LMFDB - Embedded newform 504.2.q.c.121.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [504,2,Mod(25,504)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(504, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 4, 4]))

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

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

chi := DirichletCharacter("504.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 504 = 2^{3} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	504.q (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.02446026187$
Analytic rank:	$0$
Dimension:	$22$
Relative dimension:	$11$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			121.2
Character	$\chi$	$=$	504.121
Dual form			504.2.q.c.25.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.69989 + 0.332219i) q^{3} +(-1.59750 - 2.76695i) q^{5} +(-1.66645 + 2.05498i) q^{7} +(2.77926 - 1.12947i) q^{9} +O(q^{10})$	\(q+(-1.69989 + 0.332219i) q^{3} +(-1.59750 - 2.76695i) q^{5} +(-1.66645 + 2.05498i) q^{7} +(2.77926 - 1.12947i) q^{9} +(1.14139 - 1.97695i) q^{11} +(-0.675051 + 1.16922i) q^{13} +(3.63481 + 4.17279i) q^{15} +(2.21425 + 3.83519i) q^{17} +(-3.69214 + 6.39497i) q^{19} +(2.15007 - 4.04687i) q^{21} +(3.23479 + 5.60283i) q^{23} +(-2.60400 + 4.51026i) q^{25} +(-4.34921 + 2.84330i) q^{27} +(-1.06167 - 1.83887i) q^{29} -0.632308 q^{31} +(-1.28346 + 3.73979i) q^{33} +(8.34818 + 1.32814i) q^{35} +(1.92885 - 3.34087i) q^{37} +(0.759075 - 2.21182i) q^{39} +(-5.05124 + 8.74900i) q^{41} +(4.24701 + 7.35603i) q^{43} +(-7.56506 - 5.88574i) q^{45} +6.53173 q^{47} +(-1.44591 - 6.84904i) q^{49} +(-5.03810 - 5.78379i) q^{51} +(2.39950 + 4.15606i) q^{53} -7.29349 q^{55} +(4.15170 - 12.0974i) q^{57} +6.20383 q^{59} -8.91093 q^{61} +(-2.31044 + 7.59354i) q^{63} +4.31357 q^{65} -3.01570 q^{67} +(-7.36017 - 8.44954i) q^{69} -15.3791 q^{71} +(4.36577 + 7.56173i) q^{73} +(2.92813 - 8.53206i) q^{75} +(2.16053 + 5.64002i) q^{77} -1.87610 q^{79} +(6.44859 - 6.27819i) q^{81} +(-3.00140 - 5.19857i) q^{83} +(7.07451 - 12.2534i) q^{85} +(2.41563 + 2.77317i) q^{87} +(2.65390 - 4.59668i) q^{89} +(-1.27780 - 3.33566i) q^{91} +(1.07486 - 0.210065i) q^{93} +23.5927 q^{95} +(7.44539 + 12.8958i) q^{97} +(0.939319 - 6.78363i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q - 2 q^{3} + q^{5} + 5 q^{7} + 6 q^{9}+O(q^{10}) $ 22 * q - 2 * q^3 + q^5 + 5 * q^7 + 6 * q^9	$ 22 q - 2 q^{3} + q^{5} + 5 q^{7} + 6 q^{9} + 3 q^{11} + 7 q^{13} - q^{15} - q^{17} + 13 q^{19} - 22 q^{25} - 2 q^{27} - 7 q^{29} - 12 q^{31} - 3 q^{33} + 2 q^{35} + 6 q^{37} - 4 q^{39} + 4 q^{41} + 2 q^{43} - 3 q^{45} - 34 q^{47} - 25 q^{49} + 53 q^{51} + q^{53} + 2 q^{55} - 21 q^{57} + 42 q^{59} - 62 q^{61} - 22 q^{63} + 6 q^{65} + 52 q^{67} - 40 q^{69} - 32 q^{71} + 17 q^{73} + 53 q^{75} - q^{77} + 32 q^{79} - 6 q^{81} - 36 q^{83} + 28 q^{85} - 5 q^{87} - 2 q^{89} + 15 q^{91} - 11 q^{93} + 48 q^{95} + 19 q^{97} + 24 q^{99}+O(q^{100}) $ 22 * q - 2 * q^3 + q^5 + 5 * q^7 + 6 * q^9 + 3 * q^11 + 7 * q^13 - q^15 - q^17 + 13 * q^19 - 22 * q^25 - 2 * q^27 - 7 * q^29 - 12 * q^31 - 3 * q^33 + 2 * q^35 + 6 * q^37 - 4 * q^39 + 4 * q^41 + 2 * q^43 - 3 * q^45 - 34 * q^47 - 25 * q^49 + 53 * q^51 + q^53 + 2 * q^55 - 21 * q^57 + 42 * q^59 - 62 * q^61 - 22 * q^63 + 6 * q^65 + 52 * q^67 - 40 * q^69 - 32 * q^71 + 17 * q^73 + 53 * q^75 - q^77 + 32 * q^79 - 6 * q^81 - 36 * q^83 + 28 * q^85 - 5 * q^87 - 2 * q^89 + 15 * q^91 - 11 * q^93 + 48 * q^95 + 19 * q^97 + 24 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/504\mathbb{Z}\right)^\times$.

$n$	$73$	$127$	$253$	$281$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$1$	$e\left(\frac{1}{3}\right)$

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
$3$	−1.69989	+	0.332219i	−0.981433	+	0.191807i
$3$	−1.69989	+	0.332219i	−0.981433	+	0.191807i
$4$		0			0
$5$	−1.59750	−	2.76695i	−0.714423	−	1.23742i	−0.963182	−	0.268851i	$-0.913356\pi$
$5$	−1.59750	−	2.76695i	−0.714423	−	1.23742i	0.248759	−	0.968566i	$-0.419977\pi$
$6$		0			0
$7$	−1.66645	+	2.05498i	−0.629857	+	0.776711i
$7$	−1.66645	+	2.05498i	−0.629857	+	0.776711i
$8$		0			0
$9$	2.77926	−	1.12947i	0.926420	−	0.376491i
$10$		0			0
$11$	1.14139	−	1.97695i	0.344143	−	0.596073i	−0.641055	−	0.767495i	$-0.721503\pi$
$11$	1.14139	−	1.97695i	0.344143	−	0.596073i	0.985198	+	0.171422i	$0.0548362\pi$
$12$		0			0
$13$	−0.675051	+	1.16922i	−0.187225	+	0.324284i	−0.944324	−	0.329017i	$-0.893283\pi$
$13$	−0.675051	+	1.16922i	−0.187225	+	0.324284i	0.757099	+	0.653300i	$0.226616\pi$
$14$		0			0
$15$	3.63481	+	4.17279i	0.938503	+	1.07741i
$16$		0			0
$17$	2.21425	+	3.83519i	0.537033	+	0.930169i	0.999062	+	0.0433042i	$0.0137885\pi$
$17$	2.21425	+	3.83519i	0.537033	+	0.930169i	−0.462028	+	0.886865i	$0.652878\pi$
$18$		0			0
$19$	−3.69214	+	6.39497i	−0.847034	+	1.46711i	0.0368084	+	0.999322i	$0.488281\pi$
$19$	−3.69214	+	6.39497i	−0.847034	+	1.46711i	−0.883843	+	0.467784i	$0.845052\pi$
$20$		0			0
$21$	2.15007	−	4.04687i	0.469184	−	0.883100i
$22$		0			0
$23$	3.23479	+	5.60283i	0.674501	+	1.16827i	0.976614	+	0.214999i	$0.0689747\pi$
$23$	3.23479	+	5.60283i	0.674501	+	1.16827i	−0.302113	+	0.953272i	$0.597692\pi$
$24$		0			0
$25$	−2.60400	+	4.51026i	−0.520800	+	0.902053i
$26$		0			0
$27$	−4.34921	+	2.84330i	−0.837006	+	0.547194i
$28$		0			0
$29$	−1.06167	−	1.83887i	−0.197148	−	0.341470i	0.750455	−	0.660922i	$-0.229834\pi$
$29$	−1.06167	−	1.83887i	−0.197148	−	0.341470i	−0.947602	+	0.319452i	$0.896501\pi$
$30$		0			0
$31$	−0.632308			−0.113566			−0.0567830	−	0.998387i	$-0.518084\pi$
$31$	−0.632308			−0.113566			−0.0567830	+	0.998387i	$0.518084\pi$
$32$		0			0
$33$	−1.28346	+	3.73979i	−0.223422	+	0.651014i
$34$		0			0
$35$	8.34818	+	1.32814i	1.41110	+	0.224496i
$36$		0			0
$37$	1.92885	−	3.34087i	0.317102	−	0.549236i	−0.662780	−	0.748814i	$-0.730624\pi$
$37$	1.92885	−	3.34087i	0.317102	−	0.549236i	0.979882	+	0.199578i	$0.0639570\pi$
$38$		0			0
$39$	0.759075	−	2.21182i	0.121549	−	0.354174i
$40$		0			0
$41$	−5.05124	+	8.74900i	−0.788871	+	1.36636i	0.137788	+	0.990462i	$0.456001\pi$
$41$	−5.05124	+	8.74900i	−0.788871	+	1.36636i	−0.926659	+	0.375903i	$0.877333\pi$
$42$		0			0
$43$	4.24701	+	7.35603i	0.647663	+	1.12178i	0.983680	+	0.179929i	$0.0575867\pi$
$43$	4.24701	+	7.35603i	0.647663	+	1.12178i	−0.336017	+	0.941856i	$0.609080\pi$
$44$		0			0
$45$	−7.56506	−	5.88574i	−1.12773	−	0.877395i
$46$		0			0
$47$	6.53173			0.952751			0.476375	−	0.879242i	$-0.341950\pi$
$47$	6.53173			0.952751			0.476375	+	0.879242i	$0.341950\pi$
$48$		0			0
$49$	−1.44591	−	6.84904i	−0.206559	−	0.978434i
$50$		0			0
$51$	−5.03810	−	5.78379i	−0.705475	−	0.809892i
$52$		0			0
$53$	2.39950	+	4.15606i	0.329597	+	0.570879i	0.982432	−	0.186621i	$-0.0597538\pi$
$53$	2.39950	+	4.15606i	0.329597	+	0.570879i	−0.652835	+	0.757500i	$0.726420\pi$
$54$		0			0
$55$	−7.29349			−0.983454
$56$		0			0
$57$	4.15170	−	12.0974i	0.549906	−	1.60233i
