LMFDB - Embedded newform 252.4.w.a.5.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [252,4,Mod(5,252)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(252, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 5, 5]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("252.5");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 252 = 2^{2} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	252.w (of order $6$, 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:	$14.8684813214$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			5.4
Character	$\chi$	$=$	252.5
Dual form			252.4.w.a.101.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-4.76836 - 2.06463i) q^{3} +(9.23798 + 16.0007i) q^{5} +(-13.5371 - 12.6391i) q^{7} +(18.4746 + 19.6898i) q^{9} +O(q^{10})$	\(q+(-4.76836 - 2.06463i) q^{3} +(9.23798 + 16.0007i) q^{5} +(-13.5371 - 12.6391i) q^{7} +(18.4746 + 19.6898i) q^{9} +(43.7922 + 25.2834i) q^{11} +(-68.1606 - 39.3525i) q^{13} +(-11.0146 - 95.3699i) q^{15} +(2.61183 + 4.52382i) q^{17} +(-23.3935 - 13.5062i) q^{19} +(38.4545 + 88.2171i) q^{21} +(-50.4179 + 29.1088i) q^{23} +(-108.181 + 187.374i) q^{25} +(-47.4415 - 132.031i) q^{27} +(-133.237 + 76.9242i) q^{29} +2.06045i q^{31} +(-156.616 - 210.975i) q^{33} +(77.1795 - 333.362i) q^{35} +(-184.666 + 319.851i) q^{37} +(243.766 + 328.374i) q^{39} +(-199.553 + 345.635i) q^{41} +(-152.366 - 263.906i) q^{43} +(-144.382 + 477.500i) q^{45} -294.693 q^{47} +(23.5039 + 342.194i) q^{49} +(-3.11414 - 26.9637i) q^{51} +(-431.281 + 249.000i) q^{53} +934.271i q^{55} +(83.6633 + 112.702i) q^{57} +157.928 q^{59} -726.088i q^{61} +(-1.22936 - 500.045i) q^{63} -1454.15i q^{65} -164.413 q^{67} +(300.510 - 34.7070i) q^{69} +157.652i q^{71} +(908.485 - 524.514i) q^{73} +(902.703 - 670.116i) q^{75} +(-273.256 - 895.759i) q^{77} +198.638 q^{79} +(-46.3777 + 727.523i) q^{81} +(-492.704 - 853.388i) q^{83} +(-48.2561 + 83.5820i) q^{85} +(794.141 - 91.7184i) q^{87} +(45.0433 - 78.0173i) q^{89} +(425.312 + 1394.21i) q^{91} +(4.25406 - 9.82496i) q^{93} -499.081i q^{95} +(-785.610 + 453.572i) q^{97} +(311.217 + 1329.36i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 6 q^{7} + 12 q^{9}+O(q^{10}) $ 48 * q + 6 * q^7 + 12 * q^9	$ 48 q + 6 q^{7} + 12 q^{9} + 12 q^{11} - 36 q^{13} + 66 q^{15} - 72 q^{17} + 24 q^{21} + 30 q^{23} - 600 q^{25} - 396 q^{27} + 42 q^{29} + 390 q^{35} + 84 q^{37} - 840 q^{39} - 618 q^{41} - 42 q^{43} + 366 q^{45} + 396 q^{47} + 318 q^{49} - 738 q^{51} - 1620 q^{53} + 492 q^{57} + 1500 q^{59} + 672 q^{63} - 588 q^{67} - 924 q^{69} + 564 q^{75} - 2472 q^{77} + 1608 q^{79} + 2592 q^{81} - 360 q^{85} + 2640 q^{87} + 1722 q^{89} + 540 q^{91} + 660 q^{93} - 792 q^{97} - 54 q^{99}+O(q^{100}) $ 48 * q + 6 * q^7 + 12 * q^9 + 12 * q^11 - 36 * q^13 + 66 * q^15 - 72 * q^17 + 24 * q^21 + 30 * q^23 - 600 * q^25 - 396 * q^27 + 42 * q^29 + 390 * q^35 + 84 * q^37 - 840 * q^39 - 618 * q^41 - 42 * q^43 + 366 * q^45 + 396 * q^47 + 318 * q^49 - 738 * q^51 - 1620 * q^53 + 492 * q^57 + 1500 * q^59 + 672 * q^63 - 588 * q^67 - 924 * q^69 + 564 * q^75 - 2472 * q^77 + 1608 * q^79 + 2592 * q^81 - 360 * q^85 + 2640 * q^87 + 1722 * q^89 + 540 * q^91 + 660 * q^93 - 792 * q^97 - 54 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/252\mathbb{Z}\right)^\times$.

$n$	$29$	$73$	$127$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{6}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−4.76836	−	2.06463i	−0.917672	−	0.397338i
$3$	−4.76836	−	2.06463i	−0.917672	−	0.397338i
$4$		0			0
$5$	9.23798	+	16.0007i	0.826270	+	1.43114i	0.900945	+	0.433934i	$0.142875\pi$
$5$	9.23798	+	16.0007i	0.826270	+	1.43114i	−0.0746748	+	0.997208i	$0.523792\pi$
$6$		0			0
$7$	−13.5371	−	12.6391i	−0.730932	−	0.682450i
$7$	−13.5371	−	12.6391i	−0.730932	−	0.682450i
$8$		0			0
$9$	18.4746	+	19.6898i	0.684245	+	0.729252i
$10$		0			0
$11$	43.7922	+	25.2834i	1.20035	+	0.693022i	0.960633	−	0.277821i	$-0.0896122\pi$
$11$	43.7922	+	25.2834i	1.20035	+	0.693022i	0.239717	+	0.970843i	$0.422946\pi$
$12$		0			0
$13$	−68.1606	−	39.3525i	−1.45418	−	0.839572i	−0.455466	−	0.890253i	$-0.650527\pi$
$13$	−68.1606	−	39.3525i	−1.45418	−	0.839572i	−0.998715	+	0.0506815i	$0.983861\pi$
$14$		0			0
$15$	−11.0146	−	95.3699i	−0.189598	−	1.64163i
$16$		0			0
$17$	2.61183	+	4.52382i	0.0372625	+	0.0645405i	0.884055	−	0.467383i	$-0.154803\pi$
$17$	2.61183	+	4.52382i	0.0372625	+	0.0645405i	−0.846793	+	0.531923i	$0.821470\pi$
$18$		0			0
$19$	−23.3935	−	13.5062i	−0.282465	−	0.163081i	0.352074	−	0.935972i	$-0.385477\pi$
$19$	−23.3935	−	13.5062i	−0.282465	−	0.163081i	−0.634539	+	0.772891i	$0.718810\pi$
$20$		0			0
$21$	38.4545	+	88.2171i	0.399593	+	0.916693i
$22$		0			0
$23$	−50.4179	+	29.1088i	−0.457081	+	0.263896i	−0.710816	−	0.703378i	$-0.751674\pi$
$23$	−50.4179	+	29.1088i	−0.457081	+	0.263896i	0.253735	+	0.967274i	$0.418341\pi$
$24$		0			0
$25$	−108.181	+	187.374i	−0.865444	+	1.49899i
$26$		0			0
$27$	−47.4415	−	132.031i	−0.338153	−	0.941091i
$28$		0			0
$29$	−133.237	+	76.9242i	−0.853153	+	0.492568i	−0.861713	−	0.507396i	$-0.830608\pi$
$29$	−133.237	+	76.9242i	−0.853153	+	0.492568i	0.00856075	+	0.999963i	$0.497275\pi$
$30$		0			0
$31$			2.06045i			0.0119376i	0.999982	+	0.00596882i	$0.00189995\pi$
$31$			2.06045i			0.0119376i	−0.999982	+	0.00596882i	$0.998100\pi$
$32$		0			0
$33$	−156.616	−	210.975i	−0.826163	−	1.11291i
$34$		0			0
$35$	77.1795	−	333.362i	0.372735	−	1.60996i
$36$		0			0
$37$	−184.666	+	319.851i	−0.820512	+	1.42117i	0.0847888	+	0.996399i	$0.472978\pi$
$37$	−184.666	+	319.851i	−0.820512	+	1.42117i	−0.905301	+	0.424770i	$0.860355\pi$
$38$		0			0
$39$	243.766	+	328.374i	1.00087	+	1.34825i
$40$		0			0
$41$	−199.553	+	345.635i	−0.760119	+	1.31657i	0.182669	+	0.983174i	$0.441526\pi$
$41$	−199.553	+	345.635i	−0.760119	+	1.31657i	−0.942789	+	0.333391i	$0.891807\pi$
$42$		0			0
$43$	−152.366	−	263.906i	−0.540364	−	0.935938i	−0.998883	−	0.0472536i	$-0.984953\pi$
$43$	−152.366	−	263.906i	−0.540364	−	0.935938i	0.458519	−	0.888685i	$-0.348380\pi$
$44$		0			0
$45$	−144.382	+	477.500i	−0.478293	+	1.58181i
$46$		0			0
$47$	−294.693			−0.914584			−0.457292	−	0.889317i	$-0.651181\pi$
$47$	−294.693			−0.914584			−0.457292	+	0.889317i	$0.651181\pi$
$48$		0			0
$49$	23.5039	+	342.194i	0.0685245	+	0.997649i
$50$		0			0
$51$	−3.11414	−	26.9637i	−0.00855033	−	0.0740328i
$52$		0			0
$53$	−431.281	+	249.000i	−1.11776	+	0.645336i	−0.940827	−	0.338888i	$-0.889949\pi$
$53$	−431.281	+	249.000i	−1.11776	+	0.645336i	−0.176928	+	0.984224i	$0.556616\pi$
$54$		0			0
$55$			934.271i			2.29049i
$56$		0			0
$57$	83.6633	+	112.702i	0.194412	+	0.261889i
$58$		0			0
$59$	157.928			0.348483			0.174242	−	0.984703i	$-0.444253\pi$
$59$	157.928			0.348483			0.174242	+	0.984703i	$0.444253\pi$
$60$		0			0
