LMFDB - Embedded newform 336.4.bc.d.17.4

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			17.4
Root			$-0.232749 - 2.99096i$ of defining polynomial
Character	$\chi$	$=$	336.17
Dual form			336.4.bc.d.257.4

$q$-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 $\left(\mathbb{Z}/336\mathbb{Z}\right)^\times$.

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

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	−0.999758	−	0.0220109i	$-0.992993\pi$
$5$	−5.80193	−	10.0492i	−0.518941	−	0.898832i	0.480817	−	0.876821i	$-0.340340\pi$
$6$		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	0.272050	−	0.962283i	$-0.412299\pi$
$11$	−15.5157	−	8.95800i	−0.425287	−	0.245540i	−0.697337	+	0.716743i	$0.745632\pi$
$12$		0			0
$13$		−	62.4185i		−	1.33167i	−0.746097	−	0.665837i	$-0.768075\pi$
$13$		−	62.4185i		−	1.33167i	0.746097	−	0.665837i	$-0.231925\pi$
$14$		0			0
$15$	34.1081	−	49.7211i	0.587111	−	0.855862i
$16$		0			0
$17$	10.7082	−	18.5472i	0.152772	−	0.264609i	−0.779474	−	0.626435i	$-0.784513\pi$
$17$	10.7082	−	18.5472i	0.152772	−	0.264609i	0.932245	+	0.361826i	$0.117847\pi$
$18$		0			0
$19$	−9.50747	+	5.48914i	−0.114798	+	0.0662787i	−0.556300	−	0.830982i	$-0.687779\pi$
$19$	−9.50747	+	5.48914i	−0.114798	+	0.0662787i	0.441502	+	0.897261i	$0.354446\pi$
$20$		0			0
$21$	51.0467	+	81.5796i	0.530443	+	0.847721i
$22$		0			0
$23$	59.8367	−	34.5467i	0.542470	−	0.313195i	−0.203609	−	0.979052i	$-0.565267\pi$
$23$	59.8367	−	34.5467i	0.542470	−	0.313195i	0.746079	+	0.665857i	$0.231934\pi$
$24$		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	$-0.676419\pi$
$29$		−	265.583i		−	1.70061i	0.526294	−	0.850303i	$-0.323581\pi$
$30$		0			0
$31$	−8.85795	−	5.11414i	−0.0513205	−	0.0296299i	0.474120	−	0.880460i	$-0.342766\pi$
$31$	−8.85795	−	5.11414i	−0.0513205	−	0.0296299i	−0.525441	+	0.850830i	$0.676100\pi$
$32$		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	0.816043	−	0.577991i	$-0.196163\pi$
$37$	−20.8257	−	36.0712i	−0.0925331	−	0.160272i	−0.908576	+	0.417719i	$0.862830\pi$
$38$		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	0.964638	−	0.263580i	$-0.0849033\pi$
$47$	81.8595	+	141.785i	0.254052	+	0.440031i	−0.710586	+	0.703611i	$0.751570\pi$
$48$		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	0.956784	−	0.290799i	$-0.0939211\pi$
$53$	456.586	+	263.610i	1.18334	+	0.683200i	0.226553	+	0.973999i	$0.427254\pi$
$54$		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	−0.544150	−	0.838988i	$-0.683148\pi$
$59$	205.978	−	356.765i	0.454510	−	0.787234i	0.998660	+	0.0517537i	$0.0164811\pi$
$60$		0			0
$61$	223.807	−	129.215i	0.469764	−	0.271218i	−0.246377	−	0.969174i	$-0.579240\pi$
$61$	223.807	−	129.215i	0.469764	−	0.271218i	0.716141	+	0.697956i	$0.245907\pi$
$62$		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	−0.680050	−	0.733166i	$-0.738042\pi$
$67$	161.737	−	280.137i	0.294915	−	0.510808i	0.974965	+	0.222357i	$0.0713752\pi$
$68$		0			0
$69$	296.056	+	203.091i	0.516536	+	0.354338i
$70$		0			0
$71$		−	45.4199i		−	0.0759205i	−0.999279	−	0.0379603i	$-0.987914\pi$
$71$		−	45.4199i		−	0.0759205i	0.999279	−	0.0379603i	$-0.0120860\pi$
$72$		0			0
$73$	−486.879	−	281.100i	−0.780615	−	0.450688i	0.0560334	−	0.998429i	$-0.482155\pi$
$73$	−486.879	−	281.100i	−0.780615	−	0.450688i	−0.836648	+	0.547741i	$0.815488\pi$
$74$		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	0.950435	−	0.310925i	$-0.100639\pi$