$58$		0			0
$59$	6.20383			0.807670			0.403835	−	0.914832i	$-0.367677\pi$
$59$	6.20383			0.807670			0.403835	+	0.914832i	$0.367677\pi$
$60$		0			0
$61$	−8.91093			−1.14093			−0.570464	−	0.821323i	$-0.693236\pi$
$61$	−8.91093			−1.14093			−0.570464	+	0.821323i	$0.693236\pi$
$62$		0			0
$63$	−2.31044	+	7.59354i	−0.291088	+	0.956696i
$64$		0			0
$65$	4.31357			0.535033
$66$		0			0
$67$	−3.01570			−0.368426			−0.184213	−	0.982886i	$-0.558974\pi$
$67$	−3.01570			−0.368426			−0.184213	+	0.982886i	$0.558974\pi$
$68$		0			0
$69$	−7.36017	−	8.44954i	−0.886060	−	1.01721i
$70$		0			0
$71$	−15.3791			−1.82516			−0.912580	−	0.408899i	$-0.865913\pi$
$71$	−15.3791			−1.82516			−0.912580	+	0.408899i	$0.865913\pi$
$72$		0			0
$73$	4.36577	+	7.56173i	0.510974	+	0.885033i	0.999919	+	0.0127186i	$0.00404857\pi$
$73$	4.36577	+	7.56173i	0.510974	+	0.885033i	−0.488945	+	0.872315i	$0.662618\pi$
$74$		0			0
$75$	2.92813	−	8.53206i	0.338111	−	0.985197i
$76$		0			0
$77$	2.16053	+	5.64002i	0.246215	+	0.642740i
$78$		0			0
$79$	−1.87610			−0.211078			−0.105539	−	0.994415i	$-0.533657\pi$
$79$	−1.87610			−0.211078			−0.105539	+	0.994415i	$0.533657\pi$
$80$		0			0
$81$	6.44859	−	6.27819i	0.716510	−	0.697577i
$82$		0			0
$83$	−3.00140	−	5.19857i	−0.329446	−	0.570617i	0.652956	−	0.757396i	$-0.273529\pi$
$83$	−3.00140	−	5.19857i	−0.329446	−	0.570617i	−0.982402	+	0.186779i	$0.940195\pi$
$84$		0			0
$85$	7.07451	−	12.2534i	0.767338	−	1.32907i
$86$		0			0
$87$	2.41563	+	2.77317i	0.258983	+	0.297315i
$88$		0			0
$89$	2.65390	−	4.59668i	0.281313	−	0.487248i	−0.690396	−	0.723432i	$-0.742564\pi$
$89$	2.65390	−	4.59668i	0.281313	−	0.487248i	0.971708	+	0.236184i	$0.0758969\pi$
$90$		0			0
$91$	−1.27780	−	3.33566i	−0.133949	−	0.349673i
$92$		0			0
$93$	1.07486	−	0.210065i	0.111457	−	0.0217827i
$94$		0			0
$95$	23.5927			2.42056
$96$		0			0
$97$	7.44539	+	12.8958i	0.755965	+	1.30937i	0.944893	+	0.327378i	$0.106165\pi$
$97$	7.44539	+	12.8958i	0.755965	+	1.30937i	−0.188929	+	0.981991i	$0.560502\pi$
$98$		0			0
$99$	0.939319	−	6.78363i	0.0944051	−	0.681781i
$100$		0			0
$101$	7.00299	−	12.1295i	0.696824	−	1.20693i	−0.272738	−	0.962088i	$-0.587929\pi$
$101$	7.00299	−	12.1295i	0.696824	−	1.20693i	0.969562	−	0.244846i	$-0.0787374\pi$
$102$		0			0
$103$	−8.03055	−	13.9093i	−0.791274	−	1.37053i	−0.925179	−	0.379532i	$-0.876085\pi$
$103$	−8.03055	−	13.9093i	−0.791274	−	1.37053i	0.133905	−	0.990994i	$-0.457248\pi$
$104$		0			0
$105$	−14.6322	+	0.515732i	−1.42796	+	0.0503303i
$106$		0			0
$107$	1.26820	−	2.19658i	0.122601	−	0.212352i	−0.798191	−	0.602404i	$-0.794210\pi$
$107$	1.26820	−	2.19658i	0.122601	−	0.212352i	0.920793	+	0.390052i	$0.127543\pi$
$108$		0			0
$109$	8.10946	+	14.0460i	0.776746	+	1.34536i	0.933808	+	0.357775i	$0.116464\pi$
$109$	8.10946	+	14.0460i	0.776746	+	1.34536i	−0.157062	+	0.987589i	$0.550202\pi$
$110$		0			0
$111$	−2.16894	+	6.31992i	−0.205867	+	0.599860i
$112$		0			0
$113$	1.61499	−	2.79725i	0.151926	−	0.263143i	−0.780010	−	0.625767i	$-0.784786\pi$
$113$	1.61499	−	2.79725i	0.151926	−	0.263143i	0.931935	+	0.362625i	$0.118119\pi$
$114$		0			0
$115$	10.3352	−	17.9010i	0.963759	−	1.66928i
$116$		0			0
$117$	−0.555539	+	4.01203i	−0.0513596	+	0.370912i
$118$		0			0
$119$	−11.5712	−	1.84089i	−1.06073	−	0.168754i
$120$		0			0
$121$	2.89445	+	5.01333i	0.263131	+	0.455757i
$122$		0			0
$123$	5.67997	−	16.5505i	0.512146	−	1.49231i
$124$		0			0
$125$	0.664575			0.0594414
$126$		0			0
$127$	−12.6429			−1.12187			−0.560936	−	0.827859i	$-0.689559\pi$
$127$	−12.6429			−1.12187			−0.560936	+	0.827859i	$0.689559\pi$
$128$		0			0
$129$	−9.66326	−	11.0935i	−0.850803	−	0.976730i
$130$		0			0
$131$	−9.53430	−	16.5139i	−0.833015	−	1.44282i	−0.895636	−	0.444787i	$-0.853279\pi$
$131$	−9.53430	−	16.5139i	−0.833015	−	1.44282i	0.0626210	−	0.998037i	$-0.480054\pi$
$132$		0			0
$133$	−6.98881	−	18.2442i	−0.606007	−	1.58197i
$134$		0			0
$135$	14.8151	+	7.49187i	1.27508	+	0.644797i
$136$		0			0
$137$	−3.38236	+	5.85842i	−0.288975	+	0.500519i	−0.973565	−	0.228409i	$-0.926648\pi$
$137$	−3.38236	+	5.85842i	−0.288975	+	0.500519i	0.684591	+	0.728928i	$0.259981\pi$
$138$		0			0
$139$	−6.57218	+	11.3834i	−0.557445	+	0.965524i	0.440263	+	0.897869i	$0.354885\pi$
$139$	−6.57218	+	11.3834i	−0.557445	+	0.965524i	−0.997709	+	0.0676550i	$0.978448\pi$
$140$		0			0
$141$	−11.1032	+	2.16996i	−0.935061	+	0.182744i
$142$		0			0
$143$	1.54100	+	2.66908i	0.128865	+	0.223200i
$144$		0			0
$145$	−3.39204	+	5.87518i	−0.281693	+	0.487907i
$146$		0			0
$147$	4.73328	+	11.1623i	0.390394	+	0.920648i
$148$		0			0
$149$	−0.140257	−	0.242932i	−0.0114903	−	0.0199018i	0.860223	−	0.509918i	$-0.170324\pi$
$149$	−0.140257	−	0.242932i	−0.0114903	−	0.0199018i	−0.871713	+	0.490016i	$0.836991\pi$
$150$		0			0
$151$	−4.42899	+	7.67123i	−0.360426	+	0.624276i	−0.988031	−	0.154256i	$-0.950702\pi$
$151$	−4.42899	+	7.67123i	−0.360426	+	0.624276i	0.627605	+	0.778532i	$0.284035\pi$
$152$		0			0
$153$	10.4857	+	8.15806i	0.847719	+	0.659540i
$154$		0			0
$155$	1.01011	+	1.74956i	0.0811341	+	0.140528i
$156$		0			0
$157$	−1.92894			−0.153946			−0.0769731	−	0.997033i	$-0.524526\pi$
$157$	−1.92894			−0.153946			−0.0769731	+	0.997033i	$0.524526\pi$
$158$		0			0
$159$	−5.45962	−	6.26769i	−0.432976	−	0.497060i
$160$		0			0
$161$	−16.9043	−	2.68936i	−1.33225	−	0.211952i
$162$		0			0
$163$	−12.1983	+	21.1281i	−0.955446	+	1.65488i	−0.222100	+	0.975024i	$0.571291\pi$
$163$	−12.1983	+	21.1281i	−0.955446	+	1.65488i	−0.733345	+	0.679856i	$0.762042\pi$
$164$		0			0
$165$	12.3981	−	2.42304i	0.965194	−	0.188633i
$166$		0			0
$167$	2.75658	−	4.77453i	0.213310	−	0.369464i	−0.739438	−	0.673224i	$-0.764909\pi$
$167$	2.75658	−	4.77453i	0.213310	−	0.369464i	0.952749	+	0.303760i	$0.0982421\pi$
$168$		0			0
$169$	5.58861	+	9.67976i	0.429893	+	0.744597i
$170$		0			0
$171$	−3.03848	+	21.9435i	−0.232358	+	1.67806i
$172$		0			0
$173$	12.6052			0.958355			0.479178	−	0.877718i	$-0.340935\pi$
$173$	12.6052			0.958355			0.479178	+	0.877718i	$0.340935\pi$
$174$		0			0
$175$	−4.92909	−	12.8673i	−0.372604	−	0.972676i
$176$		0			0
$177$	−10.5458	+	2.06103i	−0.792674	+	0.154916i
$178$		0			0
$179$	5.10472	+	8.84164i	0.381545	+	0.660855i	0.991283	−	0.131747i	$-0.0420588\pi$
$179$	5.10472	+	8.84164i	0.381545	+	0.660855i	−0.609738	+	0.792603i	$0.708725\pi$
$180$		0			0
$181$	−16.2398			−1.20710			−0.603548	−	0.797327i	$-0.706247\pi$
$181$	−16.2398			−1.20710			−0.603548	+	0.797327i	$0.706247\pi$
$182$		0			0
$183$	15.1476	−	2.96038i	1.11974	−	0.218837i
$184$		0			0
$185$	−12.3254			−0.906179
$186$		0			0
$187$	10.1093			0.739265
$188$		0			0
$189$	1.40479	−	13.6758i	0.102183	−	0.994766i
$190$		0			0
$191$	−3.94120			−0.285175			−0.142587	−	0.989782i	$-0.545542\pi$
$191$	−3.94120			−0.285175			−0.142587	+	0.989782i	$0.545542\pi$
$192$		0			0
$193$	−5.74112			−0.413255			−0.206627	−	0.978420i	$-0.566249\pi$
