LMFDB - Embedded newform 768.2.o.a.287.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [768,2,Mod(95,768)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(768, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([4, 3, 4]))

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

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

chi := DirichletCharacter("768.95");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 768 = 2^{8} \cdot 3 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	768.o (of order $8$, degree $4$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.13251087523$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$14$ over $\Q(\zeta_{8})$
Twist minimal:	no (minimal twist has level 96)
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			287.4
Character	$\chi$	$=$	768.287
Dual form			768.2.o.a.479.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.39698 + 1.02394i) q^{3} +(-1.20190 + 2.90164i) q^{5} +(-2.49510 + 2.49510i) q^{7} +(0.903094 - 2.86084i) q^{9} +O(q^{10})$	\(q+(-1.39698 + 1.02394i) q^{3} +(-1.20190 + 2.90164i) q^{5} +(-2.49510 + 2.49510i) q^{7} +(0.903094 - 2.86084i) q^{9} +(-1.17079 + 2.82653i) q^{11} +(-1.10922 + 0.459453i) q^{13} +(-1.29208 - 5.28419i) q^{15} +1.58794 q^{17} +(-0.645075 - 1.55735i) q^{19} +(0.930766 - 6.04043i) q^{21} +(-1.10521 + 1.10521i) q^{23} +(-3.43941 - 3.43941i) q^{25} +(1.66773 + 4.92125i) q^{27} +(8.38683 - 3.47394i) q^{29} -3.71580i q^{31} +(-1.25864 - 5.14742i) q^{33} +(-4.24102 - 10.2387i) q^{35} +(-3.90358 - 1.61692i) q^{37} +(1.07910 - 1.77762i) q^{39} +(4.79379 + 4.79379i) q^{41} +(-10.5601 - 4.37412i) q^{43} +(7.21570 + 6.05889i) q^{45} +0.00719952i q^{47} -5.45104i q^{49} +(-2.21831 + 1.62595i) q^{51} +(-8.00769 - 3.31689i) q^{53} +(-6.79441 - 6.79441i) q^{55} +(2.49579 + 1.51506i) q^{57} +(7.94232 + 3.28982i) q^{59} +(-2.39029 - 5.77068i) q^{61} +(4.88478 + 9.39140i) q^{63} -3.77076i q^{65} +(1.79590 - 0.743885i) q^{67} +(0.412283 - 2.67561i) q^{69} +(4.31833 + 4.31833i) q^{71} +(-5.47859 + 5.47859i) q^{73} +(8.32652 + 1.28303i) q^{75} +(-4.13125 - 9.97372i) q^{77} -4.77572 q^{79} +(-7.36884 - 5.16722i) q^{81} +(-3.61948 + 1.49924i) q^{83} +(-1.90854 + 4.60762i) q^{85} +(-8.15911 + 13.4406i) q^{87} +(-12.1885 + 12.1885i) q^{89} +(1.62123 - 3.91399i) q^{91} +(3.80475 + 5.19089i) q^{93} +5.29418 q^{95} -4.35108 q^{97} +(7.02894 + 5.90207i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 4 q^{3} + 8 q^{7} - 4 q^{9}+O(q^{10}) $ 56 * q - 4 * q^3 + 8 * q^7 - 4 * q^9	$ 56 q - 4 q^{3} + 8 q^{7} - 4 q^{9} + 8 q^{13} + 8 q^{15} - 8 q^{19} + 4 q^{21} - 8 q^{25} - 28 q^{27} - 8 q^{33} + 8 q^{37} + 28 q^{39} - 8 q^{43} + 4 q^{45} - 16 q^{51} - 24 q^{55} - 4 q^{57} + 40 q^{61} + 56 q^{67} + 4 q^{69} - 8 q^{73} + 16 q^{75} - 16 q^{79} + 48 q^{85} - 52 q^{87} + 40 q^{91} - 8 q^{93} - 16 q^{97} + 60 q^{99}+O(q^{100}) $ 56 * q - 4 * q^3 + 8 * q^7 - 4 * q^9 + 8 * q^13 + 8 * q^15 - 8 * q^19 + 4 * q^21 - 8 * q^25 - 28 * q^27 - 8 * q^33 + 8 * q^37 + 28 * q^39 - 8 * q^43 + 4 * q^45 - 16 * q^51 - 24 * q^55 - 4 * q^57 + 40 * q^61 + 56 * q^67 + 4 * q^69 - 8 * q^73 + 16 * q^75 - 16 * q^79 + 48 * q^85 - 52 * q^87 + 40 * q^91 - 8 * q^93 - 16 * q^97 + 60 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/768\mathbb{Z}\right)^\times$.

$n$	$257$	$511$	$517$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{1}{8}\right)$

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
$3$	−1.39698	+	1.02394i	−0.806546	+	0.591172i
$3$	−1.39698	+	1.02394i	−0.806546	+	0.591172i
$4$		0			0
$5$	−1.20190	+	2.90164i	−0.537505	+	1.29765i	0.388954	+	0.921257i	$0.372836\pi$
$5$	−1.20190	+	2.90164i	−0.537505	+	1.29765i	−0.926459	+	0.376395i	$0.877164\pi$
$6$		0			0
$7$	−2.49510	+	2.49510i	−0.943059	+	0.943059i	−0.998464	−	0.0554051i	$-0.982355\pi$
$7$	−2.49510	+	2.49510i	−0.943059	+	0.943059i	0.0554051	+	0.998464i	$0.482355\pi$
$8$		0			0
$9$	0.903094	−	2.86084i	0.301031	−	0.953614i
$10$		0			0
$11$	−1.17079	+	2.82653i	−0.353006	+	0.852232i	0.643240	+	0.765665i	$0.277590\pi$
$11$	−1.17079	+	2.82653i	−0.353006	+	0.852232i	−0.996246	+	0.0865673i	$0.972410\pi$
$12$		0			0
$13$	−1.10922	+	0.459453i	−0.307641	+	0.127429i	−0.531163	−	0.847270i	$-0.678245\pi$
$13$	−1.10922	+	0.459453i	−0.307641	+	0.127429i	0.223521	+	0.974699i	$0.428245\pi$
$14$		0			0
$15$	−1.29208	−	5.28419i	−0.333613	−	1.36437i
$16$		0			0
$17$	1.58794			0.385132			0.192566	−	0.981284i	$-0.438319\pi$
$17$	1.58794			0.385132			0.192566	+	0.981284i	$0.438319\pi$
$18$		0			0
$19$	−0.645075	−	1.55735i	−0.147990	−	0.357281i	0.832449	−	0.554102i	$-0.186938\pi$
$19$	−0.645075	−	1.55735i	−0.147990	−	0.357281i	−0.980439	+	0.196821i	$0.936938\pi$
$20$		0			0
$21$	0.930766	−	6.04043i	0.203110	−	1.31813i
$22$		0			0
$23$	−1.10521	+	1.10521i	−0.230451	+	0.230451i	−0.812881	−	0.582430i	$-0.802102\pi$
$23$	−1.10521	+	1.10521i	−0.230451	+	0.230451i	0.582430	+	0.812881i	$0.302102\pi$
$24$		0			0
$25$	−3.43941	−	3.43941i	−0.687882	−	0.687882i
$26$		0			0
$27$	1.66773	+	4.92125i	0.320955	+	0.947095i
$28$		0			0
$29$	8.38683	−	3.47394i	1.55740	−	0.645094i	0.572761	−	0.819722i	$-0.305872\pi$
$29$	8.38683	−	3.47394i	1.55740	−	0.645094i	0.984634	+	0.174628i	$0.0558723\pi$
$30$		0			0
$31$		−	3.71580i		−	0.667377i	−0.942683	−	0.333689i	$-0.891707\pi$
$31$		−	3.71580i		−	0.667377i	0.942683	−	0.333689i	$-0.108293\pi$
$32$		0			0
$33$	−1.25864	−	5.14742i	−0.219100	−	0.896051i
$34$		0			0
$35$	−4.24102	−	10.2387i	−0.716863	−	1.73066i
$36$		0			0
$37$	−3.90358	−	1.61692i	−0.641745	−	0.265820i	0.0379890	−	0.999278i	$-0.487905\pi$
$37$	−3.90358	−	1.61692i	−0.641745	−	0.265820i	−0.679734	+	0.733459i	$0.737905\pi$
$38$		0			0
$39$	1.07910	−	1.77762i	0.172794	−	0.284647i
$40$		0			0
$41$	4.79379	+	4.79379i	0.748665	+	0.748665i	0.974228	−	0.225564i	$-0.0724223\pi$
$41$	4.79379	+	4.79379i	0.748665	+	0.748665i	−0.225564	+	0.974228i	$0.572422\pi$
$42$		0			0
$43$	−10.5601	−	4.37412i	−1.61040	−	0.667048i	−0.617558	−	0.786525i	$-0.711878\pi$
$43$	−10.5601	−	4.37412i	−1.61040	−	0.667048i	−0.992837	+	0.119477i	$0.961878\pi$
$44$		0			0
$45$	7.21570	+	6.05889i	1.07565	+	0.903206i
$46$		0			0
$47$			0.00719952i			0.00105016i	1.00000		0.000525079i	$0.000167138\pi$
$47$			0.00719952i			0.00105016i	−1.00000		0.000525079i	$0.999833\pi$
$48$		0			0
$49$		−	5.45104i		−	0.778720i
$50$		0			0
$51$	−2.21831	+	1.62595i	−0.310626	+	0.227679i
$52$		0			0
$53$	−8.00769	−	3.31689i	−1.09994	−	0.455611i	−0.242478	−	0.970157i	$-0.577960\pi$
$53$	−8.00769	−	3.31689i	−1.09994	−	0.455611i	−0.857463	+	0.514546i	$0.827960\pi$
$54$		0			0
$55$	−6.79441	−	6.79441i	−0.916158	−	0.916158i
$56$		0			0
$57$	2.49579	+	1.51506i	0.330575	+	0.200675i
$58$		0			0
$59$	7.94232	+	3.28982i	1.03400	+	0.428298i	0.834156	−	0.551529i	$-0.185956\pi$
$59$	7.94232	+	3.28982i	1.03400	+	0.428298i	0.199847	+	0.979827i	$0.435956\pi$
$60$		0			0
