LMFDB - Embedded newform 756.2.be.d.107.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [756,2,Mod(107,756)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(756, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 2]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("756.107");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 756 = 2^{2} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	756.be (of order $6$, degree $2$, 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:	$6.03669039281$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$14$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			107.1
Character	$\chi$	$=$	756.107
Dual form			756.2.be.d.431.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.41404 + 0.0220675i) q^{2} +(1.99903 - 0.0624087i) q^{4} +(0.303357 + 0.175143i) q^{5} +(2.63538 + 0.234036i) q^{7} +(-2.82533 + 0.132362i) q^{8} +O(q^{10})$	\(q+(-1.41404 + 0.0220675i) q^{2} +(1.99903 - 0.0624087i) q^{4} +(0.303357 + 0.175143i) q^{5} +(2.63538 + 0.234036i) q^{7} +(-2.82533 + 0.132362i) q^{8} +(-0.432824 - 0.240965i) q^{10} +(-0.356330 - 0.617181i) q^{11} +0.127465 q^{13} +(-3.73170 - 0.272781i) q^{14} +(3.99221 - 0.249513i) q^{16} +(5.30564 - 3.06321i) q^{17} +(2.91768 + 1.68453i) q^{19} +(0.617349 + 0.331184i) q^{20} +(0.517485 + 0.864856i) q^{22} +(-2.38776 + 4.13571i) q^{23} +(-2.43865 - 4.22387i) q^{25} +(-0.180241 + 0.00281283i) q^{26} +(5.28280 + 0.303374i) q^{28} +3.39607i q^{29} +(0.00202473 - 0.00116898i) q^{31} +(-5.63964 + 0.440920i) q^{32} +(-7.43480 + 4.44859i) q^{34} +(0.758471 + 0.532565i) q^{35} +(2.17085 - 3.76003i) q^{37} +(-4.16290 - 2.31760i) q^{38} +(-0.880265 - 0.454684i) q^{40} -8.22678i q^{41} +7.55045i q^{43} +(-0.750830 - 1.21152i) q^{44} +(3.28512 - 5.90076i) q^{46} +(-1.33348 + 2.30966i) q^{47} +(6.89045 + 1.23355i) q^{49} +(3.54156 + 5.91891i) q^{50} +(0.254806 - 0.00795492i) q^{52} +(10.1596 - 5.86566i) q^{53} -0.249635i q^{55} +(-7.47679 - 0.312405i) q^{56} +(-0.0749429 - 4.80219i) q^{58} +(5.13898 + 8.90098i) q^{59} +(-2.83849 + 4.91641i) q^{61} +(-0.00283726 + 0.00169767i) q^{62} +(7.96496 - 0.747932i) q^{64} +(0.0386674 + 0.0223246i) q^{65} +(7.79435 - 4.50007i) q^{67} +(10.4149 - 6.45456i) q^{68} +(-1.08426 - 0.736332i) q^{70} +9.61361 q^{71} +(-2.15337 - 3.72974i) q^{73} +(-2.98670 + 5.36474i) q^{74} +(5.93766 + 3.18532i) q^{76} +(-0.794621 - 1.70990i) q^{77} +(-1.92240 - 1.10990i) q^{79} +(1.25476 + 0.623517i) q^{80} +(0.181544 + 11.6330i) q^{82} +5.12311 q^{83} +2.14600 q^{85} +(-0.166620 - 10.6767i) q^{86} +(1.08844 + 1.69657i) q^{88} +(7.79048 + 4.49784i) q^{89} +(0.335919 + 0.0298314i) q^{91} +(-4.51508 + 8.41642i) q^{92} +(1.83463 - 3.29538i) q^{94} +(0.590066 + 1.02203i) q^{95} -17.3426 q^{97} +(-9.77061 - 1.59223i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - 4 q^{4} + 2 q^{7}+O(q^{10}) $ 28 * q - 4 * q^4 + 2 * q^7	$ 28 q - 4 q^{4} + 2 q^{7} + 4 q^{10} + 8 q^{13} + 12 q^{16} - 42 q^{19} + 4 q^{22} + 6 q^{25} + 24 q^{28} + 30 q^{31} + 24 q^{34} + 12 q^{37} + 24 q^{46} - 14 q^{49} - 24 q^{52} - 44 q^{58} + 6 q^{61} + 8 q^{64} + 24 q^{67} - 32 q^{70} - 22 q^{73} + 48 q^{79} + 36 q^{82} - 24 q^{85} - 4 q^{88} + 16 q^{91} + 60 q^{94} - 4 q^{97}+O(q^{100}) $ 28 * q - 4 * q^4 + 2 * q^7 + 4 * q^10 + 8 * q^13 + 12 * q^16 - 42 * q^19 + 4 * q^22 + 6 * q^25 + 24 * q^28 + 30 * q^31 + 24 * q^34 + 12 * q^37 + 24 * q^46 - 14 * q^49 - 24 * q^52 - 44 * q^58 + 6 * q^61 + 8 * q^64 + 24 * q^67 - 32 * q^70 - 22 * q^73 + 48 * q^79 + 36 * q^82 - 24 * q^85 - 4 * q^88 + 16 * q^91 + 60 * q^94 - 4 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/756\mathbb{Z}\right)^\times$.

$n$	$29$	$325$	$379$
$\chi(n)$	$-1$	$e\left(\frac{1}{3}\right)$	$-1$

Coefficient data

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

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

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

$2$	−1.41404	+	0.0220675i	−0.999878	+	0.0156041i
$2$	−1.41404	+	0.0220675i	−0.999878	+	0.0156041i
$3$		0			0
$3$		0			0
$4$	1.99903	−	0.0624087i	0.999513	−	0.0312044i
$5$	0.303357	+	0.175143i	0.135665	+	0.0783264i	0.566297	−	0.824202i	$-0.308376\pi$
$5$	0.303357	+	0.175143i	0.135665	+	0.0783264i	−0.430631	+	0.902528i	$0.641709\pi$
$6$		0			0
$7$	2.63538	+	0.234036i	0.996080	+	0.0884574i
$7$	2.63538	+	0.234036i	0.996080	+	0.0884574i
$8$	−2.82533	+	0.132362i	−0.998904	+	0.0467970i
$9$		0			0
$10$	−0.432824	−	0.240965i	−0.136871	−	0.0761999i
$11$	−0.356330	−	0.617181i	−0.107437	−	0.186087i	0.807294	−	0.590149i	$-0.200931\pi$
$11$	−0.356330	−	0.617181i	−0.107437	−	0.186087i	−0.914731	+	0.404062i	$0.867598\pi$
$12$		0			0
$13$	0.127465			0.0353524			0.0176762	−	0.999844i	$-0.494373\pi$
$13$	0.127465			0.0353524			0.0176762	+	0.999844i	$0.494373\pi$
$14$	−3.73170	−	0.272781i	−0.997339	−	0.0729037i
$15$		0			0
$16$	3.99221	−	0.249513i	0.998053	−	0.0623783i
$17$	5.30564	−	3.06321i	1.28681	−	0.742938i	0.308723	−	0.951152i	$-0.400098\pi$
$17$	5.30564	−	3.06321i	1.28681	−	0.742938i	0.978083	+	0.208214i	$0.0667649\pi$
$18$		0			0
$19$	2.91768	+	1.68453i	0.669363	+	0.386457i	0.795835	−	0.605513i	$-0.207032\pi$
$19$	2.91768	+	1.68453i	0.669363	+	0.386457i	−0.126472	+	0.991970i	$0.540366\pi$
$20$	0.617349	+	0.331184i	0.138043	+	0.0740549i
$21$		0			0
$22$	0.517485	+	0.864856i	0.110328	+	0.184388i
$23$	−2.38776	+	4.13571i	−0.497881	+	0.862356i	−0.999997	−	0.00244454i	$-0.999222\pi$
$23$	−2.38776	+	4.13571i	−0.497881	+	0.862356i	0.502116	+	0.864801i	$0.332555\pi$
$24$		0			0
$25$	−2.43865	−	4.22387i	−0.487730	−	0.844773i
$26$	−0.180241	+	0.00281283i	−0.0353481	+	0.000551642i
$27$		0			0
$28$	5.28280	+	0.303374i	0.998355	+	0.0573323i
$29$			3.39607i			0.630635i	0.948986	+	0.315318i	$0.102111\pi$
$29$			3.39607i			0.630635i	−0.948986	+	0.315318i	$0.897889\pi$
$30$		0			0
$31$	0.00202473	−	0.00116898i	0.000363652	−	0.000209955i	−0.499818	−	0.866130i	$-0.666600\pi$
$31$	0.00202473	−	0.00116898i	0.000363652	−	0.000209955i	0.500182	+	0.865920i	$0.333267\pi$
$32$	−5.63964	+	0.440920i	−0.996958	+	0.0779444i
$33$		0			0
$34$	−7.43480	+	4.44859i	−1.27506	+	0.762927i
$35$	0.758471	+	0.532565i	0.128205	+	0.0900200i
$36$		0			0
$37$	2.17085	−	3.76003i	0.356886	−	0.618145i	−0.630553	−	0.776146i	$-0.717172\pi$
$37$	2.17085	−	3.76003i	0.356886	−	0.618145i	0.987439	+	0.158001i	$0.0505051\pi$
$38$	−4.16290	−	2.31760i	−0.675312	−	0.375965i
$39$		0			0
$40$	−0.880265	−	0.454684i	−0.139182	−	0.0718919i
$41$		−	8.22678i		−	1.28481i	−0.766367	−	0.642404i	$-0.777937\pi$
$41$		−	8.22678i		−	1.28481i	0.766367	−	0.642404i	$-0.222063\pi$
$42$		0			0
$43$			7.55045i			1.15143i	0.817649	+	0.575717i	$0.195277\pi$
$43$			7.55045i			1.15143i	−0.817649	+	0.575717i	$0.804723\pi$
$44$	−0.750830	−	1.21152i	−0.113192	−	0.182644i
$45$		0			0
$46$	3.28512	−	5.90076i	0.484365	−	0.870020i
$47$	−1.33348	+	2.30966i	−0.194508	+	0.336898i	−0.946739	−	0.322001i	$-0.895644\pi$
$47$	−1.33348	+	2.30966i	−0.194508	+	0.336898i	0.752231	+	0.658900i	$0.228978\pi$
$48$		0			0
$49$	6.89045	+	1.23355i	0.984351	+	0.176221i
$50$	3.54156	+	5.91891i	0.500852	+	0.837060i
$51$		0			0
$52$	0.254806	−	0.00795492i	0.0353352	−	0.00110315i
$53$	10.1596	−	5.86566i	1.39553	−	0.805710i	0.401610	−	0.915811i	$-0.368451\pi$
$53$	10.1596	−	5.86566i	1.39553	−	0.805710i	0.993920	+	0.110101i	$0.0351175\pi$
$54$		0			0
$55$		−	0.249635i		−	0.0336608i
$56$	−7.47679	−	0.312405i	−0.999128	−	0.0417469i
$57$		0			0
$58$	−0.0749429	−	4.80219i	−0.00984048	−	0.630558i
$59$	5.13898	+	8.90098i	0.669039	+	1.15881i	0.978173	+	0.207791i	$0.0666274\pi$
$59$	5.13898	+	8.90098i	0.669039	+	1.15881i	−0.309134	+	0.951018i	$0.600039\pi$
$60$		0			0
