LMFDB - Embedded newform 100.3.b.f.51.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [100,3,Mod(51,100)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(100, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("100.51");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 100 = 2^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	100.b (of order $2$, degree $1$, 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:	$2.72480264360$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{10})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + x^{2} - x + 1 $ x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	no (minimal twist has level 20)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			51.3
Root			$0.809017 - 0.587785i$ of defining polynomial
Character	$\chi$	$=$	100.51
Dual form			100.3.b.f.51.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.61803 - 1.17557i) q^{2} -3.80423i q^{3} +(1.23607 - 3.80423i) q^{4} +(-4.47214 - 6.15537i) q^{6} +8.50651i q^{7} +(-2.47214 - 7.60845i) q^{8} -5.47214 q^{9} +O(q^{10})$	\(q+(1.61803 - 1.17557i) q^{2} -3.80423i q^{3} +(1.23607 - 3.80423i) q^{4} +(-4.47214 - 6.15537i) q^{6} +8.50651i q^{7} +(-2.47214 - 7.60845i) q^{8} -5.47214 q^{9} +1.79611i q^{11} +(-14.4721 - 4.70228i) q^{12} -0.472136 q^{13} +(10.0000 + 13.7638i) q^{14} +(-12.9443 - 9.40456i) q^{16} +23.8885 q^{17} +(-8.85410 + 6.43288i) q^{18} -9.40456i q^{19} +32.3607 q^{21} +(2.11146 + 2.90617i) q^{22} +16.1150i q^{23} +(-28.9443 + 9.40456i) q^{24} +(-0.763932 + 0.555029i) q^{26} -13.4208i q^{27} +(32.3607 + 10.5146i) q^{28} +6.94427 q^{29} +47.4468i q^{31} -32.0000 q^{32} +6.83282 q^{33} +(38.6525 - 28.0827i) q^{34} +(-6.76393 + 20.8172i) q^{36} -26.3607 q^{37} +(-11.0557 - 15.2169i) q^{38} +1.79611i q^{39} -41.4164 q^{41} +(52.3607 - 38.0423i) q^{42} +2.00811i q^{43} +(6.83282 + 2.22012i) q^{44} +(18.9443 + 26.0746i) q^{46} +35.3481i q^{47} +(-35.7771 + 49.2429i) q^{48} -23.3607 q^{49} -90.8774i q^{51} +(-0.583592 + 1.79611i) q^{52} +21.6393 q^{53} +(-15.7771 - 21.7153i) q^{54} +(64.7214 - 21.0292i) q^{56} -35.7771 q^{57} +(11.2361 - 8.16348i) q^{58} +73.8644i q^{59} -26.1378 q^{61} +(55.7771 + 76.7706i) q^{62} -46.5488i q^{63} +(-51.7771 + 37.6183i) q^{64} +(11.0557 - 8.03246i) q^{66} -88.8693i q^{67} +(29.5279 - 90.8774i) q^{68} +61.3050 q^{69} -39.4144i q^{71} +(13.5279 + 41.6345i) q^{72} -137.554 q^{73} +(-42.6525 + 30.9888i) q^{74} +(-35.7771 - 11.6247i) q^{76} -15.2786 q^{77} +(2.11146 + 2.90617i) q^{78} -113.703i q^{79} -100.305 q^{81} +(-67.0132 + 48.6879i) q^{82} -21.2412i q^{83} +(40.0000 - 123.107i) q^{84} +(2.36068 + 3.24920i) q^{86} -26.4176i q^{87} +(13.6656 - 4.44023i) q^{88} +67.4427 q^{89} -4.01623i q^{91} +(61.3050 + 19.9192i) q^{92} +180.498 q^{93} +(41.5542 + 57.1944i) q^{94} +121.735i q^{96} +39.1672 q^{97} +(-37.7984 + 27.4621i) q^{98} -9.82857i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{2} - 