LMFDB - Embedded newform 275.3.f.c.232.10

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [275,3,Mod(232,275)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(275, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([1, 0])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("275.232"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 275 = 5^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	275.f (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [24] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$7.49320726991$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			232.10
Character	$\chi$	$=$	275.232
Dual form			275.3.f.c.243.10

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.94573 + 1.94573i) q^{2} +(2.32995 - 2.32995i) q^{3} +3.57173i q^{4} +9.06691 q^{6} +(4.69739 + 4.69739i) q^{7} +(0.833292 - 0.833292i) q^{8} -1.85733i q^{9} -3.31662 q^{11} +(8.32196 + 8.32196i) q^{12} +(8.25095 - 8.25095i) q^{13} +18.2797i q^{14} +17.5297 q^{16} +(-8.51563 - 8.51563i) q^{17} +(3.61387 - 3.61387i) q^{18} -1.38766i q^{19} +21.8894 q^{21} +(-6.45326 - 6.45326i) q^{22} +(-29.4914 + 29.4914i) q^{23} -3.88306i q^{24} +32.1082 q^{26} +(16.6421 + 16.6421i) q^{27} +(-16.7778 + 16.7778i) q^{28} -18.7878i q^{29} +11.9533 q^{31} +(30.7748 + 30.7748i) q^{32} +(-7.72757 + 7.72757i) q^{33} -33.1382i q^{34} +6.63389 q^{36} +(-13.2935 - 13.2935i) q^{37} +(2.70002 - 2.70002i) q^{38} -38.4486i q^{39} -3.05055 q^{41} +(42.5908 + 42.5908i) q^{42} +(-37.6277 + 37.6277i) q^{43} -11.8461i q^{44} -114.764 q^{46} +(-59.2865 - 59.2865i) q^{47} +(40.8432 - 40.8432i) q^{48} -4.86901i q^{49} -39.6820 q^{51} +(29.4702 + 29.4702i) q^{52} +(-59.2069 + 59.2069i) q^{53} +64.7619i q^{54} +7.82860 q^{56} +(-3.23318 - 3.23318i) q^{57} +(36.5560 - 36.5560i) q^{58} -89.9219i q^{59} -93.2503 q^{61} +(23.2579 + 23.2579i) q^{62} +(8.72461 - 8.72461i) q^{63} +49.6403i q^{64} -30.0715 q^{66} +(-34.1610 - 34.1610i) q^{67} +(30.4155 - 30.4155i) q^{68} +137.427i q^{69} +112.172 q^{71} +(-1.54770 - 1.54770i) q^{72} +(45.0140 - 45.0140i) q^{73} -51.7309i q^{74} +4.95636 q^{76} +(-15.5795 - 15.5795i) q^{77} +(74.8106 - 74.8106i) q^{78} +120.460i q^{79} +94.2663 q^{81} +(-5.93555 - 5.93555i) q^{82} +(-87.1999 + 87.1999i) q^{83} +78.1830i q^{84} -146.427 q^{86} +(-43.7746 - 43.7746i) q^{87} +(-2.76372 + 2.76372i) q^{88} +47.4909i q^{89} +77.5159 q^{91} +(-105.335 - 105.335i) q^{92} +(27.8505 - 27.8505i) q^{93} -230.711i q^{94} +143.408 q^{96} +(11.1746 + 11.1746i) q^{97} +(9.47378 - 9.47378i) q^{98} +6.16007i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 8 q^{6} - 128 q^{16} - 88 q^{21} + 96 q^{26} + 360 q^{31} + 176 q^{36} - 152 q^{41} + 56 q^{46} - 512 q^{51} - 1048 q^{56} + 784 q^{61} - 440 q^{66} + 728 q^{71} + 1704 q^{76} - 568 q^{81} - 328 q^{86}+ \cdots + 1568 q^{96}+O(q^{100}) $ 24 * q - 8 * q^6 - 128 * q^16 - 88 * q^21 + 96 * q^26 + 360 * q^31 + 176 * q^36 - 152 * q^41 + 56 * q^46 - 512 * q^51 - 1048 * q^56 + 784 * q^61 - 440 * q^66 + 728 * q^71 + 1704 * q^76 - 568 * q^81 - 328 * q^86 - 968 * q^91 + 1568 * q^96

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/275\mathbb{Z}\right)^\times$.

$n$	$101$	$177$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$	1.94573	+	1.94573i	0.972865	+	0.972865i	0.999641	−	0.0267763i	$-0.00852418\pi$
$2$	1.94573	+	1.94573i	0.972865	+	0.972865i	−0.0267763	+	0.999641i	$0.508524\pi$
$3$	2.32995	−	2.32995i	0.776650	−	0.776650i	−0.202610	−	0.979260i	$-0.564942\pi$
$3$	2.32995	−	2.32995i	0.776650	−	0.776650i	0.979260	+	0.202610i	$0.0649423\pi$
$4$			3.57173i			0.892933i
$5$		0			0
$5$		0			0
$6$	9.06691			1.51115
$7$	4.69739	+	4.69739i	0.671056	+	0.671056i	0.957960	−	0.286903i	$-0.0926259\pi$
$7$	4.69739	+	4.69739i	0.671056	+	0.671056i	−0.286903	+	0.957960i	$0.592626\pi$
$8$	0.833292	−	0.833292i	0.104162	−	0.104162i
$9$		−	1.85733i		−	0.206370i
$10$		0			0
$11$	−3.31662			−0.301511
$11$	−3.31662			−0.301511
$12$	8.32196	+	8.32196i	0.693496	+	0.693496i
$13$	8.25095	−	8.25095i	0.634688	−	0.634688i	−0.314552	−	0.949240i	$-0.601854\pi$
$13$	8.25095	−	8.25095i	0.634688	−	0.634688i	0.949240	+	0.314552i	$0.101854\pi$
$14$			18.2797i			1.30569i
$15$		0			0
$16$	17.5297			1.09560
$17$	−8.51563	−	8.51563i	−0.500919	−	0.500919i	0.410804	−	0.911724i	$-0.365248\pi$
$17$	−8.51563	−	8.51563i	−0.500919	−	0.500919i	−0.911724	+	0.410804i	$0.865248\pi$
$18$	3.61387	−	3.61387i	0.200770	−	0.200770i
$19$		−	1.38766i		−	0.0730349i	−0.999333	−	0.0365174i	$-0.988374\pi$
$19$		−	1.38766i		−	0.0730349i	0.999333	−	0.0365174i	$-0.0116264\pi$
$20$		0			0
$21$	21.8894			1.04235
$22$	−6.45326	−	6.45326i	−0.293330	−	0.293330i
$23$	−29.4914	+	29.4914i	−1.28223	+	1.28223i	−0.342839	+	0.939394i	$0.611388\pi$
$23$	−29.4914	+	29.4914i	−1.28223	+	1.28223i	−0.939394	+	0.342839i	$0.888612\pi$
$24$		−	3.88306i		−	0.161794i
$25$		0			0
$26$	32.1082			1.23493
$27$	16.6421	+	16.6421i	0.616373	+	0.616373i
$28$	−16.7778	+	16.7778i	−0.599208	+	0.599208i
$29$		−	18.7878i		−	0.647855i	−0.946082	−	0.323927i	$-0.894997\pi$
$29$		−	18.7878i		−	0.647855i	0.946082	−	0.323927i	$-0.105003\pi$
$30$		0			0
$31$	11.9533			0.385590			0.192795	−	0.981239i	$-0.438245\pi$
$31$	11.9533			0.385590			0.192795	+	0.981239i	$0.438245\pi$
$32$	30.7748	+	30.7748i	0.961713	+	0.961713i
$33$	−7.72757	+	7.72757i	−0.234169	+	0.234169i
$34$		−	33.1382i		−	0.974654i
$35$		0			0
$36$	6.63389			0.184275
$37$	−13.2935	−	13.2935i	−0.359282	−	0.359282i	0.504266	−	0.863548i	$-0.331763\pi$
$37$	−13.2935	−	13.2935i	−0.359282	−	0.359282i	−0.863548	+	0.504266i	$0.831763\pi$
$38$	2.70002	−	2.70002i	0.0710531	−	0.0710531i
$39$		−	38.4486i		−	0.985861i
$40$		0			0
$41$	−3.05055			−0.0744037			−0.0372018	−	0.999308i	$-0.511844\pi$
$41$	−3.05055			−0.0744037			−0.0372018	+	0.999308i	$0.511844\pi$
$42$	42.5908	+	42.5908i	1.01407	+	1.01407i
$43$	−37.6277	+	37.6277i	−0.875062	+	0.875062i	−0.993019	−	0.117956i	$-0.962366\pi$
$43$	−37.6277	+	37.6277i	−0.875062	+	0.875062i	0.117956	+	0.993019i	$0.462366\pi$
$44$		−	11.8461i		−	0.269229i
$45$		0			0
$46$	−114.764			−2.49488
$47$	−59.2865	−	59.2865i	−1.26142	−	1.26142i	−0.950407	−	0.311008i	$-0.899333\pi$
$47$	−59.2865	−	59.2865i	−1.26142	−	1.26142i	−0.311008	−	0.950407i	$-0.600667\pi$
$48$	40.8432	−	40.8432i	0.850900	−	0.850900i
$49$		−	4.86901i		−	0.0993676i
$50$		0			0
$51$	−39.6820			−0.778078
$52$	29.4702	+	29.4702i	0.566734	+	0.566734i
$53$	−59.2069	+	59.2069i	−1.11711	+	1.11711i	−0.124949	+	0.992163i	$0.539877\pi$
$53$	−59.2069	+	59.2069i	−1.11711	+	1.11711i	−0.992163	+	0.124949i	$0.960123\pi$
$54$			64.7619i			1.19929i
$55$		0			0
$56$	7.82860			0.139796
$57$	−3.23318	−	3.23318i	−0.0567225	−	0.0567225i
$58$	36.5560	−	36.5560i	0.630275	−	0.630275i
$59$		−	89.9219i		−	1.52410i	−0.647518	−	0.762050i	$-0.724193\pi$
$59$		−	89.9219i		−	1.52410i	0.647518	−	0.762050i	$-0.275807\pi$
$60$		0			0
$61$	−93.2503			−1.52869			−0.764347	−	0.644805i	$-0.776938\pi$
$61$	−93.2503			−1.52869			−0.764347	+	0.644805i	$0.776938\pi$
$62$	23.2579	+	23.2579i	0.375127	+	0.375127i
$63$	8.72461	−	8.72461i	0.138486	−	0.138486i
$64$			49.6403i			0.775630i
$65$		0			0
$66$	−30.0715			−0.455629
$67$	−34.1610	−	34.1610i	−0.509865	−	0.509865i	0.404620	−	0.914485i	$-0.367404\pi$
