LMFDB - Embedded newform 245.4.f.b.97.4

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			97.4
Character	$\chi$	$=$	245.97
Dual form			245.4.f.b.48.4

$q$-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 $\left(\mathbb{Z}/245\mathbb{Z}\right)^\times$.

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

Coefficient data

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

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

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

$2$	−3.43814	−	3.43814i	−1.21556	−	1.21556i	−0.969169	−	0.246396i	$-0.920754\pi$
$2$	−3.43814	−	3.43814i	−1.21556	−	1.21556i	−0.246396	−	0.969169i	$-0.579246\pi$
$3$	1.63468	+	1.63468i	0.314595	+	0.314595i	0.846687	−	0.532092i	$-0.178594\pi$
$3$	1.63468	+	1.63468i	0.314595	+	0.314595i	−0.532092	+	0.846687i	$0.678594\pi$
$4$			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	0.0775917	−	0.996985i	$-0.475277\pi$
$13$	−43.0940	−	43.0940i	−0.919394	−	0.919394i	−0.996985	+	0.0775917i	$0.975277\pi$
$14$		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	−0.650077	−	0.759868i	$-0.725264\pi$
$17$	7.69554	−	7.69554i	0.109791	−	0.109791i	0.759868	+	0.650077i	$0.225264\pi$
$18$	−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	−0.156384	+	0.987696i	$0.549984\pi$
$23$	−126.197	+	126.197i	−1.14408	+	1.14408i	−0.987696	+	0.156384i	$0.950016\pi$
$24$	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	$0.264384\pi$
$29$			230.609i			1.47665i	−0.674443	+	0.738326i	$0.735616\pi$
$30$	−27.3376	+	122.664i	−0.166372	+	0.746507i
$31$			137.109i			0.794372i	0.917738	+	0.397186i	$0.130013\pi$
$31$			137.109i			0.794372i	−0.917738	+	0.397186i	$0.869987\pi$
$32$	−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	0.970320	−	0.241825i	$-0.0777460\pi$
$37$	163.957	+	163.957i	0.728495	+	0.728495i	−0.241825	+	0.970320i	$0.577746\pi$
$38$	−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	$0.142465\pi$
$41$			227.230i			0.865547i	−0.901503	+	0.432774i	$0.857535\pi$
$42$		0			0
$43$	151.453	−	151.453i	0.537124	−	0.537124i	−0.385559	−	0.922683i	$-0.625992\pi$
$43$	151.453	−	151.453i	0.537124	−	0.537124i	0.922683	+	0.385559i	$0.125992\pi$
$44$		−	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	−0.233979	−	0.972242i	$-0.575175\pi$
$47$	237.880	−	237.880i	0.738262	−	0.738262i	0.972242	+	0.233979i	$0.0751748\pi$
$48$	−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	−0.861506	−	0.507747i	$-0.830478\pi$
$53$	−136.497	+	136.497i	−0.353759	+	0.353759i	0.507747	+	0.861506i	$0.330478\pi$
$54$	−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	$-0.947595\pi$
$61$		−	156.165i		−	0.327785i	0.986478	−	0.163893i	$-0.0524051\pi$
$62$	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	0.967015	−	0.254720i	$-0.0819833\pi$
$67$	390.636	+	390.636i	0.712295	+	0.712295i	−0.254720	+	0.967015i	$0.581983\pi$
$68$	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	−0.999934	−	0.0115278i	$-0.996331\pi$
$73$	−630.861	−	630.861i	−1.01146	−	1.01146i	−0.0115278	−	0.999934i	$-0.503669\pi$
$74$		−	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	$0.220942\pi$
$79$			898.356i			1.27940i	−0.768623	+	0.639702i	$0.779058\pi$
$80$	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	0.172916	−	0.984937i	$-0.444681\pi$
$83$	−614.022	−	614.022i	−0.812021	−	0.812021i	−0.984937	+	0.172916i	$0.944681\pi$
