LMFDB - Embedded newform 232.2.m.d.25.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [232,2,Mod(25,232)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(232, base_ring=CyclotomicField(14))

chi = DirichletCharacter(H, H._module([0, 0, 8]))

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

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

chi := DirichletCharacter("232.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 232 = 2^{3} \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	232.m (of order $7$, 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:	$1.85252932689$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$4$ over $\Q(\zeta_{7})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{7}]$

Embedding invariants

Embedding label			25.4
Character	$\chi$	$=$	232.25
Dual form			232.2.m.d.65.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.93897 - 1.41533i) q^{3} +(-0.0198029 + 0.0867622i) q^{5} +(-2.19840 + 1.05869i) q^{7} +(4.76390 - 5.97374i) q^{9} +O(q^{10})$	\(q+(2.93897 - 1.41533i) q^{3} +(-0.0198029 + 0.0867622i) q^{5} +(-2.19840 + 1.05869i) q^{7} +(4.76390 - 5.97374i) q^{9} +(0.732844 + 0.918957i) q^{11} +(2.13465 + 2.67676i) q^{13} +(0.0645972 + 0.283019i) q^{15} -5.92776 q^{17} +(-5.84136 - 2.81305i) q^{19} +(-4.96262 + 6.22293i) q^{21} +(-0.362180 - 1.58681i) q^{23} +(4.49771 + 2.16598i) q^{25} +(3.36853 - 14.7585i) q^{27} +(0.406024 + 5.36984i) q^{29} +(-0.0784552 + 0.343735i) q^{31} +(3.45443 + 1.66357i) q^{33} +(-0.0483198 - 0.211703i) q^{35} +(-5.47683 + 6.86773i) q^{37} +(10.0622 + 4.84568i) q^{39} +8.48054 q^{41} +(0.808927 + 3.54414i) q^{43} +(0.423956 + 0.531624i) q^{45} +(-5.46370 - 6.85126i) q^{47} +(-0.652302 + 0.817961i) q^{49} +(-17.4215 + 8.38975i) q^{51} +(2.93988 - 12.8805i) q^{53} +(-0.0942431 + 0.0453851i) q^{55} -21.1490 q^{57} +1.69844 q^{59} +(1.82856 - 0.880587i) q^{61} +(-4.14859 + 18.1762i) q^{63} +(-0.274514 + 0.132199i) q^{65} +(-0.0999855 + 0.125378i) q^{67} +(-3.31030 - 4.15099i) q^{69} +(-2.53844 - 3.18310i) q^{71} +(2.74386 + 12.0216i) q^{73} +16.2842 q^{75} +(-2.58398 - 1.24438i) q^{77} +(-4.75645 + 5.96440i) q^{79} +(-5.88751 - 25.7949i) q^{81} +(-2.05703 - 0.990613i) q^{83} +(0.117387 - 0.514305i) q^{85} +(8.79340 + 15.2071i) q^{87} +(-0.700707 + 3.07000i) q^{89} +(-7.52667 - 3.62466i) q^{91} +(0.255922 + 1.12127i) q^{93} +(0.359742 - 0.451102i) q^{95} +(6.91595 + 3.33055i) q^{97} +8.98081 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - q^{3} - 8 q^{5} + 5 q^{7} - 3 q^{9}+O(q^{10}) $ 24 * q - q^3 - 8 * q^5 + 5 * q^7 - 3 * q^9	$ 24 q - q^{3} - 8 q^{5} + 5 q^{7} - 3 q^{9} - 6 q^{11} + q^{13} - q^{15} - 16 q^{17} - 10 q^{19} - 5 q^{21} + 11 q^{23} + 10 q^{25} - 7 q^{27} - 2 q^{29} + 12 q^{31} + 13 q^{33} - 8 q^{35} + q^{37} + 34 q^{39} - 22 q^{41} + 3 q^{43} + 60 q^{45} + 9 q^{47} - 67 q^{49} - q^{51} + 19 q^{53} - 88 q^{55} - 2 q^{57} + 114 q^{59} - 11 q^{61} - 108 q^{63} + 8 q^{65} - 25 q^{67} - 84 q^{69} - 21 q^{71} + 30 q^{73} - 26 q^{75} - 22 q^{77} + 48 q^{79} + 16 q^{81} - 37 q^{83} + 8 q^{85} + 11 q^{87} - 5 q^{89} - 11 q^{91} - 18 q^{93} - 21 q^{95} + 35 q^{97} + 32 q^{99}+O(q^{100}) $ 24 * q - q^3 - 8 * q^5 + 5 * q^7 - 3 * q^9 - 6 * q^11 + q^13 - q^15 - 16 * q^17 - 10 * q^19 - 5 * q^21 + 11 * q^23 + 10 * q^25 - 7 * q^27 - 2 * q^29 + 12 * q^31 + 13 * q^33 - 8 * q^35 + q^37 + 34 * q^39 - 22 * q^41 + 3 * q^43 + 60 * q^45 + 9 * q^47 - 67 * q^49 - q^51 + 19 * q^53 - 88 * q^55 - 2 * q^57 + 114 * q^59 - 11 * q^61 - 108 * q^63 + 8 * q^65 - 25 * q^67 - 84 * q^69 - 21 * q^71 + 30 * q^73 - 26 * q^75 - 22 * q^77 + 48 * q^79 + 16 * q^81 - 37 * q^83 + 8 * q^85 + 11 * q^87 - 5 * q^89 - 11 * q^91 - 18 * q^93 - 21 * q^95 + 35 * q^97 + 32 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/232\mathbb{Z}\right)^\times$.

$n$	$89$	$117$	$175$
$\chi(n)$	$e\left(\frac{4}{7}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	2.93897	−	1.41533i	1.69681	−	0.817143i	0.702378	−	0.711804i	$-0.252122\pi$
$3$	2.93897	−	1.41533i	1.69681	−	0.817143i	0.994436	−	0.105338i	$-0.0335926\pi$
$4$		0			0
$5$	−0.0198029	+	0.0867622i	−0.00885613	+	0.0388012i	−0.979163	−	0.203076i	$-0.934906\pi$
$5$	−0.0198029	+	0.0867622i	−0.00885613	+	0.0388012i	0.970307	+	0.241877i	$0.0777632\pi$
$6$		0			0
$7$	−2.19840	+	1.05869i	−0.830917	+	0.400148i	−0.800459	−	0.599388i	$-0.795411\pi$
$7$	−2.19840	+	1.05869i	−0.830917	+	0.400148i	−0.0304578	+	0.999536i	$0.509697\pi$
$8$		0			0
$9$	4.76390	−	5.97374i	1.58797	−	1.99125i
$10$		0			0
$11$	0.732844	+	0.918957i	0.220961	+	0.277076i	0.879940	−	0.475085i	$-0.157583\pi$
$11$	0.732844	+	0.918957i	0.220961	+	0.277076i	−0.658979	+	0.752161i	$0.729011\pi$
$12$		0			0
$13$	2.13465	+	2.67676i	0.592044	+	0.742400i	0.984114	−	0.177535i	$-0.0568123\pi$
$13$	2.13465	+	2.67676i	0.592044	+	0.742400i	−0.392070	+	0.919935i	$0.628241\pi$
$14$		0			0
$15$	0.0645972	+	0.283019i	0.0166789	+	0.0730752i
$16$		0			0
$17$	−5.92776			−1.43769			−0.718846	−	0.695169i	$-0.755330\pi$
$17$	−5.92776			−1.43769			−0.718846	+	0.695169i	$0.755330\pi$
$18$		0			0
$19$	−5.84136	−	2.81305i	−1.34010	−	0.645358i	−0.379992	−	0.924990i	$-0.624073\pi$
$19$	−5.84136	−	2.81305i	−1.34010	−	0.645358i	−0.960107	+	0.279632i	$0.909788\pi$
$20$		0			0
$21$	−4.96262	+	6.22293i	−1.08293	+	1.35795i
$22$		0			0
$23$	−0.362180	−	1.58681i	−0.0755197	−	0.330873i	0.923029	−	0.384730i	$-0.125706\pi$
$23$	−0.362180	−	1.58681i	−0.0755197	−	0.330873i	−0.998549	+	0.0538572i	$0.982848\pi$
$24$		0			0
$25$	4.49771	+	2.16598i	0.899542	+	0.433196i
$26$		0			0
$27$	3.36853	−	14.7585i	0.648273	−	2.84027i
$28$		0			0
$29$	0.406024	+	5.36984i	0.0753967	+	0.997154i
$29$	0.406024	+	5.36984i	0.0753967	+	0.997154i
$30$		0			0
$31$	−0.0784552	+	0.343735i	−0.0140910	+	0.0617366i	−0.981485	−	0.191541i	$-0.938651\pi$
$31$	−0.0784552	+	0.343735i	−0.0140910	+	0.0617366i	0.967394	+	0.253278i	$0.0815086\pi$
$32$		0			0
$33$	3.45443	+	1.66357i	0.601340	+	0.289590i
$34$		0			0
$35$	−0.0483198	−	0.211703i	−0.00816754	−	0.0357843i
$36$		0			0
$37$	−5.47683	+	6.86773i	−0.900386	+	1.12905i	0.0907072	+	0.995878i	$0.471087\pi$
$37$	−5.47683	+	6.86773i	−0.900386	+	1.12905i	−0.991093	+	0.133171i	$0.957484\pi$
$38$		0			0
$39$	10.0622	+	4.84568i	1.61124	+	0.775931i
$40$		0			0
$41$	8.48054			1.32444			0.662219	−	0.749310i	$-0.269615\pi$
$41$	8.48054			1.32444			0.662219	+	0.749310i	$0.269615\pi$
$42$		0			0
$43$	0.808927	+	3.54414i	0.123360	+	0.540476i	0.998406	+	0.0564365i	$0.0179738\pi$
$43$	0.808927	+	3.54414i	0.123360	+	0.540476i	−0.875046	+	0.484040i	$0.839169\pi$
$44$		0			0
$45$	0.423956	+	0.531624i	0.0631996	+	0.0792498i
$46$		0			0
$47$	−5.46370	−	6.85126i	−0.796962	−	0.999359i	−0.999797	−	0.0201461i	$-0.993587\pi$
$47$	−5.46370	−	6.85126i	−0.796962	−	0.999359i	0.202835	−	0.979213i	$-0.434985\pi$
$48$		0			0
$49$	−0.652302	+	0.817961i	−0.0931860	+	0.116852i
$50$		0			0
$51$	−17.4215	+	8.38975i	−2.43950	+	1.17480i
$52$		0			0
$53$	2.93988	−	12.8805i	0.403824	−	1.76927i	−0.207853	−	0.978160i	$-0.566648\pi$
