LMFDB - Embedded newform 322.4.e.c.93.9

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [322,4,Mod(93,322)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("322.93"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(322, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([2, 0])) N = Newforms(chi, 4, names="a")

Level:	$ N $	$=$	$ 322 = 2 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	322.e (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [22,22,0,-44,-17] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$18.9986150218$
Analytic rank:	$0$
Dimension:	$22$
Relative dimension:	$11$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			93.9
Character	$\chi$	$=$	322.93
Dual form			322.4.e.c.277.9

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.00000 - 1.73205i) q^{2} +(2.72170 + 4.71412i) q^{3} +(-2.00000 - 3.46410i) q^{4} +(-3.53343 + 6.12007i) q^{5} +10.8868 q^{6} +(6.47254 - 17.3524i) q^{7} -8.00000 q^{8} +(-1.31529 + 2.27814i) q^{9} +(7.06685 + 12.2401i) q^{10} +(-29.6083 - 51.2831i) q^{11} +(10.8868 - 18.8565i) q^{12} +20.3418 q^{13} +(-23.5827 - 28.5632i) q^{14} -38.4677 q^{15} +(-8.00000 + 13.8564i) q^{16} +(5.28070 + 9.14644i) q^{17} +(2.63057 + 4.55628i) q^{18} +(38.4163 - 66.5390i) q^{19} +28.2674 q^{20} +(99.4177 - 16.7157i) q^{21} -118.433 q^{22} +(11.5000 - 19.9186i) q^{23} +(-21.7736 - 37.7130i) q^{24} +(37.5298 + 65.0035i) q^{25} +(20.3418 - 35.2330i) q^{26} +132.652 q^{27} +(-73.0556 + 12.2833i) q^{28} +153.342 q^{29} +(-38.4677 + 66.6280i) q^{30} +(-169.266 - 293.178i) q^{31} +(16.0000 + 27.7128i) q^{32} +(161.170 - 279.154i) q^{33} +21.1228 q^{34} +(83.3278 + 100.926i) q^{35} +10.5223 q^{36} +(34.5032 - 59.7613i) q^{37} +(-76.8327 - 133.078i) q^{38} +(55.3641 + 95.8935i) q^{39} +(28.2674 - 48.9606i) q^{40} +377.866 q^{41} +(70.4652 - 188.912i) q^{42} -238.549 q^{43} +(-118.433 + 205.132i) q^{44} +(-9.29492 - 16.0993i) q^{45} +(-23.0000 - 39.8372i) q^{46} +(95.3043 - 165.072i) q^{47} -87.0944 q^{48} +(-259.212 - 224.628i) q^{49} +150.119 q^{50} +(-28.7449 + 49.7877i) q^{51} +(-40.6835 - 70.4659i) q^{52} +(5.94023 + 10.2888i) q^{53} +(132.652 - 229.761i) q^{54} +418.475 q^{55} +(-51.7803 + 138.819i) q^{56} +418.231 q^{57} +(153.342 - 265.596i) q^{58} +(144.680 + 250.594i) q^{59} +(76.9353 + 133.256i) q^{60} +(-280.896 + 486.525i) q^{61} -677.065 q^{62} +(31.0180 + 37.5687i) q^{63} +64.0000 q^{64} +(-71.8761 + 124.493i) q^{65} +(-322.339 - 558.308i) q^{66} +(-208.109 - 360.456i) q^{67} +(21.1228 - 36.5857i) q^{68} +125.198 q^{69} +(258.137 - 43.4021i) q^{70} +125.156 q^{71} +(10.5223 - 18.2251i) q^{72} +(-267.751 - 463.758i) q^{73} +(-69.0064 - 119.523i) q^{74} +(-204.290 + 353.840i) q^{75} -307.331 q^{76} +(-1081.53 + 181.844i) q^{77} +221.456 q^{78} +(-542.495 + 939.629i) q^{79} +(-56.5348 - 97.9212i) q^{80} +(396.553 + 686.850i) q^{81} +(377.866 - 654.483i) q^{82} -828.120 q^{83} +(-256.740 - 310.961i) q^{84} -74.6358 q^{85} +(-238.549 + 413.179i) q^{86} +(417.351 + 722.873i) q^{87} +(236.866 + 410.264i) q^{88} +(441.865 - 765.333i) q^{89} -37.1797 q^{90} +(131.663 - 352.979i) q^{91} -92.0000 q^{92} +(921.383 - 1595.88i) q^{93} +(-190.609 - 330.144i) q^{94} +(271.482 + 470.221i) q^{95} +(-87.0944 + 150.852i) q^{96} +551.245 q^{97} +(-648.280 + 224.341i) q^{98} +155.773 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q + 22 q^{2} - 44 q^{4} - 17 q^{5} + 11 q^{7} - 176 q^{8} - 59 q^{9} + 34 q^{10} + 6 q^{13} + 44 q^{14} - 288 q^{15} - 176 q^{16} - 47 q^{17} + 118 q^{18} + 138 q^{19} + 136 q^{20} + 97 q^{21} + 253 q^{23}+ \cdots + 7050 q^{99}+O(q^{100}) $ 22 * q + 22 * q^2 - 44 * q^4 - 17 * q^5 + 11 * q^7 - 176 * q^8 - 59 * q^9 + 34 * q^10 + 6 * q^13 + 44 * q^14 - 288 * q^15 - 176 * q^16 - 47 * q^17 + 118 * q^18 + 138 * q^19 + 136 * q^20 + 97 * q^21 + 253 * q^23 - 350 * q^25 + 6 * q^26 - 174 * q^27 + 44 * q^28 - 502 * q^29 - 288 * q^30 + 46 * q^31 + 352 * q^32 + 222 * q^33 - 188 * q^34 + 597 * q^35 + 472 * q^36 - 475 * q^37 - 276 * q^38 + 115 * q^39 + 136 * q^40 + 1480 * q^41 + 520 * q^42 + 34 * q^43 - 875 * q^45 - 506 * q^46 + 33 * q^47 + 221 * q^49 - 1400 * q^50 - 1017 * q^51 - 12 * q^52 + 835 * q^53 - 174 * q^54 - 2646 * q^55 - 88 * q^56 + 878 * q^57 - 502 * q^58 - 1723 * q^59 + 576 * q^60 + 253 * q^61 + 184 * q^62 - 601 * q^63 + 1408 * q^64 - 1753 * q^65 - 444 * q^66 + 2573 * q^67 - 188 * q^68 + 1188 * q^70 + 2638 * q^71 + 472 * q^72 - 1159 * q^73 + 950 * q^74 - 268 * q^75 - 1104 * q^76 + 307 * q^77 + 460 * q^78 - 1095 * q^79 - 272 * q^80 + 3085 * q^81 + 1480 * q^82 - 902 * q^83 + 652 * q^84 + 5014 * q^85 + 34 * q^86 - 3540 * q^87 - 3634 * q^89 - 3500 * q^90 + 2286 * q^91 - 2024 * q^92 - 3132 * q^93 - 66 * q^94 + 4249 * q^95 - 3026 * q^97 - 1162 * q^98 + 7050 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/322\mathbb{Z}\right)^\times$.

$n$	$185$	$281$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

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 $

$2$	1.00000	−	1.73205i	0.353553	−	0.612372i
$2$	1.00000	−	1.73205i	0.353553	−	0.612372i
$3$	2.72170	+	4.71412i	0.523791	+	0.907233i	0.999616	+	0.0276930i	$0.00881610\pi$
$3$	2.72170	+	4.71412i	0.523791	+	0.907233i	−0.475825	+	0.879540i	$0.657851\pi$
$4$	−2.00000	−	3.46410i	−0.250000	−	0.433013i
$5$	−3.53343	+	6.12007i	−0.316039	+	0.547396i	−0.979658	−	0.200675i	$-0.935686\pi$
$5$	−3.53343	+	6.12007i	−0.316039	+	0.547396i	0.663619	+	0.748071i	$0.269020\pi$
$6$	10.8868			0.740752
$7$	6.47254	−	17.3524i	0.349484	−	0.936942i
$7$	6.47254	−	17.3524i	0.349484	−	0.936942i
$8$	−8.00000			−0.353553
$9$	−1.31529	+	2.27814i	−0.0487143	+	0.0843756i
$10$	7.06685	+	12.2401i	0.223473	+	0.387067i
$11$	−29.6083	−	51.2831i	−0.811567	−	1.40567i	−0.911767	−	0.410708i	$-0.865282\pi$
$11$	−29.6083	−	51.2831i	−0.811567	−	1.40567i	0.100200	−	0.994967i	$-0.468052\pi$
$12$	10.8868	−	18.8565i	0.261896	−	0.453616i
$13$	20.3418			0.433984			0.216992	−	0.976173i	$-0.430376\pi$
$13$	20.3418			0.433984			0.216992	+	0.976173i	$0.430376\pi$
$14$	−23.5827	−	28.5632i	−0.450196	−	0.545274i
$15$	−38.4677			−0.662154
$16$	−8.00000	+	13.8564i	−0.125000	+	0.216506i
$17$	5.28070	+	9.14644i	0.0753387	+	0.130490i	0.901233	−	0.433334i	$-0.142663\pi$
$17$	5.28070	+	9.14644i	0.0753387	+	0.130490i	−0.825895	+	0.563824i	$0.809330\pi$
$18$	2.63057	+	4.55628i	0.0344462	+	0.0596625i
$19$	38.4163	−	66.5390i	0.463858	−	0.803426i	−0.535291	−	0.844668i	$-0.679798\pi$
$19$	38.4163	−	66.5390i	0.463858	−	0.803426i	0.999149	+	0.0412415i	$0.0131313\pi$
$20$	28.2674			0.316039
$21$	99.4177	−	16.7157i	1.03308	−	0.173698i
$22$	−118.433			−1.14773
$23$	11.5000	−	19.9186i	0.104257	−	0.180579i
$23$	11.5000	−	19.9186i	0.104257	−	0.180579i
$24$	−21.7736	−	37.7130i	−0.185188	−	0.320755i
$25$	37.5298	+	65.0035i	0.300238	+	0.520028i
$26$	20.3418	−	35.2330i	0.153436	−	0.265760i
$27$	132.652			0.945518
$28$	−73.0556	+	12.2833i	−0.493079	+	0.0829044i
$29$	153.342			0.981893			0.490947	−	0.871190i	$-0.336651\pi$
$29$	153.342			0.981893			0.490947	+	0.871190i	$0.336651\pi$
$30$	−38.4677	+	66.6280i	−0.234107	+	0.405485i
$31$	−169.266	−	293.178i	−0.980681	−	1.69859i	−0.659746	−	0.751488i	$-0.729336\pi$
$31$	−169.266	−	293.178i	−0.980681	−	1.69859i	−0.320935	−	0.947101i	$-0.603997\pi$
$32$	16.0000	+	27.7128i	0.0883883	+	0.153093i
$33$	161.170	−	279.154i	0.850183	−	1.47256i
$34$	21.1228			0.106545
$35$	83.3278	+	100.926i	0.402428	+	0.487417i
$36$	10.5223			0.0487143
$37$	34.5032	−	59.7613i	0.153305	−	0.265532i	−0.779135	−	0.626856i	$-0.784342\pi$
$37$	34.5032	−	59.7613i	0.153305	−	0.265532i	0.932441	+	0.361323i	$0.117675\pi$
$38$	−76.8327	−	133.078i	−0.327997	−	0.568108i
$39$	55.3641	+	95.8935i	0.227317	+	0.393724i
$40$	28.2674	−	48.9606i	0.111737	−	0.193534i
$41$	377.866			1.43933			0.719667	−	0.694319i	$-0.244294\pi$
$41$	377.866			1.43933			0.719667	+	0.694319i	$0.244294\pi$
$42$	70.4652	−	188.912i	0.258881	−	0.694042i
$43$	−238.549			−0.846010			−0.423005	−	0.906127i	$-0.639025\pi$
$43$	−238.549			−0.846010			−0.423005	+	0.906127i	$0.639025\pi$
$44$	−118.433	+	205.132i	−0.405783	+	0.702837i
$45$	−9.29492	−	16.0993i	−0.0307912	−	0.0533320i
$46$	−23.0000	−	39.8372i	−0.0737210	−	0.127688i
$47$	95.3043	−	165.072i	0.295778	−	0.512303i	−0.679388	−	0.733780i	$-0.737754\pi$
$47$	95.3043	−	165.072i	0.295778	−	0.512303i	0.975166	+	0.221477i	$0.0710878\pi$
$48$	−87.0944			−0.261896
$49$	−259.212	−	224.628i	−0.755721	−	0.654893i
$50$	150.119			0.424601
$51$	−28.7449	+	49.7877i	−0.0789235	+	0.136699i
$52$	−40.6835	−	70.4659i	−0.108496	−	0.187920i
$53$	5.94023	+	10.2888i	0.0153953	+	0.0266655i	0.873620	−	0.486608i	$-0.161766\pi$
$53$	5.94023	+	10.2888i	0.0153953	+	0.0266655i	−0.858225	+	0.513274i	$0.828433\pi$
$54$	132.652	−	229.761i	0.334291	−	0.579009i
$55$	418.475			1.02595
