LMFDB - Embedded newform 440.2.y.d.361.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [440,2,Mod(81,440)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(440, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 0, 2]))

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

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

chi := DirichletCharacter("440.81");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 440 = 2^{3} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	440.y (of order $5$, degree $4$, 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:	$3.51341768894$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 3 x^{15} + 14 x^{14} - 32 x^{13} + 141 x^{12} - 220 x^{11} + 1105 x^{10} - 1935 x^{9} + \cdots + 10000 $ x^16 - 3x^15 + 14x^14 - 32x^13 + 141x^12 - 220x^11 + 1105x^10 - 1935x^9 + 9865x^8 - 18475x^7 + 34075x^6 - 18400x^5 + 23025x^4 + 26000x^3 + 41000x^2 + 25000*x + 10000
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			361.1
Root			$2.59852 - 1.88794i$ of defining polynomial
Character	$\chi$	$=$	440.361
Dual form			440.2.y.d.401.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.59852 + 1.88794i) q^{3} +(0.309017 + 0.951057i) q^{5} +(3.97176 + 2.88565i) q^{7} +(2.26096 - 6.95852i) q^{9} +(2.80658 + 1.76723i) q^{11} +(-0.248666 + 0.765314i) q^{13} +(-2.59852 - 1.88794i) q^{15} +(0.570906 + 1.75707i) q^{17} +(-4.54455 + 3.30181i) q^{19} -15.7686 q^{21} -1.60313 q^{23} +(-0.809017 + 0.587785i) q^{25} +(4.28444 + 13.1862i) q^{27} +(-6.36280 - 4.62285i) q^{29} +(1.19581 - 3.68033i) q^{31} +(-10.6294 + 0.706466i) q^{33} +(-1.51708 + 4.66909i) q^{35} +(5.40233 + 3.92502i) q^{37} +(-0.798702 - 2.45815i) q^{39} +(4.23759 - 3.07879i) q^{41} +1.05407 q^{43} +7.31662 q^{45} +(-6.99946 + 5.08541i) q^{47} +(5.28477 + 16.2649i) q^{49} +(-4.80074 - 3.48794i) q^{51} +(2.41830 - 7.44275i) q^{53} +(-0.813453 + 3.21532i) q^{55} +(5.57551 - 17.1596i) q^{57} +(-3.14961 - 2.28832i) q^{59} +(2.04656 + 6.29868i) q^{61} +(29.0599 - 21.1132i) q^{63} -0.804699 q^{65} -5.52774 q^{67} +(4.16576 - 3.02660i) q^{69} +(-3.38974 - 10.4325i) q^{71} +(-2.26518 - 1.64575i) q^{73} +(0.992547 - 3.05475i) q^{75} +(6.04746 + 15.1178i) q^{77} +(-0.902277 + 2.77692i) q^{79} +(-18.2701 - 13.2740i) q^{81} +(0.598359 + 1.84156i) q^{83} +(-1.49465 + 1.08593i) q^{85} +25.2615 q^{87} +7.32421 q^{89} +(-3.19607 + 2.32208i) q^{91} +(3.84089 + 11.8210i) q^{93} +(-4.54455 - 3.30181i) q^{95} +(2.52077 - 7.75815i) q^{97} +(18.6429 - 15.5340i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 3 q^{3} - 4 q^{5} + 8 q^{7} - 7 q^{9} - 7 q^{11} - 11 q^{13} - 3 q^{15} + 9 q^{17} - 2 q^{19} + 12 q^{21} + 20 q^{23} - 4 q^{25} - 9 q^{27} + q^{29} - 2 q^{31} - 32 q^{33} - 2 q^{35} - 16 q^{37}+ \cdots - 10 q^{99}+O(q^{100}) $ 16 * q - 3 * q^3 - 4 * q^5 + 8 * q^7 - 7 * q^9 - 7 * q^11 - 11 * q^13 - 3 * q^15 + 9 * q^17 - 2 * q^19 + 12 * q^21 + 20 * q^23 - 4 * q^25 - 9 * q^27 + q^29 - 2 * q^31 - 32 * q^33 - 2 * q^35 - 16 * q^37 + 3 * q^39 - 11 * q^41 - 16 * q^43 + 38 * q^45 - 10 * q^47 + 4 * q^49 + 26 * q^51 - 9 * q^53 + 3 * q^55 - 50 * q^57 - 60 * q^59 + 30 * q^61 + 52 * q^63 + 24 * q^65 - 4 * q^67 + 41 * q^69 - 10 * q^71 + q^73 + 2 * q^75 - 4 * q^77 + 19 * q^79 - 31 * q^81 + 64 * q^83 - 11 * q^85 + 30 * q^87 + 24 * q^89 - 9 * q^91 + 45 * q^93 - 2 * q^95 - 3 * q^97 - 10 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/440\mathbb{Z}\right)^\times$.

$n$	$111$	$177$	$221$	$321$
$\chi(n)$	$1$	$1$	$1$	$e\left(\frac{3}{5}\right)$

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			0
$2$		0			0
$3$	−2.59852	+	1.88794i	−1.50026	+	1.09000i	−0.529978	+	0.848011i	$0.677800\pi$
$3$	−2.59852	+	1.88794i	−1.50026	+	1.09000i	−0.970279	+	0.241989i	$0.922200\pi$
$4$		0			0
$5$	0.309017	+	0.951057i	0.138197	+	0.425325i
$5$	0.309017	+	0.951057i	0.138197	+	0.425325i
$6$		0			0
$7$	3.97176	+	2.88565i	1.50118	+	1.09067i	0.969907	+	0.243477i	$0.0782880\pi$
$7$	3.97176	+	2.88565i	1.50118	+	1.09067i	0.531278	+	0.847198i	$0.321712\pi$
$8$		0			0
$9$	2.26096	−	6.95852i	0.753653	−	2.31951i
$10$		0			0
$11$	2.80658	+	1.76723i	0.846216	+	0.532840i
$11$	2.80658	+	1.76723i	0.846216	+	0.532840i
$12$		0			0
$13$	−0.248666	+	0.765314i	−0.0689675	+	0.212260i	−0.979600	−	0.200957i	$-0.935595\pi$
$13$	−0.248666	+	0.765314i	−0.0689675	+	0.212260i	0.910633	+	0.413217i	$0.135595\pi$
$14$		0			0
$15$	−2.59852	−	1.88794i	−0.670935	−	0.487463i
$16$		0			0
$17$	0.570906	+	1.75707i	0.138465	+	0.426151i	0.996113	−	0.0880860i	$-0.0280750\pi$
$17$	0.570906	+	1.75707i	0.138465	+	0.426151i	−0.857648	+	0.514237i	$0.828075\pi$
$18$		0			0
$19$	−4.54455	+	3.30181i	−1.04259	+	0.757487i	−0.970790	−	0.239932i	$-0.922875\pi$
$19$	−4.54455	+	3.30181i	−1.04259	+	0.757487i	−0.0718015	+	0.997419i	$0.522875\pi$
$20$		0			0
$21$	−15.7686			−3.44100
$22$		0			0
$23$	−1.60313			−0.334275			−0.167138	−	0.985934i	$-0.553452\pi$
$23$	−1.60313			−0.334275			−0.167138	+	0.985934i	$0.553452\pi$
$24$		0			0
$25$	−0.809017	+	0.587785i	−0.161803	+	0.117557i
$26$		0			0
$27$	4.28444	+	13.1862i	0.824542	+	2.53768i
$28$		0			0
$29$	−6.36280	−	4.62285i	−1.18154	−	0.858441i	−0.189198	−	0.981939i	$-0.560589\pi$
$29$	−6.36280	−	4.62285i	−1.18154	−	0.858441i	−0.992345	+	0.123498i	$0.960589\pi$
$30$		0			0
$31$	1.19581	−	3.68033i	0.214774	−	0.661007i	−0.784395	−	0.620261i	$-0.787027\pi$
$31$	1.19581	−	3.68033i	0.214774	−	0.661007i	0.999170	−	0.0407457i	$-0.0129734\pi$
$32$		0			0
$33$	−10.6294	+	0.706466i	−1.85034	+	0.122980i
$34$		0			0
$35$	−1.51708	+	4.66909i	−0.256433	+	0.789219i
$36$		0			0
$37$	5.40233	+	3.92502i	0.888137	+	0.645269i	0.935392	−	0.353614i	$-0.115047\pi$
$37$	5.40233	+	3.92502i	0.888137	+	0.645269i	−0.0472547	+	0.998883i	$0.515047\pi$
$38$		0			0
$39$	−0.798702	−	2.45815i	−0.127895	−	0.393619i
$40$		0			0
$41$	4.23759	−	3.07879i	0.661801	−	0.480826i	−0.205470	−	0.978663i	$-0.565872\pi$
$41$	4.23759	−	3.07879i	0.661801	−	0.480826i	0.867271	+	0.497837i	$0.165872\pi$
$42$		0			0
$43$	1.05407			0.160744			0.0803718	−	0.996765i	$-0.474389\pi$
$43$	1.05407			0.160744			0.0803718	+	0.996765i	$0.474389\pi$
$44$		0			0
$45$	7.31662			1.09070
$46$		0			0
$47$	−6.99946	+	5.08541i	−1.02098	+	0.741783i	−0.966483	−	0.256731i	$-0.917355\pi$
$47$	−6.99946	+	5.08541i	−1.02098	+	0.741783i	−0.0544940	+	0.998514i	$0.517355\pi$
$48$		0			0
$49$	5.28477	+	16.2649i	0.754967	+	2.32355i
$50$		0			0
$51$	−4.80074	−	3.48794i	−0.672238	−	0.488410i
$52$		0			0
$53$	2.41830	−	7.44275i	0.332179	−	1.02234i	−0.635916	−	0.771758i	$-0.719378\pi$
$53$	2.41830	−	7.44275i	0.332179	−	1.02234i	0.968095	−	0.250583i	$-0.0806223\pi$
$54$		0			0
$55$	−0.813453	+	3.21532i	−0.109686	+	0.433554i
$56$		0			0
$57$	5.57551	−	17.1596i	0.738494	−	2.27285i
$58$		0			0
$59$	−3.14961	−	2.28832i	−0.410044	−	0.297914i	0.363576	−	0.931565i	$-0.381556\pi$