$53$	2.93988	−	12.8805i	0.403824	−	1.76927i	0.611677	−	0.791108i	$-0.290495\pi$
$54$		0			0
$55$	−0.0942431	+	0.0453851i	−0.0127077	+	0.00611973i
$56$		0			0
$57$	−21.1490			−2.80125
$58$		0			0
$59$	1.69844			0.221117			0.110559	−	0.993870i	$-0.464736\pi$
$59$	1.69844			0.221117			0.110559	+	0.993870i	$0.464736\pi$
$60$		0			0
$61$	1.82856	−	0.880587i	0.234123	−	0.112748i	−0.313145	−	0.949705i	$-0.601382\pi$
$61$	1.82856	−	0.880587i	0.234123	−	0.112748i	0.547267	+	0.836958i	$0.315668\pi$
$62$		0			0
$63$	−4.14859	+	18.1762i	−0.522674	+	2.28998i
$64$		0			0
$65$	−0.274514	+	0.132199i	−0.0340493	+	0.0163973i
$66$		0			0
$67$	−0.0999855	+	0.125378i	−0.0122152	+	0.0153173i	−0.787902	−	0.615801i	$-0.788832\pi$
$67$	−0.0999855	+	0.125378i	−0.0122152	+	0.0153173i	0.775686	+	0.631119i	$0.217404\pi$
$68$		0			0
$69$	−3.31030	−	4.15099i	−0.398514	−	0.499720i
$70$		0			0
$71$	−2.53844	−	3.18310i	−0.301257	−	0.377765i	0.608044	−	0.793904i	$-0.291955\pi$
$71$	−2.53844	−	3.18310i	−0.301257	−	0.377765i	−0.909301	+	0.416139i	$0.863383\pi$
$72$		0			0
$73$	2.74386	+	12.0216i	0.321144	+	1.40702i	0.835520	+	0.549459i	$0.185166\pi$
$73$	2.74386	+	12.0216i	0.321144	+	1.40702i	−0.514376	+	0.857565i	$0.671977\pi$
$74$		0			0
$75$	16.2842			1.88034
$76$		0			0
$77$	−2.58398	−	1.24438i	−0.294471	−	0.141810i
$78$		0			0
$79$	−4.75645	+	5.96440i	−0.535142	+	0.671047i	−0.973747	−	0.227633i	$-0.926901\pi$
$79$	−4.75645	+	5.96440i	−0.535142	+	0.671047i	0.438605	+	0.898680i	$0.355473\pi$
$80$		0			0
$81$	−5.88751	−	25.7949i	−0.654168	−	2.86610i
$82$		0			0
$83$	−2.05703	−	0.990613i	−0.225788	−	0.108734i	0.317570	−	0.948235i	$-0.397133\pi$
$83$	−2.05703	−	0.990613i	−0.225788	−	0.108734i	−0.543358	+	0.839501i	$0.682847\pi$
$84$		0			0
$85$	0.117387	−	0.514305i	0.0127324	−	0.0557842i
$86$		0			0
$87$	8.79340	+	15.2071i	0.942751	+	1.63037i
$88$		0			0
$89$	−0.700707	+	3.07000i	−0.0742748	+	0.325419i	−0.998392	−	0.0566904i	$-0.981945\pi$
$89$	−0.700707	+	3.07000i	−0.0742748	+	0.325419i	0.924117	+	0.382110i	$0.124802\pi$
$90$		0			0
$91$	−7.52667	−	3.62466i	−0.789010	−	0.379967i
$92$		0			0
$93$	0.255922	+	1.12127i	0.0265378	+	0.116270i
$94$		0			0
$95$	0.359742	−	0.451102i	0.0369088	−	0.0462821i
$96$		0			0
$97$	6.91595	+	3.33055i	0.702208	+	0.338166i	0.750687	−	0.660659i	$-0.229723\pi$
$97$	6.91595	+	3.33055i	0.702208	+	0.338166i	−0.0484782	+	0.998824i	$0.515437\pi$
$98$		0			0
$99$	8.98081			0.902605
$100$		0			0
$101$	−4.28269	−	18.7637i	−0.426143	−	1.86706i	−0.494158	−	0.869372i	$-0.664524\pi$
$101$	−4.28269	−	18.7637i	−0.426143	−	1.86706i	0.0680146	−	0.997684i	$-0.478334\pi$
$102$		0			0
$103$	−8.72593	−	10.9420i	−0.859791	−	1.07814i	−0.996166	−	0.0874869i	$-0.972116\pi$
$103$	−8.72593	−	10.9420i	−0.859791	−	1.07814i	0.136374	−	0.990657i	$-0.456455\pi$
$104$		0			0
$105$	−0.441641	−	0.553800i	−0.0430997	−	0.0540453i
$106$		0			0
$107$	8.66337	−	10.8635i	0.837520	−	1.05022i	−0.160483	−	0.987039i	$-0.551305\pi$
$107$	8.66337	−	10.8635i	0.837520	−	1.05022i	0.998002	−	0.0631777i	$-0.0201235\pi$
$108$		0			0
$109$	8.04320	−	3.87340i	0.770398	−	0.371004i	−0.00703038	−	0.999975i	$-0.502238\pi$
$109$	8.04320	−	3.87340i	0.770398	−	0.371004i	0.777429	+	0.628971i	$0.216524\pi$
$110$		0			0
$111$	−6.37612	+	27.9356i	−0.605194	+	2.65153i
$112$		0			0
$113$	3.74358	−	1.80281i	0.352166	−	0.169594i	−0.249434	−	0.968392i	$-0.580244\pi$
$113$	3.74358	−	1.80281i	0.352166	−	0.169594i	0.601600	+	0.798798i	$0.294530\pi$
$114$		0			0
$115$	0.144848			0.0135071
$116$		0			0
$117$	26.1595			2.41845
$118$		0			0
$119$	13.0316	−	6.27568i	1.19460	−	0.575290i
$120$		0			0
$121$	2.14031	−	9.37730i	0.194573	−	0.852482i
$122$		0			0
$123$	24.9240	−	12.0028i	2.24733	−	1.08226i
$124$		0			0
$125$	−0.554426	+	0.695228i	−0.0495893	+	0.0621830i
$126$		0			0
$127$	10.3912	+	13.0302i	0.922073	+	1.15624i	0.987379	+	0.158377i	$0.0506262\pi$
$127$	10.3912	+	13.0302i	0.922073	+	1.15624i	−0.0653060	+	0.997865i	$0.520802\pi$
$128$		0			0
$129$	7.39355	+	9.27122i	0.650966	+	0.816285i
$130$		0			0
$131$	−1.80822	−	7.92232i	−0.157985	−	0.692177i	−0.990424	−	0.138060i	$-0.955913\pi$
$131$	−1.80822	−	7.92232i	−0.157985	−	0.692177i	0.832439	−	0.554117i	$-0.186944\pi$
$132$		0			0
$133$	15.8198			1.37175
$134$		0			0
$135$	1.21377	+	0.584521i	0.104465	+	0.0503076i
$136$		0			0
$137$	−4.23301	+	5.30803i	−0.361651	+	0.453496i	−0.929054	−	0.369944i	$-0.879377\pi$
$137$	−4.23301	+	5.30803i	−0.361651	+	0.453496i	0.567403	+	0.823440i	$0.307948\pi$
$138$		0			0
$139$	−3.59791	−	15.7635i	−0.305171	−	1.33704i	−0.862208	−	0.506554i	$-0.830919\pi$
$139$	−3.59791	−	15.7635i	−0.305171	−	1.33704i	0.557037	−	0.830488i	$-0.311938\pi$
$140$		0			0
$141$	−25.7544	−	12.4027i	−2.16892	−	1.04449i
$142$		0			0
$143$	−0.895467	+	3.92330i	−0.0748827	+	0.328083i
$144$		0			0
$145$	−0.473939	−	0.0711109i	−0.0393585	−	0.00590544i
$146$		0			0
$147$	−0.759409	+	3.32719i	−0.0626350	+	0.274422i
$148$		0			0
$149$	0.906264	+	0.436434i	0.0742440	+	0.0357540i	0.470637	−	0.882327i	$-0.344024\pi$
$149$	0.906264	+	0.436434i	0.0742440	+	0.0357540i	−0.396393	+	0.918081i	$0.629738\pi$
$150$		0			0
$151$	−0.892340	−	3.90960i	−0.0726176	−	0.318158i	0.925553	−	0.378618i	$-0.123601\pi$
$151$	−0.892340	−	3.90960i	−0.0726176	−	0.318158i	−0.998171	+	0.0604595i	$0.980743\pi$
$152$		0			0
$153$	−28.2393	+	35.4109i	−2.28301	+	2.86280i
$154$		0			0
$155$	−0.0282695	−	0.0136139i	−0.00227066	−	0.00109349i
$156$		0			0
$157$	−13.8190			−1.10288			−0.551439	−	0.834215i	$-0.685921\pi$
$157$	−13.8190			−1.10288			−0.551439	+	0.834215i	$0.685921\pi$
$158$		0			0
$159$	−9.58992	−	42.0162i	−0.760530	−	3.33210i
$160$		0			0
$161$	2.47616	+	3.10501i	0.195149	+	0.244709i
$162$		0			0
$163$	4.69124	+	5.88263i	0.367446	+	0.460763i	0.930841	−	0.365425i	$-0.119076\pi$
$163$	4.69124	+	5.88263i	0.367446	+	0.460763i	−0.563395	+	0.826188i	$0.690505\pi$
$164$		0			0
$165$	−0.212743	+	0.266771i	−0.0165620	+	0.0207681i
$166$		0			0
$167$	−0.999854	+	0.481504i	−0.0773710	+	0.0372599i	−0.472169	−	0.881508i	$-0.656529\pi$
$167$	−0.999854	+	0.481504i	−0.0773710	+	0.0372599i	0.394798	+	0.918768i	$0.370815\pi$
$168$		0			0
$169$	0.284433	−	1.24618i	0.0218794	−	0.0958601i
$170$		0			0
$171$	−44.6321	+	21.4937i	−3.41310	+	1.64366i
$172$		0			0
$173$	−1.41764			−0.107781			−0.0538906	−	0.998547i	$-0.517162\pi$
$173$	−1.41764			−0.107781			−0.0538906	+	0.998547i	$0.517162\pi$
$174$		0			0
$175$	−12.1809			−0.920787
$176$		0			0
$177$	4.99165	−	2.40385i	0.375195	−	0.180685i
$178$		0			0
$179$	−2.31218	+	10.1303i	−0.172820	+	0.757176i	0.812008	+	0.583646i	$0.198374\pi$
$179$	−2.31218	+	10.1303i	−0.172820	+	0.757176i	−0.984829	+	0.173530i	$0.944483\pi$
$180$		0			0
$181$	12.8239	−	6.17567i	0.953193	−	0.459034i	0.108388	−	0.994109i	$-0.465431\pi$
$181$	12.8239	−	6.17567i	0.953193	−	0.459034i	0.844805	+	0.535075i	$0.179717\pi$
$182$		0			0
$183$	4.12775	−	5.17603i	0.305132	−	0.382623i
$184$		0			0
$185$	−0.487402	−	0.611183i	−0.0358345	−	0.0449351i
$186$		0			0
$187$	−4.34412	−	5.44736i	−0.317674	−	0.398350i
$188$		0			0