$56$	−51.7803	+	138.819i	−0.123561	+	0.331259i
$57$	418.231			0.971860
$58$	153.342	−	265.596i	0.347152	−	0.601284i
$59$	144.680	+	250.594i	0.319250	+	0.552958i	0.980332	−	0.197356i	$-0.0632355\pi$
$59$	144.680	+	250.594i	0.319250	+	0.552958i	−0.661081	+	0.750314i	$0.729902\pi$
$60$	76.9353	+	133.256i	0.165539	+	0.286721i
$61$	−280.896	+	486.525i	−0.589590	+	1.02120i	0.404696	+	0.914451i	$0.367377\pi$
$61$	−280.896	+	486.525i	−0.589590	+	1.02120i	−0.994286	+	0.106749i	$0.965956\pi$
$62$	−677.065			−1.38689
$63$	31.0180	+	37.5687i	0.0620302	+	0.0751304i
$64$	64.0000			0.125000
$65$	−71.8761	+	124.493i	−0.137156	+	0.237561i
$66$	−322.339	−	558.308i	−0.601170	−	1.04126i
$67$	−208.109	−	360.456i	−0.379472	−	0.657264i	0.611514	−	0.791234i	$-0.290561\pi$
$67$	−208.109	−	360.456i	−0.379472	−	0.657264i	−0.990985	+	0.133970i	$0.957228\pi$
$68$	21.1228	−	36.5857i	0.0376693	−	0.0652452i
$69$	125.198			0.218436
$70$	258.137	−	43.4021i	0.440760	−	0.0741077i
$71$	125.156			0.209201			0.104600	−	0.994514i	$-0.466644\pi$
$71$	125.156			0.209201			0.104600	+	0.994514i	$0.466644\pi$
$72$	10.5223	−	18.2251i	0.0172231	−	0.0298313i
$73$	−267.751	−	463.758i	−0.429286	−	0.743545i	0.567524	−	0.823357i	$-0.307901\pi$
$73$	−267.751	−	463.758i	−0.429286	−	0.743545i	−0.996810	+	0.0798117i	$0.974568\pi$
$74$	−69.0064	−	119.523i	−0.108403	−	0.187760i
$75$	−204.290	+	353.840i	−0.314524	+	0.544772i
$76$	−307.331			−0.463858
$77$	−1081.53	+	181.844i	−1.60067	+	0.269130i
$78$	221.456			0.321474
$79$	−542.495	+	939.629i	−0.772601	+	1.33818i	0.163532	+	0.986538i	$0.447711\pi$
$79$	−542.495	+	939.629i	−0.772601	+	1.33818i	−0.936133	+	0.351646i	$0.885622\pi$
$80$	−56.5348	−	97.9212i	−0.0790098	−	0.136849i
$81$	396.553	+	686.850i	0.543968	+	0.942180i
$82$	377.866	−	654.483i	0.508882	−	0.881409i
$83$	−828.120			−1.09516			−0.547578	−	0.836754i	$-0.684450\pi$
$83$	−828.120			−1.09516			−0.547578	+	0.836754i	$0.684450\pi$
$84$	−256.740	−	310.961i	−0.333484	−	0.403913i
$85$	−74.6358			−0.0952399
$86$	−238.549	+	413.179i	−0.299110	+	0.518073i
$87$	417.351	+	722.873i	0.514307	+	0.890806i
$88$	236.866	+	410.264i	0.286932	+	0.496981i
$89$	441.865	−	765.333i	0.526265	−	0.911518i	−0.473266	−	0.880919i	$-0.656925\pi$
$89$	441.865	−	765.333i	0.526265	−	0.911518i	0.999532	−	0.0305991i	$-0.00974151\pi$
$90$	−37.1797			−0.0435454
$91$	131.663	−	352.979i	0.151670	−	0.406618i
$92$	−92.0000			−0.104257
$93$	921.383	−	1595.88i	1.02734	−	1.77941i
$94$	−190.609	−	330.144i	−0.209147	−	0.362253i
$95$	271.482	+	470.221i	0.293195	+	0.507828i
$96$	−87.0944	+	150.852i	−0.0925941	+	0.160378i
$97$	551.245			0.577015			0.288507	−	0.957478i	$-0.406841\pi$
$97$	551.245			0.577015			0.288507	+	0.957478i	$0.406841\pi$
$98$	−648.280	+	224.341i	−0.668226	+	0.231243i
$99$	155.773			0.158140
$100$	150.119	−	260.014i	0.150119	−	0.260014i
$101$	−49.5215	−	85.7737i	−0.0487878	−	0.0845030i	0.840600	−	0.541656i	$-0.182202\pi$
$101$	−49.5215	−	85.7737i	−0.0487878	−	0.0845030i	−0.889388	+	0.457153i	$0.848869\pi$
$102$	57.4899	+	99.5754i	0.0558073	+	0.0966611i
$103$	527.933	−	914.406i	0.505036	−	0.874749i	−0.494947	−	0.868923i	$-0.664812\pi$
$103$	527.933	−	914.406i	0.505036	−	0.874749i	0.999983	−	0.00582526i	$-0.00185425\pi$
$104$	−162.734			−0.153436
$105$	−248.984	+	667.507i	−0.231412	+	0.620400i
$106$	23.7609			0.0217723
$107$	−138.592	+	240.049i	−0.125217	+	0.216882i	−0.921818	−	0.387624i	$-0.873296\pi$
$107$	−138.592	+	240.049i	−0.125217	+	0.216882i	0.796601	+	0.604506i	$0.206629\pi$
$108$	−265.305	−	459.522i	−0.236379	−	0.409421i
$109$	−172.684	−	299.097i	−0.151744	−	0.262828i	0.780125	−	0.625624i	$-0.215156\pi$
$109$	−172.684	−	299.097i	−0.151744	−	0.262828i	−0.931869	+	0.362796i	$0.881822\pi$
$110$	418.475	−	724.819i	0.362727	−	0.628262i
$111$	375.629			0.321200
$112$	188.662	+	228.505i	0.159168	+	0.192783i
$113$	−1326.83			−1.10458			−0.552289	−	0.833653i	$-0.686245\pi$
$113$	−1326.83			−1.10458			−0.552289	+	0.833653i	$0.686245\pi$
$114$	418.231	−	724.397i	0.343604	−	0.595140i
$115$	81.2688	+	140.762i	0.0658987	+	0.114140i
$116$	−306.684	−	531.193i	−0.245473	−	0.425172i
$117$	−26.7552	+	46.3414i	−0.0211412	+	0.0366176i
$118$	578.721			0.451488
$119$	192.892	−	32.4322i	0.148592	−	0.0249836i
$120$	307.741			0.234107
$121$	−1087.80	+	1884.13i	−0.817281	+	1.41557i
$122$	561.791	+	973.051i	0.416903	+	0.722097i
$123$	1028.44	+	1781.30i	0.753911	+	1.30581i
$124$	−677.065	+	1172.71i	−0.490341	+	0.849295i
$125$	−1413.79			−1.01163
$126$	96.0889	−	16.1560i	0.0679388	−	0.0114230i
$127$	355.779			0.248585			0.124292	−	0.992246i	$-0.460334\pi$
$127$	355.779			0.248585			0.124292	+	0.992246i	$0.460334\pi$
$128$	64.0000	−	110.851i	0.0441942	−	0.0765466i
$129$	−649.259	−	1124.55i	−0.443132	−	0.767528i
$130$	143.752	+	248.986i	0.0969838	+	0.167981i
$131$	−757.812	+	1312.57i	−0.505423	+	0.875418i	0.494558	+	0.869145i	$0.335330\pi$
$131$	−757.812	+	1312.57i	−0.505423	+	0.875418i	−0.999980	+	0.00627298i	$0.998003\pi$
$132$	−1289.36			−0.850183
$133$	−905.962	−	1097.29i	−0.590653	−	0.715394i
$134$	−832.437			−0.536654
$135$	−468.718	+	811.843i	−0.298821	+	0.517573i
$136$	−42.2456	−	73.1715i	−0.0266362	−	0.0461353i
$137$	1491.77	+	2583.82i	0.930294	+	1.61132i	0.782817	+	0.622251i	$0.213782\pi$
$137$	1491.77	+	2583.82i	0.930294	+	1.61132i	0.147477	+	0.989066i	$0.452885\pi$
$138$	125.198	−	216.850i	0.0772288	−	0.133764i
$139$	1507.52			0.919898			0.459949	−	0.887945i	$-0.347868\pi$
$139$	1507.52			0.919898			0.459949	+	0.887945i	$0.347868\pi$
$140$	182.962	−	490.508i	0.110451	−	0.296110i
$141$	1037.56			0.619704
$142$	125.156	−	216.776i	0.0739636	−	0.128109i
$143$	−602.284	−	1043.19i	−0.352207	−	0.610040i
$144$	−21.0446	−	36.4502i	−0.0121786	−	0.0210939i
$145$	−541.823	+	938.465i	−0.310317	+	0.537484i
$146$	−1071.00			−0.607102
$147$	353.427	−	1833.33i	0.198301	−	1.02864i
$148$	−276.026			−0.153305
$149$	230.198	−	398.714i	0.126567	−	0.219221i	−0.795777	−	0.605590i	$-0.792937\pi$
$149$	230.198	−	398.714i	0.126567	−	0.219221i	0.922345	+	0.386368i	$0.126271\pi$
$150$	408.579	+	707.680i	0.222402	+	0.385212i
$151$	781.908	+	1354.30i	0.421396	+	0.729879i	0.996076	−	0.0884989i	$-0.0282070\pi$
$151$	781.908	+	1354.30i	0.421396	+	0.729879i	−0.574680	+	0.818378i	$0.694874\pi$
$152$	−307.331	+	532.312i	−0.163999	+	0.284054i
$153$	−27.7825			−0.0146803
$154$	−766.563	+	2055.10i	−0.401113	+	1.07536i
$155$	2392.36			1.23973
$156$	221.456	−	383.574i	0.113658	−	0.196862i
$157$	1407.92	+	2438.59i	0.715696	+	1.23962i	0.962690	+	0.270605i	$0.0872237\pi$
$157$	1407.92	+	2438.59i	0.715696	+	1.23962i	−0.246994	+	0.969017i	$0.579443\pi$
$158$	1084.99	+	1879.26i	0.546311	+	0.946239i
$159$	−32.3350	+	56.0059i	−0.0161279	+	0.0279343i
$160$	−226.139			−0.111737
$161$	−271.201	−	328.477i	−0.132756	−	0.160792i
$162$	1586.21			0.769287
$163$	640.750	−	1109.81i	0.307898	−	0.533295i	−0.670004	−	0.742357i	$-0.733708\pi$
$163$	640.750	−	1109.81i	0.307898	−	0.533295i	0.977902	+	0.209062i	$0.0670411\pi$
$164$	−755.732	−	1308.97i	−0.359834	−	0.623250i
$165$	1138.96	+	1972.74i	0.537382	+	0.930773i
$166$	−828.120	+	1434.35i	−0.387196	+	0.670644i
$167$	3743.59			1.73466			0.867329	−	0.497735i	$-0.165835\pi$
$167$	3743.59			1.73466			0.867329	+	0.497735i	$0.165835\pi$
$168$	−795.341	+	133.726i	−0.365249	+	0.0614116i
$169$	−1783.21			−0.811658
$170$	−74.6358	+	129.273i	−0.0336724	+	0.0583223i
$171$	101.057	+	175.036i	0.0451930	+	0.0782766i
$172$	477.099	+	826.359i	0.211502	+	0.366333i
$173$	−1562.96	+	2707.13i	−0.686877	+	1.18971i	0.285966	+	0.958240i	$0.407686\pi$
$173$	−1562.96	+	2707.13i	−0.686877	+	1.18971i	−0.972843	+	0.231466i	$0.925648\pi$
$174$	1669.40			0.727340
$175$	1370.88	−	230.495i	0.592165	−	0.0995644i
$176$	947.465			0.405783
$177$	−787.553	+	1364.08i	−0.334441	+	0.579269i
$178$	−883.731	−	1530.67i	−0.372126	−	0.644541i
$179$	2272.78	+	3936.57i	0.949025	+	1.64376i	0.747485	+	0.664279i	$0.231261\pi$
$179$	2272.78	+	3936.57i	0.949025	+	1.64376i	0.201540	+	0.979480i	$0.435405\pi$
$180$	−37.1797	+	64.3971i	−0.0153956	+	0.0266660i
$181$	495.143			0.203335			0.101668	−	0.994818i	$-0.467582\pi$
$181$	495.143			0.203335			0.101668	+	0.994818i	$0.467582\pi$
$182$	−479.714	−	581.025i	−0.195378	−	0.236640i
$183$	−3058.05			−1.23529
$184$	−92.0000	+	159.349i	−0.0368605	+	0.0638442i
$185$	243.829	+	422.324i	0.0969009	+	0.167837i
$186$	−1842.77	−	3191.77i	−0.726442	−	1.25823i
$187$	312.705	−	541.621i	0.122285	−	0.211803i
$188$	−762.435			−0.295778
$189$	858.599	−	2301.84i	0.330444	−	0.885896i
$190$	1085.93			0.414640
$191$	397.438	−	688.383i	0.150563	−	0.260783i	−0.780871	−	0.624692i	$-0.785225\pi$
$191$	397.438	−	688.383i	0.150563	−	0.260783i	0.931435	+	0.363909i	$0.118558\pi$
$192$	174.189	+	301.704i	0.0654739	+	0.113404i
