LMFDB - Embedded newform 525.3.s.f.124.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [525,3,Mod(124,525)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(525, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 5]))

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

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

chi := DirichletCharacter("525.124");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 525 = 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	525.s (of order $6$, degree $2$, not 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:	$14.3052138789$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			124.1
Root			$-0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	525.124
Dual form			525.3.s.f.199.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.59808 - 1.50000i) q^{2} +(0.866025 + 1.50000i) q^{3} +(2.50000 + 4.33013i) q^{4} -5.19615i q^{6} +(-6.06218 - 3.50000i) q^{7} -3.00000i q^{8} +(-1.50000 + 2.59808i) q^{9} +O(q^{10})$	\(q+(-2.59808 - 1.50000i) q^{2} +(0.866025 + 1.50000i) q^{3} +(2.50000 + 4.33013i) q^{4} -5.19615i q^{6} +(-6.06218 - 3.50000i) q^{7} -3.00000i q^{8} +(-1.50000 + 2.59808i) q^{9} +(-4.33013 + 7.50000i) q^{12} -3.46410 q^{13} +(10.5000 + 18.1865i) q^{14} +(5.50000 - 9.52628i) q^{16} +(-7.79423 - 13.5000i) q^{17} +(7.79423 - 4.50000i) q^{18} +(24.0000 + 13.8564i) q^{19} -12.1244i q^{21} +(-12.9904 - 7.50000i) q^{23} +(4.50000 - 2.59808i) q^{24} +(9.00000 + 5.19615i) q^{26} -5.19615 q^{27} -35.0000i q^{28} -6.00000 q^{29} +(19.5000 - 11.2583i) q^{31} +(-38.9711 + 22.5000i) q^{32} +46.7654i q^{34} -15.0000 q^{36} +(60.6218 + 35.0000i) q^{37} +(-41.5692 - 72.0000i) q^{38} +(-3.00000 - 5.19615i) q^{39} +36.3731i q^{41} +(-18.1865 + 31.5000i) q^{42} +34.0000i q^{43} +(22.5000 + 38.9711i) q^{46} +(-12.9904 + 22.5000i) q^{47} +19.0526 q^{48} +(24.5000 + 42.4352i) q^{49} +(13.5000 - 23.3827i) q^{51} +(-8.66025 - 15.0000i) q^{52} +(36.3731 - 21.0000i) q^{53} +(13.5000 + 7.79423i) q^{54} +(-10.5000 + 18.1865i) q^{56} +48.0000i q^{57} +(15.5885 + 9.00000i) q^{58} +(-36.0000 + 20.7846i) q^{59} +(63.0000 + 36.3731i) q^{61} -67.5500 q^{62} +(18.1865 - 10.5000i) q^{63} +91.0000 q^{64} +(81.4064 - 47.0000i) q^{67} +(38.9711 - 67.5000i) q^{68} -25.9808i q^{69} +9.00000 q^{71} +(7.79423 + 4.50000i) q^{72} +(-3.46410 - 6.00000i) q^{73} +(-105.000 - 181.865i) q^{74} +138.564i q^{76} +18.0000i q^{78} +(38.5000 - 66.6840i) q^{79} +(-4.50000 - 7.79423i) q^{81} +(54.5596 - 94.5000i) q^{82} +145.492 q^{83} +(52.5000 - 30.3109i) q^{84} +(51.0000 - 88.3346i) q^{86} +(-5.19615 - 9.00000i) q^{87} +(-49.5000 - 28.5788i) q^{89} +(21.0000 + 12.1244i) q^{91} -75.0000i q^{92} +(33.7750 + 19.5000i) q^{93} +(67.5000 - 38.9711i) q^{94} +(-67.5000 - 38.9711i) q^{96} +98.7269 q^{97} -147.000i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 10 q^{4} - 6 q^{9}+O(q^{10}) $ 4 * q + 10 * q^4 - 6 * q^9	$ 4 q + 10 q^{4} - 6 q^{9} + 42 q^{14} + 22 q^{16} + 96 q^{19} + 18 q^{24} + 36 q^{26} - 24 q^{29} + 78 q^{31} - 60 q^{36} - 12 q^{39} + 90 q^{46} + 98 q^{49} + 54 q^{51} + 54 q^{54} - 42 q^{56} - 144 q^{59} + 252 q^{61} + 364 q^{64} + 36 q^{71} - 420 q^{74} + 154 q^{79} - 18 q^{81} + 210 q^{84} + 204 q^{86} - 198 q^{89} + 84 q^{91} + 270 q^{94} - 270 q^{96}+O(q^{100}) $ 4 * q + 10 * q^4 - 6 * q^9 + 42 * q^14 + 22 * q^16 + 96 * q^19 + 18 * q^24 + 36 * q^26 - 24 * q^29 + 78 * q^31 - 60 * q^36 - 12 * q^39 + 90 * q^46 + 98 * q^49 + 54 * q^51 + 54 * q^54 - 42 * q^56 - 144 * q^59 + 252 * q^61 + 364 * q^64 + 36 * q^71 - 420 * q^74 + 154 * q^79 - 18 * q^81 + 210 * q^84 + 204 * q^86 - 198 * q^89 + 84 * q^91 + 270 * q^94 - 270 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/525\mathbb{Z}\right)^\times$.

$n$	$127$	$176$	$451$
$\chi(n)$	$-1$	$1$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−2.59808	−	1.50000i	−1.29904	−	0.750000i	−0.318800	−	0.947822i	$-0.603280\pi$
$2$	−2.59808	−	1.50000i	−1.29904	−	0.750000i	−0.980238	+	0.197822i	$0.936613\pi$
$3$	0.866025	+	1.50000i	0.288675	+	0.500000i
$3$	0.866025	+	1.50000i	0.288675	+	0.500000i
$4$	2.50000	+	4.33013i	0.625000	+	1.08253i
$5$		0			0
$5$		0			0
$6$		−	5.19615i		−	0.866025i
$7$	−6.06218	−	3.50000i	−0.866025	−	0.500000i
$7$	−6.06218	−	3.50000i	−0.866025	−	0.500000i
$8$		−	3.00000i		−	0.375000i
$9$	−1.50000	+	2.59808i	−0.166667	+	0.288675i
$10$		0			0
$11$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$11$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$12$	−4.33013	+	7.50000i	−0.360844	+	0.625000i
$13$	−3.46410			−0.266469			−0.133235	−	0.991085i	$-0.542536\pi$
$13$	−3.46410			−0.266469			−0.133235	+	0.991085i	$0.542536\pi$
$14$	10.5000	+	18.1865i	0.750000	+	1.29904i
$15$		0			0
$16$	5.50000	−	9.52628i	0.343750	−	0.595392i
$17$	−7.79423	−	13.5000i	−0.458484	−	0.794118i	0.540397	−	0.841410i	$-0.318274\pi$
$17$	−7.79423	−	13.5000i	−0.458484	−	0.794118i	−0.998881	+	0.0472925i	$0.984941\pi$
$18$	7.79423	−	4.50000i	0.433013	−	0.250000i
$19$	24.0000	+	13.8564i	1.26316	+	0.729285i	0.973684	−	0.227901i	$-0.0731864\pi$
$19$	24.0000	+	13.8564i	1.26316	+	0.729285i	0.289474	+	0.957186i	$0.406520\pi$
$20$		0			0
$21$		−	12.1244i		−	0.577350i
$22$		0			0
$23$	−12.9904	−	7.50000i	−0.564799	−	0.326087i	0.190270	−	0.981732i	$-0.439064\pi$
$23$	−12.9904	−	7.50000i	−0.564799	−	0.326087i	−0.755069	+	0.655645i	$0.772397\pi$
$24$	4.50000	−	2.59808i	0.187500	−	0.108253i
$25$		0			0
$26$	9.00000	+	5.19615i	0.346154	+	0.199852i
$27$	−5.19615			−0.192450
$28$		−	35.0000i		−	1.25000i
$29$	−6.00000			−0.206897			−0.103448	−	0.994635i	$-0.532988\pi$
$29$	−6.00000			−0.206897			−0.103448	+	0.994635i	$0.532988\pi$
$30$		0			0
$31$	19.5000	−	11.2583i	0.629032	−	0.363172i	−0.151345	−	0.988481i	$-0.548360\pi$
$31$	19.5000	−	11.2583i	0.629032	−	0.363172i	0.780377	+	0.625309i	$0.215027\pi$
$32$	−38.9711	+	22.5000i	−1.21785	+	0.703125i
$33$		0			0
$34$			46.7654i			1.37545i
$35$		0			0
$36$	−15.0000			−0.416667
$37$	60.6218	+	35.0000i	1.63843	+	0.945946i	0.981375	+	0.192100i	$0.0615298\pi$
$37$	60.6218	+	35.0000i	1.63843	+	0.945946i	0.657051	+	0.753846i	$0.271804\pi$
$38$	−41.5692	−	72.0000i	−1.09393	−	1.89474i
$39$	−3.00000	−	5.19615i	−0.0769231	−	0.133235i
$40$		0			0
$41$			36.3731i			0.887148i	0.896238	+	0.443574i	$0.146290\pi$
$41$			36.3731i			0.887148i	−0.896238	+	0.443574i	$0.853710\pi$
$42$	−18.1865	+	31.5000i	−0.433013	+	0.750000i
$43$			34.0000i			0.790698i	0.918531	+	0.395349i	$0.129376\pi$
$43$			34.0000i			0.790698i	−0.918531	+	0.395349i	$0.870624\pi$
$44$		0			0
$45$		0			0
$46$	22.5000	+	38.9711i	0.489130	+	0.847199i
$47$	−12.9904	+	22.5000i	−0.276391	+	0.478723i	−0.970485	−	0.241161i	$-0.922472\pi$
$47$	−12.9904	+	22.5000i	−0.276391	+	0.478723i	0.694094	+	0.719884i	$0.255805\pi$
$48$	19.0526			0.396928
$49$	24.5000	+	42.4352i	0.500000	+	0.866025i
$50$		0			0
$51$	13.5000	−	23.3827i	0.264706	−	0.458484i
$52$	−8.66025	−	15.0000i	−0.166543	−	0.288462i
$53$	36.3731	−	21.0000i	0.686284	−	0.396226i	−0.115934	−	0.993257i	$-0.536986\pi$
$53$	36.3731	−	21.0000i	0.686284	−	0.396226i	0.802219	+	0.597030i	$0.203653\pi$
$54$	13.5000	+	7.79423i	0.250000	+	0.144338i
$55$		0			0
$56$	−10.5000	+	18.1865i	−0.187500	+	0.324760i
$57$			48.0000i			0.842105i
$58$	15.5885	+	9.00000i	0.268767	+	0.155172i
$59$	−36.0000	+	20.7846i	−0.610169	+	0.352282i	−0.773032	−	0.634367i	$-0.781261\pi$
$59$	−36.0000	+	20.7846i	−0.610169	+	0.352282i	0.162862	+	0.986649i	$0.447927\pi$
$60$		0			0
$61$	63.0000	+	36.3731i	1.03279	+	0.596280i	0.917782	−	0.397085i	$-0.129978\pi$
