LMFDB - Embedded newform 630.3.o.a.253.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("630.127");

S:= CuspForms(chi, 3);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$17.1662566547$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(i)$
Coefficient field:	$\Q(i, \sqrt{14})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 49 $ x^4 + 49
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 70)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			253.1
Root			$-1.87083 - 1.87083i$ of defining polynomial
Character	$\chi$	$=$	630.253
Dual form			630.3.o.a.127.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.00000 - 1.00000i) q^{2} -2.00000i q^{4} +(-4.87083 + 1.12917i) q^{5} +(-1.87083 + 1.87083i) q^{7} +(-2.00000 - 2.00000i) q^{8} +O(q^{10})$	\(q+(1.00000 - 1.00000i) q^{2} -2.00000i q^{4} +(-4.87083 + 1.12917i) q^{5} +(-1.87083 + 1.87083i) q^{7} +(-2.00000 - 2.00000i) q^{8} +(-3.74166 + 6.00000i) q^{10} +13.9666 q^{11} +(6.61249 + 6.61249i) q^{13} +3.74166i q^{14} -4.00000 q^{16} +(-8.09580 + 8.09580i) q^{17} -14.2583i q^{19} +(2.25834 + 9.74166i) q^{20} +(13.9666 - 13.9666i) q^{22} +(28.7083 + 28.7083i) q^{23} +(22.4499 - 11.0000i) q^{25} +13.2250 q^{26} +(3.74166 + 3.74166i) q^{28} -20.0334i q^{29} +0.775028 q^{31} +(-4.00000 + 4.00000i) q^{32} +16.1916i q^{34} +(7.00000 - 11.2250i) q^{35} +(37.2250 - 37.2250i) q^{37} +(-14.2583 - 14.2583i) q^{38} +(12.0000 + 7.48331i) q^{40} +29.6749 q^{41} +(54.4833 + 54.4833i) q^{43} -27.9333i q^{44} +57.4166 q^{46} +(64.0291 - 64.0291i) q^{47} -7.00000i q^{49} +(11.4499 - 33.4499i) q^{50} +(13.2250 - 13.2250i) q^{52} +(17.7083 + 17.7083i) q^{53} +(-68.0291 + 15.7707i) q^{55} +7.48331 q^{56} +(-20.0334 - 20.0334i) q^{58} +60.1249i q^{59} -86.9666 q^{61} +(0.775028 - 0.775028i) q^{62} +8.00000i q^{64} +(-39.6749 - 24.7417i) q^{65} +(-41.7083 + 41.7083i) q^{67} +(16.1916 + 16.1916i) q^{68} +(-4.22497 - 18.2250i) q^{70} +47.4833 q^{71} +(34.3832 + 34.3832i) q^{73} -74.4499i q^{74} -28.5167 q^{76} +(-26.1292 + 26.1292i) q^{77} +9.13348i q^{79} +(19.4833 - 4.51669i) q^{80} +(29.6749 - 29.6749i) q^{82} +(-78.9666 - 78.9666i) q^{83} +(30.2917 - 48.5748i) q^{85} +108.967 q^{86} +(-27.9333 - 27.9333i) q^{88} +80.0000i q^{89} -24.7417 q^{91} +(57.4166 - 57.4166i) q^{92} -128.058i q^{94} +(16.1001 + 69.4499i) q^{95} +(-56.5457 + 56.5457i) q^{97} +(-7.00000 - 7.00000i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{2} - 12 q^{5} - 8 q^{8}+O(q^{10}) $ 4 * q + 4 * q^2 - 12 * q^5 - 8 * q^8	$ 4 q + 4 q^{2} - 12 q^{5} - 8 q^{8} - 4 q^{11} + 4 q^{13} - 16 q^{16} + 20 q^{17} + 24 q^{20} - 4 q^{22} + 40 q^{23} + 8 q^{26} + 48 q^{31} - 16 q^{32} + 28 q^{35} + 104 q^{37} - 72 q^{38} + 48 q^{40} - 16 q^{41} + 188 q^{43} + 80 q^{46} + 84 q^{47} - 44 q^{50} + 8 q^{52} - 4 q^{53} - 100 q^{55} - 140 q^{58} - 288 q^{61} + 48 q^{62} - 24 q^{65} - 92 q^{67} - 40 q^{68} + 28 q^{70} + 160 q^{71} - 72 q^{73} - 144 q^{76} - 112 q^{77} + 48 q^{80} - 16 q^{82} - 256 q^{83} + 196 q^{85} + 376 q^{86} + 8 q^{88} - 84 q^{91} + 80 q^{92} + 244 q^{95} - 84 q^{97} - 28 q^{98}+O(q^{100}) $ 4 * q + 4 * q^2 - 12 * q^5 - 8 * q^8 - 4 * q^11 + 4 * q^13 - 16 * q^16 + 20 * q^17 + 24 * q^20 - 4 * q^22 + 40 * q^23 + 8 * q^26 + 48 * q^31 - 16 * q^32 + 28 * q^35 + 104 * q^37 - 72 * q^38 + 48 * q^40 - 16 * q^41 + 188 * q^43 + 80 * q^46 + 84 * q^47 - 44 * q^50 + 8 * q^52 - 4 * q^53 - 100 * q^55 - 140 * q^58 - 288 * q^61 + 48 * q^62 - 24 * q^65 - 92 * q^67 - 40 * q^68 + 28 * q^70 + 160 * q^71 - 72 * q^73 - 144 * q^76 - 112 * q^77 + 48 * q^80 - 16 * q^82 - 256 * q^83 + 196 * q^85 + 376 * q^86 + 8 * q^88 - 84 * q^91 + 80 * q^92 + 244 * q^95 - 84 * q^97 - 28 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	1.00000	−	1.00000i	0.500000	−	0.500000i
$2$	1.00000	−	1.00000i	0.500000	−	0.500000i
$3$		0			0
$3$		0			0
$4$		−	2.00000i		−	0.500000i
$5$	−4.87083	+	1.12917i	−0.974166	+	0.225834i
$5$	−4.87083	+	1.12917i	−0.974166	+	0.225834i
$6$		0			0
$7$	−1.87083	+	1.87083i	−0.267261	+	0.267261i
$7$	−1.87083	+	1.87083i	−0.267261	+	0.267261i
$8$	−2.00000	−	2.00000i	−0.250000	−	0.250000i
$9$		0			0
$10$	−3.74166	+	6.00000i	−0.374166	+	0.600000i
$11$	13.9666			1.26969			0.634847	−	0.772638i	$-0.281063\pi$
$11$	13.9666			1.26969			0.634847	+	0.772638i	$0.281063\pi$
$12$		0			0
$13$	6.61249	+	6.61249i	0.508653	+	0.508653i	0.914113	−	0.405460i	$-0.132889\pi$
$13$	6.61249	+	6.61249i	0.508653	+	0.508653i	−0.405460	+	0.914113i	$0.632889\pi$
$14$			3.74166i			0.267261i
$15$		0			0
$16$	−4.00000			−0.250000
$17$	−8.09580	+	8.09580i	−0.476224	+	0.476224i	−0.903922	−	0.427698i	$-0.859325\pi$
$17$	−8.09580	+	8.09580i	−0.476224	+	0.476224i	0.427698	+	0.903922i	$0.359325\pi$
$18$		0			0
$19$		−	14.2583i		−	0.750439i	−0.926936	−	0.375220i	$-0.877567\pi$
$19$		−	14.2583i		−	0.750439i	0.926936	−	0.375220i	$-0.122433\pi$
$20$	2.25834	+	9.74166i	0.112917	+	0.487083i
$21$		0			0
$22$	13.9666	−	13.9666i	0.634847	−	0.634847i
$23$	28.7083	+	28.7083i	1.24819	+	1.24819i	0.956520	+	0.291666i	$0.0942097\pi$
$23$	28.7083	+	28.7083i	1.24819	+	1.24819i	0.291666	+	0.956520i	$0.405790\pi$
$24$		0			0
$25$	22.4499	−	11.0000i	0.897998	−	0.440000i
$26$	13.2250			0.508653
$27$		0			0
$28$	3.74166	+	3.74166i	0.133631	+	0.133631i
$29$		−	20.0334i		−	0.690806i	−0.938454	−	0.345403i	$-0.887742\pi$
$29$		−	20.0334i		−	0.690806i	0.938454	−	0.345403i	$-0.112258\pi$
$30$		0			0
$31$	0.775028			0.0250009			0.0125004	−	0.999922i	$-0.496021\pi$
$31$	0.775028			0.0250009			0.0125004	+	0.999922i	$0.496021\pi$
$32$	−4.00000	+	4.00000i	−0.125000	+	0.125000i
$33$		0			0
$34$			16.1916i			0.476224i
$35$	7.00000	−	11.2250i	0.200000	−	0.320713i
$36$		0			0
$37$	37.2250	−	37.2250i	1.00608	−	1.00608i	0.00609893	−	0.999981i	$-0.498059\pi$
$37$	37.2250	−	37.2250i	1.00608	−	1.00608i	0.999981	−	0.00609893i	$-0.00194136\pi$
$38$	−14.2583	−	14.2583i	−0.375220	−	0.375220i
$39$		0			0
$40$	12.0000	+	7.48331i	0.300000	+	0.187083i
$41$	29.6749			0.723778			0.361889	−	0.932221i	$-0.382132\pi$
$41$	29.6749			0.723778			0.361889	+	0.932221i	$0.382132\pi$
$42$		0			0
$43$	54.4833	+	54.4833i	1.26705	+	1.26705i	0.947603	+	0.319451i	$0.103499\pi$
$43$	54.4833	+	54.4833i	1.26705	+	1.26705i	0.319451	+	0.947603i	$0.396501\pi$
$44$		−	27.9333i		−	0.634847i
$45$		0			0
$46$	57.4166			1.24819
$47$	64.0291	−	64.0291i	1.36232	−	1.36232i	0.491369	−	0.870952i	$-0.336497\pi$
$47$	64.0291	−	64.0291i	1.36232	−	1.36232i	0.870952	−	0.491369i	$-0.163503\pi$
$48$		0			0
$49$		−	7.00000i		−	0.142857i
$50$	11.4499	−	33.4499i	0.228999	−	0.668999i
$51$		0			0
$52$	13.2250	−	13.2250i	0.254326	−	0.254326i
$53$	17.7083	+	17.7083i	0.334119	+	0.334119i	0.854148	−	0.520030i	$-0.174079\pi$
$53$	17.7083	+	17.7083i	0.334119	+	0.334119i	−0.520030	+	0.854148i	$0.674079\pi$
$54$		0			0
$55$	−68.0291	+	15.7707i	−1.23689	+	0.286740i
$56$	7.48331			0.133631
$57$		0			0
$58$	−20.0334	−	20.0334i	−0.345403	−	0.345403i
$59$			60.1249i			1.01907i	0.860451	+	0.509533i	$0.170182\pi$
$59$			60.1249i			1.01907i	−0.860451	+	0.509533i	$0.829818\pi$
$60$		0			0
$61$	−86.9666			−1.42568			−0.712841	−	0.701325i	$-0.752592\pi$