$193$	−277.577	−	480.777i	−0.103525	−	0.179311i	0.809609	−	0.586969i	$-0.199679\pi$
$193$	−277.577	−	480.777i	−0.103525	−	0.179311i	−0.913135	+	0.407658i	$0.866346\pi$
$194$	551.245	−	954.784i	0.204005	−	0.353348i
$195$	−782.500			−0.287364
$196$	−259.711	+	1347.19i	−0.0946467	+	0.490960i
$197$	4487.43			1.62293			0.811463	−	0.584404i	$-0.198672\pi$
$197$	4487.43			1.62293			0.811463	+	0.584404i	$0.198672\pi$
$198$	155.773	−	269.807i	0.0559108	−	0.0968403i
$199$	−787.174	−	1363.43i	−0.280409	−	0.485682i	0.691077	−	0.722781i	$-0.257137\pi$
$199$	−787.174	−	1363.43i	−0.280409	−	0.485682i	−0.971485	+	0.237099i	$0.923803\pi$
$200$	−300.238	−	520.028i	−0.106150	−	0.183858i
$201$	1132.82	−	1962.10i	0.397528	−	0.688538i
$202$	−198.086			−0.0689964
$203$	992.513	−	2660.86i	0.343156	−	0.919977i
$204$	229.959			0.0789235
$205$	−1335.16	+	2312.57i	−0.454886	+	0.787886i
$206$	−1055.87	−	1828.81i	−0.357115	−	0.618541i
$207$	30.2516	+	52.3972i	0.0101576	+	0.0175935i
$208$	−162.734	+	281.864i	−0.0542480	+	0.0939602i
$209$	−4549.77			−1.50581
$210$	907.172	+	1098.76i	0.298099	+	0.361055i
$211$	−4680.39			−1.52707			−0.763534	−	0.645768i	$-0.776537\pi$
$211$	−4680.39			−1.52707			−0.763534	+	0.645768i	$0.776537\pi$
$212$	23.7609	−	41.1551i	0.00769767	−	0.0133328i
$213$	340.636	+	589.999i	0.109577	+	0.189794i
$214$	277.184	+	480.098i	0.0885418	+	0.153359i
$215$	842.896	−	1459.94i	0.267372	−	0.463102i
$216$	−1061.22			−0.334291
$217$	−6182.92	+	1039.57i	−1.93421	+	0.325211i
$218$	−690.734			−0.214598
$219$	1457.47	−	2524.42i	0.449712	−	0.778925i
$220$	−836.949	−	1449.64i	−0.256487	−	0.444248i
$221$	107.419	+	186.055i	0.0326958	+	0.0566307i
$222$	375.629	−	650.609i	0.113561	−	0.196694i
$223$	−3455.88			−1.03777			−0.518885	−	0.854844i	$-0.673653\pi$
$223$	−3455.88			−1.03777			−0.518885	+	0.854844i	$0.673653\pi$
$224$	584.445	−	98.2663i	0.174330	−	0.0293111i
$225$	−197.450			−0.0585036
$226$	−1326.83	+	2298.13i	−0.390527	+	0.676413i
$227$	−1842.04	−	3190.51i	−0.538592	−	0.932869i	−0.998980	−	0.0451515i	$-0.985623\pi$
$227$	−1842.04	−	3190.51i	−0.538592	−	0.932869i	0.460388	−	0.887718i	$-0.347710\pi$
$228$	−836.461	−	1448.79i	−0.242965	−	0.420828i
$229$	−820.433	+	1421.03i	−0.236750	+	0.410063i	−0.959780	−	0.280754i	$-0.909416\pi$
$229$	−820.433	+	1421.03i	−0.236750	+	0.410063i	0.723030	+	0.690817i	$0.242749\pi$
$230$	325.075			0.0931949
$231$	−3800.82	−	4603.52i	−1.08258	−	1.31121i
$232$	−1226.74			−0.347152
$233$	3358.53	−	5817.14i	0.944311	−	1.63560i	0.187187	−	0.982324i	$-0.440063\pi$
$233$	3358.53	−	5817.14i	0.944311	−	1.63560i	0.757124	−	0.653271i	$-0.226604\pi$
$234$	53.5104	+	92.6827i	0.0149491	+	0.0258926i
$235$	673.502	+	1166.54i	0.186955	+	0.323815i
$236$	578.721	−	1002.37i	0.159625	−	0.276479i
$237$	−5906.03			−1.61873
$238$	136.718	−	366.531i	0.0372358	−	0.0998265i
$239$	−3592.73			−0.972361			−0.486180	−	0.873859i	$-0.661610\pi$
$239$	−3592.73			−0.972361			−0.486180	+	0.873859i	$0.661610\pi$
$240$	307.741	−	533.024i	0.0827693	−	0.143361i
$241$	555.541	+	962.224i	0.148488	+	0.257188i	0.930669	−	0.365863i	$-0.119226\pi$
$241$	555.541	+	962.224i	0.148488	+	0.257188i	−0.782181	+	0.623051i	$0.785893\pi$
$242$	2175.60	+	3768.25i	0.577905	+	1.00096i
$243$	−367.786	+	637.023i	−0.0970924	+	0.168169i
$244$	2247.16			0.589590
$245$	2290.65	−	792.691i	0.597323	−	0.206707i
$246$	4113.75			1.06619
$247$	781.456	−	1353.52i	0.201307	−	0.348674i
$248$	1354.13	+	2345.42i	0.346723	+	0.600542i
$249$	−2253.89	−	3903.86i	−0.573633	−	0.993562i
$250$	−1413.79	+	2448.76i	−0.357664	+	0.619492i
$251$	4174.36			1.04973			0.524867	−	0.851184i	$-0.324115\pi$
$251$	4174.36			1.04973			0.524867	+	0.851184i	$0.324115\pi$
$252$	68.1059	−	182.587i	0.0170249	−	0.0456424i
$253$	−1361.98			−0.338447
$254$	355.779	−	616.227i	0.0878879	−	0.152226i
$255$	−203.136	−	351.842i	−0.0498858	−	0.0864048i
$256$	−128.000	−	221.703i	−0.0312500	−	0.0541266i
$257$	−3061.82	+	5303.24i	−0.743157	+	1.28719i	0.207894	+	0.978151i	$0.433339\pi$
$257$	−3061.82	+	5303.24i	−0.743157	+	1.28719i	−0.951051	+	0.309034i	$0.899994\pi$
$258$	−2597.04			−0.626684
$259$	−813.680	−	985.522i	−0.195211	−	0.236438i
$260$	575.009			0.137156
$261$	−201.689	+	349.335i	−0.0478322	+	0.0828478i
$262$	1515.62	+	2625.14i	0.357388	+	0.619014i
$263$	−2076.35	−	3596.34i	−0.486818	−	0.843194i	0.513067	−	0.858349i	$-0.328509\pi$
$263$	−2076.35	−	3596.34i	−0.486818	−	0.843194i	−0.999885	+	0.0151546i	$0.995176\pi$
$264$	−1289.36	+	2233.23i	−0.300585	+	0.520629i
$265$	−83.9575			−0.0194621
$266$	−2806.53	+	471.879i	−0.646915	+	0.108770i
$267$	4810.50			1.10261
$268$	−832.437	+	1441.82i	−0.189736	+	0.328632i
$269$	1530.37	+	2650.68i	0.346871	+	0.600798i	0.985692	−	0.168557i	$-0.0539109\pi$
$269$	1530.37	+	2650.68i	0.346871	+	0.600798i	−0.638821	+	0.769355i	$0.720578\pi$
$270$	937.435	+	1623.69i	0.211298	+	0.365979i
$271$	−1330.82	+	2305.04i	−0.298307	+	0.516684i	−0.975749	−	0.218893i	$-0.929755\pi$
$271$	−1330.82	+	2305.04i	−0.298307	+	0.516684i	0.677441	+	0.735577i	$0.263089\pi$
$272$	−168.982			−0.0376693
$273$	2022.33	−	340.027i	0.448340	−	0.0753822i
$274$	5967.07			1.31563
$275$	2222.39	−	3849.29i	0.487327	−	0.844075i
$276$	−250.396	−	433.699i	−0.0546090	−	0.0945856i
$277$	−2050.47	−	3551.51i	−0.444767	−	0.770359i	0.553269	−	0.833003i	$-0.313380\pi$
$277$	−2050.47	−	3551.51i	−0.444767	−	0.770359i	−0.998036	+	0.0626434i	$0.980047\pi$
$278$	1507.52	−	2611.09i	0.325233	−	0.563320i
$279$	890.534			0.191093
$280$	−666.622	−	807.407i	−0.142280	−	0.172328i
$281$	8582.08			1.82194			0.910968	−	0.412477i	$-0.135336\pi$
$281$	8582.08			1.82194			0.910968	+	0.412477i	$0.135336\pi$
$282$	1037.56	−	1797.10i	0.219098	−	0.379489i
$283$	−1759.32	−	3047.23i	−0.369542	−	0.640066i	0.619952	−	0.784640i	$-0.287152\pi$
$283$	−1759.32	−	3047.23i	−0.369542	−	0.640066i	−0.989494	+	0.144574i	$0.953819\pi$
$284$	−250.311	−	433.552i	−0.0523002	−	0.0905866i
$285$	−1477.79	+	2559.60i	−0.307146	+	0.531992i
$286$	−2409.14			−0.498095
$287$	2445.75	−	6556.88i	0.503025	−	1.34857i
$288$	−84.1782			−0.0172231
$289$	2400.73	−	4158.18i	0.488648	−	0.846363i
$290$	1083.65	+	1876.93i	0.219427	+	0.380059i
$291$	1500.32	+	2598.63i	0.302235	+	0.523487i
$292$	−1071.00	+	1855.03i	−0.214643	+	0.371773i
$293$	3157.18			0.629503			0.314752	−	0.949174i	$-0.398079\pi$
$293$	3157.18			0.629503			0.314752	+	0.949174i	$0.398079\pi$
$294$	−2821.99	−	2445.48i	−0.559803	−	0.485114i
$295$	−2044.87			−0.403583
$296$	−276.026	+	478.091i	−0.0542016	+	0.0938799i
$297$	−3927.61	−	6802.82i	−0.767351	−	1.32909i
$298$	−460.395	−	797.428i	−0.0894966	−	0.155013i
$299$	233.930	−	405.179i	0.0452459	−	0.0783682i
$300$	1634.32			0.314524
$301$	−1544.02	+	4139.40i	−0.295667	+	0.792662i
$302$	3127.63			0.595944
$303$	269.565	−	466.900i	0.0511092	−	0.0885238i
$304$	614.661	+	1064.62i	0.115965	+	0.200857i
$305$	−1985.05	−	3438.20i	−0.372667	−	0.645478i
$306$	−27.7825	+	48.1207i	−0.00519026	+	0.00898979i
$307$	601.675			0.111855			0.0559274	−	0.998435i	$-0.482188\pi$
$307$	601.675			0.111855			0.0559274	+	0.998435i	$0.482188\pi$
$308$	2792.98	+	3382.83i	0.516703	+	0.625826i
$309$	5747.49			1.05813
$310$	2392.36	−	4143.69i	0.438312	−	0.759179i
$311$	2066.63	+	3579.51i	0.376810	+	0.652654i	0.990596	−	0.136818i	$-0.0436877\pi$
$311$	2066.63	+	3579.51i	0.376810	+	0.652654i	−0.613786	+	0.789472i	$0.710354\pi$
$312$	−442.913	−	767.148i	−0.0803686	−	0.139203i
$313$	2772.34	−	4801.83i	0.500645	−	0.867142i	−0.499355	−	0.866398i	$-0.666430\pi$
$313$	2772.34	−	4801.83i	0.500645	−	0.867142i	1.00000		0.000744679i	$-0.000237039\pi$
$314$	5631.68			1.01215
$315$	−339.523	+	57.0861i	−0.0607300	+	0.0102109i
$316$	4339.96			0.772601
$317$	−3376.79	+	5848.77i	−0.598294	+	1.03628i	0.394779	+	0.918776i	$0.370821\pi$
$317$	−3376.79	+	5848.77i	−0.598294	+	1.03628i	−0.993073	+	0.117500i	$0.962512\pi$
$318$	64.6701	+	112.012i	0.0114041	+	0.0197526i
$319$	−4540.20	−	7863.85i	−0.796872	−	1.38022i
$320$	−226.139	+	391.685i	−0.0395049	+	0.0684245i
$321$	−1508.82			−0.262350
$322$	−840.139	+	141.258i	−0.145401	+	0.0244472i
$323$	811.460			0.139786
$324$	1586.21	−	2747.40i	0.271984	−	0.471090i
$325$	763.422	+	1322.29i	0.130299	+	0.225684i
$326$	−1281.50	−	2219.62i	−0.217717	−	0.377097i
$327$	939.985	−	1628.10i	0.158964	−	0.275334i
$328$	−3022.93			−0.508882
$329$	−2247.54	−	2722.19i	−0.376628	−	0.456169i
$330$	4555.85			0.759973
$331$	1778.00	−	3079.58i	0.295250	−	0.511387i	−0.679793	−	0.733404i	$-0.737931\pi$
$331$	1778.00	−	3079.58i	0.295250	−	0.511387i	0.975043	+	0.222016i	$0.0712638\pi$
$332$	1656.24	+	2868.69i	0.273789	+	0.474217i
$333$	90.7631	+	157.206i	0.0149363	+	0.0258704i
$334$	3743.59	−	6484.09i	0.613294	−	1.06226i
$335$	2941.35			0.479711
$336$	−563.722	+	1511.30i	−0.0915284	+	0.245381i