$61$	−2.39029	−	5.77068i	−0.306046	−	0.738859i	−0.999826	−	0.0186725i	$-0.994056\pi$
$61$	−2.39029	−	5.77068i	−0.306046	−	0.738859i	0.693780	−	0.720187i	$-0.255944\pi$
$62$		0			0
$63$	4.88478	+	9.39140i	0.615424	+	1.18320i
$64$		0			0
$65$		−	3.77076i		−	0.467705i
$66$		0			0
$67$	1.79590	−	0.743885i	0.219404	−	0.0908800i	−0.270274	−	0.962783i	$-0.587114\pi$
$67$	1.79590	−	0.743885i	0.219404	−	0.0908800i	0.489678	+	0.871903i	$0.337114\pi$
$68$		0			0
$69$	0.412283	−	2.67561i	0.0496331	−	0.322106i
$70$		0			0
$71$	4.31833	+	4.31833i	0.512491	+	0.512491i	0.915289	−	0.402798i	$-0.131962\pi$
$71$	4.31833	+	4.31833i	0.512491	+	0.512491i	−0.402798	+	0.915289i	$0.631962\pi$
$72$		0			0
$73$	−5.47859	+	5.47859i	−0.641221	+	0.641221i	−0.950855	−	0.309635i	$-0.899793\pi$
$73$	−5.47859	+	5.47859i	−0.641221	+	0.641221i	0.309635	+	0.950855i	$0.399793\pi$
$74$		0			0
$75$	8.32652	+	1.28303i	0.961464	+	0.148151i
$76$		0			0
$77$	−4.13125	−	9.97372i	−0.470799	−	1.13661i
$78$		0			0
$79$	−4.77572			−0.537311			−0.268655	−	0.963236i	$-0.586579\pi$
$79$	−4.77572			−0.537311			−0.268655	+	0.963236i	$0.586579\pi$
$80$		0			0
$81$	−7.36884	−	5.16722i	−0.818760	−	0.574136i
$82$		0			0
$83$	−3.61948	+	1.49924i	−0.397289	+	0.164563i	−0.572378	−	0.819990i	$-0.693979\pi$
$83$	−3.61948	+	1.49924i	−0.397289	+	0.164563i	0.175088	+	0.984553i	$0.443979\pi$
$84$		0			0
$85$	−1.90854	+	4.60762i	−0.207010	+	0.499767i
$86$		0			0
$87$	−8.15911	+	13.4406i	−0.874749	+	1.44099i
$88$		0			0
$89$	−12.1885	+	12.1885i	−1.29198	+	1.29198i	−0.358420	+	0.933560i	$0.616685\pi$
$89$	−12.1885	+	12.1885i	−1.29198	+	1.29198i	−0.933560	+	0.358420i	$0.883315\pi$
$90$		0			0
$91$	1.62123	−	3.91399i	0.169951	−	0.410297i
$92$		0			0
$93$	3.80475	+	5.19089i	0.394535	+	0.538270i
$94$		0			0
$95$	5.29418			0.543171
$96$		0			0
$97$	−4.35108			−0.441785			−0.220892	−	0.975298i	$-0.570897\pi$
$97$	−4.35108			−0.441785			−0.220892	+	0.975298i	$0.570897\pi$
$98$		0			0
$99$	7.02894	+	5.90207i	0.706435	+	0.593180i
$100$		0			0
$101$	−0.824264	+	1.98995i	−0.0820174	+	0.198007i	−0.959568	−	0.281476i	$-0.909176\pi$
$101$	−0.824264	+	1.98995i	−0.0820174	+	0.198007i	0.877551	+	0.479484i	$0.159176\pi$
$102$		0			0
$103$	4.97464	−	4.97464i	0.490166	−	0.490166i	−0.418192	−	0.908358i	$-0.637336\pi$
$103$	4.97464	−	4.97464i	0.490166	−	0.490166i	0.908358	+	0.418192i	$0.137336\pi$
$104$		0			0
$105$	16.4085	+	9.96072i	1.60130	+	0.972067i
$106$		0			0
$107$	3.15619	−	7.61973i	0.305121	−	0.736627i	−0.694729	−	0.719272i	$-0.744475\pi$
$107$	3.15619	−	7.61973i	0.305121	−	0.736627i	0.999849	−	0.0173549i	$-0.00552451\pi$
$108$		0			0
$109$	−3.35376	+	1.38917i	−0.321232	+	0.133059i	−0.537472	−	0.843282i	$-0.680621\pi$
$109$	−3.35376	+	1.38917i	−0.321232	+	0.133059i	0.216240	+	0.976340i	$0.430621\pi$
$110$		0			0
$111$	7.10884	−	1.73824i	0.674742	−	0.164986i
$112$		0			0
$113$	7.50843			0.706334			0.353167	−	0.935560i	$-0.385105\pi$
$113$	7.50843			0.706334			0.353167	+	0.935560i	$0.385105\pi$
$114$		0			0
$115$	−1.87856	−	4.53525i	−0.175177	−	0.422914i
$116$		0			0
$117$	0.312695	+	3.58822i	0.0289087	+	0.331731i
$118$		0			0
$119$	−3.96206	+	3.96206i	−0.363202	+	0.363202i
$120$		0			0
$121$	1.15963	+	1.15963i	0.105421	+	0.105421i
$122$		0			0
$123$	−11.6054	−	1.78827i	−1.04642	−	0.161243i
$124$		0			0
$125$	−0.394456	+	0.163389i	−0.0352813	+	0.0146140i
$126$		0			0
$127$		−	0.227205i		−	0.0201612i	−0.999949	−	0.0100806i	$-0.996791\pi$
$127$		−	0.227205i		−	0.0201612i	0.999949	−	0.0100806i	$-0.00320881\pi$
$128$		0			0
$129$	19.2310	−	4.70232i	1.69320	−	0.414016i
$130$		0			0
$131$	−3.91920	−	9.46179i	−0.342422	−	0.826680i	−0.997470	−	0.0710926i	$-0.977351\pi$
$131$	−3.91920	−	9.46179i	−0.342422	−	0.826680i	0.655048	−	0.755588i	$-0.272649\pi$
$132$		0			0
$133$	5.49527	+	2.27621i	0.476500	+	0.197373i
$134$		0			0
$135$	−16.2841	−	1.07569i	−1.40151	−	0.0925807i
$136$		0			0
$137$	−8.79196	−	8.79196i	−0.751148	−	0.751148i	0.223546	−	0.974693i	$-0.428237\pi$
$137$	−8.79196	−	8.79196i	−0.751148	−	0.751148i	−0.974693	+	0.223546i	$0.928237\pi$
$138$		0			0
$139$	17.3022	+	7.16681i	1.46756	+	0.607881i	0.966300	−	0.257418i	$-0.0828718\pi$
$139$	17.3022	+	7.16681i	1.46756	+	0.607881i	0.501255	+	0.865300i	$0.332872\pi$
$140$		0			0
$141$	−0.00737188	−	0.0100576i	−0.000620824	−	0.000847000i
$142$		0			0
$143$		−	3.67316i		−	0.307165i
$144$		0			0
$145$			28.5109i			2.36770i
$146$		0			0
$147$	5.58154	+	7.61498i	0.460357	+	0.628073i
$148$		0			0
$149$	2.70861	+	1.12194i	0.221898	+	0.0919132i	0.490863	−	0.871237i	$-0.336682\pi$
$149$	2.70861	+	1.12194i	0.221898	+	0.0919132i	−0.268965	+	0.963150i	$0.586682\pi$
$150$		0			0
$151$	4.43765	+	4.43765i	0.361130	+	0.361130i	0.864229	−	0.503099i	$-0.167807\pi$
$151$	4.43765	+	4.43765i	0.361130	+	0.361130i	−0.503099	+	0.864229i	$0.667807\pi$
$152$		0			0
$153$	1.43406	−	4.54284i	0.115937	−	0.367267i
$154$		0			0
$155$	10.7819	+	4.46601i	0.866023	+	0.358718i
$156$		0			0
$157$	8.17724	+	19.7416i	0.652615	+	1.57555i	0.808969	+	0.587851i	$0.200026\pi$
$157$	8.17724	+	19.7416i	0.652615	+	1.57555i	−0.156355	+	0.987701i	$0.549974\pi$
$158$		0			0
$159$	14.5829	−	3.56577i	1.15650	−	0.282784i
$160$		0			0
$161$		−	5.51519i		−	0.434658i
$162$		0			0
$163$	−4.18266	+	1.73251i	−0.327611	+	0.135701i	−0.540426	−	0.841392i	$-0.681737\pi$
$163$	−4.18266	+	1.73251i	−0.327611	+	0.135701i	0.212815	+	0.977093i	$0.431737\pi$
$164$		0			0
$165$	16.4487	+	2.53457i	1.28053	+	0.197316i
$166$		0			0
$167$	−2.27863	−	2.27863i	−0.176326	−	0.176326i	0.613426	−	0.789752i	$-0.289791\pi$
$167$	−2.27863	−	2.27863i	−0.176326	−	0.176326i	−0.789752	+	0.613426i	$0.789791\pi$
$168$		0			0
$169$	−8.17312	+	8.17312i	−0.628702	+	0.628702i
$170$		0			0
$171$	−5.03790	+	0.439026i	−0.385258	+	0.0335732i
$172$		0			0
$173$	5.20812	+	12.5735i	0.395966	+	0.955946i	0.988613	+	0.150484i	$0.0480831\pi$
$173$	5.20812	+	12.5735i	0.395966	+	0.955946i	−0.592647	+	0.805463i	$0.701917\pi$
$174$		0			0
$175$	17.1633			1.29743
$176$		0			0
$177$	−14.4638	+	3.53666i	−1.08717	+	0.265832i
$178$		0			0
$179$	−9.25003	+	3.83149i	−0.691380	+	0.286379i	−0.700575	−	0.713579i	$-0.747073\pi$
$179$	−9.25003	+	3.83149i	−0.691380	+	0.286379i	0.00919508	+	0.999958i	$0.497073\pi$
$180$		0			0
$181$	1.12055	−	2.70526i	0.0832901	−	0.201080i	−0.876748	−	0.480951i	$-0.840292\pi$
$181$	1.12055	−	2.70526i	0.0832901	−	0.201080i	0.960038	+	0.279871i	$0.0902916\pi$
$182$		0			0
$183$	9.24801	+	5.61399i	0.683633	+	0.414998i
$184$		0			0
$185$	9.38341	−	9.38341i	0.689882	−	0.689882i
$186$		0			0
$187$	−1.85914	+	4.48836i	−0.135954	+	0.328221i
$188$		0			0
$189$	−16.4402	−	8.11785i	−1.19585	−	0.590487i
$190$		0			0
$191$	−23.0704			−1.66931			−0.834656	−	0.550771i	$-0.814334\pi$
$191$	−23.0704			−1.66931			−0.834656	+	0.550771i	$0.814334\pi$
$192$		0			0
$193$	−6.28022			−0.452060			−0.226030	−	0.974120i	$-0.572575\pi$
$193$	−6.28022			−0.452060			−0.226030	+	0.974120i	$0.572575\pi$