$61$		−	726.088i		−	1.52403i	−0.647557	−	0.762017i	$-0.724209\pi$
$61$		−	726.088i		−	1.52403i	0.647557	−	0.762017i	$-0.275791\pi$
$62$		0			0
$63$	−1.22936	−	500.045i	−0.00245849	−	0.999997i
$64$		0			0
$65$		−	1454.15i		−	2.77485i
$66$		0			0
$67$	−164.413			−0.299794			−0.149897	−	0.988702i	$-0.547894\pi$
$67$	−164.413			−0.299794			−0.149897	+	0.988702i	$0.547894\pi$
$68$		0			0
$69$	300.510	−	34.7070i	0.524307	−	0.0605542i
$70$		0			0
$71$			157.652i			0.263519i	0.991282	+	0.131760i	$0.0420627\pi$
$71$			157.652i			0.263519i	−0.991282	+	0.131760i	$0.957937\pi$
$72$		0			0
$73$	908.485	−	524.514i	1.45658	−	0.840955i	0.457736	−	0.889088i	$-0.348661\pi$
$73$	908.485	−	524.514i	1.45658	−	0.840955i	0.998841	+	0.0481335i	$0.0153273\pi$
$74$		0			0
$75$	902.703	−	670.116i	1.38980	−	1.03171i
$76$		0			0
$77$	−273.256	−	895.759i	−0.404422	−	1.32573i
$78$		0			0
$79$	198.638			0.282892			0.141446	−	0.989946i	$-0.454825\pi$
$79$	198.638			0.282892			0.141446	+	0.989946i	$0.454825\pi$
$80$		0			0
$81$	−46.3777	+	727.523i	−0.0636183	+	0.997974i
$82$		0			0
$83$	−492.704	−	853.388i	−0.651582	−	1.12857i	−0.982739	−	0.184997i	$-0.940773\pi$
$83$	−492.704	−	853.388i	−0.651582	−	1.12857i	0.331158	−	0.943575i	$-0.392561\pi$
$84$		0			0
$85$	−48.2561	+	83.5820i	−0.0615777	+	0.106656i
$86$		0			0
$87$	794.141	−	91.7184i	0.978630	−	0.113026i
$88$		0			0
$89$	45.0433	−	78.0173i	0.0536469	−	0.0929192i	−0.837955	−	0.545740i	$-0.816249\pi$
$89$	45.0433	−	78.0173i	0.0536469	−	0.0929192i	0.891602	+	0.452820i	$0.149582\pi$
$90$		0			0
$91$	425.312	+	1394.21i	0.489942	+	1.60608i
$92$		0			0
$93$	4.25406	−	9.82496i	0.00474328	−	0.0109548i
$94$		0			0
$95$		−	499.081i		−	0.538996i
$96$		0			0
$97$	−785.610	+	453.572i	−0.822336	+	0.474776i	−0.851221	−	0.524807i	$-0.824138\pi$
$97$	−785.610	+	453.572i	−0.822336	+	0.474776i	0.0288852	+	0.999583i	$0.490804\pi$
$98$		0			0
$99$	311.217	+	1329.36i	0.315945	+	1.34955i
$100$		0			0
$101$	135.558	−	234.793i	0.133550	−	0.231315i	−0.791493	−	0.611178i	$-0.790696\pi$
$101$	135.558	−	234.793i	0.133550	−	0.231315i	0.925042	+	0.379864i	$0.124029\pi$
$102$		0			0
$103$	−470.734	+	271.779i	−0.450319	+	0.259992i	−0.707965	−	0.706248i	$-0.750387\pi$
$103$	−470.734	+	271.779i	−0.450319	+	0.259992i	0.257646	+	0.966239i	$0.417053\pi$
$104$		0			0
$105$	−1056.29	+	1430.24i	−0.981745	+	1.32931i
$106$		0			0
$107$	1091.55	+	630.207i	0.986207	+	0.569387i	0.904138	−	0.427240i	$-0.140514\pi$
$107$	1091.55	+	630.207i	0.986207	+	0.569387i	0.0820688	+	0.996627i	$0.473847\pi$
$108$		0			0
$109$	155.734	+	269.739i	0.136850	+	0.237031i	0.926303	−	0.376781i	$-0.122969\pi$
$109$	155.734	+	269.739i	0.136850	+	0.237031i	−0.789453	+	0.613811i	$0.789636\pi$
$110$		0			0
$111$	1540.93	−	1143.90i	1.31765	−	0.978147i
$112$		0			0
$113$	1020.39	+	589.120i	0.849467	+	0.490440i	0.860471	−	0.509499i	$-0.170169\pi$
$113$	1020.39	+	589.120i	0.849467	+	0.490440i	−0.0110040	+	0.999939i	$0.503503\pi$
$114$		0			0
$115$	−931.520	−	537.813i	−0.755345	−	0.436099i
$116$		0			0
$117$	−484.396	−	2069.09i	−0.382756	−	1.63494i
$118$		0			0
$119$	21.8208	−	94.2506i	0.0168093	−	0.0726045i
$120$		0			0
$121$	613.004	+	1061.75i	0.460559	+	0.797712i
$122$		0			0
$123$	1665.15	−	1236.11i	1.22066	−	0.906151i
$124$		0			0
$125$	−1687.98			−1.20782
$126$		0			0
$127$	632.178			0.441707			0.220853	−	0.975307i	$-0.429116\pi$
$127$	632.178			0.441707			0.220853	+	0.975307i	$0.429116\pi$
$128$		0			0
$129$	181.670	+	1572.98i	0.123993	+	1.07359i
$130$		0			0
$131$	1258.99	+	2180.64i	0.839686	+	1.45438i	0.890157	+	0.455654i	$0.150594\pi$
$131$	1258.99	+	2180.64i	0.839686	+	1.45438i	−0.0504710	+	0.998726i	$0.516072\pi$
$132$		0			0
$133$	145.972	+	478.508i	0.0951680	+	0.311969i
$134$		0			0
$135$	1674.33	−	1978.80i	1.06743	−	1.26154i
$136$		0			0
$137$	−555.237	−	320.566i	−0.346256	−	0.199911i	0.316779	−	0.948499i	$-0.397399\pi$
$137$	−555.237	−	320.566i	−0.346256	−	0.199911i	−0.663035	+	0.748588i	$0.730732\pi$
$138$		0			0
$139$	−2408.23	−	1390.39i	−1.46952	−	0.848428i	−0.470104	−	0.882611i	$-0.655784\pi$
$139$	−2408.23	−	1390.39i	−1.46952	−	0.848428i	−0.999416	+	0.0341833i	$0.989117\pi$
$140$		0			0
$141$	1405.21	+	608.433i	0.839289	+	0.363399i
$142$		0			0
$143$	−1989.94	−	3446.67i	−1.16368	−	2.01556i
$144$		0			0
$145$	−2461.67	−	1421.25i	−1.40987	−	0.813988i
$146$		0			0
$147$	594.428	−	1680.23i	0.333521	−	0.942743i
$148$		0			0
$149$	2234.81	−	1290.27i	1.22874	−	0.709415i	0.261975	−	0.965075i	$-0.415626\pi$
$149$	2234.81	−	1290.27i	1.22874	−	0.709415i	0.966767	+	0.255660i	$0.0822927\pi$
$150$		0			0
$151$	−781.803	+	1354.12i	−0.421339	+	0.729781i	−0.996071	−	0.0885613i	$-0.971773\pi$
$151$	−781.803	+	1354.12i	−0.421339	+	0.729781i	0.574732	+	0.818342i	$0.305106\pi$
$152$		0			0
$153$	−40.8207	+	135.002i	−0.0215697	+	0.0713352i
$154$		0			0
$155$	−32.9685	+	19.0344i	−0.0170845	+	0.00986372i
$156$		0			0
$157$			123.698i			0.0628802i	0.999506	+	0.0314401i	$0.0100093\pi$
$157$			123.698i			0.0628802i	−0.999506	+	0.0314401i	$0.989991\pi$
$158$		0			0
$159$	2570.60	−	296.888i	1.28215	−	0.148080i
$160$		0			0
$161$	1050.42	+	243.192i	0.514191	+	0.119045i
$162$		0			0
$163$	−1684.08	+	2916.90i	−0.809245	+	1.40165i	0.104142	+	0.994562i	$0.466790\pi$
$163$	−1684.08	+	2916.90i	−0.809245	+	1.40165i	−0.913387	+	0.407092i	$0.866543\pi$
$164$		0			0
$165$	1928.92	−	4454.95i	0.910100	−	2.10192i
$166$		0			0
$167$	−486.170	+	842.071i	−0.225275	+	0.390188i	−0.956402	−	0.292054i	$-0.905661\pi$
$167$	−486.170	+	842.071i	−0.225275	+	0.390188i	0.731127	+	0.682242i	$0.238995\pi$
$168$		0			0
$169$	1998.75	+	3461.93i	0.909761	+	1.57575i
$170$		0			0
$171$	−166.250	−	710.136i	−0.0743478	−	0.317576i
$172$		0			0
$173$	−2174.96			−0.955833			−0.477917	−	0.878405i	$-0.658608\pi$
$173$	−2174.96			−0.955833			−0.477917	+	0.878405i	$0.658608\pi$
$174$		0			0
$175$	3832.70	−	1169.19i	1.65557	−	0.505041i
$176$		0			0
$177$	−753.060	−	326.064i	−0.319794	−	0.138466i
$178$		0			0
$179$	−228.433	+	131.886i	−0.0953850	+	0.0550705i	−0.546934	−	0.837176i	$-0.684205\pi$
$179$	−228.433	+	131.886i	−0.0953850	+	0.0550705i	0.451549	+	0.892246i	$0.350872\pi$
$180$		0			0
$181$		−	149.976i		−	0.0615892i	−0.999526	−	0.0307946i	$-0.990196\pi$
$181$		−	149.976i		−	0.0615892i	0.999526	−	0.0307946i	$-0.00980377\pi$
$182$		0			0
$183$	−1499.10	+	3462.25i	−0.605557	+	1.39856i
$184$		0			0
$185$	−6823.78			−2.71186
$186$		0			0
$187$			264.144i			0.103295i
$188$		0			0
$189$	−1026.55	+	2386.94i	−0.395081	+	0.918646i
$190$		0			0
$191$		−	3280.50i		−	1.24277i	−0.783506	−	0.621384i	$-0.786571\pi$
$191$		−	3280.50i		−	1.24277i	0.783506	−	0.621384i	$-0.213429\pi$
$192$		0			0
$193$	5155.39			1.92276			0.961381	−	0.275221i	$-0.0887509\pi$
$193$	5155.39			1.92276			0.961381	+	0.275221i	$0.0887509\pi$