$193$	−5.74112			−0.413255			−0.206627	+	0.978420i	$0.566249\pi$
$194$		0			0
$195$	−7.33260	+	1.43305i	−0.525098	+	0.102623i
$196$		0			0
$197$	−7.67480			−0.546807			−0.273403	−	0.961899i	$-0.588149\pi$
$197$	−7.67480			−0.546807			−0.273403	+	0.961899i	$0.588149\pi$
$198$		0			0
$199$	−2.26928	−	3.93050i	−0.160865	−	0.278626i	0.774314	−	0.632801i	$-0.218095\pi$
$199$	−2.26928	−	3.93050i	−0.160865	−	0.278626i	−0.935179	+	0.354175i	$0.884762\pi$
$200$		0			0
$201$	5.12636	−	1.00187i	0.361586	−	0.0706666i
$202$		0			0
$203$	5.54807	+	0.882659i	0.389398	+	0.0619505i
$204$		0			0
$205$	32.2774			2.25435
$206$		0			0
$207$	15.3186	+	11.9181i	1.06471	+	0.828366i
$208$		0			0
$209$	8.42836	+	14.5983i	0.583002	+	1.00979i
$210$		0			0
$211$	9.84097	−	17.0451i	0.677480	−	1.17343i	−0.298257	−	0.954486i	$-0.596405\pi$
$211$	9.84097	−	17.0451i	0.677480	−	1.17343i	0.975737	−	0.218944i	$-0.0702613\pi$
$212$		0			0
$213$	26.1427	−	5.10922i	1.79127	−	0.350078i
$214$		0			0
$215$	13.5692	−	23.5025i	0.925410	−	1.60286i
$216$		0			0
$217$	1.05371	−	1.29938i	0.0715304	−	0.0882079i
$218$		0			0
$219$	−9.93348	−	11.4037i	−0.671242	−	0.770592i
$220$		0			0
$221$	−5.97891			−0.402185
$222$		0			0
$223$	6.63518	+	11.4925i	0.444324	+	0.769592i	0.998005	−	0.0631368i	$-0.0201105\pi$
$223$	6.63518	+	11.4925i	0.444324	+	0.769592i	−0.553681	+	0.832729i	$0.686777\pi$
$224$		0			0
$225$	−2.14299	+	15.4764i	−0.142866	+	1.03176i
$226$		0			0
$227$	−11.0305	+	19.1053i	−0.732118	+	1.26807i	0.223858	+	0.974622i	$0.428135\pi$
$227$	−11.0305	+	19.1053i	−0.732118	+	1.26807i	−0.955976	+	0.293445i	$0.905198\pi$
$228$		0			0
$229$	8.92359	+	15.4561i	0.589688	+	1.02137i	0.994273	+	0.106869i	$0.0340825\pi$
$229$	8.92359	+	15.4561i	0.589688	+	1.02137i	−0.404585	+	0.914500i	$0.632584\pi$
$230$		0			0
$231$	−5.54639	−	8.86966i	−0.364926	−	0.583581i
$232$		0			0
$233$	−7.84409	+	13.5864i	−0.513883	+	0.890072i	0.485987	+	0.873966i	$0.338460\pi$
$233$	−7.84409	+	13.5864i	−0.513883	+	0.890072i	−0.999870	+	0.0161061i	$0.994873\pi$
$234$		0			0
$235$	−10.4344	−	18.0730i	−0.680667	−	1.17895i
$236$		0			0
$237$	3.18917	−	0.623276i	0.207159	−	0.0404861i
$238$		0			0
$239$	−0.0639656	+	0.110792i	−0.00413759	+	0.00716652i	−0.868087	−	0.496412i	$-0.834650\pi$
$239$	−0.0639656	+	0.110792i	−0.00413759	+	0.00716652i	0.863949	+	0.503579i	$0.167984\pi$
$240$		0			0
$241$	−7.54343	+	13.0656i	−0.485915	+	0.841630i	−0.999869	−	0.0161883i	$-0.994847\pi$
$241$	−7.54343	+	13.0656i	−0.485915	+	0.841630i	0.513954	+	0.857818i	$0.328180\pi$
$242$		0			0
$243$	−8.87616	+	12.8146i	−0.569406	+	0.822056i
$244$		0			0
$245$	−16.6411	+	14.9421i	−1.06316	+	0.954616i
$246$		0			0
$247$	−4.98476	−	8.63386i	−0.317173	−	0.549359i
$248$		0			0
$249$	6.82911	+	7.83989i	0.432777	+	0.496833i
$250$		0			0
$251$	12.3738			0.781030			0.390515	−	0.920596i	$-0.372297\pi$
$251$	12.3738			0.781030			0.390515	+	0.920596i	$0.372297\pi$
$252$		0			0
$253$	14.7687			0.928499
$254$		0			0
$255$	−7.95508	+	23.1797i	−0.498167	+	1.45157i
$256$		0			0
$257$	−11.0433	−	19.1276i	−0.688865	−	1.19315i	−0.972205	−	0.234130i	$-0.924776\pi$
$257$	−11.0433	−	19.1276i	−0.688865	−	1.19315i	0.283340	−	0.959019i	$-0.408557\pi$
$258$		0			0
$259$	3.65111	+	9.53115i	0.226869	+	0.592237i
$260$		0			0
$261$	−5.02762	−	3.91157i	−0.311202	−	0.242120i
$262$		0			0
$263$	3.89678	−	6.74943i	0.240286	−	0.416187i	−0.720510	−	0.693445i	$-0.756092\pi$
$263$	3.89678	−	6.74943i	0.240286	−	0.416187i	0.960796	+	0.277257i	$0.0894255\pi$
$264$		0			0
$265$	7.66641	−	13.2786i	0.470944	−	0.815698i
$266$		0			0
$267$	−2.98423	+	8.69554i	−0.182632	+	0.532158i
$268$		0			0
$269$	−3.85738	−	6.68119i	−0.235189	−	0.407359i	0.724139	−	0.689654i	$-0.242238\pi$
$269$	−3.85738	−	6.68119i	−0.235189	−	0.407359i	−0.959328	+	0.282295i	$0.908904\pi$
$270$		0			0
$271$	12.5744	−	21.7795i	0.763839	−	1.32301i	−0.177019	−	0.984207i	$-0.556645\pi$
$271$	12.5744	−	21.7795i	0.763839	−	1.32301i	0.940858	−	0.338801i	$-0.110021\pi$
$272$		0			0
$273$	3.28029	+	5.24576i	0.198532	+	0.317488i
$274$		0			0
$275$	5.94438	+	10.2960i	0.358460	+	0.620870i
$276$		0			0
$277$	3.98137	−	6.89593i	0.239217	−	0.414336i	−0.721273	−	0.692651i	$-0.756443\pi$
$277$	3.98137	−	6.89593i	0.239217	−	0.414336i	0.960490	+	0.278315i	$0.0897759\pi$
$278$		0			0
$279$	−1.75735	+	0.714175i	−0.105210	+	0.0427565i
$280$		0			0
$281$	13.3385	+	23.1030i	0.795710	+	1.37821i	0.922388	+	0.386266i	$0.126235\pi$
$281$	13.3385	+	23.1030i	0.795710	+	1.37821i	−0.126678	+	0.991944i	$0.540431\pi$
$282$		0			0
$283$	14.4399			0.858364			0.429182	−	0.903218i	$-0.358802\pi$
$283$	14.4399			0.858364			0.429182	+	0.903218i	$0.358802\pi$
$284$		0			0
$285$	−40.1051	+	7.83795i	−2.37562	+	0.464280i
$286$		0			0
$287$	−9.56144	−	24.9600i	−0.564394	−	1.47334i
$288$		0			0
$289$	−1.30577	+	2.26166i	−0.0768099	+	0.133039i
$290$		0			0
$291$	−16.9406	−	19.4479i	−0.993074	−	1.14006i
$292$		0			0
$293$	−8.27703	+	14.3362i	−0.483549	+	0.837532i	−0.999822	−	0.0188927i	$-0.993986\pi$
$293$	−8.27703	+	14.3362i	−0.483549	+	0.837532i	0.516272	+	0.856424i	$0.327319\pi$
$294$		0			0
$295$	−9.91061	−	17.1657i	−0.577018	−	0.999424i
$296$		0			0
$297$	0.656910	+	11.8435i	0.0381178	+	0.687229i
$298$		0			0
$299$	−8.73460			−0.505135
$300$		0			0
$301$	−22.1939	−	3.53090i	−1.27924	−	0.203518i
$302$		0			0
$303$	−7.87467	+	22.9454i	−0.452388	+	1.31818i
$304$		0			0
$305$	14.2352	+	24.6561i	0.815105	+	1.41180i
$306$		0			0
$307$	10.9233			0.623425			0.311713	−	0.950176i	$-0.399097\pi$
$307$	10.9233			0.623425			0.311713	+	0.950176i	$0.399097\pi$
$308$		0			0
$309$	18.2720	+	20.9764i	1.03946	+	1.19331i
$310$		0			0
$311$	−5.25360			−0.297904			−0.148952	−	0.988844i	$-0.547590\pi$
$311$	−5.25360			−0.297904			−0.148952	+	0.988844i	$0.547590\pi$
$312$		0			0
$313$	21.5184			1.21629			0.608145	−	0.793826i	$-0.291914\pi$
$313$	21.5184			1.21629			0.608145	+	0.793826i	$0.291914\pi$
$314$		0			0
$315$	24.7019	−	5.73779i	1.39179	−	0.323288i
$316$		0			0
$317$	−17.5323			−0.984710			−0.492355	−	0.870394i	$-0.663864\pi$
$317$	−17.5323			−0.984710			−0.492355	+	0.870394i	$0.663864\pi$
$318$		0			0
$319$	−4.84714			−0.271388
$320$		0			0
$321$	−1.42605	+	4.15527i	−0.0795945	+	0.231925i
$322$		0			0
$323$	−32.7012			−1.81954
$324$		0			0
$325$	−3.51567	−	6.08932i	−0.195014	−	0.337774i
$326$		0			0
$327$	−18.4516	−	21.1826i	−1.02037	−	1.17140i
$328$		0			0
$329$	−10.8848	+	13.4226i	−0.600097	+	0.740012i
$330$		0			0
$331$	6.27589			0.344954			0.172477	−	0.985014i	$-0.444823\pi$
$331$	6.27589			0.344954			0.172477	+	0.985014i	$0.444823\pi$
$332$		0			0
$333$	1.58737	−	11.4637i	0.0869872	−	0.628209i
$334$		0			0
$335$	4.81757	+	8.34428i	0.263212	+	0.455897i
$336$		0			0
$337$	13.5924	−	23.5427i	0.740426	−	1.28246i	−0.211876	−	0.977297i	$-0.567957\pi$
$337$	13.5924	−	23.5427i	0.740426	−	1.28246i	0.952302	−	0.305159i	$-0.0987095\pi$
