LMFDB - Embedded newform 45.3.g.a.37.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [45,3,Mod(28,45)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(45, 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("45.28");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 45 = 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	45.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:	$1.22616118962$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(i)$
Coefficient field:	$\Q(i, \sqrt{10})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 25 $ x^4 + 25
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			37.1
Root			$-1.58114 - 1.58114i$ of defining polynomial
Character	$\chi$	$=$	45.37
Dual form			45.3.g.a.28.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.58114 - 1.58114i) q^{2} +1.00000i q^{4} +(-1.58114 - 4.74342i) q^{5} +(-5.00000 - 5.00000i) q^{7} +(-4.74342 + 4.74342i) q^{8} +O(q^{10})$	\(q+(-1.58114 - 1.58114i) q^{2} +1.00000i q^{4} +(-1.58114 - 4.74342i) q^{5} +(-5.00000 - 5.00000i) q^{7} +(-4.74342 + 4.74342i) q^{8} +(-5.00000 + 10.0000i) q^{10} +15.8114 q^{11} +(10.0000 - 10.0000i) q^{13} +15.8114i q^{14} +19.0000 q^{16} +(3.16228 + 3.16228i) q^{17} +18.0000i q^{19} +(4.74342 - 1.58114i) q^{20} +(-25.0000 - 25.0000i) q^{22} +(3.16228 - 3.16228i) q^{23} +(-20.0000 + 15.0000i) q^{25} -31.6228 q^{26} +(5.00000 - 5.00000i) q^{28} -47.4342i q^{29} +8.00000 q^{31} +(-11.0680 - 11.0680i) q^{32} -10.0000i q^{34} +(-15.8114 + 31.6228i) q^{35} +(10.0000 + 10.0000i) q^{37} +(28.4605 - 28.4605i) q^{38} +(30.0000 + 15.0000i) q^{40} -31.6228 q^{41} +(10.0000 - 10.0000i) q^{43} +15.8114i q^{44} -10.0000 q^{46} +(41.1096 + 41.1096i) q^{47} +1.00000i q^{49} +(55.3399 + 7.90569i) q^{50} +(10.0000 + 10.0000i) q^{52} +(-25.2982 + 25.2982i) q^{53} +(-25.0000 - 75.0000i) q^{55} +47.4342 q^{56} +(-75.0000 + 75.0000i) q^{58} +47.4342i q^{59} -58.0000 q^{61} +(-12.6491 - 12.6491i) q^{62} -41.0000i q^{64} +(-63.2456 - 31.6228i) q^{65} +(70.0000 + 70.0000i) q^{67} +(-3.16228 + 3.16228i) q^{68} +(75.0000 - 25.0000i) q^{70} +63.2456 q^{71} +(55.0000 - 55.0000i) q^{73} -31.6228i q^{74} -18.0000 q^{76} +(-79.0569 - 79.0569i) q^{77} +12.0000i q^{79} +(-30.0416 - 90.1249i) q^{80} +(50.0000 + 50.0000i) q^{82} +(-53.7587 + 53.7587i) q^{83} +(10.0000 - 20.0000i) q^{85} -31.6228 q^{86} +(-75.0000 + 75.0000i) q^{88} -100.000 q^{91} +(3.16228 + 3.16228i) q^{92} -130.000i q^{94} +(85.3815 - 28.4605i) q^{95} +(-5.00000 - 5.00000i) q^{97} +(1.58114 - 1.58114i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 20 q^{7}+O(q^{10}) $ 4 * q - 20 * q^7	$ 4 q - 20 q^{7} - 20 q^{10} + 40 q^{13} + 76 q^{16} - 100 q^{22} - 80 q^{25} + 20 q^{28} + 32 q^{31} + 40 q^{37} + 120 q^{40} + 40 q^{43} - 40 q^{46} + 40 q^{52} - 100 q^{55} - 300 q^{58} - 232 q^{61} + 280 q^{67} + 300 q^{70} + 220 q^{73} - 72 q^{76} + 200 q^{82} + 40 q^{85} - 300 q^{88} - 400 q^{91} - 20 q^{97}+O(q^{100}) $ 4 * q - 20 * q^7 - 20 * q^10 + 40 * q^13 + 76 * q^16 - 100 * q^22 - 80 * q^25 + 20 * q^28 + 32 * q^31 + 40 * q^37 + 120 * q^40 + 40 * q^43 - 40 * q^46 + 40 * q^52 - 100 * q^55 - 300 * q^58 - 232 * q^61 + 280 * q^67 + 300 * q^70 + 220 * q^73 - 72 * q^76 + 200 * q^82 + 40 * q^85 - 300 * q^88 - 400 * q^91 - 20 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/45\mathbb{Z}\right)^\times$.

$n$	$11$	$37$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$

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 $

$2$	−1.58114	−	1.58114i	−0.790569	−	0.790569i	0.191017	−	0.981587i	$-0.438821\pi$
$2$	−1.58114	−	1.58114i	−0.790569	−	0.790569i	−0.981587	+	0.191017i	$0.938821\pi$
$3$		0			0
$3$		0			0
$4$			1.00000i			0.250000i
$5$	−1.58114	−	4.74342i	−0.316228	−	0.948683i
$5$	−1.58114	−	4.74342i	−0.316228	−	0.948683i
$6$		0			0
$7$	−5.00000	−	5.00000i	−0.714286	−	0.714286i	0.253143	−	0.967429i	$-0.418536\pi$
$7$	−5.00000	−	5.00000i	−0.714286	−	0.714286i	−0.967429	+	0.253143i	$0.918536\pi$
$8$	−4.74342	+	4.74342i	−0.592927	+	0.592927i
$9$		0			0
$10$	−5.00000	+	10.0000i	−0.500000	+	1.00000i
$11$	15.8114			1.43740			0.718699	−	0.695321i	$-0.244738\pi$
$11$	15.8114			1.43740			0.718699	+	0.695321i	$0.244738\pi$
$12$		0			0
$13$	10.0000	−	10.0000i	0.769231	−	0.769231i	−0.208740	−	0.977971i	$-0.566936\pi$
$13$	10.0000	−	10.0000i	0.769231	−	0.769231i	0.977971	+	0.208740i	$0.0669363\pi$
$14$			15.8114i			1.12938i
$15$		0			0
$16$	19.0000			1.18750
$17$	3.16228	+	3.16228i	0.186016	+	0.186016i	0.793971	−	0.607955i	$-0.208010\pi$
$17$	3.16228	+	3.16228i	0.186016	+	0.186016i	−0.607955	+	0.793971i	$0.708010\pi$
$18$		0			0
$19$			18.0000i			0.947368i	0.880695	+	0.473684i	$0.157076\pi$
$19$			18.0000i			0.947368i	−0.880695	+	0.473684i	$0.842924\pi$
$20$	4.74342	−	1.58114i	0.237171	−	0.0790569i
$21$		0			0
$22$	−25.0000	−	25.0000i	−1.13636	−	1.13636i
$23$	3.16228	−	3.16228i	0.137490	−	0.137490i	−0.635012	−	0.772502i	$-0.719005\pi$
$23$	3.16228	−	3.16228i	0.137490	−	0.137490i	0.772502	+	0.635012i	$0.219005\pi$
$24$		0			0
$25$	−20.0000	+	15.0000i	−0.800000	+	0.600000i
$26$	−31.6228			−1.21626
$27$		0			0
$28$	5.00000	−	5.00000i	0.178571	−	0.178571i
$29$		−	47.4342i		−	1.63566i	−0.575459	−	0.817830i	$-0.695177\pi$
$29$		−	47.4342i		−	1.63566i	0.575459	−	0.817830i	$-0.304823\pi$
$30$		0			0
$31$	8.00000			0.258065			0.129032	−	0.991640i	$-0.458813\pi$
$31$	8.00000			0.258065			0.129032	+	0.991640i	$0.458813\pi$
$32$	−11.0680	−	11.0680i	−0.345874	−	0.345874i
$33$		0			0
$34$		−	10.0000i		−	0.294118i
$35$	−15.8114	+	31.6228i	−0.451754	+	0.903508i
$36$		0			0
$37$	10.0000	+	10.0000i	0.270270	+	0.270270i	0.829209	−	0.558939i	$-0.188791\pi$
$37$	10.0000	+	10.0000i	0.270270	+	0.270270i	−0.558939	+	0.829209i	$0.688791\pi$
$38$	28.4605	−	28.4605i	0.748960	−	0.748960i
$39$		0			0
$40$	30.0000	+	15.0000i	0.750000	+	0.375000i
$41$	−31.6228			−0.771287			−0.385644	−	0.922648i	$-0.626021\pi$
$41$	−31.6228			−0.771287			−0.385644	+	0.922648i	$0.626021\pi$
$42$		0			0
$43$	10.0000	−	10.0000i	0.232558	−	0.232558i	−0.581202	−	0.813760i	$-0.697417\pi$
$43$	10.0000	−	10.0000i	0.232558	−	0.232558i	0.813760	+	0.581202i	$0.197417\pi$
$44$			15.8114i			0.359350i
$45$		0			0
$46$	−10.0000			−0.217391
$47$	41.1096	+	41.1096i	0.874673	+	0.874673i	0.992977	−	0.118305i	$-0.0377460\pi$
$47$	41.1096	+	41.1096i	0.874673	+	0.874673i	−0.118305	+	0.992977i	$0.537746\pi$
$48$		0			0
$49$			1.00000i			0.0204082i
$50$	55.3399	+	7.90569i	1.10680	+	0.158114i
$51$		0			0
$52$	10.0000	+	10.0000i	0.192308	+	0.192308i
$53$	−25.2982	+	25.2982i	−0.477325	+	0.477325i	−0.904275	−	0.426950i	$-0.859588\pi$
$53$	−25.2982	+	25.2982i	−0.477325	+	0.477325i	0.426950	+	0.904275i	$0.359588\pi$
$54$		0			0
$55$	−25.0000	−	75.0000i	−0.454545	−	1.36364i
$56$	47.4342			0.847039
$57$		0			0
$58$	−75.0000	+	75.0000i	−1.29310	+	1.29310i
$59$			47.4342i			0.803969i	0.915646	+	0.401984i	$0.131679\pi$
$59$			47.4342i			0.803969i	−0.915646	+	0.401984i	$0.868321\pi$
$60$		0			0
$61$	−58.0000			−0.950820			−0.475410	−	0.879764i	$-0.657700\pi$
$61$	−58.0000			−0.950820			−0.475410	+	0.879764i	$0.657700\pi$
