LMFDB - Embedded newform 3150.2.bf.d.1151.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3150,2,Mod(1151,3150)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3150, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 0, 1]))

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

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

chi := DirichletCharacter("3150.1151");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3150 = 2 \cdot 3^{2} \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3150.bf (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:	$25.1528766367$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			1151.4
Character	$\chi$	$=$	3150.1151
Dual form			3150.2.bf.d.1601.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(-0.397202 - 2.61577i) q^{7} +1.00000i q^{8} +O(q^{10})$	\(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(-0.397202 - 2.61577i) q^{7} +1.00000i q^{8} +(0.429853 + 0.248176i) q^{11} -2.74440i q^{13} +(1.65187 + 2.06672i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(1.82992 - 3.16952i) q^{17} +(3.12125 - 1.80205i) q^{19} -0.496352 q^{22} +(5.56351 - 3.21210i) q^{23} +(1.37220 + 2.37672i) q^{26} +(-2.46392 - 0.963896i) q^{28} +8.87959i q^{29} +(-6.90736 - 3.98797i) q^{31} +(0.866025 + 0.500000i) q^{32} +3.65984i q^{34} +(1.14545 + 1.98397i) q^{37} +(-1.80205 + 3.12125i) q^{38} -2.22816 q^{41} -2.22575 q^{43} +(0.429853 - 0.248176i) q^{44} +(-3.21210 + 5.56351i) q^{46} +(-3.27213 - 5.66749i) q^{47} +(-6.68446 + 2.07798i) q^{49} +(-2.37672 - 1.37220i) q^{52} +(6.72594 + 3.88322i) q^{53} +(2.61577 - 0.397202i) q^{56} +(-4.43979 - 7.68995i) q^{58} +(-3.05194 + 5.28611i) q^{59} +(3.24271 - 1.87218i) q^{61} +7.97593 q^{62} -1.00000 q^{64} +(4.08889 - 7.08216i) q^{67} +(-1.82992 - 3.16952i) q^{68} -10.3761i q^{71} +(-11.3165 - 6.53361i) q^{73} +(-1.98397 - 1.14545i) q^{74} -3.60411i q^{76} +(0.478431 - 1.22297i) q^{77} +(4.44344 + 7.69627i) q^{79} +(1.92964 - 1.11408i) q^{82} +4.79091 q^{83} +(1.92756 - 1.11288i) q^{86} +(-0.248176 + 0.429853i) q^{88} +(0.743586 + 1.28793i) q^{89} +(-7.17871 + 1.09008i) q^{91} -6.42419i q^{92} +(5.66749 + 3.27213i) q^{94} -9.05174i q^{97} +(4.74992 - 5.14181i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 12 q^{4} - 4 q^{7}+O(q^{10}) $ 24 * q + 12 * q^4 - 4 * q^7	$ 24 q + 12 q^{4} - 4 q^{7} - 12 q^{16} + 12 q^{19} + 4 q^{28} + 28 q^{37} + 96 q^{43} - 8 q^{46} - 52 q^{49} - 12 q^{52} + 8 q^{58} - 12 q^{61} - 24 q^{64} - 4 q^{67} - 12 q^{73} + 4 q^{79} + 68 q^{91} - 24 q^{94}+O(q^{100}) $ 24 * q + 12 * q^4 - 4 * q^7 - 12 * q^16 + 12 * q^19 + 4 * q^28 + 28 * q^37 + 96 * q^43 - 8 * q^46 - 52 * q^49 - 12 * q^52 + 8 * q^58 - 12 * q^61 - 24 * q^64 - 4 * q^67 - 12 * q^73 + 4 * q^79 + 68 * q^91 - 24 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/3150\mathbb{Z}\right)^\times$.

$n$	$127$	$451$	$2801$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$	$-1$

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 $

$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$3$		0			0
$3$		0			0
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$		0			0
$5$		0			0
$6$		0			0
$7$	−0.397202	−	2.61577i	−0.150128	−	0.988667i
$7$	−0.397202	−	2.61577i	−0.150128	−	0.988667i
$8$			1.00000i			0.353553i
$9$		0			0
$10$		0			0
$11$	0.429853	+	0.248176i	0.129606	+	0.0748278i	0.563401	−	0.826184i	$-0.309493\pi$
$11$	0.429853	+	0.248176i	0.129606	+	0.0748278i	−0.433795	+	0.901011i	$0.642826\pi$
$12$		0			0
$13$		−	2.74440i		−	0.761160i	−0.924748	−	0.380580i	$-0.875724\pi$
$13$		−	2.74440i		−	0.761160i	0.924748	−	0.380580i	$-0.124276\pi$
$14$	1.65187	+	2.06672i	0.441481	+	0.552354i
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	1.82992	−	3.16952i	0.443821	−	0.768721i	−0.554148	−	0.832418i	$-0.686956\pi$
$17$	1.82992	−	3.16952i	0.443821	−	0.768721i	0.997969	+	0.0636974i	$0.0202893\pi$
$18$		0			0
$19$	3.12125	−	1.80205i	0.716064	−	0.413420i	−0.0972384	−	0.995261i	$-0.531001\pi$
$19$	3.12125	−	1.80205i	0.716064	−	0.413420i	0.813302	+	0.581841i	$0.197668\pi$
$20$		0			0
$21$		0			0
$22$	−0.496352			−0.105823
$23$	5.56351	−	3.21210i	1.16007	−	0.669768i	0.208751	−	0.977969i	$-0.433060\pi$
$23$	5.56351	−	3.21210i	1.16007	−	0.669768i	0.951321	+	0.308200i	$0.0997267\pi$
$24$		0			0
$25$		0			0
$26$	1.37220	+	2.37672i	0.269111	+	0.466114i
$27$		0			0
$28$	−2.46392	−	0.963896i	−0.465637	−	0.182159i
$29$			8.87959i			1.64890i	0.565937	+	0.824449i	$0.308515\pi$
$29$			8.87959i			1.64890i	−0.565937	+	0.824449i	$0.691485\pi$
$30$		0			0
$31$	−6.90736	−	3.98797i	−1.24060	−	0.716260i	−0.271383	−	0.962472i	$-0.587481\pi$
$31$	−6.90736	−	3.98797i	−1.24060	−	0.716260i	−0.969216	+	0.246211i	$0.920814\pi$
$32$	0.866025	+	0.500000i	0.153093	+	0.0883883i
$33$		0			0
$34$			3.65984i			0.627658i
$35$		0			0
$36$		0			0
$37$	1.14545	+	1.98397i	0.188311	+	0.326163i	0.944687	−	0.327973i	$-0.106366\pi$
$37$	1.14545	+	1.98397i	0.188311	+	0.326163i	−0.756377	+	0.654136i	$0.773032\pi$
$38$	−1.80205	+	3.12125i	−0.292332	+	0.506334i
$39$		0			0
$40$		0			0
$41$	−2.22816			−0.347980			−0.173990	−	0.984747i	$-0.555666\pi$
$41$	−2.22816			−0.347980			−0.173990	+	0.984747i	$0.555666\pi$
$42$		0			0
$43$	−2.22575			−0.339424			−0.169712	−	0.985494i	$-0.554284\pi$
$43$	−2.22575			−0.339424			−0.169712	+	0.985494i	$0.554284\pi$
$44$	0.429853	−	0.248176i	0.0648028	−	0.0374139i
$45$		0			0
$46$	−3.21210	+	5.56351i	−0.473598	+	0.820295i
$47$	−3.27213	−	5.66749i	−0.477289	−	0.826688i	0.522373	−	0.852717i	$-0.325047\pi$
$47$	−3.27213	−	5.66749i	−0.477289	−	0.826688i	−0.999661	+	0.0260292i	$0.991714\pi$
$48$		0			0
$49$	−6.68446	+	2.07798i	−0.954923	+	0.296854i
$50$		0			0
$51$		0			0
$52$	−2.37672	−	1.37220i	−0.329592	−	0.190290i
$53$	6.72594	+	3.88322i	0.923879	+	0.533402i	0.884870	−	0.465837i	$-0.154247\pi$
$53$	6.72594	+	3.88322i	0.923879	+	0.533402i	0.0390085	+	0.999239i	$0.487580\pi$
$54$		0			0
$55$		0			0
$56$	2.61577	−	0.397202i	0.349546	−	0.0530784i
$57$		0			0
$58$	−4.43979	−	7.68995i	−0.582973	−	1.00974i
$59$	−3.05194	+	5.28611i	−0.397328	+	0.688193i	−0.993395	−	0.114742i	$-0.963396\pi$
$59$	−3.05194	+	5.28611i	−0.397328	+	0.688193i	0.596067	+	0.802935i	$0.296729\pi$
$60$		0			0
$61$	3.24271	−	1.87218i	0.415187	−	0.239708i	−0.277829	−	0.960630i	$-0.589615\pi$
$61$	3.24271	−	1.87218i	0.415187	−	0.239708i	0.693016	+	0.720922i	$0.256282\pi$
$62$	7.97593			1.01294
$63$		0			0
$64$	−1.00000			−0.125000
$65$		0			0
$66$		0			0
$67$	4.08889	−	7.08216i	0.499537	−	0.865224i	−0.500463	−	0.865758i	$-0.666837\pi$
$67$	4.08889	−	7.08216i	0.499537	−	0.865224i	1.00000		0.000534152i	$0.000170026\pi$
$68$	−1.82992	−	3.16952i	−0.221911	−	0.384360i
$69$		0			0
$70$		0			0
$71$		−	10.3761i		−	1.23141i	−0.787975	−	0.615707i	$-0.788871\pi$
