LMFDB - Embedded newform 270.3.g.a.163.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [270,3,Mod(163,270)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(270, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 3]))

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

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

chi := DirichletCharacter("270.163");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 270 = 2 \cdot 3^{3} \cdot 5 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	270.g (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:	$7.35696713773$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(i)$
Coefficient field:	$\Q(i, \sqrt{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 9 $ x^4 + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			163.1
Root			$1.22474 - 1.22474i$ of defining polynomial
Character	$\chi$	$=$	270.163
Dual form			270.3.g.a.217.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.00000 + 1.00000i) q^{2} -2.00000i q^{4} +(-4.22474 + 2.67423i) q^{5} +(4.44949 - 4.44949i) q^{7} +(2.00000 + 2.00000i) q^{8} +O(q^{10})$	\(q+(-1.00000 + 1.00000i) q^{2} -2.00000i q^{4} +(-4.22474 + 2.67423i) q^{5} +(4.44949 - 4.44949i) q^{7} +(2.00000 + 2.00000i) q^{8} +(1.55051 - 6.89898i) q^{10} +10.2474 q^{11} +(3.55051 + 3.55051i) q^{13} +8.89898i q^{14} -4.00000 q^{16} +(-15.7753 + 15.7753i) q^{17} +19.4495i q^{19} +(5.34847 + 8.44949i) q^{20} +(-10.2474 + 10.2474i) q^{22} +(15.0227 + 15.0227i) q^{23} +(10.6969 - 22.5959i) q^{25} -7.10102 q^{26} +(-8.89898 - 8.89898i) q^{28} +35.7980i q^{29} +27.9444 q^{31} +(4.00000 - 4.00000i) q^{32} -31.5505i q^{34} +(-6.89898 + 30.6969i) q^{35} +(-38.3939 + 38.3939i) q^{37} +(-19.4495 - 19.4495i) q^{38} +(-13.7980 - 3.10102i) q^{40} +26.5403 q^{41} +(30.1918 + 30.1918i) q^{43} -20.4949i q^{44} -30.0454 q^{46} +(-10.0454 + 10.0454i) q^{47} +9.40408i q^{49} +(11.8990 + 33.2929i) q^{50} +(7.10102 - 7.10102i) q^{52} +(-47.4166 - 47.4166i) q^{53} +(-43.2929 + 27.4041i) q^{55} +17.7980 q^{56} +(-35.7980 - 35.7980i) q^{58} -78.0908i q^{59} +104.778 q^{61} +(-27.9444 + 27.9444i) q^{62} +8.00000i q^{64} +(-24.4949 - 5.50510i) q^{65} +(-85.7423 + 85.7423i) q^{67} +(31.5505 + 31.5505i) q^{68} +(-23.7980 - 37.5959i) q^{70} +62.2474 q^{71} +(52.5505 + 52.5505i) q^{73} -76.7878i q^{74} +38.8990 q^{76} +(45.5959 - 45.5959i) q^{77} -104.641i q^{79} +(16.8990 - 10.6969i) q^{80} +(-26.5403 + 26.5403i) q^{82} +(-32.2145 - 32.2145i) q^{83} +(24.4597 - 108.833i) q^{85} -60.3837 q^{86} +(20.4949 + 20.4949i) q^{88} -69.9546i q^{89} +31.5959 q^{91} +(30.0454 - 30.0454i) q^{92} -20.0908i q^{94} +(-52.0125 - 82.1691i) q^{95} +(79.1010 - 79.1010i) q^{97} +(-9.40408 - 9.40408i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{2} - 12 q^{5} + 8 q^{7} + 8 q^{8}+O(q^{10}) $ 4 * q - 4 * q^2 - 12 * q^5 + 8 * q^7 + 8 * q^8	$ 4 q - 4 q^{2} - 12 q^{5} + 8 q^{7} + 8 q^{8} + 16 q^{10} - 8 q^{11} + 24 q^{13} - 16 q^{16} - 68 q^{17} - 8 q^{20} + 8 q^{22} + 16 q^{23} - 16 q^{25} - 48 q^{26} - 16 q^{28} + 4 q^{31} + 16 q^{32} - 8 q^{35} - 36 q^{37} - 68 q^{38} - 16 q^{40} - 80 q^{41} - 36 q^{43} - 32 q^{46} + 48 q^{47} + 28 q^{50} + 48 q^{52} - 28 q^{53} - 36 q^{55} + 32 q^{56} - 104 q^{58} - 12 q^{61} - 4 q^{62} - 196 q^{67} + 136 q^{68} - 56 q^{70} + 200 q^{71} + 220 q^{73} + 136 q^{76} + 104 q^{77} + 48 q^{80} + 80 q^{82} + 72 q^{83} + 284 q^{85} + 72 q^{86} - 16 q^{88} + 48 q^{91} + 32 q^{92} + 32 q^{95} + 336 q^{97} - 116 q^{98}+O(q^{100}) $ 4 * q - 4 * q^2 - 12 * q^5 + 8 * q^7 + 8 * q^8 + 16 * q^10 - 8 * q^11 + 24 * q^13 - 16 * q^16 - 68 * q^17 - 8 * q^20 + 8 * q^22 + 16 * q^23 - 16 * q^25 - 48 * q^26 - 16 * q^28 + 4 * q^31 + 16 * q^32 - 8 * q^35 - 36 * q^37 - 68 * q^38 - 16 * q^40 - 80 * q^41 - 36 * q^43 - 32 * q^46 + 48 * q^47 + 28 * q^50 + 48 * q^52 - 28 * q^53 - 36 * q^55 + 32 * q^56 - 104 * q^58 - 12 * q^61 - 4 * q^62 - 196 * q^67 + 136 * q^68 - 56 * q^70 + 200 * q^71 + 220 * q^73 + 136 * q^76 + 104 * q^77 + 48 * q^80 + 80 * q^82 + 72 * q^83 + 284 * q^85 + 72 * q^86 - 16 * q^88 + 48 * q^91 + 32 * q^92 + 32 * q^95 + 336 * q^97 - 116 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/270\mathbb{Z}\right)^\times$.

$n$	$191$	$217$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$

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
$5$	−4.22474	+	2.67423i	−0.844949	+	0.534847i
$5$	−4.22474	+	2.67423i	−0.844949	+	0.534847i
$6$		0			0
$7$	4.44949	−	4.44949i	0.635641	−	0.635641i	−0.313836	−	0.949477i	$-0.601614\pi$
$7$	4.44949	−	4.44949i	0.635641	−	0.635641i	0.949477	+	0.313836i	$0.101614\pi$
$8$	2.00000	+	2.00000i	0.250000	+	0.250000i
$9$		0			0
$10$	1.55051	−	6.89898i	0.155051	−	0.689898i
$11$	10.2474			0.931586			0.465793	−	0.884894i	$-0.345769\pi$
$11$	10.2474			0.931586			0.465793	+	0.884894i	$0.345769\pi$
$12$		0			0
$13$	3.55051	+	3.55051i	0.273116	+	0.273116i	0.830353	−	0.557237i	$-0.188139\pi$
$13$	3.55051	+	3.55051i	0.273116	+	0.273116i	−0.557237	+	0.830353i	$0.688139\pi$
$14$			8.89898i			0.635641i
$15$		0			0
$16$	−4.00000			−0.250000
$17$	−15.7753	+	15.7753i	−0.927956	+	0.927956i	−0.997574	−	0.0696176i	$-0.977822\pi$
$17$	−15.7753	+	15.7753i	−0.927956	+	0.927956i	0.0696176	+	0.997574i	$0.477822\pi$
$18$		0			0
$19$			19.4495i			1.02366i	0.859088	+	0.511829i	$0.171032\pi$
$19$			19.4495i			1.02366i	−0.859088	+	0.511829i	$0.828968\pi$
$20$	5.34847	+	8.44949i	0.267423	+	0.422474i
$21$		0			0
$22$	−10.2474	+	10.2474i	−0.465793	+	0.465793i
$23$	15.0227	+	15.0227i	0.653161	+	0.653161i	0.953753	−	0.300592i	$-0.0971842\pi$
$23$	15.0227	+	15.0227i	0.653161	+	0.653161i	−0.300592	+	0.953753i	$0.597184\pi$
$24$		0			0
$25$	10.6969	−	22.5959i	0.427878	−	0.903837i
$26$	−7.10102			−0.273116
$27$		0			0
$28$	−8.89898	−	8.89898i	−0.317821	−	0.317821i
$29$			35.7980i			1.23441i	0.786801	+	0.617206i	$0.211736\pi$
$29$			35.7980i			1.23441i	−0.786801	+	0.617206i	$0.788264\pi$
$30$		0			0
$31$	27.9444			0.901432			0.450716	−	0.892667i	$-0.351169\pi$
$31$	27.9444			0.901432			0.450716	+	0.892667i	$0.351169\pi$
$32$	4.00000	−	4.00000i	0.125000	−	0.125000i
$33$		0			0
$34$		−	31.5505i		−	0.927956i
$35$	−6.89898	+	30.6969i	−0.197114	+	0.877055i
$36$		0			0
$37$	−38.3939	+	38.3939i	−1.03767	+	1.03767i	−0.0384103	+	0.999262i	$0.512229\pi$
$37$	−38.3939	+	38.3939i	−1.03767	+	1.03767i	−0.999262	+	0.0384103i	$0.987771\pi$
$38$	−19.4495	−	19.4495i	−0.511829	−	0.511829i
$39$		0			0
$40$	−13.7980	−	3.10102i	−0.344949	−	0.0775255i
$41$	26.5403			0.647325			0.323662	−	0.946173i	$-0.395086\pi$
$41$	26.5403			0.647325			0.323662	+	0.946173i	$0.395086\pi$
$42$		0			0
$43$	30.1918	+	30.1918i	0.702136	+	0.702136i	0.964869	−	0.262733i	$-0.0846238\pi$
$43$	30.1918	+	30.1918i	0.702136	+	0.702136i	−0.262733	+	0.964869i	$0.584624\pi$
$44$		−	20.4949i		−	0.465793i
$45$		0			0
$46$	−30.0454			−0.653161
$47$	−10.0454	+	10.0454i	−0.213732	+	0.213732i	−0.805851	−	0.592119i	$-0.798292\pi$
$47$	−10.0454	+	10.0454i	−0.213732	+	0.213732i	0.592119	+	0.805851i	$0.298292\pi$
$48$		0			0
$49$			9.40408i			0.191920i
$50$	11.8990	+	33.2929i	0.237980	+	0.665857i
$51$		0			0
$52$	7.10102	−	7.10102i	0.136558	−	0.136558i
$53$	−47.4166	−	47.4166i	−0.894652	−	0.894652i	0.100304	−	0.994957i	$-0.468018\pi$
