LMFDB - Embedded newform 784.2.bb.b.111.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [784,2,Mod(111,784)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(784, base_ring=CyclotomicField(14))

chi = DirichletCharacter(H, H._module([7, 0, 11]))

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

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

chi := DirichletCharacter("784.111");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 784 = 2^{4} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	784.bb (of order $14$, degree $6$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.26027151847$
Analytic rank:	$0$
Dimension:	$120$
Relative dimension:	$20$ over $\Q(\zeta_{14})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{14}]$

Embedding invariants

Embedding label			111.7
Character	$\chi$	$=$	784.111
Dual form			784.2.bb.b.671.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.912783 - 1.14459i) q^{3} +(-0.583523 + 0.465344i) q^{5} +(-2.34056 - 1.23360i) q^{7} +(0.190641 - 0.835251i) q^{9} +O(q^{10})$	\(q+(-0.912783 - 1.14459i) q^{3} +(-0.583523 + 0.465344i) q^{5} +(-2.34056 - 1.23360i) q^{7} +(0.190641 - 0.835251i) q^{9} +(2.76768 - 0.631705i) q^{11} +(4.35414 - 0.993805i) q^{13} +(1.06526 + 0.243138i) q^{15} +(-1.20256 + 2.49715i) q^{17} -7.65489 q^{19} +(0.724455 + 3.80500i) q^{21} +(-2.83869 - 5.89461i) q^{23} +(-0.988651 + 4.33156i) q^{25} +(-5.08707 + 2.44980i) q^{27} +(-6.35245 - 3.05918i) q^{29} +3.74877 q^{31} +(-3.24934 - 2.59126i) q^{33} +(1.93982 - 0.369333i) q^{35} +(-6.24341 - 3.00667i) q^{37} +(-5.11189 - 4.07660i) q^{39} +(-9.00202 + 7.17887i) q^{41} +(-9.26094 - 7.38535i) q^{43} +(0.277436 + 0.576101i) q^{45} +(1.75018 + 7.66806i) q^{47} +(3.95646 + 5.77463i) q^{49} +(3.95591 - 0.902910i) q^{51} +(10.6688 - 5.13783i) q^{53} +(-1.32104 + 1.65654i) q^{55} +(6.98725 + 8.76174i) q^{57} +(3.70620 - 4.64743i) q^{59} +(3.65453 - 7.58871i) q^{61} +(-1.47657 + 1.71978i) q^{63} +(-2.07828 + 2.60608i) q^{65} +2.87802i q^{67} +(-4.15582 + 8.62965i) q^{69} +(-1.64942 - 3.42506i) q^{71} +(-12.8007 - 2.92168i) q^{73} +(5.86030 - 2.82217i) q^{75} +(-7.25720 - 1.93566i) q^{77} +10.6555i q^{79} +(5.13175 + 2.47132i) q^{81} +(0.570078 - 2.49768i) q^{83} +(-0.460310 - 2.01675i) q^{85} +(2.29689 + 10.0633i) q^{87} +(8.01149 + 1.82857i) q^{89} +(-11.4171 - 3.04521i) q^{91} +(-3.42181 - 4.29082i) q^{93} +(4.46680 - 3.56215i) q^{95} -3.34444i q^{97} -2.43214i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 120 q - 24 q^{9}+O(q^{10}) $ 120 * q - 24 * q^9	$ 120 q - 24 q^{9} - 14 q^{17} + 16 q^{21} + 40 q^{25} + 32 q^{29} - 62 q^{37} - 28 q^{41} - 60 q^{49} + 14 q^{53} - 34 q^{57} - 112 q^{61} - 32 q^{65} + 112 q^{69} + 42 q^{73} + 66 q^{77} - 44 q^{81} - 12 q^{85} + 28 q^{89} - 58 q^{93}+O(q^{100}) $ 120 * q - 24 * q^9 - 14 * q^17 + 16 * q^21 + 40 * q^25 + 32 * q^29 - 62 * q^37 - 28 * q^41 - 60 * q^49 + 14 * q^53 - 34 * q^57 - 112 * q^61 - 32 * q^65 + 112 * q^69 + 42 * q^73 + 66 * q^77 - 44 * q^81 - 12 * q^85 + 28 * q^89 - 58 * q^93

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/784\mathbb{Z}\right)^\times$.

$n$	$197$	$687$	$689$
$\chi(n)$	$1$	$-1$	$e\left(\frac{11}{14}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.912783	−	1.14459i	−0.526996	−	0.660832i	0.445082	−	0.895490i	$-0.353174\pi$
$3$	−0.912783	−	1.14459i	−0.526996	−	0.660832i	−0.972078	+	0.234658i	$0.924603\pi$
$4$		0			0
$5$	−0.583523	+	0.465344i	−0.260959	+	0.208108i	−0.745225	−	0.666813i	$-0.767658\pi$
$5$	−0.583523	+	0.465344i	−0.260959	+	0.208108i	0.484266	+	0.874921i	$0.339087\pi$
$6$		0			0
$7$	−2.34056	−	1.23360i	−0.884649	−	0.466257i
$7$	−2.34056	−	1.23360i	−0.884649	−	0.466257i
$8$		0			0
$9$	0.190641	−	0.835251i	0.0635469	−	0.278417i
$10$		0			0
$11$	2.76768	−	0.631705i	0.834487	−	0.190466i	0.216131	−	0.976364i	$-0.430656\pi$
$11$	2.76768	−	0.631705i	0.834487	−	0.190466i	0.618356	+	0.785898i	$0.287799\pi$
$12$		0			0
$13$	4.35414	−	0.993805i	1.20762	−	0.275632i	0.429105	−	0.903255i	$-0.358829\pi$
$13$	4.35414	−	0.993805i	1.20762	−	0.275632i	0.778518	+	0.627623i	$0.215972\pi$
$14$		0			0
$15$	1.06526	+	0.243138i	0.275049	+	0.0627781i
$16$		0			0
$17$	−1.20256	+	2.49715i	−0.291665	+	0.605648i	−0.994386	−	0.105818i	$-0.966254\pi$
$17$	−1.20256	+	2.49715i	−0.291665	+	0.605648i	0.702721	+	0.711466i	$0.251968\pi$
$18$		0			0
$19$	−7.65489			−1.75615			−0.878076	−	0.478522i	$-0.841173\pi$
$19$	−7.65489			−1.75615			−0.878076	+	0.478522i	$0.841173\pi$
$20$		0			0
$21$	0.724455	+	3.80500i	0.158089	+	0.830320i
$22$		0			0
$23$	−2.83869	−	5.89461i	−0.591909	−	1.22911i	−0.954791	−	0.297276i	$-0.903922\pi$
$23$	−2.83869	−	5.89461i	−0.591909	−	1.22911i	0.362883	−	0.931835i	$-0.381793\pi$
$24$		0			0
$25$	−0.988651	+	4.33156i	−0.197730	+	0.866313i
$26$		0			0
$27$	−5.08707	+	2.44980i	−0.979007	+	0.471465i
$28$		0			0
$29$	−6.35245	−	3.05918i	−1.17962	−	0.568075i	−0.261819	−	0.965117i	$-0.584322\pi$
$29$	−6.35245	−	3.05918i	−1.17962	−	0.568075i	−0.917801	+	0.397042i	$0.870037\pi$
$30$		0			0
$31$	3.74877			0.673298			0.336649	−	0.941630i	$-0.390706\pi$
$31$	3.74877			0.673298			0.336649	+	0.941630i	$0.390706\pi$
$32$		0			0
$33$	−3.24934	−	2.59126i	−0.565637	−	0.451081i
$34$		0			0
$35$	1.93982	−	0.369333i	0.327889	−	0.0624286i
$36$		0			0
$37$	−6.24341	−	3.00667i	−1.02641	−	0.494293i	−0.156591	−	0.987664i	$-0.550051\pi$
$37$	−6.24341	−	3.00667i	−1.02641	−	0.494293i	−0.869819	+	0.493370i	$0.835765\pi$
$38$		0			0
$39$	−5.11189	−	4.07660i	−0.818558	−	0.652778i
$40$		0			0
$41$	−9.00202	+	7.17887i	−1.40588	+	1.12115i	−0.430003	+	0.902827i	$0.641488\pi$
$41$	−9.00202	+	7.17887i	−1.40588	+	1.12115i	−0.975876	+	0.218324i	$0.929941\pi$
$42$		0			0
$43$	−9.26094	−	7.38535i	−1.41228	−	1.12626i	−0.973771	−	0.227529i	$-0.926935\pi$
$43$	−9.26094	−	7.38535i	−1.41228	−	1.12626i	−0.438509	−	0.898727i	$-0.644493\pi$
$44$		0			0
$45$	0.277436	+	0.576101i	0.0413577	+	0.0858801i
$46$		0			0
$47$	1.75018	+	7.66806i	0.255291	+	1.11850i	0.926221	+	0.376981i	$0.123038\pi$
$47$	1.75018	+	7.66806i	0.255291	+	1.11850i	−0.670930	+	0.741520i	$0.734105\pi$
$48$		0			0
$49$	3.95646	+	5.77463i	0.565209	+	0.824948i
$50$		0			0
$51$	3.95591	−	0.902910i	0.553938	−	0.126433i
$52$		0			0
$53$	10.6688	−	5.13783i	1.46547	−	0.705735i	0.480269	−	0.877121i	$-0.340539\pi$
$53$	10.6688	−	5.13783i	1.46547	−	0.705735i	0.985204	+	0.171386i	$0.0548246\pi$
$54$		0			0
$55$	−1.32104	+	1.65654i	−0.178130	+	0.223367i
$56$		0			0
$57$	6.98725	+	8.76174i	0.925484	+	1.16052i
$58$		0			0
$59$	3.70620	−	4.64743i	0.482507	−	0.605044i	−0.479677	−	0.877445i	$-0.659246\pi$
$59$	3.70620	−	4.64743i	0.482507	−	0.605044i	0.962184	+	0.272401i	$0.0878176\pi$
$60$		0			0
$61$	3.65453	−	7.58871i	0.467915	−	0.971635i	−0.524809	−	0.851220i	$-0.675863\pi$
$61$	3.65453	−	7.58871i	0.467915	−	0.971635i	0.992724	−	0.120415i	$-0.0384224\pi$
