LMFDB - Embedded newform 1710.2.p.d.1063.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1710,2,Mod(37,1710)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1710, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 1, 2]))

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

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

chi := DirichletCharacter("1710.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1710 = 2 \cdot 3^{2} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1710.p (of order $4$, 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:	$13.6544187456$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(i)$
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} + 153x^{16} + 6416x^{12} + 78648x^{8} + 19120x^{4} + 16 $ x^20 + 153x^16 + 6416x^12 + 78648x^8 + 19120x^4 + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 2^{10} $
Twist minimal:	no (minimal twist has level 570)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			1063.4
Root			$-0.120370 - 0.120370i$ of defining polynomial
Character	$\chi$	$=$	1710.1063
Dual form			1710.2.p.d.37.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 - 0.707107i) q^{2} +1.00000i q^{4} +(1.66396 + 1.49373i) q^{5} +(-0.170229 + 0.170229i) q^{7} +(0.707107 - 0.707107i) q^{8} +O(q^{10})$	\(q+(-0.707107 - 0.707107i) q^{2} +1.00000i q^{4} +(1.66396 + 1.49373i) q^{5} +(-0.170229 + 0.170229i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-0.120370 - 2.23283i) q^{10} -3.43349 q^{11} +(4.54030 - 4.54030i) q^{13} +0.240740 q^{14} -1.00000 q^{16} +(-0.537531 + 0.537531i) q^{17} +(2.42784 - 3.62016i) q^{19} +(-1.49373 + 1.66396i) q^{20} +(2.42784 + 2.42784i) q^{22} +(-5.15769 - 5.15769i) q^{23} +(0.537531 + 4.97102i) q^{25} -6.42095 q^{26} +(-0.170229 - 0.170229i) q^{28} +5.37513 q^{29} -5.37513i q^{31} +(0.707107 + 0.707107i) q^{32} +0.760184 q^{34} +(-0.537531 + 0.0289779i) q^{35} +(-5.54122 - 5.54122i) q^{37} +(-4.27659 + 0.843095i) q^{38} +(2.23283 - 0.120370i) q^{40} +3.68222i q^{41} +(2.29224 + 2.29224i) q^{43} -3.43349i q^{44} +7.29408i q^{46} +(9.57865 - 9.57865i) q^{47} +6.94204i q^{49} +(3.13495 - 3.89514i) q^{50} +(4.54030 + 4.54030i) q^{52} +(1.93366 - 1.93366i) q^{53} +(-5.71319 - 5.12871i) q^{55} +0.240740i q^{56} +(-3.80079 - 3.80079i) q^{58} +4.20166 q^{59} +1.65954 q^{61} +(-3.80079 + 3.80079i) q^{62} -1.00000i q^{64} +(14.3369 - 0.772891i) q^{65} +(0.481480 + 0.481480i) q^{67} +(-0.537531 - 0.537531i) q^{68} +(0.400582 + 0.359601i) q^{70} -8.93130i q^{71} +(8.74888 + 8.74888i) q^{73} +7.83647i q^{74} +(3.62016 + 2.42784i) q^{76} +(0.584480 - 0.584480i) q^{77} +1.15022 q^{79} +(-1.66396 - 1.49373i) q^{80} +(2.60372 - 2.60372i) q^{82} +(9.97102 + 9.97102i) q^{83} +(-1.69736 + 0.0915034i) q^{85} -3.24172i q^{86} +(-2.42784 + 2.42784i) q^{88} -2.10098 q^{89} +1.54578i q^{91} +(5.15769 - 5.15769i) q^{92} -13.5463 q^{94} +(9.44739 - 2.39726i) q^{95} +(10.8544 + 10.8544i) q^{97} +(4.90877 - 4.90877i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 4 q^{5} - 4 q^{7}+O(q^{10}) $ 20 * q + 4 * q^5 - 4 * q^7	$ 20 q + 4 q^{5} - 4 q^{7} + 8 q^{11} - 20 q^{16} - 4 q^{17} - 44 q^{23} + 4 q^{25} + 8 q^{26} - 4 q^{28} - 4 q^{35} + 4 q^{38} + 52 q^{43} - 4 q^{47} + 16 q^{55} + 8 q^{58} + 32 q^{61} + 8 q^{62} - 4 q^{68} - 20 q^{73} + 20 q^{76} + 24 q^{77} - 4 q^{80} - 24 q^{82} + 116 q^{83} - 60 q^{85} + 44 q^{92} + 32 q^{95}+O(q^{100}) $ 20 * q + 4 * q^5 - 4 * q^7 + 8 * q^11 - 20 * q^16 - 4 * q^17 - 44 * q^23 + 4 * q^25 + 8 * q^26 - 4 * q^28 - 4 * q^35 + 4 * q^38 + 52 * q^43 - 4 * q^47 + 16 * q^55 + 8 * q^58 + 32 * q^61 + 8 * q^62 - 4 * q^68 - 20 * q^73 + 20 * q^76 + 24 * q^77 - 4 * q^80 - 24 * q^82 + 116 * q^83 - 60 * q^85 + 44 * q^92 + 32 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1710\mathbb{Z}\right)^\times$.

$n$	$191$	$1027$	$1351$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$	$-1$

Coefficient data

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

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

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

$2$	−0.707107	−	0.707107i	−0.500000	−	0.500000i
$2$	−0.707107	−	0.707107i	−0.500000	−	0.500000i
$3$		0			0
$3$		0			0
$4$			1.00000i			0.500000i
$5$	1.66396	+	1.49373i	0.744146	+	0.668017i
$5$	1.66396	+	1.49373i	0.744146	+	0.668017i
$6$		0			0
$7$	−0.170229	+	0.170229i	−0.0643405	+	0.0643405i	−0.738545	−	0.674204i	$-0.764487\pi$
$7$	−0.170229	+	0.170229i	−0.0643405	+	0.0643405i	0.674204	+	0.738545i	$0.264487\pi$
$8$	0.707107	−	0.707107i	0.250000	−	0.250000i
$9$		0			0
$10$	−0.120370	−	2.23283i	−0.0380644	−	0.706082i
$11$	−3.43349			−1.03524			−0.517618	−	0.855612i	$-0.673181\pi$
$11$	−3.43349			−1.03524			−0.517618	+	0.855612i	$0.673181\pi$
$12$		0			0
$13$	4.54030	−	4.54030i	1.25925	−	1.25925i	0.307803	−	0.951450i	$-0.400406\pi$
$13$	4.54030	−	4.54030i	1.25925	−	1.25925i	0.951450	−	0.307803i	$-0.0995936\pi$
$14$	0.240740			0.0643405
$15$		0			0
$16$	−1.00000			−0.250000
$17$	−0.537531	+	0.537531i	−0.130370	+	0.130370i	−0.769281	−	0.638911i	$-0.779385\pi$
$17$	−0.537531	+	0.537531i	−0.130370	+	0.130370i	0.638911	+	0.769281i	$0.279385\pi$
$18$		0			0
$19$	2.42784	−	3.62016i	0.556986	−	0.830522i
$19$	2.42784	−	3.62016i	0.556986	−	0.830522i
$20$	−1.49373	+	1.66396i	−0.334009	+	0.372073i
$21$		0			0
$22$	2.42784	+	2.42784i	0.517618	+	0.517618i
$23$	−5.15769	−	5.15769i	−1.07545	−	1.07545i	−0.996911	−	0.0785425i	$-0.974973\pi$
$23$	−5.15769	−	5.15769i	−1.07545	−	1.07545i	−0.0785425	−	0.996911i	$-0.525027\pi$
$24$		0			0
$25$	0.537531	+	4.97102i	0.107506	+	0.994204i
$26$	−6.42095			−1.25925
$27$		0			0
$28$	−0.170229	−	0.170229i	−0.0321703	−	0.0321703i
$29$	5.37513			0.998137			0.499069	−	0.866562i	$-0.333676\pi$
$29$	5.37513			0.998137			0.499069	+	0.866562i	$0.333676\pi$
$30$		0			0
$31$		−	5.37513i		−	0.965402i	−0.875785	−	0.482701i	$-0.839656\pi$
$31$		−	5.37513i		−	0.965402i	0.875785	−	0.482701i	$-0.160344\pi$
$32$	0.707107	+	0.707107i	0.125000	+	0.125000i
$33$		0			0
$34$	0.760184			0.130370
$35$	−0.537531	+	0.0289779i	−0.0908593	+	0.00489816i
$36$		0			0
$37$	−5.54122	−	5.54122i	−0.910972	−	0.910972i	0.0853770	−	0.996349i	$-0.472791\pi$
$37$	−5.54122	−	5.54122i	−0.910972	−	0.910972i	−0.996349	+	0.0853770i	$0.972791\pi$
$38$	−4.27659	+	0.843095i	−0.693754	+	0.136768i
$39$		0			0
$40$	2.23283	−	0.120370i	0.353041	−	0.0190322i
$41$			3.68222i			0.575066i	0.957771	+	0.287533i	$0.0928350\pi$
$41$			3.68222i			0.575066i	−0.957771	+	0.287533i	$0.907165\pi$
$42$		0			0
$43$	2.29224	+	2.29224i	0.349563	+	0.349563i	0.859947	−	0.510384i	$-0.170497\pi$
$43$	2.29224	+	2.29224i	0.349563	+	0.349563i	−0.510384	+	0.859947i	$0.670497\pi$
$44$		−	3.43349i		−	0.517618i
$45$		0			0
$46$			7.29408i			1.07545i
$47$	9.57865	−	9.57865i	1.39719	−	1.39719i	0.589208	−	0.807982i	$-0.299440\pi$
$47$	9.57865	−	9.57865i	1.39719	−	1.39719i	0.807982	−	0.589208i	$-0.200560\pi$
$48$		0			0
$49$			6.94204i			0.991721i
$50$	3.13495	−	3.89514i	0.443349	−	0.550855i
$51$		0			0
$52$	4.54030	+	4.54030i	0.629626	+	0.629626i
$53$	1.93366	−	1.93366i	0.265608	−	0.265608i	−0.561720	−	0.827328i	$-0.689860\pi$
$53$	1.93366	−	1.93366i	0.265608	−	0.265608i	0.827328	+	0.561720i	$0.189860\pi$
