LMFDB - Embedded newform 336.4.bc.d.257.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [336,4,Mod(17,336)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(336, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 3, 1]))

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

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

chi := DirichletCharacter("336.17");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 336 = 2^{4} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	336.bc (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$19.8246417619$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - x^{11} - 29x^{9} + 6x^{8} - 49x^{7} + 1564x^{6} - 441x^{5} + 486x^{4} - 21141x^{3} - 59049x + 531441 $ x^12 - x^11 - 29x^9 + 6x^8 - 49x^7 + 1564x^6 - 441x^5 + 486x^4 - 21141x^3 - 59049x + 531441
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{4}\cdot 3^{3} $
Twist minimal:	no (minimal twist has level 21)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			257.4
Root			$-0.232749 + 2.99096i$ of defining polynomial
Character	$\chi$	$=$	336.257
Dual form			336.4.bc.d.17.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.24112 - 4.68800i) q^{3} +(-5.80193 + 10.0492i) q^{5} +(18.4018 + 2.09174i) q^{7} +(-16.9548 - 21.0128i) q^{9} +O(q^{10})$	\(q+(2.24112 - 4.68800i) q^{3} +(-5.80193 + 10.0492i) q^{5} +(18.4018 + 2.09174i) q^{7} +(-16.9548 - 21.0128i) q^{9} +(-15.5157 + 8.95800i) q^{11} +62.4185i q^{13} +(34.1081 + 49.7211i) q^{15} +(10.7082 + 18.5472i) q^{17} +(-9.50747 - 5.48914i) q^{19} +(51.0467 - 81.5796i) q^{21} +(59.8367 + 34.5467i) q^{23} +(-4.82490 - 8.35697i) q^{25} +(-136.506 + 32.3918i) q^{27} +265.583i q^{29} +(-8.85795 + 5.11414i) q^{31} +(7.22254 + 92.8136i) q^{33} +(-127.786 + 172.788i) q^{35} +(-20.8257 + 36.0712i) q^{37} +(292.618 + 139.887i) q^{39} -31.0035 q^{41} +224.550 q^{43} +(309.533 - 48.4678i) q^{45} +(81.8595 - 141.785i) q^{47} +(334.249 + 76.9836i) q^{49} +(110.948 - 8.63368i) q^{51} +(456.586 - 263.610i) q^{53} -207.895i q^{55} +(-47.0405 + 32.2692i) q^{57} +(205.978 + 356.765i) q^{59} +(223.807 + 129.215i) q^{61} +(-268.044 - 422.137i) q^{63} +(-627.258 - 362.148i) q^{65} +(161.737 + 280.137i) q^{67} +(296.056 - 203.091i) q^{69} +45.4199i q^{71} +(-486.879 + 281.100i) q^{73} +(-49.9907 + 3.89016i) q^{75} +(-304.254 + 132.388i) q^{77} +(144.610 - 250.473i) q^{79} +(-154.073 + 712.532i) q^{81} -448.767 q^{83} -248.513 q^{85} +(1245.05 + 595.204i) q^{87} +(-280.814 + 486.384i) q^{89} +(-130.563 + 1148.61i) q^{91} +(4.12336 + 52.9875i) q^{93} +(110.323 - 63.6953i) q^{95} -214.364i q^{97} +(451.297 + 174.147i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 3 q^{3} + 56 q^{7} - 3 q^{9}+O(q^{10}) $ 12 * q + 3 * q^3 + 56 * q^7 - 3 * q^9	$ 12 q + 3 q^{3} + 56 q^{7} - 3 q^{9} - 6 q^{15} - 300 q^{19} + 357 q^{21} - 42 q^{25} + 930 q^{31} - 855 q^{33} + 764 q^{37} + 426 q^{39} + 1012 q^{43} + 2367 q^{45} - 336 q^{49} + 1341 q^{51} + 270 q^{57} + 2358 q^{61} - 1071 q^{63} - 792 q^{67} - 2904 q^{73} + 2418 q^{75} - 1674 q^{79} + 837 q^{81} + 348 q^{85} - 1638 q^{87} + 1218 q^{91} - 1479 q^{93} + 3354 q^{99}+O(q^{100}) $ 12 * q + 3 * q^3 + 56 * q^7 - 3 * q^9 - 6 * q^15 - 300 * q^19 + 357 * q^21 - 42 * q^25 + 930 * q^31 - 855 * q^33 + 764 * q^37 + 426 * q^39 + 1012 * q^43 + 2367 * q^45 - 336 * q^49 + 1341 * q^51 + 270 * q^57 + 2358 * q^61 - 1071 * q^63 - 792 * q^67 - 2904 * q^73 + 2418 * q^75 - 1674 * q^79 + 837 * q^81 + 348 * q^85 - 1638 * q^87 + 1218 * q^91 - 1479 * q^93 + 3354 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/336\mathbb{Z}\right)^\times$.

$n$	$85$	$113$	$127$	$241$
$\chi(n)$	$1$	$-1$	$1$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	2.24112	−	4.68800i	0.431304	−	0.902207i
$3$	2.24112	−	4.68800i	0.431304	−	0.902207i
$4$		0			0
$5$	−5.80193	+	10.0492i	−0.518941	+	0.898832i	0.480817	+	0.876821i	$0.340340\pi$
$5$	−5.80193	+	10.0492i	−0.518941	+	0.898832i	−0.999758	+	0.0220109i	$0.992993\pi$
$6$		0			0
$7$	18.4018	+	2.09174i	0.993601	+	0.112944i
$7$	18.4018	+	2.09174i	0.993601	+	0.112944i
$8$		0			0
$9$	−16.9548	−	21.0128i	−0.627954	−	0.778251i
$10$		0			0
$11$	−15.5157	+	8.95800i	−0.425287	+	0.245540i	−0.697337	−	0.716743i	$-0.745632\pi$
$11$	−15.5157	+	8.95800i	−0.425287	+	0.245540i	0.272050	+	0.962283i	$0.412299\pi$
$12$		0			0
$13$			62.4185i			1.33167i	0.746097	+	0.665837i	$0.231925\pi$
$13$			62.4185i			1.33167i	−0.746097	+	0.665837i	$0.768075\pi$
$14$		0			0
$15$	34.1081	+	49.7211i	0.587111	+	0.855862i
$16$		0			0
$17$	10.7082	+	18.5472i	0.152772	+	0.264609i	0.932245	−	0.361826i	$-0.117847\pi$
$17$	10.7082	+	18.5472i	0.152772	+	0.264609i	−0.779474	+	0.626435i	$0.784513\pi$
$18$		0			0
$19$	−9.50747	−	5.48914i	−0.114798	−	0.0662787i	0.441502	−	0.897261i	$-0.354446\pi$
$19$	−9.50747	−	5.48914i	−0.114798	−	0.0662787i	−0.556300	+	0.830982i	$0.687779\pi$
$20$		0			0
$21$	51.0467	−	81.5796i	0.530443	−	0.847721i
$22$		0			0
$23$	59.8367	+	34.5467i	0.542470	+	0.313195i	0.746079	−	0.665857i	$-0.231934\pi$
$23$	59.8367	+	34.5467i	0.542470	+	0.313195i	−0.203609	+	0.979052i	$0.565267\pi$
$24$		0			0
$25$	−4.82490	−	8.35697i	−0.0385992	−	0.0668557i
$26$		0			0
$27$	−136.506	+	32.3918i	−0.972982	+	0.230881i
$28$		0			0
$29$			265.583i			1.70061i	0.526294	+	0.850303i	$0.323581\pi$
$29$			265.583i			1.70061i	−0.526294	+	0.850303i	$0.676419\pi$
$30$		0			0
$31$	−8.85795	+	5.11414i	−0.0513205	+	0.0296299i	−0.525441	−	0.850830i	$-0.676100\pi$
$31$	−8.85795	+	5.11414i	−0.0513205	+	0.0296299i	0.474120	+	0.880460i	$0.342766\pi$
$32$		0			0
$33$	7.22254	+	92.8136i	0.0380995	+	0.489599i
$34$		0			0
$35$	−127.786	+	172.788i	−0.617138	+	0.834470i
$36$		0			0
$37$	−20.8257	+	36.0712i	−0.0925331	+	0.160272i	−0.908576	−	0.417719i	$-0.862830\pi$
$37$	−20.8257	+	36.0712i	−0.0925331	+	0.160272i	0.816043	+	0.577991i	$0.196163\pi$
$38$		0			0
$39$	292.618	+	139.887i	1.20145	+	0.574356i
$40$		0			0
$41$	−31.0035			−0.118096			−0.0590480	−	0.998255i	$-0.518807\pi$
$41$	−31.0035			−0.118096			−0.0590480	+	0.998255i	$0.518807\pi$
$42$		0			0
$43$	224.550			0.796363			0.398181	−	0.917307i	$-0.369641\pi$
$43$	224.550			0.796363			0.398181	+	0.917307i	$0.369641\pi$
$44$		0			0
$45$	309.533	−	48.4678i	1.02539	−	0.160559i
$46$		0			0
$47$	81.8595	−	141.785i	0.254052	−	0.440031i	−0.710586	−	0.703611i	$-0.751570\pi$
$47$	81.8595	−	141.785i	0.254052	−	0.440031i	0.964638	+	0.263580i	$0.0849033\pi$
$48$		0			0
$49$	334.249	+	76.9836i	0.974487	+	0.224442i
$50$		0			0
$51$	110.948	−	8.63368i	0.304623	−	0.0237050i
$52$		0			0
$53$	456.586	−	263.610i	1.18334	−	0.683200i	0.226553	−	0.973999i	$-0.427254\pi$
$53$	456.586	−	263.610i	1.18334	−	0.683200i	0.956784	+	0.290799i	$0.0939211\pi$
$54$		0			0
$55$		−	207.895i		−	0.509682i
$56$		0			0
$57$	−47.0405	+	32.2692i	−0.109310	+	0.0749853i
$58$		0			0
$59$	205.978	+	356.765i	0.454510	+	0.787234i	0.998660	−	0.0517537i	$-0.0164811\pi$
