LMFDB - Embedded newform 504.2.r.f.169.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [504,2,Mod(169,504)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(504, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 4, 0]))

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

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

chi := DirichletCharacter("504.169");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 504 = 2^{3} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	504.r (of order $3$, degree $2$, 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:	$4.02446026187$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{3})$
Coefficient field:	10.0.6095158642368.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 4x^{9} + 6x^{8} - 7x^{7} + 25x^{6} - 66x^{5} + 75x^{4} - 63x^{3} + 162x^{2} - 324x + 243 $ x^10 - 4x^9 + 6x^8 - 7x^7 + 25x^6 - 66x^5 + 75x^4 - 63x^3 + 162x^2 - 324*x + 243
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			169.2
Root			$1.72987 - 0.0867982i$ of defining polynomial
Character	$\chi$	$=$	504.169
Dual form			504.2.r.f.337.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.25506 - 1.19366i) q^{3} +(0.846320 + 1.46587i) q^{5} +(0.500000 - 0.866025i) q^{7} +(0.150339 + 2.99623i) q^{9} +O(q^{10})$	\(q+(-1.25506 - 1.19366i) q^{3} +(0.846320 + 1.46587i) q^{5} +(0.500000 - 0.866025i) q^{7} +(0.150339 + 2.99623i) q^{9} +(0.474817 - 0.822407i) q^{11} +(1.69516 + 2.93611i) q^{13} +(0.687573 - 2.84997i) q^{15} -0.300678 q^{17} +5.73697 q^{19} +(-1.66127 + 0.490080i) q^{21} +(1.17300 + 2.03169i) q^{23} +(1.06748 - 1.84894i) q^{25} +(3.38780 - 3.93990i) q^{27} +(1.01964 - 1.76607i) q^{29} +(-0.522659 - 0.905272i) q^{31} +(-1.57760 + 0.465397i) q^{33} +1.69264 q^{35} +7.22462 q^{37} +(1.37720 - 5.70844i) q^{39} +(2.56447 + 4.44179i) q^{41} +(5.25963 - 9.10995i) q^{43} +(-4.26485 + 2.75615i) q^{45} +(-3.24251 + 5.61620i) q^{47} +(-0.500000 - 0.866025i) q^{49} +(0.377368 + 0.358908i) q^{51} +1.86503 q^{53} +1.60739 q^{55} +(-7.20023 - 6.84801i) q^{57} +(4.46197 + 7.72836i) q^{59} +(-0.256177 + 0.443711i) q^{61} +(2.66998 + 1.36792i) q^{63} +(-2.86930 + 4.96978i) q^{65} +(-6.63195 - 11.4869i) q^{67} +(0.952975 - 3.95005i) q^{69} -5.04433 q^{71} -1.59027 q^{73} +(-3.54676 + 1.04631i) q^{75} +(-0.474817 - 0.822407i) q^{77} +(-6.43263 + 11.1416i) q^{79} +(-8.95480 + 0.900900i) q^{81} +(-1.98463 + 3.43748i) q^{83} +(-0.254470 - 0.440755i) q^{85} +(-3.38780 + 0.999414i) q^{87} -6.24428 q^{89} +3.39033 q^{91} +(-0.424622 + 1.76005i) q^{93} +(4.85532 + 8.40965i) q^{95} +(-5.02469 + 8.70302i) q^{97} +(2.53551 + 1.29902i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 3 q^{5} + 5 q^{7}+O(q^{10}) $ 10 * q - 3 * q^5 + 5 * q^7	$ 10 q - 3 q^{5} + 5 q^{7} + 4 q^{11} - 3 q^{13} + 15 q^{15} + 2 q^{19} + 8 q^{23} - 10 q^{25} - 9 q^{27} - 9 q^{29} - 3 q^{31} + 30 q^{33} - 6 q^{35} - 6 q^{37} - 18 q^{39} - 12 q^{41} - 5 q^{43} - 9 q^{45} + 3 q^{47} - 5 q^{49} + 9 q^{51} + 60 q^{53} + 44 q^{55} - 21 q^{57} + 7 q^{59} - 14 q^{61} + 6 q^{63} - 11 q^{65} - 8 q^{67} + 21 q^{69} - 18 q^{71} + 30 q^{73} - 51 q^{75} - 4 q^{77} - 3 q^{79} - 12 q^{81} + 20 q^{83} - 21 q^{85} + 9 q^{87} - 24 q^{89} - 6 q^{91} - 39 q^{93} - 12 q^{95} - 37 q^{97} + 60 q^{99}+O(q^{100}) $ 10 * q - 3 * q^5 + 5 * q^7 + 4 * q^11 - 3 * q^13 + 15 * q^15 + 2 * q^19 + 8 * q^23 - 10 * q^25 - 9 * q^27 - 9 * q^29 - 3 * q^31 + 30 * q^33 - 6 * q^35 - 6 * q^37 - 18 * q^39 - 12 * q^41 - 5 * q^43 - 9 * q^45 + 3 * q^47 - 5 * q^49 + 9 * q^51 + 60 * q^53 + 44 * q^55 - 21 * q^57 + 7 * q^59 - 14 * q^61 + 6 * q^63 - 11 * q^65 - 8 * q^67 + 21 * q^69 - 18 * q^71 + 30 * q^73 - 51 * q^75 - 4 * q^77 - 3 * q^79 - 12 * q^81 + 20 * q^83 - 21 * q^85 + 9 * q^87 - 24 * q^89 - 6 * q^91 - 39 * q^93 - 12 * q^95 - 37 * q^97 + 60 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/504\mathbb{Z}\right)^\times$.

$n$	$73$	$127$	$253$	$281$
$\chi(n)$	$1$	$1$	$1$	$e\left(\frac{2}{3}\right)$

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
$3$	−1.25506	−	1.19366i	−0.724608	−	0.689161i
$3$	−1.25506	−	1.19366i	−0.724608	−	0.689161i
$4$		0			0
$5$	0.846320	+	1.46587i	0.378486	+	0.655557i	0.990842	−	0.135025i	$-0.0431115\pi$
$5$	0.846320	+	1.46587i	0.378486	+	0.655557i	−0.612356	+	0.790582i	$0.709778\pi$
$6$		0			0
$7$	0.500000	−	0.866025i	0.188982	−	0.327327i
$7$	0.500000	−	0.866025i	0.188982	−	0.327327i
$8$		0			0
$9$	0.150339	+	2.99623i	0.0501130	+	0.998744i
$10$		0			0
$11$	0.474817	−	0.822407i	0.143163	−	0.247965i	−0.785523	−	0.618832i	$-0.787606\pi$
$11$	0.474817	−	0.822407i	0.143163	−	0.247965i	0.928686	+	0.370867i	$0.120939\pi$
$12$		0			0
$13$	1.69516	+	2.93611i	0.470154	+	0.814331i	0.999418	−	0.0341269i	$-0.0108650\pi$
$13$	1.69516	+	2.93611i	0.470154	+	0.814331i	−0.529264	+	0.848457i	$0.677532\pi$
$14$		0			0
$15$	0.687573	−	2.84997i	0.177531	−	0.735859i
$16$		0			0
$17$	−0.300678			−0.0729251			−0.0364625	−	0.999335i	$-0.511609\pi$
$17$	−0.300678			−0.0729251			−0.0364625	+	0.999335i	$0.511609\pi$
$18$		0			0
$19$	5.73697			1.31615			0.658076	−	0.752952i	$-0.271371\pi$
$19$	5.73697			1.31615			0.658076	+	0.752952i	$0.271371\pi$
$20$		0			0
$21$	−1.66127	+	0.490080i	−0.362519	+	0.106944i
$22$		0			0
$23$	1.17300	+	2.03169i	0.244587	+	0.423637i	0.962015	−	0.272995i	$-0.0880143\pi$
$23$	1.17300	+	2.03169i	0.244587	+	0.423637i	−0.717428	+	0.696632i	$0.754681\pi$
$24$		0			0
$25$	1.06748	−	1.84894i	0.213497	−	0.369787i
$26$		0			0
$27$	3.38780	−	3.93990i	0.651983	−	0.758233i
$28$		0			0
$29$	1.01964	−	1.76607i	0.189343	−	0.327951i	−0.755688	−	0.654931i	$-0.772698\pi$
$29$	1.01964	−	1.76607i	0.189343	−	0.327951i	0.945031	+	0.326980i	$0.106031\pi$
$30$		0			0
$31$	−0.522659	−	0.905272i	−0.0938723	−	0.162592i	0.815265	−	0.579088i	$-0.196591\pi$
$31$	−0.522659	−	0.905272i	−0.0938723	−	0.162592i	−0.909137	+	0.416496i	$0.863258\pi$
$32$		0			0
$33$	−1.57760	+	0.465397i	−0.274625	+	0.0810152i
$34$		0			0
$35$	1.69264			0.286108
$36$		0			0
$37$	7.22462			1.18772			0.593860	−	0.804568i	$-0.297603\pi$
$37$	7.22462			1.18772			0.593860	+	0.804568i	$0.297603\pi$
$38$		0			0
$39$	1.37720	−	5.70844i	0.220528	−	0.914082i
$40$		0			0
$41$	2.56447	+	4.44179i	0.400503	+	0.693691i	0.993787	−	0.111302i	$-0.0355022\pi$
$41$	2.56447	+	4.44179i	0.400503	+	0.693691i	−0.593284	+	0.804993i	$0.702169\pi$
$42$		0			0
$43$	5.25963	−	9.10995i	0.802086	−	1.38925i	−0.116154	−	0.993231i	$-0.537057\pi$
$43$	5.25963	−	9.10995i	0.802086	−	1.38925i	0.918241	−	0.396023i	$-0.129610\pi$
$44$		0			0
$45$	−4.26485	+	2.75615i	−0.635766	+	0.410862i
$46$		0			0
$47$	−3.24251	+	5.61620i	−0.472969	+	0.819207i	−0.999521	−	0.0309361i	$-0.990151\pi$
$47$	−3.24251	+	5.61620i	−0.472969	+	0.819207i	0.526552	+	0.850143i	$0.323484\pi$
$48$		0			0
$49$	−0.500000	−	0.866025i	−0.0714286	−	0.123718i
$50$		0			0
$51$	0.377368	+	0.358908i	0.0528421	+	0.0502572i
