LMFDB - Embedded newform 672.4.bb.a.271.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [672,4,Mod(271,672)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(672, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 0, 5]))

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

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

chi := DirichletCharacter("672.271");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 672 = 2^{5} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	672.bb (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$39.6492835239$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$48$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 168)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			271.18
Character	$\chi$	$=$	672.271
Dual form			672.4.bb.a.367.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.59808 + 1.50000i) q^{3} +(7.16825 - 12.4158i) q^{5} +(-12.0691 - 14.0477i) q^{7} +(4.50000 - 7.79423i) q^{9} +(8.72655 + 15.1148i) q^{11} -0.0135980 q^{13} +43.0095i q^{15} +(97.8487 - 56.4930i) q^{17} +(141.172 + 81.5059i) q^{19} +(52.4279 + 18.3934i) q^{21} +(-108.849 - 62.8441i) q^{23} +(-40.2675 - 69.7454i) q^{25} +27.0000i q^{27} -79.0227i q^{29} +(-57.5343 - 99.6523i) q^{31} +(-45.3445 - 26.1796i) q^{33} +(-260.927 + 49.1495i) q^{35} +(34.8737 + 20.1343i) q^{37} +(0.0353286 - 0.0203970i) q^{39} -387.430i q^{41} -59.4461 q^{43} +(-64.5142 - 111.742i) q^{45} +(-202.646 + 350.993i) q^{47} +(-51.6750 + 339.085i) q^{49} +(-169.479 + 293.546i) q^{51} +(-96.1083 + 55.4882i) q^{53} +250.216 q^{55} -489.036 q^{57} +(192.766 - 111.294i) q^{59} +(314.523 - 544.771i) q^{61} +(-163.802 + 30.8545i) q^{63} +(-0.0974736 + 0.168829i) q^{65} +(-132.525 - 229.540i) q^{67} +377.065 q^{69} -1023.16i q^{71} +(-952.975 + 550.200i) q^{73} +(209.236 + 120.803i) q^{75} +(107.007 - 305.010i) q^{77} +(-536.973 - 310.022i) q^{79} +(-40.5000 - 70.1481i) q^{81} +57.1755i q^{83} -1619.82i q^{85} +(118.534 + 205.307i) q^{87} +(-458.297 - 264.598i) q^{89} +(0.164115 + 0.191020i) q^{91} +(298.957 + 172.603i) q^{93} +(2023.92 - 1168.51i) q^{95} +106.812i q^{97} +157.078 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q + 432 q^{9} - 40 q^{11} - 1200 q^{25} - 456 q^{35} + 1616 q^{43} - 360 q^{49} - 336 q^{57} - 4128 q^{59} + 1440 q^{67} - 648 q^{73} - 3888 q^{81} + 104 q^{91} - 720 q^{99}+O(q^{100}) $ 96 * q + 432 * q^9 - 40 * q^11 - 1200 * q^25 - 456 * q^35 + 1616 * q^43 - 360 * q^49 - 336 * q^57 - 4128 * q^59 + 1440 * q^67 - 648 * q^73 - 3888 * q^81 + 104 * q^91 - 720 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/672\mathbb{Z}\right)^\times$.

$n$	$127$	$421$	$449$	$577$
$\chi(n)$	$-1$	$-1$	$1$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−2.59808	+	1.50000i	−0.500000	+	0.288675i
$3$	−2.59808	+	1.50000i	−0.500000	+	0.288675i
$4$		0			0
$5$	7.16825	−	12.4158i	0.641148	−	1.11050i	−0.344029	−	0.938959i	$-0.611792\pi$
$5$	7.16825	−	12.4158i	0.641148	−	1.11050i	0.985177	−	0.171541i	$-0.0548747\pi$
$6$		0			0
$7$	−12.0691	−	14.0477i	−0.651669	−	0.758504i
$7$	−12.0691	−	14.0477i	−0.651669	−	0.758504i
$8$		0			0
$9$	4.50000	−	7.79423i	0.166667	−	0.288675i
$10$		0			0
$11$	8.72655	+	15.1148i	0.239196	+	0.414299i	0.960484	−	0.278336i	$-0.0897829\pi$
$11$	8.72655	+	15.1148i	0.239196	+	0.414299i	−0.721288	+	0.692635i	$0.756450\pi$
$12$		0			0
$13$	−0.0135980			−0.000290108			−0.000145054	−	1.00000i	$-0.500046\pi$
$13$	−0.0135980			−0.000290108			−0.000145054		1.00000i	$0.500046\pi$
$14$		0			0
$15$			43.0095i			0.740333i
$16$		0			0
$17$	97.8487	−	56.4930i	1.39599	−	0.805974i	0.402019	−	0.915631i	$-0.368309\pi$
$17$	97.8487	−	56.4930i	1.39599	−	0.805974i	0.993970	+	0.109657i	$0.0349752\pi$
$18$		0			0
$19$	141.172	+	81.5059i	1.70459	+	0.984144i	0.940979	+	0.338465i	$0.109908\pi$
$19$	141.172	+	81.5059i	1.70459	+	0.984144i	0.763609	+	0.645679i	$0.223426\pi$
$20$		0			0
$21$	52.4279	+	18.3934i	0.544796	+	0.191131i
$22$		0			0
$23$	−108.849	−	62.8441i	−0.986810	−	0.569735i	−0.0824906	−	0.996592i	$-0.526287\pi$
$23$	−108.849	−	62.8441i	−0.986810	−	0.569735i	−0.904319	+	0.426857i	$0.859621\pi$
$24$		0			0
$25$	−40.2675	−	69.7454i	−0.322140	−	0.557963i
$26$		0			0
$27$			27.0000i			0.192450i
$28$		0			0
$29$		−	79.0227i		−	0.506005i	−0.967466	−	0.253002i	$-0.918582\pi$
$29$		−	79.0227i		−	0.506005i	0.967466	−	0.253002i	$-0.0814181\pi$
$30$		0			0
$31$	−57.5343	−	99.6523i	−0.333337	−	0.577357i	0.649827	−	0.760082i	$-0.274841\pi$
$31$	−57.5343	−	99.6523i	−0.333337	−	0.577357i	−0.983164	+	0.182725i	$0.941508\pi$
$32$		0			0
$33$	−45.3445	−	26.1796i	−0.239196	−	0.138100i
$34$		0			0
$35$	−260.927	+	49.1495i	−1.26013	+	0.237365i
$36$		0			0
$37$	34.8737	+	20.1343i	0.154951	+	0.0894611i	0.575471	−	0.817822i	$-0.304819\pi$
$37$	34.8737	+	20.1343i	0.154951	+	0.0894611i	−0.420520	+	0.907283i	$0.638152\pi$
$38$		0			0
$39$	0.0353286	−	0.0203970i	0.000145054	−	8.37468e-5i
$40$		0			0
$41$		−	387.430i		−	1.47577i	−0.674928	−	0.737883i	$-0.735825\pi$
$41$		−	387.430i		−	1.47577i	0.674928	−	0.737883i	$-0.264175\pi$
$42$		0			0
$43$	−59.4461			−0.210824			−0.105412	−	0.994429i	$-0.533616\pi$
$43$	−59.4461			−0.210824			−0.105412	+	0.994429i	$0.533616\pi$
$44$		0			0
$45$	−64.5142	−	111.742i	−0.213716	−	0.370167i
$46$		0			0
$47$	−202.646	+	350.993i	−0.628914	+	1.08931i	0.358856	+	0.933393i	$0.383167\pi$
$47$	−202.646	+	350.993i	−0.628914	+	1.08931i	−0.987770	+	0.155918i	$0.950167\pi$
$48$		0			0
$49$	−51.6750	+	339.085i	−0.150656	+	0.988586i
$50$		0			0
$51$	−169.479	+	293.546i	−0.465330	+	0.805974i
$52$		0			0
$53$	−96.1083	+	55.4882i	−0.249085	+	0.143809i	−0.619345	−	0.785119i	$-0.712602\pi$
$53$	−96.1083	+	55.4882i	−0.249085	+	0.143809i	0.370260	+	0.928928i	$0.379268\pi$
$54$		0			0
$55$	250.216			0.613439
$56$		0			0
$57$	−489.036			−1.13639
$58$		0			0
$59$	192.766	−	111.294i	0.425356	−	0.245579i	−0.272010	−	0.962294i	$-0.587688\pi$
$59$	192.766	−	111.294i	0.425356	−	0.245579i	0.697366	+	0.716715i	$0.254355\pi$
$60$		0			0
$61$	314.523	−	544.771i	0.660174	−	1.14345i	−0.320396	−	0.947284i	$-0.603816\pi$
$61$	314.523	−	544.771i	0.660174	−	1.14345i	0.980570	−	0.196171i	$-0.0628507\pi$
$62$		0			0
$63$	−163.802	+	30.8545i	−0.327573	+	0.0617032i
$64$		0			0
$65$	−0.0974736	+	0.168829i	−0.000186002	+	0.000322164i
$66$		0			0
$67$	−132.525	−	229.540i	−0.241649	−	0.418549i	0.719535	−	0.694456i	$-0.244355\pi$
$67$	−132.525	−	229.540i	−0.241649	−	0.418549i	−0.961184	+	0.275907i	$0.911022\pi$
$68$		0			0