$61$	63.0000	+	36.3731i	1.03279	+	0.596280i	0.115005	+	0.993365i	$0.463312\pi$
$62$	−67.5500			−1.08952
$63$	18.1865	−	10.5000i	0.288675	−	0.166667i
$64$	91.0000			1.42188
$65$		0			0
$66$		0			0
$67$	81.4064	−	47.0000i	1.21502	−	0.701493i	0.251172	−	0.967942i	$-0.419184\pi$
$67$	81.4064	−	47.0000i	1.21502	−	0.701493i	0.963849	+	0.266450i	$0.0858507\pi$
$68$	38.9711	−	67.5000i	0.573105	−	0.992647i
$69$		−	25.9808i		−	0.376533i
$70$		0			0
$71$	9.00000			0.126761			0.0633803	−	0.997989i	$-0.479812\pi$
$71$	9.00000			0.126761			0.0633803	+	0.997989i	$0.479812\pi$
$72$	7.79423	+	4.50000i	0.108253	+	0.0625000i
$73$	−3.46410	−	6.00000i	−0.0474534	−	0.0821918i	0.841323	−	0.540533i	$-0.181777\pi$
$73$	−3.46410	−	6.00000i	−0.0474534	−	0.0821918i	−0.888777	+	0.458341i	$0.848444\pi$
$74$	−105.000	−	181.865i	−1.41892	−	2.45764i
$75$		0			0
$76$			138.564i			1.82321i
$77$		0			0
$78$			18.0000i			0.230769i
$79$	38.5000	−	66.6840i	0.487342	−	0.844101i	−0.512552	−	0.858656i	$-0.671300\pi$
$79$	38.5000	−	66.6840i	0.487342	−	0.844101i	0.999894	+	0.0145553i	$0.00463326\pi$
$80$		0			0
$81$	−4.50000	−	7.79423i	−0.0555556	−	0.0962250i
$82$	54.5596	−	94.5000i	0.665361	−	1.15244i
$83$	145.492			1.75292			0.876459	−	0.481476i	$-0.159899\pi$
$83$	145.492			1.75292			0.876459	+	0.481476i	$0.159899\pi$
$84$	52.5000	−	30.3109i	0.625000	−	0.360844i
$85$		0			0
$86$	51.0000	−	88.3346i	0.593023	−	1.02715i
$87$	−5.19615	−	9.00000i	−0.0597259	−	0.103448i
$88$		0			0
$89$	−49.5000	−	28.5788i	−0.556180	−	0.321111i	0.195431	−	0.980717i	$-0.437389\pi$
$89$	−49.5000	−	28.5788i	−0.556180	−	0.321111i	−0.751611	+	0.659607i	$0.770723\pi$
$90$		0			0
$91$	21.0000	+	12.1244i	0.230769	+	0.133235i
$92$		−	75.0000i		−	0.815217i
$93$	33.7750	+	19.5000i	0.363172	+	0.209677i
$94$	67.5000	−	38.9711i	0.718085	−	0.414587i
$95$		0			0
$96$	−67.5000	−	38.9711i	−0.703125	−	0.405949i
$97$	98.7269			1.01780			0.508902	−	0.860825i	$-0.330052\pi$
$97$	98.7269			1.01780			0.508902	+	0.860825i	$0.330052\pi$
$98$		−	147.000i		−	1.50000i
$99$		0			0
$100$		0			0
$101$	144.000	−	83.1384i	1.42574	−	0.823153i	0.428961	−	0.903323i	$-0.358880\pi$
$101$	144.000	−	83.1384i	1.42574	−	0.823153i	0.996781	+	0.0801700i	$0.0255463\pi$
$102$	−70.1481	+	40.5000i	−0.687726	+	0.397059i
$103$	−64.9519	+	112.500i	−0.630601	+	1.09223i	0.356828	+	0.934170i	$0.383858\pi$
$103$	−64.9519	+	112.500i	−0.630601	+	1.09223i	−0.987429	+	0.158063i	$0.949475\pi$
$104$			10.3923i			0.0999260i
$105$		0			0
$106$	−126.000			−1.18868
$107$	166.277	+	96.0000i	1.55399	+	0.897196i	0.997811	+	0.0661336i	$0.0210663\pi$
$107$	166.277	+	96.0000i	1.55399	+	0.897196i	0.556179	+	0.831063i	$0.312267\pi$
$108$	−12.9904	−	22.5000i	−0.120281	−	0.208333i
$109$	−64.0000	−	110.851i	−0.587156	−	1.01698i	−0.994603	−	0.103755i	$-0.966914\pi$
$109$	−64.0000	−	110.851i	−0.587156	−	1.01698i	0.407447	−	0.913229i	$-0.366419\pi$
$110$		0			0
$111$			121.244i			1.09228i
$112$	−66.6840	+	38.5000i	−0.595392	+	0.343750i
$113$			183.000i			1.61947i	0.586796	+	0.809735i	$0.300389\pi$
$113$			183.000i			1.61947i	−0.586796	+	0.809735i	$0.699611\pi$
$114$	72.0000	−	124.708i	0.631579	−	1.09393i
$115$		0			0
$116$	−15.0000	−	25.9808i	−0.129310	−	0.223972i
$117$	5.19615	−	9.00000i	0.0444116	−	0.0769231i
$118$	124.708			1.05684
$119$			109.119i			0.916968i
$120$		0			0
$121$	60.5000	−	104.789i	0.500000	−	0.866025i
$122$	−109.119	−	189.000i	−0.894420	−	1.54918i
$123$	−54.5596	+	31.5000i	−0.443574	+	0.256098i
$124$	97.5000	+	56.2917i	0.786290	+	0.453965i
$125$		0			0
$126$	−63.0000			−0.500000
$127$			10.0000i			0.0787402i	0.999225	+	0.0393701i	$0.0125351\pi$
$127$			10.0000i			0.0787402i	−0.999225	+	0.0393701i	$0.987465\pi$
$128$	−80.5404	−	46.5000i	−0.629222	−	0.363281i
$129$	−51.0000	+	29.4449i	−0.395349	+	0.228255i
$130$		0			0
$131$	−189.000	−	109.119i	−1.44275	−	0.832971i	−0.444716	−	0.895672i	$-0.646695\pi$
$131$	−189.000	−	109.119i	−1.44275	−	0.832971i	−0.998032	+	0.0627008i	$0.980029\pi$
$132$		0			0
$133$	−96.9948	−	168.000i	−0.729285	−	1.26316i
$134$	−282.000			−2.10448
$135$		0			0
$136$	−40.5000	+	23.3827i	−0.297794	+	0.171932i
$137$	59.7558	−	34.5000i	0.436173	−	0.251825i	−0.265800	−	0.964028i	$-0.585636\pi$
$137$	59.7558	−	34.5000i	0.436173	−	0.251825i	0.701973	+	0.712203i	$0.252303\pi$
$138$	−38.9711	+	67.5000i	−0.282400	+	0.489130i
$139$			197.454i			1.42053i	0.703934	+	0.710265i	$0.251425\pi$
$139$			197.454i			1.42053i	−0.703934	+	0.710265i	$0.748575\pi$
$140$		0			0
$141$	−45.0000			−0.319149
$142$	−23.3827	−	13.5000i	−0.164667	−	0.0950704i
$143$		0			0
$144$	16.5000	+	28.5788i	0.114583	+	0.198464i
$145$		0			0
$146$			20.7846i			0.142360i
$147$	−42.4352	+	73.5000i	−0.288675	+	0.500000i
$148$			350.000i			2.36486i
$149$	−78.0000	+	135.100i	−0.523490	+	0.906711i	0.476136	+	0.879372i	$0.342037\pi$
$149$	−78.0000	+	135.100i	−0.523490	+	0.906711i	−0.999626	+	0.0273397i	$0.991296\pi$
$150$		0			0
$151$	43.0000	+	74.4782i	0.284768	+	0.493233i	0.972553	−	0.232682i	$-0.0747500\pi$
$151$	43.0000	+	74.4782i	0.284768	+	0.493233i	−0.687785	+	0.725915i	$0.741417\pi$
$152$	41.5692	−	72.0000i	0.273482	−	0.473684i
$153$	46.7654			0.305656
$154$		0			0
$155$		0			0
$156$	15.0000	−	25.9808i	0.0961538	−	0.166543i
$157$	84.8705	+	147.000i	0.540576	+	0.936306i	0.998871	+	0.0475054i	$0.0151271\pi$
$157$	84.8705	+	147.000i	0.540576	+	0.936306i	−0.458295	+	0.888800i	$0.651540\pi$
$158$	−200.052	+	115.500i	−1.26615	+	0.731013i
$159$	63.0000	+	36.3731i	0.396226	+	0.228761i
$160$		0			0
$161$	52.5000	+	90.9327i	0.326087	+	0.564799i
$162$			27.0000i			0.166667i
$163$	−162.813	−	94.0000i	−0.998851	−	0.576687i	−0.0909431	−	0.995856i	$-0.528988\pi$
$163$	−162.813	−	94.0000i	−0.998851	−	0.576687i	−0.907908	+	0.419169i	$0.862321\pi$
$164$	−157.500	+	90.9327i	−0.960366	+	0.554467i
$165$		0			0
$166$	−378.000	−	218.238i	−2.27711	−	1.31469i
$167$	62.3538			0.373376			0.186688	−	0.982419i	$-0.440225\pi$
$167$	62.3538			0.373376			0.186688	+	0.982419i	$0.440225\pi$
$168$	−36.3731			−0.216506
$169$	−157.000			−0.928994
$170$		0			0
$171$	−72.0000	+	41.5692i	−0.421053	+	0.243095i
$172$	−147.224	+	85.0000i	−0.855955	+	0.494186i
$173$	67.5500	−	117.000i	0.390462	−	0.676301i	−0.602048	−	0.798460i	$-0.705649\pi$
$173$	67.5500	−	117.000i	0.390462	−	0.676301i	0.992511	+	0.122159i	$0.0389818\pi$
$174$			31.1769i			0.179178i
$175$		0			0
$176$		0			0
$177$	−62.3538	−	36.0000i	−0.352282	−	0.203390i
$178$	85.7365	+	148.500i	0.481666	+	0.834270i
$179$	135.000	+	233.827i	0.754190	+	1.30630i	0.945776	+	0.324819i	$0.105304\pi$
$179$	135.000	+	233.827i	0.754190	+	1.30630i	−0.191586	+	0.981476i	$0.561363\pi$
$180$		0			0
$181$		−	41.5692i		−	0.229664i	−0.993385	−	0.114832i	$-0.963367\pi$
$181$		−	41.5692i		−	0.229664i	0.993385	−	0.114832i	$-0.0366330\pi$
$182$	−36.3731	−	63.0000i	−0.199852	−	0.346154i
$183$			126.000i			0.688525i
$184$	−22.5000	+	38.9711i	−0.122283	+	0.211800i
$185$		0			0
$186$	−58.5000	−	101.325i	−0.314516	−	0.544758i
$187$		0			0
$188$	−129.904			−0.690978
$189$	31.5000	+	18.1865i	0.166667	+	0.0962250i
$190$		0			0
$191$	−1.50000	+	2.59808i	−0.00785340	+	0.0136025i	−0.869925	−	0.493183i	$-0.835833\pi$
$191$	−1.50000	+	2.59808i	−0.00785340	+	0.0136025i	0.862072	+	0.506786i	$0.169167\pi$
$192$	78.8083	+	136.500i	0.410460	+	0.710938i
$193$	−238.157	+	137.500i	−1.23397	+	0.712435i	−0.967856	−	0.251505i	$-0.919074\pi$
$193$	−238.157	+	137.500i	−1.23397	+	0.712435i	−0.266118	+	0.963940i	$0.585741\pi$
