LMFDB - Embedded newform 656.2.u.h.529.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [656,2,Mod(305,656)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(656, base_ring=CyclotomicField(10))

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

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

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

chi := DirichletCharacter("656.305");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 656 = 2^{4} \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	656.u (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:	$5.23818637260$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$5$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 2 x^{19} + 7 x^{18} - 6 x^{17} + 60 x^{16} - 92 x^{15} + 603 x^{14} - 690 x^{13} + 2935 x^{12} + \cdots + 4096 $ x^20 - 2x^19 + 7x^18 - 6x^17 + 60x^16 - 92x^15 + 603x^14 - 690x^13 + 2935x^12 - 3168x^11 + 7811x^10 - 7928x^9 + 15482x^8 - 24314x^7 + 44829x^6 - 45930x^5 + 53273x^4 - 47528x^3 + 33216x^2 - 12800*x + 4096
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 328)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			529.3
Root			$0.645787 - 0.469192i$ of defining polynomial
Character	$\chi$	$=$	656.529
Dual form			656.2.u.h.625.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.798236 q^{3} +(0.897909 - 2.76348i) q^{5} +(-1.99043 - 1.44613i) q^{7} -2.36282 q^{9} +O(q^{10})$	\(q+0.798236 q^{3} +(0.897909 - 2.76348i) q^{5} +(-1.99043 - 1.44613i) q^{7} -2.36282 q^{9} +(0.720795 + 2.21838i) q^{11} +(3.16183 - 2.29720i) q^{13} +(0.716744 - 2.20591i) q^{15} +(-1.83272 - 5.64054i) q^{17} +(-1.22881 - 0.892785i) q^{19} +(-1.58883 - 1.15435i) q^{21} +(-1.43025 + 1.03914i) q^{23} +(-2.78550 - 2.02378i) q^{25} -4.28080 q^{27} +(1.70533 - 5.24846i) q^{29} +(-0.744676 - 2.29188i) q^{31} +(0.575365 + 1.77079i) q^{33} +(-5.78357 + 4.20201i) q^{35} +(-0.325137 + 1.00067i) q^{37} +(2.52388 - 1.83371i) q^{39} +(2.72010 + 5.79664i) q^{41} +(-4.73244 + 3.43832i) q^{43} +(-2.12160 + 6.52960i) q^{45} +(8.60402 - 6.25119i) q^{47} +(-0.292612 - 0.900567i) q^{49} +(-1.46295 - 4.50249i) q^{51} +(-2.04506 + 6.29404i) q^{53} +6.77766 q^{55} +(-0.980884 - 0.712654i) q^{57} +(9.73177 - 7.07055i) q^{59} +(5.79658 + 4.21146i) q^{61} +(4.70302 + 3.41694i) q^{63} +(-3.50924 - 10.8003i) q^{65} +(4.17182 - 12.8395i) q^{67} +(-1.14168 + 0.829477i) q^{69} +(1.91611 + 5.89717i) q^{71} -1.84789 q^{73} +(-2.22349 - 1.61546i) q^{75} +(1.77337 - 5.45789i) q^{77} +3.57097 q^{79} +3.67137 q^{81} -17.2528 q^{83} -17.2332 q^{85} +(1.36125 - 4.18951i) q^{87} +(13.4220 + 9.75163i) q^{89} -9.61543 q^{91} +(-0.594427 - 1.82946i) q^{93} +(-3.57056 + 2.59416i) q^{95} +(-4.21214 + 12.9636i) q^{97} +(-1.70311 - 5.24163i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 2 q^{3} + 2 q^{5} + 10 q^{9}+O(q^{10}) $ 20 * q - 2 * q^3 + 2 * q^5 + 10 * q^9	$ 20 q - 2 q^{3} + 2 q^{5} + 10 q^{9} - 9 q^{11} + 7 q^{13} - q^{15} - 8 q^{17} - q^{19} - 6 q^{21} + 11 q^{23} + 15 q^{25} - 2 q^{27} + 21 q^{29} + 5 q^{31} + 19 q^{33} - 4 q^{37} - 4 q^{39} + 9 q^{41} + 17 q^{43} + 11 q^{45} - 15 q^{47} - 25 q^{49} + 22 q^{51} + 10 q^{53} + 28 q^{55} - 20 q^{57} + 24 q^{59} + 15 q^{61} + 65 q^{63} - 29 q^{65} + 26 q^{67} - 47 q^{69} - 16 q^{71} + 14 q^{73} - 11 q^{75} + 12 q^{77} + 26 q^{79} - 60 q^{81} - 20 q^{83} - 94 q^{85} - 57 q^{87} + 5 q^{89} + 46 q^{91} + 43 q^{93} - 71 q^{95} - 22 q^{97} - 8 q^{99}+O(q^{100}) $ 20 * q - 2 * q^3 + 2 * q^5 + 10 * q^9 - 9 * q^11 + 7 * q^13 - q^15 - 8 * q^17 - q^19 - 6 * q^21 + 11 * q^23 + 15 * q^25 - 2 * q^27 + 21 * q^29 + 5 * q^31 + 19 * q^33 - 4 * q^37 - 4 * q^39 + 9 * q^41 + 17 * q^43 + 11 * q^45 - 15 * q^47 - 25 * q^49 + 22 * q^51 + 10 * q^53 + 28 * q^55 - 20 * q^57 + 24 * q^59 + 15 * q^61 + 65 * q^63 - 29 * q^65 + 26 * q^67 - 47 * q^69 - 16 * q^71 + 14 * q^73 - 11 * q^75 + 12 * q^77 + 26 * q^79 - 60 * q^81 - 20 * q^83 - 94 * q^85 - 57 * q^87 + 5 * q^89 + 46 * q^91 + 43 * q^93 - 71 * q^95 - 22 * q^97 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/656\mathbb{Z}\right)^\times$.

$n$	$129$	$165$	$575$
$\chi(n)$	$e\left(\frac{4}{5}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.798236			0.460862			0.230431	−	0.973089i	$-0.425986\pi$
$3$	0.798236			0.460862			0.230431	+	0.973089i	$0.425986\pi$
$4$		0			0
$5$	0.897909	−	2.76348i	0.401557	−	1.23587i	−0.522179	−	0.852836i	$-0.674881\pi$
$5$	0.897909	−	2.76348i	0.401557	−	1.23587i	0.923736	−	0.383030i	$-0.125119\pi$
$6$		0			0
$7$	−1.99043	−	1.44613i	−0.752310	−	0.546586i	0.144232	−	0.989544i	$-0.453929\pi$
$7$	−1.99043	−	1.44613i	−0.752310	−	0.546586i	−0.896542	+	0.442958i	$0.853929\pi$
$8$		0			0
$9$	−2.36282			−0.787606
$10$		0			0
$11$	0.720795	+	2.21838i	0.217328	+	0.668867i	0.998980	+	0.0451522i	$0.0143773\pi$
$11$	0.720795	+	2.21838i	0.217328	+	0.668867i	−0.781652	+	0.623715i	$0.785623\pi$
$12$		0			0
$13$	3.16183	−	2.29720i	0.876933	−	0.637129i	−0.0555054	−	0.998458i	$-0.517677\pi$
$13$	3.16183	−	2.29720i	0.876933	−	0.637129i	0.932438	+	0.361329i	$0.117677\pi$
$14$		0			0
$15$	0.716744	−	2.20591i	0.185062	−	0.569564i
$16$		0			0
$17$	−1.83272	−	5.64054i	−0.444501	−	1.36803i	−0.883030	−	0.469316i	$-0.844500\pi$
$17$	−1.83272	−	5.64054i	−0.444501	−	1.36803i	0.438529	−	0.898717i	$-0.355500\pi$
$18$		0			0
$19$	−1.22881	−	0.892785i	−0.281909	−	0.204819i	0.437841	−	0.899053i	$-0.355743\pi$
$19$	−1.22881	−	0.892785i	−0.281909	−	0.204819i	−0.719750	+	0.694234i	$0.755743\pi$
$20$		0			0
$21$	−1.58883	−	1.15435i	−0.346711	−	0.251900i
$22$		0			0
$23$	−1.43025	+	1.03914i	−0.298228	+	0.216675i	−0.726829	−	0.686819i	$-0.759007\pi$
$23$	−1.43025	+	1.03914i	−0.298228	+	0.216675i	0.428601	+	0.903494i	$0.359007\pi$
$24$		0			0
$25$	−2.78550	−	2.02378i	−0.557100	−	0.404756i
$26$		0			0
$27$	−4.28080			−0.823840
$28$		0			0
$29$	1.70533	−	5.24846i	0.316671	−	0.974614i	−0.658390	−	0.752677i	$-0.728762\pi$
$29$	1.70533	−	5.24846i	0.316671	−	0.974614i	0.975061	−	0.221937i	$-0.0712378\pi$
$30$		0			0
$31$	−0.744676	−	2.29188i	−0.133748	−	0.411633i	0.861645	−	0.507511i	$-0.169434\pi$
$31$	−0.744676	−	2.29188i	−0.133748	−	0.411633i	−0.995393	+	0.0958777i	$0.969434\pi$
$32$		0			0
$33$	0.575365	+	1.77079i	0.100158	+	0.308255i
$34$		0			0
$35$	−5.78357	+	4.20201i	−0.977602	+	0.710270i
$36$		0			0
$37$	−0.325137	+	1.00067i	−0.0534522	+	0.164509i	−0.974219	−	0.225605i	$-0.927564\pi$
$37$	−0.325137	+	1.00067i	−0.0534522	+	0.164509i	0.920767	+	0.390114i	$0.127564\pi$
$38$		0			0
$39$	2.52388	−	1.83371i	0.404145	−	0.293629i
$40$		0			0
$41$	2.72010	+	5.79664i	0.424808	+	0.905283i
$41$	2.72010	+	5.79664i	0.424808	+	0.905283i
$42$		0			0
$43$	−4.73244	+	3.43832i	−0.721691	+	0.524339i	−0.886924	−	0.461916i	$-0.847162\pi$
$43$	−4.73244	+	3.43832i	−0.721691	+	0.524339i	0.165233	+	0.986255i	$0.447162\pi$
$44$		0			0
$45$	−2.12160	+	6.52960i	−0.316269	+	0.973376i
$46$		0			0
