LMFDB - Embedded newform 1045.2.b.e.419.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1045,2,Mod(419,1045)]

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([1, 0, 0]))

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

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

chi := DirichletCharacter("1045.419");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1045 = 5 \cdot 11 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1045.b (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:	$30$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			419.5
Character	$\chi$	$=$	1045.419
Dual form			1045.2.b.e.419.26

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.39110i q^{2} +3.31399i q^{3} -3.71736 q^{4} +(1.04940 - 1.97453i) q^{5} +7.92409 q^{6} +0.907652i q^{7} +4.10637i q^{8} -7.98255 q^{9} +O(q^{10})$	\(q-2.39110i q^{2} +3.31399i q^{3} -3.71736 q^{4} +(1.04940 - 1.97453i) q^{5} +7.92409 q^{6} +0.907652i q^{7} +4.10637i q^{8} -7.98255 q^{9} +(-4.72129 - 2.50922i) q^{10} +1.00000 q^{11} -12.3193i q^{12} +4.80276i q^{13} +2.17028 q^{14} +(6.54357 + 3.47771i) q^{15} +2.38402 q^{16} +3.57904i q^{17} +19.0871i q^{18} -1.00000 q^{19} +(-3.90100 + 7.34002i) q^{20} -3.00795 q^{21} -2.39110i q^{22} -0.159316i q^{23} -13.6085 q^{24} +(-2.79751 - 4.14414i) q^{25} +11.4839 q^{26} -16.5121i q^{27} -3.37406i q^{28} +2.96605 q^{29} +(8.31554 - 15.6463i) q^{30} -8.75450 q^{31} +2.51231i q^{32} +3.31399i q^{33} +8.55783 q^{34} +(1.79218 + 0.952491i) q^{35} +29.6740 q^{36} +8.00154i q^{37} +2.39110i q^{38} -15.9163 q^{39} +(8.10813 + 4.30923i) q^{40} -4.12633 q^{41} +7.19231i q^{42} +2.33463i q^{43} -3.71736 q^{44} +(-8.37690 + 15.7618i) q^{45} -0.380939 q^{46} +6.15070i q^{47} +7.90062i q^{48} +6.17617 q^{49} +(-9.90905 + 6.68913i) q^{50} -11.8609 q^{51} -17.8536i q^{52} +10.0057i q^{53} -39.4821 q^{54} +(1.04940 - 1.97453i) q^{55} -3.72715 q^{56} -3.31399i q^{57} -7.09212i q^{58} -7.81024 q^{59} +(-24.3248 - 12.9279i) q^{60} +0.603518 q^{61} +20.9329i q^{62} -7.24537i q^{63} +10.7752 q^{64} +(9.48318 + 5.04002i) q^{65} +7.92409 q^{66} +12.2839i q^{67} -13.3045i q^{68} +0.527971 q^{69} +(2.27750 - 4.28529i) q^{70} +8.58291 q^{71} -32.7793i q^{72} -8.43389i q^{73} +19.1325 q^{74} +(13.7337 - 9.27094i) q^{75} +3.71736 q^{76} +0.907652i q^{77} +38.0575i q^{78} -16.3911 q^{79} +(2.50179 - 4.70731i) q^{80} +30.7734 q^{81} +9.86645i q^{82} +4.61071i q^{83} +11.1816 q^{84} +(7.06690 + 3.75584i) q^{85} +5.58232 q^{86} +9.82947i q^{87} +4.10637i q^{88} +7.69047 q^{89} +(37.6879 + 20.0300i) q^{90} -4.35923 q^{91} +0.592233i q^{92} -29.0124i q^{93} +14.7069 q^{94} +(-1.04940 + 1.97453i) q^{95} -8.32576 q^{96} +1.90479i q^{97} -14.7678i q^{98} -7.98255 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q - 42 q^{4} + 12 q^{6} - 40 q^{9}+O(q^{10}) $ 30 * q - 42 * q^4 + 12 * q^6 - 40 * q^9	$ 30 q - 42 q^{4} + 12 q^{6} - 40 q^{9} + 10 q^{10} + 30 q^{11} + 4 q^{14} + 4 q^{15} + 66 q^{16} - 30 q^{19} + 10 q^{20} + 14 q^{21} - 22 q^{24} - 6 q^{25} - 30 q^{29} + 14 q^{30} + 26 q^{31} - 12 q^{34} + 6 q^{35} + 78 q^{36} - 64 q^{39} - 20 q^{40} + 22 q^{41} - 42 q^{44} + 6 q^{45} + 28 q^{46} - 60 q^{49} + 64 q^{51} - 62 q^{54} - 32 q^{56} + 14 q^{59} - 28 q^{60} + 78 q^{61} - 90 q^{64} + 40 q^{65} + 12 q^{66} + 28 q^{69} + 12 q^{70} + 20 q^{71} - 42 q^{74} + 50 q^{75} + 42 q^{76} - 102 q^{79} - 40 q^{80} + 42 q^{81} - 98 q^{84} - 2 q^{85} - 52 q^{86} + 8 q^{89} + 22 q^{90} + 56 q^{91} - 40 q^{94} - 74 q^{96} - 40 q^{99}+O(q^{100}) $ 30 * q - 42 * q^4 + 12 * q^6 - 40 * q^9 + 10 * q^10 + 30 * q^11 + 4 * q^14 + 4 * q^15 + 66 * q^16 - 30 * q^19 + 10 * q^20 + 14 * q^21 - 22 * q^24 - 6 * q^25 - 30 * q^29 + 14 * q^30 + 26 * q^31 - 12 * q^34 + 6 * q^35 + 78 * q^36 - 64 * q^39 - 20 * q^40 + 22 * q^41 - 42 * q^44 + 6 * q^45 + 28 * q^46 - 60 * q^49 + 64 * q^51 - 62 * q^54 - 32 * q^56 + 14 * q^59 - 28 * q^60 + 78 * q^61 - 90 * q^64 + 40 * q^65 + 12 * q^66 + 28 * q^69 + 12 * q^70 + 20 * q^71 - 42 * q^74 + 50 * q^75 + 42 * q^76 - 102 * q^79 - 40 * q^80 + 42 * q^81 - 98 * q^84 - 2 * q^85 - 52 * q^86 + 8 * q^89 + 22 * q^90 + 56 * q^91 - 40 * q^94 - 74 * q^96 - 40 * 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 $

$2$		−	2.39110i		−	1.69076i	−0.534163	−	0.845381i	$-0.679373\pi$
$2$		−	2.39110i		−	1.69076i	0.534163	−	0.845381i	$-0.320627\pi$
$3$			3.31399i			1.91333i	0.291183	+	0.956667i	$0.405951\pi$
$3$			3.31399i			1.91333i	−0.291183	+	0.956667i	$0.594049\pi$
$4$	−3.71736			−1.85868
$5$	1.04940	−	1.97453i	0.469306	−	0.883035i
$5$	1.04940	−	1.97453i	0.469306	−	0.883035i
$6$	7.92409			3.23499
$7$			0.907652i			0.343060i	0.985179	+	0.171530i	$0.0548711\pi$
$7$			0.907652i			0.343060i	−0.985179	+	0.171530i	$0.945129\pi$
$8$			4.10637i			1.45182i
$9$	−7.98255			−2.66085
$10$	−4.72129	−	2.50922i	−1.49300	−	0.793486i
$11$	1.00000			0.301511
$11$	1.00000			0.301511
$12$		−	12.3193i		−	3.55627i
$13$			4.80276i			1.33205i	0.745931	+	0.666023i	$0.232005\pi$
$13$			4.80276i			1.33205i	−0.745931	+	0.666023i	$0.767995\pi$
$14$	2.17028			0.580033
$15$	6.54357	+	3.47771i	1.68954	+	0.897940i
$16$	2.38402			0.596005
$17$			3.57904i			0.868043i	0.900902	+	0.434022i	$0.142906\pi$
$17$			3.57904i			0.868043i	−0.900902	+	0.434022i	$0.857094\pi$
$18$			19.0871i			4.49886i
$19$	−1.00000			−0.229416
$19$	−1.00000			−0.229416
$20$	−3.90100	+	7.34002i	−0.872289	+	1.64128i
$21$	−3.00795			−0.656389
$22$		−	2.39110i		−	0.509784i
$23$		−	0.159316i		−	0.0332196i	−0.999862	−	0.0166098i	$-0.994713\pi$
$23$		−	0.159316i		−	0.0332196i	0.999862	−	0.0166098i	$-0.00528731\pi$
$24$	−13.6085			−2.77782
$25$	−2.79751	−	4.14414i	−0.559503	−	0.828828i
$26$	11.4839			2.25217
$27$		−	16.5121i		−	3.17776i
$28$		−	3.37406i		−	0.637638i
$29$	2.96605			0.550782			0.275391	−	0.961332i	$-0.411193\pi$
$29$	2.96605			0.550782			0.275391	+	0.961332i	$0.411193\pi$
$30$	8.31554	−	15.6463i	1.51820	−	2.85661i
$31$	−8.75450			−1.57236			−0.786178	−	0.618001i	$-0.787943\pi$
$31$	−8.75450			−1.57236			−0.786178	+	0.618001i	$0.787943\pi$
$32$			2.51231i			0.444117i
$33$			3.31399i			0.576892i
$34$	8.55783			1.46766
$35$	1.79218	+	0.952491i	0.302934	+	0.161000i
$36$	29.6740			4.94566
$37$			8.00154i			1.31545i	0.753260	+	0.657723i	$0.228480\pi$
$37$			8.00154i			1.31545i	−0.753260	+	0.657723i	$0.771520\pi$
$38$			2.39110i			0.387888i
$39$	−15.9163			−2.54865
$40$	8.10813	+	4.30923i	1.28201	+	0.681348i
$41$	−4.12633			−0.644424			−0.322212	−	0.946668i	$-0.604426\pi$
$41$	−4.12633			−0.644424			−0.322212	+	0.946668i	$0.604426\pi$
$42$			7.19231i			1.10980i
$43$			2.33463i			0.356027i	0.984028	+	0.178014i	$0.0569671\pi$
$43$			2.33463i			0.356027i	−0.984028	+	0.178014i	$0.943033\pi$
$44$	−3.71736			−0.560412
$45$	−8.37690	+	15.7618i	−1.24875	+	2.34962i
$46$	−0.380939			−0.0561664
$47$			6.15070i			0.897172i	0.893740	+	0.448586i	$0.148072\pi$
$47$			6.15070i			0.897172i	−0.893740	+	0.448586i	$0.851928\pi$
$48$			7.90062i			1.14036i
$49$	6.17617			0.882310
$50$	−9.90905	+	6.68913i	−1.40135	+	0.945986i
$51$	−11.8609			−1.66086
$52$		−	17.8536i		−	2.47584i
