LMFDB - Embedded newform 880.2.bo.k.801.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [880,2,Mod(81,880)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(880, 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("880.81");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 880 = 2^{4} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	880.bo (of order $5$, degree $4$, not 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:	$7.02683537787$
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:	no (minimal twist has level 440)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			801.4
Root			$2.59852 - 1.88794i$ of defining polynomial
Character	$\chi$	$=$	880.801
Dual form			880.2.bo.k.401.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

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

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/880\mathbb{Z}\right)^\times$.

$n$	$111$	$177$	$321$	$661$
$\chi(n)$	$1$	$1$	$e\left(\frac{3}{5}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	2.59852	−	1.88794i	1.50026	−	1.09000i	0.529978	−	0.848011i	$-0.322200\pi$
$3$	2.59852	−	1.88794i	1.50026	−	1.09000i	0.970279	−	0.241989i	$-0.0777998\pi$
$4$		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	$-0.921712\pi$
$7$	−3.97176	−	2.88565i	−1.50118	−	1.09067i	−0.531278	−	0.847198i	$-0.678288\pi$
$8$		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	0.0718015	−	0.997419i	$-0.477125\pi$
$19$	4.54455	−	3.30181i	1.04259	−	0.757487i	0.970790	+	0.239932i	$0.0771252\pi$
$20$		0			0
$21$	−15.7686			−3.44100
$22$		0			0
$23$	1.60313			0.334275			0.167138	−	0.985934i	$-0.446548\pi$
$23$	1.60313			0.334275			0.167138	+	0.985934i	$0.446548\pi$
$24$		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	$0.212973\pi$
$31$	−1.19581	+	3.68033i	−0.214774	+	0.661007i	−0.999170	+	0.0407457i	$0.987027\pi$
$32$		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	$-0.525611\pi$
$43$	−1.05407			−0.160744			−0.0803718	+	0.996765i	$0.525611\pi$
$44$		0			0
$45$	7.31662			1.09070
$46$		0			0
$47$	6.99946	−	5.08541i	1.02098	−	0.741783i	0.0544940	−	0.998514i	$-0.482645\pi$
$47$	6.99946	−	5.08541i	1.02098	−	0.741783i	0.966483	+	0.256731i	$0.0826454\pi$
$48$		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	0.773620	−	0.633650i	$-0.218444\pi$
$59$	3.14961	+	2.28832i	0.410044	+	0.297914i	−0.363576	+	0.931565i	$0.618444\pi$
$60$		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	$-0.390364\pi$
$67$	5.52774			0.675321			0.337661	+	0.941268i	$0.390364\pi$
$68$		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	$0.125615\pi$
$71$	3.38974	+	10.4325i	0.402288	+	1.23811i	−0.520851	+	0.853648i	$0.674385\pi$
$72$		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	−0.887382	−	0.461034i	$-0.847479\pi$
$79$	0.902277	−	2.77692i	0.101514	−	0.312428i	0.988896	+	0.148606i	$0.0474786\pi$
$80$		0			0
$81$	−18.2701	−	13.2740i	−2.03001	−	1.47489i
$82$		0			0
$83$	−0.598359	−	1.84156i	−0.0656784	−	0.202137i	0.912832	−	0.408336i	$-0.133891\pi$
$83$	−0.598359	−	1.84156i	−0.0656784	−	0.202137i	−0.978510	+	0.206198i	$0.933891\pi$
$84$		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	−0.204837	−	0.978796i	$-0.565666\pi$
$103$	−12.1688	−	8.84114i	−1.19903	−	0.871143i	−0.994189	+	0.107653i	$0.965666\pi$
$104$		0			0
$105$	−4.87278	−	14.9969i	−0.475534	−	1.46354i
$106$		0			0
