LMFDB - Embedded newform 504.3.g.b.379.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [504,3,Mod(379,504)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(504, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("504.379");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 504 = 2^{3} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	504.g (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$13.7330053238$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.0.292213762624.3
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} - 2x^{6} - 2x^{5} + 24x^{4} - 8x^{3} - 32x^{2} - 64x + 256 $ x^8 - x^7 - 2x^6 - 2x^5 + 24x^4 - 8x^3 - 32x^2 - 64x + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{5} $
Twist minimal:	no (minimal twist has level 56)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			379.4
Root			$1.37098 - 1.45617i$ of defining polynomial
Character	$\chi$	$=$	504.379
Dual form			504.3.g.b.379.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.37098 + 1.45617i) q^{2} +(-0.240837 - 3.99274i) q^{4} +6.26788i q^{5} +2.64575i q^{7} +(6.14428 + 5.12327i) q^{8} +O(q^{10})$	\(q+(-1.37098 + 1.45617i) q^{2} +(-0.240837 - 3.99274i) q^{4} +6.26788i q^{5} +2.64575i q^{7} +(6.14428 + 5.12327i) q^{8} +(-9.12707 - 8.59313i) q^{10} -9.80688 q^{11} -2.41653i q^{13} +(-3.85265 - 3.62727i) q^{14} +(-15.8840 + 1.92320i) q^{16} -6.89452 q^{17} +2.77637 q^{19} +(25.0260 - 1.50954i) q^{20} +(13.4450 - 14.2804i) q^{22} +42.8332i q^{23} -14.2863 q^{25} +(3.51887 + 3.31301i) q^{26} +(10.5638 - 0.637195i) q^{28} -37.3505i q^{29} +7.16835i q^{31} +(18.9761 - 25.7664i) q^{32} +(9.45224 - 10.0396i) q^{34} -16.5833 q^{35} +0.202653i q^{37} +(-3.80634 + 4.04285i) q^{38} +(-32.1120 + 38.5116i) q^{40} -63.5494 q^{41} -35.3384 q^{43} +(2.36186 + 39.1564i) q^{44} +(-62.3723 - 58.7234i) q^{46} -37.9129i q^{47} -7.00000 q^{49} +(19.5862 - 20.8032i) q^{50} +(-9.64858 + 0.581989i) q^{52} -54.6651i q^{53} -61.4684i q^{55} +(-13.5549 + 16.2562i) q^{56} +(54.3885 + 51.2067i) q^{58} -104.795 q^{59} -43.7668i q^{61} +(-10.4383 - 9.82765i) q^{62} +(11.5043 + 62.9575i) q^{64} +15.1465 q^{65} +31.1021 q^{67} +(1.66046 + 27.5281i) q^{68} +(22.7353 - 24.1480i) q^{70} +23.1294i q^{71} -69.2275 q^{73} +(-0.295096 - 0.277832i) q^{74} +(-0.668652 - 11.0853i) q^{76} -25.9466i q^{77} -19.9328i q^{79} +(-12.0544 - 99.5590i) q^{80} +(87.1249 - 92.5385i) q^{82} +5.11617 q^{83} -43.2140i q^{85} +(48.4482 - 51.4585i) q^{86} +(-60.2562 - 50.2433i) q^{88} +17.9889 q^{89} +6.39353 q^{91} +(171.022 - 10.3158i) q^{92} +(55.2075 + 51.9778i) q^{94} +17.4019i q^{95} +12.4864 q^{97} +(9.59685 - 10.1932i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - q^{2} + 5 q^{4} - 13 q^{8}+O(q^{10}) $ 8 * q - q^2 + 5 * q^4 - 13 * q^8	$ 8 q - q^{2} + 5 q^{4} - 13 q^{8} + 16 q^{10} + 32 q^{11} - 7 q^{14} - 71 q^{16} + 80 q^{17} + 56 q^{19} + 108 q^{20} + 66 q^{22} - 16 q^{25} - 24 q^{26} + 7 q^{28} + 19 q^{32} + 74 q^{34} - 56 q^{35} + 14 q^{38} + 84 q^{40} - 128 q^{41} - 50 q^{44} - 152 q^{46} - 56 q^{49} - 33 q^{50} + 132 q^{52} + 49 q^{56} + 24 q^{58} - 104 q^{59} - 120 q^{62} - 55 q^{64} + 72 q^{65} + 304 q^{67} + 190 q^{68} + 56 q^{70} - 112 q^{73} - 8 q^{74} + 70 q^{76} - 124 q^{80} + 450 q^{82} - 72 q^{83} - 210 q^{86} - 486 q^{88} + 512 q^{89} - 56 q^{91} + 472 q^{92} + 472 q^{94} + 64 q^{97} + 7 q^{98}+O(q^{100}) $ 8 * q - q^2 + 5 * q^4 - 13 * q^8 + 16 * q^10 + 32 * q^11 - 7 * q^14 - 71 * q^16 + 80 * q^17 + 56 * q^19 + 108 * q^20 + 66 * q^22 - 16 * q^25 - 24 * q^26 + 7 * q^28 + 19 * q^32 + 74 * q^34 - 56 * q^35 + 14 * q^38 + 84 * q^40 - 128 * q^41 - 50 * q^44 - 152 * q^46 - 56 * q^49 - 33 * q^50 + 132 * q^52 + 49 * q^56 + 24 * q^58 - 104 * q^59 - 120 * q^62 - 55 * q^64 + 72 * q^65 + 304 * q^67 + 190 * q^68 + 56 * q^70 - 112 * q^73 - 8 * q^74 + 70 * q^76 - 124 * q^80 + 450 * q^82 - 72 * q^83 - 210 * q^86 - 486 * q^88 + 512 * q^89 - 56 * q^91 + 472 * q^92 + 472 * q^94 + 64 * q^97 + 7 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/504\mathbb{Z}\right)^\times$.

$n$	$73$	$127$	$253$	$281$
$\chi(n)$	$1$	$-1$	$-1$	$1$

Coefficient data

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

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

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

$2$	−1.37098	+	1.45617i	−0.685489	+	0.728083i
$2$	−1.37098	+	1.45617i	−0.685489	+	0.728083i
$3$		0			0
$3$		0			0
$4$	−0.240837	−	3.99274i	−0.0602092	−	0.998186i
$5$			6.26788i			1.25358i	0.779190	+	0.626788i	$0.215631\pi$
$5$			6.26788i			1.25358i	−0.779190	+	0.626788i	$0.784369\pi$
$6$		0			0
$7$			2.64575i			0.377964i
$7$			2.64575i			0.377964i
$8$	6.14428	+	5.12327i	0.768035	+	0.640408i
$9$		0			0
$10$	−9.12707	−	8.59313i	−0.912707	−	0.859313i
$11$	−9.80688			−0.891535			−0.445767	−	0.895149i	$-0.647069\pi$
$11$	−9.80688			−0.891535			−0.445767	+	0.895149i	$0.647069\pi$
$12$		0			0
$13$		−	2.41653i		−	0.185887i	−0.995671	−	0.0929434i	$-0.970372\pi$
$13$		−	2.41653i		−	0.185887i	0.995671	−	0.0929434i	$-0.0296276\pi$
$14$	−3.85265	−	3.62727i	−0.275189	−	0.259091i
$15$		0			0
$16$	−15.8840	+	1.92320i	−0.992750	+	0.120200i
$17$	−6.89452			−0.405560			−0.202780	−	0.979224i	$-0.564998\pi$
$17$	−6.89452			−0.405560			−0.202780	+	0.979224i	$0.564998\pi$
$18$		0			0
$19$	2.77637			0.146125			0.0730624	−	0.997327i	$-0.476723\pi$
$19$	2.77637			0.146125			0.0730624	+	0.997327i	$0.476723\pi$
$20$	25.0260	−	1.50954i	1.25130	−	0.0754769i
$21$		0			0
$22$	13.4450	−	14.2804i	0.611137	−	0.649111i
$23$			42.8332i			1.86231i	0.364617	+	0.931157i	$0.381200\pi$
$23$			42.8332i			1.86231i	−0.364617	+	0.931157i	$0.618800\pi$
$24$		0			0
$25$	−14.2863			−0.571453
$26$	3.51887	+	3.31301i	0.135341	+	0.127423i
$27$		0			0
$28$	10.5638	−	0.637195i	0.377279	−	0.0227570i
$29$		−	37.3505i		−	1.28795i	−0.765048	−	0.643974i	$-0.777285\pi$
$29$		−	37.3505i		−	1.28795i	0.765048	−	0.643974i	$-0.222715\pi$
$30$		0			0
$31$			7.16835i			0.231237i	0.993294	+	0.115619i	$0.0368850\pi$
$31$			7.16835i			0.231237i	−0.993294	+	0.115619i	$0.963115\pi$
$32$	18.9761	−	25.7664i	0.593004	−	0.805200i
$33$		0			0
$34$	9.45224	−	10.0396i	0.278007	−	0.295281i
$35$	−16.5833			−0.473807
$36$		0			0
$37$			0.202653i			0.00547709i	0.999996	+	0.00273855i	$0.000871708\pi$
$37$			0.202653i			0.00547709i	−0.999996	+	0.00273855i	$0.999128\pi$
$38$	−3.80634	+	4.04285i	−0.100167	+	0.106391i
$39$		0			0
$40$	−32.1120	+	38.5116i	−0.802800	+	0.962790i
$41$	−63.5494			−1.54999			−0.774993	−	0.631970i	$-0.782247\pi$
$41$	−63.5494			−1.54999			−0.774993	+	0.631970i	$0.782247\pi$
$42$		0			0
$43$	−35.3384			−0.821823			−0.410911	−	0.911675i	$-0.634789\pi$
$43$	−35.3384			−0.821823			−0.410911	+	0.911675i	$0.634789\pi$
$44$	2.36186	+	39.1564i	0.0536786	+	0.889917i
$45$		0			0
$46$	−62.3723	−	58.7234i	−1.35592	−	1.27660i
$47$		−	37.9129i		−	0.806657i	−0.915055	−	0.403329i	$-0.867853\pi$
$47$		−	37.9129i		−	0.806657i	0.915055	−	0.403329i	$-0.132147\pi$
$48$		0			0
$49$	−7.00000			−0.142857