$62$		0			0
$63$	−1.47657	+	1.71978i	−0.186031	+	0.216672i
$64$		0			0
$65$	−2.07828	+	2.60608i	−0.257779	+	0.323245i
$66$		0			0
$67$			2.87802i			0.351606i	0.984425	+	0.175803i	$0.0562521\pi$
$67$			2.87802i			0.351606i	−0.984425	+	0.175803i	$0.943748\pi$
$68$		0			0
$69$	−4.15582	+	8.62965i	−0.500302	+	1.03889i
$70$		0			0
$71$	−1.64942	−	3.42506i	−0.195751	−	0.406480i	0.779871	−	0.625940i	$-0.215285\pi$
$71$	−1.64942	−	3.42506i	−0.195751	−	0.406480i	−0.975621	+	0.219460i	$0.929570\pi$
$72$		0			0
$73$	−12.8007	−	2.92168i	−1.49821	−	0.341957i	−0.606691	−	0.794937i	$-0.707504\pi$
$73$	−12.8007	−	2.92168i	−1.49821	−	0.341957i	−0.891521	+	0.452980i	$0.850361\pi$
$74$		0			0
$75$	5.86030	−	2.82217i	0.676690	−	0.325877i
$76$		0			0
$77$	−7.25720	−	1.93566i	−0.827035	−	0.220589i
$78$		0			0
$79$			10.6555i			1.19884i	0.800434	+	0.599421i	$0.204603\pi$
$79$			10.6555i			1.19884i	−0.800434	+	0.599421i	$0.795397\pi$
$80$		0			0
$81$	5.13175	+	2.47132i	0.570195	+	0.274591i
$82$		0			0
$83$	0.570078	−	2.49768i	0.0625742	−	0.274156i	−0.933956	−	0.357388i	$-0.883667\pi$
$83$	0.570078	−	2.49768i	0.0625742	−	0.274156i	0.996530	+	0.0832326i	$0.0265244\pi$
$84$		0			0
$85$	−0.460310	−	2.01675i	−0.0499276	−	0.218747i
$86$		0			0
$87$	2.29689	+	10.0633i	0.246253	+	1.07890i
$88$		0			0
$89$	8.01149	+	1.82857i	0.849217	+	0.193828i	0.624916	−	0.780692i	$-0.285133\pi$
$89$	8.01149	+	1.82857i	0.849217	+	0.193828i	0.224300	+	0.974520i	$0.427990\pi$
$90$		0			0
$91$	−11.4171	−	3.04521i	−1.19684	−	0.319225i
$92$		0			0
$93$	−3.42181	−	4.29082i	−0.354825	−	0.444937i
$94$		0			0
$95$	4.46680	−	3.56215i	0.458284	−	0.365469i
$96$		0			0
$97$		−	3.34444i		−	0.339576i	−0.985481	−	0.169788i	$-0.945692\pi$
$97$		−	3.34444i		−	0.339576i	0.985481	−	0.169788i	$-0.0543083\pi$
$98$		0			0
$99$		−	2.43214i		−	0.244439i
$100$		0			0
$101$	1.92431	−	1.53459i	0.191476	−	0.152697i	−0.523059	−	0.852296i	$-0.675209\pi$
$101$	1.92431	−	1.53459i	0.191476	−	0.152697i	0.714536	+	0.699599i	$0.246638\pi$
$102$		0			0
$103$	1.33833	+	1.67821i	0.131869	+	0.165359i	0.843382	−	0.537314i	$-0.180561\pi$
$103$	1.33833	+	1.67821i	0.131869	+	0.165359i	−0.711513	+	0.702673i	$0.751990\pi$
$104$		0			0
$105$	−2.19337	−	1.88318i	−0.214051	−	0.183780i
$106$		0			0
$107$	−12.0646	−	2.75366i	−1.16633	−	0.266207i	−0.404841	−	0.914387i	$-0.632673\pi$
$107$	−12.0646	−	2.75366i	−1.16633	−	0.266207i	−0.761487	+	0.648181i	$0.775530\pi$
$108$		0			0
$109$	−0.332533	−	1.45692i	−0.0318509	−	0.139548i	0.956502	−	0.291724i	$-0.0942290\pi$
$109$	−0.332533	−	1.45692i	−0.0318509	−	0.139548i	−0.988353	+	0.152176i	$0.951372\pi$
$110$		0			0
$111$	2.25747	+	9.89061i	0.214269	+	0.938775i
$112$		0			0
$113$	2.30656	−	10.1057i	0.216983	−	0.950665i	−0.742710	−	0.669614i	$-0.766460\pi$
$113$	2.30656	−	10.1057i	0.216983	−	0.950665i	0.959693	−	0.281051i	$-0.0906831\pi$
$114$		0			0
$115$	4.39946	+	2.11867i	0.410252	+	0.197567i
$116$		0			0
$117$		−	3.82626i		−	0.353738i
$118$		0			0
$119$	5.89516	−	4.36126i	0.540409	−	0.399796i
$120$		0			0
$121$	−2.64965	+	1.27601i	−0.240878	+	0.116001i
$122$		0			0
$123$	16.4338	+	3.75091i	1.48178	+	0.338208i
$124$		0			0
$125$	−3.05792	−	6.34983i	−0.273508	−	0.567946i
$126$		0			0
$127$	3.61869	−	7.51429i	0.321107	−	0.666786i	−0.676461	−	0.736478i	$-0.736487\pi$
$127$	3.61869	−	7.51429i	0.321107	−	0.666786i	0.997569	+	0.0696923i	$0.0222017\pi$
$128$		0			0
$129$			17.3412i			1.52681i
$130$		0			0
$131$	−4.87210	+	6.10943i	−0.425678	+	0.533783i	−0.947706	−	0.319145i	$-0.896604\pi$
$131$	−4.87210	+	6.10943i	−0.425678	+	0.533783i	0.522028	+	0.852928i	$0.325176\pi$
$132$		0			0
$133$	17.9167	+	9.44306i	1.55358	+	0.818818i
$134$		0			0
$135$	1.82842	−	3.79675i	0.157365	−	0.326772i
$136$		0			0
$137$	12.8732	−	16.1425i	1.09984	−	1.37915i	0.181479	−	0.983395i	$-0.441912\pi$
$137$	12.8732	−	16.1425i	1.09984	−	1.37915i	0.918356	−	0.395755i	$-0.129517\pi$
$138$		0			0
$139$	12.0541	+	15.1153i	1.02241	+	1.28206i	0.958798	+	0.284090i	$0.0916914\pi$
$139$	12.0541	+	15.1153i	1.02241	+	1.28206i	0.0636147	+	0.997975i	$0.479737\pi$
$140$		0			0
$141$	7.17927	−	9.00253i	0.604604	−	0.758149i
$142$		0			0
$143$	11.4231	−	5.50107i	0.955247	−	0.460022i
$144$		0			0
$145$	5.13037	−	1.17097i	0.426054	−	0.0972440i
$146$		0			0
$147$	2.99822	−	9.79953i	0.247289	−	0.808252i
$148$		0			0
$149$	−3.16108	−	13.8496i	−0.258966	−	1.13460i	−0.922360	−	0.386333i	$-0.873742\pi$
$149$	−3.16108	−	13.8496i	−0.258966	−	1.13460i	0.663394	−	0.748271i	$-0.269115\pi$
$150$		0			0
$151$	1.58908	+	3.29977i	0.129318	+	0.268531i	0.955567	−	0.294773i	$-0.0952441\pi$
$151$	1.58908	+	3.29977i	0.129318	+	0.268531i	−0.826249	+	0.563304i	$0.809530\pi$
$152$		0			0
$153$	1.85649	+	1.48050i	0.150088	+	0.119692i
$154$		0			0
$155$	−2.18749	+	1.74446i	−0.175703	+	0.140119i
$156$		0			0
$157$	5.91388	+	4.71617i	0.471979	+	0.376391i	0.830399	−	0.557170i	$-0.188113\pi$
$157$	5.91388	+	4.71617i	0.471979	+	0.376391i	−0.358419	+	0.933561i	$0.616684\pi$
$158$		0			0
$159$	−15.6190	−	7.52173i	−1.23867	−	0.596512i
$160$		0			0
$161$	−0.627447	+	17.2985i	−0.0494497	+	1.36331i
$162$		0			0
$163$	7.42935	+	5.92471i	0.581912	+	0.464059i	0.869663	−	0.493646i	$-0.164336\pi$
$163$	7.42935	+	5.92471i	0.581912	+	0.464059i	−0.287751	+	0.957705i	$0.592908\pi$
$164$		0			0
$165$	3.10189			0.241482
$166$		0			0
$167$	−2.47849	−	1.19358i	−0.191791	−	0.0923619i	0.335523	−	0.942032i	$-0.391087\pi$
$167$	−2.47849	−	1.19358i	−0.191791	−	0.0923619i	−0.527315	+	0.849670i	$0.676801\pi$
$168$		0			0
$169$	6.25832	−	3.01385i	0.481410	−	0.231835i
$170$		0			0
$171$	−1.45933	+	6.39375i	−0.111598	+	0.488943i
$172$		0			0
$173$	−10.8189	−	22.4656i	−0.822544	−	1.70803i	−0.698332	−	0.715774i	$-0.746074\pi$
$173$	−10.8189	−	22.4656i	−0.822544	−	1.70803i	−0.124212	−	0.992256i	$-0.539640\pi$
$174$		0			0
$175$	7.65741	−	8.91869i	0.578846	−	0.674190i
$176$		0			0
$177$	−8.70239			−0.654111
$178$		0			0
$179$	3.01315	−	6.25686i	0.225213	−	0.467660i	−0.757490	−	0.652846i	$-0.773575\pi$
$179$	3.01315	−	6.25686i	0.225213	−	0.467660i	0.982703	+	0.185187i	$0.0592890\pi$
$180$		0			0
$181$	−11.5309	−	2.63185i	−0.857083	−	0.195624i	−0.228671	−	0.973504i	$-0.573438\pi$
$181$	−11.5309	−	2.63185i	−0.857083	−	0.195624i	−0.628413	+	0.777880i	$0.716295\pi$
$182$		0			0
$183$	−12.0218	+	2.74389i	−0.888676	+	0.202834i
$184$		0			0
$185$	5.04231	−	1.15087i	0.370718	−	0.0846139i
$186$		0			0
$187$	−1.75085	+	7.67098i	−0.128035	+	0.560958i
$188$		0			0
$189$	14.9287	+	0.541489i	1.08590	+	0.0393875i
$190$		0			0
$191$	11.1613	−	8.90081i	0.807601	−	0.644040i	−0.130093	−	0.991502i	$-0.541528\pi$
$191$	11.1613	−	8.90081i	0.807601	−	0.644040i	0.937694	+	0.347462i	$0.112956\pi$
$192$		0			0
$193$	9.19083	+	11.5249i	0.661571	+	0.829583i	0.993513	−	0.113716i	$-0.0362755\pi$
$193$	9.19083	+	11.5249i	0.661571	+	0.829583i	−0.331943	+	0.943300i	$0.607704\pi$
