q^{42} -5.01980i q^{43} +(7.33918 - 9.06406i) q^{44} +0.156361 q^{45} +13.8995 q^{46} -4.18420 q^{47} -2.24716i q^{48} +6.98335 q^{49} -2.34872 q^{50} -0.245348 q^{51} -2.79982 q^{52} +11.5975i q^{53} +12.5013i q^{54} +(2.08709 - 2.57761i) q^{55} -0.459575i q^{56} +(0.550855 + 7.32978i) q^{57} -22.4035 q^{58} +14.0728i q^{59} -5.92985i q^{60} -8.51426i q^{61} +2.83169i q^{62} +0.0201754i q^{63} -12.0450 q^{64} -0.796203 q^{65} +(10.2090 + 8.26626i) q^{66} -7.38401i q^{67} -0.511624i q^{68} +9.97942i q^{69} -0.303057i q^{70} -8.32061i q^{71} -0.556917 q^{72} -14.6894i q^{73} +24.9129i q^{74} -1.68631i q^{75} +(-15.2848 + 1.14870i) q^{76} +(0.332591 + 0.269299i) q^{77} -3.15349i q^{78} +2.27930 q^{79} +1.33259 q^{80} -8.50647 q^{81} -7.04059 q^{82} +10.5103i q^{83} +0.765134 q^{84} -0.145494i q^{85} +11.7901i q^{86} -16.0851i q^{87} +(-7.43368 + 9.18077i) q^{88} -6.38464i q^{89} -0.367247 q^{90} -0.102735i q^{91} -20.8101 q^{92} -2.03307 q^{93} +9.82749 q^{94} +(-4.34664 + 0.326663i) q^{95} -6.73446i q^{96} -0.618546i q^{97} -16.4019 q^{98} +(0.326339 - 0.403036i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 40 q^{4} + 40 q^{5} - 28 q^{9}+O(q^{10}) \) 40 * q + 40 * q^4 + 40 * q^5 - 28 * q^9	\( 40 q + 40 q^{4} + 40 q^{5} - 28 q^{9} - 4 q^{11} + 48 q^{16} + 40 q^{20} + 24 q^{23} + 40 q^{25} - 24 q^{26} + 24 q^{36} - 28 q^{38} - 60 q^{42} - 48 q^{44} - 28 q^{45} - 36 q^{49} - 4 q^{55} - 36 q^{58} - 40 q^{64} - 28 q^{66} + 8 q^{77} + 48 q^{80} + 80 q^{81} + 8 q^{82} + 4 q^{92} + 56 q^{93} - 16 q^{99}+O(q^{100}) \) 40 * q + 40 * q^4 + 40 * q^5 - 28 * q^9 - 4 * q^11 + 48 * q^16 + 40 * q^20 + 24 * q^23 + 40 * q^25 - 24 * q^26 + 24 * q^36 - 28 * q^38 - 60 * q^42 - 48 * q^44 - 28 * q^45 - 36 * q^49 - 4 * q^55 - 36 * q^58 - 40 * q^64 - 28 * q^66 + 8 * q^77 + 48 * q^80 + 80 * q^81 + 8 * q^82 + 4 * q^92 + 56 * q^93 - 16 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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