LMFDB - Embedded newform 525.3.s.f.199.2

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			199.2
Root			$0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	525.199
Dual form			525.3.s.f.124.2

$q$-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 $\left(\mathbb{Z}/525\mathbb{Z}\right)^\times$.

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

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	$-0.396720\pi$
$2$	2.59808	−	1.50000i	1.29904	−	0.750000i	0.980238	+	0.197822i	$0.0633868\pi$
$3$	−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	$-0.833333\pi$
$11$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$12$	4.33013	+	7.50000i	0.360844	+	0.625000i
$13$	3.46410			0.266469			0.133235	−	0.991085i	$-0.457464\pi$
$13$	3.46410			0.266469			0.133235	+	0.991085i	$0.457464\pi$
$14$	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	$-0.681726\pi$
$17$	7.79423	−	13.5000i	0.458484	−	0.794118i	0.998881	+	0.0472925i	$0.0150593\pi$
$18$	−7.79423	−	4.50000i	−0.433013	−	0.250000i
$19$	24.0000	−	13.8564i	1.26316	−	0.729285i	0.289474	−	0.957186i	$-0.406520\pi$
$19$	24.0000	−	13.8564i	1.26316	−	0.729285i	0.973684	+	0.227901i	$0.0731864\pi$
$20$		0			0
$21$			12.1244i			0.577350i
$22$		0			0
$23$	12.9904	−	7.50000i	0.564799	−	0.326087i	−0.190270	−	0.981732i	$-0.560936\pi$
$23$	12.9904	−	7.50000i	0.564799	−	0.326087i	0.755069	+	0.655645i	$0.227603\pi$
$24$	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	0.780377	−	0.625309i	$-0.215027\pi$
$31$	19.5000	+	11.2583i	0.629032	+	0.363172i	−0.151345	+	0.988481i	$0.548360\pi$
$32$	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	−0.657051	+	0.753846i	$0.728196\pi$
$37$	−60.6218	+	35.0000i	−1.63843	+	0.945946i	−0.981375	+	0.192100i	$0.938470\pi$
$38$	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	$-0.853710\pi$
$41$		−	36.3731i		−	0.887148i	0.896238	−	0.443574i	$-0.146290\pi$
$42$	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	$-0.0775282\pi$
$47$	12.9904	+	22.5000i	0.276391	+	0.478723i	−0.694094	+	0.719884i	$0.744195\pi$
$48$	−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	$-0.463014\pi$
$53$	−36.3731	−	21.0000i	−0.686284	−	0.396226i	−0.802219	+	0.597030i	$0.796347\pi$
$54$	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	0.162862	−	0.986649i	$-0.447927\pi$
$59$	−36.0000	−	20.7846i	−0.610169	−	0.352282i	−0.773032	+	0.634367i	$0.781261\pi$
$60$		0			0
$61$	63.0000	−	36.3731i	1.03279	−	0.596280i	0.115005	−	0.993365i	$-0.463312\pi$
$61$	63.0000	−	36.3731i	1.03279	−	0.596280i	0.917782	+	0.397085i	$0.129978\pi$
$62$	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	$-0.580816\pi$
$67$	−81.4064	−	47.0000i	−1.21502	−	0.701493i	−0.963849	+	0.266450i	$0.914149\pi$
$68$	−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	$-0.818223\pi$
$73$	3.46410	−	6.00000i	0.0474534	−	0.0821918i	0.888777	+	0.458341i	$0.151556\pi$
$74$	−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	0.999894	−	0.0145553i	$-0.00463326\pi$
$79$	38.5000	+	66.6840i	0.487342	+	0.844101i	−0.512552	+	0.858656i	$0.671300\pi$
$80$		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	$-0.840101\pi$
$83$	−145.492			−1.75292			−0.876459	+	0.481476i	$0.840101\pi$
$84$	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	−0.751611	−	0.659607i	$-0.770723\pi$
$89$	−49.5000	+	28.5788i	−0.556180	+	0.321111i	0.195431	+	0.980717i	$0.437389\pi$
$90$		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	$-0.669948\pi$
$97$	−98.7269			−1.01780			−0.508902	+	0.860825i	$0.669948\pi$
$98$		−	147.000i		−	1.50000i
