LMFDB - Embedded newform 100.5.b.e.51.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [100,5,Mod(51,100)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(100, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 5, names="a")

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

chi := DirichletCharacter("100.51");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 100 = 2^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	100.b (of order $2$, degree $1$, 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:	$10.3369963084$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.0.1816805376000000.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 6x^{6} + 31x^{4} - 96x^{2} + 256 $ x^8 - 6x^6 + 31x^4 - 96*x^2 + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{15} $
Twist minimal:	no (minimal twist has level 20)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			51.3
Root			$1.39980 - 1.42849i$ of defining polynomial
Character	$\chi$	$=$	100.51
Dual form			100.5.b.e.51.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.79959 - 2.85697i) q^{2} +6.64118i q^{3} +(-0.324555 + 15.9967i) q^{4} +(18.9737 - 18.5926i) q^{6} -39.0703i q^{7} +(46.6107 - 43.8570i) q^{8} +36.8947 q^{9} +138.357i q^{11} +(-106.237 - 2.15543i) q^{12} -124.999 q^{13} +(-111.623 + 109.381i) q^{14} +(-255.789 - 10.3836i) q^{16} -160.412 q^{17} +(-103.290 - 105.407i) q^{18} +650.252i q^{19} +259.473 q^{21} +(395.283 - 387.344i) q^{22} +416.491i q^{23} +(291.263 + 309.551i) q^{24} +(349.947 + 357.119i) q^{26} +782.960i q^{27} +(624.997 + 12.6805i) q^{28} -236.807 q^{29} -41.5345i q^{31} +(686.440 + 759.852i) q^{32} -918.856 q^{33} +(449.088 + 458.291i) q^{34} +(-11.9744 + 590.193i) q^{36} +206.138 q^{37} +(1857.75 - 1820.44i) q^{38} -830.144i q^{39} -1816.56 q^{41} +(-726.420 - 741.307i) q^{42} +3162.64i q^{43} +(-2213.26 - 44.9046i) q^{44} +(1189.90 - 1166.01i) q^{46} -823.584i q^{47} +(68.9596 - 1698.74i) q^{48} +874.509 q^{49} -1065.32i q^{51} +(40.5692 - 1999.58i) q^{52} -4866.53 q^{53} +(2236.89 - 2191.97i) q^{54} +(-1713.51 - 1821.10i) q^{56} -4318.44 q^{57} +(662.964 + 676.551i) q^{58} -3638.55i q^{59} +4136.07 q^{61} +(-118.663 + 116.280i) q^{62} -1441.49i q^{63} +(249.122 - 4088.42i) q^{64} +(2572.42 + 2625.15i) q^{66} +3208.70i q^{67} +(52.0625 - 2566.06i) q^{68} -2766.00 q^{69} -456.333i q^{71} +(1719.69 - 1618.09i) q^{72} +5905.66 q^{73} +(-577.102 - 588.929i) q^{74} +(-10401.9 - 211.043i) q^{76} +5405.67 q^{77} +(-2371.70 + 2324.06i) q^{78} +2808.68i q^{79} -2211.32 q^{81} +(5085.63 + 5189.86i) q^{82} +3048.15i q^{83} +(-84.2134 + 4150.72i) q^{84} +(9035.57 - 8854.10i) q^{86} -1572.68i q^{87} +(6067.94 + 6448.94i) q^{88} +5143.40 q^{89} +4883.77i q^{91} +(-6662.49 - 135.174i) q^{92} +275.839 q^{93} +(-2352.96 + 2305.70i) q^{94} +(-5046.32 + 4558.78i) q^{96} +4506.56 q^{97} +(-2448.27 - 2498.45i) q^{98} +5104.65i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 48 q^{4} - 312 q^{9} - 640 q^{14} - 832 q^{16} - 960 q^{21} - 1920 q^{24} + 2496 q^{26} - 2704 q^{29} + 2176 q^{34} - 5712 q^{36} + 1456 q^{41} - 1920 q^{44} + 7040 q^{46} + 8008 q^{49} + 11520 q^{54}+ \cdots - 76800 q^{96}+O(q^{100}) $ 8 * q + 48 * q^4 - 312 * q^9 - 640 * q^14 - 832 * q^16 - 960 * q^21 - 1920 * q^24 + 2496 * q^26 - 2704 * q^29 + 2176 * q^34 - 5712 * q^36 + 1456 * q^41 - 1920 * q^44 + 7040 * q^46 + 8008 * q^49 + 11520 * q^54 - 14720 * q^56 + 6576 * q^61 - 6912 * q^64 + 46080 * q^66 + 12480 * q^69 + 23616 * q^74 - 48000 * q^76 - 19512 * q^81 - 24960 * q^84 + 37120 * q^86 - 27664 * q^89 - 10880 * q^94 - 76800 * q^96

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/100\mathbb{Z}\right)^\times$.

$n$	$51$	$77$
$\chi(n)$	$-1$	$1$

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 $

$2$	−2.79959	−	2.85697i	−0.699898	−	0.714243i
$2$	−2.79959	−	2.85697i	−0.699898	−	0.714243i
$3$			6.64118i			0.737909i	0.929447	+	0.368955i	$0.120284\pi$
$3$			6.64118i			0.737909i	−0.929447	+	0.368955i	$0.879716\pi$
$4$	−0.324555	+	15.9967i	−0.0202847	+	0.999794i
$5$		0			0
$5$		0			0
$6$	18.9737	−	18.5926i	0.527046	−	0.516462i
$7$		−	39.0703i		−	0.797354i	−0.917091	−	0.398677i	$-0.869469\pi$
$7$		−	39.0703i		−	0.797354i	0.917091	−	0.398677i	$-0.130531\pi$
$8$	46.6107	−	43.8570i	0.728293	−	0.685266i
$9$	36.8947			0.455490
$10$		0			0
$11$			138.357i			1.14345i	0.820446	+	0.571724i	$0.193725\pi$
$11$			138.357i			1.14345i	−0.820446	+	0.571724i	$0.806275\pi$
$12$	−106.237	−	2.15543i	−0.737758	−	0.0149683i
$13$	−124.999			−0.739641			−0.369821	−	0.929103i	$-0.620581\pi$
$13$	−124.999			−0.739641			−0.369821	+	0.929103i	$0.620581\pi$
$14$	−111.623	+	109.381i	−0.569504	+	0.558067i
$15$		0			0
$16$	−255.789	−	10.3836i	−0.999177	−	0.0405611i
$17$	−160.412			−0.555058			−0.277529	−	0.960717i	$-0.589515\pi$
$17$	−160.412			−0.555058			−0.277529	+	0.960717i	$0.589515\pi$
$18$	−103.290	−	105.407i	−0.318796	−	0.325330i
$19$			650.252i			1.80125i	0.434595	+	0.900626i	$0.356892\pi$
$19$			650.252i			1.80125i	−0.434595	+	0.900626i	$0.643108\pi$
$20$		0			0
$21$	259.473			0.588375
$22$	395.283	−	387.344i	0.816700	−	0.800298i
$23$			416.491i			0.787318i	0.919257	+	0.393659i	$0.128791\pi$
$23$			416.491i			0.787318i	−0.919257	+	0.393659i	$0.871209\pi$
$24$	291.263	+	309.551i	0.505664	+	0.537414i
$25$		0			0
$26$	349.947	+	357.119i	0.517674	+	0.528283i
$27$			782.960i			1.07402i
$28$	624.997	+	12.6805i	0.797190	+	0.0161741i
$29$	−236.807			−0.281578			−0.140789	−	0.990040i	$-0.544964\pi$
$29$	−236.807			−0.281578			−0.140789	+	0.990040i	$0.544964\pi$
$30$		0			0
$31$		−	41.5345i		−	0.0432201i	−0.999766	−	0.0216101i	$-0.993121\pi$
$31$		−	41.5345i		−	0.0432201i	0.999766	−	0.0216101i	$-0.00687923\pi$
$32$	686.440	+	759.852i	0.670352	+	0.742043i
$33$	−918.856			−0.843762
$34$	449.088	+	458.291i	0.388484	+	0.396446i
$35$		0			0
$36$	−11.9744	+	590.193i	−0.00923947	+	0.455396i
$37$	206.138			0.150575			0.0752877	−	0.997162i	$-0.476012\pi$
$37$	206.138			0.150575			0.0752877	+	0.997162i	$0.476012\pi$
$38$	1857.75	−	1820.44i	1.28653	−	1.26069i
$39$		−	830.144i		−	0.545788i
$40$		0			0
$41$	−1816.56			−1.08064			−0.540321	−	0.841459i	$-0.681697\pi$
$41$	−1816.56			−1.08064			−0.540321	+	0.841459i	$0.681697\pi$
$42$	−726.420	−	741.307i	−0.411803	−	0.420242i
$43$			3162.64i			1.71046i	0.518249	+	0.855230i	$0.326584\pi$
$43$			3162.64i			1.71046i	−0.518249	+	0.855230i	$0.673416\pi$
$44$	−2213.26	−	44.9046i	−1.14321	−	0.0231945i
$45$		0			0
$46$	1189.90	−	1166.01i	0.562336	−	0.551043i
$47$		−	823.584i		−	0.372831i	−0.982471	−	0.186416i	$-0.940313\pi$
$47$		−	823.584i		−	0.372831i	0.982471	−	0.186416i	$-0.0596871\pi$
$48$	68.9596	−	1698.74i	0.0299304	−	0.737302i
$49$	874.509			0.364227
$50$		0			0
$51$		−	1065.32i		−	0.409582i
$52$	40.5692	−	1999.58i	0.0150034	−	0.739489i
$53$	−4866.53			−1.73248			−0.866238	−	0.499631i	$-0.833469\pi$
$53$	−4866.53			−1.73248			−0.866238	+	0.499631i	$0.833469\pi$
$54$	2236.89	−	2191.97i	0.767110	−	0.751704i
$55$		0			0
$56$	−1713.51	−	1821.10i	−0.546400	−	0.580707i
$57$	−4318.44			−1.32916
$58$	662.964	+	676.551i	0.197076	+	0.201115i
$59$		−	3638.55i		−	1.04526i	−0.852560	−	0.522630i	$-0.824951\pi$
$59$		−	3638.55i		−	1.04526i	0.852560	−	0.522630i	$-0.175049\pi$
