LMFDB - Embedded newform 630.3.o.f.253.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [630,3,Mod(127,630)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(630, base_ring=CyclotomicField(4))

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

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("630.127");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	630.o (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:	$17.1662566547$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 8 x^{15} + 32 x^{14} + 152 x^{13} + 1954 x^{12} - 12664 x^{11} + 50336 x^{10} + 231896 x^{9} + \cdots + 2560000 $ x^16 - 8x^15 + 32x^14 + 152x^13 + 1954x^12 - 12664x^11 + 50336x^10 + 231896x^9 + 1093889x^8 - 4595248x^7 + 18837632x^6 + 86081152x^5 + 178889856x^4 + 70149120x^3 + 10035200x^2 - 7168000*x + 2560000
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{14}\cdot 5 $
Twist minimal:	no (minimal twist has level 210)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			253.8
Root			$0.170157 - 0.170157i$ of defining polynomial
Character	$\chi$	$=$	630.253
Dual form			630.3.o.f.127.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.00000 - 1.00000i) q^{2} -2.00000i q^{4} +(4.93066 + 0.829843i) q^{5} +(1.87083 - 1.87083i) q^{7} +(-2.00000 - 2.00000i) q^{8} +O(q^{10})$	\(q+(1.00000 - 1.00000i) q^{2} -2.00000i q^{4} +(4.93066 + 0.829843i) q^{5} +(1.87083 - 1.87083i) q^{7} +(-2.00000 - 2.00000i) q^{8} +(5.76050 - 4.10081i) q^{10} +5.74922 q^{11} +(15.0034 + 15.0034i) q^{13} -3.74166i q^{14} -4.00000 q^{16} +(4.78821 - 4.78821i) q^{17} +17.4017i q^{19} +(1.65969 - 9.86131i) q^{20} +(5.74922 - 5.74922i) q^{22} +(-13.2261 - 13.2261i) q^{23} +(23.6227 + 8.18334i) q^{25} +30.0069 q^{26} +(-3.74166 - 3.74166i) q^{28} -37.7271i q^{29} -27.0130 q^{31} +(-4.00000 + 4.00000i) q^{32} -9.57642i q^{34} +(10.7769 - 7.67192i) q^{35} +(11.3640 - 11.3640i) q^{37} +(17.4017 + 17.4017i) q^{38} +(-8.20163 - 11.5210i) q^{40} +53.0897 q^{41} +(37.1052 + 37.1052i) q^{43} -11.4984i q^{44} -26.4522 q^{46} +(9.39190 - 9.39190i) q^{47} -7.00000i q^{49} +(31.8061 - 15.4394i) q^{50} +(30.0069 - 30.0069i) q^{52} +(-43.8996 - 43.8996i) q^{53} +(28.3474 + 4.77095i) q^{55} -7.48331 q^{56} +(-37.7271 - 37.7271i) q^{58} +62.9694i q^{59} -1.67492 q^{61} +(-27.0130 + 27.0130i) q^{62} +8.00000i q^{64} +(61.5263 + 86.4273i) q^{65} +(28.4909 - 28.4909i) q^{67} +(-9.57642 - 9.57642i) q^{68} +(3.10499 - 18.4488i) q^{70} -47.2039 q^{71} +(-31.2071 - 31.2071i) q^{73} -22.7281i q^{74} +34.8033 q^{76} +(10.7558 - 10.7558i) q^{77} -107.134i q^{79} +(-19.7226 - 3.31937i) q^{80} +(53.0897 - 53.0897i) q^{82} +(-18.2365 - 18.2365i) q^{83} +(27.5825 - 19.6356i) q^{85} +74.2105 q^{86} +(-11.4984 - 11.4984i) q^{88} -174.675i q^{89} +56.1378 q^{91} +(-26.4522 + 26.4522i) q^{92} -18.7838i q^{94} +(-14.4406 + 85.8016i) q^{95} +(-91.5084 + 91.5084i) q^{97} +(-7.00000 - 7.00000i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 16 q^{2} + 16 q^{5} - 32 q^{8}+O(q^{10}) $ 16 * q + 16 * q^2 + 16 * q^5 - 32 * q^8	$ 16 q + 16 q^{2} + 16 q^{5} - 32 q^{8} + 24 q^{10} - 8 q^{11} - 32 q^{13} - 64 q^{16} - 56 q^{17} + 16 q^{20} - 8 q^{22} - 24 q^{23} + 40 q^{25} - 64 q^{26} - 112 q^{31} - 64 q^{32} - 28 q^{35} - 152 q^{37} - 16 q^{40} - 48 q^{46} - 80 q^{47} + 72 q^{50} - 64 q^{52} - 48 q^{53} - 24 q^{55} + 96 q^{58} + 96 q^{61} - 112 q^{62} - 16 q^{65} - 80 q^{67} + 112 q^{68} - 536 q^{71} + 168 q^{77} - 64 q^{80} + 256 q^{83} + 40 q^{85} + 16 q^{88} - 48 q^{92} - 360 q^{95} + 688 q^{97} - 112 q^{98}+O(q^{100}) $ 16 * q + 16 * q^2 + 16 * q^5 - 32 * q^8 + 24 * q^10 - 8 * q^11 - 32 * q^13 - 64 * q^16 - 56 * q^17 + 16 * q^20 - 8 * q^22 - 24 * q^23 + 40 * q^25 - 64 * q^26 - 112 * q^31 - 64 * q^32 - 28 * q^35 - 152 * q^37 - 16 * q^40 - 48 * q^46 - 80 * q^47 + 72 * q^50 - 64 * q^52 - 48 * q^53 - 24 * q^55 + 96 * q^58 + 96 * q^61 - 112 * q^62 - 16 * q^65 - 80 * q^67 + 112 * q^68 - 536 * q^71 + 168 * q^77 - 64 * q^80 + 256 * q^83 + 40 * q^85 + 16 * q^88 - 48 * q^92 - 360 * q^95 + 688 * q^97 - 112 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/630\mathbb{Z}\right)^\times$.

$n$	$127$	$281$	$451$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$	1.00000	−	1.00000i	0.500000	−	0.500000i
$2$	1.00000	−	1.00000i	0.500000	−	0.500000i
$3$		0			0
$3$		0			0
$4$		−	2.00000i		−	0.500000i
$5$	4.93066	+	0.829843i	0.986131	+	0.165969i
$5$	4.93066	+	0.829843i	0.986131	+	0.165969i
$6$		0			0
$7$	1.87083	−	1.87083i	0.267261	−	0.267261i
$7$	1.87083	−	1.87083i	0.267261	−	0.267261i
$8$	−2.00000	−	2.00000i	−0.250000	−	0.250000i
$9$		0			0
$10$	5.76050	−	4.10081i	0.576050	−	0.410081i
$11$	5.74922			0.522656			0.261328	−	0.965250i	$-0.415840\pi$
$11$	5.74922			0.522656			0.261328	+	0.965250i	$0.415840\pi$
$12$		0			0
$13$	15.0034	+	15.0034i	1.15411	+	1.15411i	0.985720	+	0.168391i	$0.0538571\pi$
$13$	15.0034	+	15.0034i	1.15411	+	1.15411i	0.168391	+	0.985720i	$0.446143\pi$
$14$		−	3.74166i		−	0.267261i
$15$		0			0
$16$	−4.00000			−0.250000
$17$	4.78821	−	4.78821i	0.281659	−	0.281659i	−0.552111	−	0.833771i	$-0.686178\pi$
$17$	4.78821	−	4.78821i	0.281659	−	0.281659i	0.833771	+	0.552111i	$0.186178\pi$
$18$		0			0
$19$			17.4017i			0.915877i	0.888984	+	0.457938i	$0.151412\pi$
$19$			17.4017i			0.915877i	−0.888984	+	0.457938i	$0.848588\pi$
$20$	1.65969	−	9.86131i	0.0829843	−	0.493066i
$21$		0			0
$22$	5.74922	−	5.74922i	0.261328	−	0.261328i
$23$	−13.2261	−	13.2261i	−0.575048	−	0.575048i	0.358487	−	0.933535i	$-0.383293\pi$
$23$	−13.2261	−	13.2261i	−0.575048	−	0.575048i	−0.933535	+	0.358487i	$0.883293\pi$
$24$		0			0
$25$	23.6227	+	8.18334i	0.944909	+	0.327333i
$26$	30.0069			1.15411
$27$		0			0
$28$	−3.74166	−	3.74166i	−0.133631	−	0.133631i
$29$		−	37.7271i		−	1.30093i	−0.759534	−	0.650467i	$-0.774573\pi$
$29$		−	37.7271i		−	1.30093i	0.759534	−	0.650467i	$-0.225427\pi$
$30$		0			0
$31$	−27.0130			−0.871386			−0.435693	−	0.900095i	$-0.643497\pi$
$31$	−27.0130			−0.871386			−0.435693	+	0.900095i	$0.643497\pi$
$32$	−4.00000	+	4.00000i	−0.125000	+	0.125000i
$33$		0			0
$34$		−	9.57642i		−	0.281659i
$35$	10.7769	−	7.67192i	0.307912	−	0.219198i
$36$		0			0
$37$	11.3640	−	11.3640i	0.307136	−	0.307136i	−0.536661	−	0.843798i	$-0.680315\pi$
$37$	11.3640	−	11.3640i	0.307136	−	0.307136i	0.843798	+	0.536661i	$0.180315\pi$
$38$	17.4017	+	17.4017i	0.457938	+	0.457938i
$39$		0			0
$40$	−8.20163	−	11.5210i	−0.205041	−	0.288025i
$41$	53.0897			1.29487			0.647435	−	0.762121i	$-0.275842\pi$
$41$	53.0897			1.29487			0.647435	+	0.762121i	$0.275842\pi$
$42$		0			0
$43$	37.1052	+	37.1052i	0.862912	+	0.862912i	0.991675	−	0.128763i	$-0.0411007\pi$
$43$	37.1052	+	37.1052i	0.862912	+	0.862912i	−0.128763	+	0.991675i	$0.541101\pi$
$44$		−	11.4984i		−	0.261328i
$45$		0			0
$46$	−26.4522			−0.575048
$47$	9.39190	−	9.39190i	0.199828	−	0.199828i	−0.600098	−	0.799926i	$-0.704872\pi$
$47$	9.39190	−	9.39190i	0.199828	−	0.199828i	0.799926	+	0.600098i	$0.204872\pi$
$48$		0			0
$49$		−	7.00000i		−	0.142857i
$50$	31.8061	−	15.4394i	0.636121	−	0.308788i
$51$		0			0
$52$	30.0069	−	30.0069i	0.577056	−	0.577056i
$53$	−43.8996	−	43.8996i	−0.828294	−	0.828294i	0.158987	−	0.987281i	$-0.449177\pi$
