LMFDB - Embedded newform 1710.2.p.c.37.10

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} + 108x^{16} + 1318x^{12} + 4652x^{8} + 5057x^{4} + 256 $ x^20 + 108x^16 + 1318x^12 + 4652x^8 + 5057x^4 + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 2^{9} $
Twist minimal:	no (minimal twist has level 570)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			37.10
Root			$0.339574 - 0.339574i$ of defining polynomial
Character	$\chi$	$=$	1710.37
Dual form			1710.2.p.c.1063.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 - 0.707107i) q^{2} -1.00000i q^{4} +(1.29975 - 1.81952i) q^{5} +(-0.728588 - 0.728588i) q^{7} +(-0.707107 - 0.707107i) q^{8} +O(q^{10})$	\(q+(0.707107 - 0.707107i) q^{2} -1.00000i q^{4} +(1.29975 - 1.81952i) q^{5} +(-0.728588 - 0.728588i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-0.367533 - 2.20566i) q^{10} +4.80832 q^{11} +(-0.531491 - 0.531491i) q^{13} -1.03038 q^{14} -1.00000 q^{16} +(3.72984 + 3.72984i) q^{17} +(2.90517 + 3.24961i) q^{19} +(-1.81952 - 1.29975i) q^{20} +(3.39999 - 3.39999i) q^{22} +(4.07973 - 4.07973i) q^{23} +(-1.62130 - 4.72984i) q^{25} -0.751642 q^{26} +(-0.728588 + 0.728588i) q^{28} +0.494819 q^{29} -8.62312i q^{31} +(-0.707107 + 0.707107i) q^{32} +5.27479 q^{34} +(-2.27266 + 0.378698i) q^{35} +(-5.47836 + 5.47836i) q^{37} +(4.35209 + 0.243552i) q^{38} +(-2.20566 + 0.367533i) q^{40} -5.82553i q^{41} +(-3.04079 + 3.04079i) q^{43} -4.80832i q^{44} -5.76961i q^{46} +(-0.910451 - 0.910451i) q^{47} -5.93832i q^{49} +(-4.49094 - 2.19807i) q^{50} +(-0.531491 + 0.531491i) q^{52} +(3.53266 + 3.53266i) q^{53} +(6.24961 - 8.74883i) q^{55} +1.03038i q^{56} +(0.349890 - 0.349890i) q^{58} -12.1307 q^{59} -5.32419 q^{61} +(-6.09747 - 6.09747i) q^{62} +1.00000i q^{64} +(-1.65786 + 0.276253i) q^{65} +(-9.19128 + 9.19128i) q^{67} +(3.72984 - 3.72984i) q^{68} +(-1.33924 + 1.87480i) q^{70} -2.06076i q^{71} +(3.31160 - 3.31160i) q^{73} +7.74758i q^{74} +(3.24961 - 2.90517i) q^{76} +(-3.50328 - 3.50328i) q^{77} -2.77074 q^{79} +(-1.29975 + 1.81952i) q^{80} +(-4.11927 - 4.11927i) q^{82} +(3.57770 - 3.57770i) q^{83} +(11.6344 - 1.93866i) q^{85} +4.30033i q^{86} +(-3.39999 - 3.39999i) q^{88} +1.08630 q^{89} +0.774476i q^{91} +(-4.07973 - 4.07973i) q^{92} -1.28757 q^{94} +(9.68873 - 1.06234i) q^{95} +(-2.81665 + 2.81665i) q^{97} +(-4.19903 - 4.19903i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 12 q^{5} - 4 q^{7}+O(q^{10}) $ 20 * q - 12 * q^5 - 4 * q^7	$ 20 q - 12 q^{5} - 4 q^{7} + 8 q^{11} - 20 q^{16} + 12 q^{17} + 4 q^{23} - 28 q^{25} - 24 q^{26} - 4 q^{28} - 4 q^{35} + 12 q^{38} - 12 q^{43} + 44 q^{47} + 64 q^{55} - 8 q^{58} + 24 q^{62} + 12 q^{68} - 4 q^{73} + 4 q^{76} - 88 q^{77} + 12 q^{80} - 8 q^{82} - 76 q^{83} - 12 q^{85} - 4 q^{92} + 24 q^{95}+O(q^{100}) $ 20 * q - 12 * q^5 - 4 * q^7 + 8 * q^11 - 20 * q^16 + 12 * q^17 + 4 * q^23 - 28 * q^25 - 24 * q^26 - 4 * q^28 - 4 * q^35 + 12 * q^38 - 12 * q^43 + 44 * q^47 + 64 * q^55 - 8 * q^58 + 24 * q^62 + 12 * q^68 - 4 * q^73 + 4 * q^76 - 88 * q^77 + 12 * q^80 - 8 * q^82 - 76 * q^83 - 12 * q^85 - 4 * q^92 + 24 * q^95

Display 100 coefficients 10 coefficients

Character values

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

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

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
$5$	1.29975	−	1.81952i	0.581266	−	0.813714i
$5$	1.29975	−	1.81952i	0.581266	−	0.813714i
$6$		0			0
$7$	−0.728588	−	0.728588i	−0.275380	−	0.275380i	0.555881	−	0.831262i	$-0.312381\pi$
$7$	−0.728588	−	0.728588i	−0.275380	−	0.275380i	−0.831262	+	0.555881i	$0.812381\pi$
$8$	−0.707107	−	0.707107i	−0.250000	−	0.250000i
$9$		0			0
$10$	−0.367533	−	2.20566i	−0.116224	−	0.697490i
$11$	4.80832			1.44976			0.724881	−	0.688874i	$-0.241895\pi$
$11$	4.80832			1.44976			0.724881	+	0.688874i	$0.241895\pi$
$12$		0			0
$13$	−0.531491	−	0.531491i	−0.147409	−	0.147409i	0.629550	−	0.776960i	$-0.283239\pi$
$13$	−0.531491	−	0.531491i	−0.147409	−	0.147409i	−0.776960	+	0.629550i	$0.783239\pi$
$14$	−1.03038			−0.275380
$15$		0			0
$16$	−1.00000			−0.250000
$17$	3.72984	+	3.72984i	0.904619	+	0.904619i	0.995831	−	0.0912125i	$-0.0290743\pi$
$17$	3.72984	+	3.72984i	0.904619	+	0.904619i	−0.0912125	+	0.995831i	$0.529074\pi$
$18$		0			0
$19$	2.90517	+	3.24961i	0.666493	+	0.745511i
$19$	2.90517	+	3.24961i	0.666493	+	0.745511i
$20$	−1.81952	−	1.29975i	−0.406857	−	0.290633i
$21$		0			0
$22$	3.39999	−	3.39999i	0.724881	−	0.724881i
$23$	4.07973	−	4.07973i	0.850682	−	0.850682i	−0.139535	−	0.990217i	$-0.544561\pi$
$23$	4.07973	−	4.07973i	0.850682	−	0.850682i	0.990217	+	0.139535i	$0.0445607\pi$
$24$		0			0
$25$	−1.62130	−	4.72984i	−0.324260	−	0.945968i
$26$	−0.751642			−0.147409
$27$		0			0
$28$	−0.728588	+	0.728588i	−0.137690	+	0.137690i
$29$	0.494819			0.0918856			0.0459428	−	0.998944i	$-0.485371\pi$
$29$	0.494819			0.0918856			0.0459428	+	0.998944i	$0.485371\pi$
$30$		0			0
$31$		−	8.62312i		−	1.54876i	−0.632722	−	0.774379i	$-0.718062\pi$
$31$		−	8.62312i		−	1.54876i	0.632722	−	0.774379i	$-0.281938\pi$
$32$	−0.707107	+	0.707107i	−0.125000	+	0.125000i
$33$		0			0
$34$	5.27479			0.904619
$35$	−2.27266	+	0.378698i	−0.384150	+	0.0640117i
$36$		0			0
$37$	−5.47836	+	5.47836i	−0.900637	+	0.900637i	−0.995491	−	0.0948538i	$-0.969762\pi$
$37$	−5.47836	+	5.47836i	−0.900637	+	0.900637i	0.0948538	+	0.995491i	$0.469762\pi$
$38$	4.35209	+	0.243552i	0.706002	+	0.0395093i
$39$		0			0
$40$	−2.20566	+	0.367533i	−0.348745	+	0.0581120i
$41$		−	5.82553i		−	0.909794i	−0.890544	−	0.454897i	$-0.849676\pi$
$41$		−	5.82553i		−	0.909794i	0.890544	−	0.454897i	$-0.150324\pi$
$42$		0			0
$43$	−3.04079	+	3.04079i	−0.463716	+	0.463716i	−0.899871	−	0.436155i	$-0.856340\pi$
$43$	−3.04079	+	3.04079i	−0.463716	+	0.463716i	0.436155	+	0.899871i	$0.356340\pi$
$44$		−	4.80832i		−	0.724881i
$45$		0			0
$46$		−	5.76961i		−	0.850682i
$47$	−0.910451	−	0.910451i	−0.132803	−	0.132803i	0.637581	−	0.770384i	$-0.279935\pi$
$47$	−0.910451	−	0.910451i	−0.132803	−	0.132803i	−0.770384	+	0.637581i	$0.779935\pi$
$48$		0			0
$49$		−	5.93832i		−	0.848331i
$50$	−4.49094	−	2.19807i	−0.635114	−	0.310854i
$51$		0			0
$52$	−0.531491	+	0.531491i	−0.0737046	+	0.0737046i
$53$	3.53266	+	3.53266i	0.485248	+	0.485248i	0.906803	−	0.421555i	$-0.138516\pi$
$53$	3.53266	+	3.53266i	0.485248	+	0.485248i	−0.421555	+	0.906803i	$0.638516\pi$
$54$		0			0
$55$	6.24961	−	8.74883i	0.842697	−	1.17969i
$56$			1.03038i			0.137690i
$57$		0			0
$58$	0.349890	−	0.349890i	0.0459428	−	0.0459428i
$59$	−12.1307			−1.57928			−0.789641	−	0.613569i	$-0.789733\pi$
$59$	−12.1307			−1.57928			−0.789641	+	0.613569i	$0.789733\pi$
$60$		0			0
$61$	−5.32419			−0.681692			−0.340846	−	0.940119i	$-0.610713\pi$
$61$	−5.32419			−0.681692			−0.340846	+	0.940119i	$0.610713\pi$
$62$	−6.09747	−	6.09747i	−0.774379	−	0.774379i
$63$		0			0
$64$			1.00000i			0.125000i
$65$	−1.65786	+	0.276253i	−0.205633	+	0.0342650i
$66$		0			0
$67$	−9.19128	+	9.19128i	−1.12289	+	1.12289i	−0.131590	+	0.991304i	$0.542008\pi$
$67$	−9.19128	+	9.19128i	−1.12289	+	1.12289i	−0.991304	+	0.131590i	$0.957992\pi$