$79$	144.610	+	250.473i	0.205949	+	0.356714i	−0.744486	+	0.667638i	$0.767305\pi$
$80$		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	0.648927	−	0.760850i	$-0.275218\pi$
$89$	−280.814	−	486.384i	−0.334452	−	0.579288i	−0.983379	+	0.181562i	$0.941885\pi$
$90$		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	$0.0357873\pi$
$97$			214.364i			0.224385i	−0.993686	+	0.112192i	$0.964213\pi$
$98$		0			0
$99$	451.297	−	174.147i	0.458152	−	0.176793i
$100$		0			0
$101$	858.845	−	1487.56i	0.846122	−	1.46553i	−0.0385219	−	0.999258i	$-0.512265\pi$
$101$	858.845	−	1487.56i	0.846122	−	1.46553i	0.884644	−	0.466268i	$-0.154402\pi$
$102$		0			0
$103$	−1002.61	+	578.855i	−0.959123	+	0.553750i	−0.895903	−	0.444250i	$-0.853470\pi$
$103$	−1002.61	+	578.855i	−0.959123	+	0.553750i	−0.0632200	+	0.998000i	$0.520137\pi$
$104$		0			0
$105$	523.644	−	986.300i	0.486690	−	0.916696i
$106$		0			0
$107$	−1054.64	+	608.897i	−0.952859	+	0.550134i	−0.893968	−	0.448131i	$-0.852090\pi$
$107$	−1054.64	+	608.897i	−0.952859	+	0.550134i	−0.0588912	+	0.998264i	$0.518757\pi$
$108$		0			0
$109$	−649.132	+	1124.33i	−0.570418	+	0.987992i	0.426105	+	0.904674i	$0.359885\pi$
$109$	−649.132	+	1124.33i	−0.570418	+	0.987992i	−0.996523	+	0.0833189i	$0.973448\pi$
$110$		0			0
$111$	122.429	−	178.471i	0.104689	−	0.152610i
$112$		0			0
$113$			1437.86i			1.19701i	0.801118	+	0.598506i	$0.204239\pi$
$113$			1437.86i			1.19701i	−0.801118	+	0.598506i	$0.795761\pi$
$114$		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	0.999180	+	0.0404852i	$0.0128904\pi$
$131$	801.637	+	1388.48i	0.534651	+	0.926043i	−0.464529	+	0.885558i	$0.653776\pi$
$132$		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	0.971539	−	0.236879i	$-0.0761246\pi$
$137$	2007.90	+	1159.26i	1.25216	+	0.722938i	0.280626	+	0.959817i	$0.409458\pi$
$138$		0			0
$139$		−	1841.57i		−	1.12374i	−0.827225	−	0.561871i	$-0.810082\pi$
$139$		−	1841.57i		−	1.12374i	0.827225	−	0.561871i	$-0.189918\pi$
$140$		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	−0.776663	−	0.629917i	$-0.783089\pi$
$149$	−1126.68	+	650.488i	−0.619470	+	0.357651i	0.157193	+	0.987568i	$0.449756\pi$
$150$		0			0
$151$	−1308.24	+	2265.94i	−0.705055	+	1.22119i	0.261616	+	0.965172i	$0.415745\pi$
$151$	−1308.24	+	2265.94i	−0.705055	+	1.22119i	−0.966672	+	0.256020i	$0.917589\pi$
$152$		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	0.279826	−	0.960051i	$-0.409723\pi$
$157$	−809.876	−	467.582i	−0.411689	−	0.237689i	−0.691515	+	0.722362i	$0.743056\pi$
$158$		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	0.797041	−	0.603926i	$-0.206398\pi$
$163$	−259.079	−	448.738i	−0.124495	−	0.215631i	−0.921535	+	0.388295i	$0.873064\pi$
$164$		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	0.999547	+	0.0301000i	$0.00958257\pi$
$173$	1196.53	+	2072.45i	0.525841	+	0.910783i	−0.473706	+	0.880683i	$0.657084\pi$
$174$		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	0.379770	−	0.925081i	$-0.376003\pi$
$179$	−554.381	−	320.072i	−0.231488	−	0.133650i	−0.611258	+	0.791431i	$0.709336\pi$
$180$		0			0
$181$		−	4204.05i		−	1.72643i	−0.504833	−	0.863217i	$-0.668446\pi$
$181$		−	4204.05i		−	1.72643i	0.504833	−	0.863217i	$-0.331554\pi$
$182$		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	−0.241563	−	0.970385i	$-0.577660\pi$
$191$	1261.85	−	728.530i	0.478033	−	0.275993i	0.719597	+	0.694392i	$0.244327\pi$
$192$		0			0
$193$	−914.633	+	1584.19i	−0.341123	+	0.590842i	−0.984642	−	0.174588i	$-0.944141\pi$