$52$		0			0
$53$	1.86503			0.256182			0.128091	−	0.991762i	$-0.459115\pi$
$53$	1.86503			0.256182			0.128091	+	0.991762i	$0.459115\pi$
$54$		0			0
$55$	1.60739			0.216740
$56$		0			0
$57$	−7.20023	−	6.84801i	−0.953694	−	0.907041i
$58$		0			0
$59$	4.46197	+	7.72836i	0.580899	+	1.00615i	0.995373	+	0.0960856i	$0.0306323\pi$
$59$	4.46197	+	7.72836i	0.580899	+	1.00615i	−0.414474	+	0.910061i	$0.636034\pi$
$60$		0			0
$61$	−0.256177	+	0.443711i	−0.0328001	+	0.0568114i	−0.881959	−	0.471325i	$-0.843776\pi$
$61$	−0.256177	+	0.443711i	−0.0328001	+	0.0568114i	0.849159	+	0.528137i	$0.177109\pi$
$62$		0			0
$63$	2.66998	+	1.36792i	0.336386	+	0.172341i
$64$		0			0
$65$	−2.86930	+	4.96978i	−0.355893	+	0.616425i
$66$		0			0
$67$	−6.63195	−	11.4869i	−0.810222	−	1.40335i	−0.912709	−	0.408611i	$-0.866013\pi$
$67$	−6.63195	−	11.4869i	−0.810222	−	1.40335i	0.102487	−	0.994734i	$-0.467320\pi$
$68$		0			0
$69$	0.952975	−	3.95005i	0.114725	−	0.475531i
$70$		0			0
$71$	−5.04433			−0.598652			−0.299326	−	0.954151i	$-0.596762\pi$
$71$	−5.04433			−0.598652			−0.299326	+	0.954151i	$0.596762\pi$
$72$		0			0
$73$	−1.59027			−0.186128			−0.0930638	−	0.995660i	$-0.529666\pi$
$73$	−1.59027			−0.186128			−0.0930638	+	0.995660i	$0.529666\pi$
$74$		0			0
$75$	−3.54676	+	1.04631i	−0.409545	+	0.120817i
$76$		0			0
$77$	−0.474817	−	0.822407i	−0.0541104	−	0.0937220i
$78$		0			0
$79$	−6.43263	+	11.1416i	−0.723727	+	1.25353i	0.235768	+	0.971809i	$0.424239\pi$
$79$	−6.43263	+	11.1416i	−0.723727	+	1.25353i	−0.959496	+	0.281723i	$0.909094\pi$
$80$		0			0
$81$	−8.95480	+	0.900900i	−0.994977	+	0.100100i
$82$		0			0
$83$	−1.98463	+	3.43748i	−0.217841	+	0.377312i	−0.954148	−	0.299336i	$-0.903235\pi$
$83$	−1.98463	+	3.43748i	−0.217841	+	0.377312i	0.736306	+	0.676648i	$0.236568\pi$
$84$		0			0
$85$	−0.254470	−	0.440755i	−0.0276011	−	0.0478065i
$86$		0			0
$87$	−3.38780	+	0.999414i	−0.363211	+	0.107148i
$88$		0			0
$89$	−6.24428			−0.661892			−0.330946	−	0.943650i	$-0.607368\pi$
$89$	−6.24428			−0.661892			−0.330946	+	0.943650i	$0.607368\pi$
$90$		0			0
$91$	3.39033			0.355403
$92$		0			0
$93$	−0.424622	+	1.76005i	−0.0440313	+	0.182508i
$94$		0			0
$95$	4.85532	+	8.40965i	0.498145	+	0.862812i
$96$		0			0
$97$	−5.02469	+	8.70302i	−0.510180	+	0.883658i	0.489750	+	0.871863i	$0.337088\pi$
$97$	−5.02469	+	8.70302i	−0.510180	+	0.883658i	−0.999930	+	0.0117950i	$0.996245\pi$
$98$		0			0
$99$	2.53551	+	1.29902i	0.254828	+	0.130557i
$100$		0			0
$101$	−8.20845	+	14.2175i	−0.816771	+	1.41469i	0.0912778	+	0.995825i	$0.470905\pi$
$101$	−8.20845	+	14.2175i	−0.816771	+	1.41469i	−0.908049	+	0.418864i	$0.862428\pi$
$102$		0			0
$103$	−2.67552	−	4.63414i	−0.263627	−	0.456615i	0.703576	−	0.710620i	$-0.251585\pi$
$103$	−2.67552	−	4.63414i	−0.263627	−	0.456615i	−0.967203	+	0.254005i	$0.918252\pi$
$104$		0			0
$105$	−2.12436	−	2.02044i	−0.207316	−	0.197175i
$106$		0			0
$107$	−17.6570			−1.70697			−0.853483	−	0.521120i	$-0.825514\pi$
$107$	−17.6570			−1.70697			−0.853483	+	0.521120i	$0.825514\pi$
$108$		0			0
$109$	17.8703			1.71167			0.855833	−	0.517253i	$-0.173045\pi$
$109$	17.8703			1.71167			0.855833	+	0.517253i	$0.173045\pi$
$110$		0			0
$111$	−9.06731	−	8.62376i	−0.860631	−	0.818531i
$112$		0			0
$113$	−9.32410	−	16.1498i	−0.877138	−	1.51925i	−0.854468	−	0.519504i	$-0.826117\pi$
$113$	−9.32410	−	16.1498i	−0.877138	−	1.51925i	−0.0226694	−	0.999743i	$-0.507217\pi$
$114$		0			0
$115$	−1.98546	+	3.43892i	−0.185145	+	0.320681i
$116$		0			0
$117$	−8.54242	+	5.52052i	−0.789747	+	0.510372i
$118$		0			0
$119$	−0.150339	+	0.260395i	−0.0137815	+	0.0238703i
$120$		0			0
$121$	5.04910	+	8.74529i	0.459009	+	0.795027i
$122$		0			0
$123$	2.08344	−	8.63581i	0.187858	−	0.778665i
$124$		0			0
$125$	12.0769			1.08019
$126$		0			0
$127$	1.35333			0.120088			0.0600441	−	0.998196i	$-0.480876\pi$
$127$	1.35333			0.120088			0.0600441	+	0.998196i	$0.480876\pi$
$128$		0			0
$129$	−17.4753	+	5.15529i	−1.53862	+	0.453898i
$130$		0			0
$131$	9.47827	+	16.4168i	0.828120	+	1.43435i	0.899511	+	0.436898i	$0.143923\pi$
$131$	9.47827	+	16.4168i	0.828120	+	1.43435i	−0.0713904	+	0.997448i	$0.522744\pi$
$132$		0			0
$133$	2.86849	−	4.96836i	0.248729	−	0.430812i
$134$		0			0
$135$	8.64254	+	1.63167i	0.743831	+	0.140431i
$136$		0			0
$137$	1.91299	−	3.31339i	0.163438	−	0.283082i	−0.772662	−	0.634818i	$-0.781075\pi$
$137$	1.91299	−	3.31339i	0.163438	−	0.283082i	0.936099	+	0.351736i	$0.114408\pi$
$138$		0			0
$139$	−11.2538	−	19.4921i	−0.954532	−	1.65330i	−0.735435	−	0.677595i	$-0.763022\pi$
$139$	−11.2538	−	19.4921i	−0.954532	−	1.65330i	−0.219097	−	0.975703i	$-0.570311\pi$
$140$		0			0
$141$	10.7734	−	3.17818i	0.907283	−	0.267651i
$142$		0			0
$143$	3.21957			0.269234
$144$		0			0
$145$	3.45178			0.286654
$146$		0			0
$147$	−0.406213	+	1.68374i	−0.0335039	+	0.138873i
$148$		0			0
$149$	−11.0505	−	19.1400i	−0.905291	−	1.56801i	−0.820527	−	0.571608i	$-0.806320\pi$
$149$	−11.0505	−	19.1400i	−0.905291	−	1.56801i	−0.0847640	−	0.996401i	$-0.527014\pi$
$150$		0			0
$151$	−2.57417	+	4.45859i	−0.209483	+	0.362835i	−0.951552	−	0.307489i	$-0.900511\pi$
$151$	−2.57417	+	4.45859i	−0.209483	+	0.362835i	0.742069	+	0.670323i	$0.233845\pi$
$152$		0			0
$153$	−0.0452036	−	0.900900i	−0.00365449	−	0.0728335i
$154$		0			0
$155$	0.884674	−	1.53230i	0.0710587	−	0.123077i
$156$		0			0
$157$	1.81812	+	3.14908i	0.145102	+	0.251324i	0.929411	−	0.369047i	$-0.120316\pi$
$157$	1.81812	+	3.14908i	0.145102	+	0.251324i	−0.784309	+	0.620370i	$0.786982\pi$
$158$		0			0
$159$	−2.34072	−	2.22622i	−0.185631	−	0.176551i
$160$		0			0
$161$	2.34600			0.184890
$162$		0			0
$163$	−5.18207			−0.405891			−0.202945	−	0.979190i	$-0.565051\pi$
$163$	−5.18207			−0.405891			−0.202945	+	0.979190i	$0.565051\pi$
$164$		0			0
$165$	−2.01737	−	1.91868i	−0.157052	−	0.149369i
$166$		0			0
$167$	−8.17010	−	14.1510i	−0.632221	−	1.09504i	−0.987097	−	0.160125i	$-0.948810\pi$
$167$	−8.17010	−	14.1510i	−0.632221	−	1.09504i	0.354876	−	0.934913i	$-0.384523\pi$
$168$		0			0
$169$	0.752836	−	1.30395i	0.0579105	−	0.100304i
$170$		0			0
$171$	0.862490	+	17.1893i	0.0659563	+	1.31450i
$172$		0			0
$173$	8.29892	−	14.3741i	0.630955	−	1.09285i	−0.356402	−	0.934333i	$-0.615997\pi$
$173$	8.29892	−	14.3741i	0.630955	−	1.09285i	0.987357	−	0.158513i	$-0.0506701\pi$
$174$		0			0
$175$	−1.06748	−	1.84894i	−0.0806942	−	0.139767i
$176$		0			0
$177$	3.62502	−	15.0256i	0.272474	−	1.12940i
$178$		0			0
$179$	3.35959			0.251107			0.125554	−	0.992087i	$-0.459929\pi$
$179$	3.35959			0.251107			0.125554	+	0.992087i	$0.459929\pi$
$180$		0			0
$181$	12.9906			0.965580			0.482790	−	0.875736i	$-0.339623\pi$
$181$	12.9906			0.965580			0.482790	+	0.875736i	$0.339623\pi$
$182$		0			0
$183$	0.851158	−	0.251094i	0.0629194	−	0.0185614i
$184$		0			0
$185$	6.11434	+	10.5903i	0.449535	+	0.778618i
$186$		0			0
$187$	−0.142767	+	0.247280i	−0.0104402	+	0.0180829i
$188$		0			0
