LMFDB - Embedded newform 504.3.g.b.379.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [504,3,Mod(379,504)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(504, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("504.379");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 504 = 2^{3} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	504.g (of order $2$, degree $1$, 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:	$13.7330053238$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.0.292213762624.3
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} - 2x^{6} - 2x^{5} + 24x^{4} - 8x^{3} - 32x^{2} - 64x + 256 $ x^8 - x^7 - 2x^6 - 2x^5 + 24x^4 - 8x^3 - 32x^2 - 64x + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{5} $
Twist minimal:	no (minimal twist has level 56)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			379.2
Root			$1.85837 - 0.739226i$ of defining polynomial
Character	$\chi$	$=$	504.379
Dual form			504.3.g.b.379.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.85837 + 0.739226i) q^{2} +(2.90709 - 2.74751i) q^{4} -3.46547i q^{5} -2.64575i q^{7} +(-3.37142 + 7.25490i) q^{8} +O(q^{10})$	\(q+(-1.85837 + 0.739226i) q^{2} +(2.90709 - 2.74751i) q^{4} -3.46547i q^{5} -2.64575i q^{7} +(-3.37142 + 7.25490i) q^{8} +(2.56177 + 6.44013i) q^{10} +2.92866 q^{11} +19.1586i q^{13} +(1.95581 + 4.91679i) q^{14} +(0.902343 - 15.9745i) q^{16} +14.3897 q^{17} +8.09744 q^{19} +(-9.52143 - 10.0744i) q^{20} +(-5.44254 + 2.16494i) q^{22} +16.7598i q^{23} +12.9905 q^{25} +(-14.1625 - 35.6038i) q^{26} +(-7.26924 - 7.69144i) q^{28} -27.1649i q^{29} -44.8923i q^{31} +(10.1319 + 30.3537i) q^{32} +(-26.7415 + 10.6373i) q^{34} -9.16878 q^{35} -39.5687i q^{37} +(-15.0480 + 5.98584i) q^{38} +(25.1416 + 11.6836i) q^{40} -45.8766 q^{41} +61.0334 q^{43} +(8.51388 - 8.04653i) q^{44} +(-12.3893 - 31.1459i) q^{46} -46.2793i q^{47} -7.00000 q^{49} +(-24.1412 + 9.60292i) q^{50} +(52.6385 + 55.6957i) q^{52} +9.69424i q^{53} -10.1492i q^{55} +(19.1947 + 8.91994i) q^{56} +(20.0810 + 50.4825i) q^{58} +114.554 q^{59} +7.48032i q^{61} +(33.1855 + 83.4265i) q^{62} +(-41.2671 - 48.9186i) q^{64} +66.3935 q^{65} -12.0590 q^{67} +(41.8323 - 39.5360i) q^{68} +(17.0390 - 6.77780i) q^{70} -129.187i q^{71} -18.2854 q^{73} +(29.2502 + 73.5334i) q^{74} +(23.5400 - 22.2478i) q^{76} -7.74851i q^{77} +42.6168i q^{79} +(-55.3593 - 3.12704i) q^{80} +(85.2558 - 33.9132i) q^{82} +109.670 q^{83} -49.8673i q^{85} +(-113.423 + 45.1174i) q^{86} +(-9.87374 + 21.2471i) q^{88} +80.9162 q^{89} +50.6889 q^{91} +(46.0478 + 48.7223i) q^{92} +(34.2109 + 86.0041i) q^{94} -28.0614i q^{95} +162.086 q^{97} +(13.0086 - 5.17458i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - q^{2} + 5 q^{4} - 13 q^{8}+O(q^{10}) $ 8 * q - q^2 + 5 * q^4 - 13 * q^8	$ 8 q - q^{2} + 5 q^{4} - 13 q^{8} + 16 q^{10} + 32 q^{11} - 7 q^{14} - 71 q^{16} + 80 q^{17} + 56 q^{19} + 108 q^{20} + 66 q^{22} - 16 q^{25} - 24 q^{26} + 7 q^{28} + 19 q^{32} + 74 q^{34} - 56 q^{35} + 14 q^{38} + 84 q^{40} - 128 q^{41} - 50 q^{44} - 152 q^{46} - 56 q^{49} - 33 q^{50} + 132 q^{52} + 49 q^{56} + 24 q^{58} - 104 q^{59} - 120 q^{62} - 55 q^{64} + 72 q^{65} + 304 q^{67} + 190 q^{68} + 56 q^{70} - 112 q^{73} - 8 q^{74} + 70 q^{76} - 124 q^{80} + 450 q^{82} - 72 q^{83} - 210 q^{86} - 486 q^{88} + 512 q^{89} - 56 q^{91} + 472 q^{92} + 472 q^{94} + 64 q^{97} + 7 q^{98}+O(q^{100}) $ 8 * q - q^2 + 5 * q^4 - 13 * q^8 + 16 * q^10 + 32 * q^11 - 7 * q^14 - 71 * q^16 + 80 * q^17 + 56 * q^19 + 108 * q^20 + 66 * q^22 - 16 * q^25 - 24 * q^26 + 7 * q^28 + 19 * q^32 + 74 * q^34 - 56 * q^35 + 14 * q^38 + 84 * q^40 - 128 * q^41 - 50 * q^44 - 152 * q^46 - 56 * q^49 - 33 * q^50 + 132 * q^52 + 49 * q^56 + 24 * q^58 - 104 * q^59 - 120 * q^62 - 55 * q^64 + 72 * q^65 + 304 * q^67 + 190 * q^68 + 56 * q^70 - 112 * q^73 - 8 * q^74 + 70 * q^76 - 124 * q^80 + 450 * q^82 - 72 * q^83 - 210 * q^86 - 486 * q^88 + 512 * q^89 - 56 * q^91 + 472 * q^92 + 472 * q^94 + 64 * q^97 + 7 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$73$	$127$	$253$	$281$
$\chi(n)$	$1$	$-1$	$-1$	$1$

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 $

$2$	−1.85837	+	0.739226i	−0.929186	+	0.369613i
$2$	−1.85837	+	0.739226i	−0.929186	+	0.369613i
$3$		0			0
$3$		0			0
$4$	2.90709	−	2.74751i	0.726772	−	0.686878i
$5$		−	3.46547i		−	0.693094i	−0.938033	−	0.346547i	$-0.887354\pi$
$5$		−	3.46547i		−	0.693094i	0.938033	−	0.346547i	$-0.112646\pi$
$6$		0			0
$7$		−	2.64575i		−	0.377964i
$7$		−	2.64575i		−	0.377964i
$8$	−3.37142	+	7.25490i	−0.421428	+	0.906862i
$9$		0			0
$10$	2.56177	+	6.44013i	0.256177	+	0.644013i
$11$	2.92866			0.266242			0.133121	−	0.991100i	$-0.457500\pi$
$11$	2.92866			0.266242			0.133121	+	0.991100i	$0.457500\pi$
$12$		0			0
$13$			19.1586i			1.47374i	0.676036	+	0.736869i	$0.263696\pi$
$13$			19.1586i			1.47374i	−0.676036	+	0.736869i	$0.736304\pi$
$14$	1.95581	+	4.91679i	0.139701	+	0.351199i
$15$		0			0
$16$	0.902343	−	15.9745i	0.0563964	−	0.998408i
$17$	14.3897			0.846456			0.423228	−	0.906023i	$-0.360897\pi$
$17$	14.3897			0.846456			0.423228	+	0.906023i	$0.360897\pi$
$18$		0			0
$19$	8.09744			0.426181			0.213090	−	0.977032i	$-0.431647\pi$
$19$	8.09744			0.426181			0.213090	+	0.977032i	$0.431647\pi$
$20$	−9.52143	−	10.0744i	−0.476071	−	0.503722i
$21$		0			0
$22$	−5.44254	+	2.16494i	−0.247388	+	0.0984064i
$23$			16.7598i			0.728687i	0.931265	+	0.364344i	$0.118707\pi$
$23$			16.7598i			0.728687i	−0.931265	+	0.364344i	$0.881293\pi$
$24$		0			0
$25$	12.9905			0.519620
$26$	−14.1625	−	35.6038i	−0.544713	−	1.36938i
$27$		0			0
$28$	−7.26924	−	7.69144i	−0.259616	−	0.274694i
$29$		−	27.1649i		−	0.936720i	−0.883538	−	0.468360i	$-0.844845\pi$
$29$		−	27.1649i		−	0.936720i	0.883538	−	0.468360i	$-0.155155\pi$
$30$		0			0
$31$		−	44.8923i		−	1.44814i	−0.689728	−	0.724069i	$-0.742270\pi$
$31$		−	44.8923i		−	1.44814i	0.689728	−	0.724069i	$-0.257730\pi$
$32$	10.1319	+	30.3537i	0.316622	+	0.948552i
$33$		0			0
$34$	−26.7415	+	10.6373i	−0.786515	+	0.312861i
$35$	−9.16878			−0.261965
$36$		0			0
$37$		−	39.5687i		−	1.06943i	−0.845034	−	0.534713i	$-0.820420\pi$
$37$		−	39.5687i		−	1.06943i	0.845034	−	0.534713i	$-0.179580\pi$
$38$	−15.0480	+	5.98584i	−0.396001	+	0.157522i
$39$		0			0
$40$	25.1416	+	11.6836i	0.628541	+	0.292089i
$41$	−45.8766			−1.11894			−0.559471	−	0.828850i	$-0.688996\pi$
$41$	−45.8766			−1.11894			−0.559471	+	0.828850i	$0.688996\pi$
$42$		0			0
$43$	61.0334			1.41938			0.709690	−	0.704514i	$-0.248835\pi$
$43$	61.0334			1.41938			0.709690	+	0.704514i	$0.248835\pi$
$44$	8.51388	−	8.04653i	0.193497	−	0.182876i
$45$		0			0
$46$	−12.3893	−	31.1459i	−0.269332	−	0.677086i
$47$		−	46.2793i		−	0.984666i	−0.870407	−	0.492333i	$-0.836144\pi$
$47$		−	46.2793i		−	0.984666i	0.870407	−	0.492333i	$-0.163856\pi$
$48$		0			0
$49$	−7.00000			−0.142857
$50$	−24.1412	+	9.60292i	−0.482824	+	0.192058i
$51$		0			0
$52$	52.6385	+	55.6957i	1.01228	+	1.07107i
