LMFDB - Embedded newform 245.4.f.b.48.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [245,4,Mod(48,245)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(245, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([3, 2]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("245.48");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 245 = 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	245.f (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:	$14.4554679514$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$36$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			48.4
Character	$\chi$	$=$	245.48
Dual form			245.4.f.b.97.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-3.43814 + 3.43814i) q^{2} +(1.63468 - 1.63468i) q^{3} -15.6416i q^{4} +(-10.9126 + 2.43206i) q^{5} +11.2405i q^{6} +(26.2728 + 26.2728i) q^{8} +21.6556i q^{9} +O(q^{10})$	\(q+(-3.43814 + 3.43814i) q^{2} +(1.63468 - 1.63468i) q^{3} -15.6416i q^{4} +(-10.9126 + 2.43206i) q^{5} +11.2405i q^{6} +(26.2728 + 26.2728i) q^{8} +21.6556i q^{9} +(29.1573 - 45.8808i) q^{10} -36.5311 q^{11} +(-25.5690 - 25.5690i) q^{12} +(-43.0940 + 43.0940i) q^{13} +(-13.8630 + 21.8143i) q^{15} -55.5261 q^{16} +(7.69554 + 7.69554i) q^{17} +(-74.4550 - 74.4550i) q^{18} +122.759 q^{19} +(38.0412 + 170.690i) q^{20} +(125.599 - 125.599i) q^{22} +(-126.197 - 126.197i) q^{23} +85.8953 q^{24} +(113.170 - 53.0802i) q^{25} -296.326i q^{26} +(79.5366 + 79.5366i) q^{27} -230.609i q^{29} +(-27.3376 - 122.664i) q^{30} -137.109i q^{31} +(-19.2757 + 19.2757i) q^{32} +(-59.7168 + 59.7168i) q^{33} -52.9166 q^{34} +338.728 q^{36} +(163.957 - 163.957i) q^{37} +(-422.062 + 422.062i) q^{38} +140.890i q^{39} +(-350.601 - 222.808i) q^{40} -227.230i q^{41} +(151.453 + 151.453i) q^{43} +571.403i q^{44} +(-52.6677 - 236.319i) q^{45} +867.763 q^{46} +(237.880 + 237.880i) q^{47} +(-90.7677 + 90.7677i) q^{48} +(-206.598 + 571.592i) q^{50} +25.1596 q^{51} +(674.057 + 674.057i) q^{52} +(-136.497 - 136.497i) q^{53} -546.915 q^{54} +(398.649 - 88.8457i) q^{55} +(200.672 - 200.672i) q^{57} +(792.864 + 792.864i) q^{58} +7.98594 q^{59} +(341.210 + 216.840i) q^{60} +156.165i q^{61} +(471.400 + 471.400i) q^{62} -576.754i q^{64} +(365.461 - 575.075i) q^{65} -410.629i q^{66} +(390.636 - 390.636i) q^{67} +(120.370 - 120.370i) q^{68} -412.584 q^{69} +271.564 q^{71} +(-568.953 + 568.953i) q^{72} +(-630.861 + 630.861i) q^{73} +1127.41i q^{74} +(98.2282 - 271.767i) q^{75} -1920.14i q^{76} +(-484.399 - 484.399i) q^{78} -898.356i q^{79} +(605.935 - 135.043i) q^{80} -324.667 q^{81} +(781.249 + 781.249i) q^{82} +(-614.022 + 614.022i) q^{83} +(-102.694 - 65.2624i) q^{85} -1041.43 q^{86} +(-376.972 - 376.972i) q^{87} +(-959.772 - 959.772i) q^{88} +1074.32 q^{89} +(993.577 + 631.419i) q^{90} +(-1973.92 + 1973.92i) q^{92} +(-224.130 - 224.130i) q^{93} -1635.73 q^{94} +(-1339.62 + 298.557i) q^{95} +63.0193i q^{96} +(174.230 + 174.230i) q^{97} -791.103i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q+O(q^{10}) $ 72 * q	$ 72 q - 32 q^{11} - 1152 q^{16} - 64 q^{18} + 576 q^{22} + 768 q^{23} + 288 q^{25} - 2512 q^{30} + 1840 q^{32} - 4640 q^{36} + 864 q^{37} + 608 q^{43} - 3552 q^{46} - 2480 q^{50} + 1056 q^{51} - 1384 q^{53} + 7872 q^{57} + 5296 q^{58} + 9104 q^{60} + 736 q^{65} + 1856 q^{67} - 6816 q^{71} - 8528 q^{72} - 5408 q^{78} - 12616 q^{81} + 5600 q^{85} + 8672 q^{86} - 10080 q^{88} + 10624 q^{92} + 416 q^{93} + 5888 q^{95}+O(q^{100}) $ 72 * q - 32 * q^11 - 1152 * q^16 - 64 * q^18 + 576 * q^22 + 768 * q^23 + 288 * q^25 - 2512 * q^30 + 1840 * q^32 - 4640 * q^36 + 864 * q^37 + 608 * q^43 - 3552 * q^46 - 2480 * q^50 + 1056 * q^51 - 1384 * q^53 + 7872 * q^57 + 5296 * q^58 + 9104 * q^60 + 736 * q^65 + 1856 * q^67 - 6816 * q^71 - 8528 * q^72 - 5408 * q^78 - 12616 * q^81 + 5600 * q^85 + 8672 * q^86 - 10080 * q^88 + 10624 * q^92 + 416 * q^93 + 5888 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/245\mathbb{Z}\right)^\times$.

$n$	$101$	$197$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$	−3.43814	+	3.43814i	−1.21556	+	1.21556i	−0.246396	+	0.969169i	$0.579246\pi$
$2$	−3.43814	+	3.43814i	−1.21556	+	1.21556i	−0.969169	+	0.246396i	$0.920754\pi$
$3$	1.63468	−	1.63468i	0.314595	−	0.314595i	−0.532092	−	0.846687i	$-0.678594\pi$
$3$	1.63468	−	1.63468i	0.314595	−	0.314595i	0.846687	+	0.532092i	$0.178594\pi$
$4$		−	15.6416i		−	1.95520i
$5$	−10.9126	+	2.43206i	−0.976054	+	0.217530i
$5$	−10.9126	+	2.43206i	−0.976054	+	0.217530i
$6$			11.2405i			0.764822i
$7$		0			0
$7$		0			0
$8$	26.2728	+	26.2728i	1.16110	+	1.16110i
$9$			21.6556i			0.802060i
$10$	29.1573	−	45.8808i	0.922035	−	1.45088i
$11$	−36.5311			−1.00132			−0.500661	−	0.865644i	$-0.666910\pi$
$11$	−36.5311			−1.00132			−0.500661	+	0.865644i	$0.666910\pi$
$12$	−25.5690	−	25.5690i	−0.615095	−	0.615095i
$13$	−43.0940	+	43.0940i	−0.919394	+	0.919394i	−0.996985	−	0.0775917i	$-0.975277\pi$
$13$	−43.0940	+	43.0940i	−0.919394	+	0.919394i	0.0775917	+	0.996985i	$0.475277\pi$
$14$		0			0
$15$	−13.8630	+	21.8143i	−0.238628	+	0.375496i
$16$	−55.5261			−0.867596
$17$	7.69554	+	7.69554i	0.109791	+	0.109791i	0.759868	−	0.650077i	$-0.225264\pi$
$17$	7.69554	+	7.69554i	0.109791	+	0.109791i	−0.650077	+	0.759868i	$0.725264\pi$
$18$	−74.4550	−	74.4550i	−0.974956	−	0.974956i
$19$	122.759			1.48225			0.741126	−	0.671366i	$-0.234292\pi$
$19$	122.759			1.48225			0.741126	+	0.671366i	$0.234292\pi$
$20$	38.0412	+	170.690i	0.425314	+	1.90838i
$21$		0			0
$22$	125.599	−	125.599i	1.21717	−	1.21717i
$23$	−126.197	−	126.197i	−1.14408	−	1.14408i	−0.987696	−	0.156384i	$-0.950016\pi$
$23$	−126.197	−	126.197i	−1.14408	−	1.14408i	−0.156384	−	0.987696i	$-0.549984\pi$
$24$	85.8953			0.730555
$25$	113.170	−	53.0802i	0.905362	−	0.424642i
$26$		−	296.326i		−	2.23517i
$27$	79.5366	+	79.5366i	0.566919	+	0.566919i
$28$		0			0
$29$		−	230.609i		−	1.47665i	−0.674443	−	0.738326i	$-0.735616\pi$
$29$		−	230.609i		−	1.47665i	0.674443	−	0.738326i	$-0.264384\pi$
$30$	−27.3376	−	122.664i	−0.166372	−	0.746507i
$31$		−	137.109i		−	0.794372i	−0.917738	−	0.397186i	$-0.869987\pi$
$31$		−	137.109i		−	0.794372i	0.917738	−	0.397186i	$-0.130013\pi$
$32$	−19.2757	+	19.2757i	−0.106484	+	0.106484i
$33$	−59.7168	+	59.7168i	−0.315011	+	0.315011i
$34$	−52.9166			−0.266915
$35$		0			0
$36$	338.728			1.56818
$37$	163.957	−	163.957i	0.728495	−	0.728495i	−0.241825	−	0.970320i	$-0.577746\pi$
$37$	163.957	−	163.957i	0.728495	−	0.728495i	0.970320	+	0.241825i	$0.0777460\pi$
$38$	−422.062	+	422.062i	−1.80177	+	1.80177i
$39$			140.890i			0.578474i
$40$	−350.601	−	222.808i	−1.38587	−	0.880724i
$41$		−	227.230i		−	0.865547i	−0.901503	−	0.432774i	$-0.857535\pi$
$41$		−	227.230i		−	0.865547i	0.901503	−	0.432774i	$-0.142465\pi$
$42$		0			0
$43$	151.453	+	151.453i	0.537124	+	0.537124i	0.922683	−	0.385559i	$-0.125992\pi$
$43$	151.453	+	151.453i	0.537124	+	0.537124i	−0.385559	+	0.922683i	$0.625992\pi$
$44$			571.403i			1.95778i
$45$	−52.6677	−	236.319i	−0.174472	−	0.782853i
$46$	867.763			2.78141
$47$	237.880	+	237.880i	0.738262	+	0.738262i	0.972242	−	0.233979i	$-0.0751748\pi$
$47$	237.880	+	237.880i	0.738262	+	0.738262i	−0.233979	+	0.972242i	$0.575175\pi$
$48$	−90.7677	+	90.7677i	−0.272941	+	0.272941i
$49$		0			0
$50$	−206.598	+	571.592i	−0.584346	+	1.61671i
$51$	25.1596			0.0690792
$52$	674.057	+	674.057i	1.79759	+	1.79759i
$53$	−136.497	−	136.497i	−0.353759	−	0.353759i	0.507747	−	0.861506i	$-0.330478\pi$
$53$	−136.497	−	136.497i	−0.353759	−	0.353759i	−0.861506	+	0.507747i	$0.830478\pi$
$54$	−546.915			−1.37825
$55$	398.649	−	88.8457i	0.977343	−	0.217817i
$56$		0			0
$57$	200.672	−	200.672i	0.466310	−	0.466310i
$58$	792.864	+	792.864i	1.79497	+	1.79497i
$59$	7.98594			0.0176217			0.00881086	−	0.999961i	$-0.497195\pi$
$59$	7.98594			0.0176217			0.00881086	+	0.999961i	$0.497195\pi$
$60$	341.210	+	216.840i	0.734167	+	0.466564i
