LMFDB - Embedded newform 525.3.f.a.449.2

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			449.2
Root			$-1.25296 + 1.25296i$ of defining polynomial
Character	$\chi$	$=$	525.449
Dual form			525.3.f.a.449.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-3.50592 q^{2} +(-2.88494 + 0.822876i) q^{3} +8.29150 q^{4} +(10.1144 - 2.88494i) q^{6} -2.64575i q^{7} -15.0457 q^{8} +(7.64575 - 4.74789i) q^{9} +O(q^{10})$	\(q-3.50592 q^{2} +(-2.88494 + 0.822876i) q^{3} +8.29150 q^{4} +(10.1144 - 2.88494i) q^{6} -2.64575i q^{7} -15.0457 q^{8} +(7.64575 - 4.74789i) q^{9} -7.01185i q^{11} +(-23.9205 + 6.82288i) q^{12} -11.6458i q^{13} +9.27580i q^{14} +19.5830 q^{16} +4.52791 q^{17} +(-26.8054 + 16.6458i) q^{18} -16.2288 q^{19} +(2.17712 + 7.63283i) q^{21} +24.5830i q^{22} +25.5635 q^{23} +(43.4059 - 12.3807i) q^{24} +40.8291i q^{26} +(-18.1506 + 19.9889i) q^{27} -21.9373i q^{28} -9.49579i q^{29} +28.7085 q^{31} -8.47380 q^{32} +(5.76988 + 20.2288i) q^{33} -15.8745 q^{34} +(63.3948 - 39.3672i) q^{36} +33.0405i q^{37} +56.8968 q^{38} +(9.58301 + 33.5973i) q^{39} +67.1946i q^{41} +(-7.63283 - 26.7601i) q^{42} -24.1255i q^{43} -58.1388i q^{44} -89.6235 q^{46} -33.0153 q^{47} +(-56.4958 + 16.1144i) q^{48} -7.00000 q^{49} +(-13.0627 + 3.72591i) q^{51} -96.5608i q^{52} +15.1877 q^{53} +(63.6346 - 70.0795i) q^{54} +39.8071i q^{56} +(46.8190 - 13.3542i) q^{57} +33.2915i q^{58} -92.3960i q^{59} -57.5203 q^{61} -100.650 q^{62} +(-12.5617 - 20.2288i) q^{63} -48.6235 q^{64} +(-20.2288 - 70.9205i) q^{66} -15.1660i q^{67} +37.5432 q^{68} +(-73.7490 + 21.0355i) q^{69} -70.5584i q^{71} +(-115.036 + 71.4353i) q^{72} -76.7895i q^{73} -115.838i q^{74} -134.561 q^{76} -18.5516 q^{77} +(-33.5973 - 117.790i) q^{78} -127.247 q^{79} +(35.9150 - 72.6024i) q^{81} -235.579i q^{82} -74.2844 q^{83} +(18.0516 + 63.2876i) q^{84} +84.5821i q^{86} +(7.81385 + 27.3948i) q^{87} +105.498i q^{88} +127.377i q^{89} -30.8118 q^{91} +211.959 q^{92} +(-82.8223 + 23.6235i) q^{93} +115.749 q^{94} +(24.4464 - 6.97288i) q^{96} +23.1660i q^{97} +24.5415 q^{98} +(-33.2915 - 53.6108i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−3.50592			−1.75296			−0.876481	−	0.481436i	$-0.840115\pi$
$2$	−3.50592			−1.75296			−0.876481	+	0.481436i	$0.840115\pi$
$3$	−2.88494	+	0.822876i	−0.961646	+	0.274292i
$3$	−2.88494	+	0.822876i	−0.961646	+	0.274292i
$4$	8.29150			2.07288
$5$		0			0
$5$		0			0
$6$	10.1144	−	2.88494i	1.68573	−	0.480823i
$7$		−	2.64575i		−	0.377964i
$7$		−	2.64575i		−	0.377964i
$8$	−15.0457			−1.88071
$9$	7.64575	−	4.74789i	0.849528	−	0.527544i
$10$		0			0
$11$		−	7.01185i		−	0.637441i	−0.947849	−	0.318720i	$-0.896747\pi$
$11$		−	7.01185i		−	0.637441i	0.947849	−	0.318720i	$-0.103253\pi$
$12$	−23.9205	+	6.82288i	−1.99337	+	0.568573i
$13$		−	11.6458i		−	0.895827i	−0.894077	−	0.447914i	$-0.852167\pi$
$13$		−	11.6458i		−	0.895827i	0.894077	−	0.447914i	$-0.147833\pi$
$14$			9.27580i			0.662557i
$15$		0			0
$16$	19.5830			1.22394
$17$	4.52791			0.266348			0.133174	−	0.991093i	$-0.457483\pi$
$17$	4.52791			0.266348			0.133174	+	0.991093i	$0.457483\pi$
$18$	−26.8054	+	16.6458i	−1.48919	+	0.924764i
$19$	−16.2288			−0.854145			−0.427073	−	0.904217i	$-0.640455\pi$
$19$	−16.2288			−0.854145			−0.427073	+	0.904217i	$0.640455\pi$
$20$		0			0
$21$	2.17712	+	7.63283i	0.103673	+	0.363468i
$22$			24.5830i			1.11741i
$23$	25.5635			1.11145			0.555727	−	0.831365i	$-0.312440\pi$
$23$	25.5635			1.11145			0.555727	+	0.831365i	$0.312440\pi$
$24$	43.4059	−	12.3807i	1.80858	−	0.515864i
$25$		0			0
$26$			40.8291i			1.57035i
$27$	−18.1506	+	19.9889i	−0.672245	+	0.740329i
$28$		−	21.9373i		−	0.783473i
$29$		−	9.49579i		−	0.327441i	−0.986507	−	0.163720i	$-0.947650\pi$
$29$		−	9.49579i		−	0.327441i	0.986507	−	0.163720i	$-0.0523495\pi$
$30$		0			0
$31$	28.7085			0.926081			0.463040	−	0.886337i	$-0.346759\pi$
$31$	28.7085			0.926081			0.463040	+	0.886337i	$0.346759\pi$
$32$	−8.47380			−0.264806
$33$	5.76988	+	20.2288i	0.174845	+	0.612993i
$34$	−15.8745			−0.466897
$35$		0			0
$36$	63.3948	−	39.3672i	1.76097	−	1.09353i
$37$			33.0405i			0.892987i	0.894787	+	0.446493i	$0.147327\pi$
$37$			33.0405i			0.892987i	−0.894787	+	0.446493i	$0.852673\pi$
$38$	56.8968			1.49728
$39$	9.58301	+	33.5973i	0.245718	+	0.861469i
$40$		0			0
$41$			67.1946i			1.63889i	0.573156	+	0.819446i	$0.305719\pi$
$41$			67.1946i			1.63889i	−0.573156	+	0.819446i	$0.694281\pi$
$42$	−7.63283	−	26.7601i	−0.181734	−	0.637146i
$43$		−	24.1255i		−	0.561058i	−0.959846	−	0.280529i	$-0.909490\pi$
$43$		−	24.1255i		−	0.561058i	0.959846	−	0.280529i	$-0.0905099\pi$
$44$		−	58.1388i		−	1.32134i
$45$		0			0
$46$	−89.6235			−1.94834
$47$	−33.0153			−0.702452			−0.351226	−	0.936291i	$-0.614235\pi$
$47$	−33.0153			−0.702452			−0.351226	+	0.936291i	$0.614235\pi$
$48$	−56.4958	+	16.1144i	−1.17700	+	0.335716i
$49$	−7.00000			−0.142857
$50$		0			0
$51$	−13.0627	+	3.72591i	−0.256132	+	0.0730570i
$52$		−	96.5608i		−	1.85694i
$53$	15.1877			0.286561			0.143281	−	0.989682i	$-0.454235\pi$
$53$	15.1877			0.286561			0.143281	+	0.989682i	$0.454235\pi$
$54$	63.6346	−	70.0795i	1.17842	−	1.29777i
$55$		0			0
$56$			39.8071i			0.710842i
$57$	46.8190	−	13.3542i	0.821386	−	0.234285i
$58$			33.2915i			0.573991i
$59$		−	92.3960i		−	1.56603i	−0.622000	−	0.783017i	$-0.713680\pi$
$59$		−	92.3960i		−	1.56603i	0.622000	−	0.783017i	$-0.286320\pi$
$60$		0			0
$61$	−57.5203			−0.942955			−0.471478	−	0.881878i	$-0.656279\pi$
$61$	−57.5203			−0.942955			−0.471478	+	0.881878i	$0.656279\pi$
$62$	−100.650			−1.62338
$63$	−12.5617	−	20.2288i	−0.199393	−	0.321091i
$64$	−48.6235			−0.759743
$65$		0			0
$66$	−20.2288	−	70.9205i	−0.306496	−	1.07455i
$67$		−	15.1660i		−	0.226358i	−0.993575	−	0.113179i	$-0.963897\pi$
$67$		−	15.1660i		−	0.226358i	0.993575	−	0.113179i	$-0.0361034\pi$
$68$	37.5432			0.552106
$69$	−73.7490	+	21.0355i	−1.06883	+	0.304863i
$70$		0			0
$71$		−	70.5584i		−	0.993781i	−0.867813	−	0.496890i	$-0.834475\pi$
$71$		−	70.5584i		−	0.993781i	0.867813	−	0.496890i	$-0.165525\pi$
$72$	−115.036	+	71.4353i	−1.59772	+	0.992157i
$73$		−	76.7895i		−	1.05191i	−0.850512	−	0.525956i	$-0.823708\pi$
$73$		−	76.7895i		−	1.05191i	0.850512	−	0.525956i	$-0.176292\pi$
$74$		−	115.838i		−	1.56537i
$75$		0			0
$76$	−134.561			−1.77054
$77$	−18.5516			−0.240930
$78$	−33.5973	−	117.790i	−0.430734	−	1.51012i
$79$	−127.247			−1.61072			−0.805361	−	0.592785i	$-0.798029\pi$
$79$	−127.247			−1.61072			−0.805361	+	0.592785i	$0.798029\pi$
$80$		0			0
$81$	35.9150	−	72.6024i	0.443395	−	0.896326i
$82$		−	235.579i		−	2.87292i
$83$	−74.2844			−0.894992			−0.447496	−	0.894286i	$-0.647684\pi$
$83$	−74.2844			−0.894992			−0.447496	+	0.894286i	$0.647684\pi$
