LMFDB - Embedded newform 171.4.y.a.53.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [171,4,Mod(53,171)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(171, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 11]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("171.53");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 171 = 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	171.y (of order $18$, degree $6$, 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:	$10.0893266110$
Analytic rank:	$0$
Dimension:	$120$
Relative dimension:	$20$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			53.9
Character	$\chi$	$=$	171.53
Dual form			171.4.y.a.71.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.02676 - 0.373709i) q^{2} +(-5.21378 - 4.37488i) q^{4} +(-4.49187 - 5.35320i) q^{5} +(9.55306 - 16.5464i) q^{7} +(8.08896 + 14.0105i) q^{8} +O(q^{10})$	\(q+(-1.02676 - 0.373709i) q^{2} +(-5.21378 - 4.37488i) q^{4} +(-4.49187 - 5.35320i) q^{5} +(9.55306 - 16.5464i) q^{7} +(8.08896 + 14.0105i) q^{8} +(2.61152 + 7.17509i) q^{10} +(21.7010 - 12.5291i) q^{11} +(-55.1705 - 9.72805i) q^{13} +(-15.9922 + 13.4191i) q^{14} +(6.38540 + 36.2134i) q^{16} +(-47.2141 + 129.720i) q^{17} +(-51.0021 - 65.2517i) q^{19} +47.5618i q^{20} +(-26.9639 + 4.75447i) q^{22} +(-74.2193 + 88.4512i) q^{23} +(13.2262 - 75.0092i) q^{25} +(53.0113 + 30.6061i) q^{26} +(-122.196 + 44.4758i) q^{28} +(-8.46316 + 3.08034i) q^{29} +(-150.551 - 86.9205i) q^{31} +(29.4512 - 167.026i) q^{32} +(96.9548 - 115.546i) q^{34} +(-131.487 + 23.1847i) q^{35} +419.365i q^{37} +(27.9816 + 86.0576i) q^{38} +(38.6664 - 106.235i) q^{40} +(61.5401 + 349.011i) q^{41} +(15.2144 - 12.7664i) q^{43} +(-167.958 - 29.6155i) q^{44} +(109.260 - 63.0814i) q^{46} +(-132.663 - 364.487i) q^{47} +(-11.0220 - 19.0907i) q^{49} +(-41.6117 + 72.0735i) q^{50} +(245.088 + 292.085i) q^{52} +(-202.318 - 169.765i) q^{53} +(-164.549 - 59.8909i) q^{55} +309.097 q^{56} +9.84076 q^{58} +(-75.3603 - 27.4289i) q^{59} +(-287.655 - 241.371i) q^{61} +(122.096 + 145.508i) q^{62} +(54.4300 - 94.2756i) q^{64} +(195.743 + 339.036i) q^{65} +(162.434 + 446.284i) q^{67} +(813.672 - 469.774i) q^{68} +(143.670 + 25.3329i) q^{70} +(371.275 - 311.537i) q^{71} +(-97.0717 - 550.521i) q^{73} +(156.720 - 430.586i) q^{74} +(-19.5547 + 563.337i) q^{76} -478.765i q^{77} +(999.614 - 176.259i) q^{79} +(165.175 - 196.848i) q^{80} +(67.2419 - 381.348i) q^{82} +(-1116.92 - 644.856i) q^{83} +(906.494 - 329.937i) q^{85} +(-20.3923 + 7.42221i) q^{86} +(351.078 + 202.695i) q^{88} +(20.8524 - 118.260i) q^{89} +(-688.012 + 819.940i) q^{91} +(773.927 - 136.464i) q^{92} +423.817i q^{94} +(-120.211 + 566.127i) q^{95} +(449.849 - 1235.95i) q^{97} +(4.18257 + 23.7205i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 120 q - 36 q^{4}+O(q^{10}) $ 120 * q - 36 * q^4	$ 120 q - 36 q^{4} - 180 q^{10} - 156 q^{13} + 180 q^{16} + 924 q^{19} + 432 q^{22} - 360 q^{25} - 624 q^{28} + 324 q^{34} + 1440 q^{40} + 1524 q^{43} + 3888 q^{46} - 3228 q^{49} - 6000 q^{52} - 4464 q^{55} + 5616 q^{58} - 5736 q^{61} - 4524 q^{64} + 372 q^{67} + 7848 q^{70} - 276 q^{73} + 4320 q^{76} + 10536 q^{79} + 3960 q^{82} - 11592 q^{85} - 11664 q^{88} - 120 q^{91} + 5904 q^{97}+O(q^{100}) $ 120 * q - 36 * q^4 - 180 * q^10 - 156 * q^13 + 180 * q^16 + 924 * q^19 + 432 * q^22 - 360 * q^25 - 624 * q^28 + 324 * q^34 + 1440 * q^40 + 1524 * q^43 + 3888 * q^46 - 3228 * q^49 - 6000 * q^52 - 4464 * q^55 + 5616 * q^58 - 5736 * q^61 - 4524 * q^64 + 372 * q^67 + 7848 * q^70 - 276 * q^73 + 4320 * q^76 + 10536 * q^79 + 3960 * q^82 - 11592 * q^85 - 11664 * q^88 - 120 * q^91 + 5904 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/171\mathbb{Z}\right)^\times$.

$n$	$20$	$154$
$\chi(n)$	$-1$	$e\left(\frac{11}{18}\right)$

Coefficient data

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

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

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

$2$	−1.02676	−	0.373709i	−0.363013	−	0.132126i	0.154073	−	0.988060i	$-0.450761\pi$
$2$	−1.02676	−	0.373709i	−0.363013	−	0.132126i	−0.517086	+	0.855933i	$0.672983\pi$
$3$		0			0
$3$		0			0
$4$	−5.21378	−	4.37488i	−0.651723	−	0.546861i
$5$	−4.49187	−	5.35320i	−0.401765	−	0.478805i	0.526792	−	0.849994i	$-0.323395\pi$
$5$	−4.49187	−	5.35320i	−0.401765	−	0.478805i	−0.928557	+	0.371189i	$0.878950\pi$
$6$		0			0
$7$	9.55306	−	16.5464i	0.515817	−	0.893421i	−0.484015	−	0.875060i	$-0.660822\pi$
$7$	9.55306	−	16.5464i	0.515817	−	0.893421i	0.999831	−	0.0183611i	$-0.00584486\pi$
$8$	8.08896	+	14.0105i	0.357485	+	0.619182i
$9$		0			0
$10$	2.61152	+	7.17509i	0.0825834	+	0.226896i
$11$	21.7010	−	12.5291i	0.594828	−	0.343424i	−0.172176	−	0.985066i	$-0.555080\pi$
$11$	21.7010	−	12.5291i	0.594828	−	0.343424i	0.767004	+	0.641642i	$0.221747\pi$
$12$		0			0
$13$	−55.1705	−	9.72805i	−1.17704	−	0.207544i	−0.449291	−	0.893385i	$-0.648323\pi$
$13$	−55.1705	−	9.72805i	−1.17704	−	0.207544i	−0.727751	+	0.685841i	$0.759434\pi$
$14$	−15.9922	+	13.4191i	−0.305293	+	0.256171i
$15$		0			0
$16$	6.38540	+	36.2134i	0.0997719	+	0.565834i
$17$	−47.2141	+	129.720i	−0.673594	+	1.85068i	−0.173198	+	0.984887i	$0.555410\pi$
$17$	−47.2141	+	129.720i	−0.673594	+	1.85068i	−0.500395	+	0.865797i	$0.666812\pi$
$18$		0			0
$19$	−51.0021	−	65.2517i	−0.615826	−	0.787883i
$19$	−51.0021	−	65.2517i	−0.615826	−	0.787883i
$20$			47.5618i			0.531758i
$21$		0			0
$22$	−26.9639	+	4.75447i	−0.261306	+	0.0460752i
$23$	−74.2193	+	88.4512i	−0.672861	+	0.801884i	−0.989170	−	0.146772i	$-0.953112\pi$
$23$	−74.2193	+	88.4512i	−0.672861	+	0.801884i	0.316310	+	0.948656i	$0.397556\pi$
$24$		0			0
$25$	13.2262	−	75.0092i	0.105809	−	0.600074i
$26$	53.0113	+	30.6061i	0.399860	+	0.230859i
$27$		0			0
$28$	−122.196	+	44.4758i	−0.824747	+	0.300183i
$29$	−8.46316	+	3.08034i	−0.0541921	+	0.0197243i	−0.368974	−	0.929440i	$-0.620291\pi$
$29$	−8.46316	+	3.08034i	−0.0541921	+	0.0197243i	0.314782	+	0.949164i	$0.398069\pi$
$30$		0			0
$31$	−150.551	−	86.9205i	−0.872249	−	0.503593i	−0.00415372	−	0.999991i	$-0.501322\pi$
$31$	−150.551	−	86.9205i	−0.872249	−	0.503593i	−0.868095	+	0.496398i	$0.834656\pi$
$32$	29.4512	−	167.026i	0.162696	−	0.922696i
$33$		0			0
$34$	96.9548	−	115.546i	0.489047	−	0.582824i
$35$	−131.487	+	23.1847i	−0.635011	+	0.111970i
$36$		0			0
$37$			419.365i			1.86333i	0.363321	+	0.931664i	$0.381643\pi$
$37$			419.365i			1.86333i	−0.363321	+	0.931664i	$0.618357\pi$
$38$	27.9816	+	86.0576i	0.119453	+	0.367378i
$39$		0			0
$40$	38.6664	−	106.235i	0.152842	−	0.419931i
$41$	61.5401	+	349.011i	0.234413	+	1.32942i	0.843846	+	0.536586i	$0.180286\pi$
$41$	61.5401	+	349.011i	0.234413	+	1.32942i	−0.609433	+	0.792838i	$0.708603\pi$
$42$		0			0
$43$	15.2144	−	12.7664i	0.0539574	−	0.0452756i	−0.615410	−	0.788207i	$-0.711010\pi$
$43$	15.2144	−	12.7664i	0.0539574	−	0.0452756i	0.669368	+	0.742931i	$0.266565\pi$
$44$	−167.958	−	29.6155i	−0.575468	−	0.101471i
$45$		0			0
$46$	109.260	−	63.0814i	0.350207	−	0.202192i
$47$	−132.663	−	364.487i	−0.411719	−	1.13119i	−0.956276	−	0.292466i	$-0.905524\pi$
$47$	−132.663	−	364.487i	−0.411719	−	1.13119i	0.544557	−	0.838724i	$-0.316698\pi$
$48$		0			0
$49$	−11.0220	−	19.0907i	−0.0321342	−	0.0556580i
$50$	−41.6117	+	72.0735i	−0.117696	+	0.203855i
$51$		0			0
$52$	245.088	+	292.085i	0.653608	+	0.778939i
$53$	−202.318	−	169.765i	−0.524349	−	0.439981i	0.341796	−	0.939774i	$-0.388965\pi$
$53$	−202.318	−	169.765i	−0.524349	−	0.439981i	−0.866145	+	0.499793i	$0.833409\pi$
$54$		0			0
$55$	−164.549	−	59.8909i	−0.403414	−	0.146831i
$56$	309.097			0.737587
$57$		0			0
$58$	9.84076			0.0222785
$59$	−75.3603	−	27.4289i	−0.166289	−	0.0605244i	0.257534	−	0.966269i	$-0.417090\pi$
$59$	−75.3603	−	27.4289i	−0.166289	−	0.0605244i	−0.423823	+	0.905745i	$0.639312\pi$
