LMFDB - Embedded newform 525.3.f.a.449.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [525,3,Mod(449,525)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(525, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1, 0]))

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

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

chi := DirichletCharacter("525.449");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 525 = 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	525.f (of order $2$, degree $1$, 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:	$8$
Coefficient field:	8.0.4337012736.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 4x^{7} + 8x^{6} + 4x^{5} + 12x^{4} - 40x^{3} + 72x^{2} + 24x + 4 $ x^8 - 4x^7 + 8x^6 + 4x^5 + 12x^4 - 40x^3 + 72x^2 + 24*x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	no (minimal twist has level 21)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			449.5
Root			$1.15355 - 1.15355i$ of defining polynomial
Character	$\chi$	$=$	525.449
Dual form			525.3.f.a.449.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.30710 q^{2} +(-2.38267 - 1.82288i) q^{3} -2.29150 q^{4} +(-3.11438 - 2.38267i) q^{6} +2.64575i q^{7} -8.22359 q^{8} +(2.35425 + 8.68663i) q^{9} +O(q^{10})$	\(q+1.30710 q^{2} +(-2.38267 - 1.82288i) q^{3} -2.29150 q^{4} +(-3.11438 - 2.38267i) q^{6} +2.64575i q^{7} -8.22359 q^{8} +(2.35425 + 8.68663i) q^{9} +2.61419i q^{11} +(5.45990 + 4.17712i) q^{12} -6.35425i q^{13} +3.45825i q^{14} -1.58301 q^{16} +12.1449 q^{17} +(3.07723 + 11.3542i) q^{18} +10.2288 q^{19} +(4.82288 - 6.30396i) q^{21} +3.41699i q^{22} +4.30231 q^{23} +(19.5941 + 14.9906i) q^{24} -8.30561i q^{26} +(10.2252 - 24.9889i) q^{27} -6.06275i q^{28} +17.3733i q^{29} +39.2915 q^{31} +30.8252 q^{32} +(4.76534 - 6.22876i) q^{33} +15.8745 q^{34} +(-5.39477 - 19.9054i) q^{36} -41.0405i q^{37} +13.3700 q^{38} +(-11.5830 + 15.1401i) q^{39} +30.2802i q^{41} +(6.30396 - 8.23987i) q^{42} -55.8745i q^{43} -5.99042i q^{44} +5.62352 q^{46} +39.9749 q^{47} +(3.77178 + 2.88562i) q^{48} -7.00000 q^{49} +(-28.9373 - 22.1386i) q^{51} +14.5608i q^{52} +105.002 q^{53} +(13.3654 - 32.6628i) q^{54} -21.7576i q^{56} +(-24.3718 - 18.6458i) q^{57} +22.7085i q^{58} +41.3640i q^{59} -20.4797 q^{61} +51.3577 q^{62} +(-22.9827 + 6.22876i) q^{63} +46.6235 q^{64} +(6.22876 - 8.14158i) q^{66} +27.1660i q^{67} -27.8300 q^{68} +(-10.2510 - 7.84257i) q^{69} +67.8049i q^{71} +(-19.3604 - 71.4353i) q^{72} +60.7895i q^{73} -53.6439i q^{74} -23.4392 q^{76} -6.91650 q^{77} +(-15.1401 + 19.7895i) q^{78} +63.2470 q^{79} +(-69.9150 + 40.9010i) q^{81} +39.5791i q^{82} +89.9435 q^{83} +(-11.0516 + 14.4455i) q^{84} -73.0333i q^{86} +(31.6693 - 41.3948i) q^{87} -21.4980i q^{88} +63.1745i q^{89} +16.8118 q^{91} -9.85875 q^{92} +(-93.6188 - 71.6235i) q^{93} +52.2510 q^{94} +(-73.4464 - 56.1906i) q^{96} -19.1660i q^{97} -9.14967 q^{98} +(-22.7085 + 6.15445i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 24 q^{4} + 28 q^{6} + 40 q^{9}+O(q^{10}) $ 8 * q + 24 * q^4 + 28 * q^6 + 40 * q^9	$ 8 q + 24 q^{4} + 28 q^{6} + 40 q^{9} + 72 q^{16} - 24 q^{19} + 28 q^{21} + 252 q^{24} + 272 q^{31} + 232 q^{36} - 8 q^{39} - 336 q^{46} - 56 q^{49} - 168 q^{51} + 308 q^{54} - 312 q^{61} - 8 q^{64} - 56 q^{66} - 336 q^{69} - 632 q^{76} - 256 q^{79} - 136 q^{81} + 28 q^{84} - 56 q^{91} + 672 q^{94} - 196 q^{96} - 224 q^{99}+O(q^{100}) $ 8 * q + 24 * q^4 + 28 * q^6 + 40 * q^9 + 72 * q^16 - 24 * q^19 + 28 * q^21 + 252 * q^24 + 272 * q^31 + 232 * q^36 - 8 * q^39 - 336 * q^46 - 56 * q^49 - 168 * q^51 + 308 * q^54 - 312 * q^61 - 8 * q^64 - 56 * q^66 - 336 * q^69 - 632 * q^76 - 256 * q^79 - 136 * q^81 + 28 * q^84 - 56 * q^91 + 672 * q^94 - 196 * q^96 - 224 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$127$	$176$	$451$
$\chi(n)$	$-1$	$-1$	$1$

Coefficient data

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

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

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

$2$	1.30710			0.653548			0.326774	−	0.945103i	$-0.394038\pi$
$2$	1.30710			0.653548			0.326774	+	0.945103i	$0.394038\pi$
$3$	−2.38267	−	1.82288i	−0.794224	−	0.607625i
$3$	−2.38267	−	1.82288i	−0.794224	−	0.607625i
$4$	−2.29150			−0.572876
$5$		0			0
$5$		0			0
$6$	−3.11438	−	2.38267i	−0.519063	−	0.397112i
$7$			2.64575i			0.377964i
$7$			2.64575i			0.377964i
$8$	−8.22359			−1.02795
$9$	2.35425	+	8.68663i	0.261583	+	0.965181i
$10$		0			0
$11$			2.61419i			0.237654i	0.992915	+	0.118827i	$0.0379133\pi$
$11$			2.61419i			0.237654i	−0.992915	+	0.118827i	$0.962087\pi$
$12$	5.45990	+	4.17712i	0.454992	+	0.348094i
$13$		−	6.35425i		−	0.488788i	−0.969676	−	0.244394i	$-0.921411\pi$
$13$		−	6.35425i		−	0.488788i	0.969676	−	0.244394i	$-0.0785891\pi$
$14$			3.45825i			0.247018i
$15$		0			0
$16$	−1.58301			−0.0989378
$17$	12.1449			0.714405			0.357202	−	0.934027i	$-0.383731\pi$
$17$	12.1449			0.714405			0.357202	+	0.934027i	$0.383731\pi$
$18$	3.07723	+	11.3542i	0.170957	+	0.630792i
$19$	10.2288			0.538356			0.269178	−	0.963090i	$-0.413248\pi$
$19$	10.2288			0.538356			0.269178	+	0.963090i	$0.413248\pi$
$20$		0			0
$21$	4.82288	−	6.30396i	0.229661	−	0.300188i
$22$			3.41699i			0.155318i
$23$	4.30231			0.187057			0.0935284	−	0.995617i	$-0.470185\pi$
$23$	4.30231			0.187057			0.0935284	+	0.995617i	$0.470185\pi$
$24$	19.5941	+	14.9906i	0.816422	+	0.624608i
$25$		0			0
$26$		−	8.30561i		−	0.319446i
$27$	10.2252	−	24.9889i	0.378713	−	0.925514i
$28$		−	6.06275i		−	0.216527i
$29$			17.3733i			0.599078i	0.954084	+	0.299539i	$0.0968328\pi$
$29$			17.3733i			0.599078i	−0.954084	+	0.299539i	$0.903167\pi$
$30$		0			0
$31$	39.2915			1.26747			0.633734	−	0.773551i	$-0.281521\pi$
$31$	39.2915			1.26747			0.633734	+	0.773551i	$0.281521\pi$
$32$	30.8252			0.963288
$33$	4.76534	−	6.22876i	0.144404	−	0.188750i
$34$	15.8745			0.466897
$35$		0			0
$36$	−5.39477	−	19.9054i	−0.149855	−	0.552929i
$37$		−	41.0405i		−	1.10920i	−0.832116	−	0.554602i	$-0.812871\pi$
$37$		−	41.0405i		−	1.10920i	0.832116	−	0.554602i	$-0.187129\pi$
$38$	13.3700			0.351841
$39$	−11.5830	+	15.1401i	−0.297000	+	0.388207i
$40$		0			0
$41$			30.2802i			0.738541i	0.929322	+	0.369270i	$0.120392\pi$
$41$			30.2802i			0.738541i	−0.929322	+	0.369270i	$0.879608\pi$
$42$	6.30396	−	8.23987i	0.150094	−	0.196187i
$43$		−	55.8745i		−	1.29941i	−0.760188	−	0.649704i	$-0.774893\pi$
$43$		−	55.8745i		−	1.29941i	0.760188	−	0.649704i	$-0.225107\pi$
$44$		−	5.99042i		−	0.136146i
$45$		0			0
$46$	5.62352			0.122251
$47$	39.9749			0.850530			0.425265	−	0.905069i	$-0.360181\pi$
$47$	39.9749			0.850530			0.425265	+	0.905069i	$0.360181\pi$
$48$	3.77178	+	2.88562i	0.0785788	+	0.0601171i
$49$	−7.00000			−0.142857
$50$		0			0
$51$	−28.9373	−	22.1386i	−0.567397	−	0.434090i
$52$			14.5608i			0.280015i
$53$	105.002			1.98116			0.990581	−	0.136928i	$-0.0437229\pi$
$53$	105.002			1.98116			0.990581	+	0.136928i	$0.0437229\pi$
$54$	13.3654	−	32.6628i	0.247507	−	0.604868i
$55$		0			0
$56$		−	21.7576i		−	0.388528i