$67$	−34.1610	−	34.1610i	−0.509865	−	0.509865i	−0.914485	+	0.404620i	$0.867404\pi$
$68$	30.4155	−	30.4155i	0.447287	−	0.447287i
$69$			137.427i			1.99169i
$70$		0			0
$71$	112.172			1.57988			0.789941	−	0.613182i	$-0.210111\pi$
$71$	112.172			1.57988			0.789941	+	0.613182i	$0.210111\pi$
$72$	−1.54770	−	1.54770i	−0.0214958	−	0.0214958i
$73$	45.0140	−	45.0140i	0.616630	−	0.616630i	−0.328036	−	0.944665i	$-0.606387\pi$
$73$	45.0140	−	45.0140i	0.616630	−	0.616630i	0.944665	+	0.328036i	$0.106387\pi$
$74$		−	51.7309i		−	0.699067i
$75$		0			0
$76$	4.95636			0.0652153
$77$	−15.5795	−	15.5795i	−0.202331	−	0.202331i
$78$	74.8106	−	74.8106i	0.959110	−	0.959110i
$79$			120.460i			1.52480i	0.647103	+	0.762402i	$0.275980\pi$
$79$			120.460i			1.52480i	−0.647103	+	0.762402i	$0.724020\pi$
$80$		0			0
$81$	94.2663			1.16378
$82$	−5.93555	−	5.93555i	−0.0723847	−	0.0723847i
$83$	−87.1999	+	87.1999i	−1.05060	+	1.05060i	−0.0519520	+	0.998650i	$0.516544\pi$
$83$	−87.1999	+	87.1999i	−1.05060	+	1.05060i	−0.998650	+	0.0519520i	$0.983456\pi$
$84$			78.1830i			0.930750i
$85$		0			0
$86$	−146.427			−1.70264
$87$	−43.7746	−	43.7746i	−0.503156	−	0.503156i
$88$	−2.76372	+	2.76372i	−0.0314059	+	0.0314059i
$89$			47.4909i			0.533605i	0.963751	+	0.266803i	$0.0859672\pi$
$89$			47.4909i			0.533605i	−0.963751	+	0.266803i	$0.914033\pi$
$90$		0			0
$91$	77.5159			0.851823
$92$	−105.335	−	105.335i	−1.14495	−	1.14495i
$93$	27.8505	−	27.8505i	0.299468	−	0.299468i
$94$		−	230.711i		−	2.45437i
$95$		0			0
$96$	143.408			1.49383
$97$	11.1746	+	11.1746i	0.115202	+	0.115202i	0.762358	−	0.647156i	$-0.224042\pi$
$97$	11.1746	+	11.1746i	0.115202	+	0.115202i	−0.647156	+	0.762358i	$0.724042\pi$
$98$	9.47378	−	9.47378i	0.0966712	−	0.0966712i
$99$			6.16007i			0.0622229i
$100$		0			0
$101$	19.6410			0.194465			0.0972326	−	0.995262i	$-0.469001\pi$
$101$	19.6410			0.194465			0.0972326	+	0.995262i	$0.469001\pi$
$102$	−77.2104	−	77.2104i	−0.756965	−	0.756965i
$103$	90.6340	−	90.6340i	0.879942	−	0.879942i	−0.113586	−	0.993528i	$-0.536234\pi$
$103$	90.6340	−	90.6340i	0.879942	−	0.879942i	0.993528	+	0.113586i	$0.0362337\pi$
$104$		−	13.7509i		−	0.132220i
$105$		0			0
$106$	−230.401			−2.17360
$107$	−64.9056	−	64.9056i	−0.606594	−	0.606594i	0.335460	−	0.942054i	$-0.391108\pi$
$107$	−64.9056	−	64.9056i	−0.606594	−	0.606594i	−0.942054	+	0.335460i	$0.891108\pi$
$108$	−59.4410	+	59.4410i	−0.550380	+	0.550380i
$109$			54.9650i			0.504266i	0.967693	+	0.252133i	$0.0811320\pi$
$109$			54.9650i			0.504266i	−0.967693	+	0.252133i	$0.918868\pi$
$110$		0			0
$111$	−61.9461			−0.558073
$112$	82.3437	+	82.3437i	0.735211	+	0.735211i
$113$	86.7160	−	86.7160i	0.767398	−	0.767398i	−0.210250	−	0.977648i	$-0.567428\pi$
$113$	86.7160	−	86.7160i	0.767398	−	0.767398i	0.977648	+	0.210250i	$0.0674277\pi$
$114$		−	12.5818i		−	0.110367i
$115$		0			0
$116$	67.1050			0.578491
$117$	−15.3247	−	15.3247i	−0.130981	−	0.130981i
$118$	174.964	−	174.964i	1.48274	−	1.48274i
$119$		−	80.0025i		−	0.672290i
$120$		0			0
$121$	11.0000			0.0909091
$122$	−181.440	−	181.440i	−1.48721	−	1.48721i
$123$	−7.10763	+	7.10763i	−0.0577856	+	0.0577856i
$124$			42.6939i			0.344306i
$125$		0			0
$126$	33.9515			0.269456
$127$	95.1205	+	95.1205i	0.748980	+	0.748980i	0.974288	−	0.225308i	$-0.0723387\pi$
$127$	95.1205	+	95.1205i	0.748980	+	0.748980i	−0.225308	+	0.974288i	$0.572339\pi$
$128$	26.5125	−	26.5125i	0.207129	−	0.207129i
$129$			175.341i			1.35923i
$130$		0			0
$131$	36.6096			0.279462			0.139731	−	0.990189i	$-0.455376\pi$
$131$	36.6096			0.279462			0.139731	+	0.990189i	$0.455376\pi$
$132$	−27.6008	−	27.6008i	−0.209097	−	0.209097i
$133$	6.51839	−	6.51839i	0.0490105	−	0.0490105i
$134$		−	132.936i		−	0.992060i
$135$		0			0
$136$	−14.1920			−0.104353
$137$	−9.43753	−	9.43753i	−0.0688871	−	0.0688871i	0.671824	−	0.740711i	$-0.265511\pi$
$137$	−9.43753	−	9.43753i	−0.0688871	−	0.0688871i	−0.740711	+	0.671824i	$0.765511\pi$
$138$	−267.395	+	267.395i	−1.93765	+	1.93765i
$139$		−	166.652i		−	1.19894i	−0.800398	−	0.599468i	$-0.795379\pi$
$139$		−	166.652i		−	1.19894i	0.800398	−	0.599468i	$-0.204621\pi$
$140$		0			0
$141$	−276.269			−1.95936
$142$	218.256	+	218.256i	1.53701	+	1.53701i
$143$	−27.3653	+	27.3653i	−0.191366	+	0.191366i
$144$		−	32.5584i		−	0.226100i
$145$		0			0
$146$	175.170			1.19980
$147$	−11.3445	−	11.3445i	−0.0771738	−	0.0771738i
$148$	47.4807	−	47.4807i	0.320815	−	0.320815i
$149$		−	47.3958i		−	0.318092i	−0.987271	−	0.159046i	$-0.949158\pi$
$149$		−	47.3958i		−	0.318092i	0.987271	−	0.159046i	$-0.0508419\pi$
$150$		0			0
$151$	197.823			1.31008			0.655042	−	0.755593i	$-0.272651\pi$
$151$	197.823			1.31008			0.655042	+	0.755593i	$0.272651\pi$
$152$	−1.15633	−	1.15633i	−0.00760743	−	0.00760743i
$153$	−15.8163	+	15.8163i	−0.103375	+	0.103375i
$154$		−	60.6270i		−	0.393682i
$155$		0			0
$156$	137.328			0.880308
$157$	216.297	+	216.297i	1.37769	+	1.37769i	0.848516	+	0.529170i	$0.177497\pi$
$157$	216.297	+	216.297i	1.37769	+	1.37769i	0.529170	+	0.848516i	$0.322503\pi$
$158$	−234.382	+	234.382i	−1.48343	+	1.48343i
$159$			275.898i			1.73521i
$160$		0			0
$161$	−277.065			−1.72090
$162$	183.417	+	183.417i	1.13220	+	1.13220i
$163$	−56.1702	+	56.1702i	−0.344603	+	0.344603i	−0.858094	−	0.513492i	$-0.828352\pi$
$163$	−56.1702	+	56.1702i	−0.344603	+	0.344603i	0.513492	+	0.858094i	$0.328352\pi$
$164$		−	10.8957i		−	0.0664375i
$165$		0			0
$166$	−339.335			−2.04419
$167$	185.183	+	185.183i	1.10888	+	1.10888i	0.993298	+	0.115582i	$0.0368733\pi$
$167$	185.183	+	185.183i	1.10888	+	1.10888i	0.115582	+	0.993298i	$0.463127\pi$
$168$	18.2403	−	18.2403i	0.108573	−	0.108573i
$169$			32.8437i			0.194341i
$170$		0			0
$171$	−2.57735			−0.0150722
$172$	−134.396	−	134.396i	−0.781372	−	0.781372i
$173$	−146.555	+	146.555i	−0.847141	+	0.847141i	−0.989775	−	0.142635i	$-0.954443\pi$
$173$	−146.555	+	146.555i	−0.847141	+	0.847141i	0.142635	+	0.989775i	$0.454443\pi$
$174$		−	170.347i		−	0.979007i
$175$		0			0
$176$	−58.1393			−0.330337
$177$	−209.513	−	209.513i	−1.18369	−	1.18369i
$178$	−92.4045	+	92.4045i	−0.519126	+	0.519126i
$179$		−	9.81684i		−	0.0548427i	−0.999624	−	0.0274213i	$-0.991270\pi$
$179$		−	9.81684i		−	0.0548427i	0.999624	−	0.0274213i	$-0.00872958\pi$
$180$		0			0
$181$	187.169			1.03408			0.517042	−	0.855960i	$-0.327033\pi$
$181$	187.169			1.03408			0.517042	+	0.855960i	$0.327033\pi$
$182$	150.825	+	150.825i	0.828709	+	0.828709i
$183$	−217.269	+	217.269i	−1.18726	+	1.18726i
$184$			49.1499i			0.267119i
$185$		0			0
$186$	108.379			0.582684
$187$	28.2431	+	28.2431i	0.151033	+	0.151033i
$188$	211.756	−	211.756i	1.12636	−	1.12636i
$189$			156.349i			0.827241i
$190$		0			0
$191$	137.592			0.720377			0.360189	−	0.932880i	$-0.382712\pi$
$191$	137.592			0.720377			0.360189	+	0.932880i	$0.382712\pi$
$192$	115.660	+	115.660i	0.602393	+	0.602393i
$193$	−123.864	+	123.864i	−0.641780	+	0.641780i	−0.950993	−	0.309213i	$-0.899934\pi$
$193$	−123.864	+	123.864i	−0.641780	+	0.641780i	0.309213	+	0.950993i	$0.399934\pi$
$194$			43.4856i			0.224152i
$195$		0			0
$196$	17.3908			0.0887286
$197$	−104.480	−	104.480i	−0.530353	−	0.530353i	0.390324	−	0.920678i	$-0.372363\pi$
