LMFDB - Embedded newform 21.4.g.a.17.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [21,4,Mod(5,21)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(21, 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("21.5");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 21 = 3 \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	21.g (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.23904011012$
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:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			17.6
Root			$-0.232749 - 2.99096i$ of defining polynomial
Character	$\chi$	$=$	21.17
Dual form			21.4.g.a.5.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(3.93653 - 2.27276i) q^{2} +(-5.18049 + 0.403134i) q^{3} +(6.33084 - 10.9653i) q^{4} +(5.80193 + 10.0492i) q^{5} +(-19.4769 + 13.3609i) q^{6} +(-18.4018 + 2.09174i) q^{7} -21.1897i q^{8} +(26.6750 - 4.17686i) q^{9} +O(q^{10})$	\(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} +(-18.4018 + 2.09174i) q^{7} -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} +(-67.6850 + 50.0569i) q^{14} +(-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} +(94.4869 - 18.2546i) q^{21} -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} +(-93.5619 + 215.024i) q^{28} +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} +(-127.786 - 172.788i) q^{35} +(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} +(330.462 - 286.606i) q^{42} -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} +(334.249 - 76.9836i) q^{49} +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} +(44.3235 + 389.928i) q^{56} +(-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} +(-482.129 + 132.659i) q^{63} +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} +(-895.738 - 389.756i) q^{70} -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} +(304.254 + 132.388i) q^{77} +(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} +(398.013 - 1151.65i) q^{84} -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} +(130.563 + 1148.61i) q^{91} -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} +(1140.82 - 1062.71i) q^{98} +(-451.297 - 174.147i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 3 q^{3} + 14 q^{4} - 56 q^{7} - 3 q^{9}+O(q^{10}) $ 12 * q - 3 * q^3 + 14 * q^4 - 56 * q^7 - 3 * q^9	$ 12 q - 3 q^{3} + 14 q^{4} - 56 q^{7} - 3 q^{9} + 30 q^{10} - 192 q^{12} + 6 q^{15} + 134 q^{16} + 66 q^{18} + 300 q^{19} + 357 q^{21} - 268 q^{22} + 414 q^{24} - 42 q^{25} - 602 q^{28} - 822 q^{30} - 930 q^{31} - 855 q^{33} + 852 q^{36} + 764 q^{37} - 426 q^{39} + 2298 q^{40} + 966 q^{42} - 1012 q^{43} + 2367 q^{45} + 608 q^{46} - 336 q^{49} - 1341 q^{51} - 3000 q^{52} - 4158 q^{54} + 270 q^{57} + 2870 q^{58} - 918 q^{60} + 2358 q^{61} + 1071 q^{63} - 548 q^{64} + 2934 q^{66} + 792 q^{67} - 4242 q^{70} - 2712 q^{72} - 2904 q^{73} - 2418 q^{75} + 4296 q^{78} + 1674 q^{79} + 837 q^{81} + 5040 q^{82} + 3864 q^{84} + 348 q^{85} + 1638 q^{87} - 554 q^{88} - 1218 q^{91} - 1479 q^{93} - 1356 q^{94} - 4410 q^{96} - 3354 q^{99}+O(q^{100}) $ 12 * q - 3 * q^3 + 14 * q^4 - 56 * q^7 - 3 * q^9 + 30 * q^10 - 192 * q^12 + 6 * q^15 + 134 * q^16 + 66 * q^18 + 300 * q^19 + 357 * q^21 - 268 * q^22 + 414 * q^24 - 42 * q^25 - 602 * q^28 - 822 * q^30 - 930 * q^31 - 855 * q^33 + 852 * q^36 + 764 * q^37 - 426 * q^39 + 2298 * q^40 + 966 * q^42 - 1012 * q^43 + 2367 * q^45 + 608 * q^46 - 336 * q^49 - 1341 * q^51 - 3000 * q^52 - 4158 * q^54 + 270 * q^57 + 2870 * q^58 - 918 * q^60 + 2358 * q^61 + 1071 * q^63 - 548 * q^64 + 2934 * q^66 + 792 * q^67 - 4242 * q^70 - 2712 * q^72 - 2904 * q^73 - 2418 * q^75 + 4296 * q^78 + 1674 * q^79 + 837 * q^81 + 5040 * q^82 + 3864 * q^84 + 348 * q^85 + 1638 * q^87 - 554 * q^88 - 1218 * q^91 - 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 $\left(\mathbb{Z}/21\mathbb{Z}\right)^\times$.

$n$	$8$	$10$
$\chi(n)$	$-1$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	3.93653	−	2.27276i	1.39177	−	0.803541i	0.398262	−	0.917272i	$-0.369614\pi$
$2$	3.93653	−	2.27276i	1.39177	−	0.803541i	0.993512	+	0.113731i	$0.0362803\pi$
$3$	−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	0.999758	+	0.0220109i	$0.00700684\pi$
$5$	5.80193	+	10.0492i	0.518941	+	0.898832i	−0.480817	+	0.876821i	$0.659660\pi$
$6$	−19.4769	+	13.3609i	−1.32524	+	0.909097i
$7$	−18.4018	+	2.09174i	−0.993601	+	0.112944i
$7$	−18.4018	+	2.09174i	−0.993601	+	0.112944i
$8$		−	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	0.272050	−	0.962283i	$-0.412299\pi$
$11$	−15.5157	−	8.95800i	−0.425287	−	0.245540i	−0.697337	+	0.716743i	$0.745632\pi$
$12$	−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	$-0.231925\pi$
$14$	−67.6850	+	50.0569i	−1.29211	+	0.955591i
$15$	−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	$-0.882153\pi$
$17$	−10.7082	+	18.5472i	−0.152772	+	0.264609i	0.779474	+	0.626435i	$0.215487\pi$
$18$	95.5138	−	77.0680i	1.25071	−	1.00917i
$19$	9.50747	−	5.48914i	0.114798	−	0.0662787i	−0.441502	−	0.897261i	$-0.645554\pi$
$19$	9.50747	−	5.48914i	0.114798	−	0.0662787i	0.556300	+	0.830982i	$0.312221\pi$
$20$	146.925			1.64267
$21$	94.4869	−	18.2546i	0.981844	−	0.189690i
$22$	−81.4374			−0.789205
$23$	59.8367	−	34.5467i	0.542470	−	0.313195i	−0.203609	−	0.979052i	$-0.565267\pi$
$23$	59.8367	−	34.5467i	0.542470	−	0.313195i	0.746079	+	0.665857i	$0.231934\pi$
$24$	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
$28$	−93.5619	+	215.024i	−0.631484	+	1.45128i
$29$			265.583i			1.70061i	0.526294	+	0.850303i	$0.323581\pi$
$29$			265.583i			1.70061i	−0.526294	+	0.850303i	$0.676419\pi$
$30$	−247.271	−	118.209i	−1.50484	−	0.719398i
$31$	8.85795	+	5.11414i	0.0513205	+	0.0296299i	0.525441	−	0.850830i	$-0.323900\pi$
$31$	8.85795	+	5.11414i	0.0513205	+	0.0296299i	−0.474120	+	0.880460i	$0.657234\pi$
$32$	166.392	+	96.0665i	0.919195	+	0.530697i
$33$	83.9902	+	40.1519i	0.443055	+	0.211805i
$34$			97.3486i			0.491034i
$35$	−127.786	−	172.788i	−0.617138	−	0.834470i
$36$	123.074	−	318.943i	0.569788	−	1.47659i
$37$	−20.8257	−	36.0712i	−0.0925331	−	0.160272i	0.816043	−	0.577991i	$-0.196163\pi$
$37$	−20.8257	−	36.0712i	−0.0925331	−	0.160272i	−0.908576	+	0.417719i	$0.862830\pi$