$57$	−24.3718	−	18.6458i	−0.427575	−	0.327118i
$58$			22.7085i			0.391526i
$59$			41.3640i			0.701085i	0.936547	+	0.350542i	$0.114003\pi$
$59$			41.3640i			0.701085i	−0.936547	+	0.350542i	$0.885997\pi$
$60$		0			0
$61$	−20.4797			−0.335733			−0.167867	−	0.985810i	$-0.553688\pi$
$61$	−20.4797			−0.335733			−0.167867	+	0.985810i	$0.553688\pi$
$62$	51.3577			0.828350
$63$	−22.9827	+	6.22876i	−0.364804	+	0.0988692i
$64$	46.6235			0.728493
$65$		0			0
$66$	6.22876	−	8.14158i	0.0943751	−	0.123357i
$67$			27.1660i			0.405463i	0.979234	+	0.202731i	$0.0649818\pi$
$67$			27.1660i			0.405463i	−0.979234	+	0.202731i	$0.935018\pi$
$68$	−27.8300			−0.409265
$69$	−10.2510	−	7.84257i	−0.148565	−	0.113660i
$70$		0			0
$71$			67.8049i			0.954999i	0.878632	+	0.477499i	$0.158457\pi$
$71$			67.8049i			0.954999i	−0.878632	+	0.477499i	$0.841543\pi$
$72$	−19.3604	−	71.4353i	−0.268894	−	0.992157i
$73$			60.7895i			0.832733i	0.909197	+	0.416367i	$0.136697\pi$
$73$			60.7895i			0.832733i	−0.909197	+	0.416367i	$0.863303\pi$
$74$		−	53.6439i		−	0.724917i
$75$		0			0
$76$	−23.4392			−0.308411
$77$	−6.91650			−0.0898246
$78$	−15.1401	+	19.7895i	−0.194104	+	0.253712i
$79$	63.2470			0.800596			0.400298	−	0.916385i	$-0.368907\pi$
$79$	63.2470			0.800596			0.400298	+	0.916385i	$0.368907\pi$
$80$		0			0
$81$	−69.9150	+	40.9010i	−0.863148	+	0.504950i
$82$			39.5791i			0.482672i
$83$	89.9435			1.08366			0.541828	−	0.840489i	$-0.317732\pi$
$83$	89.9435			1.08366			0.541828	+	0.840489i	$0.317732\pi$
$84$	−11.0516	+	14.4455i	−0.131567	+	0.171971i
$85$		0			0
$86$		−	73.0333i		−	0.849224i
$87$	31.6693	−	41.3948i	0.364015	−	0.475802i
$88$		−	21.4980i		−	0.244296i
$89$			63.1745i			0.709826i	0.934899	+	0.354913i	$0.115490\pi$
$89$			63.1745i			0.709826i	−0.934899	+	0.354913i	$0.884510\pi$
$90$		0			0
$91$	16.8118			0.184745
$92$	−9.85875			−0.107160
$93$	−93.6188	−	71.6235i	−1.00665	−	0.770145i
$94$	52.2510			0.555862
$95$		0			0
$96$	−73.4464	−	56.1906i	−0.765067	−	0.585318i
$97$		−	19.1660i		−	0.197588i	−0.995108	−	0.0987939i	$-0.968502\pi$
$97$		−	19.1660i		−	0.197588i	0.995108	−	0.0987939i	$-0.0314984\pi$
$98$	−9.14967			−0.0933639
$99$	−22.7085	+	6.15445i	−0.229379	+	0.0621662i
$100$		0			0
$101$			98.7122i			0.977348i	0.872466	+	0.488674i	$0.162519\pi$
$101$			98.7122i			0.977348i	−0.872466	+	0.488674i	$0.837481\pi$
$102$	−37.8237	−	28.9373i	−0.370821	−	0.283699i
$103$		−	56.2510i		−	0.546126i	−0.961996	−	0.273063i	$-0.911963\pi$
$103$		−	56.2510i		−	0.546126i	0.961996	−	0.273063i	$-0.0880368\pi$
$104$			52.2547i			0.502449i
$105$		0			0
$106$	137.247			1.29478
$107$	−123.137			−1.15081			−0.575406	−	0.817868i	$-0.695156\pi$
$107$	−123.137			−1.15081			−0.575406	+	0.817868i	$0.695156\pi$
$108$	−23.4312	+	57.2621i	−0.216955	+	0.530205i
$109$	−164.539			−1.50953			−0.754764	−	0.655996i	$-0.772249\pi$
$109$	−164.539			−1.50953			−0.754764	+	0.655996i	$0.772249\pi$
$110$		0			0
$111$	−74.8118	+	97.7861i	−0.673980	+	0.880956i
$112$		−	4.18824i		−	0.0373950i
$113$	−144.050			−1.27478			−0.637391	−	0.770540i	$-0.719986\pi$
$113$	−144.050			−1.27478			−0.637391	+	0.770540i	$0.719986\pi$
$114$	−31.8562	−	24.3718i	−0.279441	−	0.213787i
$115$		0			0
$116$		−	39.8109i		−	0.343197i
$117$	55.1970	−	14.9595i	0.471769	−	0.127859i
$118$			54.0667i			0.458192i
$119$			32.1323i			0.270020i
$120$		0			0
$121$	114.166			0.943521
$122$	−26.7690			−0.219418
$123$	55.1970	−	72.1477i	0.448756	−	0.586567i
$124$	−90.0366			−0.726101
$125$		0			0
$126$	−30.0405	+	8.14158i	−0.238417	+	0.0646157i
$127$			36.5830i			0.288055i	0.989574	+	0.144028i	$0.0460054\pi$
$127$			36.5830i			0.288055i	−0.989574	+	0.144028i	$0.953995\pi$
$128$	−62.3595			−0.487184
$129$	−101.852	+	133.131i	−0.789553	+	1.03202i
$130$		0			0
$131$		−	33.6855i		−	0.257141i	−0.991700	−	0.128570i	$-0.958961\pi$
$131$		−	33.6855i		−	0.257141i	0.991700	−	0.128570i	$-0.0410389\pi$
$132$	−10.9198	+	14.2732i	−0.0827257	+	0.108130i
$133$			27.0627i			0.203479i
$134$			35.5086i			0.264989i
$135$		0			0
$136$	−99.8745			−0.734371
$137$	−39.9749			−0.291788			−0.145894	−	0.989300i	$-0.546606\pi$
$137$	−39.9749			−0.291788			−0.145894	+	0.989300i	$0.546606\pi$
$138$	−13.3990	−	10.2510i	−0.0970943	−	0.0742825i
$139$	194.642			1.40030			0.700150	−	0.713995i	$-0.253116\pi$
$139$	194.642			1.40030			0.700150	+	0.713995i	$0.253116\pi$
$140$		0			0
$141$	−95.2470	−	72.8693i	−0.675511	−	0.516803i
$142$			88.6275i			0.624137i
$143$	16.6112			0.116162
$144$	−3.72679	−	13.7510i	−0.0258805	−	0.0954929i
$145$		0			0
$146$			79.4577i			0.544231i
$147$	16.6787	+	12.7601i	0.113461	+	0.0868036i
$148$			94.0445i			0.635436i
$149$		−	203.685i		−	1.36701i	−0.729945	−	0.683506i	$-0.760454\pi$
$149$		−	203.685i		−	1.36701i	0.729945	−	0.683506i	$-0.239546\pi$
$150$		0			0
$151$	165.749			1.09768			0.548838	−	0.835929i	$-0.315070\pi$
$151$	165.749			1.09768			0.548838	+	0.835929i	$0.315070\pi$
$152$	−84.1171			−0.553402
$153$	28.5921	+	105.498i	0.186876	+	0.689530i
$154$	−9.04052			−0.0587047
$155$		0			0
$156$	26.5425	−	34.6936i	0.170144	−	0.222395i
$157$			302.723i			1.92817i	0.265592	+	0.964086i	$0.414433\pi$
$157$			302.723i			1.92817i	−0.265592	+	0.964086i	$0.585567\pi$
$158$	82.6699			0.523227
$159$	−250.184	−	191.405i	−1.57349	−	1.20380i
$160$		0			0
$161$			11.3828i			0.0707008i
$162$	−91.3856	+	53.4615i	−0.564109	+	0.330009i
$163$		−	145.041i		−	0.889819i	−0.895576	−	0.444910i	$-0.853236\pi$
$163$		−	145.041i		−	0.889819i	0.895576	−	0.444910i	$-0.146764\pi$
$164$		−	69.3871i		−	0.423092i
$165$		0			0
$166$	117.565			0.708221
$167$	−19.6594			−0.117721			−0.0588604	−	0.998266i	$-0.518747\pi$
$167$	−19.6594			−0.117721			−0.0588604	+	0.998266i	$0.518747\pi$
$168$	−39.6614	+	51.8412i	−0.236080	+	0.308578i
$169$	128.624			0.761086
$170$		0			0
$171$	24.0810	+	88.8534i	0.140825	+	0.519611i
$172$			128.037i			0.744399i
$173$	19.6884			0.113806			0.0569030	−	0.998380i	$-0.481877\pi$
$173$	19.6884			0.113806			0.0569030	+	0.998380i	$0.481877\pi$
$174$	41.3948	−	54.1069i	0.237901	−	0.310959i
$175$		0			0
$176$		−	4.13828i		−	0.0235129i
$177$	75.4014	−	98.5568i	0.425997	−	0.556818i
$178$			82.5751i			0.463905i
$179$		−	341.745i		−	1.90919i	−0.297910	−	0.954594i	$-0.596289\pi$
$179$		−	341.745i		−	1.90919i	0.297910	−	0.954594i	$-0.403711\pi$
$180$		0			0
$181$	215.889			1.19276			0.596378	−	0.802704i	$-0.296606\pi$
$181$	215.889			1.19276			0.596378	+	0.802704i	$0.296606\pi$
$182$	21.9746			0.120739
$183$	48.7965	+	37.3320i	0.266648	+	0.204000i
$184$	−35.3804			−0.192285
$185$		0			0
$186$	−122.369	−	93.6188i	−0.657896	−	0.503327i
$187$			31.7490i			0.169781i
$188$	−91.6026			−0.487248
$189$	66.1144	+	27.0534i	0.349812	+	0.143140i
$190$		0			0
$191$		−	44.7112i		−	0.234090i	−0.993127	−	0.117045i	$-0.962658\pi$
$191$		−	44.7112i		−	0.234090i	0.993127	−	0.117045i	$-0.0373422\pi$
$192$	−111.089	−	84.9889i	−0.578586	−	0.442650i
$193$		−	145.122i		−	0.751925i	−0.926635	−	0.375963i	$-0.877312\pi$
$193$		−	145.122i		−	0.751925i	0.926635	−	0.375963i	$-0.122688\pi$