$50$	19.5862	−	20.8032i	0.391725	−	0.416065i
$51$		0			0
$52$	−9.64858	+	0.581989i	−0.185550	+	0.0111921i
$53$		−	54.6651i		−	1.03142i	−0.856764	−	0.515709i	$-0.827529\pi$
$53$		−	54.6651i		−	1.03142i	0.856764	−	0.515709i	$-0.172471\pi$
$54$		0			0
$55$		−	61.4684i		−	1.11761i
$56$	−13.5549	+	16.2562i	−0.242052	+	0.290290i
$57$		0			0
$58$	54.3885	+	51.2067i	0.937732	+	0.882874i
$59$	−104.795			−1.77619			−0.888093	−	0.459665i	$-0.847970\pi$
$59$	−104.795			−1.77619			−0.888093	+	0.459665i	$0.847970\pi$
$60$		0			0
$61$		−	43.7668i		−	0.717489i	−0.933436	−	0.358745i	$-0.883205\pi$
$61$		−	43.7668i		−	0.717489i	0.933436	−	0.358745i	$-0.116795\pi$
$62$	−10.4383	−	9.82765i	−0.168360	−	0.158511i
$63$		0			0
$64$	11.5043	+	62.9575i	0.179755	+	0.983711i
$65$	15.1465			0.233023
$66$		0			0
$67$	31.1021			0.464210			0.232105	−	0.972691i	$-0.425439\pi$
$67$	31.1021			0.464210			0.232105	+	0.972691i	$0.425439\pi$
$68$	1.66046	+	27.5281i	0.0244185	+	0.404824i
$69$		0			0
$70$	22.7353	−	24.1480i	0.324790	−	0.344971i
$71$			23.1294i			0.325766i	0.986645	+	0.162883i	$0.0520794\pi$
$71$			23.1294i			0.325766i	−0.986645	+	0.162883i	$0.947921\pi$
$72$		0			0
$73$	−69.2275			−0.948322			−0.474161	−	0.880438i	$-0.657249\pi$
$73$	−69.2275			−0.948322			−0.474161	+	0.880438i	$0.657249\pi$
$74$	−0.295096	−	0.277832i	−0.00398778	−	0.00375449i
$75$		0			0
$76$	−0.668652	−	11.0853i	−0.00879806	−	0.145860i
$77$		−	25.9466i		−	0.336968i
$78$		0			0
$79$		−	19.9328i		−	0.252315i	−0.992010	−	0.126157i	$-0.959736\pi$
$79$		−	19.9328i		−	0.252315i	0.992010	−	0.126157i	$-0.0402644\pi$
$80$	−12.0544	−	99.5590i	−0.150680	−	1.24449i
$81$		0			0
$82$	87.1249	−	92.5385i	1.06250	−	1.12852i
$83$	5.11617			0.0616406			0.0308203	−	0.999525i	$-0.490188\pi$
$83$	5.11617			0.0616406			0.0308203	+	0.999525i	$0.490188\pi$
$84$		0			0
$85$		−	43.2140i		−	0.508400i
$86$	48.4482	−	51.4585i	0.563351	−	0.598355i
$87$		0			0
$88$	−60.2562	−	50.2433i	−0.684730	−	0.570946i
$89$	17.9889			0.202122			0.101061	−	0.994880i	$-0.467776\pi$
$89$	17.9889			0.202122			0.101061	+	0.994880i	$0.467776\pi$
$90$		0			0
$91$	6.39353			0.0702586
$92$	171.022	−	10.3158i	1.85894	−	0.112129i
$93$		0			0
$94$	55.2075	+	51.9778i	0.587313	+	0.552955i
$95$			17.4019i			0.183178i
$96$		0			0
$97$	12.4864			0.128726			0.0643629	−	0.997927i	$-0.479498\pi$
$97$	12.4864			0.128726			0.0643629	+	0.997927i	$0.479498\pi$
$98$	9.59685	−	10.1932i	0.0979270	−	0.104012i
$99$		0			0
$100$	3.44067	+	57.0416i	0.0344067	+	0.570416i
$101$		−	68.0753i		−	0.674013i	−0.941502	−	0.337006i	$-0.890586\pi$
$101$		−	68.0753i		−	0.674013i	0.941502	−	0.337006i	$-0.109414\pi$
$102$		0			0
$103$			58.2931i			0.565952i	0.959127	+	0.282976i	$0.0913217\pi$
$103$			58.2931i			0.565952i	−0.959127	+	0.282976i	$0.908678\pi$
$104$	12.3805	−	14.8478i	0.119043	−	0.142768i
$105$		0			0
$106$	79.6015	+	74.9447i	0.750957	+	0.707026i
$107$	−135.868			−1.26979			−0.634897	−	0.772597i	$-0.718957\pi$
$107$	−135.868			−1.26979			−0.634897	+	0.772597i	$0.718957\pi$
$108$		0			0
$109$		−	44.4981i		−	0.408239i	−0.978946	−	0.204120i	$-0.934567\pi$
$109$		−	44.4981i		−	0.408239i	0.978946	−	0.204120i	$-0.0654332\pi$
$110$	89.5081	+	84.2718i	0.813710	+	0.766107i
$111$		0			0
$112$	−5.08831	−	42.0251i	−0.0454313	−	0.375224i
$113$	133.391			1.18045			0.590224	−	0.807240i	$-0.299039\pi$
$113$	133.391			1.18045			0.590224	+	0.807240i	$0.299039\pi$
$114$		0			0
$115$	−268.474			−2.33455
$116$	−149.131	+	8.99537i	−1.28561	+	0.0775463i
$117$		0			0
$118$	143.672	−	152.599i	1.21756	−	1.29321i
$119$		−	18.2412i		−	0.153287i
$120$		0			0
$121$	−24.8251			−0.205166
$122$	63.7318	+	60.0034i	0.522392	+	0.491831i
$123$		0			0
$124$	28.6214	−	1.72640i	0.230818	−	0.0139226i
$125$			67.1521i			0.537217i
$126$		0			0
$127$			130.977i			1.03131i	0.856795	+	0.515657i	$0.172452\pi$
$127$			130.977i			1.03131i	−0.856795	+	0.515657i	$0.827548\pi$
$128$	−107.449	−	69.5612i	−0.839443	−	0.543447i
$129$		0			0
$130$	−20.7655	+	22.0558i	−0.159735	+	0.169660i
$131$	53.3311			0.407108			0.203554	−	0.979064i	$-0.434751\pi$
$131$	53.3311			0.407108			0.203554	+	0.979064i	$0.434751\pi$
$132$		0			0
$133$			7.34558i			0.0552299i
$134$	−42.6403	+	45.2898i	−0.318211	+	0.337983i
$135$		0			0
$136$	−42.3619	−	35.3225i	−0.311484	−	0.259724i
$137$	57.7179			0.421299			0.210649	−	0.977562i	$-0.432442\pi$
$137$	57.7179			0.421299			0.210649	+	0.977562i	$0.432442\pi$
$138$		0			0
$139$	−172.422			−1.24045			−0.620224	−	0.784425i	$-0.712958\pi$
$139$	−172.422			−1.24045			−0.620224	+	0.784425i	$0.712958\pi$
$140$	3.99386	+	66.2127i	0.0285276	+	0.472948i
$141$		0			0
$142$	−33.6803	−	31.7099i	−0.237185	−	0.223309i
$143$			23.6986i			0.165725i
$144$		0			0
$145$	234.108			1.61454
$146$	94.9094	−	100.807i	0.650065	−	0.690457i
$147$		0			0
$148$	0.809139	−	0.0488062i	0.00546716	−	0.000329772i
$149$			219.529i			1.47335i	0.676249	+	0.736673i	$0.263604\pi$
$149$			219.529i			1.47335i	−0.676249	+	0.736673i	$0.736396\pi$
$150$		0			0
$151$			185.668i			1.22959i	0.788687	+	0.614795i	$0.210761\pi$
$151$			185.668i			1.22959i	−0.788687	+	0.614795i	$0.789239\pi$
$152$	17.0588	+	14.2241i	0.112229	+	0.0935795i
$153$		0			0
$154$	37.7825	+	35.5722i	0.245341	+	0.230988i
$155$	−44.9304			−0.289873
$156$		0			0
$157$			188.182i			1.19861i	0.800521	+	0.599305i	$0.204556\pi$
$157$			188.182i			1.19861i	−0.800521	+	0.599305i	$0.795444\pi$
$158$	29.0255	+	27.3275i	0.183706	+	0.172959i
$159$		0			0
$160$	161.501	+	118.940i	1.00938	+	0.743375i
$161$	−113.326			−0.703889
$162$		0			0
$163$	54.5154			0.334450			0.167225	−	0.985919i	$-0.446519\pi$
$163$	54.5154			0.334450			0.167225	+	0.985919i	$0.446519\pi$
$164$	15.3050	+	253.736i	0.0933235	+	1.54717i
$165$		0			0
$166$	−7.01416	+	7.45000i	−0.0422540	+	0.0448795i
$167$			266.435i			1.59542i	0.603042	+	0.797709i	$0.293955\pi$
$167$			266.435i			1.59542i	−0.603042	+	0.797709i	$0.706045\pi$
$168$		0			0
$169$	163.160			0.965446
$170$	62.9268	+	59.2455i	0.370158	+	0.348503i
$171$		0			0
$172$	8.51079	+	141.097i	0.0494813	+	0.820332i
$173$			114.835i			0.663786i	0.943317	+	0.331893i	$0.107687\pi$
$173$			114.835i			0.663786i	−0.943317	+	0.331893i	$0.892313\pi$
$174$		0			0
$175$		−	37.7980i		−	0.215989i
$176$	155.772	−	18.8606i	0.885071	−	0.107162i
$177$		0			0
$178$	−24.6624	+	26.1948i	−0.138553	+	0.147162i
$179$	−112.849			−0.630439			−0.315220	−	0.949019i	$-0.602078\pi$
$179$	−112.849			−0.630439			−0.315220	+	0.949019i	$0.602078\pi$
$180$		0			0
$181$		−	60.9470i		−	0.336724i	−0.985725	−	0.168362i	$-0.946152\pi$
$181$		−	60.9470i		−	0.336724i	0.985725	−	0.168362i	$-0.0538477\pi$
$182$	−8.76539	+	9.31004i	−0.0481615	+	0.0511541i
$183$		0			0
$184$	−219.446	+	263.179i	−1.19264	+	1.43032i
$185$	−1.27020			−0.00686595
$186$		0			0
$187$	67.6138			0.361571
$188$	−151.376	+	9.13083i	−0.805194	+	0.0485682i
$189$		0			0
$190$	−25.3401	−	23.8577i	−0.133369	−	0.125567i
$191$		−	178.459i		−	0.934342i	−0.884167	−	0.467171i	$-0.845273\pi$