$194$		0			0
$195$	4.87992			0.349459
$196$		0			0
$197$	13.4757			0.960106			0.480053	−	0.877240i	$-0.340617\pi$
$197$	13.4757			0.960106			0.480053	+	0.877240i	$0.340617\pi$
$198$		0			0
$199$	5.44906	+	6.83290i	0.386273	+	0.484371i	0.936512	−	0.350636i	$-0.114035\pi$
$199$	5.44906	+	6.83290i	0.386273	+	0.484371i	−0.550238	+	0.835008i	$0.685463\pi$
$200$		0			0
$201$	3.29416	−	2.62700i	0.232352	−	0.185295i
$202$		0			0
$203$	11.0945	+	14.9966i	0.778681	+	1.05255i
$204$		0			0
$205$	1.91224	−	8.37807i	0.133557	−	0.585150i
$206$		0			0
$207$	−5.46465	+	1.24727i	−0.379820	+	0.0866913i
$208$		0			0
$209$	−21.1863	+	4.83563i	−1.46549	+	0.334488i
$210$		0			0
$211$	3.27585	+	0.747691i	0.225519	+	0.0514731i	0.333787	−	0.942649i	$-0.391673\pi$
$211$	3.27585	+	0.747691i	0.225519	+	0.0514731i	−0.108268	+	0.994122i	$0.534531\pi$
$212$		0			0
$213$	−2.41474	+	5.01426i	−0.165455	+	0.343572i
$214$		0			0
$215$	8.84069			0.602930
$216$		0			0
$217$	−8.77422	−	4.62448i	−0.595633	−	0.313930i
$218$		0			0
$219$	8.34015	+	17.3185i	0.563575	+	1.17028i
$220$		0			0
$221$	−2.75446	+	12.0681i	−0.185285	+	0.811786i
$222$		0			0
$223$	−11.0534	+	5.32303i	−0.740190	+	0.356456i	−0.765683	−	0.643219i	$-0.777599\pi$
$223$	−11.0534	+	5.32303i	−0.740190	+	0.356456i	0.0254931	+	0.999675i	$0.491884\pi$
$224$		0			0
$225$	3.42947	+	1.65154i	0.228631	+	0.110103i
$226$		0			0
$227$	16.8406			1.11775			0.558876	−	0.829251i	$-0.311233\pi$
$227$	16.8406			1.11775			0.558876	+	0.829251i	$0.311233\pi$
$228$		0			0
$229$	−8.94811	−	7.13588i	−0.591308	−	0.471552i	0.281537	−	0.959550i	$-0.409156\pi$
$229$	−8.94811	−	7.13588i	−0.591308	−	0.471552i	−0.872845	+	0.487998i	$0.837727\pi$
$230$		0			0
$231$	4.40870	+	10.0734i	0.290071	+	0.662780i
$232$		0			0
$233$	−23.1694	−	11.1578i	−1.51788	−	0.730973i	−0.525114	−	0.851032i	$-0.675977\pi$
$233$	−23.1694	−	11.1578i	−1.51788	−	0.730973i	−0.992767	+	0.120060i	$0.961691\pi$
$234$		0			0
$235$	−4.58955	−	3.66005i	−0.299390	−	0.238755i
$236$		0			0
$237$	12.1963	−	9.72620i	0.792233	−	0.631785i
$238$		0			0
$239$	11.4121	+	9.10085i	0.738188	+	0.588685i	0.918732	−	0.394882i	$-0.129215\pi$
$239$	11.4121	+	9.10085i	0.738188	+	0.588685i	−0.180544	+	0.983567i	$0.557786\pi$
$240$		0			0
$241$	3.84677	+	7.98790i	0.247792	+	0.514546i	0.987352	−	0.158545i	$-0.0506804\pi$
$241$	3.84677	+	7.98790i	0.247792	+	0.514546i	−0.739560	+	0.673091i	$0.764966\pi$
$242$		0			0
$243$	1.91369	+	8.38441i	0.122763	+	0.537860i
$244$		0			0
$245$	−4.99587	−	1.52851i	−0.319175	−	0.0976531i
$246$		0			0
$247$	−33.3305	+	7.60746i	−2.12077	+	0.484051i
$248$		0			0
$249$	−3.37918	+	1.62733i	−0.214147	+	0.103128i
$250$		0			0
$251$	−1.64093	+	2.05766i	−0.103574	+	0.129878i	−0.830917	−	0.556396i	$-0.812184\pi$
$251$	−1.64093	+	2.05766i	−0.103574	+	0.129878i	0.727343	+	0.686274i	$0.240755\pi$
$252$		0			0
$253$	−11.5803	−	14.5212i	−0.728044	−	0.912939i
$254$		0			0
$255$	−1.88820	+	2.36772i	−0.118243	+	0.148273i
$256$		0			0
$257$	3.33144	−	6.91781i	0.207810	−	0.431521i	−0.770848	−	0.637019i	$-0.780167\pi$
$257$	3.33144	−	6.91781i	0.207810	−	0.431521i	0.978657	+	0.205498i	$0.0658815\pi$
$258$		0			0
$259$	10.9041	+	14.7392i	0.677546	+	0.915847i
$260$		0			0
$261$	−3.76622	+	4.72269i	−0.233123	+	0.292327i
$262$		0			0
$263$		−	22.0087i		−	1.35711i	−0.734548	−	0.678557i	$-0.762606\pi$
$263$		−	22.0087i		−	1.35711i	0.734548	−	0.678557i	$-0.237394\pi$
$264$		0			0
$265$	−3.83463	+	7.96270i	−0.235560	+	0.489145i
$266$		0			0
$267$	−5.21979	−	10.8390i	−0.319446	−	0.663336i
$268$		0			0
$269$	−3.94398	−	0.900187i	−0.240468	−	0.0548854i	0.100588	−	0.994928i	$-0.467928\pi$
$269$	−3.94398	−	0.900187i	−0.240468	−	0.0548854i	−0.341056	+	0.940043i	$0.610785\pi$
$270$		0			0
$271$	−2.07004	+	0.996877i	−0.125746	+	0.0605560i	−0.495699	−	0.868494i	$-0.665088\pi$
$271$	−2.07004	+	0.996877i	−0.125746	+	0.0605560i	0.369953	+	0.929050i	$0.379374\pi$
$272$		0			0
$273$	6.93581	+	15.8476i	0.419775	+	0.959138i
$274$		0			0
$275$			12.6129i			0.760588i
$276$		0			0
$277$	−6.24266	−	3.00631i	−0.375085	−	0.180632i	0.236837	−	0.971549i	$-0.423889\pi$
$277$	−6.24266	−	3.00631i	−0.375085	−	0.180632i	−0.611922	+	0.790918i	$0.709604\pi$
$278$		0			0
$279$	0.714667	−	3.13116i	0.0427860	−	0.187458i
$280$		0			0
$281$	−1.35967	−	5.95710i	−0.0811110	−	0.355371i	0.918044	−	0.396479i	$-0.129768\pi$
$281$	−1.35967	−	5.95710i	−0.0811110	−	0.355371i	−0.999155	+	0.0411087i	$0.986911\pi$
$282$		0			0
$283$	−5.18329	−	22.7095i	−0.308115	−	1.34994i	−0.857549	−	0.514402i	$-0.828014\pi$
$283$	−5.18329	−	22.7095i	−0.308115	−	1.34994i	0.549435	−	0.835537i	$-0.314843\pi$
$284$		0			0
$285$	−8.15444	−	1.86120i	−0.483027	−	0.110248i
$286$		0			0
$287$	29.9256	−	5.69771i	1.76646	−	0.336325i
$288$		0			0
$289$	5.80972	+	7.28516i	0.341748	+	0.428539i
$290$		0			0
$291$	−3.82802	+	3.05275i	−0.224403	+	0.178955i
$292$		0			0
$293$			4.30147i			0.251295i	0.992075	+	0.125647i	$0.0401008\pi$
$293$			4.30147i			0.251295i	−0.992075	+	0.125647i	$0.959899\pi$
$294$		0			0
$295$			4.43654i			0.258305i
$296$		0			0
$297$	−12.5318	+	9.99380i	−0.727170	+	0.579899i
$298$		0			0
$299$	−18.2182	−	22.8449i	−1.05358	−	1.32115i
$300$		0			0
$301$	12.5652	+	28.7102i	0.724248	+	1.65483i
$302$		0			0
$303$	−3.51296	−	0.801811i	−0.201814	−	0.0460628i
$304$		0			0
$305$	1.39886	+	6.12879i	0.0800983	+	0.350934i
$306$		0			0
$307$	−0.873487	−	3.82699i	−0.0498525	−	0.218418i	0.943866	−	0.330330i	$-0.107160\pi$
$307$	−0.873487	−	3.82699i	−0.0498525	−	0.218418i	−0.993718	+	0.111911i	$0.964303\pi$
$308$		0			0
$309$	0.699266	−	3.06368i	0.0397798	−	0.174287i
$310$		0			0
$311$	−10.5040	−	5.05848i	−0.595629	−	0.286840i	0.111680	−	0.993744i	$-0.464377\pi$
$311$	−10.5040	−	5.05848i	−0.595629	−	0.286840i	−0.707309	+	0.706904i	$0.750091\pi$
$312$		0			0
$313$			5.52163i			0.312101i	0.987749	+	0.156050i	$0.0498762\pi$
$313$			5.52163i			0.312101i	−0.987749	+	0.156050i	$0.950124\pi$
$314$		0			0
$315$	0.0613226	−	1.69065i	0.00345514	−	0.0952571i
$316$		0			0
$317$	17.4880	−	8.42177i	0.982223	−	0.473014i	0.127354	−	0.991857i	$-0.459352\pi$
$317$	17.4880	−	8.42177i	0.982223	−	0.473014i	0.854869	+	0.518843i	$0.173637\pi$
$318$		0			0
$319$	−19.5140	−	4.45395i	−1.09258	−	0.249374i
$320$		0			0
$321$	7.86052	+	16.3225i	0.438732	+	0.911036i
$322$		0			0
$323$	9.20550	−	19.1154i	0.512208	−	1.06361i
$324$		0			0
$325$			19.8428i			1.10068i
$326$		0			0
$327$	−1.36405	+	1.71047i	−0.0754324	+	0.0945892i
$328$		0			0
$329$	5.36290	−	20.1066i	0.295666	−	1.10851i
$330$		0			0
$331$	−3.14994	+	6.54091i	−0.173136	+	0.359521i	−0.969422	−	0.245400i	$-0.921081\pi$
$331$	−3.14994	+	6.54091i	−0.173136	+	0.359521i	0.796286	+	0.604921i	$0.206795\pi$
$332$		0			0
$333$	−3.70157	+	4.64163i	−0.202845	+	0.254359i
$334$		0			0
$335$	−1.33927	−	1.67939i	−0.0731720	−	0.0917547i