$99$		0			0
$100$		0			0
$101$	144.000	+	83.1384i	1.42574	+	0.823153i	0.996781	−	0.0801700i	$-0.0255463\pi$
$101$	144.000	+	83.1384i	1.42574	+	0.823153i	0.428961	+	0.903323i	$0.358880\pi$
$102$	70.1481	+	40.5000i	0.687726	+	0.397059i
$103$	64.9519	+	112.500i	0.630601	+	1.09223i	0.987429	+	0.158063i	$0.0505249\pi$
$103$	64.9519	+	112.500i	0.630601	+	1.09223i	−0.356828	+	0.934170i	$0.616142\pi$
$104$		−	10.3923i		−	0.0999260i
$105$		0			0
$106$	−126.000			−1.18868
$107$	−166.277	+	96.0000i	−1.55399	+	0.897196i	−0.556179	+	0.831063i	$0.687733\pi$
$107$	−166.277	+	96.0000i	−1.55399	+	0.897196i	−0.997811	+	0.0661336i	$0.978934\pi$
$108$	12.9904	−	22.5000i	0.120281	−	0.208333i
$109$	−64.0000	+	110.851i	−0.587156	+	1.01698i	0.407447	+	0.913229i	$0.366419\pi$
$109$	−64.0000	+	110.851i	−0.587156	+	1.01698i	−0.994603	+	0.103755i	$0.966914\pi$
$110$		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	−0.998032	−	0.0627008i	$-0.980029\pi$
$131$	−189.000	+	109.119i	−1.44275	+	0.832971i	−0.444716	+	0.895672i	$0.646695\pi$
$132$		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	$-0.414364\pi$
$137$	−59.7558	−	34.5000i	−0.436173	−	0.251825i	−0.701973	+	0.712203i	$0.747697\pi$
$138$	38.9711	+	67.5000i	0.282400	+	0.489130i
$139$		−	197.454i		−	1.42053i	−0.703934	−	0.710265i	$-0.748575\pi$
$139$		−	197.454i		−	1.42053i	0.703934	−	0.710265i	$-0.251425\pi$
$140$		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	−0.999626	−	0.0273397i	$-0.991296\pi$
$149$	−78.0000	−	135.100i	−0.523490	−	0.906711i	0.476136	−	0.879372i	$-0.342037\pi$
$150$		0			0
$151$	43.0000	−	74.4782i	0.284768	−	0.493233i	−0.687785	−	0.725915i	$-0.741417\pi$
$151$	43.0000	−	74.4782i	0.284768	−	0.493233i	0.972553	+	0.232682i	$0.0747500\pi$
$152$	−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	0.458295	+	0.888800i	$0.348460\pi$
$157$	−84.8705	+	147.000i	−0.540576	+	0.936306i	−0.998871	+	0.0475054i	$0.984873\pi$
$158$	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	$-0.471012\pi$
$163$	162.813	−	94.0000i	0.998851	−	0.576687i	0.907908	+	0.419169i	$0.137679\pi$
$164$	−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	$-0.559775\pi$
$167$	−62.3538			−0.373376			−0.186688	+	0.982419i	$0.559775\pi$
$168$	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	$-0.294351\pi$
$173$	−67.5500	−	117.000i	−0.390462	−	0.676301i	−0.992511	+	0.122159i	$0.961018\pi$
$174$		−	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	−0.191586	−	0.981476i	$-0.561363\pi$
$179$	135.000	−	233.827i	0.754190	−	1.30630i	0.945776	−	0.324819i	$-0.105304\pi$
$180$		0			0
$181$			41.5692i			0.229664i	0.993385	+	0.114832i	$0.0366330\pi$
$181$			41.5692i			0.229664i	−0.993385	+	0.114832i	$0.963367\pi$
$182$	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	0.862072	−	0.506786i	$-0.169167\pi$
$191$	−1.50000	−	2.59808i	−0.00785340	−	0.0136025i	−0.869925	+	0.493183i	$0.835833\pi$
$192$	−78.8083	+	136.500i	−0.410460	+	0.710938i
$193$	238.157	+	137.500i	1.23397	+	0.712435i	0.967856	−	0.251505i	$-0.0809256\pi$
$193$	238.157	+	137.500i	1.23397	+	0.712435i	0.266118	+	0.963940i	$0.414259\pi$
$194$	−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	0.829765	−	0.558113i	$-0.188475\pi$
$199$	151.500	+	87.4686i	0.761307	+	0.439541i	−0.0684581	+	0.997654i	$0.521808\pi$
$200$		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	$-0.513602\pi$
$223$	−19.0526			−0.0854375			−0.0427187	+	0.999087i	$0.513602\pi$
$224$	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	−0.0785766	−	0.996908i	$-0.525038\pi$
