LMFDB - Embedded newform 147.4.g.d.68.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [147,4,Mod(68,147)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(147, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 5]))

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

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

chi := DirichletCharacter("147.68");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 147 = 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	147.g (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:	$8.67328077084$
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:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3^{3} $
Twist minimal:	no (minimal twist has level 21)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			68.6
Root			$-0.232749 + 2.99096i$ of defining polynomial
Character	$\chi$	$=$	147.68
Dual form			147.4.g.d.80.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(3.93653 + 2.27276i) q^{2} +(5.18049 + 0.403134i) q^{3} +(6.33084 + 10.9653i) q^{4} +(-5.80193 + 10.0492i) q^{5} +(19.4769 + 13.3609i) q^{6} +21.1897i q^{8} +(26.6750 + 4.17686i) q^{9} +O(q^{10})$	\(q+(3.93653 + 2.27276i) q^{2} +(5.18049 + 0.403134i) q^{3} +(6.33084 + 10.9653i) q^{4} +(-5.80193 + 10.0492i) q^{5} +(19.4769 + 13.3609i) q^{6} +21.1897i q^{8} +(26.6750 + 4.17686i) q^{9} +(-45.6790 + 26.3728i) q^{10} +(-15.5157 + 8.95800i) q^{11} +(28.3764 + 59.3580i) q^{12} -62.4185i q^{13} +(-34.1081 + 49.7211i) q^{15} +(2.48762 - 4.30868i) q^{16} +(10.7082 + 18.5472i) q^{17} +(95.5138 + 77.0680i) q^{18} +(-9.50747 - 5.48914i) q^{19} -146.925 q^{20} -81.4374 q^{22} +(59.8367 + 34.5467i) q^{23} +(-8.54230 + 109.773i) q^{24} +(-4.82490 - 8.35697i) q^{25} +(141.862 - 245.712i) q^{26} +(136.506 + 32.3918i) q^{27} -265.583i q^{29} +(-247.271 + 118.209i) q^{30} +(-8.85795 + 5.11414i) q^{31} +(166.392 - 96.0665i) q^{32} +(-83.9902 + 40.1519i) q^{33} +97.3486i q^{34} +(123.074 + 318.943i) q^{36} +(-20.8257 + 36.0712i) q^{37} +(-24.9510 - 43.2163i) q^{38} +(25.1630 - 323.358i) q^{39} +(-212.941 - 122.941i) q^{40} -31.0035 q^{41} -224.550 q^{43} +(-196.455 - 113.423i) q^{44} +(-196.741 + 243.829i) q^{45} +(157.033 + 271.988i) q^{46} +(-81.8595 + 141.785i) q^{47} +(14.6241 - 21.3182i) q^{48} -43.8633i q^{50} +(47.9968 + 100.400i) q^{51} +(684.440 - 395.161i) q^{52} +(-456.586 + 263.610i) q^{53} +(463.740 + 437.755i) q^{54} -207.895i q^{55} +(-47.0405 - 32.2692i) q^{57} +(603.606 - 1045.48i) q^{58} +(-205.978 - 356.765i) q^{59} +(-761.141 - 59.2302i) q^{60} +(-223.807 - 129.215i) q^{61} -46.4928 q^{62} +833.541 q^{64} +(627.258 + 362.148i) q^{65} +(-421.886 - 32.8302i) q^{66} +(-161.737 - 280.137i) q^{67} +(-135.584 + 234.838i) q^{68} +(296.056 + 203.091i) q^{69} +45.4199i q^{71} +(-88.5066 + 565.236i) q^{72} +(486.879 - 281.100i) q^{73} +(-163.962 + 94.6635i) q^{74} +(-21.6264 - 45.2383i) q^{75} -139.004i q^{76} +(833.969 - 1215.72i) q^{78} +(-144.610 + 250.473i) q^{79} +(28.8660 + 49.9974i) q^{80} +(694.108 + 222.835i) q^{81} +(-122.046 - 70.4635i) q^{82} +448.767 q^{83} -248.513 q^{85} +(-883.949 - 510.348i) q^{86} +(107.066 - 1375.85i) q^{87} +(-189.818 - 328.774i) q^{88} +(-280.814 + 486.384i) q^{89} +(-1328.64 + 512.698i) q^{90} +874.839i q^{92} +(-47.9502 + 22.9228i) q^{93} +(-644.484 + 372.093i) q^{94} +(110.323 - 63.6953i) q^{95} +(900.720 - 430.593i) q^{96} +214.364i q^{97} +(-451.297 + 174.147i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 3 q^{3} + 14 q^{4} - 3 q^{9}+O(q^{10}) $ 12 * q + 3 * q^3 + 14 * q^4 - 3 * q^9	$ 12 q + 3 q^{3} + 14 q^{4} - 3 q^{9} - 30 q^{10} + 192 q^{12} + 6 q^{15} + 134 q^{16} + 66 q^{18} - 300 q^{19} - 268 q^{22} - 414 q^{24} - 42 q^{25} - 822 q^{30} + 930 q^{31} + 855 q^{33} + 852 q^{36} + 764 q^{37} - 426 q^{39} - 2298 q^{40} - 1012 q^{43} - 2367 q^{45} + 608 q^{46} - 1341 q^{51} + 3000 q^{52} + 4158 q^{54} + 270 q^{57} + 2870 q^{58} - 918 q^{60} - 2358 q^{61} - 548 q^{64} - 2934 q^{66} + 792 q^{67} - 2712 q^{72} + 2904 q^{73} + 2418 q^{75} + 4296 q^{78} + 1674 q^{79} + 837 q^{81} - 5040 q^{82} + 348 q^{85} - 1638 q^{87} - 554 q^{88} - 1479 q^{93} + 1356 q^{94} + 4410 q^{96} - 3354 q^{99}+O(q^{100}) $ 12 * q + 3 * q^3 + 14 * q^4 - 3 * q^9 - 30 * q^10 + 192 * q^12 + 6 * q^15 + 134 * q^16 + 66 * q^18 - 300 * q^19 - 268 * q^22 - 414 * q^24 - 42 * q^25 - 822 * q^30 + 930 * q^31 + 855 * q^33 + 852 * q^36 + 764 * q^37 - 426 * q^39 - 2298 * q^40 - 1012 * q^43 - 2367 * q^45 + 608 * q^46 - 1341 * q^51 + 3000 * q^52 + 4158 * q^54 + 270 * q^57 + 2870 * q^58 - 918 * q^60 - 2358 * q^61 - 548 * q^64 - 2934 * q^66 + 792 * q^67 - 2712 * q^72 + 2904 * q^73 + 2418 * q^75 + 4296 * q^78 + 1674 * q^79 + 837 * q^81 - 5040 * q^82 + 348 * q^85 - 1638 * q^87 - 554 * q^88 - 1479 * q^93 + 1356 * q^94 + 4410 * q^96 - 3354 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/147\mathbb{Z}\right)^\times$.

$n$	$50$	$52$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$

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 $

$2$	3.93653	+	2.27276i	1.39177	+	0.803541i	0.993512	−	0.113731i	$-0.0362803\pi$
$2$	3.93653	+	2.27276i	1.39177	+	0.803541i	0.398262	+	0.917272i	$0.369614\pi$
$3$	5.18049	+	0.403134i	0.996986	+	0.0775831i
$3$	5.18049	+	0.403134i	0.996986	+	0.0775831i
$4$	6.33084	+	10.9653i	0.791355	+	1.37067i
$5$	−5.80193	+	10.0492i	−0.518941	+	0.898832i	0.480817	+	0.876821i	$0.340340\pi$
$5$	−5.80193	+	10.0492i	−0.518941	+	0.898832i	−0.999758	+	0.0220109i	$0.992993\pi$
$6$	19.4769	+	13.3609i	1.32524	+	0.909097i
$7$		0			0
$7$		0			0
$8$			21.1897i			0.936463i
$9$	26.6750	+	4.17686i	0.987962	+	0.154699i
$10$	−45.6790	+	26.3728i	−1.44450	+	0.833980i
$11$	−15.5157	+	8.95800i	−0.425287	+	0.245540i	−0.697337	−	0.716743i	$-0.745632\pi$
$11$	−15.5157	+	8.95800i	−0.425287	+	0.245540i	0.272050	+	0.962283i	$0.412299\pi$
$12$	28.3764	+	59.3580i	0.682629	+	1.42793i
$13$		−	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
$16$	2.48762	−	4.30868i	0.0388690	−	0.0673231i
$17$	10.7082	+	18.5472i	0.152772	+	0.264609i	0.932245	−	0.361826i	$-0.117847\pi$
$17$	10.7082	+	18.5472i	0.152772	+	0.264609i	−0.779474	+	0.626435i	$0.784513\pi$
$18$	95.5138	+	77.0680i	1.25071	+	1.00917i
$19$	−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	$0.687779\pi$
$20$	−146.925			−1.64267
$21$		0			0
$22$	−81.4374			−0.789205
$23$	59.8367	+	34.5467i	0.542470	+	0.313195i	0.746079	−	0.665857i	$-0.231934\pi$
$23$	59.8367	+	34.5467i	0.542470	+	0.313195i	−0.203609	+	0.979052i	$0.565267\pi$
$24$	−8.54230	+	109.773i	−0.0726537	+	0.933641i
$25$	−4.82490	−	8.35697i	−0.0385992	−	0.0668557i
$26$	141.862	−	245.712i	1.07005	−	1.85339i
$27$	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	$-0.323581\pi$
$30$	−247.271	+	118.209i	−1.50484	+	0.719398i
$31$	−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	$0.342766\pi$
$32$	166.392	−	96.0665i	0.919195	−	0.530697i
$33$	−83.9902	+	40.1519i	−0.443055	+	0.211805i
$34$			97.3486i			0.491034i
$35$		0			0
$36$	123.074	+	318.943i	0.569788	+	1.47659i
$37$	−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	$0.196163\pi$
$38$	−24.9510	−	43.2163i	−0.106515	−	0.184490i
$39$	25.1630	−	323.358i	0.103315	−	1.32766i
$40$	−212.941	−	122.941i	−0.841723	−	0.485969i
$41$	−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	$-0.630359\pi$
$43$	−224.550			−0.796363			−0.398181	+	0.917307i	$0.630359\pi$
