LMFDB - Embedded newform 1045.2.f.b.626.17

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			626.17
Character	$\chi$	$=$	1045.626
Dual form			1045.2.f.b.626.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.233551 q^{2} -2.00145i q^{3} -1.94545 q^{4} +1.00000 q^{5} +0.467439i q^{6} -1.43314i q^{7} +0.921463 q^{8} -1.00579 q^{9} +O(q^{10})$	\(q-0.233551 q^{2} -2.00145i q^{3} -1.94545 q^{4} +1.00000 q^{5} +0.467439i q^{6} -1.43314i q^{7} +0.921463 q^{8} -1.00579 q^{9} -0.233551 q^{10} +(2.74121 + 1.86701i) q^{11} +3.89372i q^{12} +5.35008 q^{13} +0.334712i q^{14} -2.00145i q^{15} +3.67570 q^{16} +4.91740i q^{17} +0.234903 q^{18} +(3.73673 + 2.24429i) q^{19} -1.94545 q^{20} -2.86836 q^{21} +(-0.640212 - 0.436042i) q^{22} -4.98009 q^{23} -1.84426i q^{24} +1.00000 q^{25} -1.24952 q^{26} -3.99130i q^{27} +2.78812i q^{28} +4.09939 q^{29} +0.467439i q^{30} -3.87210i q^{31} -2.70139 q^{32} +(3.73673 - 5.48640i) q^{33} -1.14846i q^{34} -1.43314i q^{35} +1.95672 q^{36} +5.67729i q^{37} +(-0.872716 - 0.524155i) q^{38} -10.7079i q^{39} +0.921463 q^{40} +5.79914 q^{41} +0.669908 q^{42} -9.77410i q^{43} +(-5.33291 - 3.63219i) q^{44} -1.00579 q^{45} +1.16310 q^{46} -9.64452 q^{47} -7.35672i q^{48} +4.94610 q^{49} -0.233551 q^{50} +9.84191 q^{51} -10.4083 q^{52} -6.67111i q^{53} +0.932171i q^{54} +(2.74121 + 1.86701i) q^{55} -1.32059i q^{56} +(4.49183 - 7.47887i) q^{57} -0.957416 q^{58} -3.93187i q^{59} +3.89372i q^{60} +9.62454i q^{61} +0.904331i q^{62} +1.44145i q^{63} -6.72049 q^{64} +5.35008 q^{65} +(-0.872716 + 1.28135i) q^{66} +12.3988i q^{67} -9.56657i q^{68} +9.96739i q^{69} +0.334712i q^{70} +1.57409i q^{71} -0.926801 q^{72} -9.80194i q^{73} -1.32594i q^{74} -2.00145i q^{75} +(-7.26964 - 4.36616i) q^{76} +(2.67570 - 3.92855i) q^{77} +2.50084i q^{78} -1.60823 q^{79} +3.67570 q^{80} -11.0058 q^{81} -1.35439 q^{82} +8.47918i q^{83} +5.58027 q^{84} +4.91740i q^{85} +2.28275i q^{86} -8.20472i q^{87} +(2.52593 + 1.72038i) q^{88} -16.0172i q^{89} +0.234903 q^{90} -7.66744i q^{91} +9.68854 q^{92} -7.74981 q^{93} +2.25248 q^{94} +(3.73673 + 2.24429i) q^{95} +5.40669i q^{96} -13.9795i q^{97} -1.15516 q^{98} +(-2.75709 - 1.87783i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−0.233551			−0.165145			−0.0825726	−	0.996585i	$-0.526314\pi$
$2$	−0.233551			−0.165145			−0.0825726	+	0.996585i	$0.526314\pi$
$3$		−	2.00145i		−	1.15554i	−0.816201	−	0.577768i	$-0.803924\pi$
$3$		−	2.00145i		−	1.15554i	0.816201	−	0.577768i	$-0.196076\pi$
$4$	−1.94545			−0.972727
$5$	1.00000			0.447214
$5$	1.00000			0.447214
$6$			0.467439i			0.190831i
$7$		−	1.43314i		−	0.541677i	−0.962625	−	0.270839i	$-0.912699\pi$
$7$		−	1.43314i		−	0.541677i	0.962625	−	0.270839i	$-0.0873010\pi$
$8$	0.921463			0.325786
$9$	−1.00579			−0.335264
$10$	−0.233551			−0.0738552
$11$	2.74121	+	1.86701i	0.826507	+	0.562926i
$11$	2.74121	+	1.86701i	0.826507	+	0.562926i
$12$			3.89372i			1.12402i
$13$	5.35008			1.48385			0.741923	−	0.670485i	$-0.233914\pi$
$13$	5.35008			1.48385			0.741923	+	0.670485i	$0.233914\pi$
$14$			0.334712i			0.0894554i
$15$		−	2.00145i		−	0.516772i
$16$	3.67570			0.918925
$17$			4.91740i			1.19264i	0.802745	+	0.596322i	$0.203372\pi$
$17$			4.91740i			1.19264i	−0.802745	+	0.596322i	$0.796628\pi$
$18$	0.234903			0.0553673
$19$	3.73673	+	2.24429i	0.857265	+	0.514876i
$19$	3.73673	+	2.24429i	0.857265	+	0.514876i
$20$	−1.94545			−0.435017
$21$	−2.86836			−0.625928
$22$	−0.640212	−	0.436042i	−0.136494	−	0.0929645i
$23$	−4.98009			−1.03842			−0.519210	−	0.854646i	$-0.673774\pi$
$23$	−4.98009			−1.03842			−0.519210	+	0.854646i	$0.673774\pi$
$24$		−	1.84426i		−	0.376458i
$25$	1.00000			0.200000
$26$	−1.24952			−0.245050
$27$		−	3.99130i		−	0.768126i
$28$			2.78812i			0.526904i
$29$	4.09939			0.761238			0.380619	−	0.924732i	$-0.375711\pi$
$29$	4.09939			0.761238			0.380619	+	0.924732i	$0.375711\pi$
$30$			0.467439i			0.0853423i
$31$		−	3.87210i		−	0.695450i	−0.937597	−	0.347725i	$-0.886954\pi$
$31$		−	3.87210i		−	0.695450i	0.937597	−	0.347725i	$-0.113046\pi$
$32$	−2.70139			−0.477542
$33$	3.73673	−	5.48640i	0.650481	−	0.955059i
$34$		−	1.14846i		−	0.196959i
$35$		−	1.43314i		−	0.242246i
$36$	1.95672			0.326121
$37$			5.67729i			0.933341i	0.884431	+	0.466671i	$0.154547\pi$
$37$			5.67729i			0.933341i	−0.884431	+	0.466671i	$0.845453\pi$
$38$	−0.872716	−	0.524155i	−0.141573	−	0.0850292i
$39$		−	10.7079i		−	1.71464i
$40$	0.921463			0.145696
$41$	5.79914			0.905673			0.452837	−	0.891593i	$-0.350412\pi$
$41$	5.79914			0.905673			0.452837	+	0.891593i	$0.350412\pi$
$42$	0.669908			0.103369
$43$		−	9.77410i		−	1.49054i	−0.666765	−	0.745268i	$-0.732322\pi$
$43$		−	9.77410i		−	1.49054i	0.666765	−	0.745268i	$-0.267678\pi$
$44$	−5.33291	−	3.63219i	−0.803966	−	0.547573i
$45$	−1.00579			−0.149935
$46$	1.16310			0.171490
$47$	−9.64452			−1.40680			−0.703399	−	0.710795i	$-0.748335\pi$
$47$	−9.64452			−1.40680			−0.703399	+	0.710795i	$0.748335\pi$
$48$		−	7.35672i		−	1.06185i
$49$	4.94610			0.706586
$50$	−0.233551			−0.0330290
$51$	9.84191			1.37814
$52$	−10.4083			−1.44338
$53$		−	6.67111i		−	0.916347i	−0.888863	−	0.458173i	$-0.848504\pi$
$53$		−	6.67111i		−	0.916347i	0.888863	−	0.458173i	$-0.151496\pi$
$54$			0.932171i			0.126852i
$55$	2.74121	+	1.86701i	0.369625	+	0.251748i
$56$		−	1.32059i		−	0.176471i
$57$	4.49183	−	7.47887i	0.594957	−	0.990601i
$58$	−0.957416			−0.125715
$59$		−	3.93187i		−	0.511886i	−0.966692	−	0.255943i	$-0.917614\pi$
$59$		−	3.93187i		−	0.511886i	0.966692	−	0.255943i	$-0.0823860\pi$
$60$			3.89372i			0.502678i
$61$			9.62454i			1.23230i	0.787630	+	0.616148i	$0.211308\pi$
$61$			9.62454i			1.23230i	−0.787630	+	0.616148i	$0.788692\pi$
$62$			0.904331i			0.114850i
$63$			1.44145i			0.181605i
$64$	−6.72049			−0.840061
$65$	5.35008			0.663596
$66$	−0.872716	+	1.28135i	−0.107424	+	0.157723i
$67$			12.3988i			1.51475i	0.652980	+	0.757375i	$0.273519\pi$
$67$			12.3988i			1.51475i	−0.652980	+	0.757375i	$0.726481\pi$
$68$		−	9.56657i		−	1.16012i
$69$			9.96739i			1.19993i
$70$			0.334712i			0.0400057i
$71$			1.57409i			0.186810i	0.995628	+	0.0934051i	$0.0297752\pi$
$71$			1.57409i			0.186810i	−0.995628	+	0.0934051i	$0.970225\pi$
$72$	−0.926801			−0.109224
$73$		−	9.80194i		−	1.14723i	−0.819125	−	0.573615i	$-0.805541\pi$
$73$		−	9.80194i		−	1.14723i	0.819125	−	0.573615i	$-0.194459\pi$
$74$		−	1.32594i		−	0.154137i
$75$		−	2.00145i		−	0.231107i
$76$	−7.26964	−	4.36616i	−0.833885	−	0.500833i
$77$	2.67570	−	3.92855i	0.304924	−	0.447700i
$78$			2.50084i			0.283164i
$79$	−1.60823			−0.180940			−0.0904700	−	0.995899i	$-0.528837\pi$
$79$	−1.60823			−0.180940			−0.0904700	+	0.995899i	$0.528837\pi$
