LMFDB - Embedded newform 21.4.g.a.5.6

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			5.6
Root			$-0.232749 + 2.99096i$ of defining polynomial
Character	$\chi$	$=$	21.5
Dual form			21.4.g.a.17.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(3.93653 + 2.27276i) q^{2} +(-5.18049 - 0.403134i) q^{3} +(6.33084 + 10.9653i) q^{4} +(5.80193 - 10.0492i) q^{5} +(-19.4769 - 13.3609i) q^{6} +(-18.4018 - 2.09174i) q^{7} +21.1897i q^{8} +(26.6750 + 4.17686i) q^{9} +O(q^{10})$	\(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 $\left(\mathbb{Z}/21\mathbb{Z}\right)^\times$.

$n$	$8$	$10$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$

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	$-0.659660\pi$
$5$	5.80193	−	10.0492i	0.518941	−	0.898832i	0.999758	−	0.0220109i	$-0.00700684\pi$
$6$	−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	−0.697337	−	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	$0.231925\pi$
$13$			62.4185i			1.33167i	−0.746097	+	0.665837i	$0.768075\pi$
$14$	−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	0.779474	−	0.626435i	$-0.215487\pi$
$17$	−10.7082	−	18.5472i	−0.152772	−	0.264609i	−0.932245	+	0.361826i	$0.882153\pi$
$18$	95.5138	+	77.0680i	1.25071	+	1.00917i
$19$	9.50747	+	5.48914i	0.114798	+	0.0662787i	0.556300	−	0.830982i	$-0.312221\pi$
$19$	9.50747	+	5.48914i	0.114798	+	0.0662787i	−0.441502	+	0.897261i	$0.645554\pi$
$20$	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	0.746079	−	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
$28$	−93.5619	−	215.024i	−0.631484	−	1.45128i
$29$		−	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	−0.474120	−	0.880460i	$-0.657234\pi$
$31$	8.85795	−	5.11414i	0.0513205	−	0.0296299i	0.525441	+	0.850830i	$0.323900\pi$
$32$	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	−0.908576	−	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	$-0.481193\pi$
$41$	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	−0.710586	−	0.703611i	$-0.751570\pi$
$47$	81.8595	−	141.785i	0.254052	−	0.440031i	0.964638	+	0.263580i	$0.0849033\pi$
$48$	−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	−0.956784	−	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
$56$	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	0.998660	−	0.0517537i	$-0.0164811\pi$
$59$	205.978	+	356.765i	0.454510	+	0.787234i	−0.544150	+	0.838988i	$0.683148\pi$
$60$	−761.141	−	59.2302i	−1.63771	−	0.127443i
$61$	223.807	+	129.215i	0.469764	+	0.271218i	0.716141	−	0.697956i	$-0.245907\pi$
$61$	223.807	+	129.215i	0.469764	+	0.271218i	−0.246377	+	0.969174i	$0.579240\pi$
$62$	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	0.680050	−	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
$70$	−895.738	+	389.756i	−1.52945	+	0.665497i
$71$			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	−0.836648	−	0.547741i	$-0.815488\pi$
$73$	−486.879	+	281.100i	−0.780615	+	0.450688i	0.0560334	+	0.998429i	$0.482155\pi$
$74$	−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	−0.950435	−	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	$-0.595899\pi$
$83$	−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	−0.648927	−	0.760850i	$-0.724782\pi$
$89$	280.814	−	486.384i	0.334452	−	0.579288i	0.983379	+	0.181562i	$0.0581155\pi$
$90$	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	$-0.964213\pi$
$97$		−	214.364i		−	0.224385i	0.993686	−	0.112192i	$-0.0357873\pi$
$98$	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	−0.884644	−	0.466268i	$-0.845598\pi$
$101$	−858.845	−	1487.56i	−0.846122	−	1.46553i	0.0385219	−	0.999258i	$-0.487735\pi$
$102$	−39.2445	+	504.313i	−0.0380959	+	0.489554i
$103$	1002.61	+	578.855i	0.959123	+	0.553750i	0.895903	−	0.444250i	$-0.146530\pi$
$103$	1002.61	+	578.855i	0.959123	+	0.553750i	0.0632200	+	0.998000i	$0.479863\pi$
$104$	−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	−0.0588912	−	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
$112$	−54.7892	+	74.0838i	−0.0462240	+	0.0625024i
$113$			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
$119$	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	−0.464529	−	0.885558i	$-0.653776\pi$
$131$	801.637	−	1388.48i	0.534651	−	0.926043i	0.999180	−	0.0404852i	$-0.0128904\pi$
$132$	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	−0.971539	−	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	$-0.810082\pi$