$194$		−	25.0518i		−	0.129133i
$195$		0			0
$196$	16.0405			0.0818394
$197$	−87.4643			−0.443981			−0.221991	−	0.975049i	$-0.571255\pi$
$197$	−87.4643			−0.443981			−0.221991	+	0.975049i	$0.571255\pi$
$198$	−29.6822	+	8.04446i	−0.149910	+	0.0406286i
$199$	−65.4170			−0.328729			−0.164364	−	0.986400i	$-0.552557\pi$
$199$	−65.4170			−0.328729			−0.164364	+	0.986400i	$0.552557\pi$
$200$		0			0
$201$	49.5203	−	64.7277i	0.246369	−	0.322028i
$202$			129.026i			0.638743i
$203$	−45.9653			−0.226430
$204$	66.3098	+	50.7307i	0.325048	+	0.248680i
$205$		0			0
$206$		−	73.5254i		−	0.356919i
$207$	10.1287	+	37.3725i	0.0489309	+	0.180544i
$208$			10.0588i			0.0483597i
$209$			26.7399i			0.127942i
$210$		0			0
$211$	40.5830			0.192337			0.0961683	−	0.995365i	$-0.469341\pi$
$211$	40.5830			0.192337			0.0961683	+	0.995365i	$0.469341\pi$
$212$	−240.611			−1.13496
$213$	123.600	−	161.557i	0.580281	−	0.758483i
$214$	−160.952			−0.752110
$215$		0			0
$216$	−84.0882	+	205.498i	−0.389297	+	0.951381i
$217$			103.956i			0.479058i
$218$	−215.068			−0.986548
$219$	110.812	−	144.842i	0.505990	−	0.661377i
$220$		0			0
$221$		−	77.1716i		−	0.349193i
$222$	−97.7861	+	127.816i	−0.440478	+	0.575746i
$223$			100.959i			0.452733i	0.974042	+	0.226367i	$0.0726847\pi$
$223$			100.959i			0.452733i	−0.974042	+	0.226367i	$0.927315\pi$
$224$			81.5559i			0.364089i
$225$		0			0
$226$	−188.288			−0.833131
$227$	391.279			1.72370			0.861849	−	0.507166i	$-0.169307\pi$
$227$	391.279			1.72370			0.861849	+	0.507166i	$0.169307\pi$
$228$	55.8480	+	42.7268i	0.244947	+	0.187398i
$229$	6.81176			0.0297457			0.0148728	−	0.999889i	$-0.495266\pi$
$229$	6.81176			0.0297457			0.0148728	+	0.999889i	$0.495266\pi$
$230$		0			0
$231$	16.4797	+	12.6079i	0.0713409	+	0.0545797i
$232$		−	142.871i		−	0.615821i
$233$	116.877			0.501616			0.250808	−	0.968037i	$-0.419304\pi$
$233$	116.877			0.501616			0.250808	+	0.968037i	$0.419304\pi$
$234$	72.1477	−	19.5535i	0.308324	−	0.0835618i
$235$		0			0
$236$		−	94.7857i		−	0.401634i
$237$	−150.697	−	115.292i	−0.635852	−	0.486462i
$238$			42.0000i			0.176471i
$239$		−	59.9623i		−	0.250888i	−0.992101	−	0.125444i	$-0.959964\pi$
$239$		−	59.9623i		−	0.250888i	0.992101	−	0.125444i	$-0.0400356\pi$
$240$		0			0
$241$	134.753			0.559141			0.279570	−	0.960125i	$-0.409808\pi$
$241$	134.753			0.559141			0.279570	+	0.960125i	$0.409808\pi$
$242$	149.226			0.616636
$243$	241.142	+	29.9928i	0.992354	+	0.123427i
$244$	46.9294			0.192334
$245$		0			0
$246$	72.1477	−	94.3039i	0.293283	−	0.383349i
$247$		−	64.9961i		−	0.263142i
$248$	−323.117			−1.30289
$249$	−214.306	−	163.956i	−0.860666	−	0.658457i
$250$		0			0
$251$		−	268.248i		−	1.06872i	−0.845257	−	0.534359i	$-0.820553\pi$
$251$		−	268.248i		−	1.06872i	0.845257	−	0.534359i	$-0.179447\pi$
$252$	52.6648	−	14.2732i	0.208987	−	0.0566397i
$253$			11.2470i			0.0444547i
$254$			47.8175i			0.188258i
$255$		0			0
$256$	−268.004			−1.04689
$257$	−234.129			−0.911007			−0.455504	−	0.890234i	$-0.650541\pi$
$257$	−234.129			−0.911007			−0.455504	+	0.890234i	$0.650541\pi$
$258$	−133.131	+	174.014i	−0.516010	+	0.674474i
$259$	108.583			0.419239
$260$		0			0
$261$	−150.915	+	40.9010i	−0.578218	+	0.156709i
$262$		−	44.0301i		−	0.168054i
$263$	250.142			0.951111			0.475555	−	0.879686i	$-0.342247\pi$
$263$	250.142			0.951111			0.475555	+	0.879686i	$0.342247\pi$
$264$	−39.1882	+	51.2228i	−0.148440	+	0.194026i
$265$		0			0
$266$			35.3736i			0.132983i
$267$	115.159	−	150.524i	0.431308	−	0.563761i
$268$		−	62.2510i		−	0.232280i
$269$			340.684i			1.26648i	0.773955	+	0.633241i	$0.218276\pi$
$269$			340.684i			1.26648i	−0.773955	+	0.633241i	$0.781724\pi$
$270$		0			0
$271$	−21.2994			−0.0785955			−0.0392977	−	0.999228i	$-0.512512\pi$
$271$	−21.2994			−0.0785955			−0.0392977	+	0.999228i	$0.512512\pi$
$272$	−19.2254			−0.0706816
$273$	−40.0569	−	30.6458i	−0.146729	−	0.112255i
$274$	−52.2510			−0.190697
$275$		0			0
$276$	23.4902	+	17.9713i	0.0851093	+	0.0651133i
$277$			226.915i			0.819188i	0.912268	+	0.409594i	$0.134330\pi$
$277$			226.915i			0.819188i	−0.912268	+	0.409594i	$0.865670\pi$
$278$	254.415			0.915163
$279$	92.5020	+	341.311i	0.331548	+	1.22334i
$280$		0			0
$281$			235.489i			0.838039i	0.907977	+	0.419019i	$0.137626\pi$
$281$			235.489i			0.838039i	−0.907977	+	0.419019i	$0.862374\pi$
$282$	−124.497	−	95.2470i	−0.441479	−	0.337755i
$283$			368.634i			1.30259i	0.758823	+	0.651297i	$0.225775\pi$
$283$			368.634i			1.30259i	−0.758823	+	0.651297i	$0.774225\pi$
$284$		−	155.375i		−	0.547096i
$285$		0			0
$286$	21.7124			0.0759176
$287$	−80.1138			−0.279142
$288$	72.5703	+	267.767i	0.251980	+	0.929748i
$289$	−141.502			−0.489626
$290$		0			0
$291$	−34.9373	+	45.6663i	−0.120059	+	0.156929i
$292$		−	139.299i		−	0.477053i
$293$	−531.625			−1.81442			−0.907211	−	0.420677i	$-0.861793\pi$
$293$	−531.625			−1.81442			−0.907211	+	0.420677i	$0.861793\pi$
$294$	21.8006	+	16.6787i	0.0741519	+	0.0567303i
$295$		0			0
$296$			337.500i			1.14020i
$297$	65.3257	+	26.7307i	0.219952	+	0.0900024i
$298$		−	266.235i		−	0.893407i
$299$		−	27.3379i		−	0.0914312i
$300$		0			0
$301$	147.830			0.491130
$302$	216.650			0.717383
$303$	179.940	−	235.199i	0.593861	−	0.776233i
$304$	−16.1922			−0.0532637
$305$		0			0
$306$	37.3725	+	137.896i	0.122132	+	0.450640i
$307$		−	567.763i		−	1.84939i	−0.380706	−	0.924696i	$-0.624319\pi$
$307$		−	567.763i		−	1.84939i	0.380706	−	0.924696i	$-0.375681\pi$
$308$	15.8492			0.0514583
$309$	−102.539	+	134.028i	−0.331840	+	0.433746i
$310$		0			0
$311$		−	42.7531i		−	0.137470i	−0.997635	−	0.0687349i	$-0.978104\pi$
$311$		−	42.7531i		−	0.137470i	0.997635	−	0.0687349i	$-0.0218963\pi$
$312$	95.2539	−	124.506i	0.305301	−	0.399057i
$313$		−	158.118i		−	0.505168i	−0.967575	−	0.252584i	$-0.918720\pi$
$313$		−	158.118i		−	0.505168i	0.967575	−	0.252584i	$-0.0812804\pi$
$314$			395.688i			1.26015i
$315$		0			0
$316$	−144.931			−0.458642
$317$	140.944			0.444619			0.222309	−	0.974976i	$-0.428641\pi$
$317$	140.944			0.444619			0.222309	+	0.974976i	$0.428641\pi$
$318$	−327.015	−	250.184i	−1.02835	−	0.786743i
$319$	−45.4170			−0.142373
$320$		0			0
$321$	293.395	+	224.463i	0.914002	+	0.699262i
$322$			14.8784i			0.0462064i
$323$	124.227			0.384604
$324$	160.210	−	93.7247i	0.494477	−	0.289274i
$325$		0			0
$326$		−	189.582i		−	0.581539i
$327$	392.041	+	299.933i	1.19890	+	0.917227i
$328$		−	249.012i		−	0.759182i
$329$			105.764i			0.321470i
$330$		0			0
$331$	−258.369			−0.780570			−0.390285	−	0.920694i	$-0.627623\pi$
$331$	−258.369			−0.780570			−0.390285	+	0.920694i	$0.627623\pi$
$332$	−206.106			−0.620801
$333$	356.504	−	96.6196i	1.07058	−	0.290149i
$334$	−25.6967			−0.0769362
$335$		0			0
$336$	−7.63464	+	9.97920i	−0.0227221	+	0.0297000i
$337$		−	328.959i		−	0.976141i	−0.872804	−	0.488070i	$-0.837701\pi$
$337$		−	328.959i		−	0.976141i	0.872804	−	0.488070i	$-0.162299\pi$
$338$	168.123			0.497406
$339$	343.225	+	262.586i	1.01246	+	0.774590i
$340$		0			0
$341$			102.715i			0.301218i
$342$	31.4762	+	116.140i	0.0920357	+	0.339590i