$80$	3.67570			0.410956
$81$	−11.0058			−1.22286
$82$	−1.35439			−0.149568
$83$			8.47918i			0.930711i	0.885124	+	0.465356i	$0.154074\pi$
$83$			8.47918i			0.930711i	−0.885124	+	0.465356i	$0.845926\pi$
$84$	5.58027			0.608857
$85$			4.91740i			0.533367i
$86$			2.28275i			0.246155i
$87$		−	8.20472i		−	0.879639i
$88$	2.52593	+	1.72038i	0.269265	+	0.183394i
$89$		−	16.0172i		−	1.69782i	−0.528537	−	0.848911i	$-0.677259\pi$
$89$		−	16.0172i		−	1.69782i	0.528537	−	0.848911i	$-0.322741\pi$
$90$	0.234903			0.0247610
$91$		−	7.66744i		−	0.803766i
$92$	9.68854			1.01010
$93$	−7.74981			−0.803618
$94$	2.25248			0.232326
$95$	3.73673	+	2.24429i	0.383381	+	0.230259i
$96$			5.40669i			0.551818i
$97$		−	13.9795i		−	1.41940i	−0.704502	−	0.709702i	$-0.748830\pi$
$97$		−	13.9795i		−	1.41940i	0.704502	−	0.709702i	$-0.251170\pi$
$98$	−1.15516			−0.116689
$99$	−2.75709	−	1.87783i	−0.277098	−	0.188729i
$100$	−1.94545			−0.194545
$101$		−	2.98328i		−	0.296848i	−0.988924	−	0.148424i	$-0.952580\pi$
$101$		−	2.98328i		−	0.296848i	0.988924	−	0.148424i	$-0.0474200\pi$
$102$	−2.29858			−0.227594
$103$			3.91378i			0.385636i	0.981235	+	0.192818i	$0.0617627\pi$
$103$			3.91378i			0.385636i	−0.981235	+	0.192818i	$0.938237\pi$
$104$	4.92991			0.483417
$105$	−2.86836			−0.279924
$106$			1.55804i			0.151330i
$107$	−6.39717			−0.618437			−0.309219	−	0.950991i	$-0.600068\pi$
$107$	−6.39717			−0.618437			−0.309219	+	0.950991i	$0.600068\pi$
$108$			7.76489i			0.747177i
$109$	10.5567			1.01115			0.505575	−	0.862783i	$-0.331280\pi$
$109$	10.5567			1.01115			0.505575	+	0.862783i	$0.331280\pi$
$110$	−0.640212	−	0.436042i	−0.0610418	−	0.0415750i
$111$	11.3628			1.07851
$112$		−	5.26781i		−	0.497761i
$113$			0.0190980i			0.00179659i	1.00000		0.000898294i	$0.000285936\pi$
$113$			0.0190980i			0.00179659i	−1.00000		0.000898294i	$0.999714\pi$
$114$	−1.04907	+	1.74669i	−0.0982544	+	0.163593i
$115$	−4.98009			−0.464396
$116$	−7.97518			−0.740477
$117$	−5.38107			−0.497481
$118$			0.918291i			0.0845356i
$119$	7.04734			0.646029
$120$		−	1.84426i		−	0.168357i
$121$	4.02852	+	10.2358i	0.366229	+	0.930525i
$122$		−	2.24782i		−	0.203508i
$123$		−	11.6067i		−	1.04654i
$124$			7.53299i			0.676483i
$125$	1.00000			0.0894427
$126$		−	0.336650i		−	0.0299912i
$127$	−1.77998			−0.157948			−0.0789738	−	0.996877i	$-0.525164\pi$
$127$	−1.77998			−0.157948			−0.0789738	+	0.996877i	$0.525164\pi$
$128$	6.97235			0.616274
$129$	−19.5623			−1.72237
$130$	−1.24952			−0.109590
$131$		−	5.66242i		−	0.494728i	−0.968923	−	0.247364i	$-0.920436\pi$
$131$		−	5.66242i		−	0.494728i	0.968923	−	0.247364i	$-0.0795643\pi$
$132$	−7.26964	+	10.6735i	−0.632741	+	0.929012i
$133$	3.21639	−	5.35527i	0.278896	−	0.464361i
$134$		−	2.89574i		−	0.250154i
$135$		−	3.99130i		−	0.343517i
$136$			4.53120i			0.388547i
$137$	−7.52065			−0.642533			−0.321266	−	0.946989i	$-0.604108\pi$
$137$	−7.52065			−0.642533			−0.321266	+	0.946989i	$0.604108\pi$
$138$		−	2.32789i		−	0.198163i
$139$			12.3621i			1.04854i	0.851552	+	0.524270i	$0.175662\pi$
$139$			12.3621i			1.04854i	−0.851552	+	0.524270i	$0.824338\pi$
$140$			2.78812i			0.235639i
$141$			19.3030i			1.62561i
$142$		−	0.367630i		−	0.0308508i
$143$	14.6657	+	9.98868i	1.22641	+	0.835296i
$144$	−3.69699			−0.308083
$145$	4.09939			0.340436
$146$			2.28925i			0.189460i
$147$		−	9.89936i		−	0.816485i
$148$		−	11.0449i		−	0.907886i
$149$			15.9791i			1.30906i	0.756038	+	0.654528i	$0.227133\pi$
$149$			15.9791i			1.30906i	−0.756038	+	0.654528i	$0.772867\pi$
$150$			0.467439i			0.0381663i
$151$	−16.7389			−1.36220			−0.681098	−	0.732193i	$-0.738497\pi$
$151$	−16.7389			−1.36220			−0.681098	+	0.732193i	$0.738497\pi$
$152$	3.44326	+	2.06803i	0.279285	+	0.167739i
$153$		−	4.94588i		−	0.399851i
$154$	−0.624911	+	0.917516i	−0.0503568	+	0.0739356i
$155$		−	3.87210i		−	0.311015i
$156$			20.8318i			1.66788i
$157$	17.8951			1.42818			0.714092	−	0.700051i	$-0.246840\pi$
$157$	17.8951			1.42818			0.714092	+	0.700051i	$0.246840\pi$
$158$	0.375603			0.0298814
$159$	−13.3519			−1.05887
$160$	−2.70139			−0.213563
$161$			7.13719i			0.562489i
$162$	2.57040			0.201950
$163$	−0.0225368			−0.00176522			−0.000882609	−	1.00000i	$-0.500281\pi$
$163$	−0.0225368			−0.00176522			−0.000882609		1.00000i	$0.500281\pi$
$164$	−11.2820			−0.880973
$165$	3.73673	−	5.48640i	0.290904	−	0.427115i
$166$		−	1.98032i		−	0.153703i
$167$	−1.00831			−0.0780257			−0.0390129	−	0.999239i	$-0.512421\pi$
$167$	−1.00831			−0.0780257			−0.0390129	+	0.999239i	$0.512421\pi$
$168$	−2.64309			−0.203919
$169$	15.6234			1.20180
$170$		−	1.14846i		−	0.0880829i
$171$	−3.75838	−	2.25729i	−0.287410	−	0.172619i
$172$			19.0151i			1.44988i
$173$	−24.3866			−1.85408			−0.927040	−	0.374962i	$-0.877656\pi$
$173$	−24.3866			−1.85408			−0.927040	+	0.374962i	$0.877656\pi$
$174$			1.91622i			0.145268i
$175$		−	1.43314i		−	0.108335i
$176$	10.0759	+	6.86258i	0.759498	+	0.517287i
$177$	−7.86944			−0.591503
$178$			3.74083i			0.280387i
$179$		−	5.04062i		−	0.376753i	−0.982097	−	0.188377i	$-0.939677\pi$
$179$		−	5.04062i		−	0.376753i	0.982097	−	0.188377i	$-0.0603226\pi$
$180$	1.95672			0.145846
$181$		−	1.64532i		−	0.122295i	−0.998129	−	0.0611477i	$-0.980524\pi$
$181$		−	1.64532i		−	0.122295i	0.998129	−	0.0611477i	$-0.0194761\pi$
$182$			1.79074i			0.132738i
$183$	19.2630			1.42396
$184$	−4.58897			−0.338303
$185$			5.67729i			0.417403i
$186$	1.80997			0.132714
$187$	−9.18085	+	13.4796i	−0.671370	+	0.985729i
$188$	18.7630			1.36843
$189$	−5.72011			−0.416077
$190$	−0.872716	−	0.524155i	−0.0633134	−	0.0380262i
$191$	17.5910			1.27284			0.636422	−	0.771341i	$-0.280414\pi$
$191$	17.5910			1.27284			0.636422	+	0.771341i	$0.280414\pi$
$192$			13.4507i			0.970721i
$193$	23.1389			1.66558			0.832788	−	0.553592i	$-0.186743\pi$
$193$	23.1389			1.66558			0.832788	+	0.553592i	$0.186743\pi$
$194$			3.26492i			0.234408i
$195$		−	10.7079i		−	0.766810i
$196$	−9.62241			−0.687315
$197$			4.16708i			0.296892i	0.988921	+	0.148446i	$0.0474271\pi$
$197$			4.16708i			0.296892i	−0.988921	+	0.148446i	$0.952573\pi$
$198$	0.643921	+	0.438568i	0.0457614	+	0.0311677i
$199$	−13.2705			−0.940718			−0.470359	−	0.882475i	$-0.655876\pi$
$199$	−13.2705			−0.940718			−0.470359	+	0.882475i	$0.655876\pi$
$200$	0.921463			0.0651573
$201$	24.8155			1.75035
$202$			0.696747i			0.0490229i
$203$		−	5.87502i		−	0.412346i
$204$	−19.1470			−1.34056
$205$	5.79914			0.405029
$206$		−	0.914066i		−	0.0636860i
$207$	5.00894			0.348145
$208$	19.6653			1.36354
$209$	6.05306	+	13.1286i	0.418699	+	0.908125i
$210$	0.669908			0.0462280
$211$	−5.25036			−0.361449			−0.180725	−	0.983534i	$-0.557844\pi$
