LMFDB - Embedded newform 336.4.bc.d.257.6

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			257.6
Root			$2.70662 + 1.29391i$ of defining polynomial
Character	$\chi$	$=$	336.257
Dual form			336.4.bc.d.17.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(5.18049 + 0.403134i) q^{3} +(5.80193 - 10.0492i) q^{5} +(18.4018 + 2.09174i) q^{7} +(26.6750 + 4.17686i) q^{9} +O(q^{10})$	\(q+(5.18049 + 0.403134i) q^{3} +(5.80193 - 10.0492i) q^{5} +(18.4018 + 2.09174i) q^{7} +(26.6750 + 4.17686i) q^{9} +(15.5157 - 8.95800i) q^{11} +62.4185i q^{13} +(34.1081 - 49.7211i) q^{15} +(-10.7082 - 18.5472i) q^{17} +(-9.50747 - 5.48914i) q^{19} +(94.4869 + 18.2546i) q^{21} +(-59.8367 - 34.5467i) q^{23} +(-4.82490 - 8.35697i) q^{25} +(136.506 + 32.3918i) q^{27} -265.583i q^{29} +(-8.85795 + 5.11414i) q^{31} +(83.9902 - 40.1519i) q^{33} +(127.786 - 172.788i) q^{35} +(-20.8257 + 36.0712i) q^{37} +(-25.1630 + 323.358i) q^{39} +31.0035 q^{41} +224.550 q^{43} +(196.741 - 243.829i) q^{45} +(-81.8595 + 141.785i) q^{47} +(334.249 + 76.9836i) q^{49} +(-47.9968 - 100.400i) q^{51} +(-456.586 + 263.610i) q^{53} -207.895i q^{55} +(-47.0405 - 32.2692i) q^{57} +(-205.978 - 356.765i) q^{59} +(223.807 + 129.215i) q^{61} +(482.129 + 132.659i) q^{63} +(627.258 + 362.148i) q^{65} +(161.737 + 280.137i) q^{67} +(-296.056 - 203.091i) q^{69} -45.4199i q^{71} +(-486.879 + 281.100i) q^{73} +(-21.6264 - 45.2383i) q^{75} +(304.254 - 132.388i) q^{77} +(144.610 - 250.473i) q^{79} +(694.108 + 222.835i) q^{81} +448.767 q^{83} -248.513 q^{85} +(107.066 - 1375.85i) q^{87} +(280.814 - 486.384i) q^{89} +(-130.563 + 1148.61i) q^{91} +(-47.9502 + 22.9228i) q^{93} +(-110.323 + 63.6953i) q^{95} -214.364i q^{97} +(451.297 - 174.147i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	5.18049	+	0.403134i	0.996986	+	0.0775831i
$3$	5.18049	+	0.403134i	0.996986	+	0.0775831i
$4$		0			0
$5$	5.80193	−	10.0492i	0.518941	−	0.898832i	−0.480817	−	0.876821i	$-0.659660\pi$
$5$	5.80193	−	10.0492i	0.518941	−	0.898832i	0.999758	−	0.0220109i	$-0.00700684\pi$
$6$		0			0
$7$	18.4018	+	2.09174i	0.993601	+	0.112944i
$7$	18.4018	+	2.09174i	0.993601	+	0.112944i
$8$		0			0
$9$	26.6750	+	4.17686i	0.987962	+	0.154699i
$10$		0			0
$11$	15.5157	−	8.95800i	0.425287	−	0.245540i	−0.272050	−	0.962283i	$-0.587701\pi$
$11$	15.5157	−	8.95800i	0.425287	−	0.245540i	0.697337	+	0.716743i	$0.254368\pi$
$12$		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	0.779474	−	0.626435i	$-0.215487\pi$
$17$	−10.7082	−	18.5472i	−0.152772	−	0.264609i	−0.932245	+	0.361826i	$0.882153\pi$
$18$		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
$21$	94.4869	+	18.2546i	0.981844	+	0.189690i
$22$		0			0
$23$	−59.8367	−	34.5467i	−0.542470	−	0.313195i	0.203609	−	0.979052i	$-0.434733\pi$
$23$	−59.8367	−	34.5467i	−0.542470	−	0.313195i	−0.746079	+	0.665857i	$0.768066\pi$
$24$		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	−0.525441	−	0.850830i	$-0.676100\pi$
$31$	−8.85795	+	5.11414i	−0.0513205	+	0.0296299i	0.474120	+	0.880460i	$0.342766\pi$
$32$		0			0
$33$	83.9902	−	40.1519i	0.443055	−	0.211805i
$34$		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
$39$	−25.1630	+	323.358i	−0.103315	+	1.32766i
$40$		0			0
$41$	31.0035			0.118096			0.0590480	−	0.998255i	$-0.481193\pi$
$41$	31.0035			0.118096			0.0590480	+	0.998255i	$0.481193\pi$
$42$		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
$45$	196.741	−	243.829i	0.651742	−	0.807732i
$46$		0			0
$47$	−81.8595	+	141.785i	−0.254052	+	0.440031i	−0.964638	−	0.263580i	$-0.915097\pi$
$47$	−81.8595	+	141.785i	−0.254052	+	0.440031i	0.710586	+	0.703611i	$0.248430\pi$
$48$		0			0
$49$	334.249	+	76.9836i	0.974487	+	0.224442i
$50$		0			0
$51$	−47.9968	−	100.400i	−0.131782	−	0.275664i
$52$		0			0
$53$	−456.586	+	263.610i	−1.18334	+	0.683200i	−0.956784	−	0.290799i	$-0.906079\pi$
$53$	−456.586	+	263.610i	−1.18334	+	0.683200i	−0.226553	+	0.973999i	$0.572746\pi$