$53$			10.0057i			1.37439i	0.726473	+	0.687195i	$0.241158\pi$
$53$			10.0057i			1.37439i	−0.726473	+	0.687195i	$0.758842\pi$
$54$	−39.4821			−5.37284
$55$	1.04940	−	1.97453i	0.141501	−	0.266245i
$56$	−3.72715			−0.498061
$57$		−	3.31399i		−	0.438949i
$58$		−	7.09212i		−	0.931241i
$59$	−7.81024			−1.01681			−0.508403	−	0.861119i	$-0.669764\pi$
$59$	−7.81024			−1.01681			−0.508403	+	0.861119i	$0.669764\pi$
$60$	−24.3248	−	12.9279i	−3.14031	−	1.66898i
$61$	0.603518			0.0772726			0.0386363	−	0.999253i	$-0.487699\pi$
$61$	0.603518			0.0772726			0.0386363	+	0.999253i	$0.487699\pi$
$62$			20.9329i			2.65848i
$63$		−	7.24537i		−	0.912831i
$64$	10.7752			1.34690
$65$	9.48318	+	5.04002i	1.17624	+	0.625138i
$66$	7.92409			0.975388
$67$			12.2839i			1.50071i	0.661033	+	0.750357i	$0.270118\pi$
$67$			12.2839i			1.50071i	−0.661033	+	0.750357i	$0.729882\pi$
$68$		−	13.3045i		−	1.61341i
$69$	0.527971			0.0635602
$70$	2.27750	−	4.28529i	0.272213	−	0.512190i
$71$	8.58291			1.01860			0.509302	−	0.860588i	$-0.329904\pi$
$71$	8.58291			1.01860			0.509302	+	0.860588i	$0.329904\pi$
$72$		−	32.7793i		−	3.86307i
$73$		−	8.43389i		−	0.987112i	−0.869714	−	0.493556i	$-0.835697\pi$
$73$		−	8.43389i		−	0.987112i	0.869714	−	0.493556i	$-0.164303\pi$
$74$	19.1325			2.22411
$75$	13.7337	−	9.27094i	1.58583	−	1.07052i
$76$	3.71736			0.426410
$77$			0.907652i			0.103436i
$78$			38.0575i			4.30916i
$79$	−16.3911			−1.84414			−0.922071	−	0.387022i	$-0.873504\pi$
$79$	−16.3911			−1.84414			−0.922071	+	0.387022i	$0.873504\pi$
$80$	2.50179	−	4.70731i	0.279709	−	0.526293i
$81$	30.7734			3.41927
$82$			9.86645i			1.08957i
$83$			4.61071i			0.506092i	0.967454	+	0.253046i	$0.0814324\pi$
$83$			4.61071i			0.506092i	−0.967454	+	0.253046i	$0.918568\pi$
$84$	11.1816			1.22001
$85$	7.06690	+	3.75584i	0.766513	+	0.407378i
$86$	5.58232			0.601957
$87$			9.82947i			1.05383i
$88$			4.10637i			0.437740i
$89$	7.69047			0.815188			0.407594	−	0.913163i	$-0.366368\pi$
$89$	7.69047			0.815188			0.407594	+	0.913163i	$0.366368\pi$
$90$	37.6879	+	20.0300i	3.97266	+	2.11135i
$91$	−4.35923			−0.456972
$92$			0.592233i			0.0617445i
$93$		−	29.0124i		−	3.00844i
$94$	14.7069			1.51690
$95$	−1.04940	+	1.97453i	−0.107666	+	0.202582i
$96$	−8.32576			−0.849745
$97$			1.90479i			0.193402i	0.995313	+	0.0967009i	$0.0308290\pi$
$97$			1.90479i			0.193402i	−0.995313	+	0.0967009i	$0.969171\pi$
$98$		−	14.7678i		−	1.49178i
$99$	−7.98255			−0.802276
$100$	10.3994	+	15.4052i	1.03994	+	1.54052i
$101$	6.75399			0.672047			0.336023	−	0.941854i	$-0.390918\pi$
$101$	6.75399			0.672047			0.336023	+	0.941854i	$0.390918\pi$
$102$			28.3606i			2.80812i
$103$		−	8.46909i		−	0.834485i	−0.908795	−	0.417242i	$-0.862997\pi$
$103$		−	8.46909i		−	0.834485i	0.908795	−	0.417242i	$-0.137003\pi$
$104$	−19.7219			−1.93389
$105$	−3.15655	+	5.93928i	−0.308047	+	0.579614i
$106$	23.9247			2.32377
$107$		−	4.22371i		−	0.408321i	−0.978937	−	0.204161i	$-0.934554\pi$
$107$		−	4.22371i		−	0.408321i	0.978937	−	0.204161i	$-0.0654465\pi$
$108$			61.3815i			5.90643i
$109$	−7.79868			−0.746978			−0.373489	−	0.927635i	$-0.621839\pi$
$109$	−7.79868			−0.746978			−0.373489	+	0.927635i	$0.621839\pi$
$110$	−4.72129	−	2.50922i	−0.450157	−	0.239245i
$111$	−26.5170			−2.51689
$112$			2.16386i			0.204465i
$113$			18.3105i			1.72250i	0.508179	+	0.861251i	$0.330319\pi$
$113$			18.3105i			1.72250i	−0.508179	+	0.861251i	$0.669681\pi$
$114$	−7.92409			−0.742159
$115$	−0.314573	−	0.167186i	−0.0293341	−	0.0155902i
$116$	−11.0259			−1.02373
$117$		−	38.3383i		−	3.54437i
$118$			18.6751i			1.71918i
$119$	−3.24852			−0.297791
$120$	−14.2807	+	26.8703i	−1.30365	+	2.45291i
$121$	1.00000			0.0909091
$122$		−	1.44307i		−	0.130650i
$123$		−	13.6746i		−	1.23300i
$124$	32.5436			2.92250
$125$	−11.1184	+	1.17490i	−0.994463	+	0.105086i
$126$	−17.3244			−1.54338
$127$		−	2.30657i		−	0.204675i	−0.994750	−	0.102338i	$-0.967368\pi$
$127$		−	2.30657i		−	0.204675i	0.994750	−	0.102338i	$-0.0326322\pi$
$128$		−	20.7400i		−	1.83317i
$129$	−7.73694			−0.681199
$130$	12.0512	−	22.6752i	1.05696	−	1.98875i
$131$	−15.8512			−1.38493			−0.692464	−	0.721452i	$-0.743475\pi$
$131$	−15.8512			−1.38493			−0.692464	+	0.721452i	$0.743475\pi$
$132$		−	12.3193i		−	1.07226i
$133$		−	0.907652i		−	0.0787034i
$134$	29.3719			2.53735
$135$	−32.6037	−	17.3279i	−2.80608	−	1.49134i
$136$	−14.6968			−1.26024
$137$		−	17.8068i		−	1.52134i	−0.649139	−	0.760670i	$-0.724871\pi$
$137$		−	17.8068i		−	1.52134i	0.649139	−	0.760670i	$-0.275129\pi$
$138$		−	1.26243i		−	0.107465i
$139$	11.0618			0.938252			0.469126	−	0.883131i	$-0.344569\pi$
$139$	11.0618			0.938252			0.469126	+	0.883131i	$0.344569\pi$
$140$	−6.66218	−	3.54075i	−0.563057	−	0.299248i
$141$	−20.3834			−1.71659
$142$		−	20.5226i		−	1.72222i
$143$			4.80276i			0.401627i
$144$	−19.0306			−1.58588
$145$	3.11258	−	5.85655i	0.258486	−	0.486360i
$146$	−20.1663			−1.66897
$147$			20.4678i			1.68815i
$148$		−	29.7446i		−	2.44499i
$149$	6.61609			0.542011			0.271006	−	0.962578i	$-0.412644\pi$
$149$	6.61609			0.542011			0.271006	+	0.962578i	$0.412644\pi$
$150$	−22.1677	−	32.8385i	−1.80999	−	2.68126i
$151$	14.3204			1.16538			0.582689	−	0.812695i	$-0.302001\pi$
$151$	14.3204			1.16538			0.582689	+	0.812695i	$0.302001\pi$
$152$		−	4.10637i		−	0.333070i
$153$		−	28.5698i		−	2.30973i
$154$	2.17028			0.174887
$155$	−9.18699	+	17.2860i	−0.737917	+	1.38845i
$156$	59.1666			4.73712
$157$		−	8.94838i		−	0.714159i	−0.934074	−	0.357079i	$-0.883773\pi$
$157$		−	8.94838i		−	0.714159i	0.934074	−	0.357079i	$-0.116227\pi$
$158$			39.1927i			3.11800i
$159$	−33.1589			−2.62967
$160$	4.96062	+	2.63642i	0.392171	+	0.208427i
$161$	0.144603			0.0113963
$162$		−	73.5823i		−	5.78118i
$163$		−	13.5017i		−	1.05753i	−0.848768	−	0.528766i	$-0.822655\pi$
$163$		−	13.5017i		−	1.05753i	0.848768	−	0.528766i	$-0.177345\pi$
$164$	15.3390			1.19778
$165$	6.54357	+	3.47771i	0.509416	+	0.270739i
$166$	11.0247			0.855681
$167$		−	15.3669i		−	1.18912i	−0.804050	−	0.594561i	$-0.797326\pi$
$167$		−	15.3669i		−	1.18912i	0.804050	−	0.594561i	$-0.202674\pi$
$168$		−	12.3517i		−	0.952958i
$169$	−10.0665			−0.774345
$170$	8.98059	−	16.8977i	0.688780	−	1.29599i
$171$	7.98255			0.610441
$172$		−	8.67864i		−	0.661740i
$173$			12.2125i			0.928499i	0.885704	+	0.464250i	$0.153676\pi$
$173$			12.2125i			0.928499i	−0.885704	+	0.464250i	$0.846324\pi$
$174$	23.5032			1.78178
$175$	3.76144	−	2.53917i	0.284338	−	0.191943i
$176$	2.38402			0.179702
$177$		−	25.8831i		−	1.94549i
$178$		−	18.3887i		−	1.37829i
$179$	17.3756			1.29871			0.649356	−	0.760484i	$-0.275038\pi$
$179$	17.3756			1.29871			0.649356	+	0.760484i	$0.275038\pi$
$180$	31.1399	−	58.5921i	2.32103	−	4.36719i
$181$	11.3298			0.842134			0.421067	−	0.907030i	$-0.361656\pi$
$181$	11.3298			0.842134			0.421067	+	0.907030i	$0.361656\pi$
$182$			10.4234i			0.772630i
$183$			2.00005i			0.147848i
$184$	0.654208			0.0482289
$185$	15.7993	+	8.39683i	1.16158	+	0.617347i
$186$	−69.3714			−5.08656
$187$			3.57904i			0.261725i
$188$		−	22.8643i		−	1.66755i
$189$	14.9873			1.09016
$190$	4.72129	+	2.50922i	0.342518	+	0.182038i
$191$	−11.9980			−0.868144			−0.434072	−	0.900878i	$-0.642924\pi$