$191$		−	178.459i		−	0.934342i	0.884167	−	0.467171i	$-0.154727\pi$
$192$		0			0
$193$	221.588			1.14812			0.574062	−	0.818812i	$-0.305367\pi$
$193$	221.588			1.14812			0.574062	+	0.818812i	$0.305367\pi$
$194$	−17.1186	+	18.1823i	−0.0882402	+	0.0937231i
$195$		0			0
$196$	1.68586	+	27.9492i	0.00860132	+	0.142598i
$197$		−	242.298i		−	1.22994i	−0.788550	−	0.614970i	$-0.789168\pi$
$197$		−	242.298i		−	1.22994i	0.788550	−	0.614970i	$-0.210832\pi$
$198$		0			0
$199$			297.047i			1.49270i	0.665555	+	0.746349i	$0.268195\pi$
$199$			297.047i			1.49270i	−0.665555	+	0.746349i	$0.731805\pi$
$200$	−87.7791	−	73.1926i	−0.438895	−	0.365963i
$201$		0			0
$202$	99.1289	+	93.3297i	0.490737	+	0.462028i
$203$	98.8201			0.486798
$204$		0			0
$205$		−	398.320i		−	1.94302i
$206$	−84.8844	−	79.9186i	−0.412060	−	0.387954i
$207$		0			0
$208$	4.64747	+	38.3841i	0.0223436	+	0.184539i
$209$	−27.2275			−0.130275
$210$		0			0
$211$	−141.020			−0.668341			−0.334171	−	0.942513i	$-0.608456\pi$
$211$	−141.020			−0.668341			−0.334171	+	0.942513i	$0.608456\pi$
$212$	−218.264	+	13.1654i	−1.02955	+	0.0621009i
$213$		0			0
$214$	186.272	−	197.846i	0.870430	−	0.924515i
$215$		−	221.497i		−	1.03022i
$216$		0			0
$217$	−18.9657			−0.0873994
$218$	64.7966	+	61.0059i	0.297232	+	0.279844i
$219$		0			0
$220$	−245.427	+	14.8039i	−1.11558	+	0.0672902i
$221$			16.6608i			0.0753883i
$222$		0			0
$223$			40.8267i			0.183079i	0.995801	+	0.0915396i	$0.0291788\pi$
$223$			40.8267i			0.183079i	−0.995801	+	0.0915396i	$0.970821\pi$
$224$	68.1715	+	50.2061i	0.304337	+	0.224134i
$225$		0			0
$226$	−182.876	+	194.239i	−0.809184	+	0.859464i
$227$	−8.18598			−0.0360616			−0.0180308	−	0.999837i	$-0.505740\pi$
$227$	−8.18598			−0.0360616			−0.0180308	+	0.999837i	$0.505740\pi$
$228$		0			0
$229$			332.252i			1.45088i	0.688285	+	0.725440i	$0.258364\pi$
$229$			332.252i			1.45088i	−0.688285	+	0.725440i	$0.741636\pi$
$230$	368.071	−	390.942i	1.60031	−	1.69975i
$231$		0			0
$232$	191.356	−	229.492i	0.824812	−	0.989188i
$233$	−329.260			−1.41314			−0.706568	−	0.707646i	$-0.749757\pi$
$233$	−329.260			−1.41314			−0.706568	+	0.707646i	$0.749757\pi$
$234$		0			0
$235$	237.633			1.01121
$236$	25.2385	+	418.419i	0.106943	+	1.77296i
$237$		0			0
$238$	26.5622	+	25.0083i	0.111606	+	0.105077i
$239$			137.719i			0.576230i	0.957596	+	0.288115i	$0.0930286\pi$
$239$			137.719i			0.576230i	−0.957596	+	0.288115i	$0.906971\pi$
$240$		0			0
$241$	201.854			0.837567			0.418783	−	0.908086i	$-0.362457\pi$
$241$	201.854			0.837567			0.418783	+	0.908086i	$0.362457\pi$
$242$	34.0346	−	36.1494i	0.140639	−	0.149378i
$243$		0			0
$244$	−174.750	+	10.5407i	−0.716188	+	0.0431995i
$245$		−	43.8752i		−	0.179082i
$246$		0			0
$247$		−	6.70917i		−	0.0271627i
$248$	−36.7254	+	44.0443i	−0.148086	+	0.177598i
$249$		0			0
$250$	−97.7846	−	92.0640i	−0.391138	−	0.368256i
$251$	269.203			1.07252			0.536261	−	0.844052i	$-0.319836\pi$
$251$	269.203			1.07252			0.536261	+	0.844052i	$0.319836\pi$
$252$		0			0
$253$		−	420.061i		−	1.66032i
$254$	−190.724	−	179.566i	−0.750881	−	0.706954i
$255$		0			0
$256$	248.603	−	61.0962i	0.971104	−	0.238657i
$257$	242.359			0.943032			0.471516	−	0.881858i	$-0.343707\pi$
$257$	242.359			0.943032			0.471516	+	0.881858i	$0.343707\pi$
$258$		0			0
$259$	−0.536168			−0.00207015
$260$	−3.64784	−	60.4761i	−0.0140302	−	0.232600i
$261$		0			0
$262$	−73.1158	+	77.6589i	−0.279068	+	0.296408i
$263$		−	33.8470i		−	0.128696i	−0.997928	−	0.0643479i	$-0.979503\pi$
$263$		−	33.8470i		−	0.128696i	0.997928	−	0.0643479i	$-0.0204967\pi$
$264$		0			0
$265$	342.634			1.29296
$266$	−10.6964	−	10.0706i	−0.0402120	−	0.0378595i
$267$		0			0
$268$	−7.49053	−	124.183i	−0.0279497	−	0.463368i
$269$		−	165.598i		−	0.615606i	−0.951450	−	0.307803i	$-0.900406\pi$
$269$		−	165.598i		−	0.615606i	0.951450	−	0.307803i	$-0.0995938\pi$
$270$		0			0
$271$			148.308i			0.547263i	0.961835	+	0.273632i	$0.0882249\pi$
$271$			148.308i			0.547263i	−0.961835	+	0.273632i	$0.911775\pi$
$272$	109.513	−	13.2595i	0.402620	−	0.0487483i
$273$		0			0
$274$	−79.1300	+	84.0468i	−0.288796	+	0.306740i
$275$	140.104			0.509470
$276$		0			0
$277$		−	478.358i		−	1.72693i	−0.504413	−	0.863463i	$-0.668291\pi$
$277$		−	478.358i		−	1.72693i	0.504413	−	0.863463i	$-0.331709\pi$
$278$	236.387	−	251.075i	0.850314	−	0.903149i
$279$		0			0
$280$	−101.892	−	84.9604i	−0.363900	−	0.303430i
$281$	226.066			0.804506			0.402253	−	0.915528i	$-0.368227\pi$
$281$	226.066			0.804506			0.402253	+	0.915528i	$0.368227\pi$
$282$		0			0
$283$	−254.628			−0.899745			−0.449873	−	0.893093i	$-0.648531\pi$
$283$	−254.628			−0.899745			−0.449873	+	0.893093i	$0.648531\pi$
$284$	92.3498	−	5.57042i	0.325175	−	0.0196142i
$285$		0			0
$286$	−34.5091	−	32.4903i	−0.120661	−	0.113602i
$287$		−	168.136i		−	0.585840i
$288$		0			0
$289$	−241.466			−0.835521
$290$	−320.957	+	340.900i	−1.10675	+	1.17552i
$291$		0			0
$292$	16.6725	+	276.408i	0.0570978	+	0.946602i
$293$			149.558i			0.510437i	0.966883	+	0.255218i	$0.0821474\pi$
$293$			149.558i			0.510437i	−0.966883	+	0.255218i	$0.917853\pi$
$294$		0			0
$295$		−	656.842i		−	2.22658i
$296$	−1.03824	+	1.24515i	−0.00350758	+	0.00420660i
$297$		0			0
$298$	−319.670	−	300.969i	−1.07272	−	1.00996i
$299$	103.508			0.346180
$300$		0			0
$301$		−	93.4966i		−	0.310620i
$302$	−270.363	−	254.547i	−0.895243	−	0.842870i
$303$		0			0
$304$	−44.0998	+	5.33951i	−0.145065	+	0.0175642i
$305$	274.325			0.899427
$306$		0			0
$307$	271.779			0.885272			0.442636	−	0.896701i	$-0.354043\pi$
$307$	271.779			0.885272			0.442636	+	0.896701i	$0.354043\pi$
$308$	−103.598	+	6.24889i	−0.336357	+	0.0202886i
$309$		0			0
$310$	61.5985	−	65.4260i	0.198705	−	0.211052i
$311$			534.180i			1.71762i	0.512293	+	0.858811i	$0.328796\pi$
$311$			534.180i			1.71762i	−0.512293	+	0.858811i	$0.671204\pi$
$312$		0			0
$313$	−556.232			−1.77710			−0.888550	−	0.458780i	$-0.848287\pi$
$313$	−556.232			−1.77710			−0.888550	+	0.458780i	$0.848287\pi$
$314$	−274.024	−	257.993i	−0.872688	−	0.821634i
$315$		0			0
$316$	−79.5867	+	4.80057i	−0.251857	+	0.0151917i
$317$		−	387.459i		−	1.22227i	−0.791527	−	0.611134i	$-0.790714\pi$
$317$		−	387.459i		−	1.22227i	0.791527	−	0.611134i	$-0.209286\pi$
$318$		0			0
$319$			366.292i			1.14825i
$320$	−394.610	+	72.1076i	−1.23316	+	0.225336i
$321$		0			0
$322$	155.368	−	165.022i	0.482508	−	0.512489i
$323$	−19.1417			−0.0592624
$324$		0			0
$325$			34.5233i			0.106225i
$326$	−74.7394	+	79.3834i	−0.229262	+	0.243507i
$327$		0			0
$328$	−390.465	−	325.581i	−1.19044	−	0.992624i
$329$	100.308			0.304888
$330$		0			0
$331$	−383.205			−1.15772			−0.578860	−	0.815427i	$-0.696502\pi$
$331$	−383.205			−1.15772			−0.578860	+	0.815427i	$0.696502\pi$
$332$	−1.23216	−	20.4276i	−0.00371134	−	0.0615288i
$333$		0			0
$334$	−387.973	−	365.276i	−1.16160	−	1.09364i
$335$			194.944i			0.581923i
$336$		0			0
$337$	563.726			1.67278			0.836388	−	0.548138i	$-0.184663\pi$
$337$	563.726			1.67278			0.836388	+	0.548138i	$0.184663\pi$