4 q^{4} + 8 q^{8} - 4 q^{9}+O(q^{10}) $ 4 * q + 2 * q^2 - 4 * q^4 + 8 * q^8 - 4 * q^9	$ 4 q + 2 q^{2} - 4 q^{4} + 8 q^{8} - 4 q^{9} - 40 q^{12} + 16 q^{13} + 40 q^{14} - 16 q^{16} + 24 q^{17} - 22 q^{18} + 40 q^{21} + 80 q^{22} - 80 q^{24} - 12 q^{26} + 40 q^{28} - 8 q^{29} - 128 q^{32} - 80 q^{33} + 92 q^{34} - 36 q^{36} - 16 q^{37} - 80 q^{38} - 112 q^{41} + 120 q^{42} - 80 q^{44} + 40 q^{46} - 4 q^{49} - 56 q^{52} + 176 q^{53} + 80 q^{54} + 80 q^{56} + 36 q^{58} + 128 q^{61} + 80 q^{62} - 64 q^{64} + 80 q^{66} + 136 q^{68} + 120 q^{69} + 72 q^{72} - 264 q^{73} - 108 q^{74} - 240 q^{77} + 80 q^{78} - 276 q^{81} - 116 q^{82} + 160 q^{84} - 80 q^{86} - 160 q^{88} - 88 q^{89} + 120 q^{92} + 400 q^{93} - 120 q^{94} + 264 q^{97} - 102 q^{98}+O(q^{100}) $ 4 * q + 2 * q^2 - 4 * q^4 + 8 * q^8 - 4 * q^9 - 40 * q^12 + 16 * q^13 + 40 * q^14 - 16 * q^16 + 24 * q^17 - 22 * q^18 + 40 * q^21 + 80 * q^22 - 80 * q^24 - 12 * q^26 + 40 * q^28 - 8 * q^29 - 128 * q^32 - 80 * q^33 + 92 * q^34 - 36 * q^36 - 16 * q^37 - 80 * q^38 - 112 * q^41 + 120 * q^42 - 80 * q^44 + 40 * q^46 - 4 * q^49 - 56 * q^52 + 176 * q^53 + 80 * q^54 + 80 * q^56 + 36 * q^58 + 128 * q^61 + 80 * q^62 - 64 * q^64 + 80 * q^66 + 136 * q^68 + 120 * q^69 + 72 * q^72 - 264 * q^73 - 108 * q^74 - 240 * q^77 + 80 * q^78 - 276 * q^81 - 116 * q^82 + 160 * q^84 - 80 * q^86 - 160 * q^88 - 88 * q^89 + 120 * q^92 + 400 * q^93 - 120 * q^94 + 264 * q^97 - 102 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/100\mathbb{Z}\right)^\times$.

$n$	$51$	$77$
$\chi(n)$	$-1$	$1$

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 $

$2$	1.61803	−	1.17557i	0.809017	−	0.587785i
$2$	1.61803	−	1.17557i	0.809017	−	0.587785i
$3$		−	3.80423i		−	1.26808i	−0.773302	−	0.634038i	$-0.781396\pi$
$3$		−	3.80423i		−	1.26808i	0.773302	−	0.634038i	$-0.218604\pi$
$4$	1.23607	−	3.80423i	0.309017	−	0.951057i
$5$		0			0
$5$		0			0
$6$	−4.47214	−	6.15537i	−0.745356	−	1.02589i
$7$			8.50651i			1.21522i	0.794237	+	0.607608i	$0.207871\pi$
$7$			8.50651i			1.21522i	−0.794237	+	0.607608i	$0.792129\pi$
$8$	−2.47214	−	7.60845i	−0.309017	−	0.951057i
$9$	−5.47214			−0.608015
$10$		0			0
$11$			1.79611i			0.163283i	0.996662	+	0.0816415i	$0.0260162\pi$
$11$			1.79611i			0.163283i	−0.996662	+	0.0816415i	$0.973984\pi$
$12$	−14.4721	−	4.70228i	−1.20601	−	0.391857i
$13$	−0.472136			−0.0363182			−0.0181591	−	0.999835i	$-0.505781\pi$
$13$	−0.472136			−0.0363182			−0.0181591	+	0.999835i	$0.505781\pi$
$14$	10.0000	+	13.7638i	0.714286	+	0.983130i
$15$		0			0
$16$	−12.9443	−	9.40456i	−0.809017	−	0.587785i
$17$	23.8885			1.40521			0.702604	−	0.711581i	$-0.252020\pi$
$17$	23.8885			1.40521			0.702604	+	0.711581i	$0.252020\pi$
$18$	−8.85410	+	6.43288i	−0.491895	+	0.357382i
$19$		−	9.40456i		−	0.494977i	−0.968891	−	0.247489i	$-0.920395\pi$
$19$		−	9.40456i		−	0.494977i	0.968891	−	0.247489i	$-0.0796053\pi$