$44$	−196.455	−	113.423i	−0.673107	−	0.388618i
$45$	−196.741	+	243.829i	−0.651742	+	0.807732i
$46$	157.033	+	271.988i	0.503330	+	0.871793i
$47$	−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	$0.248430\pi$
$48$	14.6241	−	21.3182i	0.0439750	−	0.0641046i
$49$		0			0
$50$		−	43.8633i		−	0.124064i
$51$	47.9968	+	100.400i	0.131782	+	0.275664i
$52$	684.440	−	395.161i	1.82528	−	1.05383i
$53$	−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	$0.572746\pi$
$54$	463.740	+	437.755i	1.16865	+	1.10317i
$55$		−	207.895i		−	0.509682i
$56$		0			0
$57$	−47.0405	−	32.2692i	−0.109310	−	0.0749853i
$58$	603.606	−	1045.48i	1.36651	−	2.36686i
$59$	−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	$0.983519\pi$
$60$	−761.141	−	59.2302i	−1.63771	−	0.127443i
$61$	−223.807	−	129.215i	−0.469764	−	0.271218i	0.246377	−	0.969174i	$-0.420760\pi$
$61$	−223.807	−	129.215i	−0.469764	−	0.271218i	−0.716141	+	0.697956i	$0.754093\pi$
$62$	−46.4928			−0.0952352
$63$		0			0
$64$	833.541			1.62801
$65$	627.258	+	362.148i	1.19695	+	0.691060i
$66$	−421.886	−	32.8302i	−0.786826	−	0.0612290i
$67$	−161.737	−	280.137i	−0.294915	−	0.510808i	0.680050	−	0.733166i	$-0.261958\pi$
$67$	−161.737	−	280.137i	−0.294915	−	0.510808i	−0.974965	+	0.222357i	$0.928625\pi$
$68$	−135.584	+	234.838i	−0.241794	+	0.418799i
$69$	296.056	+	203.091i	0.516536	+	0.354338i
$70$		0			0
$71$			45.4199i			0.0759205i	0.999279	+	0.0379603i	$0.0120860\pi$
$71$			45.4199i			0.0759205i	−0.999279	+	0.0379603i	$0.987914\pi$
$72$	−88.5066	+	565.236i	−0.144869	+	0.925190i
$73$	486.879	−	281.100i	0.780615	−	0.450688i	−0.0560334	−	0.998429i	$-0.517845\pi$
$73$	486.879	−	281.100i	0.780615	−	0.450688i	0.836648	+	0.547741i	$0.184512\pi$
$74$	−163.962	+	94.6635i	−0.257570	+	0.148708i
$75$	−21.6264	−	45.2383i	−0.0332960	−	0.0696489i
$76$		−	139.004i		−	0.209800i
$77$		0			0
$78$	833.969	−	1215.72i	1.21062	−	1.76478i
$79$	−144.610	+	250.473i	−0.205949	+	0.356714i	−0.950435	−	0.310925i	$-0.899361\pi$
$79$	−144.610	+	250.473i	−0.205949	+	0.356714i	0.744486	+	0.667638i	$0.232695\pi$
$80$	28.8660	+	49.9974i	0.0403415	+	0.0698735i
$81$	694.108	+	222.835i	0.952137	+	0.305673i
$82$	−122.046	−	70.4635i	−0.164363	−	0.0948950i
$83$	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
$86$	−883.949	−	510.348i	−1.10836	−	0.639910i
$87$	107.066	−	1375.85i	0.131938	−	1.69548i
$88$	−189.818	−	328.774i	−0.229939	−	0.398266i
$89$	−280.814	+	486.384i	−0.334452	+	0.579288i	−0.983379	−	0.181562i	$-0.941885\pi$
$89$	−280.814	+	486.384i	−0.334452	+	0.579288i	0.648927	+	0.760850i	$0.275218\pi$
$90$	−1328.64	+	512.698i	−1.55612	+	0.600479i
$91$		0			0
$92$			874.839i			0.991394i
$93$	−47.9502	+	22.9228i	−0.0534645	+	0.0255590i
$94$	−644.484	+	372.093i	−0.707165	+	0.408282i
$95$	110.323	−	63.6953i	0.119147	−	0.0687895i
$96$	900.720	−	430.593i	0.957597	−	0.457784i
$97$			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
$100$	61.0913	−	105.813i	0.0610913	−	0.105813i
$101$	858.845	+	1487.56i	0.846122	+	1.46553i	0.884644	+	0.466268i	$0.154402\pi$
$101$	858.845	+	1487.56i	0.846122	+	1.46553i	−0.0385219	+	0.999258i	$0.512265\pi$
$102$	−39.2445	+	504.313i	−0.0380959	+	0.489554i
$103$	−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	$0.853470\pi$
$104$	1322.63			1.24706
$105$		0			0
$106$	−2396.48			−2.19592
$107$	−1054.64	−	608.897i	−0.952859	−	0.550134i	−0.0588912	−	0.998264i	$-0.518757\pi$
$107$	−1054.64	−	608.897i	−0.952859	−	0.550134i	−0.893968	+	0.448131i	$0.852090\pi$
$108$	509.008	+	1701.90i	0.453513	+	1.51634i
$109$	−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	$-0.359885\pi$
$110$	472.494	−	818.384i	0.409551	−	0.709362i
$111$	−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	$0.795761\pi$
$114$	−111.836	−	233.940i	−0.0918809	−	0.192198i
$115$	−694.337	+	400.876i	−0.563019	+	0.325059i
$116$	2912.21	−	1681.37i	2.33096	−	1.34578i
$117$	260.713	−	1665.01i	0.206008	−	1.31564i
$118$		−	1872.55i		−	1.46087i
$119$		0			0
$120$	−1053.58	−	722.741i	−0.801483	−	0.549808i
$121$	−505.009	+	874.701i	−0.379420	+	0.657175i
$122$	−587.350	−	1017.32i	−0.435870	−	0.754949i
$123$	−160.613	−	12.4986i	−0.117740	−	0.00916226i
$124$	−112.157	−	64.7536i	−0.0812254	−	0.0468955i
$125$	−1338.51			−0.957759
$126$		0			0
$127$	2686.32			1.87695			0.938475	−	0.345347i	$-0.112239\pi$
$127$	2686.32			1.87695			0.938475	+	0.345347i	$0.112239\pi$
$128$	1950.12	+	1125.90i	1.34663	+	0.777474i
$129$	−1163.28	−	90.5238i	−0.793962	−	0.0617843i
$130$	1646.15	+	2851.21i	1.11059	+	1.92360i
$131$	−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	$0.987110\pi$
$132$	−972.008	−	666.786i	−0.640928	−	0.439669i
$133$		0			0
$134$		−	1470.36i		−	0.947906i
$135$	−1117.51	+	1183.84i	−0.712444	+	0.754733i
$136$	−393.010	+	226.904i	−0.247796	+	0.143065i
$137$	−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	$0.590542\pi$
$138$	703.858	+	1472.34i	0.434176	+	0.908215i
$139$			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
$142$	−103.228	+	178.797i	−0.0610052	+	0.105664i
$143$	559.144	+	968.466i	0.326979	+	0.566344i
$144$	84.3539	−	104.543i	0.0488159	−	0.0604997i
$145$	2668.91	+	1540.90i	1.52856	+	0.882514i
$146$	2555.48			1.44858
$147$		0			0
$148$	−527.377			−0.292906
$149$	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	$0.550244\pi$
$150$	17.6828	−	227.233i	0.00962527	−	0.123690i
$151$	1308.24	+	2265.94i	0.705055	+	1.22119i	0.966672	+	0.256020i	$0.0824112\pi$
$151$	1308.24	+	2265.94i	0.705055	+	1.22119i	−0.261616	+	0.965172i	$0.584255\pi$
$152$	116.314	−	201.461i	0.0620676	−	0.107504i
$153$	208.172	+	539.472i	0.109998	+	0.285057i
$154$		0			0
$155$		−	118.688i		−	0.0615046i
$156$	3705.04	−	1771.21i	1.90154	−	0.909040i
$157$	809.876	−	467.582i	0.411689	−	0.237689i	−0.279826	−	0.960051i	$-0.590277\pi$
$157$	809.876	−	467.582i	0.411689	−	0.237689i	0.691515	+	0.722362i	$0.256944\pi$
$158$	−1138.53	+	657.329i	−0.573268	+	0.330976i
$159$	−2471.61	+	1181.56i	−1.23278	+	0.589334i
$160$			2229.49i			1.10160i
$161$		0			0
$162$	2225.92	+	2454.74i	1.07954	+	1.19051i
$163$	259.079	−	448.738i	0.124495	−	0.215631i	−0.797041	−	0.603926i	$-0.793602\pi$
$163$	259.079	−	448.738i	0.124495	−	0.215631i	0.921535	+	0.388295i	$0.126936\pi$
$164$	−196.278	−	339.964i	−0.0934559	−	0.161870i
$165$	83.8094	−	1077.00i	0.0395428	−	0.508146i
$166$	1766.58	+	1019.94i	0.825985	+	0.476883i
$167$	−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
$170$	−978.280	−	564.810i	−0.441357	−	0.254817i
$171$	−230.684	−	186.134i	−0.103163	−	0.0832399i
$172$	−1421.59	−	2462.27i	−0.630206	−	1.09155i
$173$	1196.53	−	2072.45i	0.525841	−	0.910783i	−0.473706	−	0.880683i	$-0.657084\pi$
$173$	1196.53	−	2072.45i	0.525841	−	0.910783i	0.999547	−	0.0301000i	$-0.00958257\pi$
$174$	3548.44	−	5172.74i	1.54602	−	2.25371i
$175$		0			0
$176$			89.1363i			0.0381756i
$177$	−923.244	−	1931.25i	−0.392064	−	0.820124i
$178$	−2210.87	+	1276.44i	−0.930963	+	0.537492i
$179$	−554.381	+	320.072i	−0.231488	+	0.133650i	−0.611258	−	0.791431i	$-0.709336\pi$
$179$	−554.381	+	320.072i	−0.231488	+	0.133650i	0.379770	+	0.925081i	$0.376003\pi$
$180$	−3919.21	−	613.683i	−1.62289	−	0.254118i
$181$		−	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
$184$	−732.036	+	1267.92i	−0.293296	+	0.508003i
$185$	−241.659	−	418.565i	−0.0960384	−	0.166343i
$186$	−240.855	−	18.7428i	−0.0949482	−	0.00738865i