$69$	377.065			0.657873
$70$		0			0
$71$		−	1023.16i		−	1.71023i	−0.518440	−	0.855114i	$-0.673487\pi$
$71$		−	1023.16i		−	1.71023i	0.518440	−	0.855114i	$-0.326513\pi$
$72$		0			0
$73$	−952.975	+	550.200i	−1.52791	+	0.882138i	−0.528459	+	0.848959i	$0.677230\pi$
$73$	−952.975	+	550.200i	−1.52791	+	0.882138i	−0.999449	+	0.0331792i	$0.989437\pi$
$74$		0			0
$75$	209.236	+	120.803i	0.322140	+	0.185988i
$76$		0			0
$77$	107.007	−	305.010i	0.158371	−	0.451417i
$78$		0			0
$79$	−536.973	−	310.022i	−0.764737	−	0.441521i	0.0662572	−	0.997803i	$-0.478894\pi$
$79$	−536.973	−	310.022i	−0.764737	−	0.441521i	−0.830994	+	0.556282i	$0.812228\pi$
$80$		0			0
$81$	−40.5000	−	70.1481i	−0.0555556	−	0.0962250i
$82$		0			0
$83$			57.1755i			0.0756124i	0.999285	+	0.0378062i	$0.0120370\pi$
$83$			57.1755i			0.0756124i	−0.999285	+	0.0378062i	$0.987963\pi$
$84$		0			0
$85$		−	1619.82i		−	2.06699i
$86$		0			0
$87$	118.534	+	205.307i	0.146071	+	0.253002i
$88$		0			0
$89$	−458.297	−	264.598i	−0.545835	−	0.315138i	0.201605	−	0.979467i	$-0.435384\pi$
$89$	−458.297	−	264.598i	−0.545835	−	0.315138i	−0.747441	+	0.664329i	$0.768718\pi$
$90$		0			0
$91$	0.164115	+	0.191020i	0.000189054	+	0.000220048i
$92$		0			0
$93$	298.957	+	172.603i	0.333337	+	0.192452i
$94$		0			0
$95$	2023.92	−	1168.51i	2.18578	−	1.26196i
$96$		0			0
$97$			106.812i			0.111805i	0.998436	+	0.0559026i	$0.0178036\pi$
$97$			106.812i			0.111805i	−0.998436	+	0.0559026i	$0.982196\pi$
$98$		0			0
$99$	157.078			0.159464
$100$		0			0
$101$	−144.912	−	250.995i	−0.142765	−	0.247277i	0.785772	−	0.618517i	$-0.212266\pi$
$101$	−144.912	−	250.995i	−0.142765	−	0.247277i	−0.928537	+	0.371240i	$0.878933\pi$
$102$		0			0
$103$	69.8537	−	120.990i	0.0668241	−	0.115743i	−0.830678	−	0.556754i	$-0.812047\pi$
$103$	69.8537	−	120.990i	0.0668241	−	0.115743i	0.897502	+	0.441011i	$0.145380\pi$
$104$		0			0
$105$	604.184	−	519.085i	0.561546	−	0.482452i
$106$		0			0
$107$	514.157	−	890.546i	0.464537	−	0.804602i	−0.534644	−	0.845078i	$-0.679554\pi$
$107$	514.157	−	890.546i	0.464537	−	0.804602i	0.999181	+	0.0404761i	$0.0128875\pi$
$108$		0			0
$109$	−1136.39	+	656.098i	−0.998595	+	0.576539i	−0.907832	−	0.419333i	$-0.862264\pi$
$109$	−1136.39	+	656.098i	−0.998595	+	0.576539i	−0.0907629	+	0.995873i	$0.528931\pi$
$110$		0			0
$111$	−120.806			−0.103301
$112$		0			0
$113$	763.883			0.635929			0.317965	−	0.948103i	$-0.397001\pi$
$113$	763.883			0.635929			0.317965	+	0.948103i	$0.397001\pi$
$114$		0			0
$115$	−1560.52	+	900.964i	−1.26538	+	0.730568i
$116$		0			0
$117$	−0.0611909	+	0.105986i	−4.83513e−5	+	8.37468e-5i
$118$		0			0
$119$	−1974.54	−	692.730i	−1.52106	−	0.533634i
$120$		0			0
$121$	513.195	−	888.879i	0.385571	−	0.667828i
$122$		0			0
$123$	581.145	+	1006.57i	0.426017	+	0.737883i
$124$		0			0
$125$	637.471			0.456137
$126$		0			0
$127$		−	2297.90i		−	1.60555i	−0.596279	−	0.802777i	$-0.703355\pi$
$127$		−	2297.90i		−	1.60555i	0.596279	−	0.802777i	$-0.296645\pi$
$128$		0			0
$129$	154.445	−	89.1691i	0.105412	−	0.0608597i
$130$		0			0
$131$	−2206.31	−	1273.81i	−1.47150	−	0.849570i	−0.472012	−	0.881592i	$-0.656472\pi$
$131$	−2206.31	−	1273.81i	−1.47150	−	0.849570i	−0.999487	+	0.0320218i	$0.989805\pi$
$132$		0			0
$133$	−558.850	−	2966.85i	−0.364349	−	1.93427i
$134$		0			0
$135$	335.226	+	193.543i	0.213716	+	0.123389i
$136$		0			0
$137$	985.764	+	1707.39i	0.614741	+	1.06476i	0.990430	+	0.138016i	$0.0440726\pi$
$137$	985.764	+	1707.39i	0.614741	+	1.06476i	−0.375689	+	0.926746i	$0.622594\pi$
$138$		0			0
$139$		−	2423.81i		−	1.47903i	−0.673141	−	0.739514i	$-0.735056\pi$
$139$		−	2423.81i		−	1.47903i	0.673141	−	0.739514i	$-0.264944\pi$
$140$		0			0
$141$		−	1215.88i		−	0.726207i
$142$		0			0
$143$	−0.118663	−	0.205531i	−6.93925e−5	−	0.000120191i
$144$		0			0
$145$	−981.127	−	566.454i	−0.561919	−	0.324424i
$146$		0			0
$147$	−374.372	−	958.481i	−0.210052	−	0.537784i
$148$		0			0
$149$	−517.719	−	298.905i	−0.284652	−	0.164344i	0.350875	−	0.936422i	$-0.385884\pi$
$149$	−517.719	−	298.905i	−0.284652	−	0.164344i	−0.635528	+	0.772078i	$0.719217\pi$
$150$		0			0
$151$	687.580	−	396.974i	0.370559	−	0.213943i	−0.303143	−	0.952945i	$-0.598036\pi$
$151$	687.580	−	396.974i	0.370559	−	0.213943i	0.673703	+	0.739002i	$0.264703\pi$
$152$		0			0
$153$		−	1016.87i		−	0.537316i
$154$		0			0
$155$	−1649.68			−0.854874
$156$		0			0
$157$	1088.93	+	1886.09i	0.553544	+	0.958766i	0.998015	+	0.0629729i	$0.0200582\pi$
$157$	1088.93	+	1886.09i	0.553544	+	0.958766i	−0.444472	+	0.895793i	$0.646609\pi$
$158$		0			0
$159$	166.465	−	288.325i	0.0830283	−	0.143809i
$160$		0			0
$161$	430.894	+	2287.55i	0.210927	+	1.11978i
$162$		0			0
$163$	−698.201	+	1209.32i	−0.335505	+	0.581112i	−0.983582	−	0.180463i	$-0.942240\pi$
$163$	−698.201	+	1209.32i	−0.335505	+	0.581112i	0.648077	+	0.761575i	$0.275574\pi$
$164$		0			0
$165$	−650.081	+	375.324i	−0.306719	+	0.177085i
$166$		0			0
$167$	2709.12			1.25532			0.627658	−	0.778490i	$-0.284014\pi$
$167$	2709.12			1.25532			0.627658	+	0.778490i	$0.284014\pi$
$168$		0			0
$169$	−2197.00			−1.00000
$170$		0			0
$171$	1270.55	−	733.553i	0.568196	−	0.328048i
$172$		0			0
$173$	−2134.57	+	3697.18i	−0.938081	+	1.62480i	−0.169036	+	0.985610i	$0.554065\pi$
$173$	−2134.57	+	3697.18i	−0.938081	+	1.62480i	−0.769045	+	0.639194i	$0.779268\pi$
$174$		0			0
$175$	−493.770	+	1407.43i	−0.213289	+	0.607952i
$176$		0			0
$177$	−333.881	+	578.298i	−0.141785	+	0.245579i
$178$		0			0
$179$	1236.00	+	2140.81i	0.516104	+	0.893918i	0.999825	+	0.0186963i	$0.00595155\pi$
$179$	1236.00	+	2140.81i	0.516104	+	0.893918i	−0.483721	+	0.875222i	$0.660715\pi$
$180$		0			0
$181$	1085.09			0.445601			0.222801	−	0.974864i	$-0.428480\pi$
$181$	1085.09			0.445601			0.222801	+	0.974864i	$0.428480\pi$
$182$		0			0
$183$			1887.14i			0.762303i
$184$		0			0
$185$	499.966	−	288.656i	0.198693	−	0.114716i
$186$		0			0
$187$	1707.76	+	985.977i	0.667829	+	0.385571i
$188$		0			0
$189$	379.288	−	325.865i	0.145974	−	0.125414i
$190$		0			0
$191$	3251.48	+	1877.25i	1.23178	+	0.711166i	0.967400	−	0.253254i	$-0.0815007\pi$
$191$	3251.48	+	1877.25i	1.23178	+	0.711166i	0.264376	+	0.964420i	$0.414834\pi$
$192$		0			0
$193$	−258.194	−	447.204i	−0.0962963	−	0.166790i	0.813853	−	0.581071i	$-0.197366\pi$
$193$	−258.194	−	447.204i	−0.0962963	−	0.166790i	−0.910149	+	0.414281i	$0.864033\pi$
$194$		0			0
$195$		−	0.584842i		−	0.000214776i
$196$		0			0
$197$			2723.54i			0.984995i	0.870314	+	0.492497i	$0.163916\pi$
$197$			2723.54i			0.984995i	−0.870314	+	0.492497i	$0.836084\pi$
$198$		0			0