$59$	205.978	+	356.765i	0.454510	+	0.787234i	−0.544150	+	0.838988i	$0.683148\pi$
$60$		0			0
$61$	223.807	+	129.215i	0.469764	+	0.271218i	0.716141	−	0.697956i	$-0.245907\pi$
$61$	223.807	+	129.215i	0.469764	+	0.271218i	−0.246377	+	0.969174i	$0.579240\pi$
$62$		0			0
$63$	−268.044	−	422.137i	−0.536037	−	0.844194i
$64$		0			0
$65$	−627.258	−	362.148i	−1.19695	−	0.691060i
$66$		0			0
$67$	161.737	+	280.137i	0.294915	+	0.510808i	0.974965	−	0.222357i	$-0.0713752\pi$
$67$	161.737	+	280.137i	0.294915	+	0.510808i	−0.680050	+	0.733166i	$0.738042\pi$
$68$		0			0
$69$	296.056	−	203.091i	0.516536	−	0.354338i
$70$		0			0
$71$			45.4199i			0.0759205i	0.999279	+	0.0379603i	$0.0120860\pi$
$71$			45.4199i			0.0759205i	−0.999279	+	0.0379603i	$0.987914\pi$
$72$		0			0
$73$	−486.879	+	281.100i	−0.780615	+	0.450688i	−0.836648	−	0.547741i	$-0.815488\pi$
$73$	−486.879	+	281.100i	−0.780615	+	0.450688i	0.0560334	+	0.998429i	$0.482155\pi$
$74$		0			0
$75$	−49.9907	+	3.89016i	−0.0769657	+	0.00598929i
$76$		0			0
$77$	−304.254	+	132.388i	−0.450298	+	0.195935i
$78$		0			0
$79$	144.610	−	250.473i	0.205949	−	0.356714i	−0.744486	−	0.667638i	$-0.767305\pi$
$79$	144.610	−	250.473i	0.205949	−	0.356714i	0.950435	+	0.310925i	$0.100639\pi$
$80$		0			0
$81$	−154.073	+	712.532i	−0.211348	+	0.977411i
$82$		0			0
$83$	−448.767			−0.593477			−0.296738	−	0.954959i	$-0.595899\pi$
$83$	−448.767			−0.593477			−0.296738	+	0.954959i	$0.595899\pi$
$84$		0			0
$85$	−248.513			−0.317118
$86$		0			0
$87$	1245.05	+	595.204i	1.53430	+	0.733478i
$88$		0			0
$89$	−280.814	+	486.384i	−0.334452	+	0.579288i	−0.983379	−	0.181562i	$-0.941885\pi$
$89$	−280.814	+	486.384i	−0.334452	+	0.579288i	0.648927	+	0.760850i	$0.275218\pi$
$90$		0			0
$91$	−130.563	+	1148.61i	−0.150404	+	1.32315i
$92$		0			0
$93$	4.12336	+	52.9875i	0.00459756	+	0.0590811i
$94$		0			0
$95$	110.323	−	63.6953i	0.119147	−	0.0687895i
$96$		0			0
$97$		−	214.364i		−	0.224385i	−0.993686	−	0.112192i	$-0.964213\pi$
$97$		−	214.364i		−	0.224385i	0.993686	−	0.112192i	$-0.0357873\pi$
$98$		0			0
$99$	451.297	+	174.147i	0.458152	+	0.176793i
$100$		0			0
$101$	858.845	+	1487.56i	0.846122	+	1.46553i	0.884644	+	0.466268i	$0.154402\pi$
$101$	858.845	+	1487.56i	0.846122	+	1.46553i	−0.0385219	+	0.999258i	$0.512265\pi$
$102$		0			0
$103$	−1002.61	−	578.855i	−0.959123	−	0.553750i	−0.0632200	−	0.998000i	$-0.520137\pi$
$103$	−1002.61	−	578.855i	−0.959123	−	0.553750i	−0.895903	+	0.444250i	$0.853470\pi$
$104$		0			0
$105$	523.644	+	986.300i	0.486690	+	0.916696i
$106$		0			0
$107$	−1054.64	−	608.897i	−0.952859	−	0.550134i	−0.0588912	−	0.998264i	$-0.518757\pi$
$107$	−1054.64	−	608.897i	−0.952859	−	0.550134i	−0.893968	+	0.448131i	$0.852090\pi$
$108$		0			0
$109$	−649.132	−	1124.33i	−0.570418	−	0.987992i	−0.996523	−	0.0833189i	$-0.973448\pi$
$109$	−649.132	−	1124.33i	−0.570418	−	0.987992i	0.426105	−	0.904674i	$-0.359885\pi$
$110$		0			0
$111$	122.429	+	178.471i	0.104689	+	0.152610i
$112$		0			0
$113$		−	1437.86i		−	1.19701i	−0.801118	−	0.598506i	$-0.795761\pi$
$113$		−	1437.86i		−	1.19701i	0.801118	−	0.598506i	$-0.204239\pi$
$114$		0			0
$115$	−694.337	+	400.876i	−0.563019	+	0.325059i
$116$		0			0
$117$	1311.58	−	1058.29i	1.03638	−	0.836230i
$118$		0			0
$119$	158.254	+	363.699i	0.121908	+	0.280170i
$120$		0			0
$121$	−505.009	+	874.701i	−0.379420	+	0.657175i
$122$		0			0
$123$	−69.4827	+	145.345i	−0.0509353	+	0.106547i
$124$		0			0
$125$	−1338.51			−0.957759
$126$		0			0
$127$	−2686.32			−1.87695			−0.938475	−	0.345347i	$-0.887761\pi$
$127$	−2686.32			−1.87695			−0.938475	+	0.345347i	$0.887761\pi$
$128$		0			0
$129$	503.244	−	1052.69i	0.343474	−	0.718484i
$130$		0			0
$131$	801.637	−	1388.48i	0.534651	−	0.926043i	−0.464529	−	0.885558i	$-0.653776\pi$
$131$	801.637	−	1388.48i	0.534651	−	0.926043i	0.999180	−	0.0404852i	$-0.0128904\pi$
$132$		0			0
$133$	−163.472	−	120.897i	−0.106578	−	0.0788203i
$134$		0			0
$135$	466.484	−	1559.71i	0.297396	−	0.994361i
$136$		0			0
$137$	2007.90	−	1159.26i	1.25216	−	0.722938i	0.280626	−	0.959817i	$-0.409458\pi$
$137$	2007.90	−	1159.26i	1.25216	−	0.722938i	0.971539	+	0.236879i	$0.0761246\pi$
$138$		0			0
$139$			1841.57i			1.12374i	0.827225	+	0.561871i	$0.189918\pi$
$139$			1841.57i			1.12374i	−0.827225	+	0.561871i	$0.810082\pi$
$140$		0			0
$141$	−481.230	−	701.514i	−0.287425	−	0.418994i
$142$		0			0
$143$	−559.144	−	968.466i	−0.326979	−	0.566344i
$144$		0			0
$145$	−2668.91	−	1540.90i	−1.52856	−	0.882514i
$146$		0			0
$147$	1109.99	−	1394.43i	0.622793	−	0.782386i
$148$		0			0
$149$	−1126.68	−	650.488i	−0.619470	−	0.357651i	0.157193	−	0.987568i	$-0.449756\pi$
$149$	−1126.68	−	650.488i	−0.619470	−	0.357651i	−0.776663	+	0.629917i	$0.783089\pi$
$150$		0			0
$151$	−1308.24	−	2265.94i	−0.705055	−	1.22119i	−0.966672	−	0.256020i	$-0.917589\pi$
$151$	−1308.24	−	2265.94i	−0.705055	−	1.22119i	0.261616	−	0.965172i	$-0.415745\pi$
$152$		0			0
$153$	208.172	−	539.472i	0.109998	−	0.285057i
$154$		0			0
$155$		−	118.688i		−	0.0615046i
$156$		0			0
$157$	−809.876	+	467.582i	−0.411689	+	0.237689i	−0.691515	−	0.722362i	$-0.743056\pi$
$157$	−809.876	+	467.582i	−0.411689	+	0.237689i	0.279826	+	0.960051i	$0.409723\pi$
$158$		0			0
$159$	−212.540	−	2731.26i	−0.106010	−	1.36228i
$160$		0			0
$161$	1028.84	+	760.883i	0.503625	+	0.372460i
$162$		0			0
$163$	−259.079	+	448.738i	−0.124495	+	0.215631i	−0.921535	−	0.388295i	$-0.873064\pi$
$163$	−259.079	+	448.738i	−0.124495	+	0.215631i	0.797041	+	0.603926i	$0.206398\pi$
$164$		0			0
$165$	−974.612	−	465.918i	−0.459839	−	0.219828i
$166$		0			0
$167$	3767.97			1.74595			0.872977	−	0.487761i	$-0.162186\pi$
$167$	3767.97			1.74595			0.872977	+	0.487761i	$0.162186\pi$
$168$		0			0
$169$	−1699.06			−0.773356
$170$		0			0
$171$	45.8548	+	292.845i	0.0205064	+	0.130962i
$172$		0			0
$173$	1196.53	−	2072.45i	0.525841	−	0.910783i	−0.473706	−	0.880683i	$-0.657084\pi$
$173$	1196.53	−	2072.45i	0.525841	−	0.910783i	0.999547	−	0.0301000i	$-0.00958257\pi$
$174$		0			0
$175$	−71.3059	−	163.875i	−0.0308013	−	0.0707875i
$176$		0			0
$177$	2134.14	−	166.074i	0.906280	−	0.0705246i
$178$		0			0
$179$	−554.381	+	320.072i	−0.231488	+	0.133650i	−0.611258	−	0.791431i	$-0.709336\pi$
$179$	−554.381	+	320.072i	−0.231488	+	0.133650i	0.379770	+	0.925081i	$0.376003\pi$
$180$		0			0
$181$			4204.05i			1.72643i	0.504833	+	0.863217i	$0.331554\pi$
$181$			4204.05i			1.72643i	−0.504833	+	0.863217i	$0.668446\pi$
$182$		0			0
$183$	1107.34	−	759.623i	0.447306	−	0.306847i
$184$		0			0
$185$	−241.659	−	418.565i	−0.0960384	−	0.166343i
$186$		0			0
$187$	−332.291	−	191.848i	−0.129944	−	0.0750231i
$188$		0			0
$189$	−2579.70	+	310.531i	−0.992833	+	0.119512i
$190$		0			0
$191$	1261.85	+	728.530i	0.478033	+	0.275993i	0.719597	−	0.694392i	$-0.244327\pi$
$191$	1261.85	+	728.530i	0.478033	+	0.275993i	−0.241563	+	0.970385i	$0.577660\pi$
$192$		0			0