$194$		0			0
$195$	3.86103	+	5.26767i	0.276494	+	0.377226i
$196$		0			0
$197$	−6.41739	+	15.4930i	−0.457220	+	1.10383i	0.512298	+	0.858808i	$0.328794\pi$
$197$	−6.41739	+	15.4930i	−0.457220	+	1.10383i	−0.969518	+	0.245019i	$0.921206\pi$
$198$		0			0
$199$	13.0646	−	13.0646i	0.926128	−	0.926128i	−0.0713253	−	0.997453i	$-0.522723\pi$
$199$	13.0646	−	13.0646i	0.926128	−	0.926128i	0.997453	+	0.0713253i	$0.0227229\pi$
$200$		0			0
$201$	−1.74713	+	2.87808i	−0.123233	+	0.203004i
$202$		0			0
$203$	−12.2582	+	29.5938i	−0.860354	+	2.07708i
$204$		0			0
$205$	−19.6715	+	8.14820i	−1.37392	+	0.569095i
$206$		0			0
$207$	2.16371	+	4.15992i	0.150389	+	0.289135i
$208$		0			0
$209$	5.15715			0.356727
$210$		0			0
$211$	−3.76584	−	9.09153i	−0.259251	−	0.625887i	0.739639	−	0.673004i	$-0.234996\pi$
$211$	−3.76584	−	9.09153i	−0.259251	−	0.625887i	−0.998889	+	0.0471175i	$0.984996\pi$
$212$		0			0
$213$	−10.4543	−	1.61090i	−0.716318	−	0.110377i
$214$		0			0
$215$	25.3842	−	25.3842i	1.73119	−	1.73119i
$216$		0			0
$217$	9.27129	+	9.27129i	0.629376	+	0.629376i
$218$		0			0
$219$	2.04372	−	13.2632i	0.138102	−	0.896245i
$220$		0			0
$221$	−1.76137	+	0.729583i	−0.118482	+	0.0490770i
$222$		0			0
$223$		−	8.19538i		−	0.548803i	−0.961615	−	0.274402i	$-0.911520\pi$
$223$		−	8.19538i		−	0.548803i	0.961615	−	0.274402i	$-0.0884798\pi$
$224$		0			0
$225$	−12.9457	+	6.73350i	−0.863048	+	0.448900i
$226$		0			0
$227$	7.04295	+	17.0032i	0.467457	+	1.12854i	0.965270	+	0.261256i	$0.0841366\pi$
$227$	7.04295	+	17.0032i	0.467457	+	1.12854i	−0.497813	+	0.867284i	$0.665863\pi$
$228$		0			0
$229$	−16.3558	−	6.77478i	−1.08082	−	0.447690i	−0.230023	−	0.973185i	$-0.573880\pi$
$229$	−16.3558	−	6.77478i	−1.08082	−	0.447690i	−0.850796	+	0.525495i	$0.823880\pi$
$230$		0			0
$231$	15.9837	+	9.70291i	1.05165	+	0.638405i
$232$		0			0
$233$	−19.0984	−	19.0984i	−1.25118	−	1.25118i	−0.955192	−	0.295988i	$-0.904351\pi$
$233$	−19.0984	−	19.0984i	−1.25118	−	1.25118i	−0.295988	−	0.955192i	$-0.595649\pi$
$234$		0			0
$235$	−0.0208904	−	0.00865309i	−0.00136274	−	0.000564465i
$236$		0			0
$237$	6.67158	−	4.89005i	0.433365	−	0.317643i
$238$		0			0
$239$			14.0329i			0.907716i	0.891074	+	0.453858i	$0.149953\pi$
$239$			14.0329i			0.907716i	−0.891074	+	0.453858i	$0.850047\pi$
$240$		0			0
$241$		−	28.3070i		−	1.82342i	−0.410838	−	0.911708i	$-0.634764\pi$
$241$		−	28.3070i		−	1.82342i	0.410838	−	0.911708i	$-0.365236\pi$
$242$		0			0
$243$	15.5850	−	0.326761i	0.999780	−	0.0209617i
$244$		0			0
$245$	15.8169	+	6.55159i	1.01051	+	0.418566i
$246$		0			0
$247$	1.43106	+	1.43106i	0.0910560	+	0.0910560i
$248$		0			0
$249$	3.52120	−	5.80053i	0.223147	−	0.367594i
$250$		0			0
$251$	3.35129	+	1.38815i	0.211532	+	0.0876192i	0.485933	−	0.873996i	$-0.338480\pi$
$251$	3.35129	+	1.38815i	0.211532	+	0.0876192i	−0.274402	+	0.961615i	$0.588480\pi$
$252$		0			0
$253$	−1.82994	−	4.41786i	−0.115047	−	0.277749i
$254$		0			0
$255$	−2.05174	−	8.39097i	−0.128485	−	0.525463i
$256$		0			0
$257$			25.2231i			1.57337i	0.617354	+	0.786686i	$0.288205\pi$
$257$			25.2231i			1.57337i	−0.617354	+	0.786686i	$0.711795\pi$
$258$		0			0
$259$	13.7742	−	5.70546i	0.855887	−	0.354520i
$260$		0			0
$261$	−2.36430	−	27.1307i	−0.146346	−	1.67935i
$262$		0			0
$263$	4.01798	+	4.01798i	0.247759	+	0.247759i	0.820050	−	0.572291i	$-0.193945\pi$
$263$	4.01798	+	4.01798i	0.247759	+	0.247759i	−0.572291	+	0.820050i	$0.693945\pi$
$264$		0			0
$265$	19.2489	−	19.2489i	1.18245	−	1.18245i
$266$		0			0
$267$	4.54678	−	29.5074i	0.278258	−	1.80582i
$268$		0			0
$269$	−6.02208	−	14.5386i	−0.367173	−	0.886434i	−0.994211	−	0.107445i	$-0.965733\pi$
$269$	−6.02208	−	14.5386i	−0.367173	−	0.886434i	0.627038	−	0.778989i	$-0.284267\pi$
$270$		0			0
$271$	−21.4445			−1.30266			−0.651330	−	0.758795i	$-0.725788\pi$
$271$	−21.4445			−1.30266			−0.651330	+	0.758795i	$0.725788\pi$
$272$		0			0
$273$	1.74287	+	7.12779i	0.105483	+	0.431394i
$274$		0			0
$275$	13.7484	−	5.69478i	0.829061	−	0.343408i
$276$		0			0
$277$	−4.78746	+	11.5580i	−0.287651	+	0.694450i	−0.999973	−	0.00740257i	$-0.997644\pi$
$277$	−4.78746	+	11.5580i	−0.287651	+	0.694450i	0.712322	+	0.701853i	$0.247644\pi$
$278$		0			0
$279$	−10.6303	−	3.35571i	−0.636420	−	0.200901i
$280$		0			0
$281$	3.59443	−	3.59443i	0.214426	−	0.214426i	−0.591719	−	0.806144i	$-0.701550\pi$
$281$	3.59443	−	3.59443i	0.214426	−	0.214426i	0.806144	+	0.591719i	$0.201550\pi$
$282$		0			0
$283$	6.09648	−	14.7182i	0.362398	−	0.874907i	−0.632550	−	0.774519i	$-0.717992\pi$
$283$	6.09648	−	14.7182i	0.362398	−	0.874907i	0.994948	−	0.100388i	$-0.0320083\pi$
$284$		0			0
$285$	−7.39585	+	5.42092i	−0.438092	+	0.321108i
$286$		0			0
$287$	−23.9220			−1.41207
$288$		0			0
$289$	−14.4785			−0.851674
$290$		0			0
$291$	6.07836	−	4.45524i	0.356320	−	0.261171i
$292$		0			0
$293$	−4.31868	+	10.4262i	−0.252300	+	0.609107i	−0.998389	−	0.0567399i	$-0.981929\pi$
$293$	−4.31868	+	10.4262i	−0.252300	+	0.609107i	0.746089	+	0.665846i	$0.231929\pi$
$294$		0			0
$295$	−19.0917	+	19.0917i	−1.11156	+	1.11156i
$296$		0			0
$297$	−15.8626	−	1.04785i	−0.920443	−	0.0608023i
$298$		0			0
$299$	0.718123	−	1.73370i	0.0415301	−	0.100263i
$300$		0			0
$301$	37.2623	−	15.4345i	2.14776	−	0.889632i
$302$		0			0
$303$	−0.886111	−	3.62391i	−0.0509057	−	0.208188i
$304$		0			0
$305$	19.6173			1.12328
$306$		0			0
$307$	5.67151	+	13.6922i	0.323690	+	0.781457i	0.999034	+	0.0439534i	$0.0139953\pi$
$307$	5.67151	+	13.6922i	0.323690	+	0.781457i	−0.675344	+	0.737503i	$0.736005\pi$
$308$		0			0
$309$	−1.85573	+	12.0432i	−0.105569	+	0.685114i
$310$		0			0
$311$	4.43369	−	4.43369i	0.251411	−	0.251411i	−0.570138	−	0.821549i	$-0.693110\pi$
$311$	4.43369	−	4.43369i	0.251411	−	0.251411i	0.821549	+	0.570138i	$0.193110\pi$
$312$		0			0
$313$	−1.32537	−	1.32537i	−0.0749146	−	0.0749146i	0.668657	−	0.743571i	$-0.266870\pi$
$313$	−1.32537	−	1.32537i	−0.0749146	−	0.0749146i	−0.743571	+	0.668657i	$0.766870\pi$
$314$		0			0
$315$	−33.1214	+	2.88636i	−1.86618	+	0.162628i
$316$		0			0
$317$	12.2962	−	5.09325i	0.690623	−	0.286066i	−0.00963654	−	0.999954i	$-0.503067\pi$
$317$	12.2962	−	5.09325i	0.690623	−	0.286066i	0.700260	+	0.713888i	$0.253067\pi$
$318$		0			0
$319$			27.7729i			1.55498i
$320$		0			0
$321$	3.39301	+	13.8763i	0.189379	+	0.774502i
$322$		0			0
$323$	−1.02434	−	2.47297i	−0.0569958	−	0.137600i
$324$		0			0
$325$	5.39530	+	2.23480i	0.299277	+	0.123965i
$326$		0			0
$327$	3.26270	−	5.37469i	0.180428	−	0.297221i
$328$		0			0
$329$	−0.0179635	−	0.0179635i	−0.000990361	−	0.000990361i
$330$		0			0
$331$	−22.2842	−	9.23041i	−1.22485	−	0.507349i	−0.325901	−	0.945404i	$-0.605667\pi$
$331$	−22.2842	−	9.23041i	−1.22485	−	0.507349i	−0.898948	+	0.438055i	$0.855667\pi$
$332$		0			0
$333$	−8.15105	+	9.70731i	−0.446675	+	0.531957i
$334$		0			0
$335$			6.10512i			0.333558i
$336$		0			0
$337$			3.78048i			0.205936i	0.994685	+	0.102968i	$0.0328339\pi$
$337$			3.78048i			0.205936i	−0.994685	+	0.102968i	$0.967166\pi$