$59$	−3.14961	−	2.28832i	−0.410044	−	0.297914i	−0.773620	+	0.633650i	$0.781556\pi$
$60$		0			0
$61$	2.04656	+	6.29868i	0.262036	+	0.806463i	0.992362	+	0.123364i	$0.0393682\pi$
$61$	2.04656	+	6.29868i	0.262036	+	0.806463i	−0.730326	+	0.683099i	$0.760632\pi$
$62$		0			0
$63$	29.0599	−	21.1132i	3.66120	−	2.66002i
$64$		0			0
$65$	−0.804699			−0.0998107
$66$		0			0
$67$	−5.52774			−0.675321			−0.337661	−	0.941268i	$-0.609636\pi$
$67$	−5.52774			−0.675321			−0.337661	+	0.941268i	$0.609636\pi$
$68$		0			0
$69$	4.16576	−	3.02660i	0.501499	−	0.364360i
$70$		0			0
$71$	−3.38974	−	10.4325i	−0.402288	−	1.23811i	−0.923139	−	0.384467i	$-0.874385\pi$
$71$	−3.38974	−	10.4325i	−0.402288	−	1.23811i	0.520851	−	0.853648i	$-0.325615\pi$
$72$		0			0
$73$	−2.26518	−	1.64575i	−0.265119	−	0.192620i	0.447282	−	0.894393i	$-0.352392\pi$
$73$	−2.26518	−	1.64575i	−0.265119	−	0.192620i	−0.712401	+	0.701773i	$0.752392\pi$
$74$		0			0
$75$	0.992547	−	3.05475i	0.114609	−	0.352732i
$76$		0			0
$77$	6.04746	+	15.1178i	0.689172	+	1.72284i
$78$		0			0
$79$	−0.902277	+	2.77692i	−0.101514	+	0.312428i	−0.988896	−	0.148606i	$-0.952521\pi$
$79$	−0.902277	+	2.77692i	−0.101514	+	0.312428i	0.887382	+	0.461034i	$0.152521\pi$
$80$		0			0
$81$	−18.2701	−	13.2740i	−2.03001	−	1.47489i
$82$		0			0
$83$	0.598359	+	1.84156i	0.0656784	+	0.202137i	0.978510	−	0.206198i	$-0.0661092\pi$
$83$	0.598359	+	1.84156i	0.0656784	+	0.202137i	−0.912832	+	0.408336i	$0.866109\pi$
$84$		0			0
$85$	−1.49465	+	1.08593i	−0.162118	+	0.117785i
$86$		0			0
$87$	25.2615			2.70832
$88$		0			0
$89$	7.32421			0.776365			0.388183	−	0.921583i	$-0.373103\pi$
$89$	7.32421			0.776365			0.388183	+	0.921583i	$0.373103\pi$
$90$		0			0
$91$	−3.19607	+	2.32208i	−0.335039	+	0.243420i
$92$		0			0
$93$	3.84089	+	11.8210i	0.398281	+	1.22578i
$94$		0			0
$95$	−4.54455	−	3.30181i	−0.466261	−	0.338758i
$96$		0			0
$97$	2.52077	−	7.75815i	0.255946	−	0.787721i	−0.737696	−	0.675133i	$-0.764086\pi$
$97$	2.52077	−	7.75815i	0.255946	−	0.787721i	0.993642	−	0.112587i	$-0.0359138\pi$
$98$		0			0
$99$	18.6429	−	15.5340i	1.87368	−	1.56123i
$100$		0			0
$101$	−1.97177	+	6.06848i	−0.196198	+	0.603837i	0.803762	+	0.594951i	$0.202829\pi$
$101$	−1.97177	+	6.06848i	−0.196198	+	0.603837i	−0.999961	+	0.00888592i	$0.997171\pi$
$102$		0			0
$103$	12.1688	+	8.84114i	1.19903	+	0.871143i	0.994189	−	0.107653i	$-0.0343336\pi$
$103$	12.1688	+	8.84114i	1.19903	+	0.871143i	0.204837	+	0.978796i	$0.434334\pi$
$104$		0			0
$105$	−4.87278	−	14.9969i	−0.475534	−	1.46354i
$106$		0			0
$107$	4.54470	−	3.30192i	0.439353	−	0.319208i	−0.346025	−	0.938225i	$-0.612469\pi$
$107$	4.54470	−	3.30192i	0.439353	−	0.319208i	0.785378	+	0.619017i	$0.212469\pi$
$108$		0			0
$109$	14.2032			1.36042			0.680208	−	0.733019i	$-0.261890\pi$
$109$	14.2032			1.36042			0.680208	+	0.733019i	$0.261890\pi$
$110$		0			0
$111$	−21.4482			−2.03578
$112$		0			0
$113$	−4.86698	+	3.53607i	−0.457847	+	0.332645i	−0.792686	−	0.609630i	$-0.791318\pi$
$113$	−4.86698	+	3.53607i	−0.457847	+	0.332645i	0.334839	+	0.942275i	$0.391318\pi$
$114$		0			0
$115$	−0.495394	−	1.52466i	−0.0461957	−	0.142176i
$116$		0			0
$117$	4.76323	+	3.46069i	0.440361	+	0.319941i
$118$		0			0
$119$	−2.80279	+	8.62609i	−0.256931	+	0.790752i
$120$		0			0
$121$	4.75381	+	9.91974i	0.432164	+	0.901795i
$122$		0			0
$123$	−5.19891	+	16.0006i	−0.468770	+	1.44273i
$124$		0			0
$125$	−0.809017	−	0.587785i	−0.0723607	−	0.0525731i
$126$		0			0
$127$	−0.389484	−	1.19871i	−0.0345611	−	0.106368i	0.932288	−	0.361718i	$-0.117810\pi$
$127$	−0.389484	−	1.19871i	−0.0345611	−	0.106368i	−0.966849	+	0.255349i	$0.917810\pi$
$128$		0			0
$129$	−2.73901	+	1.99001i	−0.241157	+	0.175211i
$130$		0			0
$131$	12.0760			1.05509			0.527543	−	0.849528i	$-0.323113\pi$
$131$	12.0760			1.05509			0.527543	+	0.849528i	$0.323113\pi$
$132$		0			0
$133$	−27.5777			−2.39129
$134$		0			0
$135$	−11.2168	+	8.14950i	−0.965390	+	0.701397i
$136$		0			0
$137$	−2.79354	−	8.59762i	−0.238668	−	0.734544i	−0.996614	−	0.0822266i	$-0.973797\pi$
$137$	−2.79354	−	8.59762i	−0.238668	−	0.734544i	0.757946	−	0.652318i	$-0.226203\pi$
$138$		0			0
$139$	−17.5517	−	12.7520i	−1.48871	−	1.08161i	−0.974616	−	0.223883i	$-0.928127\pi$
$139$	−17.5517	−	12.7520i	−1.48871	−	1.08161i	−0.514098	−	0.857731i	$-0.671873\pi$
$140$		0			0
$141$	8.58733	−	26.4291i	0.723184	−	2.22573i
$142$		0			0
$143$	−2.05039	+	1.70847i	−0.171462	+	0.142869i
$144$		0			0
$145$	2.43037	−	7.47992i	0.201832	−	0.621174i
$146$		0			0
$147$	−44.4396	−	32.2873i	−3.66532	−	2.66301i
$148$		0			0
$149$	−2.04612	−	6.29731i	−0.167625	−	0.515896i	0.831595	−	0.555382i	$-0.187428\pi$
$149$	−2.04612	−	6.29731i	−0.167625	−	0.515896i	−0.999220	+	0.0394859i	$0.987428\pi$
$150$		0			0
$151$	−0.910122	+	0.661242i	−0.0740646	+	0.0538111i	−0.624201	−	0.781263i	$-0.714576\pi$
$151$	−0.910122	+	0.661242i	−0.0740646	+	0.0538111i	0.550137	+	0.835075i	$0.314576\pi$
$152$		0			0
$153$	13.5174			1.09282
$154$		0			0
$155$	3.86973			0.310824
$156$		0			0
$157$	4.72544	−	3.43323i	0.377131	−	0.274002i	−0.383031	−	0.923736i	$-0.625120\pi$
$157$	4.72544	−	3.43323i	0.377131	−	0.274002i	0.760162	+	0.649734i	$0.225120\pi$
$158$		0			0
$159$	7.76745	+	23.9057i	0.615999	+	1.89585i
$160$		0			0
$161$	−6.36724	−	4.62607i	−0.501809	−	0.364585i
$162$		0			0
$163$	−4.51488	+	13.8954i	−0.353633	+	1.08837i	0.603165	+	0.797616i	$0.293906\pi$
$163$	−4.51488	+	13.8954i	−0.353633	+	1.08837i	−0.956798	+	0.290753i	$0.906094\pi$
$164$		0			0
$165$	−3.95655	−	9.89083i	−0.308017	−	0.770000i
$166$		0			0
$167$	−2.08197	+	6.40765i	−0.161108	+	0.495839i	−0.998728	−	0.0504137i	$-0.983946\pi$
$167$	−2.08197	+	6.40765i	−0.161108	+	0.495839i	0.837621	+	0.546252i	$0.183946\pi$
$168$		0			0
$169$	9.99335	+	7.26059i	0.768719	+	0.558507i
$170$		0			0
$171$	12.7006	+	39.0886i	0.971243	+	2.98918i
$172$		0			0
$173$	−2.01046	+	1.46068i	−0.152852	+	0.111054i	−0.661583	−	0.749872i	$-0.730115\pi$
$173$	−2.01046	+	1.46068i	−0.152852	+	0.111054i	0.508731	+	0.860926i	$0.330115\pi$
$174$		0			0
$175$	−4.90937			−0.371113
$176$		0			0
$177$	12.5045			0.939898
$178$		0			0
$179$	20.9334	−	15.2090i	1.56464	−	1.13677i	0.632561	−	0.774510i	$-0.282004\pi$
$179$	20.9334	−	15.2090i	1.56464	−	1.13677i	0.932075	−	0.362265i	$-0.117996\pi$
$180$		0			0
$181$	4.41663	+	13.5930i	0.328286	+	1.01036i	0.969936	+	0.243362i	$0.0782502\pi$
$181$	4.41663	+	13.5930i	0.328286	+	1.01036i	−0.641650	+	0.766998i	$0.721750\pi$
$182$		0			0
$183$	−17.2095	−	12.5035i	−1.27217	−	0.924282i
$184$		0			0
$185$	−2.06350	+	6.35081i	−0.151712	+	0.466921i
$186$		0			0
$187$	−1.50285	+	5.94028i	−0.109899	+	0.434396i
$188$		0			0
$189$	−21.0339	+	64.7357i	−1.52999	+	4.70883i
$190$		0			0
$191$	−3.17581	−	2.30736i	−0.229793	−	0.166955i	0.466931	−	0.884294i	$-0.345360\pi$