$337$	7607.26			1.22966			0.614828	−	0.788661i	$-0.289226\pi$
$337$	7607.26			1.22966			0.614828	+	0.788661i	$0.289226\pi$
$338$	−1783.21	+	3088.62i	−0.286965	+	0.497037i
$339$	−3611.22	−	6254.82i	−0.578568	−	1.00211i
$340$	149.272	+	258.546i	0.0238100	+	0.0412401i
$341$	−10023.4	+	17361.0i	−1.59178	+	2.75704i
$342$	404.227			0.0639126
$343$	−5575.61	+	3044.04i	−0.877710	+	0.479192i
$344$	1908.39			0.299110
$345$	−442.378	+	766.222i	−0.0690343	+	0.119571i
$346$	3125.92	+	5414.26i	0.485696	+	0.841249i
$347$	2983.66	+	5167.85i	0.461589	+	0.799495i	0.999040	−	0.0437993i	$-0.0139462\pi$
$347$	2983.66	+	5167.85i	0.461589	+	0.799495i	−0.537452	+	0.843295i	$0.680613\pi$
$348$	1669.40	−	2891.49i	0.257154	−	0.445403i
$349$	11089.3			1.70085			0.850426	−	0.526094i	$-0.176344\pi$
$349$	11089.3			1.70085			0.850426	+	0.526094i	$0.176344\pi$
$350$	971.653	−	2604.93i	0.148392	−	0.397827i
$351$	2698.38			0.410339
$352$	947.465	−	1641.06i	0.143466	−	0.248491i
$353$	−101.577	−	175.937i	−0.0153156	−	0.0265274i	0.858266	−	0.513205i	$-0.171542\pi$
$353$	−101.577	−	175.937i	−0.0153156	−	0.0265274i	−0.873582	+	0.486678i	$0.838209\pi$
$354$	1575.11	+	2728.16i	0.236486	+	0.409605i
$355$	−442.228	+	765.962i	−0.0661156	+	0.114516i
$356$	−3534.92			−0.526265
$357$	677.884	+	821.047i	0.100497	+	0.121721i
$358$	9091.11			1.34212
$359$	−1815.05	+	3143.75i	−0.266837	+	0.462175i	−0.968043	−	0.250783i	$-0.919312\pi$
$359$	−1815.05	+	3143.75i	−0.266837	+	0.462175i	0.701206	+	0.712959i	$0.252645\pi$
$360$	74.3594	+	128.794i	0.0108863	+	0.0188557i
$361$	477.871	+	827.697i	0.0696707	+	0.120673i
$362$	495.143	−	857.613i	0.0718899	−	0.124517i
$363$	−11842.7			−1.71234
$364$	−1486.08	+	249.864i	−0.213988	+	0.0359792i
$365$	3784.31			0.542685
$366$	−3058.05	+	5296.70i	−0.436740	+	0.756456i
$367$	−2517.55	−	4360.53i	−0.358080	−	0.620212i	0.629560	−	0.776952i	$-0.283235\pi$
$367$	−2517.55	−	4360.53i	−0.358080	−	0.620212i	−0.987640	+	0.156739i	$0.949902\pi$
$368$	184.000	+	318.697i	0.0260643	+	0.0451447i
$369$	−497.001	+	860.831i	−0.0701161	+	0.121445i
$370$	975.316			0.137039
$371$	216.984	−	36.4828i	0.0303645	−	0.00510537i
$372$	−7371.07			−1.02734
$373$	−6772.90	+	11731.0i	−0.940181	+	1.62844i	−0.175057	+	0.984558i	$0.556011\pi$
$373$	−6772.90	+	11731.0i	−0.940181	+	1.62844i	−0.765124	+	0.643883i	$0.777322\pi$
$374$	−625.410	−	1083.24i	−0.0864684	−	0.149768i
$375$	−3847.91	−	6664.78i	−0.529881	−	0.917781i
$376$	−762.435	+	1320.58i	−0.104573	+	0.181126i
$377$	3119.25			0.426126
$378$	−3128.31	−	3788.98i	−0.425669	−	0.515566i
$379$	732.186			0.0992344			0.0496172	−	0.998768i	$-0.484200\pi$
$379$	732.186			0.0992344			0.0496172	+	0.998768i	$0.484200\pi$
$380$	1085.93	−	1880.89i	0.146597	−	0.253914i
$381$	968.322	+	1677.18i	0.130206	+	0.225524i
$382$	−794.876	−	1376.77i	−0.106464	−	0.184402i
$383$	920.383	−	1594.15i	0.122792	−	0.212682i	−0.798076	−	0.602557i	$-0.794148\pi$
$383$	920.383	−	1594.15i	0.122792	−	0.212682i	0.920868	+	0.389875i	$0.127482\pi$
$384$	696.755			0.0925941
$385$	2708.59	−	7261.55i	0.358553	−	0.961254i
$386$	−1110.31			−0.146407
$387$	313.760	−	543.449i	0.0412127	−	0.0713826i
$388$	−1102.49	−	1909.57i	−0.144254	−	0.249855i
$389$	−2415.91	−	4184.49i	−0.314889	−	0.545403i	0.664525	−	0.747266i	$-0.268634\pi$
$389$	−2415.91	−	4184.49i	−0.314889	−	0.545403i	−0.979414	+	0.201863i	$0.935301\pi$
$390$	−782.500	+	1355.33i	−0.101599	+	0.175974i
$391$	242.912			0.0314184
$392$	2073.70	+	1797.03i	0.267188	+	0.231540i
$393$	−8250.15			−1.05894
$394$	4487.43	−	7772.46i	0.573791	−	0.993835i
$395$	−3833.73	−	6640.22i	−0.488344	−	0.845837i
$396$	−311.547	−	539.615i	−0.0395349	−	0.0684764i
$397$	−2806.16	+	4860.42i	−0.354754	+	0.614452i	−0.987076	−	0.160254i	$-0.948769\pi$
$397$	−2806.16	+	4860.42i	−0.354754	+	0.614452i	0.632322	+	0.774706i	$0.282102\pi$
$398$	−3148.70			−0.396558
$399$	2707.01	−	7257.31i	0.339650	−	0.910576i
$400$	−1200.95			−0.150119
$401$	−3271.36	+	5666.16i	−0.407391	+	0.705622i	−0.994597	−	0.103816i	$-0.966895\pi$
$401$	−3271.36	+	5666.16i	−0.407391	+	0.705622i	0.587205	+	0.809438i	$0.300228\pi$
$402$	−2265.64	−	3924.21i	−0.281094	−	0.486870i
$403$	−3443.17	−	5963.75i	−0.425600	−	0.737160i
$404$	−198.086	+	343.095i	−0.0243939	+	0.0422515i
$405$	−5604.76			−0.687661
$406$	−3616.22	−	4379.94i	−0.442045	−	0.535401i
$407$	−4086.32			−0.497670
$408$	229.959	−	398.302i	0.0279037	−	0.0483305i
$409$	−2130.20	−	3689.62i	−0.257535	−	0.446063i	0.708046	−	0.706166i	$-0.249577\pi$
$409$	−2130.20	−	3689.62i	−0.257535	−	0.446063i	−0.965581	+	0.260103i	$0.916244\pi$
$410$	2670.32	+	4625.13i	0.321653	+	0.557119i
$411$	−8120.28	+	14064.7i	−0.974560	+	1.68799i
$412$	−4223.46			−0.505036
$413$	5284.86	−	888.575i	0.629663	−	0.105869i
$414$	121.006			0.0143651
$415$	2926.10	−	5068.16i	0.346112	−	0.599484i
$416$	325.468	+	563.727i	0.0383591	+	0.0664399i
$417$	4103.00	+	7106.61i	0.481834	+	0.834562i
$418$	−4549.77	+	7880.43i	−0.532384	+	0.922116i
$419$	16467.6			1.92004			0.960020	−	0.279933i	$-0.0903121\pi$
$419$	16467.6			1.92004			0.960020	+	0.279933i	$0.0903121\pi$
$420$	2810.28	−	472.509i	0.326494	−	0.0548955i
$421$	−4252.38			−0.492276			−0.246138	−	0.969235i	$-0.579162\pi$
$421$	−4252.38			−0.492276			−0.246138	+	0.969235i	$0.579162\pi$
$422$	−4680.39	+	8106.67i	−0.539900	+	0.935134i
$423$	250.705	+	434.233i	0.0288172	+	0.0499129i
$424$	−47.5218	−	82.3103i	−0.00544308	−	0.00942769i
$425$	−396.367	+	686.528i	−0.0452391	+	0.0783565i
$426$	1362.54			0.154966
$427$	6624.28	+	8023.27i	0.750753	+	0.909305i
$428$	1108.74			0.125217
$429$	3278.47	−	5678.48i	0.368965	−	0.639067i
$430$	−1685.79	−	2919.88i	−0.189061	−	0.327463i
$431$	3844.36	+	6658.63i	0.429643	+	0.744164i	0.996841	−	0.0794172i	$-0.0253059\pi$
$431$	3844.36	+	6658.63i	0.429643	+	0.744164i	−0.567198	+	0.823581i	$0.691973\pi$
$432$	−1061.22	+	1838.09i	−0.118190	+	0.204711i
$433$	2752.17			0.305452			0.152726	−	0.988269i	$-0.451195\pi$
$433$	2752.17			0.305452			0.152726	+	0.988269i	$0.451195\pi$
$434$	−4382.33	+	11748.7i	−0.484697	+	1.29944i
$435$	−5898.71			−0.650165
$436$	−690.734	+	1196.39i	−0.0758720	+	0.131414i
$437$	−883.576	−	1530.40i	−0.0967212	−	0.167526i
$438$	−2914.95	−	5048.84i	−0.317995	−	0.550783i
$439$	−6868.51	+	11896.6i	−0.746733	+	1.29338i	0.202647	+	0.979252i	$0.435046\pi$
$439$	−6868.51	+	11896.6i	−0.746733	+	1.29338i	−0.949381	+	0.314128i	$0.898288\pi$
$440$	−3347.80			−0.362727
$441$	852.673	−	295.072i	0.0920714	−	0.0318618i
$442$	429.675			0.0462388
$443$	7602.81	−	13168.5i	0.815396	−	1.41231i	−0.0936469	−	0.995605i	$-0.529852\pi$
$443$	7602.81	−	13168.5i	0.815396	−	1.41231i	0.909043	−	0.416702i	$-0.136814\pi$
$444$	−751.259	−	1301.22i	−0.0802999	−	0.139084i
$445$	3122.60	+	5408.49i	0.332641	+	0.576151i
$446$	−3455.88	+	5985.75i	−0.366907	+	0.635501i
$447$	2506.12			0.265179
$448$	414.243	−	1110.55i	0.0436855	−	0.117118i
$449$	1130.68			0.118842			0.0594209	−	0.998233i	$-0.481075\pi$
$449$	1130.68			0.118842			0.0594209	+	0.998233i	$0.481075\pi$
$450$	−197.450	+	341.993i	−0.0206841	+	0.0358260i
$451$	−11188.0	−	19378.1i	−1.16812	−	2.02324i
$452$	2653.65	+	4596.26i	0.276144	+	0.478296i
$453$	−4256.24	+	7372.02i	−0.441447	+	0.764608i
$454$	−7368.16			−0.761685
$455$	1695.03	+	2053.01i	0.174647	+	0.211531i
$456$	−3345.85			−0.343604
$457$	−4589.82	+	7949.79i	−0.469809	+	0.813732i	−0.999404	−	0.0345181i	$-0.989010\pi$
$457$	−4589.82	+	7949.79i	−0.469809	+	0.813732i	0.529596	+	0.848250i	$0.322344\pi$
$458$	1640.87	+	2842.06i	0.167408	+	0.289958i
$459$	700.498	+	1213.30i	0.0712341	+	0.123381i
$460$	325.075	−	563.047i	0.0329494	−	0.0570700i
$461$	13727.6			1.38689			0.693445	−	0.720510i	$-0.256092\pi$
$461$	13727.6			1.38689			0.693445	+	0.720510i	$0.256092\pi$
$462$	−11774.3	+	1979.69i	−1.18570	+	0.199359i
$463$	11817.0			1.18614			0.593069	−	0.805151i	$-0.297916\pi$
$463$	11817.0			1.18614			0.593069	+	0.805151i	$0.297916\pi$
$464$	−1226.74	+	2124.77i	−0.122737	+	0.212586i
$465$	6511.28	+	11277.9i	0.649362	+	1.12473i
$466$	−6717.06	−	11634.3i	−0.667729	−	1.15654i
$467$	1961.83	−	3397.98i	0.194395	−	0.336702i	−0.752307	−	0.658813i	$-0.771059\pi$
$467$	1961.83	−	3397.98i	0.194395	−	0.336702i	0.946702	+	0.322111i	$0.104392\pi$
$468$	214.042			0.0211412
$469$	−7601.77	+	1278.13i	−0.748438	+	0.125839i
$470$	2694.01			0.264394
$471$	−7663.87	+	13274.2i	−0.749750	+	1.29861i
$472$	−1157.44	−	2004.75i	−0.112872	−	0.195500i
$473$	7063.03	+	12233.5i	0.686593	+	1.18921i
$474$	−5906.03	+	10229.5i	−0.572306	+	0.991263i
$475$	5767.03			0.557073
$476$	−498.133	−	603.334i	−0.0479661	−	0.0580962i
$477$	−31.2524			−0.00299989
$478$	−3592.73	+	6222.79i	−0.343781	+	0.595447i
$479$	−6554.45	−	11352.6i	−0.625220	−	1.08291i	−0.988498	−	0.151232i	$-0.951676\pi$
$479$	−6554.45	−	11352.6i	−0.625220	−	1.08291i	0.363278	−	0.931681i	$-0.381657\pi$