$338$	−223.689	+	237.589i	−0.661803	+	0.702925i
$339$		0			0
$340$	−172.543	+	10.4075i	−0.507478	+	0.0306104i
$341$		−	70.2992i		−	0.206156i
$342$		0			0
$343$		−	18.5203i		−	0.0539949i
$344$	−217.129	−	181.048i	−0.631188	−	0.526302i
$345$		0			0
$346$	−167.219	−	157.436i	−0.483291	−	0.455018i
$347$	−51.5890			−0.148671			−0.0743357	−	0.997233i	$-0.523684\pi$
$347$	−51.5890			−0.148671			−0.0743357	+	0.997233i	$0.523684\pi$
$348$		0			0
$349$			586.383i			1.68018i	0.542447	+	0.840090i	$0.317498\pi$
$349$			586.383i			1.68018i	−0.542447	+	0.840090i	$0.682502\pi$
$350$	55.0402	+	51.8203i	0.157258	+	0.148058i
$351$		0			0
$352$	−186.097	+	252.688i	−0.528683	+	0.717864i
$353$	−303.844			−0.860746			−0.430373	−	0.902651i	$-0.641618\pi$
$353$	−303.844			−0.860746			−0.430373	+	0.902651i	$0.641618\pi$
$354$		0			0
$355$	−144.972			−0.408373
$356$	−4.33239	−	71.8250i	−0.0121696	−	0.201756i
$357$		0			0
$358$	154.713	−	164.326i	0.432159	−	0.459012i
$359$			116.130i			0.323481i	0.986833	+	0.161741i	$0.0517108\pi$
$359$			116.130i			0.323481i	−0.986833	+	0.161741i	$0.948289\pi$
$360$		0			0
$361$	−353.292			−0.978648
$362$	88.7489	+	83.5570i	0.245163	+	0.230820i
$363$		0			0
$364$	−1.53980	−	25.5277i	−0.00423022	−	0.0701311i
$365$		−	433.910i		−	1.18879i
$366$		0			0
$367$			476.288i			1.29779i	0.760879	+	0.648894i	$0.224768\pi$
$367$			476.288i			1.29779i	−0.760879	+	0.648894i	$0.775232\pi$
$368$	−82.3769	−	680.363i	−0.223850	−	1.84881i
$369$		0			0
$370$	1.74142	−	1.84962i	0.00470654	−	0.00499898i
$371$	144.630			0.389839
$372$		0			0
$373$		−	49.2857i		−	0.132133i	−0.997815	−	0.0660666i	$-0.978955\pi$
$373$		−	49.2857i		−	0.132133i	0.997815	−	0.0660666i	$-0.0210450\pi$
$374$	−92.6970	+	98.4568i	−0.247853	+	0.263254i
$375$		0			0
$376$	194.238	−	232.947i	0.516590	−	0.619541i
$377$	−90.2585			−0.239412
$378$		0			0
$379$	167.511			0.441983			0.220991	−	0.975276i	$-0.429071\pi$
$379$	167.511			0.441983			0.220991	+	0.975276i	$0.429071\pi$
$380$	69.4815	−	4.19103i	0.182846	−	0.0110290i
$381$		0			0
$382$	259.866	+	244.664i	0.680278	+	0.640481i
$383$		−	513.207i		−	1.33997i	−0.742376	−	0.669983i	$-0.766301\pi$
$383$		−	513.207i		−	1.33997i	0.742376	−	0.669983i	$-0.233699\pi$
$384$		0			0
$385$	162.630			0.422416
$386$	−303.792	+	322.668i	−0.787026	+	0.835929i
$387$		0			0
$388$	−3.00719	−	49.8550i	−0.00775049	−	0.128492i
$389$			709.398i			1.82365i	0.410584	+	0.911823i	$0.365325\pi$
$389$			709.398i			1.82365i	−0.410584	+	0.911823i	$0.634675\pi$
$390$		0			0
$391$		−	295.315i		−	0.755281i
$392$	−43.0099	−	35.8629i	−0.109719	−	0.0914869i
$393$		0			0
$394$	352.826	+	332.186i	0.895498	+	0.843111i
$395$	124.937			0.316295
$396$		0			0
$397$		−	309.404i		−	0.779355i	−0.920951	−	0.389677i	$-0.872587\pi$
$397$		−	309.404i		−	0.779355i	0.920951	−	0.389677i	$-0.127413\pi$
$398$	−432.549	−	407.245i	−1.08681	−	1.02323i
$399$		0			0
$400$	226.924	−	27.4754i	0.567309	−	0.0686886i
$401$	528.073			1.31689			0.658445	−	0.752629i	$-0.271215\pi$
$401$	528.073			1.31689			0.658445	+	0.752629i	$0.271215\pi$
$402$		0			0
$403$	17.3225			0.0429839
$404$	−271.807	+	16.3950i	−0.672790	+	0.0405818i
$405$		0			0
$406$	−135.480	+	143.898i	−0.333695	+	0.354429i
$407$		−	1.98739i		−	0.00488302i
$408$		0			0
$409$	−612.830			−1.49836			−0.749181	−	0.662366i	$-0.769552\pi$
$409$	−612.830			−1.49836			−0.749181	+	0.662366i	$0.769552\pi$
$410$	580.020	+	546.088i	1.41468	+	1.33192i
$411$		0			0
$412$	232.749	−	14.0391i	0.564926	−	0.0340756i
$413$		−	277.261i		−	0.671335i
$414$		0			0
$415$			32.0676i			0.0772712i
$416$	−62.2652	−	45.8563i	−0.149676	−	0.110232i
$417$		0			0
$418$	37.3283	−	39.6478i	0.0893023	−	0.0948512i
$419$	237.642			0.567165			0.283583	−	0.958948i	$-0.408477\pi$
$419$	237.642			0.567165			0.283583	+	0.958948i	$0.408477\pi$
$420$		0			0
$421$			394.516i			0.937092i	0.883439	+	0.468546i	$0.155222\pi$
$421$			394.516i			0.937092i	−0.883439	+	0.468546i	$0.844778\pi$
$422$	193.335	−	205.348i	0.458141	−	0.486608i
$423$		0			0
$424$	280.064	−	335.878i	0.660528	−	0.792164i
$425$	98.4973			0.231758
$426$		0			0
$427$	115.796			0.271185
$428$	32.7220	+	542.486i	0.0764533	+	1.26749i
$429$		0			0
$430$	322.536	+	303.667i	0.750084	+	0.706203i
$431$		−	363.359i		−	0.843059i	−0.906815	−	0.421530i	$-0.861493\pi$
$431$		−	363.359i		−	0.843059i	0.906815	−	0.421530i	$-0.138507\pi$
$432$		0			0
$433$	119.733			0.276520			0.138260	−	0.990396i	$-0.455849\pi$
$433$	119.733			0.276520			0.138260	+	0.990396i	$0.455849\pi$
$434$	26.0015	−	27.6172i	0.0599113	−	0.0636340i
$435$		0			0
$436$	−177.669	+	10.7168i	−0.407499	+	0.0245798i
$437$			118.921i			0.272130i
$438$		0			0
$439$		−	871.477i		−	1.98514i	−0.121672	−	0.992570i	$-0.538826\pi$
$439$		−	871.477i		−	1.98514i	0.121672	−	0.992570i	$-0.461174\pi$
$440$	314.919	−	377.679i	0.715724	−	0.858361i
$441$		0			0
$442$	−24.2609	−	22.8416i	−0.0548889	−	0.0516778i
$443$	343.956			0.776424			0.388212	−	0.921570i	$-0.373093\pi$
$443$	343.956			0.776424			0.388212	+	0.921570i	$0.373093\pi$
$444$		0			0
$445$			112.752i			0.253376i
$446$	−59.4504	−	55.9725i	−0.133297	−	0.125499i
$447$		0			0
$448$	−166.570	+	30.4375i	−0.371808	+	0.0679409i
$449$	242.849			0.540866			0.270433	−	0.962739i	$-0.412833\pi$
$449$	242.849			0.540866			0.270433	+	0.962739i	$0.412833\pi$
$450$		0			0
$451$	623.222			1.38187
$452$	−32.1254	−	532.594i	−0.0710739	−	1.17831i
$453$		0			0
$454$	11.2228	−	11.9201i	0.0247198	−	0.0262558i
$455$			40.0739i			0.0880745i
$456$		0			0
$457$	−42.2571			−0.0924662			−0.0462331	−	0.998931i	$-0.514722\pi$
$457$	−42.2571			−0.0924662			−0.0462331	+	0.998931i	$0.514722\pi$
$458$	−483.814	−	455.510i	−1.05636	−	0.994563i
$459$		0			0
$460$	64.6584	+	1071.95i	0.140562	+	2.33032i
$461$			816.370i			1.77087i	0.464766	+	0.885434i	$0.346139\pi$
$461$			816.370i			1.77087i	−0.464766	+	0.885434i	$0.653861\pi$
$462$		0			0
$463$		−	115.161i		−	0.248727i	−0.992237	−	0.124363i	$-0.960311\pi$
$463$		−	115.161i		−	0.248727i	0.992237	−	0.124363i	$-0.0396889\pi$
$464$	71.8324	+	593.275i	0.154811	+	1.27861i
$465$		0			0
$466$	451.409	−	479.458i	0.968689	−	1.02888i
$467$	−603.424			−1.29213			−0.646064	−	0.763283i	$-0.723586\pi$
$467$	−603.424			−1.29213			−0.646064	+	0.763283i	$0.723586\pi$
$468$		0			0
$469$			82.2884i			0.175455i
$470$	−325.790	+	346.034i	−0.693171	+	0.736242i
$471$		0			0
$472$	−643.889	−	536.892i	−1.36417	−	1.13748i
$473$	346.559			0.732684
$474$		0			0
$475$	−39.6641			−0.0835034
$476$	−72.8324	+	4.39315i	−0.153009	+	0.00922931i
$477$		0			0
$478$	−200.542	−	188.810i	−0.419543	−	0.395000i
$479$			158.595i			0.331097i	0.986202	+	0.165548i	$0.0529394\pi$
$479$			158.595i			0.331097i	−0.986202	+	0.165548i	$0.947061\pi$
$480$		0			0
$481$	0.489715			0.00101812
$482$	−276.737	+	293.932i	−0.574143	+	0.609818i
$483$		0			0
$484$	5.97880	+	99.1201i	0.0123529	+	0.204794i
$485$			78.2633i			0.161368i
$486$		0			0
$487$			106.987i			0.219687i	0.993949	+	0.109843i	$0.0350349\pi$