$84$		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	−0.610015	−	0.792390i	$-0.708837\pi$
$97$	174.230	−	174.230i	0.182375	−	0.182375i	0.792390	+	0.610015i	$0.208837\pi$
$98$		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	$0.302296\pi$
$101$			1650.93i			1.62647i	−0.581935	+	0.813236i	$0.697704\pi$
$102$	−86.5020	−	86.5020i	−0.0839703	−	0.0839703i
$103$	463.758	+	463.758i	0.443645	+	0.443645i	0.893235	−	0.449590i	$-0.148430\pi$
$103$	463.758	+	463.758i	0.443645	+	0.443645i	−0.449590	+	0.893235i	$0.648430\pi$
$104$	−2264.39			−2.13502
$105$		0			0
$106$	938.587			0.860035
$107$	570.191	+	570.191i	0.515163	+	0.515163i	0.916104	−	0.400941i	$-0.131317\pi$
$107$	570.191	+	570.191i	0.515163	+	0.515163i	−0.400941	+	0.916104i	$0.631317\pi$
$108$	1244.08	+	1244.08i	1.10844	+	1.10844i
$109$			1811.53i			1.59186i	0.605388	+	0.795930i	$0.293018\pi$
$109$			1811.53i			1.59186i	−0.605388	+	0.795930i	$0.706982\pi$
$110$	−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	−0.804558	−	0.593875i	$-0.797598\pi$
$113$	−253.074	+	253.074i	−0.210683	+	0.210683i	0.593875	+	0.804558i	$0.297598\pi$
$114$		−	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	0.510586	−	0.859827i	$-0.329429\pi$
$127$	−499.840	−	499.840i	−0.349241	−	0.349241i	−0.859827	+	0.510586i	$0.829429\pi$
$128$	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	$-0.955950\pi$
$131$		−	413.661i		−	0.275891i	0.990440	−	0.137945i	$-0.0440499\pi$
$132$	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	0.733511	−	0.679677i	$-0.237880\pi$
$137$	86.3250	+	86.3250i	0.0538339	+	0.0538339i	−0.679677	+	0.733511i	$0.737880\pi$
$138$	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	$-0.915863\pi$
$149$		−	950.338i		−	0.522515i	0.965269	−	0.261257i	$-0.0841371\pi$
$150$	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	−0.863925	−	0.503620i	$-0.832001\pi$
$157$	−708.793	+	708.793i	−0.360305	+	0.360305i	0.503620	+	0.863925i	$0.332001\pi$
$158$	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	−0.771735	−	0.635945i	$-0.780611\pi$
$163$	−282.585	+	282.585i	−0.135790	+	0.135790i	0.635945	+	0.771735i	$0.280611\pi$
$164$	−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	−0.791467	−	0.611212i	$-0.790682\pi$
$167$	−389.010	+	389.010i	−0.180254	+	0.180254i	0.611212	+	0.791467i	$0.290682\pi$
$168$		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	0.896835	−	0.442365i	$-0.145861\pi$
$173$	1034.13	+	1034.13i	0.454470	+	0.454470i	−0.442365	+	0.896835i	$0.645861\pi$
$174$	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	$-0.926295\pi$
$179$		−	1099.17i		−	0.458973i	0.973312	−	0.229486i	$-0.0737046\pi$
$180$	−3696.40	−	823.805i	−1.53063	−	0.341127i
$181$		−	2558.15i		−	1.05053i	−0.850940	−	0.525264i	$-0.823967\pi$
$181$		−	2558.15i		−	1.05053i	0.850940	−	0.525264i	$-0.176033\pi$
$182$		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	−0.886956	−	0.461855i	$-0.847184\pi$
$193$	−1139.80	+	1139.80i	−0.425101	+	0.425101i	0.461855	+	0.886956i	$0.347184\pi$
$194$	−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	0.172527	−	0.985005i	$-0.444807\pi$
$197$	−2246.52	−	2246.52i	−0.812477	−	0.812477i	−0.985005	+	0.172527i	$0.944807\pi$
$198$	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	0.759298	−	0.650743i	$-0.225543\pi$