$71$		−	10.3761i		−	1.23141i	0.787975	−	0.615707i	$-0.211129\pi$
$72$		0			0
$73$	−11.3165	−	6.53361i	−1.32450	−	0.764701i	−0.340058	−	0.940405i	$-0.610447\pi$
$73$	−11.3165	−	6.53361i	−1.32450	−	0.764701i	−0.984443	+	0.175704i	$0.943780\pi$
$74$	−1.98397	−	1.14545i	−0.230632	−	0.133156i
$75$		0			0
$76$		−	3.60411i		−	0.413420i
$77$	0.478431	−	1.22297i	0.0545223	−	0.139370i
$78$		0			0
$79$	4.44344	+	7.69627i	0.499926	+	0.865898i	1.00000		8.52501e-5i	$-2.71360e-5\pi$
$79$	4.44344	+	7.69627i	0.499926	+	0.865898i	−0.500074	+	0.865983i	$0.666694\pi$
$80$		0			0
$81$		0			0
$82$	1.92964	−	1.11408i	0.213093	−	0.123030i
$83$	4.79091			0.525871			0.262935	−	0.964813i	$-0.415309\pi$
$83$	4.79091			0.525871			0.262935	+	0.964813i	$0.415309\pi$
$84$		0			0
$85$		0			0
$86$	1.92756	−	1.11288i	0.207854	−	0.120005i
$87$		0			0
$88$	−0.248176	+	0.429853i	−0.0264556	+	0.0458225i
$89$	0.743586	+	1.28793i	0.0788199	+	0.136520i	0.902741	−	0.430184i	$-0.141551\pi$
$89$	0.743586	+	1.28793i	0.0788199	+	0.136520i	−0.823921	+	0.566704i	$0.808218\pi$
$90$		0			0
$91$	−7.17871	+	1.09008i	−0.752534	+	0.114272i
$92$		−	6.42419i		−	0.669768i
$93$		0			0
$94$	5.66749	+	3.27213i	0.584557	+	0.337494i
$95$		0			0
$96$		0			0
$97$		−	9.05174i		−	0.919064i	−0.888161	−	0.459532i	$-0.848017\pi$
$97$		−	9.05174i		−	0.919064i	0.888161	−	0.459532i	$-0.151983\pi$
$98$	4.74992	−	5.14181i	0.479815	−	0.519401i
$99$		0			0
$100$		0			0
$101$	1.50180	−	2.60119i	0.149434	−	0.258828i	−0.781584	−	0.623800i	$-0.785588\pi$
$101$	1.50180	−	2.60119i	0.149434	−	0.258828i	0.931019	+	0.364972i	$0.118921\pi$
$102$		0			0
$103$	−12.4491	+	7.18752i	−1.22665	+	0.708207i	−0.966328	−	0.257314i	$-0.917162\pi$
$103$	−12.4491	+	7.18752i	−1.22665	+	0.708207i	−0.260323	+	0.965522i	$0.583829\pi$
$104$	2.74440			0.269111
$105$		0			0
$106$	−7.76645			−0.754344
$107$	1.84141	−	1.06314i	0.178016	−	0.102778i	−0.408344	−	0.912828i	$-0.633894\pi$
$107$	1.84141	−	1.06314i	0.178016	−	0.102778i	0.586360	+	0.810050i	$0.300560\pi$
$108$		0			0
$109$	−3.95181	+	6.84474i	−0.378515	+	0.655607i	−0.990846	−	0.134994i	$-0.956899\pi$
$109$	−3.95181	+	6.84474i	−0.378515	+	0.655607i	0.612331	+	0.790601i	$0.290232\pi$
$110$		0			0
$111$		0			0
$112$	−2.06672	+	1.65187i	−0.195287	+	0.156087i
$113$		−	12.2968i		−	1.15678i	−0.815760	−	0.578391i	$-0.803681\pi$
$113$		−	12.2968i		−	1.15678i	0.815760	−	0.578391i	$-0.196319\pi$
$114$		0			0
$115$		0			0
$116$	7.68995	+	4.43979i	0.713994	+	0.412224i
$117$		0			0
$118$		−	6.10388i		−	0.561907i
$119$	−9.01756	−	3.52771i	−0.826638	−	0.323384i
$120$		0			0
$121$	−5.37682	−	9.31292i	−0.488802	−	0.846629i
$122$	−1.87218	+	3.24271i	−0.169499	+	0.293581i
$123$		0			0
$124$	−6.90736	+	3.98797i	−0.620299	+	0.358130i
$125$		0			0
$126$		0			0
$127$	−0.753445			−0.0668574			−0.0334287	−	0.999441i	$-0.510643\pi$
$127$	−0.753445			−0.0668574			−0.0334287	+	0.999441i	$0.510643\pi$
$128$	0.866025	−	0.500000i	0.0765466	−	0.0441942i
$129$		0			0
$130$		0			0
$131$	6.35624	+	11.0093i	0.555347	+	0.961890i	0.997876	+	0.0651355i	$0.0207479\pi$
$131$	6.35624	+	11.0093i	0.555347	+	0.961890i	−0.442529	+	0.896754i	$0.645919\pi$
$132$		0			0
$133$	−5.95352	−	7.44868i	−0.516236	−	0.645882i
$134$			8.17778i			0.706452i
$135$		0			0
$136$	3.16952	+	1.82992i	0.271784	+	0.156914i
$137$	3.73673	+	2.15740i	0.319250	+	0.184319i	0.651058	−	0.759028i	$-0.274325\pi$
$137$	3.73673	+	2.15740i	0.319250	+	0.184319i	−0.331808	+	0.943347i	$0.607659\pi$
$138$		0			0
$139$			0.0681276i			0.00577851i	0.999996	+	0.00288926i	$0.000919680\pi$
$139$			0.0681276i			0.00577851i	−0.999996	+	0.00288926i	$0.999080\pi$
$140$		0			0
$141$		0			0
$142$	5.18804	+	8.98595i	0.435371	+	0.754084i
$143$	0.681094	−	1.17969i	0.0569560	−	0.0986507i
$144$		0			0
$145$		0			0
$146$	13.0672			1.08145
$147$		0			0
$148$	2.29090			0.188311
$149$	−14.4611	+	8.34911i	−1.18470	+	0.683986i	−0.957097	−	0.289768i	$-0.906422\pi$
$149$	−14.4611	+	8.34911i	−1.18470	+	0.683986i	−0.227602	+	0.973754i	$0.573088\pi$
$150$		0			0
$151$	6.51016	−	11.2759i	0.529789	−	0.917622i	−0.469607	−	0.882876i	$-0.655604\pi$
$151$	6.51016	−	11.2759i	0.529789	−	0.917622i	0.999396	−	0.0347463i	$-0.0110623\pi$
$152$	1.80205	+	3.12125i	0.146166	+	0.253167i
$153$		0			0
$154$	0.197152	+	1.29834i	0.0158870	+	0.104623i
$155$		0			0
$156$		0			0
$157$	−12.8242	−	7.40408i	−1.02349	−	0.590910i	−0.108374	−	0.994110i	$-0.534564\pi$
$157$	−12.8242	−	7.40408i	−1.02349	−	0.590910i	−0.915112	+	0.403200i	$0.867898\pi$
$158$	−7.69627	−	4.44344i	−0.612282	−	0.353501i
$159$		0			0
$160$		0			0
$161$	−10.6119	−	13.2770i	−0.836337	−	1.04637i
$162$		0			0
$163$	−7.68966	−	13.3189i	−0.602301	−	1.04322i	−0.992472	−	0.122473i	$-0.960918\pi$
$163$	−7.68966	−	13.3189i	−0.602301	−	1.04322i	0.390171	−	0.920742i	$-0.372416\pi$
$164$	−1.11408	+	1.92964i	−0.0869950	+	0.150680i
$165$		0			0
$166$	−4.14905	+	2.39546i	−0.322029	+	0.185923i
$167$	−24.5161			−1.89712			−0.948558	−	0.316603i	$-0.897458\pi$
$167$	−24.5161			−1.89712			−0.948558	+	0.316603i	$0.897458\pi$
$168$		0			0
$169$	5.46825			0.420635
$170$		0			0
$171$		0			0
$172$	−1.11288	+	1.92756i	−0.0848561	+	0.146975i
$173$	6.26213	+	10.8463i	0.476101	+	0.824631i	0.999625	−	0.0273795i	$-0.00871625\pi$
$173$	6.26213	+	10.8463i	0.476101	+	0.824631i	−0.523524	+	0.852011i	$0.675383\pi$
$174$		0			0
$175$		0			0
$176$		−	0.496352i		−	0.0374139i
$177$		0			0
$178$	−1.28793	−	0.743586i	−0.0965343	−	0.0557341i
$179$	1.58961	+	0.917762i	0.118813	+	0.0685968i	0.558229	−	0.829687i	$-0.311481\pi$
$179$	1.58961	+	0.917762i	0.118813	+	0.0685968i	−0.439416	+	0.898284i	$0.644814\pi$
$180$		0			0
$181$		−	23.6564i		−	1.75837i	−0.476481	−	0.879185i	$-0.658088\pi$
$181$		−	23.6564i		−	1.75837i	0.476481	−	0.879185i	$-0.341912\pi$
$182$	5.67191	−	4.53340i	0.420430	−	0.336038i
$183$		0			0
$184$	3.21210	+	5.56351i	0.236799	+	0.410148i
$185$		0			0
$186$		0			0
$187$	1.57319	−	0.908284i	0.115043	−	0.0664203i
$188$	−6.54425			−0.477289
$189$		0			0
$190$		0			0
$191$	−7.02253	+	4.05446i	−0.508133	+	0.293371i	−0.732066	−	0.681234i	$-0.761444\pi$
$191$	−7.02253	+	4.05446i	−0.508133	+	0.293371i	0.223933	+	0.974605i	$0.428110\pi$
$192$		0			0
$193$	−6.02502	+	10.4356i	−0.433691	+	0.751174i	−0.997188	−	0.0749438i	$-0.976122\pi$
$193$	−6.02502	+	10.4356i	−0.433691	+	0.751174i	0.563497	+	0.826118i	$0.309456\pi$
$194$	4.52587	+	7.83903i	0.324938	+	0.562810i
$195$		0			0
$196$	−1.54265	+	6.82790i	−0.110189	+	0.487707i
$197$		−	12.7463i		−	0.908137i	−0.890967	−	0.454068i	$-0.849972\pi$
$197$		−	12.7463i		−	0.908137i	0.890967	−	0.454068i	$-0.150028\pi$
$198$		0			0
$199$	16.4954	+	9.52361i	1.16933	+	0.675111i	0.953521	−	0.301325i	$-0.0974290\pi$
$199$	16.4954	+	9.52361i	1.16933	+	0.675111i	0.215805	+	0.976436i	$0.430762\pi$