$61$	−86.9666			−1.42568			−0.712841	+	0.701325i	$0.752592\pi$
$62$	0.775028	−	0.775028i	0.0125004	−	0.0125004i
$63$		0			0
$64$			8.00000i			0.125000i
$65$	−39.6749	−	24.7417i	−0.610383	−	0.380641i
$66$		0			0
$67$	−41.7083	+	41.7083i	−0.622512	+	0.622512i	−0.946173	−	0.323661i	$-0.895086\pi$
$67$	−41.7083	+	41.7083i	−0.622512	+	0.622512i	0.323661	+	0.946173i	$0.395086\pi$
$68$	16.1916	+	16.1916i	0.238112	+	0.238112i
$69$		0			0
$70$	−4.22497	−	18.2250i	−0.0603567	−	0.260357i
$71$	47.4833			0.668779			0.334390	−	0.942435i	$-0.391470\pi$
$71$	47.4833			0.668779			0.334390	+	0.942435i	$0.391470\pi$
$72$		0			0
$73$	34.3832	+	34.3832i	0.471003	+	0.471003i	0.902239	−	0.431236i	$-0.141922\pi$
$73$	34.3832	+	34.3832i	0.471003	+	0.471003i	−0.431236	+	0.902239i	$0.641922\pi$
$74$		−	74.4499i		−	1.00608i
$75$		0			0
$76$	−28.5167			−0.375220
$77$	−26.1292	+	26.1292i	−0.339340	+	0.339340i
$78$		0			0
$79$			9.13348i			0.115614i	0.998328	+	0.0578068i	$0.0184108\pi$
$79$			9.13348i			0.115614i	−0.998328	+	0.0578068i	$0.981589\pi$
$80$	19.4833	−	4.51669i	0.243541	−	0.0564586i
$81$		0			0
$82$	29.6749	−	29.6749i	0.361889	−	0.361889i
$83$	−78.9666	−	78.9666i	−0.951405	−	0.951405i	0.0474676	−	0.998873i	$-0.484885\pi$
$83$	−78.9666	−	78.9666i	−0.951405	−	0.951405i	−0.998873	+	0.0474676i	$0.984885\pi$
$84$		0			0
$85$	30.2917	−	48.5748i	0.356373	−	0.571468i
$86$	108.967			1.26705
$87$		0			0
$88$	−27.9333	−	27.9333i	−0.317423	−	0.317423i
$89$			80.0000i			0.898876i	0.893311	+	0.449438i	$0.148376\pi$
$89$			80.0000i			0.898876i	−0.893311	+	0.449438i	$0.851624\pi$
$90$		0			0
$91$	−24.7417			−0.271886
$92$	57.4166	−	57.4166i	0.624093	−	0.624093i
$93$		0			0
$94$		−	128.058i		−	1.36232i
$95$	16.1001	+	69.4499i	0.169475	+	0.731052i
$96$		0			0
$97$	−56.5457	+	56.5457i	−0.582946	+	0.582946i	−0.935712	−	0.352766i	$-0.885241\pi$
$97$	−56.5457	+	56.5457i	−0.582946	+	0.582946i	0.352766	+	0.935712i	$0.385241\pi$
$98$	−7.00000	−	7.00000i	−0.0714286	−	0.0714286i
$99$		0			0
$100$	−22.0000	−	44.8999i	−0.220000	−	0.448999i
$101$	76.5748			0.758166			0.379083	−	0.925363i	$-0.376239\pi$
$101$	76.5748			0.758166			0.379083	+	0.925363i	$0.376239\pi$
$102$		0			0
$103$	56.5457	+	56.5457i	0.548988	+	0.548988i	0.926148	−	0.377160i	$-0.123099\pi$
$103$	56.5457	+	56.5457i	0.548988	+	0.548988i	−0.377160	+	0.926148i	$0.623099\pi$
$104$		−	26.4499i		−	0.254326i
$105$		0			0
$106$	35.4166			0.334119
$107$	27.3832	−	27.3832i	0.255918	−	0.255918i	−0.567474	−	0.823392i	$-0.692079\pi$
$107$	27.3832	−	27.3832i	0.255918	−	0.255918i	0.823392	+	0.567474i	$0.192079\pi$
$108$		0			0
$109$			154.867i			1.42079i	0.703801	+	0.710397i	$0.251485\pi$
$109$			154.867i			1.42079i	−0.703801	+	0.710397i	$0.748515\pi$
$110$	−52.2583	+	83.7998i	−0.475076	+	0.761816i
$111$		0			0
$112$	7.48331	−	7.48331i	0.0668153	−	0.0668153i
$113$	−99.0247	−	99.0247i	−0.876325	−	0.876325i	0.116827	−	0.993152i	$-0.462728\pi$
$113$	−99.0247	−	99.0247i	−0.876325	−	0.876325i	−0.993152	+	0.116827i	$0.962728\pi$
$114$		0			0
$115$	−172.250	−	107.417i	−1.49782	−	0.934057i
$116$	−40.0667			−0.345403
$117$		0			0
$118$	60.1249	+	60.1249i	0.509533	+	0.509533i
$119$		−	30.2917i		−	0.254552i
$120$		0			0
$121$	74.0667			0.612122
$122$	−86.9666	+	86.9666i	−0.712841	+	0.712841i
$123$		0			0
$124$		−	1.55006i		−	0.0125004i
$125$	−96.9289	+	78.9289i	−0.775432	+	0.631432i
$126$		0			0
$127$	64.2917	−	64.2917i	0.506234	−	0.506234i	−0.407134	−	0.913368i	$-0.633472\pi$
$127$	64.2917	−	64.2917i	0.506234	−	0.506234i	0.913368	+	0.407134i	$0.133472\pi$
$128$	8.00000	+	8.00000i	0.0625000	+	0.0625000i
$129$		0			0
$130$	−64.4166	+	14.9333i	−0.495512	+	0.114871i
$131$	−146.633			−1.11934			−0.559668	−	0.828717i	$-0.689071\pi$
$131$	−146.633			−1.11934			−0.559668	+	0.828717i	$0.689071\pi$
$132$		0			0
$133$	26.6749	+	26.6749i	0.200563	+	0.200563i
$134$			83.4166i			0.622512i
$135$		0			0
$136$	32.3832			0.238112
$137$	7.34983	−	7.34983i	0.0536484	−	0.0536484i	−0.679774	−	0.733422i	$-0.737922\pi$
$137$	7.34983	−	7.34983i	0.0536484	−	0.0536484i	0.733422	+	0.679774i	$0.237922\pi$
$138$		0			0
$139$		−	53.8665i		−	0.387529i	−0.981048	−	0.193764i	$-0.937930\pi$
$139$		−	53.8665i		−	0.387529i	0.981048	−	0.193764i	$-0.0620698\pi$
$140$	−22.4499	−	14.0000i	−0.160357	−	0.100000i
$141$		0			0
$142$	47.4833	−	47.4833i	0.334390	−	0.334390i
$143$	92.3541	+	92.3541i	0.645833	+	0.645833i
$144$		0			0
$145$	22.6211	+	97.5791i	0.156008	+	0.672959i
$146$	68.7664			0.471003
$147$		0			0
$148$	−74.4499	−	74.4499i	−0.503040	−	0.503040i
$149$		−	84.6502i		−	0.568122i	−0.958806	−	0.284061i	$-0.908318\pi$
$149$		−	84.6502i		−	0.568122i	0.958806	−	0.284061i	$-0.0916818\pi$
$150$		0			0
$151$	−21.8331			−0.144590			−0.0722952	−	0.997383i	$-0.523032\pi$
$151$	−21.8331			−0.144590			−0.0722952	+	0.997383i	$0.523032\pi$
$152$	−28.5167	+	28.5167i	−0.187610	+	0.187610i
$153$		0			0
$154$			52.2583i			0.339340i
$155$	−3.77503	+	0.875139i	−0.0243550	+	0.00564606i
$156$		0			0
$157$	34.8331	−	34.8331i	0.221867	−	0.221867i	−0.587417	−	0.809284i	$-0.699855\pi$
$157$	34.8331	−	34.8331i	0.221867	−	0.221867i	0.809284	+	0.587417i	$0.199855\pi$
$158$	9.13348	+	9.13348i	0.0578068	+	0.0578068i
$159$		0			0
$160$	14.9666	−	24.0000i	0.0935414	−	0.150000i
$161$	−107.417			−0.667184
$162$		0			0
$163$	−45.2250	−	45.2250i	−0.277454	−	0.277454i	0.554638	−	0.832092i	$-0.312857\pi$
$163$	−45.2250	−	45.2250i	−0.277454	−	0.277454i	−0.832092	+	0.554638i	$0.812857\pi$
$164$		−	59.3498i		−	0.361889i
$165$		0			0
$166$	−157.933			−0.951405
$167$	78.0377	−	78.0377i	0.467292	−	0.467292i	−0.433744	−	0.901036i	$-0.642808\pi$
$167$	78.0377	−	78.0377i	0.467292	−	0.467292i	0.901036	+	0.433744i	$0.142808\pi$
$168$		0			0
$169$		−	81.5501i		−	0.482545i
$170$	−18.2831	−	78.8665i	−0.107548	−	0.463921i
$171$		0			0
$172$	108.967	−	108.967i	0.633527	−	0.633527i
$173$	102.087	+	102.087i	0.590099	+	0.590099i	0.937658	−	0.347559i	$-0.112989\pi$
$173$	102.087	+	102.087i	0.590099	+	0.590099i	−0.347559	+	0.937658i	$0.612989\pi$
$174$		0			0
$175$	−21.4209	+	62.5791i	−0.122405	+	0.357595i
$176$	−55.8665			−0.317423
$177$		0			0
$178$	80.0000	+	80.0000i	0.449438	+	0.449438i
$179$			248.250i			1.38687i	0.720519	+	0.693435i	$0.243904\pi$
$179$			248.250i			1.38687i	−0.720519	+	0.693435i	$0.756096\pi$
$180$		0			0
$181$	−17.1582			−0.0947969			−0.0473984	−	0.998876i	$-0.515093\pi$
$181$	−17.1582			−0.0947969			−0.0473984	+	0.998876i	$0.515093\pi$
$182$	−24.7417	+	24.7417i	−0.135943	+	0.135943i
$183$		0			0
$184$		−	114.833i		−	0.624093i
$185$	−139.283	+	223.350i	−0.752882	+	1.20730i
$186$		0			0
$187$	−113.071	+	113.071i	−0.604658	+	0.604658i
$188$	−128.058	−	128.058i	−0.681160	−	0.681160i
$189$		0			0
$190$	85.5501	+	53.3498i	0.450263	+	0.280789i
$191$	−200.916			−1.05192			−0.525958	−	0.850510i	$-0.676293\pi$
$191$	−200.916			−1.05192			−0.525958	+	0.850510i	$0.676293\pi$
$192$		0			0
$193$	121.800	+	121.800i	0.631087	+	0.631087i	0.948341	−	0.317254i	$-0.102761\pi$
$193$	121.800	+	121.800i	0.631087	+	0.631087i	−0.317254	+	0.948341i	$0.602761\pi$
$194$			113.091i			0.582946i
$195$		0			0
$196$	−14.0000			−0.0714286