$191$	−3.17581	−	2.30736i	−0.229793	−	0.166955i	−0.696724	+	0.717339i	$0.745360\pi$
$192$		0			0
$193$	3.26985	+	10.0636i	0.235369	+	0.724391i	0.997072	+	0.0764648i	$0.0243633\pi$
$193$	3.26985	+	10.0636i	0.235369	+	0.724391i	−0.761704	+	0.647926i	$0.775637\pi$
$194$		0			0
$195$	2.09103	−	1.51922i	0.149742	−	0.108794i
$196$		0			0
$197$	−1.89648			−0.135119			−0.0675594	−	0.997715i	$-0.521521\pi$
$197$	−1.89648			−0.135119			−0.0675594	+	0.997715i	$0.521521\pi$
$198$		0			0
$199$	13.9966			0.992189			0.496095	−	0.868268i	$-0.334767\pi$
$199$	13.9966			0.992189			0.496095	+	0.868268i	$0.334767\pi$
$200$		0			0
$201$	14.3640	−	10.4360i	1.01316	−	0.736100i
$202$		0			0
$203$	−11.9316	−	36.7217i	−0.837434	−	2.57736i
$204$		0			0
$205$	4.23759	+	3.07879i	0.295966	+	0.215032i
$206$		0			0
$207$	−3.62461	+	11.1554i	−0.251927	+	0.775353i
$208$		0			0
$209$	−18.5897	+	1.23554i	−1.28588	+	0.0854640i
$210$		0			0
$211$	8.40526	−	25.8687i	0.578642	−	1.78088i	−0.0447870	−	0.998997i	$-0.514261\pi$
$211$	8.40526	−	25.8687i	0.578642	−	1.78088i	0.623429	−	0.781880i	$-0.285739\pi$
$212$		0			0
$213$	28.5043	+	20.7096i	1.95308	+	1.41900i
$214$		0			0
$215$	0.325724	+	1.00248i	0.0222142	+	0.0683683i
$216$		0			0
$217$	15.3696	−	11.1667i	1.04336	−	0.758045i
$218$		0			0
$219$	8.99318			0.607703
$220$		0			0
$221$	−1.48667			−0.100005
$222$		0			0
$223$	−9.86282	+	7.16576i	−0.660464	+	0.479855i	−0.866819	−	0.498622i	$-0.833840\pi$
$223$	−9.86282	+	7.16576i	−0.660464	+	0.479855i	0.206356	+	0.978477i	$0.433840\pi$
$224$		0			0
$225$	2.26096	+	6.95852i	0.150731	+	0.463901i
$226$		0			0
$227$	14.0410	+	10.2014i	0.931932	+	0.677088i	0.946465	−	0.322806i	$-0.104626\pi$
$227$	14.0410	+	10.2014i	0.931932	+	0.677088i	−0.0145329	+	0.999894i	$0.504626\pi$
$228$		0			0
$229$	0.209111	−	0.643578i	0.0138185	−	0.0425288i	−0.943910	−	0.330204i	$-0.892882\pi$
$229$	0.209111	−	0.643578i	0.0138185	−	0.0425288i	0.957728	+	0.287675i	$0.0928824\pi$
$230$		0			0
$231$	−44.2560	−	27.8668i	−2.91183	−	1.83350i
$232$		0			0
$233$	0.737829	−	2.27080i	0.0483368	−	0.148765i	−0.923975	−	0.382453i	$-0.875079\pi$
$233$	0.737829	−	2.27080i	0.0483368	−	0.148765i	0.972312	+	0.233688i	$0.0750794\pi$
$234$		0			0
$235$	−6.99946	−	5.08541i	−0.456595	−	0.331735i
$236$		0			0
$237$	−2.89807	−	8.91933i	−0.188250	−	0.579373i
$238$		0			0
$239$	6.62535	−	4.81360i	0.428559	−	0.311366i	−0.352514	−	0.935807i	$-0.614673\pi$
$239$	6.62535	−	4.81360i	0.428559	−	0.311366i	0.781072	+	0.624441i	$0.214673\pi$
$240$		0			0
$241$	9.43609			0.607832			0.303916	−	0.952699i	$-0.401706\pi$
$241$	9.43609			0.607832			0.303916	+	0.952699i	$0.401706\pi$
$242$		0			0
$243$	30.9413			1.98488
$244$		0			0
$245$	−13.8357	+	10.0522i	−0.883931	+	0.642214i
$246$		0			0
$247$	−1.39685	−	4.29906i	−0.0888793	−	0.273542i
$248$		0			0
$249$	−5.03160	−	3.65567i	−0.318864	−	0.231669i
$250$		0			0
$251$	5.72227	−	17.6113i	0.361187	−	1.11162i	−0.591148	−	0.806563i	$-0.701325\pi$
$251$	5.72227	−	17.6113i	0.361187	−	1.11162i	0.952335	−	0.305055i	$-0.0986748\pi$
$252$		0			0
$253$	−4.49931	−	2.83309i	−0.282869	−	0.178115i
$254$		0			0
$255$	1.83372	−	5.64361i	0.114832	−	0.353417i
$256$		0			0
$257$	−21.8546	−	15.8783i	−1.36325	−	0.990460i	−0.998231	−	0.0594610i	$-0.981062\pi$
$257$	−21.8546	−	15.8783i	−1.36325	−	0.990460i	−0.365021	−	0.930999i	$-0.618938\pi$
$258$		0			0
$259$	10.1305	+	31.1785i	0.629479	+	1.93734i
$260$		0			0
$261$	−46.5542	+	33.8236i	−2.88163	+	2.09363i
$262$		0			0
$263$	−17.4169			−1.07397			−0.536985	−	0.843592i	$-0.680437\pi$
$263$	−17.4169			−1.07397			−0.536985	+	0.843592i	$0.680437\pi$
$264$		0			0
$265$	7.82577			0.480734
$266$		0			0
$267$	−19.0321	+	13.8276i	−1.16475	+	0.846238i
$268$		0			0
$269$	−3.21949	−	9.90857i	−0.196296	−	0.604136i	−0.999959	−	0.00905173i	$-0.997119\pi$
$269$	−3.21949	−	9.90857i	−0.196296	−	0.604136i	0.803663	−	0.595084i	$-0.202881\pi$
$270$		0			0
$271$	24.5128	+	17.8096i	1.48905	+	1.08186i	0.974498	+	0.224396i	$0.0720410\pi$
$271$	24.5128	+	17.8096i	1.48905	+	1.08186i	0.514550	+	0.857460i	$0.327959\pi$
$272$		0			0
$273$	3.92112	−	12.0680i	0.237317	−	0.730386i
$274$		0			0
$275$	−3.30932	+	0.219949i	−0.199560	+	0.0132635i
$276$		0			0
$277$	−0.969832	+	2.98484i	−0.0582716	+	0.179342i	−0.975956	−	0.217970i	$-0.930057\pi$
$277$	−0.969832	+	2.98484i	−0.0582716	+	0.179342i	0.917684	+	0.397311i	$0.130057\pi$
$278$		0			0
$279$	−22.9060	−	16.6421i	−1.37134	−	0.996339i
$280$		0			0
$281$	3.59394	+	11.0610i	0.214396	+	0.659844i	0.999196	+	0.0400944i	$0.0127659\pi$
$281$	3.59394	+	11.0610i	0.214396	+	0.659844i	−0.784800	+	0.619750i	$0.787234\pi$
$282$		0			0
$283$	1.73762	−	1.26246i	0.103291	−	0.0750454i	−0.534941	−	0.844890i	$-0.679666\pi$
$283$	1.73762	−	1.26246i	0.103291	−	0.0750454i	0.638232	+	0.769844i	$0.279666\pi$
$284$		0			0
$285$	18.0427			1.06876
$286$		0			0
$287$	25.7150			1.51791
$288$		0			0
$289$	10.9919	−	7.98611i	0.646584	−	0.469771i
$290$		0			0
$291$	8.09660	+	24.9188i	0.474631	+	1.46076i
$292$		0			0
$293$	21.1476	+	15.3646i	1.23546	+	0.897611i	0.997287	−	0.0736129i	$-0.0234529\pi$
$293$	21.1476	+	15.3646i	1.23546	+	0.897611i	0.238169	+	0.971224i	$0.423453\pi$
$294$		0			0
$295$	1.20304	−	3.70258i	0.0700438	−	0.215573i
$296$		0			0
$297$	−11.2783	+	44.5796i	−0.654435	+	2.58677i
$298$		0			0
$299$	0.398643	−	1.22690i	0.0230541	−	0.0709533i
$300$		0			0
$301$	4.18650	+	3.04167i	0.241306	+	0.175319i
$302$		0			0
$303$	−6.33323	−	19.4917i	−0.363834	−	1.11977i
$304$		0			0
$305$	−5.35797	+	3.89280i	−0.306797	+	0.222901i
$306$		0			0
$307$	−5.59232			−0.319171			−0.159585	−	0.987184i	$-0.551016\pi$
$307$	−5.59232			−0.319171			−0.159585	+	0.987184i	$0.551016\pi$
$308$		0			0
$309$	−48.3123			−2.74839
$310$		0			0
$311$	−1.38707	+	1.00777i	−0.0786536	+	0.0571452i	−0.626417	−	0.779488i	$-0.715479\pi$
$311$	−1.38707	+	1.00777i	−0.0786536	+	0.0571452i	0.547764	+	0.836633i	$0.315479\pi$
$312$		0			0
$313$	−1.63672	−	5.03732i	−0.0925131	−	0.284726i	0.894084	−	0.447898i	$-0.147827\pi$
$313$	−1.63672	−	5.03732i	−0.0925131	−	0.284726i	−0.986598	+	0.163172i	$0.947827\pi$
$314$		0			0
$315$	29.0599	+	21.1132i	1.63734	+	1.18960i
$316$		0			0
$317$	2.39112	−	7.35910i	0.134298	−	0.413328i	−0.861182	−	0.508297i	$-0.830275\pi$
$317$	2.39112	−	7.35910i	0.134298	−	0.413328i	0.995480	+	0.0949690i	$0.0302752\pi$
$318$		0			0
$319$	−9.68810	−	24.2189i	−0.542430	−	1.35600i
$320$		0			0
$321$	−5.57569	+	17.1602i	−0.311204	+	0.957789i
$322$		0			0
$323$	−8.39601	−	6.10006i	−0.467167	−	0.339416i
$324$		0			0
$325$	−0.248666	−	0.765314i	−0.0137935	−	0.0424520i
$326$		0			0
$327$	−36.9072	+	26.8147i	−2.04097	+	1.48285i
$328$		0			0
$329$	−42.4749			−2.34172
$330$		0			0
$331$	−18.7346			−1.02975			−0.514874	−	0.857266i	$-0.672161\pi$