$211$	−5.25036			−0.361449			−0.180725	+	0.983534i	$0.557844\pi$
$212$			12.9783i			0.891355i
$213$	3.15046			0.215866
$214$	1.49406			0.102132
$215$		−	9.77410i		−	0.666588i
$216$		−	3.67784i		−	0.250245i
$217$	−5.54928			−0.376710
$218$	−2.46553			−0.166986
$219$	−19.6181			−1.32567
$220$	−5.33291	−	3.63219i	−0.359545	−	0.244882i
$221$			26.3085i			1.76970i
$222$	−2.65379			−0.178111
$223$		−	19.7772i		−	1.32438i	−0.749336	−	0.662190i	$-0.769627\pi$
$223$		−	19.7772i		−	1.32438i	0.749336	−	0.662190i	$-0.230373\pi$
$224$			3.87148i			0.258674i
$225$	−1.00579			−0.0670528
$226$		−	0.00446035i		−	0.000296698i
$227$	9.63997			0.639827			0.319914	−	0.947447i	$-0.396346\pi$
$227$	9.63997			0.639827			0.319914	+	0.947447i	$0.396346\pi$
$228$	−8.73865	+	14.5498i	−0.578731	+	0.963584i
$229$	11.8034			0.779993			0.389996	−	0.920816i	$-0.372476\pi$
$229$	11.8034			0.779993			0.389996	+	0.920816i	$0.372476\pi$
$230$	1.16310			0.0766927
$231$	−7.86280	−	5.35527i	−0.517334	−	0.352351i
$232$	3.77744			0.248001
$233$			17.8273i			1.16790i	0.811788	+	0.583952i	$0.198494\pi$
$233$			17.8273i			1.16790i	−0.811788	+	0.583952i	$0.801506\pi$
$234$	1.25675			0.0821565
$235$	−9.64452			−0.629139
$236$			7.64928i			0.497926i
$237$			3.21879i			0.209083i
$238$	−1.64591			−0.106688
$239$			7.42583i			0.480337i	0.970731	+	0.240169i	$0.0772027\pi$
$239$			7.42583i			0.480337i	−0.970731	+	0.240169i	$0.922797\pi$
$240$		−	7.35672i		−	0.474874i
$241$	−18.1036			−1.16615			−0.583076	−	0.812417i	$-0.698151\pi$
$241$	−18.1036			−1.16615			−0.583076	+	0.812417i	$0.698151\pi$
$242$	−0.940862	−	2.39057i	−0.0604809	−	0.153672i
$243$			10.0535i			0.644935i
$244$		−	18.7241i		−	1.19869i
$245$	4.94610			0.315995
$246$			2.71075i			0.172831i
$247$	19.9918	+	12.0071i	1.27205	+	0.763996i
$248$		−	3.56800i		−	0.226568i
$249$	16.9706			1.07547
$250$	−0.233551			−0.0147710
$251$	−5.57383			−0.351817			−0.175909	−	0.984407i	$-0.556286\pi$
$251$	−5.57383			−0.351817			−0.175909	+	0.984407i	$0.556286\pi$
$252$		−	2.80427i		−	0.176652i
$253$	−13.6515	−	9.29790i	−0.858262	−	0.584554i
$254$	0.415715			0.0260843
$255$	9.84191			0.616325
$256$	11.8126			0.738286
$257$		−	4.17361i		−	0.260342i	−0.991492	−	0.130171i	$-0.958447\pi$
$257$		−	4.17361i		−	0.260342i	0.991492	−	0.130171i	$-0.0415527\pi$
$258$	4.56880			0.284441
$259$	8.13638			0.505570
$260$	−10.4083			−0.645498
$261$	−4.12314			−0.255216
$262$			1.32246i			0.0817019i
$263$		−	12.3508i		−	0.761581i	−0.924661	−	0.380790i	$-0.875652\pi$
$263$		−	12.3508i		−	0.761581i	0.924661	−	0.380790i	$-0.124348\pi$
$264$	3.44326	−	5.05551i	0.211918	−	0.311145i
$265$		−	6.67111i		−	0.409803i
$266$	−0.751190	+	1.25073i	−0.0460584	+	0.0766870i
$267$	−32.0576			−1.96189
$268$		−	24.1212i		−	1.47344i
$269$			31.6327i			1.92868i	0.264663	+	0.964341i	$0.414739\pi$
$269$			31.6327i			1.92868i	−0.264663	+	0.964341i	$0.585261\pi$
$270$			0.932171i			0.0567301i
$271$		−	18.9038i		−	1.14833i	−0.818741	−	0.574163i	$-0.805327\pi$
$271$		−	18.9038i		−	1.14833i	0.818741	−	0.574163i	$-0.194673\pi$
$272$			18.0749i			1.09595i
$273$	−15.3460			−0.928781
$274$	1.75645			0.106111
$275$	2.74121	+	1.86701i	0.165301	+	0.112585i
$276$		−	19.3911i		−	1.16721i
$277$		−	20.4040i		−	1.22596i	−0.790099	−	0.612979i	$-0.789971\pi$
$277$		−	20.4040i		−	1.22596i	0.790099	−	0.612979i	$-0.210029\pi$
$278$		−	2.88718i		−	0.173161i
$279$			3.89453i			0.233159i
$280$		−	1.32059i		−	0.0789203i
$281$	−31.1163			−1.85624			−0.928120	−	0.372280i	$-0.878576\pi$
$281$	−31.1163			−1.85624			−0.928120	+	0.372280i	$0.878576\pi$
$282$		−	4.50823i		−	0.268461i
$283$		−	16.5025i		−	0.980971i	−0.871449	−	0.490486i	$-0.836819\pi$
$283$		−	16.5025i		−	0.980971i	0.871449	−	0.490486i	$-0.163181\pi$
$284$		−	3.06232i		−	0.181715i
$285$	4.49183	−	7.47887i	0.266073	−	0.443010i
$286$	−3.42519	−	2.33286i	−0.202536	−	0.137945i
$287$		−	8.31100i		−	0.490583i
$288$	2.71704			0.160103
$289$	−7.18080			−0.422400
$290$	−0.957416			−0.0562214
$291$	−27.9793			−1.64017
$292$			19.0692i			1.11594i
$293$	−19.2018			−1.12178			−0.560890	−	0.827891i	$-0.689541\pi$
$293$	−19.2018			−1.12178			−0.560890	+	0.827891i	$0.689541\pi$
$294$			2.31200i			0.134839i
$295$		−	3.93187i		−	0.228923i
$296$			5.23142i			0.304070i
$297$	7.45182	−	10.9410i	0.432398	−	0.634862i
$298$		−	3.73192i		−	0.216184i
$299$	−26.6439			−1.54086
$300$			3.89372i			0.224804i
$301$	−14.0077			−0.807390
$302$	3.90939			0.224960
$303$	−5.97088			−0.343018
$304$	13.7351	+	8.24934i	0.787762	+	0.473132i
$305$			9.62454i			0.551100i
$306$			1.15511i			0.0660334i
$307$	33.3315			1.90233			0.951166	−	0.308681i	$-0.0998874\pi$
$307$	33.3315			1.90233			0.951166	+	0.308681i	$0.0998874\pi$
$308$	−5.20545	+	7.64282i	−0.296608	+	0.435490i
$309$	7.83323			0.445617
$310$			0.904331i			0.0513626i
$311$	−12.8155			−0.726698			−0.363349	−	0.931653i	$-0.618367\pi$
$311$	−12.8155			−0.726698			−0.363349	+	0.931653i	$0.618367\pi$
$312$		−	9.86695i		−	0.558606i
$313$	−0.867160			−0.0490148			−0.0245074	−	0.999700i	$-0.507802\pi$
$313$	−0.867160			−0.0490148			−0.0245074	+	0.999700i	$0.507802\pi$
$314$	−4.17941			−0.235858
$315$			1.44145i			0.0812162i
$316$	3.12874			0.176005
$317$			9.32255i			0.523606i	0.965121	+	0.261803i	$0.0843171\pi$
$317$			9.32255i			0.523606i	−0.965121	+	0.261803i	$0.915683\pi$
$318$	3.11834			0.174868
$319$	11.2373	+	7.65363i	0.629169	+	0.428521i
$320$	−6.72049			−0.375687
$321$			12.8036i			0.714627i
$322$		−	1.66689i		−	0.0928924i
$323$	−11.0361	+	18.3750i	−0.614063	+	1.02241i
$324$	21.4112			1.18951
$325$	5.35008			0.296769
$326$	0.00526348			0.000291517
$327$		−	21.1287i		−	1.16842i
$328$	5.34369			0.295056
$329$			13.8220i			0.762031i
$330$	−0.872716	+	1.28135i	−0.0480414	+	0.0705361i
$331$			24.4262i			1.34259i	0.741191	+	0.671294i	$0.234261\pi$
$331$			24.4262i			1.34259i	−0.741191	+	0.671294i	$0.765739\pi$
$332$		−	16.4959i		−	0.905328i
$333$		−	5.71018i		−	0.312916i
$334$	0.235492			0.0128856
$335$			12.3988i			0.677417i
$336$	−10.5432			−0.575181
$337$	−22.3255			−1.21615			−0.608075	−	0.793880i	$-0.708058\pi$
$337$	−22.3255			−1.21615			−0.608075	+	0.793880i	$0.708058\pi$
$338$	−3.64886			−0.198472
$339$	0.0382236			0.00207602
$340$		−	9.56657i		−	0.518820i
$341$	7.22927	−	10.6143i	0.391487	−	0.574794i
$342$	0.877771	+	0.527191i	0.0474644	+	0.0285072i
$343$		−	17.1205i		−	0.924419i
$344$		−	9.00647i		−	0.485596i
$345$			9.96739i			0.536626i
$346$	5.69551			0.306192
$347$			30.8459i			1.65589i	0.560807	+	0.827947i	$0.310491\pi$
$347$			30.8459i			1.65589i	−0.560807	+	0.827947i	$0.689509\pi$
$348$			15.9619i			0.855648i