$61$	−2.83849	+	4.91641i	−0.363432	+	0.629482i	−0.988523	−	0.151069i	$-0.951728\pi$
$61$	−2.83849	+	4.91641i	−0.363432	+	0.629482i	0.625091	+	0.780552i	$0.285062\pi$
$62$	−0.00283726	+	0.00169767i	−0.000360332	+	0.000215604i
$63$		0			0
$64$	7.96496	−	0.747932i	0.995620	−	0.0934915i
$65$	0.0386674	+	0.0223246i	0.00479610	+	0.00276903i
$66$		0			0
$67$	7.79435	−	4.50007i	0.952231	−	0.549771i	0.0584577	−	0.998290i	$-0.481382\pi$
$67$	7.79435	−	4.50007i	0.952231	−	0.549771i	0.893773	+	0.448519i	$0.148048\pi$
$68$	10.4149	−	6.45456i	1.26300	−	0.782730i
$69$		0			0
$70$	−1.08426	−	0.736332i	−0.129594	−	0.0880085i
$71$	9.61361			1.14093			0.570463	−	0.821323i	$-0.306764\pi$
$71$	9.61361			1.14093			0.570463	+	0.821323i	$0.306764\pi$
$72$		0			0
$73$	−2.15337	−	3.72974i	−0.252033	−	0.436534i	0.712053	−	0.702126i	$-0.247766\pi$
$73$	−2.15337	−	3.72974i	−0.252033	−	0.436534i	−0.964085	+	0.265593i	$0.914432\pi$
$74$	−2.98670	+	5.36474i	−0.347197	+	0.623639i
$75$		0			0
$76$	5.93766	+	3.18532i	0.681096	+	0.365382i
$77$	−0.794621	−	1.70990i	−0.0905555	−	0.194861i
$78$		0			0
$79$	−1.92240	−	1.10990i	−0.216287	−	0.124874i	0.387943	−	0.921684i	$-0.373186\pi$
$79$	−1.92240	−	1.10990i	−0.216287	−	0.124874i	−0.604230	+	0.796810i	$0.706519\pi$
$80$	1.25476	+	0.623517i	0.140287	+	0.0697113i
$81$		0			0
$82$	0.181544	+	11.6330i	0.0200482	+	1.28465i
$83$	5.12311			0.562334			0.281167	−	0.959659i	$-0.409278\pi$
$83$	5.12311			0.562334			0.281167	+	0.959659i	$0.409278\pi$
$84$		0			0
$85$	2.14600			0.232767
$86$	−0.166620	−	10.6767i	−0.0179671	−	1.15129i
$87$		0			0
$88$	1.08844	+	1.69657i	0.116028	+	0.180856i
$89$	7.79048	+	4.49784i	0.825789	+	0.476770i	0.852409	−	0.522876i	$-0.175141\pi$
$89$	7.79048	+	4.49784i	0.825789	+	0.476770i	−0.0266194	+	0.999646i	$0.508474\pi$
$90$		0			0
$91$	0.335919	+	0.0298314i	0.0352138	+	0.00312718i
$92$	−4.51508	+	8.41642i	−0.470730	+	0.877472i
$93$		0			0
$94$	1.83463	−	3.29538i	0.189228	−	0.339892i
$95$	0.590066	+	1.02203i	0.0605395	+	0.104858i
$96$		0			0
$97$	−17.3426			−1.76087			−0.880436	−	0.474165i	$-0.842750\pi$
$97$	−17.3426			−1.76087			−0.880436	+	0.474165i	$0.842750\pi$
$98$	−9.77061	−	1.59223i	−0.986980	−	0.160840i
$99$		0			0
$100$	−5.13853	−	8.29142i	−0.513853	−	0.829142i
$101$	9.20243	−	5.31302i	0.915676	−	0.528666i	0.0334227	−	0.999441i	$-0.489359\pi$
$101$	9.20243	−	5.31302i	0.915676	−	0.528666i	0.882253	+	0.470776i	$0.156026\pi$
$102$		0			0
$103$	−9.00546	−	5.19931i	−0.887335	−	0.512303i	−0.0142649	−	0.999898i	$-0.504541\pi$
$103$	−9.00546	−	5.19931i	−0.887335	−	0.512303i	−0.873070	+	0.487595i	$0.837874\pi$
$104$	−0.360130	+	0.0168715i	−0.0353137	+	0.00165439i
$105$		0			0
$106$	−14.2367	+	8.51848i	−1.38279	+	0.827388i
$107$	4.46519	−	7.73394i	0.431666	−	0.747668i	−0.565351	−	0.824851i	$-0.691259\pi$
$107$	4.46519	−	7.73394i	0.431666	−	0.747668i	0.997017	+	0.0771828i	$0.0245925\pi$
$108$		0			0
$109$	8.15380	+	14.1228i	0.780993	+	1.35272i	0.931364	+	0.364089i	$0.118620\pi$
$109$	8.15380	+	14.1228i	0.780993	+	1.35272i	−0.150371	+	0.988630i	$0.548047\pi$
$110$	0.00550882	+	0.352994i	0.000525245	+	0.0336567i
$111$		0			0
$112$	10.5794	+	0.276760i	0.999658	+	0.0261514i
$113$			8.44061i			0.794025i	0.917813	+	0.397013i	$0.129953\pi$
$113$			8.44061i			0.794025i	−0.917813	+	0.397013i	$0.870047\pi$
$114$		0			0
$115$	−1.44868	+	0.836398i	−0.135090	+	0.0779945i
$116$	0.211945	+	6.78884i	0.0196786	+	0.630328i
$117$		0			0
$118$	−7.46316	−	12.4730i	−0.687040	−	1.14823i
$119$	14.6993	−	6.83102i	1.34748	−	0.626198i
$120$		0			0
$121$	5.24606	−	9.08644i	0.476914	−	0.826040i
$122$	3.90525	−	7.01465i	0.353565	−	0.635077i
$123$		0			0
$124$	0.00397454	−	0.00246318i	0.000356924	−	0.000221200i
$125$		−	3.45988i		−	0.309461i
$126$		0			0
$127$		−	9.21826i		−	0.817988i	−0.912537	−	0.408994i	$-0.865880\pi$
$127$		−	9.21826i		−	0.817988i	0.912537	−	0.408994i	$-0.134120\pi$
$128$	−11.2463	+	1.23337i	−0.994040	+	0.109016i
$129$		0			0
$130$	−0.0551699	−	0.0307146i	−0.00483872	−	0.00269385i
$131$	−9.60458	+	16.6356i	−0.839156	+	1.45346i	0.0514445	+	0.998676i	$0.483617\pi$
$131$	−9.60458	+	16.6356i	−0.839156	+	1.45346i	−0.890601	+	0.454786i	$0.849716\pi$
$132$		0			0
$133$	7.29497	+	5.12221i	0.632554	+	0.444152i
$134$	−10.9222	+	6.53528i	−0.943536	+	0.564563i
$135$		0			0
$136$	−14.5847	+	9.35685i	−1.25063	+	0.802343i
$137$	9.16525	−	5.29156i	0.783040	−	0.452088i	−0.0544666	−	0.998516i	$-0.517346\pi$
$137$	9.16525	−	5.29156i	0.783040	−	0.452088i	0.837507	+	0.546427i	$0.184013\pi$
$138$		0			0
$139$			11.6495i			0.988101i	0.869433	+	0.494050i	$0.164484\pi$
$139$			11.6495i			0.988101i	−0.869433	+	0.494050i	$0.835516\pi$
$140$	1.54944	+	1.01728i	0.130952	+	0.0859756i
$141$		0			0
$142$	−13.5940	+	0.212148i	−1.14079	+	0.0178031i
$143$	−0.0454195	−	0.0786690i	−0.00379817	−	0.00657863i
$144$		0			0
$145$	−0.594799	+	1.03022i	−0.0493954	+	0.0855553i
$146$	3.12726	+	5.22649i	0.258814	+	0.432548i
$147$		0			0
$148$	4.10493	−	7.65188i	0.337424	−	0.628980i
$149$	−13.7343	−	7.92950i	−1.12516	−	0.649610i	−0.182445	−	0.983216i	$-0.558401\pi$
$149$	−13.7343	−	7.92950i	−1.12516	−	0.649610i	−0.942712	+	0.333606i	$0.891734\pi$
$150$		0			0
$151$	−3.21821	+	1.85804i	−0.261895	+	0.151205i	−0.625199	−	0.780466i	$-0.714982\pi$
$151$	−3.21821	+	1.85804i	−0.261895	+	0.151205i	0.363304	+	0.931671i	$0.381649\pi$
$152$	−8.46638	−	4.37315i	−0.686714	−	0.354709i
$153$		0			0
$154$	1.16136	+	2.40034i	0.0935851	+	0.193425i
$155$	0.000818955	0		6.57800e−5	0
$156$		0			0
$157$	1.00586	+	1.74221i	0.0802766	+	0.139043i	0.903369	−	0.428865i	$-0.141086\pi$
$157$	1.00586	+	1.74221i	0.0802766	+	0.139043i	−0.823092	+	0.567908i	$0.807753\pi$
$158$	2.74285	+	1.52702i	0.218210	+	0.121483i
$159$		0			0
$160$	−1.78805	−	0.853989i	−0.141358	−	0.0675138i
$161$	−7.26055	+	10.3404i	−0.572212	+	0.814934i
$162$		0			0
$163$	−14.0550	−	8.11468i	−1.10088	−	0.635590i	−0.164424	−	0.986390i	$-0.552577\pi$
$163$	−14.0550	−	8.11468i	−1.10088	−	0.635590i	−0.936451	+	0.350799i	$0.885910\pi$
$164$	−0.513423	−	16.4455i	−0.0400916	−	1.28418i
$165$		0			0
$166$	−7.24429	+	0.113054i	−0.562266	+	0.00877471i
$167$	−24.8179			−1.92047			−0.960235	−	0.279193i	$-0.909933\pi$
$167$	−24.8179			−1.92047			−0.960235	+	0.279193i	$0.909933\pi$
$168$		0			0
$169$	−12.9838			−0.998750
$170$	−3.03454	+	0.0473569i	−0.232738	+	0.00363211i
$171$		0			0
$172$	0.471214	+	15.0936i	0.0359297	+	1.15087i
$173$	−4.32404	−	2.49649i	−0.328751	−	0.189804i	0.326536	−	0.945185i	$-0.394119\pi$
$173$	−4.32404	−	2.49649i	−0.328751	−	0.189804i	−0.655286	+	0.755381i	$0.727452\pi$
$174$		0			0
$175$	−5.43823	−	11.7022i	−0.411092	−	0.884605i
$176$	−1.57654	−	2.37501i	−0.118836	−	0.179023i
$177$		0			0
$178$	−11.1153	−	6.18821i	−0.833128	−	0.463826i
$179$	−9.75634	−	16.8985i	−0.729223	−	1.26305i	−0.957212	−	0.289388i	$-0.906548\pi$
$179$	−9.75634	−	16.8985i	−0.729223	−	1.26305i	0.227989	−	0.973664i	$-0.426785\pi$
$180$		0			0
$181$	−7.80817			−0.580377			−0.290188	−	0.956970i	$-0.593718\pi$
$181$	−7.80817			−0.580377			−0.290188	+	0.956970i	$0.593718\pi$
$182$	−0.475661	−	0.0347700i	−0.0352583	−	0.00257732i
$183$		0			0
$184$	6.19878	−	12.0008i	0.456980	−	0.884711i
$185$	1.31709	−	0.760420i	0.0968341	−	0.0559072i
$186$		0			0
$187$	−3.78111	−	2.18303i	−0.276502	−	0.159639i
$188$	−2.52152	+	4.70029i	−0.183901	+	0.342804i
$189$		0			0
$190$	−0.856932	−	1.43216i	−0.0621684	−	0.103900i
$191$	−6.21530	+	10.7652i	−0.449723	+	0.778944i	−0.998368	−	0.0571120i	$-0.981811\pi$
$191$	−6.21530	+	10.7652i	−0.449723	+	0.778944i	0.548644	+	0.836056i	$0.315144\pi$
$192$		0			0
$193$	0.669942	+	1.16037i	0.0482235	+	0.0835256i	0.889130	−	0.457656i	$-0.151311\pi$
$193$	0.669942	+	1.16037i	0.0482235	+	0.0835256i	−0.840906	+	0.541181i	$0.817977\pi$