$343$		−	18.5203i		−	0.0539949i
$344$			459.489i			1.33572i
$345$		0			0
$346$	25.7347			0.0743776
$347$	−128.635			−0.370707			−0.185353	−	0.982672i	$-0.559343\pi$
$347$	−128.635			−0.370707			−0.185353	+	0.982672i	$0.559343\pi$
$348$	−72.5703	+	94.8562i	−0.208535	+	0.272575i
$349$	73.4837			0.210555			0.105277	−	0.994443i	$-0.466427\pi$
$349$	73.4837			0.210555			0.105277	+	0.994443i	$0.466427\pi$
$350$		0			0
$351$	−158.786	−	64.9737i	−0.452381	−	0.185110i
$352$			80.5830i			0.228929i
$353$	−239.685			−0.678995			−0.339498	−	0.940607i	$-0.610257\pi$
$353$	−239.685			−0.678995			−0.339498	+	0.940607i	$0.610257\pi$
$354$	98.5568	−	128.823i	0.278409	−	0.363907i
$355$		0			0
$356$		−	144.765i		−	0.406642i
$357$	58.5732	−	76.5608i	0.164071	−	0.214456i
$358$		−	446.693i		−	1.24775i
$359$			180.215i			0.501992i	0.967988	+	0.250996i	$0.0807581\pi$
$359$			180.215i			0.501992i	−0.967988	+	0.250996i	$0.919242\pi$
$360$		0			0
$361$	−256.373			−0.710173
$362$	282.187			0.779523
$363$	−272.020	−	208.110i	−0.749367	−	0.573307i
$364$	−38.5242			−0.105836
$365$		0			0
$366$	63.7817	+	48.7965i	0.174267	+	0.133324i
$367$		−	229.786i		−	0.626119i	−0.949734	−	0.313059i	$-0.898646\pi$
$367$		−	229.786i		−	0.626119i	0.949734	−	0.313059i	$-0.101354\pi$
$368$	−6.81057			−0.0185070
$369$	−263.033	+	71.2871i	−0.712826	+	0.193190i
$370$		0			0
$371$			277.808i			0.748809i
$372$	214.528	+	164.125i	0.576687	+	0.441198i
$373$			441.749i			1.18431i	0.805823	+	0.592157i	$0.201723\pi$
$373$			441.749i			1.18431i	−0.805823	+	0.592157i	$0.798277\pi$
$374$			41.4990i			0.110960i
$375$		0			0
$376$	−328.737			−0.874301
$377$	110.394			0.292822
$378$	86.4178	+	35.3614i	0.228618	+	0.0935487i
$379$	421.203			1.11135			0.555676	−	0.831399i	$-0.312459\pi$
$379$	421.203			1.11135			0.555676	+	0.831399i	$0.312459\pi$
$380$		0			0
$381$	66.6863	−	87.1653i	0.175030	−	0.228780i
$382$		−	58.4418i		−	0.152989i
$383$	595.591			1.55507			0.777534	−	0.628841i	$-0.216470\pi$
$383$	595.591			1.55507			0.777534	+	0.628841i	$0.216470\pi$
$384$	148.582	+	113.674i	0.386933	+	0.296025i
$385$		0			0
$386$		−	189.688i		−	0.491419i
$387$	485.361	−	131.542i	1.25416	−	0.339903i
$388$			43.9190i			0.113193i
$389$		−	367.347i		−	0.944336i	−0.881509	−	0.472168i	$-0.843472\pi$
$389$		−	367.347i		−	0.944336i	0.881509	−	0.472168i	$-0.156528\pi$
$390$		0			0
$391$	52.2510			0.133634
$392$	57.5651			0.146850
$393$	−61.4044	+	80.2614i	−0.156245	+	0.204227i
$394$	−114.324			−0.290163
$395$		0			0
$396$	52.0366	−	14.1029i	0.131406	−	0.0356135i
$397$		−	408.346i		−	1.02858i	−0.857616	−	0.514290i	$-0.828055\pi$
$397$		−	408.346i		−	1.02858i	0.857616	−	0.514290i	$-0.171945\pi$
$398$	−85.5062			−0.214840
$399$	49.3320	−	64.4816i	0.123639	−	0.161608i
$400$		0			0
$401$			238.817i			0.595555i	0.954635	+	0.297777i	$0.0962453\pi$
$401$			238.817i			0.595555i	−0.954635	+	0.297777i	$0.903755\pi$
$402$	64.7277	−	84.6052i	0.161014	−	0.210461i
$403$		−	249.668i		−	0.619524i
$404$		−	226.199i		−	0.559899i
$405$		0			0
$406$	−60.0810			−0.147983
$407$	107.288			0.263606
$408$	237.968	+	182.059i	0.583255	+	0.446223i
$409$	649.365			1.58769			0.793844	−	0.608121i	$-0.208076\pi$
$409$	649.365			1.58769			0.793844	+	0.608121i	$0.208076\pi$
$410$		0			0
$411$	95.2470	+	72.8693i	0.231745	+	0.177297i
$412$			128.899i			0.312862i
$413$	−109.439			−0.264985
$414$	13.2392	+	48.8495i	0.0319787	+	0.117994i
$415$		0			0
$416$		−	195.871i		−	0.470844i
$417$	−463.768	−	354.808i	−1.11215	−	0.850858i
$418$			34.9516i			0.0836163i
$419$		−	11.5178i		−	0.0274888i	−0.999906	−	0.0137444i	$-0.995625\pi$
$419$		−	11.5178i		−	0.0274888i	0.999906	−	0.0137444i	$-0.00437512\pi$
$420$		0			0
$421$	−83.9921			−0.199506			−0.0997531	−	0.995012i	$-0.531805\pi$
$421$	−83.9921			−0.199506			−0.0997531	+	0.995012i	$0.531805\pi$
$422$	53.0458			0.125701
$423$	94.1108	+	347.247i	0.222484	+	0.820915i
$424$	−863.490			−2.03653
$425$		0			0
$426$	161.557	−	211.170i	0.379241	−	0.495705i
$427$		−	54.1843i		−	0.126895i
$428$	282.168			0.659272
$429$	−39.5791	−	30.2802i	−0.0922589	−	0.0705832i
$430$		0			0
$431$		−	694.004i		−	1.61022i	−0.593127	−	0.805109i	$-0.702107\pi$
$431$		−	694.004i		−	1.61022i	0.593127	−	0.805109i	$-0.297893\pi$
$432$	−16.1866	+	39.5575i	−0.0374690	+	0.0915684i
$433$			116.834i			0.269824i	0.990858	+	0.134912i	$0.0430752\pi$
$433$			116.834i			0.269824i	−0.990858	+	0.134912i	$0.956925\pi$
$434$			135.880i			0.313087i
$435$		0			0
$436$	377.041			0.864772
$437$	44.0072			0.100703
$438$	144.842	−	189.322i	0.330688	−	0.432241i
$439$	528.073			1.20290			0.601450	−	0.798910i	$-0.294590\pi$
$439$	528.073			1.20290			0.601450	+	0.798910i	$0.294590\pi$
$440$		0			0
$441$	−16.4797	−	60.8064i	−0.0373690	−	0.137883i
$442$		−	100.871i		−	0.228214i
$443$	272.252			0.614564			0.307282	−	0.951619i	$-0.400581\pi$
$443$	272.252			0.614564			0.307282	+	0.951619i	$0.400581\pi$
$444$	171.431	−	224.077i	0.386107	−	0.504678i
$445$		0			0
$446$			131.964i			0.295883i
$447$	−371.292	+	485.314i	−0.830631	+	1.08571i
$448$			123.354i			0.275344i
$449$		−	525.770i		−	1.17098i	−0.810680	−	0.585490i	$-0.800902\pi$
$449$		−	525.770i		−	1.17098i	0.810680	−	0.585490i	$-0.199098\pi$
$450$		0			0
$451$	−79.1581			−0.175517
$452$	330.092			0.730292
$453$	−394.925	−	302.140i	−0.871800	−	0.666975i
$454$	511.439			1.12652
$455$		0			0
$456$	200.423	+	153.335i	0.439525	+	0.336261i
$457$			513.786i			1.12426i	0.827050	+	0.562129i	$0.190017\pi$
$457$			513.786i			1.12426i	−0.827050	+	0.562129i	$0.809983\pi$
$458$	8.90362			0.0194402
$459$	124.184	−	303.487i	0.270554	−	0.661192i
$460$		0			0
$461$		−	687.879i		−	1.49214i	−0.665865	−	0.746072i	$-0.731937\pi$
$461$		−	687.879i		−	1.49214i	0.665865	−	0.746072i	$-0.268063\pi$
$462$	21.5406	+	16.4797i	0.0466246	+	0.0356704i
$463$			781.061i			1.68696i	0.537162	+	0.843479i	$0.319496\pi$
$463$			781.061i			1.68696i	−0.537162	+	0.843479i	$0.680504\pi$
$464$		−	27.5020i		−	0.0592715i
$465$		0			0
$466$	152.769			0.327830
$467$	−163.353			−0.349792			−0.174896	−	0.984587i	$-0.555959\pi$
$467$	−163.353			−0.349792			−0.174896	+	0.984587i	$0.555959\pi$
$468$	−126.484	+	34.2797i	−0.270265	+	0.0732472i
$469$	−71.8745			−0.153251
$470$		0			0
$471$	551.826	−	721.289i	1.17161	−	1.53140i
$472$		−	340.161i		−	0.720679i
$473$	146.067			0.308809
$474$	−196.975	−	150.697i	−0.415560	−	0.317926i
$475$		0			0
$476$		−	73.6313i		−	0.154688i
$477$	247.200	+	912.110i	0.518239	+	1.91218i
$478$		−	78.3765i		−	0.163968i
$479$			700.159i			1.46171i	0.682533	+	0.730855i	$0.260878\pi$
$479$			700.159i			1.46171i	−0.682533	+	0.730855i	$0.739122\pi$
$480$		0			0
$481$	−260.782			−0.542166
$482$	176.135			0.365425
$483$	20.7495	−	27.1216i	0.0429596	−	0.0561523i
$484$	−261.612			−0.540520
$485$		0			0
$486$	315.195	+	39.2035i	0.648550	+	0.0806656i
$487$		−	86.5909i		−	0.177805i	−0.996040	−	0.0889023i	$-0.971664\pi$
$487$		−	86.5909i		−	0.177805i	0.996040	−	0.0889023i	$-0.0283359\pi$
$488$	168.417			0.345117
$489$	−264.391	+	345.584i	−0.540677	+	0.706716i