$53$			9.69424i			0.182910i	0.995809	+	0.0914551i	$0.0291518\pi$
$53$			9.69424i			0.182910i	−0.995809	+	0.0914551i	$0.970848\pi$
$54$		0			0
$55$		−	10.1492i		−	0.184531i
$56$	19.1947	+	8.91994i	0.342762	+	0.159285i
$57$		0			0
$58$	20.0810	+	50.4825i	0.346224	+	0.870387i
$59$	114.554			1.94159			0.970796	−	0.239907i	$-0.0771170\pi$
$59$	114.554			1.94159			0.970796	+	0.239907i	$0.0771170\pi$
$60$		0			0
$61$			7.48032i			0.122628i	0.998119	+	0.0613141i	$0.0195291\pi$
$61$			7.48032i			0.122628i	−0.998119	+	0.0613141i	$0.980471\pi$
$62$	33.1855	+	83.4265i	0.535251	+	1.34559i
$63$		0			0
$64$	−41.2671	−	48.9186i	−0.644798	−	0.764353i
$65$	66.3935			1.02144
$66$		0			0
$67$	−12.0590			−0.179985			−0.0899925	−	0.995942i	$-0.528684\pi$
$67$	−12.0590			−0.179985			−0.0899925	+	0.995942i	$0.528684\pi$
$68$	41.8323	−	39.5360i	0.615181	−	0.581412i
$69$		0			0
$70$	17.0390	−	6.77780i	0.243414	−	0.0968257i
$71$		−	129.187i		−	1.81953i	−0.415124	−	0.909765i	$-0.636262\pi$
$71$		−	129.187i		−	1.81953i	0.415124	−	0.909765i	$-0.363738\pi$
$72$		0			0
$73$	−18.2854			−0.250484			−0.125242	−	0.992126i	$-0.539971\pi$
$73$	−18.2854			−0.250484			−0.125242	+	0.992126i	$0.539971\pi$
$74$	29.2502	+	73.5334i	0.395273	+	0.993695i
$75$		0			0
$76$	23.5400	−	22.2478i	0.309737	−	0.292734i
$77$		−	7.74851i		−	0.100630i
$78$		0			0
$79$			42.6168i			0.539454i	0.962937	+	0.269727i	$0.0869334\pi$
$79$			42.6168i			0.539454i	−0.962937	+	0.269727i	$0.913067\pi$
$80$	−55.3593	−	3.12704i	−0.691991	−	0.0390880i
$81$		0			0
$82$	85.2558	−	33.9132i	1.03971	−	0.413576i
$83$	109.670			1.32133			0.660663	−	0.750683i	$-0.270275\pi$
$83$	109.670			1.32133			0.660663	+	0.750683i	$0.270275\pi$
$84$		0			0
$85$		−	49.8673i		−	0.586674i
$86$	−113.423	+	45.1174i	−1.31887	+	0.524622i
$87$		0			0
$88$	−9.87374	+	21.2471i	−0.112202	+	0.241445i
$89$	80.9162			0.909170			0.454585	−	0.890703i	$-0.349788\pi$
$89$	80.9162			0.909170			0.454585	+	0.890703i	$0.349788\pi$
$90$		0			0
$91$	50.6889			0.557020
$92$	46.0478	+	48.7223i	0.500519	+	0.529590i
$93$		0			0
$94$	34.2109	+	86.0041i	0.363945	+	0.914937i
$95$		−	28.0614i		−	0.295384i
$96$		0			0
$97$	162.086			1.67099			0.835495	−	0.549498i	$-0.185181\pi$
$97$	162.086			1.67099			0.835495	+	0.549498i	$0.185181\pi$
$98$	13.0086	−	5.17458i	0.132741	−	0.0528019i
$99$		0			0
$100$	37.7646	−	35.6916i	0.377646	−	0.356916i
$101$			106.827i			1.05769i	0.848717	+	0.528847i	$0.177375\pi$
$101$			106.827i			1.05769i	−0.848717	+	0.528847i	$0.822625\pi$
$102$		0			0
$103$		−	126.626i		−	1.22938i	−0.788768	−	0.614691i	$-0.789281\pi$
$103$		−	126.626i		−	1.22938i	0.788768	−	0.614691i	$-0.210719\pi$
$104$	−138.994	−	64.5916i	−1.33648	−	0.621074i
$105$		0			0
$106$	−7.16623	−	18.0155i	−0.0676060	−	0.169958i
$107$	−87.0191			−0.813263			−0.406632	−	0.913592i	$-0.633297\pi$
$107$	−87.0191			−0.813263			−0.406632	+	0.913592i	$0.633297\pi$
$108$		0			0
$109$			189.921i			1.74240i	0.490930	+	0.871199i	$0.336657\pi$
$109$			189.921i			1.74240i	−0.490930	+	0.871199i	$0.663343\pi$
$110$	7.50254	+	18.8610i	0.0682050	+	0.171463i
$111$		0			0
$112$	−42.2646	−	2.38737i	−0.377363	−	0.0213158i
$113$	40.1848			0.355617			0.177809	−	0.984065i	$-0.443099\pi$
$113$	40.1848			0.355617			0.177809	+	0.984065i	$0.443099\pi$
$114$		0			0
$115$	58.0806			0.505049
$116$	−74.6359	−	78.9708i	−0.643413	−	0.680783i
$117$		0			0
$118$	−212.884	+	84.6812i	−1.80410	+	0.717638i
$119$		−	38.0717i		−	0.319930i
$120$		0			0
$121$	−112.423			−0.929115
$122$	−5.52964	−	13.9012i	−0.0453249	−	0.113944i
$123$		0			0
$124$	−123.342	−	130.506i	−0.994695	−	1.05247i
$125$		−	131.655i		−	1.05324i
$126$		0			0
$127$		−	153.657i		−	1.20989i	−0.796266	−	0.604947i	$-0.793194\pi$
$127$		−	153.657i		−	1.20989i	0.796266	−	0.604947i	$-0.206806\pi$
$128$	112.851	+	60.4033i	0.881652	+	0.471901i
$129$		0			0
$130$	−123.384	+	49.0798i	−0.949107	+	0.377537i
$131$	−61.8649			−0.472251			−0.236126	−	0.971723i	$-0.575878\pi$
$131$	−61.8649			−0.472251			−0.236126	+	0.971723i	$0.575878\pi$
$132$		0			0
$133$		−	21.4238i		−	0.161081i
$134$	22.4101	−	8.91433i	0.167240	−	0.0665248i
$135$		0			0
$136$	−48.5139	+	104.396i	−0.356720	+	0.767619i
$137$	−105.943			−0.773307			−0.386653	−	0.922225i	$-0.626369\pi$
$137$	−105.943			−0.773307			−0.386653	+	0.922225i	$0.626369\pi$
$138$		0			0
$139$	−185.384			−1.33370			−0.666848	−	0.745194i	$-0.732357\pi$
$139$	−185.384			−1.33370			−0.666848	+	0.745194i	$0.732357\pi$
$140$	−26.6545	+	25.1913i	−0.190389	+	0.179938i
$141$		0			0
$142$	95.4981	+	240.077i	0.672522	+	1.69068i
$143$			56.1090i			0.392371i
$144$		0			0
$145$	−94.1392			−0.649236
$146$	33.9810	−	13.5170i	0.232747	−	0.0925823i
$147$		0			0
$148$	−108.716	−	115.030i	−0.734565	−	0.777229i
$149$			47.4096i			0.318185i	0.987264	+	0.159093i	$0.0508568\pi$
$149$			47.4096i			0.318185i	−0.987264	+	0.159093i	$0.949143\pi$
$150$		0			0
$151$		−	114.576i		−	0.758780i	−0.925237	−	0.379390i	$-0.876134\pi$
$151$		−	114.576i		−	0.758780i	0.925237	−	0.379390i	$-0.123866\pi$
$152$	−27.2999	+	58.7461i	−0.179604	+	0.386487i
$153$		0			0
$154$	5.72790	+	14.3996i	0.0371941	+	0.0935039i
$155$	−155.573			−1.00370
$156$		0			0
$157$			294.095i			1.87322i	0.350378	+	0.936608i	$0.386053\pi$
$157$			294.095i			1.87322i	−0.350378	+	0.936608i	$0.613947\pi$
$158$	−31.5035	−	79.1979i	−0.199389	−	0.501253i
$159$		0			0
$160$	105.190	−	35.1118i	0.657436	−	0.219449i
$161$	44.3423			0.275418
$162$		0			0
$163$	171.021			1.04921			0.524603	−	0.851347i	$-0.324214\pi$
$163$	171.021			1.04921			0.524603	+	0.851347i	$0.324214\pi$
$164$	−133.367	+	126.047i	−0.813216	+	0.768577i
$165$		0			0
$166$	−203.808	+	81.0709i	−1.22776	+	0.488379i
$167$			120.657i			0.722499i	0.932469	+	0.361249i	$0.117650\pi$
$167$			120.657i			0.722499i	−0.932469	+	0.361249i	$0.882350\pi$
$168$		0			0
$169$	−198.052			−1.17190
$170$	36.8632	+	92.6719i	0.216842	+	0.545129i
$171$		0			0
$172$	177.429	−	167.690i	1.03157	−	0.974942i
$173$		−	108.339i		−	0.626236i	−0.949714	−	0.313118i	$-0.898626\pi$
$173$		−	108.339i		−	0.626236i	0.949714	−	0.313118i	$-0.101374\pi$
$174$		0			0
$175$		−	34.3696i		−	0.196398i
$176$	2.64266	−	46.7840i	0.0150151	−	0.265818i
$177$		0			0
$178$	−150.372	+	59.8153i	−0.844788	+	0.336041i
$179$	161.438			0.901886			0.450943	−	0.892553i	$-0.351088\pi$
$179$	161.438			0.901886			0.450943	+	0.892553i	$0.351088\pi$
$180$		0			0
$181$			7.14696i			0.0394860i	0.999805	+	0.0197430i	$0.00628479\pi$
$181$			7.14696i			0.0394860i	−0.999805	+	0.0197430i	$0.993715\pi$
$182$	−94.1987	+	37.4705i	−0.517575	+	0.205882i
$183$		0			0
$184$	−121.591	−	56.5043i	−0.660819	−	0.307089i
$185$	−137.124			−0.741212
$186$		0			0
$187$	42.1427			0.225362
$188$	−127.153	−	134.538i	−0.676346	−	0.715628i
$189$		0			0
$190$	20.7437	+	52.1486i	0.109178	+	0.274466i
$191$		−	73.2983i		−	0.383761i	−0.981418	−	0.191880i	$-0.938541\pi$
$191$		−	73.2983i		−	0.383761i	0.981418	−	0.191880i	$-0.0614586\pi$
$192$		0			0