$38$	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	$-0.481193\pi$
$41$	31.0035			0.118096			0.0590480	+	0.998255i	$0.481193\pi$
$42$	330.462	−	286.606i	1.21408	−	1.05296i
$43$	−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	$-0.0849033\pi$
$47$	81.8595	+	141.785i	0.254052	+	0.440031i	−0.710586	+	0.703611i	$0.751570\pi$
$48$	−14.6241	−	21.3182i	−0.0439750	−	0.0641046i
$49$	334.249	−	76.9836i	0.974487	−	0.224442i
$50$			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	−0.226553	−	0.973999i	$-0.572746\pi$
$53$	−456.586	−	263.610i	−1.18334	−	0.683200i	−0.956784	+	0.290799i	$0.906079\pi$
$54$	−463.740	+	437.755i	−1.16865	+	1.10317i
$55$		−	207.895i		−	0.509682i
$56$	44.3235	+	389.928i	0.105768	+	0.930471i
$57$	−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	$-0.683148\pi$
$59$	205.978	−	356.765i	0.454510	−	0.787234i	0.998660	+	0.0517537i	$0.0164811\pi$
$60$	−761.141	+	59.2302i	−1.63771	+	0.127443i
$61$	223.807	−	129.215i	0.469764	−	0.271218i	−0.246377	−	0.969174i	$-0.579240\pi$
$61$	223.807	−	129.215i	0.469764	−	0.271218i	0.716141	+	0.697956i	$0.245907\pi$
$62$	46.4928			0.0952352
$63$	−482.129	+	132.659i	−0.964168	+	0.265293i
$64$	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	−0.974965	−	0.222357i	$-0.928625\pi$
$67$	−161.737	+	280.137i	−0.294915	+	0.510808i	0.680050	+	0.733166i	$0.261958\pi$
$68$	135.584	+	234.838i	0.241794	+	0.418799i
$69$	−296.056	+	203.091i	−0.516536	+	0.354338i
$70$	−895.738	−	389.756i	−1.52945	−	0.665497i
$71$		−	45.4199i		−	0.0759205i	−0.999279	−	0.0379603i	$-0.987914\pi$
$71$		−	45.4199i		−	0.0759205i	0.999279	−	0.0379603i	$-0.0120860\pi$
$72$	−88.5066	−	565.236i	−0.144869	−	0.925190i
$73$	−486.879	−	281.100i	−0.780615	−	0.450688i	0.0560334	−	0.998429i	$-0.482155\pi$
$73$	−486.879	−	281.100i	−0.780615	−	0.450688i	−0.836648	+	0.547741i	$0.815488\pi$
$74$	−163.962	−	94.6635i	−0.257570	−	0.148708i
$75$	21.6264	−	45.2383i	0.0332960	−	0.0696489i
$76$		−	139.004i		−	0.209800i
$77$	304.254	+	132.388i	0.450298	+	0.195935i
$78$	833.969	+	1215.72i	1.21062	+	1.76478i
$79$	−144.610	−	250.473i	−0.205949	−	0.356714i	0.744486	−	0.667638i	$-0.232695\pi$
$79$	−144.610	−	250.473i	−0.205949	−	0.356714i	−0.950435	+	0.310925i	$0.899361\pi$
$80$	−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	$-0.595899\pi$
$83$	−448.767			−0.593477			−0.296738	+	0.954959i	$0.595899\pi$
$84$	398.013	−	1151.65i	0.516986	−	1.49589i
$85$	−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	$-0.0581155\pi$
$89$	280.814	+	486.384i	0.334452	+	0.579288i	−0.648927	+	0.760850i	$0.724782\pi$
$90$	1328.64	+	512.698i	1.55612	+	0.600479i
$91$	130.563	+	1148.61i	0.150404	+	1.32315i
$92$		−	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	$0.964213\pi$
$98$	1140.82	−	1062.71i	1.17592	−	1.09541i
$99$	−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	0.0385219	+	0.999258i	$0.487735\pi$
$101$	−858.845	+	1487.56i	−0.846122	+	1.46553i	−0.884644	+	0.466268i	$0.845598\pi$
$102$	−39.2445	−	504.313i	−0.0380959	−	0.489554i
$103$	1002.61	−	578.855i	0.959123	−	0.553750i	0.0632200	−	0.998000i	$-0.479863\pi$
$103$	1002.61	−	578.855i	0.959123	−	0.553750i	0.895903	+	0.444250i	$0.146530\pi$
$104$	−1322.63			−1.24706
$105$	731.652	+	843.610i	0.680018	+	0.784075i
$106$	−2396.48			−2.19592
$107$	−1054.64	+	608.897i	−0.952859	+	0.550134i	−0.893968	−	0.448131i	$-0.852090\pi$
$107$	−1054.64	+	608.897i	−0.952859	+	0.550134i	−0.0588912	+	0.998264i	$0.518757\pi$
$108$	−509.008	+	1701.90i	−0.453513	+	1.51634i
$109$	−649.132	+	1124.33i	−0.570418	+	0.987992i	0.426105	+	0.904674i	$0.359885\pi$
$109$	−649.132	+	1124.33i	−0.570418	+	0.987992i	−0.996523	+	0.0833189i	$0.973448\pi$
$110$	−472.494	−	818.384i	−0.409551	−	0.709362i
$111$	122.429	+	178.471i	0.104689	+	0.152610i
$112$	−54.7892	−	74.0838i	−0.0462240	−	0.0625024i
$113$		−	1437.86i		−	1.19701i	−0.801118	−	0.598506i	$-0.795761\pi$
$113$		−	1437.86i		−	1.19701i	0.801118	−	0.598506i	$-0.204239\pi$
$114$	−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
$119$	158.254	−	363.699i	0.121908	−	0.280170i
$120$	−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
$126$	−1596.41	+	1617.98i	−1.12873	+	1.14398i
$127$	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	0.999180	+	0.0404852i	$0.0128904\pi$
$131$	801.637	+	1388.48i	0.534651	+	0.926043i	−0.464529	+	0.885558i	$0.653776\pi$
$132$	972.008	−	666.786i	0.640928	−	0.439669i
$133$	−163.472	+	120.897i	−0.106578	+	0.0788203i
$134$			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	−0.280626	−	0.959817i	$-0.590542\pi$
$137$	−2007.90	−	1159.26i	−1.25216	−	0.722938i	−0.971539	+	0.236879i	$0.923875\pi$
$138$	−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	$0.810082\pi$
$140$	−2703.67	+	307.329i	−1.63216	+	0.185529i
$141$	−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
$147$	−1700.54	+	533.560i	−0.954137	+	0.299369i
$148$	−527.377			−0.292906
$149$	1126.68	−	650.488i	0.619470	−	0.357651i	−0.157193	−	0.987568i	$-0.550244\pi$
$149$	1126.68	−	650.488i	0.619470	−	0.357651i	0.776663	+	0.629917i	$0.216911\pi$
$150$	−17.6828	−	227.233i	−0.00962527	−	0.123690i
$151$	1308.24	−	2265.94i	0.705055	−	1.22119i	−0.261616	−	0.965172i	$-0.584255\pi$
$151$	1308.24	−	2265.94i	0.705055	−	1.22119i	0.966672	−	0.256020i	$-0.0824112\pi$
$152$	−116.314	−	201.461i	−0.0620676	−	0.107504i
$153$	−208.172	+	539.472i	−0.109998	+	0.285057i
$154$	1498.59	−	170.346i	0.784155	−	0.0891356i
$155$			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	$-0.409723\pi$
$157$	−809.876	−	467.582i	−0.411689	−	0.237689i	−0.691515	+	0.722362i	$0.743056\pi$
$158$	−1138.53	−	657.329i	−0.573268	−	0.330976i
$159$	2471.61	+	1181.56i	1.23278	+	0.589334i
$160$			2229.49i			1.10160i
$161$	−1028.84	+	760.883i	−0.503625	+	0.372460i
$162$	2225.92	−	2454.74i	1.07954	−	1.19051i
$163$	259.079	+	448.738i	0.124495	+	0.215631i	0.921535	−	0.388295i	$-0.126936\pi$
$163$	259.079	+	448.738i	0.124495	+	0.215631i	−0.797041	+	0.603926i	$0.793602\pi$
$164$	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	$-0.162186\pi$
$167$	3767.97			1.74595			0.872977	+	0.487761i	$0.162186\pi$