$60$		0			0
$61$	−287.655	−	241.371i	−0.603778	−	0.506630i	0.288880	−	0.957365i	$-0.406717\pi$
$61$	−287.655	−	241.371i	−0.603778	−	0.506630i	−0.892657	+	0.450736i	$0.851162\pi$
$62$	122.096	+	145.508i	0.250100	+	0.298058i
$63$		0			0
$64$	54.4300	−	94.2756i	0.106309	−	0.184132i
$65$	195.743	+	339.036i	0.373521	+	0.646958i
$66$		0			0
$67$	162.434	+	446.284i	0.296186	+	0.813765i	0.995128	+	0.0985871i	$0.0314323\pi$
$67$	162.434	+	446.284i	0.296186	+	0.813765i	−0.698942	+	0.715178i	$0.746345\pi$
$68$	813.672	−	469.774i	1.45106	−	0.837771i
$69$		0			0
$70$	143.670	+	25.3329i	0.245312	+	0.0432551i
$71$	371.275	−	311.537i	0.620595	−	0.520741i	−0.277396	−	0.960756i	$-0.589471\pi$
$71$	371.275	−	311.537i	0.620595	−	0.520741i	0.897991	+	0.440015i	$0.145027\pi$
$72$		0			0
$73$	−97.0717	−	550.521i	−0.155635	−	0.882652i	−0.958203	−	0.286091i	$-0.907644\pi$
$73$	−97.0717	−	550.521i	−0.155635	−	0.882652i	0.802567	−	0.596562i	$-0.203467\pi$
$74$	156.720	−	430.586i	0.246194	−	0.676413i
$75$		0			0
$76$	−19.5547	+	563.337i	−0.0295141	+	0.850252i
$77$		−	478.765i		−	0.708576i
$78$		0			0
$79$	999.614	−	176.259i	1.42361	−	0.251021i	0.591803	−	0.806083i	$-0.298416\pi$
$79$	999.614	−	176.259i	1.42361	−	0.251021i	0.831809	+	0.555061i	$0.187305\pi$
$80$	165.175	−	196.848i	0.230839	−	0.275104i
$81$		0			0
$82$	67.2419	−	381.348i	0.0905564	−	0.513571i
$83$	−1116.92	−	644.856i	−1.47709	−	0.852797i	−0.477423	−	0.878673i	$-0.658429\pi$
$83$	−1116.92	−	644.856i	−1.47709	−	0.852797i	−0.999665	+	0.0258760i	$0.991763\pi$
$84$		0			0
$85$	906.494	−	329.937i	1.15674	−	0.421020i
$86$	−20.3923	+	7.42221i	−0.0255693	+	0.00930648i
$87$		0			0
$88$	351.078	+	202.695i	0.425284	+	0.245538i
$89$	20.8524	−	118.260i	0.0248354	−	0.140848i	−0.969869	−	0.243628i	$-0.921662\pi$
$89$	20.8524	−	118.260i	0.0248354	−	0.140848i	0.994704	+	0.102779i	$0.0327736\pi$
$90$		0			0
$91$	−688.012	+	819.940i	−0.792563	+	0.944540i
$92$	773.927	−	136.464i	0.877038	−	0.154645i
$93$		0			0
$94$			423.817i			0.465036i
$95$	−120.211	+	566.127i	−0.129825	+	0.611404i
$96$		0			0
$97$	449.849	−	1235.95i	0.470879	−	1.29373i	−0.446167	−	0.894950i	$-0.647211\pi$
$97$	449.849	−	1235.95i	0.470879	−	1.29373i	0.917046	−	0.398780i	$-0.130566\pi$
$98$	4.18257	+	23.7205i	0.00431126	+	0.0244504i
$99$		0			0
$100$	−397.115	+	333.219i	−0.397115	+	0.333219i
$101$	−1155.05	−	203.666i	−1.13793	−	0.200649i	−0.427233	−	0.904142i	$-0.640511\pi$
$101$	−1155.05	−	203.666i	−1.13793	−	0.200649i	−0.710702	+	0.703493i	$0.751623\pi$
$102$		0			0
$103$	−712.793	+	411.531i	−0.681880	+	0.393684i	−0.800563	−	0.599249i	$-0.795466\pi$
$103$	−712.793	+	411.531i	−0.681880	+	0.393684i	0.118683	+	0.992932i	$0.462133\pi$
$104$	−309.977	−	851.656i	−0.292267	−	0.802998i
$105$		0			0
$106$	144.288	+	249.915i	0.132213	+	0.228999i
$107$	51.9112	−	89.9128i	0.0469013	−	0.0812355i	−0.841622	−	0.540068i	$-0.818399\pi$
$107$	51.9112	−	89.9128i	0.0469013	−	0.0812355i	0.888523	+	0.458832i	$0.151732\pi$
$108$		0			0
$109$	−532.921	−	635.110i	−0.468299	−	0.558097i	0.479262	−	0.877672i	$-0.340904\pi$
$109$	−532.921	−	635.110i	−0.468299	−	0.558097i	−0.947561	+	0.319575i	$0.896460\pi$
$110$	146.570	+	122.987i	0.127045	+	0.106603i
$111$		0			0
$112$	660.201	+	240.294i	0.556992	+	0.202729i
$113$	659.556			0.549078			0.274539	−	0.961576i	$-0.411475\pi$
$113$	659.556			0.549078			0.274539	+	0.961576i	$0.411475\pi$
$114$		0			0
$115$	806.880			0.654278
$116$	57.6012	+	20.9651i	0.0461047	+	0.0167807i
$117$		0			0
$118$	67.1262	+	56.3256i	0.0523684	+	0.0439423i
$119$	1695.35	+	2020.44i	1.30599	+	1.55642i
$120$		0			0
$121$	−351.544	+	608.891i	−0.264120	+	0.457469i
$122$	205.149	+	355.329i	0.152240	+	0.263688i
$123$		0			0
$124$	404.672	+	1111.83i	0.293069	+	0.805201i
$125$	−1217.43	+	702.886i	−0.871125	+	0.502944i
$126$		0			0
$127$	−1670.80	−	294.606i	−1.16740	−	0.205843i	−0.443838	−	0.896107i	$-0.646383\pi$
$127$	−1670.80	−	294.606i	−1.16740	−	0.205843i	−0.723558	+	0.690264i	$0.757494\pi$
$128$	−1130.50	+	948.604i	−0.780650	+	0.655043i
$129$		0			0
$130$	−74.2792	−	421.258i	−0.0501132	−	0.284206i
$131$	205.409	−	564.357i	0.136998	−	0.376398i	−0.852155	−	0.523290i	$-0.824705\pi$
$131$	205.409	−	564.357i	0.136998	−	0.376398i	0.989153	+	0.146892i	$0.0469269\pi$
$132$		0			0
$133$	−1566.91	+	220.547i	−1.02156	+	0.143788i
$134$		−	518.928i		−	0.334542i
$135$		0			0
$136$	−2199.35	+	387.805i	−1.38671	+	0.244514i
$137$	−1061.49	+	1265.03i	−0.661964	+	0.788897i	−0.987666	−	0.156575i	$-0.949955\pi$
$137$	−1061.49	+	1265.03i	−0.661964	+	0.788897i	0.325703	+	0.945472i	$0.394399\pi$
$138$		0			0
$139$	221.349	−	1255.33i	0.135069	−	0.766013i	−0.839743	−	0.542984i	$-0.817294\pi$
$139$	221.349	−	1255.33i	0.135069	−	0.766013i	0.974812	−	0.223029i	$-0.0715944\pi$
$140$	786.977	+	454.361i	0.475083	+	0.274290i
$141$		0			0
$142$	−497.633	+	181.124i	−0.294088	+	0.107039i
$143$	−1319.14	+	480.128i	−0.771413	+	0.280771i
$144$		0			0
$145$	54.5051	+	31.4685i	0.0312166	+	0.0180229i
$146$	−106.066	+	601.528i	−0.0601236	+	0.340978i
$147$		0			0
$148$	1834.67	−	2186.48i	1.01898	−	1.21437i
$149$	−1369.62	+	241.501i	−0.753044	+	0.132782i	−0.536978	−	0.843597i	$-0.680434\pi$
$149$	−1369.62	+	241.501i	−0.753044	+	0.132782i	−0.216067	+	0.976379i	$0.569323\pi$
$150$		0			0
$151$		−	1135.54i		−	0.611977i	−0.952035	−	0.305989i	$-0.901013\pi$
$151$		−	1135.54i		−	0.611977i	0.952035	−	0.305989i	$-0.0989869\pi$
$152$	501.654	−	1242.38i	0.267694	−	0.662964i
$153$		0			0
$154$	−178.919	+	491.575i	−0.0936213	+	0.257222i
$155$	210.951	+	1196.36i	0.109316	+	0.619963i
$156$		0			0
$157$	413.929	−	347.328i	0.210415	−	0.176559i	−0.531489	−	0.847065i	$-0.678367\pi$
$157$	413.929	−	347.328i	0.210415	−	0.176559i	0.741904	+	0.670506i	$0.233923\pi$
$158$	−1092.23	−	192.590i	−0.549957	−	0.0969722i
$159$		0			0
$160$	−1026.41	+	592.600i	−0.507157	+	0.292807i
$161$	754.525	+	2073.04i	0.369347	+	1.01477i
$162$		0			0
$163$	−298.203	−	516.504i	−0.143295	−	0.248194i	0.785440	−	0.618937i	$-0.212436\pi$
$163$	−298.203	−	516.504i	−0.143295	−	0.248194i	−0.928736	+	0.370743i	$0.879103\pi$
$164$	1206.03	−	2088.90i	0.574237	−	0.994607i
$165$		0			0
$166$	905.821	+	1079.52i	0.423526	+	0.504739i
$167$	1506.45	+	1264.06i	0.698041	+	0.585726i	0.921216	−	0.389053i	$-0.127198\pi$
$167$	1506.45	+	1264.06i	0.698041	+	0.585726i	−0.223175	+	0.974778i	$0.571642\pi$
$168$		0			0
$169$	884.647	+	321.985i	0.402661	+	0.146557i
$170$	−1054.05			−0.475541
$171$		0			0
$172$	−135.176			−0.0599247
$173$	−3837.95	−	1396.90i	−1.68667	−	0.613897i	−0.692470	−	0.721447i	$-0.743477\pi$
$173$	−3837.95	−	1396.90i	−1.68667	−	0.613897i	−0.994200	+	0.107550i	$0.965700\pi$
$174$		0			0
$175$	−1114.78	−	935.413i	−0.481540	−	0.404060i
$176$	592.291	+	705.865i	0.253668	+	0.302310i
$177$		0			0
$178$	−65.6051	+	113.631i	−0.0276253	+	0.0478485i
$179$	773.834	+	1340.32i	0.323123	+	0.559666i	0.981131	−	0.193345i	$-0.0619338\pi$
$179$	773.834	+	1340.32i	0.323123	+	0.559666i	−0.658007	+	0.753012i	$0.728600\pi$
$180$		0			0
$181$	−540.228	−	1484.26i	−0.221850	−	0.609528i	0.777974	−	0.628297i	$-0.216248\pi$
$181$	−540.228	−	1484.26i	−0.221850	−	0.609528i	−0.999824	+	0.0187689i	$0.994025\pi$
$182$	1012.84	−	584.763i	0.412509	−	0.238162i
$183$		0			0
$184$	−1839.60	−	324.371i	−0.737050	−	0.129962i
$185$	2244.94	−	1883.73i	0.892170	−	0.748620i
$186$		0			0
$187$	600.675	+	3406.60i	0.234897	+	1.33217i
$188$	−902.916	+	2480.74i	−0.350276	+	0.962376i
$189$		0			0
$190$	334.994	−	536.351i	0.127911	−	0.204795i
$191$		−	1653.75i		−	0.626497i	−0.949671	−	0.313248i	$-0.898583\pi$
$191$		−	1653.75i		−	0.626497i	0.949671	−	0.313248i	$-0.101417\pi$
$192$		0			0
$193$	1860.16	−	327.996i	0.693768	−	0.122330i	0.184364	−	0.982858i	$-0.440977\pi$