$193$	−85.0705			−0.440780			−0.220390	−	0.975412i	$-0.570733\pi$
$193$	−85.0705			−0.440780			−0.220390	+	0.975412i	$0.570733\pi$
$194$	−301.216	+	119.818i	−1.55266	+	0.617620i
$195$		0			0
$196$	−20.3496	+	19.2326i	−0.103825	+	0.0981255i
$197$			140.460i			0.712996i	0.934296	+	0.356498i	$0.116029\pi$
$197$			140.460i			0.712996i	−0.934296	+	0.356498i	$0.883971\pi$
$198$		0			0
$199$			143.082i			0.719006i	0.933144	+	0.359503i	$0.117054\pi$
$199$			143.082i			0.719006i	−0.933144	+	0.359503i	$0.882946\pi$
$200$	−43.7965	+	94.2448i	−0.218982	+	0.471224i
$201$		0			0
$202$	−78.9694	−	198.524i	−0.390937	−	0.982794i
$203$	−71.8715			−0.354047
$204$		0			0
$205$			158.984i			0.775532i
$206$	93.6055	+	235.319i	0.454396	+	1.14232i
$207$		0			0
$208$	306.050	+	17.2876i	1.47139	+	0.0831135i
$209$	23.7146			0.113467
$210$		0			0
$211$	−111.955			−0.530591			−0.265295	−	0.964167i	$-0.585469\pi$
$211$	−111.955			−0.530591			−0.265295	+	0.964167i	$0.585469\pi$
$212$	26.6350	+	28.1820i	0.125637	+	0.132934i
$213$		0			0
$214$	161.714	−	64.3268i	0.755672	−	0.300593i
$215$		−	211.509i		−	0.983765i
$216$		0			0
$217$	−118.774			−0.547345
$218$	−140.395	−	352.944i	−0.644013	−	1.61901i
$219$		0			0
$220$	−27.8850	−	29.5046i	−0.126750	−	0.134112i
$221$			275.687i			1.24745i
$222$		0			0
$223$		−	311.438i		−	1.39658i	−0.715814	−	0.698291i	$-0.753944\pi$
$223$		−	311.438i		−	1.39658i	0.715814	−	0.698291i	$-0.246056\pi$
$224$	80.3082	−	26.8065i	0.358519	−	0.119672i
$225$		0			0
$226$	−74.6782	+	29.7056i	−0.330435	+	0.131441i
$227$	−74.3581			−0.327569			−0.163784	−	0.986496i	$-0.552370\pi$
$227$	−74.3581			−0.327569			−0.163784	+	0.986496i	$0.552370\pi$
$228$		0			0
$229$			78.2710i			0.341795i	0.985289	+	0.170897i	$0.0546667\pi$
$229$			78.2710i			0.341795i	−0.985289	+	0.170897i	$0.945333\pi$
$230$	−107.935	+	42.9347i	−0.469284	+	0.186673i
$231$		0			0
$232$	197.078	+	91.5842i	0.849476	+	0.394760i
$233$	−93.0573			−0.399388			−0.199694	−	0.979858i	$-0.563995\pi$
$233$	−93.0573			−0.399388			−0.199694	+	0.979858i	$0.563995\pi$
$234$		0			0
$235$	−160.380			−0.682466
$236$	333.019	−	314.738i	1.41110	−	1.33364i
$237$		0			0
$238$	28.1436	+	70.7513i	0.118250	+	0.297275i
$239$		−	291.605i		−	1.22011i	−0.792361	−	0.610053i	$-0.791148\pi$
$239$		−	291.605i		−	1.22011i	0.792361	−	0.610053i	$-0.208852\pi$
$240$		0			0
$241$	223.748			0.928413			0.464207	−	0.885727i	$-0.346340\pi$
$241$	223.748			0.928413			0.464207	+	0.885727i	$0.346340\pi$
$242$	208.924	−	83.1060i	0.863321	−	0.343413i
$243$		0			0
$244$	20.5523	+	21.7459i	0.0842306	+	0.0891227i
$245$			24.2583i			0.0990135i
$246$		0			0
$247$			155.135i			0.628079i
$248$	325.689	+	151.351i	1.31326	+	0.610285i
$249$		0			0
$250$	97.3228	+	244.664i	0.389291	+	0.978656i
$251$	310.605			1.23747			0.618734	−	0.785600i	$-0.287646\pi$
$251$	310.605			1.23747			0.618734	+	0.785600i	$0.287646\pi$
$252$		0			0
$253$			49.0838i			0.194007i
$254$	113.587	+	285.551i	0.447193	+	1.12422i
$255$		0			0
$256$	−254.372	−	28.8290i	−0.993639	−	0.112613i
$257$	−175.472			−0.682769			−0.341385	−	0.939924i	$-0.610896\pi$
$257$	−175.472			−0.682769			−0.341385	+	0.939924i	$0.610896\pi$
$258$		0			0
$259$	−104.689			−0.404205
$260$	193.012	−	182.417i	0.742354	−	0.701604i
$261$		0			0
$262$	114.968	−	45.7321i	0.438809	−	0.174550i
$263$			312.127i			1.18680i	0.804910	+	0.593398i	$0.202214\pi$
$263$			312.127i			1.18680i	−0.804910	+	0.593398i	$0.797786\pi$
$264$		0			0
$265$	33.5951			0.126774
$266$	15.8370	+	39.8134i	0.0595377	+	0.149674i
$267$		0			0
$268$	−35.0566	+	33.1323i	−0.130808	+	0.123628i
$269$			142.817i			0.530918i	0.964122	+	0.265459i	$0.0855234\pi$
$269$			142.817i			0.530918i	−0.964122	+	0.265459i	$0.914477\pi$
$270$		0			0
$271$			266.117i			0.981982i	0.871165	+	0.490991i	$0.163365\pi$
$271$			266.117i			0.981982i	−0.871165	+	0.490991i	$0.836635\pi$
$272$	12.9845	−	229.870i	0.0477371	−	0.845108i
$273$		0			0
$274$	196.882	−	78.3158i	0.718546	−	0.285824i
$275$	38.0448			0.138345
$276$		0			0
$277$		−	366.740i		−	1.32397i	−0.749516	−	0.661986i	$-0.769714\pi$
$277$		−	366.740i		−	1.32397i	0.749516	−	0.661986i	$-0.230286\pi$
$278$	344.512	−	137.040i	1.23925	−	0.492951i
$279$		0			0
$280$	30.9118	−	66.5185i	0.110399	−	0.237566i
$281$	−147.977			−0.526607			−0.263303	−	0.964713i	$-0.584812\pi$
$281$	−147.977			−0.526607			−0.263303	+	0.964713i	$0.584812\pi$
$282$		0			0
$283$	327.739			1.15809			0.579043	−	0.815297i	$-0.303426\pi$
$283$	327.739			1.15809			0.579043	+	0.815297i	$0.303426\pi$
$284$	−354.942	−	375.557i	−1.24980	−	1.32238i
$285$		0			0
$286$	−41.4772	−	104.271i	−0.145025	−	0.364585i
$287$			121.378i			0.422920i
$288$		0			0
$289$	−81.9352			−0.283513
$290$	174.946	−	69.5901i	0.603260	−	0.239966i
$291$		0			0
$292$	−53.1572	+	50.2393i	−0.182045	+	0.172052i
$293$			259.881i			0.886966i	0.896283	+	0.443483i	$0.146257\pi$
$293$			259.881i			0.886966i	−0.896283	+	0.443483i	$0.853743\pi$
$294$		0			0
$295$		−	396.983i		−	1.34571i
$296$	287.067	+	133.403i	0.969821	+	0.450685i
$297$		0			0
$298$	−35.0464	−	88.1046i	−0.117605	−	0.295653i
$299$	−321.094			−1.07389
$300$		0			0
$301$		−	161.479i		−	0.536475i
$302$	84.6974	+	212.924i	0.280455	+	0.705047i
$303$		0			0
$304$	7.30666	−	129.353i	0.0240351	−	0.425503i
$305$	25.9228			0.0849929
$306$		0			0
$307$	290.462			0.946131			0.473065	−	0.881027i	$-0.343147\pi$
$307$	290.462			0.946131			0.473065	+	0.881027i	$0.343147\pi$
$308$	−21.2891	−	22.5256i	−0.0691205	−	0.0731351i
$309$		0			0
$310$	289.112	−	115.004i	0.932620	−	0.370979i
$311$		−	74.9081i		−	0.240862i	−0.992722	−	0.120431i	$-0.961572\pi$
$311$		−	74.9081i		−	0.240862i	0.992722	−	0.120431i	$-0.0384276\pi$
$312$		0			0
$313$	284.507			0.908969			0.454485	−	0.890755i	$-0.349823\pi$
$313$	284.507			0.908969			0.454485	+	0.890755i	$0.349823\pi$
$314$	−217.403	−	546.538i	−0.692365	−	1.74057i
$315$		0			0
$316$	117.090	+	123.891i	0.370539	+	0.392060i
$317$			12.2631i			0.0386850i	0.999813	+	0.0193425i	$0.00615729\pi$
$317$			12.2631i			0.0386850i	−0.999813	+	0.0193425i	$0.993843\pi$
$318$		0			0
$319$		−	79.5567i		−	0.249394i
$320$	−169.526	+	143.010i	−0.529769	+	0.446906i
$321$		0			0
$322$	−82.4044	+	32.7790i	−0.255914	+	0.101798i
$323$	116.520			0.360743
$324$		0			0
$325$			248.880i			0.765784i
$326$	−317.820	+	126.423i	−0.974908	+	0.387800i
$327$		0			0
$328$	154.669	−	332.830i	0.471553	−	1.01473i
$329$	−122.443			−0.372169
$330$		0			0
$331$	194.466			0.587510			0.293755	−	0.955881i	$-0.405095\pi$
$331$	194.466			0.587510			0.293755	+	0.955881i	$0.405095\pi$
$332$	318.821	−	301.320i	0.960303	−	0.907590i
$333$		0			0
$334$	−89.1930	−	224.226i	−0.267045	−	0.671336i
$335$			41.7901i			0.124747i
$336$		0			0
$337$	0.596077			0.00176877			0.000884387	−	1.00000i	$-0.499718\pi$
$337$	0.596077			0.00176877			0.000884387		1.00000i	$0.499718\pi$
$338$	368.053	−	146.405i	1.08892	−	0.433150i
$339$		0			0
$340$	−137.011	−	144.969i	−0.402973	−	0.426378i