$187$	−332.291	−	191.848i	−0.129944	−	0.0750231i
$188$	−2072.96			−0.804181
$189$		0			0
$190$	579.056			0.221101
$191$	1261.85	+	728.530i	0.478033	+	0.275993i	0.719597	−	0.694392i	$-0.244327\pi$
$191$	1261.85	+	728.530i	0.478033	+	0.275993i	−0.241563	+	0.970385i	$0.577660\pi$
$192$	4318.15	+	336.028i	1.62310	+	0.126306i
$193$	−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	$0.944141\pi$
$194$	−487.196	+	843.849i	−0.180302	+	0.312293i
$195$	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	$-0.0381481\pi$
$198$	−2172.34	−	340.153i	−0.779704	−	0.122089i
$199$	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	$0.220479\pi$
$200$	177.082	−	102.238i	0.0626079	−	0.0361467i
$201$	−724.945	−	1516.45i	−0.254396	−	0.532149i
$202$			7807.78i			2.71957i
$203$		0			0
$204$	−797.063	+	1161.92i	−0.273557	+	0.398777i
$205$	179.880	−	311.562i	0.0612849	−	0.106148i
$206$	−2631.19	−	4557.36i	−0.889921	−	1.54139i
$207$	1451.84	+	1171.46i	0.487489	+	0.393344i
$208$	−268.941	−	155.273i	−0.0896525	−	0.0517609i
$209$	196.687			0.0650963
$210$		0			0
$211$	3341.96			1.09038			0.545189	−	0.838313i	$-0.316458\pi$
$211$	3341.96			1.09038			0.545189	+	0.838313i	$0.316458\pi$
$212$	−5781.14	−	3337.74i	−1.87288	−	1.08131i
$213$	−18.3103	+	235.298i	−0.00589015	+	0.0756917i
$214$	−2767.75	−	4793.88i	−0.884109	−	1.53132i
$215$	1302.83	−	2256.56i	0.413265	−	0.715796i
$216$	−686.373	+	2892.52i	−0.216212	+	0.911162i
$217$		0			0
$218$		−	5901.27i		−	1.83342i
$219$	2635.59	−	1259.96i	0.813228	−	0.388767i
$220$	2279.64	−	1316.15i	0.698605	−	0.403340i
$221$	1157.68	−	668.390i	0.352372	−	0.203442i
$222$	−887.566	+	424.305i	−0.268331	+	0.128277i
$223$		−	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
$226$	−3267.90	+	5660.17i	−0.961848	+	1.66597i
$227$	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	$0.710774\pi$
$228$	56.0370	−	720.107i	0.0162769	−	0.209168i
$229$	−91.0827	−	52.5866i	−0.0262835	−	0.0151748i	0.486801	−	0.873513i	$-0.338164\pi$
$229$	−91.0827	−	52.5866i	−0.0262835	−	0.0151748i	−0.513084	+	0.858338i	$0.671497\pi$
$230$	−3644.37			−1.04479
$231$		0			0
$232$	5627.64			1.59255
$233$	−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	$0.787013\pi$
$234$	4810.47	−	5961.82i	1.34389	−	1.66554i
$235$	−949.887	−	1645.25i	−0.263676	−	0.456700i
$236$	2608.03	−	4517.24i	0.719358	−	1.24596i
$237$	−850.127	+	1239.27i	−0.233003	+	0.339660i
$238$		0			0
$239$		−	6080.85i		−	1.64576i	−0.568212	−	0.822882i	$-0.692365\pi$
$239$		−	6080.85i		−	1.64576i	0.568212	−	0.822882i	$-0.307635\pi$
$240$	129.384	+	270.648i	0.0347989	+	0.0727927i
$241$	−4008.74	+	2314.45i	−1.07147	+	0.618616i	−0.928584	−	0.371122i	$-0.878973\pi$
$241$	−4008.74	+	2314.45i	−1.07147	+	0.618616i	−0.142891	+	0.989738i	$0.545640\pi$
$242$	−3975.96	+	2295.52i	−1.05613	+	0.609759i
$243$	3505.99	+	1434.21i	0.925552	+	0.378621i
$244$		−	3272.17i		−	0.858521i
$245$		0			0
$246$	−603.853	−	414.236i	−0.156505	−	0.107361i
$247$	−342.624	+	593.442i	−0.0882617	+	0.152874i
$248$	−108.367	−	187.698i	−0.0277473	−	0.0480597i
$249$	2324.83	+	180.913i	0.591688	+	0.0460438i
$250$	−5269.08	−	3042.10i	−1.33298	−	0.769598i
$251$	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
$254$	10574.8	+	6105.36i	2.61229	+	1.50821i
$255$	−1287.42	−	100.184i	−0.316162	−	0.0246030i
$256$	1783.64	+	3089.36i	0.435460	+	0.754239i
$257$	−2819.70	+	4883.86i	−0.684389	+	1.18540i	0.289239	+	0.957257i	$0.406598\pi$
$257$	−2819.70	+	4883.86i	−0.684389	+	1.18540i	−0.973628	+	0.228140i	$0.926736\pi$
$258$	−4373.55	−	3000.20i	−1.05537	−	0.723971i
$259$		0			0
$260$			9170.80i			2.18750i
$261$	1109.30	−	7084.42i	0.263081	−	1.68013i
$262$	−6311.33	+	3643.85i	−1.48823	+	0.859228i
$263$	3018.63	−	1742.81i	0.707745	−	0.408617i	−0.102480	−	0.994735i	$-0.532678\pi$
$263$	3018.63	−	1742.81i	0.707745	−	0.408617i	0.810226	+	0.586118i	$0.199345\pi$
$264$	−850.809	−	1779.73i	−0.198347	−	0.414905i
$265$		−	6117.79i		−	1.41816i
$266$		0			0
$267$	−1650.83	+	2406.50i	−0.378387	+	0.551594i
$268$	2047.86	−	3547.00i	0.466766	−	0.808462i
$269$	−1897.28	−	3286.18i	−0.430033	−	0.744839i	0.566842	−	0.823826i	$-0.308165\pi$
$269$	−1897.28	−	3286.18i	−0.430033	−	0.744839i	−0.996876	+	0.0789869i	$0.974831\pi$
$270$	−7089.70	+	2120.41i	−1.59802	+	0.477940i
$271$	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	$0.351655\pi$
$272$	106.552			0.0237524
$273$		0			0
$274$	−10538.9			−2.32364
$275$	149.723	+	86.4428i	0.0328315	+	0.0189553i
$276$	−352.677	+	4532.10i	−0.0769155	+	0.988406i
$277$	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	$0.712544\pi$
$278$	−4185.45	+	7249.41i	−0.902973	+	1.56399i
$279$	−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	$0.905281\pi$
$282$	−3488.75	+	1667.81i	−0.736709	+	0.352187i
$283$	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	$0.137096\pi$
$284$	−498.045	+	287.546i	−0.104062	+	0.0600801i
$285$	597.208	−	285.498i	0.124125	−	0.0593383i
$286$			5083.19i			1.05096i
$287$		0			0
$288$	4839.76	−	1867.57i	0.990227	−	0.382110i
$289$	2227.17	−	3857.57i	0.453322	−	0.785176i
$290$	7004.16	+	12131.6i	1.41827	+	2.45652i
$291$	−86.4172	+	1110.51i	−0.0174085	+	0.223709i
$292$	6164.71	+	3559.20i	1.23549	+	0.713309i
$293$	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
$296$	−764.339	−	441.291i	−0.150089	−	0.0866538i
$297$	−2408.15	+	720.235i	−0.470488	+	0.140715i
$298$	2956.80	+	5121.33i	0.574774	+	0.995539i
$299$	2156.35	−	3734.91i	0.417074	−	0.722393i
$300$	359.140	−	523.537i	0.0691165	−	0.100755i
$301$		0			0
$302$			11893.3i			2.26616i
$303$	3849.55	+	8052.54i	0.729871	+	1.52675i
$304$	−47.3019	+	27.3098i	−0.00892418	+	0.00515238i
$305$	2597.03	−	1499.40i	0.487560	−	0.281493i
$306$	−406.611	+	2596.77i	−0.0759622	+	0.485122i
$307$			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
$310$	269.748	−	467.217i	0.0494215	−	0.0856005i
$311$	−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	$-0.382139\pi$
$312$	6851.88	+	533.197i	1.24330	+	0.0967511i
$313$	2922.40	+	1687.25i	0.527743	+	0.304693i	0.740097	−	0.672500i	$-0.234780\pi$
$313$	2922.40	+	1687.25i	0.527743	+	0.304693i	−0.212354	+	0.977193i	$0.568113\pi$
$314$	4250.80			0.763970
$315$		0			0
$316$	−3662.02			−0.651914
$317$	−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	$0.733992\pi$
$318$	−12415.0	−	966.103i	−2.18930	−	0.170366i
$319$	2379.09	+	4120.71i	0.417566	+	0.723246i
$320$	−4836.15	+	8376.46i	−0.844840	+	1.46331i
$321$	−5218.09	−	3579.55i	−0.907306	−	0.622401i
$322$		0			0
$323$		−	235.116i		−	0.0405021i
$324$	1950.82	+	9021.86i	0.334503	+	1.54696i
$325$	−521.629	+	301.163i	−0.0890300	+	0.0514015i
$326$	2039.74	−	1177.65i	0.346536	−	0.200073i
$327$	−2909.57	−	6086.26i	−0.492047	−	1.02927i
$328$		−	656.957i		−	0.110593i
$329$		0			0
$330$	2777.67	−	4049.15i	0.463351	−	0.675450i
$331$	−1901.80	+	3294.02i	−0.315808	+	0.546996i	−0.979609	−	0.200913i	$-0.935609\pi$
$331$	−1901.80	+	3294.02i	−0.315808	+	0.546996i	0.663801	+	0.747910i	$0.268942\pi$
$332$	2841.07	+	4920.88i	0.469651	+	0.813459i
$333$	−706.189	+	875.212i	−0.116213	+	0.144028i
$334$	−14832.7	−	8563.68i	−2.42997	−	1.40295i
$335$	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	$0.515260\pi$
$338$	−6688.41	−	3861.56i	−1.07634	−	0.621423i
$339$	−579.649	+	7448.81i	−0.0928679	+	1.19340i
$340$	−1573.30	−	2725.03i	−0.250953	−	0.434664i
$341$	91.6249	−	158.699i	0.0145506	−	0.0252024i