$197$	215.125	−	215.125i	1.09200	−	1.09200i	0.0966898	−	0.995315i	$-0.469175\pi$
$197$	215.125	−	215.125i	1.09200	−	1.09200i	0.995315	−	0.0966898i	$-0.0308255\pi$
$198$		0			0
$199$			93.2917i			0.468803i	0.972140	+	0.234401i	$0.0753130\pi$
$199$			93.2917i			0.468803i	−0.972140	+	0.234401i	$0.924687\pi$
$200$	−66.8999	−	22.8999i	−0.334499	−	0.114499i
$201$		0			0
$202$	76.5748	−	76.5748i	0.379083	−	0.379083i
$203$	37.4790	+	37.4790i	0.184626	+	0.184626i
$204$		0			0
$205$	−144.541	+	33.5081i	−0.705080	+	0.163454i
$206$	113.091			0.548988
$207$		0			0
$208$	−26.4499	−	26.4499i	−0.127163	−	0.127163i
$209$		−	199.141i		−	0.952828i
$210$		0			0
$211$	−74.3498			−0.352369			−0.176184	−	0.984357i	$-0.556376\pi$
$211$	−74.3498			−0.352369			−0.176184	+	0.984357i	$0.556376\pi$
$212$	35.4166	−	35.4166i	0.167059	−	0.167059i
$213$		0			0
$214$		−	54.7664i		−	0.255918i
$215$	−326.900	−	203.858i	−1.52046	−	0.948176i
$216$		0			0
$217$	−1.44994	+	1.44994i	−0.00668177	+	0.00668177i
$218$	154.867	+	154.867i	0.710397	+	0.710397i
$219$		0			0
$220$	31.5414	+	136.058i	0.143370	+	0.618446i
$221$	−107.067			−0.484465
$222$		0			0
$223$	−112.929	−	112.929i	−0.506408	−	0.506408i	0.407014	−	0.913422i	$-0.366570\pi$
$223$	−112.929	−	112.929i	−0.506408	−	0.506408i	−0.913422	+	0.407014i	$0.866570\pi$
$224$		−	14.9666i		−	0.0668153i
$225$		0			0
$226$	−198.049			−0.876325
$227$	−85.7793	+	85.7793i	−0.377883	+	0.377883i	−0.870338	−	0.492455i	$-0.836100\pi$
$227$	−85.7793	+	85.7793i	−0.377883	+	0.377883i	0.492455	+	0.870338i	$0.336100\pi$
$228$		0			0
$229$		−	215.875i		−	0.942686i	−0.881950	−	0.471343i	$-0.843769\pi$
$229$		−	215.875i		−	0.942686i	0.881950	−	0.471343i	$-0.156231\pi$
$230$	−279.666	+	64.8331i	−1.21594	+	0.281883i
$231$		0			0
$232$	−40.0667	+	40.0667i	−0.172701	+	0.172701i
$233$	77.5501	+	77.5501i	0.332833	+	0.332833i	0.853661	−	0.520828i	$-0.174377\pi$
$233$	77.5501	+	77.5501i	0.332833	+	0.332833i	−0.520828	+	0.853661i	$0.674377\pi$
$234$		0			0
$235$	−239.575	+	384.174i	−1.01947	+	1.63478i
$236$	120.250			0.509533
$237$		0			0
$238$	−30.2917	−	30.2917i	−0.127276	−	0.127276i
$239$		−	30.4661i		−	0.127473i	−0.997967	−	0.0637366i	$-0.979698\pi$
$239$		−	30.4661i		−	0.127473i	0.997967	−	0.0637366i	$-0.0203017\pi$
$240$		0			0
$241$	40.3337			0.167360			0.0836799	−	0.996493i	$-0.473333\pi$
$241$	40.3337			0.167360			0.0836799	+	0.996493i	$0.473333\pi$
$242$	74.0667	−	74.0667i	0.306061	−	0.306061i
$243$		0			0
$244$			173.933i			0.712841i
$245$	7.90420	+	34.0958i	0.0322620	+	0.139167i
$246$		0			0
$247$	94.2831	−	94.2831i	0.381713	−	0.381713i
$248$	−1.55006	−	1.55006i	−0.00625022	−	0.00625022i
$249$		0			0
$250$	−18.0000	+	175.858i	−0.0720000	+	0.703432i
$251$	95.1669			0.379151			0.189575	−	0.981866i	$-0.439289\pi$
$251$	95.1669			0.379151			0.189575	+	0.981866i	$0.439289\pi$
$252$		0			0
$253$	400.958	+	400.958i	1.58481	+	1.58481i
$254$		−	128.583i		−	0.506234i
$255$		0			0
$256$	16.0000			0.0625000
$257$	−270.566	+	270.566i	−1.05279	+	1.05279i	−0.0542599	+	0.998527i	$0.517280\pi$
$257$	−270.566	+	270.566i	−1.05279	+	1.05279i	−0.998527	+	0.0542599i	$0.982720\pi$
$258$		0			0
$259$			139.283i			0.537773i
$260$	−49.4833	+	79.3498i	−0.190320	+	0.305192i
$261$		0			0
$262$	−146.633	+	146.633i	−0.559668	+	0.559668i
$263$	−183.967	−	183.967i	−0.699493	−	0.699493i	0.264808	−	0.964301i	$-0.414691\pi$
$263$	−183.967	−	183.967i	−0.699493	−	0.699493i	−0.964301	+	0.264808i	$0.914691\pi$
$264$		0			0
$265$	−106.250	−	66.2583i	−0.400942	−	0.250031i
$266$	53.3498			0.200563
$267$		0			0
$268$	83.4166	+	83.4166i	0.311256	+	0.311256i
$269$			22.4994i			0.0836411i	0.999125	+	0.0418205i	$0.0133158\pi$
$269$			22.4994i			0.0836411i	−0.999125	+	0.0418205i	$0.986684\pi$
$270$		0			0
$271$	−154.067			−0.568512			−0.284256	−	0.958748i	$-0.591747\pi$
$271$	−154.067			−0.568512			−0.284256	+	0.958748i	$0.591747\pi$
$272$	32.3832	−	32.3832i	0.119056	−	0.119056i
$273$		0			0
$274$		−	14.6997i		−	0.0536484i
$275$	313.550	−	153.633i	1.14018	−	0.558665i
$276$		0			0
$277$	336.041	−	336.041i	1.21314	−	1.21314i	0.243157	−	0.969987i	$-0.421817\pi$
$277$	336.041	−	336.041i	1.21314	−	1.21314i	0.969987	−	0.243157i	$-0.0781830\pi$
$278$	−53.8665	−	53.8665i	−0.193764	−	0.193764i
$279$		0			0
$280$	−36.4499	+	8.44994i	−0.130178	+	0.0301784i
$281$	−283.299			−1.00818			−0.504091	−	0.863650i	$-0.668172\pi$
$281$	−283.299			−1.00818			−0.504091	+	0.863650i	$0.668172\pi$
$282$		0			0
$283$	−193.321	−	193.321i	−0.683112	−	0.683112i	0.277588	−	0.960700i	$-0.410465\pi$
$283$	−193.321	−	193.321i	−0.683112	−	0.683112i	−0.960700	+	0.277588i	$0.910465\pi$
$284$		−	94.9666i		−	0.334390i
$285$		0			0
$286$	184.708			0.645833
$287$	−55.5167	+	55.5167i	−0.193438	+	0.193438i
$288$		0			0
$289$			157.916i			0.546422i
$290$	120.200	+	74.9580i	0.414484	+	0.258476i
$291$		0			0
$292$	68.7664	−	68.7664i	0.235501	−	0.235501i
$293$	346.412	+	346.412i	1.18229	+	1.18229i	0.979148	+	0.203146i	$0.0651166\pi$
$293$	346.412	+	346.412i	1.18229	+	1.18229i	0.203146	+	0.979148i	$0.434883\pi$
$294$		0			0
$295$	−67.8913	−	292.858i	−0.230140	−	0.992739i
$296$	−148.900			−0.503040
$297$		0			0
$298$	−84.6502	−	84.6502i	−0.284061	−	0.284061i
$299$			379.666i			1.26979i
$300$		0			0
$301$	−203.858			−0.677269
$302$	−21.8331	+	21.8331i	−0.0722952	+	0.0722952i
$303$		0			0
$304$			57.0334i			0.187610i
$305$	423.600	−	98.2002i	1.38885	−	0.321968i
$306$		0			0
$307$	245.512	−	245.512i	0.799715	−	0.799715i	−0.183336	−	0.983050i	$-0.558690\pi$
$307$	245.512	−	245.512i	0.799715	−	0.799715i	0.983050	+	0.183336i	$0.0586896\pi$
$308$	52.2583	+	52.2583i	0.169670	+	0.169670i
$309$		0			0
$310$	−2.89989	+	4.65017i	−0.00935448	+	0.0150005i
$311$	−325.091			−1.04531			−0.522655	−	0.852544i	$-0.675058\pi$
$311$	−325.091			−1.04531			−0.522655	+	0.852544i	$0.675058\pi$
$312$		0			0
$313$	228.012	+	228.012i	0.728472	+	0.728472i	0.970315	−	0.241843i	$-0.0777519\pi$
$313$	228.012	+	228.012i	0.728472	+	0.728472i	−0.241843	+	0.970315i	$0.577752\pi$
$314$		−	69.6663i		−	0.221867i
$315$		0			0
$316$	18.2670			0.0578068
$317$	314.800	−	314.800i	0.993059	−	0.993059i	−0.00691684	−	0.999976i	$-0.502202\pi$
$317$	314.800	−	314.800i	0.993059	−	0.993059i	0.999976	+	0.00691684i	$0.00220172\pi$
$318$		0			0
$319$		−	279.799i		−	0.877112i
$320$	−9.03337	−	38.9666i	−0.0282293	−	0.121771i
$321$		0			0
$322$	−107.417	+	107.417i	−0.333592	+	0.333592i
$323$	115.433	+	115.433i	0.357377	+	0.357377i
$324$		0			0
$325$	221.187	+	75.7126i	0.680576	+	0.232962i
$326$	−90.4499			−0.277454
$327$		0			0
$328$	−59.3498	−	59.3498i	−0.180945	−	0.180945i
$329$			239.575i			0.728191i
$330$		0			0
$331$	−65.2831			−0.197230			−0.0986149	−	0.995126i	$-0.531441\pi$
$331$	−65.2831			−0.197230			−0.0986149	+	0.995126i	$0.531441\pi$
$332$	−157.933	+	157.933i	−0.475703	+	0.475703i
$333$		0			0
$334$		−	156.075i		−	0.467292i
$335$	156.058	−	250.250i	0.465845	−	0.747014i
$336$		0			0
$337$	−18.0086	+	18.0086i	−0.0534380	+	0.0534380i	−0.733321	−	0.679883i	$-0.762031\pi$
$337$	−18.0086	+	18.0086i	−0.0534380	+	0.0534380i	0.679883	+	0.733321i	$0.262031\pi$