$193$	−914.633	−	1584.19i	−0.341123	−	0.590842i	0.643519	−	0.765430i	$-0.277474\pi$
$193$	−914.633	−	1584.19i	−0.341123	−	0.590842i	−0.984642	+	0.174588i	$0.944141\pi$
$194$		0			0
$195$	−3103.51	+	2128.97i	−1.13973	+	0.781840i
$196$		0			0
$197$			661.168i			0.239118i	0.992827	+	0.119559i	$0.0381481\pi$
$197$			661.168i			0.239118i	−0.992827	+	0.119559i	$0.961852\pi$
$198$		0			0
$199$	1687.99	−	974.564i	0.601300	−	0.347161i	−0.168253	−	0.985744i	$-0.553812\pi$
$199$	1687.99	−	974.564i	0.601300	−	0.347161i	0.769553	+	0.638583i	$0.220479\pi$
$200$		0			0
$201$	1675.76	−	130.403i	0.588053	−	0.0457609i
$202$		0			0
$203$	−555.532	+	4887.20i	−0.192073	+	1.68972i
$204$		0			0
$205$	179.880	−	311.562i	0.0612849	−	0.106148i
$206$		0			0
$207$	−288.594	−	1843.06i	−0.0969017	−	0.618850i
$208$		0			0
$209$	196.687			0.0650963
$210$		0			0
$211$	−3341.96			−1.09038			−0.545189	−	0.838313i	$-0.683542\pi$
$211$	−3341.96			−1.09038			−0.545189	+	0.838313i	$0.683542\pi$
$212$		0			0
$213$	212.929	+	101.792i	0.0684960	+	0.0327448i
$214$		0			0
$215$	−1302.83	+	2256.56i	−0.413265	+	0.715796i
$216$		0			0
$217$	−173.699	+	75.5805i	−0.0543386	+	0.0236440i
$218$		0			0
$219$	226.642	+	2912.47i	0.0699316	+	0.898659i
$220$		0			0
$221$	−1157.68	+	668.390i	−0.352372	+	0.203442i
$222$		0			0
$223$		−	2143.28i		−	0.643608i	−0.946806	−	0.321804i	$-0.895711\pi$
$223$		−	2143.28i		−	0.643608i	0.946806	−	0.321804i	$-0.104289\pi$
$224$		0			0
$225$	−93.7981	+	243.075i	−0.0277920	+	0.0720221i
$226$		0			0
$227$	−1284.55	−	2224.91i	−0.375589	−	0.650540i	0.614826	−	0.788663i	$-0.289226\pi$
$227$	−1284.55	−	2224.91i	−0.375589	−	0.650540i	−0.990415	+	0.138123i	$0.955893\pi$
$228$		0			0
$229$	91.0827	+	52.5866i	0.0262835	+	0.0151748i	0.513084	−	0.858338i	$-0.328503\pi$
$229$	91.0827	+	52.5866i	0.0262835	+	0.0151748i	−0.486801	+	0.873513i	$0.661836\pi$
$230$		0			0
$231$	−61.2350	+	1723.04i	−0.0174414	+	0.490770i
$232$		0			0
$233$	2273.94	+	1312.86i	0.639360	+	0.369135i	0.784368	−	0.620296i	$-0.212987\pi$
$233$	2273.94	+	1312.86i	0.639360	+	0.369135i	−0.145008	+	0.989431i	$0.546321\pi$
$234$		0			0
$235$	949.887	+	1645.25i	0.263676	+	0.456700i
$236$		0			0
$237$	−850.127	−	1239.27i	−0.233003	−	0.339660i
$238$		0			0
$239$		−	6080.85i		−	1.64576i	−0.568212	−	0.822882i	$-0.692365\pi$
$239$		−	6080.85i		−	1.64576i	0.568212	−	0.822882i	$-0.307635\pi$
$240$		0			0
$241$	4008.74	−	2314.45i	1.07147	−	0.618616i	0.142891	−	0.989738i	$-0.454360\pi$
$241$	4008.74	−	2314.45i	1.07147	−	0.618616i	0.928584	+	0.371122i	$0.121027\pi$
$242$		0			0
$243$	2995.06	+	2319.17i	0.790671	+	0.612241i
$244$		0			0
$245$	−2712.92	+	2912.30i	−0.707437	+	0.759428i
$246$		0			0
$247$	342.624	−	593.442i	0.0882617	−	0.152874i
$248$		0			0
$249$	−1005.74	+	2103.82i	−0.255969	+	0.535439i
$250$		0			0
$251$	−5967.85			−1.50075			−0.750373	−	0.661015i	$-0.770126\pi$
$251$	−5967.85			−1.50075			−0.750373	+	0.661015i	$0.770126\pi$
$252$		0			0
$253$	−1237.88			−0.307607
$254$		0			0
$255$	−556.948	+	1165.03i	−0.136774	+	0.286106i
$256$		0			0
$257$	−2819.70	+	4883.86i	−0.684389	+	1.18540i	0.289239	+	0.957257i	$0.406598\pi$
$257$	−2819.70	+	4883.86i	−0.684389	+	1.18540i	−0.973628	+	0.228140i	$0.926736\pi$
$258$		0			0
$259$	−458.681	+	620.211i	−0.110043	+	0.148796i
$260$		0			0
$261$	5580.64	−	4502.90i	1.32350	−	1.06790i
$262$		0			0
$263$	3018.63	−	1742.81i	0.707745	−	0.408617i	−0.102480	−	0.994735i	$-0.532678\pi$
$263$	3018.63	−	1742.81i	0.707745	−	0.408617i	0.810226	+	0.586118i	$0.199345\pi$
$264$		0			0
$265$			6117.79i			1.41816i
$266$		0			0
$267$	1650.83	+	2406.50i	0.378387	+	0.551594i
$268$		0			0
$269$	−1897.28	−	3286.18i	−0.430033	−	0.744839i	0.566842	−	0.823826i	$-0.308165\pi$
$269$	−1897.28	−	3286.18i	−0.430033	−	0.744839i	−0.996876	+	0.0789869i	$0.974831\pi$
$270$		0			0
$271$	6458.49	+	3728.81i	1.44769	+	0.835827i	0.998344	−	0.0575288i	$-0.0183221\pi$
$271$	6458.49	+	3728.81i	1.44769	+	0.835827i	0.449351	+	0.893356i	$0.351655\pi$
$272$		0			0
$273$	5092.07	+	3186.25i	1.12889	+	0.706377i
$274$		0			0
$275$	149.723	+	86.4428i	0.0328315	+	0.0189553i
$276$		0			0
$277$	1707.75	+	2957.90i	0.370428	+	0.641600i	0.989631	−	0.143631i	$-0.0458777\pi$
$277$	1707.75	+	2957.90i	0.370428	+	0.641600i	−0.619203	+	0.785231i	$0.712544\pi$
$278$		0			0
$279$	257.646	+	99.4210i	0.0552863	+	0.0213340i
$280$		0			0
$281$		−	2762.14i		−	0.586390i	−0.956053	−	0.293195i	$-0.905281\pi$
$281$		−	2762.14i		−	0.586390i	0.956053	−	0.293195i	$-0.0947185\pi$
$282$		0			0
$283$	4767.64	−	2752.60i	1.00144	−	0.578181i	0.0927647	−	0.995688i	$-0.470430\pi$
$283$	4767.64	−	2752.60i	1.00144	−	0.578181i	0.908674	+	0.417507i	$0.137096\pi$
$284$		0			0
$285$	−51.3554	−	659.946i	−0.0106738	−	0.137164i
$286$		0			0
$287$	−570.519	−	64.8515i	−0.117340	−	0.0133382i
$288$		0			0
$289$	2227.17	−	3857.57i	0.453322	−	0.785176i
$290$		0			0
$291$	−1004.94	−	480.415i	−0.202442	−	0.0967781i
$292$		0			0
$293$	4101.08			0.817705			0.408853	−	0.912600i	$-0.365929\pi$
$293$	4101.08			0.817705			0.408853	+	0.912600i	$0.365929\pi$
$294$		0			0
$295$	−4780.29			−0.943455
$296$		0			0
$297$	1827.82	−	1725.40i	0.357106	−	0.337097i
$298$		0			0
$299$	−2156.35	+	3734.91i	−0.417074	+	0.722393i
$300$		0			0
$301$	4132.12	+	469.702i	0.791267	+	0.0899441i
$302$		0			0
$303$	8898.48	−	692.459i	1.68714	−	0.131290i
$304$		0			0
$305$	−2597.03	+	1499.40i	−0.487560	+	0.281493i
$306$		0			0
$307$			8281.42i			1.53956i	0.638308	+	0.769781i	$0.279635\pi$
$307$			8281.42i			1.53956i	−0.638308	+	0.769781i	$0.720365\pi$
$308$		0			0
$309$	−4960.63	+	3402.94i	−0.913270	+	0.626493i
$310$		0			0
$311$	3435.52	+	5950.50i	0.626401	+	1.08496i	0.988268	+	0.152728i	$0.0488059\pi$
$311$	3435.52	+	5950.50i	0.626401	+	1.08496i	−0.361868	+	0.932230i	$0.617861\pi$
$312$		0			0
$313$	−2922.40	−	1687.25i	−0.527743	−	0.304693i	0.212354	−	0.977193i	$-0.431887\pi$
$313$	−2922.40	−	1687.25i	−0.527743	−	0.304693i	−0.740097	+	0.672500i	$0.765220\pi$
$314$		0			0
$315$	5797.33	−	244.428i	1.03696	−	0.0437205i
$316$		0			0
$317$	2052.28	+	1184.88i	0.363620	+	0.209936i	0.670667	−	0.741758i	$-0.266008\pi$
$317$	2052.28	+	1184.88i	0.363620	+	0.209936i	−0.307048	+	0.951694i	$0.599341\pi$
$318$		0			0
$319$	−2379.09	−	4120.71i	−0.417566	−	0.723246i
$320$		0			0
$321$	−5218.09	+	3579.55i	−0.907306	+	0.622401i
$322$		0			0
$323$		−	235.116i		−	0.0405021i
$324$		0			0
$325$	521.629	−	301.163i	0.0890300	−	0.0514015i
$326$		0			0
$327$	−6725.64	+	523.374i	−1.13740	+	0.0885096i
$328$		0			0
$329$	1802.94	−	2437.86i	0.302125	−	0.408521i
$330$		0			0
$331$	1901.80	−	3294.02i	0.315808	−	0.546996i	−0.663801	−	0.747910i	$-0.731058\pi$
$331$	1901.80	−	3294.02i	0.315808	−	0.546996i	0.979609	+	0.200913i	$0.0643910\pi$
$332$		0			0
$333$	1111.05	−	173.972i	0.182838	−	0.0286295i
$334$		0			0
$335$	−3753.55			−0.612175
$336$		0			0