$54$		0			0
$55$	−5.71319	−	5.12871i	−0.770367	−	0.691556i
$56$			0.240740i			0.0321703i
$57$		0			0
$58$	−3.80079	−	3.80079i	−0.499069	−	0.499069i
$59$	4.20166			0.547010			0.273505	−	0.961871i	$-0.411817\pi$
$59$	4.20166			0.547010			0.273505	+	0.961871i	$0.411817\pi$
$60$		0			0
$61$	1.65954			0.212483			0.106241	−	0.994340i	$-0.466118\pi$
$61$	1.65954			0.212483			0.106241	+	0.994340i	$0.466118\pi$
$62$	−3.80079	+	3.80079i	−0.482701	+	0.482701i
$63$		0			0
$64$		−	1.00000i		−	0.125000i
$65$	14.3369	−	0.772891i	1.77827	−	0.0958653i
$66$		0			0
$67$	0.481480	+	0.481480i	0.0588222	+	0.0588222i	0.735906	−	0.677084i	$-0.236757\pi$
$67$	0.481480	+	0.481480i	0.0588222	+	0.0588222i	−0.677084	+	0.735906i	$0.736757\pi$
$68$	−0.537531	−	0.537531i	−0.0651852	−	0.0651852i
$69$		0			0
$70$	0.400582	+	0.359601i	0.0478787	+	0.0429806i
$71$		−	8.93130i		−	1.05995i	−0.848013	−	0.529975i	$-0.822201\pi$
$71$		−	8.93130i		−	1.05995i	0.848013	−	0.529975i	$-0.177799\pi$
$72$		0			0
$73$	8.74888	+	8.74888i	1.02398	+	1.02398i	0.999705	+	0.0242731i	$0.00772714\pi$
$73$	8.74888	+	8.74888i	1.02398	+	1.02398i	0.0242731	+	0.999705i	$0.492273\pi$
$74$			7.83647i			0.910972i
$75$		0			0
$76$	3.62016	+	2.42784i	0.415261	+	0.278493i
$77$	0.584480	−	0.584480i	0.0666077	−	0.0666077i
$78$		0			0
$79$	1.15022			0.129410			0.0647050	−	0.997904i	$-0.479389\pi$
$79$	1.15022			0.129410			0.0647050	+	0.997904i	$0.479389\pi$
$80$	−1.66396	−	1.49373i	−0.186036	−	0.167004i
$81$		0			0
$82$	2.60372	−	2.60372i	0.287533	−	0.287533i
$83$	9.97102	+	9.97102i	1.09446	+	1.09446i	0.995046	+	0.0994159i	$0.0316974\pi$
$83$	9.97102	+	9.97102i	1.09446	+	1.09446i	0.0994159	+	0.995046i	$0.468303\pi$
$84$		0			0
$85$	−1.69736	+	0.0915034i	−0.184104	+	0.00992494i
$86$		−	3.24172i		−	0.349563i
$87$		0			0
$88$	−2.42784	+	2.42784i	−0.258809	+	0.258809i
$89$	−2.10098			−0.222703			−0.111351	−	0.993781i	$-0.535518\pi$
$89$	−2.10098			−0.222703			−0.111351	+	0.993781i	$0.535518\pi$
$90$		0			0
$91$			1.54578i			0.162042i
$92$	5.15769	−	5.15769i	0.537727	−	0.537727i
$93$		0			0
$94$	−13.5463			−1.39719
$95$	9.44739	−	2.39726i	0.969282	−	0.245953i
$96$		0			0
$97$	10.8544	+	10.8544i	1.10210	+	1.10210i	0.994157	+	0.107942i	$0.0344260\pi$
$97$	10.8544	+	10.8544i	1.10210	+	1.10210i	0.107942	+	0.994157i	$0.465574\pi$
$98$	4.90877	−	4.90877i	0.495860	−	0.495860i
$99$		0			0
$100$	−4.97102	+	0.537531i	−0.497102	+	0.0537531i
$101$	−8.90870			−0.886449			−0.443225	−	0.896411i	$-0.646166\pi$
$101$	−8.90870			−0.886449			−0.443225	+	0.896411i	$0.646166\pi$
$102$		0			0
$103$	6.26365	−	6.26365i	0.617176	−	0.617176i	−0.327630	−	0.944806i	$-0.606250\pi$
$103$	6.26365	−	6.26365i	0.617176	−	0.617176i	0.944806	+	0.327630i	$0.106250\pi$
$104$		−	6.42095i		−	0.629626i
$105$		0			0
$106$	−2.73460			−0.265608
$107$	−5.59814	−	5.59814i	−0.541193	−	0.541193i	0.382686	−	0.923879i	$-0.374999\pi$
$107$	−5.59814	−	5.59814i	−0.541193	−	0.541193i	−0.923879	+	0.382686i	$0.874999\pi$
$108$		0			0
$109$	−10.7123			−1.02605			−0.513026	−	0.858373i	$-0.671476\pi$
$109$	−10.7123			−1.02605			−0.513026	+	0.858373i	$0.671476\pi$
$110$	0.413290	+	7.66639i	0.0394056	+	0.730961i
$111$		0			0
$112$	0.170229	−	0.170229i	0.0160851	−	0.0160851i
$113$	6.81260	−	6.81260i	0.640875	−	0.640875i	−0.309895	−	0.950771i	$-0.600294\pi$
$113$	6.81260	−	6.81260i	0.640875	−	0.640875i	0.950771	+	0.309895i	$0.100294\pi$
$114$		0			0
$115$	−0.877989	−	16.2864i	−0.0818729	−	1.51872i
$116$			5.37513i			0.499069i
$117$		0			0
$118$	−2.97102	−	2.97102i	−0.273505	−	0.273505i
$119$		−	0.183007i		−	0.0167762i
$120$		0			0
$121$	0.788861			0.0717146
$122$	−1.17347	−	1.17347i	−0.106241	−	0.106241i
$123$		0			0
$124$	5.37513			0.482701
$125$	−6.53094	+	9.07451i	−0.584145	+	0.811649i
$126$		0			0
$127$	5.19935	+	5.19935i	0.461368	+	0.461368i	0.899104	−	0.437736i	$-0.144219\pi$
$127$	5.19935	+	5.19935i	0.461368	+	0.461368i	−0.437736	+	0.899104i	$0.644219\pi$
$128$	−0.707107	+	0.707107i	−0.0625000	+	0.0625000i
$129$		0			0
$130$	−10.6842	−	9.59118i	−0.937068	−	0.841202i
$131$	−2.14729			−0.187610			−0.0938048	−	0.995591i	$-0.529903\pi$
$131$	−2.14729			−0.187610			−0.0938048	+	0.995591i	$0.529903\pi$
$132$		0			0
$133$	0.202967	+	1.02955i	0.0175995	+	0.0892730i
$134$		−	0.680916i		−	0.0588222i
$135$		0			0
$136$			0.760184i			0.0651852i
$137$	13.5518	−	13.5518i	1.15781	−	1.15781i	0.172863	−	0.984946i	$-0.444698\pi$
$137$	13.5518	−	13.5518i	1.15781	−	1.15781i	0.984946	−	0.172863i	$-0.0553017\pi$
$138$		0			0
$139$		−	10.5015i		−	0.890721i	−0.895351	−	0.445361i	$-0.853075\pi$
$139$		−	10.5015i		−	0.890721i	0.895351	−	0.445361i	$-0.146925\pi$
$140$	−0.0289779	−	0.537531i	−0.00244908	−	0.0454297i
$141$		0			0
$142$	−6.31539	+	6.31539i	−0.529975	+	0.529975i
$143$	−15.5891	+	15.5891i	−1.30362	+	1.30362i
$144$		0			0
$145$	8.94401	+	8.02901i	0.742760	+	0.666773i
$146$		−	12.3728i		−	1.02398i
$147$		0			0
$148$	5.54122	−	5.54122i	0.455486	−	0.455486i
$149$		−	1.02035i		−	0.0835900i	−0.999126	−	0.0417950i	$-0.986692\pi$
$149$		−	1.02035i		−	0.0835900i	0.999126	−	0.0417950i	$-0.0133076\pi$
$150$		0			0
$151$		−	19.8394i		−	1.61451i	−0.590204	−	0.807254i	$-0.700953\pi$
$151$		−	19.8394i		−	1.61451i	0.590204	−	0.807254i	$-0.299047\pi$
$152$	−0.843095	−	4.27659i	−0.0683841	−	0.346877i
$153$		0			0
$154$	−0.826579			−0.0666077
$155$	8.02901	−	8.94401i	0.644905	−	0.718400i
$156$		0			0
$157$	−13.1863	+	13.1863i	−1.05238	+	1.05238i	−0.0538289	+	0.998550i	$0.517143\pi$
$157$	−13.1863	+	13.1863i	−1.05238	+	1.05238i	−0.998550	+	0.0538289i	$0.982857\pi$
$158$	−0.813330	−	0.813330i	−0.0647050	−	0.0647050i
$159$		0			0
$160$	0.120370	+	2.23283i	0.00951609	+	0.176520i
$161$	1.75598			0.138390
$162$		0			0
$163$	1.19921	+	1.19921i	0.0939291	+	0.0939291i	0.752510	−	0.658581i	$-0.228843\pi$
$163$	1.19921	+	1.19921i	0.0939291	+	0.0939291i	−0.658581	+	0.752510i	$0.728843\pi$
$164$	−3.68222			−0.287533
$165$		0			0
$166$		−	14.1012i		−	1.09446i
$167$	11.1290	+	11.1290i	0.861184	+	0.861184i	0.991476	−	0.130292i	$-0.0415913\pi$
$167$	11.1290	+	11.1290i	0.861184	+	0.861184i	−0.130292	+	0.991476i	$0.541591\pi$
$168$		0			0
$169$		−	28.2287i		−	2.17144i
$170$	1.26492	+	1.13551i	0.0970146	+	0.0870897i
$171$		0			0
$172$	−2.29224	+	2.29224i	−0.174782	+	0.174782i
$173$	15.2012	−	15.2012i	1.15573	−	1.15573i	0.170341	−	0.985385i	$-0.445513\pi$
$173$	15.2012	−	15.2012i	1.15573	−	1.15573i	0.985385	−	0.170341i	$-0.0544870\pi$
$174$		0			0
$175$	−0.937716	−	0.754709i	−0.0708846	−	0.0570506i
$176$	3.43349			0.258809
$177$		0			0
$178$	1.48561	+	1.48561i	0.111351	+	0.111351i
$179$	−24.9536			−1.86512			−0.932559	−	0.361019i	$-0.882429\pi$
$179$	−24.9536			−1.86512			−0.932559	+	0.361019i	$0.882429\pi$
$180$		0			0
$181$		−	15.9721i		−	1.18720i	−0.804762	−	0.593598i	$-0.797707\pi$
$181$		−	15.9721i		−	1.18720i	0.804762	−	0.593598i	$-0.202293\pi$
$182$	1.09303	−	1.09303i	0.0810210	−	0.0810210i
$183$		0			0
$184$	−7.29408			−0.537727
$185$	−0.943277	−	17.4975i	−0.0693511	−	1.28644i
$186$		0			0
$187$	1.84561	−	1.84561i	0.134964	−	0.134964i
$188$	9.57865	+	9.57865i	0.698595	+	0.698595i
$189$		0			0
$190$	−8.37543	−	4.98520i	−0.607618	−	0.361664i