$53$	−47.4166	−	47.4166i	−0.894652	−	0.894652i	−0.994957	+	0.100304i	$0.968018\pi$
$54$		0			0
$55$	−43.2929	+	27.4041i	−0.787143	+	0.498256i
$56$	17.7980			0.317821
$57$		0			0
$58$	−35.7980	−	35.7980i	−0.617206	−	0.617206i
$59$		−	78.0908i		−	1.32357i	−0.749692	−	0.661787i	$-0.769799\pi$
$59$		−	78.0908i		−	1.32357i	0.749692	−	0.661787i	$-0.230201\pi$
$60$		0			0
$61$	104.778			1.71766			0.858832	−	0.512257i	$-0.171190\pi$
$61$	104.778			1.71766			0.858832	+	0.512257i	$0.171190\pi$
$62$	−27.9444	+	27.9444i	−0.450716	+	0.450716i
$63$		0			0
$64$			8.00000i			0.125000i
$65$	−24.4949	−	5.50510i	−0.376845	−	0.0846939i
$66$		0			0
$67$	−85.7423	+	85.7423i	−1.27974	+	1.27974i	−0.338922	+	0.940814i	$0.610062\pi$
$67$	−85.7423	+	85.7423i	−1.27974	+	1.27974i	−0.940814	+	0.338922i	$0.889938\pi$
$68$	31.5505	+	31.5505i	0.463978	+	0.463978i
$69$		0			0
$70$	−23.7980	−	37.5959i	−0.339971	−	0.537085i
$71$	62.2474			0.876725			0.438362	−	0.898798i	$-0.355559\pi$
$71$	62.2474			0.876725			0.438362	+	0.898798i	$0.355559\pi$
$72$		0			0
$73$	52.5505	+	52.5505i	0.719870	+	0.719870i	0.968578	−	0.248708i	$-0.0800061\pi$
$73$	52.5505	+	52.5505i	0.719870	+	0.719870i	−0.248708	+	0.968578i	$0.580006\pi$
$74$		−	76.7878i		−	1.03767i
$75$		0			0
$76$	38.8990			0.511829
$77$	45.5959	−	45.5959i	0.592155	−	0.592155i
$78$		0			0
$79$		−	104.641i		−	1.32457i	−0.749250	−	0.662287i	$-0.769586\pi$
$79$		−	104.641i		−	1.32457i	0.749250	−	0.662287i	$-0.230414\pi$
$80$	16.8990	−	10.6969i	0.211237	−	0.133712i
$81$		0			0
$82$	−26.5403	+	26.5403i	−0.323662	+	0.323662i
$83$	−32.2145	−	32.2145i	−0.388127	−	0.388127i	0.485892	−	0.874019i	$-0.338495\pi$
$83$	−32.2145	−	32.2145i	−0.388127	−	0.388127i	−0.874019	+	0.485892i	$0.838495\pi$
$84$		0			0
$85$	24.4597	−	108.833i	0.287761	−	1.28039i
$86$	−60.3837			−0.702136
$87$		0			0
$88$	20.4949	+	20.4949i	0.232897	+	0.232897i
$89$		−	69.9546i		−	0.786007i	−0.919537	−	0.393003i	$-0.871436\pi$
$89$		−	69.9546i		−	0.786007i	0.919537	−	0.393003i	$-0.128564\pi$
$90$		0			0
$91$	31.5959			0.347208
$92$	30.0454	−	30.0454i	0.326581	−	0.326581i
$93$		0			0
$94$		−	20.0908i		−	0.213732i
$95$	−52.0125	−	82.1691i	−0.547500	−	0.864938i
$96$		0			0
$97$	79.1010	−	79.1010i	0.815474	−	0.815474i	−0.169974	−	0.985449i	$-0.554368\pi$
$97$	79.1010	−	79.1010i	0.815474	−	0.815474i	0.985449	+	0.169974i	$0.0543684\pi$
$98$	−9.40408	−	9.40408i	−0.0959600	−	0.0959600i
$99$		0			0
$100$	−45.1918	−	21.3939i	−0.451918	−	0.213939i
$101$	84.8990			0.840584			0.420292	−	0.907389i	$-0.361928\pi$
$101$	84.8990			0.840584			0.420292	+	0.907389i	$0.361928\pi$
$102$		0			0
$103$	43.0806	+	43.0806i	0.418258	+	0.418258i	0.884603	−	0.466345i	$-0.154429\pi$
$103$	43.0806	+	43.0806i	0.418258	+	0.418258i	−0.466345	+	0.884603i	$0.654429\pi$
$104$			14.2020i			0.136558i
$105$		0			0
$106$	94.8332			0.894652
$107$	53.8434	−	53.8434i	0.503209	−	0.503209i	−0.409225	−	0.912434i	$-0.634201\pi$
$107$	53.8434	−	53.8434i	0.503209	−	0.503209i	0.912434	+	0.409225i	$0.134201\pi$
$108$		0			0
$109$		−	104.576i		−	0.959408i	−0.877430	−	0.479704i	$-0.840744\pi$
$109$		−	104.576i		−	0.959408i	0.877430	−	0.479704i	$-0.159256\pi$
$110$	15.8888	−	70.6969i	0.144443	−	0.642699i
$111$		0			0
$112$	−17.7980	+	17.7980i	−0.158910	+	0.158910i
$113$	−105.283	−	105.283i	−0.931705	−	0.931705i	0.0661076	−	0.997812i	$-0.478942\pi$
$113$	−105.283	−	105.283i	−0.931705	−	0.931705i	−0.997812	+	0.0661076i	$0.978942\pi$
$114$		0			0
$115$	−103.641	−	23.2929i	−0.901229	−	0.202547i
$116$	71.5959			0.617206
$117$		0			0
$118$	78.0908	+	78.0908i	0.661787	+	0.661787i
$119$			140.384i			1.17969i
$120$		0			0
$121$	−15.9898			−0.132147
$122$	−104.778	+	104.778i	−0.858832	+	0.858832i
$123$		0			0
$124$		−	55.8888i		−	0.450716i
$125$	15.2350	+	124.068i	0.121880	+	0.992545i
$126$		0			0
$127$	−170.126	+	170.126i	−1.33957	+	1.33957i	−0.443105	+	0.896470i	$0.646123\pi$
$127$	−170.126	+	170.126i	−1.33957	+	1.33957i	−0.896470	+	0.443105i	$0.853877\pi$
$128$	−8.00000	−	8.00000i	−0.0625000	−	0.0625000i
$129$		0			0
$130$	30.0000	−	18.9898i	0.230769	−	0.146075i
$131$	−146.359			−1.11724			−0.558621	−	0.829423i	$-0.688669\pi$
$131$	−146.359			−1.11724			−0.558621	+	0.829423i	$0.688669\pi$
$132$		0			0
$133$	86.5403	+	86.5403i	0.650679	+	0.650679i
$134$		−	171.485i		−	1.27974i
$135$		0			0
$136$	−63.1010			−0.463978
$137$	35.5732	−	35.5732i	0.259658	−	0.259658i	−0.565257	−	0.824915i	$-0.691223\pi$
$137$	35.5732	−	35.5732i	0.259658	−	0.259658i	0.824915	+	0.565257i	$0.191223\pi$
$138$		0			0
$139$			123.889i			0.891286i	0.895211	+	0.445643i	$0.147025\pi$
$139$			123.889i			0.891286i	−0.895211	+	0.445643i	$0.852975\pi$
$140$	61.3939	+	13.7980i	0.438528	+	0.0985568i
$141$		0			0
$142$	−62.2474	+	62.2474i	−0.438362	+	0.438362i
$143$	36.3837	+	36.3837i	0.254431	+	0.254431i
$144$		0			0
$145$	−95.7321	−	151.237i	−0.660222	−	1.04302i
$146$	−105.101			−0.719870
$147$		0			0
$148$	76.7878	+	76.7878i	0.518836	+	0.518836i
$149$			217.237i			1.45797i	0.684531	+	0.728984i	$0.260007\pi$
$149$			217.237i			1.45797i	−0.684531	+	0.728984i	$0.739993\pi$
$150$		0			0
$151$	−142.808			−0.945749			−0.472875	−	0.881130i	$-0.656784\pi$
$151$	−142.808			−0.945749			−0.472875	+	0.881130i	$0.656784\pi$
$152$	−38.8990	+	38.8990i	−0.255914	+	0.255914i
$153$		0			0
$154$			91.1918i			0.592155i
$155$	−118.058	+	74.7298i	−0.761664	+	0.482128i
$156$		0			0
$157$	−29.8332	+	29.8332i	−0.190020	+	0.190020i	−0.795705	−	0.605685i	$-0.792899\pi$
$157$	−29.8332	+	29.8332i	−0.190020	+	0.190020i	0.605685	+	0.795705i	$0.292899\pi$
$158$	104.641	+	104.641i	0.662287	+	0.662287i
$159$		0			0
$160$	−6.20204	+	27.5959i	−0.0387628	+	0.172474i
$161$	133.687			0.830352
$162$		0			0
$163$	−61.3587	−	61.3587i	−0.376434	−	0.376434i	0.493380	−	0.869814i	$-0.335761\pi$
$163$	−61.3587	−	61.3587i	−0.376434	−	0.376434i	−0.869814	+	0.493380i	$0.835761\pi$
$164$		−	53.0806i		−	0.323662i
$165$		0			0
$166$	64.4291			0.388127
$167$	136.240	−	136.240i	0.815806	−	0.815806i	−0.169692	−	0.985497i	$-0.554277\pi$
$167$	136.240	−	136.240i	0.815806	−	0.815806i	0.985497	+	0.169692i	$0.0542772\pi$
$168$		0			0
$169$		−	143.788i		−	0.850815i
$170$	84.3735	+	133.293i	0.496315	+	0.784076i
$171$		0			0
$172$	60.3837	−	60.3837i	0.351068	−	0.351068i
$173$	149.800	+	149.800i	0.865897	+	0.865897i	0.992015	−	0.126118i	$-0.0402517\pi$
$173$	149.800	+	149.800i	0.865897	+	0.865897i	−0.126118	+	0.992015i	$0.540252\pi$
$174$		0			0
$175$	−52.9444	−	148.136i	−0.302539	−	0.846493i
$176$	−40.9898			−0.232897
$177$		0			0
$178$	69.9546	+	69.9546i	0.393003	+	0.393003i
$179$			186.252i			1.04051i	0.854010	+	0.520257i	$0.174164\pi$
$179$			186.252i			1.04051i	−0.854010	+	0.520257i	$0.825836\pi$
$180$		0			0
$181$	258.373			1.42748			0.713739	−	0.700412i	$-0.247000\pi$
$181$	258.373			1.42748			0.713739	+	0.700412i	$0.247000\pi$
$182$	−31.5959	+	31.5959i	−0.173604	+	0.173604i
$183$		0			0
$184$			60.0908i			0.326581i
$185$	59.5301	−	264.879i	0.321784	−	1.43178i
$186$		0			0
$187$	−161.656	+	161.656i	−0.864471	+	0.864471i
$188$	20.0908	+	20.0908i	0.106866	+	0.106866i
$189$		0			0
$190$	134.182	+	30.1566i	0.706219	+	0.158719i
