LMFDB - Embedded newform 21.4.g.a.17.1

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			17.1
Root			$2.70662 - 1.29391i$ of defining polynomial
Character	$\chi$	$=$	21.17
Dual form			21.4.g.a.5.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-3.93653 + 2.27276i) q^{2} +(-2.24112 - 4.68800i) q^{3} +(6.33084 - 10.9653i) q^{4} +(-5.80193 - 10.0492i) q^{5} +(19.4769 + 13.3609i) q^{6} +(-18.4018 + 2.09174i) q^{7} +21.1897i q^{8} +(-16.9548 + 21.0128i) q^{9} +O(q^{10})$	\(q+(-3.93653 + 2.27276i) q^{2} +(-2.24112 - 4.68800i) 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} +(-16.9548 + 21.0128i) q^{9} +(45.6790 + 26.3728i) q^{10} +(15.5157 + 8.95800i) q^{11} +(-65.5937 - 5.10435i) 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} +(18.9860 - 121.251i) q^{18} +(9.50747 - 5.48914i) q^{19} -146.925 q^{20} +(51.0467 + 81.5796i) q^{21} -81.4374 q^{22} +(-59.8367 + 34.5467i) q^{23} +(99.3376 - 47.4888i) 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} +(21.2635 - 273.248i) q^{30} +(8.85795 + 5.11414i) q^{31} +(-166.392 - 96.0665i) q^{32} +(7.22254 - 92.8136i) 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} +(-292.618 + 139.887i) q^{39} +(212.941 - 122.941i) q^{40} -31.0035 q^{41} +(-386.357 - 205.124i) q^{42} -224.550 q^{43} +(196.455 - 113.423i) q^{44} +(309.533 + 48.4678i) 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} +(-110.948 - 8.63368i) q^{51} +(-684.440 - 395.161i) q^{52} +(456.586 + 263.610i) q^{53} +(-610.977 + 182.733i) 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} +(329.276 + 688.783i) q^{60} +(223.807 - 129.215i) q^{61} -46.4928 q^{62} +(268.044 - 422.137i) q^{63} +833.541 q^{64} +(-627.258 + 362.148i) q^{65} +(182.511 + 381.779i) 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} +(-445.255 - 359.267i) q^{72} +(-486.879 - 281.100i) q^{73} +(163.962 + 94.6635i) q^{74} +(49.9907 + 3.89016i) 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} +(-154.073 - 712.532i) q^{81} +(122.046 - 70.4635i) q^{82} +448.767 q^{83} +(1217.72 - 43.2763i) q^{84} -248.513 q^{85} +(883.949 - 510.348i) q^{86} +(-1245.05 + 595.204i) 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} +(4.12336 - 52.9875i) q^{93} +(644.484 + 372.093i) q^{94} +(-110.323 - 63.6953i) q^{95} +(-77.4553 + 995.343i) 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	−0.993512	−	0.113731i	$-0.963720\pi$
$2$	−3.93653	+	2.27276i	−1.39177	+	0.803541i	−0.398262	+	0.917272i	$0.630386\pi$
$3$	−2.24112	−	4.68800i	−0.431304	−	0.902207i
$3$	−2.24112	−	4.68800i	−0.431304	−	0.902207i
$4$	6.33084	−	10.9653i	0.791355	−	1.37067i
$5$	−5.80193	−	10.0492i	−0.518941	−	0.898832i	−0.999758	−	0.0220109i	$-0.992993\pi$
$5$	−5.80193	−	10.0492i	−0.518941	−	0.898832i	0.480817	−	0.876821i	$-0.340340\pi$
$6$	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
$9$	−16.9548	+	21.0128i	−0.627954	+	0.778251i
$10$	45.6790	+	26.3728i	1.44450	+	0.833980i
$11$	15.5157	+	8.95800i	0.425287	+	0.245540i	0.697337	−	0.716743i	$-0.254368\pi$
$11$	15.5157	+	8.95800i	0.425287	+	0.245540i	−0.272050	+	0.962283i	$0.587701\pi$
$12$	−65.5937	−	5.10435i	−1.57794	−	0.122792i
$13$		−	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	−0.779474	−	0.626435i	$-0.784513\pi$
$17$	10.7082	−	18.5472i	0.152772	−	0.264609i	0.932245	+	0.361826i	$0.117847\pi$
$18$	18.9860	−	121.251i	0.248613	−	1.58773i
$19$	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
$21$	51.0467	+	81.5796i	0.530443	+	0.847721i
$22$	−81.4374			−0.789205
$23$	−59.8367	+	34.5467i	−0.542470	+	0.313195i	−0.746079	−	0.665857i	$-0.768066\pi$
$23$	−59.8367	+	34.5467i	−0.542470	+	0.313195i	0.203609	+	0.979052i	$0.434733\pi$
$24$	99.3376	−	47.4888i	0.844883	−	0.403900i
$25$	−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	$-0.323581\pi$
$30$	21.2635	−	273.248i	0.129406	−	1.66293i
$31$	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
$33$	7.22254	−	92.8136i	0.0380995	−	0.489599i
$34$			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
$39$	−292.618	+	139.887i	−1.20145	+	0.574356i
$40$	212.941	−	122.941i	0.841723	−	0.485969i
$41$	−31.0035			−0.118096			−0.0590480	−	0.998255i	$-0.518807\pi$
$41$	−31.0035			−0.118096			−0.0590480	+	0.998255i	$0.518807\pi$
$42$	−386.357	−	205.124i	−1.41943	−	0.753603i
$43$	−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
$45$	309.533	+	48.4678i	1.02539	+	0.160559i
$46$	157.033	−	271.988i	0.503330	−	0.871793i
$47$	−81.8595	−	141.785i	−0.254052	−	0.440031i	0.710586	−	0.703611i	$-0.248430\pi$
$47$	−81.8595	−	141.785i	−0.254052	−	0.440031i	−0.964638	+	0.263580i	$0.915097\pi$
$48$	14.6241	−	21.3182i	0.0439750	−	0.0641046i
$49$	334.249	−	76.9836i	0.974487	−	0.224442i
$50$		−	43.8633i		−	0.124064i
$51$	−110.948	−	8.63368i	−0.304623	−	0.0237050i
$52$	−684.440	−	395.161i	−1.82528	−	1.05383i
$53$	456.586	+	263.610i	1.18334	+	0.683200i	0.956784	−	0.290799i	$-0.0939211\pi$
$53$	456.586	+	263.610i	1.18334	+	0.683200i	0.226553	+	0.973999i	$0.427254\pi$
$54$	−610.977	+	182.733i	−1.53969	+	0.460496i
$55$		−	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	$-0.983519\pi$
$59$	−205.978	+	356.765i	−0.454510	+	0.787234i	0.544150	+	0.838988i	$0.316852\pi$
$60$	329.276	+	688.783i	0.708488	+	1.48202i
$61$	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
$63$	268.044	−	422.137i	0.536037	−	0.844194i
$64$	833.541			1.62801
$65$	−627.258	+	362.148i	−1.19695	+	0.691060i
$66$	182.511	+	381.779i	0.340387	+	0.712026i
$67$	−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	$0.0120860\pi$
