LMFDB - Embedded newform 126.4.m.a.41.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [126,4,Mod(41,126)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(126, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("126.41");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 126 = 2 \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	126.m (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:	$7.43424066072$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			41.4
Character	$\chi$	$=$	126.41
Dual form			126.4.m.a.83.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.73205 + 1.00000i) q^{2} +(-2.30109 - 4.65886i) q^{3} +(2.00000 - 3.46410i) q^{4} +(-2.59824 + 4.50028i) q^{5} +(8.64447 + 5.76829i) q^{6} +(-3.66839 + 18.1533i) q^{7} +8.00000i q^{8} +(-16.4100 + 21.4409i) q^{9} +O(q^{10})$	\(q+(-1.73205 + 1.00000i) q^{2} +(-2.30109 - 4.65886i) q^{3} +(2.00000 - 3.46410i) q^{4} +(-2.59824 + 4.50028i) q^{5} +(8.64447 + 5.76829i) q^{6} +(-3.66839 + 18.1533i) q^{7} +8.00000i q^{8} +(-16.4100 + 21.4409i) q^{9} -10.3929i q^{10} +(60.1559 - 34.7310i) q^{11} +(-20.7409 - 1.34651i) q^{12} +(-21.9826 - 12.6916i) q^{13} +(-11.7995 - 35.1109i) q^{14} +(26.9450 + 1.74927i) q^{15} +(-8.00000 - 13.8564i) q^{16} +102.093 q^{17} +(6.98197 - 53.5467i) q^{18} -118.577i q^{19} +(10.3929 + 18.0011i) q^{20} +(93.0151 - 24.6819i) q^{21} +(-69.4620 + 120.312i) q^{22} +(62.2408 + 35.9348i) q^{23} +(37.2709 - 18.4087i) q^{24} +(48.9983 + 84.8676i) q^{25} +50.7666 q^{26} +(137.651 + 27.1142i) q^{27} +(55.5482 + 49.0143i) q^{28} +(49.6924 - 28.6899i) q^{29} +(-48.4193 + 23.9151i) q^{30} +(50.1944 + 28.9798i) q^{31} +(27.7128 + 16.0000i) q^{32} +(-300.231 - 200.339i) q^{33} +(-176.830 + 102.093i) q^{34} +(-72.1636 - 63.6754i) q^{35} +(41.4536 + 99.7276i) q^{36} +40.2838 q^{37} +(118.577 + 205.382i) q^{38} +(-8.54470 + 131.618i) q^{39} +(-36.0022 - 20.7859i) q^{40} +(120.231 - 208.246i) q^{41} +(-136.425 + 135.765i) q^{42} +(80.2004 + 138.911i) q^{43} -277.848i q^{44} +(-53.8532 - 129.558i) q^{45} -143.739 q^{46} +(280.682 + 486.155i) q^{47} +(-46.1463 + 69.1557i) q^{48} +(-316.086 - 133.187i) q^{49} +(-169.735 - 97.9967i) q^{50} +(-234.925 - 475.637i) q^{51} +(-87.9303 + 50.7666i) q^{52} -768.800i q^{53} +(-265.533 + 90.6879i) q^{54} +360.958i q^{55} +(-145.227 - 29.3471i) q^{56} +(-552.436 + 272.857i) q^{57} +(-57.3799 + 99.3849i) q^{58} +(-86.9423 + 150.588i) q^{59} +(59.9496 - 89.8415i) q^{60} +(-357.490 + 206.397i) q^{61} -115.919 q^{62} +(-329.026 - 376.549i) q^{63} -64.0000 q^{64} +(114.232 - 65.9518i) q^{65} +(720.354 + 46.7656i) q^{66} +(271.005 - 469.395i) q^{67} +(204.186 - 353.660i) q^{68} +(24.1932 - 372.660i) q^{69} +(188.667 + 38.1254i) q^{70} +870.130i q^{71} +(-171.527 - 131.280i) q^{72} +822.641i q^{73} +(-69.7736 + 40.2838i) q^{74} +(282.637 - 423.564i) q^{75} +(-410.764 - 237.155i) q^{76} +(409.808 + 1219.44i) q^{77} +(-116.818 - 236.514i) q^{78} +(46.1797 + 79.9856i) q^{79} +83.1436 q^{80} +(-190.426 - 703.689i) q^{81} +480.923i q^{82} +(223.747 + 387.541i) q^{83} +(100.530 - 371.577i) q^{84} +(-265.262 + 459.447i) q^{85} +(-277.822 - 160.401i) q^{86} +(-248.009 - 165.492i) q^{87} +(277.848 + 481.247i) q^{88} -103.529 q^{89} +(222.834 + 170.548i) q^{90} +(311.036 - 352.499i) q^{91} +(248.963 - 143.739i) q^{92} +(19.5108 - 300.534i) q^{93} +(-972.311 - 561.364i) q^{94} +(533.632 + 308.092i) q^{95} +(10.7721 - 165.928i) q^{96} +(1263.72 - 729.611i) q^{97} +(680.664 - 85.3993i) q^{98} +(-242.491 + 1859.73i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 96 q^{4} - 12 q^{7} - 36 q^{9}+O(q^{10}) $ 48 * q + 96 * q^4 - 12 * q^7 - 36 * q^9	$ 48 q + 96 q^{4} - 12 q^{7} - 36 q^{9} + 24 q^{11} - 132 q^{14} - 120 q^{15} - 384 q^{16} + 120 q^{18} + 180 q^{21} + 348 q^{23} - 600 q^{25} - 96 q^{28} - 84 q^{29} + 192 q^{30} + 96 q^{36} - 672 q^{37} + 1368 q^{39} + 1128 q^{42} + 84 q^{43} - 1008 q^{46} - 42 q^{49} + 456 q^{50} + 2016 q^{51} - 528 q^{56} + 732 q^{57} + 504 q^{58} - 1008 q^{60} - 774 q^{63} - 3072 q^{64} - 6972 q^{65} + 1176 q^{67} + 216 q^{70} - 384 q^{72} + 2520 q^{74} + 1500 q^{77} + 2832 q^{78} + 348 q^{79} + 2268 q^{81} - 1080 q^{84} + 720 q^{85} + 1200 q^{86} + 180 q^{91} + 1392 q^{92} + 5232 q^{93} - 5892 q^{95} + 972 q^{99}+O(q^{100}) $ 48 * q + 96 * q^4 - 12 * q^7 - 36 * q^9 + 24 * q^11 - 132 * q^14 - 120 * q^15 - 384 * q^16 + 120 * q^18 + 180 * q^21 + 348 * q^23 - 600 * q^25 - 96 * q^28 - 84 * q^29 + 192 * q^30 + 96 * q^36 - 672 * q^37 + 1368 * q^39 + 1128 * q^42 + 84 * q^43 - 1008 * q^46 - 42 * q^49 + 456 * q^50 + 2016 * q^51 - 528 * q^56 + 732 * q^57 + 504 * q^58 - 1008 * q^60 - 774 * q^63 - 3072 * q^64 - 6972 * q^65 + 1176 * q^67 + 216 * q^70 - 384 * q^72 + 2520 * q^74 + 1500 * q^77 + 2832 * q^78 + 348 * q^79 + 2268 * q^81 - 1080 * q^84 + 720 * q^85 + 1200 * q^86 + 180 * q^91 + 1392 * q^92 + 5232 * q^93 - 5892 * q^95 + 972 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/126\mathbb{Z}\right)^\times$.

$n$	$29$	$73$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$

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 $

$2$	−1.73205	+	1.00000i	−0.612372	+	0.353553i
$2$	−1.73205	+	1.00000i	−0.612372	+	0.353553i
$3$	−2.30109	−	4.65886i	−0.442845	−	0.896598i
$3$	−2.30109	−	4.65886i	−0.442845	−	0.896598i
$4$	2.00000	−	3.46410i	0.250000	−	0.433013i
$5$	−2.59824	+	4.50028i	−0.232393	+	0.402517i	−0.958512	−	0.285052i	$-0.907989\pi$
$5$	−2.59824	+	4.50028i	−0.232393	+	0.402517i	0.726119	+	0.687570i	$0.241322\pi$
$6$	8.64447	+	5.76829i	0.588181	+	0.392483i
$7$	−3.66839	+	18.1533i	−0.198074	+	0.980187i
$7$	−3.66839	+	18.1533i	−0.198074	+	0.980187i
$8$			8.00000i			0.353553i
$9$	−16.4100	+	21.4409i	−0.607776	+	0.794108i
$10$		−	10.3929i		−	0.328654i
$11$	60.1559	−	34.7310i	1.64888	−	0.951981i	0.671361	−	0.741130i	$-0.265710\pi$
$11$	60.1559	−	34.7310i	1.64888	−	0.951981i	0.977518	−	0.210851i	$-0.0676235\pi$
$12$	−20.7409	−	1.34651i	−0.498950	−	0.0323920i
$13$	−21.9826	−	12.6916i	−0.468990	−	0.270771i	0.246827	−	0.969060i	$-0.420612\pi$
$13$	−21.9826	−	12.6916i	−0.468990	−	0.270771i	−0.715817	+	0.698288i	$0.753945\pi$
$14$	−11.7995	−	35.1109i	−0.225253	−	0.670269i
$15$	26.9450	+	1.74927i	0.463810	+	0.0301107i
$16$	−8.00000	−	13.8564i	−0.125000	−	0.216506i
$17$	102.093			1.45654			0.728270	−	0.685291i	$-0.240325\pi$
$17$	102.093			1.45654			0.728270	+	0.685291i	$0.240325\pi$
$18$	6.98197	−	53.5467i	0.0914259	−	0.701171i
$19$		−	118.577i		−	1.43176i	−0.698221	−	0.715882i	$-0.746025\pi$
$19$		−	118.577i		−	1.43176i	0.698221	−	0.715882i	$-0.253975\pi$
$20$	10.3929	+	18.0011i	0.116197	+	0.201259i
$21$	93.0151	−	24.6819i	0.966550	−	0.256478i
$22$	−69.4620	+	120.312i	−0.673152	+	1.16593i
$23$	62.2408	+	35.9348i	0.564266	+	0.325779i	0.754856	−	0.655891i	$-0.227707\pi$
$23$	62.2408	+	35.9348i	0.564266	+	0.325779i	−0.190590	+	0.981670i	$0.561040\pi$
$24$	37.2709	−	18.4087i	0.316995	−	0.156569i
$25$	48.9983	+	84.8676i	0.391987	+	0.678941i
$26$	50.7666			0.382929
$27$	137.651	+	27.1142i	0.981147	+	0.193264i
$28$	55.5482	+	49.0143i	0.374915	+	0.330816i
$29$	49.6924	−	28.6899i	0.318195	−	0.183710i	−0.332393	−	0.943141i	$-0.607856\pi$
$29$	49.6924	−	28.6899i	0.318195	−	0.183710i	0.650588	+	0.759431i	$0.274523\pi$
$30$	−48.4193	+	23.9151i	−0.294670	+	0.145543i
$31$	50.1944	+	28.9798i	0.290812	+	0.167901i	0.638308	−	0.769781i	$-0.279635\pi$
$31$	50.1944	+	28.9798i	0.290812	+	0.167901i	−0.347496	+	0.937682i	$0.612968\pi$
$32$	27.7128	+	16.0000i	0.153093	+	0.0883883i
$33$	−300.231	−	200.339i	−1.58374	−	1.05680i
$34$	−176.830	+	102.093i	−0.891944	+	0.514964i
$35$	−72.1636	−	63.6754i	−0.348511	−	0.307517i
$36$	41.4536	+	99.7276i	0.191915	+	0.461702i
$37$	40.2838			0.178990			0.0894948	−	0.995987i	$-0.471475\pi$
$37$	40.2838			0.178990			0.0894948	+	0.995987i	$0.471475\pi$
$38$	118.577	+	205.382i	0.506205	+	0.876773i
$39$	−8.54470	+	131.618i	−0.0350833	+	0.540405i
$40$	−36.0022	−	20.7859i	−0.142311	−	0.0821635i
$41$	120.231	−	208.246i	0.457973	−	0.793233i	−0.540881	−	0.841099i	$-0.681909\pi$
$41$	120.231	−	208.246i	0.457973	−	0.793233i	0.998854	+	0.0478668i	$0.0152423\pi$
$42$	−136.425	+	135.765i	−0.501210	+	0.498787i
$43$	80.2004	+	138.911i	0.284429	+	0.492646i	0.972471	−	0.233026i	$-0.0748626\pi$
$43$	80.2004	+	138.911i	0.284429	+	0.492646i	−0.688041	+	0.725671i	$0.741529\pi$
$44$		−	277.848i		−	0.951981i
$45$	−53.8532	−	129.558i	−0.178399	−	0.429186i
$46$	−143.739			−0.460721
$47$	280.682	+	486.155i	0.871099	+	1.50879i	0.860861	+	0.508841i	$0.169926\pi$
$47$	280.682	+	486.155i	0.871099	+	1.50879i	0.0102389	+	0.999948i	$0.496741\pi$
$48$	−46.1463	+	69.1557i	−0.138764	+	0.207954i
$49$	−316.086	−	133.187i	−0.921533	−	0.388300i
$50$	−169.735	−	97.9967i	−0.480084	−	0.277176i
$51$	−234.925	−	475.637i	−0.645021	−	1.30593i
$52$	−87.9303	+	50.7666i	−0.234495	+	0.135386i
$53$		−	768.800i		−	1.99251i	−0.0864839	−	0.996253i	$-0.527563\pi$
$53$		−	768.800i		−	1.99251i	0.0864839	−	0.996253i	$-0.472437\pi$
$54$	−265.533	+	90.6879i	−0.669156	+	0.228538i
$55$			360.958i			0.884937i
$56$	−145.227	−	29.3471i	−0.346548	−	0.0700299i
$57$	−552.436	+	272.857i	−1.28372	+	0.634050i
$58$	−57.3799	+	99.3849i	−0.129903	+	0.224998i