$53$	−43.8996	−	43.8996i	−0.828294	−	0.828294i	−0.987281	+	0.158987i	$0.949177\pi$
$54$		0			0
$55$	28.3474	+	4.77095i	0.515407	+	0.0867445i
$56$	−7.48331			−0.133631
$57$		0			0
$58$	−37.7271	−	37.7271i	−0.650467	−	0.650467i
$59$			62.9694i			1.06728i	0.845713	+	0.533639i	$0.179176\pi$
$59$			62.9694i			1.06728i	−0.845713	+	0.533639i	$0.820824\pi$
$60$		0			0
$61$	−1.67492			−0.0274577			−0.0137288	−	0.999906i	$-0.504370\pi$
$61$	−1.67492			−0.0274577			−0.0137288	+	0.999906i	$0.504370\pi$
$62$	−27.0130	+	27.0130i	−0.435693	+	0.435693i
$63$		0			0
$64$			8.00000i			0.125000i
$65$	61.5263	+	86.4273i	0.946559	+	1.32965i
$66$		0			0
$67$	28.4909	−	28.4909i	0.425238	−	0.425238i	−0.461765	−	0.887003i	$-0.652784\pi$
$67$	28.4909	−	28.4909i	0.425238	−	0.425238i	0.887003	+	0.461765i	$0.152784\pi$
$68$	−9.57642	−	9.57642i	−0.140830	−	0.140830i
$69$		0			0
$70$	3.10499	−	18.4488i	0.0443570	−	0.263555i
$71$	−47.2039			−0.664844			−0.332422	−	0.943131i	$-0.607866\pi$
$71$	−47.2039			−0.664844			−0.332422	+	0.943131i	$0.607866\pi$
$72$		0			0
$73$	−31.2071	−	31.2071i	−0.427495	−	0.427495i	0.460279	−	0.887774i	$-0.347749\pi$
$73$	−31.2071	−	31.2071i	−0.427495	−	0.427495i	−0.887774	+	0.460279i	$0.847749\pi$
$74$		−	22.7281i		−	0.307136i
$75$		0			0
$76$	34.8033			0.457938
$77$	10.7558	−	10.7558i	0.139686	−	0.139686i
$78$		0			0
$79$		−	107.134i		−	1.35612i	−0.735006	−	0.678061i	$-0.762821\pi$
$79$		−	107.134i		−	1.35612i	0.735006	−	0.678061i	$-0.237179\pi$
$80$	−19.7226	−	3.31937i	−0.246533	−	0.0414921i
$81$		0			0
$82$	53.0897	−	53.0897i	0.647435	−	0.647435i
$83$	−18.2365	−	18.2365i	−0.219716	−	0.219716i	0.588662	−	0.808379i	$-0.299655\pi$
$83$	−18.2365	−	18.2365i	−0.219716	−	0.219716i	−0.808379	+	0.588662i	$0.799655\pi$
$84$		0			0
$85$	27.5825	−	19.6356i	0.324500	−	0.231007i
$86$	74.2105			0.862912
$87$		0			0
$88$	−11.4984	−	11.4984i	−0.130664	−	0.130664i
$89$		−	174.675i		−	1.96265i	−0.192368	−	0.981323i	$-0.561617\pi$
$89$		−	174.675i		−	1.96265i	0.192368	−	0.981323i	$-0.438383\pi$
$90$		0			0
$91$	56.1378			0.616898
$92$	−26.4522	+	26.4522i	−0.287524	+	0.287524i
$93$		0			0
$94$		−	18.7838i		−	0.199828i
$95$	−14.4406	+	85.8016i	−0.152007	+	0.903175i
$96$		0			0
$97$	−91.5084	+	91.5084i	−0.943385	+	0.943385i	−0.998481	−	0.0550959i	$-0.982454\pi$
$97$	−91.5084	+	91.5084i	−0.943385	+	0.943385i	0.0550959	+	0.998481i	$0.482454\pi$
$98$	−7.00000	−	7.00000i	−0.0714286	−	0.0714286i
$99$		0			0
$100$	16.3667	−	47.2454i	0.163667	−	0.472454i
$101$	182.855			1.81045			0.905223	−	0.424937i	$-0.139704\pi$
$101$	182.855			1.81045			0.905223	+	0.424937i	$0.139704\pi$
$102$		0			0
$103$	−46.6226	−	46.6226i	−0.452647	−	0.452647i	0.443586	−	0.896232i	$-0.353706\pi$
$103$	−46.6226	−	46.6226i	−0.452647	−	0.452647i	−0.896232	+	0.443586i	$0.853706\pi$
$104$		−	60.0138i		−	0.577056i
$105$		0			0
$106$	−87.7991			−0.828294
$107$	−57.5651	+	57.5651i	−0.537992	+	0.537992i	−0.922939	−	0.384947i	$-0.874220\pi$
$107$	−57.5651	+	57.5651i	−0.537992	+	0.537992i	0.384947	+	0.922939i	$0.374220\pi$
$108$		0			0
$109$			205.254i			1.88307i	0.336920	+	0.941533i	$0.390615\pi$
$109$			205.254i			1.88307i	−0.336920	+	0.941533i	$0.609385\pi$
$110$	33.1184	−	23.5765i	0.301076	−	0.214331i
$111$		0			0
$112$	−7.48331	+	7.48331i	−0.0668153	+	0.0668153i
$113$	−32.6037	−	32.6037i	−0.288528	−	0.288528i	0.547970	−	0.836498i	$-0.315401\pi$
$113$	−32.6037	−	32.6037i	−0.288528	−	0.288528i	−0.836498	+	0.547970i	$0.815401\pi$
$114$		0			0
$115$	−54.2378	−	76.1890i	−0.471633	−	0.662513i
$116$	−75.4542			−0.650467
$117$		0			0
$118$	62.9694	+	62.9694i	0.533639	+	0.533639i
$119$		−	17.9158i		−	0.150553i
$120$		0			0
$121$	−87.9465			−0.726831
$122$	−1.67492	+	1.67492i	−0.0137288	+	0.0137288i
$123$		0			0
$124$			54.0259i			0.435693i
$125$	109.685	+	59.9524i	0.877477	+	0.479619i
$126$		0			0
$127$	−103.735	+	103.735i	−0.816814	+	0.816814i	−0.985645	−	0.168831i	$-0.946001\pi$
$127$	−103.735	+	103.735i	−0.816814	+	0.816814i	0.168831	+	0.985645i	$0.446001\pi$
$128$	8.00000	+	8.00000i	0.0625000	+	0.0625000i
$129$		0			0
$130$	147.954	+	24.9010i	1.13810	+	0.191546i
$131$	−157.999			−1.20610			−0.603049	−	0.797704i	$-0.706048\pi$
$131$	−157.999			−1.20610			−0.603049	+	0.797704i	$0.706048\pi$
$132$		0			0
$133$	32.5555	+	32.5555i	0.244778	+	0.244778i
$134$		−	56.9819i		−	0.425238i
$135$		0			0
$136$	−19.1528			−0.140830
$137$	36.9574	−	36.9574i	0.269762	−	0.269762i	−0.559242	−	0.829004i	$-0.688908\pi$
$137$	36.9574	−	36.9574i	0.269762	−	0.269762i	0.829004	+	0.559242i	$0.188908\pi$
$138$		0			0
$139$			132.183i			0.950960i	0.879727	+	0.475480i	$0.157726\pi$
$139$			132.183i			0.950960i	−0.879727	+	0.475480i	$0.842274\pi$
$140$	−15.3438	−	21.5538i	−0.109599	−	0.153956i
$141$		0			0
$142$	−47.2039	+	47.2039i	−0.332422	+	0.332422i
$143$	86.2581	+	86.2581i	0.603203	+	0.603203i
$144$		0			0
$145$	31.3076	−	186.019i	0.215914	−	1.28289i
$146$	−62.4143			−0.427495
$147$		0			0
$148$	−22.7281	−	22.7281i	−0.153568	−	0.153568i
$149$			255.329i			1.71362i	0.515634	+	0.856809i	$0.327556\pi$
$149$			255.329i			1.71362i	−0.515634	+	0.856809i	$0.672444\pi$
$150$		0			0
$151$	−210.524			−1.39420			−0.697098	−	0.716976i	$-0.745526\pi$
$151$	−210.524			−1.39420			−0.697098	+	0.716976i	$0.745526\pi$
$152$	34.8033	−	34.8033i	0.228969	−	0.228969i
$153$		0			0
$154$		−	21.5116i		−	0.139686i
$155$	−133.192	−	22.4165i	−0.859301	−	0.144623i
$156$		0			0
$157$	−181.671	+	181.671i	−1.15714	+	1.15714i	−0.172052	+	0.985088i	$0.555040\pi$
$157$	−181.671	+	181.671i	−1.15714	+	1.15714i	−0.985088	+	0.172052i	$0.944960\pi$
$158$	−107.134	−	107.134i	−0.678061	−	0.678061i
$159$		0			0
$160$	−23.0420	+	16.4033i	−0.144012	+	0.102520i
$161$	−49.4876			−0.307376
$162$		0			0
$163$	155.563	+	155.563i	0.954376	+	0.954376i	0.999004	−	0.0446274i	$-0.0142101\pi$
$163$	155.563	+	155.563i	0.954376	+	0.954376i	−0.0446274	+	0.999004i	$0.514210\pi$
$164$		−	106.179i		−	0.647435i
$165$		0			0
$166$	−36.4729			−0.219716
$167$	−76.0788	+	76.0788i	−0.455562	+	0.455562i	−0.897195	−	0.441634i	$-0.854399\pi$
$167$	−76.0788	+	76.0788i	−0.455562	+	0.455562i	0.441634	+	0.897195i	$0.354399\pi$
$168$		0			0
$169$			281.207i			1.66395i
$170$	7.94692	−	47.2180i	0.0467466	−	0.277753i
$171$		0			0
$172$	74.2105	−	74.2105i	0.431456	−	0.431456i
$173$	−28.9323	−	28.9323i	−0.167239	−	0.167239i	0.618526	−	0.785765i	$-0.287730\pi$
$173$	−28.9323	−	28.9323i	−0.167239	−	0.167239i	−0.785765	+	0.618526i	$0.787730\pi$
$174$		0			0
$175$	59.5037	−	28.8844i	0.340021	−	0.165054i
$176$	−22.9969			−0.130664
$177$		0			0
$178$	−174.675	−	174.675i	−0.981323	−	0.981323i
$179$		−	126.849i		−	0.708653i	−0.935122	−	0.354327i	$-0.884710\pi$
$179$		−	126.849i		−	0.708653i	0.935122	−	0.354327i	$-0.115290\pi$
$180$		0			0
$181$	307.681			1.69989			0.849947	−	0.526867i	$-0.176634\pi$
$181$	307.681			1.69989			0.849947	+	0.526867i	$0.176634\pi$
$182$	56.1378	−	56.1378i	0.308449	−	0.308449i
$183$		0			0
$184$			52.9044i			0.287524i
$185$	65.4626	−	46.6018i	0.353852	−	0.251902i
$186$		0			0
$187$	27.5285	−	27.5285i	0.147211	−	0.147211i
$188$	−18.7838	−	18.7838i	−0.0999139	−	0.0999139i