$71$			45.4199i			0.0759205i	−0.999279	+	0.0379603i	$0.987914\pi$
$72$	−445.255	−	359.267i	−0.728803	−	0.588056i
$73$	−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
$75$	49.9907	+	3.89016i	0.0769657	+	0.00598929i
$76$		−	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
$81$	−154.073	−	712.532i	−0.211348	−	0.977411i
$82$	122.046	−	70.4635i	0.164363	−	0.0948950i
$83$	448.767			0.593477			0.296738	−	0.954959i	$-0.404101\pi$
$83$	448.767			0.593477			0.296738	+	0.954959i	$0.404101\pi$
$84$	1217.72	−	43.2763i	1.58171	−	0.0562123i
$85$	−248.513			−0.317118
$86$	883.949	−	510.348i	1.10836	−	0.639910i
$87$	−1245.05	+	595.204i	−1.53430	+	0.733478i
$88$	−189.818	+	328.774i	−0.229939	+	0.398266i
$89$	−280.814	−	486.384i	−0.334452	−	0.579288i	0.648927	−	0.760850i	$-0.275218\pi$
$89$	−280.814	−	486.384i	−0.334452	−	0.579288i	−0.983379	+	0.181562i	$0.941885\pi$
$90$	−1328.64	+	512.698i	−1.55612	+	0.600479i
$91$	130.563	+	1148.61i	0.150404	+	1.32315i
$92$			874.839i			0.991394i
$93$	4.12336	−	52.9875i	0.00459756	−	0.0590811i
$94$	644.484	+	372.093i	0.707165	+	0.408282i
$95$	−110.323	−	63.6953i	−0.119147	−	0.0687895i
$96$	−77.4553	+	995.343i	−0.0823463	+	1.05820i
$97$			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	$-0.512265\pi$
$101$	858.845	−	1487.56i	0.846122	−	1.46553i	0.884644	−	0.466268i	$-0.154402\pi$
$102$	456.370	−	218.170i	0.443014	−	0.211785i
$103$	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
$105$	523.644	−	986.300i	0.486690	−	0.916696i
$106$	−2396.48			−2.19592
$107$	1054.64	−	608.897i	0.952859	−	0.550134i	0.0588912	−	0.998264i	$-0.481243\pi$
$107$	1054.64	−	608.897i	0.952859	−	0.550134i	0.893968	+	0.448131i	$0.147910\pi$
$108$	1219.38	−	1291.76i	1.08644	−	1.15093i
$109$	−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	$0.204239\pi$
$113$			1437.86i			1.19701i	−0.801118	+	0.598506i	$0.795761\pi$
$114$	258.517	+	20.1172i	0.212389	+	0.0165276i
$115$	694.337	+	400.876i	0.563019	+	0.325059i
$116$	−2912.21	−	1681.37i	−2.33096	−	1.34578i
$117$	1311.58	+	1058.29i	1.03638	+	0.836230i
$118$		−	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
$123$	69.4827	+	145.345i	0.0509353	+	0.106547i
$124$	112.157	−	64.7536i	0.0812254	−	0.0468955i
$125$	−1338.51			−0.957759
$126$	−95.7483	+	2270.95i	−0.0676979	+	1.60565i
$127$	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
$129$	503.244	+	1052.69i	0.343474	+	0.718484i
$130$	1646.15	−	2851.21i	1.11059	−	1.92360i
$131$	−801.637	−	1388.48i	−0.534651	−	0.926043i	−0.999180	−	0.0404852i	$-0.987110\pi$
$131$	−801.637	−	1388.48i	−0.534651	−	0.926043i	0.464529	−	0.885558i	$-0.346224\pi$
$132$	−972.008	−	666.786i	−0.640928	−	0.439669i
$133$	−163.472	+	120.897i	−0.106578	+	0.0788203i
$134$		−	1470.36i		−	0.947906i
$135$	−466.484	−	1559.71i	−0.297396	−	0.994361i
$136$	393.010	+	226.904i	0.247796	+	0.143065i
$137$	2007.90	+	1159.26i	1.25216	+	0.722938i	0.971539	−	0.236879i	$-0.0761246\pi$
$137$	2007.90	+	1159.26i	1.25216	+	0.722938i	0.280626	+	0.959817i	$0.409458\pi$
$138$	−1627.01	−	126.610i	−1.00363	−	0.0780998i
$139$			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
$144$	−132.714	−	20.7809i	−0.0768022	−	0.0120260i
$145$	−2668.91	+	1540.90i	−1.52856	+	0.882514i
$146$	2555.48			1.44858
$147$	−1109.99	−	1394.43i	−0.622793	−	0.782386i
$148$	−527.377			−0.292906
$149$	−1126.68	+	650.488i	−0.619470	+	0.357651i	−0.776663	−	0.629917i	$-0.783089\pi$
$149$	−1126.68	+	650.488i	−0.619470	+	0.357651i	0.157193	+	0.987568i	$0.449756\pi$
$150$	−205.631	+	98.3029i	−0.111931	+	0.0535093i
$151$	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
$156$	−318.606	+	4094.26i	−0.163518	+	2.10130i
$157$	−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
$159$	212.540	−	2731.26i	0.106010	−	1.36228i
$160$			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
$165$	−974.612	+	465.918i	−0.459839	+	0.219828i
$166$	−1766.58	+	1019.94i	−0.825985	+	0.476883i
$167$	−3767.97			−1.74595			−0.872977	−	0.487761i	$-0.837814\pi$
$167$	−3767.97			−1.74595			−0.872977	+	0.487761i	$0.837814\pi$
$168$	−1728.65	+	1081.67i	−0.793859	+	0.496740i
$169$	−1699.06			−0.773356
$170$	978.280	−	564.810i	0.441357	−	0.254817i
$171$	−45.8548	+	292.845i	−0.0205064	+	0.130962i
$172$	−1421.59	+	2462.27i	−0.630206	+	1.09155i
$173$	1196.53	+	2072.45i	0.525841	+	0.910783i	0.999547	+	0.0301000i	$0.00958257\pi$
$173$	1196.53	+	2072.45i	0.525841	+	0.910783i	−0.473706	+	0.880683i	$0.657084\pi$
$174$	3548.44	−	5172.74i	1.54602	−	2.25371i
$175$	71.3059	−	163.875i	0.0308013	−	0.0707875i
$176$			89.1363i			0.0381756i
$177$	2134.14	+	166.074i	0.906280	+	0.0705246i
$178$	2210.87	+	1276.44i	0.930963	+	0.537492i
$179$	554.381	+	320.072i	0.231488	+	0.133650i	0.611258	−	0.791431i	$-0.290664\pi$
$179$	554.381	+	320.072i	0.231488	+	0.133650i	−0.379770	+	0.925081i	$0.623997\pi$
$180$	2491.07	−	3087.29i	1.03152	−	1.27841i
$181$		−	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
$186$	104.196	+	217.958i	0.0410753	+	0.0859219i
$187$	332.291	−	191.848i	0.129944	−	0.0750231i
$188$	−2072.96			−0.804181
$189$	−2579.70	−	310.531i	−0.992833	−	0.119512i
$190$	579.056			0.221101
$191$	−1261.85	+	728.530i	−0.478033	+	0.275993i	−0.719597	−	0.694392i	$-0.755673\pi$
$191$	−1261.85	+	728.530i	−0.478033	+	0.275993i	0.241563	+	0.970385i	$0.422340\pi$
$192$	−1868.07	−	3907.64i	−0.702167	−	1.46880i
$193$	−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	$-0.961852\pi$
$197$		−	661.168i		−	0.239118i	0.992827	−	0.119559i	$-0.0381481\pi$
$198$	1380.75	−	1711.22i	0.495584	−	0.614199i
