LMFDB - Embedded newform 630.3.o.f.127.8

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			127.8
Root			$0.170157 + 0.170157i$ of defining polynomial
Character	$\chi$	$=$	630.127
Dual form			630.3.o.f.253.8

$q$-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 $\left(\mathbb{Z}/630\mathbb{Z}\right)^\times$.

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

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	0.168391	−	0.985720i	$-0.446143\pi$
$13$	15.0034	−	15.0034i	1.15411	−	1.15411i	0.985720	−	0.168391i	$-0.0538571\pi$
$14$			3.74166i			0.267261i
$15$		0			0
$16$	−4.00000			−0.250000
$17$	4.78821	+	4.78821i	0.281659	+	0.281659i	0.833771	−	0.552111i	$-0.186178\pi$
$17$	4.78821	+	4.78821i	0.281659	+	0.281659i	−0.552111	+	0.833771i	$0.686178\pi$
$18$		0			0
$19$		−	17.4017i		−	0.915877i	−0.888984	−	0.457938i	$-0.848588\pi$
$19$		−	17.4017i		−	0.915877i	0.888984	−	0.457938i	$-0.151412\pi$
$20$	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	−0.933535	−	0.358487i	$-0.883293\pi$
$23$	−13.2261	+	13.2261i	−0.575048	+	0.575048i	0.358487	+	0.933535i	$0.383293\pi$
$24$		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	$0.225427\pi$
$29$			37.7271i			1.30093i	−0.759534	+	0.650467i	$0.774573\pi$
$30$		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	0.843798	−	0.536661i	$-0.180315\pi$
$37$	11.3640	+	11.3640i	0.307136	+	0.307136i	−0.536661	+	0.843798i	$0.680315\pi$
$38$	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	−0.128763	−	0.991675i	$-0.541101\pi$
$43$	37.1052	−	37.1052i	0.862912	−	0.862912i	0.991675	+	0.128763i	$0.0411007\pi$
$44$			11.4984i			0.261328i
$45$		0			0
$46$	−26.4522			−0.575048
$47$	9.39190	+	9.39190i	0.199828	+	0.199828i	0.799926	−	0.600098i	$-0.204872\pi$
$47$	9.39190	+	9.39190i	0.199828	+	0.199828i	−0.600098	+	0.799926i	$0.704872\pi$
$48$		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	−0.987281	−	0.158987i	$-0.949177\pi$
$53$	−43.8996	+	43.8996i	−0.828294	+	0.828294i	0.158987	+	0.987281i	$0.449177\pi$
$54$		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	$-0.820824\pi$
$59$		−	62.9694i		−	1.06728i	0.845713	−	0.533639i	$-0.179176\pi$
$60$		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	0.887003	−	0.461765i	$-0.152784\pi$
$67$	28.4909	+	28.4909i	0.425238	+	0.425238i	−0.461765	+	0.887003i	$0.652784\pi$
$68$	−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	−0.887774	−	0.460279i	$-0.847749\pi$
$73$	−31.2071	+	31.2071i	−0.427495	+	0.427495i	0.460279	+	0.887774i	$0.347749\pi$
$74$			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	$0.237179\pi$
$79$			107.134i			1.35612i	−0.735006	+	0.678061i	$0.762821\pi$
$80$	−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	−0.808379	−	0.588662i	$-0.799655\pi$
$83$	−18.2365	+	18.2365i	−0.219716	+	0.219716i	0.588662	+	0.808379i	$0.299655\pi$
$84$		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	$0.438383\pi$
$89$			174.675i			1.96265i	−0.192368	+	0.981323i	$0.561617\pi$
$90$		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	0.0550959	−	0.998481i	$-0.482454\pi$
$97$	−91.5084	−	91.5084i	−0.943385	−	0.943385i	−0.998481	+	0.0550959i	$0.982454\pi$
$98$	−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	−0.896232	−	0.443586i	$-0.853706\pi$