$61$			156.165i			0.327785i	0.986478	+	0.163893i	$0.0524051\pi$
$61$			156.165i			0.327785i	−0.986478	+	0.163893i	$0.947595\pi$
$62$	471.400	+	471.400i	0.965611	+	0.965611i
$63$		0			0
$64$		−	576.754i		−	1.12647i
$65$	365.461	−	575.075i	0.697382	−	1.09737i
$66$		−	410.629i		−	0.765832i
$67$	390.636	−	390.636i	0.712295	−	0.712295i	−0.254720	−	0.967015i	$-0.581983\pi$
$67$	390.636	−	390.636i	0.712295	−	0.712295i	0.967015	+	0.254720i	$0.0819833\pi$
$68$	120.370	−	120.370i	0.214662	−	0.214662i
$69$	−412.584			−0.719844
$70$		0			0
$71$	271.564			0.453925			0.226963	−	0.973903i	$-0.427120\pi$
$71$	271.564			0.453925			0.226963	+	0.973903i	$0.427120\pi$
$72$	−568.953	+	568.953i	−0.931274	+	0.931274i
$73$	−630.861	+	630.861i	−1.01146	+	1.01146i	−0.0115278	+	0.999934i	$0.503669\pi$
$73$	−630.861	+	630.861i	−1.01146	+	1.01146i	−0.999934	+	0.0115278i	$0.996331\pi$
$74$			1127.41i			1.77107i
$75$	98.2282	−	271.767i	0.151232	−	0.418413i
$76$		−	1920.14i		−	2.89809i
$77$		0			0
$78$	−484.399	−	484.399i	−0.703172	−	0.703172i
$79$		−	898.356i		−	1.27940i	−0.768623	−	0.639702i	$-0.779058\pi$
$79$		−	898.356i		−	1.27940i	0.768623	−	0.639702i	$-0.220942\pi$
$80$	605.935	−	135.043i	0.846820	−	0.188728i
$81$	−324.667			−0.445360
$82$	781.249	+	781.249i	1.05213	+	1.05213i
$83$	−614.022	+	614.022i	−0.812021	+	0.812021i	−0.984937	−	0.172916i	$-0.944681\pi$
$83$	−614.022	+	614.022i	−0.812021	+	0.812021i	0.172916	+	0.984937i	$0.444681\pi$
$84$		0			0
$85$	−102.694	−	65.2624i	−0.131044	−	0.0832789i
$86$	−1041.43			−1.30582
$87$	−376.972	−	376.972i	−0.464548	−	0.464548i
$88$	−959.772	−	959.772i	−1.16264	−	1.16264i
$89$	1074.32			1.27952			0.639762	−	0.768573i	$-0.279033\pi$
$89$	1074.32			1.27952			0.639762	+	0.768573i	$0.279033\pi$
$90$	993.577	+	631.419i	1.16369	+	0.739527i
$91$		0			0
$92$	−1973.92	+	1973.92i	−2.23690	+	2.23690i
$93$	−224.130	−	224.130i	−0.249906	−	0.249906i
$94$	−1635.73			−1.79481
$95$	−1339.62	+	298.557i	−1.44676	+	0.322434i
$96$			63.0193i			0.0669988i
$97$	174.230	+	174.230i	0.182375	+	0.182375i	0.792390	−	0.610015i	$-0.208837\pi$
$97$	174.230	+	174.230i	0.182375	+	0.182375i	−0.610015	+	0.792390i	$0.708837\pi$
$98$		0			0
$99$		−	791.103i		−	0.803119i
$100$	−830.258	−	1770.16i	−0.830258	−	1.77016i
$101$		−	1650.93i		−	1.62647i	−0.581935	−	0.813236i	$-0.697704\pi$
$101$		−	1650.93i		−	1.62647i	0.581935	−	0.813236i	$-0.302296\pi$
$102$	−86.5020	+	86.5020i	−0.0839703	+	0.0839703i
$103$	463.758	−	463.758i	0.443645	−	0.443645i	−0.449590	−	0.893235i	$-0.648430\pi$
$103$	463.758	−	463.758i	0.443645	−	0.443645i	0.893235	+	0.449590i	$0.148430\pi$
$104$	−2264.39			−2.13502
$105$		0			0
$106$	938.587			0.860035
$107$	570.191	−	570.191i	0.515163	−	0.515163i	−0.400941	−	0.916104i	$-0.631317\pi$
$107$	570.191	−	570.191i	0.515163	−	0.515163i	0.916104	+	0.400941i	$0.131317\pi$
$108$	1244.08	−	1244.08i	1.10844	−	1.10844i
$109$		−	1811.53i		−	1.59186i	−0.605388	−	0.795930i	$-0.706982\pi$
$109$		−	1811.53i		−	1.59186i	0.605388	−	0.795930i	$-0.293018\pi$
$110$	−1065.15	+	1676.07i	−0.923253	+	1.45280i
$111$		−	536.035i		−	0.458362i
$112$		0			0
$113$	−253.074	−	253.074i	−0.210683	−	0.210683i	0.593875	−	0.804558i	$-0.297598\pi$
$113$	−253.074	−	253.074i	−0.210683	−	0.210683i	−0.804558	+	0.593875i	$0.797598\pi$
$114$			1379.87i			1.13366i
$115$	1684.05	+	1070.22i	1.36556	+	0.867812i
$116$	−3607.08			−2.88715
$117$	−933.226	−	933.226i	−0.737409	−	0.737409i
$118$	−27.4568	+	27.4568i	−0.0214203	+	0.0214203i
$119$		0			0
$120$	−937.342	+	208.902i	−0.713060	+	0.158917i
$121$	3.51929			0.00264409
$122$	−536.917	−	536.917i	−0.398444	−	0.398444i
$123$	−371.450	−	371.450i	−0.272297	−	0.272297i
$124$	−2144.60			−1.55315
$125$	−1105.89	+	854.480i	−0.791309	+	0.611416i
$126$		0			0
$127$	−499.840	+	499.840i	−0.349241	+	0.349241i	−0.859827	−	0.510586i	$-0.829429\pi$
$127$	−499.840	+	499.840i	−0.349241	+	0.349241i	0.510586	+	0.859827i	$0.329429\pi$
$128$	1828.75	+	1828.75i	1.26282	+	1.26282i
$129$	495.155			0.337953
$130$	720.682	+	3233.69i	0.486215	+	2.18164i
$131$			413.661i			0.275891i	0.990440	+	0.137945i	$0.0440499\pi$
$131$			413.661i			0.275891i	−0.990440	+	0.137945i	$0.955950\pi$
$132$	934.064	+	934.064i	0.615908	+	0.615908i
$133$		0			0
$134$			2686.12i			1.73168i
$135$	−1061.39	−	674.514i	−0.676665	−	0.430022i
$136$			404.366i			0.254957i
$137$	86.3250	−	86.3250i	0.0538339	−	0.0538339i	−0.679677	−	0.733511i	$-0.737880\pi$
$137$	86.3250	−	86.3250i	0.0538339	−	0.0538339i	0.733511	+	0.679677i	$0.237880\pi$
$138$	1418.52	−	1418.52i	0.875017	−	0.875017i
$139$	−0.984410			−0.000600695			−0.000300347	−	1.00000i	$-0.500096\pi$
$139$	−0.984410			−0.000600695			−0.000300347		1.00000i	$0.500096\pi$
$140$		0			0
$141$	777.717			0.464508
$142$	−933.674	+	933.674i	−0.551776	+	0.551776i
$143$	1574.27	−	1574.27i	0.920608	−	0.920608i
$144$		−	1202.45i		−	0.695863i
$145$	560.853	+	2516.54i	0.321216	+	1.44129i
$146$		−	4337.97i		−	2.45899i
$147$		0			0
$148$	−2564.54	−	2564.54i	−1.42435	−	1.42435i
$149$			950.338i			0.522515i	0.965269	+	0.261257i	$0.0841371\pi$
$149$			950.338i			0.522515i	−0.965269	+	0.261257i	$0.915863\pi$
$150$	596.650	+	1272.09i	0.324775	+	0.692440i
$151$	1107.37			0.596798			0.298399	−	0.954441i	$-0.403547\pi$
$151$	1107.37			0.596798			0.298399	+	0.954441i	$0.403547\pi$
$152$	3225.21	+	3225.21i	1.72105	+	1.72105i
$153$	−166.652	+	166.652i	−0.0880587	+	0.0880587i
$154$		0			0
$155$	333.457	+	1496.22i	0.172800	+	0.775350i
$156$	2203.74			1.13103
$157$	−708.793	−	708.793i	−0.360305	−	0.360305i	0.503620	−	0.863925i	$-0.332001\pi$
$157$	−708.793	−	708.793i	−0.360305	−	0.360305i	−0.863925	+	0.503620i	$0.832001\pi$
$158$	3088.67	+	3088.67i	1.55520	+	1.55520i
$159$	−446.257			−0.222582
$160$	163.468	−	257.228i	0.0807707	−	0.127098i
$161$		0			0
$162$	1116.25	−	1116.25i	0.541364	−	0.541364i
$163$	−282.585	−	282.585i	−0.135790	−	0.135790i	0.635945	−	0.771735i	$-0.280611\pi$
$163$	−282.585	−	282.585i	−0.135790	−	0.135790i	−0.771735	+	0.635945i	$0.780611\pi$
$164$	−3554.24			−1.69231
$165$	506.431	−	796.901i	0.238943	−	0.375992i
$166$		−	4222.19i		−	1.97413i
$167$	−389.010	−	389.010i	−0.180254	−	0.180254i	0.611212	−	0.791467i	$-0.290682\pi$
$167$	−389.010	−	389.010i	−0.180254	−	0.180254i	−0.791467	+	0.611212i	$0.790682\pi$
$168$		0			0
$169$		−	1517.18i		−	0.690569i
$170$	577.459	−	128.696i	0.260524	−	0.0580621i
$171$			2658.42i			1.18886i
$172$	2368.96	−	2368.96i	1.05018	−	1.05018i
$173$	1034.13	−	1034.13i	0.454470	−	0.454470i	−0.442365	−	0.896835i	$-0.645861\pi$
$173$	1034.13	−	1034.13i	0.454470	−	0.454470i	0.896835	+	0.442365i	$0.145861\pi$
$174$	2592.16			1.12938
$175$		0			0
$176$	2028.43			0.868742
$177$	13.0545	−	13.0545i	0.00554371	−	0.00554371i
$178$	−3693.66	+	3693.66i	−1.55534	+	1.55534i
$179$			1099.17i			0.458973i	0.973312	+	0.229486i	$0.0737046\pi$
$179$			1099.17i			0.458973i	−0.973312	+	0.229486i	$0.926295\pi$
$180$	−3696.40	+	823.805i	−1.53063	+	0.341127i
$181$			2558.15i			1.05053i	0.850940	+	0.525264i	$0.176033\pi$
$181$			2558.15i			1.05053i	−0.850940	+	0.525264i	$0.823967\pi$
$182$		0			0
$183$	255.281	+	255.281i	0.103120	+	0.103120i
$184$		−	6631.07i		−	2.65679i
$185$	−1390.44	+	2187.95i	−0.552581	+	0.869519i
$186$	1541.18			0.607553
$187$	−281.126	−	281.126i	−0.109936	−	0.109936i
$188$	3720.81	−	3720.81i	1.44345	−	1.44345i
$189$		0			0
$190$	3579.32	−	5632.27i	1.36669	−	2.15057i
$191$	−828.154			−0.313734			−0.156867	−	0.987620i	$-0.550139\pi$
$191$	−828.154			−0.313734			−0.156867	+	0.987620i	$0.550139\pi$
$192$	−942.810	−	942.810i	−0.354383	−	0.354383i
$193$	−1139.80	−	1139.80i	−0.425101	−	0.425101i	0.461855	−	0.886956i	$-0.347184\pi$
$193$	−1139.80	−	1139.80i	−0.425101	−	0.425101i	−0.886956	+	0.461855i	$0.847184\pi$
$194$	−1198.05			−0.443377
$195$	−342.653	−	1537.48i	−0.125835	−	0.564621i
$196$		0			0