$199$	−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
$201$	1675.76	+	130.403i	0.588053	+	0.0457609i
$202$			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
$207$	288.594	−	1843.06i	0.0969017	−	0.618850i
$208$	268.941	−	155.273i	0.0896525	−	0.0517609i
$209$	196.687			0.0650963
$210$	180.279	+	5072.72i	0.0592401	+	1.66691i
$211$	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
$213$	212.929	−	101.792i	0.0684960	−	0.0327448i
$214$	−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
$219$	−226.642	+	2912.47i	−0.0699316	+	0.898659i
$220$	−2279.64	−	1316.15i	−0.698605	−	0.403340i
$221$	−1157.68	−	668.390i	−0.352372	−	0.203442i
$222$	76.3241	−	980.807i	0.0230745	−	0.296520i
$223$		−	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	−0.614826	−	0.788663i	$-0.710774\pi$
$227$	1284.55	−	2224.91i	0.375589	−	0.650540i	0.990415	+	0.138123i	$0.0441070\pi$
$228$	−651.649	+	311.524i	−0.189283	+	0.0904876i
$229$	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
$231$	61.2350	+	1723.04i	0.0174414	+	0.490770i
$232$	5627.64			1.59255
$233$	2273.94	−	1312.86i	0.639360	−	0.369135i	−0.145008	−	0.989431i	$-0.546321\pi$
$233$	2273.94	−	1312.86i	0.639360	−	0.369135i	0.784368	+	0.620296i	$0.212987\pi$
$234$	−7568.32	−	1185.08i	−2.11435	−	0.331072i
$235$	−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	$-0.307635\pi$
$240$	−299.080	−	23.2737i	−0.0804397	−	0.00625963i
$241$	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
$243$	−2995.06	+	2319.17i	−0.790671	+	0.612241i
$244$		−	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
$249$	−1005.74	−	2103.82i	−0.255969	−	0.535439i
$250$	5269.08	−	3042.10i	1.33298	−	0.769598i
$251$	5967.85			1.50075			0.750373	−	0.661015i	$-0.229874\pi$
$251$	5967.85			1.50075			0.750373	+	0.661015i	$0.229874\pi$
$252$	−2931.93	−	5611.67i	−0.732914	−	1.40279i
$253$	−1237.88			−0.307607
$254$	−10574.8	+	6105.36i	−2.61229	+	1.50821i
$255$	556.948	+	1165.03i	0.136774	+	0.286106i
$256$	1783.64	−	3089.36i	0.435460	−	0.754239i
$257$	−2819.70	−	4883.86i	−0.684389	−	1.18540i	−0.973628	−	0.228140i	$-0.926736\pi$
$257$	−2819.70	−	4883.86i	−0.684389	−	1.18540i	0.289239	−	0.957257i	$-0.406598\pi$
$258$	−4373.55	−	3000.20i	−1.05537	−	0.723971i
$259$	458.681	+	620.211i	0.110043	+	0.148796i
$260$			9170.80i			2.18750i
$261$	5580.64	+	4502.90i	1.32350	+	1.06790i
$262$	6311.33	+	3643.85i	1.48823	+	0.859228i
$263$	−3018.63	−	1742.81i	−0.707745	−	0.408617i	0.102480	−	0.994735i	$-0.467322\pi$
$263$	−3018.63	−	1742.81i	−0.707745	−	0.408617i	−0.810226	+	0.586118i	$0.800655\pi$
$264$	1966.70	+	153.044i	0.458492	+	0.0356788i
$265$		−	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	$-0.974831\pi$
$269$	−1897.28	+	3286.18i	−0.430033	+	0.744839i	0.566842	+	0.823826i	$0.308165\pi$
$270$	5381.17	+	5079.65i	1.21292	+	1.14495i
$271$	−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
$273$	5092.07	−	3186.25i	1.12889	−	0.706377i
$274$	−10538.9			−2.32364
$275$	−149.723	+	86.4428i	−0.0328315	+	0.0189553i
$276$	4101.25	−	1960.62i	0.894443	−	0.427592i
$277$	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	$0.0947185\pi$
$281$			2762.14i			0.586390i	−0.956053	+	0.293195i	$0.905281\pi$
$282$	300.007	−	3855.25i	0.0633516	−	0.814102i
$283$	−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
$285$	−51.3554	+	659.946i	−0.0106738	+	0.137164i
$286$			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
$291$	1004.94	−	480.415i	0.202442	−	0.0967781i
$292$	−6164.71	+	3559.20i	−1.23549	+	0.713309i
$293$	4101.08			0.817705			0.408853	−	0.912600i	$-0.365929\pi$
$293$	4101.08			0.817705			0.408853	+	0.912600i	$0.365929\pi$
$294$	7538.72	+	2966.48i	1.49547	+	0.588465i
$295$	4780.29			0.943455
$296$	764.339	−	441.291i	0.150089	−	0.0866538i
$297$	1827.82	+	1725.40i	0.357106	+	0.337097i
$298$	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
$303$	−8898.48	−	692.459i	−1.68714	−	0.131290i
$304$	47.3019	+	27.3098i	0.00892418	+	0.00515238i
$305$	−2597.03	−	1499.40i	−0.487560	−	0.281493i
$306$	−2045.56	−	1650.52i	−0.382147	−	0.308346i
$307$			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	$0.382139\pi$
$311$	−3435.52	+	5950.50i	−0.626401	+	1.08496i	−0.988268	+	0.152728i	$0.951194\pi$
$312$	−2964.18	−	6200.50i	−0.537864	−	1.12511i
$313$	−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
$315$	−5797.33	−	244.428i	−1.03696	−	0.0437205i
$316$	−3662.02			−0.651914
$317$	2052.28	−	1184.88i	0.363620	−	0.209936i	−0.307048	−	0.951694i	$-0.599341\pi$
$317$	2052.28	−	1184.88i	0.363620	−	0.209936i	0.670667	+	0.741758i	$0.266008\pi$
$318$	5370.81	+	11234.7i	0.947107	+	1.98117i
$319$	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
$324$	−8788.57	−	2821.47i	−1.50696	−	0.483791i
$325$	521.629	+	301.163i	0.0890300	+	0.0514015i
$326$	−2039.74	−	1177.65i	−0.346536	−	0.200073i
$327$	6725.64	+	523.374i	1.13740	+	0.0885096i
$328$		−	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
$333$	1111.05	+	173.972i	0.182838	+	0.0286295i
$334$	14832.7	−	8563.68i	2.42997	−	1.40295i
$335$	3753.55			0.612175
$336$	−224.516	+	422.883i	−0.0364534	+	0.0686612i
$337$	−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
$339$	6740.69	−	3222.42i	1.07995	−	0.516276i
$340$	−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
$345$	323.213	−	4153.46i	0.0504383	−	0.648159i
$346$	−9420.35	−	5438.84i	−1.46370	−	0.845069i
$347$	−4137.14	−	2388.58i	−0.640039	−	0.369527i	0.144590	−	0.989492i	$-0.453814\pi$
$347$	−4137.14	−	2388.58i	−0.640039	−	0.369527i	−0.784630	+	0.619965i	$0.787147\pi$