$168$	−386.811	−	2002.15i	−0.177638	−	0.919461i
$169$	−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	−0.999547	−	0.0301000i	$-0.990417\pi$
$173$	−1196.53	−	2072.45i	−0.525841	−	0.910783i	0.473706	−	0.880683i	$-0.342916\pi$
$174$	−3548.44	−	5172.74i	−1.54602	−	2.25371i
$175$	71.3059	−	163.875i	0.0308013	−	0.0707875i
$176$		−	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	0.379770	−	0.925081i	$-0.376003\pi$
$179$	−554.381	−	320.072i	−0.231488	−	0.133650i	−0.611258	+	0.791431i	$0.709336\pi$
$180$	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	$-0.331554\pi$
$182$	3124.48	+	4224.79i	1.27254	+	1.72067i
$183$	−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
$189$	2444.19	−	881.600i	0.940680	−	0.339296i
$190$	579.056			0.221101
$191$	1261.85	−	728.530i	0.478033	−	0.275993i	−0.241563	−	0.970385i	$-0.577660\pi$
$191$	1261.85	−	728.530i	0.478033	−	0.275993i	0.719597	+	0.694392i	$0.244327\pi$
$192$	−4318.15	+	336.028i	−1.62310	+	0.126306i
$193$	−914.633	+	1584.19i	−0.341123	+	0.590842i	−0.984642	−	0.174588i	$-0.944141\pi$
$193$	−914.633	+	1584.19i	−0.341123	+	0.590842i	0.643519	+	0.765430i	$0.277474\pi$
$194$	487.196	+	843.849i	0.180302	+	0.312293i
$195$	−3103.51	+	2128.97i	−1.13973	+	0.781840i
$196$	1271.93	−	4152.53i	0.463531	−	1.51331i
$197$			661.168i			0.239118i	0.992827	+	0.119559i	$0.0381481\pi$
$197$			661.168i			0.239118i	−0.992827	+	0.119559i	$0.961852\pi$
$198$	−2172.34	+	340.153i	−0.779704	+	0.122089i
$199$	−1687.99	−	974.564i	−0.601300	−	0.347161i	0.168253	−	0.985744i	$-0.446188\pi$
$199$	−1687.99	−	974.564i	−0.601300	−	0.347161i	−0.769553	+	0.638583i	$0.779521\pi$
$200$	177.082	+	102.238i	0.0626079	+	0.0361467i
$201$	724.945	−	1516.45i	0.254396	−	0.532149i
$202$			7807.78i			2.71957i
$203$	−555.532	−	4887.20i	−0.192073	−	1.68972i
$204$	−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
$210$	4797.49	+	1658.03i	1.57647	+	0.544832i
$211$	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
$217$	−173.699	−	75.5805i	−0.0543386	−	0.0236440i
$218$			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	$-0.104289\pi$
$224$	−3262.85	−	1419.74i	−0.973252	−	0.423484i
$225$	−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	$-0.955893\pi$
$227$	−1284.55	+	2224.91i	−0.375589	+	0.650540i	0.614826	+	0.788663i	$0.289226\pi$
$228$	56.0370	+	720.107i	0.0162769	+	0.209168i
$229$	91.0827	−	52.5866i	0.0262835	−	0.0151748i	−0.486801	−	0.873513i	$-0.661836\pi$
$229$	91.0827	−	52.5866i	0.0262835	−	0.0151748i	0.513084	+	0.858338i	$0.328503\pi$
$230$	3644.37			1.04479
$231$	−1629.56	−	563.180i	−0.464142	−	0.160409i
$232$	5627.64			1.59255
$233$	−2273.94	+	1312.86i	−0.639360	+	0.369135i	−0.784368	−	0.620296i	$-0.787013\pi$
$233$	−2273.94	+	1312.86i	−0.639360	+	0.369135i	0.145008	+	0.989431i	$0.453679\pi$
$234$	−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
$238$	−203.628	−	1791.38i	−0.0554591	−	0.487892i
$239$			6080.85i			1.64576i	0.568212	+	0.822882i	$0.307635\pi$
$239$			6080.85i			1.64576i	−0.568212	+	0.822882i	$0.692365\pi$
$240$	129.384	−	270.648i	0.0347989	−	0.0727927i
$241$	4008.74	+	2314.45i	1.07147	+	0.618616i	0.928584	−	0.371122i	$-0.121027\pi$
$241$	4008.74	+	2314.45i	1.07147	+	0.618616i	0.142891	+	0.989738i	$0.454360\pi$
$242$	−3975.96	−	2295.52i	−1.05613	−	0.609759i
$243$	−3505.99	+	1434.21i	−0.925552	+	0.378621i
$244$		−	3272.17i		−	0.858521i
$245$	2712.92	+	2912.30i	0.707437	+	0.759428i
$246$	−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	$-0.770126\pi$
$251$	−5967.85			−1.50075			−0.750373	+	0.661015i	$0.770126\pi$
$252$	−1597.64	+	6126.55i	−0.399371	+	1.53149i
$253$	−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	0.973628	+	0.228140i	$0.0732643\pi$
$257$	2819.70	+	4883.86i	0.684389	+	1.18540i	−0.289239	+	0.957257i	$0.593402\pi$
$258$	4373.55	−	3000.20i	1.05537	−	0.723971i
$259$	458.681	+	620.211i	0.110043	+	0.148796i
$260$		−	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	0.810226	−	0.586118i	$-0.199345\pi$
$263$	3018.63	+	1742.81i	0.707745	+	0.408617i	−0.102480	+	0.994735i	$0.532678\pi$
$264$	850.809	−	1779.73i	0.198347	−	0.414905i
$265$		−	6117.79i		−	1.41816i
$266$	−368.744	+	847.448i	−0.0849968	+	0.195340i
$267$	−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	$-0.691835\pi$
$269$	1897.28	−	3286.18i	0.430033	−	0.744839i	0.996876	+	0.0789869i	$0.0251685\pi$
$270$	−7089.70	−	2120.41i	−1.59802	−	0.477940i
$271$	−6458.49	+	3728.81i	−1.44769	+	0.835827i	−0.998344	−	0.0575288i	$-0.981678\pi$
$271$	−6458.49	+	3728.81i	−1.44769	+	0.835827i	−0.449351	+	0.893356i	$0.648345\pi$
$272$	−106.552			−0.0237524
$273$	−1139.43	−	5897.72i	−0.252605	−	1.30750i
$274$	−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	−0.619203	−	0.785231i	$-0.712544\pi$
$277$	1707.75	−	2957.90i	0.370428	−	0.641600i	0.989631	+	0.143631i	$0.0458777\pi$
$278$	4185.45	+	7249.41i	0.902973	+	1.56399i
$279$	257.646	+	99.4210i	0.0552863	+	0.0213340i
$280$	−3661.32	+	2707.76i	−0.781450	+	0.577927i
$281$		−	2762.14i		−	0.586390i	−0.956053	−	0.293195i	$-0.905281\pi$
$281$		−	2762.14i		−	0.586390i	0.956053	−	0.293195i	$-0.0947185\pi$
$282$	−3488.75	−	1667.81i	−0.736709	−	0.352187i
$283$	−4767.64	−	2752.60i	−1.00144	−	0.578181i	−0.0927647	−	0.995688i	$-0.529570\pi$
$283$	−4767.64	−	2752.60i	−1.00144	−	0.578181i	−0.908674	+	0.417507i	$0.862904\pi$
$284$	−498.045	−	287.546i	−0.104062	−	0.0600801i
$285$	−597.208	−	285.498i	−0.124125	−	0.0593383i
$286$			5083.19i			1.05096i
$287$	−570.519	+	64.8515i	−0.117340	+	0.0133382i
$288$	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	$-0.634071\pi$
$293$	−4101.08			−0.817705			−0.408853	+	0.912600i	$0.634071\pi$
$294$	−5481.58	+	5965.29i	−1.08739	+	1.18334i
$295$	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
$301$	4132.12	−	469.702i	0.791267	−	0.0899441i
$302$		−	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	$0.720365\pi$
$308$	3377.86	−	2498.12i	0.624908	−	0.462155i
$309$	−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	−0.361868	−	0.932230i	$-0.617861\pi$
$311$	3435.52	−	5950.50i	0.626401	−	1.08496i	0.988268	−	0.152728i	$-0.0488059\pi$