$197$	−2246.52	+	2246.52i	−0.812477	+	0.812477i	−0.985005	−	0.172527i	$-0.944807\pi$
$197$	−2246.52	+	2246.52i	−0.812477	+	0.812477i	0.172527	+	0.985005i	$0.444807\pi$
$198$	2719.92	+	2719.92i	0.976244	+	0.976244i
$199$	3868.28			1.37796			0.688982	−	0.724778i	$-0.258058\pi$
$199$	3868.28			1.37796			0.688982	+	0.724778i	$0.258058\pi$
$200$	4367.86	+	1578.73i	1.54427	+	0.558165i
$201$		−	1277.13i		−	0.448169i
$202$	5676.12	+	5676.12i	1.97708	+	1.97708i
$203$		0			0
$204$		−	393.535i		−	0.135063i
$205$	552.638	+	2479.68i	0.188282	+	0.844821i
$206$			3188.93i			1.07856i
$207$	2732.87	−	2732.87i	0.917621	−	0.917621i
$208$	2392.84	−	2392.84i	0.797662	−	0.797662i
$209$	−4484.51			−1.48421
$210$		0			0
$211$	−4515.36			−1.47322			−0.736612	−	0.676316i	$-0.763575\pi$
$211$	−4515.36			−1.47322			−0.736612	+	0.676316i	$0.763575\pi$
$212$	−2135.02	+	2135.02i	−0.691669	+	0.691669i
$213$	443.921	−	443.921i	0.142803	−	0.142803i
$214$			3920.79i			1.25243i
$215$	−2021.09	−	1284.40i	−0.641102	−	0.407421i
$216$			4179.29i			1.31650i
$217$		0			0
$218$	6228.28	+	6228.28i	1.93501	+	1.93501i
$219$			2062.52i			0.636402i
$220$	−1389.69	−	6235.50i	−0.425875	−	1.91090i
$221$	−663.263			−0.201882
$222$	1842.96	+	1842.96i	0.557169	+	0.557169i
$223$	361.498	−	361.498i	0.108555	−	0.108555i	−0.650743	−	0.759298i	$-0.725543\pi$
$223$	361.498	−	361.498i	0.108555	−	0.108555i	0.759298	+	0.650743i	$0.225543\pi$
$224$		0			0
$225$	1149.48	+	2450.77i	0.340588	+	0.726154i
$226$	1740.20			0.512198
$227$	2486.39	+	2486.39i	0.726992	+	0.726992i	0.970020	−	0.243027i	$-0.0781404\pi$
$227$	2486.39	+	2486.39i	0.726992	+	0.726992i	−0.243027	+	0.970020i	$0.578140\pi$
$228$	−3138.82	−	3138.82i	−0.911727	−	0.911727i
$229$	−2209.84			−0.637688			−0.318844	−	0.947807i	$-0.603295\pi$
$229$	−2209.84			−0.637688			−0.318844	+	0.947807i	$0.603295\pi$
$230$	−9469.56	+	2110.45i	−2.71480	+	0.605039i
$231$		0			0
$232$	6058.72	−	6058.72i	1.71455	−	1.71455i
$233$	−2220.92	−	2220.92i	−0.624451	−	0.624451i	0.322215	−	0.946666i	$-0.395572\pi$
$233$	−2220.92	−	2220.92i	−0.624451	−	0.624451i	−0.946666	+	0.322215i	$0.895572\pi$
$234$	6417.12			1.79274
$235$	−3174.43	−	2017.35i	−0.881178	−	0.559990i
$236$		−	124.913i		−	0.0344539i
$237$	−1468.53	−	1468.53i	−0.402495	−	0.402495i
$238$		0			0
$239$		−	749.777i		−	0.202925i	−0.994839	−	0.101462i	$-0.967648\pi$
$239$		−	749.777i		−	0.202925i	0.994839	−	0.101462i	$-0.0323522\pi$
$240$	769.760	−	1211.26i	0.207033	−	0.325778i
$241$		−	5897.58i		−	1.57633i	−0.615462	−	0.788167i	$-0.711030\pi$
$241$		−	5897.58i		−	1.57633i	0.615462	−	0.788167i	$-0.288970\pi$
$242$	−12.0998	+	12.0998i	−0.00321407	+	0.00321407i
$243$	−2678.22	+	2678.22i	−0.707027	+	0.707027i
$244$	2442.67			0.640885
$245$		0			0
$246$	2554.19			0.661989
$247$	−5290.16	+	5290.16i	−1.36277	+	1.36277i
$248$	3602.24	−	3602.24i	0.922347	−	0.922347i
$249$			2007.47i			0.510915i
$250$	864.376	−	6740.01i	0.218672	−	1.70510i
$251$			3068.86i			0.771732i	0.922555	+	0.385866i	$0.126097\pi$
$251$			3068.86i			0.771732i	−0.922555	+	0.385866i	$0.873903\pi$
$252$		0			0
$253$	4610.10	+	4610.10i	1.14559	+	1.14559i
$254$		−	3437.03i		−	0.849050i
$255$	−274.556	+	61.1895i	−0.0674251	+	0.0150268i
$256$	−7960.97			−1.94360
$257$	−1678.06	−	1678.06i	−0.407293	−	0.407293i	0.473501	−	0.880794i	$-0.342990\pi$
$257$	−1678.06	−	1678.06i	−0.407293	−	0.407293i	−0.880794	+	0.473501i	$0.842990\pi$
$258$	−1702.41	+	1702.41i	−0.410804	+	0.410804i
$259$		0			0
$260$	−8995.07	−	5716.38i	−2.14558	−	1.36352i
$261$	4993.97			1.18436
$262$	−1422.22	−	1422.22i	−0.335363	−	0.335363i
$263$	−2326.55	−	2326.55i	−0.545481	−	0.545481i	0.379649	−	0.925130i	$-0.376045\pi$
$263$	−2326.55	−	2326.55i	−0.545481	−	0.545481i	−0.925130	+	0.379649i	$0.876045\pi$
$264$	−3137.85			−0.731520
$265$	1821.50	+	1157.57i	0.422241	+	0.268335i
$266$		0			0
$267$	1756.17	−	1756.17i	0.402532	−	0.402532i
$268$	−6110.15	−	6110.15i	−1.39268	−	1.39268i
$269$	6869.66			1.55706			0.778532	−	0.627605i	$-0.215965\pi$
$269$	6869.66			1.55706			0.778532	+	0.627605i	$0.215965\pi$
$270$	5968.27	−	1330.13i	1.34525	−	0.299811i
$271$		−	7059.95i		−	1.58252i	−0.611483	−	0.791258i	$-0.709427\pi$
$271$		−	7059.95i		−	1.58252i	0.611483	−	0.791258i	$-0.290573\pi$
$272$	−427.303	−	427.303i	−0.0952539	−	0.0952539i
$273$		0			0
$274$			593.595i			0.130877i
$275$	−4134.23	+	1939.08i	−0.906558	+	0.425203i
$276$			6453.46i			1.40744i
$277$	−760.327	+	760.327i	−0.164923	+	0.164923i	−0.784744	−	0.619821i	$-0.787205\pi$
$277$	−760.327	+	760.327i	−0.164923	+	0.164923i	0.619821	+	0.784744i	$0.287205\pi$
$278$	3.38454	−	3.38454i	0.000730184	−	0.000730184i
$279$	2969.18			0.637134
$280$		0			0
$281$	−1015.21			−0.215524			−0.107762	−	0.994177i	$-0.534369\pi$
$281$	−1015.21			−0.215524			−0.107762	+	0.994177i	$0.534369\pi$
$282$	−2673.90	+	2673.90i	−0.564639	+	0.564639i
$283$	−4511.69	+	4511.69i	−0.947675	+	0.947675i	−0.998698	−	0.0510225i	$-0.983752\pi$
$283$	−4511.69	+	4511.69i	−0.947675	+	0.947675i	0.0510225	+	0.998698i	$0.483752\pi$
$284$		−	4247.68i		−	0.887513i
$285$	−1701.81	+	2677.90i	−0.353707	+	0.556579i
$286$			10825.1i			2.23812i
$287$		0			0
$288$	−417.427	−	417.427i	−0.0854066	−	0.0854066i
$289$		−	4794.56i		−	0.975892i
$290$	−10580.5	−	6723.92i	−2.14244	−	1.36153i
$291$	569.622			0.114749
$292$	9867.65	+	9867.65i	1.97761	+	1.97761i
$293$	6725.58	−	6725.58i	1.34100	−	1.34100i	0.445930	−	0.895068i	$-0.352873\pi$
$293$	6725.58	−	6725.58i	1.34100	−	1.34100i	0.895068	−	0.445930i	$-0.147127\pi$
$294$		0			0
$295$	−87.1475	+	19.4223i	−0.0171997	+	0.00383325i
$296$	8615.19			1.69171
$297$	−2905.56	−	2905.56i	−0.567668	−	0.567668i
$298$	−3267.39	−	3267.39i	−0.635150	−	0.635150i
$299$	10876.6			2.10372
$300$	−4250.86	−	1536.44i	−0.818079	−	0.295688i
$301$		0			0
$302$	−3807.29	+	3807.29i	−0.725446	+	0.725446i
$303$	−2698.75	−	2698.75i	−0.511680	−	0.511680i
$304$	−6816.32			−1.28600
$305$	−379.803	−	1704.17i	−0.0713031	−	0.319936i
$306$		−	1145.94i		−	0.214082i
$307$	−6263.08	−	6263.08i	−1.16434	−	1.16434i	−0.983515	−	0.180827i	$-0.942123\pi$
$307$	−6263.08	−	6263.08i	−1.16434	−	1.16434i	−0.180827	−	0.983515i	$-0.557877\pi$
$308$		0			0
$309$		−	1516.20i		−	0.279137i
$310$	−6290.68	−	3997.73i	−1.15254	−	0.732439i
$311$		−	2792.17i		−	0.509097i	−0.967060	−	0.254549i	$-0.918073\pi$
$311$		−	2792.17i		−	0.509097i	0.967060	−	0.254549i	$-0.0819269\pi$
$312$	−3701.57	+	3701.57i	−0.671667	+	0.671667i
$313$	−2044.33	+	2044.33i	−0.369178	+	0.369178i	−0.867177	−	0.498000i	$-0.834068\pi$
$313$	−2044.33	+	2044.33i	−0.369178	+	0.369178i	0.498000	+	0.867177i	$0.334068\pi$
$314$	4873.85			0.875947
$315$		0			0
$316$	−14051.7			−2.50149
$317$	4230.33	−	4230.33i	0.749523	−	0.749523i	−0.224867	−	0.974390i	$-0.572195\pi$
$317$	4230.33	−	4230.33i	0.749523	−	0.749523i	0.974390	+	0.224867i	$0.0721946\pi$
$318$	1534.29	−	1534.29i	0.270563	−	0.270563i
$319$			8424.38i			1.47860i
$320$	1402.70	+	6293.89i	0.245041	+	1.09950i
$321$		−	1864.16i		−	0.324135i
$322$		0			0
$323$	944.695	+	944.695i	0.162738	+	0.162738i
$324$			5078.30i			0.870765i
$325$	−2589.52	+	7164.39i	−0.441971	+	1.22280i
$326$	1943.13			0.330122
$327$	−2961.27	−	2961.27i	−0.500792	−	0.500792i
$328$	5969.97	−	5969.97i	1.00499	−	1.00499i
$329$		0			0
$330$	998.673	+	4481.03i	0.166591	+	0.747493i
$331$	4904.17			0.814373			0.407186	−	0.913345i	$-0.366510\pi$
$331$	4904.17			0.814373			0.407186	+	0.913345i	$0.366510\pi$
$332$	9604.27	+	9604.27i	1.58766	+	1.58766i
$333$	3550.58	+	3550.58i	0.584296	+	0.584296i
$334$	2674.94			0.438222
$335$	−3312.81	+	5212.90i	−0.540292	+	0.850183i
$336$		0			0
$337$	976.895	−	976.895i	0.157908	−	0.157908i	−0.623731	−	0.781639i	$-0.714384\pi$
$337$	976.895	−	976.895i	0.157908	−	0.157908i	0.781639	+	0.623731i	$0.214384\pi$
$338$	5216.27	+	5216.27i	0.839432	+	0.839432i
$339$	−827.391			−0.132560