$348$	−1355.63	+	17420.6i	−0.208820	+	2.68345i
$349$		−	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	−0.714102	−	0.700041i	$-0.753165\pi$
$353$	1652.78	−	2862.69i	0.249202	−	0.431631i	0.963305	+	0.268410i	$0.0864982\pi$
$354$	−8778.54	+	4196.62i	−1.31801	+	0.630078i
$355$	456.436	−	263.524i	0.0682398	−	0.0393982i
$356$	−7111.16			−1.05868
$357$	2059.69	−	73.1991i	0.305351	−	0.0108518i
$358$	−2909.78			−0.429572
$359$	−359.154	+	207.358i	−0.0528006	+	0.0304845i	−0.526168	−	0.850381i	$-0.676372\pi$
$359$	−359.154	+	207.358i	−0.0528006	+	0.0304845i	0.473367	+	0.880865i	$0.343038\pi$
$360$	−1027.02	+	6558.92i	−0.150357	+	0.960237i
$361$	−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
$366$	6085.52	+	473.561i	0.869113	+	0.0676323i
$367$	−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
$369$	525.657	−	651.470i	0.0741588	−	0.0919083i
$370$		−	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
$375$	2999.76	+	6274.93i	0.413085	+	0.864096i
$376$	3004.38	−	1734.58i	0.412072	−	0.237910i
$377$	−16577.3			−2.26465
$378$	10860.8	−	4640.61i	1.47783	−	0.631448i
$379$	−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
$381$	−6020.38	−	12593.5i	−0.809536	−	1.69340i
$382$	3311.54	−	5735.76i	0.443543	−	0.768239i
$383$	2555.45	+	4426.17i	0.340933	+	0.590513i	0.984606	−	0.174787i	$-0.0559237\pi$
$383$	2555.45	+	4426.17i	0.340933	+	0.590513i	−0.643673	+	0.765300i	$0.722590\pi$
$384$	9648.70	+	6618.89i	1.28225	+	0.879606i
$385$	434.863	+	3825.63i	0.0575654	+	0.506421i
$386$		−	8314.95i		−	1.09642i
$387$	3807.19	−	4718.42i	0.500079	−	0.619770i
$388$	2350.57	+	1357.10i	0.307557	+	0.177568i
$389$	6339.84	+	3660.31i	0.826331	+	0.477083i	0.852595	−	0.522572i	$-0.175028\pi$
$389$	6339.84	+	3660.31i	0.826331	+	0.477083i	−0.0262636	+	0.999655i	$0.508361\pi$
$390$	−17055.7	−	1327.24i	−2.21448	−	0.172326i
$391$			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
$396$	−947.507	+	6051.13i	−0.120237	+	0.767880i
$397$	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
$399$	933.127	+	495.414i	0.117080	+	0.0621597i
$400$	−48.0100			−0.00600125
$401$	8447.68	−	4877.27i	1.05201	−	0.607379i	0.128800	−	0.991671i	$-0.458887\pi$
$401$	8447.68	−	4877.27i	1.05201	−	0.607379i	0.923212	+	0.384291i	$0.125554\pi$
$402$	−6893.03	+	3295.25i	−0.855207	+	0.408836i
$403$	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
$408$	182.945	−	2350.95i	0.0221989	−	0.285268i
$409$	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
$411$	934.676	−	12011.1i	0.112176	−	1.44152i
$412$		−	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
$417$	8633.30	−	4127.19i	1.01385	−	0.484675i
$418$	−774.264	+	447.021i	−0.0905992	+	0.0523075i
$419$	12777.4			1.48977			0.744887	−	0.667191i	$-0.232504\pi$
$419$	12777.4			1.48977			0.744887	+	0.667191i	$0.232504\pi$
$420$	−7500.01	−	11986.0i	−0.871340	−	1.39252i
$421$	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
$423$	4367.20	+	683.831i	0.501987	+	0.0786029i
$424$	−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
$429$	−5793.28	−	450.820i	−0.651987	−	0.0507361i
$430$	−10257.2	−	5922.01i	−1.15034	−	0.664151i
$431$	3279.13	+	1893.21i	0.366474	+	0.211584i	0.671917	−	0.740627i	$-0.265471\pi$
$431$	3279.13	+	1893.21i	0.366474	+	0.211584i	−0.305443	+	0.952210i	$0.598805\pi$
$432$	200.008	+	668.737i	0.0222752	+	0.0744783i
$433$			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
$438$	−5727.15	−	11980.1i	−0.624780	−	1.30692i
$439$	−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
$441$	−4049.47	+	8328.74i	−0.437261	+	0.899335i
$442$	6076.35			0.653897
$443$	−9266.95	+	5350.27i	−0.993873	+	0.573813i	−0.906430	−	0.422356i	$-0.861203\pi$
$443$	−9266.95	+	5350.27i	−0.993873	+	0.573813i	−0.0874435	+	0.996169i	$0.527870\pi$
$444$	1181.92	+	2472.35i	0.126332	+	0.264262i
$445$	−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	$0.932278\pi$
$450$	921.688	+	743.691i	0.0965529	+	0.0779065i
$451$	−481.042	−	277.729i	−0.0502248	−	0.0289973i
$452$	15766.6	+	9102.86i	1.64071	+	0.947262i
$453$	−13554.7	−	1054.79i	−1.40586	−	0.109401i
$454$			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
$459$	2062.51	−	2184.93i	0.209737	−	0.222187i
$460$	8791.47	−	5075.76i	0.891097	−	0.514475i
$461$	−1289.80			−0.130308			−0.0651542	−	0.997875i	$-0.520754\pi$
$461$	−1289.80			−0.130308			−0.0651542	+	0.997875i	$0.520754\pi$
$462$	−4157.11	−	6643.63i	−0.418628	−	0.669025i
$463$	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
$465$	−556.408	+	265.993i	−0.0554899	+	0.0265272i
$466$	−5967.63	+	10336.2i	−0.593230	+	1.02750i
$467$	−3931.83	−	6810.13i	−0.389600	−	0.674808i	0.602795	−	0.797896i	$-0.294054\pi$
$467$	−3931.83	−	6810.13i	−0.389600	−	0.674808i	−0.992396	+	0.123088i	$0.960720\pi$
$468$	19907.9	−	7682.11i	1.96633	−	0.758772i
$469$	2390.27	−	5493.32i	0.235336	−	0.540849i
$470$		−	8635.44i		−	0.847496i
$471$	−376.996	+	4844.61i	−0.0368813	+	0.473944i
$472$	−7559.75	−	4364.63i	−0.737216	−	0.425632i
$473$	−3484.06	−	2011.52i	−0.338683	−	0.195539i
$474$	529.983	−	6810.57i	0.0513564	−	0.659958i
$475$			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	$-0.776954\pi$
$479$	1847.13	−	3199.33i	0.176196	−	0.305180i	0.940574	+	0.339588i	$0.110288\pi$
$480$	10451.8	−	4996.55i	0.993873	−	0.475125i
$481$	−2251.51	+	1299.91i	−0.213430	+	0.123224i
$482$	−21040.7			−1.98833
$483$	−5872.77	−	3117.96i	−0.553251	−	0.293731i
$484$	−12788.5			−1.20103
$485$	2154.19	−	1243.72i	0.201684	−	0.116442i