$189$		0			0
$190$	71.3609	+	100.242i	0.375584	+	0.527591i
$191$	−71.4969			−0.374329			−0.187165	−	0.982329i	$-0.559930\pi$
$191$	−71.4969			−0.374329			−0.187165	+	0.982329i	$0.559930\pi$
$192$		0			0
$193$	−155.347	−	155.347i	−0.804908	−	0.804908i	0.178950	−	0.983858i	$-0.442730\pi$
$193$	−155.347	−	155.347i	−0.804908	−	0.804908i	−0.983858	+	0.178950i	$0.942730\pi$
$194$			183.017i			0.943385i
$195$		0			0
$196$	−14.0000			−0.0714286
$197$	−190.520	+	190.520i	−0.967107	+	0.967107i	−0.999476	−	0.0323691i	$-0.989695\pi$
$197$	−190.520	+	190.520i	−0.967107	+	0.967107i	0.0323691	+	0.999476i	$0.489695\pi$
$198$		0			0
$199$		−	173.246i		−	0.870582i	−0.900290	−	0.435291i	$-0.856646\pi$
$199$		−	173.246i		−	0.870582i	0.900290	−	0.435291i	$-0.143354\pi$
$200$	−30.8788	−	63.6121i	−0.154394	−	0.318061i
$201$		0			0
$202$	182.855	−	182.855i	0.905223	−	0.905223i
$203$	−70.5809	−	70.5809i	−0.347689	−	0.347689i
$204$		0			0
$205$	261.767	+	44.0561i	1.27691	+	0.214908i
$206$	−93.2452			−0.452647
$207$		0			0
$208$	−60.0138	−	60.0138i	−0.288528	−	0.288528i
$209$			100.046i			0.478689i
$210$		0			0
$211$	53.9193			0.255542			0.127771	−	0.991804i	$-0.459218\pi$
$211$	53.9193			0.255542			0.127771	+	0.991804i	$0.459218\pi$
$212$	−87.7991	+	87.7991i	−0.414147	+	0.414147i
$213$		0			0
$214$			115.130i			0.537992i
$215$	152.162	+	213.745i	0.707728	+	0.994161i
$216$		0			0
$217$	−50.5366	+	50.5366i	−0.232888	+	0.232888i
$218$	205.254	+	205.254i	0.941533	+	0.941533i
$219$		0			0
$220$	9.54189	−	56.6948i	0.0433722	−	0.257704i
$221$	143.679			0.650133
$222$		0			0
$223$	−146.512	−	146.512i	−0.657006	−	0.657006i	0.297664	−	0.954671i	$-0.403792\pi$
$223$	−146.512	−	146.512i	−0.657006	−	0.657006i	−0.954671	+	0.297664i	$0.903792\pi$
$224$			14.9666i			0.0668153i
$225$		0			0
$226$	−65.2073			−0.288528
$227$	−162.897	+	162.897i	−0.717607	+	0.717607i	−0.968115	−	0.250508i	$-0.919402\pi$
$227$	−162.897	+	162.897i	−0.717607	+	0.717607i	0.250508	+	0.968115i	$0.419402\pi$
$228$		0			0
$229$		−	176.209i		−	0.769470i	−0.923027	−	0.384735i	$-0.874293\pi$
$229$		−	176.209i		−	0.769470i	0.923027	−	0.384735i	$-0.125707\pi$
$230$	−130.427	−	21.9512i	−0.567073	−	0.0954399i
$231$		0			0
$232$	−75.4542	+	75.4542i	−0.325234	+	0.325234i
$233$	18.3615	+	18.3615i	0.0788049	+	0.0788049i	0.745411	−	0.666606i	$-0.232253\pi$
$233$	18.3615	+	18.3615i	0.0788049	+	0.0788049i	−0.666606	+	0.745411i	$0.732253\pi$
$234$		0			0
$235$	54.1020	−	38.5144i	0.230221	−	0.163891i
$236$	125.939			0.533639
$237$		0			0
$238$	−17.9158	−	17.9158i	−0.0752767	−	0.0752767i
$239$			275.093i			1.15102i	0.817795	+	0.575509i	$0.195196\pi$
$239$			275.093i			1.15102i	−0.817795	+	0.575509i	$0.804804\pi$
$240$		0			0
$241$	338.925			1.40633			0.703164	−	0.711028i	$-0.251770\pi$
$241$	338.925			1.40633			0.703164	+	0.711028i	$0.251770\pi$
$242$	−87.9465	+	87.9465i	−0.363415	+	0.363415i
$243$		0			0
$244$			3.34984i			0.0137288i
$245$	5.80890	−	34.5146i	0.0237098	−	0.140876i
$246$		0			0
$247$	−261.085	+	261.085i	−1.05702	+	1.05702i
$248$	54.0259	+	54.0259i	0.217846	+	0.217846i
$249$		0			0
$250$	169.637	−	49.7323i	0.678548	−	0.198929i
$251$	−72.1187			−0.287326			−0.143663	−	0.989627i	$-0.545888\pi$
$251$	−72.1187			−0.287326			−0.143663	+	0.989627i	$0.545888\pi$
$252$		0			0
$253$	−76.0397	−	76.0397i	−0.300552	−	0.300552i
$254$			207.471i			0.816814i
$255$		0			0
$256$	16.0000			0.0625000
$257$	12.2256	−	12.2256i	0.0475703	−	0.0475703i	−0.682921	−	0.730492i	$-0.739291\pi$
$257$	12.2256	−	12.2256i	0.0475703	−	0.0475703i	0.730492	+	0.682921i	$0.239291\pi$
$258$		0			0
$259$		−	42.5204i		−	0.164171i
$260$	172.855	−	123.053i	0.664826	−	0.473279i
$261$		0			0
$262$	−157.999	+	157.999i	−0.603049	+	0.603049i
$263$	−275.733	−	275.733i	−1.04842	−	1.04842i	−0.998767	−	0.0496495i	$-0.984190\pi$
$263$	−275.733	−	275.733i	−1.04842	−	1.04842i	−0.0496495	−	0.998767i	$-0.515810\pi$
$264$		0			0
$265$	−180.024	−	252.883i	−0.679335	−	0.954277i
$266$	65.1110			0.244778
$267$		0			0
$268$	−56.9819	−	56.9819i	−0.212619	−	0.212619i
$269$		−	275.988i		−	1.02598i	−0.858395	−	0.512989i	$-0.828538\pi$
$269$		−	275.988i		−	1.02598i	0.858395	−	0.512989i	$-0.171462\pi$
$270$		0			0
$271$	295.698			1.09114			0.545568	−	0.838067i	$-0.316314\pi$
$271$	295.698			1.09114			0.545568	+	0.838067i	$0.316314\pi$
$272$	−19.1528	+	19.1528i	−0.0704149	+	0.0704149i
$273$		0			0
$274$		−	73.9148i		−	0.269762i
$275$	135.812	+	47.0478i	0.493862	+	0.171083i
$276$		0			0
$277$	−21.4676	+	21.4676i	−0.0775005	+	0.0775005i	−0.744794	−	0.667294i	$-0.767452\pi$
$277$	−21.4676	+	21.4676i	−0.0775005	+	0.0775005i	0.667294	+	0.744794i	$0.267452\pi$
$278$	132.183	+	132.183i	0.475480	+	0.475480i
$279$		0			0
$280$	−36.8976	−	6.20997i	−0.131777	−	0.0221785i
$281$	−74.2011			−0.264061			−0.132030	−	0.991246i	$-0.542150\pi$
$281$	−74.2011			−0.264061			−0.132030	+	0.991246i	$0.542150\pi$
$282$		0			0
$283$	−322.473	−	322.473i	−1.13948	−	1.13948i	−0.988543	−	0.150937i	$-0.951771\pi$
$283$	−322.473	−	322.473i	−1.13948	−	1.13948i	−0.150937	−	0.988543i	$-0.548229\pi$
$284$			94.4079i			0.332422i
$285$		0			0
$286$	172.516			0.603203
$287$	99.3217	−	99.3217i	0.346069	−	0.346069i
$288$		0			0
$289$			243.146i			0.841336i
$290$	−154.712	−	217.327i	−0.533489	−	0.749403i
$291$		0			0
$292$	−62.4143	+	62.4143i	−0.213747	+	0.213747i
$293$	145.754	+	145.754i	0.497456	+	0.497456i	0.910645	−	0.413189i	$-0.135585\pi$
$293$	145.754	+	145.754i	0.497456	+	0.497456i	−0.413189	+	0.910645i	$0.635585\pi$
$294$		0			0
$295$	−52.2547	+	310.480i	−0.177134	+	1.05248i
$296$	−45.4562			−0.153568
$297$		0			0
$298$	255.329	+	255.329i	0.856809	+	0.856809i
$299$		−	396.874i		−	1.32734i
$300$		0			0
$301$	138.835			0.461246
$302$	−210.524	+	210.524i	−0.697098	+	0.697098i
$303$		0			0
$304$		−	69.6066i		−	0.228969i
$305$	−8.25845	−	1.38992i	−0.0270769	−	0.00455711i
$306$		0			0
$307$	−308.104	+	308.104i	−1.00360	+	1.00360i	−0.00360237	+	0.999994i	$0.501147\pi$
$307$	−308.104	+	308.104i	−1.00360	+	1.00360i	−0.999994	+	0.00360237i	$0.998853\pi$
$308$	−21.5116	−	21.5116i	−0.0698429	−	0.0698429i
$309$		0			0
$310$	−155.608	+	110.775i	−0.501962	+	0.357339i
$311$	29.1191			0.0936304			0.0468152	−	0.998904i	$-0.485093\pi$
$311$	29.1191			0.0936304			0.0468152	+	0.998904i	$0.485093\pi$
$312$		0			0
$313$	12.1714	+	12.1714i	0.0388863	+	0.0388863i	0.726283	−	0.687396i	$-0.241246\pi$
$313$	12.1714	+	12.1714i	0.0388863	+	0.0388863i	−0.687396	+	0.726283i	$0.741246\pi$
$314$			363.342i			1.15714i
$315$		0			0
$316$	−214.267			−0.678061
$317$	−219.192	+	219.192i	−0.691456	+	0.691456i	−0.962552	−	0.271096i	$-0.912614\pi$
$317$	−219.192	+	219.192i	−0.691456	+	0.691456i	0.271096	+	0.962552i	$0.412614\pi$
$318$		0			0
$319$		−	216.901i		−	0.679941i
$320$	−6.63874	+	39.4452i	−0.0207461	+	0.123266i
$321$		0			0
$322$	−49.4876	+	49.4876i	−0.153688	+	0.153688i
$323$	83.3228	+	83.3228i	0.257965	+	0.257965i
$324$		0			0
$325$	231.644	+	477.201i	0.712751	+	1.46831i
$326$	311.127			0.954376
$327$		0			0
$328$	−106.179	−	106.179i	−0.323718	−	0.323718i
$329$		−	35.1413i		−	0.106812i
$330$		0			0
$331$	276.111			0.834171			0.417086	−	0.908867i	$-0.363052\pi$