$340$	−1020.81	+	1606.30i	−0.162827	+	0.256217i
$341$			5008.74i			0.795421i
$342$	−9140.00	−	9140.00i	−1.44513	−	1.44513i
$343$		0			0
$344$			7958.16i			1.24731i
$345$	4502.37	−	1003.43i	0.702606	−	0.156588i
$346$			7110.94i			1.10487i
$347$	357.261	−	357.261i	0.0552702	−	0.0552702i	−0.678931	−	0.734202i	$-0.737557\pi$
$347$	357.261	−	357.261i	0.0552702	−	0.0552702i	0.734202	+	0.678931i	$0.237557\pi$
$348$	−5896.44	+	5896.44i	−0.908282	+	0.908282i
$349$	2840.46			0.435663			0.217831	−	0.975986i	$-0.430102\pi$
$349$	2840.46			0.435663			0.217831	+	0.975986i	$0.430102\pi$
$350$		0			0
$351$	−6855.09			−1.04244
$352$	704.161	−	704.161i	0.106625	−	0.106625i
$353$	4216.68	−	4216.68i	0.635782	−	0.635782i	−0.313730	−	0.949512i	$-0.601579\pi$
$353$	4216.68	−	4216.68i	0.635782	−	0.635782i	0.949512	+	0.313730i	$0.101579\pi$
$354$			89.7663i			0.0134775i
$355$	−2963.47	+	660.459i	−0.443055	+	0.0987423i
$356$		−	16804.0i		−	2.50172i
$357$		0			0
$358$	−3779.11	−	3779.11i	−0.557911	−	0.557911i
$359$			12750.5i			1.87451i	0.348649	+	0.937253i	$0.386641\pi$
$359$			12750.5i			1.87451i	−0.348649	+	0.937253i	$0.613359\pi$
$360$	4825.03	−	7592.49i	0.706393	−	1.11155i
$361$	8210.73			1.19707
$362$	−8795.25	−	8795.25i	−1.27698	−	1.27698i
$363$	5.75292	−	5.75292i	0.000831819	−	0.000831819i
$364$		0			0
$365$	5350.05	−	8418.63i	0.767217	−	1.20726i
$366$	−1755.38			−0.250697
$367$	−7302.48	−	7302.48i	−1.03865	−	1.03865i	−0.999222	−	0.0394322i	$-0.987445\pi$
$367$	−7302.48	−	7302.48i	−1.03865	−	1.03865i	−0.0394322	−	0.999222i	$-0.512555\pi$
$368$	7007.21	+	7007.21i	0.992599	+	0.992599i
$369$	4920.82			0.694221
$370$	−2741.93	−	12303.0i	−0.385260	−	1.72866i
$371$		0			0
$372$	−3505.75	+	3505.75i	−0.488614	+	0.488614i
$373$	4067.46	+	4067.46i	0.564625	+	0.564625i	0.930618	−	0.365993i	$-0.119270\pi$
$373$	4067.46	+	4067.46i	0.564625	+	0.564625i	−0.365993	+	0.930618i	$0.619270\pi$
$374$	1933.10			0.267268
$375$	−410.973	+	3204.58i	−0.0565935	+	0.441291i
$376$			12499.5i			1.71440i
$377$	9937.84	+	9937.84i	1.35763	+	1.35763i
$378$		0			0
$379$		−	3568.88i		−	0.483697i	−0.970314	−	0.241849i	$-0.922246\pi$
$379$		−	3568.88i		−	0.483697i	0.970314	−	0.241849i	$-0.0777538\pi$
$380$	4669.89	+	20953.7i	0.630422	+	2.82870i
$381$			1634.16i			0.219739i
$382$	2847.31	−	2847.31i	0.381364	−	0.381364i
$383$	−1082.62	+	1082.62i	−0.144437	+	0.144437i	−0.775628	−	0.631191i	$-0.782566\pi$
$383$	−1082.62	+	1082.62i	−0.144437	+	0.144437i	0.631191	+	0.775628i	$0.282566\pi$
$384$	5978.87			0.794552
$385$		0			0
$386$	7837.56			1.03348
$387$	−3279.80	+	3279.80i	−0.430805	+	0.430805i
$388$	2725.23	−	2725.23i	0.356579	−	0.356579i
$389$			2102.89i			0.274089i	0.990565	+	0.137044i	$0.0437603\pi$
$389$			2102.89i			0.274089i	−0.990565	+	0.137044i	$0.956240\pi$
$390$	6464.15	+	4107.97i	0.839295	+	0.533373i
$391$		−	1942.30i		−	0.251219i
$392$		0			0
$393$	676.205	+	676.205i	0.0867939	+	0.0867939i
$394$		−	15447.7i		−	1.97524i
$395$	2184.85	+	9803.41i	0.278309	+	1.24877i
$396$	−12374.1			−1.57026
$397$	7625.38	+	7625.38i	0.963997	+	0.963997i	0.999374	−	0.0353766i	$-0.0112631\pi$
$397$	7625.38	+	7625.38i	0.963997	+	0.963997i	−0.0353766	+	0.999374i	$0.511263\pi$
$398$	−13299.7	+	13299.7i	−1.67501	+	1.67501i
$399$		0			0
$400$	−6283.90	+	2947.34i	−0.785488	+	0.368417i
$401$	1009.87			0.125761			0.0628807	−	0.998021i	$-0.479971\pi$
$401$	1009.87			0.125761			0.0628807	+	0.998021i	$0.479971\pi$
$402$	4390.95	+	4390.95i	0.544778	+	0.544778i
$403$	5908.58	+	5908.58i	0.730340	+	0.730340i
$404$	−25823.1			−3.18007
$405$	3542.97	−	789.609i	0.434695	−	0.0968790i
$406$		0			0
$407$	−5989.51	+	5989.51i	−0.729457	+	0.729457i
$408$	661.011	+	661.011i	0.0802081	+	0.0802081i
$409$	−10265.7			−1.24109			−0.620547	−	0.784169i	$-0.713090\pi$
$409$	−10265.7			−1.24109			−0.620547	+	0.784169i	$0.713090\pi$
$410$	−10425.5	−	6625.43i	−1.25580	−	0.798065i
$411$		−	282.228i		−	0.0338718i
$412$	−7253.90	−	7253.90i	−0.867413	−	0.867413i
$413$		0			0
$414$			18791.9i			2.23085i
$415$	5207.25	−	8193.92i	0.615937	−	0.969214i
$416$		−	1661.33i		−	0.195802i
$417$	−1.60920	+	1.60920i	−0.000188976	+	0.000188976i
$418$	15418.4	−	15418.4i	1.80415	−	1.80415i
$419$	−5463.78			−0.637047			−0.318524	−	0.947915i	$-0.603187\pi$
$419$	−5463.78			−0.637047			−0.318524	+	0.947915i	$0.603187\pi$
$420$		0			0
$421$	854.085			0.0988731			0.0494365	−	0.998777i	$-0.484257\pi$
$421$	854.085			0.0988731			0.0494365	+	0.998777i	$0.484257\pi$
$422$	15524.4	−	15524.4i	1.79080	−	1.79080i
$423$	−5151.43	+	5151.43i	−0.592131	+	0.592131i
$424$		−	7172.28i		−	0.821502i
$425$	1279.39	+	462.425i	0.146022	+	0.0527786i
$426$			3052.52i			0.347172i
$427$		0			0
$428$	−8918.68	−	8918.68i	−1.00724	−	1.00724i
$429$		−	5146.87i		−	0.579238i
$430$	11364.7	−	2532.82i	1.27455	−	0.284054i
$431$	−1160.19			−0.129662			−0.0648309	−	0.997896i	$-0.520651\pi$
$431$	−1160.19			−0.129662			−0.0648309	+	0.997896i	$0.520651\pi$
$432$	−4416.36	−	4416.36i	−0.491857	−	0.491857i
$433$	3549.00	−	3549.00i	0.393889	−	0.393889i	−0.482182	−	0.876071i	$-0.660156\pi$
$433$	3549.00	−	3549.00i	0.393889	−	0.393889i	0.876071	+	0.482182i	$0.160156\pi$
$434$		0			0
$435$	5030.57	+	3196.93i	0.554477	+	0.352371i
$436$	−28335.1			−3.11240
$437$	−15491.8	−	15491.8i	−1.69582	−	1.69582i
$438$	−7091.21	−	7091.21i	−0.773587	−	0.773587i
$439$	546.723			0.0594389			0.0297194	−	0.999558i	$-0.490539\pi$
$439$	546.723			0.0594389			0.0297194	+	0.999558i	$0.490539\pi$
$440$	12807.8	+	8139.40i	1.38770	+	0.881888i
$441$		0			0
$442$	2280.39	−	2280.39i	0.245400	−	0.245400i
$443$	−12556.1	−	12556.1i	−1.34663	−	1.34663i	−0.889296	−	0.457332i	$-0.848805\pi$
$443$	−12556.1	−	12556.1i	−1.34663	−	1.34663i	−0.457332	−	0.889296i	$-0.651195\pi$
$444$	−8384.42			−0.896187
$445$	−11723.6	+	2612.81i	−1.24888	+	0.278335i
$446$			2485.76i			0.263910i
$447$	1553.50	+	1553.50i	0.164381	+	0.164381i
$448$		0			0
$449$		−	17447.1i		−	1.83380i	−0.399112	−	0.916902i	$-0.630682\pi$
$449$		−	17447.1i		−	1.83380i	0.399112	−	0.916902i	$-0.369318\pi$
$450$	−12378.2	−	4474.00i	−1.29669	−	0.468681i
$451$			8300.97i			0.866691i
$452$	−3958.47	+	3958.47i	−0.411926	+	0.411926i
$453$	1810.20	−	1810.20i	0.187750	−	0.187750i
$454$	−17097.1			−1.76741
$455$		0			0
$456$	10544.4			1.08287
$457$	6548.22	−	6548.22i	0.670269	−	0.670269i	−0.287509	−	0.957778i	$-0.592827\pi$
$457$	6548.22	−	6548.22i	0.670269	−	0.670269i	0.957778	+	0.287509i	$0.0928270\pi$
$458$	7597.74	−	7597.74i	0.775151	−	0.775151i
$459$			1224.15i			0.124485i
$460$	16739.9	−	26341.2i	1.69674	−	2.66993i
$461$			11684.1i			1.18044i	0.807243	+	0.590219i	$0.200959\pi$
$461$			11684.1i			1.18044i	−0.807243	+	0.590219i	$0.799041\pi$
$462$		0			0
$463$	−9508.03	−	9508.03i	−0.954375	−	0.954375i	0.0446288	−	0.999004i	$-0.485789\pi$
$463$	−9508.03	−	9508.03i	−0.954375	−	0.954375i	−0.999004	+	0.0446288i	$0.985789\pi$
$464$			12804.8i			1.28114i
$465$	2990.94	+	1900.75i	0.298283	+	0.189559i
$466$	15271.6			1.51812
$467$	−9490.95	−	9490.95i	−0.940447	−	0.940447i	0.0578767	−	0.998324i	$-0.481567\pi$
$467$	−9490.95	−	9490.95i	−0.940447	−	0.940447i	−0.998324	+	0.0578767i	$0.981567\pi$
$468$	−14597.1	+	14597.1i	−1.44178	+	1.44178i
$469$		0			0
$470$	17850.0	−	3978.18i	1.75183	−	0.390425i
$471$	−2317.30			−0.226700
$472$	209.813	+	209.813i	0.0204606	+	0.0204606i
$473$	−5532.73	−	5532.73i	−0.537833	−	0.537833i
$474$	10098.0			0.978516
$475$	13892.6	−	6516.06i	1.34197	−	0.629426i
$476$		0			0
$477$	2955.92	−	2955.92i	0.283736	−	0.283736i
$478$	2577.84	+	2577.84i	0.246668	+	0.246668i
$479$	−722.275			−0.0688968			−0.0344484	−	0.999406i	$-0.510967\pi$
$479$	−722.275			−0.0688968			−0.0344484	+	0.999406i	$0.510967\pi$
$480$	−153.267	−	687.705i	−0.0145742	−	0.0653944i
$481$			14131.1i			1.33955i
$482$	20276.7	+	20276.7i	1.91614	+	1.91614i
$483$		0			0
$484$		−	55.0472i		−	0.00516972i