$194$	−256.500	−	148.090i	−1.32216	−	0.763352i
$195$		0			0
$196$	−122.500	+	212.176i	−0.625000	+	1.08253i
$197$		−	180.000i		−	0.913706i	−0.889542	−	0.456853i	$-0.848977\pi$
$197$		−	180.000i		−	0.913706i	0.889542	−	0.456853i	$-0.151023\pi$
$198$		0			0
$199$	151.500	−	87.4686i	0.761307	−	0.439541i	−0.0684581	−	0.997654i	$-0.521808\pi$
$199$	151.500	−	87.4686i	0.761307	−	0.439541i	0.829765	+	0.558113i	$0.188475\pi$
$200$		0			0
$201$	141.000	+	81.4064i	0.701493	+	0.405007i
$202$	−498.831			−2.46946
$203$	36.3731	+	21.0000i	0.179178	+	0.103448i
$204$	135.000			0.661765
$205$		0			0
$206$	337.500	−	194.856i	1.63835	−	0.945902i
$207$	38.9711	−	22.5000i	0.188266	−	0.108696i
$208$	−19.0526	+	33.0000i	−0.0915988	+	0.158654i
$209$		0			0
$210$		0			0
$211$	−68.0000			−0.322275			−0.161137	−	0.986932i	$-0.551516\pi$
$211$	−68.0000			−0.322275			−0.161137	+	0.986932i	$0.551516\pi$
$212$	181.865	+	105.000i	0.857855	+	0.495283i
$213$	7.79423	+	13.5000i	0.0365926	+	0.0633803i
$214$	−288.000	−	498.831i	−1.34579	−	2.33098i
$215$		0			0
$216$			15.5885i			0.0721688i
$217$	−157.617			−0.726344
$218$			384.000i			1.76147i
$219$	6.00000	−	10.3923i	0.0273973	−	0.0474534i
$220$		0			0
$221$	27.0000	+	46.7654i	0.122172	+	0.211608i
$222$	181.865	−	315.000i	0.819213	−	1.41892i
$223$	19.0526			0.0854375			0.0427187	−	0.999087i	$-0.486398\pi$
$223$	19.0526			0.0854375			0.0427187	+	0.999087i	$0.486398\pi$
$224$	315.000			1.40625
$225$		0			0
$226$	274.500	−	475.448i	1.21460	−	2.10375i
$227$	−187.061	−	324.000i	−0.824059	−	1.42731i	−0.902636	−	0.430405i	$-0.858371\pi$
$227$	−187.061	−	324.000i	−0.824059	−	1.42731i	0.0785766	−	0.996908i	$-0.474962\pi$
$228$	−207.846	+	120.000i	−0.911606	+	0.526316i
$229$	270.000	+	155.885i	1.17904	+	0.680719i	0.955792	−	0.294043i	$-0.0950010\pi$
$229$	270.000	+	155.885i	1.17904	+	0.680719i	0.223247	+	0.974762i	$0.428334\pi$
$230$		0			0
$231$		0			0
$232$			18.0000i			0.0775862i
$233$	−337.750	−	195.000i	−1.44957	−	0.836910i	−0.451115	−	0.892466i	$-0.648974\pi$
$233$	−337.750	−	195.000i	−1.44957	−	0.836910i	−0.998456	+	0.0555560i	$0.982307\pi$
$234$	−27.0000	+	15.5885i	−0.115385	+	0.0666173i
$235$		0			0
$236$	−180.000	−	103.923i	−0.762712	−	0.440352i
$237$	133.368			0.562734
$238$	163.679	−	283.500i	0.687726	−	1.19118i
$239$	−357.000			−1.49372			−0.746862	−	0.664979i	$-0.768440\pi$
$239$	−357.000			−1.49372			−0.746862	+	0.664979i	$0.768440\pi$
$240$		0			0
$241$	−42.0000	+	24.2487i	−0.174274	+	0.100617i	−0.584600	−	0.811322i	$-0.698748\pi$
$241$	−42.0000	+	24.2487i	−0.174274	+	0.100617i	0.410326	+	0.911939i	$0.365415\pi$
$242$	−314.367	+	181.500i	−1.29904	+	0.750000i
$243$	7.79423	−	13.5000i	0.0320750	−	0.0555556i
$244$			363.731i			1.49070i
$245$		0			0
$246$	189.000			0.768293
$247$	−83.1384	−	48.0000i	−0.336593	−	0.194332i
$248$	−33.7750	−	58.5000i	−0.136189	−	0.235887i
$249$	126.000	+	218.238i	0.506024	+	0.876459i
$250$		0			0
$251$			290.985i			1.15930i	0.814865	+	0.579650i	$0.196811\pi$
$251$			290.985i			1.15930i	−0.814865	+	0.579650i	$0.803189\pi$
$252$	90.9327	+	52.5000i	0.360844	+	0.208333i
$253$		0			0
$254$	15.0000	−	25.9808i	0.0590551	−	0.102286i
$255$		0			0
$256$	−42.5000	−	73.6122i	−0.166016	−	0.287547i
$257$	72.7461	−	126.000i	0.283059	−	0.490272i	−0.689078	−	0.724687i	$-0.741984\pi$
$257$	72.7461	−	126.000i	0.283059	−	0.490272i	0.972137	+	0.234415i	$0.0753175\pi$
$258$	176.669			0.684764
$259$	−245.000	−	424.352i	−0.945946	−	1.63843i
$260$		0			0
$261$	9.00000	−	15.5885i	0.0344828	−	0.0597259i
$262$	327.358	+	567.000i	1.24946	+	2.16412i
$263$	−148.090	+	85.5000i	−0.563081	+	0.325095i	−0.754381	−	0.656437i	$-0.772063\pi$
$263$	−148.090	+	85.5000i	−0.563081	+	0.325095i	0.191300	+	0.981532i	$0.438730\pi$
$264$		0			0
$265$		0			0
$266$			581.969i			2.18785i
$267$		−	99.0000i		−	0.370787i
$268$	407.032	+	235.000i	1.51878	+	0.876866i
$269$	360.000	−	207.846i	1.33829	−	0.772662i	0.351736	−	0.936099i	$-0.385591\pi$
$269$	360.000	−	207.846i	1.33829	−	0.772662i	0.986554	+	0.163437i	$0.0522581\pi$
$270$		0			0
$271$	−205.500	−	118.645i	−0.758303	−	0.437806i	0.0703834	−	0.997520i	$-0.477578\pi$
$271$	−205.500	−	118.645i	−0.758303	−	0.437806i	−0.828686	+	0.559714i	$0.810911\pi$
$272$	−171.473			−0.630416
$273$			42.0000i			0.153846i
$274$	−207.000			−0.755474
$275$		0			0
$276$	112.500	−	64.9519i	0.407609	−	0.235333i
$277$	112.583	−	65.0000i	0.406438	−	0.234657i	−0.282820	−	0.959173i	$-0.591270\pi$
$277$	112.583	−	65.0000i	0.406438	−	0.234657i	0.689258	+	0.724516i	$0.257937\pi$
$278$	296.181	−	513.000i	1.06540	−	1.84532i
$279$			67.5500i			0.242115i
$280$		0			0
$281$	−225.000			−0.800712			−0.400356	−	0.916360i	$-0.631113\pi$
$281$	−225.000			−0.800712			−0.400356	+	0.916360i	$0.631113\pi$
$282$	116.913	+	67.5000i	0.414587	+	0.239362i
$283$	62.3538	+	108.000i	0.220332	+	0.381625i	0.954909	−	0.296900i	$-0.0959527\pi$
$283$	62.3538	+	108.000i	0.220332	+	0.381625i	−0.734577	+	0.678525i	$0.762619\pi$
$284$	22.5000	+	38.9711i	0.0792254	+	0.137222i
$285$		0			0
$286$		0			0
$287$	127.306	−	220.500i	0.443574	−	0.768293i
$288$		−	135.000i		−	0.468750i
$289$	23.0000	−	39.8372i	0.0795848	−	0.137845i
$290$		0			0
$291$	85.5000	+	148.090i	0.293814	+	0.508902i
$292$	17.3205	−	30.0000i	0.0593168	−	0.102740i
$293$	207.846			0.709372			0.354686	−	0.934985i	$-0.384588\pi$
$293$	207.846			0.709372			0.354686	+	0.934985i	$0.384588\pi$
$294$	220.500	−	127.306i	0.750000	−	0.433013i
$295$		0			0
$296$	105.000	−	181.865i	0.354730	−	0.614410i
$297$		0			0
$298$	405.300	−	234.000i	1.36007	−	0.785235i
$299$	45.0000	+	25.9808i	0.150502	+	0.0868922i
$300$		0			0
$301$	119.000	−	206.114i	0.395349	−	0.684764i
$302$		−	258.000i		−	0.854305i
$303$	249.415	+	144.000i	0.823153	+	0.475248i
$304$	264.000	−	152.420i	0.868421	−	0.501383i
$305$		0			0
$306$	−121.500	−	70.1481i	−0.397059	−	0.229242i
$307$	−34.6410			−0.112837			−0.0564186	−	0.998407i	$-0.517968\pi$
$307$	−34.6410			−0.112837			−0.0564186	+	0.998407i	$0.517968\pi$
$308$		0			0
$309$	−225.000			−0.728155
$310$		0			0
$311$	−265.500	+	153.286i	−0.853698	+	0.492883i	−0.861897	−	0.507084i	$-0.830723\pi$
$311$	−265.500	+	153.286i	−0.853698	+	0.492883i	0.00819903	+	0.999966i	$0.497390\pi$
$312$	−15.5885	+	9.00000i	−0.0499630	+	0.0288462i
$313$	127.306	−	220.500i	0.406728	−	0.704473i	−0.587793	−	0.809011i	$-0.700003\pi$
$313$	127.306	−	220.500i	0.406728	−	0.704473i	0.994521	+	0.104538i	$0.0333365\pi$
$314$		−	509.223i		−	1.62173i
$315$		0			0
$316$	385.000			1.21835
$317$	509.223	+	294.000i	1.60638	+	0.927445i	0.990171	+	0.139863i	$0.0446664\pi$
$317$	509.223	+	294.000i	1.60638	+	0.927445i	0.616211	+	0.787581i	$0.288667\pi$
$318$	−109.119	−	189.000i	−0.343142	−	0.594340i
$319$		0			0
$320$		0			0
$321$			332.554i			1.03599i
$322$		−	315.000i		−	0.978261i
$323$		−	432.000i		−	1.33746i
$324$	22.5000	−	38.9711i	0.0694444	−	0.120281i
$325$		0			0
$326$	282.000	+	488.438i	0.865031	+	1.49828i
$327$	110.851	−	192.000i	0.338995	−	0.587156i
$328$	109.119			0.332680
$329$	157.500	−	90.9327i	0.478723	−	0.276391i
$330$		0			0
$331$	−35.0000	+	60.6218i	−0.105740	+	0.183147i	−0.914040	−	0.405623i	$-0.867055\pi$
$331$	−35.0000	+	60.6218i	−0.105740	+	0.183147i	0.808300	+	0.588771i	$0.200388\pi$
$332$	363.731	+	630.000i	1.09557	+	1.89759i
$333$	−181.865	+	105.000i	−0.546142	+	0.315315i
$334$	−162.000	−	93.5307i	−0.485030	−	0.280032i
$335$		0			0
$336$	−115.500	−	66.6840i	−0.343750	−	0.198464i
$337$			611.000i			1.81306i	0.422145	+	0.906528i	$0.361277\pi$