$227$	187.061	−	324.000i	0.824059	−	1.42731i	0.902636	−	0.430405i	$-0.141629\pi$
$228$	207.846	+	120.000i	0.911606	+	0.526316i
$229$	270.000	−	155.885i	1.17904	−	0.680719i	0.223247	−	0.974762i	$-0.428334\pi$
$229$	270.000	−	155.885i	1.17904	−	0.680719i	0.955792	+	0.294043i	$0.0950010\pi$
$230$		0			0
$231$		0			0
$232$			18.0000i			0.0775862i
$233$	337.750	−	195.000i	1.44957	−	0.836910i	0.451115	−	0.892466i	$-0.351026\pi$
$233$	337.750	−	195.000i	1.44957	−	0.836910i	0.998456	+	0.0555560i	$0.0176931\pi$
$234$	−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	0.410326	−	0.911939i	$-0.365415\pi$
$241$	−42.0000	−	24.2487i	−0.174274	−	0.100617i	−0.584600	+	0.811322i	$0.698748\pi$
$242$	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	$-0.803189\pi$
$251$		−	290.985i		−	1.15930i	0.814865	−	0.579650i	$-0.196811\pi$
$252$	−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	$-0.258016\pi$
$257$	−72.7461	−	126.000i	−0.283059	−	0.490272i	−0.972137	+	0.234415i	$0.924683\pi$
$258$	−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	$-0.227937\pi$
$263$	148.090	+	85.5000i	0.563081	+	0.325095i	−0.191300	+	0.981532i	$0.561270\pi$
$264$		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	0.986554	−	0.163437i	$-0.0522581\pi$
$269$	360.000	+	207.846i	1.33829	+	0.772662i	0.351736	+	0.936099i	$0.385591\pi$
$270$		0			0
$271$	−205.500	+	118.645i	−0.758303	+	0.437806i	−0.828686	−	0.559714i	$-0.810911\pi$
$271$	−205.500	+	118.645i	−0.758303	+	0.437806i	0.0703834	+	0.997520i	$0.477578\pi$
$272$	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	$-0.408730\pi$
$277$	−112.583	−	65.0000i	−0.406438	−	0.234657i	−0.689258	+	0.724516i	$0.742063\pi$
$278$	−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	$-0.904047\pi$
$283$	−62.3538	+	108.000i	−0.220332	+	0.381625i	0.734577	+	0.678525i	$0.237381\pi$
$284$	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	$-0.615412\pi$
$293$	−207.846			−0.709372			−0.354686	+	0.934985i	$0.615412\pi$
$294$	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	$-0.482032\pi$
$307$	34.6410			0.112837			0.0564186	+	0.998407i	$0.482032\pi$
$308$		0			0
$309$	−225.000			−0.728155
$310$		0			0
$311$	−265.500	−	153.286i	−0.853698	−	0.492883i	0.00819903	−	0.999966i	$-0.497390\pi$
$311$	−265.500	−	153.286i	−0.853698	−	0.492883i	−0.861897	+	0.507084i	$0.830723\pi$
$312$	15.5885	+	9.00000i	0.0499630	+	0.0288462i
$313$	−127.306	−	220.500i	−0.406728	−	0.704473i	0.587793	−	0.809011i	$-0.299997\pi$
$313$	−127.306	−	220.500i	−0.406728	−	0.704473i	−0.994521	+	0.104538i	$0.966664\pi$
$314$			509.223i			1.62173i
$315$		0			0
$316$	385.000			1.21835
$317$	−509.223	+	294.000i	−1.60638	+	0.927445i	−0.616211	+	0.787581i	$0.711333\pi$
$317$	−509.223	+	294.000i	−1.60638	+	0.927445i	−0.990171	+	0.139863i	$0.955334\pi$
$318$	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	0.808300	−	0.588771i	$-0.200388\pi$
$331$	−35.0000	−	60.6218i	−0.105740	−	0.183147i	−0.914040	+	0.405623i	$0.867055\pi$
$332$	−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	$-0.291937\pi$
$347$	77.9423	+	45.0000i	0.224618	+	0.129683i	−0.383469	+	0.923554i	$0.625271\pi$
$348$	−25.9808	−	45.0000i	−0.0746574	−	0.129310i
$349$			235.559i			0.674954i	0.941334	+	0.337477i	$0.109574\pi$
$349$			235.559i			0.674954i	−0.941334	+	0.337477i	$0.890426\pi$
$350$		0			0
$351$	18.0000			0.0512821
$352$		0			0
$353$	−75.3442	+	130.500i	−0.213440	+	0.369688i	−0.952789	−	0.303634i	$-0.901800\pi$
$353$	−75.3442	+	130.500i	−0.213440	+	0.369688i	0.739349	+	0.673322i	$0.235133\pi$