$338$		0			0
$339$	−10.4891	+	7.68818i	−0.569690	+	0.417565i
$340$		0			0
$341$	10.5028	+	4.35041i	0.568760	+	0.235588i
$342$		0			0
$343$	−3.86481	−	3.86481i	−0.208680	−	0.208680i
$344$		0			0
$345$	7.26813	+	4.41211i	0.391303	+	0.237540i
$346$		0			0
$347$	−33.8475	−	14.0201i	−1.81703	−	0.752638i	−0.978017	−	0.208526i	$-0.933134\pi$
$347$	−33.8475	−	14.0201i	−1.81703	−	0.752638i	−0.839012	−	0.544113i	$-0.816866\pi$
$348$		0			0
$349$	−1.91399	−	4.62078i	−0.102454	−	0.247345i	0.864338	−	0.502912i	$-0.167738\pi$
$349$	−1.91399	−	4.62078i	−0.102454	−	0.247345i	−0.966791	+	0.255567i	$0.917738\pi$
$350$		0			0
$351$	−4.11095	−	4.69249i	−0.219427	−	0.250467i
$352$		0			0
$353$			10.1457i			0.540002i	0.962860	+	0.270001i	$0.0870241\pi$
$353$			10.1457i			0.540002i	−0.962860	+	0.270001i	$0.912976\pi$
$354$		0			0
$355$	−17.7204	+	7.34003i	−0.940501	+	0.389568i
$356$		0			0
$357$	1.47800	−	9.59183i	0.0782240	−	0.507653i
$358$		0			0
$359$	−14.1291	−	14.1291i	−0.745703	−	0.745703i	0.227966	−	0.973669i	$-0.426793\pi$
$359$	−14.1291	−	14.1291i	−0.745703	−	0.745703i	−0.973669	+	0.227966i	$0.926793\pi$
$360$		0			0
$361$	11.4258	−	11.4258i	0.601359	−	0.601359i
$362$		0			0
$363$	−2.80736	−	0.432585i	−0.147348	−	0.0227048i
$364$		0			0
$365$	−9.31218	−	22.4816i	−0.487422	−	1.17674i
$366$		0			0
$367$	−15.2535			−0.796226			−0.398113	−	0.917336i	$-0.630335\pi$
$367$	−15.2535			−0.796226			−0.398113	+	0.917336i	$0.630335\pi$
$368$		0			0
$369$	18.0435	−	9.38505i	0.939309	−	0.488566i
$370$		0			0
$371$	28.2560	−	11.7040i	1.46698	−	0.607642i
$372$		0			0
$373$	11.7359	−	28.3331i	0.607664	−	1.46703i	−0.257869	−	0.966180i	$-0.583020\pi$
$373$	11.7359	−	28.3331i	0.607664	−	1.46703i	0.865533	−	0.500851i	$-0.166980\pi$
$374$		0			0
$375$	0.383746	−	0.632151i	0.0198166	−	0.0326441i
$376$		0			0
$377$	−7.70671	+	7.70671i	−0.396916	+	0.396916i
$378$		0			0
$379$	−6.39117	+	15.4297i	−0.328293	+	0.792568i	0.670427	+	0.741976i	$0.266111\pi$
$379$	−6.39117	+	15.4297i	−0.328293	+	0.792568i	−0.998719	+	0.0505927i	$0.983889\pi$
$380$		0			0
$381$	0.232644	+	0.317401i	0.0119187	+	0.0162609i
$382$		0			0
$383$	13.8717			0.708812			0.354406	−	0.935092i	$-0.384683\pi$
$383$	13.8717			0.708812			0.354406	+	0.935092i	$0.384683\pi$
$384$		0			0
$385$	33.9054			1.72798
$386$		0			0
$387$	−22.0504	+	26.2605i	−1.12089	+	1.33489i
$388$		0			0
$389$	5.70564	−	13.7746i	0.289287	−	0.698402i	−0.710700	−	0.703496i	$-0.751621\pi$
$389$	5.70564	−	13.7746i	0.289287	−	0.698402i	0.999987	+	0.00509391i	$0.00162145\pi$
$390$		0			0
$391$	−1.75500	+	1.75500i	−0.0887540	+	0.0887540i
$392$		0			0
$393$	15.1633	+	9.20488i	0.764889	+	0.464325i
$394$		0			0
$395$	5.73993	−	13.8574i	0.288807	−	0.697242i
$396$		0			0
$397$	−10.1491	+	4.20389i	−0.509368	+	0.210987i	−0.622540	−	0.782588i	$-0.713899\pi$
$397$	−10.1491	+	4.20389i	−0.509368	+	0.210987i	0.113171	+	0.993575i	$0.463899\pi$
$398$		0			0
$399$	−10.0075	+	2.44700i	−0.501000	+	0.122503i
$400$		0			0
$401$	−17.5270			−0.875254			−0.437627	−	0.899157i	$-0.644181\pi$
$401$	−17.5270			−0.875254			−0.437627	+	0.899157i	$0.644181\pi$
$402$		0			0
$403$	1.70723	+	4.12163i	0.0850434	+	0.205313i
$404$		0			0
$405$	23.8500	−	15.1712i	1.18512	−	0.753865i
$406$		0			0
$407$	9.14054	−	9.14054i	0.453080	−	0.453080i
$408$		0			0
$409$	−14.1295	−	14.1295i	−0.698661	−	0.698661i	0.265461	−	0.964122i	$-0.414476\pi$
$409$	−14.1295	−	14.1295i	−0.698661	−	0.698661i	−0.964122	+	0.265461i	$0.914476\pi$
$410$		0			0
$411$	21.2846	+	3.27973i	1.04989	+	0.161777i
$412$		0			0
$413$	−28.0253	+	11.6085i	−1.37904	+	0.571215i
$414$		0			0
$415$		−	12.3043i		−	0.603997i
$416$		0			0
$417$	−31.5092	+	7.70455i	−1.54301	+	0.377294i
$418$		0			0
$419$	−6.19905	−	14.9658i	−0.302844	−	0.731129i	−0.999900	−	0.0141131i	$-0.995508\pi$
$419$	−6.19905	−	14.9658i	−0.302844	−	0.731129i	0.697057	−	0.717016i	$-0.254492\pi$
$420$		0			0
$421$	32.5621	+	13.4877i	1.58698	+	0.657348i	0.989500	−	0.144535i	$-0.0461687\pi$
$421$	32.5621	+	13.4877i	1.58698	+	0.657348i	0.597480	+	0.801884i	$0.296169\pi$
$422$		0			0
$423$	0.0205967	+	0.00650185i	0.00100145	+	0.000316131i
$424$		0			0
$425$	−5.46157	−	5.46157i	−0.264925	−	0.264925i
$426$		0			0
$427$	20.3624	+	8.43439i	0.985407	+	0.408169i
$428$		0			0
$429$	3.76110	+	5.13133i	0.181587	+	0.247743i
$430$		0			0
$431$			24.2039i			1.16586i	0.812523	+	0.582930i	$0.198094\pi$
$431$			24.2039i			1.16586i	−0.812523	+	0.582930i	$0.801906\pi$
$432$		0			0
$433$		−	17.6654i		−	0.848945i	−0.905441	−	0.424473i	$-0.860459\pi$
$433$		−	17.6654i		−	0.848945i	0.905441	−	0.424473i	$-0.139541\pi$
$434$		0			0
$435$	−29.1934	−	39.8290i	−1.39972	−	1.90966i
$436$		0			0
$437$	2.43413	+	1.00825i	0.116440	+	0.0482312i
$438$		0			0
$439$	12.5412	+	12.5412i	0.598558	+	0.598558i	0.939929	−	0.341370i	$-0.110891\pi$
$439$	12.5412	+	12.5412i	0.598558	+	0.598558i	−0.341370	+	0.939929i	$0.610891\pi$
$440$		0			0
$441$	−15.5946	−	4.92280i	−0.742599	−	0.234419i
$442$		0			0
$443$	4.94039	+	2.04638i	0.234725	+	0.0972262i	0.496946	−	0.867782i	$-0.334455\pi$
$443$	4.94039	+	2.04638i	0.234725	+	0.0972262i	−0.262221	+	0.965008i	$0.584455\pi$
$444$		0			0
$445$	−20.7173	−	50.0160i	−0.982095	−	2.37099i
$446$		0			0
$447$	−4.93267	+	1.20613i	−0.233307	+	0.0570478i
$448$		0			0
$449$		−	6.38209i		−	0.301189i	−0.988596	−	0.150595i	$-0.951881\pi$
$449$		−	6.38209i		−	0.301189i	0.988596	−	0.150595i	$-0.0481188\pi$
$450$		0			0
$451$	−19.1623	+	7.93730i	−0.902319	+	0.373753i
$452$		0			0
$453$	−10.7432	−	1.65541i	−0.504758	−	0.0777779i
$454$		0			0
$455$	9.40842	+	9.40842i	0.441074	+	0.441074i
$456$		0			0
$457$	−15.1406	+	15.1406i	−0.708248	+	0.708248i	−0.966167	−	0.257918i	$-0.916963\pi$
$457$	−15.1406	+	15.1406i	−0.708248	+	0.708248i	0.257918	+	0.966167i	$0.416963\pi$
$458$		0			0
$459$	2.64825	+	7.81464i	0.123610	+	0.364756i
$460$		0			0
$461$	7.93553	+	19.1581i	0.369595	+	0.892280i	0.993817	+	0.111033i	$0.0354161\pi$
$461$	7.93553	+	19.1581i	0.369595	+	0.892280i	−0.624222	+	0.781247i	$0.714584\pi$
$462$		0			0
$463$	21.2770			0.988826			0.494413	−	0.869227i	$-0.335383\pi$
$463$	21.2770			0.988826			0.494413	+	0.869227i	$0.335383\pi$
$464$		0			0
$465$	−19.6350	+	4.80110i	−0.910551	+	0.222646i
$466$		0			0
$467$	−19.2375	+	7.96843i	−0.890205	+	0.368735i	−0.780446	−	0.625223i	$-0.785008\pi$
$467$	−19.2375	+	7.96843i	−0.890205	+	0.368735i	−0.109759	+	0.993958i	$0.535008\pi$
$468$		0			0
$469$	−2.62487	+	6.33701i	−0.121205	+	0.292616i
$470$		0			0
$471$	−31.6376	−	19.2056i	−1.45779	−	0.884946i
$472$		0			0
$473$	24.7272	−	24.7272i	1.13696	−	1.13696i
$474$		0			0
$475$	−3.13768	+	7.57504i	−0.143967	+	0.347567i
$476$		0			0
$477$	−16.7208	+	19.9133i	−0.765593	+	0.911766i
$478$		0			0
$479$	6.03976			0.275964			0.137982	−	0.990435i	$-0.455938\pi$
$479$	6.03976			0.275964			0.137982	+	0.990435i	$0.455938\pi$
$480$		0			0
$481$	5.07282			0.231301