$331$	276.111			0.834171			0.417086	+	0.908867i	$0.363052\pi$
$332$	−36.4729	+	36.4729i	−0.109858	+	0.109858i
$333$		0			0
$334$			152.158i			0.455562i
$335$	164.122	−	116.836i	0.489916	−	0.348764i
$336$		0			0
$337$	276.393	−	276.393i	0.820157	−	0.820157i	−0.165973	−	0.986130i	$-0.553077\pi$
$337$	276.393	−	276.393i	0.820157	−	0.820157i	0.986130	+	0.165973i	$0.0530766\pi$
$338$	281.207	+	281.207i	0.831973	+	0.831973i
$339$		0			0
$340$	−39.2711	−	55.1650i	−0.115503	−	0.162250i
$341$	−155.303			−0.455435
$342$		0			0
$343$	−13.0958	−	13.0958i	−0.0381802	−	0.0381802i
$344$		−	148.421i		−	0.431456i
$345$		0			0
$346$	−57.8647			−0.167239
$347$	158.084	−	158.084i	0.455573	−	0.455573i	−0.441626	−	0.897199i	$-0.645598\pi$
$347$	158.084	−	158.084i	0.455573	−	0.455573i	0.897199	+	0.441626i	$0.145598\pi$
$348$		0			0
$349$		−	452.412i		−	1.29631i	−0.761508	−	0.648155i	$-0.775541\pi$
$349$		−	452.412i		−	1.29631i	0.761508	−	0.648155i	$-0.224459\pi$
$350$	30.6192	−	88.3881i	0.0874835	−	0.252538i
$351$		0			0
$352$	−22.9969	+	22.9969i	−0.0653320	+	0.0653320i
$353$	−481.681	−	481.681i	−1.36453	−	1.36453i	−0.868039	−	0.496495i	$-0.834620\pi$
$353$	−481.681	−	481.681i	−1.36453	−	1.36453i	−0.496495	−	0.868039i	$-0.665380\pi$
$354$		0			0
$355$	−232.746	−	39.1718i	−0.655624	−	0.110343i
$356$	−349.351			−0.981323
$357$		0			0
$358$	−126.849	−	126.849i	−0.354327	−	0.354327i
$359$			485.514i			1.35241i	0.736716	+	0.676203i	$0.236376\pi$
$359$			485.514i			1.35241i	−0.736716	+	0.676203i	$0.763624\pi$
$360$		0			0
$361$	58.1823			0.161170
$362$	307.681	−	307.681i	0.849947	−	0.849947i
$363$		0			0
$364$		−	112.276i		−	0.308449i
$365$	−127.975	−	179.769i	−0.350615	−	0.492517i
$366$		0			0
$367$	205.331	−	205.331i	0.559486	−	0.559486i	−0.369675	−	0.929161i	$-0.620531\pi$
$367$	205.331	−	205.331i	0.559486	−	0.559486i	0.929161	+	0.369675i	$0.120531\pi$
$368$	52.9044	+	52.9044i	0.143762	+	0.143762i
$369$		0			0
$370$	18.8607	−	112.064i	0.0509750	−	0.302877i
$371$	−164.257			−0.442742
$372$		0			0
$373$	−24.9803	−	24.9803i	−0.0669714	−	0.0669714i	0.672828	−	0.739799i	$-0.265079\pi$
$373$	−24.9803	−	24.9803i	−0.0669714	−	0.0669714i	−0.739799	+	0.672828i	$0.765079\pi$
$374$		−	55.0569i		−	0.147211i
$375$		0			0
$376$	−37.5676			−0.0999139
$377$	566.037	−	566.037i	1.50142	−	1.50142i
$378$		0			0
$379$			356.423i			0.940429i	0.882552	+	0.470215i	$0.155823\pi$
$379$			356.423i			0.940429i	−0.882552	+	0.470215i	$0.844177\pi$
$380$	171.603	+	28.8813i	0.451587	+	0.0760034i
$381$		0			0
$382$	−71.4969	+	71.4969i	−0.187165	+	0.187165i
$383$	−480.677	−	480.677i	−1.25503	−	1.25503i	−0.953436	−	0.301596i	$-0.902481\pi$
$383$	−480.677	−	480.677i	−1.25503	−	1.25503i	−0.301596	−	0.953436i	$-0.597519\pi$
$384$		0			0
$385$	61.9588	−	44.1075i	0.160932	−	0.114565i
$386$	−310.695			−0.804908
$387$		0			0
$388$	183.017	+	183.017i	0.471693	+	0.471693i
$389$		−	169.784i		−	0.436461i	−0.975897	−	0.218231i	$-0.929971\pi$
$389$		−	169.784i		−	0.436461i	0.975897	−	0.218231i	$-0.0700285\pi$
$390$		0			0
$391$	−126.659			−0.323935
$392$	−14.0000	+	14.0000i	−0.0357143	+	0.0357143i
$393$		0			0
$394$			381.040i			0.967107i
$395$	88.9040	−	528.239i	0.225073	−	1.33731i
$396$		0			0
$397$	−66.1208	+	66.1208i	−0.166551	+	0.166551i	−0.785462	−	0.618910i	$-0.787574\pi$
$397$	−66.1208	+	66.1208i	−0.166551	+	0.166551i	0.618910	+	0.785462i	$0.287574\pi$
$398$	−173.246	−	173.246i	−0.435291	−	0.435291i
$399$		0			0
$400$	−94.4909	−	32.7333i	−0.236227	−	0.0818334i
$401$	213.860			0.533318			0.266659	−	0.963791i	$-0.414080\pi$
$401$	213.860			0.533318			0.266659	+	0.963791i	$0.414080\pi$
$402$		0			0
$403$	−405.288	−	405.288i	−1.00568	−	1.00568i
$404$		−	365.710i		−	0.905223i
$405$		0			0
$406$	−141.162			−0.347689
$407$	65.3344	−	65.3344i	0.160527	−	0.160527i
$408$		0			0
$409$			300.366i			0.734391i	0.930144	+	0.367196i	$0.119682\pi$
$409$			300.366i			0.734391i	−0.930144	+	0.367196i	$0.880318\pi$
$410$	305.823	−	217.711i	0.745910	−	0.531002i
$411$		0			0
$412$	−93.2452	+	93.2452i	−0.226323	+	0.226323i
$413$	117.805	+	117.805i	0.285242	+	0.285242i
$414$		0			0
$415$	−74.7843	−	105.051i	−0.180203	−	0.253135i
$416$	−120.028			−0.288528
$417$		0			0
$418$	100.046	+	100.046i	0.239344	+	0.239344i
$419$			696.907i			1.66326i	0.555328	+	0.831632i	$0.312593\pi$
$419$			696.907i			1.66326i	−0.555328	+	0.831632i	$0.687407\pi$
$420$		0			0
$421$	−114.980			−0.273111			−0.136555	−	0.990632i	$-0.543603\pi$
$421$	−114.980			−0.273111			−0.136555	+	0.990632i	$0.543603\pi$
$422$	53.9193	−	53.9193i	0.127771	−	0.127771i
$423$		0			0
$424$			175.598i			0.414147i
$425$	152.294	−	73.9270i	0.358339	−	0.173946i
$426$		0			0
$427$	−3.13349	+	3.13349i	−0.00733838	+	0.00733838i
$428$	115.130	+	115.130i	0.268996	+	0.268996i
$429$		0			0
$430$	365.906	+	61.5830i	0.850945	+	0.143216i
$431$	724.694			1.68143			0.840713	−	0.541481i	$-0.182136\pi$
$431$	724.694			1.68143			0.840713	+	0.541481i	$0.182136\pi$
$432$		0			0
$433$	100.327	+	100.327i	0.231703	+	0.231703i	0.813403	−	0.581700i	$-0.197612\pi$
$433$	100.327	+	100.327i	0.231703	+	0.231703i	−0.581700	+	0.813403i	$0.697612\pi$
$434$			101.073i			0.232888i
$435$		0			0
$436$	410.509			0.941533
$437$	230.156	−	230.156i	0.526673	−	0.526673i
$438$		0			0
$439$		−	685.890i		−	1.56239i	−0.624286	−	0.781195i	$-0.714610\pi$
$439$		−	685.890i		−	1.56239i	0.624286	−	0.781195i	$-0.285390\pi$
$440$	−47.1529	−	66.2367i	−0.107166	−	0.150538i
$441$		0			0
$442$	143.679	−	143.679i	0.325066	−	0.325066i
$443$	−339.752	−	339.752i	−0.766935	−	0.766935i	0.210631	−	0.977566i	$-0.432448\pi$
$443$	−339.752	−	339.752i	−0.766935	−	0.766935i	−0.977566	+	0.210631i	$0.932448\pi$
$444$		0			0
$445$	144.953	−	861.264i	0.325737	−	1.93543i
$446$	−293.025			−0.657006
$447$		0			0
$448$	14.9666	+	14.9666i	0.0334077	+	0.0334077i
$449$			226.637i			0.504758i	0.967628	+	0.252379i	$0.0812130\pi$
$449$			226.637i			0.504758i	−0.967628	+	0.252379i	$0.918787\pi$
$450$		0			0
$451$	305.224			0.676772
$452$	−65.2073	+	65.2073i	−0.144264	+	0.144264i
$453$		0			0
$454$			325.794i			0.717607i
$455$	276.796	+	46.5855i	0.608343	+	0.102386i
$456$		0			0
$457$	−266.282	+	266.282i	−0.582675	+	0.582675i	−0.935637	−	0.352963i	$-0.885174\pi$
$457$	−266.282	+	266.282i	−0.582675	+	0.582675i	0.352963	+	0.935637i	$0.385174\pi$
$458$	−176.209	−	176.209i	−0.384735	−	0.384735i
$459$		0			0
$460$	−152.378	+	108.476i	−0.331256	+	0.235816i
$461$	121.199			0.262905			0.131453	−	0.991322i	$-0.458036\pi$
$461$	121.199			0.262905			0.131453	+	0.991322i	$0.458036\pi$
$462$		0			0
$463$	−565.604	−	565.604i	−1.22161	−	1.22161i	−0.967061	−	0.254547i	$-0.918074\pi$
$463$	−565.604	−	565.604i	−1.22161	−	1.22161i	−0.254547	−	0.967061i	$-0.581926\pi$
$464$			150.908i			0.325234i
$465$		0			0
$466$	36.7231			0.0788049
$467$	279.536	−	279.536i	0.598578	−	0.598578i	−0.341356	−	0.939934i	$-0.610886\pi$
$467$	279.536	−	279.536i	0.598578	−	0.598578i	0.939934	+	0.341356i	$0.110886\pi$
$468$		0			0
$469$		−	106.603i		−	0.227299i
$470$	15.5876	−	92.6165i	0.0331651	−	0.197056i
$471$		0			0
$472$	125.939	−	125.939i	0.266819	−	0.266819i