$62$	−12.6491	−	12.6491i	−0.204018	−	0.204018i
$63$		0			0
$64$		−	41.0000i		−	0.640625i
$65$	−63.2456	−	31.6228i	−0.973009	−	0.486504i
$66$		0			0
$67$	70.0000	+	70.0000i	1.04478	+	1.04478i	0.998949	+	0.0458267i	$0.0145922\pi$
$67$	70.0000	+	70.0000i	1.04478	+	1.04478i	0.0458267	+	0.998949i	$0.485408\pi$
$68$	−3.16228	+	3.16228i	−0.0465041	+	0.0465041i
$69$		0			0
$70$	75.0000	−	25.0000i	1.07143	−	0.357143i
$71$	63.2456			0.890782			0.445391	−	0.895336i	$-0.353065\pi$
$71$	63.2456			0.890782			0.445391	+	0.895336i	$0.353065\pi$
$72$		0			0
$73$	55.0000	−	55.0000i	0.753425	−	0.753425i	−0.221692	−	0.975117i	$-0.571158\pi$
$73$	55.0000	−	55.0000i	0.753425	−	0.753425i	0.975117	+	0.221692i	$0.0711580\pi$
$74$		−	31.6228i		−	0.427335i
$75$		0			0
$76$	−18.0000			−0.236842
$77$	−79.0569	−	79.0569i	−1.02671	−	1.02671i
$78$		0			0
$79$			12.0000i			0.151899i	0.997112	+	0.0759494i	$0.0241987\pi$
$79$			12.0000i			0.151899i	−0.997112	+	0.0759494i	$0.975801\pi$
$80$	−30.0416	−	90.1249i	−0.375520	−	1.12656i
$81$		0			0
$82$	50.0000	+	50.0000i	0.609756	+	0.609756i
$83$	−53.7587	+	53.7587i	−0.647695	+	0.647695i	−0.952436	−	0.304740i	$-0.901430\pi$
$83$	−53.7587	+	53.7587i	−0.647695	+	0.647695i	0.304740	+	0.952436i	$0.401430\pi$
$84$		0			0
$85$	10.0000	−	20.0000i	0.117647	−	0.235294i
$86$	−31.6228			−0.367707
$87$		0			0
$88$	−75.0000	+	75.0000i	−0.852273	+	0.852273i
$89$		0			0		1.00000			$0$
$89$		0			0		−1.00000			$\pi$
$90$		0			0
$91$	−100.000			−1.09890
$92$	3.16228	+	3.16228i	0.0343726	+	0.0343726i
$93$		0			0
$94$		−	130.000i		−	1.38298i
$95$	85.3815	−	28.4605i	0.898753	−	0.299584i
$96$		0			0
$97$	−5.00000	−	5.00000i	−0.0515464	−	0.0515464i	0.680864	−	0.732410i	$-0.261605\pi$
$97$	−5.00000	−	5.00000i	−0.0515464	−	0.0515464i	−0.732410	+	0.680864i	$0.761605\pi$
$98$	1.58114	−	1.58114i	0.0161341	−	0.0161341i
$99$		0			0
$100$	−15.0000	−	20.0000i	−0.150000	−	0.200000i
$101$	15.8114			0.156548			0.0782742	−	0.996932i	$-0.475059\pi$
$101$	15.8114			0.156548			0.0782742	+	0.996932i	$0.475059\pi$
$102$		0			0
$103$	−35.0000	+	35.0000i	−0.339806	+	0.339806i	−0.856294	−	0.516488i	$-0.827239\pi$
$103$	−35.0000	+	35.0000i	−0.339806	+	0.339806i	0.516488	+	0.856294i	$0.327239\pi$
$104$			94.8683i			0.912195i
$105$		0			0
$106$	80.0000			0.754717
$107$	60.0833	+	60.0833i	0.561526	+	0.561526i	0.929741	−	0.368215i	$-0.120031\pi$
$107$	60.0833	+	60.0833i	0.561526	+	0.561526i	−0.368215	+	0.929741i	$0.620031\pi$
$108$		0			0
$109$			162.000i			1.48624i	0.669159	+	0.743119i	$0.266655\pi$
$109$			162.000i			1.48624i	−0.669159	+	0.743119i	$0.733345\pi$
$110$	−79.0569	+	158.114i	−0.718699	+	1.43740i
$111$		0			0
$112$	−95.0000	−	95.0000i	−0.848214	−	0.848214i
$113$	117.004	−	117.004i	1.03544	−	1.03544i	0.0360874	−	0.999349i	$-0.488511\pi$
$113$	117.004	−	117.004i	1.03544	−	1.03544i	0.999349	−	0.0360874i	$-0.0114895\pi$
$114$		0			0
$115$	−20.0000	−	10.0000i	−0.173913	−	0.0869565i
$116$	47.4342			0.408915
$117$		0			0
$118$	75.0000	−	75.0000i	0.635593	−	0.635593i
$119$		−	31.6228i		−	0.265738i
$120$		0			0
$121$	129.000			1.06612
$122$	91.7061	+	91.7061i	0.751689	+	0.751689i
$123$		0			0
$124$			8.00000i			0.0645161i
$125$	102.774	+	71.1512i	0.822192	+	0.569210i
$126$		0			0
$127$	55.0000	+	55.0000i	0.433071	+	0.433071i	0.889672	−	0.456601i	$-0.150933\pi$
$127$	55.0000	+	55.0000i	0.433071	+	0.433071i	−0.456601	+	0.889672i	$0.650933\pi$
$128$	−109.099	+	109.099i	−0.852333	+	0.852333i
$129$		0			0
$130$	50.0000	+	150.000i	0.384615	+	1.15385i
$131$	−173.925			−1.32767			−0.663837	−	0.747877i	$-0.731073\pi$
$131$	−173.925			−1.32767			−0.663837	+	0.747877i	$0.731073\pi$
$132$		0			0
$133$	90.0000	−	90.0000i	0.676692	−	0.676692i
$134$		−	221.359i		−	1.65194i
$135$		0			0
$136$	−30.0000			−0.220588
$137$	−15.8114	−	15.8114i	−0.115412	−	0.115412i	0.647042	−	0.762454i	$-0.276006\pi$
$137$	−15.8114	−	15.8114i	−0.115412	−	0.115412i	−0.762454	+	0.647042i	$0.776006\pi$
$138$		0			0
$139$		−	102.000i		−	0.733813i	−0.930258	−	0.366906i	$-0.880417\pi$
$139$		−	102.000i		−	0.733813i	0.930258	−	0.366906i	$-0.119583\pi$
$140$	−31.6228	−	15.8114i	−0.225877	−	0.112938i
$141$		0			0
$142$	−100.000	−	100.000i	−0.704225	−	0.704225i
$143$	158.114	−	158.114i	1.10569	−	1.10569i
$144$		0			0
$145$	−225.000	+	75.0000i	−1.55172	+	0.517241i
$146$	−173.925			−1.19127
$147$		0			0
$148$	−10.0000	+	10.0000i	−0.0675676	+	0.0675676i
$149$			47.4342i			0.318350i	0.987250	+	0.159175i	$0.0508834\pi$
$149$			47.4342i			0.318350i	−0.987250	+	0.159175i	$0.949117\pi$
$150$		0			0
$151$	−22.0000			−0.145695			−0.0728477	−	0.997343i	$-0.523209\pi$
$151$	−22.0000			−0.145695			−0.0728477	+	0.997343i	$0.523209\pi$
$152$	−85.3815	−	85.3815i	−0.561720	−	0.561720i
$153$		0			0
$154$			250.000i			1.62338i
$155$	−12.6491	−	37.9473i	−0.0816072	−	0.244821i
$156$		0			0
$157$	−200.000	−	200.000i	−1.27389	−	1.27389i	−0.944032	−	0.329853i	$-0.893001\pi$
$157$	−200.000	−	200.000i	−1.27389	−	1.27389i	−0.329853	−	0.944032i	$-0.606999\pi$
$158$	18.9737	−	18.9737i	0.120086	−	0.120086i
$159$		0			0
$160$	−35.0000	+	70.0000i	−0.218750	+	0.437500i
$161$	−31.6228			−0.196415
$162$		0			0
$163$	100.000	−	100.000i	0.613497	−	0.613497i	−0.330359	−	0.943856i	$-0.607170\pi$
$163$	100.000	−	100.000i	0.613497	−	0.613497i	0.943856	+	0.330359i	$0.107170\pi$
$164$		−	31.6228i		−	0.192822i
$165$		0			0
$166$	170.000			1.02410
$167$	−148.627	−	148.627i	−0.889982	−	0.889982i	0.104539	−	0.994521i	$-0.466663\pi$
$167$	−148.627	−	148.627i	−0.889982	−	0.889982i	−0.994521	+	0.104539i	$0.966663\pi$
$168$		0			0
$169$		−	31.0000i		−	0.183432i
$170$	−47.4342	+	15.8114i	−0.279024	+	0.0930082i
$171$		0			0
$172$	10.0000	+	10.0000i	0.0581395	+	0.0581395i
$173$	−110.680	+	110.680i	−0.639767	+	0.639767i	−0.950498	−	0.310731i	$-0.899426\pi$
$173$	−110.680	+	110.680i	−0.639767	+	0.639767i	0.310731	+	0.950498i	$0.399426\pi$
$174$		0			0
$175$	175.000	+	25.0000i	1.00000	+	0.142857i
$176$	300.416			1.70691
$177$		0			0
$178$		0			0
$179$			142.302i			0.794986i	0.917605	+	0.397493i	$0.130120\pi$
$179$			142.302i			0.794986i	−0.917605	+	0.397493i	$0.869880\pi$
$180$		0			0
$181$	218.000			1.20442			0.602210	−	0.798338i	$-0.294287\pi$
$181$	218.000			1.20442			0.602210	+	0.798338i	$0.294287\pi$
$182$	158.114	+	158.114i	0.868758	+	0.868758i
$183$		0			0
$184$			30.0000i			0.163043i
$185$	31.6228	−	63.2456i	0.170934	−	0.341868i
$186$		0			0
$187$	50.0000	+	50.0000i	0.267380	+	0.267380i
$188$	−41.1096	+	41.1096i	−0.218668	+	0.218668i
$189$		0			0
$190$	−180.000	−	90.0000i	−0.947368	−	0.473684i
$191$	158.114			0.827821			0.413911	−	0.910317i	$-0.364163\pi$
$191$	158.114			0.827821			0.413911	+	0.910317i	$0.364163\pi$
$192$		0			0
$193$	−125.000	+	125.000i	−0.647668	+	0.647668i	−0.952429	−	0.304761i	$-0.901424\pi$
$193$	−125.000	+	125.000i	−0.647668	+	0.647668i	0.304761	+	0.952429i	$0.401424\pi$
$194$			15.8114i			0.0815020i
$195$		0			0
$196$	−1.00000			−0.00510204
$197$	145.465	+	145.465i	0.738400	+	0.738400i	0.972268	−	0.233868i	$-0.0751385\pi$
$197$	145.465	+	145.465i	0.738400	+	0.738400i	−0.233868	+	0.972268i	$0.575138\pi$