$487$			106.987i			0.219687i	−0.993949	+	0.109843i	$0.964965\pi$
$488$	224.229	−	268.916i	0.459486	−	0.551057i
$489$		0			0
$490$	63.8895	+	60.1519i	0.130387	+	0.122759i
$491$	−616.591			−1.25579			−0.627893	−	0.778299i	$-0.716083\pi$
$491$	−616.591			−1.25579			−0.627893	+	0.778299i	$0.716083\pi$
$492$		0			0
$493$			257.514i			0.522340i
$494$	9.76967	+	9.19813i	0.0197767	+	0.0186197i
$495$		0			0
$496$	−13.7862	−	113.862i	−0.0277947	−	0.229561i
$497$	−61.1947			−0.123128
$498$		0			0
$499$	554.090			1.11040			0.555200	−	0.831717i	$-0.312642\pi$
$499$	554.090			1.11040			0.555200	+	0.831717i	$0.312642\pi$
$500$	268.121	−	16.1727i	0.536242	−	0.0323454i
$501$		0			0
$502$	−369.072	+	392.004i	−0.735202	+	0.780885i
$503$			148.158i			0.294548i	0.989096	+	0.147274i	$0.0470499\pi$
$503$			148.158i			0.294548i	−0.989096	+	0.147274i	$0.952950\pi$
$504$		0			0
$505$	426.688			0.844926
$506$	611.678	+	575.894i	1.20885	+	1.13813i
$507$		0			0
$508$	522.957	−	31.5440i	1.02944	−	0.0620946i
$509$		−	182.889i		−	0.359310i	−0.983730	−	0.179655i	$-0.942502\pi$
$509$		−	182.889i		−	0.359310i	0.983730	−	0.179655i	$-0.0574981\pi$
$510$		0			0
$511$		−	183.159i		−	0.358432i
$512$	−251.863	+	445.768i	−0.491919	+	0.870641i
$513$		0			0
$514$	−332.269	+	352.915i	−0.646438	+	0.686605i
$515$	−365.374			−0.709464
$516$		0			0
$517$			371.807i			0.719163i
$518$	0.735075	−	0.780750i	0.00141906	−	0.00150724i
$519$		0			0
$520$	93.0644	+	77.5996i	0.178970	+	0.149230i
$521$	−98.2461			−0.188572			−0.0942861	−	0.995545i	$-0.530057\pi$
$521$	−98.2461			−0.188572			−0.0942861	+	0.995545i	$0.530057\pi$
$522$		0			0
$523$	−574.764			−1.09898			−0.549488	−	0.835502i	$-0.685177\pi$
$523$	−574.764			−1.09898			−0.549488	+	0.835502i	$0.685177\pi$
$524$	−12.8441	−	212.937i	−0.0245116	−	0.406369i
$525$		0			0
$526$	49.2868	+	46.4035i	0.0937012	+	0.0882196i
$527$		−	49.4223i		−	0.0937805i
$528$		0			0
$529$	−1305.69			−2.46822
$530$	−469.744	+	498.933i	−0.886310	+	0.941382i
$531$		0			0
$532$	29.3290	−	1.76909i	0.0551297	−	0.00332535i
$533$			153.569i			0.288122i
$534$		0			0
$535$		−	851.604i		−	1.59178i
$536$	191.100	+	159.344i	0.356529	+	0.297284i
$537$		0			0
$538$	241.138	+	227.031i	0.448212	+	0.421991i
$539$	68.6482			0.127362
$540$		0			0
$541$			370.654i			0.685128i	0.939495	+	0.342564i	$0.111295\pi$
$541$			370.654i			0.685128i	−0.939495	+	0.342564i	$0.888705\pi$
$542$	−215.962	−	203.328i	−0.398453	−	0.375143i
$543$		0			0
$544$	−130.831	+	177.647i	−0.240499	+	0.326557i
$545$	278.909			0.511759
$546$		0			0
$547$	−56.5966			−0.103467			−0.0517336	−	0.998661i	$-0.516475\pi$
$547$	−56.5966			−0.103467			−0.0517336	+	0.998661i	$0.516475\pi$
$548$	−13.9006	−	230.453i	−0.0253661	−	0.420534i
$549$		0			0
$550$	−192.080	+	204.015i	−0.349236	+	0.370936i
$551$		−	103.699i		−	0.188201i
$552$		0			0
$553$	52.7374			0.0953659
$554$	696.569	+	655.819i	1.25734	+	1.18379i
$555$		0			0
$556$	41.5257	+	688.438i	0.0746864	+	1.23820i
$557$		−	151.525i		−	0.272037i	−0.990706	−	0.136019i	$-0.956569\pi$
$557$		−	151.525i		−	0.272037i	0.990706	−	0.136019i	$-0.0434307\pi$
$558$		0			0
$559$			85.3962i			0.152766i
$560$	263.408	−	31.8929i	0.470372	−	0.0569516i
$561$		0			0
$562$	−309.932	+	329.190i	−0.551480	+	0.585747i
$563$	318.048			0.564917			0.282458	−	0.959280i	$-0.408850\pi$
$563$	318.048			0.564917			0.282458	+	0.959280i	$0.408850\pi$
$564$		0			0
$565$			836.076i			1.47978i
$566$	349.089	−	370.780i	0.616766	−	0.655089i
$567$		0			0
$568$	−118.498	+	142.114i	−0.208624	+	0.250200i
$569$	−356.654			−0.626808			−0.313404	−	0.949620i	$-0.601469\pi$
$569$	−356.654			−0.626808			−0.313404	+	0.949620i	$0.601469\pi$
$570$		0			0
$571$	831.014			1.45537			0.727683	−	0.685914i	$-0.240597\pi$
$571$	831.014			1.45537			0.727683	+	0.685914i	$0.240597\pi$
$572$	94.6224	−	5.70750i	0.165424	−	0.00997815i
$573$		0			0
$574$	244.834	+	230.511i	0.426540	+	0.401587i
$575$		−	611.929i		−	1.06422i
$576$		0			0
$577$	771.483			1.33706			0.668530	−	0.743685i	$-0.266924\pi$
$577$	771.483			1.33706			0.668530	+	0.743685i	$0.266924\pi$
$578$	331.044	−	351.614i	0.572741	−	0.608328i
$579$		0			0
$580$	−56.3819	−	934.734i	−0.0972102	−	1.61161i
$581$			13.5361i			0.0232980i
$582$		0			0
$583$			536.094i			0.919544i
$584$	−425.353	−	354.671i	−0.728344	−	0.607313i
$585$		0			0
$586$	−217.781	−	205.041i	−0.371640	−	0.349899i
$587$	−144.376			−0.245956			−0.122978	−	0.992409i	$-0.539244\pi$
$587$	−144.376			−0.245956			−0.122978	+	0.992409i	$0.539244\pi$
$588$		0			0
$589$			19.9020i			0.0337894i
$590$	956.471	+	900.516i	1.62114	+	1.52630i
$591$		0			0
$592$	−0.389741	−	3.21893i	−0.000658347	−	0.00543738i
$593$	−838.926			−1.41471			−0.707357	−	0.706856i	$-0.750113\pi$
$593$	−838.926			−1.41471			−0.707357	+	0.706856i	$0.750113\pi$
$594$		0			0
$595$	114.334			0.192157
$596$	876.521	−	52.8706i	1.47067	−	0.0887090i
$597$		0			0
$598$	−141.907	+	150.724i	−0.237302	+	0.252048i
$599$			711.341i			1.18755i	0.804632	+	0.593774i	$0.202363\pi$
$599$			711.341i			1.18755i	−0.804632	+	0.593774i	$0.797637\pi$
$600$		0			0
$601$	−356.394			−0.593002			−0.296501	−	0.955033i	$-0.595820\pi$
$601$	−356.394			−0.593002			−0.296501	+	0.955033i	$0.595820\pi$
$602$	136.147	+	128.182i	0.226157	+	0.212927i
$603$		0			0
$604$	741.324	−	44.7157i	1.22736	−	0.0740326i
$605$		−	155.601i		−	0.257191i
$606$		0			0
$607$		−	60.3719i		−	0.0994595i	−0.998763	−	0.0497298i	$-0.984164\pi$
$607$		−	60.3719i		−	0.0994595i	0.998763	−	0.0497298i	$-0.0158360\pi$
$608$	52.6847	−	71.5370i	0.0866525	−	0.117660i
$609$		0			0
$610$	−376.094	+	399.463i	−0.616548	+	0.654858i
$611$	−91.6176			−0.149947
$612$		0			0
$613$		−	482.989i		−	0.787911i	−0.919130	−	0.393955i	$-0.871106\pi$
$613$		−	482.989i		−	0.787911i	0.919130	−	0.393955i	$-0.128894\pi$
$614$	−372.603	+	395.755i	−0.606845	+	0.644552i
$615$		0			0
$616$	132.931	−	159.423i	0.215797	−	0.258803i
$617$	−712.490			−1.15476			−0.577382	−	0.816474i	$-0.695926\pi$
$617$	−712.490			−1.15476			−0.577382	+	0.816474i	$0.695926\pi$
$618$		0			0
$619$	−93.0817			−0.150374			−0.0751872	−	0.997169i	$-0.523955\pi$
$619$	−93.0817			−0.150374			−0.0751872	+	0.997169i	$0.523955\pi$
$620$	10.8209	+	179.395i	0.0174530	+	0.289347i
$621$		0			0
$622$	−777.855	−	732.350i	−1.25057	−	1.17741i
$623$			47.5941i			0.0763951i
$624$		0			0
$625$	−778.059			−1.24489
$626$	762.582	−	809.966i	1.21818	−	1.29388i
$627$		0			0
$628$	751.362	−	45.3211i	1.19644	−	0.0721674i
$629$		−	1.39719i		−	0.00222129i
$630$		0			0
$631$		−	610.573i		−	0.967628i	−0.875171	−	0.483814i	$-0.839251\pi$
$631$		−	610.573i		−	0.967628i	0.875171	−	0.483814i	$-0.160749\pi$
$632$	102.121	−	122.473i	0.161584	−	0.193786i
$633$		0			0
$634$	564.205	+	531.198i	0.889912	+	0.837852i
$635$	−820.947			−1.29283
$636$		0			0
$637$			16.9157i			0.0265553i
$638$	−533.381	−	502.178i	−0.836021	−	0.787113i
$639$		0			0
$640$	436.002	−	673.476i	0.681252	−	1.05231i
$641$	−590.153			−0.920676			−0.460338	−	0.887744i	$-0.652272\pi$