$193$	1860.16	−	327.996i	0.693768	−	0.122330i	0.509403	+	0.860528i	$0.329866\pi$
$194$	−923.772	+	1100.91i	−0.341871	+	0.407426i
$195$		0			0
$196$	−26.0532	+	147.755i	−0.00949460	+	0.0538465i
$197$	1372.16	+	792.214i	0.496254	+	0.286512i	0.727165	−	0.686462i	$-0.240837\pi$
$197$	1372.16	+	792.214i	0.496254	+	0.286512i	−0.230911	+	0.972975i	$0.574171\pi$
$198$		0			0
$199$	−2001.13	+	728.352i	−0.712846	+	0.259455i	−0.672886	−	0.739746i	$-0.734945\pi$
$199$	−2001.13	+	728.352i	−0.712846	+	0.259455i	−0.0399607	+	0.999201i	$0.512723\pi$
$200$	1157.90	−	421.442i	0.409380	−	0.149002i
$201$		0			0
$202$	1109.84	+	640.766i	0.386575	+	0.223189i
$203$	−29.8806	+	169.461i	−0.0103311	+	0.0585905i
$204$		0			0
$205$	1591.90	−	1897.15i	0.542355	−	0.646354i
$206$	885.659	−	156.165i	0.299547	−	0.0528183i
$207$		0			0
$208$		−	2060.03i		−	0.686718i
$209$	−1924.34	−	777.019i	−0.636888	−	0.257165i
$210$		0			0
$211$	747.181	−	2052.86i	0.243782	−	0.669786i	−0.756100	−	0.654456i	$-0.772898\pi$
$211$	747.181	−	2052.86i	0.243782	−	0.669786i	0.999882	−	0.0153302i	$-0.00487996\pi$
$212$	312.140	+	1770.23i	0.101122	+	0.573491i
$213$		0			0
$214$	−86.9014	+	72.9189i	−0.0277591	+	0.0232927i
$215$	−136.682	−	24.1007i	−0.0433564	−	0.00764490i
$216$		0			0
$217$	−2876.44	+	1660.71i	−0.899841	+	0.519523i
$218$	309.834	+	851.261i	0.0962595	+	0.264471i
$219$		0			0
$220$	595.907	+	1032.14i	0.182618	+	0.316304i
$221$	3866.74	−	6697.40i	1.17695	−	2.03853i
$222$		0			0
$223$	272.714	+	325.008i	0.0818937	+	0.0975971i	0.805435	−	0.592684i	$-0.201932\pi$
$223$	272.714	+	325.008i	0.0818937	+	0.0975971i	−0.723542	+	0.690281i	$0.757487\pi$
$224$	−2482.33	−	2082.92i	−0.740435	−	0.621298i
$225$		0			0
$226$	−677.203	−	246.482i	−0.199323	−	0.0725475i
$227$	3939.83			1.15196			0.575982	−	0.817463i	$-0.304620\pi$
$227$	3939.83			1.15196			0.575982	+	0.817463i	$0.304620\pi$
$228$		0			0
$229$	1301.54			0.375580			0.187790	−	0.982209i	$-0.439867\pi$
$229$	1301.54			0.375580			0.187790	+	0.982209i	$0.439867\pi$
$230$	−828.470	−	301.538i	−0.237512	−	0.0864472i
$231$		0			0
$232$	−111.615	−	93.6564i	−0.0315858	−	0.0265036i
$233$	−2074.81	−	2472.66i	−0.583371	−	0.695234i	0.390947	−	0.920413i	$-0.372148\pi$
$233$	−2074.81	−	2472.66i	−0.583371	−	0.695234i	−0.974317	+	0.225179i	$0.927703\pi$
$234$		0			0
$235$	−1355.27	+	2347.40i	−0.376205	+	0.651606i
$236$	272.914	+	472.701i	0.0752762	+	0.130382i
$237$		0			0
$238$	−985.657	−	2708.07i	−0.268448	−	0.737555i
$239$	−5423.52	+	3131.27i	−1.46786	+	0.847469i	−0.999352	−	0.0359911i	$-0.988541\pi$
$239$	−5423.52	+	3131.27i	−1.46786	+	0.847469i	−0.468507	+	0.883460i	$0.655208\pi$
$240$		0			0
$241$	7096.32	+	1251.27i	1.89674	+	0.334446i	0.995168	−	0.0981849i	$-0.0313036\pi$
$241$	7096.32	+	1251.27i	1.89674	+	0.334446i	0.901571	+	0.432631i	$0.142415\pi$
$242$	588.498	−	493.808i	0.156323	−	0.131170i
$243$		0			0
$244$	443.800	+	2516.91i	0.116440	+	0.660365i
$245$	−52.6869	+	144.756i	−0.0137389	+	0.0377474i
$246$		0			0
$247$	2179.04	+	4096.12i	0.561332	+	1.05518i
$248$		−	2812.39i		−	0.720108i
$249$		0			0
$250$	1512.68	−	266.727i	0.382682	−	0.0674772i
$251$	4223.49	−	5033.36i	1.06209	−	1.26575i	0.0994256	−	0.995045i	$-0.468299\pi$
$251$	4223.49	−	5033.36i	1.06209	−	1.26575i	0.962663	−	0.270703i	$-0.0872561\pi$
$252$		0			0
$253$	−502.423	+	2849.38i	−0.124850	+	0.708060i
$254$	1605.40	+	926.881i	0.396583	+	0.228967i
$255$		0			0
$256$	696.893	−	253.648i	0.170140	−	0.0619258i
$257$	−3525.46	+	1283.16i	−0.855690	+	0.311446i	−0.732358	−	0.680920i	$-0.761580\pi$
$257$	−3525.46	+	1283.16i	−0.855690	+	0.311446i	−0.123332	+	0.992365i	$0.539358\pi$
$258$		0			0
$259$	6938.97	+	4006.22i	1.66474	+	0.961136i
$260$	462.684	−	2624.01i	0.110363	−	0.625901i
$261$		0			0
$262$	−421.811	+	502.694i	−0.0994639	+	0.118537i
$263$	5217.46	−	919.979i	1.22328	−	0.215697i	0.475543	−	0.879693i	$-0.342252\pi$
$263$	5217.46	−	919.979i	1.22328	−	0.215697i	0.747737	+	0.663996i	$0.231141\pi$
$264$		0			0
$265$			1845.61i			0.427829i
$266$	1691.25	+	359.119i	0.389840	+	0.0827781i
$267$		0			0
$268$	1105.54	−	3037.46i	0.251985	−	0.692322i
$269$	−1004.71	−	5698.00i	−0.227726	−	1.29150i	−0.857404	−	0.514643i	$-0.827924\pi$
$269$	−1004.71	−	5698.00i	−0.227726	−	1.29150i	0.629678	−	0.776856i	$-0.283187\pi$
$270$		0			0
$271$	−1239.10	+	1039.73i	−0.277750	+	0.233060i	−0.771012	−	0.636821i	$-0.780249\pi$
$271$	−1239.10	+	1039.73i	−0.277750	+	0.233060i	0.493262	+	0.869881i	$0.335805\pi$
$272$	−4999.07	−	881.471i	−1.11439	−	0.196496i
$273$		0			0
$274$	1562.64	−	902.193i	0.344536	−	0.198918i
$275$	−652.777	−	1793.49i	−0.143141	−	0.393278i
$276$		0			0
$277$	−1703.14	−	2949.93i	−0.369430	−	0.639871i	0.620047	−	0.784565i	$-0.287114\pi$
$277$	−1703.14	−	2949.93i	−0.369430	−	0.639871i	−0.989476	+	0.144694i	$0.953780\pi$
$278$	−696.400	+	1206.20i	−0.150242	+	0.260227i
$279$		0			0
$280$	−1388.43	−	1654.66i	−0.296337	−	0.353160i
$281$	−1712.42	−	1436.89i	−0.363538	−	0.305045i	0.442661	−	0.896689i	$-0.354035\pi$
$281$	−1712.42	−	1436.89i	−0.363538	−	0.305045i	−0.806199	+	0.591644i	$0.798479\pi$
$282$		0			0
$283$	1210.23	+	440.489i	0.254208	+	0.0925242i	0.465981	−	0.884795i	$-0.345702\pi$
$283$	1210.23	+	440.489i	0.254208	+	0.0925242i	−0.211773	+	0.977319i	$0.567924\pi$
$284$	−3298.69			−0.689229
$285$		0			0
$286$	1533.86			0.317131
$287$	6362.77	+	2315.86i	1.30865	+	0.476309i
$288$		0			0
$289$	−10834.4	−	9091.17i	−2.20526	−	1.85043i
$290$	−44.2034	−	52.6796i	−0.00895074	−	0.0106671i
$291$		0			0
$292$	−1902.36	+	3294.98i	−0.381257	+	0.660356i
$293$	4227.55	+	7322.32i	0.842921	+	1.45998i	0.887414	+	0.460972i	$0.152499\pi$
$293$	4227.55	+	7322.32i	0.842921	+	1.45998i	−0.0444934	+	0.999010i	$0.514167\pi$
$294$		0			0
$295$	191.676	+	526.626i	0.0378299	+	0.103937i
$296$	−5875.51	+	3392.23i	−1.15374	+	0.666112i
$297$		0			0
$298$	1496.52	+	263.876i	0.290909	+	0.0512951i
$299$	4955.18	−	4157.89i	0.958412	−	0.804203i
$300$		0			0
$301$	−65.8935	−	373.700i	−0.0126181	−	0.0715606i
$302$	−424.360	+	1165.92i	−0.0808581	+	0.222156i
$303$		0			0
$304$	2037.32	−	2263.62i	0.384369	−	0.427064i
$305$			2624.08i			0.492638i
$306$		0			0
$307$	1792.01	−	315.979i	0.333144	−	0.0587423i	−0.00457421	−	0.999990i	$-0.501456\pi$
$307$	1792.01	−	315.979i	0.333144	−	0.0587423i	0.337718	+	0.941247i	$0.390345\pi$
$308$	−2094.54	+	2496.18i	−0.387492	+	0.461795i
$309$		0			0
$310$	230.496	−	1307.21i	0.0422300	−	0.239498i
$311$	−1489.75	−	860.109i	−0.271628	−	0.156824i	0.358000	−	0.933722i	$-0.383459\pi$
$311$	−1489.75	−	860.109i	−0.271628	−	0.156824i	−0.629627	+	0.776898i	$0.716792\pi$
$312$		0			0
$313$	1506.16	−	548.196i	0.271990	−	0.0989964i	−0.202424	−	0.979298i	$-0.564882\pi$
$313$	1506.16	−	548.196i	0.271990	−	0.0989964i	0.474415	+	0.880302i	$0.342660\pi$
$314$	−554.804	+	201.932i	−0.0997114	+	0.0362920i
$315$		0			0
$316$	−5982.88	−	3454.22i	−1.06507	−	0.614921i
$317$	−545.188	+	3091.91i	−0.0965956	+	0.547821i	0.897651	+	0.440707i	$0.145272\pi$
$317$	−545.188	+	3091.91i	−0.0965956	+	0.547821i	−0.994247	+	0.107114i	$0.965839\pi$
$318$		0			0
$319$	−145.065	+	172.882i	−0.0254612	+	0.0303434i
$320$	−749.168	+	132.099i	−0.130874	+	0.0230767i
$321$		0			0
$322$		−	2410.48i		−	0.417177i
$323$	10872.4	−	3535.17i	1.87294	−	0.608986i
$324$		0			0
$325$	−1459.39	+	4009.63i	−0.249084	+	0.684352i
$326$	113.160	+	641.765i	0.0192251	+	0.109031i
$327$		0			0
$328$	−4392.02	+	3685.34i	−0.739356	+	0.620394i
$329$	−7298.28	−	1286.88i	−1.22300	−	0.215648i
$330$		0			0
$331$	−7994.76	+	4615.77i	−1.32759	+	0.766483i	−0.984926	−	0.172976i	$-0.944662\pi$
$331$	−7994.76	+	4615.77i	−1.32759	+	0.766483i	−0.342662	+	0.939459i	$0.611328\pi$
$332$	3002.23	+	8248.56i	0.496291	+	1.36355i
$333$		0			0