$191$	−11.9980			−0.868144			−0.434072	+	0.900878i	$0.642924\pi$
$192$			35.7090i			2.57707i
$193$		−	23.1493i		−	1.66632i	−0.553031	−	0.833161i	$-0.686529\pi$
$193$		−	23.1493i		−	1.66632i	0.553031	−	0.833161i	$-0.313471\pi$
$194$	4.55453			0.326996
$195$	−16.7026	+	31.4272i	−1.19610	+	2.25055i
$196$	−22.9590			−1.63993
$197$			1.66139i			0.118369i	0.998247	+	0.0591845i	$0.0188500\pi$
$197$			1.66139i			0.118369i	−0.998247	+	0.0591845i	$0.981150\pi$
$198$			19.0871i			1.35646i
$199$	−5.31215			−0.376569			−0.188284	−	0.982115i	$-0.560293\pi$
$199$	−5.31215			−0.376569			−0.188284	+	0.982115i	$0.560293\pi$
$200$	17.0174	−	11.4876i	1.20331	−	0.812297i
$201$	−40.7086			−2.87137
$202$		−	16.1495i		−	1.13627i
$203$			2.69214i			0.188951i
$204$	44.0912			3.08700
$205$	−4.33017	+	8.14754i	−0.302432	+	0.569049i
$206$	−20.2504			−1.41092
$207$			1.27174i			0.0883923i
$208$			11.4499i			0.793906i
$209$	−1.00000			−0.0691714
$210$	14.2014	+	7.54762i	0.979990	+	0.520835i
$211$	11.2546			0.774799			0.387399	−	0.921912i	$-0.373373\pi$
$211$	11.2546			0.774799			0.387399	+	0.921912i	$0.373373\pi$
$212$		−	37.1948i		−	2.55455i
$213$			28.4437i			1.94893i
$214$	−10.0993			−0.690374
$215$	4.60978	+	2.44996i	0.314385	+	0.167086i
$216$	67.8049			4.61354
$217$		−	7.94604i		−	0.539412i
$218$			18.6474i			1.26296i
$219$	27.9499			1.88868
$220$	−3.90100	+	7.34002i	−0.263005	+	0.494864i
$221$	−17.1892			−1.15627
$222$			63.4049i			4.25546i
$223$		−	1.43220i		−	0.0959072i	−0.998850	−	0.0479536i	$-0.984730\pi$
$223$		−	1.43220i		−	0.0959072i	0.998850	−	0.0479536i	$-0.0152700\pi$
$224$	−2.28030			−0.152359
$225$	22.3313	+	33.0808i	1.48875	+	2.20539i
$226$	43.7821			2.91234
$227$		−	1.11781i		−	0.0741914i	−0.999312	−	0.0370957i	$-0.988189\pi$
$227$		−	1.11781i		−	0.0741914i	0.999312	−	0.0370957i	$-0.0118106\pi$
$228$			12.3193i			0.815865i
$229$	14.7072			0.971882			0.485941	−	0.873992i	$-0.338477\pi$
$229$	14.7072			0.971882			0.485941	+	0.873992i	$0.338477\pi$
$230$	−0.399758	+	0.752175i	−0.0263593	+	0.0495970i
$231$	−3.00795			−0.197909
$232$			12.1797i			0.799636i
$233$		−	24.1225i		−	1.58031i	−0.612904	−	0.790157i	$-0.709999\pi$
$233$		−	24.1225i		−	1.58031i	0.612904	−	0.790157i	$-0.290001\pi$
$234$	−91.6706			−5.99269
$235$	12.1447	+	6.45455i	0.792234	+	0.421049i
$236$	29.0334			1.88992
$237$		−	54.3199i		−	3.52846i
$238$			7.76753i			0.503494i
$239$	−1.47959			−0.0957069			−0.0478535	−	0.998854i	$-0.515238\pi$
$239$	−1.47959			−0.0957069			−0.0478535	+	0.998854i	$0.515238\pi$
$240$	15.6000	+	8.29093i	1.00698	+	0.535177i
$241$	−13.0927			−0.843375			−0.421687	−	0.906741i	$-0.638562\pi$
$241$	−13.0927			−0.843375			−0.421687	+	0.906741i	$0.638562\pi$
$242$		−	2.39110i		−	0.153706i
$243$			52.4466i			3.36445i
$244$	−2.24349			−0.143625
$245$	6.48128	−	12.1950i	0.414074	−	0.779111i
$246$	−32.6974			−2.08471
$247$		−	4.80276i		−	0.305592i
$248$		−	35.9492i		−	2.28278i
$249$	−15.2799			−0.968323
$250$	2.80930	+	26.5853i	0.177676	+	1.68140i
$251$	−10.1057			−0.637868			−0.318934	−	0.947777i	$-0.603325\pi$
$251$	−10.1057			−0.637868			−0.318934	+	0.947777i	$0.603325\pi$
$252$			26.9336i			1.69666i
$253$		−	0.159316i		−	0.0100161i
$254$	−5.51524			−0.346057
$255$	−12.4468	+	23.4197i	−0.779451	+	1.46660i
$256$	−28.0409			−1.75256
$257$			20.8353i			1.29967i	0.760074	+	0.649836i	$0.225162\pi$
$257$			20.8353i			1.29967i	−0.760074	+	0.649836i	$0.774838\pi$
$258$			18.4998i			1.15175i
$259$	−7.26261			−0.451277
$260$	−35.2523	−	18.7355i	−2.18626	−	1.16193i
$261$	−23.6767			−1.46555
$262$			37.9019i			2.34158i
$263$		−	18.1621i		−	1.11992i	−0.828518	−	0.559962i	$-0.810816\pi$
$263$		−	18.1621i		−	1.11992i	0.828518	−	0.559962i	$-0.189184\pi$
$264$	−13.6085			−0.837543
$265$	19.7566	+	10.5000i	1.21364	+	0.645010i
$266$	−2.17028			−0.133069
$267$			25.4862i			1.55973i
$268$		−	45.6635i		−	2.78934i
$269$	5.07585			0.309480			0.154740	−	0.987955i	$-0.450546\pi$
$269$	5.07585			0.309480			0.154740	+	0.987955i	$0.450546\pi$
$270$	−41.4326	+	77.9586i	−2.52151	+	4.74441i
$271$	10.1822			0.618522			0.309261	−	0.950977i	$-0.399918\pi$
$271$	10.1822			0.618522			0.309261	+	0.950977i	$0.399918\pi$
$272$			8.53249i			0.517358i
$273$		−	14.4465i		−	0.874340i
$274$	−42.5779			−2.57222
$275$	−2.79751	−	4.14414i	−0.168696	−	0.249901i
$276$	−1.96265			−0.118138
$277$		−	28.3706i		−	1.70462i	−0.523035	−	0.852311i	$-0.675200\pi$
$277$		−	28.3706i		−	1.70462i	0.523035	−	0.852311i	$-0.324800\pi$
$278$		−	26.4499i		−	1.58636i
$279$	69.8833			4.18380
$280$	−3.91128	+	7.35936i	−0.233743	+	0.439806i
$281$	29.3966			1.75365			0.876827	−	0.480806i	$-0.159656\pi$
$281$	29.3966			1.75365			0.876827	+	0.480806i	$0.159656\pi$
$282$			48.7387i			2.90235i
$283$			29.1332i			1.73179i	0.500229	+	0.865893i	$0.333249\pi$
$283$			29.1332i			1.73179i	−0.500229	+	0.865893i	$0.666751\pi$
$284$	−31.9057			−1.89326
$285$	−6.54357	−	3.47771i	−0.387608	−	0.206002i
$286$	11.4839			0.679056
$287$		−	3.74527i		−	0.221076i
$288$		−	20.0546i		−	1.18173i
$289$	4.19051			0.246500
$290$	−14.0036	−	7.44248i	−0.822319	−	0.437038i
$291$	−6.31245			−0.370042
$292$			31.3518i			1.83472i
$293$			13.7298i			0.802104i	0.916055	+	0.401052i	$0.131355\pi$
$293$			13.7298i			0.802104i	−0.916055	+	0.401052i	$0.868645\pi$
$294$	48.9405			2.85427
$295$	−8.19608	+	15.4215i	−0.477194	+	0.897876i
$296$	−32.8573			−1.90979
$297$		−	16.5121i		−	0.958131i
$298$		−	15.8197i		−	0.916412i
$299$	0.765154			0.0442500
$300$	−51.0529	+	34.4634i	−2.94754	+	1.98974i
$301$	−2.11903			−0.122139
$302$		−	34.2415i		−	1.97038i
$303$			22.3827i			1.28585i
$304$	−2.38402			−0.136733
$305$	0.633333	−	1.19166i	0.0362645	−	0.0682344i
$306$	−68.3133			−3.90521
$307$			24.2744i			1.38541i	0.721220	+	0.692706i	$0.243582\pi$
$307$			24.2744i			1.38541i	−0.721220	+	0.692706i	$0.756418\pi$
$308$		−	3.37406i		−	0.192255i
$309$	28.0665			1.59665
$310$	41.3326	+	21.9670i	2.34753	+	1.24764i
$311$	12.0690			0.684371			0.342186	−	0.939632i	$-0.388833\pi$
$311$	12.0690			0.684371			0.342186	+	0.939632i	$0.388833\pi$
$312$		−	65.3582i		−	3.70018i
$313$			21.6408i			1.22321i	0.791164	+	0.611604i	$0.209476\pi$
$313$			21.6408i			1.22321i	−0.791164	+	0.611604i	$0.790524\pi$
$314$	−21.3965			−1.20747
$315$	−14.3062	−	7.60330i	−0.806062	−	0.428398i
$316$	60.9315			3.42766
$317$			3.90023i			0.219059i	0.993984	+	0.109529i	$0.0349344\pi$
$317$			3.90023i			0.219059i	−0.993984	+	0.109529i	$0.965066\pi$
$318$			79.2861i			4.44615i
$319$	2.96605			0.166067
$320$	11.3075	−	21.2759i	0.632110	−	1.18936i
$321$	13.9973			0.781255
$322$		−	0.345760i		−	0.0192685i
$323$		−	3.57904i		−	0.199143i
$324$	−114.396			−6.35532
$325$	19.9033	−	13.4358i	1.10404	−	0.745283i
$326$	−32.2838			−1.78803
$327$		−	25.8448i		−	1.42922i
$328$		−	16.9442i		−	0.935587i
$329$	−5.58269			−0.307784
$330$	8.31554	−	15.6463i	0.457756	−	0.861302i
$331$	1.86620			0.102575			0.0512877	−	0.998684i	$-0.483667\pi$
$331$	1.86620			0.102575			0.0512877	+	0.998684i	$0.483667\pi$
$332$		−	17.1397i		−	0.940661i
$333$		−	63.8727i		−	3.50020i
$334$	−36.7437			−2.01052