$194$	24.5231	−	0.382707i	1.76066	−	0.0274768i
$195$		0			0
$196$	13.8512	+	2.03587i	0.989370	+	0.145419i
$197$			12.0610i			0.859312i	0.902993	+	0.429656i	$0.141365\pi$
$197$			12.0610i			0.859312i	−0.902993	+	0.429656i	$0.858635\pi$
$198$		0			0
$199$	−10.2777	+	5.93383i	−0.728566	+	0.420638i	−0.817897	−	0.575364i	$-0.804860\pi$
$199$	−10.2777	+	5.93383i	−0.728566	+	0.420638i	0.0893311	+	0.996002i	$0.471527\pi$
$200$	7.44907	+	11.6110i	0.526728	+	0.821023i
$201$		0			0
$202$	−12.8954	+	7.71591i	−0.907315	+	0.542889i
$203$	−0.794805	+	8.94995i	−0.0557844	+	0.628163i
$204$		0			0
$205$	1.44086	−	2.49565i	0.100634	−	0.174304i
$206$	12.8488	+	7.15331i	0.895221	+	0.498394i
$207$		0			0
$208$	0.508867	−	0.0318042i	0.0352836	−	0.00220522i
$209$		−	2.40099i		−	0.166080i
$210$		0			0
$211$		−	2.47485i		−	0.170376i	−0.996365	−	0.0851878i	$-0.972851\pi$
$211$		−	2.47485i		−	0.170376i	0.996365	−	0.0851878i	$-0.0271490\pi$
$212$	19.9433	−	12.3596i	1.36971	−	0.848864i
$213$		0			0
$214$	−6.14329	+	11.0346i	−0.419947	+	0.754313i
$215$	−1.32241	+	2.29048i	−0.0901876	+	0.156210i
$216$		0			0
$217$	0.00560952	−	0.00260684i	0.000380799	−	0.000176964i
$218$	−11.8415	−	19.7903i	−0.802006	−	1.34037i
$219$		0			0
$220$	−0.0155794	−	0.499027i	−0.00105036	−	0.0336444i
$221$	0.676283	−	0.390452i	0.0454917	−	0.0262647i
$222$		0			0
$223$			7.76582i			0.520038i	0.965604	+	0.260019i	$0.0837288\pi$
$223$			7.76582i			0.520038i	−0.965604	+	0.260019i	$0.916271\pi$
$224$	−14.9658	−	0.157889i	−0.999944	−	0.0105494i
$225$		0			0
$226$	−0.186263	−	11.9354i	−0.0123900	−	0.793929i
$227$	−8.03290	−	13.9134i	−0.533163	−	0.923465i	−0.999250	−	0.0387259i	$-0.987670\pi$
$227$	−8.03290	−	13.9134i	−0.533163	−	0.923465i	0.466087	−	0.884739i	$-0.345663\pi$
$228$		0			0
$229$	−5.54735	+	9.60830i	−0.366579	+	0.634934i	−0.989028	−	0.147726i	$-0.952805\pi$
$229$	−5.54735	+	9.60830i	−0.366579	+	0.634934i	0.622449	+	0.782660i	$0.286138\pi$
$230$	2.03004	−	1.21467i	0.133857	−	0.0800930i
$231$		0			0
$232$	−0.449511	−	9.59503i	−0.0295119	−	0.629944i
$233$	−3.11180	−	1.79660i	−0.203861	−	0.117699i	0.394594	−	0.918855i	$-0.370885\pi$
$233$	−3.11180	−	1.79660i	−0.203861	−	0.117699i	−0.598455	+	0.801156i	$0.704218\pi$
$234$		0			0
$235$	−0.809041	+	0.467100i	−0.0527760	+	0.0304703i
$236$	10.8285	+	17.4726i	0.704873	+	1.13737i
$237$		0			0
$238$	−20.6346	+	9.98372i	−1.33755	+	0.647148i
$239$	6.15253			0.397974			0.198987	−	0.980002i	$-0.436235\pi$
$239$	6.15253			0.397974			0.198987	+	0.980002i	$0.436235\pi$
$240$		0			0
$241$	−6.27143	−	10.8624i	−0.403978	−	0.699711i	0.590224	−	0.807240i	$-0.299040\pi$
$241$	−6.27143	−	10.8624i	−0.403978	−	0.699711i	−0.994202	+	0.107529i	$0.965706\pi$
$242$	−7.21763	+	12.9644i	−0.463967	+	0.833381i
$243$		0			0
$244$	−5.36739	+	10.0052i	−0.343612	+	0.640516i
$245$	1.87422	+	1.58102i	0.119739	+	0.101008i
$246$		0			0
$247$	0.371903	+	0.214718i	0.0236636	+	0.0136622i
$248$	−0.00556580	+	0.00357075i	−0.000353429	+	0.000226743i
$249$		0			0
$250$	0.0763510	+	4.89242i	0.00482886	+	0.309424i
$251$	0.485661			0.0306547			0.0153273	−	0.999883i	$-0.495121\pi$
$251$	0.485661			0.0306547			0.0153273	+	0.999883i	$0.495121\pi$
$252$		0			0
$253$	3.40331			0.213964
$254$	0.203424	+	13.0350i	0.0127640	+	0.817889i
$255$		0			0
$256$	15.8755	−	1.99222i	0.992218	−	0.124514i
$257$	−25.2361	−	14.5701i	−1.57418	−	0.908855i	−0.995648	−	0.0931975i	$-0.970291\pi$
$257$	−25.2361	−	14.5701i	−1.57418	−	0.908855i	−0.578535	−	0.815657i	$-0.696375\pi$
$258$		0			0
$259$	6.60101	−	9.40105i	0.410167	−	0.584153i
$260$	0.0786903	+	0.0422143i	0.00488017	+	0.00261802i
$261$		0			0
$262$	13.2142	−	23.7354i	0.816374	−	1.46638i
$263$	−11.6832	−	20.2359i	−0.720416	−	1.24780i	−0.960833	−	0.277127i	$-0.910618\pi$
$263$	−11.6832	−	20.2359i	−0.720416	−	1.24780i	0.240418	−	0.970670i	$-0.422716\pi$
$264$		0			0
$265$	4.10932			0.252433
$266$	−10.4284	−	7.08204i	−0.639407	−	0.434227i
$267$		0			0
$268$	15.3003	−	9.48219i	0.934612	−	0.579217i
$269$	−24.1233	+	13.9276i	−1.47082	+	0.849180i	−0.999463	−	0.0327619i	$-0.989570\pi$
$269$	−24.1233	+	13.9276i	−1.47082	+	0.849180i	−0.471359	+	0.881941i	$0.656236\pi$
$270$		0			0
$271$	24.8590	+	14.3523i	1.51008	+	0.871843i	0.999931	+	0.0117552i	$0.00374189\pi$
$271$	24.8590	+	14.3523i	1.51008	+	0.871843i	0.510146	+	0.860088i	$0.329591\pi$
$272$	20.4169	−	13.5528i	1.23796	−	0.821760i
$273$		0			0
$274$	−12.8433	+	7.68474i	−0.775890	+	0.464252i
$275$	−1.73793	+	3.01018i	−0.104801	+	0.181521i
$276$		0			0
$277$	13.4773	+	23.3434i	0.809773	+	1.40257i	0.913021	+	0.407912i	$0.133743\pi$
$277$	13.4773	+	23.3434i	0.809773	+	1.40257i	−0.103248	+	0.994656i	$0.532924\pi$
$278$	−0.257076	−	16.4729i	−0.0154184	−	0.987980i
$279$		0			0
$280$	−2.21342	−	1.40428i	−0.132277	−	0.0839217i
$281$			25.3505i			1.51228i	0.654409	+	0.756141i	$0.272918\pi$
$281$			25.3505i			1.51228i	−0.654409	+	0.756141i	$0.727082\pi$
$282$		0			0
$283$	2.20500	−	1.27306i	0.131074	−	0.0756754i	−0.433029	−	0.901380i	$-0.642555\pi$
$283$	2.20500	−	1.27306i	0.131074	−	0.0756754i	0.564103	+	0.825704i	$0.309222\pi$
$284$	19.2179	−	0.599973i	1.14037	−	0.0356018i
$285$		0			0
$286$	0.0659611	+	0.110239i	0.00390036	+	0.00651856i
$287$	1.92537	−	21.6807i	0.113651	−	1.27977i
$288$		0			0
$289$	10.2665	−	17.7822i	0.603914	−	1.04601i
$290$	0.818336	−	1.46990i	0.0480544	−	0.0863157i
$291$		0			0
$292$	−4.53741	−	7.32147i	−0.265532	−	0.428456i
$293$			4.66529i			0.272549i	0.990671	+	0.136274i	$0.0435129\pi$
$293$			4.66529i			0.272549i	−0.990671	+	0.136274i	$0.956487\pi$
$294$		0			0
$295$			3.60023i			0.209614i
$296$	−5.63569	+	10.9107i	−0.327568	+	0.634169i
$297$		0			0
$298$	19.5958	+	10.9096i	1.13516	+	0.631974i
$299$	−0.304355	+	0.527159i	−0.0176013	+	0.0304864i
$300$		0			0
$301$	−1.76708	+	19.8983i	−0.101853	+	1.14692i
$302$	4.50969	−	2.69836i	0.259503	−	0.155273i
$303$		0			0
$304$	12.0683	+	5.99698i	0.692166	+	0.343950i
$305$	−1.72215	+	0.994285i	−0.0986101	+	0.0569326i
$306$		0			0
$307$		−	16.7333i		−	0.955020i	−0.878626	−	0.477510i	$-0.841539\pi$
$307$		−	16.7333i		−	0.955020i	0.878626	−	0.477510i	$-0.158461\pi$
$308$	−1.69518	−	3.36855i	−0.0965919	−	0.191941i
$309$		0			0
$310$	−0.00115804		1.80723e-5i	−6.57720e−5		1.02644e-6i
$311$	15.6845	+	27.1664i	0.889389	+	1.54047i	0.840599	+	0.541657i	$0.182203\pi$
$311$	15.6845	+	27.1664i	0.889389	+	1.54047i	0.0487894	+	0.998809i	$0.484464\pi$
$312$		0			0
$313$	11.3777	−	19.7068i	0.643107	−	1.11389i	−0.341629	−	0.939835i	$-0.610979\pi$
$313$	11.3777	−	19.7068i	0.643107	−	1.11389i	0.984735	−	0.174058i	$-0.0556882\pi$
$314$	−1.46078	−	2.44135i	−0.0824364	−	0.137774i
$315$		0			0
$316$	−3.91220	−	2.09875i	−0.220079	−	0.118064i
$317$	5.10594	+	2.94792i	0.286778	+	0.165572i	0.636488	−	0.771287i	$-0.280386\pi$
$317$	5.10594	+	2.94792i	0.286778	+	0.165572i	−0.349710	+	0.936858i	$0.613720\pi$
$318$		0			0
$319$	2.09599	−	1.21012i	0.117353	−	0.0677538i
$320$	2.54722	+	1.16812i	0.142394	+	0.0652998i
$321$		0			0
$322$	10.0385	−	14.7819i	0.559426	−	0.823764i
$323$	20.6402			1.14845
$324$		0			0
$325$	−0.310842	−	0.538395i	−0.0172424	−	0.0298648i
$326$	20.0535	+	11.1643i	1.11066	+	0.618335i
$327$		0			0
$328$	1.08891	+	23.2434i	0.0601252	+	1.28340i
$329$	−4.05477	+	5.77474i	−0.223547	+	0.318372i
$330$		0			0
$331$	−7.41160	−	4.27909i	−0.407378	−	0.235200i	0.282284	−	0.959331i	$-0.408908\pi$
$331$	−7.41160	−	4.27909i	−0.407378	−	0.235200i	−0.689663	+	0.724131i	$0.742241\pi$
$332$	10.2412	−	0.319727i	0.562061	−	0.0175473i
$333$		0			0
$334$	35.0936	−	0.547670i	1.92024	−	0.0299672i
$335$	3.15262			0.172246
$336$		0			0
$337$	−26.1588			−1.42496			−0.712479	−	0.701693i	$-0.752428\pi$