$189$	8.21933	+	36.0112i	0.597868	+	2.61943i
$190$		0			0
$191$	20.3400			1.47175			0.735875	−	0.677118i	$-0.236771\pi$
$191$	20.3400			1.47175			0.735875	+	0.677118i	$0.236771\pi$
$192$		0			0
$193$	−2.42233	−	1.16653i	−0.174363	−	0.0839690i	0.344666	−	0.938725i	$-0.387992\pi$
$193$	−2.42233	−	1.16653i	−0.174363	−	0.0839690i	−0.519029	+	0.854756i	$0.673706\pi$
$194$		0			0
$195$	−0.619682	+	0.777057i	−0.0443764	+	0.0556462i
$196$		0			0
$197$	−1.20773	−	5.29142i	−0.0860474	−	0.376998i	0.913508	−	0.406821i	$-0.133363\pi$
$197$	−1.20773	−	5.29142i	−0.0860474	−	0.376998i	−0.999555	+	0.0298229i	$0.990506\pi$
$198$		0			0
$199$	19.9097	+	9.58801i	1.41136	+	0.679676i	0.975431	−	0.220304i	$-0.0707049\pi$
$199$	19.9097	+	9.58801i	1.41136	+	0.679676i	0.435931	+	0.899980i	$0.356419\pi$
$200$		0			0
$201$	−0.116403	+	0.509994i	−0.00821042	+	0.0359722i
$202$		0			0
$203$	−6.57761	−	11.3752i	−0.461658	−	0.798382i
$204$		0			0
$205$	−0.167939	+	0.735790i	−0.0117294	+	0.0513898i
$206$		0			0
$207$	−11.2046	−	5.39585i	−0.778773	−	0.375037i
$208$		0			0
$209$	−1.69573	−	7.42948i	−0.117296	−	0.513908i
$210$		0			0
$211$	−7.81009	+	9.79355i	−0.537669	+	0.674215i	−0.974255	−	0.225447i	$-0.927616\pi$
$211$	−7.81009	+	9.79355i	−0.537669	+	0.674215i	0.436587	+	0.899662i	$0.356187\pi$
$212$		0			0
$213$	−11.9655	−	5.76230i	−0.819866	−	0.394827i
$214$		0			0
$215$	−0.323516			−0.0220636
$216$		0			0
$217$	−0.191434	−	0.838726i	−0.0129954	−	0.0569364i
$218$		0			0
$219$	25.0787	+	31.4477i	1.69466	+	2.12504i
$220$		0			0
$221$	−12.6537	−	15.8672i	−0.851178	−	1.06734i
$222$		0			0
$223$	−11.1484	+	13.9796i	−0.746550	+	0.936144i	−0.999509	−	0.0313332i	$-0.990025\pi$
$223$	−11.1484	+	13.9796i	−0.746550	+	0.936144i	0.252959	+	0.967477i	$0.418596\pi$
$224$		0			0
$225$	34.3657	−	16.5496i	2.29104	−	1.10331i
$226$		0			0
$227$	−0.463168	+	2.02927i	−0.0307415	+	0.134687i	−0.987970	−	0.154646i	$-0.950576\pi$
$227$	−0.463168	+	2.02927i	−0.0307415	+	0.134687i	0.957228	+	0.289333i	$0.0934335\pi$
$228$		0			0
$229$	9.33501	−	4.49550i	0.616875	−	0.297071i	−0.0992295	−	0.995065i	$-0.531638\pi$
$229$	9.33501	−	4.49550i	0.616875	−	0.297071i	0.716104	+	0.697993i	$0.245924\pi$
$230$		0			0
$231$	−9.35543			−0.615542
$232$		0			0
$233$	−3.92218			−0.256951			−0.128475	−	0.991713i	$-0.541008\pi$
$233$	−3.92218			−0.256951			−0.128475	+	0.991713i	$0.541008\pi$
$234$		0			0
$235$	0.702627	−	0.338367i	0.0458344	−	0.0220727i
$236$		0			0
$237$	−5.53744	+	24.2611i	−0.359696	+	1.57593i
$238$		0			0
$239$	−4.69705	+	2.26198i	−0.303827	+	0.146315i	−0.579585	−	0.814912i	$-0.696785\pi$
$239$	−4.69705	+	2.26198i	−0.303827	+	0.146315i	0.275758	+	0.961227i	$0.411071\pi$
$240$		0			0
$241$	−15.5595	+	19.5110i	−1.00227	+	1.25681i	−0.0359850	+	0.999352i	$0.511457\pi$
$241$	−15.5595	+	19.5110i	−1.00227	+	1.25681i	−0.966289	+	0.257460i	$0.917115\pi$
$242$		0			0
$243$	−25.4963	−	31.9714i	−1.63559	−	2.05097i
$244$		0			0
$245$	−0.0580506	−	0.0727932i	−0.00370872	−	0.00465059i
$246$		0			0
$247$	−4.93937	−	21.6408i	−0.314284	−	1.37697i
$248$		0			0
$249$	−7.44759			−0.471972
$250$		0			0
$251$	14.6712	+	7.06530i	0.926040	+	0.445957i	0.835224	−	0.549910i	$-0.185338\pi$
$251$	14.6712	+	7.06530i	0.926040	+	0.445957i	0.0908165	+	0.995868i	$0.471052\pi$
$252$		0			0
$253$	1.19279	−	1.49571i	0.0749901	−	0.0940347i
$254$		0			0
$255$	−0.382917	−	1.67767i	−0.0239792	−	0.105060i
$256$		0			0
$257$	5.03347	+	2.42399i	0.313979	+	0.151204i	0.584236	−	0.811584i	$-0.301394\pi$
$257$	5.03347	+	2.42399i	0.313979	+	0.151204i	−0.270257	+	0.962788i	$0.587109\pi$
$258$		0			0
$259$	4.76944	−	20.8963i	0.296359	−	1.29843i
$260$		0			0
$261$	34.0123	+	23.1559i	2.10531	+	1.43331i
$262$		0			0
$263$	−1.01152	+	4.43178i	−0.0623733	+	0.273275i	−0.996492	−	0.0836871i	$-0.973330\pi$
$263$	−1.01152	+	4.43178i	−0.0623733	+	0.273275i	0.934119	+	0.356962i	$0.116188\pi$
$264$		0			0
$265$	1.05932	+	0.510141i	0.0650734	+	0.0313377i
$266$		0			0
$267$	2.28571	+	10.0144i	0.139883	+	0.612869i
$268$		0			0
$269$	4.95043	−	6.20764i	0.301833	−	0.378487i	−0.607666	−	0.794193i	$-0.707894\pi$
$269$	4.95043	−	6.20764i	0.301833	−	0.378487i	0.909499	+	0.415706i	$0.136466\pi$
$270$		0			0
$271$	21.1641	+	10.1921i	1.28563	+	0.619127i	0.946831	−	0.321732i	$-0.104265\pi$
$271$	21.1641	+	10.1921i	1.28563	+	0.619127i	0.338799	+	0.940859i	$0.389979\pi$
$272$		0			0
$273$	−27.2508			−1.64929
$274$		0			0
$275$	1.30567	+	5.72053i	0.0787350	+	0.344961i
$276$		0			0
$277$	−0.190987	−	0.239490i	−0.0114753	−	0.0143896i	0.776061	−	0.630658i	$-0.217215\pi$
$277$	−0.190987	−	0.239490i	−0.0114753	−	0.0143896i	−0.787536	+	0.616269i	$0.788644\pi$
$278$		0			0
$279$	1.67963	+	2.10619i	0.100557	+	0.126094i
$280$		0			0
$281$	−3.43101	+	4.30235i	−0.204677	+	0.256657i	−0.873566	−	0.486705i	$-0.838199\pi$
$281$	−3.43101	+	4.30235i	−0.204677	+	0.256657i	0.668889	+	0.743362i	$0.266770\pi$
$282$		0			0
$283$	−6.66333	+	3.20889i	−0.396094	+	0.190749i	−0.621318	−	0.783558i	$-0.713403\pi$
$283$	−6.66333	+	3.20889i	−0.396094	+	0.190749i	0.225225	+	0.974307i	$0.427688\pi$
$284$		0			0
$285$	0.418811	−	1.83493i	0.0248082	−	0.108692i
$286$		0			0
$287$	−18.6436	+	8.97829i	−1.10050	+	0.529972i
$288$		0			0
$289$	18.1383			1.06696
$290$		0			0
$291$	25.0396			1.46785
$292$		0			0
$293$	−20.2533	+	9.75349i	−1.18321	+	0.569805i	−0.918846	−	0.394617i	$-0.870877\pi$
$293$	−20.2533	+	9.75349i	−1.18321	+	0.569805i	−0.264367	+	0.964422i	$0.585163\pi$
$294$		0			0
$295$	−0.0336339	+	0.147360i	−0.00195824	+	0.00857963i
$296$		0			0
$297$	16.0310	−	7.72013i	0.930213	−	0.447967i
$298$		0			0
$299$	3.47439	−	4.35675i	0.200929	−	0.251957i
$300$		0			0
$301$	−5.53050	−	6.93503i	−0.318773	−	0.399728i
$302$		0			0
$303$	−39.1435	−	49.0845i	−2.24874	−	2.81983i
$304$		0			0
$305$	0.0401909	+	0.176088i	0.00230132	+	0.0100828i
$306$		0			0
$307$	−30.3690			−1.73325			−0.866625	−	0.498960i	$-0.833715\pi$
$307$	−30.3690			−1.73325			−0.866625	+	0.498960i	$0.833715\pi$
$308$		0			0
$309$	−41.1318	−	19.8080i	−2.33990	−	1.12684i
$310$		0			0
$311$	−6.84203	+	8.57964i	−0.387976	+	0.486507i	−0.937015	−	0.349290i	$-0.886423\pi$
$311$	−6.84203	+	8.57964i	−0.387976	+	0.486507i	0.549038	+	0.835797i	$0.314994\pi$
$312$		0			0
$313$	−3.33338	−	14.6045i	−0.188414	−	0.825495i	−0.977453	−	0.211152i	$-0.932278\pi$
$313$	−3.33338	−	14.6045i	−0.188414	−	0.825495i	0.789039	−	0.614343i	$-0.210579\pi$
$314$		0			0
$315$	−1.49485	−	0.719882i	−0.0842253	−	0.0405608i
$316$		0			0
$317$	−3.12235	+	13.6799i	−0.175369	+	0.768340i	0.808361	+	0.588687i	$0.200355\pi$
$317$	−3.12235	+	13.6799i	−0.175369	+	0.768340i	−0.983730	+	0.179654i	$0.942502\pi$
$318$		0			0
$319$	−4.63710	+	4.30837i	−0.259628	+	0.241222i
$320$		0			0
$321$	10.0859	−	44.1891i	0.562939	−	2.46640i
$322$		0			0
$323$	34.6262	+	16.6751i	1.92665	+	0.927826i
$324$		0			0
$325$	3.80320	+	16.6629i	0.210964	+	0.924292i
$326$		0			0
$327$	18.1566	−	22.7676i	1.00406	−	1.25905i
$328$		0			0
$329$	19.2648	+	9.27742i	1.06210	+	0.511481i
$330$		0			0