$335$	24.2548	+	12.8907i	1.32518	+	0.704294i
$336$	−7.17101			−0.391211
$337$		−	21.3254i		−	1.16167i	−0.814021	−	0.580835i	$-0.802726\pi$
$337$		−	21.3254i		−	1.16167i	0.814021	−	0.580835i	$-0.197274\pi$
$338$			24.0700i			1.30923i
$339$	−60.6807			−3.29572
$340$	−26.2702	−	13.9618i	−1.42470	−	0.757185i
$341$	−8.75450			−0.474083
$342$		−	19.0871i		−	1.03211i
$343$			11.9594i			0.645745i
$344$	−9.58683			−0.516887
$345$	0.554053	−	1.04249i	0.0298292	−	0.0561259i
$346$	29.2013			1.56987
$347$			27.3244i			1.46685i	0.679770	+	0.733426i	$0.262080\pi$
$347$			27.3244i			1.46685i	−0.679770	+	0.733426i	$0.737920\pi$
$348$		−	36.5396i		−	1.95873i
$349$	3.07102			0.164388			0.0821940	−	0.996616i	$-0.473807\pi$
$349$	3.07102			0.164388			0.0821940	+	0.996616i	$0.473807\pi$
$350$	−6.07140	−	8.99397i	−0.324530	−	0.480748i
$351$	79.3038			4.23292
$352$			2.51231i			0.133906i
$353$		−	2.05954i		−	0.109618i	−0.998497	−	0.0548091i	$-0.982545\pi$
$353$		−	2.05954i		−	0.109618i	0.998497	−	0.0548091i	$-0.0174550\pi$
$354$	−61.8890			−3.28936
$355$	9.00691	−	16.9472i	0.478037	−	0.899463i
$356$	−28.5882			−1.51517
$357$		−	10.7656i		−	0.569774i
$358$		−	41.5467i		−	2.19581i
$359$	0.330271			0.0174310			0.00871552	−	0.999962i	$-0.497226\pi$
$359$	0.330271			0.0174310			0.00871552	+	0.999962i	$0.497226\pi$
$360$	−64.7236	−	34.3986i	−3.41123	−	1.81297i
$361$	1.00000			0.0526316
$362$		−	27.0906i		−	1.42385i
$363$			3.31399i			0.173940i
$364$	16.2048			0.849363
$365$	−16.6529	−	8.85054i	−0.871655	−	0.463258i
$366$	4.78233			0.249976
$367$		−	8.16820i		−	0.426377i	−0.977011	−	0.213188i	$-0.931615\pi$
$367$		−	8.16820i		−	0.426377i	0.977011	−	0.213188i	$-0.0683848\pi$
$368$		−	0.379812i		−	0.0197990i
$369$	32.9386			1.71471
$370$	20.0776	−	37.7776i	1.04379	−	1.96396i
$371$	−9.08170			−0.471498
$372$			107.849i			5.59172i
$373$			12.9054i			0.668218i	0.942534	+	0.334109i	$0.108435\pi$
$373$			12.9054i			0.668218i	−0.942534	+	0.334109i	$0.891565\pi$
$374$	8.55783			0.442515
$375$	−3.89361	−	36.8464i	−0.201065	−	1.90274i
$376$	−25.2570			−1.30253
$377$			14.2452i			0.733667i
$378$		−	35.8360i		−	1.84321i
$379$	−28.6728			−1.47282			−0.736411	−	0.676534i	$-0.763481\pi$
$379$	−28.6728			−1.47282			−0.736411	+	0.676534i	$0.763481\pi$
$380$	3.90100	−	7.34002i	0.200117	−	0.376535i
$381$	7.64396			0.391612
$382$			28.6884i			1.46783i
$383$		−	26.9020i		−	1.37463i	−0.726361	−	0.687313i	$-0.758790\pi$
$383$		−	26.9020i		−	1.37463i	0.726361	−	0.687313i	$-0.241210\pi$
$384$	68.7322			3.50747
$385$	1.79218	+	0.952491i	0.0913381	+	0.0485434i
$386$	−55.3522			−2.81735
$387$		−	18.6363i		−	0.947335i
$388$		−	7.08077i		−	0.359472i
$389$	6.06774			0.307647			0.153823	−	0.988098i	$-0.450841\pi$
$389$	6.06774			0.307647			0.153823	+	0.988098i	$0.450841\pi$
$390$	75.1455	+	39.9376i	3.80514	+	2.02232i
$391$	0.570196			0.0288361
$392$			25.3616i			1.28095i
$393$		−	52.5308i		−	2.64983i
$394$	3.97255			0.200134
$395$	−17.2008	+	32.3646i	−0.865467	+	1.62844i
$396$	29.6740			1.49117
$397$			34.3926i			1.72611i	0.505107	+	0.863057i	$0.331453\pi$
$397$			34.3926i			1.72611i	−0.505107	+	0.863057i	$0.668547\pi$
$398$			12.7019i			0.636688i
$399$	3.00795			0.150586
$400$	−6.66933	−	9.87972i	−0.333466	−	0.493986i
$401$	−28.8835			−1.44237			−0.721185	−	0.692742i	$-0.756402\pi$
$401$	−28.8835			−1.44237			−0.721185	+	0.692742i	$0.756402\pi$
$402$			97.3384i			4.85480i
$403$		−	42.0458i		−	2.09445i
$404$	−25.1070			−1.24912
$405$	32.2937	−	60.7630i	1.60469	−	3.01934i
$406$	6.43718			0.319472
$407$			8.00154i			0.396622i
$408$		−	48.7052i		−	2.41127i
$409$	−25.5952			−1.26560			−0.632800	−	0.774316i	$-0.718094\pi$
$409$	−25.5952			−1.26560			−0.632800	+	0.774316i	$0.718094\pi$
$410$	19.4816	+	10.3539i	0.962127	+	0.511341i
$411$	59.0117			2.91083
$412$			31.4826i			1.55104i
$413$		−	7.08898i		−	0.348826i
$414$	3.04087			0.149450
$415$	9.10398	+	4.83849i	0.446897	+	0.237512i
$416$	−12.0660			−0.591584
$417$			36.6588i			1.79519i
$418$			2.39110i			0.116952i
$419$	−22.8984			−1.11866			−0.559329	−	0.828946i	$-0.688941\pi$
$419$	−22.8984			−1.11866			−0.559329	+	0.828946i	$0.688941\pi$
$420$	11.7340	−	22.0784i	0.572561	−	1.07732i
$421$	19.1750			0.934533			0.467267	−	0.884116i	$-0.345239\pi$
$421$	19.1750			0.934533			0.467267	+	0.884116i	$0.345239\pi$
$422$		−	26.9109i		−	1.31000i
$423$		−	49.0983i		−	2.38724i
$424$	−41.0871			−1.99537
$425$	14.8320	−	10.0124i	0.719459	−	0.485673i
$426$	68.0117			3.29518
$427$			0.547784i			0.0265091i
$428$			15.7010i			0.758937i
$429$	−15.9163			−0.768447
$430$	5.85810	−	11.0224i	0.282503	−	0.531550i
$431$	−3.38640			−0.163117			−0.0815586	−	0.996669i	$-0.525990\pi$
$431$	−3.38640			−0.163117			−0.0815586	+	0.996669i	$0.525990\pi$
$432$		−	39.3652i		−	1.89396i
$433$			20.7630i			0.997808i	0.866657	+	0.498904i	$0.166264\pi$
$433$			20.7630i			0.997808i	−0.866657	+	0.498904i	$0.833736\pi$
$434$	−18.9998			−0.912018
$435$	19.4086	+	10.3151i	0.930569	+	0.494569i
$436$	28.9905			1.38839
$437$			0.159316i			0.00762110i
$438$		−	66.8309i		−	3.19330i
$439$	−2.94907			−0.140751			−0.0703756	−	0.997521i	$-0.522420\pi$
$439$	−2.94907			−0.140751			−0.0703756	+	0.997521i	$0.522420\pi$
$440$	8.10813	+	4.30923i	0.386540	+	0.205434i
$441$	−49.3016			−2.34769
$442$			41.1012i			1.95498i
$443$			14.4624i			0.687130i	0.939129	+	0.343565i	$0.111635\pi$
$443$			14.4624i			0.687130i	−0.939129	+	0.343565i	$0.888365\pi$
$444$	98.5733			4.67808
$445$	8.07038	−	15.1850i	0.382573	−	0.719840i
$446$	−3.42453			−0.162156
$447$			21.9257i			1.03705i
$448$			9.78014i			0.462068i
$449$	31.3106			1.47764			0.738819	−	0.673904i	$-0.235384\pi$
$449$	31.3106			1.47764			0.738819	+	0.673904i	$0.235384\pi$
$450$	79.0995	−	53.3963i	3.72879	−	2.51713i
$451$	−4.12633			−0.194301
$452$		−	68.0665i		−	3.20158i
$453$			47.4577i			2.22976i
$454$	−2.67278			−0.125440
$455$	−4.57458	+	8.60742i	−0.214460	+	0.403522i
$456$	13.6085			0.637275
$457$			35.8569i			1.67731i	0.544661	+	0.838656i	$0.316658\pi$
$457$			35.8569i			1.67731i	−0.544661	+	0.838656i	$0.683342\pi$
$458$		−	35.1665i		−	1.64322i
$459$	59.0975			2.75843
$460$	1.16938	+	0.621490i	0.0545226	+	0.0289771i
$461$	−0.256953			−0.0119675			−0.00598374	−	0.999982i	$-0.501905\pi$
$461$	−0.256953			−0.0119675			−0.00598374	+	0.999982i	$0.501905\pi$
$462$			7.19231i			0.334616i
$463$		−	0.808212i		−	0.0375608i	−0.999824	−	0.0187804i	$-0.994022\pi$
$463$		−	0.808212i		−	0.0375608i	0.999824	−	0.0187804i	$-0.00597834\pi$
$464$	7.07113			0.328269
$465$	−57.2857	−	30.4456i	−2.65656	−	1.41188i
$466$	−57.6792			−2.67194
$467$			33.0240i			1.52817i	0.645116	+	0.764084i	$0.276809\pi$
$467$			33.0240i			1.52817i	−0.645116	+	0.764084i	$0.723191\pi$
$468$			142.517i			6.58785i
$469$	−11.1495			−0.514835
$470$	15.4335	−	29.0392i	0.711893	−	1.33948i
$471$	29.6549			1.36642
$472$		−	32.0717i		−	1.47622i
$473$			2.33463i			0.107346i
$474$	−129.884			−5.96579
$475$	2.79751	+	4.14414i	0.128359	+	0.190146i
$476$	12.0759			0.553498
$477$		−	79.8711i		−	3.65705i
$478$			3.53785i			0.161818i
$479$	−9.97890			−0.455948			−0.227974	−	0.973667i	$-0.573210\pi$