$223$	361.498	+	361.498i	0.108555	+	0.108555i	−0.650743	+	0.759298i	$0.725543\pi$
$224$		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	−0.243027	−	0.970020i	$-0.578140\pi$
$227$	2486.39	−	2486.39i	0.726992	−	0.726992i	0.970020	+	0.243027i	$0.0781404\pi$
$228$	−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	−0.946666	−	0.322215i	$-0.895572\pi$
$233$	−2220.92	+	2220.92i	−0.624451	+	0.624451i	0.322215	+	0.946666i	$0.395572\pi$
$234$	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	$0.0323522\pi$
$239$			749.777i			0.202925i	−0.994839	+	0.101462i	$0.967648\pi$
$240$	769.760	+	1211.26i	0.207033	+	0.325778i
$241$			5897.58i			1.57633i	0.615462	+	0.788167i	$0.288970\pi$
$241$			5897.58i			1.57633i	−0.615462	+	0.788167i	$0.711030\pi$
$242$	−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	$-0.873903\pi$
$251$		−	3068.86i		−	0.771732i	0.922555	−	0.385866i	$-0.126097\pi$
$252$		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	−0.880794	−	0.473501i	$-0.842990\pi$
$257$	−1678.06	+	1678.06i	−0.407293	+	0.407293i	0.473501	+	0.880794i	$0.342990\pi$
$258$	−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	−0.925130	−	0.379649i	$-0.876045\pi$
$263$	−2326.55	+	2326.55i	−0.545481	+	0.545481i	0.379649	+	0.925130i	$0.376045\pi$
$264$	−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	$0.290573\pi$
$271$			7059.95i			1.58252i	−0.611483	+	0.791258i	$0.709427\pi$
$272$	−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	0.619821	−	0.784744i	$-0.287205\pi$
$277$	−760.327	−	760.327i	−0.164923	−	0.164923i	−0.784744	+	0.619821i	$0.787205\pi$
$278$	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	0.0510225	−	0.998698i	$-0.483752\pi$
$283$	−4511.69	−	4511.69i	−0.947675	−	0.947675i	−0.998698	+	0.0510225i	$0.983752\pi$
$284$			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	0.895068	+	0.445930i	$0.147127\pi$
$293$	6725.58	+	6725.58i	1.34100	+	1.34100i	0.445930	+	0.895068i	$0.352873\pi$
$294$		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	−0.180827	+	0.983515i	$0.557877\pi$
$307$	−6263.08	+	6263.08i	−1.16434	+	1.16434i	−0.983515	+	0.180827i	$0.942123\pi$
$308$		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	$0.0819269\pi$
$311$			2792.17i			0.509097i	−0.967060	+	0.254549i	$0.918073\pi$
$312$	−3701.57	−	3701.57i	−0.671667	−	0.671667i
$313$	−2044.33	−	2044.33i	−0.369178	−	0.369178i	0.498000	−	0.867177i	$-0.334068\pi$
$313$	−2044.33	−	2044.33i	−0.369178	−	0.369178i	−0.867177	+	0.498000i	$0.834068\pi$
$314$	4873.85			0.875947
$315$		0			0
$316$	−14051.7			−2.50149
$317$	4230.33	+	4230.33i	0.749523	+	0.749523i	0.974390	−	0.224867i	$-0.0721946\pi$
$317$	4230.33	+	4230.33i	0.749523	+	0.749523i	−0.224867	+	0.974390i	$0.572195\pi$
$318$	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	0.781639	−	0.623731i	$-0.214384\pi$
$337$	976.895	+	976.895i	0.157908	+	0.157908i	−0.623731	+	0.781639i	$0.714384\pi$
$338$	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	0.734202	−	0.678931i	$-0.237557\pi$
$347$	357.261	+	357.261i	0.0552702	+	0.0552702i	−0.678931	+	0.734202i	$0.737557\pi$
$348$	−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	0.949512	−	0.313730i	$-0.101579\pi$
$353$	4216.68	+	4216.68i	0.635782	+	0.635782i	−0.313730	+	0.949512i	$0.601579\pi$
$354$		−	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	$-0.613359\pi$