$199$	−2259.07	−	3912.82i	−0.804729	−	1.39383i	−0.916474	−	0.400095i	$-0.868977\pi$
$199$	−2259.07	−	3912.82i	−0.804729	−	1.39383i	0.111744	−	0.993737i	$-0.464356\pi$
$200$		0			0
$201$	688.620	+	397.575i	0.241649	+	0.139516i
$202$		0			0
$203$	−1110.09	+	953.730i	−0.383807	+	0.329748i
$204$		0			0
$205$	−4810.24	−	2777.20i	−1.63884	−	0.946184i
$206$		0			0
$207$	−979.643	+	565.597i	−0.328937	+	0.189912i
$208$		0			0
$209$			2845.06i			0.941612i
$210$		0			0
$211$	−693.490			−0.226265			−0.113132	−	0.993580i	$-0.536088\pi$
$211$	−693.490			−0.226265			−0.113132	+	0.993580i	$0.536088\pi$
$212$		0			0
$213$	1534.73	+	2658.24i	0.493700	+	0.855114i
$214$		0			0
$215$	−426.124	+	738.069i	−0.135169	+	0.234120i
$216$		0			0
$217$	−705.499	+	2010.93i	−0.220702	+	0.629083i
$218$		0			0
$219$	1650.60	−	2858.93i	0.509303	−	0.882138i
$220$		0			0
$221$	−1.33054	+	0.768190i	−0.000404987	+	0.000233819i
$222$		0			0
$223$	−3875.20			−1.16369			−0.581844	−	0.813300i	$-0.697669\pi$
$223$	−3875.20			−1.16369			−0.581844	+	0.813300i	$0.697669\pi$
$224$		0			0
$225$	−724.816			−0.214760
$226$		0			0
$227$	−1611.42	+	930.351i	−0.471160	+	0.272024i	−0.716725	−	0.697356i	$-0.754360\pi$
$227$	−1611.42	+	930.351i	−0.471160	+	0.272024i	0.245565	+	0.969380i	$0.421027\pi$
$228$		0			0
$229$	665.716	−	1153.05i	0.192104	−	0.332733i	−0.753844	−	0.657054i	$-0.771802\pi$
$229$	665.716	−	1153.05i	0.192104	−	0.332733i	0.945947	+	0.324321i	$0.105136\pi$
$230$		0			0
$231$	179.502	+	952.949i	0.0511272	+	0.271426i
$232$		0			0
$233$	1454.66	−	2519.54i	0.409004	−	0.708415i	−0.585775	−	0.810474i	$-0.699210\pi$
$233$	1454.66	−	2519.54i	0.409004	−	0.708415i	0.994778	+	0.102059i	$0.0325430\pi$
$234$		0			0
$235$	2905.23	+	5032.01i	0.806453	+	1.39682i
$236$		0			0
$237$	1860.13			0.509824
$238$		0			0
$239$			2878.18i			0.778971i	0.921033	+	0.389486i	$0.127347\pi$
$239$			2878.18i			0.778971i	−0.921033	+	0.389486i	$0.872653\pi$
$240$		0			0
$241$	2620.03	−	1512.68i	0.700296	−	0.404316i	−0.107162	−	0.994242i	$-0.534176\pi$
$241$	2620.03	−	1512.68i	0.700296	−	0.404316i	0.807458	+	0.589926i	$0.200843\pi$
$242$		0			0
$243$	210.444	+	121.500i	0.0555556	+	0.0320750i
$244$		0			0
$245$	3839.58	+	3072.23i	1.00123	+	0.801133i
$246$		0			0
$247$	−1.91966	−	1.10831i	−0.000494514	−	0.000285508i
$248$		0			0
$249$	−85.7633	−	148.546i	−0.0218274	−	0.0378062i
$250$		0			0
$251$		−	6545.00i		−	1.64588i	−0.568126	−	0.822942i	$-0.692331\pi$
$251$		−	6545.00i		−	1.64588i	0.568126	−	0.822942i	$-0.307669\pi$
$252$		0			0
$253$		−	2193.65i		−	0.545112i
$254$		0			0
$255$	2429.73	+	4208.42i	0.596690	+	1.03350i
$256$		0			0
$257$	1072.74	+	619.345i	0.260372	+	0.150326i	0.624504	−	0.781022i	$-0.285301\pi$
$257$	1072.74	+	619.345i	0.260372	+	0.150326i	−0.364132	+	0.931347i	$0.618634\pi$
$258$		0			0
$259$	−138.052	−	732.897i	−0.0331202	−	0.175830i
$260$		0			0
$261$	−615.921	−	355.602i	−0.146071	−	0.0843342i
$262$		0			0
$263$	809.679	−	467.468i	0.189836	−	0.109602i	−0.402070	−	0.915609i	$-0.631709\pi$
$263$	809.679	−	467.468i	0.189836	−	0.109602i	0.591906	+	0.806007i	$0.298376\pi$
$264$		0			0
$265$			1591.01i			0.368812i
$266$		0			0
$267$	1587.59			0.363890
$268$		0			0
$269$	−556.221	−	963.402i	−0.126072	−	0.218363i	0.796079	−	0.605192i	$-0.206904\pi$
$269$	−556.221	−	963.402i	−0.126072	−	0.218363i	−0.922151	+	0.386829i	$0.873570\pi$
$270$		0			0
$271$	−2696.04	+	4669.69i	−0.604329	+	1.04673i	0.387829	+	0.921731i	$0.373225\pi$
$271$	−2696.04	+	4669.69i	−0.604329	+	1.04673i	−0.992157	+	0.124996i	$0.960108\pi$
$272$		0			0
$273$	−0.712913	−	0.250112i	−0.000158049	−	5.54486e-5i
$274$		0			0
$275$	702.793	−	1217.27i	0.154109	−	0.266925i
$276$		0			0
$277$	1478.86	−	853.823i	0.320781	−	0.185203i	−0.330960	−	0.943645i	$-0.607372\pi$
$277$	1478.86	−	853.823i	0.320781	−	0.185203i	0.651741	+	0.758442i	$0.274039\pi$
$278$		0			0
$279$	−1035.62			−0.222225
$280$		0			0
$281$	214.055			0.0454429			0.0227214	−	0.999742i	$-0.492767\pi$
$281$	214.055			0.0454429			0.0227214	+	0.999742i	$0.492767\pi$
$282$		0			0
$283$	3145.91	−	1816.29i	0.660795	−	0.381510i	−0.131785	−	0.991278i	$-0.542071\pi$
$283$	3145.91	−	1816.29i	0.660795	−	0.381510i	0.792580	+	0.609768i	$0.208738\pi$
$284$		0			0
$285$	−3505.53	+	6071.75i	−0.728595	+	1.26196i
$286$		0			0
$287$	−5442.50	+	4675.92i	−1.11937	+	0.961711i
$288$		0			0
$289$	3926.42	−	6800.76i	0.799189	−	1.38424i
$290$		0			0
$291$	−160.218	−	277.505i	−0.0322754	−	0.0559026i
$292$		0			0
$293$	620.515			0.123723			0.0618615	−	0.998085i	$-0.480296\pi$
$293$	620.515			0.123723			0.0618615	+	0.998085i	$0.480296\pi$
$294$		0			0
$295$		−	3191.12i		−	0.629811i
$296$		0			0
$297$	−408.100	+	235.617i	−0.0797319	+	0.0460332i
$298$		0			0
$299$	1.48013	+	0.854552i	0.000286281	+	0.000165284i
$300$		0			0
$301$	717.459	+	835.080i	0.137388	+	0.159911i
$302$		0			0
$303$	752.985	+	434.736i	0.142765	+	0.0824255i
$304$		0			0
$305$	−4509.16	−	7810.10i	−0.846538	−	1.46625i
$306$		0			0
$307$			5779.18i			1.07438i	0.843461	+	0.537191i	$0.180514\pi$
$307$			5779.18i			1.07438i	−0.843461	+	0.537191i	$0.819486\pi$
$308$		0			0
$309$			419.122i			0.0771619i
$310$		0			0
$311$	1260.47	+	2183.20i	0.229823	+	0.398065i	0.957755	−	0.287584i	$-0.0928520\pi$
$311$	1260.47	+	2183.20i	0.229823	+	0.398065i	−0.727933	+	0.685649i	$0.759519\pi$
$312$		0			0
$313$	−6168.58	−	3561.43i	−1.11396	−	0.643144i	−0.174106	−	0.984727i	$-0.555703\pi$
$313$	−6168.58	−	3561.43i	−1.11396	−	0.643144i	−0.939851	+	0.341583i	$0.889037\pi$
$314$		0			0
$315$	−791.089	+	2254.90i	−0.141501	+	0.403330i
$316$		0			0
$317$	1901.44	+	1097.79i	0.336894	+	0.194506i	0.658898	−	0.752233i	$-0.271023\pi$
$317$	1901.44	+	1097.79i	0.336894	+	0.194506i	−0.322004	+	0.946738i	$0.604356\pi$
$318$		0			0
$319$	1194.41	−	689.595i	0.209637	−	0.121034i
$320$		0			0
$321$			3084.94i			0.536401i
$322$		0			0
$323$	18418.1			3.17278
$324$		0			0
$325$	0.547557	+	0.948396i	9.34553e−5	+	0.000161869i
$326$		0			0
$327$	1968.29	−	3409.18i	0.332865	−	0.576539i
$328$		0			0
$329$	7376.39	−	1389.45i	1.23609	−	0.232836i
$330$		0			0
$331$	−3370.28	+	5837.50i	−0.559660	+	0.969360i	0.437864	+	0.899041i	$0.355735\pi$
$331$	−3370.28	+	5837.50i	−0.559660	+	0.969360i	−0.997525	+	0.0703191i	$0.977598\pi$
$332$		0			0
$333$	313.863	−	181.209i	0.0516504	−	0.0298204i
$334$		0			0
$335$	−3799.89			−0.619732
$336$		0			0
$337$	−3202.38			−0.517641			−0.258820	−	0.965925i	$-0.583334\pi$
$337$	−3202.38			−0.517641			−0.258820	+	0.965925i	$0.583334\pi$
