LMFDB - Embedded newform 126.4.m.a.41.9

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			41.9
Character	$\chi$	$=$	126.41
Dual form			126.4.m.a.83.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.73205 + 1.00000i) q^{2} +(2.30109 + 4.65886i) q^{3} +(2.00000 - 3.46410i) q^{4} +(2.59824 - 4.50028i) q^{5} +(-8.64447 - 5.76829i) q^{6} +(17.5554 + 5.89974i) q^{7} +8.00000i q^{8} +(-16.4100 + 21.4409i) q^{9} +O(q^{10})$	\(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} +(17.5554 + 5.89974i) 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} +(-36.3066 + 7.33678i) 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} +(12.9106 + 95.3641i) 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} +(-117.726 - 152.265i) 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} +(273.386 + 207.145i) 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} +(-47.1979 + 140.443i) 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} +(-414.580 + 279.590i) 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} +(-61.3157 + 182.453i) 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} +(1260.97 - 254.814i) 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} +(356.172 + 146.005i) 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	−0.726119	−	0.687570i	$-0.758678\pi$
$5$	2.59824	−	4.50028i	0.232393	−	0.402517i	0.958512	+	0.285052i	$0.0920110\pi$
$6$	−8.64447	−	5.76829i	−0.588181	−	0.392483i
$7$	17.5554	+	5.89974i	0.947904	+	0.318556i
$7$	17.5554	+	5.89974i	0.947904	+	0.318556i
$8$			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	0.715817	−	0.698288i	$-0.246055\pi$
$13$	21.9826	+	12.6916i	0.468990	+	0.270771i	−0.246827	+	0.969060i	$0.579388\pi$
$14$	−36.3066	+	7.33678i	−0.693097	+	0.140060i
$15$	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	$-0.759675\pi$
$17$	−102.093			−1.45654			−0.728270	+	0.685291i	$0.759675\pi$
$18$	6.98197	−	53.5467i	0.0914259	−	0.701171i
$19$			118.577i			1.43176i	0.698221	+	0.715882i	$0.253975\pi$
$19$			118.577i			1.43176i	−0.698221	+	0.715882i	$0.746025\pi$
$20$	−10.3929	−	18.0011i	−0.116197	−	0.201259i
$21$	12.9106	+	95.3641i	0.134158	+	0.990960i
$22$	−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	0.347496	−	0.937682i	$-0.387032\pi$
$31$	−50.1944	−	28.9798i	−0.290812	−	0.167901i	−0.638308	+	0.769781i	$0.720365\pi$
$32$	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	−0.998854	−	0.0478668i	$-0.984758\pi$
$41$	−120.231	+	208.246i	−0.457973	+	0.793233i	0.540881	+	0.841099i	$0.318091\pi$
$42$	−117.726	−	152.265i	−0.432512	−	0.559405i
$43$	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	$-0.830074\pi$
$47$	−280.682	−	486.155i	−0.871099	−	1.50879i	−0.0102389	−	0.999948i	$-0.503259\pi$
$48$	46.1463	−	69.1557i	0.138764	−	0.207954i
$49$	273.386	+	207.145i	0.797044	+	0.603921i
$50$	−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
$56$	−47.1979	+	140.443i	−0.112627	+	0.335135i
$57$	−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	−0.754016	−	0.656856i	$-0.771886\pi$
$59$	86.9423	−	150.588i	0.191846	−	0.332287i	0.945862	+	0.324569i	$0.105219\pi$
$60$	59.9496	−	89.8415i	0.128991	−	0.193308i
$61$	357.490	−	206.397i	0.750360	−	0.433220i	−0.0754642	−	0.997149i	$-0.524044\pi$
$61$	357.490	−	206.397i	0.750360	−	0.433220i	0.825824	+	0.563928i	$0.190711\pi$
$62$	115.919			0.237447
$63$	−414.580	+	279.590i	−0.829082	+	0.559128i
$64$	−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
$70$	−61.3157	+	182.453i	−0.104695	+	0.311532i