$194$		0			0
$195$	−3002.29	+	6933.93i	−1.10255	+	2.54640i
$196$		0			0
$197$			2422.36i			0.876071i	0.898958	+	0.438035i	$0.144326\pi$
$197$			2422.36i			0.876071i	−0.898958	+	0.438035i	$0.855674\pi$
$198$		0			0
$199$	−408.371	+	235.773i	−0.145471	+	0.0839875i	−0.570969	−	0.820972i	$-0.693432\pi$
$199$	−408.371	+	235.773i	−0.145471	+	0.0839875i	0.425498	+	0.904959i	$0.360099\pi$
$200$		0			0
$201$	783.980	+	339.452i	0.275113	+	0.119120i
$202$		0			0
$203$	2775.89	+	642.670i	0.959750	+	0.222200i
$204$		0			0
$205$	−7373.85			−2.51225
$206$		0			0
$207$	−1504.60	−	454.946i	−0.505202	−	0.152758i
$208$		0			0
$209$	−682.968	−	1182.94i	−0.226038	−	0.391509i
$210$		0			0
$211$	38.7447	−	67.1077i	0.0126412	−	0.0218952i	−0.859636	−	0.510908i	$-0.829309\pi$
$211$	38.7447	−	67.1077i	0.0126412	−	0.0218952i	0.872277	+	0.489012i	$0.162643\pi$
$212$		0			0
$213$	325.493	−	751.743i	0.104706	−	0.241824i
$214$		0			0
$215$	2815.12	−	4875.92i	0.892974	−	1.54668i
$216$		0			0
$217$	26.0423	−	27.8924i	0.00814684	−	0.00872561i
$218$		0			0
$219$	−5414.91	+	625.389i	−1.67080	+	0.192967i
$220$		0			0
$221$		−	411.129i		−	0.125138i
$222$		0			0
$223$	3593.68	−	2074.81i	1.07915	−	0.623047i	0.148482	−	0.988915i	$-0.452561\pi$
$223$	3593.68	−	2074.81i	1.07915	−	0.623047i	0.930667	+	0.365868i	$0.119228\pi$
$224$		0			0
$225$	−5687.96	+	1331.61i	−1.68532	+	0.394551i
$226$		0			0
$227$	−181.153	+	313.767i	−0.0529673	+	0.0917420i	−0.891293	−	0.453427i	$-0.850201\pi$
$227$	−181.153	+	313.767i	−0.0529673	+	0.0917420i	0.838326	+	0.545169i	$0.183535\pi$
$228$		0			0
$229$	1984.21	−	1145.59i	0.572579	−	0.330579i	−0.185600	−	0.982625i	$-0.559423\pi$
$229$	1984.21	−	1145.59i	0.572579	−	0.330579i	0.758179	+	0.652047i	$0.226089\pi$
$230$		0			0
$231$	−546.425	+	4835.48i	−0.155637	+	1.37728i
$232$		0			0
$233$	5724.54	+	3305.07i	1.60956	+	0.929280i	0.989468	+	0.144750i	$0.0462378\pi$
$233$	5724.54	+	3305.07i	1.60956	+	0.929280i	0.620091	+	0.784530i	$0.287096\pi$
$234$		0			0
$235$	−2722.37	−	4715.29i	−0.755694	−	1.30890i
$236$		0			0
$237$	−947.178	−	410.114i	−0.259603	−	0.112404i
$238$		0			0
$239$	−2242.86	−	1294.92i	−0.607024	−	0.350466i	0.164776	−	0.986331i	$-0.447310\pi$
$239$	−2242.86	−	1294.92i	−0.607024	−	0.350466i	−0.771800	+	0.635866i	$0.780643\pi$
$240$		0			0
$241$	−1004.65	−	580.036i	−0.268528	−	0.155035i	0.359690	−	0.933072i	$-0.382882\pi$
$241$	−1004.65	−	580.036i	−0.268528	−	0.155035i	−0.628219	+	0.778037i	$0.716216\pi$
$242$		0			0
$243$	1723.21	−	3373.34i	0.454914	−	0.890535i
$244$		0			0
$245$	−5258.19	+	3537.26i	−1.37116	+	0.922396i
$246$		0			0
$247$	1063.01	+	1841.19i	0.273837	+	0.474299i
$248$		0			0
$249$	587.461	+	5086.52i	0.149513	+	1.29456i
$250$		0			0
$251$	−3533.26			−0.888516			−0.444258	−	0.895899i	$-0.646533\pi$
$251$	−3533.26			−0.888516			−0.444258	+	0.895899i	$0.646533\pi$
$252$		0			0
$253$	−2943.88			−0.731543
$254$		0			0
$255$	402.668	−	298.918i	0.0988866	−	0.0734078i
$256$		0			0
$257$	3613.85	+	6259.37i	0.877142	+	1.51925i	0.854463	+	0.519512i	$0.173886\pi$
$257$	3613.85	+	6259.37i	0.877142	+	1.51925i	0.0226791	+	0.999743i	$0.492780\pi$
$258$		0			0
$259$	6542.49	−	1995.82i	1.56962	−	0.478820i
$260$		0			0
$261$	−3976.12	−	1202.26i	−0.942971	−	0.285127i
$262$		0			0
$263$	−2522.96	−	1456.63i	−0.591530	−	0.341520i	0.174172	−	0.984715i	$-0.444275\pi$
$263$	−2522.96	−	1456.63i	−0.591530	−	0.341520i	−0.765702	+	0.643195i	$0.777608\pi$
$264$		0			0
$265$	−7968.33	−	4600.52i	−1.84713	−	1.06644i
$266$		0			0
$267$	−375.860	+	279.017i	−0.0861507	+	0.0639534i
$268$		0			0
$269$	2237.45	+	3875.37i	0.507136	+	0.878386i	0.999966	+	0.00825986i	$0.00262922\pi$
$269$	2237.45	+	3875.37i	0.507136	+	0.878386i	−0.492830	+	0.870126i	$0.664037\pi$
$270$		0			0
$271$	1000.29	+	577.515i	0.224218	+	0.129452i	0.607902	−	0.794012i	$-0.292011\pi$
$271$	1000.29	+	577.515i	0.224218	+	0.129452i	−0.383684	+	0.923464i	$0.625345\pi$
$272$		0			0
$273$	850.486	−	7526.21i	0.188549	−	1.66852i
$274$		0			0
$275$	−9474.93	+	5470.35i	−2.07767	+	1.19954i
$276$		0			0
$277$	−2626.80	+	4549.75i	−0.569780	+	0.986889i	0.426807	+	0.904343i	$0.359638\pi$
$277$	−2626.80	+	4549.75i	−0.569780	+	0.986889i	−0.996587	+	0.0825458i	$0.973695\pi$
$278$		0			0
$279$	−40.5698	+	38.0659i	−0.00870556	+	0.00816827i
$280$		0			0
$281$	2917.67	−	1684.52i	0.619409	−	0.357616i	−0.157230	−	0.987562i	$-0.550256\pi$
$281$	2917.67	−	1684.52i	0.619409	−	0.357616i	0.776639	+	0.629946i	$0.216923\pi$
$282$		0			0
$283$			3799.74i			0.798132i	0.916922	+	0.399066i	$0.130665\pi$
$283$			3799.74i			0.798132i	−0.916922	+	0.399066i	$0.869335\pi$
$284$		0			0
$285$	−1030.42	+	2379.80i	−0.214164	+	0.494622i
$286$		0			0
$287$	7069.89	−	2156.71i	1.45409	−	0.443577i
$288$		0			0
$289$	2442.86	−	4231.15i	0.497223	−	0.861216i
$290$		0			0
$291$	4682.53	−	540.804i	0.943282	−	0.108943i
$292$		0			0
$293$	−3501.18	+	6064.21i	−0.698092	+	1.20913i	0.271036	+	0.962569i	$0.412634\pi$
$293$	−3501.18	+	6064.21i	−0.698092	+	1.20913i	−0.969127	+	0.246561i	$0.920699\pi$
$294$		0			0
$295$	1458.94	+	2526.96i	0.287941	+	0.498729i
$296$		0			0
$297$	1260.64	−	6981.43i	0.246296	−	1.36399i
$298$		0			0
$299$	4582.02			0.886238
$300$		0			0
$301$	−1272.96	+	5498.30i	−0.243761	+	1.05288i
$302$		0			0
$303$	−1131.15	+	839.702i	−0.214465	+	0.159207i
$304$		0			0
$305$	11617.9	−	6707.59i	2.18111	−	1.25926i
$306$		0			0
$307$			5403.08i			1.00446i	0.864734	+	0.502231i	$0.167487\pi$
$307$			5403.08i			1.00446i	−0.864734	+	0.502231i	$0.832513\pi$
$308$		0			0
$309$	2805.76	−	324.047i	0.516550	−	0.0596583i
$310$		0			0
$311$	238.054			0.0434045			0.0217023	−	0.999764i	$-0.493091\pi$
$311$	238.054			0.0434045			0.0217023	+	0.999764i	$0.493091\pi$
$312$		0			0
$313$		−	10051.0i		−	1.81506i	−0.419982	−	0.907532i	$-0.637964\pi$
$313$		−	10051.0i		−	1.81506i	0.419982	−	0.907532i	$-0.362036\pi$
$314$		0			0
$315$	7989.70	−	4639.08i	1.42911	−	0.829786i
$316$		0			0
$317$			3108.20i			0.550706i	0.961343	+	0.275353i	$0.0887947\pi$
$317$			3108.20i			0.550706i	−0.961343	+	0.275353i	$0.911205\pi$
$318$		0			0
$319$	−7779.63			−1.36544
$320$		0			0
$321$	−3903.77	−	5258.70i	−0.678776	−	0.914368i
$322$		0			0
$323$		−	141.104i		−	0.0243072i
$324$		0			0
$325$	14747.3	−	8514.36i	2.51703	−	1.45321i
$326$		0			0
$327$	−185.685	−	1607.75i	−0.0314018	−	0.271892i
$328$		0			0
$329$	3989.28	+	3724.67i	0.668499	+	0.624158i
$330$		0			0
$331$	2933.55			0.487137			0.243569	−	0.969884i	$-0.421682\pi$
$331$	2933.55			0.487137			0.243569	+	0.969884i	$0.421682\pi$
$332$		0			0
$333$	−9709.45	+	2273.08i	−1.59782	+	0.374067i
$334$		0			0
$335$	−1518.84	−	2630.71i	−0.247711	−	0.429048i
$336$		0			0
$337$	3915.68	−	6782.16i	0.632940	−	1.09628i	−0.354008	−	0.935242i	$-0.615181\pi$