$485$	−2325.04	−	1477.57i	−0.217680	−	0.138336i
$486$		−	18416.1i		−	1.71888i
$487$	10188.6	−	10188.6i	0.948032	−	0.948032i	−0.0506831	−	0.998715i	$-0.516140\pi$
$487$	10188.6	−	10188.6i	0.948032	−	0.948032i	0.998715	+	0.0506831i	$0.0161399\pi$
$488$	−4102.89	+	4102.89i	−0.380592	+	0.380592i
$489$	−923.873			−0.0854376
$490$		0			0
$491$	12781.9			1.17482			0.587412	−	0.809288i	$-0.300147\pi$
$491$	12781.9			1.17482			0.587412	+	0.809288i	$0.300147\pi$
$492$	−5810.06	+	5810.06i	−0.532394	+	0.532394i
$493$	1774.66	−	1774.66i	0.162123	−	0.162123i
$494$		−	36376.6i		−	3.31308i
$495$	1924.01	+	8633.00i	0.174702	+	0.783888i
$496$			7613.14i			0.689194i
$497$		0			0
$498$	−6901.94	−	6901.94i	−0.621051	−	0.621051i
$499$			6445.96i			0.578279i	0.957287	+	0.289139i	$0.0933691\pi$
$499$			6445.96i			0.578279i	−0.957287	+	0.289139i	$0.906631\pi$
$500$	13365.4	+	17297.8i	1.19544	+	1.54716i
$501$	−1271.82			−0.113414
$502$	−10551.2	−	10551.2i	−0.938090	−	0.938090i
$503$	7078.21	−	7078.21i	0.627439	−	0.627439i	−0.319984	−	0.947423i	$-0.603678\pi$
$503$	7078.21	−	7078.21i	0.627439	−	0.627439i	0.947423	+	0.319984i	$0.103678\pi$
$504$		0			0
$505$	4015.15	+	18015.9i	0.353806	+	1.58752i
$506$	−31700.3			−2.78508
$507$	−2480.11	−	2480.11i	−0.217250	−	0.217250i
$508$	7818.28	+	7818.28i	0.682834	+	0.682834i
$509$	6361.92			0.554002			0.277001	−	0.960870i	$-0.410659\pi$
$509$	6361.92			0.554002			0.277001	+	0.960870i	$0.410659\pi$
$510$	733.585	−	1154.34i	0.0636935	−	0.100226i
$511$		0			0
$512$	12740.9	−	12740.9i	1.09975	−	1.09975i
$513$	9763.81	+	9763.81i	0.840318	+	0.840318i
$514$	11538.8			0.990182
$515$	−3932.92	+	6188.70i	−0.336515	+	0.529527i
$516$		−	7745.00i		−	0.660764i
$517$	−8690.00	−	8690.00i	−0.739238	−	0.739238i
$518$		0			0
$519$		−	3380.94i		−	0.285948i
$520$	24710.5	−	5507.14i	2.08389	−	0.464431i
$521$		−	17923.9i		−	1.50722i	−0.657322	−	0.753609i	$-0.728311\pi$
$521$		−	17923.9i		−	1.50722i	0.657322	−	0.753609i	$-0.271689\pi$
$522$	−17170.0	+	17170.0i	−1.43967	+	1.43967i
$523$	−567.052	+	567.052i	−0.0474100	+	0.0474100i	−0.730414	−	0.683004i	$-0.760673\pi$
$523$	−567.052	+	567.052i	−0.0474100	+	0.0474100i	0.683004	+	0.730414i	$0.260673\pi$
$524$	6470.30			0.539421
$525$		0			0
$526$	15998.0			1.32613
$527$	1055.13	−	1055.13i	0.0872147	−	0.0872147i
$528$	3315.84	−	3315.84i	0.273302	−	0.273302i
$529$			19684.2i			1.61784i
$530$	−10242.4	+	2282.70i	−0.839440	+	0.187083i
$531$			172.940i			0.0141337i
$532$		0			0
$533$	9792.26	+	9792.26i	0.795779	+	0.795779i
$534$			12075.9i			0.978607i
$535$	−4835.53	+	7609.01i	−0.390763	+	0.614890i
$536$	20526.2			1.65409
$537$	1796.80	+	1796.80i	0.144391	+	0.144391i
$538$	−23618.8	+	23618.8i	−1.89271	+	1.89271i
$539$		0			0
$540$	−10550.5	+	16601.8i	−0.840777	+	1.32301i
$541$	13307.8			1.05757			0.528785	−	0.848756i	$-0.322648\pi$
$541$	13307.8			1.05757			0.528785	+	0.848756i	$0.322648\pi$
$542$	24273.1	+	24273.1i	1.92365	+	1.92365i
$543$	4181.76	+	4181.76i	0.330491	+	0.330491i
$544$	−296.674			−0.0233819
$545$	4405.74	+	19768.5i	0.346277	+	1.55374i
$546$		0			0
$547$	−9565.99	+	9565.99i	−0.747737	+	0.747737i	−0.974054	−	0.226317i	$-0.927331\pi$
$547$	−9565.99	+	9565.99i	−0.747737	+	0.747737i	0.226317	+	0.974054i	$0.427331\pi$
$548$	−1350.26	−	1350.26i	−0.105256	−	0.105256i
$549$	−3381.85			−0.262903
$550$	7547.23	−	20880.9i	0.585118	−	1.61884i
$551$		−	28309.2i		−	2.18877i
$552$	−10839.7	−	10839.7i	−0.835813	−	0.835813i
$553$		0			0
$554$		−	5228.22i		−	0.400949i
$555$	1303.67	+	5849.54i	0.0997074	+	0.447386i
$556$			15.3977i			0.00117448i
$557$	−2756.28	+	2756.28i	−0.209672	+	0.209672i	−0.804128	−	0.594456i	$-0.797367\pi$
$557$	−2756.28	+	2756.28i	−0.209672	+	0.209672i	0.594456	+	0.804128i	$0.297367\pi$
$558$	−10208.5	+	10208.5i	−0.774477	+	0.774477i
$559$	−13053.4			−0.987656
$560$		0			0
$561$	−919.105			−0.0691705
$562$	3490.43	−	3490.43i	0.261984	−	0.261984i
$563$	−3982.05	+	3982.05i	−0.298087	+	0.298087i	−0.840264	−	0.542177i	$-0.817600\pi$
$563$	−3982.05	+	3982.05i	−0.298087	+	0.298087i	0.542177	+	0.840264i	$0.317600\pi$
$564$		−	12164.7i		−	0.908203i
$565$	3377.19	+	2146.21i	0.251468	+	0.159808i
$566$		−	31023.6i		−	2.30392i
$567$		0			0
$568$	7134.73	+	7134.73i	0.527054	+	0.527054i
$569$			15195.3i			1.11955i	0.828646	+	0.559773i	$0.189112\pi$
$569$			15195.3i			1.11955i	−0.828646	+	0.559773i	$0.810888\pi$
$570$	−3355.94	−	15058.0i	−0.246605	−	1.10651i
$571$	3539.41			0.259404			0.129702	−	0.991553i	$-0.458598\pi$
$571$	3539.41			0.259404			0.129702	+	0.991553i	$0.458598\pi$
$572$	−24624.0	−	24624.0i	−1.79997	−	1.79997i
$573$	−1353.77	+	1353.77i	−0.0986991	+	0.0986991i
$574$		0			0
$575$	−20980.3	−	7583.16i	−1.52163	−	0.549982i
$576$	12490.0			0.903498
$577$	10735.4	+	10735.4i	0.774562	+	0.774562i	0.978900	−	0.204338i	$-0.0655042\pi$
$577$	10735.4	+	10735.4i	0.774562	+	0.774562i	−0.204338	+	0.978900i	$0.565504\pi$
$578$	16484.3	+	16484.3i	1.18626	+	1.18626i
$579$	−3726.42			−0.267469
$580$	39362.7	−	8772.63i	2.81801	−	0.628040i
$581$		0			0
$582$	−1958.44	+	1958.44i	−0.139484	+	0.139484i
$583$	4986.36	+	4986.36i	0.354227	+	0.354227i
$584$	−33148.9			−2.34882
$585$	12453.6	+	7914.28i	0.880159	+	0.559342i
$586$			46246.9i			3.26014i
$587$	−982.935	−	982.935i	−0.0691143	−	0.0691143i	0.671705	−	0.740819i	$-0.265562\pi$
$587$	−982.935	−	982.935i	−0.0691143	−	0.0691143i	−0.740819	+	0.671705i	$0.765562\pi$
$588$		0			0
$589$		−	16831.4i		−	1.17746i
$590$	232.849	−	366.401i	0.0162478	−	0.0255670i
$591$			7344.71i			0.511203i
$592$	−9103.88	+	9103.88i	−0.632039	+	0.632039i
$593$	−15202.9	+	15202.9i	−1.05280	+	1.05280i	−0.0542721	+	0.998526i	$0.517284\pi$
$593$	−15202.9	+	15202.9i	−1.05280	+	1.05280i	−0.998526	+	0.0542721i	$0.982716\pi$
$594$	19979.4			1.38008
$595$		0			0
$596$	14864.8			1.02162
$597$	6323.41	−	6323.41i	0.433501	−	0.433501i
$598$	−37395.4	+	37395.4i	−2.55721	+	2.55721i
$599$		−	18930.9i		−	1.29131i	−0.763629	−	0.645655i	$-0.776584\pi$
$599$		−	18930.9i		−	1.29131i	0.763629	−	0.645655i	$-0.223416\pi$
$600$	9720.79	−	4559.34i	0.661416	−	0.310224i
$601$		−	17782.5i		−	1.20693i	−0.797389	−	0.603465i	$-0.793786\pi$
$601$		−	17782.5i		−	1.20693i	0.797389	−	0.603465i	$-0.206214\pi$
$602$		0			0
$603$	8459.46	+	8459.46i	0.571303	+	0.571303i
$604$		−	17321.0i		−	1.16686i
$605$	−38.4046	+	8.55911i	−0.00258078	+	0.000575169i
$606$	18557.3			1.24396
$607$	−4710.45	−	4710.45i	−0.314977	−	0.314977i	0.531857	−	0.846834i	$-0.321494\pi$
$607$	−4710.45	−	4710.45i	−0.314977	−	0.314977i	−0.846834	+	0.531857i	$0.821494\pi$
$608$	−2366.26	+	2366.26i	−0.157836	+	0.157836i
$609$		0			0
$610$	7164.98	+	4553.36i	0.475577	+	0.302230i
$611$	−20502.4			−1.35751
$612$	2606.69	+	2606.69i	0.172172	+	0.172172i
$613$	803.919	+	803.919i	0.0529690	+	0.0529690i	0.733095	−	0.680126i	$-0.238075\pi$
$613$	803.919	+	803.919i	0.0529690	+	0.0529690i	−0.680126	+	0.733095i	$0.738075\pi$
$614$	43066.7			2.83067
$615$	4956.88	+	3150.10i	0.325009	+	0.206544i
$616$		0			0
$617$	17773.8	−	17773.8i	1.15972	−	1.15972i	0.175179	−	0.984537i	$-0.443950\pi$
$617$	17773.8	−	17773.8i	1.15972	−	1.15972i	0.984537	−	0.175179i	$-0.0560505\pi$
$618$	5212.89	+	5212.89i	0.339309	+	0.339309i
$619$	11891.5			0.772147			0.386074	−	0.922468i	$-0.373831\pi$
$619$	11891.5			0.772147			0.386074	+	0.922468i	$0.373831\pi$
$620$	23403.2	−	5215.80i	1.51596	−	0.337857i
$621$		−	20074.5i		−	1.29720i
$622$	9599.85	+	9599.85i	0.618841	+	0.618841i
$623$		0			0
$624$		−	7823.08i		−	0.501881i
$625$	9989.98	−	12014.2i	0.639359	−	0.768908i
$626$		−	14057.4i		−	0.897519i
$627$	−7330.76	+	7330.76i	−0.466926	+	0.466926i
$628$	−11086.6	+	11086.6i	−0.704466	+	0.704466i
$629$	2523.47			0.159964
$630$		0			0
$631$	−23901.0			−1.50790			−0.753949	−	0.656933i	$-0.771853\pi$
$631$	−23901.0			−1.50790			−0.753949	+	0.656933i	$0.771853\pi$