$331$	−16.6065			−0.912775			−0.456388	−	0.889781i	$-0.650857\pi$
$331$	−16.6065			−0.912775			−0.456388	+	0.889781i	$0.650857\pi$
$332$		0			0
$333$	14.9350	+	65.4344i	0.818431	+	3.58578i
$334$		0			0
$335$	−0.00889805	−	0.0111578i	−0.000486152	−	0.000609616i
$336$		0			0
$337$	10.5219	+	13.1941i	0.573166	+	0.718727i	0.980930	−	0.194360i	$-0.0622630\pi$
$337$	10.5219	+	13.1941i	0.573166	+	0.718727i	−0.407765	+	0.913087i	$0.633692\pi$
$338$		0			0
$339$	8.45068	−	10.5968i	0.458978	−	0.575540i
$340$		0			0
$341$	−0.373373	+	0.179807i	−0.0202193	+	0.00973709i
$342$		0			0
$343$	4.36877	−	19.1408i	0.235891	−	1.03351i
$344$		0			0
$345$	0.425702	−	0.205007i	0.0229190	−	0.0110372i
$346$		0			0
$347$	5.81539			0.312186			0.156093	−	0.987742i	$-0.450110\pi$
$347$	5.81539			0.312186			0.156093	+	0.987742i	$0.450110\pi$
$348$		0			0
$349$	−31.7937			−1.70188			−0.850940	−	0.525263i	$-0.823967\pi$
$349$	−31.7937			−1.70188			−0.850940	+	0.525263i	$0.823967\pi$
$350$		0			0
$351$	46.6955	−	22.4874i	2.49242	−	1.20029i
$352$		0			0
$353$	−3.49252	+	15.3017i	−0.185888	+	0.814429i	0.792867	+	0.609395i	$0.208588\pi$
$353$	−3.49252	+	15.3017i	−0.185888	+	0.814429i	−0.978755	+	0.205034i	$0.934270\pi$
$354$		0			0
$355$	0.326441	−	0.157206i	0.0173257	−	0.00834362i
$356$		0			0
$357$	29.4172	−	36.8880i	1.55692	−	1.95232i
$358$		0			0
$359$	−3.38392	−	4.24330i	−0.178596	−	0.223953i	0.684473	−	0.729038i	$-0.260032\pi$
$359$	−3.38392	−	4.24330i	−0.178596	−	0.223953i	−0.863069	+	0.505086i	$0.831461\pi$
$360$		0			0
$361$	14.3619	+	18.0092i	0.755889	+	0.947855i
$362$		0			0
$363$	−6.98171	−	30.5888i	−0.366444	−	1.60550i
$364$		0			0
$365$	−1.09736			−0.0574383
$366$		0			0
$367$	13.6073	+	6.55294i	0.710296	+	0.342060i	0.753901	−	0.656988i	$-0.228170\pi$
$367$	13.6073	+	6.55294i	0.710296	+	0.342060i	−0.0436048	+	0.999049i	$0.513884\pi$
$368$		0			0
$369$	40.4005	−	50.6606i	2.10316	−	2.63728i
$370$		0			0
$371$	7.17342	+	31.4288i	0.372426	+	1.63170i
$372$		0			0
$373$	−21.3086	−	10.2617i	−1.10332	−	0.531329i	−0.208617	−	0.977998i	$-0.566896\pi$
$373$	−21.3086	−	10.2617i	−1.10332	−	0.531329i	−0.894700	+	0.446668i	$0.852610\pi$
$374$		0			0
$375$	−0.645461	+	2.82795i	−0.0333315	+	0.146035i
$376$		0			0
$377$	−13.5071	+	12.5495i	−0.695649	+	0.646334i
$378$		0			0
$379$	−1.28398	+	5.62548i	−0.0659536	+	0.288961i	−0.997140	−	0.0755831i	$-0.975918\pi$
$379$	−1.28398	+	5.62548i	−0.0659536	+	0.288961i	0.931186	+	0.364545i	$0.118775\pi$
$380$		0			0
$381$	48.9816	+	23.5883i	2.50940	+	1.20846i
$382$		0			0
$383$	2.80175	+	12.2753i	0.143163	+	0.627236i	0.994689	+	0.102925i	$0.0328201\pi$
$383$	2.80175	+	12.2753i	0.143163	+	0.627236i	−0.851527	+	0.524311i	$0.824323\pi$
$384$		0			0
$385$	0.159135	−	0.199549i	0.00811028	−	0.0101700i
$386$		0			0
$387$	25.0254	+	12.0516i	1.27211	+	0.612618i
$388$		0			0
$389$	−24.4195			−1.23812			−0.619059	−	0.785344i	$-0.712486\pi$
$389$	−24.4195			−1.23812			−0.619059	+	0.785344i	$0.712486\pi$
$390$		0			0
$391$	2.14691	+	9.40624i	0.108574	+	0.475694i
$392$		0			0
$393$	−16.5270	−	20.7242i	−0.833678	−	1.04540i
$394$		0			0
$395$	−0.423293	−	0.530792i	−0.0212982	−	0.0267070i
$396$		0			0
$397$	11.8019	−	14.7992i	0.592322	−	0.742748i	−0.391837	−	0.920034i	$-0.628160\pi$
$397$	11.8019	−	14.7992i	0.592322	−	0.742748i	0.984159	+	0.177286i	$0.0567319\pi$
$398$		0			0
$399$	46.4939	−	22.3903i	2.32760	−	1.12092i
$400$		0			0
$401$	2.02678	−	8.87989i	0.101212	−	0.443441i	−0.898775	−	0.438410i	$-0.855542\pi$
$401$	2.02678	−	8.87989i	0.101212	−	0.443441i	0.999987	−	0.00503026i	$-0.00160119\pi$
$402$		0			0
$403$	−1.08757	+	0.523746i	−0.0541757	+	0.0260897i
$404$		0			0
$405$	2.35461			0.117001
$406$		0			0
$407$	−10.3248			−0.511782
$408$		0			0
$409$	17.3582	−	8.35926i	0.858307	−	0.413339i	0.0476525	−	0.998864i	$-0.484826\pi$
$409$	17.3582	−	8.35926i	0.858307	−	0.413339i	0.810654	+	0.585525i	$0.199112\pi$
$410$		0			0
$411$	−4.92806	+	21.5913i	−0.243083	+	1.06502i
$412$		0			0
$413$	−3.73384	+	1.79812i	−0.183730	+	0.0884798i
$414$		0			0
$415$	0.126683	−	0.158855i	0.00621862	−	0.00779790i
$416$		0			0
$417$	−32.8847	−	41.2362i	−1.61037	−	2.01934i
$418$		0			0
$419$	6.92843	+	8.68797i	0.338476	+	0.424435i	0.921717	−	0.387864i	$-0.126787\pi$
$419$	6.92843	+	8.68797i	0.338476	+	0.424435i	−0.583241	+	0.812299i	$0.698216\pi$
$420$		0			0
$421$	−2.51112	−	11.0019i	−0.122384	−	0.536201i	−0.998532	−	0.0541588i	$-0.982752\pi$
$421$	−2.51112	−	11.0019i	−0.122384	−	0.536201i	0.876148	−	0.482042i	$-0.160105\pi$
$422$		0			0
$423$	−66.9562			−3.25552
$424$		0			0
$425$	−26.6613	−	12.8394i	−1.29326	−	0.622803i
$426$		0			0
$427$	−3.08763	+	3.87176i	−0.149421	+	0.187368i
$428$		0			0
$429$	2.92102	+	12.7978i	0.141028	+	0.617885i
$430$		0			0
$431$	6.63468	+	3.19510i	0.319582	+	0.153902i	0.586796	−	0.809735i	$-0.300389\pi$
$431$	6.63468	+	3.19510i	0.319582	+	0.153902i	−0.267215	+	0.963637i	$0.586103\pi$
$432$		0			0
$433$	−1.43779	+	6.29935i	−0.0690956	+	0.302727i	−0.997654	−	0.0684590i	$-0.978192\pi$
$433$	−1.43779	+	6.29935i	−0.0690956	+	0.302727i	0.928558	+	0.371186i	$0.121049\pi$
$434$		0			0
$435$	−1.49354	+	0.461789i	−0.0716097	+	0.0221411i
$436$		0			0
$437$	−2.34816	+	10.2880i	−0.112328	+	0.492140i
$438$		0			0
$439$	22.9014	+	11.0288i	1.09303	+	0.526374i	0.891459	−	0.453101i	$-0.149682\pi$
$439$	22.9014	+	11.0288i	1.09303	+	0.526374i	0.201567	+	0.979475i	$0.435397\pi$
$440$		0			0
$441$	1.77879	+	7.79337i	0.0847041	+	0.371113i
$442$		0			0
$443$	−20.0899	+	25.1919i	−0.954500	+	1.19690i	0.0258558	+	0.999666i	$0.491769\pi$
$443$	−20.0899	+	25.1919i	−0.954500	+	1.19690i	−0.980355	+	0.197239i	$0.936803\pi$
$444$		0			0
$445$	−0.252484	−	0.121590i	−0.0119689	−	0.00576391i
$446$		0			0
$447$	3.28118			0.155195
$448$		0			0
$449$	1.49871	+	6.56628i	0.0707285	+	0.309882i	0.997901	−	0.0647518i	$-0.0206256\pi$
$449$	1.49871	+	6.56628i	0.0707285	+	0.309882i	−0.927173	+	0.374634i	$0.877768\pi$
$450$		0			0
$451$	6.21491	+	7.79325i	0.292649	+	0.366970i
$452$		0			0
$453$	−8.15594	−	10.2272i	−0.383199	−	0.480517i
$454$		0			0
$455$	0.463533	−	0.581252i	0.0217308	−	0.0272495i
$456$		0			0
$457$	−2.63395	+	1.26844i	−0.123211	+	0.0593353i	−0.494474	−	0.869193i	$-0.664639\pi$
$457$	−2.63395	+	1.26844i	−0.123211	+	0.0593353i	0.371263	+	0.928528i	$0.378925\pi$
$458$		0			0
$459$	−19.9678	+	87.4847i	−0.932017	+	4.08343i
$460$		0			0
$461$	24.1972	−	11.6527i	1.12697	−	0.542722i	0.224934	−	0.974374i	$-0.427783\pi$
$461$	24.1972	−	11.6527i	1.12697	−	0.542722i	0.902040	+	0.431652i	$0.142069\pi$
$462$		0			0
$463$	25.5726			1.18846			0.594229	−	0.804296i	$-0.297457\pi$
$463$	25.5726			1.18846			0.594229	+	0.804296i	$0.297457\pi$
$464$		0			0
$465$	−0.102351			−0.00474644
$466$		0			0
$467$	−32.0870	+	15.4523i	−1.48481	+	0.715047i	−0.988235	−	0.152946i	$-0.951124\pi$
$467$	−32.0870	+	15.4523i	−1.48481	+	0.715047i	−0.496576	+	0.867993i	$0.665410\pi$
$468$		0			0
$469$	0.0870713	−	0.381484i	0.00402058	−	0.0176153i
$470$		0			0
$471$	−40.6137	+	19.5585i	−1.87138	+	0.901209i
$472$		0			0