$60$		0			0
$61$	4136.07			1.11155			0.555774	−	0.831334i	$-0.312422\pi$
$61$	4136.07			1.11155			0.555774	+	0.831334i	$0.312422\pi$
$62$	−118.663	+	116.280i	−0.0308696	+	0.0302497i
$63$		−	1441.49i		−	0.363186i
$64$	249.122	−	4088.42i	0.0608207	−	0.998149i
$65$		0			0
$66$	2572.42	+	2625.15i	0.590547	+	0.602650i
$67$			3208.70i			0.714792i	0.933953	+	0.357396i	$0.116335\pi$
$67$			3208.70i			0.714792i	−0.933953	+	0.357396i	$0.883665\pi$
$68$	52.0625	−	2566.06i	0.0112592	−	0.554944i
$69$	−2766.00			−0.580970
$70$		0			0
$71$		−	456.333i		−	0.0905243i	−0.998975	−	0.0452621i	$-0.985588\pi$
$71$		−	456.333i		−	0.0905243i	0.998975	−	0.0452621i	$-0.0144123\pi$
$72$	1719.69	−	1618.09i	0.331730	−	0.312132i
$73$	5905.66			1.10821			0.554106	−	0.832446i	$-0.313060\pi$
$73$	5905.66			1.10821			0.554106	+	0.832446i	$0.313060\pi$
$74$	−577.102	−	588.929i	−0.105387	−	0.107547i
$75$		0			0
$76$	−10401.9	−	211.043i	−1.80088	−	0.0365379i
$77$	5405.67			0.911733
$78$	−2371.70	+	2324.06i	−0.389825	+	0.381996i
$79$			2808.68i			0.450037i	0.974354	+	0.225018i	$0.0722442\pi$
$79$			2808.68i			0.450037i	−0.974354	+	0.225018i	$0.927756\pi$
$80$		0			0
$81$	−2211.32			−0.337039
$82$	5085.63	+	5189.86i	0.756340	+	0.771841i
$83$			3048.15i			0.442466i	0.975221	+	0.221233i	$0.0710082\pi$
$83$			3048.15i			0.442466i	−0.975221	+	0.221233i	$0.928992\pi$
$84$	−84.2134	+	4150.72i	−0.0119350	+	0.588254i
$85$		0			0
$86$	9035.57	−	8854.10i	1.22168	−	1.19715i
$87$		−	1572.68i		−	0.207779i
$88$	6067.94	+	6448.94i	0.783567	+	0.832765i
$89$	5143.40			0.649337			0.324668	−	0.945828i	$-0.394747\pi$
$89$	5143.40			0.649337			0.324668	+	0.945828i	$0.394747\pi$
$90$		0			0
$91$			4883.77i			0.589756i
$92$	−6662.49	−	135.174i	−0.787156	−	0.0159705i
$93$	275.839			0.0318925
$94$	−2352.96	+	2305.70i	−0.266292	+	0.260944i
$95$		0			0
$96$	−5046.32	+	4558.78i	−0.547561	+	0.494659i
$97$	4506.56			0.478963			0.239481	−	0.970901i	$-0.423023\pi$
$97$	4506.56			0.478963			0.239481	+	0.970901i	$0.423023\pi$
$98$	−2448.27	−	2498.45i	−0.254922	−	0.260146i
$99$			5104.65i			0.520829i
$100$		0			0
$101$	−1737.92			−0.170368			−0.0851840	−	0.996365i	$-0.527148\pi$
$101$	−1737.92			−0.170368			−0.0851840	+	0.996365i	$0.527148\pi$
$102$	−3043.60	+	2982.47i	−0.292541	+	0.286666i
$103$		−	12672.6i		−	1.19452i	−0.802049	−	0.597258i	$-0.796257\pi$
$103$		−	12672.6i		−	1.19452i	0.802049	−	0.597258i	$-0.203743\pi$
$104$	−5826.31	+	5482.10i	−0.538675	+	0.506851i
$105$		0			0
$106$	13624.3	+	13903.5i	1.21256	+	1.23741i
$107$		−	6987.88i		−	0.610349i	−0.952297	−	0.305174i	$-0.901285\pi$
$107$		−	6987.88i		−	0.610349i	0.952297	−	0.305174i	$-0.0987147\pi$
$108$	−12524.8	−	254.114i	−1.07380	−	0.0217862i
$109$	811.156			0.0682734			0.0341367	−	0.999417i	$-0.489132\pi$
$109$	811.156			0.0682734			0.0341367	+	0.999417i	$0.489132\pi$
$110$		0			0
$111$			1369.00i			0.111111i
$112$	−405.692	+	9993.77i	−0.0323415	+	0.796698i
$113$	6342.41			0.496704			0.248352	−	0.968670i	$-0.420111\pi$
$113$	6342.41			0.496704			0.248352	+	0.968670i	$0.420111\pi$
$114$	12089.9	+	12337.7i	0.930277	+	0.949343i
$115$		0			0
$116$	76.8570	−	3788.13i	0.00571173	−	0.281520i
$117$	−4611.81			−0.336899
$118$	−10395.2	+	10186.5i	−0.746569	+	0.731576i
$119$			6267.34i			0.442577i
$120$		0			0
$121$	−4501.74			−0.307475
$122$	−11579.3	−	11816.6i	−0.777970	−	0.793914i
$123$		−	12064.1i		−	0.797416i
$124$	664.416	+	13.4803i	0.0432112	+	0.000876707i
$125$		0			0
$126$	−4118.28	+	4035.58i	−0.259403	+	0.254194i
$127$		−	7702.06i		−	0.477529i	−0.971078	−	0.238764i	$-0.923258\pi$
$127$		−	7702.06i		−	0.477529i	0.971078	−	0.238764i	$-0.0767424\pi$
$128$	−12377.9	+	10734.2i	−0.755489	+	0.655162i
$129$	−21003.7			−1.26216
$130$		0			0
$131$		−	15619.8i		−	0.910192i	−0.890442	−	0.455096i	$-0.849605\pi$
$131$		−	15619.8i		−	0.910192i	0.890442	−	0.455096i	$-0.150395\pi$
$132$	298.220	−	14698.7i	0.0171155	−	0.843588i
$133$	25405.6			1.43624
$134$	9167.16	−	8983.06i	0.510535	−	0.500282i
$135$		0			0
$136$	−7476.91	+	7035.18i	−0.404245	+	0.380362i
$137$	−3770.61			−0.200896			−0.100448	−	0.994942i	$-0.532028\pi$
$137$	−3770.61			−0.200896			−0.100448	+	0.994942i	$0.532028\pi$
$138$	7743.66	+	7902.37i	0.406620	+	0.414953i
$139$			7001.21i			0.362363i	0.983450	+	0.181181i	$0.0579921\pi$
$139$			7001.21i			0.362363i	−0.983450	+	0.181181i	$0.942008\pi$
$140$		0			0
$141$	5469.57			0.275116
$142$	−1303.73	+	1277.55i	−0.0646563	+	0.0633578i
$143$		−	17294.6i		−	0.845742i
$144$	−9437.26	−	383.101i	−0.455115	−	0.0184751i
$145$		0			0
$146$	−16533.5	−	16872.3i	−0.775636	−	0.791532i
$147$			5807.78i			0.268766i
$148$	−66.9031	+	3297.53i	−0.00305438	+	0.150544i
$149$	29966.7			1.34979			0.674894	−	0.737914i	$-0.264189\pi$
$149$	29966.7			1.34979			0.674894	+	0.737914i	$0.264189\pi$
$150$		0			0
$151$			12397.1i			0.543710i	0.962338	+	0.271855i	$0.0876372\pi$
$151$			12397.1i			0.543710i	−0.962338	+	0.271855i	$0.912363\pi$
$152$	28518.1	+	30308.7i	1.23434	+	1.31184i
$153$	−5918.34			−0.252823
$154$	−15133.7	−	15443.8i	−0.638121	−	0.651199i
$155$		0			0
$156$	13279.6	+	269.428i	0.545676	+	0.0110712i
$157$	18293.8			0.742171			0.371085	−	0.928599i	$-0.378986\pi$
$157$	18293.8			0.742171			0.371085	+	0.928599i	$0.378986\pi$
$158$	8024.32	−	7863.16i	0.321436	−	0.314980i
$159$		−	32319.5i		−	1.27841i
$160$		0			0
$161$	16272.5			0.627771
$162$	6190.79	+	6317.66i	0.235893	+	0.240728i
$163$			26437.3i			0.995043i	0.867452	+	0.497522i	$0.165756\pi$
$163$			26437.3i			0.995043i	−0.867452	+	0.497522i	$0.834244\pi$
$164$	589.574	−	29059.0i	0.0219205	−	1.08042i
$165$		0			0
$166$	8708.47	−	8533.58i	0.316028	−	0.309681i
$167$			16417.6i			0.588677i	0.955701	+	0.294339i	$0.0950993\pi$
$167$			16417.6i			0.588677i	−0.955701	+	0.294339i	$0.904901\pi$
$168$	12094.2	−	11379.7i	0.428509	−	0.403193i
$169$	−12936.2			−0.452931
$170$		0			0
$171$			23990.8i			0.820452i
$172$	−50591.8	−	1026.45i	−1.71011	−	0.0346962i
$173$	−14503.0			−0.484581			−0.242291	−	0.970204i	$-0.577899\pi$
$173$	−14503.0			−0.484581			−0.242291	+	0.970204i	$0.577899\pi$
$174$	−4493.10	+	4402.86i	−0.148405	+	0.145424i
$175$		0			0
$176$	1436.65	−	35390.3i	0.0463795	−	1.14251i
$177$	24164.3			0.771307
$178$	−14399.4	−	14694.5i	−0.454470	−	0.463784i
$179$		−	29882.7i		−	0.932640i	−0.884616	−	0.466320i	$-0.845580\pi$
$179$		−	29882.7i		−	0.932640i	0.884616	−	0.466320i	$-0.154420\pi$
$180$		0			0
$181$	−13028.0			−0.397669			−0.198834	−	0.980033i	$-0.563716\pi$
$181$	−13028.0			−0.397669			−0.198834	+	0.980033i	$0.563716\pi$
$182$	13952.8	−	13672.6i	0.421229	−	0.412769i
$183$			27468.4i			0.820221i
$184$	18266.1	+	19413.0i	0.539522	+	0.573398i
$185$		0			0
$186$	−772.236	−	788.062i	−0.0223215	−	0.0227790i
$187$		−	22194.1i		−	0.634680i
$188$	13174.6	+	267.299i	0.372754	+	0.00756277i
$189$	30590.5			0.856374
$190$		0			0
$191$		−	53818.5i		−	1.47525i	−0.675212	−	0.737624i	$-0.735948\pi$
$191$		−	53818.5i		−	1.47525i	0.675212	−	0.737624i	$-0.264052\pi$
$192$	27151.9	+	1654.46i	0.736543	+	0.0448802i
$193$	−48440.5			−1.30045			−0.650225	−	0.759741i	$-0.725326\pi$
$193$	−48440.5			−1.30045			−0.650225	+	0.759741i	$0.725326\pi$
$194$	−12616.5	−	12875.1i	−0.335225	−	0.342096i
$195$		0			0