$68$	3.72984	−	3.72984i	0.452309	−	0.452309i
$69$		0			0
$70$	−1.33924	+	1.87480i	−0.160069	+	0.224081i
$71$		−	2.06076i		−	0.244567i	−0.992495	−	0.122284i	$-0.960978\pi$
$71$		−	2.06076i		−	0.244567i	0.992495	−	0.122284i	$-0.0390217\pi$
$72$		0			0
$73$	3.31160	−	3.31160i	0.387594	−	0.387594i	−0.486235	−	0.873828i	$-0.661630\pi$
$73$	3.31160	−	3.31160i	0.387594	−	0.387594i	0.873828	+	0.486235i	$0.161630\pi$
$74$			7.74758i			0.900637i
$75$		0			0
$76$	3.24961	−	2.90517i	0.372756	−	0.333246i
$77$	−3.50328	−	3.50328i	−0.399236	−	0.399236i
$78$		0			0
$79$	−2.77074			−0.311733			−0.155866	−	0.987778i	$-0.549817\pi$
$79$	−2.77074			−0.311733			−0.155866	+	0.987778i	$0.549817\pi$
$80$	−1.29975	+	1.81952i	−0.145316	+	0.203428i
$81$		0			0
$82$	−4.11927	−	4.11927i	−0.454897	−	0.454897i
$83$	3.57770	−	3.57770i	0.392703	−	0.392703i	−0.482947	−	0.875650i	$-0.660433\pi$
$83$	3.57770	−	3.57770i	0.392703	−	0.392703i	0.875650	+	0.482947i	$0.160433\pi$
$84$		0			0
$85$	11.6344	−	1.93866i	1.26192	−	0.210277i
$86$			4.30033i			0.463716i
$87$		0			0
$88$	−3.39999	−	3.39999i	−0.362441	−	0.362441i
$89$	1.08630			0.115147			0.0575736	−	0.998341i	$-0.481664\pi$
$89$	1.08630			0.115147			0.0575736	+	0.998341i	$0.481664\pi$
$90$		0			0
$91$			0.774476i			0.0811872i
$92$	−4.07973	−	4.07973i	−0.425341	−	0.425341i
$93$		0			0
$94$	−1.28757			−0.132803
$95$	9.68873	−	1.06234i	0.994042	−	0.108994i
$96$		0			0
$97$	−2.81665	+	2.81665i	−0.285988	+	0.285988i	−0.835491	−	0.549503i	$-0.814817\pi$
$97$	−2.81665	+	2.81665i	−0.285988	+	0.285988i	0.549503	+	0.835491i	$0.314817\pi$
$98$	−4.19903	−	4.19903i	−0.424166	−	0.424166i
$99$		0			0
$100$	−4.72984	+	1.62130i	−0.472984	+	0.162130i
$101$	14.0592			1.39894			0.699470	−	0.714662i	$-0.253419\pi$
$101$	14.0592			1.39894			0.699470	+	0.714662i	$0.253419\pi$
$102$		0			0
$103$	6.63327	+	6.63327i	0.653596	+	0.653596i	0.953857	−	0.300261i	$-0.0970739\pi$
$103$	6.63327	+	6.63327i	0.653596	+	0.653596i	−0.300261	+	0.953857i	$0.597074\pi$
$104$			0.751642i			0.0737046i
$105$		0			0
$106$	4.99593			0.485248
$107$	1.54262	−	1.54262i	0.149131	−	0.149131i	−0.628599	−	0.777730i	$-0.716371\pi$
$107$	1.54262	−	1.54262i	0.149131	−	0.149131i	0.777730	+	0.628599i	$0.216371\pi$
$108$		0			0
$109$	18.4286			1.76514			0.882569	−	0.470183i	$-0.155812\pi$
$109$	18.4286			1.76514			0.882569	+	0.470183i	$0.155812\pi$
$110$	−1.76721	−	10.6055i	−0.168497	−	1.01119i
$111$		0			0
$112$	0.728588	+	0.728588i	0.0688451	+	0.0688451i
$113$	−5.25913	−	5.25913i	−0.494738	−	0.494738i	0.415058	−	0.909795i	$-0.363761\pi$
$113$	−5.25913	−	5.25913i	−0.494738	−	0.494738i	−0.909795	+	0.415058i	$0.863761\pi$
$114$		0			0
$115$	−2.12052	−	12.7258i	−0.197740	−	1.18668i
$116$		−	0.494819i		−	0.0459428i
$117$		0			0
$118$	−8.57770	+	8.57770i	−0.789641	+	0.789641i
$119$		−	5.43503i		−	0.498229i
$120$		0			0
$121$	12.1199			1.10181
$122$	−3.76477	+	3.76477i	−0.340846	+	0.340846i
$123$		0			0
$124$	−8.62312			−0.774379
$125$	−10.7133	−	3.19762i	−0.958229	−	0.286004i
$126$		0			0
$127$	−9.35800	+	9.35800i	−0.830388	+	0.830388i	−0.987570	−	0.157181i	$-0.949759\pi$
$127$	−9.35800	+	9.35800i	−0.830388	+	0.830388i	0.157181	+	0.987570i	$0.449759\pi$
$128$	0.707107	+	0.707107i	0.0625000	+	0.0625000i
$129$		0			0
$130$	−0.976946	+	1.36763i	−0.0856839	+	0.119949i
$131$	−12.6267			−1.10320			−0.551601	−	0.834108i	$-0.685983\pi$
$131$	−12.6267			−1.10320			−0.551601	+	0.834108i	$0.685983\pi$
$132$		0			0
$133$	0.250951	−	4.48430i	0.0217602	−	0.388838i
$134$			12.9984i			1.12289i
$135$		0			0
$136$		−	5.27479i		−	0.452309i
$137$	−0.378698	−	0.378698i	−0.0323544	−	0.0323544i	0.690745	−	0.723099i	$-0.257283\pi$
$137$	−0.378698	−	0.378698i	−0.0323544	−	0.0323544i	−0.723099	+	0.690745i	$0.757283\pi$
$138$		0			0
$139$			22.7942i			1.93338i	0.255957	+	0.966688i	$0.417609\pi$
$139$			22.7942i			1.93338i	−0.255957	+	0.966688i	$0.582391\pi$
$140$	0.378698	+	2.27266i	0.0320058	+	0.192075i
$141$		0			0
$142$	−1.45718	−	1.45718i	−0.122284	−	0.122284i
$143$	−2.55558	−	2.55558i	−0.213708	−	0.213708i
$144$		0			0
$145$	0.643141	−	0.900333i	0.0534100	−	0.0747686i
$146$		−	4.68331i		−	0.387594i
$147$		0			0
$148$	5.47836	+	5.47836i	0.450319	+	0.450319i
$149$		−	15.8801i		−	1.30095i	−0.759529	−	0.650473i	$-0.774571\pi$
$149$		−	15.8801i		−	1.30095i	0.759529	−	0.650473i	$-0.225429\pi$
$150$		0			0
$151$			13.3507i			1.08646i	0.839583	+	0.543231i	$0.182799\pi$
$151$			13.3507i			1.08646i	−0.839583	+	0.543231i	$0.817201\pi$
$152$	0.243552	−	4.35209i	0.0197547	−	0.353001i
$153$		0			0
$154$	−4.95439			−0.399236
$155$	−15.6899	−	11.2079i	−1.26025	−	0.900240i
$156$		0			0
$157$	11.7372	+	11.7372i	0.936727	+	0.936727i	0.998114	−	0.0613870i	$-0.0195524\pi$
$157$	11.7372	+	11.7372i	0.936727	+	0.936727i	−0.0613870	+	0.998114i	$0.519552\pi$
$158$	−1.95921	+	1.95921i	−0.155866	+	0.155866i
$159$		0			0
$160$	0.367533	+	2.20566i	0.0290560	+	0.174372i
$161$	−5.94489			−0.468523
$162$		0			0
$163$	−0.988668	+	0.988668i	−0.0774384	+	0.0774384i	−0.744765	−	0.667327i	$-0.767438\pi$
$163$	−0.988668	+	0.988668i	−0.0774384	+	0.0774384i	0.667327	+	0.744765i	$0.267438\pi$
$164$	−5.82553			−0.454897
$165$		0			0
$166$		−	5.05963i		−	0.392703i
$167$	7.42584	−	7.42584i	0.574629	−	0.574629i	−0.358790	−	0.933418i	$-0.616811\pi$
$167$	7.42584	−	7.42584i	0.574629	−	0.574629i	0.933418	+	0.358790i	$0.116811\pi$
$168$		0			0
$169$		−	12.4350i		−	0.956541i
$170$	6.85591	−	9.59758i	0.525824	−	0.736101i
$171$		0			0
$172$	3.04079	+	3.04079i	0.231858	+	0.231858i
$173$	11.0462	+	11.0462i	0.839825	+	0.839825i	0.988836	−	0.149011i	$-0.0476090\pi$
$173$	11.0462	+	11.0462i	0.839825	+	0.839825i	−0.149011	+	0.988836i	$0.547609\pi$
$174$		0			0
$175$	−2.26484	+	4.62737i	−0.171206	+	0.349796i
$176$	−4.80832			−0.362441
$177$		0			0
$178$	0.768128	−	0.768128i	0.0575736	−	0.0575736i
$179$	−19.0425			−1.42330			−0.711652	−	0.702532i	$-0.752053\pi$
$179$	−19.0425			−1.42330			−0.711652	+	0.702532i	$0.752053\pi$
$180$		0			0
$181$		−	1.78110i		−	0.132388i	−0.997807	−	0.0661941i	$-0.978914\pi$
$181$		−	1.78110i		−	0.132388i	0.997807	−	0.0661941i	$-0.0210857\pi$
$182$	0.547637	+	0.547637i	0.0405936	+	0.0405936i
$183$		0			0
$184$	−5.76961			−0.425341
$185$	2.84749	+	17.0885i	0.209351	+	1.25637i
$186$		0			0
$187$	17.9343	+	17.9343i	1.31148	+	1.31148i
$188$	−0.910451	+	0.910451i	−0.0664014	+	0.0664014i
$189$		0			0
$190$	6.09977	−	7.60215i	0.442524	−	0.551518i
$191$	14.8650			1.07559			0.537797	−	0.843075i	$-0.319257\pi$
$191$	14.8650			1.07559			0.537797	+	0.843075i	$0.319257\pi$
$192$		0			0
$193$	−5.04632	−	5.04632i	−0.363242	−	0.363242i	0.501763	−	0.865005i	$-0.332685\pi$
$193$	−5.04632	−	5.04632i	−0.363242	−	0.363242i	−0.865005	+	0.501763i	$0.832685\pi$
$194$			3.98335i			0.285988i
$195$		0			0
$196$	−5.93832			−0.424166
$197$	7.66209	+	7.66209i	0.545901	+	0.545901i	0.925253	−	0.379351i	$-0.123853\pi$
$197$	7.66209	+	7.66209i	0.545901	+	0.545901i	−0.379351	+	0.925253i	$0.623853\pi$
$198$		0			0
$199$			20.9302i			1.48370i	0.670565	+	0.741851i	$0.266052\pi$