$337$	−26.1588			−1.42496			−0.712479	+	0.701693i	$0.752428\pi$
$338$	18.3596	−	0.286519i	0.998629	−	0.0155846i
$339$		0			0
$340$	4.28992	−	0.133929i	0.232653	−	0.00726334i
$341$	−0.00144294		0.000833084i	−7.81398e−5		4.51140e-5i
$342$		0			0
$343$	17.8703	+	4.86349i	0.964904	+	0.262604i
$344$	−0.999393	−	21.3325i	−0.0538837	−	1.15017i
$345$		0			0
$346$	6.16946	+	3.43471i	0.331672	+	0.184651i
$347$	−18.3826	−	31.8396i	−0.986830	−	1.70924i	−0.633505	−	0.773738i	$-0.718385\pi$
$347$	−18.3826	−	31.8396i	−0.986830	−	1.70924i	−0.353324	−	0.935501i	$-0.614949\pi$
$348$		0			0
$349$	9.93465			0.531790			0.265895	−	0.964002i	$-0.414333\pi$
$349$	9.93465			0.531790			0.265895	+	0.964002i	$0.414333\pi$
$350$	7.94812	+	16.4274i	0.424845	+	0.878082i
$351$		0			0
$352$	2.28170	+	3.32357i	0.121615	+	0.177147i
$353$	−10.7415	+	6.20163i	−0.571715	+	0.330080i	−0.757834	−	0.652447i	$-0.773742\pi$
$353$	−10.7415	+	6.20163i	−0.571715	+	0.330080i	0.186119	+	0.982527i	$0.440409\pi$
$354$		0			0
$355$	2.91635	+	1.68376i	0.154784	+	0.0893646i
$356$	15.8541	+	8.50510i	0.840265	+	0.450769i
$357$		0			0
$358$	14.1688	+	23.6799i	0.748843	+	1.25152i
$359$	8.25328	−	14.2951i	0.435592	−	0.754467i	−0.561752	−	0.827306i	$-0.689873\pi$
$359$	8.25328	−	14.2951i	0.435592	−	0.754467i	0.997344	+	0.0728388i	$0.0232059\pi$
$360$		0			0
$361$	−3.82474	−	6.62465i	−0.201302	−	0.348666i
$362$	11.0411	−	0.172307i	0.580306	−	0.00905624i
$363$		0			0
$364$	0.673372	+	0.0386696i	0.0352943	+	0.00202684i
$365$		−	1.50859i		−	0.0789633i
$366$		0			0
$367$	10.7204	−	6.18944i	0.559602	−	0.323086i	−0.193384	−	0.981123i	$-0.561946\pi$
$367$	10.7204	−	6.18944i	0.559602	−	0.323086i	0.752986	+	0.658037i	$0.228613\pi$
$368$	−8.50051	+	17.1064i	−0.443120	+	0.891734i
$369$		0			0
$370$	−1.84563	+	1.10433i	−0.0959500	+	0.0574114i
$371$	28.1472	−	13.0805i	1.46133	−	0.679106i
$372$		0			0
$373$	10.5698	−	18.3074i	0.547282	−	0.947920i	−0.451178	−	0.892434i	$-0.648996\pi$
$373$	10.5698	−	18.3074i	0.547282	−	0.947920i	0.998459	−	0.0554855i	$-0.0176707\pi$
$374$	5.39483	+	3.00345i	0.278960	+	0.155305i
$375$		0			0
$376$	3.46181	−	6.70204i	0.178529	−	0.345632i
$377$			0.432880i			0.0222945i
$378$		0			0
$379$			18.9297i			0.972352i	0.873861	+	0.486176i	$0.161609\pi$
$379$			18.9297i			0.972352i	−0.873861	+	0.486176i	$0.838391\pi$
$380$	1.24334	+	2.00623i	0.0637821	+	0.102917i
$381$		0			0
$382$	8.55113	−	15.3596i	0.437514	−	0.785867i
$383$	−3.25973	+	5.64601i	−0.166564	+	0.288498i	−0.937210	−	0.348766i	$-0.886601\pi$
$383$	−3.25973	+	5.64601i	−0.166564	+	0.288498i	0.770645	+	0.637264i	$0.219934\pi$
$384$		0			0
$385$	0.0584236	−	0.657883i	0.00297754	−	0.0335288i
$386$	−0.972933	−	1.62603i	−0.0495210	−	0.0827629i
$387$		0			0
$388$	−34.6683	+	1.08233i	−1.76001	+	0.0549469i
$389$	−14.7537	+	8.51806i	−0.748043	+	0.431883i	−0.824986	−	0.565153i	$-0.808817\pi$
$389$	−14.7537	+	8.51806i	−0.748043	+	0.431883i	0.0769436	+	0.997035i	$0.475484\pi$
$390$		0			0
$391$			29.2568i			1.47958i
$392$	−19.6311	−	2.57315i	−0.991519	−	0.129964i
$393$		0			0
$394$	−0.266157	−	17.0548i	−0.0134088	−	0.859207i
$395$	−0.388783	−	0.673392i	−0.0195618	−	0.0338820i
$396$		0			0
$397$	−7.32945	+	12.6950i	−0.367854	+	0.637142i	−0.989230	−	0.146370i	$-0.953241\pi$
$397$	−7.32945	+	12.6950i	−0.367854	+	0.637142i	0.621375	+	0.783513i	$0.286574\pi$
$398$	14.4021	−	8.61748i	0.721914	−	0.431955i
$399$		0			0
$400$	−10.7895	−	16.2541i	−0.539476	−	0.812704i
$401$	5.41239	+	3.12484i	0.270282	+	0.156047i	0.629016	−	0.777393i	$-0.283458\pi$
$401$	5.41239	+	3.12484i	0.270282	+	0.156047i	−0.358734	+	0.933440i	$0.616791\pi$
$402$		0			0
$403$	0.000258082	0	0.000149004i	1.28560e−5	0	7.42241e-6i
$404$	18.0643	−	11.1952i	0.898733	−	0.556981i
$405$		0			0
$406$	0.926384	−	12.6731i	0.0459757	−	0.628957i
$407$	−3.09416			−0.153372
$408$		0			0
$409$	−14.5140	−	25.1389i	−0.717670	−	1.24304i	−0.961921	−	0.273329i	$-0.911875\pi$
$409$	−14.5140	−	25.1389i	−0.717670	−	1.24304i	0.244251	−	0.969712i	$-0.421458\pi$
$410$	−1.98237	+	3.56075i	−0.0979022	+	0.175853i
$411$		0			0
$412$	−18.3266	−	9.83153i	−0.902889	−	0.484365i
$413$	11.4600	+	24.6602i	0.563911	+	1.21345i
$414$		0			0
$415$	1.55413	+	0.897278i	0.0762893	+	0.0440456i
$416$	−0.718857	+	0.0562019i	−0.0352449	+	0.00275552i
$417$		0			0
$418$	0.0529838	+	3.39509i	0.00259152	+	0.166060i
$419$	−5.94826			−0.290591			−0.145296	−	0.989388i	$-0.546413\pi$
$419$	−5.94826			−0.290591			−0.145296	+	0.989388i	$0.546413\pi$
$420$		0			0
$421$	26.2986			1.28172			0.640858	−	0.767660i	$-0.278579\pi$
$421$	26.2986			1.28172			0.640858	+	0.767660i	$0.278579\pi$
$422$	0.0546137	+	3.49954i	0.00265855	+	0.170355i
$423$		0			0
$424$	−27.9279	+	17.9171i	−1.35630	+	0.870134i
$425$	−25.8772	−	14.9402i	−1.25523	−	0.724706i
$426$		0			0
$427$	−8.63112	+	12.2923i	−0.417689	+	0.594866i
$428$	8.44337	−	15.7390i	0.408126	−	0.760774i
$429$		0			0
$430$	1.81940	−	3.26802i	0.0877391	−	0.157598i
$431$	−3.94092	−	6.82587i	−0.189827	−	0.328790i	0.755365	−	0.655304i	$-0.227459\pi$
$431$	−3.94092	−	6.82587i	−0.189827	−	0.328790i	−0.945193	+	0.326514i	$0.894126\pi$
$432$		0			0
$433$	−28.8906			−1.38839			−0.694196	−	0.719786i	$-0.744240\pi$
$433$	−28.8906			−1.38839			−0.694196	+	0.719786i	$0.744240\pi$
$434$	−0.00787456	+	0.00380997i	−0.000377991	+	0.000182884i
$435$		0			0
$436$	17.1811	+	27.7230i	0.822823	+	1.32769i
$437$	−13.9334	+	8.04447i	−0.666527	+	0.384819i
$438$		0			0
$439$	22.8209	+	13.1757i	1.08918	+	0.628840i	0.933359	−	0.358945i	$-0.116864\pi$
$439$	22.8209	+	13.1757i	1.08918	+	0.628840i	0.155824	+	0.987785i	$0.450197\pi$
$440$	0.0330422	+	0.705300i	0.00157522	+	0.0336239i
$441$		0			0
$442$	−0.947676	+	0.567040i	−0.0450764	+	0.0269713i
$443$	−11.8798	+	20.5764i	−0.564425	+	0.977613i	0.432678	+	0.901549i	$0.357569\pi$
$443$	−11.8798	+	20.5764i	−0.564425	+	0.977613i	−0.997103	+	0.0760641i	$0.975765\pi$
$444$		0			0
$445$	1.57553	+	2.72890i	0.0746873	+	0.129362i
$446$	−0.171372	−	10.9812i	−0.00811471	−	0.519974i
$447$		0			0
$448$	21.1657	−	0.106995i	0.999987	−	0.00505506i
$449$		−	36.0964i		−	1.70350i	−0.523951	−	0.851748i	$-0.675543\pi$
$449$		−	36.0964i		−	1.70350i	0.523951	−	0.851748i	$-0.324457\pi$
$450$		0			0
$451$	−5.07741	+	2.93145i	−0.239086	+	0.138036i
$452$	0.526767	+	16.8730i	0.0247771	+	0.793639i
$453$		0			0
$454$	11.6659	+	19.4969i	0.547507	+	0.915033i
$455$	0.0966784	+	0.0678834i	0.00453235	+	0.00318242i
$456$		0			0
$457$	9.98422	−	17.2932i	0.467042	−	0.808941i	−0.532249	−	0.846588i	$-0.678653\pi$
$457$	9.98422	−	17.2932i	0.467042	−	0.808941i	0.999291	+	0.0376473i	$0.0119863\pi$
$458$	7.63216	−	13.7089i	0.356627	−	0.640577i
$459$		0			0
$460$	−2.84376	+	1.76239i	−0.132591	+	0.0821720i
$461$			3.90222i			0.181744i	0.995863	+	0.0908722i	$0.0289655\pi$
$461$			3.90222i			0.181744i	−0.995863	+	0.0908722i	$0.971035\pi$
$462$		0			0
$463$		−	11.0279i		−	0.512510i	−0.966609	−	0.256255i	$-0.917511\pi$
$463$		−	11.0279i		−	0.512510i	0.966609	−	0.256255i	$-0.0824887\pi$
$464$	0.847366	+	13.5578i	0.0393380	+	0.629407i
$465$		0			0
$466$	4.43985	+	2.47179i	0.205672	+	0.114504i
$467$	−19.2572	+	33.3545i	−0.891119	+	1.54346i	−0.0525832	+	0.998617i	$0.516745\pi$
$467$	−19.2572	+	33.3545i	−0.891119	+	1.54346i	−0.838536	+	0.544847i	$0.816588\pi$
$468$		0			0
$469$	21.5942	−	10.0352i	0.997129	−	0.463384i
$470$	1.13371	−	0.678353i	0.0522942	−	0.0312901i
$471$		0			0
$472$	−15.6975	−	24.4680i	−0.722535	−	1.12623i
$473$	4.66000	−	2.69045i	0.214267	−	0.123707i
$474$		0			0
$475$		−	16.4319i		−	0.753946i
$476$	28.9579	−	14.5727i	1.32728	−	0.667941i
$477$		0			0
$478$	−8.69993	+	0.135771i	−0.397926	+	0.00621002i
$479$	−7.41054	−	12.8354i	−0.338596	−	0.586466i	0.645573	−	0.763699i	$-0.276619\pi$