$196$	−283.827	+	13989.3i	−0.00738824	+	0.364152i
$197$	−74216.3			−1.91235			−0.956174	−	0.292798i	$-0.905414\pi$
$197$	−74216.3			−1.91235			−0.956174	+	0.292798i	$0.905414\pi$
$198$	14583.8	−	14290.9i	0.371998	−	0.364527i
$199$			13240.2i			0.334341i	0.985928	+	0.167170i	$0.0534630\pi$
$199$			13240.2i			0.334341i	−0.985928	+	0.167170i	$0.946537\pi$
$200$		0			0
$201$	−21309.6			−0.527452
$202$	4865.48	+	4965.19i	0.119240	+	0.121684i
$203$			9252.13i			0.224517i
$204$	17041.7	+	345.757i	0.409498	+	0.00830826i
$205$		0			0
$206$	−36205.3	+	35478.2i	−0.853174	+	0.836040i
$207$			15366.3i			0.358615i
$208$	31973.5	+	1297.95i	0.739032	+	0.0300006i
$209$	−89967.1			−2.05964
$210$		0			0
$211$			4466.51i			0.100324i	0.998741	+	0.0501618i	$0.0159737\pi$
$211$			4466.51i			0.100324i	−0.998741	+	0.0501618i	$0.984026\pi$
$212$	1579.46	−	77848.4i	0.0351428	−	1.73212i
$213$	3030.59			0.0667987
$214$	−19964.2	+	19563.2i	−0.435937	+	0.427182i
$215$		0			0
$216$	34338.3	+	36494.4i	0.735989	+	0.782201i
$217$	−1622.77			−0.0344617
$218$	−2270.91	−	2317.45i	−0.0477844	−	0.0487637i
$219$			39220.6i			0.817760i
$220$		0			0
$221$	20051.4			0.410544
$222$	3911.19	−	3832.64i	0.0793602	−	0.0777664i
$223$		−	4344.79i		−	0.0873694i	−0.999045	−	0.0436847i	$-0.986090\pi$
$223$		−	4344.79i		−	0.0873694i	0.999045	−	0.0436847i	$-0.0139097\pi$
$224$	29687.7	−	26819.5i	0.591671	−	0.534508i
$225$		0			0
$226$	−17756.2	−	18120.1i	−0.347642	−	0.354767i
$227$			62311.6i			1.20925i	0.796509	+	0.604626i	$0.206677\pi$
$227$			62311.6i			1.20925i	−0.796509	+	0.604626i	$0.793323\pi$
$228$	1401.57	−	69080.9i	0.0269616	−	1.32889i
$229$	78625.5			1.49931			0.749657	−	0.661827i	$-0.230219\pi$
$229$	78625.5			1.49931			0.749657	+	0.661827i	$0.230219\pi$
$230$		0			0
$231$			35900.0i			0.672777i
$232$	−11037.8	+	10385.7i	−0.205071	+	0.192956i
$233$	−2464.06			−0.0453878			−0.0226939	−	0.999742i	$-0.507224\pi$
$233$	−2464.06			−0.0453878			−0.0226939	+	0.999742i	$0.507224\pi$
$234$	12911.2	+	13175.8i	0.235795	+	0.240628i
$235$		0			0
$236$	58204.8	+	1180.91i	1.04505	+	0.0212028i
$237$	−18653.0			−0.332086
$238$	17905.6	−	17546.0i	0.316108	−	0.309759i
$239$			54386.5i			0.952128i	0.879411	+	0.476064i	$0.157937\pi$
$239$			54386.5i			0.952128i	−0.879411	+	0.476064i	$0.842063\pi$
$240$		0			0
$241$	4097.25			0.0705437			0.0352718	−	0.999378i	$-0.488770\pi$
$241$	4097.25			0.0705437			0.0352718	+	0.999378i	$0.488770\pi$
$242$	12603.0	+	12861.3i	0.215201	+	0.219612i
$243$			48734.0i			0.825315i
$244$	−1342.38	+	66163.5i	−0.0225474	+	1.11132i
$245$		0			0
$246$	−34466.8	+	33774.6i	−0.569548	+	0.558110i
$247$		−	81281.1i		−	1.33228i
$248$	−1821.58	−	1935.96i	−0.0296173	−	0.0314769i
$249$	−20243.3			−0.326500
$250$		0			0
$251$		−	48310.9i		−	0.766828i	−0.923577	−	0.383414i	$-0.874748\pi$
$251$		−	48310.9i		−	0.766828i	0.923577	−	0.383414i	$-0.125252\pi$
$252$	23059.0	+	467.842i	0.363112	+	0.00736713i
$253$	−57624.6			−0.900258
$254$	−22004.6	+	21562.6i	−0.341071	+	0.334222i
$255$		0			0
$256$	65320.4	+	5312.05i	0.996710	+	0.0810554i
$257$	24560.5			0.371853			0.185927	−	0.982564i	$-0.440471\pi$
$257$	24560.5			0.371853			0.185927	+	0.982564i	$0.440471\pi$
$258$	58801.7	+	60006.9i	0.883387	+	0.901491i
$259$		−	8053.87i		−	0.120062i
$260$		0			0
$261$	−8736.92			−0.128256
$262$	−44625.3	+	43729.1i	−0.650098	+	0.637042i
$263$			83305.2i			1.20437i	0.798356	+	0.602186i	$0.205703\pi$
$263$			83305.2i			1.20437i	−0.798356	+	0.602186i	$0.794297\pi$
$264$	−42828.6	+	40298.3i	−0.614505	+	0.578201i
$265$		0			0
$266$	−71125.2	−	72582.9i	−1.00522	−	1.02582i
$267$			34158.2i			0.479152i
$268$	−51328.6	−	1041.40i	−0.714645	−	0.0144993i
$269$	26533.4			0.366681			0.183341	−	0.983049i	$-0.441309\pi$
$269$	26533.4			0.366681			0.183341	+	0.983049i	$0.441309\pi$
$270$		0			0
$271$			110062.i			1.49864i	0.662207	+	0.749321i	$0.269620\pi$
$271$			110062.i			1.49864i	−0.662207	+	0.749321i	$0.730380\pi$
$272$	41031.6	+	1665.66i	0.554601	+	0.0225137i
$273$	−32434.0			−0.435186
$274$	10556.2	+	10772.5i	0.140606	+	0.143488i
$275$		0			0
$276$	897.719	−	44246.8i	0.0117848	−	0.580850i
$277$	111083.			1.44773			0.723864	−	0.689942i	$-0.242364\pi$
$277$	111083.			1.44773			0.723864	+	0.689942i	$0.242364\pi$
$278$	20002.2	−	19600.5i	0.258815	−	0.253617i
$279$		−	1532.40i		−	0.0196863i
$280$		0			0
$281$	−66386.2			−0.840747			−0.420374	−	0.907351i	$-0.638101\pi$
$281$	−66386.2			−0.840747			−0.420374	+	0.907351i	$0.638101\pi$
$282$	−15312.6	−	15626.4i	−0.192553	−	0.196499i
$283$		−	123904.i		−	1.54708i	−0.633747	−	0.773540i	$-0.718484\pi$
$283$		−	123904.i		−	1.54708i	0.633747	−	0.773540i	$-0.281516\pi$
$284$	7299.83	+	148.105i	0.0905057	+	0.00183626i
$285$		0			0
$286$	−49410.1	+	48417.8i	−0.604065	+	0.591933i
$287$			70973.6i			0.861654i
$288$	25326.0	+	28034.5i	0.305338	+	0.337993i
$289$	−57789.1			−0.691911
$290$		0			0
$291$			29928.9i			0.353431i
$292$	−1916.71	+	94471.2i	−0.0224798	+	1.10798i
$293$	79770.8			0.929199			0.464600	−	0.885521i	$-0.346198\pi$
$293$	79770.8			0.929199			0.464600	+	0.885521i	$0.346198\pi$
$294$	16592.6	−	16259.4i	0.191964	−	0.188109i
$295$		0			0
$296$	9608.23	−	9040.59i	0.109663	−	0.103184i
$297$	−108328.			−1.22809
$298$	−83894.5	−	85613.9i	−0.944715	−	0.964077i
$299$		−	52061.1i		−	0.582333i
$300$		0			0
$301$	123565.			1.36384
$302$	35418.3	−	34707.0i	0.388341	−	0.380542i
$303$		−	11541.9i		−	0.125716i
$304$	6751.98	−	166328.i	0.0730607	−	1.79977i
$305$		0			0
$306$	16568.9	+	16908.5i	0.176950	+	0.180577i
$307$		−	102607.i		−	1.08868i	−0.838865	−	0.544340i	$-0.816780\pi$
$307$		−	102607.i		−	1.08868i	0.838865	−	0.544340i	$-0.183220\pi$
$308$	−1754.44	+	86472.9i	−0.0184942	+	0.911546i
$309$	84161.2			0.881445
$310$		0			0
$311$		−	113118.i		−	1.16953i	−0.811203	−	0.584764i	$-0.801187\pi$
$311$		−	113118.i		−	1.16953i	0.811203	−	0.584764i	$-0.198813\pi$
$312$	−36407.6	−	38693.6i	−0.374010	−	0.397494i
$313$	180078.			1.83811			0.919055	−	0.394128i	$-0.128953\pi$
$313$	180078.			1.83811			0.919055	+	0.394128i	$0.128953\pi$
$314$	−51215.1	−	52264.7i	−0.519444	−	0.530090i
$315$		0			0
$316$	−44929.6	−	911.572i	−0.449944	−	0.00912887i
$317$	19461.2			0.193665			0.0968324	−	0.995301i	$-0.469129\pi$
$317$	19461.2			0.193665			0.0968324	+	0.995301i	$0.469129\pi$
$318$	−92335.8	+	90481.5i	−0.913095	+	0.894757i
$319$		−	32764.0i		−	0.321970i
$320$		0			0
$321$	46407.8			0.450382
$322$	−45556.3	−	46489.9i	−0.439376	−	0.448381i
$323$		−	104308.i		−	0.999799i
$324$	717.694	−	35373.8i	0.00683675	−	0.336970i
$325$		0			0
$326$	75530.6	−	74013.7i	0.710702	−	0.696429i
$327$			5387.04i			0.0503796i
$328$	−84671.2	+	79668.9i	−0.787024	+	0.740527i
$329$	−32177.7			−0.297278
$330$		0			0
$331$		−	62028.6i		−	0.566156i	−0.959097	−	0.283078i	$-0.908644\pi$
$331$		−	62028.6i		−	0.566156i	0.959097	−	0.283078i	$-0.0913555\pi$
$332$	−48760.4	−	989.293i	−0.442375	−	0.00897530i
$333$	7605.38			0.0685856
$334$	46904.6	−	45962.6i	0.420458	−	0.412014i
$335$		0			0
$336$	−66370.5	−	2694.28i	−0.587891	−	0.0238651i
$337$	26723.7			0.235308			0.117654	−	0.993055i	$-0.462463\pi$
$337$	26723.7			0.235308			0.117654	+	0.993055i	$0.462463\pi$
$338$	36216.0	+	36958.2i	0.317006	+	0.323503i