$191$	−188.924			−0.989131			−0.494565	−	0.869140i	$-0.664673\pi$
$191$	−188.924			−0.989131			−0.494565	+	0.869140i	$0.664673\pi$
$192$		0			0
$193$	−181.237	−	181.237i	−0.939053	−	0.939053i	0.0591935	−	0.998247i	$-0.481147\pi$
$193$	−181.237	−	181.237i	−0.939053	−	0.939053i	−0.998247	+	0.0591935i	$0.981147\pi$
$194$			158.202i			0.815474i
$195$		0			0
$196$	18.8082			0.0959600
$197$	−181.775	+	181.775i	−0.922717	+	0.922717i	−0.997221	−	0.0745037i	$-0.976263\pi$
$197$	−181.775	+	181.775i	−0.922717	+	0.922717i	0.0745037	+	0.997221i	$0.476263\pi$
$198$		0			0
$199$		−	67.3235i		−	0.338309i	−0.985590	−	0.169154i	$-0.945896\pi$
$199$		−	67.3235i		−	0.338309i	0.985590	−	0.169154i	$-0.0541037\pi$
$200$	66.5857	−	23.7980i	0.332929	−	0.118990i
$201$		0			0
$202$	−84.8990	+	84.8990i	−0.420292	+	0.420292i
$203$	159.283	+	159.283i	0.784644	+	0.784644i
$204$		0			0
$205$	−112.126	+	70.9750i	−0.546956	+	0.346220i
$206$	−86.1612			−0.418258
$207$		0			0
$208$	−14.2020	−	14.2020i	−0.0682790	−	0.0682790i
$209$			199.308i			0.953625i
$210$		0			0
$211$	191.520			0.907677			0.453839	−	0.891084i	$-0.350054\pi$
$211$	191.520			0.907677			0.453839	+	0.891084i	$0.350054\pi$
$212$	−94.8332	+	94.8332i	−0.447326	+	0.447326i
$213$		0			0
$214$			107.687i			0.503209i
$215$	−208.293	−	46.8128i	−0.968804	−	0.217734i
$216$		0			0
$217$	124.338	−	124.338i	0.572987	−	0.572987i
$218$	104.576	+	104.576i	0.479704	+	0.479704i
$219$		0			0
$220$	54.8082	+	86.5857i	0.249128	+	0.393571i
$221$	−112.020			−0.506880
$222$		0			0
$223$	8.36888	+	8.36888i	0.0375286	+	0.0375286i	0.725622	−	0.688093i	$-0.241552\pi$
$223$	8.36888	+	8.36888i	0.0375286	+	0.0375286i	−0.688093	+	0.725622i	$0.741552\pi$
$224$		−	35.5959i		−	0.158910i
$225$		0			0
$226$	210.565			0.931705
$227$	6.91148	−	6.91148i	0.0304470	−	0.0304470i	−0.691719	−	0.722166i	$-0.743146\pi$
$227$	6.91148	−	6.91148i	0.0304470	−	0.0304470i	0.722166	+	0.691719i	$0.243146\pi$
$228$		0			0
$229$		−	246.242i		−	1.07529i	−0.843171	−	0.537646i	$-0.819314\pi$
$229$		−	246.242i		−	1.07529i	0.843171	−	0.537646i	$-0.180686\pi$
$230$	126.934	−	80.3485i	0.551888	−	0.349341i
$231$		0			0
$232$	−71.5959	+	71.5959i	−0.308603	+	0.308603i
$233$	−182.586	−	182.586i	−0.783630	−	0.783630i	0.196812	−	0.980441i	$-0.436941\pi$
$233$	−182.586	−	182.586i	−0.783630	−	0.783630i	−0.980441	+	0.196812i	$0.936941\pi$
$234$		0			0
$235$	15.5755	−	69.3031i	0.0662788	−	0.294907i
$236$	−156.182			−0.661787
$237$		0			0
$238$	−140.384	−	140.384i	−0.589847	−	0.589847i
$239$			174.409i			0.729743i	0.931058	+	0.364872i	$0.118887\pi$
$239$			174.409i			0.729743i	−0.931058	+	0.364872i	$0.881113\pi$
$240$		0			0
$241$	−190.333			−0.789762			−0.394881	−	0.918732i	$-0.629214\pi$
$241$	−190.333			−0.789762			−0.394881	+	0.918732i	$0.629214\pi$
$242$	15.9898	−	15.9898i	0.0660735	−	0.0660735i
$243$		0			0
$244$		−	209.555i		−	0.858832i
$245$	−25.1487	−	39.7298i	−0.102648	−	0.162163i
$246$		0			0
$247$	−69.0556	+	69.0556i	−0.279577	+	0.279577i
$248$	55.8888	+	55.8888i	0.225358	+	0.225358i
$249$		0			0
$250$	−139.303	−	108.833i	−0.557212	−	0.435333i
$251$	421.707			1.68011			0.840054	−	0.542503i	$-0.182523\pi$
$251$	421.707			1.68011			0.840054	+	0.542503i	$0.182523\pi$
$252$		0			0
$253$	153.944	+	153.944i	0.608476	+	0.608476i
$254$		−	340.252i		−	1.33957i
$255$		0			0
$256$	16.0000			0.0625000
$257$	88.6288	−	88.6288i	0.344859	−	0.344859i	−0.513331	−	0.858191i	$-0.671589\pi$
$257$	88.6288	−	88.6288i	0.344859	−	0.344859i	0.858191	+	0.513331i	$0.171589\pi$
$258$		0			0
$259$			341.666i			1.31917i
$260$	−11.0102	+	48.9898i	−0.0423469	+	0.188422i
$261$		0			0
$262$	146.359	−	146.359i	0.558621	−	0.558621i
$263$	25.1214	+	25.1214i	0.0955187	+	0.0955187i	0.753251	−	0.657733i	$-0.228484\pi$
$263$	25.1214	+	25.1214i	0.0955187	+	0.0955187i	−0.657733	+	0.753251i	$0.728484\pi$
$264$		0			0
$265$	327.126	+	73.5199i	1.23444	+	0.277434i
$266$	−173.081			−0.650679
$267$		0			0
$268$	171.485	+	171.485i	0.639868	+	0.639868i
$269$		−	197.621i		−	0.734650i	−0.930093	−	0.367325i	$-0.880274\pi$
$269$		−	197.621i		−	0.734650i	0.930093	−	0.367325i	$-0.119726\pi$
$270$		0			0
$271$	−158.258			−0.583977			−0.291988	−	0.956422i	$-0.594317\pi$
$271$	−158.258			−0.583977			−0.291988	+	0.956422i	$0.594317\pi$
$272$	63.1010	−	63.1010i	0.231989	−	0.231989i
$273$		0			0
$274$			71.1464i			0.259658i
$275$	109.616	−	231.551i	0.398605	−	0.842002i
$276$		0			0
$277$	82.7321	−	82.7321i	0.298672	−	0.298672i	−0.541822	−	0.840494i	$-0.682265\pi$
$277$	82.7321	−	82.7321i	0.298672	−	0.298672i	0.840494	+	0.541822i	$0.182265\pi$
$278$	−123.889	−	123.889i	−0.445643	−	0.445643i
$279$		0			0
$280$	−75.1918	+	47.5959i	−0.268542	+	0.169985i
$281$	123.353			0.438979			0.219489	−	0.975615i	$-0.429561\pi$
$281$	123.353			0.438979			0.219489	+	0.975615i	$0.429561\pi$
$282$		0			0
$283$	−194.980	−	194.980i	−0.688974	−	0.688974i	0.273031	−	0.962005i	$-0.411974\pi$
$283$	−194.980	−	194.980i	−0.688974	−	0.688974i	−0.962005	+	0.273031i	$0.911974\pi$
$284$		−	124.495i		−	0.438362i
$285$		0			0
$286$	−72.7673			−0.254431
$287$	118.091	−	118.091i	0.411466	−	0.411466i
$288$		0			0
$289$		−	208.717i		−	0.722205i
$290$	246.969	+	55.5051i	0.851619	+	0.191397i
$291$		0			0
$292$	105.101	−	105.101i	0.359935	−	0.359935i
$293$	−52.9921	−	52.9921i	−0.180860	−	0.180860i	0.610870	−	0.791731i	$-0.290820\pi$
$293$	−52.9921	−	52.9921i	−0.180860	−	0.180860i	−0.791731	+	0.610870i	$0.790820\pi$
$294$		0			0
$295$	208.833	+	329.914i	0.707909	+	1.11835i
$296$	−153.576			−0.518836
$297$		0			0
$298$	−217.237	−	217.237i	−0.728984	−	0.728984i
$299$			106.677i			0.356778i
$300$		0			0
$301$	268.677			0.892613
$302$	142.808	−	142.808i	0.472875	−	0.472875i
$303$		0			0
$304$		−	77.7980i		−	0.255914i
$305$	−442.658	+	280.200i	−1.45134	+	0.918688i
$306$		0			0
$307$	186.106	−	186.106i	0.606207	−	0.606207i	−0.335746	−	0.941953i	$-0.608988\pi$
$307$	186.106	−	186.106i	0.606207	−	0.606207i	0.941953	+	0.335746i	$0.108988\pi$
$308$	−91.1918	−	91.1918i	−0.296077	−	0.296077i
$309$		0			0
$310$	43.3281	−	192.788i	0.139768	−	0.621896i
$311$	−246.858			−0.793756			−0.396878	−	0.917871i	$-0.629906\pi$
$311$	−246.858			−0.793756			−0.396878	+	0.917871i	$0.629906\pi$
$312$		0			0
$313$	−210.161	−	210.161i	−0.671442	−	0.671442i	0.286607	−	0.958048i	$-0.407473\pi$
$313$	−210.161	−	210.161i	−0.671442	−	0.671442i	−0.958048	+	0.286607i	$0.907473\pi$
$314$		−	59.6663i		−	0.190020i
$315$		0			0
$316$	−209.283			−0.662287
$317$	244.361	−	244.361i	0.770855	−	0.770855i	−0.207401	−	0.978256i	$-0.566501\pi$
$317$	244.361	−	244.361i	0.770855	−	0.770855i	0.978256	+	0.207401i	$0.0665005\pi$
$318$		0			0
$319$			366.838i			1.14996i
$320$	−21.3939	−	33.7980i	−0.0668559	−	0.105619i
$321$		0			0
$322$	−133.687	+	133.687i	−0.415176	+	0.415176i
$323$	−306.821	−	306.821i	−0.949909	−	0.949909i
$324$		0			0
$325$	118.207	−	42.2474i	0.363713	−	0.129992i
$326$	122.717			0.376434
$327$		0			0
$328$	53.0806	+	53.0806i	0.161831	+	0.161831i
$329$			89.3939i			0.271714i
$330$		0			0
$331$	−551.464			−1.66606			−0.833028	−	0.553231i	$-0.813395\pi$
$331$	−551.464			−1.66606			−0.833028	+	0.553231i	$0.813395\pi$
$332$	−64.4291	+	64.4291i	−0.194063	+	0.194063i