$486$	6519.24	−	15936.5i	0.608475	−	1.48744i
$487$	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	$-0.965138\pi$
$491$		−	2378.40i		−	0.218607i	0.994008	−	0.109303i	$-0.0348620\pi$
$492$	2033.64	+	158.253i	0.186348	+	0.0145012i
$493$	−4925.81	−	2843.92i	−0.449995	−	0.259805i
$494$	2697.50	+	1557.40i	0.245680	+	0.141844i
$495$	4368.45	+	3524.81i	0.396661	+	0.320057i
$496$			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
$501$	8444.48	+	17664.3i	0.753037	+	1.57521i
$502$	−23492.6	+	13563.5i	−2.08870	+	1.20591i
$503$	−16095.2			−1.42674			−0.713370	−	0.700788i	$-0.752832\pi$
$503$	−16095.2			−1.42674			−0.713370	+	0.700788i	$0.752832\pi$
$504$	8944.97	+	5679.78i	0.790557	+	0.501979i
$505$	−19931.9			−1.75635
$506$	4872.94	−	2813.39i	0.428120	−	0.247175i
$507$	3807.81	+	7965.21i	0.333552	+	0.697727i
$508$	17006.7	−	29456.5i	1.48533	−	2.57267i
$509$	1575.31	+	2728.52i	0.137180	+	0.237603i	0.926428	−	0.376472i	$-0.122863\pi$
$509$	1575.31	+	2728.52i	0.137180	+	0.237603i	−0.789248	+	0.614074i	$0.789529\pi$
$510$	−4840.28	−	3320.37i	−0.420257	−	0.288291i
$511$	9547.42	+	4154.30i	0.826522	+	0.359639i
$512$		−	1799.30i		−	0.155310i
$513$	1475.63	−	441.335i	0.126999	−	0.0379832i
$514$	22199.7	+	12817.0i	1.90503	+	1.09987i
$515$	−11634.1	−	6716.95i	−0.995456	−	0.574727i
$516$	14729.1	+	1146.18i	1.25661	+	0.0977867i
$517$		−	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	$-0.900468\pi$
$521$	−2489.60	+	4312.12i	−0.209350	+	0.362605i	0.742160	+	0.670223i	$0.233802\pi$
$522$	−32202.3	−	5042.36i	−2.70011	−	0.422793i
$523$	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
$525$	−928.053	+	32.9820i	−0.0771496	+	0.00274181i
$526$	15843.9			1.31336
$527$	189.705	−	109.526i	0.0156806	−	0.00905322i
$528$	417.871	−	199.765i	0.0344423	−	0.0164653i
$529$	−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
$534$	1029.15	−	13225.2i	0.0834005	−	1.07174i
$535$	−12237.9	−	7065.56i	−0.988955	−	0.570973i
$536$	−5936.03	−	3427.17i	−0.478353	−	0.276177i
$537$	258.064	−	3316.26i	0.0207379	−	0.266494i
$538$		−	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
$543$	−19708.6	+	9421.79i	−1.55760	+	0.744618i
$544$	−3563.52	+	2057.40i	−0.280854	+	0.162151i
$545$	15064.9			1.18405
$546$	−12803.5	+	24115.8i	−1.00355	+	1.89022i
$547$	−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
$549$	−1079.43	+	6893.63i	−0.0839142	+	0.535907i
$550$	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
$555$	2503.82	+	194.842i	0.191498	+	0.0149019i
$556$	20193.5	+	11658.7i	1.54028	+	0.889279i
$557$	−125.920	−	72.6999i	−0.00957881	−	0.00553033i	0.495203	−	0.868777i	$-0.335094\pi$
$557$	−125.920	−	72.6999i	−0.00957881	−	0.00553033i	−0.504782	+	0.863247i	$0.668427\pi$
$558$	788.273	−	976.941i	0.0598033	−	0.0741169i
$559$			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	$-0.786507\pi$
$563$	1958.12	−	3391.56i	0.146581	−	0.253885i	0.929962	+	0.367657i	$0.119840\pi$
$564$	4645.75	+	9718.03i	0.346846	+	0.725537i
$565$	14449.4	−	8342.36i	1.07591	−	0.621178i
$566$	25024.0			1.85837
$567$	4325.65	+	12789.6i	0.320388	+	0.947286i
$568$	−962.437			−0.0710968
$569$	−7404.97	+	4275.26i	−0.545576	+	0.314988i	−0.747336	−	0.664447i	$-0.768667\pi$
$569$	−7404.97	+	4275.26i	−0.545576	+	0.314988i	0.201760	+	0.979435i	$0.435334\pi$
$570$	−1297.73	−	2714.61i	−0.0953616	−	0.199478i
$571$	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
$576$	−14132.5	+	17515.0i	−1.02231	+	1.26700i
$577$	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
$579$	9476.49	+	737.439i	0.680189	+	0.0529307i
$580$			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
$585$	3025.28	−	19320.6i	0.213812	−	1.36548i
$586$	−16144.0	+	9320.76i	−1.13806	+	0.657059i
$587$	18034.7			1.26809			0.634047	−	0.773294i	$-0.281392\pi$
$587$	18034.7			1.26809			0.634047	+	0.773294i	$0.281392\pi$
$588$	−22317.6	+	3343.51i	−1.56524	+	0.234497i
$589$	112.289			0.00785532
$590$	−18817.7	+	10864.4i	−1.31308	+	0.758104i
$591$	−3099.56	+	1481.76i	−0.215734	+	0.103133i
$592$	103.613	−	179.463i	0.00719335	−	0.0124592i
$593$	11358.1	+	19672.8i	0.786547	+	1.36234i	0.928071	+	0.372404i	$0.121466\pi$
$593$	11358.1	+	19672.8i	0.786547	+	1.36234i	−0.141524	+	0.989935i	$0.545200\pi$
$594$	−11116.7	−	2637.90i	−0.767882	−	0.182213i
$595$	4573.08	−	519.826i	0.315089	−	0.0358165i
$596$			16472.5i			1.13212i
$597$	−785.759	+	10097.4i	−0.0538677	+	0.692229i
$598$	−16977.1	−	9801.73i	−1.16094	−	0.670272i
$599$	11720.4	+	6766.78i	0.799471	+	0.461575i	0.843286	−	0.537465i	$-0.180618\pi$
$599$	11720.4	+	6766.78i	0.799471	+	0.461575i	−0.0438153	+	0.999040i	$0.513951\pi$
$600$	−82.4314	+	1059.29i	−0.00560875	+	0.0720755i
$601$		−	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
$606$	36602.9	−	17498.2i	2.45362	−	1.17296i
$607$	−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
$609$	21666.2	−	13557.1i	1.44164	−	0.902074i
$610$	13631.1			0.904763
$611$	−8849.99	+	5109.54i	−0.585977	+	0.338314i
$612$	7233.39	+	1132.63i	0.477766	+	0.0748103i
$613$	−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	$-0.906153\pi$
$617$		−	8906.76i		−	0.581155i	0.956851	−	0.290578i	$-0.0938474\pi$
$618$	27261.7	+	2121.44i	1.77448	+	0.138086i
$619$	−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
$621$	−9287.07	+	2777.60i	−0.600124	+	0.179487i
$622$		−	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
$627$	−440.799	−	922.069i	−0.0280763	−	0.0587303i
$628$	−10254.4	+	5920.38i	−0.651584	+	0.376192i
$629$	−892.024			−0.0565458
$630$	23376.9	−	12213.7i	1.47834	−	0.772391i