$193$	−914.633	+	1584.19i	−0.341123	+	0.590842i	0.643519	+	0.765430i	$0.277474\pi$
$194$		0			0
$195$	−3103.51	−	2128.97i	−1.13973	−	0.781840i
$196$		0			0
$197$		−	661.168i		−	0.239118i	−0.992827	−	0.119559i	$-0.961852\pi$
$197$		−	661.168i		−	0.239118i	0.992827	−	0.119559i	$-0.0381481\pi$
$198$		0			0
$199$	1687.99	+	974.564i	0.601300	+	0.347161i	0.769553	−	0.638583i	$-0.220479\pi$
$199$	1687.99	+	974.564i	0.601300	+	0.347161i	−0.168253	+	0.985744i	$0.553812\pi$
$200$		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	$0.104289\pi$
$223$			2143.28i			0.643608i	−0.946806	+	0.321804i	$0.895711\pi$
$224$		0			0
$225$	−93.7981	−	243.075i	−0.0277920	−	0.0720221i
$226$		0			0
$227$	−1284.55	+	2224.91i	−0.375589	+	0.650540i	−0.990415	−	0.138123i	$-0.955893\pi$
$227$	−1284.55	+	2224.91i	−0.375589	+	0.650540i	0.614826	+	0.788663i	$0.289226\pi$
$228$		0			0
$229$	91.0827	−	52.5866i	0.0262835	−	0.0151748i	−0.486801	−	0.873513i	$-0.661836\pi$
$229$	91.0827	−	52.5866i	0.0262835	−	0.0151748i	0.513084	+	0.858338i	$0.328503\pi$
$230$		0			0
$231$	−61.2350	−	1723.04i	−0.0174414	−	0.490770i
$232$		0			0
$233$	2273.94	−	1312.86i	0.639360	−	0.369135i	−0.145008	−	0.989431i	$-0.546321\pi$
$233$	2273.94	−	1312.86i	0.639360	−	0.369135i	0.784368	+	0.620296i	$0.212987\pi$
$234$		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	$0.307635\pi$
$239$			6080.85i			1.64576i	−0.568212	+	0.822882i	$0.692365\pi$
$240$		0			0
$241$	4008.74	+	2314.45i	1.07147	+	0.618616i	0.928584	−	0.371122i	$-0.121027\pi$
$241$	4008.74	+	2314.45i	1.07147	+	0.618616i	0.142891	+	0.989738i	$0.454360\pi$
$242$		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	−0.973628	−	0.228140i	$-0.926736\pi$
$257$	−2819.70	−	4883.86i	−0.684389	−	1.18540i	0.289239	−	0.957257i	$-0.406598\pi$
$258$		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	0.810226	−	0.586118i	$-0.199345\pi$
$263$	3018.63	+	1742.81i	0.707745	+	0.408617i	−0.102480	+	0.994735i	$0.532678\pi$
$264$		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	−0.996876	−	0.0789869i	$-0.974831\pi$
$269$	−1897.28	+	3286.18i	−0.430033	+	0.744839i	0.566842	+	0.823826i	$0.308165\pi$
$270$		0			0
$271$	6458.49	−	3728.81i	1.44769	−	0.835827i	0.449351	−	0.893356i	$-0.351655\pi$
$271$	6458.49	−	3728.81i	1.44769	−	0.835827i	0.998344	+	0.0575288i	$0.0183221\pi$
$272$		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	−0.619203	−	0.785231i	$-0.712544\pi$
$277$	1707.75	−	2957.90i	0.370428	−	0.641600i	0.989631	+	0.143631i	$0.0458777\pi$
$278$		0			0
$279$	257.646	−	99.4210i	0.0552863	−	0.0213340i
$280$		0			0
$281$			2762.14i			0.586390i	0.956053	+	0.293195i	$0.0947185\pi$
$281$			2762.14i			0.586390i	−0.956053	+	0.293195i	$0.905281\pi$
$282$		0			0
$283$	4767.64	+	2752.60i	1.00144	+	0.578181i	0.908674	−	0.417507i	$-0.137096\pi$
$283$	4767.64	+	2752.60i	1.00144	+	0.578181i	0.0927647	+	0.995688i	$0.470430\pi$
$284$		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	$-0.720365\pi$
$307$		−	8281.42i		−	1.53956i	0.638308	−	0.769781i	$-0.279635\pi$
$308$		0			0
$309$	−4960.63	−	3402.94i	−0.913270	−	0.626493i
$310$		0			0
$311$	3435.52	−	5950.50i	0.626401	−	1.08496i	−0.361868	−	0.932230i	$-0.617861\pi$
$311$	3435.52	−	5950.50i	0.626401	−	1.08496i	0.988268	−	0.152728i	$-0.0488059\pi$
$312$		0			0
$313$	−2922.40	+	1687.25i	−0.527743	+	0.304693i	−0.740097	−	0.672500i	$-0.765220\pi$