$336$		0			0
$337$	13.5523	−	16.9941i	0.738243	−	0.925727i	−0.260972	−	0.965346i	$-0.584043\pi$
$337$	13.5523	−	16.9941i	0.738243	−	0.925727i	0.999215	+	0.0396190i	$0.0126144\pi$
$338$		0			0
$339$	−13.6723	+	6.58424i	−0.742579	+	0.357607i
$340$		0			0
$341$	10.3754	−	2.36811i	0.561859	−	0.128241i
$342$		0			0
$343$	−2.13677	−	18.3966i	−0.115374	−	0.993322i
$344$		0			0
$345$	−1.59074	−	6.96948i	−0.0856425	−	0.375224i
$346$		0			0
$347$	−7.07694	−	14.6954i	−0.379910	−	0.788891i	−0.999991	−	0.00435293i	$-0.998614\pi$
$347$	−7.07694	−	14.6954i	−0.379910	−	0.788891i	0.620081	−	0.784538i	$-0.287100\pi$
$348$		0			0
$349$	−18.1017	−	14.4356i	−0.968959	−	0.772719i	0.00487266	−	0.999988i	$-0.498449\pi$
$349$	−18.1017	−	14.4356i	−0.968959	−	0.772719i	−0.973832	+	0.227269i	$0.927020\pi$
$350$		0			0
$351$	−19.7152	+	15.7223i	−1.05232	+	0.839197i
$352$		0			0
$353$	−18.4378	−	14.7036i	−0.981344	−	0.782596i	−0.00525946	−	0.999986i	$-0.501674\pi$
$353$	−18.4378	−	14.7036i	−0.981344	−	0.782596i	−0.976085	+	0.217390i	$0.930246\pi$
$354$		0			0
$355$	2.55631	+	1.23105i	0.135675	+	0.0653375i
$356$		0			0
$357$	−10.3729	−	2.76669i	−0.548991	−	0.146429i
$358$		0			0
$359$	6.17766	+	4.92652i	0.326044	+	0.260012i	0.772807	−	0.634641i	$-0.218852\pi$
$359$	6.17766	+	4.92652i	0.326044	+	0.260012i	−0.446763	+	0.894652i	$0.647423\pi$
$360$		0			0
$361$	39.5973			2.08407
$362$		0			0
$363$	3.87907	+	1.86806i	0.203598	+	0.0980478i
$364$		0			0
$365$	8.82910	−	4.25187i	0.462136	−	0.222553i
$366$		0			0
$367$	−2.55991	+	11.2157i	−0.133626	+	0.585454i	0.863131	+	0.504981i	$0.168500\pi$
$367$	−2.55991	+	11.2157i	−0.133626	+	0.585454i	−0.996757	+	0.0804736i	$0.974357\pi$
$368$		0			0
$369$	4.28001	+	8.88754i	0.222809	+	0.462667i
$370$		0			0
$371$	−31.3090	−	1.13563i	−1.62548	−	0.0589591i
$372$		0			0
$373$	−11.4606			−0.593406			−0.296703	−	0.954970i	$-0.595887\pi$
$373$	−11.4606			−0.593406			−0.296703	+	0.954970i	$0.595887\pi$
$374$		0			0
$375$	−4.47676	+	9.29609i	−0.231179	+	0.480048i
$376$		0			0
$377$	−30.6997	−	7.00701i	−1.58111	−	0.360879i
$378$		0			0
$379$	8.07633	−	1.84337i	0.414853	−	0.0946876i	−0.00999950	−	0.999950i	$-0.503183\pi$
$379$	8.07633	−	1.84337i	0.414853	−	0.0946876i	0.424853	+	0.905262i	$0.360326\pi$
$380$		0			0
$381$	−11.9039	+	2.71699i	−0.609855	+	0.139195i
$382$		0			0
$383$	7.21831	−	31.6255i	0.368838	−	1.61599i	−0.361137	−	0.932513i	$-0.617611\pi$
$383$	7.21831	−	31.6255i	0.368838	−	1.61599i	0.729975	−	0.683474i	$-0.239532\pi$
$384$		0			0
$385$	5.13549	−	2.24759i	0.261729	−	0.114548i
$386$		0			0
$387$	−7.93414	+	6.32726i	−0.403315	+	0.321633i
$388$		0			0
$389$	16.7804	+	21.0420i	0.850801	+	1.06687i	0.996984	+	0.0776132i	$0.0247299\pi$
$389$	16.7804	+	21.0420i	0.850801	+	1.06687i	−0.146182	+	0.989258i	$0.546699\pi$
$390$		0			0
$391$	18.1334			0.917048
$392$		0			0
$393$	11.4400			0.577071
$394$		0			0
$395$	−4.95849	−	6.21775i	−0.249489	−	0.312849i
$396$		0			0
$397$	−5.45246	+	4.34819i	−0.273651	+	0.218230i	−0.750693	−	0.660651i	$-0.770280\pi$
$397$	−5.45246	+	4.34819i	−0.273651	+	0.218230i	0.477042	+	0.878880i	$0.341709\pi$
$398$		0			0
$399$	−5.54562	−	29.1269i	−0.277628	−	1.45817i
$400$		0			0
$401$	−7.85804	+	34.4283i	−0.392412	+	1.71927i	0.263700	+	0.964605i	$0.415057\pi$
$401$	−7.85804	+	34.4283i	−0.392412	+	1.71927i	−0.656112	+	0.754664i	$0.727800\pi$
$402$		0			0
$403$	16.3227	−	3.72554i	0.813090	−	0.185582i
$404$		0			0
$405$	−4.14451	+	0.945957i	−0.205942	+	0.0470050i
$406$		0			0
$407$	−19.1791	−	4.37750i	−0.950673	−	0.216985i
$408$		0			0
$409$	2.11195	−	4.38551i	0.104429	−	0.216850i	−0.842206	−	0.539155i	$-0.818744\pi$
$409$	2.11195	−	4.38551i	0.104429	−	0.216850i	0.946636	+	0.322306i	$0.104458\pi$
$410$		0			0
$411$	−30.2271			−1.49099
$412$		0			0
$413$	−14.4077	+	6.30564i	−0.708955	+	0.310280i
$414$		0			0
$415$	0.829625	+	1.72273i	0.0407247	+	0.0845656i
$416$		0			0
$417$	6.29815	−	27.5940i	0.308422	−	1.35128i
$418$		0			0
$419$	24.8980	−	11.9902i	1.21635	−	0.585761i	0.288054	−	0.957614i	$-0.406992\pi$
$419$	24.8980	−	11.9902i	1.21635	−	0.585761i	0.928292	+	0.371853i	$0.121278\pi$
$420$		0			0
$421$	31.8253	+	15.3262i	1.55107	+	0.746955i	0.996373	−	0.0850982i	$-0.0271204\pi$
$421$	31.8253	+	15.3262i	1.55107	+	0.746955i	0.554696	+	0.832053i	$0.312835\pi$
$422$		0			0
$423$	6.73841			0.327633
$424$		0			0
$425$	−9.62765	−	7.67780i	−0.467010	−	0.372428i
$426$		0			0
$427$	−17.9151	+	13.2536i	−0.866972	+	0.641388i
$428$		0			0
$429$	−16.7233	−	8.05351i	−0.807408	−	0.388827i
$430$		0			0
$431$	−16.7037	−	13.3207i	−0.804587	−	0.641637i	0.132323	−	0.991207i	$-0.457756\pi$
$431$	−16.7037	−	13.3207i	−0.804587	−	0.641637i	−0.936910	+	0.349570i	$0.886328\pi$
$432$		0			0
$433$	−9.69579	+	7.73213i	−0.465950	+	0.371583i	−0.828140	−	0.560522i	$-0.810601\pi$
$433$	−9.69579	+	7.73213i	−0.465950	+	0.371583i	0.362190	+	0.932104i	$0.382029\pi$
$434$		0			0
$435$	−6.02320	−	4.80334i	−0.288790	−	0.230303i
$436$		0			0
$437$	21.7299	+	45.1226i	1.03948	+	2.15851i
$438$		0			0
$439$	−3.73252	−	16.3533i	−0.178144	−	0.780499i	−0.982487	−	0.186333i	$-0.940340\pi$
$439$	−3.73252	−	16.3533i	−0.178144	−	0.780499i	0.804343	−	0.594165i	$-0.202518\pi$
$440$		0			0
$441$	5.57753	−	2.20376i	0.265597	−	0.104941i
$442$		0			0
$443$	5.88301	−	1.34276i	0.279510	−	0.0637964i	−0.0804677	−	0.996757i	$-0.525641\pi$
$443$	5.88301	−	1.34276i	0.279510	−	0.0637964i	0.359978	+	0.932961i	$0.382784\pi$
$444$		0			0
$445$	−5.52580	+	2.66109i	−0.261948	+	0.126148i
$446$		0			0
$447$	−12.9668	+	16.2598i	−0.613308	+	0.769064i
$448$		0			0
$449$	2.38463	+	2.99023i	0.112538	+	0.141118i	0.834910	−	0.550387i	$-0.185520\pi$
$449$	2.38463	+	2.99023i	0.112538	+	0.141118i	−0.722372	+	0.691504i	$0.756948\pi$
$450$		0			0
$451$	−20.3798	+	25.5554i	−0.959647	+	1.20336i
$452$		0			0
$453$	2.32640	−	4.83083i	0.109304	−	0.226972i
$454$		0			0
$455$	8.07920	−	3.53593i	0.378759	−	0.165767i
$456$		0			0
$457$	−10.6215	+	13.3189i	−0.496851	+	0.623032i	−0.965516	−	0.260344i	$-0.916164\pi$
$457$	−10.6215	+	13.3189i	−0.496851	+	0.623032i	0.468664	+	0.883376i	$0.344735\pi$
$458$		0			0
$459$		−	15.6492i		−	0.730443i
$460$		0			0
$461$	0.0359041	−	0.0745555i	0.00167222	−	0.00347240i	−0.900131	−	0.435619i	$-0.856529\pi$
$461$	0.0359041	−	0.0745555i	0.00167222	−	0.00347240i	0.901803	+	0.432147i	$0.142244\pi$
$462$		0			0
$463$	4.40999	+	9.15745i	0.204950	+	0.425583i	0.977955	−	0.208818i	$-0.0669615\pi$
$463$	4.40999	+	9.15745i	0.204950	+	0.425583i	−0.773005	+	0.634400i	$0.781247\pi$
$464$		0			0
$465$	3.99341	+	0.911469i	0.185190	+	0.0422684i
$466$		0			0
$467$	−11.5662	+	5.56998i	−0.535219	+	0.257748i	−0.681912	−	0.731434i	$-0.738851\pi$
$467$	−11.5662	+	5.56998i	−0.535219	+	0.257748i	0.146693	+	0.989182i	$0.453137\pi$
$468$		0			0
$469$	3.55032	−	6.73618i	0.163939	−	0.311048i
$470$		0			0