$312$	6851.88	−	533.197i	1.24330	−	0.0967511i
$313$	−2922.40	+	1687.25i	−0.527743	+	0.304693i	−0.740097	−	0.672500i	$-0.765220\pi$
$313$	−2922.40	+	1687.25i	−0.527743	+	0.304693i	0.212354	+	0.977193i	$0.431887\pi$
$314$	−4250.80			−0.763970
$315$	−4130.40	−	4075.36i	−0.738800	−	0.728954i
$316$	−3662.02			−0.651914
$317$	−2052.28	+	1184.88i	−0.363620	+	0.209936i	−0.670667	−	0.741758i	$-0.733992\pi$
$317$	−2052.28	+	1184.88i	−0.363620	+	0.209936i	0.307048	+	0.951694i	$0.400659\pi$
$318$	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
$322$	−2320.74	+	5333.53i	−0.401646	+	0.923063i
$323$			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
$329$	−1802.94	−	2437.86i	−0.302125	−	0.408521i
$330$	2777.67	+	4049.15i	0.463351	+	0.675450i
$331$	−1901.80	−	3294.02i	−0.315808	−	0.546996i	0.663801	−	0.747910i	$-0.268942\pi$
$331$	−1901.80	−	3294.02i	−0.315808	−	0.546996i	−0.979609	+	0.200913i	$0.935609\pi$
$332$	−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
$336$	313.701	+	361.703i	0.0509338	+	0.0587278i
$337$	−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
$343$	−5989.74	+	2115.80i	−0.942903	+	0.333068i
$344$			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	0.784630	−	0.619965i	$-0.212853\pi$
$347$	4137.14	+	2388.58i	0.640039	+	0.369527i	−0.144590	+	0.989492i	$0.546186\pi$
$348$	−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	$-0.190852\pi$
$350$	−91.7507	−	807.161i	−0.0140122	−	0.123270i
$351$	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	$-0.913502\pi$
$353$	−1652.78	+	2862.69i	−0.249202	+	0.431631i	0.714102	+	0.700041i	$0.246835\pi$
$354$	754.889	+	9700.74i	0.113339	+	1.45647i
$355$	456.436	−	263.524i	0.0682398	−	0.0393982i
$356$	7111.16			1.05868
$357$	−673.213	+	1947.94i	−0.0998046	+	0.288784i
$358$	−2909.78			−0.429572
$359$	359.154	−	207.358i	0.0528006	−	0.0304845i	−0.473367	−	0.880865i	$-0.656962\pi$
$359$	359.154	−	207.358i	0.0528006	−	0.0304845i	0.526168	+	0.850381i	$0.323628\pi$
$360$	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
$364$	13421.5	+	5839.99i	1.93263	+	0.840930i
$365$		−	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	$-0.335057\pi$
$367$	−65.9242	−	38.0613i	−0.00937661	−	0.00541359i	−0.504681	+	0.863306i	$0.668390\pi$
$368$	297.702	+	171.878i	0.0421706	+	0.0243472i
$369$	827.018	−	129.497i	0.116674	−	0.0182693i
$370$		−	2196.93i		−	0.308683i
$371$	8953.38	+	3895.82i	1.25293	+	0.545178i
$372$	−554.921	+	380.669i	−0.0773423	+	0.0530559i
$373$	6150.49	+	10653.0i	0.853781	+	1.47879i	0.877771	+	0.479080i	$0.159030\pi$
$373$	6150.49	+	10653.0i	0.853781	+	1.47879i	−0.0239900	+	0.999712i	$0.507637\pi$
$374$	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
$378$	7617.95	−	9025.49i	1.03657	−	1.22810i
$379$	−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	$-0.277410\pi$
$383$	−2555.45	−	4426.17i	−0.340933	−	0.590513i	−0.984606	+	0.174787i	$0.944076\pi$
$384$	−9648.70	+	6618.89i	−1.28225	+	0.879606i
$385$	434.863	+	3825.63i	0.0575654	+	0.506421i
$386$			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	0.0262636	−	0.999655i	$-0.491639\pi$
$389$	−6339.84	−	3660.31i	−0.826331	−	0.477083i	−0.852595	+	0.522572i	$0.824972\pi$
$390$	−7378.43	+	15434.3i	−0.958004	+	2.00396i
$391$			1479.73i			0.191390i
$392$	−1631.26	−	7082.65i	−0.210182	−	0.912572i
$393$	−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	$-0.481818\pi$
$397$	7516.61	−	4339.72i	0.950247	−	0.548625i	0.893158	+	0.449744i	$0.148485\pi$
$398$	−8859.79			−1.11583
$399$	798.129	−	692.207i	0.100141	−	0.0868514i
$400$	−48.0100			−0.00600125
$401$	−8447.68	+	4877.27i	−1.05201	+	0.607379i	−0.923212	−	0.384291i	$-0.874446\pi$
$401$	−8447.68	+	4877.27i	−1.05201	+	0.607379i	−0.128800	+	0.991671i	$0.541113\pi$
$402$	−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
$406$	−13294.3	−	17976.0i	−1.62508	−	2.19737i
$407$			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	$-0.267651\pi$
$409$	2935.32	+	1694.71i	0.354871	+	0.204885i	−0.311958	+	0.950096i	$0.600985\pi$
$410$	1416.21	+	817.649i	0.170589	+	0.0984897i
$411$	10869.3	+	5196.10i	1.30448	+	0.623612i
$412$		−	14658.5i		−	1.75285i
$413$	−3044.10	+	6995.95i	−0.362689	+	0.833531i
$414$	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	$-0.767496\pi$
$419$	−12777.4			−1.48977			−0.744887	+	0.667191i	$0.767496\pi$
$420$	13882.4	−	2682.05i	1.61284	−	0.311597i
$421$	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
$427$	−3848.17	+	2845.94i	−0.436126	+	0.322540i
$428$			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	0.305443	−	0.952210i	$-0.401195\pi$
$431$	−3279.13	−	1893.21i	−0.366474	−	0.211584i	−0.671917	+	0.740627i	$0.734529\pi$
$432$	−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	$0.943323\pi$
$434$	−855.548	+	97.2510i	−0.0946259	+	0.0107562i
$435$	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	$-0.724383\pi$
$439$	−2872.90	+	1658.67i	−0.312337	+	0.180328i	0.335635	+	0.941992i	$0.391049\pi$
$440$	−4405.24			−0.477299
$441$	8594.54	−	3449.65i	0.928035	−	0.372492i
$442$	6076.35			0.653897
$443$	9266.95	−	5350.27i	0.993873	−	0.573813i	0.0874435	−	0.996169i	$-0.472130\pi$
$443$	9266.95	−	5350.27i	0.993873	−	0.573813i	0.906430	+	0.422356i	$0.138797\pi$
$444$	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
$448$	−15338.6	+	1743.55i	−1.61759	+	0.183873i
$449$		−	4017.92i		−	0.422310i	−0.977453	−	0.211155i	$-0.932278\pi$
$449$		−	4017.92i		−	0.422310i	0.977453	−	0.211155i	$-0.0677225\pi$
$450$	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
$455$	−10785.1	+	7976.22i	−1.11124	+	0.821826i
$456$	683.777	+	996.777i	0.0702210	+	0.102365i
$457$	−4584.83	−	7941.15i	−0.469298	−	0.812848i	0.530086	−	0.847944i	$-0.322160\pi$
$457$	−4584.83	−	7941.15i	−0.469298	−	0.812848i	−0.999384	+	0.0350961i	$0.988826\pi$
$458$	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	$-0.479246\pi$
$461$	1289.80			0.130308			0.0651542	+	0.997875i	$0.479246\pi$
$462$	−7694.76	+	1486.61i	−0.774876	+	0.149704i
$463$	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	$-0.0392798\pi$
$467$	3931.83	+	6810.13i	0.389600	+	0.674808i	−0.602795	+	0.797896i	$0.705946\pi$