$341$		−	131.474i		−	0.385555i
$342$		0			0
$343$			18.5203i			0.0539949i
$344$	−205.769	+	442.791i	−0.598166	+	1.28718i
$345$		0			0
$346$	80.0869	+	201.334i	0.231465	+	0.581890i
$347$	204.867			0.590394			0.295197	−	0.955436i	$-0.404615\pi$
$347$	204.867			0.590394			0.295197	+	0.955436i	$0.404615\pi$
$348$		0			0
$349$			128.396i			0.367898i	0.982936	+	0.183949i	$0.0588882\pi$
$349$			128.396i			0.367898i	−0.982936	+	0.183949i	$0.941112\pi$
$350$	25.4069	+	63.8716i	0.0725913	+	0.182490i
$351$		0			0
$352$	29.6729	+	88.8956i	0.0842980	+	0.252544i
$353$	190.841			0.540627			0.270314	−	0.962772i	$-0.412873\pi$
$353$	190.841			0.540627			0.270314	+	0.962772i	$0.412873\pi$
$354$		0			0
$355$	−447.692			−1.26111
$356$	235.231	−	222.318i	0.660760	−	0.624489i
$357$		0			0
$358$	−300.011	+	119.339i	−0.838020	+	0.333349i
$359$			215.704i			0.600847i	0.953806	+	0.300424i	$0.0971281\pi$
$359$			215.704i			0.600847i	−0.953806	+	0.300424i	$0.902872\pi$
$360$		0			0
$361$	−295.432			−0.818370
$362$	−5.28322	−	13.2817i	−0.0145945	−	0.0366898i
$363$		0			0
$364$	147.357	−	139.268i	0.404827	−	0.382605i
$365$			63.3674i			0.173609i
$366$		0			0
$367$			454.789i			1.23921i	0.784915	+	0.619604i	$0.212707\pi$
$367$			454.789i			1.23921i	−0.784915	+	0.619604i	$0.787293\pi$
$368$	267.730	+	15.1231i	0.727527	+	0.0410954i
$369$		0			0
$370$	254.828	−	101.366i	0.688724	−	0.273962i
$371$	25.6485			0.0691335
$372$		0			0
$373$			360.748i			0.967153i	0.875302	+	0.483576i	$0.160662\pi$
$373$			360.748i			0.967153i	−0.875302	+	0.483576i	$0.839338\pi$
$374$	−78.3168	+	31.1530i	−0.209403	+	0.0832967i
$375$		0			0
$376$	335.751	+	156.027i	0.892956	+	0.414965i
$377$	520.441			1.38048
$378$		0			0
$379$	−268.427			−0.708250			−0.354125	−	0.935198i	$-0.615221\pi$
$379$	−268.427			−0.708250			−0.354125	+	0.935198i	$0.615221\pi$
$380$	−77.0992	−	81.5771i	−0.202893	−	0.214677i
$381$		0			0
$382$	54.1840	+	136.215i	0.141843	+	0.356585i
$383$			581.532i			1.51836i	0.650881	+	0.759180i	$0.274400\pi$
$383$			581.532i			1.51836i	−0.650881	+	0.759180i	$0.725600\pi$
$384$		0			0
$385$	−26.8522			−0.0697461
$386$	158.093	−	62.8863i	0.409566	−	0.162918i
$387$		0			0
$388$	471.199	−	445.334i	1.21443	−	1.14777i
$389$		−	512.278i		−	1.31691i	−0.752620	−	0.658455i	$-0.771210\pi$
$389$		−	512.278i		−	1.31691i	0.752620	−	0.658455i	$-0.228790\pi$
$390$		0			0
$391$			241.169i			0.616801i
$392$	23.5999	−	50.7843i	0.0602039	−	0.129552i
$393$		0			0
$394$	−103.832	−	261.027i	−0.263532	−	0.662505i
$395$	147.687			0.373892
$396$		0			0
$397$			81.3250i			0.204849i	0.994741	+	0.102424i	$0.0326600\pi$
$397$			81.3250i			0.204849i	−0.994741	+	0.102424i	$0.967340\pi$
$398$	−105.770	−	265.900i	−0.265754	−	0.668090i
$399$		0			0
$400$	11.7219	−	207.517i	0.0293047	−	0.518793i
$401$	−527.441			−1.31531			−0.657657	−	0.753318i	$-0.728452\pi$
$401$	−527.441			−1.31531			−0.657657	+	0.753318i	$0.728452\pi$
$402$		0			0
$403$	860.073			2.13418
$404$	293.509	+	310.556i	0.726507	+	0.768703i
$405$		0			0
$406$	133.564	−	53.1293i	0.328975	−	0.130860i
$407$		−	115.883i		−	0.284726i
$408$		0			0
$409$	−58.6727			−0.143454			−0.0717270	−	0.997424i	$-0.522851\pi$
$409$	−58.6727			−0.143454			−0.0717270	+	0.997424i	$0.522851\pi$
$410$	−117.525	−	295.452i	−0.286647	−	0.720614i
$411$		0			0
$412$	−347.908	−	368.114i	−0.844436	−	0.893481i
$413$		−	303.081i		−	0.733853i
$414$		0			0
$415$		−	380.058i		−	0.915803i
$416$	−581.533	+	194.113i	−1.39792	+	0.466618i
$417$		0			0
$418$	−44.0706	+	17.5305i	−0.105432	+	0.0419389i
$419$	−760.704			−1.81552			−0.907761	−	0.419487i	$-0.862210\pi$
$419$	−760.704			−1.81552			−0.907761	+	0.419487i	$0.862210\pi$
$420$		0			0
$421$			46.2918i			0.109957i	0.998488	+	0.0549784i	$0.0175090\pi$
$421$			46.2918i			0.109957i	−0.998488	+	0.0549784i	$0.982491\pi$
$422$	208.053	−	82.7598i	0.493017	−	0.196113i
$423$		0			0
$424$	−70.3307	−	32.6834i	−0.165874	−	0.0770834i
$425$	186.930			0.439835
$426$		0			0
$427$	19.7911			0.0463491
$428$	−252.972	+	239.086i	−0.591057	+	0.558613i
$429$		0			0
$430$	156.353	+	393.063i	0.363612	+	0.914100i
$431$		−	336.176i		−	0.779991i	−0.920817	−	0.389996i	$-0.872477\pi$
$431$		−	336.176i		−	0.779991i	0.920817	−	0.389996i	$-0.127523\pi$
$432$		0			0
$433$	−372.694			−0.860725			−0.430363	−	0.902656i	$-0.641614\pi$
$433$	−372.694			−0.860725			−0.430363	+	0.902656i	$0.641614\pi$
$434$	220.726	−	87.8007i	0.508585	−	0.202306i
$435$		0			0
$436$	521.811	+	552.118i	1.19682	+	1.26633i
$437$			135.711i			0.310553i
$438$		0			0
$439$		−	397.478i		−	0.905418i	−0.891658	−	0.452709i	$-0.850458\pi$
$439$		−	397.478i		−	0.905418i	0.891658	−	0.452709i	$-0.149542\pi$
$440$	73.6313	+	34.2172i	0.167344	+	0.0777663i
$441$		0			0
$442$	−203.795	−	512.329i	−0.461075	−	1.15912i
$443$	−273.530			−0.617450			−0.308725	−	0.951151i	$-0.599902\pi$
$443$	−273.530			−0.617450			−0.308725	+	0.951151i	$0.599902\pi$
$444$		0			0
$445$		−	280.413i		−	0.630141i
$446$	230.223	+	578.767i	0.516195	+	1.29768i
$447$		0			0
$448$	−129.426	+	109.182i	−0.288898	+	0.243711i
$449$	−428.702			−0.954792			−0.477396	−	0.878688i	$-0.658419\pi$
$449$	−428.702			−0.954792			−0.477396	+	0.878688i	$0.658419\pi$
$450$		0			0
$451$	−134.357			−0.297909
$452$	116.821	−	110.408i	0.258453	−	0.244266i
$453$		0			0
$454$	138.185	−	54.9674i	0.304372	−	0.121074i
$455$		−	175.661i		−	0.386068i
$456$		0			0
$457$	10.0500			0.0219913			0.0109956	−	0.999940i	$-0.496500\pi$
$457$	10.0500			0.0219913			0.0109956	+	0.999940i	$0.496500\pi$
$458$	−57.8600	−	145.457i	−0.126332	−	0.317591i
$459$		0			0
$460$	168.846	−	159.577i	0.367056	−	0.346907i
$461$			825.802i			1.79133i	0.444732	+	0.895664i	$0.353299\pi$
$461$			825.802i			1.79133i	−0.444732	+	0.895664i	$0.646701\pi$
$462$		0			0
$463$		−	114.707i		−	0.247748i	−0.992298	−	0.123874i	$-0.960468\pi$
$463$		−	114.707i		−	0.247748i	0.992298	−	0.123874i	$-0.0395318\pi$
$464$	−433.946	−	24.5120i	−0.935229	−	0.0528277i
$465$		0			0
$466$	172.935	−	68.7904i	0.371105	−	0.147619i
$467$	201.727			0.431964			0.215982	−	0.976397i	$-0.430705\pi$
$467$	201.727			0.431964			0.215982	+	0.976397i	$0.430705\pi$
$468$		0			0
$469$			31.9051i			0.0680280i
$470$	298.045	−	118.557i	0.634138	−	0.252248i
$471$		0			0
$472$	−386.209	+	831.077i	−0.818240	+	1.76076i
$473$	178.746			0.377899
$474$		0			0
$475$	105.190			0.221452
$476$	−104.602	−	110.678i	−0.219753	−	0.232516i
$477$		0			0
$478$	215.562	+	541.911i	0.450967	+	1.13371i
$479$			597.538i			1.24747i	0.781636	+	0.623735i	$0.214385\pi$
$479$			597.538i			1.24747i	−0.781636	+	0.623735i	$0.785615\pi$
$480$		0			0
$481$	758.081			1.57605
$482$	−415.806	+	165.400i	−0.862668	+	0.343154i
$483$		0			0
$484$	−326.824	+	308.884i	−0.675255	+	0.638189i
$485$		−	561.705i		−	1.15815i
$486$		0			0
$487$			345.125i			0.708675i	0.935118	+	0.354337i	$0.115294\pi$
$487$			345.125i			0.708675i	−0.935118	+	0.354337i	$0.884706\pi$
$488$	−54.2689	−	25.2193i	−0.111207	−	0.0516789i
$489$		0			0