$84$	18.0516	+	63.2876i	0.214900	+	0.753424i
$85$		0			0
$86$			84.5821i			0.983513i
$87$	7.81385	+	27.3948i	0.0898144	+	0.314882i
$88$			105.498i			1.19884i
$89$			127.377i			1.43121i	0.698507	+	0.715603i	$0.253848\pi$
$89$			127.377i			1.43121i	−0.698507	+	0.715603i	$0.746152\pi$
$90$		0			0
$91$	−30.8118			−0.338591
$92$	211.959			2.30391
$93$	−82.8223	+	23.6235i	−0.890562	+	0.254016i
$94$	115.749			1.23137
$95$		0			0
$96$	24.4464	−	6.97288i	0.254650	−	0.0726342i
$97$			23.1660i			0.238825i	0.992845	+	0.119412i	$0.0381011\pi$
$97$			23.1660i			0.238825i	−0.992845	+	0.119412i	$0.961899\pi$
$98$	24.5415			0.250423
$99$	−33.2915	−	53.6108i	−0.336278	−	0.541524i
$100$		0			0
$101$		−	134.907i		−	1.33571i	−0.744290	−	0.667857i	$-0.767212\pi$
$101$		−	134.907i		−	1.33571i	0.744290	−	0.667857i	$-0.232788\pi$
$102$	45.7970	−	13.0627i	0.448990	−	0.128066i
$103$		−	119.749i		−	1.16261i	−0.813685	−	0.581306i	$-0.802542\pi$
$103$		−	119.749i		−	1.16261i	0.813685	−	0.581306i	$-0.197458\pi$
$104$			175.218i			1.68479i
$105$		0			0
$106$	−53.2470			−0.502331
$107$	−77.8544			−0.727611			−0.363806	−	0.931475i	$-0.618523\pi$
$107$	−77.8544			−0.727611			−0.363806	+	0.931475i	$0.618523\pi$
$108$	−150.496	+	165.738i	−1.39348	+	1.53461i
$109$	36.5385			0.335216			0.167608	−	0.985854i	$-0.446396\pi$
$109$	36.5385			0.335216			0.167608	+	0.985854i	$0.446396\pi$
$110$		0			0
$111$	−27.1882	−	95.3199i	−0.244939	−	0.858738i
$112$		−	51.8118i		−	0.462605i
$113$	−21.7596			−0.192563			−0.0962815	−	0.995354i	$-0.530695\pi$
$113$	−21.7596			−0.192563			−0.0962815	+	0.995354i	$0.530695\pi$
$114$	−164.144	+	46.8190i	−1.43986	+	0.410693i
$115$		0			0
$116$		−	78.7343i		−	0.678744i
$117$	−55.2928	−	89.0405i	−0.472588	−	0.761030i
$118$			323.933i			2.74520i
$119$		−	11.9797i		−	0.100670i
$120$		0			0
$121$	71.8340			0.593669
$122$	201.662			1.65296
$123$	−55.2928	−	193.852i	−0.449535	−	1.57603i
$124$	238.037			1.91965
$125$		0			0
$126$	44.0405	+	70.9205i	0.349528	+	0.562861i
$127$			15.4170i			0.121394i	0.998156	+	0.0606968i	$0.0193323\pi$
$127$			15.4170i			0.121394i	−0.998156	+	0.0606968i	$0.980668\pi$
$128$	204.366			1.59661
$129$	19.8523	+	69.6006i	0.153894	+	0.539539i
$130$		0			0
$131$			183.110i			1.39779i	0.715226	+	0.698893i	$0.246324\pi$
$131$			183.110i			1.39779i	−0.715226	+	0.698893i	$0.753676\pi$
$132$	47.8410	+	167.727i	0.362432	+	1.27066i
$133$			42.9373i			0.322836i
$134$			53.1709i			0.396798i
$135$		0			0
$136$	−68.1255			−0.500923
$137$	33.0153			0.240987			0.120494	−	0.992714i	$-0.461552\pi$
$137$	33.0153			0.240987			0.120494	+	0.992714i	$0.461552\pi$
$138$	258.558	−	73.7490i	1.87361	−	0.534413i
$139$	−64.6418			−0.465049			−0.232525	−	0.972591i	$-0.574699\pi$
$139$	−64.6418			−0.465049			−0.232525	+	0.972591i	$0.574699\pi$
$140$		0			0
$141$	95.2470	−	27.1675i	0.675511	−	0.192677i
$142$			247.373i			1.74206i
$143$	−81.6582			−0.571037
$144$	149.727	−	92.9780i	1.03977	−	0.645681i
$145$		0			0
$146$			269.218i			1.84396i
$147$	20.1946	−	5.76013i	0.137378	−	0.0391846i
$148$			273.956i			1.85105i
$149$		−	195.736i		−	1.31366i	−0.754037	−	0.656832i	$-0.771896\pi$
$149$		−	195.736i		−	1.31366i	0.754037	−	0.656832i	$-0.228104\pi$
$150$		0			0
$151$	102.251			0.677159			0.338579	−	0.940938i	$-0.390054\pi$
$151$	102.251			0.677159			0.338579	+	0.940938i	$0.390054\pi$
$152$	244.173			1.60640
$153$	34.6193	−	21.4980i	0.226270	−	0.140510i
$154$	65.0405			0.422341
$155$		0			0
$156$	79.4575	+	278.572i	0.509343	+	1.78572i
$157$		−	104.723i		−	0.667025i	−0.942746	−	0.333512i	$-0.891766\pi$
$157$		−	104.723i		−	0.667025i	0.942746	−	0.333512i	$-0.108234\pi$
$158$	446.118			2.82353
$159$	−43.8157	+	12.4976i	−0.275570	+	0.0786014i
$160$		0			0
$161$		−	67.6345i		−	0.420090i
$162$	−125.915	+	254.539i	−0.777255	+	1.57123i
$163$		−	70.9595i		−	0.435334i	−0.976023	−	0.217667i	$-0.930155\pi$
$163$		−	70.9595i		−	0.435334i	0.976023	−	0.217667i	$-0.0698447\pi$
$164$			557.144i			3.39722i
$165$		0			0
$166$	260.435			1.56889
$167$	−206.992			−1.23947			−0.619735	−	0.784811i	$-0.712760\pi$
$167$	−206.992			−1.23947			−0.619735	+	0.784811i	$0.712760\pi$
$168$	−32.7563	−	114.841i	−0.194978	−	0.683578i
$169$	33.3765			0.197494
$170$		0			0
$171$	−124.081	+	77.0524i	−0.725620	+	0.450599i
$172$		−	200.037i		−	1.16300i
$173$	−108.464			−0.626958			−0.313479	−	0.949595i	$-0.601494\pi$
$173$	−108.464			−0.626958			−0.313479	+	0.949595i	$0.601494\pi$
$174$	−27.3948	−	96.0440i	−0.157441	−	0.551977i
$175$		0			0
$176$		−	137.313i		−	0.780188i
$177$	76.0304	+	266.557i	0.429550	+	1.50597i
$178$		−	446.575i		−	2.50885i
$179$		−	159.357i		−	0.890261i	−0.895466	−	0.445131i	$-0.853157\pi$
$179$		−	159.357i		−	0.890261i	0.895466	−	0.445131i	$-0.146843\pi$
$180$		0			0
$181$	−233.889			−1.29220			−0.646102	−	0.763251i	$-0.723602\pi$
$181$	−233.889			−1.29220			−0.646102	+	0.763251i	$0.723602\pi$
$182$	108.024			0.593537
$183$	165.942	−	47.3320i	0.906789	−	0.258645i
$184$	−384.620			−2.09032
$185$		0			0
$186$	290.369	−	82.8223i	1.56112	−	0.445281i
$187$		−	31.7490i		−	0.169781i
$188$	−273.746			−1.45610
$189$	52.8856	+	48.0220i	0.279818	+	0.254085i
$190$		0			0
$191$		−	288.210i		−	1.50895i	−0.656328	−	0.754476i	$-0.727891\pi$
$191$		−	288.210i		−	1.50895i	0.656328	−	0.754476i	$-0.272109\pi$
$192$	140.276	−	40.0111i	0.730604	−	0.208391i
$193$			77.1216i			0.399594i	0.979837	+	0.199797i	$0.0640282\pi$
$193$			77.1216i			0.399594i	−0.979837	+	0.199797i	$0.935972\pi$
$194$		−	81.2183i		−	0.418651i
$195$		0			0
$196$	−58.0405			−0.296125
$197$	−136.433			−0.692554			−0.346277	−	0.938132i	$-0.612554\pi$
$197$	−136.433			−0.692554			−0.346277	+	0.938132i	$0.612554\pi$
$198$	116.717	+	187.956i	0.589482	+	0.949270i
$199$	−86.5830			−0.435090			−0.217545	−	0.976050i	$-0.569805\pi$
$199$	−86.5830			−0.435090			−0.217545	+	0.976050i	$0.569805\pi$
$200$		0			0
$201$	12.4797	+	43.7530i	0.0620883	+	0.217677i
$202$			472.974i			2.34145i
$203$	−25.1235			−0.123761
$204$	−108.310	+	30.8934i	−0.530930	+	0.151438i
$205$		0			0
$206$			419.831i			2.03801i
$207$	195.452	−	121.373i	0.944212	−	0.586341i
$208$		−	228.059i		−	1.09644i
$209$			113.794i			0.544467i
$210$		0			0
$211$	19.4170			0.0920237			0.0460118	−	0.998941i	$-0.485349\pi$
$211$	19.4170			0.0920237			0.0460118	+	0.998941i	$0.485349\pi$
$212$	125.929			0.594005
$213$	58.0608	+	203.557i	0.272586	+	0.955666i
$214$	272.952			1.27547
$215$		0			0
$216$	273.088	−	300.746i	1.26430	−	1.39234i
$217$		−	75.9555i		−	0.350026i
$218$	−128.101			−0.587621
$219$	63.1882	+	221.533i	0.288531	+	1.01157i
$220$		0			0
$221$		−	52.7309i		−	0.238601i
$222$	95.3199	+	334.184i	0.429369	+	1.50533i