$641$	−590.153			−0.920676			−0.460338	+	0.887744i	$0.652272\pi$
$642$		0			0
$643$	−257.971			−0.401199			−0.200600	−	0.979673i	$-0.564289\pi$
$643$	−257.971			−0.401199			−0.200600	+	0.979673i	$0.564289\pi$
$644$	27.2931	+	452.482i	0.0423806	+	0.702612i
$645$		0			0
$646$	26.2429	−	27.8735i	0.0406237	−	0.0431479i
$647$			379.964i			0.587271i	0.955918	+	0.293635i	$0.0948651\pi$
$647$			379.964i			0.587271i	−0.955918	+	0.293635i	$0.905135\pi$
$648$		0			0
$649$	1027.71			1.58353
$650$	−50.2716	−	47.3307i	−0.0773410	−	0.0728164i
$651$		0			0
$652$	−13.1293	−	217.666i	−0.0201370	−	0.333843i
$653$		−	952.773i		−	1.45907i	−0.683943	−	0.729535i	$-0.739736\pi$
$653$		−	952.773i		−	1.45907i	0.683943	−	0.729535i	$-0.260264\pi$
$654$		0			0
$655$			334.273i			0.510340i
$656$	1009.42	−	122.218i	1.53875	−	0.186308i
$657$		0			0
$658$	−137.520	+	146.065i	−0.208997	+	0.221984i
$659$	963.119			1.46149			0.730743	−	0.682653i	$-0.239174\pi$
$659$	963.119			1.46149			0.730743	+	0.682653i	$0.239174\pi$
$660$		0			0
$661$		−	71.6817i		−	0.108444i	−0.998529	−	0.0542222i	$-0.982732\pi$
$661$		−	71.6817i		−	0.108444i	0.998529	−	0.0542222i	$-0.0172679\pi$
$662$	525.366	−	558.010i	0.793604	−	0.842915i
$663$		0			0
$664$	31.4352	+	26.2115i	0.0473422	+	0.0394752i
$665$	−46.0412			−0.0692349
$666$		0			0
$667$	1599.84			2.39856
$668$	1063.81	−	64.1674i	1.59252	−	0.0960589i
$669$		0			0
$670$	−283.871	−	267.264i	−0.423688	−	0.398902i
$671$			429.216i			0.639667i
$672$		0			0
$673$	−712.783			−1.05911			−0.529556	−	0.848275i	$-0.677642\pi$
$673$	−712.783			−1.05911			−0.529556	+	0.848275i	$0.677642\pi$
$674$	−772.856	+	820.878i	−1.14667	+	1.21792i
$675$		0			0
$676$	−39.2951	−	651.458i	−0.0581288	−	0.963695i
$677$			767.527i			1.13372i	0.823815	+	0.566859i	$0.191841\pi$
$677$			767.527i			1.13372i	−0.823815	+	0.566859i	$0.808159\pi$
$678$		0			0
$679$			33.0359i			0.0486538i
$680$	221.397	−	265.519i	0.325584	−	0.390469i
$681$		0			0
$682$	102.367	+	96.3786i	0.150099	+	0.141318i
$683$	484.354			0.709156			0.354578	−	0.935026i	$-0.384625\pi$
$683$	484.354			0.709156			0.354578	+	0.935026i	$0.384625\pi$
$684$		0			0
$685$			361.769i			0.528130i
$686$	26.9686	+	25.3909i	0.0393128	+	0.0370129i
$687$		0			0
$688$	561.315	−	67.9628i	0.815864	−	0.0987831i
$689$	−132.100			−0.191727
$690$		0			0
$691$	−574.851			−0.831912			−0.415956	−	0.909385i	$-0.636553\pi$
$691$	−574.851			−0.831912			−0.415956	+	0.909385i	$0.636553\pi$
$692$	458.507	−	27.6565i	0.662582	−	0.0399661i
$693$		0			0
$694$	70.7274	−	75.1221i	0.101913	−	0.108245i
$695$		−	1080.72i		−	1.55500i
$696$		0			0
$697$	438.143			0.628612
$698$	−853.871	−	803.918i	−1.22331	−	1.15175i
$699$		0			0
$700$	−150.918	+	9.10317i	−0.215597	+	0.0130045i
$701$		−	143.138i		−	0.204191i	−0.994775	−	0.102096i	$-0.967445\pi$
$701$		−	143.138i		−	0.204191i	0.994775	−	0.102096i	$-0.0325548\pi$
$702$		0			0
$703$			0.562638i			0.000800339i
$704$	−112.821	−	617.417i	−0.160258	−	0.877013i
$705$		0			0
$706$	416.563	−	442.446i	0.590032	−	0.626695i
$707$	180.110			0.254753
$708$		0			0
$709$		−	255.311i		−	0.360101i	−0.983657	−	0.180050i	$-0.942374\pi$
$709$		−	255.311i		−	0.360101i	0.983657	−	0.180050i	$-0.0576261\pi$
$710$	198.754	−	211.104i	0.279935	−	0.297329i
$711$		0			0
$712$	110.529	+	92.1618i	0.155237	+	0.129441i
$713$	−307.044			−0.430636
$714$		0			0
$715$	−148.540			−0.207748
$716$	27.1781	+	450.576i	0.0379583	+	0.629296i
$717$		0			0
$718$	−169.104	−	159.211i	−0.235521	−	0.221743i
$719$		−	415.630i		−	0.578067i	−0.957319	−	0.289034i	$-0.906666\pi$
$719$		−	415.630i		−	0.578067i	0.957319	−	0.289034i	$-0.0933340\pi$
$720$		0			0
$721$	−154.229			−0.213910
$722$	484.355	−	514.451i	0.670852	−	0.712537i
$723$		0			0
$724$	−243.346	+	14.6783i	−0.336113	+	0.0202739i
$725$			533.601i			0.736001i
$726$		0			0
$727$			896.838i			1.23361i	0.787114	+	0.616807i	$0.211574\pi$
$727$			896.838i			1.23361i	−0.787114	+	0.616807i	$0.788426\pi$
$728$	39.2836	+	32.7558i	0.0539610	+	0.0449942i
$729$		0			0
$730$	631.845	+	594.881i	0.865541	+	0.814905i
$731$	243.641			0.333299
$732$		0			0
$733$		−	509.059i		−	0.694487i	−0.937775	−	0.347244i	$-0.887118\pi$
$733$		−	509.059i		−	0.694487i	0.937775	−	0.347244i	$-0.112882\pi$
$734$	−693.555	−	652.981i	−0.944898	−	0.889620i
$735$		0			0
$736$	1103.66	+	812.808i	1.49954	+	1.10436i
$737$	−305.014			−0.413859
$738$		0			0
$739$	741.427			1.00328			0.501642	−	0.865075i	$-0.332729\pi$
$739$	741.427			1.00328			0.501642	+	0.865075i	$0.332729\pi$
$740$	0.305911	+	5.07159i	0.000413394	+	0.00685350i
$741$		0			0
$742$	−198.285	+	210.606i	−0.267231	+	0.283835i
$743$		−	1344.98i		−	1.81021i	−0.425191	−	0.905104i	$-0.639793\pi$
$743$		−	1344.98i		−	1.81021i	0.425191	−	0.905104i	$-0.360207\pi$
$744$		0			0
$745$	−1375.98			−1.84695
$746$	71.7681	+	67.5696i	0.0962039	+	0.0905759i
$747$		0			0
$748$	−16.2839	−	269.964i	−0.0217699	−	0.360915i
$749$		−	359.473i		−	0.479937i
$750$		0			0
$751$			27.6931i			0.0368749i	0.999830	+	0.0184375i	$0.00586916\pi$
$751$			27.6931i			0.0368749i	−0.999830	+	0.0184375i	$0.994131\pi$
$752$	72.9141	+	602.208i	0.0969602	+	0.800809i
$753$		0			0
$754$	123.742	−	131.431i	0.164115	−	0.174312i
$755$	−1163.74			−1.54138
$756$		0			0
$757$			1341.69i			1.77238i	0.463318	+	0.886192i	$0.346659\pi$
$757$			1341.69i			1.77238i	−0.463318	+	0.886192i	$0.653341\pi$
$758$	−229.654	+	243.924i	−0.302974	+	0.321800i
$759$		0			0
$760$	−89.1548	+	106.922i	−0.117309	+	0.140687i
$761$	112.001			0.147176			0.0735881	−	0.997289i	$-0.476555\pi$
$761$	112.001			0.147176			0.0735881	+	0.997289i	$0.476555\pi$
$762$		0			0
$763$	117.731			0.154300
$764$	−712.542	+	42.9796i	−0.932647	+	0.0562560i
$765$		0			0
$766$	747.314	+	703.596i	0.975606	+	0.918532i
$767$			253.240i			0.330169i
$768$		0			0
$769$	140.749			0.183028			0.0915142	−	0.995804i	$-0.470829\pi$
$769$	140.749			0.183028			0.0915142	+	0.995804i	$0.470829\pi$
$770$	−222.962	+	236.816i	−0.289561	+	0.307553i
$771$		0			0
$772$	−53.3665	−	884.743i	−0.0691276	−	1.14604i
$773$			1325.14i			1.71428i	0.515087	+	0.857138i	$0.327760\pi$
$773$			1325.14i			1.71428i	−0.515087	+	0.857138i	$0.672240\pi$
$774$		0			0
$775$		−	102.409i		−	0.132141i
$776$	76.7200	+	63.9712i	0.0988660	+	0.0824371i
$777$		0			0
$778$	−1033.00	−	972.570i	−1.32777	−	1.25009i
$779$	−176.437			−0.226491
$780$		0			0
$781$		−	226.827i		−	0.290432i
$782$	430.027	+	404.870i	0.549907	+	0.517737i
$783$		0			0
$784$	111.188	−	13.4624i	0.141821	−	0.0171714i
$785$	−1179.50			−1.50255
$786$		0			0
$787$	−327.801			−0.416519			−0.208260	−	0.978074i	$-0.566780\pi$
$787$	−327.801			−0.416519			−0.208260	+	0.978074i	$0.566780\pi$
$788$	−967.434	+	58.3544i	−1.22771	+	0.0740538i
$789$		0			0
$790$	−171.285	+	181.929i	−0.216817	+	0.230289i
$791$			352.918i			0.446167i
$792$		0			0
$793$	−105.764			−0.133372
$794$	450.543	+	424.186i	0.567435	+	0.534239i
$795$		0			0
$796$	1186.03	−	71.5399i	1.48999	−	0.0898742i
$797$		−	393.650i		−	0.493915i	−0.969026	−	0.246958i	$-0.920569\pi$