$54$		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	$-0.316852\pi$
$59$	−205.978	−	356.765i	−0.454510	−	0.787234i	−0.998660	+	0.0517537i	$0.983519\pi$
$60$		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
$63$	482.129	+	132.659i	0.964168	+	0.265293i
$64$		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	$-0.987914\pi$
$71$		−	45.4199i		−	0.0759205i	0.999279	−	0.0379603i	$-0.0120860\pi$
$72$		0			0
$73$	−486.879	+	281.100i	−0.780615	+	0.450688i	−0.836648	−	0.547741i	$-0.815488\pi$
$73$	−486.879	+	281.100i	−0.780615	+	0.450688i	0.0560334	+	0.998429i	$0.482155\pi$
$74$		0			0
$75$	−21.6264	−	45.2383i	−0.0332960	−	0.0696489i
$76$		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
$81$	694.108	+	222.835i	0.952137	+	0.305673i
$82$		0			0
$83$	448.767			0.593477			0.296738	−	0.954959i	$-0.404101\pi$
$83$	448.767			0.593477			0.296738	+	0.954959i	$0.404101\pi$
$84$		0			0
$85$	−248.513			−0.317118
$86$		0			0
$87$	107.066	−	1375.85i	0.131938	−	1.69548i
$88$		0			0
$89$	280.814	−	486.384i	0.334452	−	0.579288i	−0.648927	−	0.760850i	$-0.724782\pi$
$89$	280.814	−	486.384i	0.334452	−	0.579288i	0.983379	+	0.181562i	$0.0581155\pi$
$90$		0			0
$91$	−130.563	+	1148.61i	−0.150404	+	1.32315i
$92$		0			0
$93$	−47.9502	+	22.9228i	−0.0534645	+	0.0255590i
$94$		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	$-0.845598\pi$
$101$	−858.845	−	1487.56i	−0.846122	−	1.46553i	0.0385219	−	0.999258i	$-0.487735\pi$
$102$		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
$105$	731.652	−	843.610i	0.680018	−	0.784075i
$106$		0			0
$107$	1054.64	+	608.897i	0.952859	+	0.550134i	0.893968	−	0.448131i	$-0.147910\pi$
$107$	1054.64	+	608.897i	0.952859	+	0.550134i	0.0588912	+	0.998264i	$0.481243\pi$
$108$		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	$0.204239\pi$
$113$			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
$117$	−260.713	+	1665.01i	−0.206008	+	1.31564i
$118$		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
$123$	160.613	+	12.4986i	0.117740	+	0.00916226i
$124$		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
$129$	1163.28	+	90.5238i	0.793962	+	0.0617843i
$130$		0			0
$131$	−801.637	+	1388.48i	−0.534651	+	0.926043i	0.464529	+	0.885558i	$0.346224\pi$
$131$	−801.637	+	1388.48i	−0.534651	+	0.926043i	−0.999180	+	0.0404852i	$0.987110\pi$
$132$		0			0
$133$	−163.472	−	120.897i	−0.106578	−	0.0788203i
$134$		0			0
$135$	1117.51	−	1183.84i	0.712444	−	0.754733i
$136$		0			0
$137$	−2007.90	+	1159.26i	−1.25216	+	0.722938i	−0.971539	−	0.236879i	$-0.923875\pi$
$137$	−2007.90	+	1159.26i	−1.25216	+	0.722938i	−0.280626	+	0.959817i	$0.590542\pi$
$138$		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
$147$	1700.54	+	533.560i	0.954137	+	0.299369i
$148$		0			0
$149$	1126.68	+	650.488i	0.619470	+	0.357651i	0.776663	−	0.629917i	$-0.216911\pi$
$149$	1126.68	+	650.488i	0.619470	+	0.357651i	−0.157193	+	0.987568i	$0.550244\pi$
$150$		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
$159$	−2471.61	+	1181.56i	−1.23278	+	0.589334i
$160$		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
$165$	83.8094	−	1077.00i	0.0395428	−	0.508146i
$166$		0			0
$167$	−3767.97			−1.74595			−0.872977	−	0.487761i	$-0.837814\pi$
$167$	−3767.97			−1.74595			−0.872977	+	0.487761i	$0.837814\pi$
$168$		0			0
$169$	−1699.06			−0.773356
$170$		0			0
$171$	−230.684	−	186.134i	−0.103163	−	0.0832399i
$172$		0			0
$173$	−1196.53	+	2072.45i	−0.525841	+	0.910783i	0.473706	+	0.880683i	$0.342916\pi$
$173$	−1196.53	+	2072.45i	−0.525841	+	0.910783i	−0.999547	+	0.0301000i	$0.990417\pi$
$174$		0			0
$175$	−71.3059	−	163.875i	−0.0308013	−	0.0707875i
$176$		0			0
$177$	−923.244	−	1931.25i	−0.392064	−	0.820124i
$178$		0			0
$179$	554.381	−	320.072i	0.231488	−	0.133650i	−0.379770	−	0.925081i	$-0.623997\pi$
$179$	554.381	−	320.072i	0.231488	−	0.133650i	0.611258	+	0.791431i	$0.290664\pi$