$223$			175.041i			0.784935i	0.919766	+	0.392468i	$0.128378\pi$
$223$			175.041i			0.784935i	−0.919766	+	0.392468i	$0.871622\pi$
$224$			22.4196i			0.100087i
$225$		0			0
$226$	76.2876			0.337556
$227$	−177.574			−0.782264			−0.391132	−	0.920335i	$-0.627916\pi$
$227$	−177.574			−0.782264			−0.391132	+	0.920335i	$0.627916\pi$
$228$	388.200	−	110.727i	1.70263	−	0.485644i
$229$	−40.8118			−0.178217			−0.0891087	−	0.996022i	$-0.528402\pi$
$229$	−40.8118			−0.178217			−0.0891087	+	0.996022i	$0.528402\pi$
$230$		0			0
$231$	53.5203	−	15.2657i	0.231689	−	0.0660851i
$232$			142.871i			0.615821i
$233$	−387.696			−1.66393			−0.831965	−	0.554828i	$-0.812784\pi$
$233$	−387.696			−1.66393			−0.831965	+	0.554828i	$0.812784\pi$
$234$	193.852	+	312.169i	0.828429	+	1.33406i
$235$		0			0
$236$		−	766.102i		−	3.24619i
$237$	367.100	−	104.708i	1.54895	−	0.441808i
$238$			42.0000i			0.176471i
$239$			49.5229i			0.207209i	0.994619	+	0.103604i	$0.0330376\pi$
$239$			49.5229i			0.207209i	−0.994619	+	0.103604i	$0.966962\pi$
$240$		0			0
$241$	325.247			1.34957			0.674786	−	0.738013i	$-0.264236\pi$
$241$	325.247			1.34957			0.674786	+	0.738013i	$0.264236\pi$
$242$	−251.845			−1.04068
$243$	−43.8699	+	239.007i	−0.180535	+	0.983569i
$244$	−476.929			−1.95463
$245$		0			0
$246$	193.852	+	679.631i	0.788017	+	2.76273i
$247$			188.996i			0.765166i
$248$	−431.939			−1.74169
$249$	214.306	−	61.1268i	0.860666	−	0.245489i
$250$		0			0
$251$		−	263.732i		−	1.05073i	−0.850878	−	0.525364i	$-0.823929\pi$
$251$		−	263.732i		−	1.05073i	0.850878	−	0.525364i	$-0.176071\pi$
$252$	−104.156	−	167.727i	−0.413316	−	0.665582i
$253$		−	179.247i		−	0.708486i
$254$		−	54.0508i		−	0.212798i
$255$		0			0
$256$	−521.996			−2.03905
$257$	−151.181			−0.588252			−0.294126	−	0.955767i	$-0.595029\pi$
$257$	−151.181			−0.588252			−0.294126	+	0.955767i	$0.595029\pi$
$258$	−69.6006	−	244.014i	−0.269770	−	0.945792i
$259$	87.4170			0.337517
$260$		0			0
$261$	−45.0850	−	72.6024i	−0.172739	−	0.278170i
$262$		−	641.970i		−	2.45027i
$263$	−114.389			−0.434941			−0.217470	−	0.976067i	$-0.569781\pi$
$263$	−114.389			−0.434941			−0.217470	+	0.976067i	$0.569781\pi$
$264$	−86.8118	−	304.355i	−0.328832	−	1.15286i
$265$		0			0
$266$		−	150.535i		−	0.565920i
$267$	−104.816	−	367.476i	−0.392568	−	1.37631i
$268$		−	125.749i		−	0.469213i
$269$		−	4.76170i		−	0.0177015i	−0.999961	−	0.00885074i	$-0.997183\pi$
$269$		−	4.76170i		−	0.0177015i	0.999961	−	0.00885074i	$-0.00281731\pi$
$270$		0			0
$271$	−518.701			−1.91402			−0.957012	−	0.290048i	$-0.906329\pi$
$271$	−518.701			−1.91402			−0.957012	+	0.290048i	$0.906329\pi$
$272$	88.6701			0.325993
$273$	88.8901	−	25.3542i	0.325605	−	0.0928727i
$274$	−115.749			−0.422442
$275$		0			0
$276$	−611.490	+	174.416i	−2.21554	+	0.631943i
$277$			121.085i			0.437130i	0.975822	+	0.218565i	$0.0701375\pi$
$277$			121.085i			0.437130i	−0.975822	+	0.218565i	$0.929862\pi$
$278$	226.629			0.815213
$279$	219.498	−	136.305i	0.786731	−	0.488548i
$280$		0			0
$281$			407.255i			1.44931i	0.689113	+	0.724654i	$0.258000\pi$
$281$			407.255i			1.44931i	−0.689113	+	0.724654i	$0.742000\pi$
$282$	−333.929	+	95.2470i	−1.18415	+	0.337755i
$283$		−	398.634i		−	1.40860i	−0.709902	−	0.704300i	$-0.751261\pi$
$283$		−	398.634i		−	1.40860i	0.709902	−	0.704300i	$-0.248739\pi$
$284$		−	585.036i		−	2.05998i
$285$		0			0
$286$	286.288			1.00101
$287$	177.780			0.619443
$288$	−64.7886	+	40.2327i	−0.224960	+	0.139697i
$289$	−268.498			−0.929059
$290$		0			0
$291$	−19.0627	−	66.8325i	−0.0655077	−	0.229665i
$292$		−	636.701i		−	2.18048i
$293$	−2.53426			−0.00864935			−0.00432468	−	0.999991i	$-0.501377\pi$
$293$	−2.53426			−0.00864935			−0.00432468	+	0.999991i	$0.501377\pi$
$294$	−70.8006	+	20.1946i	−0.240819	+	0.0686890i
$295$		0			0
$296$		−	497.117i		−	1.67945i
$297$	140.159	+	127.269i	0.471916	+	0.428516i
$298$			686.235i			2.30280i
$299$		−	297.706i		−	0.995671i
$300$		0			0
$301$	−63.8301			−0.212060
$302$	−358.484			−1.18703
$303$	111.012	+	389.199i	0.366375	+	1.28448i
$304$	−317.808			−1.04542
$305$		0			0
$306$	−121.373	+	75.3705i	−0.396642	+	0.246309i
$307$		−	86.2366i		−	0.280901i	−0.990088	−	0.140451i	$-0.955145\pi$
$307$		−	86.2366i		−	0.280901i	0.990088	−	0.140451i	$-0.0448551\pi$
$308$	−153.821			−0.499418
$309$	98.5385	+	345.469i	0.318895	+	1.11802i
$310$		0			0
$311$			151.777i			0.488028i	0.969772	+	0.244014i	$0.0784643\pi$
$311$			151.777i			0.488028i	−0.969772	+	0.244014i	$0.921536\pi$
$312$	−144.183	−	505.494i	−0.462125	−	1.62017i
$313$			318.118i			1.01635i	0.861254	+	0.508175i	$0.169680\pi$
$313$			318.118i			1.01635i	−0.861254	+	0.508175i	$0.830320\pi$
$314$			367.150i			1.16927i
$315$		0			0
$316$	−1055.07			−3.33883
$317$	364.020			1.14833			0.574164	−	0.818740i	$-0.305327\pi$
$317$	364.020			1.14833			0.574164	+	0.818740i	$0.305327\pi$
$318$	153.615	−	43.8157i	0.483064	−	0.137785i
$319$	−66.5830			−0.208724
$320$		0			0
$321$	224.605	−	64.0645i	0.699705	−	0.199578i
$322$			237.122i			0.736402i
$323$	−73.4823			−0.227500
$324$	297.790	−	601.983i	0.919104	−	1.85797i
$325$		0			0
$326$			248.779i			0.763124i
$327$	−105.412	+	30.0667i	−0.322359	+	0.0919470i
$328$		−	1010.99i		−	3.08228i
$329$			87.3502i			0.265502i
$330$		0			0
$331$	154.369			0.466370			0.233185	−	0.972432i	$-0.425085\pi$
$331$	154.369			0.466370			0.233185	+	0.972432i	$0.425085\pi$
$332$	−615.929			−1.85521
$333$	156.873	+	252.620i	0.471090	+	0.758617i
$334$	725.697			2.17274
$335$		0			0
$336$	42.6346	+	149.474i	0.126889	+	0.444862i
$337$		−	403.041i		−	1.19597i	−0.801509	−	0.597983i	$-0.795969\pi$
$337$		−	403.041i		−	1.19597i	0.801509	−	0.597983i	$-0.204031\pi$
$338$	−117.015			−0.346199
$339$	62.7752	−	17.9055i	0.185178	−	0.0528185i
$340$		0			0
$341$		−	201.300i		−	0.590321i
$342$	435.019	−	270.140i	1.27198	−	0.789883i
$343$			18.5203i			0.0539949i
$344$			362.984i			1.05519i
$345$		0			0
$346$	380.265			1.09903
$347$	−471.242			−1.35805			−0.679023	−	0.734117i	$-0.737596\pi$
$347$	−471.242			−1.35805			−0.679023	+	0.734117i	$0.737596\pi$
$348$	64.7886	+	227.144i	0.186174	+	0.652712i
$349$	364.516			1.04446			0.522230	−	0.852805i	$-0.325100\pi$
$349$	364.516			1.04446			0.522230	+	0.852805i	$0.325100\pi$
$350$		0			0
$351$	232.786	+	211.377i	0.663207	+	0.602215i
$352$			59.4170i			0.168798i
$353$	86.3420			0.244595			0.122297	−	0.992493i	$-0.460974\pi$
$353$	86.3420			0.244595			0.122297	+	0.992493i	$0.460974\pi$
$354$	−266.557	−	934.528i	−0.752985	−	2.63991i
$355$		0			0
$356$			1056.15i			2.96671i
$357$	9.85782	+	34.5608i	0.0276129	+	0.0968089i
$358$			558.693i			1.56059i
$359$		−	372.068i		−	1.03640i	−0.855259	−	0.518200i	$-0.826602\pi$