$198$		0			0
$199$		−	18.0000i		−	0.0904523i	−0.998977	−	0.0452261i	$-0.985599\pi$
$199$		−	18.0000i		−	0.0904523i	0.998977	−	0.0452261i	$-0.0144008\pi$
$200$	23.7171	−	166.020i	0.118585	−	0.830098i
$201$		0			0
$202$	−25.0000	−	25.0000i	−0.123762	−	0.123762i
$203$	−237.171	+	237.171i	−1.16833	+	1.16833i
$204$		0			0
$205$	50.0000	+	150.000i	0.243902	+	0.731707i
$206$	110.680			0.537280
$207$		0			0
$208$	190.000	−	190.000i	0.913462	−	0.913462i
$209$			284.605i			1.36175i
$210$		0			0
$211$	−298.000			−1.41232			−0.706161	−	0.708051i	$-0.749575\pi$
$211$	−298.000			−1.41232			−0.706161	+	0.708051i	$0.749575\pi$
$212$	−25.2982	−	25.2982i	−0.119331	−	0.119331i
$213$		0			0
$214$		−	190.000i		−	0.887850i
$215$	−63.2456	−	31.6228i	−0.294165	−	0.147083i
$216$		0			0
$217$	−40.0000	−	40.0000i	−0.184332	−	0.184332i
$218$	256.144	−	256.144i	1.17497	−	1.17497i
$219$		0			0
$220$	75.0000	−	25.0000i	0.340909	−	0.113636i
$221$	63.2456			0.286179
$222$		0			0
$223$	−215.000	+	215.000i	−0.964126	+	0.964126i	−0.999378	−	0.0352529i	$-0.988776\pi$
$223$	−215.000	+	215.000i	−0.964126	+	0.964126i	0.0352529	+	0.999378i	$0.488776\pi$
$224$			110.680i			0.494106i
$225$		0			0
$226$	−370.000			−1.63717
$227$	−271.956	−	271.956i	−1.19804	−	1.19804i	−0.974752	−	0.223292i	$-0.928320\pi$
$227$	−271.956	−	271.956i	−1.19804	−	1.19804i	−0.223292	−	0.974752i	$-0.571680\pi$
$228$		0			0
$229$			78.0000i			0.340611i	0.985391	+	0.170306i	$0.0544755\pi$
$229$			78.0000i			0.340611i	−0.985391	+	0.170306i	$0.945524\pi$
$230$	15.8114	+	47.4342i	0.0687452	+	0.206235i
$231$		0			0
$232$	225.000	+	225.000i	0.969828	+	0.969828i
$233$	−110.680	+	110.680i	−0.475020	+	0.475020i	−0.903535	−	0.428515i	$-0.859037\pi$
$233$	−110.680	+	110.680i	−0.475020	+	0.475020i	0.428515	+	0.903535i	$0.359037\pi$
$234$		0			0
$235$	130.000	−	260.000i	0.553191	−	1.10638i
$236$	−47.4342			−0.200992
$237$		0			0
$238$	−50.0000	+	50.0000i	−0.210084	+	0.210084i
$239$		−	379.473i		−	1.58775i	−0.608078	−	0.793877i	$-0.708059\pi$
$239$		−	379.473i		−	1.58775i	0.608078	−	0.793877i	$-0.291941\pi$
$240$		0			0
$241$	212.000			0.879668			0.439834	−	0.898079i	$-0.355037\pi$
$241$	212.000			0.879668			0.439834	+	0.898079i	$0.355037\pi$
$242$	−203.967	−	203.967i	−0.842838	−	0.842838i
$243$		0			0
$244$		−	58.0000i		−	0.237705i
$245$	4.74342	−	1.58114i	0.0193609	−	0.00645363i
$246$		0			0
$247$	180.000	+	180.000i	0.728745	+	0.728745i
$248$	−37.9473	+	37.9473i	−0.153013	+	0.153013i
$249$		0			0
$250$	−50.0000	−	275.000i	−0.200000	−	1.10000i
$251$	−363.662			−1.44885			−0.724426	−	0.689352i	$-0.757895\pi$
$251$	−363.662			−1.44885			−0.724426	+	0.689352i	$0.757895\pi$
$252$		0			0
$253$	50.0000	−	50.0000i	0.197628	−	0.197628i
$254$		−	173.925i		−	0.684745i
$255$		0			0
$256$	181.000			0.707031
$257$	306.741	+	306.741i	1.19354	+	1.19354i	0.976065	+	0.217480i	$0.0697836\pi$
$257$	306.741	+	306.741i	1.19354	+	1.19354i	0.217480	+	0.976065i	$0.430216\pi$
$258$		0			0
$259$		−	100.000i		−	0.386100i
$260$	31.6228	−	63.2456i	0.121626	−	0.243252i
$261$		0			0
$262$	275.000	+	275.000i	1.04962	+	1.04962i
$263$	287.767	−	287.767i	1.09417	−	1.09417i	0.0990940	−	0.995078i	$-0.468406\pi$
$263$	287.767	−	287.767i	1.09417	−	1.09417i	0.995078	−	0.0990940i	$-0.0315945\pi$
$264$		0			0
$265$	160.000	+	80.0000i	0.603774	+	0.301887i
$266$	−284.605			−1.06994
$267$		0			0
$268$	−70.0000	+	70.0000i	−0.261194	+	0.261194i
$269$		−	142.302i		−	0.529006i	−0.964385	−	0.264503i	$-0.914792\pi$
$269$		−	142.302i		−	0.529006i	0.964385	−	0.264503i	$-0.0852078\pi$
$270$		0			0
$271$	−178.000			−0.656827			−0.328413	−	0.944534i	$-0.606514\pi$
$271$	−178.000			−0.656827			−0.328413	+	0.944534i	$0.606514\pi$
$272$	60.0833	+	60.0833i	0.220894	+	0.220894i
$273$		0			0
$274$			50.0000i			0.182482i
$275$	−316.228	+	237.171i	−1.14992	+	0.862439i
$276$		0			0
$277$	−230.000	−	230.000i	−0.830325	−	0.830325i	0.157236	−	0.987561i	$-0.449742\pi$
$277$	−230.000	−	230.000i	−0.830325	−	0.830325i	−0.987561	+	0.157236i	$0.949742\pi$
$278$	−161.276	+	161.276i	−0.580130	+	0.580130i
$279$		0			0
$280$	−75.0000	−	225.000i	−0.267857	−	0.803571i
$281$	158.114			0.562683			0.281341	−	0.959608i	$-0.409221\pi$
$281$	158.114			0.562683			0.281341	+	0.959608i	$0.409221\pi$
$282$		0			0
$283$	−350.000	+	350.000i	−1.23675	+	1.23675i	−0.275427	+	0.961322i	$0.588819\pi$
$283$	−350.000	+	350.000i	−1.23675	+	1.23675i	−0.961322	+	0.275427i	$0.911181\pi$
$284$			63.2456i			0.222696i
$285$		0			0
$286$	−500.000			−1.74825
$287$	158.114	+	158.114i	0.550919	+	0.550919i
$288$		0			0
$289$		−	269.000i		−	0.930796i
$290$	474.342	+	237.171i	1.63566	+	0.817830i
$291$		0			0
$292$	55.0000	+	55.0000i	0.188356	+	0.188356i
$293$	202.386	−	202.386i	0.690736	−	0.690736i	−0.271658	−	0.962394i	$-0.587572\pi$
$293$	202.386	−	202.386i	0.690736	−	0.690736i	0.962394	+	0.271658i	$0.0875718\pi$
$294$		0			0
$295$	225.000	−	75.0000i	0.762712	−	0.254237i
$296$	−94.8683			−0.320501
$297$		0			0
$298$	75.0000	−	75.0000i	0.251678	−	0.251678i
$299$		−	63.2456i		−	0.211524i
$300$		0			0
$301$	−100.000			−0.332226
$302$	34.7851	+	34.7851i	0.115182	+	0.115182i
$303$		0			0
$304$			342.000i			1.12500i
$305$	91.7061	+	275.118i	0.300676	+	0.902027i
$306$		0			0
$307$	190.000	+	190.000i	0.618893	+	0.618893i	0.945247	−	0.326355i	$-0.105820\pi$
$307$	190.000	+	190.000i	0.618893	+	0.618893i	−0.326355	+	0.945247i	$0.605820\pi$
$308$	79.0569	−	79.0569i	0.256678	−	0.256678i
$309$		0			0
$310$	−40.0000	+	80.0000i	−0.129032	+	0.258065i
$311$	252.982			0.813448			0.406724	−	0.913551i	$-0.366671\pi$
$311$	252.982			0.813448			0.406724	+	0.913551i	$0.366671\pi$
$312$		0			0
$313$	145.000	−	145.000i	0.463259	−	0.463259i	−0.436463	−	0.899722i	$-0.643769\pi$
$313$	145.000	−	145.000i	0.463259	−	0.463259i	0.899722	+	0.436463i	$0.143769\pi$
$314$			632.456i			2.01419i
$315$		0			0
$316$	−12.0000			−0.0379747
$317$	−15.8114	−	15.8114i	−0.0498782	−	0.0498782i	0.681728	−	0.731606i	$-0.261229\pi$
$317$	−15.8114	−	15.8114i	−0.0498782	−	0.0498782i	−0.731606	+	0.681728i	$0.761229\pi$
$318$		0			0
$319$		−	750.000i		−	2.35110i
$320$	−194.480	+	64.8267i	−0.607750	+	0.202583i
$321$		0			0
$322$	50.0000	+	50.0000i	0.155280	+	0.155280i
$323$	−56.9210	+	56.9210i	−0.176226	+	0.176226i
$324$		0			0
$325$	−50.0000	+	350.000i	−0.153846	+	1.07692i
$326$	−316.228			−0.970024
$327$		0			0
$328$	150.000	−	150.000i	0.457317	−	0.457317i
$329$		−	411.096i		−	1.24953i
$330$		0			0
$331$	482.000			1.45619			0.728097	−	0.685474i	$-0.240405\pi$
$331$	482.000			1.45619			0.728097	+	0.685474i	$0.240405\pi$
$332$	−53.7587	−	53.7587i	−0.161924	−	0.161924i
$333$		0			0
$334$			470.000i			1.40719i
$335$	221.359	−	442.719i	0.660774	−	1.32155i
$336$		0			0
$337$	−155.000	−	155.000i	−0.459941	−	0.459941i	0.438695	−	0.898636i	$-0.355441\pi$
$337$	−155.000	−	155.000i	−0.459941	−	0.459941i	−0.898636	+	0.438695i	$0.855441\pi$
$338$	−49.0153	+	49.0153i	−0.145016	+	0.145016i
$339$		0			0
$340$	20.0000	+	10.0000i	0.0588235	+	0.0294118i
$341$	126.491			0.370942
$342$		0			0
$343$	−240.000	+	240.000i	−0.699708	+	0.699708i