$71$			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	$-0.770780\pi$
$73$		−	822.641i		−	1.31894i	0.751729	−	0.659472i	$-0.229220\pi$
$74$	−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
$77$	1260.97	−	254.814i	1.86624	−	0.377126i
$78$	−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	0.679296	−	0.733864i	$-0.262285\pi$
$83$	−223.747	−	387.541i	−0.295897	−	0.512508i	−0.975193	+	0.221356i	$0.928952\pi$
$84$	356.172	+	146.005i	0.462638	+	0.189648i
$85$	−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	$-0.480363\pi$
$89$	103.529			0.123304			0.0616518	+	0.998098i	$0.480363\pi$
$90$	−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	−0.984175	−	0.177201i	$-0.943296\pi$
$97$	−1263.72	+	729.611i	−1.32280	+	0.763720i	−0.338627	+	0.940921i	$0.609962\pi$
$98$	−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	$0.00412518\pi$
$101$	518.868	+	898.706i	0.511181	+	0.885392i	−0.488735	+	0.872432i	$0.662541\pi$
$102$	882.539	+	588.902i	0.856709	+	0.571666i
$103$	−722.747	−	417.278i	−0.691402	−	0.399181i	0.112735	−	0.993625i	$-0.464039\pi$
$103$	−722.747	−	417.278i	−0.691402	−	0.399181i	−0.804137	+	0.594444i	$0.797372\pi$
$104$	−101.533	+	175.861i	−0.0957321	+	0.165813i
$105$	462.710	+	189.677i	0.430056	+	0.176292i
$106$	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
$112$	−58.6943	−	290.453i	−0.0495186	−	0.245047i
$113$	−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
$119$	−1792.28	−	602.321i	−1.38066	−	0.463989i
$120$	−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
$126$	438.483	−	898.844i	0.310025	−	0.635519i
$127$	−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	−0.982918	−	0.184046i	$-0.941080\pi$
$131$	−497.894	+	862.377i	−0.332070	+	0.575162i	0.650848	+	0.759208i	$0.274414\pi$
$132$	1294.46	−	639.354i	0.853544	−	0.421580i
$133$	−699.576	+	2081.68i	−0.456097	+	1.35718i
$134$			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	0.00594676	−	0.999982i	$-0.498107\pi$
$139$	−1404.59	−	810.939i	−0.857090	−	0.494841i	−0.863037	+	0.505141i	$0.831440\pi$
$140$	−76.2508	−	377.333i	−0.0460312	−	0.227789i
$141$	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
$147$	−335.973	+	1750.33i	−0.188507	+	0.982072i
$148$	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	0.962892	−	0.269887i	$-0.0869865\pi$
$157$	2381.51	+	1374.97i	1.21061	+	0.698945i	0.247717	+	0.968833i	$0.420320\pi$
$158$	−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	−0.936207	−	0.351450i	$-0.885689\pi$
$167$	−353.366	+	612.049i	−0.163738	+	0.283603i	0.772468	+	0.635054i	$0.219022\pi$
$168$	−762.913	+	103.285i	−0.350357	+	0.0474320i
$169$	−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	$-0.988363\pi$
$173$	−1209.00	−	2094.04i	−0.531319	−	0.920272i	0.468012	−	0.883722i	$-0.344970\pi$
$174$	−595.057	−	38.6313i	−0.259259	−	0.0168312i
$175$	359.490	+	1778.96i	0.155285	+	0.768440i
$176$	−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	$-0.831600\pi$
$181$		−	2458.04i		−	1.00942i	0.863290	−	0.504709i	$-0.168400\pi$
$182$	−891.229	−	299.509i	−0.362979	−	0.121984i
$183$	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
$189$	−2256.56	−	1288.11i	−0.868468	−	0.495746i
$190$	−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
$196$	1264.34	−	532.748i	0.460766	−	0.194150i
$197$			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	$0.0436691\pi$
$199$			767.839i			0.273521i	−0.990604	+	0.136760i	$0.956331\pi$
$200$	−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