$349$			22.7996i			1.22043i	0.792235	+	0.610216i	$0.208918\pi$
$349$			22.7996i			1.22043i	−0.792235	+	0.610216i	$0.791082\pi$
$350$			0.334712i			0.0178911i
$351$		−	21.3538i		−	1.13978i
$352$	−7.40508	−	5.04353i	−0.394692	−	0.268821i
$353$	4.04143			0.215103			0.107552	−	0.994199i	$-0.465699\pi$
$353$	4.04143			0.215103			0.107552	+	0.994199i	$0.465699\pi$
$354$	1.83791			0.0976839
$355$			1.57409i			0.0835440i
$356$			31.1608i			1.65152i
$357$		−	14.1049i		−	0.746509i
$358$			1.17724i			0.0622190i
$359$		−	2.16029i		−	0.114016i	−0.998374	−	0.0570080i	$-0.981844\pi$
$359$		−	2.16029i		−	0.114016i	0.998374	−	0.0570080i	$-0.0181560\pi$
$360$	−0.926801			−0.0488467
$361$	8.92632	+	16.7726i	0.469806	+	0.882770i
$362$			0.384265i			0.0201965i
$363$	20.4864	−	8.06286i	1.07526	−	0.423191i
$364$			14.9167i			0.781845i
$365$		−	9.80194i		−	0.513057i
$366$	−4.49889			−0.235161
$367$	2.10528			0.109895			0.0549475	−	0.998489i	$-0.482501\pi$
$367$	2.10528			0.109895			0.0549475	+	0.998489i	$0.482501\pi$
$368$	−18.3053			−0.954231
$369$	−5.83273			−0.303640
$370$		−	1.32594i		−	0.0689321i
$371$	−9.56065			−0.496364
$372$	15.0769			0.781701
$373$	−5.82412			−0.301562			−0.150781	−	0.988567i	$-0.548179\pi$
$373$	−5.82412			−0.301562			−0.150781	+	0.988567i	$0.548179\pi$
$374$	2.14419	−	3.14818i	0.110874	−	0.162788i
$375$		−	2.00145i		−	0.103354i
$376$	−8.88707			−0.458316
$377$	21.9321			1.12956
$378$	1.33593			0.0687131
$379$		−	34.5045i		−	1.77238i	−0.463323	−	0.886189i	$-0.653343\pi$
$379$		−	34.5045i		−	1.77238i	0.463323	−	0.886189i	$-0.346657\pi$
$380$	−7.26964	−	4.36616i	−0.372925	−	0.223980i
$381$			3.56253i			0.182514i
$382$	−4.10840			−0.210204
$383$		−	3.21013i		−	0.164030i	−0.996631	−	0.0820150i	$-0.973864\pi$
$383$		−	3.21013i		−	0.164030i	0.996631	−	0.0820150i	$-0.0261356\pi$
$384$		−	13.9548i		−	0.712128i
$385$	2.67570	−	3.92855i	0.136366	−	0.200218i
$386$	−5.40411			−0.275062
$387$			9.83071i			0.499723i
$388$			27.1965i			1.38069i
$389$	24.4290			1.23860			0.619299	−	0.785155i	$-0.287417\pi$
$389$	24.4290			1.23860			0.619299	+	0.785155i	$0.287417\pi$
$390$			2.50084i			0.126635i
$391$		−	24.4891i		−	1.23847i
$392$	4.55765			0.230196
$393$	−11.3330			−0.571676
$394$		−	0.973223i		−	0.0490303i
$395$	−1.60823			−0.0809188
$396$	5.36380	+	3.65323i	0.269541	+	0.183582i
$397$	−0.646226			−0.0324331			−0.0162166	−	0.999869i	$-0.505162\pi$
$397$	−0.646226			−0.0324331			−0.0162166	+	0.999869i	$0.505162\pi$
$398$	3.09932			0.155355
$399$	−10.7183	−	6.43744i	−0.536586	−	0.322275i
$400$	3.67570			0.183785
$401$		−	3.14296i		−	0.156952i	−0.996916	−	0.0784760i	$-0.974995\pi$
$401$		−	3.14296i		−	0.156952i	0.996916	−	0.0784760i	$-0.0250054\pi$
$402$	−5.79567			−0.289062
$403$		−	20.7161i		−	1.03194i
$404$			5.80384i			0.288752i
$405$	−11.0058			−0.546881
$406$			1.37211i			0.0680969i
$407$	−10.5996	+	15.5627i	−0.525402	+	0.771413i
$408$	9.06896			0.448980
$409$	−29.6853			−1.46784			−0.733922	−	0.679234i	$-0.762312\pi$
$409$	−29.6853			−1.46784			−0.733922	+	0.679234i	$0.762312\pi$
$410$	−1.35439			−0.0668887
$411$			15.0522i			0.742470i
$412$		−	7.61408i		−	0.375119i
$413$	−5.63494			−0.277277
$414$	−1.16984			−0.0574945
$415$			8.47918i			0.416227i
$416$	−14.4527			−0.708600
$417$	24.7421			1.21163
$418$	−1.41370	−	3.06619i	−0.0691461	−	0.149972i
$419$	0.297415			0.0145297			0.00726484	−	0.999974i	$-0.497688\pi$
$419$	0.297415			0.0145297			0.00726484	+	0.999974i	$0.497688\pi$
$420$	5.58027			0.272289
$421$		−	2.43711i		−	0.118777i	−0.998235	−	0.0593887i	$-0.981085\pi$
$421$		−	2.43711i		−	0.118777i	0.998235	−	0.0593887i	$-0.0189151\pi$
$422$	1.22622			0.0596916
$423$	9.70039			0.471649
$424$		−	6.14718i		−	0.298533i
$425$			4.91740i			0.238529i
$426$	−0.735792			−0.0356492
$427$	13.7934			0.667507
$428$	12.4454			0.601571
$429$	19.9918	−	29.3527i	0.965215	−	1.41716i
$430$			2.28275i			0.110084i
$431$	−1.72591			−0.0831339			−0.0415670	−	0.999136i	$-0.513235\pi$
$431$	−1.72591			−0.0831339			−0.0415670	+	0.999136i	$0.513235\pi$
$432$		−	14.6708i		−	0.705851i
$433$		−	24.1597i		−	1.16104i	−0.814245	−	0.580522i	$-0.802849\pi$
$433$		−	24.1597i		−	1.16104i	0.814245	−	0.580522i	$-0.197151\pi$
$434$	1.29604			0.0622118
$435$		−	8.20472i		−	0.393386i
$436$	−20.5376			−0.983573
$437$	−18.6093	−	11.1768i	−0.890202	−	0.534657i
$438$	4.58181			0.218927
$439$	19.0644			0.909892			0.454946	−	0.890519i	$-0.349658\pi$
$439$	19.0644			0.909892			0.454946	+	0.890519i	$0.349658\pi$
$440$	2.52593	+	1.72038i	0.120419	+	0.0820161i
$441$	−4.97475			−0.236893
$442$		−	6.14436i		−	0.292258i
$443$	−5.55652			−0.263998			−0.131999	−	0.991250i	$-0.542140\pi$
$443$	−5.55652			−0.263998			−0.131999	+	0.991250i	$0.542140\pi$
$444$	−22.1058			−1.04910
$445$		−	16.0172i		−	0.759289i
$446$			4.61898i			0.218715i
$447$	31.9813			1.51266
$448$			9.63143i			0.455042i
$449$			7.91048i			0.373319i	0.982425	+	0.186659i	$0.0597661\pi$
$449$			7.91048i			0.373319i	−0.982425	+	0.186659i	$0.940234\pi$
$450$	0.234903			0.0110735
$451$	15.8967	+	10.8271i	0.748546	+	0.509827i
$452$		−	0.0371543i		−	0.00174759i
$453$			33.5021i			1.57407i
$454$	−2.25142			−0.105664
$455$		−	7.66744i		−	0.359455i
$456$	4.13906	−	6.89150i	0.193829	−	0.322724i
$457$			19.0924i			0.893104i	0.894758	+	0.446552i	$0.147348\pi$
$457$			19.0924i			0.893104i	−0.894758	+	0.446552i	$0.852652\pi$
$458$	−2.75670			−0.128812
$459$	19.6268			0.916102
$460$	9.68854			0.451730
$461$		−	17.8733i		−	0.832445i	−0.909263	−	0.416222i	$-0.863354\pi$
$461$		−	17.8733i		−	0.832445i	0.909263	−	0.416222i	$-0.136646\pi$
$462$	1.83636	+	1.25073i	0.0854352	+	0.0581891i
$463$	−32.9388			−1.53080			−0.765398	−	0.643557i	$-0.777458\pi$
$463$	−32.9388			−1.53080			−0.765398	+	0.643557i	$0.777458\pi$
$464$	15.0681			0.699521
$465$	−7.74981			−0.359389
$466$		−	4.16357i		−	0.192874i
$467$	−7.27956			−0.336858			−0.168429	−	0.985714i	$-0.553869\pi$
$467$	−7.27956			−0.336858			−0.168429	+	0.985714i	$0.553869\pi$
$468$	10.4686			0.483913
$469$	17.7692			0.820506
$470$	2.25248			0.103899
$471$		−	35.8161i		−	1.65032i
$472$		−	3.62308i		−	0.166766i
$473$	18.2484	−	26.7929i	0.839061	−	1.23194i
$474$		−	0.751750i		−	0.0345290i
$475$	3.73673	+	2.24429i	0.171453	+	0.102975i
$476$	−13.7103			−0.628409
$477$			6.70975i			0.307218i
$478$		−	1.73431i		−	0.0793254i
$479$			39.1765i			1.79002i	0.446048	+	0.895009i	$0.352831\pi$
$479$			39.1765i			1.79002i	−0.446048	+	0.895009i	$0.647169\pi$
$480$			5.40669i			0.246780i
$481$			30.3740i			1.38494i
$482$	4.22810			0.192584
$483$	14.2847			0.649977
$484$	−7.83729	−	19.9132i	−0.356241	−	0.905147i
$485$		−	13.9795i		−	0.634777i