$103$	−46.6226	+	46.6226i	−0.452647	+	0.452647i	0.443586	+	0.896232i	$0.353706\pi$
$104$			60.0138i			0.577056i
$105$		0			0
$106$	−87.7991			−0.828294
$107$	−57.5651	−	57.5651i	−0.537992	−	0.537992i	0.384947	−	0.922939i	$-0.374220\pi$
$107$	−57.5651	−	57.5651i	−0.537992	−	0.537992i	−0.922939	+	0.384947i	$0.874220\pi$
$108$		0			0
$109$		−	205.254i		−	1.88307i	−0.336920	−	0.941533i	$-0.609385\pi$
$109$		−	205.254i		−	1.88307i	0.336920	−	0.941533i	$-0.390615\pi$
$110$	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	−0.836498	−	0.547970i	$-0.815401\pi$
$113$	−32.6037	+	32.6037i	−0.288528	+	0.288528i	0.547970	+	0.836498i	$0.315401\pi$
$114$		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	0.168831	−	0.985645i	$-0.446001\pi$
$127$	−103.735	−	103.735i	−0.816814	−	0.816814i	−0.985645	+	0.168831i	$0.946001\pi$
$128$	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	0.829004	−	0.559242i	$-0.188908\pi$
$137$	36.9574	+	36.9574i	0.269762	+	0.269762i	−0.559242	+	0.829004i	$0.688908\pi$
$138$		0			0
$139$		−	132.183i		−	0.950960i	−0.879727	−	0.475480i	$-0.842274\pi$
$139$		−	132.183i		−	0.950960i	0.879727	−	0.475480i	$-0.157726\pi$
$140$	−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	$-0.672444\pi$
$149$		−	255.329i		−	1.71362i	0.515634	−	0.856809i	$-0.327556\pi$
$150$		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	−0.985088	−	0.172052i	$-0.944960\pi$
$157$	−181.671	−	181.671i	−1.15714	−	1.15714i	−0.172052	−	0.985088i	$-0.555040\pi$
$158$	−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	−0.0446274	−	0.999004i	$-0.514210\pi$
$163$	155.563	−	155.563i	0.954376	−	0.954376i	0.999004	+	0.0446274i	$0.0142101\pi$
$164$			106.179i			0.647435i
$165$		0			0
$166$	−36.4729			−0.219716
$167$	−76.0788	−	76.0788i	−0.455562	−	0.455562i	0.441634	−	0.897195i	$-0.354399\pi$
$167$	−76.0788	−	76.0788i	−0.455562	−	0.455562i	−0.897195	+	0.441634i	$0.854399\pi$
$168$		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	−0.785765	−	0.618526i	$-0.787730\pi$
$173$	−28.9323	+	28.9323i	−0.167239	+	0.167239i	0.618526	+	0.785765i	$0.287730\pi$
$174$		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	$0.115290\pi$
$179$			126.849i			0.708653i	−0.935122	+	0.354327i	$0.884710\pi$
$180$		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	−0.983858	−	0.178950i	$-0.942730\pi$
$193$	−155.347	+	155.347i	−0.804908	+	0.804908i	0.178950	+	0.983858i	$0.442730\pi$
$194$		−	183.017i		−	0.943385i
$195$		0			0
$196$	−14.0000			−0.0714286
$197$	−190.520	−	190.520i	−0.967107	−	0.967107i	0.0323691	−	0.999476i	$-0.489695\pi$
$197$	−190.520	−	190.520i	−0.967107	−	0.967107i	−0.999476	+	0.0323691i	$0.989695\pi$
$198$		0			0
$199$			173.246i			0.870582i	0.900290	+	0.435291i	$0.143354\pi$
$199$			173.246i			0.870582i	−0.900290	+	0.435291i	$0.856646\pi$
$200$	−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	−0.954671	−	0.297664i	$-0.903792\pi$
$223$	−146.512	+	146.512i	−0.657006	+	0.657006i	0.297664	+	0.954671i	$0.403792\pi$
$224$		−	14.9666i		−	0.0668153i
$225$		0			0
$226$	−65.2073			−0.288528
$227$	−162.897	−	162.897i	−0.717607	−	0.717607i	0.250508	−	0.968115i	$-0.419402\pi$
$227$	−162.897	−	162.897i	−0.717607	−	0.717607i	−0.968115	+	0.250508i	$0.919402\pi$
$228$		0			0