$203$	1041.64	−	210.492i	0.360140	−	0.0727765i
$204$	−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
$210$	−991.115	+	134.179i	−0.325683	+	0.0440916i
$211$	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	−0.463098	−	0.886307i	$-0.653262\pi$
$223$	242.822	−	140.193i	0.0729172	−	0.0420988i	0.536015	+	0.844208i	$0.319929\pi$
$224$	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	$-0.981322\pi$
$227$	−1880.81	−	3257.66i	−0.549928	−	0.952503i	0.448351	−	0.893858i	$-0.352012\pi$
$228$	−159.666	+	2459.41i	−0.0463777	+	0.714379i
$229$	1848.81	+	1067.41i	0.533504	+	0.308019i	0.742442	−	0.669910i	$-0.233667\pi$
$229$	1848.81	+	1067.41i	0.533504	+	0.308019i	−0.208938	+	0.977929i	$0.567001\pi$
$230$	−373.468	+	646.866i	−0.107069	+	0.185448i
$231$	4088.74	+	5288.31i	1.16459	+	1.50626i
$232$	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
$238$	3706.65	−	749.033i	1.00952	−	0.204003i
$239$	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	−0.161078	−	0.986942i	$-0.551497\pi$
$241$	2293.80	−	1324.33i	0.613099	−	0.353973i	0.774177	+	0.632969i	$0.218164\pi$
$242$			6987.94i			1.85621i
$243$	2840.20	−	2506.42i	0.749791	−	0.661675i
$244$		−	1651.18i		−	0.433220i
$245$	1642.53	−	692.102i	0.428316	−	0.180477i
$246$	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	$-0.570990\pi$
$251$	−1759.07			−0.442358			−0.221179	+	0.975233i	$0.570990\pi$
$252$	139.369	+	1995.33i	0.0348390	+	0.498785i
$253$	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	−0.964559	−	0.263868i	$-0.915002\pi$
$257$	−1045.51	+	1810.87i	−0.253763	+	0.439530i	0.710796	+	0.703398i	$0.248335\pi$
$258$	107.991	−	1663.43i	0.0260589	−	0.401398i
$259$	707.199	+	237.664i	0.169665	+	0.0570182i
$260$		−	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
$266$	−869.977	−	4305.15i	−0.200533	−	0.992352i
$267$	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	$-0.535874\pi$
$269$	−992.346			−0.224923			−0.112462	+	0.993656i	$0.535874\pi$
$270$	281.797	−	1430.60i	0.0635170	−	0.322458i
$271$			3247.79i			0.728005i	0.931398	+	0.364002i	$0.118590\pi$
$271$			3247.79i			0.728005i	−0.931398	+	0.364002i	$0.881410\pi$
$272$	816.743	+	1414.64i	0.182067	+	0.315350i
$273$	−926.520	+	2260.20i	−0.205405	+	0.501076i
$274$	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	0.754636	−	0.656144i	$-0.227814\pi$
$283$	2683.74	+	1549.46i	0.563716	+	0.325462i	−0.190920	+	0.981606i	$0.561147\pi$
$284$	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	$0.464556\pi$
$293$	−4037.87	+	6993.80i	−0.805102	+	1.39448i	−0.916222	+	0.400671i	$0.868777\pi$
$294$	−1168.41	−	3367.63i	−0.231778	−	0.668041i
$295$	−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
$301$	588.413	+	2911.81i	0.112676	+	0.557587i
$302$	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	$-0.691245\pi$
$307$		−	8874.14i		−	1.64975i	0.565314	−	0.824876i	$-0.308755\pi$
$308$	1639.23	−	4877.74i	0.303259	−	0.902387i
$309$	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	−0.642830	−	0.766009i	$-0.722240\pi$
$311$	1875.54	−	3248.53i	0.341968	−	0.592307i	0.984798	+	0.173702i	$0.0555731\pi$
$312$	−1052.95	−	68.3576i	−0.191062	−	0.0124038i
$313$	8535.10	−	4927.74i	1.54132	−	0.889880i	0.542561	−	0.840016i	$-0.317455\pi$
$313$	8535.10	−	4927.74i	1.54132	−	0.889880i	0.998756	−	0.0498640i	$-0.0158788\pi$
$314$	−5499.87			−0.988458
$315$	181.057	+	2592.17i	0.0323854	+	0.463657i
$316$	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
$322$	−2523.40	−	848.023i	−0.436719	−	0.146765i