$479$	−9.97890			−0.455948			−0.227974	+	0.973667i	$0.573210\pi$
$480$	−8.73707	+	16.4394i	−0.398791	+	0.750355i
$481$	−38.4295			−1.75223
$482$			31.3059i			1.42595i
$483$			0.479213i			0.0218050i
$484$	−3.71736			−0.168971
$485$	3.76105	+	1.99889i	0.170781	+	0.0907647i
$486$	125.405			5.68848
$487$			17.8238i			0.807674i	0.914831	+	0.403837i	$0.132324\pi$
$487$			17.8238i			0.807674i	−0.914831	+	0.403837i	$0.867676\pi$
$488$			2.47827i			0.112186i
$489$	44.7444			2.02341
$490$	−29.1595	−	15.4974i	−1.31729	−	0.700100i
$491$	−30.8805			−1.39362			−0.696810	−	0.717256i	$-0.745398\pi$
$491$	−30.8805			−1.39362			−0.696810	+	0.717256i	$0.745398\pi$
$492$			50.8334i			2.29175i
$493$			10.6156i			0.478103i
$494$	−11.4839			−0.516684
$495$	−8.37690	+	15.7618i	−0.376513	+	0.708438i
$496$	−20.8709			−0.937132
$497$			7.79029i			0.349442i
$498$			36.5357i			1.63720i
$499$	−9.67994			−0.433334			−0.216667	−	0.976246i	$-0.569519\pi$
$499$	−9.67994			−0.433334			−0.216667	+	0.976246i	$0.569519\pi$
$500$	41.3312	−	4.36752i	1.84839	−	0.195321i
$501$	50.9256			2.27519
$502$			24.1638i			1.07848i
$503$			9.37341i			0.417940i	0.977922	+	0.208970i	$0.0670110\pi$
$503$			9.37341i			0.417940i	−0.977922	+	0.208970i	$0.932989\pi$
$504$	29.7522			1.32527
$505$	7.08764	−	13.3359i	0.315396	−	0.593441i
$506$	−0.380939			−0.0169348
$507$		−	33.3603i		−	1.48158i
$508$			8.57434i			0.380425i
$509$	29.0755			1.28875			0.644374	−	0.764710i	$-0.277118\pi$
$509$	29.0755			1.28875			0.644374	+	0.764710i	$0.277118\pi$
$510$	55.9987	+	29.7616i	2.47967	+	1.31787i
$511$	7.65503			0.338639
$512$			25.5687i			1.12999i
$513$			16.5121i			0.729028i
$514$	49.8193			2.19744
$515$	−16.7225	−	8.88748i	−0.736879	−	0.391629i
$516$	28.7609			1.26613
$517$			6.15070i			0.270507i
$518$			17.3656i			0.763002i
$519$	−40.4721			−1.77653
$520$	−20.6962	+	38.9414i	−0.907587	+	1.70769i
$521$	9.00008			0.394300			0.197150	−	0.980373i	$-0.436831\pi$
$521$	9.00008			0.394300			0.197150	+	0.980373i	$0.436831\pi$
$522$			56.6132i			2.47789i
$523$		−	11.5638i		−	0.505651i	−0.967512	−	0.252825i	$-0.918640\pi$
$523$		−	11.5638i		−	0.505651i	0.967512	−	0.252825i	$-0.0813598\pi$
$524$	58.9246			2.57413
$525$	8.41479	+	12.4654i	0.367251	+	0.544034i
$526$	−43.4274			−1.89352
$527$		−	31.3327i		−	1.36487i
$528$			7.90062i			0.343831i
$529$	22.9746			0.998896
$530$	25.1066	−	47.2399i	1.09056	−	2.05197i
$531$	62.3456			2.70557
$532$			3.37406i			0.146284i
$533$		−	19.8177i		−	0.858402i
$534$	60.9399			2.63713
$535$	−8.33982	−	4.43236i	−0.360562	−	0.191628i
$536$	−50.4421			−2.17877
$537$			57.5826i			2.48487i
$538$		−	12.1369i		−	0.523257i
$539$	6.17617			0.266026
$540$	121.199	+	64.4138i	5.21559	+	2.77193i
$541$	−23.3991			−1.00601			−0.503003	−	0.864285i	$-0.667772\pi$
$541$	−23.3991			−1.00601			−0.503003	+	0.864285i	$0.667772\pi$
$542$		−	24.3465i		−	1.04577i
$543$			37.5467i			1.61128i
$544$	−8.99163			−0.385513
$545$	−8.18394	+	15.3987i	−0.350562	+	0.659608i
$546$	−34.5429			−1.47830
$547$		−	12.3118i		−	0.526417i	−0.964739	−	0.263208i	$-0.915219\pi$
$547$		−	12.3118i		−	0.526417i	0.964739	−	0.263208i	$-0.0847806\pi$
$548$			66.1943i			2.82768i
$549$	−4.81761			−0.205611
$550$	−9.90905	+	6.68913i	−0.422524	+	0.285226i
$551$	−2.96605			−0.126358
$552$			2.16804i			0.0922780i
$553$		−	14.8774i		−	0.632651i
$554$	−67.8368			−2.88211
$555$	−27.8270	+	52.3586i	−1.18119	+	2.22250i
$556$	−41.1207			−1.74391
$557$		−	33.2490i		−	1.40880i	−0.709801	−	0.704402i	$-0.751215\pi$
$557$		−	33.2490i		−	1.40880i	0.709801	−	0.704402i	$-0.248785\pi$
$558$		−	167.098i		−	7.07381i
$559$	−11.2126			−0.474244
$560$	4.27260	+	2.27076i	0.180550	+	0.0959570i
$561$	−11.8609			−0.500767
$562$		−	70.2902i		−	2.96501i
$563$			17.0918i			0.720332i	0.932888	+	0.360166i	$0.117280\pi$
$563$			17.0918i			0.720332i	−0.932888	+	0.360166i	$0.882720\pi$
$564$	75.7722			3.19059
$565$	36.1545	+	19.2150i	1.52103	+	0.808382i
$566$	69.6603			2.92804
$567$			27.9316i			1.17302i
$568$			35.2446i			1.47883i
$569$	−6.26048			−0.262453			−0.131227	−	0.991352i	$-0.541892\pi$
$569$	−6.26048			−0.262453			−0.131227	+	0.991352i	$0.541892\pi$
$570$	−8.31554	+	15.6463i	−0.348300	+	0.655352i
$571$	42.8778			1.79438			0.897189	−	0.441647i	$-0.145605\pi$
$571$	42.8778			1.79438			0.897189	+	0.441647i	$0.145605\pi$
$572$		−	17.8536i		−	0.746495i
$573$		−	39.7613i		−	1.66105i
$574$	−8.95530			−0.373787
$575$	−0.660226	+	0.445688i	−0.0275333	+	0.0185865i
$576$	−86.0137			−3.58390
$577$		−	3.16509i		−	0.131764i	−0.997827	−	0.0658822i	$-0.979014\pi$
$577$		−	3.16509i		−	0.131764i	0.997827	−	0.0658822i	$-0.0209862\pi$
$578$		−	10.0199i		−	0.416774i
$579$	76.7166			3.18823
$580$	−11.5706	+	21.7709i	−0.480441	+	0.903986i
$581$	−4.18492			−0.173620
$582$			15.0937i			0.625654i
$583$			10.0057i			0.414394i
$584$	34.6327			1.43311
$585$	−75.6999	−	40.2322i	−3.12981	−	1.66340i
$586$	32.8293			1.35617
$587$		−	27.6985i		−	1.14324i	−0.820519	−	0.571619i	$-0.806315\pi$
$587$		−	27.6985i		−	1.14324i	0.820519	−	0.571619i	$-0.193685\pi$
$588$		−	76.0860i		−	3.13773i
$589$	8.75450			0.360723
$590$	36.8744	+	19.5976i	1.51810	+	0.806822i
$591$	−5.50583			−0.226480
$592$			19.0758i			0.784012i
$593$		−	39.6320i		−	1.62749i	−0.581220	−	0.813746i	$-0.697425\pi$
$593$		−	39.6320i		−	1.62749i	0.581220	−	0.813746i	$-0.302575\pi$
$594$	−39.4821			−1.61997
$595$	−3.40900	+	6.41428i	−0.139755	+	0.262960i
$596$	−24.5944			−1.00742
$597$		−	17.6044i		−	0.720502i
$598$		−	1.82956i		−	0.0748163i
$599$	11.6640			0.476576			0.238288	−	0.971194i	$-0.423414\pi$
$599$	11.6640			0.476576			0.238288	+	0.971194i	$0.423414\pi$
$600$	38.0699	+	56.3954i	1.55420	+	2.30233i
$601$	1.71009			0.0697561			0.0348781	−	0.999392i	$-0.488896\pi$
$601$	1.71009			0.0697561			0.0348781	+	0.999392i	$0.488896\pi$
$602$			5.06680i			0.206508i
$603$		−	98.0566i		−	3.99317i
$604$	−53.2340			−2.16606
$605$	1.04940	−	1.97453i	0.0426642	−	0.0802759i
$606$	53.5192			2.17407
$607$		−	8.97345i		−	0.364221i	−0.983278	−	0.182111i	$-0.941707\pi$
$607$		−	8.97345i		−	0.364221i	0.983278	−	0.182111i	$-0.0582929\pi$
$608$		−	2.51231i		−	0.101887i
$609$	−8.92174			−0.361527
$610$	−2.84938	−	1.51436i	−0.115368	−	0.0613147i
$611$	−29.5403			−1.19507
$612$			106.204i			4.29305i
$613$		−	14.0363i		−	0.566922i	−0.958984	−	0.283461i	$-0.908517\pi$
$613$		−	14.0363i		−	0.566922i	0.958984	−	0.283461i	$-0.0914827\pi$
$614$	58.0425			2.34240
$615$	−27.0009	−	14.3502i	−1.08878	−	0.578654i
$616$	−3.72715			−0.150171
$617$			36.6485i			1.47541i	0.675120	+	0.737707i	$0.264092\pi$
$617$			36.6485i			1.47541i	−0.675120	+	0.737707i	$0.735908\pi$
$618$		−	67.1098i		−	2.69955i
$619$	29.9727			1.20471			0.602353	−	0.798230i	$-0.294230\pi$
$619$	29.9727			1.20471			0.602353	+	0.798230i	$0.294230\pi$
$620$	34.1513	−	64.2582i	1.37155	−	2.58067i
$621$	−2.63064			−0.105564
$622$		−	28.8582i		−	1.15711i
$623$			6.98026i			0.279658i
$624$	−37.9448			−1.51901
$625$	−9.34783	+	23.1866i	−0.373913	+	0.927464i
$626$	51.7452			2.06816
$627$		−	3.31399i		−	0.132348i
$628$			33.2643i			1.32739i
$629$	−28.6378			−1.14186
$630$	−18.1803	+	34.2075i	−0.724319	+	1.36286i