$342$	−485.058	−	1257.01i	−0.0766927	−	0.198747i
$343$		0			0
$344$		−	4758.16i		−	0.745764i
$345$	−3758.61	+	1796.82i	−0.586542	+	0.280399i
$346$	9420.35	−	5438.84i	1.46370	−	0.845069i
$347$	4137.14	−	2388.58i	0.640039	−	0.369527i	−0.144590	−	0.989492i	$-0.546186\pi$
$347$	4137.14	−	2388.58i	0.640039	−	0.369527i	0.784630	+	0.619965i	$0.212853\pi$
$348$	15764.5	−	7536.29i	2.42835	−	1.16088i
$349$		−	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
$352$	−1721.13	+	2981.08i	−0.260615	+	0.451398i
$353$	1652.78	+	2862.69i	0.249202	+	0.431631i	0.963305	−	0.268410i	$-0.0864982\pi$
$353$	1652.78	+	2862.69i	0.249202	+	0.431631i	−0.714102	+	0.700041i	$0.753165\pi$
$354$	754.889	−	9700.74i	0.113339	−	1.45647i
$355$	−456.436	−	263.524i	−0.0682398	−	0.0393982i
$356$	−7111.16			−1.05868
$357$		0			0
$358$	−2909.78			−0.429572
$359$	359.154	+	207.358i	0.0528006	+	0.0304845i	0.526168	−	0.850381i	$-0.323628\pi$
$359$	359.154	+	207.358i	0.0528006	+	0.0304845i	−0.473367	+	0.880865i	$0.656962\pi$
$360$	−5166.68	−	4168.89i	−0.756411	−	0.610332i
$361$	−3369.24	−	5835.69i	−0.491214	−	0.850808i
$362$	9554.78	−	16549.4i	1.38726	−	2.40281i
$363$	−2968.81	+	4327.79i	−0.429263	+	0.625758i
$364$		0			0
$365$			6523.69i			0.935522i
$366$	−2632.64	−	5507.00i	−0.375985	−	0.786490i
$367$	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	$0.331610\pi$
$368$	297.702	−	171.878i	0.0421706	−	0.0243472i
$369$	−827.018	−	129.497i	−0.116674	−	0.0182693i
$370$		−	2196.93i		−	0.308683i
$371$		0			0
$372$	−554.921	−	380.669i	−0.0773423	−	0.0530559i
$373$	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	$-0.159030\pi$
$374$	−872.048	−	1510.43i	−0.120568	−	0.208830i
$375$	−6934.13	−	539.598i	−0.954872	−	0.0743059i
$376$	−3004.38	−	1734.58i	−0.412072	−	0.237910i
$377$	−16577.3			−2.26465
$378$		0			0
$379$	−1429.02			−0.193678			−0.0968389	−	0.995300i	$-0.530873\pi$
$379$	−1429.02			−0.193678			−0.0968389	+	0.995300i	$0.530873\pi$
$380$	1396.88	+	806.490i	0.188575	+	0.108874i
$381$	13916.5	+	1082.95i	1.87129	+	0.145620i
$382$	3311.54	+	5735.76i	0.443543	+	0.768239i
$383$	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	$0.0559237\pi$
$384$	9648.70	+	6618.89i	1.28225	+	0.879606i
$385$		0			0
$386$		−	8314.95i		−	1.09642i
$387$	−5989.87	−	937.915i	−0.786776	−	0.123196i
$388$	−2350.57	+	1357.10i	−0.307557	+	0.177568i
$389$	−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	$0.491639\pi$
$390$	7378.43	+	15434.3i	0.958004	+	2.00396i
$391$			1479.73i			0.191390i
$392$		0			0
$393$	−4712.61	+	6869.82i	−0.604885	+	0.881772i
$394$	1502.67	−	2602.71i	0.192141	−	0.332798i
$395$	−1678.04	−	2906.45i	−0.213750	−	0.370227i
$396$	−4766.68	−	3846.13i	−0.604885	−	0.488069i
$397$	−7516.61	−	4339.72i	−0.950247	−	0.548625i	−0.0570893	−	0.998369i	$-0.518182\pi$
$397$	−7516.61	−	4339.72i	−0.950247	−	0.548625i	−0.893158	+	0.449744i	$0.851515\pi$
$398$	8859.79			1.11583
$399$		0			0
$400$	−48.0100			−0.00600125
$401$	−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	$0.874446\pi$
$402$	592.750	−	7617.17i	0.0735415	−	0.945049i
$403$	319.217	+	552.899i	0.0394573	+	0.0683421i
$404$	−10874.4	+	18835.1i	−1.33917	+	2.31950i
$405$	−6266.49	+	5682.38i	−0.768851	+	0.697185i
$406$		0			0
$407$		−	746.226i		−	0.0908822i
$408$	−2127.45	+	1017.04i	−0.258149	+	0.123409i
$409$	−2935.32	+	1694.71i	−0.354871	+	0.204885i	−0.666828	−	0.745211i	$-0.732349\pi$
$409$	−2935.32	+	1694.71i	−0.354871	+	0.204885i	0.311958	+	0.950096i	$0.399015\pi$
$410$	1416.21	−	817.649i	0.170589	−	0.0984897i
$411$	−10869.3	+	5196.10i	−1.30448	+	0.623612i
$412$		−	14658.5i		−	1.75285i
$413$		0			0
$414$	3052.78	+	7911.18i	0.362406	+	0.939163i
$415$	−2603.72	+	4509.77i	−0.307979	+	0.533436i
$416$	−5996.32	−	10385.9i	−0.706716	−	1.22407i
$417$	−742.400	+	9540.25i	−0.0871834	+	1.12036i
$418$	774.264	+	447.021i	0.0905992	+	0.0523075i
$419$	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	$0.280167\pi$
$422$	13155.7	+	7595.46i	1.51756	+	0.876164i
$423$	−2775.81	+	3440.19i	−0.319065	+	0.395432i
$424$	−5585.82	−	9674.93i	−0.639791	−	1.10815i
$425$	103.332	−	178.976i	0.0117937	−	0.0204273i
$426$	−606.853	+	884.641i	−0.0690191	+	0.100613i
$427$		0			0
$428$		−	15419.3i		−	1.74140i
$429$	2506.22	+	5242.54i	0.282055	+	0.590005i
$430$	10257.2	−	5922.01i	1.15034	−	0.664151i
$431$	−3279.13	+	1893.21i	−0.366474	+	0.211584i	−0.671917	−	0.740627i	$-0.734529\pi$
$431$	−3279.13	+	1893.21i	−0.366474	+	0.211584i	0.305443	+	0.952210i	$0.401195\pi$
$432$	479.140	−	507.581i	0.0533625	−	0.0565301i
$433$			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
$436$	8219.10	−	14235.9i	0.902806	−	1.56371i
$437$	−379.264	−	656.904i	−0.0415163	−	0.0719084i
$438$	13238.7	+	1030.20i	1.44422	+	0.112386i
$439$	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	$0.608951\pi$
$440$	4405.24			0.477299
$441$		0			0
$442$	6076.35			0.653897
$443$	9266.95	+	5350.27i	0.993873	+	0.573813i	0.906430	−	0.422356i	$-0.138797\pi$
$443$	9266.95	+	5350.27i	0.993873	+	0.573813i	0.0874435	+	0.996169i	$0.472130\pi$
$444$	−2732.07	−	212.603i	−0.292023	−	0.0227246i
$445$	−3258.53	−	5643.94i	−0.347122	−	0.601232i
$446$	4871.15	−	8437.07i	0.517165	−	0.895756i
$447$	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	$0.932278\pi$
$450$	183.211	−	1170.05i	0.0191925	−	0.122571i
$451$	481.042	−	277.729i	0.0502248	−	0.0289973i
$452$	−15766.6	+	9102.86i	−1.64071	+	0.947262i
$453$	5863.87	+	12266.1i	0.608186	+	1.27221i
$454$			11677.9i			1.20720i
$455$		0			0
$456$	683.777	−	996.777i	0.0702210	−	0.102365i
$457$	−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	$0.322160\pi$
$458$	−239.033	−	414.018i	−0.0243871	−	0.0422397i
$459$	860.955	+	2878.65i	0.0875510	+	0.292732i
$460$	−8791.47	−	5075.76i	−0.891097	−	0.514475i
$461$	−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	$-0.386135\pi$
$463$	6976.52			0.700273			0.350137	+	0.936699i	$0.386135\pi$
$464$	−1144.31	−	660.670i	−0.114490	−	0.0661009i
$465$	47.8470	−	614.860i	0.00477172	−	0.0613192i
$466$	−5967.63	−	10336.2i	−0.593230	−	1.02750i
$467$	−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	$0.294054\pi$
$468$	19907.9	−	7682.11i	1.96633	−	0.758772i
$469$		0			0
$470$		−	8635.44i		−	0.847496i
$471$	4384.05	−	2095.82i	0.428889	−	0.205032i
$472$	7559.75	−	4364.63i	0.737216	−	0.425632i
$473$	3484.06	−	2011.52i	0.338683	−	0.195539i
$474$	−6163.12	+	2946.31i	−0.597218	+	0.285503i
$475$			105.938i			0.0102332i
$476$		0			0
$477$	−13280.5	+	5124.69i	−1.27478	+	0.491915i
$478$	13820.3	−	23937.5i	1.32244	−	2.29053i
$479$	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	$0.776954\pi$
$480$	−898.781	+	11549.8i	−0.0854657	+	1.09828i
$481$	2251.51	+	1299.91i	0.213430	+	0.123224i
$482$	−21040.7			−1.98833
$483$		0			0
$484$	−12788.5			−1.20103
$485$	−2154.19	−	1243.72i	−0.201684	−	0.116442i
$486$	10541.8	+	13614.1i	0.983921	+	1.27067i
$487$	526.359	+	911.681i	0.0489766	+	0.0848300i	0.889474	−	0.456985i	$-0.151071\pi$
$487$	526.359	+	911.681i	0.0489766	+	0.0848300i	−0.840498	+	0.541815i	$0.817737\pi$
$488$	2738.04	−	4742.42i	0.253986	−	0.439917i
$489$	1523.06	−	2220.24i	0.140849	−	0.205322i
$490$		0			0
$491$		−	2378.40i		−	0.218607i	−0.994008	−	0.109303i	$-0.965138\pi$
$491$		−	2378.40i		−	0.218607i	0.994008	−	0.109303i	$-0.0348620\pi$
$492$	−879.767	−	1840.31i	−0.0806158	−	0.168633i