$323$		−	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
$329$	−2059.30	−	10190.6i	−0.345085	−	1.70768i
$330$	−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
$336$	1218.12	−	941.807i	0.197779	−	0.152916i
$337$	−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	−0.390735	−	0.920503i	$-0.627779\pi$
$349$	1376.19	−	794.545i	0.211077	−	0.121865i	0.601812	+	0.798638i	$0.294446\pi$
$350$	−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	0.658343	−	0.752718i	$-0.271258\pi$
$353$	−2140.24	−	3707.01i	−0.322702	−	0.558936i	−0.981045	+	0.193782i	$0.937924\pi$
$354$	−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
$357$	−1318.08	−	9736.00i	−0.195406	−	1.44337i
$358$	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
$364$	1843.16	−	372.463i	0.265407	−	0.0536329i
$365$	−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	0.325714	−	0.945468i	$-0.394395\pi$
$367$	9191.74	−	5306.86i	1.30737	−	0.754811i	0.981657	+	0.190657i	$0.0610619\pi$
$368$		−	1149.91i		−	0.162889i
$369$	−2492.00	−	5995.17i	−0.351567	−	0.845788i
$370$			418.668i			0.0588256i
$371$	4535.72	−	13496.6i	0.634725	−	1.88871i
$372$	−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
$378$	5196.58	−	25.4898i	0.707098	−	0.00346840i
$379$	−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	−0.960139	−	0.279522i	$-0.909824\pi$
$383$	−1783.89	+	3089.79i	−0.237997	+	0.412222i	0.722143	+	0.691744i	$0.243157\pi$
$384$	553.246	+	369.171i	0.0735227	+	0.0490603i
$385$	2129.56	−	6336.77i	0.281902	−	0.838835i
$386$			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
$392$	−1657.16	+	2187.09i	−0.213518	+	0.281798i
$393$	−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	$-0.946621\pi$
$397$		−	2640.60i		−	0.333823i	0.985972	−	0.166911i	$-0.0533794\pi$
$398$	−767.839	−	1329.94i	−0.0967042	−	0.167497i
$399$	−11308.0	+	1530.90i	−1.41882	+	0.192083i
$400$	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	0.816937	−	0.576727i	$-0.195670\pi$
$409$	6004.66	+	3466.79i	0.725945	+	0.419124i	−0.0909920	+	0.995852i	$0.529004\pi$
$410$	−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	$0.462496\pi$
$419$	−6872.07	+	11902.8i	−0.801247	+	1.38780i	−0.918796	+	0.394733i	$0.870837\pi$
$420$	1582.48	−	1223.52i	0.183850	−	0.142147i
$421$	−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
$427$	7493.58	−	1514.29i	0.849274	−	0.171620i
$428$	−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	$-0.929600\pi$
$433$		−	3953.10i		−	0.438739i	0.975642	−	0.219369i	$-0.0703999\pi$
$434$	2035.01	+	683.892i	0.225077	+	0.0756403i
$435$	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	−0.929473	−	0.368889i	$-0.879738\pi$
$439$	−9885.56	+	5707.43i	−1.07474	+	0.620503i	−0.145270	+	0.989392i	$0.546405\pi$
$440$	2887.66			0.312872
$441$	−8927.63	+	2462.41i	−0.964003	+	0.265890i
$442$	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
$448$	−1123.55	−	377.583i	−0.118488	−	0.0398195i
$449$		−	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
$455$	2394.49	−	483.874i	0.246715	−	0.0498557i
$456$	−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	$0.165087\pi$
$461$	8547.34	+	14804.4i	0.863534	+	1.49569i	−0.00496117	+	0.999988i	$0.501579\pi$
$462$	−12370.2	−	5070.89i	−1.24570	−	0.510648i
$463$	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	$-0.595500\pi$
$467$	−5965.17			−0.591081			−0.295541	+	0.955330i	$0.595500\pi$
$468$	−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	0.530260	−	0.847835i	$-0.322094\pi$