$337$	3915.68	−	6782.16i	0.632940	−	1.09628i	0.986948	−	0.161041i	$-0.0514852\pi$
$338$		0			0
$339$	−3649.26	−	4915.86i	−0.584662	−	0.787589i
$340$		0			0
$341$	−52.0951	+	90.2314i	−0.00827305	+	0.0143293i
$342$		0			0
$343$	4006.86	−	4929.37i	0.630759	−	0.775979i
$344$		0			0
$345$	3331.44	+	4487.73i	0.519880	+	0.700323i
$346$		0			0
$347$			2567.19i			0.397159i	0.980085	+	0.198579i	$0.0636328\pi$
$347$			2567.19i			0.397159i	−0.980085	+	0.198579i	$0.936367\pi$
$348$		0			0
$349$	−164.687	+	95.0820i	−0.0252593	+	0.0145834i	−0.512576	−	0.858642i	$-0.671309\pi$
$349$	−164.687	+	95.0820i	−0.0252593	+	0.0145834i	0.487317	+	0.873225i	$0.337976\pi$
$350$		0			0
$351$	−1962.13	+	10866.3i	−0.298379	+	1.65242i
$352$		0			0
$353$	−2552.60	+	4421.23i	−0.384875	+	0.666624i	−0.991752	−	0.128172i	$-0.959089\pi$
$353$	−2552.60	+	4421.23i	−0.384875	+	0.666624i	0.606877	+	0.794796i	$0.292422\pi$
$354$		0			0
$355$	−2522.54	+	1456.39i	−0.377134	+	0.217738i
$356$		0			0
$357$	−298.642	+	404.369i	−0.0442740	+	0.0599482i
$358$		0			0
$359$	−1813.09	−	1046.79i	−0.266550	−	0.153893i	0.360769	−	0.932655i	$-0.382514\pi$
$359$	−1813.09	−	1046.79i	−0.266550	−	0.153893i	−0.627319	+	0.778763i	$0.715848\pi$
$360$		0			0
$361$	−3064.66	−	5308.15i	−0.446809	−	0.773896i
$362$		0			0
$363$	−730.898	−	6328.46i	−0.105681	−	0.915036i
$364$		0			0
$365$	16785.1	+	9690.90i	2.40705	+	1.38971i
$366$		0			0
$367$	5884.58	+	3397.46i	0.836982	+	0.483232i	0.856237	−	0.516583i	$-0.172796\pi$
$367$	5884.58	+	3397.46i	0.836982	+	0.483232i	−0.0192551	+	0.999815i	$0.506129\pi$
$368$		0			0
$369$	−10492.2	+	2456.32i	−1.48022	+	0.346534i
$370$		0			0
$371$	8985.43	+	2080.29i	1.25741	+	0.291115i
$372$		0			0
$373$	−3360.32	−	5820.24i	−0.466463	−	0.807937i	0.532804	−	0.846239i	$-0.321138\pi$
$373$	−3360.32	−	5820.24i	−0.466463	−	0.807937i	−0.999266	+	0.0383019i	$0.987805\pi$
$374$		0			0
$375$	8048.92	+	3485.06i	1.10839	+	0.479914i
$376$		0			0
$377$	12108.7			1.65418
$378$		0			0
$379$	−11495.7			−1.55804			−0.779018	−	0.627001i	$-0.784282\pi$
$379$	−11495.7			−1.55804			−0.779018	+	0.627001i	$0.784282\pi$
$380$		0			0
$381$	−3014.46	−	1305.21i	−0.405342	−	0.175507i
$382$		0			0
$383$	−6785.46	−	11752.8i	−0.905276	−	1.56798i	−0.820547	−	0.571579i	$-0.806331\pi$
$383$	−6785.46	−	11752.8i	−0.905276	−	1.56798i	−0.0847288	−	0.996404i	$-0.527002\pi$
$384$		0			0
$385$	11808.4	−	12647.3i	1.56315	−	1.67420i
$386$		0			0
$387$	2381.36	−	7875.63i	0.312794	−	1.03447i
$388$		0			0
$389$	−5438.17	−	3139.73i	−0.708808	−	0.409230i	0.101812	−	0.994804i	$-0.467536\pi$
$389$	−5438.17	−	3139.73i	−0.708808	−	0.409230i	−0.810619	+	0.585573i	$0.800869\pi$
$390$		0			0
$391$	−263.366	−	152.055i	−0.0340639	−	0.0196668i
$392$		0			0
$393$	−1501.13	−	12997.5i	−0.192676	−	1.66828i
$394$		0			0
$395$	1835.01	+	3178.33i	0.233746	+	0.404859i
$396$		0			0
$397$	9881.78	+	5705.25i	1.24925	+	0.721255i	0.970960	−	0.239242i	$-0.0768990\pi$
$397$	9881.78	+	5705.25i	1.24925	+	0.721255i	0.278290	+	0.960497i	$0.410232\pi$
$398$		0			0
$399$	291.896	−	2583.08i	0.0366243	−	0.324100i
$400$		0			0
$401$	3084.49	−	1780.83i	0.384120	−	0.221772i	−0.295489	−	0.955346i	$-0.595483\pi$
$401$	3084.49	−	1780.83i	0.384120	−	0.221772i	0.679609	+	0.733574i	$0.262149\pi$
$402$		0			0
$403$	81.0838	−	140.441i	0.0100225	−	0.0173595i
$404$		0			0
$405$	−12069.3	+	5978.77i	−1.48081	+	0.733549i
$406$		0			0
$407$	−16173.9	+	9338.00i	−1.96980	+	1.13727i
$408$		0			0
$409$			4392.06i			0.530986i	0.964113	+	0.265493i	$0.0855347\pi$
$409$			4392.06i			0.530986i	−0.964113	+	0.265493i	$0.914465\pi$
$410$		0			0
$411$	1985.72	+	2674.94i	0.238318	+	0.321034i
$412$		0			0
$413$	−2137.89	−	1996.08i	−0.254718	−	0.237822i
$414$		0			0
$415$	9103.18	−	15767.2i	1.07676	−	1.86501i
$416$		0			0
$417$	8612.67	+	11602.0i	1.01142	+	1.36247i
$418$		0			0
$419$	1251.47	−	2167.61i	0.145915	−	0.252731i	−0.783799	−	0.621014i	$-0.786721\pi$
$419$	1251.47	−	2167.61i	0.145915	−	0.252731i	0.929714	+	0.368283i	$0.120054\pi$
$420$		0			0
$421$	−464.674	−	804.839i	−0.0537929	−	0.0931721i	0.837875	−	0.545862i	$-0.183798\pi$
$421$	−464.674	−	804.839i	−0.0537929	−	0.0931721i	−0.891668	+	0.452690i	$0.850464\pi$
$422$		0			0
$423$	−5444.35	−	5802.46i	−0.625799	−	0.666963i
$424$		0			0
$425$	−1130.20			−0.128994
$426$		0			0
$427$	−9177.13	+	9829.10i	−1.04008	+	1.11397i
$428$		0			0
$429$	2372.64	+	20543.5i	0.267022	+	2.31200i
$430$		0			0
$431$	6571.40	−	3794.00i	0.734416	−	0.424015i	−0.0856193	−	0.996328i	$-0.527287\pi$
$431$	6571.40	−	3794.00i	0.734416	−	0.424015i	0.820036	+	0.572312i	$0.193954\pi$
$432$		0			0
$433$			5016.66i			0.556779i	0.960468	+	0.278389i	$0.0898006\pi$
$433$			5016.66i			0.556779i	−0.960468	+	0.278389i	$0.910199\pi$
$434$		0			0
$435$	8803.81	+	11859.5i	0.970369	+	1.30717i
$436$		0			0
$437$	1572.60			0.172146
$438$		0			0
$439$			546.491i			0.0594137i	0.999559	+	0.0297068i	$0.00945737\pi$
$439$			546.491i			0.0594137i	−0.999559	+	0.0297068i	$0.990543\pi$
$440$		0			0
$441$	−6303.51	+	6784.68i	−0.680651	+	0.732608i
$442$		0			0
$443$		−	10415.7i		−	1.11707i	−0.829480	−	0.558537i	$-0.811363\pi$
$443$		−	10415.7i		−	1.11707i	0.829480	−	0.558537i	$-0.188637\pi$
$444$		0			0
$445$	1664.44			0.177307
$446$		0			0
$447$	−13320.3	+	1538.41i	−1.40946	+	0.162784i
$448$		0			0
$449$			13773.8i			1.44772i	0.689945	+	0.723862i	$0.257635\pi$
$449$			13773.8i			1.44772i	−0.689945	+	0.723862i	$0.742365\pi$
$450$		0			0
$451$	−17477.7	+	10090.8i	−1.82482	+	1.05356i
$452$		0			0
$453$	6523.68	−	4842.81i	0.676621	−	0.502285i
$454$		0			0
$455$	−18379.2	+	19684.9i	−1.89370	+	2.02823i
$456$		0			0
$457$	2810.45			0.287675			0.143837	−	0.989601i	$-0.454056\pi$
$457$	2810.45			0.287675			0.143837	+	0.989601i	$0.454056\pi$
$458$		0			0
$459$	473.378	−	559.461i	0.0481381	−	0.0568919i
$460$		0			0
$461$	438.471	+	759.453i	0.0442985	+	0.0767273i	0.887325	−	0.461146i	$-0.152561\pi$
$461$	438.471	+	759.453i	0.0442985	+	0.0767273i	−0.843026	+	0.537873i	$0.819228\pi$
$462$		0			0
$463$	2755.40	−	4772.49i	0.276575	−	0.479042i	−0.693956	−	0.720017i	$-0.744134\pi$
$463$	2755.40	−	4772.49i	0.276575	−	0.479042i	0.970531	+	0.240975i	$0.0774672\pi$
$464$		0			0
$465$	196.505	−	22.6951i	0.0195972	−	0.00226335i
$466$		0			0
$467$	2699.99	−	4676.53i	0.267539	−	0.463392i	−0.700686	−	0.713469i	$-0.747123\pi$
$467$	2699.99	−	4676.53i	0.267539	−	0.463392i	0.968226	+	0.250078i	$0.0804562\pi$
$468$		0			0
$469$	2225.67	+	2078.04i	0.219129	+	0.204595i
$470$		0			0
$471$	255.391	−	589.838i	0.0249847	−	0.0577034i
$472$		0			0
$473$		−	15409.4i		−	1.49794i
$474$		0			0
$475$	5061.44	−	2922.22i	0.488915	−	0.282275i
$476$		0			0
$477$	−12870.5	−	3891.66i	−1.23543	−	0.373558i
$478$		0			0
$479$	−1673.81	+	2899.13i	−0.159663	+	0.276544i	−0.934747	−	0.355314i	$-0.884374\pi$