$490$		0			0
$491$			741.494i			1.51017i	0.655627	+	0.755085i	$0.272404\pi$
$491$			741.494i			1.51017i	−0.655627	+	0.755085i	$0.727596\pi$
$492$	−126.484	+	165.327i	−0.257081	+	0.336030i
$493$			210.996i			0.427984i
$494$		−	84.9560i		−	0.171976i
$495$		0			0
$496$	−62.1987			−0.125401
$497$	−179.395			−0.360956
$498$	−280.118	−	214.306i	−0.562486	−	0.430333i
$499$	−379.814			−0.761151			−0.380575	−	0.924750i	$-0.624274\pi$
$499$	−379.814			−0.761151			−0.380575	+	0.924750i	$0.624274\pi$
$500$		0			0
$501$	46.8419	+	35.8366i	0.0934967	+	0.0715302i
$502$		−	350.626i		−	0.698458i
$503$	−465.808			−0.926059			−0.463029	−	0.886343i	$-0.653238\pi$
$503$	−465.808			−0.926059			−0.463029	+	0.886343i	$0.653238\pi$
$504$	189.000	−	51.2228i	0.375000	−	0.101632i
$505$		0			0
$506$			14.7010i			0.0290533i
$507$	−306.468	−	234.465i	−0.604473	−	0.462455i
$508$		−	83.8301i		−	0.165020i
$509$		−	750.503i		−	1.47447i	−0.675639	−	0.737233i	$-0.736132\pi$
$509$		−	750.503i		−	1.47447i	0.675639	−	0.737233i	$-0.263868\pi$
$510$		0			0
$511$	−160.834			−0.314744
$512$	−100.868			−0.197009
$513$	104.592	−	255.605i	0.203882	−	0.498256i
$514$	−306.029			−0.595387
$515$		0			0
$516$	233.395	−	305.069i	0.452315	−	0.591219i
$517$			104.502i			0.202131i
$518$	141.928			0.273993
$519$	−46.9111	−	35.8896i	−0.0903875	−	0.0691514i
$520$		0			0
$521$			726.946i			1.39529i	0.716443	+	0.697645i	$0.245769\pi$
$521$			726.946i			1.39529i	−0.716443	+	0.697645i	$0.754231\pi$
$522$	−197.260	+	53.4615i	−0.377893	+	0.102417i
$523$		−	624.707i		−	1.19447i	−0.802067	−	0.597234i	$-0.796266\pi$
$523$		−	624.707i		−	1.19447i	0.802067	−	0.597234i	$-0.203734\pi$
$524$			77.1903i			0.147310i
$525$		0			0
$526$	326.959			0.621596
$527$	477.190			0.905485
$528$	−7.54356	+	9.86015i	−0.0142871	+	0.0186745i
$529$	−510.490			−0.965010
$530$		0			0
$531$	−359.314	+	97.3812i	−0.676674	+	0.183392i
$532$		−	62.0144i		−	0.116568i
$533$	192.408			0.360990
$534$	150.524	−	196.749i	0.281881	−	0.368445i
$535$		0			0
$536$		−	223.402i		−	0.416795i
$537$	−622.958	+	814.265i	−1.16007	+	1.51632i
$538$			445.306i			0.827706i
$539$		−	18.2993i		−	0.0339505i
$540$		0			0
$541$	−291.757			−0.539292			−0.269646	−	0.962960i	$-0.586907\pi$
$541$	−291.757			−0.539292			−0.269646	+	0.962960i	$0.586907\pi$
$542$	−27.8403			−0.0513659
$543$	−514.392	−	393.539i	−0.947315	−	0.724749i
$544$	374.369			0.688178
$545$		0			0
$546$	−52.3582	−	40.0569i	−0.0958941	−	0.0733643i
$547$		−	204.952i		−	0.374683i	−0.982295	−	0.187342i	$-0.940013\pi$
$547$		−	204.952i		−	0.374683i	0.982295	−	0.187342i	$-0.0599871\pi$
$548$	91.6026			0.167158
$549$	−48.2144	−	177.900i	−0.0878222	−	0.324044i
$550$		0			0
$551$			177.707i			0.322517i
$552$	84.2999	+	64.4941i	0.152717	+	0.116837i
$553$			167.336i			0.302597i
$554$			296.599i			0.535378i
$555$		0			0
$556$	−446.022			−0.802198
$557$	−503.883			−0.904637			−0.452318	−	0.891857i	$-0.649403\pi$
$557$	−503.883			−0.904637			−0.452318	+	0.891857i	$0.649403\pi$
$558$	120.909	+	446.125i	0.216683	+	0.799508i
$559$	−355.041			−0.635135
$560$		0			0
$561$	57.8745	−	75.6475i	0.103163	−	0.134844i
$562$			307.806i			0.547698i
$563$	−108.735			−0.193135			−0.0965674	−	0.995326i	$-0.530786\pi$
$563$	−108.735			−0.193135			−0.0965674	+	0.995326i	$0.530786\pi$
$564$	218.259	+	166.980i	0.386984	+	0.296064i
$565$		0			0
$566$			481.840i			0.851307i
$567$	−108.214	−	184.978i	−0.190853	−	0.326239i
$568$		−	557.600i		−	0.981690i
$569$			434.871i			0.764273i	0.924106	+	0.382136i	$0.124812\pi$
$569$			434.871i			0.764273i	−0.924106	+	0.382136i	$0.875188\pi$
$570$		0			0
$571$	119.122			0.208619			0.104310	−	0.994545i	$-0.466737\pi$
$571$	119.122			0.208619			0.104310	+	0.994545i	$0.466737\pi$
$572$	−38.0646			−0.0665466
$573$	−81.5029	+	106.532i	−0.142239	+	0.185920i
$574$	−104.716			−0.182433
$575$		0			0
$576$	109.763	+	405.001i	0.190561	+	0.703127i
$577$			655.417i			1.13590i	0.823061	+	0.567952i	$0.192264\pi$
$577$			655.417i			1.13590i	−0.823061	+	0.567952i	$0.807736\pi$
$578$	−184.957			−0.319994
$579$	−264.539	+	345.777i	−0.456889	+	0.597197i
$580$		0			0
$581$			237.968i			0.409584i
$582$	−45.6663	+	59.6902i	−0.0784645	+	0.102560i
$583$			274.494i			0.470830i
$584$		−	499.908i		−	0.856007i
$585$		0			0
$586$	−694.885			−1.18581
$587$	736.236			1.25424			0.627118	−	0.778925i	$-0.284235\pi$
$587$	736.236			1.25424			0.627118	+	0.778925i	$0.284235\pi$
$588$	−38.2193	−	29.2399i	−0.0649988	−	0.0497277i
$589$	401.903			0.682348
$590$		0			0
$591$	208.399	+	159.437i	0.352620	+	0.269774i
$592$			64.9674i			0.109742i
$593$	−832.884			−1.40453			−0.702263	−	0.711917i	$-0.747827\pi$
$593$	−832.884			−1.40453			−0.702263	+	0.711917i	$0.747827\pi$
$594$	85.3869	+	34.9396i	0.143749	+	0.0588209i
$595$		0			0
$596$			466.744i			0.783127i
$597$	155.867	+	119.247i	0.261084	+	0.199744i
$598$		−	35.7333i		−	0.0597546i
$599$		−	69.3290i		−	0.115741i	−0.998324	−	0.0578706i	$-0.981569\pi$
$599$		−	69.3290i		−	0.115741i	0.998324	−	0.0578706i	$-0.0184311\pi$
$600$		0			0
$601$	−161.720			−0.269085			−0.134543	−	0.990908i	$-0.542957\pi$
$601$	−161.720			−0.269085			−0.134543	+	0.990908i	$0.542957\pi$
$602$	193.228			0.320977
$603$	−235.981	+	63.9555i	−0.391345	+	0.106062i
$604$	−379.814			−0.628832
$605$		0			0
$606$	235.199	−	307.427i	0.388117	−	0.507305i
$607$		−	929.608i		−	1.53148i	−0.643151	−	0.765740i	$-0.722373\pi$
$607$		−	929.608i		−	1.53148i	0.643151	−	0.765740i	$-0.277627\pi$
$608$	315.304			0.518592
$609$	109.520	+	83.7891i	0.179836	+	0.137585i
$610$		0			0
$611$		−	254.010i		−	0.415729i
$612$	−65.5188	−	241.749i	−0.107057	−	0.395015i
$613$			297.940i			0.486036i	0.970022	+	0.243018i	$0.0781373\pi$
$613$			297.940i			0.486036i	−0.970022	+	0.243018i	$0.921863\pi$
$614$		−	742.121i		−	1.20867i
$615$		0			0
$616$	56.8784			0.0923351
$617$	−975.575			−1.58116			−0.790579	−	0.612360i	$-0.790220\pi$
$617$	−975.575			−1.58116			−0.790579	+	0.612360i	$0.790220\pi$
$618$	−134.028	+	175.187i	−0.216873	+	0.283474i
$619$	−357.034			−0.576792			−0.288396	−	0.957511i	$-0.593122\pi$
$619$	−357.034			−0.576792			−0.288396	+	0.957511i	$0.593122\pi$
$620$		0			0
$621$	43.9921	−	107.510i	0.0708408	−	0.173124i
$622$		−	55.8824i		−	0.0898431i
$623$	−167.144			−0.268289
$624$	18.3360	−	23.9668i	0.0293845	−	0.0384084i
$625$		0			0
$626$		−	206.675i		−	0.330151i
$627$	48.7435	−	63.7124i	0.0777409	−	0.101615i
$628$		−	693.690i		−	1.10460i
$629$		−	498.432i		−	0.792420i
$630$		0			0
$631$	−813.223			−1.28879			−0.644393	−	0.764695i	$-0.722890\pi$
$631$	−813.223			−1.28879			−0.644393	+	0.764695i	$0.722890\pi$
$632$	−520.118			−0.822971
$633$	−96.6960	−	73.9778i	−0.152758	−	0.116869i
$634$	184.227			0.290579
$635$		0			0
$636$	573.298	+	438.605i	0.901412	+	0.689630i
$637$			44.4797i			0.0698269i
$638$	−59.3643			−0.0930475
$639$	−588.996	+	159.630i	−0.921747	+	0.249812i
$640$		0			0
$641$			646.727i			1.00893i	0.863431	+	0.504467i	$0.168311\pi$
$641$			646.727i			1.00893i	−0.863431	+	0.504467i	$0.831689\pi$