$199$			20.9302i			1.48370i	−0.670565	+	0.741851i	$0.733948\pi$
$200$	−2.19807	+	4.49094i	−0.155427	+	0.317557i
$201$		0			0
$202$	9.94134	−	9.94134i	0.699470	−	0.699470i
$203$	−0.360520	−	0.360520i	−0.0253035	−	0.0253035i
$204$		0			0
$205$	−10.5997	−	7.57173i	−0.740312	−	0.528832i
$206$	9.38086			0.653596
$207$		0			0
$208$	0.531491	+	0.531491i	0.0368523	+	0.0368523i
$209$	13.9690	+	15.6252i	0.966256	+	1.08081i
$210$		0			0
$211$		−	27.6388i		−	1.90273i	−0.308062	−	0.951366i	$-0.599681\pi$
$211$		−	27.6388i		−	1.90273i	0.308062	−	0.951366i	$-0.400319\pi$
$212$	3.53266	−	3.53266i	0.242624	−	0.242624i
$213$		0			0
$214$		−	2.18160i		−	0.149131i
$215$	1.58051	+	9.48504i	0.107790	+	0.646875i
$216$		0			0
$217$	−6.28270	+	6.28270i	−0.426498	+	0.426498i
$218$	13.0310	−	13.0310i	0.882569	−	0.882569i
$219$		0			0
$220$	−8.74883	−	6.24961i	−0.589846	−	0.421349i
$221$		−	3.96475i		−	0.266698i
$222$		0			0
$223$	8.04571	+	8.04571i	0.538781	+	0.538781i	0.923171	−	0.384390i	$-0.125588\pi$
$223$	8.04571	+	8.04571i	0.538781	+	0.538781i	−0.384390	+	0.923171i	$0.625588\pi$
$224$	1.03038			0.0688451
$225$		0			0
$226$	−7.43754			−0.494738
$227$	−1.98330	+	1.98330i	−0.131636	+	0.131636i	−0.769855	−	0.638219i	$-0.779671\pi$
$227$	−1.98330	+	1.98330i	−0.131636	+	0.131636i	0.638219	+	0.769855i	$0.279671\pi$
$228$		0			0
$229$		−	19.6443i		−	1.29813i	−0.760732	−	0.649066i	$-0.775160\pi$
$229$		−	19.6443i		−	1.29813i	0.760732	−	0.649066i	$-0.224840\pi$
$230$	−10.4979	−	7.49905i	−0.692212	−	0.494473i
$231$		0			0
$232$	−0.349890	−	0.349890i	−0.0229714	−	0.0229714i
$233$	4.73992	−	4.73992i	0.310523	−	0.310523i	−0.534589	−	0.845112i	$-0.679534\pi$
$233$	4.73992	−	4.73992i	0.310523	−	0.310523i	0.845112	+	0.534589i	$0.179534\pi$
$234$		0			0
$235$	−2.83994	+	0.473225i	−0.185257	+	0.0308698i
$236$			12.1307i			0.789641i
$237$		0			0
$238$	−3.84315	−	3.84315i	−0.249114	−	0.249114i
$239$			21.1851i			1.37035i	0.728378	+	0.685176i	$0.240275\pi$
$239$			21.1851i			1.37035i	−0.728378	+	0.685176i	$0.759725\pi$
$240$		0			0
$241$		−	16.2784i		−	1.04859i	−0.851538	−	0.524293i	$-0.824329\pi$
$241$		−	16.2784i		−	1.04859i	0.851538	−	0.524293i	$-0.175671\pi$
$242$	8.57008	−	8.57008i	0.550905	−	0.550905i
$243$		0			0
$244$			5.32419i			0.340846i
$245$	−10.8049	−	7.71833i	−0.690299	−	0.493106i
$246$		0			0
$247$	0.183064	−	3.27121i	0.0116481	−	0.208142i
$248$	−6.09747	+	6.09747i	−0.387190	+	0.387190i
$249$		0			0
$250$	−9.83652	+	5.31441i	−0.622116	+	0.336113i
$251$	−5.24992			−0.331372			−0.165686	−	0.986179i	$-0.552984\pi$
$251$	−5.24992			−0.331372			−0.165686	+	0.986179i	$0.552984\pi$
$252$		0			0
$253$	19.6166	−	19.6166i	1.23329	−	1.23329i
$254$			13.2342i			0.830388i
$255$		0			0
$256$	1.00000			0.0625000
$257$	−16.0320	+	16.0320i	−1.00005	+	1.00005i	−4.94079e−5		1.00000i	$0.500016\pi$
$257$	−16.0320	+	16.0320i	−1.00005	+	1.00005i	−1.00000		4.94079e-5i	$0.999984\pi$
$258$		0			0
$259$	7.98294			0.496036
$260$	0.276253	+	1.65786i	0.0171325	+	0.102816i
$261$		0			0
$262$	−8.92844	+	8.92844i	−0.551601	+	0.551601i
$263$	5.94999	−	5.94999i	0.366892	−	0.366892i	−0.499450	−	0.866342i	$-0.666465\pi$
$263$	5.94999	−	5.94999i	0.366892	−	0.366892i	0.866342	+	0.499450i	$0.166465\pi$
$264$		0			0
$265$	11.0193	−	1.83617i	0.676911	−	0.112795i
$266$	−2.99343	−	3.34833i	−0.183539	−	0.205299i
$267$		0			0
$268$	9.19128	+	9.19128i	0.561447	+	0.561447i
$269$	26.2880			1.60281			0.801404	−	0.598123i	$-0.204087\pi$
$269$	26.2880			1.60281			0.801404	+	0.598123i	$0.204087\pi$
$270$		0			0
$271$	−11.9318			−0.724802			−0.362401	−	0.932022i	$-0.618043\pi$
$271$	−11.9318			−0.724802			−0.362401	+	0.932022i	$0.618043\pi$
$272$	−3.72984	−	3.72984i	−0.226155	−	0.226155i
$273$		0			0
$274$	−0.535560			−0.0323544
$275$	−7.79573	−	22.7426i	−0.470100	−	1.37143i
$276$		0			0
$277$	−13.1943	−	13.1943i	−0.792771	−	0.792771i	0.189173	−	0.981944i	$-0.439419\pi$
$277$	−13.1943	−	13.1943i	−0.792771	−	0.792771i	−0.981944	+	0.189173i	$0.939419\pi$
$278$	16.1179	+	16.1179i	0.966688	+	0.966688i
$279$		0			0
$280$	1.87480	+	1.33924i	0.112040	+	0.0800346i
$281$			25.4814i			1.52009i	0.649870	+	0.760045i	$0.274823\pi$
$281$			25.4814i			1.52009i	−0.649870	+	0.760045i	$0.725177\pi$
$282$		0			0
$283$	−14.9451	+	14.9451i	−0.888392	+	0.888392i	−0.994369	−	0.105977i	$-0.966203\pi$
$283$	−14.9451	+	14.9451i	−0.888392	+	0.888392i	0.105977	+	0.994369i	$0.466203\pi$
$284$	−2.06076			−0.122284
$285$		0			0
$286$	−3.61413			−0.213708
$287$	−4.24441	+	4.24441i	−0.250540	+	0.250540i
$288$		0			0
$289$			10.8234i			0.636671i
$290$	−0.181862	−	1.09140i	−0.0106793	−	0.0640893i
$291$		0			0
$292$	−3.31160	−	3.31160i	−0.193797	−	0.193797i
$293$	19.3388	+	19.3388i	1.12978	+	1.12978i	0.990212	+	0.139570i	$0.0445719\pi$
$293$	19.3388	+	19.3388i	1.12978	+	1.12978i	0.139570	+	0.990212i	$0.455428\pi$
$294$		0			0
$295$	−15.7669	+	22.0720i	−0.917982	+	1.28508i
$296$	7.74758			0.450319
$297$		0			0
$298$	−11.2289	−	11.2289i	−0.650473	−	0.650473i
$299$	−4.33668			−0.250797
$300$		0			0
$301$	4.43097			0.255397
$302$	9.44035	+	9.44035i	0.543231	+	0.543231i
$303$		0			0
$304$	−2.90517	−	3.24961i	−0.166623	−	0.186378i
$305$	−6.92011	+	9.68746i	−0.396244	+	0.554702i
$306$		0			0
$307$	−0.00353863	+	0.00353863i	−0.000201960	+	0.000201960i	−0.707208	−	0.707006i	$-0.750045\pi$
$307$	−0.00353863	+	0.00353863i	−0.000201960	+	0.000201960i	0.707006	+	0.707208i	$0.250045\pi$
$308$	−3.50328	+	3.50328i	−0.199618	+	0.199618i
$309$		0			0
$310$	−19.0196	+	3.16928i	−1.08024	+	0.180003i
$311$	11.6925			0.663019			0.331509	−	0.943452i	$-0.392442\pi$
$311$	11.6925			0.663019			0.331509	+	0.943452i	$0.392442\pi$
$312$		0			0
$313$	−16.6688	+	16.6688i	−0.942174	+	0.942174i	−0.998417	−	0.0562432i	$-0.982088\pi$
$313$	−16.6688	+	16.6688i	−0.942174	+	0.942174i	0.0562432	+	0.998417i	$0.482088\pi$
$314$	16.5988			0.936727
$315$		0			0
$316$			2.77074i			0.155866i
$317$	−6.96737	+	6.96737i	−0.391327	+	0.391327i	−0.875160	−	0.483834i	$-0.839244\pi$
$317$	−6.96737	+	6.96737i	−0.391327	+	0.391327i	0.483834	+	0.875160i	$0.339244\pi$
$318$		0			0
$319$	2.37925			0.133212
$320$	1.81952	+	1.29975i	0.101714	+	0.0726582i
$321$		0			0
$322$	−4.20367	+	4.20367i	−0.234261	+	0.234261i
$323$	−1.28468	+	22.9564i	−0.0714818	+	1.27733i
$324$		0			0
$325$	−1.65216	+	3.37558i	−0.0916454	+	0.187243i
$326$			1.39819i			0.0774384i
$327$		0			0
$328$	−4.11927	+	4.11927i	−0.227449	+	0.227449i
$329$			1.32669i			0.0731426i
$330$		0			0
$331$			12.2381i			0.672669i	0.941743	+	0.336335i	$0.109187\pi$
$331$			12.2381i			0.672669i	−0.941743	+	0.336335i	$0.890813\pi$
$332$	−3.57770	−	3.57770i	−0.196352	−	0.196352i
$333$		0			0
$334$		−	10.5017i		−	0.574629i
$335$	4.77735	+	28.6701i	0.261015	+	1.56641i
$336$		0			0
$337$	18.9918	−	18.9918i	1.03455	−	1.03455i	0.0351664	−	0.999381i	$-0.488804\pi$
$337$	18.9918	−	18.9918i	1.03455	−	1.03455i	0.999381	−	0.0351664i	$-0.0111961\pi$
$338$	−8.79290	−	8.79290i	−0.478271	−	0.478271i
$339$		0			0
$340$	−1.93866	−	11.6344i	−0.105138	−	0.630962i
$341$		−	41.4627i		−	2.24533i