$139$		−	1841.57i		−	1.12374i	0.827225	−	0.561871i	$-0.189918\pi$
$140$	−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	0.776663	−	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
$154$	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	−0.691515	−	0.722362i	$-0.743056\pi$
$157$	−809.876	+	467.582i	−0.411689	+	0.237689i	0.279826	+	0.960051i	$0.409723\pi$
$158$	−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	−0.797041	−	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	$-0.162186\pi$
$167$	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	0.473706	+	0.880683i	$0.342916\pi$
$173$	−1196.53	+	2072.45i	−0.525841	+	0.910783i	−0.999547	+	0.0301000i	$0.990417\pi$
$174$	−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	−0.611258	−	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	$0.331554\pi$
$181$			4204.05i			1.72643i	−0.504833	+	0.863217i	$0.668446\pi$
$182$	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	0.719597	−	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
$196$	1271.93	+	4152.53i	0.463531	+	1.51331i
$197$		−	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	−0.769553	−	0.638583i	$-0.779521\pi$
$199$	−1687.99	+	974.564i	−0.601300	+	0.347161i	0.168253	+	0.985744i	$0.446188\pi$
$200$	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	$0.104289\pi$
$223$			2143.28i			0.643608i	−0.946806	+	0.321804i	$0.895711\pi$
$224$	−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	0.614826	−	0.788663i	$-0.289226\pi$
$227$	−1284.55	−	2224.91i	−0.375589	−	0.650540i	−0.990415	+	0.138123i	$0.955893\pi$
$228$	56.0370	−	720.107i	0.0162769	−	0.209168i
$229$	91.0827	+	52.5866i	0.0262835	+	0.0151748i	0.513084	−	0.858338i	$-0.328503\pi$
$229$	91.0827	+	52.5866i	0.0262835	+	0.0151748i	−0.486801	+	0.873513i	$0.661836\pi$
$230$	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	0.145008	−	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
$238$	−203.628	+	1791.38i	−0.0554591	+	0.487892i
$239$		−	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	0.142891	−	0.989738i	$-0.454360\pi$
$241$	4008.74	−	2314.45i	1.07147	−	0.618616i	0.928584	+	0.371122i	$0.121027\pi$
$242$	−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	−0.289239	−	0.957257i	$-0.593402\pi$
$257$	2819.70	−	4883.86i	0.684389	−	1.18540i	0.973628	−	0.228140i	$-0.0732643\pi$
$258$	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	−0.102480	−	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
$266$	−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	0.996876	−	0.0789869i	$-0.0251685\pi$
$269$	1897.28	+	3286.18i	0.430033	+	0.744839i	−0.566842	+	0.823826i	$0.691835\pi$
$270$	−7089.70	+	2120.41i	−1.59802	+	0.477940i
$271$	−6458.49	−	3728.81i	−1.44769	−	0.835827i	−0.449351	−	0.893356i	$-0.648345\pi$
$271$	−6458.49	−	3728.81i	−1.44769	−	0.835827i	−0.998344	+	0.0575288i	$0.981678\pi$
$272$	−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	0.989631	−	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
$280$	−3661.32	−	2707.76i	−0.781450	−	0.577927i
$281$			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	−0.908674	−	0.417507i	$-0.862904\pi$
$283$	−4767.64	+	2752.60i	−1.00144	+	0.578181i	−0.0927647	+	0.995688i	$0.529570\pi$
$284$	−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	$-0.720365\pi$
$307$		−	8281.42i		−	1.53956i	0.638308	−	0.769781i	$-0.279635\pi$
$308$	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	0.988268	+	0.152728i	$0.0488059\pi$
$311$	3435.52	+	5950.50i	0.626401	+	1.08496i	−0.361868	+	0.932230i	$0.617861\pi$
$312$	6851.88	+	533.197i	1.24330	+	0.0967511i
$313$	−2922.40	−	1687.25i	−0.527743	−	0.304693i	0.212354	−	0.977193i	$-0.431887\pi$
$313$	−2922.40	−	1687.25i	−0.527743	−	0.304693i	−0.740097	+	0.672500i	$0.765220\pi$
$314$	−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	0.307048	−	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
$322$	−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	−0.979609	−	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
$336$	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	−0.144590	−	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	$0.190852\pi$
$349$			7358.26i			1.12859i	−0.825573	+	0.564296i	$0.809148\pi$
$350$	−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	0.714102	−	0.700041i	$-0.246835\pi$