$180$		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
$189$	2444.19	+	881.600i	0.940680	+	0.339296i
$190$		0			0
$191$	−1261.85	−	728.530i	−0.478033	−	0.275993i	0.241563	−	0.970385i	$-0.422340\pi$
$191$	−1261.85	−	728.530i	−0.478033	−	0.275993i	−0.719597	+	0.694392i	$0.755673\pi$
$192$		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	$-0.961852\pi$
$197$		−	661.168i		−	0.239118i	0.992827	−	0.119559i	$-0.0381481\pi$
$198$		0			0
$199$	1687.99	−	974.564i	0.601300	−	0.347161i	−0.168253	−	0.985744i	$-0.553812\pi$
$199$	1687.99	−	974.564i	0.601300	−	0.347161i	0.769553	+	0.638583i	$0.220479\pi$
$200$		0			0
$201$	724.945	+	1516.45i	0.254396	+	0.532149i
$202$		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
$207$	−1451.84	−	1171.46i	−0.487489	−	0.393344i
$208$		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
$213$	18.3103	−	235.298i	0.00589015	−	0.0756917i
$214$		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
$219$	−2635.59	+	1259.96i	−0.813228	+	0.388767i
$220$		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	0.990415	−	0.138123i	$-0.0441070\pi$
$227$	1284.55	+	2224.91i	0.375589	+	0.650540i	−0.614826	+	0.788663i	$0.710774\pi$
$228$		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
$231$	1629.56	−	563.180i	0.464142	−	0.160409i
$232$		0			0
$233$	−2273.94	−	1312.86i	−0.639360	−	0.369135i	0.145008	−	0.989431i	$-0.453679\pi$
$233$	−2273.94	−	1312.86i	−0.639360	−	0.369135i	−0.784368	+	0.620296i	$0.787013\pi$
$234$		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	0.142891	−	0.989738i	$-0.454360\pi$
$241$	4008.74	−	2314.45i	1.07147	−	0.618616i	0.928584	+	0.371122i	$0.121027\pi$
$242$		0			0
$243$	3505.99	+	1434.21i	0.925552	+	0.378621i
$244$		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
$249$	2324.83	+	180.913i	0.591688	+	0.0460438i
$250$		0			0
$251$	5967.85			1.50075			0.750373	−	0.661015i	$-0.229874\pi$
$251$	5967.85			1.50075			0.750373	+	0.661015i	$0.229874\pi$
$252$		0			0
$253$	−1237.88			−0.307607
$254$		0			0
$255$	−1287.42	−	100.184i	−0.316162	−	0.0246030i
$256$		0			0
$257$	2819.70	−	4883.86i	0.684389	−	1.18540i	−0.289239	−	0.957257i	$-0.593402\pi$
$257$	2819.70	−	4883.86i	0.684389	−	1.18540i	0.973628	−	0.228140i	$-0.0732643\pi$
$258$		0			0
$259$	−458.681	+	620.211i	−0.110043	+	0.148796i
$260$		0			0
$261$	1109.30	−	7084.42i	0.263081	−	1.68013i
$262$		0			0
$263$	−3018.63	+	1742.81i	−0.707745	+	0.408617i	−0.810226	−	0.586118i	$-0.800655\pi$
$263$	−3018.63	+	1742.81i	−0.707745	+	0.408617i	0.102480	+	0.994735i	$0.467322\pi$
$264$		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	$-0.0251685\pi$
$269$	1897.28	+	3286.18i	0.430033	+	0.744839i	−0.566842	+	0.823826i	$0.691835\pi$
$270$		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
$273$	−1139.43	+	5897.72i	−0.252605	+	1.30750i
$274$		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	$0.0947185\pi$
$281$			2762.14i			0.586390i	−0.956053	+	0.293195i	$0.905281\pi$
$282$		0			0
$283$	4767.64	−	2752.60i	1.00144	−	0.578181i	0.0927647	−	0.995688i	$-0.470430\pi$
$283$	4767.64	−	2752.60i	1.00144	−	0.578181i	0.908674	+	0.417507i	$0.137096\pi$
$284$		0			0
$285$	−597.208	+	285.498i	−0.124125	+	0.0593383i
$286$		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
$291$	86.4172	−	1110.51i	0.0174085	−	0.223709i
$292$		0			0
$293$	−4101.08			−0.817705			−0.408853	−	0.912600i	$-0.634071\pi$
$293$	−4101.08			−0.817705			−0.408853	+	0.912600i	$0.634071\pi$
$294$		0			0
$295$	−4780.29			−0.943455
$296$		0			0
$297$	2408.15	−	720.235i	0.470488	−	0.140715i
$298$		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
$303$	−3849.55	−	8052.54i	−0.729871	−	1.52675i
$304$		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	$-0.951194\pi$
$311$	−3435.52	−	5950.50i	−0.626401	−	1.08496i	0.361868	−	0.932230i	$-0.382139\pi$
$312$		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
$315$	4130.40	−	4075.36i	0.738800	−	0.728954i