$471$		−	11.0738i		−	0.510255i
$472$		0			0
$473$	−30.2967	−	14.5901i	−1.39304	−	0.670854i
$474$		0			0
$475$	7.56801	−	33.1576i	0.347244	−	1.52138i
$476$		0			0
$477$	−2.25747	−	9.89061i	−0.103362	−	0.452860i
$478$		0			0
$479$	6.68066	+	29.2699i	0.305247	+	1.33737i	0.862089	+	0.506756i	$0.169156\pi$
$479$	6.68066	+	29.2699i	0.305247	+	1.33737i	−0.556842	+	0.830618i	$0.687987\pi$
$480$		0			0
$481$	−30.1728	−	6.88673i	−1.37576	−	0.314008i
$482$		0			0
$483$	20.3725	−	15.0716i	0.926981	−	0.685783i
$484$		0			0
$485$	1.55631	+	1.95155i	0.0706685	+	0.0886155i
$486$		0			0
$487$	4.26640	−	3.40234i	0.193329	−	0.154175i	−0.522041	−	0.852920i	$-0.674829\pi$
$487$	4.26640	−	3.40234i	0.193329	−	0.154175i	0.715371	+	0.698745i	$0.246258\pi$
$488$		0			0
$489$		−	13.9116i		−	0.629103i
$490$		0			0
$491$		−	14.7035i		−	0.663560i	−0.943357	−	0.331780i	$-0.892351\pi$
$491$		−	14.7035i		−	0.663560i	0.943357	−	0.331780i	$-0.107649\pi$
$492$		0			0
$493$	15.2785	−	12.1842i	0.688107	−	0.548747i
$494$		0			0
$495$	1.13178	+	1.41921i	0.0508697	+	0.0637886i
$496$		0			0
$497$	−0.364578	+	10.0513i	−0.0163536	+	0.450863i
$498$		0			0
$499$	−42.6862	−	9.74284i	−1.91090	−	0.436149i	−0.999708	−	0.0241572i	$-0.992310\pi$
$499$	−42.6862	−	9.74284i	−1.91090	−	0.436149i	−0.911187	−	0.411992i	$-0.864833\pi$
$500$		0			0
$501$	0.896163	+	3.92635i	0.0400376	+	0.175416i
$502$		0			0
$503$	7.20446	+	31.5648i	0.321231	+	1.40740i	0.835366	+	0.549695i	$0.185256\pi$
$503$	7.20446	+	31.5648i	0.321231	+	1.40740i	−0.514135	+	0.857709i	$0.671887\pi$
$504$		0			0
$505$	−0.408769	+	1.79093i	−0.0181900	+	0.0796955i
$506$		0			0
$507$	−9.16213	−	4.41225i	−0.406904	−	0.195955i
$508$		0			0
$509$		−	18.7995i		−	0.833275i	−0.909073	−	0.416638i	$-0.863208\pi$
$509$		−	18.7995i		−	0.833275i	0.909073	−	0.416638i	$-0.136792\pi$
$510$		0			0
$511$	26.3567	+	22.6294i	1.16595	+	1.00106i
$512$		0			0
$513$	38.9409	−	18.7530i	1.71928	−	0.827963i
$514$		0			0
$515$	−1.56189	−	0.356491i	−0.0688250	−	0.0157089i
$516$		0			0
$517$	9.68790	+	20.1171i	0.426073	+	0.884751i
$518$		0			0
$519$	−15.8387	+	32.8895i	−0.695243	+	1.44369i
$520$		0			0
$521$			15.5108i			0.679540i	0.940509	+	0.339770i	$0.110349\pi$
$521$			15.5108i			0.679540i	−0.940509	+	0.339770i	$0.889651\pi$
$522$		0			0
$523$	−11.0902	+	13.9067i	−0.484941	+	0.608097i	−0.962759	−	0.270362i	$-0.912856\pi$
$523$	−11.0902	+	13.9067i	−0.484941	+	0.608097i	0.477818	+	0.878459i	$0.341428\pi$
$524$		0			0
$525$	−17.1978	−	0.623795i	−0.750575	−	0.0272247i
$526$		0			0
$527$	−4.50813	+	9.36124i	−0.196377	+	0.407782i
$528$		0			0
$529$	−12.3480	+	15.4839i	−0.536868	+	0.673212i
$530$		0			0
$531$	−3.17522	−	3.98160i	−0.137793	−	0.172787i
$532$		0			0
$533$	−32.0617	+	40.2041i	−1.38875	+	1.74143i
$534$		0			0
$535$	8.32136	−	4.00735i	0.359764	−	0.173253i
$536$		0			0
$537$	−9.91192	+	2.26233i	−0.427731	+	0.0976268i
$538$		0			0
$539$	14.5981	+	13.4830i	0.628784	+	0.580755i
$540$		0			0
$541$	−1.60462	−	7.03030i	−0.0689881	−	0.302256i	0.928649	−	0.370959i	$-0.120971\pi$
$541$	−1.60462	−	7.03030i	−0.0689881	−	0.302256i	−0.997637	+	0.0687029i	$0.978114\pi$
$542$		0			0
$543$	7.51279	+	15.6005i	0.322405	+	0.669480i
$544$		0			0
$545$	0.872011	+	0.695405i	0.0373528	+	0.0297879i
$546$		0			0
$547$	7.53685	−	6.01043i	0.322252	−	0.256988i	−0.448979	−	0.893542i	$-0.648212\pi$
$547$	7.53685	−	6.01043i	0.322252	−	0.256988i	0.771232	+	0.636554i	$0.219641\pi$
$548$		0			0
$549$	−5.64178	−	4.49917i	−0.240785	−	0.192020i
$550$		0			0
$551$	48.6273	+	23.4177i	2.07159	+	0.997626i
$552$		0			0
$553$	13.1447	−	24.9400i	0.558969	−	1.06056i
$554$		0			0
$555$	−5.91981	−	4.72089i	−0.251282	−	0.200391i
$556$		0			0
$557$	4.57373			0.193795			0.0968976	−	0.995294i	$-0.469108\pi$
$557$	4.57373			0.193795			0.0968976	+	0.995294i	$0.469108\pi$
$558$		0			0
$559$	−47.6631	−	22.9533i	−2.01593	−	0.970822i
$560$		0			0
$561$	10.3783	−	4.99793i	0.438173	−	0.211013i
$562$		0			0
$563$	2.49552	−	10.9336i	0.105174	−	0.460796i	−0.894726	−	0.446616i	$-0.852629\pi$
$563$	2.49552	−	10.9336i	0.105174	−	0.460796i	0.999899	−	0.0141801i	$-0.00451381\pi$
$564$		0			0
$565$	3.35670	+	6.97025i	0.141217	+	0.293241i
$566$		0			0
$567$	−8.96257	−	12.1148i	−0.376392	−	0.508774i
$568$		0			0
$569$	34.8208			1.45976			0.729882	−	0.683573i	$-0.239575\pi$
$569$	34.8208			1.45976			0.729882	+	0.683573i	$0.239575\pi$
$570$		0			0
$571$	0.143914	−	0.298840i	0.00602259	−	0.0125060i	−0.897936	−	0.440126i	$-0.854934\pi$
$571$	0.143914	−	0.298840i	0.00602259	−	0.0125060i	0.903958	+	0.427620i	$0.140648\pi$
$572$		0			0
$573$	−20.3756	−	4.65061i	−0.851204	−	0.194282i
$574$		0			0
$575$	28.3393	−	6.46827i	1.18183	−	0.269746i
$576$		0			0
$577$	−14.2014	+	3.24139i	−0.591214	+	0.134941i	−0.507653	−	0.861562i	$-0.669487\pi$
$577$	−14.2014	+	3.24139i	−0.591214	+	0.134941i	−0.0835615	+	0.996503i	$0.526630\pi$
$578$		0			0
$579$	4.80214	−	21.0395i	0.199570	−	0.874373i
$580$		0			0
$581$	−4.41544	+	5.14272i	−0.183183	+	0.213356i
$582$		0			0
$583$	26.2823	−	20.9594i	1.08850	−	0.868050i
$584$		0			0
$585$	1.78053	+	2.23271i	0.0736158	+	0.0923113i
$586$		0			0
$587$	17.1275			0.706929			0.353464	−	0.935448i	$-0.385004\pi$
$587$	17.1275			0.706929			0.353464	+	0.935448i	$0.385004\pi$
$588$		0			0
$589$	−28.6964			−1.18241
$590$		0			0
$591$	−12.3004	−	15.4242i	−0.505971	−	0.634468i
$592$		0			0
$593$	7.08018	−	5.64625i	0.290748	−	0.231864i	−0.467243	−	0.884129i	$-0.654753\pi$
$593$	7.08018	−	5.64625i	0.290748	−	0.231864i	0.757991	+	0.652265i	$0.226181\pi$
$594$		0			0
$595$	−1.41048	+	5.28817i	−0.0578239	+	0.216794i
$596$		0			0
$597$	2.84709	−	12.4739i	0.116524	−	0.510523i
$598$		0			0
$599$	−22.3946	+	5.11142i	−0.915018	+	0.208847i	−0.654007	−	0.756489i	$-0.726913\pi$
$599$	−22.3946	+	5.11142i	−0.915018	+	0.208847i	−0.261012	+	0.965336i	$0.584056\pi$
$600$		0			0
$601$	30.9570	−	7.06574i	1.26276	−	0.288217i	0.461828	−	0.886969i	$-0.347194\pi$
$601$	30.9570	−	7.06574i	1.26276	−	0.288217i	0.800935	+	0.598752i	$0.204336\pi$
$602$		0			0
$603$	2.40387	+	0.548667i	0.0978930	+	0.0223434i
$604$		0			0
$605$	0.952351	−	1.97758i	0.0387186	−	0.0804000i
$606$		0			0
$607$	0.455111			0.0184724			0.00923619	−	0.999957i	$-0.497060\pi$
$607$	0.455111			0.0184724			0.00923619	+	0.999957i	$0.497060\pi$
$608$		0			0
$609$	7.03811	−	26.3873i	0.285199	−	1.06927i
$610$		0			0
$611$	15.2411	+	31.6485i	0.616589	+	1.28036i
$612$		0			0
$613$	−6.55574	+	28.7226i	−0.264784	+	1.16009i	0.651209	+	0.758899i	$0.274262\pi$
$613$	−6.55574	+	28.7226i	−0.264784	+	1.16009i	−0.915993	+	0.401195i	$0.868595\pi$
$614$		0			0
$615$	−11.3349	+	5.45862i	−0.457069	+	0.220113i
$616$		0			0
$617$	−18.9663	−	9.13371i	−0.763556	−	0.367709i	0.0112263	−	0.999937i	$-0.496426\pi$
$617$	−18.9663	−	9.13371i	−0.763556	−	0.367709i	−0.774783	+	0.632228i	$0.782141\pi$
$618$		0			0