$200$		0			0
$201$		0			0
$202$			3.00359i			0.211332i
$203$	23.2269	−	3.52699i	1.63021	−	0.247546i
$204$		0			0
$205$		0			0
$206$	7.18752	−	12.4491i	0.500778	−	0.867373i
$207$		0			0
$208$	−2.37672	+	1.37220i	−0.164796	+	0.0951450i
$209$	1.78891			0.123741
$210$		0			0
$211$	−8.92057			−0.614117			−0.307059	−	0.951691i	$-0.599345\pi$
$211$	−8.92057			−0.614117			−0.307059	+	0.951691i	$0.599345\pi$
$212$	6.72594	−	3.88322i	0.461939	−	0.266701i
$213$		0			0
$214$	−1.06314	+	1.84141i	−0.0726748	+	0.125876i
$215$		0			0
$216$		0			0
$217$	−7.68797	+	19.6521i	−0.521893	+	1.33407i
$218$		−	7.90363i		−	0.535301i
$219$		0			0
$220$		0			0
$221$	−8.69843	−	5.02204i	−0.585120	−	0.337819i
$222$		0			0
$223$		−	23.5443i		−	1.57664i	−0.615265	−	0.788320i	$-0.710951\pi$
$223$		−	23.5443i		−	1.57664i	0.615265	−	0.788320i	$-0.289049\pi$
$224$	0.963896	−	2.46392i	0.0644030	−	0.164628i
$225$		0			0
$226$	6.14838	+	10.6493i	0.408984	+	0.708382i
$227$	4.66223	−	8.07522i	0.309443	−	0.535971i	−0.668797	−	0.743445i	$-0.733191\pi$
$227$	4.66223	−	8.07522i	0.309443	−	0.535971i	0.978241	+	0.207473i	$0.0665240\pi$
$228$		0			0
$229$	20.1545	−	11.6362i	1.33185	−	0.768944i	0.346266	−	0.938136i	$-0.387449\pi$
$229$	20.1545	−	11.6362i	1.33185	−	0.768944i	0.985583	+	0.169193i	$0.0541160\pi$
$230$		0			0
$231$		0			0
$232$	−8.87959			−0.582973
$233$	10.9295	−	6.31017i	0.716018	−	0.413393i	−0.0972676	−	0.995258i	$-0.531010\pi$
$233$	10.9295	−	6.31017i	0.716018	−	0.413393i	0.813285	+	0.581865i	$0.197677\pi$
$234$		0			0
$235$		0			0
$236$	3.05194	+	5.28611i	0.198664	+	0.344097i
$237$		0			0
$238$	9.57329	−	1.45370i	0.620544	−	0.0942292i
$239$		−	16.1198i		−	1.04270i	−0.853342	−	0.521351i	$-0.825428\pi$
$239$		−	16.1198i		−	1.04270i	0.853342	−	0.521351i	$-0.174572\pi$
$240$		0			0
$241$	−18.3222	−	10.5783i	−1.18024	−	0.681411i	−0.224168	−	0.974550i	$-0.571966\pi$
$241$	−18.3222	−	10.5783i	−1.18024	−	0.681411i	−0.956070	+	0.293140i	$0.905300\pi$
$242$	9.31292	+	5.37682i	0.598657	+	0.345635i
$243$		0			0
$244$		−	3.74436i		−	0.239708i
$245$		0			0
$246$		0			0
$247$	−4.94556	−	8.56597i	−0.314679	−	0.545039i
$248$	3.98797	−	6.90736i	0.253236	−	0.438618i
$249$		0			0
$250$		0			0
$251$	−6.06317			−0.382704			−0.191352	−	0.981522i	$-0.561287\pi$
$251$	−6.06317			−0.382704			−0.191352	+	0.981522i	$0.561287\pi$
$252$		0			0
$253$	3.18866			0.200469
$254$	0.652503	−	0.376723i	0.0409416	−	0.0236377i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	5.49266	+	9.51357i	0.342623	+	0.593440i	0.984919	−	0.173016i	$-0.0553513\pi$
$257$	5.49266	+	9.51357i	0.342623	+	0.593440i	−0.642296	+	0.766457i	$0.722018\pi$
$258$		0			0
$259$	4.73464	−	3.78426i	0.294196	−	0.235143i
$260$		0			0
$261$		0			0
$262$	−11.0093	−	6.35624i	−0.680159	−	0.392690i
$263$	−1.15937	−	0.669365i	−0.0714901	−	0.0412748i	0.463829	−	0.885925i	$-0.346475\pi$
$263$	−1.15937	−	0.669365i	−0.0714901	−	0.0412748i	−0.535319	+	0.844650i	$0.679809\pi$
$264$		0			0
$265$		0			0
$266$	8.88024	+	3.47399i	0.544482	+	0.213004i
$267$		0			0
$268$	−4.08889	−	7.08216i	−0.249769	−	0.432612i
$269$	−0.311161	+	0.538946i	−0.0189718	+	0.0328601i	−0.875355	−	0.483480i	$-0.839373\pi$
$269$	−0.311161	+	0.538946i	−0.0189718	+	0.0328601i	0.856384	+	0.516340i	$0.172706\pi$
$270$		0			0
$271$	18.4634	−	10.6598i	1.12157	−	0.647539i	0.179769	−	0.983709i	$-0.442465\pi$
$271$	18.4634	−	10.6598i	1.12157	−	0.647539i	0.941801	+	0.336170i	$0.109132\pi$
$272$	−3.65984			−0.221911
$273$		0			0
$274$	−4.31480			−0.260667
$275$		0			0
$276$		0			0
$277$	0.593544	−	1.02805i	0.0356626	−	0.0617694i	−0.847643	−	0.530567i	$-0.821979\pi$
$277$	0.593544	−	1.02805i	0.0356626	−	0.0617694i	0.883306	+	0.468797i	$0.155312\pi$
$278$	−0.0340638	−	0.0590003i	−0.00204301	−	0.00353860i
$279$		0			0
$280$		0			0
$281$		−	1.97593i		−	0.117874i	−0.998262	−	0.0589370i	$-0.981229\pi$
$281$		−	1.97593i		−	0.117874i	0.998262	−	0.0589370i	$-0.0187711\pi$
$282$		0			0
$283$	23.4960	+	13.5654i	1.39669	+	0.806382i	0.994045	−	0.108972i	$-0.0347560\pi$
$283$	23.4960	+	13.5654i	1.39669	+	0.806382i	0.402650	+	0.915354i	$0.368089\pi$
$284$	−8.98595	−	5.18804i	−0.533218	−	0.307853i
$285$		0			0
$286$			1.36219i			0.0805479i
$287$	0.885030	+	5.82835i	0.0522417	+	0.344036i
$288$		0			0
$289$	1.80278	+	3.12250i	0.106046	+	0.183677i
$290$		0			0
$291$		0			0
$292$	−11.3165	+	6.53361i	−0.662250	+	0.382350i
$293$	−10.3808			−0.606456			−0.303228	−	0.952918i	$-0.598064\pi$
$293$	−10.3808			−0.606456			−0.303228	+	0.952918i	$0.598064\pi$
$294$		0			0
$295$		0			0
$296$	−1.98397	+	1.14545i	−0.115316	+	0.0665778i
$297$		0			0
$298$	8.34911	−	14.4611i	0.483651	−	0.837708i
$299$	−8.81529	−	15.2685i	−0.509801	−	0.883002i
$300$		0			0
$301$	0.884074	+	5.82205i	0.0509572	+	0.335577i
$302$			13.0203i			0.749235i
$303$		0			0
$304$	−3.12125	−	1.80205i	−0.179016	−	0.103355i
$305$		0			0
$306$		0			0
$307$		−	14.1364i		−	0.806808i	−0.915022	−	0.403404i	$-0.867827\pi$
$307$		−	14.1364i		−	0.806808i	0.915022	−	0.403404i	$-0.132173\pi$
$308$	−0.819908	−	1.02582i	−0.0467186	−	0.0584515i
$309$		0			0
$310$		0			0
$311$	3.32643	−	5.76155i	0.188625	−	0.326708i	−0.756167	−	0.654378i	$-0.772930\pi$
$311$	3.32643	−	5.76155i	0.188625	−	0.326708i	0.944792	+	0.327671i	$0.106264\pi$
$312$		0			0
$313$	−10.5184	+	6.07282i	−0.594537	+	0.343256i	−0.766890	−	0.641779i	$-0.778197\pi$
$313$	−10.5184	+	6.07282i	−0.594537	+	0.343256i	0.172352	+	0.985035i	$0.444863\pi$
$314$	14.8082			0.835673
$315$		0			0
$316$	8.88688			0.499926
$317$	−26.6051	+	15.3605i	−1.49429	+	0.862730i	−0.999979	−	0.00655283i	$-0.997914\pi$
$317$	−26.6051	+	15.3605i	−1.49429	+	0.862730i	−0.494314	+	0.869283i	$0.664581\pi$
$318$		0			0
$319$	−2.20370	+	3.81692i	−0.123383	+	0.213706i
$320$		0			0
$321$		0			0
$322$	15.8287	+	6.19225i	0.882099	+	0.345081i
$323$		−	13.1905i		−	0.733937i
$324$		0			0
$325$		0			0
$326$	13.3189	+	7.68966i	0.737665	+	0.425891i
$327$		0			0
$328$		−	2.22816i		−	0.123030i
$329$	−13.5251	+	10.8103i	−0.745664	+	0.595989i
$330$		0			0
$331$	15.5140	+	26.8710i	0.852724	+	1.47696i	0.878741	+	0.477300i	$0.158384\pi$
$331$	15.5140	+	26.8710i	0.852724	+	1.47696i	−0.0260166	+	0.999662i	$0.508282\pi$
$332$	2.39546	−	4.14905i	0.131468	−	0.227709i
$333$		0			0
$334$	21.2316	−	12.2581i	1.16174	−	0.670732i
$335$		0			0
$336$		0			0
$337$	6.91470			0.376668			0.188334	−	0.982105i	$-0.439691\pi$
$337$	6.91470			0.376668			0.188334	+	0.982105i	$0.439691\pi$
$338$	−4.73565	+	2.73413i	−0.257585	+	0.148717i
$339$		0			0
$340$		0			0
$341$	−1.97943	−	3.42848i	−0.107192	−	0.185663i
$342$		0			0
$343$	8.09058	+	16.6596i	0.436850	+	0.899534i
$344$		−	2.22575i		−	0.120005i
$345$		0			0
$346$	−10.8463	−	6.26213i	−0.583103	−	0.336654i