$316$		0			0
$317$	−2052.28	−	1184.88i	−0.363620	−	0.209936i	0.307048	−	0.951694i	$-0.400659\pi$
$317$	−2052.28	−	1184.88i	−0.363620	−	0.209936i	−0.670667	+	0.741758i	$0.733992\pi$
$318$		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
$327$	−2909.57	−	6086.26i	−0.492047	−	1.02927i
$328$		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
$333$	−706.189	+	875.212i	−0.116213	+	0.144028i
$334$		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
$339$	−579.649	+	7448.81i	−0.0928679	+	1.19340i
$340$		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
$345$	−3758.61	+	1796.82i	−0.586542	+	0.280399i
$346$		0			0
$347$	−4137.14	+	2388.58i	−0.640039	+	0.369527i	−0.784630	−	0.619965i	$-0.787147\pi$
$347$	−4137.14	+	2388.58i	−0.640039	+	0.369527i	0.144590	+	0.989492i	$0.453814\pi$
$348$		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	0.714102	−	0.700041i	$-0.246835\pi$
$353$	−1652.78	−	2862.69i	−0.249202	−	0.431631i	−0.963305	+	0.268410i	$0.913502\pi$
$354$		0			0
$355$	−456.436	−	263.524i	−0.0682398	−	0.0393982i
$356$		0			0
$357$	−673.213	−	1947.94i	−0.0998046	−	0.288784i
$358$		0			0
$359$	−359.154	−	207.358i	−0.0528006	−	0.0304845i	0.473367	−	0.880865i	$-0.343038\pi$
$359$	−359.154	−	207.358i	−0.0528006	−	0.0304845i	−0.526168	+	0.850381i	$0.676372\pi$
$360$		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
$369$	827.018	+	129.497i	0.116674	+	0.0182693i
$370$		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
$375$	6934.13	+	539.598i	0.954872	+	0.0743059i
$376$		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
$381$	−13916.5	−	1082.95i	−1.87129	−	0.145620i
$382$		0			0
$383$	2555.45	−	4426.17i	0.340933	−	0.590513i	−0.643673	−	0.765300i	$-0.722590\pi$
$383$	2555.45	−	4426.17i	0.340933	−	0.590513i	0.984606	+	0.174787i	$0.0559237\pi$
$384$		0			0
$385$	434.863	−	3825.63i	0.0575654	−	0.506421i
$386$		0			0
$387$	5989.87	+	937.915i	0.786776	+	0.123196i
$388$		0			0
$389$	−6339.84	+	3660.31i	−0.826331	+	0.477083i	−0.852595	−	0.522572i	$-0.824972\pi$
$389$	−6339.84	+	3660.31i	−0.826331	+	0.477083i	0.0262636	+	0.999655i	$0.491639\pi$
$390$		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
$399$	−798.129	−	692.207i	−0.100141	−	0.0868514i
$400$		0			0
$401$	−8447.68	−	4877.27i	−1.05201	−	0.607379i	−0.128800	−	0.991671i	$-0.541113\pi$
$401$	−8447.68	−	4877.27i	−1.05201	−	0.607379i	−0.923212	+	0.384291i	$0.874446\pi$
$402$		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
$411$	−10869.3	+	5196.10i	−1.30448	+	0.623612i
$412$		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
$417$	−742.400	+	9540.25i	−0.0871834	+	1.12036i
$418$		0			0
$419$	12777.4			1.48977			0.744887	−	0.667191i	$-0.232504\pi$
$419$	12777.4			1.48977			0.744887	+	0.667191i	$0.232504\pi$
$420$		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
$423$	−2775.81	+	3440.19i	−0.319065	+	0.395432i
$424$		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
$429$	2506.22	+	5242.54i	0.282055	+	0.590005i
$430$		0			0
$431$	3279.13	−	1893.21i	0.366474	−	0.211584i	−0.305443	−	0.952210i	$-0.598805\pi$
$431$	3279.13	−	1893.21i	0.366474	−	0.211584i	0.671917	+	0.740627i	$0.265471\pi$
$432$		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
$441$	8594.54	+	3449.65i	0.928035	+	0.372492i
$442$		0			0
$443$	−9266.95	−	5350.27i	−0.993873	−	0.573813i	−0.0874435	−	0.996169i	$-0.527870\pi$
$443$	−9266.95	−	5350.27i	−0.993873	−	0.573813i	−0.906430	+	0.422356i	$0.861203\pi$
$444$		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
$453$	−5863.87	−	12266.1i	−0.608186	−	1.27221i
$454$		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
$459$	−860.955	−	2878.65i	−0.0875510	−	0.292732i
$460$		0			0
$461$	1289.80			0.130308			0.0651542	−	0.997875i	$-0.479246\pi$
$461$	1289.80			0.130308			0.0651542	+	0.997875i	$0.479246\pi$
$462$		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