$479$	−1673.81	+	2899.13i	−0.159663	+	0.276544i	0.775084	+	0.631858i	$0.217707\pi$
$480$		0			0
$481$	25173.9	−	14534.2i	2.38635	−	1.37776i
$482$		0			0
$483$	−4506.69	−	3328.36i	−0.424558	−	0.313552i
$484$		0			0
$485$	−14514.9	−	8380.18i	−1.35894	−	0.784587i
$486$		0			0
$487$	8565.82	+	14836.4i	0.797032	+	1.38050i	0.921541	+	0.388281i	$0.126931\pi$
$487$	8565.82	+	14836.4i	0.797032	+	1.38050i	−0.124510	+	0.992218i	$0.539736\pi$
$488$		0			0
$489$	14052.6	−	10431.9i	1.29955	−	0.964715i
$490$		0			0
$491$	7540.00	+	4353.22i	0.693025	+	0.400118i	0.804744	−	0.593622i	$-0.202302\pi$
$491$	7540.00	+	4353.22i	0.693025	+	0.400118i	−0.111719	+	0.993740i	$0.535636\pi$
$492$		0			0
$493$	−695.983	−	401.826i	−0.0635811	−	0.0367086i
$494$		0			0
$495$	−18395.6	+	17260.3i	−1.67035	+	1.56726i
$496$		0			0
$497$	1992.59	−	2134.15i	0.179839	−	0.192615i
$498$		0			0
$499$	1926.02	+	3335.97i	0.172787	+	0.299275i	0.939393	−	0.342842i	$-0.111390\pi$
$499$	1926.02	+	3335.97i	0.172787	+	0.299275i	−0.766606	+	0.642117i	$0.778056\pi$
$500$		0			0
$501$	4056.80	−	3011.54i	0.361765	−	0.268554i
$502$		0			0
$503$	10923.9			0.968338			0.484169	−	0.874975i	$-0.339122\pi$
$503$	10923.9			0.968338			0.484169	+	0.874975i	$0.339122\pi$
$504$		0			0
$505$	5009.12			0.441392
$506$		0			0
$507$	−2383.15	−	20634.4i	−0.208756	−	1.80751i
$508$		0			0
$509$	−4664.62	−	8079.37i	−0.406200	−	0.703559i	0.588260	−	0.808672i	$-0.299813\pi$
$509$	−4664.62	−	8079.37i	−0.406200	−	0.703559i	−0.994460	+	0.105113i	$0.966480\pi$
$510$		0			0
$511$	−18927.6	−	4382.10i	−1.63857	−	0.379359i
$512$		0			0
$513$	−673.426	+	3729.43i	−0.0579580	+	0.320972i
$514$		0			0
$515$	−8697.27	−	5021.37i	−0.744170	−	0.429647i
$516$		0			0
$517$	−12905.3	−	7450.86i	−1.09782	−	0.633827i
$518$		0			0
$519$	10371.0	+	4490.49i	0.877142	+	0.379789i
$520$		0			0
$521$	−7245.30	−	12549.2i	−0.609256	−	1.05526i	−0.991363	−	0.131144i	$-0.958135\pi$
$521$	−7245.30	−	12549.2i	−0.609256	−	1.05526i	0.382107	−	0.924118i	$-0.375198\pi$
$522$		0			0
$523$	−17900.5	−	10334.9i	−1.49662	−	0.864076i	−0.496631	−	0.867962i	$-0.665430\pi$
$523$	−17900.5	−	10334.9i	−1.49662	−	0.864076i	−0.999992	+	0.00388547i	$0.998763\pi$
$524$		0			0
$525$	−20689.6	−	2338.00i	−1.71994	−	0.194359i
$526$		0			0
$527$	−9.32109	+	5.38153i	−0.000770461	+	0.000444826i
$528$		0			0
$529$	−4388.85	+	7601.72i	−0.360718	+	0.624782i
$530$		0			0
$531$	2917.67	+	3109.58i	0.238448	+	0.254132i
$532$		0			0
$533$	27203.3	−	15705.8i	2.21070	−	1.27635i
$534$		0			0
$535$			23287.4i			1.88187i
$536$		0			0
$537$	1361.55	−	157.251i	0.109414	−	0.0126366i
$538$		0			0
$539$	−7622.55	+	15579.7i	−0.609140	+	1.24502i
$540$		0			0
$541$	3008.56	−	5210.98i	0.239091	−	0.414118i	−0.721363	−	0.692557i	$-0.756484\pi$
$541$	3008.56	−	5210.98i	0.239091	−	0.414118i	0.960454	+	0.278440i	$0.0898173\pi$
$542$		0			0
$543$	−309.645	+	715.141i	−0.0244717	+	0.0565187i
$544$		0			0
$545$	−2877.33	+	4983.69i	−0.226150	+	0.391702i
$546$		0			0
$547$	−4198.40	−	7271.84i	−0.328173	−	0.568412i	0.653976	−	0.756515i	$-0.273100\pi$
$547$	−4198.40	−	7271.84i	−0.328173	−	0.568412i	−0.982149	+	0.188103i	$0.939766\pi$
$548$		0			0
$549$	14296.5	−	13414.2i	1.11141	−	1.04281i
$550$		0			0
$551$	4155.83			0.321314
$552$		0			0
$553$	−2688.97	−	2510.61i	−0.206775	−	0.193060i
$554$		0			0
$555$	32538.3	+	14088.6i	2.48860	+	1.07753i
$556$		0			0
$557$	−12485.8	+	7208.68i	−0.949803	+	0.548369i	−0.893020	−	0.450017i	$-0.851418\pi$
$557$	−12485.8	+	7208.68i	−0.949803	+	0.548369i	−0.0567836	+	0.998387i	$0.518085\pi$
$558$		0			0
$559$			23984.0i			1.81470i
$560$		0			0
$561$	545.360	−	1259.54i	0.0410430	−	0.0947908i
$562$		0			0
$563$	−21699.3			−1.62437			−0.812183	−	0.583403i	$-0.801721\pi$
$563$	−21699.3			−1.62437			−0.812183	+	0.583403i	$0.801721\pi$
$564$		0			0
$565$			21769.1i			1.62094i
$566$		0			0
$567$	9823.09	−	9262.35i	0.727568	−	0.686036i
$568$		0			0
$569$			16645.8i			1.22641i	0.789924	+	0.613204i	$0.210120\pi$
$569$			16645.8i			1.22641i	−0.789924	+	0.613204i	$0.789880\pi$
$570$		0			0
$571$	−7884.90			−0.577886			−0.288943	−	0.957346i	$-0.593304\pi$
$571$	−7884.90			−0.577886			−0.288943	+	0.957346i	$0.593304\pi$
$572$		0			0
$573$	−6773.02	+	15642.6i	−0.493799	+	1.14045i
$574$		0			0
$575$		−	12596.0i		−	0.913549i
$576$		0			0
$577$	−6891.32	+	3978.71i	−0.497209	+	0.287064i	−0.727560	−	0.686044i	$-0.759346\pi$
$577$	−6891.32	+	3978.71i	−0.497209	+	0.287064i	0.230351	+	0.973108i	$0.426012\pi$
$578$		0			0
$579$	−24582.8	−	10644.0i	−1.76447	−	0.763987i
$580$		0			0
$581$	−4116.34	+	17779.7i	−0.293932	+	1.26958i
$582$		0			0
$583$	−25182.3			−1.78893
$584$		0			0
$585$	28632.0	−	26864.9i	2.02357	−	1.89868i
$586$		0			0
$587$	−9647.97	−	16710.8i	−0.678389	−	1.17500i	−0.975466	−	0.220150i	$-0.929345\pi$
$587$	−9647.97	−	16710.8i	−0.678389	−	1.17500i	0.297077	−	0.954853i	$-0.403988\pi$
$588$		0			0
$589$	27.8289	−	48.2010i	0.00194680	−	0.00337196i
$590$		0			0
$591$	5001.27	−	11550.7i	0.348096	−	0.803946i
$592$		0			0
$593$	1389.88	−	2407.34i	0.0962488	−	0.166708i	−0.813880	−	0.581033i	$-0.802649\pi$
$593$	1389.88	−	2407.34i	0.0962488	−	0.166708i	0.910129	+	0.414325i	$0.135982\pi$
$594$		0			0
$595$	1709.65	−	521.538i	0.117796	−	0.0359344i
$596$		0			0
$597$	2434.05	−	281.117i	0.166866	−	0.0192720i
$598$		0			0
$599$			8034.96i			0.548079i	0.961718	+	0.274040i	$0.0883600\pi$
$599$			8034.96i			0.548079i	−0.961718	+	0.274040i	$0.911640\pi$
$600$		0			0
$601$	−14763.4	+	8523.64i	−1.00201	+	0.578514i	−0.908844	−	0.417137i	$-0.863034\pi$
$601$	−14763.4	+	8523.64i	−1.00201	+	0.578514i	−0.0931710	+	0.995650i	$0.529700\pi$
$602$		0			0
$603$	−3037.46	−	3237.26i	−0.205133	−	0.218626i
$604$		0			0
$605$	−11325.8	+	19616.9i	−0.761092	+	1.31825i
$606$		0			0
$607$	−8538.22	+	4929.54i	−0.570932	+	0.329628i	−0.757521	−	0.652810i	$-0.773590\pi$
$607$	−8538.22	+	4929.54i	−0.570932	+	0.329628i	0.186590	+	0.982438i	$0.440256\pi$
$608$		0			0
$609$	−11909.6	−	8795.67i	−0.792447	−	0.585252i
$610$		0			0
$611$	20086.5	+	11596.9i	1.32997	+	0.767859i
$612$		0			0
$613$	492.242	+	852.589i	0.0324331	+	0.0561758i	0.881786	−	0.471649i	$-0.156341\pi$
$613$	492.242	+	852.589i	0.0324331	+	0.0561758i	−0.849353	+	0.527825i	$0.823008\pi$
$614$		0			0
$615$	35161.2	+	15224.3i	2.30543	+	0.998215i
$616$		0			0
$617$	5359.59	+	3094.36i	0.349706	+	0.201903i	0.664556	−	0.747239i	$-0.268621\pi$
$617$	5359.59	+	3094.36i	0.349706	+	0.201903i	−0.314850	+	0.949142i	$0.601954\pi$
$618$		0			0
$619$	14551.3	+	8401.21i	0.944858	+	0.545514i	0.891480	−	0.453060i	$-0.149668\pi$
$619$	14551.3	+	8401.21i	0.944858	+	0.545514i	0.0533783	+	0.998574i	$0.483001\pi$
$620$		0			0
$621$	6235.18	+	5275.79i	0.402913	+	0.340918i
$622$		0			0
$623$	−1595.83	+	486.815i	−0.102625	+	0.0313063i
$624$		0			0