$482$		0			0
$483$	5.64723	+	7.70460i	0.256958	+	0.350572i
$484$		0			0
$485$	5.22955	−	12.6252i	0.237462	−	0.573283i
$486$		0			0
$487$	−17.2191	+	17.2191i	−0.780272	+	0.780272i	−0.979877	−	0.199604i	$-0.936034\pi$
$487$	−17.2191	+	17.2191i	−0.780272	+	0.780272i	0.199604	+	0.979877i	$0.436034\pi$
$488$		0			0
$489$	4.06909	−	6.70307i	0.184011	−	0.303123i
$490$		0			0
$491$	8.94510	−	21.5954i	0.403687	−	0.974586i	−0.583076	−	0.812418i	$-0.698151\pi$
$491$	8.94510	−	21.5954i	0.403687	−	0.974586i	0.986763	−	0.162169i	$-0.0518489\pi$
$492$		0			0
$493$	13.3178	−	5.51640i	0.599802	−	0.248446i
$494$		0			0
$495$	−25.5737	+	13.3017i	−1.14945	+	0.597869i
$496$		0			0
$497$	−21.5493			−0.966619
$498$		0			0
$499$	11.8494	+	28.6070i	0.530453	+	1.28063i	0.931224	+	0.364449i	$0.118743\pi$
$499$	11.8494	+	28.6070i	0.530453	+	1.28063i	−0.400770	+	0.916179i	$0.631257\pi$
$500$		0			0
$501$	5.51638	+	0.850016i	0.246454	+	0.0379759i
$502$		0			0
$503$	4.08261	−	4.08261i	0.182035	−	0.182035i	−0.610207	−	0.792242i	$-0.708914\pi$
$503$	4.08261	−	4.08261i	0.182035	−	0.182035i	0.792242	+	0.610207i	$0.208914\pi$
$504$		0			0
$505$	−4.78343	−	4.78343i	−0.212860	−	0.212860i
$506$		0			0
$507$	3.04888	−	19.7865i	0.135406	−	0.878747i
$508$		0			0
$509$	−1.90443	+	0.788843i	−0.0844126	+	0.0349648i	−0.424490	−	0.905433i	$-0.639547\pi$
$509$	−1.90443	+	0.788843i	−0.0844126	+	0.0349648i	0.340078	+	0.940397i	$0.389547\pi$
$510$		0			0
$511$		−	27.3393i		−	1.20942i
$512$		0			0
$513$	6.58829	−	5.77181i	0.290880	−	0.254832i
$514$		0			0
$515$	8.45560	+	20.4136i	0.372598	+	0.899532i
$516$		0			0
$517$	−0.0203497	−	0.00842912i	−0.000894978	−	0.000370712i
$518$		0			0
$519$	−20.1501	−	12.2321i	−0.884493	−	0.536930i
$520$		0			0
$521$	16.1433	+	16.1433i	0.707249	+	0.707249i	0.965956	−	0.258707i	$-0.0832963\pi$
$521$	16.1433	+	16.1433i	0.707249	+	0.707249i	−0.258707	+	0.965956i	$0.583296\pi$
$522$		0			0
$523$	−3.37011	−	1.39594i	−0.147364	−	0.0610404i	0.307782	−	0.951457i	$-0.400413\pi$
$523$	−3.37011	−	1.39594i	−0.147364	−	0.0610404i	−0.455147	+	0.890416i	$0.650413\pi$
$524$		0			0
$525$	−23.9768	+	17.5742i	−1.04643	+	0.767002i
$526$		0			0
$527$		−	5.90046i		−	0.257028i
$528$		0			0
$529$			20.5570i			0.893784i
$530$		0			0
$531$	16.5843	−	19.7507i	0.719698	−	0.857108i
$532$		0			0
$533$	−7.51988	−	3.11484i	−0.325722	−	0.134919i
$534$		0			0
$535$	18.3163	+	18.3163i	0.791881	+	0.791881i
$536$		0			0
$537$	8.99888	−	14.8240i	0.388330	−	0.639702i
$538$		0			0
$539$	15.4075	+	6.38202i	0.663650	+	0.274893i
$540$		0			0
$541$	11.3007	+	27.2823i	0.485855	+	1.17296i	0.956788	+	0.290788i	$0.0939174\pi$
$541$	11.3007	+	27.2823i	0.485855	+	1.17296i	−0.470933	+	0.882169i	$0.656083\pi$
$542$		0			0
$543$	1.20463	+	4.92656i	0.0516957	+	0.211419i
$544$		0			0
$545$		−	11.4010i		−	0.488367i
$546$		0			0
$547$	8.83261	−	3.65859i	0.377655	−	0.156430i	−0.185778	−	0.982592i	$-0.559480\pi$
$547$	8.83261	−	3.65859i	0.377655	−	0.156430i	0.563433	+	0.826162i	$0.309480\pi$
$548$		0			0
$549$	−18.6677	+	1.62679i	−0.796716	+	0.0694296i
$550$		0			0
$551$	−10.8203	−	10.8203i	−0.460959	−	0.460959i
$552$		0			0
$553$	11.9159	−	11.9159i	0.506715	−	0.506715i
$554$		0			0
$555$	−3.50037	+	22.7165i	−0.148582	+	0.964261i
$556$		0			0
$557$	−6.59515	−	15.9221i	−0.279445	−	0.674641i	0.720375	−	0.693585i	$-0.243970\pi$
$557$	−6.59515	−	15.9221i	−0.279445	−	0.674641i	−0.999821	+	0.0189437i	$0.993970\pi$
$558$		0			0
$559$	13.7231			0.580426
$560$		0			0
$561$	−1.99863	−	8.17379i	−0.0843824	−	0.345098i
$562$		0			0
$563$	−22.9846	+	9.52054i	−0.968687	+	0.401243i	−0.810223	−	0.586122i	$-0.800654\pi$
$563$	−22.9846	+	9.52054i	−0.968687	+	0.401243i	−0.158464	+	0.987365i	$0.550654\pi$
$564$		0			0
$565$	−9.02437	+	21.7867i	−0.379658	+	0.916575i
$566$		0			0
$567$	31.2787	−	5.49327i	1.31358	−	0.230696i
$568$		0			0
$569$	−18.8785	+	18.8785i	−0.791426	+	0.791426i	−0.981726	−	0.190300i	$-0.939054\pi$
$569$	−18.8785	+	18.8785i	−0.791426	+	0.791426i	0.190300	+	0.981726i	$0.439054\pi$
$570$		0			0
$571$	0.935866	−	2.25938i	0.0391648	−	0.0945521i	−0.903087	−	0.429458i	$-0.858705\pi$
$571$	0.935866	−	2.25938i	0.0391648	−	0.0945521i	0.942252	+	0.334906i	$0.108705\pi$
$572$		0			0
$573$	32.2288	−	23.6227i	1.34638	−	0.986851i
$574$		0			0
$575$	7.60250			0.317046
$576$		0			0
$577$	22.5985			0.940787			0.470394	−	0.882457i	$-0.344112\pi$
$577$	22.5985			0.940787			0.470394	+	0.882457i	$0.344112\pi$
$578$		0			0
$579$	8.77333	−	6.43057i	0.364607	−	0.267245i
$580$		0			0
$581$	5.29021	−	12.7717i	0.219475	−	0.529860i
$582$		0			0
$583$	18.7506	−	18.7506i	0.776572	−	0.776572i
$584$		0			0
$585$	−10.7876	−	3.40535i	−0.446010	−	0.140794i
$586$		0			0
$587$	−1.29597	+	3.12875i	−0.0534905	+	0.129137i	−0.948366	−	0.317179i	$-0.897264\pi$
$587$	−1.29597	+	3.12875i	−0.0534905	+	0.129137i	0.894875	+	0.446316i	$0.147264\pi$
$588$		0			0
$589$	−5.78680	+	2.39697i	−0.238441	+	0.0987654i
$590$		0			0
$591$	−6.89890	−	28.2143i	−0.283783	−	1.16058i
$592$		0			0
$593$	41.2238			1.69286			0.846428	−	0.532503i	$-0.178748\pi$
$593$	41.2238			1.69286			0.846428	+	0.532503i	$0.178748\pi$
$594$		0			0
$595$	−6.73448	−	16.2585i	−0.276087	−	0.666532i
$596$		0			0
$597$	−4.87361	+	31.6284i	−0.199463	+	1.29446i
$598$		0			0
$599$	−20.8013	+	20.8013i	−0.849919	+	0.849919i	−0.990123	−	0.140204i	$-0.955224\pi$
$599$	−20.8013	+	20.8013i	−0.849919	+	0.849919i	0.140204	+	0.990123i	$0.455224\pi$
$600$		0			0
$601$	19.5712	+	19.5712i	0.798327	+	0.798327i	0.982832	−	0.184505i	$-0.0590680\pi$
$601$	19.5712	+	19.5712i	0.798327	+	0.798327i	−0.184505	+	0.982832i	$0.559068\pi$
$602$		0			0
$603$	−0.506274	−	5.80958i	−0.0206171	−	0.236584i
$604$		0			0
$605$	−4.75857	+	1.97107i	−0.193464	+	0.0801352i
$606$		0			0
$607$			44.8841i			1.82179i	0.412639	+	0.910895i	$0.364607\pi$
$607$			44.8841i			1.82179i	−0.412639	+	0.910895i	$0.635393\pi$
$608$		0			0
$609$	−13.1779	−	53.8935i	−0.533996	−	2.18387i
$610$		0			0
$611$	−0.00330784	−	0.00798583i	−0.000133821	−	0.000323072i
$612$		0			0
$613$	−24.6508	−	10.2107i	−0.995636	−	0.412406i	−0.175441	−	0.984490i	$-0.556135\pi$
$613$	−24.6508	−	10.2107i	−0.995636	−	0.412406i	−0.820195	+	0.572084i	$0.806135\pi$
$614$		0			0
$615$	19.1374	−	31.5253i	0.771694	−	1.27122i
$616$		0			0
$617$	5.98992	+	5.98992i	0.241145	+	0.241145i	0.817324	−	0.576179i	$-0.195457\pi$
$617$	5.98992	+	5.98992i	0.241145	+	0.241145i	−0.576179	+	0.817324i	$0.695457\pi$
$618$		0			0
$619$	0.646750	+	0.267893i	0.0259951	+	0.0107675i	0.395643	−	0.918404i	$-0.370522\pi$
$619$	0.646750	+	0.267893i	0.0259951	+	0.0107675i	−0.369648	+	0.929172i	$0.620522\pi$
$620$		0			0
$621$	−7.28217	−	3.59581i	−0.292224	−	0.144295i
$622$		0			0
$623$		−	60.8231i		−	2.43683i
$624$		0			0
$625$		−	25.6612i		−	1.02645i
$626$		0			0
$627$	−7.20442	+	5.28061i	−0.287717	+	0.210887i
$628$		0			0
$629$	−6.19865	−	2.56756i	−0.247156	−	0.102375i
$630$		0			0