$313$	−2922.40	+	1687.25i	−0.527743	+	0.304693i	0.212354	+	0.977193i	$0.431887\pi$
$314$		0			0
$315$	5797.33	+	244.428i	1.03696	+	0.0437205i
$316$		0			0
$317$	2052.28	−	1184.88i	0.363620	−	0.209936i	−0.307048	−	0.951694i	$-0.599341\pi$
$317$	2052.28	−	1184.88i	0.363620	−	0.209936i	0.670667	+	0.741758i	$0.266008\pi$
$318$		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	0.979609	−	0.200913i	$-0.0643910\pi$
$331$	1901.80	+	3294.02i	0.315808	+	0.546996i	−0.663801	+	0.747910i	$0.731058\pi$
$332$		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	0.784630	−	0.619965i	$-0.212853\pi$
$347$	4137.14	+	2388.58i	0.640039	+	0.369527i	−0.144590	+	0.989492i	$0.546186\pi$
$348$		0			0
$349$		−	7358.26i		−	1.12859i	−0.825573	−	0.564296i	$-0.809148\pi$
$349$		−	7358.26i		−	1.12859i	0.825573	−	0.564296i	$-0.190852\pi$
$350$		0			0
$351$	−2021.84	+	8520.47i	−0.307459	+	1.29569i
$352$		0			0
$353$	1652.78	−	2862.69i	0.249202	−	0.431631i	−0.714102	−	0.700041i	$-0.753165\pi$
$353$	1652.78	−	2862.69i	0.249202	−	0.431631i	0.963305	+	0.268410i	$0.0864982\pi$
$354$		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	−0.473367	−	0.880865i	$-0.656962\pi$
$359$	359.154	−	207.358i	0.0528006	−	0.0304845i	0.526168	+	0.850381i	$0.323628\pi$
$360$		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	0.504681	−	0.863306i	$-0.331610\pi$
$367$	65.9242	+	38.0613i	0.00937661	+	0.00541359i	−0.495304	+	0.868720i	$0.664943\pi$
$368$		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	0.877771	+	0.479080i	$0.159030\pi$
$373$	6150.49	+	10653.0i	0.853781	+	1.47879i	−0.0239900	+	0.999712i	$0.507637\pi$
$374$		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	0.643673	−	0.765300i	$-0.277410\pi$
$383$	−2555.45	−	4426.17i	−0.340933	−	0.590513i	−0.984606	+	0.174787i	$0.944076\pi$
$384$		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	0.852595	−	0.522572i	$-0.175028\pi$
$389$	6339.84	+	3660.31i	0.826331	+	0.477083i	−0.0262636	+	0.999655i	$0.508361\pi$
$390$		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	0.0570893	−	0.998369i	$-0.481818\pi$
$397$	7516.61	−	4339.72i	0.950247	−	0.548625i	0.893158	+	0.449744i	$0.148485\pi$
$398$		0			0
$399$	−933.127	−	495.414i	−0.117080	−	0.0621597i
$400$		0			0
$401$	8447.68	−	4877.27i	1.05201	−	0.607379i	0.128800	−	0.991671i	$-0.458887\pi$
$401$	8447.68	−	4877.27i	1.05201	−	0.607379i	0.923212	+	0.384291i	$0.125554\pi$
$402$		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	0.666828	−	0.745211i	$-0.267651\pi$
$409$	2935.32	+	1694.71i	0.354871	+	0.204885i	−0.311958	+	0.950096i	$0.600985\pi$
$410$		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	0.305443	−	0.952210i	$-0.401195\pi$
$431$	−3279.13	−	1893.21i	−0.366474	−	0.211584i	−0.671917	+	0.740627i	$0.734529\pi$
$432$		0			0
$433$			3191.67i			0.354230i	0.984190	+	0.177115i	$0.0566765\pi$
$433$			3191.67i			0.354230i	−0.984190	+	0.177115i	$0.943323\pi$
$434$		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	−0.335635	−	0.941992i	$-0.608951\pi$
$439$	2872.90	−	1658.67i	0.312337	−	0.180328i	0.647972	+	0.761664i	$0.275617\pi$
$440$		0			0
$441$	−4049.47	+	8328.74i	−0.437261	+	0.899335i
$442$		0			0
$443$	9266.95	−	5350.27i	0.993873	−	0.573813i	0.0874435	−	0.996169i	$-0.472130\pi$
$443$	9266.95	−	5350.27i	0.993873	−	0.573813i	0.906430	+	0.422356i	$0.138797\pi$
$444$		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	$0.0677225\pi$
$449$			4017.92i			0.422310i	−0.977453	+	0.211155i	$0.932278\pi$