$47$	8.60402	−	6.25119i	1.25503	−	0.911829i	0.256523	−	0.966538i	$-0.417423\pi$
$47$	8.60402	−	6.25119i	1.25503	−	0.911829i	0.998502	+	0.0547086i	$0.0174230\pi$
$48$		0			0
$49$	−0.292612	−	0.900567i	−0.0418017	−	0.128652i
$50$		0			0
$51$	−1.46295	−	4.50249i	−0.204854	−	0.630474i
$52$		0			0
$53$	−2.04506	+	6.29404i	−0.280910	+	0.864553i	0.706685	+	0.707529i	$0.250190\pi$
$53$	−2.04506	+	6.29404i	−0.280910	+	0.864553i	−0.987595	+	0.157024i	$0.949810\pi$
$54$		0			0
$55$	6.77766			0.913899
$56$		0			0
$57$	−0.980884	−	0.712654i	−0.129921	−	0.0943933i
$58$		0			0
$59$	9.73177	−	7.07055i	1.26697	−	0.920507i	0.267891	−	0.963449i	$-0.413673\pi$
$59$	9.73177	−	7.07055i	1.26697	−	0.920507i	0.999078	+	0.0429422i	$0.0136731\pi$
$60$		0			0
$61$	5.79658	+	4.21146i	0.742176	+	0.539222i	0.893392	−	0.449279i	$-0.148319\pi$
$61$	5.79658	+	4.21146i	0.742176	+	0.539222i	−0.151216	+	0.988501i	$0.548319\pi$
$62$		0			0
$63$	4.70302	+	3.41694i	0.592524	+	0.430494i
$64$		0			0
$65$	−3.50924	−	10.8003i	−0.435267	−	1.33962i
$66$		0			0
$67$	4.17182	−	12.8395i	0.509669	−	1.56860i	−0.283109	−	0.959088i	$-0.591366\pi$
$67$	4.17182	−	12.8395i	0.509669	−	1.56860i	0.792778	−	0.609511i	$-0.208634\pi$
$68$		0			0
$69$	−1.14168	+	0.829477i	−0.137442	+	0.0998574i
$70$		0			0
$71$	1.91611	+	5.89717i	0.227400	+	0.699865i	0.998039	+	0.0625934i	$0.0199371\pi$
$71$	1.91611	+	5.89717i	0.227400	+	0.699865i	−0.770639	+	0.637272i	$0.780063\pi$
$72$		0			0
$73$	−1.84789			−0.216280			−0.108140	−	0.994136i	$-0.534489\pi$
$73$	−1.84789			−0.216280			−0.108140	+	0.994136i	$0.534489\pi$
$74$		0			0
$75$	−2.22349	−	1.61546i	−0.256746	−	0.186537i
$76$		0			0
$77$	1.77337	−	5.45789i	0.202095	−	0.621984i
$78$		0			0
$79$	3.57097			0.401766			0.200883	−	0.979615i	$-0.435619\pi$
$79$	3.57097			0.401766			0.200883	+	0.979615i	$0.435619\pi$
$80$		0			0
$81$	3.67137			0.407930
$82$		0			0
$83$	−17.2528			−1.89375			−0.946873	−	0.321608i	$-0.895777\pi$
$83$	−17.2528			−1.89375			−0.946873	+	0.321608i	$0.895777\pi$
$84$		0			0
$85$	−17.2332			−1.86920
$86$		0			0
$87$	1.36125	−	4.18951i	0.145942	−	0.449162i
$88$		0			0
$89$	13.4220	+	9.75163i	1.42273	+	1.03367i	0.991314	+	0.131516i	$0.0419843\pi$
$89$	13.4220	+	9.75163i	1.42273	+	1.03367i	0.431412	+	0.902155i	$0.358016\pi$
$90$		0			0
$91$	−9.61543			−1.00797
$92$		0			0
$93$	−0.594427	−	1.82946i	−0.0616392	−	0.189706i
$94$		0			0
$95$	−3.57056	+	2.59416i	−0.366331	+	0.266155i
$96$		0			0
$97$	−4.21214	+	12.9636i	−0.427678	+	1.31626i	0.472730	+	0.881208i	$0.343269\pi$
$97$	−4.21214	+	12.9636i	−0.427678	+	1.31626i	−0.900407	+	0.435048i	$0.856731\pi$
$98$		0			0
$99$	−1.70311	−	5.24163i	−0.171169	−	0.526804i
$100$		0			0
$101$	6.02614	+	4.37825i	0.599624	+	0.435652i	0.845745	−	0.533587i	$-0.179156\pi$
$101$	6.02614	+	4.37825i	0.599624	+	0.435652i	−0.246122	+	0.969239i	$0.579156\pi$
$102$		0			0
$103$	7.41810	+	5.38956i	0.730927	+	0.531049i	0.889856	−	0.456241i	$-0.150804\pi$
$103$	7.41810	+	5.38956i	0.730927	+	0.531049i	−0.158930	+	0.987290i	$0.550804\pi$
$104$		0			0
$105$	−4.61666	+	3.35420i	−0.450540	+	0.327336i
$106$		0			0
$107$	2.78645	+	2.02448i	0.269376	+	0.195713i	0.714270	−	0.699870i	$-0.246759\pi$
$107$	2.78645	+	2.02448i	0.269376	+	0.195713i	−0.444894	+	0.895583i	$0.646759\pi$
$108$		0			0
$109$	6.88044			0.659026			0.329513	−	0.944151i	$-0.393115\pi$
$109$	6.88044			0.659026			0.329513	+	0.944151i	$0.393115\pi$
$110$		0			0
$111$	−0.259536	+	0.798771i	−0.0246341	+	0.0758159i
$112$		0			0
$113$	−1.22622	−	3.77391i	−0.115353	−	0.355019i	0.876668	−	0.481097i	$-0.159761\pi$
$113$	−1.22622	−	3.77391i	−0.115353	−	0.355019i	−0.992020	+	0.126077i	$0.959761\pi$
$114$		0			0
$115$	1.58740	+	4.88552i	0.148026	+	0.455577i
$116$		0			0
$117$	−7.47082	+	5.42787i	−0.690678	+	0.501807i
$118$		0			0
$119$	−4.50906	+	13.8774i	−0.413344	+	1.27214i
$120$		0			0
$121$	4.49752	−	3.26764i	0.408866	−	0.297058i
$122$		0			0
$123$	2.17128	+	4.62709i	0.195778	+	0.417211i
$124$		0			0
$125$	3.65998	−	2.65913i	0.327358	−	0.237840i
$126$		0			0
$127$	1.97012	−	6.06340i	0.174820	−	0.538040i	−0.824806	−	0.565416i	$-0.808715\pi$
$127$	1.97012	−	6.06340i	0.174820	−	0.538040i	0.999625	+	0.0273770i	$0.00871545\pi$
$128$		0			0
$129$	−3.77761	+	2.74459i	−0.332600	+	0.241648i
$130$		0			0
$131$	6.27399	+	19.3094i	0.548161	+	1.68707i	0.713352	+	0.700806i	$0.247176\pi$
$131$	6.27399	+	19.3094i	0.548161	+	1.68707i	−0.165191	+	0.986262i	$0.552824\pi$
$132$		0			0
$133$	1.15478	+	3.55405i	0.100132	+	0.308175i
$134$		0			0
$135$	−3.84377	+	11.8299i	−0.330819	+	1.01816i
$136$		0			0
$137$	6.72508			0.574562			0.287281	−	0.957846i	$-0.407249\pi$
$137$	6.72508			0.574562			0.287281	+	0.957846i	$0.407249\pi$
$138$		0			0
$139$	−7.84191	−	5.69748i	−0.665142	−	0.483254i	0.203253	−	0.979126i	$-0.434849\pi$
$139$	−7.84191	−	5.69748i	−0.665142	−	0.483254i	−0.868396	+	0.495872i	$0.834849\pi$
$140$		0			0
$141$	6.86804	−	4.98993i	0.578394	−	0.420228i
$142$		0			0
$143$	7.37510	+	5.35832i	0.616737	+	0.448085i
$144$		0			0
$145$	−12.9728	−	9.42527i	−1.07733	−	0.782726i
$146$		0			0
$147$	−0.233574	−	0.718865i	−0.0192648	−	0.0592910i
$148$		0			0
$149$	−1.29059	+	3.97204i	−0.105730	+	0.325402i	−0.989901	−	0.141760i	$-0.954724\pi$
$149$	−1.29059	+	3.97204i	−0.105730	+	0.325402i	0.884171	+	0.467163i	$0.154724\pi$
$150$		0			0
$151$	9.83152	−	7.14302i	0.800078	−	0.581290i	−0.110859	−	0.993836i	$-0.535360\pi$
$151$	9.83152	−	7.14302i	0.800078	−	0.581290i	0.910937	+	0.412546i	$0.135360\pi$
$152$		0			0
$153$	4.33039	+	13.3276i	0.350092	+	1.07747i
$154$		0			0
$155$	−7.00220			−0.562431
$156$		0			0
$157$	−17.1487	−	12.4592i	−1.36861	−	0.994355i	−0.997844	−	0.0656300i	$-0.979094\pi$
$157$	−17.1487	−	12.4592i	−1.36861	−	0.994355i	−0.370769	−	0.928725i	$-0.620906\pi$
$158$		0			0
$159$	−1.63244	+	5.02413i	−0.129461	+	0.398439i
$160$		0			0
$161$	4.34954			0.342791
$162$		0			0
$163$	−11.4036			−0.893200			−0.446600	−	0.894734i	$-0.647365\pi$
$163$	−11.4036			−0.893200			−0.446600	+	0.894734i	$0.647365\pi$
$164$		0			0
$165$	5.41017			0.421181
$166$		0			0
$167$	10.0315			0.776258			0.388129	−	0.921605i	$-0.373121\pi$
$167$	10.0315			0.776258			0.388129	+	0.921605i	$0.373121\pi$
$168$		0			0
$169$	0.702792	−	2.16297i	0.0540609	−	0.166382i
$170$		0			0
$171$	2.90346	+	2.10949i	0.222033	+	0.161317i
$172$		0			0
$173$	5.85206			0.444924			0.222462	−	0.974941i	$-0.428591\pi$
$173$	5.85206			0.444924			0.222462	+	0.974941i	$0.428591\pi$
$174$		0			0
$175$	2.61768	+	8.05638i	0.197878	+	0.609005i
$176$		0			0
$177$	7.76826	−	5.64397i	0.583898	−	0.424227i
$178$		0			0
$179$	−2.46741	+	7.59390i	−0.184423	+	0.567595i	−0.999938	−	0.0111409i	$-0.996454\pi$
$179$	−2.46741	+	7.59390i	−0.184423	+	0.567595i	0.815515	+	0.578736i	$0.196454\pi$
$180$		0			0
$181$	1.94357	+	5.98169i	0.144464	+	0.444615i	0.996942	−	0.0781488i	$-0.0249009\pi$