$338$		0			0
$339$	−1.81601	+	5.29155i	−0.0986322	+	0.287397i
$340$		0			0
$341$	−0.721712	+	1.25004i	−0.0390829	+	0.0676936i
$342$		0			0
$343$	16.4842	+	8.44222i	0.890063	+	0.455837i
$344$		0			0
$345$	−11.6216	+	33.8633i	−0.625685	+	1.82314i
$346$		0			0
$347$	−19.1808			−1.02968			−0.514840	−	0.857286i	$-0.672149\pi$
$347$	−19.1808			−1.02968			−0.514840	+	0.857286i	$0.672149\pi$
$348$		0			0
$349$	10.1028	+	17.4985i	0.540789	+	0.936675i	0.998859	+	0.0477584i	$0.0152078\pi$
$349$	10.1028	+	17.4985i	0.540789	+	0.936675i	−0.458069	+	0.888916i	$0.651459\pi$
$350$		0			0
$351$	−0.388515	−	7.00457i	−0.0207374	−	0.373876i
$352$		0			0
$353$	14.2499	−	24.6816i	0.758448	−	1.31367i	−0.185193	−	0.982702i	$-0.559291\pi$
$353$	14.2499	−	24.6816i	0.758448	−	1.31367i	0.943642	−	0.330969i	$-0.107376\pi$
$354$		0			0
$355$	24.5680	+	42.5531i	1.30394	+	2.25848i
$356$		0			0
$357$	20.2813	−	0.714841i	1.07340	−	0.0378334i
$358$		0			0
$359$	15.4572	−	26.7727i	0.815802	−	1.41301i	−0.0929489	−	0.995671i	$-0.529629\pi$
$359$	15.4572	−	26.7727i	0.815802	−	1.41301i	0.908751	−	0.417339i	$-0.137037\pi$
$360$		0			0
$361$	−17.7638	−	30.7677i	−0.934934	−	1.61935i
$362$		0			0
$363$	−6.58576	−	7.56052i	−0.345663	−	0.396824i
$364$		0			0
$365$	13.9486	−	24.1597i	0.730103	−	1.26458i
$366$		0			0
$367$	3.41547	−	5.91577i	0.178286	−	0.308801i	−0.763007	−	0.646390i	$-0.776278\pi$
$367$	3.41547	−	5.91577i	0.178286	−	0.308801i	0.941294	+	0.337589i	$0.109611\pi$
$368$		0			0
$369$	−4.15696	+	30.0210i	−0.216403	+	1.56283i
$370$		0			0
$371$	−12.5393	−	1.99491i	−0.651007	−	0.103571i
$372$		0			0
$373$	−3.38245	−	5.85858i	−0.175137	−	0.303346i	0.765072	−	0.643945i	$-0.222703\pi$
$373$	−3.38245	−	5.85858i	−0.175137	−	0.303346i	−0.940209	+	0.340599i	$0.889370\pi$
$374$		0			0
$375$	−1.12970	+	0.220784i	−0.0583377	+	0.0114012i
$376$		0			0
$377$	2.86673			0.147644
$378$		0			0
$379$	−7.62967			−0.391910			−0.195955	−	0.980613i	$-0.562781\pi$
$379$	−7.62967			−0.391910			−0.195955	+	0.980613i	$0.562781\pi$
$380$		0			0
$381$	21.4915	−	4.20019i	1.10104	−	0.215182i
$382$		0			0
$383$	3.21132	+	5.56217i	0.164091	+	0.284214i	0.936332	−	0.351116i	$-0.114198\pi$
$383$	3.21132	+	5.56217i	0.164091	+	0.284214i	−0.772241	+	0.635329i	$0.780864\pi$
$384$		0			0
$385$	12.1542	−	14.9880i	0.619436	−	0.763860i
$386$		0			0
$387$	20.1120	+	15.6475i	1.02235	+	0.795405i
$388$		0			0
$389$	7.92675	−	13.7295i	0.401902	−	0.696115i	−0.592053	−	0.805899i	$-0.701683\pi$
$389$	7.92675	−	13.7295i	0.401902	−	0.696115i	0.993955	+	0.109784i	$0.0350159\pi$
$390$		0			0
$391$	−14.3253	+	24.8121i	−0.724460	+	1.25480i
$392$		0			0
$393$	21.6935	+	24.9043i	1.09429	+	1.25626i
$394$		0			0
$395$	2.99707	+	5.19107i	0.150799	+	0.261191i
$396$		0			0
$397$	−8.56287	+	14.8313i	−0.429758	+	0.744363i	−0.996852	−	0.0792903i	$-0.974735\pi$
$397$	−8.56287	+	14.8313i	−0.429758	+	0.744363i	0.567093	+	0.823654i	$0.308068\pi$
$398$		0			0
$399$	17.9413	+	28.6913i	0.898187	+	1.43636i
$400$		0			0
$401$	−11.8845	−	20.5846i	−0.593486	−	1.02795i	−0.993759	−	0.111552i	$-0.964418\pi$
$401$	−11.8845	−	20.5846i	−0.593486	−	1.02795i	0.400273	−	0.916396i	$-0.368915\pi$
$402$		0			0
$403$	0.426840	−	0.739309i	0.0212624	−	0.0368276i
$404$		0			0
$405$	−27.6730	−	7.81350i	−1.37508	−	0.388256i
$406$		0			0
$407$	−4.40316	−	7.62649i	−0.218256	−	0.378031i
$408$		0			0
$409$	15.1189			0.747582			0.373791	−	0.927513i	$-0.378058\pi$
$409$	15.1189			0.747582			0.373791	+	0.927513i	$0.378058\pi$
$410$		0			0
$411$	3.80337	−	11.0824i	0.187606	−	0.546653i
$412$		0			0
$413$	−10.3383	+	12.7488i	−0.508717	+	0.627326i
$414$		0			0
$415$	−9.58945	+	16.6094i	−0.470728	+	0.815324i
$416$		0			0
$417$	7.39023	−	21.5339i	0.361901	−	1.05452i
$418$		0			0
$419$	2.82673	−	4.89604i	0.138095	−	0.239187i	−0.788681	−	0.614803i	$-0.789236\pi$
$419$	2.82673	−	4.89604i	0.138095	−	0.239187i	0.926775	+	0.375616i	$0.122569\pi$
$420$		0			0
$421$	−12.5088	−	21.6658i	−0.609640	−	1.05593i	−0.991300	−	0.131625i	$-0.957981\pi$
$421$	−12.5088	−	21.6658i	−0.609640	−	1.05593i	0.381660	−	0.924303i	$-0.375353\pi$
$422$		0			0
$423$	18.1534	−	7.37741i	0.882648	−	0.358702i
$424$		0			0
$425$	−23.0636			−1.11875
$426$		0			0
$427$	14.8496	−	18.3118i	0.718622	−	0.886171i
$428$		0			0
$429$	−3.50625	−	4.02520i	−0.169283	−	0.194339i
$430$		0			0
$431$	10.4514	+	18.1024i	0.503428	+	0.871962i	0.999992	+	0.00396247i	$0.00126130\pi$
$431$	10.4514	+	18.1024i	0.503428	+	0.871962i	−0.496564	+	0.868000i	$0.665405\pi$
$432$		0			0
$433$	−21.2708			−1.02221			−0.511104	−	0.859519i	$-0.670763\pi$
$433$	−21.2708			−1.02221			−0.511104	+	0.859519i	$0.670763\pi$
$434$		0			0
$435$	3.81425	−	11.1141i	0.182879	−	0.532879i
$436$		0			0
$437$	−47.7732			−2.28530
$438$		0			0
$439$	17.1817			0.820040			0.410020	−	0.912077i	$-0.365522\pi$
$439$	17.1817			0.820040			0.410020	+	0.912077i	$0.365522\pi$
$440$		0			0
$441$	−11.7544	−	17.4021i	−0.559732	−	0.828674i
$442$		0			0
$443$	−12.7436			−0.605467			−0.302734	−	0.953075i	$-0.597899\pi$
$443$	−12.7436			−0.605467			−0.302734	+	0.953075i	$0.597899\pi$
$444$		0			0
$445$	−16.9584			−0.803905
$446$		0			0
$447$	0.319128	+	0.366362i	0.0150942	+	0.0173283i
$448$		0			0
$449$	31.5913			1.49088			0.745442	−	0.666570i	$-0.232238\pi$
$449$	31.5913			1.49088			0.745442	+	0.666570i	$0.232238\pi$
$450$		0			0
$451$	11.5309	+	19.9721i	0.542969	+	0.940449i
$452$		0			0
$453$	4.98027	−	14.5117i	0.233994	−	0.681817i
$454$		0			0
$455$	−7.18833	+	8.86432i	−0.336994	+	0.415566i
$456$		0			0
$457$	−7.30486			−0.341707			−0.170853	−	0.985296i	$-0.554652\pi$
$457$	−7.30486			−0.341707			−0.170853	+	0.985296i	$0.554652\pi$
$458$		0			0
$459$	−20.5348	−	10.3843i	−0.958483	−	0.484696i
$460$		0			0
$461$	−13.3651	−	23.1491i	−0.622477	−	1.07816i	−0.989023	−	0.147761i	$-0.952793\pi$
$461$	−13.3651	−	23.1491i	−0.622477	−	1.07816i	0.366546	−	0.930400i	$-0.380540\pi$
$462$		0			0
$463$	−1.75608	+	3.04161i	−0.0816117	+	0.141356i	−0.903942	−	0.427654i	$-0.859340\pi$
$463$	−1.75608	+	3.04161i	−0.0816117	+	0.141356i	0.822331	+	0.569010i	$0.192673\pi$
$464$		0			0
$465$	−2.29832	−	2.63849i	−0.106582	−	0.122357i
$466$		0			0
$467$	−7.80239	+	13.5141i	−0.361052	+	0.625360i	−0.988134	−	0.153593i	$-0.950915\pi$
$467$	−7.80239	+	13.5141i	−0.361052	+	0.625360i	0.627083	+	0.778953i	$0.284249\pi$
$468$		0			0
$469$	5.02550	−	6.19721i	0.232056	−	0.286161i
$470$		0			0
$471$	3.27899	−	0.640831i	0.151088	−	0.0295279i
$472$		0			0
$473$	19.3900			0.891554
$474$		0			0
$475$	−19.2287	−	33.3050i	−0.882272	−	1.52814i
$476$		0			0
$477$	11.3630	+	8.84061i	0.520276	+	0.404784i
$478$		0			0
$479$	8.54444	−	14.7994i	0.390405	−	0.676202i	−0.602098	−	0.798422i	$-0.705668\pi$
$479$	8.54444	−	14.7994i	0.390405	−	0.676202i	0.992503	+	0.122221i	$0.0390015\pi$
$480$		0			0
$481$	2.60415	+	4.51052i	0.118739	+	0.205662i
$482$		0			0