$334$	−1074.37	−	1860.86i	−0.176009	−	0.304856i
$335$	1659.42	−	2874.19i	0.270637	−	0.468758i
$336$		0			0
$337$	4194.73	+	4999.09i	0.678046	+	0.808064i	0.989855	−	0.142081i	$-0.0453793\pi$
$337$	4194.73	+	4999.09i	0.678046	+	0.808064i	−0.311809	+	0.950145i	$0.600935\pi$
$338$	−787.988	−	661.201i	−0.126807	−	0.106404i
$339$		0			0
$340$	−6169.70	−	2245.59i	−0.984115	−	0.358189i
$341$	−4356.14			−0.691784
$342$		0			0
$343$	6132.22			0.965332
$344$	301.931	+	109.894i	0.0473228	+	0.0172241i
$345$		0			0
$346$	3418.61	+	2868.55i	0.531172	+	0.445706i
$347$	6767.67	+	8065.40i	1.04700	+	1.24776i	0.968017	+	0.250885i	$0.0807217\pi$
$347$	6767.67	+	8065.40i	1.04700	+	1.24776i	0.0789795	+	0.996876i	$0.474834\pi$
$348$		0			0
$349$	5270.27	−	9128.37i	0.808341	−	1.40009i	−0.105671	−	0.994401i	$-0.533699\pi$
$349$	5270.27	−	9128.37i	0.808341	−	1.40009i	0.914012	−	0.405687i	$-0.132968\pi$
$350$	795.038	+	1377.05i	0.121419	+	0.210303i
$351$		0			0
$352$	−1453.56	−	3993.63i	−0.220100	−	0.604719i
$353$	−5189.48	+	2996.15i	−0.782459	+	0.451753i	−0.837301	−	0.546742i	$-0.815868\pi$
$353$	−5189.48	+	2996.15i	−0.782459	+	0.451753i	0.0548419	+	0.998495i	$0.482535\pi$
$354$		0			0
$355$	−3335.44	−	588.128i	−0.498667	−	0.0879284i
$356$	−626.093	+	525.354i	−0.0932103	+	0.0782127i
$357$		0			0
$358$	−293.650	−	1665.37i	−0.0433516	−	0.245859i
$359$	−4059.28	+	11152.8i	−0.596771	+	1.63961i	0.160895	+	0.986972i	$0.448562\pi$
$359$	−4059.28	+	11152.8i	−0.596771	+	1.63961i	−0.757666	+	0.652643i	$0.773660\pi$
$360$		0			0
$361$	−1656.57	+	6655.95i	−0.241518	+	0.970396i
$362$			1725.87i			0.250579i
$363$		0			0
$364$	7174.29	−	1265.02i	1.03306	−	0.182157i
$365$	−2511.02	+	2992.51i	−0.360089	+	0.429138i
$366$		0			0
$367$	−317.137	+	1798.57i	−0.0451074	+	0.255817i	−0.999020	−	0.0442689i	$-0.985904\pi$
$367$	−317.137	+	1798.57i	−0.0451074	+	0.255817i	0.953912	+	0.300086i	$0.0970153\pi$
$368$	−3677.04	−	2122.94i	−0.520866	−	0.300722i
$369$		0			0
$370$	−3008.98	+	1095.18i	−0.422782	+	0.153880i
$371$	−4741.75	+	1725.85i	−0.663556	+	0.241515i
$372$		0			0
$373$	−5746.38	−	3317.67i	−0.797685	−	0.460543i	0.0449763	−	0.998988i	$-0.485679\pi$
$373$	−5746.38	−	3317.67i	−0.797685	−	0.460543i	−0.842661	+	0.538445i	$0.819012\pi$
$374$	656.329	−	3722.23i	0.0907432	−	0.514630i
$375$		0			0
$376$	4033.54	−	4806.99i	0.553229	−	0.659313i
$377$	496.883	−	87.6139i	0.0678800	−	0.0119691i
$378$		0			0
$379$		−	2511.14i		−	0.340339i	−0.985415	−	0.170170i	$-0.945568\pi$
$379$		−	2511.14i		−	0.340339i	0.985415	−	0.170170i	$-0.0544315\pi$
$380$	3103.49	−	2425.75i	0.418962	−	0.327470i
$381$		0			0
$382$	−618.020	+	1698.00i	−0.0827765	+	0.227427i
$383$	−1614.98	−	9158.99i	−0.215461	−	1.22194i	−0.880105	−	0.474779i	$-0.842528\pi$
$383$	−1614.98	−	9158.99i	−0.215461	−	1.22194i	0.664644	−	0.747160i	$-0.268583\pi$
$384$		0			0
$385$	−2562.92	+	2150.55i	−0.339269	+	0.284681i
$386$	−2032.51	−	358.386i	−0.268010	−	0.0472574i
$387$		0			0
$388$	−7752.56	+	4475.94i	−1.01437	+	0.585648i
$389$	−3526.18	−	9688.09i	−0.459600	−	1.26274i	−0.925784	−	0.378052i	$-0.876594\pi$
$389$	−3526.18	−	9688.09i	−0.459600	−	1.26274i	0.466185	−	0.884687i	$-0.345628\pi$
$390$		0			0
$391$	−7969.65	−	13803.8i	−1.03080	−	1.78540i
$392$	178.313	−	308.848i	0.0229750	−	0.0397938i
$393$		0			0
$394$	−1112.81	−	1326.20i	−0.142291	−	0.169576i
$395$	−5433.68	−	4559.40i	−0.692148	−	0.580781i
$396$		0			0
$397$	−4607.91	−	1677.14i	−0.582531	−	0.212024i	0.0339105	−	0.999425i	$-0.489204\pi$
$397$	−4607.91	−	1677.14i	−0.582531	−	0.212024i	−0.616441	+	0.787401i	$0.711426\pi$
$398$	2326.87			0.293054
$399$		0			0
$400$	2800.79			0.350099
$401$	−2396.16	−	872.132i	−0.298401	−	0.108609i	0.188481	−	0.982077i	$-0.439644\pi$
$401$	−2396.16	−	872.132i	−0.298401	−	0.108609i	−0.486882	+	0.873468i	$0.661866\pi$
$402$		0			0
$403$	7460.39	+	6260.01i	0.922156	+	0.773780i
$404$	5131.15	+	6115.06i	0.631891	+	0.753059i
$405$		0			0
$406$	94.0094	−	162.829i	0.0114916	−	0.0199041i
$407$	5254.26	+	9100.64i	0.639911	+	1.10836i
$408$		0			0
$409$	789.489	+	2169.10i	0.0954467	+	0.262238i	0.978223	−	0.207555i	$-0.0665507\pi$
$409$	789.489	+	2169.10i	0.0954467	+	0.262238i	−0.882777	+	0.469793i	$0.844329\pi$
$410$	−2343.47	+	1353.00i	−0.282282	+	0.162976i
$411$		0			0
$412$	5516.75	+	972.753i	0.659687	+	0.116321i
$413$	−1173.77	+	984.910i	−0.139849	+	0.117347i
$414$		0			0
$415$	1565.03	+	8875.73i	0.185119	+	1.04986i
$416$	−3249.67	+	8928.40i	−0.383001	+	1.05229i
$417$		0			0
$418$	1685.45	+	1516.95i	0.197221	+	0.177504i
$419$			6841.40i			0.797671i	0.917022	+	0.398836i	$0.130586\pi$
$419$			6841.40i			0.797671i	−0.917022	+	0.398836i	$0.869414\pi$
$420$		0			0
$421$	1336.82	−	235.717i	0.154757	−	0.0272878i	−0.0957330	−	0.995407i	$-0.530519\pi$
$421$	1336.82	−	235.717i	0.154757	−	0.0272878i	0.250490	+	0.968119i	$0.419408\pi$
$422$	−1534.35	+	1828.56i	−0.176992	+	0.210931i
$423$		0			0
$424$	741.947	−	4207.79i	0.0849815	−	0.481954i
$425$	9105.71	+	5257.18i	1.03927	+	0.600025i
$426$		0			0
$427$	−6741.81	+	2453.82i	−0.764073	+	0.278100i
$428$	−664.012	+	241.681i	−0.0749912	+	0.0272946i
$429$		0			0
$430$	131.332	+	75.8247i	0.0147288	+	0.00850370i
$431$	2205.75	−	12509.4i	0.246514	−	1.39805i	−0.570437	−	0.821341i	$-0.693226\pi$
$431$	2205.75	−	12509.4i	0.246514	−	1.39805i	0.816951	−	0.576707i	$-0.195663\pi$
$432$		0			0
$433$	8937.43	−	10651.2i	0.991929	−	1.18214i	0.00866258	−	0.999962i	$-0.497243\pi$
$433$	8937.43	−	10651.2i	0.991929	−	1.18214i	0.983267	−	0.182173i	$-0.0583130\pi$
$434$	3574.03	−	630.198i	0.395297	−	0.0697015i
$435$		0			0
$436$			5642.79i			0.619818i
$437$	9556.93	+	331.742i	1.04616	+	0.0363144i
$438$		0			0
$439$	−2629.41	+	7224.26i	−0.285866	+	0.785410i	0.710768	+	0.703427i	$0.248348\pi$
$439$	−2629.41	+	7224.26i	−0.285866	+	0.785410i	−0.996634	+	0.0819832i	$0.973875\pi$
$440$	−491.929	−	2789.87i	−0.0532995	−	0.302277i
$441$		0			0
$442$	−6473.08	+	5431.56i	−0.696591	+	0.584509i
$443$	−12954.5	−	2284.22i	−1.38936	−	0.244981i	−0.571594	−	0.820537i	$-0.693675\pi$
$443$	−12954.5	−	2284.22i	−1.38936	−	0.244981i	−0.817762	+	0.575556i	$0.804786\pi$
$444$		0			0
$445$	−726.735	+	419.580i	−0.0774169	+	0.0446967i
$446$	−158.553	−	435.620i	−0.0168334	−	0.0462494i
$447$		0			0
$448$	−1039.95	−	1801.24i	−0.109672	−	0.189957i
$449$	3981.53	−	6896.21i	0.418485	−	0.724838i	−0.577302	−	0.816531i	$-0.695894\pi$
$449$	3981.53	−	6896.21i	0.418485	−	0.724838i	0.995787	+	0.0916928i	$0.0292278\pi$
$450$		0			0
$451$	5708.28	+	6802.86i	0.595992	+	0.710275i
$452$	−3438.78	−	2885.48i	−0.357847	−	0.300269i
$453$		0			0
$454$	−4045.25	−	1472.35i	−0.418178	−	0.152204i
$455$	7479.76			0.770674
$456$		0			0
$457$	3938.81			0.403172			0.201586	−	0.979471i	$-0.435390\pi$
$457$	3938.81			0.403172			0.201586	+	0.979471i	$0.435390\pi$
$458$	−1336.36	−	486.396i	−0.136341	−	0.0496240i
$459$		0			0
$460$	−4206.90	−	3530.01i	−0.426408	−	0.357799i
$461$	3222.21	+	3840.08i	0.325539	+	0.387962i	0.903847	−	0.427857i	$-0.140731\pi$
$461$	3222.21	+	3840.08i	0.325539	+	0.387962i	−0.578308	+	0.815819i	$0.696287\pi$
$462$		0			0
$463$	−5806.80	+	10057.7i	−0.582861	+	1.00955i	0.412277	+	0.911059i	$0.364734\pi$
$463$	−5806.80	+	10057.7i	−0.582861	+	1.00955i	−0.995138	+	0.0984871i	$0.968600\pi$
$464$	−165.590	−	286.811i	−0.0165675	−	0.0286958i
$465$		0			0
$466$	1206.27	+	3314.20i	0.119913	+	0.329458i
$467$	1449.35	−	836.781i	0.143614	−	0.0829156i	−0.426471	−	0.904501i	$-0.640243\pi$
$467$	1449.35	−	836.781i	0.143614	−	0.0829156i	0.570085	+	0.821586i	$0.306910\pi$
$468$		0			0
$469$	8936.14	+	1575.68i	0.879813	+	0.155135i
$470$	2268.78	−	1903.73i	0.222661	−	0.186835i
$471$		0			0
$472$	−225.294	−	1277.71i	−0.0219703	−	0.124600i
$473$	170.216	−	467.665i	0.0165466	−	0.0454614i
$474$		0			0