$229$			176.209i			0.769470i	0.923027	+	0.384735i	$0.125707\pi$
$229$			176.209i			0.769470i	−0.923027	+	0.384735i	$0.874293\pi$
$230$	−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	−0.666606	−	0.745411i	$-0.732253\pi$
$233$	18.3615	−	18.3615i	0.0788049	−	0.0788049i	0.745411	+	0.666606i	$0.232253\pi$
$234$		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	$-0.804804\pi$
$239$		−	275.093i		−	1.15102i	0.817795	−	0.575509i	$-0.195196\pi$
$240$		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	0.730492	−	0.682921i	$-0.239291\pi$
$257$	12.2256	+	12.2256i	0.0475703	+	0.0475703i	−0.682921	+	0.730492i	$0.739291\pi$
$258$		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	−0.0496495	+	0.998767i	$0.515810\pi$
$263$	−275.733	+	275.733i	−1.04842	+	1.04842i	−0.998767	+	0.0496495i	$0.984190\pi$
$264$		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	$0.171462\pi$
$269$			275.988i			1.02598i	−0.858395	+	0.512989i	$0.828538\pi$
$270$		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	0.667294	−	0.744794i	$-0.267452\pi$
$277$	−21.4676	−	21.4676i	−0.0775005	−	0.0775005i	−0.744794	+	0.667294i	$0.767452\pi$
$278$	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	−0.150937	+	0.988543i	$0.548229\pi$
$283$	−322.473	+	322.473i	−1.13948	+	1.13948i	−0.988543	+	0.150937i	$0.951771\pi$
$284$		−	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	−0.413189	−	0.910645i	$-0.635585\pi$
$293$	145.754	−	145.754i	0.497456	−	0.497456i	0.910645	+	0.413189i	$0.135585\pi$
$294$		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	−0.999994	−	0.00360237i	$-0.998853\pi$
$307$	−308.104	−	308.104i	−1.00360	−	1.00360i	−0.00360237	−	0.999994i	$-0.501147\pi$
$308$	−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	−0.687396	−	0.726283i	$-0.741246\pi$
$313$	12.1714	−	12.1714i	0.0388863	−	0.0388863i	0.726283	+	0.687396i	$0.241246\pi$
$314$		−	363.342i		−	1.15714i
$315$		0			0
$316$	−214.267			−0.678061
$317$	−219.192	−	219.192i	−0.691456	−	0.691456i	0.271096	−	0.962552i	$-0.412614\pi$
$317$	−219.192	−	219.192i	−0.691456	−	0.691456i	−0.962552	+	0.271096i	$0.912614\pi$
$318$		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	0.986130	−	0.165973i	$-0.0530766\pi$
$337$	276.393	+	276.393i	0.820157	+	0.820157i	−0.165973	+	0.986130i	$0.553077\pi$
$338$	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	0.897199	−	0.441626i	$-0.145598\pi$
$347$	158.084	+	158.084i	0.455573	+	0.455573i	−0.441626	+	0.897199i	$0.645598\pi$
$348$		0			0
$349$			452.412i			1.29631i	0.761508	+	0.648155i	$0.224459\pi$
$349$			452.412i			1.29631i	−0.761508	+	0.648155i	$0.775541\pi$
$350$	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	−0.496495	+	0.868039i	$0.665380\pi$
$353$	−481.681	+	481.681i	−1.36453	+	1.36453i	−0.868039	+	0.496495i	$0.834620\pi$
$354$		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	$-0.763624\pi$
$359$		−	485.514i		−	1.35241i	0.736716	−	0.676203i	$-0.236376\pi$
$360$		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	0.929161	−	0.369675i	$-0.120531\pi$
$367$	205.331	+	205.331i	0.559486	+	0.559486i	−0.369675	+	0.929161i	$0.620531\pi$
$368$	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	−0.739799	−	0.672828i	$-0.765079\pi$
$373$	−24.9803	+	24.9803i	−0.0669714	+	0.0669714i	0.672828	+	0.739799i	$0.265079\pi$