$333$		0			0
$334$			272.479i			0.815806i
$335$	132.944	−	591.535i	0.396849	−	1.76578i
$336$		0			0
$337$	−38.7832	+	38.7832i	−0.115084	+	0.115084i	−0.762303	−	0.647220i	$-0.775932\pi$
$337$	−38.7832	+	38.7832i	−0.115084	+	0.115084i	0.647220	+	0.762303i	$0.275932\pi$
$338$	143.788	+	143.788i	0.425408	+	0.425408i
$339$		0			0
$340$	−217.666	−	48.9194i	−0.640195	−	0.143881i
$341$	286.359			0.839762
$342$		0			0
$343$	259.868	+	259.868i	0.757634	+	0.757634i
$344$			120.767i			0.351068i
$345$		0			0
$346$	−299.601			−0.865897
$347$	402.722	−	402.722i	1.16058	−	1.16058i	0.176234	−	0.984348i	$-0.443609\pi$
$347$	402.722	−	402.722i	1.16058	−	1.16058i	0.984348	−	0.176234i	$-0.0563914\pi$
$348$		0			0
$349$			491.272i			1.40766i	0.710370	+	0.703829i	$0.248528\pi$
$349$			491.272i			1.40766i	−0.710370	+	0.703829i	$0.751472\pi$
$350$	201.081	+	95.1918i	0.574516	+	0.271977i
$351$		0			0
$352$	40.9898	−	40.9898i	0.116448	−	0.116448i
$353$	−68.5857	−	68.5857i	−0.194294	−	0.194294i	0.603255	−	0.797549i	$-0.293870\pi$
$353$	−68.5857	−	68.5857i	−0.194294	−	0.194294i	−0.797549	+	0.603255i	$0.793870\pi$
$354$		0			0
$355$	−262.980	+	166.464i	−0.740788	+	0.468913i
$356$	−139.909			−0.393003
$357$		0			0
$358$	−186.252	−	186.252i	−0.520257	−	0.520257i
$359$		−	353.773i		−	0.985440i	−0.870188	−	0.492720i	$-0.836003\pi$
$359$		−	353.773i		−	0.985440i	0.870188	−	0.492720i	$-0.163997\pi$
$360$		0			0
$361$	−17.2827			−0.0478744
$362$	−258.373	+	258.373i	−0.713739	+	0.713739i
$363$		0			0
$364$		−	63.1918i		−	0.173604i
$365$	−362.545	−	81.4801i	−0.993274	−	0.223233i
$366$		0			0
$367$	240.702	−	240.702i	0.655862	−	0.655862i	−0.298536	−	0.954398i	$-0.596498\pi$
$367$	240.702	−	240.702i	0.655862	−	0.655862i	0.954398	+	0.298536i	$0.0964983\pi$
$368$	−60.0908	−	60.0908i	−0.163290	−	0.163290i
$369$		0			0
$370$	205.348	+	324.409i	0.554996	+	0.876780i
$371$	−421.959			−1.13736
$372$		0			0
$373$	423.060	+	423.060i	1.13421	+	1.13421i	0.989470	+	0.144740i	$0.0462345\pi$
$373$	423.060	+	423.060i	1.13421	+	1.13421i	0.144740	+	0.989470i	$0.453765\pi$
$374$		−	323.312i		−	0.864471i
$375$		0			0
$376$	−40.1816			−0.106866
$377$	−127.101	+	127.101i	−0.337138	+	0.337138i
$378$		0			0
$379$			57.1066i			0.150677i	0.997158	+	0.0753386i	$0.0240038\pi$
$379$			57.1066i			0.150677i	−0.997158	+	0.0753386i	$0.975996\pi$
$380$	−164.338	+	104.025i	−0.432469	+	0.273750i
$381$		0			0
$382$	188.924	−	188.924i	0.494565	−	0.494565i
$383$	362.487	+	362.487i	0.946441	+	0.946441i	0.998637	−	0.0521957i	$-0.0166219\pi$
$383$	362.487	+	362.487i	0.946441	+	0.946441i	−0.0521957	+	0.998637i	$0.516622\pi$
$384$		0			0
$385$	−70.6969	+	314.565i	−0.183628	+	0.817053i
$386$	362.474			0.939053
$387$		0			0
$388$	−158.202	−	158.202i	−0.407737	−	0.407737i
$389$		−	477.106i		−	1.22649i	−0.789892	−	0.613246i	$-0.789863\pi$
$389$		−	477.106i		−	1.22649i	0.789892	−	0.613246i	$-0.210137\pi$
$390$		0			0
$391$	−473.974			−1.21221
$392$	−18.8082	+	18.8082i	−0.0479800	+	0.0479800i
$393$		0			0
$394$		−	363.551i		−	0.922717i
$395$	279.835	+	442.083i	0.708444	+	1.11920i
$396$		0			0
$397$	130.297	−	130.297i	0.328205	−	0.328205i	−0.523699	−	0.851904i	$-0.675448\pi$
$397$	130.297	−	130.297i	0.328205	−	0.328205i	0.851904	+	0.523699i	$0.175448\pi$
$398$	67.3235	+	67.3235i	0.169154	+	0.169154i
$399$		0			0
$400$	−42.7878	+	90.3837i	−0.106969	+	0.225959i
$401$	91.7821			0.228883			0.114442	−	0.993430i	$-0.463492\pi$
$401$	91.7821			0.228883			0.114442	+	0.993430i	$0.463492\pi$
$402$		0			0
$403$	99.2168	+	99.2168i	0.246196	+	0.246196i
$404$		−	169.798i		−	0.420292i
$405$		0			0
$406$	−318.565			−0.784644
$407$	−393.439	+	393.439i	−0.966681	+	0.966681i
$408$		0			0
$409$			23.2520i			0.0568509i	0.999596	+	0.0284255i	$0.00904933\pi$
$409$			23.2520i			0.0568509i	−0.999596	+	0.0284255i	$0.990951\pi$
$410$	41.1510	−	183.101i	0.100368	−	0.446588i
$411$		0			0
$412$	86.1612	−	86.1612i	0.209129	−	0.209129i
$413$	−347.464	−	347.464i	−0.841318	−	0.841318i
$414$		0			0
$415$	222.247	+	49.9490i	0.535536	+	0.120359i
$416$	28.4041			0.0682790
$417$		0			0
$418$	−199.308	−	199.308i	−0.476813	−	0.476813i
$419$			675.551i			1.61229i	0.591716	+	0.806146i	$0.298451\pi$
$419$			675.551i			1.61229i	−0.591716	+	0.806146i	$0.701549\pi$
$420$		0			0
$421$	307.252			0.729815			0.364907	−	0.931044i	$-0.381101\pi$
$421$	307.252			0.729815			0.364907	+	0.931044i	$0.381101\pi$
$422$	−191.520	+	191.520i	−0.453839	+	0.453839i
$423$		0			0
$424$		−	189.666i		−	0.447326i
$425$	187.709	+	525.203i	0.441669	+	1.23577i
$426$		0			0
$427$	466.207	−	466.207i	1.09182	−	1.09182i
$428$	−107.687	−	107.687i	−0.251605	−	0.251605i
$429$		0			0
$430$	255.106	−	161.480i	0.593269	−	0.375535i
$431$	680.120			1.57801			0.789003	−	0.614390i	$-0.210598\pi$
$431$	680.120			1.57801			0.789003	+	0.614390i	$0.210598\pi$
$432$		0			0
$433$	−416.479	−	416.479i	−0.961845	−	0.961845i	0.0374530	−	0.999298i	$-0.488076\pi$
$433$	−416.479	−	416.479i	−0.961845	−	0.961845i	−0.999298	+	0.0374530i	$0.988076\pi$
$434$			248.677i			0.572987i
$435$		0			0
$436$	−209.151			−0.479704
$437$	−292.184	+	292.184i	−0.668613	+	0.668613i
$438$		0			0
$439$		−	325.277i		−	0.740950i	−0.928842	−	0.370475i	$-0.879195\pi$
$439$		−	325.277i		−	0.740950i	0.928842	−	0.370475i	$-0.120805\pi$
$440$	−141.394	−	31.7775i	−0.321350	−	0.0722217i
$441$		0			0
$442$	112.020	−	112.020i	0.253440	−	0.253440i
$443$	−310.330	−	310.330i	−0.700520	−	0.700520i	0.264002	−	0.964522i	$-0.414957\pi$
$443$	−310.330	−	310.330i	−0.700520	−	0.700520i	−0.964522	+	0.264002i	$0.914957\pi$
$444$		0			0
$445$	187.075	+	295.540i	0.420393	+	0.664136i
$446$	−16.7378			−0.0375286
$447$		0			0
$448$	35.5959	+	35.5959i	0.0794552	+	0.0794552i
$449$			184.697i			0.411352i	0.978620	+	0.205676i	$0.0659393\pi$
$449$			184.697i			0.411352i	−0.978620	+	0.205676i	$0.934061\pi$
$450$		0			0
$451$	271.970			0.603039
$452$	−210.565	+	210.565i	−0.465852	+	0.465852i
$453$		0			0
$454$			13.8230i			0.0304470i
$455$	−133.485	+	84.4949i	−0.293373	+	0.185703i
$456$		0			0
$457$	520.182	−	520.182i	1.13825	−	1.13825i	0.149490	−	0.988763i	$-0.452237\pi$
$457$	520.182	−	520.182i	1.13825	−	1.13825i	0.988763	−	0.149490i	$-0.0477631\pi$
$458$	246.242	+	246.242i	0.537646	+	0.537646i
$459$		0			0
$460$	−46.5857	+	207.283i	−0.101273	+	0.450614i
$461$	808.286			1.75333			0.876666	−	0.481099i	$-0.159762\pi$
$461$	808.286			1.75333			0.876666	+	0.481099i	$0.159762\pi$
$462$		0			0
$463$	−38.8934	−	38.8934i	−0.0840029	−	0.0840029i	0.663857	−	0.747860i	$-0.268918\pi$
$463$	−38.8934	−	38.8934i	−0.0840029	−	0.0840029i	−0.747860	+	0.663857i	$0.768918\pi$
$464$		−	143.192i		−	0.308603i
$465$		0			0
$466$	365.171			0.783630
$467$	−80.8411	+	80.8411i	−0.173107	+	0.173107i	−0.788343	−	0.615236i	$-0.789061\pi$
$467$	−80.8411	+	80.8411i	−0.173107	+	0.173107i	0.615236	+	0.788343i	$0.289061\pi$
$468$		0			0
$469$			763.019i			1.62691i
$470$	53.7276	+	84.8786i	0.114314	+	0.180593i
$471$		0			0
$472$	156.182	−	156.182i	0.330893	−	0.330893i
$473$	309.389	+	309.389i	0.654100	+	0.654100i
$474$		0			0
$475$	439.479	+	208.050i	0.925219	+	0.438000i
$476$	280.767			0.589847
$477$		0			0
$478$	−174.409	−	174.409i	−0.364872	−	0.364872i