$490$	−17.9324	−	45.0809i	−0.0365967	−	0.0920019i
$491$	−373.498			−0.760689			−0.380344	−	0.924845i	$-0.624195\pi$
$491$	−373.498			−0.760689			−0.380344	+	0.924845i	$0.624195\pi$
$492$		0			0
$493$		−	390.896i		−	0.792892i
$494$	−114.680	−	288.299i	−0.232146	−	0.583602i
$495$		0			0
$496$	−717.133	−	40.5082i	−1.44583	−	0.0816698i
$497$	−341.796			−0.687718
$498$		0			0
$499$	−850.317			−1.70404			−0.852021	−	0.523508i	$-0.824623\pi$
$499$	−850.317			−1.70404			−0.852021	+	0.523508i	$0.824623\pi$
$500$	−361.724	−	382.733i	−0.723448	−	0.765466i
$501$		0			0
$502$	−577.219	+	229.607i	−1.14984	+	0.457384i
$503$			459.256i			0.913033i	0.889715	+	0.456517i	$0.150903\pi$
$503$			459.256i			0.913033i	−0.889715	+	0.456517i	$0.849097\pi$
$504$		0			0
$505$	370.206			0.733082
$506$	−36.2840	−	91.2159i	−0.0717075	−	0.180269i
$507$		0			0
$508$	−422.174	−	446.694i	−0.831050	−	0.879318i
$509$			673.910i			1.32399i	0.749509	+	0.661994i	$0.230290\pi$
$509$			673.910i			1.32399i	−0.749509	+	0.661994i	$0.769710\pi$
$510$		0			0
$511$			48.3785i			0.0946742i
$512$	494.028	−	134.463i	0.964898	−	0.262623i
$513$		0			0
$514$	326.092	−	129.713i	0.634419	−	0.252360i
$515$	−438.820			−0.852078
$516$		0			0
$517$		−	135.536i		−	0.262159i
$518$	194.551	−	77.3888i	0.375581	−	0.149399i
$519$		0			0
$520$	−223.841	+	481.678i	−0.430463	+	0.926304i
$521$	486.473			0.933729			0.466864	−	0.884329i	$-0.345384\pi$
$521$	486.473			0.933729			0.466864	+	0.884329i	$0.345384\pi$
$522$		0			0
$523$	−680.087			−1.30036			−0.650179	−	0.759781i	$-0.725306\pi$
$523$	−680.087			−1.30036			−0.650179	+	0.759781i	$0.725306\pi$
$524$	−179.847	+	169.975i	−0.343219	+	0.324379i
$525$		0			0
$526$	−230.732	−	580.048i	−0.438655	−	1.10275i
$527$		−	645.988i		−	1.22578i
$528$		0			0
$529$	248.109			0.469015
$530$	−62.4322	+	24.8344i	−0.117797	+	0.0468573i
$531$		0			0
$532$	−58.8622	−	62.2809i	−0.110643	−	0.117069i
$533$		−	878.931i		−	1.64903i
$534$		0			0
$535$			301.562i			0.563668i
$536$	40.6559	−	87.4868i	0.0758507	−	0.163222i
$537$		0			0
$538$	−105.574	−	265.407i	−0.196234	−	0.493321i
$539$	−20.5006			−0.0380346
$540$		0			0
$541$		−	794.999i		−	1.46950i	−0.678339	−	0.734749i	$-0.737300\pi$
$541$		−	794.999i		−	1.46950i	0.678339	−	0.734749i	$-0.262700\pi$
$542$	−196.721	−	494.544i	−0.362953	−	0.912444i
$543$		0			0
$544$	145.796	+	436.781i	0.268006	+	0.802907i
$545$	658.167			1.20765
$546$		0			0
$547$	−736.752			−1.34690			−0.673448	−	0.739235i	$-0.735187\pi$
$547$	−736.752			−1.34690			−0.673448	+	0.739235i	$0.735187\pi$
$548$	−307.986	+	291.080i	−0.562018	+	0.531168i
$549$		0			0
$550$	−70.7013	+	28.1237i	−0.128548	+	0.0511340i
$551$		−	219.966i		−	0.399212i
$552$		0			0
$553$	112.754			0.203894
$554$	271.104	+	681.540i	0.489357	+	1.23022i
$555$		0			0
$556$	−538.927	+	509.344i	−0.969294	+	0.916087i
$557$			415.758i			0.746423i	0.927746	+	0.373212i	$0.121743\pi$
$557$			415.758i			0.746423i	−0.927746	+	0.373212i	$0.878257\pi$
$558$		0			0
$559$			1169.31i			2.09179i
$560$	−8.27338	+	146.467i	−0.0147739	+	0.261548i
$561$		0			0
$562$	274.995	−	109.388i	0.489316	−	0.194641i
$563$	96.4996			0.171402			0.0857012	−	0.996321i	$-0.472687\pi$
$563$	96.4996			0.171402			0.0857012	+	0.996321i	$0.472687\pi$
$564$		0			0
$565$		−	139.259i		−	0.246476i
$566$	−609.060	+	242.273i	−1.07608	+	0.428044i
$567$		0			0
$568$	937.235	+	435.542i	1.65006	+	0.766800i
$569$	−347.953			−0.611517			−0.305759	−	0.952109i	$-0.598910\pi$
$569$	−347.953			−0.611517			−0.305759	+	0.952109i	$0.598910\pi$
$570$		0			0
$571$	−13.7251			−0.0240370			−0.0120185	−	0.999928i	$-0.503826\pi$
$571$	−13.7251			−0.0240370			−0.0120185	+	0.999928i	$0.503826\pi$
$572$	154.160	+	163.114i	0.269511	+	0.285164i
$573$		0			0
$574$	−89.7259	−	225.566i	−0.156317	−	0.392972i
$575$			217.718i			0.378641i
$576$		0			0
$577$	−827.320			−1.43383			−0.716915	−	0.697161i	$-0.754446\pi$
$577$	−827.320			−1.43383			−0.716915	+	0.697161i	$0.754446\pi$
$578$	152.266	−	60.5686i	0.263436	−	0.104790i
$579$		0			0
$580$	−273.671	+	258.649i	−0.471847	+	0.445946i
$581$		−	290.160i		−	0.499414i
$582$		0			0
$583$			28.3911i			0.0486983i
$584$	61.6476	−	132.658i	0.105561	−	0.227155i
$585$		0			0
$586$	−192.111	−	482.955i	−0.327834	−	0.824156i
$587$	675.987			1.15160			0.575798	−	0.817592i	$-0.304692\pi$
$587$	675.987			1.15160			0.575798	+	0.817592i	$0.304692\pi$
$588$		0			0
$589$		−	363.512i		−	0.617169i
$590$	293.460	+	737.743i	0.497391	+	1.25041i
$591$		0			0
$592$	−632.092	−	35.7046i	−1.06772	−	0.0603118i
$593$	414.116			0.698341			0.349171	−	0.937059i	$-0.386463\pi$
$593$	414.116			0.698341			0.349171	+	0.937059i	$0.386463\pi$
$594$		0			0
$595$	−131.936			−0.221742
$596$	130.258	+	137.824i	0.218554	+	0.231248i
$597$		0			0
$598$	596.712	−	237.361i	0.997847	−	0.396925i
$599$		−	723.303i		−	1.20752i	−0.797167	−	0.603759i	$-0.793669\pi$
$599$		−	723.303i		−	1.20752i	0.797167	−	0.603759i	$-0.206331\pi$
$600$		0			0
$601$	68.7503			0.114393			0.0571966	−	0.998363i	$-0.481784\pi$
$601$	68.7503			0.114393			0.0571966	+	0.998363i	$0.481784\pi$
$602$	119.370	+	300.088i	0.198288	+	0.498485i
$603$		0			0
$604$	−314.798	−	333.082i	−0.521189	−	0.551460i
$605$			389.599i			0.643965i
$606$		0			0
$607$			141.263i			0.232724i	0.993207	+	0.116362i	$0.0371232\pi$
$607$			141.263i			0.232724i	−0.993207	+	0.116362i	$0.962877\pi$
$608$	82.0424	+	245.787i	0.134938	+	0.404255i
$609$		0			0
$610$	−48.1742	+	19.1628i	−0.0789742	+	0.0314145i
$611$	886.646			1.45114
$612$		0			0
$613$			96.7370i			0.157809i	0.996882	+	0.0789046i	$0.0251422\pi$
$613$			96.7370i			0.157809i	−0.996882	+	0.0789046i	$0.974858\pi$
$614$	−539.787	+	214.717i	−0.879131	+	0.349702i
$615$		0			0
$616$	56.2146	+	26.1235i	0.0912575	+	0.0424082i
$617$	−580.418			−0.940709			−0.470355	−	0.882478i	$-0.655874\pi$
$617$	−580.418			−0.940709			−0.470355	+	0.882478i	$0.655874\pi$
$618$		0			0
$619$	157.945			0.255161			0.127581	−	0.991828i	$-0.459279\pi$
$619$	157.945			0.255161			0.127581	+	0.991828i	$0.459279\pi$
$620$	−452.264	+	427.439i	−0.729459	+	0.689417i
$621$		0			0
$622$	55.3740	+	139.207i	0.0890257	+	0.223806i
$623$		−	214.084i		−	0.343634i
$624$		0			0
$625$	−131.484			−0.210375
$626$	−528.720	+	210.315i	−0.844601	+	0.335967i
$627$		0			0
$628$	808.030	+	854.961i	1.28667	+	1.36140i
$629$		−	569.384i		−	0.905221i
$630$		0			0
$631$			771.793i			1.22313i	0.791195	+	0.611564i	$0.209459\pi$
$631$			771.793i			1.22313i	−0.791195	+	0.611564i	$0.790541\pi$
$632$	−309.181	−	143.679i	−0.489210	−	0.227341i
$633$		0			0
$634$	−9.06523	−	22.7895i	−0.0142985	−	0.0359455i
$635$	−532.493			−0.838571
$636$		0			0
$637$		−	134.110i		−	0.210534i
$638$	58.8104	+	147.846i	0.0921793	+	0.231733i
$639$		0			0
$640$	209.326	−	391.083i	0.327072	−	0.611068i
$641$	586.903			0.915605			0.457802	−	0.889054i	$-0.348637\pi$
$641$	586.903			0.915605			0.457802	+	0.889054i	$0.348637\pi$
$642$		0			0
$643$	865.328			1.34577			0.672883	−	0.739749i	$-0.265056\pi$