$642$	383.495	+	293.395i	0.597344	+	0.457001i
$643$			144.561i			0.224822i	0.993662	+	0.112411i	$0.0358574\pi$
$643$			144.561i			0.224822i	−0.993662	+	0.112411i	$0.964143\pi$
$644$		−	26.0838i		−	0.0405028i
$645$		0			0
$646$	162.376			0.251357
$647$	−716.654			−1.10766			−0.553828	−	0.832631i	$-0.686834\pi$
$647$	−716.654			−1.10766			−0.553828	+	0.832631i	$0.686834\pi$
$648$	574.953	−	336.353i	0.887273	−	0.519063i
$649$	−108.133			−0.166615
$650$		0			0
$651$	189.498	−	247.692i	0.291088	−	0.380479i
$652$			332.361i			0.509756i
$653$	−378.999			−0.580397			−0.290199	−	0.956966i	$-0.593721\pi$
$653$	−378.999			−0.580397			−0.290199	+	0.956966i	$0.593721\pi$
$654$	512.435	+	392.041i	0.783540	+	0.599452i
$655$		0			0
$656$		−	47.9337i		−	0.0730696i
$657$	−528.056	+	143.114i	−0.803738	+	0.217829i
$658$			138.243i			0.210096i
$659$			710.721i			1.07848i	0.842151	+	0.539242i	$0.181289\pi$
$659$			710.721i			1.07848i	−0.842151	+	0.539242i	$0.818711\pi$
$660$		0			0
$661$	91.5045			0.138433			0.0692167	−	0.997602i	$-0.477950\pi$
$661$	91.5045			0.138433			0.0692167	+	0.997602i	$0.477950\pi$
$662$	−337.712			−0.510139
$663$	−140.674	+	183.875i	−0.212178	+	0.277337i
$664$	−739.659			−1.11394
$665$		0			0
$666$	465.984	−	126.291i	0.699676	−	0.189626i
$667$			74.7451i			0.112062i
$668$	45.0495			0.0674394
$669$	184.037	−	240.553i	0.275092	−	0.359571i
$670$		0			0
$671$		−	53.5379i		−	0.0797883i
$672$	148.666	−	194.321i	0.221230	−	0.289168i
$673$			645.806i			0.959594i	0.877380	+	0.479797i	$0.159290\pi$
$673$			645.806i			0.959594i	−0.877380	+	0.479797i	$0.840710\pi$
$674$		−	429.981i		−	0.637954i
$675$		0			0
$676$	−294.741			−0.436008
$677$	−335.571			−0.495674			−0.247837	−	0.968802i	$-0.579720\pi$
$677$	−335.571			−0.495674			−0.247837	+	0.968802i	$0.579720\pi$
$678$	448.627	+	343.225i	0.661692	+	0.506231i
$679$	50.7085			0.0746811
$680$		0			0
$681$	−932.290	−	713.254i	−1.36900	−	1.04736i
$682$			134.259i			0.196860i
$683$	113.336			0.165939			0.0829694	−	0.996552i	$-0.473560\pi$
$683$	113.336			0.165939			0.0829694	+	0.996552i	$0.473560\pi$
$684$	−55.1818	−	203.608i	−0.0806751	−	0.297672i
$685$		0			0
$686$		−	24.2077i		−	0.0352882i
$687$	−16.2302	−	12.4170i	−0.0236247	−	0.0180742i
$688$			88.4496i			0.128561i
$689$		−	667.206i		−	0.968369i
$690$		0			0
$691$	565.667			0.818620			0.409310	−	0.912395i	$-0.365769\pi$
$691$	565.667			0.818620			0.409310	+	0.912395i	$0.365769\pi$
$692$	−45.1161			−0.0651967
$693$	−16.2832	−	60.0810i	−0.0234966	−	0.0866970i
$694$	−168.138			−0.242274
$695$		0			0
$696$	−260.435	+	340.414i	−0.374189	+	0.489100i
$697$			367.749i			0.527617i
$698$	96.0501			0.137608
$699$	−278.478	−	213.051i	−0.398395	−	0.304794i
$700$		0			0
$701$		−	872.955i		−	1.24530i	−0.782501	−	0.622650i	$-0.786056\pi$
$701$		−	872.955i		−	1.24530i	0.782501	−	0.622650i	$-0.213944\pi$
$702$	−207.548	−	84.9268i	−0.295652	−	0.120978i
$703$		−	419.793i		−	0.597146i
$704$			121.883i			0.173129i
$705$		0			0
$706$	−313.292			−0.443756
$707$	−261.168			−0.369403
$708$	−172.783	+	225.843i	−0.244043	+	0.318988i
$709$	−1092.04			−1.54025			−0.770125	−	0.637894i	$-0.779806\pi$
$709$	−1092.04			−1.54025			−0.770125	+	0.637894i	$0.779806\pi$
$710$		0			0
$711$	148.899	+	549.404i	0.209422	+	0.772720i
$712$		−	519.522i		−	0.729665i
$713$	169.044			0.237088
$714$	76.5608	−	100.072i	0.107228	−	0.140157i
$715$		0			0
$716$			783.109i			1.09373i
$717$	−109.304	+	142.871i	−0.152446	+	0.199262i
$718$			235.558i			0.328076i
$719$			901.769i			1.25420i	0.778939	+	0.627099i	$0.215758\pi$
$719$			901.769i			1.25420i	−0.778939	+	0.627099i	$0.784242\pi$
$720$		0			0
$721$	148.826			0.206416
$722$	−335.103			−0.464132
$723$	−321.072	−	245.638i	−0.444083	−	0.339748i
$724$	−494.710			−0.683301
$725$		0			0
$726$	−355.556	−	272.020i	−0.489747	−	0.374683i
$727$		−	297.506i		−	0.409224i	−0.978843	−	0.204612i	$-0.934407\pi$
$727$		−	297.506i		−	0.409224i	0.978843	−	0.204612i	$-0.0655933\pi$
$728$	−138.253			−0.189908
$729$	−519.889	−	511.035i	−0.713153	−	0.701008i
$730$		0			0
$731$		−	678.589i		−	0.928302i
$732$	−111.817	−	85.5464i	−0.152756	−	0.116867i
$733$			456.966i			0.623419i	0.950177	+	0.311709i	$0.100902\pi$
$733$			456.966i			0.623419i	−0.950177	+	0.311709i	$0.899098\pi$
$734$		−	300.352i		−	0.409198i
$735$		0			0
$736$	132.620			0.180190
$737$	−71.0171			−0.0963597
$738$	−343.809	+	93.1790i	−0.465865	+	0.126259i
$739$	332.199			0.449525			0.224762	−	0.974414i	$-0.427839\pi$
$739$	332.199			0.449525			0.224762	+	0.974414i	$0.427839\pi$
$740$		0			0
$741$	−118.480	+	154.864i	−0.159892	+	0.208994i
$742$			363.122i			0.489382i
$743$	−64.5346			−0.0868568			−0.0434284	−	0.999057i	$-0.513828\pi$
$743$	−64.5346			−0.0868568			−0.0434284	+	0.999057i	$0.513828\pi$
$744$	769.882	+	589.003i	1.03479	+	0.791670i
$745$		0			0
$746$			577.408i			0.774005i
$747$	211.749	+	781.306i	0.283466	+	1.04592i
$748$		−	72.7530i		−	0.0972633i
$749$		−	325.790i		−	0.434966i
$750$		0			0
$751$	−611.668			−0.814471			−0.407236	−	0.913323i	$-0.633507\pi$
$751$	−611.668			−0.814471			−0.407236	+	0.913323i	$0.633507\pi$
$752$	−63.2805			−0.0841496
$753$	−488.983	+	639.148i	−0.649380	+	0.848802i
$754$	144.295			0.191373
$755$		0			0
$756$	−151.501	−	61.9930i	−0.200399	−	0.0820014i
$757$			207.357i			0.273919i	0.990577	+	0.136960i	$0.0437330\pi$
$757$			207.357i			0.273919i	−0.990577	+	0.136960i	$0.956267\pi$
$758$	550.552			0.726322
$759$	20.5020	−	26.7980i	0.0270118	−	0.0353070i
$760$		0			0
$761$		−	337.770i		−	0.443851i	−0.975064	−	0.221925i	$-0.928766\pi$
$761$		−	337.770i		−	0.443851i	0.975064	−	0.221925i	$-0.0712341\pi$
$762$	87.1653	−	113.933i	0.114390	−	0.149519i
$763$		−	435.328i		−	0.570548i
$764$			102.456i			0.134104i
$765$		0			0
$766$	778.494			1.01631
$767$	262.837			0.342682
$768$	638.565	+	488.538i	0.831465	+	0.636117i
$769$	1042.22			1.35529			0.677646	−	0.735388i	$-0.263000\pi$
$769$	1042.22			1.35529			0.677646	+	0.735388i	$0.263000\pi$
$770$		0			0
$771$	557.852	+	426.788i	0.723544	+	0.553551i
$772$			332.546i			0.430760i
$773$	291.448			0.377035			0.188517	−	0.982070i	$-0.439632\pi$
$773$	291.448			0.377035			0.188517	+	0.982070i	$0.439632\pi$
$774$	634.413	−	171.939i	0.819655	−	0.222143i
$775$		0			0
$776$			157.613i			0.203110i
$777$	−258.718	−	197.933i	−0.332970	−	0.254740i
$778$		−	480.157i		−	0.617168i
$779$			309.729i			0.397598i
$780$		0			0
$781$	−177.255			−0.226959
$782$	68.2970			0.0873363
$783$	434.138	+	177.646i	0.554455	+	0.226878i
$784$	11.0810			0.0141340
$785$		0			0
$786$	−80.2614	+	104.909i	−0.102114	+	0.133472i
$787$		−	293.889i		−	0.373429i	−0.982414	−	0.186715i	$-0.940216\pi$
$787$		−	293.889i		−	0.373429i	0.982414	−	0.186715i	$-0.0597840\pi$
$788$	200.425			0.254346
$789$	−596.006	−	455.978i	−0.755395	−	0.577919i
$790$		0			0
$791$		−	381.122i		−	0.481822i
$792$	186.745	−	50.6117i	0.235790	−	0.0639037i
$793$			130.133i			0.164103i
$794$		−	533.748i		−	0.672226i
$795$		0			0
$796$	149.903			0.188321
$797$	568.764			0.713631			0.356816	−	0.934175i	$-0.383862\pi$