$631$	−20.4610			−0.814538			−0.407269	−	0.913308i	$-0.633519\pi$
$631$	−20.4610			−0.814538			−0.407269	+	0.913308i	$0.633519\pi$
$632$		−	67.3078i		−	2.67736i
$633$			37.2977i			1.48245i
$634$	9.32583			0.370376
$635$	−4.55439	−	2.42052i	−0.180735	−	0.0960553i
$636$	123.263			4.88771
$637$			29.6626i			1.17528i
$638$		−	7.09212i		−	0.280780i
$639$	−68.5135			−2.71035
$640$	−40.9517	−	21.7646i	−1.61876	−	0.860320i
$641$	13.8089			0.545419			0.272709	−	0.962096i	$-0.412080\pi$
$641$	13.8089			0.545419			0.272709	+	0.962096i	$0.412080\pi$
$642$		−	33.4690i		−	1.32092i
$643$		−	3.93163i		−	0.155048i	−0.996990	−	0.0775242i	$-0.975298\pi$
$643$		−	3.93163i		−	0.155048i	0.996990	−	0.0775242i	$-0.0247015\pi$
$644$	−0.537541			−0.0211821
$645$	−8.11915	+	15.2768i	−0.319691	+	0.601523i
$646$	−8.55783			−0.336703
$647$			34.9182i			1.37278i	0.727235	+	0.686389i	$0.240805\pi$
$647$			34.9182i			1.37278i	−0.727235	+	0.686389i	$0.759195\pi$
$648$			126.367i			4.96417i
$649$	−7.81024			−0.306579
$650$	−32.1263	−	47.5908i	−1.26010	−	1.86666i
$651$	26.3331			1.03208
$652$			50.1904i			1.96561i
$653$			4.79484i			0.187637i	0.995589	+	0.0938184i	$0.0299073\pi$
$653$			4.79484i			0.187637i	−0.995589	+	0.0938184i	$0.970093\pi$
$654$	−61.7974			−2.41647
$655$	−16.6343	+	31.2987i	−0.649956	+	1.22294i
$656$	−9.83724			−0.384080
$657$			67.3240i			2.62656i
$658$			13.3488i			0.520389i
$659$	−13.5528			−0.527943			−0.263972	−	0.964530i	$-0.585033\pi$
$659$	−13.5528			−0.527943			−0.263972	+	0.964530i	$0.585033\pi$
$660$	−24.3248	−	12.9279i	−0.946840	−	0.503217i
$661$	38.7807			1.50840			0.754198	−	0.656647i	$-0.228026\pi$
$661$	38.7807			1.50840			0.754198	+	0.656647i	$0.228026\pi$
$662$		−	4.46226i		−	0.173431i
$663$		−	56.9650i		−	2.21234i
$664$	−18.9333			−0.734754
$665$	−1.79218	−	0.952491i	−0.0694979	−	0.0369360i
$666$	−152.726			−5.91801
$667$		−	0.472538i		−	0.0182968i
$668$			57.1241i			2.21020i
$669$	4.74630			0.183503
$670$	30.8230	−	57.9957i	1.19079	−	2.24057i
$671$	0.603518			0.0232986
$672$		−	7.55689i		−	0.291513i
$673$		−	1.54247i		−	0.0594580i	−0.999558	−	0.0297290i	$-0.990536\pi$
$673$		−	1.54247i		−	0.0594580i	0.999558	−	0.0297290i	$-0.00946444\pi$
$674$	−50.9912			−1.96411
$675$	−68.4286	+	46.1929i	−2.63382	+	1.77797i
$676$	37.4207			1.43926
$677$		−	23.5358i		−	0.904553i	−0.891878	−	0.452276i	$-0.850612\pi$
$677$		−	23.5358i		−	0.904553i	0.891878	−	0.452276i	$-0.149388\pi$
$678$			145.094i			5.57229i
$679$	−1.72888			−0.0663484
$680$	−15.4229	+	29.0193i	−0.591440	+	1.11284i
$681$	3.70440			0.141953
$682$			20.9329i			0.801562i
$683$			13.1897i			0.504689i	0.967637	+	0.252345i	$0.0812017\pi$
$683$			13.1897i			0.504689i	−0.967637	+	0.252345i	$0.918798\pi$
$684$	−29.6740			−1.13461
$685$	−35.1601	−	18.6865i	−1.34340	−	0.713975i
$686$	28.5960			1.09180
$687$			48.7397i			1.85954i
$688$			5.56580i			0.212194i
$689$	−48.0550			−1.83075
$690$	−2.49270	−	1.32480i	−0.0948956	−	0.0504341i
$691$	10.1794			0.387244			0.193622	−	0.981076i	$-0.437976\pi$
$691$	10.1794			0.387244			0.193622	+	0.981076i	$0.437976\pi$
$692$		−	45.3982i		−	1.72578i
$693$		−	7.24537i		−	0.275229i
$694$	65.3354			2.48010
$695$	11.6083	−	21.8419i	0.440328	−	0.828509i
$696$	−40.3634			−1.52997
$697$		−	14.7683i		−	0.559388i
$698$		−	7.34311i		−	0.277941i
$699$	79.9417			3.02367
$700$	−13.9826	+	9.43899i	−0.528493	+	0.356760i
$701$	19.3491			0.730807			0.365404	−	0.930849i	$-0.380931\pi$
$701$	19.3491			0.730807			0.365404	+	0.930849i	$0.380931\pi$
$702$		−	189.623i		−	7.15687i
$703$		−	8.00154i		−	0.301784i
$704$	10.7752			0.406106
$705$	−21.3903	+	40.2475i	−0.805607	+	1.51581i
$706$	−4.92456			−0.185338
$707$			6.13027i			0.230552i
$708$			96.2166i			3.61604i
$709$	−1.72744			−0.0648753			−0.0324376	−	0.999474i	$-0.510327\pi$
$709$	−1.72744			−0.0648753			−0.0324376	+	0.999474i	$0.510327\pi$
$710$	−40.5224	−	21.5364i	−1.52078	−	0.808247i
$711$	130.843			4.90698
$712$			31.5799i			1.18351i
$713$			1.39473i			0.0522330i
$714$	−25.7415			−0.963352
$715$	9.48318	+	5.04002i	0.354651	+	0.188486i
$716$	−64.5912			−2.41389
$717$		−	4.90336i		−	0.183119i
$718$		−	0.789710i		−	0.0294717i
$719$	−23.1430			−0.863088			−0.431544	−	0.902092i	$-0.642031\pi$
$719$	−23.1430			−0.863088			−0.431544	+	0.902092i	$0.642031\pi$
$720$	−19.9707	+	37.5763i	−0.744264	+	1.40039i
$721$	7.68699			0.286278
$722$		−	2.39110i		−	0.0889875i
$723$		−	43.3891i		−	1.61366i
$724$	−42.1167			−1.56526
$725$	−8.29757	−	12.2917i	−0.308164	−	0.456504i
$726$	7.92409			0.294090
$727$			11.2305i			0.416514i	0.978074	+	0.208257i	$0.0667791\pi$
$727$			11.2305i			0.416514i	−0.978074	+	0.208257i	$0.933221\pi$
$728$		−	17.9006i		−	0.663440i
$729$	−81.4872			−3.01805
$730$	−21.1625	+	39.8188i	−0.783260	+	1.47376i
$731$	−8.35571			−0.309047
$732$		−	7.43491i		−	0.274802i
$733$			31.1816i			1.15172i	0.817548	+	0.575860i	$0.195333\pi$
$733$			31.1816i			1.15172i	−0.817548	+	0.575860i	$0.804667\pi$
$734$	−19.5310			−0.720902
$735$	40.4142	+	21.4789i	1.49070	+	0.792262i
$736$	0.400249			0.0147534
$737$			12.2839i			0.452482i
$738$		−	78.7595i		−	2.89918i
$739$	−42.7549			−1.57277			−0.786383	−	0.617739i	$-0.788049\pi$
$739$	−42.7549			−1.57277			−0.786383	+	0.617739i	$0.788049\pi$
$740$	−58.7315	−	31.2140i	−2.15901	−	1.14745i
$741$	15.9163			0.584700
$742$			21.7152i			0.797192i
$743$		−	19.8100i		−	0.726759i	−0.931641	−	0.363380i	$-0.881623\pi$
$743$		−	19.8100i		−	0.726759i	0.931641	−	0.363380i	$-0.118377\pi$
$744$	119.135			4.36772
$745$	6.94293	−	13.0637i	0.254369	−	0.478615i
$746$	30.8582			1.12980
$747$		−	36.8053i		−	1.34663i
$748$		−	13.3045i		−	0.486462i
$749$	3.83365			0.140079
$750$	−88.1034	+	9.31001i	−3.21708	+	0.339953i
$751$	6.14518			0.224241			0.112120	−	0.993695i	$-0.464236\pi$
$751$	6.14518			0.224241			0.112120	+	0.993695i	$0.464236\pi$
$752$			14.6634i			0.534719i
$753$		−	33.4903i		−	1.22045i
$754$	34.0618			1.24046
$755$	15.0279	−	28.2760i	0.546920	−	1.02907i
$756$	−55.7130			−2.02626
$757$		−	6.29333i		−	0.228735i	−0.993439	−	0.114367i	$-0.963516\pi$
$757$		−	6.29333i		−	0.228735i	0.993439	−	0.114367i	$-0.0364841\pi$
$758$			68.5595i			2.49019i
$759$	0.527971			0.0191641
$760$	−8.10813	−	4.30923i	−0.294113	−	0.156312i
$761$	34.4999			1.25062			0.625310	−	0.780377i	$-0.284973\pi$
$761$	34.4999			1.25062			0.625310	+	0.780377i	$0.284973\pi$
$762$		−	18.2775i		−	0.662123i
$763$		−	7.07848i		−	0.256258i
$764$	44.6008			1.61360
$765$	−56.4119	−	29.9812i	−2.03958	−	1.08397i
$766$	−64.3253			−2.32417
$767$		−	37.5107i		−	1.35443i
$768$		−	92.9275i		−	3.35323i
$769$	−35.4977			−1.28008			−0.640040	−	0.768342i	$-0.721082\pi$
$769$	−35.4977			−1.28008			−0.640040	+	0.768342i	$0.721082\pi$
$770$	2.27750	−	4.28529i	0.0820754	−	0.154431i
$771$	−69.0481			−2.48671
$772$			86.0541i			3.09715i
$773$			42.1875i			1.51738i	0.651453	+	0.758689i	$0.274160\pi$
$773$			42.1875i			1.51738i	−0.651453	+	0.758689i	$0.725840\pi$
$774$	−44.5612			−1.60172
$775$	24.4909	+	36.2799i	0.879737	+	1.30321i
$776$	−7.82175			−0.280785
$777$		−	24.0682i		−	0.863443i
$778$		−	14.5086i		−	0.520158i