$337$			611.000i			1.81306i	−0.422145	+	0.906528i	$0.638723\pi$
$338$	407.898	+	235.500i	1.20680	+	0.696746i
$339$	−274.500	+	158.483i	−0.809735	+	0.467500i
$340$		0			0
$341$		0			0
$342$	249.415			0.729285
$343$		−	343.000i		−	1.00000i
$344$	102.000			0.296512
$345$		0			0
$346$	−351.000	+	202.650i	−1.01445	+	0.585693i
$347$	−77.9423	+	45.0000i	−0.224618	+	0.129683i	−0.608087	−	0.793871i	$-0.708063\pi$
$347$	−77.9423	+	45.0000i	−0.224618	+	0.129683i	0.383469	+	0.923554i	$0.374729\pi$
$348$	25.9808	−	45.0000i	0.0746574	−	0.129310i
$349$		−	235.559i		−	0.674954i	−0.941334	−	0.337477i	$-0.890426\pi$
$349$		−	235.559i		−	0.674954i	0.941334	−	0.337477i	$-0.109574\pi$
$350$		0			0
$351$	18.0000			0.0512821
$352$		0			0
$353$	75.3442	+	130.500i	0.213440	+	0.369688i	0.952789	−	0.303634i	$-0.0982000\pi$
$353$	75.3442	+	130.500i	0.213440	+	0.369688i	−0.739349	+	0.673322i	$0.764867\pi$
$354$	108.000	+	187.061i	0.305085	+	0.528422i
$355$		0			0
$356$		−	285.788i		−	0.802776i
$357$	−163.679	+	94.5000i	−0.458484	+	0.264706i
$358$		−	810.000i		−	2.26257i
$359$	−129.000	+	223.435i	−0.359331	+	0.622380i	−0.987849	−	0.155415i	$-0.950329\pi$
$359$	−129.000	+	223.435i	−0.359331	+	0.622380i	0.628518	+	0.777795i	$0.283662\pi$
$360$		0			0
$361$	203.500	+	352.472i	0.563712	+	0.976378i
$362$	−62.3538	+	108.000i	−0.172248	+	0.298343i
$363$	209.578			0.577350
$364$			121.244i			0.333087i
$365$		0			0
$366$	189.000	−	327.358i	0.516393	−	0.894420i
$367$	31.1769	+	54.0000i	0.0849507	+	0.147139i	0.905370	−	0.424623i	$-0.139593\pi$
$367$	31.1769	+	54.0000i	0.0849507	+	0.147139i	−0.820419	+	0.571762i	$0.806260\pi$
$368$	−142.894	+	82.5000i	−0.388299	+	0.224185i
$369$	−94.5000	−	54.5596i	−0.256098	−	0.147858i
$370$		0			0
$371$	−294.000			−0.792453
$372$			195.000i			0.524194i
$373$	−510.955	−	295.000i	−1.36985	−	0.790885i	−0.378944	−	0.925420i	$-0.623713\pi$
$373$	−510.955	−	295.000i	−1.36985	−	0.790885i	−0.990909	+	0.134535i	$0.957046\pi$
$374$		0			0
$375$		0			0
$376$	67.5000	+	38.9711i	0.179521	+	0.103647i
$377$	20.7846			0.0551316
$378$	−54.5596	−	94.5000i	−0.144338	−	0.250000i
$379$	98.0000			0.258575			0.129288	−	0.991607i	$-0.458731\pi$
$379$	98.0000			0.258575			0.129288	+	0.991607i	$0.458731\pi$
$380$		0			0
$381$	−15.0000	+	8.66025i	−0.0393701	+	0.0227303i
$382$	7.79423	−	4.50000i	0.0204037	−	0.0117801i
$383$	96.1288	−	166.500i	0.250989	−	0.434726i	−0.712809	−	0.701358i	$-0.752578\pi$
$383$	96.1288	−	166.500i	0.250989	−	0.434726i	0.963798	+	0.266632i	$0.0859108\pi$
$384$		−	161.081i		−	0.419481i
$385$		0			0
$386$	825.000			2.13731
$387$	−88.3346	−	51.0000i	−0.228255	−	0.131783i
$388$	246.817	+	427.500i	0.636127	+	1.10180i
$389$	258.000	+	446.869i	0.663239	+	1.14876i	0.979760	+	0.200178i	$0.0641521\pi$
$389$	258.000	+	446.869i	0.663239	+	1.14876i	−0.316520	+	0.948586i	$0.602515\pi$
$390$		0			0
$391$			233.827i			0.598023i
$392$	127.306	−	73.5000i	0.324760	−	0.187500i
$393$		−	378.000i		−	0.961832i
$394$	−270.000	+	467.654i	−0.685279	+	1.18694i
$395$		0			0
$396$		0			0
$397$	24.2487	−	42.0000i	0.0610799	−	0.105793i	−0.833868	−	0.551963i	$-0.813879\pi$
$397$	24.2487	−	42.0000i	0.0610799	−	0.105793i	0.894948	+	0.446170i	$0.147212\pi$
$398$	−524.811			−1.31862
$399$	168.000	−	290.985i	0.421053	−	0.729285i
$400$		0			0
$401$	129.000	−	223.435i	0.321696	−	0.557193i	−0.659142	−	0.752018i	$-0.729081\pi$
$401$	129.000	−	223.435i	0.321696	−	0.557193i	0.980838	+	0.194825i	$0.0624138\pi$
$402$	−244.219	−	423.000i	−0.607510	−	1.05224i
$403$	−67.5500	+	39.0000i	−0.167618	+	0.0967742i
$404$	720.000	+	415.692i	1.78218	+	1.02894i
$405$		0			0
$406$	−63.0000	−	109.119i	−0.155172	−	0.268767i
$407$		0			0
$408$	−70.1481	−	40.5000i	−0.171932	−	0.0992647i
$409$	538.500	−	310.903i	1.31663	−	0.760154i	0.333442	−	0.942771i	$-0.391790\pi$
$409$	538.500	−	310.903i	1.31663	−	0.760154i	0.983184	+	0.182616i	$0.0584566\pi$
$410$		0			0
$411$	103.500	+	59.7558i	0.251825	+	0.145391i
$412$	−649.519			−1.57650
$413$	290.985			0.704563
$414$	−135.000			−0.326087
$415$		0			0
$416$	135.000	−	77.9423i	0.324519	−	0.187361i
$417$	−296.181	+	171.000i	−0.710265	+	0.410072i
$418$		0			0
$419$		−	239.023i		−	0.570461i	−0.958459	−	0.285230i	$-0.907930\pi$
$419$		−	239.023i		−	0.570461i	0.958459	−	0.285230i	$-0.0920701\pi$
$420$		0			0
$421$	182.000			0.432304			0.216152	−	0.976360i	$-0.430649\pi$
$421$	182.000			0.432304			0.216152	+	0.976360i	$0.430649\pi$
$422$	176.669	+	102.000i	0.418647	+	0.241706i
$423$	−38.9711	−	67.5000i	−0.0921304	−	0.159574i
$424$	−63.0000	−	109.119i	−0.148585	−	0.257357i
$425$		0			0
$426$		−	46.7654i		−	0.109778i
$427$	−254.611	−	441.000i	−0.596280	−	1.03279i
$428$			960.000i			2.24299i
$429$		0			0
$430$		0			0
$431$	−148.500	−	257.210i	−0.344548	−	0.596774i	0.640724	−	0.767771i	$-0.278634\pi$
$431$	−148.500	−	257.210i	−0.344548	−	0.596774i	−0.985271	+	0.170997i	$0.945301\pi$
$432$	−28.5788	+	49.5000i	−0.0661547	+	0.114583i
$433$	−725.729			−1.67605			−0.838025	−	0.545632i	$-0.816289\pi$
$433$	−725.729			−1.67605			−0.838025	+	0.545632i	$0.816289\pi$
$434$	409.500	+	236.425i	0.943548	+	0.544758i
$435$		0			0
$436$	320.000	−	554.256i	0.733945	−	1.27123i
$437$	−207.846	−	360.000i	−0.475620	−	0.823799i
$438$	−31.1769	+	18.0000i	−0.0711802	+	0.0410959i
$439$	82.5000	+	47.6314i	0.187927	+	0.108500i	0.591012	−	0.806663i	$-0.298729\pi$
$439$	82.5000	+	47.6314i	0.187927	+	0.108500i	−0.403085	+	0.915163i	$0.632062\pi$
$440$		0			0
$441$	−147.000			−0.333333
$442$		−	162.000i		−	0.366516i
$443$	561.184	+	324.000i	1.26678	+	0.731377i	0.974378	−	0.224918i	$-0.0722114\pi$
$443$	561.184	+	324.000i	1.26678	+	0.731377i	0.292404	+	0.956295i	$0.405545\pi$
$444$	−525.000	+	303.109i	−1.18243	+	0.682678i
$445$		0			0
$446$	−49.5000	−	28.5788i	−0.110987	−	0.0640781i
$447$	−270.200			−0.604474
$448$	−551.658	−	318.500i	−1.23138	−	0.710938i
$449$	687.000			1.53007			0.765033	−	0.643991i	$-0.222722\pi$
$449$	687.000			1.53007			0.765033	+	0.643991i	$0.222722\pi$
$450$		0			0
$451$		0			0
$452$	−792.413	+	457.500i	−1.75313	+	1.01217i
$453$	−74.4782	+	129.000i	−0.164411	+	0.284768i
$454$			1122.37i			2.47218i
$455$		0			0
$456$	144.000			0.315789
$457$	−313.501	−	181.000i	−0.685998	−	0.396061i	0.116113	−	0.993236i	$-0.462957\pi$
$457$	−313.501	−	181.000i	−0.685998	−	0.396061i	−0.802111	+	0.597175i	$0.796290\pi$
$458$	−467.654	−	810.000i	−1.02108	−	1.76856i
$459$	40.5000	+	70.1481i	0.0882353	+	0.152828i
$460$		0			0
$461$		−	571.577i		−	1.23986i	−0.784656	−	0.619931i	$-0.787160\pi$
$461$		−	571.577i		−	1.23986i	0.784656	−	0.619931i	$-0.212840\pi$
$462$		0			0
$463$			257.000i			0.555076i	0.960715	+	0.277538i	$0.0895184\pi$
$463$			257.000i			0.555076i	−0.960715	+	0.277538i	$0.910482\pi$
$464$	−33.0000	+	57.1577i	−0.0711207	+	0.123185i
$465$		0			0
$466$	585.000	+	1013.25i	1.25536	+	2.17436i
$467$	−420.888	+	729.000i	−0.901260	+	1.56103i	−0.0753993	+	0.997153i	$0.524023\pi$
$467$	−420.888	+	729.000i	−0.901260	+	1.56103i	−0.825861	+	0.563874i	$0.809310\pi$
$468$	51.9615			0.111029
$469$	−658.000			−1.40299
$470$		0			0
$471$	−147.000	+	254.611i	−0.312102	+	0.540576i
$472$	62.3538	+	108.000i	0.132106	+	0.228814i
$473$		0			0
$474$	−346.500	−	200.052i	−0.731013	−	0.422050i
$475$		0			0
$476$	−472.500	+	272.798i	−0.992647	+	0.573105i
$477$			126.000i			0.264151i
$478$	927.513	+	535.500i	1.94040	+	1.12029i
$479$	−454.500	+	262.406i	−0.948852	+	0.547820i	−0.892724	−	0.450604i	$-0.851209\pi$
$479$	−454.500	+	262.406i	−0.948852	+	0.547820i	−0.0561277	+	0.998424i	$0.517875\pi$