$59$	−86.9423	+	150.588i	−0.191846	+	0.332287i	−0.945862	−	0.324569i	$-0.894781\pi$
$59$	−86.9423	+	150.588i	−0.191846	+	0.332287i	0.754016	+	0.656856i	$0.228114\pi$
$60$	59.9496	−	89.8415i	0.128991	−	0.193308i
$61$	−357.490	+	206.397i	−0.750360	+	0.433220i	−0.825824	−	0.563928i	$-0.809289\pi$
$61$	−357.490	+	206.397i	−0.750360	+	0.433220i	0.0754642	+	0.997149i	$0.475956\pi$
$62$	−115.919			−0.237447
$63$	−329.026	−	376.549i	−0.657990	−	0.753027i
$64$	−64.0000			−0.125000
$65$	114.232	−	65.9518i	0.217980	−	0.125851i
$66$	720.354	+	46.7656i	1.34348	+	0.0872189i
$67$	271.005	−	469.395i	0.494157	−	0.855906i	−0.505820	−	0.862639i	$-0.668810\pi$
$67$	271.005	−	469.395i	0.494157	−	0.855906i	0.999977	+	0.00673345i	$0.00214334\pi$
$68$	204.186	−	353.660i	0.364135	−	0.630700i
$69$	24.1932	−	372.660i	0.0422105	−	0.650189i
$70$	188.667	+	38.1254i	0.322142	+	0.0650980i
$71$			870.130i			1.45444i	0.686403	+	0.727221i	$0.259188\pi$
$71$			870.130i			1.45444i	−0.686403	+	0.727221i	$0.740812\pi$
$72$	−171.527	−	131.280i	−0.280760	−	0.214881i
$73$			822.641i			1.31894i	0.751729	+	0.659472i	$0.229220\pi$
$73$			822.641i			1.31894i	−0.751729	+	0.659472i	$0.770780\pi$
$74$	−69.7736	+	40.2838i	−0.109608	+	0.0632824i
$75$	282.637	−	423.564i	0.435148	−	0.652120i
$76$	−410.764	−	237.155i	−0.619972	−	0.357941i
$77$	409.808	+	1219.44i	0.606518	+	1.80477i
$78$	−116.818	−	236.514i	−0.169578	−	0.343333i
$79$	46.1797	+	79.9856i	0.0657674	+	0.113912i	0.897034	−	0.441961i	$-0.145717\pi$
$79$	46.1797	+	79.9856i	0.0657674	+	0.113912i	−0.831267	+	0.555874i	$0.812384\pi$
$80$	83.1436			0.116197
$81$	−190.426	−	703.689i	−0.261216	−	0.965280i
$82$			480.923i			0.647672i
$83$	223.747	+	387.541i	0.295897	+	0.512508i	0.975193	−	0.221356i	$-0.0710482\pi$
$83$	223.747	+	387.541i	0.295897	+	0.512508i	−0.679296	+	0.733864i	$0.737715\pi$
$84$	100.530	−	371.577i	0.130579	−	0.482648i
$85$	−265.262	+	459.447i	−0.338490	+	0.586282i
$86$	−277.822	−	160.401i	−0.348353	−	0.201122i
$87$	−248.009	−	165.492i	−0.305625	−	0.203938i
$88$	277.848	+	481.247i	0.336576	+	0.582967i
$89$	−103.529			−0.123304			−0.0616518	−	0.998098i	$-0.519637\pi$
$89$	−103.529			−0.123304			−0.0616518	+	0.998098i	$0.519637\pi$
$90$	222.834	+	170.548i	0.260987	+	0.199748i
$91$	311.036	−	352.499i	0.358301	−	0.406065i
$92$	248.963	−	143.739i	0.282133	−	0.162889i
$93$	19.5108	−	300.534i	0.0217545	−	0.335096i
$94$	−972.311	−	561.364i	−1.06687	−	0.615960i
$95$	533.632	+	308.092i	0.576310	+	0.332733i
$96$	10.7721	−	165.928i	0.0114523	−	0.176405i
$97$	1263.72	−	729.611i	1.32280	−	0.763720i	0.338627	−	0.940921i	$-0.390038\pi$
$97$	1263.72	−	729.611i	1.32280	−	0.763720i	0.984175	+	0.177201i	$0.0567043\pi$
$98$	680.664	−	85.3993i	0.701606	−	0.0880269i
$99$	−242.491	+	1859.73i	−0.246174	+	1.88798i
$100$	391.987			0.391987
$101$	−518.868	−	898.706i	−0.511181	−	0.885392i	−0.999916	−	0.0129593i	$-0.995875\pi$
$101$	−518.868	−	898.706i	−0.511181	−	0.885392i	0.488735	−	0.872432i	$-0.337459\pi$
$102$	882.539	+	588.902i	0.856709	+	0.571666i
$103$	722.747	+	417.278i	0.691402	+	0.399181i	0.804137	−	0.594444i	$-0.202628\pi$
$103$	722.747	+	417.278i	0.691402	+	0.399181i	−0.112735	+	0.993625i	$0.535961\pi$
$104$	101.533	−	175.861i	0.0957321	−	0.165813i
$105$	−130.600	+	482.723i	−0.121383	+	0.448657i
$106$	768.800	+	1331.60i	0.704457	+	1.22016i
$107$		−	770.696i		−	0.696318i	−0.937436	−	0.348159i	$-0.886807\pi$
$107$		−	770.696i		−	0.696318i	0.937436	−	0.348159i	$-0.113193\pi$
$108$	369.229	−	422.609i	0.328973	−	0.376533i
$109$	−1119.19			−0.983475			−0.491737	−	0.870744i	$-0.663638\pi$
$109$	−1119.19			−0.983475			−0.491737	+	0.870744i	$0.663638\pi$
$110$	−360.958	−	625.197i	−0.312872	−	0.541911i
$111$	−92.6967	−	187.677i	−0.0792647	−	0.160482i
$112$	280.887	−	94.3958i	0.236976	−	0.0796390i
$113$	−109.193	−	63.0425i	−0.0909026	−	0.0524826i	0.453860	−	0.891073i	$-0.350047\pi$
$113$	−109.193	−	63.0425i	−0.0909026	−	0.0524826i	−0.544762	+	0.838591i	$0.683380\pi$
$114$	683.989	−	1025.04i	0.561943	−	0.842137i
$115$	−323.433	+	186.734i	−0.262263	+	0.151418i
$116$		−	229.520i		−	0.183710i
$117$	632.854	−	263.057i	0.500063	−	0.207860i
$118$		−	347.769i		−	0.271311i
$119$	−374.517	+	1853.32i	−0.288503	+	1.42768i
$120$	−13.9942	+	215.560i	−0.0106457	+	0.163982i
$121$	1746.99	−	3025.87i	1.31254	−	2.27338i
$122$	412.794	−	714.981i	0.306333	−	0.530584i
$123$	−1246.85	−	80.9459i	−0.914022	−	0.0593386i
$124$	200.778	−	115.919i	0.145406	−	0.0839503i
$125$	−1158.80			−0.829167
$126$	946.438	+	323.176i	0.669170	+	0.228499i
$127$	−668.605			−0.467158			−0.233579	−	0.972338i	$-0.575044\pi$
$127$	−668.605			−0.467158			−0.233579	+	0.972338i	$0.575044\pi$
$128$	110.851	−	64.0000i	0.0765466	−	0.0441942i
$129$	462.620	−	693.290i	0.315747	−	0.473184i
$130$	−131.904	+	228.464i	−0.0889901	+	0.154135i
$131$	497.894	−	862.377i	0.332070	−	0.575162i	−0.650848	−	0.759208i	$-0.725586\pi$
$131$	497.894	−	862.377i	0.332070	−	0.575162i	0.982918	+	0.184046i	$0.0589196\pi$
$132$	−1294.46	+	639.354i	−0.853544	+	0.421580i
$133$	2152.57	+	434.988i	1.40340	+	0.283596i
$134$			1084.02i			0.698844i
$135$	−479.672	+	549.019i	−0.305804	+	0.350015i
$136$			816.743i			0.514964i
$137$	−620.242	+	358.097i	−0.386794	+	0.223316i	−0.680770	−	0.732497i	$-0.738355\pi$
$137$	−620.242	+	358.097i	−0.386794	+	0.223316i	0.293976	+	0.955813i	$0.405021\pi$
$138$	330.757	+	669.660i	0.204028	+	0.413082i
$139$	1404.59	+	810.939i	0.857090	+	0.494841i	0.863037	−	0.505141i	$-0.168560\pi$
$139$	1404.59	+	810.939i	0.857090	+	0.494841i	−0.00594676	+	0.999982i	$0.501893\pi$
$140$	−364.905	+	122.631i	−0.220287	+	0.0740303i
$141$	1619.06	−	2426.35i	0.967015	−	1.44919i
$142$	−870.130	−	1507.11i	−0.514223	−	0.890660i
$143$	−1763.17			−1.03108
$144$	428.374	+	55.8557i	0.247902	+	0.0323239i
$145$			298.173i			0.170772i
$146$	−822.641	−	1424.86i	−0.466317	−	0.807685i
$147$	106.843	+	1779.07i	0.0599473	+	0.998202i
$148$	80.5676	−	139.547i	0.0447474	−	0.0775048i
$149$	337.428	+	194.814i	0.185525	+	0.107113i	0.589886	−	0.807487i	$-0.299173\pi$
$149$	337.428	+	194.814i	0.185525	+	0.107113i	−0.404361	+	0.914599i	$0.632506\pi$
$150$	−65.9767	+	1016.27i	−0.0359132	+	0.553188i
$151$	−573.297	−	992.979i	−0.308968	−	0.535149i	0.669169	−	0.743111i	$-0.266650\pi$
$151$	−573.297	−	992.979i	−0.308968	−	0.535149i	−0.978137	+	0.207962i	$0.933317\pi$
$152$	948.619			0.506205
$153$	−1675.34	+	2188.97i	−0.885250	+	1.15665i
$154$	−1929.24	−	1702.32i	−1.00950	−	0.890757i
$155$	−260.834	+	150.593i	−0.135166	+	0.0780380i
$156$	438.850	+	292.836i	0.225231	+	0.150293i
$157$	−2381.51	−	1374.97i	−1.21061	−	0.698945i	−0.247717	−	0.968833i	$-0.579680\pi$
$157$	−2381.51	−	1374.97i	−1.21061	−	0.698945i	−0.962892	+	0.269887i	$0.913013\pi$
$158$	−159.971	−	92.3594i	−0.0805482	−	0.0465046i
$159$	−3581.73	+	1769.08i	−1.78648	+	0.882372i
$160$	−144.009	+	83.1436i	−0.0711557	+	0.0410817i
$161$	−880.659	+	998.055i	−0.431091	+	0.488557i
$162$	1033.52	+	1028.40i	0.501239	+	0.498757i
$163$	−2839.35			−1.36438			−0.682192	−	0.731173i	$-0.738973\pi$
$163$	−2839.35			−1.36438			−0.682192	+	0.731173i	$0.738973\pi$
$164$	−480.923	−	832.983i	−0.228987	−	0.396616i
$165$	1681.65	−	830.596i	0.793432	−	0.391890i
$166$	−775.083	−	447.494i	−0.362398	−	0.209231i
$167$	353.366	−	612.049i	0.163738	−	0.283603i	−0.772468	−	0.635054i	$-0.780978\pi$
$167$	353.366	−	612.049i	0.163738	−	0.283603i	0.936207	+	0.351450i	$0.114311\pi$
$168$	197.455	+	744.121i	0.0906786	+	0.341727i
$169$	−776.345	−	1344.67i	−0.353366	−	0.612047i
$170$		−	1061.05i		−	0.478697i
$171$	2542.41	+	1945.85i	1.13698	+	0.870193i
$172$	641.603			0.284429
$173$	1209.00	+	2094.04i	0.531319	+	0.920272i	0.999332	+	0.0365503i	$0.0116369\pi$
$173$	1209.00	+	2094.04i	0.531319	+	0.920272i	−0.468012	+	0.883722i	$0.655030\pi$
$174$	595.057	+	38.6313i	0.259259	+	0.0168312i
$175$	−1720.37	+	578.155i	−0.743131	+	0.249739i
$176$	−962.494	−	555.696i	−0.412220	−	0.237995i
$177$	901.633	+	58.5343i	0.382886	+	0.0248571i
$178$	179.317	−	103.529i	0.0755077	−	0.0435944i
$179$		−	597.957i		−	0.249684i	−0.992177	−	0.124842i	$-0.960158\pi$
$179$		−	597.957i		−	0.249684i	0.992177	−	0.124842i	$-0.0398424\pi$
$180$	−556.508	−	72.5632i	−0.230443	−	0.0300475i
$181$			2458.04i			1.00942i	0.863290	+	0.504709i	$0.168400\pi$
$181$			2458.04i			1.00942i	−0.863290	+	0.504709i	$0.831600\pi$
$182$	−186.232	+	921.581i	−0.0758484	+	0.375342i
$183$	1784.19	+	1190.56i	0.720718	+	0.480922i
$184$	−287.478	+	497.927i	−0.115180	+	0.199498i
$185$	−104.667	+	181.288i	−0.0415960	+	0.0720464i
$186$	266.740	+	540.051i	0.105152	+	0.212895i
$187$	6141.49	−	3545.79i	2.40166	−	1.38660i
$188$	2245.46			0.871099
$189$	−997.171	+	2399.36i	−0.383775	+	0.923427i
$190$	−1232.37			−0.470555
$191$	−162.422	+	93.7746i	−0.0615312	+	0.0355251i	−0.530450	−	0.847716i	$-0.677977\pi$
$191$	−162.422	+	93.7746i	−0.0615312	+	0.0355251i	0.468919	+	0.883241i	$0.344644\pi$
$192$	147.270	+	298.167i	0.0553556	+	0.112075i
$193$	1766.36	−	3059.43i	0.658785	−	1.14105i	−0.322146	−	0.946690i	$-0.604404\pi$
$193$	1766.36	−	3059.43i	0.658785	−	1.14105i	0.980931	−	0.194358i	$-0.0622624\pi$
$194$	−1459.22	+	2527.45i	−0.540031	+	0.935362i
$195$	−570.118	−	380.429i	−0.209369	−	0.139708i