$344$			94.8683i			0.275780i
$345$		0			0
$346$	350.000			1.01156
$347$	164.438	+	164.438i	0.473886	+	0.473886i	0.903170	−	0.429284i	$-0.141234\pi$
$347$	164.438	+	164.438i	0.473886	+	0.473886i	−0.429284	+	0.903170i	$0.641234\pi$
$348$		0			0
$349$			318.000i			0.911175i	0.890191	+	0.455587i	$0.150571\pi$
$349$			318.000i			0.911175i	−0.890191	+	0.455587i	$0.849429\pi$
$350$	−237.171	−	316.228i	−0.677631	−	0.903508i
$351$		0			0
$352$	−175.000	−	175.000i	−0.497159	−	0.497159i
$353$	−224.522	+	224.522i	−0.636039	+	0.636039i	−0.949576	−	0.313537i	$-0.898486\pi$
$353$	−224.522	+	224.522i	−0.636039	+	0.636039i	0.313537	+	0.949576i	$0.398486\pi$
$354$		0			0
$355$	−100.000	−	300.000i	−0.281690	−	0.845070i
$356$		0			0
$357$		0			0
$358$	225.000	−	225.000i	0.628492	−	0.628492i
$359$		−	284.605i		−	0.792772i	−0.918084	−	0.396386i	$-0.870264\pi$
$359$		−	284.605i		−	0.792772i	0.918084	−	0.396386i	$-0.129736\pi$
$360$		0			0
$361$	37.0000			0.102493
$362$	−344.688	−	344.688i	−0.952178	−	0.952178i
$363$		0			0
$364$		−	100.000i		−	0.274725i
$365$	−347.851	−	173.925i	−0.953015	−	0.476508i
$366$		0			0
$367$	−185.000	−	185.000i	−0.504087	−	0.504087i	0.408618	−	0.912705i	$-0.366011\pi$
$367$	−185.000	−	185.000i	−0.504087	−	0.504087i	−0.912705	+	0.408618i	$0.866011\pi$
$368$	60.0833	−	60.0833i	0.163270	−	0.163270i
$369$		0			0
$370$	−150.000	+	50.0000i	−0.405405	+	0.135135i
$371$	252.982			0.681893
$372$		0			0
$373$	100.000	−	100.000i	0.268097	−	0.268097i	−0.560236	−	0.828333i	$-0.689290\pi$
$373$	100.000	−	100.000i	0.268097	−	0.268097i	0.828333	+	0.560236i	$0.189290\pi$
$374$		−	158.114i		−	0.422764i
$375$		0			0
$376$	−390.000			−1.03723
$377$	−474.342	−	474.342i	−1.25820	−	1.25820i
$378$		0			0
$379$			558.000i			1.47230i	0.676821	+	0.736148i	$0.263357\pi$
$379$			558.000i			1.47230i	−0.676821	+	0.736148i	$0.736643\pi$
$380$	28.4605	+	85.3815i	0.0748960	+	0.224688i
$381$		0			0
$382$	−250.000	−	250.000i	−0.654450	−	0.654450i
$383$	−281.443	+	281.443i	−0.734837	+	0.734837i	−0.971574	−	0.236737i	$-0.923922\pi$
$383$	−281.443	+	281.443i	−0.734837	+	0.734837i	0.236737	+	0.971574i	$0.423922\pi$
$384$		0			0
$385$	−250.000	+	500.000i	−0.649351	+	1.29870i
$386$	395.285			1.02405
$387$		0			0
$388$	5.00000	−	5.00000i	0.0128866	−	0.0128866i
$389$			521.776i			1.34133i	0.741762	+	0.670663i	$0.233990\pi$
$389$			521.776i			1.34133i	−0.741762	+	0.670663i	$0.766010\pi$
$390$		0			0
$391$	20.0000			0.0511509
$392$	−4.74342	−	4.74342i	−0.0121006	−	0.0121006i
$393$		0			0
$394$		−	460.000i		−	1.16751i
$395$	56.9210	−	18.9737i	0.144104	−	0.0480346i
$396$		0			0
$397$	−260.000	−	260.000i	−0.654912	−	0.654912i	0.299260	−	0.954172i	$-0.403260\pi$
$397$	−260.000	−	260.000i	−0.654912	−	0.654912i	−0.954172	+	0.299260i	$0.903260\pi$
$398$	−28.4605	+	28.4605i	−0.0715088	+	0.0715088i
$399$		0			0
$400$	−380.000	+	285.000i	−0.950000	+	0.712500i
$401$	252.982			0.630878			0.315439	−	0.948946i	$-0.397848\pi$
$401$	252.982			0.630878			0.315439	+	0.948946i	$0.397848\pi$
$402$		0			0
$403$	80.0000	−	80.0000i	0.198511	−	0.198511i
$404$			15.8114i			0.0391371i
$405$		0			0
$406$	750.000			1.84729
$407$	158.114	+	158.114i	0.388486	+	0.388486i
$408$		0			0
$409$			348.000i			0.850856i	0.904992	+	0.425428i	$0.139876\pi$
$409$			348.000i			0.850856i	−0.904992	+	0.425428i	$0.860124\pi$
$410$	158.114	−	316.228i	0.385644	−	0.771287i
$411$		0			0
$412$	−35.0000	−	35.0000i	−0.0849515	−	0.0849515i
$413$	237.171	−	237.171i	0.574263	−	0.574263i
$414$		0			0
$415$	340.000	+	170.000i	0.819277	+	0.409639i
$416$	−221.359			−0.532114
$417$		0			0
$418$	450.000	−	450.000i	1.07656	−	1.07656i
$419$			616.644i			1.47170i	0.677142	+	0.735852i	$0.263218\pi$
$419$			616.644i			1.47170i	−0.677142	+	0.735852i	$0.736782\pi$
$420$		0			0
$421$	338.000			0.802850			0.401425	−	0.915892i	$-0.368515\pi$
$421$	338.000			0.802850			0.401425	+	0.915892i	$0.368515\pi$
$422$	471.179	+	471.179i	1.11654	+	1.11654i
$423$		0			0
$424$		−	240.000i		−	0.566038i
$425$	−110.680	−	15.8114i	−0.260423	−	0.0372033i
$426$		0			0
$427$	290.000	+	290.000i	0.679157	+	0.679157i
$428$	−60.0833	+	60.0833i	−0.140381	+	0.140381i
$429$		0			0
$430$	50.0000	+	150.000i	0.116279	+	0.348837i
$431$	−221.359			−0.513595			−0.256797	−	0.966465i	$-0.582667\pi$
$431$	−221.359			−0.513595			−0.256797	+	0.966465i	$0.582667\pi$
$432$		0			0
$433$	145.000	−	145.000i	0.334873	−	0.334873i	−0.519561	−	0.854434i	$-0.673904\pi$
$433$	145.000	−	145.000i	0.334873	−	0.334873i	0.854434	+	0.519561i	$0.173904\pi$
$434$			126.491i			0.291454i
$435$		0			0
$436$	−162.000			−0.371560
$437$	56.9210	+	56.9210i	0.130254	+	0.130254i
$438$		0			0
$439$		−	78.0000i		−	0.177677i	−0.996046	−	0.0888383i	$-0.971685\pi$
$439$		−	78.0000i		−	0.177677i	0.996046	−	0.0888383i	$-0.0283154\pi$
$440$	474.342	+	237.171i	1.07805	+	0.539025i
$441$		0			0
$442$	−100.000	−	100.000i	−0.226244	−	0.226244i
$443$	−196.061	+	196.061i	−0.442576	+	0.442576i	−0.892877	−	0.450301i	$-0.851317\pi$
$443$	−196.061	+	196.061i	−0.442576	+	0.442576i	0.450301	+	0.892877i	$0.351317\pi$
$444$		0			0
$445$		0			0
$446$	679.890			1.52442
$447$		0			0
$448$	−205.000	+	205.000i	−0.457589	+	0.457589i
$449$		−	284.605i		−	0.633864i	−0.948448	−	0.316932i	$-0.897347\pi$
$449$		−	284.605i		−	0.633864i	0.948448	−	0.316932i	$-0.102653\pi$
$450$		0			0
$451$	−500.000			−1.10865
$452$	117.004	+	117.004i	0.258859	+	0.258859i
$453$		0			0
$454$			860.000i			1.89427i
$455$	158.114	+	474.342i	0.347503	+	1.04251i
$456$		0			0
$457$	−365.000	−	365.000i	−0.798687	−	0.798687i	0.184201	−	0.982889i	$-0.441030\pi$
$457$	−365.000	−	365.000i	−0.798687	−	0.798687i	−0.982889	+	0.184201i	$0.941030\pi$
$458$	123.329	−	123.329i	0.269277	−	0.269277i
$459$		0			0
$460$	10.0000	−	20.0000i	0.0217391	−	0.0434783i
$461$	−838.004			−1.81780			−0.908898	−	0.417019i	$-0.863075\pi$
$461$	−838.004			−1.81780			−0.908898	+	0.417019i	$0.863075\pi$
$462$		0			0
$463$	−35.0000	+	35.0000i	−0.0755940	+	0.0755940i	−0.743893	−	0.668299i	$-0.767023\pi$
$463$	−35.0000	+	35.0000i	−0.0755940	+	0.0755940i	0.668299	+	0.743893i	$0.267023\pi$
$464$		−	901.249i		−	1.94235i
$465$		0			0
$466$	350.000			0.751073
$467$	117.004	+	117.004i	0.250544	+	0.250544i	0.821194	−	0.570649i	$-0.193308\pi$
$467$	117.004	+	117.004i	0.250544	+	0.250544i	−0.570649	+	0.821194i	$0.693308\pi$
$468$		0			0
$469$		−	700.000i		−	1.49254i
$470$	−616.644	+	205.548i	−1.31201	+	0.437336i
$471$		0			0
$472$	−225.000	−	225.000i	−0.476695	−	0.476695i
$473$	158.114	−	158.114i	0.334279	−	0.334279i
$474$		0			0
$475$	−270.000	−	360.000i	−0.568421	−	0.757895i
$476$	31.6228			0.0664344
$477$		0			0
$478$	−600.000	+	600.000i	−1.25523	+	1.25523i
$479$			379.473i			0.792220i	0.918203	+	0.396110i	$0.129640\pi$
$479$			379.473i			0.792220i	−0.918203	+	0.396110i	$0.870360\pi$
$480$		0			0
$481$	200.000			0.415800
$482$	−335.201	−	335.201i	−0.695439	−	0.695439i
$483$		0			0
$484$			129.000i			0.266529i
$485$	−15.8114	+	31.6228i	−0.0326008	+	0.0652016i
$486$		0			0
$487$	−125.000	−	125.000i	−0.256674	−	0.256674i	0.567026	−	0.823700i	$-0.308094\pi$