$480$	−615.483	−	1066.05i	−0.0585267	−	0.101371i
$481$	701.856	−	1215.65i	0.0665320	−	0.115237i
$482$	2222.16			0.209993
$483$	810.350	−	2172.49i	0.0763400	−	0.204662i
$484$	8702.41			0.817281
$485$	−1947.78	+	3373.66i	−0.182359	+	0.315855i
$486$	735.571	+	1274.05i	0.0686547	+	0.118913i
$487$	−1811.60	−	3137.79i	−0.168566	−	0.291965i	0.769350	−	0.638827i	$-0.220580\pi$
$487$	−1811.60	−	3137.79i	−0.168566	−	0.291965i	−0.937916	+	0.346863i	$0.887247\pi$
$488$	2247.16	−	3892.20i	0.208452	−	0.361049i
$489$	6975.71			0.645097
$490$	917.668	−	4760.21i	0.0846041	−	0.438866i
$491$	6124.55			0.562927			0.281464	−	0.959572i	$-0.409180\pi$
$491$	6124.55			0.562927			0.281464	+	0.959572i	$0.409180\pi$
$492$	4113.75	−	7125.22i	0.376955	−	0.652906i
$493$	809.753	+	1402.53i	0.0739745	+	0.128128i
$494$	−1562.91	−	2707.04i	−0.142346	−	0.246550i
$495$	−550.414	+	953.344i	−0.0499783	+	0.0865649i
$496$	5416.52			0.490341
$497$	810.076	−	2171.75i	0.0731124	−	0.196009i
$498$	−9015.58			−0.811240
$499$	−5863.34	+	10155.6i	−0.526010	+	0.911076i	0.473531	+	0.880777i	$0.342979\pi$
$499$	−5863.34	+	10155.6i	−0.526010	+	0.911076i	−0.999541	+	0.0302990i	$0.990354\pi$
$500$	2827.58	+	4897.52i	0.252907	+	0.438047i
$501$	10188.9	+	17647.7i	0.908598	+	1.57374i
$502$	4174.36	−	7230.20i	0.371137	−	0.642828i
$503$	−1144.58			−0.101460			−0.0507298	−	0.998712i	$-0.516155\pi$
$503$	−1144.58			−0.101460			−0.0507298	+	0.998712i	$0.516155\pi$
$504$	−248.144	−	300.550i	−0.0219310	−	0.0265626i
$505$	699.921			0.0616754
$506$	−1361.98	+	2359.02i	−0.119659	+	0.207255i
$507$	−4853.37	−	8406.28i	−0.425139	−	0.736363i
$508$	−711.557	−	1232.45i	−0.0621462	−	0.107640i
$509$	−9228.50	+	15984.2i	−0.803627	+	1.39192i	0.113587	+	0.993528i	$0.463766\pi$
$509$	−9228.50	+	15984.2i	−0.803627	+	1.39192i	−0.917214	+	0.398394i	$0.869568\pi$
$510$	−812.545			−0.0705492
$511$	−9780.35	+	1644.43i	−0.846688	+	0.142359i
$512$	−512.000			−0.0441942
$513$	5096.02	−	8826.57i	0.438586	−	0.759654i
$514$	6123.65	+	10606.5i	0.525491	+	0.910178i
$515$	3730.82	+	6461.97i	0.319223	+	0.552910i
$516$	−2597.04	+	4498.20i	−0.221566	+	0.383764i
$517$	−11287.2			−0.960174
$518$	−2520.65	+	423.813i	−0.213805	+	0.0359484i
$519$	−17015.6			−1.43912
$520$	575.009	−	995.944i	0.0484919	−	0.0839905i
$521$	−5380.03	−	9318.49i	−0.452406	−	0.783590i	0.546129	−	0.837701i	$-0.316101\pi$
$521$	−5380.03	−	9318.49i	−0.452406	−	0.783590i	−0.998535	+	0.0541108i	$0.982768\pi$
$522$	403.377	+	698.670i	0.0338225	+	0.0585823i
$523$	8189.08	−	14183.9i	0.684672	−	1.18589i	−0.288868	−	0.957369i	$-0.593279\pi$
$523$	8189.08	−	14183.9i	0.684672	−	1.18589i	0.973540	−	0.228518i	$-0.0733878\pi$
$524$	6062.50			0.505423
$525$	4817.71	+	5835.16i	0.400499	+	0.485081i
$526$	−8305.40			−0.688465
$527$	1787.69	−	3096.37i	0.147766	−	0.255939i
$528$	2578.71	+	4466.46i	0.212546	+	0.368140i
$529$	−264.500	−	458.127i	−0.0217391	−	0.0376533i
$530$	−83.9575	+	145.419i	−0.00688090	+	0.0119181i
$531$	−761.184			−0.0622082
$532$	−1989.21	+	5332.93i	−0.162111	+	0.434609i
$533$	7686.45			0.624648
$534$	4810.50	−	8332.02i	0.389832	−	0.675210i
$535$	−979.411	−	1696.39i	−0.0791469	−	0.137087i
$536$	1664.87	+	2883.65i	0.134163	+	0.232378i
$537$	−12371.6	+	21428.3i	−0.994182	+	1.72197i
$538$	6121.48			0.490549
$539$	−3844.79	+	19944.1i	−0.307249	+	1.59379i
$540$	3749.74			0.298821
$541$	4639.88	−	8036.51i	0.368732	−	0.638663i	−0.620635	−	0.784099i	$-0.713125\pi$
$541$	4639.88	−	8036.51i	0.368732	−	0.638663i	0.989368	+	0.145436i	$0.0464586\pi$
$542$	2661.63	+	4610.08i	0.210935	+	0.365351i
$543$	1347.63	+	2334.16i	0.106505	+	0.184473i
$544$	−168.982	+	292.686i	−0.0133181	+	0.0230677i
$545$	2440.66			0.191828
$546$	1433.39	−	3842.80i	0.112350	−	0.301203i
$547$	12380.3			0.967718			0.483859	−	0.875146i	$-0.339235\pi$
$547$	12380.3			0.967718			0.483859	+	0.875146i	$0.339235\pi$
$548$	5967.07	−	10335.3i	0.465147	−	0.805658i
$549$	−738.916	−	1279.84i	−0.0574429	−	0.0994940i
$550$	−4444.77	−	7698.57i	−0.344592	−	0.596851i
$551$	5890.84	−	10203.2i	0.455460	−	0.788879i
$552$	−1001.59			−0.0772288
$553$	12793.5	+	15495.4i	0.983789	+	1.19156i
$554$	−8201.86			−0.628996
$555$	−1327.26	+	2298.88i	−0.101512	+	0.175823i
$556$	−3015.03	−	5222.19i	−0.229975	−	0.398328i
$557$	2884.45	+	4996.02i	0.219422	+	0.380050i	0.954631	−	0.297790i	$-0.0962495\pi$
$557$	2884.45	+	4996.02i	0.219422	+	0.380050i	−0.735209	+	0.677840i	$0.762916\pi$
$558$	890.534	−	1542.45i	0.0675615	−	0.117020i
$559$	−4852.51			−0.367154
$560$	−2065.09	+	347.217i	−0.155832	+	0.0262010i
$561$	3404.35			0.256207
$562$	8582.08	−	14864.6i	0.644152	−	1.11570i
$563$	−1559.68	−	2701.45i	−0.116754	−	0.202225i	0.801725	−	0.597693i	$-0.203916\pi$
$563$	−1559.68	−	2701.45i	−0.116754	−	0.202225i	−0.918480	+	0.395468i	$0.870582\pi$
$564$	−2075.12	−	3594.21i	−0.154926	−	0.268339i
$565$	4688.24	−	8120.27i	0.349090	−	0.604641i
$566$	−7037.27			−0.522612
$567$	14485.2	−	2435.49i	1.07288	−	0.180389i
$568$	−1001.25			−0.0739636
$569$	−2376.64	+	4116.46i	−0.175104	+	0.303289i	−0.940197	−	0.340631i	$-0.889359\pi$
$569$	−2376.64	+	4116.46i	−0.175104	+	0.303289i	0.765093	+	0.643919i	$0.222693\pi$
$570$	2955.57	+	5119.20i	0.217185	+	0.376175i
$571$	11718.5	+	20297.0i	0.858851	+	1.48757i	0.873026	+	0.487674i	$0.162154\pi$
$571$	11718.5	+	20297.0i	0.858851	+	1.48757i	−0.0141750	+	0.999900i	$0.504512\pi$
$572$	−2409.14	+	4172.75i	−0.176103	+	0.305020i
$573$	4326.82			0.315455
$574$	−8911.10	−	10793.0i	−0.647983	−	0.784831i
$575$	1726.37			0.125208
$576$	−84.1782	+	145.801i	−0.00608928	+	0.0105469i
$577$	−1280.91	−	2218.60i	−0.0924175	−	0.160072i	0.816110	−	0.577896i	$-0.196126\pi$
$577$	−1280.91	−	2218.60i	−0.0924175	−	0.160072i	−0.908528	+	0.417824i	$0.862793\pi$
$578$	−4801.46	−	8316.37i	−0.345526	−	0.598469i
$579$	1510.96	−	2617.06i	0.108451	−	0.187843i
$580$	4334.58			0.310317
$581$	−5360.04	+	14369.9i	−0.382740	+	1.02610i
$582$	6001.29			0.427425
$583$	351.760	−	609.266i	0.0249887	−	0.0432817i
$584$	2142.01	+	3710.07i	0.151776	+	0.262883i
$585$	−189.075	−	327.488i	−0.0133629	−	0.0231452i
$586$	3157.18	−	5468.40i	0.222563	−	0.385490i
$587$	6248.52			0.439359			0.219680	−	0.975572i	$-0.429499\pi$
$587$	6248.52			0.439359			0.219680	+	0.975572i	$0.429499\pi$
$588$	−7057.69	+	2442.35i	−0.494990	+	0.171294i
$589$	−26010.4			−1.81959
$590$	−2044.87	+	3541.82i	−0.142688	+	0.247143i
$591$	12213.4	+	21154.3i	0.850074	+	1.47237i
$592$	552.051	+	956.181i	0.0383263	+	0.0663831i
$593$	9125.00	−	15805.0i	0.631904	−	1.09449i	−0.355258	−	0.934768i	$-0.615607\pi$
$593$	9125.00	−	15805.0i	0.631904	−	1.09449i	0.987162	−	0.159721i	$-0.0510596\pi$
$594$	−15710.5			−1.08520
$595$	−483.083	+	1295.11i	−0.0332848	+	0.0892343i
$596$	−1841.58			−0.126567
$597$	4284.90	−	7421.67i	0.293751	−	0.508792i
$598$	−467.860	−	810.358i	−0.0319937	−	0.0554147i
$599$	4848.02	+	8397.02i	0.330692	+	0.572776i	0.982648	−	0.185481i	$-0.0593844\pi$
$599$	4848.02	+	8397.02i	0.330692	+	0.572776i	−0.651955	+	0.758257i	$0.726051\pi$
$600$	1634.32	−	2830.72i	0.111201	−	0.192606i
$601$	−9471.96			−0.642877			−0.321439	−	0.946930i	$-0.604166\pi$
$601$	−9471.96			−0.642877			−0.321439	+	0.946930i	$0.604166\pi$
$602$	5625.64	+	6813.73i	0.380870	+	0.461307i
$603$	1094.89			0.0739427
$604$	3127.63	−	5417.22i	0.210698	−	0.364940i
$605$	−7687.33	−	13314.8i	−0.516586	−	0.894753i
$606$	−539.130	−	933.800i	−0.0361397	−	0.0625958i
$607$	6500.05	−	11258.4i	0.434644	−	0.752826i	−0.562622	−	0.826714i	$-0.690207\pi$
$607$	6500.05	−	11258.4i	0.434644	−	0.752826i	0.997267	+	0.0738883i	$0.0235408\pi$
$608$	2458.65			0.163999
$609$	15244.9	−	2563.22i	1.01438	−	0.170553i
$610$	−7940.19			−0.527031
$611$	1938.66	−	3357.85i	0.128363	−	0.222331i
$612$	55.5650	+	96.2414i	0.00367007	+	0.00635674i
$613$	−9174.16	−	15890.1i	−0.604471	−	1.04697i	−0.992135	−	0.125174i	$-0.960051\pi$
$613$	−9174.16	−	15890.1i	−0.604471	−	1.04697i	0.387664	−	0.921801i	$-0.373282\pi$
$614$	601.675	−	1042.13i	0.0395466	−	0.0684968i
$615$	−14535.6			−0.953061
$616$	8652.20	−	1454.75i	0.565921	−	0.0951518i
$617$	11707.8			0.763922			0.381961	−	0.924179i	$-0.375249\pi$
$617$	11707.8			0.763922			0.381961	+	0.924179i	$0.375249\pi$
$618$	5747.49	−	9954.95i	0.374107	−	0.647972i
$619$	8197.26	+	14198.1i	0.532271	+	0.921921i	0.999290	+	0.0376735i	$0.0119947\pi$
$619$	8197.26	+	14198.1i	0.532271	+	0.921921i	−0.467019	+	0.884247i	$0.654672\pi$
$620$	−4784.72	−	8287.37i	−0.309934	−	0.536821i
$621$	1525.50	−	2642.25i	0.0985770	−	0.170740i
$622$	8266.52			0.532890
$623$	−10420.4	−	12621.1i	−0.670119	−	0.811642i
$624$	−1771.65			−0.113658
$625$	304.301	−	527.064i	0.0194752	−	0.0337321i
$626$	−5544.68	−	9603.66i	−0.354009	−	0.613162i
$627$	−12383.1	−	21448.1i	−0.788729	−	1.36612i