$479$	−7.41054	−	12.8354i	−0.338596	−	0.586466i	−0.984169	+	0.177233i	$0.943285\pi$
$480$		0			0
$481$	0.276708	−	0.479272i	0.0126168	−	0.0218529i
$482$	9.10777	+	15.2215i	0.414847	+	0.693322i
$483$		0			0
$484$	9.91993	−	18.4914i	0.450906	−	0.840519i
$485$	−5.26099	−	3.03743i	−0.238889	−	0.137923i
$486$		0			0
$487$	−7.45460	+	4.30391i	−0.337800	+	0.195029i	−0.659299	−	0.751881i	$-0.729147\pi$
$487$	−7.45460	+	4.30391i	−0.337800	+	0.195029i	0.321499	+	0.946910i	$0.395813\pi$
$488$	7.36893	−	14.2662i	0.333576	−	0.645800i
$489$		0			0
$490$	−2.68511	−	2.19427i	−0.121301	−	0.0991270i
$491$	8.74870			0.394823			0.197412	−	0.980321i	$-0.436746\pi$
$491$	8.74870			0.394823			0.197412	+	0.980321i	$0.436746\pi$
$492$		0			0
$493$	10.4029	+	18.0184i	0.468523	+	0.811506i
$494$	−0.530624	−	0.295413i	−0.0238739	−	0.0132913i
$495$		0			0
$496$	0.00779148	−	0.00517201i	0.000349848	−	0.000232230i
$497$	25.3355	+	2.24993i	1.13645	+	0.100923i
$498$		0			0
$499$	25.1145	+	14.4998i	1.12428	+	0.649102i	0.942490	−	0.334236i	$-0.108478\pi$
$499$	25.1145	+	14.4998i	1.12428	+	0.649102i	0.181788	+	0.983338i	$0.441811\pi$
$500$	−0.215927	−	6.91640i	−0.00965654	−	0.309311i
$501$		0			0
$502$	−0.686745	+	0.0107173i	−0.0306509	+	0.000478338i
$503$	−27.7583			−1.23768			−0.618841	−	0.785516i	$-0.712397\pi$
$503$	−27.7583			−1.23768			−0.618841	+	0.785516i	$0.712397\pi$
$504$		0			0
$505$	3.72216			0.165634
$506$	−4.81243	+	0.0751026i	−0.213938	+	0.00333872i
$507$		0			0
$508$	−0.575300	−	18.4275i	−0.0255248	−	0.817590i
$509$	−18.3756	−	10.6092i	−0.814484	−	0.470243i	0.0340265	−	0.999421i	$-0.489167\pi$
$509$	−18.3756	−	10.6092i	−0.814484	−	0.470243i	−0.848511	+	0.529178i	$0.822500\pi$
$510$		0			0
$511$	−4.80205	−	10.3333i	−0.212430	−	0.457117i
$512$	−22.4046	+	3.16741i	−0.990154	+	0.139981i
$513$		0			0
$514$	36.0064	+	20.0458i	1.58817	+	0.884181i
$515$	−1.82125	−	3.15449i	−0.0802537	−	0.139003i
$516$		0			0
$517$	1.90064			0.0835899
$518$	−9.12664	+	13.4391i	−0.401002	+	0.590482i
$519$		0			0
$520$	−0.112203	−	0.0579563i	−0.00492042	−	0.00254155i
$521$	−20.9834	+	12.1148i	−0.919300	+	0.530758i	−0.883412	−	0.468598i	$-0.844759\pi$
$521$	−20.9834	+	12.1148i	−0.919300	+	0.530758i	−0.0358883	+	0.999356i	$0.511426\pi$
$522$		0			0
$523$	−18.7115	−	10.8031i	−0.818195	−	0.472385i	0.0315989	−	0.999501i	$-0.489940\pi$
$523$	−18.7115	−	10.8031i	−0.818195	−	0.472385i	−0.849794	+	0.527116i	$0.823273\pi$
$524$	−18.1616	+	33.8545i	−0.793393	+	1.47894i
$525$		0			0
$526$	16.9671	+	28.3565i	0.739799	+	1.23640i
$527$	0.00716166	−	0.0124044i	0.000311967	−	0.000540343i
$528$		0			0
$529$	0.0972459	+	0.168435i	0.00422808	+	0.00732325i
$530$	−5.81075	+	0.0906824i	−0.252403	+	0.00393899i
$531$		0			0
$532$	14.9025	+	9.78416i	0.646105	+	0.424197i
$533$		−	1.04863i		−	0.0454210i
$534$		0			0
$535$	2.70909	−	1.56409i	0.117124	−	0.0676217i
$536$	−21.4259	+	13.7458i	−0.925460	+	0.593730i
$537$		0			0
$538$	33.8040	−	20.2265i	1.45739	−	0.872027i
$539$	−1.69395	−	4.69221i	−0.0729636	−	0.202108i
$540$		0			0
$541$	−20.2054	+	34.9967i	−0.868696	+	1.50463i	−0.00536596	+	0.999986i	$0.501708\pi$
$541$	−20.2054	+	34.9967i	−0.868696	+	1.50463i	−0.863330	+	0.504640i	$0.831625\pi$
$542$	−35.4684	−	19.7462i	−1.52350	−	0.848174i
$543$		0			0
$544$	−28.5713	+	19.6148i	−1.22498	+	0.840977i
$545$			5.71233i			0.244689i
$546$		0			0
$547$		−	21.7198i		−	0.928670i	−0.885660	−	0.464335i	$-0.846293\pi$
$547$		−	21.7198i		−	0.928670i	0.885660	−	0.464335i	$-0.153707\pi$
$548$	17.9913	−	11.1500i	0.768552	−	0.476302i
$549$		0			0
$550$	2.39107	−	4.29487i	0.101956	−	0.183134i
$551$	−5.72078	+	9.90868i	−0.243713	+	0.422124i
$552$		0			0
$553$	−4.80651	−	3.37492i	−0.204394	−	0.143516i
$554$	−19.5726	−	32.7111i	−0.831560	−	1.38976i
$555$		0			0
$556$	0.727032	+	23.2877i	0.0308330	+	0.987620i
$557$	36.2866	−	20.9501i	1.53751	−	0.887684i	0.538530	−	0.842606i	$-0.318980\pi$
$557$	36.2866	−	20.9501i	1.53751	−	0.887684i	0.998983	−	0.0450775i	$-0.0143535\pi$
$558$		0			0
$559$			0.962418i			0.0407059i
$560$	3.16086	+	1.93686i	0.133571	+	0.0818474i
$561$		0			0
$562$	−0.559421	−	35.8466i	−0.0235978	−	1.51210i
$563$	−1.21907	−	2.11148i	−0.0513775	−	0.0889885i	0.839193	−	0.543834i	$-0.183028\pi$
$563$	−1.21907	−	2.11148i	−0.0513775	−	0.0889885i	−0.890570	+	0.454845i	$0.849695\pi$
$564$		0			0
$565$	−1.47831	+	2.56052i	−0.0621932	+	0.107722i
$566$	−3.08987	+	1.84881i	−0.129877	+	0.0777114i
$567$		0			0
$568$	−27.1616	+	1.27248i	−1.13968	+	0.0533919i
$569$	−7.19227	−	4.15246i	−0.301515	−	0.174080i	0.341608	−	0.939843i	$-0.389028\pi$
$569$	−7.19227	−	4.15246i	−0.301515	−	0.174080i	−0.643123	+	0.765762i	$0.722362\pi$
$570$		0			0
$571$	40.3829	−	23.3151i	1.68997	−	0.975705i	0.735442	−	0.677588i	$-0.236975\pi$
$571$	40.3829	−	23.3151i	1.68997	−	0.975705i	0.954529	−	0.298117i	$-0.0963586\pi$
$572$	−0.0957045	−	0.154427i	−0.00400161	−	0.00645691i
$573$		0			0
$574$	−2.24411	+	30.6999i	−0.0936672	+	1.28139i
$575$	23.2916			0.971327
$576$		0			0
$577$	−4.32922	−	7.49843i	−0.180228	−	0.312164i	0.761730	−	0.647894i	$-0.224350\pi$
$577$	−4.32922	−	7.49843i	−0.180228	−	0.312164i	−0.941958	+	0.335730i	$0.891017\pi$
$578$	−14.1249	+	25.3713i	−0.587519	+	1.05531i
$579$		0			0
$580$	−1.12472	+	2.09656i	−0.0467016	+	0.0870550i
$581$	13.5013	+	1.19899i	0.560130	+	0.0497426i
$582$		0			0
$583$	−7.24034	−	4.18021i	−0.299864	−	0.173127i
$584$	6.57765	+	10.2527i	0.272185	+	0.424261i
$585$		0			0
$586$	−0.102951	−	6.59691i	−0.00425287	−	0.272516i
$587$	−16.5890			−0.684700			−0.342350	−	0.939573i	$-0.611223\pi$
$587$	−16.5890			−0.684700			−0.342350	+	0.939573i	$0.611223\pi$
$588$		0			0
$589$	0.00787670			0.000324554
$590$	−0.0794481	−	5.09088i	−0.00327083	−	0.209588i
$591$		0			0
$592$	7.72833	−	15.5525i	0.317632	−	0.639203i
$593$	35.4794	+	20.4840i	1.45696	+	0.841178i	0.998861	−	0.0477210i	$-0.0151958\pi$
$593$	35.4794	+	20.4840i	1.45696	+	0.841178i	0.458103	+	0.888899i	$0.348529\pi$
$594$		0			0
$595$	5.65553	+	0.502243i	0.231854	+	0.0205899i
$596$	−27.9501	−	14.9941i	−1.14488	−	0.614184i
$597$		0			0
$598$	0.418738	−	0.752140i	0.0171235	−	0.0307573i
$599$	−10.5150	−	18.2125i	−0.429632	−	0.744144i	0.567209	−	0.823574i	$-0.308023\pi$
$599$	−10.5150	−	18.2125i	−0.429632	−	0.744144i	−0.996840	+	0.0794302i	$0.974690\pi$
$600$		0			0
$601$	−1.20122			−0.0489988			−0.0244994	−	0.999700i	$-0.507799\pi$
$601$	−1.20122			−0.0489988			−0.0244994	+	0.999700i	$0.507799\pi$
$602$	2.05962	−	28.1760i	0.0839438	−	1.14837i
$603$		0			0
$604$	−6.31734	+	3.91511i	−0.257049	+	0.159304i
$605$	3.18286	−	1.83762i	0.129401	−	0.0747100i
$606$		0			0
$607$	−26.7657	−	15.4532i	−1.08638	−	0.627224i	−0.153773	−	0.988106i	$-0.549142\pi$
$607$	−26.7657	−	15.4532i	−1.08638	−	0.627224i	−0.932612	+	0.360882i	$0.882476\pi$
$608$	−17.1974	−	8.21366i	−0.697449	−	0.333108i
$609$		0			0
$610$	2.41325	−	1.44396i	0.0977098	−	0.0584644i
$611$	−0.169972	+	0.294400i	−0.00687634	+	0.0119102i
$612$		0			0
$613$	2.49089	+	4.31434i	0.100606	+	0.174255i	0.911934	−	0.410336i	$-0.134589\pi$
$613$	2.49089	+	4.31434i	0.100606	+	0.174255i	−0.811329	+	0.584590i	$0.801255\pi$
$614$	0.369262	+	23.6616i	0.0149022	+	0.954903i
$615$		0			0
$616$	2.47139	+	4.72585i	0.0995752	+	0.190410i
$617$			15.4858i			0.623435i	0.950175	+	0.311718i	$0.100904\pi$
$617$			15.4858i			0.623435i	−0.950175	+	0.311718i	$0.899096\pi$
$618$		0			0
$619$	−21.9439	+	12.6693i	−0.881998	+	0.509222i	−0.871317	−	0.490721i	$-0.836733\pi$
$619$	−21.9439	+	12.6693i	−0.881998	+	0.509222i	−0.0106814	+	0.999943i	$0.503400\pi$
$620$	0.00163711		5.11099e-5i	6.57480e−5		2.05262e-6i
$621$		0			0
$622$	−22.7781	−	38.0683i	−0.913318	−	1.52640i