$339$			42121.1i			0.366522i
$340$		0			0
$341$	5746.61			0.0494200
$342$	68541.1	−	67164.6i	0.586001	−	0.574233i
$343$		−	127975.i		−	1.08777i
$344$	138704.	+	147413.i	1.17212	+	1.24572i
$345$		0			0
$346$	40602.6	+	41434.7i	0.339157	+	0.346108i
$347$		−	138874.i		−	1.15335i	−0.816974	−	0.576675i	$-0.804350\pi$
$347$		−	138874.i		−	1.15335i	0.816974	−	0.576675i	$-0.195650\pi$
$348$	25157.7	+	510.422i	0.207736	+	0.00421474i
$349$	−74063.7			−0.608072			−0.304036	−	0.952661i	$-0.598334\pi$
$349$	−74063.7			−0.608072			−0.304036	+	0.952661i	$0.598334\pi$
$350$		0			0
$351$		−	97869.5i		−	0.794389i
$352$	−105131.	+	94974.0i	−0.848489	+	0.766513i
$353$	−22898.3			−0.183761			−0.0918805	−	0.995770i	$-0.529288\pi$
$353$	−22898.3			−0.183761			−0.0918805	+	0.995770i	$0.529288\pi$
$354$	−67650.2	−	69036.6i	−0.539837	−	0.550901i
$355$		0			0
$356$	−1669.32	+	82277.4i	−0.0131716	+	0.649203i
$357$	−41622.6			−0.326582
$358$	−85374.0	+	83659.4i	−0.666131	+	0.652753i
$359$		−	216833.i		−	1.68242i	−0.540705	−	0.841212i	$-0.681842\pi$
$359$		−	216833.i		−	1.68242i	0.540705	−	0.841212i	$-0.318158\pi$
$360$		0			0
$361$	−292507.			−2.24451
$362$	36473.2	+	37220.7i	0.278328	+	0.284032i
$363$		−	29896.9i		−	0.226889i
$364$	−78124.2	−	1585.05i	−0.589634	−	0.0119630i
$365$		0			0
$366$	78476.4	−	76900.3i	0.585837	−	0.574071i
$367$			17075.9i			0.126780i	0.997989	+	0.0633900i	$0.0201912\pi$
$367$			17075.9i			0.126780i	−0.997989	+	0.0633900i	$0.979809\pi$
$368$	4324.69	−	106534.i	0.0319345	−	0.786670i
$369$	−67021.4			−0.492221
$370$		0			0
$371$			190137.i			1.38140i
$372$	−89.5249	+	4412.51i	−0.000646931	+	0.0318860i
$373$	−8495.42			−0.0610615			−0.0305307	−	0.999534i	$-0.509720\pi$
$373$	−8495.42			−0.0610615			−0.0305307	+	0.999534i	$0.509720\pi$
$374$	−63408.0	+	62134.5i	−0.453316	+	0.444212i
$375$		0			0
$376$	−36120.0	−	38387.9i	−0.255489	−	0.271530i
$377$	29600.7			0.208267
$378$	−85641.0	−	87396.2i	−0.599374	−	0.611658i
$379$		−	59878.5i		−	0.416862i	−0.978037	−	0.208431i	$-0.933164\pi$
$379$		−	59878.5i		−	0.416862i	0.978037	−	0.208431i	$-0.0668357\pi$
$380$		0			0
$381$	51150.8			0.352373
$382$	−153758.	+	150670.i	−1.05368	+	1.03252i
$383$			144186.i			0.982935i	0.870896	+	0.491467i	$0.163539\pi$
$383$			144186.i			0.982935i	−0.870896	+	0.491467i	$0.836461\pi$
$384$	−71287.6	−	82204.1i	−0.483450	−	0.557482i
$385$		0			0
$386$	135614.	+	138393.i	0.910183	+	0.928837i
$387$			116685.i			0.779097i
$388$	−1462.63	+	72090.1i	−0.00971562	+	0.478864i
$389$	237951.			1.57249			0.786247	−	0.617913i	$-0.212021\pi$
$389$	237951.			1.57249			0.786247	+	0.617913i	$0.212021\pi$
$390$		0			0
$391$		−	66810.1i		−	0.437007i
$392$	40761.5	−	38353.4i	0.265264	−	0.249592i
$393$	103734.			0.671639
$394$	207776.	+	212034.i	1.33845	+	1.36588i
$395$		0			0
$396$	−81657.5	−	1656.74i	−0.520722	−	0.0105649i
$397$	267251.			1.69566			0.847828	−	0.530271i	$-0.177910\pi$
$397$	267251.			1.69566			0.847828	+	0.530271i	$0.177910\pi$
$398$	37826.9	−	37067.2i	0.238800	−	0.234004i
$399$			168723.i			1.05981i
$400$		0			0
$401$	17276.0			0.107437			0.0537185	−	0.998556i	$-0.482893\pi$
$401$	17276.0			0.107437			0.0537185	+	0.998556i	$0.482893\pi$
$402$	59658.1	+	60880.8i	0.369163	+	0.376728i
$403$			5191.79i			0.0319674i
$404$	564.052	−	27801.1i	0.00345586	−	0.170333i
$405$		0			0
$406$	26433.1	−	25902.2i	0.160360	−	0.157139i
$407$			28520.7i			0.172175i
$408$	−46721.9	−	49655.5i	−0.280673	−	0.298296i
$409$	−126218.			−0.754530			−0.377265	−	0.926105i	$-0.623135\pi$
$409$	−126218.			−0.754530			−0.377265	+	0.926105i	$0.623135\pi$
$410$		0			0
$411$		−	25041.3i		−	0.148243i
$412$	202720.	+	4112.97i	1.19427	+	0.0242304i
$413$	−142159.			−0.833442
$414$	43901.1	−	43019.4i	0.256138	−	0.250994i
$415$		0			0
$416$	−85804.6	−	94981.1i	−0.495820	−	0.548846i
$417$	−46496.3			−0.267391
$418$	251871.	+	257033.i	1.44154	+	1.47108i
$419$			270580.i			1.54123i	0.637299	+	0.770617i	$0.280052\pi$
$419$			270580.i			1.54123i	−0.637299	+	0.770617i	$0.719948\pi$
$420$		0			0
$421$	260404.			1.46921			0.734605	−	0.678495i	$-0.237368\pi$
$421$	260404.			1.46921			0.734605	+	0.678495i	$0.237368\pi$
$422$	12760.7	−	12504.4i	0.0716554	−	0.0702163i
$423$		−	30385.9i		−	0.169821i
$424$	−226832.	+	213431.i	−1.26175	+	1.18721i
$425$		0			0
$426$	−8484.42	−	8658.31i	−0.0467523	−	0.0477105i
$427$		−	161598.i		−	0.886296i
$428$	111783.	+	2267.95i	0.610223	+	0.0123807i
$429$	114856.			0.624081
$430$		0			0
$431$			326771.i			1.75909i	0.475814	+	0.879546i	$0.342153\pi$
$431$			326771.i			1.75909i	−0.475814	+	0.879546i	$0.657847\pi$
$432$	8129.97	−	200273.i	0.0435634	−	1.07314i
$433$	164821.			0.879099			0.439549	−	0.898218i	$-0.355138\pi$
$433$	164821.			0.879099			0.439549	+	0.898218i	$0.355138\pi$
$434$	4543.09	+	4636.20i	0.0241197	+	0.0246140i
$435$		0			0
$436$	−263.265	+	12975.8i	−0.00138491	+	0.0682593i
$437$	−270824.			−1.41816
$438$	112052.	−	109802.i	0.584079	−	0.572349i
$439$			273776.i			1.42058i	0.703907	+	0.710292i	$0.251437\pi$
$439$			273776.i			1.42058i	−0.703907	+	0.710292i	$0.748563\pi$
$440$		0			0
$441$	32264.7			0.165902
$442$	−56135.7	−	57286.1i	−0.287339	−	0.293228i
$443$			10446.4i			0.0532305i	0.999646	+	0.0266153i	$0.00847290\pi$
$443$			10446.4i			0.0532305i	−0.999646	+	0.0266153i	$0.991527\pi$
$444$	−21899.5	−	444.316i	−0.111088	−	0.00225385i
$445$		0			0
$446$	−12412.9	+	12163.7i	−0.0624029	+	0.0611497i
$447$			199014.i			0.996022i
$448$	−159736.	−	9733.27i	−0.795878	−	0.0484956i
$449$	−193840.			−0.961502			−0.480751	−	0.876857i	$-0.659636\pi$
$449$	−193840.			−0.961502			−0.480751	+	0.876857i	$0.659636\pi$
$450$		0			0
$451$		−	251334.i		−	1.23566i
$452$	−2058.46	+	101458.i	−0.0100755	+	0.496601i
$453$	−82331.7			−0.401209
$454$	178022.	−	174447.i	0.863699	−	0.846354i
$455$		0			0
$456$	−201286.	+	189394.i	−0.968018	+	0.910829i
$457$	−31679.4			−0.151686			−0.0758428	−	0.997120i	$-0.524165\pi$
$457$	−31679.4			−0.151686			−0.0758428	+	0.997120i	$0.524165\pi$
$458$	−220119.	−	224631.i	−1.04937	−	1.07087i
$459$		−	125596.i		−	0.596143i
$460$		0			0
$461$	−92279.5			−0.434213			−0.217107	−	0.976148i	$-0.569662\pi$
$461$	−92279.5			−0.434213			−0.217107	+	0.976148i	$0.569662\pi$
$462$	102565.	−	100505.i	0.480526	−	0.470875i
$463$			196264.i			0.915542i	0.889070	+	0.457771i	$0.151352\pi$
$463$			196264.i			0.915542i	−0.889070	+	0.457771i	$0.848648\pi$
$464$	60572.7	+	2458.92i	0.281346	+	0.0114211i
$465$		0			0
$466$	6898.35	+	7039.73i	0.0317668	+	0.0324179i
$467$			261041.i			1.19695i	0.801142	+	0.598475i	$0.204226\pi$
$467$			261041.i			1.19695i	−0.801142	+	0.598475i	$0.795774\pi$
$468$	1496.79	−	73773.8i	0.00683390	−	0.336830i
$469$	125365.			0.569942
$470$		0			0
$471$			121492.i			0.547655i
$472$	−159576.	−	169596.i	−0.716281	−	0.761255i
$473$	−437574.			−1.95582
$474$	52220.7	+	53291.0i	0.232427	+	0.237190i
$475$		0			0
$476$	−100257.	−	2034.10i	−0.442486	−	0.00897755i
$477$	−179549.			−0.789125
$478$	155381.	−	152260.i	0.680051	−	0.666393i
$479$		−	105637.i		−	0.460410i	−0.973142	−	0.230205i	$-0.926060\pi$
$479$		−	105637.i		−	0.460410i	0.973142	−	0.230205i	$-0.0739396\pi$
$480$		0			0
$481$	−25767.1			−0.111372
$482$	−11470.6	−	11705.7i	−0.0493734	−	0.0503853i