$493$	4925.81	−	2843.92i	0.449995	−	0.259805i
$494$	−2697.50	+	1557.40i	−0.245680	+	0.141844i
$495$	868.348	−	5545.59i	0.0788471	−	0.503547i
$496$			50.8881i			0.00460674i
$497$		0			0
$498$	8740.60	+	5995.95i	0.786497	+	0.539528i
$499$	−9385.74	+	16256.6i	−0.842011	+	1.45840i	0.0461818	+	0.998933i	$0.485295\pi$
$499$	−9385.74	+	16256.6i	−0.842011	+	1.45840i	−0.888192	+	0.459472i	$0.848039\pi$
$500$	−8473.89	−	14677.2i	−0.757928	−	1.31277i
$501$	−19519.9	−	1519.00i	−1.74069	−	0.135457i
$502$	23492.6	+	13563.5i	2.08870	+	1.20591i
$503$	−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
$506$	−4872.94	−	2813.39i	−0.428120	−	0.247175i
$507$	−8801.98	−	684.950i	−0.771025	−	0.0599994i
$508$	17006.7	+	29456.5i	1.48533	+	2.57267i
$509$	1575.31	−	2728.52i	0.137180	−	0.237603i	−0.789248	−	0.614074i	$-0.789529\pi$
$509$	1575.31	−	2728.52i	0.137180	−	0.237603i	0.926428	+	0.376472i	$0.122863\pi$
$510$	−4840.28	−	3320.37i	−0.420257	−	0.288291i
$511$		0			0
$512$		−	1799.30i		−	0.155310i
$513$	−1120.02	−	1057.26i	−0.0963940	−	0.0909928i
$514$	−22199.7	+	12817.0i	−1.90503	+	1.09987i
$515$	11634.1	−	6716.95i	0.995456	−	0.574727i
$516$	−6371.92	−	13328.9i	−0.543621	−	1.13715i
$517$		−	2933.19i		−	0.249519i
$518$		0			0
$519$	7034.08	−	10253.9i	0.594917	−	0.867241i
$520$	−7673.82	+	13291.4i	−0.647152	+	1.12090i
$521$	−2489.60	−	4312.12i	−0.209350	−	0.362605i	0.742160	−	0.670223i	$-0.233802\pi$
$521$	−2489.60	−	4312.12i	−0.209350	−	0.362605i	−0.951510	+	0.307618i	$0.900468\pi$
$522$	20468.0	−	25366.9i	1.71620	−	2.12697i
$523$	−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	$0.862889\pi$
$524$	−20300.1			−1.69240
$525$		0			0
$526$	15843.9			1.31336
$527$	−189.705	−	109.526i	−0.0156806	−	0.00905322i
$528$	−35.9338	+	461.770i	−0.00296178	+	0.0380605i
$529$	−3696.55	−	6402.61i	−0.303818	−	0.526228i
$530$	13904.2	−	24082.9i	1.13955	−	1.97376i
$531$	−4004.31	−	10377.0i	−0.327254	−	0.848069i
$532$		0			0
$533$			1935.19i			0.157265i
$534$	−11967.9	+	5721.33i	−0.969857	+	0.463644i
$535$	12237.9	−	7065.56i	0.988955	−	0.570973i
$536$	5936.03	−	3427.17i	0.478353	−	0.276177i
$537$	−3001.00	+	1434.64i	−0.241159	+	0.115287i
$538$		−	17248.2i		−	1.38220i
$539$		0			0
$540$	−20056.0	−	4759.15i	−1.59828	−	0.379261i
$541$	−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	$0.234439\pi$
$542$	16949.3	+	29357.1i	1.34324	+	2.32656i
$543$	1694.79	−	21779.0i	0.133942	−	1.72123i
$544$	3563.52	+	2057.40i	0.280854	+	0.162151i
$545$	15064.9			1.18405
$546$		0			0
$547$	−9266.96			−0.724363			−0.362181	−	0.932108i	$-0.617968\pi$
$547$	−9266.96			−0.724363			−0.362181	+	0.932108i	$0.617968\pi$
$548$	−25423.4	−	14678.2i	−1.98181	−	1.14420i
$549$	−5430.34	−	4381.63i	−0.422152	−	0.340625i
$550$	392.927	+	680.569i	0.0304627	+	0.0527629i
$551$	−1457.82	+	2525.03i	−0.112714	+	0.195226i
$552$	−4303.45	+	6273.36i	−0.331824	+	0.483717i
$553$		0			0
$554$			15525.2i			1.19062i
$555$	−1083.17	−	2265.79i	−0.0828435	−	0.173293i
$556$	−20193.5	+	11658.7i	−1.54028	+	0.889279i
$557$	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	$0.331573\pi$
$558$	−1240.19	−	194.194i	−0.0940888	−	0.0147328i
$559$			14016.1i			1.06050i
$560$		0			0
$561$	−1644.09	−	1127.83i	−0.123732	−	0.0848785i
$562$	−6277.68	+	10873.3i	−0.471188	+	0.816122i
$563$	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	$0.786507\pi$
$564$	−10738.9	−	835.679i	−0.801757	−	0.0623909i
$565$	−14449.4	−	8342.36i	−1.07591	−	0.621178i
$566$	25024.0			1.85837
$567$		0			0
$568$	−962.437			−0.0710968
$569$	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	$0.564666\pi$
$570$	2999.79	+	233.437i	0.220434	+	0.0171537i
$571$	11956.8	+	20709.8i	0.876318	+	1.51783i	0.855352	+	0.518047i	$0.173341\pi$
$571$	11956.8	+	20709.8i	0.876318	+	1.51783i	0.0209659	+	0.999780i	$0.493326\pi$
$572$	−7079.71	+	12262.4i	−0.517513	+	0.896359i
$573$	6243.32	+	4282.84i	0.455180	+	0.312248i
$574$		0			0
$575$		−	666.737i		−	0.0483563i
$576$	22234.7	+	3481.58i	1.60841	+	0.251851i
$577$	−11347.8	+	6551.66i	−0.818745	+	0.472703i	−0.849983	−	0.526809i	$-0.823388\pi$
$577$	−11347.8	+	6551.66i	−0.818745	+	0.472703i	0.0312386	+	0.999512i	$0.490055\pi$
$578$	17534.6	−	10123.6i	1.26184	−	0.728525i
$579$	−4099.61	−	8575.60i	−0.294255	−	0.615527i
$580$			39020.7i			2.79353i
$581$		0			0
$582$	−2864.10	+	4175.15i	−0.203988	+	0.297363i
$583$	4722.83	−	8180.18i	0.335506	−	0.581113i
$584$	5956.43	+	10316.8i	0.422053	+	0.731017i
$585$	15219.5	+	12280.3i	1.07564	+	0.867908i
$586$	16144.0	+	9320.76i	1.13806	+	0.657059i
$587$	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
$590$	18817.7	+	10864.4i	1.31308	+	0.758104i
$591$	266.539	−	3425.18i	0.0185515	−	0.238398i
$592$	103.613	+	179.463i	0.00719335	+	0.0124592i
$593$	11358.1	−	19672.8i	0.786547	−	1.36234i	−0.141524	−	0.989935i	$-0.545200\pi$
$593$	11358.1	−	19672.8i	0.786547	−	1.36234i	0.928071	−	0.372404i	$-0.121466\pi$
$594$	−11116.7	−	2637.90i	−0.767882	−	0.182213i
$595$		0			0
$596$			16472.5i			1.13212i
$597$	9137.52	−	4368.23i	0.626422	−	0.299464i
$598$	16977.1	−	9801.73i	1.16094	−	0.670272i
$599$	−11720.4	+	6766.78i	−0.799471	+	0.461575i	−0.843286	−	0.537465i	$-0.819382\pi$
$599$	−11720.4	+	6766.78i	−0.799471	+	0.461575i	0.0438153	+	0.999040i	$0.486049\pi$
$600$	958.587	−	458.257i	0.0652236	−	0.0311804i
$601$		−	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
$604$	−16564.6	+	28690.7i	−1.11590	+	1.93279i
$605$	−5860.05	−	10149.9i	−0.393794	−	0.682070i
$606$	−3147.58	+	40448.1i	−0.210993	+	2.71138i
$607$	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	$0.580291\pi$
$608$	−2109.29			−0.140696
$609$		0			0
$610$	13631.1			0.904763
$611$	8849.99	+	5109.54i	0.585977	+	0.338314i
$612$	−4597.58	+	5697.99i	−0.303670	+	0.376352i
$613$	−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	$0.933515\pi$
$614$	−18821.7	+	32600.1i	−1.23710	+	2.14272i
$615$	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	$-0.0938474\pi$
$618$	−11793.6	−	24670.1i	−0.767653	−	1.60579i
$619$	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	$0.259993\pi$
$620$	1301.45	−	751.392i	0.0843024	−	0.0486720i
$621$	7049.01	+	6654.03i	0.455502	+	0.429979i
$622$		−	31232.4i		−	2.01335i
$623$		0			0
$624$	−1330.65	−	912.811i	−0.0853665	−	0.0585604i
$625$	8369.05	−	14495.6i	0.535619	−	0.927720i
$626$	7669.40	+	13283.8i	0.489666	+	0.848127i
$627$	1018.93	+	79.2911i	0.0649000	+	0.00505037i
$628$	10254.4	+	5920.38i	0.651584	+	0.376192i
$629$	−892.024			−0.0565458
$630$		0			0
$631$	−12628.6			−0.796728			−0.398364	−	0.917227i	$-0.630422\pi$
$631$	−12628.6			−0.796728			−0.398364	+	0.917227i	$0.630422\pi$
$632$	−5307.45	−	3064.26i	−0.334049	−	0.192863i
$633$	17313.0	+	1347.26i	1.08709	+	0.0845950i
$634$	−5385.90	−	9328.65i	−0.337384	−	0.584366i
$635$	−15585.9	+	26995.5i	−0.974026	+	1.68706i
$636$	−28603.6	−	19621.7i	−1.78334	−	1.22335i
$637$		0			0
$638$			21628.4i			1.34213i
$639$	−189.713	+	1211.58i	−0.0117448	+	0.0750066i
$640$	−22629.0	+	13064.8i	−1.39764	+	0.806926i
$641$	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	$0.234436\pi$
$642$	−12405.7	−	25950.4i	−0.762640	−	1.59530i
$643$			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
$646$	534.360	−	925.539i	0.0325451	−	0.0563697i
$647$	−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	$0.908682\pi$
$648$	−4721.82	+	14708.0i	−0.286251	+	0.891641i