$181$	1.94357	+	5.98169i	0.144464	+	0.444615i	−0.852477	+	0.522764i	$0.824901\pi$
$182$		0			0
$183$	4.62704	+	3.36174i	0.342041	+	0.248507i
$184$		0			0
$185$	2.47339	+	1.79702i	0.181847	+	0.132120i
$186$		0			0
$187$	11.1919	−	8.13136i	0.818429	−	0.594624i
$188$		0			0
$189$	8.52061	+	6.19059i	0.619783	+	0.450299i
$190$		0			0
$191$	−20.2047			−1.46196			−0.730980	−	0.682399i	$-0.760937\pi$
$191$	−20.2047			−1.46196			−0.730980	+	0.682399i	$0.760937\pi$
$192$		0			0
$193$	−1.20159	+	3.69811i	−0.0864922	+	0.266196i	−0.984943	−	0.172878i	$-0.944693\pi$
$193$	−1.20159	+	3.69811i	−0.0864922	+	0.266196i	0.898451	+	0.439074i	$0.144693\pi$
$194$		0			0
$195$	−2.80120	−	8.62121i	−0.200598	−	0.617378i
$196$		0			0
$197$	1.85947	+	5.72285i	0.132481	+	0.407736i	0.995190	−	0.0979658i	$-0.0312336\pi$
$197$	1.85947	+	5.72285i	0.132481	+	0.407736i	−0.862708	+	0.505702i	$0.831234\pi$
$198$		0			0
$199$	−4.88317	+	3.54783i	−0.346159	+	0.251499i	−0.747256	−	0.664536i	$-0.768629\pi$
$199$	−4.88317	+	3.54783i	−0.346159	+	0.251499i	0.401097	+	0.916036i	$0.368629\pi$
$200$		0			0
$201$	3.33010	−	10.2490i	0.234887	−	0.722907i
$202$		0			0
$203$	−10.9843	+	7.98054i	−0.770945	+	0.560124i
$204$		0			0
$205$	18.4613	−	2.31209i	1.28939	−	0.161483i
$206$		0			0
$207$	3.37942	−	2.45529i	0.234886	−	0.170655i
$208$		0			0
$209$	1.09481	−	3.36949i	0.0757299	−	0.233073i
$210$		0			0
$211$	−16.4369	+	11.9421i	−1.13156	+	0.822129i	−0.985922	−	0.167209i	$-0.946525\pi$
$211$	−16.4369	+	11.9421i	−1.13156	+	0.822129i	−0.145642	+	0.989337i	$0.546525\pi$
$212$		0			0
$213$	1.52951	+	4.70733i	0.104800	+	0.322541i
$214$		0			0
$215$	5.25243	+	16.1653i	0.358213	+	1.10247i
$216$		0			0
$217$	−1.83213	+	5.63871i	−0.124373	+	0.382780i
$218$		0			0
$219$	−1.47506			−0.0996751
$220$		0			0
$221$	−18.7522	−	13.6243i	−1.26141	−	0.916469i
$222$		0			0
$223$	22.2957	−	16.1987i	1.49303	−	1.08475i	0.519970	−	0.854184i	$-0.325943\pi$
$223$	22.2957	−	16.1987i	1.49303	−	1.08475i	0.973057	−	0.230564i	$-0.0740570\pi$
$224$		0			0
$225$	6.58163	+	4.78183i	0.438775	+	0.318789i
$226$		0			0
$227$	17.2810	+	12.5554i	1.14698	+	0.833331i	0.988077	−	0.153963i	$-0.0492037\pi$
$227$	17.2810	+	12.5554i	1.14698	+	0.833331i	0.158905	+	0.987294i	$0.449204\pi$
$228$		0			0
$229$	−4.90040	−	15.0819i	−0.323828	−	0.996639i	−0.971967	−	0.235117i	$-0.924453\pi$
$229$	−4.90040	−	15.0819i	−0.323828	−	0.996639i	0.648139	−	0.761522i	$-0.275547\pi$
$230$		0			0
$231$	1.41557	−	4.35668i	0.0931378	−	0.286649i
$232$		0			0
$233$	−10.3839	+	7.54437i	−0.680274	+	0.494248i	−0.873448	−	0.486917i	$-0.838122\pi$
$233$	−10.3839	+	7.54437i	−0.680274	+	0.494248i	0.193175	+	0.981164i	$0.438122\pi$
$234$		0			0
$235$	−9.54940	−	29.3900i	−0.622934	−	1.91720i
$236$		0			0
$237$	2.85048			0.185159
$238$		0			0
$239$	9.26028	+	6.72799i	0.598998	+	0.435197i	0.845523	−	0.533939i	$-0.179289\pi$
$239$	9.26028	+	6.72799i	0.598998	+	0.435197i	−0.246525	+	0.969136i	$0.579289\pi$
$240$		0			0
$241$	8.66987	−	26.6831i	0.558476	−	1.71881i	−0.128108	−	0.991760i	$-0.540891\pi$
$241$	8.66987	−	26.6831i	0.558476	−	1.71881i	0.686584	−	0.727051i	$-0.259109\pi$
$242$		0			0
$243$	15.7730			1.01184
$244$		0			0
$245$	−2.75144			−0.175783
$246$		0			0
$247$	−5.93620			−0.377712
$248$		0			0
$249$	−13.7718			−0.872755
$250$		0			0
$251$	−8.02492	+	24.6982i	−0.506529	+	1.55893i	0.291657	+	0.956523i	$0.405793\pi$
$251$	−8.02492	+	24.6982i	−0.506529	+	1.55893i	−0.798186	+	0.602412i	$0.794207\pi$
$252$		0			0
$253$	−3.33612	−	2.42383i	−0.209740	−	0.152385i
$254$		0			0
$255$	−13.7561			−0.861442
$256$		0			0
$257$	3.51394	+	10.8148i	0.219194	+	0.674609i	0.998829	+	0.0483752i	$0.0154043\pi$
$257$	3.51394	+	10.8148i	0.219194	+	0.674609i	−0.779636	+	0.626233i	$0.784596\pi$
$258$		0			0
$259$	2.09426	−	1.52157i	0.130131	−	0.0945456i
$260$		0			0
$261$	−4.02938	+	12.4011i	−0.249412	+	0.767612i
$262$		0			0
$263$	−9.16637	−	28.2112i	−0.565223	−	1.73958i	−0.667289	−	0.744799i	$-0.732545\pi$
$263$	−9.16637	−	28.2112i	−0.565223	−	1.73958i	0.102066	−	0.994778i	$-0.467455\pi$
$264$		0			0
$265$	15.5572	+	11.3029i	0.955670	+	0.694335i
$266$		0			0
$267$	10.7139	+	7.78411i	0.655680	+	0.476380i
$268$		0			0
$269$	−12.2311	+	8.88640i	−0.745742	+	0.541813i	−0.894504	−	0.447060i	$-0.852471\pi$
$269$	−12.2311	+	8.88640i	−0.745742	+	0.541813i	0.148762	+	0.988873i	$0.452471\pi$
$270$		0			0
$271$	−3.81219	−	2.76972i	−0.231574	−	0.168248i	0.465947	−	0.884812i	$-0.345714\pi$
$271$	−3.81219	−	2.76972i	−0.231574	−	0.168248i	−0.697521	+	0.716564i	$0.745714\pi$
$272$		0			0
$273$	−7.67539			−0.464536
$274$		0			0
$275$	2.48175	−	7.63803i	0.149655	−	0.460590i
$276$		0			0
$277$	−3.20745	−	9.87151i	−0.192717	−	0.593122i	−0.999996	−	0.00295129i	$-0.999061\pi$
$277$	−3.20745	−	9.87151i	−0.192717	−	0.593122i	0.807279	−	0.590170i	$-0.200939\pi$
$278$		0			0
$279$	1.75953	+	5.41529i	0.105341	+	0.324205i
$280$		0			0
$281$	−10.0725	+	7.31809i	−0.600874	+	0.436561i	−0.846189	−	0.532883i	$-0.821109\pi$
$281$	−10.0725	+	7.31809i	−0.600874	+	0.436561i	0.245315	+	0.969443i	$0.421109\pi$
$282$		0			0
$283$	7.62700	−	23.4735i	0.453378	−	1.39535i	−0.419651	−	0.907686i	$-0.637847\pi$
$283$	7.62700	−	23.4735i	0.453378	−	1.39535i	0.873029	−	0.487669i	$-0.162153\pi$
$284$		0			0
$285$	−2.85015	+	2.07075i	−0.168828	+	0.122661i
$286$		0			0
$287$	2.96853	−	15.4714i	0.175227	−	0.913248i
$288$		0			0
$289$	−14.7036	+	10.6828i	−0.864916	+	0.628398i
$290$		0			0
$291$	−3.36228	+	10.3480i	−0.197100	+	0.606612i
$292$		0			0
$293$	−12.8065	+	9.30449i	−0.748166	+	0.543574i	−0.895258	−	0.445549i	$-0.853009\pi$
$293$	−12.8065	+	9.30449i	−0.748166	+	0.543574i	0.147092	+	0.989123i	$0.453009\pi$
$294$		0			0
$295$	−10.8011	−	33.2423i	−0.628863	−	1.93544i
$296$		0			0
$297$	−3.08558	−	9.49643i	−0.179043	−	0.551039i
$298$		0			0
$299$	−2.13509	+	6.57115i	−0.123476	+	0.380019i
$300$		0			0
$301$	14.3918			0.829532
$302$		0			0
$303$	4.81029	+	3.49488i	0.276344	+	0.200775i
$304$		0			0
$305$	16.8431	−	12.2372i	0.964432	−	0.700701i
$306$		0			0
$307$	−15.2812	−	11.1025i	−0.872146	−	0.633651i	0.0590159	−	0.998257i	$-0.481204\pi$
$307$	−15.2812	−	11.1025i	−0.872146	−	0.633651i	−0.931162	+	0.364606i	$0.881204\pi$
$308$		0			0
$309$	5.92139	+	4.30214i	0.336856	+	0.244740i
$310$		0			0
$311$	−4.37591	−	13.4677i	−0.248135	−	0.763682i	−0.995105	−	0.0988239i	$-0.968492\pi$
$311$	−4.37591	−	13.4677i	−0.248135	−	0.763682i	0.746970	−	0.664858i	$-0.231508\pi$
$312$		0			0
$313$	0.0543472	−	0.167263i	0.00307188	−	0.00945429i	−0.949509	−	0.313740i	$-0.898418\pi$
$313$	0.0543472	−	0.167263i	0.00307188	−	0.00945429i	0.952581	+	0.304286i	$0.0984179\pi$
$314$		0			0
$315$	13.6655	−	9.92859i	0.769966	−	0.559413i
$316$		0			0
$317$	−2.84305	−	8.75001i	−0.159682	−	0.491450i	0.838923	−	0.544249i	$-0.183185\pi$
$317$	−2.84305	−	8.75001i	−0.159682	−	0.491450i	−0.998605	+	0.0527998i	$0.983185\pi$
$318$		0			0
$319$	12.8723			0.720708