$197$	−104.480	−	104.480i	−0.530353	−	0.530353i	−0.920678	+	0.390324i	$0.872363\pi$
$198$	−11.9858	+	11.9858i	−0.0605345	+	0.0605345i
$199$			50.3008i			0.252768i	0.991981	+	0.126384i	$0.0403371\pi$
$199$			50.3008i			0.252768i	−0.991981	+	0.126384i	$0.959663\pi$
$200$		0			0
$201$	−159.187			−0.791973
$202$	38.2161	+	38.2161i	0.189188	+	0.189188i
$203$	88.2536	−	88.2536i	0.434747	−	0.434747i
$204$		−	141.733i		−	0.694772i
$205$		0			0
$206$	352.699			1.71213
$207$	54.7752	+	54.7752i	0.264615	+	0.264615i
$208$	144.636	−	144.636i	0.695367	−	0.695367i
$209$			4.60236i			0.0220208i
$210$		0			0
$211$	35.3826			0.167690			0.0838449	−	0.996479i	$-0.473280\pi$
$211$	35.3826			0.167690			0.0838449	+	0.996479i	$0.473280\pi$
$212$	−211.471	−	211.471i	−0.997506	−	0.997506i
$213$	261.354	−	261.354i	1.22702	−	1.22702i
$214$		−	252.578i		−	1.18027i
$215$		0			0
$216$	27.7354			0.128405
$217$	56.1492	+	56.1492i	0.258752	+	0.258752i
$218$	−106.947	+	106.947i	−0.490583	+	0.490583i
$219$		−	209.761i		−	0.957811i
$220$		0			0
$221$	−140.524			−0.635855
$222$	−120.530	−	120.530i	−0.542930	−	0.542930i
$223$	162.802	−	162.802i	0.730054	−	0.730054i	−0.240576	−	0.970630i	$-0.577336\pi$
$223$	162.802	−	162.802i	0.730054	−	0.730054i	0.970630	+	0.240576i	$0.0773363\pi$
$224$			289.123i			1.29073i
$225$		0			0
$226$	337.452			1.49315
$227$	−85.9899	−	85.9899i	−0.378810	−	0.378810i	0.491863	−	0.870673i	$-0.336316\pi$
$227$	−85.9899	−	85.9899i	−0.378810	−	0.378810i	−0.870673	+	0.491863i	$0.836316\pi$
$228$	11.5481	−	11.5481i	0.0506494	−	0.0506494i
$229$		−	171.077i		−	0.747062i	−0.927618	−	0.373531i	$-0.878147\pi$
$229$		−	171.077i		−	0.747062i	0.927618	−	0.373531i	$-0.121853\pi$
$230$		0			0
$231$	−72.5988			−0.314281
$232$	−15.6557	−	15.6557i	−0.0674816	−	0.0674816i
$233$	−163.710	+	163.710i	−0.702619	+	0.702619i	−0.964972	−	0.262353i	$-0.915501\pi$
$233$	−163.710	+	163.710i	−0.702619	+	0.702619i	0.262353	+	0.964972i	$0.415501\pi$
$234$		−	59.6356i		−	0.254853i
$235$		0			0
$236$	321.177			1.36092
$237$	280.665	+	280.665i	1.18424	+	1.18424i
$238$	155.663	−	155.663i	0.654047	−	0.654047i
$239$		−	33.4764i		−	0.140069i	−0.997545	−	0.0700344i	$-0.977689\pi$
$239$		−	33.4764i		−	0.140069i	0.997545	−	0.0700344i	$-0.0223109\pi$
$240$		0			0
$241$	209.783			0.870467			0.435233	−	0.900318i	$-0.356666\pi$
$241$	209.783			0.870467			0.435233	+	0.900318i	$0.356666\pi$
$242$	21.4030	+	21.4030i	0.0884423	+	0.0884423i
$243$	69.8572	−	69.8572i	0.287478	−	0.287478i
$244$		−	333.065i		−	1.36502i
$245$		0			0
$246$	−27.6591			−0.112435
$247$	−11.4495	−	11.4495i	−0.0463544	−	0.0463544i
$248$	9.96058	−	9.96058i	0.0401636	−	0.0401636i
$249$			406.343i			1.63190i
$250$		0			0
$251$	310.212			1.23590			0.617952	−	0.786216i	$-0.287963\pi$
$251$	310.212			1.23590			0.617952	+	0.786216i	$0.287963\pi$
$252$	31.1620	+	31.1620i	0.123659	+	0.123659i
$253$	97.8118	−	97.8118i	0.386608	−	0.386608i
$254$			370.158i			1.45731i
$255$		0			0
$256$	301.734			1.17865
$257$	33.6050	+	33.6050i	0.130759	+	0.130759i	0.769457	−	0.638698i	$-0.220527\pi$
$257$	33.6050	+	33.6050i	0.130759	+	0.130759i	−0.638698	+	0.769457i	$0.720527\pi$
$258$	−341.167	+	341.167i	−1.32235	+	1.32235i
$259$		−	124.889i		−	0.482197i
$260$		0			0
$261$	−34.8951			−0.133698
$262$	71.2324	+	71.2324i	0.271879	+	0.271879i
$263$	−26.6309	+	26.6309i	−0.101258	+	0.101258i	−0.755921	−	0.654663i	$-0.772811\pi$
$263$	−26.6309	+	26.6309i	−0.101258	+	0.101258i	0.654663	+	0.755921i	$0.272811\pi$
$264$			12.8786i			0.0487828i
$265$		0			0
$266$	25.3661			0.0953612
$267$	110.651	+	110.651i	0.414425	+	0.414425i
$268$	122.014	−	122.014i	0.455275	−	0.455275i
$269$		−	98.9960i		−	0.368015i	−0.982925	−	0.184007i	$-0.941093\pi$
$269$		−	98.9960i		−	0.368015i	0.982925	−	0.184007i	$-0.0589071\pi$
$270$		0			0
$271$	22.5104			0.0830640			0.0415320	−	0.999137i	$-0.486776\pi$
$271$	22.5104			0.0830640			0.0415320	+	0.999137i	$0.486776\pi$
$272$	−149.276	−	149.276i	−0.548809	−	0.548809i
$273$	180.608	−	180.608i	0.661568	−	0.661568i
$274$		−	36.7258i		−	0.134036i
$275$		0			0
$276$	−490.852			−1.77845
$277$	−371.516	−	371.516i	−1.34121	−	1.34121i	−0.894854	−	0.446360i	$-0.852720\pi$
$277$	−371.516	−	371.516i	−1.34121	−	1.34121i	−0.446360	−	0.894854i	$-0.647280\pi$
$278$	324.260	−	324.260i	1.16640	−	1.16640i
$279$		−	22.2012i		−	0.0795742i
$280$		0			0
$281$	−482.822			−1.71823			−0.859114	−	0.511785i	$-0.828984\pi$
$281$	−482.822			−1.71823			−0.859114	+	0.511785i	$0.828984\pi$
$282$	−537.546	−	537.546i	−1.90619	−	1.90619i
$283$	−351.916	+	351.916i	−1.24352	+	1.24352i	−0.284987	+	0.958531i	$0.591989\pi$
$283$	−351.916	+	351.916i	−1.24352	+	1.24352i	−0.958531	+	0.284987i	$0.908011\pi$
$284$			400.647i			1.41073i
$285$		0			0
$286$	−106.491			−0.372346
$287$	−14.3296	−	14.3296i	−0.0499290	−	0.0499290i
$288$	57.1590	−	57.1590i	0.198469	−	0.198469i
$289$		−	143.968i		−	0.498160i
$290$		0			0
$291$	52.0726			0.178944
$292$	160.778	+	160.778i	0.550609	+	0.550609i
$293$	110.219	−	110.219i	0.376173	−	0.376173i	−0.493546	−	0.869719i	$-0.664300\pi$
$293$	110.219	−	110.219i	0.376173	−	0.376173i	0.869719	+	0.493546i	$0.164300\pi$
$294$		−	44.1469i		−	0.150159i
$295$		0			0
$296$	−22.1547			−0.0748468
$297$	−55.1955	−	55.1955i	−0.185843	−	0.185843i
$298$	92.2194	−	92.2194i	0.309461	−	0.309461i
$299$			486.663i			1.62764i
$300$		0			0
$301$	−353.504			−1.17443
$302$	384.909	+	384.909i	1.27453	+	1.27453i
$303$	45.7625	−	45.7625i	0.151031	−	0.151031i
$304$		−	24.3252i		−	0.0800173i
$305$		0			0
$306$	−61.5487			−0.201139
$307$	252.602	+	252.602i	0.822807	+	0.822807i	0.986510	−	0.163702i	$-0.0523437\pi$
$307$	252.602	+	252.602i	0.822807	+	0.822807i	−0.163702	+	0.986510i	$0.552344\pi$
$308$	55.6458	−	55.6458i	0.180668	−	0.180668i
$309$		−	422.346i		−	1.36681i
$310$		0			0
$311$	−432.725			−1.39140			−0.695700	−	0.718333i	$-0.744906\pi$
$311$	−432.725			−1.39140			−0.695700	+	0.718333i	$0.744906\pi$
$312$	−32.0389	−	32.0389i	−0.102689	−	0.102689i
$313$	195.153	−	195.153i	0.623492	−	0.623492i	−0.322930	−	0.946423i	$-0.604668\pi$
$313$	195.153	−	195.153i	0.623492	−	0.623492i	0.946423	+	0.322930i	$0.104668\pi$
$314$			841.710i			2.68061i
$315$		0			0
$316$	−430.249			−1.36155
$317$	−160.830	−	160.830i	−0.507349	−	0.507349i	0.406363	−	0.913712i	$-0.366797\pi$
$317$	−160.830	−	160.830i	−0.507349	−	0.507349i	−0.913712	+	0.406363i	$0.866797\pi$
$318$	−536.824	+	536.824i	−1.68813	+	1.68813i
$319$			62.3121i			0.195336i
$320$		0			0
$321$	−302.454			−0.942223
$322$	−539.094	−	539.094i	−1.67420	−	1.67420i
$323$	−11.8168	+	11.8168i	−0.0365846	+	0.0365846i
$324$			336.694i			1.03918i
$325$		0			0
$326$	−218.584			−0.670504
$327$	128.066	+	128.066i	0.391638	+	0.391638i
$328$	−2.54200	+	2.54200i	−0.00775000	+	0.00775000i
$329$		−	556.984i		−	1.69296i
$330$		0			0
$331$	304.835			0.920952			0.460476	−	0.887672i	$-0.347679\pi$
$331$	304.835			0.920952			0.460476	+	0.887672i	$0.347679\pi$
$332$	−311.455	−	311.455i	−0.938117	−	0.938117i
$333$	−24.6903	+	24.6903i	−0.0741452	+	0.0741452i
$334$			720.632i			2.15758i
$335$		0			0
$336$	383.713			1.14200
$337$	−107.040	−	107.040i	−0.317627	−	0.317627i	0.530228	−	0.847855i	$-0.322106\pi$
$337$	−107.040	−	107.040i	−0.317627	−	0.317627i	−0.847855	+	0.530228i	$0.822106\pi$