$479$	−4917.95	−	8518.13i	−0.469116	−	0.812533i	−0.999377	+	0.0353015i	$0.988761\pi$
$480$	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
$483$	−2623.32	+	6399.48i	−0.247133	+	0.602870i
$484$	−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
$490$	−2152.85	+	2841.29i	−0.198481	+	0.261952i
$491$	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
$497$	−5133.54	+	15275.5i	−0.463321	+	1.37867i
$498$	−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	$-0.228323\pi$
$503$	17002.6			1.50717			0.753586	+	0.657350i	$0.228323\pi$
$504$	−2236.72	−	3316.64i	−0.197681	−	0.293125i
$505$	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	$0.342733\pi$
$509$	−6032.90	+	10449.3i	−0.525351	+	0.909934i	−0.999564	+	0.0295243i	$0.990601\pi$
$510$	4943.27	−	2441.56i	0.429199	−	0.211989i
$511$	4853.37	−	14441.8i	0.420157	−	1.25023i
$512$		−	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
$518$	−1462.57	+	295.553i	−0.124057	+	0.0250693i
$519$	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	$-0.344436\pi$
$521$	11166.5			0.938988			0.469494	+	0.882936i	$0.344436\pi$
$522$	−1189.30	−	2861.18i	−0.0997209	−	0.239905i
$523$			13008.8i			1.08764i	0.839201	+	0.543821i	$0.183023\pi$
$523$			13008.8i			1.08764i	−0.839201	+	0.543821i	$0.816977\pi$
$524$	1991.57	+	3449.51i	0.166035	+	0.287581i
$525$	−7460.73	+	5768.37i	−0.620215	+	0.479528i
$526$	−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
$546$	−655.425	−	4841.31i	−0.0513729	−	0.379467i
$547$	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
$553$	338.810	+	1676.63i	0.0260537	+	0.128929i
$554$	−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
$560$	−1459.62	−	490.525i	−0.110143	−	0.0370152i
$561$	−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	$-0.523814\pi$
$563$	11037.3	−	19117.2i	0.826232	−	1.43107i	0.900974	−	0.433872i	$-0.142853\pi$
$564$	−5167.00	−	10461.3i	−0.385762	−	0.781026i
$565$	−567.418	+	327.599i	−0.0422503	+	0.0243932i
$566$	−6197.83			−0.460272
$567$	808.569	−	13477.0i	0.0598884	−	0.998205i
$568$	−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
$574$	2837.32	−	8442.81i	0.206320	−	0.613931i
$575$			7042.97i			0.510804i
$576$	1050.24	−	1372.22i	0.0759720	−	0.0992635i
$577$			8285.59i			0.597805i	0.954284	+	0.298903i	$0.0966206\pi$
$577$			8285.59i			0.597805i	−0.954284	+	0.298903i	$0.903379\pi$
$578$	−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
$581$	−1641.58	−	8123.51i	−0.117219	−	0.580069i
$582$	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	0.891025	−	0.453955i	$-0.149987\pi$
$587$	744.882	+	1290.17i	0.0523758	+	0.0907175i	−0.838649	+	0.544672i	$0.816654\pi$
$588$	5391.37	+	4664.50i	0.378123	+	0.327144i
$589$	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	$-0.506532\pi$
$593$	−592.599			−0.0410373			−0.0205187	+	0.999789i	$0.506532\pi$
$594$	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	−0.0912431	−	0.995829i	$-0.529084\pi$
$601$	10690.0	−	6171.88i	0.725548	−	0.418895i	0.816791	+	0.576933i	$0.195751\pi$
$602$	−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	0.357366	−	0.933964i	$-0.383675\pi$
$607$	−4079.51	−	2355.31i	−0.272788	−	0.157494i	−0.630154	+	0.776470i	$0.717008\pi$
$608$	−1897.24	+	3286.11i	−0.126551	+	0.219193i
$609$	3377.55	+	4368.47i	0.224738	+	0.290672i
$610$	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
$616$	2038.51	+	10087.7i	0.133334	+	0.659815i
$617$	−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	−0.844626	−	0.535358i	$-0.820177\pi$