$623$	19.4782	+	13.6768i	0.780379	+	0.547948i
$624$		0			0
$625$	−11.5873	+	20.0697i	−0.463491	+	0.802790i
$626$	−15.6537	+	28.1173i	−0.625647	+	1.12379i
$627$		0			0
$628$	2.11947	+	3.41994i	0.0845762	+	0.136470i
$629$		−	26.5991i		−	1.06058i
$630$		0			0
$631$			12.6823i			0.504876i	0.967613	+	0.252438i	$0.0812323\pi$
$631$			12.6823i			0.504876i	−0.967613	+	0.252438i	$0.918768\pi$
$632$	5.57833	+	2.88138i	0.221894	+	0.114615i
$633$		0			0
$634$	−7.28507	−	4.05580i	−0.289327	−	0.161076i
$635$	1.61451	−	2.79642i	0.0640701	−	0.110973i
$636$		0			0
$637$	0.878291	+	0.157234i	0.0347992	+	0.00622985i
$638$	−2.93712	+	1.75742i	−0.116282	+	0.0695768i
$639$		0			0
$640$	−3.62765	−	1.59556i	−0.143396	−	0.0630699i
$641$	14.7613	−	8.52242i	0.583035	−	0.336615i	−0.179304	−	0.983794i	$-0.557385\pi$
$641$	14.7613	−	8.52242i	0.583035	−	0.336615i	0.762338	+	0.647179i	$0.224051\pi$
$642$		0			0
$643$			37.1996i			1.46701i	0.679685	+	0.733504i	$0.262117\pi$
$643$			37.1996i			1.46701i	−0.679685	+	0.733504i	$0.737883\pi$
$644$	−13.8687	+	21.1238i	−0.546503	+	0.832393i
$645$		0			0
$646$	−29.1862	+	0.455479i	−1.14831	+	0.0179206i
$647$	7.31238	+	12.6654i	0.287479	+	0.497929i	0.973207	−	0.229929i	$-0.0738494\pi$
$647$	7.31238	+	12.6654i	0.287479	+	0.497929i	−0.685728	+	0.727858i	$0.740516\pi$
$648$		0			0
$649$	3.66235	−	6.34337i	0.143760	−	0.248999i
$650$	0.451425	+	0.754453i	0.0177063	+	0.0295921i
$651$		0			0
$652$	−28.6028	−	15.3443i	−1.12017	−	0.600929i
$653$	35.1095	+	20.2705i	1.37394	+	0.793245i	0.991422	−	0.130703i	$-0.0417235\pi$
$653$	35.1095	+	20.2705i	1.37394	+	0.793245i	0.382519	+	0.923948i	$0.375057\pi$
$654$		0			0
$655$	−5.82723	+	3.36435i	−0.227689	+	0.131456i
$656$	−2.05269	−	32.8430i	−0.0801441	−	1.28230i
$657$		0			0
$658$	5.60618	−	8.25520i	0.218552	−	0.321821i
$659$	2.98301			0.116201			0.0581007	−	0.998311i	$-0.481496\pi$
$659$	2.98301			0.116201			0.0581007	+	0.998311i	$0.481496\pi$
$660$		0			0
$661$	15.4040	+	26.6805i	0.599146	+	1.03775i	0.992947	+	0.118556i	$0.0378264\pi$
$661$	15.4040	+	26.6805i	0.599146	+	1.03775i	−0.393801	+	0.919196i	$0.628840\pi$
$662$	10.5747	+	5.88725i	0.410999	+	0.228815i
$663$		0			0
$664$	−14.4745	+	0.678105i	−0.561718	+	0.0263156i
$665$	1.31586	+	2.83152i	0.0510268	+	0.109802i
$666$		0			0
$667$	−14.0452	−	8.10900i	−0.543832	−	0.313982i
$668$	−49.6117	+	1.54886i	−1.91953	+	0.0599270i
$669$		0			0
$670$	−4.45794	+	0.0695705i	−0.172225	+	0.00268774i
$671$	4.04576			0.156185
$672$		0			0
$673$	15.4848			0.596894			0.298447	−	0.954426i	$-0.403531\pi$
$673$	15.4848			0.596894			0.298447	+	0.954426i	$0.403531\pi$
$674$	36.9896	−	0.577258i	1.42478	−	0.0222352i
$675$		0			0
$676$	−25.9549	+	0.810299i	−0.998264	+	0.0311654i
$677$	−25.3739	−	14.6496i	−0.975199	−	0.563032i	−0.0743819	−	0.997230i	$-0.523698\pi$
$677$	−25.3739	−	14.6496i	−0.975199	−	0.563032i	−0.900817	+	0.434198i	$0.857032\pi$
$678$		0			0
$679$	−45.7043	−	4.05879i	−1.75397	−	0.155762i
$680$	−6.06316	+	0.284049i	−0.232512	+	0.0108928i
$681$		0			0
$682$	0.00205877	+	0.00114617i	7.88342e−5	+	4.38892e-5i
$683$	1.53968	+	2.66681i	0.0589143	+	0.102043i	0.893978	−	0.448110i	$-0.147903\pi$
$683$	1.53968	+	2.66681i	0.0589143	+	0.102043i	−0.835064	+	0.550153i	$0.814569\pi$
$684$		0			0
$685$	3.70712			0.141642
$686$	−25.3766	−	6.48282i	−0.968884	−	0.247515i
$687$		0			0
$688$	1.88394	+	30.1430i	0.0718245	+	1.14919i
$689$	1.29499	−	0.747665i	0.0493354	−	0.0284838i
$690$		0			0
$691$	−19.1882	−	11.0783i	−0.729952	−	0.421438i	0.0884525	−	0.996080i	$-0.471808\pi$
$691$	−19.1882	−	11.0783i	−0.729952	−	0.421438i	−0.818405	+	0.574642i	$0.805141\pi$
$692$	−8.79967	−	4.72068i	−0.334513	−	0.179453i
$693$		0			0
$694$	26.6964	+	44.6169i	1.01338	+	1.69363i
$695$	−2.04034	+	3.53397i	−0.0773944	+	0.134051i
$696$		0			0
$697$	−25.2004	−	43.6483i	−0.954532	−	1.65330i
$698$	−14.0480	+	0.219233i	−0.531725	+	0.00829809i
$699$		0			0
$700$	−11.6015	−	23.0537i	−0.438495	−	0.871346i
$701$		−	33.1595i		−	1.25242i	−0.779656	−	0.626208i	$-0.784606\pi$
$701$		−	33.1595i		−	1.25242i	0.779656	−	0.626208i	$-0.215394\pi$
$702$		0			0
$703$	12.6677	−	7.31372i	0.477773	−	0.275842i
$704$	−3.29976	−	4.64931i	−0.124364	−	0.175228i
$705$		0			0
$706$	15.0521	−	9.00641i	0.566495	−	0.338961i
$707$	25.4953	−	11.8481i	0.958850	−	0.445595i
$708$		0			0
$709$	−7.67372	+	13.2913i	−0.288193	+	0.499164i	−0.973378	−	0.229204i	$-0.926388\pi$
$709$	−7.67372	+	13.2913i	−0.288193	+	0.499164i	0.685186	+	0.728368i	$0.259721\pi$
$710$	−4.16100	−	2.31655i	−0.156160	−	0.0869384i
$711$		0			0
$712$	−22.6060	−	11.6767i	−0.847196	−	0.437603i
$713$			0.0111649i			0.000418130i
$714$		0			0
$715$		−	0.0318197i		−	0.00118999i
$716$	−20.5578	−	33.1716i	−0.768281	−	1.23968i
$717$		0			0
$718$	−11.3550	+	20.3960i	−0.423766	+	0.761172i
$719$	−14.9962	+	25.9742i	−0.559264	+	0.968674i	0.438294	+	0.898832i	$0.355583\pi$
$719$	−14.9962	+	25.9742i	−0.559264	+	0.968674i	−0.997558	+	0.0698422i	$0.977750\pi$
$720$		0			0
$721$	−22.5160	−	15.8098i	−0.838539	−	0.588786i
$722$	5.55454	+	9.28313i	0.206718	+	0.345482i
$723$		0			0
$724$	−15.6087	+	0.487298i	−0.580094	+	0.0181103i
$725$	14.3446	−	8.28184i	0.532744	−	0.307580i
$726$		0			0
$727$		−	41.1692i		−	1.52688i	−0.645879	−	0.763440i	$-0.723509\pi$
$727$		−	41.1692i		−	1.52688i	0.645879	−	0.763440i	$-0.276491\pi$
$728$	−0.953029	−	0.0398207i	−0.0353216	−	0.00147585i
$729$		0			0
$730$	0.0332908	+	2.13321i	0.00123215	+	0.0789537i
$731$	23.1286	+	40.0600i	0.855444	+	1.48167i
$732$		0			0
$733$	−16.3313	+	28.2866i	−0.603209	+	1.04479i	0.389123	+	0.921186i	$0.372778\pi$
$733$	−16.3313	+	28.2866i	−0.603209	+	1.04479i	−0.992332	+	0.123603i	$0.960555\pi$
$734$	−15.0225	+	8.98870i	−0.554492	+	0.331779i
$735$		0			0
$736$	11.6426	−	24.3768i	0.429151	−	0.898540i
$737$	−5.55471	−	3.20702i	−0.204611	−	0.118132i
$738$		0			0
$739$	−15.9487	+	9.20799i	−0.586683	+	0.338721i	−0.763785	−	0.645471i	$-0.776661\pi$
$739$	−15.9487	+	9.20799i	−0.586683	+	0.338721i	0.177102	+	0.984192i	$0.443328\pi$
$740$	2.58543	−	1.60230i	0.0950424	−	0.0589016i
$741$		0			0
$742$	−39.5127	+	19.1175i	−1.45056	+	0.701826i
$743$	22.5175			0.826088			0.413044	−	0.910711i	$-0.364466\pi$
$743$	22.5175			0.826088			0.413044	+	0.910711i	$0.364466\pi$
$744$		0			0
$745$	−2.77759	−	4.81093i	−0.101763	−	0.176259i
$746$	−14.5421	+	26.1206i	−0.532424	+	0.956344i
$747$		0			0
$748$	−7.69479	−	4.12795i	−0.281349	−	0.150933i
$749$	13.5775	−	19.3368i	0.496111	−	0.706553i
$750$		0			0
$751$	−27.5078	−	15.8816i	−1.00377	−	0.579529i	−0.0944107	−	0.995533i	$-0.530097\pi$
$751$	−27.5078	−	15.8816i	−1.00377	−	0.579529i	−0.909362	+	0.416005i	$0.863430\pi$
$752$	−4.74725	+	9.55336i	−0.173114	+	0.348375i
$753$		0			0
$754$	−0.00955259	−	0.612111i	−0.000347885	−	0.0222918i
$755$	−1.30169			−0.0473733
$756$		0			0
$757$	−7.32709			−0.266308			−0.133154	−	0.991095i	$-0.542510\pi$
$757$	−7.32709			−0.266308			−0.133154	+	0.991095i	$0.542510\pi$
$758$	−0.417730	−	26.7673i	−0.0151727	−	0.972233i
$759$		0			0
$760$	−1.80241	−	2.80945i	−0.0653802	−	0.101910i
$761$	4.23458	+	2.44483i	0.153503	+	0.0886252i	0.574784	−	0.818305i	$-0.305086\pi$
$761$	4.23458	+	2.44483i	0.153503	+	0.0886252i	−0.421281	+	0.906930i	$0.638419\pi$
$762$		0			0
$763$	18.1831	+	39.1272i	0.658273	+	1.41650i
$764$	−11.7527	+	21.9078i	−0.425198	+	0.792598i
$765$		0			0
$766$	4.48479	−	8.05563i	0.162042	−	0.291062i
$767$	0.655040	+	1.13456i	0.0236521	+	0.0409667i
$768$		0			0
$769$	10.3531			0.373343			0.186672	−	0.982422i	$-0.440230\pi$
$769$	10.3531			0.373343			0.186672	+	0.982422i	$0.440230\pi$
$770$	−0.0680956	+	0.931563i	−0.00245399	+	0.0335712i
$771$		0			0
$772$	1.41165	+	2.27781i	0.0508064	+	0.0819801i