$479$			311.773i			0.650883i	0.945562	+	0.325442i	$0.105513\pi$
$479$			311.773i			0.650883i	−0.945562	+	0.325442i	$0.894487\pi$
$480$		0			0
$481$	−272.636			−0.566810
$482$	190.333	−	190.333i	0.394881	−	0.394881i
$483$		0			0
$484$			31.9796i			0.0660735i
$485$	−122.647	+	545.716i	−0.252880	+	1.12519i
$486$		0			0
$487$	−323.424	+	323.424i	−0.664116	+	0.664116i	−0.956348	−	0.292232i	$-0.905602\pi$
$487$	−323.424	+	323.424i	−0.664116	+	0.664116i	0.292232	+	0.956348i	$0.405602\pi$
$488$	209.555	+	209.555i	0.429416	+	0.429416i
$489$		0			0
$490$	64.8786	+	14.5811i	0.132405	+	0.0297574i
$491$	−753.914			−1.53547			−0.767733	−	0.640770i	$-0.778615\pi$
$491$	−753.914			−1.53547			−0.767733	+	0.640770i	$0.778615\pi$
$492$		0			0
$493$	−564.722	−	564.722i	−1.14548	−	1.14548i
$494$		−	138.111i		−	0.279577i
$495$		0			0
$496$	−111.778			−0.225358
$497$	276.969	−	276.969i	0.557282	−	0.557282i
$498$		0			0
$499$		−	535.388i		−	1.07292i	−0.843925	−	0.536461i	$-0.819761\pi$
$499$		−	535.388i		−	1.07292i	0.843925	−	0.536461i	$-0.180239\pi$
$500$	248.136	−	30.4699i	0.496272	−	0.0609398i
$501$		0			0
$502$	−421.707	+	421.707i	−0.840054	+	0.840054i
$503$	209.704	+	209.704i	0.416906	+	0.416906i	0.884136	−	0.467230i	$-0.154748\pi$
$503$	209.704	+	209.704i	0.416906	+	0.416906i	−0.467230	+	0.884136i	$0.654748\pi$
$504$		0			0
$505$	−358.677	+	227.040i	−0.710251	+	0.449584i
$506$	−307.889			−0.608476
$507$		0			0
$508$	340.252	+	340.252i	0.669787	+	0.669787i
$509$			57.2122i			0.112401i	0.998419	+	0.0562006i	$0.0178986\pi$
$509$			57.2122i			0.112401i	−0.998419	+	0.0562006i	$0.982101\pi$
$510$		0			0
$511$	467.646			0.915158
$512$	−16.0000	+	16.0000i	−0.0312500	+	0.0312500i
$513$		0			0
$514$			177.258i			0.344859i
$515$	−297.212	−	66.7969i	−0.577111	−	0.129703i
$516$		0			0
$517$	−102.940	+	102.940i	−0.199110	+	0.199110i
$518$	−341.666	−	341.666i	−0.659587	−	0.659587i
$519$		0			0
$520$	−37.9796	−	60.0000i	−0.0730377	−	0.115385i
$521$	344.611			0.661441			0.330720	−	0.943729i	$-0.392708\pi$
$521$	344.611			0.661441			0.330720	+	0.943729i	$0.392708\pi$
$522$		0			0
$523$	−66.7923	−	66.7923i	−0.127710	−	0.127710i	0.640363	−	0.768073i	$-0.278784\pi$
$523$	−66.7923	−	66.7923i	−0.127710	−	0.127710i	−0.768073	+	0.640363i	$0.778784\pi$
$524$			292.717i			0.558621i
$525$		0			0
$526$	−50.2429			−0.0955187
$527$	−440.830	+	440.830i	−0.836489	+	0.836489i
$528$		0			0
$529$		−	77.6367i		−	0.146761i
$530$	−400.646	+	253.606i	−0.755936	+	0.478502i
$531$		0			0
$532$	173.081	−	173.081i	0.325339	−	0.325339i
$533$	94.2316	+	94.2316i	0.176795	+	0.176795i
$534$		0			0
$535$	−83.4847	+	371.464i	−0.156046	+	0.694326i
$536$	−342.969			−0.639868
$537$		0			0
$538$	197.621	+	197.621i	0.367325	+	0.367325i
$539$			96.3678i			0.178790i
$540$		0			0
$541$	−943.383			−1.74378			−0.871888	−	0.489706i	$-0.837104\pi$
$541$	−943.383			−1.74378			−0.871888	+	0.489706i	$0.837104\pi$
$542$	158.258	−	158.258i	0.291988	−	0.291988i
$543$		0			0
$544$			126.202i			0.231989i
$545$	279.659	+	441.805i	0.513137	+	0.810651i
$546$		0			0
$547$	669.929	−	669.929i	1.22473	−	1.22473i	0.258802	−	0.965930i	$-0.416672\pi$
$547$	669.929	−	669.929i	1.22473	−	1.22473i	0.965930	−	0.258802i	$-0.0833277\pi$
$548$	−71.1464	−	71.1464i	−0.129829	−	0.129829i
$549$		0			0
$550$	121.934	+	341.167i	0.221699	+	0.620303i
$551$	−696.252			−1.26362
$552$		0			0
$553$	−465.601	−	465.601i	−0.841954	−	0.841954i
$554$			165.464i			0.298672i
$555$		0			0
$556$	247.778			0.445643
$557$	128.586	−	128.586i	0.230854	−	0.230854i	−0.582195	−	0.813049i	$-0.697806\pi$
$557$	128.586	−	128.586i	0.230854	−	0.230854i	0.813049	+	0.582195i	$0.197806\pi$
$558$		0			0
$559$			214.393i			0.383529i
$560$	27.5959	−	122.788i	0.0492784	−	0.219264i
$561$		0			0
$562$	−123.353	+	123.353i	−0.219489	+	0.219489i
$563$	53.5301	+	53.5301i	0.0950801	+	0.0950801i	0.753047	−	0.657967i	$-0.228583\pi$
$563$	53.5301	+	53.5301i	0.0950801	+	0.0950801i	−0.657967	+	0.753047i	$0.728583\pi$
$564$		0			0
$565$	726.343	+	163.242i	1.28556	+	0.288924i
$566$	389.959			0.688974
$567$		0			0
$568$	124.495	+	124.495i	0.219181	+	0.219181i
$569$		−	449.959i		−	0.790789i	−0.918511	−	0.395395i	$-0.870608\pi$
$569$		−	449.959i		−	0.790789i	0.918511	−	0.395395i	$-0.129392\pi$
$570$		0			0
$571$	28.7526			0.0503547			0.0251774	−	0.999683i	$-0.491985\pi$
$571$	28.7526			0.0503547			0.0251774	+	0.999683i	$0.491985\pi$
$572$	72.7673	−	72.7673i	0.127216	−	0.127216i
$573$		0			0
$574$			236.182i			0.411466i
$575$	500.149	−	178.755i	0.869824	−	0.310878i
$576$		0			0
$577$	−664.135	+	664.135i	−1.15101	+	1.15101i	−0.164665	+	0.986350i	$0.552654\pi$
$577$	−664.135	+	664.135i	−1.15101	+	1.15101i	−0.986350	+	0.164665i	$0.947346\pi$
$578$	208.717	+	208.717i	0.361103	+	0.361103i
$579$		0			0
$580$	−302.474	+	191.464i	−0.521508	+	0.330111i
$581$	−286.677			−0.493419
$582$		0			0
$583$	−485.899	−	485.899i	−0.833446	−	0.833446i
$584$			210.202i			0.359935i
$585$		0			0
$586$	105.984			0.180860
$587$	304.083	−	304.083i	0.518029	−	0.518029i	−0.398946	−	0.916975i	$-0.630624\pi$
$587$	304.083	−	304.083i	0.518029	−	0.518029i	0.916975	+	0.398946i	$0.130624\pi$
$588$		0			0
$589$			543.504i			0.922757i
$590$	−538.747	−	121.081i	−0.913130	−	0.205221i
$591$		0			0
$592$	153.576	−	153.576i	0.259418	−	0.259418i
$593$	−588.102	−	588.102i	−0.991741	−	0.991741i	0.00822539	−	0.999966i	$-0.497382\pi$
$593$	−588.102	−	588.102i	−0.991741	−	0.991741i	−0.999966	+	0.00822539i	$0.997382\pi$
$594$		0			0
$595$	−375.419	−	593.085i	−0.630956	−	0.996782i
$596$	434.474			0.728984
$597$		0			0
$598$	−106.677	−	106.677i	−0.178389	−	0.178389i
$599$			160.252i			0.267533i	0.991013	+	0.133766i	$0.0427072\pi$
$599$			160.252i			0.267533i	−0.991013	+	0.133766i	$0.957293\pi$
$600$		0			0
$601$	−1157.79			−1.92644			−0.963218	−	0.268722i	$-0.913399\pi$
$601$	−1157.79			−1.92644			−0.963218	+	0.268722i	$0.913399\pi$
$602$	−268.677	+	268.677i	−0.446307	+	0.446307i
$603$		0			0
$604$			285.616i			0.472875i
$605$	67.5528	−	42.7605i	0.111658	−	0.0706785i
$606$		0			0
$607$	312.303	−	312.303i	0.514503	−	0.514503i	−0.401400	−	0.915903i	$-0.631476\pi$
$607$	312.303	−	312.303i	0.514503	−	0.514503i	0.915903	+	0.401400i	$0.131476\pi$
$608$	77.7980	+	77.7980i	0.127957	+	0.127957i
$609$		0			0
$610$	162.459	−	722.858i	0.266326	−	1.18501i
$611$	−71.3326			−0.116747
$612$		0			0
$613$	687.959	+	687.959i	1.12228	+	1.12228i	0.991398	+	0.130885i	$0.0417818\pi$
$613$	687.959	+	687.959i	1.12228	+	1.12228i	0.130885	+	0.991398i	$0.458218\pi$
$614$			372.211i			0.606207i
$615$		0			0
$616$	182.384			0.296077
$617$	−213.421	+	213.421i	−0.345901	+	0.345901i	−0.858580	−	0.512679i	$-0.828653\pi$
$617$	−213.421	+	213.421i	−0.345901	+	0.345901i	0.512679	+	0.858580i	$0.328653\pi$
$618$		0			0
$619$			86.9082i			0.140401i	0.997533	+	0.0702004i	$0.0223639\pi$
$619$			86.9082i			0.140401i	−0.997533	+	0.0702004i	$0.977636\pi$
$620$	149.460	+	236.116i	0.241064	+	0.380832i
$621$		0			0
$622$	246.858	−	246.858i	0.396878	−	0.396878i
$623$	−311.262	−	311.262i	−0.499618	−	0.499618i
$624$		0			0
$625$	−396.151	−	483.414i	−0.633842	−	0.773463i
$626$	420.322			0.671442
$627$		0			0
$628$	59.6663	+	59.6663i	0.0950101	+	0.0950101i