$320$		0			0
$321$	2.22425	+	1.61601i	0.124145	+	0.0901969i
$322$		0			0
$323$	−2.78372	+	8.56741i	−0.154890	+	0.476703i
$324$		0			0
$325$	−13.4563			−0.746421
$326$		0			0
$327$	5.49221			0.303720
$328$		0			0
$329$	−26.1657			−1.44256
$330$		0			0
$331$	−11.5868			−0.636870			−0.318435	−	0.947945i	$-0.603157\pi$
$331$	−11.5868			−0.636870			−0.318435	+	0.947945i	$0.603157\pi$
$332$		0			0
$333$	0.768240	−	2.36440i	0.0420993	−	0.129568i
$334$		0			0
$335$	−31.7359	−	23.0575i	−1.73392	−	1.25976i
$336$		0			0
$337$	18.5090			1.00825			0.504125	−	0.863631i	$-0.331815\pi$
$337$	18.5090			1.00825			0.504125	+	0.863631i	$0.331815\pi$
$338$		0			0
$339$	−0.978811	−	3.01247i	−0.0531617	−	0.163615i
$340$		0			0
$341$	4.54749	−	3.30395i	0.246261	−	0.178919i
$342$		0			0
$343$	−6.04184	+	18.5949i	−0.326229	+	1.00403i
$344$		0			0
$345$	1.26712	+	3.89980i	0.0682195	+	0.209958i
$346$		0			0
$347$	1.08095	+	0.785359i	0.0580287	+	0.0421603i	0.616421	−	0.787416i	$-0.288582\pi$
$347$	1.08095	+	0.785359i	0.0580287	+	0.0421603i	−0.558393	+	0.829577i	$0.688582\pi$
$348$		0			0
$349$	2.42305	+	1.76045i	0.129703	+	0.0942348i	0.650745	−	0.759296i	$-0.274457\pi$
$349$	2.42305	+	1.76045i	0.129703	+	0.0942348i	−0.521042	+	0.853531i	$0.674457\pi$
$350$		0			0
$351$	−13.5351	+	9.83385i	−0.722452	+	0.524892i
$352$		0			0
$353$	7.54046	+	5.47846i	0.401338	+	0.291589i	0.770086	−	0.637940i	$-0.220213\pi$
$353$	7.54046	+	5.47846i	0.401338	+	0.291589i	−0.368748	+	0.929530i	$0.620213\pi$
$354$		0			0
$355$	18.0172			0.956254
$356$		0			0
$357$	−3.59929	+	11.0775i	−0.190495	+	0.586282i
$358$		0			0
$359$	−10.6338	−	32.7274i	−0.561230	−	1.72729i	−0.678896	−	0.734235i	$-0.737541\pi$
$359$	−10.6338	−	32.7274i	−0.561230	−	1.72729i	0.117666	−	0.993053i	$-0.462459\pi$
$360$		0			0
$361$	−5.15841	−	15.8759i	−0.271495	−	0.835576i
$362$		0			0
$363$	3.59009	−	2.60835i	0.188431	−	0.136903i
$364$		0			0
$365$	−1.65924	+	5.10662i	−0.0868487	+	0.267293i
$366$		0			0
$367$	23.8966	−	17.3619i	1.24739	−	0.906282i	0.249322	−	0.968421i	$-0.419792\pi$
$367$	23.8966	−	17.3619i	1.24739	−	0.906282i	0.998068	+	0.0621388i	$0.0197921\pi$
$368$		0			0
$369$	−6.42711	−	13.6964i	−0.334582	−	0.713007i
$370$		0			0
$371$	13.1725	−	9.57040i	0.683884	−	0.496870i
$372$		0			0
$373$	10.7097	−	32.9612i	0.554529	−	1.70667i	−0.142654	−	0.989773i	$-0.545564\pi$
$373$	10.7097	−	32.9612i	0.554529	−	1.70667i	0.697183	−	0.716893i	$-0.254436\pi$
$374$		0			0
$375$	2.92153	−	2.12261i	0.150867	−	0.109611i
$376$		0			0
$377$	−6.66481	−	20.5122i	−0.343255	−	1.05643i
$378$		0			0
$379$	0.675642	+	2.07941i	0.0347054	+	0.106812i	0.966909	−	0.255123i	$-0.0821161\pi$
$379$	0.675642	+	2.07941i	0.0347054	+	0.106812i	−0.932203	+	0.361935i	$0.882116\pi$
$380$		0			0
$381$	1.57262	−	4.84002i	0.0805677	−	0.247962i
$382$		0			0
$383$	22.2058			1.13467			0.567333	−	0.823489i	$-0.307975\pi$
$383$	22.2058			1.13467			0.567333	+	0.823489i	$0.307975\pi$
$384$		0			0
$385$	−13.4904	−	9.80137i	−0.687536	−	0.499524i
$386$		0			0
$387$	11.1819	−	8.12413i	0.568408	−	0.412973i
$388$		0			0
$389$	6.74301	+	4.89909i	0.341884	+	0.248393i	0.745456	−	0.666554i	$-0.232232\pi$
$389$	6.74301	+	4.89909i	0.341884	+	0.248393i	−0.403572	+	0.914948i	$0.632232\pi$
$390$		0			0
$391$	8.48256	+	6.16294i	0.428981	+	0.311673i
$392$		0			0
$393$	5.00813	+	15.4134i	0.252627	+	0.777505i
$394$		0			0
$395$	3.20641	−	9.86832i	0.161332	−	0.496529i
$396$		0			0
$397$	−4.45553	+	3.23713i	−0.223617	+	0.162467i	−0.693953	−	0.720020i	$-0.744133\pi$
$397$	−4.45553	+	3.23713i	−0.223617	+	0.162467i	0.470337	+	0.882487i	$0.344133\pi$
$398$		0			0
$399$	0.921787	+	2.83697i	0.0461471	+	0.142026i
$400$		0			0
$401$	28.2757			1.41202			0.706011	−	0.708201i	$-0.250493\pi$
$401$	28.2757			1.41202			0.706011	+	0.708201i	$0.250493\pi$
$402$		0			0
$403$	−7.61943	−	5.53584i	−0.379551	−	0.275760i
$404$		0			0
$405$	3.29656	−	10.1458i	0.163807	−	0.504147i
$406$		0			0
$407$	−2.45422			−0.121651
$408$		0			0
$409$	−17.1665			−0.848826			−0.424413	−	0.905469i	$-0.639520\pi$
$409$	−17.1665			−0.848826			−0.424413	+	0.905469i	$0.639520\pi$
$410$		0			0
$411$	5.36820			0.264794
$412$		0			0
$413$	−29.5953			−1.45629
$414$		0			0
$415$	−15.4915	+	47.6779i	−0.760447	+	2.34042i
$416$		0			0
$417$	−6.25970	−	4.54794i	−0.306539	−	0.222713i
$418$		0			0
$419$	15.6385			0.763990			0.381995	−	0.924164i	$-0.375237\pi$
$419$	15.6385			0.763990			0.381995	+	0.924164i	$0.375237\pi$
$420$		0			0
$421$	7.05179	+	21.7032i	0.343683	+	1.05775i	0.962285	+	0.272044i	$0.0876995\pi$
$421$	7.05179	+	21.7032i	0.343683	+	1.05775i	−0.618602	+	0.785705i	$0.712301\pi$
$422$		0			0
$423$	−20.3297	+	14.7704i	−0.988466	+	0.718163i
$424$		0			0
$425$	−6.31019	+	19.4208i	−0.306089	+	0.942045i
$426$		0			0
$427$	−5.44734	−	16.7652i	−0.263615	−	0.811325i
$428$		0			0
$429$	5.88707	+	4.27721i	0.284230	+	0.206505i
$430$		0			0
$431$	−13.1832	−	9.57813i	−0.635011	−	0.461362i	0.223122	−	0.974791i	$-0.428375\pi$
$431$	−13.1832	−	9.57813i	−0.635011	−	0.461362i	−0.858133	+	0.513428i	$0.828375\pi$
$432$		0			0
$433$	30.0009	−	21.7970i	1.44175	−	1.04749i	0.454080	−	0.890961i	$-0.349968\pi$
$433$	30.0009	−	21.7970i	1.44175	−	1.04749i	0.987673	−	0.156534i	$-0.0500321\pi$
$434$		0			0
$435$	−10.3553	−	7.52359i	−0.496501	−	0.360729i
$436$		0			0
$437$	2.68524			0.128452
$438$		0			0
$439$	5.07740	−	15.6266i	0.242331	−	0.745818i	−0.753733	−	0.657181i	$-0.771749\pi$
$439$	5.07740	−	15.6266i	0.242331	−	0.745818i	0.996064	−	0.0886375i	$-0.0282513\pi$
$440$		0			0
$441$	0.691389	+	2.12788i	0.0329233	+	0.101327i
$442$		0			0
$443$	−0.453932	−	1.39706i	−0.0215670	−	0.0663763i	0.939694	−	0.342017i	$-0.111110\pi$
$443$	−0.453932	−	1.39706i	−0.0215670	−	0.0663763i	−0.961261	+	0.275641i	$0.911110\pi$
$444$		0			0
$445$	39.0001	−	28.3353i	1.84878	−	1.34322i
$446$		0			0
$447$	−1.03020	+	3.17063i	−0.0487267	+	0.149965i
$448$		0			0
$449$	15.0241	−	10.9156i	0.709029	−	0.515140i	−0.173831	−	0.984775i	$-0.555615\pi$
$449$	15.0241	−	10.9156i	0.709029	−	0.515140i	0.882860	+	0.469636i	$0.155615\pi$
$450$		0			0
$451$	−10.8985	+	10.2124i	−0.513191	+	0.480884i
$452$		0			0
$453$	7.84788	−	5.70182i	0.368725	−	0.267895i
$454$		0			0
$455$	−8.63379	+	26.5721i	−0.404758	+	1.24572i
$456$		0			0
$457$	−17.5959	+	12.7842i	−0.823101	+	0.598018i	−0.917599	−	0.397507i	$-0.869875\pi$
$457$	−17.5959	+	12.7842i	−0.823101	+	0.598018i	0.0944983	+	0.995525i	$0.469875\pi$
$458$		0			0
$459$	7.84552	+	24.1460i	0.366197	+	1.12704i
$460$		0			0
$461$	−9.08111	−	27.9488i	−0.422949	−	1.30170i	−0.904944	−	0.425530i	$-0.860088\pi$
$461$	−9.08111	−	27.9488i	−0.422949	−	1.30170i	0.481995	−	0.876174i	$-0.339912\pi$
$462$		0			0
$463$	−11.5553	+	35.5637i	−0.537022	+	1.65278i	0.202218	+	0.979341i	$0.435185\pi$
$463$	−11.5553	+	35.5637i	−0.537022	+	1.65278i	−0.739239	+	0.673443i	$0.764815\pi$
$464$		0			0
$465$	−5.58941			−0.259203