$342$		0			0
$343$	−9.42671	+	9.42671i	−0.508994	+	0.508994i
$344$	4.30033			0.231858
$345$		0			0
$346$	15.6216			0.839825
$347$	−1.51527	−	1.51527i	−0.0813438	−	0.0813438i	0.665264	−	0.746608i	$-0.268319\pi$
$347$	−1.51527	−	1.51527i	−0.0813438	−	0.0813438i	−0.746608	+	0.665264i	$0.768319\pi$
$348$		0			0
$349$			21.3136i			1.14089i	0.821336	+	0.570444i	$0.193229\pi$
$349$			21.3136i			1.14089i	−0.821336	+	0.570444i	$0.806771\pi$
$350$	1.67056	+	4.87353i	0.0892950	+	0.260501i
$351$		0			0
$352$	−3.39999	+	3.39999i	−0.181220	+	0.181220i
$353$	−9.37463	+	9.37463i	−0.498961	+	0.498961i	−0.911115	−	0.412153i	$-0.864777\pi$
$353$	−9.37463	+	9.37463i	−0.498961	+	0.498961i	0.412153	+	0.911115i	$0.364777\pi$
$354$		0			0
$355$	−3.74959	−	2.67847i	−0.199008	−	0.142158i
$356$		−	1.08630i		−	0.0575736i
$357$		0			0
$358$	−13.4651	+	13.4651i	−0.711652	+	0.711652i
$359$			30.1209i			1.58972i	0.606792	+	0.794861i	$0.292456\pi$
$359$			30.1209i			1.58972i	−0.606792	+	0.794861i	$0.707544\pi$
$360$		0			0
$361$	−2.11992	+	18.8814i	−0.111575	+	0.993756i
$362$	−1.25943	−	1.25943i	−0.0661941	−	0.0661941i
$363$		0			0
$364$	0.774476			0.0405936
$365$	−1.72127	−	10.3298i	−0.0900954	−	0.540685i
$366$		0			0
$367$	−10.0986	−	10.0986i	−0.527140	−	0.527140i	0.392578	−	0.919719i	$-0.371583\pi$
$367$	−10.0986	−	10.0986i	−0.527140	−	0.527140i	−0.919719	+	0.392578i	$0.871583\pi$
$368$	−4.07973	+	4.07973i	−0.212671	+	0.212671i
$369$		0			0
$370$	14.0969	+	10.0699i	0.732861	+	0.523510i
$371$		−	5.14771i		−	0.267256i
$372$		0			0
$373$	11.5759	+	11.5759i	0.599377	+	0.599377i	0.940147	−	0.340770i	$-0.110688\pi$
$373$	11.5759	+	11.5759i	0.599377	+	0.599377i	−0.340770	+	0.940147i	$0.610688\pi$
$374$	25.3629			1.31148
$375$		0			0
$376$			1.28757i			0.0664014i
$377$	−0.262992	−	0.262992i	−0.0135448	−	0.0135448i
$378$		0			0
$379$	30.6895			1.57641			0.788206	−	0.615412i	$-0.211010\pi$
$379$	30.6895			1.57641			0.788206	+	0.615412i	$0.211010\pi$
$380$	−1.06234	−	9.68873i	−0.0544971	−	0.497021i
$381$		0			0
$382$	10.5111	−	10.5111i	0.537797	−	0.537797i
$383$	6.71232	+	6.71232i	0.342983	+	0.342983i	0.857488	−	0.514504i	$-0.172024\pi$
$383$	6.71232	+	6.71232i	0.342983	+	0.342983i	−0.514504	+	0.857488i	$0.672024\pi$
$384$		0			0
$385$	−10.9277	+	1.82090i	−0.556926	+	0.0928017i
$386$	−7.13657			−0.363242
$387$		0			0
$388$	2.81665	+	2.81665i	0.142994	+	0.142994i
$389$		−	1.69598i		−	0.0859894i	−0.999075	−	0.0429947i	$-0.986310\pi$
$389$		−	1.69598i		−	0.0859894i	0.999075	−	0.0429947i	$-0.0136899\pi$
$390$		0			0
$391$	30.4335			1.53909
$392$	−4.19903	+	4.19903i	−0.212083	+	0.212083i
$393$		0			0
$394$	10.8358			0.545901
$395$	−3.60127	+	5.04142i	−0.181199	+	0.253661i
$396$		0			0
$397$	−17.6346	−	17.6346i	−0.885057	−	0.885057i	0.108986	−	0.994043i	$-0.465240\pi$
$397$	−17.6346	−	17.6346i	−0.885057	−	0.885057i	−0.994043	+	0.108986i	$0.965240\pi$
$398$	14.7999	+	14.7999i	0.741851	+	0.741851i
$399$		0			0
$400$	1.62130	+	4.72984i	0.0810651	+	0.236492i
$401$			1.30146i			0.0649918i	0.999472	+	0.0324959i	$0.0103456\pi$
$401$			1.30146i			0.0649918i	−0.999472	+	0.0324959i	$0.989654\pi$
$402$		0			0
$403$	−4.58311	+	4.58311i	−0.228301	+	0.228301i
$404$		−	14.0592i		−	0.699470i
$405$		0			0
$406$	−0.509852			−0.0253035
$407$	−26.3417	+	26.3417i	−1.30571	+	1.30571i
$408$		0			0
$409$	18.8682			0.932971			0.466485	−	0.884529i	$-0.345520\pi$
$409$	18.8682			0.932971			0.466485	+	0.884529i	$0.345520\pi$
$410$	−12.8491	+	2.14107i	−0.634572	+	0.105740i
$411$		0			0
$412$	6.63327	−	6.63327i	0.326798	−	0.326798i
$413$	8.83828	+	8.83828i	0.434903	+	0.434903i
$414$		0			0
$415$	−1.85958	−	11.1598i	−0.0912831	−	0.547813i
$416$	0.751642			0.0368523
$417$		0			0
$418$	20.9262	+	1.17107i	1.02354	+	0.0572791i
$419$		−	20.1568i		−	0.984725i	−0.870390	−	0.492363i	$-0.836133\pi$
$419$		−	20.1568i		−	0.984725i	0.870390	−	0.492363i	$-0.163867\pi$
$420$		0			0
$421$			8.85286i			0.431462i	0.976453	+	0.215731i	$0.0692134\pi$
$421$			8.85286i			0.431462i	−0.976453	+	0.215731i	$0.930787\pi$
$422$	−19.5436	−	19.5436i	−0.951366	−	0.951366i
$423$		0			0
$424$		−	4.99593i		−	0.242624i
$425$	11.5943	−	23.6887i	0.562408	−	1.14907i
$426$		0			0
$427$	3.87914	+	3.87914i	0.187725	+	0.187725i
$428$	−1.54262	−	1.54262i	−0.0745656	−	0.0745656i
$429$		0			0
$430$	7.82453	+	5.58935i	0.377332	+	0.269542i
$431$		−	25.3047i		−	1.21889i	−0.792830	−	0.609443i	$-0.791393\pi$
$431$		−	25.3047i		−	1.21889i	0.792830	−	0.609443i	$-0.208607\pi$
$432$		0			0
$433$	6.00560	+	6.00560i	0.288611	+	0.288611i	0.836531	−	0.547920i	$-0.184580\pi$
$433$	6.00560	+	6.00560i	0.288611	+	0.288611i	−0.547920	+	0.836531i	$0.684580\pi$
$434$			8.88509i			0.426498i
$435$		0			0
$436$		−	18.4286i		−	0.882569i
$437$	25.1099	+	1.40520i	1.20117	+	0.0672198i
$438$		0			0
$439$	−38.4260			−1.83397			−0.916986	−	0.398919i	$-0.869386\pi$
$439$	−38.4260			−1.83397			−0.916986	+	0.398919i	$0.869386\pi$
$440$	−10.6055	+	1.76721i	−0.505597	+	0.0842486i
$441$		0			0
$442$	−2.80350	−	2.80350i	−0.133349	−	0.133349i
$443$	−27.7457	+	27.7457i	−1.31824	+	1.31824i	−0.403066	+	0.915171i	$0.632055\pi$
$443$	−27.7457	+	27.7457i	−1.31824	+	1.31824i	−0.915171	+	0.403066i	$0.867945\pi$
$444$		0			0
$445$	1.41191	−	1.97654i	0.0669311	−	0.0936969i
$446$	11.3784			0.538781
$447$		0			0
$448$	0.728588	−	0.728588i	0.0344226	−	0.0344226i
$449$	−28.1598			−1.32894			−0.664472	−	0.747313i	$-0.731344\pi$
$449$	−28.1598			−1.32894			−0.664472	+	0.747313i	$0.731344\pi$
$450$		0			0
$451$		−	28.0110i		−	1.31899i
$452$	−5.25913	+	5.25913i	−0.247369	+	0.247369i
$453$		0			0
$454$			2.80480i			0.131636i
$455$	1.40917	+	1.00663i	0.0660631	+	0.0471913i
$456$		0			0
$457$	−19.5575	−	19.5575i	−0.914859	−	0.914859i	0.0817904	−	0.996650i	$-0.473936\pi$
$457$	−19.5575	−	19.5575i	−0.914859	−	0.914859i	−0.996650	+	0.0817904i	$0.973936\pi$
$458$	−13.8906	−	13.8906i	−0.649066	−	0.649066i
$459$		0			0
$460$	−12.7258	+	2.12052i	−0.593342	+	0.0988698i
$461$	−9.61570			−0.447848			−0.223924	−	0.974607i	$-0.571887\pi$
$461$	−9.61570			−0.447848			−0.223924	+	0.974607i	$0.571887\pi$
$462$		0			0
$463$	16.6735	−	16.6735i	0.774882	−	0.774882i	−0.204074	−	0.978956i	$-0.565418\pi$
$463$	16.6735	−	16.6735i	0.774882	−	0.774882i	0.978956	+	0.204074i	$0.0654182\pi$
$464$	−0.494819			−0.0229714
$465$		0			0
$466$		−	6.70326i		−	0.310523i
$467$	17.1190	+	17.1190i	0.792171	+	0.792171i	0.981847	−	0.189676i	$-0.0607437\pi$
$467$	17.1190	+	17.1190i	0.792171	+	0.792171i	−0.189676	+	0.981847i	$0.560744\pi$
$468$		0			0
$469$	13.3933			0.618446
$470$	−1.67352	+	2.34276i	−0.0771938	+	0.108064i
$471$		0			0
$472$	8.57770	+	8.57770i	0.394820	+	0.394820i
$473$	−14.6211	+	14.6211i	−0.672278	+	0.672278i
$474$		0			0
$475$	10.6600	−	19.0096i	0.489113	−	0.872221i
$476$	−5.43503			−0.249114
$477$		0			0
$478$	14.9801	+	14.9801i	0.685176	+	0.685176i
$479$		−	14.2801i		−	0.652474i	−0.945288	−	0.326237i	$-0.894219\pi$
$479$		−	14.2801i		−	0.652474i	0.945288	−	0.326237i	$-0.105781\pi$
$480$		0			0
$481$	5.82340			0.265524
$482$	−11.5106	−	11.5106i	−0.524293	−	0.524293i