$191$	−2.91580			−0.210980			−0.105490	−	0.994420i	$-0.533641\pi$
$191$	−2.91580			−0.210980			−0.105490	+	0.994420i	$0.533641\pi$
$192$		0			0
$193$	−6.67601	+	6.67601i	−0.480550	+	0.480550i	−0.905307	−	0.424758i	$-0.860359\pi$
$193$	−6.67601	+	6.67601i	−0.480550	+	0.480550i	0.424758	+	0.905307i	$0.360359\pi$
$194$		−	15.3505i		−	1.10210i
$195$		0			0
$196$	−6.94204			−0.495860
$197$	4.08263	−	4.08263i	0.290875	−	0.290875i	−0.546551	−	0.837426i	$-0.684059\pi$
$197$	4.08263	−	4.08263i	0.290875	−	0.290875i	0.837426	+	0.546551i	$0.184059\pi$
$198$		0			0
$199$			8.23662i			0.583879i	0.956437	+	0.291939i	$0.0943006\pi$
$199$			8.23662i			0.583879i	−0.956437	+	0.291939i	$0.905699\pi$
$200$	3.89514	+	3.13495i	0.275428	+	0.221675i
$201$		0			0
$202$	6.29940	+	6.29940i	0.443225	+	0.443225i
$203$	−0.915004	+	0.915004i	−0.0642207	+	0.0642207i
$204$		0			0
$205$	−5.50024	+	6.12706i	−0.384154	+	0.427933i
$206$	−8.85814			−0.617176
$207$		0			0
$208$	−4.54030	+	4.54030i	−0.314813	+	0.314813i
$209$	−8.33598	+	12.4298i	−0.576612	+	0.859787i
$210$		0			0
$211$		−	14.6136i		−	1.00604i	−0.864275	−	0.503020i	$-0.832222\pi$
$211$		−	14.6136i		−	1.00604i	0.864275	−	0.503020i	$-0.167778\pi$
$212$	1.93366	+	1.93366i	0.132804	+	0.132804i
$213$		0			0
$214$			7.91697i			0.541193i
$215$	0.390206	+	7.23819i	0.0266118	+	0.493640i
$216$		0			0
$217$	0.915004	+	0.915004i	0.0621145	+	0.0621145i
$218$	7.57474	+	7.57474i	0.513026	+	0.513026i
$219$		0			0
$220$	5.12871	−	5.71319i	0.345778	−	0.385183i
$221$			4.88110i			0.328339i
$222$		0			0
$223$	−15.9582	+	15.9582i	−1.06864	+	1.06864i	−0.0711734	+	0.997464i	$0.522674\pi$
$223$	−15.9582	+	15.9582i	−1.06864	+	1.06864i	−0.997464	+	0.0711734i	$0.977326\pi$
$224$	−0.240740			−0.0160851
$225$		0			0
$226$	−9.63447			−0.640875
$227$	−5.87132	−	5.87132i	−0.389694	−	0.389694i	0.484885	−	0.874578i	$-0.338862\pi$
$227$	−5.87132	−	5.87132i	−0.389694	−	0.389694i	−0.874578	+	0.484885i	$0.838862\pi$
$228$		0			0
$229$			10.2825i			0.679487i	0.940518	+	0.339743i	$0.110340\pi$
$229$			10.2825i			0.679487i	−0.940518	+	0.339743i	$0.889660\pi$
$230$	−10.8954	+	12.1371i	−0.718421	+	0.800294i
$231$		0			0
$232$	3.80079	−	3.80079i	0.249534	−	0.249534i
$233$	−14.4725	−	14.4725i	−0.948123	−	0.948123i	0.0505960	−	0.998719i	$-0.483888\pi$
$233$	−14.4725	−	14.4725i	−0.948123	−	0.948123i	−0.998719	+	0.0505960i	$0.983888\pi$
$234$		0			0
$235$	30.2464	−	1.63056i	1.97306	−	0.106366i
$236$			4.20166i			0.273505i
$237$		0			0
$238$	−0.129405	+	0.129405i	−0.00838810	+	0.00838810i
$239$			21.4459i			1.38722i	0.720352	+	0.693609i	$0.243980\pi$
$239$			21.4459i			1.38722i	−0.720352	+	0.693609i	$0.756020\pi$
$240$		0			0
$241$		−	1.51636i		−	0.0976773i	−0.998807	−	0.0488387i	$-0.984448\pi$
$241$		−	1.51636i		−	0.0976773i	0.998807	−	0.0488387i	$-0.0155520\pi$
$242$	−0.557809	−	0.557809i	−0.0358573	−	0.0358573i
$243$		0			0
$244$			1.65954i			0.106241i
$245$	−10.3696	+	11.5513i	−0.662486	+	0.737985i
$246$		0			0
$247$	−5.41348	−	27.4598i	−0.344451	−	1.74722i
$248$	−3.80079	−	3.80079i	−0.241351	−	0.241351i
$249$		0			0
$250$	11.0347	−	1.79858i	0.697897	−	0.113752i
$251$	−11.6524			−0.735495			−0.367748	−	0.929926i	$-0.619871\pi$
$251$	−11.6524			−0.735495			−0.367748	+	0.929926i	$0.619871\pi$
$252$		0			0
$253$	17.7089	+	17.7089i	1.11335	+	1.11335i
$254$		−	7.35299i		−	0.461368i
$255$		0			0
$256$	1.00000			0.0625000
$257$	1.00645	+	1.00645i	0.0627804	+	0.0627804i	0.737800	−	0.675020i	$-0.235865\pi$
$257$	1.00645	+	1.00645i	0.0627804	+	0.0627804i	−0.675020	+	0.737800i	$0.735865\pi$
$258$		0			0
$259$	1.88655			0.117225
$260$	0.772891	+	14.3369i	0.0479327	+	0.889135i
$261$		0			0
$262$	1.51836	+	1.51836i	0.0938048	+	0.0938048i
$263$	−0.396280	−	0.396280i	−0.0244357	−	0.0244357i	0.694783	−	0.719219i	$-0.255500\pi$
$263$	−0.396280	−	0.396280i	−0.0244357	−	0.0244357i	−0.719219	+	0.694783i	$0.755500\pi$
$264$		0			0
$265$	6.10589	−	0.329165i	0.375082	−	0.0202204i
$266$	0.584480	−	0.871519i	0.0358368	−	0.0534362i
$267$		0			0
$268$	−0.481480	+	0.481480i	−0.0294111	+	0.0294111i
$269$	20.9263			1.27590			0.637948	−	0.770079i	$-0.279783\pi$
$269$	20.9263			1.27590			0.637948	+	0.770079i	$0.279783\pi$
$270$		0			0
$271$	−16.9175			−1.02767			−0.513834	−	0.857890i	$-0.671775\pi$
$271$	−16.9175			−1.02767			−0.513834	+	0.857890i	$0.671775\pi$
$272$	0.537531	−	0.537531i	0.0325926	−	0.0325926i
$273$		0			0
$274$	−19.1651			−1.15781
$275$	−1.84561	−	17.0680i	−0.111294	−	1.02924i
$276$		0			0
$277$	15.6769	−	15.6769i	0.941931	−	0.941931i	−0.0564732	−	0.998404i	$-0.517986\pi$
$277$	15.6769	−	15.6769i	0.941931	−	0.941931i	0.998404	+	0.0564732i	$0.0179856\pi$
$278$	−7.42565	+	7.42565i	−0.445361	+	0.445361i
$279$		0			0
$280$	−0.359601	+	0.400582i	−0.0214903	+	0.0239394i
$281$			10.3485i			0.617342i	0.951169	+	0.308671i	$0.0998842\pi$
$281$			10.3485i			0.617342i	−0.951169	+	0.308671i	$0.900116\pi$
$282$		0			0
$283$	6.03331	+	6.03331i	0.358643	+	0.358643i	0.863313	−	0.504670i	$-0.168386\pi$
$283$	6.03331	+	6.03331i	0.358643	+	0.358643i	−0.504670	+	0.863313i	$0.668386\pi$
$284$	8.93130			0.529975
$285$		0			0
$286$	22.0463			1.30362
$287$	−0.626820	−	0.626820i	−0.0370000	−	0.0370000i
$288$		0			0
$289$			16.4221i			0.966007i
$290$	−0.647005	−	12.0017i	−0.0379935	−	0.704766i
$291$		0			0
$292$	−8.74888	+	8.74888i	−0.511989	+	0.511989i
$293$	−6.64005	+	6.64005i	−0.387916	+	0.387916i	−0.873943	−	0.486028i	$-0.838445\pi$
$293$	−6.64005	+	6.64005i	−0.387916	+	0.387916i	0.486028	+	0.873943i	$0.338445\pi$
$294$		0			0
$295$	6.99140	+	6.27615i	0.407055	+	0.365412i
$296$	−7.83647			−0.455486
$297$		0			0
$298$	−0.721494	+	0.721494i	−0.0417950	+	0.0417950i
$299$	−46.8349			−2.70853
$300$		0			0
$301$	−0.780412			−0.0449822
$302$	−14.0286	+	14.0286i	−0.807254	+	0.807254i
$303$		0			0
$304$	−2.42784	+	3.62016i	−0.139246	+	0.207631i
$305$	2.76141	+	2.47891i	0.158118	+	0.141942i
$306$		0			0
$307$	6.21426	+	6.21426i	0.354667	+	0.354667i	0.861843	−	0.507176i	$-0.169311\pi$
$307$	6.21426	+	6.21426i	0.354667	+	0.354667i	−0.507176	+	0.861843i	$0.669311\pi$
$308$	0.584480	+	0.584480i	0.0333038	+	0.0333038i
$309$		0			0
$310$	−12.0017	+	0.647005i	−0.681653	+	0.0367474i
$311$	4.55027			0.258022			0.129011	−	0.991643i	$-0.458820\pi$
$311$	4.55027			0.258022			0.129011	+	0.991643i	$0.458820\pi$
$312$		0			0
$313$	20.0429	+	20.0429i	1.13289	+	1.13289i	0.989694	+	0.143197i	$0.0457382\pi$
$313$	20.0429	+	20.0429i	1.13289	+	1.13289i	0.143197	+	0.989694i	$0.454262\pi$
$314$	18.6482			1.05238
$315$		0			0
$316$			1.15022i			0.0647050i
$317$	−21.4280	−	21.4280i	−1.20351	−	1.20351i	−0.973090	−	0.230424i	$-0.925989\pi$
$317$	−21.4280	−	21.4280i	−1.20351	−	1.20351i	−0.230424	−	0.973090i	$-0.574011\pi$
$318$		0			0
$319$	−18.4555			−1.03331
$320$	1.49373	−	1.66396i	0.0835021	−	0.0930182i
$321$		0			0
$322$	−1.24166	−	1.24166i	−0.0691952	−	0.0691952i
$323$	0.640907	+	3.25099i	0.0356610	+	0.180890i
$324$		0			0
$325$	25.0105	+	20.1294i	1.38733	+	1.11658i
$326$		−	1.69593i		−	0.0939291i
$327$		0			0
$328$	2.60372	+	2.60372i	0.143766	+	0.143766i
$329$			3.26113i			0.179792i
$330$		0			0
$331$			31.9582i			1.75658i	0.478125	+	0.878292i	$0.341317\pi$