$338$	−63.9049	+	63.9049i	−0.189068	+	0.189068i
$339$		−	404.088i		−	1.19200i
$340$		0			0
$341$	−39.6445			−0.116260
$342$	−5.01482	−	5.01482i	−0.0146632	−	0.0146632i
$343$	253.044	−	253.044i	0.737737	−	0.737737i
$344$			62.7097i			0.182296i
$345$		0			0
$346$	−570.314			−1.64831
$347$	283.178	+	283.178i	0.816074	+	0.816074i	0.985537	−	0.169463i	$-0.0542032\pi$
$347$	283.178	+	283.178i	0.816074	+	0.816074i	−0.169463	+	0.985537i	$0.554203\pi$
$348$	156.351	−	156.351i	0.449285	−	0.449285i
$349$		−	278.263i		−	0.797315i	−0.917100	−	0.398657i	$-0.869476\pi$
$349$		−	278.263i		−	0.797315i	0.917100	−	0.398657i	$-0.130524\pi$
$350$		0			0
$351$	274.626			0.782409
$352$	−102.069	−	102.069i	−0.289967	−	0.289967i
$353$	−126.294	+	126.294i	−0.357774	+	0.357774i	−0.862992	−	0.505218i	$-0.831412\pi$
$353$	−126.294	+	126.294i	−0.357774	+	0.357774i	0.505218	+	0.862992i	$0.331412\pi$
$354$		−	815.313i		−	2.30315i
$355$		0			0
$356$	−169.625			−0.476474
$357$	−186.402	−	186.402i	−0.522134	−	0.522134i
$358$	19.1009	−	19.1009i	0.0533545	−	0.0533545i
$359$		−	426.950i		−	1.18928i	−0.803993	−	0.594638i	$-0.797295\pi$
$359$		−	426.950i		−	1.18928i	0.803993	−	0.594638i	$-0.202705\pi$
$360$		0			0
$361$	359.074			0.994666
$362$	364.181	+	364.181i	1.00602	+	1.00602i
$363$	25.6294	−	25.6294i	0.0706045	−	0.0706045i
$364$			276.866i			0.760621i
$365$		0			0
$366$	−845.492			−2.31009
$367$	232.750	+	232.750i	0.634197	+	0.634197i	0.949118	−	0.314921i	$-0.101978\pi$
$367$	232.750	+	232.750i	0.634197	+	0.634197i	−0.314921	+	0.949118i	$0.601978\pi$
$368$	−516.973	+	516.973i	−1.40482	+	1.40482i
$369$			5.66588i			0.0153547i
$370$		0			0
$371$	−556.236			−1.49929
$372$	99.4747	+	99.4747i	0.267405	+	0.267405i
$373$	160.235	−	160.235i	0.429585	−	0.429585i	−0.458902	−	0.888487i	$-0.651757\pi$
$373$	160.235	−	160.235i	0.429585	−	0.429585i	0.888487	+	0.458902i	$0.151757\pi$
$374$			109.907i			0.293869i
$375$		0			0
$376$	−98.8060			−0.262782
$377$	−155.017	−	155.017i	−0.411186	−	0.411186i
$378$	−304.212	+	304.212i	−0.804794	+	0.804794i
$379$		−	635.237i		−	1.67609i	−0.545603	−	0.838044i	$-0.683699\pi$
$379$		−	635.237i		−	1.67609i	0.545603	−	0.838044i	$-0.316301\pi$
$380$		0			0
$381$	443.252			1.16339
$382$	267.717	+	267.717i	0.700830	+	0.700830i
$383$	4.36679	−	4.36679i	0.0114015	−	0.0114015i	−0.701383	−	0.712785i	$-0.747434\pi$
$383$	4.36679	−	4.36679i	0.0114015	−	0.0114015i	0.712785	+	0.701383i	$0.247434\pi$
$384$		−	123.546i		−	0.321734i
$385$		0			0
$386$	−482.010			−1.24873
$387$	69.8871	+	69.8871i	0.180587	+	0.180587i
$388$	−39.9127	+	39.9127i	−0.102868	+	0.102868i
$389$		−	192.401i		−	0.494605i	−0.968938	−	0.247303i	$-0.920456\pi$
$389$		−	192.401i		−	0.494605i	0.968938	−	0.247303i	$-0.0795442\pi$
$390$		0			0
$391$	502.275			1.28459
$392$	−4.05731	−	4.05731i	−0.0103503	−	0.0103503i
$393$	85.2985	−	85.2985i	0.217044	−	0.217044i
$394$		−	406.578i		−	1.03192i
$395$		0			0
$396$	−22.0021			−0.0555609
$397$	−280.596	−	280.596i	−0.706791	−	0.706791i	0.259068	−	0.965859i	$-0.416585\pi$
$397$	−280.596	−	280.596i	−0.706791	−	0.706791i	−0.965859	+	0.259068i	$0.916585\pi$
$398$	−97.8717	+	97.8717i	−0.245909	+	0.245909i
$399$		−	30.3751i		−	0.0761280i
$400$		0			0
$401$	419.293			1.04562			0.522809	−	0.852450i	$-0.324884\pi$
$401$	419.293			1.04562			0.522809	+	0.852450i	$0.324884\pi$
$402$	−309.734	−	309.734i	−0.770483	−	0.770483i
$403$	98.6259	−	98.6259i	0.244729	−	0.244729i
$404$			70.1524i			0.173644i
$405$		0			0
$406$	343.436			0.845900
$407$	44.0894	+	44.0894i	0.108328	+	0.108328i
$408$	−33.0667	+	33.0667i	−0.0810458	+	0.0810458i
$409$			181.384i			0.443481i	0.975106	+	0.221740i	$0.0711738\pi$
$409$			181.384i			0.443481i	−0.975106	+	0.221740i	$0.928826\pi$
$410$		0			0
$411$	−43.9779			−0.107002
$412$	323.721	+	323.721i	0.785730	+	0.785730i
$413$	422.398	−	422.398i	1.02276	−	1.02276i
$414$			213.156i			0.514869i
$415$		0			0
$416$	507.843			1.22078
$417$	−388.291	−	388.291i	−0.931154	−	0.931154i
$418$	−8.95494	+	8.95494i	−0.0214233	+	0.0214233i
$419$		−	1.48155i		−	0.00353591i	−0.999998	−	0.00176796i	$-0.999437\pi$
$419$		−	1.48155i		−	0.00353591i	0.999998	−	0.00176796i	$-0.000562758\pi$
$420$		0			0
$421$	−581.421			−1.38105			−0.690524	−	0.723310i	$-0.742620\pi$
$421$	−581.421			−1.38105			−0.690524	+	0.723310i	$0.742620\pi$
$422$	68.8449	+	68.8449i	0.163140	+	0.163140i
$423$	−110.115	+	110.115i	−0.260318	+	0.260318i
$424$			98.6734i			0.232720i
$425$		0			0
$426$	1017.05			2.38744
$427$	−438.033	−	438.033i	−1.02584	−	1.02584i
$428$	231.825	−	231.825i	0.541648	−	0.541648i
$429$			127.520i			0.297248i
$430$		0			0
$431$	267.721			0.621163			0.310581	−	0.950547i	$-0.399476\pi$
$431$	267.721			0.621163			0.310581	+	0.950547i	$0.399476\pi$
$432$	291.730	+	291.730i	0.675300	+	0.675300i
$433$	−90.9590	+	90.9590i	−0.210067	+	0.210067i	−0.804296	−	0.594229i	$-0.797457\pi$
$433$	−90.9590	+	90.9590i	−0.210067	+	0.210067i	0.594229	+	0.804296i	$0.297457\pi$
$434$			218.503i			0.503462i
$435$		0			0
$436$	−196.320			−0.450276
$437$	40.9240	+	40.9240i	0.0936477	+	0.0936477i
$438$	408.138	−	408.138i	0.931821	−	0.931821i
$439$			656.521i			1.49549i	0.663985	+	0.747746i	$0.268864\pi$
$439$			656.521i			1.49549i	−0.663985	+	0.747746i	$0.731136\pi$
$440$		0			0
$441$	−9.04336			−0.0205065
$442$	−273.422	−	273.422i	−0.618602	−	0.618602i
$443$	−539.996	+	539.996i	−1.21895	+	1.21895i	−0.250953	+	0.967999i	$0.580744\pi$
$443$	−539.996	+	539.996i	−1.21895	+	1.21895i	−0.967999	+	0.250953i	$0.919256\pi$
$444$		−	221.255i		−	0.498322i
$445$		0			0
$446$	633.538			1.42049
$447$	−110.430	−	110.430i	−0.247046	−	0.247046i
$448$	−233.180	+	233.180i	−0.520492	+	0.520492i
$449$			892.268i			1.98723i	0.112802	+	0.993617i	$0.464017\pi$
$449$			892.268i			1.98723i	−0.112802	+	0.993617i	$0.535983\pi$
$450$		0			0
$451$	10.1175			0.0224335
$452$	309.726	+	309.726i	0.685235	+	0.685235i
$453$	460.917	−	460.917i	1.01748	−	1.01748i
$454$		−	334.626i		−	0.737063i
$455$		0			0
$456$	−5.38837			−0.0118166
$457$	−236.647	−	236.647i	−0.517827	−	0.517827i	0.399086	−	0.916913i	$-0.369327\pi$
$457$	−236.647	−	236.647i	−0.517827	−	0.517827i	−0.916913	+	0.399086i	$0.869327\pi$
$458$	332.870	−	332.870i	0.726791	−	0.726791i
$459$		−	283.435i		−	0.617506i
$460$		0			0
$461$	379.208			0.822577			0.411288	−	0.911505i	$-0.365079\pi$
$461$	379.208			0.822577			0.411288	+	0.911505i	$0.365079\pi$
$462$	−141.258	−	141.258i	−0.305753	−	0.305753i
$463$	220.388	−	220.388i	0.475999	−	0.475999i	−0.427850	−	0.903850i	$-0.640729\pi$
$463$	220.388	−	220.388i	0.475999	−	0.475999i	0.903850	+	0.427850i	$0.140729\pi$
$464$		−	329.344i		−	0.709792i
$465$		0			0
$466$	−637.071			−1.36711
$467$	324.041	+	324.041i	0.693878	+	0.693878i	0.963083	−	0.269205i	$-0.0867609\pi$
$467$	324.041	+	324.041i	0.693878	+	0.693878i	−0.269205	+	0.963083i	$0.586761\pi$
$468$	54.7359	−	54.7359i	0.116957	−	0.116957i
$469$		−	320.935i		−	0.684296i
$470$		0			0
$471$	1007.92			2.13996
$472$	−74.9312	−	74.9312i	−0.158753	−	0.158753i
$473$	124.797	−	124.797i	0.263841	−	0.263841i
$474$			1092.20i			2.30421i
$475$		0			0
$476$	285.748			0.600310
$477$	109.967	+	109.967i	0.230539	+	0.230539i