$486$		−	2.34801i		−	0.106508i
$487$		−	5.75305i		−	0.260696i	−0.991468	−	0.130348i	$-0.958391\pi$
$487$		−	5.75305i		−	0.260696i	0.991468	−	0.130348i	$-0.0416094\pi$
$488$			8.86866i			0.401465i
$489$			0.0451062i			0.00203977i
$490$	−1.15516			−0.0521850
$491$		−	35.6419i		−	1.60850i	−0.594294	−	0.804248i	$-0.702568\pi$
$491$		−	35.6419i		−	1.60850i	0.594294	−	0.804248i	$-0.297432\pi$
$492$			22.5803i			1.01800i
$493$			20.1584i			0.907887i
$494$	−4.66910	−	2.80428i	−0.210073	−	0.126170i
$495$	−2.75709	−	1.87783i	−0.123922	−	0.0844021i
$496$		−	14.2327i		−	0.639066i
$497$	2.25590			0.101191
$498$	−3.96350			−0.177609
$499$	−0.523154			−0.0234196			−0.0117098	−	0.999931i	$-0.503727\pi$
$499$	−0.523154			−0.0234196			−0.0117098	+	0.999931i	$0.503727\pi$
$500$	−1.94545			−0.0870034
$501$			2.01809i			0.0901615i
$502$	1.30177			0.0581009
$503$		−	4.85001i		−	0.216251i	−0.994137	−	0.108126i	$-0.965515\pi$
$503$		−	4.85001i		−	0.216251i	0.994137	−	0.108126i	$-0.0344849\pi$
$504$			1.32824i			0.0591644i
$505$		−	2.98328i		−	0.132754i
$506$	3.18831	+	2.17153i	0.141738	+	0.0965363i
$507$		−	31.2694i		−	1.38872i
$508$	3.46287			0.153640
$509$			31.5282i			1.39746i	0.715384	+	0.698731i	$0.246252\pi$
$509$			31.5282i			1.39746i	−0.715384	+	0.698731i	$0.753748\pi$
$510$	−2.29858			−0.101783
$511$	−14.0476			−0.621429
$512$	−16.7035			−0.738199
$513$	8.95764	−	14.9144i	0.395490	−	0.658488i
$514$			0.974748i			0.0429943i
$515$			3.91378i			0.172462i
$516$	38.0576			1.67539
$517$	−26.4377	−	18.0065i	−1.16273	−	0.791923i
$518$	−1.90026			−0.0834924
$519$			48.8085i			2.14246i
$520$	4.92991			0.216191
$521$		−	40.0097i		−	1.75286i	−0.481530	−	0.876429i	$-0.659919\pi$
$521$		−	40.0097i		−	1.75286i	0.481530	−	0.876429i	$-0.340081\pi$
$522$	0.962962			0.0421477
$523$	34.7925			1.52137			0.760685	−	0.649121i	$-0.224863\pi$
$523$	34.7925			1.52137			0.760685	+	0.649121i	$0.224863\pi$
$524$			11.0160i			0.481235i
$525$	−2.86836			−0.125186
$526$			2.88453i			0.125771i
$527$	19.0407			0.829424
$528$	13.7351	−	20.1664i	0.597744	−	0.877628i
$529$	1.80130			0.0783175
$530$			1.55804i			0.0676769i
$531$			3.95465i			0.171617i
$532$	−6.25734	+	10.4184i	−0.271290	+	0.451697i
$533$	31.0259			1.34388
$534$	7.48707			0.323997
$535$	−6.39717			−0.276574
$536$			11.4250i			0.493485i
$537$	−10.0885			−0.435352
$538$		−	7.38784i		−	0.318513i
$539$	13.5583	+	9.23444i	0.583998	+	0.397755i
$540$			7.76489i			0.334148i
$541$			37.5787i			1.61564i	0.589432	+	0.807818i	$0.299351\pi$
$541$			37.5787i			1.61564i	−0.589432	+	0.807818i	$0.700649\pi$
$542$			4.41500i			0.189641i
$543$	−3.29302			−0.141317
$544$		−	13.2838i		−	0.569538i
$545$	10.5567			0.452200
$546$	3.58406			0.153384
$547$	18.8898			0.807672			0.403836	−	0.914831i	$-0.367677\pi$
$547$	18.8898			0.807672			0.403836	+	0.914831i	$0.367677\pi$
$548$	14.6311			0.625009
$549$		−	9.68029i		−	0.413145i
$550$	−0.640212	−	0.436042i	−0.0272987	−	0.0185929i
$551$	15.3183	+	9.20023i	0.652583	+	0.391943i
$552$			9.18458i			0.390922i
$553$			2.30482i			0.0980111i
$554$			4.76537i			0.202461i
$555$	11.3628			0.482324
$556$		−	24.0499i		−	1.01994i
$557$		−	5.18028i		−	0.219495i	−0.993959	−	0.109748i	$-0.964996\pi$
$557$		−	5.18028i		−	0.219495i	0.993959	−	0.109748i	$-0.0350043\pi$
$558$		−	0.909570i		−	0.0385052i
$559$		−	52.2923i		−	2.21173i
$560$		−	5.26781i		−	0.222605i
$561$	26.9788	+	18.3750i	1.13905	+	0.775793i
$562$	7.26722			0.306549
$563$	−23.2936			−0.981709			−0.490855	−	0.871242i	$-0.663315\pi$
$563$	−23.2936			−0.981709			−0.490855	+	0.871242i	$0.663315\pi$
$564$		−	37.5531i		−	1.58127i
$565$			0.0190980i			0.000803458i
$566$			3.85417i			0.162003i
$567$			15.7728i			0.662397i
$568$			1.45047i			0.0608602i
$569$	−4.92012			−0.206262			−0.103131	−	0.994668i	$-0.532886\pi$
$569$	−4.92012			−0.206262			−0.103131	+	0.994668i	$0.532886\pi$
$570$	−1.04907	+	1.74669i	−0.0439407	+	0.0731610i
$571$		−	24.1258i		−	1.00963i	−0.863226	−	0.504817i	$-0.831560\pi$
$571$		−	24.1258i		−	1.00963i	0.863226	−	0.504817i	$-0.168440\pi$
$572$	−28.5315	−	19.4325i	−1.19296	−	0.812515i
$573$		−	35.2076i		−	1.47082i
$574$			1.94104i			0.0810174i
$575$	−4.98009			−0.207684
$576$	6.75942			0.281642
$577$	−2.20983			−0.0919962			−0.0459981	−	0.998942i	$-0.514647\pi$
$577$	−2.20983			−0.0919962			−0.0459981	+	0.998942i	$0.514647\pi$
$578$	1.67708			0.0697574
$579$		−	46.3113i		−	1.92463i
$580$	−7.97518			−0.331151
$581$	12.1519			0.504145
$582$	6.53457			0.270867
$583$	12.4550	−	18.2869i	0.515835	−	0.757367i
$584$		−	9.03212i		−	0.373752i
$585$	−5.38107			−0.222480
$586$	4.48458			0.185256
$587$	−3.33295			−0.137565			−0.0687827	−	0.997632i	$-0.521912\pi$
$587$	−3.33295			−0.137565			−0.0687827	+	0.997632i	$0.521912\pi$
$588$			19.2587i			0.794217i
$589$	8.69012	−	14.4690i	0.358070	−	0.596185i
$590$			0.918291i			0.0378055i
$591$	8.34019			0.343069
$592$			20.8680i			0.857671i
$593$			33.5903i			1.37939i	0.724101	+	0.689694i	$0.242255\pi$
$593$			33.5903i			1.37939i	−0.724101	+	0.689694i	$0.757745\pi$
$594$	−1.74038	+	2.55528i	−0.0714085	+	0.104844i
$595$	7.04734			0.288913
$596$		−	31.0865i		−	1.27335i
$597$			26.5601i			1.08703i
$598$	6.22270			0.254465
$599$			5.73415i			0.234291i	0.993115	+	0.117146i	$0.0373744\pi$
$599$			5.73415i			0.234291i	−0.993115	+	0.117146i	$0.962626\pi$
$600$		−	1.84426i		−	0.0752916i
$601$	19.4981			0.795342			0.397671	−	0.917528i	$-0.369819\pi$
$601$	19.4981			0.795342			0.397671	+	0.917528i	$0.369819\pi$
$602$	3.27150			0.133337
$603$		−	12.4706i		−	0.507842i
$604$	32.5648			1.32504
$605$	4.02852	+	10.2358i	0.163782	+	0.416143i
$606$	1.39450			0.0566478
$607$	−7.65408			−0.310669			−0.155335	−	0.987862i	$-0.549646\pi$
$607$	−7.65408			−0.310669			−0.155335	+	0.987862i	$0.549646\pi$
$608$	−10.0944	−	6.06270i	−0.409380	−	0.245875i
$609$	−11.7585			−0.476480
$610$		−	2.24782i		−	0.0910114i
$611$	−51.5990			−2.08747
$612$			9.62199i			0.388946i
$613$		−	16.5092i		−	0.666801i	−0.942785	−	0.333400i	$-0.891804\pi$
$613$		−	16.5092i		−	0.666801i	0.942785	−	0.333400i	$-0.108196\pi$
$614$	−7.78460			−0.314161
$615$		−	11.6067i		−	0.468026i
$616$	2.46556	−	3.62002i	0.0993402	−	0.145855i
$617$	28.3193			1.14009			0.570046	−	0.821613i	$-0.306925\pi$
$617$	28.3193			1.14009			0.570046	+	0.821613i	$0.306925\pi$
$618$	−1.82945			−0.0735914
$619$	8.48004			0.340842			0.170421	−	0.985371i	$-0.445487\pi$
$619$	8.48004			0.340842			0.170421	+	0.985371i	$0.445487\pi$
$620$			7.53299i			0.302532i
$621$			19.8770i			0.797638i
$622$	2.99306			0.120011
$623$	−22.9550			−0.919671
$624$		−	39.3591i		−	1.57562i
$625$	1.00000			0.0400000