$337$	−592.955			−0.0958466			−0.0479233	−	0.998851i	$-0.515260\pi$
$337$	−592.955			−0.0958466			−0.0479233	+	0.998851i	$0.515260\pi$
$338$		0			0
$339$	−6740.69	−	3222.42i	−1.07995	−	0.516276i
$340$		0			0
$341$	91.6249	−	158.699i	0.0145506	−	0.0252024i
$342$		0			0
$343$	5989.74	+	2115.80i	0.942903	+	0.333068i
$344$		0			0
$345$	323.213	+	4153.46i	0.0504383	+	0.648159i
$346$		0			0
$347$	4137.14	−	2388.58i	0.640039	−	0.369527i	−0.144590	−	0.989492i	$-0.546186\pi$
$347$	4137.14	−	2388.58i	0.640039	−	0.369527i	0.784630	+	0.619965i	$0.212853\pi$
$348$		0			0
$349$			7358.26i			1.12859i	0.825573	+	0.564296i	$0.190852\pi$
$349$			7358.26i			1.12859i	−0.825573	+	0.564296i	$0.809148\pi$
$350$		0			0
$351$	−2021.84	−	8520.47i	−0.307459	−	1.29569i
$352$		0			0
$353$	1652.78	+	2862.69i	0.249202	+	0.431631i	0.963305	−	0.268410i	$-0.0864982\pi$
$353$	1652.78	+	2862.69i	0.249202	+	0.431631i	−0.714102	+	0.700041i	$0.753165\pi$
$354$		0			0
$355$	−456.436	−	263.524i	−0.0682398	−	0.0393982i
$356$		0			0
$357$	2059.69	+	73.1991i	0.305351	+	0.0108518i
$358$		0			0
$359$	359.154	+	207.358i	0.0528006	+	0.0304845i	0.526168	−	0.850381i	$-0.323628\pi$
$359$	359.154	+	207.358i	0.0528006	+	0.0304845i	−0.473367	+	0.880865i	$0.656962\pi$
$360$		0			0
$361$	−3369.24	−	5835.69i	−0.491214	−	0.850808i
$362$		0			0
$363$	2968.81	+	4327.79i	0.429263	+	0.625758i
$364$		0			0
$365$		−	6523.69i		−	0.935522i
$366$		0			0
$367$	65.9242	−	38.0613i	0.00937661	−	0.00541359i	−0.495304	−	0.868720i	$-0.664943\pi$
$367$	65.9242	−	38.0613i	0.00937661	−	0.00541359i	0.504681	+	0.863306i	$0.331610\pi$
$368$		0			0
$369$	525.657	+	651.470i	0.0741588	+	0.0919083i
$370$		0			0
$371$	8953.38	−	3895.82i	1.25293	−	0.545178i
$372$		0			0
$373$	6150.49	−	10653.0i	0.853781	−	1.47879i	−0.0239900	−	0.999712i	$-0.507637\pi$
$373$	6150.49	−	10653.0i	0.853781	−	1.47879i	0.877771	−	0.479080i	$-0.159030\pi$
$374$		0			0
$375$	−2999.76	+	6274.93i	−0.413085	+	0.864096i
$376$		0			0
$377$	−16577.3			−2.26465
$378$		0			0
$379$	1429.02			0.193678			0.0968389	−	0.995300i	$-0.469127\pi$
$379$	1429.02			0.193678			0.0968389	+	0.995300i	$0.469127\pi$
$380$		0			0
$381$	−6020.38	+	12593.5i	−0.809536	+	1.69340i
$382$		0			0
$383$	−2555.45	+	4426.17i	−0.340933	+	0.590513i	−0.984606	−	0.174787i	$-0.944076\pi$
$383$	−2555.45	+	4426.17i	−0.340933	+	0.590513i	0.643673	+	0.765300i	$0.277410\pi$
$384$		0			0
$385$	434.863	−	3825.63i	0.0575654	−	0.506421i
$386$		0			0
$387$	−3807.19	−	4718.42i	−0.500079	−	0.619770i
$388$		0			0
$389$	6339.84	−	3660.31i	0.826331	−	0.477083i	−0.0262636	−	0.999655i	$-0.508361\pi$
$389$	6339.84	−	3660.31i	0.826331	−	0.477083i	0.852595	+	0.522572i	$0.175028\pi$
$390$		0			0
$391$			1479.73i			0.191390i
$392$		0			0
$393$	−4712.61	−	6869.82i	−0.604885	−	0.881772i
$394$		0			0
$395$	1678.04	+	2906.45i	0.213750	+	0.370227i
$396$		0			0
$397$	7516.61	+	4339.72i	0.950247	+	0.548625i	0.893158	−	0.449744i	$-0.148485\pi$
$397$	7516.61	+	4339.72i	0.950247	+	0.548625i	0.0570893	+	0.998369i	$0.481818\pi$
$398$		0			0
$399$	−933.127	+	495.414i	−0.117080	+	0.0621597i
$400$		0			0
$401$	8447.68	+	4877.27i	1.05201	+	0.607379i	0.923212	−	0.384291i	$-0.125554\pi$
$401$	8447.68	+	4877.27i	1.05201	+	0.607379i	0.128800	+	0.991671i	$0.458887\pi$
$402$		0			0
$403$	−319.217	−	552.899i	−0.0394573	−	0.0683421i
$404$		0			0
$405$	−6266.49	−	5682.38i	−0.768851	−	0.697185i
$406$		0			0
$407$		−	746.226i		−	0.0908822i
$408$		0			0
$409$	2935.32	−	1694.71i	0.354871	−	0.204885i	−0.311958	−	0.950096i	$-0.600985\pi$
$409$	2935.32	−	1694.71i	0.354871	−	0.204885i	0.666828	+	0.745211i	$0.267651\pi$
$410$		0			0
$411$	−934.676	−	12011.1i	−0.112176	−	1.44152i
$412$		0			0
$413$	3044.10	+	6995.95i	0.362689	+	0.833531i
$414$		0			0
$415$	2603.72	−	4509.77i	0.307979	−	0.533436i
$416$		0			0
$417$	8633.30	+	4127.19i	1.01385	+	0.484675i
$418$		0			0
$419$	−12777.4			−1.48977			−0.744887	−	0.667191i	$-0.767496\pi$
$419$	−12777.4			−1.48977			−0.744887	+	0.667191i	$0.767496\pi$
$420$		0			0
$421$	11005.4			1.27404			0.637020	−	0.770848i	$-0.280167\pi$
$421$	11005.4			1.27404			0.637020	+	0.770848i	$0.280167\pi$
$422$		0			0
$423$	−4367.20	+	683.831i	−0.501987	+	0.0786029i
$424$		0			0
$425$	103.332	−	178.976i	0.0117937	−	0.0204273i
$426$		0			0
$427$	3848.17	+	2845.94i	0.436126	+	0.322540i
$428$		0			0
$429$	−5793.28	+	450.820i	−0.651987	+	0.0507361i
$430$		0			0
$431$	−3279.13	+	1893.21i	−0.366474	+	0.211584i	−0.671917	−	0.740627i	$-0.734529\pi$
$431$	−3279.13	+	1893.21i	−0.366474	+	0.211584i	0.305443	+	0.952210i	$0.401195\pi$
$432$		0			0
$433$		−	3191.67i		−	0.354230i	−0.984190	−	0.177115i	$-0.943323\pi$
$433$		−	3191.67i		−	0.354230i	0.984190	−	0.177115i	$-0.0566765\pi$
$434$		0			0
$435$	−13205.1	+	9058.53i	−1.45548	+	0.998444i
$436$		0			0
$437$	−379.264	−	656.904i	−0.0415163	−	0.0719084i
$438$		0			0
$439$	2872.90	+	1658.67i	0.312337	+	0.180328i	0.647972	−	0.761664i	$-0.275617\pi$
$439$	2872.90	+	1658.67i	0.312337	+	0.180328i	−0.335635	+	0.941992i	$0.608951\pi$
$440$		0			0
$441$	−4049.47	−	8328.74i	−0.437261	−	0.899335i
$442$		0			0
$443$	9266.95	+	5350.27i	0.993873	+	0.573813i	0.906430	−	0.422356i	$-0.138797\pi$
$443$	9266.95	+	5350.27i	0.993873	+	0.573813i	0.0874435	+	0.996169i	$0.472130\pi$
$444$		0			0
$445$	−3258.53	−	5643.94i	−0.347122	−	0.601232i
$446$		0			0
$447$	−5574.51	+	3824.05i	−0.589855	+	0.404634i
$448$		0			0
$449$		−	4017.92i		−	0.422310i	−0.977453	−	0.211155i	$-0.932278\pi$
$449$		−	4017.92i		−	0.422310i	0.977453	−	0.211155i	$-0.0677225\pi$
$450$		0			0
$451$	481.042	−	277.729i	0.0502248	−	0.0289973i
$452$		0			0
$453$	−13554.7	+	1054.79i	−1.40586	+	0.109401i
$454$		0			0
$455$	−10785.1	−	7976.22i	−1.11124	−	0.821826i
$456$		0			0
$457$	−4584.83	+	7941.15i	−0.469298	+	0.812848i	−0.999384	−	0.0350961i	$-0.988826\pi$
$457$	−4584.83	+	7941.15i	−0.469298	+	0.812848i	0.530086	+	0.847944i	$0.322160\pi$
$458$		0			0
$459$	−2062.51	−	2184.93i	−0.209737	−	0.222187i
$460$		0			0
$461$	−1289.80			−0.130308			−0.0651542	−	0.997875i	$-0.520754\pi$
$461$	−1289.80			−0.130308			−0.0651542	+	0.997875i	$0.520754\pi$
$462$		0			0
$463$	−6976.52			−0.700273			−0.350137	−	0.936699i	$-0.613865\pi$
$463$	−6976.52			−0.700273			−0.350137	+	0.936699i	$0.613865\pi$
$464$		0			0
$465$	−556.408	−	265.993i	−0.0554899	−	0.0265272i
$466$		0			0
$467$	3931.83	−	6810.13i	0.389600	−	0.674808i	−0.602795	−	0.797896i	$-0.705946\pi$
$467$	3931.83	−	6810.13i	0.389600	−	0.674808i	0.992396	+	0.123088i	$0.0392798\pi$
$468$		0			0
$469$	2390.27	+	5493.32i	0.235336	+	0.540849i
$470$		0			0
$471$	376.996	+	4844.61i	0.0368813	+	0.473944i
$472$		0			0
$473$	−3484.06	+	2011.52i	−0.338683	+	0.195539i
$474$		0			0
$475$			105.938i			0.0102332i
$476$		0			0
$477$	−13280.5	−	5124.69i	−1.27478	−	0.491915i
$478$		0			0
$479$	−1847.13	−	3199.33i	−0.176196	−	0.305180i	0.764379	−	0.644767i	$-0.223046\pi$