$480$		0			0
$481$	−210.000	−	121.244i	−0.436590	−	0.252066i
$482$	145.492			0.301851
$483$	−90.9327	+	157.500i	−0.188266	+	0.326087i
$484$	605.000			1.25000
$485$		0			0
$486$	−40.5000	+	23.3827i	−0.0833333	+	0.0481125i
$487$	695.418	−	401.500i	1.42796	−	0.824435i	0.431004	−	0.902350i	$-0.358160\pi$
$487$	695.418	−	401.500i	1.42796	−	0.824435i	0.996960	+	0.0779148i	$0.0248262\pi$
$488$	109.119	−	189.000i	0.223605	−	0.387295i
$489$		−	325.626i		−	0.665901i
$490$		0			0
$491$	−678.000			−1.38086			−0.690428	−	0.723401i	$-0.742578\pi$
$491$	−678.000			−1.38086			−0.690428	+	0.723401i	$0.742578\pi$
$492$	−272.798	−	157.500i	−0.554467	−	0.320122i
$493$	46.7654	+	81.0000i	0.0948588	+	0.164300i
$494$	144.000	+	249.415i	0.291498	+	0.504889i
$495$		0			0
$496$		−	247.683i		−	0.499361i
$497$	−54.5596	−	31.5000i	−0.109778	−	0.0633803i
$498$		−	756.000i		−	1.51807i
$499$	−283.000	+	490.170i	−0.567134	+	0.982305i	0.429713	+	0.902965i	$0.358615\pi$
$499$	−283.000	+	490.170i	−0.567134	+	0.982305i	−0.996848	+	0.0793400i	$0.974719\pi$
$500$		0			0
$501$	54.0000	+	93.5307i	0.107784	+	0.186688i
$502$	436.477	−	756.000i	0.869476	−	1.50598i
$503$	−83.1384			−0.165285			−0.0826426	−	0.996579i	$-0.526336\pi$
$503$	−83.1384			−0.165285			−0.0826426	+	0.996579i	$0.526336\pi$
$504$	−31.5000	−	54.5596i	−0.0625000	−	0.108253i
$505$		0			0
$506$		0			0
$507$	−135.966	−	235.500i	−0.268177	−	0.464497i
$508$	−43.3013	+	25.0000i	−0.0852387	+	0.0492126i
$509$	−108.000	−	62.3538i	−0.212181	−	0.122503i	0.390144	−	0.920754i	$-0.372425\pi$
$509$	−108.000	−	62.3538i	−0.212181	−	0.122503i	−0.602324	+	0.798251i	$0.705759\pi$
$510$		0			0
$511$			48.4974i			0.0949069i
$512$			627.000i			1.22461i
$513$	−124.708	−	72.0000i	−0.243095	−	0.140351i
$514$	−378.000	+	218.238i	−0.735409	+	0.424588i
$515$		0			0
$516$	−255.000	−	147.224i	−0.494186	−	0.285318i
$517$		0			0
$518$			1470.00i			2.83784i
$519$	234.000			0.450867
$520$		0			0
$521$	544.500	−	314.367i	1.04511	−	0.603392i	0.123830	−	0.992303i	$-0.460482\pi$
$521$	544.500	−	314.367i	1.04511	−	0.603392i	0.921275	+	0.388911i	$0.127149\pi$
$522$	−46.7654	+	27.0000i	−0.0895888	+	0.0517241i
$523$	−64.0859	+	111.000i	−0.122535	+	0.212237i	−0.920767	−	0.390114i	$-0.872436\pi$
$523$	−64.0859	+	111.000i	−0.122535	+	0.212237i	0.798232	+	0.602351i	$0.205769\pi$
$524$		−	1091.19i		−	2.08243i
$525$		0			0
$526$	513.000			0.975285
$527$	−303.975	−	175.500i	−0.576802	−	0.333017i
$528$		0			0
$529$	−152.000	−	263.272i	−0.287335	−	0.497678i
$530$		0			0
$531$		−	124.708i		−	0.234854i
$532$	484.974	−	840.000i	0.911606	−	1.57895i
$533$		−	126.000i		−	0.236398i
$534$	−148.500	+	257.210i	−0.278090	+	0.481666i
$535$		0			0
$536$	−141.000	−	244.219i	−0.263060	−	0.455633i
$537$	−233.827	+	405.000i	−0.435432	+	0.754190i
$538$	−1247.08			−2.31799
$539$		0			0
$540$		0			0
$541$	−22.0000	+	38.1051i	−0.0406654	+	0.0704346i	−0.885642	−	0.464369i	$-0.846281\pi$
$541$	−22.0000	+	38.1051i	−0.0406654	+	0.0704346i	0.844976	+	0.534804i	$0.179614\pi$
$542$	355.936	+	616.500i	0.656709	+	1.13745i
$543$	62.3538	−	36.0000i	0.114832	−	0.0662983i
$544$	607.500	+	350.740i	1.11673	+	0.644743i
$545$		0			0
$546$	63.0000	−	109.119i	0.115385	−	0.199852i
$547$			376.000i			0.687386i	0.939082	+	0.343693i	$0.111678\pi$
$547$			376.000i			0.687386i	−0.939082	+	0.343693i	$0.888322\pi$
$548$	298.779	+	172.500i	0.545217	+	0.314781i
$549$	−189.000	+	109.119i	−0.344262	+	0.198760i
$550$		0			0
$551$	−144.000	−	83.1384i	−0.261343	−	0.150886i
$552$	−77.9423			−0.141200
$553$	−466.788	+	269.500i	−0.844101	+	0.487342i
$554$	−390.000			−0.703971
$555$		0			0
$556$	−855.000	+	493.634i	−1.53777	+	0.887832i
$557$	67.5500	−	39.0000i	0.121275	−	0.0700180i	−0.438136	−	0.898909i	$-0.644361\pi$
$557$	67.5500	−	39.0000i	0.121275	−	0.0700180i	0.559410	+	0.828891i	$0.311028\pi$
$558$	101.325	−	175.500i	0.181586	−	0.314516i
$559$		−	117.779i		−	0.210697i
$560$		0			0
$561$		0			0
$562$	584.567	+	337.500i	1.04016	+	0.600534i
$563$	290.985	+	504.000i	0.516846	+	0.895204i	0.999809	+	0.0195631i	$0.00622751\pi$
$563$	290.985	+	504.000i	0.516846	+	0.895204i	−0.482962	+	0.875641i	$0.660439\pi$
$564$	−112.500	−	194.856i	−0.199468	−	0.345489i
$565$		0			0
$566$		−	374.123i		−	0.660995i
$567$			63.0000i			0.111111i
$568$		−	27.0000i		−	0.0475352i
$569$	118.500	−	205.248i	0.208260	−	0.360717i	−0.742906	−	0.669395i	$-0.766553\pi$
$569$	118.500	−	205.248i	0.208260	−	0.360717i	0.951167	+	0.308678i	$0.0998866\pi$
$570$		0			0
$571$	290.000	+	502.295i	0.507881	+	0.879676i	0.999958	+	0.00912412i	$0.00290434\pi$
$571$	290.000	+	502.295i	0.507881	+	0.879676i	−0.492077	+	0.870551i	$0.663762\pi$
$572$		0			0
$573$	−5.19615			−0.00906833
$574$	−661.500	+	381.917i	−1.15244	+	0.665361i
$575$		0			0
$576$	−136.500	+	236.425i	−0.236979	+	0.410460i
$577$	−204.382	−	354.000i	−0.354215	−	0.613518i	0.632768	−	0.774341i	$-0.281919\pi$
$577$	−204.382	−	354.000i	−0.354215	−	0.613518i	−0.986983	+	0.160823i	$0.948585\pi$
$578$	−119.512	+	69.0000i	−0.206767	+	0.119377i
$579$	−412.500	−	238.157i	−0.712435	−	0.411325i
$580$		0			0
$581$	−882.000	−	509.223i	−1.51807	−	0.876459i
$582$		−	513.000i		−	0.881443i
$583$		0			0
$584$	−18.0000	+	10.3923i	−0.0308219	+	0.0177950i
$585$		0			0
$586$	−540.000	−	311.769i	−0.921502	−	0.532029i
$587$	1049.62			1.78811			0.894057	−	0.447953i	$-0.147847\pi$
$587$	1049.62			1.78811			0.894057	+	0.447953i	$0.147847\pi$
$588$	−424.352			−0.721688
$589$	624.000			1.05942
$590$		0			0
$591$	270.000	−	155.885i	0.456853	−	0.263764i
$592$	666.840	−	385.000i	1.12642	−	0.650338i
$593$	418.290	−	724.500i	0.705380	−	1.22175i	−0.261174	−	0.965292i	$-0.584110\pi$
$593$	418.290	−	724.500i	0.705380	−	1.22175i	0.966554	−	0.256462i	$-0.0825569\pi$
$594$		0			0
$595$		0			0
$596$	−780.000			−1.30872
$597$	262.406	+	151.500i	0.439541	+	0.253769i
$598$	−77.9423	−	135.000i	−0.130338	−	0.225753i
$599$	−19.5000	−	33.7750i	−0.0325543	−	0.0563856i	0.849289	−	0.527928i	$-0.177031\pi$
$599$	−19.5000	−	33.7750i	−0.0325543	−	0.0563856i	−0.881844	+	0.471542i	$0.843698\pi$
$600$		0			0
$601$		−	20.7846i		−	0.0345834i	−0.999850	−	0.0172917i	$-0.994496\pi$
$601$		−	20.7846i		−	0.0345834i	0.999850	−	0.0172917i	$-0.00550439\pi$
$602$	−618.342	+	357.000i	−1.02715	+	0.593023i
$603$			282.000i			0.467662i
$604$	−215.000	+	372.391i	−0.355960	+	0.616541i
$605$		0			0
$606$	−432.000	−	748.246i	−0.712871	−	1.23473i
$607$	−125.574	+	217.500i	−0.206876	+	0.358320i	−0.950729	−	0.310024i	$-0.899663\pi$
$607$	−125.574	+	217.500i	−0.206876	+	0.358320i	0.743853	+	0.668343i	$0.232996\pi$
$608$	−1247.08			−2.05111
$609$			72.7461i			0.119452i
$610$		0			0
$611$	45.0000	−	77.9423i	0.0736498	−	0.127565i
$612$	116.913	+	202.500i	0.191035	+	0.330882i
$613$	677.232	−	391.000i	1.10478	−	0.637847i	0.167310	−	0.985904i	$-0.446492\pi$
$613$	677.232	−	391.000i	1.10478	−	0.637847i	0.937473	+	0.348058i	$0.113159\pi$
$614$	90.0000	+	51.9615i	0.146580	+	0.0846279i
$615$		0			0
$616$		0			0
$617$			1011.00i			1.63857i	0.573384	+	0.819287i	$0.305630\pi$
$617$			1011.00i			1.63857i	−0.573384	+	0.819287i	$0.694370\pi$
$618$	584.567	+	337.500i	0.945902	+	0.546117i
$619$	−87.0000	+	50.2295i	−0.140549	+	0.0811462i	−0.568626	−	0.822596i	$-0.692525\pi$
$619$	−87.0000	+	50.2295i	−0.140549	+	0.0811462i	0.428076	+	0.903743i	$0.359191\pi$
$620$		0			0
$621$	67.5000	+	38.9711i	0.108696	+	0.0627555i
$622$	919.719			1.47865
$623$	200.052	+	346.500i	0.321111	+	0.556180i
$624$	−66.0000			−0.105769
$625$		0			0