$354$	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	0.628518	−	0.777795i	$-0.283662\pi$
$359$	−129.000	−	223.435i	−0.359331	−	0.622380i	−0.987849	+	0.155415i	$0.950329\pi$
$360$		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	$-0.860407\pi$
$367$	−31.1769	+	54.0000i	−0.0849507	+	0.147139i	0.820419	+	0.571762i	$0.193740\pi$
$368$	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	$-0.376287\pi$
$373$	510.955	−	295.000i	1.36985	−	0.790885i	0.990909	+	0.134535i	$0.0429541\pi$
$374$		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	$-0.247422\pi$
$383$	−96.1288	−	166.500i	−0.250989	−	0.434726i	−0.963798	+	0.266632i	$0.914089\pi$
$384$			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	−0.316520	−	0.948586i	$-0.602515\pi$
$389$	258.000	−	446.869i	0.663239	−	1.14876i	0.979760	−	0.200178i	$-0.0641521\pi$
$390$		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	$-0.186121\pi$
$397$	−24.2487	−	42.0000i	−0.0610799	−	0.105793i	−0.894948	+	0.446170i	$0.852788\pi$
$398$	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	0.980838	−	0.194825i	$-0.0624138\pi$
$401$	129.000	+	223.435i	0.321696	+	0.557193i	−0.659142	+	0.752018i	$0.729081\pi$
$402$	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	0.983184	−	0.182616i	$-0.0584566\pi$
$409$	538.500	+	310.903i	1.31663	+	0.760154i	0.333442	+	0.942771i	$0.391790\pi$
$410$		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	$0.0920701\pi$
$419$			239.023i			0.570461i	−0.958459	+	0.285230i	$0.907930\pi$
$420$		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	−0.985271	−	0.170997i	$-0.945301\pi$
$431$	−148.500	+	257.210i	−0.344548	+	0.596774i	0.640724	+	0.767771i	$0.278634\pi$
$432$	28.5788	+	49.5000i	0.0661547	+	0.114583i
$433$	725.729			1.67605			0.838025	−	0.545632i	$-0.183711\pi$
$433$	725.729			1.67605			0.838025	+	0.545632i	$0.183711\pi$
$434$	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	−0.403085	−	0.915163i	$-0.632062\pi$
$439$	82.5000	−	47.6314i	0.187927	−	0.108500i	0.591012	+	0.806663i	$0.298729\pi$
$440$		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	$-0.927789\pi$
$443$	−561.184	+	324.000i	−1.26678	+	0.731377i	−0.292404	+	0.956295i	$0.594455\pi$
$444$	−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	$-0.537043\pi$
$457$	313.501	−	181.000i	0.685998	−	0.396061i	0.802111	+	0.597175i	$0.203710\pi$
$458$	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	$0.212840\pi$
$461$			571.577i			1.23986i	−0.784656	+	0.619931i	$0.787160\pi$
$462$		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	0.825861	+	0.563874i	$0.190690\pi$
$467$	420.888	+	729.000i	0.901260	+	1.56103i	0.0753993	+	0.997153i	$0.475977\pi$
$468$	−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	−0.0561277	−	0.998424i	$-0.517875\pi$
$479$	−454.500	−	262.406i	−0.948852	−	0.547820i	−0.892724	+	0.450604i	$0.851209\pi$
$480$		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	$-0.641840\pi$
$487$	−695.418	−	401.500i	−1.42796	−	0.824435i	−0.996960	+	0.0779148i	$0.975174\pi$
$488$	−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	−0.996848	−	0.0793400i	$-0.974719\pi$
$499$	−283.000	−	490.170i	−0.567134	−	0.982305i	0.429713	−	0.902965i	$-0.358615\pi$
$500$		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	$-0.473664\pi$
$503$	83.1384			0.165285			0.0826426	+	0.996579i	$0.473664\pi$
$504$	−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	−0.602324	−	0.798251i	$-0.705759\pi$
$509$	−108.000	+	62.3538i	−0.212181	+	0.122503i	0.390144	+	0.920754i	$0.372425\pi$