$643$	865.328			1.34577			0.672883	+	0.739749i	$0.265056\pi$
$644$	128.907	−	121.831i	0.200166	−	0.189179i
$645$		0			0
$646$	−216.538	+	86.1347i	−0.335197	+	0.133335i
$647$			132.883i			0.205383i	0.994713	+	0.102691i	$0.0327454\pi$
$647$			132.883i			0.205383i	−0.994713	+	0.102691i	$0.967255\pi$
$648$		0			0
$649$	335.489			0.516933
$650$	−183.978	−	462.511i	−0.283044	−	0.711555i
$651$		0			0
$652$	497.173	−	469.882i	0.762535	−	0.720677i
$653$		−	364.309i		−	0.557900i	−0.960306	−	0.278950i	$-0.910014\pi$
$653$		−	364.309i		−	0.557900i	0.960306	−	0.278950i	$-0.0899865\pi$
$654$		0			0
$655$			214.391i			0.327315i
$656$	−41.3964	+	732.858i	−0.0631043	+	1.11716i
$657$		0			0
$658$	227.546	−	90.5134i	0.345814	−	0.137558i
$659$	18.8972			0.0286756			0.0143378	−	0.999897i	$-0.495436\pi$
$659$	18.8972			0.0286756			0.0143378	+	0.999897i	$0.495436\pi$
$660$		0			0
$661$		−	339.106i		−	0.513019i	−0.966542	−	0.256510i	$-0.917427\pi$
$661$		−	339.106i		−	0.513019i	0.966542	−	0.256510i	$-0.0825725\pi$
$662$	−361.390	+	143.754i	−0.545906	+	0.217151i
$663$		0			0
$664$	−369.744	+	795.645i	−0.556843	+	1.19826i
$665$	−74.2436			−0.111644
$666$		0			0
$667$	455.278			0.682576
$668$	331.508	+	350.762i	0.496269	+	0.525092i
$669$		0			0
$670$	−30.8923	−	77.6616i	−0.0461080	−	0.115913i
$671$			21.9073i			0.0326487i
$672$		0			0
$673$	674.869			1.00278			0.501389	−	0.865222i	$-0.332823\pi$
$673$	674.869			1.00278			0.501389	+	0.865222i	$0.332823\pi$
$674$	−1.10773	+	0.440635i	−0.00164352	+	0.000653762i
$675$		0			0
$676$	−575.754	+	544.149i	−0.851706	+	0.804954i
$677$		−	988.747i		−	1.46048i	−0.683189	−	0.730242i	$-0.739407\pi$
$677$		−	988.747i		−	1.46048i	0.683189	−	0.730242i	$-0.260593\pi$
$678$		0			0
$679$		−	428.839i		−	0.631575i
$680$	361.782	+	168.123i	0.532032	+	0.247240i
$681$		0			0
$682$	97.1892	+	244.328i	0.142506	+	0.358252i
$683$	518.125			0.758602			0.379301	−	0.925273i	$-0.376165\pi$
$683$	518.125			0.758602			0.379301	+	0.925273i	$0.376165\pi$
$684$		0			0
$685$			367.143i			0.535975i
$686$	−13.6907	−	34.4175i	−0.0199572	−	0.0501713i
$687$		0			0
$688$	55.0730	−	974.980i	0.0800480	−	1.41712i
$689$	−185.728			−0.269562
$690$		0			0
$691$	−617.021			−0.892940			−0.446470	−	0.894799i	$-0.647319\pi$
$691$	−617.021			−0.892940			−0.446470	+	0.894799i	$0.647319\pi$
$692$	−297.662	−	314.951i	−0.430148	−	0.455131i
$693$		0			0
$694$	−380.718	+	151.443i	−0.548585	+	0.218217i
$695$			642.442i			0.924377i
$696$		0			0
$697$	−660.153			−0.947135
$698$	−94.9140	−	238.608i	−0.135980	−	0.341846i
$699$		0			0
$700$	−94.4311	−	99.9157i	−0.134902	−	0.142737i
$701$		−	97.6954i		−	0.139366i	−0.997569	−	0.0696829i	$-0.977801\pi$
$701$		−	97.6954i		−	0.139366i	0.997569	−	0.0696829i	$-0.0221987\pi$
$702$		0			0
$703$		−	320.405i		−	0.455768i
$704$	−120.857	−	143.266i	−0.171672	−	0.203503i
$705$		0			0
$706$	−354.654	+	141.075i	−0.502343	+	0.199823i
$707$	282.638			0.399771
$708$		0			0
$709$		−	1249.74i		−	1.76269i	−0.472476	−	0.881343i	$-0.656640\pi$
$709$		−	1249.74i		−	1.76269i	0.472476	−	0.881343i	$-0.343360\pi$
$710$	831.979	−	330.946i	1.17180	−	0.466121i
$711$		0			0
$712$	−272.802	+	587.038i	−0.383149	+	0.824492i
$713$	752.386			1.05524
$714$		0			0
$715$	194.444			0.271950
$716$	469.314	−	443.552i	0.655466	−	0.619486i
$717$		0			0
$718$	−159.454	−	400.859i	−0.222081	−	0.558299i
$719$		−	424.744i		−	0.590743i	−0.955382	−	0.295372i	$-0.904557\pi$
$719$		−	424.744i		−	0.590743i	0.955382	−	0.295372i	$-0.0954435\pi$
$720$		0			0
$721$	−335.022			−0.464663
$722$	549.022	−	218.391i	0.760418	−	0.302480i
$723$		0			0
$724$	19.6364	+	20.7768i	0.0271220	+	0.0286973i
$725$		−	352.886i		−	0.486739i
$726$		0			0
$727$			79.1445i			0.108865i	0.998517	+	0.0544323i	$0.0173349\pi$
$727$			79.1445i			0.108865i	−0.998517	+	0.0544323i	$0.982665\pi$
$728$	−170.893	+	367.742i	−0.234744	+	0.505141i
$729$		0			0
$730$	−46.8428	−	117.760i	−0.0641683	−	0.161315i
$731$	878.255			1.20144
$732$		0			0
$733$			663.766i			0.905548i	0.891625	+	0.452774i	$0.149566\pi$
$733$			663.766i			0.905548i	−0.891625	+	0.452774i	$0.850434\pi$
$734$	−336.192	−	845.167i	−0.458027	−	1.15145i
$735$		0			0
$736$	−508.721	+	169.809i	−0.691198	+	0.230718i
$737$	−35.3167			−0.0479196
$738$		0			0
$739$	832.112			1.12600			0.562998	−	0.826458i	$-0.309648\pi$
$739$	832.112			1.12600			0.562998	+	0.826458i	$0.309648\pi$
$740$	−398.633	+	376.751i	−0.538693	+	0.509123i
$741$		0			0
$742$	−47.6645	+	18.9601i	−0.0642379	+	0.0255527i
$743$			283.217i			0.381180i	0.981670	+	0.190590i	$0.0610401\pi$
$743$			283.217i			0.381180i	−0.981670	+	0.190590i	$0.938960\pi$
$744$		0			0
$745$	164.297			0.220532
$746$	−266.674	−	670.404i	−0.357472	−	0.898665i
$747$		0			0
$748$	122.513	−	115.788i	0.163787	−	0.154796i
$749$			230.231i			0.307385i
$750$		0			0
$751$			374.981i			0.499309i	0.968335	+	0.249654i	$0.0803170\pi$
$751$			374.981i			0.499309i	−0.968335	+	0.249654i	$0.919683\pi$
$752$	−739.290	−	41.7598i	−0.983099	−	0.0555316i
$753$		0			0
$754$	−967.173	+	384.723i	−1.28272	+	0.510243i
$755$	−397.059			−0.525906
$756$		0			0
$757$			63.0951i			0.0833488i	0.999131	+	0.0416744i	$0.0132692\pi$
$757$			63.0951i			0.0833488i	−0.999131	+	0.0416744i	$0.986731\pi$
$758$	498.837	−	198.428i	0.658096	−	0.261779i
$759$		0			0
$760$	203.583	+	94.6069i	0.267872	+	0.124483i
$761$	−467.505			−0.614330			−0.307165	−	0.951656i	$-0.599380\pi$
$761$	−467.505			−0.614330			−0.307165	+	0.951656i	$0.599380\pi$
$762$		0			0
$763$	502.485			0.658564
$764$	−201.388	−	213.085i	−0.263597	−	0.278907i
$765$		0			0
$766$	−429.884	−	1080.70i	−0.561206	−	1.41084i
$767$			2194.69i			2.86140i
$768$		0			0
$769$	900.573			1.17110			0.585548	−	0.810638i	$-0.300879\pi$
$769$	900.573			1.17110			0.585548	+	0.810638i	$0.300879\pi$
$770$	49.9014	−	19.8499i	0.0648070	−	0.0257790i
$771$		0			0
$772$	−247.308	+	233.732i	−0.320347	+	0.302762i
$773$		−	1222.76i		−	1.58184i	−0.611920	−	0.790919i	$-0.709603\pi$
$773$		−	1222.76i		−	1.58184i	0.611920	−	0.790919i	$-0.290397\pi$
$774$		0			0
$775$		−	583.173i		−	0.752482i
$776$	−546.460	+	1175.92i	−0.704201	+	1.51536i
$777$		0			0
$778$	378.689	+	952.003i	0.486747	+	1.22365i
$779$	−371.483			−0.476872
$780$		0			0
$781$		−	378.344i		−	0.484435i
$782$	−178.279	−	448.182i	−0.227978	−	0.573123i
$783$		0			0
$784$	−6.31640	+	111.822i	−0.00805663	+	0.142630i
$785$	1019.18			1.29832
$786$		0			0
$787$	862.942			1.09650			0.548248	−	0.836316i	$-0.315295\pi$
$787$	862.942			1.09650			0.548248	+	0.836316i	$0.315295\pi$
$788$	385.916	+	408.330i	0.489741	+	0.518186i
$789$		0			0
$790$	−274.458	+	109.174i	−0.347415	+	0.138195i
$791$		−	106.319i		−	0.134411i
$792$		0			0
$793$	−143.312			−0.180722
$794$	−60.1175	−	151.132i	−0.0757148	−	0.190343i
$795$		0			0
$796$	393.120	+	415.953i	0.493869	+	0.522554i
$797$			1078.34i			1.35300i	0.736442	+	0.676500i	$0.236504\pi$
$797$			1078.34i			1.35300i	−0.736442	+	0.676500i	$0.763496\pi$