$338$		0			0
$339$	−1984.63	+	1145.82i	−0.317965	+	0.183577i
$340$		0			0
$341$	1004.15	−	1739.24i	0.159466	−	0.276203i
$342$		0			0
$343$	5387.03	−	3366.53i	0.848024	−	0.529958i
$344$		0			0
$345$	2702.89	−	4681.55i	0.421794	−	0.730568i
$346$		0			0
$347$	2395.49	+	4149.10i	0.370595	+	0.641889i	0.989657	−	0.143453i	$-0.0458205\pi$
$347$	2395.49	+	4149.10i	0.370595	+	0.641889i	−0.619062	+	0.785342i	$0.712487\pi$
$348$		0			0
$349$	2226.98			0.341568			0.170784	−	0.985308i	$-0.445370\pi$
$349$	2226.98			0.341568			0.170784	+	0.985308i	$0.445370\pi$
$350$		0			0
$351$		−	0.367145i		−	5.58312e-5i
$352$		0			0
$353$	−2615.57	+	1510.10i	−0.394371	+	0.227690i	−0.684052	−	0.729433i	$-0.739784\pi$
$353$	−2615.57	+	1510.10i	−0.394371	+	0.227690i	0.289682	+	0.957123i	$0.406451\pi$
$354$		0			0
$355$	−12703.3	−	7334.23i	−1.89921	−	1.09651i
$356$		0			0
$357$	6169.10	−	1162.04i	0.914575	−	0.172274i
$358$		0			0
$359$	3403.84	+	1965.21i	0.500411	+	0.288913i	0.728883	−	0.684638i	$-0.240040\pi$
$359$	3403.84	+	1965.21i	0.500411	+	0.288913i	−0.228472	+	0.973550i	$0.573373\pi$
$360$		0			0
$361$	9856.93	+	17072.7i	1.43708	+	2.48910i
$362$		0			0
$363$			3079.17i			0.445219i
$364$		0			0
$365$			15775.9i			2.26232i
$366$		0			0
$367$	695.065	+	1203.89i	0.0988613	+	0.171233i	0.911214	−	0.411934i	$-0.135147\pi$
$367$	695.065	+	1203.89i	0.0988613	+	0.171233i	−0.812352	+	0.583167i	$0.801813\pi$
$368$		0			0
$369$	−3019.72	−	1743.44i	−0.426017	−	0.245961i
$370$		0			0
$371$	1939.42	+	680.409i	0.271401	+	0.0952158i
$372$		0			0
$373$	−10511.1	−	6068.57i	−1.45910	−	0.842409i	−0.460128	−	0.887852i	$-0.652197\pi$
$373$	−10511.1	−	6068.57i	−1.45910	−	0.842409i	−0.998967	+	0.0454434i	$0.985530\pi$
$374$		0			0
$375$	−1656.20	+	956.206i	−0.228069	+	0.131675i
$376$		0			0
$377$			1.07455i			0.000146796i
$378$		0			0
$379$	−321.051			−0.0435127			−0.0217563	−	0.999763i	$-0.506926\pi$
$379$	−321.051			−0.0435127			−0.0217563	+	0.999763i	$0.506926\pi$
$380$		0			0
$381$	3446.85	+	5970.11i	0.463484	+	0.802777i
$382$		0			0
$383$	−5584.09	+	9671.92i	−0.744996	+	1.29037i	0.205200	+	0.978720i	$0.434215\pi$
$383$	−5584.09	+	9671.92i	−0.744996	+	1.29037i	−0.950197	+	0.311651i	$0.899118\pi$
$384$		0			0
$385$	−3019.88	−	3514.96i	−0.399759	−	0.465296i
$386$		0			0
$387$	−267.507	+	463.336i	−0.0351374	+	0.0608597i
$388$		0			0
$389$	5487.56	−	3168.25i	0.715246	−	0.412947i	−0.0977547	−	0.995211i	$-0.531166\pi$
$389$	5487.56	−	3168.25i	0.715246	−	0.412947i	0.813000	+	0.582263i	$0.197833\pi$
$390$		0			0
$391$	−14201.0			−1.83677
$392$		0			0
$393$	7642.89			0.980999
$394$		0			0
$395$	−7698.31	+	4444.62i	−0.980618	+	0.566160i
$396$		0			0
$397$	2394.19	−	4146.85i	0.302672	−	0.524243i	−0.674068	−	0.738669i	$-0.735455\pi$
$397$	2394.19	−	4146.85i	0.302672	−	0.524243i	0.976740	+	0.214426i	$0.0687880\pi$
$398$		0			0
$399$	5902.21	+	6869.82i	0.740551	+	0.861958i
$400$		0			0
$401$	4608.04	−	7981.36i	0.573852	−	0.993940i	−0.422314	−	0.906450i	$-0.638782\pi$
$401$	4608.04	−	7981.36i	0.573852	−	0.993940i	0.996165	−	0.0874903i	$-0.0278847\pi$
$402$		0			0
$403$	0.782349	+	1.35507i	9.67037e−5	+	0.000167496i
$404$		0			0
$405$	−1161.26			−0.142477
$406$		0			0
$407$			702.812i			0.0855948i
$408$		0			0
$409$	−10106.2	+	5834.81i	−1.22181	+	0.705411i	−0.965303	−	0.261132i	$-0.915904\pi$
$409$	−10106.2	+	5834.81i	−1.22181	+	0.705411i	−0.256504	+	0.966543i	$0.582571\pi$
$410$		0			0
$411$	−5122.18	−	2957.29i	−0.614741	−	0.354921i
$412$		0			0
$413$	−3889.92	−	1364.71i	−0.463464	−	0.162598i
$414$		0			0
$415$	709.878	+	409.848i	0.0839676	+	0.0484787i
$416$		0			0
$417$	3635.71	+	6297.24i	0.426958	+	0.739514i
$418$		0			0
$419$		−	1594.55i		−	0.185916i	−0.995670	−	0.0929582i	$-0.970368\pi$
$419$		−	1594.55i		−	0.185916i	0.995670	−	0.0929582i	$-0.0296323\pi$
$420$		0			0
$421$			14519.0i			1.68079i	0.541975	+	0.840394i	$0.317677\pi$
$421$			14519.0i			1.68079i	−0.541975	+	0.840394i	$0.682323\pi$
$422$		0			0
$423$	1823.81	+	3158.94i	0.209638	+	0.363104i
$424$		0			0
$425$	−7880.26	−	4549.67i	−0.899409	−	0.519274i
$426$		0			0
$427$	−11448.8	+	2156.55i	−1.29753	+	0.244409i
$428$		0			0
$429$	0.616593	+	0.355990i	6.93925e−5	+	4.00638e-5i
$430$		0			0
$431$	8079.55	−	4664.73i	0.902966	−	0.521328i	0.0248046	−	0.999692i	$-0.492104\pi$
$431$	8079.55	−	4664.73i	0.902966	−	0.521328i	0.878161	+	0.478365i	$0.158770\pi$
$432$		0			0
$433$			7452.02i			0.827069i	0.910488	+	0.413535i	$0.135706\pi$
$433$			7452.02i			0.827069i	−0.910488	+	0.413535i	$0.864294\pi$
$434$		0			0
$435$	3398.72			0.374612
$436$		0			0
$437$	−10244.3	−	17743.7i	−1.12140	−	1.94233i
$438$		0			0
$439$	4973.45	−	8614.28i	0.540706	−	0.936531i	−0.458157	−	0.888871i	$-0.651490\pi$
$439$	4973.45	−	8614.28i	0.540706	−	0.936531i	0.998864	−	0.0476596i	$-0.0151763\pi$
$440$		0			0
$441$	2410.37	+	1928.65i	0.260271	+	0.208255i
$442$		0			0
$443$	3025.34	−	5240.04i	0.324466	−	0.561991i	−0.656939	−	0.753944i	$-0.728149\pi$
$443$	3025.34	−	5240.04i	0.324466	−	0.561991i	0.981404	+	0.191953i	$0.0614822\pi$
$444$		0			0
$445$	−6570.37	+	3793.40i	−0.699922	+	0.404100i
$446$		0			0
$447$	1793.43			0.189768
$448$		0			0
$449$	4126.16			0.433687			0.216844	−	0.976206i	$-0.430424\pi$
$449$	4126.16			0.433687			0.216844	+	0.976206i	$0.430424\pi$
$450$		0			0
$451$	5855.94	−	3380.93i	0.611409	−	0.352997i
$452$		0			0
$453$	−1190.92	+	2062.74i	−0.123520	+	0.213943i
$454$		0			0
$455$	3.54808	−	0.668334i	0.000365574	−	6.88615e-5i
$456$		0			0
$457$	−55.1701	+	95.5574i	−0.00564715	+	0.00978116i	−0.868835	−	0.495101i	$-0.835131\pi$
$457$	−55.1701	+	95.5574i	−0.00564715	+	0.00978116i	0.863188	+	0.504883i	$0.168464\pi$
$458$		0			0
$459$	1525.31	+	2641.92i	0.155110	+	0.268658i
$460$		0			0
$461$	9429.10			0.952618			0.476309	−	0.879278i	$-0.341974\pi$
$461$	9429.10			0.952618			0.476309	+	0.879278i	$0.341974\pi$
$462$		0			0
$463$		−	9382.12i		−	0.941737i	−0.882203	−	0.470868i	$-0.843941\pi$
$463$		−	9382.12i		−	0.941737i	0.882203	−	0.470868i	$-0.156059\pi$
$464$		0			0
$465$	4285.99	−	2474.52i	0.427437	−	0.246781i
$466$		0			0
$467$	6270.05	+	3620.01i	0.621292	+	0.358703i	0.777372	−	0.629042i	$-0.216552\pi$
$467$	6270.05	+	3620.01i	0.621292	+	0.358703i	−0.156080	+	0.987744i	$0.549886\pi$
$468$		0			0
$469$	−1625.05	+	4632.01i	−0.159996	+	0.456047i
$470$		0			0
$471$	−5658.27	−	3266.80i	−0.553544	−	0.319589i
$472$		0			0
$473$	−518.759	−	898.517i	−0.0504283	−	0.0873443i
$474$		0			0
$475$		−	13128.2i		−	1.26813i
$476$		0			0