$331$	−18.7346			−1.02975			−0.514874	+	0.857266i	$0.672161\pi$
$332$		0			0
$333$	39.5267	−	28.7179i	2.16605	−	1.57373i
$334$		0			0
$335$	−1.70817	−	5.25719i	−0.0933271	−	0.287231i
$336$		0			0
$337$	8.74014	+	6.35008i	0.476106	+	0.345911i	0.799816	−	0.600245i	$-0.204930\pi$
$337$	8.74014	+	6.35008i	0.476106	+	0.345911i	−0.323710	+	0.946156i	$0.604930\pi$
$338$		0			0
$339$	5.97108	−	18.3771i	0.324305	−	0.998107i
$340$		0			0
$341$	9.86013	−	8.21588i	0.533956	−	0.444915i
$342$		0			0
$343$	−15.3253	+	47.1665i	−0.827490	+	2.54675i
$344$		0			0
$345$	4.16576	+	3.02660i	0.224277	+	0.162947i
$346$		0			0
$347$	−4.77524	−	14.6967i	−0.256348	−	0.788959i	−0.993561	−	0.113298i	$-0.963859\pi$
$347$	−4.77524	−	14.6967i	−0.256348	−	0.788959i	0.737213	−	0.675661i	$-0.236141\pi$
$348$		0			0
$349$	23.0541	−	16.7498i	1.23406	−	0.896595i	0.236870	−	0.971541i	$-0.423878\pi$
$349$	23.0541	−	16.7498i	1.23406	−	0.896595i	0.997188	+	0.0749459i	$0.0238784\pi$
$350$		0			0
$351$	−11.1570			−0.595514
$352$		0			0
$353$	−16.7619			−0.892148			−0.446074	−	0.894996i	$-0.647178\pi$
$353$	−16.7619			−0.892148			−0.446074	+	0.894996i	$0.647178\pi$
$354$		0			0
$355$	8.87445	−	6.44766i	0.471007	−	0.342206i
$356$		0			0
$357$	−9.00241	−	27.7066i	−0.476458	−	1.46639i
$358$		0			0
$359$	12.1482	+	8.82619i	0.641158	+	0.465828i	0.860248	−	0.509876i	$-0.170309\pi$
$359$	12.1482	+	8.82619i	0.641158	+	0.465828i	−0.219090	+	0.975705i	$0.570309\pi$
$360$		0			0
$361$	3.87967	−	11.9404i	0.204193	−	0.628442i
$362$		0			0
$363$	−31.0807	−	16.8018i	−1.63131	−	0.881865i
$364$		0			0
$365$	0.865221	−	2.66288i	0.0452877	−	0.139381i
$366$		0			0
$367$	16.5287	+	12.0088i	0.862793	+	0.626856i	0.928643	−	0.370974i	$-0.120976\pi$
$367$	16.5287	+	12.0088i	0.862793	+	0.626856i	−0.0658502	+	0.997830i	$0.520976\pi$
$368$		0			0
$369$	−11.8428	−	36.4484i	−0.616511	−	1.89743i
$370$		0			0
$371$	31.0821	−	22.5825i	1.61370	−	1.17242i
$372$		0			0
$373$	16.8624			0.873101			0.436550	−	0.899680i	$-0.356200\pi$
$373$	16.8624			0.873101			0.436550	+	0.899680i	$0.356200\pi$
$374$		0			0
$375$	3.21195			0.165864
$376$		0			0
$377$	5.12014	−	3.72000i	0.263701	−	0.191590i
$378$		0			0
$379$	−7.51646	−	23.1333i	−0.386095	−	1.18828i	−0.935683	−	0.352842i	$-0.885215\pi$
$379$	−7.51646	−	23.1333i	−0.386095	−	1.18828i	0.549588	−	0.835436i	$-0.314785\pi$
$380$		0			0
$381$	3.27517	+	2.37955i	0.167792	+	0.121908i
$382$		0			0
$383$	3.89293	−	11.9812i	0.198919	−	0.612211i	−0.800989	−	0.598679i	$-0.795693\pi$
$383$	3.89293	−	11.9812i	0.198919	−	0.612211i	0.999908	−	0.0135318i	$-0.00430743\pi$
$384$		0			0
$385$	−12.5091	+	10.4231i	−0.637525	+	0.531213i
$386$		0			0
$387$	2.38320	−	7.33474i	0.121145	−	0.372846i
$388$		0			0
$389$	16.7848	+	12.1949i	0.851023	+	0.618304i	0.925428	−	0.378924i	$-0.123706\pi$
$389$	16.7848	+	12.1949i	0.851023	+	0.618304i	−0.0744052	+	0.997228i	$0.523706\pi$
$390$		0			0
$391$	−0.915235	−	2.81680i	−0.0462854	−	0.142452i
$392$		0			0
$393$	−31.3798	+	22.7988i	−1.58290	+	1.15005i
$394$		0			0
$395$	−2.91983			−0.146913
$396$		0			0
$397$	−3.76055			−0.188737			−0.0943683	−	0.995537i	$-0.530083\pi$
$397$	−3.76055			−0.188737			−0.0943683	+	0.995537i	$0.530083\pi$
$398$		0			0
$399$	71.6613	−	52.0650i	3.58755	−	2.60651i
$400$		0			0
$401$	−5.20744	−	16.0268i	−0.260047	−	0.800342i	−0.992793	−	0.119840i	$-0.961762\pi$
$401$	−5.20744	−	16.0268i	−0.260047	−	0.800342i	0.732746	−	0.680502i	$-0.238238\pi$
$402$		0			0
$403$	2.51925	+	1.83034i	0.125493	+	0.0911759i
$404$		0			0
$405$	6.97854	−	21.4777i	0.346766	−	1.06724i
$406$		0			0
$407$	8.22566	+	20.5630i	0.407731	+	1.01927i
$408$		0			0
$409$	6.70934	−	20.6492i	0.331756	−	1.02104i	−0.636543	−	0.771242i	$-0.719636\pi$
$409$	6.70934	−	20.6492i	0.331756	−	1.02104i	0.968298	−	0.249797i	$-0.0803639\pi$
$410$		0			0
$411$	23.4908	+	17.0671i	1.15872	+	0.841857i
$412$		0			0
$413$	−5.90618	−	18.1773i	−0.290624	−	0.894449i
$414$		0			0
$415$	−1.56652	+	1.13815i	−0.0768977	+	0.0558694i
$416$		0			0
$417$	69.6835			3.41241
$418$		0			0
$419$	−39.1675			−1.91346			−0.956729	−	0.290981i	$-0.906018\pi$
$419$	−39.1675			−1.91346			−0.956729	+	0.290981i	$0.906018\pi$
$420$		0			0
$421$	6.82952	−	4.96194i	0.332850	−	0.241830i	−0.408789	−	0.912629i	$-0.634049\pi$
$421$	6.82952	−	4.96194i	0.332850	−	0.241830i	0.741639	+	0.670799i	$0.234049\pi$
$422$		0			0
$423$	19.5614	+	60.2038i	0.951108	+	2.92721i
$424$		0			0
$425$	−1.49465	−	1.08593i	−0.0725012	−	0.0526752i
$426$		0			0
$427$	−10.0473	+	30.9225i	−0.486224	+	1.49644i
$428$		0			0
$429$	2.10249	−	8.31049i	0.101509	−	0.401234i
$430$		0			0
$431$	0.523478	−	1.61110i	0.0252151	−	0.0776040i	−0.937657	−	0.347562i	$-0.887010\pi$
$431$	0.523478	−	1.61110i	0.0252151	−	0.0776040i	0.962872	+	0.269958i	$0.0870097\pi$
$432$		0			0
$433$	−32.2752	−	23.4493i	−1.55105	−	1.12690i	−0.942898	−	0.333081i	$-0.891912\pi$
$433$	−32.2752	−	23.4493i	−1.55105	−	1.12690i	−0.608150	−	0.793822i	$-0.708088\pi$
$434$		0			0
$435$	7.80624	+	24.0251i	0.374281	+	1.15192i
$436$		0			0
$437$	7.28549	−	5.29322i	0.348512	−	0.253209i
$438$		0			0
$439$	−0.598520			−0.0285658			−0.0142829	−	0.999898i	$-0.504547\pi$
$439$	−0.598520			−0.0285658			−0.0142829	+	0.999898i	$0.504547\pi$
$440$		0			0
$441$	125.128			5.95847
$442$		0			0
$443$	29.5783	−	21.4899i	1.40531	−	1.02102i	0.411325	−	0.911489i	$-0.365066\pi$
$443$	29.5783	−	21.4899i	1.40531	−	1.02102i	0.993984	−	0.109528i	$-0.0349340\pi$
$444$		0			0
$445$	2.26331	+	6.96574i	0.107291	+	0.330208i
$446$		0			0
$447$	17.2058	+	12.5008i	0.813807	+	0.591266i
$448$		0			0
$449$	−11.1274	+	34.2468i	−0.525137	+	1.61620i	0.238909	+	0.971042i	$0.423210\pi$
$449$	−11.1274	+	34.2468i	−0.525137	+	1.61620i	−0.764045	+	0.645162i	$0.776790\pi$
$450$		0			0
$451$	17.3341	−	1.15208i	0.816230	−	0.0542496i
$452$		0			0
$453$	1.11659	−	3.43650i	0.0524619	−	0.161461i
$454$		0			0
$455$	−3.19607	−	2.32208i	−0.149834	−	0.108861i
$456$		0			0
$457$	−3.34802	−	10.3041i	−0.156614	−	0.482007i	0.841707	−	0.539934i	$-0.181551\pi$
$457$	−3.34802	−	10.3041i	−0.156614	−	0.482007i	−0.998321	+	0.0579270i	$0.981551\pi$
$458$		0			0
$459$	−20.7230	+	15.0561i	−0.967265	+	0.702759i
$460$		0			0
$461$	5.70020			0.265485			0.132742	−	0.991151i	$-0.457622\pi$
$461$	5.70020			0.265485			0.132742	+	0.991151i	$0.457622\pi$
$462$		0			0
$463$	−6.28911			−0.292280			−0.146140	−	0.989264i	$-0.546685\pi$
$463$	−6.28911			−0.292280			−0.146140	+	0.989264i	$0.546685\pi$
$464$		0			0
$465$	−10.0556	+	7.30580i	−0.466316	+	0.338798i
$466$		0			0
$467$	0.242605	+	0.746662i	0.0112264	+	0.0345514i	0.956513	−	0.291690i	$-0.0942177\pi$
$467$	0.242605	+	0.746662i	0.0112264	+	0.0345514i	−0.945286	+	0.326242i	$0.894218\pi$
$468$		0			0
$469$	−21.9549	−	15.9511i	−1.01378	−	0.736555i
$470$		0			0