$625$	−2070.99	−	3587.06i	−0.132543	−	0.229572i
$626$		0			0
$627$	814.317	+	7050.74i	0.0518671	+	0.449090i
$628$		0			0
$629$	−1929.27			−0.122297
$630$		0			0
$631$	−28945.5			−1.82615			−0.913077	−	0.407788i	$-0.866300\pi$
$631$	−28945.5			−1.82615			−0.913077	+	0.407788i	$0.866300\pi$
$632$		0			0
$633$	−323.301	+	240.001i	−0.0203003	+	0.0150698i
$634$		0			0
$635$	5840.05	+	10115.3i	0.364969	+	0.632145i
$636$		0			0
$637$	11864.2	−	24249.1i	0.737951	−	1.50829i
$638$		0			0
$639$	−3104.14	+	2912.56i	−0.192172	+	0.180312i
$640$		0			0
$641$	−18742.7	−	10821.1i	−1.15490	−	0.666783i	−0.204825	−	0.978799i	$-0.565663\pi$
$641$	−18742.7	−	10821.1i	−1.15490	−	0.666783i	−0.950077	+	0.312015i	$0.898996\pi$
$642$		0			0
$643$	15889.2	+	9173.63i	0.974508	+	0.562632i	0.900608	−	0.434633i	$-0.143122\pi$
$643$	15889.2	+	9173.63i	0.974508	+	0.562632i	0.0739003	+	0.997266i	$0.476455\pi$
$644$		0			0
$645$	−23490.5	+	17438.0i	−1.43401	+	1.06453i
$646$		0			0
$647$	−11759.1	−	20367.4i	−0.714527	−	1.23760i	−0.963142	−	0.268994i	$-0.913309\pi$
$647$	−11759.1	−	20367.4i	−0.714527	−	1.23760i	0.248615	−	0.968602i	$-0.420025\pi$
$648$		0			0
$649$	6916.03	+	3992.97i	0.418302	+	0.241507i
$650$		0			0
$651$	−181.766	+	79.2333i	−0.0109431	+	0.00477020i
$652$		0			0
$653$	10503.4	−	6064.13i	0.629447	−	0.363411i	−0.151091	−	0.988520i	$-0.548279\pi$
$653$	10503.4	−	6064.13i	0.629447	−	0.363411i	0.780538	+	0.625109i	$0.214945\pi$
$654$		0			0
$655$	−23261.1	+	40289.5i	−1.38762	+	2.40342i
$656$		0			0
$657$	27111.5	+	8197.71i	1.60992	+	0.486793i
$658$		0			0
$659$	6667.42	−	3849.44i	0.394121	−	0.227546i	−0.289823	−	0.957080i	$-0.593596\pi$
$659$	6667.42	−	3849.44i	0.394121	−	0.227546i	0.683944	+	0.729534i	$0.260263\pi$
$660$		0			0
$661$			1849.96i			0.108858i	0.998518	+	0.0544290i	$0.0173338\pi$
$661$			1849.96i			0.108858i	−0.998518	+	0.0544290i	$0.982666\pi$
$662$		0			0
$663$	−848.829	+	1960.41i	−0.0497221	+	0.114836i
$664$		0			0
$665$	−6307.96	+	6756.09i	−0.367838	+	0.393970i
$666$		0			0
$667$	4478.34	−	7756.72i	0.259973	−	0.450287i
$668$		0			0
$669$	−21419.7	+	2473.84i	−1.23787	+	0.142966i
$670$		0			0
$671$	18358.0	−	31797.0i	1.05619	−	1.82937i
$672$		0			0
$673$	−1372.38	−	2377.03i	−0.0786052	−	0.136148i	0.824043	−	0.566527i	$-0.191713\pi$
$673$	−1372.38	−	2377.03i	−0.0786052	−	0.136148i	−0.902648	+	0.430379i	$0.858380\pi$
$674$		0			0
$675$	29871.5	+	5393.92i	1.70334	+	0.307574i
$676$		0			0
$677$	−13024.0			−0.739368			−0.369684	−	0.929157i	$-0.620534\pi$
$677$	−13024.0			−0.739368			−0.369684	+	0.929157i	$0.620534\pi$
$678$		0			0
$679$	16367.6	+	3789.41i	0.925083	+	0.214174i
$680$		0			0
$681$	1511.62	−	1122.14i	0.0850592	−	0.0631432i
$682$		0			0
$683$	8703.77	−	5025.13i	0.487614	−	0.281524i	−0.235970	−	0.971760i	$-0.575827\pi$
$683$	8703.77	−	5025.13i	0.487614	−	0.281524i	0.723584	+	0.690236i	$0.242493\pi$
$684$		0			0
$685$		−	11845.5i		−	0.660723i
$686$		0			0
$687$	−11826.7	+	1365.91i	−0.656791	+	0.0758553i
$688$		0			0
$689$	39195.2			2.16722
$690$		0			0
$691$		−	4308.93i		−	0.237221i	−0.992941	−	0.118610i	$-0.962156\pi$
$691$		−	4308.93i		−	0.237221i	0.992941	−	0.118610i	$-0.0378439\pi$
$692$		0			0
$693$	12589.0	−	21929.2i	0.690069	−	1.20205i
$694$		0			0
$695$		−	51377.6i		−	2.80412i
$696$		0			0
$697$	−2084.79			−0.113296
$698$		0			0
$699$	−20473.0	−	27578.8i	−1.10781	−	1.49231i
$700$		0			0
$701$		−	25140.9i		−	1.35458i	−0.735717	−	0.677289i	$-0.763155\pi$
$701$		−	25140.9i		−	1.35458i	0.735717	−	0.677289i	$-0.236845\pi$
$702$		0			0
$703$	8639.98	−	4988.29i	0.463532	−	0.267620i
$704$		0			0
$705$	3245.94	+	28104.9i	0.173403	+	1.50141i
$706$		0			0
$707$	−4802.64	+	1465.07i	−0.255476	+	0.0779345i
$708$		0			0
$709$	−28831.3			−1.52720			−0.763598	−	0.645693i	$-0.776569\pi$
$709$	−28831.3			−1.52720			−0.763598	+	0.645693i	$0.776569\pi$
$710$		0			0
$711$	3669.76	+	3911.14i	0.193568	+	0.206300i
$712$		0			0
$713$	−59.9771	−	103.883i	−0.00315030	−	0.00545647i
$714$		0			0
$715$	36766.0	−	63680.5i	1.92303	−	3.33079i
$716$		0			0
$717$	8021.26	+	10805.3i	0.417796	+	0.562806i
$718$		0			0
$719$	−16062.6	+	27821.2i	−0.833147	+	1.44305i	0.0623840	+	0.998052i	$0.480130\pi$
$719$	−16062.6	+	27821.2i	−0.833147	+	1.44305i	−0.895531	+	0.445000i	$0.853204\pi$
$720$		0			0
$721$	9807.41	+	2270.60i	0.506584	+	0.117284i
$722$		0			0
$723$	3592.98	+	4840.05i	0.184820	+	0.248968i
$724$		0			0
$725$		−	33286.8i		−	1.70516i
$726$		0			0
$727$	32959.3	−	19029.0i	1.68142	−	0.970768i	0.720699	−	0.693249i	$-0.243821\pi$
$727$	32959.3	−	19029.0i	1.68142	−	0.970768i	0.960720	−	0.277519i	$-0.0895121\pi$
$728$		0			0
$729$	−15181.6	+	12527.5i	−0.771306	+	0.636465i
$730$		0			0
$731$	795.911	−	1378.56i	0.0402706	−	0.0697507i
$732$		0			0
$733$	5067.94	−	2925.97i	0.255373	−	0.147440i	−0.366849	−	0.930281i	$-0.619563\pi$
$733$	5067.94	−	2925.97i	0.255373	−	0.147440i	0.622222	+	0.782841i	$0.286230\pi$
$734$		0			0
$735$	32376.1	−	6010.71i	1.62478	−	0.301644i
$736$		0			0
$737$	−7200.00	−	4156.92i	−0.359858	−	0.207764i
$738$		0			0
$739$	16427.7	+	28453.7i	0.817733	+	1.41635i	0.907349	+	0.420378i	$0.138103\pi$
$739$	16427.7	+	28453.7i	0.817733	+	1.41635i	−0.0896163	+	0.995976i	$0.528564\pi$
$740$		0			0
$741$	−1267.45	−	10974.2i	−0.0628352	−	0.544057i
$742$		0			0
$743$	−1622.71	−	936.871i	−0.0801230	−	0.0462590i	0.459403	−	0.888228i	$-0.348063\pi$
$743$	−1622.71	−	936.871i	−0.0801230	−	0.0462590i	−0.539526	+	0.841969i	$0.681397\pi$
$744$		0			0
$745$	41290.2	+	23838.9i	2.03055	+	1.17234i
$746$		0			0
$747$	7700.54	−	25467.3i	0.377173	−	1.24739i
$748$		0			0
$749$	−6811.10	−	22327.4i	−0.332273	−	1.08922i
$750$		0			0
$751$	9160.00	+	15865.6i	0.445077	+	0.770897i	0.998058	−	0.0622978i	$-0.0198429\pi$
$751$	9160.00	+	15865.6i	0.445077	+	0.770897i	−0.552980	+	0.833194i	$0.686510\pi$
$752$		0			0
$753$	16847.9	+	7294.87i	0.815366	+	0.353041i
$754$		0			0
$755$	−28889.1			−1.39256
$756$		0			0
$757$	−17389.8			−0.834934			−0.417467	−	0.908692i	$-0.637082\pi$
$757$	−17389.8			−0.834934			−0.417467	+	0.908692i	$0.637082\pi$
$758$		0			0
$759$	14037.5	+	6078.03i	0.671316	+	0.290670i
$760$		0			0
$761$	−2251.59	−	3899.87i	−0.107254	−	0.185769i	0.807403	−	0.590000i	$-0.200872\pi$
$761$	−2251.59	−	3899.87i	−0.107254	−	0.185769i	−0.914657	+	0.404231i	$0.867539\pi$
$762$		0			0
$763$	1301.09	−	5619.82i	0.0617336	−	0.266646i
$764$		0			0
$765$	−2537.23	+	593.991i	−0.119913	+	0.0280729i
$766$		0			0
$767$	−10764.5	−	6214.88i	−0.506758	−	0.292577i
$768$		0			0
$769$	8677.31	+	5009.84i	0.406907	+	0.234928i	0.689460	−	0.724324i	$-0.257848\pi$
$769$	8677.31	+	5009.84i	0.406907	+	0.234928i	−0.282553	+	0.959252i	$0.591181\pi$
$770$		0			0
$771$	−4308.87	−	37308.2i	−0.201271	−	1.74270i
$772$		0			0
$773$	15195.6	+	26319.5i	0.707046	+	1.22464i	0.965948	+	0.258736i	$0.0833059\pi$