$483$		0			0
$484$		−	12.1199i		−	0.550905i
$485$	1.46401	+	8.78590i	0.0664774	+	0.398947i
$486$		0			0
$487$	−13.6790	+	13.6790i	−0.619856	+	0.619856i	−0.945494	−	0.325639i	$-0.894421\pi$
$487$	−13.6790	+	13.6790i	−0.619856	+	0.619856i	0.325639	+	0.945494i	$0.394421\pi$
$488$	3.76477	+	3.76477i	0.170423	+	0.170423i
$489$		0			0
$490$	−13.0979	+	2.18253i	−0.591702	+	0.0985965i
$491$	−6.60655			−0.298150			−0.149075	−	0.988826i	$-0.547630\pi$
$491$	−6.60655			−0.298150			−0.149075	+	0.988826i	$0.547630\pi$
$492$		0			0
$493$	1.84560	+	1.84560i	0.0831215	+	0.0831215i
$494$	−2.18365	−	2.44254i	−0.0982471	−	0.109895i
$495$		0			0
$496$			8.62312i			0.387190i
$497$	−1.50144	+	1.50144i	−0.0673490	+	0.0673490i
$498$		0			0
$499$			35.7269i			1.59935i	0.600430	+	0.799677i	$0.294996\pi$
$499$			35.7269i			1.59935i	−0.600430	+	0.799677i	$0.705004\pi$
$500$	−3.19762	+	10.7133i	−0.143002	+	0.479114i
$501$		0			0
$502$	−3.71225	+	3.71225i	−0.165686	+	0.165686i
$503$	8.52003	−	8.52003i	0.379889	−	0.379889i	−0.491173	−	0.871062i	$-0.663432\pi$
$503$	8.52003	−	8.52003i	0.379889	−	0.379889i	0.871062	+	0.491173i	$0.163432\pi$
$504$		0			0
$505$	18.2734	−	25.5809i	0.813156	−	1.13834i
$506$		−	27.7421i		−	1.23329i
$507$		0			0
$508$	9.35800	+	9.35800i	0.415194	+	0.415194i
$509$	13.4408			0.595753			0.297877	−	0.954604i	$-0.403722\pi$
$509$	13.4408			0.595753			0.297877	+	0.954604i	$0.403722\pi$
$510$		0			0
$511$	−4.82559			−0.213471
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$		0			0
$514$			22.6727i			1.00005i
$515$	20.6910	−	3.44777i	0.911752	−	0.151927i
$516$		0			0
$517$	−4.37774	−	4.37774i	−0.192533	−	0.192533i
$518$	5.64479	−	5.64479i	0.248018	−	0.248018i
$519$		0			0
$520$	1.36763	+	0.976946i	0.0599744	+	0.0428419i
$521$		−	13.5544i		−	0.593831i	−0.954904	−	0.296916i	$-0.904042\pi$
$521$		−	13.5544i		−	0.593831i	0.954904	−	0.296916i	$-0.0959580\pi$
$522$		0			0
$523$	5.40357	+	5.40357i	0.236282	+	0.236282i	0.815308	−	0.579027i	$-0.196567\pi$
$523$	5.40357	+	5.40357i	0.236282	+	0.236282i	−0.579027	+	0.815308i	$0.696567\pi$
$524$			12.6267i			0.551601i
$525$		0			0
$526$		−	8.41456i		−	0.366892i
$527$	32.1629	−	32.1629i	1.40104	−	1.40104i
$528$		0			0
$529$		−	10.2884i		−	0.447321i
$530$	6.49346	−	9.09020i	0.282058	−	0.394853i
$531$		0			0
$532$	−4.48430	−	0.250951i	−0.194419	−	0.0108801i
$533$	−3.09622	+	3.09622i	−0.134112	+	0.134112i
$534$		0			0
$535$	−0.801810	−	4.81186i	−0.0346653	−	0.208035i
$536$	12.9984			0.561447
$537$		0			0
$538$	18.5884	−	18.5884i	0.801404	−	0.801404i
$539$		−	28.5533i		−	1.22988i
$540$		0			0
$541$	7.68488			0.330399			0.165200	−	0.986260i	$-0.447173\pi$
$541$	7.68488			0.330399			0.165200	+	0.986260i	$0.447173\pi$
$542$	−8.43702	+	8.43702i	−0.362401	+	0.362401i
$543$		0			0
$544$	−5.27479			−0.226155
$545$	23.9525	−	33.5312i	1.02601	−	1.43632i
$546$		0			0
$547$	−17.8604	+	17.8604i	−0.763656	+	0.763656i	−0.976981	−	0.213325i	$-0.931571\pi$
$547$	−17.8604	+	17.8604i	−0.763656	+	0.763656i	0.213325	+	0.976981i	$0.431571\pi$
$548$	−0.378698	+	0.378698i	−0.0161772	+	0.0161772i
$549$		0			0
$550$	−21.5938	−	10.5690i	−0.920765	−	0.450664i
$551$	1.43754	+	1.60797i	0.0612411	+	0.0685018i
$552$		0			0
$553$	2.01873	+	2.01873i	0.0858451	+	0.0858451i
$554$	−18.6596			−0.792771
$555$		0			0
$556$	22.7942			0.966688
$557$	−12.5198	−	12.5198i	−0.530480	−	0.530480i	0.390235	−	0.920715i	$-0.372394\pi$
$557$	−12.5198	−	12.5198i	−0.530480	−	0.530480i	−0.920715	+	0.390235i	$0.872394\pi$
$558$		0			0
$559$	3.23231			0.136712
$560$	2.27266	−	0.378698i	0.0960375	−	0.0160029i
$561$		0			0
$562$	18.0180	+	18.0180i	0.760045	+	0.760045i
$563$	−11.0759	−	11.0759i	−0.466791	−	0.466791i	0.434082	−	0.900873i	$-0.357073\pi$
$563$	−11.0759	−	11.0759i	−0.466791	−	0.466791i	−0.900873	+	0.434082i	$0.857073\pi$
$564$		0			0
$565$	−16.4046	+	2.73354i	−0.690149	+	0.115001i
$566$			21.1355i			0.888392i
$567$		0			0
$568$	−1.45718	+	1.45718i	−0.0611418	+	0.0611418i
$569$	43.4414			1.82116			0.910579	−	0.413336i	$-0.135636\pi$
$569$	43.4414			1.82116			0.910579	+	0.413336i	$0.135636\pi$
$570$		0			0
$571$	15.6768			0.656052			0.328026	−	0.944669i	$-0.393617\pi$
$571$	15.6768			0.656052			0.328026	+	0.944669i	$0.393617\pi$
$572$	−2.55558	+	2.55558i	−0.106854	+	0.106854i
$573$		0			0
$574$			6.00250i			0.250540i
$575$	−25.9109	−	12.6820i	−1.08056	−	0.528876i
$576$		0			0
$577$	6.59569	+	6.59569i	0.274582	+	0.274582i	0.830942	−	0.556359i	$-0.187802\pi$
$577$	6.59569	+	6.59569i	0.274582	+	0.274582i	−0.556359	+	0.830942i	$0.687802\pi$
$578$	7.65330	+	7.65330i	0.318335	+	0.318335i
$579$		0			0
$580$	−0.900333	−	0.643141i	−0.0373843	−	0.0267050i
$581$	−5.21334			−0.216286
$582$		0			0
$583$	16.9861	+	16.9861i	0.703494	+	0.703494i
$584$	−4.68331			−0.193797
$585$		0			0
$586$	27.3491			1.12978
$587$	23.8623	+	23.8623i	0.984904	+	0.984904i	0.999888	−	0.0149835i	$-0.00476957\pi$
$587$	23.8623	+	23.8623i	0.984904	+	0.984904i	−0.0149835	+	0.999888i	$0.504770\pi$
$588$		0			0
$589$	28.0218	−	25.0517i	1.15462	−	1.03224i
$590$	4.45843	+	26.7561i	0.183551	+	1.10153i
$591$		0			0
$592$	5.47836	−	5.47836i	0.225159	−	0.225159i
$593$	−22.7988	+	22.7988i	−0.936236	+	0.936236i	−0.998085	−	0.0618495i	$-0.980300\pi$
$593$	−22.7988	+	22.7988i	−0.936236	+	0.936236i	0.0618495	+	0.998085i	$0.480300\pi$
$594$		0			0
$595$	−9.88915	−	7.06418i	−0.405416	−	0.289603i
$596$	−15.8801			−0.650473
$597$		0			0
$598$	−3.06650	+	3.06650i	−0.125398	+	0.125398i
$599$	11.4248			0.466805			0.233402	−	0.972380i	$-0.425014\pi$
$599$	11.4248			0.466805			0.233402	+	0.972380i	$0.425014\pi$
$600$		0			0
$601$		−	7.14156i		−	0.291310i	−0.989335	−	0.145655i	$-0.953471\pi$
$601$		−	7.14156i		−	0.291310i	0.989335	−	0.145655i	$-0.0465290\pi$
$602$	3.13317	−	3.13317i	0.127698	−	0.127698i
$603$		0			0
$604$	13.3507			0.543231
$605$	15.7529	−	22.0524i	0.640445	−	0.896559i
$606$		0			0
$607$	6.44190	−	6.44190i	0.261469	−	0.261469i	−0.564182	−	0.825651i	$-0.690808\pi$
$607$	6.44190	−	6.44190i	0.261469	−	0.261469i	0.825651	+	0.564182i	$0.190808\pi$
$608$	−4.35209	−	0.243552i	−0.176501	−	0.00987733i
$609$		0			0
$610$	1.95681	+	11.7433i	0.0792290	+	0.475473i
$611$			0.967793i			0.0391527i
$612$		0			0
$613$	−21.1379	+	21.1379i	−0.853752	+	0.853752i	−0.990593	−	0.136841i	$-0.956305\pi$
$613$	−21.1379	+	21.1379i	−0.853752	+	0.853752i	0.136841	+	0.990593i	$0.456305\pi$
$614$			0.00500438i			0.000201960i
$615$		0			0
$616$			4.95439i			0.199618i
$617$	9.52678	+	9.52678i	0.383534	+	0.383534i	0.872373	−	0.488840i	$-0.162580\pi$
$617$	9.52678	+	9.52678i	0.383534	+	0.383534i	−0.488840	+	0.872373i	$0.662580\pi$
$618$		0			0
$619$		−	6.57762i		−	0.264377i	−0.991225	−	0.132188i	$-0.957800\pi$
$619$		−	6.57762i		−	0.264377i	0.991225	−	0.132188i	$-0.0422004\pi$
$620$	−11.2079	+	15.6899i	−0.450120	+	0.630123i
$621$		0			0
$622$	8.26782	−	8.26782i	0.331509	−	0.331509i
$623$	−0.791463	−	0.791463i	−0.0317093	−	0.0317093i
$624$		0			0
$625$	−19.7428	+	15.3370i	−0.789710	+	0.613480i
$626$			23.5732i			0.942174i
$627$		0			0