$338$	−81.5501	−	81.5501i	−0.241272	−	0.241272i
$339$		0			0
$340$	−97.1496	−	60.5834i	−0.285734	−	0.178187i
$341$	10.8245			0.0317435
$342$		0			0
$343$	13.0958	+	13.0958i	0.0381802	+	0.0381802i
$344$		−	217.933i		−	0.633527i
$345$		0			0
$346$	204.174			0.590099
$347$	−137.625	+	137.625i	−0.396615	+	0.396615i	−0.877037	−	0.480422i	$-0.840483\pi$
$347$	−137.625	+	137.625i	−0.396615	+	0.396615i	0.480422	+	0.877037i	$0.340483\pi$
$348$		0			0
$349$		−	496.174i		−	1.42170i	−0.703342	−	0.710852i	$-0.748310\pi$
$349$		−	496.174i		−	1.42170i	0.703342	−	0.710852i	$-0.251690\pi$
$350$	41.1582	+	84.0000i	0.117595	+	0.240000i
$351$		0			0
$352$	−55.8665	+	55.8665i	−0.158712	+	0.158712i
$353$	−92.1625	−	92.1625i	−0.261084	−	0.261084i	0.564411	−	0.825494i	$-0.309104\pi$
$353$	−92.1625	−	92.1625i	−0.261084	−	0.261084i	−0.825494	+	0.564411i	$0.809104\pi$
$354$		0			0
$355$	−231.283	+	53.6168i	−0.651502	+	0.151033i
$356$	160.000			0.449438
$357$		0			0
$358$	248.250	+	248.250i	0.693435	+	0.693435i
$359$		−	592.232i		−	1.64967i	−0.565372	−	0.824836i	$-0.691267\pi$
$359$		−	592.232i		−	1.64967i	0.565372	−	0.824836i	$-0.308733\pi$
$360$		0			0
$361$	157.700			0.436841
$362$	−17.1582	+	17.1582i	−0.0473984	+	0.0473984i
$363$		0			0
$364$			49.4833i			0.135943i
$365$	−206.299	−	128.650i	−0.565203	−	0.352466i
$366$		0			0
$367$	42.0872	−	42.0872i	0.114679	−	0.114679i	−0.647439	−	0.762118i	$-0.724160\pi$
$367$	42.0872	−	42.0872i	0.114679	−	0.114679i	0.762118	+	0.647439i	$0.224160\pi$
$368$	−114.833	−	114.833i	−0.312047	−	0.312047i
$369$		0			0
$370$	84.0667	+	362.633i	0.227207	+	0.980089i
$371$	−66.2583			−0.178594
$372$		0			0
$373$	−160.133	−	160.133i	−0.429312	−	0.429312i	0.459082	−	0.888394i	$-0.348178\pi$
$373$	−160.133	−	160.133i	−0.429312	−	0.429312i	−0.888394	+	0.459082i	$0.848178\pi$
$374$			226.142i			0.604658i
$375$		0			0
$376$	−256.116			−0.681160
$377$	132.470	−	132.470i	0.351380	−	0.351380i
$378$		0			0
$379$		−	749.066i		−	1.97643i	−0.153084	−	0.988213i	$-0.548920\pi$
$379$		−	749.066i		−	1.97643i	0.153084	−	0.988213i	$-0.451080\pi$
$380$	138.900	−	32.2002i	0.365526	−	0.0847374i
$381$		0			0
$382$	−200.916	+	200.916i	−0.525958	+	0.525958i
$383$	295.399	+	295.399i	0.771278	+	0.771278i	0.978330	−	0.207052i	$-0.0663870\pi$
$383$	295.399	+	295.399i	0.771278	+	0.771278i	−0.207052	+	0.978330i	$0.566387\pi$
$384$		0			0
$385$	97.7664	−	156.775i	0.253939	−	0.407208i
$386$	243.600			0.631087
$387$		0			0
$388$	113.091	+	113.091i	0.291473	+	0.291473i
$389$			387.116i			0.995157i	0.867419	+	0.497579i	$0.165777\pi$
$389$			387.116i			0.995157i	−0.867419	+	0.497579i	$0.834223\pi$
$390$		0			0
$391$	−464.833			−1.18883
$392$	−14.0000	+	14.0000i	−0.0357143	+	0.0357143i
$393$		0			0
$394$		−	430.250i		−	1.09200i
$395$	−10.3133	−	44.4876i	−0.0261095	−	0.112627i
$396$		0			0
$397$	−282.203	+	282.203i	−0.710840	+	0.710840i	−0.966711	−	0.255871i	$-0.917638\pi$
$397$	−282.203	+	282.203i	−0.710840	+	0.710840i	0.255871	+	0.966711i	$0.417638\pi$
$398$	93.2917	+	93.2917i	0.234401	+	0.234401i
$399$		0			0
$400$	−89.7998	+	44.0000i	−0.224499	+	0.110000i
$401$	95.6502			0.238529			0.119265	−	0.992863i	$-0.461946\pi$
$401$	95.6502			0.238529			0.119265	+	0.992863i	$0.461946\pi$
$402$		0			0
$403$	5.12486	+	5.12486i	0.0127168	+	0.0127168i
$404$		−	153.150i		−	0.379083i
$405$		0			0
$406$	74.9580			0.184626
$407$	519.907	−	519.907i	1.27741	−	1.27741i
$408$		0			0
$409$			113.875i			0.278423i	0.990263	+	0.139212i	$0.0444568\pi$
$409$			113.875i			0.278423i	−0.990263	+	0.139212i	$0.955543\pi$
$410$	−111.033	+	178.049i	−0.270813	+	0.434267i
$411$		0			0
$412$	113.091	−	113.091i	0.274494	−	0.274494i
$413$	−112.483	−	112.483i	−0.272357	−	0.272357i
$414$		0			0
$415$	473.800	+	295.466i	1.14169	+	0.711966i
$416$	−52.8999			−0.127163
$417$		0			0
$418$	−199.141	−	199.141i	−0.476414	−	0.476414i
$419$		−	445.158i		−	1.06243i	−0.847237	−	0.531215i	$-0.821736\pi$
$419$		−	445.158i		−	1.06243i	0.847237	−	0.531215i	$-0.178264\pi$
$420$		0			0
$421$	164.333			0.390339			0.195169	−	0.980770i	$-0.437474\pi$
$421$	164.333			0.390339			0.195169	+	0.980770i	$0.437474\pi$
$422$	−74.3498	+	74.3498i	−0.176184	+	0.176184i
$423$		0			0
$424$		−	70.8331i		−	0.167059i
$425$	−92.6965	+	270.804i	−0.218109	+	0.637186i
$426$		0			0
$427$	162.700	−	162.700i	0.381030	−	0.381030i
$428$	−54.7664	−	54.7664i	−0.127959	−	0.127959i
$429$		0			0
$430$	−530.758	+	123.042i	−1.23432	+	0.286144i
$431$	−466.199			−1.08167			−0.540834	−	0.841129i	$-0.681891\pi$
$431$	−466.199			−1.08167			−0.540834	+	0.841129i	$0.681891\pi$
$432$		0			0
$433$	221.274	+	221.274i	0.511026	+	0.511026i	0.914841	−	0.403814i	$-0.132316\pi$
$433$	221.274	+	221.274i	0.511026	+	0.511026i	−0.403814	+	0.914841i	$0.632316\pi$
$434$			2.89989i			0.00668177i
$435$		0			0
$436$	309.733			0.710397
$437$	409.333	−	409.333i	0.936688	−	0.936688i
$438$		0			0
$439$		−	32.5662i		−	0.0741827i	−0.999312	−	0.0370913i	$-0.988191\pi$
$439$		−	32.5662i		−	0.0741827i	0.999312	−	0.0370913i	$-0.0118092\pi$
$440$	167.600	+	104.517i	0.380908	+	0.237538i
$441$		0			0
$442$	−107.067	+	107.067i	−0.242232	+	0.242232i
$443$	−312.849	−	312.849i	−0.706206	−	0.706206i	0.259529	−	0.965735i	$-0.416433\pi$
$443$	−312.849	−	312.849i	−0.706206	−	0.706206i	−0.965735	+	0.259529i	$0.916433\pi$
$444$		0			0
$445$	−90.3337	−	389.666i	−0.202997	−	0.875655i
$446$	−225.858			−0.506408
$447$		0			0
$448$	−14.9666	−	14.9666i	−0.0334077	−	0.0334077i
$449$			276.582i			0.615996i	0.951387	+	0.307998i	$0.0996591\pi$
$449$			276.582i			0.615996i	−0.951387	+	0.307998i	$0.900341\pi$
$450$		0			0
$451$	414.459			0.918977
$452$	−198.049	+	198.049i	−0.438163	+	0.438163i
$453$		0			0
$454$			171.559i			0.377883i
$455$	120.512	−	27.9376i	0.264862	−	0.0614013i
$456$		0			0
$457$	77.4413	−	77.4413i	0.169456	−	0.169456i	−0.617284	−	0.786740i	$-0.711767\pi$
$457$	77.4413	−	77.4413i	0.169456	−	0.169456i	0.786740	+	0.617284i	$0.211767\pi$
$458$	−215.875	−	215.875i	−0.471343	−	0.471343i
$459$		0			0
$460$	−214.833	+	344.499i	−0.467029	+	0.748912i
$461$	615.600			1.33536			0.667678	−	0.744450i	$-0.267288\pi$
$461$	615.600			1.33536			0.667678	+	0.744450i	$0.267288\pi$
$462$		0			0
$463$	146.566	+	146.566i	0.316558	+	0.316558i	0.847443	−	0.530886i	$-0.178141\pi$
$463$	146.566	+	146.566i	0.316558	+	0.316558i	−0.530886	+	0.847443i	$0.678141\pi$
$464$			80.1335i			0.172701i
$465$		0			0
$466$	155.100			0.332833
$467$	95.0711	−	95.0711i	0.203578	−	0.203578i	−0.597953	−	0.801531i	$-0.704019\pi$
$467$	95.0711	−	95.0711i	0.203578	−	0.203578i	0.801531	+	0.597953i	$0.204019\pi$
$468$		0			0
$469$		−	156.058i		−	0.332747i
$470$	144.600	+	623.749i	0.307659	+	1.32713i
$471$		0			0
$472$	120.250	−	120.250i	0.254766	−	0.254766i
$473$	760.948	+	760.948i	1.60877	+	1.60877i
$474$		0			0
$475$	−156.842	−	320.099i	−0.330193	−	0.673893i
$476$	−60.5834			−0.127276
$477$		0			0
$478$	−30.4661	−	30.4661i	−0.0637366	−	0.0637366i
$479$			32.0667i			0.0669452i	0.999440	+	0.0334726i	$0.0106566\pi$
$479$			32.0667i			0.0669452i	−0.999440	+	0.0334726i	$0.989343\pi$
$480$		0			0
$481$	492.299			1.02349
$482$	40.3337	−	40.3337i	0.0836799	−	0.0836799i