$483$	29.6290	−	1.04431i	1.34817	−	0.0475179i
$484$		0			0
$485$	23.7880	−	41.2020i	1.08016	−	1.87089i
$486$		0			0
$487$	−12.9335	−	22.4014i	−0.586072	−	1.01511i	−0.994741	−	0.102423i	$-0.967340\pi$
$487$	−12.9335	−	22.4014i	−0.586072	−	1.01511i	0.408669	−	0.912683i	$-0.365993\pi$
$488$		0			0
$489$	13.7167	−	39.9680i	0.620289	−	1.80741i
$490$		0			0
$491$	−7.51452	+	13.0155i	−0.339126	+	0.587383i	−0.984269	−	0.176679i	$-0.943465\pi$
$491$	−7.51452	+	13.0155i	−0.339126	+	0.587383i	0.645143	+	0.764062i	$0.276798\pi$
$492$		0			0
$493$	4.70160	−	8.14342i	0.211750	−	0.366761i
$494$		0			0
$495$	−20.2705	+	8.23779i	−0.911092	+	0.370261i
$496$		0			0
$497$	25.6284	−	31.6037i	1.14959	−	1.41762i
$498$		0			0
$499$	−7.62094	−	13.1999i	−0.341160	−	0.590907i	0.643488	−	0.765456i	$-0.277487\pi$
$499$	−7.62094	−	13.1999i	−0.341160	−	0.590907i	−0.984648	+	0.174549i	$0.944153\pi$
$500$		0			0
$501$	−3.09969	+	9.03197i	−0.138484	+	0.403519i
$502$		0			0
$503$	18.6284			0.830599			0.415299	−	0.909685i	$-0.363677\pi$
$503$	18.6284			0.830599			0.415299	+	0.909685i	$0.363677\pi$
$504$		0			0
$505$	−44.7491			−1.99131
$506$		0			0
$507$	−12.7158	−	14.5979i	−0.564730	−	0.648316i
$508$		0			0
$509$	3.72333	+	6.44899i	0.165034	+	0.285847i	0.936667	−	0.350221i	$-0.113893\pi$
$509$	3.72333	+	6.44899i	0.165034	+	0.285847i	−0.771634	+	0.636067i	$0.780560\pi$
$510$		0			0
$511$	−22.8145	−	3.62964i	−1.00926	−	0.160566i
$512$		0			0
$513$	−2.12495	−	38.3109i	−0.0938188	−	1.69147i
$514$		0			0
$515$	−25.6576	+	44.4402i	−1.13061	+	1.95827i
$516$		0			0
$517$	7.45527	−	12.9129i	0.327882	−	0.567909i
$518$		0			0
$519$	−21.4275	+	4.18768i	−0.940561	+	0.183819i
$520$		0			0
$521$	−11.3853	−	19.7200i	−0.498800	−	0.863947i	0.501199	−	0.865332i	$-0.332893\pi$
$521$	−11.3853	−	19.7200i	−0.498800	−	0.863947i	−0.999999	+	0.00138491i	$0.999559\pi$
$522$		0			0
$523$	16.5092	−	28.5949i	0.721899	−	1.25037i	−0.238339	−	0.971182i	$-0.576603\pi$
$523$	16.5092	−	28.5949i	0.721899	−	1.25037i	0.960238	−	0.279184i	$-0.0900639\pi$
$524$		0			0
$525$	12.6537	+	20.2355i	0.552252	+	0.883148i
$526$		0			0
$527$	−1.40009	−	2.42502i	−0.0609887	−	0.105636i
$528$		0			0
$529$	−9.42780	+	16.3294i	−0.409904	+	0.709975i
$530$		0			0
$531$	17.2421	−	7.00705i	0.748242	−	0.304080i
$532$		0			0
$533$	−6.81969	−	11.8120i	−0.295393	−	0.511636i
$534$		0			0
$535$	−8.10378			−0.350357
$536$		0			0
$537$	−11.6148	−	13.3339i	−0.501217	−	0.575402i
$538$		0			0
$539$	−15.1906	−	4.95894i	−0.654304	−	0.213597i
$540$		0			0
$541$	8.53464	−	14.7824i	0.366933	−	0.635546i	−0.622151	−	0.782897i	$-0.713741\pi$
$541$	8.53464	−	14.7824i	0.366933	−	0.635546i	0.989084	+	0.147351i	$0.0470745\pi$
$542$		0			0
$543$	27.6059	−	5.39517i	1.18468	−	0.231529i
$544$		0			0
$545$	25.9097	−	44.8769i	1.10985	−	1.92232i
$546$		0			0
$547$	16.3574	+	28.3318i	0.699390	+	1.21138i	0.968678	+	0.248319i	$0.0798782\pi$
$547$	16.3574	+	28.3318i	0.699390	+	1.21138i	−0.269288	+	0.963060i	$0.586788\pi$
$548$		0			0
$549$	−24.7658	+	10.0646i	−1.05698	+	0.429548i
$550$		0			0
$551$	15.6794			0.667963
$552$		0			0
$553$	3.12642	−	3.85536i	0.132949	−	0.163946i
$554$		0			0
$555$	20.9518	−	4.09472i	0.889353	−	0.173811i
$556$		0			0
$557$	17.0783	+	29.5806i	0.723633	+	1.25337i	0.959534	+	0.281592i	$0.0908623\pi$
$557$	17.0783	+	29.5806i	0.723633	+	1.25337i	−0.235902	+	0.971777i	$0.575804\pi$
$558$		0			0
$559$	−11.4678			−0.485036
$560$		0			0
$561$	−17.1847	+	3.35850i	−0.725539	+	0.141796i
$562$		0			0
$563$	−9.67074			−0.407573			−0.203786	−	0.979015i	$-0.565325\pi$
$563$	−9.67074			−0.407573			−0.203786	+	0.979015i	$0.565325\pi$
$564$		0			0
$565$	−10.3198			−0.434157
$566$		0			0
$567$	2.15536	+	23.7140i	0.0905168	+	0.995895i
$568$		0			0
$569$	11.1274			0.466484			0.233242	−	0.972419i	$-0.425067\pi$
$569$	11.1274			0.466484			0.233242	+	0.972419i	$0.425067\pi$
$570$		0			0
$571$	0.729305			0.0305205			0.0152602	−	0.999884i	$-0.495142\pi$
$571$	0.729305			0.0305205			0.0152602	+	0.999884i	$0.495142\pi$
$572$		0			0
$573$	6.69960	−	1.30934i	0.279880	−	0.0546984i
$574$		0			0
$575$	−33.6937			−1.40512
$576$		0			0
$577$	9.49359	+	16.4434i	0.395223	+	0.684547i	0.993130	−	0.117019i	$-0.0373338\pi$
$577$	9.49359	+	16.4434i	0.395223	+	0.684547i	−0.597906	+	0.801566i	$0.704001\pi$
$578$		0			0
$579$	9.75928	−	1.90731i	0.405582	−	0.0792650i
$580$		0			0
$581$	15.6846	+	2.49532i	0.650709	+	0.103523i
$582$		0			0
$583$	10.9551			0.453714
$584$		0			0
$585$	11.9885	−	4.87206i	0.495665	−	0.201435i
$586$		0			0
$587$	−1.30535	−	2.26093i	−0.0538775	−	0.0933185i	0.837829	−	0.545933i	$-0.183825\pi$
$587$	−1.30535	−	2.26093i	−0.0538775	−	0.0933185i	−0.891706	+	0.452615i	$0.850491\pi$
$588$		0			0
$589$	2.33457	−	4.04359i	0.0961942	−	0.166613i
$590$		0			0
$591$	13.0463	−	2.54971i	0.536654	−	0.104881i
$592$		0			0
$593$	−7.92622	+	13.7286i	−0.325491	+	0.563767i	−0.981612	−	0.190889i	$-0.938863\pi$
$593$	−7.92622	+	13.7286i	−0.325491	+	0.563767i	0.656121	+	0.754656i	$0.272196\pi$
$594$		0			0
$595$	13.3913	+	34.9576i	0.548988	+	1.43312i
$596$		0			0
$597$	5.16331	+	5.92753i	0.211320	+	0.242598i
$598$		0			0
$599$	15.8610			0.648063			0.324032	−	0.946046i	$-0.394962\pi$
$599$	15.8610			0.648063			0.324032	+	0.946046i	$0.394962\pi$
$600$		0			0
$601$	0.834141	+	1.44477i	0.0340253	+	0.0589336i	0.882537	−	0.470244i	$-0.155834\pi$
$601$	0.834141	+	1.44477i	0.0340253	+	0.0589336i	−0.848511	+	0.529177i	$0.822501\pi$
$602$		0			0
$603$	−8.38142	+	3.40615i	−0.341318	+	0.138709i
$604$		0			0
$605$	9.24774	−	16.0176i	0.375974	−	0.651207i
$606$		0			0
$607$	18.2555	+	31.6194i	0.740968	+	1.28339i	0.952055	+	0.305926i	$0.0989661\pi$
$607$	18.2555	+	31.6194i	0.740968	+	1.28339i	−0.211088	+	0.977467i	$0.567701\pi$
$608$		0			0
$609$	−9.72435	+	0.342747i	−0.394050	+	0.0138888i
$610$		0			0
$611$	−4.40925	+	7.63705i	−0.178379	+	0.308962i
$612$		0			0
$613$	18.2957	+	31.6891i	0.738958	+	1.27991i	0.952965	+	0.303080i	$0.0980150\pi$
$613$	18.2957	+	31.6891i	0.738958	+	1.27991i	−0.214007	+	0.976832i	$0.568652\pi$
$614$		0			0
$615$	−54.8680	+	10.7232i	−2.21249	+	0.432399i
$616$		0			0
$617$	−5.10936	+	8.84967i	−0.205695	+	0.356274i	−0.950354	−	0.311171i	$-0.899279\pi$
$617$	−5.10936	+	8.84967i	−0.205695	+	0.356274i	0.744659	+	0.667445i	$0.232612\pi$
$618$		0			0
$619$	12.3664	−	21.4193i	0.497049	−	0.860914i	−0.502945	−	0.864318i	$-0.667750\pi$
$619$	12.3664	−	21.4193i	0.497049	−	0.860914i	0.999994	+	0.00340432i	$0.00108363\pi$
$620$		0			0
$621$	−29.9993	−	15.1704i	−1.20383	−	0.608767i
$622$		0			0
$623$	5.02353	+	13.1138i	0.201264	+	0.525395i
$624$		0			0
$625$	11.9584	+	20.7125i	0.478334	+	0.828499i
$626$		0			0
$627$	−19.1771	−	22.0155i	−0.765861	−	0.879216i
$628$		0			0
$629$	17.0838			0.681177
$630$		0			0
$631$	42.1420			1.67765			0.838823	−	0.544404i	$-0.183244\pi$
$631$	42.1420			1.67765			0.838823	+	0.544404i	$0.183244\pi$
$632$		0			0