$477$			998.787i			0.0958728i
$478$		0			0
$479$	4352.19	+	7538.22i	0.415150	+	0.719060i	0.995444	−	0.0953464i	$-0.0303959\pi$
$479$	4352.19	+	7538.22i	0.415150	+	0.719060i	−0.580294	+	0.814407i	$0.697063\pi$
$480$		0			0
$481$	−0.474211	−	0.273786i	−4.49525e−5	−	2.59533e-5i
$482$		0			0
$483$	−4550.82	−	5296.89i	−0.428715	−	0.498999i
$484$		0			0
$485$	1326.15	+	765.654i	0.124160	+	0.0716836i
$486$		0			0
$487$	5116.57	−	2954.05i	0.476086	−	0.274868i	−0.242698	−	0.970102i	$-0.578032\pi$
$487$	5116.57	−	2954.05i	0.476086	−	0.274868i	0.718784	+	0.695234i	$0.244699\pi$
$488$		0			0
$489$		−	4189.21i		−	0.387408i
$490$		0			0
$491$	−2879.70			−0.264682			−0.132341	−	0.991204i	$-0.542249\pi$
$491$	−2879.70			−0.264682			−0.132341	+	0.991204i	$0.542249\pi$
$492$		0			0
$493$	−4464.23	−	7732.27i	−0.407827	−	0.706377i
$494$		0			0
$495$	1125.97	−	1950.24i	0.102240	−	0.177085i
$496$		0			0
$497$	−14373.0	+	12348.5i	−1.29721	+	1.11450i
$498$		0			0
$499$	10301.7	−	17843.1i	0.924186	−	1.60074i	0.131320	−	0.991340i	$-0.458078\pi$
$499$	10301.7	−	17843.1i	0.924186	−	1.60074i	0.792865	−	0.609397i	$-0.208588\pi$
$500$		0			0
$501$	−7038.49	+	4063.67i	−0.627658	+	0.362378i
$502$		0			0
$503$	−10122.2			−0.897274			−0.448637	−	0.893714i	$-0.648090\pi$
$503$	−10122.2			−0.897274			−0.448637	+	0.893714i	$0.648090\pi$
$504$		0			0
$505$	−4155.06			−0.366134
$506$		0			0
$507$	5707.97	−	3295.50i	0.500000	−	0.288675i
$508$		0			0
$509$	−452.319	+	783.440i	−0.0393884	+	0.0682227i	−0.885048	−	0.465501i	$-0.845874\pi$
$509$	−452.319	+	783.440i	−0.0393884	+	0.0682227i	0.845659	+	0.533723i	$0.179208\pi$
$510$		0			0
$511$	19230.6	+	6746.69i	1.66479	+	0.584062i
$512$		0			0
$513$	−2200.66	+	3811.65i	−0.189399	+	0.328048i
$514$		0			0
$515$	−1001.46	−	1734.57i	−0.0856883	−	0.148416i
$516$		0			0
$517$	−7073.60			−0.601734
$518$		0			0
$519$		−	12807.4i		−	1.08320i
$520$		0			0
$521$	10554.3	−	6093.53i	0.887510	−	0.512404i	0.0143826	−	0.999897i	$-0.495422\pi$
$521$	10554.3	−	6093.53i	0.887510	−	0.512404i	0.873127	+	0.487493i	$0.162088\pi$
$522$		0			0
$523$	−4054.18	−	2340.68i	−0.338962	−	0.195700i	0.320851	−	0.947130i	$-0.396031\pi$
$523$	−4054.18	−	2340.68i	−0.338962	−	0.195700i	−0.659813	+	0.751430i	$0.729364\pi$
$524$		0			0
$525$	−828.290	−	4397.26i	−0.0688563	−	0.365547i
$526$		0			0
$527$	−11259.3	−	6500.57i	−0.930671	−	0.537323i
$528$		0			0
$529$	1815.26	+	3144.13i	0.149196	+	0.258414i
$530$		0			0
$531$		−	2003.28i		−	0.163720i
$532$		0			0
$533$			5.26826i			0.000428131i
$534$		0			0
$535$	−7371.21	−	12767.3i	−0.595673	−	1.03174i
$536$		0			0
$537$	−6422.42	−	3707.99i	−0.516104	−	0.297973i
$538$		0			0
$539$	−5576.15	+	2177.98i	−0.445607	+	0.174049i
$540$		0			0
$541$	−11836.3	−	6833.70i	−0.940634	−	0.543075i	−0.0504750	−	0.998725i	$-0.516074\pi$
$541$	−11836.3	−	6833.70i	−0.940634	−	0.543075i	−0.890159	+	0.455650i	$0.849407\pi$
$542$		0			0
$543$	−2819.14	+	1627.63i	−0.222801	+	0.128634i
$544$		0			0
$545$			18812.3i			1.47859i
$546$		0			0
$547$	14251.9			1.11402			0.557009	−	0.830506i	$-0.311949\pi$
$547$	14251.9			1.11402			0.557009	+	0.830506i	$0.311949\pi$
$548$		0			0
$549$	−2830.71	−	4902.94i	−0.220058	−	0.381151i
$550$		0			0
$551$	6440.82	−	11155.8i	0.497982	−	0.862530i
$552$		0			0
$553$	2125.68	+	11284.9i	0.163460	+	0.867781i
$554$		0			0
$555$	−865.967	+	1499.90i	−0.0662310	+	0.114716i
$556$		0			0
$557$	9512.61	−	5492.11i	0.723631	−	0.417788i	−0.0924567	−	0.995717i	$-0.529472\pi$
$557$	9512.61	−	5492.11i	0.723631	−	0.417788i	0.816088	+	0.577928i	$0.196139\pi$
$558$		0			0
$559$	0.808346			6.11617e−5
$560$		0			0
$561$	−5915.86			−0.445219
$562$		0			0
$563$	−1766.78	+	1020.05i	−0.132257	+	0.0763588i	−0.564669	−	0.825318i	$-0.690996\pi$
$563$	−1766.78	+	1020.05i	−0.132257	+	0.0763588i	0.432412	+	0.901676i	$0.357663\pi$
$564$		0			0
$565$	5475.70	−	9484.19i	0.407725	−	0.706200i
$566$		0			0
$567$	−496.621	+	1415.55i	−0.0367832	+	0.104846i
$568$		0			0
$569$	910.229	−	1576.56i	0.0670629	−	0.116156i	−0.830544	−	0.556953i	$-0.811971\pi$
$569$	910.229	−	1576.56i	0.0670629	−	0.116156i	0.897607	+	0.440796i	$0.145304\pi$
$570$		0			0
$571$	−632.042	−	1094.73i	−0.0463225	−	0.0802329i	0.841935	−	0.539580i	$-0.181417\pi$
$571$	−632.042	−	1094.73i	−0.0463225	−	0.0802329i	−0.888257	+	0.459347i	$0.848084\pi$
$572$		0			0
$573$	−11263.5			−0.821184
$574$		0			0
$575$			10122.3i			0.734138i
$576$		0			0
$577$	19613.3	−	11323.7i	1.41510	−	0.817008i	0.419236	−	0.907877i	$-0.362298\pi$
$577$	19613.3	−	11323.7i	1.41510	−	0.817008i	0.995863	+	0.0908695i	$0.0289646\pi$
$578$		0			0
$579$	1341.61	+	774.581i	0.0962963	+	0.0555967i
$580$		0			0
$581$	803.184	−	690.056i	0.0573523	−	0.0492742i
$582$		0			0
$583$	−1677.39	−	968.440i	−0.119160	−	0.0687971i
$584$		0			0
$585$	0.877262	+	1.51946i	6.20006e−5	+	0.000107388i
$586$		0			0
$587$			22223.9i			1.56265i	0.624122	+	0.781327i	$0.285457\pi$
$587$			22223.9i			1.56265i	−0.624122	+	0.781327i	$0.714543\pi$
$588$		0			0
$589$		−	18757.5i		−	1.31221i
$590$		0			0
$591$	−4085.31	−	7075.96i	−0.284344	−	0.492497i
$592$		0			0
$593$	−15704.3	−	9066.88i	−1.08752	−	0.627879i	−0.154603	−	0.987977i	$-0.549410\pi$
$593$	−15704.3	−	9066.88i	−1.08752	−	0.627879i	−0.932915	+	0.360098i	$0.882743\pi$
$594$		0			0
$595$	−22754.8	+	19549.8i	−1.56782	+	1.34700i
$596$		0			0
$597$	11738.5	+	6777.21i	0.804729	+	0.464611i
$598$		0			0
$599$	23274.1	−	13437.3i	1.58757	−	0.916584i	0.593864	−	0.804566i	$-0.297602\pi$
$599$	23274.1	−	13437.3i	1.58757	−	0.916584i	0.993706	−	0.112018i	$-0.0357316\pi$
$600$		0			0
$601$			2069.10i			0.140433i	0.997532	+	0.0702167i	$0.0223691\pi$
$601$			2069.10i			0.140433i	−0.997532	+	0.0702167i	$0.977631\pi$
$602$		0			0
$603$	−2385.45			−0.161100
$604$		0			0
$605$	−7357.41	−	12743.4i	−0.494416	−	0.856353i
$606$		0			0
$607$	−3262.04	+	5650.02i	−0.218126	+	0.377804i	−0.954235	−	0.299058i	$-0.903328\pi$
$607$	−3262.04	+	5650.02i	−0.218126	+	0.377804i	0.736109	+	0.676863i	$0.236661\pi$
$608$		0			0
$609$	1453.49	−	4142.99i	0.0967134	−	0.275669i
$610$		0			0
$611$	2.75557	−	4.77279i	0.000182453	−	0.000316017i
$612$		0			0
$613$	24391.0	−	14082.2i	1.60709	−	0.927852i	0.617069	−	0.786909i	$-0.288320\pi$
$613$	24391.0	−	14082.2i	1.60709	−	0.927852i	0.990018	−	0.140943i	$-0.0450133\pi$
$614$		0			0
$615$	16663.2			1.09256
$616$		0			0
$617$	2680.20			0.174880			0.0874398	−	0.996170i	$-0.472131\pi$
$617$	2680.20			0.174880			0.0874398	+	0.996170i	$0.472131\pi$
$618$		0			0