$798$		0			0
$799$		−	665.947i		−	0.833476i
$800$	131.619	+	394.309i	0.164523	+	0.492887i
$801$		0			0
$802$	980.180	−	389.898i	1.22217	−	0.486157i
$803$	−53.5516			−0.0666894
$804$		0			0
$805$		−	153.667i		−	0.190891i
$806$	−1598.33	+	635.788i	−1.98305	+	0.788819i
$807$		0			0
$808$	−775.020	−	360.159i	−0.959183	−	0.445741i
$809$	−333.388			−0.412099			−0.206050	−	0.978542i	$-0.566061\pi$
$809$	−333.388			−0.412099			−0.206050	+	0.978542i	$0.566061\pi$
$810$		0			0
$811$	−1246.04			−1.53642			−0.768211	−	0.640197i	$-0.778853\pi$
$811$	−1246.04			−1.53642			−0.768211	+	0.640197i	$0.778853\pi$
$812$	−208.937	+	197.468i	−0.257312	+	0.243187i
$813$		0			0
$814$	85.6640	+	215.354i	0.105238	+	0.264563i
$815$		−	592.667i		−	0.727199i
$816$		0			0
$817$	494.214			0.604913
$818$	109.036	−	43.3724i	0.133295	−	0.0530224i
$819$		0			0
$820$	436.811	+	462.181i	0.532696	+	0.563636i
$821$		−	1458.68i		−	1.77671i	−0.459162	−	0.888353i	$-0.651850\pi$
$821$		−	1458.68i		−	1.77671i	0.459162	−	0.888353i	$-0.348150\pi$
$822$		0			0
$823$			464.047i			0.563848i	0.959437	+	0.281924i	$0.0909725\pi$
$823$			464.047i			0.563848i	−0.959437	+	0.281924i	$0.909027\pi$
$824$	918.661	+	426.911i	1.11488	+	0.518095i
$825$		0			0
$826$	224.045	+	563.237i	0.271241	+	0.681885i
$827$	−1077.41			−1.30279			−0.651394	−	0.758739i	$-0.725816\pi$
$827$	−1077.41			−1.30279			−0.651394	+	0.758739i	$0.725816\pi$
$828$		0			0
$829$		−	35.9354i		−	0.0433479i	−0.999765	−	0.0216740i	$-0.993100\pi$
$829$		−	35.9354i		−	0.0433479i	0.999765	−	0.0216740i	$-0.00689958\pi$
$830$	280.949	+	706.290i	0.338493	+	0.850951i
$831$		0			0
$832$	937.211	−	790.619i	1.12646	−	0.950263i
$833$	−100.728			−0.120922
$834$		0			0
$835$	418.134			0.500760
$836$	68.9406	−	65.1563i	0.0824648	−	0.0779381i
$837$		0			0
$838$	1413.67	−	562.332i	1.68696	−	0.671041i
$839$			734.676i			0.875656i	0.899059	+	0.437828i	$0.144252\pi$
$839$			734.676i			0.875656i	−0.899059	+	0.437828i	$0.855748\pi$
$840$		0			0
$841$	103.069			0.122555
$842$	−34.2201	−	86.0274i	−0.0406415	−	0.102170i
$843$		0			0
$844$	−325.462	+	307.597i	−0.385619	+	0.364451i
$845$			686.342i			0.812239i
$846$		0			0
$847$			297.443i			0.351173i
$848$	154.861	+	8.74753i	0.182619	+	0.0103155i
$849$		0			0
$850$	−347.386	+	138.184i	−0.408689	+	0.162569i
$851$	663.164			0.779276
$852$		0			0
$853$		−	402.566i		−	0.471942i	−0.971760	−	0.235971i	$-0.924173\pi$
$853$		−	402.566i		−	0.471942i	0.971760	−	0.235971i	$-0.0758270\pi$
$854$	−36.7791	+	14.6301i	−0.0430669	+	0.0171312i
$855$		0			0
$856$	293.378	−	631.315i	0.342731	−	0.737517i
$857$	−552.003			−0.644110			−0.322055	−	0.946721i	$-0.604374\pi$
$857$	−552.003			−0.644110			−0.322055	+	0.946721i	$0.604374\pi$
$858$		0			0
$859$	−330.117			−0.384303			−0.192152	−	0.981365i	$-0.561547\pi$
$859$	−330.117			−0.384303			−0.192152	+	0.981365i	$0.561547\pi$
$860$	−581.125	−	614.877i	−0.675727	−	0.714973i
$861$		0			0
$862$	248.510	+	624.740i	0.288295	+	0.724757i
$863$		−	1116.67i		−	1.29394i	−0.762516	−	0.646969i	$-0.776036\pi$
$863$		−	1116.67i		−	1.29394i	0.762516	−	0.646969i	$-0.223964\pi$
$864$		0			0
$865$	−375.445			−0.434041
$866$	692.604	−	275.505i	0.799774	−	0.318135i
$867$		0			0
$868$	−345.286	+	326.333i	−0.397795	+	0.375959i
$869$			124.810i			0.143625i
$870$		0			0
$871$		−	231.033i		−	0.265251i
$872$	−1377.86	−	640.305i	−1.58011	−	0.734294i
$873$		0			0
$874$	−100.321	−	252.202i	−0.114784	−	0.288561i
$875$	−348.326			−0.398087
$876$		0			0
$877$		−	0.747441i		−	0.000852270i	−1.00000		0.000426135i	$-0.999864\pi$
$877$		−	0.747441i		−	0.000852270i	1.00000		0.000426135i	$-0.000135643\pi$
$878$	293.826	+	738.662i	0.334654	+	0.841301i
$879$		0			0
$880$	−162.129	−	9.15805i	−0.184237	−	0.0104069i
$881$	247.826			0.281301			0.140650	−	0.990059i	$-0.455081\pi$
$881$	247.826			0.281301			0.140650	+	0.990059i	$0.455081\pi$
$882$		0			0
$883$	−1613.74			−1.82757			−0.913784	−	0.406200i	$-0.866854\pi$
$883$	−1613.74			−1.82757			−0.913784	+	0.406200i	$0.866854\pi$
$884$	757.454	+	801.448i	0.856849	+	0.906615i
$885$		0			0
$886$	508.321	−	202.201i	0.573726	−	0.228217i
$887$		−	1110.59i		−	1.25207i	−0.779795	−	0.626034i	$-0.784677\pi$
$887$		−	1110.59i		−	1.25207i	0.779795	−	0.626034i	$-0.215323\pi$
$888$		0			0
$889$	−406.537			−0.457297
$890$	207.288	+	521.111i	0.232908	+	0.585518i
$891$		0			0
$892$	−855.680	−	905.378i	−0.959282	−	1.01500i
$893$		−	374.744i		−	0.419646i
$894$		0			0
$895$		−	559.458i		−	0.625092i
$896$	159.812	−	298.577i	0.178362	−	0.333233i
$897$		0			0
$898$	796.687	−	316.907i	0.887179	−	0.352904i
$899$	−1219.49			−1.35650
$900$		0			0
$901$			139.498i			0.154825i
$902$	249.685	−	99.3202i	0.276813	−	0.110111i
$903$		0			0
$904$	−135.480	+	291.536i	−0.149867	+	0.322496i
$905$	24.7676			0.0273675
$906$		0			0
$907$	−518.009			−0.571123			−0.285562	−	0.958360i	$-0.592180\pi$
$907$	−518.009			−0.571123			−0.285562	+	0.958360i	$0.592180\pi$
$908$	−216.166	+	204.300i	−0.238068	+	0.225000i
$909$		0			0
$910$	129.853	+	326.443i	0.142696	+	0.358729i
$911$		−	1065.61i		−	1.16972i	−0.811135	−	0.584860i	$-0.801150\pi$
$911$		−	1065.61i		−	1.16972i	0.811135	−	0.584860i	$-0.198850\pi$
$912$		0			0
$913$	321.186			0.351792
$914$	−18.6767	+	7.42923i	−0.0204340	+	0.00812826i
$915$		0			0
$916$	215.051	+	227.541i	0.234772	+	0.248407i
$917$			163.679i			0.178494i
$918$		0			0
$919$			1183.66i			1.28799i	0.765030	+	0.643994i	$0.222724\pi$
$919$			1183.66i			1.28799i	−0.765030	+	0.643994i	$0.777276\pi$
$920$	−195.814	+	421.369i	−0.212842	+	0.458010i
$921$		0			0
$922$	−610.454	−	1534.65i	−0.662098	−	1.66448i
$923$	2475.03			2.68151
$924$		0			0
$925$		−	514.018i		−	0.555695i
$926$	84.7946	+	213.169i	0.0915708	+	0.230204i
$927$		0			0
$928$	824.554	−	275.232i	0.888528	−	0.296586i
$929$	379.019			0.407986			0.203993	−	0.978972i	$-0.434608\pi$
$929$	379.019			0.407986			0.203993	+	0.978972i	$0.434608\pi$
$930$		0			0
$931$	−56.6821			−0.0608830
$932$	−270.526	+	255.676i	−0.290264	+	0.274331i
$933$		0			0
$934$	−374.884	+	149.122i	−0.401375	+	0.159660i
$935$		−	146.044i		−	0.156197i
$936$		0			0
$937$	1316.09			1.40458			0.702289	−	0.711892i	$-0.252161\pi$
$937$	1316.09			1.40458			0.702289	+	0.711892i	$0.252161\pi$
$938$	−23.5851	−	59.2916i	−0.0251440	−	0.0632106i
$939$		0			0
$940$	−466.238	+	440.645i	−0.495998	+	0.468771i
$941$		−	497.031i		−	0.528194i	−0.964496	−	0.264097i	$-0.914926\pi$
$941$		−	497.031i		−	0.528194i	0.964496	−	0.264097i	$-0.0850739\pi$
$942$		0			0
$943$		−	768.883i		−	0.815359i
$944$	103.367	−	1829.95i	0.109499	−	1.93850i
$945$		0			0
$946$	−332.176	+	132.134i	−0.351138	+	0.139676i
$947$	−808.487			−0.853735			−0.426867	−	0.904314i	$-0.640383\pi$
$947$	−808.487			−0.853735			−0.426867	+	0.904314i	$0.640383\pi$
$948$		0			0
$949$		−	350.322i		−	0.369148i
$950$	−195.482	+	77.7590i	−0.205770	+	0.0818516i
$951$		0			0
$952$	276.206	+	128.356i	0.290133	+	0.134827i