$347$	−6.49006	−	3.74704i	−0.348405	−	0.201152i	0.315578	−	0.948900i	$-0.397802\pi$
$347$	−6.49006	−	3.74704i	−0.348405	−	0.201152i	−0.663982	+	0.747748i	$0.731135\pi$
$348$		0			0
$349$		−	12.4552i		−	0.666714i	−0.942801	−	0.333357i	$-0.891819\pi$
$349$		−	12.4552i		−	0.666714i	0.942801	−	0.333357i	$-0.108181\pi$
$350$		0			0
$351$		0			0
$352$	0.248176	+	0.429853i	0.0132278	+	0.0229113i
$353$	−9.47011	+	16.4027i	−0.504043	+	0.873028i	0.495946	+	0.868353i	$0.334821\pi$
$353$	−9.47011	+	16.4027i	−0.504043	+	0.873028i	−0.999989	+	0.00467471i	$0.998512\pi$
$354$		0			0
$355$		0			0
$356$	1.48717			0.0788199
$357$		0			0
$358$	−1.83552			−0.0970105
$359$	23.0590	−	13.3131i	1.21701	−	0.702639i	0.252730	−	0.967537i	$-0.418671\pi$
$359$	23.0590	−	13.3131i	1.21701	−	0.702639i	0.964277	+	0.264898i	$0.0853381\pi$
$360$		0			0
$361$	−3.00520	+	5.20516i	−0.158168	+	0.273956i
$362$	11.8282	+	20.4871i	0.621677	+	1.07678i
$363$		0			0
$364$	−2.64532	+	6.76199i	−0.138652	+	0.354425i
$365$		0			0
$366$		0			0
$367$	−9.45017	−	5.45606i	−0.493295	−	0.284804i	0.232646	−	0.972562i	$-0.425262\pi$
$367$	−9.45017	−	5.45606i	−0.493295	−	0.284804i	−0.725940	+	0.687758i	$0.758595\pi$
$368$	−5.56351	−	3.21210i	−0.290018	−	0.167442i
$369$		0			0
$370$		0			0
$371$	7.48604	−	19.1359i	0.388656	−	0.993487i
$372$		0			0
$373$	−11.2539	−	19.4924i	−0.582707	−	1.00928i	−0.995157	−	0.0982976i	$-0.968660\pi$
$373$	−11.2539	−	19.4924i	−0.582707	−	1.00928i	0.412450	−	0.910980i	$-0.364673\pi$
$374$	−0.908284	+	1.57319i	−0.0469663	+	0.0813480i
$375$		0			0
$376$	5.66749	−	3.27213i	0.292278	−	0.168747i
$377$	24.3692			1.25508
$378$		0			0
$379$	−3.25909			−0.167408			−0.0837040	−	0.996491i	$-0.526675\pi$
$379$	−3.25909			−0.167408			−0.0837040	+	0.996491i	$0.526675\pi$
$380$		0			0
$381$		0			0
$382$	4.05446	−	7.02253i	0.207444	−	0.359304i
$383$	−8.66098	−	15.0013i	−0.442555	−	0.766528i	0.555323	−	0.831635i	$-0.312595\pi$
$383$	−8.66098	−	15.0013i	−0.442555	−	0.766528i	−0.997878	+	0.0651064i	$0.979261\pi$
$384$		0			0
$385$		0			0
$386$		−	12.0500i		−	0.613331i
$387$		0			0
$388$	−7.83903	−	4.52587i	−0.397967	−	0.229766i
$389$	−27.4515	−	15.8491i	−1.39185	−	0.803582i	−0.398326	−	0.917244i	$-0.630409\pi$
$389$	−27.4515	−	15.8491i	−1.39185	−	0.803582i	−0.993520	+	0.113662i	$0.963742\pi$
$390$		0			0
$391$		−	23.5115i		−	1.18903i
$392$	−2.07798	−	6.68446i	−0.104954	−	0.337616i
$393$		0			0
$394$	6.37315	+	11.0386i	0.321075	+	0.556118i
$395$		0			0
$396$		0			0
$397$	29.0224	−	16.7561i	1.45659	−	0.840964i	0.457750	−	0.889081i	$-0.348655\pi$
$397$	29.0224	−	16.7561i	1.45659	−	0.840964i	0.998842	+	0.0481170i	$0.0153220\pi$
$398$	−19.0472			−0.954751
$399$		0			0
$400$		0			0
$401$	−31.0404	+	17.9212i	−1.55008	+	0.894940i	−0.551947	+	0.833879i	$0.686115\pi$
$401$	−31.0404	+	17.9212i	−1.55008	+	0.894940i	−0.998134	+	0.0610611i	$0.980552\pi$
$402$		0			0
$403$	−10.9446	+	18.9566i	−0.545189	+	0.944295i
$404$	−1.50180	−	2.60119i	−0.0747171	−	0.129414i
$405$		0			0
$406$	−18.3516	+	14.6679i	−0.910775	+	0.727957i
$407$			1.13709i			0.0563635i
$408$		0			0
$409$	−21.3474	−	12.3249i	−1.05556	−	0.609429i	−0.131361	−	0.991335i	$-0.541935\pi$
$409$	−21.3474	−	12.3249i	−1.05556	−	0.609429i	−0.924201	+	0.381905i	$0.875268\pi$
$410$		0			0
$411$		0			0
$412$			14.3750i			0.708207i
$413$	15.0395	+	5.88350i	0.740044	+	0.289508i
$414$		0			0
$415$		0			0
$416$	1.37220	−	2.37672i	0.0672777	−	0.116528i
$417$		0			0
$418$	−1.54924	+	0.894453i	−0.0757757	+	0.0437491i
$419$	10.6574			0.520646			0.260323	−	0.965522i	$-0.416171\pi$
$419$	10.6574			0.520646			0.260323	+	0.965522i	$0.416171\pi$
$420$		0			0
$421$	22.6815			1.10543			0.552714	−	0.833371i	$-0.313592\pi$
$421$	22.6815			1.10543			0.552714	+	0.833371i	$0.313592\pi$
$422$	7.72544	−	4.46028i	0.376068	−	0.217123i
$423$		0			0
$424$	−3.88322	+	6.72594i	−0.188586	+	0.326641i
$425$		0			0
$426$		0			0
$427$	−6.18520	−	7.73854i	−0.299323	−	0.374494i
$428$		−	2.12628i		−	0.102778i
$429$		0			0
$430$		0			0
$431$	−26.0439	−	15.0364i	−1.25449	−	0.724279i	−0.282491	−	0.959270i	$-0.591161\pi$
$431$	−26.0439	−	15.0364i	−1.25449	−	0.724279i	−0.971998	+	0.234991i	$0.924494\pi$
$432$		0			0
$433$			14.9203i			0.717025i	0.933525	+	0.358512i	$0.116716\pi$
$433$			14.9203i			0.717025i	−0.933525	+	0.358512i	$0.883284\pi$
$434$	−3.16806	−	20.8632i	−0.152072	−	1.00146i
$435$		0			0
$436$	3.95181	+	6.84474i	0.189258	+	0.327804i
$437$	11.5767	−	20.0515i	0.553791	−	0.959194i
$438$		0			0
$439$	11.1126	−	6.41586i	0.530375	−	0.306212i	−0.210794	−	0.977530i	$-0.567605\pi$
$439$	11.1126	−	6.41586i	0.530375	−	0.306212i	0.741169	+	0.671318i	$0.234272\pi$
$440$		0			0
$441$		0			0
$442$	10.0441			0.477748
$443$	17.6792	−	10.2071i	0.839963	−	0.484953i	−0.0172887	−	0.999851i	$-0.505503\pi$
$443$	17.6792	−	10.2071i	0.839963	−	0.484953i	0.857252	+	0.514898i	$0.172170\pi$
$444$		0			0
$445$		0			0
$446$	11.7721	+	20.3899i	0.557426	+	0.965491i
$447$		0			0
$448$	0.397202	+	2.61577i	0.0187660	+	0.123583i
$449$			20.8404i			0.983519i	0.870731	+	0.491760i	$0.163646\pi$
$449$			20.8404i			0.983519i	−0.870731	+	0.491760i	$0.836354\pi$
$450$		0			0
$451$	−0.957782	−	0.552976i	−0.0451002	−	0.0260386i
$452$	−10.6493	−	6.14838i	−0.500901	−	0.289196i
$453$		0			0
$454$			9.32446i			0.437619i
$455$		0			0
$456$		0			0
$457$	8.01424	+	13.8811i	0.374890	+	0.649329i	0.990311	−	0.138870i	$-0.0443470\pi$
$457$	8.01424	+	13.8811i	0.374890	+	0.649329i	−0.615420	+	0.788199i	$0.711014\pi$
$458$	−11.6362	+	20.1545i	−0.543725	+	0.941760i
$459$		0			0
$460$		0			0
$461$	−1.98400			−0.0924039			−0.0462020	−	0.998932i	$-0.514712\pi$
$461$	−1.98400			−0.0924039			−0.0462020	+	0.998932i	$0.514712\pi$
$462$		0			0
$463$	36.3987			1.69159			0.845796	−	0.533506i	$-0.179126\pi$
$463$	36.3987			1.69159			0.845796	+	0.533506i	$0.179126\pi$
$464$	7.68995	−	4.43979i	0.356997	−	0.206112i
$465$		0			0
$466$	−6.31017	+	10.9295i	−0.292313	+	0.506301i
$467$	15.5372	+	26.9113i	0.718977	+	1.24530i	0.961405	+	0.275136i	$0.0887227\pi$
$467$	15.5372	+	26.9113i	0.718977	+	1.24530i	−0.242428	+	0.970169i	$0.577944\pi$
$468$		0			0
$469$	−20.1494	−	7.88253i	−0.930413	−	0.363981i
$470$		0			0
$471$		0			0
$472$	−5.28611	−	3.05194i	−0.243313	−	0.140477i
$473$	−0.956747	−	0.552378i	−0.0439913	−	0.0253984i
$474$		0			0
$475$		0			0
$476$	−7.56386	+	6.04558i	−0.346689	+	0.277099i
$477$		0			0
$478$	8.05990	+	13.9601i	0.368651	+	0.638522i
$479$	18.2404	−	31.5933i	0.833426	−	1.44354i	−0.0618788	−	0.998084i	$-0.519709\pi$
$479$	18.2404	−	31.5933i	0.833426	−	1.44354i	0.895305	−	0.445453i	$-0.146957\pi$
$480$		0			0
$481$	5.44483	−	3.14357i	0.248263	−	0.143335i
$482$	21.1567			0.963660
$483$		0			0
$484$	−10.7536			−0.488802
$485$		0			0
$486$		0			0