$619$	−3985.34	+	2300.94i	−0.258780	+	0.149406i	−0.623778	−	0.781602i	$-0.714403\pi$
$619$	−3985.34	+	2300.94i	−0.258780	+	0.149406i	0.364998	+	0.931008i	$0.381070\pi$
$620$		0			0
$621$	1696.79	−	2938.93i	0.109646	−	0.189912i
$622$		0			0
$623$	1814.23	+	9631.45i	0.116670	+	0.619384i
$624$		0			0
$625$	9602.99	−	16632.9i	0.614592	−	1.06450i
$626$		0			0
$627$	−4267.59	−	7391.68i	−0.271820	−	0.470806i
$628$		0			0
$629$	4549.79			0.288413
$630$		0			0
$631$		−	28417.5i		−	1.79284i	−0.443206	−	0.896420i	$-0.646159\pi$
$631$		−	28417.5i		−	1.79284i	0.443206	−	0.896420i	$-0.353841\pi$
$632$		0			0
$633$	1801.74	−	1040.23i	0.113132	−	0.0653169i
$634$		0			0
$635$	−28530.2	−	16471.9i	−1.78297	−	1.02940i
$636$		0			0
$637$	0.702675	−	4.61087i	4.37064e−5	−	0.000286796i
$638$		0			0
$639$	−7974.71	−	4604.20i	−0.493700	−	0.285038i
$640$		0			0
$641$	857.499	+	1485.23i	0.0528380	+	0.0915181i	0.891235	−	0.453543i	$-0.149840\pi$
$641$	857.499	+	1485.23i	0.0528380	+	0.0915181i	−0.838397	+	0.545061i	$0.816507\pi$
$642$		0			0
$643$			5665.36i			0.347465i	0.984793	+	0.173733i	$0.0555828\pi$
$643$			5665.36i			0.347465i	−0.984793	+	0.173733i	$0.944417\pi$
$644$		0			0
$645$		−	2556.75i		−	0.156080i
$646$		0			0
$647$	−5809.92	−	10063.1i	−0.353032	−	0.611469i	0.633747	−	0.773540i	$-0.281516\pi$
$647$	−5809.92	−	10063.1i	−0.353032	−	0.611469i	−0.986779	+	0.162071i	$0.948183\pi$
$648$		0			0
$649$	3364.36	+	1942.42i	0.203487	+	0.117483i
$650$		0			0
$651$	−1183.46	−	6282.81i	−0.0712496	−	0.378253i
$652$		0			0
$653$	16057.9	+	9271.01i	0.962317	+	0.555594i	0.896885	−	0.442263i	$-0.145824\pi$
$653$	16057.9	+	9271.01i	0.962317	+	0.555594i	0.0654313	+	0.997857i	$0.479158\pi$
$654$		0			0
$655$	−31630.8	+	18262.0i	−1.88690	+	1.08940i
$656$		0			0
$657$			9903.61i			0.588092i
$658$		0			0
$659$	−7570.77			−0.447519			−0.223760	−	0.974644i	$-0.571833\pi$
$659$	−7570.77			−0.447519			−0.223760	+	0.974644i	$0.571833\pi$
$660$		0			0
$661$	9925.25	+	17191.0i	0.584036	+	1.01158i	0.994995	+	0.0999258i	$0.0318605\pi$
$661$	9925.25	+	17191.0i	0.584036	+	1.01158i	−0.410959	+	0.911654i	$0.634806\pi$
$662$		0			0
$663$	2.30457	−	3.99163i	0.000134996	−	0.000233819i
$664$		0			0
$665$	−40841.7	−	14328.5i	−2.38161	−	0.835544i
$666$		0			0
$667$	−4966.11	+	8601.55i	−0.288289	+	0.499331i
$668$		0			0
$669$	10068.1	−	5812.80i	0.581844	−	0.335928i
$670$		0			0
$671$	10978.8			0.631643
$672$		0			0
$673$	−6328.13			−0.362454			−0.181227	−	0.983441i	$-0.558007\pi$
$673$	−6328.13			−0.362454			−0.181227	+	0.983441i	$0.558007\pi$
$674$		0			0
$675$	1883.13	−	1087.22i	0.107380	−	0.0619959i
$676$		0			0
$677$	−7175.39	+	12428.1i	−0.407345	+	0.705542i	−0.994591	−	0.103866i	$-0.966879\pi$
$677$	−7175.39	+	12428.1i	−0.407345	+	0.705542i	0.587246	+	0.809408i	$0.300212\pi$
$678$		0			0
$679$	1500.46	−	1289.12i	0.0848046	−	0.0728599i
$680$		0			0
$681$	2791.05	−	4834.25i	0.157053	−	0.272024i
$682$		0			0
$683$	14738.8	+	25528.3i	0.825716	+	1.43018i	0.901371	+	0.433048i	$0.142562\pi$
$683$	14738.8	+	25528.3i	0.825716	+	1.43018i	−0.0756553	+	0.997134i	$0.524105\pi$
$684$		0			0
$685$	28264.8			1.57656
$686$		0			0
$687$			3994.30i			0.221822i
$688$		0			0
$689$	1.30688	−	0.754527i	7.22614e−5	−	4.17201e-5i
$690$		0			0
$691$	1274.09	+	735.599i	0.0701430	+	0.0404971i	0.534661	−	0.845066i	$-0.320439\pi$
$691$	1274.09	+	735.599i	0.0701430	+	0.0404971i	−0.464518	+	0.885564i	$0.653773\pi$
$692$		0			0
$693$	−1895.78	−	2206.58i	−0.103918	−	0.120954i
$694$		0			0
$695$	−30093.5	−	17374.5i	−1.64246	−	0.948275i
$696$		0			0
$697$	−21887.1	−	37909.6i	−1.18943	−	2.06015i
$698$		0			0
$699$			8727.95i			0.472277i
$700$		0			0
$701$		−	36181.3i		−	1.94943i	−0.223460	−	0.974713i	$-0.571735\pi$
$701$		−	36181.3i		−	1.94943i	0.223460	−	0.974713i	$-0.428265\pi$
$702$		0			0
$703$	3282.13	+	5684.82i	0.176085	+	0.304989i
$704$		0			0
$705$	−15096.0	−	8715.70i	−0.806453	−	0.465606i
$706$		0			0
$707$	−1776.95	+	5064.96i	−0.0945246	+	0.269430i
$708$		0			0
$709$	−13668.1	−	7891.26i	−0.723998	−	0.418001i	0.0922242	−	0.995738i	$-0.470602\pi$
$709$	−13668.1	−	7891.26i	−0.723998	−	0.418001i	−0.816223	+	0.577738i	$0.803936\pi$
$710$		0			0
$711$	−4832.76	+	2790.19i	−0.254912	+	0.147174i
$712$		0			0
$713$			14462.8i			0.759656i
$714$		0			0
$715$	−3.40243			−0.000177963
$716$		0			0
$717$	−4317.27	−	7477.74i	−0.224870	−	0.389486i
$718$		0			0
$719$	−7498.23	+	12987.3i	−0.388925	+	0.673638i	−0.992305	−	0.123816i	$-0.960487\pi$
$719$	−7498.23	+	12987.3i	−0.388925	+	0.673638i	0.603380	+	0.797454i	$0.293820\pi$
$720$		0			0
$721$	−2542.70	+	478.956i	−0.131339	+	0.0247396i
$722$		0			0
$723$	−4538.03	+	7860.10i	−0.233432	+	0.404316i
$724$		0			0
$725$	−5511.47	+	3182.05i	−0.282332	+	0.163005i
$726$		0			0
$727$	23460.4			1.19684			0.598418	−	0.801184i	$-0.295796\pi$
$727$	23460.4			1.19684			0.598418	+	0.801184i	$0.295796\pi$
$728$		0			0
$729$	−729.000			−0.0370370
$730$		0			0
$731$	−5816.73	+	3358.29i	−0.294308	+	0.169919i
$732$		0			0
$733$	−15323.6	+	26541.3i	−0.772157	+	1.33742i	0.164221	+	0.986424i	$0.447489\pi$
$733$	−15323.6	+	26541.3i	−0.772157	+	1.33742i	−0.936378	+	0.350992i	$0.885844\pi$
$734$		0			0
$735$	−14583.9	−	2222.51i	−0.731883	−	0.111536i
$736$		0			0
$737$	2312.97	−	4006.18i	0.115603	−	0.200230i
$738$		0			0
$739$	12993.6	+	22505.6i	0.646791	+	1.12028i	0.983885	+	0.178804i	$0.0572229\pi$
$739$	12993.6	+	22505.6i	0.646791	+	1.12028i	−0.337093	+	0.941471i	$0.609444\pi$
$740$		0			0
$741$	6.64989			0.000329676
$742$		0			0
$743$		−	31662.8i		−	1.56339i	−0.623664	−	0.781693i	$-0.714357\pi$
$743$		−	31662.8i		−	1.56339i	0.623664	−	0.781693i	$-0.285643\pi$
$744$		0			0
$745$	−7422.27	+	4285.25i	−0.365008	+	0.210738i
$746$		0			0
$747$	445.639	+	257.290i	0.0218274	+	0.0126021i
$748$		0			0
$749$	−18715.5	+	3525.35i	−0.913017	+	0.171981i
$750$		0			0
$751$	20071.7	+	11588.4i	0.975267	+	0.563070i	0.900838	−	0.434156i	$-0.142953\pi$
$751$	20071.7	+	11588.4i	0.975267	+	0.563070i	0.0744288	+	0.997226i	$0.476287\pi$
$752$		0			0
$753$	9817.50	+	17004.4i	0.475125	+	0.822942i
$754$		0			0
$755$		−	11382.4i		−	0.548675i
$756$		0			0
$757$			21080.0i			1.01211i	0.862501	+	0.506055i	$0.168897\pi$
$757$			21080.0i			1.01211i	−0.862501	+	0.506055i	$0.831103\pi$
$758$		0			0
$759$	3290.47	+	5699.26i	0.157360	+	0.272556i
$760$		0			0
$761$	−5731.49	−	3309.08i	−0.273017	−	0.157627i	0.357241	−	0.934012i	$-0.383718\pi$
$761$	−5731.49	−	3309.08i	−0.273017	−	0.157627i	−0.630258	+	0.776386i	$0.717051\pi$
$762$		0			0