$189$	−1.71815	−	4.90387i	−0.124977	−	0.356704i
$190$		0			0
$191$	0.422193	−	0.731260i	0.0305488	−	0.0529121i	−0.850347	−	0.526223i	$-0.823608\pi$
$191$	0.422193	−	0.731260i	0.0305488	−	0.0529121i	0.880896	+	0.473311i	$0.156941\pi$
$192$		0			0
$193$	−3.12679	−	5.41576i	−0.225071	−	0.389835i	0.731270	−	0.682089i	$-0.238928\pi$
$193$	−3.12679	−	5.41576i	−0.225071	−	0.389835i	−0.956341	+	0.292254i	$0.905595\pi$
$194$		0			0
$195$	9.53338	−	2.81238i	0.682700	−	0.201399i
$196$		0			0
$197$	13.4213			0.956228			0.478114	−	0.878298i	$-0.341321\pi$
$197$	13.4213			0.956228			0.478114	+	0.878298i	$0.341321\pi$
$198$		0			0
$199$	1.86503			0.132209			0.0661043	−	0.997813i	$-0.478943\pi$
$199$	1.86503			0.132209			0.0661043	+	0.997813i	$0.478943\pi$
$200$		0			0
$201$	−5.38798	+	22.3330i	−0.380039	+	1.57525i
$202$		0			0
$203$	−1.01964	−	1.76607i	−0.0715649	−	0.123954i
$204$		0			0
$205$	−4.34072	+	7.51835i	−0.303169	+	0.525104i
$206$		0			0
$207$	−5.91107	+	3.82001i	−0.410848	+	0.265509i
$208$		0			0
$209$	2.72401	−	4.71813i	0.188424	−	0.326360i
$210$		0			0
$211$	4.03008	+	6.98030i	0.277442	+	0.480544i	0.970748	−	0.240099i	$-0.0771800\pi$
$211$	4.03008	+	6.98030i	0.277442	+	0.480544i	−0.693306	+	0.720643i	$0.743847\pi$
$212$		0			0
$213$	6.33093	+	6.02123i	0.433788	+	0.412568i
$214$		0			0
$215$	17.8053			1.21431
$216$		0			0
$217$	−1.04532			−0.0709608
$218$		0			0
$219$	1.99589	+	1.89825i	0.134869	+	0.128272i
$220$		0			0
$221$	−0.509698	−	0.882824i	−0.0342860	−	0.0593851i
$222$		0			0
$223$	−7.79085	+	13.4941i	−0.521714	+	0.903635i	0.477967	+	0.878378i	$0.341374\pi$
$223$	−7.79085	+	13.4941i	−0.521714	+	0.903635i	−0.999681	+	0.0252571i	$0.991960\pi$
$224$		0			0
$225$	5.70033	+	2.92046i	0.380022	+	0.194697i
$226$		0			0
$227$	−9.11891	+	15.7944i	−0.605244	+	1.04831i	0.386769	+	0.922176i	$0.373591\pi$
$227$	−9.11891	+	15.7944i	−0.605244	+	1.04831i	−0.992013	+	0.126136i	$0.959742\pi$
$228$		0			0
$229$	−8.54576	−	14.8017i	−0.564719	−	0.978123i	−0.997076	−	0.0764200i	$-0.975651\pi$
$229$	−8.54576	−	14.8017i	−0.564719	−	0.978123i	0.432356	−	0.901703i	$-0.357682\pi$
$230$		0			0
$231$	−0.385754	+	1.59894i	−0.0253808	+	0.105203i
$232$		0			0
$233$	−13.8882			−0.909843			−0.454922	−	0.890531i	$-0.650333\pi$
$233$	−13.8882			−0.909843			−0.454922	+	0.890531i	$0.650333\pi$
$234$		0			0
$235$	−10.9768			−0.716049
$236$		0			0
$237$	21.3727	−	6.30501i	1.38830	−	0.409555i
$238$		0			0
$239$	6.79464	+	11.7687i	0.439509	+	0.761252i	0.997652	−	0.0684931i	$-0.0218191\pi$
$239$	6.79464	+	11.7687i	0.439509	+	0.761252i	−0.558143	+	0.829745i	$0.688486\pi$
$240$		0			0
$241$	−7.31780	+	12.6748i	−0.471381	+	0.816455i	−0.999464	−	0.0327373i	$-0.989578\pi$
$241$	−7.31780	+	12.6748i	−0.471381	+	0.816455i	0.528083	+	0.849193i	$0.322911\pi$
$242$		0			0
$243$	12.3142	+	9.55832i	0.789953	+	0.613167i
$244$		0			0
$245$	0.846320	−	1.46587i	0.0540694	−	0.0936510i
$246$		0			0
$247$	9.72511	+	16.8444i	0.618794	+	1.07178i
$248$		0			0
$249$	6.59402	−	1.94526i	0.417879	−	0.123276i
$250$		0			0
$251$	−23.6805			−1.49470			−0.747351	−	0.664429i	$-0.768675\pi$
$251$	−23.6805			−1.49470			−0.747351	+	0.664429i	$0.768675\pi$
$252$		0			0
$253$	2.22784			0.140063
$254$		0			0
$255$	−0.206738	+	0.856923i	−0.0129464	+	0.0536626i
$256$		0			0
$257$	−6.08965	−	10.5476i	−0.379862	−	0.657940i	0.611180	−	0.791492i	$-0.290695\pi$
$257$	−6.08965	−	10.5476i	−0.379862	−	0.657940i	−0.991042	+	0.133551i	$0.957362\pi$
$258$		0			0
$259$	3.61231	−	6.25670i	0.224458	−	0.388773i
$260$		0			0
$261$	5.44485	+	2.78957i	0.337028	+	0.172670i
$262$		0			0
$263$	11.4729	−	19.8716i	0.707449	−	1.22534i	−0.258351	−	0.966051i	$-0.583179\pi$
$263$	11.4729	−	19.8716i	0.707449	−	1.22534i	0.965800	−	0.259287i	$-0.0834876\pi$
$264$		0			0
$265$	1.57841	+	2.73389i	0.0969612	+	0.167942i
$266$		0			0
$267$	7.83693	+	7.45356i	0.479612	+	0.456151i
$268$		0			0
$269$	30.5332			1.86164			0.930821	−	0.365476i	$-0.119094\pi$
$269$	30.5332			1.86164			0.930821	+	0.365476i	$0.119094\pi$
$270$		0			0
$271$	−5.13773			−0.312095			−0.156048	−	0.987750i	$-0.549875\pi$
$271$	−5.13773			−0.312095			−0.156048	+	0.987750i	$0.549875\pi$
$272$		0			0
$273$	−4.25506	−	4.04691i	−0.257528	−	0.244930i
$274$		0			0
$275$	−1.01372	−	1.75581i	−0.0611296	−	0.105880i
$276$		0			0
$277$	4.33632	−	7.51073i	0.260544	−	0.451276i	−0.705842	−	0.708369i	$-0.749431\pi$
$277$	4.33632	−	7.51073i	0.260544	−	0.451276i	0.966387	+	0.257093i	$0.0827646\pi$
$278$		0			0
$279$	2.63383	−	1.70210i	0.157683	−	0.101902i
$280$		0			0
$281$	2.69818	−	4.67339i	0.160960	−	0.278791i	−0.774253	−	0.632876i	$-0.781874\pi$
$281$	2.69818	−	4.67339i	0.160960	−	0.278791i	0.935213	+	0.354085i	$0.115208\pi$
$282$		0			0
$283$	−7.58933	−	13.1451i	−0.451139	−	0.781395i	0.547318	−	0.836924i	$-0.315649\pi$
$283$	−7.58933	−	13.1451i	−0.451139	−	0.781395i	−0.998457	+	0.0555294i	$0.982315\pi$
$284$		0			0
$285$	3.94459	−	16.3502i	0.233657	−	0.968503i
$286$		0			0
$287$	5.12894			0.302751
$288$		0			0
$289$	−16.9096			−0.994682
$290$		0			0
$291$	16.6947	−	4.92500i	0.978663	−	0.288709i
$292$		0			0
$293$	−10.7029	−	18.5380i	−0.625270	−	1.08300i	−0.988489	−	0.151295i	$-0.951656\pi$
$293$	−10.7029	−	18.5380i	−0.625270	−	1.08300i	0.363219	−	0.931704i	$-0.381678\pi$
$294$		0			0
$295$	−7.55251	+	13.0813i	−0.439724	+	0.761625i
$296$		0			0
$297$	−1.63161	−	4.65688i	−0.0946757	−	0.270220i
$298$		0			0
$299$	−3.97685	+	6.88810i	−0.229987	+	0.398349i
$300$		0			0
$301$	−5.25963	−	9.10995i	−0.303160	−	0.525089i
$302$		0			0
$303$	27.2729	−	8.04560i	1.56679	−	0.462208i
$304$		0			0
$305$	−0.867230			−0.0496575
$306$		0			0
$307$	12.5259			0.714893			0.357447	−	0.933934i	$-0.383647\pi$
$307$	12.5259			0.714893			0.357447	+	0.933934i	$0.383647\pi$
$308$		0			0
$309$	−2.17367	+	9.00978i	−0.123656	+	0.512549i
$310$		0			0
$311$	−4.30243	−	7.45202i	−0.243968	−	0.422565i	0.717873	−	0.696174i	$-0.245116\pi$
$311$	−4.30243	−	7.45202i	−0.243968	−	0.422565i	−0.961841	+	0.273609i	$0.911783\pi$
$312$		0			0
$313$	6.70560	−	11.6144i	0.379023	−	0.656487i	−0.611897	−	0.790937i	$-0.709593\pi$
$313$	6.70560	−	11.6144i	0.379023	−	0.656487i	0.990920	+	0.134450i	$0.0429268\pi$
$314$		0			0
$315$	0.254470	+	5.07154i	0.0143377	+	0.285749i
$316$		0			0
$317$	5.65753	−	9.79913i	0.317759	−	0.550374i	−0.662261	−	0.749273i	$-0.730403\pi$
$317$	5.65753	−	9.79913i	0.317759	−	0.550374i	0.980020	+	0.198899i	$0.0637365\pi$
$318$		0			0
$319$	−0.968287	−	1.67712i	−0.0542137	−	0.0939008i
$320$		0			0
$321$	22.1605	+	21.0765i	1.23688	+	1.17638i
$322$		0			0
$323$	−1.72498			−0.0959805
$324$		0			0
$325$	7.23825			0.401506
$326$		0			0
$327$	−22.4283	−	21.3311i	−1.24029	−	1.17961i
$328$		0			0
$329$	3.24251	+	5.61620i	0.178766	+	0.309631i
$330$		0			0
$331$	−14.1119	+	24.4426i	−0.775662	+	1.34349i	0.158760	+	0.987317i	$0.449250\pi$