$331$			31.9582i			1.75658i	−0.478125	+	0.878292i	$0.658683\pi$
$332$	−9.97102	+	9.97102i	−0.547231	+	0.547231i
$333$		0			0
$334$		−	15.7387i		−	0.861184i
$335$	0.0819620	+	1.52037i	0.00447806	+	0.0830665i
$336$		0			0
$337$	−6.27191	−	6.27191i	−0.341653	−	0.341653i	0.515336	−	0.856988i	$-0.327667\pi$
$337$	−6.27191	−	6.27191i	−0.341653	−	0.341653i	−0.856988	+	0.515336i	$0.827667\pi$
$338$	−19.9607	+	19.9607i	−1.08572	+	1.08572i
$339$		0			0
$340$	−0.0915034	−	1.69736i	−0.00496247	−	0.0920521i
$341$			18.4555i			0.999420i
$342$		0			0
$343$	−2.37334	−	2.37334i	−0.128148	−	0.128148i
$344$	3.24172			0.174782
$345$		0			0
$346$	−21.4978			−1.15573
$347$	9.84922	−	9.84922i	0.528734	−	0.528734i	−0.391461	−	0.920195i	$-0.628030\pi$
$347$	9.84922	−	9.84922i	0.528734	−	0.528734i	0.920195	+	0.391461i	$0.128030\pi$
$348$		0			0
$349$			23.7919i			1.27355i	0.771049	+	0.636776i	$0.219732\pi$
$349$			23.7919i			1.27355i	−0.771049	+	0.636776i	$0.780268\pi$
$350$	0.129405	+	1.19672i	0.00691701	+	0.0639676i
$351$		0			0
$352$	−2.42784	−	2.42784i	−0.129405	−	0.129405i
$353$	16.4474	+	16.4474i	0.875407	+	0.875407i	0.993055	−	0.117649i	$-0.0375356\pi$
$353$	16.4474	+	16.4474i	0.875407	+	0.875407i	−0.117649	+	0.993055i	$0.537536\pi$
$354$		0			0
$355$	13.3410	−	14.8613i	0.708065	−	0.788758i
$356$		−	2.10098i		−	0.111351i
$357$		0			0
$358$	17.6448	+	17.6448i	0.932559	+	0.932559i
$359$		−	9.08979i		−	0.479741i	−0.970805	−	0.239870i	$-0.922895\pi$
$359$		−	9.08979i		−	0.479741i	0.970805	−	0.239870i	$-0.0771050\pi$
$360$		0			0
$361$	−7.21114	−	17.5784i	−0.379534	−	0.925178i
$362$	−11.2940	+	11.2940i	−0.593598	+	0.593598i
$363$		0			0
$364$	−1.54578			−0.0810210
$365$	1.48931	+	27.6263i	0.0779542	+	1.44602i
$366$		0			0
$367$	17.6931	−	17.6931i	0.923570	−	0.923570i	−0.0737098	−	0.997280i	$-0.523484\pi$
$367$	17.6931	−	17.6931i	0.923570	−	0.923570i	0.997280	+	0.0737098i	$0.0234839\pi$
$368$	5.15769	+	5.15769i	0.268863	+	0.268863i
$369$		0			0
$370$	−11.7056	+	13.0396i	−0.608545	+	0.677896i
$371$			0.658329i			0.0341787i
$372$		0			0
$373$	−4.93586	+	4.93586i	−0.255569	+	0.255569i	−0.823249	−	0.567680i	$-0.807841\pi$
$373$	−4.93586	+	4.93586i	−0.255569	+	0.255569i	0.567680	+	0.823249i	$0.307841\pi$
$374$	−2.61008			−0.134964
$375$		0			0
$376$		−	13.5463i		−	0.698595i
$377$	24.4047	−	24.4047i	1.25691	−	1.25691i
$378$		0			0
$379$	9.44824			0.485324			0.242662	−	0.970111i	$-0.421979\pi$
$379$	9.44824			0.485324			0.242662	+	0.970111i	$0.421979\pi$
$380$	2.39726	+	9.44739i	0.122977	+	0.484641i
$381$		0			0
$382$	2.06179	+	2.06179i	0.105490	+	0.105490i
$383$	−17.3196	+	17.3196i	−0.884991	+	0.884991i	−0.994037	−	0.109046i	$-0.965221\pi$
$383$	−17.3196	+	17.3196i	−0.884991	+	0.884991i	0.109046	+	0.994037i	$0.465221\pi$
$384$		0			0
$385$	1.84561	−	0.0994955i	0.0940609	−	0.00507076i
$386$	9.44130			0.480550
$387$		0			0
$388$	−10.8544	+	10.8544i	−0.551049	+	0.551049i
$389$		−	20.3705i		−	1.03283i	−0.856340	−	0.516413i	$-0.827267\pi$
$389$		−	20.3705i		−	1.03283i	0.856340	−	0.516413i	$-0.172733\pi$
$390$		0			0
$391$	5.54484			0.280415
$392$	4.90877	+	4.90877i	0.247930	+	0.247930i
$393$		0			0
$394$	−5.77371			−0.290875
$395$	1.91392	+	1.71812i	0.0963000	+	0.0864481i
$396$		0			0
$397$	13.9251	−	13.9251i	0.698883	−	0.698883i	−0.265287	−	0.964170i	$-0.585467\pi$
$397$	13.9251	−	13.9251i	0.698883	−	0.698883i	0.964170	+	0.265287i	$0.0854666\pi$
$398$	5.82417	−	5.82417i	0.291939	−	0.291939i
$399$		0			0
$400$	−0.537531	−	4.97102i	−0.0268765	−	0.248551i
$401$			0.407767i			0.0203629i	0.999948	+	0.0101815i	$0.00324092\pi$
$401$			0.407767i			0.0203629i	−0.999948	+	0.0101815i	$0.996759\pi$
$402$		0			0
$403$	−24.4047	−	24.4047i	−1.21569	−	1.21569i
$404$		−	8.90870i		−	0.443225i
$405$		0			0
$406$	1.29401			0.0642207
$407$	19.0257	+	19.0257i	0.943071	+	0.943071i
$408$		0			0
$409$	6.82208			0.337330			0.168665	−	0.985673i	$-0.446054\pi$
$409$	6.82208			0.337330			0.168665	+	0.985673i	$0.446054\pi$
$410$	8.22175	−	0.443229i	0.406043	−	0.0218895i
$411$		0			0
$412$	6.26365	+	6.26365i	0.308588	+	0.308588i
$413$	−0.715245	+	0.715245i	−0.0351949	+	0.0351949i
$414$		0			0
$415$	1.69736	+	31.4854i	0.0833200	+	1.54556i
$416$	6.42095			0.314813
$417$		0			0
$418$	14.6836	−	2.89476i	0.718199	−	0.141587i
$419$			30.8811i			1.50864i	0.656507	+	0.754320i	$0.272033\pi$
$419$			30.8811i			1.50864i	−0.656507	+	0.754320i	$0.727967\pi$
$420$		0			0
$421$		−	5.62994i		−	0.274386i	−0.990544	−	0.137193i	$-0.956192\pi$
$421$		−	5.62994i		−	0.274386i	0.990544	−	0.137193i	$-0.0438081\pi$
$422$	−10.3334	+	10.3334i	−0.503020	+	0.503020i
$423$		0			0
$424$		−	2.73460i		−	0.132804i
$425$	−2.96102	−	2.38314i	−0.143630	−	0.115599i
$426$		0			0
$427$	−0.282502	+	0.282502i	−0.0136712	+	0.0136712i
$428$	5.59814	−	5.59814i	0.270597	−	0.270597i
$429$		0			0
$430$	4.84226	−	5.39409i	0.233514	−	0.260126i
$431$			8.03322i			0.386947i	0.981106	+	0.193473i	$0.0619753\pi$
$431$			8.03322i			0.386947i	−0.981106	+	0.193473i	$0.938025\pi$
$432$		0			0
$433$	−27.5643	+	27.5643i	−1.32466	+	1.32466i	−0.414695	+	0.909960i	$0.636112\pi$
$433$	−27.5643	+	27.5643i	−1.32466	+	1.32466i	−0.909960	+	0.414695i	$0.863888\pi$
$434$		−	1.29401i		−	0.0621145i
$435$		0			0
$436$		−	10.7123i		−	0.513026i
$437$	−31.1938	+	6.14960i	−1.49220	+	0.294175i
$438$		0			0
$439$	−2.72959			−0.130276			−0.0651381	−	0.997876i	$-0.520749\pi$
$439$	−2.72959			−0.130276			−0.0651381	+	0.997876i	$0.520749\pi$
$440$	−7.66639	+	0.413290i	−0.365481	+	0.0197028i
$441$		0			0
$442$	3.45146	−	3.45146i	0.164169	−	0.164169i
$443$	21.7450	+	21.7450i	1.03313	+	1.03313i	0.999432	+	0.0337029i	$0.0107300\pi$
$443$	21.7450	+	21.7450i	1.03313	+	1.03313i	0.0337029	+	0.999432i	$0.489270\pi$
$444$		0			0
$445$	−3.49594	−	3.13829i	−0.165723	−	0.148769i
$446$	22.5682			1.06864
$447$		0			0
$448$	0.170229	+	0.170229i	0.00804257	+	0.00804257i
$449$	−6.33780			−0.299099			−0.149550	−	0.988754i	$-0.547782\pi$
$449$	−6.33780			−0.299099			−0.149550	+	0.988754i	$0.547782\pi$
$450$		0			0
$451$		−	12.6429i		−	0.595329i
$452$	6.81260	+	6.81260i	0.320438	+	0.320438i
$453$		0			0
$454$			8.30331i			0.389694i
$455$	−2.30898	+	2.57212i	−0.108247	+	0.120583i
$456$		0			0
$457$	−14.1287	+	14.1287i	−0.660915	+	0.660915i	−0.955596	−	0.294681i	$-0.904787\pi$
$457$	−14.1287	+	14.1287i	−0.660915	+	0.660915i	0.294681	+	0.955596i	$0.404787\pi$
$458$	7.27083	−	7.27083i	0.339743	−	0.339743i
$459$		0			0
$460$	16.2864	−	0.877989i	0.759358	−	0.0409365i
$461$	10.3701			0.482984			0.241492	−	0.970403i	$-0.422363\pi$
$461$	10.3701			0.482984			0.241492	+	0.970403i	$0.422363\pi$
$462$		0			0
$463$	−21.5966	−	21.5966i	−1.00368	−	1.00368i	−0.999993	−	0.00368676i	$-0.998826\pi$
$463$	−21.5966	−	21.5966i	−1.00368	−	1.00368i	−0.00368676	−	0.999993i	$-0.501174\pi$
$464$	−5.37513			−0.249534
$465$		0			0
$466$			20.4672i			0.948123i
$467$	−5.68112	+	5.68112i	−0.262891	+	0.262891i	−0.826228	−	0.563337i	$-0.809517\pi$
$467$	−5.68112	+	5.68112i	−0.262891	+	0.262891i	0.563337	+	0.826228i	$0.309517\pi$
$468$		0			0
$469$	−0.163924			−0.00756930
$470$	−22.5404	−	20.2345i	−1.03971	−	0.933346i
$471$		0			0
$472$	2.97102	−	2.97102i	0.136752	−	0.136752i
$473$	−7.87039	−	7.87039i	−0.361881	−	0.361881i