$196$	−1093.54	+	828.580i	−0.398522	+	0.301960i
$197$			2086.51i			0.754609i	0.926089	+	0.377304i	$0.123149\pi$
$197$			2086.51i			0.754609i	−0.926089	+	0.377304i	$0.876851\pi$
$198$	−1439.73	−	3463.64i	−0.516752	−	1.24318i
$199$		−	767.839i		−	0.273521i	−0.990604	−	0.136760i	$-0.956331\pi$
$199$		−	767.839i		−	0.273521i	0.990604	−	0.136760i	$-0.0436691\pi$
$200$	−678.941	+	391.987i	−0.240042	+	0.138588i
$201$	−2810.45	−	182.455i	−0.986239	−	0.0640269i
$202$	1797.41	+	1037.74i	0.626066	+	0.361460i
$203$	338.526	+	1007.33i	0.117044	+	0.348279i
$204$	−2117.50	−	137.469i	−0.726740	−	0.0471802i
$205$	624.776	+	1082.14i	0.212860	+	0.368684i
$206$	−1669.11			−0.564527
$207$	−1791.84	+	744.813i	−0.601651	+	0.250087i
$208$			406.132i			0.135386i
$209$	−4118.31	−	7133.13i	−1.36301	−	2.36081i
$210$	−256.518	−	966.701i	−0.0842924	−	0.317660i
$211$	974.845	−	1688.48i	0.318062	−	0.550900i	−0.662022	−	0.749485i	$-0.730301\pi$
$211$	974.845	−	1688.48i	0.318062	−	0.550900i	0.980084	+	0.198585i	$0.0636346\pi$
$212$	−2663.20	−	1537.60i	−0.862781	−	0.498127i
$213$	4053.81	−	2002.25i	1.30405	−	0.644093i
$214$	770.696	+	1334.89i	0.246186	+	0.426406i
$215$	−833.519			−0.264398
$216$	−216.914	+	1101.21i	−0.0683292	+	0.346888i
$217$	−710.212	+	804.886i	−0.222177	+	0.251794i
$218$	1938.49	−	1119.19i	0.602253	−	0.347711i
$219$	3832.57	−	1892.97i	1.18256	−	0.584088i
$220$	1250.39	+	721.915i	0.383189	+	0.221234i
$221$	−2244.26	−	1295.73i	−0.683102	−	0.394389i
$222$	348.232	+	232.369i	0.105278	+	0.0702503i
$223$	−242.822	+	140.193i	−0.0729172	+	0.0420988i	−0.536015	−	0.844208i	$-0.680071\pi$
$223$	−242.822	+	140.193i	−0.0729172	+	0.0420988i	0.463098	+	0.886307i	$0.346738\pi$
$224$	−392.114	+	444.385i	−0.116961	+	0.132552i
$225$	−2623.70	−	342.105i	−0.777393	−	0.101364i
$226$	252.170			0.0742217
$227$	1880.81	+	3257.66i	0.549928	+	0.952503i	0.998279	+	0.0586458i	$0.0186782\pi$
$227$	1880.81	+	3257.66i	0.549928	+	0.952503i	−0.448351	+	0.893858i	$0.647988\pi$
$228$	−159.666	+	2459.41i	−0.0463777	+	0.714379i
$229$	−1848.81	−	1067.41i	−0.533504	−	0.308019i	0.208938	−	0.977929i	$-0.432999\pi$
$229$	−1848.81	−	1067.41i	−0.533504	−	0.308019i	−0.742442	+	0.669910i	$0.766333\pi$
$230$	373.468	−	646.866i	0.107069	−	0.185448i
$231$	4738.17	−	4715.27i	1.34956	−	1.34304i
$232$	229.520	+	397.540i	0.0649513	+	0.112499i
$233$		−	1520.42i		−	0.427493i	−0.976889	−	0.213747i	$-0.931433\pi$
$233$		−	1520.42i		−	0.427493i	0.976889	−	0.213747i	$-0.0685667\pi$
$234$	−833.077	+	1088.48i	−0.232735	+	0.304087i
$235$	−2917.11			−0.809751
$236$	347.769	+	602.354i	0.0959230	+	0.166144i
$237$	266.378	−	399.199i	0.0730089	−	0.109412i
$238$	−1204.64	−	3584.57i	−0.328090	−	0.976274i
$239$	591.644	+	341.586i	0.160127	+	0.0924492i	0.577922	−	0.816092i	$-0.303864\pi$
$239$	591.644	+	341.586i	0.160127	+	0.0924492i	−0.417795	+	0.908541i	$0.637197\pi$
$240$	−191.321	−	387.354i	−0.0514571	−	0.104182i
$241$	−2293.80	+	1324.33i	−0.613099	+	0.353973i	−0.774177	−	0.632969i	$-0.781836\pi$
$241$	−2293.80	+	1324.33i	−0.613099	+	0.353973i	0.161078	+	0.986942i	$0.448503\pi$
$242$			6987.94i			1.85621i
$243$	−2840.20	+	2506.42i	−0.749791	+	0.661675i
$244$			1651.18i			0.433220i
$245$	1420.64	−	1076.42i	0.370456	−	0.280695i
$246$	2240.55	−	1106.65i	0.580701	−	0.286818i
$247$	−1504.94	+	2606.64i	−0.387681	+	0.671483i
$248$	−231.838	+	401.555i	−0.0593618	+	0.102818i
$249$	1290.64	−	1934.18i	0.328478	−	0.492263i
$250$	2007.09	−	1158.80i	0.507759	−	0.293155i
$251$	1759.07			0.442358			0.221179	−	0.975233i	$-0.429010\pi$
$251$	1759.07			0.442358			0.221179	+	0.975233i	$0.429010\pi$
$252$	−1962.46	+	386.681i	−0.490568	+	0.0966611i
$253$	4992.20			1.24054
$254$	1158.06	−	668.605i	0.286075	−	0.165165i
$255$	2750.89	+	178.589i	0.675558	+	0.0438574i
$256$	−128.000	+	221.703i	−0.0312500	+	0.0541266i
$257$	1045.51	−	1810.87i	0.253763	−	0.439530i	−0.710796	−	0.703398i	$-0.751665\pi$
$257$	1045.51	−	1810.87i	0.253763	−	0.439530i	0.964559	+	0.263868i	$0.0849984\pi$
$258$	−107.991	+	1663.43i	−0.0260589	+	0.401398i
$259$	−147.777	+	731.285i	−0.0354533	+	0.175443i
$260$		−	527.614i		−	0.125851i
$261$	−200.312	+	1536.25i	−0.0475058	+	0.364336i
$262$			1991.57i			0.469618i
$263$	1430.81	−	826.078i	0.335466	−	0.193681i	−0.322799	−	0.946467i	$-0.604624\pi$
$263$	1430.81	−	826.078i	0.335466	−	0.193681i	0.658265	+	0.752786i	$0.271291\pi$
$264$	1602.71	−	2401.85i	0.373636	−	0.559938i
$265$	3459.82	+	1997.53i	0.802018	+	0.463045i
$266$	−4163.36	+	1399.15i	−0.959668	+	0.322509i
$267$	238.229	+	482.326i	0.0546044	+	0.110554i
$268$	−1084.02	−	1877.58i	−0.247079	−	0.427953i
$269$	992.346			0.224923			0.112462	−	0.993656i	$-0.464126\pi$
$269$	992.346			0.224923			0.112462	+	0.993656i	$0.464126\pi$
$270$	281.797	−	1430.60i	0.0635170	−	0.322458i
$271$		−	3247.79i		−	0.728005i	−0.931398	−	0.364002i	$-0.881410\pi$
$271$		−	3247.79i		−	0.728005i	0.931398	−	0.364002i	$-0.118590\pi$
$272$	−816.743	−	1414.64i	−0.182067	−	0.315350i
$273$	−2357.96	−	637.942i	−0.522749	−	0.141429i
$274$	716.194	−	1240.48i	0.157908	−	0.273505i
$275$	5895.07	+	3403.52i	1.29268	+	0.746328i
$276$	−1242.55	−	829.129i	−0.270988	−	0.180825i
$277$	3534.60	+	6122.11i	0.766692	+	1.32795i	0.939347	+	0.342967i	$0.111432\pi$
$277$	3534.60	+	6122.11i	0.766692	+	1.32795i	−0.172655	+	0.984982i	$0.555235\pi$
$278$	−3243.75			−0.699811
$279$	−1445.04	+	600.658i	−0.310080	+	0.128891i
$280$	509.403	−	577.309i	0.108724	−	0.123217i
$281$	−1427.07	+	823.921i	−0.302961	+	0.174915i	−0.643772	−	0.765217i	$-0.722632\pi$
$281$	−1427.07	+	823.921i	−0.302961	+	0.174915i	0.340811	+	0.940132i	$0.389298\pi$
$282$	−377.941	+	5821.61i	−0.0798087	+	1.22933i
$283$	−2683.74	−	1549.46i	−0.563716	−	0.325462i	0.190920	−	0.981606i	$-0.438853\pi$
$283$	−2683.74	−	1549.46i	−0.563716	−	0.325462i	−0.754636	+	0.656144i	$0.772186\pi$
$284$	3014.22	+	1740.26i	0.629792	+	0.363611i
$285$	207.425	−	3195.06i	0.0431115	−	0.664067i
$286$	3053.91	−	1763.17i	0.631403	−	0.364541i
$287$	3339.30	+	2946.51i	0.686803	+	0.606018i
$288$	−797.821	+	331.629i	−0.163236	+	0.0678521i
$289$	5509.96			1.12151
$290$	−298.173	−	516.451i	−0.0603770	−	0.104576i
$291$	−6307.10	−	4208.61i	−1.27055	−	0.847812i
$292$	2849.71	+	1645.28i	0.571119	+	0.329736i
$293$	4037.87	−	6993.80i	0.805102	−	1.39448i	−0.111120	−	0.993807i	$-0.535444\pi$
$293$	4037.87	−	6993.80i	0.805102	−	1.39448i	0.916222	−	0.400671i	$-0.131223\pi$
$294$	−1964.13	−	2974.61i	−0.389628	−	0.590077i
$295$	−451.793	−	782.529i	−0.0891675	−	0.154443i
$296$			322.270i			0.0632824i
$297$	9222.22	−	3149.68i	1.80178	−	0.615364i
$298$	−779.256			−0.151480
$299$	−912.142	−	1579.88i	−0.176423	−	0.305574i
$300$	−901.997	−	1826.21i	−0.173589	−	0.351454i
$301$	−2815.91	+	946.323i	−0.539223	+	0.181213i
$302$	1985.96	+	1146.59i	0.378408	+	0.218474i
$303$	−2992.98	+	4485.34i	−0.567466	+	0.850415i
$304$	−1643.06	+	948.619i	−0.309986	+	0.178971i
$305$		−	2145.07i		−	0.402710i
$306$	712.809	−	5466.74i	0.133165	−	1.02128i
$307$			8874.14i			1.64975i	0.565314	+	0.824876i	$0.308755\pi$
$307$			8874.14i			1.64975i	−0.565314	+	0.824876i	$0.691245\pi$
$308$	5043.86	+	1019.26i	0.933119	+	0.188563i
$309$	280.934	−	4327.37i	0.0517210	−	0.796685i
$310$	301.185	−	521.668i	0.0551812	−	0.0955767i
$311$	−1875.54	+	3248.53i	−0.341968	+	0.592307i	−0.984798	−	0.173702i	$-0.944427\pi$
$311$	−1875.54	+	3248.53i	−0.341968	+	0.592307i	0.642830	+	0.766009i	$0.277760\pi$
$312$	−1052.95	−	68.3576i	−0.191062	−	0.0124038i
$313$	−8535.10	+	4927.74i	−1.54132	+	0.889880i	−0.542561	+	0.840016i	$0.682545\pi$
$313$	−8535.10	+	4927.74i	−1.54132	+	0.889880i	−0.998756	+	0.0498640i	$0.984121\pi$
$314$	5499.87			0.988458
$315$	2549.46	−	502.344i	0.456019	−	0.0898536i
$316$	369.438			0.0657674
$317$	−6558.91	+	3786.79i	−1.16210	+	0.670938i	−0.951806	−	0.306700i	$-0.900775\pi$
$317$	−6558.91	+	3786.79i	−1.16210	+	0.670938i	−0.210293	+	0.977638i	$0.567442\pi$
$318$	4434.66	−	6645.87i	0.782024	−	1.17196i
$319$	1992.86	−	3451.74i	0.349777	−	0.605831i
$320$	166.287	−	288.018i	0.0290492	−	0.0503147i
$321$	−3590.57	+	1773.44i	−0.624317	+	0.308361i
$322$	527.291	−	2609.34i	0.0912571	−	0.451593i
$323$		−	12105.9i		−	2.08542i
$324$	−2818.50	−	747.723i	−0.483283	−	0.128210i
$325$		−	2487.48i		−	0.424555i
$326$	4917.89	−	2839.35i	0.835512	−	0.482383i
$327$	2575.35	+	5214.14i	0.435527	+	0.881782i
$328$	1665.97	+	961.846i	0.280450	+	0.161918i
$329$	−9854.99	+	3311.90i	−1.65144	+	0.554988i
$330$	−2082.11	+	3120.29i	−0.347322	+	0.520503i
$331$	2142.09	+	3710.22i	0.355710	+	0.616109i	0.987239	−	0.159244i	$-0.0509056\pi$
$331$	2142.09	+	3710.22i	0.355710	+	0.616109i	−0.631529	+	0.775352i	$0.717572\pi$
$332$	1789.98			0.295897
$333$	−661.056	+	863.722i	−0.108786	+	0.142137i
$334$			1413.47i			0.231561i
$335$	1408.27	+	2439.20i	0.229678	+	0.397814i
$336$	−1086.12	−	1091.40i	−0.176348	−	0.177205i
$337$	−4339.07	+	7515.50i	−0.701378	+	1.21482i	0.266605	+	0.963806i	$0.414098\pi$
$337$	−4339.07	+	7515.50i	−0.701378	+	1.21482i	−0.967983	+	0.251017i	$0.919235\pi$
$338$	2689.34	+	1552.69i	0.432783	+	0.249867i
$339$	−42.4436	+	653.781i	−0.00680006	+	0.104745i
$340$	1061.05	+	1837.79i	0.169245	+	0.293141i
$341$	4025.99			0.639353