$450$		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	0.530086	−	0.847944i	$-0.322160\pi$
$457$	−4584.83	−	7941.15i	−0.469298	−	0.812848i	−0.999384	+	0.0350961i	$0.988826\pi$
$458$		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	0.992396	−	0.123088i	$-0.0392798\pi$
$467$	3931.83	+	6810.13i	0.389600	+	0.674808i	−0.602795	+	0.797896i	$0.705946\pi$
$468$		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	−0.940574	−	0.339588i	$-0.889712\pi$
$479$	−1847.13	+	3199.33i	−0.176196	+	0.305180i	0.764379	+	0.644767i	$0.223046\pi$
$480$		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	−0.889474	−	0.456985i	$-0.848929\pi$
$487$	−526.359	+	911.681i	−0.0489766	+	0.0848300i	0.840498	+	0.541815i	$0.182263\pi$
$488$		0			0
$489$	1523.06	−	2220.24i	0.140849	−	0.205322i
$490$		0			0
$491$			2378.40i			0.218607i	0.994008	+	0.109303i	$0.0348620\pi$
$491$			2378.40i			0.218607i	−0.994008	+	0.109303i	$0.965138\pi$
$492$		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	0.888192	+	0.459472i	$0.151961\pi$
$499$	9385.74	+	16256.6i	0.842011	+	1.45840i	−0.0461818	+	0.998933i	$0.514705\pi$
$500$		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	0.926428	−	0.376472i	$-0.122863\pi$
$509$	1575.31	+	2728.52i	0.137180	+	0.237603i	−0.789248	+	0.614074i	$0.789529\pi$
$510$		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	−0.951510	−	0.307618i	$-0.900468\pi$
$521$	−2489.60	+	4312.12i	−0.209350	+	0.362605i	0.742160	+	0.670223i	$0.233802\pi$
$522$		0			0
$523$	−11977.0	+	6914.92i	−1.00137	+	0.578142i	−0.908654	−	0.417550i	$-0.862889\pi$
$523$	−11977.0	+	6914.92i	−1.00137	+	0.578142i	−0.0927181	+	0.995692i	$0.529556\pi$
$524$		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	0.740815	−	0.671709i	$-0.234439\pi$
$541$	−2658.97	−	4605.48i	−0.211309	−	0.365998i	−0.952124	+	0.305711i	$0.901106\pi$
$542$		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	0.495203	−	0.868777i	$-0.335094\pi$
$557$	−125.920	−	72.6999i	−0.00957881	−	0.00553033i	−0.504782	+	0.863247i	$0.668427\pi$
$558$		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	−0.929962	−	0.367657i	$-0.880160\pi$
$563$	−1958.12	+	3391.56i	−0.146581	+	0.253885i	0.783381	+	0.621542i	$0.213493\pi$
$564$		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	−0.747336	−	0.664447i	$-0.768667\pi$
$569$	−7404.97	+	4275.26i	−0.545576	+	0.314988i	0.201760	+	0.979435i	$0.435334\pi$
$570$		0			0
$571$	−11956.8	+	20709.8i	−0.876318	+	1.51783i	−0.0209659	+	0.999780i	$0.506674\pi$
$571$	−11956.8	+	20709.8i	−0.876318	+	1.51783i	−0.855352	+	0.518047i	$0.826659\pi$
$572$		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	0.849983	−	0.526809i	$-0.176612\pi$
$577$	11347.8	+	6551.66i	0.818745	+	0.472703i	−0.0312386	+	0.999512i	$0.509945\pi$
$578$		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	0.928071	+	0.372404i	$0.121466\pi$
$593$	11358.1	+	19672.8i	0.786547	+	1.36234i	−0.141524	+	0.989935i	$0.545200\pi$
$594$		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	0.0438153	−	0.999040i	$-0.486049\pi$
$599$	−11720.4	−	6766.78i	−0.799471	−	0.461575i	−0.843286	+	0.537465i	$0.819382\pi$
$600$		0			0
$601$		−	3667.98i		−	0.248952i	−0.992223	−	0.124476i	$-0.960275\pi$
$601$		−	3667.98i		−	0.248952i	0.992223	−	0.124476i	$-0.0397250\pi$
$602$		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	−0.249575	−	0.968355i	$-0.580291\pi$
$607$	6942.92	−	4008.50i	0.464258	−	0.268039i	0.713833	+	0.700316i	$0.246958\pi$