$474$		0			0
$475$	19.3009	+	10.1229i	0.885588	+	0.464471i
$476$	0.183007			0.00838810
$477$		0			0
$478$	15.1645	−	15.1645i	0.693609	−	0.693609i
$479$			18.3301i			0.837524i	0.908096	+	0.418762i	$0.137536\pi$
$479$			18.3301i			0.837524i	−0.908096	+	0.418762i	$0.862464\pi$
$480$		0			0
$481$	−50.3176			−2.29429
$482$	−1.07223	+	1.07223i	−0.0488387	+	0.0488387i
$483$		0			0
$484$			0.788861i			0.0358573i
$485$	1.84774	+	34.2749i	0.0839014	+	1.55634i
$486$		0			0
$487$	−8.21504	−	8.21504i	−0.372259	−	0.372259i	0.496040	−	0.868299i	$-0.334787\pi$
$487$	−8.21504	−	8.21504i	−0.372259	−	0.372259i	−0.868299	+	0.496040i	$0.834787\pi$
$488$	1.17347	−	1.17347i	0.0531206	−	0.0531206i
$489$		0			0
$490$	15.5004	−	0.835615i	0.700236	−	0.0377492i
$491$	−5.85271			−0.264129			−0.132065	−	0.991241i	$-0.542161\pi$
$491$	−5.85271			−0.264129			−0.132065	+	0.991241i	$0.542161\pi$
$492$		0			0
$493$	−2.88930	+	2.88930i	−0.130128	+	0.130128i
$494$	−15.5891	+	23.2449i	−0.701386	+	1.04584i
$495$		0			0
$496$			5.37513i			0.241351i
$497$	1.52037	+	1.52037i	0.0681978	+	0.0681978i
$498$		0			0
$499$			24.4054i			1.09254i	0.837610	+	0.546268i	$0.183952\pi$
$499$			24.4054i			1.09254i	−0.837610	+	0.546268i	$0.816048\pi$
$500$	−9.07451	−	6.53094i	−0.405825	−	0.292073i
$501$		0			0
$502$	8.23952	+	8.23952i	0.367748	+	0.367748i
$503$	−19.8672	−	19.8672i	−0.885836	−	0.885836i	0.108284	−	0.994120i	$-0.465464\pi$
$503$	−19.8672	−	19.8672i	−0.885836	−	0.885836i	−0.994120	+	0.108284i	$0.965464\pi$
$504$		0			0
$505$	−14.8237	−	13.3072i	−0.659647	−	0.592163i
$506$		−	25.0442i		−	1.11335i
$507$		0			0
$508$	−5.19935	+	5.19935i	−0.230684	+	0.230684i
$509$	19.2340			0.852534			0.426267	−	0.904597i	$-0.359828\pi$
$509$	19.2340			0.852534			0.426267	+	0.904597i	$0.359828\pi$
$510$		0			0
$511$	−2.97863			−0.131767
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$		0			0
$514$		−	1.42333i		−	0.0627804i
$515$	19.7787	−	1.06626i	0.871553	−	0.0469848i
$516$		0			0
$517$	−32.8882	+	32.8882i	−1.44642	+	1.44642i
$518$	−1.33400	−	1.33400i	−0.0586124	−	0.0586124i
$519$		0			0
$520$	9.59118	−	10.6842i	0.420601	−	0.468534i
$521$			19.1370i			0.838407i	0.907892	+	0.419204i	$0.137691\pi$
$521$			19.1370i			0.838407i	−0.907892	+	0.419204i	$0.862309\pi$
$522$		0			0
$523$	−13.3664	+	13.3664i	−0.584471	+	0.584471i	−0.936129	−	0.351657i	$-0.885618\pi$
$523$	−13.3664	+	13.3664i	−0.584471	+	0.584471i	0.351657	+	0.936129i	$0.385618\pi$
$524$		−	2.14729i		−	0.0938048i
$525$		0			0
$526$			0.560424i			0.0244357i
$527$	2.88930	+	2.88930i	0.125860	+	0.125860i
$528$		0			0
$529$			30.2036i			1.31320i
$530$	−4.55027	−	4.08476i	−0.197651	−	0.177431i
$531$		0			0
$532$	−1.02955	+	0.202967i	−0.0446365	+	0.00879973i
$533$	16.7184	+	16.7184i	0.724153	+	0.724153i
$534$		0			0
$535$	−0.952967	−	17.6772i	−0.0412003	−	0.764253i
$536$	0.680916			0.0294111
$537$		0			0
$538$	−14.7971	−	14.7971i	−0.637948	−	0.637948i
$539$		−	23.8354i		−	1.02667i
$540$		0			0
$541$	−36.4227			−1.56593			−0.782967	−	0.622063i	$-0.786295\pi$
$541$	−36.4227			−1.56593			−0.782967	+	0.622063i	$0.786295\pi$
$542$	11.9625	+	11.9625i	0.513834	+	0.513834i
$543$		0			0
$544$	−0.760184			−0.0325926
$545$	−17.8249	−	16.0013i	−0.763533	−	0.685421i
$546$		0			0
$547$	7.49691	+	7.49691i	0.320545	+	0.320545i	0.848976	−	0.528431i	$-0.177220\pi$
$547$	7.49691	+	7.49691i	0.320545	+	0.320545i	−0.528431	+	0.848976i	$0.677220\pi$
$548$	13.5518	+	13.5518i	0.578904	+	0.578904i
$549$		0			0
$550$	−10.7638	+	13.3739i	−0.458971	+	0.570266i
$551$	13.0500	−	19.4588i	0.555948	−	0.828975i
$552$		0			0
$553$	−0.195801	+	0.195801i	−0.00832631	+	0.00832631i
$554$	−22.1704			−0.941931
$555$		0			0
$556$	10.5015			0.445361
$557$	−6.66081	+	6.66081i	−0.282228	+	0.282228i	−0.833997	−	0.551769i	$-0.813953\pi$
$557$	−6.66081	+	6.66081i	−0.282228	+	0.282228i	0.551769	+	0.833997i	$0.313953\pi$
$558$		0			0
$559$	20.8149			0.880377
$560$	0.537531	−	0.0289779i	0.0227148	−	0.00122454i
$561$		0			0
$562$	7.31752	−	7.31752i	0.308671	−	0.308671i
$563$	18.2264	−	18.2264i	0.768150	−	0.768150i	−0.209631	−	0.977781i	$-0.567226\pi$
$563$	18.2264	−	18.2264i	0.768150	−	0.768150i	0.977781	+	0.209631i	$0.0672261\pi$
$564$		0			0
$565$	21.5121	−	1.15970i	0.905020	−	0.0487890i
$566$		−	8.53238i		−	0.358643i
$567$		0			0
$568$	−6.31539	−	6.31539i	−0.264988	−	0.264988i
$569$	−12.9797			−0.544138			−0.272069	−	0.962278i	$-0.587708\pi$
$569$	−12.9797			−0.544138			−0.272069	+	0.962278i	$0.587708\pi$
$570$		0			0
$571$	−4.34400			−0.181791			−0.0908954	−	0.995860i	$-0.528973\pi$
$571$	−4.34400			−0.181791			−0.0908954	+	0.995860i	$0.528973\pi$
$572$	−15.5891	−	15.5891i	−0.651812	−	0.651812i
$573$		0			0
$574$			0.886458i			0.0370000i
$575$	22.8666	−	28.4114i	0.953602	−	1.18484i
$576$		0			0
$577$	22.6630	−	22.6630i	0.943474	−	0.943474i	−0.0550121	−	0.998486i	$-0.517520\pi$
$577$	22.6630	−	22.6630i	0.943474	−	0.943474i	0.998486	+	0.0550121i	$0.0175197\pi$
$578$	11.6122	−	11.6122i	0.483004	−	0.483004i
$579$		0			0
$580$	−8.02901	+	8.94401i	−0.333386	+	0.371380i
$581$	−3.39472			−0.140837
$582$		0			0
$583$	−6.63919	+	6.63919i	−0.274967	+	0.274967i
$584$	12.3728			0.511989
$585$		0			0
$586$	9.39045			0.387916
$587$	1.52632	−	1.52632i	0.0629979	−	0.0629979i	−0.674906	−	0.737904i	$-0.735816\pi$
$587$	1.52632	−	1.52632i	0.0629979	−	0.0629979i	0.737904	+	0.674906i	$0.235816\pi$
$588$		0			0
$589$	−19.4588	−	13.0500i	−0.801788	−	0.537715i
$590$	−0.505754	−	9.38157i	−0.0208216	−	0.386233i
$591$		0			0
$592$	5.54122	+	5.54122i	0.227743	+	0.227743i
$593$	−2.34436	−	2.34436i	−0.0962714	−	0.0962714i	0.657331	−	0.753602i	$-0.271685\pi$
$593$	−2.34436	−	2.34436i	−0.0962714	−	0.0962714i	−0.753602	+	0.657331i	$0.771685\pi$
$594$		0			0
$595$	0.273363	−	0.304516i	0.0112068	−	0.0124839i
$596$	1.02035			0.0417950
$597$		0			0
$598$	33.1173	+	33.1173i	1.35427	+	1.35427i
$599$	20.2744			0.828391			0.414195	−	0.910188i	$-0.364063\pi$
$599$	20.2744			0.828391			0.414195	+	0.910188i	$0.364063\pi$
$600$		0			0
$601$			18.2726i			0.745354i	0.927961	+	0.372677i	$0.121560\pi$
$601$			18.2726i			0.745354i	−0.927961	+	0.372677i	$0.878440\pi$
$602$	0.551834	+	0.551834i	0.0224911	+	0.0224911i
$603$		0			0
$604$	19.8394			0.807254
$605$	1.31263	+	1.17835i	0.0533662	+	0.0479066i
$606$		0			0
$607$	−21.4067	−	21.4067i	−0.868872	−	0.868872i	0.123476	−	0.992348i	$-0.460596\pi$
$607$	−21.4067	−	21.4067i	−0.868872	−	0.868872i	−0.992348	+	0.123476i	$0.960596\pi$
$608$	4.27659	−	0.843095i	0.173438	−	0.0341920i
$609$		0			0
$610$	−0.199759	−	3.70547i	−0.00808802	−	0.150030i
$611$		−	86.9799i		−	3.51883i
$612$		0			0
$613$	−21.6012	−	21.6012i	−0.872462	−	0.872462i	0.120278	−	0.992740i	$-0.461621\pi$
$613$	−21.6012	−	21.6012i	−0.872462	−	0.872462i	−0.992740	+	0.120278i	$0.961621\pi$
$614$		−	8.78829i		−	0.354667i
$615$		0			0
$616$		−	0.826579i		−	0.0333038i
$617$	−13.3582	+	13.3582i	−0.537782	+	0.537782i	−0.922877	−	0.385095i	$-0.874169\pi$
$617$	−13.3582	+	13.3582i	−0.537782	+	0.537782i	0.385095	+	0.922877i	$0.374169\pi$
$618$		0			0
$619$		−	35.7297i		−	1.43610i	−0.695993	−	0.718049i	$-0.745035\pi$
$619$		−	35.7297i		−	1.43610i	0.695993	−	0.718049i	$-0.254965\pi$