$465$	−47.8470	+	614.860i	−0.00477172	+	0.0613192i
$466$		0			0
$467$	−3931.83	+	6810.13i	−0.389600	+	0.674808i	−0.992396	−	0.123088i	$-0.960720\pi$
$467$	−3931.83	+	6810.13i	−0.389600	+	0.674808i	0.602795	+	0.797896i	$0.294054\pi$
$468$		0			0
$469$	2390.27	+	5493.32i	0.235336	+	0.540849i
$470$		0			0
$471$	−4384.05	+	2095.82i	−0.428889	+	0.205032i
$472$		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	$-0.110288\pi$
$479$	1847.13	+	3199.33i	0.176196	+	0.305180i	−0.764379	+	0.644767i	$0.776954\pi$
$480$		0			0
$481$	−2251.51	−	1299.91i	−0.213430	−	0.123224i
$482$		0			0
$483$	−5023.14	−	4356.51i	−0.473211	−	0.410410i
$484$		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	$0.0348620\pi$
$491$			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
$495$	868.348	−	5545.59i	0.0788471	−	0.503547i
$496$		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
$501$	−19519.9	−	1519.00i	−1.74069	−	0.135457i
$502$		0			0
$503$	−16095.2			−1.42674			−0.713370	−	0.700788i	$-0.752832\pi$
$503$	−16095.2			−1.42674			−0.713370	+	0.700788i	$0.752832\pi$
$504$		0			0
$505$	−19931.9			−1.75635
$506$		0			0
$507$	−8801.98	−	684.950i	−0.771025	−	0.0599994i
$508$		0			0
$509$	−1575.31	+	2728.52i	−0.137180	+	0.237603i	−0.926428	−	0.376472i	$-0.877137\pi$
$509$	−1575.31	+	2728.52i	−0.137180	+	0.237603i	0.789248	+	0.614074i	$0.210471\pi$
$510$		0			0
$511$	−9547.42	+	4154.30i	−0.826522	+	0.359639i
$512$		0			0
$513$	−1120.02	−	1057.26i	−0.0963940	−	0.0909928i
$514$		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	$-0.0995318\pi$
$521$	2489.60	+	4312.12i	0.209350	+	0.362605i	−0.742160	+	0.670223i	$0.766198\pi$
$522$		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
$525$	−303.336	−	877.700i	−0.0252165	−	0.0729638i
$526$		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
$537$	3001.00	−	1434.64i	0.241159	−	0.115287i
$538$		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
$543$	−1694.79	+	21779.0i	−0.133942	+	1.72123i
$544$		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
$549$	5430.34	+	4381.63i	0.422152	+	0.340625i
$550$		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
$555$	1083.17	+	2265.79i	0.0828435	+	0.173293i
$556$		0			0
$557$	125.920	−	72.6999i	0.00957881	−	0.00553033i	−0.495203	−	0.868777i	$-0.664906\pi$
$557$	125.920	−	72.6999i	0.00957881	−	0.00553033i	0.504782	+	0.863247i	$0.331573\pi$
$558$		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	$-0.119840\pi$
$563$	1958.12	+	3391.56i	0.146581	+	0.253885i	−0.783381	+	0.621542i	$0.786507\pi$
$564$		0			0
$565$	14449.4	+	8342.36i	1.07591	+	0.621178i
$566$		0			0
$567$	12306.7	+	5552.46i	0.911521	+	0.411254i
$568$		0			0
$569$	7404.97	+	4275.26i	0.545576	+	0.314988i	0.747336	−	0.664447i	$-0.231333\pi$
$569$	7404.97	+	4275.26i	0.545576	+	0.314988i	−0.201760	+	0.979435i	$0.564666\pi$
$570$		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
$579$	−4099.61	−	8575.60i	−0.294255	−	0.615527i
$580$		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
$585$	15219.5	+	12280.3i	1.07564	+	0.867908i
$586$		0			0
$587$	18034.7			1.26809			0.634047	−	0.773294i	$-0.281392\pi$
$587$	18034.7			1.26809			0.634047	+	0.773294i	$0.281392\pi$
$588$		0			0
$589$	112.289			0.00785532
$590$		0			0
$591$	266.539	−	3425.18i	0.0185515	−	0.238398i
$592$		0			0
$593$	−11358.1	+	19672.8i	−0.786547	+	1.36234i	0.141524	+	0.989935i	$0.454800\pi$
$593$	−11358.1	+	19672.8i	−0.786547	+	1.36234i	−0.928071	+	0.372404i	$0.878534\pi$
$594$		0			0
$595$	−4573.08	−	519.826i	−0.315089	−	0.0358165i
$596$		0			0
$597$	9137.52	−	4368.23i	0.626422	−	0.299464i
$598$		0			0
$599$	11720.4	−	6766.78i	0.799471	−	0.461575i	−0.0438153	−	0.999040i	$-0.513951\pi$
$599$	11720.4	−	6766.78i	0.799471	−	0.461575i	0.843286	+	0.537465i	$0.180618\pi$
$600$		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
$609$	4848.12	−	25094.1i	0.322588	−	1.66973i