$475$	−5569.04	+	2962.60i	−0.537948	+	0.286176i
$476$		−	17951.1i		−	1.72855i
$477$		0			0
$478$	6738.82	−	1188.24i	0.644825	−	0.113700i
$479$	−2094.64	+	2496.29i	−0.199805	+	0.238118i	−0.856638	−	0.515918i	$-0.827451\pi$
$479$	−2094.64	+	2496.29i	−0.199805	+	0.238118i	0.656833	+	0.754036i	$0.271895\pi$
$480$		0			0
$481$	4079.60	−	23136.6i	0.386723	−	2.19322i
$482$	−6818.58	−	3936.71i	−0.644353	−	0.372017i
$483$		0			0
$484$	4496.70	−	1636.67i	0.422305	−	0.153706i
$485$	−8636.96	+	3143.60i	−0.808627	+	0.294316i
$486$		0			0
$487$	16948.9	+	9785.48i	1.57706	+	0.910518i	0.995266	+	0.0971839i	$0.0309835\pi$
$487$	16948.9	+	9785.48i	1.57706	+	0.910518i	0.581797	+	0.813334i	$0.302350\pi$
$488$	1054.90	−	5982.63i	0.0978546	−	0.554961i
$489$		0			0
$490$	108.193	−	128.940i	0.00997484	−	0.0118876i
$491$	1805.40	−	318.341i	0.165940	−	0.0292597i	−0.0900607	−	0.995936i	$-0.528706\pi$
$491$	1805.40	−	318.341i	0.165940	−	0.0292597i	0.256001	+	0.966677i	$0.417595\pi$
$492$		0			0
$493$		−	1243.27i		−	0.113579i
$494$	−706.588	−	5020.05i	−0.0643540	−	0.457212i
$495$		0			0
$496$	2186.36	−	6006.98i	0.197924	−	0.543793i
$497$	−1607.99	−	9119.39i	−0.145128	−	0.823060i
$498$		0			0
$499$	13291.5	−	11152.9i	1.19240	−	1.00055i	0.192590	−	0.981279i	$-0.438311\pi$
$499$	13291.5	−	11152.9i	1.19240	−	1.00055i	0.999814	−	0.0192670i	$-0.00613327\pi$
$500$	9422.48	+	1661.44i	0.842773	+	0.148604i
$501$		0			0
$502$	−6217.51	+	3589.68i	−0.552791	+	0.319154i
$503$	4141.92	+	11379.8i	0.367155	+	1.00875i	0.976438	+	0.215798i	$0.0692352\pi$
$503$	4141.92	+	11379.8i	0.367155	+	1.00875i	−0.609283	+	0.792953i	$0.708543\pi$
$504$		0			0
$505$	4098.05	+	7098.03i	0.361111	+	0.625462i
$506$	1580.71	−	2737.86i	0.138875	−	0.240539i
$507$		0			0
$508$	7422.30	+	8845.56i	0.648251	+	0.772555i
$509$	−13427.2	−	11266.8i	−1.16926	−	0.981123i	−0.169266	−	0.985570i	$-0.554140\pi$
$509$	−13427.2	−	11266.8i	−1.16926	−	0.981123i	−0.999990	+	0.00444765i	$0.998584\pi$
$510$		0			0
$511$	−10036.5	−	3652.98i	−0.868860	−	0.316239i
$512$	10995.8			0.949121
$513$		0			0
$514$	4099.32			0.351777
$515$	5404.79	+	1967.18i	0.462453	+	0.168319i
$516$		0			0
$517$	−7445.61	−	6247.61i	−0.633380	−	0.531469i
$518$	−5627.48	−	6706.57i	−0.477330	−	0.568860i
$519$		0			0
$520$	−3166.71	+	5484.90i	−0.267056	+	0.462555i
$521$	7187.90	+	12449.8i	0.604430	+	1.04690i	0.992141	+	0.125122i	$0.0399323\pi$
$521$	7187.90	+	12449.8i	0.604430	+	1.04690i	−0.387712	+	0.921781i	$0.626734\pi$
$522$		0			0
$523$	−4579.81	−	12582.9i	−0.382909	−	1.05203i	−0.970126	−	0.242604i	$-0.921999\pi$
$523$	−4579.81	−	12582.9i	−0.382909	−	1.05203i	0.587217	−	0.809430i	$-0.300224\pi$
$524$	−3539.96	+	2043.80i	−0.295122	+	0.170389i
$525$		0			0
$526$	−5700.87	−	1005.22i	−0.472566	−	0.0833261i
$527$	18383.4	−	15425.5i	1.51953	−	1.27504i
$528$		0			0
$529$	−202.320	−	1147.41i	−0.0166286	−	0.0943055i
$530$	689.720	−	1894.99i	0.0565274	−	0.155308i
$531$		0			0
$532$	9134.38	+	5705.15i	0.744409	+	0.464943i
$533$		−	19853.8i		−	1.61344i
$534$		0			0
$535$	−714.499	+	125.986i	−0.0577393	+	0.0101810i
$536$	−4938.74	+	5885.76i	−0.397987	+	0.474302i
$537$		0			0
$538$	−1097.80	+	6225.93i	−0.0879731	+	0.498920i
$539$	−478.378	−	276.192i	−0.0382286	−	0.0220713i
$540$		0			0
$541$	8538.52	−	3107.77i	0.678558	−	0.246975i	0.0203296	−	0.999793i	$-0.493528\pi$
$541$	8538.52	−	3107.77i	0.678558	−	0.246975i	0.658228	+	0.752819i	$0.271306\pi$
$542$	1660.82	−	604.488i	0.131620	−	0.0479058i
$543$		0			0
$544$	20276.0	+	11706.4i	1.59803	+	0.922622i
$545$	−1006.06	+	5705.66i	−0.0790733	+	0.448447i
$546$		0			0
$547$	−4904.33	+	5844.75i	−0.383353	+	0.456862i	−0.922869	−	0.385113i	$-0.874162\pi$
$547$	−4904.33	+	5844.75i	−0.383353	+	0.456862i	0.539517	+	0.841975i	$0.318607\pi$
$548$	11068.7	−	1951.72i	0.862834	−	0.152141i
$549$		0			0
$550$			2085.43i			0.161678i
$551$	632.637	+	395.132i	0.0489133	+	0.0305503i
$552$		0			0
$553$	6632.93	−	18223.8i	0.510056	−	1.40137i
$554$	646.299	+	3665.34i	0.0495643	+	0.281093i
$555$		0			0
$556$	−6645.99	+	5576.65i	−0.506929	+	0.425364i
$557$	−6839.48	−	1205.98i	−0.520283	−	0.0917400i	−0.0926615	−	0.995698i	$-0.529537\pi$
$557$	−6839.48	−	1205.98i	−0.520283	−	0.0917400i	−0.427622	+	0.903958i	$0.640649\pi$
$558$		0			0
$559$	−963.576	+	556.321i	−0.0729068	+	0.0420928i
$560$	−1679.20	−	4613.56i	−0.126713	−	0.348140i
$561$		0			0
$562$	1221.26	+	2115.28i	0.0916649	+	0.158768i
$563$	8727.13	−	15115.8i	0.653294	−	1.13154i	−0.329024	−	0.944322i	$-0.606720\pi$
$563$	8727.13	−	15115.8i	0.653294	−	1.13154i	0.982318	−	0.187218i	$-0.0599469\pi$
$564$		0			0
$565$	−2962.64	−	3530.73i	−0.220600	−	0.262901i
$566$	−1078.00	−	904.550i	−0.0800561	−	0.0671750i
$567$		0			0
$568$	7368.01	+	2681.74i	0.544287	+	0.198104i
$569$	−16278.6			−1.19936			−0.599679	−	0.800240i	$-0.704705\pi$
$569$	−16278.6			−1.19936			−0.599679	+	0.800240i	$0.704705\pi$
$570$		0			0
$571$	−23492.9			−1.72180			−0.860901	−	0.508773i	$-0.830099\pi$
$571$	−23492.9			−1.72180			−0.860901	+	0.508773i	$0.830099\pi$
$572$	8978.22	+	3267.80i	0.656291	+	0.238870i
$573$		0			0
$574$	−5667.56	−	4755.65i	−0.412124	−	0.345813i
$575$	5653.02	+	6737.00i	0.409995	+	0.488613i
$576$		0			0
$577$	2634.09	−	4562.37i	0.190049	−	0.329175i	−0.755217	−	0.655475i	$-0.772469\pi$
$577$	2634.09	−	4562.37i	0.190049	−	0.329175i	0.945266	+	0.326300i	$0.105802\pi$
$578$	7726.88	+	13383.3i	0.556048	+	0.963103i
$579$		0			0
$580$	−146.507	−	402.524i	−0.0104885	−	0.0288170i
$581$	−21340.1	+	12320.7i	−1.52381	+	0.879775i
$582$		0			0
$583$	−6517.50	−	1149.21i	−0.462997	−	0.0816389i
$584$	6927.86	−	5813.17i	0.490885	−	0.411902i
$585$		0			0
$586$	−1604.24	−	9098.12i	−0.113090	−	0.641365i
$587$	−4998.01	+	13731.9i	−0.351431	+	0.965549i	0.630480	+	0.776206i	$0.282858\pi$
$587$	−4998.01	+	13731.9i	−0.351431	+	0.965549i	−0.981911	+	0.189343i	$0.939364\pi$
$588$		0			0
$589$	2006.69	+	14256.8i	0.140381	+	0.997355i
$590$		−	612.347i		−	0.0427287i
$591$		0			0
$592$	−15186.6	+	2677.81i	−1.05434	+	0.185908i
$593$	−9960.87	+	11870.9i	−0.689787	+	0.822056i	−0.991330	−	0.131396i	$-0.958054\pi$
$593$	−9960.87	+	11870.9i	−0.689787	+	0.822056i	0.301543	+	0.953453i	$0.402498\pi$
$594$		0			0
$595$	3200.53	−	18151.1i	0.220519	−	1.25063i
$596$	8197.44	+	4732.79i	0.563390	+	0.325273i
$597$		0			0
$598$	−6641.60	+	2417.34i	−0.454173	+	0.165305i
$599$	−7411.15	+	2697.44i	−0.505528	+	0.183997i	−0.582179	−	0.813061i	$-0.697800\pi$
$599$	−7411.15	+	2697.44i	−0.505528	+	0.183997i	0.0766506	+	0.997058i	$0.475577\pi$
$600$		0			0
$601$	2579.64	+	1489.35i	0.175084	+	0.101085i	0.584981	−	0.811047i	$-0.301102\pi$
$601$	2579.64	+	1489.35i	0.175084	+	0.101085i	−0.409897	+	0.912132i	$0.634435\pi$
$602$	−71.9986	+	408.324i	−0.00487449	+	0.0276446i
$603$		0			0
$604$	−4967.83	+	5920.43i	−0.334666	+	0.398840i
$605$	4838.61	−	853.177i	0.325153	−	0.0573332i
$606$		0			0
$607$			15489.8i			1.03577i	0.855452	+	0.517883i	$0.173280\pi$
$607$			15489.8i			1.03577i	−0.855452	+	0.517883i	$0.826720\pi$
$608$	−12400.8	+	6596.93i	−0.827168	+	0.440034i
$609$		0			0
$610$	980.643	−	2694.29i	0.0650903	−	0.178834i
$611$	3773.31	+	21399.5i	0.249839	+	1.41691i
$612$		0			0
$613$	−9333.78	+	7831.97i	−0.614989	+	0.516037i	−0.896224	−	0.443602i	$-0.853700\pi$
$613$	−9333.78	+	7831.97i	−0.614989	+	0.516037i	0.281235	+	0.959639i	$0.409256\pi$
$614$	−1958.04	−	345.255i	−0.128697	−	0.0226928i
$615$		0			0
$616$	6707.73	−	3872.71i	0.438737	−	0.253305i
$617$	4535.24	+	12460.5i	0.295919	+	0.813031i	0.995171	+	0.0981555i	$0.0312943\pi$
$617$	4535.24	+	12460.5i	0.295919	+	0.813031i	−0.699252	+	0.714875i	$0.746484\pi$
$618$		0			0
$619$	−8561.76	−	14829.4i	−0.555939	−	0.962915i	−0.997830	−	0.0658460i	$-0.979025\pi$
$619$	−8561.76	−	14829.4i	−0.555939	−	0.962915i	0.441891	−	0.897069i	$-0.354308\pi$