$628$	11.7372	−	11.7372i	0.468363	−	0.468363i
$629$	−40.8668			−1.62947
$630$		0			0
$631$	−17.0875			−0.680241			−0.340121	−	0.940382i	$-0.610468\pi$
$631$	−17.0875			−0.680241			−0.340121	+	0.940382i	$0.610468\pi$
$632$	1.95921	+	1.95921i	0.0779332	+	0.0779332i
$633$		0			0
$634$			9.85335i			0.391327i
$635$	4.86401	+	29.1901i	0.193022	+	1.15837i
$636$		0			0
$637$	−3.15616	+	3.15616i	−0.125052	+	0.125052i
$638$	1.68238	−	1.68238i	0.0666062	−	0.0666062i
$639$		0			0
$640$	2.20566	−	0.367533i	0.0871862	−	0.0145280i
$641$		−	46.7376i		−	1.84602i	−0.384773	−	0.923011i	$-0.625720\pi$
$641$		−	46.7376i		−	1.84602i	0.384773	−	0.923011i	$-0.374280\pi$
$642$		0			0
$643$	−7.16897	+	7.16897i	−0.282717	+	0.282717i	−0.834191	−	0.551475i	$-0.814065\pi$
$643$	−7.16897	+	7.16897i	−0.282717	+	0.282717i	0.551475	+	0.834191i	$0.314065\pi$
$644$			5.94489i			0.234261i
$645$		0			0
$646$	15.3242	+	17.1410i	0.602922	+	0.674404i
$647$	6.19558	+	6.19558i	0.243574	+	0.243574i	0.818327	−	0.574753i	$-0.194902\pi$
$647$	6.19558	+	6.19558i	0.243574	+	0.243574i	−0.574753	+	0.818327i	$0.694902\pi$
$648$		0			0
$649$	−58.3282			−2.28958
$650$	1.21864	+	3.55515i	0.0477989	+	0.139444i
$651$		0			0
$652$	0.988668	+	0.988668i	0.0387192	+	0.0387192i
$653$	−17.2336	+	17.2336i	−0.674401	+	0.674401i	−0.958728	−	0.284326i	$-0.908230\pi$
$653$	−17.2336	+	17.2336i	−0.674401	+	0.674401i	0.284326	+	0.958728i	$0.408230\pi$
$654$		0			0
$655$	−16.4116	+	22.9746i	−0.641253	+	0.897690i
$656$			5.82553i			0.227449i
$657$		0			0
$658$	0.938110	+	0.938110i	0.0365713	+	0.0365713i
$659$	21.6005			0.841436			0.420718	−	0.907191i	$-0.361778\pi$
$659$	21.6005			0.841436			0.420718	+	0.907191i	$0.361778\pi$
$660$		0			0
$661$		−	1.49297i		−	0.0580696i	−0.999578	−	0.0290348i	$-0.990757\pi$
$661$		−	1.49297i		−	0.0580696i	0.999578	−	0.0290348i	$-0.00924337\pi$
$662$	8.65367	+	8.65367i	0.336335	+	0.336335i
$663$		0			0
$664$	−5.05963			−0.196352
$665$	−7.83310	−	6.28508i	−0.303755	−	0.243725i
$666$		0			0
$667$	2.01873	−	2.01873i	0.0781655	−	0.0781655i
$668$	−7.42584	−	7.42584i	−0.287314	−	0.287314i
$669$		0			0
$670$	23.6509	+	16.8947i	0.913714	+	0.652700i
$671$	−25.6004			−0.988291
$672$		0			0
$673$	−8.49705	−	8.49705i	−0.327537	−	0.327537i	0.524112	−	0.851649i	$-0.324397\pi$
$673$	−8.49705	−	8.49705i	−0.327537	−	0.327537i	−0.851649	+	0.524112i	$0.824397\pi$
$674$		−	26.8584i		−	1.03455i
$675$		0			0
$676$	−12.4350			−0.478271
$677$	5.92660	−	5.92660i	0.227778	−	0.227778i	−0.583986	−	0.811764i	$-0.698508\pi$
$677$	5.92660	−	5.92660i	0.227778	−	0.227778i	0.811764	+	0.583986i	$0.198508\pi$
$678$		0			0
$679$	4.10436			0.157511
$680$	−9.59758	−	6.85591i	−0.368050	−	0.262912i
$681$		0			0
$682$	−29.3186	−	29.3186i	−1.12267	−	1.12267i
$683$	−26.3647	−	26.3647i	−1.00882	−	1.00882i	−0.999961	−	0.00885484i	$-0.997181\pi$
$683$	−26.3647	−	26.3647i	−1.00882	−	1.00882i	−0.00885484	−	0.999961i	$-0.502819\pi$
$684$		0			0
$685$	−1.18126	+	0.196836i	−0.0451337	+	0.00752071i
$686$			13.3314i			0.508994i
$687$		0			0
$688$	3.04079	−	3.04079i	0.115929	−	0.115929i
$689$		−	3.75515i		−	0.143060i
$690$		0			0
$691$	19.3186			0.734913			0.367456	−	0.930041i	$-0.380229\pi$
$691$	19.3186			0.734913			0.367456	+	0.930041i	$0.380229\pi$
$692$	11.0462	−	11.0462i	0.419912	−	0.419912i
$693$		0			0
$694$	−2.14291			−0.0813438
$695$	41.4744	+	29.6267i	1.57322	+	1.12381i
$696$		0			0
$697$	21.7283	−	21.7283i	0.823017	−	0.823017i
$698$	15.0710	+	15.0710i	0.570444	+	0.570444i
$699$		0			0
$700$	4.62737	+	2.26484i	0.174898	+	0.0856031i
$701$	−8.82340			−0.333255			−0.166628	−	0.986020i	$-0.553288\pi$
$701$	−8.82340			−0.333255			−0.166628	+	0.986020i	$0.553288\pi$
$702$		0			0
$703$	−33.7181	−	1.88694i	−1.27170	−	0.0711672i
$704$			4.80832i			0.181220i
$705$		0			0
$706$			13.2577i			0.498961i
$707$	−10.2434	−	10.2434i	−0.385241	−	0.385241i
$708$		0			0
$709$			1.20583i			0.0452859i	0.999744	+	0.0226429i	$0.00720808\pi$
$709$			1.20583i			0.0452859i	−0.999744	+	0.0226429i	$0.992792\pi$
$710$	−4.54533	+	0.757396i	−0.170583	+	0.0284246i
$711$		0			0
$712$	−0.768128	−	0.768128i	−0.0287868	−	0.0287868i
$713$	−35.1800	−	35.1800i	−1.31750	−	1.31750i
$714$		0			0
$715$	−7.97154	+	1.32831i	−0.298119	+	0.0496761i
$716$			19.0425i			0.711652i
$717$		0			0
$718$	21.2987	+	21.2987i	0.794861	+	0.794861i
$719$		−	9.38938i		−	0.350165i	−0.984554	−	0.175082i	$-0.943981\pi$
$719$		−	9.38938i		−	0.350165i	0.984554	−	0.175082i	$-0.0560192\pi$
$720$		0			0
$721$		−	9.66585i		−	0.359975i
$722$	11.8521	+	14.8502i	0.441091	+	0.552665i
$723$		0			0
$724$	−1.78110			−0.0661941
$725$	−0.802251	−	2.34042i	−0.0297949	−	0.0869209i
$726$		0			0
$727$	−17.4688	−	17.4688i	−0.647884	−	0.647884i	0.304597	−	0.952481i	$-0.401478\pi$
$727$	−17.4688	−	17.4688i	−0.647884	−	0.647884i	−0.952481	+	0.304597i	$0.901478\pi$
$728$	0.547637	−	0.547637i	0.0202968	−	0.0202968i
$729$		0			0
$730$	−8.52138	−	6.08713i	−0.315390	−	0.225295i
$731$	−22.6833			−0.838973
$732$		0			0
$733$	13.1840	−	13.1840i	0.486963	−	0.486963i	−0.420383	−	0.907347i	$-0.638104\pi$
$733$	13.1840	−	13.1840i	0.486963	−	0.486963i	0.907347	+	0.420383i	$0.138104\pi$
$734$	−14.2815			−0.527140
$735$		0			0
$736$			5.76961i			0.212671i
$737$	−44.1946	+	44.1946i	−1.62793	+	1.62793i
$738$		0			0
$739$		−	47.8710i		−	1.76096i	−0.474080	−	0.880482i	$-0.657219\pi$
$739$		−	47.8710i		−	1.76096i	0.474080	−	0.880482i	$-0.342781\pi$
$740$	17.0885	−	2.84749i	0.628185	−	0.104676i
$741$		0			0
$742$	−3.63998	−	3.63998i	−0.133628	−	0.133628i
$743$	−19.4260	−	19.4260i	−0.712670	−	0.712670i	0.254423	−	0.967093i	$-0.418114\pi$
$743$	−19.4260	−	19.4260i	−0.712670	−	0.712670i	−0.967093	+	0.254423i	$0.918114\pi$
$744$		0			0
$745$	−28.8941	−	20.6401i	−1.05860	−	0.756196i
$746$	16.3708			0.599377
$747$		0			0
$748$	17.9343	−	17.9343i	0.655741	−	0.655741i
$749$	−2.24788			−0.0821356
$750$		0			0
$751$		−	23.5009i		−	0.857559i	−0.903409	−	0.428779i	$-0.858944\pi$
$751$		−	23.5009i		−	0.857559i	0.903409	−	0.428779i	$-0.141056\pi$
$752$	0.910451	+	0.910451i	0.0332007	+	0.0332007i
$753$		0			0
$754$	−0.371927			−0.0135448
$755$	24.2918	+	17.3525i	0.884069	+	0.631523i
$756$		0			0
$757$	19.2062	+	19.2062i	0.698060	+	0.698060i	0.963992	−	0.265932i	$-0.0856796\pi$
$757$	19.2062	+	19.2062i	0.698060	+	0.698060i	−0.265932	+	0.963992i	$0.585680\pi$
$758$	21.7007	−	21.7007i	0.788206	−	0.788206i
$759$		0			0
$760$	−7.60215	−	6.09977i	−0.275759	−	0.221262i
$761$	23.7982			0.862685			0.431343	−	0.902188i	$-0.358040\pi$
$761$	23.7982			0.862685			0.431343	+	0.902188i	$0.358040\pi$
$762$		0			0
$763$	−13.4268	−	13.4268i	−0.486084	−	0.486084i
$764$		−	14.8650i		−	0.537797i
$765$		0			0
$766$	9.49265			0.342983
$767$	6.44736	+	6.44736i	0.232801	+	0.232801i
$768$		0			0
$769$			28.9884i			1.04535i	0.852532	+	0.522675i	$0.175066\pi$
$769$			28.9884i			1.04535i	−0.852532	+	0.522675i	$0.824934\pi$
$770$	−6.43947	+	9.01461i	−0.232062	+	0.324864i
$771$		0			0
$772$	−5.04632	+	5.04632i	−0.181621	+	0.181621i
$773$	−29.2365	−	29.2365i	−1.05156	−	1.05156i	−0.998596	−	0.0529667i	$-0.983132\pi$