$610$		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	$-0.906153\pi$
$617$		−	8906.76i		−	0.581155i	0.956851	−	0.290578i	$-0.0938474\pi$
$618$		0			0
$619$	6091.73	−	3517.06i	0.395553	−	0.228373i	−0.289010	−	0.957326i	$-0.593326\pi$
$619$	6091.73	−	3517.06i	0.395553	−	0.228373i	0.684563	+	0.728953i	$0.259993\pi$
$620$		0			0
$621$	−7049.01	−	6654.03i	−0.455502	−	0.429979i
$622$		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
$627$	−1018.93	−	79.2911i	−0.0649000	−	0.00505037i
$628$		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
$633$	−17313.0	−	1347.26i	−1.08709	−	0.0845950i
$634$		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
$639$	189.713	−	1211.58i	0.0117448	−	0.0750066i
$640$		0			0
$641$	8593.58	−	4961.51i	0.529526	−	0.305722i	−0.211297	−	0.977422i	$-0.567769\pi$
$641$	8593.58	−	4961.51i	0.529526	−	0.305722i	0.740823	+	0.671700i	$0.234436\pi$
$642$		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	0.724620	−	0.689149i	$-0.242015\pi$
$647$	−3859.39	−	6684.67i	−0.234511	−	0.406184i	−0.959130	+	0.282965i	$0.908682\pi$
$648$		0			0
$649$	−6391.80	−	3690.30i	−0.386595	−	0.223201i
$650$		0			0
$651$	−930.316	+	321.520i	−0.0560092	+	0.0193569i
$652$		0			0
$653$	9846.89	+	5685.11i	0.590105	+	0.340697i	0.765139	−	0.643865i	$-0.222670\pi$
$653$	9846.89	+	5685.11i	0.590105	+	0.340697i	−0.175034	+	0.984562i	$0.556004\pi$
$654$		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	0.588219	−	0.808702i	$-0.299829\pi$
$661$	26896.6	−	15528.7i	1.58268	−	0.913763i	0.994466	−	0.105062i	$-0.0335041\pi$
$662$		0			0
$663$	6266.83	−	2995.88i	0.367094	−	0.175491i
$664$		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
$669$	864.027	−	11103.2i	0.0499331	−	0.641668i
$670$		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
$675$	−387.928	−	1297.06i	−0.0221205	−	0.0739612i
$676$		0			0
$677$	12478.3	−	21613.0i	0.708389	−	1.22697i	−0.257066	−	0.966394i	$-0.582756\pi$
$677$	12478.3	−	21613.0i	0.708389	−	1.22697i	0.965455	−	0.260571i	$-0.0839110\pi$
$678$		0			0
$679$	448.394	−	3944.67i	0.0253428	−	0.222949i
$680$		0			0
$681$	5757.68	+	12044.0i	0.323986	+	0.677718i
$682$		0			0
$683$	9706.83	−	5604.24i	0.543809	−	0.313968i	−0.202812	−	0.979218i	$-0.565008\pi$
$683$	9706.83	−	5604.24i	0.543809	−	0.313968i	0.746621	+	0.665249i	$0.231675\pi$
$684$		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
$693$	8668.93	−	2260.62i	0.475188	−	0.123916i
$694$		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
$705$	4257.62	+	8906.14i	0.227449	+	0.475780i
$706$		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
$711$	4903.67	−	6077.33i	0.258653	−	0.320560i
$712$		0			0
$713$	706.707			0.0371197
$714$		0			0
$715$	12976.5			0.678731
$716$		0			0
$717$	−2451.40	+	31501.8i	−0.127684	+	1.64080i
$718$		0			0
$719$	4150.10	−	7188.19i	0.215261	−	0.372843i	−0.738092	−	0.674700i	$-0.764273\pi$
$719$	4150.10	−	7188.19i	0.215261	−	0.372843i	0.953353	+	0.301857i	$0.0976064\pi$
$720$		0			0
$721$	−17238.9	−	12749.1i	−0.890443	−	0.658533i
$722$		0			0
$723$	21700.3	−	10373.9i	1.11624	−	0.533623i
$724$		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
$735$	15228.3	−	13993.5i	0.764223	−	0.702254i
$736$		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	$-0.963255\pi$
$743$		−	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
$747$	11970.8	+	1874.44i	0.586332	+	0.0918100i
$748$		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
$753$	30916.4	+	2405.84i	1.49622	+	0.116433i
$754$		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
$759$	−6412.81	−	499.030i	−0.306680	−	0.0238651i
$760$		0			0
$761$	−11215.0	+	19424.9i	−0.534221	+	0.925298i	0.464980	+	0.885321i	$0.346062\pi$
$761$	−11215.0	+	19424.9i	−0.534221	+	0.925298i	−0.999201	+	0.0399765i	$0.987272\pi$
$762$		0			0
$763$	−9593.35	−	22047.4i	−0.455180	−	1.04610i
$764$		0			0
$765$	−6629.08	−	1038.01i	−0.313301	−	0.0490577i