$953$	1345.58			1.41194			0.705969	−	0.708243i	$-0.250512\pi$
$953$	1345.58			1.41194			0.705969	+	0.708243i	$0.250512\pi$
$954$		0			0
$955$	−254.013			−0.265982
$956$	−801.190	−	847.723i	−0.838064	−	0.886740i
$957$		0			0
$958$	−441.715	−	1110.45i	−0.461081	−	1.15913i
$959$			280.299i			0.292283i
$960$		0			0
$961$	−1054.32			−1.09710
$962$	−1408.80	+	560.393i	−1.46444	+	0.582529i
$963$		0			0
$964$	650.454	−	614.749i	0.674745	−	0.637707i
$965$			294.809i			0.305502i
$966$		0			0
$967$			140.279i			0.145066i	0.997366	+	0.0725330i	$0.0231083\pi$
$967$			140.279i			0.145066i	−0.997366	+	0.0725330i	$0.976892\pi$
$968$	379.025	−	815.617i	0.391555	−	0.842579i
$969$		0			0
$970$	415.227	+	1043.86i	0.428069	+	1.07614i
$971$	−1438.67			−1.48164			−0.740820	−	0.671704i	$-0.765563\pi$
$971$	−1438.67			−1.48164			−0.740820	+	0.671704i	$0.765563\pi$
$972$		0			0
$973$			490.479i			0.504090i
$974$	−255.125	−	641.370i	−0.261935	−	0.658491i
$975$		0			0
$976$	119.495	+	6.74981i	0.122433	+	0.00691579i
$977$	−902.190			−0.923428			−0.461714	−	0.887029i	$-0.652765\pi$
$977$	−902.190			−0.923428			−0.461714	+	0.887029i	$0.652765\pi$
$978$		0			0
$979$	236.976			0.242059
$980$	66.6500	+	70.5211i	0.0680102	+	0.0719603i
$981$		0			0
$982$	694.098	−	276.100i	0.706821	−	0.281160i
$983$		−	503.193i		−	0.511896i	−0.966691	−	0.255948i	$-0.917612\pi$
$983$		−	503.193i		−	0.511896i	0.966691	−	0.255948i	$-0.0823875\pi$
$984$		0			0
$985$	486.761			0.494173
$986$	288.960	+	726.430i	0.293063	+	0.736744i
$987$		0			0
$988$	426.237	+	450.993i	0.431414	+	0.456470i
$989$			1022.91i			1.03428i
$990$		0			0
$991$			906.322i			0.914553i	0.889325	+	0.457277i	$0.151175\pi$
$991$			906.322i			0.914553i	−0.889325	+	0.457277i	$0.848825\pi$
$992$	1362.64	−	454.844i	1.37363	−	0.458512i
$993$		0			0
$994$	635.183	−	252.664i	0.639017	−	0.254189i
$995$	495.847			0.498339
$996$		0			0
$997$		−	608.625i		−	0.610457i	−0.952279	−	0.305228i	$-0.901267\pi$
$997$		−	608.625i		−	0.610457i	0.952279	−	0.305228i	$-0.0987328\pi$
$998$	1580.20	−	628.576i	1.58337	−	0.629836i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.3.g.b.379.2		8
3.2	odd	2		56.3.g.b.43.7	✓	8
4.3	odd	2		2016.3.g.b.1135.4		8
8.3	odd	2	inner	504.3.g.b.379.1		8
8.5	even	2		2016.3.g.b.1135.5		8
12.11	even	2		224.3.g.b.15.4		8
21.2	odd	6		392.3.k.o.67.2		16
21.5	even	6		392.3.k.n.67.2		16
21.11	odd	6		392.3.k.o.275.4		16
21.17	even	6		392.3.k.n.275.4		16
21.20	even	2		392.3.g.m.99.7		8
24.5	odd	2		224.3.g.b.15.3		8
24.11	even	2		56.3.g.b.43.8	yes	8
48.5	odd	4		1792.3.d.j.1023.7		16
48.11	even	4		1792.3.d.j.1023.9		16
48.29	odd	4		1792.3.d.j.1023.10		16
48.35	even	4		1792.3.d.j.1023.8		16
84.83	odd	2		1568.3.g.m.687.5		8
168.11	even	6		392.3.k.o.275.2		16
168.59	odd	6		392.3.k.n.275.2		16
168.83	odd	2		392.3.g.m.99.8		8
168.107	even	6		392.3.k.o.67.4		16
168.125	even	2		1568.3.g.m.687.6		8
168.131	odd	6		392.3.k.n.67.4		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
56.3.g.b.43.7	✓	8	3.2	odd	2
56.3.g.b.43.8	yes	8	24.11	even	2
224.3.g.b.15.3		8	24.5	odd	2
224.3.g.b.15.4		8	12.11	even	2
392.3.g.m.99.7		8	21.20	even	2
392.3.g.m.99.8		8	168.83	odd	2
392.3.k.n.67.2		16	21.5	even	6
392.3.k.n.67.4		16	168.131	odd	6
392.3.k.n.275.2		16	168.59	odd	6
392.3.k.n.275.4		16	21.17	even	6
392.3.k.o.67.2		16	21.2	odd	6
392.3.k.o.67.4		16	168.107	even	6
392.3.k.o.275.2		16	168.11	even	6
392.3.k.o.275.4		16	21.11	odd	6
504.3.g.b.379.1		8	8.3	odd	2	inner
504.3.g.b.379.2		8	1.1	even	1	trivial
1568.3.g.m.687.5		8	84.83	odd	2
1568.3.g.m.687.6		8	168.125	even	2
1792.3.d.j.1023.7		16	48.5	odd	4
1792.3.d.j.1023.8		16	48.35	even	4
1792.3.d.j.1023.9		16	48.11	even	4
1792.3.d.j.1023.10		16	48.29	odd	4
2016.3.g.b.1135.4		8	4.3	odd	2
2016.3.g.b.1135.5		8	8.5	even	2

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:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	504.g (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.85837 + 0.739226i) q^{2} +(2.90709 - 2.74751i) q^{4} -3.46547i q^{5} -2.64575i q^{7} +(-3.37142 + 7.25490i) q^{8} +O(q^{10})\)	\(q+(-1.85837 + 0.739226i) q^{2} +(2.90709 - 2.74751i) q^{4} -3.46547i q^{5} -2.64575i q^{7} +(-3.37142 + 7.25490i) q^{8} +(2.56177 + 6.44013i) q^{10} +2.92866 q^{11} +19.1586i q^{13} +(1.95581 + 4.91679i) q^{14} +(0.902343 - 15.9745i) q^{16} +14.3897 q^{17} +8.09744 q^{19} +(-9.52143 - 10.0744i) q^{20} +(-5.44254 + 2.16494i) q^{22} +16.7598i q^{23} +12.9905 q^{25} +(-14.1625 - 35.6038i) q^{26} +(-7.26924 - 7.69144i) q^{28} -27.1649i q^{29} -44.8923i q^{31} +(10.1319 + 30.3537i) q^{32} +(-26.7415 + 10.6373i) q^{34} -9.16878 q^{35} -39.5687i q^{37} +(-15.0480 + 5.98584i) q^{38} +(25.1416 + 11.6836i) q^{40} -45.8766 q^{41} +61.0334 q^{43} +(8.51388 - 8.04653i) q^{44} +(-12.3893 - 31.1459i) q^{46} -46.2793i q^{47} -7.00000 q^{49} +(-24.1412 + 9.60292i) q^{50} +(52.6385 + 55.6957i) q^{52} +9.69424i q^{53} -10.1492i q^{55} +(19.1947 + 8.91994i) q^{56} +(20.0810 + 50.4825i) q^{58} +114.554 q^{59} +7.48032i q^{61} +(33.1855 + 83.4265i) q^{62} +(-41.2671 - 48.9186i) q^{64} +66.3935 q^{65} -12.0590 q^{67} +(41.8323 - 39.5360i) q^{68} +(17.0390 - 6.77780i) q^{70} -129.187i q^{71} -18.2854 q^{73} +(29.2502 + 73.5334i) q^{74} +(23.5400 - 22.2478i) q^{76} -7.74851i q^{77} +42.6168i q^{79} +(-55.3593 - 3.12704i) q^{80} +(85.2558 - 33.9132i) q^{82} +109.670 q^{83} -49.8673i q^{85} +(-113.423 + 45.1174i) q^{86} +(-9.87374 + 21.2471i) q^{88} +80.9162 q^{89} +50.6889 q^{91} +(46.0478 + 48.7223i) q^{92} +(34.2109 + 86.0041i) q^{94} -28.0614i q^{95} +162.086 q^{97} +(13.0086 - 5.17458i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - q^{2} + 5 q^{4} - 13 q^{8}+O(q^{10}) \) 8 * q - q^2 + 5 * q^4 - 13 * q^8	\( 8 q - q^{2} + 5 q^{4} - 13 q^{8} + 16 q^{10} + 32 q^{11} - 7 q^{14} - 71 q^{16} + 80 q^{17} + 56 q^{19} + 108 q^{20} + 66 q^{22} - 16 q^{25} - 24 q^{26} + 7 q^{28} + 19 q^{32} + 74 q^{34} - 56 q^{35} + 14 q^{38} + 84 q^{40} - 128 q^{41} - 50 q^{44} - 152 q^{46} - 56 q^{49} - 33 q^{50} + 132 q^{52} + 49 q^{56} + 24 q^{58} - 104 q^{59} - 120 q^{62} - 55 q^{64} + 72 q^{65} + 304 q^{67} + 190 q^{68} + 56 q^{70} - 112 q^{73} - 8 q^{74} + 70 q^{76} - 124 q^{80} + 450 q^{82} - 72 q^{83} - 210 q^{86} - 486 q^{88} + 512 q^{89} - 56 q^{91} + 472 q^{92} + 472 q^{94} + 64 q^{97} + 7 q^{98}+O(q^{100}) \) 8 * q - q^2 + 5 * q^4 - 13 * q^8 + 16 * q^10 + 32 * q^11 - 7 * q^14 - 71 * q^16 + 80 * q^17 + 56 * q^19 + 108 * q^20 + 66 * q^22 - 16 * q^25 - 24 * q^26 + 7 * q^28 + 19 * q^32 + 74 * q^34 - 56 * q^35 + 14 * q^38 + 84 * q^40 - 128 * q^41 - 50 * q^44 - 152 * q^46 - 56 * q^49 - 33 * q^50 + 132 * q^52 + 49 * q^56 + 24 * q^58 - 104 * q^59 - 120 * q^62 - 55 * q^64 + 72 * q^65 + 304 * q^67 + 190 * q^68 + 56 * q^70 - 112 * q^73 - 8 * q^74 + 70 * q^76 - 124 * q^80 + 450 * q^82 - 72 * q^83 - 210 * q^86 - 486 * q^88 + 512 * q^89 - 56 * q^91 + 472 * q^92 + 472 * q^94 + 64 * q^97 + 7 * q^98

Introduction

L-functions

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