$619$	5.28200			0.212302			0.106151	−	0.994350i	$-0.466147\pi$
$619$	5.28200			0.212302			0.106151	+	0.994350i	$0.466147\pi$
$620$		0			0
$621$	28.8813	+	23.0320i	1.15897	+	0.924244i
$622$		0			0
$623$	−16.4957	−	14.1629i	−0.660885	−	0.567423i
$624$		0			0
$625$	−15.2756	−	7.35635i	−0.611024	−	0.294254i
$626$		0			0
$627$	24.8733	+	19.8358i	0.993344	+	0.792166i
$628$		0			0
$629$	15.0162	−	11.9750i	0.598736	−	0.477476i
$630$		0			0
$631$	12.0725	+	9.62751i	0.480599	+	0.383265i	0.833609	−	0.552354i	$-0.186270\pi$
$631$	12.0725	+	9.62751i	0.480599	+	0.383265i	−0.353010	+	0.935620i	$0.614842\pi$
$632$		0			0
$633$	−2.13434	−	4.43199i	−0.0848322	−	0.176156i
$634$		0			0
$635$	1.38514	+	6.06870i	0.0549676	+	0.240829i
$636$		0			0
$637$	22.9659	+	21.2116i	0.909941	+	0.840435i
$638$		0			0
$639$	−3.17524	+	0.724727i	−0.125610	+	0.0286698i
$640$		0			0
$641$	−13.9476	+	6.71679i	−0.550896	+	0.265297i	−0.688557	−	0.725182i	$-0.741756\pi$
$641$	−13.9476	+	6.71679i	−0.550896	+	0.265297i	0.137662	+	0.990479i	$0.456041\pi$
$642$		0			0
$643$	5.10534	−	6.40189i	0.201335	−	0.252466i	−0.670906	−	0.741542i	$-0.734095\pi$
$643$	5.10534	−	6.40189i	0.201335	−	0.252466i	0.872241	+	0.489076i	$0.162666\pi$
$644$		0			0
$645$	−8.06964	−	10.1190i	−0.317742	−	0.398435i
$646$		0			0
$647$	6.91336	−	8.66907i	0.271792	−	0.340816i	−0.627138	−	0.778908i	$-0.715774\pi$
$647$	6.91336	−	8.66907i	0.271792	−	0.340816i	0.898930	+	0.438091i	$0.144345\pi$
$648$		0			0
$649$	7.32178	−	15.2038i	0.287405	−	0.596803i
$650$		0			0
$651$	2.71581	+	14.2641i	0.106441	+	0.559053i
$652$		0			0
$653$	−20.3303	+	25.4934i	−0.795587	+	0.997635i	0.204238	+	0.978921i	$0.434528\pi$
$653$	−20.3303	+	25.4934i	−0.795587	+	0.997635i	−0.999825	+	0.0187135i	$0.994043\pi$
$654$		0			0
$655$		−	5.83219i		−	0.227883i
$656$		0			0
$657$	−4.88068	+	10.1348i	−0.190413	+	0.395398i
$658$		0			0
$659$	−1.32499	−	2.75137i	−0.0516143	−	0.107178i	0.873567	−	0.486705i	$-0.161801\pi$
$659$	−1.32499	−	2.75137i	−0.0516143	−	0.107178i	−0.925181	+	0.379526i	$0.876087\pi$
$660$		0			0
$661$	−45.3445	−	10.3496i	−1.76370	−	0.402552i	−0.786961	−	0.617002i	$-0.788347\pi$
$661$	−45.3445	−	10.3496i	−1.76370	−	0.402552i	−0.976735	+	0.214450i	$0.931204\pi$
$662$		0			0
$663$	16.3273	−	7.86280i	0.634098	−	0.305366i
$664$		0			0
$665$	−14.8491	+	2.82720i	−0.575823	+	0.109634i
$666$		0			0
$667$			46.1293i			1.78613i
$668$		0			0
$669$	16.1821	+	7.79287i	0.625634	+	0.301290i
$670$		0			0
$671$	5.32075	−	23.3117i	0.205405	−	0.899938i
$672$		0			0
$673$	1.32432	+	5.80221i	0.0510486	+	0.223659i	0.994017	−	0.109223i	$-0.0348362\pi$
$673$	1.32432	+	5.80221i	0.0510486	+	0.223659i	−0.942969	+	0.332882i	$0.891979\pi$
$674$		0			0
$675$	−5.58214	−	24.4569i	−0.214857	−	0.941348i
$676$		0			0
$677$	−7.08002	−	1.61597i	−0.272107	−	0.0621067i	0.0842899	−	0.996441i	$-0.473138\pi$
$677$	−7.08002	−	1.61597i	−0.272107	−	0.0621067i	−0.356397	+	0.934335i	$0.615995\pi$
$678$		0			0
$679$	−4.12570	+	7.82787i	−0.158330	+	0.300406i
$680$		0			0
$681$	−15.3718	−	19.2757i	−0.589050	−	0.738646i
$682$		0			0
$683$	−9.45025	+	7.53633i	−0.361604	+	0.288370i	−0.787391	−	0.616454i	$-0.788569\pi$
$683$	−9.45025	+	7.53633i	−0.361604	+	0.288370i	0.425787	+	0.904823i	$0.359997\pi$
$684$		0			0
$685$			15.4100i			0.588786i
$686$		0			0
$687$			16.7555i			0.639261i
$688$		0			0
$689$	41.3475	−	32.9735i	1.57522	−	1.25619i
$690$		0			0
$691$	4.44921	+	5.57913i	0.169256	+	0.212240i	0.859224	−	0.511600i	$-0.170947\pi$
$691$	4.44921	+	5.57913i	0.169256	+	0.212240i	−0.689968	+	0.723840i	$0.742375\pi$
$692$		0			0
$693$	−3.00028	+	5.69257i	−0.113971	+	0.216243i
$694$		0			0
$695$	−14.0676	−	3.21085i	−0.533616	−	0.121794i
$696$		0			0
$697$	−7.10122	−	31.1125i	−0.268978	−	1.17847i
$698$		0			0
$699$	8.37751	+	36.7043i	0.316866	+	1.38828i
$700$		0			0
$701$	1.42298	−	6.23450i	0.0537454	−	0.235474i	−0.940920	−	0.338629i	$-0.890037\pi$
$701$	1.42298	−	6.23450i	0.0537454	−	0.235474i	0.994665	+	0.103155i	$0.0328939\pi$
$702$		0			0
$703$	47.7926	+	23.0157i	1.80253	+	0.868054i
$704$		0			0
$705$			8.59401i			0.323669i
$706$		0			0
$707$	−6.39704	+	1.21797i	−0.240586	+	0.0458064i
$708$		0			0
$709$	23.1413	−	11.1443i	0.869090	−	0.418532i	0.0544622	−	0.998516i	$-0.482656\pi$
$709$	23.1413	−	11.1443i	0.869090	−	0.418532i	0.814628	+	0.579984i	$0.196941\pi$
$710$		0			0
$711$	8.90006	+	2.03138i	0.333778	+	0.0761827i
$712$		0			0
$713$	−10.6416	−	22.0975i	−0.398531	−	0.827558i
$714$		0			0
$715$	−4.10574	+	8.52566i	−0.153546	+	0.318842i
$716$		0			0
$717$		−	21.3693i		−	0.798052i
$718$		0			0
$719$	−16.2410	+	20.3656i	−0.605688	+	0.759509i	−0.986252	−	0.165246i	$-0.947158\pi$
$719$	−16.2410	+	20.3656i	−0.605688	+	0.759509i	0.380564	+	0.924754i	$0.375730\pi$
$720$		0			0
$721$	−1.06220	−	5.57892i	−0.0395584	−	0.207770i
$722$		0			0
$723$	5.63163	−	11.6942i	0.209443	−	0.434912i
$724$		0			0
$725$	19.5314	−	24.4916i	0.725377	−	0.909594i
$726$		0			0
$727$	5.87310	+	7.36464i	0.217821	+	0.273139i	0.878722	−	0.477334i	$-0.158397\pi$
$727$	5.87310	+	7.36464i	0.217821	+	0.273139i	−0.660901	+	0.750474i	$0.729825\pi$
$728$		0			0
$729$	18.5038	−	23.2031i	0.685327	−	0.859372i
$730$		0			0
$731$	29.5792	−	14.2446i	1.09403	−	0.526856i
$732$		0			0
$733$	−3.32048	+	0.757878i	−0.122645	+	0.0279929i	−0.283403	−	0.959001i	$-0.591463\pi$
$733$	−3.32048	+	0.757878i	−0.122645	+	0.0279929i	0.160758	+	0.986994i	$0.448606\pi$
$734$		0			0
$735$	2.81062	+	7.11345i	0.103671	+	0.262384i
$736$		0			0
$737$	1.81806	+	7.96543i	0.0669690	+	0.293410i
$738$		0			0
$739$	15.4618	+	32.1068i	0.568772	+	1.18107i	0.964838	+	0.262846i	$0.0846610\pi$
$739$	15.4618	+	32.1068i	0.568772	+	1.18107i	−0.396066	+	0.918222i	$0.629625\pi$
$740$		0			0
$741$	39.1310	+	31.2059i	1.43751	+	1.14638i
$742$		0			0
$743$	40.2744	−	32.1178i	1.47753	−	1.17829i	0.534682	−	0.845054i	$-0.320432\pi$
$743$	40.2744	−	32.1178i	1.47753	−	1.17829i	0.942844	−	0.333234i	$-0.108140\pi$
$744$		0			0
$745$	8.28938	+	6.61056i	0.303700	+	0.242192i
$746$		0			0
$747$	−1.97751	−	0.952318i	−0.0723532	−	0.0348435i
$748$		0			0
$749$	24.8410	+	21.3280i	0.907670	+	0.779308i
$750$		0			0
$751$	−13.5100	−	10.7739i	−0.492987	−	0.393144i	0.345198	−	0.938530i	$-0.387812\pi$
$751$	−13.5100	−	10.7739i	−0.492987	−	0.393144i	−0.838185	+	0.545386i	$0.816383\pi$
$752$		0			0
$753$	3.85299			0.140411
$754$		0			0
$755$	−2.46279	−	1.18602i	−0.0896302	−	0.0431636i
$756$		0			0
$757$	−16.9022	+	8.13966i	−0.614320	+	0.295841i	−0.715051	−	0.699073i	$-0.753596\pi$
$757$	−16.9022	+	8.13966i	−0.614320	+	0.295841i	0.100730	+	0.994914i	$0.467882\pi$
$758$		0			0
$759$	−6.05059	+	26.5094i	−0.219623	+	0.962229i
$760$		0			0
$761$	−18.2606	−	37.9185i	−0.661946	−	1.37455i	−0.913555	−	0.406716i	$-0.866674\pi$
$761$	−18.2606	−	37.9185i	−0.661946	−	1.37455i	0.251608	−	0.967829i	$-0.419040\pi$
$762$		0			0