$629$		−	1211.35i		−	1.92583i
$630$		0			0
$631$	302.298			0.479078			0.239539	−	0.970887i	$-0.423004\pi$
$631$	302.298			0.479078			0.239539	+	0.970887i	$0.423004\pi$
$632$	209.283	−	209.283i	0.331143	−	0.331143i
$633$		0			0
$634$			488.722i			0.770855i
$635$	263.782	−	1173.70i	0.415405	−	1.84834i
$636$		0			0
$637$	−33.3893	+	33.3893i	−0.0524165	+	0.0524165i
$638$	−366.838	−	366.838i	−0.574981	−	0.574981i
$639$		0			0
$640$	55.1918	+	12.4041i	0.0862372	+	0.0193814i
$641$	667.060			1.04066			0.520328	−	0.853967i	$-0.325810\pi$
$641$	667.060			1.04066			0.520328	+	0.853967i	$0.325810\pi$
$642$		0			0
$643$	246.581	+	246.581i	0.383485	+	0.383485i	0.872356	−	0.488871i	$-0.162591\pi$
$643$	246.581	+	246.581i	0.383485	+	0.383485i	−0.488871	+	0.872356i	$0.662591\pi$
$644$		−	267.373i		−	0.415176i
$645$		0			0
$646$	613.641			0.949909
$647$	43.7900	−	43.7900i	0.0676817	−	0.0676817i	−0.672456	−	0.740137i	$-0.734760\pi$
$647$	43.7900	−	43.7900i	0.0676817	−	0.0676817i	0.740137	+	0.672456i	$0.234760\pi$
$648$		0			0
$649$		−	800.232i		−	1.23302i
$650$	−75.9592	+	160.454i	−0.116860	+	0.246852i
$651$		0			0
$652$	−122.717	+	122.717i	−0.188217	+	0.188217i
$653$	72.4268	+	72.4268i	0.110914	+	0.110914i	0.760386	−	0.649472i	$-0.225010\pi$
$653$	72.4268	+	72.4268i	0.110914	+	0.110914i	−0.649472	+	0.760386i	$0.725010\pi$
$654$		0			0
$655$	618.328	−	391.397i	0.944012	−	0.597553i
$656$	−106.161			−0.161831
$657$		0			0
$658$	−89.3939	−	89.3939i	−0.135857	−	0.135857i
$659$		−	346.636i		−	0.526003i	−0.964795	−	0.263001i	$-0.915288\pi$
$659$		−	346.636i		−	0.526003i	0.964795	−	0.263001i	$-0.0847124\pi$
$660$		0			0
$661$	−474.152			−0.717325			−0.358663	−	0.933467i	$-0.616767\pi$
$661$	−474.152			−0.717325			−0.358663	+	0.933467i	$0.616767\pi$
$662$	551.464	−	551.464i	0.833028	−	0.833028i
$663$		0			0
$664$		−	128.858i		−	0.194063i
$665$	−597.040	−	134.182i	−0.897804	−	0.201777i
$666$		0			0
$667$	−537.782	+	537.782i	−0.806270	+	0.806270i
$668$	−272.479	−	272.479i	−0.407903	−	0.407903i
$669$		0			0
$670$	458.590	+	724.479i	0.684463	+	1.08131i
$671$	1073.70			1.60015
$672$		0			0
$673$	−70.7332	−	70.7332i	−0.105101	−	0.105101i	0.652601	−	0.757702i	$-0.273678\pi$
$673$	−70.7332	−	70.7332i	−0.105101	−	0.105101i	−0.757702	+	0.652601i	$0.773678\pi$
$674$		−	77.5663i		−	0.115084i
$675$		0			0
$676$	−287.576			−0.425408
$677$	−162.009	+	162.009i	−0.239305	+	0.239305i	−0.816562	−	0.577258i	$-0.804123\pi$
$677$	−162.009	+	162.009i	−0.239305	+	0.239305i	0.577258	+	0.816562i	$0.304123\pi$
$678$		0			0
$679$		−	703.918i		−	1.03670i
$680$	266.586	−	168.747i	0.392038	−	0.248157i
$681$		0			0
$682$	−286.359	+	286.359i	−0.419881	+	0.419881i
$683$	855.304	+	855.304i	1.25228	+	1.25228i	0.954697	+	0.297578i	$0.0961789\pi$
$683$	855.304	+	855.304i	1.25228	+	1.25228i	0.297578	+	0.954697i	$0.403821\pi$
$684$		0			0
$685$	−55.1566	+	245.419i	−0.0805206	+	0.358276i
$686$	−519.737			−0.757634
$687$		0			0
$688$	−120.767	−	120.767i	−0.175534	−	0.175534i
$689$		−	336.706i		−	0.488688i
$690$		0			0
$691$	122.430			0.177178			0.0885891	−	0.996068i	$-0.471764\pi$
$691$	122.430			0.177178			0.0885891	+	0.996068i	$0.471764\pi$
$692$	299.601	−	299.601i	0.432949	−	0.432949i
$693$		0			0
$694$			805.444i			1.16058i
$695$	−331.308	−	523.398i	−0.476702	−	0.753091i
$696$		0			0
$697$	−418.680	+	418.680i	−0.600689	+	0.600689i
$698$	−491.272	−	491.272i	−0.703829	−	0.703829i
$699$		0			0
$700$	−296.272	+	105.889i	−0.423246	+	0.151270i
$701$	−1322.17			−1.88613			−0.943063	−	0.332613i	$-0.892070\pi$
$701$	−1322.17			−1.88613			−0.943063	+	0.332613i	$0.892070\pi$
$702$		0			0
$703$	−746.741	−	746.741i	−1.06222	−	1.06222i
$704$			81.9796i			0.116448i
$705$		0			0
$706$	137.171			0.194294
$707$	377.757	−	377.757i	0.534310	−	0.534310i
$708$		0			0
$709$			779.909i			1.10001i	0.835160	+	0.550006i	$0.185375\pi$
$709$			779.909i			1.10001i	−0.835160	+	0.550006i	$0.814625\pi$
$710$	96.5153	−	429.444i	0.135937	−	0.604851i
$711$		0			0
$712$	139.909	−	139.909i	0.196502	−	0.196502i
$713$	419.800	+	419.800i	0.588780	+	0.588780i
$714$		0			0
$715$	−251.010	−	56.4133i	−0.351063	−	0.0788997i
$716$	372.504			0.520257
$717$		0			0
$718$	353.773	+	353.773i	0.492720	+	0.492720i
$719$		−	572.652i		−	0.796456i	−0.917287	−	0.398228i	$-0.869625\pi$
$719$		−	572.652i		−	0.796456i	0.917287	−	0.398228i	$-0.130375\pi$
$720$		0			0
$721$	383.373			0.531725
$722$	17.2827	−	17.2827i	0.0239372	−	0.0239372i
$723$		0			0
$724$		−	516.747i		−	0.713739i
$725$	808.888	+	382.929i	1.11571	+	0.528177i
$726$		0			0
$727$	231.748	−	231.748i	0.318773	−	0.318773i	−0.529523	−	0.848296i	$-0.677629\pi$
$727$	231.748	−	231.748i	0.318773	−	0.318773i	0.848296	+	0.529523i	$0.177629\pi$
$728$	63.1918	+	63.1918i	0.0868020	+	0.0868020i
$729$		0			0
$730$	444.025	−	281.065i	0.608253	−	0.385020i
$731$	−952.568			−1.30310
$732$		0			0
$733$	739.626	+	739.626i	1.00904	+	1.00904i	0.999959	+	0.00908011i	$0.00289033\pi$
$733$	739.626	+	739.626i	1.00904	+	1.00904i	0.00908011	+	0.999959i	$0.497110\pi$
$734$			481.403i			0.655862i
$735$		0			0
$736$	120.182			0.163290
$737$	−878.640	+	878.640i	−1.19218	+	1.19218i
$738$		0			0
$739$		−	506.539i		−	0.685439i	−0.939438	−	0.342719i	$-0.888652\pi$
$739$		−	506.539i		−	0.685439i	0.939438	−	0.342719i	$-0.111348\pi$
$740$	−529.757	−	119.060i	−0.715888	−	0.160892i
$741$		0			0
$742$	421.959	−	421.959i	0.568678	−	0.568678i
$743$	10.7219	+	10.7219i	0.0144306	+	0.0144306i	0.714285	−	0.699855i	$-0.246752\pi$
$743$	10.7219	+	10.7219i	0.0144306	+	0.0144306i	−0.699855	+	0.714285i	$0.746752\pi$
$744$		0			0
$745$	−580.943	−	917.772i	−0.779790	−	1.23191i
$746$	−846.120			−1.13421
$747$		0			0
$748$	323.312	+	323.312i	0.432236	+	0.432236i
$749$		−	479.151i		−	0.639721i
$750$		0			0
$751$	813.075			1.08266			0.541328	−	0.840811i	$-0.317922\pi$
$751$	813.075			1.08266			0.541328	+	0.840811i	$0.317922\pi$
$752$	40.1816	−	40.1816i	0.0534330	−	0.0534330i
$753$		0			0
$754$		−	254.202i		−	0.337138i
$755$	603.328	−	381.903i	0.799110	−	0.505831i
$756$		0			0
$757$	132.514	−	132.514i	0.175052	−	0.175052i	−0.614143	−	0.789195i	$-0.710498\pi$
$757$	132.514	−	132.514i	0.175052	−	0.175052i	0.789195	+	0.614143i	$0.210498\pi$
$758$	−57.1066	−	57.1066i	−0.0753386	−	0.0753386i
$759$		0			0
$760$	60.3133	−	268.363i	0.0793596	−	0.353110i
$761$	−412.252			−0.541724			−0.270862	−	0.962618i	$-0.587309\pi$
$761$	−412.252			−0.541724			−0.270862	+	0.962618i	$0.587309\pi$
$762$		0			0
$763$	−465.308	−	465.308i	−0.609840	−	0.609840i
$764$			377.848i			0.494565i
$765$		0			0
$766$	−724.974			−0.946441
$767$	277.262	−	277.262i	0.361489	−	0.361489i
$768$		0			0
$769$		−	867.393i		−	1.12795i	−0.825792	−	0.563975i	$-0.809272\pi$
$769$		−	867.393i		−	1.12795i	0.825792	−	0.563975i	$-0.190728\pi$
$770$	−243.868	−	385.262i	−0.316712	−	0.500341i
$771$		0			0
$772$	−362.474	+	362.474i	−0.469527	+	0.469527i
$773$	−295.578	−	295.578i	−0.382377	−	0.382377i	0.489581	−	0.871958i	$-0.337150\pi$
$773$	−295.578	−	295.578i	−0.382377	−	0.382377i	−0.871958	+	0.489581i	$0.837150\pi$
$774$		0			0
$775$	298.919	−	631.429i	0.385702	−	0.814747i
$776$	316.404			0.407737
$777$		0			0
$778$	477.106	+	477.106i	0.613246	+	0.613246i