$620$	4134.10	−	7160.47i	0.267789	−	0.463825i
$621$		0			0
$622$	1208.18	+	1439.86i	0.0778839	+	0.0928184i
$623$	−1757.57	−	1474.78i	−0.113026	−	0.0948405i
$624$		0			0
$625$	284.623	+	103.594i	0.0182159	+	0.00663003i
$626$	−1751.32			−0.111816
$627$		0			0
$628$	−3677.65			−0.233685
$629$	−54399.8	−	19799.9i	−3.44843	−	1.25513i
$630$		0			0
$631$	10029.9	+	8416.08i	0.632779	+	0.530965i	0.901791	−	0.432172i	$-0.142253\pi$
$631$	10029.9	+	8416.08i	0.632779	+	0.530965i	−0.269012	+	0.963137i	$0.586697\pi$
$632$	10555.3	+	12579.3i	0.664348	+	0.791739i
$633$		0			0
$634$	1715.25	−	2970.90i	0.107447	−	0.186103i
$635$	5927.91	+	10267.4i	0.370460	+	0.641655i
$636$		0			0
$637$	422.375	+	1160.47i	0.0262718	+	0.0721811i
$638$	213.555	−	123.296i	0.0132519	−	0.00765099i
$639$		0			0
$640$	10156.1	+	1790.80i	0.627276	+	0.110606i
$641$	−10507.9	+	8817.20i	−0.647486	+	0.543305i	−0.906307	−	0.422620i	$-0.861110\pi$
$641$	−10507.9	+	8817.20i	−0.647486	+	0.543305i	0.258821	+	0.965925i	$0.416666\pi$
$642$		0			0
$643$	2842.52	+	16120.7i	0.174336	+	0.988707i	0.938908	+	0.344169i	$0.111839\pi$
$643$	2842.52	+	16120.7i	0.174336	+	0.988707i	−0.764572	+	0.644538i	$0.777050\pi$
$644$	5135.38	−	14109.4i	0.314227	−	0.863333i
$645$		0			0
$646$	−12484.5	−	433.364i	−0.760364	−	0.0263939i
$647$		−	6379.48i		−	0.387640i	−0.981037	−	0.193820i	$-0.937912\pi$
$647$		−	6379.48i		−	0.387640i	0.981037	−	0.193820i	$-0.0620878\pi$
$648$		0			0
$649$	−1979.05	+	348.961i	−0.119699	+	0.0211062i
$650$	2996.87	−	3571.53i	0.180842	−	0.215519i
$651$		0			0
$652$	−704.875	+	3997.54i	−0.0423390	+	0.240116i
$653$	9638.64	+	5564.87i	0.577625	+	0.333492i	0.760189	−	0.649702i	$-0.225106\pi$
$653$	9638.64	+	5564.87i	0.577625	+	0.333492i	−0.182564	+	0.983194i	$0.558440\pi$
$654$		0			0
$655$	−3943.79	+	1435.42i	−0.235262	+	0.0856283i
$656$	−12245.9	+	4457.15i	−0.728846	+	0.265278i
$657$		0			0
$658$	7012.64	+	4048.75i	0.415473	+	0.239873i
$659$	−1314.49	+	7454.85i	−0.0777015	+	0.440667i	0.920993	+	0.389580i	$0.127380\pi$
$659$	−1314.49	+	7454.85i	−0.0777015	+	0.440667i	−0.998694	+	0.0510873i	$0.983731\pi$
$660$		0			0
$661$	6467.72	−	7707.93i	0.380583	−	0.453561i	−0.541415	−	0.840755i	$-0.682111\pi$
$661$	6467.72	−	7707.93i	0.380583	−	0.453561i	0.921998	+	0.387194i	$0.126556\pi$
$662$	9933.63	−	1751.57i	0.583204	−	0.102835i
$663$		0			0
$664$		−	20864.9i		−	1.21945i
$665$	8218.97	+	7397.30i	0.479275	+	0.431361i
$666$		0			0
$667$	355.671	−	977.197i	0.0206471	−	0.0567275i
$668$	−2324.19	−	13181.1i	−0.134619	−	0.763462i
$669$		0			0
$670$	−2777.93	+	2330.96i	−0.160180	+	0.134407i
$671$	−9266.57	−	1633.95i	−0.533133	−	0.0940057i
$672$		0			0
$673$	−22460.8	+	12967.8i	−1.28648	+	0.742749i	−0.978024	−	0.208490i	$-0.933145\pi$
$673$	−22460.8	+	12967.8i	−1.28648	+	0.742749i	−0.308455	+	0.951239i	$0.599812\pi$
$674$	−2438.77	−	6700.45i	−0.139374	−	0.382926i
$675$		0			0
$676$	−3203.71	−	5548.99i	−0.182278	−	0.315714i
$677$	2879.85	−	4988.05i	0.163489	−	0.283171i	−0.772629	−	0.634858i	$-0.781059\pi$
$677$	2879.85	−	4988.05i	0.163489	−	0.283171i	0.936118	+	0.351687i	$0.114392\pi$
$678$		0			0
$679$	−16153.1	−	19250.5i	−0.912958	−	1.08802i
$680$	11955.2	+	10031.6i	0.674206	+	0.565726i
$681$		0			0
$682$	4472.70	+	1627.93i	0.251127	+	0.0914026i
$683$	−524.910			−0.0294072			−0.0147036	−	0.999892i	$-0.504680\pi$
$683$	−524.910			−0.0294072			−0.0147036	+	0.999892i	$0.504680\pi$
$684$		0			0
$685$	11540.0			0.643682
$686$	−6296.30	−	2291.67i	−0.350429	−	0.127546i
$687$		0			0
$688$	559.463	+	469.445i	0.0310019	+	0.0260137i
$689$	9510.49	+	11334.2i	0.525865	+	0.626701i
$690$		0			0
$691$	−8123.39	+	14070.1i	−0.447219	+	0.774606i	−0.998204	−	0.0599095i	$-0.980919\pi$
$691$	−8123.39	+	14070.1i	−0.447219	+	0.774606i	0.550985	+	0.834515i	$0.314252\pi$
$692$	13899.0	+	24073.7i	0.763525	+	1.32246i
$693$		0			0
$694$	−3934.64	−	10810.3i	−0.215212	−	0.591290i
$695$	−7714.31	+	4453.86i	−0.421036	+	0.243085i
$696$		0			0
$697$	−48179.1	−	8495.28i	−2.61824	−	0.461667i
$698$	−8822.64	+	7403.07i	−0.478427	+	0.401448i
$699$		0			0
$700$	1719.91	+	9754.08i	0.0928663	+	0.526671i
$701$	8737.82	−	24007.0i	0.470789	−	1.29348i	−0.446330	−	0.894868i	$-0.647269\pi$
$701$	8737.82	−	24007.0i	0.470789	−	1.29348i	0.917119	−	0.398613i	$-0.130508\pi$
$702$		0			0
$703$	27364.3	−	21388.5i	1.46808	−	1.14748i
$704$		−	2727.84i		−	0.146036i
$705$		0			0
$706$	6448.02	−	1136.96i	0.343732	−	0.0606091i
$707$	−14404.2	+	17166.2i	−0.766230	+	0.913157i
$708$		0			0
$709$	5068.89	−	28747.1i	0.268500	−	1.52274i	−0.490382	−	0.871508i	$-0.663143\pi$
$709$	5068.89	−	28747.1i	0.268500	−	1.52274i	0.758881	−	0.651229i	$-0.225746\pi$
$710$	3204.89	+	1850.35i	0.169405	+	0.0978060i
$711$		0			0
$712$	1825.55	−	664.447i	0.0960891	−	0.0349736i
$713$	18862.0	−	6865.20i	0.990725	−	0.360594i
$714$		0			0
$715$	8495.63	+	4904.95i	0.444361	+	0.256552i
$716$	1829.14	−	10373.6i	0.0954724	−	0.541451i
$717$		0			0
$718$	8335.79	−	9934.21i	0.433272	−	0.516353i
$719$	−21970.2	+	3873.95i	−1.13957	+	0.200937i	−0.711418	−	0.702769i	$-0.751947\pi$
$719$	−21970.2	+	3873.95i	−1.13957	+	0.200937i	−0.428153	+	0.903706i	$0.640836\pi$
$720$		0			0
$721$			15725.5i			0.812274i
$722$	4188.28	−	6214.97i	0.215889	−	0.320356i
$723$		0			0
$724$	−3676.85	+	10102.1i	−0.188742	+	0.518564i
$725$	119.119	+	675.556i	0.00610202	+	0.0346063i
$726$		0			0
$727$	−3808.02	+	3195.31i	−0.194266	+	0.163009i	−0.734733	−	0.678357i	$-0.762692\pi$
$727$	−3808.02	+	3195.31i	−0.194266	+	0.163009i	0.540466	+	0.841366i	$0.318248\pi$
$728$	−17053.1	−	3006.92i	−0.868171	−	0.153082i
$729$		0			0
$730$	3696.53	−	2134.19i	0.187418	−	0.108206i
$731$	937.715	+	2576.35i	0.0474455	+	0.130355i
$732$		0			0
$733$	−8489.19	−	14703.7i	−0.427770	−	0.740919i	0.568905	−	0.822403i	$-0.307367\pi$
$733$	−8489.19	−	14703.7i	−0.427770	−	0.740919i	−0.996675	+	0.0814843i	$0.974034\pi$
$734$	997.766	−	1728.18i	0.0501747	−	0.0869051i
$735$		0			0
$736$	12587.8	+	15001.5i	0.630424	+	0.751310i
$737$	9116.52	+	7649.67i	0.455646	+	0.382333i
$738$		0			0
$739$	−6175.36	−	2247.65i	−0.307394	−	0.111882i	0.183717	−	0.982979i	$-0.441187\pi$
$739$	−6175.36	−	2247.65i	−0.307394	−	0.111882i	−0.491111	+	0.871097i	$0.663409\pi$
$740$	−19945.8			−0.990839
$741$		0			0
$742$	5513.59			0.272790
$743$	5534.49	+	2014.39i	0.273271	+	0.0994626i	0.475021	−	0.879975i	$-0.342440\pi$
$743$	5534.49	+	2014.39i	0.273271	+	0.0994626i	−0.201750	+	0.979437i	$0.564663\pi$
$744$		0			0
$745$	7444.95	+	6247.06i	0.366124	+	0.307214i
$746$	4660.29	+	5553.92i	0.228720	+	0.272578i
$747$		0			0
$748$	11771.7	−	20389.2i	0.575422	−	0.996659i
$749$	−991.821	−	1717.89i	−0.0483850	−	0.0838053i
$750$		0			0
$751$	3929.29	+	10795.6i	0.190921	+	0.524552i	0.997810	−	0.0661524i	$-0.0210723\pi$
$751$	3929.29	+	10795.6i	0.190921	+	0.524552i	−0.806888	+	0.590704i	$0.798850\pi$
$752$	12352.2	−	7131.56i	0.598988	−	0.345826i
$753$		0			0
$754$	−542.920	−	95.7314i	−0.0262228	−	0.00462378i
$755$	−6078.75	+	5100.67i	−0.293018	+	0.245871i
$756$		0			0
$757$	1749.49	+	9921.88i	0.0839980	+	0.476376i	0.997568	+	0.0696954i	$0.0222027\pi$
$757$	1749.49	+	9921.88i	0.0839980	+	0.476376i	−0.913570	+	0.406681i	$0.866686\pi$
$758$	−938.435	+	2578.33i	−0.0449677	+	0.123548i
$759$		0			0
$760$	−8904.09	+	2895.17i	−0.424981	+	0.138182i
$761$		−	19688.7i		−	0.937862i	−0.883235	−	0.468931i	$-0.844639\pi$
$761$		−	19688.7i		−	0.937862i	0.883235	−	0.468931i	$-0.155361\pi$
$762$		0			0
$763$	−15599.8	+	2750.67i	−0.740172	+	0.130512i
$764$	−7234.95	+	8622.28i	−0.342606	+	0.408302i
$765$		0			0
$766$	−1764.61	+	10007.6i	−0.0832348	+	0.472048i
$767$	3890.84	+	2246.37i	0.183168	+	0.105752i
$768$		0			0
$769$	−15579.7	+	5670.55i	−0.730584	+	0.265911i	−0.680412	−	0.732830i	$-0.738199\pi$