$342$	−6349.43	−	827.904i	−1.00391	−	0.130900i
$343$	3577.31	−	5249.42i	0.563139	−	0.826362i
$344$	−1111.29	+	641.603i	−0.174177	+	0.100561i
$345$	1614.22	+	1077.14i	0.251903	+	0.168090i
$346$	−4188.08	−	2417.99i	−0.650731	−	0.375700i
$347$	−3447.16	−	1990.22i	−0.533294	−	0.307898i	0.209062	−	0.977902i	$-0.432959\pi$
$347$	−3447.16	−	1990.22i	−0.533294	−	0.307898i	−0.742357	+	0.670005i	$0.766292\pi$
$348$	−1069.30	+	528.145i	−0.164714	+	0.0813551i
$349$	−1376.19	+	794.545i	−0.211077	+	0.121865i	−0.601812	−	0.798638i	$-0.705554\pi$
$349$	−1376.19	+	794.545i	−0.211077	+	0.121865i	0.390735	+	0.920503i	$0.372221\pi$
$350$	2401.62	−	2721.77i	0.366777	−	0.415670i
$351$	−2681.80	−	2343.06i	−0.407817	−	0.356305i
$352$	2222.78			0.336576
$353$	2140.24	+	3707.01i	0.322702	+	0.558936i	0.981045	−	0.193782i	$-0.0620756\pi$
$353$	2140.24	+	3707.01i	0.322702	+	0.558936i	−0.658343	+	0.752718i	$0.728742\pi$
$354$	−1620.21	+	800.248i	−0.243257	+	0.120149i
$355$	−3915.83	−	2260.80i	−0.585438	−	0.338003i
$356$	−207.057	+	358.634i	−0.0308259	+	0.0533920i
$357$	9496.18	−	2519.85i	1.40782	−	0.373570i
$358$	597.957	+	1035.69i	0.0882766	+	0.152900i
$359$		−	2470.23i		−	0.363158i	−0.983376	−	0.181579i	$-0.941879\pi$
$359$		−	2470.23i		−	0.363158i	0.983376	−	0.181579i	$-0.0581208\pi$
$360$	1036.46	−	430.825i	0.151740	−	0.0630736i
$361$	−7201.61			−1.04995
$362$	−2458.04	−	4257.45i	−0.356883	−	0.618140i
$363$	−18117.1	−	1176.17i	−2.61956	−	0.170063i
$364$	−599.019	−	1782.46i	−0.0862558	−	0.256665i
$365$	−3702.12	−	2137.42i	−0.530897	−	0.306514i
$366$	−4280.87	−	277.916i	−0.611379	−	0.0396909i
$367$	−9191.74	+	5306.86i	−1.30737	+	0.754811i	−0.981657	−	0.190657i	$-0.938938\pi$
$367$	−9191.74	+	5306.86i	−1.30737	+	0.754811i	−0.325714	+	0.945468i	$0.605605\pi$
$368$		−	1149.91i		−	0.162889i
$369$	2492.00	+	5995.17i	0.351567	+	0.845788i
$370$		−	418.668i		−	0.0588256i
$371$	13956.3	+	2820.26i	1.95303	+	0.394665i
$372$	−1002.06	−	668.655i	−0.139662	−	0.0931940i
$373$	−6865.02	+	11890.6i	−0.952968	+	1.65059i	−0.214017	+	0.976830i	$0.568655\pi$
$373$	−6865.02	+	11890.6i	−0.952968	+	1.65059i	−0.738951	+	0.673759i	$0.764678\pi$
$374$	−7091.58	+	12283.0i	−0.980473	+	1.69823i
$375$	2666.50	+	5398.67i	0.367193	+	0.743430i
$376$	−3889.24	+	2245.46i	−0.533437	+	0.307980i
$377$	−1456.49			−0.198974
$378$	−672.207	−	5152.98i	−0.0914672	−	0.701166i
$379$	−6480.26			−0.878282			−0.439141	−	0.898418i	$-0.644717\pi$
$379$	−6480.26			−0.878282			−0.439141	+	0.898418i	$0.644717\pi$
$380$	2134.53	−	1232.37i	0.288155	−	0.166366i
$381$	1538.52	+	3114.94i	0.206879	+	0.418853i
$382$	187.549	−	324.845i	0.0251200	−	0.0435092i
$383$	1783.89	−	3089.79i	0.237997	−	0.412222i	−0.722143	−	0.691744i	$-0.756843\pi$
$383$	1783.89	−	3089.79i	0.237997	−	0.412222i	0.960139	+	0.279522i	$0.0901760\pi$
$384$	−553.246	−	369.171i	−0.0735227	−	0.0490603i
$385$	−6552.58	−	1324.13i	−0.867403	−	0.175283i
$386$			7065.44i			0.931662i
$387$	−4294.47	−	559.957i	−0.564083	−	0.0735509i
$388$		−	5836.89i		−	0.763720i
$389$	−3454.88	+	1994.67i	−0.450307	+	0.259985i	−0.707960	−	0.706253i	$-0.750384\pi$
$389$	−3454.88	+	1994.67i	−0.450307	+	0.259985i	0.257653	+	0.966237i	$0.417051\pi$
$390$	1367.90	+	88.8047i	0.177606	+	0.0115303i
$391$	6354.35	+	3668.68i	0.821875	+	0.474510i
$392$	1065.50	−	2528.69i	0.137285	−	0.325811i
$393$	−5163.39	−	335.209i	−0.662745	−	0.0430256i
$394$	−2086.51	−	3613.95i	−0.266794	−	0.462102i
$395$	−479.943			−0.0611356
$396$	5957.32	+	4559.48i	0.755976	+	0.578592i
$397$			2640.60i			0.333823i	0.985972	+	0.166911i	$0.0533794\pi$
$397$			2640.60i			0.333823i	−0.985972	+	0.166911i	$0.946621\pi$
$398$	767.839	+	1329.94i	0.0967042	+	0.167497i
$399$	−2926.72	−	11029.5i	−0.367216	−	1.38387i
$400$	783.973	−	1357.88i	0.0979967	−	0.169735i
$401$	3855.14	+	2225.76i	0.480091	+	0.277180i	0.720454	−	0.693502i	$-0.243933\pi$
$401$	3855.14	+	2225.76i	0.480091	+	0.277180i	−0.240364	+	0.970683i	$0.577267\pi$
$402$	5050.30	−	2494.43i	0.626582	−	0.309480i
$403$	−735.602	−	1274.10i	−0.0909254	−	0.157487i
$404$	−4150.94			−0.511181
$405$	3661.57	+	971.381i	0.449247	+	0.119181i
$406$	−1593.67	−	1406.22i	−0.194810	−	0.171895i
$407$	2423.31	−	1399.10i	0.295132	−	0.170395i
$408$	3805.09	−	1879.40i	0.461716	−	0.228049i
$409$	−6004.66	−	3466.79i	−0.725945	−	0.419124i	0.0909920	−	0.995852i	$-0.470996\pi$
$409$	−6004.66	−	3466.79i	−0.725945	−	0.419124i	−0.816937	+	0.576727i	$0.804330\pi$
$410$	−2164.29	−	1249.55i	−0.260699	−	0.150515i
$411$	3095.56	+	2065.61i	0.371515	+	0.247905i
$412$	2890.99	−	1669.11i	0.345701	−	0.199590i
$413$	−2414.74	−	2130.71i	−0.287704	−	0.253863i
$414$	2358.75	−	3081.90i	0.280015	−	0.365862i
$415$	−2325.39			−0.275058
$416$	−406.132	−	703.442i	−0.0478661	−	0.0829065i
$417$	545.968	−	8409.82i	0.0641155	−	0.987603i
$418$	14266.3	+	8236.63i	1.66934	+	0.963796i
$419$	6872.07	−	11902.8i	0.801247	−	1.38780i	−0.117549	−	0.993067i	$-0.537504\pi$
$419$	6872.07	−	11902.8i	0.801247	−	1.38780i	0.918796	−	0.394733i	$-0.129163\pi$
$420$	1411.00	+	1417.86i	0.163928	+	0.164725i
$421$	−2314.21	−	4008.32i	−0.267904	−	0.464023i	0.700417	−	0.713734i	$-0.252998\pi$
$421$	−2314.21	−	4008.32i	−0.267904	−	0.464023i	−0.968320	+	0.249711i	$0.919664\pi$
$422$			3899.38i			0.449808i
$423$	−15029.6	−	1959.71i	−1.72758	−	0.225259i
$424$	6150.40			0.704457
$425$	5002.38	+	8664.38i	0.570944	+	0.988904i
$426$	−5019.16	+	7521.81i	−0.570843	+	0.855476i
$427$	−2435.38	−	7246.78i	−0.276010	−	0.821303i
$428$	−2669.77	−	1541.39i	−0.301515	−	0.174079i
$429$	4057.22	+	8214.38i	0.456607	+	0.924462i
$430$	1443.70	−	833.519i	0.161910	−	0.0934787i
$431$		−	8546.12i		−	0.955110i	−0.878602	−	0.477555i	$-0.841523\pi$
$431$		−	8546.12i		−	0.955110i	0.878602	−	0.477555i	$-0.158477\pi$
$432$	−725.503	−	2124.26i	−0.0808004	−	0.236583i
$433$			3953.10i			0.438739i	0.975642	+	0.219369i	$0.0703999\pi$
$433$			3953.10i			0.438739i	−0.975642	+	0.219369i	$0.929600\pi$
$434$	425.236	−	2104.32i	0.0470323	−	0.232743i
$435$	1389.15	−	686.124i	0.153114	−	0.0756255i
$436$	−2238.38	+	3876.98i	−0.245869	+	0.425857i
$437$	4261.05	−	7380.36i	0.466439	−	0.807896i
$438$	−4745.24	+	7111.30i	−0.517662	+	0.775778i
$439$	9885.56	−	5707.43i	1.07474	−	0.620503i	0.145270	−	0.989392i	$-0.453595\pi$
$439$	9885.56	−	5707.43i	1.07474	−	0.620503i	0.929473	+	0.368889i	$0.120262\pi$
$440$	−2887.66			−0.312872
$441$	8042.61	−	4591.58i	0.868438	−	0.495797i
$442$	5182.90			0.557750
$443$	−11273.0	+	6508.45i	−1.20902	+	0.698026i	−0.962545	−	0.271124i	$-0.912605\pi$
$443$	−11273.0	+	6508.45i	−1.20902	+	0.698026i	−0.246472	+	0.969150i	$0.579271\pi$
$444$	−835.524	−	54.2425i	−0.0893068	−	0.00579783i
$445$	268.992	−	465.908i	0.0286549	−	0.0496318i
$446$	280.386	−	485.643i	0.0297683	−	0.0515603i
$447$	131.159	−	2020.31i	0.0138784	−	0.213775i
$448$	234.777	−	1161.81i	0.0247593	−	0.122523i
$449$		−	611.494i		−	0.0642721i	−0.999484	−	0.0321361i	$-0.989769\pi$
$449$		−	611.494i		−	0.0642721i	0.999484	−	0.0321361i	$-0.0102310\pi$
$450$	4886.49	−	2031.16i	0.511892	−	0.212777i
$451$		−	16702.9i		−	1.74393i
$452$	−436.771	+	252.170i	−0.0454513	+	0.0262413i
$453$	−3306.94	+	4955.85i	−0.342988	+	0.514009i
$454$	−6515.31	−	3761.62i	−0.673522	−	0.388858i
$455$	778.197	+	2315.62i	0.0801811	+	0.238589i
$456$	−2182.86	−	4419.49i	−0.224171	−	0.453863i
$457$	5266.83	+	9122.42i	0.539107	+	0.933761i	0.998952	+	0.0457621i	$0.0145716\pi$
$457$	5266.83	+	9122.42i	0.539107	+	0.933761i	−0.459845	+	0.887999i	$0.652095\pi$
$458$	4269.63			0.435605
$459$	14053.2	+	2768.17i	1.42908	+	0.281497i
$460$			1493.87i			0.151418i
$461$	−8547.34	−	14804.4i	−0.863534	−	1.49569i	−0.868495	−	0.495697i	$-0.834913\pi$
$461$	−8547.34	−	14804.4i	−0.863534	−	1.49569i	0.00496117	−	0.999988i	$-0.498421\pi$
$462$	−3491.49	+	12905.3i	−0.351599	+	1.29958i
$463$	3296.13	−	5709.07i	0.330852	−	0.573052i	−0.651827	−	0.758367i	$-0.725997\pi$
$463$	3296.13	−	5709.07i	0.330852	−	0.573052i	0.982679	+	0.185315i	$0.0593307\pi$
$464$	−795.079	−	459.039i	−0.0795488	−	0.0459275i
$465$	1301.79	+	868.662i	0.129826	+	0.0866307i
$466$	1520.42	+	2633.44i	0.151142	+	0.261785i
$467$	5965.17			0.591081			0.295541	−	0.955330i	$-0.404500\pi$
$467$	5965.17			0.591081			0.295541	+	0.955330i	$0.404500\pi$
$468$	354.450	−	2718.38i	0.0350096	−	0.268499i
$469$	7526.92	+	6641.56i	0.741068	+	0.653900i
$470$	5052.59	−	2917.11i	0.495869	−	0.286290i
$471$	−925.703	+	14259.1i	−0.0905608	+	1.39495i
$472$	−1204.71	−	695.538i	−0.117481	−	0.0678278i
$473$	9649.05	+	5570.88i	0.937979	+	0.541542i
$474$	−62.1814	+	957.811i	−0.00602550	+	0.0928137i
$475$	10063.4	−	5810.10i	0.972083	−	0.561233i
$476$	5671.07	+	5004.01i	0.546078	+	0.481846i
$477$	16483.8	+	12616.0i	1.58227	+	1.21100i
$478$	−1366.34			−0.130743
$479$	4917.95	+	8518.13i	0.469116	+	0.812533i	0.999377	−	0.0353015i	$-0.0112392\pi$
$479$	4917.95	+	8518.13i	0.469116	+	0.812533i	−0.530260	+	0.847835i	$0.677906\pi$
$480$	718.732	+	479.597i	0.0683447	+	0.0456052i
$481$	−885.541	−	511.268i	−0.0839443	−	0.0484653i
$482$	2648.66	−	4587.61i	0.250297	−	0.433527i
$483$	6676.27	+	1806.25i	0.628946	+	0.170160i
$484$	−6987.94	−	12103.5i	−0.656268	−	1.13669i
$485$			7582.82i			0.709934i
$486$	2412.95	−	7181.45i	0.225214	−	0.670283i