$620$	8.94401	+	8.02901i	0.359200	+	0.322453i
$621$		0			0
$622$	−3.21753	−	3.21753i	−0.129011	−	0.129011i
$623$	0.357647	−	0.357647i	0.0143288	−	0.0143288i
$624$		0			0
$625$	−24.4221	+	5.34416i	−0.976885	+	0.213766i
$626$		−	28.3449i		−	1.13289i
$627$		0			0
$628$	−13.1863	−	13.1863i	−0.526190	−	0.526190i
$629$	5.95716			0.237528
$630$		0			0
$631$	−5.92905			−0.236032			−0.118016	−	0.993012i	$-0.537653\pi$
$631$	−5.92905			−0.236032			−0.118016	+	0.993012i	$0.537653\pi$
$632$	0.813330	−	0.813330i	0.0323525	−	0.0323525i
$633$		0			0
$634$			30.3037i			1.20351i
$635$	0.885081	+	16.4180i	0.0351234	+	0.651527i
$636$		0			0
$637$	31.5190	+	31.5190i	1.24883	+	1.24883i
$638$	13.0500	+	13.0500i	0.516654	+	0.516654i
$639$		0			0
$640$	−2.23283	+	0.120370i	−0.0882602	+	0.00475805i
$641$			6.60094i			0.260721i	0.991467	+	0.130361i	$0.0416135\pi$
$641$			6.60094i			0.260721i	−0.991467	+	0.130361i	$0.958386\pi$
$642$		0			0
$643$	13.4065	+	13.4065i	0.528700	+	0.528700i	0.920185	−	0.391484i	$-0.128038\pi$
$643$	13.4065	+	13.4065i	0.528700	+	0.528700i	−0.391484	+	0.920185i	$0.628038\pi$
$644$			1.75598i			0.0691952i
$645$		0			0
$646$	1.84561	−	2.75199i	0.0726145	−	0.108275i
$647$	−10.3980	+	10.3980i	−0.408788	+	0.408788i	−0.881316	−	0.472528i	$-0.843342\pi$
$647$	−10.3980	+	10.3980i	−0.408788	+	0.408788i	0.472528	+	0.881316i	$0.343342\pi$
$648$		0			0
$649$	−14.4264			−0.566284
$650$	−3.45146	−	31.9187i	−0.135377	−	1.25195i
$651$		0			0
$652$	−1.19921	+	1.19921i	−0.0469646	+	0.0469646i
$653$	9.88773	+	9.88773i	0.386937	+	0.386937i	0.873593	−	0.486657i	$-0.161784\pi$
$653$	9.88773	+	9.88773i	0.386937	+	0.386937i	−0.486657	+	0.873593i	$0.661784\pi$
$654$		0			0
$655$	−3.57301	−	3.20748i	−0.139609	−	0.125326i
$656$		−	3.68222i		−	0.143766i
$657$		0			0
$658$	2.30597	−	2.30597i	0.0898959	−	0.0898959i
$659$	13.1768			0.513294			0.256647	−	0.966505i	$-0.417382\pi$
$659$	13.1768			0.513294			0.256647	+	0.966505i	$0.417382\pi$
$660$		0			0
$661$		−	27.6493i		−	1.07543i	−0.843126	−	0.537716i	$-0.819287\pi$
$661$		−	27.6493i		−	1.07543i	0.843126	−	0.537716i	$-0.180713\pi$
$662$	22.5979	−	22.5979i	0.878292	−	0.878292i
$663$		0			0
$664$	14.1012			0.547231
$665$	−1.20014	+	2.01630i	−0.0465393	+	0.0781889i
$666$		0			0
$667$	−27.7233	−	27.7233i	−1.07345	−	1.07345i
$668$	−11.1290	+	11.1290i	−0.430592	+	0.430592i
$669$		0			0
$670$	1.01711	−	1.13302i	0.0392942	−	0.0437723i
$671$	−5.69802			−0.219970
$672$		0			0
$673$	15.0414	−	15.0414i	0.579804	−	0.579804i	−0.355045	−	0.934849i	$-0.615535\pi$
$673$	15.0414	−	15.0414i	0.579804	−	0.579804i	0.934849	+	0.355045i	$0.115535\pi$
$674$			8.86982i			0.341653i
$675$		0			0
$676$	28.2287			1.08572
$677$	32.6303	+	32.6303i	1.25408	+	1.25408i	0.953873	+	0.300211i	$0.0970571\pi$
$677$	32.6303	+	32.6303i	1.25408	+	1.25408i	0.300211	+	0.953873i	$0.402943\pi$
$678$		0			0
$679$	−3.69547			−0.141819
$680$	−1.13551	+	1.26492i	−0.0435448	+	0.0485073i
$681$		0			0
$682$	13.0500	−	13.0500i	0.499710	−	0.499710i
$683$	−19.7427	+	19.7427i	−0.755435	+	0.755435i	−0.975488	−	0.220053i	$-0.929377\pi$
$683$	−19.7427	+	19.7427i	−0.755435	+	0.755435i	0.220053	+	0.975488i	$0.429377\pi$
$684$		0			0
$685$	42.7924	−	2.30691i	1.63501	−	0.0881425i
$686$			3.35641i			0.128148i
$687$		0			0
$688$	−2.29224	−	2.29224i	−0.0873908	−	0.0873908i
$689$		−	17.5588i		−	0.668936i
$690$		0			0
$691$	−1.07506			−0.0408973			−0.0204486	−	0.999791i	$-0.506509\pi$
$691$	−1.07506			−0.0408973			−0.0204486	+	0.999791i	$0.506509\pi$
$692$	15.2012	+	15.2012i	0.577863	+	0.577863i
$693$		0			0
$694$	−13.9289			−0.528734
$695$	15.6864	−	17.4740i	0.595017	−	0.662827i
$696$		0			0
$697$	−1.97931	−	1.97931i	−0.0749715	−	0.0749715i
$698$	16.8234	−	16.8234i	0.636776	−	0.636776i
$699$		0			0
$700$	0.754709	−	0.937716i	0.0285253	−	0.0354423i
$701$	−49.0251			−1.85165			−0.925827	−	0.377947i	$-0.876630\pi$
$701$	−49.0251			−1.85165			−0.925827	+	0.377947i	$0.876630\pi$
$702$		0			0
$703$	−33.5134	+	6.60689i	−1.26398	+	0.249184i
$704$			3.43349i			0.129405i
$705$		0			0
$706$		−	23.2601i		−	0.875407i
$707$	1.51652	−	1.51652i	0.0570346	−	0.0570346i
$708$		0			0
$709$			1.20397i			0.0452160i	0.999744	+	0.0226080i	$0.00719696\pi$
$709$			1.20397i			0.0452160i	−0.999744	+	0.0226080i	$0.992803\pi$
$710$	−19.9420	+	1.07506i	−0.748412	+	0.0403464i
$711$		0			0
$712$	−1.48561	+	1.48561i	−0.0556757	+	0.0556757i
$713$	−27.7233	+	27.7233i	−1.03825	+	1.03825i
$714$		0			0
$715$	−49.2255	+	2.65371i	−1.84093	+	0.0992433i
$716$		−	24.9536i		−	0.932559i
$717$		0			0
$718$	−6.42745	+	6.42745i	−0.239870	+	0.239870i
$719$		−	13.0396i		−	0.486297i	−0.969989	−	0.243148i	$-0.921820\pi$
$719$		−	13.0396i		−	0.486297i	0.969989	−	0.243148i	$-0.0781802\pi$
$720$		0			0
$721$			2.13251i			0.0794189i
$722$	−7.33075	+	17.5288i	−0.272822	+	0.652356i
$723$		0			0
$724$	15.9721			0.593598
$725$	2.88930	+	26.7199i	0.107306	+	0.992352i
$726$		0			0
$727$	−11.3275	+	11.3275i	−0.420115	+	0.420115i	−0.885243	−	0.465129i	$-0.846008\pi$
$727$	−11.3275	+	11.3275i	−0.420115	+	0.420115i	0.465129	+	0.885243i	$0.346008\pi$
$728$	1.09303	+	1.09303i	0.0405105	+	0.0405105i
$729$		0			0
$730$	18.4816	−	20.5878i	0.684035	−	0.761989i
$731$	−2.46430			−0.0911454
$732$		0			0
$733$	30.7800	+	30.7800i	1.13689	+	1.13689i	0.989005	+	0.147882i	$0.0472456\pi$
$733$	30.7800	+	30.7800i	1.13689	+	1.13689i	0.147882	+	0.989005i	$0.452754\pi$
$734$	−25.0218			−0.923570
$735$		0			0
$736$		−	7.29408i		−	0.268863i
$737$	−1.65316	−	1.65316i	−0.0608949	−	0.0608949i
$738$		0			0
$739$		−	44.9834i		−	1.65474i	−0.561656	−	0.827371i	$-0.689835\pi$
$739$		−	44.9834i		−	1.65474i	0.561656	−	0.827371i	$-0.310165\pi$
$740$	17.4975	−	0.943277i	0.643220	−	0.0346756i
$741$		0			0
$742$	0.465509	−	0.465509i	0.0170894	−	0.0170894i
$743$	−16.4071	+	16.4071i	−0.601917	+	0.601917i	−0.940821	−	0.338904i	$-0.889944\pi$
$743$	−16.4071	+	16.4071i	−0.601917	+	0.601917i	0.338904	+	0.940821i	$0.389944\pi$
$744$		0			0
$745$	1.52412	−	1.69782i	0.0558396	−	0.0622032i
$746$	6.98036			0.255569
$747$		0			0
$748$	1.84561	+	1.84561i	0.0674821	+	0.0674821i
$749$	1.90593			0.0696413
$750$		0			0
$751$		−	10.0580i		−	0.367021i	−0.983018	−	0.183510i	$-0.941254\pi$
$751$		−	10.0580i		−	0.367021i	0.983018	−	0.183510i	$-0.0587461\pi$
$752$	−9.57865	+	9.57865i	−0.349297	+	0.349297i
$753$		0			0
$754$	−34.5135			−1.25691
$755$	29.6348	−	33.0120i	1.07852	−	1.20143i
$756$		0			0
$757$	−0.0674583	+	0.0674583i	−0.00245182	+	0.00245182i	−0.708332	−	0.705880i	$-0.750552\pi$
$757$	−0.0674583	+	0.0674583i	−0.00245182	+	0.00245182i	0.705880	+	0.708332i	$0.250552\pi$
$758$	−6.68092	−	6.68092i	−0.242662	−	0.242662i
$759$		0			0
$760$	4.98520	−	8.37543i	0.180832	−	0.303809i
$761$	−15.9170			−0.576990			−0.288495	−	0.957481i	$-0.593155\pi$
$761$	−15.9170			−0.576990			−0.288495	+	0.957481i	$0.593155\pi$
$762$		0			0
$763$	1.82355	−	1.82355i	0.0660168	−	0.0660168i
$764$		−	2.91580i		−	0.105490i
$765$		0			0
$766$	24.4936			0.884991
$767$	19.0768	−	19.0768i	0.688823	−	0.688823i
$768$		0			0
$769$			4.99203i			0.180017i	0.995941	+	0.0900087i	$0.0286895\pi$
$769$			4.99203i			0.180017i	−0.995941	+	0.0900087i	$0.971311\pi$