$632$	23602.3	−	23602.3i	1.48552	−	1.48552i
$633$	−7381.19	+	7381.19i	−0.463469	+	0.463469i
$634$			29088.9i			1.82219i
$635$	4238.92	−	6670.19i	0.264908	−	0.416848i
$636$			6980.17i			0.435191i
$637$		0			0
$638$	−28964.2	−	28964.2i	−1.79734	−	1.79734i
$639$			5880.88i			0.364075i
$640$	−24404.1	−	15508.8i	−1.50728	−	0.957876i
$641$	−2074.58			−0.127833			−0.0639165	−	0.997955i	$-0.520359\pi$
$641$	−2074.58			−0.127833			−0.0639165	+	0.997955i	$0.520359\pi$
$642$	6409.25	+	6409.25i	0.394008	+	0.394008i
$643$	12479.8	−	12479.8i	0.765406	−	0.765406i	−0.211888	−	0.977294i	$-0.567961\pi$
$643$	12479.8	−	12479.8i	0.765406	−	0.765406i	0.977294	+	0.211888i	$0.0679613\pi$
$644$		0			0
$645$	−5403.43	+	1204.24i	−0.329860	+	0.0735149i
$646$	−6495.98			−0.395636
$647$	6299.12	+	6299.12i	0.382757	+	0.382757i	0.872095	−	0.489337i	$-0.162761\pi$
$647$	6299.12	+	6299.12i	0.382757	+	0.382757i	−0.489337	+	0.872095i	$0.662761\pi$
$648$	−8529.90	−	8529.90i	−0.517108	−	0.517108i
$649$	−291.735			−0.0176450
$650$	−15729.0	−	33535.3i	−0.949144	−	2.02363i
$651$		0			0
$652$	−4420.07	+	4420.07i	−0.265496	+	0.265496i
$653$	−9485.73	−	9485.73i	−0.568462	−	0.568462i	0.363236	−	0.931697i	$-0.381672\pi$
$653$	−9485.73	−	9485.73i	−0.568462	−	0.568462i	−0.931697	+	0.363236i	$0.881672\pi$
$654$	20362.5			1.21749
$655$	−1006.05	−	4514.12i	−0.0600145	−	0.269284i
$656$			12617.2i			0.750945i
$657$	−13661.7	−	13661.7i	−0.811252	−	0.811252i
$658$		0			0
$659$			15987.7i			0.945057i	0.881315	+	0.472529i	$0.156659\pi$
$659$			15987.7i			0.945057i	−0.881315	+	0.472529i	$0.843341\pi$
$660$	−12464.8	−	7921.38i	−0.735137	−	0.467181i
$661$		−	4308.47i		−	0.253525i	−0.991933	−	0.126763i	$-0.959541\pi$
$661$		−	4308.47i		−	0.253525i	0.991933	−	0.126763i	$-0.0404586\pi$
$662$	−16861.2	+	16861.2i	−0.989923	+	0.989923i
$663$	−1084.22	+	1084.22i	−0.0635110	+	0.0635110i
$664$	−32264.1			−1.88568
$665$		0			0
$666$	−24414.8			−1.42050
$667$	−29102.1	+	29102.1i	−1.68941	+	1.68941i
$668$	−6084.73	+	6084.73i	−0.352433	+	0.352433i
$669$		−	1181.87i		−	0.0683015i
$670$	−6532.79	−	29312.6i	−0.376692	−	1.69021i
$671$		−	5704.88i		−	0.328218i
$672$		0			0
$673$	10710.4	+	10710.4i	0.613456	+	0.613456i	0.943845	−	0.330389i	$-0.107180\pi$
$673$	10710.4	+	10710.4i	0.613456	+	0.613456i	−0.330389	+	0.943845i	$0.607180\pi$
$674$			6717.40i			0.383894i
$675$	13223.0	+	4779.35i	0.754004	+	0.272529i
$676$	−23731.1			−1.35020
$677$	5827.60	+	5827.60i	0.330832	+	0.330832i	0.852902	−	0.522071i	$-0.174840\pi$
$677$	5827.60	+	5827.60i	0.330832	+	0.330832i	−0.522071	+	0.852902i	$0.674840\pi$
$678$	2844.68	−	2844.68i	0.161135	−	0.161135i
$679$		0			0
$680$	−983.441	−	4412.69i	−0.0554607	−	0.248851i
$681$	8128.91			0.457417
$682$	−17220.7	−	17220.7i	−0.966886	−	0.966886i
$683$	−12178.9	−	12178.9i	−0.682302	−	0.682302i	0.278216	−	0.960518i	$-0.410257\pi$
$683$	−12178.9	−	12178.9i	−0.682302	−	0.682302i	−0.960518	+	0.278216i	$0.910257\pi$
$684$	41581.8			2.32445
$685$	−732.084	+	1151.98i	−0.0408343	+	0.0642553i
$686$		0			0
$687$	−3612.39	+	3612.39i	−0.200613	+	0.200613i
$688$	−8409.58	−	8409.58i	−0.466006	−	0.466006i
$689$	11764.4			0.650488
$690$	−12029.8	+	18929.7i	−0.663721	+	1.04441i
$691$			23733.9i			1.30663i	0.757086	+	0.653315i	$0.226622\pi$
$691$			23733.9i			1.30663i	−0.757086	+	0.653315i	$0.773378\pi$
$692$	−16175.4	−	16175.4i	−0.888577	−	0.888577i
$693$		0			0
$694$			2456.62i			0.134369i
$695$	10.7425	−	2.39414i	0.000586311	−	0.000130669i
$696$		−	19808.2i		−	1.07878i
$697$	1748.66	−	1748.66i	0.0950291	−	0.0950291i
$698$	−9765.89	+	9765.89i	−0.529576	+	0.529576i
$699$	−7260.99			−0.392898
$700$		0			0
$701$	−2641.08			−0.142300			−0.0711501	−	0.997466i	$-0.522667\pi$
$701$	−2641.08			−0.142300			−0.0711501	+	0.997466i	$0.522667\pi$
$702$	23568.7	−	23568.7i	1.26716	−	1.26716i
$703$	20127.1	−	20127.1i	1.07981	−	1.07981i
$704$			21069.4i			1.12796i
$705$	−8486.92	+	1891.45i	−0.453384	+	0.101044i
$706$			28995.0i			1.54567i
$707$		0			0
$708$	−204.193	−	204.193i	−0.0108390	−	0.0108390i
$709$			17803.8i			0.943068i	0.881848	+	0.471534i	$0.156300\pi$
$709$			17803.8i			0.943068i	−0.881848	+	0.471534i	$0.843700\pi$
$710$	7918.07	−	12459.6i	0.418535	−	0.658590i
$711$	19454.5			1.02616
$712$	28225.3	+	28225.3i	1.48566	+	1.48566i
$713$	−17302.7	+	17302.7i	−0.908825	+	0.908825i
$714$		0			0
$715$	−13350.7	+	21008.1i	−0.698303	+	1.09882i
$716$	17192.8			0.897381
$717$	−1225.65	−	1225.65i	−0.0638392	−	0.0638392i
$718$	−43838.1	−	43838.1i	−2.27858	−	2.27858i
$719$	−27837.5			−1.44390			−0.721950	−	0.691945i	$-0.756754\pi$
$719$	−27837.5			−1.44390			−0.721950	+	0.691945i	$0.756754\pi$
$720$	2924.43	+	13121.9i	0.151371	+	0.679200i
$721$		0			0
$722$	−28229.6	+	28229.6i	−1.45512	+	1.45512i
$723$	−9640.68	−	9640.68i	−0.495907	−	0.495907i
$724$	40013.4			2.05399
$725$	−12240.7	−	26098.0i	−0.627048	−	1.33690i
$726$			39.5587i			0.00202226i
$727$	16901.8	+	16901.8i	0.862246	+	0.862246i	0.991599	−	0.129353i	$-0.0412899\pi$
$727$	16901.8	+	16901.8i	0.862246	+	0.862246i	−0.129353	+	0.991599i	$0.541290\pi$
$728$		0			0
$729$		−	9.93984i		−	0.000504996i
$730$	10550.2	+	47338.6i	0.534905	+	2.40011i
$731$			2331.02i			0.117942i
$732$	3992.99	−	3992.99i	0.201619	−	0.201619i
$733$	14387.3	−	14387.3i	0.724978	−	0.724978i	−0.244637	−	0.969615i	$-0.578669\pi$
$733$	14387.3	−	14387.3i	0.724978	−	0.724978i	0.969615	+	0.244637i	$0.0786687\pi$
$734$	50213.8			2.52510
$735$		0			0
$736$	4865.06			0.243653
$737$	−14270.3	+	14270.3i	−0.713236	+	0.713236i
$738$	−16918.4	+	16918.4i	−0.843870	+	0.843870i
$739$			8775.84i			0.436840i	0.975855	+	0.218420i	$0.0700902\pi$
$739$			8775.84i			0.436840i	−0.975855	+	0.218420i	$0.929910\pi$
$740$	34222.9	+	21748.7i	1.70008	+	1.08040i
$741$			17295.5i			0.857444i
$742$		0			0
$743$	24208.9	+	24208.9i	1.19534	+	1.19534i	0.975546	+	0.219795i	$0.0705388\pi$
$743$	24208.9	+	24208.9i	1.19534	+	1.19534i	0.219795	+	0.975546i	$0.429461\pi$
$744$		−	11777.0i		−	0.580332i
$745$	−2311.28	−	10370.7i	−0.113663	−	0.510002i
$746$	−27969.0			−1.37268
$747$	−13297.0	−	13297.0i	−0.651289	−	0.651289i
$748$	−4397.26	+	4397.26i	−0.214946	+	0.214946i
$749$		0			0
$750$	−9604.81	−	12430.8i	−0.467624	−	0.605210i
$751$	−38485.2			−1.86997			−0.934983	−	0.354692i	$-0.884586\pi$
$751$	−38485.2			−1.86997			−0.934983	+	0.354692i	$0.884586\pi$
$752$	−13208.5	−	13208.5i	−0.640513	−	0.640513i
$753$	5016.62	+	5016.62i	0.242783	+	0.242783i
$754$	−68335.3			−3.30056
$755$	−12084.3	+	2693.19i	−0.582507	+	0.129821i
$756$		0			0
$757$	4414.65	−	4414.65i	0.211959	−	0.211959i	−0.593140	−	0.805099i	$-0.702112\pi$
$757$	4414.65	−	4414.65i	0.211959	−	0.211959i	0.805099	+	0.593140i	$0.202112\pi$
$758$	12270.3	+	12270.3i	0.587966	+	0.587966i
$759$	15072.1			0.720795
$760$	−43039.4	−	27351.6i	−2.05421	−	1.30546i
$761$			20123.5i			0.958577i	0.877657	+	0.479289i	$0.159105\pi$
$761$			20123.5i			0.958577i	−0.877657	+	0.479289i	$0.840895\pi$
$762$	−5618.47	−	5618.47i	−0.267107	−	0.267107i
$763$		0			0
$764$			12953.6i			0.613411i
$765$	1413.30	−	2223.91i	0.0667946	−	0.105105i
$766$		−	7444.38i		−	0.351144i
$767$	−344.146	+	344.146i	−0.0162013	+	0.0162013i
$768$	−13013.7	+	13013.7i	−0.611446	+	0.611446i
$769$	−18145.5			−0.850900			−0.425450	−	0.904982i	$-0.639884\pi$
$769$	−18145.5			−0.850900			−0.425450	+	0.904982i	$0.639884\pi$
$770$		0			0
$771$	−5486.19			−0.256265
$772$	−17828.2	+	17828.2i	−0.831156	+	0.831156i
$773$	27647.1	−	27647.1i	1.28641	−	1.28641i	0.349462	−	0.936950i	$-0.386364\pi$
$773$	27647.1	−	27647.1i	1.28641	−	1.28641i	0.936950	−	0.349462i	$-0.113636\pi$
$774$		−	22552.8i		−	1.04734i
$775$	−7277.78	−	15516.7i	−0.337323	−	0.719194i
$776$			9155.00i			0.423512i
$777$		0			0
$778$	−7230.01	−	7230.01i	−0.333173	−	0.333173i
$779$		−	27894.5i		−	1.28296i
$780$	−24048.6	+	5359.63i	−1.10395	+	0.246033i
$781$	−9920.52			−0.454525