$487$	3271.87			0.304441			0.152220	−	0.988347i	$-0.451358\pi$
$487$	3271.87			0.304441			0.152220	+	0.988347i	$0.451358\pi$
$488$	−1651.18	−	2859.92i	−0.153167	−	0.265292i
$489$	6533.59	+	13228.1i	0.604211	+	1.22330i
$490$	−1384.20	+	3285.06i	−0.127616	+	0.302865i
$491$	10148.1	+	5858.99i	0.932741	+	0.538518i	0.887677	−	0.460466i	$-0.152318\pi$
$491$	10148.1	+	5858.99i	0.932741	+	0.538518i	0.0450633	+	0.998984i	$0.485651\pi$
$492$	−2774.11	+	4157.32i	−0.254200	+	0.380948i
$493$	5073.25	−	2929.04i	0.463463	−	0.267581i
$494$		−	6019.77i		−	0.548264i
$495$	−7739.26	−	5923.30i	−0.702735	−	0.537844i
$496$		−	927.353i		−	0.0839503i
$497$	−15795.7	−	3191.98i	−1.42563	−	0.288088i
$498$	−301.278	+	4640.73i	−0.0271096	+	0.417582i
$499$	237.204	−	410.849i	0.0212800	−	0.0368580i	−0.855189	−	0.518316i	$-0.826559\pi$
$499$	237.204	−	410.849i	0.0212800	−	0.0368580i	0.876469	+	0.481458i	$0.159893\pi$
$500$	−2317.59	+	4014.19i	−0.207292	+	0.359040i
$501$	−3664.58	−	237.906i	−0.326789	−	0.0212152i
$502$	−3046.81	+	1759.07i	−0.270888	+	0.156397i
$503$	−17002.6			−1.50717			−0.753586	−	0.657350i	$-0.771677\pi$
$503$	−17002.6			−1.50717			−0.753586	+	0.657350i	$0.771677\pi$
$504$	3012.39	−	2632.21i	0.266235	−	0.232634i
$505$	5392.57			0.475180
$506$	−8646.75	+	4992.20i	−0.759673	+	0.438598i
$507$	−4478.18	+	6711.08i	−0.392274	+	0.587869i
$508$	−1337.21	+	2316.12i	−0.116790	+	0.202285i
$509$	6032.90	−	10449.3i	0.525351	−	0.909934i	−0.474213	−	0.880410i	$-0.657267\pi$
$509$	6032.90	−	10449.3i	0.525351	−	0.909934i	0.999564	−	0.0295243i	$-0.00939924\pi$
$510$	−4943.27	+	2441.56i	−0.429199	+	0.211989i
$511$	−14933.7	−	3017.77i	−1.29281	−	0.261249i
$512$		−	512.000i		−	0.0441942i
$513$	3215.13	−	16322.3i	0.276709	−	1.40477i
$514$			4182.03i			0.358875i
$515$	−3755.74	+	2168.37i	−0.321354	+	0.185534i
$516$	−1476.39	−	2989.14i	−0.125958	−	0.255019i
$517$	33769.3	+	19496.7i	2.87268	+	1.65854i
$518$	−475.328	−	1414.40i	−0.0403180	−	0.119971i
$519$	6973.84	−	10451.1i	0.589822	−	0.883918i
$520$	527.614	+	913.855i	0.0444950	+	0.0770677i
$521$	−11166.5			−0.938988			−0.469494	−	0.882936i	$-0.655564\pi$
$521$	−11166.5			−0.938988			−0.469494	+	0.882936i	$0.655564\pi$
$522$	−1189.30	−	2861.18i	−0.0997209	−	0.239905i
$523$		−	13008.8i		−	1.08764i	−0.839201	−	0.543821i	$-0.816977\pi$
$523$		−	13008.8i		−	1.08764i	0.839201	−	0.543821i	$-0.183023\pi$
$524$	−1991.57	−	3449.51i	−0.166035	−	0.287581i
$525$	6652.28	+	6684.59i	0.553008	+	0.555694i
$526$	−1652.16	+	2861.62i	−0.136953	+	0.237210i
$527$	5124.50	+	2958.63i	0.423580	+	0.244554i
$528$	−374.125	+	5762.83i	−0.0308365	+	0.474991i
$529$	−3500.89	−	6063.71i	−0.287736	−	0.498374i
$530$	−7990.10			−0.654845
$531$	−1802.04	−	4335.27i	−0.147272	−	0.354303i
$532$	5811.99	−	6586.76i	0.473650	−	0.536790i
$533$	−5285.96	+	3051.85i	−0.429569	+	0.248012i
$534$	−894.950	−	597.184i	−0.0725249	−	0.0483945i
$535$	3468.35	+	2002.45i	0.280280	+	0.161820i
$536$	3755.16	+	2168.04i	0.302608	+	0.174711i
$537$	−2785.80	+	1375.95i	−0.223866	+	0.110571i
$538$	−1718.79	+	992.346i	−0.137737	+	0.0795224i
$539$	−23640.1	+	2966.00i	−1.88915	+	0.237022i
$540$	942.514	+	2759.67i	0.0751099	+	0.219921i
$541$	22519.6			1.78964			0.894820	−	0.446427i	$-0.147304\pi$
$541$	22519.6			1.78964			0.894820	+	0.446427i	$0.147304\pi$
$542$	3247.79	+	5625.34i	0.257389	+	0.445810i
$543$	11451.7	−	5656.17i	0.905042	−	0.447016i
$544$	2829.28	+	1633.49i	0.222986	+	0.128741i
$545$	2907.92	−	5036.66i	0.228553	−	0.395866i
$546$	4722.06	−	1253.02i	0.370120	−	0.0982127i
$547$	1854.23	+	3211.62i	0.144938	+	0.251040i	0.929350	−	0.369200i	$-0.120368\pi$
$547$	1854.23	+	3211.62i	0.144938	+	0.251040i	−0.784412	+	0.620241i	$0.787035\pi$
$548$			2864.77i			0.223316i
$549$	1441.06	−	11051.9i	0.112027	−	0.859168i
$550$	−13614.1			−1.05547
$551$	−3401.98	−	5892.40i	−0.263029	−	0.455580i
$552$	2981.28	+	193.546i	0.229877	+	0.0149237i
$553$	−1621.41	+	544.896i	−0.124682	+	0.0419012i
$554$	−12244.2	−	7069.20i	−0.939002	−	0.542133i
$555$	1085.45	+	70.4674i	0.0830173	+	0.00538951i
$556$	5618.35	−	3243.75i	0.428545	−	0.247421i
$557$			13908.2i			1.05800i	0.848620	+	0.529002i	$0.177434\pi$
$557$			13908.2i			1.05800i	−0.848620	+	0.529002i	$0.822566\pi$
$558$	1902.23	−	2485.41i	0.144315	−	0.188559i
$559$		−	4071.50i		−	0.308061i
$560$	−305.003	+	1509.33i	−0.0230156	+	0.113894i
$561$	−30651.5	−	20453.1i	−2.30678	−	1.53927i
$562$	1647.84	−	2854.14i	0.123683	−	0.214226i
$563$	−11037.3	+	19117.2i	−0.826232	+	1.43107i	0.0747429	+	0.997203i	$0.476186\pi$
$563$	−11037.3	+	19117.2i	−0.826232	+	1.43107i	−0.900974	+	0.433872i	$0.857147\pi$
$564$	−5167.00	−	10461.3i	−0.385762	−	0.781026i
$565$	567.418	−	327.599i	0.0422503	−	0.0243932i
$566$	6197.83			0.460272
$567$	13472.9	−	875.460i	0.997895	−	0.0648428i
$568$	−6961.04			−0.514223
$569$	7973.63	−	4603.58i	0.587472	−	0.339177i	−0.176625	−	0.984278i	$-0.556518\pi$
$569$	7973.63	−	4603.58i	0.587472	−	0.339177i	0.764097	+	0.645101i	$0.223185\pi$
$570$	2835.79	+	5741.44i	0.208383	+	0.421899i
$571$	−5236.02	+	9069.05i	−0.383749	+	0.664672i	−0.991595	−	0.129383i	$-0.958700\pi$
$571$	−5236.02	+	9069.05i	−0.383749	+	0.664672i	0.607846	+	0.794055i	$0.292034\pi$
$572$	−3526.35	+	6107.81i	−0.257769	+	0.446469i
$573$	810.631	+	540.919i	0.0591005	+	0.0394367i
$574$	−8730.35	−	1764.21i	−0.634839	−	0.128287i
$575$			7042.97i			0.510804i
$576$	1050.24	−	1372.22i	0.0759720	−	0.0992635i
$577$		−	8285.59i		−	0.597805i	−0.954284	−	0.298903i	$-0.903379\pi$
$577$		−	8285.59i		−	0.597805i	0.954284	−	0.298903i	$-0.0966206\pi$
$578$	−9543.53	+	5509.96i	−0.686779	+	0.396512i
$579$	−18318.0	−	1189.21i	−1.31480	−	0.0853573i
$580$	1032.90	+	596.346i	0.0739464	+	0.0426930i
$581$	−7855.96	+	2640.10i	−0.560964	+	0.188519i
$582$	15132.8	+	982.428i	1.07779	+	0.0699707i
$583$	−26701.2	−	46247.8i	−1.89683	−	3.28540i
$584$	−6581.13			−0.466317
$585$	−460.473	+	3531.50i	−0.0325440	+	0.249589i
$586$			16151.5i			1.13859i
$587$	−744.882	−	1290.17i	−0.0523758	−	0.0907175i	0.838649	−	0.544672i	$-0.183346\pi$
$587$	−744.882	−	1290.17i	−0.0523758	−	0.0907175i	−0.891025	+	0.453955i	$0.850013\pi$
$588$	6376.58	+	3188.04i	0.447221	+	0.223592i
$589$	3436.35	−	5951.93i	0.240394	−	0.416375i
$590$	1565.06	+	903.587i	0.109207	+	0.0630510i
$591$	9720.77	−	4801.26i	0.676581	−	0.334175i
$592$	−322.270	−	558.189i	−0.0223737	−	0.0387524i
$593$	592.599			0.0410373			0.0205187	−	0.999789i	$-0.493468\pi$
$593$	592.599			0.0410373			0.0205187	+	0.999789i	$0.493468\pi$
$594$	−12823.7	+	14677.6i	−0.885795	+	1.01386i
$595$	−7367.40	−	6500.81i	−0.507620	−	0.447911i
$596$	1349.71	−	779.256i	0.0927623	−	0.0535563i
$597$	−3577.25	+	1766.87i	−0.245238	+	0.121127i
$598$	3159.75	+	1824.28i	0.216073	+	0.124750i
$599$	5059.84	+	2921.30i	0.345141	+	0.199267i	0.662543	−	0.749024i	$-0.269477\pi$
$599$	5059.84	+	2921.30i	0.345141	+	0.199267i	−0.317402	+	0.948291i	$0.602810\pi$
$600$	3388.52	+	2261.09i	0.230559	+	0.153848i
$601$	−10690.0	+	6171.88i	−0.725548	+	0.418895i	−0.816791	−	0.576933i	$-0.804249\pi$
$601$	−10690.0	+	6171.88i	−0.725548	+	0.418895i	0.0912431	+	0.995829i	$0.470916\pi$
$602$	3930.97	−	4454.99i	0.266137	−	0.301614i
$603$	5617.07	+	13513.3i	0.379345	+	0.912614i
$604$	−4586.37			−0.308968
$605$	9078.17	+	15723.8i	0.610049	+	1.05664i
$606$	698.660	−	10761.8i	0.0468336	−	0.721401i
$607$	4079.51	+	2355.31i	0.272788	+	0.157494i	0.630154	−	0.776470i	$-0.282992\pi$
$607$	4079.51	+	2355.31i	0.272788	+	0.157494i	−0.357366	+	0.933964i	$0.616325\pi$
$608$	1897.24	−	3286.11i	0.126551	−	0.219193i
$609$	3914.02	−	3895.10i	0.260434	−	0.259175i
$610$	2145.07	+	3715.38i	0.142380	+	0.246609i
$611$		−	14249.3i		−	0.943475i
$612$	4232.12	+	10181.5i	0.279531	+	0.672487i
$613$	−3465.96			−0.228366			−0.114183	−	0.993460i	$-0.536425\pi$
$613$	−3465.96			−0.228366			−0.114183	+	0.993460i	$0.536425\pi$
$614$	−8874.14	−	15370.5i	−0.583275	−	1.01026i
$615$	3603.89	−	5400.86i	0.236297	−	0.354120i
$616$	−9755.48	+	3278.46i	−0.638084	+	0.214437i
$617$	−22256.0	−	12849.5i	−1.45218	−	0.838415i	−0.453572	−	0.891220i	$-0.649850\pi$
$617$	−22256.0	−	12849.5i	−1.45218	−	0.838415i	−0.998605	+	0.0528050i	$0.983184\pi$
$618$	3840.78	+	7776.16i	0.249998	+	0.506154i
$619$	12371.3	−	7142.59i	0.803305	−	0.463788i	−0.0413205	−	0.999146i	$-0.513156\pi$
$619$	12371.3	−	7142.59i	0.803305	−	0.463788i	0.844626	+	0.535358i	$0.179823\pi$
$620$			1204.74i			0.0780380i
$621$	7593.17	+	6634.07i	0.490666	+	0.428689i
$622$		−	7502.17i		−	0.483616i
$623$	379.784	−	1879.39i	0.0244233	−	0.120861i
$624$	1892.11	−	934.548i	0.121387	−	0.0599549i
$625$	−3113.96	+	5393.54i	−0.199294	+	0.345187i
$626$	9855.48	−	17070.2i	0.629240	−	1.08988i
$627$	−23755.6	+	35600.6i	−1.51309	+	2.26755i
$628$	−9526.06	+	5499.87i	−0.605304	+	0.349473i
$629$	4112.69			0.260705
$630$	−3913.45	+	3419.55i	−0.247485	+	0.216251i
$631$	11002.4			0.694133			0.347066	−	0.937841i	$-0.387178\pi$
$631$	11002.4			0.694133			0.347066	+	0.937841i	$0.387178\pi$
$632$	−639.885	+	369.438i	−0.0402741	+	0.0232523i
$633$	−10109.6	−	656.319i	−0.634788	−	0.0412106i
$634$	7573.58	−	13117.8i	0.474425	−	0.821728i
$635$	1737.19	−	3008.91i	0.108564	−	0.188039i