$478$	65.1361	−	65.1361i	0.136268	−	0.136268i
$479$			112.034i			0.233891i	0.993138	+	0.116945i	$0.0373102\pi$
$479$			112.034i			0.233891i	−0.993138	+	0.116945i	$0.962690\pi$
$480$		0			0
$481$	−219.367			−0.456065
$482$	408.180	+	408.180i	0.846847	+	0.846847i
$483$	−645.547	+	645.547i	−1.33654	+	1.33654i
$484$			39.2891i			0.0811757i
$485$		0			0
$486$	271.847			0.559355
$487$	226.535	+	226.535i	0.465163	+	0.465163i	0.900343	−	0.435180i	$-0.143315\pi$
$487$	226.535	+	226.535i	0.465163	+	0.465163i	−0.435180	+	0.900343i	$0.643315\pi$
$488$	−77.7048	+	77.7048i	−0.159231	+	0.159231i
$489$			261.748i			0.535271i
$490$		0			0
$491$	−584.100			−1.18961			−0.594807	−	0.803869i	$-0.702771\pi$
$491$	−584.100			−1.18961			−0.594807	+	0.803869i	$0.702771\pi$
$492$	−25.3865	−	25.3865i	−0.0515987	−	0.0515987i
$493$	−159.990	+	159.990i	−0.324523	+	0.324523i
$494$		−	44.5554i		−	0.0901931i
$495$		0			0
$496$	209.537			0.422453
$497$	526.914	+	526.914i	1.06019	+	1.06019i
$498$	−790.634	+	790.634i	−1.58762	+	1.58762i
$499$		−	260.989i		−	0.523023i	−0.965200	−	0.261512i	$-0.915779\pi$
$499$		−	260.989i		−	0.523023i	0.965200	−	0.261512i	$-0.0842210\pi$
$500$		0			0
$501$	862.934			1.72242
$502$	603.588	+	603.588i	1.20237	+	1.20237i
$503$	211.141	−	211.141i	0.419763	−	0.419763i	−0.465359	−	0.885122i	$-0.654075\pi$
$503$	211.141	−	211.141i	0.419763	−	0.419763i	0.885122	+	0.465359i	$0.154075\pi$
$504$		−	14.5403i		−	0.0288498i
$505$		0			0
$506$	380.631			0.752234
$507$	76.5241	+	76.5241i	0.150935	+	0.150935i
$508$	−339.745	+	339.745i	−0.668789	+	0.668789i
$509$			413.771i			0.812909i	0.913671	+	0.406454i	$0.133235\pi$
$509$			413.771i			0.812909i	−0.913671	+	0.406454i	$0.866765\pi$
$510$		0			0
$511$	422.897			0.827586
$512$	481.043	+	481.043i	0.939536	+	0.939536i
$513$	23.0936	−	23.0936i	0.0450167	−	0.0450167i
$514$			130.773i			0.254421i
$515$		0			0
$516$	−626.272			−1.21371
$517$	196.631	+	196.631i	0.380331	+	0.380331i
$518$	243.001	−	243.001i	0.469113	−	0.469113i
$519$			682.933i			1.31586i
$520$		0			0
$521$	−375.677			−0.721068			−0.360534	−	0.932746i	$-0.617406\pi$
$521$	−375.677			−0.721068			−0.360534	+	0.932746i	$0.617406\pi$
$522$	−67.8965	−	67.8965i	−0.130070	−	0.130070i
$523$	287.569	−	287.569i	0.549846	−	0.549846i	−0.376550	−	0.926396i	$-0.622890\pi$
$523$	287.569	−	287.569i	0.549846	−	0.549846i	0.926396	+	0.376550i	$0.122890\pi$
$524$			130.760i			0.249541i
$525$		0			0
$526$	−103.633			−0.197021
$527$	−101.790	−	101.790i	−0.193149	−	0.193149i
$528$	−135.462	+	135.462i	−0.256556	+	0.256556i
$529$		−	1210.48i		−	2.28824i
$530$		0			0
$531$	−167.015			−0.314529
$532$	23.2820	+	23.2820i	0.0437631	+	0.0437631i
$533$	−25.1699	+	25.1699i	−0.0472231	+	0.0472231i
$534$			430.595i			0.806359i
$535$		0			0
$536$	−56.9321			−0.106217
$537$	−22.8727	−	22.8727i	−0.0425936	−	0.0425936i
$538$	192.620	−	192.620i	0.358029	−	0.358029i
$539$			16.1487i			0.0299604i
$540$		0			0
$541$	345.340			0.638336			0.319168	−	0.947698i	$-0.396597\pi$
$541$	345.340			0.638336			0.319168	+	0.947698i	$0.396597\pi$
$542$	43.7991	+	43.7991i	0.0808101	+	0.0808101i
$543$	436.095	−	436.095i	0.803121	−	0.803121i
$544$		−	524.134i		−	0.963481i
$545$		0			0
$546$	702.829			1.28723
$547$	644.463	+	644.463i	1.17818	+	1.17818i	0.980208	+	0.197968i	$0.0634342\pi$
$547$	644.463	+	644.463i	1.17818	+	1.17818i	0.197968	+	0.980208i	$0.436566\pi$
$548$	33.7083	−	33.7083i	0.0615115	−	0.0615115i
$549$			173.197i			0.315477i
$550$		0			0
$551$	−26.0711			−0.0473160
$552$	114.517	+	114.517i	0.207458	+	0.207458i
$553$	−565.846	+	565.846i	−1.02323	+	1.02323i
$554$		−	1445.74i		−	2.60964i
$555$		0			0
$556$	595.237			1.07057
$557$	−314.588	−	314.588i	−0.564790	−	0.564790i	0.365874	−	0.930664i	$-0.380770\pi$
$557$	−314.588	−	314.588i	−0.564790	−	0.564790i	−0.930664	+	0.365874i	$0.880770\pi$
$558$	43.1975	−	43.1975i	0.0774150	−	0.0774150i
$559$			620.928i			1.11078i
$560$		0			0
$561$	131.610			0.234599
$562$	−939.441	−	939.441i	−1.67160	−	1.67160i
$563$	−384.532	+	384.532i	−0.683005	+	0.683005i	−0.960676	−	0.277671i	$-0.910437\pi$
$563$	−384.532	+	384.532i	−0.683005	+	0.683005i	0.277671	+	0.960676i	$0.410437\pi$
$564$		−	986.760i		−	1.74957i
$565$		0			0
$566$	−1369.47			−2.41955
$567$	442.806	+	442.806i	0.780963	+	0.780963i
$568$	93.4718	−	93.4718i	0.164563	−	0.164563i
$569$		−	342.503i		−	0.601938i	−0.953634	−	0.300969i	$-0.902690\pi$
$569$		−	342.503i		−	0.601938i	0.953634	−	0.300969i	$-0.0973100\pi$
$570$		0			0
$571$	−995.752			−1.74387			−0.871937	−	0.489618i	$-0.837136\pi$
$571$	−995.752			−1.74387			−0.871937	+	0.489618i	$0.837136\pi$
$572$	−97.7415	−	97.7415i	−0.170877	−	0.170877i
$573$	320.583	−	320.583i	0.559481	−	0.559481i
$574$		−	55.7632i		−	0.0971484i
$575$		0			0
$576$	92.1986			0.160067
$577$	−581.964	−	581.964i	−1.00860	−	1.00860i	−0.999963	−	0.00864073i	$-0.997250\pi$
$577$	−581.964	−	581.964i	−1.00860	−	1.00860i	−0.00864073	−	0.999963i	$-0.502750\pi$
$578$	280.123	−	280.123i	0.484642	−	0.484642i
$579$			577.192i			0.996877i
$580$		0			0
$581$	−819.225			−1.41003
$582$	101.319	+	101.319i	0.174088	+	0.174088i
$583$	196.367	−	196.367i	0.336822	−	0.336822i
$584$		−	75.0196i		−	0.128458i
$585$		0			0
$586$	428.912			0.731931
$587$	127.566	+	127.566i	0.217318	+	0.217318i	0.807367	−	0.590049i	$-0.200892\pi$
$587$	127.566	+	127.566i	0.217318	+	0.217318i	−0.590049	+	0.807367i	$0.700892\pi$
$588$	40.5197	−	40.5197i	0.0689111	−	0.0689111i
$589$		−	16.5871i		−	0.0281615i
$590$		0			0
$591$	−486.865			−0.823798
$592$	−233.030	−	233.030i	−0.393631	−	0.393631i
$593$	−190.867	+	190.867i	−0.321866	+	0.321866i	−0.849483	−	0.527617i	$-0.823086\pi$
$593$	−190.867	+	190.867i	−0.321866	+	0.321866i	0.527617	+	0.849483i	$0.323086\pi$
$594$		−	214.791i		−	0.361601i
$595$		0			0
$596$	169.285			0.284035
$597$	117.198	+	117.198i	0.196312	+	0.196312i
$598$	−946.916	+	946.916i	−1.58347	+	1.58347i
$599$		−	1049.59i		−	1.75224i	−0.482096	−	0.876118i	$-0.660124\pi$
$599$		−	1049.59i		−	1.75224i	0.482096	−	0.876118i	$-0.339876\pi$
$600$		0			0
$601$	113.596			0.189012			0.0945062	−	0.995524i	$-0.469873\pi$
$601$	113.596			0.189012			0.0945062	+	0.995524i	$0.469873\pi$
$602$	−687.823	−	687.823i	−1.14256	−	1.14256i
$603$	−63.4482	+	63.4482i	−0.105221	+	0.105221i
$604$			706.569i			1.16982i
$605$		0			0
$606$	178.083			0.293866
$607$	725.396	+	725.396i	1.19505	+	1.19505i	0.975630	+	0.219421i	$0.0704169\pi$
$607$	725.396	+	725.396i	1.19505	+	1.19505i	0.219421	+	0.975630i	$0.429583\pi$
$608$	42.7051	−	42.7051i	0.0702386	−	0.0702386i
$609$		−	411.253i		−	0.675292i
$610$		0			0
$611$	−978.340			−1.60121
$612$	−56.4917	−	56.4917i	−0.0923068	−	0.0923068i
$613$	−110.938	+	110.938i	−0.180975	+	0.180975i	−0.791781	−	0.610806i	$-0.790846\pi$
$613$	−110.938	+	110.938i	−0.180975	+	0.180975i	0.610806	+	0.791781i	$0.290846\pi$
$614$			982.990i			1.60096i
$615$		0			0
$616$	−25.9645			−0.0421502
$617$	−362.476	−	362.476i	−0.587481	−	0.587481i	0.349467	−	0.936949i	$-0.386363\pi$
$617$	−362.476	−	362.476i	−0.587481	−	0.587481i	−0.936949	+	0.349467i	$0.886363\pi$
$618$	821.771	−	821.771i	1.32973	−	1.32973i
$619$			742.446i			1.19943i	0.800214	+	0.599714i	$0.204719\pi$
$619$			742.446i			1.19943i	−0.800214	+	0.599714i	$0.795281\pi$