$782$	6677.91	+	6677.91i	0.305373	+	0.305373i
$783$	18341.8	−	18341.8i	0.837143	−	0.837143i
$784$		0			0
$785$	9458.61	+	6010.96i	0.430054	+	0.273300i
$786$	−4649.77			−0.211007
$787$	398.444	+	398.444i	0.0180470	+	0.0180470i	0.716073	−	0.698026i	$-0.245938\pi$
$787$	398.444	+	398.444i	0.0180470	+	0.0180470i	−0.698026	+	0.716073i	$0.745938\pi$
$788$	35139.1	+	35139.1i	1.58855	+	1.58855i
$789$	−7606.36			−0.343211
$790$	−41217.3	−	26193.6i	−1.85626	−	1.17966i
$791$		0			0
$792$	20784.5	−	20784.5i	0.932504	−	0.932504i
$793$	−6729.78	−	6729.78i	−0.301364	−	0.301364i
$794$	−52434.2			−2.34360
$795$	4869.83	−	1085.32i	0.217252	−	0.0484182i
$796$		−	60505.9i		−	2.69419i
$797$	−20102.6	−	20102.6i	−0.893438	−	0.893438i	0.101407	−	0.994845i	$-0.467666\pi$
$797$	−20102.6	−	20102.6i	−0.893438	−	0.893438i	−0.994845	+	0.101407i	$0.967666\pi$
$798$		0			0
$799$			3661.23i			0.162109i
$800$	−1158.28	+	3204.59i	−0.0511890	+	0.141624i
$801$			23265.0i			1.02625i
$802$	−3472.06	+	3472.06i	−0.152871	+	0.152871i
$803$	23046.0	−	23046.0i	1.01280	−	1.01280i
$804$	−19976.3			−0.876258
$805$		0			0
$806$	−40629.0			−1.77555
$807$	11229.7	−	11229.7i	0.489845	−	0.489845i
$808$	43374.5	−	43374.5i	1.88850	−	1.88850i
$809$		−	41416.5i		−	1.79991i	−0.435982	−	0.899955i	$-0.643599\pi$
$809$		−	41416.5i		−	1.79991i	0.435982	−	0.899955i	$-0.356401\pi$
$810$	−9466.42	+	14896.0i	−0.410637	+	0.646163i
$811$			23291.9i			1.00850i	0.863559	+	0.504248i	$0.168230\pi$
$811$			23291.9i			1.00850i	−0.863559	+	0.504248i	$0.831770\pi$
$812$		0			0
$813$	−11540.8	−	11540.8i	−0.497852	−	0.497852i
$814$		−	41185.5i		−	1.77341i
$815$	3771.00	+	2396.47i	0.162076	+	0.103000i
$816$	−1397.01			−0.0599328
$817$	18592.2	+	18592.2i	0.796153	+	0.796153i
$818$	35295.0	−	35295.0i	1.50863	−	1.50863i
$819$		0			0
$820$	38786.1	−	8644.12i	1.65179	−	0.368129i
$821$	40570.0			1.72461			0.862304	−	0.506391i	$-0.169021\pi$
$821$	40570.0			1.72461			0.862304	+	0.506391i	$0.169021\pi$
$822$	970.340	+	970.340i	0.0411733	+	0.0411733i
$823$	1023.46	+	1023.46i	0.0433482	+	0.0433482i	0.728449	−	0.685100i	$-0.240242\pi$
$823$	1023.46	+	1023.46i	0.0433482	+	0.0433482i	−0.685100	+	0.728449i	$0.740242\pi$
$824$	24368.4			1.03023
$825$	−3588.38	+	9927.94i	−0.151432	+	0.418965i
$826$		0			0
$827$	7402.23	−	7402.23i	0.311246	−	0.311246i	−0.534146	−	0.845392i	$-0.679367\pi$
$827$	7402.23	−	7402.23i	0.311246	−	0.311246i	0.845392	+	0.534146i	$0.179367\pi$
$828$	−42746.3	−	42746.3i	−1.79413	−	1.79413i
$829$	−37230.4			−1.55979			−0.779894	−	0.625911i	$-0.784727\pi$
$829$	−37230.4			−1.55979			−0.779894	+	0.625911i	$0.784727\pi$
$830$	10268.6	+	46075.1i	0.429432	+	1.92685i
$831$			2485.79i			0.103768i
$832$	24854.6	+	24854.6i	1.03567	+	1.03567i
$833$		0			0
$834$		−	11.0653i		−	0.000459424i
$835$	5191.21	+	3299.02i	0.215149	+	0.136727i
$836$			70144.8i			2.90192i
$837$	10905.2	−	10905.2i	0.450345	−	0.450345i
$838$	18785.2	−	18785.2i	0.774373	−	0.774373i
$839$	−22615.9			−0.930615			−0.465308	−	0.885149i	$-0.654056\pi$
$839$	−22615.9			−0.930615			−0.465308	+	0.885149i	$0.654056\pi$
$840$		0			0
$841$	−28791.3			−1.18050
$842$	−2936.46	+	2936.46i	−0.120187	+	0.120187i
$843$	−1659.55	+	1659.55i	−0.0678029	+	0.0678029i
$844$			70627.3i			2.88044i
$845$	3689.87	+	16556.4i	0.150219	+	0.674032i
$846$		−	35422.7i		−	1.43955i
$847$		0			0
$848$	7579.12	+	7579.12i	0.306920	+	0.306920i
$849$			14750.4i			0.596268i
$850$	−5988.58	+	2808.83i	−0.241655	+	0.113343i
$851$	−41381.6			−1.66691
$852$	−6943.62	−	6943.62i	−0.279207	−	0.279207i
$853$	7541.07	−	7541.07i	0.302698	−	0.302698i	−0.539371	−	0.842068i	$-0.681338\pi$
$853$	7541.07	−	7541.07i	0.302698	−	0.302698i	0.842068	+	0.539371i	$0.181338\pi$
$854$		0			0
$855$	−6465.42	−	29010.3i	−0.258612	−	1.16039i
$856$	29961.0			1.19631
$857$	−6769.22	−	6769.22i	−0.269816	−	0.269816i	0.559210	−	0.829026i	$-0.311105\pi$
$857$	−6769.22	−	6769.22i	−0.269816	−	0.269816i	−0.829026	+	0.559210i	$0.811105\pi$
$858$	17695.6	+	17695.6i	0.704101	+	0.704101i
$859$	21986.0			0.873284			0.436642	−	0.899635i	$-0.356168\pi$
$859$	21986.0			0.873284			0.436642	+	0.899635i	$0.356168\pi$
$860$	−20090.1	+	31613.0i	−0.796588	+	1.25348i
$861$		0			0
$862$	3988.88	−	3988.88i	0.157612	−	0.157612i
$863$	−4510.11	−	4510.11i	−0.177898	−	0.177898i	0.612541	−	0.790439i	$-0.290147\pi$
$863$	−4510.11	−	4510.11i	−0.177898	−	0.177898i	−0.790439	+	0.612541i	$0.790147\pi$
$864$	−3066.24			−0.120736
$865$	−8769.97	+	13800.1i	−0.344726	+	0.542447i
$866$			24403.9i			0.957595i
$867$	−7837.59	−	7837.59i	−0.307011	−	0.307011i
$868$		0			0
$869$			32817.9i			1.28110i
$870$	−28287.3	+	6304.29i	−1.10233	+	0.245673i
$871$			33668.1i			1.30976i
$872$	47593.8	−	47593.8i	1.84831	−	1.84831i
$873$	−3773.06	+	3773.06i	−0.146276	+	0.146276i
$874$	106526.			4.12275
$875$		0			0
$876$	32261.0			1.24429
$877$	4673.51	−	4673.51i	0.179947	−	0.179947i	−0.611386	−	0.791333i	$-0.709388\pi$
$877$	4673.51	−	4673.51i	0.179947	−	0.179947i	0.791333	+	0.611386i	$0.209388\pi$
$878$	−1879.71	+	1879.71i	−0.0722518	+	0.0722518i
$879$		−	21988.4i		−	0.843743i
$880$	−22135.5	+	4933.26i	−0.847939	+	0.188977i
$881$			26453.1i			1.01161i	0.862648	+	0.505805i	$0.168805\pi$
$881$			26453.1i			1.01161i	−0.862648	+	0.505805i	$0.831195\pi$
$882$		0			0
$883$	−5892.09	−	5892.09i	−0.224558	−	0.224558i	0.585857	−	0.810415i	$-0.300758\pi$
$883$	−5892.09	−	5892.09i	−0.224558	−	0.224558i	−0.810415	+	0.585857i	$0.800758\pi$
$884$			10374.5i			0.394718i
$885$	−110.709	+	174.208i	−0.00420503	+	0.00661688i
$886$	86338.9			3.27383
$887$	−10935.8	−	10935.8i	−0.413965	−	0.413965i	0.469152	−	0.883117i	$-0.344559\pi$
$887$	−10935.8	−	10935.8i	−0.413965	−	0.413965i	−0.883117	+	0.469152i	$0.844559\pi$
$888$	14083.1	−	14083.1i	0.532205	−	0.532205i
$889$		0			0
$890$	31324.2	−	49290.6i	1.17977	−	1.85643i
$891$	11860.4			0.445948
$892$	−5654.39	−	5654.39i	−0.212246	−	0.212246i
$893$	29201.8	+	29201.8i	1.09429	+	1.09429i
$894$	−10682.3			−0.399631
$895$	−2673.25	−	11994.9i	−0.0998402	−	0.447982i
$896$		0			0
$897$	17779.9	−	17779.9i	0.661820	−	0.661820i
$898$	59985.4	+	59985.4i	2.22911	+	2.22911i
$899$	−31618.5			−1.17301
$900$	38333.9	−	17979.7i	1.41977	−	0.665916i
$901$		−	2100.83i		−	0.0776790i
$902$	−28539.9	−	28539.9i	−1.05352	−	1.05352i
$903$		0			0
$904$		−	13297.9i		−	0.489249i
$905$	−6221.56	−	27916.0i	−0.228521	−	1.02537i
$906$			12447.4i			0.456444i
$907$	10067.0	−	10067.0i	0.368543	−	0.368543i	−0.498403	−	0.866946i	$-0.666080\pi$
$907$	10067.0	−	10067.0i	0.368543	−	0.368543i	0.866946	+	0.498403i	$0.166080\pi$
$908$	38891.0	−	38891.0i	1.42141	−	1.42141i
$909$	35751.9			1.30453
$910$		0			0
$911$	2046.69			0.0744346			0.0372173	−	0.999307i	$-0.488151\pi$
$911$	2046.69			0.0744346			0.0372173	+	0.999307i	$0.488151\pi$
$912$	−11142.5	+	11142.5i	−0.404568	+	0.404568i
$913$	22430.9	−	22430.9i	0.813093	−	0.813093i
$914$			45027.4i			1.62951i
$915$	−3406.64	−	2164.92i	−0.123082	−	0.0782187i
$916$			34565.4i			1.24680i
$917$		0			0
$918$	−4208.81	−	4208.81i	−0.151320	−	0.151320i
$919$		−	1800.55i		−	0.0646298i	−0.999478	−	0.0323149i	$-0.989712\pi$
$919$		−	1800.55i		−	0.0646298i	0.999478	−	0.0323149i	$-0.0102879\pi$
$920$	16127.2	+	72362.3i	0.577931	+	2.59317i
$921$	−20476.3			−0.732593
$922$	−40171.5	−	40171.5i	−1.43490	−	1.43490i
$923$	−11702.8	+	11702.8i	−0.417336	+	0.417336i
$924$		0			0
$925$	9852.15	−	27257.9i	0.350202	−	0.968900i
$926$	65379.8			2.32021
$927$	10043.0	+	10043.0i	0.355830	+	0.355830i
$928$	4445.14	+	4445.14i	0.157240	+	0.157240i
$929$	−6362.05			−0.224685			−0.112342	−	0.993670i	$-0.535835\pi$
$929$	−6362.05			−0.224685			−0.112342	+	0.993670i	$0.535835\pi$
$930$	−16818.3	+	3748.24i	−0.593004	+	0.132161i
$931$		0			0
$932$	−34738.6	+	34738.6i	−1.22092	+	1.22092i
$933$	−4564.31	−	4564.31i	−0.160159	−	0.160159i
$934$	65262.4			2.28635