$107$	−4.54470	+	3.30192i	−0.439353	+	0.319208i	−0.785378	−	0.619017i	$-0.787531\pi$
$107$	−4.54470	+	3.30192i	−0.439353	+	0.319208i	0.346025	+	0.938225i	$0.387531\pi$
$108$		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	0.966849	−	0.255349i	$-0.0821905\pi$
$127$	0.389484	+	1.19871i	0.0345611	+	0.106368i	−0.932288	+	0.361718i	$0.882190\pi$
$128$		0			0
$129$	−2.73901	+	1.99001i	−0.241157	+	0.175211i
$130$		0			0
$131$	−12.0760			−1.05509			−0.527543	−	0.849528i	$-0.676887\pi$
$131$	−12.0760			−1.05509			−0.527543	+	0.849528i	$0.676887\pi$
$132$		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	$0.0718734\pi$
$139$	17.5517	+	12.7520i	1.48871	+	1.08161i	0.514098	+	0.857731i	$0.328127\pi$
$140$		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	−0.550137	−	0.835075i	$-0.685424\pi$
$151$	0.910122	−	0.661242i	0.0740646	−	0.0538111i	0.624201	+	0.781263i	$0.285424\pi$
$152$		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	$-0.706094\pi$
$163$	4.51488	−	13.8954i	0.353633	−	1.08837i	0.956798	−	0.290753i	$-0.0939059\pi$
$164$		0			0
$165$	−3.95655	−	9.89083i	−0.308017	−	0.770000i
$166$		0			0
$167$	2.08197	−	6.40765i	0.161108	−	0.495839i	−0.837621	−	0.546252i	$-0.816054\pi$
$167$	2.08197	−	6.40765i	0.161108	−	0.495839i	0.998728	+	0.0504137i	$0.0160540\pi$
$168$		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	$0.717996\pi$
$179$	−20.9334	+	15.2090i	−1.56464	+	1.13677i	−0.932075	+	0.362265i	$0.882004\pi$
$180$		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	0.696724	−	0.717339i	$-0.254640\pi$
$191$	3.17581	+	2.30736i	0.229793	+	0.166955i	−0.466931	+	0.884294i	$0.654640\pi$
$192$		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	$-0.665233\pi$
$199$	−13.9966			−0.992189			−0.496095	+	0.868268i	$0.665233\pi$
$200$		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	$0.485739\pi$
$211$	−8.40526	+	25.8687i	−0.578642	+	1.78088i	−0.623429	+	0.781880i	$0.714261\pi$
$212$		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	−0.206356	−	0.978477i	$-0.566160\pi$
$223$	9.86282	−	7.16576i	0.660464	−	0.479855i	0.866819	+	0.498622i	$0.166160\pi$
$224$		0			0
$225$	2.26096	+	6.95852i	0.150731	+	0.463901i
$226$		0			0
$227$	−14.0410	−	10.2014i	−0.931932	−	0.677088i	0.0145329	−	0.999894i	$-0.495374\pi$
$227$	−14.0410	−	10.2014i	−0.931932	−	0.677088i	−0.946465	+	0.322806i	$0.895374\pi$
$228$		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	−0.781072	−	0.624441i	$-0.785327\pi$
$239$	−6.62535	+	4.81360i	−0.428559	+	0.311366i	0.352514	+	0.935807i	$0.385327\pi$
$240$		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	$0.298675\pi$
$251$	−5.72227	+	17.6113i	−0.361187	+	1.11162i	−0.952335	+	0.305055i	$0.901325\pi$
$252$		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	$-0.319563\pi$
$263$	17.4169			1.07397			0.536985	+	0.843592i	$0.319563\pi$
$264$		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	$-0.927959\pi$
$271$	−24.5128	−	17.8096i	−1.48905	−	1.08186i	−0.514550	−	0.857460i	$-0.672041\pi$
$272$		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	−0.638232	−	0.769844i	$-0.720334\pi$
$283$	−1.73762	+	1.26246i	−0.103291	+	0.0750454i	0.534941	+	0.844890i	$0.320334\pi$
$284$		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	$-0.448984\pi$
$307$	5.59232			0.319171			0.159585	+	0.987184i	$0.448984\pi$
$308$		0			0
$309$	−48.3123			−2.74839
$310$		0			0