$631$	−30.5844	−	30.5844i	−1.21755	−	1.21755i	−0.968489	−	0.249056i	$-0.919880\pi$
$631$	−30.5844	−	30.5844i	−1.21755	−	1.21755i	−0.249056	−	0.968489i	$-0.580120\pi$
$632$		0			0
$633$	14.5700	+	8.84468i	0.579104	+	0.351544i
$634$		0			0
$635$	0.659267	+	0.273077i	0.0261622	+	0.0108367i
$636$		0			0
$637$	2.50450	+	6.04639i	0.0992317	+	0.239567i
$638$		0			0
$639$	16.2539	−	8.45420i	0.642995	−	0.334443i
$640$		0			0
$641$			0.218800i			0.00864208i	0.999991	+	0.00432104i	$0.00137543\pi$
$641$			0.218800i			0.00864208i	−0.999991	+	0.00432104i	$0.998625\pi$
$642$		0			0
$643$	45.2083	−	18.7259i	1.78284	−	0.738478i	0.790877	−	0.611976i	$-0.209625\pi$
$643$	45.2083	−	18.7259i	1.78284	−	0.738478i	0.991966	−	0.126502i	$-0.0403750\pi$
$644$		0			0
$645$	−9.46928	+	61.4532i	−0.372853	+	2.41972i
$646$		0			0
$647$	21.0610	+	21.0610i	0.827992	+	0.827992i	0.987239	−	0.159247i	$-0.0509065\pi$
$647$	21.0610	+	21.0610i	0.827992	+	0.827992i	−0.159247	+	0.987239i	$0.550907\pi$
$648$		0			0
$649$	−18.5976	+	18.5976i	−0.730018	+	0.730018i
$650$		0			0
$651$	−22.4450	−	3.45854i	−0.879690	−	0.135551i
$652$		0			0
$653$	12.4762	+	30.1202i	0.488231	+	1.17869i	0.955610	+	0.294636i	$0.0951985\pi$
$653$	12.4762	+	30.1202i	0.488231	+	1.17869i	−0.467379	+	0.884057i	$0.654802\pi$
$654$		0			0
$655$	32.1652			1.25680
$656$		0			0
$657$	10.7257	+	20.6211i	0.418450	+	0.804504i
$658$		0			0
$659$	5.90137	−	2.44443i	0.229885	−	0.0952213i	−0.264768	−	0.964312i	$-0.585295\pi$
$659$	5.90137	−	2.44443i	0.229885	−	0.0952213i	0.494652	+	0.869091i	$0.335295\pi$
$660$		0			0
$661$	16.4720	−	39.7669i	0.640687	−	1.54675i	−0.185069	−	0.982726i	$-0.559251\pi$
$661$	16.4720	−	39.7669i	0.640687	−	1.54675i	0.825755	−	0.564029i	$-0.190749\pi$
$662$		0			0
$663$	1.71354	−	2.82275i	0.0665485	−	0.109626i
$664$		0			0
$665$	−13.2095	+	13.2095i	−0.512242	+	0.512242i
$666$		0			0
$667$	−5.42975	+	13.1086i	−0.210241	+	0.507567i
$668$		0			0
$669$	8.39158	+	11.4488i	0.324437	+	0.442635i
$670$		0			0
$671$	19.1095			0.737716
$672$		0			0
$673$	−24.1661			−0.931534			−0.465767	−	0.884907i	$-0.654222\pi$
$673$	−24.1661			−0.931534			−0.465767	+	0.884907i	$0.654222\pi$
$674$		0			0
$675$	11.1902	−	22.6622i	0.430710	−	0.872268i
$676$		0			0
$677$	−2.32047	+	5.60211i	−0.0891829	+	0.215307i	−0.962178	−	0.272423i	$-0.912175\pi$
$677$	−2.32047	+	5.60211i	−0.0891829	+	0.215307i	0.872995	+	0.487730i	$0.162175\pi$
$678$		0			0
$679$	10.8564	−	10.8564i	0.416629	−	0.416629i
$680$		0			0
$681$	−27.2491	−	16.5415i	−1.04419	−	0.633872i
$682$		0			0
$683$	−9.07979	+	21.9205i	−0.347428	+	0.838766i	0.649494	+	0.760367i	$0.274981\pi$
$683$	−9.07979	+	21.9205i	−0.347428	+	0.838766i	−0.996922	+	0.0783994i	$0.975019\pi$
$684$		0			0
$685$	36.0781	−	14.9440i	1.37847	−	0.570982i
$686$		0			0
$687$	29.7856	−	7.28310i	1.13639	−	0.277868i
$688$		0			0
$689$	10.4062			0.396446
$690$		0			0
$691$	7.03092	+	16.9741i	0.267469	+	0.645726i	0.999363	−	0.0356919i	$-0.0113635\pi$
$691$	7.03092	+	16.9741i	0.267469	+	0.645726i	−0.731894	+	0.681418i	$0.761363\pi$
$692$		0			0
$693$	−32.2641	+	2.81165i	−1.22561	+	0.106806i
$694$		0			0
$695$	−41.5910	+	41.5910i	−1.57764	+	1.57764i
$696$		0			0
$697$	7.61225	+	7.61225i	0.288334	+	0.288334i
$698$		0			0
$699$	46.2357	+	7.12444i	1.74880	+	0.269471i
$700$		0			0
$701$	36.7215	−	15.2105i	1.38695	−	0.574495i	0.440621	−	0.897693i	$-0.354758\pi$
$701$	36.7215	−	15.2105i	1.38695	−	0.574495i	0.946331	+	0.323199i	$0.104758\pi$
$702$		0			0
$703$			7.12228i			0.268622i
$704$		0			0
$705$	0.0380437	−	0.00930235i	0.00143281	−	0.000350347i
$706$		0			0
$707$	−2.90850	−	7.02174i	−0.109385	−	0.264080i
$708$		0			0
$709$	10.3771	+	4.29832i	0.389719	+	0.161427i	0.568934	−	0.822383i	$-0.307356\pi$
$709$	10.3771	+	4.29832i	0.389719	+	0.161427i	−0.179215	+	0.983810i	$0.557356\pi$
$710$		0			0
$711$	−4.31292	+	13.6626i	−0.161747	+	0.512387i
$712$		0			0
$713$	4.10672	+	4.10672i	0.153798	+	0.153798i
$714$		0			0
$715$	10.6582	+	4.41476i	0.398593	+	0.165103i
$716$		0			0
$717$	−14.3689	−	19.6037i	−0.536616	−	0.732114i
$718$		0			0
$719$			36.3807i			1.35677i	0.734706	+	0.678386i	$0.237320\pi$
$719$			36.3807i			1.35677i	−0.734706	+	0.678386i	$0.762680\pi$
$720$		0			0
$721$			24.8245i			0.924511i
$722$		0			0
$723$	28.9847	+	39.5443i	1.07795	+	1.47067i
$724$		0			0
$725$	−40.7940	−	16.8974i	−1.51505	−	0.627555i
$726$		0			0
$727$	14.9398	+	14.9398i	0.554085	+	0.554085i	0.927617	−	0.373532i	$-0.121853\pi$
$727$	14.9398	+	14.9398i	0.554085	+	0.554085i	−0.373532	+	0.927617i	$0.621853\pi$
$728$		0			0
$729$	−21.4374	+	16.4146i	−0.793976	+	0.607949i
$730$		0			0
$731$	−16.7687	−	6.94584i	−0.620214	−	0.256901i
$732$		0			0
$733$	9.90466	+	23.9120i	0.365837	+	0.883208i	0.994423	+	0.105468i	$0.0336341\pi$
$733$	9.90466	+	23.9120i	0.365837	+	0.883208i	−0.628586	+	0.777740i	$0.716366\pi$
$734$		0			0
$735$	−28.8044	+	7.04317i	−1.06246	+	0.259791i
$736$		0			0
$737$			5.94710i			0.219064i
$738$		0			0
$739$	−15.6631	+	6.48787i	−0.576177	+	0.238660i	−0.651691	−	0.758484i	$-0.725940\pi$
$739$	−15.6631	+	6.48787i	−0.576177	+	0.238660i	0.0755143	+	0.997145i	$0.475940\pi$
$740$		0			0
$741$	−3.46447	−	0.533839i	−0.127271	−	0.0196110i
$742$		0			0
$743$	23.8582	+	23.8582i	0.875271	+	0.875271i	0.993041	−	0.117770i	$-0.0375745\pi$
$743$	23.8582	+	23.8582i	0.875271	+	0.875271i	−0.117770	+	0.993041i	$0.537574\pi$
$744$		0			0
$745$	−6.51095	+	6.51095i	−0.238543	+	0.238543i
$746$		0			0
$747$	1.02035	+	11.7087i	0.0373327	+	0.428399i
$748$		0			0
$749$	11.1370	+	26.8870i	0.406936	+	0.982429i
$750$		0			0
$751$	−26.8230			−0.978784			−0.489392	−	0.872064i	$-0.662781\pi$
$751$	−26.8230			−0.978784			−0.489392	+	0.872064i	$0.662781\pi$
$752$		0			0
$753$	−6.10306	+	1.49231i	−0.222408	+	0.0543826i
$754$		0			0
$755$	−18.2100	+	7.54284i	−0.662731	+	0.274512i
$756$		0			0
$757$	−10.3411	+	24.9657i	−0.375854	+	0.907392i	0.616879	+	0.787058i	$0.288397\pi$
$757$	−10.3411	+	24.9657i	−0.375854	+	0.907392i	−0.992733	+	0.120334i	$0.961603\pi$
$758$		0			0
$759$	7.08001	+	4.29791i	0.256988	+	0.156004i
$760$		0			0
$761$	−22.4659	+	22.4659i	−0.814388	+	0.814388i	−0.985288	−	0.170901i	$-0.945332\pi$
$761$	−22.4659	+	22.4659i	−0.814388	+	0.814388i	0.170901	+	0.985288i	$0.445332\pi$
$762$		0			0
$763$	4.90184	−	11.8341i	0.177459	−	0.428423i
$764$		0			0
$765$	11.4581	+	9.62114i	0.414268	+	0.347853i
$766$		0			0
$767$	−10.3213			−0.372680
$768$		0			0
$769$	19.7988			0.713963			0.356982	−	0.934111i	$-0.383806\pi$
$769$	19.7988			0.713963			0.356982	+	0.934111i	$0.383806\pi$
$770$		0			0
$771$	−25.8269	−	35.2361i	−0.930133	−	1.26900i
$772$		0			0
$773$	−4.91415	+	11.8638i	−0.176750	+	0.426711i	−0.987281	−	0.158984i	$-0.949178\pi$
$773$	−4.91415	+	11.8638i	−0.176750	+	0.426711i	0.810532	+	0.585695i	$0.199178\pi$
$774$		0			0
$775$	−12.7801	+	12.7801i	−0.459076	+	0.459076i
$776$		0			0
$777$	−13.4002	+	22.0743i	−0.480729	+	0.791913i