$468$	−19907.9	−	7682.11i	−1.96633	−	0.758772i
$469$	2390.27	−	5493.32i	0.235336	−	0.540849i
$470$			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
$476$	−2986.20	−	4037.83i	−0.287547	−	0.388810i
$477$	−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	$-0.889712\pi$
$479$	−1847.13	+	3199.33i	−0.176196	+	0.305180i	0.764379	+	0.644767i	$0.223046\pi$
$480$	−898.781	−	11549.8i	−0.0854657	−	1.09828i
$481$	−2251.51	+	1299.91i	−0.213430	+	0.123224i
$482$	21040.7			1.98833
$483$	5023.14	−	4356.51i	0.473211	−	0.410410i
$484$	−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	−0.840498	−	0.541815i	$-0.817737\pi$
$487$	526.359	−	911.681i	0.0489766	−	0.0848300i	0.889474	+	0.456985i	$0.151071\pi$
$488$	−2738.04	−	4742.42i	−0.253986	−	0.439917i
$489$	−1523.06	−	2220.24i	−0.140849	−	0.205322i
$490$	17298.4	+	5298.55i	1.59482	+	0.488498i
$491$			2378.40i			0.218607i	0.994008	+	0.109303i	$0.0348620\pi$
$491$			2378.40i			0.218607i	−0.994008	+	0.109303i	$0.965138\pi$
$492$	−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
$497$	95.0069	+	835.807i	0.00857474	+	0.0754347i
$498$	8740.60	−	5995.95i	0.786497	−	0.539528i
$499$	−9385.74	−	16256.6i	−0.842011	−	1.45840i	−0.888192	−	0.459472i	$-0.848039\pi$
$499$	−9385.74	−	16256.6i	−0.842011	−	1.45840i	0.0461818	−	0.998933i	$-0.485295\pi$
$500$	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	$-0.247168\pi$
$503$	16095.2			1.42674			0.713370	+	0.700788i	$0.247168\pi$
$504$	2811.01	+	10216.2i	0.248437	+	0.902908i
$505$	−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	$-0.210471\pi$
$509$	−1575.31	−	2728.52i	−0.137180	−	0.237603i	−0.926428	+	0.376472i	$0.877137\pi$
$510$	4840.28	−	3320.37i	0.420257	−	0.288291i
$511$	9547.42	+	4154.30i	0.826522	+	0.359639i
$512$			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
$518$	3215.20	+	1399.01i	0.272718	+	0.118666i
$519$	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	$-0.766198\pi$
$521$	2489.60	−	4312.12i	0.209350	−	0.362605i	0.951510	+	0.307618i	$0.0995318\pi$
$522$	20468.0	+	25366.9i	1.71620	+	2.12697i
$523$	11977.0	−	6914.92i	1.00137	−	0.578142i	0.0927181	−	0.995692i	$-0.470444\pi$
$523$	11977.0	−	6914.92i	1.00137	−	0.578142i	0.908654	+	0.417550i	$0.137111\pi$
$524$	20300.1			1.69240
$525$	−303.336	+	877.700i	−0.0252165	+	0.0729638i
$526$	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
$532$	290.760	+	2557.91i	0.0236956	+	0.208458i
$533$		−	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
$539$	−5875.73	−	1799.75i	−0.469547	−	0.143823i
$540$	−20056.0	+	4759.15i	−1.59828	+	0.379261i
$541$	−2658.97	−	4605.48i	−0.211309	−	0.365998i	0.740815	−	0.671709i	$-0.234439\pi$
$541$	−2658.97	−	4605.48i	−0.211309	−	0.365998i	−0.952124	+	0.305711i	$0.901106\pi$
$542$	−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
$546$	−17889.5	−	20626.9i	−1.40220	−	1.61676i
$547$	−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
$553$	3185.01	+	4306.65i	0.244920	+	0.331171i
$554$		−	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	0.504782	−	0.863247i	$-0.331573\pi$
$557$	125.920	+	72.6999i	0.00957881	+	0.00553033i	−0.495203	+	0.868777i	$0.664906\pi$
$558$	1240.19	−	194.194i	0.0940888	−	0.0147328i
$559$			14016.1i			1.06050i
$560$	426.603	−	980.420i	0.0321916	−	0.0739827i
$561$	−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	$-0.880160\pi$
$563$	−1958.12	+	3391.56i	−0.146581	+	0.253885i	0.783381	+	0.621542i	$0.213493\pi$
$564$	−10738.9	+	835.679i	−0.801757	+	0.0623909i
$565$	14449.4	−	8342.36i	1.07591	−	0.621178i
$566$	−25024.0			−1.85837
$567$	−12306.7	+	5552.46i	−0.911521	+	0.411254i
$568$	−962.437			−0.0710968
$569$	7404.97	−	4275.26i	0.545576	−	0.314988i	−0.201760	−	0.979435i	$-0.564666\pi$
$569$	7404.97	−	4275.26i	0.545576	−	0.314988i	0.747336	+	0.664447i	$0.231333\pi$
$570$	−2999.79	+	233.437i	−0.220434	+	0.0171537i
$571$	11956.8	−	20709.8i	0.876318	−	1.51783i	0.0209659	−	0.999780i	$-0.493326\pi$
$571$	11956.8	−	20709.8i	0.876318	−	1.51783i	0.855352	−	0.518047i	$-0.173341\pi$
$572$	7079.71	+	12262.4i	0.517513	+	0.896359i
$573$	−6243.32	+	4282.84i	−0.455180	+	0.312248i
$574$	−2098.47	+	1551.94i	−0.152593	+	0.112852i
$575$			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	$-0.176612\pi$
$577$	11347.8	+	6551.66i	0.818745	+	0.472703i	−0.0312386	+	0.999512i	$0.509945\pi$
$578$	17534.6	+	10123.6i	1.26184	+	0.728525i
$579$	4099.61	−	8575.60i	0.294255	−	0.615527i
$580$			39020.7i			2.79353i
$581$	8258.10	−	938.706i	0.589679	−	0.0670294i
$582$	−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	$-0.718608\pi$
$587$	−18034.7			−1.26809			−0.634047	+	0.773294i	$0.718608\pi$
$588$	−4915.19	+	22024.9i	−0.344726	+	1.54471i
$589$	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	−0.928071	−	0.372404i	$-0.878534\pi$
$593$	−11358.1	−	19672.8i	−0.786547	−	1.36234i	0.141524	−	0.989935i	$-0.454800\pi$
$594$	11116.7	−	2637.90i	0.767882	−	0.182213i
$595$	4573.08	−	519.826i	0.315089	−	0.0358165i
$596$		−	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	0.0438153	−	0.999040i	$-0.486049\pi$
$599$	−11720.4	−	6766.78i	−0.799471	−	0.461575i	−0.843286	+	0.537465i	$0.819382\pi$
$600$	−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	$-0.0397250\pi$
$602$	15198.7	−	11240.3i	1.02899	−	0.760997i
$603$	−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	$-0.753042\pi$
$607$	−6942.92	+	4008.50i	−0.464258	+	0.268039i	0.249575	+	0.968355i	$0.419709\pi$
$608$	2109.29			0.140696
$609$	4848.12	+	25094.1i	0.322588	+	1.66973i
$610$	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	−0.978266	−	0.207352i	$-0.933515\pi$
$613$	−4698.26	+	8137.63i	−0.309561	+	0.536176i	0.668705	+	0.743528i	$0.266849\pi$
$614$	18821.7	+	32600.1i	1.23710	+	2.14272i
$615$	−1057.47	−	1541.53i	−0.0693355	−	0.101074i
$616$	2805.27	−	6447.06i	0.183486	−	0.421688i
$617$			8906.76i			0.581155i	0.956851	+	0.290578i	$0.0938474\pi$
$617$			8906.76i			0.581155i	−0.956851	+	0.290578i	$0.906153\pi$
$618$	−11793.6	+	24670.1i	−0.767653	+	1.60579i
$619$	−6091.73	−	3517.06i	−0.395553	−	0.228373i	0.289010	−	0.957326i	$-0.406674\pi$
$619$	−6091.73	−	3517.06i	−0.395553	−	0.228373i	−0.684563	+	0.728953i	$0.740007\pi$