$483$		0			0
$484$		−	148.133i		−	0.306061i
$485$	211.575	−	339.274i	0.436237	−	0.699535i
$486$		0			0
$487$	−449.324	+	449.324i	−0.922636	+	0.922636i	−0.997215	−	0.0745786i	$-0.976239\pi$
$487$	−449.324	+	449.324i	−0.922636	+	0.922636i	0.0745786	+	0.997215i	$0.476239\pi$
$488$	173.933	+	173.933i	0.356421	+	0.356421i
$489$		0			0
$490$	42.0000	+	26.1916i	0.0857143	+	0.0534522i
$491$	−322.216			−0.656245			−0.328123	−	0.944635i	$-0.606416\pi$
$491$	−322.216			−0.656245			−0.328123	+	0.944635i	$0.606416\pi$
$492$		0			0
$493$	162.186	+	162.186i	0.328978	+	0.328978i
$494$		−	188.566i		−	0.381713i
$495$		0			0
$496$	−3.10011			−0.00625022
$497$	−88.8331	+	88.8331i	−0.178739	+	0.178739i
$498$		0			0
$499$		−	925.648i		−	1.85501i	−0.373816	−	0.927503i	$-0.621951\pi$
$499$		−	925.648i		−	1.85501i	0.373816	−	0.927503i	$-0.378049\pi$
$500$	157.858	+	193.858i	0.315716	+	0.387716i
$501$		0			0
$502$	95.1669	−	95.1669i	0.189575	−	0.189575i
$503$	−158.029	−	158.029i	−0.314173	−	0.314173i	0.532351	−	0.846524i	$-0.321309\pi$
$503$	−158.029	−	158.029i	−0.314173	−	0.314173i	−0.846524	+	0.532351i	$0.821309\pi$
$504$		0			0
$505$	−372.983	+	86.4661i	−0.738580	+	0.171220i
$506$	801.916			1.58481
$507$		0			0
$508$	−128.583	−	128.583i	−0.253117	−	0.253117i
$509$		−	972.299i		−	1.91021i	−0.296260	−	0.955107i	$-0.595740\pi$
$509$		−	972.299i		−	1.91021i	0.296260	−	0.955107i	$-0.404260\pi$
$510$		0			0
$511$	−128.650			−0.251762
$512$	16.0000	−	16.0000i	0.0312500	−	0.0312500i
$513$		0			0
$514$			541.132i			1.05279i
$515$	−339.274	−	211.575i	−0.658785	−	0.410825i
$516$		0			0
$517$	894.270	−	894.270i	1.72973	−	1.72973i
$518$	139.283	+	139.283i	0.268886	+	0.268886i
$519$		0			0
$520$	29.8665	+	128.833i	0.0574356	+	0.247756i
$521$	178.525			0.342659			0.171329	−	0.985214i	$-0.445194\pi$
$521$	178.525			0.342659			0.171329	+	0.985214i	$0.445194\pi$
$522$		0			0
$523$	412.241	+	412.241i	0.788224	+	0.788224i	0.981203	−	0.192979i	$-0.0618149\pi$
$523$	412.241	+	412.241i	0.788224	+	0.788224i	−0.192979	+	0.981203i	$0.561815\pi$
$524$			293.266i			0.559668i
$525$		0			0
$526$	−367.933			−0.699493
$527$	−6.27447	+	6.27447i	−0.0119060	+	0.0119060i
$528$		0			0
$529$			1119.33i			2.11594i
$530$	−172.508	+	39.9914i	−0.325487	+	0.0754554i
$531$		0			0
$532$	53.3498	−	53.3498i	0.100282	−	0.100282i
$533$	196.225	+	196.225i	0.368152	+	0.368152i
$534$		0			0
$535$	−102.459	+	164.299i	−0.191511	+	0.307101i
$536$	166.833			0.311256
$537$		0			0
$538$	22.4994	+	22.4994i	0.0418205	+	0.0418205i
$539$		−	97.7664i		−	0.181385i
$540$		0			0
$541$	485.133			0.896735			0.448367	−	0.893849i	$-0.352006\pi$
$541$	485.133			0.896735			0.448367	+	0.893849i	$0.352006\pi$
$542$	−154.067	+	154.067i	−0.284256	+	0.284256i
$543$		0			0
$544$		−	64.7664i		−	0.119056i
$545$	−174.871	−	754.328i	−0.320864	−	1.38409i
$546$		0			0
$547$	92.0172	−	92.0172i	0.168222	−	0.168222i	−0.617976	−	0.786197i	$-0.712047\pi$
$547$	92.0172	−	92.0172i	0.168222	−	0.168222i	0.786197	+	0.617976i	$0.212047\pi$
$548$	−14.6997	−	14.6997i	−0.0268242	−	0.0268242i
$549$		0			0
$550$	159.917	−	467.183i	0.290758	−	0.849424i
$551$	−285.643			−0.518408
$552$		0			0
$553$	−17.0872	−	17.0872i	−0.0308991	−	0.0308991i
$554$		−	672.082i		−	1.21314i
$555$		0			0
$556$	−107.733			−0.193764
$557$	201.283	−	201.283i	0.361370	−	0.361370i	−0.502947	−	0.864317i	$-0.667751\pi$
$557$	201.283	−	201.283i	0.361370	−	0.361370i	0.864317	+	0.502947i	$0.167751\pi$
$558$		0			0
$559$			720.540i			1.28898i
$560$	−28.0000	+	44.8999i	−0.0500000	+	0.0801784i
$561$		0			0
$562$	−283.299	+	283.299i	−0.504091	+	0.504091i
$563$	200.949	+	200.949i	0.356926	+	0.356926i	0.862679	−	0.505753i	$-0.168785\pi$
$563$	200.949	+	200.949i	0.356926	+	0.356926i	−0.505753	+	0.862679i	$0.668785\pi$
$564$		0			0
$565$	594.148	+	370.517i	1.05159	+	0.655782i
$566$	−386.642			−0.683112
$567$		0			0
$568$	−94.9666	−	94.9666i	−0.167195	−	0.167195i
$569$		−	724.349i		−	1.27302i	−0.771268	−	0.636510i	$-0.780377\pi$
$569$		−	724.349i		−	1.27302i	0.771268	−	0.636510i	$-0.219623\pi$
$570$		0			0
$571$	−650.850			−1.13984			−0.569922	−	0.821699i	$-0.693026\pi$
$571$	−650.850			−1.13984			−0.569922	+	0.821699i	$0.693026\pi$
$572$	184.708	−	184.708i	0.322917	−	0.322917i
$573$		0			0
$574$			111.033i			0.193438i
$575$	960.291	+	328.708i	1.67007	+	0.571667i
$576$		0			0
$577$	−758.711	+	758.711i	−1.31492	+	1.31492i	−0.397187	+	0.917738i	$0.630013\pi$
$577$	−758.711	+	758.711i	−1.31492	+	1.31492i	−0.917738	+	0.397187i	$0.869987\pi$
$578$	157.916	+	157.916i	0.273211	+	0.273211i
$579$		0			0
$580$	195.158	−	45.2422i	0.336480	−	0.0780038i
$581$	295.466			0.508547
$582$		0			0
$583$	247.325	+	247.325i	0.424228	+	0.424228i
$584$		−	137.533i		−	0.235501i
$585$		0			0
$586$	692.825			1.18229
$587$	−422.865	+	422.865i	−0.720384	+	0.720384i	−0.968683	−	0.248299i	$-0.920128\pi$
$587$	−422.865	+	422.865i	−0.720384	+	0.720384i	0.248299	+	0.968683i	$0.420128\pi$
$588$		0			0
$589$		−	11.0506i		−	0.0187617i
$590$	−360.749	−	224.967i	−0.611439	−	0.381299i
$591$		0			0
$592$	−148.900	+	148.900i	−0.251520	+	0.251520i
$593$	633.245	+	633.245i	1.06787	+	1.06787i	0.997523	+	0.0703447i	$0.0224099\pi$
$593$	633.245	+	633.245i	1.06787	+	1.06787i	0.0703447	+	0.997523i	$0.477590\pi$
$594$		0			0
$595$	34.2045	+	147.546i	0.0574866	+	0.247976i
$596$	−169.300			−0.284061
$597$		0			0
$598$	379.666	+	379.666i	0.634893	+	0.634893i
$599$			688.733i			1.14980i	0.818222	+	0.574902i	$0.194960\pi$
$599$			688.733i			1.14980i	−0.818222	+	0.574902i	$0.805040\pi$
$600$		0			0
$601$	−651.739			−1.08443			−0.542213	−	0.840241i	$-0.682413\pi$
$601$	−651.739			−1.08443			−0.542213	+	0.840241i	$0.682413\pi$
$602$	−203.858	+	203.858i	−0.338634	+	0.338634i
$603$		0			0
$604$			43.6663i			0.0722952i
$605$	−360.766	+	83.6340i	−0.596308	+	0.138238i
$606$		0			0
$607$	203.678	−	203.678i	0.335549	−	0.335549i	−0.519140	−	0.854689i	$-0.673748\pi$
$607$	203.678	−	203.678i	0.335549	−	0.335549i	0.854689	+	0.519140i	$0.173748\pi$
$608$	57.0334	+	57.0334i	0.0938049	+	0.0938049i
$609$		0			0
$610$	325.399	−	521.800i	0.533442	−	0.855409i
$611$	846.783			1.38590
$612$		0			0
$613$	357.766	+	357.766i	0.583632	+	0.583632i	0.935899	−	0.352267i	$-0.114589\pi$
$613$	357.766	+	357.766i	0.583632	+	0.583632i	−0.352267	+	0.935899i	$0.614589\pi$
$614$		−	491.025i		−	0.799715i
$615$		0			0
$616$	104.517			0.169670
$617$	−328.174	+	328.174i	−0.531887	+	0.531887i	−0.921134	−	0.389246i	$-0.872735\pi$
$617$	−328.174	+	328.174i	−0.531887	+	0.531887i	0.389246	+	0.921134i	$0.372735\pi$
$618$		0			0
$619$		−	949.733i		−	1.53430i	−0.641466	−	0.767151i	$-0.721674\pi$
$619$		−	949.733i		−	1.53430i	0.641466	−	0.767151i	$-0.278326\pi$
$620$	1.75028	+	7.55006i	0.00282303	+	0.0121775i
$621$		0			0
$622$	−325.091	+	325.091i	−0.522655	+	0.522655i
$623$	−149.666	−	149.666i	−0.240235	−	0.240235i
$624$		0			0
$625$	383.000	−	493.899i	0.612800	−	0.790238i
$626$	456.024			0.728472
$627$		0			0
$628$	−69.6663	−	69.6663i	−0.110934	−	0.110934i
$629$			602.732i			0.958238i
$630$		0			0
$631$	−646.266			−1.02419			−0.512097	−	0.858928i	$-0.671131\pi$