$479$	−1847.13	−	3199.33i	−0.176196	−	0.305180i	−0.940574	+	0.339588i	$0.889712\pi$
$480$		0			0
$481$	−2251.51	−	1299.91i	−0.213430	−	0.123224i
$482$		0			0
$483$	5872.77	−	3117.96i	0.553251	−	0.293731i
$484$		0			0
$485$	2154.19	+	1243.72i	0.201684	+	0.116442i
$486$		0			0
$487$	−526.359	−	911.681i	−0.0489766	−	0.0848300i	0.840498	−	0.541815i	$-0.182263\pi$
$487$	−526.359	−	911.681i	−0.0489766	−	0.0848300i	−0.889474	+	0.456985i	$0.848929\pi$
$488$		0			0
$489$	1523.06	+	2220.24i	0.140849	+	0.205322i
$490$		0			0
$491$		−	2378.40i		−	0.218607i	−0.994008	−	0.109303i	$-0.965138\pi$
$491$		−	2378.40i		−	0.218607i	0.994008	−	0.109303i	$-0.0348620\pi$
$492$		0			0
$493$	−4925.81	+	2843.92i	−0.449995	+	0.259805i
$494$		0			0
$495$	−4368.45	+	3524.81i	−0.396661	+	0.320057i
$496$		0			0
$497$	−95.0069	+	835.807i	−0.00857474	+	0.0754347i
$498$		0			0
$499$	9385.74	−	16256.6i	0.842011	−	1.45840i	−0.0461818	−	0.998933i	$-0.514705\pi$
$499$	9385.74	−	16256.6i	0.842011	−	1.45840i	0.888192	−	0.459472i	$-0.151961\pi$
$500$		0			0
$501$	8444.48	−	17664.3i	0.753037	−	1.57521i
$502$		0			0
$503$	16095.2			1.42674			0.713370	−	0.700788i	$-0.247168\pi$
$503$	16095.2			1.42674			0.713370	+	0.700788i	$0.247168\pi$
$504$		0			0
$505$	−19931.9			−1.75635
$506$		0			0
$507$	−3807.81	+	7965.21i	−0.333552	+	0.697727i
$508$		0			0
$509$	1575.31	−	2728.52i	0.137180	−	0.237603i	−0.789248	−	0.614074i	$-0.789529\pi$
$509$	1575.31	−	2728.52i	0.137180	−	0.237603i	0.926428	+	0.376472i	$0.122863\pi$
$510$		0			0
$511$	−9547.42	+	4154.30i	−0.826522	+	0.359639i
$512$		0			0
$513$	1475.63	+	441.335i	0.126999	+	0.0379832i
$514$		0			0
$515$	11634.1	−	6716.95i	0.995456	−	0.574727i
$516$		0			0
$517$			2933.19i			0.249519i
$518$		0			0
$519$	−7034.08	−	10253.9i	−0.594917	−	0.867241i
$520$		0			0
$521$	−2489.60	−	4312.12i	−0.209350	−	0.362605i	0.742160	−	0.670223i	$-0.233802\pi$
$521$	−2489.60	−	4312.12i	−0.209350	−	0.362605i	−0.951510	+	0.307618i	$0.900468\pi$
$522$		0			0
$523$	−11977.0	−	6914.92i	−1.00137	−	0.578142i	−0.0927181	−	0.995692i	$-0.529556\pi$
$523$	−11977.0	−	6914.92i	−1.00137	−	0.578142i	−0.908654	+	0.417550i	$0.862889\pi$
$524$		0			0
$525$	−928.053	−	32.9820i	−0.0771496	−	0.00274181i
$526$		0			0
$527$	−189.705	−	109.526i	−0.0156806	−	0.00905322i
$528$		0			0
$529$	−3696.55	−	6402.61i	−0.303818	−	0.526228i
$530$		0			0
$531$	4004.31	−	10377.0i	0.327254	−	0.848069i
$532$		0			0
$533$		−	1935.19i		−	0.157265i
$534$		0			0
$535$	12237.9	−	7065.56i	0.988955	−	0.570973i
$536$		0			0
$537$	258.064	+	3316.26i	0.0207379	+	0.266494i
$538$		0			0
$539$	−5875.73	+	1799.75i	−0.469547	+	0.143823i
$540$		0			0
$541$	−2658.97	+	4605.48i	−0.211309	+	0.365998i	−0.952124	−	0.305711i	$-0.901106\pi$
$541$	−2658.97	+	4605.48i	−0.211309	+	0.365998i	0.740815	+	0.671709i	$0.234439\pi$
$542$		0			0
$543$	19708.6	+	9421.79i	1.55760	+	0.744618i
$544$		0			0
$545$	15064.9			1.18405
$546$		0			0
$547$	9266.96			0.724363			0.362181	−	0.932108i	$-0.382032\pi$
$547$	9266.96			0.724363			0.362181	+	0.932108i	$0.382032\pi$
$548$		0			0
$549$	−1079.43	−	6893.63i	−0.0839142	−	0.535907i
$550$		0			0
$551$	1457.82	−	2525.03i	0.112714	−	0.195226i
$552$		0			0
$553$	3185.01	−	4306.65i	0.244920	−	0.331171i
$554$		0			0
$555$	−2503.82	+	194.842i	−0.191498	+	0.0149019i
$556$		0			0
$557$	−125.920	+	72.6999i	−0.00957881	+	0.00553033i	−0.504782	−	0.863247i	$-0.668427\pi$
$557$	−125.920	+	72.6999i	−0.00957881	+	0.00553033i	0.495203	+	0.868777i	$0.335094\pi$
$558$		0			0
$559$			14016.1i			1.06050i
$560$		0			0
$561$	−1644.09	+	1127.83i	−0.123732	+	0.0848785i
$562$		0			0
$563$	−1958.12	−	3391.56i	−0.146581	−	0.253885i	0.783381	−	0.621542i	$-0.213493\pi$
$563$	−1958.12	−	3391.56i	−0.146581	−	0.253885i	−0.929962	+	0.367657i	$0.880160\pi$
$564$		0			0
$565$	14449.4	+	8342.36i	1.07591	+	0.621178i
$566$		0			0
$567$	−4325.65	+	12789.6i	−0.320388	+	0.947286i
$568$		0			0
$569$	−7404.97	−	4275.26i	−0.545576	−	0.314988i	0.201760	−	0.979435i	$-0.435334\pi$
$569$	−7404.97	−	4275.26i	−0.545576	−	0.314988i	−0.747336	+	0.664447i	$0.768667\pi$
$570$		0			0
$571$	−11956.8	−	20709.8i	−0.876318	−	1.51783i	−0.855352	−	0.518047i	$-0.826659\pi$
$571$	−11956.8	−	20709.8i	−0.876318	−	1.51783i	−0.0209659	−	0.999780i	$-0.506674\pi$
$572$		0			0
$573$	6243.32	−	4282.84i	0.455180	−	0.312248i
$574$		0			0
$575$		−	666.737i		−	0.0483563i
$576$		0			0
$577$	11347.8	−	6551.66i	0.818745	−	0.472703i	−0.0312386	−	0.999512i	$-0.509945\pi$
$577$	11347.8	−	6551.66i	0.818745	−	0.472703i	0.849983	+	0.526809i	$0.176612\pi$
$578$		0			0
$579$	−9476.49	+	737.439i	−0.680189	+	0.0529307i
$580$		0			0
$581$	−8258.10	−	938.706i	−0.589679	−	0.0670294i
$582$		0			0
$583$	−4722.83	+	8180.18i	−0.335506	+	0.581113i
$584$		0			0
$585$	3025.28	+	19320.6i	0.213812	+	1.36548i
$586$		0			0
$587$	−18034.7			−1.26809			−0.634047	−	0.773294i	$-0.718608\pi$
$587$	−18034.7			−1.26809			−0.634047	+	0.773294i	$0.718608\pi$
$588$		0			0
$589$	112.289			0.00785532
$590$		0			0
$591$	3099.56	+	1481.76i	0.215734	+	0.103133i
$592$		0			0
$593$	11358.1	−	19672.8i	0.786547	−	1.36234i	−0.141524	−	0.989935i	$-0.545200\pi$
$593$	11358.1	−	19672.8i	0.786547	−	1.36234i	0.928071	−	0.372404i	$-0.121466\pi$
$594$		0			0
$595$	−4573.08	−	519.826i	−0.315089	−	0.0358165i
$596$		0			0
$597$	−785.759	−	10097.4i	−0.0538677	−	0.692229i
$598$		0			0
$599$	−11720.4	+	6766.78i	−0.799471	+	0.461575i	−0.843286	−	0.537465i	$-0.819382\pi$
$599$	−11720.4	+	6766.78i	−0.799471	+	0.461575i	0.0438153	+	0.999040i	$0.486049\pi$
$600$		0			0
$601$			3667.98i			0.248952i	0.992223	+	0.124476i	$0.0397250\pi$
$601$			3667.98i			0.248952i	−0.992223	+	0.124476i	$0.960275\pi$
$602$		0			0
$603$	3144.24	−	8148.20i	0.212344	−	0.550282i
$604$		0			0
$605$	−5860.05	−	10149.9i	−0.393794	−	0.682070i
$606$		0			0
$607$	6942.92	+	4008.50i	0.464258	+	0.268039i	0.713833	−	0.700316i	$-0.246958\pi$
$607$	6942.92	+	4008.50i	0.464258	+	0.268039i	−0.249575	+	0.968355i	$0.580291\pi$
$608$		0			0
$609$	21666.2	+	13557.1i	1.44164	+	0.902074i
$610$		0			0
$611$	8849.99	+	5109.54i	0.585977	+	0.338314i
$612$		0			0
$613$	−4698.26	−	8137.63i	−0.309561	−	0.536176i	0.668705	−	0.743528i	$-0.266849\pi$
$613$	−4698.26	−	8137.63i	−0.309561	−	0.536176i	−0.978266	+	0.207352i	$0.933515\pi$
$614$		0			0
$615$	−1057.47	−	1541.53i	−0.0693355	−	0.101074i
$616$		0			0
$617$			8906.76i			0.581155i	0.956851	+	0.290578i	$0.0938474\pi$
$617$			8906.76i			0.581155i	−0.956851	+	0.290578i	$0.906153\pi$
$618$		0			0
$619$	6091.73	−	3517.06i	0.395553	−	0.228373i	−0.289010	−	0.957326i	$-0.593326\pi$
$619$	6091.73	−	3517.06i	0.395553	−	0.228373i	0.684563	+	0.728953i	$0.259993\pi$
$620$		0			0
$621$	−9287.07	−	2777.60i	−0.600124	−	0.179487i
$622$		0			0
$623$	−6184.86	+	8362.93i	−0.397739	+	0.537807i
$624$		0			0
$625$	8369.05	−	14495.6i	0.535619	−	0.927720i
$626$		0			0
$627$	440.799	−	922.069i	0.0280763	−	0.0587303i