$649$	6391.80	+	3690.30i	0.386595	+	0.223201i
$650$	−2737.88			−0.165213
$651$		0			0
$652$	6560.75			0.394078
$653$	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	$0.556004\pi$
$654$	2379.00	−	30571.5i	0.142242	−	1.82789i
$655$	−9302.09	−	16111.7i	−0.554905	−	0.961123i
$656$	−77.1249	+	133.584i	−0.00459028	+	0.00795060i
$657$	14161.6	−	5464.70i	0.840938	−	0.324503i
$658$		0			0
$659$			19795.1i			1.17012i	0.810990	+	0.585060i	$0.198929\pi$
$659$			19795.1i			1.17012i	−0.810990	+	0.585060i	$0.801071\pi$
$660$	12340.2	−	5899.30i	0.727792	−	0.347924i
$661$	−26896.6	+	15528.7i	−1.58268	+	0.913763i	−0.588219	+	0.808702i	$0.700171\pi$
$661$	−26896.6	+	15528.7i	−1.58268	+	0.913763i	−0.994466	+	0.105062i	$0.966496\pi$
$662$	−14973.0	+	8644.67i	−0.879068	+	0.507530i
$663$	6266.83	−	2995.88i	0.367094	−	0.175491i
$664$			9509.25i			0.555769i
$665$		0			0
$666$	−4769.08	+	1840.30i	−0.277474	+	0.107072i
$667$	9175.03	−	15891.6i	0.532621	−	0.922527i
$668$	−23854.4	−	41317.1i	−1.38167	−	2.39312i
$669$	864.027	−	11103.2i	0.0499331	−	0.641668i
$670$	14776.0	+	8530.91i	0.852008	+	0.491907i
$671$	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	$0.451127\pi$
$674$	−2334.18	−	1347.64i	−0.133397	−	0.0770166i
$675$	−387.928	−	1297.06i	−0.0221205	−	0.0739612i
$676$	−10756.5	−	18630.8i	−0.611999	−	1.06001i
$677$	−12478.3	+	21613.0i	−0.708389	+	1.22697i	0.257066	+	0.966394i	$0.417244\pi$
$677$	−12478.3	+	21613.0i	−0.708389	+	1.22697i	−0.965455	+	0.260571i	$0.916089\pi$
$678$	−19211.1	+	28005.1i	−1.08820	+	1.58632i
$679$		0			0
$680$		−	5265.93i		−	0.296970i
$681$	5757.68	+	12044.0i	0.323986	+	0.677718i
$682$	721.368	−	416.482i	0.0405023	−	0.0233840i
$683$	−9706.83	+	5604.24i	−0.543809	+	0.313968i	−0.746621	−	0.665249i	$-0.768325\pi$
$683$	−9706.83	+	5604.24i	−0.543809	+	0.313968i	0.202812	+	0.979218i	$0.434992\pi$
$684$	580.599	−	3707.92i	0.0324558	−	0.207274i
$685$		−	26903.9i		−	1.50065i
$686$		0			0
$687$	−450.654	−	309.143i	−0.0250269	−	0.0171682i
$688$	−558.595	+	967.516i	−0.0309538	+	0.0536136i
$689$	16454.1	+	28499.4i	0.909800	+	1.57582i
$690$	−18879.6	−	1469.17i	−1.04164	−	0.0810584i
$691$	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	$0.569320\pi$
$692$	30300.2			1.66451
$693$		0			0
$694$	21714.7			1.18772
$695$	−18506.4	−	10684.7i	−1.01006	−	0.583156i
$696$	29153.9	+	2268.69i	1.58775	+	0.123555i
$697$	−331.992	−	575.027i	−0.0180418	−	0.0312492i
$698$	16723.5	−	28966.0i	0.906870	−	1.57074i
$699$	−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	$-0.271368\pi$
$702$	27324.0	−	28945.9i	1.46906	−	1.55626i
$703$	396.000	−	228.631i	0.0212453	−	0.0122660i
$704$	−12933.0	+	7466.86i	−0.692372	+	0.399741i
$705$	−4257.62	−	8906.14i	−0.227449	−	0.475780i
$706$			15025.4i			0.800977i
$707$		0			0
$708$	15331.9	−	22350.1i	0.813855	−	1.18640i
$709$	−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	$0.979484\pi$
$710$	−1197.85	−	2074.74i	−0.0633162	−	0.109667i
$711$	−4903.67	+	6077.33i	−0.258653	+	0.320560i
$712$	−10306.4	−	5950.38i	−0.542482	−	0.313202i
$713$	−706.707			−0.0371197
$714$		0			0
$715$	−12976.5			−0.678731
$716$	−7019.40	−	4052.65i	−0.366379	−	0.211529i
$717$	2451.40	−	31501.8i	0.127684	−	1.64080i
$718$	942.547	+	1632.54i	0.0489910	+	0.0848549i
$719$	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	$0.0976064\pi$
$720$	561.167	+	1454.25i	0.0290465	+	0.0752731i
$721$		0			0
$722$		−	30629.8i		−	1.57884i
$723$	−21700.3	+	10373.9i	−1.11624	+	0.533623i
$724$	46098.8	−	26615.2i	2.36637	−	1.36622i
$725$	−2219.47	+	1281.41i	−0.113695	+	0.0656420i
$726$	−21522.8	+	10289.1i	−1.10026	+	0.525983i
$727$			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
$730$	−14826.8	+	25680.7i	−0.751730	+	1.30203i
$731$	−2404.53	−	4164.77i	−0.121662	−	0.210724i
$732$	1319.12	−	16951.4i	0.0666067	−	0.855933i
$733$	−4885.73	−	2820.78i	−0.246192	−	0.142139i	0.371827	−	0.928302i	$-0.378731\pi$
$733$	−4885.73	−	2820.78i	−0.246192	−	0.142139i	−0.618019	+	0.786163i	$0.712065\pi$
$734$	346.017			0.0174001
$735$		0			0
$736$	13275.1			0.664847
$737$	5018.93	+	2897.68i	0.250848	+	0.144827i
$738$	−2961.26	−	2389.38i	−0.147704	−	0.119179i
$739$	5691.08	+	9857.24i	0.283288	+	0.490669i	0.972193	−	0.234183i	$-0.0752415\pi$
$739$	5691.08	+	9857.24i	0.283288	+	0.490669i	−0.688905	+	0.724852i	$0.741908\pi$
$740$	3059.81	−	5299.74i	0.152001	−	0.263273i
$741$	−2014.20	+	2936.20i	−0.0998560	+	0.145565i
$742$		0			0
$743$			4665.46i			0.230362i	0.993345	+	0.115181i	$0.0367449\pi$
$743$			4665.46i			0.230362i	−0.993345	+	0.115181i	$0.963255\pi$
$744$	−485.728	−	1016.05i	−0.0239350	−	0.0500676i
$745$	−13073.8	+	7548.17i	−0.642936	+	0.371200i
$746$	48423.2	−	27957.1i	2.37654	−	1.37210i
$747$	11970.8	+	1874.44i	0.586332	+	0.0918100i
$748$		−	4858.24i		−	0.237480i
$749$		0			0
$750$	−26070.0	−	17883.7i	−1.26926	−	0.870696i
$751$	4780.43	−	8279.95i	0.232277	−	0.402316i	−0.726200	−	0.687483i	$-0.758716\pi$
$751$	4780.43	−	8279.95i	0.232277	−	0.402316i	0.958478	+	0.285167i	$0.0920489\pi$
$752$	407.270	+	705.413i	0.0197495	+	0.0342071i
$753$	30916.4	+	2405.84i	1.49622	+	0.116433i
$754$	−65257.0	−	37676.1i	−3.15188	−	1.81974i
$755$	−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	$0.226187\pi$
$758$	−5625.38	−	3247.82i	−0.269556	−	0.155628i
$759$	−6412.81	−	499.030i	−0.306680	−	0.0238651i
$760$	1349.69	+	2337.73i	0.0644188	+	0.111577i
$761$	11215.0	−	19424.9i	0.534221	−	0.925298i	−0.464980	−	0.885321i	$-0.653938\pi$
$761$	11215.0	−	19424.9i	0.534221	−	0.925298i	0.999201	−	0.0399765i	$-0.0127283\pi$
$762$	52321.3	+	35891.8i	2.48740	+	1.70633i
$763$		0			0
$764$			18448.8i			0.873633i
$765$	−6629.08	−	1038.01i	−0.313301	−	0.0490577i
$766$	20119.2	−	11615.8i	0.949003	−	0.547907i
$767$	−22268.7	+	12856.8i	−1.04834	+	0.605259i
$768$	7994.73	+	16723.5i	0.375631	+	0.785750i
$769$			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
$772$	11580.8	−	20058.5i	0.539899	−	0.935132i
$773$	11104.6	+	19233.7i	0.516693	+	0.894938i	0.999812	+	0.0193838i	$0.00617045\pi$
$773$	11104.6	+	19233.7i	0.516693	+	0.894938i	−0.483119	+	0.875555i	$0.660496\pi$
$774$	−21447.7	−	17305.6i	−0.996021	−	0.803668i
$775$	85.4774	+	49.3504i	0.00396185	+	0.00228738i
$776$	−4542.31			−0.210128
$777$		0			0
$778$	−33276.0			−1.53342
$779$	294.765	+	170.183i	0.0135572	+	0.00782725i
$780$	−3697.06	+	47509.3i	−0.169713	+	2.18090i
$781$	−406.872	−	704.722i	−0.0186415	−	0.0322880i
$782$	−3363.07	+	5825.01i	−0.153789	+	0.266371i
$783$	8602.71	−	36253.6i	0.392638	−	1.65466i
$784$		0			0
$785$			10851.5i			0.493385i
$786$	−34164.8	+	16332.6i	−1.55040	+	0.741177i
$787$	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	$0.182937\pi$
$788$	7249.94	−	4185.75i	0.327752	−	0.189227i
$789$	16340.6	−	7811.69i	0.737314	−	0.352476i
$790$		−	15255.1i		−	0.687029i
$791$		0			0
$792$	−3690.14	−	9562.87i	−0.165560	−	0.429043i
$793$	−8065.42	+	13969.7i	−0.361175	+	0.625573i
$794$	−19726.2	−	34166.9i	−0.881685	−	1.52712i
$795$	2466.29	−	31693.1i	0.110025	−	1.41389i
$796$	21372.9	+	12339.6i	0.951684	+	0.549455i
$797$	−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
$800$	−1605.65	−	927.022i	−0.0709603	−	0.0409690i
$801$	−9522.26	+	11801.4i	−0.420041	+	0.520575i
$802$	−22169.7	−	38399.0i	−0.976108	−	1.69067i
$803$	−5036.18	+	8722.92i	−0.221324	+	0.383344i
$804$	12038.9	−	17549.7i	0.528082	−	0.769812i
$805$		0			0