$374$			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	$-0.844177\pi$
$379$		−	356.423i		−	0.940429i	0.882552	−	0.470215i	$-0.155823\pi$
$380$	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	−0.301596	+	0.953436i	$0.597519\pi$
$383$	−480.677	+	480.677i	−1.25503	+	1.25503i	−0.953436	+	0.301596i	$0.902481\pi$
$384$		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	$0.0700285\pi$
$389$			169.784i			0.436461i	−0.975897	+	0.218231i	$0.929971\pi$
$390$		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	0.618910	−	0.785462i	$-0.287574\pi$
$397$	−66.1208	−	66.1208i	−0.166551	−	0.166551i	−0.785462	+	0.618910i	$0.787574\pi$
$398$	−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	$-0.880318\pi$
$409$		−	300.366i		−	0.734391i	0.930144	−	0.367196i	$-0.119682\pi$
$410$	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	$-0.687407\pi$
$419$		−	696.907i		−	1.66326i	0.555328	−	0.831632i	$-0.312593\pi$
$420$		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	−0.581700	−	0.813403i	$-0.697612\pi$
$433$	100.327	−	100.327i	0.231703	−	0.231703i	0.813403	+	0.581700i	$0.197612\pi$
$434$		−	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	$0.285390\pi$
$439$			685.890i			1.56239i	−0.624286	+	0.781195i	$0.714610\pi$
$440$	−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	−0.977566	−	0.210631i	$-0.932448\pi$
$443$	−339.752	+	339.752i	−0.766935	+	0.766935i	0.210631	+	0.977566i	$0.432448\pi$
$444$		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	$-0.918787\pi$
$449$		−	226.637i		−	0.504758i	0.967628	−	0.252379i	$-0.0812130\pi$
$450$		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	0.352963	−	0.935637i	$-0.385174\pi$
$457$	−266.282	−	266.282i	−0.582675	−	0.582675i	−0.935637	+	0.352963i	$0.885174\pi$
$458$	−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	−0.254547	+	0.967061i	$0.581926\pi$
$463$	−565.604	+	565.604i	−1.22161	+	1.22161i	−0.967061	+	0.254547i	$0.918074\pi$
$464$		−	150.908i		−	0.325234i
$465$		0			0
$466$	36.7231			0.0788049
$467$	279.536	+	279.536i	0.598578	+	0.598578i	0.939934	−	0.341356i	$-0.110886\pi$
$467$	279.536	+	279.536i	0.598578	+	0.598578i	−0.341356	+	0.939934i	$0.610886\pi$
$468$		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	$-0.966049\pi$
$479$		−	101.987i		−	0.212916i	0.994317	−	0.106458i	$-0.0339510\pi$
$480$		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	0.915721	−	0.401815i	$-0.131620\pi$
$487$	250.272	+	250.272i	0.513907	+	0.513907i	−0.401815	+	0.915721i	$0.631620\pi$
$488$	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	$0.123579\pi$
$499$			377.798i			0.757110i	−0.925579	+	0.378555i	$0.876421\pi$
$500$	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	−0.452243	−	0.891895i	$-0.649376\pi$
$503$	221.145	−	221.145i	0.439651	−	0.439651i	0.891895	+	0.452243i	$0.149376\pi$
$504$		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	$0.195535\pi$
$509$			586.753i			1.15276i	−0.817183	+	0.576378i	$0.804465\pi$
$510$		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	−0.354465	−	0.935069i	$-0.615337\pi$
$523$	303.656	−	303.656i	0.580604	−	0.580604i	0.935069	+	0.354465i	$0.115337\pi$
$524$		−	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	0.995472	−	0.0950533i	$-0.0303021\pi$