$353$	−1652.78	−	2862.69i	−0.249202	−	0.431631i	−0.963305	+	0.268410i	$0.913502\pi$
$354$	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	0.526168	−	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
$364$	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	−0.504681	−	0.863306i	$-0.668390\pi$
$367$	−65.9242	+	38.0613i	−0.00937661	+	0.00541359i	0.495304	+	0.868720i	$0.335057\pi$
$368$	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	−0.0239900	−	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
$378$	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	−0.984606	−	0.174787i	$-0.944076\pi$
$383$	−2555.45	+	4426.17i	−0.340933	+	0.590513i	0.643673	+	0.765300i	$0.277410\pi$
$384$	−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	−0.852595	−	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
$392$	−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	0.893158	−	0.449744i	$-0.148485\pi$
$397$	7516.61	+	4339.72i	0.950247	+	0.548625i	0.0570893	+	0.998369i	$0.481818\pi$
$398$	−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	−0.128800	−	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
$406$	−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	−0.311958	−	0.950096i	$-0.600985\pi$
$409$	2935.32	−	1694.71i	0.354871	−	0.204885i	0.666828	+	0.745211i	$0.267651\pi$
$410$	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	−0.671917	−	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	$-0.943323\pi$
$433$		−	3191.67i		−	0.354230i	0.984190	−	0.177115i	$-0.0566765\pi$
$434$	−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	0.335635	−	0.941992i	$-0.391049\pi$
$439$	−2872.90	−	1658.67i	−0.312337	−	0.180328i	−0.647972	+	0.761664i	$0.724383\pi$
$440$	−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	0.906430	−	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
$448$	−15338.6	−	1743.55i	−1.61759	−	0.183873i
$449$			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
$455$	−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	−0.999384	−	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	$-0.479246\pi$
$461$	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	−0.602795	−	0.797896i	$-0.705946\pi$
$467$	3931.83	−	6810.13i	0.389600	−	0.674808i	0.992396	+	0.123088i	$0.0392798\pi$
$468$	−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	0.764379	−	0.644767i	$-0.223046\pi$
$479$	−1847.13	−	3199.33i	−0.176196	−	0.305180i	−0.940574	+	0.339588i	$0.889712\pi$
$480$	−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	0.889474	−	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
$490$	17298.4	−	5298.55i	1.59482	−	0.488498i
$491$		−	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
$497$	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	0.0461818	+	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	$-0.247168\pi$
$503$	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	−0.926428	−	0.376472i	$-0.877137\pi$
$509$	−1575.31	+	2728.52i	−0.137180	+	0.237603i	0.789248	+	0.614074i	$0.210471\pi$
$510$	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	0.951510	−	0.307618i	$-0.0995318\pi$
$521$	2489.60	+	4312.12i	0.209350	+	0.362605i	−0.742160	+	0.670223i	$0.766198\pi$
$522$	20468.0	−	25366.9i	1.71620	−	2.12697i
$523$	11977.0	+	6914.92i	1.00137	+	0.578142i	0.908654	−	0.417550i	$-0.137111\pi$
$523$	11977.0	+	6914.92i	1.00137	+	0.578142i	0.0927181	+	0.995692i	$0.470444\pi$
$524$	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	−0.952124	−	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
$546$	−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	−0.495203	−	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
$560$	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	0.783381	−	0.621542i	$-0.213493\pi$
$563$	−1958.12	−	3391.56i	−0.146581	−	0.253885i	−0.929962	+	0.367657i	$0.880160\pi$
$564$	−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	0.747336	−	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
$574$	−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	−0.0312386	−	0.999512i	$-0.509945\pi$
$577$	11347.8	−	6551.66i	0.818745	−	0.472703i	0.849983	+	0.526809i	$0.176612\pi$
$578$	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	0.141524	+	0.989935i	$0.454800\pi$