$636$	−1035.20	+	15945.6i	−0.0645412	+	0.994160i
$637$	5258.02	+	6939.44i	0.327049	+	0.431633i
$638$			7971.45i			0.494659i
$639$	−18656.4	−	14278.8i	−1.15498	−	0.883976i
$640$			665.149i			0.0410817i
$641$	−9886.03	+	5707.70i	−0.609165	+	0.351702i	−0.772639	−	0.634846i	$-0.781063\pi$
$641$	−9886.03	+	5707.70i	−0.609165	+	0.351702i	0.163474	+	0.986548i	$0.447730\pi$
$642$	4445.60	−	6662.26i	0.273293	−	0.409561i
$643$	7061.92	+	4077.20i	0.433118	+	0.250061i	0.700674	−	0.713482i	$-0.252883\pi$
$643$	7061.92	+	4077.20i	0.433118	+	0.250061i	−0.267556	+	0.963542i	$0.586216\pi$
$644$	1696.05	+	5046.80i	0.103779	+	0.308807i
$645$	1918.00	+	3883.25i	0.117087	+	0.237059i
$646$	12105.9	+	20968.1i	0.737308	+	1.27705i
$647$	20551.0			1.24875			0.624376	−	0.781124i	$-0.285353\pi$
$647$	20551.0			1.24875			0.624376	+	0.781124i	$0.285353\pi$
$648$	5629.52	−	1523.41i	0.341278	−	0.0923537i
$649$			12078.4i			0.730535i
$650$	2487.48	+	4308.44i	0.150103	+	0.259986i
$651$	5384.11	+	1456.66i	0.324148	+	0.0876975i
$652$	−5678.69	+	9835.78i	−0.341096	+	0.590796i
$653$	10707.0	+	6181.69i	0.641650	+	0.370457i	0.785250	−	0.619179i	$-0.212534\pi$
$653$	10707.0	+	6181.69i	0.641650	+	0.370457i	−0.143600	+	0.989636i	$0.545868\pi$
$654$	−9674.78	−	6455.80i	−0.578462	−	0.385997i
$655$	2587.29	+	4481.32i	0.154342	+	0.267328i
$656$	−3847.39			−0.228987
$657$	−17638.2	−	13499.5i	−1.04738	−	0.801623i
$658$	13757.4	−	15591.4i	0.815077	−	0.923731i
$659$	22860.8	−	13198.7i	1.35134	−	0.780194i	0.362899	−	0.931829i	$-0.381787\pi$
$659$	22860.8	−	13198.7i	1.35134	−	0.780194i	0.988437	+	0.151635i	$0.0484538\pi$
$660$	486.033	−	7486.60i	0.0286648	−	0.441539i
$661$	−2806.25	−	1620.19i	−0.165129	−	0.0953374i	0.415158	−	0.909749i	$-0.363726\pi$
$661$	−2806.25	−	1620.19i	−0.165129	−	0.0953374i	−0.580287	+	0.814412i	$0.697060\pi$
$662$	−7420.43	−	4284.19i	−0.435655	−	0.251525i
$663$	−872.353	+	13437.3i	−0.0511001	+	0.787121i
$664$	−3100.33	+	1789.98i	−0.181199	+	0.104615i
$665$	−7550.47	+	8556.98i	−0.440293	+	0.498986i
$666$	281.260	−	2157.07i	0.0163643	−	0.125502i
$667$	4123.87			0.239395
$668$	−1413.47	−	2448.19i	−0.0818692	−	0.141802i
$669$	1211.90	+	808.675i	0.0700367	+	0.0467342i
$670$	−4878.39	−	2816.54i	−0.281297	−	0.162407i
$671$	−14336.8	+	24832.0i	−0.824835	+	1.42866i
$672$	2972.62	+	804.236i	0.170642	+	0.0461668i
$673$	−1749.04	−	3029.43i	−0.100179	−	0.173516i	0.811579	−	0.584242i	$-0.198608\pi$
$673$	−1749.04	−	3029.43i	−0.100179	−	0.173516i	−0.911758	+	0.410727i	$0.865275\pi$
$674$		−	17356.3i		−	0.991898i
$675$	4443.55	+	13010.7i	0.253381	+	0.741897i
$676$	−6210.76			−0.353366
$677$	−16223.0	−	28099.0i	−0.920973	−	1.59517i	−0.797913	−	0.602773i	$-0.794063\pi$
$677$	−16223.0	−	28099.0i	−0.920973	−	1.59517i	−0.123060	−	0.992399i	$-0.539271\pi$
$678$	−580.266	−	1174.82i	−0.0328687	−	0.0665470i
$679$	8609.03	+	25617.3i	0.486575	+	1.44787i
$680$	−3675.57	−	2122.09i	−0.207282	−	0.119674i
$681$	10849.1	−	16258.6i	0.610480	−	0.914876i
$682$	−6973.21	+	4025.99i	−0.391522	+	0.226045i
$683$		−	13676.1i		−	0.766179i	−0.923711	−	0.383090i	$-0.874860\pi$
$683$		−	13676.1i		−	0.766179i	0.923711	−	0.383090i	$-0.125140\pi$
$684$	11825.4	−	4915.46i	0.661049	−	0.274777i
$685$		−	3721.68i		−	0.207589i
$686$	−946.660	+	12669.6i	−0.0526875	+	0.705141i
$687$	−718.637	+	11069.5i	−0.0399094	+	0.614744i
$688$	1283.21	−	2222.58i	0.0711073	−	0.123161i
$689$	−9757.34	+	16900.2i	−0.539514	+	0.934465i
$690$	−3873.04	−	251.439i	−0.213687	−	0.0138726i
$691$	−26470.2	+	15282.6i	−1.45727	+	0.841355i	−0.998876	−	0.0473939i	$-0.984908\pi$
$691$	−26470.2	+	15282.6i	−1.45727	+	0.841355i	−0.458394	+	0.888749i	$0.651575\pi$
$692$	9671.97			0.531319
$693$	−32870.7	−	11224.2i	−1.80181	−	0.615257i
$694$	7960.87			0.435433
$695$	−7298.90	+	4214.02i	−0.398364	+	0.229996i
$696$	1323.94	−	1984.07i	0.0721030	−	0.108055i
$697$	12274.7	−	21260.4i	0.667056	−	1.15537i
$698$	1589.09	−	2752.39i	0.0861719	−	0.149254i
$699$	−7083.41	+	3498.62i	−0.383289	+	0.189313i
$700$	−1437.96	+	7115.86i	−0.0776425	+	0.384220i
$701$			28456.9i			1.53324i	0.642100	+	0.766621i	$0.278063\pi$
$701$			28456.9i			1.53324i	−0.642100	+	0.766621i	$0.721937\pi$
$702$	6988.07	+	1376.50i	0.375709	+	0.0740064i
$703$		−	4776.75i		−	0.256271i
$704$	−3849.98	+	2222.78i	−0.206110	+	0.118998i
$705$	6712.54	+	13590.4i	0.358594	+	0.726021i
$706$	−7414.02	−	4280.49i	−0.395227	−	0.228185i
$707$	18217.9	−	6122.37i	0.969101	−	0.325680i
$708$	2006.03	−	3006.28i	0.106485	−	0.159580i
$709$	−8817.91	−	15273.1i	−0.467085	−	0.809015i	0.532208	−	0.846614i	$-0.321363\pi$
$709$	−8817.91	−	15273.1i	−0.467085	−	0.809015i	−0.999293	+	0.0375985i	$0.988029\pi$
$710$	9043.21			0.478008
$711$	−2472.77	−	322.425i	−0.130431	−	0.0170069i
$712$		−	828.230i		−	0.0435944i
$713$	2082.76	+	3607.45i	0.109397	+	0.189481i
$714$	−13928.0	+	13860.7i	−0.730032	+	0.726503i
$715$	4581.14	−	7934.77i	0.239615	−	0.415026i
$716$	−2071.39	−	1195.91i	−0.108116	−	0.0624210i
$717$	229.974	−	3542.41i	0.0119784	−	0.184510i
$718$	2470.23	+	4278.56i	0.128396	+	0.222388i
$719$	29112.4			1.51003			0.755014	−	0.655709i	$-0.227630\pi$
$719$	29112.4			1.51003			0.755014	+	0.655709i	$0.227630\pi$
$720$	−1364.38	+	1782.68i	−0.0706216	+	0.0922728i
$721$	−10226.3	+	11589.5i	−0.528221	+	0.598635i
$722$	12473.6	−	7201.61i	0.642961	−	0.371213i
$723$	11448.1	+	7639.11i	0.588880	+	0.392948i
$724$	8514.90	+	4916.08i	0.437091	+	0.252354i
$725$	4869.69	+	2811.52i	0.249456	+	0.144024i
$726$	32555.8	−	16079.9i	1.66427	−	0.822012i
$727$	22919.1	−	13232.3i	1.16922	−	0.675049i	0.215723	−	0.976455i	$-0.430789\pi$
$727$	22919.1	−	13232.3i	1.16922	−	0.675049i	0.953496	+	0.301406i	$0.0974558\pi$
$728$	2819.99	+	2488.29i	0.143566	+	0.126679i
$729$	18212.6	+	7464.60i	0.925298	+	0.379241i
$730$	8549.67			0.433476
$731$	8187.89	+	14181.8i	0.414282	+	0.717558i
$732$	7692.60	−	3799.51i	0.388425	−	0.191850i
$733$	−6094.22	−	3518.50i	−0.307088	−	0.177297i	0.338535	−	0.940954i	$-0.390069\pi$
$733$	−6094.22	−	3518.50i	−0.307088	−	0.177297i	−0.645623	+	0.763657i	$0.723402\pi$
$734$	10613.7	−	18383.5i	0.533732	−	0.924451i
$735$	−8283.94	−	4141.64i	−0.415725	−	0.207846i
$736$	1149.91	+	1991.71i	0.0575901	+	0.0997490i
$737$		−	37649.1i		−	1.88171i
$738$	−10311.4	−	7891.93i	−0.514321	−	0.393640i
$739$	−3555.93			−0.177005			−0.0885027	−	0.996076i	$-0.528208\pi$
$739$	−3555.93			−0.177005			−0.0885027	+	0.996076i	$0.528208\pi$
$740$	418.668	+	725.153i	0.0207980	+	0.0360232i
$741$	15607.0	+	1013.21i	0.773733	+	0.0502310i
$742$	−26993.2	+	9071.44i	−1.33552	+	0.448818i
$743$	10659.6	+	6154.30i	0.526328	+	0.303875i	0.739520	−	0.673135i	$-0.235053\pi$
$743$	10659.6	+	6154.30i	0.526328	+	0.303875i	−0.213192	+	0.977010i	$0.568386\pi$
$744$	2404.27	+	156.086i	0.118474	+	0.00769139i
$745$	−1753.43	+	1012.35i	−0.0862294	+	0.0497845i
$746$		−	27460.1i		−	1.34770i
$747$	−11980.9	−	1562.20i	−0.586826	−	0.0765164i
$748$		−	28366.3i		−	1.38660i
$749$	13990.7	+	2827.21i	0.682522	+	0.137923i
$750$	−10017.2	−	6684.28i	−0.487701	−	0.325434i
$751$	−11706.2	+	20275.7i	−0.568793	+	0.985179i	0.427893	+	0.903830i	$0.359256\pi$
$751$	−11706.2	+	20275.7i	−0.568793	+	0.985179i	−0.996686	+	0.0813490i	$0.974077\pi$
$752$	4490.91	−	7778.49i	0.217775	−	0.377197i
$753$	−4047.79	−	8195.28i	−0.195896	−	0.396617i
$754$	2522.71	−	1456.49i	0.121846	−	0.0703478i
$755$	5958.25			0.287209
$756$	6317.28	+	8253.02i	0.303912	+	0.397036i
$757$	−33427.8			−1.60496			−0.802481	−	0.596678i	$-0.796487\pi$
$757$	−33427.8			−1.60496			−0.802481	+	0.596678i	$0.796487\pi$
$758$	11224.1	−	6480.26i	0.537836	−	0.310520i
$759$	−11487.5	−	23258.0i	−0.549368	−	1.11227i
$760$	−2464.74	+	4269.05i	−0.117639	+	0.203756i
$761$	2315.87	−	4011.20i	0.110316	−	0.191072i	−0.805582	−	0.592484i	$-0.798147\pi$
$761$	2315.87	−	4011.20i	0.110316	−	0.191072i	0.915898	+	0.401412i	$0.131480\pi$
$762$	−5779.73	−	3856.71i	−0.274774	−	0.183351i
$763$	4105.62	−	20317.0i	0.194801	−	0.963989i
$764$			750.197i			0.0355251i
$765$	−5498.02	−	13227.0i	−0.259845	−	0.625126i
$766$			7135.57i			0.336578i
$767$	3822.43	−	2206.88i	0.179948	−	0.103893i
$768$	1327.42	+	86.1766i	0.0623687	+	0.00404900i
$769$	−34829.0	−	20108.5i	−1.63325	−	0.942955i	−0.983083	−	0.183160i	$-0.941367\pi$
$769$	−34829.0	−	20108.5i	−1.63325	−	0.942955i	−0.650163	−	0.759795i	$-0.725299\pi$
$770$	12673.5	−	4259.11i	0.593146	−	0.199335i
$771$	−10842.4	−	703.893i	−0.506459	−	0.0328795i
$772$	−7065.44	−	12237.7i	−0.329392	−	0.570524i
$773$	12424.8			0.578124			0.289062	−	0.957310i	$-0.406657\pi$
$773$	12424.8			0.578124			0.289062	+	0.957310i	$0.406657\pi$
$774$	7998.20	−	3324.60i	0.371433	−	0.154393i
$775$			5679.84i			0.263259i
$776$	5836.89	+	10109.8i	0.270016	+	0.467681i
$777$	3747.00	−	994.281i	0.173002	−	0.0459069i
$778$	3989.35	−	6909.76i	0.183837	−	0.318415i
$779$	−24693.3	−	14256.7i	−1.13572	−	0.655710i
$780$	−2458.08	+	1214.09i	−0.112838	+	0.0557325i
$781$	30220.5	+	52343.4i	1.38460	+	2.39820i
$782$	−14674.7			−0.671058
$783$	7618.12	−	2601.83i	0.347701	−	0.118751i
$784$	683.194	+	5445.31i	0.0311222	+	0.248055i
$785$	12375.5	−	7144.99i	0.562675	−	0.324860i
$786$	9278.47	−	4582.79i	0.421059	−	0.207968i
$787$	−15562.6	−	8985.07i	−0.704888	−	0.406967i	0.104277	−	0.994548i	$-0.466747\pi$