$770$	−1.37540	−	1.23469i	−0.0495658	−	0.0444951i
$771$		0			0
$772$	−6.67601	−	6.67601i	−0.240275	−	0.240275i
$773$	0.387825	−	0.387825i	0.0139491	−	0.0139491i	−0.700098	−	0.714047i	$-0.746860\pi$
$773$	0.387825	−	0.387825i	0.0139491	−	0.0139491i	0.714047	+	0.700098i	$0.246860\pi$
$774$		0			0
$775$	26.7199	−	2.88930i	0.959807	−	0.103787i
$776$	15.3505			0.551049
$777$		0			0
$778$	−14.4041	+	14.4041i	−0.516413	+	0.516413i
$779$	13.3302	+	8.93985i	0.477605	+	0.320303i
$780$		0			0
$781$			30.6655i			1.09730i
$782$	−3.92079	−	3.92079i	−0.140207	−	0.140207i
$783$		0			0
$784$		−	6.94204i		−	0.247930i
$785$	−41.6382	+	2.24469i	−1.48613	+	0.0801163i
$786$		0			0
$787$	33.2308	+	33.2308i	1.18455	+	1.18455i	0.978552	+	0.205999i	$0.0660445\pi$
$787$	33.2308	+	33.2308i	1.18455	+	1.18455i	0.205999	+	0.978552i	$0.433956\pi$
$788$	4.08263	+	4.08263i	0.145438	+	0.145438i
$789$		0			0
$790$	−0.138452	−	2.56824i	−0.00492591	−	0.0913740i
$791$			2.31940i			0.0824685i
$792$		0			0
$793$	7.53482	−	7.53482i	0.267569	−	0.267569i
$794$	−19.6931			−0.698883
$795$		0			0
$796$	−8.23662			−0.291939
$797$	−12.3179	−	12.3179i	−0.436324	−	0.436324i	0.454449	−	0.890773i	$-0.349836\pi$
$797$	−12.3179	−	12.3179i	−0.436324	−	0.436324i	−0.890773	+	0.454449i	$0.849836\pi$
$798$		0			0
$799$			10.2976i			0.364304i
$800$	−3.13495	+	3.89514i	−0.110837	+	0.137714i
$801$		0			0
$802$	0.288335	−	0.288335i	0.0101815	−	0.0101815i
$803$	−30.0392	−	30.0392i	−1.06006	−	1.06006i
$804$		0			0
$805$	2.92188	+	2.62296i	0.102983	+	0.0924472i
$806$			34.5135i			1.21569i
$807$		0			0
$808$	−6.29940	+	6.29940i	−0.221612	+	0.221612i
$809$			9.46048i			0.332613i	0.986074	+	0.166306i	$0.0531841\pi$
$809$			9.46048i			0.332613i	−0.986074	+	0.166306i	$0.946816\pi$
$810$		0			0
$811$			3.82726i			0.134393i	0.997740	+	0.0671967i	$0.0214055\pi$
$811$			3.82726i			0.134393i	−0.997740	+	0.0671967i	$0.978594\pi$
$812$	−0.915004	−	0.915004i	−0.0321103	−	0.0321103i
$813$		0			0
$814$		−	26.9065i		−	0.943071i
$815$	0.204140	+	3.78673i	0.00715071	+	0.132643i
$816$		0			0
$817$	13.8635	−	2.73308i	0.485022	−	0.0956182i
$818$	−4.82394	−	4.82394i	−0.168665	−	0.168665i
$819$		0			0
$820$	−6.12706	−	5.50024i	−0.213966	−	0.192077i
$821$	−2.99180			−0.104415			−0.0522073	−	0.998636i	$-0.516626\pi$
$821$	−2.99180			−0.104415			−0.0522073	+	0.998636i	$0.516626\pi$
$822$		0			0
$823$	−32.6466	−	32.6466i	−1.13799	−	1.13799i	−0.988810	−	0.149179i	$-0.952337\pi$
$823$	−32.6466	−	32.6466i	−1.13799	−	1.13799i	−0.149179	−	0.988810i	$-0.547663\pi$
$824$		−	8.85814i		−	0.308588i
$825$		0			0
$826$	1.01151			0.0351949
$827$	24.8297	+	24.8297i	0.863413	+	0.863413i	0.991733	−	0.128320i	$-0.0409585\pi$
$827$	24.8297	+	24.8297i	0.863413	+	0.863413i	−0.128320	+	0.991733i	$0.540958\pi$
$828$		0			0
$829$	24.2255			0.841388			0.420694	−	0.907203i	$-0.361787\pi$
$829$	24.2255			0.841388			0.420694	+	0.907203i	$0.361787\pi$
$830$	21.0633	−	23.4638i	0.731119	−	0.814439i
$831$		0			0
$832$	−4.54030	−	4.54030i	−0.157407	−	0.157407i
$833$	−3.73156	−	3.73156i	−0.129291	−	0.129291i
$834$		0			0
$835$	1.89447	+	35.1418i	0.0655609	+	1.21613i
$836$	−12.4298	−	8.33598i	−0.429893	−	0.288306i
$837$		0			0
$838$	21.8362	−	21.8362i	0.754320	−	0.754320i
$839$	−14.8623			−0.513105			−0.256552	−	0.966530i	$-0.582587\pi$
$839$	−14.8623			−0.513105			−0.256552	+	0.966530i	$0.582587\pi$
$840$		0			0
$841$	−0.107945			−0.00372223
$842$	−3.98097	+	3.98097i	−0.137193	+	0.137193i
$843$		0			0
$844$	14.6136			0.503020
$845$	42.1660	−	46.9714i	1.45056	−	1.61586i
$846$		0			0
$847$	−0.134287	+	0.134287i	−0.00461416	+	0.00461416i
$848$	−1.93366	+	1.93366i	−0.0664021	+	0.0664021i
$849$		0			0
$850$	0.408622	+	3.77889i	0.0140156	+	0.129615i
$851$			57.1599i			1.95941i
$852$		0			0
$853$	2.50921	+	2.50921i	0.0859138	+	0.0859138i	0.748758	−	0.662844i	$-0.230651\pi$
$853$	2.50921	+	2.50921i	0.0859138	+	0.0859138i	−0.662844	+	0.748758i	$0.730651\pi$
$854$	0.399518			0.0136712
$855$		0			0
$856$	−7.91697			−0.270597
$857$	3.30288	+	3.30288i	0.112824	+	0.112824i	0.761265	−	0.648441i	$-0.224579\pi$
$857$	3.30288	+	3.30288i	0.112824	+	0.112824i	−0.648441	+	0.761265i	$0.724579\pi$
$858$		0			0
$859$			9.52716i			0.325063i	0.986703	+	0.162531i	$0.0519659\pi$
$859$			9.52716i			0.325063i	−0.986703	+	0.162531i	$0.948034\pi$
$860$	−7.23819	+	0.390206i	−0.246820	+	0.0133059i
$861$		0			0
$862$	5.68035	−	5.68035i	0.193473	−	0.193473i
$863$	−14.4388	+	14.4388i	−0.491503	+	0.491503i	−0.908779	−	0.417277i	$-0.862985\pi$
$863$	−14.4388	+	14.4388i	−0.491503	+	0.491503i	0.417277	+	0.908779i	$0.362985\pi$
$864$		0			0
$865$	48.0007	−	2.58769i	1.63207	−	0.0879840i
$866$	38.9818			1.32466
$867$		0			0
$868$	−0.915004	+	0.915004i	−0.0310573	+	0.0310573i
$869$	−3.94928			−0.133970
$870$		0			0
$871$	4.37213			0.148144
$872$	−7.57474	+	7.57474i	−0.256513	+	0.256513i
$873$		0			0
$874$	26.4057	+	17.7089i	0.893188	+	0.599012i
$875$	−0.432989	−	2.65650i	−0.0146377	−	0.0898062i
$876$		0			0
$877$	−27.0374	−	27.0374i	−0.912987	−	0.912987i	0.0835187	−	0.996506i	$-0.473384\pi$
$877$	−27.0374	−	27.0374i	−0.912987	−	0.912987i	−0.996506	+	0.0835187i	$0.973384\pi$
$878$	1.93011	+	1.93011i	0.0651381	+	0.0651381i
$879$		0			0
$880$	5.71319	+	5.12871i	0.192592	+	0.172889i
$881$	15.9706			0.538063			0.269031	−	0.963131i	$-0.413296\pi$
$881$	15.9706			0.538063			0.269031	+	0.963131i	$0.413296\pi$
$882$		0			0
$883$	−8.39528	−	8.39528i	−0.282524	−	0.282524i	0.551591	−	0.834115i	$-0.314021\pi$
$883$	−8.39528	−	8.39528i	−0.282524	−	0.282524i	−0.834115	+	0.551591i	$0.814021\pi$
$884$	−4.88110			−0.164169
$885$		0			0
$886$		−	30.7520i		−	1.03313i
$887$	−18.4894	−	18.4894i	−0.620814	−	0.620814i	0.324925	−	0.945740i	$-0.394661\pi$
$887$	−18.4894	−	18.4894i	−0.620814	−	0.620814i	−0.945740	+	0.324925i	$0.894661\pi$
$888$		0			0
$889$	−1.77016			−0.0593693
$890$	0.252895	+	4.69111i	0.00847705	+	0.157246i
$891$		0			0
$892$	−15.9582	−	15.9582i	−0.534319	−	0.534319i
$893$	−11.4208	−	57.9317i	−0.382182	−	1.93861i
$894$		0			0
$895$	−41.5218	−	37.2739i	−1.38792	−	1.24593i
$896$		−	0.240740i		−	0.00804257i
$897$		0			0
$898$	4.48150	+	4.48150i	0.149550	+	0.149550i
$899$		−	28.8921i		−	0.963604i
$900$		0			0
$901$			2.07880i			0.0692549i
$902$	−8.93985	+	8.93985i	−0.297664	+	0.297664i
$903$		0			0
$904$		−	9.63447i		−	0.320438i
$905$	23.8580	−	26.5769i	0.793068	−	0.883447i
$906$		0			0
$907$	−15.6355	−	15.6355i	−0.519169	−	0.519169i	0.398151	−	0.917320i	$-0.369652\pi$
$907$	−15.6355	−	15.6355i	−0.519169	−	0.519169i	−0.917320	+	0.398151i	$0.869652\pi$
$908$	5.87132	−	5.87132i	0.194847	−	0.194847i
$909$		0			0
$910$	3.45146	−	0.186066i	0.114415	−	0.00616803i
$911$		−	21.2778i		−	0.704964i	−0.935819	−	0.352482i	$-0.885338\pi$
$911$		−	21.2778i		−	0.704964i	0.935819	−	0.352482i	$-0.114662\pi$
$912$		0			0
$913$	−34.2354	−	34.2354i	−1.13303	−	1.13303i
$914$	19.9811			0.660915
$915$		0			0
$916$	−10.2825			−0.339743
$917$	0.365531	−	0.365531i	0.0120709	−	0.0120709i
$918$		0			0
$919$			19.7132i			0.650277i	0.945666	+	0.325139i	$0.105411\pi$
$919$			19.7132i			0.650277i	−0.945666	+	0.325139i	$0.894589\pi$
$920$	−12.1371	−	10.8954i	−0.400147	−	0.359211i
$921$		0			0
$922$	−7.33277	−	7.33277i	−0.241492	−	0.241492i