$547$	492.529	+	492.529i	0.900419	+	0.900419i	−0.0950533	+	0.995472i	$0.530302\pi$
$548$	−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	0.256716	−	0.966487i	$-0.417359\pi$
$557$	−395.342	−	395.342i	−0.709771	−	0.709771i	−0.966487	+	0.256716i	$0.917359\pi$
$558$		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	−0.982137	−	0.188167i	$-0.939746\pi$
$563$	−447.005	+	447.005i	−0.793971	+	0.793971i	0.188167	+	0.982137i	$0.439746\pi$
$564$		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	$0.0109939\pi$
$569$			39.2969i			0.0690631i	−0.999404	+	0.0345316i	$0.989006\pi$
$570$		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	0.991984	+	0.126365i	$0.0403311\pi$
$577$	645.287	+	645.287i	1.11835	+	1.11835i	0.126365	+	0.991984i	$0.459669\pi$
$578$	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	0.118997	−	0.992895i	$-0.462032\pi$
$587$	−512.978	−	512.978i	−0.873898	−	0.873898i	−0.992895	+	0.118997i	$0.962032\pi$
$588$		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	−0.310259	−	0.950652i	$-0.600416\pi$
$593$	379.753	−	379.753i	0.640393	−	0.640393i	0.950652	+	0.310259i	$0.100416\pi$
$594$		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	$0.0445599\pi$
$599$			167.160i			0.279065i	−0.990218	+	0.139532i	$0.955440\pi$
$600$		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	0.365674	−	0.930743i	$-0.380839\pi$
$607$	−342.997	−	342.997i	−0.565069	−	0.565069i	−0.930743	+	0.365674i	$0.880839\pi$
$608$	−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	−0.913995	−	0.405725i	$-0.867019\pi$
$613$	−311.569	+	311.569i	−0.508270	+	0.508270i	0.405725	+	0.913995i	$0.367019\pi$
$614$		−	616.208i		−	1.00360i
$615$		0			0
$616$	−43.0232			−0.0698429
$617$	−442.165	−	442.165i	−0.716636	−	0.716636i	0.251279	−	0.967915i	$-0.419149\pi$
$617$	−442.165	−	442.165i	−0.716636	−	0.716636i	−0.967915	+	0.251279i	$0.919149\pi$
$618$		0			0
$619$		−	375.146i		−	0.606052i	−0.952982	−	0.303026i	$-0.902003\pi$
$619$		−	375.146i		−	0.606052i	0.952982	−	0.303026i	$-0.0979968\pi$
$620$	−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	−0.128919	−	0.991655i	$-0.541151\pi$
$643$	554.739	−	554.739i	0.862736	−	0.862736i	0.991655	+	0.128919i	$0.0411509\pi$
$644$		−	98.9751i		−	0.153688i
$645$		0			0
$646$	166.646			0.257965
$647$	−337.971	−	337.971i	−0.522367	−	0.522367i	0.395919	−	0.918285i	$-0.370426\pi$
$647$	−337.971	−	337.971i	−0.522367	−	0.522367i	−0.918285	+	0.395919i	$0.870426\pi$
$648$		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	−0.935051	−	0.354514i	$-0.884646\pi$
$653$	−379.091	+	379.091i	−0.580537	+	0.580537i	0.354514	+	0.935051i	$0.384646\pi$
$654$		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	$0.250205\pi$
$659$			932.566i			1.41512i	−0.706652	+	0.707561i	$0.749795\pi$
$660$		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	−0.479008	−	0.877811i	$-0.659003\pi$
$673$	268.394	−	268.394i	0.398803	−	0.398803i	0.877811	+	0.479008i	$0.159003\pi$
$674$			552.786i			0.820157i
$675$		0			0
$676$	562.414			0.831973
$677$	317.565	+	317.565i	0.469076	+	0.469076i	0.901615	−	0.432539i	$-0.142382\pi$
$677$	317.565	+	317.565i	0.469076	+	0.469076i	−0.432539	+	0.901615i	$0.642382\pi$
$678$		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	−0.104741	+	0.994500i	$0.533401\pi$