$510$		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	0.921275	−	0.388911i	$-0.127149\pi$
$521$	544.500	+	314.367i	1.04511	+	0.603392i	0.123830	+	0.992303i	$0.460482\pi$
$522$	46.7654	+	27.0000i	0.0895888	+	0.0517241i
$523$	64.0859	+	111.000i	0.122535	+	0.212237i	0.920767	−	0.390114i	$-0.127564\pi$
$523$	64.0859	+	111.000i	0.122535	+	0.212237i	−0.798232	+	0.602351i	$0.794231\pi$
$524$			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	0.844976	−	0.534804i	$-0.179614\pi$
$541$	−22.0000	−	38.1051i	−0.0406654	−	0.0704346i	−0.885642	+	0.464369i	$0.846281\pi$
$542$	−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	$-0.355639\pi$
$557$	−67.5500	−	39.0000i	−0.121275	−	0.0700180i	−0.559410	+	0.828891i	$0.688972\pi$
$558$	−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	0.482962	+	0.875641i	$0.339561\pi$
$563$	−290.985	+	504.000i	−0.516846	+	0.895204i	−0.999809	+	0.0195631i	$0.993772\pi$
$564$	−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	0.951167	−	0.308678i	$-0.0998866\pi$
$569$	118.500	+	205.248i	0.208260	+	0.360717i	−0.742906	+	0.669395i	$0.766553\pi$
$570$		0			0
$571$	290.000	−	502.295i	0.507881	−	0.879676i	−0.492077	−	0.870551i	$-0.663762\pi$
$571$	290.000	−	502.295i	0.507881	−	0.879676i	0.999958	−	0.00912412i	$-0.00290434\pi$
$572$		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	$-0.718081\pi$
$577$	204.382	−	354.000i	0.354215	−	0.613518i	0.986983	+	0.160823i	$0.0514148\pi$
$578$	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	$-0.852153\pi$
$587$	−1049.62			−1.78811			−0.894057	+	0.447953i	$0.852153\pi$
$588$	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	−0.966554	−	0.256462i	$-0.917443\pi$
$593$	−418.290	−	724.500i	−0.705380	−	1.22175i	0.261174	−	0.965292i	$-0.415890\pi$
$594$		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	−0.881844	−	0.471542i	$-0.843698\pi$
$599$	−19.5000	+	33.7750i	−0.0325543	+	0.0563856i	0.849289	+	0.527928i	$0.177031\pi$
$600$		0			0
$601$			20.7846i			0.0345834i	0.999850	+	0.0172917i	$0.00550439\pi$
$601$			20.7846i			0.0345834i	−0.999850	+	0.0172917i	$0.994496\pi$
$602$	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	$-0.100337\pi$
$607$	125.574	+	217.500i	0.206876	+	0.358320i	−0.743853	+	0.668343i	$0.767004\pi$
$608$	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	$-0.553508\pi$
$613$	−677.232	−	391.000i	−1.10478	−	0.637847i	−0.937473	+	0.348058i	$0.886841\pi$
$614$	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	0.428076	−	0.903743i	$-0.359191\pi$
$619$	−87.0000	−	50.2295i	−0.140549	−	0.0811462i	−0.568626	+	0.822596i	$0.692525\pi$
$620$		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	−0.719978	−	0.693997i	$-0.755848\pi$
$641$	154.500	−	267.602i	0.241030	−	0.417476i	0.961008	+	0.276521i	$0.0891816\pi$
$642$	−498.831	−	864.000i	−0.776995	−	1.34579i
$643$	−491.902			−0.765012			−0.382506	−	0.923953i	$-0.624939\pi$
$643$	−491.902			−0.765012			−0.382506	+	0.923953i	$0.624939\pi$
$644$	−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	0.109458	−	0.993991i	$-0.465088\pi$
$647$	592.361	−	1026.00i	0.915551	−	1.58578i	0.806093	−	0.591789i	$-0.201578\pi$
$648$	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	$-0.794366\pi$
$653$	−441.673	+	255.000i	−0.676375	+	0.390505i	0.122113	+	0.992516i	$0.461033\pi$
$654$	−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	0.984287	+	0.176575i	$0.0565020\pi$
$661$	1077.00	+	621.806i	1.62935	+	0.940705i	0.645062	+	0.764130i	$0.276831\pi$
$662$	−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	$-0.289398\pi$