$779$			516.195i			0.662639i
$780$		0			0
$781$	637.878			0.816745
$782$	473.974	−	473.974i	0.606105	−	0.606105i
$783$		0			0
$784$		−	37.6163i		−	0.0479800i
$785$	46.2566	−	205.818i	0.0589256	−	0.262189i
$786$		0			0
$787$	179.899	−	179.899i	0.228588	−	0.228588i	−0.583514	−	0.812103i	$-0.698323\pi$
$787$	179.899	−	179.899i	0.228588	−	0.228588i	0.812103	+	0.583514i	$0.198323\pi$
$788$	363.551	+	363.551i	0.461359	+	0.461359i
$789$		0			0
$790$	−721.918	−	162.247i	−0.913821	−	0.205377i
$791$	−936.908			−1.18446
$792$		0			0
$793$	372.014	+	372.014i	0.469122	+	0.469122i
$794$			260.595i			0.328205i
$795$		0			0
$796$	−134.647			−0.169154
$797$	40.0023	−	40.0023i	0.0501911	−	0.0501911i	−0.681566	−	0.731757i	$-0.738701\pi$
$797$	40.0023	−	40.0023i	0.0501911	−	0.0501911i	0.731757	+	0.681566i	$0.238701\pi$
$798$		0			0
$799$		−	316.938i		−	0.396668i
$800$	−47.5959	−	133.171i	−0.0594949	−	0.166464i
$801$		0			0
$802$	−91.7821	+	91.7821i	−0.114442	+	0.114442i
$803$	538.509	+	538.509i	0.670621	+	0.670621i
$804$		0			0
$805$	−564.792	+	357.510i	−0.701605	+	0.444111i
$806$	−198.434			−0.246196
$807$		0			0
$808$	169.798	+	169.798i	0.210146	+	0.210146i
$809$			135.875i			0.167954i	0.996468	+	0.0839771i	$0.0267623\pi$
$809$			135.875i			0.167954i	−0.996468	+	0.0839771i	$0.973238\pi$
$810$		0			0
$811$	1361.17			1.67838			0.839192	−	0.543835i	$-0.183028\pi$
$811$	1361.17			1.67838			0.839192	+	0.543835i	$0.183028\pi$
$812$	318.565	−	318.565i	0.392322	−	0.392322i
$813$		0			0
$814$		−	786.879i		−	0.966681i
$815$	423.312	+	95.1373i	0.519402	+	0.116733i
$816$		0			0
$817$	−587.216	+	587.216i	−0.718746	+	0.718746i
$818$	−23.2520	−	23.2520i	−0.0284255	−	0.0284255i
$819$		0			0
$820$	141.950	+	224.252i	0.173110	+	0.273478i
$821$	369.630			0.450219			0.225110	−	0.974333i	$-0.427726\pi$
$821$	369.630			0.450219			0.225110	+	0.974333i	$0.427726\pi$
$822$		0			0
$823$	752.514	+	752.514i	0.914355	+	0.914355i	0.996611	−	0.0822561i	$-0.0262125\pi$
$823$	752.514	+	752.514i	0.914355	+	0.914355i	−0.0822561	+	0.996611i	$0.526213\pi$
$824$			172.322i			0.209129i
$825$		0			0
$826$	694.929			0.841318
$827$	263.579	−	263.579i	0.318717	−	0.318717i	−0.529557	−	0.848274i	$-0.677642\pi$
$827$	263.579	−	263.579i	0.318717	−	0.318717i	0.848274	+	0.529557i	$0.177642\pi$
$828$		0			0
$829$		−	367.171i		−	0.442909i	−0.975171	−	0.221454i	$-0.928920\pi$
$829$		−	367.171i		−	0.442909i	0.975171	−	0.221454i	$-0.0710804\pi$
$830$	−272.196	+	172.298i	−0.327947	+	0.207589i
$831$		0			0
$832$	−28.4041	+	28.4041i	−0.0341395	+	0.0341395i
$833$	−148.352	−	148.352i	−0.178093	−	0.178093i
$834$		0			0
$835$	−211.241	+	939.914i	−0.252983	+	1.12565i
$836$	398.615			0.476813
$837$		0			0
$838$	−675.551	−	675.551i	−0.806146	−	0.806146i
$839$			601.970i			0.717486i	0.933436	+	0.358743i	$0.116794\pi$
$839$			601.970i			0.717486i	−0.933436	+	0.358743i	$0.883206\pi$
$840$		0			0
$841$	−440.494			−0.523774
$842$	−307.252	+	307.252i	−0.364907	+	0.364907i
$843$		0			0
$844$		−	383.040i		−	0.453839i
$845$	384.522	+	607.467i	0.455056	+	0.718895i
$846$		0			0
$847$	−71.1464	+	71.1464i	−0.0839981	+	0.0839981i
$848$	189.666	+	189.666i	0.223663	+	0.223663i
$849$		0			0
$850$	−712.913	−	337.494i	−0.838721	−	0.397052i
$851$	−1153.56			−1.35553
$852$		0			0
$853$	370.767	+	370.767i	0.434663	+	0.434663i	0.890211	−	0.455548i	$-0.150557\pi$
$853$	370.767	+	370.767i	0.434663	+	0.434663i	−0.455548	+	0.890211i	$0.650557\pi$
$854$			932.413i			1.09182i
$855$		0			0
$856$	215.373			0.251605
$857$	128.073	−	128.073i	0.149443	−	0.149443i	−0.628426	−	0.777869i	$-0.716301\pi$
$857$	128.073	−	128.073i	0.149443	−	0.149443i	0.777869	+	0.628426i	$0.216301\pi$
$858$		0			0
$859$			518.610i			0.603737i	0.953350	+	0.301868i	$0.0976103\pi$
$859$			518.610i			0.603737i	−0.953350	+	0.301868i	$0.902390\pi$
$860$	−93.6255	+	416.586i	−0.108867	+	0.484402i
$861$		0			0
$862$	−680.120	+	680.120i	−0.789003	+	0.789003i
$863$	519.729	+	519.729i	0.602235	+	0.602235i	0.940905	−	0.338670i	$-0.109977\pi$
$863$	519.729	+	519.729i	0.602235	+	0.602235i	−0.338670	+	0.940905i	$0.609977\pi$
$864$		0			0
$865$	−1033.47	−	232.267i	−1.19476	−	0.268517i
$866$	832.958			0.961845
$867$		0			0
$868$	−248.677	−	248.677i	−0.286494	−	0.286494i
$869$		−	1072.31i		−	1.23395i
$870$		0			0
$871$	−608.858			−0.699033
$872$	209.151	−	209.151i	0.239852	−	0.239852i
$873$		0			0
$874$		−	584.368i		−	0.668613i
$875$	619.828	+	484.252i	0.708374	+	0.553431i
$876$		0			0
$877$	−339.915	+	339.915i	−0.387588	+	0.387588i	−0.873826	−	0.486238i	$-0.838369\pi$
$877$	−339.915	+	339.915i	−0.387588	+	0.387588i	0.486238	+	0.873826i	$0.338369\pi$
$878$	325.277	+	325.277i	0.370475	+	0.370475i
$879$		0			0
$880$	173.171	−	109.616i	0.196786	−	0.124564i
$881$	1325.62			1.50468			0.752340	−	0.658775i	$-0.228925\pi$
$881$	1325.62			1.50468			0.752340	+	0.658775i	$0.228925\pi$
$882$		0			0
$883$	393.358	+	393.358i	0.445479	+	0.445479i	0.893848	−	0.448370i	$-0.147995\pi$
$883$	393.358	+	393.358i	0.445479	+	0.445479i	−0.448370	+	0.893848i	$0.647995\pi$
$884$			224.041i			0.253440i
$885$		0			0
$886$	620.661			0.700520
$887$	−430.936	+	430.936i	−0.485836	+	0.485836i	−0.906989	−	0.421153i	$-0.861625\pi$
$887$	−430.936	+	430.936i	−0.485836	+	0.485836i	0.421153	+	0.906989i	$0.361625\pi$
$888$		0			0
$889$			1513.95i			1.70298i
$890$	−482.615	−	108.465i	−0.542264	−	0.121871i
$891$		0			0
$892$	16.7378	−	16.7378i	0.0187643	−	0.0187643i
$893$	−195.378	−	195.378i	−0.218788	−	0.218788i
$894$		0			0
$895$	−498.082	−	786.867i	−0.556516	−	0.879181i
$896$	−71.1918			−0.0794552
$897$		0			0
$898$	−184.697	−	184.697i	−0.205676	−	0.205676i
$899$			1000.35i			1.11274i
$900$		0			0
$901$	1496.02			1.66040
$902$	−271.970	+	271.970i	−0.301519	+	0.301519i
$903$		0			0
$904$		−	421.131i		−	0.465852i
$905$	−1091.56	+	690.951i	−1.20615	+	0.763482i
$906$		0			0
$907$	−1199.45	+	1199.45i	−1.32244	+	1.32244i	−0.410644	+	0.911796i	$0.634696\pi$
$907$	−1199.45	+	1199.45i	−1.32244	+	1.32244i	−0.911796	+	0.410644i	$0.865304\pi$
$908$	−13.8230	−	13.8230i	−0.0152235	−	0.0152235i
$909$		0			0
$910$	48.9898	−	217.980i	0.0538349	−	0.239538i
$911$	−1159.45			−1.27273			−0.636363	−	0.771390i	$-0.719562\pi$
$911$	−1159.45			−1.27273			−0.636363	+	0.771390i	$0.719562\pi$
$912$		0			0
$913$	−330.117	−	330.117i	−0.361574	−	0.361574i
$914$			1040.36i			1.13825i
$915$		0			0
$916$	−492.484			−0.537646
$917$	−651.221	+	651.221i	−0.710165	+	0.710165i
$918$		0			0
$919$		−	279.362i		−	0.303985i	−0.988382	−	0.151993i	$-0.951431\pi$
$919$		−	279.362i		−	0.303985i	0.988382	−	0.151993i	$-0.0485690\pi$
$920$	−160.697	−	253.868i	−0.174671	−	0.275944i
$921$		0			0
$922$	−808.286	+	808.286i	−0.876666	+	0.876666i
$923$	221.010	+	221.010i	0.239448	+	0.239448i
$924$		0			0
$925$	456.848	+	1278.24i	0.493890	+	1.38188i
$926$	77.7867			0.0840029
$927$		0			0
$928$	143.192	+	143.192i	0.154302	+	0.154302i
$929$			1140.90i			1.22810i	0.789269	+	0.614048i	$0.210460\pi$
$929$			1140.90i			1.22810i	−0.789269	+	0.614048i	$0.789540\pi$
$930$		0			0
$931$	−182.905			−0.196460
$932$	−365.171	+	365.171i	−0.391815	+	0.391815i
$933$		0			0
$934$		−	161.682i		−	0.173107i