$487$	−7.06672	+	12.2399i	−0.320224	+	0.554644i	−0.980534	−	0.196349i	$-0.937091\pi$
$487$	−7.06672	+	12.2399i	−0.320224	+	0.554644i	0.660310	+	0.750993i	$0.270425\pi$
$488$	1.87218	+	3.24271i	0.0847496	+	0.146791i
$489$		0			0
$490$		0			0
$491$		−	32.5466i		−	1.46881i	−0.678714	−	0.734403i	$-0.737462\pi$
$491$		−	32.5466i		−	1.46881i	0.678714	−	0.734403i	$-0.262538\pi$
$492$		0			0
$493$	28.1440	+	16.2489i	1.26754	+	0.731815i
$494$	8.56597	+	4.94556i	0.385401	+	0.222511i
$495$		0			0
$496$			7.97593i			0.358130i
$497$	−27.1414	+	4.12140i	−1.21746	+	0.184870i
$498$		0			0
$499$	−5.87396	−	10.1740i	−0.262955	−	0.455451i	0.704071	−	0.710130i	$-0.251364\pi$
$499$	−5.87396	−	10.1740i	−0.262955	−	0.455451i	−0.967026	+	0.254679i	$0.918030\pi$
$500$		0			0
$501$		0			0
$502$	5.25086	−	3.03158i	0.234357	−	0.135306i
$503$	−24.5250			−1.09352			−0.546758	−	0.837291i	$-0.684138\pi$
$503$	−24.5250			−1.09352			−0.546758	+	0.837291i	$0.684138\pi$
$504$		0			0
$505$		0			0
$506$	−2.76146	+	1.59433i	−0.122762	+	0.0708766i
$507$		0			0
$508$	−0.376723	+	0.652503i	−0.0167144	+	0.0289501i
$509$	−5.84634	−	10.1262i	−0.259135	−	0.448834i	0.706876	−	0.707338i	$-0.250104\pi$
$509$	−5.84634	−	10.1262i	−0.259135	−	0.448834i	−0.966010	+	0.258503i	$0.916771\pi$
$510$		0			0
$511$	−12.5954	+	32.1966i	−0.557189	+	1.42429i
$512$		−	1.00000i		−	0.0441942i
$513$		0			0
$514$	−9.51357	−	5.49266i	−0.419626	−	0.242271i
$515$		0			0
$516$		0			0
$517$		−	3.24825i		−	0.142858i
$518$	−2.20819	+	5.64459i	−0.0970221	+	0.248009i
$519$		0			0
$520$		0			0
$521$	−14.8674	+	25.7511i	−0.651354	+	1.12818i	0.331441	+	0.943476i	$0.392465\pi$
$521$	−14.8674	+	25.7511i	−0.651354	+	1.12818i	−0.982795	+	0.184702i	$0.940868\pi$
$522$		0			0
$523$	−4.90024	+	2.82915i	−0.214272	+	0.123710i	−0.603295	−	0.797518i	$-0.706146\pi$
$523$	−4.90024	+	2.82915i	−0.214272	+	0.123710i	0.389023	+	0.921228i	$0.372813\pi$
$524$	12.7125			0.555347
$525$		0			0
$526$	1.33873			0.0583714
$527$	−25.2799	+	14.5953i	−1.10121	+	0.635783i
$528$		0			0
$529$	9.13513	−	15.8225i	0.397179	−	0.687935i
$530$		0			0
$531$		0			0
$532$	−9.42751	+	1.43156i	−0.408734	+	0.0620660i
$533$			6.11497i			0.264869i
$534$		0			0
$535$		0			0
$536$	7.08216	+	4.08889i	0.305903	+	0.176613i
$537$		0			0
$538$		−	0.622322i		−	0.0268302i
$539$	−3.38904	−	0.765697i	−0.145976	−	0.0329809i
$540$		0			0
$541$	17.6742	+	30.6126i	0.759874	+	1.31614i	0.942915	+	0.333035i	$0.108073\pi$
$541$	17.6742	+	30.6126i	0.759874	+	1.31614i	−0.183041	+	0.983105i	$0.558594\pi$
$542$	−10.6598	+	18.4634i	−0.457879	+	0.793070i
$543$		0			0
$544$	3.16952	−	1.82992i	0.135892	−	0.0784572i
$545$		0			0
$546$		0			0
$547$	−21.4806			−0.918445			−0.459223	−	0.888321i	$-0.651872\pi$
$547$	−21.4806			−0.918445			−0.459223	+	0.888321i	$0.651872\pi$
$548$	3.73673	−	2.15740i	0.159625	−	0.0921595i
$549$		0			0
$550$		0			0
$551$	16.0015	+	27.7154i	0.681687	+	1.18072i
$552$		0			0
$553$	18.3667	−	14.6800i	0.781031	−	0.624256i
$554$			1.18709i			0.0504345i
$555$		0			0
$556$	0.0590003	+	0.0340638i	0.00250217	+	0.00144463i
$557$	34.4939	+	19.9150i	1.46155	+	0.843828i	0.999083	−	0.0428076i	$-0.0136303\pi$
$557$	34.4939	+	19.9150i	1.46155	+	0.843828i	0.462469	+	0.886635i	$0.346964\pi$
$558$		0			0
$559$			6.10836i			0.258356i
$560$		0			0
$561$		0			0
$562$	0.987964	+	1.71120i	0.0416747	+	0.0721828i
$563$	−5.17056	+	8.95567i	−0.217913	+	0.377437i	−0.954170	−	0.299266i	$-0.903258\pi$
$563$	−5.17056	+	8.95567i	−0.217913	+	0.377437i	0.736257	+	0.676702i	$0.236592\pi$
$564$		0			0
$565$		0			0
$566$	−27.1309			−1.14040
$567$		0			0
$568$	10.3761			0.435371
$569$	−24.3464	+	14.0564i	−1.02065	+	0.589275i	−0.914293	−	0.405053i	$-0.867253\pi$
$569$	−24.3464	+	14.0564i	−1.02065	+	0.589275i	−0.106361	+	0.994328i	$0.533920\pi$
$570$		0			0
$571$	13.7146	−	23.7544i	0.573938	−	0.994090i	−0.422218	−	0.906494i	$-0.638748\pi$
$571$	13.7146	−	23.7544i	0.573938	−	0.994090i	0.996156	−	0.0875958i	$-0.0279184\pi$
$572$	−0.681094	−	1.17969i	−0.0284780	−	0.0493253i
$573$		0			0
$574$	−3.68063	−	4.60498i	−0.153627	−	0.192208i
$575$		0			0
$576$		0			0
$577$	11.2914	+	6.51910i	0.470068	+	0.271394i	0.716268	−	0.697825i	$-0.245849\pi$
$577$	11.2914	+	6.51910i	0.470068	+	0.271394i	−0.246200	+	0.969219i	$0.579182\pi$
$578$	−3.12250	−	1.80278i	−0.129879	−	0.0749857i
$579$		0			0
$580$		0			0
$581$	−1.90296	−	12.5319i	−0.0789481	−	0.519911i
$582$		0			0
$583$	1.92744	+	3.33843i	0.0798266	+	0.138264i
$584$	6.53361	−	11.3165i	0.270363	−	0.468282i
$585$		0			0
$586$	8.99008	−	5.19042i	0.371377	−	0.214414i
$587$	−35.0223			−1.44553			−0.722763	−	0.691096i	$-0.757128\pi$
$587$	−35.0223			−1.44553			−0.722763	+	0.691096i	$0.757128\pi$
$588$		0			0
$589$	−28.7461			−1.18446
$590$		0			0
$591$		0			0
$592$	1.14545	−	1.98397i	0.0470776	−	0.0815409i
$593$	8.19370	+	14.1919i	0.336475	+	0.582792i	0.983767	−	0.179450i	$-0.0574319\pi$
$593$	8.19370	+	14.1919i	0.336475	+	0.582792i	−0.647292	+	0.762242i	$0.724099\pi$
$594$		0			0
$595$		0			0
$596$			16.6982i			0.683986i
$597$		0			0
$598$	15.2685	+	8.81529i	0.624376	+	0.360484i
$599$	26.0718	+	15.0526i	1.06527	+	0.615032i	0.926884	−	0.375347i	$-0.122476\pi$
$599$	26.0718	+	15.0526i	1.06527	+	0.615032i	0.138382	+	0.990379i	$0.455810\pi$
$600$		0			0
$601$		−	1.75569i		−	0.0716162i	−0.999359	−	0.0358081i	$-0.988599\pi$
$601$		−	1.75569i		−	0.0716162i	0.999359	−	0.0358081i	$-0.0114005\pi$
$602$	−3.67666	−	4.60001i	−0.149849	−	0.187482i
$603$		0			0
$604$	−6.51016	−	11.2759i	−0.264895	−	0.458811i
$605$		0			0
$606$		0			0
$607$	15.6511	−	9.03616i	0.635258	−	0.366766i	−0.147528	−	0.989058i	$-0.547132\pi$
$607$	15.6511	−	9.03616i	0.635258	−	0.366766i	0.782785	+	0.622292i	$0.213798\pi$
$608$	3.60411			0.146166
$609$		0			0
$610$		0			0
$611$	−15.5539	+	8.98003i	−0.629242	+	0.363293i
$612$		0			0
$613$	−6.42507	+	11.1285i	−0.259506	+	0.449478i	−0.966110	−	0.258132i	$-0.916893\pi$
$613$	−6.42507	+	11.1285i	−0.259506	+	0.449478i	0.706604	+	0.707610i	$0.250226\pi$
$614$	7.06821	+	12.2425i	0.285250	+	0.494067i
$615$		0			0
$616$	1.22297	+	0.478431i	0.0492749	+	0.0192765i
$617$		−	37.3633i		−	1.50419i	−0.659055	−	0.752094i	$-0.729044\pi$
$617$		−	37.3633i		−	1.50419i	0.659055	−	0.752094i	$-0.270956\pi$
$618$		0			0
$619$	23.7213	+	13.6955i	0.953439	+	0.550468i	0.894147	−	0.447773i	$-0.147783\pi$
$619$	23.7213	+	13.6955i	0.953439	+	0.550468i	0.0592911	+	0.998241i	$0.481116\pi$
$620$		0			0
$621$		0			0
$622$			6.65287i			0.266756i
$623$	3.07356	−	2.45661i	0.123140	−	0.0984222i
$624$		0			0
$625$		0			0
$626$	6.07282	−	10.5184i	0.242719	−	0.420401i
$627$		0			0
$628$	−12.8242	+	7.40408i	−0.511743	+	0.295455i
$629$	8.38432			0.334305
$630$		0			0
$631$	−4.09420			−0.162987			−0.0814937	−	0.996674i	$-0.525969\pi$