$608$		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	−0.978266	−	0.207352i	$-0.933515\pi$
$613$	−4698.26	+	8137.63i	−0.309561	+	0.536176i	0.668705	+	0.743528i	$0.266849\pi$
$614$		0			0
$615$	−1057.47	+	1541.53i	−0.0693355	+	0.101074i
$616$		0			0
$617$		−	8906.76i		−	0.581155i	−0.956851	−	0.290578i	$-0.906153\pi$
$617$		−	8906.76i		−	0.581155i	0.956851	−	0.290578i	$-0.0938474\pi$
$618$		0			0
$619$	6091.73	+	3517.06i	0.395553	+	0.228373i	0.684563	−	0.728953i	$-0.259993\pi$
$619$	6091.73	+	3517.06i	0.395553	+	0.228373i	−0.289010	+	0.957326i	$0.593326\pi$
$620$		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	0.211297	−	0.977422i	$-0.432231\pi$
$641$	−8593.58	−	4961.51i	−0.529526	−	0.305722i	−0.740823	+	0.671700i	$0.765564\pi$
$642$		0			0
$643$		−	294.191i		−	0.0180432i	−0.999959	−	0.00902160i	$-0.997128\pi$
$643$		−	294.191i		−	0.0180432i	0.999959	−	0.00902160i	$-0.00287170\pi$
$644$		0			0
$645$	7658.97	−	11164.9i	0.467553	−	0.681576i
$646$		0			0
$647$	3859.39	−	6684.67i	0.234511	−	0.406184i	−0.724620	−	0.689149i	$-0.757985\pi$
$647$	3859.39	−	6684.67i	0.234511	−	0.406184i	0.959130	+	0.282965i	$0.0913179\pi$
$648$		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	−0.765139	−	0.643865i	$-0.777330\pi$
$653$	−9846.89	+	5685.11i	−0.590105	+	0.340697i	0.175034	+	0.984562i	$0.443996\pi$
$654$		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	$-0.801071\pi$
$659$		−	19795.1i		−	1.17012i	0.810990	−	0.585060i	$-0.198929\pi$
$660$		0			0
$661$	26896.6	+	15528.7i	1.58268	+	0.913763i	0.994466	+	0.105062i	$0.0335041\pi$
$661$	26896.6	+	15528.7i	1.58268	+	0.913763i	0.588219	+	0.808702i	$0.299829\pi$
$662$		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	−0.965455	−	0.260571i	$-0.916089\pi$
$677$	−12478.3	−	21613.0i	−0.708389	−	1.22697i	0.257066	−	0.966394i	$-0.417244\pi$
$678$		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	0.202812	−	0.979218i	$-0.434992\pi$
$683$	−9706.83	−	5604.24i	−0.543809	−	0.313968i	−0.746621	+	0.665249i	$0.768325\pi$
$684$		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	−0.216057	−	0.976381i	$-0.569320\pi$
$691$	9472.37	−	5468.88i	0.521485	−	0.301079i	0.737542	+	0.675301i	$0.235986\pi$
$692$		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	$-0.728632\pi$
$701$		−	27949.3i		−	1.50589i	0.658082	−	0.752947i	$-0.271368\pi$
$702$		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	−0.997924	−	0.0644082i	$-0.979484\pi$
$709$	−10472.7	−	18139.3i	−0.554741	−	0.960840i	0.443183	−	0.896431i	$-0.353849\pi$
$710$		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	0.738092	−	0.674700i	$-0.235727\pi$
$719$	−4150.10	−	7188.19i	−0.215261	−	0.372843i	−0.953353	+	0.301857i	$0.902394\pi$
$720$		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	$-0.820530\pi$
$727$		−	20951.5i		−	1.06884i	0.845218	−	0.534421i	$-0.179470\pi$
$728$		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	−0.371827	−	0.928302i	$-0.621269\pi$
$733$	4885.73	−	2820.78i	0.246192	−	0.142139i	0.618019	+	0.786163i	$0.287935\pi$
$734$		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	−0.972193	−	0.234183i	$-0.924758\pi$
$739$	−5691.08	+	9857.24i	−0.283288	+	0.490669i	0.688905	+	0.724852i	$0.258092\pi$
$740$		0			0
$741$	−2014.20	+	2936.20i	−0.0998560	+	0.145565i
$742$		0			0
$743$		−	4665.46i		−	0.230362i	−0.993345	−	0.115181i	$-0.963255\pi$
$743$		−	4665.46i		−	0.230362i	0.993345	−	0.115181i	$-0.0367449\pi$