$593$	−11358.1	+	19672.8i	−0.786547	+	1.36234i	−0.928071	+	0.372404i	$0.878534\pi$
$594$	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	−0.843286	−	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	$0.0397250\pi$
$601$			3667.98i			0.248952i	−0.992223	+	0.124476i	$0.960275\pi$
$602$	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	0.249575	−	0.968355i	$-0.419709\pi$
$607$	−6942.92	−	4008.50i	−0.464258	−	0.268039i	−0.713833	+	0.700316i	$0.753042\pi$
$608$	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	0.668705	−	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
$616$	2805.27	+	6447.06i	0.183486	+	0.421688i
$617$		−	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	−0.684563	−	0.728953i	$-0.740007\pi$
$619$	−6091.73	+	3517.06i	−0.395553	+	0.228373i	0.289010	+	0.957326i	$0.406674\pi$
$620$	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	−0.211297	−	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	$-0.997128\pi$
$643$		−	294.191i		−	0.0180432i	0.999959	−	0.00902160i	$-0.00287170\pi$
$644$	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	0.959130	−	0.282965i	$-0.0913179\pi$
$647$	3859.39	+	6684.67i	0.234511	+	0.406184i	−0.724620	+	0.689149i	$0.757985\pi$
$648$	−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	0.765139	−	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
$658$	−12638.0	+	5499.07i	−0.748753	+	0.325800i
$659$			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	$-0.299829\pi$
$661$	26896.6	−	15528.7i	1.58268	−	0.913763i	0.994466	−	0.105062i	$-0.0335041\pi$
$662$	−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	−0.257066	−	0.966394i	$-0.582756\pi$
$677$	12478.3	−	21613.0i	0.708389	−	1.22697i	0.965455	−	0.260571i	$-0.0839110\pi$
$678$	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	−0.746621	−	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
$686$	−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	0.216057	−	0.976381i	$-0.430680\pi$
$691$	−9472.37	−	5468.88i	−0.521485	−	0.301079i	−0.737542	+	0.675301i	$0.764014\pi$
$692$	−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	$-0.728632\pi$
$701$		−	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
$707$	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	0.443183	+	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
$714$	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	−0.953353	−	0.301857i	$-0.902394\pi$
$719$	−4150.10	+	7188.19i	−0.215261	+	0.372843i	0.738092	+	0.674700i	$0.235727\pi$
$720$	−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	$-0.820530\pi$
$727$		−	20951.5i		−	1.06884i	0.845218	−	0.534421i	$-0.179470\pi$
$728$	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	0.618019	−	0.786163i	$-0.287935\pi$
$733$	4885.73	+	2820.78i	0.246192	+	0.142139i	−0.371827	+	0.928302i	$0.621269\pi$
$734$	−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	0.972193	−	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
$742$	44099.5	+	5012.83i	2.18186	+	0.248015i
$743$			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
$749$	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	−0.726200	−	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
$756$	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	0.464980	+	0.885321i	$0.346062\pi$
$761$	−11215.0	+	19424.9i	−0.534221	+	0.925298i	−0.999201	+	0.0399765i	$0.987272\pi$
$762$	−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	$-0.782883\pi$
$769$		−	26887.4i		−	1.26084i	0.776254	−	0.630420i	$-0.217117\pi$
$770$	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	−0.999812	−	0.0193838i	$-0.993830\pi$
$773$	−11104.6	−	19233.7i	−0.516693	−	0.894938i	0.483119	−	0.875555i	$-0.339504\pi$
$774$	−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	−0.839348	−	0.543594i	$-0.817063\pi$
$787$	−17403.2	+	10047.8i	−0.788257	+	0.455100i	0.0510919	+	0.998694i	$0.483730\pi$
$788$	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	−0.751174	−	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	$-0.968459\pi$
$811$		−	4569.51i		−	0.197851i	0.995095	−	0.0989255i	$-0.0315405\pi$
$812$	−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	−0.912948	−	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
$826$	3916.90	−	34458.3i	0.164996	−	1.45152i
$827$		−	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	−0.850887	−	0.525349i	$-0.823935\pi$