$483$			108068.i			0.463238i
$484$	1461.06	−	72013.0i	0.00623704	−	0.307412i
$485$		0			0
$486$	139232.	−	136435.i	0.589475	−	0.577637i
$487$		−	332629.i		−	1.40250i	−0.712916	−	0.701249i	$-0.752626\pi$
$487$		−	332629.i		−	1.40250i	0.712916	−	0.701249i	$-0.247374\pi$
$488$	192785.	−	181396.i	0.809532	−	0.761706i
$489$	−175575.			−0.734252
$490$		0			0
$491$			94449.4i			0.391775i	0.980626	+	0.195887i	$0.0627587\pi$
$491$			94449.4i			0.391775i	−0.980626	+	0.195887i	$0.937241\pi$
$492$	192986.	+	3915.47i	0.797252	+	0.0161754i
$493$	37986.6			0.156292
$494$	−232218.	+	227554.i	−0.951571	+	0.932461i
$495$		0			0
$496$	−431.279	+	10624.1i	−0.00175305	+	0.0431846i
$497$	−17829.1			−0.0721799
$498$	56673.1	+	57834.6i	0.228517	+	0.233200i
$499$		−	301032.i		−	1.20896i	−0.796621	−	0.604479i	$-0.793381\pi$
$499$		−	301032.i		−	1.20896i	0.796621	−	0.604479i	$-0.206619\pi$
$500$		0			0
$501$	−109032.			−0.434390
$502$	−138023.	+	135251.i	−0.547701	+	0.536702i
$503$			3184.75i			0.0125875i	0.999980	+	0.00629374i	$0.00200337\pi$
$503$			3184.75i			0.0125875i	−0.999980	+	0.00629374i	$0.997997\pi$
$504$	−63219.3	−	67188.8i	−0.248879	−	0.264506i
$505$		0			0
$506$	161325.	+	164632.i	0.630089	+	0.643003i
$507$		−	85911.4i		−	0.334222i
$508$	123208.	+	2499.75i	0.477431	+	0.00968653i
$509$	159009.			0.613741			0.306871	−	0.951751i	$-0.400718\pi$
$509$	159009.			0.613741			0.306871	+	0.951751i	$0.400718\pi$
$510$		0			0
$511$		−	230736.i		−	0.883637i
$512$	−167694.	−	201490.i	−0.639702	−	0.768623i
$513$	−509121.			−1.93458
$514$	−68759.5	−	70168.7i	−0.260260	−	0.265593i
$515$		0			0
$516$	6816.85	−	335990.i	0.0256026	−	1.26190i
$517$	113949.			0.426313
$518$	−23009.7	+	22547.6i	−0.0857533	+	0.0840311i
$519$		−	96317.3i		−	0.357577i
$520$		0			0
$521$	36476.2			0.134380			0.0671899	−	0.997740i	$-0.478597\pi$
$521$	36476.2			0.134380			0.0671899	+	0.997740i	$0.478597\pi$
$522$	24459.8	+	24961.1i	0.0897661	+	0.0916058i
$523$			449988.i			1.64512i	0.568679	+	0.822559i	$0.307454\pi$
$523$			449988.i			1.64512i	−0.568679	+	0.822559i	$0.692546\pi$
$524$	249865.	+	5069.49i	0.910004	+	0.0184630i
$525$		0			0
$526$	238000.	−	233221.i	0.860214	−	0.842938i
$527$			6662.63i			0.0239897i
$528$	235034.	+	9541.07i	0.843067	+	0.0342239i
$529$	106376.			0.380130
$530$		0			0
$531$		−	134243.i		−	0.476105i
$532$	−8245.51	+	406405.i	−0.0291336	+	1.43594i
$533$	227069.			0.799287
$534$	97589.1	−	95629.2i	0.342230	−	0.335357i
$535$		0			0
$536$	140724.	+	149560.i	0.489823	+	0.520578i
$537$	198457.			0.688204
$538$	−74282.8	−	75805.2i	−0.256640	−	0.261899i
$539$			120995.i			0.416475i
$540$		0			0
$541$	−247407.			−0.845314			−0.422657	−	0.906290i	$-0.638903\pi$
$541$	−247407.			−0.845314			−0.422657	+	0.906290i	$0.638903\pi$
$542$	314443.	−	308128.i	1.07039	−	1.04890i
$543$		−	86521.5i		−	0.293443i
$544$	−110113.	−	121889.i	−0.372084	−	0.411877i
$545$		0			0
$546$	90802.0	+	92663.0i	0.304586	+	0.310829i
$547$			313468.i			1.04765i	0.851824	+	0.523827i	$0.175496\pi$
$547$			313468.i			1.04765i	−0.851824	+	0.523827i	$0.824504\pi$
$548$	1223.77	−	60317.3i	0.00407511	−	0.200854i
$549$	152599.			0.506298
$550$		0			0
$551$		−	153984.i		−	0.507193i
$552$	−128925.	+	121308.i	−0.423116	+	0.398119i
$553$	109736.			0.358839
$554$	−310987.	−	317360.i	−1.01326	−	1.03403i
$555$		0			0
$556$	−111996.	−	2272.28i	−0.362288	−	0.00735042i
$557$	−123970.			−0.399581			−0.199790	−	0.979839i	$-0.564026\pi$
$557$	−123970.			−0.399581			−0.199790	+	0.979839i	$0.564026\pi$
$558$	−4378.03	+	4290.10i	−0.0140608	+	0.0137784i
$559$		−	395328.i		−	1.26513i
$560$		0			0
$561$	147395.			0.468336
$562$	185854.	+	189663.i	0.588437	+	0.600497i
$563$			81897.7i			0.258378i	0.991620	+	0.129189i	$0.0412373\pi$
$563$			81897.7i			0.258378i	−0.991620	+	0.129189i	$0.958763\pi$
$564$	−1775.18	+	87495.2i	−0.00558064	+	0.275059i
$565$		0			0
$566$	−353990.	+	346881.i	−1.10499	+	1.08280i
$567$			86396.9i			0.268740i
$568$	−20013.4	−	21270.0i	−0.0620332	−	0.0659282i
$569$	−479808.			−1.48198			−0.740990	−	0.671516i	$-0.765644\pi$
$569$	−479808.			−1.48198			−0.740990	+	0.671516i	$0.765644\pi$
$570$		0			0
$571$			314368.i			0.964199i	0.876116	+	0.482100i	$0.160126\pi$
$571$			314368.i			0.964199i	−0.876116	+	0.482100i	$0.839874\pi$
$572$	276656.	+	5613.05i	0.845568	+	0.0171556i
$573$	357419.			1.08860
$574$	202769.	−	198697.i	0.615430	−	0.603070i
$575$		0			0
$576$	9191.26	−	150841.i	0.0277032	−	0.454646i
$577$	229486.			0.689294			0.344647	−	0.938732i	$-0.387999\pi$
$577$	229486.			0.689294			0.344647	+	0.938732i	$0.387999\pi$
$578$	161786.	+	165102.i	0.484267	+	0.494192i
$579$		−	321702.i		−	0.959615i
$580$		0			0
$581$	119092.			0.352802
$582$	85506.0	−	83788.7i	0.252436	−	0.247366i
$583$		−	673319.i		−	1.98100i
$584$	275267.	−	259005.i	0.807103	−	0.759420i
$585$		0			0
$586$	−223326.	−	227903.i	−0.650345	−	0.663674i
$587$			308124.i			0.894230i	0.894476	+	0.447115i	$0.147549\pi$
$587$			308124.i			0.894230i	−0.894476	+	0.447115i	$0.852451\pi$
$588$	−92905.3	−	1884.94i	−0.268711	−	0.00545185i
$589$	27007.9			0.0778503
$590$		0			0
$591$		−	492884.i		−	1.41114i
$592$	−52727.8	−	2140.46i	−0.150452	−	0.00610750i
$593$	379121.			1.07812			0.539062	−	0.842266i	$-0.318779\pi$
$593$	379121.			1.07812			0.539062	+	0.842266i	$0.318779\pi$
$594$	303275.	+	309491.i	0.859536	+	0.877151i
$595$		0			0
$596$	−9725.84	+	479368.i	−0.0273801	+	1.34951i
$597$	−87930.7			−0.246713
$598$	−148737.	+	145750.i	−0.415927	+	0.407574i
$599$			415907.i			1.15916i	0.814916	+	0.579579i	$0.196783\pi$
$599$			415907.i			1.15916i	−0.814916	+	0.579579i	$0.803217\pi$
$600$		0			0
$601$	95042.6			0.263130			0.131565	−	0.991308i	$-0.458000\pi$
$601$	95042.6			0.263130			0.131565	+	0.991308i	$0.458000\pi$
$602$	−345933.	−	353023.i	−0.954550	−	0.974113i
$603$			118384.i			0.325580i
$604$	−198313.	−	4023.56i	−0.543599	−	0.0110290i
$605$		0			0
$606$	−32974.8	+	32312.5i	−0.0897918	+	0.0879885i
$607$		−	253259.i		−	0.687364i	−0.939086	−	0.343682i	$-0.888326\pi$
$607$		−	253259.i		−	0.687364i	0.939086	−	0.343682i	$-0.111674\pi$
$608$	−494095.	+	446359.i	−1.33661	+	1.20747i
$609$	−61445.1			−0.165673
$610$		0			0
$611$			102947.i			0.275761i
$612$	1920.83	−	94673.9i	0.00512844	−	0.252771i
$613$	−427719.			−1.13825			−0.569125	−	0.822251i	$-0.692718\pi$
$613$	−427719.			−1.13825			−0.569125	+	0.822251i	$0.692718\pi$
$614$	−293145.	+	287258.i	−0.777581	+	0.761965i
$615$		0			0
$616$	251962.	−	237076.i	0.664009	−	0.624780i
$617$	−283218.			−0.743962			−0.371981	−	0.928240i	$-0.621321\pi$
$617$	−283218.			−0.743962			−0.371981	+	0.928240i	$0.621321\pi$
$618$	−235617.	−	240446.i	−0.616922	−	0.629565i
$619$			647178.i			1.68905i	0.535517	+	0.844525i	$0.320117\pi$
$619$			647178.i			1.68905i	−0.535517	+	0.844525i	$0.679883\pi$
$620$		0			0
$621$	−326096.			−0.845595
$622$	−323175.	+	316684.i	−0.835327	+	0.818551i
$623$		−	200954.i		−	0.517751i
$624$	−8619.91	+	212342.i	−0.0221378	+	0.545339i
$625$		0			0
$626$	−504145.	−	514477.i	−1.28649	−	1.31286i
$627$		−	597488.i		−	1.51983i
$628$	−5937.34	+	292640.i	−0.0150547	+	0.742018i
$629$	−33066.9			−0.0835781
$630$		0			0
$631$			552250.i			1.38700i	0.720455	+	0.693501i	$0.243933\pi$