$773$	−29.2365	−	29.2365i	−1.05156	−	1.05156i	−0.0529667	−	0.998596i	$-0.516868\pi$
$774$		0			0
$775$	−40.7860	+	13.9807i	−1.46508	+	0.502201i
$776$	3.98335			0.142994
$777$		0			0
$778$	−1.19924	−	1.19924i	−0.0429947	−	0.0429947i
$779$	18.9307	−	16.9242i	0.678262	−	0.606371i
$780$		0			0
$781$		−	9.90878i		−	0.354564i
$782$	21.5197	−	21.5197i	0.769543	−	0.769543i
$783$		0			0
$784$			5.93832i			0.212083i
$785$	36.6113	−	6.10062i	1.30671	−	0.217740i
$786$		0			0
$787$	12.6866	−	12.6866i	0.452228	−	0.452228i	−0.443866	−	0.896093i	$-0.646393\pi$
$787$	12.6866	−	12.6866i	0.452228	−	0.452228i	0.896093	+	0.443866i	$0.146393\pi$
$788$	7.66209	−	7.66209i	0.272951	−	0.272951i
$789$		0			0
$790$	1.01834	+	6.11130i	0.0362308	+	0.217430i
$791$			7.66348i			0.272482i
$792$		0			0
$793$	2.82976	+	2.82976i	0.100488	+	0.100488i
$794$	−24.9391			−0.885057
$795$		0			0
$796$	20.9302			0.741851
$797$	−15.7202	+	15.7202i	−0.556838	+	0.556838i	−0.928406	−	0.371568i	$-0.878820\pi$
$797$	−15.7202	+	15.7202i	−0.556838	+	0.556838i	0.371568	+	0.928406i	$0.378820\pi$
$798$		0			0
$799$		−	6.79167i		−	0.240272i
$800$	4.49094	+	2.19807i	0.158779	+	0.0777134i
$801$		0			0
$802$	0.920271	+	0.920271i	0.0324959	+	0.0324959i
$803$	15.9232	−	15.9232i	0.561919	−	0.561919i
$804$		0			0
$805$	−7.72686	+	10.8168i	−0.272336	+	0.381243i
$806$			6.48150i			0.228301i
$807$		0			0
$808$	−9.94134	−	9.94134i	−0.349735	−	0.349735i
$809$		−	11.4400i		−	0.402210i	−0.979570	−	0.201105i	$-0.935547\pi$
$809$		−	11.4400i		−	0.402210i	0.979570	−	0.201105i	$-0.0644533\pi$
$810$		0			0
$811$		−	17.5878i		−	0.617592i	−0.951128	−	0.308796i	$-0.900074\pi$
$811$		−	17.5878i		−	0.617592i	0.951128	−	0.308796i	$-0.0999260\pi$
$812$	−0.360520	+	0.360520i	−0.0126518	+	0.0126518i
$813$		0			0
$814$			37.2528i			1.30571i
$815$	0.513880	+	3.08392i	0.0180004	+	0.108025i
$816$		0			0
$817$	−18.7154	−	1.04735i	−0.654769	−	0.0366422i
$818$	13.3418	−	13.3418i	0.466485	−	0.466485i
$819$		0			0
$820$	−7.57173	+	10.5997i	−0.264416	+	0.370156i
$821$	−13.1354			−0.458428			−0.229214	−	0.973376i	$-0.573616\pi$
$821$	−13.1354			−0.458428			−0.229214	+	0.973376i	$0.573616\pi$
$822$		0			0
$823$	−23.2779	+	23.2779i	−0.811417	+	0.811417i	−0.984846	−	0.173429i	$-0.944515\pi$
$823$	−23.2779	+	23.2779i	−0.811417	+	0.811417i	0.173429	+	0.984846i	$0.444515\pi$
$824$		−	9.38086i		−	0.326798i
$825$		0			0
$826$	12.4992			0.434903
$827$	−33.6240	+	33.6240i	−1.16922	+	1.16922i	−0.186828	+	0.982393i	$0.559821\pi$
$827$	−33.6240	+	33.6240i	−1.16922	+	1.16922i	−0.982393	+	0.186828i	$0.940179\pi$
$828$		0			0
$829$	−22.3434			−0.776020			−0.388010	−	0.921655i	$-0.626837\pi$
$829$	−22.3434			−0.776020			−0.388010	+	0.921655i	$0.626837\pi$
$830$	−9.20609	−	6.57625i	−0.319548	−	0.228265i
$831$		0			0
$832$	0.531491	−	0.531491i	0.0184261	−	0.0184261i
$833$	22.1490	−	22.1490i	0.767416	−	0.767416i
$834$		0			0
$835$	−3.85973	−	23.1632i	−0.133571	−	0.801595i
$836$	15.6252	−	13.9690i	0.540407	−	0.483128i
$837$		0			0
$838$	−14.2530	−	14.2530i	−0.492363	−	0.492363i
$839$	31.3884			1.08365			0.541824	−	0.840492i	$-0.317734\pi$
$839$	31.3884			1.08365			0.541824	+	0.840492i	$0.317734\pi$
$840$		0			0
$841$	−28.7552			−0.991557
$842$	6.25992	+	6.25992i	0.215731	+	0.215731i
$843$		0			0
$844$	−27.6388			−0.951366
$845$	−22.6258	−	16.1624i	−0.778351	−	0.556005i
$846$		0			0
$847$	−8.83043	−	8.83043i	−0.303417	−	0.303417i
$848$	−3.53266	−	3.53266i	−0.121312	−	0.121312i
$849$		0			0
$850$	−8.55203	−	24.9489i	−0.293332	−	0.855740i
$851$			44.7005i			1.53231i
$852$		0			0
$853$	−16.0193	+	16.0193i	−0.548490	+	0.548490i	−0.926004	−	0.377514i	$-0.876779\pi$
$853$	−16.0193	+	16.0193i	−0.548490	+	0.548490i	0.377514	+	0.926004i	$0.376779\pi$
$854$	5.48593			0.187725
$855$		0			0
$856$	−2.18160			−0.0745656
$857$	14.3582	−	14.3582i	0.490467	−	0.490467i	−0.417986	−	0.908453i	$-0.637264\pi$
$857$	14.3582	−	14.3582i	0.490467	−	0.490467i	0.908453	+	0.417986i	$0.137264\pi$
$858$		0			0
$859$			23.5232i			0.802602i	0.915946	+	0.401301i	$0.131442\pi$
$859$			23.5232i			0.802602i	−0.915946	+	0.401301i	$0.868558\pi$
$860$	9.48504	−	1.58051i	0.323437	−	0.0538950i
$861$		0			0
$862$	−17.8931	−	17.8931i	−0.609443	−	0.609443i
$863$	−34.2060	−	34.2060i	−1.16439	−	1.16439i	−0.983505	−	0.180881i	$-0.942105\pi$
$863$	−34.2060	−	34.2060i	−1.16439	−	1.16439i	−0.180881	−	0.983505i	$-0.557895\pi$
$864$		0			0
$865$	34.4560	−	5.74146i	1.17154	−	0.195216i
$866$	8.49320			0.288611
$867$		0			0
$868$	6.28270	+	6.28270i	0.213249	+	0.213249i
$869$	−13.3226			−0.451938
$870$		0			0
$871$	9.77017			0.331050
$872$	−13.0310	−	13.0310i	−0.441284	−	0.441284i
$873$		0			0
$874$	18.7490	−	16.7617i	0.634193	−	0.566974i
$875$	5.47585	+	10.1353i	0.185118	+	0.342637i
$876$		0			0
$877$	34.2759	−	34.2759i	1.15742	−	1.15742i	0.172387	−	0.985029i	$-0.444852\pi$
$877$	34.2759	−	34.2759i	1.15742	−	1.15742i	0.985029	−	0.172387i	$-0.0551479\pi$
$878$	−27.1713	+	27.1713i	−0.916986	+	0.916986i
$879$		0			0
$880$	−6.24961	+	8.74883i	−0.210674	+	0.294923i
$881$	16.2818			0.548548			0.274274	−	0.961652i	$-0.411562\pi$
$881$	16.2818			0.548548			0.274274	+	0.961652i	$0.411562\pi$
$882$		0			0
$883$	−16.4556	+	16.4556i	−0.553774	+	0.553774i	−0.927528	−	0.373754i	$-0.878070\pi$
$883$	−16.4556	+	16.4556i	−0.553774	+	0.553774i	0.373754	+	0.927528i	$0.378070\pi$
$884$	−3.96475			−0.133349
$885$		0			0
$886$			39.2383i			1.31824i
$887$	20.1627	−	20.1627i	0.676997	−	0.676997i	−0.282322	−	0.959320i	$-0.591105\pi$
$887$	20.1627	−	20.1627i	0.676997	−	0.676997i	0.959320	+	0.282322i	$0.0911047\pi$
$888$		0			0
$889$	13.6363			0.457345
$890$	−0.399250	−	2.39600i	−0.0133829	−	0.0803140i
$891$		0			0
$892$	8.04571	−	8.04571i	0.269390	−	0.269390i
$893$	0.313590	−	5.60363i	0.0104939	−	0.187518i
$894$		0			0
$895$	−24.7505	+	34.6482i	−0.827318	+	1.15816i
$896$		−	1.03038i		−	0.0344226i
$897$		0			0
$898$	−19.9120	+	19.9120i	−0.664472	+	0.664472i
$899$		−	4.26689i		−	0.142309i
$900$		0			0
$901$			26.3525i			0.877929i
$902$	−19.8068	−	19.8068i	−0.659493	−	0.659493i
$903$		0			0
$904$			7.43754i			0.247369i
$905$	−3.24075	−	2.31499i	−0.107726	−	0.0769527i
$906$		0			0
$907$	−36.3346	+	36.3346i	−1.20647	+	1.20647i	−0.234309	+	0.972162i	$0.575283\pi$
$907$	−36.3346	+	36.3346i	−1.20647	+	1.20647i	−0.972162	+	0.234309i	$0.924717\pi$
$908$	1.98330	+	1.98330i	0.0658180	+	0.0658180i
$909$		0			0
$910$	1.70823	−	0.284645i	0.0566272	−	0.00943590i
$911$			9.50181i			0.314809i	0.987534	+	0.157405i	$0.0503127\pi$
$911$			9.50181i			0.314809i	−0.987534	+	0.157405i	$0.949687\pi$
$912$		0			0
$913$	17.2027	−	17.2027i	0.569326	−	0.569326i
$914$	−27.6584			−0.914859
$915$		0			0
$916$	−19.6443			−0.649066
$917$	9.19968	+	9.19968i	0.303800	+	0.303800i
$918$		0			0
$919$			3.20583i			0.105751i	0.998601	+	0.0528753i	$0.0168386\pi$
$919$			3.20583i			0.105751i	−0.998601	+	0.0528753i	$0.983161\pi$
$920$	−7.49905	+	10.4979i	−0.247236	+	0.346106i
$921$		0			0
$922$	−6.79932	+	6.79932i	−0.223924	+	0.223924i
$923$	−1.09527	+	1.09527i	−0.0360514	+	0.0360514i