$620$	1301.45	+	751.392i	0.0843024	+	0.0486720i
$621$	−7049.01	+	6654.03i	−0.455502	+	0.429979i
$622$		−	31232.4i		−	2.01335i
$623$	−6184.86	−	8362.93i	−0.397739	−	0.537807i
$624$	−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
$630$	−25521.8	−	6655.37i	−1.61399	−	0.420883i
$631$	−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
$637$	−4805.19	−	20863.3i	−0.298883	−	1.29770i
$638$		−	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	0.740823	−	0.671700i	$-0.234436\pi$
$641$	8593.58	+	4961.51i	0.529526	+	0.305722i	−0.211297	+	0.977422i	$0.567769\pi$
$642$	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	$0.997128\pi$
$644$	1829.94	+	16098.6i	0.111972	+	0.985051i
$645$	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	$-0.757985\pi$
$647$	3859.39	−	6684.67i	0.234511	−	0.406184i	0.959130	+	0.282965i	$0.0913179\pi$
$648$	−4721.82	−	14708.0i	−0.286251	−	0.891641i
$649$	−6391.80	+	3690.30i	−0.386595	+	0.223201i
$650$	2737.88			0.165213
$651$	930.316	+	321.520i	0.0560092	+	0.0193569i
$652$	6560.75			0.394078
$653$	9846.89	−	5685.11i	0.590105	−	0.340697i	−0.175034	−	0.984562i	$-0.556004\pi$
$653$	9846.89	−	5685.11i	0.590105	−	0.340697i	0.765139	+	0.643865i	$0.222670\pi$
$654$	−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
$658$	−12638.0	−	5499.07i	−0.748753	−	0.325800i
$659$		−	19795.1i		−	1.17012i	−0.810990	−	0.585060i	$-0.801071\pi$
$659$		−	19795.1i		−	1.17012i	0.810990	−	0.585060i	$-0.198929\pi$
$660$	12340.2	+	5899.30i	0.727792	+	0.347924i
$661$	26896.6	+	15528.7i	1.58268	+	0.913763i	0.994466	+	0.105062i	$0.0335041\pi$
$661$	26896.6	+	15528.7i	1.58268	+	0.913763i	0.588219	+	0.808702i	$0.299829\pi$
$662$	−14973.0	−	8644.67i	−0.879068	−	0.507530i
$663$	−6266.83	−	2995.88i	−0.367094	−	0.175491i
$664$			9509.25i			0.555769i
$665$	−2163.38	−	941.337i	−0.126154	−	0.0548924i
$666$	−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
$672$	17475.5	+	6039.59i	1.00317	+	0.346700i
$673$	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	0.965455	+	0.260571i	$0.0839110\pi$
$677$	12478.3	+	21613.0i	0.708389	+	1.22697i	−0.257066	+	0.966394i	$0.582756\pi$
$678$	19211.1	+	28005.1i	1.08820	+	1.58632i
$679$	−448.394	−	3944.67i	−0.0253428	−	0.222949i
$680$			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	0.202812	−	0.979218i	$-0.434992\pi$
$683$	−9706.83	−	5604.24i	−0.543809	−	0.313968i	−0.746621	+	0.665249i	$0.768325\pi$
$684$	−580.599	−	3707.92i	−0.0324558	−	0.207274i
$685$		−	26903.9i		−	1.50065i
$686$	−18770.1	+	21942.1i	−1.04467	+	1.22122i
$687$	−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	$-0.764014\pi$
$691$	−9472.37	+	5468.88i	−0.521485	+	0.301079i	0.216057	+	0.976381i	$0.430680\pi$
$692$	−30300.2			−1.66451
$693$	8668.93	+	2260.62i	0.475188	+	0.123916i
$694$	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
$700$	−1345.52	−	1819.36i	−0.0726513	−	0.0982363i
$701$			27949.3i			1.50589i	0.658082	+	0.752947i	$0.271368\pi$
$701$			27949.3i			1.50589i	−0.658082	+	0.752947i	$0.728632\pi$
$702$	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
$707$	12692.7	−	29170.3i	0.675186	−	1.55171i
$708$	15331.9	+	22350.1i	0.813855	+	1.18640i
$709$	−10472.7	−	18139.3i	−0.554741	−	0.960840i	−0.997924	−	0.0644082i	$-0.979484\pi$
$709$	−10472.7	−	18139.3i	−0.554741	−	0.960840i	0.443183	−	0.896431i	$-0.353849\pi$
$710$	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
$714$	1777.06	+	9198.16i	0.0931441	+	0.482118i
$715$	−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	$-0.235727\pi$
$719$	−4150.10	−	7188.19i	−0.215261	−	0.372843i	−0.953353	+	0.301857i	$0.902394\pi$
$720$	−561.167	+	1454.25i	−0.0290465	+	0.0752731i
$721$	−17238.9	+	12749.1i	−0.890443	+	0.658533i
$722$			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	$0.820530\pi$
$728$	24338.7	−	2766.61i	1.23908	−	0.140848i
$729$	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	$-0.621269\pi$
$733$	4885.73	−	2820.78i	0.246192	−	0.142139i	0.618019	+	0.786163i	$0.287935\pi$
$734$	−346.017			−0.0174001
$735$	−15228.3	−	13993.5i	−0.764223	−	0.702254i
$736$	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	−0.688905	−	0.724852i	$-0.741908\pi$
$739$	5691.08	−	9857.24i	0.283288	−	0.490669i	0.972193	+	0.234183i	$0.0752415\pi$
$740$	−3059.81	−	5299.74i	−0.152001	−	0.263273i
$741$	2014.20	+	2936.20i	0.0998560	+	0.145565i
$742$	44099.5	−	5012.83i	2.18186	−	0.248015i
$743$		−	4665.46i		−	0.230362i	−0.993345	−	0.115181i	$-0.963255\pi$
$743$		−	4665.46i		−	0.230362i	0.993345	−	0.115181i	$-0.0367449\pi$
$744$	−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
$749$	18133.6	−	13410.8i	0.884628	−	0.654233i
$750$	−26070.0	+	17883.7i	−1.26926	+	0.870696i
$751$	4780.43	+	8279.95i	0.232277	+	0.402316i	0.958478	−	0.285167i	$-0.0920489\pi$
$751$	4780.43	+	8279.95i	0.232277	+	0.402316i	−0.726200	+	0.687483i	$0.758716\pi$
$752$	−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
$756$	5806.71	−	32382.6i	0.279349	−	1.55786i
$757$	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	−0.999201	−	0.0399765i	$-0.987272\pi$
$761$	−11215.0	−	19424.9i	−0.534221	−	0.925298i	0.464980	−	0.885321i	$-0.346062\pi$
$762$	−52321.3	+	35891.8i	−2.48740	+	1.70633i
$763$	9593.35	−	22047.4i	0.455180	−	1.04610i
$764$		−	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	$0.782883\pi$
$770$	10406.6	+	14071.4i	0.487048	+	0.658567i
$771$	−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	0.483119	+	0.875555i	$0.339504\pi$
$773$	−11104.6	+	19233.7i	−0.516693	+	0.894938i	−0.999812	+	0.0193838i	$0.993830\pi$
$774$	−21447.7	+	17305.6i	−0.996021	+	0.803668i
$775$	−85.4774	+	49.3504i	−0.00396185	+	0.00228738i
$776$	4542.31			0.210128
$777$	−2626.22	−	3028.09i	−0.121255	−	0.139810i
$778$	−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
$784$	1163.18	+	1248.67i	0.0529875	+	0.0568817i
$785$		−	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	$-0.483730\pi$
$787$	−17403.2	−	10047.8i	−0.788257	−	0.455100i	−0.839348	+	0.543594i	$0.817063\pi$
$788$	7249.94	+	4185.75i	0.327752	+	0.189227i
$789$	−16340.6	−	7811.69i	−0.737314	−	0.352476i
$790$		−	15255.1i		−	0.687029i