$766$		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	$-0.993830\pi$
$773$	−11104.6	−	19233.7i	−0.516693	−	0.894938i	0.483119	−	0.875555i	$-0.339504\pi$
$774$		0			0
$775$	85.4774	+	49.3504i	0.00396185	+	0.00228738i
$776$		0			0
$777$	−2626.22	+	3028.09i	−0.121255	+	0.139810i
$778$		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
$789$	−16340.6	+	7811.69i	−0.737314	+	0.352476i
$790$		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
$795$	−2466.29	+	31693.1i	−0.110025	+	1.41389i
$796$		0			0
$797$	14300.8			0.635583			0.317791	−	0.948161i	$-0.397059\pi$
$797$	14300.8			0.635583			0.317791	+	0.948161i	$0.397059\pi$
$798$		0			0
$799$	3506.27			0.155248
$800$		0			0
$801$	9522.26	−	11801.4i	0.420041	−	0.520575i
$802$		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
$807$	8504.05	+	17788.9i	0.370950	+	0.775958i
$808$		0			0
$809$	−12772.9	+	7374.43i	−0.555093	+	0.320483i	−0.751174	−	0.660104i	$-0.770512\pi$
$809$	−12772.9	+	7374.43i	−0.555093	+	0.320483i	0.196080	+	0.980588i	$0.437179\pi$
$810$		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
$819$	−8280.36	+	30093.8i	−0.353283	+	1.28396i
$820$		0			0
$821$	−40528.1	−	23398.9i	−1.72283	−	0.994674i	−0.912948	−	0.408076i	$-0.866200\pi$
$821$	−40528.1	−	23398.9i	−1.72283	−	0.994674i	−0.809878	−	0.586598i	$-0.800467\pi$
$822$		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	$0.347531\pi$
$827$			42212.0i			1.77492i	−0.460888	+	0.887458i	$0.652469\pi$
$828$		0			0
$829$	−19605.0	+	11319.0i	−0.821364	+	0.474215i	−0.850887	−	0.525349i	$-0.823935\pi$
$829$	−19605.0	+	11319.0i	−0.821364	+	0.474215i	0.0295225	+	0.999564i	$0.490601\pi$
$830$		0			0
$831$	7654.54	+	16011.8i	0.319534	+	0.668405i
$832$		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
$837$	−1374.82	+	411.184i	−0.0567749	+	0.0169804i
$838$		0			0
$839$	−39480.0			−1.62455			−0.812277	−	0.583272i	$-0.801772\pi$
$839$	−39480.0			−1.62455			−0.812277	+	0.583272i	$0.801772\pi$
$840$		0			0
$841$	−46145.4			−1.89206
$842$		0			0
$843$	−1113.51	+	14309.3i	−0.0454940	+	0.584623i
$844$		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
$849$	25808.4	−	12337.8i	1.04328	−	0.498743i
$850$		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	0.845249	−	0.534373i	$-0.179452\pi$
$857$	−1007.45	−	1744.96i	−0.0401562	−	0.0695526i	−0.885405	+	0.464820i	$0.846119\pi$
$858$		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
$861$	2929.43	+	565.958i	0.115952	+	0.0224016i
$862$		0			0
$863$	−5979.04	−	3452.00i	−0.235839	−	0.136162i	0.377424	−	0.926041i	$-0.376810\pi$
$863$	−5979.04	−	3452.00i	−0.235839	−	0.136162i	−0.613263	+	0.789879i	$0.710143\pi$
$864$		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
$873$	895.367	−	5718.14i	0.0347120	−	0.221684i
$874$		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
$879$	−21245.6	−	1653.28i	−0.815241	−	0.0634401i
$880$		0			0
$881$	7244.25			0.277032			0.138516	−	0.990360i	$-0.455767\pi$
$881$	7244.25			0.277032			0.138516	+	0.990360i	$0.455767\pi$
$882$		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
$885$	−24764.2	−	1927.10i	−0.940611	−	0.0731962i
$886$		0			0
$887$	8933.98	−	15474.1i	0.338189	−	0.585761i	−0.645903	−	0.763420i	$-0.723519\pi$
$887$	8933.98	−	15474.1i	0.338189	−	0.585761i	0.984092	+	0.177659i	$0.0568523\pi$
$888$		0			0
$889$	−49433.1	−	5619.10i	−1.86494	−	0.211990i
$890$		0			0
$891$	12765.7	−	2760.37i	0.479986	−	0.103789i
$892$		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
$903$	21217.1	+	4099.08i	0.781904	+	0.151062i
$904$		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	$-0.731456\pi$
$911$		−	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
$915$	14058.4	−	6720.66i	0.507929	−	0.242818i
$916$		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
$921$	−3338.52	+	42901.8i	−0.119444	+	1.53492i
$922$		0			0
$923$	2835.04			0.101101
$924$		0			0
$925$	401.928			0.0142868