$473$	213.326	+	213.326i	0.451006	+	0.451006i
$474$		0			0
$475$	−142.404	+	411.075i	−0.299797	+	0.865420i
$476$	−35.8317			−0.0752767
$477$		0			0
$478$	275.093	+	275.093i	0.575509	+	0.575509i
$479$			101.987i			0.212916i	0.994317	+	0.106458i	$0.0339510\pi$
$479$			101.987i			0.212916i	−0.994317	+	0.106458i	$0.966049\pi$
$480$		0			0
$481$	341.000			0.708939
$482$	338.925	−	338.925i	0.703164	−	0.703164i
$483$		0			0
$484$			175.893i			0.363415i
$485$	−527.134	+	375.259i	−1.08687	+	0.773729i
$486$		0			0
$487$	250.272	−	250.272i	0.513907	−	0.513907i	−0.401815	−	0.915721i	$-0.631620\pi$
$487$	250.272	−	250.272i	0.513907	−	0.513907i	0.915721	+	0.401815i	$0.131620\pi$
$488$	3.34984	+	3.34984i	0.00686442	+	0.00686442i
$489$		0			0
$490$	−28.7057	−	40.3235i	−0.0585830	−	0.0822928i
$491$	648.021			1.31980			0.659899	−	0.751355i	$-0.270599\pi$
$491$	648.021			1.31980			0.659899	+	0.751355i	$0.270599\pi$
$492$		0			0
$493$	−180.645	−	180.645i	−0.366421	−	0.366421i
$494$			522.170i			1.05702i
$495$		0			0
$496$	108.052			0.217846
$497$	−88.3105	+	88.3105i	−0.177687	+	0.177687i
$498$		0			0
$499$		−	377.798i		−	0.757110i	−0.925579	−	0.378555i	$-0.876421\pi$
$499$		−	377.798i		−	0.757110i	0.925579	−	0.378555i	$-0.123579\pi$
$500$	119.905	−	219.369i	0.239809	−	0.438738i
$501$		0			0
$502$	−72.1187	+	72.1187i	−0.143663	+	0.143663i
$503$	221.145	+	221.145i	0.439651	+	0.439651i	0.891895	−	0.452243i	$-0.149376\pi$
$503$	221.145	+	221.145i	0.439651	+	0.439651i	−0.452243	+	0.891895i	$0.649376\pi$
$504$		0			0
$505$	901.595	+	151.741i	1.78534	+	0.300477i
$506$	−152.079			−0.300552
$507$		0			0
$508$	207.471	+	207.471i	0.408407	+	0.408407i
$509$		−	586.753i		−	1.15276i	−0.817183	−	0.576378i	$-0.804465\pi$
$509$		−	586.753i		−	1.15276i	0.817183	−	0.576378i	$-0.195535\pi$
$510$		0			0
$511$	−116.766			−0.228506
$512$	16.0000	−	16.0000i	0.0312500	−	0.0312500i
$513$		0			0
$514$		−	24.4511i		−	0.0475703i
$515$	−191.191	−	268.569i	−0.371244	−	0.521494i
$516$		0			0
$517$	53.9961	−	53.9961i	0.104441	−	0.104441i
$518$	−42.5204	−	42.5204i	−0.0820857	−	0.0820857i
$519$		0			0
$520$	49.8020	−	295.907i	0.0957731	−	0.569052i
$521$	466.427			0.895253			0.447626	−	0.894221i	$-0.352269\pi$
$521$	466.427			0.895253			0.447626	+	0.894221i	$0.352269\pi$
$522$		0			0
$523$	303.656	+	303.656i	0.580604	+	0.580604i	0.935069	−	0.354465i	$-0.115337\pi$
$523$	303.656	+	303.656i	0.580604	+	0.580604i	−0.354465	+	0.935069i	$0.615337\pi$
$524$			315.998i			0.603049i
$525$		0			0
$526$	−551.467			−1.04842
$527$	−129.344	+	129.344i	−0.245434	+	0.245434i
$528$		0			0
$529$		−	179.140i		−	0.338639i
$530$	−432.907	−	72.8595i	−0.816806	−	0.137471i
$531$		0			0
$532$	65.1110	−	65.1110i	0.122389	−	0.122389i
$533$	796.528	+	796.528i	1.49442	+	1.49442i
$534$		0			0
$535$	−331.604	+	236.064i	−0.619820	+	0.441241i
$536$	−113.964			−0.212619
$537$		0			0
$538$	−275.988	−	275.988i	−0.512989	−	0.512989i
$539$		−	40.2445i		−	0.0746652i
$540$		0			0
$541$	465.245			0.859973			0.429986	−	0.902835i	$-0.358518\pi$
$541$	465.245			0.859973			0.429986	+	0.902835i	$0.358518\pi$
$542$	295.698	−	295.698i	0.545568	−	0.545568i
$543$		0			0
$544$			38.3057i			0.0704149i
$545$	−170.329	+	1012.04i	−0.312530	+	1.85695i
$546$		0			0
$547$	492.529	−	492.529i	0.900419	−	0.900419i	−0.0950533	−	0.995472i	$-0.530302\pi$
$547$	492.529	−	492.529i	0.900419	−	0.900419i	0.995472	+	0.0950533i	$0.0303021\pi$
$548$	−73.9148	−	73.9148i	−0.134881	−	0.134881i
$549$		0			0
$550$	182.860	−	88.7644i	0.332473	−	0.161390i
$551$	656.514			1.19150
$552$		0			0
$553$	−200.429	−	200.429i	−0.362439	−	0.362439i
$554$			42.9353i			0.0775005i
$555$		0			0
$556$	264.367			0.475480
$557$	−395.342	+	395.342i	−0.709771	+	0.709771i	−0.966487	−	0.256716i	$-0.917359\pi$
$557$	−395.342	+	395.342i	−0.709771	+	0.709771i	0.256716	+	0.966487i	$0.417359\pi$
$558$		0			0
$559$			1113.41i			1.99179i
$560$	−43.1076	+	30.6877i	−0.0769779	+	0.0547994i
$561$		0			0
$562$	−74.2011	+	74.2011i	−0.132030	+	0.132030i
$563$	−447.005	−	447.005i	−0.793971	−	0.793971i	0.188167	−	0.982137i	$-0.439746\pi$
$563$	−447.005	−	447.005i	−0.793971	−	0.793971i	−0.982137	+	0.188167i	$0.939746\pi$
$564$		0			0
$565$	−133.701	−	187.813i	−0.236640	−	0.332413i
$566$	−644.946			−1.13948
$567$		0			0
$568$	94.4079	+	94.4079i	0.166211	+	0.166211i
$569$		−	39.2969i		−	0.0690631i	−0.999404	−	0.0345316i	$-0.989006\pi$
$569$		−	39.2969i		−	0.0690631i	0.999404	−	0.0345316i	$-0.0109939\pi$
$570$		0			0
$571$	−824.326			−1.44365			−0.721826	−	0.692074i	$-0.756697\pi$
$571$	−824.326			−1.44365			−0.721826	+	0.692074i	$0.756697\pi$
$572$	172.516	−	172.516i	0.301602	−	0.301602i
$573$		0			0
$574$		−	198.643i		−	0.346069i
$575$	−204.203	−	420.670i	−0.355136	−	0.731600i
$576$		0			0
$577$	645.287	−	645.287i	1.11835	−	1.11835i	0.126365	−	0.991984i	$-0.459669\pi$
$577$	645.287	−	645.287i	1.11835	−	1.11835i	0.991984	−	0.126365i	$-0.0403311\pi$
$578$	243.146	+	243.146i	0.420668	+	0.420668i
$579$		0			0
$580$	−372.039	−	62.6151i	−0.641446	−	0.107957i
$581$	−68.2346			−0.117443
$582$		0			0
$583$	−252.388	−	252.388i	−0.432913	−	0.432913i
$584$			124.829i			0.213747i
$585$		0			0
$586$	291.509			0.497456
$587$	−512.978	+	512.978i	−0.873898	+	0.873898i	−0.992895	−	0.118997i	$-0.962032\pi$
$587$	−512.978	+	512.978i	−0.873898	+	0.873898i	0.118997	+	0.992895i	$0.462032\pi$
$588$		0			0
$589$		−	470.070i		−	0.798082i
$590$	258.226	+	362.735i	0.437670	+	0.614805i
$591$		0			0
$592$	−45.4562	+	45.4562i	−0.0767841	+	0.0767841i
$593$	379.753	+	379.753i	0.640393	+	0.640393i	0.950652	−	0.310259i	$-0.100416\pi$
$593$	379.753	+	379.753i	0.640393	+	0.640393i	−0.310259	+	0.950652i	$0.600416\pi$
$594$		0			0
$595$	14.8673	−	88.3369i	0.0249871	−	0.148465i
$596$	510.658			0.856809
$597$		0			0
$598$	−396.874	−	396.874i	−0.663669	−	0.663669i
$599$		−	167.160i		−	0.279065i	−0.990218	−	0.139532i	$-0.955440\pi$
$599$		−	167.160i		−	0.279065i	0.990218	−	0.139532i	$-0.0445599\pi$
$600$		0			0
$601$	649.442			1.08060			0.540302	−	0.841472i	$-0.318310\pi$
$601$	649.442			1.08060			0.540302	+	0.841472i	$0.318310\pi$
$602$	138.835	−	138.835i	0.230623	−	0.230623i
$603$		0			0
$604$			421.047i			0.697098i
$605$	−433.634	−	72.9818i	−0.716750	−	0.120631i
$606$		0			0
$607$	−342.997	+	342.997i	−0.565069	+	0.565069i	−0.930743	−	0.365674i	$-0.880839\pi$
$607$	−342.997	+	342.997i	−0.565069	+	0.565069i	0.365674	+	0.930743i	$0.380839\pi$
$608$	−69.6066	−	69.6066i	−0.114485	−	0.114485i
$609$		0			0
$610$	−9.64837	+	6.86853i	−0.0158170	+	0.0112599i
$611$	281.822			0.461247
$612$		0			0
$613$	−311.569	−	311.569i	−0.508270	−	0.508270i	0.405725	−	0.913995i	$-0.367019\pi$
$613$	−311.569	−	311.569i	−0.508270	−	0.508270i	−0.913995	+	0.405725i	$0.867019\pi$
$614$			616.208i			1.00360i
$615$		0			0
$616$	−43.0232			−0.0698429
$617$	−442.165	+	442.165i	−0.716636	+	0.716636i	−0.967915	−	0.251279i	$-0.919149\pi$
$617$	−442.165	+	442.165i	−0.716636	+	0.716636i	0.251279	+	0.967915i	$0.419149\pi$
$618$		0			0
$619$			375.146i			0.606052i	0.952982	+	0.303026i	$0.0979968\pi$
$619$			375.146i			0.606052i	−0.952982	+	0.303026i	$0.902003\pi$
$620$	−44.8330	+	266.383i	−0.0723113	+	0.429650i