$619$	−12371.3	+	7142.59i	−0.803305	+	0.463788i	0.0413205	+	0.999146i	$0.486844\pi$
$620$			1204.74i			0.0780380i
$621$	−7593.17	−	6634.07i	−0.490666	−	0.428689i
$622$			7502.17i			0.483616i
$623$	1817.49	+	610.792i	0.116880	+	0.0392791i
$624$	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
$630$	−2905.77	−	4308.71i	−0.183759	−	0.272481i
$631$	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
$637$	3380.72	+	8023.29i	0.210281	+	0.499049i
$638$			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	0.267556	−	0.963542i	$-0.413784\pi$
$643$	−7061.92	−	4077.20i	−0.433118	−	0.250061i	−0.700674	+	0.713482i	$0.747117\pi$
$644$	5218.68	−	1054.58i	0.319324	−	0.0645285i
$645$	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	$-0.714647\pi$
$647$	−20551.0			−1.24875			−0.624376	+	0.781124i	$0.714647\pi$
$648$	5629.52	−	1523.41i	0.341278	−	0.0923537i
$649$		−	12078.4i		−	0.730535i
$650$	−2487.48	−	4308.44i	−0.150103	−	0.259986i
$651$	2115.59	−	5160.89i	0.127368	−	0.310709i
$652$	−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	0.580287	−	0.814412i	$-0.302940\pi$
$661$	2806.25	+	1620.19i	0.165129	+	0.0953374i	−0.415158	+	0.909749i	$0.636274\pi$
$662$	−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
$672$	−1168.04	+	2849.38i	−0.0670506	+	0.163567i
$673$	−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	$0.205937\pi$
$677$	16223.0	+	28099.0i	0.920973	+	1.59517i	0.123060	+	0.992399i	$0.460729\pi$
$678$	580.266	+	1174.82i	0.0328687	+	0.0665470i
$679$	−26489.7	+	5353.00i	−1.49718	+	0.302547i
$680$	−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
$686$	−11445.5	−	5514.96i	−0.637014	−	0.306942i
$687$	−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	0.458394	−	0.888749i	$-0.348425\pi$
$691$	26470.2	−	15282.6i	1.45727	−	0.841355i	0.998876	+	0.0473939i	$0.0150916\pi$
$692$	−9671.97			−0.531319
$693$	−15229.0	+	31217.8i	−0.834777	+	1.71120i
$694$	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
$700$	6881.49	+	2312.62i	0.371566	+	0.124870i
$701$			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
$707$	3806.82	+	18838.3i	0.202504	+	1.00211i
$708$	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
$714$	12019.0	+	15545.2i	0.629971	+	0.814795i
$715$	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	$-0.772370\pi$
$719$	−29112.4			−1.51003			−0.755014	+	0.655709i	$0.772370\pi$
$720$	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	−0.953496	−	0.301406i	$-0.902544\pi$
$727$	−22919.1	+	13232.3i	−1.16922	+	0.675049i	−0.215723	+	0.976455i	$0.569211\pi$
$728$	−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	0.645623	−	0.763657i	$-0.276598\pi$
$733$	6094.22	+	3518.50i	0.307088	+	0.177297i	−0.338535	+	0.940954i	$0.609931\pi$
$734$	−10613.7	+	18383.5i	−0.533732	+	0.924451i
$735$	7004.02	+	6059.74i	0.351493	+	0.304104i
$736$	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
$742$	5640.52	+	27912.6i	0.279070	+	1.38100i
$743$	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
$749$	4546.91	−	13529.9i	0.221816	−	0.660043i
$750$	−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
$756$	−8975.25	+	5240.73i	−0.431781	+	0.252121i
$757$	−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	−0.915898	−	0.401412i	$-0.868520\pi$
$761$	−2315.87	+	4011.20i	−0.110316	+	0.191072i	0.805582	+	0.592484i	$0.201853\pi$
$762$	5779.73	+	3856.71i	0.274774	+	0.183351i
$763$	−19647.8	−	6602.92i	−0.932240	−	0.313292i
$764$			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	$0.0586327\pi$