$631$			552250.i			1.38700i	−0.720455	+	0.693501i	$0.756067\pi$
$632$	123180.	+	130915.i	0.308395	+	0.327759i
$633$	−29662.9			−0.0740297
$634$	−54483.4	−	55600.0i	−0.135546	−	0.138324i
$635$		0			0
$636$	517006.	+	10489.5i	1.27815	+	0.0259322i
$637$	−109313.			−0.269397
$638$	−93605.7	+	91725.9i	−0.229965	+	0.225346i
$639$		−	16836.3i		−	0.0412329i
$640$		0			0
$641$	394430.			0.959962			0.479981	−	0.877279i	$-0.340644\pi$
$641$	394430.			0.959962			0.479981	+	0.877279i	$0.340644\pi$
$642$	−129923.	−	132586.i	−0.315222	−	0.321682i
$643$		−	320916.i		−	0.776192i	−0.921619	−	0.388096i	$-0.873133\pi$
$643$		−	320916.i		−	0.776192i	0.921619	−	0.388096i	$-0.126867\pi$
$644$	−5281.31	+	260306.i	−0.0127342	+	0.627642i
$645$		0			0
$646$	−298005.	+	292020.i	−0.714099	+	0.699758i
$647$		−	378985.i		−	0.905344i	−0.891677	−	0.452672i	$-0.850471\pi$
$647$		−	378985.i		−	0.905344i	0.891677	−	0.452672i	$-0.149529\pi$
$648$	−103071.	+	96981.8i	−0.245463	+	0.230962i
$649$	503420.			1.19520
$650$		0			0
$651$		−	10777.1i		−	0.0254296i
$652$	−422910.	−	8580.37i	−0.994838	−	0.0201842i
$653$	205104.			0.481003			0.240501	−	0.970649i	$-0.422688\pi$
$653$	205104.			0.481003			0.240501	+	0.970649i	$0.422688\pi$
$654$	15390.6	−	15081.5i	0.0359832	−	0.0352606i
$655$		0			0
$656$	464657.	+	18862.5i	1.07975	+	0.0438320i
$657$	217887.			0.504779
$658$	90084.5	+	91930.7i	0.208065	+	0.212329i
$659$			204237.i			0.470288i	0.971961	+	0.235144i	$0.0755562\pi$
$659$			204237.i			0.470288i	−0.971961	+	0.235144i	$0.924444\pi$
$660$		0			0
$661$	549151.			1.25687			0.628433	−	0.777864i	$-0.283697\pi$
$661$	549151.			1.25687			0.628433	+	0.777864i	$0.283697\pi$
$662$	−177214.	+	173655.i	−0.404373	+	0.396252i
$663$			133165.i			0.302944i
$664$	133683.	+	142076.i	0.303207	+	0.322245i
$665$		0			0
$666$	−21292.0	−	21728.4i	−0.0480029	−	0.0489867i
$667$		−	98628.1i		−	0.221691i
$668$	−262628.	−	5328.42i	−0.588556	−	0.0119411i
$669$	28854.6			0.0644707
$670$		0			0
$671$			572255.i			1.27100i
$672$	178113.	+	197161.i	0.394418	+	0.436600i
$673$	506727.			1.11878			0.559389	−	0.828905i	$-0.311036\pi$
$673$	506727.			1.11878			0.559389	+	0.828905i	$0.311036\pi$
$674$	−74815.5	−	76348.8i	−0.164692	−	0.168067i
$675$		0			0
$676$	4198.50	−	206936.i	0.00918757	−	0.452838i
$677$	548346.			1.19640			0.598202	−	0.801346i	$-0.295882\pi$
$677$	548346.			1.19640			0.598202	+	0.801346i	$0.295882\pi$
$678$	120339.	−	117922.i	0.261786	−	0.256528i
$679$		−	176073.i		−	0.381903i
$680$		0			0
$681$	−413823.			−0.892319
$682$	−16088.2	−	16417.9i	−0.0345890	−	0.0352979i
$683$		−	537201.i		−	1.15158i	−0.817596	−	0.575792i	$-0.804694\pi$
$683$		−	537201.i		−	1.15158i	0.817596	−	0.575792i	$-0.195306\pi$
$684$	−383774.	−	7786.35i	−0.820283	−	0.0166426i
$685$		0			0
$686$	−365621.	+	358279.i	−0.776933	+	0.761329i
$687$			522166.i			1.10636i
$688$	32839.7	−	808969.i	0.0693781	−	1.70905i
$689$	608313.			1.28141
$690$		0			0
$691$		−	197108.i		−	0.412808i	−0.978467	−	0.206404i	$-0.933824\pi$
$691$		−	197108.i		−	0.412808i	0.978467	−	0.206404i	$-0.0661760\pi$
$692$	4707.03	−	232001.i	0.00982958	−	0.484481i
$693$	199440.			0.415285
$694$	−396758.	+	388790.i	−0.823771	+	0.807227i
$695$		0			0
$696$	−68973.1	−	73303.8i	−0.142384	−	0.151324i
$697$	291397.			0.599819
$698$	207348.	+	211598.i	0.425588	+	0.434311i
$699$		−	16364.3i		−	0.0334921i
$700$		0			0
$701$	−555586.			−1.13062			−0.565308	−	0.824880i	$-0.691243\pi$
$701$	−555586.			−1.13062			−0.565308	+	0.824880i	$0.691243\pi$
$702$	−279610.	+	273995.i	−0.567386	+	0.555992i
$703$			134041.i			0.271224i
$704$	565662.	+	34467.8i	1.14133	+	0.0695454i
$705$		0			0
$706$	64105.9	+	65419.7i	0.128614	+	0.131250i
$707$			67901.2i			0.135844i
$708$	−7842.65	+	386549.i	−0.0156457	+	0.771149i
$709$	−833981.			−1.65907			−0.829533	−	0.558458i	$-0.811393\pi$
$709$	−833981.			−1.65907			−0.829533	+	0.558458i	$0.811393\pi$
$710$		0			0
$711$			103625.i			0.204987i
$712$	239737.	−	225574.i	0.472907	−	0.444968i
$713$	17298.8			0.0340280
$714$	116526.	+	118914.i	0.228574	+	0.233259i
$715$		0			0
$716$	478025.	+	9698.59i	0.932448	+	0.0189183i
$717$	−361191.			−0.702585
$718$	−619484.	+	607043.i	−1.20166	+	1.17753i
$719$			450137.i			0.870737i	0.900252	+	0.435368i	$0.143382\pi$
$719$			450137.i			0.870737i	−0.900252	+	0.435368i	$0.856618\pi$
$720$		0			0
$721$	−495124.			−0.952452
$722$	818899.	+	835683.i	1.57093	+	1.60312i
$723$			27210.6i			0.0520548i
$724$	4228.31	−	208406.i	0.00806659	−	0.397587i
$725$		0			0
$726$	−85414.5	+	83699.2i	−0.162054	+	0.158799i
$727$		−	281881.i		−	0.533331i	−0.963789	−	0.266666i	$-0.914078\pi$
$727$		−	281881.i		−	0.533331i	0.963789	−	0.266666i	$-0.0859219\pi$
$728$	214187.	+	227636.i	0.404140	+	0.429515i
$729$	−502768.			−0.946047
$730$		0			0
$731$		−	507324.i		−	0.949404i
$732$	−439404.	−	8915.01i	−0.820052	−	0.0166379i
$733$	59324.7			0.110415			0.0552074	−	0.998475i	$-0.482418\pi$
$733$	59324.7			0.110415			0.0552074	+	0.998475i	$0.482418\pi$
$734$	48785.2	−	47805.5i	0.0905516	−	0.0887331i
$735$		0			0
$736$	−316472.	+	285896.i	−0.584224	+	0.527780i
$737$	−443947.			−0.817328
$738$	187633.	+	191478.i	0.344505	+	0.351565i
$739$			11842.3i			0.0216845i	0.999941	+	0.0108422i	$0.00345126\pi$
$739$			11842.3i			0.0216845i	−0.999941	+	0.0108422i	$0.996549\pi$
$740$		0			0
$741$	539803.			0.983102
$742$	543215.	−	532306.i	0.986652	−	0.966837i
$743$		−	8652.18i		−	0.0156728i	−0.999969	−	0.00783642i	$-0.997506\pi$
$743$		−	8652.18i		−	0.0156728i	0.999969	−	0.00783642i	$-0.00249444\pi$
$744$	12857.0	−	12097.5i	0.0232271	−	0.0218549i
$745$		0			0
$746$	23783.7	+	24271.2i	0.0427368	+	0.0436127i
$747$			112460.i			0.201539i
$748$	355033.	+	7203.22i	0.634550	+	0.0128743i
$749$	−273019.			−0.486664
$750$		0			0
$751$		−	952787.i		−	1.68934i	−0.535291	−	0.844668i	$-0.679798\pi$
$751$		−	952787.i		−	1.68934i	0.535291	−	0.844668i	$-0.320202\pi$
$752$	−8551.80	+	210664.i	−0.0151224	+	0.372524i
$753$	320842.			0.565850
$754$	−82870.0	−	84568.4i	−0.145765	−	0.148753i
$755$		0			0
$756$	−9928.32	+	489348.i	−0.0173713	+	0.856197i
$757$	605031.			1.05581			0.527905	−	0.849303i	$-0.322978\pi$
$757$	605031.			1.05581			0.527905	+	0.849303i	$0.322978\pi$
$758$	−171071.	+	167635.i	−0.297741	+	0.291761i
$759$		−	382696.i		−	0.664309i
$760$		0			0
$761$	229134.			0.395659			0.197830	−	0.980236i	$-0.436611\pi$
$761$	229134.			0.395659			0.197830	+	0.980236i	$0.436611\pi$
$762$	−143201.	−	146136.i	−0.246625	−	0.251680i
$763$		−	31692.1i		−	0.0544380i
$764$	860919.	+	17467.1i	1.47494	+	0.0299250i
$765$		0			0
$766$	411934.	−	403661.i	0.702054	−	0.687954i
$767$			454816.i			0.773117i
$768$	−35278.3	+	433805.i	−0.0598115	+	0.735481i
$769$	802587.			1.35719			0.678593	−	0.734515i	$-0.262590\pi$
$769$	802587.			1.35719			0.678593	+	0.734515i	$0.262590\pi$
$770$		0			0
$771$			163111.i			0.274394i
$772$	15721.6	−	774888.i	0.0263793	−	1.30018i
$773$	−285645.			−0.478045			−0.239022	−	0.971014i	$-0.576827\pi$
$773$	−285645.			−0.478045			−0.239022	+	0.971014i	$0.576827\pi$
$774$	333364.	−	326669.i	0.556464	−	0.545288i
$775$		0			0
$776$	210054.	−	197644.i	0.348825	−	0.328217i
$777$	53487.2			0.0885948
$778$	−666167.	−	679820.i	−1.10059	−	1.12314i
$779$		−	1.18122e6i		−	1.94651i