$631$	−646.266			−1.02419			−0.512097	+	0.858928i	$0.671131\pi$
$632$	18.2670	−	18.2670i	0.0289034	−	0.0289034i
$633$		0			0
$634$		−	629.600i		−	0.993059i
$635$	−240.558	+	385.750i	−0.378831	+	0.607481i
$636$		0			0
$637$	46.2874	−	46.2874i	0.0726647	−	0.0726647i
$638$	−279.799	−	279.799i	−0.438556	−	0.438556i
$639$		0			0
$640$	−48.0000	−	29.9333i	−0.0750000	−	0.0467707i
$641$	−409.899			−0.639468			−0.319734	−	0.947507i	$-0.603593\pi$
$641$	−409.899			−0.639468			−0.319734	+	0.947507i	$0.603593\pi$
$642$		0			0
$643$	−125.487	−	125.487i	−0.195158	−	0.195158i	0.602763	−	0.797921i	$-0.294067\pi$
$643$	−125.487	−	125.487i	−0.195158	−	0.195158i	−0.797921	+	0.602763i	$0.794067\pi$
$644$			214.833i			0.333592i
$645$		0			0
$646$	230.865			0.357377
$647$	−694.291	+	694.291i	−1.07309	+	1.07309i	−0.0759830	+	0.997109i	$0.524209\pi$
$647$	−694.291	+	694.291i	−1.07309	+	1.07309i	−0.997109	+	0.0759830i	$0.975791\pi$
$648$		0			0
$649$			839.742i			1.29390i
$650$	296.900	−	145.475i	0.456769	−	0.223807i
$651$		0			0
$652$	−90.4499	+	90.4499i	−0.138727	+	0.138727i
$653$	−187.784	−	187.784i	−0.287571	−	0.287571i	0.548548	−	0.836119i	$-0.315181\pi$
$653$	−187.784	−	187.784i	−0.287571	−	0.287571i	−0.836119	+	0.548548i	$0.815181\pi$
$654$		0			0
$655$	714.224	−	165.574i	1.09042	−	0.252784i
$656$	−118.700			−0.180945
$657$		0			0
$658$	239.575	+	239.575i	0.364095	+	0.364095i
$659$		−	144.983i		−	0.220004i	−0.993931	−	0.110002i	$-0.964914\pi$
$659$		−	144.983i		−	0.220004i	0.993931	−	0.110002i	$-0.0350858\pi$
$660$		0			0
$661$	−433.266			−0.655470			−0.327735	−	0.944770i	$-0.606285\pi$
$661$	−433.266			−0.655470			−0.327735	+	0.944770i	$0.606285\pi$
$662$	−65.2831	+	65.2831i	−0.0986149	+	0.0986149i
$663$		0			0
$664$			315.867i			0.475703i
$665$	−160.049	−	99.8084i	−0.240676	−	0.150088i
$666$		0			0
$667$	575.124	−	575.124i	0.862254	−	0.862254i
$668$	−156.075	−	156.075i	−0.233646	−	0.233646i
$669$		0			0
$670$	−94.1916	−	406.308i	−0.140584	−	0.606430i
$671$	−1214.63			−1.81018
$672$		0			0
$673$	−783.315	−	783.315i	−1.16392	−	1.16392i	−0.983611	−	0.180305i	$-0.942291\pi$
$673$	−783.315	−	783.315i	−1.16392	−	1.16392i	−0.180305	−	0.983611i	$-0.557709\pi$
$674$			36.0172i			0.0534380i
$675$		0			0
$676$	−163.100			−0.241272
$677$	−232.380	+	232.380i	−0.343250	+	0.343250i	−0.857588	−	0.514338i	$-0.828038\pi$
$677$	−232.380	+	232.380i	−0.343250	+	0.343250i	0.514338	+	0.857588i	$0.328038\pi$
$678$		0			0
$679$		−	211.575i		−	0.311598i
$680$	−157.733	+	36.5662i	−0.231960	+	0.0537738i
$681$		0			0
$682$	10.8245	−	10.8245i	0.0158717	−	0.0158717i
$683$	−18.6997	−	18.6997i	−0.0273787	−	0.0273787i	0.693285	−	0.720664i	$-0.256163\pi$
$683$	−18.6997	−	18.6997i	−0.0273787	−	0.0273787i	−0.720664	+	0.693285i	$0.756163\pi$
$684$		0			0
$685$	−27.5006	+	44.0990i	−0.0401468	+	0.0643781i
$686$	26.1916			0.0381802
$687$		0			0
$688$	−217.933	−	217.933i	−0.316763	−	0.316763i
$689$			234.192i			0.339901i
$690$		0			0
$691$	−736.598			−1.06599			−0.532995	−	0.846119i	$-0.678933\pi$
$691$	−736.598			−1.06599			−0.532995	+	0.846119i	$0.678933\pi$
$692$	204.174	−	204.174i	0.295050	−	0.295050i
$693$		0			0
$694$			275.251i			0.396615i
$695$	60.8245	+	262.375i	0.0875173	+	0.377517i
$696$		0			0
$697$	−240.242	+	240.242i	−0.344680	+	0.344680i
$698$	−496.174	−	496.174i	−0.710852	−	0.710852i
$699$		0			0
$700$	125.158	+	42.8418i	0.178797	+	0.0612025i
$701$	−518.483			−0.739634			−0.369817	−	0.929105i	$-0.620580\pi$
$701$	−518.483			−0.739634			−0.369817	+	0.929105i	$0.620580\pi$
$702$		0			0
$703$	−530.766	−	530.766i	−0.755002	−	0.755002i
$704$			111.733i			0.158712i
$705$		0			0
$706$	−184.325			−0.261084
$707$	−143.258	+	143.258i	−0.202628	+	0.202628i
$708$		0			0
$709$			758.765i			1.07019i	0.844792	+	0.535095i	$0.179724\pi$
$709$			758.765i			1.07019i	−0.844792	+	0.535095i	$0.820276\pi$
$710$	−177.666	+	284.900i	−0.250234	+	0.401267i
$711$		0			0
$712$	160.000	−	160.000i	0.224719	−	0.224719i
$713$	22.2497	+	22.2497i	0.0312058	+	0.0312058i
$714$		0			0
$715$	−554.125	−	345.558i	−0.775000	−	0.483297i
$716$	496.499			0.693435
$717$		0			0
$718$	−592.232	−	592.232i	−0.824836	−	0.824836i
$719$		−	16.7341i		−	0.0232742i	−0.999932	−	0.0116371i	$-0.996296\pi$
$719$		−	16.7341i		−	0.0232742i	0.999932	−	0.0116371i	$-0.00370429\pi$
$720$		0			0
$721$	−211.575			−0.293446
$722$	157.700	−	157.700i	0.218421	−	0.218421i
$723$		0			0
$724$			34.3165i			0.0473984i
$725$	−220.367	−	449.748i	−0.303955	−	0.620342i
$726$		0			0
$727$	34.7836	−	34.7836i	0.0478455	−	0.0478455i	−0.682779	−	0.730625i	$-0.739229\pi$
$727$	34.7836	−	34.7836i	0.0478455	−	0.0478455i	0.730625	+	0.682779i	$0.239229\pi$
$728$	49.4833	+	49.4833i	0.0679716	+	0.0679716i
$729$		0			0
$730$	−334.949	+	77.6491i	−0.458835	+	0.106369i
$731$	−882.172			−1.20680
$732$		0			0
$733$	−754.703	−	754.703i	−1.02961	−	1.02961i	−0.999548	−	0.0300602i	$-0.990430\pi$
$733$	−754.703	−	754.703i	−1.02961	−	1.02961i	−0.0300602	−	0.999548i	$-0.509570\pi$
$734$		−	84.1744i		−	0.114679i
$735$		0			0
$736$	−229.666			−0.312047
$737$	−582.524	+	582.524i	−0.790399	+	0.790399i
$738$		0			0
$739$			303.549i			0.410756i	0.978683	+	0.205378i	$0.0658424\pi$
$739$			303.549i			0.410756i	−0.978683	+	0.205378i	$0.934158\pi$
$740$	446.700	+	278.566i	0.603648	+	0.376441i
$741$		0			0
$742$	−66.2583	+	66.2583i	−0.0892970	+	0.0892970i
$743$	−549.424	−	549.424i	−0.739467	−	0.739467i	0.233008	−	0.972475i	$-0.425143\pi$
$743$	−549.424	−	549.424i	−0.739467	−	0.739467i	−0.972475	+	0.233008i	$0.925143\pi$
$744$		0			0
$745$	95.5845	+	412.316i	0.128301	+	0.553445i
$746$	−320.267			−0.429312
$747$		0			0
$748$	226.142	+	226.142i	0.302329	+	0.302329i
$749$			102.459i			0.136794i
$750$		0			0
$751$	4.50056			0.00599275			0.00299638	−	0.999996i	$-0.499046\pi$
$751$	4.50056			0.00599275			0.00299638	+	0.999996i	$0.499046\pi$
$752$	−256.116	+	256.116i	−0.340580	+	0.340580i
$753$		0			0
$754$		−	264.941i		−	0.351380i
$755$	106.346	−	24.6534i	0.140855	−	0.0326535i
$756$		0			0
$757$	−342.532	+	342.532i	−0.452486	+	0.452486i	−0.896179	−	0.443693i	$-0.853668\pi$
$757$	−342.532	+	342.532i	−0.452486	+	0.452486i	0.443693	+	0.896179i	$0.353668\pi$
$758$	−749.066	−	749.066i	−0.988213	−	0.988213i
$759$		0			0
$760$	106.700	−	171.100i	0.140394	−	0.225132i
$761$	198.267			0.260535			0.130267	−	0.991479i	$-0.458416\pi$
$761$	198.267			0.260535			0.130267	+	0.991479i	$0.458416\pi$
$762$		0			0
$763$	−289.729	−	289.729i	−0.379723	−	0.379723i
$764$			401.832i			0.525958i
$765$		0			0
$766$	590.799			0.771278
$767$	−397.575	+	397.575i	−0.518350	+	0.518350i
$768$		0			0
$769$			423.158i			0.550271i	0.961405	+	0.275135i	$0.0887227\pi$
$769$			423.158i			0.550271i	−0.961405	+	0.275135i	$0.911277\pi$
$770$	−59.0086	−	254.541i	−0.0766346	−	0.330573i
$771$		0			0
$772$	243.600	−	243.600i	0.315543	−	0.315543i
$773$	−893.620	−	893.620i	−1.15604	−	1.15604i	−0.985319	−	0.170722i	$-0.945390\pi$
$773$	−893.620	−	893.620i	−1.15604	−	1.15604i	−0.170722	−	0.985319i	$-0.554610\pi$
$774$		0			0
$775$	17.3993	−	8.52531i	0.0224508	−	0.0110004i
$776$	226.183			0.291473
$777$		0			0
$778$	387.116	+	387.116i	0.497579	+	0.497579i