$359$		−	12750.5i		−	1.87451i	0.348649	−	0.937253i	$-0.386641\pi$
$360$	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	−0.0394322	+	0.999222i	$0.512555\pi$
$367$	−7302.48	+	7302.48i	−1.03865	+	1.03865i	−0.999222	+	0.0394322i	$0.987445\pi$
$368$	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	−0.365993	−	0.930618i	$-0.619270\pi$
$373$	4067.46	−	4067.46i	0.564625	−	0.564625i	0.930618	+	0.365993i	$0.119270\pi$
$374$	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	$0.0777538\pi$
$379$			3568.88i			0.483697i	−0.970314	+	0.241849i	$0.922246\pi$
$380$	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	0.631191	−	0.775628i	$-0.282566\pi$
$383$	−1082.62	−	1082.62i	−0.144437	−	0.144437i	−0.775628	+	0.631191i	$0.782566\pi$
$384$	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	$-0.956240\pi$
$389$		−	2102.89i		−	0.274089i	0.990565	−	0.137044i	$-0.0437603\pi$
$390$	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	−0.0353766	−	0.999374i	$-0.511263\pi$
$397$	7625.38	−	7625.38i	0.963997	−	0.963997i	0.999374	+	0.0353766i	$0.0112631\pi$
$398$	−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	0.876071	−	0.482182i	$-0.160156\pi$
$433$	3549.00	+	3549.00i	0.393889	+	0.393889i	−0.482182	+	0.876071i	$0.660156\pi$
$434$		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	−0.457332	+	0.889296i	$0.651195\pi$
$443$	−12556.1	+	12556.1i	−1.34663	+	1.34663i	−0.889296	+	0.457332i	$0.848805\pi$
$444$	−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	$0.369318\pi$
$449$			17447.1i			1.83380i	−0.399112	+	0.916902i	$0.630682\pi$
$450$	−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	0.957778	−	0.287509i	$-0.0928270\pi$
$457$	6548.22	+	6548.22i	0.670269	+	0.670269i	−0.287509	+	0.957778i	$0.592827\pi$
$458$	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	$-0.799041\pi$
$461$		−	11684.1i		−	1.18044i	0.807243	−	0.590219i	$-0.200959\pi$
$462$		0			0
$463$	−9508.03	+	9508.03i	−0.954375	+	0.954375i	−0.999004	−	0.0446288i	$-0.985789\pi$
$463$	−9508.03	+	9508.03i	−0.954375	+	0.954375i	0.0446288	+	0.999004i	$0.485789\pi$
$464$		−	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	−0.998324	−	0.0578767i	$-0.981567\pi$
$467$	−9490.95	+	9490.95i	−0.940447	+	0.940447i	0.0578767	+	0.998324i	$0.481567\pi$
$468$	−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	0.998715	−	0.0506831i	$-0.0161399\pi$
$487$	10188.6	+	10188.6i	0.948032	+	0.948032i	−0.0506831	+	0.998715i	$0.516140\pi$
$488$	−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	$-0.906631\pi$
$499$		−	6445.96i		−	0.578279i	0.957287	−	0.289139i	$-0.0933691\pi$
$500$	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	0.947423	−	0.319984i	$-0.103678\pi$
$503$	7078.21	+	7078.21i	0.627439	+	0.627439i	−0.319984	+	0.947423i	$0.603678\pi$
$504$		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	$0.271689\pi$
$521$			17923.9i			1.50722i	−0.657322	+	0.753609i	$0.728311\pi$
$522$	−17170.0	−	17170.0i	−1.43967	−	1.43967i
$523$	−567.052	−	567.052i	−0.0474100	−	0.0474100i	0.683004	−	0.730414i	$-0.260673\pi$
$523$	−567.052	−	567.052i	−0.0474100	−	0.0474100i	−0.730414	+	0.683004i	$0.760673\pi$
$524$	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	0.226317	−	0.974054i	$-0.427331\pi$
$547$	−9565.99	−	9565.99i	−0.747737	−	0.747737i	−0.974054	+	0.226317i	$0.927331\pi$