$631$	−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
$633$	−7489.74	−	15667.1i	−0.470285	−	0.983747i
$634$	−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
$639$	−954.399	−	770.084i	−0.0590852	−	0.0476746i
$640$	22629.0	+	13064.8i	1.39764	+	0.806926i
$641$	−8593.58	−	4961.51i	−0.529526	−	0.305722i	0.211297	−	0.977422i	$-0.432231\pi$
$641$	−8593.58	−	4961.51i	−0.529526	−	0.305722i	−0.740823	+	0.671700i	$0.765564\pi$
$642$	28676.6	+	2231.55i	1.76289	+	0.137184i
$643$			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	−0.959130	−	0.282965i	$-0.908682\pi$
$647$	−3859.39	+	6684.67i	−0.234511	+	0.406184i	0.724620	+	0.689149i	$0.242015\pi$
$648$	15098.4	−	3264.76i	0.915309	−	0.197920i
$649$	−6391.80	+	3690.30i	−0.386595	+	0.223201i
$650$	−2737.88			−0.165213
$651$	34.9592	+	983.688i	0.00210470	+	0.0592224i
$652$	6560.75			0.394078
$653$	−9846.89	+	5685.11i	−0.590105	+	0.340697i	−0.765139	−	0.643865i	$-0.777330\pi$
$653$	−9846.89	+	5685.11i	−0.590105	+	0.340697i	0.175034	+	0.984562i	$0.443996\pi$
$654$	−27665.2	+	13225.5i	−1.65412	+	0.790759i
$655$	−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	$0.801071\pi$
$660$	−1061.17	+	13636.6i	−0.0625847	+	0.804248i
$661$	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
$663$	−538.901	+	6925.17i	−0.0315674	+	0.405658i
$664$			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
$669$	−10047.7	+	4803.34i	−0.580667	+	0.277590i
$670$	−14776.0	+	8530.91i	−0.852008	+	0.491907i
$671$	4630.04			0.266380
$672$	−656.690	−	18478.1i	−0.0376970	−	1.06072i
$673$	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
$675$	−929.322	+	984.486i	−0.0529920	+	0.0561376i
$676$	−10756.5	+	18630.8i	−0.611999	+	1.06001i
$677$	−12478.3	−	21613.0i	−0.708389	−	1.22697i	−0.965455	−	0.260571i	$-0.916089\pi$
$677$	−12478.3	−	21613.0i	−0.708389	−	1.22697i	0.257066	−	0.966394i	$-0.417244\pi$
$678$	−19211.1	+	28005.1i	−1.08820	+	1.58632i
$679$	−448.394	−	3944.67i	−0.0253428	−	0.222949i
$680$		−	5265.93i		−	0.296970i
$681$	−13309.2	−	1035.69i	−0.748914	−	0.0582788i
$682$	−721.368	−	416.482i	−0.0405023	−	0.0233840i
$683$	9706.83	+	5604.24i	0.543809	+	0.313968i	0.746621	−	0.665249i	$-0.231675\pi$
$683$	9706.83	+	5604.24i	0.543809	+	0.313968i	−0.202812	+	0.979218i	$0.565008\pi$
$684$	2920.85	+	2356.77i	0.163277	+	0.131745i
$685$		−	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
$690$	8167.47	+	17084.8i	0.450624	+	0.942620i
$691$	−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
$693$	7940.39	−	4148.61i	0.435253	−	0.227407i
$694$	21714.7			1.18772
$695$	18506.4	−	10684.7i	1.01006	−	0.583156i
$696$	−12612.2	−	26382.4i	−0.686875	−	1.43681i
$697$	−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	$-0.271368\pi$
$702$	11405.9	+	38136.2i	0.613230	+	2.05037i
$703$	−396.000	−	228.631i	−0.0212453	−	0.0122660i
$704$	12933.0	+	7466.86i	0.692372	+	0.399741i
$705$	9841.76	+	765.863i	0.525762	+	0.0409136i
$706$			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
$711$	7714.96	+	1208.04i	0.406939	+	0.0637200i
$712$	10306.4	−	5950.38i	0.542482	−	0.313202i
$713$	−706.707			−0.0371197
$714$	−7941.66	+	4969.32i	−0.416259	+	0.260465i
$715$	−12976.5			−0.678731
$716$	7019.40	−	4052.65i	0.366379	−	0.211529i
$717$	−28507.1	+	13627.9i	−1.48482	+	0.709825i
$718$	942.547	−	1632.54i	0.0489910	−	0.0848549i
$719$	4150.10	+	7188.19i	0.215261	+	0.372843i	0.953353	−	0.301857i	$-0.0976064\pi$
$719$	4150.10	+	7188.19i	0.215261	+	0.372843i	−0.738092	+	0.674700i	$0.764273\pi$
$720$	561.167	+	1454.25i	0.0290465	+	0.0752731i
$721$	−17238.9	+	12749.1i	−0.890443	+	0.658533i
$722$		−	30629.8i		−	1.57884i
$723$	1866.06	−	23979.9i	0.0959884	−	1.23350i
$724$	−46098.8	−	26615.2i	−2.36637	−	1.36622i
$725$	2219.47	+	1281.41i	0.113695	+	0.0656420i
$726$	1850.81	−	23783.9i	0.0946141	−	1.21584i
$727$			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
$732$	−15339.9	+	7333.32i	−0.774563	+	0.370283i
$733$	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
$735$	−7572.89	+	19245.0i	−0.380041	+	0.965799i
$736$	13275.1			0.664847
$737$	−5018.93	+	2897.68i	−0.250848	+	0.144827i
$738$	−588.632	+	3759.22i	−0.0293602	+	0.187505i
$739$	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	$0.0367449\pi$
$743$			4665.46i			0.230362i	−0.993345	+	0.115181i	$0.963255\pi$
$744$	1122.79	+	87.3730i	0.0553273	+	0.00430544i
$745$	13073.8	+	7548.17i	0.642936	+	0.371200i
$746$	−48423.2	−	27957.1i	−2.37654	−	1.37210i
$747$	−7608.73	+	9429.84i	−0.372676	+	0.461874i
$748$		−	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
$753$	−13374.7	−	27977.3i	−0.647278	−	1.35398i
$754$	65257.0	−	37676.1i	3.15188	−	1.81974i
$755$	−30361.4			−1.46353
$756$	−19736.7	+	26321.3i	−0.949495	+	1.26627i
$757$	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
$759$	2774.23	+	5803.17i	0.132672	+	0.277525i
$760$	1349.69	−	2337.73i	0.0644188	−	0.111577i
$761$	11215.0	+	19424.9i	0.534221	+	0.925298i	0.999201	+	0.0399765i	$0.0127283\pi$
$761$	11215.0	+	19424.9i	0.534221	+	0.925298i	−0.464980	+	0.885321i	$0.653938\pi$
$762$	52321.3	+	35891.8i	2.48740	+	1.70633i
$763$	9593.35	−	22047.4i	0.455180	−	1.04610i
$764$			18448.8i			0.873633i
$765$	4213.48	−	5221.95i	0.199136	−	0.246797i
$766$	−20119.2	−	11615.8i	−0.949003	−	0.547907i
$767$	22268.7	+	12856.8i	1.04834	+	0.605259i
$768$	−18480.3	−	1438.09i	−0.868295	−	0.0675687i
$769$			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	$-0.660496\pi$
$773$	11104.6	−	19233.7i	0.516693	−	0.894938i	0.999812	−	0.0193838i	$-0.00617045\pi$