$628$	5631.68	−	9754.36i	0.357848	−	0.619811i
$629$	728.804			0.0461992
$630$	−240.647	+	645.157i	−0.0152184	+	0.0407995i
$631$	−20099.8			−1.26808			−0.634041	−	0.773299i	$-0.718605\pi$
$631$	−20099.8			−1.26808			−0.634041	+	0.773299i	$0.718605\pi$
$632$	4339.96	−	7517.03i	0.273156	−	0.473120i
$633$	−12738.6	−	22063.9i	−0.799864	−	1.38541i
$634$	6753.57	+	11697.5i	0.423058	+	0.732758i
$635$	−1257.12	+	2177.39i	−0.0785625	+	0.136074i
$636$	258.680			0.0161279
$637$	−5272.84	−	4569.34i	−0.327971	−	0.284213i
$638$	−18160.8			−1.12695
$639$	−164.615	+	285.122i	−0.0101911	+	0.0176514i
$640$	452.278	+	783.369i	0.0279342	+	0.0483834i
$641$	−8295.14	−	14367.6i	−0.511136	−	0.885314i	−0.999917	−	0.0129073i	$-0.995891\pi$
$641$	−8295.14	−	14367.6i	−0.511136	−	0.885314i	0.488780	−	0.872407i	$-0.337442\pi$
$642$	−1508.82	+	2613.36i	−0.0927548	+	0.160656i
$643$	23133.2			1.41879			0.709396	−	0.704810i	$-0.248968\pi$
$643$	23133.2			1.41879			0.709396	+	0.704810i	$0.248968\pi$
$644$	−595.474	+	1596.42i	−0.0364363	+	0.0976830i
$645$	9176.43			0.560189
$646$	811.460	−	1405.49i	0.0494218	−	0.0856010i
$647$	11482.6	+	19888.5i	0.697725	+	1.20850i	0.969253	+	0.246065i	$0.0791378\pi$
$647$	11482.6	+	19888.5i	0.697725	+	1.20850i	−0.271528	+	0.962431i	$0.587529\pi$
$648$	−3172.42	−	5494.80i	−0.192322	−	0.333111i
$649$	8567.48	−	14839.3i	0.518186	−	0.897525i
$650$	3053.69			0.184270
$651$	−21728.7	−	26317.6i	−1.30817	−	1.58444i
$652$	−5126.00			−0.307898
$653$	−12323.3	+	21344.6i	−0.738512	+	1.27914i	0.214653	+	0.976690i	$0.431138\pi$
$653$	−12323.3	+	21344.6i	−0.738512	+	1.27914i	−0.953165	+	0.302450i	$0.902195\pi$
$654$	−1879.97	−	3256.20i	−0.112405	−	0.194691i
$655$	−5355.35	−	9275.73i	−0.319467	−	0.553333i
$656$	−3022.93	+	5235.86i	−0.179917	+	0.311625i
$657$	1408.68			0.0836494
$658$	−6962.52	+	1170.65i	−0.412503	+	0.0693567i
$659$	15924.1			0.941295			0.470647	−	0.882321i	$-0.344020\pi$
$659$	15924.1			0.941295			0.470647	+	0.882321i	$0.344020\pi$
$660$	4555.85	−	7890.96i	0.268691	−	0.465387i
$661$	−5335.78	−	9241.84i	−0.313975	−	0.543821i	0.665244	−	0.746626i	$-0.268328\pi$
$661$	−5335.78	−	9241.84i	−0.313975	−	0.543821i	−0.979219	+	0.202805i	$0.934994\pi$
$662$	−3556.00	−	6159.17i	−0.208773	−	0.361605i
$663$	−584.722	+	1012.77i	−0.0342515	+	0.0593253i
$664$	6624.96			0.387196
$665$	9916.66	−	1667.35i	0.578273	−	0.0972286i
$666$	363.053			0.0211231
$667$	1763.43	−	3054.36i	0.102369	−	0.177309i
$668$	−7487.18	−	12968.2i	−0.433664	−	0.751129i
$669$	−9405.85	−	16291.4i	−0.543574	−	0.941499i
$670$	2941.35	−	5094.57i	0.169604	−	0.293762i
$671$	33267.3			1.91397
$672$	2053.92	+	2487.69i	0.117904	+	0.142805i
$673$	−23453.7			−1.34335			−0.671675	−	0.740846i	$-0.734425\pi$
$673$	−23453.7			−1.34335			−0.671675	+	0.740846i	$0.734425\pi$
$674$	7607.26	−	13176.2i	0.434749	−	0.753007i
$675$	4978.42	+	8622.88i	0.283881	+	0.491696i
$676$	3566.43	+	6177.23i	0.202915	+	0.351458i
$677$	−7204.23	+	12478.1i	−0.408982	+	0.708378i	−0.994776	−	0.102082i	$-0.967450\pi$
$677$	−7204.23	+	12478.1i	−0.408982	+	0.708378i	0.585794	+	0.810460i	$0.300783\pi$
$678$	−14444.9			−0.818219
$679$	3567.95	−	9565.43i	0.201658	−	0.540629i
$680$	597.086			0.0336724
$681$	10027.0	−	17367.2i	0.564220	−	0.977257i
$682$	20046.7	+	34722.0i	1.12556	+	1.94952i
$683$	6276.70	+	10871.6i	0.351641	+	0.609061i	0.986537	−	0.163537i	$-0.0522903\pi$
$683$	6276.70	+	10871.6i	0.351641	+	0.609061i	−0.634896	+	0.772598i	$0.718957\pi$
$684$	404.227	−	700.142i	0.0225965	−	0.0391383i
$685$	−21084.2			−1.17604
$686$	−303.167	+	12701.3i	−0.0168731	+	0.706905i
$687$	−8931.89			−0.496030
$688$	1908.39	−	3305.44i	0.105751	−	0.183166i
$689$	120.835	+	209.292i	0.00668133	+	0.0115724i
$690$	884.757	+	1532.44i	0.0488146	+	0.0845494i
$691$	11137.1	−	19290.0i	0.613134	−	1.06198i	−0.377575	−	0.925979i	$-0.623242\pi$
$691$	11137.1	−	19290.0i	0.613134	−	1.06198i	0.990709	−	0.136000i	$-0.0434246\pi$
$692$	12503.7			0.686877
$693$	1008.25	−	2703.04i	0.0552673	−	0.148168i
$694$	11934.6			0.652785
$695$	−5326.69	+	9226.11i	−0.290724	+	0.503548i
$696$	−3338.81	−	5782.98i	−0.181835	−	0.314947i
$697$	1995.40	+	3456.13i	0.108438	+	0.187819i
$698$	11089.3	−	19207.3i	0.601342	−	1.04156i
$699$	36563.6			1.97849
$700$	−3540.22	−	4287.88i	−0.191154	−	0.231524i
$701$	16964.2			0.914024			0.457012	−	0.889461i	$-0.348920\pi$
$701$	16964.2			0.914024			0.457012	+	0.889461i	$0.348920\pi$
$702$	2698.38	−	4673.74i	0.145077	−	0.251280i
$703$	−2650.97	−	4591.62i	−0.142224	−	0.246339i
$704$	−1894.93	−	3282.12i	−0.101446	−	0.175709i
$705$	−3666.14	+	6349.93i	−0.195851	+	0.339223i
$706$	−406.309			−0.0216596
$707$	−1808.91	+	304.143i	−0.0962250	+	0.0161789i
$708$	6300.42			0.334441
$709$	−13493.7	+	23371.8i	−0.714763	+	1.23801i	0.248287	+	0.968686i	$0.420132\pi$
$709$	−13493.7	+	23371.8i	−0.714763	+	1.23801i	−0.963051	+	0.269320i	$0.913201\pi$
$710$	884.457	+	1531.92i	0.0467508	+	0.0809748i
$711$	−1427.07	−	2471.76i	−0.0752734	−	0.130377i
$712$	−3534.92	+	6122.66i	−0.186063	+	0.322270i
$713$	−7786.25			−0.408972
$714$	2099.98	−	353.082i	0.110070	−	0.0185067i
$715$	8512.51			0.445244
$716$	9091.11	−	15746.3i	0.474512	−	0.821880i
$717$	−9778.32	−	16936.5i	−0.509314	−	0.882157i
$718$	3630.09	+	6287.51i	0.188682	+	0.326807i
$719$	6753.79	−	11697.9i	0.350311	−	0.606757i	−0.635993	−	0.771695i	$-0.719409\pi$
$719$	6753.79	−	11697.9i	0.350311	−	0.606757i	0.986304	+	0.164938i	$0.0527425\pi$
$720$	297.438			0.0153956
$721$	−12450.1	−	15079.4i	−0.643087	−	0.778901i
$722$	1911.48			0.0985292
$723$	−3024.03	+	5237.77i	−0.155553	+	0.269426i
$724$	−990.287	−	1715.23i	−0.0508339	−	0.0880468i
$725$	5754.90	+	9967.78i	0.294802	+	0.510612i
$726$	−11842.7	+	20512.1i	−0.605403	+	1.04859i
$727$	−12991.8			−0.662777			−0.331388	−	0.943494i	$-0.607517\pi$
$727$	−12991.8			−0.662777			−0.331388	+	0.943494i	$0.607517\pi$
$728$	−1053.30	+	2823.83i	−0.0536236	+	0.143761i
$729$	17409.8			0.884512
$730$	3784.31	−	6554.62i	0.191868	−	0.332325i
$731$	−1259.71	−	2181.88i	−0.0637373	−	0.110396i
$732$	6116.10	+	10593.4i	0.308822	+	0.534895i
$733$	−677.394	+	1173.28i	−0.0341339	+	0.0591216i	−0.882588	−	0.470148i	$-0.844201\pi$
$733$	−677.394	+	1173.28i	−0.0341339	+	0.0591216i	0.848454	+	0.529269i	$0.177534\pi$
$734$	−10070.2			−0.506401
$735$	9971.30	+	8640.93i	0.500404	+	0.433640i
$736$	736.000			0.0368605
$737$	−12323.5	+	21345.0i	−0.615933	+	1.06683i
$738$	994.002	+	1721.66i	0.0495796	+	0.0858744i
$739$	8294.44	+	14366.4i	0.412877	+	0.715124i	0.995203	−	0.0978317i	$-0.0311907\pi$
$739$	8294.44	+	14366.4i	0.412877	+	0.715124i	−0.582326	+	0.812955i	$0.697857\pi$
$740$	975.316	−	1689.30i	0.0484505	−	0.0839187i
$741$	8507.55			0.421771
$742$	153.794	−	412.309i	0.00760908	−	0.0203994i
$743$	−29256.6			−1.44458			−0.722288	−	0.691593i	$-0.756909\pi$
$743$	−29256.6			−1.44458			−0.722288	+	0.691593i	$0.756909\pi$
$744$	−7371.07	+	12767.1i	−0.363221	+	0.629117i
$745$	1626.77	+	2817.65i	0.0800005	+	0.138565i
$746$	13545.8	+	23462.0i	0.664808	+	1.15148i
$747$	1089.21	−	1886.57i	0.0533498	−	0.0924045i
$748$	−2501.64			−0.122285
$749$	3268.38	+	3958.63i	0.159445	+	0.193118i
$750$	−15391.7			−0.749365
$751$	7107.16	−	12310.0i	0.345332	−	0.598132i	−0.640082	−	0.768306i	$-0.721100\pi$
$751$	7107.16	−	12310.0i	0.345332	−	0.598132i	0.985414	+	0.170174i	$0.0544331\pi$
$752$	1524.87	+	2641.15i	0.0739445	+	0.128076i
$753$	11361.3	+	19678.4i	0.549841	+	0.952353i
$754$	3119.25	−	5402.69i	0.150658	−	0.260948i
$755$	−11051.3			−0.532710
$756$	−9691.01	+	1629.41i	−0.466215	+	0.0783876i
$757$	16229.5			0.779223			0.389612	−	0.920979i	$-0.372609\pi$
$757$	16229.5			0.779223			0.389612	+	0.920979i	$0.372609\pi$
$758$	732.186	−	1268.18i	0.0350847	−	0.0607684i
$759$	−3706.90	−	6420.54i	−0.177275	−	0.307050i
$760$	−2171.86	−	3761.77i	−0.103660	−	0.179544i
$761$	3036.95	−	5260.16i	0.144664	−	0.250566i	−0.784583	−	0.620023i	$-0.787123\pi$
$761$	3036.95	−	5260.16i	0.144664	−	0.250566i	0.929248	+	0.369458i	$0.120456\pi$
$762$	3873.29			0.184140
$763$	−6307.75	+	1060.56i	−0.299287	+	0.0503209i
$764$	−3179.50			−0.150563
$765$	98.1674	−	170.031i	0.00463954	−	0.00803592i
$766$	−1840.77	−	3188.30i	−0.0868272	−	0.150389i
$767$	2943.05	+	5097.52i	0.138549	+	0.239975i
$768$	696.755	−	1206.81i	0.0327369	−	0.0567021i
$769$	9079.48			0.425766			0.212883	−	0.977078i	$-0.431715\pi$
$769$	9079.48			0.425766			0.212883	+	0.977078i	$0.431715\pi$
$770$	−9868.77	−	11953.0i	−0.461878	−	0.559422i
$771$	−33333.5			−1.55704
$772$	−1110.31	+	1923.11i	−0.0517627	+	0.0896557i
$773$	1306.40	+	2262.75i	0.0607866	+	0.105285i	0.894817	−	0.446433i	$-0.147306\pi$
$773$	1306.40	+	2262.75i	0.0607866	+	0.105285i	−0.834031	+	0.551718i	$0.813972\pi$
$774$	−627.521	−	1086.90i	−0.0291418	−	0.0504751i
$775$	12705.1	−	22005.8i	0.588876	−	1.01996i