$359$		−	372.068i		−	1.03640i	0.855259	−	0.518200i	$-0.173398\pi$
$360$		0			0
$361$	−97.6275			−0.270436
$362$	819.997			2.26518
$363$	−207.237	+	59.1104i	−0.570900	+	0.162839i
$364$	−255.476			−0.701857
$365$		0			0
$366$	−581.782	+	165.942i	−1.58957	+	0.453395i
$367$			161.786i			0.440833i	0.975406	+	0.220416i	$0.0707416\pi$
$367$			161.786i			0.440833i	−0.975406	+	0.220416i	$0.929258\pi$
$368$	500.609			1.36035
$369$	319.033	+	513.753i	0.864587	+	1.39228i
$370$		0			0
$371$		−	40.1830i		−	0.108310i
$372$	−686.721	+	195.875i	−1.84602	+	0.526544i
$373$			378.251i			1.01408i	0.861923	+	0.507039i	$0.169260\pi$
$373$			378.251i			1.01408i	−0.861923	+	0.507039i	$0.830740\pi$
$374$			111.310i			0.297619i
$375$		0			0
$376$	496.737			1.32111
$377$	−110.586			−0.293330
$378$	−185.413	−	168.361i	−0.490510	−	0.445401i
$379$	50.7974			0.134030			0.0670151	−	0.997752i	$-0.478652\pi$
$379$	50.7974			0.134030			0.0670151	+	0.997752i	$0.478652\pi$
$380$		0			0
$381$	−12.6863	−	44.4771i	−0.0332973	−	0.116738i
$382$			1010.44i			2.64514i
$383$	−113.381			−0.296034			−0.148017	−	0.988985i	$-0.547289\pi$
$383$	−113.381			−0.296034			−0.148017	+	0.988985i	$0.547289\pi$
$384$	−589.582	+	168.167i	−1.53537	+	0.437936i
$385$		0			0
$386$		−	270.382i		−	0.700472i
$387$	−114.545	−	184.458i	−0.295983	−	0.476634i
$388$			192.081i			0.495054i
$389$			725.584i			1.86526i	0.360841	+	0.932628i	$0.382490\pi$
$389$			725.584i			1.86526i	−0.360841	+	0.932628i	$0.617510\pi$
$390$		0			0
$391$	115.749			0.296033
$392$	105.320			0.268673
$393$	−150.677	−	528.261i	−0.383402	−	1.34418i
$394$	478.324			1.21402
$395$		0			0
$396$	−276.037	−	444.514i	−0.697062	−	1.12251i
$397$			94.3464i			0.237648i	0.992915	+	0.118824i	$0.0379125\pi$
$397$			94.3464i			0.237648i	−0.992915	+	0.118824i	$0.962088\pi$
$398$	303.553			0.762697
$399$	−35.3320	−	123.871i	−0.0885514	−	0.310455i
$400$		0			0
$401$		−	677.665i		−	1.68994i	−0.534815	−	0.844969i	$-0.679619\pi$
$401$		−	677.665i		−	1.68994i	0.534815	−	0.844969i	$-0.320381\pi$
$402$	−43.7530	−	153.395i	−0.108838	−	0.381579i
$403$		−	334.332i		−	0.829608i
$404$		−	1118.58i		−	2.76877i
$405$		0			0
$406$	88.0810			0.216948
$407$	231.675			0.569226
$408$	196.538	−	56.0588i	0.481711	−	0.137399i
$409$	−17.3647			−0.0424564			−0.0212282	−	0.999775i	$-0.506758\pi$
$409$	−17.3647			−0.0424564			−0.0212282	+	0.999775i	$0.506758\pi$
$410$		0			0
$411$	−95.2470	+	27.1675i	−0.231745	+	0.0661009i
$412$		−	992.899i		−	2.40995i
$413$	−244.457			−0.591905
$414$	−685.239	+	425.523i	−1.65517	+	1.02783i
$415$		0			0
$416$			98.6838i			0.237221i
$417$	186.488	−	53.1922i	0.447213	−	0.127559i
$418$		−	398.952i		−	0.954430i
$419$		−	136.071i		−	0.324752i	−0.986729	−	0.162376i	$-0.948084\pi$
$419$		−	136.071i		−	0.324752i	0.986729	−	0.162376i	$-0.0519157\pi$
$420$		0			0
$421$	423.992			1.00711			0.503554	−	0.863964i	$-0.332026\pi$
$421$	423.992			1.00711			0.503554	+	0.863964i	$0.332026\pi$
$422$	−68.0745			−0.161314
$423$	−252.427	+	156.753i	−0.596753	+	0.370574i
$424$	−228.510			−0.538938
$425$		0			0
$426$	−203.557	−	713.655i	−0.477833	−	1.67525i
$427$			152.184i			0.356404i
$428$	−645.530			−1.50825
$429$	235.579	−	67.1946i	0.549135	−	0.156631i
$430$		0			0
$431$			340.244i			0.789430i	0.918804	+	0.394715i	$0.129157\pi$
$431$			340.244i			0.789430i	−0.918804	+	0.394715i	$0.870843\pi$
$432$	−355.443	+	391.442i	−0.822786	+	0.906117i
$433$			159.166i			0.367589i	0.982965	+	0.183794i	$0.0588381\pi$
$433$			159.166i			0.367589i	−0.982965	+	0.183794i	$0.941162\pi$
$434$			266.294i			0.613581i
$435$		0			0
$436$	302.959			0.694861
$437$	−414.863			−0.949343
$438$	−221.533	−	776.678i	−0.505783	−	1.77324i
$439$	−128.073			−0.291738			−0.145869	−	0.989304i	$-0.546598\pi$
$439$	−128.073			−0.291738			−0.145869	+	0.989304i	$0.546598\pi$
$440$		0			0
$441$	−53.5203	+	33.2353i	−0.121361	+	0.0753634i
$442$			184.871i			0.418259i
$443$	197.340			0.445463			0.222731	−	0.974880i	$-0.428503\pi$
$443$	197.340			0.445463			0.222731	+	0.974880i	$0.428503\pi$
$444$	−225.431	−	790.345i	−0.507728	−	1.78006i
$445$		0			0
$446$		−	613.679i		−	1.37596i
$447$	161.066	+	564.686i	0.360327	+	1.26328i
$448$			128.646i			0.287156i
$449$		−	148.101i		−	0.329847i	−0.986306	−	0.164923i	$-0.947262\pi$
$449$		−	148.101i		−	0.329847i	0.986306	−	0.164923i	$-0.0527377\pi$
$450$		0			0
$451$	471.158			1.04470
$452$	−180.420			−0.399159
$453$	−294.988	+	84.1398i	−0.651187	+	0.185739i
$454$	622.561			1.37128
$455$		0			0
$456$	−704.423	+	200.924i	−1.54479	+	0.440622i
$457$			122.214i			0.267428i	0.991020	+	0.133714i	$0.0426903\pi$
$457$			122.214i			0.267428i	−0.991020	+	0.133714i	$0.957310\pi$
$458$	143.083			0.312408
$459$	−82.1843	+	90.5079i	−0.179051	+	0.197185i
$460$		0			0
$461$			602.089i			1.30605i	0.757337	+	0.653025i	$0.226500\pi$
$461$			602.089i			1.30605i	−0.757337	+	0.653025i	$0.773500\pi$
$462$	−187.638	+	53.5203i	−0.406143	+	0.115845i
$463$		−	637.061i		−	1.37594i	−0.725738	−	0.687971i	$-0.758502\pi$
$463$		−	637.061i		−	1.37594i	0.725738	−	0.687971i	$-0.241498\pi$
$464$		−	185.956i		−	0.400767i
$465$		0			0
$466$	1359.23			2.91681
$467$	−767.706			−1.64391			−0.821955	−	0.569553i	$-0.807116\pi$
$467$	−767.706			−1.64391			−0.821955	+	0.569553i	$0.807116\pi$
$468$	−458.460	−	738.280i	−0.979616	−	1.57752i
$469$	−40.1255			−0.0855554
$470$		0			0
$471$	86.1739	+	302.119i	0.182959	+	0.641442i
$472$			1390.16i			2.94526i
$473$	−169.164			−0.357641
$474$	−1287.02	+	367.100i	−2.71524	+	0.774473i
$475$		0			0
$476$		−	99.3299i		−	0.208676i
$477$	116.122	−	72.1097i	0.243442	−	0.151173i
$478$		−	173.624i		−	0.363229i
$479$		−	393.855i		−	0.822245i	−0.911580	−	0.411122i	$-0.865137\pi$
$479$		−	393.855i		−	0.822245i	0.911580	−	0.411122i	$-0.134863\pi$
$480$		0			0
$481$	384.782			0.799962
$482$	−1140.29			−2.36575
$483$	55.6548	+	195.122i	0.115227	+	0.403978i
$484$	595.612			1.23060
$485$		0			0
$486$	153.805	−	837.941i	0.316470	−	1.72416i
$487$		−	573.409i		−	1.17743i	−0.808340	−	0.588716i	$-0.799634\pi$
$487$		−	573.409i		−	1.17743i	0.808340	−	0.588716i	$-0.200366\pi$
$488$	865.432			1.77343
$489$	58.3908	+	204.714i	0.119409	+	0.418638i
$490$		0			0
$491$		−	170.796i		−	0.347853i	−0.984759	−	0.173927i	$-0.944354\pi$
$491$		−	170.796i		−	0.347853i	0.984759	−	0.173927i	$-0.0556455\pi$
$492$	−458.460	−	1607.33i	−0.931830	−	3.26692i
$493$		−	42.9961i		−	0.0872131i
$494$		−	662.606i		−	1.34131i
$495$		0			0
$496$	562.199			1.13347
$497$	−186.680			−0.375614
$498$	−751.340	+	214.306i	−1.50871	+	0.430333i
$499$	847.814			1.69903			0.849513	−	0.527567i	$-0.176896\pi$
$499$	847.814			1.69903			0.849513	+	0.527567i	$0.176896\pi$
$500$		0			0