$923$	−40.5508	−	40.5508i	−1.33475	−	1.33475i
$924$		0			0
$925$	24.5670	−	30.5241i	0.807757	−	1.00363i
$926$			30.5422i			1.00368i
$927$		0			0
$928$	3.80079	+	3.80079i	0.124767	+	0.124767i
$929$			44.9199i			1.47377i	0.676016	+	0.736887i	$0.263705\pi$
$929$			44.9199i			1.47377i	−0.676016	+	0.736887i	$0.736295\pi$
$930$		0			0
$931$	25.1313	+	16.8542i	0.823646	+	0.552374i
$932$	14.4725	−	14.4725i	0.474062	−	0.474062i
$933$		0			0
$934$	8.03432			0.262891
$935$	5.82786	−	0.314176i	0.190591	−	0.0102747i
$936$		0			0
$937$	11.9641	−	11.9641i	0.390851	−	0.390851i	−0.484140	−	0.874991i	$-0.660867\pi$
$937$	11.9641	−	11.9641i	0.390851	−	0.390851i	0.874991	+	0.484140i	$0.160867\pi$
$938$	0.115912	+	0.115912i	0.00378465	+	0.00378465i
$939$		0			0
$940$	1.63056	+	30.2464i	0.0531831	+	0.986530i
$941$		−	37.3163i		−	1.21648i	−0.793755	−	0.608238i	$-0.791877\pi$
$941$		−	37.3163i		−	1.21648i	0.793755	−	0.608238i	$-0.208123\pi$
$942$		0			0
$943$	18.9917	−	18.9917i	0.618456	−	0.618456i
$944$	−4.20166			−0.136752
$945$		0			0
$946$			11.1304i			0.361881i
$947$	−21.4508	+	21.4508i	−0.697057	+	0.697057i	−0.963775	−	0.266717i	$-0.914061\pi$
$947$	−21.4508	+	21.4508i	−0.697057	+	0.697057i	0.266717	+	0.963775i	$0.414061\pi$
$948$		0			0
$949$	79.4451			2.57890
$950$	−6.48984	−	20.8058i	−0.210558	−	0.675030i
$951$		0			0
$952$	−0.129405	−	0.129405i	−0.00419405	−	0.00419405i
$953$	24.4941	−	24.4941i	0.793442	−	0.793442i	−0.188610	−	0.982052i	$-0.560398\pi$
$953$	24.4941	−	24.4941i	0.793442	−	0.793442i	0.982052	+	0.188610i	$0.0603982\pi$
$954$		0			0
$955$	−4.85178	−	4.35543i	−0.157000	−	0.140938i
$956$	−21.4459			−0.693609
$957$		0			0
$958$	12.9613	−	12.9613i	0.418762	−	0.418762i
$959$			4.61382i			0.148988i
$960$		0			0
$961$	2.10794			0.0679982
$962$	35.5799	+	35.5799i	1.14714	+	1.14714i
$963$		0			0
$964$	1.51636			0.0488387
$965$	−21.0808	+	1.13645i	−0.678614	+	0.0365836i
$966$		0			0
$967$	34.3368	−	34.3368i	1.10420	−	1.10420i	0.110299	−	0.993898i	$-0.464819\pi$
$967$	34.3368	−	34.3368i	1.10420	−	1.10420i	0.993898	−	0.110299i	$-0.0351809\pi$
$968$	0.557809	−	0.557809i	0.0179287	−	0.0179287i
$969$		0			0
$970$	22.9295	−	25.5426i	0.736221	−	0.820122i
$971$		−	23.0276i		−	0.738992i	−0.929232	−	0.369496i	$-0.879530\pi$
$971$		−	23.0276i		−	0.738992i	0.929232	−	0.369496i	$-0.120470\pi$
$972$		0			0
$973$	1.78765	+	1.78765i	0.0573095	+	0.0573095i
$974$			11.6178i			0.372259i
$975$		0			0
$976$	−1.65954			−0.0531206
$977$	32.7527	+	32.7527i	1.04785	+	1.04785i	0.998796	+	0.0490563i	$0.0156214\pi$
$977$	32.7527	+	32.7527i	1.04785	+	1.04785i	0.0490563	+	0.998796i	$0.484379\pi$
$978$		0			0
$979$	7.21368			0.230550
$980$	−11.5513	−	10.3696i	−0.368992	−	0.331243i
$981$		0			0
$982$	4.13849	+	4.13849i	0.132065	+	0.132065i
$983$	4.11107	−	4.11107i	0.131123	−	0.131123i	−0.638499	−	0.769622i	$-0.720445\pi$
$983$	4.11107	−	4.11107i	0.131123	−	0.131123i	0.769622	+	0.638499i	$0.220445\pi$
$984$		0			0
$985$	12.8917	−	0.694982i	0.410763	−	0.0221440i
$986$	4.08609			0.130128
$987$		0			0
$988$	27.4598	−	5.41348i	0.873612	−	0.172226i
$989$		−	23.6453i		−	0.751878i
$990$		0			0
$991$			39.6215i			1.25862i	0.777155	+	0.629309i	$0.216662\pi$
$991$			39.6215i			1.25862i	−0.777155	+	0.629309i	$0.783338\pi$
$992$	3.80079	−	3.80079i	0.120675	−	0.120675i
$993$		0			0
$994$		−	2.15012i		−	0.0681978i
$995$	−12.3033	+	13.7054i	−0.390041	+	0.434491i
$996$		0			0
$997$	23.8300	−	23.8300i	0.754705	−	0.754705i	−0.220649	−	0.975353i	$-0.570817\pi$
$997$	23.8300	−	23.8300i	0.754705	−	0.754705i	0.975353	+	0.220649i	$0.0708174\pi$
$998$	17.2572	−	17.2572i	0.546268	−	0.546268i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1710.2.p.d.1063.4		20
3.2	odd	2		570.2.m.a.493.7	yes	20
5.2	odd	4	inner	1710.2.p.d.37.9		20
15.2	even	4		570.2.m.a.37.2	✓	20
19.18	odd	2	inner	1710.2.p.d.1063.9		20
57.56	even	2		570.2.m.a.493.2	yes	20
95.37	even	4	inner	1710.2.p.d.37.4		20
285.227	odd	4		570.2.m.a.37.7	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.m.a.37.2	✓	20	15.2	even	4
570.2.m.a.37.7	yes	20	285.227	odd	4
570.2.m.a.493.2	yes	20	57.56	even	2
570.2.m.a.493.7	yes	20	3.2	odd	2
1710.2.p.d.37.4		20	95.37	even	4	inner
1710.2.p.d.37.9		20	5.2	odd	4	inner
1710.2.p.d.1063.4		20	1.1	even	1	trivial
1710.2.p.d.1063.9		20	19.18	odd	2	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:	\( N \)	\(=\)	\( 1710 = 2 \cdot 3^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1710.p (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 - 0.707107i) q^{2} +1.00000i q^{4} +(1.66396 + 1.49373i) q^{5} +(-0.170229 + 0.170229i) q^{7} +(0.707107 - 0.707107i) q^{8} +O(q^{10})\)	\(q+(-0.707107 - 0.707107i) q^{2} +1.00000i q^{4} +(1.66396 + 1.49373i) q^{5} +(-0.170229 + 0.170229i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-0.120370 - 2.23283i) q^{10} -3.43349 q^{11} +(4.54030 - 4.54030i) q^{13} +0.240740 q^{14} -1.00000 q^{16} +(-0.537531 + 0.537531i) q^{17} +(2.42784 - 3.62016i) q^{19} +(-1.49373 + 1.66396i) q^{20} +(2.42784 + 2.42784i) q^{22} +(-5.15769 - 5.15769i) q^{23} +(0.537531 + 4.97102i) q^{25} -6.42095 q^{26} +(-0.170229 - 0.170229i) q^{28} +5.37513 q^{29} -5.37513i q^{31} +(0.707107 + 0.707107i) q^{32} +0.760184 q^{34} +(-0.537531 + 0.0289779i) q^{35} +(-5.54122 - 5.54122i) q^{37} +(-4.27659 + 0.843095i) q^{38} +(2.23283 - 0.120370i) q^{40} +3.68222i q^{41} +(2.29224 + 2.29224i) q^{43} -3.43349i q^{44} +7.29408i q^{46} +(9.57865 - 9.57865i) q^{47} +6.94204i q^{49} +(3.13495 - 3.89514i) q^{50} +(4.54030 + 4.54030i) q^{52} +(1.93366 - 1.93366i) q^{53} +(-5.71319 - 5.12871i) q^{55} +0.240740i q^{56} +(-3.80079 - 3.80079i) q^{58} +4.20166 q^{59} +1.65954 q^{61} +(-3.80079 + 3.80079i) q^{62} -1.00000i q^{64} +(14.3369 - 0.772891i) q^{65} +(0.481480 + 0.481480i) q^{67} +(-0.537531 - 0.537531i) q^{68} +(0.400582 + 0.359601i) q^{70} -8.93130i q^{71} +(8.74888 + 8.74888i) q^{73} +7.83647i q^{74} +(3.62016 + 2.42784i) q^{76} +(0.584480 - 0.584480i) q^{77} +1.15022 q^{79} +(-1.66396 - 1.49373i) q^{80} +(2.60372 - 2.60372i) q^{82} +(9.97102 + 9.97102i) q^{83} +(-1.69736 + 0.0915034i) q^{85} -3.24172i q^{86} +(-2.42784 + 2.42784i) q^{88} -2.10098 q^{89} +1.54578i q^{91} +(5.15769 - 5.15769i) q^{92} -13.5463 q^{94} +(9.44739 - 2.39726i) q^{95} +(10.8544 + 10.8544i) q^{97} +(4.90877 - 4.90877i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 4 q^{5} - 4 q^{7}+O(q^{10}) \) 20 * q + 4 * q^5 - 4 * q^7	\( 20 q + 4 q^{5} - 4 q^{7} + 8 q^{11} - 20 q^{16} - 4 q^{17} - 44 q^{23} + 4 q^{25} + 8 q^{26} - 4 q^{28} - 4 q^{35} + 4 q^{38} + 52 q^{43} - 4 q^{47} + 16 q^{55} + 8 q^{58} + 32 q^{61} + 8 q^{62} - 4 q^{68} - 20 q^{73} + 20 q^{76} + 24 q^{77} - 4 q^{80} - 24 q^{82} + 116 q^{83} - 60 q^{85} + 44 q^{92} + 32 q^{95}+O(q^{100}) \) 20 * q + 4 * q^5 - 4 * q^7 + 8 * q^11 - 20 * q^16 - 4 * q^17 - 44 * q^23 + 4 * q^25 + 8 * q^26 - 4 * q^28 - 4 * q^35 + 4 * q^38 + 52 * q^43 - 4 * q^47 + 16 * q^55 + 8 * q^58 + 32 * q^61 + 8 * q^62 - 4 * q^68 - 20 * q^73 + 20 * q^76 + 24 * q^77 - 4 * q^80 - 24 * q^82 + 116 * q^83 - 60 * q^85 + 44 * q^92 + 32 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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