$779$	4.12633			0.147841
$780$	62.0895	−	116.826i	2.22316	−	4.18304i
$781$	8.58291			0.307121
$782$		−	1.36340i		−	0.0487549i
$783$		−	48.9758i		−	1.75025i
$784$	14.7241			0.525861
$785$	−17.6688	−	9.39044i	−0.630627	−	0.335159i
$786$	−125.606			−4.48023
$787$		−	45.5168i		−	1.62250i	−0.584701	−	0.811249i	$-0.698788\pi$
$787$		−	45.5168i		−	1.62250i	0.584701	−	0.811249i	$-0.301212\pi$
$788$		−	6.17597i		−	0.220010i
$789$	60.1891			2.14279
$790$	77.3871	+	41.1289i	2.75331	+	1.46330i
$791$	−16.6195			−0.590922
$792$		−	32.7793i		−	1.16476i
$793$			2.89855i			0.102931i
$794$	82.2360			2.91845
$795$	−34.7970	+	65.4731i	−1.23412	+	2.32209i
$796$	19.7472			0.699920
$797$			32.1787i			1.13983i	0.821704	+	0.569915i	$0.193024\pi$
$797$			32.1787i			1.13983i	−0.821704	+	0.569915i	$0.806976\pi$
$798$		−	7.19231i		−	0.254605i
$799$	−22.0136			−0.778784
$800$	10.4114	−	7.02821i	0.368097	−	0.248485i
$801$	−61.3895			−2.16909
$802$			69.0632i			2.43871i
$803$		−	8.43389i		−	0.297626i
$804$	151.328			5.33694
$805$	0.151747	−	0.285523i	0.00534836	−	0.0100633i
$806$	−100.536			−3.54122
$807$			16.8213i			0.592139i
$808$			27.7343i			0.975691i
$809$	−14.0643			−0.494475			−0.247238	−	0.968955i	$-0.579523\pi$
$809$	−14.0643			−0.494475			−0.247238	+	0.968955i	$0.579523\pi$
$810$	−145.290	−	77.2174i	−5.10498	−	2.71314i
$811$	31.7138			1.11362			0.556812	−	0.830639i	$-0.312025\pi$
$811$	31.7138			1.11362			0.556812	+	0.830639i	$0.312025\pi$
$812$		−	10.0076i		−	0.351200i
$813$			33.7436i			1.18344i
$814$	19.1325			0.670593
$815$	−26.6594	−	14.1687i	−0.933837	−	0.496306i
$816$	−28.2766			−0.989879
$817$		−	2.33463i		−	0.0816782i
$818$			61.2006i			2.13983i
$819$	34.7978			1.21593
$820$	16.0968	−	30.2873i	0.562124	−	1.05768i
$821$	54.3282			1.89607			0.948034	−	0.318170i	$-0.103068\pi$
$821$	54.3282			1.89607			0.948034	+	0.318170i	$0.103068\pi$
$822$		−	141.103i		−	4.92153i
$823$			0.0239052i			0.000833284i	1.00000		0.000416642i	$0.000132621\pi$
$823$			0.0239052i			0.000833284i	−1.00000		0.000416642i	$0.999867\pi$
$824$	34.7772			1.21152
$825$	13.7337	−	9.27094i	0.478145	−	0.322773i
$826$	−16.9504			−0.589781
$827$			0.635541i			0.0220999i	0.999939	+	0.0110500i	$0.00351738\pi$
$827$			0.635541i			0.0220999i	−0.999939	+	0.0110500i	$0.996483\pi$
$828$		−	4.72753i		−	0.164293i
$829$	18.6434			0.647513			0.323757	−	0.946140i	$-0.395054\pi$
$829$	18.6434			0.647513			0.323757	+	0.946140i	$0.395054\pi$
$830$	11.5693	−	21.7685i	0.401577	−	0.755596i
$831$	94.0198			3.26151
$832$			51.7507i			1.79413i
$833$			22.1047i			0.765883i
$834$	87.6548			3.03524
$835$	−30.3423	−	16.1260i	−1.05004	−	0.558063i
$836$	3.71736			0.128567
$837$			144.556i			4.99657i
$838$			54.7523i			1.89139i
$839$	−13.4740			−0.465175			−0.232587	−	0.972576i	$-0.574719\pi$
$839$	−13.4740			−0.465175			−0.232587	+	0.972576i	$0.574719\pi$
$840$	−24.3889	−	12.9619i	−0.841496	−	0.447229i
$841$	−20.2025			−0.696639
$842$		−	45.8494i		−	1.58007i
$843$			97.4201i			3.35533i
$844$	−41.8373			−1.44010
$845$	−10.5638	+	19.8766i	−0.363405	+	0.683774i
$846$	−117.399			−4.03625
$847$			0.907652i			0.0311873i
$848$			23.8538i			0.819144i
$849$	−96.5471			−3.31349
$850$	−23.9406	−	35.4649i	−0.821157	−	1.21643i
$851$	1.27477			0.0436986
$852$		−	105.735i		−	3.62243i
$853$		−	14.6865i		−	0.502855i	−0.967876	−	0.251428i	$-0.919100\pi$
$853$		−	14.6865i		−	0.502855i	0.967876	−	0.251428i	$-0.0809000\pi$
$854$	1.30981			0.0448207
$855$	8.37690	−	15.7618i	0.286484	−	0.539041i
$856$	17.3441			0.592809
$857$			22.0020i			0.751573i	0.926706	+	0.375787i	$0.122627\pi$
$857$			22.0020i			0.751573i	−0.926706	+	0.375787i	$0.877373\pi$
$858$			38.0575i			1.29926i
$859$	−24.7894			−0.845803			−0.422901	−	0.906176i	$-0.638988\pi$
$859$	−24.7894			−0.845803			−0.422901	+	0.906176i	$0.638988\pi$
$860$	−17.1362	−	9.10737i	−0.584340	−	0.310559i
$861$	12.4118			0.422992
$862$			8.09722i			0.275792i
$863$			53.6587i			1.82657i	0.407327	+	0.913283i	$0.366461\pi$
$863$			53.6587i			1.82657i	−0.407327	+	0.913283i	$0.633539\pi$
$864$	41.4835			1.41130
$865$	24.1139	+	12.8158i	0.819898	+	0.435751i
$866$	49.6465			1.68706
$867$			13.8873i			0.471638i
$868$			29.5383i			1.00259i
$869$	−16.3911			−0.556030
$870$	24.6643	−	46.4078i	0.836199	−	1.57337i
$871$	−58.9964			−1.99902
$872$		−	32.0242i		−	1.08448i
$873$		−	15.2051i		−	0.514613i
$874$	0.380939			0.0128855
$875$	−1.06640	−	10.0917i	−0.0360509	−	0.341161i
$876$	−103.900			−3.51044
$877$			15.8532i			0.535323i	0.963513	+	0.267662i	$0.0862509\pi$
$877$			15.8532i			0.535323i	−0.963513	+	0.267662i	$0.913749\pi$
$878$			7.05151i			0.237977i
$879$	−45.5005			−1.53469
$880$	2.50179	−	4.70731i	0.0843354	−	0.158683i
$881$	−24.4503			−0.823753			−0.411876	−	0.911240i	$-0.635126\pi$
$881$	−24.4503			−0.823753			−0.411876	+	0.911240i	$0.635126\pi$
$882$			117.885i			3.96939i
$883$			41.9824i			1.41282i	0.707802	+	0.706411i	$0.249687\pi$
$883$			41.9824i			1.41282i	−0.707802	+	0.706411i	$0.750313\pi$
$884$	63.8985			2.14914
$885$	−51.1068	−	27.1617i	−1.71794	−	0.913032i
$886$	34.5810			1.16177
$887$			9.33740i			0.313519i	0.987637	+	0.156760i	$0.0501048\pi$
$887$			9.33740i			0.313519i	−0.987637	+	0.156760i	$0.949895\pi$
$888$		−	108.889i		−	3.65407i
$889$	2.09356			0.0702158
$890$	−36.3089	−	19.2971i	−1.21708	−	0.646840i
$891$	30.7734			1.03095
$892$			5.32400i			0.178261i
$893$		−	6.15070i		−	0.205825i
$894$	52.4265			1.75340
$895$	18.2340	−	34.3086i	0.609494	−	1.14681i
$896$	18.8247			0.628889
$897$			2.53572i			0.0846651i
$898$		−	74.8668i		−	2.49834i
$899$	−25.9663			−0.866025
$900$	−83.0134	−	122.973i	−2.76711	−	4.09911i
$901$	−35.8108			−1.19303
$902$			9.86645i			0.328517i
$903$		−	7.02244i		−	0.233692i
$904$	−75.1894			−2.50076
$905$	11.8895	−	22.3709i	0.395219	−	0.743634i
$906$	113.476			3.76999
$907$		−	19.0768i		−	0.633435i	−0.948520	−	0.316718i	$-0.897419\pi$
$907$		−	19.0768i		−	0.633435i	0.948520	−	0.316718i	$-0.102581\pi$
$908$			4.15528i			0.137898i
$909$	−53.9140			−1.78822
$910$	20.5812	+	10.9383i	0.682260	+	0.362600i
$911$	52.1806			1.72882			0.864409	−	0.502789i	$-0.167693\pi$
$911$	52.1806			1.72882			0.864409	+	0.502789i	$0.167693\pi$
$912$		−	7.90062i		−	0.261616i
$913$			4.61071i			0.152592i
$914$	85.7373			2.83594
$915$	3.94916	+	2.09886i	0.130555	+	0.0693862i
$916$	−54.6720			−1.80641
$917$		−	14.3874i		−	0.475113i
$918$		−	141.308i		−	4.66386i
$919$	−25.4335			−0.838974			−0.419487	−	0.907761i	$-0.637790\pi$
$919$	−25.4335			−0.838974			−0.419487	+	0.907761i	$0.637790\pi$
$920$	0.686527	−	1.29175i	0.0226341	−	0.0425878i
$921$	−80.4451			−2.65076
$922$			0.614399i			0.0202342i
$923$			41.2216i			1.35683i
$924$	11.1816			0.367848
$925$	33.1595	−	22.3844i	1.09028	−	0.735995i
$926$	−1.93251			−0.0635064
$927$			67.6050i			2.22044i
$928$			7.45163i			0.244612i
$929$	37.9395			1.24476			0.622378	−	0.782717i	$-0.286167\pi$
$929$	37.9395			1.24476			0.622378	+	0.782717i	$0.286167\pi$
$930$	−72.7985	+	136.976i	−2.38716	+	4.49161i
$931$	−6.17617			−0.202416
$932$			89.6718i			2.93730i
$933$			39.9966i			1.30943i
$934$	78.9637			2.58377