$311$	1.38707	−	1.00777i	0.0786536	−	0.0571452i	−0.547764	−	0.836633i	$-0.684521\pi$
$311$	1.38707	−	1.00777i	0.0786536	−	0.0571452i	0.626417	+	0.779488i	$0.284521\pi$
$312$		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	$-0.327839\pi$
$331$	18.7346			1.02975			0.514874	+	0.857266i	$0.327839\pi$
$332$		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	$0.0361415\pi$
$347$	4.77524	+	14.6967i	0.256348	+	0.788959i	−0.737213	+	0.675661i	$0.763859\pi$
$348$		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	0.219090	−	0.975705i	$-0.429691\pi$
$359$	−12.1482	−	8.82619i	−0.641158	−	0.465828i	−0.860248	+	0.509876i	$0.829691\pi$
$360$		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	0.0658502	−	0.997830i	$-0.479024\pi$
$367$	−16.5287	−	12.0088i	−0.862793	−	0.626856i	−0.928643	+	0.370974i	$0.879024\pi$
$368$		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	$0.114785\pi$
$379$	7.51646	+	23.1333i	0.386095	+	1.18828i	−0.549588	+	0.835436i	$0.685215\pi$
$380$		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	$0.204307\pi$
$383$	−3.89293	+	11.9812i	−0.198919	+	0.612211i	−0.999908	+	0.0135318i	$0.995693\pi$
$384$		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	$-0.0939817\pi$
$419$	39.1675			1.91346			0.956729	+	0.290981i	$0.0939817\pi$
$420$		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	−0.962872	−	0.269958i	$-0.912990\pi$
$431$	−0.523478	+	1.61110i	−0.0252151	+	0.0776040i	0.937657	+	0.347562i	$0.112990\pi$
$432$		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	$-0.495453\pi$
$439$	0.598520			0.0285658			0.0142829	+	0.999898i	$0.495453\pi$
$440$		0			0
$441$	125.128			5.95847
$442$		0			0
$443$	−29.5783	+	21.4899i	−1.40531	+	1.02102i	−0.411325	+	0.911489i	$0.634934\pi$
$443$	−29.5783	+	21.4899i	−1.40531	+	1.02102i	−0.993984	+	0.109528i	$0.965066\pi$
$444$		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	$-0.453315\pi$
$463$	6.28911			0.292280			0.146140	+	0.989264i	$0.453315\pi$
$464$		0			0
$465$	−10.0556	+	7.30580i	−0.466316	+	0.338798i
$466$		0			0
$467$	−0.242605	−	0.746662i	−0.0112264	−	0.0345514i	0.945286	−	0.326242i	$-0.105782\pi$
$467$	−0.242605	−	0.746662i	−0.0112264	−	0.0345514i	−0.956513	+	0.291690i	$0.905782\pi$
$468$		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	$-0.756986\pi$
$479$	−11.9144	−	36.6687i	−0.544382	−	1.67544i	0.178073	−	0.984017i	$-0.443014\pi$
$480$		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	−0.254663	−	0.967030i	$-0.581965\pi$
$487$	12.9394	−	9.40105i	0.586342	−	0.426002i	0.841005	+	0.541027i	$0.181965\pi$
$488$		0			0
$489$	−14.5016	−	44.6312i	−0.655783	−	2.01829i
$490$		0			0
$491$	−20.4310	−	14.8440i	−0.922037	−	0.669899i	0.0219933	−	0.999758i	$-0.492999\pi$
$491$	−20.4310	−	14.8440i	−0.922037	−	0.669899i	−0.944030	+	0.329859i	$0.892999\pi$
$492$		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	0.494231	−	0.869330i	$-0.335450\pi$
$499$	−4.01699	−	2.91851i	−0.179825	−	0.130651i	−0.674056	+	0.738680i	$0.735450\pi$
$500$		0			0
$501$	−6.68718	−	20.5810i	−0.298761	−	0.919493i
$502$		0			0
$503$	−16.3333	+	11.8668i	−0.728265	+	0.529116i	−0.889014	−	0.457880i	$-0.848609\pi$
$503$	−16.3333	+	11.8668i	−0.728265	+	0.529116i	0.160749	+	0.986995i	$0.448609\pi$
$504$		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	$0.0720879\pi$
$523$	7.27440	+	22.3883i	0.318087	+	0.978972i	−0.656377	+	0.754433i	$0.727912\pi$