$501$	597.158	−	170.328i	1.19193	−	0.339977i
$502$			924.626i			1.84188i
$503$	−197.624			−0.392891			−0.196445	−	0.980515i	$-0.562940\pi$
$503$	−197.624			−0.392891			−0.196445	+	0.980515i	$0.562940\pi$
$504$	189.000	+	304.355i	0.375000	+	0.603880i
$505$		0			0
$506$			628.427i			1.24195i
$507$	−96.2891	+	27.4647i	−0.189919	+	0.0541710i
$508$			127.830i			0.251634i
$509$		−	491.448i		−	0.965516i	−0.875754	−	0.482758i	$-0.839635\pi$
$509$		−	491.448i		−	0.965516i	0.875754	−	0.482758i	$-0.160365\pi$
$510$		0			0
$511$	−203.166			−0.397585
$512$	1012.62			1.97777
$513$	294.562	−	324.395i	0.574194	−	0.632348i
$514$	530.029			1.03118
$515$		0			0
$516$	164.605	+	577.093i	0.319002	+	1.11840i
$517$			231.498i			0.447772i
$518$	−306.477			−0.591655
$519$	312.911	−	89.2521i	0.602912	−	0.171969i
$520$		0			0
$521$			870.010i			1.66988i	0.550338	+	0.834942i	$0.314499\pi$
$521$			870.010i			1.66988i	−0.550338	+	0.834942i	$0.685501\pi$
$522$	158.064	+	254.539i	0.302806	+	0.487622i
$523$			798.707i			1.52716i	0.645710	+	0.763582i	$0.276561\pi$
$523$			798.707i			1.52716i	−0.645710	+	0.763582i	$0.723439\pi$
$524$			1518.26i			2.89744i
$525$		0			0
$526$	401.041			0.762434
$527$	129.989			0.246659
$528$	112.992	+	396.140i	0.213999	+	0.750265i
$529$	124.490			0.235331
$530$		0			0
$531$	−438.686	−	706.437i	−0.826151	−	1.33039i
$532$			356.014i			0.669200i
$533$	782.531			1.46816
$534$	367.476	+	1288.34i	0.688157	+	2.41263i
$535$		0			0
$536$			228.183i			0.425714i
$537$	131.131	+	459.735i	0.244191	+	0.856117i
$538$			16.6941i			0.0310300i
$539$			49.0829i			0.0910630i
$540$		0			0
$541$	−736.243			−1.36089			−0.680446	−	0.732798i	$-0.738214\pi$
$541$	−736.243			−1.36089			−0.680446	+	0.732798i	$0.738214\pi$
$542$	1818.52			3.35521
$543$	674.755	−	192.461i	1.24264	−	0.354441i
$544$	−38.3686			−0.0705305
$545$		0			0
$546$	−311.642	+	88.8901i	−0.570773	+	0.162802i
$547$			228.952i			0.418559i	0.977856	+	0.209279i	$0.0671118\pi$
$547$			228.952i			0.418559i	−0.977856	+	0.209279i	$0.932888\pi$
$548$	273.746			0.499537
$549$	−439.786	+	273.100i	−0.801067	+	0.497450i
$550$		0			0
$551$			154.105i			0.279682i
$552$	1109.60	−	316.494i	2.01015	−	0.573359i
$553$			336.664i			0.608796i
$554$		−	424.515i		−	0.766272i
$555$		0			0
$556$	−535.978			−0.963989
$557$	906.288			1.62709			0.813544	−	0.581503i	$-0.197535\pi$
$557$	906.288			1.62709			0.813544	+	0.581503i	$0.197535\pi$
$558$	−769.543	+	477.875i	−1.37911	+	0.856406i
$559$	−280.959			−0.502611
$560$		0			0
$561$	26.1255	+	91.5940i	0.0465695	+	0.163269i
$562$		−	1427.81i		−	2.54058i
$563$	458.616			0.814593			0.407297	−	0.913296i	$-0.366471\pi$
$563$	458.616			0.814593			0.407297	+	0.913296i	$0.366471\pi$
$564$	789.741	−	225.259i	1.40025	−	0.399396i
$565$		0			0
$566$			1397.58i			2.46922i
$567$	−192.088	−	95.0222i	−0.338779	−	0.167588i
$568$			1061.60i			1.86901i
$569$			577.428i			1.01481i	0.861707	+	0.507406i	$0.169395\pi$
$569$			577.428i			1.01481i	−0.861707	+	0.507406i	$0.830605\pi$
$570$		0			0
$571$	−103.122			−0.180598			−0.0902991	−	0.995915i	$-0.528782\pi$
$571$	−103.122			−0.180598			−0.0902991	+	0.995915i	$0.528782\pi$
$572$	−677.069			−1.18369
$573$	237.161	+	831.468i	0.413893	+	1.45108i
$574$	−623.284			−1.08586
$575$		0			0
$576$	−371.763	+	230.859i	−0.645423	+	0.400797i
$577$			676.583i			1.17259i	0.810099	+	0.586294i	$0.199414\pi$
$577$			676.583i			1.17259i	−0.810099	+	0.586294i	$0.800586\pi$
$578$	941.334			1.62860
$579$	−63.4615	−	222.491i	−0.109605	−	0.384268i
$580$		0			0
$581$			196.538i			0.338275i
$582$	66.8325	+	234.310i	0.114833	+	0.402594i
$583$		−	106.494i		−	0.182666i
$584$			1155.35i			1.97834i
$585$		0			0
$586$	8.88492			0.0151620
$587$	158.683			0.270329			0.135164	−	0.990823i	$-0.456844\pi$
$587$	158.683			0.270329			0.135164	+	0.990823i	$0.456844\pi$
$588$	167.443	−	47.7601i	0.284768	−	0.0812247i
$589$	−465.903			−0.791007
$590$		0			0
$591$	393.601	−	112.267i	0.665992	−	0.189962i
$592$			647.033i			1.09296i
$593$	935.371			1.57735			0.788677	−	0.614807i	$-0.210766\pi$
$593$	935.371			1.57735			0.788677	+	0.614807i	$0.210766\pi$
$594$	−491.387	−	446.196i	−0.827251	−	0.751172i
$595$		0			0
$596$		−	1622.94i		−	2.72306i
$597$	249.787	−	71.2470i	0.418403	−	0.119342i
$598$			1043.73i			1.74537i
$599$		−	73.7665i		−	0.123149i	−0.998102	−	0.0615747i	$-0.980388\pi$
$599$		−	73.7665i		−	0.123149i	0.998102	−	0.0615747i	$-0.0196122\pi$
$600$		0			0
$601$	−934.280			−1.55454			−0.777271	−	0.629166i	$-0.783397\pi$
$601$	−934.280			−1.55454			−0.777271	+	0.629166i	$0.783397\pi$
$602$	223.783			0.371733
$603$	−72.0066	−	115.956i	−0.119414	−	0.192298i
$604$	847.814			1.40367
$605$		0			0
$606$	−389.199	−	1364.50i	−0.642242	−	2.25165i
$607$			181.608i			0.299189i	0.988747	+	0.149595i	$0.0477968\pi$
$607$			181.608i			0.299189i	−0.988747	+	0.149595i	$0.952203\pi$
$608$	137.519			0.226183
$609$	72.4797	−	20.6735i	0.119014	−	0.0339466i
$610$		0			0
$611$			384.488i			0.629276i
$612$	287.046	−	178.251i	0.469029	−	0.291260i
$613$		−	897.940i		−	1.46483i	−0.680859	−	0.732414i	$-0.738394\pi$
$613$		−	897.940i		−	1.46483i	0.680859	−	0.732414i	$-0.261606\pi$
$614$			302.339i			0.492409i
$615$		0			0
$616$	279.122			0.453119
$617$	1169.69			1.89576			0.947882	−	0.318622i	$-0.103220\pi$
$617$	1169.69			1.89576			0.947882	+	0.318622i	$0.103220\pi$
$618$	−345.469	−	1211.19i	−0.559011	−	1.95985i
$619$	−1208.97			−1.95310			−0.976548	−	0.215301i	$-0.930927\pi$
$619$	−1208.97			−1.95310			−0.976548	+	0.215301i	$0.930927\pi$
$620$		0			0
$621$	−463.992	+	510.985i	−0.747169	+	0.822842i
$622$		−	532.118i		−	0.855495i
$623$	337.009			0.540945
$624$	187.664	+	657.936i	0.300744	+	1.05438i
$625$		0			0
$626$		−	1115.30i		−	1.78162i
$627$	−93.6380	−	328.288i	−0.149343	−	0.523585i
$628$		−	868.310i		−	1.38266i
$629$			149.604i			0.237845i
$630$		0			0
$631$	901.223			1.42825			0.714123	−	0.700020i	$-0.246826\pi$
$631$	901.223			1.42825			0.714123	+	0.700020i	$0.246826\pi$
$632$	1914.52			3.02930
$633$	−56.0169	+	15.9778i	−0.0884942	+	0.0252413i
$634$	−1276.23			−2.01298
$635$		0			0
$636$	−363.298	+	103.624i	−0.571223	+	0.162931i
$637$			81.5203i			0.127975i
$638$	233.435			0.365886
$639$	−335.004	−	539.472i	−0.524263	−	0.844245i
$640$		0			0
$641$			528.629i			0.824694i	0.911027	+	0.412347i	$0.135291\pi$
$641$			528.629i			0.824694i	−0.911027	+	0.412347i	$0.864709\pi$
$642$	−787.449	+	224.605i	−1.22656	+	0.349852i
$643$			33.4392i			0.0520050i	0.999662	+	0.0260025i	$0.00827779\pi$
$643$			33.4392i			0.0520050i	−0.999662	+	0.0260025i	$0.991722\pi$
$644$		−	560.792i		−	0.870795i
$645$		0			0
$646$	257.624			0.398798
$647$	−786.308			−1.21531			−0.607657	−	0.794200i	$-0.707890\pi$