$683$	−750.781	+	750.781i	−1.09924	+	1.09924i	−0.994500	+	0.104741i	$0.966599\pi$
$684$		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	$0.0271745\pi$
$709$			120.909i			0.170535i	−0.996358	+	0.0852674i	$0.972826\pi$
$710$	−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	$0.0349688\pi$
$719$			157.658i			0.219274i	−0.993972	+	0.109637i	$0.965031\pi$
$720$		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	0.737769	−	0.675053i	$-0.235879\pi$
$727$	45.5944	+	45.5944i	0.0627159	+	0.0627159i	−0.675053	+	0.737769i	$0.735879\pi$
$728$	−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	−0.703671	−	0.710526i	$-0.748457\pi$
$733$	5.02444	−	5.02444i	0.00685462	−	0.00685462i	0.710526	+	0.703671i	$0.248457\pi$
$734$			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	$-0.695724\pi$
$739$		−	1207.29i		−	1.63368i	0.576865	−	0.816839i	$-0.304276\pi$
$740$	−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	−0.589322	−	0.807898i	$-0.700605\pi$
$743$	162.402	−	162.402i	0.218577	−	0.218577i	0.807898	+	0.589322i	$0.200605\pi$
$744$		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	0.808429	−	0.588593i	$-0.200318\pi$
$757$	166.416	+	166.416i	0.219836	+	0.219836i	−0.588593	+	0.808429i	$0.700318\pi$
$758$	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	$-0.894110\pi$
$769$		−	502.250i		−	0.653121i	0.945176	−	0.326560i	$-0.105890\pi$
$770$	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	−0.452224	−	0.891904i	$-0.649369\pi$
$773$	339.873	−	339.873i	0.439681	−	0.439681i	0.891904	+	0.452224i	$0.149369\pi$
$774$		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	0.999081	−	0.0428547i	$-0.0136452\pi$
$787$	752.550	+	752.550i	0.956227	+	0.956227i	−0.0428547	+	0.999081i	$0.513645\pi$
$788$	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	0.812511	−	0.582947i	$-0.198100\pi$
$797$	182.962	+	182.962i	0.229564	+	0.229564i	−0.582947	+	0.812511i	$0.698100\pi$
$798$		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	$0.101785\pi$
$809$			508.611i			0.628690i	−0.949309	+	0.314345i	$0.898215\pi$
$810$		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	−0.458782	−	0.888549i	$-0.651714\pi$
$823$	353.698	−	353.698i	0.429767	−	0.429767i	0.888549	+	0.458782i	$0.151714\pi$
$824$		−	186.490i		−	0.226323i
$825$		0			0
$826$	235.610			0.285242
$827$	−57.1544	−	57.1544i	−0.0691105	−	0.0691105i	0.671707	−	0.740817i	$-0.265562\pi$
$827$	−57.1544	−	57.1544i	−0.0691105	−	0.0691105i	−0.740817	+	0.671707i	$0.765562\pi$
$828$		0			0
$829$		−	260.205i		−	0.313878i	−0.987608	−	0.156939i	$-0.949837\pi$
$829$		−	260.205i		−	0.313878i	0.987608	−	0.156939i	$-0.0501626\pi$
$830$	−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	$-0.854200\pi$
$839$		−	742.004i		−	0.884391i	0.896919	−	0.442196i	$-0.145800\pi$
$840$		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	0.0277980	−	0.999614i	$-0.491150\pi$
$853$	876.382	−	876.382i	1.02741	−	1.02741i	0.999614	−	0.0277980i	$-0.00884953\pi$
$854$		−	6.26698i		−	0.00733838i
$855$		0			0
$856$	230.261			0.268996
$857$	−953.370	−	953.370i	−1.11245	−	1.11245i	−0.992818	−	0.119632i	$-0.961828\pi$
$857$	−953.370	−	953.370i	−1.11245	−	1.11245i	−0.119632	−	0.992818i	$-0.538172\pi$
$858$		0			0