$626$	−661.500	+	381.917i	−1.05671	+	0.610091i
$627$		0			0
$628$	−424.352	+	735.000i	−0.675720	+	1.17038i
$629$		−	1091.19i		−	1.73480i
$630$		0			0
$631$	395.000			0.625990			0.312995	−	0.949755i	$-0.398668\pi$
$631$	395.000			0.625990			0.312995	+	0.949755i	$0.398668\pi$
$632$	−200.052	−	115.500i	−0.316538	−	0.182753i
$633$	−58.8897	−	102.000i	−0.0930327	−	0.161137i
$634$	−882.000	−	1527.67i	−1.39117	−	2.40957i
$635$		0			0
$636$			363.731i			0.571904i
$637$	−84.8705	−	147.000i	−0.133235	−	0.230769i
$638$		0			0
$639$	−13.5000	+	23.3827i	−0.0211268	+	0.0365926i
$640$		0			0
$641$	154.500	+	267.602i	0.241030	+	0.417476i	0.961008	−	0.276521i	$-0.0891816\pi$
$641$	154.500	+	267.602i	0.241030	+	0.417476i	−0.719978	+	0.693997i	$0.755848\pi$
$642$	498.831	−	864.000i	0.776995	−	1.34579i
$643$	491.902			0.765012			0.382506	−	0.923953i	$-0.375061\pi$
$643$	491.902			0.765012			0.382506	+	0.923953i	$0.375061\pi$
$644$	−262.500	+	454.663i	−0.407609	+	0.705999i
$645$		0			0
$646$	−648.000	+	1122.37i	−1.00310	+	1.73741i
$647$	−592.361	−	1026.00i	−0.915551	−	1.58578i	−0.806093	−	0.591789i	$-0.798422\pi$
$647$	−592.361	−	1026.00i	−0.915551	−	1.58578i	−0.109458	−	0.993991i	$-0.534912\pi$
$648$	−23.3827	+	13.5000i	−0.0360844	+	0.0208333i
$649$		0			0
$650$		0			0
$651$	−136.500	−	236.425i	−0.209677	−	0.363172i
$652$		−	940.000i		−	1.44172i
$653$	441.673	+	255.000i	0.676375	+	0.390505i	0.798488	−	0.602011i	$-0.205634\pi$
$653$	441.673	+	255.000i	0.676375	+	0.390505i	−0.122113	+	0.992516i	$0.538967\pi$
$654$	−576.000	+	332.554i	−0.880734	+	0.508492i
$655$		0			0
$656$	346.500	+	200.052i	0.528201	+	0.304957i
$657$	20.7846			0.0316356
$658$	−545.596			−0.829173
$659$	−102.000			−0.154780			−0.0773900	−	0.997001i	$-0.524659\pi$
$659$	−102.000			−0.154780			−0.0773900	+	0.997001i	$0.524659\pi$
$660$		0			0
$661$	1077.00	−	621.806i	1.62935	−	0.940705i	0.645062	−	0.764130i	$-0.276831\pi$
$661$	1077.00	−	621.806i	1.62935	−	0.940705i	0.984287	−	0.176575i	$-0.0565020\pi$
$662$	181.865	−	105.000i	0.274721	−	0.158610i
$663$	−46.7654	+	81.0000i	−0.0705360	+	0.122172i
$664$		−	436.477i		−	0.657345i
$665$		0			0
$666$	630.000			0.945946
$667$	77.9423	+	45.0000i	0.116855	+	0.0674663i
$668$	155.885	+	270.000i	0.233360	+	0.404192i
$669$	16.5000	+	28.5788i	0.0246637	+	0.0427187i
$670$		0			0
$671$		0			0
$672$	272.798	+	472.500i	0.405949	+	0.703125i
$673$		−	533.000i		−	0.791976i	−0.918256	−	0.395988i	$-0.870402\pi$
$673$		−	533.000i		−	0.791976i	0.918256	−	0.395988i	$-0.129598\pi$
$674$	916.500	−	1587.42i	1.35979	−	2.35523i
$675$		0			0
$676$	−392.500	−	679.830i	−0.580621	−	1.00567i
$677$	254.611	−	441.000i	0.376088	−	0.651403i	−0.614401	−	0.788994i	$-0.710602\pi$
$677$	254.611	−	441.000i	0.376088	−	0.651403i	0.990489	+	0.137590i	$0.0439358\pi$
$678$	950.896			1.40250
$679$	−598.500	−	345.544i	−0.881443	−	0.508902i
$680$		0			0
$681$	324.000	−	561.184i	0.475771	−	0.824059i
$682$		0			0
$683$	436.477	−	252.000i	0.639058	−	0.368960i	−0.145193	−	0.989403i	$-0.546380\pi$
$683$	436.477	−	252.000i	0.639058	−	0.368960i	0.784252	+	0.620443i	$0.213047\pi$
$684$	−360.000	−	207.846i	−0.526316	−	0.303869i
$685$		0			0
$686$	−514.500	+	891.140i	−0.750000	+	1.29904i
$687$			540.000i			0.786026i
$688$	323.894	+	187.000i	0.470775	+	0.271802i
$689$	−126.000	+	72.7461i	−0.182874	+	0.105582i
$690$		0			0
$691$	−312.000	−	180.133i	−0.451520	−	0.260685i	0.256952	−	0.966424i	$-0.417282\pi$
$691$	−312.000	−	180.133i	−0.451520	−	0.260685i	−0.708472	+	0.705739i	$0.750615\pi$
$692$	675.500			0.976156
$693$		0			0
$694$	270.000			0.389049
$695$		0			0
$696$	−27.0000	+	15.5885i	−0.0387931	+	0.0223972i
$697$	491.036	−	283.500i	0.704500	−	0.406743i
$698$	−353.338	+	612.000i	−0.506215	+	0.876791i
$699$		−	675.500i		−	0.966380i
$700$		0			0
$701$	−78.0000			−0.111270			−0.0556348	−	0.998451i	$-0.517718\pi$
$701$	−78.0000			−0.111270			−0.0556348	+	0.998451i	$0.517718\pi$
$702$	−46.7654	−	27.0000i	−0.0666173	−	0.0384615i
$703$	969.948	+	1680.00i	1.37973	+	2.38976i
$704$		0			0
$705$		0			0
$706$		−	452.065i		−	0.640319i
$707$	−1163.94			−1.64631
$708$		−	360.000i		−	0.508475i
$709$	65.0000	−	112.583i	0.0916784	−	0.158792i	−0.816539	−	0.577290i	$-0.804110\pi$
$709$	65.0000	−	112.583i	0.0916784	−	0.158792i	0.908217	+	0.418498i	$0.137443\pi$
$710$		0			0
$711$	115.500	+	200.052i	0.162447	+	0.281367i
$712$	−85.7365	+	148.500i	−0.120416	+	0.208567i
$713$	−337.750			−0.473703
$714$	567.000			0.794118
$715$		0			0
$716$	−675.000	+	1169.13i	−0.942737	+	1.63287i
$717$	−309.171	−	535.500i	−0.431201	−	0.746862i
$718$	670.304	−	387.000i	0.933571	−	0.538997i
$719$	670.500	+	387.113i	0.932545	+	0.538405i	0.887616	−	0.460585i	$-0.152360\pi$
$719$	670.500	+	387.113i	0.932545	+	0.538405i	0.0449296	+	0.998990i	$0.485694\pi$
$720$		0			0
$721$	787.500	−	454.663i	1.09223	−	0.630601i
$722$		−	1221.00i		−	1.69114i
$723$	−72.7461	−	42.0000i	−0.100617	−	0.0580913i
$724$	180.000	−	103.923i	0.248619	−	0.143540i
$725$		0			0
$726$	−544.500	−	314.367i	−0.750000	−	0.433013i
$727$	−659.911			−0.907719			−0.453859	−	0.891073i	$-0.649953\pi$
$727$	−659.911			−0.907719			−0.453859	+	0.891073i	$0.649953\pi$
$728$	36.3731	−	63.0000i	0.0499630	−	0.0865385i
$729$	27.0000			0.0370370
$730$		0			0
$731$	459.000	−	265.004i	0.627907	−	0.362522i
$732$	−545.596	+	315.000i	−0.745350	+	0.430328i
$733$	55.4256	−	96.0000i	0.0756148	−	0.130969i	−0.825739	−	0.564053i	$-0.809241\pi$
$733$	55.4256	−	96.0000i	0.0756148	−	0.130969i	0.901353	+	0.433084i	$0.142575\pi$
$734$		−	187.061i		−	0.254852i
$735$		0			0
$736$	675.000			0.917120
$737$		0			0
$738$	163.679	+	283.500i	0.221787	+	0.384146i
$739$	−77.0000	−	133.368i	−0.104195	−	0.180471i	0.809214	−	0.587514i	$-0.199893\pi$
$739$	−77.0000	−	133.368i	−0.104195	−	0.180471i	−0.913409	+	0.407043i	$0.866560\pi$
$740$		0			0
$741$		−	166.277i		−	0.224395i
$742$	763.834	+	441.000i	1.02943	+	0.594340i
$743$			1371.00i			1.84522i	0.385732	+	0.922611i	$0.373949\pi$
$743$			1371.00i			1.84522i	−0.385732	+	0.922611i	$0.626051\pi$
$744$	58.5000	−	101.325i	0.0786290	−	0.136189i
$745$		0			0
$746$	885.000	+	1532.86i	1.18633	+	2.05478i
$747$	−218.238	+	378.000i	−0.292153	+	0.506024i
$748$		0			0
$749$	−672.000	−	1163.94i	−0.897196	−	1.55399i
$750$		0			0
$751$	−263.000	+	455.529i	−0.350200	+	0.606564i	−0.986284	−	0.165056i	$-0.947220\pi$
$751$	−263.000	+	455.529i	−0.350200	+	0.606564i	0.636085	+	0.771619i	$0.280553\pi$
$752$	142.894	+	247.500i	0.190019	+	0.329122i
$753$	−436.477	+	252.000i	−0.579650	+	0.334661i
$754$	−54.0000	−	31.1769i	−0.0716180	−	0.0413487i
$755$		0			0
$756$			181.865i			0.240563i
$757$			1100.00i			1.45310i	0.687111	+	0.726552i	$0.258878\pi$
$757$			1100.00i			1.45310i	−0.687111	+	0.726552i	$0.741122\pi$
$758$	−254.611	−	147.000i	−0.335899	−	0.193931i
$759$		0			0
$760$		0			0
$761$	175.500	+	101.325i	0.230618	+	0.133147i	0.610857	−	0.791741i	$-0.290825\pi$
$761$	175.500	+	101.325i	0.230618	+	0.133147i	−0.380239	+	0.924888i	$0.624158\pi$
$762$	51.9615			0.0681910
$763$			896.000i			1.17431i
$764$	−15.0000			−0.0196335
$765$		0			0
$766$	−499.500	+	288.386i	−0.652089	+	0.376484i
$767$	124.708	−	72.0000i	0.162591	−	0.0938722i
$768$	73.6122	−	127.500i	0.0958492	−	0.166016i
$769$			602.754i			0.783815i	0.920005	+	0.391907i	$0.128185\pi$
$769$			602.754i			0.783815i	−0.920005	+	0.391907i	$0.871815\pi$
$770$		0			0
$771$	252.000			0.326848
$772$	−1190.78	−	687.500i	−1.54247	−	0.890544i
$773$	−649.519	−	1125.00i	−0.840258	−	1.45537i	−0.889677	−	0.456591i	$-0.849070\pi$