$797$	568.764			0.713631			0.356816	+	0.934175i	$0.383862\pi$
$798$	64.4816	−	84.2836i	0.0808041	−	0.105619i
$799$	485.490			0.607622
$800$		0			0
$801$	−548.774	+	148.729i	−0.685111	+	0.185679i
$802$			312.157i			0.389223i
$803$	−158.915			−0.197902
$804$	−113.476	+	148.324i	−0.141139	+	0.184482i
$805$		0			0
$806$		−	326.340i		−	0.404888i
$807$	621.024	−	811.737i	0.769546	−	1.00587i
$808$		−	811.768i		−	1.00466i
$809$		−	183.697i		−	0.227067i	−0.993534	−	0.113534i	$-0.963783\pi$
$809$		−	183.697i		−	0.227067i	0.993534	−	0.113534i	$-0.0362169\pi$
$810$		0			0
$811$	−544.663			−0.671594			−0.335797	−	0.941934i	$-0.609006\pi$
$811$	−544.663			−0.671594			−0.335797	+	0.941934i	$0.609006\pi$
$812$	105.330			0.129716
$813$	50.7494	+	38.8261i	0.0624224	+	0.0477566i
$814$	140.235			0.172279
$815$		0			0
$816$	45.8078	+	35.0455i	0.0561370	+	0.0429479i
$817$		−	571.527i		−	0.699543i
$818$	848.781			1.03763
$819$	39.5791	+	146.038i	0.0483261	+	0.178312i
$820$		0			0
$821$		−	1188.78i		−	1.44797i	−0.689818	−	0.723983i	$-0.742309\pi$
$821$		−	1188.78i		−	1.44797i	0.689818	−	0.723983i	$-0.257691\pi$
$822$	124.497	+	95.2470i	0.151456	+	0.115872i
$823$			1265.15i			1.53724i	0.639704	+	0.768621i	$0.279057\pi$
$823$			1265.15i			1.53724i	−0.639704	+	0.768621i	$0.720943\pi$
$824$			462.585i			0.561390i
$825$		0			0
$826$	−143.047			−0.173180
$827$	790.941			0.956398			0.478199	−	0.878252i	$-0.341290\pi$
$827$	790.941			0.956398			0.478199	+	0.878252i	$0.341290\pi$
$828$	−23.2099	−	85.6393i	−0.0280313	−	0.103429i
$829$	−99.1961			−0.119658			−0.0598288	−	0.998209i	$-0.519055\pi$
$829$	−99.1961			−0.119658			−0.0598288	+	0.998209i	$0.519055\pi$
$830$		0			0
$831$	413.638	−	540.664i	0.497759	−	0.650619i
$832$		−	296.257i		−	0.356079i
$833$	−85.0141			−0.102058
$834$	−606.188	−	463.768i	−0.726844	−	0.556076i
$835$		0			0
$836$		−	61.2746i		−	0.0732950i
$837$	401.765	−	981.851i	0.480006	−	1.17306i
$838$		−	15.0549i		−	0.0179652i
$839$			243.824i			0.290612i	0.989387	+	0.145306i	$0.0464167\pi$
$839$			243.824i			0.290612i	−0.989387	+	0.145306i	$0.953583\pi$
$840$		0			0
$841$	539.170			0.641106
$842$	−109.786			−0.130387
$843$	429.267	−	561.093i	0.509214	−	0.665591i
$844$	−92.9961			−0.110185
$845$		0			0
$846$	123.012	+	453.885i	0.145404	+	0.536507i
$847$			302.055i			0.356617i
$848$	−166.218			−0.196012
$849$	671.974	−	878.334i	0.791489	−	1.03455i
$850$		0			0
$851$		−	176.569i		−	0.207484i
$852$	−283.230	+	370.208i	−0.332429	+	0.434516i
$853$		−	1122.06i		−	1.31543i	−0.753268	−	0.657713i	$-0.771524\pi$
$853$		−	1122.06i		−	1.31543i	0.753268	−	0.657713i	$-0.228476\pi$
$854$		−	70.8240i		−	0.0829321i
$855$		0			0
$856$	1012.63			1.18298
$857$	871.489			1.01691			0.508453	−	0.861090i	$-0.330217\pi$
$857$	871.489			1.01691			0.508453	+	0.861090i	$0.330217\pi$
$858$	−51.7336	−	39.5791i	−0.0602956	−	0.0461295i
$859$	1674.92			1.94985			0.974925	−	0.222533i	$-0.0714324\pi$
$859$	1674.92			1.94985			0.974925	+	0.222533i	$0.0714324\pi$
$860$		0			0
$861$	190.885	+	146.038i	0.221701	+	0.169614i
$862$		−	907.129i		−	1.05235i
$863$	−1320.74			−1.53041			−0.765205	−	0.643787i	$-0.777362\pi$
$863$	−1320.74			−1.53041			−0.765205	+	0.643787i	$0.777362\pi$
$864$	315.195	−	770.288i	0.364810	−	0.891537i
$865$		0			0
$866$			152.713i			0.176343i
$867$	337.153	+	257.940i	0.388873	+	0.297509i
$868$		−	238.214i		−	0.274441i
$869$			165.340i			0.190264i
$870$		0			0
$871$	172.620			0.198186
$872$	1353.10			1.55172
$873$	166.488	−	45.1216i	0.190708	−	0.0516856i
$874$	57.5217			0.0658142
$875$		0			0
$876$	−253.925	+	331.905i	−0.289869	+	0.378887i
$877$			344.790i			0.393147i	0.980489	+	0.196573i	$0.0629814\pi$
$877$			344.790i			0.393147i	−0.980489	+	0.196573i	$0.937019\pi$
$878$	690.242			0.786152
$879$	1266.69	+	969.087i	1.44106	+	1.10249i
$880$		0			0
$881$		−	518.737i		−	0.588805i	−0.955682	−	0.294403i	$-0.904879\pi$
$881$		−	518.737i		−	0.588805i	0.955682	−	0.294403i	$-0.0951206\pi$
$882$	−21.5406	−	79.4797i	−0.0244224	−	0.0901131i
$883$		−	584.008i		−	0.661391i	−0.943738	−	0.330695i	$-0.892717\pi$
$883$		−	584.008i		−	0.661391i	0.943738	−	0.330695i	$-0.107283\pi$
$884$			176.839i			0.200044i
$885$		0			0
$886$	355.859			0.401646
$887$	−263.213			−0.296745			−0.148373	−	0.988932i	$-0.547403\pi$
$887$	−263.213			−0.296745			−0.148373	+	0.988932i	$0.547403\pi$
$888$	615.221	−	804.153i	0.692817	−	0.905577i
$889$	−96.7895			−0.108875
$890$		0			0
$891$	−106.923	−	182.771i	−0.120003	−	0.205130i
$892$		−	231.349i		−	0.259360i
$893$	408.893			0.457887
$894$	−485.314	+	634.351i	−0.542857	+	0.709565i
$895$		0			0
$896$		−	164.988i		−	0.184138i
$897$	−49.8336	+	65.1373i	−0.0555559	+	0.0726168i
$898$		−	687.231i		−	0.765291i
$899$			682.621i			0.759312i
$900$		0			0
$901$	1275.23			1.41535
$902$	−103.467			−0.114709
$903$	−352.230	−	269.476i	−0.390067	−	0.298423i
$904$	1184.61			1.31041
$905$		0			0
$906$	−516.205	−	394.925i	−0.569763	−	0.435900i
$907$			1501.72i			1.65570i	0.560951	+	0.827849i	$0.310435\pi$
$907$			1501.72i			1.65570i	−0.560951	+	0.827849i	$0.689565\pi$
$908$	−896.618			−0.987464
$909$	−857.476	+	232.393i	−0.943318	+	0.255658i
$910$		0			0
$911$		−	879.178i		−	0.965069i	−0.875877	−	0.482534i	$-0.839716\pi$
$911$		−	879.178i		−	0.965069i	0.875877	−	0.482534i	$-0.160284\pi$
$912$	38.5806	+	29.5163i	0.0423033	+	0.0323644i
$913$			235.129i			0.257535i
$914$			671.567i			0.734756i
$915$		0			0
$916$	−15.6092			−0.0170406
$917$	89.1234			0.0971901
$918$	162.321	−	396.686i	0.176820	−	0.432120i
$919$	−76.9882			−0.0837739			−0.0418869	−	0.999122i	$-0.513337\pi$
$919$	−76.9882			−0.0837739			−0.0418869	+	0.999122i	$0.513337\pi$
$920$		0			0
$921$	−1034.96	+	1352.79i	−1.12374	+	1.46883i
$922$		−	899.123i		−	0.975188i
$923$	430.849			0.466792
$924$	−37.7634	−	28.8911i	−0.0408694	−	0.0312674i
$925$		0			0
$926$			1020.92i			1.10251i
$927$	488.631	−	132.429i	0.527110	−	0.142857i
$928$			535.535i			0.577085i
$929$			1629.76i			1.75431i	0.480204	+	0.877157i	$0.340563\pi$
$929$			1629.76i			1.75431i	−0.480204	+	0.877157i	$0.659437\pi$
$930$		0			0
$931$	−71.6013			−0.0769079
$932$	−267.823			−0.287364
$933$	−77.9336	+	101.867i	−0.0835301	+	0.109182i
$934$	−213.517			−0.228605
$935$		0			0
$936$	−453.918	+	123.021i	−0.484955	+	0.131432i
$937$			497.720i			0.531185i	0.964085	+	0.265592i	$0.0855676\pi$
$937$			497.720i			0.531185i	−0.964085	+	0.265592i	$0.914432\pi$
$938$	−93.9468			−0.100157
$939$	−288.229	+	376.742i	−0.306953	+	0.401217i
$940$		0			0
$941$			238.894i			0.253873i	0.991911	+	0.126936i	$0.0405144\pi$
$941$			238.894i			0.253873i	−0.991911	+	0.126936i	$0.959486\pi$
$942$	721.289	−	942.793i	0.765700	−	1.00084i
$943$			130.275i			0.138149i
$944$		−	65.4794i		−	0.0693638i
$945$		0			0
$946$	190.923			0.201821
$947$	667.910			0.705291			0.352645	−	0.935757i	$-0.385282\pi$
$947$	667.910			0.705291			0.352645	+	0.935757i	$0.385282\pi$
$948$	345.322	+	264.191i	0.364264	+	0.278682i
$949$	386.272			0.407030
$950$		0			0
$951$	−335.824	−	256.924i	−0.353127	−	0.270162i