$763$	−1.01895	+	3.82023i	−0.0368883	+	0.138302i
$764$		0			0
$765$	−1.77225			−0.0640757
$766$		0			0
$767$	11.5187	−	23.9188i	0.415916	−	0.863659i
$768$		0			0
$769$	15.5717	+	3.55413i	0.561529	+	0.128165i	0.493858	−	0.869542i	$-0.335586\pi$
$769$	15.5717	+	3.55413i	0.561529	+	0.128165i	0.0676707	+	0.997708i	$0.478443\pi$
$770$		0			0
$771$	−10.9590	+	2.50131i	−0.394677	+	0.0900825i
$772$		0			0
$773$	36.3233	−	8.29057i	1.30646	−	0.298191i	0.488045	−	0.872819i	$-0.337710\pi$
$773$	36.3233	−	8.29057i	1.30646	−	0.298191i	0.818415	+	0.574628i	$0.194853\pi$
$774$		0			0
$775$	−3.70622	+	16.2380i	−0.133131	+	0.583287i
$776$		0			0
$777$	6.91731	−	25.9344i	0.248157	−	0.930391i
$778$		0			0
$779$	68.9095	−	54.9535i	2.46894	−	1.96891i
$780$		0			0
$781$	−6.72871	−	8.43753i	−0.240772	−	0.301919i
$782$		0			0
$783$	39.8097			1.42268
$784$		0			0
$785$	−5.64552			−0.201497
$786$		0			0
$787$	−27.1158	−	34.0021i	−0.966572	−	1.21204i	−0.977248	−	0.212100i	$-0.931970\pi$
$787$	−27.1158	−	34.0021i	−0.966572	−	1.21204i	0.0106758	−	0.999943i	$-0.496602\pi$
$788$		0			0
$789$	−25.1910	+	20.0892i	−0.896824	+	0.715193i
$790$		0			0
$791$	−17.8650	+	20.8077i	−0.635208	+	0.739835i
$792$		0			0
$793$	8.37065	−	36.6742i	0.297251	−	1.30234i
$794$		0			0
$795$	12.6142	−	2.87912i	0.447381	−	0.102112i
$796$		0			0
$797$	19.5452	−	4.46107i	0.692327	−	0.158019i	0.138142	−	0.990412i	$-0.455887\pi$
$797$	19.5452	−	4.46107i	0.692327	−	0.158019i	0.554185	+	0.832393i	$0.313030\pi$
$798$		0			0
$799$	−21.2530	−	4.85086i	−0.751878	−	0.171611i
$800$		0			0
$801$	3.05463	−	6.34301i	0.107930	−	0.224119i
$802$		0			0
$803$	−37.2740			−1.31537
$804$		0			0
$805$	−7.68362	−	10.3861i	−0.270812	−	0.366060i
$806$		0			0
$807$	2.56965	+	5.33593i	0.0904559	+	0.187834i
$808$		0			0
$809$	0.768601	−	3.36746i	0.0270226	−	0.118394i	−0.959618	−	0.281307i	$-0.909232\pi$
$809$	0.768601	−	3.36746i	0.0270226	−	0.118394i	0.986640	+	0.162914i	$0.0520892\pi$
$810$		0			0
$811$	−19.7053	+	9.48958i	−0.691948	+	0.333224i	−0.746593	−	0.665281i	$-0.768312\pi$
$811$	−19.7053	+	9.48958i	−0.691948	+	0.333224i	0.0546451	+	0.998506i	$0.482597\pi$
$812$		0			0
$813$	3.03051	+	1.45942i	0.106285	+	0.0511840i
$814$		0			0
$815$	−7.09222			−0.248430
$816$		0			0
$817$	70.8914	+	56.5340i	2.48018	+	1.97788i
$818$		0			0
$819$	−4.72008	+	8.95561i	−0.164933	+	0.312934i
$820$		0			0
$821$	33.4886	+	16.1273i	1.16876	+	0.562845i	0.914617	−	0.404322i	$-0.132492\pi$
$821$	33.4886	+	16.1273i	1.16876	+	0.562845i	0.254143	+	0.967167i	$0.418207\pi$
$822$		0			0
$823$	−16.4790	−	13.1416i	−0.574424	−	0.458087i	0.292683	−	0.956209i	$-0.405452\pi$
$823$	−16.4790	−	13.1416i	−0.574424	−	0.458087i	−0.867107	+	0.498122i	$0.834023\pi$
$824$		0			0
$825$	14.4367	−	11.5129i	0.502620	−	0.400826i
$826$		0			0
$827$	25.5756	+	20.3958i	0.889350	+	0.709233i	0.957497	−	0.288442i	$-0.0931374\pi$
$827$	25.5756	+	20.3958i	0.889350	+	0.709233i	−0.0681473	+	0.997675i	$0.521709\pi$
$828$		0			0
$829$	−8.66507	−	17.9932i	−0.300950	−	0.624930i	0.694576	−	0.719420i	$-0.255592\pi$
$829$	−8.66507	−	17.9932i	−0.300950	−	0.624930i	−0.995526	+	0.0944902i	$0.969878\pi$
$830$		0			0
$831$	2.25720	+	9.88942i	0.0783012	+	0.343060i
$832$		0			0
$833$	−19.1780	+	2.93552i	−0.664480	+	0.101710i
$834$		0			0
$835$	2.00168	−	0.456871i	0.0692710	−	0.0158107i
$836$		0			0
$837$	−19.0702	+	9.18374i	−0.659163	+	0.317436i
$838$		0			0
$839$	−19.1156	+	23.9703i	−0.659945	+	0.827545i	−0.993337	−	0.115243i	$-0.963235\pi$
$839$	−19.1156	+	23.9703i	−0.659945	+	0.827545i	0.333392	+	0.942788i	$0.391807\pi$
$840$		0			0
$841$	12.9138	+	16.1934i	0.445304	+	0.558394i
$842$		0			0
$843$	−5.57737	+	6.99381i	−0.192095	+	0.240879i
$844$		0			0
$845$	−2.24940	+	4.67092i	−0.0773816	+	0.160685i
$846$		0			0
$847$	7.77576	+	0.282040i	0.267178	+	0.00969102i
$848$		0			0
$849$	−21.2619	+	26.6616i	−0.729707	+	0.915024i
$850$		0			0
$851$			45.3375i			1.55415i
$852$		0			0
$853$	4.72558	−	9.81277i	0.161801	−	0.335983i	−0.804268	−	0.594266i	$-0.797443\pi$
$853$	4.72558	−	9.81277i	0.161801	−	0.335983i	0.966069	+	0.258283i	$0.0831568\pi$
$854$		0			0
$855$	−2.12374	−	4.40999i	−0.0726304	−	0.150819i
$856$		0			0
$857$	−4.85761	−	1.10872i	−0.165933	−	0.0378730i	0.138747	−	0.990328i	$-0.455692\pi$
$857$	−4.85761	−	1.10872i	−0.165933	−	0.0378730i	−0.304680	+	0.952455i	$0.598550\pi$
$858$		0			0
$859$	36.2912	−	17.4769i	1.23824	−	0.596304i	0.303904	−	0.952703i	$-0.401710\pi$
$859$	36.2912	−	17.4769i	1.23824	−	0.596304i	0.934334	+	0.356398i	$0.115995\pi$
$860$		0			0
$861$	−33.8372	−	29.0519i	−1.15317	−	0.990088i
$862$		0			0
$863$		−	45.7020i		−	1.55571i	−0.628441	−	0.777857i	$-0.716307\pi$
$863$		−	45.7020i		−	1.55571i	0.628441	−	0.777857i	$-0.283693\pi$
$864$		0			0
$865$	16.7673	+	8.07470i	0.570105	+	0.274548i
$866$		0			0
$867$	3.03554	−	13.2995i	0.103092	−	0.451676i
$868$		0			0
$869$	6.73116	+	29.4911i	0.228339	+	1.00042i
$870$		0			0
$871$	2.86019	+	12.5313i	0.0969137	+	0.424607i
$872$		0			0
$873$	−2.79345	−	0.637586i	−0.0945438	−	0.0215790i
$874$		0			0
$875$	−0.675903	+	18.6344i	−0.0228497	+	0.629959i
$876$		0			0
$877$	8.86076	+	11.1110i	0.299206	+	0.375193i	0.908595	−	0.417679i	$-0.137156\pi$
$877$	8.86076	+	11.1110i	0.299206	+	0.375193i	−0.609388	+	0.792872i	$0.708585\pi$
$878$		0			0
$879$	4.92344	−	3.92631i	0.166064	−	0.132431i
$880$		0			0
$881$		−	55.0950i		−	1.85620i	−0.372332	−	0.928099i	$-0.621442\pi$
$881$		−	55.0950i		−	1.85620i	0.372332	−	0.928099i	$-0.378558\pi$
$882$		0			0
$883$		−	3.88004i		−	0.130574i	−0.997867	−	0.0652869i	$-0.979204\pi$
$883$		−	3.88004i		−	0.130574i	0.997867	−	0.0652869i	$-0.0207963\pi$
$884$		0			0
$885$	5.07804	−	4.04960i	0.170696	−	0.136126i
$886$		0			0
$887$	−7.87252	−	9.87183i	−0.264333	−	0.331464i	0.631897	−	0.775052i	$-0.282277\pi$
$887$	−7.87252	−	9.87183i	−0.264333	−	0.331464i	−0.896231	+	0.443589i	$0.853705\pi$
$888$		0			0
$889$	−17.7394	+	13.1237i	−0.594961	+	0.440153i
$890$		0			0
$891$	15.7642	+	3.59808i	0.528121	+	0.120540i
$892$		0			0
$893$	−13.3975	−	58.6981i	−0.448329	−	1.96426i
$894$		0			0
$895$	1.15335	+	5.05317i	0.0385523	+	0.168909i
$896$		0			0
$897$	−9.51885	+	41.7048i	−0.317825	+	1.39248i
$898$		0			0
$899$	−23.8138	−	11.4681i	−0.794236	−	0.382484i
$900$		0			0
$901$			32.8202i			1.09340i
$902$		0			0
$903$	21.3921	−	40.5883i	0.711886	−	1.35069i
$904$		0			0
$905$	7.95324	−	3.83008i	0.264375	−	0.127316i
$906$		0			0
$907$	15.2535	+	3.48150i	0.506483	+	0.115601i	0.468124	−	0.883663i	$-0.344930\pi$
$907$	15.2535	+	3.48150i	0.506483	+	0.115601i	0.0383587	+	0.999264i	$0.487787\pi$
$908$		0			0
$909$	−0.914915	−	1.89984i	−0.0303458	−	0.0630137i
$910$		0			0
$911$	−13.8819	+	28.8260i	−0.459927	+	0.955049i	0.534049	+	0.845454i	$0.320670\pi$
$911$	−13.8819	+	28.8260i	−0.459927	+	0.955049i	−0.993976	+	0.109595i	$0.965044\pi$
$912$		0			0
$913$		−	7.27289i		−	0.240698i