$935$	7.06690	+	3.75584i	0.231112	+	0.122829i
$936$	157.431			5.14579
$937$			49.3386i			1.61182i	0.592038	+	0.805910i	$0.298324\pi$
$937$			49.3386i			1.61182i	−0.592038	+	0.805910i	$0.701676\pi$
$938$			26.6595i			0.870463i
$939$	−71.7174			−2.34041
$940$	−45.1463	−	23.9939i	−1.47251	−	0.782593i
$941$	−7.71975			−0.251657			−0.125828	−	0.992052i	$-0.540159\pi$
$941$	−7.71975			−0.251657			−0.125828	+	0.992052i	$0.540159\pi$
$942$		−	70.9077i		−	2.31030i
$943$			0.657388i			0.0214075i
$944$	−18.6198			−0.606022
$945$	15.7277	−	29.5928i	0.511620	−	0.962652i
$946$	5.58232			0.181497
$947$			6.78507i			0.220485i	0.993905	+	0.110243i	$0.0351628\pi$
$947$			6.78507i			0.220485i	−0.993905	+	0.110243i	$0.964837\pi$
$948$			201.927i			6.55827i
$949$	40.5059			1.31488
$950$	9.90905	−	6.68913i	0.321492	−	0.217024i
$951$	−12.9253			−0.419133
$952$		−	13.3396i		−	0.432339i
$953$			6.14106i			0.198929i	0.995041	+	0.0994643i	$0.0317129\pi$
$953$			6.14106i			0.198929i	−0.995041	+	0.0994643i	$0.968287\pi$
$954$	−190.980			−6.18320
$955$	−12.5907	+	23.6904i	−0.407426	+	0.766602i
$956$	5.50017			0.177888
$957$			9.82947i			0.317742i
$958$			23.8605i			0.770899i
$959$	16.1624			0.521911
$960$	70.5083	+	37.4730i	2.27565	+	1.20944i
$961$	45.6413			1.47230
$962$			91.8887i			2.96261i
$963$			33.7159i			1.08648i
$964$	48.6702			1.56756
$965$	−45.7089	−	24.2929i	−1.47142	−	0.782016i
$966$	1.14585			0.0368670
$967$		−	15.3317i		−	0.493035i	−0.969138	−	0.246518i	$-0.920714\pi$
$967$		−	15.3317i		−	0.493035i	0.969138	−	0.246518i	$-0.0792863\pi$
$968$			4.10637i			0.131984i
$969$	11.8609			0.381027
$970$	4.77953	−	8.99305i	0.153462	−	0.288749i
$971$	−15.3042			−0.491136			−0.245568	−	0.969379i	$-0.578975\pi$
$971$	−15.3042			−0.491136			−0.245568	+	0.969379i	$0.578975\pi$
$972$		−	194.963i		−	6.25343i
$973$			10.0403i			0.321877i
$974$	42.6185			1.36558
$975$	44.5261	+	65.9594i	1.42598	+	2.11239i
$976$	1.43880			0.0460548
$977$			53.8363i			1.72238i	0.508286	+	0.861188i	$0.330279\pi$
$977$			53.8363i			1.72238i	−0.508286	+	0.861188i	$0.669721\pi$
$978$		−	106.988i		−	3.42111i
$979$	7.69047			0.245788
$980$	−24.0932	+	45.3332i	−0.769630	+	1.44812i
$981$	62.2533			1.98760
$982$			73.8384i			2.35628i
$983$			3.87925i			0.123729i	0.998085	+	0.0618644i	$0.0197046\pi$
$983$			3.87925i			0.123729i	−0.998085	+	0.0618644i	$0.980295\pi$
$984$	56.1530			1.79009
$985$	3.28046	+	1.74346i	0.104524	+	0.0555514i
$986$	25.3830			0.808358
$987$		−	18.5010i		−	0.588893i
$988$			17.8536i			0.567997i
$989$	0.371942			0.0118271
$990$	37.6879	+	20.0300i	1.19780	+	0.636595i
$991$	43.6663			1.38711			0.693553	−	0.720406i	$-0.256045\pi$
$991$	43.6663			1.38711			0.693553	+	0.720406i	$0.256045\pi$
$992$		−	21.9940i		−	0.698310i
$993$			6.18456i			0.196261i
$994$	18.6274			0.590824
$995$	−5.57458	+	10.4890i	−0.176726	+	0.332523i
$996$	56.8007			1.79980
$997$		−	47.7827i		−	1.51329i	−0.653824	−	0.756647i	$-0.726836\pi$
$997$		−	47.7827i		−	1.51329i	0.653824	−	0.756647i	$-0.273164\pi$
$998$			23.1457i			0.732664i
$999$	132.122			4.18017

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1045.2.b.e.419.5	✓	30
5.2	odd	4		5225.2.a.bc.1.26		30
5.3	odd	4		5225.2.a.bc.1.5		30
5.4	even	2	inner	1045.2.b.e.419.26	yes	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1045.2.b.e.419.5	✓	30	1.1	even	1	trivial
1045.2.b.e.419.26	yes	30	5.4	even	2	inner
5225.2.a.bc.1.5		30	5.3	odd	4
5225.2.a.bc.1.26		30	5.2	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-2.39110i q^{2} +3.31399i q^{3} -3.71736 q^{4} +(1.04940 - 1.97453i) q^{5} +7.92409 q^{6} +0.907652i q^{7} +4.10637i q^{8} -7.98255 q^{9} +O(q^{10})\)	\(q-2.39110i q^{2} +3.31399i q^{3} -3.71736 q^{4} +(1.04940 - 1.97453i) q^{5} +7.92409 q^{6} +0.907652i q^{7} +4.10637i q^{8} -7.98255 q^{9} +(-4.72129 - 2.50922i) q^{10} +1.00000 q^{11} -12.3193i q^{12} +4.80276i q^{13} +2.17028 q^{14} +(6.54357 + 3.47771i) q^{15} +2.38402 q^{16} +3.57904i q^{17} +19.0871i q^{18} -1.00000 q^{19} +(-3.90100 + 7.34002i) q^{20} -3.00795 q^{21} -2.39110i q^{22} -0.159316i q^{23} -13.6085 q^{24} +(-2.79751 - 4.14414i) q^{25} +11.4839 q^{26} -16.5121i q^{27} -3.37406i q^{28} +2.96605 q^{29} +(8.31554 - 15.6463i) q^{30} -8.75450 q^{31} +2.51231i q^{32} +3.31399i q^{33} +8.55783 q^{34} +(1.79218 + 0.952491i) q^{35} +29.6740 q^{36} +8.00154i q^{37} +2.39110i q^{38} -15.9163 q^{39} +(8.10813 + 4.30923i) q^{40} -4.12633 q^{41} +7.19231i q^{42} +2.33463i q^{43} -3.71736 q^{44} +(-8.37690 + 15.7618i) q^{45} -0.380939 q^{46} +6.15070i q^{47} +7.90062i q^{48} +6.17617 q^{49} +(-9.90905 + 6.68913i) q^{50} -11.8609 q^{51} -17.8536i q^{52} +10.0057i q^{53} -39.4821 q^{54} +(1.04940 - 1.97453i) q^{55} -3.72715 q^{56} -3.31399i q^{57} -7.09212i q^{58} -7.81024 q^{59} +(-24.3248 - 12.9279i) q^{60} +0.603518 q^{61} +20.9329i q^{62} -7.24537i q^{63} +10.7752 q^{64} +(9.48318 + 5.04002i) q^{65} +7.92409 q^{66} +12.2839i q^{67} -13.3045i q^{68} +0.527971 q^{69} +(2.27750 - 4.28529i) q^{70} +8.58291 q^{71} -32.7793i q^{72} -8.43389i q^{73} +19.1325 q^{74} +(13.7337 - 9.27094i) q^{75} +3.71736 q^{76} +0.907652i q^{77} +38.0575i q^{78} -16.3911 q^{79} +(2.50179 - 4.70731i) q^{80} +30.7734 q^{81} +9.86645i q^{82} +4.61071i q^{83} +11.1816 q^{84} +(7.06690 + 3.75584i) q^{85} +5.58232 q^{86} +9.82947i q^{87} +4.10637i q^{88} +7.69047 q^{89} +(37.6879 + 20.0300i) q^{90} -4.35923 q^{91} +0.592233i q^{92} -29.0124i q^{93} +14.7069 q^{94} +(-1.04940 + 1.97453i) q^{95} -8.32576 q^{96} +1.90479i q^{97} -14.7678i q^{98} -7.98255 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q - 42 q^{4} + 12 q^{6} - 40 q^{9}+O(q^{10}) \) 30 * q - 42 * q^4 + 12 * q^6 - 40 * q^9	\( 30 q - 42 q^{4} + 12 q^{6} - 40 q^{9} + 10 q^{10} + 30 q^{11} + 4 q^{14} + 4 q^{15} + 66 q^{16} - 30 q^{19} + 10 q^{20} + 14 q^{21} - 22 q^{24} - 6 q^{25} - 30 q^{29} + 14 q^{30} + 26 q^{31} - 12 q^{34} + 6 q^{35} + 78 q^{36} - 64 q^{39} - 20 q^{40} + 22 q^{41} - 42 q^{44} + 6 q^{45} + 28 q^{46} - 60 q^{49} + 64 q^{51} - 62 q^{54} - 32 q^{56} + 14 q^{59} - 28 q^{60} + 78 q^{61} - 90 q^{64} + 40 q^{65} + 12 q^{66} + 28 q^{69} + 12 q^{70} + 20 q^{71} - 42 q^{74} + 50 q^{75} + 42 q^{76} - 102 q^{79} - 40 q^{80} + 42 q^{81} - 98 q^{84} - 2 q^{85} - 52 q^{86} + 8 q^{89} + 22 q^{90} + 56 q^{91} - 40 q^{94} - 74 q^{96} - 40 q^{99}+O(q^{100}) \) 30 * q - 42 * q^4 + 12 * q^6 - 40 * q^9 + 10 * q^10 + 30 * q^11 + 4 * q^14 + 4 * q^15 + 66 * q^16 - 30 * q^19 + 10 * q^20 + 14 * q^21 - 22 * q^24 - 6 * q^25 - 30 * q^29 + 14 * q^30 + 26 * q^31 - 12 * q^34 + 6 * q^35 + 78 * q^36 - 64 * q^39 - 20 * q^40 + 22 * q^41 - 42 * q^44 + 6 * q^45 + 28 * q^46 - 60 * q^49 + 64 * q^51 - 62 * q^54 - 32 * q^56 + 14 * q^59 - 28 * q^60 + 78 * q^61 - 90 * q^64 + 40 * q^65 + 12 * q^66 + 28 * q^69 + 12 * q^70 + 20 * q^71 - 42 * q^74 + 50 * q^75 + 42 * q^76 - 102 * q^79 - 40 * q^80 + 42 * q^81 - 98 * q^84 - 2 * q^85 - 52 * q^86 + 8 * q^89 + 22 * q^90 + 56 * q^91 - 40 * q^94 - 74 * q^96 - 40 * q^99

Introduction

L-functions

Modular forms

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Database

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