$763$	22931.9	+	8045.23i	1.08806	+	0.381726i
$764$		0			0
$765$	−12625.3	−	7289.20i	−0.596690	−	0.344499i
$766$		0			0
$767$	−2.62123	+	1.51337i	−0.000123399	+	7.12444e-5i
$768$		0			0
$769$		−	30464.7i		−	1.42859i	−0.699844	−	0.714296i	$-0.746747\pi$
$769$		−	30464.7i		−	1.42859i	0.699844	−	0.714296i	$-0.253253\pi$
$770$		0			0
$771$	−3716.07			−0.173581
$772$		0			0
$773$	−13374.8	−	23165.8i	−0.622325	−	1.07790i	−0.989052	−	0.147570i	$-0.952855\pi$
$773$	−13374.8	−	23165.8i	−0.622325	−	1.07790i	0.366727	−	0.930329i	$-0.380478\pi$
$774$		0			0
$775$	−4633.53	+	8025.51i	−0.214763	+	0.371980i
$776$		0			0
$777$	1458.01	+	1697.04i	0.0673179	+	0.0783540i
$778$		0			0
$779$	31577.9	−	54694.5i	1.45237	−	2.51557i
$780$		0			0
$781$	15464.8	−	8928.61i	0.708546	−	0.409079i
$782$		0			0
$783$	2133.61			0.0973807
$784$		0			0
$785$	31223.0			1.41961
$786$		0			0
$787$	19932.1	−	11507.8i	0.902798	−	0.521231i	0.0246914	−	0.999695i	$-0.492140\pi$
$787$	19932.1	−	11507.8i	0.902798	−	0.521231i	0.878107	+	0.478464i	$0.158806\pi$
$788$		0			0
$789$	−1402.40	+	2429.04i	−0.0632787	+	0.109602i
$790$		0			0
$791$	−9219.35	−	10730.8i	−0.414415	−	0.482355i
$792$		0			0
$793$	−4.27688	+	7.40777i	−0.000191521	+	0.000331725i
$794$		0			0
$795$	−2386.52	−	4133.57i	−0.106467	−	0.184406i
$796$		0			0
$797$	36331.6			1.61472			0.807359	−	0.590060i	$-0.200896\pi$
$797$	36331.6			1.61472			0.807359	+	0.590060i	$0.200896\pi$
$798$		0			0
$799$			45792.3i			2.02755i
$800$		0			0
$801$	−4124.67	+	2381.38i	−0.181945	+	0.105046i
$802$		0			0
$803$	−16632.4	−	9602.70i	−0.730938	−	0.422007i
$804$		0			0
$805$	31490.4	+	11047.8i	1.37875	+	0.483708i
$806$		0			0
$807$	2890.21	+	1668.66i	0.126072	+	0.0727877i
$808$		0			0
$809$	16290.8	+	28216.4i	0.707976	+	1.22625i	0.965607	+	0.260007i	$0.0837250\pi$
$809$	16290.8	+	28216.4i	0.707976	+	1.22625i	−0.257630	+	0.966244i	$0.582942\pi$
$810$		0			0
$811$			13370.1i			0.578898i	0.957193	+	0.289449i	$0.0934720\pi$
$811$			13370.1i			0.578898i	−0.957193	+	0.289449i	$0.906528\pi$
$812$		0			0
$813$		−	16176.3i		−	0.697818i
$814$		0			0
$815$	10009.8	+	17337.4i	0.430216	+	0.745157i
$816$		0			0
$817$	−8392.15	−	4845.21i	−0.359369	−	0.207482i
$818$		0			0
$819$	2.22737	−	0.419559i	9.50313e−5	−	1.79006e-5i
$820$		0			0
$821$	−22344.3	−	12900.5i	−0.949845	−	0.548393i	−0.0568122	−	0.998385i	$-0.518094\pi$
$821$	−22344.3	−	12900.5i	−0.949845	−	0.548393i	−0.893033	+	0.449992i	$0.851427\pi$
$822$		0			0
$823$	−15322.0	+	8846.18i	−0.648958	+	0.374676i	−0.788057	−	0.615602i	$-0.788913\pi$
$823$	−15322.0	+	8846.18i	−0.648958	+	0.374676i	0.139099	+	0.990279i	$0.455579\pi$
$824$		0			0
$825$			4216.76i			0.177950i
$826$		0			0
$827$	32331.0			1.35944			0.679722	−	0.733470i	$-0.262100\pi$
$827$	32331.0			1.35944			0.679722	+	0.733470i	$0.262100\pi$
$828$		0			0
$829$	17484.5	+	30284.1i	0.732524	+	1.26877i	0.955801	+	0.294014i	$0.0949911\pi$
$829$	17484.5	+	30284.1i	0.732524	+	1.26877i	−0.223277	+	0.974755i	$0.571676\pi$
$830$		0			0
$831$	−2561.47	+	4436.59i	−0.106927	+	0.185203i
$832$		0			0
$833$	14099.6	+	36098.3i	0.586461	+	1.50148i
$834$		0			0
$835$	19419.6	−	33635.7i	0.804842	−	1.39403i
$836$		0			0
$837$	2690.61	−	1553.43i	0.111112	−	0.0641508i
$838$		0			0
$839$	−620.863			−0.0255478			−0.0127739	−	0.999918i	$-0.504066\pi$
$839$	−620.863			−0.0255478			−0.0127739	+	0.999918i	$0.504066\pi$
$840$		0			0
$841$	18144.4			0.743959
$842$		0			0
$843$	−556.131	+	321.082i	−0.0227214	+	0.0131182i
$844$		0			0
$845$	−15748.6	+	27277.4i	−0.641147	+	1.11050i
$846$		0			0
$847$	−18680.5	+	3518.75i	−0.757815	+	0.142746i
$848$		0			0
$849$	−5448.87	+	9437.73i	−0.220265	+	0.381510i
$850$		0			0
$851$	−2530.65	−	4383.21i	−0.101938	−	0.176562i
$852$		0			0
$853$	−48976.5			−1.96591			−0.982955	−	0.183844i	$-0.941146\pi$
$853$	−48976.5			−1.96591			−0.982955	+	0.183844i	$0.941146\pi$
$854$		0			0
$855$		−	21033.2i		−	0.841309i
$856$		0			0
$857$	41178.0	−	23774.1i	1.64132	−	0.947618i	0.660959	−	0.750422i	$-0.270150\pi$
$857$	41178.0	−	23774.1i	1.64132	−	0.947618i	0.980364	−	0.197196i	$-0.0631836\pi$
$858$		0			0
$859$	5907.86	+	3410.90i	0.234661	+	0.135481i	0.612720	−	0.790300i	$-0.290075\pi$
$859$	5907.86	+	3410.90i	0.234661	+	0.135481i	−0.378060	+	0.925781i	$0.623409\pi$
$860$		0			0
$861$	7126.14	−	20312.2i	0.282065	−	0.803991i
$862$		0			0
$863$	3901.64	+	2252.61i	0.153897	+	0.0888526i	0.574971	−	0.818174i	$-0.305013\pi$
$863$	3901.64	+	2252.61i	0.153897	+	0.0888526i	−0.421074	+	0.907026i	$0.638347\pi$
$864$		0			0
$865$	30602.2	+	53004.6i	1.20290	+	2.08348i
$866$		0			0
$867$			23558.5i			0.922825i
$868$		0			0
$869$		−	10821.7i		−	0.422440i
$870$		0			0
$871$	1.80207	+	3.12128i	7.01043e−5	+	0.000121424i
$872$		0			0
$873$	832.516	+	480.653i	0.0322754	+	0.0186342i
$874$		0			0
$875$	−7693.68	−	8954.99i	−0.297250	−	0.345982i
$876$		0			0
$877$	19331.7	+	11161.2i	0.744339	+	0.429745i	0.823645	−	0.567106i	$-0.191937\pi$
$877$	19331.7	+	11161.2i	0.744339	+	0.429745i	−0.0793055	+	0.996850i	$0.525270\pi$
$878$		0			0
$879$	−1612.14	+	930.772i	−0.0618615	+	0.0357158i
$880$		0			0
$881$		−	10311.4i		−	0.394325i	−0.980371	−	0.197162i	$-0.936827\pi$
$881$		−	10311.4i		−	0.394325i	0.980371	−	0.197162i	$-0.0631726\pi$
$882$		0			0
$883$	−30437.2			−1.16002			−0.580008	−	0.814611i	$-0.696951\pi$
$883$	−30437.2			−1.16002			−0.580008	+	0.814611i	$0.696951\pi$
$884$		0			0
$885$	4786.68	+	8290.77i	0.181811	+	0.314905i
$886$		0			0
$887$	76.5737	−	132.629i	0.00289864	−	0.00502059i	−0.864572	−	0.502508i	$-0.832411\pi$
$887$	76.5737	−	132.629i	0.00289864	−	0.00502059i	0.867471	+	0.497488i	$0.165744\pi$
$888$		0			0
$889$	−32280.1	+	27733.5i	−1.21782	+	1.04629i
$890$		0			0
$891$	706.850	−	1224.30i	0.0265773	−	0.0460332i
$892$		0			0
$893$	−57216.0	+	33033.7i	−2.14408	+	1.23788i
$894$		0			0
$895$	35439.7			1.32360
$896$		0			0
$897$	−5.12731			−0.000190854
$898$		0			0
$899$	−7874.79	+	4546.51i	−0.292146	+	0.168670i
$900$		0			0
$901$	−6269.39	+	10858.9i	−0.231813	+	0.401512i
$902$		0			0
$903$	−3116.63	−	1093.41i	−0.114856	−	0.0402951i
$904$		0			0
$905$	7778.17	−	13472.2i	0.285696	−	0.494840i
$906$		0			0
$907$	−8377.82	−	14510.8i	−0.306705	−	0.531228i	0.670935	−	0.741516i	$-0.265893\pi$
$907$	−8377.82	−	14510.8i	−0.306705	−	0.531228i	−0.977639	+	0.210288i	$0.932560\pi$
$908$		0			0
$909$	−2608.42			−0.0951768
$910$		0			0
$911$			30395.6i			1.10543i	0.833369	+	0.552717i	$0.186409\pi$
$911$			30395.6i			1.10543i	−0.833369	+	0.552717i	$0.813591\pi$
$912$		0			0