$779$		−	423.115i		−	0.543152i
$780$		0			0
$781$	663.182			0.849145
$782$	−464.833	+	464.833i	−0.594416	+	0.594416i
$783$		0			0
$784$			28.0000i			0.0357143i
$785$	−130.334	+	208.999i	−0.166030	+	0.266241i
$786$		0			0
$787$	−820.137	+	820.137i	−1.04211	+	1.04211i	−0.0430313	+	0.999074i	$0.513702\pi$
$787$	−820.137	+	820.137i	−1.04211	+	1.04211i	−0.999074	+	0.0430313i	$0.986298\pi$
$788$	−430.250	−	430.250i	−0.546002	−	0.546002i
$789$		0			0
$790$	−54.8009	−	34.1744i	−0.0693682	−	0.0432587i
$791$	370.517			0.468416
$792$		0			0
$793$	−575.066	−	575.066i	−0.725177	−	0.725177i
$794$			564.407i			0.710840i
$795$		0			0
$796$	186.583			0.234401
$797$	300.653	−	300.653i	0.377231	−	0.377231i	−0.492871	−	0.870102i	$-0.664053\pi$
$797$	300.653	−	300.653i	0.377231	−	0.377231i	0.870102	+	0.492871i	$0.164053\pi$
$798$		0			0
$799$			1036.73i			1.29754i
$800$	−45.7998	+	133.800i	−0.0572497	+	0.167250i
$801$		0			0
$802$	95.6502	−	95.6502i	0.119265	−	0.119265i
$803$	480.217	+	480.217i	0.598029	+	0.598029i
$804$		0			0
$805$	523.208	−	121.292i	0.649947	−	0.150673i
$806$	10.2497			0.0127168
$807$		0			0
$808$	−153.150	−	153.150i	−0.189542	−	0.189542i
$809$			1060.03i			1.31030i	0.755498	+	0.655150i	$0.227395\pi$
$809$			1060.03i			1.31030i	−0.755498	+	0.655150i	$0.772605\pi$
$810$		0			0
$811$	726.801			0.896179			0.448089	−	0.893989i	$-0.352105\pi$
$811$	726.801			0.896179			0.448089	+	0.893989i	$0.352105\pi$
$812$	74.9580	−	74.9580i	0.0923128	−	0.0923128i
$813$		0			0
$814$		−	1039.81i		−	1.27741i
$815$	271.350	+	169.216i	0.332945	+	0.207627i
$816$		0			0
$817$	776.842	−	776.842i	0.950847	−	0.950847i
$818$	113.875	+	113.875i	0.139212	+	0.139212i
$819$		0			0
$820$	67.0161	+	289.083i	0.0817270	+	0.352540i
$821$	−775.314			−0.944354			−0.472177	−	0.881504i	$-0.656532\pi$
$821$	−775.314			−0.944354			−0.472177	+	0.881504i	$0.656532\pi$
$822$		0			0
$823$	724.025	+	724.025i	0.879738	+	0.879738i	0.993507	−	0.113769i	$-0.0362923\pi$
$823$	724.025	+	724.025i	0.879738	+	0.879738i	−0.113769	+	0.993507i	$0.536292\pi$
$824$		−	226.183i		−	0.274494i
$825$		0			0
$826$	−224.967			−0.272357
$827$	−301.457	+	301.457i	−0.364519	+	0.364519i	−0.865474	−	0.500954i	$-0.832982\pi$
$827$	−301.457	+	301.457i	−0.364519	+	0.364519i	0.500954	+	0.865474i	$0.332982\pi$
$828$		0			0
$829$		−	126.325i		−	0.152382i	−0.997093	−	0.0761912i	$-0.975724\pi$
$829$		−	126.325i		−	0.152382i	0.997093	−	0.0761912i	$-0.0242760\pi$
$830$	769.266	−	178.334i	0.926826	−	0.214860i
$831$		0			0
$832$	−52.8999	+	52.8999i	−0.0635816	+	0.0635816i
$833$	56.6706	+	56.6706i	0.0680319	+	0.0680319i
$834$		0			0
$835$	−291.990	+	468.226i	−0.349689	+	0.560750i
$836$	−398.282			−0.476414
$837$		0			0
$838$	−445.158	−	445.158i	−0.531215	−	0.531215i
$839$		−	176.166i		−	0.209971i	−0.994474	−	0.104986i	$-0.966520\pi$
$839$		−	176.166i		−	0.209971i	0.994474	−	0.104986i	$-0.0334796\pi$
$840$		0			0
$841$	439.664			0.522787
$842$	164.333	−	164.333i	0.195169	−	0.195169i
$843$		0			0
$844$			148.700i			0.176184i
$845$	92.0840	+	397.216i	0.108975	+	0.470079i
$846$		0			0
$847$	−138.566	+	138.566i	−0.163596	+	0.163596i
$848$	−70.8331	−	70.8331i	−0.0835297	−	0.0835297i
$849$		0			0
$850$	178.108	+	363.501i	0.209538	+	0.427648i
$851$	2137.33			2.51155
$852$		0			0
$853$	−221.234	−	221.234i	−0.259359	−	0.259359i	0.565434	−	0.824793i	$-0.308709\pi$
$853$	−221.234	−	221.234i	−0.259359	−	0.259359i	−0.824793	+	0.565434i	$0.808709\pi$
$854$		−	325.399i		−	0.381030i
$855$		0			0
$856$	−109.533			−0.127959
$857$	777.533	−	777.533i	0.907273	−	0.907273i	−0.0887786	−	0.996051i	$-0.528296\pi$
$857$	777.533	−	777.533i	0.907273	−	0.907273i	0.996051	+	0.0887786i	$0.0282963\pi$
$858$		0			0
$859$			62.7987i			0.0731067i	0.999332	+	0.0365534i	$0.0116379\pi$
$859$			62.7987i			0.0731067i	−0.999332	+	0.0365534i	$0.988362\pi$
$860$	−407.716	+	653.800i	−0.474088	+	0.760232i
$861$		0			0
$862$	−466.199	+	466.199i	−0.540834	+	0.540834i
$863$	681.874	+	681.874i	0.790121	+	0.790121i	0.981513	−	0.191393i	$-0.0613005\pi$
$863$	681.874	+	681.874i	0.790121	+	0.790121i	−0.191393	+	0.981513i	$0.561300\pi$
$864$		0			0
$865$	−612.523	−	381.975i	−0.708119	−	0.441590i
$866$	442.549			0.511026
$867$		0			0
$868$	2.89989	+	2.89989i	0.00334089	+	0.00334089i
$869$			127.564i			0.146794i
$870$		0			0
$871$	−551.591			−0.633285
$872$	309.733	−	309.733i	0.355198	−	0.355198i
$873$		0			0
$874$		−	818.665i		−	0.936688i
$875$	33.6749	−	329.000i	0.0384856	−	0.376000i
$876$		0			0
$877$	−1019.15	+	1019.15i	−1.16208	+	1.16208i	−0.178066	+	0.984018i	$0.556984\pi$
$877$	−1019.15	+	1019.15i	−1.16208	+	1.16208i	−0.984018	+	0.178066i	$0.943016\pi$
$878$	−32.5662	−	32.5662i	−0.0370913	−	0.0370913i
$879$		0			0
$880$	272.116	−	63.0829i	0.309223	−	0.0716851i
$881$	77.5673			0.0880446			0.0440223	−	0.999031i	$-0.485983\pi$
$881$	77.5673			0.0880446			0.0440223	+	0.999031i	$0.485983\pi$
$882$		0			0
$883$	954.566	+	954.566i	1.08105	+	1.08105i	0.996412	+	0.0846371i	$0.0269731\pi$
$883$	954.566	+	954.566i	1.08105	+	1.08105i	0.0846371	+	0.996412i	$0.473027\pi$
$884$			214.133i			0.242232i
$885$		0			0
$886$	−625.699			−0.706206
$887$	−307.150	+	307.150i	−0.346279	+	0.346279i	−0.858722	−	0.512442i	$-0.828741\pi$
$887$	−307.150	+	307.150i	−0.346279	+	0.346279i	0.512442	+	0.858722i	$0.328741\pi$
$888$		0			0
$889$			240.558i			0.270593i
$890$	−480.000	−	299.333i	−0.539326	−	0.336329i
$891$		0			0
$892$	−225.858	+	225.858i	−0.253204	+	0.253204i
$893$	−912.948	−	912.948i	−1.02234	−	1.02234i
$894$		0			0
$895$	−280.316	−	1209.18i	−0.313203	−	1.35104i
$896$	−29.9333			−0.0334077
$897$		0			0
$898$	276.582	+	276.582i	0.307998	+	0.307998i
$899$		−	15.5264i		−	0.0172708i
$900$		0			0
$901$	−286.726			−0.318230
$902$	414.459	−	414.459i	0.459488	−	0.459488i
$903$		0			0
$904$			396.099i			0.438163i
$905$	83.5748	−	19.3746i	0.0923479	−	0.0214084i
$906$		0			0
$907$	−608.192	+	608.192i	−0.670553	+	0.670553i	−0.957844	−	0.287290i	$-0.907246\pi$
$907$	−608.192	+	608.192i	−0.670553	+	0.670553i	0.287290	+	0.957844i	$0.407246\pi$
$908$	171.559	+	171.559i	0.188941	+	0.188941i
$909$		0			0
$910$	92.5748	−	148.450i	0.101731	−	0.163132i
$911$	−1336.46			−1.46703			−0.733515	−	0.679673i	$-0.762122\pi$
$911$	−1336.46			−1.46703			−0.733515	+	0.679673i	$0.762122\pi$
$912$		0			0
$913$	−1102.90	−	1102.90i	−1.20799	−	1.20799i
$914$		−	154.883i		−	0.169456i
$915$		0			0
$916$	−431.750			−0.471343
$917$	274.325	−	274.325i	0.299155	−	0.299155i
$918$		0			0
$919$			358.632i			0.390241i	0.980779	+	0.195121i	$0.0625099\pi$
$919$			358.632i			0.390241i	−0.980779	+	0.195121i	$0.937490\pi$
$920$	129.666	+	559.333i	0.140942	+	0.607970i
$921$		0			0
$922$	615.600	−	615.600i	0.667678	−	0.667678i
$923$	313.983	+	313.983i	0.340176	+	0.340176i
$924$		0			0
$925$	426.224	−	1245.17i	0.460783	−	1.34613i
$926$	293.132			0.316558
$927$		0			0
$928$	80.1335	+	80.1335i	0.0863507	+	0.0863507i
$929$			399.023i			0.429518i	0.976667	+	0.214759i	$0.0688967\pi$
$929$			399.023i			0.429518i	−0.976667	+	0.214759i	$0.931103\pi$
$930$		0			0
$931$	−99.8084			−0.107206
$932$	155.100	−	155.100i	0.166416	−	0.166416i