$647$	−786.308			−1.21531			−0.607657	+	0.794200i	$0.707890\pi$
$648$	−540.366	+	1092.35i	−0.833898	+	1.68573i
$649$	−647.867			−0.998254
$650$		0			0
$651$	62.5020	+	219.127i	0.0960092	+	0.336601i
$652$		−	588.361i		−	0.902394i
$653$	385.807			0.590823			0.295412	−	0.955370i	$-0.404543\pi$
$653$	385.807			0.590823			0.295412	+	0.955370i	$0.404543\pi$
$654$	369.565	−	105.412i	0.565084	−	0.161180i
$655$		0			0
$656$			1315.87i			2.00590i
$657$	−364.588	−	587.114i	−0.554929	−	0.893628i
$658$		−	306.243i		−	0.465415i
$659$			97.2583i			0.147585i	0.997274	+	0.0737924i	$0.0235102\pi$
$659$			97.2583i			0.147585i	−0.997274	+	0.0737924i	$0.976490\pi$
$660$		0			0
$661$	−961.505			−1.45462			−0.727311	−	0.686309i	$-0.759230\pi$
$661$	−961.505			−1.45462			−0.727311	+	0.686309i	$0.759230\pi$
$662$	−541.205			−0.817530
$663$	43.3910	+	152.125i	0.0654464	+	0.229450i
$664$	1117.66			1.68322
$665$		0			0
$666$	−549.984	−	885.665i	−0.825802	−	1.32983i
$667$		−	242.745i		−	0.363936i
$668$	−1716.27			−2.56927
$669$	−144.037	−	504.981i	−0.215301	−	0.754830i
$670$		0			0
$671$			403.323i			0.601078i
$672$	−18.4485	−	64.6791i	−0.0274531	−	0.0962487i
$673$		−	1089.81i		−	1.61933i	−0.586895	−	0.809663i	$-0.699650\pi$
$673$		−	1089.81i		−	1.61933i	0.586895	−	0.809663i	$-0.300350\pi$
$674$			1413.03i			2.09648i
$675$		0			0
$676$	276.741			0.409380
$677$	1252.56			1.85016			0.925080	−	0.379771i	$-0.123997\pi$
$677$	1252.56			1.85016			0.925080	+	0.379771i	$0.123997\pi$
$678$	−220.085	+	62.7752i	−0.324609	+	0.0925888i
$679$	61.2915			0.0902673
$680$		0			0
$681$	512.290	−	146.121i	0.752262	−	0.214569i
$682$			705.741i			1.03481i
$683$	−341.097			−0.499409			−0.249705	−	0.968322i	$-0.580334\pi$
$683$	−341.097			−0.499409			−0.249705	+	0.968322i	$0.580334\pi$
$684$	−1028.82	+	638.880i	−1.50412	+	0.934035i
$685$		0			0
$686$		−	64.9306i		−	0.0946510i
$687$	117.739	−	33.5830i	0.171382	−	0.0488836i
$688$		−	472.450i		−	0.686700i
$689$		−	176.873i		−	0.256709i
$690$		0			0
$691$	−783.667			−1.13411			−0.567053	−	0.823682i	$-0.691916\pi$
$691$	−783.667			−1.13411			−0.567053	+	0.823682i	$0.691916\pi$
$692$	−899.327			−1.29961
$693$	−141.841	+	88.0810i	−0.204677	+	0.127101i
$694$	1652.14			2.38060
$695$		0			0
$696$	−117.565	−	412.173i	−0.168915	−	0.592203i
$697$			304.251i			0.436515i
$698$	−1277.97			−1.83090
$699$	1118.48	−	319.025i	1.60011	−	0.456402i
$700$		0			0
$701$		−	1331.76i		−	1.89979i	−0.312562	−	0.949897i	$-0.601187\pi$
$701$		−	1331.76i		−	1.89979i	0.312562	−	0.949897i	$-0.398813\pi$
$702$	−816.129	−	741.073i	−1.16258	−	1.05566i
$703$		−	536.207i		−	0.762740i
$704$			340.941i			0.484291i
$705$		0			0
$706$	−302.708			−0.428766
$707$	−356.930			−0.504852
$708$	630.406	+	2210.16i	0.890404	+	3.12169i
$709$	−763.963			−1.07752			−0.538761	−	0.842459i	$-0.681107\pi$
$709$	−763.963			−1.07752			−0.538761	+	0.842459i	$0.681107\pi$
$710$		0			0
$711$	−972.899	+	604.155i	−1.36835	+	0.849726i
$712$		−	1916.48i		−	2.69168i
$713$	733.888			1.02930
$714$	−34.5608	−	121.167i	−0.0484045	−	0.169702i
$715$		0			0
$716$		−	1321.31i		−	1.84540i
$717$	−40.7512	−	142.871i	−0.0568357	−	0.199262i
$718$			1304.44i			1.81677i
$719$			623.715i			0.867476i	0.901039	+	0.433738i	$0.142806\pi$
$719$			623.715i			0.867476i	−0.901039	+	0.433738i	$0.857194\pi$
$720$		0			0
$721$	−316.826			−0.439426
$722$	342.274			0.474064
$723$	−938.318	+	267.638i	−1.29781	+	0.370177i
$724$	−1939.29			−2.67858
$725$		0			0
$726$	726.556	−	207.237i	1.00077	−	0.285450i
$727$		−	678.494i		−	0.933279i	−0.884448	−	0.466640i	$-0.845464\pi$
$727$		−	678.494i		−	0.933279i	0.884448	−	0.466640i	$-0.154536\pi$
$728$	463.584			0.636791
$729$	−70.1111	−	725.621i	−0.0961744	−	0.995364i
$730$		0			0
$731$		−	109.238i		−	0.149436i
$732$	1375.91	−	392.454i	1.87966	−	0.536139i
$733$		−	394.966i		−	0.538835i	−0.963023	−	0.269417i	$-0.913169\pi$
$733$		−	394.966i		−	0.538835i	0.963023	−	0.269417i	$-0.0868311\pi$
$734$		−	567.208i		−	0.772763i
$735$		0			0
$736$	−216.620			−0.294320
$737$	−106.342			−0.144290
$738$	−1118.50	−	1801.18i	−1.51559	−	2.44062i
$739$	−292.199			−0.395397			−0.197699	−	0.980263i	$-0.563347\pi$
$739$	−292.199			−0.395397			−0.197699	+	0.980263i	$0.563347\pi$
$740$		0			0
$741$	−155.520	−	545.242i	−0.209879	−	0.735819i
$742$			140.878i			0.189863i
$743$	−383.452			−0.516086			−0.258043	−	0.966133i	$-0.583078\pi$
$743$	−383.452			−0.516086			−0.258043	+	0.966133i	$0.583078\pi$
$744$	1246.12	−	355.432i	1.67489	−	0.477731i
$745$		0			0
$746$		−	1326.12i		−	1.77764i
$747$	−567.960	+	352.694i	−0.760321	+	0.472147i
$748$		−	263.247i		−	0.351935i
$749$			205.983i			0.275011i
$750$		0			0
$751$	−696.332			−0.927206			−0.463603	−	0.886043i	$-0.653444\pi$
$751$	−696.332			−0.927206			−0.463603	+	0.886043i	$0.653444\pi$
$752$	−646.538			−0.859758
$753$	217.019	+	760.852i	0.288206	+	1.01043i
$754$	387.705			0.514197
$755$		0			0
$756$	438.501	+	398.174i	0.580028	+	0.526686i
$757$		−	967.357i		−	1.27788i	−0.769256	−	0.638941i	$-0.779373\pi$
$757$		−	967.357i		−	1.27788i	0.769256	−	0.638941i	$-0.220627\pi$
$758$	−178.092			−0.234950
$759$	147.498	+	517.117i	0.194332	+	0.681313i
$760$		0			0
$761$			89.7059i			0.117879i	0.998262	+	0.0589395i	$0.0187719\pi$
$761$			89.7059i			0.117879i	−0.998262	+	0.0589395i	$0.981228\pi$
$762$	44.4771	+	155.933i	0.0583689	+	0.204637i
$763$		−	96.6719i		−	0.126700i
$764$		−	2389.69i		−	3.12787i
$765$		0			0
$766$	397.506			0.518937
$767$	−1076.02			−1.40290
$768$	1505.93	−	429.538i	1.96084	−	0.559294i
$769$	−926.219			−1.20445			−0.602223	−	0.798328i	$-0.705718\pi$
$769$	−926.219			−1.20445			−0.602223	+	0.798328i	$0.705718\pi$
$770$		0			0
$771$	436.148	−	124.403i	0.565691	−	0.161353i
$772$			639.454i			0.828308i
$773$	424.125			0.548674			0.274337	−	0.961634i	$-0.411542\pi$
$773$	424.125			0.548674			0.274337	+	0.961634i	$0.411542\pi$
$774$	401.587	+	646.694i	0.518846	+	0.835522i
$775$		0			0
$776$		−	348.548i		−	0.449160i
$777$	−252.193	+	71.9333i	−0.324572	+	0.0925783i
$778$		−	2543.84i		−	3.26972i
$779$		−	1090.48i		−	1.39985i
$780$		0			0
$781$	−494.745			−0.633476
$782$	−405.807			−0.518935
$783$	189.810	+	172.354i	0.242414	+	0.220120i
$784$	−137.081			−0.174848
$785$		0			0
$786$	528.261	+	1852.04i	0.672088	+	2.35629i
$787$			155.889i			0.198080i	0.995083	+	0.0990399i	$0.0315772\pi$
$787$			155.889i			0.198080i	−0.995083	+	0.0990399i	$0.968423\pi$
$788$	−1131.24			−1.43558
$789$	330.006	−	94.1282i	0.418259	−	0.119301i
$790$		0			0
$791$			57.5705i			0.0727820i
$792$	500.893	+	806.612i	0.632441	+	1.01845i
$793$			669.867i			0.844725i
$794$		−	330.771i		−	0.416588i
$795$		0			0