$797$		−	393.650i		−	0.493915i	0.969026	−	0.246958i	$-0.0794308\pi$
$798$		0			0
$799$			261.391i			0.327148i
$800$	−271.099	+	368.107i	−0.338873	+	0.460134i
$801$		0			0
$802$	−723.976	+	768.961i	−0.902713	+	0.958804i
$803$	678.906			0.845462
$804$		0			0
$805$		−	710.314i		−	0.882378i
$806$	−23.7488	+	25.2245i	−0.0294650	+	0.0312959i
$807$		0			0
$808$	348.768	−	418.273i	0.431643	−	0.517665i
$809$	−416.641			−0.515008			−0.257504	−	0.966277i	$-0.582900\pi$
$809$	−416.641			−0.515008			−0.257504	+	0.966277i	$0.582900\pi$
$810$		0			0
$811$	−748.707			−0.923190			−0.461595	−	0.887091i	$-0.652723\pi$
$811$	−748.707			−0.923190			−0.461595	+	0.887091i	$0.652723\pi$
$812$	−23.7995	−	394.563i	−0.0293098	−	0.485915i
$813$		0			0
$814$	2.89397	+	2.72467i	0.00355524	+	0.00334726i
$815$			341.696i			0.419259i
$816$		0			0
$817$	−98.1124			−0.120089
$818$	840.176	−	892.382i	1.02711	−	1.09093i
$819$		0			0
$820$	−1590.39	+	95.9302i	−1.93950	+	0.116988i
$821$		−	554.169i		−	0.674993i	−0.941327	−	0.337496i	$-0.890420\pi$
$821$		−	554.169i		−	0.674993i	0.941327	−	0.337496i	$-0.109580\pi$
$822$		0			0
$823$			121.452i			0.147572i	0.997274	+	0.0737861i	$0.0235082\pi$
$823$			121.452i			0.147572i	−0.997274	+	0.0737861i	$0.976492\pi$
$824$	−298.651	+	358.169i	−0.362441	+	0.434671i
$825$		0			0
$826$	403.738	+	380.119i	0.488787	+	0.460193i
$827$	1516.61			1.83386			0.916932	−	0.399043i	$-0.130657\pi$
$827$	1516.61			1.83386			0.916932	+	0.399043i	$0.130657\pi$
$828$		0			0
$829$		−	325.042i		−	0.392089i	−0.980595	−	0.196044i	$-0.937190\pi$
$829$		−	325.042i		−	0.392089i	0.980595	−	0.196044i	$-0.0628097\pi$
$830$	−46.6957	−	43.9639i	−0.0562599	−	0.0529686i
$831$		0			0
$832$	152.139	−	27.8005i	0.182859	−	0.0334140i
$833$	48.2617			0.0579372
$834$		0			0
$835$	−1669.98			−1.99998
$836$	6.55740	+	108.713i	0.00784377	+	0.130039i
$837$		0			0
$838$	−325.802	+	346.046i	−0.388785	+	0.412943i
$839$			1165.70i			1.38939i	0.719303	+	0.694696i	$0.244461\pi$
$839$			1165.70i			1.38939i	−0.719303	+	0.694696i	$0.755539\pi$
$840$		0			0
$841$	−554.058			−0.658808
$842$	−574.480	−	540.872i	−0.682280	−	0.642366i
$843$		0			0
$844$	33.9628	+	563.057i	0.0402403	+	0.667129i
$845$			1022.67i			1.21026i
$846$		0			0
$847$		−	65.6810i		−	0.0775454i
$848$	105.132	+	868.301i	0.123976	+	1.02394i
$849$		0			0
$850$	−135.038	+	143.428i	−0.158868	+	0.168739i
$851$	−8.68026			−0.0102001
$852$		0			0
$853$		−	151.949i		−	0.178134i	−0.996026	−	0.0890672i	$-0.971611\pi$
$853$		−	151.949i		−	0.178134i	0.996026	−	0.0890672i	$-0.0283886\pi$
$854$	−158.754	+	168.618i	−0.185895	+	0.197445i
$855$		0			0
$856$	−834.810	−	696.087i	−0.975246	−	0.813186i
$857$	−412.018			−0.480768			−0.240384	−	0.970678i	$-0.577273\pi$
$857$	−412.018			−0.480768			−0.240384	+	0.970678i	$0.577273\pi$
$858$		0			0
$859$	159.993			0.186255			0.0931274	−	0.995654i	$-0.470314\pi$
$859$	159.993			0.186255			0.0931274	+	0.995654i	$0.470314\pi$
$860$	−884.380	+	53.3446i	−1.02835	+	0.0620286i
$861$		0			0
$862$	529.110	+	498.157i	0.613817	+	0.577908i
$863$		−	992.910i		−	1.15053i	−0.817966	−	0.575266i	$-0.804898\pi$
$863$		−	992.910i		−	1.15053i	0.817966	−	0.575266i	$-0.195102\pi$
$864$		0			0
$865$	−719.772			−0.832107
$866$	−164.152	+	174.352i	−0.189552	+	0.201330i
$867$		0			0
$868$	4.56763	+	75.7250i	0.00526225	+	0.0872408i
$869$			195.479i			0.224947i
$870$		0			0
$871$		−	75.1590i		−	0.0862905i
$872$	227.975	−	273.409i	0.261440	−	0.313542i
$873$		0			0
$874$	−173.169	−	163.038i	−0.198133	−	0.186542i
$875$	−177.668			−0.203049
$876$		0			0
$877$		−	825.096i		−	0.940817i	−0.882449	−	0.470408i	$-0.844107\pi$
$877$		−	825.096i		−	0.940817i	0.882449	−	0.470408i	$-0.155893\pi$
$878$	1269.01	+	1194.78i	1.44535	+	1.36079i
$879$		0			0
$880$	118.216	+	976.363i	0.134336	+	1.10950i
$881$	−1352.83			−1.53556			−0.767780	−	0.640714i	$-0.778639\pi$
$881$	−1352.83			−1.53556			−0.767780	+	0.640714i	$0.778639\pi$
$882$		0			0
$883$	−1013.40			−1.14768			−0.573838	−	0.818969i	$-0.694546\pi$
$883$	−1013.40			−1.14768			−0.573838	+	0.818969i	$0.694546\pi$
$884$	66.5223	−	4.01254i	0.0752515	−	0.00453907i
$885$		0			0
$886$	−471.556	+	500.857i	−0.532230	+	0.565301i
$887$			233.760i			0.263540i	0.991280	+	0.131770i	$0.0420661\pi$
$887$			233.760i			0.263540i	−0.991280	+	0.131770i	$0.957934\pi$
$888$		0			0
$889$	−346.532			−0.389800
$890$	−164.186	−	154.581i	−0.184478	−	0.173686i
$891$		0			0
$892$	163.010	−	9.83257i	0.182747	−	0.0110231i
$893$		−	105.260i		−	0.117873i
$894$		0			0
$895$		−	707.322i		−	0.790304i
$896$	184.042	−	284.283i	0.205404	−	0.317280i
$897$		0			0
$898$	−332.941	+	353.628i	−0.370758	+	0.393795i
$899$	267.741			0.297821
$900$		0			0
$901$			376.890i			0.418302i
$902$	−854.423	+	907.514i	−0.947254	+	1.00611i
$903$		0			0
$904$	819.589	+	683.396i	0.906625	+	0.755968i
$905$	382.008			0.422109
$906$		0			0
$907$	−203.590			−0.224465			−0.112233	−	0.993682i	$-0.535800\pi$
$907$	−203.590			−0.224465			−0.112233	+	0.993682i	$0.535800\pi$
$908$	1.97149	+	32.6845i	0.00217124	+	0.0359961i
$909$		0			0
$910$	−58.3542	−	54.9404i	−0.0641255	−	0.0603741i
$911$		−	712.022i		−	0.781583i	−0.920479	−	0.390792i	$-0.872201\pi$
$911$		−	712.022i		−	0.781583i	0.920479	−	0.390792i	$-0.127799\pi$
$912$		0			0
$913$	−50.1737			−0.0549548
$914$	57.9335	−	61.5333i	0.0633846	−	0.0673231i
$915$		0			0
$916$	1326.60	−	80.0185i	1.44825	−	0.0873564i
$917$			141.101i			0.153872i
$918$		0			0
$919$		−	786.783i		−	0.856129i	−0.903748	−	0.428065i	$-0.859196\pi$
$919$		−	786.783i		−	0.856129i	0.903748	−	0.428065i	$-0.140804\pi$
$920$	−1649.58	−	1375.46i	−1.79302	−	1.49507i
$921$		0			0
$922$	−1188.77	−	1119.23i	−1.28934	−	1.21391i
$923$	55.8929			0.0605557
$924$		0			0
$925$		−	2.89516i		−	0.00312990i
$926$	167.693	+	157.883i	0.181094	+	0.170500i
$927$		0			0
$928$	−962.387	−	708.767i	−1.03705	−	0.763757i
$929$	1657.99			1.78471			0.892353	−	0.451338i	$-0.149053\pi$
$929$	1657.99			1.78471			0.892353	+	0.451338i	$0.149053\pi$
$930$		0			0
$931$	−19.4346			−0.0208750
$932$	79.2981	+	1314.65i	0.0850838	+	1.41057i
$933$		0			0
$934$	827.281	−	878.685i	0.885740	−	0.940776i
$935$			423.795i			0.453257i
$936$		0			0
$937$	333.736			0.356175			0.178088	−	0.984015i	$-0.443009\pi$
$937$	333.736			0.356175			0.178088	+	0.984015i	$0.443009\pi$
$938$	−119.825	−	112.816i	−0.127746	−	0.120272i
$939$		0			0
$940$	−57.2309	−	948.809i	−0.0608840	−	1.00937i
$941$		−	543.324i		−	0.577390i	−0.957421	−	0.288695i	$-0.906779\pi$
$941$		−	543.324i		−	0.577390i	0.957421	−	0.288695i	$-0.0932214\pi$
$942$		0			0
$943$		−	2722.03i		−	2.88656i
$944$	1664.56	−	201.542i	1.76331	−	0.213497i
$945$		0			0
$946$	−475.125	+	504.648i	−0.502247	+	0.533454i
$947$	359.728			0.379861			0.189930	−	0.981798i	$-0.439174\pi$
$947$	359.728			0.379861			0.189930	+	0.981798i	$0.439174\pi$
$948$		0			0
$949$			167.290i			0.176281i
$950$	54.3786	−	57.7575i	0.0572406	−	0.0607974i
$951$		0			0
$952$	93.4545	−	112.079i	0.0981665	−	0.117730i