$791$	3007.63	+	26459.1i	0.135195	+	1.18935i
$792$	−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	$-0.397059\pi$
$797$	14300.8			0.635583			0.317791	+	0.948161i	$0.397059\pi$
$798$	1568.64	−	4538.85i	0.0695855	−	0.201345i
$799$	−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
$805$	−13615.5	−	5924.44i	−0.596130	−	0.259390i
$806$		−	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	0.196080	−	0.980588i	$-0.437179\pi$
$809$	−12772.9	−	7374.43i	−0.555093	−	0.320483i	−0.751174	+	0.660104i	$0.770512\pi$
$810$	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	$0.968459\pi$
$812$	−57106.8	−	24848.5i	−2.46805	−	1.07390i
$813$	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
$819$	8280.36	+	30093.8i	0.353283	+	1.28396i
$820$	4555.18			0.193992
$821$	−40528.1	+	23398.9i	−1.72283	+	0.994674i	−0.809878	+	0.586598i	$0.800467\pi$
$821$	−40528.1	+	23398.9i	−1.72283	+	0.994674i	−0.912948	+	0.408076i	$0.866200\pi$
$822$	54596.6	−	4248.58i	2.31664	−	0.180275i
$823$	13086.7	−	22666.8i	0.554281	−	0.960043i	−0.443678	−	0.896186i	$-0.646327\pi$
$823$	13086.7	−	22666.8i	0.554281	−	0.960043i	0.997959	−	0.0638567i	$-0.0203401\pi$
$824$	−12265.8	−	21245.0i	−0.518566	−	0.898183i
$825$	−740.792	+	508.175i	−0.0312619	+	0.0214453i
$826$	3916.90	+	34458.3i	0.164996	+	1.45152i
$827$			42212.0i			1.77492i	0.460888	+	0.887458i	$0.347531\pi$
$827$			42212.0i			1.77492i	−0.460888	+	0.887458i	$0.652469\pi$
$828$	−3654.08	−	23336.3i	−0.153367	−	0.979460i
$829$	−19605.0	−	11319.0i	−0.821364	−	0.474215i	0.0295225	−	0.999564i	$-0.490601\pi$
$829$	−19605.0	−	11319.0i	−0.821364	−	0.474215i	−0.850887	+	0.525349i	$0.823935\pi$
$830$	−20499.2	−	11835.2i	−0.857275	−	0.494948i
$831$	−7654.54	+	16011.8i	−0.319534	+	0.668405i
$832$		−	52028.3i		−	2.16798i
$833$	−2151.38	+	7023.73i	−0.0894850	+	0.292146i
$834$	−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	$-0.198228\pi$
$839$	39480.0			1.62455			0.812277	+	0.583272i	$0.198228\pi$
$840$	17875.9	−	15503.5i	0.734257	−	0.636812i
$841$	−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
$847$	11122.7	+	15039.7i	0.451216	+	0.610117i
$848$		−	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	$0.655180\pi$
$854$	−8680.29	+	19949.1i	−0.347814	+	0.799347i
$855$	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	$-0.846119\pi$
$857$	−1007.45	+	1744.96i	−0.0401562	+	0.0695526i	0.845249	+	0.534373i	$0.179452\pi$
$858$	−2049.21	−	26333.4i	−0.0815370	−	1.04780i
$859$	15844.5	−	9147.83i	0.629345	−	0.363353i	−0.151153	−	0.988510i	$-0.548299\pi$
$859$	15844.5	−	9147.83i	0.629345	−	0.363353i	0.780499	+	0.625158i	$0.214965\pi$
$860$	−32991.9			−1.30816
$861$	2929.43	−	565.958i	0.115952	−	0.0224016i
$862$	−17211.2			−0.680064
$863$	5979.04	−	3452.00i	0.235839	−	0.136162i	−0.377424	−	0.926041i	$-0.623190\pi$
$863$	5979.04	−	3452.00i	0.235839	−	0.136162i	0.613263	+	0.789879i	$0.289857\pi$
$864$	−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
$868$	−1928.43	+	1426.18i	−0.0754091	+	0.0557693i
$869$			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
$875$	−24630.9	+	2799.82i	−0.951631	+	0.108173i
$876$	30501.4	−	20923.6i	1.17642	−	0.807012i
$877$	−208.597	−	361.300i	−0.00803171	−	0.0139113i	0.861982	−	0.506940i	$-0.169223\pi$
$877$	−208.597	−	361.300i	−0.00803171	−	0.0139113i	−0.870013	+	0.493028i	$0.835890\pi$
$878$	−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	$-0.455767\pi$
$881$	7244.25			0.277032			0.138516	+	0.990360i	$0.455767\pi$
$882$	25992.4	−	33112.9i	0.992303	−	1.26414i
$883$	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	$-0.276481\pi$
$887$	−8933.98	−	15474.1i	−0.338189	−	0.585761i	−0.984092	+	0.177659i	$0.943148\pi$
$888$	3781.75	−	2594.24i	0.142914	−	0.0980370i
$889$	−49433.1	+	5619.10i	−1.86494	+	0.211990i
$890$			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
$896$	−33530.6	+	24797.8i	−1.25020	+	0.924592i
$897$	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
$903$	−21217.1	+	4099.08i	−0.781904	+	0.151062i
$904$	−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	−0.799687	−	0.600417i	$-0.795001\pi$
$907$	3281.49	−	5683.71i	0.120132	−	0.208076i	0.919820	+	0.392341i	$0.128335\pi$
$908$	16264.6	+	28171.1i	0.594449	+	1.02962i
$909$	−16696.3	+	43268.0i	−0.609221	+	1.57878i
$910$	−24328.0	+	55910.6i	−0.886225	+	2.03672i
$911$		−	41084.1i		−	1.49416i	−0.664735	−	0.747079i	$-0.731456\pi$
$911$		−	41084.1i		−	1.49416i	0.664735	−	0.747079i	$-0.268544\pi$
$912$	−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
$917$	−17655.9	−	23873.6i	−0.635821	−	0.859732i
$918$	−3153.29	−	13288.6i	−0.113371	−	0.477767i
$919$	−2762.34	−	4784.51i	−0.0991524	−	0.171737i	0.812182	−	0.583405i	$-0.198280\pi$
$919$	−2762.34	−	4784.51i	−0.0991524	−	0.171737i	−0.911334	+	0.411668i	$0.864946\pi$
$920$	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
$924$	−16491.9	+	14303.2i	−0.587169	+	0.509244i
$925$	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	$-0.0194962\pi$
$929$	12630.2	+	21876.1i	0.446052	+	0.772585i	−0.552073	+	0.833796i	$0.686163\pi$
$930$	−1585.78	−	2311.67i	−0.0559136	−	0.0815082i
$931$	2755.29	−	2566.66i	0.0969936	−	0.0903533i
$932$			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	$-0.296820\pi$
$938$	−3075.61	−	27057.1i	−0.107060	−	0.941841i
$939$	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	−0.0584406	−	0.998291i	$-0.518613\pi$
$941$	24112.4	−	41763.8i	0.835325	−	1.44683i	0.893766	−	0.448534i	$-0.148054\pi$
$942$	22021.2	−	1713.64i	0.761667	−	0.0592712i
$943$	1855.15	−	1071.07i	0.0640635	−	0.0369871i
$944$	2049.58			0.0706654
$945$	23040.4	+	19447.2i	0.793127	+	0.669438i
$946$	18286.8			0.628493
$947$	−21340.2	+	12320.8i	−0.732275	+	0.422779i	−0.819254	−	0.573431i	$-0.805612\pi$
$947$	−21340.2	+	12320.8i	−0.732275	+	0.422779i	0.0869787	+	0.996210i	$0.472279\pi$
$948$	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
$952$	−7706.69	−	3353.36i	−0.262369	−	0.114163i
$953$		−	13271.1i		−	0.451095i	−0.974232	−	0.225548i	$-0.927583\pi$
$953$		−	13271.1i		−	0.451095i	0.974232	−	0.225548i	$-0.0724171\pi$
$954$	−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