$769$	−15579.7	+	5670.55i	−0.730584	+	0.265911i	−0.0501719	+	0.998741i	$0.515977\pi$
$770$	3435.18	−	1250.30i	0.160773	−	0.0585166i
$771$		0			0
$772$	−11133.4	−	6427.88i	−0.519042	−	0.299669i
$773$	−5068.11	+	28742.7i	−0.235818	+	1.33739i	0.605066	+	0.796175i	$0.293147\pi$
$773$	−5068.11	+	28742.7i	−0.235818	+	1.33739i	−0.840884	+	0.541215i	$0.817965\pi$
$774$		0			0
$775$	−8511.04	+	10143.1i	−0.394485	+	0.470129i
$776$	20955.1	−	3694.95i	0.969387	−	0.170929i
$777$		0			0
$778$			11265.1i			0.519117i
$779$	19634.9	−	21815.9i	0.903072	−	1.00338i
$780$		0			0
$781$	4153.78	−	11412.4i	0.190312	−	0.522878i
$782$	3024.28	+	17151.5i	0.138297	+	0.784319i
$783$		0			0
$784$	620.959	−	521.047i	0.0282871	−	0.0237357i
$785$	−3718.63	−	655.694i	−0.169075	−	0.0298124i
$786$		0			0
$787$	−7153.14	+	4129.87i	−0.323992	+	0.187057i	−0.653171	−	0.757211i	$-0.726562\pi$
$787$	−7153.14	+	4129.87i	−0.323992	+	0.187057i	0.329178	+	0.944268i	$0.393228\pi$
$788$	−3688.28	−	10133.5i	−0.166738	−	0.458109i
$789$		0			0
$790$	3875.18	+	6712.01i	0.174523	+	0.302282i
$791$	6300.78	−	10913.3i	0.283224	−	0.490558i
$792$		0			0
$793$	13522.0	+	16114.9i	0.605524	+	0.721635i
$794$	4104.44	+	3444.04i	0.183452	+	0.153935i
$795$		0			0
$796$	13619.9	+	4957.25i	0.606464	+	0.220735i
$797$	8216.48			0.365173			0.182586	−	0.983190i	$-0.441553\pi$
$797$	8216.48			0.365173			0.182586	+	0.983190i	$0.441553\pi$
$798$		0			0
$799$	53544.7			2.37081
$800$	−12139.0	−	4418.22i	−0.536471	−	0.195259i
$801$		0			0
$802$	2134.35	+	1790.94i	0.0939734	+	0.0788530i
$803$	−9004.09	−	10730.7i	−0.395700	−	0.471577i
$804$		0			0
$805$	7708.18	−	13351.0i	0.337488	−	0.584546i
$806$	−5320.59	−	9215.53i	−0.232518	−	0.402733i
$807$		0			0
$808$	−6489.67	−	17830.2i	−0.282557	−	0.776318i
$809$	35978.4	−	20772.2i	1.56358	−	0.902732i	0.566687	−	0.823933i	$-0.308225\pi$
$809$	35978.4	−	20772.2i	1.56358	−	0.902732i	0.996891	−	0.0787991i	$-0.0251086\pi$
$810$		0			0
$811$	35857.3	+	6322.62i	1.55255	+	0.273757i	0.883132	−	0.469125i	$-0.155431\pi$
$811$	35857.3	+	6322.62i	1.55255	+	0.273757i	0.669422	+	0.742882i	$0.266542\pi$
$812$	897.166	−	752.811i	0.0387738	−	0.0325351i
$813$		0			0
$814$	−1993.85	−	11307.7i	−0.0858533	−	0.486898i
$815$	−1425.46	+	3916.41i	−0.0612657	+	0.168326i
$816$		0			0
$817$	−1608.99	−	341.651i	−0.0689002	−	0.0146302i
$818$		−	2522.18i		−	0.107807i
$819$		0			0
$820$	−16599.6	+	2926.96i	−0.706931	+	0.124651i
$821$	4890.72	−	5828.53i	0.207902	−	0.247768i	−0.652010	−	0.758210i	$-0.726074\pi$
$821$	4890.72	−	5828.53i	0.207902	−	0.247768i	0.859912	+	0.510443i	$0.170518\pi$
$822$		0			0
$823$	3366.90	−	19094.6i	0.142604	−	0.808745i	−0.826657	−	0.562707i	$-0.809760\pi$
$823$	3366.90	−	19094.6i	0.142604	−	0.808745i	0.969260	−	0.246038i	$-0.0791289\pi$
$824$	−11531.5	−	6657.73i	−0.487524	−	0.281472i
$825$		0			0
$826$	1573.25	−	572.615i	0.0662715	−	0.0241209i
$827$	30831.8	−	11221.9i	1.29641	−	0.471853i	0.400581	−	0.916261i	$-0.368808\pi$
$827$	30831.8	−	11221.9i	1.29641	−	0.471853i	0.895824	+	0.444409i	$0.146586\pi$
$828$		0			0
$829$	16458.5	+	9502.34i	0.689540	+	0.398106i	0.803440	−	0.595386i	$-0.203001\pi$
$829$	16458.5	+	9502.34i	0.689540	+	0.398106i	−0.113900	+	0.993492i	$0.536334\pi$
$830$	1710.03	−	9698.08i	0.0715134	−	0.405573i
$831$		0			0
$832$	−3920.05	+	4671.73i	−0.163345	+	0.194667i
$833$	2996.83	−	528.423i	0.124651	−	0.0219793i
$834$		0			0
$835$		−	13742.4i		−	0.569549i
$836$	6633.74	+	12470.0i	0.274441	+	0.515889i
$837$		0			0
$838$	2556.69	−	7024.45i	0.105393	−	0.289565i
$839$	−7538.49	−	42752.9i	−0.310200	−	1.75923i	−0.597959	−	0.801527i	$-0.704021\pi$
$839$	−7538.49	−	42752.9i	−0.310200	−	1.75923i	0.287759	−	0.957703i	$-0.407090\pi$
$840$		0			0
$841$	−18620.9	+	15624.8i	−0.763497	+	0.640650i
$842$	−1460.68	−	257.557i	−0.0597842	−	0.0105416i
$843$		0			0
$844$	−12876.7	+	7434.35i	−0.525158	+	0.303200i
$845$	−2250.07	−	6182.01i	−0.0916031	−	0.251677i
$846$		0			0
$847$	6716.64	+	11633.6i	0.272475	+	0.471941i
$848$	4855.88	−	8410.63i	0.196641	−	0.340592i
$849$		0			0
$850$	−7384.69	−	8800.73i	−0.297992	−	0.355132i
$851$	−37093.3	−	31125.0i	−1.49417	−	1.25376i
$852$		0			0
$853$	184.023	+	66.9791i	0.00738669	+	0.00268853i	0.345711	−	0.938341i	$-0.387638\pi$
$853$	184.023	+	66.9791i	0.00738669	+	0.00268853i	−0.338324	+	0.941030i	$0.609860\pi$
$854$	7839.21			0.314113
$855$		0			0
$856$	1679.63			0.0670661
$857$	12538.9	+	4563.79i	0.499792	+	0.181909i	0.579600	−	0.814901i	$-0.303209\pi$
$857$	12538.9	+	4563.79i	0.499792	+	0.181909i	−0.0798086	+	0.996810i	$0.525431\pi$
$858$		0			0
$859$	−636.366	−	533.975i	−0.0252765	−	0.0212095i	0.630062	−	0.776545i	$-0.283030\pi$
$859$	−636.366	−	533.975i	−0.0252765	−	0.0212095i	−0.655338	+	0.755335i	$0.727474\pi$
$860$	607.191	+	723.623i	0.0240756	+	0.0286922i
$861$		0			0
$862$	−6939.66	+	12019.8i	−0.274206	+	0.474939i
$863$	−18598.3	−	32213.3i	−0.733598	−	1.27063i	−0.955336	−	0.295522i	$-0.904506\pi$
$863$	−18598.3	−	32213.3i	−0.733598	−	1.27063i	0.221738	−	0.975106i	$-0.428827\pi$
$864$		0			0
$865$	9761.68	+	26820.0i	0.383708	+	1.05423i
$866$	−13157.0	+	7596.21i	−0.516274	+	0.298071i
$867$		0			0
$868$	22262.6	+	3925.49i	0.870554	+	0.153502i
$869$	19484.3	−	16349.3i	0.760597	−	0.638217i
$870$		0			0
$871$	−4620.10	−	26201.9i	−0.179732	−	1.01931i
$872$	4587.43	−	12603.9i	0.178154	−	0.489473i
$873$		0			0
$874$	−9688.67	−	3912.13i	−0.374970	−	0.151407i
$875$			26858.9i			1.03771i
$876$		0			0
$877$	8374.99	−	1476.74i	0.322467	−	0.0568596i	−0.0100718	−	0.999949i	$-0.503206\pi$
$877$	8374.99	−	1476.74i	0.322467	−	0.0568596i	0.332538	+	0.943090i	$0.392095\pi$
$878$	5399.54	−	6434.92i	0.207546	−	0.247344i
$879$		0			0
$880$	1118.14	−	6341.30i	0.0428325	−	0.242915i
$881$	−647.493	−	373.830i	−0.0247612	−	0.0142959i	0.487568	−	0.873085i	$-0.337884\pi$
$881$	−647.493	−	373.830i	−0.0247612	−	0.0142959i	−0.512329	+	0.858789i	$0.671217\pi$
$882$		0			0
$883$	27766.7	−	10106.3i	1.05824	−	0.385167i	0.246472	−	0.969150i	$-0.420729\pi$
$883$	27766.7	−	10106.3i	1.05824	−	0.385167i	0.811766	+	0.583983i	$0.198506\pi$
$884$	−49460.7	+	18002.2i	−1.88184	+	0.684933i
$885$		0			0
$886$	12447.4	+	7186.53i	0.471986	+	0.272502i
$887$	1018.01	−	5773.41i	0.0385359	−	0.218548i	−0.959459	−	0.281850i	$-0.909052\pi$
$887$	1018.01	−	5773.41i	0.0385359	−	0.218548i	0.997994	+	0.0633019i	$0.0201631\pi$
$888$		0			0
$889$	−20835.9	+	24831.3i	−0.786067	+	0.936798i
$890$	902.981	−	159.220i	0.0340090	−	0.00599670i
$891$		0			0
$892$		−	2887.62i		−	0.108391i
$893$	−17017.3	+	27246.1i	−0.637697	+	1.02100i
$894$		0			0
$895$	3699.04	−	10163.0i	0.138151	−	0.379567i
$896$	4896.21	+	27767.8i	0.182557	+	1.03533i
$897$		0			0
$898$	−6665.24	+	5592.80i	−0.247686	+	0.207833i
$899$	1541.88	+	271.875i	0.0572020	+	0.0100863i
$900$		0			0
$901$	31574.1	−	18229.3i	1.16746	−	0.674035i
$902$	−3318.72	−	9118.11i	−0.122507	−	0.336585i
$903$		0			0
$904$	5335.12	+	9240.70i	0.196287	+	0.339979i
$905$	−5518.93	+	9559.07i	−0.202713	+	0.351110i
$906$		0			0
$907$	20538.0	+	24476.3i	0.751879	+	0.896054i	0.997305	−	0.0733610i	$-0.0233725\pi$
$907$	20538.0	+	24476.3i	0.751879	+	0.896054i	−0.245427	+	0.969415i	$0.578928\pi$
$908$	−20541.4	−	17236.3i	−0.750761	−	0.629963i
$909$		0			0
$910$	−7679.90	−	2795.25i	−0.279765	−	0.101826i
$911$	46413.8			1.68799			0.843994	−	0.536353i	$-0.180199\pi$
$911$	46413.8			1.68799			0.843994	+	0.536353i	$0.180199\pi$
$912$		0			0
$913$	−32317.9			−1.17148
$914$	−4044.20	−	1471.97i	−0.146357	−	0.0532696i
$915$		0			0
$916$	−6785.93	−	5694.07i	−0.244774	−	0.205390i
$917$	−7375.79	−	8790.12i	−0.265616	−	0.316549i
$918$		0			0
$919$	−4163.77	+	7211.85i	−0.149456	+	0.258865i	−0.931026	−	0.364952i	$-0.881086\pi$