$774$	−4263.31	+	27227.0i	−0.197986	+	1.26441i
$775$	−85.4774	+	49.3504i	−0.00396185	+	0.00228738i
$776$	−4542.31			−0.210128
$777$	1879.59	−	3540.27i	0.0867824	−	0.163457i
$778$	−33276.0			−1.53342
$779$	−294.765	+	170.183i	−0.0135572	+	0.00782725i
$780$	42992.7	−	20552.9i	1.97357	−	0.943476i
$781$	−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
$786$	2937.92	−	37753.9i	0.133323	−	1.71328i
$787$	−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
$789$	−1405.17	+	18057.2i	−0.0634035	+	0.814770i
$790$		−	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
$795$	−28680.2	+	13710.7i	−1.27947	+	0.611659i
$796$	−21372.9	+	12339.6i	−0.951684	+	0.549455i
$797$	−14300.8			−0.635583			−0.317791	−	0.948161i	$-0.602941\pi$
$797$	−14300.8			−0.635583			−0.317791	+	0.948161i	$0.602941\pi$
$798$	−4799.24	+	170.560i	−0.212896	+	0.00756610i
$799$	−3506.27			−0.155248
$800$	1605.65	−	927.022i	0.0709603	−	0.0409690i
$801$	14981.4	+	2345.84i	0.660851	+	0.103478i
$802$	−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
$807$	19657.6	+	1529.71i	0.857474	+	0.0667266i
$808$	31521.1	+	18198.7i	1.37241	+	0.792362i
$809$	12772.9	+	7374.43i	0.555093	+	0.320483i	0.751174	−	0.660104i	$-0.229488\pi$
$809$	12772.9	+	7374.43i	0.555093	+	0.320483i	−0.196080	+	0.980588i	$0.562821\pi$
$810$	11753.6	−	36611.1i	0.509850	−	1.58813i
$811$			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
$816$	−238.795	−	499.515i	−0.0102445	−	0.0214296i
$817$	−2134.91	+	1232.59i	−0.0914209	+	0.0527819i
$818$	−15406.6			−0.658532
$819$	−26349.1	−	16730.9i	−1.12419	−	0.713827i
$820$	4555.18			0.193992
$821$	40528.1	−	23398.9i	1.72283	−	0.994674i	0.809878	−	0.586598i	$-0.199533\pi$
$821$	40528.1	−	23398.9i	1.72283	−	0.994674i	0.912948	−	0.408076i	$-0.133800\pi$
$822$	23618.9	+	49406.3i	1.00220	+	2.09640i
$823$	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	$-0.652469\pi$
$827$		−	42212.0i		−	1.77492i	0.460888	−	0.887458i	$-0.347531\pi$
$828$	−18382.8	−	14832.7i	−0.771553	−	0.622550i
$829$	−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
$831$	−17693.9	−	1376.90i	−0.738623	−	0.0574779i
$832$		−	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
$837$	1043.50	+	985.033i	0.0430929	+	0.0406783i
$838$	−50298.5	+	29039.8i	−2.07343	+	1.19709i
$839$	−39480.0			−1.62455			−0.812277	−	0.583272i	$-0.801772\pi$
$839$	−39480.0			−1.62455			−0.812277	+	0.583272i	$0.801772\pi$
$840$	20899.4	+	11095.9i	0.858452	+	0.455767i
$841$	−46145.4			−1.89206
$842$	−43323.1	+	25012.6i	−1.77317	+	1.02374i
$843$	12948.9	−	6190.30i	0.529045	−	0.252912i
$844$	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
$849$	−2219.33	+	28519.6i	−0.0897141	+	1.15288i
$850$	−813.539	−	469.697i	−0.0328284	−	0.0189535i
$851$	2492.28	+	1438.92i	0.100393	+	0.0579618i
$852$	231.839	−	2979.26i	0.00932240	−	0.119798i
$853$			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	−0.845249	−	0.534373i	$-0.820548\pi$
$857$	1007.45	−	1744.96i	0.0401562	−	0.0695526i	0.885405	+	0.464820i	$0.153881\pi$
$858$	23830.0	−	11392.1i	0.948186	−	0.453285i
$859$	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
$861$	−1582.63	−	2529.26i	−0.0626432	−	0.100112i
$862$	−17211.2			−0.680064
$863$	−5979.04	+	3452.00i	−0.235839	+	0.136162i	−0.613263	−	0.789879i	$-0.710143\pi$
$863$	−5979.04	+	3452.00i	−0.235839	+	0.136162i	0.377424	+	0.926041i	$0.376810\pi$
$864$	−19601.7	−	18503.3i	−0.771832	−	0.728584i
$865$	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
$870$	−72570.0	−	5647.23i	−2.82799	−	0.220068i
$871$	17485.7	+	10095.4i	0.680230	+	0.392731i
$872$	−23824.2	−	13754.9i	−0.925218	−	0.534175i
$873$	−4504.37	−	3634.48i	−0.174628	−	0.140903i
$874$		−	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
$879$	−9191.02	−	19225.9i	−0.352680	−	0.737739i
$880$	895.753	−	517.163i	0.0343134	−	0.0198109i
$881$	−7244.25			−0.277032			−0.138516	−	0.990360i	$-0.544233\pi$
$881$	−7244.25			−0.277032			−0.138516	+	0.990360i	$0.544233\pi$
$882$	−2988.32	−	41989.8i	−0.114084	−	1.60303i
$883$	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
$885$	−10713.2	−	22410.0i	−0.406916	−	0.851191i
$886$	24319.7	−	42123.0i	0.922164	−	1.59724i
$887$	8933.98	+	15474.1i	0.338189	+	0.585761i	0.984092	−	0.177659i	$-0.0568523\pi$
$887$	8933.98	+	15474.1i	0.338189	+	0.585761i	−0.645903	+	0.763420i	$0.723519\pi$
$888$	−3781.75	−	2594.24i	−0.142914	−	0.0980370i
$889$	−49433.1	+	5619.10i	−1.86494	+	0.211990i
$890$		−	29623.4i		−	1.11571i
$891$	3992.32	−	12435.6i	0.150110	−	0.467575i
$892$	−23501.8	−	13568.8i	−0.882172	−	0.509322i
$893$	−1556.55	−	898.677i	−0.0583293	−	0.0336765i
$894$	−30635.3	−	2383.97i	−1.14608	−	0.0891856i
$895$		−	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
$900$	−3259.22	−	510.340i	−0.120712	−	0.0189015i
$901$	9778.43	−	5645.58i	0.361561	−	0.208747i
$902$	2524.85			0.0932020
$903$	−11462.5	−	18318.7i	−0.422425	−	0.675093i
$904$	−30467.9			−1.12096
$905$	−42247.5	+	24391.6i	−1.55177	+	0.895917i
$906$	55755.7	−	26654.3i	2.04455	−	0.977405i
$907$	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	$0.268544\pi$
$911$			41084.1i			1.49416i	−0.664735	+	0.747079i	$0.731456\pi$
$912$	22.0190	−	282.956i	0.000799475	−	0.0102737i
$913$	6962.94	+	4020.05i	0.252398	+	0.145722i
$914$	36096.6	+	20840.4i	1.30631	+	0.754200i
$915$	−1208.92	+	15535.2i	−0.0436782	+	0.561288i
$916$		−	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
$921$	38823.3	−	18559.7i	1.38900	−	0.664020i
$922$	5077.35	−	2931.41i	0.181360	−	0.104708i
$923$	2835.04			0.101101