$773$	5.48545	−	3.16703i	0.197298	−	0.113910i	−0.398097	−	0.917344i	$-0.630329\pi$
$773$	5.48545	−	3.16703i	0.197298	−	0.113910i	0.595395	+	0.803433i	$0.296996\pi$
$774$		0			0
$775$	−0.00987522	−	0.00570146i	−0.000354728	−	0.000204802i
$776$	48.9985	−	2.29550i	1.75894	−	0.0824036i
$777$		0			0
$778$	20.6744	−	12.3705i	0.741212	−	0.443503i
$779$	13.8582	−	24.0031i	0.496522	−	0.860002i
$780$		0			0
$781$	−3.42561	−	5.93334i	−0.122578	−	0.212312i
$782$	−0.645625	−	41.3703i	−0.0230875	−	1.47940i
$783$		0			0
$784$	27.8159	+	3.20533i	0.993426	+	0.114476i
$785$			0.704680i			0.0251511i
$786$		0			0
$787$	1.48926	−	0.859826i	0.0530865	−	0.0306495i	−0.473222	−	0.880943i	$-0.656909\pi$
$787$	1.48926	−	0.859826i	0.0530865	−	0.0306495i	0.526308	+	0.850294i	$0.323576\pi$
$788$	0.752713	+	24.1103i	0.0268143	+	0.858894i
$789$		0			0
$790$	0.564615	+	0.943625i	0.0200881	+	0.0335727i
$791$	−1.97541	+	22.2442i	−0.0702374	+	0.790913i
$792$		0			0
$793$	−0.361808	+	0.626670i	−0.0128482	+	0.0222537i
$794$	10.0840	−	18.1130i	0.357868	−	0.642805i
$795$		0			0
$796$	−20.1751	+	12.5033i	−0.715086	+	0.443168i
$797$		−	3.60991i		−	0.127870i	−0.997954	−	0.0639348i	$-0.979635\pi$
$797$		−	3.60991i		−	0.127870i	0.997954	−	0.0639348i	$-0.0203650\pi$
$798$		0			0
$799$			16.3390i			0.578031i
$800$	15.6155	+	22.7458i	0.552091	+	0.804187i
$801$		0			0
$802$	−7.72230	−	4.29922i	−0.272684	−	0.151811i
$803$	−1.53462	+	2.65804i	−0.0541555	+	0.0938001i
$804$		0			0
$805$	−4.01358	+	1.86518i	−0.141460	+	0.0657390i
$806$	−0.000361651	0	0.000216393i	−1.27386e−5	0	7.62211e-6i
$807$		0			0
$808$	−25.2966	+	16.2291i	−0.889932	+	0.570937i
$809$	9.63889	−	5.56502i	0.338885	−	0.195656i	−0.320894	−	0.947115i	$-0.603983\pi$
$809$	9.63889	−	5.56502i	0.338885	−	0.195656i	0.659779	+	0.751460i	$0.270650\pi$
$810$		0			0
$811$		−	40.8908i		−	1.43587i	−0.696110	−	0.717936i	$-0.745087\pi$
$811$		−	40.8908i		−	1.43587i	0.696110	−	0.717936i	$-0.254913\pi$
$812$	−1.03028	+	17.9408i	−0.0361558	+	0.629598i
$813$		0			0
$814$	4.37527	−	0.0682803i	0.153353	−	0.00239322i
$815$	−2.84246	−	4.92329i	−0.0995670	−	0.172455i
$816$		0			0
$817$	−12.7189	+	22.0298i	−0.444979	+	0.770727i
$818$	21.0781	+	35.2272i	0.736979	+	1.23169i
$819$		0			0
$820$	2.72457	−	5.07879i	0.0951463	−	0.177359i
$821$	28.0807	+	16.2124i	0.980024	+	0.565817i	0.902277	−	0.431156i	$-0.141894\pi$
$821$	28.0807	+	16.2124i	0.980024	+	0.565817i	0.0777465	+	0.996973i	$0.475228\pi$
$822$		0			0
$823$	−8.66266	+	5.00139i	−0.301961	+	0.174337i	−0.643324	−	0.765594i	$-0.722445\pi$
$823$	−8.66266	+	5.00139i	−0.301961	+	0.174337i	0.341362	+	0.939932i	$0.389112\pi$
$824$	26.1316	+	13.4978i	0.910337	+	0.470217i
$825$		0			0
$826$	−16.7491	−	34.6176i	−0.582777	−	1.20450i
$827$	28.0825			0.976525			0.488263	−	0.872697i	$-0.337631\pi$
$827$	28.0825			0.976525			0.488263	+	0.872697i	$0.337631\pi$
$828$		0			0
$829$	22.9592	+	39.7666i	0.797407	+	1.38115i	0.921299	+	0.388854i	$0.127129\pi$
$829$	22.9592	+	39.7666i	0.797407	+	1.38115i	−0.123892	+	0.992296i	$0.539538\pi$
$830$	−2.21741	−	1.23449i	−0.0769673	−	0.0428498i
$831$		0			0
$832$	1.01525	−	0.0953351i	0.0351976	−	0.00330515i
$833$	40.3369	−	14.5622i	1.39759	−	0.504549i
$834$		0			0
$835$	−7.52869	−	4.34669i	−0.260541	−	0.150423i
$836$	−0.149842	−	4.79964i	−0.00518241	−	0.165999i
$837$		0			0
$838$	8.41108	−	0.131263i	0.290556	−	0.00453441i
$839$	22.9019			0.790662			0.395331	−	0.918539i	$-0.370630\pi$
$839$	22.9019			0.790662			0.395331	+	0.918539i	$0.370630\pi$
$840$		0			0
$841$	17.4667			0.602299
$842$	−37.1873	+	0.580344i	−1.28156	+	0.0200000i
$843$		0			0
$844$	−0.154452	−	4.94728i	−0.00531646	−	0.170293i
$845$	−3.93871	−	2.27402i	−0.135496	−	0.0782285i
$846$		0			0
$847$	15.9519	−	22.7185i	0.548114	−	0.780615i
$848$	39.0958	−	25.9519i	1.34255	−	0.891192i
$849$		0			0
$850$	36.9211	+	20.5550i	1.26638	+	0.705032i
$851$	10.3669	+	17.9561i	0.355374	+	0.615526i
$852$		0			0
$853$	10.6107			0.363304			0.181652	−	0.983363i	$-0.441856\pi$
$853$	10.6107			0.363304			0.181652	+	0.983363i	$0.441856\pi$
$854$	11.9335	−	17.5723i	0.408356	−	0.601312i
$855$		0			0
$856$	−11.5919	+	22.4419i	−0.396205	+	0.767049i
$857$	27.1454	−	15.6724i	0.927268	−	0.535358i	0.0413213	−	0.999146i	$-0.486843\pi$
$857$	27.1454	−	15.6724i	0.927268	−	0.535358i	0.885946	+	0.463788i	$0.153510\pi$
$858$		0			0
$859$	−8.41769	−	4.85995i	−0.287208	−	0.165819i	0.349474	−	0.936946i	$-0.386360\pi$
$859$	−8.41769	−	4.85995i	−0.287208	−	0.165819i	−0.636682	+	0.771127i	$0.719694\pi$
$860$	−2.50059	+	4.66126i	−0.0852693	+	0.158948i
$861$		0			0
$862$	5.72325	+	9.56509i	0.194935	+	0.325788i
$863$	−22.7910	+	39.4752i	−0.775815	+	1.34375i	0.158520	+	0.987356i	$0.449328\pi$
$863$	−22.7910	+	39.4752i	−0.775815	+	1.34375i	−0.934335	+	0.356395i	$0.884006\pi$
$864$		0			0
$865$	−0.874485	−	1.51465i	−0.0297334	−	0.0514997i
$866$	40.8525	−	0.637543i	1.38822	−	0.0216646i
$867$		0			0
$868$	0.0110509	−	0.00556123i	0.000375091	−	0.000188760i
$869$			1.58196i			0.0536644i
$870$		0			0
$871$	0.993506	−	0.573601i	0.0336637	−	0.0194357i
$872$	−24.9065	−	38.8223i	−0.843440	−	1.31469i
$873$		0			0
$874$	19.5249	−	11.6827i	0.660441	−	0.395173i
$875$	0.809738	−	9.11811i	0.0273741	−	0.308248i
$876$		0			0
$877$	−4.86133	+	8.42007i	−0.164155	+	0.284326i	−0.936355	−	0.351054i	$-0.885823\pi$
$877$	−4.86133	+	8.42007i	−0.164155	+	0.284326i	0.772200	+	0.635380i	$0.219157\pi$
$878$	−32.5605	−	18.1273i	−1.09886	−	0.611767i
$879$		0			0
$880$	−0.0622872	−	0.996595i	−0.00209970	−	0.0335952i
$881$		−	7.59560i		−	0.255902i	−0.991780	−	0.127951i	$-0.959160\pi$
$881$		−	7.59560i		−	0.255902i	0.991780	−	0.127951i	$-0.0408401\pi$
$882$		0			0
$883$			12.2076i			0.410817i	0.978676	+	0.205409i	$0.0658524\pi$
$883$			12.2076i			0.410817i	−0.978676	+	0.205409i	$0.934148\pi$
$884$	1.32754	−	0.822730i	0.0446500	−	0.0276714i
$885$		0			0
$886$	16.3444	−	29.3580i	0.549101	−	0.986301i
$887$	14.1560	−	24.5189i	0.475312	−	0.823264i	−0.524288	−	0.851541i	$-0.675669\pi$
$887$	14.1560	−	24.5189i	0.475312	−	0.823264i	0.999600	+	0.0282768i	$0.00900198\pi$
$888$		0			0
$889$	2.15741	−	24.2936i	0.0723571	−	0.814782i
$890$	−2.28809	−	3.82401i	−0.0766968	−	0.128181i
$891$		0			0
$892$	0.484655	+	15.5241i	0.0162274	+	0.519784i
$893$	−7.78136	+	4.49257i	−0.260393	+	0.150338i
$894$		0			0
$895$		−	6.83503i		−	0.228470i
$896$	−29.9269	+	0.618371i	−0.999787	+	0.0206583i
$897$		0			0
$898$	0.796558	+	51.0419i	0.0265815	+	1.70329i
$899$	0.00396994	+	0.00687614i	0.000132405	+	0.000229332i
$900$		0			0
$901$	35.9355	−	62.2421i	1.19719	−	2.07359i
$902$	7.11498	−	4.25723i	0.236903	−	0.141750i
$903$		0			0
$904$	−1.11722	−	23.8475i	−0.0371580	−	0.793156i
$905$	−2.36866	−	1.36755i	−0.0787370	−	0.0454588i
$906$		0			0
$907$	−5.89877	+	3.40566i	−0.195865	+	0.113083i	−0.594725	−	0.803929i	$-0.702739\pi$
$907$	−5.89877	+	3.40566i	−0.195865	+	0.113083i	0.398860	+	0.917012i	$0.369406\pi$
$908$	−16.9263	−	27.3119i	−0.561719	−	0.906378i
$909$		0			0
$910$	−0.138205	−	0.0938565i	−0.00458146	−	0.00311131i
$911$	−33.1107			−1.09701			−0.548503	−	0.836148i	$-0.684802\pi$
$911$	−33.1107			−1.09701			−0.548503	+	0.836148i	$0.684802\pi$
$912$		0			0
$913$	−1.82552	−	3.16189i	−0.0604158	−	0.104643i
$914$	−13.7365	+	24.6736i	−0.454362	+	0.816130i
$915$		0			0
$916$	−10.4897	+	19.5534i	−0.346588	+	0.646064i
$917$	−29.2051	+	41.5934i	−0.964436	+	1.37353i
$918$		0			0
$919$	38.7490	+	22.3718i	1.27821	+	0.737976i	0.976520	−	0.215429i	$-0.0691149\pi$
$919$	38.7490	+	22.3718i	1.27821	+	0.737976i	0.301693	+	0.953405i	$0.402448\pi$
$920$	3.98230	−	2.55485i	0.131293	−	0.0842309i
$921$		0			0
$922$	−0.0861122	−	5.51790i	−0.00283595	−	0.181722i
$923$	1.22540			0.0403345