$769$	34829.0	+	20108.5i	1.63325	+	0.942955i	0.650163	+	0.759795i	$0.274701\pi$
$770$	2648.27	+	13105.2i	0.123944	+	0.613347i
$771$	−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	$-0.593343\pi$
$773$	−12424.8			−0.578124			−0.289062	+	0.957310i	$0.593343\pi$
$774$	7998.20	−	3324.60i	0.371433	−	0.154393i
$775$		−	5679.84i		−	0.263259i
$776$	−5836.89	−	10109.8i	−0.270016	−	0.467681i
$777$	520.087	+	3841.63i	0.0240129	+	0.177372i
$778$	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	0.809165	−	0.587581i	$-0.199920\pi$
$787$	15562.6	+	8985.07i	0.704888	+	0.406967i	−0.104277	+	0.994548i	$0.533253\pi$
$788$	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	$-0.639437\pi$
$797$	12873.8	−	22298.2i	0.572165	−	0.991018i	0.996343	−	0.0854396i	$-0.0272295\pi$
$798$	18055.2	−	13959.6i	0.800936	−	0.619255i
$799$	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
$805$	6779.68	−	1370.03i	0.296835	−	0.0599840i
$806$	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	$-0.735638\pi$
$811$		−	34102.2i		−	1.47656i	0.674495	−	0.738280i	$-0.264362\pi$
$812$	1354.11	−	4029.31i	0.0585219	−	0.174139i
$813$	−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
$819$	−12662.0	+	884.410i	−0.540226	+	0.0377336i
$820$	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
$826$	−2051.75	+	6105.24i	−0.0864278	+	0.257177i
$827$			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	$-0.974975\pi$
$829$		−	3749.17i		−	0.157074i	0.996911	−	0.0785368i	$-0.0250248\pi$
$830$	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
$833$	−27910.8	−	21148.0i	−1.16093	−	0.879634i
$834$	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	0.990930	−	0.134380i	$-0.0429044\pi$
$839$	9212.62	+	15956.7i	0.379088	+	0.656600i	−0.611842	+	0.790980i	$0.709571\pi$
$840$	−1517.42	+	3701.68i	−0.0623285	+	0.152048i
$841$	−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	0.241838	−	0.970317i	$-0.422250\pi$
$853$	29972.1	−	17304.4i	1.20308	−	0.694596i	0.961238	+	0.275720i	$0.0889164\pi$
$854$	−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	$0.0709127\pi$
$857$	17034.5	+	29504.7i	0.678984	+	1.17603i	−0.296303	+	0.955094i	$0.595754\pi$
$858$	−15241.7	−	10170.5i	−0.606460	−	0.404680i
$859$	21418.1	+	12365.8i	0.850731	+	0.491170i	0.860897	−	0.508779i	$-0.169903\pi$
$859$	21418.1	+	12365.8i	0.850731	+	0.491170i	−0.0101665	+	0.999948i	$0.503236\pi$
$860$	1667.04	−	2887.39i	0.0660994	−	0.114488i
$861$	−21411.4	−	8777.13i	−0.847502	−	0.347414i
$862$	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
$868$	−4208.63	+	850.473i	−0.164574	+	0.0332568i
$869$	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
$875$	20343.2	+	6836.60i	0.785971	+	0.264136i
$876$	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	$-0.466666\pi$
$881$	5466.82			0.209060			0.104530	+	0.994522i	$0.466666\pi$
$882$	13000.7	−	13192.7i	0.496323	−	0.503651i
$883$	−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	−0.503152	−	0.864198i	$-0.667827\pi$
$887$	13125.1	−	22733.3i	0.496841	−	0.860554i	0.999993	+	0.00364396i	$0.00115991\pi$
$888$	−1501.41	+	741.574i	−0.0567389	+	0.0280243i
$889$	−11737.6	−	3944.59i	−0.442821	−	0.148816i
$890$			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
$896$	2323.62	−	469.554i	0.0866371	−	0.0175075i
$897$	−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
$903$	−12211.7	+	9441.67i	−0.450034	+	0.347950i
$904$	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
$924$	26496.7	−	3587.18i	0.943375	−	0.127716i