$548$	−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	0.594456	−	0.804128i	$-0.297367\pi$
$557$	−2756.28	−	2756.28i	−0.209672	−	0.209672i	−0.804128	+	0.594456i	$0.797367\pi$
$558$	−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	0.542177	−	0.840264i	$-0.317600\pi$
$563$	−3982.05	−	3982.05i	−0.298087	−	0.298087i	−0.840264	+	0.542177i	$0.817600\pi$
$564$			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	$-0.810888\pi$
$569$		−	15195.3i		−	1.11955i	0.828646	−	0.559773i	$-0.189112\pi$
$570$	−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	−0.204338	−	0.978900i	$-0.565504\pi$
$577$	10735.4	−	10735.4i	0.774562	−	0.774562i	0.978900	+	0.204338i	$0.0655042\pi$
$578$	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	−0.740819	−	0.671705i	$-0.765562\pi$
$587$	−982.935	+	982.935i	−0.0691143	+	0.0691143i	0.671705	+	0.740819i	$0.265562\pi$
$588$		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	−0.998526	−	0.0542721i	$-0.982716\pi$
$593$	−15202.9	−	15202.9i	−1.05280	−	1.05280i	−0.0542721	−	0.998526i	$-0.517284\pi$
$594$	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	$0.223416\pi$
$599$			18930.9i			1.29131i	−0.763629	+	0.645655i	$0.776584\pi$
$600$	9720.79	+	4559.34i	0.661416	+	0.310224i
$601$			17782.5i			1.20693i	0.797389	+	0.603465i	$0.206214\pi$
$601$			17782.5i			1.20693i	−0.797389	+	0.603465i	$0.793786\pi$
$602$		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	−0.846834	−	0.531857i	$-0.821494\pi$
$607$	−4710.45	+	4710.45i	−0.314977	+	0.314977i	0.531857	+	0.846834i	$0.321494\pi$
$608$	−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	−0.680126	−	0.733095i	$-0.738075\pi$
$613$	803.919	−	803.919i	0.0529690	−	0.0529690i	0.733095	+	0.680126i	$0.238075\pi$
$614$	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	0.984537	+	0.175179i	$0.0560505\pi$
$617$	17773.8	+	17773.8i	1.15972	+	1.15972i	0.175179	+	0.984537i	$0.443950\pi$
$618$	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	0.977294	−	0.211888i	$-0.0679613\pi$
$643$	12479.8	+	12479.8i	0.765406	+	0.765406i	−0.211888	+	0.977294i	$0.567961\pi$
$644$		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	−0.489337	−	0.872095i	$-0.662761\pi$
$647$	6299.12	−	6299.12i	0.382757	−	0.382757i	0.872095	+	0.489337i	$0.162761\pi$
$648$	−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	−0.931697	−	0.363236i	$-0.881672\pi$
$653$	−9485.73	+	9485.73i	−0.568462	+	0.568462i	0.363236	+	0.931697i	$0.381672\pi$
$654$	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	$-0.843341\pi$
$659$		−	15987.7i		−	0.945057i	0.881315	−	0.472529i	$-0.156659\pi$
$660$	−12464.8	+	7921.38i	−0.735137	+	0.467181i
$661$			4308.47i			0.253525i	0.991933	+	0.126763i	$0.0404586\pi$
$661$			4308.47i			0.253525i	−0.991933	+	0.126763i	$0.959541\pi$
$662$	−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	−0.330389	−	0.943845i	$-0.607180\pi$
$673$	10710.4	−	10710.4i	0.613456	−	0.613456i	0.943845	+	0.330389i	$0.107180\pi$
$674$		−	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	−0.522071	−	0.852902i	$-0.674840\pi$
$677$	5827.60	−	5827.60i	0.330832	−	0.330832i	0.852902	+	0.522071i	$0.174840\pi$
$678$	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	−0.960518	−	0.278216i	$-0.910257\pi$
$683$	−12178.9	+	12178.9i	−0.682302	+	0.682302i	0.278216	+	0.960518i	$0.410257\pi$