$331$	−14.1119	+	24.4426i	−0.775662	+	1.34349i	−0.934422	+	0.356169i	$0.884083\pi$
$332$		0			0
$333$	1.08614	+	21.6466i	0.0595202	+	1.18623i
$334$		0			0
$335$	11.2255	−	19.4432i	0.613315	−	1.06229i
$336$		0			0
$337$	−7.44257	−	12.8909i	−0.405423	−	0.702213i	0.588948	−	0.808171i	$-0.299542\pi$
$337$	−7.44257	−	12.8909i	−0.405423	−	0.702213i	−0.994371	+	0.105958i	$0.966209\pi$
$338$		0			0
$339$	−7.57515	+	31.3988i	−0.411426	+	1.70535i
$340$		0			0
$341$	−0.992670			−0.0537561
$342$		0			0
$343$	−1.00000			−0.0539949
$344$		0			0
$345$	6.59679	−	1.94607i	0.355159	−	0.104773i
$346$		0			0
$347$	6.54418	+	11.3348i	0.351310	+	0.608486i	0.986479	−	0.163886i	$-0.0524031\pi$
$347$	6.54418	+	11.3348i	0.351310	+	0.608486i	−0.635169	+	0.772373i	$0.719070\pi$
$348$		0			0
$349$	−15.2633	+	26.4367i	−0.817023	+	1.41513i	0.0908426	+	0.995865i	$0.471044\pi$
$349$	−15.2633	+	26.4367i	−0.817023	+	1.41513i	−0.907866	+	0.419261i	$0.862289\pi$
$350$		0			0
$351$	17.3109	+	3.26820i	0.923985	+	0.174444i
$352$		0			0
$353$	3.80446	−	6.58951i	0.202491	−	0.350724i	−0.746840	−	0.665004i	$-0.768430\pi$
$353$	3.80446	−	6.58951i	0.202491	−	0.350724i	0.949330	+	0.314280i	$0.101763\pi$
$354$		0			0
$355$	−4.26912	−	7.39433i	−0.226581	−	0.392450i
$356$		0			0
$357$	0.499507	−	0.147356i	0.0264367	−	0.00779892i
$358$		0			0
$359$	1.99575			0.105332			0.0526658	−	0.998612i	$-0.483228\pi$
$359$	1.99575			0.105332			0.0526658	+	0.998612i	$0.483228\pi$
$360$		0			0
$361$	13.9129			0.732256
$362$		0			0
$363$	4.10202	−	17.0028i	0.215300	−	0.892414i
$364$		0			0
$365$	−1.34588	−	2.33114i	−0.0704467	−	0.122017i
$366$		0			0
$367$	5.86262	−	10.1544i	0.306026	−	0.530053i	−0.671463	−	0.741038i	$-0.734334\pi$
$367$	5.86262	−	10.1544i	0.306026	−	0.530053i	0.977489	+	0.210985i	$0.0676671\pi$
$368$		0			0
$369$	−12.9231	+	8.35151i	−0.672749	+	0.434762i
$370$		0			0
$371$	0.932516	−	1.61516i	0.0484138	−	0.0838552i
$372$		0			0
$373$	6.36135	+	11.0182i	0.329378	+	0.570500i	0.982389	−	0.186849i	$-0.0598276\pi$
$373$	6.36135	+	11.0182i	0.329378	+	0.570500i	−0.653010	+	0.757349i	$0.726494\pi$
$374$		0			0
$375$	−15.1572	−	14.4158i	−0.782717	−	0.744428i
$376$		0			0
$377$	6.91385			0.356081
$378$		0			0
$379$	0.751468			0.0386003			0.0193002	−	0.999814i	$-0.493856\pi$
$379$	0.751468			0.0386003			0.0193002	+	0.999814i	$0.493856\pi$
$380$		0			0
$381$	−1.69850	−	1.61542i	−0.0870169	−	0.0827602i
$382$		0			0
$383$	6.65501	+	11.5268i	0.340055	+	0.588993i	0.984443	−	0.175706i	$-0.0562210\pi$
$383$	6.65501	+	11.5268i	0.340055	+	0.588993i	−0.644388	+	0.764699i	$0.722888\pi$
$384$		0			0
$385$	0.803694	−	1.39204i	0.0409601	−	0.0709449i
$386$		0			0
$387$	28.0862	+	14.3895i	1.42770	+	0.731459i
$388$		0			0
$389$	−3.15954	+	5.47249i	−0.160195	+	0.277466i	−0.934939	−	0.354809i	$-0.884546\pi$
$389$	−3.15954	+	5.47249i	−0.160195	+	0.277466i	0.774743	+	0.632276i	$0.217879\pi$
$390$		0			0
$391$	−0.352695	−	0.610885i	−0.0178365	−	0.0308938i
$392$		0			0
$393$	7.70040	−	31.9180i	0.388434	−	1.61005i
$394$		0			0
$395$	−21.7763			−1.09568
$396$		0			0
$397$	−18.0085			−0.903823			−0.451911	−	0.892063i	$-0.649258\pi$
$397$	−18.0085			−0.903823			−0.451911	+	0.892063i	$0.649258\pi$
$398$		0			0
$399$	−9.53067	+	2.81158i	−0.477130	+	0.140755i
$400$		0			0
$401$	−12.5907	−	21.8077i	−0.628747	−	1.08902i	−0.987803	−	0.155706i	$-0.950235\pi$
$401$	−12.5907	−	21.8077i	−0.628747	−	1.08902i	0.359056	−	0.933316i	$-0.383099\pi$
$402$		0			0
$403$	1.77199	−	3.06917i	0.0882689	−	0.152886i
$404$		0			0
$405$	−8.89923	−	12.3641i	−0.442206	−	0.614378i
$406$		0			0
$407$	3.43037	−	5.94158i	0.170037	−	0.294513i
$408$		0			0
$409$	−13.9660	−	24.1898i	−0.690574	−	1.19611i	−0.971650	−	0.236424i	$-0.924025\pi$
$409$	−13.9660	−	24.1898i	−0.690574	−	1.19611i	0.281076	−	0.959685i	$-0.409309\pi$
$410$		0			0
$411$	−6.35598	+	1.87504i	−0.313517	+	0.0924887i
$412$		0			0
$413$	8.92394			0.439118
$414$		0			0
$415$	−6.71853			−0.329800
$416$		0			0
$417$	−9.14286	+	37.8969i	−0.447728	+	1.85582i
$418$		0			0
$419$	−17.2178	−	29.8221i	−0.841143	−	1.45690i	−0.888929	−	0.458045i	$-0.848550\pi$
$419$	−17.2178	−	29.8221i	−0.841143	−	1.45690i	0.0477860	−	0.998858i	$-0.484783\pi$
$420$		0			0
$421$	−17.7450	+	30.7352i	−0.864838	+	1.49794i	0.00236917	+	0.999997i	$0.499246\pi$
$421$	−17.7450	+	30.7352i	−0.864838	+	1.49794i	−0.867208	+	0.497947i	$0.834087\pi$
$422$		0			0
$423$	−17.3149	−	8.87099i	−0.841879	−	0.431322i
$424$		0			0
$425$	−0.320969	+	0.555934i	−0.0155693	+	0.0269668i
$426$		0			0
$427$	0.256177	+	0.443711i	0.0123973	+	0.0214727i
$428$		0			0
$429$	−4.04075	−	3.84308i	−0.195089	−	0.185546i
$430$		0			0
$431$	3.04684			0.146761			0.0733805	−	0.997304i	$-0.476621\pi$
$431$	3.04684			0.146761			0.0733805	+	0.997304i	$0.476621\pi$
$432$		0			0
$433$	−5.83630			−0.280475			−0.140237	−	0.990118i	$-0.544787\pi$
$433$	−5.83630			−0.280475			−0.140237	+	0.990118i	$0.544787\pi$
$434$		0			0
$435$	−4.33218	−	4.12026i	−0.207712	−	0.197551i
$436$		0			0
$437$	6.72946	+	11.6558i	0.321914	+	0.557571i
$438$		0			0
$439$	2.71733	−	4.70655i	0.129691	−	0.224632i	−0.793866	−	0.608093i	$-0.791935\pi$
$439$	2.71733	−	4.70655i	0.129691	−	0.224632i	0.923557	+	0.383461i	$0.125268\pi$
$440$		0			0
$441$	2.51964	−	1.62831i	0.119983	−	0.0775387i
$442$		0			0
$443$	8.95305	−	15.5071i	0.425372	−	0.736766i	−0.571083	−	0.820892i	$-0.693477\pi$
$443$	8.95305	−	15.5071i	0.425372	−	0.736766i	0.996455	+	0.0841262i	$0.0268099\pi$
$444$		0			0
$445$	−5.28466	−	9.15330i	−0.250517	−	0.433908i
$446$		0			0
$447$	−8.97771	+	37.2123i	−0.424631	+	1.76008i
$448$		0			0
$449$	−24.0642			−1.13566			−0.567830	−	0.823146i	$-0.692217\pi$
$449$	−24.0642			−1.13566			−0.567830	+	0.823146i	$0.692217\pi$
$450$		0			0
$451$	4.87061			0.229348
$452$		0			0
$453$	8.55278	−	2.52310i	0.401844	−	0.118545i
$454$		0			0
$455$	2.86930	+	4.96978i	0.134515	+	0.232987i
$456$		0			0
$457$	−9.35657	+	16.2061i	−0.437682	+	0.758087i	−0.997510	−	0.0705212i	$-0.977534\pi$
$457$	−9.35657	+	16.2061i	−0.437682	+	0.758087i	0.559828	+	0.828609i	$0.310867\pi$
$458$		0			0
$459$	−1.01864	+	1.18464i	−0.0475459	+	0.0552942i
$460$		0			0
$461$	−20.1590	+	34.9164i	−0.938897	+	1.62622i	−0.171364	+	0.985208i	$0.554817\pi$
$461$	−20.1590	+	34.9164i	−0.938897	+	1.62622i	−0.767533	+	0.641010i	$0.778516\pi$
$462$		0			0
$463$	16.0903	+	27.8691i	0.747778	+	1.29519i	0.948886	+	0.315620i	$0.102212\pi$
$463$	16.0903	+	27.8691i	0.747778	+	1.29519i	−0.201108	+	0.979569i	$0.564454\pi$
$464$		0			0
$465$	−2.93937	+	0.867122i	−0.136310	+	0.0402118i
$466$		0			0
$467$	−2.33670			−0.108129			−0.0540647	−	0.998537i	$-0.517218\pi$
$467$	−2.33670			−0.108129			−0.0540647	+	0.998537i	$0.517218\pi$
$468$		0			0
$469$	−13.2639			−0.612470
$470$		0			0
$471$	1.47709	−	6.12250i	0.0680607	−	0.282110i
$472$		0			0
$473$	−4.99473	−	8.65112i	−0.229658	−	0.397779i
$474$		0			0