$524$		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	−0.953095	−	0.302671i	$-0.902122\pi$
$547$	−22.4469	+	16.3086i	−0.959760	+	0.697306i	−0.00666505	+	0.999978i	$0.502122\pi$
$548$		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	$-0.678706\pi$
$563$	9.39334	−	28.9097i	0.395882	−	1.21840i	0.928273	−	0.371901i	$-0.121294\pi$
$564$		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	$-0.254825\pi$
$571$	33.2773			1.39261			0.696307	+	0.717744i	$0.254825\pi$
$572$		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	0.885463	−	0.464709i	$-0.153841\pi$
$587$	17.3745	+	12.6233i	0.717121	+	0.521019i	−0.168342	+	0.985729i	$0.553841\pi$
$588$		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	$-0.760959\pi$
$599$	−13.2330	−	40.7271i	−0.540687	−	1.66406i	0.190341	−	0.981718i	$-0.439041\pi$
$600$		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	$0.363300\pi$
$607$	−11.2073	+	34.4924i	−0.454889	+	1.40000i	−0.871266	+	0.490812i	$0.836700\pi$
$608$		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	−0.211890	−	0.977293i	$-0.567962\pi$
$619$	16.2239	−	11.7873i	0.652093	−	0.473773i	0.863984	+	0.503520i	$0.167962\pi$
$620$		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	0.374491	−	0.927230i	$-0.377817\pi$
$631$	−9.83771	−	7.14751i	−0.391633	−	0.284538i	−0.766124	+	0.642692i	$0.777817\pi$
$632$		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	0.996009	−	0.0892482i	$-0.0284464\pi$
$643$	3.49329	+	10.7513i	0.137762	+	0.423988i	−0.858247	+	0.513236i	$0.828446\pi$
$644$		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	$0.236709\pi$
$647$	−6.54599	+	20.1465i	−0.257350	+	0.792041i	−0.993358	+	0.115068i	$0.963291\pi$
$648$		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	$-0.435842\pi$
$659$	10.2784			0.400391			0.200195	+	0.979756i	$0.435842\pi$
$660$		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	$-0.570702\pi$
$683$	−11.5145			−0.440590			−0.220295	+	0.975433i	$0.570702\pi$
$684$		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	$0.242575\pi$
$691$	−7.03598	+	21.6545i	−0.267661	+	0.823777i	−0.991068	+	0.133355i	$0.957425\pi$
$692$		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	0.893718	−	0.448630i	$-0.148088\pi$
$719$	19.9288	+	14.4791i	0.743219	+	0.539981i	−0.150498	+	0.988610i	$0.548088\pi$
$720$		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	$-0.303708\pi$
$727$	31.1865			1.15664			0.578321	+	0.815809i	$0.303708\pi$
$728$		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	−0.959182	−	0.282791i	$-0.908740\pi$
$739$	−0.461240	+	1.41955i	−0.0169670	+	0.0522190i	0.942215	+	0.335010i	$0.108740\pi$
$740$		0			0
$741$	11.7461	+	8.53403i	0.431503	+	0.313505i
$742$		0			0
$743$	−3.07996	−	9.47913i	−0.112993	−	0.347755i	0.878530	−	0.477686i	$-0.158524\pi$
$743$	−3.07996	−	9.47913i	−0.112993	−	0.347755i	−0.991523	+	0.129931i	$0.958524\pi$
$744$		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	−0.410257	−	0.911970i	$-0.634561\pi$
$751$	9.05170	−	6.57644i	0.330301	−	0.239978i	0.740558	+	0.671992i	$0.234561\pi$
$752$		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	$0.180255\pi$
$787$	13.3680	+	41.1425i	0.476518	+	1.46657i	−0.367380	+	0.930071i	$0.619745\pi$
$788$		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	−0.967962	−	0.251096i	$-0.919209\pi$
$811$	−29.2832	+	21.2755i	−1.02827	+	0.747084i	−0.0603105	+	0.998180i	$0.519209\pi$