$633$	−11.0659	+	32.2441i	−0.439829	+	1.28159i
$634$		0			0
$635$	20.1969	+	34.9821i	0.801491	+	1.38822i
$636$		0			0
$637$	8.98411	+	2.93285i	0.355964	+	0.116204i
$638$		0			0
$639$	−42.7424	+	17.3702i	−1.69086	+	0.687155i
$640$		0			0
$641$	1.16519	−	2.01817i	0.0460222	−	0.0797128i	−0.842097	−	0.539327i	$-0.818679\pi$
$641$	1.16519	−	2.01817i	0.0460222	−	0.0797128i	0.888119	+	0.459614i	$0.152012\pi$
$642$		0			0
$643$	16.5035	−	28.5850i	0.650836	−	1.12728i	−0.332085	−	0.943250i	$-0.607752\pi$
$643$	16.5035	−	28.5850i	0.650836	−	1.12728i	0.982920	−	0.184031i	$-0.0589147\pi$
$644$		0			0
$645$	−15.2582	+	44.4596i	−0.600789	+	1.75060i
$646$		0			0
$647$	−10.4187	−	18.0458i	−0.409603	−	0.709452i	0.585243	−	0.810858i	$-0.300999\pi$
$647$	−10.4187	−	18.0458i	−0.409603	−	0.709452i	−0.994845	+	0.101406i	$0.967666\pi$
$648$		0			0
$649$	7.08101	−	12.2647i	0.277954	−	0.481430i
$650$		0			0
$651$	−1.35951	+	2.55887i	−0.0532834	+	0.100290i
$652$		0			0
$653$	24.4176	+	42.2925i	0.955534	+	1.65503i	0.733142	+	0.680075i	$0.238053\pi$
$653$	24.4176	+	42.2925i	0.955534	+	1.65503i	0.222391	+	0.974958i	$0.428614\pi$
$654$		0			0
$655$	−30.4620	+	52.7618i	−1.19025	+	2.06157i
$656$		0			0
$657$	20.6744	+	16.0850i	0.806584	+	0.627536i
$658$		0			0
$659$	0.272662	+	0.472265i	0.0106214	+	0.0183968i	0.871287	−	0.490773i	$-0.163286\pi$
$659$	0.272662	+	0.472265i	0.0106214	+	0.0183968i	−0.860666	+	0.509170i	$0.829952\pi$
$660$		0			0
$661$	−46.4250			−1.80572			−0.902861	−	0.429933i	$-0.858537\pi$
$661$	−46.4250			−1.80572			−0.902861	+	0.429933i	$0.858537\pi$
$662$		0			0
$663$	10.1635	−	1.98631i	0.394718	−	0.0771418i
$664$		0			0
$665$	−39.3160	+	48.4827i	−1.52461	+	1.88008i
$666$		0			0
$667$	6.86858	−	11.8967i	0.265953	−	0.460643i
$668$		0			0
$669$	−15.0971	−	17.3316i	−0.583687	−	0.670079i
$670$		0			0
$671$	−10.1709	+	17.6165i	−0.392642	+	0.680076i
$672$		0			0
$673$	−16.9838	−	29.4168i	−0.654677	−	1.13393i	−0.981975	−	0.189013i	$-0.939471\pi$
$673$	−16.9838	−	29.4168i	−0.654677	−	1.13393i	0.327298	−	0.944921i	$-0.393862\pi$
$674$		0			0
$675$	−1.49869	−	27.0201i	−0.0576847	−	1.04000i
$676$		0			0
$677$	31.2851			1.20238			0.601191	−	0.799105i	$-0.294693\pi$
$677$	31.2851			1.20238			0.601191	+	0.799105i	$0.294693\pi$
$678$		0			0
$679$	−38.9080	−	6.18999i	−1.49315	−	0.237550i
$680$		0			0
$681$	12.4035	−	36.1415i	0.475301	−	1.38495i
$682$		0			0
$683$	0.289712	+	0.501795i	0.0110855	+	0.0192007i	0.871515	−	0.490369i	$-0.163138\pi$
$683$	0.289712	+	0.501795i	0.0110855	+	0.0192007i	−0.860429	+	0.509570i	$0.829805\pi$
$684$		0			0
$685$	21.6133			0.825801
$686$		0			0
$687$	−20.3040	−	23.3091i	−0.774644	−	0.889299i
$688$		0			0
$689$	−6.47915			−0.246836
$690$		0			0
$691$	2.21565			0.0842872			0.0421436	−	0.999112i	$-0.486581\pi$
$691$	2.21565			0.0842872			0.0421436	+	0.999112i	$0.486581\pi$
$692$		0			0
$693$	12.3749	+	13.2348i	0.470085	+	0.502750i
$694$		0			0
$695$	41.9962			1.59301
$696$		0			0
$697$	−44.7387			−1.69460
$698$		0			0
$699$	8.82046	−	25.7013i	0.333620	−	0.972112i
$700$		0			0
$701$	4.74299			0.179140			0.0895702	−	0.995981i	$-0.471451\pi$
$701$	4.74299			0.179140			0.0895702	+	0.995981i	$0.471451\pi$
$702$		0			0
$703$	14.2432	+	24.6699i	0.537192	+	0.930444i
$704$		0			0
$705$	23.7416	+	27.2556i	0.894159	+	1.02650i
$706$		0			0
$707$	13.2559	+	34.6043i	0.498539	+	1.30143i
$708$		0			0
$709$	−23.3765			−0.877923			−0.438962	−	0.898506i	$-0.644654\pi$
$709$	−23.3765			−0.877923			−0.438962	+	0.898506i	$0.644654\pi$
$710$		0			0
$711$	−5.21417	+	2.11900i	−0.195547	+	0.0794688i
$712$		0			0
$713$	−2.04539	−	3.54272i	−0.0766004	−	0.132676i
$714$		0			0
$715$	4.92348	−	8.52771i	0.184128	−	0.318918i
$716$		0			0
$717$	0.0719275	−	0.209584i	0.00268618	−	0.00782707i
$718$		0			0
$719$	13.0256	−	22.5610i	0.485772	−	0.841382i	−0.514094	−	0.857734i	$-0.671872\pi$
$719$	13.0256	−	22.5610i	0.485772	−	0.841382i	0.999866	+	0.0163516i	$0.00520511\pi$
$720$		0			0
$721$	41.9659	+	6.67649i	1.56289	+	0.248645i
$722$		0			0
$723$	8.48237	−	24.7162i	0.315463	−	0.919205i
$724$		0			0
$725$	11.0584			0.410698
$726$		0			0
$727$	5.79712	+	10.0409i	0.215003	+	0.372396i	0.953274	−	0.302108i	$-0.0976905\pi$
$727$	5.79712	+	10.0409i	0.215003	+	0.372396i	−0.738270	+	0.674505i	$0.764357\pi$
$728$		0			0
$729$	10.8313	−	24.7322i	0.401158	−	0.916009i
$730$		0			0
$731$	−18.8078	+	32.5761i	−0.695633	+	1.20487i
$732$		0			0
$733$	17.6743	+	30.6128i	0.652816	+	1.13071i	0.982436	+	0.186597i	$0.0597459\pi$
$733$	17.6743	+	30.6128i	0.652816	+	1.13071i	−0.329620	+	0.944114i	$0.606921\pi$
$734$		0			0
$735$	23.3240	−	30.9284i	0.860319	−	1.14081i
$736$		0			0
$737$	−3.44210	+	5.96189i	−0.126791	+	0.219609i
$738$		0			0
$739$	4.66968	+	8.08812i	0.171777	+	0.297526i	0.939041	−	0.343805i	$-0.111716\pi$
$739$	4.66968	+	8.08812i	0.171777	+	0.297526i	−0.767264	+	0.641331i	$0.778383\pi$
$740$		0			0
$741$	11.3419	+	13.0206i	0.416654	+	0.478323i
$742$		0			0
$743$	−14.6308	+	25.3412i	−0.536750	+	0.929679i	0.462326	+	0.886710i	$0.347015\pi$
$743$	−14.6308	+	25.3412i	−0.536750	+	0.929679i	−0.999076	+	0.0429687i	$0.986318\pi$
$744$		0			0
$745$	−0.448120	+	0.776167i	−0.0164179	+	0.0284366i
$746$		0			0
$747$	−14.2133	−	11.0582i	−0.520038	−	0.404598i
$748$		0			0
$749$	2.40056	+	6.26662i	0.0877146	+	0.228977i
$750$		0			0
$751$	−13.3106	−	23.0547i	−0.485712	−	0.841278i	0.514153	−	0.857699i	$-0.328106\pi$
$751$	−13.3106	−	23.0547i	−0.485712	−	0.841278i	−0.999865	+	0.0164202i	$0.994773\pi$
$752$		0			0
$753$	−21.0342	+	4.11083i	−0.766529	+	0.149807i
$754$		0			0
$755$	28.3012			1.02999
$756$		0			0
$757$	−35.3183			−1.28367			−0.641833	−	0.766845i	$-0.721826\pi$
$757$	−35.3183			−1.28367			−0.641833	+	0.766845i	$0.721826\pi$
$758$		0			0
$759$	−25.1052	+	4.90644i	−0.911260	+	0.178092i
$760$		0			0
$761$	−15.7824	−	27.3359i	−0.572112	−	0.990927i	−0.996349	−	0.0853760i	$-0.972791\pi$
$761$	−15.7824	−	27.3359i	−0.572112	−	0.990927i	0.424237	−	0.905551i	$-0.360542\pi$
$762$		0			0
$763$	−42.3783	−	6.74210i	−1.53420	−	0.244080i
$764$		0			0
$765$	5.82203	−	42.0459i	0.210496	−	1.52017i
$766$		0			0
$767$	−4.18790	+	7.25366i	−0.151216	+	0.261914i
$768$		0			0
$769$	−23.8477	+	41.3055i	−0.859972	+	1.48951i	0.0119829	+	0.999928i	$0.496186\pi$
$769$	−23.8477	+	41.3055i	−0.859972	+	1.48951i	−0.871955	+	0.489587i	$0.837148\pi$
$770$		0			0
$771$	25.1270	+	28.8461i	0.904928	+	1.03887i
$772$		0			0
$773$	20.7219	+	35.8914i	0.745314	+	1.29092i	0.950048	+	0.312105i	$0.101034\pi$
$773$	20.7219	+	35.8914i	0.745314	+	1.29092i	−0.204733	+	0.978818i	$0.565633\pi$
$774$		0			0
$775$	1.64653	−	2.85188i	0.0591452	−	0.102442i
$776$		0			0
$777$	−9.37291	−	14.9889i	−0.336251	−	0.537725i
$778$		0			0
$779$	−37.2997	−	64.6050i	−1.33640	−	2.31472i
$780$		0			0
$781$	−17.5536	+	30.4036i	−0.628116	+	1.08793i
$782$		0			0
$783$	9.84590	+	4.97898i	0.351864	+	0.177934i