$787$	−15562.6	−	8985.07i	−0.704888	−	0.406967i	−0.809165	+	0.587581i	$0.800080\pi$
$788$	7227.89	+	4173.03i	0.326755	+	0.188652i
$789$	−7141.01	−	4765.06i	−0.322214	−	0.215007i
$790$	831.286	−	479.943i	0.0374378	−	0.0216147i
$791$	1544.99	−	1750.95i	0.0694483	−	0.0787061i
$792$	−14877.9	−	1939.93i	−0.667502	−	0.0870357i
$793$	10478.1			0.469215
$794$	−2640.60	−	4573.65i	−0.118024	−	0.204424i
$795$	1344.84	−	20715.3i	0.0599958	−	0.924145i
$796$	−2659.87	−	1535.68i	−0.118438	−	0.0683802i
$797$	−12873.8	+	22298.2i	−0.572165	+	0.991018i	0.424179	+	0.905578i	$0.360563\pi$
$797$	−12873.8	+	22298.2i	−0.572165	+	0.991018i	−0.996343	+	0.0854396i	$0.972771\pi$
$798$	16098.7	+	16176.9i	0.714146	+	0.717615i
$799$	28655.6	+	49633.0i	1.26879	+	2.19761i
$800$			3135.89i			0.138588i
$801$	1698.90	−	2219.75i	0.0749410	−	0.0979164i
$802$	−8903.06			−0.391992
$803$	28571.2	+	49486.7i	1.25561	+	2.17478i
$804$	−6252.95	+	9370.78i	−0.274284	+	0.411047i
$805$	−2203.36	−	6556.39i	−0.0964700	−	0.287059i
$806$	2548.20	+	1471.20i	0.111360	+	0.0642939i
$807$	−2283.48	−	4623.20i	−0.0996062	−	0.201666i
$808$	7189.64	−	4150.94i	0.313033	−	0.180730i
$809$			23810.9i			1.03479i	0.855746	+	0.517396i	$0.173099\pi$
$809$			23810.9i			1.03479i	−0.855746	+	0.517396i	$0.826901\pi$
$810$	−7313.41	+	1979.09i	−0.317243	+	0.0858496i
$811$			34102.2i			1.47656i	0.674495	+	0.738280i	$0.264362\pi$
$811$			34102.2i			1.47656i	−0.674495	+	0.738280i	$0.735638\pi$
$812$	4166.54	+	841.968i	0.180070	+	0.0363883i
$813$	−15131.0	+	7473.46i	−0.652728	+	0.322393i
$814$	−2798.19	+	4846.61i	−0.120487	+	0.208690i
$815$	7377.29	−	12777.8i	0.317074	−	0.549188i
$816$	−4711.21	+	7060.31i	−0.202115	+	0.302892i
$817$	16471.7	−	9509.96i	0.705353	−	0.407236i
$818$	13867.2			0.592731
$819$	2453.81	+	12453.4i	0.104692	+	0.531327i
$820$	4998.21			0.212860
$821$	19703.4	−	11375.8i	0.837581	−	0.483578i	−0.0188604	−	0.999822i	$-0.506004\pi$
$821$	19703.4	−	11375.8i	0.837581	−	0.483578i	0.856441	+	0.516245i	$0.172670\pi$
$822$	−7427.27	−	482.181i	−0.315153	−	0.0204598i
$823$	10422.3	−	18051.9i	0.441431	−	0.764581i	−0.556365	−	0.830938i	$-0.687804\pi$
$823$	10422.3	−	18051.9i	0.441431	−	0.764581i	0.997796	+	0.0663569i	$0.0211376\pi$
$824$	−3338.22	+	5781.97i	−0.141132	+	0.244447i
$825$	2291.44	−	35296.1i	0.0967001	−	1.48952i
$826$	6313.16	+	1275.75i	0.265936	+	0.0537399i
$827$			21810.9i			0.917099i	0.888669	+	0.458550i	$0.151631\pi$
$827$			21810.9i			0.917099i	−0.888669	+	0.458550i	$0.848369\pi$
$828$	−1003.58	+	7696.75i	−0.0421218	+	0.323044i
$829$			3749.17i			0.157074i	0.996911	+	0.0785368i	$0.0250248\pi$
$829$			3749.17i			0.157074i	−0.996911	+	0.0785368i	$0.974975\pi$
$830$	4027.70	−	2325.39i	0.168438	−	0.0972477i
$831$	20388.6	−	30554.8i	0.851111	−	1.27549i
$832$	1406.88	+	812.265i	0.0586237	+	0.0338464i
$833$	−32270.1	−	13597.4i	−1.34225	−	0.565574i
$834$	7464.17	+	15112.2i	0.309908	+	0.627449i
$835$	1836.26	+	3180.50i	0.0761035	+	0.131815i
$836$	−32946.5			−1.36301
$837$	6123.55	+	5350.08i	0.252881	+	0.220939i
$838$			27488.3i			1.13313i
$839$	−9212.62	−	15956.7i	−0.379088	−	0.656600i	0.611842	−	0.790980i	$-0.290429\pi$
$839$	−9212.62	−	15956.7i	−0.379088	−	0.656600i	−0.990930	+	0.134380i	$0.957096\pi$
$840$	−3861.79	−	1044.80i	−0.158624	−	0.0429154i
$841$	−10548.3	+	18270.1i	−0.432501	+	0.749114i
$842$	8016.64	+	4628.41i	0.328114	+	0.189437i
$843$	7122.35	+	4752.61i	0.290993	+	0.194174i
$844$	−3899.38	−	6753.92i	−0.159031	−	0.275450i
$845$	8068.51			0.328480
$846$	27991.7	−	11635.3i	1.13756	−	0.472848i
$847$	48520.9	+	42813.6i	1.96836	+	1.73683i
$848$	−10652.8	+	6150.40i	−0.431390	+	0.249063i
$849$	−1043.18	+	16068.6i	−0.0421694	+	0.649556i
$850$	−17328.8	−	10004.8i	−0.699260	−	0.403718i
$851$	2507.30	+	1447.59i	0.100998	+	0.0583110i
$852$	1171.64	−	18047.3i	0.0471122	−	0.725693i
$853$	−29972.1	+	17304.4i	−1.20308	+	0.694596i	−0.961238	−	0.275720i	$-0.911084\pi$
$853$	−29972.1	+	17304.4i	−1.20308	+	0.694596i	−0.241838	+	0.970317i	$0.577750\pi$
$854$	11465.0	+	10116.4i	0.459395	+	0.405359i
$855$	−15362.7	+	6385.77i	−0.614493	+	0.255425i
$856$	6165.57			0.246186
$857$	−17034.5	−	29504.7i	−0.678984	−	1.17603i	−0.975287	−	0.220941i	$-0.929087\pi$
$857$	−17034.5	−	29504.7i	−0.678984	−	1.17603i	0.296303	−	0.955094i	$-0.404246\pi$
$858$	−15241.7	−	10170.5i	−0.606460	−	0.404680i
$859$	−21418.1	−	12365.8i	−0.850731	−	0.491170i	0.0101665	−	0.999948i	$-0.496764\pi$
$859$	−21418.1	−	12365.8i	−0.850731	−	0.491170i	−0.860897	+	0.508779i	$0.830097\pi$
$860$	−1667.04	+	2887.39i	−0.0660994	+	0.114488i
$861$	6043.37	−	22337.5i	0.239207	−	0.884159i
$862$	8546.12	+	14802.3i	0.337682	+	0.584883i
$863$		−	11353.1i		−	0.447816i	−0.974610	−	0.223908i	$-0.928118\pi$
$863$		−	11353.1i		−	0.447816i	0.974610	−	0.223908i	$-0.0718815\pi$
$864$	3380.87	+	2953.83i	0.133124	+	0.116309i
$865$	−12565.0			−0.493901
$866$	−3953.10	−	6846.97i	−0.155118	−	0.268671i
$867$	−12678.9	−	25670.1i	−0.496653	−	1.00554i
$868$	1367.78	+	4070.02i	0.0534858	+	0.159154i
$869$	5555.96	+	3207.73i	0.216885	+	0.125219i
$870$	−1719.95	+	2577.55i	−0.0670250	+	0.100445i
$871$	−11914.8	+	6879.00i	−0.463509	+	0.267607i
$872$		−	8953.50i		−	0.347711i
$873$	−5094.12	+	39068.3i	−0.197491	+	1.51462i
$874$			17044.2i			0.659644i
$875$	4250.92	−	21036.0i	0.164237	−	0.812739i
$876$	1107.69	−	17062.4i	0.0427232	−	0.658086i
$877$	24041.1	−	41640.4i	0.925667	−	1.60330i	0.135181	−	0.990821i	$-0.456838\pi$
$877$	24041.1	−	41640.4i	0.925667	−	1.60330i	0.790486	−	0.612481i	$-0.209828\pi$
$878$	−11414.9	+	19771.1i	−0.438762	+	0.759958i
$879$	−41874.6	−	2718.51i	−1.60682	−	0.104315i
$880$	5001.58	−	2887.66i	0.191594	−	0.110617i
$881$	−5466.82			−0.209060			−0.104530	−	0.994522i	$-0.533334\pi$
$881$	−5466.82			−0.209060			−0.104530	+	0.994522i	$0.533334\pi$
$882$	−9338.62	+	15995.5i	−0.356517	+	0.610652i
$883$	−36040.8			−1.37358			−0.686788	−	0.726857i	$-0.740980\pi$
$883$	−36040.8			−1.37358			−0.686788	+	0.726857i	$0.740980\pi$
$884$	−8977.05	+	5182.90i	−0.341551	+	0.197195i
$885$	−2606.08	+	3905.51i	−0.0989856	+	0.148342i
$886$	13016.9	−	22545.9i	0.493579	−	0.854904i
$887$	−13125.1	+	22733.3i	−0.496841	+	0.860554i	−0.999993	−	0.00364396i	$-0.998840\pi$
$887$	−13125.1	+	22733.3i	−0.496841	+	0.860554i	0.503152	+	0.864198i	$0.332173\pi$
$888$	1501.41	−	741.574i	0.0567389	−	0.0280243i
$889$	2452.70	−	12137.4i	0.0925321	−	0.457902i
$890$			1075.97i			0.0405242i
$891$	−35895.1	−	35717.4i	−1.34964	−	1.34296i
$892$			1121.55i			0.0420988i
$893$	57647.1	−	33282.5i	2.16023	−	1.24721i
$894$	1793.14	+	3630.44i	0.0670822	+	0.135817i
$895$	2690.98	+	1553.64i	0.100502	+	0.0580249i
$896$	755.167	+	2247.09i	0.0281566	+	0.0837837i
$897$	−5261.50	+	7884.98i	−0.195849	+	0.293503i
$898$	611.494	+	1059.14i	0.0227236	+	0.0393585i
$899$	3325.71			0.123380
$900$	−6432.49	+	8404.55i	−0.238240	+	0.311280i
$901$		−	78489.0i		−	2.90216i
$902$	16702.9	+	28930.3i	0.616571	+	1.06793i
$903$	10888.4	+	10941.3i	0.401268	+	0.403217i
$904$	504.340	−	873.542i	0.0185554	−	0.0321389i
$905$	−11061.9	−	6386.57i	−0.406308	−	0.234582i
$906$	771.949	−	11890.7i	0.0283072	−	0.436029i
$907$	176.103	+	305.020i	0.00644699	+	0.0111665i	0.869231	−	0.494406i	$-0.164615\pi$
$907$	176.103	+	305.020i	0.00644699	+	0.0111665i	−0.862784	+	0.505573i	$0.831281\pi$
$908$	15046.5			0.549928
$909$	27783.7	+	3622.72i	1.01378	+	0.132187i
$910$	−3663.50	−	3232.58i	−0.133455	−	0.117757i
$911$	−37914.5	+	21889.9i	−1.37888	+	0.796099i	−0.992025	−	0.126040i	$-0.959773\pi$
$911$	−37914.5	+	21889.9i	−1.37888	+	0.796099i	−0.386859	+	0.922139i	$0.626440\pi$
$912$	8200.31	+	5471.91i	0.297741	+	0.198677i
$913$	26919.4	+	15541.9i	0.975797	+	0.563377i
$914$	−18244.8	−	10533.7i	−0.660269	−	0.381206i
$915$	−9993.60	+	4936.01i	−0.361069	+	0.178338i
$916$	−7395.22	+	4269.63i	−0.266752	+	0.154009i
$917$	13828.5	+	12202.0i	0.497992	+	0.439416i
$918$	−27109.0	+	9258.59i	−0.974653	+	0.332875i
$919$	−15685.5			−0.563020			−0.281510	−	0.959558i	$-0.590835\pi$
$919$	−15685.5			−0.563020			−0.281510	+	0.959558i	$0.590835\pi$
$920$	−1493.87	−	2587.46i	−0.0535343	−	0.0927240i
$921$	41343.4	−	20420.2i	1.47916	−	0.730584i
$922$	29608.8	+	17094.7i	1.05761	+	0.610611i
$923$	11043.4	−	19127.7i	0.393821	−	0.682118i
$924$	−6857.82	−	25844.1i	−0.244162	−	0.920137i
$925$	1973.84	+	3418.79i	0.0701615	+	0.121523i
$926$			13184.5i			0.467895i
$927$	−20807.1	+	8648.84i	−0.737210	+	0.306435i
$928$	1836.16			0.0649513
$929$	−557.048	−	964.835i	−0.0196729	−	0.0340745i	0.856021	−	0.516940i	$-0.172929\pi$
$929$	−557.048	−	964.835i	−0.0196729	−	0.0340745i	−0.875694	+	0.482866i	$0.839596\pi$
$930$	−3123.43	−	202.774i	−0.110131	−	0.00714971i
$931$	−15793.0	+	37480.6i	−0.555954	+	1.31942i
$932$	−5266.88	−	3040.84i	−0.185110	−	0.106873i
$933$	19450.3	+	1262.72i	0.682500	+	0.0443081i
$934$	−10332.0	+	5965.17i	−0.361962	+	0.208979i
$935$			36851.2i			1.28894i
$936$	2104.46	+	5062.83i	0.0734897	+	0.176799i
$937$			28817.1i			1.00471i	0.864661	+	0.502355i	$0.167533\pi$
$937$			28817.1i			1.00471i	−0.864661	+	0.502355i	$0.832467\pi$
$938$	−19678.6	−	3976.61i	−0.684998	−	0.138423i
$939$	42597.7	+	28424.7i	1.48043	+	0.987863i