$684$	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	$-0.773378\pi$
$691$		−	23733.9i		−	1.30663i	0.757086	−	0.653315i	$-0.226622\pi$
$692$	−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	$-0.843700\pi$
$709$		−	17803.8i		−	0.943068i	0.881848	−	0.471534i	$-0.156300\pi$
$710$	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	−0.129353	−	0.991599i	$-0.541290\pi$
$727$	16901.8	−	16901.8i	0.862246	−	0.862246i	0.991599	+	0.129353i	$0.0412899\pi$
$728$		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	0.969615	−	0.244637i	$-0.0786687\pi$
$733$	14387.3	+	14387.3i	0.724978	+	0.724978i	−0.244637	+	0.969615i	$0.578669\pi$
$734$	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	$-0.929910\pi$
$739$		−	8775.84i		−	0.436840i	0.975855	−	0.218420i	$-0.0700902\pi$
$740$	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	0.219795	−	0.975546i	$-0.429461\pi$
$743$	24208.9	−	24208.9i	1.19534	−	1.19534i	0.975546	−	0.219795i	$-0.0705388\pi$
$744$			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	0.805099	−	0.593140i	$-0.202112\pi$
$757$	4414.65	+	4414.65i	0.211959	+	0.211959i	−0.593140	+	0.805099i	$0.702112\pi$
$758$	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	$-0.840895\pi$
$761$		−	20123.5i		−	0.958577i	0.877657	−	0.479289i	$-0.159105\pi$
$762$	−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	0.936950	+	0.349462i	$0.113636\pi$
$773$	27647.1	+	27647.1i	1.28641	+	1.28641i	0.349462	+	0.936950i	$0.386364\pi$
$774$			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	−0.698026	−	0.716073i	$-0.745938\pi$
$787$	398.444	−	398.444i	0.0180470	−	0.0180470i	0.716073	+	0.698026i	$0.245938\pi$
$788$	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	−0.994845	−	0.101407i	$-0.967666\pi$
$797$	−20102.6	+	20102.6i	−0.893438	+	0.893438i	0.101407	+	0.994845i	$0.467666\pi$
$798$		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	$0.356401\pi$
$809$			41416.5i			1.79991i	−0.435982	+	0.899955i	$0.643599\pi$
$810$	−9466.42	−	14896.0i	−0.410637	−	0.646163i
$811$		−	23291.9i		−	1.00850i	−0.863559	−	0.504248i	$-0.831770\pi$
$811$		−	23291.9i		−	1.00850i	0.863559	−	0.504248i	$-0.168230\pi$
$812$		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	−0.685100	−	0.728449i	$-0.740242\pi$
$823$	1023.46	−	1023.46i	0.0433482	−	0.0433482i	0.728449	+	0.685100i	$0.240242\pi$
$824$	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	0.845392	−	0.534146i	$-0.179367\pi$
$827$	7402.23	+	7402.23i	0.311246	+	0.311246i	−0.534146	+	0.845392i	$0.679367\pi$
$828$	−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	0.842068	−	0.539371i	$-0.181338\pi$
$853$	7541.07	+	7541.07i	0.302698	+	0.302698i	−0.539371	+	0.842068i	$0.681338\pi$
$854$		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	−0.829026	−	0.559210i	$-0.811105\pi$
$857$	−6769.22	+	6769.22i	−0.269816	+	0.269816i	0.559210	+	0.829026i	$0.311105\pi$
$858$	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	−0.790439	−	0.612541i	$-0.790147\pi$
$863$	−4510.11	+	4510.11i	−0.177898	+	0.177898i	0.612541	+	0.790439i	$0.290147\pi$
$864$	−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	0.791333	−	0.611386i	$-0.209388\pi$
$877$	4673.51	+	4673.51i	0.179947	+	0.179947i	−0.611386	+	0.791333i	$0.709388\pi$
$878$	−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	$-0.831195\pi$