$628$		0			0
$629$	−892.024			−0.0565458
$630$		0			0
$631$	12628.6			0.796728			0.398364	−	0.917227i	$-0.369578\pi$
$631$	12628.6			0.796728			0.398364	+	0.917227i	$0.369578\pi$
$632$		0			0
$633$	−7489.74	+	15667.1i	−0.470285	+	0.983747i
$634$		0			0
$635$	15585.9	−	26995.5i	0.974026	−	1.68706i
$636$		0			0
$637$	−4805.19	+	20863.3i	−0.298883	+	1.29770i
$638$		0			0
$639$	954.399	−	770.084i	0.0590852	−	0.0476746i
$640$		0			0
$641$	−8593.58	+	4961.51i	−0.529526	+	0.305722i	−0.740823	−	0.671700i	$-0.765564\pi$
$641$	−8593.58	+	4961.51i	−0.529526	+	0.305722i	0.211297	+	0.977422i	$0.432231\pi$
$642$		0			0
$643$			294.191i			0.0180432i	0.999959	+	0.00902160i	$0.00287170\pi$
$643$			294.191i			0.0180432i	−0.999959	+	0.00902160i	$0.997128\pi$
$644$		0			0
$645$	7658.97	+	11164.9i	0.467553	+	0.681576i
$646$		0			0
$647$	3859.39	+	6684.67i	0.234511	+	0.406184i	0.959130	−	0.282965i	$-0.0913179\pi$
$647$	3859.39	+	6684.67i	0.234511	+	0.406184i	−0.724620	+	0.689149i	$0.757985\pi$
$648$		0			0
$649$	−6391.80	−	3690.30i	−0.386595	−	0.223201i
$650$		0			0
$651$	−34.9592	+	983.688i	−0.00210470	+	0.0592224i
$652$		0			0
$653$	−9846.89	−	5685.11i	−0.590105	−	0.340697i	0.175034	−	0.984562i	$-0.443996\pi$
$653$	−9846.89	−	5685.11i	−0.590105	−	0.340697i	−0.765139	+	0.643865i	$0.777330\pi$
$654$		0			0
$655$	9302.09	+	16111.7i	0.554905	+	0.961123i
$656$		0			0
$657$	14161.6	+	5464.70i	0.840938	+	0.324503i
$658$		0			0
$659$			19795.1i			1.17012i	0.810990	+	0.585060i	$0.198929\pi$
$659$			19795.1i			1.17012i	−0.810990	+	0.585060i	$0.801071\pi$
$660$		0			0
$661$	26896.6	−	15528.7i	1.58268	−	0.913763i	0.588219	−	0.808702i	$-0.299829\pi$
$661$	26896.6	−	15528.7i	1.58268	−	0.913763i	0.994466	−	0.105062i	$-0.0335041\pi$
$662$		0			0
$663$	538.901	+	6925.17i	0.0315674	+	0.405658i
$664$		0			0
$665$	2163.38	−	941.337i	0.126154	−	0.0548924i
$666$		0			0
$667$	−9175.03	+	15891.6i	−0.532621	+	0.922527i
$668$		0			0
$669$	−10047.7	−	4803.34i	−0.580667	−	0.277590i
$670$		0			0
$671$	−4630.04			−0.266380
$672$		0			0
$673$	5340.26			0.305872			0.152936	−	0.988236i	$-0.451127\pi$
$673$	5340.26			0.305872			0.152936	+	0.988236i	$0.451127\pi$
$674$		0			0
$675$	929.322	+	984.486i	0.0529920	+	0.0561376i
$676$		0			0
$677$	−12478.3	+	21613.0i	−0.708389	+	1.22697i	0.257066	+	0.966394i	$0.417244\pi$
$677$	−12478.3	+	21613.0i	−0.708389	+	1.22697i	−0.965455	+	0.260571i	$0.916089\pi$
$678$		0			0
$679$	448.394	−	3944.67i	0.0253428	−	0.222949i
$680$		0			0
$681$	−13309.2	+	1035.69i	−0.748914	+	0.0582788i
$682$		0			0
$683$	−9706.83	+	5604.24i	−0.543809	+	0.313968i	−0.746621	−	0.665249i	$-0.768325\pi$
$683$	−9706.83	+	5604.24i	−0.543809	+	0.313968i	0.202812	+	0.979218i	$0.434992\pi$
$684$		0			0
$685$			26903.9i			1.50065i
$686$		0			0
$687$	450.654	−	309.143i	0.0250269	−	0.0171682i
$688$		0			0
$689$	16454.1	+	28499.4i	0.909800	+	1.57582i
$690$		0			0
$691$	9472.37	+	5468.88i	0.521485	+	0.301079i	0.737542	−	0.675301i	$-0.235986\pi$
$691$	9472.37	+	5468.88i	0.521485	+	0.301079i	−0.216057	+	0.976381i	$0.569320\pi$
$692$		0			0
$693$	7940.39	+	4148.61i	0.435253	+	0.227407i
$694$		0			0
$695$	−18506.4	−	10684.7i	−1.01006	−	0.583156i
$696$		0			0
$697$	−331.992	−	575.027i	−0.0180418	−	0.0312492i
$698$		0			0
$699$	11250.9	−	7717.97i	0.608795	−	0.417626i
$700$		0			0
$701$			27949.3i			1.50589i	0.658082	+	0.752947i	$0.271368\pi$
$701$			27949.3i			1.50589i	−0.658082	+	0.752947i	$0.728632\pi$
$702$		0			0
$703$	396.000	−	228.631i	0.0212453	−	0.0122660i
$704$		0			0
$705$	9841.76	−	765.863i	0.525762	−	0.0409136i
$706$		0			0
$707$	12692.7	+	29170.3i	0.675186	+	1.55171i
$708$		0			0
$709$	−10472.7	+	18139.3i	−0.554741	+	0.960840i	0.443183	+	0.896431i	$0.353849\pi$
$709$	−10472.7	+	18139.3i	−0.554741	+	0.960840i	−0.997924	+	0.0644082i	$0.979484\pi$
$710$		0			0
$711$	−7714.96	+	1208.04i	−0.406939	+	0.0637200i
$712$		0			0
$713$	−706.707			−0.0371197
$714$		0			0
$715$	12976.5			0.678731
$716$		0			0
$717$	−28507.1	−	13627.9i	−1.48482	−	0.709825i
$718$		0			0
$719$	−4150.10	+	7188.19i	−0.215261	+	0.372843i	−0.953353	−	0.301857i	$-0.902394\pi$
$719$	−4150.10	+	7188.19i	−0.215261	+	0.372843i	0.738092	+	0.674700i	$0.235727\pi$
$720$		0			0
$721$	−17238.9	−	12749.1i	−0.890443	−	0.658533i
$722$		0			0
$723$	−1866.06	−	23979.9i	−0.0959884	−	1.23350i
$724$		0			0
$725$	2219.47	−	1281.41i	0.113695	−	0.0656420i
$726$		0			0
$727$			20951.5i			1.06884i	0.845218	+	0.534421i	$0.179470\pi$
$727$			20951.5i			1.06884i	−0.845218	+	0.534421i	$0.820530\pi$
$728$		0			0
$729$	17584.5	−	8843.31i	0.893388	−	0.449287i
$730$		0			0
$731$	2404.53	+	4164.77i	0.121662	+	0.210724i
$732$		0			0
$733$	4885.73	+	2820.78i	0.246192	+	0.142139i	0.618019	−	0.786163i	$-0.287935\pi$
$733$	4885.73	+	2820.78i	0.246192	+	0.142139i	−0.371827	+	0.928302i	$0.621269\pi$
$734$		0			0
$735$	7572.89	+	19245.0i	0.380041	+	0.965799i
$736$		0			0
$737$	−5018.93	−	2897.68i	−0.250848	−	0.144827i
$738$		0			0
$739$	−5691.08	−	9857.24i	−0.283288	−	0.490669i	0.688905	−	0.724852i	$-0.258092\pi$
$739$	−5691.08	−	9857.24i	−0.283288	−	0.490669i	−0.972193	+	0.234183i	$0.924758\pi$
$740$		0			0
$741$	−2014.20	−	2936.20i	−0.0998560	−	0.145565i
$742$		0			0
$743$			4665.46i			0.230362i	0.993345	+	0.115181i	$0.0367449\pi$
$743$			4665.46i			0.230362i	−0.993345	+	0.115181i	$0.963255\pi$
$744$		0			0
$745$	13073.8	−	7548.17i	0.642936	−	0.371200i
$746$		0			0
$747$	7608.73	+	9429.84i	0.372676	+	0.461874i
$748$		0			0
$749$	−18133.6	−	13410.8i	−0.884628	−	0.654233i
$750$		0			0
$751$	−4780.43	+	8279.95i	−0.232277	+	0.402316i	−0.958478	−	0.285167i	$-0.907951\pi$
$751$	−4780.43	+	8279.95i	−0.232277	+	0.402316i	0.726200	+	0.687483i	$0.241284\pi$
$752$		0			0
$753$	−13374.7	+	27977.3i	−0.647278	+	1.35398i
$754$		0			0
$755$	30361.4			1.46353
$756$		0			0
$757$	31574.1			1.51596			0.757979	−	0.652279i	$-0.226187\pi$
$757$	31574.1			1.51596			0.757979	+	0.652279i	$0.226187\pi$
$758$		0			0
$759$	−2774.23	+	5803.17i	−0.132672	+	0.277525i
$760$		0			0
$761$	11215.0	−	19424.9i	0.534221	−	0.925298i	−0.464980	−	0.885321i	$-0.653938\pi$
$761$	11215.0	−	19424.9i	0.534221	−	0.925298i	0.999201	−	0.0399765i	$-0.0127283\pi$
$762$		0			0
$763$	−9593.35	−	22047.4i	−0.455180	−	1.04610i
$764$		0			0
$765$	4213.48	+	5221.95i	0.199136	+	0.246797i
$766$		0			0
$767$	−22268.7	+	12856.8i	−1.04834	+	0.605259i
$768$		0			0
$769$		−	26887.4i		−	1.26084i	−0.776254	−	0.630420i	$-0.782883\pi$
$769$		−	26887.4i		−	1.26084i	0.776254	−	0.630420i	$-0.217117\pi$
$770$		0			0
$771$	16576.3	+	24164.1i	0.774293	+	1.12873i
$772$		0			0
$773$	11104.6	+	19233.7i	0.516693	+	0.894938i	0.999812	+	0.0193838i	$0.00617045\pi$
$773$	11104.6	+	19233.7i	0.516693	+	0.894938i	−0.483119	+	0.875555i	$0.660496\pi$
$774$		0			0
$775$	85.4774	+	49.3504i	0.00396185	+	0.00228738i
$776$		0			0
$777$	1879.59	+	3540.27i	0.0867824	+	0.163457i