$626$	0.202526			0.00809456
$627$	26.2762	−	12.1149i	1.04937	−	0.483822i
$628$	−34.8141			−1.38923
$629$	−27.9175			−1.11314
$630$		−	0.336650i		−	0.0134125i
$631$	−30.3910			−1.20985			−0.604924	−	0.796284i	$-0.706796\pi$
$631$	−30.3910			−1.20985			−0.604924	+	0.796284i	$0.706796\pi$
$632$	−1.48192			−0.0589478
$633$			10.5083i			0.417668i
$634$		−	2.17729i		−	0.0864711i
$635$	−1.77998			−0.0706363
$636$	25.9754			1.02999
$637$	26.4620			1.04846
$638$	−2.62448	−	1.78751i	−0.103904	−	0.0707682i
$639$		−	1.58321i		−	0.0626307i
$640$	6.97235			0.275606
$641$		−	46.7801i		−	1.84770i	−0.382753	−	0.923851i	$-0.625024\pi$
$641$		−	46.7801i		−	1.84770i	0.382753	−	0.923851i	$-0.374976\pi$
$642$		−	2.99029i		−	0.118017i
$643$	−27.4601			−1.08292			−0.541459	−	0.840727i	$-0.682128\pi$
$643$	−27.4601			−1.08292			−0.541459	+	0.840727i	$0.682128\pi$
$644$		−	13.8851i		−	0.547148i
$645$	−19.5623			−0.770267
$646$	2.57748	−	4.29149i	0.101410	−	0.168846i
$647$	−30.0287			−1.18055			−0.590275	−	0.807202i	$-0.700981\pi$
$647$	−30.0287			−1.18055			−0.590275	+	0.807202i	$0.700981\pi$
$648$	−10.1414			−0.398392
$649$	7.34086	−	10.7781i	0.288154	−	0.423078i
$650$	−1.24952			−0.0490100
$651$			11.1066i			0.435302i
$652$	0.0438443			0.00171708
$653$	−44.9046			−1.75725			−0.878626	−	0.477511i	$-0.841539\pi$
$653$	−44.9046			−1.75725			−0.878626	+	0.477511i	$0.841539\pi$
$654$			4.93462i			0.192959i
$655$		−	5.66242i		−	0.221249i
$656$	21.3159			0.832246
$657$			9.85872i			0.384625i
$658$		−	3.22813i		−	0.125846i
$659$	5.10834			0.198993			0.0994964	−	0.995038i	$-0.468277\pi$
$659$	5.10834			0.198993			0.0994964	+	0.995038i	$0.468277\pi$
$660$	−7.26964	+	10.6735i	−0.282970	+	0.415467i
$661$		−	10.0930i		−	0.392572i	−0.980547	−	0.196286i	$-0.937112\pi$
$661$		−	10.0930i		−	0.392572i	0.980547	−	0.196286i	$-0.0628881\pi$
$662$		−	5.70476i		−	0.221722i
$663$	52.6551			2.04495
$664$			7.81325i			0.303213i
$665$	3.21639	−	5.35527i	0.124726	−	0.207669i
$666$			1.33362i			0.0516766i
$667$	−20.4154			−0.790486
$668$	1.96163			0.0758977
$669$	−39.5830			−1.53037
$670$		−	2.89574i		−	0.111872i
$671$	−17.9692	+	26.3829i	−0.693691	+	1.01850i
$672$	7.74856			0.298907
$673$	17.9732			0.692817			0.346409	−	0.938084i	$-0.387401\pi$
$673$	17.9732			0.692817			0.346409	+	0.938084i	$0.387401\pi$
$674$	5.21414			0.200841
$675$		−	3.99130i		−	0.153625i
$676$	−30.3946			−1.16902
$677$	−1.31718			−0.0506233			−0.0253116	−	0.999680i	$-0.508058\pi$
$677$	−1.31718			−0.0506233			−0.0253116	+	0.999680i	$0.508058\pi$
$678$	−0.00892715			−0.000342845
$679$	−20.0347			−0.768859
$680$			4.53120i			0.173764i
$681$		−	19.2939i		−	0.739344i
$682$	−1.68840	+	2.47897i	−0.0646522	+	0.0949245i
$683$			11.5918i			0.443550i	0.975098	+	0.221775i	$0.0711850\pi$
$683$			11.5918i			0.443550i	−0.975098	+	0.221775i	$0.928815\pi$
$684$	7.31175	+	4.39145i	0.279572	+	0.167911i
$685$	−7.52065			−0.287349
$686$			3.99850i			0.152663i
$687$		−	23.6240i		−	0.901310i
$688$		−	35.9267i		−	1.36969i
$689$		−	35.6910i		−	1.35972i
$690$		−	2.32789i		−	0.0886212i
$691$	9.15183			0.348152			0.174076	−	0.984732i	$-0.444306\pi$
$691$	9.15183			0.348152			0.174076	+	0.984732i	$0.444306\pi$
$692$	47.4431			1.80351
$693$	−2.69120	+	3.95131i	−0.102230	+	0.150098i
$694$		−	7.20407i		−	0.273463i
$695$			12.3621i			0.468921i
$696$		−	7.56035i		−	0.286574i
$697$			28.5167i			1.08015i
$698$		−	5.32485i		−	0.201549i
$699$	35.6804			1.34956
$700$			2.78812i			0.105381i
$701$			13.8844i			0.524405i	0.965013	+	0.262202i	$0.0844488\pi$
$701$			13.8844i			0.524405i	−0.965013	+	0.262202i	$0.915551\pi$
$702$			4.98719i			0.188229i
$703$	−12.7415	+	21.2145i	−0.480555	+	0.800121i
$704$	−18.4223	−	12.5472i	−0.694317	−	0.472892i
$705$			19.3030i			0.726993i
$706$	−0.943878			−0.0355233
$707$	−4.27547			−0.160796
$708$	15.3096			0.575371
$709$	−11.9309			−0.448073			−0.224036	−	0.974581i	$-0.571923\pi$
$709$	−11.9309			−0.448073			−0.224036	+	0.974581i	$0.571923\pi$
$710$		−	0.367630i		−	0.0137969i
$711$	1.61755			0.0606627
$712$		−	14.7593i		−	0.553127i
$713$			19.2834i			0.722169i
$714$			3.29420i			0.123282i
$715$	14.6657	+	9.98868i	0.548467	+	0.373556i
$716$			9.80629i			0.366478i
$717$	14.8624			0.555047
$718$			0.504538i			0.0188292i
$719$	34.4328			1.28413			0.642064	−	0.766651i	$-0.278078\pi$
$719$	34.4328			1.28413			0.642064	+	0.766651i	$0.278078\pi$
$720$	−3.69699			−0.137779
$721$	5.60901			0.208890
$722$	−2.08475	−	3.91726i	−0.0775863	−	0.145785i
$723$			36.2333i			1.34753i
$724$			3.20089i			0.118960i
$725$	4.09939			0.152248
$726$	−4.78460	+	1.88309i	−0.177573	+	0.0698879i
$727$	1.08357			0.0401873			0.0200937	−	0.999798i	$-0.493604\pi$
$727$	1.08357			0.0401873			0.0200937	+	0.999798i	$0.493604\pi$
$728$		−	7.06526i		−	0.261856i
$729$	−12.8956			−0.477616
$730$			2.28925i			0.0847289i
$731$	48.0631			1.77768
$732$	−37.4753			−1.38513
$733$			35.7456i			1.32029i	0.751136	+	0.660147i	$0.229506\pi$
$733$			35.7456i			1.32029i	−0.751136	+	0.660147i	$0.770494\pi$
$734$	−0.491690			−0.0181486
$735$		−	9.89936i		−	0.365143i
$736$	13.4532			0.495890
$737$	−23.1487	+	33.9877i	−0.852693	+	1.25195i
$738$	1.36224			0.0501447
$739$		−	4.50860i		−	0.165852i	−0.996556	−	0.0829258i	$-0.973574\pi$
$739$		−	4.50860i		−	0.165852i	0.996556	−	0.0829258i	$-0.0264265\pi$
$740$		−	11.0449i		−	0.406019i
$741$	24.0317	−	40.0126i	0.882825	−	1.46990i
$742$	2.23290			0.0819722
$743$	−11.2067			−0.411133			−0.205567	−	0.978643i	$-0.565904\pi$
$743$	−11.2067			−0.411133			−0.205567	+	0.978643i	$0.565904\pi$
$744$	−7.14116			−0.261808
$745$			15.9791i			0.585428i
$746$	1.36023			0.0498014
$747$		−	8.52830i		−	0.312034i
$748$	17.8609	−	26.2240i	0.653060	−	0.958845i
$749$			9.16806i			0.334994i
$750$			0.467439i			0.0170685i
$751$			46.6128i			1.70092i	0.526037	+	0.850462i	$0.323677\pi$
$751$			46.6128i			1.70092i	−0.526037	+	0.850462i	$0.676323\pi$
$752$	−35.4504			−1.29274
$753$			11.1557i			0.406538i
$754$	−5.12226			−0.186542
$755$	−16.7389			−0.609192
$756$	11.1282			0.404729
$757$	−48.7771			−1.77283			−0.886416	−	0.462889i	$-0.846813\pi$
$757$	−48.7771			−1.77283			−0.886416	+	0.462889i	$0.846813\pi$
$758$			8.05855i			0.292700i
$759$	−18.6093	+	27.3228i	−0.675473	+	0.991753i
$760$	3.44326	+	2.06803i	0.124900	+	0.0750154i
$761$			50.5432i			1.83219i	0.400960	+	0.916096i	$0.368677\pi$
$761$			50.5432i			1.83219i	−0.400960	+	0.916096i	$0.631323\pi$
$762$		−	0.832032i		−	0.0301413i
$763$		−	15.1293i		−	0.547717i
$764$	−34.2226			−1.23813
$765$		−	4.94588i		−	0.178819i
$766$			0.749728i			0.0270888i
$767$		−	21.0359i		−	0.759561i
$768$		−	23.6423i		−	0.853117i