$784$		0			0
$785$	3.08148	+	5.33728i	0.109983	+	0.190496i
$786$		0			0
$787$	−26.3177			−0.938125			−0.469063	−	0.883165i	$-0.655408\pi$
$787$	−26.3177			−0.938125			−0.469063	+	0.883165i	$0.655408\pi$
$788$		0			0
$789$	−4.38182	+	12.7679i	−0.155997	+	0.454548i
$790$		0			0
$791$	3.05700	+	7.98024i	0.108694	+	0.283745i
$792$		0			0
$793$	6.01533	−	10.4189i	0.213611	−	0.369984i
$794$		0			0
$795$	−8.62065	+	25.1191i	−0.305743	+	0.890883i
$796$		0			0
$797$	8.42109	−	14.5858i	0.298290	−	0.516654i	−0.677455	−	0.735565i	$-0.736917\pi$
$797$	8.42109	−	14.5858i	0.298290	−	0.516654i	0.975745	+	0.218911i	$0.0702503\pi$
$798$		0			0
$799$	14.4629	+	25.0504i	0.511659	+	0.886220i
$800$		0			0
$801$	2.18405	−	15.7729i	0.0771695	−	0.557308i
$802$		0			0
$803$	19.9322			0.703392
$804$		0			0
$805$	19.5633	+	51.0697i	0.689516	+	1.79997i
$806$		0			0
$807$	8.77675	+	10.0758i	0.308956	+	0.354685i
$808$		0			0
$809$	−11.8734	−	20.5653i	−0.417445	−	0.723036i	0.578237	−	0.815869i	$-0.303741\pi$
$809$	−11.8734	−	20.5653i	−0.417445	−	0.723036i	−0.995682	+	0.0928330i	$0.970408\pi$
$810$		0			0
$811$	21.9596			0.771107			0.385553	−	0.922686i	$-0.374011\pi$
$811$	21.9596			0.771107			0.385553	+	0.922686i	$0.374011\pi$
$812$		0			0
$813$	−14.1395	+	41.2002i	−0.495895	+	1.44495i
$814$		0			0
$815$	77.9471			2.73037
$816$		0			0
$817$	−62.7221			−2.19437
$818$		0			0
$819$	−7.31887	−	7.82745i	−0.255742	−	0.273513i
$820$		0			0
$821$	−21.2208			−0.740610			−0.370305	−	0.928910i	$-0.620747\pi$
$821$	−21.2208			−0.740610			−0.370305	+	0.928910i	$0.620747\pi$
$822$		0			0
$823$	13.0785			0.455890			0.227945	−	0.973674i	$-0.426799\pi$
$823$	13.0785			0.455890			0.227945	+	0.973674i	$0.426799\pi$
$824$		0			0
$825$	−13.5253	−	15.5272i	−0.470891	−	0.540587i
$826$		0			0
$827$	−25.8079			−0.897427			−0.448714	−	0.893676i	$-0.648118\pi$
$827$	−25.8079			−0.897427			−0.448714	+	0.893676i	$0.648118\pi$
$828$		0			0
$829$	−6.21392	−	10.7628i	−0.215818	−	0.373808i	0.737707	−	0.675121i	$-0.235909\pi$
$829$	−6.21392	−	10.7628i	−0.215818	−	0.373808i	−0.953525	+	0.301313i	$0.902575\pi$
$830$		0			0
$831$	−4.47693	+	13.0450i	−0.155303	+	0.452526i
$832$		0			0
$833$	23.0657	−	20.7108i	0.799180	−	0.717587i
$834$		0			0
$835$	−17.6145			−0.609575
$836$		0			0
$837$	2.75004	−	1.79784i	0.0950554	−	0.0621426i
$838$		0			0
$839$	0.492155	+	0.852437i	0.0169911	+	0.0294294i	0.874396	−	0.485213i	$-0.161258\pi$
$839$	0.492155	+	0.852437i	0.0169911	+	0.0294294i	−0.857405	+	0.514643i	$0.827925\pi$
$840$		0			0
$841$	12.2457	−	21.2102i	0.422266	−	0.731386i
$842$		0			0
$843$	−30.3493	−	34.8413i	−1.04529	−	1.20000i
$844$		0			0
$845$	17.8556	−	30.9268i	0.614251	−	1.06391i
$846$		0			0
$847$	−15.1257	−	2.40640i	−0.519727	−	0.0826849i
$848$		0			0
$849$	−24.5463	+	4.79721i	−0.842427	+	0.164640i
$850$		0			0
$851$	24.9578			0.855542
$852$		0			0
$853$	−4.66990	−	8.08850i	−0.159894	−	0.276945i	0.774936	−	0.632040i	$-0.217782\pi$
$853$	−4.66990	−	8.08850i	−0.159894	−	0.276945i	−0.934830	+	0.355095i	$0.884449\pi$
$854$		0			0
$855$	65.5704	−	26.6473i	2.24246	−	0.911319i
$856$		0			0
$857$	5.78991	−	10.0284i	0.197779	−	0.342564i	−0.750029	−	0.661405i	$-0.769960\pi$
$857$	5.78991	−	10.0284i	0.197779	−	0.342564i	0.947808	+	0.318841i	$0.103294\pi$
$858$		0			0
$859$	26.8214	+	46.4560i	0.915134	+	1.58506i	0.806705	+	0.590954i	$0.201249\pi$
$859$	26.8214	+	46.4560i	0.915134	+	1.58506i	0.108429	+	0.994104i	$0.465418\pi$
$860$		0			0
$861$	24.5456	+	39.2527i	0.836511	+	1.33773i
$862$		0			0
$863$	−4.80485	+	8.32225i	−0.163559	+	0.283293i	−0.936143	−	0.351620i	$-0.885631\pi$
$863$	−4.80485	+	8.32225i	−0.163559	+	0.283293i	0.772584	+	0.634913i	$0.218964\pi$
$864$		0			0
$865$	−20.1368	−	34.8779i	−0.684671	−	1.18588i
$866$		0			0
$867$	1.46830	−	4.27837i	0.0498661	−	0.145301i
$868$		0			0
$869$	−2.14137	+	3.70896i	−0.0726409	+	0.125818i
$870$		0			0
$871$	2.03575	−	3.52602i	0.0689788	−	0.119475i
$872$		0			0
$873$	35.2581	+	27.4314i	1.19331	+	0.928413i
$874$		0			0
$875$	−1.10748	+	1.36569i	−0.0374396	+	0.0461687i
$876$		0			0
$877$	0.532415	+	0.922170i	0.0179784	+	0.0311395i	0.874875	−	0.484349i	$-0.160944\pi$
$877$	0.532415	+	0.922170i	0.0179784	+	0.0311395i	−0.856896	+	0.515489i	$0.827610\pi$
$878$		0			0
$879$	9.30728	−	27.1198i	0.313927	−	0.914729i
$880$		0			0
$881$	−20.7526			−0.699171			−0.349586	−	0.936904i	$-0.613678\pi$
$881$	−20.7526			−0.699171			−0.349586	+	0.936904i	$0.613678\pi$
$882$		0			0
$883$	−8.80560			−0.296332			−0.148166	−	0.988963i	$-0.547337\pi$
$883$	−8.80560			−0.296332			−0.148166	+	0.988963i	$0.547337\pi$
$884$		0			0
$885$	22.5497	+	25.8873i	0.758000	+	0.870192i
$886$		0			0
$887$	−10.0074	−	17.3334i	−0.336017	−	0.581998i	0.647663	−	0.761927i	$-0.275746\pi$
$887$	−10.0074	−	17.3334i	−0.336017	−	0.581998i	−0.983680	+	0.179929i	$0.942413\pi$
$888$		0			0
$889$	21.0686	−	25.9809i	0.706619	−	0.871370i
$890$		0			0
$891$	−5.05131	−	19.9144i	−0.169225	−	0.667158i
$892$		0			0
$893$	−24.1160	+	41.7702i	−0.807013	+	1.39779i
$894$		0			0
$895$	16.3096	−	28.2490i	0.545169	−	0.944260i
$896$		0			0
$897$	14.8479	−	2.90180i	0.495756	−	0.0968883i
$898$		0			0
$899$	0.671304	+	1.16273i	0.0223892	+	0.0387793i
$900$		0			0
$901$	−10.6262	+	18.4051i	−0.354009	+	0.613162i
$902$		0			0
$903$	38.9003	−	1.37109i	1.29452	−	0.0456271i
$904$		0			0
$905$	25.9431	+	44.9347i	0.862377	+	1.49368i
$906$		0			0
$907$	−12.5307	+	21.7039i	−0.416076	+	0.720665i	−0.995541	−	0.0943323i	$-0.969928\pi$
$907$	−12.5307	+	21.7039i	−0.416076	+	0.720665i	0.579465	+	0.814997i	$0.303262\pi$
$908$		0			0
$909$	5.76317	−	41.6208i	0.191152	−	1.38048i
$910$		0			0
$911$	4.86265	+	8.42236i	0.161107	+	0.279045i	0.935266	−	0.353946i	$-0.115160\pi$
$911$	4.86265	+	8.42236i	0.161107	+	0.279045i	−0.774159	+	0.632991i	$0.781827\pi$
$912$		0			0
$913$	−13.7031			−0.453506
$914$		0			0
$915$	−32.3895	−	37.1835i	−1.07076	−	1.22925i
$916$		0			0
$917$	49.8241	+	7.92668i	1.64534	+	0.261762i
$918$		0			0
$919$	−23.2582	+	40.2844i	−0.767217	+	1.32886i	0.171849	+	0.985123i	$0.445026\pi$
$919$	−23.2582	+	40.2844i	−0.767217	+	1.32886i	−0.939066	+	0.343736i	$0.888308\pi$
$920$		0			0
$921$	−18.5684	+	3.62892i	−0.611850	+	0.119577i
$922$		0			0
$923$	10.3817	−	17.9815i	0.341716	−	0.591870i
$924$		0			0
$925$	10.0455	+	17.3993i	0.330293	+	0.572085i
$926$		0			0
$927$	−38.0292	−	29.5874i	−1.24904	−	0.971776i
$928$		0			0
$929$	34.4680			1.13086			0.565429	−	0.824797i	$-0.308711\pi$
$929$	34.4680			1.13086			0.565429	+	0.824797i	$0.308711\pi$
$930$		0			0
$931$	49.1379	+	16.0410i	1.61043	+	0.525723i
$932$		0			0
$933$	8.93054	−	1.74534i	0.292373	−	0.0571400i
$934$		0			0
$935$	−16.1496	−	27.9719i	−0.528148	−	0.914779i
$936$		0			0
$937$	27.1376			0.886547			0.443274	−	0.896386i	$-0.353817\pi$
$937$	27.1376			0.886547			0.443274	+	0.896386i	$0.353817\pi$
$938$		0			0