$914$		0			0
$915$	5.73813	−	7.19538i	0.189697	−	0.237872i
$916$		0			0
$917$	18.9401	−	8.28927i	0.625456	−	0.273736i
$918$		0			0
$919$	23.6354	−	49.0794i	0.779660	−	1.61898i	−0.00573224	−	0.999984i	$-0.501825\pi$
$919$	23.6354	−	49.0794i	0.779660	−	1.61898i	0.785393	−	0.618998i	$-0.212461\pi$
$920$		0			0
$921$	−3.58305	+	4.49300i	−0.118066	+	0.148050i
$922$		0			0
$923$	−10.5857	−	13.2740i	−0.348432	−	0.436920i
$924$		0			0
$925$	19.1961	−	24.0712i	0.631165	−	0.791456i
$926$		0			0
$927$	1.65687	−	0.797905i	0.0544187	−	0.0262066i
$928$		0			0
$929$	29.4374	−	6.71889i	0.965809	−	0.220440i	0.289599	−	0.957148i	$-0.406478\pi$
$929$	29.4374	−	6.71889i	0.965809	−	0.220440i	0.676211	+	0.736708i	$0.263621\pi$
$930$		0			0
$931$	−30.2863	−	44.2042i	−0.992593	−	1.44873i
$932$		0			0
$933$	3.79801	+	16.6402i	0.124341	+	0.544774i
$934$		0			0
$935$	−2.54798	−	5.29094i	−0.0833279	−	0.173032i
$936$		0			0
$937$	25.9883	+	20.7249i	0.848999	+	0.677054i	0.948082	−	0.318025i	$-0.103020\pi$
$937$	25.9883	+	20.7249i	0.848999	+	0.677054i	−0.0990830	+	0.995079i	$0.531591\pi$
$938$		0			0
$939$	6.32002	−	5.04005i	0.206246	−	0.164476i
$940$		0			0
$941$	−11.0991	−	8.85126i	−0.361821	−	0.288543i	0.425658	−	0.904884i	$-0.360043\pi$
$941$	−11.0991	−	8.85126i	−0.361821	−	0.288543i	−0.787479	+	0.616341i	$0.788614\pi$
$942$		0			0
$943$	67.8706	+	32.6848i	2.21017	+	1.06436i
$944$		0			0
$945$	−8.96320	+	6.63099i	−0.291573	+	0.215706i
$946$		0			0
$947$	16.4689	+	13.1335i	0.535168	+	0.426782i	0.853420	−	0.521224i	$-0.174524\pi$
$947$	16.4689	+	13.1335i	0.535168	+	0.426782i	−0.318252	+	0.948006i	$0.603096\pi$
$948$		0			0
$949$	−58.6398			−1.90353
$950$		0			0
$951$	−25.6023	−	12.3294i	−0.830210	−	0.399808i
$952$		0			0
$953$	−22.8440	+	11.0011i	−0.739990	+	0.356360i	−0.765605	−	0.643312i	$-0.777560\pi$
$953$	−22.8440	+	11.0011i	−0.739990	+	0.356360i	0.0256146	+	0.999672i	$0.491846\pi$
$954$		0			0
$955$	−2.37091	+	10.3876i	−0.0767209	+	0.336136i
$956$		0			0
$957$	12.7141	+	26.4012i	0.410989	+	0.853428i
$958$		0			0
$959$	−50.0440	+	21.9022i	−1.61601	+	0.707258i
$960$		0			0
$961$	−16.9468			−0.546669
$962$		0			0
$963$	−4.60000	+	9.55200i	−0.148233	+	0.307809i
$964$		0			0
$965$	−10.7261	−	2.44817i	−0.345286	−	0.0788092i
$966$		0			0
$967$	−18.4090	+	4.20173i	−0.591993	+	0.135118i	−0.508014	−	0.861349i	$-0.669620\pi$
$967$	−18.4090	+	4.20173i	−0.591993	+	0.135118i	−0.0839791	+	0.996468i	$0.526763\pi$
$968$		0			0
$969$	−30.2820	+	6.91167i	−0.972798	+	0.222035i
$970$		0			0
$971$	−5.15127	+	22.5692i	−0.165312	+	0.724279i	0.822518	+	0.568740i	$0.192569\pi$
$971$	−5.15127	+	22.5692i	−0.165312	+	0.724279i	−0.987830	+	0.155540i	$0.950288\pi$
$972$		0			0
$973$	−9.56704	−	50.2482i	−0.306705	−	1.61088i
$974$		0			0
$975$	22.7119	−	18.1121i	0.727363	−	0.580053i
$976$		0			0
$977$	−12.9016	−	16.1781i	−0.412759	−	0.517583i	0.531379	−	0.847134i	$-0.321674\pi$
$977$	−12.9016	−	16.1781i	−0.412759	−	0.517583i	−0.944138	+	0.329551i	$0.893103\pi$
$978$		0			0
$979$	23.3284			0.745578
$980$		0			0
$981$	−1.28029			−0.0408766
$982$		0			0
$983$	20.1774	+	25.3017i	0.643560	+	0.806999i	0.991443	−	0.130539i	$-0.0416709\pi$
$983$	20.1774	+	25.3017i	0.643560	+	0.806999i	−0.347883	+	0.937538i	$0.613099\pi$
$984$		0			0
$985$	−7.86339	+	6.27084i	−0.250548	+	0.199806i
$986$		0			0
$987$	−27.9091	+	12.2146i	−0.888355	+	0.388796i
$988$		0			0
$989$	−17.2448	+	75.5544i	−0.548353	+	2.40249i
$990$		0			0
$991$	−19.7064	+	4.49786i	−0.625994	+	0.142879i	−0.523739	−	0.851879i	$-0.675463\pi$
$991$	−19.7064	+	4.49786i	−0.625994	+	0.142879i	−0.102256	+	0.994758i	$0.532606\pi$
$992$		0			0
$993$	10.3619	−	2.36504i	0.328825	−	0.0750521i
$994$		0			0
$995$	−6.35929	−	1.45147i	−0.201603	−	0.0460146i
$996$		0			0
$997$	9.01881	−	18.7278i	0.285629	−	0.593114i	−0.707949	−	0.706263i	$-0.750380\pi$
$997$	9.01881	−	18.7278i	0.285629	−	0.593114i	0.993578	+	0.113149i	$0.0360938\pi$
$998$		0			0
$999$	39.1264			1.23790

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	784.2.bb.b.111.7	✓	120
4.3	odd	2	inner	784.2.bb.b.111.14	yes	120
49.34	odd	14	inner	784.2.bb.b.671.14	yes	120
196.83	even	14	inner	784.2.bb.b.671.7	yes	120

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
784.2.bb.b.111.7	✓	120	1.1	even	1	trivial
784.2.bb.b.111.14	yes	120	4.3	odd	2	inner
784.2.bb.b.671.7	yes	120	196.83	even	14	inner
784.2.bb.b.671.14	yes	120	49.34	odd	14	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:	\( N \)	\(=\)	\( 784 = 2^{4} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	784.bb (of order \(14\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.912783 - 1.14459i) q^{3} +(-0.583523 + 0.465344i) q^{5} +(-2.34056 - 1.23360i) q^{7} +(0.190641 - 0.835251i) q^{9} +O(q^{10})\)	\(q+(-0.912783 - 1.14459i) q^{3} +(-0.583523 + 0.465344i) q^{5} +(-2.34056 - 1.23360i) q^{7} +(0.190641 - 0.835251i) q^{9} +(2.76768 - 0.631705i) q^{11} +(4.35414 - 0.993805i) q^{13} +(1.06526 + 0.243138i) q^{15} +(-1.20256 + 2.49715i) q^{17} -7.65489 q^{19} +(0.724455 + 3.80500i) q^{21} +(-2.83869 - 5.89461i) q^{23} +(-0.988651 + 4.33156i) q^{25} +(-5.08707 + 2.44980i) q^{27} +(-6.35245 - 3.05918i) q^{29} +3.74877 q^{31} +(-3.24934 - 2.59126i) q^{33} +(1.93982 - 0.369333i) q^{35} +(-6.24341 - 3.00667i) q^{37} +(-5.11189 - 4.07660i) q^{39} +(-9.00202 + 7.17887i) q^{41} +(-9.26094 - 7.38535i) q^{43} +(0.277436 + 0.576101i) q^{45} +(1.75018 + 7.66806i) q^{47} +(3.95646 + 5.77463i) q^{49} +(3.95591 - 0.902910i) q^{51} +(10.6688 - 5.13783i) q^{53} +(-1.32104 + 1.65654i) q^{55} +(6.98725 + 8.76174i) q^{57} +(3.70620 - 4.64743i) q^{59} +(3.65453 - 7.58871i) q^{61} +(-1.47657 + 1.71978i) q^{63} +(-2.07828 + 2.60608i) q^{65} +2.87802i q^{67} +(-4.15582 + 8.62965i) q^{69} +(-1.64942 - 3.42506i) q^{71} +(-12.8007 - 2.92168i) q^{73} +(5.86030 - 2.82217i) q^{75} +(-7.25720 - 1.93566i) q^{77} +10.6555i q^{79} +(5.13175 + 2.47132i) q^{81} +(0.570078 - 2.49768i) q^{83} +(-0.460310 - 2.01675i) q^{85} +(2.29689 + 10.0633i) q^{87} +(8.01149 + 1.82857i) q^{89} +(-11.4171 - 3.04521i) q^{91} +(-3.42181 - 4.29082i) q^{93} +(4.46680 - 3.56215i) q^{95} -3.34444i q^{97} -2.43214i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 120 q - 24 q^{9}+O(q^{10}) \) 120 * q - 24 * q^9	\( 120 q - 24 q^{9} - 14 q^{17} + 16 q^{21} + 40 q^{25} + 32 q^{29} - 62 q^{37} - 28 q^{41} - 60 q^{49} + 14 q^{53} - 34 q^{57} - 112 q^{61} - 32 q^{65} + 112 q^{69} + 42 q^{73} + 66 q^{77} - 44 q^{81} - 12 q^{85} + 28 q^{89} - 58 q^{93}+O(q^{100}) \) 120 * q - 24 * q^9 - 14 * q^17 + 16 * q^21 + 40 * q^25 + 32 * q^29 - 62 * q^37 - 28 * q^41 - 60 * q^49 + 14 * q^53 - 34 * q^57 - 112 * q^61 - 32 * q^65 + 112 * q^69 + 42 * q^73 + 66 * q^77 - 44 * q^81 - 12 * q^85 + 28 * q^89 - 58 * q^93

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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