$773$	15195.6	+	26319.5i	0.707046	+	1.22464i	−0.258902	+	0.965904i	$0.583361\pi$
$774$		0			0
$775$	−386.074	−	222.900i	−0.0178944	−	0.0103314i
$776$		0			0
$777$	−35317.6	−	3991.00i	−1.63065	−	0.184268i
$778$		0			0
$779$	9336.46	−	5390.41i	0.429414	−	0.247922i
$780$		0			0
$781$	−3985.99	+	6903.94i	−0.182625	+	0.316315i
$782$		0			0
$783$	16477.4	+	13942.0i	0.752047	+	0.636331i
$784$		0			0
$785$	−1979.25	+	1142.72i	−0.0899905	+	0.0519560i
$786$		0			0
$787$			20274.0i			0.918285i	0.888363	+	0.459143i	$0.151843\pi$
$787$			20274.0i			0.918285i	−0.888363	+	0.459143i	$0.848157\pi$
$788$		0			0
$789$	9023.00	+	12154.7i	0.407132	+	0.548441i
$790$		0			0
$791$	−6367.04	−	20871.7i	−0.286202	−	0.938197i
$792$		0			0
$793$	−28573.4	+	49490.6i	−1.27954	+	2.21622i
$794$		0			0
$795$	28497.5	+	38388.6i	1.27133	+	1.71258i
$796$		0			0
$797$	2740.80	−	4747.21i	0.121812	−	0.210985i	−0.798670	−	0.601769i	$-0.794463\pi$
$797$	2740.80	−	4747.21i	0.121812	−	0.210985i	0.920482	+	0.390784i	$0.127796\pi$
$798$		0			0
$799$	−769.689	−	1333.14i	−0.0340797	−	0.0590277i
$800$		0			0
$801$	2368.30	−	554.444i	0.104469	−	0.0244573i
$802$		0			0
$803$	53046.0			2.33120
$804$		0			0
$805$	5812.54	+	19054.0i	0.254491	+	0.834244i
$806$		0			0
$807$	−2667.76	−	23098.7i	−0.116369	−	1.00757i
$808$		0			0
$809$	−7125.44	+	4113.88i	−0.309663	+	0.178784i	−0.646776	−	0.762680i	$-0.723883\pi$
$809$	−7125.44	+	4113.88i	−0.309663	+	0.178784i	0.337113	+	0.941464i	$0.390550\pi$
$810$		0			0
$811$		−	24169.5i		−	1.04649i	−0.852181	−	0.523247i	$-0.824721\pi$
$811$		−	24169.5i		−	1.04649i	0.852181	−	0.523247i	$-0.175279\pi$
$812$		0			0
$813$	−3577.37	−	4819.02i	−0.154322	−	0.207885i
$814$		0			0
$815$	−62229.8			−2.67462
$816$		0			0
$817$			8231.59i			0.352493i
$818$		0			0
$819$	−19594.3	+	34131.8i	−0.835994	+	1.45624i
$820$		0			0
$821$			12449.7i			0.529230i	0.964354	+	0.264615i	$0.0852449\pi$
$821$			12449.7i			0.529230i	−0.964354	+	0.264615i	$0.914755\pi$
$822$		0			0
$823$	−38170.6			−1.61670			−0.808351	−	0.588701i	$-0.799639\pi$
$823$	−38170.6			−1.61670			−0.808351	+	0.588701i	$0.799639\pi$
$824$		0			0
$825$	56474.2	−	6522.42i	2.38325	−	0.275250i
$826$		0			0
$827$		−	12733.5i		−	0.535415i	−0.963500	−	0.267707i	$-0.913734\pi$
$827$		−	12733.5i		−	0.535415i	0.963500	−	0.267707i	$-0.0862660\pi$
$828$		0			0
$829$	−2221.11	+	1282.36i	−0.0930549	+	0.0537253i	−0.545805	−	0.837912i	$-0.683776\pi$
$829$	−2221.11	+	1282.36i	−0.0930549	+	0.0537253i	0.452750	+	0.891637i	$0.350443\pi$
$830$		0			0
$831$	21919.1	−	16271.5i	0.915000	−	0.679245i
$832$		0			0
$833$	−1486.64	+	1000.08i	−0.0618354	+	0.0415975i
$834$		0			0
$835$	−17964.9			−0.744552
$836$		0			0
$837$	272.044	−	97.7506i	0.0112344	−	0.00403674i
$838$		0			0
$839$	6493.35	+	11246.8i	0.267194	+	0.462793i	0.968136	−	0.250425i	$-0.0805703\pi$
$839$	6493.35	+	11246.8i	0.267194	+	0.462793i	−0.700942	+	0.713218i	$0.747237\pi$
$840$		0			0
$841$	−359.831	+	623.246i	−0.0147538	+	0.0255544i
$842$		0			0
$843$	−17390.4	+	2008.49i	−0.710509	+	0.0820593i
$844$		0			0
$845$	−36928.7	+	63962.5i	−1.50342	+	2.60399i
$846$		0			0
$847$	5121.40	−	22120.9i	0.207761	−	0.897382i
$848$		0			0
$849$	7845.06	−	18118.6i	0.317128	−	0.732423i
$850$		0			0
$851$		−	21501.7i		−	0.866119i
$852$		0			0
$853$	−9158.91	+	5287.90i	−0.367638	+	0.212256i	−0.672426	−	0.740164i	$-0.734748\pi$
$853$	−9158.91	+	5287.90i	−0.367638	+	0.212256i	0.304788	+	0.952420i	$0.401414\pi$
$854$		0			0
$855$	9826.82	−	9220.33i	0.393064	−	0.368805i
$856$		0			0
$857$	−14495.5	+	25106.9i	−0.577778	+	1.00074i	0.417955	+	0.908468i	$0.362747\pi$
$857$	−14495.5	+	25106.9i	−0.577778	+	1.00074i	−0.995734	+	0.0922740i	$0.970586\pi$
$858$		0			0
$859$	−20910.0	+	12072.4i	−0.830546	+	0.479516i	−0.854040	−	0.520208i	$-0.825854\pi$
$859$	−20910.0	+	12072.4i	−0.830546	+	0.479516i	0.0234937	+	0.999724i	$0.492521\pi$
$860$		0			0
$861$	−38164.6	−	4312.73i	−1.51062	−	0.170705i
$862$		0			0
$863$	16715.3	+	9650.60i	0.659324	+	0.380661i	0.792019	−	0.610496i	$-0.209030\pi$
$863$	16715.3	+	9650.60i	0.659324	+	0.380661i	−0.132695	+	0.991157i	$0.542363\pi$
$864$		0			0
$865$	−20092.2	−	34800.8i	−0.789776	−	1.36793i
$866$		0			0
$867$	−20384.2	+	15132.1i	−0.798482	+	0.592748i
$868$		0			0
$869$	8698.79	+	5022.25i	0.339570	+	0.196051i
$870$		0			0
$871$	11206.5	+	6470.06i	0.435955	+	0.251699i
$872$		0			0
$873$	−23444.6	−	7088.95i	−0.908911	−	0.274828i
$874$		0			0
$875$	22850.3	+	21334.7i	0.882837	+	0.824278i
$876$		0			0
$877$	3447.12	+	5970.58i	0.132726	+	0.229889i	0.924727	−	0.380632i	$-0.124294\pi$
$877$	3447.12	+	5970.58i	0.132726	+	0.229889i	−0.792000	+	0.610521i	$0.790960\pi$
$878$		0			0
$879$	29215.2	−	21687.8i	1.12105	−	0.832207i
$880$		0			0
$881$	2203.54			0.0842668			0.0421334	−	0.999112i	$-0.486585\pi$
$881$	2203.54			0.0842668			0.0421334	+	0.999112i	$0.486585\pi$
$882$		0			0
$883$	34188.4			1.30298			0.651491	−	0.758656i	$-0.274144\pi$
$883$	34188.4			1.30298			0.651491	+	0.758656i	$0.274144\pi$
$884$		0			0
$885$	−1739.52	−	15061.6i	−0.0660717	−	0.572080i
$886$		0			0
$887$	14248.8	+	24679.7i	0.539378	+	0.934230i	0.998938	+	0.0460830i	$0.0146739\pi$
$887$	14248.8	+	24679.7i	0.539378	+	0.934230i	−0.459560	+	0.888147i	$0.651993\pi$
$888$		0			0
$889$	−8557.84	−	7990.20i	−0.322858	−	0.301443i
$890$		0			0
$891$	−20425.3	+	30687.3i	−0.767982	+	1.15383i
$892$		0			0
$893$	6893.91	+	3980.20i	0.258338	+	0.149151i
$894$		0			0
$895$	−4220.53	−	2436.72i	−0.157628	−	0.0910063i
$896$		0			0
$897$	−21848.8	−	9460.18i	−0.813276	−	0.352136i
$898$		0			0
$899$	−158.498	−	274.527i	−0.00588010	−	0.0101846i
$900$		0			0
$901$	−2252.87	−	1300.69i	−0.0833006	−	0.0480936i
$902$		0			0
$903$	17421.9	−	23589.7i	0.642042	−	0.869342i
$904$		0			0
$905$	2399.72	−	1385.48i	0.0881428	−	0.0508893i
$906$		0			0
$907$	−1583.03	+	2741.89i	−0.0579533	+	0.100378i	−0.893547	−	0.448971i	$-0.851791\pi$
$907$	−1583.03	+	2741.89i	−0.0579533	+	0.100378i	0.835593	+	0.549349i	$0.185124\pi$
$908$		0			0
$909$	7127.41	−	1668.60i	0.260067	−	0.0608844i
$910$		0			0
$911$	16808.6	−	9704.48i	0.611301	−	0.352935i	−0.162173	−	0.986762i	$-0.551850\pi$
$911$	16808.6	−	9704.48i	0.611301	−	0.352935i	0.773474	+	0.633827i	$0.218517\pi$
$912$		0			0
$913$		−	49829.0i		−	1.80624i
$914$		0			0
$915$	−69247.0	+	7997.60i	−2.50190	+	0.288953i
$916$		0			0
$917$	10518.4	−	45432.1i	0.378787	−	1.63610i
$918$		0			0
$919$	−6737.87	+	11670.3i	−0.241852	+	0.418899i	−0.961242	−	0.275707i	$-0.911088\pi$
$919$	−6737.87	+	11670.3i	−0.241852	+	0.418899i	0.719390	+	0.694606i	$0.244421\pi$
$920$		0			0
$921$	11155.3	−	25763.8i	0.399111	−	0.921767i
$922$		0			0
$923$	6204.02	−	10745.7i	0.221243	−	0.383205i
$924$		0			0
$925$	−39954.6	−	69203.4i	−1.42022	−	2.45989i