$780$		0			0
$781$	63137.0			0.103510
$782$	−190874.	+	187041.i	−0.312129	+	0.305861i
$783$		−	185411.i		−	0.302420i
$784$	−223690.	−	9080.58i	−0.363927	−	0.0147734i
$785$		0			0
$786$	−290413.	−	296365.i	−0.470079	−	0.479713i
$787$			369344.i			0.596324i	0.954515	+	0.298162i	$0.0963735\pi$
$787$			369344.i			0.596324i	−0.954515	+	0.298162i	$0.903627\pi$
$788$	24087.3	−	1.18722e6i	0.0387914	−	1.91196i
$789$	−553245.			−0.888717
$790$		0			0
$791$		−	247800.i		−	0.396048i
$792$	223875.	+	237931.i	0.356907	+	0.379316i
$793$	−517006.			−0.822146
$794$	−748193.	−	763527.i	−1.18679	−	1.21111i
$795$		0			0
$796$	−211800.	−	4297.18i	−0.334272	−	0.00678200i
$797$	282731.			0.445100			0.222550	−	0.974921i	$-0.428562\pi$
$797$	282731.			0.445100			0.222550	+	0.974921i	$0.428562\pi$
$798$	482037.	−	472356.i	0.756962	−	0.741760i
$799$			132113.i			0.206943i
$800$		0			0
$801$	189764.			0.295766
$802$	−48365.7	−	49357.0i	−0.0751950	−	0.0767361i
$803$			817092.i			1.26718i
$804$	6916.14	−	340883.i	0.0106992	−	0.527343i
$805$		0			0
$806$	14832.8	−	14534.9i	0.0228325	−	0.0223739i
$807$			176213.i			0.270577i
$808$	−81005.9	+	76220.2i	−0.124078	+	0.116747i
$809$	866021.			1.32322			0.661609	−	0.749849i	$-0.269874\pi$
$809$	866021.			1.32322			0.661609	+	0.749849i	$0.269874\pi$
$810$		0			0
$811$			550380.i			0.836798i	0.908263	+	0.418399i	$0.137409\pi$
$811$			550380.i			0.836798i	−0.908263	+	0.418399i	$0.862591\pi$
$812$	−148004.	−	3002.83i	−0.224471	−	0.00455427i
$813$	−730940.			−1.10586
$814$	81482.7	−	79846.3i	0.122975	−	0.120505i
$815$		0			0
$816$	−11061.9	+	272498.i	−0.0166131	+	0.409245i
$817$	−2.05651e6			−3.08097
$818$	353360.	+	360602.i	0.528094	+	0.538917i
$819$			180185.i			0.268628i
$820$		0			0
$821$	60251.5			0.0893884			0.0446942	−	0.999001i	$-0.485769\pi$
$821$	60251.5			0.0893884			0.0446942	+	0.999001i	$0.485769\pi$
$822$	−71542.3	+	70105.5i	−0.105881	+	0.103755i
$823$			760386.i			1.12262i	0.827604	+	0.561312i	$0.189703\pi$
$823$			760386.i			1.12262i	−0.827604	+	0.561312i	$0.810297\pi$
$824$	−555784.	−	590680.i	−0.818561	−	0.869957i
$825$		0			0
$826$	397988.	+	406145.i	0.583325	+	0.595280i
$827$		−	1.18336e6i		−	1.73024i	−0.501568	−	0.865118i	$-0.667243\pi$
$827$		−	1.18336e6i		−	1.73024i	0.501568	−	0.865118i	$-0.332757\pi$
$828$	−245810.	−	4987.22i	−0.358542	−	0.00727441i
$829$	−518356.			−0.754257			−0.377129	−	0.926161i	$-0.623089\pi$
$829$	−518356.			−0.754257			−0.377129	+	0.926161i	$0.623089\pi$
$830$		0			0
$831$			737721.i			1.06829i
$832$	−31140.1	+	511049.i	−0.0449855	+	0.738272i
$833$	−140281.			−0.202167
$834$	130171.	+	132839.i	0.187146	+	0.190982i
$835$		0			0
$836$	29199.3	−	1.43918e6i	0.0417792	−	2.05922i
$837$	32519.9			0.0464193
$838$	773040.	−	757515.i	1.10081	−	1.07871i
$839$		−	519063.i		−	0.737388i	−0.929551	−	0.368694i	$-0.879805\pi$
$839$		−	519063.i		−	0.737388i	0.929551	−	0.368694i	$-0.120195\pi$
$840$		0			0
$841$	−651203.			−0.920714
$842$	−729026.	−	743967.i	−1.02830	−	1.04937i
$843$		−	440883.i		−	0.620395i
$844$	−71449.4	−	1449.63i	−0.100303	−	0.00203503i
$845$		0			0
$846$	−86811.5	+	85068.0i	−0.121293	+	0.118857i
$847$			175885.i			0.245166i
$848$	1.24481e6	+	50532.2i	1.73105	+	0.0702711i
$849$	822870.			1.14161
$850$		0			0
$851$			85854.6i			0.118551i
$852$	−983.595	+	48479.5i	−0.00135499	+	0.0667850i
$853$	−1.08704e6			−1.49398			−0.746992	−	0.664834i	$-0.768502\pi$
$853$	−1.08704e6			−1.49398			−0.746992	+	0.664834i	$0.768502\pi$
$854$	−461679.	+	452407.i	−0.633031	+	0.620317i
$855$		0			0
$856$	−306468.	−	325710.i	−0.418251	−	0.444512i
$857$	1.32143e6			1.79921			0.899605	−	0.436705i	$-0.143854\pi$
$857$	1.32143e6			1.79921			0.899605	+	0.436705i	$0.143854\pi$
$858$	−321551.	−	328141.i	−0.436793	−	0.445745i
$859$		−	54795.2i		−	0.0742602i	−0.999310	−	0.0371301i	$-0.988178\pi$
$859$		−	54795.2i		−	0.0742602i	0.999310	−	0.0371301i	$-0.0118216\pi$
$860$		0			0
$861$	−471349.			−0.635823
$862$	933574.	−	914825.i	1.25642	−	1.23119i
$863$			1.00023e6i			1.34300i	0.741002	+	0.671502i	$0.234351\pi$
$863$			1.00023e6i			1.34300i	−0.741002	+	0.671502i	$0.765649\pi$
$864$	−594934.	+	537456.i	−0.796969	+	0.719971i
$865$		0			0
$866$	−461433.	−	470890.i	−0.615280	−	0.627890i
$867$		−	383788.i		−	0.510568i
$868$	526.678	−	25958.9i	0.000699046	−	0.0344546i
$869$	−388601.			−0.514594
$870$		0			0
$871$		−	401085.i		−	0.528689i
$872$	37808.6	−	35574.9i	0.0497230	−	0.0467854i
$873$	166268.			0.218163
$874$	758198.	+	773737.i	0.992567	+	1.01291i
$875$		0			0
$876$	−627401.	−	12729.3i	−0.817592	−	0.0165880i
$877$	−403840.			−0.525061			−0.262531	−	0.964924i	$-0.584557\pi$
$877$	−403840.			−0.525061			−0.262531	+	0.964924i	$0.584557\pi$
$878$	782171.	−	766463.i	1.01464	−	0.994264i
$879$			529773.i			0.685665i
$880$		0			0
$881$	642029.			0.827185			0.413593	−	0.910462i	$-0.364274\pi$
$881$	642029.			0.827185			0.413593	+	0.910462i	$0.364274\pi$
$882$	−90328.1	−	92179.3i	−0.116114	−	0.118494i
$883$		−	238590.i		−	0.306006i	−0.988226	−	0.153003i	$-0.951106\pi$
$883$		−	238590.i		−	0.306006i	0.988226	−	0.153003i	$-0.0488945\pi$
$884$	−6507.78	+	320756.i	−0.00832776	+	0.410459i
$885$		0			0
$886$	29845.2	−	29245.8i	0.0380195	−	0.0372560i
$887$			439336.i			0.558406i	0.960232	+	0.279203i	$0.0900702\pi$
$887$			439336.i			0.558406i	−0.960232	+	0.279203i	$0.909930\pi$
$888$	60040.2	+	63810.1i	0.0761406	+	0.0809214i
$889$	−300922.			−0.380759
$890$		0			0
$891$		−	305952.i		−	0.385387i
$892$	69502.4	+	1410.13i	0.0873514	+	0.00177226i
$893$	535537.			0.671563
$894$	568577.	−	557159.i	0.711401	−	0.697114i
$895$		0			0
$896$	419388.	+	483610.i	0.522396	+	0.602392i
$897$	345748.			0.429709
$898$	542673.	+	553795.i	0.672954	+	0.686746i
$899$			9835.67i			0.0121698i
$900$		0			0
$901$	780648.			0.961625
$902$	−718054.	+	703634.i	−0.882560	+	0.864836i
$903$			820621.i			1.00639i
$904$	295624.	−	278159.i	0.361746	−	0.340374i
$905$		0			0
$906$	230495.	+	235219.i	0.280806	+	0.286561i
$907$			1.10959e6i			1.34880i	0.738368	+	0.674398i	$0.235597\pi$
$907$			1.10959e6i			1.34880i	−0.738368	+	0.674398i	$0.764403\pi$
$908$	−996780.	−	20223.6i	−1.20900	−	0.0245293i
$909$	−64120.1			−0.0776008
$910$		0			0
$911$			249223.i			0.300297i	0.988663	+	0.150148i	$0.0479752\pi$
$911$			249223.i			0.300297i	−0.988663	+	0.150148i	$0.952025\pi$
$912$	1.10461e6	+	44841.1i	1.32807	+	0.0539122i
$913$	−421734.			−0.505937
$914$	88689.4	+	90507.0i	0.106164	+	0.108340i
$915$		0			0
$916$	−25518.3	+	1.25775e6i	−0.0304131	+	1.49900i
$917$	−610271.			−0.725745
$918$	−358824.	+	351618.i	−0.425791	+	0.417239i
$919$			385756.i			0.456753i	0.973573	+	0.228376i	$0.0733417\pi$
$919$			385756.i			0.456753i	−0.973573	+	0.228376i	$0.926658\pi$
$920$		0			0
$921$	681432.			0.803347
$922$	258345.	+	263640.i	0.303905	+	0.310134i
$923$			57041.3i			0.0669555i
$924$	−574282.	−	11651.5i	−0.672638	−	0.0136471i
$925$		0			0
$926$	560720.	−	549459.i	0.653919	−	0.640786i
$927$		−	467552.i		−	0.544090i
$928$	−162554.	−	179938.i	−0.188756	−	0.208943i
$929$	297906.			0.345182			0.172591	−	0.984994i	$-0.444786\pi$
$929$	297906.			0.345182			0.172591	+	0.984994i	$0.444786\pi$
$930$		0			0
$931$			568651.i			0.656064i
$932$	799.722	−	39416.8i	0.000920677	−	0.0453784i