$778$		0			0
$779$	4.37326	−	10.5580i	0.156688	−	0.378279i
$780$		0			0
$781$	−17.2617	+	7.15005i	−0.617674	+	0.255849i
$782$		0			0
$783$	31.0831	+	35.4801i	1.11082	+	1.26795i
$784$		0			0
$785$	−67.1112			−2.39530
$786$		0			0
$787$	1.39030	+	3.35649i	0.0495589	+	0.119646i	0.946720	−	0.322057i	$-0.104374\pi$
$787$	1.39030	+	3.35649i	0.0495589	+	0.119646i	−0.897161	+	0.441703i	$0.854374\pi$
$788$		0			0
$789$	−9.72720	−	1.49886i	−0.346298	−	0.0533608i
$790$		0			0
$791$	−18.7343	+	18.7343i	−0.666114	+	0.666114i
$792$		0			0
$793$	5.30271	+	5.30271i	0.188305	+	0.188305i
$794$		0			0
$795$	−7.18055	+	46.5999i	−0.254668	+	1.65273i
$796$		0			0
$797$	1.39468	−	0.577696i	0.0494021	−	0.0204630i	−0.357846	−	0.933781i	$-0.616489\pi$
$797$	1.39468	−	0.577696i	0.0494021	−	0.0204630i	0.407248	+	0.913318i	$0.366489\pi$
$798$		0			0
$799$			0.0114324i			0.000404449i
$800$		0			0
$801$	23.8621	+	45.8768i	0.843125	+	1.62098i
$802$		0			0
$803$	−9.07115	−	21.8997i	−0.320114	−	0.772823i
$804$		0			0
$805$	16.0031	+	6.62870i	0.564035	+	0.233631i
$806$		0			0
$807$	23.2994	+	14.1438i	0.820177	+	0.497887i
$808$		0			0
$809$	33.8616	+	33.8616i	1.19051	+	1.19051i	0.976924	+	0.213586i	$0.0685143\pi$
$809$	33.8616	+	33.8616i	1.19051	+	1.19051i	0.213586	+	0.976924i	$0.431486\pi$
$810$		0			0
$811$	−2.09779	−	0.868935i	−0.0736635	−	0.0305124i	0.345547	−	0.938401i	$-0.387693\pi$
$811$	−2.09779	−	0.868935i	−0.0736635	−	0.0305124i	−0.419211	+	0.907889i	$0.637693\pi$
$812$		0			0
$813$	29.9575	−	21.9579i	1.05065	−	0.770096i
$814$		0			0
$815$		−	14.2189i		−	0.498065i
$816$		0			0
$817$			19.2674i			0.674080i
$818$		0			0
$819$	−9.73318	−	8.17277i	−0.340105	−	0.285580i
$820$		0			0
$821$	−23.5971	−	9.77426i	−0.823546	−	0.341124i	−0.0692016	−	0.997603i	$-0.522045\pi$
$821$	−23.5971	−	9.77426i	−0.823546	−	0.341124i	−0.754345	+	0.656479i	$0.772045\pi$
$822$		0			0
$823$	8.56830	+	8.56830i	0.298672	+	0.298672i	0.840494	−	0.541821i	$-0.182265\pi$
$823$	8.56830	+	8.56830i	0.298672	+	0.298672i	−0.541821	+	0.840494i	$0.682265\pi$
$824$		0			0
$825$	−13.3751	+	22.0330i	−0.465662	+	0.767092i
$826$		0			0
$827$	29.9643	+	12.4116i	1.04196	+	0.431594i	0.837015	−	0.547180i	$-0.184299\pi$
$827$	29.9643	+	12.4116i	1.04196	+	0.431594i	0.204945	+	0.978774i	$0.434299\pi$
$828$		0			0
$829$	12.9154	+	31.1806i	0.448571	+	1.08295i	0.972858	+	0.231404i	$0.0743318\pi$
$829$	12.9154	+	31.1806i	0.448571	+	1.08295i	−0.524287	+	0.851542i	$0.675668\pi$
$830$		0			0
$831$	−5.14668	−	21.0483i	−0.178536	−	0.730157i
$832$		0			0
$833$		−	8.65591i		−	0.299910i
$834$		0			0
$835$	9.35045	−	3.87308i	0.323586	−	0.134034i
$836$		0			0
$837$	18.2864	−	6.19694i	0.632069	−	0.214198i
$838$		0			0
$839$	−17.3187	−	17.3187i	−0.597908	−	0.597908i	0.341848	−	0.939755i	$-0.388947\pi$
$839$	−17.3187	−	17.3187i	−0.597908	−	0.597908i	−0.939755	+	0.341848i	$0.888947\pi$
$840$		0			0
$841$	37.7646	−	37.7646i	1.30223	−	1.30223i
$842$		0			0
$843$	−1.34086	+	8.70181i	−0.0461816	+	0.299706i
$844$		0			0
$845$	−13.8922	−	33.5387i	−0.477906	−	1.15377i
$846$		0			0
$847$	−5.78677			−0.198836
$848$		0			0
$849$	6.55392	+	26.8035i	0.224930	+	0.919892i
$850$		0			0
$851$	6.10129	−	2.52724i	0.209149	−	0.0866325i
$852$		0			0
$853$	2.56433	−	6.19084i	0.0878010	−	0.211970i	−0.873880	−	0.486142i	$-0.838404\pi$
$853$	2.56433	−	6.19084i	0.0878010	−	0.211970i	0.961681	+	0.274172i	$0.0884037\pi$
$854$		0			0
$855$	4.78114	−	15.1458i	0.163512	−	0.517976i
$856$		0			0
$857$	35.6407	−	35.6407i	1.21746	−	1.21746i	0.248947	−	0.968517i	$-0.419916\pi$
$857$	35.6407	−	35.6407i	1.21746	−	1.21746i	0.968517	−	0.248947i	$-0.0800843\pi$
$858$		0			0
$859$	−12.4360	+	30.0231i	−0.424310	+	1.02438i	0.556751	+	0.830679i	$0.312048\pi$
$859$	−12.4360	+	30.0231i	−0.424310	+	1.02438i	−0.981062	+	0.193696i	$0.937952\pi$
$860$		0			0
$861$	33.4185	−	24.4947i	1.13890	−	0.834776i
$862$		0			0
$863$	17.2288			0.586474			0.293237	−	0.956040i	$-0.405267\pi$
$863$	17.2288			0.586474			0.293237	+	0.956040i	$0.405267\pi$
$864$		0			0
$865$	−42.7434			−1.45332
$866$		0			0
$867$	20.2261	−	14.8251i	0.686914	−	0.503486i
$868$		0			0
$869$	5.59136	−	13.4987i	0.189674	−	0.457913i
$870$		0			0
$871$	−1.65026	+	1.65026i	−0.0559169	+	0.0559169i
$872$		0			0
$873$	−3.92943	+	12.4477i	−0.132991	+	0.421292i
$874$		0			0
$875$	0.576536	−	1.39188i	0.0194905	−	0.0470541i
$876$		0			0
$877$	−32.9430	+	13.6454i	−1.11241	+	0.460774i	−0.861766	−	0.507306i	$-0.830641\pi$
$877$	−32.9430	+	13.6454i	−1.11241	+	0.460774i	−0.250641	+	0.968080i	$0.580641\pi$
$878$		0			0
$879$	−4.64272	−	18.9873i	−0.156595	−	0.640425i
$880$		0			0
$881$	3.11591			0.104978			0.0524889	−	0.998622i	$-0.483285\pi$
$881$	3.11591			0.104978			0.0524889	+	0.998622i	$0.483285\pi$
$882$		0			0
$883$	−16.3029	−	39.3586i	−0.548635	−	1.32452i	−0.918494	−	0.395435i	$-0.870594\pi$
$883$	−16.3029	−	39.3586i	−0.548635	−	1.32452i	0.369859	−	0.929088i	$-0.379406\pi$
$884$		0			0
$885$	7.12193	−	46.2195i	0.239401	−	1.55365i
$886$		0			0
$887$	9.96917	−	9.96917i	0.334732	−	0.334732i	−0.519648	−	0.854380i	$-0.673937\pi$
$887$	9.96917	−	9.96917i	0.334732	−	0.334732i	0.854380	+	0.519648i	$0.173937\pi$
$888$		0			0
$889$	0.566900	+	0.566900i	0.0190132	+	0.0190132i
$890$		0			0
$891$	23.2327	−	14.7786i	0.778324	−	0.495100i
$892$		0			0
$893$	0.0112122	−	0.00464423i	0.000375201	−	0.000155413i
$894$		0			0
$895$		−	31.4453i		−	1.05110i
$896$		0			0
$897$	0.772005	+	3.15726i	0.0257765	+	0.105418i
$898$		0			0
$899$	−12.9085	−	31.1638i	−0.430521	−	1.03937i
$900$		0			0
$901$	−12.7157	−	5.26702i	−0.423622	−	0.175470i
$902$		0			0
$903$	−36.2505	+	59.7161i	−1.20634	+	1.98723i
$904$		0			0
$905$	6.50288	+	6.50288i	0.216163	+	0.216163i
$906$		0			0
$907$	34.3481	+	14.2274i	1.14051	+	0.472414i	0.871340	−	0.490679i	$-0.163251\pi$
$907$	34.3481	+	14.2274i	1.14051	+	0.472414i	0.269168	+	0.963093i	$0.413251\pi$
$908$		0			0
$909$	4.94855	+	4.15520i	0.164133	+	0.137819i
$910$		0			0
$911$		−	30.8862i		−	1.02331i	−0.859192	−	0.511653i	$-0.829033\pi$
$911$		−	30.8862i		−	1.02331i	0.859192	−	0.511653i	$-0.170967\pi$
$912$		0			0
$913$		−	11.9859i		−	0.396674i
$914$		0			0
$915$	−27.4049	+	20.0869i	−0.905979	+	0.664054i
$916$		0			0
$917$	33.3869	+	13.8293i	1.10253	+	0.456684i
$918$		0			0
$919$	23.4030	+	23.4030i	0.771993	+	0.771993i	0.978455	−	0.206462i	$-0.0661949\pi$
$919$	23.4030	+	23.4030i	0.771993	+	0.771993i	−0.206462	+	0.978455i	$0.566195\pi$
$920$		0			0
$921$	−21.9430	−	13.3205i	−0.723046	−	0.438924i
$922$		0			0
$923$	−6.77403	−	2.80589i	−0.222970	−	0.0923571i
$924$		0			0
$925$	7.86478	+	18.9873i	0.258592	+	0.624297i
$926$		0			0
$927$	−9.73910	−	18.7242i	−0.319874	−	0.614985i
$928$		0			0
$929$		−	47.8573i		−	1.57015i	−0.619402	−	0.785074i	$-0.712625\pi$
$929$		−	47.8573i		−	1.57015i	0.619402	−	0.785074i	$-0.287375\pi$
$930$		0			0
$931$	−8.48918	+	3.51633i	−0.278221	+	0.115243i
$932$		0			0