$778$		0			0
$779$	294.765	+	170.183i	0.0135572	+	0.00782725i
$780$		0			0
$781$	−406.872	−	704.722i	−0.0186415	−	0.0322880i
$782$		0			0
$783$	−8602.71	−	36253.6i	−0.392638	−	1.65466i
$784$		0			0
$785$		−	10851.5i		−	0.493385i
$786$		0			0
$787$	17403.2	−	10047.8i	0.788257	−	0.455100i	−0.0510919	−	0.998694i	$-0.516270\pi$
$787$	17403.2	−	10047.8i	0.788257	−	0.455100i	0.839348	+	0.543594i	$0.182937\pi$
$788$		0			0
$789$	−1405.17	−	18057.2i	−0.0634035	−	0.814770i
$790$		0			0
$791$	3007.63	−	26459.1i	0.135195	−	1.18935i
$792$		0			0
$793$	−8065.42	+	13969.7i	−0.361175	+	0.625573i
$794$		0			0
$795$	28680.2	+	13710.7i	1.27947	+	0.611659i
$796$		0			0
$797$	−14300.8			−0.635583			−0.317791	−	0.948161i	$-0.602941\pi$
$797$	−14300.8			−0.635583			−0.317791	+	0.948161i	$0.602941\pi$
$798$		0			0
$799$	3506.27			0.155248
$800$		0			0
$801$	14981.4	−	2345.84i	0.660851	−	0.103478i
$802$		0			0
$803$	5036.18	−	8722.92i	0.221324	−	0.383344i
$804$		0			0
$805$	−13615.5	+	5924.44i	−0.596130	+	0.259390i
$806$		0			0
$807$	−19657.6	+	1529.71i	−0.857474	+	0.0667266i
$808$		0			0
$809$	12772.9	−	7374.43i	0.555093	−	0.320483i	−0.196080	−	0.980588i	$-0.562821\pi$
$809$	12772.9	−	7374.43i	0.555093	−	0.320483i	0.751174	+	0.660104i	$0.229488\pi$
$810$		0			0
$811$			4569.51i			0.197851i	0.995095	+	0.0989255i	$0.0315405\pi$
$811$			4569.51i			0.197851i	−0.995095	+	0.0989255i	$0.968459\pi$
$812$		0			0
$813$	31954.9	−	21920.7i	1.37848	−	0.945624i
$814$		0			0
$815$	−3006.32	−	5207.09i	−0.129211	−	0.223799i
$816$		0			0
$817$	−2134.91	−	1232.59i	−0.0914209	−	0.0527819i
$818$		0			0
$819$	26349.1	−	16730.9i	1.12419	−	0.713827i
$820$		0			0
$821$	40528.1	+	23398.9i	1.72283	+	0.994674i	0.912948	+	0.408076i	$0.133800\pi$
$821$	40528.1	+	23398.9i	1.72283	+	0.994674i	0.809878	+	0.586598i	$0.199533\pi$
$822$		0			0
$823$	−13086.7	−	22666.8i	−0.554281	−	0.960043i	−0.997959	−	0.0638567i	$-0.979660\pi$
$823$	−13086.7	−	22666.8i	−0.554281	−	0.960043i	0.443678	−	0.896186i	$-0.353673\pi$
$824$		0			0
$825$	740.792	−	508.175i	0.0312619	−	0.0214453i
$826$		0			0
$827$		−	42212.0i		−	1.77492i	−0.460888	−	0.887458i	$-0.652469\pi$
$827$		−	42212.0i		−	1.77492i	0.460888	−	0.887458i	$-0.347531\pi$
$828$		0			0
$829$	−19605.0	+	11319.0i	−0.821364	+	0.474215i	−0.850887	−	0.525349i	$-0.823935\pi$
$829$	−19605.0	+	11319.0i	−0.821364	+	0.474215i	0.0295225	+	0.999564i	$0.490601\pi$
$830$		0			0
$831$	17693.9	−	1376.90i	0.738623	−	0.0574779i
$832$		0			0
$833$	2151.38	+	7023.73i	0.0894850	+	0.292146i
$834$		0			0
$835$	−21861.5	+	37865.3i	−0.906047	+	1.56932i
$836$		0			0
$837$	1043.50	−	985.033i	0.0430929	−	0.0406783i
$838$		0			0
$839$	39480.0			1.62455			0.812277	−	0.583272i	$-0.198228\pi$
$839$	39480.0			1.62455			0.812277	+	0.583272i	$0.198228\pi$
$840$		0			0
$841$	−46145.4			−1.89206
$842$		0			0
$843$	−12948.9	−	6190.30i	−0.529045	−	0.252912i
$844$		0			0
$845$	9857.85	−	17074.3i	0.401326	−	0.695117i
$846$		0			0
$847$	−11122.7	+	15039.7i	−0.451216	+	0.610117i
$848$		0			0
$849$	−2219.33	−	28519.6i	−0.0897141	−	1.15288i
$850$		0			0
$851$	−2492.28	+	1438.92i	−0.100393	+	0.0579618i
$852$		0			0
$853$		−	44021.1i		−	1.76700i	−0.468430	−	0.883501i	$-0.655180\pi$
$853$		−	44021.1i		−	1.76700i	0.468430	−	0.883501i	$-0.344820\pi$
$854$		0			0
$855$	−3208.92	−	1238.26i	−0.128354	−	0.0495295i
$856$		0			0
$857$	1007.45	+	1744.96i	0.0401562	+	0.0695526i	0.885405	−	0.464820i	$-0.153881\pi$
$857$	1007.45	+	1744.96i	0.0401562	+	0.0695526i	−0.845249	+	0.534373i	$0.820548\pi$
$858$		0			0
$859$	−15844.5	−	9147.83i	−0.629345	−	0.363353i	0.151153	−	0.988510i	$-0.451701\pi$
$859$	−15844.5	−	9147.83i	−0.629345	−	0.363353i	−0.780499	+	0.625158i	$0.785035\pi$
$860$		0			0
$861$	−1582.63	+	2529.26i	−0.0626432	+	0.100112i
$862$		0			0
$863$	5979.04	+	3452.00i	0.235839	+	0.136162i	0.613263	−	0.789879i	$-0.289857\pi$
$863$	5979.04	+	3452.00i	0.235839	+	0.136162i	−0.377424	+	0.926041i	$0.623190\pi$
$864$		0			0
$865$	13884.4	+	24048.4i	0.545761	+	0.945285i
$866$		0			0
$867$	−13092.9	−	19086.3i	−0.512872	−	0.747639i
$868$		0			0
$869$			5181.68i			0.202274i
$870$		0			0
$871$	−17485.7	+	10095.4i	−0.680230	+	0.392731i
$872$		0			0
$873$	−4504.37	+	3634.48i	−0.174628	+	0.140903i
$874$		0			0
$875$	−24630.9	−	2799.82i	−0.951631	−	0.108173i
$876$		0			0
$877$	−208.597	+	361.300i	−0.00803171	+	0.0139113i	−0.870013	−	0.493028i	$-0.835890\pi$
$877$	−208.597	+	361.300i	−0.00803171	+	0.0139113i	0.861982	+	0.506940i	$0.169223\pi$
$878$		0			0
$879$	9191.02	−	19225.9i	0.352680	−	0.737739i
$880$		0			0
$881$	−7244.25			−0.277032			−0.138516	−	0.990360i	$-0.544233\pi$
$881$	−7244.25			−0.277032			−0.138516	+	0.990360i	$0.544233\pi$
$882$		0			0
$883$	−38284.4			−1.45908			−0.729542	−	0.683936i	$-0.760267\pi$
$883$	−38284.4			−1.45908			−0.729542	+	0.683936i	$0.760267\pi$
$884$		0			0
$885$	−10713.2	+	22410.0i	−0.406916	+	0.851191i
$886$		0			0
$887$	−8933.98	+	15474.1i	−0.338189	+	0.585761i	−0.984092	−	0.177659i	$-0.943148\pi$
$887$	−8933.98	+	15474.1i	−0.338189	+	0.585761i	0.645903	+	0.763420i	$0.276481\pi$
$888$		0			0
$889$	−49433.1	−	5619.10i	−1.86494	−	0.211990i
$890$		0			0
$891$	−3992.32	−	12435.6i	−0.150110	−	0.467575i
$892$		0			0
$893$	−1556.55	+	898.677i	−0.0583293	+	0.0336765i
$894$		0			0
$895$		−	7428.15i		−	0.277425i
$896$		0			0
$897$	12676.6	+	18479.4i	0.471862	+	0.687858i
$898$		0			0
$899$	−1358.23	−	2352.52i	−0.0503887	−	0.0872758i
$900$		0			0
$901$	9778.43	+	5645.58i	0.361561	+	0.208747i
$902$		0			0
$903$	11462.5	−	18318.7i	0.422425	−	0.675093i
$904$		0			0
$905$	−42247.5	−	24391.6i	−1.55177	−	0.895917i
$906$		0			0
$907$	−3281.49	−	5683.71i	−0.120132	−	0.208076i	0.799687	−	0.600417i	$-0.204999\pi$
$907$	−3281.49	−	5683.71i	−0.120132	−	0.208076i	−0.919820	+	0.392341i	$0.871665\pi$
$908$		0			0
$909$	16696.3	−	43268.0i	0.609221	−	1.57878i
$910$		0			0
$911$			41084.1i			1.49416i	0.664735	+	0.747079i	$0.268544\pi$
$911$			41084.1i			1.49416i	−0.664735	+	0.747079i	$0.731456\pi$
$912$		0			0
$913$	6962.94	−	4020.05i	0.252398	−	0.145722i
$914$		0			0
$915$	1208.92	+	15535.2i	0.0436782	+	0.561288i
$916$		0			0
$917$	17655.9	−	23873.6i	0.635821	−	0.859732i
$918$		0			0
$919$	2762.34	−	4784.51i	0.0991524	−	0.171737i	−0.812182	−	0.583405i	$-0.801720\pi$
$919$	2762.34	−	4784.51i	0.0991524	−	0.171737i	0.911334	+	0.411668i	$0.135054\pi$
$920$		0			0
$921$	38823.3	+	18559.7i	1.38900	+	0.664020i
$922$		0			0
$923$	−2835.04			−0.101101
$924$		0			0
$925$	401.928			0.0142868
$926$		0			0
$927$	4835.59	+	30881.9i	0.171329	+	1.09417i
$928$		0			0
$929$	−12630.2	+	21876.1i	−0.446052	+	0.772585i	−0.998125	−	0.0612109i	$-0.980504\pi$
$929$	−12630.2	+	21876.1i	−0.446052	+	0.772585i	0.552073	+	0.833796i	$0.313837\pi$
$930$		0			0
$931$	−2755.29	−	2566.66i	−0.0969936	−	0.0903533i
$932$		0			0
$933$	35595.4	−	2769.95i	1.24903	−	0.0971962i