$933$	751237.			0.863006
$934$	745788.	−	730810.i	0.854912	−	0.837743i
$935$		0			0
$936$	−214960.	+	202260.i	−0.245361	+	0.230865i
$937$	−661095.			−0.752982			−0.376491	−	0.926420i	$-0.622869\pi$
$937$	−661095.			−0.752982			−0.376491	+	0.926420i	$0.622869\pi$
$938$	−350971.	−	358164.i	−0.398901	−	0.407077i
$939$			1.19593e6i			1.35636i
$940$		0			0
$941$	−1.71686e6			−1.93890			−0.969448	−	0.245298i	$-0.921114\pi$
$941$	−1.71686e6			−1.93890			−0.969448	+	0.245298i	$0.921114\pi$
$942$	347100.	−	340129.i	0.391158	−	0.383303i
$943$		−	756581.i		−	0.850809i
$944$	−37781.4	+	930702.i	−0.0423969	+	1.04440i
$945$		0			0
$946$	1.22503e6	+	1.25014e6i	1.36888	+	1.39693i
$947$			659116.i			0.734957i	0.930032	+	0.367478i	$0.119779\pi$
$947$			659116.i			0.734957i	−0.930032	+	0.367478i	$0.880221\pi$
$948$	6053.92	−	298386.i	0.00673628	−	0.332018i
$949$	−738204.			−0.819679
$950$		0			0
$951$			129245.i			0.142907i
$952$	274867.	+	292125.i	0.303283	+	0.322326i
$953$	−870368.			−0.958335			−0.479167	−	0.877724i	$-0.659061\pi$
$953$	−870368.			−0.958335			−0.479167	+	0.877724i	$0.659061\pi$
$954$	502664.	+	512966.i	0.552307	+	0.563627i
$955$		0			0
$956$	−870005.	−	17651.4i	−0.951933	−	0.0193136i
$957$	217592.			0.237585
$958$	−301801.	+	295740.i	−0.328844	+	0.322240i
$959$			147319.i			0.160185i
$960$		0			0
$961$	921796.			0.998132
$962$	72137.4	+	73615.8i	0.0779489	+	0.0795465i
$963$		−	257815.i		−	0.278007i
$964$	−1329.78	+	65542.4i	−0.00143096	+	0.0705291i
$965$		0			0
$966$	308748.	−	302548.i	0.330864	−	0.324220i
$967$			1.50355e6i			1.60792i	0.594682	+	0.803961i	$0.297278\pi$
$967$			1.50355e6i			1.60792i	−0.594682	+	0.803961i	$0.702722\pi$
$968$	−209829.	+	197433.i	−0.223932	+	0.210702i
$969$	692729.			0.737761
$970$		0			0
$971$		−	1.39973e6i		−	1.48459i	−0.670074	−	0.742295i	$-0.733738\pi$
$971$		−	1.39973e6i		−	1.48459i	0.670074	−	0.742295i	$-0.266262\pi$
$972$	−779584.	−	15816.9i	−0.825145	−	0.0167413i
$973$	273540.			0.288931
$974$	−950311.	+	931226.i	−1.00172	+	0.981606i
$975$		0			0
$976$	−1.05796e6	−	42947.4i	−1.11063	−	0.0450855i
$977$	1.27509e6			1.33583			0.667917	−	0.744236i	$-0.267186\pi$
$977$	1.27509e6			1.33583			0.667917	+	0.744236i	$0.267186\pi$
$978$	491539.	+	501613.i	0.513902	+	0.524434i
$979$			711626.i			0.742483i
$980$		0			0
$981$	29927.3			0.0310978
$982$	269839.	−	264420.i	0.279822	−	0.274202i
$983$		−	652901.i		−	0.675679i	−0.941204	−	0.337839i	$-0.890304\pi$
$983$		−	652901.i		−	0.675679i	0.941204	−	0.337839i	$-0.109696\pi$
$984$	−529096.	−	562317.i	−0.546442	−	0.580752i
$985$		0			0
$986$	−106347.	−	108527.i	−0.109389	−	0.111630i
$987$		−	213698.i		−	0.219365i
$988$	1.30023e6	+	26380.2i	1.33201	+	0.0270249i
$989$	−1.31721e6			−1.34668
$990$		0			0
$991$			817175.i			0.832086i	0.909345	+	0.416043i	$0.136583\pi$
$991$			817175.i			0.832086i	−0.909345	+	0.416043i	$0.863417\pi$
$992$	31560.1	−	28511.0i	0.0320712	−	0.0289727i
$993$	411943.			0.417772
$994$	49914.2	+	50937.2i	0.0505186	+	0.0515539i
$995$		0			0
$996$	6570.08	−	323827.i	0.00662296	−	0.326433i
$997$	−295553.			−0.297335			−0.148667	−	0.988887i	$-0.547498\pi$
$997$	−295553.			−0.297335			−0.148667	+	0.988887i	$0.547498\pi$
$998$	−860038.	+	842766.i	−0.863489	+	0.846147i
$999$			161398.i			0.161721i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	100.5.b.e.51.3		8
4.3	odd	2	inner	100.5.b.e.51.4		8
5.2	odd	4		20.5.d.c.19.7	yes	8
5.3	odd	4		20.5.d.c.19.2	yes	8
5.4	even	2	inner	100.5.b.e.51.6		8
15.2	even	4		180.5.f.g.19.2		8
15.8	even	4		180.5.f.g.19.7		8
20.3	even	4		20.5.d.c.19.8	yes	8
20.7	even	4		20.5.d.c.19.1	✓	8
20.19	odd	2	inner	100.5.b.e.51.5		8
40.3	even	4		320.5.h.f.319.4		8
40.13	odd	4		320.5.h.f.319.6		8
40.27	even	4		320.5.h.f.319.5		8
40.37	odd	4		320.5.h.f.319.3		8
60.23	odd	4		180.5.f.g.19.1		8
60.47	odd	4		180.5.f.g.19.8		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
20.5.d.c.19.1	✓	8	20.7	even	4
20.5.d.c.19.2	yes	8	5.3	odd	4
20.5.d.c.19.7	yes	8	5.2	odd	4
20.5.d.c.19.8	yes	8	20.3	even	4
100.5.b.e.51.3		8	1.1	even	1	trivial
100.5.b.e.51.4		8	4.3	odd	2	inner
100.5.b.e.51.5		8	20.19	odd	2	inner
100.5.b.e.51.6		8	5.4	even	2	inner
180.5.f.g.19.1		8	60.23	odd	4
180.5.f.g.19.2		8	15.2	even	4
180.5.f.g.19.7		8	15.8	even	4
180.5.f.g.19.8		8	60.47	odd	4
320.5.h.f.319.3		8	40.37	odd	4
320.5.h.f.319.4		8	40.3	even	4
320.5.h.f.319.5		8	40.27	even	4
320.5.h.f.319.6		8	40.13	odd	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:	\( N \)	\(=\)	\( 100 = 2^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	100.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.79959 - 2.85697i) q^{2} +6.64118i q^{3} +(-0.324555 + 15.9967i) q^{4} +(18.9737 - 18.5926i) q^{6} -39.0703i q^{7} +(46.6107 - 43.8570i) q^{8} +36.8947 q^{9} +138.357i q^{11} +(-106.237 - 2.15543i) q^{12} -124.999 q^{13} +(-111.623 + 109.381i) q^{14} +(-255.789 - 10.3836i) q^{16} -160.412 q^{17} +(-103.290 - 105.407i) q^{18} +650.252i q^{19} +259.473 q^{21} +(395.283 - 387.344i) q^{22} +416.491i q^{23} +(291.263 + 309.551i) q^{24} +(349.947 + 357.119i) q^{26} +782.960i q^{27} +(624.997 + 12.6805i) q^{28} -236.807 q^{29} -41.5345i q^{31} +(686.440 + 759.852i) q^{32} -918.856 q^{33} +(449.088 + 458.291i) q^{34} +(-11.9744 + 590.193i) q^{36} +206.138 q^{37} +(1857.75 - 1820.44i) q^{38} -830.144i q^{39} -1816.56 q^{41} +(-726.420 - 741.307i) q^{42} +3162.64i q^{43} +(-2213.26 - 44.9046i) q^{44} +(1189.90 - 1166.01i) q^{46} -823.584i q^{47} +(68.9596 - 1698.74i) q^{48} +874.509 q^{49} -1065.32i q^{51} +(40.5692 - 1999.58i) q^{52} -4866.53 q^{53} +(2236.89 - 2191.97i) q^{54} +(-1713.51 - 1821.10i) q^{56} -4318.44 q^{57} +(662.964 + 676.551i) q^{58} -3638.55i q^{59} +4136.07 q^{61} +(-118.663 + 116.280i) q^{62} -1441.49i q^{63} +(249.122 - 4088.42i) q^{64} +(2572.42 + 2625.15i) q^{66} +3208.70i q^{67} +(52.0625 - 2566.06i) q^{68} -2766.00 q^{69} -456.333i q^{71} +(1719.69 - 1618.09i) q^{72} +5905.66 q^{73} +(-577.102 - 588.929i) q^{74} +(-10401.9 - 211.043i) q^{76} +5405.67 q^{77} +(-2371.70 + 2324.06i) q^{78} +2808.68i q^{79} -2211.32 q^{81} +(5085.63 + 5189.86i) q^{82} +3048.15i q^{83} +(-84.2134 + 4150.72i) q^{84} +(9035.57 - 8854.10i) q^{86} -1572.68i q^{87} +(6067.94 + 6448.94i) q^{88} +5143.40 q^{89} +4883.77i q^{91} +(-6662.49 - 135.174i) q^{92} +275.839 q^{93} +(-2352.96 + 2305.70i) q^{94} +(-5046.32 + 4558.78i) q^{96} +4506.56 q^{97} +(-2448.27 - 2498.45i) q^{98} +5104.65i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 48 q^{4} - 312 q^{9} - 640 q^{14} - 832 q^{16} - 960 q^{21} - 1920 q^{24} + 2496 q^{26} - 2704 q^{29} + 2176 q^{34} - 5712 q^{36} + 1456 q^{41} - 1920 q^{44} + 7040 q^{46} + 8008 q^{49} + 11520 q^{54}+ \cdots - 76800 q^{96}+O(q^{100}) \) 8 * q + 48 * q^4 - 312 * q^9 - 640 * q^14 - 832 * q^16 - 960 * q^21 - 1920 * q^24 + 2496 * q^26 - 2704 * q^29 + 2176 * q^34 - 5712 * q^36 + 1456 * q^41 - 1920 * q^44 + 7040 * q^46 + 8008 * q^49 + 11520 * q^54 - 14720 * q^56 + 6576 * q^61 - 6912 * q^64 + 46080 * q^66 + 12480 * q^69 + 23616 * q^74 - 48000 * q^76 - 19512 * q^81 - 24960 * q^84 + 37120 * q^86 - 27664 * q^89 - 10880 * q^94 - 76800 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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