$471$	−5.79743	+	17.8427i	−0.267132	+	0.822147i
$472$		0			0
$473$	2.95832	+	1.86278i	0.136024	+	0.0856505i
$474$		0			0
$475$	1.73586	−	5.34244i	0.0796469	−	0.245128i
$476$		0			0
$477$	−46.3228	−	33.6555i	−2.12098	−	1.54098i
$478$		0			0
$479$	11.9144	+	36.6687i	0.544382	+	1.67544i	0.722455	+	0.691418i	$0.243014\pi$
$479$	11.9144	+	36.6687i	0.544382	+	1.67544i	−0.178073	+	0.984017i	$0.556986\pi$
$480$		0			0
$481$	−4.34725	+	3.15846i	−0.198217	+	0.144013i
$482$		0			0
$483$	25.2791			1.15024
$484$		0			0
$485$	8.15740			0.370408
$486$		0			0
$487$	−12.9394	+	9.40105i	−0.586342	+	0.426002i	−0.841005	−	0.541027i	$-0.818035\pi$
$487$	−12.9394	+	9.40105i	−0.586342	+	0.426002i	0.254663	+	0.967030i	$0.418035\pi$
$488$		0			0
$489$	−14.5016	−	44.6312i	−0.655783	−	2.01829i
$490$		0			0
$491$	20.4310	+	14.8440i	0.922037	+	0.669899i	0.944030	−	0.329859i	$-0.107001\pi$
$491$	20.4310	+	14.8440i	0.922037	+	0.669899i	−0.0219933	+	0.999758i	$0.507001\pi$
$492$		0			0
$493$	4.49009	−	13.8191i	0.202224	−	0.622380i
$494$		0			0
$495$	20.5347	+	12.9301i	0.922965	+	0.581166i
$496$		0			0
$497$	16.6415	−	51.2171i	0.746472	−	2.29740i
$498$		0			0
$499$	4.01699	+	2.91851i	0.179825	+	0.130651i	0.674056	−	0.738680i	$-0.264550\pi$
$499$	4.01699	+	2.91851i	0.179825	+	0.130651i	−0.494231	+	0.869330i	$0.664550\pi$
$500$		0			0
$501$	−6.68718	−	20.5810i	−0.298761	−	0.919493i
$502$		0			0
$503$	16.3333	−	11.8668i	0.728265	−	0.529116i	−0.160749	−	0.986995i	$-0.551391\pi$
$503$	16.3333	−	11.8668i	0.728265	−	0.529116i	0.889014	+	0.457880i	$0.151391\pi$
$504$		0			0
$505$	−6.38078			−0.283941
$506$		0			0
$507$	−39.6755			−1.76205
$508$		0			0
$509$	−29.3380	+	21.3153i	−1.30038	+	0.944785i	−0.999959	−	0.00902031i	$-0.997129\pi$
$509$	−29.3380	+	21.3153i	−1.30038	+	0.944785i	−0.300426	+	0.953805i	$0.597129\pi$
$510$		0			0
$511$	−4.24769	−	13.0730i	−0.187907	−	0.578317i
$512$		0			0
$513$	−63.0091	−	45.7788i	−2.78192	−	2.02118i
$514$		0			0
$515$	−4.64806	+	14.3053i	−0.204818	+	0.630365i
$516$		0			0
$517$	−28.6317	+	1.90296i	−1.25922	+	0.0836922i
$518$		0			0
$519$	2.46654	−	7.59122i	0.108269	−	0.333218i
$520$		0			0
$521$	8.96230	+	6.51149i	0.392646	+	0.285274i	0.766539	−	0.642198i	$-0.221977\pi$
$521$	8.96230	+	6.51149i	0.392646	+	0.285274i	−0.373893	+	0.927472i	$0.621977\pi$
$522$		0			0
$523$	−7.27440	−	22.3883i	−0.318087	−	0.978972i	−0.974465	−	0.224540i	$-0.927912\pi$
$523$	−7.27440	−	22.3883i	−0.318087	−	0.978972i	0.656377	−	0.754433i	$-0.272088\pi$
$524$		0			0
$525$	12.7571	−	9.26857i	0.556765	−	0.404514i
$526$		0			0
$527$	7.14928			0.311428
$528$		0			0
$529$	−20.4300			−0.888260
$530$		0			0
$531$	−23.0445	+	16.7428i	−1.00004	+	0.726575i
$532$		0			0
$533$	1.30250	+	4.00868i	0.0564175	+	0.173635i
$534$		0			0
$535$	4.54470	+	3.30192i	0.196484	+	0.142754i
$536$		0			0
$537$	−25.6823	+	79.0419i	−1.10827	+	3.41091i
$538$		0			0
$539$	−13.9116	+	54.9880i	−0.599214	+	2.36850i
$540$		0			0
$541$	−7.91146	+	24.3490i	−0.340140	+	1.04684i	0.623994	+	0.781429i	$0.285509\pi$
$541$	−7.91146	+	24.3490i	−0.340140	+	1.04684i	−0.964134	+	0.265415i	$0.914491\pi$
$542$		0			0
$543$	−37.1394	−	26.9834i	−1.59381	−	1.15797i
$544$		0			0
$545$	4.38902	+	13.5080i	0.188005	+	0.578619i
$546$		0			0
$547$	22.4469	−	16.3086i	0.959760	−	0.697306i	0.00666505	−	0.999978i	$-0.497878\pi$
$547$	22.4469	−	16.3086i	0.959760	−	0.697306i	0.953095	+	0.302671i	$0.0978784\pi$
$548$		0			0
$549$	48.4566			2.06808
$550$		0			0
$551$	44.1798			1.88212
$552$		0			0
$553$	−11.5969	+	8.42561i	−0.493149	+	0.358294i
$554$		0			0
$555$	−6.62787	−	20.3985i	−0.281337	−	0.865868i
$556$		0			0
$557$	−6.31807	−	4.59035i	−0.267705	−	0.194499i	0.445832	−	0.895117i	$-0.352908\pi$
$557$	−6.31807	−	4.59035i	−0.267705	−	0.194499i	−0.713537	+	0.700617i	$0.752908\pi$
$558$		0			0
$559$	−0.262110	+	0.806692i	−0.0110861	+	0.0341194i
$560$		0			0
$561$	−7.30968	−	18.2732i	−0.308615	−	0.771496i
$562$		0			0
$563$	−9.39334	+	28.9097i	−0.395882	+	1.21840i	0.532391	+	0.846499i	$0.321294\pi$
$563$	−9.39334	+	28.9097i	−0.395882	+	1.21840i	−0.928273	+	0.371901i	$0.878706\pi$
$564$		0			0
$565$	−4.86698	−	3.53607i	−0.204755	−	0.148763i
$566$		0			0
$567$	−34.2602	−	105.442i	−1.43879	−	4.42815i
$568$		0			0
$569$	1.60201	−	1.16393i	0.0671598	−	0.0487945i	−0.553699	−	0.832717i	$-0.686784\pi$
$569$	1.60201	−	1.16393i	0.0671598	−	0.0487945i	0.620859	+	0.783923i	$0.286784\pi$
$570$		0			0
$571$	−33.2773			−1.39261			−0.696307	−	0.717744i	$-0.745175\pi$
$571$	−33.2773			−1.39261			−0.696307	+	0.717744i	$0.745175\pi$
$572$		0			0
$573$	12.6085			0.526729
$574$		0			0
$575$	1.29696	−	0.942295i	0.0540869	−	0.0392964i
$576$		0			0
$577$	11.1165	+	34.2129i	0.462784	+	1.42430i	0.861748	+	0.507336i	$0.169370\pi$
$577$	11.1165	+	34.2129i	0.462784	+	1.42430i	−0.398964	+	0.916966i	$0.630630\pi$
$578$		0			0
$579$	−27.4961	−	19.9771i	−1.14270	−	0.830220i
$580$		0			0
$581$	−2.93756	+	9.04089i	−0.121871	+	0.375079i
$582$		0			0
$583$	19.9402	−	16.6150i	0.825839	−	0.688124i
$584$		0			0
$585$	−1.81939	+	5.59951i	−0.0752226	+	0.231511i
$586$		0			0
$587$	−17.3745	−	12.6233i	−0.717121	−	0.521019i	0.168342	−	0.985729i	$-0.446159\pi$
$587$	−17.3745	−	12.6233i	−0.717121	−	0.521019i	−0.885463	+	0.464709i	$0.846159\pi$
$588$		0			0
$589$	6.71732	+	20.6738i	0.276782	+	0.851848i
$590$		0			0
$591$	4.92805	−	3.58044i	0.202713	−	0.147280i
$592$		0			0
$593$	14.2405			0.584787			0.292393	−	0.956298i	$-0.405548\pi$
$593$	14.2405			0.584787			0.292393	+	0.956298i	$0.405548\pi$
$594$		0			0
$595$	−9.07001			−0.371834
$596$		0			0
$597$	−36.3703	+	26.4246i	−1.48854	+	1.08149i
$598$		0			0
$599$	13.2330	+	40.7271i	0.540687	+	1.66406i	0.731029	+	0.682347i	$0.239041\pi$
$599$	13.2330	+	40.7271i	0.540687	+	1.66406i	−0.190341	+	0.981718i	$0.560959\pi$
$600$		0			0
$601$	−12.8041	−	9.30269i	−0.522288	−	0.379465i	0.295177	−	0.955443i	$-0.404621\pi$
$601$	−12.8041	−	9.30269i	−0.522288	−	0.379465i	−0.817465	+	0.575978i	$0.804621\pi$
$602$		0			0
$603$	−12.4980	+	38.4649i	−0.508958	+	1.56641i
$604$		0			0
$605$	−7.96523	+	7.58651i	−0.323833	+	0.308435i
$606$		0			0
$607$	11.2073	−	34.4924i	0.454889	−	1.40000i	−0.416377	−	0.909192i	$-0.636700\pi$
$607$	11.2073	−	34.4924i	0.454889	−	1.40000i	0.871266	−	0.490812i	$-0.163300\pi$
$608$		0			0
$609$	100.333	+	72.8960i	4.06569	+	2.95389i
$610$		0			0
$611$	−2.15141	−	6.62136i	−0.0870367	−	0.267871i
$612$		0			0
$613$	−31.5049	+	22.8896i	−1.27247	+	0.924504i	−0.999298	−	0.0374608i	$-0.988073\pi$
$613$	−31.5049	+	22.8896i	−1.27247	+	0.924504i	−0.273173	+	0.961965i	$0.588073\pi$
$614$		0			0
$615$	−16.8240			−0.678411
$616$		0			0
$617$	−30.2869			−1.21931			−0.609653	−	0.792669i	$-0.708691\pi$
$617$	−30.2869			−1.21931			−0.609653	+	0.792669i	$0.708691\pi$
$618$		0			0