$959$	39373.8	+	17132.4i	1.32580	+	0.576888i
$960$	−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
$966$	9872.46	−	28565.9i	0.328821	−	0.951441i
$967$	−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	−0.875947	−	0.482407i	$-0.839763\pi$
$971$	−25892.6	−	44847.3i	−0.855750	−	1.48220i	0.0201966	−	0.999796i	$-0.493571\pi$
$972$	−6469.20	+	47524.1i	−0.213477	+	1.56825i
$973$	−3852.10	−	33888.2i	−0.126920	−	1.11655i
$974$		−	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	0.847639	−	0.530573i	$-0.178023\pi$
$977$	24796.0	+	14316.0i	0.811969	+	0.468790i	−0.0356703	+	0.999364i	$0.511357\pi$
$978$	−11041.6	−	5278.49i	−0.361014	−	0.172584i
$979$		−	10062.1i		−	0.328485i
$980$	49109.4	−	11310.8i	1.60076	−	0.368683i
$981$	−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	0.250288	+	0.968171i	$0.419475\pi$
$983$	−21984.3	+	38077.9i	−0.713317	+	1.23550i	−0.963605	+	0.267330i	$0.913859\pi$
$984$	264.841	+	3403.36i	0.00858012	+	0.110259i
$985$	−6644.24	+	3836.06i	−0.214927	+	0.124088i
$986$	−25854.1			−0.835055
$987$	10322.9	+	11902.5i	0.332909	+	0.383850i
$988$	−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	−0.718648	−	0.695374i	$-0.755239\pi$
$991$	7577.33	−	13124.3i	0.242888	−	0.420694i	0.961536	+	0.274680i	$0.0885720\pi$
$992$	982.594	+	1701.90i	0.0314490	+	0.0544712i
$993$	11180.2	+	16298.0i	0.357294	+	0.520846i
$994$	2273.58	+	3074.25i	0.0725490	+	0.0980979i
$995$		−	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	$-0.477843\pi$
$997$	−23912.6	−	13806.0i	−0.759599	−	0.438555i	−0.829152	+	0.559023i	$0.811176\pi$
$998$	−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	21.4.g.a.17.6	yes	12
3.2	odd	2	inner	21.4.g.a.17.1	yes	12
4.3	odd	2		336.4.bc.d.17.6		12
7.2	even	3		147.4.g.d.68.1		12
7.3	odd	6		147.4.c.a.146.11		12
7.4	even	3		147.4.c.a.146.12		12
7.5	odd	6	inner	21.4.g.a.5.1	✓	12
7.6	odd	2		147.4.g.d.80.6		12
12.11	even	2		336.4.bc.d.17.4		12
21.2	odd	6		147.4.g.d.68.6		12
21.5	even	6	inner	21.4.g.a.5.6	yes	12
21.11	odd	6		147.4.c.a.146.1		12
21.17	even	6		147.4.c.a.146.2		12
21.20	even	2		147.4.g.d.80.1		12
28.19	even	6		336.4.bc.d.257.4		12
84.47	odd	6		336.4.bc.d.257.6		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
21.4.g.a.5.1	✓	12	7.5	odd	6	inner
21.4.g.a.5.6	yes	12	21.5	even	6	inner
21.4.g.a.17.1	yes	12	3.2	odd	2	inner
21.4.g.a.17.6	yes	12	1.1	even	1	trivial
147.4.c.a.146.1		12	21.11	odd	6
147.4.c.a.146.2		12	21.17	even	6
147.4.c.a.146.11		12	7.3	odd	6
147.4.c.a.146.12		12	7.4	even	3
147.4.g.d.68.1		12	7.2	even	3
147.4.g.d.68.6		12	21.2	odd	6
147.4.g.d.80.1		12	21.20	even	2
147.4.g.d.80.6		12	7.6	odd	2
336.4.bc.d.17.4		12	12.11	even	2
336.4.bc.d.17.6		12	4.3	odd	2
336.4.bc.d.257.4		12	28.19	even	6
336.4.bc.d.257.6		12	84.47	odd	6

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:	\( N \)	\(=\)	\( 21 = 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	21.g (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(3.93653 - 2.27276i) q^{2} +(-5.18049 + 0.403134i) q^{3} +(6.33084 - 10.9653i) q^{4} +(5.80193 + 10.0492i) q^{5} +(-19.4769 + 13.3609i) q^{6} +(-18.4018 + 2.09174i) q^{7} -21.1897i q^{8} +(26.6750 - 4.17686i) q^{9} +O(q^{10})\)	\(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} +(-18.4018 + 2.09174i) q^{7} -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} +(-67.6850 + 50.0569i) q^{14} +(-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} +(94.4869 - 18.2546i) q^{21} -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} +(-93.5619 + 215.024i) q^{28} +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} +(-127.786 - 172.788i) q^{35} +(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} +(330.462 - 286.606i) q^{42} -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} +(334.249 - 76.9836i) q^{49} +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} +(44.3235 + 389.928i) q^{56} +(-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} +(-482.129 + 132.659i) q^{63} +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} +(-895.738 - 389.756i) q^{70} -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} +(304.254 + 132.388i) q^{77} +(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} +(398.013 - 1151.65i) q^{84} -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} +(130.563 + 1148.61i) q^{91} -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} +(1140.82 - 1062.71i) q^{98} +(-451.297 - 174.147i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 3 q^{3} + 14 q^{4} - 56 q^{7} - 3 q^{9}+O(q^{10}) \) 12 * q - 3 * q^3 + 14 * q^4 - 56 * q^7 - 3 * q^9	\( 12 q - 3 q^{3} + 14 q^{4} - 56 q^{7} - 3 q^{9} + 30 q^{10} - 192 q^{12} + 6 q^{15} + 134 q^{16} + 66 q^{18} + 300 q^{19} + 357 q^{21} - 268 q^{22} + 414 q^{24} - 42 q^{25} - 602 q^{28} - 822 q^{30} - 930 q^{31} - 855 q^{33} + 852 q^{36} + 764 q^{37} - 426 q^{39} + 2298 q^{40} + 966 q^{42} - 1012 q^{43} + 2367 q^{45} + 608 q^{46} - 336 q^{49} - 1341 q^{51} - 3000 q^{52} - 4158 q^{54} + 270 q^{57} + 2870 q^{58} - 918 q^{60} + 2358 q^{61} + 1071 q^{63} - 548 q^{64} + 2934 q^{66} + 792 q^{67} - 4242 q^{70} - 2712 q^{72} - 2904 q^{73} - 2418 q^{75} + 4296 q^{78} + 1674 q^{79} + 837 q^{81} + 5040 q^{82} + 3864 q^{84} + 348 q^{85} + 1638 q^{87} - 554 q^{88} - 1218 q^{91} - 1479 q^{93} - 1356 q^{94} - 4410 q^{96} - 3354 q^{99}+O(q^{100}) \) 12 * q - 3 * q^3 + 14 * q^4 - 56 * q^7 - 3 * q^9 + 30 * q^10 - 192 * q^12 + 6 * q^15 + 134 * q^16 + 66 * q^18 + 300 * q^19 + 357 * q^21 - 268 * q^22 + 414 * q^24 - 42 * q^25 - 602 * q^28 - 822 * q^30 - 930 * q^31 - 855 * q^33 + 852 * q^36 + 764 * q^37 - 426 * q^39 + 2298 * q^40 + 966 * q^42 - 1012 * q^43 + 2367 * q^45 + 608 * q^46 - 336 * q^49 - 1341 * q^51 - 3000 * q^52 - 4158 * q^54 + 270 * q^57 + 2870 * q^58 - 918 * q^60 + 2358 * q^61 + 1071 * q^63 - 548 * q^64 + 2934 * q^66 + 792 * q^67 - 4242 * q^70 - 2712 * q^72 - 2904 * q^73 - 2418 * q^75 + 4296 * q^78 + 1674 * q^79 + 837 * q^81 + 5040 * q^82 + 3864 * q^84 + 348 * q^85 + 1638 * q^87 - 554 * q^88 - 1218 * q^91 - 1479 * q^93 - 1356 * q^94 - 4410 * q^96 - 3354 * q^99

Introduction

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