$631$	−4.09420			−0.162987			−0.0814937	+	0.996674i	$0.525969\pi$
$632$	−7.69627	+	4.44344i	−0.306141	+	0.176751i
$633$		0			0
$634$	15.3605	−	26.6051i	0.610043	−	1.05662i
$635$		0			0
$636$		0			0
$637$	5.70280	+	18.3449i	0.225953	+	0.726850i
$638$		−	4.40740i		−	0.174491i
$639$		0			0
$640$		0			0
$641$	28.4700	+	16.4371i	1.12450	+	0.649228i	0.942545	−	0.334080i	$-0.108426\pi$
$641$	28.4700	+	16.4371i	1.12450	+	0.649228i	0.181951	+	0.983308i	$0.441759\pi$
$642$		0			0
$643$			48.1790i			1.89999i	0.312261	+	0.949996i	$0.398914\pi$
$643$			48.1790i			1.89999i	−0.312261	+	0.949996i	$0.601086\pi$
$644$	−16.8042	+	2.55170i	−0.662178	+	0.100551i
$645$		0			0
$646$	6.59524	+	11.4233i	0.259486	+	0.449443i
$647$	−2.64703	+	4.58478i	−0.104065	+	0.180246i	−0.913356	−	0.407162i	$-0.866518\pi$
$647$	−2.64703	+	4.58478i	−0.104065	+	0.180246i	0.809291	+	0.587408i	$0.199852\pi$
$648$		0			0
$649$	−2.62377	+	1.51483i	−0.102992	+	0.0594625i
$650$		0			0
$651$		0			0
$652$	−15.3793			−0.602301
$653$	−43.4057	+	25.0603i	−1.69860	+	0.980686i	−0.751503	+	0.659729i	$0.770671\pi$
$653$	−43.4057	+	25.0603i	−1.69860	+	0.980686i	−0.947094	+	0.320956i	$0.895996\pi$
$654$		0			0
$655$		0			0
$656$	1.11408	+	1.92964i	0.0434975	+	0.0753399i
$657$		0			0
$658$	6.30798	−	16.1245i	0.245911	−	0.628599i
$659$			2.20149i			0.0857579i	0.999080	+	0.0428790i	$0.0136530\pi$
$659$			2.20149i			0.0857579i	−0.999080	+	0.0428790i	$0.986347\pi$
$660$		0			0
$661$	−33.7612	−	19.4921i	−1.31316	−	0.758153i	−0.330542	−	0.943791i	$-0.607231\pi$
$661$	−33.7612	−	19.4921i	−1.31316	−	0.758153i	−0.982618	+	0.185638i	$0.940565\pi$
$662$	−26.8710	−	15.5140i	−1.04437	−	0.602967i
$663$		0			0
$664$			4.79091i			0.185923i
$665$		0			0
$666$		0			0
$667$	28.5221	+	49.4017i	1.10438	+	1.91284i
$668$	−12.2581	+	21.2316i	−0.474279	+	0.821475i
$669$		0			0
$670$		0			0
$671$	1.85852			0.0717473
$672$		0			0
$673$	43.4830			1.67615			0.838074	−	0.545556i	$-0.183682\pi$
$673$	43.4830			1.67615			0.838074	+	0.545556i	$0.183682\pi$
$674$	−5.98830	+	3.45735i	−0.230661	+	0.133172i
$675$		0			0
$676$	2.73413	−	4.73565i	0.105159	−	0.182140i
$677$	−20.8309	−	36.0802i	−0.800597	−	1.38668i	−0.919223	−	0.393736i	$-0.871182\pi$
$677$	−20.8309	−	36.0802i	−0.800597	−	1.38668i	0.118626	−	0.992939i	$-0.462151\pi$
$678$		0			0
$679$	−23.6772	+	3.59537i	−0.908648	+	0.137978i
$680$		0			0
$681$		0			0
$682$	3.42848	+	1.97943i	0.131283	+	0.0757965i
$683$	41.3332	+	23.8637i	1.58157	+	0.913120i	0.994631	+	0.103490i	$0.0330010\pi$
$683$	41.3332	+	23.8637i	1.58157	+	0.913120i	0.586940	+	0.809630i	$0.300332\pi$
$684$		0			0
$685$		0			0
$686$	−15.3365	−	10.3824i	−0.585548	−	0.396400i
$687$		0			0
$688$	1.11288	+	1.92756i	0.0424280	+	0.0734875i
$689$	10.6571	−	18.4587i	0.406004	−	0.703220i
$690$		0			0
$691$	33.6953	−	19.4540i	1.28183	−	0.740066i	0.304648	−	0.952465i	$-0.401461\pi$
$691$	33.6953	−	19.4540i	1.28183	−	0.740066i	0.977183	+	0.212399i	$0.0681277\pi$
$692$	12.5243			0.476101
$693$		0			0
$694$	7.49408			0.284471
$695$		0			0
$696$		0			0
$697$	−4.07736	+	7.06219i	−0.154441	+	0.267500i
$698$	6.22762	+	10.7866i	0.235719	+	0.408277i
$699$		0			0
$700$		0			0
$701$			8.73610i			0.329958i	0.986297	+	0.164979i	$0.0527556\pi$
$701$			8.73610i			0.329958i	−0.986297	+	0.164979i	$0.947244\pi$
$702$		0			0
$703$	7.15046	+	4.12832i	0.269685	+	0.155703i
$704$	−0.429853	−	0.248176i	−0.0162007	−	0.00935348i
$705$		0			0
$706$		−	18.9402i		−	0.712824i
$707$	−7.40061	−	2.89515i	−0.278329	−	0.108883i
$708$		0			0
$709$	−8.25544	−	14.2988i	−0.310039	−	0.537004i	0.668331	−	0.743864i	$-0.267009\pi$
$709$	−8.25544	−	14.2988i	−0.310039	−	0.537004i	−0.978371	+	0.206860i	$0.933676\pi$
$710$		0			0
$711$		0			0
$712$	−1.28793	+	0.743586i	−0.0482671	+	0.0278671i
$713$	−51.2389			−1.91891
$714$		0			0
$715$		0			0
$716$	1.58961	−	0.917762i	0.0594066	−	0.0342984i
$717$		0			0
$718$	−13.3131	+	23.0590i	−0.496841	+	0.860554i
$719$	22.5570	+	39.0699i	0.841234	+	1.45706i	0.888852	+	0.458195i	$0.151504\pi$
$719$	22.5570	+	39.0699i	0.841234	+	1.45706i	−0.0476171	+	0.998866i	$0.515163\pi$
$720$		0			0
$721$	23.7457	+	29.7092i	0.884336	+	1.10643i
$722$		−	6.01040i		−	0.223684i
$723$		0			0
$724$	−20.4871	−	11.8282i	−0.761396	−	0.439592i
$725$		0			0
$726$		0			0
$727$		−	31.9760i		−	1.18593i	−0.805230	−	0.592963i	$-0.797958\pi$
$727$		−	31.9760i		−	1.18593i	0.805230	−	0.592963i	$-0.202042\pi$
$728$	−1.09008	−	7.17871i	−0.0404012	−	0.266061i
$729$		0			0
$730$		0			0
$731$	−4.07295	+	7.05456i	−0.150644	+	0.260922i
$732$		0			0
$733$	−40.4618	+	23.3606i	−1.49449	+	0.862844i	−0.999980	−	0.00632839i	$-0.997986\pi$
$733$	−40.4618	+	23.3606i	−1.49449	+	0.862844i	−0.494509	+	0.869172i	$0.664652\pi$
$734$	10.9121			0.402773
$735$		0			0
$736$	6.42419			0.236799
$737$	3.51524	−	2.02953i	0.129486	−	0.0747586i
$738$		0			0
$739$	4.59353	−	7.95623i	0.168976	−	0.292675i	−0.769084	−	0.639147i	$-0.779287\pi$
$739$	4.59353	−	7.95623i	0.168976	−	0.292675i	0.938060	+	0.346473i	$0.112621\pi$
$740$		0			0
$741$		0			0
$742$	3.08485	+	20.3152i	0.113248	+	0.745795i
$743$			28.5353i			1.04686i	0.852069	+	0.523430i	$0.175348\pi$
$743$			28.5353i			1.04686i	−0.852069	+	0.523430i	$0.824652\pi$
$744$		0			0
$745$		0			0
$746$	19.4924	+	11.2539i	0.713667	+	0.412036i
$747$		0			0
$748$		−	1.81657i		−	0.0664203i
$749$	−3.51234	−	4.39442i	−0.128338	−	0.160569i
$750$		0			0
$751$	21.4749	+	37.1956i	0.783629	+	1.35729i	0.929814	+	0.368029i	$0.119967\pi$
$751$	21.4749	+	37.1956i	0.783629	+	1.35729i	−0.146185	+	0.989257i	$0.546700\pi$
$752$	−3.27213	+	5.66749i	−0.119322	+	0.206672i
$753$		0			0
$754$	−21.1043	+	12.1846i	−0.768574	+	0.443736i
$755$		0			0
$756$		0			0
$757$	19.4415			0.706612			0.353306	−	0.935508i	$-0.385057\pi$
$757$	19.4415			0.706612			0.353306	+	0.935508i	$0.385057\pi$
$758$	2.82245	−	1.62954i	0.102516	−	0.0591877i
$759$		0			0
$760$		0			0
$761$	24.9154	+	43.1547i	0.903182	+	1.56436i	0.823339	+	0.567550i	$0.192109\pi$
$761$	24.9154	+	43.1547i	0.903182	+	1.56436i	0.0798434	+	0.996807i	$0.474558\pi$
$762$		0			0
$763$	19.4739	+	7.61827i	0.705003	+	0.275800i
$764$			8.10892i			0.293371i
$765$		0			0
$766$	15.0013	+	8.66098i	0.542017	+	0.312934i
$767$	14.5072	+	8.37575i	0.523825	+	0.302431i
$768$		0			0
$769$		−	29.5025i		−	1.06389i	−0.846779	−	0.531944i	$-0.821462\pi$
$769$		−	29.5025i		−	1.06389i	0.846779	−	0.531944i	$-0.178538\pi$
$770$		0			0
$771$		0			0
$772$	6.02502	+	10.4356i	0.216845	+	0.375587i
$773$	−12.6641	+	21.9349i	−0.455498	+	0.788945i	−0.998717	−	0.0506458i	$-0.983872\pi$
$773$	−12.6641	+	21.9349i	−0.455498	+	0.788945i	0.543219	+	0.839591i	$0.317205\pi$
$774$		0			0
$775$		0			0
$776$	9.05174			0.324938
$777$		0			0
$778$	31.6982			1.13644