$926$		0			0
$927$	−14047.9	−	4247.67i	−0.497728	−	0.150498i
$928$		0			0
$929$	26118.8			0.922423			0.461211	−	0.887290i	$-0.347415\pi$
$929$	26118.8			0.922423			0.461211	+	0.887290i	$0.347415\pi$
$930$		0			0
$931$	4071.91	−	8322.55i	0.143342	−	0.292976i
$932$		0			0
$933$	−1135.13	−	491.493i	−0.0398311	−	0.0172463i
$934$		0			0
$935$	−4226.48	+	2440.16i	−0.147830	+	0.0853494i
$936$		0			0
$937$			34858.9i			1.21536i	0.794183	+	0.607679i	$0.207899\pi$
$937$			34858.9i			1.21536i	−0.794183	+	0.607679i	$0.792101\pi$
$938$		0			0
$939$	−20751.6	+	47926.8i	−0.721195	+	1.66563i
$940$		0			0
$941$	−23270.5			−0.806161			−0.403081	−	0.915164i	$-0.632061\pi$
$941$	−23270.5			−0.806161			−0.403081	+	0.915164i	$0.632061\pi$
$942$		0			0
$943$		−	23235.0i		−	0.802369i
$944$		0			0
$945$	−47675.8	+	5625.07i	−1.64116	+	0.193633i
$946$		0			0
$947$			21281.9i			0.730273i	0.930954	+	0.365137i	$0.118978\pi$
$947$			21281.9i			0.730273i	−0.930954	+	0.365137i	$0.881022\pi$
$948$		0			0
$949$	−82563.8			−2.82417
$950$		0			0
$951$	6417.27	−	14821.0i	0.218816	−	0.505367i
$952$		0			0
$953$			4409.79i			0.149892i	0.997188	+	0.0749461i	$0.0238785\pi$
$953$			4409.79i			0.149892i	−0.997188	+	0.0749461i	$0.976122\pi$
$954$		0			0
$955$	52490.2	−	30305.2i	1.77858	−	1.02686i
$956$		0			0
$957$	37096.1	+	16062.1i	1.25303	+	0.542542i
$958$		0			0
$959$	3464.59	+	11357.3i	0.116661	+	0.382424i
$960$		0			0
$961$	29786.8			0.999857
$962$		0			0
$963$	7757.31	+	33135.3i	0.259580	+	1.10879i
$964$		0			0
$965$	47625.4	+	82489.6i	1.58872	+	2.75175i
$966$		0			0
$967$	−5443.52	+	9428.46i	−0.181026	+	0.313546i	−0.942230	−	0.334966i	$-0.891275\pi$
$967$	−5443.52	+	9428.46i	−0.181026	+	0.313546i	0.761204	+	0.648512i	$0.224608\pi$
$968$		0			0
$969$	−291.327	+	672.835i	−0.00965819	+	0.0223061i
$970$		0			0
$971$	−10600.7	+	18361.0i	−0.350354	+	0.606830i	−0.986311	−	0.164894i	$-0.947272\pi$
$971$	−10600.7	+	18361.0i	−0.350354	+	0.606830i	0.635958	+	0.771724i	$0.280605\pi$
$972$		0			0
$973$	15027.0	+	49259.8i	0.495110	+	1.62302i
$974$		0			0
$975$	−87899.5	+	10151.9i	−2.88722	+	0.333456i
$976$		0			0
$977$		−	54447.6i		−	1.78294i	−0.453080	−	0.891470i	$-0.649675\pi$
$977$		−	54447.6i		−	1.78294i	0.453080	−	0.891470i	$-0.350325\pi$
$978$		0			0
$979$	3945.09	−	2277.70i	0.128790	−	0.0743570i
$980$		0			0
$981$	−2433.99	+	8049.70i	−0.0792164	+	0.261985i
$982$		0			0
$983$	−18546.9	+	32124.1i	−0.601783	+	1.04232i	0.390768	+	0.920489i	$0.372209\pi$
$983$	−18546.9	+	32124.1i	−0.601783	+	1.04232i	−0.992551	+	0.121830i	$0.961124\pi$
$984$		0			0
$985$	−38759.3	+	22377.7i	−1.25378	+	0.723871i
$986$		0			0
$987$	−11332.3	−	25997.0i	−0.365462	−	0.838393i
$988$		0			0
$989$	15364.0	+	8870.41i	0.493981	+	0.285200i
$990$		0			0
$991$	−359.692	−	623.005i	−0.0115298	−	0.0199701i	0.860203	−	0.509952i	$-0.170337\pi$
$991$	−359.692	−	623.005i	−0.0115298	−	0.0199701i	−0.871733	+	0.489982i	$0.837003\pi$
$992$		0			0
$993$	−13988.2	−	6056.69i	−0.447032	−	0.193558i
$994$		0			0
$995$	−7545.05	−	4356.14i	−0.240396	−	0.138793i
$996$		0			0
$997$	8519.24	+	4918.59i	0.270619	+	0.156242i	0.629169	−	0.777269i	$-0.283395\pi$
$997$	8519.24	+	4918.59i	0.270619	+	0.156242i	−0.358550	+	0.933511i	$0.616729\pi$
$998$		0			0
$999$	50991.3	+	9207.53i	1.61491	+	0.291605i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	252.4.w.a.5.4	✓	48
3.2	odd	2		756.4.w.a.341.1		48
7.3	odd	6		252.4.bm.a.185.13	yes	48
9.2	odd	6		252.4.bm.a.173.13	yes	48
9.7	even	3		756.4.bm.a.89.1		48
21.17	even	6		756.4.bm.a.17.1		48
63.38	even	6	inner	252.4.w.a.101.4	yes	48
63.52	odd	6		756.4.w.a.521.1		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.4.w.a.5.4	✓	48	1.1	even	1	trivial
252.4.w.a.101.4	yes	48	63.38	even	6	inner
252.4.bm.a.173.13	yes	48	9.2	odd	6
252.4.bm.a.185.13	yes	48	7.3	odd	6
756.4.w.a.341.1		48	3.2	odd	2
756.4.w.a.521.1		48	63.52	odd	6
756.4.bm.a.17.1		48	21.17	even	6
756.4.bm.a.89.1		48	9.7	even	3

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:	\( N \)	\(=\)	\( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	252.w (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-4.76836 - 2.06463i) q^{3} +(9.23798 + 16.0007i) q^{5} +(-13.5371 - 12.6391i) q^{7} +(18.4746 + 19.6898i) q^{9} +O(q^{10})\)	\(q+(-4.76836 - 2.06463i) q^{3} +(9.23798 + 16.0007i) q^{5} +(-13.5371 - 12.6391i) q^{7} +(18.4746 + 19.6898i) q^{9} +(43.7922 + 25.2834i) q^{11} +(-68.1606 - 39.3525i) q^{13} +(-11.0146 - 95.3699i) q^{15} +(2.61183 + 4.52382i) q^{17} +(-23.3935 - 13.5062i) q^{19} +(38.4545 + 88.2171i) q^{21} +(-50.4179 + 29.1088i) q^{23} +(-108.181 + 187.374i) q^{25} +(-47.4415 - 132.031i) q^{27} +(-133.237 + 76.9242i) q^{29} +2.06045i q^{31} +(-156.616 - 210.975i) q^{33} +(77.1795 - 333.362i) q^{35} +(-184.666 + 319.851i) q^{37} +(243.766 + 328.374i) q^{39} +(-199.553 + 345.635i) q^{41} +(-152.366 - 263.906i) q^{43} +(-144.382 + 477.500i) q^{45} -294.693 q^{47} +(23.5039 + 342.194i) q^{49} +(-3.11414 - 26.9637i) q^{51} +(-431.281 + 249.000i) q^{53} +934.271i q^{55} +(83.6633 + 112.702i) q^{57} +157.928 q^{59} -726.088i q^{61} +(-1.22936 - 500.045i) q^{63} -1454.15i q^{65} -164.413 q^{67} +(300.510 - 34.7070i) q^{69} +157.652i q^{71} +(908.485 - 524.514i) q^{73} +(902.703 - 670.116i) q^{75} +(-273.256 - 895.759i) q^{77} +198.638 q^{79} +(-46.3777 + 727.523i) q^{81} +(-492.704 - 853.388i) q^{83} +(-48.2561 + 83.5820i) q^{85} +(794.141 - 91.7184i) q^{87} +(45.0433 - 78.0173i) q^{89} +(425.312 + 1394.21i) q^{91} +(4.25406 - 9.82496i) q^{93} -499.081i q^{95} +(-785.610 + 453.572i) q^{97} +(311.217 + 1329.36i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 6 q^{7} + 12 q^{9}+O(q^{10}) \) 48 * q + 6 * q^7 + 12 * q^9	\( 48 q + 6 q^{7} + 12 q^{9} + 12 q^{11} - 36 q^{13} + 66 q^{15} - 72 q^{17} + 24 q^{21} + 30 q^{23} - 600 q^{25} - 396 q^{27} + 42 q^{29} + 390 q^{35} + 84 q^{37} - 840 q^{39} - 618 q^{41} - 42 q^{43} + 366 q^{45} + 396 q^{47} + 318 q^{49} - 738 q^{51} - 1620 q^{53} + 492 q^{57} + 1500 q^{59} + 672 q^{63} - 588 q^{67} - 924 q^{69} + 564 q^{75} - 2472 q^{77} + 1608 q^{79} + 2592 q^{81} - 360 q^{85} + 2640 q^{87} + 1722 q^{89} + 540 q^{91} + 660 q^{93} - 792 q^{97} - 54 q^{99}+O(q^{100}) \) 48 * q + 6 * q^7 + 12 * q^9 + 12 * q^11 - 36 * q^13 + 66 * q^15 - 72 * q^17 + 24 * q^21 + 30 * q^23 - 600 * q^25 - 396 * q^27 + 42 * q^29 + 390 * q^35 + 84 * q^37 - 840 * q^39 - 618 * q^41 - 42 * q^43 + 366 * q^45 + 396 * q^47 + 318 * q^49 - 738 * q^51 - 1620 * q^53 + 492 * q^57 + 1500 * q^59 + 672 * q^63 - 588 * q^67 - 924 * q^69 + 564 * q^75 - 2472 * q^77 + 1608 * q^79 + 2592 * q^81 - 360 * q^85 + 2640 * q^87 + 1722 * q^89 + 540 * q^91 + 660 * q^93 - 792 * q^97 - 54 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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