$881$		−	26453.1i		−	1.01161i	0.862648	−	0.505805i	$-0.168805\pi$
$882$		0			0
$883$	−5892.09	+	5892.09i	−0.224558	+	0.224558i	−0.810415	−	0.585857i	$-0.800758\pi$
$883$	−5892.09	+	5892.09i	−0.224558	+	0.224558i	0.585857	+	0.810415i	$0.300758\pi$
$884$		−	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	−0.883117	−	0.469152i	$-0.844559\pi$
$887$	−10935.8	+	10935.8i	−0.413965	+	0.413965i	0.469152	+	0.883117i	$0.344559\pi$
$888$	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	0.866946	−	0.498403i	$-0.166080\pi$
$907$	10067.0	+	10067.0i	0.368543	+	0.368543i	−0.498403	+	0.866946i	$0.666080\pi$
$908$	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	$0.0102879\pi$
$919$			1800.55i			0.0646298i	−0.999478	+	0.0323149i	$0.989712\pi$
$920$	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	−0.737446	−	0.675406i	$-0.763968\pi$
$937$	−1779.41	+	1779.41i	−0.0620391	+	0.0620391i	0.675406	+	0.737446i	$0.263968\pi$
$938$		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	$-0.892930\pi$
$941$		−	19055.0i		−	0.660124i	0.943959	−	0.330062i	$-0.107070\pi$
$942$	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	0.828264	−	0.560338i	$-0.189329\pi$
$947$	7808.02	+	7808.02i	0.267927	+	0.267927i	−0.560338	+	0.828264i	$0.689329\pi$
$948$	−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	−0.825489	−	0.564418i	$-0.809101\pi$
$953$	−7680.65	+	7680.65i	−0.261071	+	0.261071i	0.564418	+	0.825489i	$0.309101\pi$
$954$		−	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	0.863233	−	0.504806i	$-0.168436\pi$
$967$	10778.0	+	10778.0i	0.358426	+	0.358426i	−0.504806	+	0.863233i	$0.668436\pi$
$968$	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	$0.247650\pi$
$971$			42473.1i			1.40373i	−0.712308	+	0.701867i	$0.752350\pi$
$972$	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	0.548940	−	0.835862i	$-0.315032\pi$
$977$	−8762.06	−	8762.06i	−0.286922	−	0.286922i	−0.835862	+	0.548940i	$0.815032\pi$
$978$	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	0.997505	−	0.0705894i	$-0.0224880\pi$
$983$	28567.4	+	28567.4i	0.926916	+	0.926916i	−0.0705894	+	0.997505i	$0.522488\pi$
$984$			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	−0.586483	−	0.809962i	$-0.699488\pi$
$997$	7035.24	−	7035.24i	0.223479	−	0.223479i	0.809962	+	0.586483i	$0.199488\pi$
$998$	−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.97.4	yes	72
5.3	odd	4	inner	245.4.f.b.48.3	✓	72
7.2	even	3		245.4.l.d.227.3		144
7.3	odd	6		245.4.l.d.117.33		144
7.4	even	3		245.4.l.d.117.34		144
7.5	odd	6		245.4.l.d.227.4		144
7.6	odd	2	inner	245.4.f.b.97.3	yes	72
35.3	even	12		245.4.l.d.68.3		144
35.13	even	4	inner	245.4.f.b.48.4	yes	72
35.18	odd	12		245.4.l.d.68.4		144
35.23	odd	12		245.4.l.d.178.33		144
35.33	even	12		245.4.l.d.178.34		144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
245.4.f.b.48.3	✓	72	5.3	odd	4	inner
245.4.f.b.48.4	yes	72	35.13	even	4	inner
245.4.f.b.97.3	yes	72	7.6	odd	2	inner
245.4.f.b.97.4	yes	72	1.1	even	1	trivial
245.4.l.d.68.3		144	35.3	even	12
245.4.l.d.68.4		144	35.18	odd	12
245.4.l.d.117.33		144	7.3	odd	6
245.4.l.d.117.34		144	7.4	even	3
245.4.l.d.178.33		144	35.23	odd	12
245.4.l.d.178.34		144	35.33	even	12
245.4.l.d.227.3		144	7.2	even	3
245.4.l.d.227.4		144	7.5	odd	6

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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