$924$		0			0
$925$	−21.1758			−0.696256
$926$	0.243358	+	15.5939i	0.00799725	+	0.512448i
$927$		0			0
$928$	−1.49740	−	19.1527i	−0.0491545	−	0.628717i
$929$	−35.1764	−	20.3091i	−1.15410	−	0.666319i	−0.204216	−	0.978926i	$-0.565465\pi$
$929$	−35.1764	−	20.3091i	−1.15410	−	0.666319i	−0.949883	+	0.312606i	$0.898798\pi$
$930$		0			0
$931$	18.0262	+	15.2063i	0.590786	+	0.498365i
$932$	−6.33268	−	3.39724i	−0.207434	−	0.111280i
$933$		0			0
$934$	26.4945	−	47.5896i	0.866926	−	1.55718i
$935$	−0.764685	−	1.32447i	−0.0250079	−	0.0433149i
$936$		0			0
$937$	15.8390			0.517437			0.258718	−	0.965953i	$-0.416700\pi$
$937$	15.8390			0.517437			0.258718	+	0.965953i	$0.416700\pi$
$938$	−30.3137	+	14.6668i	−0.989777	+	0.478887i
$939$		0			0
$940$	−1.58814	+	0.984237i	−0.0517995	+	0.0321023i
$941$	35.2983	−	20.3795i	1.15069	−	0.664352i	0.201636	−	0.979461i	$-0.435374\pi$
$941$	35.2983	−	20.3795i	1.15069	−	0.664352i	0.949056	+	0.315109i	$0.102041\pi$
$942$		0			0
$943$	34.0236	+	19.6435i	1.10796	+	0.639682i
$944$	22.7368	+	34.2524i	0.740021	+	1.11482i
$945$		0			0
$946$	−6.53006	+	3.90724i	−0.212310	+	0.127035i
$947$	−10.9987	+	19.0503i	−0.357411	+	0.619053i	−0.987527	−	0.157447i	$-0.949674\pi$
$947$	−10.9987	+	19.0503i	−0.357411	+	0.619053i	0.630117	+	0.776500i	$0.283007\pi$
$948$		0			0
$949$	−0.274479	−	0.475412i	−0.00890997	−	0.0154325i
$950$	0.362610	+	23.2354i	0.0117646	+	0.753854i
$951$		0			0
$952$	−40.6261	+	21.2455i	−1.31670	+	0.688570i
$953$		−	23.9613i		−	0.776184i	−0.921621	−	0.388092i	$-0.873134\pi$
$953$		−	23.9613i		−	0.776184i	0.921621	−	0.388092i	$-0.126866\pi$
$954$		0			0
$955$	−3.77091	+	2.17714i	−0.122024	+	0.0704504i
$956$	12.2991	−	0.383972i	0.397780	−	0.0124185i
$957$		0			0
$958$	10.7621	+	17.9863i	0.347706	+	0.581111i
$959$	25.3923	−	11.8003i	0.819961	−	0.381050i
$960$		0			0
$961$	−15.5000	+	26.8468i	−0.500000	+	0.866025i
$962$	−0.380700	+	0.683816i	−0.0122743	+	0.0220471i
$963$		0			0
$964$	−13.2147	−	21.3229i	−0.425616	−	0.686764i
$965$			0.469343i			0.0151087i
$966$		0			0
$967$		−	53.1580i		−	1.70945i	−0.519084	−	0.854723i	$-0.673727\pi$
$967$		−	53.1580i		−	1.70945i	0.519084	−	0.854723i	$-0.326273\pi$
$968$	−13.6191	+	26.3666i	−0.437736	+	0.847453i
$969$		0			0
$970$	7.50628	+	4.17896i	0.241012	+	0.134178i
$971$	−20.7550	+	35.9488i	−0.666060	+	1.15365i	0.312936	+	0.949774i	$0.398687\pi$
$971$	−20.7550	+	35.9488i	−0.666060	+	1.15365i	−0.978997	+	0.203876i	$0.934646\pi$
$972$		0			0
$973$	−2.72641	+	30.7010i	−0.0874048	+	0.984227i
$974$	10.4461	−	6.25042i	0.334716	−	0.200276i
$975$		0			0
$976$	−10.1051	+	20.3356i	−0.323458	+	0.650927i
$977$	22.0401	−	12.7249i	0.705127	−	0.407105i	−0.104127	−	0.994564i	$-0.533205\pi$
$977$	22.0401	−	12.7249i	0.705127	−	0.407105i	0.809254	+	0.587459i	$0.199872\pi$
$978$		0			0
$979$		−	6.41085i		−	0.204892i
$980$	3.84528	+	3.04354i	0.122833	+	0.0972222i
$981$		0			0
$982$	−12.3710	+	0.193062i	−0.394775	+	0.00616085i
$983$	11.7347	+	20.3252i	0.374280	+	0.648273i	0.990219	−	0.139522i	$-0.0445564\pi$
$983$	11.7347	+	20.3252i	0.374280	+	0.648273i	−0.615939	+	0.787794i	$0.711223\pi$
$984$		0			0
$985$	−2.11241	+	3.65879i	−0.0673068	+	0.116579i
$986$	−15.1078	−	25.2491i	−0.481129	−	0.804096i
$987$		0			0
$988$	0.756843	+	0.406017i	0.0240784	+	0.0129171i
$989$	−31.2265	−	18.0286i	−0.992945	−	0.573277i
$990$		0			0
$991$	−48.6218	+	28.0718i	−1.54452	+	0.891731i	−0.545979	+	0.837799i	$0.683842\pi$
$991$	−48.6218	+	28.0718i	−1.54452	+	0.891731i	−0.998545	+	0.0539326i	$0.982824\pi$
$992$	−0.0109033	+	0.00748537i	−0.000346181	+	0.000237661i
$993$		0			0
$994$	−35.8751	−	2.62241i	−1.13789	−	0.0831777i
$995$	−4.15708			−0.131788
$996$		0			0
$997$	−12.9528	−	22.4350i	−0.410221	−	0.710523i	0.584693	−	0.811255i	$-0.301215\pi$
$997$	−12.9528	−	22.4350i	−0.410221	−	0.710523i	−0.994914	+	0.100732i	$0.967882\pi$
$998$	−35.8329	−	19.9492i	−1.13427	−	0.631480i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	756.2.be.d.107.1	yes	28
3.2	odd	2	inner	756.2.be.d.107.14	yes	28
4.3	odd	2		756.2.be.c.107.5	✓	28
7.4	even	3		756.2.be.c.431.10	yes	28
12.11	even	2		756.2.be.c.107.10	yes	28
21.11	odd	6		756.2.be.c.431.5	yes	28
28.11	odd	6	inner	756.2.be.d.431.14	yes	28
84.11	even	6	inner	756.2.be.d.431.1	yes	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
756.2.be.c.107.5	✓	28	4.3	odd	2
756.2.be.c.107.10	yes	28	12.11	even	2
756.2.be.c.431.5	yes	28	21.11	odd	6
756.2.be.c.431.10	yes	28	7.4	even	3
756.2.be.d.107.1	yes	28	1.1	even	1	trivial
756.2.be.d.107.14	yes	28	3.2	odd	2	inner
756.2.be.d.431.1	yes	28	84.11	even	6	inner
756.2.be.d.431.14	yes	28	28.11	odd	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:	\( N \)	\(=\)	\( 756 = 2^{2} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	756.be (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.41404 + 0.0220675i) q^{2} +(1.99903 - 0.0624087i) q^{4} +(0.303357 + 0.175143i) q^{5} +(2.63538 + 0.234036i) q^{7} +(-2.82533 + 0.132362i) q^{8} +O(q^{10})\)	\(q+(-1.41404 + 0.0220675i) q^{2} +(1.99903 - 0.0624087i) q^{4} +(0.303357 + 0.175143i) q^{5} +(2.63538 + 0.234036i) q^{7} +(-2.82533 + 0.132362i) q^{8} +(-0.432824 - 0.240965i) q^{10} +(-0.356330 - 0.617181i) q^{11} +0.127465 q^{13} +(-3.73170 - 0.272781i) q^{14} +(3.99221 - 0.249513i) q^{16} +(5.30564 - 3.06321i) q^{17} +(2.91768 + 1.68453i) q^{19} +(0.617349 + 0.331184i) q^{20} +(0.517485 + 0.864856i) q^{22} +(-2.38776 + 4.13571i) q^{23} +(-2.43865 - 4.22387i) q^{25} +(-0.180241 + 0.00281283i) q^{26} +(5.28280 + 0.303374i) q^{28} +3.39607i q^{29} +(0.00202473 - 0.00116898i) q^{31} +(-5.63964 + 0.440920i) q^{32} +(-7.43480 + 4.44859i) q^{34} +(0.758471 + 0.532565i) q^{35} +(2.17085 - 3.76003i) q^{37} +(-4.16290 - 2.31760i) q^{38} +(-0.880265 - 0.454684i) q^{40} -8.22678i q^{41} +7.55045i q^{43} +(-0.750830 - 1.21152i) q^{44} +(3.28512 - 5.90076i) q^{46} +(-1.33348 + 2.30966i) q^{47} +(6.89045 + 1.23355i) q^{49} +(3.54156 + 5.91891i) q^{50} +(0.254806 - 0.00795492i) q^{52} +(10.1596 - 5.86566i) q^{53} -0.249635i q^{55} +(-7.47679 - 0.312405i) q^{56} +(-0.0749429 - 4.80219i) q^{58} +(5.13898 + 8.90098i) q^{59} +(-2.83849 + 4.91641i) q^{61} +(-0.00283726 + 0.00169767i) q^{62} +(7.96496 - 0.747932i) q^{64} +(0.0386674 + 0.0223246i) q^{65} +(7.79435 - 4.50007i) q^{67} +(10.4149 - 6.45456i) q^{68} +(-1.08426 - 0.736332i) q^{70} +9.61361 q^{71} +(-2.15337 - 3.72974i) q^{73} +(-2.98670 + 5.36474i) q^{74} +(5.93766 + 3.18532i) q^{76} +(-0.794621 - 1.70990i) q^{77} +(-1.92240 - 1.10990i) q^{79} +(1.25476 + 0.623517i) q^{80} +(0.181544 + 11.6330i) q^{82} +5.12311 q^{83} +2.14600 q^{85} +(-0.166620 - 10.6767i) q^{86} +(1.08844 + 1.69657i) q^{88} +(7.79048 + 4.49784i) q^{89} +(0.335919 + 0.0298314i) q^{91} +(-4.51508 + 8.41642i) q^{92} +(1.83463 - 3.29538i) q^{94} +(0.590066 + 1.02203i) q^{95} -17.3426 q^{97} +(-9.77061 - 1.59223i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 4 q^{4} + 2 q^{7}+O(q^{10}) \) 28 * q - 4 * q^4 + 2 * q^7	\( 28 q - 4 q^{4} + 2 q^{7} + 4 q^{10} + 8 q^{13} + 12 q^{16} - 42 q^{19} + 4 q^{22} + 6 q^{25} + 24 q^{28} + 30 q^{31} + 24 q^{34} + 12 q^{37} + 24 q^{46} - 14 q^{49} - 24 q^{52} - 44 q^{58} + 6 q^{61} + 8 q^{64} + 24 q^{67} - 32 q^{70} - 22 q^{73} + 48 q^{79} + 36 q^{82} - 24 q^{85} - 4 q^{88} + 16 q^{91} + 60 q^{94} - 4 q^{97}+O(q^{100}) \) 28 * q - 4 * q^4 + 2 * q^7 + 4 * q^10 + 8 * q^13 + 12 * q^16 - 42 * q^19 + 4 * q^22 + 6 * q^25 + 24 * q^28 + 30 * q^31 + 24 * q^34 + 12 * q^37 + 24 * q^46 - 14 * q^49 - 24 * q^52 - 44 * q^58 + 6 * q^61 + 8 * q^64 + 24 * q^67 - 32 * q^70 - 22 * q^73 + 48 * q^79 + 36 * q^82 - 24 * q^85 - 4 * q^88 + 16 * q^91 + 60 * q^94 - 4 * q^97

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