$933$		0			0
$934$		−	190.142i		−	0.203578i
$935$	423.073	−	678.426i	0.452485	−	0.725590i
$936$		0			0
$937$	149.237	−	149.237i	0.159271	−	0.159271i	−0.622973	−	0.782244i	$-0.714075\pi$
$937$	149.237	−	149.237i	0.159271	−	0.159271i	0.782244	+	0.622973i	$0.214075\pi$
$938$	−156.058	−	156.058i	−0.166373	−	0.166373i
$939$		0			0
$940$	768.349	+	479.150i	0.817392	+	0.509734i
$941$	719.397			0.764503			0.382251	−	0.924058i	$-0.375149\pi$
$941$	719.397			0.764503			0.382251	+	0.924058i	$0.375149\pi$
$942$		0			0
$943$	851.916	+	851.916i	0.903410	+	0.903410i
$944$		−	240.499i		−	0.254766i
$945$		0			0
$946$	1521.90			1.60877
$947$	35.9408	−	35.9408i	0.0379522	−	0.0379522i	−0.687876	−	0.725828i	$-0.741457\pi$
$947$	35.9408	−	35.9408i	0.0379522	−	0.0379522i	0.725828	+	0.687876i	$0.241457\pi$
$948$		0			0
$949$			454.717i			0.479154i
$950$	−476.941	−	163.257i	−0.502043	−	0.171850i
$951$		0			0
$952$	−60.5834	+	60.5834i	−0.0636381	+	0.0636381i
$953$	−178.057	−	178.057i	−0.186838	−	0.186838i	0.607489	−	0.794328i	$-0.292177\pi$
$953$	−178.057	−	178.057i	−0.186838	−	0.186838i	−0.794328	+	0.607489i	$0.792177\pi$
$954$		0			0
$955$	978.628	−	226.869i	1.02474	−	0.237559i
$956$	−60.9321			−0.0637366
$957$		0			0
$958$	32.0667	+	32.0667i	0.0334726	+	0.0334726i
$959$			27.5006i			0.0286763i
$960$		0			0
$961$	−960.399			−0.999375
$962$	492.299	−	492.299i	0.511746	−	0.511746i
$963$		0			0
$964$		−	80.6674i		−	0.0836799i
$965$	−730.799	−	455.733i	−0.757304	−	0.472262i
$966$		0			0
$967$	−288.417	+	288.417i	−0.298259	+	0.298259i	−0.840332	−	0.542073i	$-0.817640\pi$
$967$	−288.417	+	288.417i	−0.298259	+	0.298259i	0.542073	+	0.840332i	$0.317640\pi$
$968$	−148.133	−	148.133i	−0.153030	−	0.153030i
$969$		0			0
$970$	−127.700	−	550.849i	−0.131649	−	0.567886i
$971$	212.474			0.218819			0.109410	−	0.993997i	$-0.465104\pi$
$971$	212.474			0.218819			0.109410	+	0.993997i	$0.465104\pi$
$972$		0			0
$973$	100.775	+	100.775i	0.103571	+	0.103571i
$974$			898.648i			0.922636i
$975$		0			0
$976$	347.867			0.356421
$977$	−53.5662	+	53.5662i	−0.0548272	+	0.0548272i	−0.733989	−	0.679162i	$-0.762344\pi$
$977$	−53.5662	+	53.5662i	−0.0548272	+	0.0548272i	0.679162	+	0.733989i	$0.262344\pi$
$978$		0			0
$979$			1117.33i			1.14130i
$980$	68.1916	−	15.8084i	0.0695833	−	0.0161310i
$981$		0			0
$982$	−322.216	+	322.216i	−0.328123	+	0.328123i
$983$	−612.070	−	612.070i	−0.622655	−	0.622655i	0.323554	−	0.946210i	$-0.395122\pi$
$983$	−612.070	−	612.070i	−0.622655	−	0.622655i	−0.946210	+	0.323554i	$0.895122\pi$
$984$		0			0
$985$	−804.924	+	1290.75i	−0.817181	+	1.31041i
$986$	324.372			0.328978
$987$		0			0
$988$	−188.566	−	188.566i	−0.190856	−	0.190856i
$989$			3128.25i			3.16304i
$990$		0			0
$991$	−699.666			−0.706020			−0.353010	−	0.935619i	$-0.614842\pi$
$991$	−699.666			−0.706020			−0.353010	+	0.935619i	$0.614842\pi$
$992$	−3.10011	+	3.10011i	−0.00312511	+	0.00312511i
$993$		0			0
$994$			177.666i			0.178739i
$995$	−105.342	−	454.408i	−0.105872	−	0.456691i
$996$		0			0
$997$	682.529	−	682.529i	0.684582	−	0.684582i	−0.276447	−	0.961029i	$-0.589157\pi$
$997$	682.529	−	682.529i	0.684582	−	0.684582i	0.961029	+	0.276447i	$0.0891570\pi$
$998$	−925.648	−	925.648i	−0.927503	−	0.927503i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	630.3.o.a.253.1		4
3.2	odd	2		70.3.f.a.43.2	✓	4
5.2	odd	4	inner	630.3.o.a.127.1		4
12.11	even	2		560.3.bh.b.113.1		4
15.2	even	4		70.3.f.a.57.2	yes	4
15.8	even	4		350.3.f.b.57.1		4
15.14	odd	2		350.3.f.b.43.1		4
21.20	even	2		490.3.f.d.393.1		4
60.47	odd	4		560.3.bh.b.337.1		4
105.62	odd	4		490.3.f.d.197.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
70.3.f.a.43.2	✓	4	3.2	odd	2
70.3.f.a.57.2	yes	4	15.2	even	4
350.3.f.b.43.1		4	15.14	odd	2
350.3.f.b.57.1		4	15.8	even	4
490.3.f.d.197.1		4	105.62	odd	4
490.3.f.d.393.1		4	21.20	even	2
560.3.bh.b.113.1		4	12.11	even	2
560.3.bh.b.337.1		4	60.47	odd	4
630.3.o.a.127.1		4	5.2	odd	4	inner
630.3.o.a.253.1		4	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(1.00000 - 1.00000i) q^{2} -2.00000i q^{4} +(-4.87083 + 1.12917i) q^{5} +(-1.87083 + 1.87083i) q^{7} +(-2.00000 - 2.00000i) q^{8} +O(q^{10})\)	\(q+(1.00000 - 1.00000i) q^{2} -2.00000i q^{4} +(-4.87083 + 1.12917i) q^{5} +(-1.87083 + 1.87083i) q^{7} +(-2.00000 - 2.00000i) q^{8} +(-3.74166 + 6.00000i) q^{10} +13.9666 q^{11} +(6.61249 + 6.61249i) q^{13} +3.74166i q^{14} -4.00000 q^{16} +(-8.09580 + 8.09580i) q^{17} -14.2583i q^{19} +(2.25834 + 9.74166i) q^{20} +(13.9666 - 13.9666i) q^{22} +(28.7083 + 28.7083i) q^{23} +(22.4499 - 11.0000i) q^{25} +13.2250 q^{26} +(3.74166 + 3.74166i) q^{28} -20.0334i q^{29} +0.775028 q^{31} +(-4.00000 + 4.00000i) q^{32} +16.1916i q^{34} +(7.00000 - 11.2250i) q^{35} +(37.2250 - 37.2250i) q^{37} +(-14.2583 - 14.2583i) q^{38} +(12.0000 + 7.48331i) q^{40} +29.6749 q^{41} +(54.4833 + 54.4833i) q^{43} -27.9333i q^{44} +57.4166 q^{46} +(64.0291 - 64.0291i) q^{47} -7.00000i q^{49} +(11.4499 - 33.4499i) q^{50} +(13.2250 - 13.2250i) q^{52} +(17.7083 + 17.7083i) q^{53} +(-68.0291 + 15.7707i) q^{55} +7.48331 q^{56} +(-20.0334 - 20.0334i) q^{58} +60.1249i q^{59} -86.9666 q^{61} +(0.775028 - 0.775028i) q^{62} +8.00000i q^{64} +(-39.6749 - 24.7417i) q^{65} +(-41.7083 + 41.7083i) q^{67} +(16.1916 + 16.1916i) q^{68} +(-4.22497 - 18.2250i) q^{70} +47.4833 q^{71} +(34.3832 + 34.3832i) q^{73} -74.4499i q^{74} -28.5167 q^{76} +(-26.1292 + 26.1292i) q^{77} +9.13348i q^{79} +(19.4833 - 4.51669i) q^{80} +(29.6749 - 29.6749i) q^{82} +(-78.9666 - 78.9666i) q^{83} +(30.2917 - 48.5748i) q^{85} +108.967 q^{86} +(-27.9333 - 27.9333i) q^{88} +80.0000i q^{89} -24.7417 q^{91} +(57.4166 - 57.4166i) q^{92} -128.058i q^{94} +(16.1001 + 69.4499i) q^{95} +(-56.5457 + 56.5457i) q^{97} +(-7.00000 - 7.00000i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{2} - 12 q^{5} - 8 q^{8}+O(q^{10}) \) 4 * q + 4 * q^2 - 12 * q^5 - 8 * q^8	\( 4 q + 4 q^{2} - 12 q^{5} - 8 q^{8} - 4 q^{11} + 4 q^{13} - 16 q^{16} + 20 q^{17} + 24 q^{20} - 4 q^{22} + 40 q^{23} + 8 q^{26} + 48 q^{31} - 16 q^{32} + 28 q^{35} + 104 q^{37} - 72 q^{38} + 48 q^{40} - 16 q^{41} + 188 q^{43} + 80 q^{46} + 84 q^{47} - 44 q^{50} + 8 q^{52} - 4 q^{53} - 100 q^{55} - 140 q^{58} - 288 q^{61} + 48 q^{62} - 24 q^{65} - 92 q^{67} - 40 q^{68} + 28 q^{70} + 160 q^{71} - 72 q^{73} - 144 q^{76} - 112 q^{77} + 48 q^{80} - 16 q^{82} - 256 q^{83} + 196 q^{85} + 376 q^{86} + 8 q^{88} - 84 q^{91} + 80 q^{92} + 244 q^{95} - 84 q^{97} - 28 q^{98}+O(q^{100}) \) 4 * q + 4 * q^2 - 12 * q^5 - 8 * q^8 - 4 * q^11 + 4 * q^13 - 16 * q^16 + 20 * q^17 + 24 * q^20 - 4 * q^22 + 40 * q^23 + 8 * q^26 + 48 * q^31 - 16 * q^32 + 28 * q^35 + 104 * q^37 - 72 * q^38 + 48 * q^40 - 16 * q^41 + 188 * q^43 + 80 * q^46 + 84 * q^47 - 44 * q^50 + 8 * q^52 - 4 * q^53 - 100 * q^55 - 140 * q^58 - 288 * q^61 + 48 * q^62 - 24 * q^65 - 92 * q^67 - 40 * q^68 + 28 * q^70 + 160 * q^71 - 72 * q^73 - 144 * q^76 - 112 * q^77 + 48 * q^80 - 16 * q^82 - 256 * q^83 + 196 * q^85 + 376 * q^86 + 8 * q^88 - 84 * q^91 + 80 * q^92 + 244 * q^95 - 84 * q^97 - 28 * q^98

Introduction

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