$475$	6.12413	−	10.6073i	0.280994	−	0.486696i
$476$		0			0
$477$	0.280387	+	5.58806i	0.0128380	+	0.255860i
$478$		0			0
$479$	20.7517	−	35.9430i	0.948169	−	1.64228i	0.198889	−	0.980022i	$-0.436267\pi$
$479$	20.7517	−	35.9430i	0.948169	−	1.64228i	0.749279	−	0.662254i	$-0.230400\pi$
$480$		0			0
$481$	12.2469	+	21.2123i	0.558411	+	0.967197i
$482$		0			0
$483$	−2.94436	−	2.80033i	−0.133973	−	0.127419i
$484$		0			0
$485$	−17.0100			−0.772384
$486$		0			0
$487$	−29.1835			−1.32243			−0.661216	−	0.750195i	$-0.729959\pi$
$487$	−29.1835			−1.32243			−0.661216	+	0.750195i	$0.729959\pi$
$488$		0			0
$489$	6.50379	+	6.18564i	0.294112	+	0.279724i
$490$		0			0
$491$	−16.8729	−	29.2248i	−0.761465	−	1.31890i	−0.942095	−	0.335346i	$-0.891147\pi$
$491$	−16.8729	−	29.2248i	−0.761465	−	1.31890i	0.180630	−	0.983551i	$-0.442186\pi$
$492$		0			0
$493$	−0.306584	+	0.531019i	−0.0138078	+	0.0239159i
$494$		0			0
$495$	0.241653	+	4.81611i	0.0108615	+	0.216468i
$496$		0			0
$497$	−2.52217	+	4.36852i	−0.113135	+	0.195955i
$498$		0			0
$499$	14.5193	+	25.1481i	0.649972	+	1.12578i	0.983129	+	0.182913i	$0.0585525\pi$
$499$	14.5193	+	25.1481i	0.649972	+	1.12578i	−0.333158	+	0.942871i	$0.608114\pi$
$500$		0			0
$501$	−6.63760	+	27.5127i	−0.296546	+	1.22918i
$502$		0			0
$503$	−23.1322			−1.03141			−0.515707	−	0.856765i	$-0.672471\pi$
$503$	−23.1322			−1.03141			−0.515707	+	0.856765i	$0.672471\pi$
$504$		0			0
$505$	−27.7879			−1.23655
$506$		0			0
$507$	−2.50133	+	0.737900i	−0.111088	+	0.0327713i
$508$		0			0
$509$	12.6431	+	21.8986i	0.560398	+	0.970637i	0.997462	+	0.0712068i	$0.0226850\pi$
$509$	12.6431	+	21.8986i	0.560398	+	0.970637i	−0.437064	+	0.899430i	$0.643982\pi$
$510$		0			0
$511$	−0.795137	+	1.37722i	−0.0351748	+	0.0609245i
$512$		0			0
$513$	19.4357	−	22.6031i	0.858109	−	0.997950i
$514$		0			0
$515$	4.52870	−	7.84393i	0.199558	−	0.345645i
$516$		0			0
$517$	3.07920	+	5.33333i	0.135423	+	0.234560i
$518$		0			0
$519$	−27.5735	+	8.13427i	−1.21034	+	0.357055i
$520$		0			0
$521$	26.1095			1.14388			0.571939	−	0.820296i	$-0.306191\pi$
$521$	26.1095			1.14388			0.571939	+	0.820296i	$0.306191\pi$
$522$		0			0
$523$	−7.58463			−0.331653			−0.165826	−	0.986155i	$-0.553029\pi$
$523$	−7.58463			−0.331653			−0.165826	+	0.986155i	$0.553029\pi$
$524$		0			0
$525$	−0.867253	+	3.59474i	−0.0378500	+	0.156887i
$526$		0			0
$527$	0.157152	+	0.272195i	0.00684565	+	0.0118570i
$528$		0			0
$529$	8.74815	−	15.1522i	0.380354	−	0.658793i
$530$		0			0
$531$	−22.4851	+	14.5310i	−0.975772	+	0.630590i
$532$		0			0
$533$	−8.69439	+	15.0591i	−0.376596	+	0.652283i
$534$		0			0
$535$	−14.9435	−	25.8829i	−0.646063	−	1.11901i
$536$		0			0
$537$	−4.21648	−	4.01021i	−0.181954	−	0.173054i
$538$		0			0
$539$	−0.949634			−0.0409036
$540$		0			0
$541$	−28.0683			−1.20675			−0.603375	−	0.797458i	$-0.706178\pi$
$541$	−28.0683			−1.20675			−0.603375	+	0.797458i	$0.706178\pi$
$542$		0			0
$543$	−16.3039	−	15.5063i	−0.699667	−	0.665441i
$544$		0			0
$545$	15.1240	+	26.1955i	0.647841	+	1.12209i
$546$		0			0
$547$	12.1404	−	21.0277i	0.519084	−	0.899080i	−0.480670	−	0.876902i	$-0.659606\pi$
$547$	12.1404	−	21.0277i	0.519084	−	0.899080i	0.999754	−	0.0221785i	$-0.00706023\pi$
$548$		0			0
$549$	−1.36797	−	0.700858i	−0.0583837	−	0.0299119i
$550$		0			0
$551$	5.84966	−	10.1319i	0.249204	−	0.431634i
$552$		0			0
$553$	6.43263	+	11.1416i	0.273543	+	0.473791i
$554$		0			0
$555$	4.96745	−	20.5900i	0.210857	−	0.873995i
$556$		0			0
$557$	−25.7678			−1.09182			−0.545909	−	0.837844i	$-0.683816\pi$
$557$	−25.7678			−1.09182			−0.545909	+	0.837844i	$0.683816\pi$
$558$		0			0
$559$	35.6638			1.50842
$560$		0			0
$561$	0.474349	−	0.139935i	0.0200270	−	0.00590804i
$562$		0			0
$563$	−0.0281457	−	0.0487497i	−0.00118620	−	0.00205456i	0.865432	−	0.501027i	$-0.167044\pi$
$563$	−0.0281457	−	0.0487497i	−0.00118620	−	0.00205456i	−0.866618	+	0.498972i	$0.833711\pi$
$564$		0			0
$565$	15.7823	−	27.3358i	0.663968	−	1.15003i
$566$		0			0
$567$	−3.69720	+	8.20553i	−0.155268	+	0.344600i
$568$		0			0
$569$	−16.7575	+	29.0248i	−0.702510	+	1.21678i	0.265072	+	0.964229i	$0.414604\pi$
$569$	−16.7575	+	29.0248i	−0.702510	+	1.21678i	−0.967582	+	0.252555i	$0.918729\pi$
$570$		0			0
$571$	−11.1923	−	19.3856i	−0.468382	−	0.811261i	0.530965	−	0.847393i	$-0.321829\pi$
$571$	−11.1923	−	19.3856i	−0.468382	−	0.811261i	−0.999347	+	0.0361328i	$0.988496\pi$
$572$		0			0
$573$	−1.40276	+	0.413817i	−0.0586009	+	0.0172875i
$574$		0			0
$575$	5.00863			0.208874
$576$		0			0
$577$	15.4029			0.641231			0.320615	−	0.947210i	$-0.396110\pi$
$577$	15.4029			0.641231			0.320615	+	0.947210i	$0.396110\pi$
$578$		0			0
$579$	−2.54029	+	10.5294i	−0.105571	+	0.437588i
$580$		0			0
$581$	1.98463	+	3.43748i	0.0823363	+	0.142611i
$582$		0			0
$583$	0.885549	−	1.53382i	0.0366757	−	0.0635241i
$584$		0			0
$585$	−15.3220	−	7.84994i	−0.633486	−	0.324555i
$586$		0			0
$587$	6.58418	−	11.4041i	0.271758	−	0.470699i	−0.697554	−	0.716532i	$-0.745728\pi$
$587$	6.58418	−	11.4041i	0.271758	−	0.470699i	0.969312	+	0.245833i	$0.0790615\pi$
$588$		0			0
$589$	−2.99848	−	5.19352i	−0.123550	−	0.213995i
$590$		0			0
$591$	−16.8445	−	16.0205i	−0.692890	−	0.658995i
$592$		0			0
$593$	8.87156			0.364311			0.182156	−	0.983270i	$-0.441693\pi$
$593$	8.87156			0.364311			0.182156	+	0.983270i	$0.441693\pi$
$594$		0			0
$595$	−0.508939			−0.0208645
$596$		0			0
$597$	−2.34072	−	2.22622i	−0.0957994	−	0.0911130i
$598$		0			0
$599$	23.1000	+	40.0103i	0.943839	+	1.63478i	0.758058	+	0.652187i	$0.226148\pi$
$599$	23.1000	+	40.0103i	0.943839	+	1.63478i	0.185781	+	0.982591i	$0.440519\pi$
$600$		0			0
$601$	−12.7492	+	22.0822i	−0.520049	+	0.900751i	0.479680	+	0.877444i	$0.340753\pi$
$601$	−12.7492	+	22.0822i	−0.520049	+	0.900751i	−0.999728	+	0.0233072i	$0.992580\pi$
$602$		0			0
$603$	33.4203	−	21.5978i	1.36098	−	0.879530i
$604$		0			0
$605$	−8.54631	+	14.8026i	−0.347457	+	0.601813i
$606$		0			0
$607$	7.09153	+	12.2829i	0.287836	+	0.498547i	0.973293	−	0.229566i	$-0.0737308\pi$
$607$	7.09153	+	12.2829i	0.287836	+	0.498547i	−0.685457	+	0.728113i	$0.740397\pi$
$608$		0			0
$609$	−0.828385	+	3.43363i	−0.0335678	+	0.139138i
$610$		0			0
$611$	−21.9864			−0.889473
$612$		0			0
$613$	35.4110			1.43024			0.715118	−	0.699004i	$-0.246373\pi$
$613$	35.4110			1.43024			0.715118	+	0.699004i	$0.246373\pi$
$614$		0			0
$615$	14.4222	−	4.25461i	0.581560	−	0.171562i
$616$		0			0
$617$	14.0185	+	24.2808i	0.564365	+	0.977508i	0.997108	+	0.0759913i	$0.0242121\pi$
$617$	14.0185	+	24.2808i	0.564365	+	0.977508i	−0.432744	+	0.901517i	$0.642455\pi$
$618$		0			0
$619$	21.5834	−	37.3835i	0.867510	−	1.50257i	0.00297630	−	0.999996i	$-0.499053\pi$
$619$	21.5834	−	37.3835i	0.867510	−	1.50257i	0.864533	−	0.502575i	$-0.167614\pi$
$620$		0			0
$621$	11.9785	+	2.26149i	0.480682	+	0.0907503i
$622$		0			0
$623$	−3.12214	+	5.40770i	−0.125086	+	0.216655i
$624$		0			0