$620$		0			0
$621$	−981.594			−1.58067
$622$	−841.967	−	841.967i	−1.35364	−	1.35364i
$623$	−223.083	+	223.083i	−0.358079	+	0.358079i
$624$		−	673.991i		−	1.08011i
$625$		0			0
$626$	759.430			1.21315
$627$	10.7233	+	10.7233i	0.0171025	+	0.0171025i
$628$	−772.554	+	772.554i	−1.23018	+	1.23018i
$629$			226.404i			0.359943i
$630$		0			0
$631$	401.361			0.636072			0.318036	−	0.948079i	$-0.396977\pi$
$631$	401.361			0.636072			0.318036	+	0.948079i	$0.396977\pi$
$632$	100.378	+	100.378i	0.158826	+	0.158826i
$633$	82.4396	−	82.4396i	0.130236	−	0.130236i
$634$		−	625.862i		−	0.987164i
$635$		0			0
$636$	−985.435			−1.54943
$637$	−40.1740	−	40.1740i	−0.0630674	−	0.0630674i
$638$	−121.242	+	121.242i	−0.190035	+	0.190035i
$639$		−	208.340i		−	0.326041i
$640$		0			0
$641$	−326.998			−0.510137			−0.255069	−	0.966923i	$-0.582098\pi$
$641$	−326.998			−0.510137			−0.255069	+	0.966923i	$0.582098\pi$
$642$	−588.493	−	588.493i	−0.916656	−	0.916656i
$643$	−543.234	+	543.234i	−0.844843	+	0.844843i	−0.989484	−	0.144641i	$-0.953797\pi$
$643$	−543.234	+	543.234i	−0.844843	+	0.844843i	0.144641	+	0.989484i	$0.453797\pi$
$644$		−	989.602i		−	1.53665i
$645$		0			0
$646$	−45.9847			−0.0711837
$647$	−672.400	−	672.400i	−1.03926	−	1.03926i	−0.999197	−	0.0400605i	$-0.987245\pi$
$647$	−672.400	−	672.400i	−1.03926	−	1.03926i	−0.0400605	−	0.999197i	$-0.512755\pi$
$648$	78.5514	−	78.5514i	0.121221	−	0.121221i
$649$			298.237i			0.459533i
$650$		0			0
$651$	261.650			0.401920
$652$	−200.625	−	200.625i	−0.307707	−	0.307707i
$653$	5.81723	−	5.81723i	0.00890847	−	0.00890847i	−0.702639	−	0.711547i	$-0.747995\pi$
$653$	5.81723	−	5.81723i	0.00890847	−	0.00890847i	0.711547	+	0.702639i	$0.247995\pi$
$654$			498.362i			0.762022i
$655$		0			0
$656$	−53.4751			−0.0815169
$657$	−83.6058	−	83.6058i	−0.127254	−	0.127254i
$658$	1083.74	−	1083.74i	1.64702	−	1.64702i
$659$		−	159.043i		−	0.241340i	−0.992693	−	0.120670i	$-0.961496\pi$
$659$		−	159.043i		−	0.241340i	0.992693	−	0.120670i	$-0.0385044\pi$
$660$		0			0
$661$	34.4265			0.0520825			0.0260412	−	0.999661i	$-0.491710\pi$
$661$	34.4265			0.0520825			0.0260412	+	0.999661i	$0.491710\pi$
$662$	593.127	+	593.127i	0.895962	+	0.895962i
$663$	−327.414	+	327.414i	−0.493837	+	0.493837i
$664$			145.326i			0.218865i
$665$		0			0
$666$	−96.0815			−0.144266
$667$	554.077	+	554.077i	0.830701	+	0.830701i
$668$	−661.424	+	661.424i	−0.990156	+	0.990156i
$669$		−	758.641i		−	1.13399i
$670$		0			0
$671$	309.276			0.460918
$672$	673.641	+	673.641i	1.00244	+	1.00244i
$673$	−536.654	+	536.654i	−0.797406	+	0.797406i	−0.982686	−	0.185280i	$-0.940681\pi$
$673$	−536.654	+	536.654i	−0.797406	+	0.797406i	0.185280	+	0.982686i	$0.440681\pi$
$674$		−	416.544i		−	0.618017i
$675$		0			0
$676$	−117.309			−0.173534
$677$	−492.035	−	492.035i	−0.726787	−	0.726787i	0.243191	−	0.969978i	$-0.421806\pi$
$677$	−492.035	−	492.035i	−0.726787	−	0.726787i	−0.969978	+	0.243191i	$0.921806\pi$
$678$	786.246	−	786.246i	1.15965	−	1.15965i
$679$			104.983i			0.154614i
$680$		0			0
$681$	−400.704			−0.588406
$682$	−77.1376	−	77.1376i	−0.113105	−	0.113105i
$683$	412.797	−	412.797i	0.604388	−	0.604388i	−0.337086	−	0.941474i	$-0.609441\pi$
$683$	412.797	−	412.797i	0.604388	−	0.604388i	0.941474	+	0.337086i	$0.109441\pi$
$684$		−	9.20560i		−	0.0134585i
$685$		0			0
$686$	984.710			1.43544
$687$	−398.601	−	398.601i	−0.580206	−	0.580206i
$688$	−659.600	+	659.600i	−0.958721	+	0.958721i
$689$			977.027i			1.41804i
$690$		0			0
$691$	213.120			0.308423			0.154212	−	0.988038i	$-0.450716\pi$
$691$	213.120			0.308423			0.154212	+	0.988038i	$0.450716\pi$
$692$	−523.457	−	523.457i	−0.756440	−	0.756440i
$693$	−28.9363	+	28.9363i	−0.0417551	+	0.0417551i
$694$			1101.97i			1.58786i
$695$		0			0
$696$	−72.9541			−0.104819
$697$	25.9773	+	25.9773i	0.0372702	+	0.0372702i
$698$	541.425	−	541.425i	0.775680	−	0.775680i
$699$			762.873i			1.09138i
$700$		0			0
$701$	−991.452			−1.41434			−0.707170	−	0.707044i	$-0.750028\pi$
$701$	−991.452			−1.41434			−0.707170	+	0.707044i	$0.750028\pi$
$702$	534.347	+	534.347i	0.761178	+	0.761178i
$703$	−18.4468	+	18.4468i	−0.0262401	+	0.0262401i
$704$		−	164.638i		−	0.233861i
$705$		0			0
$706$	−491.470			−0.696132
$707$	92.2614	+	92.2614i	0.130497	+	0.130497i
$708$	748.326	−	748.326i	1.05696	−	1.05696i
$709$			407.203i			0.574335i	0.957880	+	0.287167i	$0.0927136\pi$
$709$			407.203i			0.574335i	−0.957880	+	0.287167i	$0.907286\pi$
$710$		0			0
$711$	223.733			0.314674
$712$	39.5738	+	39.5738i	0.0555812	+	0.0555812i
$713$	−352.518	+	352.518i	−0.494416	+	0.494416i
$714$		−	725.375i		−	1.01593i
$715$		0			0
$716$	35.0631			0.0489709
$717$	−77.9984	−	77.9984i	−0.108784	−	0.108784i
$718$	830.730	−	830.730i	1.15701	−	1.15701i
$719$			322.825i			0.448992i	0.974475	+	0.224496i	$0.0720736\pi$
$719$			322.825i			0.448992i	−0.974475	+	0.224496i	$0.927926\pi$
$720$		0			0
$721$	851.487			1.18098
$722$	698.662	+	698.662i	0.967676	+	0.967676i
$723$	488.783	−	488.783i	0.676048	−	0.676048i
$724$			668.518i			0.923368i
$725$		0			0
$726$	99.7360			0.137377
$727$	76.4125	+	76.4125i	0.105107	+	0.105107i	0.757704	−	0.652598i	$-0.226321\pi$
$727$	76.4125	+	76.4125i	0.105107	+	0.105107i	−0.652598	+	0.757704i	$0.726321\pi$
$728$	64.5934	−	64.5934i	0.0887272	−	0.0887272i
$729$			522.869i			0.717242i
$730$		0			0
$731$	640.847			0.876671
$732$	−776.025	−	776.025i	−1.06014	−	1.06014i
$733$	−458.236	+	458.236i	−0.625152	+	0.625152i	−0.946844	−	0.321692i	$-0.895748\pi$
$733$	−458.236	+	458.236i	−0.625152	+	0.625152i	0.321692	+	0.946844i	$0.395748\pi$
$734$			905.739i			1.23398i
$735$		0			0
$736$	−1815.18			−2.46628
$737$	113.299	+	113.299i	0.153730	+	0.153730i
$738$	−11.0243	+	11.0243i	−0.0149380	+	0.0149380i
$739$			833.837i			1.12833i	0.825661	+	0.564166i	$0.190802\pi$
$739$			833.837i			1.12833i	−0.825661	+	0.564166i	$0.809198\pi$
$740$		0			0
$741$	−53.3537			−0.0720023
$742$	−1082.29	−	1082.29i	−1.45861	−	1.45861i
$743$	433.108	−	433.108i	0.582918	−	0.582918i	−0.352786	−	0.935704i	$-0.614766\pi$
$743$	433.108	−	433.108i	0.582918	−	0.582918i	0.935704	+	0.352786i	$0.114766\pi$
$744$		−	46.4153i		−	0.0623861i
$745$		0			0
$746$	623.549			0.835856
$747$	161.959	+	161.959i	0.216813	+	0.216813i
$748$	−100.877	+	100.877i	−0.134862	+	0.134862i
$749$		−	609.774i		−	0.814118i
$750$		0			0
$751$	752.215			1.00162			0.500809	−	0.865558i	$-0.333036\pi$
$751$	752.215			1.00162			0.500809	+	0.865558i	$0.333036\pi$
$752$	−1039.27	−	1039.27i	−1.38201	−	1.38201i
$753$	722.778	−	722.778i	0.959864	−	0.959864i
$754$		−	603.243i		−	0.800057i
$755$		0			0
$756$	−558.435			−0.738671
$757$	445.110	+	445.110i	0.587992	+	0.587992i	0.937087	−	0.349095i	$-0.113511\pi$
$757$	445.110	+	445.110i	0.587992	+	0.587992i	−0.349095	+	0.937087i	$0.613511\pi$
$758$	1236.00	−	1236.00i	1.63061	−	1.63061i
$759$		−	455.793i		−	0.600518i
$760$		0			0
$761$	−1172.60			−1.54086			−0.770431	−	0.637523i	$-0.779959\pi$
$761$	−1172.60			−1.54086			−0.770431	+	0.637523i	$0.779959\pi$
$762$	862.448	+	862.448i	1.13182	+	1.13182i
$763$	−258.192	+	258.192i	−0.338391	+	0.338391i
$764$			491.442i			0.643249i
$765$		0			0
$766$	16.9932			0.0221843
$767$	−741.941	−	741.941i	−0.967328	−	0.967328i