$952$		−	264.243i		−	0.277566i
$953$	−11.3247			−0.0118832			−0.00594162	−	0.999982i	$-0.501891\pi$
$953$	−11.3247			−0.0118832			−0.00594162	+	0.999982i	$0.501891\pi$
$954$	323.114	+	1192.21i	0.338694	+	1.24970i
$955$		0			0
$956$			137.404i			0.143728i
$957$	108.214	+	82.7895i	0.113076	+	0.0865094i
$958$			915.174i			0.955296i
$959$		−	105.764i		−	0.110285i
$960$		0			0
$961$	582.822			0.606475
$962$	−340.866			−0.354331
$963$	−289.895	−	1069.64i	−0.301033	−	1.11074i
$964$	−308.787			−0.320318
$965$		0			0
$966$	27.1216	−	35.4504i	0.0280761	−	0.0366982i
$967$		−	830.324i		−	0.858660i	−0.903148	−	0.429330i	$-0.858750\pi$
$967$		−	830.324i		−	0.858660i	0.903148	−	0.429330i	$-0.141250\pi$
$968$	−938.855			−0.969891
$969$	−295.992	−	226.450i	−0.305461	−	0.233695i
$970$		0			0
$971$			1217.58i			1.25394i	0.779044	+	0.626970i	$0.215705\pi$
$971$			1217.58i			1.25394i	−0.779044	+	0.626970i	$0.784295\pi$
$972$	−552.577	−	68.7286i	−0.568495	−	0.0707085i
$973$			514.974i			0.529264i
$974$		−	113.183i		−	0.116204i
$975$		0			0
$976$	32.4195			0.0332167
$977$	−424.579			−0.434574			−0.217287	−	0.976108i	$-0.569721\pi$
$977$	−424.579			−0.434574			−0.217287	+	0.976108i	$0.569721\pi$
$978$	−345.584	+	451.711i	−0.353358	+	0.461872i
$979$	−165.150			−0.168693
$980$		0			0
$981$	−387.365	−	1429.29i	−0.394867	−	1.45697i
$982$			969.203i			0.986968i
$983$	76.7273			0.0780542			0.0390271	−	0.999238i	$-0.487574\pi$
$983$	76.7273			0.0780542			0.0390271	+	0.999238i	$0.487574\pi$
$984$	−453.918	+	593.313i	−0.461298	+	0.602961i
$985$		0			0
$986$			275.792i			0.279708i
$987$	192.794	−	252.000i	0.195333	−	0.255319i
$988$			148.939i			0.150748i
$989$		−	240.389i		−	0.243063i
$990$		0			0
$991$	181.271			0.182917			0.0914585	−	0.995809i	$-0.470847\pi$
$991$	181.271			0.182917			0.0914585	+	0.995809i	$0.470847\pi$
$992$	1211.17			1.22094
$993$	615.608	+	470.974i	0.619947	+	0.474294i
$994$	−234.486			−0.235902
$995$		0			0
$996$	491.082	+	375.705i	0.493055	+	0.377214i
$997$			1184.43i			1.18800i	0.804466	+	0.593998i	$0.202451\pi$
$997$			1184.43i			1.18800i	−0.804466	+	0.593998i	$0.797549\pi$
$998$	−496.453			−0.497448
$999$	−1025.56	−	419.649i	−1.02658	−	0.420069i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	525.3.f.a.449.5		8
3.2	odd	2	inner	525.3.f.a.449.3		8
5.2	odd	4		21.3.b.a.8.3	yes	4
5.3	odd	4		525.3.c.a.176.2		4
5.4	even	2	inner	525.3.f.a.449.4		8
15.2	even	4		21.3.b.a.8.2	✓	4
15.8	even	4		525.3.c.a.176.3		4
15.14	odd	2	inner	525.3.f.a.449.6		8
20.7	even	4		336.3.d.c.113.3		4
35.2	odd	12		147.3.h.e.116.3		8
35.12	even	12		147.3.h.c.116.3		8
35.17	even	12		147.3.h.c.128.2		8
35.27	even	4		147.3.b.f.50.3		4
35.32	odd	12		147.3.h.e.128.2		8
40.27	even	4		1344.3.d.b.449.2		4
40.37	odd	4		1344.3.d.f.449.3		4
45.2	even	12		567.3.r.c.134.2		8
45.7	odd	12		567.3.r.c.134.3		8
45.22	odd	12		567.3.r.c.512.2		8
45.32	even	12		567.3.r.c.512.3		8
60.47	odd	4		336.3.d.c.113.4		4
105.2	even	12		147.3.h.e.116.2		8
105.17	odd	12		147.3.h.c.128.3		8
105.32	even	12		147.3.h.e.128.3		8
105.47	odd	12		147.3.h.c.116.2		8
105.62	odd	4		147.3.b.f.50.2		4
120.77	even	4		1344.3.d.f.449.4		4
120.107	odd	4		1344.3.d.b.449.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
21.3.b.a.8.2	✓	4	15.2	even	4
21.3.b.a.8.3	yes	4	5.2	odd	4
147.3.b.f.50.2		4	105.62	odd	4
147.3.b.f.50.3		4	35.27	even	4
147.3.h.c.116.2		8	105.47	odd	12
147.3.h.c.116.3		8	35.12	even	12
147.3.h.c.128.2		8	35.17	even	12
147.3.h.c.128.3		8	105.17	odd	12
147.3.h.e.116.2		8	105.2	even	12
147.3.h.e.116.3		8	35.2	odd	12
147.3.h.e.128.2		8	35.32	odd	12
147.3.h.e.128.3		8	105.32	even	12
336.3.d.c.113.3		4	20.7	even	4
336.3.d.c.113.4		4	60.47	odd	4
525.3.c.a.176.2		4	5.3	odd	4
525.3.c.a.176.3		4	15.8	even	4
525.3.f.a.449.3		8	3.2	odd	2	inner
525.3.f.a.449.4		8	5.4	even	2	inner
525.3.f.a.449.5		8	1.1	even	1	trivial
525.3.f.a.449.6		8	15.14	odd	2	inner
567.3.r.c.134.2		8	45.2	even	12
567.3.r.c.134.3		8	45.7	odd	12
567.3.r.c.512.2		8	45.22	odd	12
567.3.r.c.512.3		8	45.32	even	12
1344.3.d.b.449.1		4	120.107	odd	4
1344.3.d.b.449.2		4	40.27	even	4
1344.3.d.f.449.3		4	40.37	odd	4
1344.3.d.f.449.4		4	120.77	even	4

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.f (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+1.30710 q^{2} +(-2.38267 - 1.82288i) q^{3} -2.29150 q^{4} +(-3.11438 - 2.38267i) q^{6} +2.64575i q^{7} -8.22359 q^{8} +(2.35425 + 8.68663i) q^{9} +O(q^{10})\)	\(q+1.30710 q^{2} +(-2.38267 - 1.82288i) q^{3} -2.29150 q^{4} +(-3.11438 - 2.38267i) q^{6} +2.64575i q^{7} -8.22359 q^{8} +(2.35425 + 8.68663i) q^{9} +2.61419i q^{11} +(5.45990 + 4.17712i) q^{12} -6.35425i q^{13} +3.45825i q^{14} -1.58301 q^{16} +12.1449 q^{17} +(3.07723 + 11.3542i) q^{18} +10.2288 q^{19} +(4.82288 - 6.30396i) q^{21} +3.41699i q^{22} +4.30231 q^{23} +(19.5941 + 14.9906i) q^{24} -8.30561i q^{26} +(10.2252 - 24.9889i) q^{27} -6.06275i q^{28} +17.3733i q^{29} +39.2915 q^{31} +30.8252 q^{32} +(4.76534 - 6.22876i) q^{33} +15.8745 q^{34} +(-5.39477 - 19.9054i) q^{36} -41.0405i q^{37} +13.3700 q^{38} +(-11.5830 + 15.1401i) q^{39} +30.2802i q^{41} +(6.30396 - 8.23987i) q^{42} -55.8745i q^{43} -5.99042i q^{44} +5.62352 q^{46} +39.9749 q^{47} +(3.77178 + 2.88562i) q^{48} -7.00000 q^{49} +(-28.9373 - 22.1386i) q^{51} +14.5608i q^{52} +105.002 q^{53} +(13.3654 - 32.6628i) q^{54} -21.7576i q^{56} +(-24.3718 - 18.6458i) q^{57} +22.7085i q^{58} +41.3640i q^{59} -20.4797 q^{61} +51.3577 q^{62} +(-22.9827 + 6.22876i) q^{63} +46.6235 q^{64} +(6.22876 - 8.14158i) q^{66} +27.1660i q^{67} -27.8300 q^{68} +(-10.2510 - 7.84257i) q^{69} +67.8049i q^{71} +(-19.3604 - 71.4353i) q^{72} +60.7895i q^{73} -53.6439i q^{74} -23.4392 q^{76} -6.91650 q^{77} +(-15.1401 + 19.7895i) q^{78} +63.2470 q^{79} +(-69.9150 + 40.9010i) q^{81} +39.5791i q^{82} +89.9435 q^{83} +(-11.0516 + 14.4455i) q^{84} -73.0333i q^{86} +(31.6693 - 41.3948i) q^{87} -21.4980i q^{88} +63.1745i q^{89} +16.8118 q^{91} -9.85875 q^{92} +(-93.6188 - 71.6235i) q^{93} +52.2510 q^{94} +(-73.4464 - 56.1906i) q^{96} -19.1660i q^{97} -9.14967 q^{98} +(-22.7085 + 6.15445i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 24 q^{4} + 28 q^{6} + 40 q^{9}+O(q^{10}) \) 8 * q + 24 * q^4 + 28 * q^6 + 40 * q^9	\( 8 q + 24 q^{4} + 28 q^{6} + 40 q^{9} + 72 q^{16} - 24 q^{19} + 28 q^{21} + 252 q^{24} + 272 q^{31} + 232 q^{36} - 8 q^{39} - 336 q^{46} - 56 q^{49} - 168 q^{51} + 308 q^{54} - 312 q^{61} - 8 q^{64} - 56 q^{66} - 336 q^{69} - 632 q^{76} - 256 q^{79} - 136 q^{81} + 28 q^{84} - 56 q^{91} + 672 q^{94} - 196 q^{96} - 224 q^{99}+O(q^{100}) \) 8 * q + 24 * q^4 + 28 * q^6 + 40 * q^9 + 72 * q^16 - 24 * q^19 + 28 * q^21 + 252 * q^24 + 272 * q^31 + 232 * q^36 - 8 * q^39 - 336 * q^46 - 56 * q^49 - 168 * q^51 + 308 * q^54 - 312 * q^61 - 8 * q^64 - 56 * q^66 - 336 * q^69 - 632 * q^76 - 256 * q^79 - 136 * q^81 + 28 * q^84 - 56 * q^91 + 672 * q^94 - 196 * q^96 - 224 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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