$473$	−2.66410	+	3.34067i	−0.122495	+	0.153604i
$474$		0			0
$475$	−20.1797	−	25.3046i	−0.925908	−	1.16105i
$476$		0			0
$477$	−62.9393	−	78.9233i	−2.88179	−	3.61365i
$478$		0			0
$479$	−2.35766	−	10.3296i	−0.107724	−	0.471970i	−0.999798	−	0.0200813i	$-0.993607\pi$
$479$	−2.35766	−	10.3296i	−0.107724	−	0.471970i	0.892074	−	0.451889i	$-0.149250\pi$
$480$		0			0
$481$	−30.0744			−1.37127
$482$		0			0
$483$	11.6720	+	5.62093i	0.531094	+	0.255761i
$484$		0			0
$485$	−0.425921	+	0.534088i	−0.0193401	+	0.0242517i
$486$		0			0
$487$	4.49879	+	19.7105i	0.203860	+	0.893167i	0.968560	+	0.248781i	$0.0800299\pi$
$487$	4.49879	+	19.7105i	0.203860	+	0.893167i	−0.764700	+	0.644386i	$0.777113\pi$
$488$		0			0
$489$	22.1133	+	10.6492i	0.999997	+	0.481573i
$490$		0			0
$491$	−4.45110	+	19.5016i	−0.200876	+	0.880093i	0.769530	+	0.638611i	$0.220491\pi$
$491$	−4.45110	+	19.5016i	−0.200876	+	0.880093i	−0.970405	+	0.241482i	$0.922366\pi$
$492$		0			0
$493$	−2.40681	−	31.8311i	−0.108397	−	1.43360i
$494$		0			0
$495$	−0.177846	+	0.779194i	−0.00799358	+	0.0350222i
$496$		0			0
$497$	8.95043	+	4.31030i	0.401482	+	0.193343i
$498$		0			0
$499$	−4.24914	−	18.6167i	−0.190218	−	0.833398i	−0.976498	−	0.215528i	$-0.930853\pi$
$499$	−4.24914	−	18.6167i	−0.190218	−	0.833398i	0.786280	−	0.617870i	$-0.212004\pi$
$500$		0			0
$501$	−2.25705	+	2.83025i	−0.100838	+	0.126446i
$502$		0			0
$503$	−9.19298	−	4.42711i	−0.409895	−	0.197395i	0.217562	−	0.976047i	$-0.430190\pi$
$503$	−9.19298	−	4.42711i	−0.409895	−	0.197395i	−0.627456	+	0.778652i	$0.715904\pi$
$504$		0			0
$505$	1.71279			0.0762181
$506$		0			0
$507$	−0.927822	−	4.06505i	−0.0412060	−	0.180535i
$508$		0			0
$509$	13.7893	+	17.2912i	0.611200	+	0.766421i	0.987077	−	0.160249i	$-0.0512297\pi$
$509$	13.7893	+	17.2912i	0.611200	+	0.766421i	−0.375876	+	0.926670i	$0.622658\pi$
$510$		0			0
$511$	−18.7593	−	23.5234i	−0.829862	−	1.04061i
$512$		0			0
$513$	−61.1931	+	76.7337i	−2.70174	+	3.38787i
$514$		0			0
$515$	1.12215	−	0.540398i	0.0494477	−	0.0238128i
$516$		0			0
$517$	2.29198	−	10.0418i	0.100801	−	0.441638i
$518$		0			0
$519$	−4.16640	+	2.00643i	−0.182885	+	0.0880727i
$520$		0			0
$521$	0.736874			0.0322830			0.0161415	−	0.999870i	$-0.494862\pi$
$521$	0.736874			0.0322830			0.0161415	+	0.999870i	$0.494862\pi$
$522$		0			0
$523$	2.95427			0.129181			0.0645905	−	0.997912i	$-0.479426\pi$
$523$	2.95427			0.129181			0.0645905	+	0.997912i	$0.479426\pi$
$524$		0			0
$525$	−35.7992	+	17.2400i	−1.56240	+	0.752414i
$526$		0			0
$527$	0.465064	−	2.03758i	0.0202585	−	0.0887583i
$528$		0			0
$529$	18.3355	−	8.82990i	0.797195	−	0.383909i
$530$		0			0
$531$	8.09118	−	10.1460i	0.351127	−	0.440300i
$532$		0			0
$533$	18.1030	+	22.7004i	0.784126	+	0.983263i
$534$		0			0
$535$	0.770983	+	0.966782i	0.0333325	+	0.0417976i
$536$		0			0
$537$	7.54235	+	33.0452i	0.325476	+	1.42601i
$538$		0			0
$539$	−1.22971			−0.0529672
$540$		0			0
$541$	−1.24430	−	0.599222i	−0.0534965	−	0.0257626i	0.406944	−	0.913453i	$-0.366594\pi$
$541$	−1.24430	−	0.599222i	−0.0534965	−	0.0257626i	−0.460441	+	0.887690i	$0.652309\pi$
$542$		0			0
$543$	28.9484	−	36.3002i	1.24230	−	1.55779i
$544$		0			0
$545$	0.176786	+	0.774550i	0.00757268	+	0.0331781i
$546$		0			0
$547$	4.00722	+	1.92977i	0.171336	+	0.0825112i	0.517586	−	0.855631i	$-0.326831\pi$
$547$	4.00722	+	1.92977i	0.171336	+	0.0825112i	−0.346250	+	0.938142i	$0.612545\pi$
$548$		0			0
$549$	3.45067	−	15.1184i	0.147271	−	0.645236i
$550$		0			0
$551$	12.7339	−	32.5093i	0.542482	−	1.38494i
$552$		0			0
$553$	4.14210	−	18.1477i	0.176140	−	0.771720i
$554$		0			0
$555$	−2.29749	−	1.10641i	−0.0975229	−	0.0469646i
$556$		0			0
$557$	9.05581	+	39.6761i	0.383707	+	1.68113i	0.685751	+	0.727836i	$0.259474\pi$
$557$	9.05581	+	39.6761i	0.383707	+	1.68113i	−0.302044	+	0.953294i	$0.597669\pi$
$558$		0			0
$559$	−7.76005	+	9.73079i	−0.328215	+	0.411569i
$560$		0			0
$561$	−20.4771	−	9.86123i	−0.864542	−	0.416341i
$562$		0			0
$563$	−5.56939			−0.234722			−0.117361	−	0.993089i	$-0.537443\pi$
$563$	−5.56939			−0.234722			−0.117361	+	0.993089i	$0.537443\pi$
$564$		0			0
$565$	0.0822822	+	0.360502i	0.00346164	+	0.0151664i
$566$		0			0
$567$	40.2519	+	50.4743i	1.69042	+	2.11972i
$568$		0			0
$569$	22.7561	+	28.5353i	0.953986	+	1.19626i	0.980481	+	0.196611i	$0.0629937\pi$
$569$	22.7561	+	28.5353i	0.953986	+	1.19626i	−0.0264957	+	0.999649i	$0.508435\pi$
$570$		0			0
$571$	18.3688	−	23.0337i	0.768708	−	0.963930i	−0.231251	−	0.972894i	$-0.574282\pi$
$571$	18.3688	−	23.0337i	0.768708	−	0.963930i	0.999960	+	0.00896414i	$0.00285341\pi$
$572$		0			0
$573$	59.7786	−	28.7878i	2.49729	−	1.20263i
$574$		0			0
$575$	1.80803	−	7.92149i	0.0754000	−	0.330349i
$576$		0			0
$577$	−11.5230	+	5.54917i	−0.479707	+	0.231015i	−0.658080	−	0.752948i	$-0.728631\pi$
$577$	−11.5230	+	5.54917i	−0.479707	+	0.231015i	0.178373	+	0.983963i	$0.442917\pi$
$578$		0			0
$579$	−8.77020			−0.364477
$580$		0			0
$581$	5.57092			0.231121
$582$		0			0
$583$	13.9911	−	6.73774i	0.579451	−	0.279049i
$584$		0			0
$585$	−0.518035	+	2.26966i	−0.0214181	+	0.0938388i
$586$		0			0
$587$	29.8854	−	14.3921i	1.23350	−	0.594024i	0.300462	−	0.953794i	$-0.402859\pi$
$587$	29.8854	−	14.3921i	1.23350	−	0.594024i	0.933041	+	0.359770i	$0.117145\pi$
$588$		0			0
$589$	1.42523	−	1.78718i	0.0587255	−	0.0736394i
$590$		0			0
$591$	−11.0386	−	13.8420i	−0.454068	−	0.569383i
$592$		0			0
$593$	−13.0910	−	16.4156i	−0.537583	−	0.674108i	0.436655	−	0.899629i	$-0.356163\pi$
$593$	−13.0910	−	16.4156i	−0.537583	−	0.674108i	−0.974238	+	0.225521i	$0.927592\pi$
$594$		0			0
$595$	0.286428	+	1.25492i	0.0117424	+	0.0514469i
$596$		0			0
$597$	72.0842			2.95021
$598$		0			0
$599$	−22.9385	−	11.0466i	−0.937240	−	0.451351i	−0.0980451	−	0.995182i	$-0.531259\pi$
$599$	−22.9385	−	11.0466i	−0.937240	−	0.451351i	−0.839195	+	0.543831i	$0.816973\pi$
$600$		0			0
$601$	−12.2008	+	15.2994i	−0.497683	+	0.624075i	−0.965705	−	0.259642i	$-0.916395\pi$
$601$	−12.2008	+	15.2994i	−0.497683	+	0.624075i	0.468022	+	0.883717i	$0.344967\pi$
$602$		0			0
$603$	0.272654	+	1.19457i	0.0111033	+	0.0486469i
$604$		0			0
$605$	0.771211	+	0.371396i	0.0313542	+	0.0150994i
$606$		0			0
$607$	−7.66118	+	33.5658i	−0.310958	+	1.36239i	0.541984	+	0.840389i	$0.317673\pi$
$607$	−7.66118	+	33.5658i	−0.310958	+	1.36239i	−0.852942	+	0.522006i	$0.825184\pi$
$608$		0			0
$609$	−35.4311	−	24.1218i	−1.43574	−	0.977465i
$610$		0			0
$611$	6.67613	−	29.2500i	0.270087	−	1.18333i
$612$		0			0
$613$	−10.6531	−	5.13025i	−0.430273	−	0.207209i	0.206196	−	0.978511i	$-0.433892\pi$
$613$	−10.6531	−	5.13025i	−0.430273	−	0.207209i	−0.636469	+	0.771302i	$0.719606\pi$
$614$		0			0
$615$	0.547820	+	2.40015i	0.0220902	+	0.0967836i
$616$		0			0
$617$	−13.4319	+	16.8430i	−0.540747	+	0.678075i	−0.974869	−	0.222779i	$-0.928487\pi$
$617$	−13.4319	+	16.8430i	−0.540747	+	0.678075i	0.434122	+	0.900854i	$0.357059\pi$
$618$		0			0
$619$	15.9865	+	7.69871i	0.642553	+	0.309437i	0.726637	−	0.687022i	$-0.241082\pi$
$619$	15.9865	+	7.69871i	0.642553	+	0.309437i	−0.0840843	+	0.996459i	$0.526797\pi$
$620$		0			0