$925$	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	0.875694	−	0.482866i	$-0.160404\pi$
$929$	557.048	+	964.835i	0.0196729	+	0.0340745i	−0.856021	+	0.516940i	$0.827071\pi$
$930$	3123.43	+	202.774i	0.110131	+	0.00714971i
$931$	−24562.7	+	32417.4i	−0.864673	+	1.14118i
$932$	−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	$-0.832467\pi$
$937$		−	28817.1i		−	1.00471i	0.864661	−	0.502355i	$-0.167533\pi$
$938$	−6395.44	+	19030.4i	−0.222621	+	0.662437i
$939$	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	−0.830517	−	0.556993i	$-0.811955\pi$
$941$	1937.24	−	3355.39i	0.0671117	−	0.116241i	0.897629	+	0.440752i	$0.145288\pi$
$942$	−12655.7	−	25623.1i	−0.437734	−	0.886249i
$943$	−14966.5	+	8640.93i	−0.516837	+	0.298396i
$944$	−2782.15			−0.0959230
$945$	−11659.9	+	6808.33i	−0.401372	+	0.234365i
$946$	−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
$952$	4818.57	−	14338.3i	0.164045	−	0.488137i
$953$		−	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
$959$	−13001.3	+	2627.28i	−0.437783	+	0.0884664i
$960$	−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
$966$	−1855.75	−	13707.5i	−0.0618094	−	0.456556i
$967$	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	$-0.546399\pi$
$971$	−8789.79			−0.290502			−0.145251	+	0.989395i	$0.546399\pi$
$972$	−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	$0.194104\pi$
$983$	27918.3	+	48355.9i	0.905855	+	1.56899i	0.0860899	+	0.996287i	$0.472563\pi$
$984$	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
$987$	42738.0	−	33043.5i	1.37828	−	1.06564i
$988$	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
$994$	−6383.95	−	31591.5i	−0.203709	−	1.00807i
$995$	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	−0.601644	−	0.798764i	$-0.705487\pi$
$997$	−6633.45	+	3829.82i	−0.210716	+	0.121657i	0.390928	+	0.920421i	$0.372154\pi$
$998$			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.41.9	yes	48
3.2	odd	2		378.4.m.a.125.21		48
7.6	odd	2	inner	126.4.m.a.41.4	✓	48
9.2	odd	6	inner	126.4.m.a.83.4	yes	48
9.4	even	3		1134.4.d.b.1133.47		48
9.5	odd	6		1134.4.d.b.1133.2		48
9.7	even	3		378.4.m.a.251.22		48
21.20	even	2		378.4.m.a.125.22		48
63.13	odd	6		1134.4.d.b.1133.1		48
63.20	even	6	inner	126.4.m.a.83.9	yes	48
63.34	odd	6		378.4.m.a.251.21		48
63.41	even	6		1134.4.d.b.1133.48		48

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-1.73205 + 1.00000i) q^{2} +(2.30109 + 4.65886i) q^{3} +(2.00000 - 3.46410i) q^{4} +(2.59824 - 4.50028i) q^{5} +(-8.64447 - 5.76829i) q^{6} +(17.5554 + 5.89974i) q^{7} +8.00000i q^{8} +(-16.4100 + 21.4409i) q^{9} +O(q^{10})\)	\(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} +(17.5554 + 5.89974i) 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} +(-36.3066 + 7.33678i) 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} +(12.9106 + 95.3641i) 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} +(-117.726 - 152.265i) 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} +(273.386 + 207.145i) 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} +(-47.1979 + 140.443i) 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} +(-414.580 + 279.590i) 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} +(-61.3157 + 182.453i) 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} +(1260.97 - 254.814i) 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} +(356.172 + 146.005i) 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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