$769$			24.6122i			0.887540i	0.896141	+	0.443770i	$0.146359\pi$
$769$			24.6122i			0.887540i	−0.896141	+	0.443770i	$0.853641\pi$
$770$	−0.624911	+	0.917516i	−0.0225202	+	0.0330650i
$771$	−8.35326			−0.300835
$772$	−45.0157			−1.62015
$773$			50.2038i			1.80571i	0.429949	+	0.902853i	$0.358531\pi$
$773$			50.2038i			1.80571i	−0.429949	+	0.902853i	$0.641469\pi$
$774$		−	2.29597i		−	0.0825269i
$775$		−	3.87210i		−	0.139090i
$776$		−	12.8816i		−	0.462423i
$777$		−	16.2845i		−	0.584204i
$778$	−5.70540			−0.204548
$779$	21.6698	+	13.0150i	0.776402	+	0.466309i
$780$			20.8318i			0.745896i
$781$	−2.93885	+	4.31492i	−0.105160	+	0.154400i
$782$			5.71944i			0.204527i
$783$		−	16.3619i		−	0.584727i
$784$	18.1804			0.649299
$785$	17.8951			0.638704
$786$	2.64684			0.0944095
$787$	−41.9843			−1.49658			−0.748290	−	0.663372i	$-0.769125\pi$
$787$	−41.9843			−1.49658			−0.748290	+	0.663372i	$0.769125\pi$
$788$		−	8.10686i		−	0.288795i
$789$	−24.7194			−0.880034
$790$	0.375603			0.0133634
$791$	0.0273702			0.000973171
$792$	−2.54056	−	1.73035i	−0.0902748	−	0.0614853i
$793$			51.4921i			1.82854i
$794$	0.150926			0.00535618
$795$	−13.3519			−0.473542
$796$	25.8171			0.915062
$797$		−	20.6457i		−	0.731307i	−0.930751	−	0.365654i	$-0.880845\pi$
$797$		−	20.6457i		−	0.731307i	0.930751	−	0.365654i	$-0.119155\pi$
$798$	2.50326	+	1.50347i	0.0886146	+	0.0532222i
$799$		−	47.4260i		−	1.67781i
$800$	−2.70139			−0.0955085
$801$			16.1100i			0.569219i
$802$			0.734041i			0.0259199i
$803$	18.3004	−	26.8692i	0.645806	−	0.948194i
$804$	−48.2774			−1.70261
$805$			7.13719i			0.251553i
$806$			4.83825i			0.170420i
$807$	63.3113			2.22866
$808$		−	2.74898i		−	0.0967089i
$809$			29.5837i			1.04011i	0.854134	+	0.520053i	$0.174088\pi$
$809$			29.5837i			1.04011i	−0.854134	+	0.520053i	$0.825912\pi$
$810$	2.57040			0.0903147
$811$	22.9005			0.804145			0.402073	−	0.915608i	$-0.368290\pi$
$811$	22.9005			0.804145			0.402073	+	0.915608i	$0.368290\pi$
$812$			11.4296i			0.401100i
$813$	−37.8351			−1.32693
$814$	2.47554	−	3.63467i	0.0867676	−	0.127395i
$815$	−0.0225368			−0.000789430
$816$	36.1759			1.26641
$817$	21.9359	−	36.5232i	0.767441	−	1.27778i
$818$	6.93302			0.242407
$819$			7.71185i			0.269474i
$820$	−11.2820			−0.393983
$821$		−	2.38708i		−	0.0833097i	−0.999132	−	0.0416549i	$-0.986737\pi$
$821$		−	2.38708i		−	0.0833097i	0.999132	−	0.0416549i	$-0.0132630\pi$
$822$		−	3.51545i		−	0.122615i
$823$	2.81919			0.0982707			0.0491354	−	0.998792i	$-0.484353\pi$
$823$	2.81919			0.0982707			0.0491354	+	0.998792i	$0.484353\pi$
$824$			3.60640i			0.125635i
$825$	3.73673	−	5.48640i	0.130096	−	0.191012i
$826$	1.31604			0.0457910
$827$	−20.8027			−0.723380			−0.361690	−	0.932298i	$-0.617800\pi$
$827$	−20.8027			−0.723380			−0.361690	+	0.932298i	$0.617800\pi$
$828$	−9.74466			−0.338650
$829$			14.4518i			0.501933i	0.967996	+	0.250967i	$0.0807484\pi$
$829$			14.4518i			0.501933i	−0.967996	+	0.250967i	$0.919252\pi$
$830$		−	1.98032i		−	0.0687379i
$831$	−40.8376			−1.41664
$832$	−35.9552			−1.24652
$833$			24.3219i			0.842705i
$834$	−5.77853			−0.200094
$835$	−1.00831			−0.0348942
$836$	−11.7760	−	25.5411i	−0.407280	−	0.883358i
$837$	−15.4547			−0.534193
$838$	−0.0694615			−0.00239951
$839$			24.6330i			0.850426i	0.905093	+	0.425213i	$0.139801\pi$
$839$			24.6330i			0.850426i	−0.905093	+	0.425213i	$0.860199\pi$
$840$	−2.64309			−0.0911953
$841$	−12.1950			−0.420516
$842$			0.569188i			0.0196155i
$843$			62.2776i			2.14495i
$844$	10.2143			0.351592
$845$	15.6234			0.537461
$846$	−2.26553			−0.0778906
$847$	14.6693	−	5.77344i	0.504044	−	0.198378i
$848$		−	24.5210i		−	0.842054i
$849$	−33.0289			−1.13355
$850$		−	1.14846i		−	0.0393919i
$851$		−	28.2734i		−	0.969201i
$852$	−6.12907			−0.209979
$853$		−	43.1839i		−	1.47859i	−0.673382	−	0.739294i	$-0.735159\pi$
$853$		−	43.1839i		−	1.47859i	0.673382	−	0.739294i	$-0.264841\pi$
$854$	−3.22144			−0.110236
$855$	−3.75838	−	2.25729i	−0.128534	−	0.0771977i
$856$	−5.89475			−0.201478
$857$	12.9640			0.442843			0.221422	−	0.975178i	$-0.428930\pi$
$857$	12.9640			0.442843			0.221422	+	0.975178i	$0.428930\pi$
$858$	−4.66910	+	6.85534i	−0.159401	+	0.234037i
$859$	33.7825			1.15264			0.576322	−	0.817223i	$-0.304488\pi$
$859$	33.7825			1.15264			0.576322	+	0.817223i	$0.304488\pi$
$860$			19.0151i			0.648408i
$861$	−16.6340			−0.566886
$862$	0.403086			0.0137292
$863$			33.0229i			1.12411i	0.827099	+	0.562056i	$0.189990\pi$
$863$			33.0229i			1.12411i	−0.827099	+	0.562056i	$0.810010\pi$
$864$			10.7821i			0.366813i
$865$	−24.3866			−0.829170
$866$			5.64252i			0.191741i
$867$			14.3720i			0.488099i
$868$	10.7959			0.366436
$869$	−4.40850	−	3.00259i	−0.149548	−	0.101856i
$870$			1.91622i			0.0649659i
$871$			66.3345i			2.24766i
$872$	9.72762			0.329419
$873$			14.0605i			0.475875i
$874$	4.34620	+	2.61034i	0.147013	+	0.0882961i
$875$		−	1.43314i		−	0.0484491i
$876$	38.1660			1.28951
$877$	−56.4257			−1.90536			−0.952681	−	0.303973i	$-0.901687\pi$
$877$	−56.4257			−1.90536			−0.952681	+	0.303973i	$0.901687\pi$
$878$	−4.45249			−0.150264
$879$			38.4313i			1.29626i
$880$	10.0759	+	6.86258i	0.339658	+	0.231338i
$881$	−27.1919			−0.916120			−0.458060	−	0.888921i	$-0.651456\pi$
$881$	−27.1919			−0.916120			−0.458060	+	0.888921i	$0.651456\pi$
$882$	1.16186			0.0391217
$883$	15.7324			0.529436			0.264718	−	0.964326i	$-0.414721\pi$
$883$	15.7324			0.529436			0.264718	+	0.964326i	$0.414721\pi$
$884$		−	51.1820i		−	1.72144i
$885$	−7.86944			−0.264528
$886$	1.29773			0.0435981
$887$	19.9602			0.670199			0.335099	−	0.942183i	$-0.391230\pi$
$887$	19.9602			0.670199			0.335099	+	0.942183i	$0.391230\pi$
$888$	10.4704			0.351364
$889$			2.55096i			0.0855566i
$890$			3.74083i			0.125393i
$891$	−30.1691	−	20.5479i	−1.01070	−	0.688381i
$892$			38.4756i			1.28826i
$893$	−36.0390	−	21.6451i	−1.20600	−	0.724326i
$894$	−7.46924			−0.249809
$895$		−	5.04062i		−	0.168489i
$896$		−	9.99238i		−	0.333822i
$897$			53.3264i			1.78052i
$898$		−	1.84750i		−	0.0616518i
$899$		−	15.8733i		−	0.529403i
$900$	1.95672			0.0652241
$901$	32.8045			1.09288
$902$	−3.71268	−	2.52867i	−0.123619	−	0.0841955i
$903$			28.0357i			0.932968i
$904$			0.0175981i			0.000585304i
$905$		−	1.64532i		−	0.0546922i
$906$		−	7.82443i		−	0.259949i
$907$			6.66988i			0.221470i	0.993850	+	0.110735i	$0.0353205\pi$
$907$			6.66988i			0.221470i	−0.993850	+	0.110735i	$0.964680\pi$
$908$	−18.7541			−0.622377
$909$			3.00056i			0.0995223i
$910$			1.79074i			0.0593623i
$911$			13.8160i			0.457743i	0.973457	+	0.228872i	$0.0735036\pi$
$911$			13.8160i			0.457743i	−0.973457	+	0.228872i	$0.926496\pi$
$912$	16.5106	−	27.4901i	0.546721	−	0.910288i