$773$	−649.519	−	1125.00i	−0.840258	−	1.45537i	0.0494194	−	0.998778i	$-0.484263\pi$
$774$	153.000	+	265.004i	0.197674	+	0.342382i
$775$		0			0
$776$		−	296.181i		−	0.381676i
$777$	424.352	−	735.000i	0.546142	−	0.945946i
$778$		−	1548.00i		−	1.98972i
$779$	−504.000	+	872.954i	−0.646983	+	1.12061i
$780$		0			0
$781$		0			0
$782$	350.740	−	607.500i	0.448517	−	0.776854i
$783$	31.1769			0.0398173
$784$	539.000			0.687500
$785$		0			0
$786$	−567.000	+	982.073i	−0.721374	+	1.24946i
$787$	57.1577	+	99.0000i	0.0726273	+	0.125794i	0.900052	−	0.435782i	$-0.143528\pi$
$787$	57.1577	+	99.0000i	0.0726273	+	0.125794i	−0.827425	+	0.561577i	$0.810195\pi$
$788$	779.423	−	450.000i	0.989115	−	0.571066i
$789$	−256.500	−	148.090i	−0.325095	−	0.187694i
$790$		0			0
$791$	640.500	−	1109.38i	0.809735	−	1.40250i
$792$		0			0
$793$	−218.238	−	126.000i	−0.275206	−	0.158890i
$794$	−126.000	+	72.7461i	−0.158690	+	0.0916198i
$795$		0			0
$796$	757.500	+	437.343i	0.951633	+	0.549426i
$797$	426.084			0.534610			0.267305	−	0.963612i	$-0.413867\pi$
$797$	426.084			0.534610			0.267305	+	0.963612i	$0.413867\pi$
$798$	−872.954	+	504.000i	−1.09393	+	0.631579i
$799$	405.000			0.506884
$800$		0			0
$801$	148.500	−	85.7365i	0.185393	−	0.107037i
$802$	−670.304	+	387.000i	−0.835790	+	0.482544i
$803$		0			0
$804$			814.064i			1.01252i
$805$		0			0
$806$	234.000			0.290323
$807$	623.538	+	360.000i	0.772662	+	0.446097i
$808$	−249.415	−	432.000i	−0.308682	−	0.534653i
$809$	351.000	+	607.950i	0.433869	+	0.751483i	0.997203	−	0.0747464i	$-0.0238147\pi$
$809$	351.000	+	607.950i	0.433869	+	0.751483i	−0.563334	+	0.826230i	$0.690481\pi$
$810$		0			0
$811$		−	1167.40i		−	1.43946i	−0.694254	−	0.719730i	$-0.744266\pi$
$811$		−	1167.40i		−	1.43946i	0.694254	−	0.719730i	$-0.255734\pi$
$812$			210.000i			0.258621i
$813$		−	411.000i		−	0.505535i
$814$		0			0
$815$		0			0
$816$	−148.500	−	257.210i	−0.181985	−	0.315208i
$817$	−471.118	+	816.000i	−0.576644	+	0.998776i
$818$	−1865.42			−2.28046
$819$	−63.0000	+	36.3731i	−0.0769231	+	0.0444116i
$820$		0			0
$821$	−30.0000	+	51.9615i	−0.0365408	+	0.0632905i	−0.883717	−	0.468021i	$-0.844967\pi$
$821$	−30.0000	+	51.9615i	−0.0365408	+	0.0632905i	0.847177	+	0.531311i	$0.178301\pi$
$822$	−179.267	−	310.500i	−0.218087	−	0.377737i
$823$	323.894	−	187.000i	0.393552	−	0.227217i	−0.290146	−	0.956982i	$-0.593704\pi$
$823$	323.894	−	187.000i	0.393552	−	0.227217i	0.683698	+	0.729765i	$0.260371\pi$
$824$	337.500	+	194.856i	0.409587	+	0.236475i
$825$		0			0
$826$	−756.000	−	436.477i	−0.915254	−	0.528422i
$827$			864.000i			1.04474i	0.852719	+	0.522370i	$0.174952\pi$
$827$			864.000i			1.04474i	−0.852719	+	0.522370i	$0.825048\pi$
$828$	194.856	+	112.500i	0.235333	+	0.135870i
$829$	−366.000	+	211.310i	−0.441496	+	0.254898i	−0.704232	−	0.709970i	$-0.748708\pi$
$829$	−366.000	+	211.310i	−0.441496	+	0.254898i	0.262736	+	0.964868i	$0.415375\pi$
$830$		0			0
$831$	195.000	+	112.583i	0.234657	+	0.135479i
$832$	−315.233			−0.378886
$833$	381.917	−	661.500i	0.458484	−	0.794118i
$834$	1026.00			1.23022
$835$		0			0
$836$		0			0
$837$	−101.325	+	58.5000i	−0.121057	+	0.0698925i
$838$	−358.535	+	621.000i	−0.427845	+	0.741050i
$839$			909.327i			1.08382i	0.840436	+	0.541911i	$0.182299\pi$
$839$			909.327i			1.08382i	−0.840436	+	0.541911i	$0.817701\pi$
$840$		0			0
$841$	−805.000			−0.957194
$842$	−472.850	−	273.000i	−0.561579	−	0.324228i
$843$	−194.856	−	337.500i	−0.231146	−	0.400356i
$844$	−170.000	−	294.449i	−0.201422	−	0.348873i
$845$		0			0
$846$			233.827i			0.276391i
$847$	−733.524	+	423.500i	−0.866025	+	0.500000i
$848$		−	462.000i		−	0.544811i
$849$	−108.000	+	187.061i	−0.127208	+	0.220332i
$850$		0			0
$851$	−525.000	−	909.327i	−0.616921	−	1.06854i
$852$	−38.9711	+	67.5000i	−0.0457408	+	0.0792254i
$853$	405.300			0.475146			0.237573	−	0.971370i	$-0.423648\pi$
$853$	405.300			0.475146			0.237573	+	0.971370i	$0.423648\pi$
$854$			1527.67i			1.78884i
$855$		0			0
$856$	288.000	−	498.831i	0.336449	−	0.582746i
$857$	166.277	+	288.000i	0.194022	+	0.336056i	0.946579	−	0.322471i	$-0.104513\pi$
$857$	166.277	+	288.000i	0.194022	+	0.336056i	−0.752557	+	0.658527i	$0.771180\pi$
$858$		0			0
$859$	−807.000	−	465.922i	−0.939464	−	0.542400i	−0.0496721	−	0.998766i	$-0.515818\pi$
$859$	−807.000	−	465.922i	−0.939464	−	0.542400i	−0.889792	+	0.456366i	$0.849151\pi$
$860$		0			0
$861$	441.000			0.512195
$862$			891.000i			1.03364i
$863$	−584.567	−	337.500i	−0.677366	−	0.391078i	0.121496	−	0.992592i	$-0.461231\pi$
$863$	−584.567	−	337.500i	−0.677366	−	0.391078i	−0.798862	+	0.601514i	$0.794564\pi$
$864$	202.500	−	116.913i	0.234375	−	0.135316i
$865$		0			0
$866$	1885.50	+	1088.59i	2.17725	+	1.25704i
$867$	79.6743			0.0918966
$868$	−394.042	−	682.500i	−0.453965	−	0.786290i
$869$		0			0
$870$		0			0
$871$	−282.000	+	162.813i	−0.323766	+	0.186926i
$872$	−332.554	+	192.000i	−0.381369	+	0.220183i
$873$	−148.090	+	256.500i	−0.169634	+	0.293814i
$874$			1247.08i			1.42686i
$875$		0			0
$876$	60.0000			0.0684932
$877$	−429.549	−	248.000i	−0.489793	−	0.282782i	0.234695	−	0.972069i	$-0.424591\pi$
$877$	−429.549	−	248.000i	−0.489793	−	0.282782i	−0.724489	+	0.689287i	$0.757924\pi$
$878$	−142.894	−	247.500i	−0.162750	−	0.281891i
$879$	180.000	+	311.769i	0.204778	+	0.354686i
$880$		0			0
$881$		−	462.458i		−	0.524923i	−0.964942	−	0.262462i	$-0.915466\pi$
$881$		−	462.458i		−	0.524923i	0.964942	−	0.262462i	$-0.0845343\pi$
$882$	381.917	+	220.500i	0.433013	+	0.250000i
$883$			388.000i			0.439411i	0.975566	+	0.219706i	$0.0705097\pi$
$883$			388.000i			0.439411i	−0.975566	+	0.219706i	$0.929490\pi$
$884$	−135.000	+	233.827i	−0.152715	+	0.264510i
$885$		0			0
$886$	−972.000	−	1683.55i	−1.09707	−	1.90017i
$887$	530.008	−	918.000i	0.597528	−	1.03495i	−0.395657	−	0.918399i	$-0.629483\pi$
$887$	530.008	−	918.000i	0.597528	−	1.03495i	0.993185	−	0.116551i	$-0.0371838\pi$
$888$	363.731			0.409607
$889$	35.0000	−	60.6218i	0.0393701	−	0.0681910i
$890$		0			0
$891$		0			0
$892$	47.6314	+	82.5000i	0.0533984	+	0.0924888i
$893$	−623.538	+	360.000i	−0.698251	+	0.403135i
$894$	702.000	+	405.300i	0.785235	+	0.453356i
$895$		0			0
$896$	325.500	+	563.783i	0.363281	+	0.629222i
$897$			90.0000i			0.100334i
$898$	−1784.88	−	1030.50i	−1.98762	−	1.14755i
$899$	−117.000	+	67.5500i	−0.130145	+	0.0751390i
$900$		0			0
$901$	−567.000	−	327.358i	−0.629301	−	0.363327i
$902$		0			0
$903$	412.228			0.456510
$904$	549.000			0.607301
$905$		0			0
$906$	387.000	−	223.435i	0.427152	−	0.246617i
$907$	−1359.66	+	785.000i	−1.49907	+	0.865491i	−0.999999	−	0.00106856i	$-0.999660\pi$
$907$	−1359.66	+	785.000i	−1.49907	+	0.865491i	−0.499074	+	0.866559i	$0.666327\pi$
$908$	935.307	−	1620.00i	1.03007	−	1.78414i
$909$			498.831i			0.548769i
$910$		0			0
$911$	−555.000			−0.609221			−0.304610	−	0.952477i	$-0.598526\pi$
$911$	−555.000			−0.609221			−0.304610	+	0.952477i	$0.598526\pi$
$912$	457.261	+	264.000i	0.501383	+	0.289474i
$913$		0			0
$914$	543.000	+	940.504i	0.594092	+	1.02900i
$915$		0			0
$916$			1558.85i			1.70180i
$917$	763.834	+	1323.00i	0.832971	+	1.44275i
$918$		−	243.000i		−	0.264706i
$919$	−746.500	+	1292.98i	−0.812296	+	1.40694i	0.0989574	+	0.995092i	$0.468449\pi$
$919$	−746.500	+	1292.98i	−0.812296	+	1.40694i	−0.911253	+	0.411846i	$0.864884\pi$
$920$		0			0
$921$	−30.0000	−	51.9615i	−0.0325733	−	0.0564186i
$922$	−857.365	+	1485.00i	−0.929897	+	1.61063i
$923$	−31.1769			−0.0337778
$924$		0			0
$925$		0			0
$926$	385.500	−	667.706i	0.416307	−	0.721064i
$927$	−194.856	−	337.500i	−0.210200	−	0.364078i