$806$			2902.01i			0.126822i
$807$	−8504.05	−	17788.9i	−0.370950	−	0.775958i
$808$	−31521.1	+	18198.7i	−1.37241	+	0.792362i
$809$	−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	$0.437179\pi$
$810$	−37582.9	+	8126.65i	−1.63028	+	0.352520i
$811$			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
$814$	1695.99	−	2937.54i	0.0730276	−	0.126487i
$815$	3006.32	+	5207.09i	0.129211	+	0.223799i
$816$	551.990	+	42.9546i	0.0236808	+	0.00184278i
$817$	2134.91	+	1232.59i	0.0914209	+	0.0527819i
$818$	−15406.6			−0.658532
$819$		0			0
$820$	4555.18			0.193992
$821$	−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	$-0.800467\pi$
$822$	−54596.6	−	4248.58i	−2.31664	−	0.180275i
$823$	13086.7	+	22666.8i	0.554281	+	0.960043i	0.997959	+	0.0638567i	$0.0203401\pi$
$823$	13086.7	+	22666.8i	0.554281	+	0.960043i	−0.443678	+	0.896186i	$0.646327\pi$
$824$	12265.8	−	21245.0i	0.518566	−	0.898183i
$825$	740.792	+	508.175i	0.0312619	+	0.0214453i
$826$		0			0
$827$		−	42212.0i		−	1.77492i	−0.460888	−	0.887458i	$-0.652469\pi$
$827$		−	42212.0i		−	1.77492i	0.460888	−	0.887458i	$-0.347531\pi$
$828$	−3654.08	+	23336.3i	−0.153367	+	0.979460i
$829$	19605.0	−	11319.0i	0.821364	−	0.474215i	−0.0295225	−	0.999564i	$-0.509399\pi$
$829$	19605.0	−	11319.0i	0.821364	−	0.474215i	0.850887	+	0.525349i	$0.176065\pi$
$830$	−20499.2	+	11835.2i	−0.857275	+	0.494948i
$831$	7654.54	+	16011.8i	0.319534	+	0.668405i
$832$		−	52028.3i		−	2.16798i
$833$		0			0
$834$	−24605.1	+	35868.2i	−1.02159	+	1.48923i
$835$	21861.5	−	37865.3i	0.906047	−	1.56932i
$836$	1245.19	+	2156.74i	0.0515143	+	0.0892253i
$837$	−1374.82	+	411.184i	−0.0567749	+	0.0169804i
$838$	50298.5	+	29039.8i	2.07343	+	1.19709i
$839$	−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
$842$	43323.1	+	25012.6i	1.77317	+	1.02374i
$843$	−1113.51	+	14309.3i	−0.0454940	+	0.584623i
$844$	21157.4	+	36645.7i	0.862877	+	1.49455i
$845$	9857.85	−	17074.3i	0.401326	−	0.695117i
$846$	−18745.8	+	7233.65i	−0.761812	+	0.293969i
$847$		0			0
$848$			2623.04i			0.106221i
$849$	25808.4	−	12337.8i	1.04328	−	0.498743i
$850$	813.539	−	469.697i	0.0328284	−	0.0189535i
$851$	−2492.28	+	1438.92i	−0.100393	+	0.0579618i
$852$	−2696.04	+	1288.85i	−0.108409	+	0.0518256i
$853$			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
$856$	12902.4	−	22347.6i	0.515180	−	0.892317i
$857$	1007.45	+	1744.96i	0.0401562	+	0.0695526i	0.885405	−	0.464820i	$-0.153881\pi$
$857$	1007.45	+	1744.96i	0.0401562	+	0.0695526i	−0.845249	+	0.534373i	$0.820548\pi$
$858$	−2049.21	+	26333.4i	−0.0815370	+	1.04780i
$859$	−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	$0.785035\pi$
$860$	32991.9			1.30816
$861$		0			0
$862$	−17211.2			−0.680064
$863$	5979.04	+	3452.00i	0.235839	+	0.136162i	0.613263	−	0.789879i	$-0.289857\pi$
$863$	5979.04	+	3452.00i	0.235839	+	0.136162i	−0.377424	+	0.926041i	$0.623190\pi$
$864$	25825.2	−	7723.88i	1.01689	−	0.304134i
$865$	13884.4	+	24048.4i	0.545761	+	0.945285i
$866$	−7253.88	+	12564.1i	−0.284638	+	0.493008i
$867$	13092.9	−	19086.3i	0.512872	−	0.747639i
$868$		0			0
$869$		−	5181.68i		−	0.202274i
$870$	31394.4	+	65671.1i	1.22341	+	2.55915i
$871$	−17485.7	+	10095.4i	−0.680230	+	0.392731i
$872$	23824.2	−	13754.9i	0.925218	−	0.534175i
$873$	−895.367	+	5718.14i	−0.0347120	+	0.221684i
$874$		−	3447.90i		−	0.133440i
$875$		0			0
$876$	30501.4	+	20923.6i	1.17642	+	0.807012i
$877$	−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	$0.169223\pi$
$878$	7539.50	+	13058.8i	0.289802	+	0.501951i
$879$	21245.6	+	1653.28i	0.815241	+	0.0634401i
$880$	−895.753	−	517.163i	−0.0343134	−	0.0198109i
$881$	−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	$-0.239733\pi$
$883$	38284.4			1.45908			0.729542	+	0.683936i	$0.239733\pi$
$884$	14658.2	+	8462.94i	0.557704	+	0.321990i
$885$	24764.2	+	1927.10i	0.940611	+	0.0731962i
$886$	24319.7	+	42123.0i	0.922164	+	1.59724i
$887$	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	$0.0568523\pi$
$888$	−3781.75	−	2594.24i	−0.142914	−	0.0980370i
$889$		0			0
$890$		−	29623.4i		−	1.11571i
$891$	−12765.7	+	2760.37i	−0.479986	+	0.103789i
$892$	23501.8	−	13568.8i	0.882172	−	0.509322i
$893$	1556.55	−	898.677i	0.0583293	−	0.0336765i
$894$	13253.1	+	27723.0i	0.495805	+	1.03713i
$895$		−	7428.15i		−	0.277425i
$896$		0			0
$897$	12676.6	−	18479.4i	0.471862	−	0.687858i
$898$	−9131.74	+	15816.6i	−0.339343	+	0.587760i
$899$	1358.23	+	2352.52i	0.0503887	+	0.0872758i
$900$	2071.58	−	2567.40i	0.0767250	−	0.0950887i
$901$	−9778.43	−	5645.58i	−0.361561	−	0.208747i
$902$	2524.85			0.0932020
$903$		0			0
$904$	−30467.9			−1.12096
$905$	42247.5	+	24391.6i	1.55177	+	0.895917i
$906$	−4794.58	+	61613.0i	−0.175816	+	2.25933i
$907$	3281.49	+	5683.71i	0.120132	+	0.208076i	0.919820	−	0.392341i	$-0.128335\pi$
$907$	3281.49	+	5683.71i	0.120132	+	0.208076i	−0.799687	+	0.600417i	$0.795001\pi$
$908$	−16264.6	+	28171.1i	−0.594449	+	1.02962i
$909$	16696.3	+	43268.0i	0.609221	+	1.57878i
$910$		0			0
$911$			41084.1i			1.49416i	0.664735	+	0.747079i	$0.268544\pi$
$911$			41084.1i			1.49416i	−0.664735	+	0.747079i	$0.731456\pi$
$912$	−256.057	+	122.409i	−0.00929702	+	0.00444448i
$913$	−6962.94	+	4020.05i	−0.252398	+	0.145722i
$914$	−36096.6	+	20840.4i	−1.30631	+	0.754200i
$915$	14058.4	−	6720.66i	0.507929	−	0.242818i
$916$		−	1331.67i		−	0.0480345i
$917$		0			0
$918$	−3153.29	+	13288.6i	−0.113371	+	0.477767i
$919$	−2762.34	+	4784.51i	−0.0991524	+	0.171737i	−0.911334	−	0.411668i	$-0.864946\pi$
$919$	−2762.34	+	4784.51i	−0.0991524	+	0.171737i	0.812182	+	0.583405i	$0.198280\pi$
$920$	−8494.45	−	14712.8i	−0.304406	−	0.527247i
$921$	−3338.52	+	42901.8i	−0.119444	+	1.53492i
$922$	−5077.35	−	2931.41i	−0.181360	−	0.104708i
$923$	2835.04			0.101101
$924$		0			0
$925$	401.928			0.0142868
$926$	27463.3	+	15855.9i	0.974622	+	0.562698i
$927$	−24326.7	−	19628.7i	−0.861912	−	0.695459i
$928$	−25513.6	−	44190.9i	−0.902507	−	1.56319i
$929$	−12630.2	+	21876.1i	−0.446052	+	0.772585i	−0.998125	−	0.0612109i	$-0.980504\pi$
$929$	−12630.2	+	21876.1i	−0.446052	+	0.772585i	0.552073	+	0.833796i	$0.313837\pi$
$930$	1585.78	−	2311.67i	0.0559136	−	0.0815082i
$931$		0			0
$932$		−	33246.1i		−	1.16847i
$933$	−15398.8	−	32211.5i	−0.540338	−	1.13029i
$934$	−30955.5	+	17872.2i	−1.08447	+	0.626120i
$935$	3855.86	−	2226.18i	0.134866	−	0.0778651i
$936$	35281.1	+	5524.45i	1.23205	+	0.192919i
$937$		−	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
$940$	12027.2	−	20831.7i	0.417322	−	0.722823i
$941$	−24112.4	−	41763.8i	−0.835325	−	1.44683i	−0.893766	−	0.448534i	$-0.851946\pi$
$941$	−24112.4	−	41763.8i	−0.835325	−	1.44683i	0.0584406	−	0.998291i	$-0.481387\pi$
$942$	22021.2	+	1713.64i	0.761667	+	0.0592712i
$943$	−1855.15	−	1071.07i	−0.0640635	−	0.0369871i
$944$	−2049.58			−0.0706654
$945$		0			0
$946$	18286.8			0.628493
$947$	−21340.2	−	12320.8i	−0.732275	−	0.422779i	0.0869787	−	0.996210i	$-0.472279\pi$
$947$	−21340.2	−	12320.8i	−0.732275	−	0.422779i	−0.819254	+	0.573431i	$0.805612\pi$
$948$	−18971.1	−	1476.29i	−0.649950	−	0.0505776i
$949$	−17545.8	−	30390.2i	−0.600170	−	1.03952i
$950$	−240.772	+	417.029i	−0.00822281	+	0.0142423i
$951$	−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	$0.927583\pi$
$954$	−63926.1	−	10009.8i	−2.16948	−	0.339705i
$955$	−14642.4	+	8453.77i	−0.496142	+	0.286448i
$956$	66678.6	−	38496.9i	2.25580	−	1.30238i
$957$	10663.7	+	22306.4i	0.360196	+	0.753462i