$913$	−15.8308	+	23.2433i	−0.523922	+	0.769240i
$914$		−	4.45903i		−	0.147492i
$915$	19.2630			0.636816
$916$	−22.9630			−0.758720
$917$	−8.11506			−0.267983
$918$	−4.58386			−0.151290
$919$		−	2.22908i		−	0.0735306i	−0.999324	−	0.0367653i	$-0.988295\pi$
$919$		−	2.22908i		−	0.0735306i	0.999324	−	0.0367653i	$-0.0117054\pi$
$920$	−4.58897			−0.151294
$921$		−	66.7113i		−	2.19821i
$922$			4.17433i			0.137474i
$923$			8.42152i			0.277198i
$924$	15.2967	+	10.4184i	0.503225	+	0.342741i
$925$			5.67729i			0.186668i
$926$	7.69287			0.252804
$927$		−	3.93645i		−	0.129290i
$928$	−11.0741			−0.363524
$929$	5.45045			0.178823			0.0894117	−	0.995995i	$-0.471501\pi$
$929$	5.45045			0.178823			0.0894117	+	0.995995i	$0.471501\pi$
$930$	1.80997			0.0593513
$931$	18.4822	+	11.1005i	0.605731	+	0.363804i
$932$		−	34.6822i		−	1.13605i
$933$			25.6495i			0.839726i
$934$	1.70015			0.0556305
$935$	−9.18085	+	13.4796i	−0.300246	+	0.440831i
$936$	−4.95846			−0.162072
$937$		−	10.0919i		−	0.329688i	−0.986320	−	0.164844i	$-0.947288\pi$
$937$		−	10.0919i		−	0.329688i	0.986320	−	0.164844i	$-0.0527120\pi$
$938$	−4.15001			−0.135503
$939$			1.73558i			0.0566384i
$940$	18.7630			0.611981
$941$	5.95604			0.194161			0.0970807	−	0.995277i	$-0.469049\pi$
$941$	5.95604			0.194161			0.0970807	+	0.995277i	$0.469049\pi$
$942$			8.36487i			0.272542i
$943$	−28.8802			−0.940470
$944$		−	14.4524i		−	0.470385i
$945$	−5.72011			−0.186075
$946$	−4.26192	+	6.25750i	−0.138567	+	0.203449i
$947$	−17.5736			−0.571065			−0.285533	−	0.958369i	$-0.592170\pi$
$947$	−17.5736			−0.571065			−0.285533	+	0.958369i	$0.592170\pi$
$948$		−	6.26200i		−	0.203380i
$949$		−	52.4412i		−	1.70231i
$950$	−0.872716	−	0.524155i	−0.0283146	−	0.0170058i
$951$	18.6586			0.605046
$952$	6.49386			0.210467
$953$	−60.7494			−1.96787			−0.983934	−	0.178535i	$-0.942864\pi$
$953$	−60.7494			−1.96787			−0.983934	+	0.178535i	$0.942864\pi$
$954$		−	1.56707i		−	0.0507356i
$955$	17.5910			0.569233
$956$		−	14.4466i		−	0.467237i
$957$	15.3183	−	22.4909i	0.495171	−	0.727028i
$958$		−	9.14968i		−	0.295613i
$959$			10.7782i			0.348046i
$960$			13.4507i			0.434120i
$961$	16.0068			0.516350
$962$		−	7.09387i		−	0.228715i
$963$	6.43422			0.207340
$964$	35.2196			1.13435
$965$	23.1389			0.744868
$966$	−3.33620			−0.107340
$967$			36.3265i			1.16818i	0.811688	+	0.584091i	$0.198549\pi$
$967$			36.3265i			1.16818i	−0.811688	+	0.584091i	$0.801451\pi$
$968$	3.71213	+	9.43189i	0.119312	+	0.303152i
$969$	36.7766	+	22.0881i	1.18143	+	0.709573i
$970$			3.26492i			0.104830i
$971$			32.9217i			1.05651i	0.849087	+	0.528253i	$0.177153\pi$
$971$			32.9217i			1.05651i	−0.849087	+	0.528253i	$0.822847\pi$
$972$		−	19.5587i		−	0.627346i
$973$	17.7167			0.567971
$974$			1.34363i			0.0430526i
$975$		−	10.7079i		−	0.342928i
$976$			35.3769i			1.13239i
$977$		−	37.7452i		−	1.20758i	−0.797145	−	0.603788i	$-0.793657\pi$
$977$		−	37.7452i		−	1.20758i	0.797145	−	0.603788i	$-0.206343\pi$
$978$		−	0.0105346i		−	0.000336859i
$979$	29.9044	−	43.9066i	0.955748	−	1.40326i
$980$	−9.62241			−0.307377
$981$	−10.6179			−0.339002
$982$			8.32418i			0.265635i
$983$			37.1835i			1.18597i	0.805214	+	0.592985i	$0.202050\pi$
$983$			37.1835i			1.18597i	−0.805214	+	0.592985i	$0.797950\pi$
$984$		−	10.6951i		−	0.340948i
$985$			4.16708i			0.132774i
$986$		−	4.70799i		−	0.149933i
$987$	27.6640			0.880554
$988$	−38.8932	−	23.3593i	−1.23736	−	0.743160i
$989$			48.6759i			1.54780i
$990$	0.643921	+	0.438568i	0.0204651	+	0.0139386i
$991$		−	58.3125i		−	1.85236i	−0.377085	−	0.926179i	$-0.623073\pi$
$991$		−	58.3125i		−	1.85236i	0.377085	−	0.926179i	$-0.376927\pi$
$992$			10.4600i			0.332107i
$993$	48.8879			1.55141
$994$	−0.526866			−0.0167112
$995$	−13.2705			−0.420702
$996$	−33.0156			−1.04614
$997$		−	45.4438i		−	1.43922i	−0.694379	−	0.719610i	$-0.744321\pi$
$997$		−	45.4438i		−	1.43922i	0.694379	−	0.719610i	$-0.255679\pi$
$998$	0.122183			0.00386763
$999$	22.6598			0.716924

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1045.2.f.b.626.17	✓	40
11.10	odd	2	inner	1045.2.f.b.626.23	yes	40
19.18	odd	2	inner	1045.2.f.b.626.24	yes	40
209.208	even	2	inner	1045.2.f.b.626.18	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1045.2.f.b.626.17	✓	40	1.1	even	1	trivial
1045.2.f.b.626.18	yes	40	209.208	even	2	inner
1045.2.f.b.626.23	yes	40	11.10	odd	2	inner
1045.2.f.b.626.24	yes	40	19.18	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)

\(f(q)\)	\(=\)	\(q-0.233551 q^{2} -2.00145i q^{3} -1.94545 q^{4} +1.00000 q^{5} +0.467439i q^{6} -1.43314i q^{7} +0.921463 q^{8} -1.00579 q^{9} +O(q^{10})\)	\(q-0.233551 q^{2} -2.00145i q^{3} -1.94545 q^{4} +1.00000 q^{5} +0.467439i q^{6} -1.43314i q^{7} +0.921463 q^{8} -1.00579 q^{9} -0.233551 q^{10} +(2.74121 + 1.86701i) q^{11} +3.89372i q^{12} +5.35008 q^{13} +0.334712i q^{14} -2.00145i q^{15} +3.67570 q^{16} +4.91740i q^{17} +0.234903 q^{18} +(3.73673 + 2.24429i) q^{19} -1.94545 q^{20} -2.86836 q^{21} +(-0.640212 - 0.436042i) q^{22} -4.98009 q^{23} -1.84426i q^{24} +1.00000 q^{25} -1.24952 q^{26} -3.99130i q^{27} +2.78812i q^{28} +4.09939 q^{29} +0.467439i q^{30} -3.87210i q^{31} -2.70139 q^{32} +(3.73673 - 5.48640i) q^{33} -1.14846i q^{34} -1.43314i q^{35} +1.95672 q^{36} +5.67729i q^{37} +(-0.872716 - 0.524155i) q^{38} -10.7079i q^{39} +0.921463 q^{40} +5.79914 q^{41} +0.669908 q^{42} -9.77410i q^{43} +(-5.33291 - 3.63219i) q^{44} -1.00579 q^{45} +1.16310 q^{46} -9.64452 q^{47} -7.35672i q^{48} +4.94610 q^{49} -0.233551 q^{50} +9.84191 q^{51} -10.4083 q^{52} -6.67111i q^{53} +0.932171i q^{54} +(2.74121 + 1.86701i) q^{55} -1.32059i q^{56} +(4.49183 - 7.47887i) q^{57} -0.957416 q^{58} -3.93187i q^{59} +3.89372i q^{60} +9.62454i q^{61} +0.904331i q^{62} +1.44145i q^{63} -6.72049 q^{64} +5.35008 q^{65} +(-0.872716 + 1.28135i) q^{66} +12.3988i q^{67} -9.56657i q^{68} +9.96739i q^{69} +0.334712i q^{70} +1.57409i q^{71} -0.926801 q^{72} -9.80194i q^{73} -1.32594i q^{74} -2.00145i q^{75} +(-7.26964 - 4.36616i) q^{76} +(2.67570 - 3.92855i) q^{77} +2.50084i q^{78} -1.60823 q^{79} +3.67570 q^{80} -11.0058 q^{81} -1.35439 q^{82} +8.47918i q^{83} +5.58027 q^{84} +4.91740i q^{85} +2.28275i q^{86} -8.20472i q^{87} +(2.52593 + 1.72038i) q^{88} -16.0172i q^{89} +0.234903 q^{90} -7.66744i q^{91} +9.68854 q^{92} -7.74981 q^{93} +2.25248 q^{94} +(3.73673 + 2.24429i) q^{95} +5.40669i q^{96} -13.9795i q^{97} -1.15516 q^{98} +(-2.75709 - 1.87783i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 40 q^{4} + 40 q^{5} - 28 q^{9}+O(q^{10}) \) 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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