$779$	−6.95465	+	4.01527i	−0.249176	+	0.143862i
$780$		0			0
$781$	2.57509	−	4.46019i	0.0921440	−	0.159598i
$782$	11.7558	+	20.3616i	0.420385	+	0.728129i
$783$		0			0
$784$	5.14181	+	4.74992i	0.183636	+	0.169640i
$785$		0			0
$786$		0			0
$787$	−5.89278	−	3.40220i	−0.210055	−	0.121275i	0.391282	−	0.920271i	$-0.372032\pi$
$787$	−5.89278	−	3.40220i	−0.210055	−	0.121275i	−0.601337	+	0.798996i	$0.705365\pi$
$788$	−11.0386	−	6.37315i	−0.393235	−	0.227034i
$789$		0			0
$790$		0			0
$791$	−32.1655	+	4.88430i	−1.14367	+	0.173666i
$792$		0			0
$793$	−5.13802	−	8.89931i	−0.182456	−	0.316024i
$794$	−16.7561	+	29.0224i	−0.594651	+	1.02997i
$795$		0			0
$796$	16.4954	−	9.52361i	0.584663	−	0.337556i
$797$	−31.6373			−1.12065			−0.560326	−	0.828272i	$-0.689324\pi$
$797$	−31.6373			−1.12065			−0.560326	+	0.828272i	$0.689324\pi$
$798$		0			0
$799$	−23.9509			−0.847323
$800$		0			0
$801$		0			0
$802$	17.9212	−	31.0404i	0.632818	−	1.09607i
$803$	−3.24297	−	5.61698i	−0.114442	−	0.198219i
$804$		0			0
$805$		0			0
$806$		−	21.8892i		−	0.771013i
$807$		0			0
$808$	2.60119	+	1.50180i	0.0915094	+	0.0528330i
$809$	22.9302	+	13.2388i	0.806183	+	0.465450i	0.845629	−	0.533772i	$-0.179226\pi$
$809$	22.9302	+	13.2388i	0.806183	+	0.465450i	−0.0394457	+	0.999222i	$0.512559\pi$
$810$		0			0
$811$			25.4799i			0.894720i	0.894354	+	0.447360i	$0.147636\pi$
$811$			25.4799i			0.894720i	−0.894354	+	0.447360i	$0.852364\pi$
$812$	8.55899	−	21.8786i	0.300362	−	0.767788i
$813$		0			0
$814$	−0.568545	−	0.984749i	−0.0199275	−	0.0345154i
$815$		0			0
$816$		0			0
$817$	−6.94713	+	4.01093i	−0.243049	+	0.140325i
$818$	24.6499			0.861863
$819$		0			0
$820$		0			0
$821$	−32.9335	+	19.0141i	−1.14939	+	0.663598i	−0.948738	−	0.316065i	$-0.897638\pi$
$821$	−32.9335	+	19.0141i	−1.14939	+	0.663598i	−0.200649	+	0.979663i	$0.564305\pi$
$822$		0			0
$823$	−1.78791	+	3.09676i	−0.0623228	+	0.107946i	−0.895503	−	0.445055i	$-0.853184\pi$
$823$	−1.78791	+	3.09676i	−0.0623228	+	0.107946i	0.833181	+	0.553001i	$0.186517\pi$
$824$	−7.18752	−	12.4491i	−0.250389	−	0.433687i
$825$		0			0
$826$	−15.9663	+	2.42447i	−0.555539	+	0.0843582i
$827$			15.0648i			0.523855i	0.965088	+	0.261927i	$0.0843581\pi$
$827$			15.0648i			0.523855i	−0.965088	+	0.261927i	$0.915642\pi$
$828$		0			0
$829$	−27.5046	−	15.8798i	−0.955273	−	0.551527i	−0.0605582	−	0.998165i	$-0.519288\pi$
$829$	−27.5046	−	15.8798i	−0.955273	−	0.551527i	−0.894715	+	0.446637i	$0.852621\pi$
$830$		0			0
$831$		0			0
$832$			2.74440i			0.0951450i
$833$	−5.64586	+	24.9890i	−0.195617	+	0.865819i
$834$		0			0
$835$		0			0
$836$	0.894453	−	1.54924i	0.0309353	−	0.0535815i
$837$		0			0
$838$	−9.22954	+	5.32868i	−0.318829	+	0.184076i
$839$	15.1305			0.522362			0.261181	−	0.965290i	$-0.415888\pi$
$839$	15.1305			0.522362			0.261181	+	0.965290i	$0.415888\pi$
$840$		0			0
$841$	−49.8470			−1.71886
$842$	−19.6427	+	11.3407i	−0.676933	+	0.390828i
$843$		0			0
$844$	−4.46028	+	7.72544i	−0.153529	+	0.265920i
$845$		0			0
$846$		0			0
$847$	−22.2247	+	17.7636i	−0.763651	+	0.610365i
$848$		−	7.76645i		−	0.266701i
$849$		0			0
$850$		0			0
$851$	12.7454	+	7.35858i	0.436908	+	0.252249i
$852$		0			0
$853$		−	12.1586i		−	0.416302i	−0.978097	−	0.208151i	$-0.933255\pi$
$853$		−	12.1586i		−	0.416302i	0.978097	−	0.208151i	$-0.0667445\pi$
$854$	9.22581	+	3.60917i	0.315701	+	0.123503i
$855$		0			0
$856$	1.06314	+	1.84141i	0.0363374	+	0.0629382i
$857$	15.6668	−	27.1356i	0.535167	−	0.926936i	−0.463989	−	0.885841i	$-0.653582\pi$
$857$	15.6668	−	27.1356i	0.535167	−	0.926936i	0.999155	−	0.0410947i	$-0.0130845\pi$
$858$		0			0
$859$	−12.7872	+	7.38268i	−0.436293	+	0.251894i	−0.702024	−	0.712153i	$-0.747720\pi$
$859$	−12.7872	+	7.38268i	−0.436293	+	0.251894i	0.265731	+	0.964047i	$0.414387\pi$
$860$		0			0
$861$		0			0
$862$	30.0728			1.02429
$863$	12.4950	−	7.21398i	0.425334	−	0.245567i	−0.272023	−	0.962291i	$-0.587693\pi$
$863$	12.4950	−	7.21398i	0.425334	−	0.245567i	0.697357	+	0.716724i	$0.254359\pi$
$864$		0			0
$865$		0			0
$866$	−7.46016	−	12.9214i	−0.253507	−	0.439086i
$867$		0			0
$868$	13.1752	+	16.4840i	0.447196	+	0.559504i
$869$			4.41102i			0.149634i
$870$		0			0
$871$	−19.4363	−	11.2216i	−0.658574	−	0.380228i
$872$	−6.84474	−	3.95181i	−0.231792	−	0.133825i
$873$		0			0
$874$			23.1535i			0.783179i
$875$		0			0
$876$		0			0
$877$	5.28153	+	9.14788i	0.178345	+	0.308902i	0.941314	−	0.337533i	$-0.109592\pi$
$877$	5.28153	+	9.14788i	0.178345	+	0.308902i	−0.762969	+	0.646435i	$0.776259\pi$
$878$	−6.41586	+	11.1126i	−0.216525	+	0.375032i
$879$		0			0
$880$		0			0
$881$	13.4300			0.452469			0.226234	−	0.974073i	$-0.427358\pi$
$881$	13.4300			0.452469			0.226234	+	0.974073i	$0.427358\pi$
$882$		0			0
$883$	−4.06019			−0.136636			−0.0683181	−	0.997664i	$-0.521763\pi$
$883$	−4.06019			−0.136636			−0.0683181	+	0.997664i	$0.521763\pi$
$884$	−8.69843	+	5.02204i	−0.292560	+	0.168909i
$885$		0			0
$886$	−10.2071	+	17.6792i	−0.342913	+	0.593943i
$887$	16.5177	+	28.6095i	0.554611	+	0.960614i	0.997934	+	0.0642519i	$0.0204661\pi$
$887$	16.5177	+	28.6095i	0.554611	+	0.960614i	−0.443323	+	0.896362i	$0.646201\pi$
$888$		0			0
$889$	0.299270	+	1.97084i	0.0100372	+	0.0660997i
$890$		0			0
$891$		0			0
$892$	−20.3899	−	11.7721i	−0.682705	−	0.394160i
$893$	−20.4262	−	11.7931i	−0.683538	−	0.394641i
$894$		0			0
$895$		0			0
$896$	−1.65187	−	2.06672i	−0.0551851	−	0.0690442i
$897$		0			0
$898$	−10.4202	−	18.0483i	−0.347727	−	0.602280i
$899$	35.4115	−	61.3345i	1.18104	−	2.04562i
$900$		0			0
$901$	24.6159	−	14.2120i	0.820074	−	0.473470i
$902$	1.10595			0.0368241
$903$		0			0
$904$	12.2968			0.408984
$905$		0			0
$906$		0			0
$907$	−13.6659	+	23.6700i	−0.453768	+	0.785949i	−0.998616	−	0.0525853i	$-0.983254\pi$
$907$	−13.6659	+	23.6700i	−0.453768	+	0.785949i	0.544848	+	0.838535i	$0.316587\pi$
$908$	−4.66223	−	8.07522i	−0.154722	−	0.267986i
$909$		0			0
$910$		0			0
$911$			1.06838i			0.0353972i	0.999843	+	0.0176986i	$0.00563393\pi$
$911$			1.06838i			0.0353972i	−0.999843	+	0.0176986i	$0.994366\pi$
$912$		0			0
$913$	2.05939	+	1.18899i	0.0681558	+	0.0393498i
$914$	−13.8811	−	8.01424i	−0.459145	−	0.265087i
$915$		0			0
$916$		−	23.2725i		−	0.768944i
$917$	26.2731	−	20.9994i	0.867615	−	0.693460i
$918$		0			0
$919$	26.8653	+	46.5320i	0.886203	+	1.53495i	0.844329	+	0.535826i	$0.180000\pi$
$919$	26.8653	+	46.5320i	0.886203	+	1.53495i	0.0418743	+	0.999123i	$0.486667\pi$
$920$		0			0
$921$		0			0
$922$	1.71819	−	0.991998i	0.0565856	−	0.0326697i
$923$	−28.4761			−0.937303
$924$		0			0
$925$		0			0
$926$	−31.5222	+	18.1994i	−1.03588	+	0.598068i
$927$		0			0
$928$	−4.43979	+	7.68995i	−0.145743	+	0.252435i
$929$	4.80716	+	8.32625i	0.157718	+	0.273175i	0.934045	−	0.357154i	$-0.116253\pi$
$929$	4.80716	+	8.32625i	0.157718	+	0.273175i	−0.776327	+	0.630330i	$0.782920\pi$