$487$	−125.000	−	125.000i	−0.256674	−	0.256674i	−0.823700	+	0.567026i	$0.808094\pi$
$488$	275.118	−	275.118i	0.563767	−	0.563767i
$489$		0			0
$490$	−10.0000	−	5.00000i	−0.0204082	−	0.0102041i
$491$	−458.530			−0.933870			−0.466935	−	0.884292i	$-0.654642\pi$
$491$	−458.530			−0.933870			−0.466935	+	0.884292i	$0.654642\pi$
$492$		0			0
$493$	150.000	−	150.000i	0.304260	−	0.304260i
$494$		−	569.210i		−	1.15225i
$495$		0			0
$496$	152.000			0.306452
$497$	−316.228	−	316.228i	−0.636273	−	0.636273i
$498$		0			0
$499$			222.000i			0.444890i	0.974945	+	0.222445i	$0.0714037\pi$
$499$			222.000i			0.444890i	−0.974945	+	0.222445i	$0.928596\pi$
$500$	−71.1512	+	102.774i	−0.142302	+	0.205548i
$501$		0			0
$502$	575.000	+	575.000i	1.14542	+	1.14542i
$503$	458.530	−	458.530i	0.911591	−	0.911591i	−0.0848065	−	0.996397i	$-0.527027\pi$
$503$	458.530	−	458.530i	0.911591	−	0.911591i	0.996397	+	0.0848065i	$0.0270272\pi$
$504$		0			0
$505$	−25.0000	−	75.0000i	−0.0495050	−	0.148515i
$506$	−158.114			−0.312478
$507$		0			0
$508$	−55.0000	+	55.0000i	−0.108268	+	0.108268i
$509$		−	237.171i		−	0.465954i	−0.972482	−	0.232977i	$-0.925153\pi$
$509$		−	237.171i		−	0.465954i	0.972482	−	0.232977i	$-0.0748468\pi$
$510$		0			0
$511$	−550.000			−1.07632
$512$	150.208	+	150.208i	0.293375	+	0.293375i
$513$		0			0
$514$		−	970.000i		−	1.88716i
$515$	221.359	+	110.680i	0.429824	+	0.214912i
$516$		0			0
$517$	650.000	+	650.000i	1.25725	+	1.25725i
$518$	−158.114	+	158.114i	−0.305239	+	0.305239i
$519$		0			0
$520$	450.000	−	150.000i	0.865385	−	0.288462i
$521$	−790.569			−1.51741			−0.758704	−	0.651436i	$-0.774167\pi$
$521$	−790.569			−1.51741			−0.758704	+	0.651436i	$0.774167\pi$
$522$		0			0
$523$	370.000	−	370.000i	0.707457	−	0.707457i	−0.258543	−	0.966000i	$-0.583242\pi$
$523$	370.000	−	370.000i	0.707457	−	0.707457i	0.966000	+	0.258543i	$0.0832423\pi$
$524$		−	173.925i		−	0.331918i
$525$		0			0
$526$	−910.000			−1.73004
$527$	25.2982	+	25.2982i	0.0480042	+	0.0480042i
$528$		0			0
$529$			509.000i			0.962193i
$530$	−126.491	−	379.473i	−0.238662	−	0.715987i
$531$		0			0
$532$	90.0000	+	90.0000i	0.169173	+	0.169173i
$533$	−316.228	+	316.228i	−0.593298	+	0.593298i
$534$		0			0
$535$	190.000	−	380.000i	0.355140	−	0.710280i
$536$	−664.078			−1.23895
$537$		0			0
$538$	−225.000	+	225.000i	−0.418216	+	0.418216i
$539$			15.8114i			0.0293347i
$540$		0			0
$541$	362.000			0.669131			0.334566	−	0.942372i	$-0.391410\pi$
$541$	362.000			0.669131			0.334566	+	0.942372i	$0.391410\pi$
$542$	281.443	+	281.443i	0.519267	+	0.519267i
$543$		0			0
$544$		−	70.0000i		−	0.128676i
$545$	768.433	−	256.144i	1.40997	−	0.469990i
$546$		0			0
$547$	490.000	+	490.000i	0.895795	+	0.895795i	0.995061	−	0.0992657i	$-0.0316494\pi$
$547$	490.000	+	490.000i	0.895795	+	0.895795i	−0.0992657	+	0.995061i	$0.531649\pi$
$548$	15.8114	−	15.8114i	0.0288529	−	0.0288529i
$549$		0			0
$550$	875.000	+	125.000i	1.59091	+	0.227273i
$551$	853.815			1.54957
$552$		0			0
$553$	60.0000	−	60.0000i	0.108499	−	0.108499i
$554$			727.324i			1.31286i
$555$		0			0
$556$	102.000			0.183453
$557$	−252.982	−	252.982i	−0.454187	−	0.454187i	0.442555	−	0.896742i	$-0.354072\pi$
$557$	−252.982	−	252.982i	−0.454187	−	0.454187i	−0.896742	+	0.442555i	$0.854072\pi$
$558$		0			0
$559$		−	200.000i		−	0.357782i
$560$	−300.416	+	600.833i	−0.536458	+	1.07292i
$561$		0			0
$562$	−250.000	−	250.000i	−0.444840	−	0.444840i
$563$	202.386	−	202.386i	0.359477	−	0.359477i	−0.504143	−	0.863620i	$-0.668192\pi$
$563$	202.386	−	202.386i	0.359477	−	0.359477i	0.863620	+	0.504143i	$0.168192\pi$
$564$		0			0
$565$	−740.000	−	370.000i	−1.30973	−	0.654867i
$566$	1106.80			1.95547
$567$		0			0
$568$	−300.000	+	300.000i	−0.528169	+	0.528169i
$569$		−	189.737i		−	0.333456i	−0.986003	−	0.166728i	$-0.946680\pi$
$569$		−	189.737i		−	0.333456i	0.986003	−	0.166728i	$-0.0533202\pi$
$570$		0			0
$571$	−658.000			−1.15236			−0.576182	−	0.817321i	$-0.695458\pi$
$571$	−658.000			−1.15236			−0.576182	+	0.817321i	$0.695458\pi$
$572$	158.114	+	158.114i	0.276423	+	0.276423i
$573$		0			0
$574$		−	500.000i		−	0.871080i
$575$	−15.8114	+	110.680i	−0.0274981	+	0.192486i
$576$		0			0
$577$	−35.0000	−	35.0000i	−0.0606586	−	0.0606586i	0.676127	−	0.736785i	$-0.263657\pi$
$577$	−35.0000	−	35.0000i	−0.0606586	−	0.0606586i	−0.736785	+	0.676127i	$0.763657\pi$
$578$	−425.326	+	425.326i	−0.735859	+	0.735859i
$579$		0			0
$580$	−75.0000	−	225.000i	−0.129310	−	0.387931i
$581$	537.587			0.925279
$582$		0			0
$583$	−400.000	+	400.000i	−0.686106	+	0.686106i
$584$			521.776i			0.893452i
$585$		0			0
$586$	−640.000			−1.09215
$587$	154.952	+	154.952i	0.263972	+	0.263972i	0.826666	−	0.562694i	$-0.190235\pi$
$587$	154.952	+	154.952i	0.263972	+	0.263972i	−0.562694	+	0.826666i	$0.690235\pi$
$588$		0			0
$589$			144.000i			0.244482i
$590$	−474.342	−	237.171i	−0.803969	−	0.401984i
$591$		0			0
$592$	190.000	+	190.000i	0.320946	+	0.320946i
$593$	−167.601	+	167.601i	−0.282632	+	0.282632i	−0.834158	−	0.551526i	$-0.814046\pi$
$593$	−167.601	+	167.601i	−0.282632	+	0.282632i	0.551526	+	0.834158i	$0.314046\pi$
$594$		0			0
$595$	−150.000	+	50.0000i	−0.252101	+	0.0840336i
$596$	−47.4342			−0.0795875
$597$		0			0
$598$	−100.000	+	100.000i	−0.167224	+	0.167224i
$599$			1043.55i			1.74216i	0.491144	+	0.871078i	$0.336579\pi$
$599$			1043.55i			1.74216i	−0.491144	+	0.871078i	$0.663421\pi$
$600$		0			0
$601$	−382.000			−0.635607			−0.317804	−	0.948157i	$-0.602945\pi$
$601$	−382.000			−0.635607			−0.317804	+	0.948157i	$0.602945\pi$
$602$	158.114	+	158.114i	0.262648	+	0.262648i
$603$		0			0
$604$		−	22.0000i		−	0.0364238i
$605$	−203.967	−	611.901i	−0.337135	−	1.01141i
$606$		0			0
$607$	655.000	+	655.000i	1.07908	+	1.07908i	0.996592	+	0.0824851i	$0.0262857\pi$
$607$	655.000	+	655.000i	1.07908	+	1.07908i	0.0824851	+	0.996592i	$0.473714\pi$
$608$	199.223	−	199.223i	0.327670	−	0.327670i
$609$		0			0
$610$	290.000	−	580.000i	0.475410	−	0.950820i
$611$	822.192			1.34565
$612$		0			0
$613$	−620.000	+	620.000i	−1.01142	+	1.01142i	−0.0114852	+	0.999934i	$0.503656\pi$
$613$	−620.000	+	620.000i	−1.01142	+	1.01142i	−0.999934	+	0.0114852i	$0.996344\pi$
$614$		−	600.833i		−	0.978555i
$615$		0			0
$616$	750.000			1.21753
$617$	−34.7851	−	34.7851i	−0.0563777	−	0.0563777i	0.678356	−	0.734734i	$-0.262693\pi$
$617$	−34.7851	−	34.7851i	−0.0563777	−	0.0563777i	−0.734734	+	0.678356i	$0.762693\pi$
$618$		0			0
$619$		−	258.000i		−	0.416801i	−0.978044	−	0.208401i	$-0.933174\pi$
$619$		−	258.000i		−	0.416801i	0.978044	−	0.208401i	$-0.0668258\pi$
$620$	37.9473	−	12.6491i	0.0612054	−	0.0204018i
$621$		0			0
$622$	−400.000	−	400.000i	−0.643087	−	0.643087i
$623$		0			0
$624$		0			0
$625$	175.000	−	600.000i	0.280000	−	0.960000i
$626$	−458.530			−0.732476
$627$		0			0
$628$	200.000	−	200.000i	0.318471	−	0.318471i
$629$			63.2456i			0.100549i
$630$		0			0
$631$	812.000			1.28685			0.643423	−	0.765511i	$-0.277514\pi$
$631$	812.000			1.28685			0.643423	+	0.765511i	$0.277514\pi$
$632$	−56.9210	−	56.9210i	−0.0900649	−	0.0900649i
$633$		0			0
$634$			50.0000i			0.0788644i
$635$	173.925	−	347.851i	0.273898	−	0.547796i