$20$		0			0
$21$	32.3607			1.54098
$22$	2.11146	+	2.90617i	0.0959753	+	0.132099i
$23$			16.1150i			0.700650i	0.936628	+	0.350325i	$0.113929\pi$
$23$			16.1150i			0.700650i	−0.936628	+	0.350325i	$0.886071\pi$
$24$	−28.9443	+	9.40456i	−1.20601	+	0.391857i
$25$		0			0
$26$	−0.763932	+	0.555029i	−0.0293820	+	0.0213473i
$27$		−	13.4208i		−	0.497066i
$28$	32.3607	+	10.5146i	1.15574	+	0.375522i
$29$	6.94427			0.239458			0.119729	−	0.992807i	$-0.461797\pi$
$29$	6.94427			0.239458			0.119729	+	0.992807i	$0.461797\pi$
$30$		0			0
$31$			47.4468i			1.53054i	0.643708	+	0.765271i	$0.277395\pi$
$31$			47.4468i			1.53054i	−0.643708	+	0.765271i	$0.722605\pi$
$32$	−32.0000			−1.00000
$33$	6.83282			0.207055
$34$	38.6525	−	28.0827i	1.13684	−	0.825961i
$35$		0			0
$36$	−6.76393	+	20.8172i	−0.187887	+	0.578257i
$37$	−26.3607			−0.712451			−0.356225	−	0.934400i	$-0.615936\pi$
$37$	−26.3607			−0.712451			−0.356225	+	0.934400i	$0.615936\pi$
$38$	−11.0557	−	15.2169i	−0.290940	−	0.400445i
$39$			1.79611i			0.0460542i
$40$		0			0
$41$	−41.4164			−1.01016			−0.505078	−	0.863074i	$-0.668536\pi$
$41$	−41.4164			−1.01016			−0.505078	+	0.863074i	$0.668536\pi$
$42$	52.3607	−	38.0423i	1.24668	−	0.905768i
$43$			2.00811i			0.0467003i	0.999727	+	0.0233502i	$0.00743326\pi$
$43$			2.00811i			0.0467003i	−0.999727	+	0.0233502i	$0.992567\pi$
$44$	6.83282	+	2.22012i	0.155291	+	0.0504572i
$45$		0			0
$46$	18.9443	+	26.0746i	0.411832	+	0.566838i
$47$			35.3481i			0.752087i	0.926602	+	0.376044i	$0.122716\pi$
$47$			35.3481i			0.752087i	−0.926602	+	0.376044i	$0.877284\pi$
$48$	−35.7771	+	49.2429i	−0.745356	+	1.02589i
$49$	−23.3607			−0.476749
$50$		0			0
$51$		−	90.8774i		−	1.78191i
$52$	−0.583592	+	1.79611i	−0.0112229	+	0.0345406i
$53$	21.6393			0.408289			0.204145	−	0.978941i	$-0.434559\pi$
$53$	21.6393			0.408289			0.204145	+	0.978941i	$0.434559\pi$
$54$	−15.7771	−	21.7153i	−0.292168	−	0.402135i
$55$		0			0
$56$	64.7214	−	21.0292i	1.15574	−	0.375522i
$57$	−35.7771			−0.627668
$58$	11.2361	−	8.16348i	0.193725	−	0.140750i
$59$			73.8644i			1.25194i	0.779848	+	0.625970i	$0.215297\pi$
$59$			73.8644i			1.25194i	−0.779848	+	0.625970i	$0.784703\pi$
$60$		0			0
$61$	−26.1378			−0.428488			−0.214244	−	0.976780i	$-0.568729\pi$
$61$	−26.1378			−0.428488			−0.214244	+	0.976780i	$0.568729\pi$
$62$	55.7771	+	76.7706i	0.899630	+	1.23824i
$63$		−	46.5488i		−	0.738869i
$64$	−51.7771	+	37.6183i	−0.809017	+	0.587785i
$65$		0			0
$66$	11.0557	−	8.03246i	0.167511	−	0.121704i
$67$		−	88.8693i		−	1.32641i	−0.748439	−	0.663204i	$-0.769196\pi$
$67$		−	88.8693i		−	1.32641i	0.748439	−	0.663204i	$-0.230804\pi$
$68$	29.5279	−	90.8774i	0.434233	−	1.33643i
$69$	61.3050			0.888478
$70$		0			0
$71$		−	39.4144i		−	0.555132i	−0.960707	−	0.277566i	$-0.910472\pi$
$71$		−	39.4144i		−	0.555132i	0.960707	−	0.277566i	$-0.0895277\pi$
$72$	13.5279	+	41.6345i	0.187887	+	0.578257i