$621$	−24.6389			−0.988727
$622$		0			0
$623$	−1.70975	−	7.49092i	−0.0684998	−	0.300117i
$624$		0			0
$625$	15.5132	+	19.4530i	0.620529	+	0.778118i
$626$		0			0
$627$	−15.4989	−	19.4350i	−0.618966	−	0.776159i
$628$		0			0
$629$	32.4653	−	40.7103i	1.29448	−	1.62322i
$630$		0			0
$631$	−15.4755	+	7.45262i	−0.616071	+	0.296684i	−0.715773	−	0.698333i	$-0.753925\pi$
$631$	−15.4755	+	7.45262i	−0.616071	+	0.296684i	0.0997018	+	0.995017i	$0.468211\pi$
$632$		0			0
$633$	−9.09249	+	39.8368i	−0.361394	+	1.58337i
$634$		0			0
$635$	−1.33630	+	0.643530i	−0.0530296	+	0.0255377i
$636$		0			0
$637$	−3.58192			−0.141921
$638$		0			0
$639$	−31.1079			−1.23061
$640$		0			0
$641$	−9.98994	+	4.81090i	−0.394579	+	0.190019i	−0.620643	−	0.784093i	$-0.713128\pi$
$641$	−9.98994	+	4.81090i	−0.394579	+	0.190019i	0.226064	+	0.974112i	$0.427414\pi$
$642$		0			0
$643$	5.53961	−	24.2706i	0.218461	−	0.957139i	−0.740155	−	0.672436i	$-0.765248\pi$
$643$	5.53961	−	24.2706i	0.218461	−	0.957139i	0.958616	−	0.284703i	$-0.0918949\pi$
$644$		0			0
$645$	−0.950805	+	0.457883i	−0.0374379	+	0.0180291i
$646$		0			0
$647$	−19.2382	+	24.1240i	−0.756333	+	0.948412i	−0.999769	−	0.0215051i	$-0.993154\pi$
$647$	−19.2382	+	24.1240i	−0.756333	+	0.948412i	0.243435	+	0.969917i	$0.421726\pi$
$648$		0			0
$649$	1.24469	+	1.56079i	0.0488583	+	0.0612663i
$650$		0			0
$651$	−1.74969	−	2.19405i	−0.0685759	−	0.0859915i
$652$		0			0
$653$	−7.98505	−	34.9848i	−0.312479	−	1.36906i	−0.850432	−	0.526085i	$-0.823659\pi$
$653$	−7.98505	−	34.9848i	−0.312479	−	1.36906i	0.537953	−	0.842975i	$-0.319198\pi$
$654$		0			0
$655$	0.723166			0.0282564
$656$		0			0
$657$	84.8855	+	40.8787i	3.31170	+	1.59483i
$658$		0			0
$659$	10.5872	−	13.2759i	0.412419	−	0.517158i	−0.531623	−	0.846981i	$-0.678418\pi$
$659$	10.5872	−	13.2759i	0.412419	−	0.517158i	0.944043	+	0.329823i	$0.106989\pi$
$660$		0			0
$661$	−0.308018	−	1.34951i	−0.0119805	−	0.0524900i	0.968584	−	0.248685i	$-0.0799985\pi$
$661$	−0.308018	−	1.34951i	−0.0119805	−	0.0524900i	−0.980565	+	0.196195i	$0.937141\pi$
$662$		0			0
$663$	−59.6461	−	28.7241i	−2.31646	−	1.11555i
$664$		0			0
$665$	−0.313278	+	1.37256i	−0.0121484	+	0.0532256i
$666$		0			0
$667$	8.37387	−	2.58913i	0.324238	−	0.100251i
$668$		0			0
$669$	−12.9789	+	56.8643i	−0.501793	+	2.19850i
$670$		0			0
$671$	2.14927	+	1.03503i	0.0829716	+	0.0399570i
$672$		0			0
$673$	−1.28483	−	5.62921i	−0.0495266	−	0.216990i	0.944109	−	0.329634i	$-0.106925\pi$
$673$	−1.28483	−	5.62921i	−0.0495266	−	0.216990i	−0.993635	+	0.112644i	$0.964068\pi$
$674$		0			0
$675$	47.1172	−	59.0832i	1.81354	−	2.27411i
$676$		0			0
$677$	−6.89448	−	3.32021i	−0.264976	−	0.127606i	0.296679	−	0.954977i	$-0.404121\pi$
$677$	−6.89448	−	3.32021i	−0.264976	−	0.127606i	−0.561655	+	0.827371i	$0.689835\pi$
$678$		0			0
$679$	−18.7300			−0.718793
$680$		0			0
$681$	1.51086	+	6.61950i	0.0578962	+	0.253660i
$682$		0			0
$683$	−20.1470	−	25.2636i	−0.770905	−	0.966684i	0.229072	−	0.973409i	$-0.426431\pi$
$683$	−20.1470	−	25.2636i	−0.770905	−	0.966684i	−0.999977	+	0.00672515i	$0.997859\pi$
$684$		0			0
$685$	−0.376710	−	0.472380i	−0.0143934	−	0.0180487i
$686$		0			0
$687$	21.0727	−	26.4243i	0.803972	−	1.00815i
$688$		0			0
$689$	40.7535	−	19.6259i	1.55259	−	0.747686i
$690$		0			0
$691$	7.38499	−	32.3558i	0.280938	−	1.23087i	−0.615655	−	0.788016i	$-0.711108\pi$
$691$	7.38499	−	32.3558i	0.280938	−	1.23087i	0.896593	−	0.442855i	$-0.146034\pi$
$692$		0			0
$693$	−19.7434	+	9.50792i	−0.749990	+	0.361176i
$694$		0			0
$695$	1.43892			0.0545815
$696$		0			0
$697$	−50.2706			−1.90414
$698$		0			0
$699$	−11.5272	+	5.55119i	−0.435997	+	0.209965i
$700$		0			0
$701$	5.63738	−	24.6990i	0.212921	−	0.932867i	−0.749649	−	0.661835i	$-0.769778\pi$
$701$	5.63738	−	24.6990i	0.212921	−	0.932867i	0.962570	−	0.271032i	$-0.0873650\pi$
$702$		0			0
$703$	51.3114	−	24.7103i	1.93525	−	0.931966i
$704$		0			0
$705$	1.58610	−	1.98890i	0.0597359	−	0.0749064i
$706$		0			0
$707$	29.2800	+	36.7160i	1.10119	+	1.38085i
$708$		0			0
$709$	20.9224	+	26.2359i	0.785758	+	0.985310i	0.999964	+	0.00852090i	$0.00271232\pi$
$709$	20.9224	+	26.2359i	0.785758	+	0.985310i	−0.214206	+	0.976789i	$0.568716\pi$
$710$		0			0
$711$	12.9705	+	56.8276i	0.486433	+	2.13120i
$712$		0			0
$713$	0.573858			0.0214911
$714$		0			0
$715$	−0.322661	−	0.155385i	−0.0120668	−	0.00581108i
$716$		0			0
$717$	−10.6030	+	13.2958i	−0.395977	+	0.496540i
$718$		0			0
$719$	−4.14468	−	18.1590i	−0.154571	−	0.677218i	−0.991522	−	0.129941i	$-0.958521\pi$
$719$	−4.14468	−	18.1590i	−0.154571	−	0.677218i	0.836951	−	0.547278i	$-0.184336\pi$
$720$		0			0
$721$	30.7673	+	14.8167i	1.14583	+	0.551804i
$722$		0			0
$723$	−18.1143	+	79.3640i	−0.673678	+	2.95158i
$724$		0			0
$725$	−9.80480	+	25.0314i	−0.364141	+	0.929643i
$726$		0			0
$727$	8.48432	−	37.1722i	0.314666	−	1.37864i	−0.532102	−	0.846680i	$-0.678598\pi$
$727$	8.48432	−	37.1722i	0.314666	−	1.37864i	0.846768	−	0.531962i	$-0.178545\pi$
$728$		0			0
$729$	−48.6690	−	23.4377i	−1.80255	−	0.868064i
$730$		0			0
$731$	−4.79512	−	21.0088i	−0.177354	−	0.777039i
$732$		0			0
$733$	7.39976	−	9.27900i	0.273316	−	0.342728i	−0.626162	−	0.779693i	$-0.715375\pi$
$733$	7.39976	−	9.27900i	0.273316	−	0.342728i	0.899478	+	0.436965i	$0.143947\pi$
$734$		0			0
$735$	−0.273636	−	0.131776i	−0.0100932	−	0.00486063i
$736$		0			0
$737$	−0.188491			−0.00694314
$738$		0			0
$739$	−0.130636	−	0.572353i	−0.00480552	−	0.0210543i	0.972468	−	0.233035i	$-0.0748657\pi$
$739$	−0.130636	−	0.572353i	−0.00480552	−	0.0210543i	−0.977274	+	0.211981i	$0.932009\pi$
$740$		0			0
$741$	−45.1456	−	56.6107i	−1.65846	−	2.07965i
$742$		0			0
$743$	8.57986	+	10.7588i	0.314764	+	0.394702i	0.913896	−	0.405949i	$-0.133059\pi$
$743$	8.57986	+	10.7588i	0.314764	+	0.394702i	−0.599132	+	0.800651i	$0.704487\pi$
$744$		0			0
$745$	−0.0558126	+	0.0699868i	−0.00204482	+	0.00256412i
$746$		0			0
$747$	−15.7171	+	7.56898i	−0.575060	+	0.276934i
$748$		0			0
$749$	−7.54441	+	33.0542i	−0.275667	+	1.20777i
$750$		0			0
$751$	−28.1618	+	13.5620i	−1.02764	+	0.494884i	−0.870228	−	0.492649i	$-0.836029\pi$
$751$	−28.1618	+	13.5620i	−1.02764	+	0.494884i	−0.157409	+	0.987533i	$0.550314\pi$
$752$		0			0
$753$	53.1180			1.93573
$754$		0			0
$755$	0.356876			0.0129880
$756$		0			0
$757$	9.54889	−	4.59850i	0.347060	−	0.167135i	−0.252230	−	0.967667i	$-0.581164\pi$
$757$	9.54889	−	4.59850i	0.347060	−	0.167135i	0.599290	+	0.800532i	$0.295450\pi$
$758$		0			0
$759$	1.38864	−	6.08405i	0.0504046	−	0.220837i
$760$		0			0
$761$	33.7586	−	16.2573i	1.22375	−	0.589326i	0.293396	−	0.955991i	$-0.405215\pi$
$761$	33.7586	−	16.2573i	1.22375	−	0.589326i	0.930353	+	0.366665i	$0.119500\pi$
$762$		0			0
$763$	−13.5814	+	17.0306i	−0.491680	+	0.616547i
$764$		0			0
$765$	−2.51311	−	3.15134i	−0.0908616	−	0.113937i
$766$		0			0
$767$	3.62556	+	4.54631i	0.130911	+	0.164158i
$768$		0			0
$769$	−7.85149	−	34.3996i	−0.283132	−	1.24048i	−0.893753	−	0.448559i	$-0.851937\pi$
$769$	−7.85149	−	34.3996i	−0.283132	−	1.24048i	0.610621	−	0.791923i	$-0.290920\pi$
$770$		0			0