$625$	4.88353	+	8.45853i	0.195341	+	0.338341i
$626$		0			0
$627$	−9.05065	+	2.66997i	−0.361448	+	0.106628i
$628$		0			0
$629$	−2.17228			−0.0866146
$630$		0			0
$631$	−4.97939			−0.198226			−0.0991132	−	0.995076i	$-0.531601\pi$
$631$	−4.97939			−0.198226			−0.0991132	+	0.995076i	$0.531601\pi$
$632$		0			0
$633$	3.27414	−	13.5712i	0.130136	−	0.539408i
$634$		0			0
$635$	1.14535	+	1.98380i	0.0454517	+	0.0787247i
$636$		0			0
$637$	1.69516	−	2.93611i	0.0671649	−	0.116333i
$638$		0			0
$639$	−0.758360	−	15.1140i	−0.0300002	−	0.597900i
$640$		0			0
$641$	−6.30128	+	10.9141i	−0.248886	+	0.431083i	−0.963217	−	0.268725i	$-0.913398\pi$
$641$	−6.30128	+	10.9141i	−0.248886	+	0.431083i	0.714331	+	0.699808i	$0.246731\pi$
$642$		0			0
$643$	2.75433	+	4.77064i	0.108620	+	0.188136i	0.915212	−	0.402974i	$-0.132023\pi$
$643$	2.75433	+	4.77064i	0.108620	+	0.188136i	−0.806591	+	0.591110i	$0.798690\pi$
$644$		0			0
$645$	−22.3467	−	21.2536i	−0.879901	−	0.836858i
$646$		0			0
$647$	21.1617			0.831952			0.415976	−	0.909376i	$-0.363440\pi$
$647$	21.1617			0.831952			0.415976	+	0.909376i	$0.363440\pi$
$648$		0			0
$649$	8.47448			0.332652
$650$		0			0
$651$	1.31193	+	1.24776i	0.0514188	+	0.0489035i
$652$		0			0
$653$	−23.7703	−	41.1714i	−0.930205	−	1.61116i	−0.782969	−	0.622061i	$-0.786296\pi$
$653$	−23.7703	−	41.1714i	−0.930205	−	1.61116i	−0.147236	−	0.989101i	$-0.547038\pi$
$654$		0			0
$655$	−16.0433	+	27.7878i	−0.626864	+	1.08576i
$656$		0			0
$657$	−0.239080	−	4.76483i	−0.00932741	−	0.185894i
$658$		0			0
$659$	−7.27512	+	12.6009i	−0.283398	+	0.490860i	−0.972220	−	0.234071i	$-0.924795\pi$
$659$	−7.27512	+	12.6009i	−0.283398	+	0.490860i	0.688821	+	0.724931i	$0.258129\pi$
$660$		0			0
$661$	−14.0932	−	24.4102i	−0.548163	−	0.949446i	−0.998401	−	0.0565370i	$-0.981994\pi$
$661$	−14.0932	−	24.4102i	−0.548163	−	0.949446i	0.450238	−	0.892909i	$-0.351339\pi$
$662$		0			0
$663$	−0.414093	+	1.71640i	−0.0160820	+	0.0666595i
$664$		0			0
$665$	9.71063			0.376562
$666$		0			0
$667$	4.78415			0.185243
$668$		0			0
$669$	25.8854	−	7.63628i	1.00079	−	0.295236i
$670$		0			0
$671$	0.243274	+	0.421363i	0.00939150	+	0.0162666i
$672$		0			0
$673$	5.62630	−	9.74503i	0.216878	−	0.375643i	−0.736974	−	0.675921i	$-0.763746\pi$
$673$	5.62630	−	9.74503i	0.216878	−	0.375643i	0.953852	+	0.300278i	$0.0970793\pi$
$674$		0			0
$675$	−3.66819	−	10.4696i	−0.141189	−	0.402976i
$676$		0			0
$677$	−12.9436	+	22.4189i	−0.497462	+	0.861630i	−0.999996	−	0.00292776i	$-0.999068\pi$
$677$	−12.9436	+	22.4189i	−0.497462	+	0.861630i	0.502533	+	0.864558i	$0.332401\pi$
$678$		0			0
$679$	5.02469	+	8.70302i	0.192830	+	0.333991i
$680$		0			0
$681$	30.2980	−	8.93800i	1.16102	−	0.342505i
$682$		0			0
$683$	0.360573			0.0137970			0.00689848	−	0.999976i	$-0.497804\pi$
$683$	0.360573			0.0137970			0.00689848	+	0.999976i	$0.497804\pi$
$684$		0			0
$685$	6.47600			0.247435
$686$		0			0
$687$	−6.94280	+	28.7777i	−0.264884	+	1.09794i
$688$		0			0
$689$	3.16153	+	5.47594i	0.120445	+	0.208617i
$690$		0			0
$691$	3.99148	−	6.91345i	0.151843	−	0.263000i	−0.780062	−	0.625702i	$-0.784813\pi$
$691$	3.99148	−	6.91345i	0.151843	−	0.263000i	0.931905	+	0.362702i	$0.118146\pi$
$692$		0			0
$693$	2.39274	−	1.54630i	0.0908926	−	0.0587391i
$694$		0			0
$695$	19.0486	−	32.9931i	0.722554	−	1.25150i
$696$		0			0
$697$	−0.771079	−	1.33555i	−0.0292067	−	0.0505875i
$698$		0			0
$699$	17.4304	+	16.5778i	0.659279	+	0.627029i
$700$		0			0
$701$	18.9665			0.716355			0.358177	−	0.933654i	$-0.383398\pi$
$701$	18.9665			0.716355			0.358177	+	0.933654i	$0.383398\pi$
$702$		0			0
$703$	41.4474			1.56322
$704$		0			0
$705$	13.7765	+	13.1026i	0.518854	+	0.493473i
$706$		0			0
$707$	8.20845	+	14.2175i	0.308711	+	0.534702i
$708$		0			0
$709$	19.5152	−	33.8013i	0.732909	−	1.26944i	−0.222726	−	0.974881i	$-0.571496\pi$
$709$	19.5152	−	33.8013i	0.732909	−	1.26944i	0.955635	−	0.294554i	$-0.0951711\pi$
$710$		0			0
$711$	−34.3500	−	17.5986i	−1.28823	−	0.660000i
$712$		0			0
$713$	1.22616	−	2.12376i	0.0459199	−	0.0795356i
$714$		0			0
$715$	2.72479	+	4.71947i	0.101901	+	0.176498i
$716$		0			0
$717$	5.52015	−	22.8809i	0.206154	−	0.854502i
$718$		0			0
$719$	47.5157			1.77204			0.886018	−	0.463652i	$-0.153461\pi$
$719$	47.5157			1.77204			0.886018	+	0.463652i	$0.153461\pi$
$720$		0			0
$721$	−5.35104			−0.199283
$722$		0			0
$723$	24.3137	−	7.17262i	0.904236	−	0.266752i
$724$		0			0
$725$	−2.17690	−	3.77051i	−0.0808482	−	0.140033i
$726$		0			0
$727$	−14.1949	+	24.5863i	−0.526460	+	0.911856i	0.473064	+	0.881028i	$0.343148\pi$
$727$	−14.1949	+	24.5863i	−0.526460	+	0.911856i	−0.999525	+	0.0308282i	$0.990186\pi$
$728$		0			0
$729$	−4.04556	−	26.6952i	−0.149836	−	0.988711i
$730$		0			0
$731$	−1.58145	+	2.73916i	−0.0584922	+	0.101312i
$732$		0			0
$733$	−7.45675	−	12.9155i	−0.275422	−	0.477044i	0.694820	−	0.719184i	$-0.255484\pi$
$733$	−7.45675	−	12.9155i	−0.275422	−	0.477044i	−0.970241	+	0.242140i	$0.922151\pi$
$734$		0			0
$735$	−2.81193	+	0.829530i	−0.103720	+	0.0305977i
$736$		0			0
$737$	−12.5959			−0.463974
$738$		0			0
$739$	28.8731			1.06211			0.531057	−	0.847336i	$-0.321795\pi$
$739$	28.8731			1.06211			0.531057	+	0.847336i	$0.321795\pi$
$740$		0			0
$741$	7.90094	−	32.7492i	0.290248	−	1.20307i
$742$		0			0
$743$	−7.15034	−	12.3848i	−0.262320	−	0.454352i	0.704538	−	0.709667i	$-0.251154\pi$
$743$	−7.15034	−	12.3848i	−0.262320	−	0.454352i	−0.966858	+	0.255314i	$0.917821\pi$
$744$		0			0
$745$	18.7045	−	32.3971i	0.685279	−	1.18694i
$746$		0			0
$747$	−10.5978	−	5.42962i	−0.387755	−	0.198659i
$748$		0			0
$749$	−8.82850	+	15.2914i	−0.322586	+	0.558736i
$750$		0			0
$751$	15.8543	+	27.4605i	0.578532	+	1.00205i	0.995648	+	0.0931937i	$0.0297076\pi$
$751$	15.8543	+	27.4605i	0.578532	+	1.00205i	−0.417116	+	0.908853i	$0.636959\pi$
$752$		0			0
$753$	29.7204	+	28.2666i	1.08307	+	1.03009i
$754$		0			0
$755$	−8.71427			−0.317145
$756$		0			0
$757$	−13.3387			−0.484805			−0.242403	−	0.970176i	$-0.577935\pi$
$757$	−13.3387			−0.484805			−0.242403	+	0.970176i	$0.577935\pi$
$758$		0			0
$759$	−2.79606	−	2.65929i	−0.101491	−	0.0965260i
$760$		0			0
$761$	16.5303	+	28.6314i	0.599225	+	1.03789i	0.992936	+	0.118653i	$0.0378577\pi$
$761$	16.5303	+	28.6314i	0.599225	+	1.03789i	−0.393711	+	0.919234i	$0.628809\pi$
$762$		0			0
$763$	8.93515	−	15.4761i	0.323474	−	0.560274i
$764$		0			0
$765$	1.28235	−	0.828713i	0.0463633	−	0.0299622i
$766$		0			0
$767$	−15.1275	+	26.2017i	−0.546224	+	0.946088i
$768$		0			0
$769$	−8.61119	−	14.9150i	−0.310528	−	0.537850i	0.667949	−	0.744207i	$-0.267172\pi$
$769$	−8.61119	−	14.9150i	−0.310528	−	0.537850i	−0.978477	+	0.206357i	$0.933839\pi$
$770$		0			0
$771$	−4.94740	+	20.5068i	−0.178176	+	0.738535i
$772$		0			0
$773$	−0.753102			−0.0270872			−0.0135436	−	0.999908i	$-0.504311\pi$
$773$	−0.753102			−0.0270872			−0.0135436	+	0.999908i	$0.504311\pi$
$774$		0			0
$775$	−2.23172			−0.0801658
$776$		0			0