$926$		0			0
$927$	−24326.7	−	19628.7i	−0.861912	−	0.695459i
$928$		0			0
$929$	12630.2	−	21876.1i	0.446052	−	0.772585i	−0.552073	−	0.833796i	$-0.686163\pi$
$929$	12630.2	−	21876.1i	0.446052	−	0.772585i	0.998125	+	0.0612109i	$0.0194962\pi$
$930$		0			0
$931$	−2755.29	−	2566.66i	−0.0969936	−	0.0903533i
$932$		0			0
$933$	−15398.8	−	32211.5i	−0.540338	−	1.13029i
$934$		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	$0.148054\pi$
$941$	24112.4	+	41763.8i	0.835325	+	1.44683i	−0.0584406	+	0.998291i	$0.518613\pi$
$942$		0			0
$943$	−1855.15	−	1071.07i	−0.0640635	−	0.0369871i
$944$		0			0
$945$	23040.4	−	19447.2i	0.793127	−	0.669438i
$946$		0			0
$947$	21340.2	+	12320.8i	0.732275	+	0.422779i	0.819254	−	0.573431i	$-0.194388\pi$
$947$	21340.2	+	12320.8i	0.732275	+	0.422779i	−0.0869787	+	0.996210i	$0.527721\pi$
$948$		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
$957$	−10663.7	−	22306.4i	−0.360196	−	0.753462i
$958$		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
$963$	25589.2	+	20647.4i	0.856284	+	0.690917i
$964$		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
$969$	−94.7830	+	1218.01i	−0.00314228	+	0.0403800i
$970$		0			0
$971$	25892.6	−	44847.3i	0.855750	−	1.48220i	−0.0201966	−	0.999796i	$-0.506429\pi$
$971$	25892.6	−	44847.3i	0.855750	−	1.48220i	0.875947	−	0.482407i	$-0.160237\pi$
$972$		0			0
$973$	−3852.10	+	33888.2i	−0.126920	+	1.11655i
$974$		0			0
$975$	2823.70	−	1349.88i	0.0927496	−	0.0443394i
$976$		0			0
$977$	24796.0	−	14316.0i	0.811969	−	0.468790i	−0.0356703	−	0.999364i	$-0.511357\pi$
$977$	24796.0	−	14316.0i	0.811969	−	0.468790i	0.847639	+	0.530573i	$0.178023\pi$
$978$		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	$0.0861414\pi$
$983$	21984.3	+	38077.9i	0.713317	+	1.23550i	−0.250288	+	0.968171i	$0.580525\pi$
$984$		0			0
$985$	−6644.24	−	3836.06i	−0.214927	−	0.124088i
$986$		0			0
$987$	−10322.9	+	11902.5i	−0.332909	+	0.383850i
$988$		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
$999$	−4011.23	+	4249.34i	−0.127037	+	0.134578i

Twists

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

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

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)

\(f(q)\)	\(=\)	\(q+(5.18049 + 0.403134i) q^{3} +(5.80193 - 10.0492i) q^{5} +(18.4018 + 2.09174i) q^{7} +(26.6750 + 4.17686i) q^{9} +O(q^{10})\)	\(q+(5.18049 + 0.403134i) q^{3} +(5.80193 - 10.0492i) q^{5} +(18.4018 + 2.09174i) q^{7} +(26.6750 + 4.17686i) q^{9} +(15.5157 - 8.95800i) q^{11} +62.4185i q^{13} +(34.1081 - 49.7211i) q^{15} +(-10.7082 - 18.5472i) q^{17} +(-9.50747 - 5.48914i) q^{19} +(94.4869 + 18.2546i) q^{21} +(-59.8367 - 34.5467i) q^{23} +(-4.82490 - 8.35697i) q^{25} +(136.506 + 32.3918i) q^{27} -265.583i q^{29} +(-8.85795 + 5.11414i) q^{31} +(83.9902 - 40.1519i) q^{33} +(127.786 - 172.788i) q^{35} +(-20.8257 + 36.0712i) q^{37} +(-25.1630 + 323.358i) q^{39} +31.0035 q^{41} +224.550 q^{43} +(196.741 - 243.829i) q^{45} +(-81.8595 + 141.785i) q^{47} +(334.249 + 76.9836i) q^{49} +(-47.9968 - 100.400i) q^{51} +(-456.586 + 263.610i) q^{53} -207.895i q^{55} +(-47.0405 - 32.2692i) q^{57} +(-205.978 - 356.765i) q^{59} +(223.807 + 129.215i) q^{61} +(482.129 + 132.659i) q^{63} +(627.258 + 362.148i) q^{65} +(161.737 + 280.137i) q^{67} +(-296.056 - 203.091i) q^{69} -45.4199i q^{71} +(-486.879 + 281.100i) q^{73} +(-21.6264 - 45.2383i) q^{75} +(304.254 - 132.388i) q^{77} +(144.610 - 250.473i) q^{79} +(694.108 + 222.835i) q^{81} +448.767 q^{83} -248.513 q^{85} +(107.066 - 1375.85i) q^{87} +(280.814 - 486.384i) q^{89} +(-130.563 + 1148.61i) q^{91} +(-47.9502 + 22.9228i) q^{93} +(-110.323 + 63.6953i) q^{95} -214.364i q^{97} +(451.297 - 174.147i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 3 q^{3} + 56 q^{7} - 3 q^{9}+O(q^{10}) \) 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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