$919$	−4163.77	+	7211.85i	−0.149456	+	0.258865i	0.781571	+	0.623817i	$0.214419\pi$
$920$	6526.82	+	11304.8i	0.233895	+	0.405117i
$921$		0			0
$922$	−1873.35	−	5147.00i	−0.0669150	−	0.183848i
$923$	−23514.1	+	13575.9i	−0.838543	+	0.484133i
$924$		0			0
$925$	31456.2	+	5546.58i	1.11813	+	0.197157i
$926$	9720.81	−	8156.73i	0.344974	−	0.289467i
$927$		0			0
$928$	265.246	+	1504.29i	0.00938269	+	0.0532119i
$929$	−8010.52	+	22008.7i	−0.282903	+	0.777269i	0.714110	+	0.700033i	$0.246831\pi$
$929$	−8010.52	+	22008.7i	−0.282903	+	0.777269i	−0.997013	+	0.0772353i	$0.975391\pi$
$930$		0			0
$931$	−683.555	+	1692.87i	−0.0240629	+	0.0595936i
$932$			21969.0i			0.772123i
$933$		0			0
$934$	−1800.84	+	317.536i	−0.0630891	+	0.0111243i
$935$	15538.0	−	18517.5i	0.543474	−	0.647688i
$936$		0			0
$937$	−7508.84	+	42584.7i	−0.261796	+	1.48472i	0.516209	+	0.856462i	$0.327343\pi$
$937$	−7508.84	+	42584.7i	−0.261796	+	1.48472i	−0.778006	+	0.628257i	$0.783769\pi$
$938$	−8586.39	−	4957.36i	−0.298887	−	0.172562i
$939$		0			0
$940$	17335.7	−	6309.67i	0.601519	−	0.218935i
$941$	36138.5	−	13153.4i	1.25195	−	0.455672i	0.370889	−	0.928677i	$-0.379053\pi$
$941$	36138.5	−	13153.4i	1.25195	−	0.455672i	0.881059	+	0.473006i	$0.156831\pi$
$942$		0			0
$943$	−35437.9	−	20460.1i	−1.22377	−	0.706545i
$944$	512.088	−	2904.20i	0.0176558	−	0.100131i
$945$		0			0
$946$	−349.541	+	416.567i	−0.0120133	+	0.0143169i
$947$	2254.56	−	397.540i	0.0773636	−	0.0136413i	−0.134832	−	0.990868i	$-0.543050\pi$
$947$	2254.56	−	397.540i	0.0773636	−	0.0136413i	0.212196	+	0.977227i	$0.431938\pi$
$948$		0			0
$949$			31316.9i			1.07122i
$950$	6825.20	−	960.669i	0.233093	−	0.0328087i
$951$		0			0
$952$	−14593.8	+	40096.0i	−0.496834	+	1.36504i
$953$	−433.779	−	2460.08i	−0.0147445	−	0.0836200i	0.976548	−	0.215302i	$-0.0690735\pi$
$953$	−433.779	−	2460.08i	−0.0147445	−	0.0836200i	−0.991292	+	0.131682i	$0.957962\pi$
$954$		0			0
$955$	−8852.83	+	7428.41i	−0.299970	+	0.251704i
$956$	41976.0	+	7401.50i	1.42008	+	0.250399i
$957$		0			0
$958$	3083.57	−	1780.30i	0.103993	−	0.0600406i
$959$	10791.3	+	29648.7i	0.363366	+	0.998339i
$960$		0			0
$961$	214.842	+	372.118i	0.00721165	+	0.0124910i
$962$	−12835.1	+	22231.0i	−0.430167	+	0.745070i
$963$		0			0
$964$	−31524.5	−	37569.4i	−1.05325	−	1.25522i
$965$	−10111.4	−	8484.49i	−0.337304	−	0.283031i
$966$		0			0
$967$	−51551.3	−	18763.1i	−1.71435	−	0.623973i	−0.717025	−	0.697047i	$-0.754497\pi$
$967$	−51551.3	−	18763.1i	−1.71435	−	0.623973i	−0.997327	+	0.0730739i	$0.976719\pi$
$968$	−11374.5			−0.377676
$969$		0			0
$970$	10042.8			0.332429
$971$	14110.5	+	5135.79i	0.466351	+	0.169738i	0.564499	−	0.825434i	$-0.309070\pi$
$971$	14110.5	+	5135.79i	0.466351	+	0.169738i	−0.0981477	+	0.995172i	$0.531292\pi$
$972$		0			0
$973$	−18656.6	−	15654.8i	−0.614701	−	0.515795i
$974$	−13745.5	−	16381.3i	−0.452192	−	0.538901i
$975$		0			0
$976$	6904.08	−	11958.2i	0.226429	−	0.392186i
$977$	14086.4	+	24398.3i	0.461272	+	0.798946i	0.999025	−	0.0441562i	$-0.0140599\pi$
$977$	14086.4	+	24398.3i	0.461272	+	0.798946i	−0.537753	+	0.843103i	$0.680727\pi$
$978$		0			0
$979$	−1029.17	−	2827.62i	−0.0335980	−	0.0923096i
$980$	907.989	−	524.228i	0.0295966	−	0.0170876i
$981$		0			0
$982$	−1972.68	−	347.836i	−0.0641045	−	0.0113034i
$983$	−7916.63	+	6642.84i	−0.256868	+	0.215538i	−0.762123	−	0.647432i	$-0.775843\pi$
$983$	−7916.63	+	6642.84i	−0.256868	+	0.215538i	0.505255	+	0.862970i	$0.331398\pi$
$984$		0			0
$985$	−1922.66	−	10903.9i	−0.0621940	−	0.352719i
$986$	−464.622	+	1276.54i	−0.0150067	+	0.0412305i
$987$		0			0
$988$	6559.01	−	30889.3i	0.211204	−	0.994657i
$989$			2293.24i			0.0737318i
$990$		0			0
$991$	22751.5	−	4011.70i	0.729288	−	0.128593i	0.203338	−	0.979109i	$-0.434821\pi$
$991$	22751.5	−	4011.70i	0.729288	−	0.128593i	0.525950	+	0.850516i	$0.323710\pi$
$992$	−18951.9	+	22585.9i	−0.606575	+	0.722888i
$993$		0			0
$994$	−1756.98	+	9964.32i	−0.0560644	+	0.317957i
$995$	12887.8	+	7440.80i	0.410625	+	0.237074i
$996$		0			0
$997$	806.496	−	293.541i	0.0256188	−	0.00932450i	−0.329179	−	0.944268i	$-0.606772\pi$
$997$	806.496	−	293.541i	0.0256188	−	0.00932450i	0.354798	+	0.934943i	$0.384550\pi$
$998$	−17815.1	+	6484.16i	−0.565057	+	0.205664i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	171.4.y.a.53.9	✓	120
3.2	odd	2	inner	171.4.y.a.53.12	yes	120
19.14	odd	18	inner	171.4.y.a.71.12	yes	120
57.14	even	18	inner	171.4.y.a.71.9	yes	120

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
171.4.y.a.53.9	✓	120	1.1	even	1	trivial
171.4.y.a.53.12	yes	120	3.2	odd	2	inner
171.4.y.a.71.9	yes	120	57.14	even	18	inner
171.4.y.a.71.12	yes	120	19.14	odd	18	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 171 = 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	171.y (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.02676 - 0.373709i) q^{2} +(-5.21378 - 4.37488i) q^{4} +(-4.49187 - 5.35320i) q^{5} +(9.55306 - 16.5464i) q^{7} +(8.08896 + 14.0105i) q^{8} +O(q^{10})\)	\(q+(-1.02676 - 0.373709i) q^{2} +(-5.21378 - 4.37488i) q^{4} +(-4.49187 - 5.35320i) q^{5} +(9.55306 - 16.5464i) q^{7} +(8.08896 + 14.0105i) q^{8} +(2.61152 + 7.17509i) q^{10} +(21.7010 - 12.5291i) q^{11} +(-55.1705 - 9.72805i) q^{13} +(-15.9922 + 13.4191i) q^{14} +(6.38540 + 36.2134i) q^{16} +(-47.2141 + 129.720i) q^{17} +(-51.0021 - 65.2517i) q^{19} +47.5618i q^{20} +(-26.9639 + 4.75447i) q^{22} +(-74.2193 + 88.4512i) q^{23} +(13.2262 - 75.0092i) q^{25} +(53.0113 + 30.6061i) q^{26} +(-122.196 + 44.4758i) q^{28} +(-8.46316 + 3.08034i) q^{29} +(-150.551 - 86.9205i) q^{31} +(29.4512 - 167.026i) q^{32} +(96.9548 - 115.546i) q^{34} +(-131.487 + 23.1847i) q^{35} +419.365i q^{37} +(27.9816 + 86.0576i) q^{38} +(38.6664 - 106.235i) q^{40} +(61.5401 + 349.011i) q^{41} +(15.2144 - 12.7664i) q^{43} +(-167.958 - 29.6155i) q^{44} +(109.260 - 63.0814i) q^{46} +(-132.663 - 364.487i) q^{47} +(-11.0220 - 19.0907i) q^{49} +(-41.6117 + 72.0735i) q^{50} +(245.088 + 292.085i) q^{52} +(-202.318 - 169.765i) q^{53} +(-164.549 - 59.8909i) q^{55} +309.097 q^{56} +9.84076 q^{58} +(-75.3603 - 27.4289i) q^{59} +(-287.655 - 241.371i) q^{61} +(122.096 + 145.508i) q^{62} +(54.4300 - 94.2756i) q^{64} +(195.743 + 339.036i) q^{65} +(162.434 + 446.284i) q^{67} +(813.672 - 469.774i) q^{68} +(143.670 + 25.3329i) q^{70} +(371.275 - 311.537i) q^{71} +(-97.0717 - 550.521i) q^{73} +(156.720 - 430.586i) q^{74} +(-19.5547 + 563.337i) q^{76} -478.765i q^{77} +(999.614 - 176.259i) q^{79} +(165.175 - 196.848i) q^{80} +(67.2419 - 381.348i) q^{82} +(-1116.92 - 644.856i) q^{83} +(906.494 - 329.937i) q^{85} +(-20.3923 + 7.42221i) q^{86} +(351.078 + 202.695i) q^{88} +(20.8524 - 118.260i) q^{89} +(-688.012 + 819.940i) q^{91} +(773.927 - 136.464i) q^{92} +423.817i q^{94} +(-120.211 + 566.127i) q^{95} +(449.849 - 1235.95i) q^{97} +(4.18257 + 23.7205i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 120 q - 36 q^{4}+O(q^{10}) \) 120 * q - 36 * q^4	\( 120 q - 36 q^{4} - 180 q^{10} - 156 q^{13} + 180 q^{16} + 924 q^{19} + 432 q^{22} - 360 q^{25} - 624 q^{28} + 324 q^{34} + 1440 q^{40} + 1524 q^{43} + 3888 q^{46} - 3228 q^{49} - 6000 q^{52} - 4464 q^{55} + 5616 q^{58} - 5736 q^{61} - 4524 q^{64} + 372 q^{67} + 7848 q^{70} - 276 q^{73} + 4320 q^{76} + 10536 q^{79} + 3960 q^{82} - 11592 q^{85} - 11664 q^{88} - 120 q^{91} + 5904 q^{97}+O(q^{100}) \) 120 * q - 36 * q^4 - 180 * q^10 - 156 * q^13 + 180 * q^16 + 924 * q^19 + 432 * q^22 - 360 * q^25 - 624 * q^28 + 324 * q^34 + 1440 * q^40 + 1524 * q^43 + 3888 * q^46 - 3228 * q^49 - 6000 * q^52 - 4464 * q^55 + 5616 * q^58 - 5736 * q^61 - 4524 * q^64 + 372 * q^67 + 7848 * q^70 - 276 * q^73 + 4320 * q^76 + 10536 * q^79 + 3960 * q^82 - 11592 * q^85 - 11664 * q^88 - 120 * q^91 + 5904 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more