$934$		0			0
$935$	3855.86	−	2226.18i	0.134866	−	0.0778651i
$936$		0			0
$937$			46069.3i			1.60621i	0.595838	+	0.803105i	$0.296820\pi$
$937$			46069.3i			1.60621i	−0.595838	+	0.803105i	$0.703180\pi$
$938$		0			0
$939$	−14459.3	+	9918.89i	−0.502514	+	0.344718i
$940$		0			0
$941$	−24112.4	−	41763.8i	−0.835325	−	1.44683i	−0.893766	−	0.448534i	$-0.851946\pi$
$941$	−24112.4	−	41763.8i	−0.835325	−	1.44683i	0.0584406	−	0.998291i	$-0.481387\pi$
$942$		0			0
$943$	−1855.15	−	1071.07i	−0.0640635	−	0.0369871i
$944$		0			0
$945$	11846.6	−	27725.7i	0.407800	−	0.954409i
$946$		0			0
$947$	−21340.2	−	12320.8i	−0.732275	−	0.422779i	0.0869787	−	0.996210i	$-0.472279\pi$
$947$	−21340.2	−	12320.8i	−0.732275	−	0.422779i	−0.819254	+	0.573431i	$0.805612\pi$
$948$		0			0
$949$	−17545.8	−	30390.2i	−0.600170	−	1.03952i
$950$		0			0
$951$	10154.1	−	6965.62i	0.346236	−	0.237514i
$952$		0			0
$953$		−	13271.1i		−	0.451095i	−0.974232	−	0.225548i	$-0.927583\pi$
$953$		−	13271.1i		−	0.451095i	0.974232	−	0.225548i	$-0.0724171\pi$
$954$		0			0
$955$	−14642.4	+	8453.77i	−0.496142	+	0.286448i
$956$		0			0
$957$	−24649.7	+	1918.19i	−0.832615	+	0.0647922i
$958$		0			0
$959$	39373.8	−	17132.4i	1.32580	−	0.576888i
$960$		0			0
$961$	−14843.2	+	25709.2i	−0.498244	+	0.862984i
$962$		0			0
$963$	5086.56	+	32484.6i	0.170210	+	1.08702i
$964$		0			0
$965$	21226.6			0.708090
$966$		0			0
$967$	15785.8			0.524959			0.262480	−	0.964938i	$-0.415460\pi$
$967$	15785.8			0.524959			0.262480	+	0.964938i	$0.415460\pi$
$968$		0			0
$969$	−1102.22	−	526.922i	−0.0365413	−	0.0174687i
$970$		0			0
$971$	−25892.6	+	44847.3i	−0.855750	+	1.48220i	0.0201966	+	0.999796i	$0.493571\pi$
$971$	−25892.6	+	44847.3i	−0.855750	+	1.48220i	−0.875947	+	0.482407i	$0.839763\pi$
$972$		0			0
$973$	−3852.10	+	33888.2i	−0.126920	+	1.11655i
$974$		0			0
$975$	−242.818	−	3120.34i	−0.00797578	−	0.102493i
$976$		0			0
$977$	−24796.0	+	14316.0i	−0.811969	+	0.468790i	−0.847639	−	0.530573i	$-0.821977\pi$
$977$	−24796.0	+	14316.0i	−0.811969	+	0.468790i	0.0356703	+	0.999364i	$0.488643\pi$
$978$		0			0
$979$		−	10062.1i		−	0.328485i
$980$		0			0
$981$	−12619.4	+	32702.8i	−0.410710	+	1.06434i
$982$		0			0
$983$	−21984.3	−	38077.9i	−0.713317	−	1.23550i	−0.963605	−	0.267330i	$-0.913859\pi$
$983$	−21984.3	−	38077.9i	−0.713317	−	1.23550i	0.250288	−	0.968171i	$-0.419475\pi$
$984$		0			0
$985$	−6644.24	−	3836.06i	−0.214927	−	0.124088i
$986$		0			0
$987$	−7388.10	−	13915.7i	−0.238263	−	0.448776i
$988$		0			0
$989$	13436.3	+	7757.47i	0.432003	+	0.249417i
$990$		0			0
$991$	−7577.33	−	13124.3i	−0.242888	−	0.420694i	0.718648	−	0.695374i	$-0.244761\pi$
$991$	−7577.33	−	13124.3i	−0.242888	−	0.420694i	−0.961536	+	0.274680i	$0.911428\pi$
$992$		0			0
$993$	−11180.2	−	16298.0i	−0.357294	−	0.520846i
$994$		0			0
$995$			22617.4i			0.720624i
$996$		0			0
$997$	−23912.6	+	13806.0i	−0.759599	+	0.438555i	−0.829152	−	0.559023i	$-0.811176\pi$
$997$	−23912.6	+	13806.0i	−0.759599	+	0.438555i	0.0695525	+	0.997578i	$0.477843\pi$
$998$		0			0
$999$	1674.42	−	5598.50i	0.0530292	−	0.177306i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	336.4.bc.d.257.4		12
3.2	odd	2	inner	336.4.bc.d.257.6		12
4.3	odd	2		21.4.g.a.5.1	✓	12
7.3	odd	6	inner	336.4.bc.d.17.6		12
12.11	even	2		21.4.g.a.5.6	yes	12
21.17	even	6	inner	336.4.bc.d.17.4		12
28.3	even	6		21.4.g.a.17.6	yes	12
28.11	odd	6		147.4.g.d.80.6		12
28.19	even	6		147.4.c.a.146.12		12
28.23	odd	6		147.4.c.a.146.11		12
28.27	even	2		147.4.g.d.68.1		12
84.11	even	6		147.4.g.d.80.1		12
84.23	even	6		147.4.c.a.146.2		12
84.47	odd	6		147.4.c.a.146.1		12
84.59	odd	6		21.4.g.a.17.1	yes	12
84.83	odd	2		147.4.g.d.68.6		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
21.4.g.a.5.1	✓	12	4.3	odd	2
21.4.g.a.5.6	yes	12	12.11	even	2
21.4.g.a.17.1	yes	12	84.59	odd	6
21.4.g.a.17.6	yes	12	28.3	even	6
147.4.c.a.146.1		12	84.47	odd	6
147.4.c.a.146.2		12	84.23	even	6
147.4.c.a.146.11		12	28.23	odd	6
147.4.c.a.146.12		12	28.19	even	6
147.4.g.d.68.1		12	28.27	even	2
147.4.g.d.68.6		12	84.83	odd	2
147.4.g.d.80.1		12	84.11	even	6
147.4.g.d.80.6		12	28.11	odd	6
336.4.bc.d.17.4		12	21.17	even	6	inner
336.4.bc.d.17.6		12	7.3	odd	6	inner
336.4.bc.d.257.4		12	1.1	even	1	trivial
336.4.bc.d.257.6		12	3.2	odd	2	inner

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:	\( N \)	\(=\)	\( 336 = 2^{4} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	336.bc (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(2.24112 - 4.68800i) q^{3} +(-5.80193 + 10.0492i) q^{5} +(18.4018 + 2.09174i) q^{7} +(-16.9548 - 21.0128i) q^{9} +O(q^{10})\)	\(q+(2.24112 - 4.68800i) q^{3} +(-5.80193 + 10.0492i) q^{5} +(18.4018 + 2.09174i) q^{7} +(-16.9548 - 21.0128i) q^{9} +(-15.5157 + 8.95800i) q^{11} +62.4185i q^{13} +(34.1081 + 49.7211i) q^{15} +(10.7082 + 18.5472i) q^{17} +(-9.50747 - 5.48914i) q^{19} +(51.0467 - 81.5796i) q^{21} +(59.8367 + 34.5467i) q^{23} +(-4.82490 - 8.35697i) q^{25} +(-136.506 + 32.3918i) q^{27} +265.583i q^{29} +(-8.85795 + 5.11414i) q^{31} +(7.22254 + 92.8136i) q^{33} +(-127.786 + 172.788i) q^{35} +(-20.8257 + 36.0712i) q^{37} +(292.618 + 139.887i) q^{39} -31.0035 q^{41} +224.550 q^{43} +(309.533 - 48.4678i) q^{45} +(81.8595 - 141.785i) q^{47} +(334.249 + 76.9836i) q^{49} +(110.948 - 8.63368i) q^{51} +(456.586 - 263.610i) q^{53} -207.895i q^{55} +(-47.0405 + 32.2692i) q^{57} +(205.978 + 356.765i) q^{59} +(223.807 + 129.215i) q^{61} +(-268.044 - 422.137i) q^{63} +(-627.258 - 362.148i) q^{65} +(161.737 + 280.137i) q^{67} +(296.056 - 203.091i) q^{69} +45.4199i q^{71} +(-486.879 + 281.100i) q^{73} +(-49.9907 + 3.89016i) q^{75} +(-304.254 + 132.388i) q^{77} +(144.610 - 250.473i) q^{79} +(-154.073 + 712.532i) q^{81} -448.767 q^{83} -248.513 q^{85} +(1245.05 + 595.204i) q^{87} +(-280.814 + 486.384i) q^{89} +(-130.563 + 1148.61i) q^{91} +(4.12336 + 52.9875i) q^{93} +(110.323 - 63.6953i) q^{95} -214.364i q^{97} +(451.297 + 174.147i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 3 q^{3} + 56 q^{7} - 3 q^{9}+O(q^{10}) \) 12 * q + 3 * q^3 + 56 * q^7 - 3 * q^9	\( 12 q + 3 q^{3} + 56 q^{7} - 3 q^{9} - 6 q^{15} - 300 q^{19} + 357 q^{21} - 42 q^{25} + 930 q^{31} - 855 q^{33} + 764 q^{37} + 426 q^{39} + 1012 q^{43} + 2367 q^{45} - 336 q^{49} + 1341 q^{51} + 270 q^{57} + 2358 q^{61} - 1071 q^{63} - 792 q^{67} - 2904 q^{73} + 2418 q^{75} - 1674 q^{79} + 837 q^{81} + 348 q^{85} - 1638 q^{87} + 1218 q^{91} - 1479 q^{93} + 3354 q^{99}+O(q^{100}) \) 12 * q + 3 * q^3 + 56 * q^7 - 3 * q^9 - 6 * q^15 - 300 * q^19 + 357 * q^21 - 42 * q^25 + 930 * q^31 - 855 * q^33 + 764 * q^37 + 426 * q^39 + 1012 * q^43 + 2367 * q^45 - 336 * q^49 + 1341 * q^51 + 270 * q^57 + 2358 * q^61 - 1071 * q^63 - 792 * q^67 - 2904 * q^73 + 2418 * q^75 - 1674 * q^79 + 837 * q^81 + 348 * q^85 - 1638 * q^87 + 1218 * q^91 - 1479 * q^93 + 3354 * q^99

Introduction

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