$940$	−5834.23	+	10105.2i	−0.202438	+	0.350633i
$941$	−1937.24	+	3355.39i	−0.0671117	+	0.116241i	−0.897629	−	0.440752i	$-0.854712\pi$
$941$	−1937.24	+	3355.39i	−0.0671117	+	0.116241i	0.830517	+	0.556993i	$0.188045\pi$
$942$	−12655.7	−	25623.1i	−0.437734	−	0.886249i
$943$	14966.5	−	8640.93i	0.516837	−	0.298396i
$944$	2782.15			0.0959230
$945$	−8206.89	−	10721.6i	−0.282508	−	0.369074i
$946$	−22283.5			−0.765856
$947$	−21854.0	+	12617.4i	−0.749905	+	0.432958i	−0.825660	−	0.564169i	$-0.809197\pi$
$947$	−21854.0	+	12617.4i	−0.749905	+	0.432958i	0.0757547	+	0.997126i	$0.475863\pi$
$948$	−850.109	−	1721.16i	−0.0291248	−	0.0589669i
$949$	10440.7	−	18083.8i	0.357132	−	0.618571i
$950$	−11620.2	+	20126.8i	−0.396851	+	0.687367i
$951$	32734.8	+	21843.3i	1.11619	+	0.744814i
$952$	−14826.6	−	2996.13i	−0.504761	−	0.102001i
$953$		−	34412.3i		−	1.16970i	−0.811141	−	0.584850i	$-0.801153\pi$
$953$		−	34412.3i		−	1.16970i	0.811141	−	0.584850i	$-0.198847\pi$
$954$	−41166.7	−	5367.74i	−1.39709	−	0.182167i
$955$		−	974.594i		−	0.0330232i
$956$	2366.58	−	1366.34i	0.0800633	−	0.0462246i
$957$	−20666.9	−	1341.70i	−0.698084	−	0.0453198i
$958$	−17036.3	−	9835.89i	−0.574548	−	0.331715i
$959$	−4225.36	−	12573.1i	−0.142277	−	0.423364i
$960$	−1724.48	−	111.954i	−0.0579763	−	0.00376384i
$961$	−13215.8	−	22890.5i	−0.443619	−	0.768370i
$962$	2045.07			0.0685402
$963$	16524.4	+	12647.1i	0.552952	+	0.423206i
$964$			10594.6i			0.353973i
$965$	9178.85	+	15898.2i	0.306194	+	0.530344i
$966$	−13369.9	+	3547.75i	−0.445310	+	0.118165i
$967$	27144.6	−	47015.8i	0.902700	−	1.56352i	0.0787258	−	0.996896i	$-0.474915\pi$
$967$	27144.6	−	47015.8i	0.902700	−	1.56352i	0.823975	−	0.566627i	$-0.191752\pi$
$968$	24206.9	+	13975.9i	0.803761	+	0.464052i
$969$	−56399.8	+	27856.8i	−1.86978	+	0.923519i
$970$	−7582.82	−	13133.8i	−0.251000	−	0.434744i
$971$	8789.79			0.290502			0.145251	−	0.989395i	$-0.453601\pi$
$971$	8789.79			0.290502			0.145251	+	0.989395i	$0.453601\pi$
$972$	3002.10	+	14851.6i	0.0990662	+	0.490088i
$973$	−19873.8	+	22523.1i	−0.654804	+	0.742093i
$974$	−5667.04	+	3271.87i	−0.186431	+	0.107636i
$975$	−11588.8	+	5723.91i	−0.380655	+	0.188012i
$976$	5719.84	+	3302.35i	0.187590	+	0.108305i
$977$	−31969.0	−	18457.3i	−1.04686	−	0.604402i	−0.125088	−	0.992146i	$-0.539921\pi$
$977$	−31969.0	−	18457.3i	−1.04686	−	0.604402i	−0.921767	+	0.387743i	$0.873255\pi$
$978$	−24544.6	−	16378.2i	−0.802506	−	0.535497i
$979$	−6227.86	+	3595.66i	−0.203313	+	0.117383i
$980$	−887.551	−	7074.10i	−0.0289304	−	0.230586i
$981$	18365.8	−	23996.4i	0.597733	−	0.780986i
$982$	−23435.9			−0.761579
$983$	−27918.3	−	48355.9i	−0.905855	−	1.56899i	−0.819765	−	0.572700i	$-0.805896\pi$
$983$	−27918.3	−	48355.9i	−0.905855	−	1.56899i	−0.0860899	−	0.996287i	$-0.527437\pi$
$984$	647.567	−	9974.80i	0.0209794	−	0.323156i
$985$	−9389.89	−	5421.26i	−0.303743	−	0.175366i
$986$	−5858.08	+	10146.5i	−0.189208	+	0.327718i
$987$	38106.9	+	38292.0i	1.22893	+	1.23490i
$988$	6019.77	+	10426.5i	0.193840	+	0.335741i
$989$			11527.9i			0.370644i
$990$	19328.1	+	2520.19i	0.620492	+	0.0809061i
$991$	−20640.6			−0.661626			−0.330813	−	0.943696i	$-0.607323\pi$
$991$	−20640.6			−0.661626			−0.330813	+	0.943696i	$0.607323\pi$
$992$	927.353	+	1606.22i	0.0296809	+	0.0514089i
$993$	12356.2	−	18517.3i	0.394877	−	0.591770i
$994$	30551.0	−	10267.1i	0.974868	−	0.327618i
$995$	3455.49	+	1995.03i	0.110097	+	0.0635645i
$996$	−4118.90	−	8339.26i	−0.131037	−	0.265301i
$997$	6633.45	−	3829.82i	0.210716	−	0.121657i	−0.390928	−	0.920421i	$-0.627846\pi$
$997$	6633.45	−	3829.82i	0.210716	−	0.121657i	0.601644	+	0.798764i	$0.294513\pi$
$998$			948.816i			0.0300944i
$999$	5545.11	+	1092.26i	0.175615	+	0.0345923i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	126.4.m.a.41.4	✓	48
3.2	odd	2		378.4.m.a.125.22		48
7.6	odd	2	inner	126.4.m.a.41.9	yes	48
9.2	odd	6	inner	126.4.m.a.83.9	yes	48
9.4	even	3		1134.4.d.b.1133.1		48
9.5	odd	6		1134.4.d.b.1133.48		48
9.7	even	3		378.4.m.a.251.21		48
21.20	even	2		378.4.m.a.125.21		48
63.13	odd	6		1134.4.d.b.1133.47		48
63.20	even	6	inner	126.4.m.a.83.4	yes	48
63.34	odd	6		378.4.m.a.251.22		48
63.41	even	6		1134.4.d.b.1133.2		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.4.m.a.41.4	✓	48	1.1	even	1	trivial
126.4.m.a.41.9	yes	48	7.6	odd	2	inner
126.4.m.a.83.4	yes	48	63.20	even	6	inner
126.4.m.a.83.9	yes	48	9.2	odd	6	inner
378.4.m.a.125.21		48	21.20	even	2
378.4.m.a.125.22		48	3.2	odd	2
378.4.m.a.251.21		48	9.7	even	3
378.4.m.a.251.22		48	63.34	odd	6
1134.4.d.b.1133.1		48	9.4	even	3
1134.4.d.b.1133.2		48	63.41	even	6
1134.4.d.b.1133.47		48	63.13	odd	6
1134.4.d.b.1133.48		48	9.5	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 126 = 2 \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	126.m (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.73205 + 1.00000i) q^{2} +(-2.30109 - 4.65886i) q^{3} +(2.00000 - 3.46410i) q^{4} +(-2.59824 + 4.50028i) q^{5} +(8.64447 + 5.76829i) q^{6} +(-3.66839 + 18.1533i) q^{7} +8.00000i q^{8} +(-16.4100 + 21.4409i) q^{9} +O(q^{10})\)	\(q+(-1.73205 + 1.00000i) q^{2} +(-2.30109 - 4.65886i) q^{3} +(2.00000 - 3.46410i) q^{4} +(-2.59824 + 4.50028i) q^{5} +(8.64447 + 5.76829i) q^{6} +(-3.66839 + 18.1533i) q^{7} +8.00000i q^{8} +(-16.4100 + 21.4409i) q^{9} -10.3929i q^{10} +(60.1559 - 34.7310i) q^{11} +(-20.7409 - 1.34651i) q^{12} +(-21.9826 - 12.6916i) q^{13} +(-11.7995 - 35.1109i) q^{14} +(26.9450 + 1.74927i) q^{15} +(-8.00000 - 13.8564i) q^{16} +102.093 q^{17} +(6.98197 - 53.5467i) q^{18} -118.577i q^{19} +(10.3929 + 18.0011i) q^{20} +(93.0151 - 24.6819i) q^{21} +(-69.4620 + 120.312i) q^{22} +(62.2408 + 35.9348i) q^{23} +(37.2709 - 18.4087i) q^{24} +(48.9983 + 84.8676i) q^{25} +50.7666 q^{26} +(137.651 + 27.1142i) q^{27} +(55.5482 + 49.0143i) q^{28} +(49.6924 - 28.6899i) q^{29} +(-48.4193 + 23.9151i) q^{30} +(50.1944 + 28.9798i) q^{31} +(27.7128 + 16.0000i) q^{32} +(-300.231 - 200.339i) q^{33} +(-176.830 + 102.093i) q^{34} +(-72.1636 - 63.6754i) q^{35} +(41.4536 + 99.7276i) q^{36} +40.2838 q^{37} +(118.577 + 205.382i) q^{38} +(-8.54470 + 131.618i) q^{39} +(-36.0022 - 20.7859i) q^{40} +(120.231 - 208.246i) q^{41} +(-136.425 + 135.765i) q^{42} +(80.2004 + 138.911i) q^{43} -277.848i q^{44} +(-53.8532 - 129.558i) q^{45} -143.739 q^{46} +(280.682 + 486.155i) q^{47} +(-46.1463 + 69.1557i) q^{48} +(-316.086 - 133.187i) q^{49} +(-169.735 - 97.9967i) q^{50} +(-234.925 - 475.637i) q^{51} +(-87.9303 + 50.7666i) q^{52} -768.800i q^{53} +(-265.533 + 90.6879i) q^{54} +360.958i q^{55} +(-145.227 - 29.3471i) q^{56} +(-552.436 + 272.857i) q^{57} +(-57.3799 + 99.3849i) q^{58} +(-86.9423 + 150.588i) q^{59} +(59.9496 - 89.8415i) q^{60} +(-357.490 + 206.397i) q^{61} -115.919 q^{62} +(-329.026 - 376.549i) q^{63} -64.0000 q^{64} +(114.232 - 65.9518i) q^{65} +(720.354 + 46.7656i) q^{66} +(271.005 - 469.395i) q^{67} +(204.186 - 353.660i) q^{68} +(24.1932 - 372.660i) q^{69} +(188.667 + 38.1254i) q^{70} +870.130i q^{71} +(-171.527 - 131.280i) q^{72} +822.641i q^{73} +(-69.7736 + 40.2838i) q^{74} +(282.637 - 423.564i) q^{75} +(-410.764 - 237.155i) q^{76} +(409.808 + 1219.44i) q^{77} +(-116.818 - 236.514i) q^{78} +(46.1797 + 79.9856i) q^{79} +83.1436 q^{80} +(-190.426 - 703.689i) q^{81} +480.923i q^{82} +(223.747 + 387.541i) q^{83} +(100.530 - 371.577i) q^{84} +(-265.262 + 459.447i) q^{85} +(-277.822 - 160.401i) q^{86} +(-248.009 - 165.492i) q^{87} +(277.848 + 481.247i) q^{88} -103.529 q^{89} +(222.834 + 170.548i) q^{90} +(311.036 - 352.499i) q^{91} +(248.963 - 143.739i) q^{92} +(19.5108 - 300.534i) q^{93} +(-972.311 - 561.364i) q^{94} +(533.632 + 308.092i) q^{95} +(10.7721 - 165.928i) q^{96} +(1263.72 - 729.611i) q^{97} +(680.664 - 85.3993i) q^{98} +(-242.491 + 1859.73i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 96 q^{4} - 12 q^{7} - 36 q^{9}+O(q^{10}) \) 48 * q + 96 * q^4 - 12 * q^7 - 36 * q^9	\( 48 q + 96 q^{4} - 12 q^{7} - 36 q^{9} + 24 q^{11} - 132 q^{14} - 120 q^{15} - 384 q^{16} + 120 q^{18} + 180 q^{21} + 348 q^{23} - 600 q^{25} - 96 q^{28} - 84 q^{29} + 192 q^{30} + 96 q^{36} - 672 q^{37} + 1368 q^{39} + 1128 q^{42} + 84 q^{43} - 1008 q^{46} - 42 q^{49} + 456 q^{50} + 2016 q^{51} - 528 q^{56} + 732 q^{57} + 504 q^{58} - 1008 q^{60} - 774 q^{63} - 3072 q^{64} - 6972 q^{65} + 1176 q^{67} + 216 q^{70} - 384 q^{72} + 2520 q^{74} + 1500 q^{77} + 2832 q^{78} + 348 q^{79} + 2268 q^{81} - 1080 q^{84} + 720 q^{85} + 1200 q^{86} + 180 q^{91} + 1392 q^{92} + 5232 q^{93} - 5892 q^{95} + 972 q^{99}+O(q^{100}) \) 48 * q + 96 * q^4 - 12 * q^7 - 36 * q^9 + 24 * q^11 - 132 * q^14 - 120 * q^15 - 384 * q^16 + 120 * q^18 + 180 * q^21 + 348 * q^23 - 600 * q^25 - 96 * q^28 - 84 * q^29 + 192 * q^30 + 96 * q^36 - 672 * q^37 + 1368 * q^39 + 1128 * q^42 + 84 * q^43 - 1008 * q^46 - 42 * q^49 + 456 * q^50 + 2016 * q^51 - 528 * q^56 + 732 * q^57 + 504 * q^58 - 1008 * q^60 - 774 * q^63 - 3072 * q^64 - 6972 * q^65 + 1176 * q^67 + 216 * q^70 - 384 * q^72 + 2520 * q^74 + 1500 * q^77 + 2832 * q^78 + 348 * q^79 + 2268 * q^81 - 1080 * q^84 + 720 * q^85 + 1200 * q^86 + 180 * q^91 + 1392 * q^92 + 5232 * q^93 - 5892 * q^95 + 972 * q^99

Introduction

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