$859$			808.979i			0.941768i	0.882195	+	0.470884i	$0.156065\pi$
$859$			808.979i			0.941768i	−0.882195	+	0.470884i	$0.843935\pi$
$860$	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	−0.865986	−	0.500068i	$-0.833308\pi$
$863$	−315.788	+	315.788i	−0.365919	+	0.365919i	0.500068	+	0.865986i	$0.333308\pi$
$864$		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	0.521452	−	0.853281i	$-0.325391\pi$
$877$	−291.014	−	291.014i	−0.331829	−	0.331829i	−0.853281	+	0.521452i	$0.825391\pi$
$878$	−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	0.546042	−	0.837758i	$-0.316134\pi$
$883$	1221.90	−	1221.90i	1.38380	−	1.38380i	0.837758	−	0.546042i	$-0.183866\pi$
$884$			287.359i			0.325066i
$885$		0			0
$886$	−679.505			−0.766935
$887$	−67.8606	−	67.8606i	−0.0765058	−	0.0765058i	0.667818	−	0.744324i	$-0.267228\pi$
$887$	−67.8606	−	67.8606i	−0.0765058	−	0.0765058i	−0.744324	+	0.667818i	$0.767228\pi$
$888$		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	0.622991	−	0.782229i	$-0.285917\pi$
$907$	−144.428	−	144.428i	−0.159237	−	0.159237i	−0.782229	+	0.622991i	$0.785917\pi$
$908$	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	$0.247418\pi$
$919$			1289.08i			1.40269i	−0.712820	+	0.701347i	$0.752582\pi$
$920$	−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	$-0.867824\pi$
$929$		−	749.538i		−	0.806823i	0.915019	−	0.403411i	$-0.132176\pi$
$930$		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	0.586990	−	0.809594i	$-0.300313\pi$
$937$	−208.580	−	208.580i	−0.222605	−	0.222605i	−0.809594	+	0.586990i	$0.800313\pi$
$938$	−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	0.538381	−	0.842702i	$-0.319036\pi$
$947$	−288.192	−	288.192i	−0.304321	−	0.304321i	−0.842702	+	0.538381i	$0.819036\pi$
$948$		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	−0.430072	−	0.902794i	$-0.641512\pi$
$953$	450.504	−	450.504i	0.472722	−	0.472722i	0.902794	+	0.430072i	$0.141512\pi$
$954$		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	0.990501	−	0.137505i	$-0.0439082\pi$
$967$	824.848	+	824.848i	0.852997	+	0.852997i	−0.137505	+	0.990501i	$0.543908\pi$
$968$	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	0.639206	−	0.769036i	$-0.279263\pi$
$977$	−126.844	−	126.844i	−0.129830	−	0.129830i	−0.769036	+	0.639206i	$0.779263\pi$
$978$		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	0.211839	−	0.977305i	$-0.432055\pi$
$983$	1168.93	−	1168.93i	1.18914	−	1.18914i	0.977305	−	0.211839i	$-0.0679451\pi$
$984$		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	−1.00000		0.000649790i	$-0.999793\pi$
$997$	−997.648	−	997.648i	−1.00065	−	1.00065i	−0.000649790	−	1.00000i	$-0.500207\pi$
$998$	−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.127.8		16
3.2	odd	2		210.3.l.b.127.1	yes	16
5.3	odd	4	inner	630.3.o.f.253.8		16
15.2	even	4		1050.3.l.h.43.6		16
15.8	even	4		210.3.l.b.43.1	✓	16
15.14	odd	2		1050.3.l.h.757.6		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.3.l.b.43.1	✓	16	15.8	even	4
210.3.l.b.127.1	yes	16	3.2	odd	2
630.3.o.f.127.8		16	1.1	even	1	trivial
630.3.o.f.253.8		16	5.3	odd	4	inner
1050.3.l.h.43.6		16	15.2	even	4
1050.3.l.h.757.6		16	15.14	odd	2

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

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