$619$	−16.2239	+	11.7873i	−0.652093	+	0.473773i	−0.863984	−	0.503520i	$-0.832038\pi$
$619$	−16.2239	+	11.7873i	−0.652093	+	0.473773i	0.211890	+	0.977293i	$0.432038\pi$
$620$		0			0
$621$	−6.86851	−	21.1391i	−0.275624	−	0.848283i
$622$		0			0
$623$	29.0900	+	21.1351i	1.16547	+	0.846761i
$624$		0			0
$625$	0.309017	−	0.951057i	0.0123607	−	0.0380423i
$626$		0			0
$627$	45.9731	−	38.3067i	1.83599	−	1.52982i
$628$		0			0
$629$	−3.81230	+	11.7331i	−0.152007	+	0.467828i
$630$		0			0
$631$	9.83771	+	7.14751i	0.391633	+	0.284538i	0.766124	−	0.642692i	$-0.222183\pi$
$631$	9.83771	+	7.14751i	0.391633	+	0.284538i	−0.374491	+	0.927230i	$0.622183\pi$
$632$		0			0
$633$	26.9973	+	83.0890i	1.07304	+	3.30249i
$634$		0			0
$635$	1.01968	−	0.740843i	0.0404649	−	0.0293995i
$636$		0			0
$637$	−13.7619			−0.545265
$638$		0			0
$639$	−80.2590			−3.17500
$640$		0			0
$641$	−13.9056	+	10.1030i	−0.549239	+	0.399046i	−0.827505	−	0.561458i	$-0.810240\pi$
$641$	−13.9056	+	10.1030i	−0.549239	+	0.399046i	0.278266	+	0.960504i	$0.410240\pi$
$642$		0			0
$643$	−3.49329	−	10.7513i	−0.137762	−	0.423988i	0.858247	−	0.513236i	$-0.171554\pi$
$643$	−3.49329	−	10.7513i	−0.137762	−	0.423988i	−0.996009	+	0.0892482i	$0.971554\pi$
$644$		0			0
$645$	−2.73901	−	1.99001i	−0.107849	−	0.0783566i
$646$		0			0
$647$	6.54599	−	20.1465i	0.257350	−	0.792041i	−0.736008	−	0.676973i	$-0.763291\pi$
$647$	6.54599	−	20.1465i	0.257350	−	0.792041i	0.993358	−	0.115068i	$-0.0367085\pi$
$648$		0			0
$649$	−4.79564	−	11.9884i	−0.188245	−	0.470587i
$650$		0			0
$651$	−18.8563	+	58.0338i	−0.739037	+	2.27452i
$652$		0			0
$653$	−10.0991	−	7.33746i	−0.395210	−	0.287137i	0.372377	−	0.928082i	$-0.378543\pi$
$653$	−10.0991	−	7.33746i	−0.395210	−	0.287137i	−0.767587	+	0.640945i	$0.778543\pi$
$654$		0			0
$655$	3.73170	+	11.4850i	0.145809	+	0.448755i
$656$		0			0
$657$	−16.5734	+	12.0413i	−0.646591	+	0.469776i
$658$		0			0
$659$	−10.2784			−0.400391			−0.200195	−	0.979756i	$-0.564158\pi$
$659$	−10.2784			−0.400391			−0.200195	+	0.979756i	$0.564158\pi$
$660$		0			0
$661$	−39.9264			−1.55296			−0.776478	−	0.630145i	$-0.782996\pi$
$661$	−39.9264			−1.55296			−0.776478	+	0.630145i	$0.782996\pi$
$662$		0			0
$663$	3.86315	−	2.80675i	0.150032	−	0.109005i
$664$		0			0
$665$	−8.52199	−	26.2280i	−0.330469	−	1.01708i
$666$		0			0
$667$	10.2004	+	7.41101i	0.394961	+	0.286956i
$668$		0			0
$669$	12.1003	−	37.2408i	0.467823	−	1.43981i
$670$		0			0
$671$	−5.38735	+	21.2945i	−0.207976	+	0.822065i
$672$		0			0
$673$	6.46751	−	19.9049i	0.249304	−	0.767279i	−0.745595	−	0.666400i	$-0.767834\pi$
$673$	6.46751	−	19.9049i	0.249304	−	0.767279i	0.994899	−	0.100879i	$-0.0321656\pi$
$674$		0			0
$675$	−11.2168	−	8.14950i	−0.431736	−	0.313674i
$676$		0			0
$677$	5.83665	+	17.9634i	0.224321	+	0.690388i	0.998360	+	0.0572503i	$0.0182333\pi$
$677$	5.83665	+	17.9634i	0.224321	+	0.690388i	−0.774039	+	0.633138i	$0.781767\pi$
$678$		0			0
$679$	32.3992	−	23.5394i	1.24337	−	0.903360i
$680$		0			0
$681$	−55.7453			−2.13616
$682$		0			0
$683$	11.5145			0.440590			0.220295	−	0.975433i	$-0.429298\pi$
$683$	11.5145			0.440590			0.220295	+	0.975433i	$0.429298\pi$
$684$		0			0
$685$	7.31357	−	5.31362i	0.279437	−	0.203023i
$686$		0			0
$687$	0.671654	+	2.06714i	0.0256252	+	0.0788663i
$688$		0			0
$689$	5.09470	+	3.70152i	0.194093	+	0.141017i
$690$		0			0
$691$	7.03598	−	21.6545i	0.267661	−	0.823777i	−0.723407	−	0.690422i	$-0.757425\pi$
$691$	7.03598	−	21.6545i	0.267661	−	0.823777i	0.991068	−	0.133355i	$-0.0425750\pi$
$692$		0			0
$693$	118.871	−	7.90057i	4.51553	−	0.300118i
$694$		0			0
$695$	6.70415	−	20.6332i	0.254303	−	0.782664i
$696$		0			0
$697$	7.82891	+	5.68804i	0.296541	+	0.215450i
$698$		0			0
$699$	2.36987	+	7.29370i	0.0896366	+	0.275873i
$700$		0			0
$701$	5.36640	−	3.89892i	0.202686	−	0.147260i	−0.481812	−	0.876274i	$-0.660021\pi$
$701$	5.36640	−	3.89892i	0.202686	−	0.147260i	0.684498	+	0.729014i	$0.260021\pi$
$702$		0			0
$703$	−37.5108			−1.41475
$704$		0			0
$705$	27.7892			1.04660
$706$		0			0
$707$	−25.3429	+	18.4127i	−0.953119	+	0.692482i
$708$		0			0
$709$	−11.5294	−	35.4840i	−0.432997	−	1.33263i	−0.895125	−	0.445815i	$-0.852914\pi$
$709$	−11.5294	−	35.4840i	−0.432997	−	1.33263i	0.462128	−	0.886813i	$-0.347086\pi$
$710$		0			0
$711$	17.2832	+	12.5570i	0.648172	+	0.470925i
$712$		0			0
$713$	−1.91704	+	5.90004i	−0.0717937	+	0.220958i
$714$		0			0
$715$	−2.25845	−	1.42209i	−0.0844614	−	0.0531831i
$716$		0			0
$717$	−8.12835	+	25.0165i	−0.303559	+	0.934258i
$718$		0			0
$719$	−19.9288	−	14.4791i	−0.743219	−	0.539981i	0.150498	−	0.988610i	$-0.451912\pi$
$719$	−19.9288	−	14.4791i	−0.743219	−	0.539981i	−0.893718	+	0.448630i	$0.851912\pi$
$720$		0			0
$721$	22.8190	+	70.2298i	0.849825	+	2.61549i
$722$		0			0
$723$	−24.5199	+	17.8147i	−0.911904	+	0.662537i
$724$		0			0
$725$	7.86486			0.292094
$726$		0			0
$727$	−31.1865			−1.15664			−0.578321	−	0.815809i	$-0.696292\pi$
$727$	−31.1865			−1.15664			−0.578321	+	0.815809i	$0.696292\pi$
$728$		0			0
$729$	−25.5914	+	18.5932i	−0.947830	+	0.688639i
$730$		0			0
$731$	0.601773	+	1.85207i	0.0222574	+	0.0685011i
$732$		0			0
$733$	9.94743	+	7.22723i	0.367417	+	0.266944i	0.756139	−	0.654411i	$-0.227083\pi$
$733$	9.94743	+	7.22723i	0.367417	+	0.266944i	−0.388722	+	0.921355i	$0.627083\pi$
$734$		0			0
$735$	16.9744	−	52.2419i	0.626111	−	1.92697i
$736$		0			0
$737$	−15.5141	−	9.76878i	−0.571468	−	0.359838i
$738$		0			0
$739$	0.461240	−	1.41955i	0.0169670	−	0.0522190i	−0.942215	−	0.335010i	$-0.891260\pi$
$739$	0.461240	−	1.41955i	0.0169670	−	0.0522190i	0.959182	+	0.282791i	$0.0912603\pi$
$740$		0			0
$741$	11.7461	+	8.53403i	0.431503	+	0.313505i
$742$		0			0
$743$	3.07996	+	9.47913i	0.112993	+	0.347755i	0.991523	−	0.129931i	$-0.0414755\pi$
$743$	3.07996	+	9.47913i	0.112993	+	0.347755i	−0.878530	+	0.477686i	$0.841476\pi$
$744$		0			0
$745$	5.35682	−	3.89195i	0.196259	−	0.142590i
$746$		0			0
$747$	14.1674			0.518358
$748$		0			0
$749$	27.5786			1.00770
$750$		0			0
$751$	−9.05170	+	6.57644i	−0.330301	+	0.239978i	−0.740558	−	0.671992i	$-0.765439\pi$
$751$	−9.05170	+	6.57644i	−0.330301	+	0.239978i	0.410257	+	0.911970i	$0.365439\pi$
$752$		0			0
$753$	18.3796	+	56.5667i	0.669791	+	2.06141i
$754$		0			0
$755$	−0.910122	−	0.661242i	−0.0331227	−	0.0240651i
$756$		0			0
$757$	13.5297	−	41.6402i	0.491746	−	1.51344i	−0.330222	−	0.943903i	$-0.607124\pi$
$757$	13.5297	−	41.6402i	0.491746	−	1.51344i	0.821968	−	0.569534i	$-0.192876\pi$
$758$		0			0
$759$	17.0403	−	1.13256i	0.618522	−	0.0411092i
$760$		0			0
$761$	−0.436179	+	1.34242i	−0.0158115	+	0.0486628i	−0.958651	−	0.284584i	$-0.908144\pi$
$761$	−0.436179	+	1.34242i	−0.0158115	+	0.0486628i	0.942839	+	0.333247i	$0.108144\pi$
$762$		0			0
$763$	56.4115	+	40.9854i	2.04224	+	1.48377i
$764$		0			0
$765$	4.17710	+	12.8558i	0.151023	+	0.464802i
$766$		0			0