$621$		0			0
$622$	29.1191	−	29.1191i	0.0468152	−	0.0468152i
$623$	−326.788	−	326.788i	−0.524539	−	0.524539i
$624$		0			0
$625$	491.066	+	386.625i	0.785706	+	0.618601i
$626$	24.3428			0.0388863
$627$		0			0
$628$	363.342	+	363.342i	0.578570	+	0.578570i
$629$		−	108.827i		−	0.173016i
$630$		0			0
$631$	−973.951			−1.54350			−0.771752	−	0.635924i	$-0.780619\pi$
$631$	−973.951			−1.54350			−0.771752	+	0.635924i	$0.780619\pi$
$632$	−214.267	+	214.267i	−0.339030	+	0.339030i
$633$		0			0
$634$			438.383i			0.691456i
$635$	−597.568	+	425.400i	−0.941051	+	0.669921i
$636$		0			0
$637$	105.024	−	105.024i	0.164873	−	0.164873i
$638$	−216.901	−	216.901i	−0.339971	−	0.339971i
$639$		0			0
$640$	32.8065	+	46.0840i	0.0512602	+	0.0720062i
$641$	−487.398			−0.760371			−0.380185	−	0.924910i	$-0.624140\pi$
$641$	−487.398			−0.760371			−0.380185	+	0.924910i	$0.624140\pi$
$642$		0			0
$643$	554.739	+	554.739i	0.862736	+	0.862736i	0.991655	−	0.128919i	$-0.0411509\pi$
$643$	554.739	+	554.739i	0.862736	+	0.862736i	−0.128919	+	0.991655i	$0.541151\pi$
$644$			98.9751i			0.153688i
$645$		0			0
$646$	166.646			0.257965
$647$	−337.971	+	337.971i	−0.522367	+	0.522367i	−0.918285	−	0.395919i	$-0.870426\pi$
$647$	−337.971	+	337.971i	−0.522367	+	0.522367i	0.395919	+	0.918285i	$0.370426\pi$
$648$		0			0
$649$			362.025i			0.557819i
$650$	708.845	+	245.557i	1.09053	+	0.377779i
$651$		0			0
$652$	311.127	−	311.127i	0.477188	−	0.477188i
$653$	−379.091	−	379.091i	−0.580537	−	0.580537i	0.354514	−	0.935051i	$-0.384646\pi$
$653$	−379.091	−	379.091i	−0.580537	−	0.580537i	−0.935051	+	0.354514i	$0.884646\pi$
$654$		0			0
$655$	−779.038	−	131.114i	−1.18937	−	0.200174i
$656$	−212.359			−0.323718
$657$		0			0
$658$	−35.1413	−	35.1413i	−0.0534062	−	0.0534062i
$659$		−	932.566i		−	1.41512i	−0.706652	−	0.707561i	$-0.749795\pi$
$659$		−	932.566i		−	1.41512i	0.706652	−	0.707561i	$-0.250205\pi$
$660$		0			0
$661$	435.268			0.658500			0.329250	−	0.944243i	$-0.393204\pi$
$661$	435.268			0.658500			0.329250	+	0.944243i	$0.393204\pi$
$662$	276.111	−	276.111i	0.417086	−	0.417086i
$663$		0			0
$664$			72.9459i			0.109858i
$665$	133.504	+	187.536i	0.200758	+	0.282009i
$666$		0			0
$667$	−498.983	+	498.983i	−0.748100	+	0.748100i
$668$	152.158	+	152.158i	0.227781	+	0.227781i
$669$		0			0
$670$	47.2860	−	280.958i	0.0705761	−	0.419340i
$671$	−9.62948			−0.0143509
$672$		0			0
$673$	268.394	+	268.394i	0.398803	+	0.398803i	0.877811	−	0.479008i	$-0.159003\pi$
$673$	268.394	+	268.394i	0.398803	+	0.398803i	−0.479008	+	0.877811i	$0.659003\pi$
$674$		−	552.786i		−	0.820157i
$675$		0			0
$676$	562.414			0.831973
$677$	317.565	−	317.565i	0.469076	−	0.469076i	−0.432539	−	0.901615i	$-0.642382\pi$
$677$	317.565	−	317.565i	0.469076	−	0.469076i	0.901615	+	0.432539i	$0.142382\pi$
$678$		0			0
$679$			342.393i			0.504261i
$680$	−94.4361	−	15.8938i	−0.138877	−	0.0233733i
$681$		0			0
$682$	−155.303	+	155.303i	−0.227718	+	0.227718i
$683$	−750.781	−	750.781i	−1.09924	−	1.09924i	−0.994500	−	0.104741i	$-0.966599\pi$
$683$	−750.781	−	750.781i	−1.09924	−	1.09924i	−0.104741	−	0.994500i	$-0.533401\pi$
$684$		0			0
$685$	212.893	−	151.555i	0.310793	−	0.221249i
$686$	−26.1916			−0.0381802
$687$		0			0
$688$	−148.421	−	148.421i	−0.215728	−	0.215728i
$689$		−	1317.29i		−	1.91189i
$690$		0			0
$691$	−630.352			−0.912231			−0.456116	−	0.889921i	$-0.650760\pi$
$691$	−630.352			−0.912231			−0.456116	+	0.889921i	$0.650760\pi$
$692$	−57.8647	+	57.8647i	−0.0836194	+	0.0836194i
$693$		0			0
$694$		−	316.168i		−	0.455573i
$695$	−109.691	+	651.751i	−0.157829	+	0.937771i
$696$		0			0
$697$	254.205	−	254.205i	0.364712	−	0.364712i
$698$	−452.412	−	452.412i	−0.648155	−	0.648155i
$699$		0			0
$700$	−57.7689	−	119.007i	−0.0825270	−	0.170011i
$701$	1143.23			1.63085			0.815425	−	0.578863i	$-0.196503\pi$
$701$	1143.23			1.63085			0.815425	+	0.578863i	$0.196503\pi$
$702$		0			0
$703$	197.753	+	197.753i	0.281299	+	0.281299i
$704$			45.9937i			0.0653320i
$705$		0			0
$706$	−963.362			−1.36453
$707$	342.090	−	342.090i	0.483862	−	0.483862i
$708$		0			0
$709$		−	120.909i		−	0.170535i	−0.996358	−	0.0852674i	$-0.972826\pi$
$709$		−	120.909i		−	0.170535i	0.996358	−	0.0852674i	$-0.0271745\pi$
$710$	−271.918	+	193.575i	−0.382983	+	0.272640i
$711$		0			0
$712$	−349.351	+	349.351i	−0.490661	+	0.490661i
$713$	357.276	+	357.276i	0.501089	+	0.501089i
$714$		0			0
$715$	353.728	+	496.889i	0.494725	+	0.694950i
$716$	−253.698			−0.354327
$717$		0			0
$718$	485.514	+	485.514i	0.676203	+	0.676203i
$719$		−	157.658i		−	0.219274i	−0.993972	−	0.109637i	$-0.965031\pi$
$719$		−	157.658i		−	0.219274i	0.993972	−	0.109637i	$-0.0349688\pi$
$720$		0			0
$721$	−174.446			−0.241950
$722$	58.1823	−	58.1823i	0.0805849	−	0.0805849i
$723$		0			0
$724$		−	615.362i		−	0.849947i
$725$	308.734	−	891.217i	0.425839	−	1.22926i
$726$		0			0
$727$	45.5944	−	45.5944i	0.0627159	−	0.0627159i	−0.675053	−	0.737769i	$-0.735879\pi$
$727$	45.5944	−	45.5944i	0.0627159	−	0.0627159i	0.737769	+	0.675053i	$0.235879\pi$
$728$	−112.276	−	112.276i	−0.154225	−	0.154225i
$729$		0			0
$730$	−307.743	−	51.7940i	−0.421566	−	0.0709507i
$731$	355.335			0.486095
$732$		0			0
$733$	5.02444	+	5.02444i	0.00685462	+	0.00685462i	0.710526	−	0.703671i	$-0.248457\pi$
$733$	5.02444	+	5.02444i	0.00685462	+	0.00685462i	−0.703671	+	0.710526i	$0.748457\pi$
$734$		−	410.663i		−	0.559486i
$735$		0			0
$736$	105.809			0.143762
$737$	163.801	−	163.801i	0.222253	−	0.222253i
$738$		0			0
$739$			1207.29i			1.63368i	0.576865	+	0.816839i	$0.304276\pi$
$739$			1207.29i			1.63368i	−0.576865	+	0.816839i	$0.695724\pi$
$740$	−93.2037	−	130.925i	−0.125951	−	0.176926i
$741$		0			0
$742$	−164.257	+	164.257i	−0.221371	+	0.221371i
$743$	162.402	+	162.402i	0.218577	+	0.218577i	0.807898	−	0.589322i	$-0.200605\pi$
$743$	162.402	+	162.402i	0.218577	+	0.218577i	−0.589322	+	0.807898i	$0.700605\pi$
$744$		0			0
$745$	−211.883	+	1258.94i	−0.284407	+	1.68985i
$746$	−49.9606			−0.0669714
$747$		0			0
$748$	−55.0569	−	55.0569i	−0.0736055	−	0.0736055i
$749$			215.389i			0.287569i
$750$		0			0
$751$	−1054.43			−1.40404			−0.702020	−	0.712157i	$-0.747718\pi$
$751$	−1054.43			−1.40404			−0.702020	+	0.712157i	$0.747718\pi$
$752$	−37.5676	+	37.5676i	−0.0499569	+	0.0499569i
$753$		0			0
$754$		−	1132.07i		−	1.50142i
$755$	−1038.02	−	174.701i	−1.37486	−	0.231393i
$756$		0			0
$757$	166.416	−	166.416i	0.219836	−	0.219836i	−0.588593	−	0.808429i	$-0.700318\pi$
$757$	166.416	−	166.416i	0.219836	−	0.219836i	0.808429	+	0.588593i	$0.200318\pi$
$758$	356.423	+	356.423i	0.470215	+	0.470215i
$759$		0			0
$760$	200.484	−	142.722i	0.263795	−	0.187792i
$761$	−1422.52			−1.86928			−0.934640	−	0.355596i	$-0.884278\pi$
$761$	−1422.52			−1.86928			−0.934640	+	0.355596i	$0.884278\pi$
$762$		0			0
$763$	383.996	+	383.996i	0.503271	+	0.503271i
$764$			142.994i			0.187165i
$765$		0			0
$766$	−961.354			−1.25503
$767$	−944.758	+	944.758i	−1.23176	+	1.23176i
$768$		0			0
$769$			502.250i			0.653121i	0.945176	+	0.326560i	$0.105890\pi$
$769$			502.250i			0.653121i	−0.945176	+	0.326560i	$0.894110\pi$
$770$	17.8512	−	106.066i	0.0231834	−	0.137748i
$771$		0			0
$772$	−310.695	+	310.695i	−0.402454	+	0.402454i