$958$			16792.3i			0.566321i
$959$		0			0
$960$	−28430.5	+	41444.5i	−0.955822	+	1.39335i
$961$	−14843.2	+	25709.2i	−0.498244	+	0.862984i
$962$	5908.75	+	10234.3i	0.198031	+	0.343000i
$963$	−25589.2	−	20647.4i	−0.856284	−	0.690917i
$964$	−50757.4	−	29304.8i	−1.69583	−	0.979090i
$965$	21226.6			0.708090
$966$		0			0
$967$	−15785.8			−0.524959			−0.262480	−	0.964938i	$-0.584540\pi$
$967$	−15785.8			−0.524959			−0.262480	+	0.964938i	$0.584540\pi$
$968$	−18534.7	−	10701.0i	−0.615421	−	0.355313i
$969$	94.7830	−	1218.01i	0.00314228	−	0.0403800i
$970$	−5653.36	−	9791.91i	−0.187133	−	0.324123i
$971$	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	$-0.160237\pi$
$972$	6469.20	+	47524.1i	0.213477	+	1.56825i
$973$		0			0
$974$			4785.15i			0.157419i
$975$	−2823.70	+	1349.88i	−0.0927496	+	0.0443394i
$976$	−1113.50	+	642.877i	−0.0365186	+	0.0210840i
$977$	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	$0.178023\pi$
$978$	11041.6	−	5278.49i	0.361014	−	0.172584i
$979$		−	10062.1i		−	0.328485i
$980$		0			0
$981$	−12619.4	−	32702.8i	−0.410710	−	1.06434i
$982$	5405.53	−	9362.65i	0.175659	−	0.304251i
$983$	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	$0.580525\pi$
$984$	264.841	−	3403.36i	0.00858012	−	0.110259i
$985$	6644.24	+	3836.06i	0.214927	+	0.124088i
$986$	25854.1			0.835055
$987$		0			0
$988$	−8676.39			−0.279385
$989$	−13436.3	−	7757.47i	−0.432003	−	0.249417i
$990$	16022.0	−	19856.8i	0.514358	−	0.637466i
$991$	7577.33	+	13124.3i	0.242888	+	0.420694i	0.961536	−	0.274680i	$-0.0885720\pi$
$991$	7577.33	+	13124.3i	0.242888	+	0.420694i	−0.718648	+	0.695374i	$0.755239\pi$
$992$	−982.594	+	1701.90i	−0.0314490	+	0.0544712i
$993$	−11180.2	+	16298.0i	−0.357294	+	0.520846i
$994$		0			0
$995$			22617.4i			0.720624i
$996$	12734.4	+	26637.9i	0.405125	+	0.847444i
$997$	23912.6	−	13806.0i	0.759599	−	0.438555i	−0.0695525	−	0.997578i	$-0.522157\pi$
$997$	23912.6	−	13806.0i	0.759599	−	0.438555i	0.829152	+	0.559023i	$0.188824\pi$
$998$	−73894.4	+	42663.0i	−2.34378	+	1.35318i
$999$	−4011.23	+	4249.34i	−0.127037	+	0.134578i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	147.4.g.d.68.6		12
3.2	odd	2	inner	147.4.g.d.68.1		12
7.2	even	3		147.4.c.a.146.1		12
7.3	odd	6	inner	147.4.g.d.80.1		12
7.4	even	3		21.4.g.a.17.1	yes	12
7.5	odd	6		147.4.c.a.146.2		12
7.6	odd	2		21.4.g.a.5.6	yes	12
21.2	odd	6		147.4.c.a.146.12		12
21.5	even	6		147.4.c.a.146.11		12
21.11	odd	6		21.4.g.a.17.6	yes	12
21.17	even	6	inner	147.4.g.d.80.6		12
21.20	even	2		21.4.g.a.5.1	✓	12
28.11	odd	6		336.4.bc.d.17.4		12
28.27	even	2		336.4.bc.d.257.6		12
84.11	even	6		336.4.bc.d.17.6		12
84.83	odd	2		336.4.bc.d.257.4		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
21.4.g.a.5.1	✓	12	21.20	even	2
21.4.g.a.5.6	yes	12	7.6	odd	2
21.4.g.a.17.1	yes	12	7.4	even	3
21.4.g.a.17.6	yes	12	21.11	odd	6
147.4.c.a.146.1		12	7.2	even	3
147.4.c.a.146.2		12	7.5	odd	6
147.4.c.a.146.11		12	21.5	even	6
147.4.c.a.146.12		12	21.2	odd	6
147.4.g.d.68.1		12	3.2	odd	2	inner
147.4.g.d.68.6		12	1.1	even	1	trivial
147.4.g.d.80.1		12	7.3	odd	6	inner
147.4.g.d.80.6		12	21.17	even	6	inner
336.4.bc.d.17.4		12	28.11	odd	6
336.4.bc.d.17.6		12	84.11	even	6
336.4.bc.d.257.4		12	84.83	odd	2
336.4.bc.d.257.6		12	28.27	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 147 = 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	147.g (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(3.93653 + 2.27276i) q^{2} +(5.18049 + 0.403134i) q^{3} +(6.33084 + 10.9653i) q^{4} +(-5.80193 + 10.0492i) q^{5} +(19.4769 + 13.3609i) q^{6} +21.1897i q^{8} +(26.6750 + 4.17686i) q^{9} +O(q^{10})\)	\(q+(3.93653 + 2.27276i) q^{2} +(5.18049 + 0.403134i) q^{3} +(6.33084 + 10.9653i) q^{4} +(-5.80193 + 10.0492i) q^{5} +(19.4769 + 13.3609i) q^{6} +21.1897i q^{8} +(26.6750 + 4.17686i) q^{9} +(-45.6790 + 26.3728i) q^{10} +(-15.5157 + 8.95800i) q^{11} +(28.3764 + 59.3580i) q^{12} -62.4185i q^{13} +(-34.1081 + 49.7211i) q^{15} +(2.48762 - 4.30868i) q^{16} +(10.7082 + 18.5472i) q^{17} +(95.5138 + 77.0680i) q^{18} +(-9.50747 - 5.48914i) q^{19} -146.925 q^{20} -81.4374 q^{22} +(59.8367 + 34.5467i) q^{23} +(-8.54230 + 109.773i) q^{24} +(-4.82490 - 8.35697i) q^{25} +(141.862 - 245.712i) q^{26} +(136.506 + 32.3918i) q^{27} -265.583i q^{29} +(-247.271 + 118.209i) q^{30} +(-8.85795 + 5.11414i) q^{31} +(166.392 - 96.0665i) q^{32} +(-83.9902 + 40.1519i) q^{33} +97.3486i q^{34} +(123.074 + 318.943i) q^{36} +(-20.8257 + 36.0712i) q^{37} +(-24.9510 - 43.2163i) q^{38} +(25.1630 - 323.358i) q^{39} +(-212.941 - 122.941i) q^{40} -31.0035 q^{41} -224.550 q^{43} +(-196.455 - 113.423i) q^{44} +(-196.741 + 243.829i) q^{45} +(157.033 + 271.988i) q^{46} +(-81.8595 + 141.785i) q^{47} +(14.6241 - 21.3182i) q^{48} -43.8633i q^{50} +(47.9968 + 100.400i) q^{51} +(684.440 - 395.161i) q^{52} +(-456.586 + 263.610i) q^{53} +(463.740 + 437.755i) q^{54} -207.895i q^{55} +(-47.0405 - 32.2692i) q^{57} +(603.606 - 1045.48i) q^{58} +(-205.978 - 356.765i) q^{59} +(-761.141 - 59.2302i) q^{60} +(-223.807 - 129.215i) q^{61} -46.4928 q^{62} +833.541 q^{64} +(627.258 + 362.148i) q^{65} +(-421.886 - 32.8302i) q^{66} +(-161.737 - 280.137i) q^{67} +(-135.584 + 234.838i) q^{68} +(296.056 + 203.091i) q^{69} +45.4199i q^{71} +(-88.5066 + 565.236i) q^{72} +(486.879 - 281.100i) q^{73} +(-163.962 + 94.6635i) q^{74} +(-21.6264 - 45.2383i) q^{75} -139.004i q^{76} +(833.969 - 1215.72i) q^{78} +(-144.610 + 250.473i) q^{79} +(28.8660 + 49.9974i) q^{80} +(694.108 + 222.835i) q^{81} +(-122.046 - 70.4635i) q^{82} +448.767 q^{83} -248.513 q^{85} +(-883.949 - 510.348i) q^{86} +(107.066 - 1375.85i) q^{87} +(-189.818 - 328.774i) q^{88} +(-280.814 + 486.384i) q^{89} +(-1328.64 + 512.698i) q^{90} +874.839i q^{92} +(-47.9502 + 22.9228i) q^{93} +(-644.484 + 372.093i) q^{94} +(110.323 - 63.6953i) q^{95} +(900.720 - 430.593i) q^{96} +214.364i q^{97} +(-451.297 + 174.147i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 3 q^{3} + 14 q^{4} - 3 q^{9}+O(q^{10}) \) 12 * q + 3 * q^3 + 14 * q^4 - 3 * q^9	\( 12 q + 3 q^{3} + 14 q^{4} - 3 q^{9} - 30 q^{10} + 192 q^{12} + 6 q^{15} + 134 q^{16} + 66 q^{18} - 300 q^{19} - 268 q^{22} - 414 q^{24} - 42 q^{25} - 822 q^{30} + 930 q^{31} + 855 q^{33} + 852 q^{36} + 764 q^{37} - 426 q^{39} - 2298 q^{40} - 1012 q^{43} - 2367 q^{45} + 608 q^{46} - 1341 q^{51} + 3000 q^{52} + 4158 q^{54} + 270 q^{57} + 2870 q^{58} - 918 q^{60} - 2358 q^{61} - 548 q^{64} - 2934 q^{66} + 792 q^{67} - 2712 q^{72} + 2904 q^{73} + 2418 q^{75} + 4296 q^{78} + 1674 q^{79} + 837 q^{81} - 5040 q^{82} + 348 q^{85} - 1638 q^{87} - 554 q^{88} - 1479 q^{93} + 1356 q^{94} + 4410 q^{96} - 3354 q^{99}+O(q^{100}) \) 12 * q + 3 * q^3 + 14 * q^4 - 3 * q^9 - 30 * q^10 + 192 * q^12 + 6 * q^15 + 134 * q^16 + 66 * q^18 - 300 * q^19 - 268 * q^22 - 414 * q^24 - 42 * q^25 - 822 * q^30 + 930 * q^31 + 855 * q^33 + 852 * q^36 + 764 * q^37 - 426 * q^39 - 2298 * q^40 - 1012 * q^43 - 2367 * q^45 + 608 * q^46 - 1341 * q^51 + 3000 * q^52 + 4158 * q^54 + 270 * q^57 + 2870 * q^58 - 918 * q^60 - 2358 * q^61 - 548 * q^64 - 2934 * q^66 + 792 * q^67 - 2712 * q^72 + 2904 * q^73 + 2418 * q^75 + 4296 * q^78 + 1674 * q^79 + 837 * q^81 - 5040 * q^82 + 348 * q^85 - 1638 * q^87 - 554 * q^88 - 1479 * q^93 + 1356 * q^94 + 4410 * q^96 - 3354 * q^99

Introduction

L-functions

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