$796$	−717.903			−0.901888
$797$	719.191			0.902373			0.451186	−	0.892430i	$-0.351001\pi$
$797$	719.191			0.902373			0.451186	+	0.892430i	$0.351001\pi$
$798$	123.871	+	434.284i	0.155227	+	0.544215i
$799$	−149.490			−0.187097
$800$		0			0
$801$	604.774	+	973.895i	0.755023	+	1.21585i
$802$			2375.84i			2.96240i
$803$	−538.437			−0.670531
$804$	103.476	+	362.778i	0.128701	+	0.451217i
$805$		0			0
$806$			1172.14i			1.45427i
$807$	3.91828	+	13.7372i	0.00485537	+	0.0170226i
$808$			2029.77i			2.51209i
$809$		−	212.244i		−	0.262353i	−0.991359	−	0.131176i	$-0.958125\pi$
$809$		−	212.244i		−	0.262353i	0.991359	−	0.131176i	$-0.0418755\pi$
$810$		0			0
$811$	1058.66			1.30538			0.652690	−	0.757625i	$-0.273641\pi$
$811$	1058.66			1.30538			0.652690	+	0.757625i	$0.273641\pi$
$812$	−208.311			−0.256541
$813$	1496.42	−	426.826i	1.84061	−	0.525001i
$814$	−812.235			−0.997832
$815$		0			0
$816$	−255.808	+	72.9645i	−0.313490	+	0.0894172i
$817$			391.527i			0.479225i
$818$	60.8792			0.0744244
$819$	−235.579	+	146.291i	−0.287642	+	0.178621i
$820$		0			0
$821$		−	818.571i		−	0.997042i	−0.866878	−	0.498521i	$-0.833877\pi$
$821$		−	818.571i		−	0.997042i	0.866878	−	0.498521i	$-0.166123\pi$
$822$	333.929	−	95.2470i	0.406240	−	0.115872i
$823$			206.850i			0.251336i	0.992072	+	0.125668i	$0.0401074\pi$
$823$			206.850i			0.251336i	−0.992072	+	0.125668i	$0.959893\pi$
$824$			1801.71i			2.18654i
$825$		0			0
$826$	857.047			1.03759
$827$	438.639			0.530398			0.265199	−	0.964194i	$-0.414562\pi$
$827$	438.639			0.530398			0.265199	+	0.964194i	$0.414562\pi$
$828$	1620.59	−	1006.36i	1.95723	−	1.21541i
$829$	−654.804			−0.789872			−0.394936	−	0.918709i	$-0.629233\pi$
$829$	−654.804			−0.789872			−0.394936	+	0.918709i	$0.629233\pi$
$830$		0			0
$831$	−99.6379	−	349.323i	−0.119901	−	0.420364i
$832$			566.257i			0.680598i
$833$	−31.6954			−0.0380497
$834$	−653.812	+	186.488i	−0.783947	+	0.223606i
$835$		0			0
$836$			943.520i			1.12861i
$837$	−521.077	+	573.851i	−0.622553	+	0.685604i
$838$			477.055i			0.569278i
$839$			50.9710i			0.0607521i	0.999539	+	0.0303761i	$0.00967049\pi$
$839$			50.9710i			0.0607521i	−0.999539	+	0.0303761i	$0.990330\pi$
$840$		0			0
$841$	750.830			0.892782
$842$	−1486.48			−1.76542
$843$	−335.121	−	1174.91i	−0.397533	−	1.39372i
$844$	160.996			0.190754
$845$		0			0
$846$	884.988	−	549.564i	1.04609	−	0.649603i
$847$		−	190.055i		−	0.224386i
$848$	297.422			0.350733
$849$	328.026	+	1150.03i	0.386368	+	1.35458i
$850$		0			0
$851$			844.630i			0.992514i
$852$	481.411	+	1687.79i	0.565037	+	1.98098i
$853$		−	883.941i		−	1.03627i	−0.855298	−	0.518137i	$-0.826626\pi$
$853$		−	883.941i		−	1.03627i	0.855298	−	0.518137i	$-0.173374\pi$
$854$		−	533.547i		−	0.624762i
$855$		0			0
$856$	1171.37			1.36843
$857$	556.521			0.649382			0.324691	−	0.945820i	$-0.394740\pi$
$857$	556.521			0.649382			0.324691	+	0.945820i	$0.394740\pi$
$858$	−825.922	+	235.579i	−0.962613	+	0.274568i
$859$	643.078			0.748636			0.374318	−	0.927300i	$-0.377877\pi$
$859$	643.078			0.748636			0.374318	+	0.927300i	$0.377877\pi$
$860$		0			0
$861$	−512.885	+	146.291i	−0.595685	+	0.169908i
$862$		−	1192.87i		−	1.38384i
$863$	−204.892			−0.237419			−0.118709	−	0.992929i	$-0.537876\pi$
$863$	−204.892			−0.237419			−0.118709	+	0.992929i	$0.537876\pi$
$864$	153.805	−	169.382i	0.178015	−	0.196044i
$865$		0			0
$866$		−	558.024i		−	0.644369i
$867$	774.601	−	220.940i	0.893426	−	0.254833i
$868$		−	629.786i		−	0.725559i
$869$			892.237i			1.02674i
$870$		0			0
$871$	−176.620			−0.202778
$872$	−549.747			−0.630444
$873$	109.990	+	177.122i	0.125991	+	0.202888i
$874$	1454.48			1.66416
$875$		0			0
$876$	523.925	+	1836.84i	0.598088	+	2.09685i
$877$			207.210i			0.236272i	0.992997	+	0.118136i	$0.0376919\pi$
$877$			207.210i			0.236272i	−0.992997	+	0.118136i	$0.962308\pi$
$878$	449.015			0.511406
$879$	7.31119	−	2.08538i	0.00831762	−	0.00237245i
$880$		0			0
$881$		−	1391.37i		−	1.57931i	−0.613552	−	0.789654i	$-0.710260\pi$
$881$		−	1391.37i		−	1.57931i	0.613552	−	0.789654i	$-0.289740\pi$
$882$	187.638	−	116.520i	0.212741	−	0.132109i
$883$		−	1091.99i		−	1.23668i	−0.785909	−	0.618342i	$-0.787805\pi$
$883$		−	1091.99i		−	1.23668i	0.785909	−	0.618342i	$-0.212195\pi$
$884$		−	437.219i		−	0.494591i
$885$		0			0
$886$	−691.859			−0.780879
$887$	149.449			0.168488			0.0842439	−	0.996445i	$-0.473153\pi$
$887$	149.449			0.168488			0.0842439	+	0.996445i	$0.473153\pi$
$888$	409.066	+	1434.15i	0.460659	+	1.61504i
$889$	40.7895			0.0458825
$890$		0			0
$891$	−509.077	−	251.831i	−0.571355	−	0.282638i
$892$			1451.35i			1.62707i
$893$	535.797			0.599996
$894$	−564.686	−	1979.75i	−0.631640	−	2.21448i
$895$		0			0
$896$		−	540.700i		−	0.603460i
$897$	244.975	+	858.863i	0.273104	+	0.957483i
$898$			519.231i			0.578209i
$899$		−	272.610i		−	0.303237i
$900$		0			0
$901$	68.7687			0.0763249
$902$	−1651.84			−1.83131
$903$	184.146	−	52.5242i	0.203927	−	0.0581663i
$904$	327.388			0.362155
$905$		0			0
$906$	1034.21	−	294.988i	1.14151	−	0.325594i
$907$		−	593.718i		−	0.654595i	−0.944921	−	0.327297i	$-0.893862\pi$
$907$		−	593.718i		−	0.654595i	0.944921	−	0.327297i	$-0.106138\pi$
$908$	−1472.35			−1.62154
$909$	−640.524	−	1031.47i	−0.704647	−	1.13473i
$910$		0			0
$911$			1133.75i			1.24451i	0.782815	+	0.622254i	$0.213783\pi$
$911$			1133.75i			1.24451i	−0.782815	+	0.622254i	$0.786217\pi$
$912$	916.856	−	261.516i	1.00532	−	0.286750i
$913$			520.871i			0.570504i
$914$		−	428.474i		−	0.468790i
$915$		0			0
$916$	−338.391			−0.369422
$917$	484.464			0.528314
$918$	288.132	−	317.314i	0.313869	−	0.345658i
$919$	684.988			0.745363			0.372681	−	0.927959i	$-0.378438\pi$
$919$	684.988			0.745363			0.372681	+	0.927959i	$0.378438\pi$
$920$		0			0
$921$	70.9620	+	248.787i	0.0770489	+	0.270128i
$922$		−	2110.88i		−	2.28945i
$923$	−821.706			−0.890256
$924$	443.763	−	126.575i	0.480263	−	0.136986i
$925$		0			0
$926$			2233.49i			2.41197i
$927$	−568.556	−	915.571i	−0.613328	−	0.987671i
$928$			80.4654i			0.0867084i
$929$			192.317i			0.207015i	0.994629	+	0.103507i	$0.0330066\pi$
$929$			192.317i			0.207015i	−0.994629	+	0.103507i	$0.966993\pi$
$930$		0			0
$931$	113.601			0.122021
$932$	−3214.58			−3.44912
$933$	−124.893	−	437.867i	−0.133862	−	0.469310i
$934$	2691.52			2.88171
$935$		0			0
$936$	831.918	+	1339.68i	0.888801	+	1.43128i
$937$			1270.28i			1.35569i	0.735206	+	0.677844i	$0.237086\pi$
$937$			1270.28i			1.35569i	−0.735206	+	0.677844i	$0.762914\pi$
$938$	140.677			0.149975
$939$	−261.771	−	917.750i	−0.278777	−	0.977370i
$940$		0			0
$941$			156.951i			0.166791i	0.996517	+	0.0833957i	$0.0265766\pi$
$941$			156.951i			0.166791i	−0.996517	+	0.0833957i	$0.973423\pi$