$777$	−12.0021	+	3.54064i	−0.430571	+	0.127020i
$778$		0			0
$779$	14.7123	+	25.4824i	0.527122	+	0.913002i
$780$		0			0
$781$	−2.39514	+	4.14850i	−0.0857047	+	0.148445i
$782$		0			0
$783$	−3.50379	−	10.0004i	−0.125215	−	0.357385i
$784$		0			0
$785$	−3.07742	+	5.33026i	−0.109838	+	0.190245i
$786$		0			0
$787$	21.1905	+	36.7031i	0.755360	+	1.30832i	0.945195	+	0.326506i	$0.105871\pi$
$787$	21.1905	+	36.7031i	0.755360	+	1.30832i	−0.189835	+	0.981816i	$0.560795\pi$
$788$		0			0
$789$	−38.1192	+	11.2453i	−1.35708	+	0.400343i
$790$		0			0
$791$	−18.6482			−0.663054
$792$		0			0
$793$	−1.73705			−0.0616844
$794$		0			0
$795$	1.28235	−	5.31529i	0.0454801	−	0.188514i
$796$		0			0
$797$	−0.893289	−	1.54722i	−0.0316419	−	0.0548054i	0.849771	−	0.527152i	$-0.176740\pi$
$797$	−0.893289	−	1.54722i	−0.0316419	−	0.0548054i	−0.881413	+	0.472347i	$0.843407\pi$
$798$		0			0
$799$	0.974952	−	1.68867i	0.0344913	−	0.0597407i
$800$		0			0
$801$	−0.938758	−	18.7093i	−0.0331694	−	0.661061i
$802$		0			0
$803$	−0.755089	+	1.30785i	−0.0266465	+	0.0461531i
$804$		0			0
$805$	1.98546	+	3.43892i	0.0699784	+	0.121206i
$806$		0			0
$807$	−38.3209	−	36.4463i	−1.34896	−	1.28297i
$808$		0			0
$809$	39.5870			1.39180			0.695902	−	0.718137i	$-0.255005\pi$
$809$	39.5870			1.39180			0.695902	+	0.718137i	$0.255005\pi$
$810$		0			0
$811$	28.8730			1.01387			0.506935	−	0.861984i	$-0.330778\pi$
$811$	28.8730			1.01387			0.506935	+	0.861984i	$0.330778\pi$
$812$		0			0
$813$	6.44815	+	6.13272i	0.226147	+	0.215084i
$814$		0			0
$815$	−4.38569	−	7.59623i	−0.153624	−	0.266084i
$816$		0			0
$817$	30.1744	−	52.2635i	1.05567	−	1.82847i
$818$		0			0
$819$	0.509698	+	10.1582i	0.0178103	+	0.354956i
$820$		0			0
$821$	8.72151	−	15.1061i	0.304383	−	0.527206i	−0.672741	−	0.739878i	$-0.734883\pi$
$821$	8.72151	−	15.1061i	0.304383	−	0.527206i	0.977124	+	0.212672i	$0.0682165\pi$
$822$		0			0
$823$	9.05386	+	15.6817i	0.315598	+	0.546631i	0.979564	−	0.201131i	$-0.0644616\pi$
$823$	9.05386	+	15.6817i	0.315598	+	0.546631i	−0.663967	+	0.747762i	$0.731128\pi$
$824$		0			0
$825$	−0.823573	+	3.41369i	−0.0286731	+	0.118849i
$826$		0			0
$827$	−12.3460			−0.429314			−0.214657	−	0.976689i	$-0.568863\pi$
$827$	−12.3460			−0.429314			−0.214657	+	0.976689i	$0.568863\pi$
$828$		0			0
$829$	−37.7766			−1.31203			−0.656017	−	0.754746i	$-0.727760\pi$
$829$	−37.7766			−1.31203			−0.656017	+	0.754746i	$0.727760\pi$
$830$		0			0
$831$	−14.4076	+	4.25029i	−0.499795	+	0.147441i
$832$		0			0
$833$	0.150339	+	0.260395i	0.00520894	+	0.00902214i
$834$		0			0
$835$	13.8290	−	23.9526i	0.478573	−	0.828914i
$836$		0			0
$837$	−5.33734	−	1.00766i	−0.184486	−	0.0348299i
$838$		0			0
$839$	−19.9004	+	34.4685i	−0.687038	+	1.18998i	0.285754	+	0.958303i	$0.407756\pi$
$839$	−19.9004	+	34.4685i	−0.687038	+	1.18998i	−0.972792	+	0.231681i	$0.925577\pi$
$840$		0			0
$841$	12.4207	+	21.5132i	0.428299	+	0.741835i
$842$		0			0
$843$	−8.96482	+	2.64465i	−0.308765	+	0.0910866i
$844$		0			0
$845$	2.54856			0.0876732
$846$		0			0
$847$	10.0982			0.346978
$848$		0			0
$849$	−6.16577	+	25.5570i	−0.211609	+	0.877112i
$850$		0			0
$851$	8.47446	+	14.6782i	0.290501	+	0.503162i
$852$		0			0
$853$	−8.82985	+	15.2937i	−0.302328	+	0.523648i	−0.976663	−	0.214778i	$-0.931097\pi$
$853$	−8.82985	+	15.2937i	−0.302328	+	0.523648i	0.674335	+	0.738426i	$0.264431\pi$
$854$		0			0
$855$	−24.4673	+	15.8119i	−0.836765	+	0.540757i
$856$		0			0
$857$	10.0647	−	17.4326i	0.343804	−	0.595486i	−0.641332	−	0.767264i	$-0.721618\pi$
$857$	10.0647	−	17.4326i	0.343804	−	0.595486i	0.985136	+	0.171777i	$0.0549510\pi$
$858$		0			0
$859$	−10.1584	−	17.5948i	−0.346599	−	0.600327i	0.639044	−	0.769170i	$-0.279330\pi$
$859$	−10.1584	−	17.5948i	−0.346599	−	0.600327i	−0.985643	+	0.168843i	$0.945997\pi$
$860$		0			0
$861$	−6.43711	−	6.12222i	−0.219376	−	0.208645i
$862$		0			0
$863$	2.42304			0.0824812			0.0412406	−	0.999149i	$-0.486869\pi$
$863$	2.42304			0.0824812			0.0412406	+	0.999149i	$0.486869\pi$
$864$		0			0
$865$	28.0942			0.955230
$866$		0			0
$867$	21.2225	+	20.1843i	0.720754	+	0.685496i
$868$		0			0
$869$	6.10864	+	10.5805i	0.207222	+	0.358918i
$870$		0			0
$871$	22.4845	−	38.9443i	0.761858	−	1.31958i
$872$		0			0
$873$	−26.8317	−	13.7467i	−0.908114	−	0.465256i
$874$		0			0
$875$	6.03847	−	10.4589i	0.204137	−	0.353576i
$876$		0			0
$877$	19.3743	+	33.5573i	0.654224	+	1.13315i	0.982088	+	0.188424i	$0.0603380\pi$
$877$	19.3743	+	33.5573i	0.654224	+	1.13315i	−0.327864	+	0.944725i	$0.606329\pi$
$878$		0			0
$879$	−8.69532	+	36.0418i	−0.293286	+	1.21566i
$880$		0			0
$881$	−2.18153			−0.0734975			−0.0367487	−	0.999325i	$-0.511700\pi$
$881$	−2.18153			−0.0734975			−0.0367487	+	0.999325i	$0.511700\pi$
$882$		0			0
$883$	−13.4286			−0.451908			−0.225954	−	0.974138i	$-0.572550\pi$
$883$	−13.4286			−0.451908			−0.225954	+	0.974138i	$0.572550\pi$
$884$		0			0
$885$	25.0935	−	7.40268i	0.843510	−	0.248838i
$886$		0			0
$887$	−9.99837	−	17.3177i	−0.335712	−	0.581471i	0.647909	−	0.761718i	$-0.275644\pi$
$887$	−9.99837	−	17.3177i	−0.335712	−	0.581471i	−0.983621	+	0.180247i	$0.942310\pi$
$888$		0			0
$889$	0.676663	−	1.17201i	0.0226946	−	0.0393081i
$890$		0			0
$891$	−3.51098	+	7.79225i	−0.117622	+	0.261050i
$892$		0			0
$893$	−18.6022	+	32.2200i	−0.622499	+	1.07820i
$894$		0			0
$895$	2.84329	+	4.92472i	0.0950406	+	0.164615i
$896$		0			0
$897$	13.2132	−	3.89795i	0.441177	−	0.130149i
$898$		0			0
$899$	−2.13170			−0.0710962
$900$		0			0
$901$	−0.560774			−0.0186821
$902$		0			0
$903$	−4.27307	+	17.7117i	−0.142199	+	0.589410i
$904$		0			0
$905$	10.9942	+	19.0425i	0.365458	+	0.632993i
$906$		0			0
$907$	−14.9799	+	25.9460i	−0.497401	+	0.861523i	−0.999996	−	0.00299870i	$-0.999045\pi$
$907$	−14.9799	+	25.9460i	−0.497401	+	0.861523i	0.502595	+	0.864522i	$0.332379\pi$
$908$		0			0
$909$	−43.8328	−	22.4570i	−1.45384	−	0.744851i
$910$		0			0
$911$	−10.8134	+	18.7294i	−0.358264	+	0.620531i	−0.987671	−	0.156545i	$-0.949964\pi$
$911$	−10.8134	+	18.7294i	−0.358264	+	0.620531i	0.629407	+	0.777076i	$0.283298\pi$
$912$		0			0
$913$	1.88467	+	3.26435i	0.0623735	+	0.108034i
$914$		0			0
$915$	1.08842	+	1.03518i	0.0359822	+	0.0342220i
$916$		0			0
$917$	18.9565			0.626000
$918$		0			0
$919$	2.01792			0.0665650			0.0332825	−	0.999446i	$-0.489404\pi$
$919$	2.01792			0.0665650			0.0332825	+	0.999446i	$0.489404\pi$
$920$		0			0
$921$	−15.7208	−	14.9518i	−0.518017	−	0.492677i
$922$		0			0
$923$	−8.55097	−	14.8107i	−0.281459	−	0.487501i
$924$		0			0
$925$	7.71217	−	13.3579i	0.253575	−	0.439204i
$926$		0			0
$927$	13.4827	−	8.71317i	0.442831	−	0.286178i
$928$		0			0
$929$	12.5900	−	21.8066i	0.413065	−	0.715450i	−0.582158	−	0.813076i	$-0.697791\pi$
$929$	12.5900	−	21.8066i	0.413065	−	0.715450i	0.995223	+	0.0976255i	$0.0311247\pi$
$930$		0			0
$931$	−2.86849	−	4.96836i	−0.0940108	−	0.162832i
$932$		0			0
$933$	−3.49541	+	14.4884i	−0.114434	+	0.474328i