$776$	−4409.96			−0.204005
$777$	2431.28	−	6518.08i	0.112254	−	0.300946i
$778$	−9663.66			−0.445320
$779$	14516.2	−	25142.8i	0.667648	−	1.15640i
$780$	1565.00	+	2710.66i	0.0718410	+	0.124432i
$781$	−3705.65	−	6418.37i	−0.169780	−	0.294068i
$782$	242.912	−	420.736i	0.0111081	−	0.0192398i
$783$	20341.2			0.928398
$784$	5186.24	−	1794.73i	0.236254	−	0.0817568i
$785$	−19899.1			−0.904752
$786$	−8250.15	+	14289.7i	−0.374393	+	0.648468i
$787$	−4121.59	−	7138.81i	−0.186682	−	0.323343i	0.757460	−	0.652882i	$-0.226440\pi$
$787$	−4121.59	−	7138.81i	−0.186682	−	0.323343i	−0.944142	+	0.329539i	$0.893107\pi$
$788$	−8974.87	−	15544.9i	−0.405732	−	0.702748i
$789$	11302.4	−	19576.3i	0.509982	−	0.883315i
$790$	−15334.9			−0.690623
$791$	−8587.93	+	23023.6i	−0.386033	+	1.03493i
$792$	−1246.19			−0.0559108
$793$	−5713.91	+	9896.78i	−0.255872	+	0.443184i
$794$	5612.33	+	9720.83i	0.250849	+	0.434483i
$795$	−228.507	−	395.786i	−0.0101941	−	0.0176567i
$796$	−3148.70	+	5453.70i	−0.140204	+	0.242841i
$797$	9141.47			0.406283			0.203141	−	0.979149i	$-0.434885\pi$
$797$	9141.47			0.406283			0.203141	+	0.979149i	$0.434885\pi$
$798$	−9863.02	−	11946.0i	−0.437528	−	0.529930i
$799$	2013.09			0.0891341
$800$	−1200.95	+	2080.11i	−0.0530752	+	0.0919289i
$801$	1162.36	+	2013.26i	0.0512733	+	0.0888079i
$802$	6542.72	+	11332.3i	0.288069	+	0.498950i
$803$	−15855.3	+	27462.2i	−0.696789	+	1.20687i
$804$	−9062.57			−0.397528
$805$	2968.57	−	499.124i	0.129973	−	0.0218532i
$806$	−13772.7			−0.601889
$807$	−8330.41	+	14428.7i	−0.363376	+	0.629385i
$808$	396.172	+	686.189i	0.0172491	+	0.0298763i
$809$	−6775.42	−	11735.4i	−0.294451	−	0.510004i	0.680406	−	0.732835i	$-0.261804\pi$
$809$	−6775.42	−	11735.4i	−0.294451	−	0.510004i	−0.974857	+	0.222831i	$0.928470\pi$
$810$	−5604.76	+	9707.73i	−0.243125	+	0.421105i
$811$	8593.49			0.372082			0.186041	−	0.982542i	$-0.440434\pi$
$811$	8593.49			0.372082			0.186041	+	0.982542i	$0.440434\pi$
$812$	−11202.5	+	1883.54i	−0.484151	+	0.0814033i
$813$	−14488.3			−0.625003
$814$	−4086.32	+	7077.72i	−0.175953	+	0.304759i
$815$	4528.08	+	7842.87i	0.194616	+	0.337084i
$816$	−459.919	−	796.603i	−0.0197309	−	0.0341749i
$817$	−9164.19	+	15872.8i	−0.392429	+	0.679707i
$818$	−8520.81			−0.364209
$819$	630.960	+	764.214i	0.0269201	+	0.0326054i
$820$	10681.3			0.454886
$821$	−7294.29	+	12634.1i	−0.310076	+	0.537068i	−0.978379	−	0.206822i	$-0.933688\pi$
$821$	−7294.29	+	12634.1i	−0.310076	+	0.537068i	0.668302	+	0.743890i	$0.267021\pi$
$822$	16240.6	+	28129.5i	0.689118	+	1.19359i
$823$	11967.3	+	20728.0i	0.506869	+	0.877923i	0.999968	+	0.00795024i	$0.00253067\pi$
$823$	11967.3	+	20728.0i	0.506869	+	0.877923i	−0.493099	+	0.869973i	$0.664136\pi$
$824$	−4223.46	+	7315.25i	−0.178557	+	0.309270i
$825$	24194.7			1.02103
$826$	3745.80	−	10042.2i	0.157788	−	0.423019i
$827$	−39607.7			−1.66541			−0.832706	−	0.553715i	$-0.813210\pi$
$827$	−39607.7			−1.66541			−0.832706	+	0.553715i	$0.813210\pi$
$828$	121.006	−	209.589i	0.00507881	−	0.00879676i
$829$	−15461.2	−	26779.5i	−0.647755	−	1.12194i	−0.983658	−	0.180048i	$-0.942375\pi$
$829$	−15461.2	−	26779.5i	−0.647755	−	1.12194i	0.335903	−	0.941897i	$-0.390959\pi$
$830$	−5852.20	−	10136.3i	−0.244738	−	0.423899i
$831$	11161.5	−	19332.3i	0.465930	−	0.807015i
$832$	1301.87			0.0542480
$833$	685.727	−	3557.06i	0.0285222	−	0.147953i
$834$	16412.0			0.681417
$835$	−13227.7	+	22911.1i	−0.548220	+	0.949545i
$836$	9099.53	+	15760.9i	0.376452	+	0.652034i
$837$	−22453.6	−	38890.8i	−0.927252	−	1.60605i
$838$	16467.6	−	28522.8i	0.678836	−	1.17578i
$839$	−40349.1			−1.66032			−0.830158	−	0.557528i	$-0.811750\pi$
$839$	−40349.1			−1.66032			−0.830158	+	0.557528i	$0.811750\pi$
$840$	1991.87	−	5340.06i	0.0818167	−	0.219345i
$841$	−875.206			−0.0358853
$842$	−4252.38	+	7365.34i	−0.174046	+	0.301456i
$843$	23357.8	+	40457.0i	0.954314	+	1.65292i
$844$	9360.78	+	16213.3i	0.381767	+	0.661240i
$845$	6300.85	−	10913.4i	0.256516	−	0.444298i
$846$	1002.82			0.0407537
$847$	25653.3	+	31071.1i	1.04068	+	1.26047i
$848$	−190.087			−0.00769767
$849$	9576.66	−	16587.3i	0.387126	−	0.670522i
$850$	792.734	+	1373.06i	0.0319889	+	0.0554064i
$851$	−793.574	−	1374.51i	−0.0319664	−	0.0553673i
$852$	1362.54	−	2360.00i	0.0547887	−	0.0948969i
$853$	−37021.2			−1.48603			−0.743014	−	0.669275i	$-0.766605\pi$
$853$	−37021.2			−1.48603			−0.743014	+	0.669275i	$0.766605\pi$
$854$	20521.0	−	3450.32i	0.822265	−	0.138252i
$855$	−1428.31			−0.0571311
$856$	1108.74	−	1920.39i	0.0442709	−	0.0766794i
$857$	−17738.2	−	30723.4i	−0.707029	−	1.22461i	−0.965954	−	0.258713i	$-0.916702\pi$
$857$	−17738.2	−	30723.4i	−0.707029	−	1.22461i	0.258925	−	0.965897i	$-0.416632\pi$
$858$	−6556.95	−	11357.0i	−0.260898	−	0.451889i
$859$	16023.7	−	27753.8i	0.636461	−	1.10238i	−0.349742	−	0.936846i	$-0.613731\pi$
$859$	16023.7	−	27753.8i	0.636461	−	1.10238i	0.986203	−	0.165538i	$-0.0529359\pi$
$860$	−6743.17			−0.267372
$861$	37566.5	−	6316.29i	1.48695	−	0.250010i
$862$	15377.4			0.607608
$863$	−17563.9	+	30421.6i	−0.692796	+	1.19996i	0.278122	+	0.960546i	$0.410288\pi$
$863$	−17563.9	+	30421.6i	−0.692796	+	1.19996i	−0.970918	+	0.239412i	$0.923045\pi$
$864$	2122.44	+	3676.17i	0.0835728	+	0.144752i
$865$	−11045.2	−	19130.9i	−0.434160	−	0.751988i
$866$	2752.17	−	4766.90i	0.107994	−	0.187051i
$867$	26136.2			1.02380
$868$	15967.0	+	19339.1i	0.624374	+	0.756236i
$869$	64249.4			2.50807
$870$	−5898.71	+	10216.9i	−0.229868	+	0.398143i
$871$	−4233.31	−	7332.30i	−0.164684	−	0.285242i
$872$	1381.47	+	2392.77i	0.0536496	+	0.0929238i
$873$	−725.044	+	1255.81i	−0.0281088	+	0.0486859i
$874$	−3534.30			−0.136784
$875$	−9150.82	+	24532.7i	−0.353548	+	0.947836i
$876$	−11659.8			−0.449712
$877$	−7830.33	+	13562.5i	−0.301495	+	0.522205i	−0.976475	−	0.215631i	$-0.930819\pi$
$877$	−7830.33	+	13562.5i	−0.301495	+	0.522205i	0.674980	+	0.737836i	$0.264152\pi$
$878$	13737.0	+	23793.2i	0.528020	+	0.914558i
$879$	8592.89	+	14883.3i	0.329728	+	0.571106i
$880$	−3347.80	+	5798.56i	−0.128243	+	0.222124i
$881$	1733.30			0.0662842			0.0331421	−	0.999451i	$-0.489449\pi$
$881$	1733.30			0.0662842			0.0331421	+	0.999451i	$0.489449\pi$
$882$	341.594	−	1771.95i	0.0130409	−	0.0676468i
$883$	−31775.4			−1.21102			−0.605509	−	0.795839i	$-0.707030\pi$
$883$	−31775.4			−1.21102			−0.605509	+	0.795839i	$0.707030\pi$
$884$	429.675	−	744.218i	0.0163479	−	0.0283154i
$885$	−5565.52	−	9639.76i	−0.211393	−	0.366143i
$886$	−15205.6	−	26336.9i	−0.576572	−	0.998652i
$887$	−11934.8	+	20671.6i	−0.451781	+	0.782508i	−0.998497	−	0.0548107i	$-0.982544\pi$
$887$	−11934.8	+	20671.6i	−0.451781	+	0.782508i	0.546716	+	0.837318i	$0.315878\pi$
$888$	−3005.04			−0.113561
$889$	2302.79	−	6173.62i	0.0868764	−	0.232909i
$890$	12490.4			0.470425
$891$	23482.5	−	40672.9i	0.882933	−	1.52928i
$892$	6911.75	+	11971.5i	0.259442	+	0.449367i
$893$	−7322.49	−	12682.9i	−0.274398	−	0.475272i
$894$	2506.12	−	4340.72i	0.0937551	−	0.162389i
$895$	−32122.8			−1.19972
$896$	−1509.29	−	1828.04i	−0.0562745	−	0.0681592i
$897$	2546.75			0.0947977
$898$	1130.68	−	1958.39i	0.0420169	−	0.0727754i
$899$	−25955.6	−	44956.5i	−0.962924	−	1.66783i
$900$	394.899	+	683.985i	0.0146259	+	0.0253328i
$901$	−62.7371	+	108.664i	−0.00231973	+	0.00401789i
$902$	−44751.8			−1.65197
$903$	−23716.0	+	3987.52i	−0.873997	+	0.146950i
$904$	10614.6			0.390527
$905$	−1749.55	+	3030.31i	−0.0642620	+	0.111305i
$906$	8512.47	+	14744.0i	0.312150	+	0.540660i
$907$	3748.50	+	6492.59i	0.137229	+	0.237688i	0.926447	−	0.376426i	$-0.122847\pi$
$907$	3748.50	+	6492.59i	0.137229	+	0.237688i	−0.789218	+	0.614114i	$0.789514\pi$
$908$	−7368.16	+	12762.0i	−0.269296	+	0.466435i
$909$	260.539			0.00950665
$910$	5250.95	−	882.874i	0.191283	−	0.0321615i
$911$	33271.5			1.21003			0.605013	−	0.796216i	$-0.293168\pi$
$911$	33271.5			1.21003			0.605013	+	0.796216i	$0.293168\pi$
$912$	−3345.85	+	5795.17i	−0.121482	+	0.210414i
$913$	24519.2	+	42468.5i	0.888793	+	1.53943i
$914$	9179.63	+	15899.6i	0.332205	+	0.575396i
$915$	10805.4	−	18715.5i	0.390399	−	0.676192i
$916$	6563.47			0.236750
$917$	17871.3	+	21645.5i	0.643579	+	0.779497i
$918$	2801.99			0.100740
$919$	−19795.0	+	34285.9i	−0.710529	+	1.23067i	0.254130	+	0.967170i	$0.418211\pi$
$919$	−19795.0	+	34285.9i	−0.710529	+	1.23067i	−0.964659	+	0.263502i	$0.915122\pi$
$920$	−650.150	−	1126.09i	−0.0232987	−	0.0403546i
$921$	1637.58	+	2836.37i	0.0585885	+	0.101478i
$922$	13727.6	−	23776.8i	0.490339	−	0.849293i
$923$	2545.89			0.0907897
$924$	−8345.42	+	22373.5i	−0.297126	+	0.796572i
$925$	5179.60			0.184113
$926$	11817.0	−	20467.6i	0.419363	−	0.726359i
$927$	1388.76	+	2405.41i	0.0492049	+	0.0852255i
$928$	2453.47	+	4249.54i	0.0867879	+	0.150321i
$929$	433.517	−	750.873i	0.0153103	−	0.0265181i	−0.858269	−	0.513200i	$-0.828460\pi$