$636$		0			0
$637$	10.0000	+	10.0000i	0.0156986	+	0.0156986i
$638$	−1185.85	+	1185.85i	−1.85871	+	1.85871i
$639$		0			0
$640$	690.000	+	345.000i	1.07812	+	0.539062i
$641$	442.719			0.690669			0.345335	−	0.938480i	$-0.387765\pi$
$641$	442.719			0.690669			0.345335	+	0.938480i	$0.387765\pi$
$642$		0			0
$643$	820.000	−	820.000i	1.27527	−	1.27527i	0.331989	−	0.943283i	$-0.392280\pi$
$643$	820.000	−	820.000i	1.27527	−	1.27527i	0.943283	−	0.331989i	$-0.107720\pi$
$644$		−	31.6228i		−	0.0491037i
$645$		0			0
$646$	180.000			0.278638
$647$	−679.890	−	679.890i	−1.05083	−	1.05083i	−0.998637	−	0.0521974i	$-0.983378\pi$
$647$	−679.890	−	679.890i	−1.05083	−	1.05083i	−0.0521974	−	0.998637i	$-0.516622\pi$
$648$		0			0
$649$			750.000i			1.15562i
$650$	632.456	−	474.342i	0.973009	−	0.729756i
$651$		0			0
$652$	100.000	+	100.000i	0.153374	+	0.153374i
$653$	515.451	−	515.451i	0.789359	−	0.789359i	−0.192030	−	0.981389i	$-0.561507\pi$
$653$	515.451	−	515.451i	0.789359	−	0.789359i	0.981389	+	0.192030i	$0.0615072\pi$
$654$		0			0
$655$	275.000	+	825.000i	0.419847	+	1.25954i
$656$	−600.833			−0.915904
$657$		0			0
$658$	−650.000	+	650.000i	−0.987842	+	0.987842i
$659$		−	901.249i		−	1.36760i	−0.729669	−	0.683801i	$-0.760326\pi$
$659$		−	901.249i		−	1.36760i	0.729669	−	0.683801i	$-0.239674\pi$
$660$		0			0
$661$	−802.000			−1.21331			−0.606657	−	0.794964i	$-0.707490\pi$
$661$	−802.000			−1.21331			−0.606657	+	0.794964i	$0.707490\pi$
$662$	−762.109	−	762.109i	−1.15122	−	1.15122i
$663$		0			0
$664$		−	510.000i		−	0.768072i
$665$	−569.210	−	284.605i	−0.855955	−	0.427977i
$666$		0			0
$667$	−150.000	−	150.000i	−0.224888	−	0.224888i
$668$	148.627	−	148.627i	0.222496	−	0.222496i
$669$		0			0
$670$	−1050.00	+	350.000i	−1.56716	+	0.522388i
$671$	−917.061			−1.36671
$672$		0			0
$673$	775.000	−	775.000i	1.15156	−	1.15156i	0.165320	−	0.986240i	$-0.447134\pi$
$673$	775.000	−	775.000i	1.15156	−	1.15156i	0.986240	−	0.165320i	$-0.0528658\pi$
$674$			490.153i			0.727230i
$675$		0			0
$676$	31.0000			0.0458580
$677$	496.478	+	496.478i	0.733349	+	0.733349i	0.971282	−	0.237932i	$-0.0764696\pi$
$677$	496.478	+	496.478i	0.733349	+	0.733349i	−0.237932	+	0.971282i	$0.576470\pi$
$678$		0			0
$679$			50.0000i			0.0736377i
$680$	47.4342	+	142.302i	0.0697561	+	0.209268i
$681$		0			0
$682$	−200.000	−	200.000i	−0.293255	−	0.293255i
$683$	60.0833	−	60.0833i	0.0879697	−	0.0879697i	−0.661753	−	0.749722i	$-0.730187\pi$
$683$	60.0833	−	60.0833i	0.0879697	−	0.0879697i	0.749722	+	0.661753i	$0.230187\pi$
$684$		0			0
$685$	−50.0000	+	100.000i	−0.0729927	+	0.145985i
$686$	758.947			1.10634
$687$		0			0
$688$	190.000	−	190.000i	0.276163	−	0.276163i
$689$			505.964i			0.734346i
$690$		0			0
$691$	−562.000			−0.813314			−0.406657	−	0.913581i	$-0.633306\pi$
$691$	−562.000			−0.813314			−0.406657	+	0.913581i	$0.633306\pi$
$692$	−110.680	−	110.680i	−0.159942	−	0.159942i
$693$		0			0
$694$		−	520.000i		−	0.749280i
$695$	−483.828	+	161.276i	−0.696156	+	0.232052i
$696$		0			0
$697$	−100.000	−	100.000i	−0.143472	−	0.143472i
$698$	502.802	−	502.802i	0.720347	−	0.720347i
$699$		0			0
$700$	−25.0000	+	175.000i	−0.0357143	+	0.250000i
$701$	−363.662			−0.518776			−0.259388	−	0.965773i	$-0.583521\pi$
$701$	−363.662			−0.518776			−0.259388	+	0.965773i	$0.583521\pi$
$702$		0			0
$703$	−180.000	+	180.000i	−0.256046	+	0.256046i
$704$		−	648.267i		−	0.920834i
$705$		0			0
$706$	710.000			1.00567
$707$	−79.0569	−	79.0569i	−0.111820	−	0.111820i
$708$		0			0
$709$			498.000i			0.702398i	0.936301	+	0.351199i	$0.114226\pi$
$709$			498.000i			0.702398i	−0.936301	+	0.351199i	$0.885774\pi$
$710$	−316.228	+	632.456i	−0.445391	+	0.890782i
$711$		0			0
$712$		0			0
$713$	25.2982	−	25.2982i	0.0354814	−	0.0354814i
$714$		0			0
$715$	−1000.00	−	500.000i	−1.39860	−	0.699301i
$716$	−142.302			−0.198747
$717$		0			0
$718$	−450.000	+	450.000i	−0.626741	+	0.626741i
$719$		−	569.210i		−	0.791669i	−0.918322	−	0.395834i	$-0.870455\pi$
$719$		−	569.210i		−	0.791669i	0.918322	−	0.395834i	$-0.129545\pi$
$720$		0			0
$721$	350.000			0.485437
$722$	−58.5021	−	58.5021i	−0.0810279	−	0.0810279i
$723$		0			0
$724$			218.000i			0.301105i
$725$	711.512	+	948.683i	0.981397	+	1.30853i
$726$		0			0
$727$	−905.000	−	905.000i	−1.24484	−	1.24484i	−0.957969	−	0.286873i	$-0.907384\pi$
$727$	−905.000	−	905.000i	−1.24484	−	1.24484i	−0.286873	−	0.957969i	$-0.592616\pi$
$728$	474.342	−	474.342i	0.651568	−	0.651568i
$729$		0			0
$730$	275.000	+	825.000i	0.376712	+	1.13014i
$731$	63.2456			0.0865192
$732$		0			0
$733$	550.000	−	550.000i	0.750341	−	0.750341i	−0.224202	−	0.974543i	$-0.571977\pi$
$733$	550.000	−	550.000i	0.750341	−	0.750341i	0.974543	+	0.224202i	$0.0719774\pi$
$734$			585.021i			0.797032i
$735$		0			0
$736$	−70.0000			−0.0951087
$737$	1106.80	+	1106.80i	1.50176	+	1.50176i
$738$		0			0
$739$			198.000i			0.267930i	0.990986	+	0.133965i	$0.0427709\pi$
$739$			198.000i			0.267930i	−0.990986	+	0.133965i	$0.957229\pi$
$740$	63.2456	+	31.6228i	0.0854670	+	0.0427335i
$741$		0			0
$742$	−400.000	−	400.000i	−0.539084	−	0.539084i
$743$	−964.495	+	964.495i	−1.29811	+	1.29811i	−0.368468	+	0.929640i	$0.620118\pi$
$743$	−964.495	+	964.495i	−1.29811	+	1.29811i	−0.929640	+	0.368468i	$0.879882\pi$
$744$		0			0
$745$	225.000	−	75.0000i	0.302013	−	0.100671i
$746$	−316.228			−0.423898
$747$		0			0
$748$	−50.0000	+	50.0000i	−0.0668449	+	0.0668449i
$749$		−	600.833i		−	0.802180i
$750$		0			0
$751$	728.000			0.969374			0.484687	−	0.874688i	$-0.338933\pi$
$751$	728.000			0.969374			0.484687	+	0.874688i	$0.338933\pi$
$752$	781.083	+	781.083i	1.03867	+	1.03867i
$753$		0			0
$754$			1500.00i			1.98939i
$755$	34.7851	+	104.355i	0.0460729	+	0.138219i
$756$		0			0
$757$	−170.000	−	170.000i	−0.224571	−	0.224571i	0.585849	−	0.810420i	$-0.300761\pi$
$757$	−170.000	−	170.000i	−0.224571	−	0.224571i	−0.810420	+	0.585849i	$0.800761\pi$
$758$	882.275	−	882.275i	1.16395	−	1.16395i
$759$		0			0
$760$	−270.000	+	540.000i	−0.355263	+	0.710526i
$761$	−31.6228			−0.0415542			−0.0207771	−	0.999784i	$-0.506614\pi$
$761$	−31.6228			−0.0415542			−0.0207771	+	0.999784i	$0.506614\pi$
$762$		0			0
$763$	810.000	−	810.000i	1.06160	−	1.06160i
$764$			158.114i			0.206955i
$765$		0			0
$766$	890.000			1.16188
$767$	474.342	+	474.342i	0.618438	+	0.618438i
$768$		0			0
$769$		−	318.000i		−	0.413524i	−0.978391	−	0.206762i	$-0.933707\pi$
$769$		−	318.000i		−	0.413524i	0.978391	−	0.206762i	$-0.0662926\pi$
$770$	1185.85	−	395.285i	1.54007	−	0.513357i
$771$		0			0
$772$	−125.000	−	125.000i	−0.161917	−	0.161917i
$773$	−452.206	+	452.206i	−0.585001	+	0.585001i	−0.936273	−	0.351272i	$-0.885749\pi$
$773$	−452.206	+	452.206i	−0.585001	+	0.585001i	0.351272	+	0.936273i	$0.385749\pi$
$774$		0			0
$775$	−160.000	+	120.000i	−0.206452	+	0.154839i
$776$	47.4342			0.0611265
$777$		0			0
$778$	825.000	−	825.000i	1.06041	−	1.06041i
$779$		−	569.210i		−	0.730693i
$780$		0			0
$781$	1000.00			1.28041
$782$	−31.6228	−	31.6228i	−0.0404383	−	0.0404383i
$783$		0			0
$784$			19.0000i			0.0242347i
$785$	−632.456	+	1264.91i	−0.805676	+	1.61135i
$786$		0			0