$773$	339.873	+	339.873i	0.439681	+	0.439681i	0.891904	−	0.452224i	$-0.149369\pi$
$773$	339.873	+	339.873i	0.439681	+	0.439681i	−0.452224	+	0.891904i	$0.649369\pi$
$774$		0			0
$775$	−638.120	−	221.056i	−0.823380	−	0.285234i
$776$	366.033			0.471693
$777$		0			0
$778$	−169.784	−	169.784i	−0.218231	−	0.218231i
$779$			923.848i			1.18594i
$780$		0			0
$781$	−271.386			−0.347485
$782$	−126.659	+	126.659i	−0.161968	+	0.161968i
$783$		0			0
$784$			28.0000i			0.0357143i
$785$	−1046.52	+	744.999i	−1.33314	+	0.949043i
$786$		0			0
$787$	752.550	−	752.550i	0.956227	−	0.956227i	−0.0428547	−	0.999081i	$-0.513645\pi$
$787$	752.550	−	752.550i	0.956227	−	0.956227i	0.999081	+	0.0428547i	$0.0136452\pi$
$788$	381.040	+	381.040i	0.483553	+	0.483553i
$789$		0			0
$790$	−439.335	−	617.143i	−0.556120	−	0.781193i
$791$	−121.992			−0.154225
$792$		0			0
$793$	−25.1296	−	25.1296i	−0.0316892	−	0.0316892i
$794$			132.242i			0.166551i
$795$		0			0
$796$	−346.492			−0.435291
$797$	182.962	−	182.962i	0.229564	−	0.229564i	−0.582947	−	0.812511i	$-0.698100\pi$
$797$	182.962	−	182.962i	0.229564	−	0.229564i	0.812511	+	0.582947i	$0.198100\pi$
$798$		0			0
$799$		−	89.9408i		−	0.112567i
$800$	−127.224	+	61.7575i	−0.159030	+	0.0771969i
$801$		0			0
$802$	213.860	−	213.860i	0.266659	−	0.266659i
$803$	−179.417	−	179.417i	−0.223433	−	0.223433i
$804$		0			0
$805$	−244.006	−	41.0669i	−0.303113	−	0.0510148i
$806$	−810.575			−1.00568
$807$		0			0
$808$	−365.710	−	365.710i	−0.452611	−	0.452611i
$809$		−	508.611i		−	0.628690i	−0.949309	−	0.314345i	$-0.898215\pi$
$809$		−	508.611i		−	0.628690i	0.949309	−	0.314345i	$-0.101785\pi$
$810$		0			0
$811$	−768.233			−0.947267			−0.473633	−	0.880722i	$-0.657058\pi$
$811$	−768.233			−0.947267			−0.473633	+	0.880722i	$0.657058\pi$
$812$	−141.162	+	141.162i	−0.173845	+	0.173845i
$813$		0			0
$814$		−	130.669i		−	0.160527i
$815$	637.936	+	896.122i	0.782744	+	1.09954i
$816$		0			0
$817$	−645.693	+	645.693i	−0.790321	+	0.790321i
$818$	300.366	+	300.366i	0.367196	+	0.367196i
$819$		0			0
$820$	88.1122	−	523.534i	0.107454	−	0.638456i
$821$	−103.940			−0.126602			−0.0633011	−	0.997994i	$-0.520163\pi$
$821$	−103.940			−0.126602			−0.0633011	+	0.997994i	$0.520163\pi$
$822$		0			0
$823$	353.698	+	353.698i	0.429767	+	0.429767i	0.888549	−	0.458782i	$-0.151714\pi$
$823$	353.698	+	353.698i	0.429767	+	0.429767i	−0.458782	+	0.888549i	$0.651714\pi$
$824$			186.490i			0.226323i
$825$		0			0
$826$	235.610			0.285242
$827$	−57.1544	+	57.1544i	−0.0691105	+	0.0691105i	−0.740817	−	0.671707i	$-0.765562\pi$
$827$	−57.1544	+	57.1544i	−0.0691105	+	0.0691105i	0.671707	+	0.740817i	$0.265562\pi$
$828$		0			0
$829$			260.205i			0.313878i	0.987608	+	0.156939i	$0.0501626\pi$
$829$			260.205i			0.313878i	−0.987608	+	0.156939i	$0.949837\pi$
$830$	−179.835	−	30.2668i	−0.216669	−	0.0364660i
$831$		0			0
$832$	−120.028	+	120.028i	−0.144264	+	0.144264i
$833$	−33.5175	−	33.5175i	−0.0402371	−	0.0402371i
$834$		0			0
$835$	−438.252	+	311.985i	−0.524852	+	0.373635i
$836$	200.092			0.239344
$837$		0			0
$838$	696.907	+	696.907i	0.831632	+	0.831632i
$839$			742.004i			0.884391i	0.896919	+	0.442196i	$0.145800\pi$
$839$			742.004i			0.884391i	−0.896919	+	0.442196i	$0.854200\pi$
$840$		0			0
$841$	−582.334			−0.692430
$842$	−114.980	+	114.980i	−0.136555	+	0.136555i
$843$		0			0
$844$		−	107.839i		−	0.127771i
$845$	−233.357	+	1386.53i	−0.276163	+	1.64087i
$846$		0			0
$847$	−164.533	+	164.533i	−0.194254	+	0.194254i
$848$	175.598	+	175.598i	0.207073	+	0.207073i
$849$		0			0
$850$	78.3671	−	226.221i	0.0921966	−	0.266143i
$851$	−300.604			−0.353236
$852$		0			0
$853$	876.382	+	876.382i	1.02741	+	1.02741i	0.999614	+	0.0277980i	$0.00884953\pi$
$853$	876.382	+	876.382i	1.02741	+	1.02741i	0.0277980	+	0.999614i	$0.491150\pi$
$854$			6.26698i			0.00733838i
$855$		0			0
$856$	230.261			0.268996
$857$	−953.370	+	953.370i	−1.11245	+	1.11245i	−0.119632	+	0.992818i	$0.538172\pi$
$857$	−953.370	+	953.370i	−1.11245	+	1.11245i	−0.992818	+	0.119632i	$0.961828\pi$
$858$		0			0
$859$		−	808.979i		−	0.941768i	−0.882195	−	0.470884i	$-0.843935\pi$
$859$		−	808.979i		−	0.941768i	0.882195	−	0.470884i	$-0.156065\pi$
$860$	427.489	−	304.323i	0.497080	−	0.353864i
$861$		0			0
$862$	724.694	−	724.694i	0.840713	−	0.840713i
$863$	−315.788	−	315.788i	−0.365919	−	0.365919i	0.500068	−	0.865986i	$-0.333308\pi$
$863$	−315.788	−	315.788i	−0.365919	−	0.365919i	−0.865986	+	0.500068i	$0.833308\pi$
$864$		0			0
$865$	−118.646	−	166.665i	−0.137163	−	0.192676i
$866$	200.655			0.231703
$867$		0			0
$868$	101.073	+	101.073i	0.116444	+	0.116444i
$869$		−	615.934i		−	0.708785i
$870$		0			0
$871$	854.925			0.981544
$872$	410.509	−	410.509i	0.470767	−	0.470767i
$873$		0			0
$874$		−	460.312i		−	0.526673i
$875$	317.362	−	93.0405i	0.362699	−	0.106332i
$876$		0			0
$877$	−291.014	+	291.014i	−0.331829	+	0.331829i	−0.853281	−	0.521452i	$-0.825391\pi$
$877$	−291.014	+	291.014i	−0.331829	+	0.331829i	0.521452	+	0.853281i	$0.325391\pi$
$878$	−685.890	−	685.890i	−0.781195	−	0.781195i
$879$		0			0
$880$	−113.390	−	19.0838i	−0.128852	−	0.0216861i
$881$	−368.877			−0.418702			−0.209351	−	0.977841i	$-0.567135\pi$
$881$	−368.877			−0.418702			−0.209351	+	0.977841i	$0.567135\pi$
$882$		0			0
$883$	1221.90	+	1221.90i	1.38380	+	1.38380i	0.837758	+	0.546042i	$0.183866\pi$
$883$	1221.90	+	1221.90i	1.38380	+	1.38380i	0.546042	+	0.837758i	$0.316134\pi$
$884$		−	287.359i		−	0.325066i
$885$		0			0
$886$	−679.505			−0.766935
$887$	−67.8606	+	67.8606i	−0.0765058	+	0.0765058i	−0.744324	−	0.667818i	$-0.767228\pi$
$887$	−67.8606	+	67.8606i	−0.0765058	+	0.0765058i	0.667818	+	0.744324i	$0.267228\pi$
$888$		0			0
$889$			388.142i			0.436606i
$890$	−716.311	−	1006.22i	−0.804844	−	1.13058i
$891$		0			0
$892$	−293.025	+	293.025i	−0.328503	+	0.328503i
$893$	163.435	+	163.435i	0.183018	+	0.183018i
$894$		0			0
$895$	105.265	−	625.448i	0.117614	−	0.698825i
$896$	29.9333			0.0334077
$897$		0			0
$898$	226.637	+	226.637i	0.252379	+	0.252379i
$899$			1019.12i			1.13362i
$900$		0			0
$901$	−420.401			−0.466594
$902$	305.224	−	305.224i	0.338386	−	0.338386i
$903$		0			0
$904$			130.415i			0.144264i
$905$	1517.07	+	255.327i	1.67632	+	0.282129i
$906$		0			0
$907$	−144.428	+	144.428i	−0.159237	+	0.159237i	−0.782229	−	0.622991i	$-0.785917\pi$
$907$	−144.428	+	144.428i	−0.159237	+	0.159237i	0.622991	+	0.782229i	$0.285917\pi$
$908$	325.794	+	325.794i	0.358804	+	0.358804i
$909$		0			0
$910$	323.381	−	230.210i	0.355364	−	0.252978i
$911$	−423.332			−0.464689			−0.232345	−	0.972634i	$-0.574640\pi$
$911$	−423.332			−0.464689			−0.232345	+	0.972634i	$0.574640\pi$
$912$		0			0
$913$	−104.845	−	104.845i	−0.114836	−	0.114836i
$914$			532.565i			0.582675i
$915$		0			0
$916$	−352.417			−0.384735
$917$	−295.589	+	295.589i	−0.322343	+	0.322343i
$918$		0			0
$919$		−	1289.08i		−	1.40269i	−0.712820	−	0.701347i	$-0.752582\pi$
$919$		−	1289.08i		−	1.40269i	0.712820	−	0.701347i	$-0.247418\pi$
$920$	−43.9023	+	260.853i	−0.0477199	+	0.283536i
$921$		0			0
$922$	121.199	−	121.199i	0.131453	−	0.131453i
$923$	−708.222	−	708.222i	−0.767304	−	0.767304i
$924$		0			0
$925$	361.446	−	175.454i	0.390752	−	0.189680i