$744$		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	0.726200	−	0.687483i	$-0.241284\pi$
$751$	−4780.43	−	8279.95i	−0.232277	−	0.402316i	−0.958478	+	0.285167i	$0.907951\pi$
$752$		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	0.999201	+	0.0399765i	$0.0127283\pi$
$761$	11215.0	+	19424.9i	0.534221	+	0.925298i	−0.464980	+	0.885321i	$0.653938\pi$
$762$		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	$0.217117\pi$
$769$			26887.4i			1.26084i	−0.776254	+	0.630420i	$0.782883\pi$
$770$		0			0
$771$	16576.3	−	24164.1i	0.774293	−	1.12873i
$772$		0			0
$773$	11104.6	−	19233.7i	0.516693	−	0.894938i	−0.483119	−	0.875555i	$-0.660496\pi$
$773$	11104.6	−	19233.7i	0.516693	−	0.894938i	0.999812	−	0.0193838i	$-0.00617045\pi$
$774$		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	0.839348	−	0.543594i	$-0.182937\pi$
$787$	17403.2	+	10047.8i	0.788257	+	0.455100i	−0.0510919	+	0.998694i	$0.516270\pi$
$788$		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	0.751174	−	0.660104i	$-0.229488\pi$
$809$	12772.9	+	7374.43i	0.555093	+	0.320483i	−0.196080	+	0.980588i	$0.562821\pi$
$810$		0			0
$811$		−	4569.51i		−	0.197851i	−0.995095	−	0.0989255i	$-0.968459\pi$
$811$		−	4569.51i		−	0.197851i	0.995095	−	0.0989255i	$-0.0315405\pi$
$812$		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	0.809878	−	0.586598i	$-0.199533\pi$
$821$	40528.1	−	23398.9i	1.72283	−	0.994674i	0.912948	−	0.408076i	$-0.133800\pi$
$822$		0			0
$823$	−13086.7	+	22666.8i	−0.554281	+	0.960043i	0.443678	+	0.896186i	$0.353673\pi$
$823$	−13086.7	+	22666.8i	−0.554281	+	0.960043i	−0.997959	+	0.0638567i	$0.979660\pi$
$824$		0			0
$825$	740.792	+	508.175i	0.0312619	+	0.0214453i
$826$		0			0
$827$			42212.0i			1.77492i	0.460888	+	0.887458i	$0.347531\pi$
$827$			42212.0i			1.77492i	−0.460888	+	0.887458i	$0.652469\pi$
$828$		0			0
$829$	−19605.0	−	11319.0i	−0.821364	−	0.474215i	0.0295225	−	0.999564i	$-0.490601\pi$
$829$	−19605.0	−	11319.0i	−0.821364	−	0.474215i	−0.850887	+	0.525349i	$0.823935\pi$
$830$		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	$0.344820\pi$
$853$			44021.1i			1.76700i	−0.468430	+	0.883501i	$0.655180\pi$
$854$		0			0
$855$	−3208.92	+	1238.26i	−0.128354	+	0.0495295i
$856$		0			0
$857$	1007.45	−	1744.96i	0.0401562	−	0.0695526i	−0.845249	−	0.534373i	$-0.820548\pi$
$857$	1007.45	−	1744.96i	0.0401562	−	0.0695526i	0.885405	+	0.464820i	$0.153881\pi$
$858$		0			0
$859$	−15844.5	+	9147.83i	−0.629345	+	0.363353i	−0.780499	−	0.625158i	$-0.785035\pi$
$859$	−15844.5	+	9147.83i	−0.629345	+	0.363353i	0.151153	+	0.988510i	$0.451701\pi$
$860$		0			0
$861$	−1582.63	−	2529.26i	−0.0626432	−	0.100112i
$862$		0			0
$863$	5979.04	−	3452.00i	0.235839	−	0.136162i	−0.377424	−	0.926041i	$-0.623190\pi$
$863$	5979.04	−	3452.00i	0.235839	−	0.136162i	0.613263	+	0.789879i	$0.289857\pi$
$864$		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	0.861982	−	0.506940i	$-0.169223\pi$
$877$	−208.597	−	361.300i	−0.00803171	−	0.0139113i	−0.870013	+	0.493028i	$0.835890\pi$
$878$		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	0.645903	−	0.763420i	$-0.276481\pi$
$887$	−8933.98	−	15474.1i	−0.338189	−	0.585761i	−0.984092	+	0.177659i	$0.943148\pi$
$888$		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	−0.919820	−	0.392341i	$-0.871665\pi$
$907$	−3281.49	+	5683.71i	−0.120132	+	0.208076i	0.799687	+	0.600417i	$0.204999\pi$
$908$		0			0
$909$	16696.3	+	43268.0i	0.609221	+	1.57878i