$787$	250.000	+	250.000i	0.317662	+	0.317662i	0.847869	−	0.530207i	$-0.177886\pi$
$787$	250.000	+	250.000i	0.317662	+	0.317662i	−0.530207	+	0.847869i	$0.677886\pi$
$788$	−145.465	+	145.465i	−0.184600	+	0.184600i
$789$		0			0
$790$	−120.000	−	60.0000i	−0.151899	−	0.0759494i
$791$	−1170.04			−1.47919
$792$		0			0
$793$	−580.000	+	580.000i	−0.731400	+	0.731400i
$794$			822.192i			1.03551i
$795$		0			0
$796$	18.0000			0.0226131
$797$	−888.600	−	888.600i	−1.11493	−	1.11493i	−0.992474	−	0.122457i	$-0.960923\pi$
$797$	−888.600	−	888.600i	−1.11493	−	1.11493i	−0.122457	−	0.992474i	$-0.539077\pi$
$798$		0			0
$799$			260.000i			0.325407i
$800$	387.379	+	55.3399i	0.484224	+	0.0691748i
$801$		0			0
$802$	−400.000	−	400.000i	−0.498753	−	0.498753i
$803$	869.626	−	869.626i	1.08297	−	1.08297i
$804$		0			0
$805$	50.0000	+	150.000i	0.0621118	+	0.186335i
$806$	−252.982			−0.313874
$807$		0			0
$808$	−75.0000	+	75.0000i	−0.0928218	+	0.0928218i
$809$			569.210i			0.703597i	0.936076	+	0.351799i	$0.114430\pi$
$809$			569.210i			0.703597i	−0.936076	+	0.351799i	$0.885570\pi$
$810$		0			0
$811$	−142.000			−0.175092			−0.0875462	−	0.996160i	$-0.527903\pi$
$811$	−142.000			−0.175092			−0.0875462	+	0.996160i	$0.527903\pi$
$812$	−237.171	−	237.171i	−0.292082	−	0.292082i
$813$		0			0
$814$		−	500.000i		−	0.614251i
$815$	−632.456	−	316.228i	−0.776019	−	0.388010i
$816$		0			0
$817$	180.000	+	180.000i	0.220318	+	0.220318i
$818$	550.236	−	550.236i	0.672661	−	0.672661i
$819$		0			0
$820$	−150.000	+	50.0000i	−0.182927	+	0.0609756i
$821$	869.626			1.05923			0.529614	−	0.848239i	$-0.322337\pi$
$821$	869.626			1.05923			0.529614	+	0.848239i	$0.322337\pi$
$822$		0			0
$823$	−1115.00	+	1115.00i	−1.35480	+	1.35480i	−0.474595	+	0.880204i	$0.657406\pi$
$823$	−1115.00	+	1115.00i	−1.35480	+	1.35480i	−0.880204	+	0.474595i	$0.842594\pi$
$824$		−	332.039i		−	0.402960i
$825$		0			0
$826$	−750.000			−0.907990
$827$	−25.2982	−	25.2982i	−0.0305904	−	0.0305904i	0.691646	−	0.722237i	$-0.256886\pi$
$827$	−25.2982	−	25.2982i	−0.0305904	−	0.0305904i	−0.722237	+	0.691646i	$0.756886\pi$
$828$		0			0
$829$		−	1062.00i		−	1.28106i	−0.767933	−	0.640531i	$-0.778714\pi$
$829$		−	1062.00i		−	1.28106i	0.767933	−	0.640531i	$-0.221286\pi$
$830$	−268.794	−	806.381i	−0.323848	−	0.971543i
$831$		0			0
$832$	−410.000	−	410.000i	−0.492788	−	0.492788i
$833$	−3.16228	+	3.16228i	−0.00379625	+	0.00379625i
$834$		0			0
$835$	−470.000	+	940.000i	−0.562874	+	1.12575i
$836$	−284.605			−0.340437
$837$		0			0
$838$	975.000	−	975.000i	1.16348	−	1.16348i
$839$		−	474.342i		−	0.565365i	−0.959213	−	0.282683i	$-0.908776\pi$
$839$		−	474.342i		−	0.565365i	0.959213	−	0.282683i	$-0.0912244\pi$
$840$		0			0
$841$	−1409.00			−1.67539
$842$	−534.425	−	534.425i	−0.634709	−	0.634709i
$843$		0			0
$844$		−	298.000i		−	0.353081i
$845$	−147.046	+	49.0153i	−0.174019	+	0.0580063i
$846$		0			0
$847$	−645.000	−	645.000i	−0.761511	−	0.761511i
$848$	−480.666	+	480.666i	−0.566823	+	0.566823i
$849$		0			0
$850$	150.000	+	200.000i	0.176471	+	0.235294i
$851$	63.2456			0.0743191
$852$		0			0
$853$	−80.0000	+	80.0000i	−0.0937866	+	0.0937866i	−0.752443	−	0.658657i	$-0.771125\pi$
$853$	−80.0000	+	80.0000i	−0.0937866	+	0.0937866i	0.658657	+	0.752443i	$0.271125\pi$
$854$		−	917.061i		−	1.07384i
$855$		0			0
$856$	−570.000			−0.665888
$857$	−243.495	−	243.495i	−0.284125	−	0.284125i	0.550626	−	0.834752i	$-0.314389\pi$
$857$	−243.495	−	243.495i	−0.284125	−	0.284125i	−0.834752	+	0.550626i	$0.814389\pi$
$858$		0			0
$859$			1482.00i			1.72526i	0.505834	+	0.862631i	$0.331185\pi$
$859$			1482.00i			1.72526i	−0.505834	+	0.862631i	$0.668815\pi$
$860$	31.6228	−	63.2456i	0.0367707	−	0.0735413i
$861$		0			0
$862$	350.000	+	350.000i	0.406032	+	0.406032i
$863$	−964.495	+	964.495i	−1.11761	+	1.11761i	−0.125515	+	0.992092i	$0.540058\pi$
$863$	−964.495	+	964.495i	−1.11761	+	1.11761i	−0.992092	+	0.125515i	$0.959942\pi$
$864$		0			0
$865$	700.000	+	350.000i	0.809249	+	0.404624i
$866$	−458.530			−0.529481
$867$		0			0
$868$	40.0000	−	40.0000i	0.0460829	−	0.0460829i
$869$			189.737i			0.218339i
$870$		0			0
$871$	1400.00			1.60735
$872$	−768.433	−	768.433i	−0.881231	−	0.881231i
$873$		0			0
$874$		−	180.000i		−	0.205950i
$875$	−158.114	−	869.626i	−0.180702	−	0.993859i
$876$		0			0
$877$	700.000	+	700.000i	0.798176	+	0.798176i	0.982808	−	0.184632i	$-0.0591094\pi$
$877$	700.000	+	700.000i	0.798176	+	0.798176i	−0.184632	+	0.982808i	$0.559109\pi$
$878$	−123.329	+	123.329i	−0.140466	+	0.140466i
$879$		0			0
$880$	−475.000	−	1425.00i	−0.539773	−	1.61932i
$881$	1201.67			1.36398			0.681990	−	0.731362i	$-0.261115\pi$
$881$	1201.67			1.36398			0.681990	+	0.731362i	$0.261115\pi$
$882$		0			0
$883$	640.000	−	640.000i	0.724802	−	0.724802i	−0.244777	−	0.969579i	$-0.578715\pi$
$883$	640.000	−	640.000i	0.724802	−	0.724802i	0.969579	+	0.244777i	$0.0787149\pi$
$884$			63.2456i			0.0715447i
$885$		0			0
$886$	620.000			0.699774
$887$	135.978	+	135.978i	0.153301	+	0.153301i	0.779591	−	0.626290i	$-0.215427\pi$
$887$	135.978	+	135.978i	0.153301	+	0.153301i	−0.626290	+	0.779591i	$0.715427\pi$
$888$		0			0
$889$		−	550.000i		−	0.618673i
$890$		0			0
$891$		0			0
$892$	−215.000	−	215.000i	−0.241031	−	0.241031i
$893$	−739.973	+	739.973i	−0.828637	+	0.828637i
$894$		0			0
$895$	675.000	−	225.000i	0.754190	−	0.251397i
$896$	1090.99			1.21762
$897$		0			0
$898$	−450.000	+	450.000i	−0.501114	+	0.501114i
$899$		−	379.473i		−	0.422106i
$900$		0			0
$901$	−160.000			−0.177580
$902$	790.569	+	790.569i	0.876463	+	0.876463i
$903$		0			0
$904$			1110.00i			1.22788i
$905$	−344.688	−	1034.06i	−0.380871	−	1.14261i
$906$		0			0
$907$	40.0000	+	40.0000i	0.0441014	+	0.0441014i	0.728814	−	0.684712i	$-0.240072\pi$
$907$	40.0000	+	40.0000i	0.0441014	+	0.0441014i	−0.684712	+	0.728814i	$0.740072\pi$
$908$	271.956	−	271.956i	0.299511	−	0.299511i
$909$		0			0
$910$	500.000	−	1000.00i	0.549451	−	1.09890i
$911$	−411.096			−0.451258			−0.225629	−	0.974213i	$-0.572444\pi$
$911$	−411.096			−0.451258			−0.225629	+	0.974213i	$0.572444\pi$
$912$		0			0
$913$	−850.000	+	850.000i	−0.930997	+	0.930997i
$914$			1154.23i			1.26284i
$915$		0			0
$916$	−78.0000			−0.0851528
$917$	869.626	+	869.626i	0.948338	+	0.948338i
$918$		0			0
$919$		−	792.000i		−	0.861806i	−0.902398	−	0.430903i	$-0.858195\pi$
$919$		−	792.000i		−	0.861806i	0.902398	−	0.430903i	$-0.141805\pi$
$920$	142.302	−	47.4342i	0.154677	−	0.0515589i
$921$		0			0
$922$	1325.00	+	1325.00i	1.43709	+	1.43709i
$923$	632.456	−	632.456i	0.685217	−	0.685217i
$924$		0			0
$925$	−350.000	−	50.0000i	−0.378378	−	0.0540541i
$926$	110.680			0.119525
$927$		0			0
$928$	−525.000	+	525.000i	−0.565733	+	0.565733i
$929$			1233.29i			1.32754i	0.747935	+	0.663772i	$0.231045\pi$
$929$			1233.29i			1.32754i	−0.747935	+	0.663772i	$0.768955\pi$
$930$		0			0
$931$	−18.0000			−0.0193340
$932$	−110.680	−	110.680i	−0.118755	−	0.118755i
$933$		0			0
$934$		−	370.000i		−	0.396146i
$935$	158.114	−	316.228i	0.169106	−	0.338212i
$936$		0			0
$937$	865.000	+	865.000i	0.923159	+	0.923159i	0.997251	−	0.0740924i	$-0.0236060\pi$
$937$	865.000	+	865.000i	0.923159	+	0.923159i	−0.0740924	+	0.997251i	$0.523606\pi$