$928$	233.827	−	135.000i	0.251969	−	0.145474i
$929$	792.000	+	457.261i	0.852530	+	0.492208i	0.861504	−	0.507752i	$-0.169523\pi$
$929$	792.000	+	457.261i	0.852530	+	0.492208i	−0.00897395	+	0.999960i	$0.502857\pi$
$930$		0			0
$931$			1357.93i			1.45857i
$932$		−	1950.00i		−	2.09227i
$933$	−459.859	−	265.500i	−0.492883	−	0.284566i
$934$	2187.00	−	1262.67i	2.34154	−	1.35189i
$935$		0			0
$936$	−27.0000	−	15.5885i	−0.0288462	−	0.0166543i
$937$	−672.036			−0.717221			−0.358610	−	0.933487i	$-0.616749\pi$
$937$	−672.036			−0.717221			−0.358610	+	0.933487i	$0.616749\pi$
$938$	1709.53	+	987.000i	1.82253	+	1.05224i
$939$	441.000			0.469649
$940$		0			0
$941$	63.0000	−	36.3731i	0.0669501	−	0.0386536i	−0.466151	−	0.884705i	$-0.654360\pi$
$941$	63.0000	−	36.3731i	0.0669501	−	0.0386536i	0.533101	+	0.846051i	$0.321026\pi$
$942$	763.834	−	441.000i	0.810865	−	0.468153i
$943$	272.798	−	472.500i	0.289287	−	0.501060i
$944$			457.261i			0.484387i
$945$		0			0
$946$		0			0
$947$	−997.661	−	576.000i	−1.05350	−	0.608237i	−0.129870	−	0.991531i	$-0.541456\pi$
$947$	−997.661	−	576.000i	−1.05350	−	0.608237i	−0.923626	+	0.383294i	$0.874789\pi$
$948$	333.420	+	577.500i	0.351709	+	0.609177i
$949$	12.0000	+	20.7846i	0.0126449	+	0.0219016i
$950$		0			0
$951$			1018.45i			1.07092i
$952$	327.358			0.343863
$953$		−	426.000i		−	0.447009i	−0.974703	−	0.223505i	$-0.928250\pi$
$953$		−	426.000i		−	0.447009i	0.974703	−	0.223505i	$-0.0717498\pi$
$954$	189.000	−	327.358i	0.198113	−	0.343142i
$955$		0			0
$956$	−892.500	−	1545.86i	−0.933577	−	1.61700i
$957$		0			0
$958$	1574.43			1.64346
$959$	−483.000			−0.503650
$960$		0			0
$961$	−227.000	+	393.176i	−0.236212	+	0.409132i
$962$	363.731	+	630.000i	0.378098	+	0.654886i
$963$	−498.831	+	288.000i	−0.517997	+	0.299065i
$964$	−210.000	−	121.244i	−0.217842	−	0.125771i
$965$		0			0
$966$	472.500	−	272.798i	0.489130	−	0.282400i
$967$		−	341.000i		−	0.352637i	−0.984333	−	0.176319i	$-0.943581\pi$
$967$		−	341.000i		−	0.352637i	0.984333	−	0.176319i	$-0.0564189\pi$
$968$	−314.367	−	181.500i	−0.324760	−	0.187500i
$969$	648.000	−	374.123i	0.668731	−	0.386092i
$970$		0			0
$971$	1215.00	+	701.481i	1.25129	+	0.722431i	0.971365	−	0.237592i	$-0.0763580\pi$
$971$	1215.00	+	701.481i	1.25129	+	0.722431i	0.279922	+	0.960023i	$0.409691\pi$
$972$	77.9423			0.0801875
$973$	691.088	−	1197.00i	0.710265	−	1.23022i
$974$	−2409.00			−2.47331
$975$		0			0
$976$	693.000	−	400.104i	0.710041	−	0.409942i
$977$	75.3442	−	43.5000i	0.0771179	−	0.0445241i	−0.460945	−	0.887429i	$-0.652490\pi$
$977$	75.3442	−	43.5000i	0.0771179	−	0.0445241i	0.538063	+	0.842905i	$0.319156\pi$
$978$	−488.438	+	846.000i	−0.499426	+	0.865031i
$979$		0			0
$980$		0			0
$981$	384.000			0.391437
$982$	1761.50	+	1017.00i	1.79378	+	1.03564i
$983$	−467.654	−	810.000i	−0.475741	−	0.824008i	0.523873	−	0.851797i	$-0.324487\pi$
$983$	−467.654	−	810.000i	−0.475741	−	0.824008i	−0.999614	+	0.0277886i	$0.991153\pi$
$984$	94.5000	+	163.679i	0.0960366	+	0.166340i
$985$		0			0
$986$		−	280.592i		−	0.284576i
$987$	272.798	+	157.500i	0.276391	+	0.159574i
$988$		−	480.000i		−	0.485830i
$989$	255.000	−	441.673i	0.257836	−	0.446585i
$990$		0			0
$991$	143.500	+	248.549i	0.144803	+	0.250807i	0.929300	−	0.369327i	$-0.120412\pi$
$991$	143.500	+	248.549i	0.144803	+	0.250807i	−0.784496	+	0.620134i	$0.787078\pi$
$992$	−506.625	+	877.500i	−0.510711	+	0.884577i
$993$	−121.244			−0.122098
$994$	94.5000	+	163.679i	0.0950704	+	0.164667i
$995$		0			0
$996$	−630.000	+	1091.19i	−0.632530	+	1.09557i
$997$	−325.626	−	564.000i	−0.326605	−	0.565697i	0.655231	−	0.755429i	$-0.272571\pi$
$997$	−325.626	−	564.000i	−0.326605	−	0.565697i	−0.981836	+	0.189732i	$0.939238\pi$
$998$	1470.51	−	849.000i	1.47346	−	0.850701i
$999$	−315.000	−	181.865i	−0.315315	−	0.182047i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	525.3.s.f.124.1		4
5.2	odd	4		525.3.o.i.376.1	yes	2
5.3	odd	4		525.3.o.a.376.1	✓	2
5.4	even	2	inner	525.3.s.f.124.2		4
7.3	odd	6	inner	525.3.s.f.199.2		4
35.3	even	12		525.3.o.a.451.1	yes	2
35.17	even	12		525.3.o.i.451.1	yes	2
35.24	odd	6	inner	525.3.s.f.199.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
525.3.o.a.376.1	✓	2	5.3	odd	4
525.3.o.a.451.1	yes	2	35.3	even	12
525.3.o.i.376.1	yes	2	5.2	odd	4
525.3.o.i.451.1	yes	2	35.17	even	12
525.3.s.f.124.1		4	1.1	even	1	trivial
525.3.s.f.124.2		4	5.4	even	2	inner
525.3.s.f.199.1		4	35.24	odd	6	inner
525.3.s.f.199.2		4	7.3	odd	6	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	525.s (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-2.59808 - 1.50000i) q^{2} +(0.866025 + 1.50000i) q^{3} +(2.50000 + 4.33013i) q^{4} -5.19615i q^{6} +(-6.06218 - 3.50000i) q^{7} -3.00000i q^{8} +(-1.50000 + 2.59808i) q^{9} +O(q^{10})\)	\(q+(-2.59808 - 1.50000i) q^{2} +(0.866025 + 1.50000i) q^{3} +(2.50000 + 4.33013i) q^{4} -5.19615i q^{6} +(-6.06218 - 3.50000i) q^{7} -3.00000i q^{8} +(-1.50000 + 2.59808i) q^{9} +(-4.33013 + 7.50000i) q^{12} -3.46410 q^{13} +(10.5000 + 18.1865i) q^{14} +(5.50000 - 9.52628i) q^{16} +(-7.79423 - 13.5000i) q^{17} +(7.79423 - 4.50000i) q^{18} +(24.0000 + 13.8564i) q^{19} -12.1244i q^{21} +(-12.9904 - 7.50000i) q^{23} +(4.50000 - 2.59808i) q^{24} +(9.00000 + 5.19615i) q^{26} -5.19615 q^{27} -35.0000i q^{28} -6.00000 q^{29} +(19.5000 - 11.2583i) q^{31} +(-38.9711 + 22.5000i) q^{32} +46.7654i q^{34} -15.0000 q^{36} +(60.6218 + 35.0000i) q^{37} +(-41.5692 - 72.0000i) q^{38} +(-3.00000 - 5.19615i) q^{39} +36.3731i q^{41} +(-18.1865 + 31.5000i) q^{42} +34.0000i q^{43} +(22.5000 + 38.9711i) q^{46} +(-12.9904 + 22.5000i) q^{47} +19.0526 q^{48} +(24.5000 + 42.4352i) q^{49} +(13.5000 - 23.3827i) q^{51} +(-8.66025 - 15.0000i) q^{52} +(36.3731 - 21.0000i) q^{53} +(13.5000 + 7.79423i) q^{54} +(-10.5000 + 18.1865i) q^{56} +48.0000i q^{57} +(15.5885 + 9.00000i) q^{58} +(-36.0000 + 20.7846i) q^{59} +(63.0000 + 36.3731i) q^{61} -67.5500 q^{62} +(18.1865 - 10.5000i) q^{63} +91.0000 q^{64} +(81.4064 - 47.0000i) q^{67} +(38.9711 - 67.5000i) q^{68} -25.9808i q^{69} +9.00000 q^{71} +(7.79423 + 4.50000i) q^{72} +(-3.46410 - 6.00000i) q^{73} +(-105.000 - 181.865i) q^{74} +138.564i q^{76} +18.0000i q^{78} +(38.5000 - 66.6840i) q^{79} +(-4.50000 - 7.79423i) q^{81} +(54.5596 - 94.5000i) q^{82} +145.492 q^{83} +(52.5000 - 30.3109i) q^{84} +(51.0000 - 88.3346i) q^{86} +(-5.19615 - 9.00000i) q^{87} +(-49.5000 - 28.5788i) q^{89} +(21.0000 + 12.1244i) q^{91} -75.0000i q^{92} +(33.7750 + 19.5000i) q^{93} +(67.5000 - 38.9711i) q^{94} +(-67.5000 - 38.9711i) q^{96} +98.7269 q^{97} -147.000i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 10 q^{4} - 6 q^{9}+O(q^{10}) \) 4 * q + 10 * q^4 - 6 * q^9	\( 4 q + 10 q^{4} - 6 q^{9} + 42 q^{14} + 22 q^{16} + 96 q^{19} + 18 q^{24} + 36 q^{26} - 24 q^{29} + 78 q^{31} - 60 q^{36} - 12 q^{39} + 90 q^{46} + 98 q^{49} + 54 q^{51} + 54 q^{54} - 42 q^{56} - 144 q^{59} + 252 q^{61} + 364 q^{64} + 36 q^{71} - 420 q^{74} + 154 q^{79} - 18 q^{81} + 210 q^{84} + 204 q^{86} - 198 q^{89} + 84 q^{91} + 270 q^{94} - 270 q^{96}+O(q^{100}) \) 4 * q + 10 * q^4 - 6 * q^9 + 42 * q^14 + 22 * q^16 + 96 * q^19 + 18 * q^24 + 36 * q^26 - 24 * q^29 + 78 * q^31 - 60 * q^36 - 12 * q^39 + 90 * q^46 + 98 * q^49 + 54 * q^51 + 54 * q^54 - 42 * q^56 - 144 * q^59 + 252 * q^61 + 364 * q^64 + 36 * q^71 - 420 * q^74 + 154 * q^79 - 18 * q^81 + 210 * q^84 + 204 * q^86 - 198 * q^89 + 84 * q^91 + 270 * q^94 - 270 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

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