$929$	433.517	−	750.873i	0.0153103	−	0.0265181i	0.873579	+	0.486682i	$0.161793\pi$
$930$	26045.1			0.918337
$931$	−24904.5	+	8618.35i	−0.876706	+	0.303389i
$932$	−26868.2			−0.944311
$933$	−11249.5	+	19484.7i	−0.394739	+	0.683709i
$934$	−3923.65	−	6795.97i	−0.137458	−	0.238084i
$935$	2209.84	+	3827.55i	0.0772935	+	0.133876i
$936$	214.042	−	370.731i	0.00747454	−	0.0129463i
$937$	−13213.5			−0.460689			−0.230344	−	0.973109i	$-0.573985\pi$
$937$	−13213.5			−0.460689			−0.230344	+	0.973109i	$0.573985\pi$
$938$	−5387.98	+	14444.8i	−0.187552	+	0.502814i
$939$	30181.9			1.04893
$940$	2694.01	−	4666.16i	0.0934774	−	0.161908i
$941$	−10425.0	−	18056.6i	−0.361153	−	0.625536i	0.626998	−	0.779021i	$-0.284284\pi$
$941$	−10425.0	−	18056.6i	−0.361153	−	0.625536i	−0.988151	+	0.153485i	$0.950950\pi$
$942$	15327.7	+	26548.4i	0.530154	+	0.918253i
$943$	4345.46	−	7526.55i	0.150061	−	0.259913i
$944$	−4629.77			−0.159625
$945$	11053.6	+	13388.1i	0.380502	+	0.460861i
$946$	28252.1			0.970990
$947$	9118.95	−	15794.5i	0.312910	−	0.541977i	−0.666081	−	0.745880i	$-0.732029\pi$
$947$	9118.95	−	15794.5i	0.312910	−	0.541977i	0.978991	+	0.203903i	$0.0653627\pi$
$948$	11812.1	+	20459.1i	0.404682	+	0.700929i
$949$	−5446.52	−	9433.66i	−0.186303	−	0.322686i
$950$	5767.03	−	9988.79i	0.196955	−	0.341136i
$951$	−36762.4			−1.25352
$952$	−1543.14	+	259.457i	−0.0525351	+	0.00883305i
$953$	−27324.0			−0.928762			−0.464381	−	0.885636i	$-0.653723\pi$
$953$	−27324.0			−0.928762			−0.464381	+	0.885636i	$0.653723\pi$
$954$	−31.2524	+	54.1307i	−0.00106062	+	0.00183705i
$955$	2808.63	+	4864.70i	0.0951678	+	0.164835i
$956$	7185.45	+	12445.6i	0.243090	+	0.421044i
$957$	24714.1	−	42806.1i	0.834789	−	1.44590i
$958$	−26217.8			−0.884195
$959$	54491.0	−	9161.91i	1.83483	−	0.308502i
$960$	−2461.93			−0.0827693
$961$	−42406.6	+	73450.4i	−1.42347	+	2.46552i
$962$	−1403.71	−	2431.30i	−0.0470452	−	0.0814847i
$963$	−364.577	−	631.465i	−0.0121997	−	0.0211305i
$964$	2222.16	−	3848.90i	0.0742438	−	0.128594i
$965$	3923.19			0.130872
$966$	−2952.51	−	3576.06i	−0.0983391	−	0.119107i
$967$	−18434.0			−0.613029			−0.306514	−	0.951866i	$-0.599163\pi$
$967$	−18434.0			−0.613029			−0.306514	+	0.951866i	$0.599163\pi$
$968$	8702.41	−	15073.0i	0.288953	−	0.500480i
$969$	2208.55	+	3825.32i	0.0732186	+	0.126818i
$970$	3895.56	+	6747.32i	0.128947	+	0.223344i
$971$	−3841.26	+	6653.25i	−0.126953	+	0.219890i	−0.922495	−	0.386009i	$-0.873853\pi$
$971$	−3841.26	+	6653.25i	−0.126953	+	0.219890i	0.795541	+	0.605899i	$0.207187\pi$
$972$	2942.28			0.0970924
$973$	9757.46	−	26159.0i	0.321490	−	0.861891i
$974$	−7246.41			−0.238388
$975$	−4155.61	+	7197.73i	−0.136498	+	0.236422i
$976$	−4494.33	−	7784.41i	−0.147398	−	0.255300i
$977$	−15053.4	−	26073.3i	−0.492939	−	0.853795i	0.507028	−	0.861929i	$-0.330744\pi$
$977$	−15053.4	−	26073.3i	−0.492939	−	0.853795i	−0.999967	+	0.00813471i	$0.997411\pi$
$978$	6975.71	−	12082.3i	0.228076	−	0.395040i
$979$	−52331.5			−1.70840
$980$	−7327.26	−	6349.66i	−0.238838	−	0.206972i
$981$	908.513			0.0295684
$982$	6124.55	−	10608.0i	0.199025	−	0.344721i
$983$	7718.81	+	13369.4i	0.250449	+	0.433791i	0.963650	−	0.267169i	$-0.0860883\pi$
$983$	7718.81	+	13369.4i	0.250449	+	0.433791i	−0.713200	+	0.700960i	$0.752755\pi$
$984$	−8227.49	−	14250.4i	−0.266548	−	0.461674i
$985$	−15856.0	+	27463.4i	−0.512908	+	0.888383i
$986$	3239.01			0.104616
$987$	6715.64	−	18004.1i	0.216577	−	0.580626i
$988$	−6251.64			−0.201307
$989$	−2743.32	+	4751.56i	−0.0882026	+	0.152771i
$990$	1100.83	+	1906.69i	0.0353400	+	0.0612106i
$991$	−25596.8	−	44335.0i	−0.820494	−	1.42114i	−0.905315	−	0.424741i	$-0.860365\pi$
$991$	−25596.8	−	44335.0i	−0.820494	−	1.42114i	0.0848214	−	0.996396i	$-0.472968\pi$
$992$	5416.52	−	9381.69i	0.173362	−	0.300271i
$993$	19356.7			0.618597
$994$	−2951.51	−	3574.85i	−0.0941814	−	0.114072i
$995$	11125.7			0.354480
$996$	−9015.58	+	15615.4i	−0.286817	+	0.496781i
$997$	8365.41	+	14489.3i	0.265732	+	0.460262i	0.967755	−	0.251892i	$-0.0810529\pi$
$997$	8365.41	+	14489.3i	0.265732	+	0.460262i	−0.702023	+	0.712154i	$0.747720\pi$
$998$	11726.7	+	20311.2i	0.371945	+	0.644228i
$999$	4576.94	−	7927.49i	0.144953	−	0.251066i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	322.4.e.c.93.9	✓	22
7.2	even	3		2254.4.a.t.1.3		11
7.4	even	3	inner	322.4.e.c.277.9	yes	22
7.5	odd	6		2254.4.a.s.1.9		11

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
322.4.e.c.93.9	✓	22	1.1	even	1	trivial
322.4.e.c.277.9	yes	22	7.4	even	3	inner
2254.4.a.s.1.9		11	7.5	odd	6
2254.4.a.t.1.3		11	7.2	even	3

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 322 = 2 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	322.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.00000 - 1.73205i) q^{2} +(2.72170 + 4.71412i) q^{3} +(-2.00000 - 3.46410i) q^{4} +(-3.53343 + 6.12007i) q^{5} +10.8868 q^{6} +(6.47254 - 17.3524i) q^{7} -8.00000 q^{8} +(-1.31529 + 2.27814i) q^{9} +(7.06685 + 12.2401i) q^{10} +(-29.6083 - 51.2831i) q^{11} +(10.8868 - 18.8565i) q^{12} +20.3418 q^{13} +(-23.5827 - 28.5632i) q^{14} -38.4677 q^{15} +(-8.00000 + 13.8564i) q^{16} +(5.28070 + 9.14644i) q^{17} +(2.63057 + 4.55628i) q^{18} +(38.4163 - 66.5390i) q^{19} +28.2674 q^{20} +(99.4177 - 16.7157i) q^{21} -118.433 q^{22} +(11.5000 - 19.9186i) q^{23} +(-21.7736 - 37.7130i) q^{24} +(37.5298 + 65.0035i) q^{25} +(20.3418 - 35.2330i) q^{26} +132.652 q^{27} +(-73.0556 + 12.2833i) q^{28} +153.342 q^{29} +(-38.4677 + 66.6280i) q^{30} +(-169.266 - 293.178i) q^{31} +(16.0000 + 27.7128i) q^{32} +(161.170 - 279.154i) q^{33} +21.1228 q^{34} +(83.3278 + 100.926i) q^{35} +10.5223 q^{36} +(34.5032 - 59.7613i) q^{37} +(-76.8327 - 133.078i) q^{38} +(55.3641 + 95.8935i) q^{39} +(28.2674 - 48.9606i) q^{40} +377.866 q^{41} +(70.4652 - 188.912i) q^{42} -238.549 q^{43} +(-118.433 + 205.132i) q^{44} +(-9.29492 - 16.0993i) q^{45} +(-23.0000 - 39.8372i) q^{46} +(95.3043 - 165.072i) q^{47} -87.0944 q^{48} +(-259.212 - 224.628i) q^{49} +150.119 q^{50} +(-28.7449 + 49.7877i) q^{51} +(-40.6835 - 70.4659i) q^{52} +(5.94023 + 10.2888i) q^{53} +(132.652 - 229.761i) q^{54} +418.475 q^{55} +(-51.7803 + 138.819i) q^{56} +418.231 q^{57} +(153.342 - 265.596i) q^{58} +(144.680 + 250.594i) q^{59} +(76.9353 + 133.256i) q^{60} +(-280.896 + 486.525i) q^{61} -677.065 q^{62} +(31.0180 + 37.5687i) q^{63} +64.0000 q^{64} +(-71.8761 + 124.493i) q^{65} +(-322.339 - 558.308i) q^{66} +(-208.109 - 360.456i) q^{67} +(21.1228 - 36.5857i) q^{68} +125.198 q^{69} +(258.137 - 43.4021i) q^{70} +125.156 q^{71} +(10.5223 - 18.2251i) q^{72} +(-267.751 - 463.758i) q^{73} +(-69.0064 - 119.523i) q^{74} +(-204.290 + 353.840i) q^{75} -307.331 q^{76} +(-1081.53 + 181.844i) q^{77} +221.456 q^{78} +(-542.495 + 939.629i) q^{79} +(-56.5348 - 97.9212i) q^{80} +(396.553 + 686.850i) q^{81} +(377.866 - 654.483i) q^{82} -828.120 q^{83} +(-256.740 - 310.961i) q^{84} -74.6358 q^{85} +(-238.549 + 413.179i) q^{86} +(417.351 + 722.873i) q^{87} +(236.866 + 410.264i) q^{88} +(441.865 - 765.333i) q^{89} -37.1797 q^{90} +(131.663 - 352.979i) q^{91} -92.0000 q^{92} +(921.383 - 1595.88i) q^{93} +(-190.609 - 330.144i) q^{94} +(271.482 + 470.221i) q^{95} +(-87.0944 + 150.852i) q^{96} +551.245 q^{97} +(-648.280 + 224.341i) q^{98} +155.773 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q + 22 q^{2} - 44 q^{4} - 17 q^{5} + 11 q^{7} - 176 q^{8} - 59 q^{9} + 34 q^{10} + 6 q^{13} + 44 q^{14} - 288 q^{15} - 176 q^{16} - 47 q^{17} + 118 q^{18} + 138 q^{19} + 136 q^{20} + 97 q^{21} + 253 q^{23}+ \cdots + 7050 q^{99}+O(q^{100}) \) 22 * q + 22 * q^2 - 44 * q^4 - 17 * q^5 + 11 * q^7 - 176 * q^8 - 59 * q^9 + 34 * q^10 + 6 * q^13 + 44 * q^14 - 288 * q^15 - 176 * q^16 - 47 * q^17 + 118 * q^18 + 138 * q^19 + 136 * q^20 + 97 * q^21 + 253 * q^23 - 350 * q^25 + 6 * q^26 - 174 * q^27 + 44 * q^28 - 502 * q^29 - 288 * q^30 + 46 * q^31 + 352 * q^32 + 222 * q^33 - 188 * q^34 + 597 * q^35 + 472 * q^36 - 475 * q^37 - 276 * q^38 + 115 * q^39 + 136 * q^40 + 1480 * q^41 + 520 * q^42 + 34 * q^43 - 875 * q^45 - 506 * q^46 + 33 * q^47 + 221 * q^49 - 1400 * q^50 - 1017 * q^51 - 12 * q^52 + 835 * q^53 - 174 * q^54 - 2646 * q^55 - 88 * q^56 + 878 * q^57 - 502 * q^58 - 1723 * q^59 + 576 * q^60 + 253 * q^61 + 184 * q^62 - 601 * q^63 + 1408 * q^64 - 1753 * q^65 - 444 * q^66 + 2573 * q^67 - 188 * q^68 + 1188 * q^70 + 2638 * q^71 + 472 * q^72 - 1159 * q^73 + 950 * q^74 - 268 * q^75 - 1104 * q^76 + 307 * q^77 + 460 * q^78 - 1095 * q^79 - 272 * q^80 + 3085 * q^81 + 1480 * q^82 - 902 * q^83 + 652 * q^84 + 5014 * q^85 + 34 * q^86 - 3540 * q^87 - 3634 * q^89 - 3500 * q^90 + 2286 * q^91 - 2024 * q^92 - 3132 * q^93 - 66 * q^94 + 4249 * q^95 - 3026 * q^97 - 1162 * q^98 + 7050 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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