$829$	−19605.0	+	11319.0i	−0.821364	+	0.474215i	0.0295225	+	0.999564i	$0.490601\pi$
$830$	−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	$-0.655180\pi$
$853$		−	44021.1i		−	1.76700i	0.468430	−	0.883501i	$-0.344820\pi$
$854$	−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	0.845249	−	0.534373i	$-0.179452\pi$
$857$	−1007.45	−	1744.96i	−0.0401562	−	0.0695526i	−0.885405	+	0.464820i	$0.846119\pi$
$858$	−2049.21	+	26333.4i	−0.0815370	+	1.04780i
$859$	15844.5	+	9147.83i	0.629345	+	0.363353i	0.780499	−	0.625158i	$-0.214965\pi$
$859$	15844.5	+	9147.83i	0.629345	+	0.363353i	−0.151153	+	0.988510i	$0.548299\pi$
$860$	−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	0.613263	−	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
$868$	−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	−0.870013	−	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	$-0.455767\pi$
$881$	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	−0.984092	−	0.177659i	$-0.943148\pi$
$887$	−8933.98	+	15474.1i	−0.338189	+	0.585761i	0.645903	+	0.763420i	$0.276481\pi$
$888$	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	0.919820	−	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
$910$	−24328.0	−	55910.6i	−0.886225	−	2.03672i
$911$			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
$917$	−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	−0.911334	−	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
$924$	−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	−0.552073	−	0.833796i	$-0.686163\pi$
$929$	12630.2	−	21876.1i	0.446052	−	0.772585i	0.998125	+	0.0612109i	$0.0194962\pi$
$930$	−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	$0.296820\pi$
$937$			46069.3i			1.60621i	−0.595838	+	0.803105i	$0.703180\pi$
$938$	−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	0.893766	+	0.448534i	$0.148054\pi$
$941$	24112.4	+	41763.8i	0.835325	+	1.44683i	−0.0584406	+	0.998291i	$0.518613\pi$
$942$	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	0.0869787	−	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
$952$	−7706.69	+	3353.36i	−0.262369	+	0.114163i
$953$			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
$959$	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	0.0201966	+	0.999796i	$0.493571\pi$
$971$	−25892.6	+	44847.3i	−0.855750	+	1.48220i	−0.875947	+	0.482407i	$0.839763\pi$
$972$	−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	−0.0356703	−	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
$980$	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	−0.963605	−	0.267330i	$-0.913859\pi$
$983$	−21984.3	−	38077.9i	−0.713317	−	1.23550i	0.250288	−	0.968171i	$-0.419475\pi$
$984$	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	0.961536	−	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
$994$	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	−0.829152	−	0.559023i	$-0.811176\pi$
$997$	−23912.6	+	13806.0i	−0.759599	+	0.438555i	0.0695525	+	0.997578i	$0.477843\pi$
$998$	−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.5.6	yes	12
3.2	odd	2	inner	21.4.g.a.5.1	✓	12
4.3	odd	2		336.4.bc.d.257.6		12
7.2	even	3		147.4.c.a.146.2		12
7.3	odd	6	inner	21.4.g.a.17.1	yes	12
7.4	even	3		147.4.g.d.80.1		12
7.5	odd	6		147.4.c.a.146.1		12
7.6	odd	2		147.4.g.d.68.6		12
12.11	even	2		336.4.bc.d.257.4		12
21.2	odd	6		147.4.c.a.146.11		12
21.5	even	6		147.4.c.a.146.12		12
21.11	odd	6		147.4.g.d.80.6		12
21.17	even	6	inner	21.4.g.a.17.6	yes	12
21.20	even	2		147.4.g.d.68.1		12
28.3	even	6		336.4.bc.d.17.4		12
84.59	odd	6		336.4.bc.d.17.6		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
21.4.g.a.5.1	✓	12	3.2	odd	2	inner
21.4.g.a.5.6	yes	12	1.1	even	1	trivial
21.4.g.a.17.1	yes	12	7.3	odd	6	inner
21.4.g.a.17.6	yes	12	21.17	even	6	inner
147.4.c.a.146.1		12	7.5	odd	6
147.4.c.a.146.2		12	7.2	even	3
147.4.c.a.146.11		12	21.2	odd	6
147.4.c.a.146.12		12	21.5	even	6
147.4.g.d.68.1		12	21.20	even	2
147.4.g.d.68.6		12	7.6	odd	2
147.4.g.d.80.1		12	7.4	even	3
147.4.g.d.80.6		12	21.11	odd	6
336.4.bc.d.17.4		12	28.3	even	6
336.4.bc.d.17.6		12	84.59	odd	6
336.4.bc.d.257.4		12	12.11	even	2
336.4.bc.d.257.6		12	4.3	odd	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:	\( N \)	\(=\)	\( 21 = 3 \cdot 7 \)
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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