$771$	18.2240			0.656320
$772$		0			0
$773$	13.9657	+	6.72554i	0.502312	+	0.241901i	0.667841	−	0.744304i	$-0.267219\pi$
$773$	13.9657	+	6.72554i	0.502312	+	0.241901i	−0.165529	+	0.986205i	$0.552933\pi$
$774$		0			0
$775$	−1.09739	+	1.37609i	−0.0394195	+	0.0494305i
$776$		0			0
$777$	−15.5580	−	68.1639i	−0.558139	−	2.44537i
$778$		0			0
$779$	−49.5379	−	23.8562i	−1.77488	−	0.854736i
$780$		0			0
$781$	1.06486	−	4.66543i	0.0381035	−	0.166942i
$782$		0			0
$783$	80.6183	+	12.0961i	2.88106	+	0.432281i
$784$		0			0
$785$	0.273657	−	1.19897i	0.00976723	−	0.0427930i
$786$		0			0
$787$	−41.3950	−	19.9348i	−1.47557	−	0.710597i	−0.488751	−	0.872423i	$-0.662547\pi$
$787$	−41.3950	−	19.9348i	−1.47557	−	0.710597i	−0.986819	+	0.161826i	$0.948262\pi$
$788$		0			0
$789$	3.29960	+	14.4565i	0.117469	+	0.514665i
$790$		0			0
$791$	−6.32125	+	7.92660i	−0.224758	+	0.281838i
$792$		0			0
$793$	6.26044	+	3.01487i	0.222315	+	0.107061i
$794$		0			0
$795$	3.83532			0.136025
$796$		0			0
$797$	−2.86148	−	12.5369i	−0.101359	−	0.444081i	−0.999986	−	0.00536777i	$-0.998291\pi$
$797$	−2.86148	−	12.5369i	−0.101359	−	0.444081i	0.898627	−	0.438714i	$-0.144566\pi$
$798$		0			0
$799$	32.3875	+	40.6126i	1.14579	+	1.43677i
$800$		0			0
$801$	15.0013	+	18.8110i	0.530044	+	0.664655i
$802$		0			0
$803$	−9.03653	+	11.3315i	−0.318892	+	0.399878i
$804$		0			0
$805$	−0.318433	+	0.153349i	−0.0112233	+	0.00540484i
$806$		0			0
$807$	5.76328	−	25.2506i	0.202877	−	0.888862i
$808$		0			0
$809$	15.8436	−	7.62988i	0.557032	−	0.268252i	−0.134116	−	0.990966i	$-0.542820\pi$
$809$	15.8436	−	7.62988i	0.557032	−	0.268252i	0.691148	+	0.722713i	$0.257105\pi$
$810$		0			0
$811$	19.1408			0.672125			0.336063	−	0.941840i	$-0.390905\pi$
$811$	19.1408			0.672125			0.336063	+	0.941840i	$0.390905\pi$
$812$		0			0
$813$	76.6260			2.68739
$814$		0			0
$815$	−0.603290	+	0.290529i	−0.0211323	+	0.0101768i
$816$		0			0
$817$	5.24461	−	22.9781i	0.183486	−	0.803903i
$818$		0			0
$819$	−57.5091	+	27.6949i	−2.00953	+	0.967739i
$820$		0			0
$821$	−5.64263	+	7.07563i	−0.196929	+	0.246941i	−0.870485	−	0.492195i	$-0.836195\pi$
$821$	−5.64263	+	7.07563i	−0.196929	+	0.246941i	0.673556	+	0.739136i	$0.264766\pi$
$822$		0			0
$823$	29.3587	+	36.8146i	1.02338	+	1.28328i	0.958412	+	0.285388i	$0.0921226\pi$
$823$	29.3587	+	36.8146i	1.02338	+	1.28328i	0.0649663	+	0.997887i	$0.479306\pi$
$824$		0			0
$825$	11.9338	+	14.9645i	0.415481	+	0.520997i
$826$		0			0
$827$	2.93566	+	12.8620i	0.102083	+	0.447255i	0.999975	+	0.00703934i	$0.00224071\pi$
$827$	2.93566	+	12.8620i	0.102083	+	0.447255i	−0.897892	+	0.440215i	$0.854902\pi$
$828$		0			0
$829$	13.1960			0.458316			0.229158	−	0.973389i	$-0.426403\pi$
$829$	13.1960			0.458316			0.229158	+	0.973389i	$0.426403\pi$
$830$		0			0
$831$	−0.900262	−	0.433543i	−0.0312297	−	0.0150395i
$832$		0			0
$833$	3.86669	−	4.84868i	0.133973	−	0.167997i
$834$		0			0
$835$	−0.0219764	−	0.0962847i	−0.000760523	−	0.00333207i
$836$		0			0
$837$	4.80872	+	2.31576i	0.166214	+	0.0800443i
$838$		0			0
$839$	10.6981	−	46.8716i	0.369340	−	1.61819i	−0.359254	−	0.933240i	$-0.616969\pi$
$839$	10.6981	−	46.8716i	0.369340	−	1.61819i	0.728594	−	0.684946i	$-0.240174\pi$
$840$		0			0
$841$	−28.6703	+	4.36056i	−0.988631	+	0.150364i
$842$		0			0
$843$	−3.99438	+	17.5005i	−0.137574	+	0.602750i
$844$		0			0
$845$	0.102489	+	0.0493560i	0.00352572	+	0.00169790i
$846$		0			0
$847$	5.22243	+	22.8810i	0.179445	+	0.786200i
$848$		0			0
$849$	−15.0417	+	18.8617i	−0.516229	+	0.647330i
$850$		0			0
$851$	12.8814	+	6.20336i	0.441569	+	0.212648i
$852$		0			0
$853$	6.64118			0.227390			0.113695	−	0.993516i	$-0.463731\pi$
$853$	6.64118			0.227390			0.113695	+	0.993516i	$0.463731\pi$
$854$		0			0
$855$	−0.980993	−	4.29801i	−0.0335493	−	0.146989i
$856$		0			0
$857$	−30.5985	−	38.3693i	−1.04522	−	1.31067i	−0.948988	−	0.315312i	$-0.897891\pi$
$857$	−30.5985	−	38.3693i	−1.04522	−	1.31067i	−0.0962363	−	0.995359i	$-0.530680\pi$
$858$		0			0
$859$	−16.5078	−	20.7001i	−0.563239	−	0.706280i	0.415914	−	0.909404i	$-0.363462\pi$
$859$	−16.5078	−	20.7001i	−0.563239	−	0.706280i	−0.979153	+	0.203124i	$0.934890\pi$
$860$		0			0
$861$	−42.0857	+	52.7738i	−1.43428	+	1.79853i
$862$		0			0
$863$	−40.1851	+	19.3521i	−1.36792	+	0.658754i	−0.966387	−	0.257092i	$-0.917236\pi$
$863$	−40.1851	+	19.3521i	−1.36792	+	0.658754i	−0.401530	+	0.915846i	$0.631521\pi$
$864$		0			0
$865$	0.0280734	−	0.122998i	0.000954525	−	0.00418205i
$866$		0			0
$867$	53.3080	−	25.6718i	1.81043	−	0.871859i
$868$		0			0
$869$	−8.96676			−0.304176
$870$		0			0
$871$	−0.549040			−0.0186035
$872$		0			0
$873$	52.8427	−	25.4477i	1.78846	−	0.861275i
$874$		0			0
$875$	0.482816	−	2.11535i	0.0163222	−	0.0715120i
$876$		0			0
$877$	−8.77459	+	4.22562i	−0.296297	+	0.142689i	−0.576126	−	0.817361i	$-0.695436\pi$
$877$	−8.77459	+	4.22562i	−0.296297	+	0.142689i	0.279829	+	0.960050i	$0.409722\pi$
$878$		0			0
$879$	−45.7195	+	57.3304i	−1.54208	+	1.93371i
$880$		0			0
$881$	−1.53281	−	1.92209i	−0.0516418	−	0.0647568i	0.755340	−	0.655333i	$-0.227472\pi$
$881$	−1.53281	−	1.92209i	−0.0516418	−	0.0647568i	−0.806982	+	0.590577i	$0.798900\pi$
$882$		0			0
$883$	15.5805	+	19.5373i	0.524325	+	0.657482i	0.971521	−	0.236953i	$-0.0761489\pi$
$883$	15.5805	+	19.5373i	0.524325	+	0.657482i	−0.447196	+	0.894436i	$0.647577\pi$
$884$		0			0
$885$	0.109714	+	0.480690i	0.00368800	+	0.0161582i
$886$		0			0
$887$	3.32291			0.111572			0.0557861	−	0.998443i	$-0.482233\pi$
$887$	3.32291			0.111572			0.0557861	+	0.998443i	$0.482233\pi$
$888$		0			0
$889$	−36.6390	−	17.6444i	−1.22883	−	0.591775i
$890$		0			0
$891$	19.3898	−	24.3140i	0.649581	−	0.814549i
$892$		0			0
$893$	12.6425	+	55.3903i	0.423064	+	1.85357i
$894$		0			0
$895$	−0.833141	−	0.401219i	−0.0278488	−	0.0134113i
$896$		0			0
$897$	4.04488	−	17.7218i	0.135055	−	0.591713i
$898$		0			0
$899$	−1.87765	−	0.281727i	−0.0626233	−	0.00939613i
$900$		0			0
$901$	−17.4269	+	76.3523i	−0.580575	+	2.54366i
$902$		0			0
$903$	−26.0693	−	12.5543i	−0.867533	−	0.417782i
$904$		0			0
$905$	0.281864	+	1.23493i	0.00936947	+	0.0410503i
$906$		0			0
$907$	−3.61118	+	4.52828i	−0.119907	+	0.150359i	−0.838162	−	0.545421i	$-0.816370\pi$
$907$	−3.61118	+	4.52828i	−0.119907	+	0.150359i	0.718255	+	0.695780i	$0.244941\pi$
$908$		0			0
$909$	−132.492	−	63.8046i	−4.39447	−	2.11627i
$910$		0			0
$911$	−7.05255			−0.233661			−0.116831	−	0.993152i	$-0.537273\pi$
$911$	−7.05255			−0.233661			−0.116831	+	0.993152i	$0.537273\pi$
$912$		0			0
$913$	−0.597150	−	2.61628i	−0.0197628	−	0.0865864i
$914$		0			0
$915$	0.367343	+	0.460633i	0.0121440	+	0.0152281i
$916$		0			0
$917$	12.3625	+	15.5021i	0.408246	+	0.511924i
$918$		0			0
$919$	12.6586	−	15.8733i	0.417567	−	0.523613i	−0.527910	−	0.849300i	$-0.677024\pi$
$919$	12.6586	−	15.8733i	0.417567	−	0.523613i	0.945478	+	0.325687i	$0.105596\pi$
$920$		0			0
$921$	−89.2535	+	42.9822i	−2.94100	+	1.41631i
$922$		0			0
$923$	3.10174	−	13.5896i	0.102095	−	0.447307i
$924$		0			0
$925$	−39.5086	+	19.0263i	−1.29903	+	0.625582i
$926$		0			0
$927$	−106.934			−3.51217
$928$		0			0