$924$		0			0
$925$	34.7939	+	17.0297i	1.14402	+	0.559933i
$926$		−	23.5799i		−	0.774882i
$927$		0			0
$928$	−0.349890	+	0.349890i	−0.0114857	+	0.0114857i
$929$			0.680198i			0.0223166i	0.999938	+	0.0111583i	$0.00355187\pi$
$929$			0.680198i			0.0223166i	−0.999938	+	0.0111583i	$0.996448\pi$
$930$		0			0
$931$	19.2972	−	17.2519i	0.632441	−	0.565407i
$932$	−4.73992	−	4.73992i	−0.155261	−	0.155261i
$933$		0			0
$934$	24.2099			0.792171
$935$	55.9418	−	9.32168i	1.82949	−	0.304852i
$936$		0			0
$937$	20.6037	+	20.6037i	0.673093	+	0.673093i	0.958428	−	0.285335i	$-0.0921048\pi$
$937$	20.6037	+	20.6037i	0.673093	+	0.673093i	−0.285335	+	0.958428i	$0.592105\pi$
$938$	9.47051	−	9.47051i	0.309223	−	0.309223i
$939$		0			0
$940$	0.473225	+	2.83994i	0.0154349	+	0.0926286i
$941$		−	16.5409i		−	0.539220i	−0.962970	−	0.269610i	$-0.913105\pi$
$941$		−	16.5409i		−	0.539220i	0.962970	−	0.269610i	$-0.0868947\pi$
$942$		0			0
$943$	−23.7666	−	23.7666i	−0.773946	−	0.773946i
$944$	12.1307			0.394820
$945$		0			0
$946$			20.6773i			0.672278i
$947$	−21.1699	−	21.1699i	−0.687929	−	0.687929i	0.273845	−	0.961774i	$-0.411704\pi$
$947$	−21.1699	−	21.1699i	−0.687929	−	0.687929i	−0.961774	+	0.273845i	$0.911704\pi$
$948$		0			0
$949$	−3.52017			−0.114270
$950$	−5.90409	−	20.9796i	−0.191554	−	0.680667i
$951$		0			0
$952$	−3.84315	+	3.84315i	−0.124557	+	0.124557i
$953$	28.1289	+	28.1289i	0.911186	+	0.911186i	0.996366	−	0.0851800i	$-0.0271465\pi$
$953$	28.1289	+	28.1289i	0.911186	+	0.911186i	−0.0851800	+	0.996366i	$0.527147\pi$
$954$		0			0
$955$	19.3208	−	27.0471i	0.625205	−	0.875225i
$956$	21.1851			0.685176
$957$		0			0
$958$	−10.0976	−	10.0976i	−0.326237	−	0.326237i
$959$			0.551830i			0.0178195i
$960$		0			0
$961$	−43.3582			−1.39865
$962$	4.11777	−	4.11777i	0.132762	−	0.132762i
$963$		0			0
$964$	−16.2784			−0.524293
$965$	−15.7408	+	2.62292i	−0.506715	+	0.0844349i
$966$		0			0
$967$	−2.96462	−	2.96462i	−0.0953359	−	0.0953359i	0.657830	−	0.753166i	$-0.271474\pi$
$967$	−2.96462	−	2.96462i	−0.0953359	−	0.0953359i	−0.753166	+	0.657830i	$0.771474\pi$
$968$	−8.57008	−	8.57008i	−0.275453	−	0.275453i
$969$		0			0
$970$	7.24778	+	5.17736i	0.232712	+	0.166235i
$971$			4.90480i			0.157403i	0.996898	+	0.0787013i	$0.0250773\pi$
$971$			4.90480i			0.157403i	−0.996898	+	0.0787013i	$0.974923\pi$
$972$		0			0
$973$	16.6076	−	16.6076i	0.532414	−	0.532414i
$974$			19.3451i			0.619856i
$975$		0			0
$976$	5.32419			0.170423
$977$	−11.6920	+	11.6920i	−0.374061	+	0.374061i	−0.868954	−	0.494893i	$-0.835207\pi$
$977$	−11.6920	+	11.6920i	−0.374061	+	0.374061i	0.494893	+	0.868954i	$0.335207\pi$
$978$		0			0
$979$	5.22326			0.166936
$980$	−7.71833	+	10.8049i	−0.246553	+	0.345149i
$981$		0			0
$982$	−4.67154	+	4.67154i	−0.149075	+	0.149075i
$983$	−24.4836	−	24.4836i	−0.780907	−	0.780907i	0.199077	−	0.979984i	$-0.436206\pi$
$983$	−24.4836	−	24.4836i	−0.780907	−	0.780907i	−0.979984	+	0.199077i	$0.936206\pi$
$984$		0			0
$985$	23.9001	−	3.98252i	0.761521	−	0.126894i
$986$	2.61007			0.0831215
$987$		0			0
$988$	−3.27121	−	0.183064i	−0.104071	−	0.00582404i
$989$			24.8112i			0.788950i
$990$		0			0
$991$		−	56.2681i		−	1.78741i	−0.448650	−	0.893707i	$-0.648095\pi$
$991$		−	56.2681i		−	1.78741i	0.448650	−	0.893707i	$-0.351905\pi$
$992$	6.09747	+	6.09747i	0.193595	+	0.193595i
$993$		0			0
$994$			2.12336i			0.0673490i
$995$	38.0829	+	27.2040i	1.20731	+	0.862425i
$996$		0			0
$997$	−2.01280	−	2.01280i	−0.0637459	−	0.0637459i	0.674515	−	0.738261i	$-0.264353\pi$
$997$	−2.01280	−	2.01280i	−0.0637459	−	0.0637459i	−0.738261	+	0.674515i	$0.764353\pi$
$998$	25.2627	+	25.2627i	0.799677	+	0.799677i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1710.2.p.c.37.10		20
3.2	odd	2		570.2.m.b.37.1	✓	20
5.3	odd	4	inner	1710.2.p.c.1063.5		20
15.8	even	4		570.2.m.b.493.6	yes	20
19.18	odd	2	inner	1710.2.p.c.37.5		20
57.56	even	2		570.2.m.b.37.6	yes	20
95.18	even	4	inner	1710.2.p.c.1063.10		20
285.113	odd	4		570.2.m.b.493.1	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.m.b.37.1	✓	20	3.2	odd	2
570.2.m.b.37.6	yes	20	57.56	even	2
570.2.m.b.493.1	yes	20	285.113	odd	4
570.2.m.b.493.6	yes	20	15.8	even	4
1710.2.p.c.37.5		20	19.18	odd	2	inner
1710.2.p.c.37.10		20	1.1	even	1	trivial
1710.2.p.c.1063.5		20	5.3	odd	4	inner
1710.2.p.c.1063.10		20	95.18	even	4	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)

\(f(q)\)	\(=\)	\(q+(0.707107 - 0.707107i) q^{2} -1.00000i q^{4} +(1.29975 - 1.81952i) q^{5} +(-0.728588 - 0.728588i) q^{7} +(-0.707107 - 0.707107i) q^{8} +O(q^{10})\)	\(q+(0.707107 - 0.707107i) q^{2} -1.00000i q^{4} +(1.29975 - 1.81952i) q^{5} +(-0.728588 - 0.728588i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-0.367533 - 2.20566i) q^{10} +4.80832 q^{11} +(-0.531491 - 0.531491i) q^{13} -1.03038 q^{14} -1.00000 q^{16} +(3.72984 + 3.72984i) q^{17} +(2.90517 + 3.24961i) q^{19} +(-1.81952 - 1.29975i) q^{20} +(3.39999 - 3.39999i) q^{22} +(4.07973 - 4.07973i) q^{23} +(-1.62130 - 4.72984i) q^{25} -0.751642 q^{26} +(-0.728588 + 0.728588i) q^{28} +0.494819 q^{29} -8.62312i q^{31} +(-0.707107 + 0.707107i) q^{32} +5.27479 q^{34} +(-2.27266 + 0.378698i) q^{35} +(-5.47836 + 5.47836i) q^{37} +(4.35209 + 0.243552i) q^{38} +(-2.20566 + 0.367533i) q^{40} -5.82553i q^{41} +(-3.04079 + 3.04079i) q^{43} -4.80832i q^{44} -5.76961i q^{46} +(-0.910451 - 0.910451i) q^{47} -5.93832i q^{49} +(-4.49094 - 2.19807i) q^{50} +(-0.531491 + 0.531491i) q^{52} +(3.53266 + 3.53266i) q^{53} +(6.24961 - 8.74883i) q^{55} +1.03038i q^{56} +(0.349890 - 0.349890i) q^{58} -12.1307 q^{59} -5.32419 q^{61} +(-6.09747 - 6.09747i) q^{62} +1.00000i q^{64} +(-1.65786 + 0.276253i) q^{65} +(-9.19128 + 9.19128i) q^{67} +(3.72984 - 3.72984i) q^{68} +(-1.33924 + 1.87480i) q^{70} -2.06076i q^{71} +(3.31160 - 3.31160i) q^{73} +7.74758i q^{74} +(3.24961 - 2.90517i) q^{76} +(-3.50328 - 3.50328i) q^{77} -2.77074 q^{79} +(-1.29975 + 1.81952i) q^{80} +(-4.11927 - 4.11927i) q^{82} +(3.57770 - 3.57770i) q^{83} +(11.6344 - 1.93866i) q^{85} +4.30033i q^{86} +(-3.39999 - 3.39999i) q^{88} +1.08630 q^{89} +0.774476i q^{91} +(-4.07973 - 4.07973i) q^{92} -1.28757 q^{94} +(9.68873 - 1.06234i) q^{95} +(-2.81665 + 2.81665i) q^{97} +(-4.19903 - 4.19903i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 12 q^{5} - 4 q^{7}+O(q^{10}) \) 20 * q - 12 * q^5 - 4 * q^7	\( 20 q - 12 q^{5} - 4 q^{7} + 8 q^{11} - 20 q^{16} + 12 q^{17} + 4 q^{23} - 28 q^{25} - 24 q^{26} - 4 q^{28} - 4 q^{35} + 12 q^{38} - 12 q^{43} + 44 q^{47} + 64 q^{55} - 8 q^{58} + 24 q^{62} + 12 q^{68} - 4 q^{73} + 4 q^{76} - 88 q^{77} + 12 q^{80} - 8 q^{82} - 76 q^{83} - 12 q^{85} - 4 q^{92} + 24 q^{95}+O(q^{100}) \) 20 * q - 12 * q^5 - 4 * q^7 + 8 * q^11 - 20 * q^16 + 12 * q^17 + 4 * q^23 - 28 * q^25 - 24 * q^26 - 4 * q^28 - 4 * q^35 + 12 * q^38 - 12 * q^43 + 44 * q^47 + 64 * q^55 - 8 * q^58 + 24 * q^62 + 12 * q^68 - 4 * q^73 + 4 * q^76 - 88 * q^77 + 12 * q^80 - 8 * q^82 - 76 * q^83 - 12 * q^85 - 4 * q^92 + 24 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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