$677$	−254.611	−	441.000i	−0.376088	−	0.651403i	−0.990489	+	0.137590i	$0.956064\pi$
$678$	−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	$-0.453620\pi$
$683$	−436.477	−	252.000i	−0.639058	−	0.368960i	−0.784252	+	0.620443i	$0.786953\pi$
$684$	−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	−0.708472	−	0.705739i	$-0.750615\pi$
$691$	−312.000	+	180.133i	−0.451520	+	0.260685i	0.256952	+	0.966424i	$0.417282\pi$
$692$	−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	0.908217	−	0.418498i	$-0.137443\pi$
$709$	65.0000	+	112.583i	0.0916784	+	0.158792i	−0.816539	+	0.577290i	$0.804110\pi$
$710$		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	0.0449296	−	0.998990i	$-0.485694\pi$
$719$	670.500	−	387.113i	0.932545	−	0.538405i	0.887616	+	0.460585i	$0.152360\pi$
$720$		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	$-0.350047\pi$
$727$	659.911			0.907719			0.453859	+	0.891073i	$0.350047\pi$
$728$	−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	$-0.190759\pi$
$733$	−55.4256	−	96.0000i	−0.0756148	−	0.130969i	−0.901353	+	0.433084i	$0.857425\pi$
$734$			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	−0.913409	−	0.407043i	$-0.866560\pi$
$739$	−77.0000	+	133.368i	−0.104195	+	0.180471i	0.809214	+	0.587514i	$0.199893\pi$
$740$		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	0.636085	−	0.771619i	$-0.280553\pi$
$751$	−263.000	−	455.529i	−0.350200	−	0.606564i	−0.986284	+	0.165056i	$0.947220\pi$
$752$	−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	−0.380239	−	0.924888i	$-0.624158\pi$
$761$	175.500	−	101.325i	0.230618	−	0.133147i	0.610857	+	0.791741i	$0.290825\pi$
$762$	−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	$-0.871815\pi$
$769$		−	602.754i		−	0.783815i	0.920005	−	0.391907i	$-0.128185\pi$
$770$		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	−0.0494194	−	0.998778i	$-0.515737\pi$
$773$	649.519	−	1125.00i	0.840258	−	1.45537i	0.889677	−	0.456591i	$-0.150930\pi$
$774$	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	$-0.856472\pi$
$787$	−57.1577	+	99.0000i	−0.0726273	+	0.125794i	0.827425	+	0.561577i	$0.189805\pi$
$788$	−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	$-0.586133\pi$
$797$	−426.084			−0.534610			−0.267305	+	0.963612i	$0.586133\pi$
$798$	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	−0.563334	−	0.826230i	$-0.690481\pi$
$809$	351.000	−	607.950i	0.433869	−	0.751483i	0.997203	+	0.0747464i	$0.0238147\pi$
$810$		0			0
$811$			1167.40i			1.43946i	0.694254	+	0.719730i	$0.255734\pi$
$811$			1167.40i			1.43946i	−0.694254	+	0.719730i	$0.744266\pi$
$812$			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	0.847177	−	0.531311i	$-0.178301\pi$
$821$	−30.0000	−	51.9615i	−0.0365408	−	0.0632905i	−0.883717	+	0.468021i	$0.844967\pi$
$822$	179.267	−	310.500i	0.218087	−	0.377737i
$823$	−323.894	−	187.000i	−0.393552	−	0.227217i	0.290146	−	0.956982i	$-0.406296\pi$
$823$	−323.894	−	187.000i	−0.393552	−	0.227217i	−0.683698	+	0.729765i	$0.739629\pi$
$824$	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	0.262736	−	0.964868i	$-0.415375\pi$
$829$	−366.000	−	211.310i	−0.441496	−	0.254898i	−0.704232	+	0.709970i	$0.748708\pi$
$830$		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	$-0.817701\pi$
$839$		−	909.327i		−	1.08382i	0.840436	−	0.541911i	$-0.182299\pi$
$840$		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	$-0.576352\pi$
$853$	−405.300			−0.475146			−0.237573	+	0.971370i	$0.576352\pi$
$854$		−	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	$-0.895487\pi$
$857$	−166.277	+	288.000i	−0.194022	+	0.336056i	0.752557	+	0.658527i	$0.228820\pi$