$466$		0			0
$467$	22.0230	+	16.0006i	1.01910	+	0.740421i	0.966099	−	0.258174i	$-0.0831207\pi$
$467$	22.0230	+	16.0006i	1.01910	+	0.740421i	0.0530031	+	0.998594i	$0.483121\pi$
$468$		0			0
$469$	−26.8713	+	19.5232i	−1.24080	+	0.901496i
$470$		0			0
$471$	−13.6887	−	9.94541i	−0.630741	−	0.458260i
$472$		0			0
$473$	−11.0386	−	8.02003i	−0.507557	−	0.368761i
$474$		0			0
$475$	1.61605	+	4.97370i	0.0741496	+	0.228209i
$476$		0			0
$477$	4.83210	−	14.8717i	0.221247	−	0.680927i
$478$		0			0
$479$	−13.7870	+	10.0168i	−0.629942	+	0.457680i	−0.856380	−	0.516346i	$-0.827292\pi$
$479$	−13.7870	+	10.0168i	−0.629942	+	0.457680i	0.226438	+	0.974026i	$0.427292\pi$
$480$		0			0
$481$	1.27071	+	3.91085i	0.0579395	+	0.178319i
$482$		0			0
$483$	3.47196			0.157980
$484$		0			0
$485$	32.0426	+	23.2803i	1.45498	+	1.05710i
$486$		0			0
$487$	−7.05033	+	21.6987i	−0.319481	+	0.983262i	0.654389	+	0.756158i	$0.272926\pi$
$487$	−7.05033	+	21.6987i	−0.319481	+	0.983262i	−0.973870	+	0.227104i	$0.927074\pi$
$488$		0			0
$489$	−9.10278			−0.411642
$490$		0			0
$491$	15.6516			0.706346			0.353173	−	0.935558i	$-0.385103\pi$
$491$	15.6516			0.706346			0.353173	+	0.935558i	$0.385103\pi$
$492$		0			0
$493$	−32.7295			−1.47406
$494$		0			0
$495$	−16.0144			−0.719793
$496$		0			0
$497$	4.71420	−	14.5088i	0.211461	−	0.650809i
$498$		0			0
$499$	−14.3191	−	10.4034i	−0.641010	−	0.465721i	0.219187	−	0.975683i	$-0.429659\pi$
$499$	−14.3191	−	10.4034i	−0.641010	−	0.465721i	−0.860197	+	0.509962i	$0.829659\pi$
$500$		0			0
$501$	8.00748			0.357748
$502$		0			0
$503$	2.93200	+	9.02376i	0.130731	+	0.402350i	0.994902	−	0.100850i	$-0.0321562\pi$
$503$	2.93200	+	9.02376i	0.130731	+	0.402350i	−0.864170	+	0.503199i	$0.832156\pi$
$504$		0			0
$505$	17.5101	−	12.7219i	0.779191	−	0.566115i
$506$		0			0
$507$	0.560994	−	1.72656i	0.0249146	−	0.0766793i
$508$		0			0
$509$	7.59317	+	23.3694i	0.336561	+	1.03583i	0.965948	+	0.258737i	$0.0833062\pi$
$509$	7.59317	+	23.3694i	0.336561	+	1.03583i	−0.629387	+	0.777092i	$0.716694\pi$
$510$		0			0
$511$	3.67810	+	2.67230i	0.162710	+	0.118215i
$512$		0			0
$513$	5.26030	+	3.82183i	0.232248	+	0.168738i
$514$		0			0
$515$	21.5547	−	15.6604i	0.949815	−	0.690081i
$516$		0			0
$517$	20.0693	+	14.5812i	0.882645	+	0.641279i
$518$		0			0
$519$	4.67132			0.205048
$520$		0			0
$521$	−13.5880	+	41.8196i	−0.595301	+	1.83215i	−0.0420792	+	0.999114i	$0.513398\pi$
$521$	−13.5880	+	41.8196i	−0.595301	+	1.83215i	−0.553222	+	0.833034i	$0.686602\pi$
$522$		0			0
$523$	0.319506	+	0.983337i	0.0139710	+	0.0429983i	0.957799	−	0.287439i	$-0.0928038\pi$
$523$	0.319506	+	0.983337i	0.0139710	+	0.0429983i	−0.943828	+	0.330437i	$0.892804\pi$
$524$		0			0
$525$	2.08952	+	6.43090i	0.0911943	+	0.280667i
$526$		0			0
$527$	−11.5626	+	8.40075i	−0.503677	+	0.365942i
$528$		0			0
$529$	−6.14158	+	18.9018i	−0.267025	+	0.821819i
$530$		0			0
$531$	−22.9944	+	16.7064i	−0.997873	+	0.724997i
$532$		0			0
$533$	21.9165	+	12.0794i	0.949311	+	0.523215i
$534$		0			0
$535$	8.09658	−	5.88251i	0.350046	−	0.254323i
$536$		0			0
$537$	−1.96957	+	6.06173i	−0.0849934	+	0.261583i
$538$		0			0
$539$	1.78689	−	1.29825i	0.0769667	−	0.0559196i
$540$		0			0
$541$	−11.2139	−	34.5128i	−0.482122	−	1.48382i	−0.836106	−	0.548568i	$-0.815173\pi$
$541$	−11.2139	−	34.5128i	−0.482122	−	1.48382i	0.353984	−	0.935252i	$-0.384827\pi$
$542$		0			0
$543$	1.55143	+	4.77480i	0.0665781	+	0.204906i
$544$		0			0
$545$	6.17801	−	19.0140i	0.264637	−	0.814468i
$546$		0			0
$547$	−2.31716			−0.0990745			−0.0495372	−	0.998772i	$-0.515775\pi$
$547$	−2.31716			−0.0990745			−0.0495372	+	0.998772i	$0.515775\pi$
$548$		0			0
$549$	−13.6963	−	9.95092i	−0.584542	−	0.424695i
$550$		0			0
$551$	−6.78127	+	4.92688i	−0.288892	+	0.209892i
$552$		0			0
$553$	−7.10776	−	5.16409i	−0.302253	−	0.219599i
$554$		0			0
$555$	1.97435	+	1.43445i	0.0838064	+	0.0608889i
$556$		0			0
$557$	−1.77740	−	5.47028i	−0.0753109	−	0.231783i	0.906314	−	0.422606i	$-0.138884\pi$
$557$	−1.77740	−	5.47028i	−0.0753109	−	0.231783i	−0.981625	+	0.190823i	$0.938884\pi$
$558$		0			0
$559$	−7.06465	+	21.7427i	−0.298803	+	0.919620i
$560$		0			0
$561$	8.93374	−	6.49074i	0.377183	−	0.274039i
$562$		0			0
$563$	0.632322	+	1.94609i	0.0266492	+	0.0820177i	0.963497	−	0.267721i	$-0.0862705\pi$
$563$	0.632322	+	1.94609i	0.0266492	+	0.0820177i	−0.936847	+	0.349738i	$0.886270\pi$
$564$		0			0
$565$	−11.5302			−0.485077
$566$		0			0
$567$	−7.30759	−	5.30927i	−0.306890	−	0.222969i
$568$		0			0
$569$	−4.11990	+	12.6797i	−0.172715	+	0.531563i	−0.999522	−	0.0309238i	$-0.990155\pi$
$569$	−4.11990	+	12.6797i	−0.172715	+	0.531563i	0.826807	+	0.562486i	$0.190155\pi$
$570$		0			0
$571$	20.3679			0.852372			0.426186	−	0.904636i	$-0.359857\pi$
$571$	20.3679			0.852372			0.426186	+	0.904636i	$0.359857\pi$
$572$		0			0
$573$	−16.1281			−0.673762
$574$		0			0
$575$	6.08695			0.253843
$576$		0			0
$577$	−15.6083			−0.649780			−0.324890	−	0.945752i	$-0.605327\pi$
$577$	−15.6083			−0.649780			−0.324890	+	0.945752i	$0.605327\pi$
$578$		0			0
$579$	−0.959151	+	2.95196i	−0.0398610	+	0.122679i
$580$		0			0
$581$	34.3405	+	24.9498i	1.42468	+	1.03509i
$582$		0			0
$583$	−15.4366			−0.639320
$584$		0			0
$585$	8.29169	+	25.5192i	0.342819	+	1.05509i
$586$		0			0
$587$	20.9355	−	15.2105i	0.864100	−	0.627805i	−0.0648972	−	0.997892i	$-0.520672\pi$
$587$	20.9355	−	15.2105i	0.864100	−	0.627805i	0.928997	+	0.370087i	$0.120672\pi$
$588$		0			0
$589$	−1.13109	+	3.48112i	−0.0466056	+	0.143437i
$590$		0			0
$591$	1.48429	+	4.56819i	0.0610557	+	0.187910i
$592$		0			0
$593$	−8.06134	−	5.85690i	−0.331039	−	0.240514i	0.409832	−	0.912161i	$-0.365587\pi$
$593$	−8.06134	−	5.85690i	−0.331039	−	0.240514i	−0.740872	+	0.671647i	$0.765587\pi$
$594$		0			0
$595$	34.3013	+	24.9214i	1.40622	+	1.02168i
$596$		0			0
$597$	−3.89792	+	2.83201i	−0.159531	+	0.115906i
$598$		0			0
$599$	27.0123	+	19.6255i	1.10369	+	0.801878i	0.981658	−	0.190648i	$-0.0610589\pi$
$599$	27.0123	+	19.6255i	1.10369	+	0.801878i	0.122032	+	0.992526i	$0.461059\pi$
$600$		0			0
$601$	−2.08104			−0.0848874			−0.0424437	−	0.999099i	$-0.513514\pi$
$601$	−2.08104			−0.0848874			−0.0424437	+	0.999099i	$0.513514\pi$
$602$		0			0
$603$	−9.85725	+	30.3375i	−0.401418	+	1.23544i
$604$		0			0
$605$	−4.99170	−	15.3629i	−0.202941	−	0.624589i
$606$		0			0
$607$	−13.5846	−	41.8092i	−0.551383	−	1.69698i	−0.705310	−	0.708899i	$-0.749192\pi$
$607$	−13.5846	−	41.8092i	−0.551383	−	1.69698i	0.153927	−	0.988082i	$-0.450808\pi$
$608$		0			0
$609$	−8.76804	+	6.37036i	−0.355299	+	0.258140i
$610$		0			0
$611$	12.8442	−	39.5303i	0.519620	−	1.59923i
$612$		0			0
$613$	−6.09453	+	4.42794i	−0.246156	+	0.178843i	−0.704021	−	0.710179i	$-0.748614\pi$
$613$	−6.09453	+	4.42794i	−0.246156	+	0.178843i	0.457866	+	0.889021i	$0.348614\pi$
$614$		0			0
$615$	14.7365	−	1.84559i	0.594232	−	0.0744215i
$616$		0			0
$617$	−28.3632	+	20.6071i	−1.14186	+	0.829610i	−0.987377	−	0.158386i	$-0.949371\pi$