$933$	−1.65393	+	10.7336i	−0.0541473	+	0.351402i
$934$		0			0
$935$	−10.7891	−	10.7891i	−0.352841	−	0.352841i
$936$		0			0
$937$	−3.90002	+	3.90002i	−0.127408	+	0.127408i	−0.767935	−	0.640527i	$-0.778716\pi$
$937$	−3.90002	+	3.90002i	−0.127408	+	0.127408i	0.640527	+	0.767935i	$0.278716\pi$
$938$		0			0
$939$	3.20862	+	0.494415i	0.104709	+	0.0161346i
$940$		0			0
$941$	13.7353	+	33.1599i	0.447758	+	1.08098i	0.973160	+	0.230129i	$0.0739149\pi$
$941$	13.7353	+	33.1599i	0.447758	+	1.08098i	−0.525402	+	0.850854i	$0.676085\pi$
$942$		0			0
$943$	−10.5963			−0.345062
$944$		0			0
$945$	43.3144	−	37.9465i	1.40902	−	1.23440i
$946$		0			0
$947$	35.7987	−	14.8283i	1.16330	−	0.481855i	0.284329	−	0.958727i	$-0.408229\pi$
$947$	35.7987	−	14.8283i	1.16330	−	0.481855i	0.878973	+	0.476871i	$0.158229\pi$
$948$		0			0
$949$	3.55979	−	8.59410i	0.115556	−	0.278976i
$950$		0			0
$951$	−11.9623	+	19.7057i	−0.387905	+	0.639002i
$952$		0			0
$953$	16.3341	−	16.3341i	0.529112	−	0.529112i	−0.391195	−	0.920308i	$-0.627938\pi$
$953$	16.3341	−	16.3341i	0.529112	−	0.529112i	0.920308	+	0.391195i	$0.127938\pi$
$954$		0			0
$955$	27.7282	−	66.9418i	0.897264	−	2.16619i
$956$		0			0
$957$	−28.4378	−	38.7981i	−0.919263	−	1.25417i
$958$		0			0
$959$	43.8736			1.41675
$960$		0			0
$961$	17.1928			0.554608
$962$		0			0
$963$	−18.9485	−	15.9107i	−0.610607	−	0.512715i
$964$		0			0
$965$	7.54819	−	18.2229i	0.242985	−	0.586617i
$966$		0			0
$967$	32.9294	−	32.9294i	1.05894	−	1.05894i	0.0607878	−	0.998151i	$-0.480639\pi$
$967$	32.9294	−	32.9294i	1.05894	−	1.05894i	0.998151	−	0.0607878i	$-0.0193613\pi$
$968$		0			0
$969$	3.96316	+	2.40583i	0.127315	+	0.0772863i
$970$		0			0
$971$	1.99488	−	4.81606i	0.0640187	−	0.154555i	−0.888633	−	0.458620i	$-0.848344\pi$
$971$	1.99488	−	4.81606i	0.0640187	−	0.154555i	0.952651	+	0.304065i	$0.0983440\pi$
$972$		0			0
$973$	−61.0527	+	25.2888i	−1.95726	+	0.810723i
$974$		0			0
$975$	−9.82541	+	2.40249i	−0.314665	+	0.0769411i
$976$		0			0
$977$	−32.1515			−1.02862			−0.514309	−	0.857605i	$-0.671952\pi$
$977$	−32.1515			−1.02862			−0.514309	+	0.857605i	$0.671952\pi$
$978$		0			0
$979$	−20.1811	−	48.7214i	−0.644990	−	1.55714i
$980$		0			0
$981$	0.945445	+	10.8491i	0.0301857	+	0.346386i
$982$		0			0
$983$	−13.6974	+	13.6974i	−0.436879	+	0.436879i	−0.890960	−	0.454081i	$-0.849968\pi$
$983$	−13.6974	+	13.6974i	−0.436879	+	0.436879i	0.454081	+	0.890960i	$0.349968\pi$
$984$		0			0
$985$	−37.2419	−	37.2419i	−1.18663	−	1.18663i
$986$		0			0
$987$	0.0434882	+	0.00670107i	0.00138425	+	0.000213298i
$988$		0			0
$989$	16.5053	−	6.83674i	0.524840	−	0.217396i
$990$		0			0
$991$			31.4404i			0.998739i	0.866389	+	0.499369i	$0.166435\pi$
$991$			31.4404i			0.998739i	−0.866389	+	0.499369i	$0.833565\pi$
$992$		0			0
$993$	40.5819	−	9.92298i	1.28783	−	0.314896i
$994$		0			0
$995$	22.2065	+	53.6112i	0.703993	+	1.69959i
$996$		0			0
$997$	−31.5711	−	13.0772i	−0.999867	−	0.414158i	−0.178119	−	0.984009i	$-0.557001\pi$
$997$	−31.5711	−	13.0772i	−0.999867	−	0.414158i	−0.821748	+	0.569851i	$0.807001\pi$
$998$		0			0
$999$	1.44713	−	21.9071i	0.0457852	−	0.693109i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	768.2.o.a.287.4		56
3.2	odd	2	inner	768.2.o.a.287.1		56
4.3	odd	2		768.2.o.b.287.11		56
8.3	odd	2		96.2.o.a.59.4	✓	56
8.5	even	2		384.2.o.a.143.11		56
12.11	even	2		768.2.o.b.287.14		56
24.5	odd	2		384.2.o.a.143.14		56
24.11	even	2		96.2.o.a.59.11	yes	56
32.3	odd	8		384.2.o.a.239.14		56
32.13	even	8		768.2.o.b.479.14		56
32.19	odd	8	inner	768.2.o.a.479.1		56
32.29	even	8		96.2.o.a.83.11	yes	56
96.29	odd	8		96.2.o.a.83.4	yes	56
96.35	even	8		384.2.o.a.239.11		56
96.77	odd	8		768.2.o.b.479.11		56
96.83	even	8	inner	768.2.o.a.479.4		56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
96.2.o.a.59.4	✓	56	8.3	odd	2
96.2.o.a.59.11	yes	56	24.11	even	2
96.2.o.a.83.4	yes	56	96.29	odd	8
96.2.o.a.83.11	yes	56	32.29	even	8
384.2.o.a.143.11		56	8.5	even	2
384.2.o.a.143.14		56	24.5	odd	2
384.2.o.a.239.11		56	96.35	even	8
384.2.o.a.239.14		56	32.3	odd	8
768.2.o.a.287.1		56	3.2	odd	2	inner
768.2.o.a.287.4		56	1.1	even	1	trivial
768.2.o.a.479.1		56	32.19	odd	8	inner
768.2.o.a.479.4		56	96.83	even	8	inner
768.2.o.b.287.11		56	4.3	odd	2
768.2.o.b.287.14		56	12.11	even	2
768.2.o.b.479.11		56	96.77	odd	8
768.2.o.b.479.14		56	32.13	even	8

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:	\( N \)	\(=\)	\( 768 = 2^{8} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	768.o (of order \(8\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.39698 + 1.02394i) q^{3} +(-1.20190 + 2.90164i) q^{5} +(-2.49510 + 2.49510i) q^{7} +(0.903094 - 2.86084i) q^{9} +O(q^{10})\)	\(q+(-1.39698 + 1.02394i) q^{3} +(-1.20190 + 2.90164i) q^{5} +(-2.49510 + 2.49510i) q^{7} +(0.903094 - 2.86084i) q^{9} +(-1.17079 + 2.82653i) q^{11} +(-1.10922 + 0.459453i) q^{13} +(-1.29208 - 5.28419i) q^{15} +1.58794 q^{17} +(-0.645075 - 1.55735i) q^{19} +(0.930766 - 6.04043i) q^{21} +(-1.10521 + 1.10521i) q^{23} +(-3.43941 - 3.43941i) q^{25} +(1.66773 + 4.92125i) q^{27} +(8.38683 - 3.47394i) q^{29} -3.71580i q^{31} +(-1.25864 - 5.14742i) q^{33} +(-4.24102 - 10.2387i) q^{35} +(-3.90358 - 1.61692i) q^{37} +(1.07910 - 1.77762i) q^{39} +(4.79379 + 4.79379i) q^{41} +(-10.5601 - 4.37412i) q^{43} +(7.21570 + 6.05889i) q^{45} +0.00719952i q^{47} -5.45104i q^{49} +(-2.21831 + 1.62595i) q^{51} +(-8.00769 - 3.31689i) q^{53} +(-6.79441 - 6.79441i) q^{55} +(2.49579 + 1.51506i) q^{57} +(7.94232 + 3.28982i) q^{59} +(-2.39029 - 5.77068i) q^{61} +(4.88478 + 9.39140i) q^{63} -3.77076i q^{65} +(1.79590 - 0.743885i) q^{67} +(0.412283 - 2.67561i) q^{69} +(4.31833 + 4.31833i) q^{71} +(-5.47859 + 5.47859i) q^{73} +(8.32652 + 1.28303i) q^{75} +(-4.13125 - 9.97372i) q^{77} -4.77572 q^{79} +(-7.36884 - 5.16722i) q^{81} +(-3.61948 + 1.49924i) q^{83} +(-1.90854 + 4.60762i) q^{85} +(-8.15911 + 13.4406i) q^{87} +(-12.1885 + 12.1885i) q^{89} +(1.62123 - 3.91399i) q^{91} +(3.80475 + 5.19089i) q^{93} +5.29418 q^{95} -4.35108 q^{97} +(7.02894 + 5.90207i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 4 q^{3} + 8 q^{7} - 4 q^{9}+O(q^{10}) \) 56 * q - 4 * q^3 + 8 * q^7 - 4 * q^9	\( 56 q - 4 q^{3} + 8 q^{7} - 4 q^{9} + 8 q^{13} + 8 q^{15} - 8 q^{19} + 4 q^{21} - 8 q^{25} - 28 q^{27} - 8 q^{33} + 8 q^{37} + 28 q^{39} - 8 q^{43} + 4 q^{45} - 16 q^{51} - 24 q^{55} - 4 q^{57} + 40 q^{61} + 56 q^{67} + 4 q^{69} - 8 q^{73} + 16 q^{75} - 16 q^{79} + 48 q^{85} - 52 q^{87} + 40 q^{91} - 8 q^{93} - 16 q^{97} + 60 q^{99}+O(q^{100}) \) 56 * q - 4 * q^3 + 8 * q^7 - 4 * q^9 + 8 * q^13 + 8 * q^15 - 8 * q^19 + 4 * q^21 - 8 * q^25 - 28 * q^27 - 8 * q^33 + 8 * q^37 + 28 * q^39 - 8 * q^43 + 4 * q^45 - 16 * q^51 - 24 * q^55 - 4 * q^57 + 40 * q^61 + 56 * q^67 + 4 * q^69 - 8 * q^73 + 16 * q^75 - 16 * q^79 + 48 * q^85 - 52 * q^87 + 40 * q^91 - 8 * q^93 - 16 * q^97 + 60 * q^99

Introduction

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