$858$		0			0
$859$	−807.000	+	465.922i	−0.939464	+	0.542400i	−0.889792	−	0.456366i	$-0.849151\pi$
$859$	−807.000	+	465.922i	−0.939464	+	0.542400i	−0.0496721	+	0.998766i	$0.515818\pi$
$860$		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	$-0.538769\pi$
$863$	584.567	−	337.500i	0.677366	−	0.391078i	0.798862	+	0.601514i	$0.205436\pi$
$864$	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	$-0.575409\pi$
$877$	429.549	−	248.000i	0.489793	−	0.282782i	0.724489	+	0.689287i	$0.242076\pi$
$878$	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	$0.0845343\pi$
$881$			462.458i			0.524923i	−0.964942	+	0.262462i	$0.915466\pi$
$882$	−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	−0.993185	−	0.116551i	$-0.962816\pi$
$887$	−530.008	−	918.000i	−0.597528	−	1.03495i	0.395657	−	0.918399i	$-0.370517\pi$
$888$	−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	$-0.000340134\pi$
$907$	1359.66	+	785.000i	1.49907	+	0.865491i	0.499074	+	0.866559i	$0.333673\pi$
$908$	−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	−0.911253	−	0.411846i	$-0.864884\pi$
$919$	−746.500	−	1292.98i	−0.812296	−	1.40694i	0.0989574	−	0.995092i	$-0.468449\pi$
$920$		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	−0.00897395	−	0.999960i	$-0.502857\pi$
$929$	792.000	−	457.261i	0.852530	−	0.492208i	0.861504	+	0.507752i	$0.169523\pi$
$930$		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	$-0.383251\pi$
$937$	672.036			0.717221			0.358610	+	0.933487i	$0.383251\pi$
$938$	−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	0.533101	−	0.846051i	$-0.321026\pi$
$941$	63.0000	+	36.3731i	0.0669501	+	0.0386536i	−0.466151	+	0.884705i	$0.654360\pi$
$942$	−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	$-0.458544\pi$
$947$	997.661	−	576.000i	1.05350	−	0.608237i	0.923626	+	0.383294i	$0.125211\pi$
$948$	−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	0.279922	−	0.960023i	$-0.409691\pi$
$971$	1215.00	−	701.481i	1.25129	−	0.722431i	0.971365	+	0.237592i	$0.0763580\pi$
$972$	−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	$-0.347510\pi$
$977$	−75.3442	−	43.5000i	−0.0771179	−	0.0445241i	−0.538063	+	0.842905i	$0.680844\pi$
$978$	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	$-0.675513\pi$
$983$	467.654	−	810.000i	0.475741	−	0.824008i	0.999614	+	0.0277886i	$0.00884651\pi$
$984$	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	−0.784496	−	0.620134i	$-0.787078\pi$
$991$	143.500	−	248.549i	0.144803	−	0.250807i	0.929300	+	0.369327i	$0.120412\pi$
$992$	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	$-0.727429\pi$
$997$	325.626	−	564.000i	0.326605	−	0.565697i	0.981836	+	0.189732i	$0.0607619\pi$
$998$	−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.199.2		4
5.2	odd	4		525.3.o.i.451.1	yes	2
5.3	odd	4		525.3.o.a.451.1	yes	2
5.4	even	2	inner	525.3.s.f.199.1		4
7.5	odd	6	inner	525.3.s.f.124.1		4
35.12	even	12		525.3.o.i.376.1	yes	2
35.19	odd	6	inner	525.3.s.f.124.2		4
35.33	even	12		525.3.o.a.376.1	✓	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
525.3.o.a.376.1	✓	2	35.33	even	12
525.3.o.a.451.1	yes	2	5.3	odd	4
525.3.o.i.376.1	yes	2	35.12	even	12
525.3.o.i.451.1	yes	2	5.2	odd	4
525.3.s.f.124.1		4	7.5	odd	6	inner
525.3.s.f.124.2		4	35.19	odd	6	inner
525.3.s.f.199.1		4	5.4	even	2	inner
525.3.s.f.199.2		4	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 525 = 3 \cdot 5^{2} \cdot 7 \)
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

Database

Properties

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