$617$	−28.3632	+	20.6071i	−1.14186	+	0.829610i	−0.154483	+	0.987996i	$0.549371\pi$
$618$		0			0
$619$	−13.9542	+	42.9466i	−0.560866	+	1.72617i	0.119059	+	0.992887i	$0.462012\pi$
$619$	−13.9542	+	42.9466i	−0.560866	+	1.72617i	−0.679925	+	0.733282i	$0.737988\pi$
$620$		0			0
$621$	6.12261	−	4.44834i	0.245692	−	0.178506i
$622$		0			0
$623$	−12.6133	−	38.8198i	−0.505342	−	1.55528i
$624$		0			0
$625$	−9.38195	−	28.8747i	−0.375278	−	1.15499i
$626$		0			0
$627$	0.873920	−	2.68965i	0.0349010	−	0.107414i
$628$		0			0
$629$	6.24021			0.248813
$630$		0			0
$631$	−16.5520	−	12.0258i	−0.658927	−	0.478738i	0.207374	−	0.978262i	$-0.433508\pi$
$631$	−16.5520	−	12.0258i	−0.658927	−	0.478738i	−0.866300	+	0.499524i	$0.833508\pi$
$632$		0			0
$633$	−13.1205	+	9.53263i	−0.521494	+	0.378888i
$634$		0			0
$635$	−14.9871	−	10.8888i	−0.594745	−	0.432107i
$636$		0			0
$637$	−2.99397	−	2.17525i	−0.118626	−	0.0861865i
$638$		0			0
$639$	−4.52741	−	13.9339i	−0.179102	−	0.551218i
$640$		0			0
$641$	10.6333	−	32.7260i	0.419991	−	1.29260i	−0.487718	−	0.873001i	$-0.662171\pi$
$641$	10.6333	−	32.7260i	0.419991	−	1.29260i	0.907710	−	0.419599i	$-0.137829\pi$
$642$		0			0
$643$	−20.6264	+	14.9859i	−0.813425	+	0.590988i	−0.914822	−	0.403858i	$-0.867669\pi$
$643$	−20.6264	+	14.9859i	−0.813425	+	0.590988i	0.101396	+	0.994846i	$0.467669\pi$
$644$		0			0
$645$	4.19268	+	12.9037i	0.165087	+	0.508084i
$646$		0			0
$647$	−11.1198			−0.437166			−0.218583	−	0.975818i	$-0.570143\pi$
$647$	−11.1198			−0.437166			−0.218583	+	0.975818i	$0.570143\pi$
$648$		0			0
$649$	22.6998	+	16.4924i	0.891044	+	0.647382i
$650$		0			0
$651$	−1.46247	+	4.50102i	−0.0573187	+	0.176409i
$652$		0			0
$653$	29.6012			1.15838			0.579192	−	0.815191i	$-0.303368\pi$
$653$	29.6012			1.15838			0.579192	+	0.815191i	$0.303368\pi$
$654$		0			0
$655$	58.9945			2.30511
$656$		0			0
$657$	4.36624			0.170343
$658$		0			0
$659$	14.7924			0.576231			0.288116	−	0.957596i	$-0.406971\pi$
$659$	14.7924			0.576231			0.288116	+	0.957596i	$0.406971\pi$
$660$		0			0
$661$	−6.78317	+	20.8765i	−0.263835	+	0.812000i	0.728125	+	0.685445i	$0.240392\pi$
$661$	−6.78317	+	20.8765i	−0.263835	+	0.812000i	−0.991960	+	0.126556i	$0.959608\pi$
$662$		0			0
$663$	−14.9687	−	10.8754i	−0.581336	−	0.422366i
$664$		0			0
$665$	10.8584			0.421072
$666$		0			0
$667$	3.01482	+	9.27867i	0.116734	+	0.359272i
$668$		0			0
$669$	17.7972	−	12.9304i	0.688080	−	0.499919i
$670$		0			0
$671$	−5.16447	+	15.8946i	−0.199372	+	0.613605i
$672$		0			0
$673$	13.1223	+	40.3863i	0.505827	+	1.55678i	0.799376	+	0.600831i	$0.205164\pi$
$673$	13.1223	+	40.3863i	0.505827	+	1.55678i	−0.293549	+	0.955944i	$0.594836\pi$
$674$		0			0
$675$	11.9241	+	8.66340i	0.458961	+	0.333454i
$676$		0			0
$677$	−11.8645	−	8.62004i	−0.455988	−	0.331295i	0.335967	−	0.941874i	$-0.390937\pi$
$677$	−11.8645	−	8.62004i	−0.455988	−	0.331295i	−0.791956	+	0.610579i	$0.790937\pi$
$678$		0			0
$679$	27.1310	−	19.7118i	1.04119	−	0.756471i
$680$		0			0
$681$	13.7943	+	10.0222i	0.528600	+	0.384050i
$682$		0			0
$683$	22.0761			0.844717			0.422359	−	0.906429i	$-0.361202\pi$
$683$	22.0761			0.844717			0.422359	+	0.906429i	$0.361202\pi$
$684$		0			0
$685$	6.03851	−	18.5846i	0.230720	−	0.710082i
$686$		0			0
$687$	−3.91168	−	12.0389i	−0.149240	−	0.459313i
$688$		0			0
$689$	7.99256	+	24.5986i	0.304492	+	0.937131i
$690$		0			0
$691$	−4.85498	+	3.52735i	−0.184692	+	0.134187i	−0.676289	−	0.736636i	$-0.736413\pi$
$691$	−4.85498	+	3.52735i	−0.184692	+	0.134187i	0.491597	+	0.870823i	$0.336413\pi$
$692$		0			0
$693$	−4.19016	+	12.8960i	−0.159171	+	0.489878i
$694$		0			0
$695$	−22.7862	+	16.5551i	−0.864330	+	0.627973i
$696$		0			0
$697$	27.7110	−	25.9665i	1.04963	−	0.983551i
$698$		0			0
$699$	−8.28883	+	6.02219i	−0.313512	+	0.227780i
$700$		0			0
$701$	−1.60509	+	4.93997i	−0.0606235	+	0.186580i	−0.976782	−	0.214237i	$-0.931274\pi$
$701$	−1.60509	+	4.93997i	−0.0606235	+	0.186580i	0.916158	+	0.400817i	$0.131274\pi$
$702$		0			0
$703$	1.29292	−	0.939358i	0.0487632	−	0.0354286i
$704$		0			0
$705$	−7.62268	−	23.4602i	−0.287087	−	0.883562i
$706$		0			0
$707$	−5.66308	−	17.4292i	−0.212982	−	0.655491i
$708$		0			0
$709$	−12.8319	+	39.4925i	−0.481911	+	1.48317i	0.354494	+	0.935058i	$0.384653\pi$
$709$	−12.8319	+	39.4925i	−0.481911	+	1.48317i	−0.836405	+	0.548112i	$0.815347\pi$
$710$		0			0
$711$	−8.43756			−0.316433
$712$		0			0
$713$	3.44665	+	2.50414i	0.129078	+	0.0937806i
$714$		0			0
$715$	21.4298	−	15.5696i	0.801428	−	0.582272i
$716$		0			0
$717$	7.39189	+	5.37052i	0.276055	+	0.200566i
$718$		0			0
$719$	6.38534	+	4.63922i	0.238133	+	0.173014i	0.700451	−	0.713700i	$-0.252982\pi$
$719$	6.38534	+	4.63922i	0.238133	+	0.173014i	−0.462318	+	0.886714i	$0.652982\pi$
$720$		0			0
$721$	−6.97117	−	21.4551i	−0.259620	−	0.799028i
$722$		0			0
$723$	6.92061	−	21.2994i	0.257380	−	0.792135i
$724$		0			0
$725$	−15.3719	+	11.1683i	−0.570899	+	0.414782i
$726$		0			0
$727$	−1.94453	−	5.98463i	−0.0721185	−	0.221958i	0.908500	−	0.417885i	$-0.137228\pi$
$727$	−1.94453	−	5.98463i	−0.0721185	−	0.221958i	−0.980618	+	0.195927i	$0.937228\pi$
$728$		0			0
$729$	1.57648			0.0583882
$730$		0			0
$731$	28.0673	+	20.3921i	1.03811	+	0.754227i
$732$		0			0
$733$	−9.64303	+	29.6782i	−0.356174	+	1.09619i	0.599152	+	0.800635i	$0.295504\pi$
$733$	−9.64303	+	29.6782i	−0.356174	+	1.09619i	−0.955326	+	0.295554i	$0.904496\pi$
$734$		0			0
$735$	−2.19630			−0.0810117
$736$		0			0
$737$	31.4900			1.15995
$738$		0			0
$739$	−11.3530			−0.417625			−0.208813	−	0.977956i	$-0.566960\pi$
$739$	−11.3530			−0.417625			−0.208813	+	0.977956i	$0.566960\pi$
$740$		0			0
$741$	−4.73849			−0.174073
$742$		0			0
$743$	−6.25670	+	19.2561i	−0.229536	+	0.706439i	0.768263	+	0.640134i	$0.221121\pi$
$743$	−6.25670	+	19.2561i	−0.229536	+	0.706439i	−0.997799	+	0.0663055i	$0.978879\pi$
$744$		0			0
$745$	9.81782	+	7.13306i	0.359697	+	0.261335i
$746$		0			0
$747$	40.7654			1.49153
$748$		0			0
$749$	−2.61857	−	8.05914i	−0.0956806	−	0.294474i
$750$		0			0
$751$	−18.4611	+	13.4128i	−0.673656	+	0.489440i	−0.871247	−	0.490845i	$-0.836688\pi$
$751$	−18.4611	+	13.4128i	−0.673656	+	0.489440i	0.197591	+	0.980285i	$0.436688\pi$
$752$		0			0
$753$	−6.40578	+	19.7150i	−0.233440	+	0.718454i
$754$		0			0
$755$	−10.9118	−	33.5830i	−0.397120	−	1.22221i
$756$		0			0
$757$	−43.0272	−	31.2611i	−1.56385	−	1.13620i	−0.932764	−	0.360489i	$-0.882610\pi$
$757$	−43.0272	−	31.2611i	−1.56385	−	1.13620i	−0.631085	−	0.775714i	$-0.717390\pi$
$758$		0			0
$759$	−2.66301	−	1.93479i	−0.0966612	−	0.0702285i
$760$		0			0
$761$	−36.2434	+	26.3324i	−1.31382	+	0.954547i	−0.313835	+	0.949478i	$0.601614\pi$
$761$	−36.2434	+	26.3324i	−1.31382	+	0.954547i	−0.999987	+	0.00506961i	$0.998386\pi$
$762$		0			0
$763$	−13.6950	−	9.95000i	−0.495792	−	0.360214i
$764$		0			0
$765$	40.7188			1.47219
$766$		0			0
$767$	14.5277	−	44.7117i	0.524565	−	1.61445i