$812$		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	$-0.724512\pi$
$823$	9.28714	−	28.5829i	0.323729	−	0.996336i	0.972011	−	0.234936i	$-0.0754879\pi$
$824$		0			0
$825$	8.18410	−	6.81934i	0.284934	−	0.237419i
$826$		0			0
$827$	0.194302	−	0.597999i	0.00675653	−	0.0207945i	−0.947621	−	0.319396i	$-0.896520\pi$
$827$	0.194302	−	0.597999i	0.00675653	−	0.0207945i	0.954378	+	0.298601i	$0.0965201\pi$
$828$		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	−0.499415	−	0.866363i	$-0.666452\pi$
$839$	4.93041	−	3.58215i	0.170217	−	0.123670i	0.669632	+	0.742693i	$0.266452\pi$
$840$		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	$-0.641791\pi$
$859$	−25.2561			−0.861725			−0.430863	+	0.902417i	$0.641791\pi$
$860$		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	$-0.976801\pi$
$863$	−6.85295	−	21.0912i	−0.233277	−	0.717954i	0.764068	−	0.645136i	$-0.223199\pi$
$864$		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	−0.636830	−	0.771004i	$-0.719755\pi$
$883$	−2.98200	+	2.16655i	−0.100352	+	0.0729102i	0.536478	+	0.843915i	$0.319755\pi$
$884$		0			0
$885$	3.86411	+	11.8925i	0.129891	+	0.399762i
$886$		0			0
$887$	7.33074	+	5.32609i	0.246142	+	0.178833i	0.704015	−	0.710185i	$-0.251389\pi$
$887$	7.33074	+	5.32609i	0.246142	+	0.178833i	−0.457873	+	0.889018i	$0.651389\pi$
$888$		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	$-0.918803\pi$
$907$	−10.0323	−	30.8764i	−0.333119	−	1.02523i	0.634523	−	0.772904i	$-0.281197\pi$
$908$		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	$0.423232\pi$
$911$	−15.8507	+	48.7836i	−0.525158	+	1.61627i	−0.764002	+	0.645214i	$0.776768\pi$
$912$		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	0.868557	−	0.495590i	$-0.165048\pi$
$919$	−3.80213	−	11.7018i	−0.125421	−	0.386006i	−0.993978	+	0.109584i	$0.965048\pi$
$920$		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	$-0.617052\pi$
$947$	−22.1259			−0.718996			−0.359498	+	0.933146i	$0.617052\pi$
$948$		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	$-0.236561\pi$
$967$	45.7942			1.47264			0.736321	+	0.676632i	$0.236561\pi$
$968$		0			0
$969$	33.3337			1.07083
$970$		0			0
$971$	47.5115	−	34.5191i	1.52472	−	1.10777i	0.565630	−	0.824659i	$-0.308633\pi$
$971$	47.5115	−	34.5191i	1.52472	−	1.10777i	0.959087	−	0.283113i	$-0.0913670\pi$
$972$		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	0.0719774	−	0.997406i	$-0.477069\pi$
$983$	−26.7869	−	19.4618i	−0.854370	−	0.620736i	−0.926347	+	0.376670i	$0.877069\pi$
$984$		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	$-0.564271\pi$
$991$	−12.6263			−0.401088			−0.200544	+	0.979685i	$0.564271\pi$
$992$		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	880.2.bo.k.801.4		16
4.3	odd	2		440.2.y.d.361.1	✓	16
11.4	even	5		9680.2.a.df.1.1		8
11.5	even	5	inner	880.2.bo.k.401.4		16
11.7	odd	10		9680.2.a.de.1.1		8
44.7	even	10		4840.2.a.bh.1.8		8
44.15	odd	10		4840.2.a.bg.1.8		8
44.27	odd	10		440.2.y.d.401.1	yes	16

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

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:	\( N \)	\(=\)	\( 880 = 2^{4} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	880.bo (of order \(5\), degree \(4\), not minimal)

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

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Database

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