$935$	3751.54	+	2384.11i	0.131218	+	0.0833889i
$936$		−	49036.9i		−	1.71241i
$937$	−1779.41	−	1779.41i	−0.0620391	−	0.0620391i	0.675406	−	0.737446i	$-0.263968\pi$
$937$	−1779.41	−	1779.41i	−0.0620391	−	0.0620391i	−0.737446	+	0.675406i	$0.763968\pi$
$938$		0			0
$939$			6683.68i			0.232283i
$940$	−31554.6	+	49653.0i	−1.09489	+	1.72288i
$941$			19055.0i			0.660124i	0.943959	+	0.330062i	$0.107070\pi$
$941$			19055.0i			0.660124i	−0.943959	+	0.330062i	$0.892930\pi$
$942$	7967.21	−	7967.21i	0.275569	−	0.275569i
$943$	−28675.7	+	28675.7i	−0.990255	+	0.990255i
$944$	−443.428			−0.0152885
$945$		0			0
$946$	38044.6			1.30754
$947$	7808.02	−	7808.02i	0.267927	−	0.267927i	−0.560338	−	0.828264i	$-0.689329\pi$
$947$	7808.02	−	7808.02i	0.267927	−	0.267927i	0.828264	+	0.560338i	$0.189329\pi$
$948$	−22970.1	+	22970.1i	−0.786956	+	0.786956i
$949$		−	54372.6i		−	1.85986i
$950$	−25361.7	+	70167.9i	−0.866149	+	2.39637i
$951$		−	13830.5i		−	0.471593i
$952$		0			0
$953$	−7680.65	−	7680.65i	−0.261071	−	0.261071i	0.564418	−	0.825489i	$-0.309101\pi$
$953$	−7680.65	−	7680.65i	−0.261071	−	0.261071i	−0.825489	+	0.564418i	$0.809101\pi$
$954$			20325.7i			0.689799i
$955$	9037.33	−	2014.12i	0.306221	−	0.0682465i
$956$	−11727.7			−0.396758
$957$	13771.2	+	13771.2i	0.465162	+	0.465162i
$958$	2483.28	−	2483.28i	0.0837485	−	0.0837485i
$959$		0			0
$960$	12581.5	+	7995.55i	0.422985	+	0.268808i
$961$	10992.1			0.368973
$962$	−48584.6	−	48584.6i	−1.62831	−	1.62831i
$963$	12347.8	+	12347.8i	0.413191	+	0.413191i
$964$	−92247.4			−3.08204
$965$	15210.2	+	9666.12i	0.507393	+	0.322449i
$966$		0			0
$967$	10778.0	−	10778.0i	0.358426	−	0.358426i	−0.504806	−	0.863233i	$-0.668436\pi$
$967$	10778.0	−	10778.0i	0.358426	−	0.358426i	0.863233	+	0.504806i	$0.168436\pi$
$968$	92.4614	+	92.4614i	0.00307006	+	0.00307006i
$969$	3088.56			0.102393
$970$	13073.9	−	2913.73i	0.432760	−	0.0964478i
$971$		−	42473.1i		−	1.40373i	−0.712308	−	0.701867i	$-0.752350\pi$
$971$		−	42473.1i		−	1.40373i	0.712308	−	0.701867i	$-0.247650\pi$
$972$	41891.5	+	41891.5i	1.38238	+	1.38238i
$973$		0			0
$974$			70059.9i			2.30479i
$975$	7478.47	+	15944.6i	0.245644	+	0.523728i
$976$		−	8671.25i		−	0.284385i
$977$	−8762.06	+	8762.06i	−0.286922	+	0.286922i	−0.835862	−	0.548940i	$-0.815032\pi$
$977$	−8762.06	+	8762.06i	−0.286922	+	0.286922i	0.548940	+	0.835862i	$0.315032\pi$
$978$	3176.40	−	3176.40i	0.103855	−	0.103855i
$979$	−39246.0			−1.28121
$980$		0			0
$981$	39229.7			1.27677
$982$	−43945.9	+	43945.9i	−1.42808	+	1.42808i
$983$	28567.4	−	28567.4i	0.926916	−	0.926916i	−0.0705894	−	0.997505i	$-0.522488\pi$
$983$	28567.4	−	28567.4i	0.926916	−	0.926916i	0.997505	+	0.0705894i	$0.0224880\pi$
$984$		−	19518.0i		−	0.632330i
$985$	19051.7	−	29979.1i	0.616283	−	0.969760i
$986$			12203.0i			0.394142i
$987$		0			0
$988$	82746.5	+	82746.5i	2.66449	+	2.66449i
$989$		−	38225.7i		−	1.22902i
$990$	−36296.4	−	23066.4i	−1.16523	−	0.740504i
$991$	−18319.3			−0.587218			−0.293609	−	0.955926i	$-0.594856\pi$
$991$	−18319.3			−0.587218			−0.293609	+	0.955926i	$0.594856\pi$
$992$	2642.87	+	2642.87i	0.0845880	+	0.0845880i
$993$	8016.76	−	8016.76i	0.256198	−	0.256198i
$994$		0			0
$995$	−42213.0	+	9407.88i	−1.34497	+	0.299748i
$996$	31399.9			0.998940
$997$	7035.24	+	7035.24i	0.223479	+	0.223479i	0.809962	−	0.586483i	$-0.199488\pi$
$997$	7035.24	+	7035.24i	0.223479	+	0.223479i	−0.586483	+	0.809962i	$0.699488\pi$
$998$	−22162.1	−	22162.1i	−0.702935	−	0.702935i
$999$	26081.1			0.825996

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	245.4.f.b.48.4	yes	72
5.2	odd	4	inner	245.4.f.b.97.3	yes	72
7.2	even	3		245.4.l.d.178.34		144
7.3	odd	6		245.4.l.d.68.4		144
7.4	even	3		245.4.l.d.68.3		144
7.5	odd	6		245.4.l.d.178.33		144
7.6	odd	2	inner	245.4.f.b.48.3	✓	72
35.2	odd	12		245.4.l.d.227.4		144
35.12	even	12		245.4.l.d.227.3		144
35.17	even	12		245.4.l.d.117.34		144
35.27	even	4	inner	245.4.f.b.97.4	yes	72
35.32	odd	12		245.4.l.d.117.33		144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
245.4.f.b.48.3	✓	72	7.6	odd	2	inner
245.4.f.b.48.4	yes	72	1.1	even	1	trivial
245.4.f.b.97.3	yes	72	5.2	odd	4	inner
245.4.f.b.97.4	yes	72	35.27	even	4	inner
245.4.l.d.68.3		144	7.4	even	3
245.4.l.d.68.4		144	7.3	odd	6
245.4.l.d.117.33		144	35.32	odd	12
245.4.l.d.117.34		144	35.17	even	12
245.4.l.d.178.33		144	7.5	odd	6
245.4.l.d.178.34		144	7.2	even	3
245.4.l.d.227.3		144	35.12	even	12
245.4.l.d.227.4		144	35.2	odd	12

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:	\( N \)	\(=\)	\( 245 = 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	245.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-3.43814 + 3.43814i) q^{2} +(1.63468 - 1.63468i) q^{3} -15.6416i q^{4} +(-10.9126 + 2.43206i) q^{5} +11.2405i q^{6} +(26.2728 + 26.2728i) q^{8} +21.6556i q^{9} +O(q^{10})\)	\(q+(-3.43814 + 3.43814i) q^{2} +(1.63468 - 1.63468i) q^{3} -15.6416i q^{4} +(-10.9126 + 2.43206i) q^{5} +11.2405i q^{6} +(26.2728 + 26.2728i) q^{8} +21.6556i q^{9} +(29.1573 - 45.8808i) q^{10} -36.5311 q^{11} +(-25.5690 - 25.5690i) q^{12} +(-43.0940 + 43.0940i) q^{13} +(-13.8630 + 21.8143i) q^{15} -55.5261 q^{16} +(7.69554 + 7.69554i) q^{17} +(-74.4550 - 74.4550i) q^{18} +122.759 q^{19} +(38.0412 + 170.690i) q^{20} +(125.599 - 125.599i) q^{22} +(-126.197 - 126.197i) q^{23} +85.8953 q^{24} +(113.170 - 53.0802i) q^{25} -296.326i q^{26} +(79.5366 + 79.5366i) q^{27} -230.609i q^{29} +(-27.3376 - 122.664i) q^{30} -137.109i q^{31} +(-19.2757 + 19.2757i) q^{32} +(-59.7168 + 59.7168i) q^{33} -52.9166 q^{34} +338.728 q^{36} +(163.957 - 163.957i) q^{37} +(-422.062 + 422.062i) q^{38} +140.890i q^{39} +(-350.601 - 222.808i) q^{40} -227.230i q^{41} +(151.453 + 151.453i) q^{43} +571.403i q^{44} +(-52.6677 - 236.319i) q^{45} +867.763 q^{46} +(237.880 + 237.880i) q^{47} +(-90.7677 + 90.7677i) q^{48} +(-206.598 + 571.592i) q^{50} +25.1596 q^{51} +(674.057 + 674.057i) q^{52} +(-136.497 - 136.497i) q^{53} -546.915 q^{54} +(398.649 - 88.8457i) q^{55} +(200.672 - 200.672i) q^{57} +(792.864 + 792.864i) q^{58} +7.98594 q^{59} +(341.210 + 216.840i) q^{60} +156.165i q^{61} +(471.400 + 471.400i) q^{62} -576.754i q^{64} +(365.461 - 575.075i) q^{65} -410.629i q^{66} +(390.636 - 390.636i) q^{67} +(120.370 - 120.370i) q^{68} -412.584 q^{69} +271.564 q^{71} +(-568.953 + 568.953i) q^{72} +(-630.861 + 630.861i) q^{73} +1127.41i q^{74} +(98.2282 - 271.767i) q^{75} -1920.14i q^{76} +(-484.399 - 484.399i) q^{78} -898.356i q^{79} +(605.935 - 135.043i) q^{80} -324.667 q^{81} +(781.249 + 781.249i) q^{82} +(-614.022 + 614.022i) q^{83} +(-102.694 - 65.2624i) q^{85} -1041.43 q^{86} +(-376.972 - 376.972i) q^{87} +(-959.772 - 959.772i) q^{88} +1074.32 q^{89} +(993.577 + 631.419i) q^{90} +(-1973.92 + 1973.92i) q^{92} +(-224.130 - 224.130i) q^{93} -1635.73 q^{94} +(-1339.62 + 298.557i) q^{95} +63.0193i q^{96} +(174.230 + 174.230i) q^{97} -791.103i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q+O(q^{10}) \) 72 * q	\( 72 q - 32 q^{11} - 1152 q^{16} - 64 q^{18} + 576 q^{22} + 768 q^{23} + 288 q^{25} - 2512 q^{30} + 1840 q^{32} - 4640 q^{36} + 864 q^{37} + 608 q^{43} - 3552 q^{46} - 2480 q^{50} + 1056 q^{51} - 1384 q^{53} + 7872 q^{57} + 5296 q^{58} + 9104 q^{60} + 736 q^{65} + 1856 q^{67} - 6816 q^{71} - 8528 q^{72} - 5408 q^{78} - 12616 q^{81} + 5600 q^{85} + 8672 q^{86} - 10080 q^{88} + 10624 q^{92} + 416 q^{93} + 5888 q^{95}+O(q^{100}) \) 72 * q - 32 * q^11 - 1152 * q^16 - 64 * q^18 + 576 * q^22 + 768 * q^23 + 288 * q^25 - 2512 * q^30 + 1840 * q^32 - 4640 * q^36 + 864 * q^37 + 608 * q^43 - 3552 * q^46 - 2480 * q^50 + 1056 * q^51 - 1384 * q^53 + 7872 * q^57 + 5296 * q^58 + 9104 * q^60 + 736 * q^65 + 1856 * q^67 - 6816 * q^71 - 8528 * q^72 - 5408 * q^78 - 12616 * q^81 + 5600 * q^85 + 8672 * q^86 - 10080 * q^88 + 10624 * q^92 + 416 * q^93 + 5888 * q^95

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