$929$	−51.6227			−1.69369			−0.846843	−	0.531843i	$-0.821500\pi$
$929$	−51.6227			−1.69369			−0.846843	+	0.531843i	$0.821500\pi$
$930$		0			0
$931$	6.11130	−	2.94304i	0.200290	−	0.0964544i
$932$		0			0
$933$	−7.96548	+	34.8990i	−0.260778	+	1.14254i
$934$		0			0
$935$	0.558651	−	0.269032i	0.0182698	−	0.00879829i
$936$		0			0
$937$	1.76297	−	2.21069i	0.0575937	−	0.0722202i	−0.752200	−	0.658935i	$-0.771007\pi$
$937$	1.76297	−	2.21069i	0.0575937	−	0.0722202i	0.809794	+	0.586714i	$0.199579\pi$
$938$		0			0
$939$	−30.4669	−	38.2043i	−0.994250	−	1.24675i
$940$		0			0
$941$	−15.3467	−	19.2442i	−0.500289	−	0.627343i	0.466005	−	0.884782i	$-0.345693\pi$
$941$	−15.3467	−	19.2442i	−0.500289	−	0.627343i	−0.966295	+	0.257439i	$0.917121\pi$
$942$		0			0
$943$	−3.07148	−	13.4570i	−0.100021	−	0.438221i
$944$		0			0
$945$	−3.28718			−0.106932
$946$		0			0
$947$	−28.8896	−	13.9125i	−0.938785	−	0.452095i	−0.0990443	−	0.995083i	$-0.531579\pi$
$947$	−28.8896	−	13.9125i	−0.938785	−	0.452095i	−0.839740	+	0.542988i	$0.817293\pi$
$948$		0			0
$949$	−26.3218	+	33.0066i	−0.854443	+	1.07144i
$950$		0			0
$951$	10.1851	+	44.6240i	0.330276	+	1.44703i
$952$		0			0
$953$	39.4806	+	19.0128i	1.27890	+	0.615886i	0.945107	−	0.326760i	$-0.105957\pi$
$953$	39.4806	+	19.0128i	1.27890	+	0.615886i	0.333794	+	0.942646i	$0.391671\pi$
$954$		0			0
$955$	−0.402791	+	1.76474i	−0.0130340	+	0.0571057i
$956$		0			0
$957$	−7.53051	+	19.2252i	−0.243427	+	0.621462i
$958$		0			0
$959$	3.68628	−	16.1506i	0.119036	−	0.521531i
$960$		0			0
$961$	27.8180	+	13.3965i	0.897356	+	0.432144i
$962$		0			0
$963$	−23.6245	−	103.505i	−0.761287	−	3.33542i
$964$		0			0
$965$	0.149180	−	0.187066i	0.00480228	−	0.00602187i
$966$		0			0
$967$	−11.5851	−	5.57907i	−0.372550	−	0.179411i	0.238234	−	0.971208i	$-0.423431\pi$
$967$	−11.5851	−	5.57907i	−0.372550	−	0.179411i	−0.610784	+	0.791797i	$0.709146\pi$
$968$		0			0
$969$	125.366			4.02733
$970$		0			0
$971$	−7.96383	−	34.8918i	−0.255571	−	1.11973i	−0.925930	−	0.377694i	$-0.876717\pi$
$971$	−7.96383	−	34.8918i	−0.255571	−	1.11973i	0.670359	−	0.742037i	$-0.266140\pi$
$972$		0			0
$973$	24.5984	+	30.8454i	0.788587	+	0.988857i
$974$		0			0
$975$	34.7610	+	43.5890i	1.11324	+	1.39596i
$976$		0			0
$977$	8.27077	−	10.3712i	0.264605	−	0.331805i	−0.631724	−	0.775193i	$-0.717652\pi$
$977$	8.27077	−	10.3712i	0.264605	−	0.331805i	0.896329	+	0.443389i	$0.146224\pi$
$978$		0			0
$979$	−3.33471	+	1.60591i	−0.106578	+	0.0513251i
$980$		0			0
$981$	15.1783	−	66.5005i	0.484606	−	2.12320i
$982$		0			0
$983$	28.9374	−	13.9355i	0.922961	−	0.444475i	0.0888338	−	0.996046i	$-0.471686\pi$
$983$	28.9374	−	13.9355i	0.922961	−	0.444475i	0.834127	+	0.551572i	$0.185972\pi$
$984$		0			0
$985$	0.483012			0.0153900
$986$		0			0
$987$	69.7492			2.22014
$988$		0			0
$989$	5.33091	−	2.56723i	0.169513	−	0.0816332i
$990$		0			0
$991$	−10.6800	+	46.7922i	−0.339262	+	1.48640i	0.461349	+	0.887219i	$0.347365\pi$
$991$	−10.6800	+	46.7922i	−0.339262	+	1.48640i	−0.800611	+	0.599184i	$0.795492\pi$
$992$		0			0
$993$	−48.8060	+	23.5037i	−1.54881	+	0.745868i
$994$		0			0
$995$	−1.22615	+	1.53754i	−0.0388715	+	0.0487433i
$996$		0			0
$997$	4.07525	+	5.11021i	0.129065	+	0.161842i	0.842165	−	0.539220i	$-0.181281\pi$
$997$	4.07525	+	5.11021i	0.129065	+	0.161842i	−0.713100	+	0.701062i	$0.752710\pi$
$998$		0			0
$999$	82.9084	+	103.964i	2.62311	+	3.28927i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	232.2.m.d.25.4	✓	24
4.3	odd	2		464.2.u.i.257.1		24
29.6	even	14		6728.2.a.bb.1.12		12
29.7	even	7	inner	232.2.m.d.65.4	yes	24
29.23	even	7		6728.2.a.z.1.1		12
116.7	odd	14		464.2.u.i.65.1		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
232.2.m.d.25.4	✓	24	1.1	even	1	trivial
232.2.m.d.65.4	yes	24	29.7	even	7	inner
464.2.u.i.65.1		24	116.7	odd	14
464.2.u.i.257.1		24	4.3	odd	2
6728.2.a.z.1.1		12	29.23	even	7
6728.2.a.bb.1.12		12	29.6	even	14

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:	\( N \)	\(=\)	\( 232 = 2^{3} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	232.m (of order \(7\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(2.93897 - 1.41533i) q^{3} +(-0.0198029 + 0.0867622i) q^{5} +(-2.19840 + 1.05869i) q^{7} +(4.76390 - 5.97374i) q^{9} +O(q^{10})\)	\(q+(2.93897 - 1.41533i) q^{3} +(-0.0198029 + 0.0867622i) q^{5} +(-2.19840 + 1.05869i) q^{7} +(4.76390 - 5.97374i) q^{9} +(0.732844 + 0.918957i) q^{11} +(2.13465 + 2.67676i) q^{13} +(0.0645972 + 0.283019i) q^{15} -5.92776 q^{17} +(-5.84136 - 2.81305i) q^{19} +(-4.96262 + 6.22293i) q^{21} +(-0.362180 - 1.58681i) q^{23} +(4.49771 + 2.16598i) q^{25} +(3.36853 - 14.7585i) q^{27} +(0.406024 + 5.36984i) q^{29} +(-0.0784552 + 0.343735i) q^{31} +(3.45443 + 1.66357i) q^{33} +(-0.0483198 - 0.211703i) q^{35} +(-5.47683 + 6.86773i) q^{37} +(10.0622 + 4.84568i) q^{39} +8.48054 q^{41} +(0.808927 + 3.54414i) q^{43} +(0.423956 + 0.531624i) q^{45} +(-5.46370 - 6.85126i) q^{47} +(-0.652302 + 0.817961i) q^{49} +(-17.4215 + 8.38975i) q^{51} +(2.93988 - 12.8805i) q^{53} +(-0.0942431 + 0.0453851i) q^{55} -21.1490 q^{57} +1.69844 q^{59} +(1.82856 - 0.880587i) q^{61} +(-4.14859 + 18.1762i) q^{63} +(-0.274514 + 0.132199i) q^{65} +(-0.0999855 + 0.125378i) q^{67} +(-3.31030 - 4.15099i) q^{69} +(-2.53844 - 3.18310i) q^{71} +(2.74386 + 12.0216i) q^{73} +16.2842 q^{75} +(-2.58398 - 1.24438i) q^{77} +(-4.75645 + 5.96440i) q^{79} +(-5.88751 - 25.7949i) q^{81} +(-2.05703 - 0.990613i) q^{83} +(0.117387 - 0.514305i) q^{85} +(8.79340 + 15.2071i) q^{87} +(-0.700707 + 3.07000i) q^{89} +(-7.52667 - 3.62466i) q^{91} +(0.255922 + 1.12127i) q^{93} +(0.359742 - 0.451102i) q^{95} +(6.91595 + 3.33055i) q^{97} +8.98081 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - q^{3} - 8 q^{5} + 5 q^{7} - 3 q^{9}+O(q^{10}) \) 24 * q - q^3 - 8 * q^5 + 5 * q^7 - 3 * q^9	\( 24 q - q^{3} - 8 q^{5} + 5 q^{7} - 3 q^{9} - 6 q^{11} + q^{13} - q^{15} - 16 q^{17} - 10 q^{19} - 5 q^{21} + 11 q^{23} + 10 q^{25} - 7 q^{27} - 2 q^{29} + 12 q^{31} + 13 q^{33} - 8 q^{35} + q^{37} + 34 q^{39} - 22 q^{41} + 3 q^{43} + 60 q^{45} + 9 q^{47} - 67 q^{49} - q^{51} + 19 q^{53} - 88 q^{55} - 2 q^{57} + 114 q^{59} - 11 q^{61} - 108 q^{63} + 8 q^{65} - 25 q^{67} - 84 q^{69} - 21 q^{71} + 30 q^{73} - 26 q^{75} - 22 q^{77} + 48 q^{79} + 16 q^{81} - 37 q^{83} + 8 q^{85} + 11 q^{87} - 5 q^{89} - 11 q^{91} - 18 q^{93} - 21 q^{95} + 35 q^{97} + 32 q^{99}+O(q^{100}) \) 24 * q - q^3 - 8 * q^5 + 5 * q^7 - 3 * q^9 - 6 * q^11 + q^13 - q^15 - 16 * q^17 - 10 * q^19 - 5 * q^21 + 11 * q^23 + 10 * q^25 - 7 * q^27 - 2 * q^29 + 12 * q^31 + 13 * q^33 - 8 * q^35 + q^37 + 34 * q^39 - 22 * q^41 + 3 * q^43 + 60 * q^45 + 9 * q^47 - 67 * q^49 - q^51 + 19 * q^53 - 88 * q^55 - 2 * q^57 + 114 * q^59 - 11 * q^61 - 108 * q^63 + 8 * q^65 - 25 * q^67 - 84 * q^69 - 21 * q^71 + 30 * q^73 - 26 * q^75 - 22 * q^77 + 48 * q^79 + 16 * q^81 - 37 * q^83 + 8 * q^85 + 11 * q^87 - 5 * q^89 - 11 * q^91 - 18 * q^93 - 21 * q^95 + 35 * q^97 + 32 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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