$768$		0			0
$769$	8.45764	+	26.0299i	0.304990	+	0.938663i	0.979681	+	0.200563i	$0.0642770\pi$
$769$	8.45764	+	26.0299i	0.304990	+	0.938663i	−0.674691	+	0.738101i	$0.735723\pi$
$770$		0			0
$771$	2.80496	+	8.63277i	0.101018	+	0.310901i
$772$		0			0
$773$	−33.4385	+	24.2945i	−1.20270	+	0.873811i	−0.994547	−	0.104285i	$-0.966745\pi$
$773$	−33.4385	+	24.2945i	−1.20270	+	0.873811i	−0.208151	+	0.978097i	$0.566745\pi$
$774$		0			0
$775$	−2.56397	+	7.89108i	−0.0921004	+	0.283456i
$776$		0			0
$777$	1.67171	−	1.21457i	0.0599724	−	0.0435725i
$778$		0			0
$779$	1.83266	−	9.55146i	0.0656618	−	0.342216i
$780$		0			0
$781$	−11.7010	+	8.50130i	−0.418696	+	0.304201i
$782$		0			0
$783$	−7.30016	+	22.4676i	−0.260886	+	0.802925i
$784$		0			0
$785$	−49.8288	+	36.2027i	−1.77847	+	1.29213i
$786$		0			0
$787$	10.0608	+	30.9641i	0.358630	+	1.10375i	0.953875	+	0.300205i	$0.0970551\pi$
$787$	10.0608	+	30.9641i	0.358630	+	1.10375i	−0.595245	+	0.803544i	$0.702945\pi$
$788$		0			0
$789$	−7.31693	−	22.5192i	−0.260490	−	0.801705i
$790$		0			0
$791$	−3.01687	+	9.28496i	−0.107267	+	0.330135i
$792$		0			0
$793$	28.0023			0.994392
$794$		0			0
$795$	12.4183	+	9.02242i	0.440432	+	0.319992i
$796$		0			0
$797$	−18.2933	+	13.2909i	−0.647983	+	0.470787i	−0.862584	−	0.505914i	$-0.831155\pi$
$797$	−18.2933	+	13.2909i	−0.647983	+	0.470787i	0.214600	+	0.976702i	$0.431155\pi$
$798$		0			0
$799$	−51.0289	−	37.0747i	−1.80527	−	1.31161i
$800$		0			0
$801$	−31.7137	−	23.0413i	−1.12055	−	0.814126i
$802$		0			0
$803$	−1.33195	−	4.09933i	−0.0470036	−	0.144662i
$804$		0			0
$805$	3.90549	−	12.0199i	0.137650	−	0.423644i
$806$		0			0
$807$	−9.76329	+	7.09345i	−0.343684	+	0.249701i
$808$		0			0
$809$	−0.0864554	−	0.266082i	−0.00303961	−	0.00935496i	0.949525	−	0.313691i	$-0.101566\pi$
$809$	−0.0864554	−	0.266082i	−0.00303961	−	0.00935496i	−0.952565	+	0.304336i	$0.901566\pi$
$810$		0			0
$811$	−32.1834			−1.13011			−0.565057	−	0.825052i	$-0.691146\pi$
$811$	−32.1834			−1.13011			−0.565057	+	0.825052i	$0.691146\pi$
$812$		0			0
$813$	−3.04303	−	2.21089i	−0.106724	−	0.0775392i
$814$		0			0
$815$	−10.2394	+	31.5137i	−0.358671	+	1.10388i
$816$		0			0
$817$	8.88497			0.310846
$818$		0			0
$819$	22.7195			0.793885
$820$		0			0
$821$	−52.4771			−1.83146			−0.915731	−	0.401791i	$-0.868388\pi$
$821$	−52.4771			−1.83146			−0.915731	+	0.401791i	$0.868388\pi$
$822$		0			0
$823$	46.5553			1.62282			0.811408	−	0.584481i	$-0.198702\pi$
$823$	46.5553			1.62282			0.811408	+	0.584481i	$0.198702\pi$
$824$		0			0
$825$	1.98102	−	6.09695i	0.0689702	−	0.212269i
$826$		0			0
$827$	−9.94037	−	7.22210i	−0.345660	−	0.251137i	0.401386	−	0.915909i	$-0.368529\pi$
$827$	−9.94037	−	7.22210i	−0.345660	−	0.251137i	−0.747046	+	0.664772i	$0.768529\pi$
$828$		0			0
$829$	21.1899			0.735955			0.367977	−	0.929835i	$-0.380050\pi$
$829$	21.1899			0.735955			0.367977	+	0.929835i	$0.380050\pi$
$830$		0			0
$831$	−2.56030	−	7.87980i	−0.0888159	−	0.273347i
$832$		0			0
$833$	−4.54341	+	3.30098i	−0.157420	+	0.114372i
$834$		0			0
$835$	9.00735	−	27.7218i	0.311712	−	0.959351i
$836$		0			0
$837$	3.18780	+	9.81105i	0.110187	+	0.339120i
$838$		0			0
$839$	14.2063	+	10.3215i	0.490456	+	0.356337i	0.805360	−	0.592787i	$-0.201972\pi$
$839$	14.2063	+	10.3215i	0.490456	+	0.356337i	−0.314904	+	0.949124i	$0.601972\pi$
$840$		0			0
$841$	−1.17665	−	0.854886i	−0.0405741	−	0.0294788i
$842$		0			0
$843$	−8.04022	+	5.84156i	−0.276920	+	0.201194i
$844$		0			0
$845$	−5.34628	−	3.88430i	−0.183918	−	0.133624i
$846$		0			0
$847$	−13.6774			−0.469962
$848$		0			0
$849$	6.08815	−	18.7374i	0.208945	−	0.643066i
$850$		0			0
$851$	−0.574806	−	1.76907i	−0.0197041	−	0.0606429i
$852$		0			0
$853$	−3.71015	−	11.4187i	−0.127033	−	0.390968i	0.867233	−	0.497903i	$-0.165896\pi$
$853$	−3.71015	−	11.4187i	−0.127033	−	0.390968i	−0.994266	+	0.106935i	$0.965896\pi$
$854$		0			0
$855$	8.43658	−	6.12953i	0.288525	−	0.209626i
$856$		0			0
$857$	13.3615	−	41.1226i	0.456421	−	1.40472i	−0.413037	−	0.910714i	$-0.635532\pi$
$857$	13.3615	−	41.1226i	0.456421	−	1.40472i	0.869458	−	0.494006i	$-0.164468\pi$
$858$		0			0
$859$	−29.8930	+	21.7185i	−1.01994	+	0.741027i	−0.966270	−	0.257532i	$-0.917091\pi$
$859$	−29.8930	+	21.7185i	−1.01994	+	0.741027i	−0.0536661	+	0.998559i	$0.517091\pi$
$860$		0			0
$861$	2.36959	−	12.3498i	0.0807554	−	0.420881i
$862$		0			0
$863$	0.233266	−	0.169478i	0.00794048	−	0.00576910i	−0.583808	−	0.811892i	$-0.698438\pi$
$863$	0.233266	−	0.169478i	0.00794048	−	0.00576910i	0.591748	+	0.806123i	$0.298438\pi$
$864$		0			0
$865$	5.25461	−	16.1720i	0.178662	−	0.549866i
$866$		0			0
$867$	−11.7369	+	8.52738i	−0.398607	+	0.289605i
$868$		0			0
$869$	2.57394	+	7.92178i	0.0873150	+	0.268728i
$870$		0			0
$871$	−16.3044	−	50.1799i	−0.552455	−	1.70028i
$872$		0			0
$873$	9.95251	−	30.6307i	0.336841	−	1.03669i
$874$		0			0
$875$	−11.1304			−0.376275
$876$		0			0
$877$	35.6186	+	25.8784i	1.20276	+	0.873853i	0.994553	−	0.104233i	$-0.0332388\pi$
$877$	35.6186	+	25.8784i	1.20276	+	0.873853i	0.208202	+	0.978086i	$0.433239\pi$
$878$		0			0
$879$	−10.2226	+	7.42718i	−0.344801	+	0.250513i
$880$		0			0
$881$	24.3049	+	17.6586i	0.818854	+	0.594932i	0.916384	−	0.400300i	$-0.131094\pi$
$881$	24.3049	+	17.6586i	0.818854	+	0.594932i	−0.0975301	+	0.995233i	$0.531094\pi$
$882$		0			0
$883$	7.18443	+	5.21979i	0.241775	+	0.175660i	0.702074	−	0.712104i	$-0.252258\pi$
$883$	7.18443	+	5.21979i	0.241775	+	0.175660i	−0.460299	+	0.887764i	$0.652258\pi$
$884$		0			0
$885$	−8.62181	−	26.5352i	−0.289819	−	0.891971i
$886$		0			0
$887$	14.2622	−	43.8945i	0.478878	−	1.47383i	−0.361778	−	0.932264i	$-0.617830\pi$
$887$	14.2622	−	43.8945i	0.478878	−	1.47383i	0.840656	−	0.541569i	$-0.182170\pi$
$888$		0			0
$889$	−12.6898	+	9.21970i	−0.425603	+	0.309219i
$890$		0			0
$891$	2.64631	+	8.14449i	0.0886546	+	0.272851i
$892$		0			0
$893$	−16.1537			−0.540563
$894$		0			0
$895$	18.7701	+	13.6373i	0.627415	+	0.455843i
$896$		0			0
$897$	−1.70431	+	5.24533i	−0.0569053	+	0.175136i
$898$		0			0
$899$	−13.2987			−0.443537
$900$		0			0
$901$	39.2498			1.30760
$902$		0			0
$903$	11.4881			0.382300
$904$		0			0
$905$	18.2754			0.607495
$906$		0			0
$907$	−6.88585	+	21.1925i	−0.228641	+	0.703685i	0.769261	+	0.638935i	$0.220625\pi$
$907$	−6.88585	+	21.1925i	−0.228641	+	0.703685i	−0.997902	+	0.0647495i	$0.979375\pi$
$908$		0			0
$909$	−14.2387	−	10.3450i	−0.472267	−	0.343122i
$910$		0			0
$911$	−28.8297			−0.955170			−0.477585	−	0.878585i	$-0.658488\pi$
$911$	−28.8297			−0.955170			−0.477585	+	0.878585i	$0.658488\pi$
$912$		0			0
$913$	−12.4358	−	38.2734i	−0.411564	−	1.26666i
$914$		0			0
$915$	13.4448	−	9.76819i	0.444470	−	0.322926i
$916$		0			0
$917$	15.4359	−	47.5069i	0.509739	−	1.56882i
$918$		0			0
$919$	8.00969	+	24.6513i	0.264215	+	0.813171i	0.991873	+	0.127231i	$0.0406090\pi$
$919$	8.00969	+	24.6513i	0.264215	+	0.813171i	−0.727658	+	0.685940i	$0.759391\pi$
$920$		0			0