$934$		0			0
$935$	−0.483306			−0.0158058
$936$		0			0
$937$	−40.2353			−1.31443			−0.657214	−	0.753704i	$-0.728265\pi$
$937$	−40.2353			−1.31443			−0.657214	+	0.753704i	$0.728265\pi$
$938$		0			0
$939$	−22.2796	+	6.57257i	−0.727069	+	0.214488i
$940$		0			0
$941$	7.21699	+	12.5002i	0.235267	+	0.407495i	0.959350	−	0.282218i	$-0.0910702\pi$
$941$	7.21699	+	12.5002i	0.235267	+	0.407495i	−0.724083	+	0.689713i	$0.757737\pi$
$942$		0			0
$943$	−6.01623	+	10.4204i	−0.195915	+	0.339335i
$944$		0			0
$945$	5.73433	−	6.66883i	0.186538	−	0.216937i
$946$		0			0
$947$	−24.5734	+	42.5624i	−0.798528	+	1.38309i	0.122047	+	0.992524i	$0.461054\pi$
$947$	−24.5734	+	42.5624i	−0.798528	+	1.38309i	−0.920575	+	0.390566i	$0.872279\pi$
$948$		0			0
$949$	−2.69578	−	4.66922i	−0.0875086	−	0.151569i
$950$		0			0
$951$	−18.7974	+	5.54529i	−0.609547	+	0.179818i
$952$		0			0
$953$	−19.9466			−0.646135			−0.323068	−	0.946376i	$-0.604714\pi$
$953$	−19.9466			−0.646135			−0.323068	+	0.946376i	$0.604714\pi$
$954$		0			0
$955$	1.42924			0.0462492
$956$		0			0
$957$	−0.786662	+	3.26069i	−0.0254292	+	0.105403i
$958$		0			0
$959$	−1.91299	−	3.31339i	−0.0617736	−	0.106995i
$960$		0			0
$961$	14.9537	−	25.9005i	0.482376	−	0.835500i
$962$		0			0
$963$	−2.65453	−	52.9044i	−0.0855412	−	1.70482i
$964$		0			0
$965$	5.29253	−	9.16693i	0.170373	−	0.295094i
$966$		0			0
$967$	21.9057	+	37.9418i	0.704439	+	1.22012i	0.966893	+	0.255180i	$0.0821348\pi$
$967$	21.9057	+	37.9418i	0.704439	+	1.22012i	−0.262454	+	0.964944i	$0.584532\pi$
$968$		0			0
$969$	2.16495	+	2.05905i	0.0695482	+	0.0661461i
$970$		0			0
$971$	0.349912			0.0112292			0.00561461	−	0.999984i	$-0.498213\pi$
$971$	0.349912			0.0112292			0.00561461	+	0.999984i	$0.498213\pi$
$972$		0			0
$973$	−22.5075			−0.721558
$974$		0			0
$975$	−9.08441	−	8.64002i	−0.290934	−	0.276702i
$976$		0			0
$977$	−27.0841	−	46.9110i	−0.866497	−	1.50082i	−0.865553	−	0.500817i	$-0.833033\pi$
$977$	−27.0841	−	46.9110i	−0.866497	−	1.50082i	−0.000943440	−	1.00000i	$-0.500300\pi$
$978$		0			0
$979$	−2.96489	+	5.13534i	−0.0947583	+	0.164126i
$980$		0			0
$981$	2.68660	+	53.5436i	0.0857766	+	1.70951i
$982$		0			0
$983$	19.3605	−	33.5334i	0.617504	−	1.06955i	−0.372436	−	0.928058i	$-0.621477\pi$
$983$	19.3605	−	33.5334i	0.617504	−	1.06955i	0.989940	−	0.141490i	$-0.0451894\pi$
$984$		0			0
$985$	11.3587	+	19.6739i	0.361919	+	0.626862i
$986$		0			0
$987$	2.63431	−	10.9191i	0.0838509	−	0.347559i
$988$		0			0
$989$	24.6782			0.784720
$990$		0			0
$991$	−20.5862			−0.653943			−0.326971	−	0.945034i	$-0.606028\pi$
$991$	−20.5862			−0.653943			−0.326971	+	0.945034i	$0.606028\pi$
$992$		0			0
$993$	46.8875	−	13.8320i	1.48793	−	0.438944i
$994$		0			0
$995$	1.57841	+	2.73389i	0.0500391	+	0.0866702i
$996$		0			0
$997$	3.06503	−	5.30879i	0.0970706	−	0.168131i	−0.813400	−	0.581704i	$-0.802386\pi$
$997$	3.06503	−	5.30879i	0.0970706	−	0.168131i	0.910471	+	0.413573i	$0.135719\pi$
$998$		0			0
$999$	24.4756	−	28.4642i	0.774374	−	0.900569i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.2.r.f.169.2	✓	10
3.2	odd	2		1512.2.r.f.505.2		10
4.3	odd	2		1008.2.r.n.673.4		10
9.2	odd	6		4536.2.a.bc.1.4		5
9.4	even	3	inner	504.2.r.f.337.2	yes	10
9.5	odd	6		1512.2.r.f.1009.2		10
9.7	even	3		4536.2.a.bd.1.2		5
12.11	even	2		3024.2.r.n.2017.2		10
36.7	odd	6		9072.2.a.cn.1.2		5
36.11	even	6		9072.2.a.cm.1.4		5
36.23	even	6		3024.2.r.n.1009.2		10
36.31	odd	6		1008.2.r.n.337.4		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.r.f.169.2	✓	10	1.1	even	1	trivial
504.2.r.f.337.2	yes	10	9.4	even	3	inner
1008.2.r.n.337.4		10	36.31	odd	6
1008.2.r.n.673.4		10	4.3	odd	2
1512.2.r.f.505.2		10	3.2	odd	2
1512.2.r.f.1009.2		10	9.5	odd	6
3024.2.r.n.1009.2		10	36.23	even	6
3024.2.r.n.2017.2		10	12.11	even	2
4536.2.a.bc.1.4		5	9.2	odd	6
4536.2.a.bd.1.2		5	9.7	even	3
9072.2.a.cm.1.4		5	36.11	even	6
9072.2.a.cn.1.2		5	36.7	odd	6

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:	\( N \)	\(=\)	\( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	504.r (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.25506 - 1.19366i) q^{3} +(0.846320 + 1.46587i) q^{5} +(0.500000 - 0.866025i) q^{7} +(0.150339 + 2.99623i) q^{9} +O(q^{10})\)	\(q+(-1.25506 - 1.19366i) q^{3} +(0.846320 + 1.46587i) q^{5} +(0.500000 - 0.866025i) q^{7} +(0.150339 + 2.99623i) q^{9} +(0.474817 - 0.822407i) q^{11} +(1.69516 + 2.93611i) q^{13} +(0.687573 - 2.84997i) q^{15} -0.300678 q^{17} +5.73697 q^{19} +(-1.66127 + 0.490080i) q^{21} +(1.17300 + 2.03169i) q^{23} +(1.06748 - 1.84894i) q^{25} +(3.38780 - 3.93990i) q^{27} +(1.01964 - 1.76607i) q^{29} +(-0.522659 - 0.905272i) q^{31} +(-1.57760 + 0.465397i) q^{33} +1.69264 q^{35} +7.22462 q^{37} +(1.37720 - 5.70844i) q^{39} +(2.56447 + 4.44179i) q^{41} +(5.25963 - 9.10995i) q^{43} +(-4.26485 + 2.75615i) q^{45} +(-3.24251 + 5.61620i) q^{47} +(-0.500000 - 0.866025i) q^{49} +(0.377368 + 0.358908i) q^{51} +1.86503 q^{53} +1.60739 q^{55} +(-7.20023 - 6.84801i) q^{57} +(4.46197 + 7.72836i) q^{59} +(-0.256177 + 0.443711i) q^{61} +(2.66998 + 1.36792i) q^{63} +(-2.86930 + 4.96978i) q^{65} +(-6.63195 - 11.4869i) q^{67} +(0.952975 - 3.95005i) q^{69} -5.04433 q^{71} -1.59027 q^{73} +(-3.54676 + 1.04631i) q^{75} +(-0.474817 - 0.822407i) q^{77} +(-6.43263 + 11.1416i) q^{79} +(-8.95480 + 0.900900i) q^{81} +(-1.98463 + 3.43748i) q^{83} +(-0.254470 - 0.440755i) q^{85} +(-3.38780 + 0.999414i) q^{87} -6.24428 q^{89} +3.39033 q^{91} +(-0.424622 + 1.76005i) q^{93} +(4.85532 + 8.40965i) q^{95} +(-5.02469 + 8.70302i) q^{97} +(2.53551 + 1.29902i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 3 q^{5} + 5 q^{7}+O(q^{10}) \) 10 * q - 3 * q^5 + 5 * q^7	\( 10 q - 3 q^{5} + 5 q^{7} + 4 q^{11} - 3 q^{13} + 15 q^{15} + 2 q^{19} + 8 q^{23} - 10 q^{25} - 9 q^{27} - 9 q^{29} - 3 q^{31} + 30 q^{33} - 6 q^{35} - 6 q^{37} - 18 q^{39} - 12 q^{41} - 5 q^{43} - 9 q^{45} + 3 q^{47} - 5 q^{49} + 9 q^{51} + 60 q^{53} + 44 q^{55} - 21 q^{57} + 7 q^{59} - 14 q^{61} + 6 q^{63} - 11 q^{65} - 8 q^{67} + 21 q^{69} - 18 q^{71} + 30 q^{73} - 51 q^{75} - 4 q^{77} - 3 q^{79} - 12 q^{81} + 20 q^{83} - 21 q^{85} + 9 q^{87} - 24 q^{89} - 6 q^{91} - 39 q^{93} - 12 q^{95} - 37 q^{97} + 60 q^{99}+O(q^{100}) \) 10 * q - 3 * q^5 + 5 * q^7 + 4 * q^11 - 3 * q^13 + 15 * q^15 + 2 * q^19 + 8 * q^23 - 10 * q^25 - 9 * q^27 - 9 * q^29 - 3 * q^31 + 30 * q^33 - 6 * q^35 - 6 * q^37 - 18 * q^39 - 12 * q^41 - 5 * q^43 - 9 * q^45 + 3 * q^47 - 5 * q^49 + 9 * q^51 + 60 * q^53 + 44 * q^55 - 21 * q^57 + 7 * q^59 - 14 * q^61 + 6 * q^63 - 11 * q^65 - 8 * q^67 + 21 * q^69 - 18 * q^71 + 30 * q^73 - 51 * q^75 - 4 * q^77 - 3 * q^79 - 12 * q^81 + 20 * q^83 - 21 * q^85 + 9 * q^87 - 24 * q^89 - 6 * q^91 - 39 * q^93 - 12 * q^95 - 37 * q^97 + 60 * q^99

Introduction

L-functions

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Database

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