$935$	250.649	−	1115.26i	0.268074	−	1.19279i
$936$		0			0
$937$	−267.535	+	267.535i	−0.285523	+	0.285523i	−0.835307	−	0.549784i	$-0.814710\pi$
$937$	−267.535	+	267.535i	−0.285523	+	0.285523i	0.549784	+	0.835307i	$0.314710\pi$
$938$	−763.019	−	763.019i	−0.813453	−	0.813453i
$939$		0			0
$940$	−138.606	−	31.1510i	−0.147453	−	0.0331394i
$941$	859.065			0.912928			0.456464	−	0.889742i	$-0.349116\pi$
$941$	859.065			0.912928			0.456464	+	0.889742i	$0.349116\pi$
$942$		0			0
$943$	398.707	+	398.707i	0.422807	+	0.422807i
$944$			312.363i			0.330893i
$945$		0			0
$946$	−618.779			−0.654100
$947$	−675.159	+	675.159i	−0.712945	+	0.712945i	−0.967150	−	0.254205i	$-0.918186\pi$
$947$	−675.159	+	675.159i	−0.712945	+	0.712945i	0.254205	+	0.967150i	$0.418186\pi$
$948$		0			0
$949$			373.162i			0.393216i
$950$	−647.529	+	231.429i	−0.681610	+	0.243610i
$951$		0			0
$952$	−280.767	+	280.767i	−0.294924	+	0.294924i
$953$	297.873	+	297.873i	0.312563	+	0.312563i	0.845902	−	0.533338i	$-0.179063\pi$
$953$	297.873	+	297.873i	0.312563	+	0.312563i	−0.533338	+	0.845902i	$0.679063\pi$
$954$		0			0
$955$	798.156	−	505.227i	0.835765	−	0.529034i
$956$	348.817			0.364872
$957$		0			0
$958$	−311.773	−	311.773i	−0.325442	−	0.325442i
$959$		−	316.565i		−	0.330099i
$960$		0			0
$961$	−180.111			−0.187421
$962$	272.636	−	272.636i	0.283405	−	0.283405i
$963$		0			0
$964$			380.665i			0.394881i
$965$	1250.35	+	281.010i	1.29570	+	0.291202i
$966$		0			0
$967$	140.955	−	140.955i	0.145765	−	0.145765i	−0.630458	−	0.776223i	$-0.717133\pi$
$967$	140.955	−	140.955i	0.145765	−	0.145765i	0.776223	+	0.630458i	$0.217133\pi$
$968$	−31.9796	−	31.9796i	−0.0330368	−	0.0330368i
$969$		0			0
$970$	−423.069	−	668.363i	−0.436154	−	0.689034i
$971$	−1252.45			−1.28985			−0.644927	−	0.764245i	$-0.723112\pi$
$971$	−1252.45			−1.28985			−0.644927	+	0.764245i	$0.723112\pi$
$972$		0			0
$973$	551.242	+	551.242i	0.566538	+	0.566538i
$974$		−	646.849i		−	0.664116i
$975$		0			0
$976$	−419.110			−0.429416
$977$	−192.172	+	192.172i	−0.196696	+	0.196696i	−0.798582	−	0.601886i	$-0.794416\pi$
$977$	−192.172	+	192.172i	−0.196696	+	0.196696i	0.601886	+	0.798582i	$0.294416\pi$
$978$		0			0
$979$		−	716.856i		−	0.732233i
$980$	−79.4597	+	50.2974i	−0.0810813	+	0.0513239i
$981$		0			0
$982$	753.914	−	753.914i	0.767733	−	0.767733i
$983$	994.178	+	994.178i	1.01137	+	1.01137i	0.999935	+	0.0114370i	$0.00364060\pi$
$983$	994.178	+	994.178i	1.01137	+	1.01137i	0.0114370	+	0.999935i	$0.496359\pi$
$984$		0			0
$985$	281.844	−	1254.06i	0.286136	−	1.27316i
$986$	1129.44			1.14548
$987$		0			0
$988$	138.111	+	138.111i	0.139789	+	0.139789i
$989$			907.126i			0.917215i
$990$		0			0
$991$	651.166			0.657080			0.328540	−	0.944490i	$-0.393444\pi$
$991$	651.166			0.657080			0.328540	+	0.944490i	$0.393444\pi$
$992$	111.778	−	111.778i	0.112679	−	0.112679i
$993$		0			0
$994$			553.939i			0.557282i
$995$	180.039	+	284.424i	0.180943	+	0.285854i
$996$		0			0
$997$	−430.853	+	430.853i	−0.432149	+	0.432149i	−0.889359	−	0.457210i	$-0.848849\pi$
$997$	−430.853	+	430.853i	−0.432149	+	0.432149i	0.457210	+	0.889359i	$0.348849\pi$
$998$	535.388	+	535.388i	0.536461	+	0.536461i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	270.3.g.a.163.1	✓	4
3.2	odd	2		270.3.g.d.163.2	yes	4
5.2	odd	4	inner	270.3.g.a.217.1	yes	4
5.3	odd	4		1350.3.g.h.757.1		4
5.4	even	2		1350.3.g.h.1243.1		4
15.2	even	4		270.3.g.d.217.2	yes	4
15.8	even	4		1350.3.g.b.757.1		4
15.14	odd	2		1350.3.g.b.1243.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
270.3.g.a.163.1	✓	4	1.1	even	1	trivial
270.3.g.a.217.1	yes	4	5.2	odd	4	inner
270.3.g.d.163.2	yes	4	3.2	odd	2
270.3.g.d.217.2	yes	4	15.2	even	4
1350.3.g.b.757.1		4	15.8	even	4
1350.3.g.b.1243.1		4	15.14	odd	2
1350.3.g.h.757.1		4	5.3	odd	4
1350.3.g.h.1243.1		4	5.4	even	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:	\( N \)	\(=\)	\( 270 = 2 \cdot 3^{3} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	270.g (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.00000 + 1.00000i) q^{2} -2.00000i q^{4} +(-4.22474 + 2.67423i) q^{5} +(4.44949 - 4.44949i) q^{7} +(2.00000 + 2.00000i) q^{8} +O(q^{10})\)	\(q+(-1.00000 + 1.00000i) q^{2} -2.00000i q^{4} +(-4.22474 + 2.67423i) q^{5} +(4.44949 - 4.44949i) q^{7} +(2.00000 + 2.00000i) q^{8} +(1.55051 - 6.89898i) q^{10} +10.2474 q^{11} +(3.55051 + 3.55051i) q^{13} +8.89898i q^{14} -4.00000 q^{16} +(-15.7753 + 15.7753i) q^{17} +19.4495i q^{19} +(5.34847 + 8.44949i) q^{20} +(-10.2474 + 10.2474i) q^{22} +(15.0227 + 15.0227i) q^{23} +(10.6969 - 22.5959i) q^{25} -7.10102 q^{26} +(-8.89898 - 8.89898i) q^{28} +35.7980i q^{29} +27.9444 q^{31} +(4.00000 - 4.00000i) q^{32} -31.5505i q^{34} +(-6.89898 + 30.6969i) q^{35} +(-38.3939 + 38.3939i) q^{37} +(-19.4495 - 19.4495i) q^{38} +(-13.7980 - 3.10102i) q^{40} +26.5403 q^{41} +(30.1918 + 30.1918i) q^{43} -20.4949i q^{44} -30.0454 q^{46} +(-10.0454 + 10.0454i) q^{47} +9.40408i q^{49} +(11.8990 + 33.2929i) q^{50} +(7.10102 - 7.10102i) q^{52} +(-47.4166 - 47.4166i) q^{53} +(-43.2929 + 27.4041i) q^{55} +17.7980 q^{56} +(-35.7980 - 35.7980i) q^{58} -78.0908i q^{59} +104.778 q^{61} +(-27.9444 + 27.9444i) q^{62} +8.00000i q^{64} +(-24.4949 - 5.50510i) q^{65} +(-85.7423 + 85.7423i) q^{67} +(31.5505 + 31.5505i) q^{68} +(-23.7980 - 37.5959i) q^{70} +62.2474 q^{71} +(52.5505 + 52.5505i) q^{73} -76.7878i q^{74} +38.8990 q^{76} +(45.5959 - 45.5959i) q^{77} -104.641i q^{79} +(16.8990 - 10.6969i) q^{80} +(-26.5403 + 26.5403i) q^{82} +(-32.2145 - 32.2145i) q^{83} +(24.4597 - 108.833i) q^{85} -60.3837 q^{86} +(20.4949 + 20.4949i) q^{88} -69.9546i q^{89} +31.5959 q^{91} +(30.0454 - 30.0454i) q^{92} -20.0908i q^{94} +(-52.0125 - 82.1691i) q^{95} +(79.1010 - 79.1010i) q^{97} +(-9.40408 - 9.40408i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{2} - 12 q^{5} + 8 q^{7} + 8 q^{8}+O(q^{10}) \) 4 * q - 4 * q^2 - 12 * q^5 + 8 * q^7 + 8 * q^8	\( 4 q - 4 q^{2} - 12 q^{5} + 8 q^{7} + 8 q^{8} + 16 q^{10} - 8 q^{11} + 24 q^{13} - 16 q^{16} - 68 q^{17} - 8 q^{20} + 8 q^{22} + 16 q^{23} - 16 q^{25} - 48 q^{26} - 16 q^{28} + 4 q^{31} + 16 q^{32} - 8 q^{35} - 36 q^{37} - 68 q^{38} - 16 q^{40} - 80 q^{41} - 36 q^{43} - 32 q^{46} + 48 q^{47} + 28 q^{50} + 48 q^{52} - 28 q^{53} - 36 q^{55} + 32 q^{56} - 104 q^{58} - 12 q^{61} - 4 q^{62} - 196 q^{67} + 136 q^{68} - 56 q^{70} + 200 q^{71} + 220 q^{73} + 136 q^{76} + 104 q^{77} + 48 q^{80} + 80 q^{82} + 72 q^{83} + 284 q^{85} + 72 q^{86} - 16 q^{88} + 48 q^{91} + 32 q^{92} + 32 q^{95} + 336 q^{97} - 116 q^{98}+O(q^{100}) \) 4 * q - 4 * q^2 - 12 * q^5 + 8 * q^7 + 8 * q^8 + 16 * q^10 - 8 * q^11 + 24 * q^13 - 16 * q^16 - 68 * q^17 - 8 * q^20 + 8 * q^22 + 16 * q^23 - 16 * q^25 - 48 * q^26 - 16 * q^28 + 4 * q^31 + 16 * q^32 - 8 * q^35 - 36 * q^37 - 68 * q^38 - 16 * q^40 - 80 * q^41 - 36 * q^43 - 32 * q^46 + 48 * q^47 + 28 * q^50 + 48 * q^52 - 28 * q^53 - 36 * q^55 + 32 * q^56 - 104 * q^58 - 12 * q^61 - 4 * q^62 - 196 * q^67 + 136 * q^68 - 56 * q^70 + 200 * q^71 + 220 * q^73 + 136 * q^76 + 104 * q^77 + 48 * q^80 + 80 * q^82 + 72 * q^83 + 284 * q^85 + 72 * q^86 - 16 * q^88 + 48 * q^91 + 32 * q^92 + 32 * q^95 + 336 * q^97 - 116 * q^98

Introduction

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