$921$	−12.1980	−	8.86239i	−0.401939	−	0.292026i
$922$		0			0
$923$	19.6054	+	14.2441i	0.645319	+	0.468852i
$924$		0			0
$925$	2.93081	−	2.12936i	0.0963643	−	0.0700128i
$926$		0			0
$927$	−17.5276	−	12.7346i	−0.575682	−	0.418258i
$928$		0			0
$929$	−1.69608			−0.0556466			−0.0278233	−	0.999613i	$-0.508858\pi$
$929$	−1.69608			−0.0556466			−0.0278233	+	0.999613i	$0.508858\pi$
$930$		0			0
$931$	−0.444448	+	1.36787i	−0.0145662	+	0.0448301i
$932$		0			0
$933$	−3.49301	−	10.7504i	−0.114356	−	0.351952i
$934$		0			0
$935$	−12.4216	−	38.2297i	−0.406229	−	1.25024i
$936$		0			0
$937$	10.9245	−	7.93711i	0.356888	−	0.259294i	−0.394865	−	0.918739i	$-0.629209\pi$
$937$	10.9245	−	7.93711i	0.356888	−	0.259294i	0.751753	+	0.659445i	$0.229209\pi$
$938$		0			0
$939$	0.0433819	−	0.133516i	0.00141571	−	0.00435712i
$940$		0			0
$941$	16.7554	−	12.1735i	0.546211	−	0.396846i	−0.280176	−	0.959949i	$-0.590393\pi$
$941$	16.7554	−	12.1735i	0.546211	−	0.396846i	0.826387	+	0.563103i	$0.190393\pi$
$942$		0			0
$943$	−9.91393	−	5.46409i	−0.322842	−	0.177935i
$944$		0			0
$945$	24.7583	−	17.9880i	0.805387	−	0.585148i
$946$		0			0
$947$	7.28428	−	22.4187i	0.236707	−	0.728510i	−0.760183	−	0.649709i	$-0.774891\pi$
$947$	7.28428	−	22.4187i	0.236707	−	0.728510i	0.996890	−	0.0788011i	$-0.0251092\pi$
$948$		0			0
$949$	−5.84272	+	4.24499i	−0.189663	+	0.137798i
$950$		0			0
$951$	−2.26943	−	6.98458i	−0.0735912	−	0.226490i
$952$		0			0
$953$	−2.99039	−	9.20346i	−0.0968681	−	0.298129i	0.890868	−	0.454262i	$-0.150097\pi$
$953$	−2.99039	−	9.20346i	−0.0968681	−	0.298129i	−0.987736	+	0.156133i	$0.950097\pi$
$954$		0			0
$955$	−18.1420	+	55.8353i	−0.587061	+	1.80679i
$956$		0			0
$957$	10.2751			0.332147
$958$		0			0
$959$	−13.3858	−	9.72533i	−0.432249	−	0.314047i
$960$		0			0
$961$	20.3814	−	14.8079i	0.657464	−	0.477675i
$962$		0			0
$963$	−6.58388	−	4.78347i	−0.212163	−	0.154145i
$964$		0			0
$965$	9.14073	+	6.64113i	0.294250	+	0.213785i
$966$		0			0
$967$	0.925245	+	2.84761i	0.0297539	+	0.0915730i	0.964831	−	0.262872i	$-0.0846697\pi$
$967$	0.925245	+	2.84761i	0.0297539	+	0.0915730i	−0.935077	+	0.354445i	$0.884670\pi$
$968$		0			0
$969$	−2.22207	+	6.83881i	−0.0713830	+	0.219694i
$970$		0			0
$971$	23.8526	−	17.3299i	0.765467	−	0.556144i	−0.135116	−	0.990830i	$-0.543141\pi$
$971$	23.8526	−	17.3299i	0.765467	−	0.556144i	0.900582	+	0.434686i	$0.143141\pi$
$972$		0			0
$973$	7.36945	+	22.6808i	0.236254	+	0.727114i
$974$		0			0
$975$	−10.7413			−0.343997
$976$		0			0
$977$	34.4568	+	25.0343i	1.10237	+	0.800919i	0.981445	−	0.191743i	$-0.0614139\pi$
$977$	34.4568	+	25.0343i	1.10237	+	0.800919i	0.120925	+	0.992662i	$0.461414\pi$
$978$		0			0
$979$	−11.9583	+	36.8040i	−0.382190	+	1.17626i
$980$		0			0
$981$	−16.2572			−0.519053
$982$		0			0
$983$	42.2266			1.34682			0.673410	−	0.739269i	$-0.264829\pi$
$983$	42.2266			1.34682			0.673410	+	0.739269i	$0.264829\pi$
$984$		0			0
$985$	17.4846			0.557106
$986$		0			0
$987$	−20.8864			−0.664822
$988$		0			0
$989$	3.19569	−	9.83532i	0.101617	−	0.312745i
$990$		0			0
$991$	35.7990	+	26.0095i	1.13719	+	0.826219i	0.986726	−	0.162396i	$-0.0519222\pi$
$991$	35.7990	+	26.0095i	1.13719	+	0.826219i	0.150467	+	0.988615i	$0.451922\pi$
$992$		0			0
$993$	−9.24903			−0.293509
$994$		0			0
$995$	5.41972	+	16.6802i	0.171817	+	0.528797i
$996$		0			0
$997$	4.37403	−	3.17792i	0.138527	−	0.100646i	−0.516364	−	0.856369i	$-0.672715\pi$
$997$	4.37403	−	3.17792i	0.138527	−	0.100646i	0.654891	+	0.755724i	$0.272715\pi$
$998$		0			0
$999$	1.39185	−	4.28366i	0.0440361	−	0.135529i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	656.2.u.h.529.3		20
4.3	odd	2		328.2.m.c.201.3	✓	20
41.10	even	5	inner	656.2.u.h.625.3		20
164.51	odd	10		328.2.m.c.297.3	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
328.2.m.c.201.3	✓	20	4.3	odd	2
328.2.m.c.297.3	yes	20	164.51	odd	10
656.2.u.h.529.3		20	1.1	even	1	trivial
656.2.u.h.625.3		20	41.10	even	5	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 656 = 2^{4} \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	656.u (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+0.798236 q^{3} +(0.897909 - 2.76348i) q^{5} +(-1.99043 - 1.44613i) q^{7} -2.36282 q^{9} +O(q^{10})\)	\(q+0.798236 q^{3} +(0.897909 - 2.76348i) q^{5} +(-1.99043 - 1.44613i) q^{7} -2.36282 q^{9} +(0.720795 + 2.21838i) q^{11} +(3.16183 - 2.29720i) q^{13} +(0.716744 - 2.20591i) q^{15} +(-1.83272 - 5.64054i) q^{17} +(-1.22881 - 0.892785i) q^{19} +(-1.58883 - 1.15435i) q^{21} +(-1.43025 + 1.03914i) q^{23} +(-2.78550 - 2.02378i) q^{25} -4.28080 q^{27} +(1.70533 - 5.24846i) q^{29} +(-0.744676 - 2.29188i) q^{31} +(0.575365 + 1.77079i) q^{33} +(-5.78357 + 4.20201i) q^{35} +(-0.325137 + 1.00067i) q^{37} +(2.52388 - 1.83371i) q^{39} +(2.72010 + 5.79664i) q^{41} +(-4.73244 + 3.43832i) q^{43} +(-2.12160 + 6.52960i) q^{45} +(8.60402 - 6.25119i) q^{47} +(-0.292612 - 0.900567i) q^{49} +(-1.46295 - 4.50249i) q^{51} +(-2.04506 + 6.29404i) q^{53} +6.77766 q^{55} +(-0.980884 - 0.712654i) q^{57} +(9.73177 - 7.07055i) q^{59} +(5.79658 + 4.21146i) q^{61} +(4.70302 + 3.41694i) q^{63} +(-3.50924 - 10.8003i) q^{65} +(4.17182 - 12.8395i) q^{67} +(-1.14168 + 0.829477i) q^{69} +(1.91611 + 5.89717i) q^{71} -1.84789 q^{73} +(-2.22349 - 1.61546i) q^{75} +(1.77337 - 5.45789i) q^{77} +3.57097 q^{79} +3.67137 q^{81} -17.2528 q^{83} -17.2332 q^{85} +(1.36125 - 4.18951i) q^{87} +(13.4220 + 9.75163i) q^{89} -9.61543 q^{91} +(-0.594427 - 1.82946i) q^{93} +(-3.57056 + 2.59416i) q^{95} +(-4.21214 + 12.9636i) q^{97} +(-1.70311 - 5.24163i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 2 q^{3} + 2 q^{5} + 10 q^{9}+O(q^{10}) \) 20 * q - 2 * q^3 + 2 * q^5 + 10 * q^9	\( 20 q - 2 q^{3} + 2 q^{5} + 10 q^{9} - 9 q^{11} + 7 q^{13} - q^{15} - 8 q^{17} - q^{19} - 6 q^{21} + 11 q^{23} + 15 q^{25} - 2 q^{27} + 21 q^{29} + 5 q^{31} + 19 q^{33} - 4 q^{37} - 4 q^{39} + 9 q^{41} + 17 q^{43} + 11 q^{45} - 15 q^{47} - 25 q^{49} + 22 q^{51} + 10 q^{53} + 28 q^{55} - 20 q^{57} + 24 q^{59} + 15 q^{61} + 65 q^{63} - 29 q^{65} + 26 q^{67} - 47 q^{69} - 16 q^{71} + 14 q^{73} - 11 q^{75} + 12 q^{77} + 26 q^{79} - 60 q^{81} - 20 q^{83} - 94 q^{85} - 57 q^{87} + 5 q^{89} + 46 q^{91} + 43 q^{93} - 71 q^{95} - 22 q^{97} - 8 q^{99}+O(q^{100}) \) 20 * q - 2 * q^3 + 2 * q^5 + 10 * q^9 - 9 * q^11 + 7 * q^13 - q^15 - 8 * q^17 - q^19 - 6 * q^21 + 11 * q^23 + 15 * q^25 - 2 * q^27 + 21 * q^29 + 5 * q^31 + 19 * q^33 - 4 * q^37 - 4 * q^39 + 9 * q^41 + 17 * q^43 + 11 * q^45 - 15 * q^47 - 25 * q^49 + 22 * q^51 + 10 * q^53 + 28 * q^55 - 20 * q^57 + 24 * q^59 + 15 * q^61 + 65 * q^63 - 29 * q^65 + 26 * q^67 - 47 * q^69 - 16 * q^71 + 14 * q^73 - 11 * q^75 + 12 * q^77 + 26 * q^79 - 60 * q^81 - 20 * q^83 - 94 * q^85 - 57 * q^87 + 5 * q^89 + 46 * q^91 + 43 * q^93 - 71 * q^95 - 22 * q^97 - 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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