$938$	−1106.80	+	1106.80i	−1.17995	+	1.17995i
$939$		0			0
$940$	260.000	+	130.000i	0.276596	+	0.138298i
$941$	964.495			1.02497			0.512484	−	0.858697i	$-0.328725\pi$
$941$	964.495			1.02497			0.512484	+	0.858697i	$0.328725\pi$
$942$		0			0
$943$	−100.000	+	100.000i	−0.106045	+	0.106045i
$944$			901.249i			0.954713i
$945$		0			0
$946$	−500.000			−0.528541
$947$	−841.166	−	841.166i	−0.888243	−	0.888243i	0.106112	−	0.994354i	$-0.466160\pi$
$947$	−841.166	−	841.166i	−0.888243	−	0.888243i	−0.994354	+	0.106112i	$0.966160\pi$
$948$		0			0
$949$		−	1100.00i		−	1.15911i
$950$	−142.302	+	996.117i	−0.149792	+	1.04854i
$951$		0			0
$952$	150.000	+	150.000i	0.157563	+	0.157563i
$953$	1141.58	−	1141.58i	1.19788	−	1.19788i	0.223083	−	0.974799i	$-0.428388\pi$
$953$	1141.58	−	1141.58i	1.19788	−	1.19788i	0.974799	−	0.223083i	$-0.0716122\pi$
$954$		0			0
$955$	−250.000	−	750.000i	−0.261780	−	0.785340i
$956$	379.473			0.396939
$957$		0			0
$958$	600.000	−	600.000i	0.626305	−	0.626305i
$959$			158.114i			0.164874i
$960$		0			0
$961$	−897.000			−0.933403
$962$	−316.228	−	316.228i	−0.328719	−	0.328719i
$963$		0			0
$964$			212.000i			0.219917i
$965$	790.569	+	395.285i	0.819243	+	0.409621i
$966$		0			0
$967$	−1145.00	−	1145.00i	−1.18407	−	1.18407i	−0.978679	−	0.205395i	$-0.934152\pi$
$967$	−1145.00	−	1145.00i	−1.18407	−	1.18407i	−0.205395	−	0.978679i	$-0.565848\pi$
$968$	−611.901	+	611.901i	−0.632129	+	0.632129i
$969$		0			0
$970$	75.0000	−	25.0000i	0.0773196	−	0.0257732i
$971$	1628.57			1.67721			0.838606	−	0.544738i	$-0.183371\pi$
$971$	1628.57			1.67721			0.838606	+	0.544738i	$0.183371\pi$
$972$		0			0
$973$	−510.000	+	510.000i	−0.524152	+	0.524152i
$974$			395.285i			0.405836i
$975$		0			0
$976$	−1102.00			−1.12910
$977$	762.109	+	762.109i	0.780050	+	0.780050i	0.979839	−	0.199789i	$-0.0640256\pi$
$977$	762.109	+	762.109i	0.780050	+	0.780050i	−0.199789	+	0.979839i	$0.564026\pi$
$978$		0			0
$979$		0			0
$980$	1.58114	+	4.74342i	0.00161341	+	0.00484022i
$981$		0			0
$982$	725.000	+	725.000i	0.738289	+	0.738289i
$983$	−167.601	+	167.601i	−0.170499	+	0.170499i	−0.787199	−	0.616699i	$-0.788469\pi$
$983$	−167.601	+	167.601i	−0.170499	+	0.170499i	0.616699	+	0.787199i	$0.288469\pi$
$984$		0			0
$985$	460.000	−	920.000i	0.467005	−	0.934010i
$986$	−474.342			−0.481077
$987$		0			0
$988$	−180.000	+	180.000i	−0.182186	+	0.182186i
$989$		−	63.2456i		−	0.0639490i
$990$		0			0
$991$	2.00000			0.00201816			0.00100908	−	0.999999i	$-0.499679\pi$
$991$	2.00000			0.00201816			0.00100908	+	0.999999i	$0.499679\pi$
$992$	−88.5438	−	88.5438i	−0.0892578	−	0.0892578i
$993$		0			0
$994$			1000.00i			1.00604i
$995$	−85.3815	+	28.4605i	−0.0858105	+	0.0286035i
$996$		0			0
$997$	310.000	+	310.000i	0.310933	+	0.310933i	0.845271	−	0.534338i	$-0.179439\pi$
$997$	310.000	+	310.000i	0.310933	+	0.310933i	−0.534338	+	0.845271i	$0.679439\pi$
$998$	351.013	−	351.013i	0.351716	−	0.351716i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	45.3.g.a.37.1	yes	4
3.2	odd	2	inner	45.3.g.a.37.2	yes	4
4.3	odd	2		720.3.bh.j.577.1		4
5.2	odd	4		225.3.g.g.118.2		4
5.3	odd	4	inner	45.3.g.a.28.1	✓	4
5.4	even	2		225.3.g.g.82.2		4
9.2	odd	6		405.3.l.g.352.2		8
9.4	even	3		405.3.l.g.217.2		8
9.5	odd	6		405.3.l.g.217.1		8
9.7	even	3		405.3.l.g.352.1		8
12.11	even	2		720.3.bh.j.577.2		4
15.2	even	4		225.3.g.g.118.1		4
15.8	even	4	inner	45.3.g.a.28.2	yes	4
15.14	odd	2		225.3.g.g.82.1		4
20.3	even	4		720.3.bh.j.433.1		4
45.13	odd	12		405.3.l.g.298.1		8
45.23	even	12		405.3.l.g.298.2		8
45.38	even	12		405.3.l.g.28.1		8
45.43	odd	12		405.3.l.g.28.2		8
60.23	odd	4		720.3.bh.j.433.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
45.3.g.a.28.1	✓	4	5.3	odd	4	inner
45.3.g.a.28.2	yes	4	15.8	even	4	inner
45.3.g.a.37.1	yes	4	1.1	even	1	trivial
45.3.g.a.37.2	yes	4	3.2	odd	2	inner
225.3.g.g.82.1		4	15.14	odd	2
225.3.g.g.82.2		4	5.4	even	2
225.3.g.g.118.1		4	15.2	even	4
225.3.g.g.118.2		4	5.2	odd	4
405.3.l.g.28.1		8	45.38	even	12
405.3.l.g.28.2		8	45.43	odd	12
405.3.l.g.217.1		8	9.5	odd	6
405.3.l.g.217.2		8	9.4	even	3
405.3.l.g.298.1		8	45.13	odd	12
405.3.l.g.298.2		8	45.23	even	12
405.3.l.g.352.1		8	9.7	even	3
405.3.l.g.352.2		8	9.2	odd	6
720.3.bh.j.433.1		4	20.3	even	4
720.3.bh.j.433.2		4	60.23	odd	4
720.3.bh.j.577.1		4	4.3	odd	2
720.3.bh.j.577.2		4	12.11	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:	\( N \)	\(=\)	\( 45 = 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	45.g (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.58114 - 1.58114i) q^{2} +1.00000i q^{4} +(-1.58114 - 4.74342i) q^{5} +(-5.00000 - 5.00000i) q^{7} +(-4.74342 + 4.74342i) q^{8} +O(q^{10})\)	\(q+(-1.58114 - 1.58114i) q^{2} +1.00000i q^{4} +(-1.58114 - 4.74342i) q^{5} +(-5.00000 - 5.00000i) q^{7} +(-4.74342 + 4.74342i) q^{8} +(-5.00000 + 10.0000i) q^{10} +15.8114 q^{11} +(10.0000 - 10.0000i) q^{13} +15.8114i q^{14} +19.0000 q^{16} +(3.16228 + 3.16228i) q^{17} +18.0000i q^{19} +(4.74342 - 1.58114i) q^{20} +(-25.0000 - 25.0000i) q^{22} +(3.16228 - 3.16228i) q^{23} +(-20.0000 + 15.0000i) q^{25} -31.6228 q^{26} +(5.00000 - 5.00000i) q^{28} -47.4342i q^{29} +8.00000 q^{31} +(-11.0680 - 11.0680i) q^{32} -10.0000i q^{34} +(-15.8114 + 31.6228i) q^{35} +(10.0000 + 10.0000i) q^{37} +(28.4605 - 28.4605i) q^{38} +(30.0000 + 15.0000i) q^{40} -31.6228 q^{41} +(10.0000 - 10.0000i) q^{43} +15.8114i q^{44} -10.0000 q^{46} +(41.1096 + 41.1096i) q^{47} +1.00000i q^{49} +(55.3399 + 7.90569i) q^{50} +(10.0000 + 10.0000i) q^{52} +(-25.2982 + 25.2982i) q^{53} +(-25.0000 - 75.0000i) q^{55} +47.4342 q^{56} +(-75.0000 + 75.0000i) q^{58} +47.4342i q^{59} -58.0000 q^{61} +(-12.6491 - 12.6491i) q^{62} -41.0000i q^{64} +(-63.2456 - 31.6228i) q^{65} +(70.0000 + 70.0000i) q^{67} +(-3.16228 + 3.16228i) q^{68} +(75.0000 - 25.0000i) q^{70} +63.2456 q^{71} +(55.0000 - 55.0000i) q^{73} -31.6228i q^{74} -18.0000 q^{76} +(-79.0569 - 79.0569i) q^{77} +12.0000i q^{79} +(-30.0416 - 90.1249i) q^{80} +(50.0000 + 50.0000i) q^{82} +(-53.7587 + 53.7587i) q^{83} +(10.0000 - 20.0000i) q^{85} -31.6228 q^{86} +(-75.0000 + 75.0000i) q^{88} -100.000 q^{91} +(3.16228 + 3.16228i) q^{92} -130.000i q^{94} +(85.3815 - 28.4605i) q^{95} +(-5.00000 - 5.00000i) q^{97} +(1.58114 - 1.58114i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 20 q^{7}+O(q^{10}) \) 4 * q - 20 * q^7	\( 4 q - 20 q^{7} - 20 q^{10} + 40 q^{13} + 76 q^{16} - 100 q^{22} - 80 q^{25} + 20 q^{28} + 32 q^{31} + 40 q^{37} + 120 q^{40} + 40 q^{43} - 40 q^{46} + 40 q^{52} - 100 q^{55} - 300 q^{58} - 232 q^{61} + 280 q^{67} + 300 q^{70} + 220 q^{73} - 72 q^{76} + 200 q^{82} + 40 q^{85} - 300 q^{88} - 400 q^{91} - 20 q^{97}+O(q^{100}) \) 4 * q - 20 * q^7 - 20 * q^10 + 40 * q^13 + 76 * q^16 - 100 * q^22 - 80 * q^25 + 20 * q^28 + 32 * q^31 + 40 * q^37 + 120 * q^40 + 40 * q^43 - 40 * q^46 + 40 * q^52 - 100 * q^55 - 300 * q^58 - 232 * q^61 + 280 * q^67 + 300 * q^70 + 220 * q^73 - 72 * q^76 + 200 * q^82 + 40 * q^85 - 300 * q^88 - 400 * q^91 - 20 * q^97

Introduction

L-functions

Modular forms

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