$939$	−36.5789	+	7.14880i	−1.19371	+	0.233292i
$940$		0			0
$941$	−10.0390			−0.327262			−0.163631	−	0.986522i	$-0.552321\pi$
$941$	−10.0390			−0.327262			−0.163631	+	0.986522i	$0.552321\pi$
$942$		0			0
$943$	−65.3589			−2.12838
$944$		0			0
$945$	−40.0843	+	17.9600i	−1.30394	+	0.584240i
$946$		0			0
$947$	−17.0977			−0.555599			−0.277800	−	0.960639i	$-0.589605\pi$
$947$	−17.0977			−0.555599			−0.277800	+	0.960639i	$0.589605\pi$
$948$		0			0
$949$	−11.7885			−0.382669
$950$		0			0
$951$	29.8029	−	5.82455i	0.966427	−	0.188874i
$952$		0			0
$953$	−2.79843			−0.0906500			−0.0453250	−	0.998972i	$-0.514432\pi$
$953$	−2.79843			−0.0906500			−0.0453250	+	0.998972i	$0.514432\pi$
$954$		0			0
$955$	6.29605	+	10.9051i	0.203736	+	0.352880i
$956$		0			0
$957$	8.23961	−	1.61031i	0.266349	−	0.0520539i
$958$		0			0
$959$	−6.40244	−	16.7134i	−0.206746	−	0.539705i
$960$		0			0
$961$	−30.6002			−0.987103
$962$		0			0
$963$	1.04368	−	7.53728i	0.0336320	−	0.242885i
$964$		0			0
$965$	9.17143	+	15.8854i	0.295239	+	0.511369i
$966$		0			0
$967$	4.97799	−	8.62213i	0.160081	−	0.277269i	−0.774816	−	0.632186i	$-0.782158\pi$
$967$	4.97799	−	8.62213i	0.160081	−	0.277269i	0.934898	+	0.354917i	$0.115491\pi$
$968$		0			0
$969$	55.5885	−	10.8640i	1.78576	−	0.349000i
$970$		0			0
$971$	−1.13634	+	1.96819i	−0.0364668	+	0.0631623i	−0.883683	−	0.468086i	$-0.844944\pi$
$971$	−1.13634	+	1.96819i	−0.0364668	+	0.0631623i	0.847216	+	0.531249i	$0.178277\pi$
$972$		0			0
$973$	−12.4404	−	32.4755i	−0.398822	−	1.04112i
$974$		0			0
$975$	7.99924	+	9.18320i	0.256181	+	0.294098i
$976$		0			0
$977$	16.8466			0.538971			0.269485	−	0.963004i	$-0.413146\pi$
$977$	16.8466			0.538971			0.269485	+	0.963004i	$0.413146\pi$
$978$		0			0
$979$	−6.05828	−	10.4932i	−0.193623	−	0.335366i
$980$		0			0
$981$	38.4029	+	29.8781i	1.22611	+	0.953934i
$982$		0			0
$983$	10.7661	−	18.6475i	0.343386	−	0.594762i	−0.641673	−	0.766978i	$-0.721759\pi$
$983$	10.7661	−	18.6475i	0.343386	−	0.594762i	0.985059	+	0.172216i	$0.0550928\pi$
$984$		0			0
$985$	12.2605	+	21.2358i	0.390651	+	0.676628i
$986$		0			0
$987$	14.0437	−	26.4331i	0.447016	−	0.841374i
$988$		0			0
$989$	−27.4764	+	47.5905i	−0.873699	+	1.51329i
$990$		0			0
$991$	−16.8227	−	29.1378i	−0.534392	−	0.925594i	−0.999193	−	0.0401785i	$-0.987207\pi$
$991$	−16.8227	−	29.1378i	−0.534392	−	0.925594i	0.464801	−	0.885415i	$-0.346126\pi$
$992$		0			0
$993$	−10.6683	+	2.08497i	−0.338549	+	0.0661645i
$994$		0			0
$995$	−7.25033	+	12.5579i	−0.229851	+	0.398113i
$996$		0			0
$997$	−6.99406	+	12.1141i	−0.221504	+	0.383656i	−0.955265	−	0.295752i	$-0.904430\pi$
$997$	−6.99406	+	12.1141i	−0.221504	+	0.383656i	0.733761	+	0.679408i	$0.237763\pi$
$998$		0			0
$999$	1.11012	+	20.0145i	0.0351227	+	0.633230i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.2.q.c.121.2	yes	22
3.2	odd	2		1512.2.q.d.793.10		22
4.3	odd	2		1008.2.q.l.625.10		22
7.4	even	3		504.2.t.c.193.9	yes	22
9.2	odd	6		1512.2.t.c.289.2		22
9.7	even	3		504.2.t.c.457.9	yes	22
12.11	even	2		3024.2.q.l.2305.10		22
21.11	odd	6		1512.2.t.c.361.2		22
28.11	odd	6		1008.2.t.l.193.3		22
36.7	odd	6		1008.2.t.l.961.3		22
36.11	even	6		3024.2.t.k.289.2		22
63.11	odd	6		1512.2.q.d.1369.10		22
63.25	even	3	inner	504.2.q.c.25.2	✓	22
84.11	even	6		3024.2.t.k.1873.2		22
252.11	even	6		3024.2.q.l.2881.10		22
252.151	odd	6		1008.2.q.l.529.10		22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.q.c.25.2	✓	22	63.25	even	3	inner
504.2.q.c.121.2	yes	22	1.1	even	1	trivial
504.2.t.c.193.9	yes	22	7.4	even	3
504.2.t.c.457.9	yes	22	9.7	even	3
1008.2.q.l.529.10		22	252.151	odd	6
1008.2.q.l.625.10		22	4.3	odd	2
1008.2.t.l.193.3		22	28.11	odd	6
1008.2.t.l.961.3		22	36.7	odd	6
1512.2.q.d.793.10		22	3.2	odd	2
1512.2.q.d.1369.10		22	63.11	odd	6
1512.2.t.c.289.2		22	9.2	odd	6
1512.2.t.c.361.2		22	21.11	odd	6
3024.2.q.l.2305.10		22	12.11	even	2
3024.2.q.l.2881.10		22	252.11	even	6
3024.2.t.k.289.2		22	36.11	even	6
3024.2.t.k.1873.2		22	84.11	even	6

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:	\( N \)	\(=\)	\( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	504.q (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.69989 + 0.332219i) q^{3} +(-1.59750 - 2.76695i) q^{5} +(-1.66645 + 2.05498i) q^{7} +(2.77926 - 1.12947i) q^{9} +O(q^{10})\)	\(q+(-1.69989 + 0.332219i) q^{3} +(-1.59750 - 2.76695i) q^{5} +(-1.66645 + 2.05498i) q^{7} +(2.77926 - 1.12947i) q^{9} +(1.14139 - 1.97695i) q^{11} +(-0.675051 + 1.16922i) q^{13} +(3.63481 + 4.17279i) q^{15} +(2.21425 + 3.83519i) q^{17} +(-3.69214 + 6.39497i) q^{19} +(2.15007 - 4.04687i) q^{21} +(3.23479 + 5.60283i) q^{23} +(-2.60400 + 4.51026i) q^{25} +(-4.34921 + 2.84330i) q^{27} +(-1.06167 - 1.83887i) q^{29} -0.632308 q^{31} +(-1.28346 + 3.73979i) q^{33} +(8.34818 + 1.32814i) q^{35} +(1.92885 - 3.34087i) q^{37} +(0.759075 - 2.21182i) q^{39} +(-5.05124 + 8.74900i) q^{41} +(4.24701 + 7.35603i) q^{43} +(-7.56506 - 5.88574i) q^{45} +6.53173 q^{47} +(-1.44591 - 6.84904i) q^{49} +(-5.03810 - 5.78379i) q^{51} +(2.39950 + 4.15606i) q^{53} -7.29349 q^{55} +(4.15170 - 12.0974i) q^{57} +6.20383 q^{59} -8.91093 q^{61} +(-2.31044 + 7.59354i) q^{63} +4.31357 q^{65} -3.01570 q^{67} +(-7.36017 - 8.44954i) q^{69} -15.3791 q^{71} +(4.36577 + 7.56173i) q^{73} +(2.92813 - 8.53206i) q^{75} +(2.16053 + 5.64002i) q^{77} -1.87610 q^{79} +(6.44859 - 6.27819i) q^{81} +(-3.00140 - 5.19857i) q^{83} +(7.07451 - 12.2534i) q^{85} +(2.41563 + 2.77317i) q^{87} +(2.65390 - 4.59668i) q^{89} +(-1.27780 - 3.33566i) q^{91} +(1.07486 - 0.210065i) q^{93} +23.5927 q^{95} +(7.44539 + 12.8958i) q^{97} +(0.939319 - 6.78363i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q - 2 q^{3} + q^{5} + 5 q^{7} + 6 q^{9}+O(q^{10}) \) 22 * q - 2 * q^3 + q^5 + 5 * q^7 + 6 * q^9	\( 22 q - 2 q^{3} + q^{5} + 5 q^{7} + 6 q^{9} + 3 q^{11} + 7 q^{13} - q^{15} - q^{17} + 13 q^{19} - 22 q^{25} - 2 q^{27} - 7 q^{29} - 12 q^{31} - 3 q^{33} + 2 q^{35} + 6 q^{37} - 4 q^{39} + 4 q^{41} + 2 q^{43} - 3 q^{45} - 34 q^{47} - 25 q^{49} + 53 q^{51} + q^{53} + 2 q^{55} - 21 q^{57} + 42 q^{59} - 62 q^{61} - 22 q^{63} + 6 q^{65} + 52 q^{67} - 40 q^{69} - 32 q^{71} + 17 q^{73} + 53 q^{75} - q^{77} + 32 q^{79} - 6 q^{81} - 36 q^{83} + 28 q^{85} - 5 q^{87} - 2 q^{89} + 15 q^{91} - 11 q^{93} + 48 q^{95} + 19 q^{97} + 24 q^{99}+O(q^{100}) \) 22 * q - 2 * q^3 + q^5 + 5 * q^7 + 6 * q^9 + 3 * q^11 + 7 * q^13 - q^15 - q^17 + 13 * q^19 - 22 * q^25 - 2 * q^27 - 7 * q^29 - 12 * q^31 - 3 * q^33 + 2 * q^35 + 6 * q^37 - 4 * q^39 + 4 * q^41 + 2 * q^43 - 3 * q^45 - 34 * q^47 - 25 * q^49 + 53 * q^51 + q^53 + 2 * q^55 - 21 * q^57 + 42 * q^59 - 62 * q^61 - 22 * q^63 + 6 * q^65 + 52 * q^67 - 40 * q^69 - 32 * q^71 + 17 * q^73 + 53 * q^75 - q^77 + 32 * q^79 - 6 * q^81 - 36 * q^83 + 28 * q^85 - 5 * q^87 - 2 * q^89 + 15 * q^91 - 11 * q^93 + 48 * q^95 + 19 * q^97 + 24 * q^99

Introduction

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