$768$	703.025	−	703.025i	0.915397	−	0.915397i
$769$			943.570i			1.22701i	0.789691	+	0.613505i	$0.210241\pi$
$769$			943.570i			1.22701i	−0.789691	+	0.613505i	$0.789759\pi$
$770$		0			0
$771$	156.596			0.203108
$772$	−442.407	−	442.407i	−0.573067	−	0.573067i
$773$	605.699	−	605.699i	0.783569	−	0.783569i	−0.196862	−	0.980431i	$-0.563075\pi$
$773$	605.699	−	605.699i	0.783569	−	0.783569i	0.980431	+	0.196862i	$0.0630752\pi$
$774$			271.963i			0.351373i
$775$		0			0
$776$	18.6234			0.0239993
$777$	−290.985	−	290.985i	−0.374499	−	0.374499i
$778$	374.361	−	374.361i	0.481184	−	0.481184i
$779$			4.23313i			0.00543406i
$780$		0			0
$781$	−372.031			−0.476353
$782$	977.291	+	977.291i	1.24973	+	1.24973i
$783$	312.668	−	312.668i	0.399320	−	0.399320i
$784$		−	85.3521i		−	0.108867i
$785$		0			0
$786$	331.936			0.422310
$787$	−478.071	−	478.071i	−0.607459	−	0.607459i	0.334822	−	0.942281i	$-0.391324\pi$
$787$	−478.071	−	478.071i	−0.607459	−	0.607459i	−0.942281	+	0.334822i	$0.891324\pi$
$788$	373.173	−	373.173i	0.473570	−	0.473570i
$789$			124.097i			0.157284i
$790$		0			0
$791$	814.678			1.02993
$792$	5.13314	+	5.13314i	0.00648124	+	0.00648124i
$793$	−769.404	+	769.404i	−0.970244	+	0.970244i
$794$		−	1091.93i		−	1.37522i
$795$		0			0
$796$	−179.661			−0.225705
$797$	721.889	+	721.889i	0.905758	+	0.905758i	0.995927	−	0.0901681i	$-0.0287404\pi$
$797$	721.889	+	721.889i	0.905758	+	0.905758i	−0.0901681	+	0.995927i	$0.528740\pi$
$798$	59.1017	−	59.1017i	0.0740623	−	0.0740623i
$799$			1009.72i			1.26373i
$800$		0			0
$801$	88.2063			0.110120
$802$	815.831	+	815.831i	1.01725	+	1.01725i
$803$	−149.294	+	149.294i	−0.185921	+	0.185921i
$804$		−	568.572i		−	0.707179i
$805$		0			0
$806$	383.799			0.476177
$807$	−230.656	−	230.656i	−0.285819	−	0.285819i
$808$	16.3667	−	16.3667i	0.0202558	−	0.0202558i
$809$		−	1130.38i		−	1.39725i	−0.715487	−	0.698626i	$-0.753795\pi$
$809$		−	1130.38i		−	1.39725i	0.715487	−	0.698626i	$-0.246205\pi$
$810$		0			0
$811$	885.040			1.09129			0.545647	−	0.838015i	$-0.316284\pi$
$811$	885.040			1.09129			0.545647	+	0.838015i	$0.316284\pi$
$812$	315.218	+	315.218i	0.388200	+	0.388200i
$813$	52.4480	−	52.4480i	0.0645117	−	0.0645117i
$814$			171.572i			0.210777i
$815$		0			0
$816$	−695.611			−0.852465
$817$	52.2145	+	52.2145i	0.0639101	+	0.0639101i
$818$	−352.924	+	352.924i	−0.431447	+	0.431447i
$819$		−	143.973i		−	0.175791i
$820$		0			0
$821$	656.727			0.799911			0.399956	−	0.916535i	$-0.369026\pi$
$821$	656.727			0.799911			0.399956	+	0.916535i	$0.369026\pi$
$822$	−85.5692	−	85.5692i	−0.104099	−	0.104099i
$823$	−266.121	+	266.121i	−0.323354	+	0.323354i	−0.850052	−	0.526698i	$-0.823430\pi$
$823$	−266.121	+	266.121i	−0.323354	+	0.323354i	0.526698	+	0.850052i	$0.323430\pi$
$824$		−	151.049i		−	0.183312i
$825$		0			0
$826$	1643.75			1.99001
$827$	−308.533	−	308.533i	−0.373075	−	0.373075i	0.495521	−	0.868596i	$-0.334977\pi$
$827$	−308.533	−	308.533i	−0.373075	−	0.373075i	−0.868596	+	0.495521i	$0.834977\pi$
$828$	−195.642	+	195.642i	−0.236283	+	0.236283i
$829$			853.146i			1.02913i	0.857452	+	0.514563i	$0.172046\pi$
$829$			853.146i			1.02913i	−0.857452	+	0.514563i	$0.827954\pi$
$830$		0			0
$831$	−1731.23			−2.08331
$832$	409.580	+	409.580i	0.492284	+	0.492284i
$833$	−41.4627	+	41.4627i	−0.0497751	+	0.0497751i
$834$		−	1511.02i		−	1.81178i
$835$		0			0
$836$	−16.4384			−0.0196631
$837$	198.927	+	198.927i	0.237667	+	0.237667i
$838$	2.88269	−	2.88269i	0.00343997	−	0.00343997i
$839$			153.643i			0.183126i	0.995799	+	0.0915630i	$0.0291863\pi$
$839$			153.643i			0.183126i	−0.995799	+	0.0915630i	$0.970814\pi$
$840$		0			0
$841$	488.019			0.580284
$842$	−1131.29	−	1131.29i	−1.34357	−	1.34357i
$843$	−1124.95	+	1124.95i	−1.33446	+	1.33446i
$844$			126.377i			0.149736i
$845$		0			0
$846$	−428.507			−0.506510
$847$	51.6713	+	51.6713i	0.0610051	+	0.0610051i
$848$	−1037.88	+	1037.88i	−1.22391	+	1.22391i
$849$			1639.89i			1.93156i
$850$		0			0
$851$	784.084			0.921368
$852$	933.488	+	933.488i	1.09564	+	1.09564i
$853$	103.006	−	103.006i	0.120757	−	0.120757i	−0.644146	−	0.764903i	$-0.722787\pi$
$853$	103.006	−	103.006i	0.120757	−	0.120757i	0.764903	+	0.644146i	$0.222787\pi$
$854$		−	1704.59i		−	1.99601i
$855$		0			0
$856$	−108.171			−0.126368
$857$	−826.015	−	826.015i	−0.963845	−	0.963845i	0.0355235	−	0.999369i	$-0.488690\pi$
$857$	−826.015	−	826.015i	−0.963845	−	0.963845i	−0.999369	+	0.0355235i	$0.988690\pi$
$858$	−248.119	+	248.119i	−0.289183	+	0.289183i
$859$		−	1329.82i		−	1.54811i	−0.633121	−	0.774053i	$-0.718226\pi$
$859$		−	1329.82i		−	1.54811i	0.633121	−	0.774053i	$-0.281774\pi$
$860$		0			0
$861$	−66.7746			−0.0775547
$862$	520.913	+	520.913i	0.604308	+	0.604308i
$863$	−764.324	+	764.324i	−0.885659	+	0.885659i	−0.994103	−	0.108444i	$-0.965413\pi$
$863$	−764.324	+	764.324i	−0.885659	+	0.885659i	0.108444	+	0.994103i	$0.465413\pi$
$864$			1024.31i			1.18555i
$865$		0			0
$866$	−353.963			−0.408734
$867$	−335.439	−	335.439i	−0.386896	−	0.386896i
$868$	−200.550	+	200.550i	−0.231049	+	0.231049i
$869$		−	399.519i		−	0.459746i
$870$		0			0
$871$	−563.721			−0.647211
$872$	45.8019	+	45.8019i	0.0525251	+	0.0525251i
$873$	20.7549	−	20.7549i	0.0237743	−	0.0237743i
$874$			159.254i			0.182213i
$875$		0			0
$876$	749.209			0.855261
$877$	865.671	+	865.671i	0.987083	+	0.987083i	0.999918	−	0.0128350i	$-0.00408561\pi$
$877$	865.671	+	865.671i	0.987083	+	0.987083i	−0.0128350	+	0.999918i	$0.504086\pi$
$878$	−1277.41	+	1277.41i	−1.45491	+	1.45491i
$879$		−	513.608i		−	0.584310i
$880$		0			0
$881$	902.531			1.02444			0.512220	−	0.858854i	$-0.328823\pi$
$881$	902.531			1.02444			0.512220	+	0.858854i	$0.328823\pi$
$882$	−17.5959	−	17.5959i	−0.0199501	−	0.0199501i
$883$	675.764	−	675.764i	0.765305	−	0.765305i	−0.211971	−	0.977276i	$-0.567988\pi$
$883$	675.764	−	675.764i	0.765305	−	0.765305i	0.977276	+	0.211971i	$0.0679883\pi$
$884$		−	501.914i		−	0.567776i
$885$		0			0
$886$	−2101.37			−2.37175
$887$	−767.416	−	767.416i	−0.865181	−	0.865181i	0.126753	−	0.991934i	$-0.459544\pi$
$887$	−767.416	−	767.416i	−0.865181	−	0.865181i	−0.991934	+	0.126753i	$0.959544\pi$
$888$	−51.6193	+	51.6193i	−0.0581298	+	0.0581298i
$889$			893.636i			1.00522i
$890$		0			0
$891$	−312.646			−0.350893
$892$	581.486	+	581.486i	0.651890	+	0.651890i
$893$	−82.2697	+	82.2697i	−0.0921273	+	0.0921273i
$894$		−	429.733i		−	0.480686i
$895$		0			0
$896$	249.079			0.277990
$897$	1133.90	+	1133.90i	1.26410	+	1.26410i
$898$	−1736.11	+	1736.11i	−1.93331	+	1.93331i
$899$		−	224.576i		−	0.249806i
$900$		0			0
$901$	1008.37			1.11917
$902$	19.6860	+	19.6860i	0.0218248	+	0.0218248i
$903$	−823.646	+	823.646i	−0.912122	+	0.912122i
$904$		−	144.520i		−	0.159867i
$905$		0			0
$906$	1793.64			1.97973
$907$	−839.766	−	839.766i	−0.925873	−	0.925873i	0.0715635	−	0.997436i	$-0.477201\pi$
$907$	−839.766	−	839.766i	−0.925873	−	0.925873i	−0.997436	+	0.0715635i	$0.977201\pi$
$908$	307.133	−	307.133i	0.338252	−	0.338252i
$909$		−	36.4798i		−	0.0401318i
$910$		0			0
$911$	479.304			0.526130			0.263065	−	0.964778i	$-0.415267\pi$
$911$	479.304			0.526130			0.263065	+	0.964778i	$0.415267\pi$
$912$	−56.6766	−	56.6766i	−0.0621454	−	0.0621454i
$913$	289.209	−	289.209i	0.316768	−	0.316768i