$953$	904.225			0.948820			0.474410	−	0.880304i	$-0.342661\pi$
$953$	904.225			0.948820			0.474410	+	0.880304i	$0.342661\pi$
$954$		0			0
$955$	1118.56			1.17127
$956$	549.877	−	33.1678i	0.575185	−	0.0346944i
$957$		0			0
$958$	−230.941	−	217.431i	−0.241066	−	0.226963i
$959$			152.707i			0.159236i
$960$		0			0
$961$	909.615			0.946529
$962$	−0.671389	+	0.713107i	−0.000697910	+	0.000741275i
$963$		0			0
$964$	−48.6138	−	805.949i	−0.0504293	−	0.836047i
$965$			1388.89i			1.43926i
$966$		0			0
$967$		−	920.961i		−	0.952390i	−0.879340	−	0.476195i	$-0.842016\pi$
$967$		−	920.961i		−	0.952390i	0.879340	−	0.476195i	$-0.157984\pi$
$968$	−152.532	−	127.185i	−0.157575	−	0.131390i
$969$		0			0
$970$	−113.964	−	107.297i	−0.117489	−	0.110616i
$971$	−1327.31			−1.36695			−0.683476	−	0.729973i	$-0.739532\pi$
$971$	−1327.31			−1.36695			−0.683476	+	0.729973i	$0.739532\pi$
$972$		0			0
$973$		−	456.186i		−	0.468845i
$974$	−155.791	−	146.677i	−0.159950	−	0.150593i
$975$		0			0
$976$	84.1724	+	695.192i	0.0862422	+	0.712287i
$977$	688.490			0.704698			0.352349	−	0.935869i	$-0.385383\pi$
$977$	688.490			0.704698			0.352349	+	0.935869i	$0.385383\pi$
$978$		0			0
$979$	−176.415			−0.180199
$980$	−175.182	+	10.5668i	−0.178757	+	0.0107824i
$981$		0			0
$982$	845.333	−	897.859i	0.860828	−	0.914317i
$983$		−	1687.08i		−	1.71625i	−0.513438	−	0.858127i	$-0.671628\pi$
$983$		−	1687.08i		−	1.71625i	0.513438	−	0.858127i	$-0.328372\pi$
$984$		0			0
$985$	1518.70			1.54182
$986$	−374.983	−	353.046i	−0.380307	−	0.358058i
$987$		0			0
$988$	−26.7880	+	1.61582i	−0.0271134	+	0.00163544i
$989$		−	1513.66i		−	1.53049i
$990$		0			0
$991$			1139.22i			1.14957i	0.818304	+	0.574785i	$0.194914\pi$
$991$			1139.22i			1.14957i	−0.818304	+	0.574785i	$0.805086\pi$
$992$	184.703	+	136.027i	0.186192	+	0.137124i
$993$		0			0
$994$	83.8966	−	89.1096i	0.0844030	−	0.0896475i
$995$	−1861.85			−1.87121
$996$		0			0
$997$		−	206.085i		−	0.206705i	−0.994645	−	0.103353i	$-0.967043\pi$
$997$		−	206.085i		−	0.206705i	0.994645	−	0.103353i	$-0.0329570\pi$
$998$	−759.645	+	806.847i	−0.761168	+	0.808464i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.3.g.b.379.4		8
3.2	odd	2		56.3.g.b.43.5	✓	8
4.3	odd	2		2016.3.g.b.1135.8		8
8.3	odd	2	inner	504.3.g.b.379.3		8
8.5	even	2		2016.3.g.b.1135.1		8
12.11	even	2		224.3.g.b.15.7		8
21.2	odd	6		392.3.k.o.67.1		16
21.5	even	6		392.3.k.n.67.1		16
21.11	odd	6		392.3.k.o.275.6		16
21.17	even	6		392.3.k.n.275.6		16
21.20	even	2		392.3.g.m.99.5		8
24.5	odd	2		224.3.g.b.15.8		8
24.11	even	2		56.3.g.b.43.6	yes	8
48.5	odd	4		1792.3.d.j.1023.16		16
48.11	even	4		1792.3.d.j.1023.2		16
48.29	odd	4		1792.3.d.j.1023.1		16
48.35	even	4		1792.3.d.j.1023.15		16
84.83	odd	2		1568.3.g.m.687.2		8
168.11	even	6		392.3.k.o.275.1		16
168.59	odd	6		392.3.k.n.275.1		16
168.83	odd	2		392.3.g.m.99.6		8
168.107	even	6		392.3.k.o.67.6		16
168.125	even	2		1568.3.g.m.687.1		8
168.131	odd	6		392.3.k.n.67.6		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
56.3.g.b.43.5	✓	8	3.2	odd	2
56.3.g.b.43.6	yes	8	24.11	even	2
224.3.g.b.15.7		8	12.11	even	2
224.3.g.b.15.8		8	24.5	odd	2
392.3.g.m.99.5		8	21.20	even	2
392.3.g.m.99.6		8	168.83	odd	2
392.3.k.n.67.1		16	21.5	even	6
392.3.k.n.67.6		16	168.131	odd	6
392.3.k.n.275.1		16	168.59	odd	6
392.3.k.n.275.6		16	21.17	even	6
392.3.k.o.67.1		16	21.2	odd	6
392.3.k.o.67.6		16	168.107	even	6
392.3.k.o.275.1		16	168.11	even	6
392.3.k.o.275.6		16	21.11	odd	6
504.3.g.b.379.3		8	8.3	odd	2	inner
504.3.g.b.379.4		8	1.1	even	1	trivial
1568.3.g.m.687.1		8	168.125	even	2
1568.3.g.m.687.2		8	84.83	odd	2
1792.3.d.j.1023.1		16	48.29	odd	4
1792.3.d.j.1023.2		16	48.11	even	4
1792.3.d.j.1023.15		16	48.35	even	4
1792.3.d.j.1023.16		16	48.5	odd	4
2016.3.g.b.1135.1		8	8.5	even	2
2016.3.g.b.1135.8		8	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	504.g (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.37098 + 1.45617i) q^{2} +(-0.240837 - 3.99274i) q^{4} +6.26788i q^{5} +2.64575i q^{7} +(6.14428 + 5.12327i) q^{8} +O(q^{10})\)	\(q+(-1.37098 + 1.45617i) q^{2} +(-0.240837 - 3.99274i) q^{4} +6.26788i q^{5} +2.64575i q^{7} +(6.14428 + 5.12327i) q^{8} +(-9.12707 - 8.59313i) q^{10} -9.80688 q^{11} -2.41653i q^{13} +(-3.85265 - 3.62727i) q^{14} +(-15.8840 + 1.92320i) q^{16} -6.89452 q^{17} +2.77637 q^{19} +(25.0260 - 1.50954i) q^{20} +(13.4450 - 14.2804i) q^{22} +42.8332i q^{23} -14.2863 q^{25} +(3.51887 + 3.31301i) q^{26} +(10.5638 - 0.637195i) q^{28} -37.3505i q^{29} +7.16835i q^{31} +(18.9761 - 25.7664i) q^{32} +(9.45224 - 10.0396i) q^{34} -16.5833 q^{35} +0.202653i q^{37} +(-3.80634 + 4.04285i) q^{38} +(-32.1120 + 38.5116i) q^{40} -63.5494 q^{41} -35.3384 q^{43} +(2.36186 + 39.1564i) q^{44} +(-62.3723 - 58.7234i) q^{46} -37.9129i q^{47} -7.00000 q^{49} +(19.5862 - 20.8032i) q^{50} +(-9.64858 + 0.581989i) q^{52} -54.6651i q^{53} -61.4684i q^{55} +(-13.5549 + 16.2562i) q^{56} +(54.3885 + 51.2067i) q^{58} -104.795 q^{59} -43.7668i q^{61} +(-10.4383 - 9.82765i) q^{62} +(11.5043 + 62.9575i) q^{64} +15.1465 q^{65} +31.1021 q^{67} +(1.66046 + 27.5281i) q^{68} +(22.7353 - 24.1480i) q^{70} +23.1294i q^{71} -69.2275 q^{73} +(-0.295096 - 0.277832i) q^{74} +(-0.668652 - 11.0853i) q^{76} -25.9466i q^{77} -19.9328i q^{79} +(-12.0544 - 99.5590i) q^{80} +(87.1249 - 92.5385i) q^{82} +5.11617 q^{83} -43.2140i q^{85} +(48.4482 - 51.4585i) q^{86} +(-60.2562 - 50.2433i) q^{88} +17.9889 q^{89} +6.39353 q^{91} +(171.022 - 10.3158i) q^{92} +(55.2075 + 51.9778i) q^{94} +17.4019i q^{95} +12.4864 q^{97} +(9.59685 - 10.1932i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - q^{2} + 5 q^{4} - 13 q^{8}+O(q^{10}) \) 8 * q - q^2 + 5 * q^4 - 13 * q^8	\( 8 q - q^{2} + 5 q^{4} - 13 q^{8} + 16 q^{10} + 32 q^{11} - 7 q^{14} - 71 q^{16} + 80 q^{17} + 56 q^{19} + 108 q^{20} + 66 q^{22} - 16 q^{25} - 24 q^{26} + 7 q^{28} + 19 q^{32} + 74 q^{34} - 56 q^{35} + 14 q^{38} + 84 q^{40} - 128 q^{41} - 50 q^{44} - 152 q^{46} - 56 q^{49} - 33 q^{50} + 132 q^{52} + 49 q^{56} + 24 q^{58} - 104 q^{59} - 120 q^{62} - 55 q^{64} + 72 q^{65} + 304 q^{67} + 190 q^{68} + 56 q^{70} - 112 q^{73} - 8 q^{74} + 70 q^{76} - 124 q^{80} + 450 q^{82} - 72 q^{83} - 210 q^{86} - 486 q^{88} + 512 q^{89} - 56 q^{91} + 472 q^{92} + 472 q^{94} + 64 q^{97} + 7 q^{98}+O(q^{100}) \) 8 * q - q^2 + 5 * q^4 - 13 * q^8 + 16 * q^10 + 32 * q^11 - 7 * q^14 - 71 * q^16 + 80 * q^17 + 56 * q^19 + 108 * q^20 + 66 * q^22 - 16 * q^25 - 24 * q^26 + 7 * q^28 + 19 * q^32 + 74 * q^34 - 56 * q^35 + 14 * q^38 + 84 * q^40 - 128 * q^41 - 50 * q^44 - 152 * q^46 - 56 * q^49 - 33 * q^50 + 132 * q^52 + 49 * q^56 + 24 * q^58 - 104 * q^59 - 120 * q^62 - 55 * q^64 + 72 * q^65 + 304 * q^67 + 190 * q^68 + 56 * q^70 - 112 * q^73 - 8 * q^74 + 70 * q^76 - 124 * q^80 + 450 * q^82 - 72 * q^83 - 210 * q^86 - 486 * q^88 + 512 * q^89 - 56 * q^91 + 472 * q^92 + 472 * q^94 + 64 * q^97 + 7 * q^98

Introduction

L-functions

Modular forms

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