$930$		0			0
$931$	−17.1192	+	18.5316i	−0.561061	+	0.607350i
$932$		−	12.6203i		−	0.413393i
$933$		0			0
$934$	−26.9113	−	15.5372i	−0.880563	−	0.508394i
$935$		0			0
$936$		0			0
$937$		−	12.8030i		−	0.418256i	−0.977888	−	0.209128i	$-0.932937\pi$
$937$		−	12.8030i		−	0.418256i	0.977888	−	0.209128i	$-0.0670626\pi$
$938$	21.3912	−	3.24823i	0.698446	−	0.106059i
$939$		0			0
$940$		0			0
$941$	24.2221	−	41.9538i	0.789616	−	1.36766i	−0.136586	−	0.990628i	$-0.543613\pi$
$941$	24.2221	−	41.9538i	0.789616	−	1.36766i	0.926202	−	0.377028i	$-0.123054\pi$
$942$		0			0
$943$	−12.3964	+	7.15707i	−0.403682	+	0.233066i
$944$	6.10388			0.198664
$945$		0			0
$946$	1.10476			0.0359187
$947$	−32.9055	+	18.9980i	−1.06929	+	0.617353i	−0.927986	−	0.372614i	$-0.878461\pi$
$947$	−32.9055	+	18.9980i	−1.06929	+	0.617353i	−0.141300	+	0.989967i	$0.545128\pi$
$948$		0			0
$949$	−17.9308	+	31.0571i	−0.582060	+	1.00816i
$950$		0			0
$951$		0			0
$952$	3.52771	−	9.01756i	0.114334	−	0.292261i
$953$		−	15.2394i		−	0.493652i	−0.969060	−	0.246826i	$-0.920612\pi$
$953$		−	15.2394i		−	0.493652i	0.969060	−	0.246826i	$-0.0793877\pi$
$954$		0			0
$955$		0			0
$956$	−13.9601	−	8.05990i	−0.451503	−	0.260676i
$957$		0			0
$958$			36.4809i			1.17864i
$959$	4.15902	−	10.6313i	0.134302	−	0.343303i
$960$		0			0
$961$	16.3078	+	28.2459i	0.526057	+	0.911157i
$962$	−3.14357	+	5.44483i	−0.101353	+	0.175548i
$963$		0			0
$964$	−18.3222	+	10.5783i	−0.590119	+	0.340705i
$965$		0			0
$966$		0			0
$967$	27.7458			0.892244			0.446122	−	0.894972i	$-0.352805\pi$
$967$	27.7458			0.892244			0.446122	+	0.894972i	$0.352805\pi$
$968$	9.31292	−	5.37682i	0.299329	−	0.172817i
$969$		0			0
$970$		0			0
$971$	10.2730	+	17.7934i	0.329677	+	0.571018i	0.982448	−	0.186538i	$-0.0597268\pi$
$971$	10.2730	+	17.7934i	0.329677	+	0.571018i	−0.652771	+	0.757556i	$0.726393\pi$
$972$		0			0
$973$	0.178206	−	0.0270604i	0.00571302	−	0.000867518i
$974$		−	14.1334i		−	0.452865i
$975$		0			0
$976$	−3.24271	−	1.87218i	−0.103797	−	0.0599270i
$977$	6.60604	+	3.81400i	0.211346	+	0.122021i	0.601937	−	0.798544i	$-0.294396\pi$
$977$	6.60604	+	3.81400i	0.211346	+	0.122021i	−0.390591	+	0.920564i	$0.627729\pi$
$978$		0			0
$979$			0.738160i			0.0235917i
$980$		0			0
$981$		0			0
$982$	16.2733	+	28.1861i	0.519301	+	0.899456i
$983$	−11.8347	+	20.4984i	−0.377470	+	0.653797i	−0.990693	−	0.136113i	$-0.956539\pi$
$983$	−11.8347	+	20.4984i	−0.377470	+	0.653797i	0.613224	+	0.789909i	$0.289872\pi$
$984$		0			0
$985$		0			0
$986$	−32.4979			−1.03494
$987$		0			0
$988$	−9.89113			−0.314679
$989$	−12.3830	+	7.14933i	−0.393757	+	0.227336i
$990$		0			0
$991$	−13.3947	+	23.2003i	−0.425497	+	0.736982i	−0.996467	−	0.0839887i	$-0.973234\pi$
$991$	−13.3947	+	23.2003i	−0.425497	+	0.736982i	0.570970	+	0.820971i	$0.306567\pi$
$992$	−3.98797	−	6.90736i	−0.126618	−	0.219309i
$993$		0			0
$994$	21.4444	−	17.1399i	0.680176	−	0.543646i
$995$		0			0
$996$		0			0
$997$	36.5656	+	21.1111i	1.15804	+	0.668596i	0.950834	−	0.309700i	$-0.100229\pi$
$997$	36.5656	+	21.1111i	1.15804	+	0.668596i	0.207209	+	0.978297i	$0.433562\pi$
$998$	10.1740	+	5.87396i	0.322053	+	0.185937i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3150.2.bf.d.1151.4	✓	24
3.2	odd	2	inner	3150.2.bf.d.1151.9	yes	24
5.2	odd	4		3150.2.bp.g.899.11		24
5.3	odd	4		3150.2.bp.h.899.2		24
5.4	even	2		3150.2.bf.e.1151.9	yes	24
7.5	odd	6	inner	3150.2.bf.d.1601.9	yes	24
15.2	even	4		3150.2.bp.h.899.11		24
15.8	even	4		3150.2.bp.g.899.2		24
15.14	odd	2		3150.2.bf.e.1151.4	yes	24
21.5	even	6	inner	3150.2.bf.d.1601.4	yes	24
35.12	even	12		3150.2.bp.g.1349.2		24
35.19	odd	6		3150.2.bf.e.1601.4	yes	24
35.33	even	12		3150.2.bp.h.1349.11		24
105.47	odd	12		3150.2.bp.h.1349.2		24
105.68	odd	12		3150.2.bp.g.1349.11		24
105.89	even	6		3150.2.bf.e.1601.9	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3150.2.bf.d.1151.4	✓	24	1.1	even	1	trivial
3150.2.bf.d.1151.9	yes	24	3.2	odd	2	inner
3150.2.bf.d.1601.4	yes	24	21.5	even	6	inner
3150.2.bf.d.1601.9	yes	24	7.5	odd	6	inner
3150.2.bf.e.1151.4	yes	24	15.14	odd	2
3150.2.bf.e.1151.9	yes	24	5.4	even	2
3150.2.bf.e.1601.4	yes	24	35.19	odd	6
3150.2.bf.e.1601.9	yes	24	105.89	even	6
3150.2.bp.g.899.2		24	15.8	even	4
3150.2.bp.g.899.11		24	5.2	odd	4
3150.2.bp.g.1349.2		24	35.12	even	12
3150.2.bp.g.1349.11		24	105.68	odd	12
3150.2.bp.h.899.2		24	5.3	odd	4
3150.2.bp.h.899.11		24	15.2	even	4
3150.2.bp.h.1349.2		24	105.47	odd	12
3150.2.bp.h.1349.11		24	35.33	even	12

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:	\( N \)	\(=\)	\( 3150 = 2 \cdot 3^{2} \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3150.bf (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(-0.397202 - 2.61577i) q^{7} +1.00000i q^{8} +O(q^{10})\)	\(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(-0.397202 - 2.61577i) q^{7} +1.00000i q^{8} +(0.429853 + 0.248176i) q^{11} -2.74440i q^{13} +(1.65187 + 2.06672i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(1.82992 - 3.16952i) q^{17} +(3.12125 - 1.80205i) q^{19} -0.496352 q^{22} +(5.56351 - 3.21210i) q^{23} +(1.37220 + 2.37672i) q^{26} +(-2.46392 - 0.963896i) q^{28} +8.87959i q^{29} +(-6.90736 - 3.98797i) q^{31} +(0.866025 + 0.500000i) q^{32} +3.65984i q^{34} +(1.14545 + 1.98397i) q^{37} +(-1.80205 + 3.12125i) q^{38} -2.22816 q^{41} -2.22575 q^{43} +(0.429853 - 0.248176i) q^{44} +(-3.21210 + 5.56351i) q^{46} +(-3.27213 - 5.66749i) q^{47} +(-6.68446 + 2.07798i) q^{49} +(-2.37672 - 1.37220i) q^{52} +(6.72594 + 3.88322i) q^{53} +(2.61577 - 0.397202i) q^{56} +(-4.43979 - 7.68995i) q^{58} +(-3.05194 + 5.28611i) q^{59} +(3.24271 - 1.87218i) q^{61} +7.97593 q^{62} -1.00000 q^{64} +(4.08889 - 7.08216i) q^{67} +(-1.82992 - 3.16952i) q^{68} -10.3761i q^{71} +(-11.3165 - 6.53361i) q^{73} +(-1.98397 - 1.14545i) q^{74} -3.60411i q^{76} +(0.478431 - 1.22297i) q^{77} +(4.44344 + 7.69627i) q^{79} +(1.92964 - 1.11408i) q^{82} +4.79091 q^{83} +(1.92756 - 1.11288i) q^{86} +(-0.248176 + 0.429853i) q^{88} +(0.743586 + 1.28793i) q^{89} +(-7.17871 + 1.09008i) q^{91} -6.42419i q^{92} +(5.66749 + 3.27213i) q^{94} -9.05174i q^{97} +(4.74992 - 5.14181i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 12 q^{4} - 4 q^{7}+O(q^{10}) \) 24 * q + 12 * q^4 - 4 * q^7	\( 24 q + 12 q^{4} - 4 q^{7} - 12 q^{16} + 12 q^{19} + 4 q^{28} + 28 q^{37} + 96 q^{43} - 8 q^{46} - 52 q^{49} - 12 q^{52} + 8 q^{58} - 12 q^{61} - 24 q^{64} - 4 q^{67} - 12 q^{73} + 4 q^{79} + 68 q^{91} - 24 q^{94}+O(q^{100}) \) 24 * q + 12 * q^4 - 4 * q^7 - 12 * q^16 + 12 * q^19 + 4 * q^28 + 28 * q^37 + 96 * q^43 - 8 * q^46 - 52 * q^49 - 12 * q^52 + 8 * q^58 - 12 * q^61 - 24 * q^64 - 4 * q^67 - 12 * q^73 + 4 * q^79 + 68 * q^91 - 24 * q^94

Introduction

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