$910$		0			0
$911$		−	41084.1i		−	1.49416i	−0.664735	−	0.747079i	$-0.731456\pi$
$911$		−	41084.1i		−	1.49416i	0.664735	−	0.747079i	$-0.268544\pi$
$912$		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	0.911334	−	0.411668i	$-0.135054\pi$
$919$	2762.34	+	4784.51i	0.0991524	+	0.171737i	−0.812182	+	0.583405i	$0.801720\pi$
$920$		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	0.552073	−	0.833796i	$-0.313837\pi$
$929$	−12630.2	−	21876.1i	−0.446052	−	0.772585i	−0.998125	+	0.0612109i	$0.980504\pi$
$930$		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	$-0.703180\pi$
$937$		−	46069.3i		−	1.60621i	0.595838	−	0.803105i	$-0.296820\pi$
$938$		0			0
$939$	−14459.3	−	9918.89i	−0.502514	−	0.344718i
$940$		0			0
$941$	−24112.4	+	41763.8i	−0.835325	+	1.44683i	0.0584406	+	0.998291i	$0.481387\pi$
$941$	−24112.4	+	41763.8i	−0.835325	+	1.44683i	−0.893766	+	0.448534i	$0.851946\pi$
$942$		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	−0.819254	−	0.573431i	$-0.805612\pi$
$947$	−21340.2	+	12320.8i	−0.732275	+	0.422779i	0.0869787	+	0.996210i	$0.472279\pi$
$948$		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	$0.0724171\pi$
$953$			13271.1i			0.451095i	−0.974232	+	0.225548i	$0.927583\pi$
$954$		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	−0.875947	−	0.482407i	$-0.839763\pi$
$971$	−25892.6	−	44847.3i	−0.855750	−	1.48220i	0.0201966	−	0.999796i	$-0.493571\pi$
$972$		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	0.0356703	−	0.999364i	$-0.488643\pi$
$977$	−24796.0	−	14316.0i	−0.811969	−	0.468790i	−0.847639	+	0.530573i	$0.821977\pi$
$978$		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	0.250288	+	0.968171i	$0.419475\pi$
$983$	−21984.3	+	38077.9i	−0.713317	+	1.23550i	−0.963605	+	0.267330i	$0.913859\pi$
$984$		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	−0.961536	−	0.274680i	$-0.911428\pi$
$991$	−7577.33	+	13124.3i	−0.242888	+	0.420694i	0.718648	+	0.695374i	$0.244761\pi$
$992$		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	0.0695525	−	0.997578i	$-0.477843\pi$
$997$	−23912.6	−	13806.0i	−0.759599	−	0.438555i	−0.829152	+	0.559023i	$0.811176\pi$
$998$		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.17.4		12
3.2	odd	2	inner	336.4.bc.d.17.6		12
4.3	odd	2		21.4.g.a.17.1	yes	12
7.5	odd	6	inner	336.4.bc.d.257.6		12
12.11	even	2		21.4.g.a.17.6	yes	12
21.5	even	6	inner	336.4.bc.d.257.4		12
28.3	even	6		147.4.c.a.146.2		12
28.11	odd	6		147.4.c.a.146.1		12
28.19	even	6		21.4.g.a.5.6	yes	12
28.23	odd	6		147.4.g.d.68.6		12
28.27	even	2		147.4.g.d.80.1		12
84.11	even	6		147.4.c.a.146.12		12
84.23	even	6		147.4.g.d.68.1		12
84.47	odd	6		21.4.g.a.5.1	✓	12
84.59	odd	6		147.4.c.a.146.11		12
84.83	odd	2		147.4.g.d.80.6		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
21.4.g.a.5.1	✓	12	84.47	odd	6
21.4.g.a.5.6	yes	12	28.19	even	6
21.4.g.a.17.1	yes	12	4.3	odd	2
21.4.g.a.17.6	yes	12	12.11	even	2
147.4.c.a.146.1		12	28.11	odd	6
147.4.c.a.146.2		12	28.3	even	6
147.4.c.a.146.11		12	84.59	odd	6
147.4.c.a.146.12		12	84.11	even	6
147.4.g.d.68.1		12	84.23	even	6
147.4.g.d.68.6		12	28.23	odd	6
147.4.g.d.80.1		12	28.27	even	2
147.4.g.d.80.6		12	84.83	odd	2
336.4.bc.d.17.4		12	1.1	even	1	trivial
336.4.bc.d.17.6		12	3.2	odd	2	inner
336.4.bc.d.257.4		12	21.5	even	6	inner
336.4.bc.d.257.6		12	7.5	odd	6	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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