$914$		−	920.902i		−	1.00755i
$915$		0			0
$916$	611.042			0.667076
$917$	171.970	+	171.970i	0.187535	+	0.187535i
$918$	551.488	−	551.488i	0.600750	−	0.600750i
$919$		−	909.910i		−	0.990109i	−0.868862	−	0.495055i	$-0.835148\pi$
$919$		−	909.910i		−	0.990109i	0.868862	−	0.495055i	$-0.164852\pi$
$920$		0			0
$921$	1177.10			1.27807
$922$	737.836	+	737.836i	0.800256	+	0.800256i
$923$	925.523	−	925.523i	1.00273	−	1.00273i
$924$		−	259.304i		−	0.280632i
$925$		0			0
$926$	857.630			0.926166
$927$	−168.337	−	168.337i	−0.181594	−	0.181594i
$928$	578.191	−	578.191i	0.623050	−	0.623050i
$929$			1025.02i			1.10336i	0.834057	+	0.551678i	$0.186012\pi$
$929$			1025.02i			1.10336i	−0.834057	+	0.551678i	$0.813988\pi$
$930$		0			0
$931$	−6.75654			−0.00725730
$932$	−584.729	−	584.729i	−0.627391	−	0.627391i
$933$	−1008.23	+	1008.23i	−1.08063	+	1.08063i
$934$			1260.99i			1.35010i
$935$		0			0
$936$	−25.5400			−0.0272863
$937$	−1089.69	−	1089.69i	−1.16296	−	1.16296i	−0.983825	−	0.179132i	$-0.942671\pi$
$937$	−1089.69	−	1089.69i	−1.16296	−	1.16296i	−0.179132	−	0.983825i	$-0.557329\pi$
$938$	624.453	−	624.453i	0.665728	−	0.665728i
$939$		−	909.394i		−	0.968470i
$940$		0			0
$941$	−861.318			−0.915322			−0.457661	−	0.889127i	$-0.651313\pi$
$941$	−861.318			−0.915322			−0.457661	+	0.889127i	$0.651313\pi$
$942$	1961.14	+	1961.14i	2.08189	+	2.08189i
$943$	89.9649	−	89.9649i	0.0954028	−	0.0954028i
$944$		−	1576.30i		−	1.66981i
$945$		0			0
$946$	485.642			0.513364
$947$	576.202	+	576.202i	0.608450	+	0.608450i	0.942541	−	0.334091i	$-0.108429\pi$
$947$	576.202	+	576.202i	0.608450	+	0.608450i	−0.334091	+	0.942541i	$0.608429\pi$
$948$	−1002.46	+	1002.46i	−1.05745	+	1.05745i
$949$		−	742.816i		−	0.782736i
$950$		0			0
$951$	−749.449			−0.788065
$952$	−66.6655	−	66.6655i	−0.0700268	−	0.0700268i
$953$	−1037.42	+	1037.42i	−1.08858	+	1.08858i	−0.0929099	+	0.995675i	$0.529617\pi$
$953$	−1037.42	+	1037.42i	−1.08858	+	1.08858i	−0.995675	+	0.0929099i	$0.970383\pi$
$954$			427.932i			0.448566i
$955$		0			0
$956$	119.569			0.125072
$957$	145.184	+	145.184i	0.151707	+	0.151707i
$958$	−217.987	+	217.987i	−0.227544	+	0.227544i
$959$		−	88.6635i		−	0.0924542i
$960$		0			0
$961$	−818.119			−0.851321
$962$	−426.829	−	426.829i	−0.443690	−	0.443690i
$963$	−120.551	+	120.551i	−0.125183	+	0.125183i
$964$			749.287i			0.777269i
$965$		0			0
$966$	−2512.12			−2.60054
$967$	322.978	+	322.978i	0.334000	+	0.334000i	0.854103	−	0.520103i	$-0.174107\pi$
$967$	322.978	+	322.978i	0.334000	+	0.334000i	−0.520103	+	0.854103i	$0.674107\pi$
$968$	9.16622	−	9.16622i	0.00946923	−	0.00946923i
$969$			55.0652i			0.0568268i
$970$		0			0
$971$	−190.074			−0.195751			−0.0978754	−	0.995199i	$-0.531205\pi$
$971$	−190.074			−0.195751			−0.0978754	+	0.995199i	$0.531205\pi$
$972$	249.511	+	249.511i	0.256699	+	0.256699i
$973$	782.831	−	782.831i	0.804554	−	0.804554i
$974$			881.550i			0.905082i
$975$		0			0
$976$	−1634.65			−1.67484
$977$	275.997	+	275.997i	0.282494	+	0.282494i	0.834103	−	0.551609i	$-0.185986\pi$
$977$	275.997	+	275.997i	0.282494	+	0.282494i	−0.551609	+	0.834103i	$0.685986\pi$
$978$	−509.290	+	509.290i	−0.520747	+	0.520747i
$979$		−	157.509i		−	0.160888i
$980$		0			0
$981$	102.088			0.104065
$982$	−1136.50	−	1136.50i	−1.15733	−	1.15733i
$983$	496.618	−	496.618i	0.505206	−	0.505206i	−0.407845	−	0.913051i	$-0.633720\pi$
$983$	496.618	−	496.618i	0.505206	−	0.505206i	0.913051	+	0.407845i	$0.133720\pi$
$984$			11.8455i			0.0120381i
$985$		0			0
$986$	−622.594			−0.631434
$987$	−1297.75	−	1297.75i	−1.31484	−	1.31484i
$988$	40.8947	−	40.8947i	0.0413914	−	0.0413914i
$989$		−	2219.38i		−	2.24407i
$990$		0			0
$991$	856.829			0.864610			0.432305	−	0.901727i	$-0.357700\pi$
$991$	856.829			0.864610			0.432305	+	0.901727i	$0.357700\pi$
$992$	367.860	+	367.860i	0.370827	+	0.370827i
$993$	710.251	−	710.251i	0.715257	−	0.715257i
$994$			2050.47i			2.06284i
$995$		0			0
$996$	−1451.35			−1.45718
$997$	533.591	+	533.591i	0.535196	+	0.535196i	0.922114	−	0.386918i	$-0.126460\pi$
$997$	533.591	+	533.591i	0.535196	+	0.535196i	−0.386918	+	0.922114i	$0.626460\pi$
$998$	507.813	−	507.813i	0.508831	−	0.508831i
$999$		−	442.461i		−	0.442904i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	275.3.f.c.232.10	yes	24
5.2	odd	4	inner	275.3.f.c.243.3	yes	24
5.3	odd	4	inner	275.3.f.c.243.10	yes	24
5.4	even	2	inner	275.3.f.c.232.3	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
275.3.f.c.232.3	✓	24	5.4	even	2	inner
275.3.f.c.232.10	yes	24	1.1	even	1	trivial
275.3.f.c.243.3	yes	24	5.2	odd	4	inner
275.3.f.c.243.10	yes	24	5.3	odd	4	inner

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 275 = 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	275.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.94573 + 1.94573i) q^{2} +(2.32995 - 2.32995i) q^{3} +3.57173i q^{4} +9.06691 q^{6} +(4.69739 + 4.69739i) q^{7} +(0.833292 - 0.833292i) q^{8} -1.85733i q^{9} -3.31662 q^{11} +(8.32196 + 8.32196i) q^{12} +(8.25095 - 8.25095i) q^{13} +18.2797i q^{14} +17.5297 q^{16} +(-8.51563 - 8.51563i) q^{17} +(3.61387 - 3.61387i) q^{18} -1.38766i q^{19} +21.8894 q^{21} +(-6.45326 - 6.45326i) q^{22} +(-29.4914 + 29.4914i) q^{23} -3.88306i q^{24} +32.1082 q^{26} +(16.6421 + 16.6421i) q^{27} +(-16.7778 + 16.7778i) q^{28} -18.7878i q^{29} +11.9533 q^{31} +(30.7748 + 30.7748i) q^{32} +(-7.72757 + 7.72757i) q^{33} -33.1382i q^{34} +6.63389 q^{36} +(-13.2935 - 13.2935i) q^{37} +(2.70002 - 2.70002i) q^{38} -38.4486i q^{39} -3.05055 q^{41} +(42.5908 + 42.5908i) q^{42} +(-37.6277 + 37.6277i) q^{43} -11.8461i q^{44} -114.764 q^{46} +(-59.2865 - 59.2865i) q^{47} +(40.8432 - 40.8432i) q^{48} -4.86901i q^{49} -39.6820 q^{51} +(29.4702 + 29.4702i) q^{52} +(-59.2069 + 59.2069i) q^{53} +64.7619i q^{54} +7.82860 q^{56} +(-3.23318 - 3.23318i) q^{57} +(36.5560 - 36.5560i) q^{58} -89.9219i q^{59} -93.2503 q^{61} +(23.2579 + 23.2579i) q^{62} +(8.72461 - 8.72461i) q^{63} +49.6403i q^{64} -30.0715 q^{66} +(-34.1610 - 34.1610i) q^{67} +(30.4155 - 30.4155i) q^{68} +137.427i q^{69} +112.172 q^{71} +(-1.54770 - 1.54770i) q^{72} +(45.0140 - 45.0140i) q^{73} -51.7309i q^{74} +4.95636 q^{76} +(-15.5795 - 15.5795i) q^{77} +(74.8106 - 74.8106i) q^{78} +120.460i q^{79} +94.2663 q^{81} +(-5.93555 - 5.93555i) q^{82} +(-87.1999 + 87.1999i) q^{83} +78.1830i q^{84} -146.427 q^{86} +(-43.7746 - 43.7746i) q^{87} +(-2.76372 + 2.76372i) q^{88} +47.4909i q^{89} +77.5159 q^{91} +(-105.335 - 105.335i) q^{92} +(27.8505 - 27.8505i) q^{93} -230.711i q^{94} +143.408 q^{96} +(11.1746 + 11.1746i) q^{97} +(9.47378 - 9.47378i) q^{98} +6.16007i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 8 q^{6} - 128 q^{16} - 88 q^{21} + 96 q^{26} + 360 q^{31} + 176 q^{36} - 152 q^{41} + 56 q^{46} - 512 q^{51} - 1048 q^{56} + 784 q^{61} - 440 q^{66} + 728 q^{71} + 1704 q^{76} - 568 q^{81} - 328 q^{86}+ \cdots + 1568 q^{96}+O(q^{100}) \) 24 * q - 8 * q^6 - 128 * q^16 - 88 * q^21 + 96 * q^26 + 360 * q^31 + 176 * q^36 - 152 * q^41 + 56 * q^46 - 512 * q^51 - 1048 * q^56 + 784 * q^61 - 440 * q^66 + 728 * q^71 + 1704 * q^76 - 568 * q^81 - 328 * q^86 - 968 * q^91 + 1568 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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