$767$	2.53449	−	1.84141i	0.0915150	−	0.0664895i
$768$		0			0
$769$	42.9335			1.54822			0.774111	−	0.633049i	$-0.218197\pi$
$769$	42.9335			1.54822			0.774111	+	0.633049i	$0.218197\pi$
$770$		0			0
$771$	86.7668			3.12483
$772$		0			0
$773$	−5.74193	+	4.17176i	−0.206523	+	0.150048i	−0.686239	−	0.727376i	$-0.740740\pi$
$773$	−5.74193	+	4.17176i	−0.206523	+	0.150048i	0.479716	+	0.877424i	$0.340740\pi$
$774$		0			0
$775$	1.19581	+	3.68033i	0.0429548	+	0.132201i
$776$		0			0
$777$	−85.1873	−	61.8922i	−3.05608	−	2.22037i
$778$		0			0
$779$	−9.09237	+	27.9834i	−0.325768	+	1.00261i
$780$		0			0
$781$	8.92310	−	35.2702i	0.319294	−	1.26207i
$782$		0			0
$783$	33.6965	−	103.707i	1.20422	−	3.70620i
$784$		0			0
$785$	4.72544	+	3.43323i	0.168658	+	0.122537i
$786$		0			0
$787$	−13.3680	−	41.1425i	−0.476518	−	1.46657i	−0.843899	−	0.536502i	$-0.819745\pi$
$787$	−13.3680	−	41.1425i	−0.476518	−	1.46657i	0.367380	−	0.930071i	$-0.380255\pi$
$788$		0			0
$789$	45.2581	−	32.8820i	1.61123	−	1.17063i
$790$		0			0
$791$	−29.5343			−1.05012
$792$		0			0
$793$	−5.32938			−0.189252
$794$		0			0
$795$	−20.3354	+	14.7746i	−0.721224	+	0.524000i
$796$		0			0
$797$	−10.9136	−	33.5887i	−0.386580	−	1.18977i	−0.935327	−	0.353783i	$-0.884895\pi$
$797$	−10.9136	−	33.5887i	−0.386580	−	1.18977i	0.548747	−	0.835988i	$-0.315105\pi$
$798$		0			0
$799$	−12.9314	−	9.39524i	−0.457482	−	0.332380i
$800$		0			0
$801$	16.5597	−	50.9657i	0.585110	−	1.80078i
$802$		0			0
$803$	−3.44899	−	8.62201i	−0.121712	−	0.304264i
$804$		0			0
$805$	2.43207	−	7.48514i	0.0857192	−	0.263816i
$806$		0			0
$807$	27.0726	+	19.6694i	0.953002	+	0.692397i
$808$		0			0
$809$	1.26081	+	3.88037i	0.0443277	+	0.136427i	0.970771	−	0.240008i	$-0.0771500\pi$
$809$	1.26081	+	3.88037i	0.0443277	+	0.136427i	−0.926443	+	0.376434i	$0.877150\pi$
$810$		0			0
$811$	29.2832	−	21.2755i	1.02827	−	0.747084i	0.0603105	−	0.998180i	$-0.480791\pi$
$811$	29.2832	−	21.2755i	1.02827	−	0.747084i	0.967962	+	0.251096i	$0.0807909\pi$
$812$		0			0
$813$	−97.3205			−3.41318
$814$		0			0
$815$	−14.6105			−0.511782
$816$		0			0
$817$	−4.79026	+	3.48032i	−0.167590	+	0.121761i
$818$		0			0
$819$	8.93206	+	27.4901i	0.312111	+	0.960580i
$820$		0			0
$821$	13.0058	+	9.44930i	0.453907	+	0.329783i	0.791136	−	0.611640i	$-0.209490\pi$
$821$	13.0058	+	9.44930i	0.453907	+	0.329783i	−0.337229	+	0.941423i	$0.609490\pi$
$822$		0			0
$823$	−9.28714	+	28.5829i	−0.323729	+	0.996336i	0.648282	+	0.761401i	$0.275488\pi$
$823$	−9.28714	+	28.5829i	−0.323729	+	0.996336i	−0.972011	+	0.234936i	$0.924512\pi$
$824$		0			0
$825$	8.18410	−	6.81934i	0.284934	−	0.237419i
$826$		0			0
$827$	−0.194302	+	0.597999i	−0.00675653	+	0.0207945i	−0.954378	−	0.298601i	$-0.903480\pi$
$827$	−0.194302	+	0.597999i	−0.00675653	+	0.0207945i	0.947621	+	0.319396i	$0.103480\pi$
$828$		0			0
$829$	−3.98624	−	2.89618i	−0.138448	−	0.100588i	0.516406	−	0.856344i	$-0.327270\pi$
$829$	−3.98624	−	2.89618i	−0.138448	−	0.100588i	−0.654854	+	0.755756i	$0.727270\pi$
$830$		0			0
$831$	−3.11505	−	9.58715i	−0.108060	−	0.332574i
$832$		0			0
$833$	−25.5613	+	18.5714i	−0.885648	+	0.643461i
$834$		0			0
$835$	−6.73740			−0.233157
$836$		0			0
$837$	53.6528			1.85451
$838$		0			0
$839$	−4.93041	+	3.58215i	−0.170217	+	0.123670i	−0.669632	−	0.742693i	$-0.733548\pi$
$839$	−4.93041	+	3.58215i	−0.170217	+	0.123670i	0.499415	+	0.866363i	$0.333548\pi$
$840$		0			0
$841$	10.1531	+	31.2479i	0.350106	+	1.07751i
$842$		0			0
$843$	−30.2214	−	21.9571i	−1.04088	−	0.756244i
$844$		0			0
$845$	−3.81712	+	11.7479i	−0.131313	+	0.404140i
$846$		0			0
$847$	−9.74396	+	53.1167i	−0.334807	+	1.82511i
$848$		0			0
$849$	−2.13181	+	6.56105i	−0.0731637	+	0.225175i
$850$		0			0
$851$	−8.66062	−	6.29231i	−0.296882	−	0.215697i
$852$		0			0
$853$	5.01793	+	15.4436i	0.171811	+	0.528778i	0.999473	−	0.0324471i	$-0.0103301\pi$
$853$	5.01793	+	15.4436i	0.171811	+	0.528778i	−0.827663	+	0.561225i	$0.810330\pi$
$854$		0			0
$855$	−33.2507	+	24.1581i	−1.13715	+	0.826188i
$856$		0			0
$857$	42.8315			1.46310			0.731548	−	0.681790i	$-0.238798\pi$
$857$	42.8315			1.46310			0.731548	+	0.681790i	$0.238798\pi$
$858$		0			0
$859$	25.2561			0.861725			0.430863	−	0.902417i	$-0.358209\pi$
$859$	25.2561			0.861725			0.430863	+	0.902417i	$0.358209\pi$
$860$		0			0
$861$	−66.8211	+	48.5483i	−2.27726	+	1.65452i
$862$		0			0
$863$	6.85295	+	21.0912i	0.233277	+	0.717954i	0.997345	+	0.0728179i	$0.0231992\pi$
$863$	6.85295	+	21.0912i	0.233277	+	0.717954i	−0.764068	+	0.645136i	$0.776801\pi$
$864$		0			0
$865$	−2.01046	−	1.46068i	−0.0683575	−	0.0496647i
$866$		0			0
$867$	−13.4855	+	41.5041i	−0.457992	+	1.40955i
$868$		0			0
$869$	−7.43977	+	6.19913i	−0.252377	+	0.210291i
$870$		0			0
$871$	1.37456	−	4.23046i	0.0465752	−	0.143344i
$872$		0			0
$873$	−48.2858	−	35.0817i	−1.63423	−	1.18734i
$874$		0			0
$875$	−1.51708	−	4.66909i	−0.0512866	−	0.157844i
$876$		0			0
$877$	−15.6589	+	11.3769i	−0.528764	+	0.384170i	−0.819895	−	0.572513i	$-0.805968\pi$
$877$	−15.6589	+	11.3769i	−0.528764	+	0.384170i	0.291131	+	0.956683i	$0.405968\pi$
$878$		0			0
$879$	−83.9599			−2.83190
$880$		0			0
$881$	−34.6226			−1.16646			−0.583232	−	0.812306i	$-0.698212\pi$
$881$	−34.6226			−1.16646			−0.583232	+	0.812306i	$0.698212\pi$
$882$		0			0
$883$	2.98200	−	2.16655i	0.100352	−	0.0729102i	−0.536478	−	0.843915i	$-0.680245\pi$
$883$	2.98200	−	2.16655i	0.100352	−	0.0729102i	0.636830	+	0.771004i	$0.280245\pi$
$884$		0			0
$885$	3.86411	+	11.8925i	0.129891	+	0.399762i
$886$		0			0
$887$	−7.33074	−	5.32609i	−0.246142	−	0.178833i	0.457873	−	0.889018i	$-0.348611\pi$
$887$	−7.33074	−	5.32609i	−0.246142	−	0.178833i	−0.704015	+	0.710185i	$0.748611\pi$
$888$		0			0
$889$	1.91212	−	5.88490i	0.0641305	−	0.197373i
$890$		0			0
$891$	−27.8183	−	69.5418i	−0.931947	−	2.32974i
$892$		0			0
$893$	15.0184	−	46.2218i	0.502571	−	1.54675i
$894$		0			0
$895$	20.9334	+	15.2090i	0.699727	+	0.508381i
$896$		0			0
$897$	1.28042	+	3.94073i	0.0427520	+	0.131577i
$898$		0			0
$899$	−24.6223	+	17.8892i	−0.821200	+	0.596637i
$900$		0			0
$901$	14.4580			0.481667
$902$		0			0
$903$	−16.6212			−0.553118
$904$		0			0
$905$	−11.5629	+	8.40093i	−0.384364	+	0.279256i
$906$		0			0
$907$	10.0323	+	30.8764i	0.333119	+	1.02523i	0.967641	+	0.252329i	$0.0811967\pi$
$907$	10.0323	+	30.8764i	0.333119	+	1.02523i	−0.634523	+	0.772904i	$0.718803\pi$
$908$		0			0
$909$	37.7696	+	27.4412i	1.25274	+	0.910167i
$910$		0			0
$911$	15.8507	−	48.7836i	0.525158	−	1.61627i	−0.238844	−	0.971058i	$-0.576768\pi$
$911$	15.8507	−	48.7836i	0.525158	−	1.61627i	0.764002	−	0.645214i	$-0.223232\pi$
$912$		0			0
$913$	−1.57511	+	6.22593i	−0.0521287	+	0.206048i
$914$		0			0
$915$	6.57346	−	20.2310i	0.217312	−	0.668817i
$916$		0			0
$917$	47.9631	+	34.8472i	1.58388	+	1.15076i
$918$		0			0