$942$	−302.119	−	1059.21i	−0.320721	−	1.12442i
$943$			1717.73i			1.82155i
$944$		−	1809.39i		−	1.91673i
$945$		0			0
$946$	593.077			0.626931
$947$	879.945			0.929193			0.464596	−	0.885523i	$-0.346199\pi$
$947$	879.945			0.929193			0.464596	+	0.885523i	$0.346199\pi$
$948$	3043.81	−	868.191i	3.21077	−	0.915813i
$949$	−894.272			−0.942331
$950$		0			0
$951$	−1050.18	+	299.543i	−1.10429	+	0.314977i
$952$			180.243i			0.189331i
$953$	−563.276			−0.591056			−0.295528	−	0.955334i	$-0.595495\pi$
$953$	−563.276			−0.591056			−0.295528	+	0.955334i	$0.595495\pi$
$954$	−407.114	+	252.811i	−0.426744	+	0.265001i
$955$		0			0
$956$			410.619i			0.429518i
$957$	192.088	−	54.7895i	0.200719	−	0.0572513i
$958$			1380.83i			1.44136i
$959$		−	87.3502i		−	0.0910847i
$960$		0			0
$961$	−136.822			−0.142375
$962$	−1349.02			−1.40230
$963$	−595.255	+	369.644i	−0.618126	+	0.383847i
$964$	2696.79			2.79750
$965$		0			0
$966$	−195.122	−	684.081i	−0.201989	−	0.708159i
$967$		−	237.676i		−	0.245787i	−0.992420	−	0.122893i	$-0.960783\pi$
$967$		−	237.676i		−	0.245787i	0.992420	−	0.122893i	$-0.0392173\pi$
$968$	−1080.79			−1.11652
$969$	211.992	−	60.4668i	0.218774	−	0.0624013i
$970$		0			0
$971$		−	1355.00i		−	1.39546i	−0.716359	−	0.697732i	$-0.754192\pi$
$971$		−	1355.00i		−	1.39546i	0.716359	−	0.697732i	$-0.245808\pi$
$972$	−363.748	+	1981.73i	−0.374226	+	2.03882i
$973$			171.026i			0.175772i
$974$			2010.33i			2.06399i
$975$		0			0
$976$	−1126.42			−1.15412
$977$	−493.726			−0.505349			−0.252674	−	0.967551i	$-0.581310\pi$
$977$	−493.726			−0.505349			−0.252674	+	0.967551i	$0.581310\pi$
$978$	−204.714	−	717.711i	−0.209319	−	0.733856i
$979$	893.150			0.912309
$980$		0			0
$981$	279.365	−	173.481i	0.284775	−	0.176841i
$982$			598.797i			0.609773i
$983$	1538.05			1.56465			0.782325	−	0.622870i	$-0.214034\pi$
$983$	1538.05			1.56465			0.782325	+	0.622870i	$0.214034\pi$
$984$	831.918	+	2916.64i	0.845445	+	2.96406i
$985$		0			0
$986$			150.741i			0.152881i
$987$	−71.8783	−	252.000i	−0.0728251	−	0.255319i
$988$			1567.06i			1.58609i
$989$		−	616.731i		−	0.623590i
$990$		0			0
$991$	1514.73			1.52849			0.764243	−	0.644929i	$-0.223113\pi$
$991$	1514.73			1.52849			0.764243	+	0.644929i	$0.223113\pi$
$992$	−243.270			−0.245232
$993$	−445.344	+	127.026i	−0.448483	+	0.127922i
$994$	654.486			0.658437
$995$		0			0
$996$	1776.92	−	506.833i	1.78405	−	0.508868i
$997$		−	1826.43i		−	1.83193i	−0.401260	−	0.915964i	$-0.631428\pi$
$997$		−	1826.43i		−	1.83193i	0.401260	−	0.915964i	$-0.368572\pi$
$998$	−2972.37			−2.97833
$999$	−660.443	−	599.705i	−0.661104	−	0.600306i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	525.3.f.a.449.2		8
3.2	odd	2	inner	525.3.f.a.449.8		8
5.2	odd	4		21.3.b.a.8.1	✓	4
5.3	odd	4		525.3.c.a.176.4		4
5.4	even	2	inner	525.3.f.a.449.7		8
15.2	even	4		21.3.b.a.8.4	yes	4
15.8	even	4		525.3.c.a.176.1		4
15.14	odd	2	inner	525.3.f.a.449.1		8
20.7	even	4		336.3.d.c.113.1		4
35.2	odd	12		147.3.h.e.116.1		8
35.12	even	12		147.3.h.c.116.1		8
35.17	even	12		147.3.h.c.128.4		8
35.27	even	4		147.3.b.f.50.1		4
35.32	odd	12		147.3.h.e.128.4		8
40.27	even	4		1344.3.d.b.449.4		4
40.37	odd	4		1344.3.d.f.449.1		4
45.2	even	12		567.3.r.c.134.4		8
45.7	odd	12		567.3.r.c.134.1		8
45.22	odd	12		567.3.r.c.512.4		8
45.32	even	12		567.3.r.c.512.1		8
60.47	odd	4		336.3.d.c.113.2		4
105.2	even	12		147.3.h.e.116.4		8
105.17	odd	12		147.3.h.c.128.1		8
105.32	even	12		147.3.h.e.128.1		8
105.47	odd	12		147.3.h.c.116.4		8
105.62	odd	4		147.3.b.f.50.4		4
120.77	even	4		1344.3.d.f.449.2		4
120.107	odd	4		1344.3.d.b.449.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
21.3.b.a.8.1	✓	4	5.2	odd	4
21.3.b.a.8.4	yes	4	15.2	even	4
147.3.b.f.50.1		4	35.27	even	4
147.3.b.f.50.4		4	105.62	odd	4
147.3.h.c.116.1		8	35.12	even	12
147.3.h.c.116.4		8	105.47	odd	12
147.3.h.c.128.1		8	105.17	odd	12
147.3.h.c.128.4		8	35.17	even	12
147.3.h.e.116.1		8	35.2	odd	12
147.3.h.e.116.4		8	105.2	even	12
147.3.h.e.128.1		8	105.32	even	12
147.3.h.e.128.4		8	35.32	odd	12
336.3.d.c.113.1		4	20.7	even	4
336.3.d.c.113.2		4	60.47	odd	4
525.3.c.a.176.1		4	15.8	even	4
525.3.c.a.176.4		4	5.3	odd	4
525.3.f.a.449.1		8	15.14	odd	2	inner
525.3.f.a.449.2		8	1.1	even	1	trivial
525.3.f.a.449.7		8	5.4	even	2	inner
525.3.f.a.449.8		8	3.2	odd	2	inner
567.3.r.c.134.1		8	45.7	odd	12
567.3.r.c.134.4		8	45.2	even	12
567.3.r.c.512.1		8	45.32	even	12
567.3.r.c.512.4		8	45.22	odd	12
1344.3.d.b.449.3		4	120.107	odd	4
1344.3.d.b.449.4		4	40.27	even	4
1344.3.d.f.449.1		4	40.37	odd	4
1344.3.d.f.449.2		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)

\(f(q)\)	\(=\)	\(q-3.50592 q^{2} +(-2.88494 + 0.822876i) q^{3} +8.29150 q^{4} +(10.1144 - 2.88494i) q^{6} -2.64575i q^{7} -15.0457 q^{8} +(7.64575 - 4.74789i) q^{9} +O(q^{10})\)	\(q-3.50592 q^{2} +(-2.88494 + 0.822876i) q^{3} +8.29150 q^{4} +(10.1144 - 2.88494i) q^{6} -2.64575i q^{7} -15.0457 q^{8} +(7.64575 - 4.74789i) q^{9} -7.01185i q^{11} +(-23.9205 + 6.82288i) q^{12} -11.6458i q^{13} +9.27580i q^{14} +19.5830 q^{16} +4.52791 q^{17} +(-26.8054 + 16.6458i) q^{18} -16.2288 q^{19} +(2.17712 + 7.63283i) q^{21} +24.5830i q^{22} +25.5635 q^{23} +(43.4059 - 12.3807i) q^{24} +40.8291i q^{26} +(-18.1506 + 19.9889i) q^{27} -21.9373i q^{28} -9.49579i q^{29} +28.7085 q^{31} -8.47380 q^{32} +(5.76988 + 20.2288i) q^{33} -15.8745 q^{34} +(63.3948 - 39.3672i) q^{36} +33.0405i q^{37} +56.8968 q^{38} +(9.58301 + 33.5973i) q^{39} +67.1946i q^{41} +(-7.63283 - 26.7601i) q^{42} -24.1255i q^{43} -58.1388i q^{44} -89.6235 q^{46} -33.0153 q^{47} +(-56.4958 + 16.1144i) q^{48} -7.00000 q^{49} +(-13.0627 + 3.72591i) q^{51} -96.5608i q^{52} +15.1877 q^{53} +(63.6346 - 70.0795i) q^{54} +39.8071i q^{56} +(46.8190 - 13.3542i) q^{57} +33.2915i q^{58} -92.3960i q^{59} -57.5203 q^{61} -100.650 q^{62} +(-12.5617 - 20.2288i) q^{63} -48.6235 q^{64} +(-20.2288 - 70.9205i) q^{66} -15.1660i q^{67} +37.5432 q^{68} +(-73.7490 + 21.0355i) q^{69} -70.5584i q^{71} +(-115.036 + 71.4353i) q^{72} -76.7895i q^{73} -115.838i q^{74} -134.561 q^{76} -18.5516 q^{77} +(-33.5973 - 117.790i) q^{78} -127.247 q^{79} +(35.9150 - 72.6024i) q^{81} -235.579i q^{82} -74.2844 q^{83} +(18.0516 + 63.2876i) q^{84} +84.5821i q^{86} +(7.81385 + 27.3948i) q^{87} +105.498i q^{88} +127.377i q^{89} -30.8118 q^{91} +211.959 q^{92} +(-82.8223 + 23.6235i) q^{93} +115.749 q^{94} +(24.4464 - 6.97288i) q^{96} +23.1660i q^{97} +24.5415 q^{98} +(-33.2915 - 53.6108i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 24 q^{4} + 28 q^{6} + 40 q^{9}+O(q^{10}) \) 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

Fields

Representations

Groups

Database

Properties

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