$913$	−864.198	+	498.945i	−0.0313262	+	0.0180862i
$914$		0			0
$915$	23430.3	+	13527.5i	0.846538	+	0.488749i
$916$		0			0
$917$	8733.99	+	46367.3i	0.314527	+	1.66978i
$918$		0			0
$919$	22204.2	+	12819.6i	0.797005	+	0.460151i	0.842423	−	0.538817i	$-0.181129\pi$
$919$	22204.2	+	12819.6i	0.797005	+	0.460151i	−0.0454180	+	0.998968i	$0.514462\pi$
$920$		0			0
$921$	−8668.77	−	15014.7i	−0.310147	−	0.537191i
$922$		0			0
$923$			13.9128i			0.000496150i
$924$		0			0
$925$		−	3243.04i		−	0.115276i
$926$		0			0
$927$	−628.683	−	1088.91i	−0.0222747	−	0.0385809i
$928$		0			0
$929$	4081.79	+	2356.63i	0.144154	+	0.0832275i	0.570342	−	0.821407i	$-0.306811\pi$
$929$	4081.79	+	2356.63i	0.144154	+	0.0832275i	−0.426188	+	0.904635i	$0.640144\pi$
$930$		0			0
$931$	−34932.5	+	43657.6i	−1.22972	+	1.53686i
$932$		0			0
$933$	−6549.61	−	3781.42i	−0.229823	−	0.132688i
$934$		0			0
$935$	24483.3	−	14135.5i	0.856354	−	0.494416i
$936$		0			0
$937$		−	36696.5i		−	1.27943i	−0.768614	−	0.639713i	$-0.779053\pi$
$937$		−	36696.5i		−	1.27943i	0.768614	−	0.639713i	$-0.220947\pi$
$938$		0			0
$939$	21368.6			0.742638
$940$		0			0
$941$	22166.4	+	38393.3i	0.767910	+	1.33006i	0.938694	+	0.344751i	$0.112037\pi$
$941$	22166.4	+	38393.3i	0.767910	+	1.33006i	−0.170784	+	0.985309i	$0.554630\pi$
$942$		0			0
$943$	−24347.7	+	42171.5i	−0.840796	+	1.45630i
$944$		0			0
$945$	−1327.04	−	7045.03i	−0.0456810	−	0.242513i
$946$		0			0
$947$	−4439.42	+	7689.30i	−0.152335	+	0.263853i	−0.932086	−	0.362238i	$-0.882013\pi$
$947$	−4439.42	+	7689.30i	−0.152335	+	0.263853i	0.779750	+	0.626091i	$0.215346\pi$
$948$		0			0
$949$	12.9585	−	7.48161i	0.000443258	−	0.000255915i
$950$		0			0
$951$	−6586.77			−0.224596
$952$		0			0
$953$	9873.81			0.335618			0.167809	−	0.985820i	$-0.446331\pi$
$953$	9873.81			0.335618			0.167809	+	0.985820i	$0.446331\pi$
$954$		0			0
$955$	46614.9	−	26913.1i	1.57950	−	0.911925i
$956$		0			0
$957$	−2068.79	+	3583.24i	−0.0698791	+	0.121034i
$958$		0			0
$959$	12087.7	−	34454.3i	0.407019	−	1.16016i
$960$		0			0
$961$	8275.12	−	14332.9i	0.277772	−	0.481116i
$962$		0			0
$963$	−4627.41	−	8014.92i	−0.154846	−	0.268201i
$964$		0			0
$965$	−7403.18			−0.246960
$966$		0			0
$967$			37987.8i			1.26329i	0.775256	+	0.631647i	$0.217621\pi$
$967$			37987.8i			1.26329i	−0.775256	+	0.631647i	$0.782379\pi$
$968$		0			0
$969$	−47851.5	+	27627.1i	−1.58639	+	0.915903i
$970$		0			0
$971$	−15678.8	−	9052.15i	−0.518184	−	0.299173i	0.218008	−	0.975947i	$-0.430044\pi$
$971$	−15678.8	−	9052.15i	−0.518184	−	0.299173i	−0.736191	+	0.676774i	$0.763378\pi$
$972$		0			0
$973$	−34048.9	+	29253.1i	−1.12185	+	0.963836i
$974$		0			0
$975$	−2.84519	−	1.64267i	−9.34553e−5	−	5.39565e-5i
$976$		0			0
$977$	−17975.5	−	31134.4i	−0.588624	−	1.01953i	−0.994413	−	0.105560i	$-0.966336\pi$
$977$	−17975.5	−	31134.4i	−0.588624	−	1.01953i	0.405789	−	0.913967i	$-0.366997\pi$
$978$		0			0
$979$		−	9236.09i		−	0.301519i
$980$		0			0
$981$			11809.8i			0.384359i
$982$		0			0
$983$	−8106.45	−	14040.8i	−0.263027	−	0.455576i	0.704018	−	0.710182i	$-0.251387\pi$
$983$	−8106.45	−	14040.8i	−0.263027	−	0.455576i	−0.967045	+	0.254606i	$0.918054\pi$
$984$		0			0
$985$	33814.8	+	19523.0i	1.09384	+	0.631527i
$986$		0			0
$987$	−17080.2	+	14674.5i	−0.550831	+	0.473246i
$988$		0			0
$989$	6470.66	+	3735.84i	0.208043	+	0.120114i
$990$		0			0
$991$	15142.2	−	8742.34i	0.485375	−	0.280232i	−0.237278	−	0.971442i	$-0.576255\pi$
$991$	15142.2	−	8742.34i	0.485375	−	0.280232i	0.722654	+	0.691210i	$0.242922\pi$
$992$		0			0
$993$		−	20221.7i		−	0.646240i
$994$		0			0
$995$	−64774.3			−2.06380
$996$		0			0
$997$	12042.3	+	20857.9i	0.382531	+	0.662562i	0.991423	−	0.130690i	$-0.0417193\pi$
$997$	12042.3	+	20857.9i	0.382531	+	0.662562i	−0.608893	+	0.793253i	$0.708386\pi$
$998$		0			0
$999$	−543.627	+	941.589i	−0.0172168	+	0.0298204i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	672.4.bb.a.271.18		96
4.3	odd	2		168.4.t.a.19.10	✓	96
7.3	odd	6	inner	672.4.bb.a.367.17		96
8.3	odd	2	inner	672.4.bb.a.271.17		96
8.5	even	2		168.4.t.a.19.22	yes	96
28.3	even	6		168.4.t.a.115.22	yes	96
56.3	even	6	inner	672.4.bb.a.367.18		96
56.45	odd	6		168.4.t.a.115.10	yes	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
168.4.t.a.19.10	✓	96	4.3	odd	2
168.4.t.a.19.22	yes	96	8.5	even	2
168.4.t.a.115.10	yes	96	56.45	odd	6
168.4.t.a.115.22	yes	96	28.3	even	6
672.4.bb.a.271.17		96	8.3	odd	2	inner
672.4.bb.a.271.18		96	1.1	even	1	trivial
672.4.bb.a.367.17		96	7.3	odd	6	inner
672.4.bb.a.367.18		96	56.3	even	6	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:	\( N \)	\(=\)	\( 672 = 2^{5} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	672.bb (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-2.59808 + 1.50000i) q^{3} +(7.16825 - 12.4158i) q^{5} +(-12.0691 - 14.0477i) q^{7} +(4.50000 - 7.79423i) q^{9} +(8.72655 + 15.1148i) q^{11} -0.0135980 q^{13} +43.0095i q^{15} +(97.8487 - 56.4930i) q^{17} +(141.172 + 81.5059i) q^{19} +(52.4279 + 18.3934i) q^{21} +(-108.849 - 62.8441i) q^{23} +(-40.2675 - 69.7454i) q^{25} +27.0000i q^{27} -79.0227i q^{29} +(-57.5343 - 99.6523i) q^{31} +(-45.3445 - 26.1796i) q^{33} +(-260.927 + 49.1495i) q^{35} +(34.8737 + 20.1343i) q^{37} +(0.0353286 - 0.0203970i) q^{39} -387.430i q^{41} -59.4461 q^{43} +(-64.5142 - 111.742i) q^{45} +(-202.646 + 350.993i) q^{47} +(-51.6750 + 339.085i) q^{49} +(-169.479 + 293.546i) q^{51} +(-96.1083 + 55.4882i) q^{53} +250.216 q^{55} -489.036 q^{57} +(192.766 - 111.294i) q^{59} +(314.523 - 544.771i) q^{61} +(-163.802 + 30.8545i) q^{63} +(-0.0974736 + 0.168829i) q^{65} +(-132.525 - 229.540i) q^{67} +377.065 q^{69} -1023.16i q^{71} +(-952.975 + 550.200i) q^{73} +(209.236 + 120.803i) q^{75} +(107.007 - 305.010i) q^{77} +(-536.973 - 310.022i) q^{79} +(-40.5000 - 70.1481i) q^{81} +57.1755i q^{83} -1619.82i q^{85} +(118.534 + 205.307i) q^{87} +(-458.297 - 264.598i) q^{89} +(0.164115 + 0.191020i) q^{91} +(298.957 + 172.603i) q^{93} +(2023.92 - 1168.51i) q^{95} +106.812i q^{97} +157.078 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q + 432 q^{9} - 40 q^{11} - 1200 q^{25} - 456 q^{35} + 1616 q^{43} - 360 q^{49} - 336 q^{57} - 4128 q^{59} + 1440 q^{67} - 648 q^{73} - 3888 q^{81} + 104 q^{91} - 720 q^{99}+O(q^{100}) \) 96 * q + 432 * q^9 - 40 * q^11 - 1200 * q^25 - 456 * q^35 + 1616 * q^43 - 360 * q^49 - 336 * q^57 - 4128 * q^59 + 1440 * q^67 - 648 * q^73 - 3888 * q^81 + 104 * q^91 - 720 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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