$919$	3.80213	+	11.7018i	0.125421	+	0.386006i	0.993978	−	0.109584i	$-0.0349519\pi$
$919$	3.80213	+	11.7018i	0.125421	+	0.386006i	−0.868557	+	0.495590i	$0.834952\pi$
$920$		0			0
$921$	14.5318	−	10.5580i	0.478838	−	0.347896i
$922$		0			0
$923$	8.82708			0.290547
$924$		0			0
$925$	−6.67764			−0.219559
$926$		0			0
$927$	89.0343	−	64.6872i	2.92427	−	2.12461i
$928$		0			0
$929$	5.68141	+	17.4856i	0.186401	+	0.573683i	0.999970	−	0.00778542i	$-0.00247820\pi$
$929$	5.68141	+	17.4856i	0.186401	+	0.573683i	−0.813569	+	0.581469i	$0.802478\pi$
$930$		0			0
$931$	−77.7203	−	56.4671i	−2.54718	−	1.85064i
$932$		0			0
$933$	1.70173	−	5.23740i	0.0557123	−	0.171465i
$934$		0			0
$935$	−6.11394	+	0.406354i	−0.199947	+	0.0132892i
$936$		0			0
$937$	3.96318	−	12.1974i	0.129472	−	0.398472i	−0.865218	−	0.501396i	$-0.832820\pi$
$937$	3.96318	−	12.1974i	0.129472	−	0.398472i	0.994689	+	0.102924i	$0.0328198\pi$
$938$		0			0
$939$	13.7632	+	9.99955i	0.449145	+	0.326323i
$940$		0			0
$941$	−2.66548	−	8.20351i	−0.0868922	−	0.267427i	0.898164	−	0.439661i	$-0.144901\pi$
$941$	−2.66548	−	8.20351i	−0.0868922	−	0.267427i	−0.985056	+	0.172234i	$0.944901\pi$
$942$		0			0
$943$	−6.79340	+	4.93570i	−0.221224	+	0.160728i
$944$		0			0
$945$	−68.0671			−2.21422
$946$		0			0
$947$	22.1259			0.718996			0.359498	−	0.933146i	$-0.382948\pi$
$947$	22.1259			0.718996			0.359498	+	0.933146i	$0.382948\pi$
$948$		0			0
$949$	1.82279	−	1.32433i	0.0591702	−	0.0429896i
$950$		0			0
$951$	7.68014	+	23.6370i	0.249046	+	0.766484i
$952$		0			0
$953$	24.6623	+	17.9182i	0.798889	+	0.580427i	0.910588	−	0.413315i	$-0.135629\pi$
$953$	24.6623	+	17.9182i	0.798889	+	0.580427i	−0.111699	+	0.993742i	$0.535629\pi$
$954$		0			0
$955$	1.21305	−	3.73338i	0.0392534	−	0.120809i
$956$		0			0
$957$	70.8985	+	44.6429i	2.29182	+	1.44310i
$958$		0			0
$959$	13.7145	−	42.2089i	0.442864	−	1.36300i
$960$		0			0
$961$	12.9647	+	9.41938i	0.418215	+	0.303851i
$962$		0			0
$963$	−12.7011	−	39.0898i	−0.409286	−	1.25965i
$964$		0			0
$965$	−8.56057	+	6.21962i	−0.275575	+	0.200217i
$966$		0			0
$967$	−45.7942			−1.47264			−0.736321	−	0.676632i	$-0.763439\pi$
$967$	−45.7942			−1.47264			−0.736321	+	0.676632i	$0.763439\pi$
$968$		0			0
$969$	33.3337			1.07083
$970$		0			0
$971$	−47.5115	+	34.5191i	−1.52472	+	1.10777i	−0.565630	+	0.824659i	$0.691367\pi$
$971$	−47.5115	+	34.5191i	−1.52472	+	1.10777i	−0.959087	+	0.283113i	$0.908633\pi$
$972$		0			0
$973$	−32.9131	−	101.296i	−1.05515	−	3.24741i
$974$		0			0
$975$	2.09103	+	1.51922i	0.0669665	+	0.0486540i
$976$		0			0
$977$	−7.02964	+	21.6350i	−0.224898	+	0.692166i	0.773404	+	0.633914i	$0.218553\pi$
$977$	−7.02964	+	21.6350i	−0.224898	+	0.692166i	−0.998302	+	0.0582518i	$0.981447\pi$
$978$		0			0
$979$	20.5560	+	12.9436i	0.656973	+	0.413678i
$980$		0			0
$981$	32.1128	−	98.8329i	1.02528	−	3.15549i
$982$		0			0
$983$	26.7869	+	19.4618i	0.854370	+	0.620736i	0.926347	−	0.376670i	$-0.122931\pi$
$983$	26.7869	+	19.4618i	0.854370	+	0.620736i	−0.0719774	+	0.997406i	$0.522931\pi$
$984$		0			0
$985$	−0.586045	−	1.80366i	−0.0186730	−	0.0574694i
$986$		0			0
$987$	110.372	−	80.1900i	3.51318	−	2.55247i
$988$		0			0
$989$	−1.68980			−0.0537326
$990$		0			0
$991$	12.6263			0.401088			0.200544	−	0.979685i	$-0.435729\pi$
$991$	12.6263			0.401088			0.200544	+	0.979685i	$0.435729\pi$
$992$		0			0
$993$	48.6823	−	35.3698i	1.54489	−	1.12243i
$994$		0			0
$995$	4.32517	+	13.3115i	0.137117	+	0.422003i
$996$		0			0
$997$	15.4413	+	11.2188i	0.489032	+	0.355303i	0.804812	−	0.593530i	$-0.202266\pi$
$997$	15.4413	+	11.2188i	0.489032	+	0.355303i	−0.315780	+	0.948832i	$0.602266\pi$
$998$		0			0
$999$	−28.6100	+	88.0525i	−0.905180	+	2.78586i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	440.2.y.d.361.1	✓	16
4.3	odd	2		880.2.bo.k.801.4		16
11.4	even	5		4840.2.a.bg.1.8		8
11.5	even	5	inner	440.2.y.d.401.1	yes	16
11.7	odd	10		4840.2.a.bh.1.8		8
44.7	even	10		9680.2.a.de.1.1		8
44.15	odd	10		9680.2.a.df.1.1		8
44.27	odd	10		880.2.bo.k.401.4		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
440.2.y.d.361.1	✓	16	1.1	even	1	trivial
440.2.y.d.401.1	yes	16	11.5	even	5	inner
880.2.bo.k.401.4		16	44.27	odd	10
880.2.bo.k.801.4		16	4.3	odd	2
4840.2.a.bg.1.8		8	11.4	even	5
4840.2.a.bh.1.8		8	11.7	odd	10
9680.2.a.de.1.1		8	44.7	even	10
9680.2.a.df.1.1		8	44.15	odd	10

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:	\( N \)	\(=\)	\( 440 = 2^{3} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	440.y (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.59852 + 1.88794i) q^{3} +(0.309017 + 0.951057i) q^{5} +(3.97176 + 2.88565i) q^{7} +(2.26096 - 6.95852i) q^{9} +(2.80658 + 1.76723i) q^{11} +(-0.248666 + 0.765314i) q^{13} +(-2.59852 - 1.88794i) q^{15} +(0.570906 + 1.75707i) q^{17} +(-4.54455 + 3.30181i) q^{19} -15.7686 q^{21} -1.60313 q^{23} +(-0.809017 + 0.587785i) q^{25} +(4.28444 + 13.1862i) q^{27} +(-6.36280 - 4.62285i) q^{29} +(1.19581 - 3.68033i) q^{31} +(-10.6294 + 0.706466i) q^{33} +(-1.51708 + 4.66909i) q^{35} +(5.40233 + 3.92502i) q^{37} +(-0.798702 - 2.45815i) q^{39} +(4.23759 - 3.07879i) q^{41} +1.05407 q^{43} +7.31662 q^{45} +(-6.99946 + 5.08541i) q^{47} +(5.28477 + 16.2649i) q^{49} +(-4.80074 - 3.48794i) q^{51} +(2.41830 - 7.44275i) q^{53} +(-0.813453 + 3.21532i) q^{55} +(5.57551 - 17.1596i) q^{57} +(-3.14961 - 2.28832i) q^{59} +(2.04656 + 6.29868i) q^{61} +(29.0599 - 21.1132i) q^{63} -0.804699 q^{65} -5.52774 q^{67} +(4.16576 - 3.02660i) q^{69} +(-3.38974 - 10.4325i) q^{71} +(-2.26518 - 1.64575i) q^{73} +(0.992547 - 3.05475i) q^{75} +(6.04746 + 15.1178i) q^{77} +(-0.902277 + 2.77692i) q^{79} +(-18.2701 - 13.2740i) q^{81} +(0.598359 + 1.84156i) q^{83} +(-1.49465 + 1.08593i) q^{85} +25.2615 q^{87} +7.32421 q^{89} +(-3.19607 + 2.32208i) q^{91} +(3.84089 + 11.8210i) q^{93} +(-4.54455 - 3.30181i) q^{95} +(2.52077 - 7.75815i) q^{97} +(18.6429 - 15.5340i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 3 q^{3} - 4 q^{5} + 8 q^{7} - 7 q^{9} - 7 q^{11} - 11 q^{13} - 3 q^{15} + 9 q^{17} - 2 q^{19} + 12 q^{21} + 20 q^{23} - 4 q^{25} - 9 q^{27} + q^{29} - 2 q^{31} - 32 q^{33} - 2 q^{35} - 16 q^{37}+ \cdots - 10 q^{99}+O(q^{100}) \) 16 * q - 3 * q^3 - 4 * q^5 + 8 * q^7 - 7 * q^9 - 7 * q^11 - 11 * q^13 - 3 * q^15 + 9 * q^17 - 2 * q^19 + 12 * q^21 + 20 * q^23 - 4 * q^25 - 9 * q^27 + q^29 - 2 * q^31 - 32 * q^33 - 2 * q^35 - 16 * q^37 + 3 * q^39 - 11 * q^41 - 16 * q^43 + 38 * q^45 - 10 * q^47 + 4 * q^49 + 26 * q^51 - 9 * q^53 + 3 * q^55 - 50 * q^57 - 60 * q^59 + 30 * q^61 + 52 * q^63 + 24 * q^65 - 4 * q^67 + 41 * q^69 - 10 * q^71 + q^73 + 2 * q^75 - 4 * q^77 + 19 * q^79 - 31 * q^81 + 64 * q^83 - 11 * q^85 + 30 * q^87 + 24 * q^89 - 9 * q^91 + 45 * q^93 - 2 * q^95 - 3 * q^97 - 10 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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