$924$	19281.4	+	10236.8i	0.686484	+	0.364467i
$925$	401.928			0.0142868
$926$	−27463.3	+	15855.9i	−0.974622	+	0.562698i
$927$	−4835.59	+	30881.9i	−0.171329	+	1.09417i
$928$	−25513.6	+	44190.9i	−0.902507	+	1.56319i
$929$	−12630.2	−	21876.1i	−0.446052	−	0.772585i	0.552073	−	0.833796i	$-0.313837\pi$
$929$	−12630.2	−	21876.1i	−0.446052	−	0.772585i	−0.998125	+	0.0612109i	$0.980504\pi$
$930$	1585.78	−	2311.67i	0.0559136	−	0.0815082i
$931$	2755.29	−	2566.66i	0.0969936	−	0.0903533i
$932$		−	33246.1i		−	1.16847i
$933$	35595.4	+	2769.95i	1.24903	+	0.0971962i
$934$	30955.5	+	17872.2i	1.08447	+	0.626120i
$935$	−3855.86	−	2226.18i	−0.134866	−	0.0778651i
$936$	−22424.9	+	27792.1i	−0.783098	+	0.970528i
$937$		−	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	$0.481387\pi$
$941$	−24112.4	+	41763.8i	−0.835325	+	1.44683i	−0.893766	+	0.448534i	$0.851946\pi$
$942$	−9526.56	−	19927.8i	−0.329503	−	0.689259i
$943$	1855.15	−	1071.07i	0.0640635	−	0.0369871i
$944$	−2049.58			−0.0706654
$945$	11846.6	+	27725.7i	0.407800	+	0.954409i
$946$	18286.8			0.628493
$947$	21340.2	−	12320.8i	0.732275	−	0.422779i	−0.0869787	−	0.996210i	$-0.527721\pi$
$947$	21340.2	−	12320.8i	0.732275	−	0.422779i	0.819254	+	0.573431i	$0.194388\pi$
$948$	8207.04	+	17167.6i	0.281173	+	0.588162i
$949$	−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	$0.927583\pi$
$954$	40631.8	−	50356.8i	1.37893	−	1.70897i
$955$	14642.4	+	8453.77i	0.496142	+	0.286448i
$956$	−66678.6	−	38496.9i	−2.25580	−	1.30238i
$957$	−24649.7	−	1918.19i	−0.832615	−	0.0647922i
$958$			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
$963$	−5086.56	+	32484.6i	−0.170210	+	1.08702i
$964$	50757.4	−	29304.8i	1.69583	−	0.979090i
$965$	21226.6			0.708090
$966$	30204.7	−	1073.44i	1.00602	−	0.0357530i
$967$	−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
$969$	−1102.22	+	526.922i	−0.0365413	+	0.0174687i
$970$	−5653.36	+	9791.91i	−0.187133	+	0.324123i
$971$	25892.6	+	44847.3i	0.855750	+	1.48220i	0.875947	+	0.482407i	$0.160237\pi$
$971$	25892.6	+	44847.3i	0.855750	+	1.48220i	−0.0201966	+	0.999796i	$0.506429\pi$
$972$	6469.20	+	47524.1i	0.213477	+	1.56825i
$973$	−3852.10	−	33888.2i	−0.126920	−	1.11655i
$974$			4785.15i			0.157419i
$975$	242.818	−	3120.34i	0.00797578	−	0.102493i
$976$	1113.50	+	642.877i	0.0365186	+	0.0210840i
$977$	−24796.0	−	14316.0i	−0.811969	−	0.468790i	0.0356703	−	0.999364i	$-0.488643\pi$
$977$	−24796.0	−	14316.0i	−0.811969	−	0.468790i	−0.847639	+	0.530573i	$0.821977\pi$
$978$	−949.497	+	12201.6i	−0.0310446	+	0.398940i
$979$		−	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	$-0.580525\pi$
$983$	21984.3	−	38077.9i	0.713317	−	1.23550i	0.963605	−	0.267330i	$-0.0861414\pi$
$984$	−3079.82	+	1472.32i	−0.0997774	+	0.0476990i
$985$	−6644.24	+	3836.06i	−0.214927	+	0.124088i
$986$	25854.1			0.835055
$987$	7388.10	−	13915.7i	0.238263	−	0.448776i
$988$	−8676.39			−0.279385
$989$	13436.3	−	7757.47i	0.432003	−	0.249417i
$990$	−25207.5	−	3947.09i	−0.809241	−	0.126714i
$991$	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
$996$	−29436.3	−	2290.66i	−0.936471	−	0.0728740i
$997$	−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
$999$	−1674.42	−	5598.50i	−0.0530292	−	0.177306i

Twists

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

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

\(f(q)\)	\(=\)	\(q+(-3.93653 + 2.27276i) q^{2} +(-2.24112 - 4.68800i) q^{3} +(6.33084 - 10.9653i) q^{4} +(-5.80193 - 10.0492i) q^{5} +(19.4769 + 13.3609i) q^{6} +(-18.4018 + 2.09174i) q^{7} +21.1897i q^{8} +(-16.9548 + 21.0128i) q^{9} +O(q^{10})\)	\(q+(-3.93653 + 2.27276i) q^{2} +(-2.24112 - 4.68800i) 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} +(-16.9548 + 21.0128i) q^{9} +(45.6790 + 26.3728i) q^{10} +(15.5157 + 8.95800i) q^{11} +(-65.5937 - 5.10435i) 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} +(18.9860 - 121.251i) q^{18} +(9.50747 - 5.48914i) q^{19} -146.925 q^{20} +(51.0467 + 81.5796i) q^{21} -81.4374 q^{22} +(-59.8367 + 34.5467i) q^{23} +(99.3376 - 47.4888i) 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} +(21.2635 - 273.248i) q^{30} +(8.85795 + 5.11414i) q^{31} +(-166.392 - 96.0665i) q^{32} +(7.22254 - 92.8136i) 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} +(-292.618 + 139.887i) q^{39} +(212.941 - 122.941i) q^{40} -31.0035 q^{41} +(-386.357 - 205.124i) q^{42} -224.550 q^{43} +(196.455 - 113.423i) q^{44} +(309.533 + 48.4678i) 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} +(-110.948 - 8.63368i) q^{51} +(-684.440 - 395.161i) q^{52} +(456.586 + 263.610i) q^{53} +(-610.977 + 182.733i) 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} +(329.276 + 688.783i) q^{60} +(223.807 - 129.215i) q^{61} -46.4928 q^{62} +(268.044 - 422.137i) q^{63} +833.541 q^{64} +(-627.258 + 362.148i) q^{65} +(182.511 + 381.779i) 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} +(-445.255 - 359.267i) q^{72} +(-486.879 - 281.100i) q^{73} +(163.962 + 94.6635i) q^{74} +(49.9907 + 3.89016i) 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} +(-154.073 - 712.532i) q^{81} +(122.046 - 70.4635i) q^{82} +448.767 q^{83} +(1217.72 - 43.2763i) q^{84} -248.513 q^{85} +(883.949 - 510.348i) q^{86} +(-1245.05 + 595.204i) 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} +(4.12336 - 52.9875i) q^{93} +(644.484 + 372.093i) q^{94} +(-110.323 - 63.6953i) q^{95} +(-77.4553 + 995.343i) 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

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more