$926$	−1131.21			−1.22161
$927$		0			0
$928$	150.908	+	150.908i	0.162617	+	0.162617i
$929$			749.538i			0.806823i	0.915019	+	0.403411i	$0.132176\pi$
$929$			749.538i			0.806823i	−0.915019	+	0.403411i	$0.867824\pi$
$930$		0			0
$931$	121.812			0.130840
$932$	36.7231	−	36.7231i	0.0394025	−	0.0394025i
$933$		0			0
$934$		−	559.072i		−	0.598578i
$935$	158.578	−	112.889i	0.169602	−	0.120737i
$936$		0			0
$937$	−208.580	+	208.580i	−0.222605	+	0.222605i	−0.809594	−	0.586990i	$-0.800313\pi$
$937$	−208.580	+	208.580i	−0.222605	+	0.222605i	0.586990	+	0.809594i	$0.300313\pi$
$938$	−106.603	−	106.603i	−0.113650	−	0.113650i
$939$		0			0
$940$	−77.0289	−	108.204i	−0.0819456	−	0.115111i
$941$	1017.80			1.08161			0.540807	−	0.841147i	$-0.318119\pi$
$941$	1017.80			1.08161			0.540807	+	0.841147i	$0.318119\pi$
$942$		0			0
$943$	−702.170	−	702.170i	−0.744613	−	0.744613i
$944$		−	251.877i		−	0.266819i
$945$		0			0
$946$	426.652			0.451006
$947$	−288.192	+	288.192i	−0.304321	+	0.304321i	−0.842702	−	0.538381i	$-0.819036\pi$
$947$	−288.192	+	288.192i	−0.304321	+	0.304321i	0.538381	+	0.842702i	$0.319036\pi$
$948$		0			0
$949$		−	936.429i		−	0.986753i
$950$	268.671	+	553.478i	0.282811	+	0.582609i
$951$		0			0
$952$	−35.8317	+	35.8317i	−0.0376383	+	0.0376383i
$953$	450.504	+	450.504i	0.472722	+	0.472722i	0.902794	−	0.430072i	$-0.141512\pi$
$953$	450.504	+	450.504i	0.472722	+	0.472722i	−0.430072	+	0.902794i	$0.641512\pi$
$954$		0			0
$955$	−352.527	−	59.3312i	−0.369138	−	0.0621269i
$956$	550.187			0.575509
$957$		0			0
$958$	101.987	+	101.987i	0.106458	+	0.106458i
$959$		−	138.282i		−	0.144194i
$960$		0			0
$961$	−231.300			−0.240687
$962$	341.000	−	341.000i	0.354470	−	0.354470i
$963$		0			0
$964$		−	677.850i		−	0.703164i
$965$	−637.050	−	894.878i	−0.660155	−	0.927334i
$966$		0			0
$967$	824.848	−	824.848i	0.852997	−	0.852997i	−0.137505	−	0.990501i	$-0.543908\pi$
$967$	824.848	−	824.848i	0.852997	−	0.852997i	0.990501	+	0.137505i	$0.0439082\pi$
$968$	175.893	+	175.893i	0.181708	+	0.181708i
$969$		0			0
$970$	−151.875	+	902.392i	−0.156572	+	0.930301i
$971$	770.810			0.793831			0.396916	−	0.917855i	$-0.370081\pi$
$971$	770.810			0.793831			0.396916	+	0.917855i	$0.370081\pi$
$972$		0			0
$973$	247.293	+	247.293i	0.254155	+	0.254155i
$974$		−	500.545i		−	0.513907i
$975$		0			0
$976$	6.69968			0.00686442
$977$	−126.844	+	126.844i	−0.129830	+	0.129830i	−0.769036	−	0.639206i	$-0.779263\pi$
$977$	−126.844	+	126.844i	−0.129830	+	0.129830i	0.639206	+	0.769036i	$0.279263\pi$
$978$		0			0
$979$		−	1004.25i		−	1.02579i
$980$	−69.0292	−	11.6178i	−0.0704379	−	0.0118549i
$981$		0			0
$982$	648.021	−	648.021i	0.659899	−	0.659899i
$983$	1168.93	+	1168.93i	1.18914	+	1.18914i	0.977305	+	0.211839i	$0.0679451\pi$
$983$	1168.93	+	1168.93i	1.18914	+	1.18914i	0.211839	+	0.977305i	$0.432055\pi$
$984$		0			0
$985$	−1097.49	+	781.287i	−1.11420	+	0.793185i
$986$	−361.291			−0.366421
$987$		0			0
$988$	522.170	+	522.170i	0.528512	+	0.528512i
$989$		−	981.515i		−	0.992432i
$990$		0			0
$991$	1475.28			1.48868			0.744339	−	0.667802i	$-0.232765\pi$
$991$	1475.28			1.48868			0.744339	+	0.667802i	$0.232765\pi$
$992$	108.052	−	108.052i	0.108923	−	0.108923i
$993$		0			0
$994$			176.621i			0.177687i
$995$	143.767	−	854.215i	0.144489	−	0.858508i
$996$		0			0
$997$	−997.648	+	997.648i	−1.00065	+	1.00065i	−0.000649790		1.00000i	$0.500207\pi$
$997$	−997.648	+	997.648i	−1.00065	+	1.00065i	−1.00000		0.000649790i	$0.999793\pi$
$998$	−377.798	−	377.798i	−0.378555	−	0.378555i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	630.3.o.f.253.8		16
3.2	odd	2		210.3.l.b.43.1	✓	16
5.2	odd	4	inner	630.3.o.f.127.8		16
15.2	even	4		210.3.l.b.127.1	yes	16
15.8	even	4		1050.3.l.h.757.6		16
15.14	odd	2		1050.3.l.h.43.6		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.3.l.b.43.1	✓	16	3.2	odd	2
210.3.l.b.127.1	yes	16	15.2	even	4
630.3.o.f.127.8		16	5.2	odd	4	inner
630.3.o.f.253.8		16	1.1	even	1	trivial
1050.3.l.h.43.6		16	15.14	odd	2
1050.3.l.h.757.6		16	15.8	even	4

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:	\( N \)	\(=\)	\( 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	630.o (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.00000 - 1.00000i) q^{2} -2.00000i q^{4} +(4.93066 + 0.829843i) q^{5} +(1.87083 - 1.87083i) q^{7} +(-2.00000 - 2.00000i) q^{8} +O(q^{10})\)	\(q+(1.00000 - 1.00000i) q^{2} -2.00000i q^{4} +(4.93066 + 0.829843i) q^{5} +(1.87083 - 1.87083i) q^{7} +(-2.00000 - 2.00000i) q^{8} +(5.76050 - 4.10081i) q^{10} +5.74922 q^{11} +(15.0034 + 15.0034i) q^{13} -3.74166i q^{14} -4.00000 q^{16} +(4.78821 - 4.78821i) q^{17} +17.4017i q^{19} +(1.65969 - 9.86131i) q^{20} +(5.74922 - 5.74922i) q^{22} +(-13.2261 - 13.2261i) q^{23} +(23.6227 + 8.18334i) q^{25} +30.0069 q^{26} +(-3.74166 - 3.74166i) q^{28} -37.7271i q^{29} -27.0130 q^{31} +(-4.00000 + 4.00000i) q^{32} -9.57642i q^{34} +(10.7769 - 7.67192i) q^{35} +(11.3640 - 11.3640i) q^{37} +(17.4017 + 17.4017i) q^{38} +(-8.20163 - 11.5210i) q^{40} +53.0897 q^{41} +(37.1052 + 37.1052i) q^{43} -11.4984i q^{44} -26.4522 q^{46} +(9.39190 - 9.39190i) q^{47} -7.00000i q^{49} +(31.8061 - 15.4394i) q^{50} +(30.0069 - 30.0069i) q^{52} +(-43.8996 - 43.8996i) q^{53} +(28.3474 + 4.77095i) q^{55} -7.48331 q^{56} +(-37.7271 - 37.7271i) q^{58} +62.9694i q^{59} -1.67492 q^{61} +(-27.0130 + 27.0130i) q^{62} +8.00000i q^{64} +(61.5263 + 86.4273i) q^{65} +(28.4909 - 28.4909i) q^{67} +(-9.57642 - 9.57642i) q^{68} +(3.10499 - 18.4488i) q^{70} -47.2039 q^{71} +(-31.2071 - 31.2071i) q^{73} -22.7281i q^{74} +34.8033 q^{76} +(10.7558 - 10.7558i) q^{77} -107.134i q^{79} +(-19.7226 - 3.31937i) q^{80} +(53.0897 - 53.0897i) q^{82} +(-18.2365 - 18.2365i) q^{83} +(27.5825 - 19.6356i) q^{85} +74.2105 q^{86} +(-11.4984 - 11.4984i) q^{88} -174.675i q^{89} +56.1378 q^{91} +(-26.4522 + 26.4522i) q^{92} -18.7838i q^{94} +(-14.4406 + 85.8016i) q^{95} +(-91.5084 + 91.5084i) q^{97} +(-7.00000 - 7.00000i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 16 q^{2} + 16 q^{5} - 32 q^{8}+O(q^{10}) \) 16 * q + 16 * q^2 + 16 * q^5 - 32 * q^8	\( 16 q + 16 q^{2} + 16 q^{5} - 32 q^{8} + 24 q^{10} - 8 q^{11} - 32 q^{13} - 64 q^{16} - 56 q^{17} + 16 q^{20} - 8 q^{22} - 24 q^{23} + 40 q^{25} - 64 q^{26} - 112 q^{31} - 64 q^{32} - 28 q^{35} - 152 q^{37} - 16 q^{40} - 48 q^{46} - 80 q^{47} + 72 q^{50} - 64 q^{52} - 48 q^{53} - 24 q^{55} + 96 q^{58} + 96 q^{61} - 112 q^{62} - 16 q^{65} - 80 q^{67} + 112 q^{68} - 536 q^{71} + 168 q^{77} - 64 q^{80} + 256 q^{83} + 40 q^{85} + 16 q^{88} - 48 q^{92} - 360 q^{95} + 688 q^{97} - 112 q^{98}+O(q^{100}) \) 16 * q + 16 * q^2 + 16 * q^5 - 32 * q^8 + 24 * q^10 - 8 * q^11 - 32 * q^13 - 64 * q^16 - 56 * q^17 + 16 * q^20 - 8 * q^22 - 24 * q^23 + 40 * q^25 - 64 * q^26 - 112 * q^31 - 64 * q^32 - 28 * q^35 - 152 * q^37 - 16 * q^40 - 48 * q^46 - 80 * q^47 + 72 * q^50 - 64 * q^52 - 48 * q^53 - 24 * q^55 + 96 * q^58 + 96 * q^61 - 112 * q^62 - 16 * q^65 - 80 * q^67 + 112 * q^68 - 536 * q^71 + 168 * q^77 - 64 * q^80 + 256 * q^83 + 40 * q^85 + 16 * q^88 - 48 * q^92 - 360 * q^95 + 688 * q^97 - 112 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more