$73$	−137.554			−1.88430			−0.942152	−	0.335186i	$-0.891201\pi$
$73$	−137.554			−1.88430			−0.942152	+	0.335186i	$0.891201\pi$
$74$	−42.6525	+	30.9888i	−0.576385	+	0.418768i
$75$		0			0
$76$	−35.7771	−	11.6247i	−0.470751	−	0.152956i
$77$	−15.2786			−0.198424
$78$	2.11146	+	2.90617i	0.0270700	+	0.0372586i
$79$		−	113.703i		−	1.43928i	−0.694350	−	0.719638i	$-0.744308\pi$
$79$		−	113.703i		−	1.43928i	0.694350	−	0.719638i	$-0.255692\pi$
$80$		0			0
$81$	−100.305			−1.23833
$82$	−67.0132	+	48.6879i	−0.817234	+	0.593755i
$83$		−	21.2412i		−	0.255919i	−0.991779	−	0.127959i	$-0.959157\pi$
$83$		−	21.2412i		−	0.255919i	0.991779	−	0.127959i	$-0.0408427\pi$
$84$	40.0000	−	123.107i	0.476190	−	1.46556i
$85$		0			0
$86$	2.36068	+	3.24920i	0.0274498	+	0.0377814i
$87$		−	26.4176i		−	0.303650i
$88$	13.6656	−	4.44023i	0.155291	−	0.0504572i
$89$	67.4427			0.757783			0.378892	−	0.925441i	$-0.376305\pi$
$89$	67.4427			0.757783			0.378892	+	0.925441i	$0.376305\pi$
$90$		0			0
$91$		−	4.01623i		−	0.0441344i
$92$	61.3050	+	19.9192i	0.666358	+	0.216513i
$93$	180.498			1.94084
$94$	41.5542	+	57.1944i	0.442066	+	0.608451i
$95$		0			0
$96$			121.735i			1.26808i
$97$	39.1672			0.403785			0.201893	−	0.979408i	$-0.435291\pi$
$97$	39.1672			0.403785			0.201893	+	0.979408i	$0.435291\pi$
$98$	−37.7984	+	27.4621i	−0.385698	+	0.280226i
$99$		−	9.82857i		−	0.0992785i
$100$		0			0
$101$	99.8885			0.988995			0.494498	−	0.869179i	$-0.335352\pi$
$101$	99.8885			0.988995			0.494498	+	0.869179i	$0.335352\pi$
$102$	−106.833	−	147.043i	−1.04738	−	1.44160i
$103$			35.7721i			0.347302i	0.984807	+	0.173651i	$0.0555565\pi$
$103$			35.7721i			0.347302i	−0.984807	+	0.173651i	$0.944444\pi$
$104$	1.16718	+	3.59222i	0.0112229	+	0.0345406i
$105$		0			0
$106$	35.0132	−	25.4385i	0.330313	−	0.239986i
$107$			121.099i			1.13177i	0.824485	+	0.565884i	$0.191465\pi$
$107$			121.099i			1.13177i	−0.824485	+	0.565884i	$0.808535\pi$
$108$	−51.0557	−	16.5890i	−0.472738	−	0.153602i
$109$	−197.469			−1.81164			−0.905821	−	0.423660i	$-0.860745\pi$
$109$	−197.469			−1.81164			−0.905821	+	0.423660i	$0.860745\pi$
$110$		0			0
$111$			100.282i			0.903441i
$112$	80.0000	−	110.111i	0.714286	−	0.983130i
$113$	−81.2786			−0.719280			−0.359640	−	0.933091i	$-0.617100\pi$
$113$	−81.2786			−0.719280			−0.359640	+	0.933091i	$0.617100\pi$
$114$	−57.8885	+	42.0585i	−0.507794	+	0.368934i
$115$		0			0
$116$	8.58359	−	26.4176i	0.0739965	−	0.227738i
$117$	2.58359			0.0220820
$118$	86.8328	+	119.515i	0.735871	+	1.01284i
$119$			203.208i			1.70763i
$120$		0			0
$121$	117.774			0.973339
$122$	−42.2918	+	30.7268i	−0.346654	+	0.251859i
$123$			157.557i			1.28095i
$124$	180.498	+	58.6475i	1.45563	+	0.472964i
$125$		0			0
$126$	−54.7214	−	75.3175i	−0.434297	−	0.597758i
$127$			1.84616i			0.0145367i	0.999974	+	0.00726834i	$0.00231361\pi$
$127$			1.84616i			0.0145367i	−0.999974	+	0.00726834i	$0.997686\pi$
$128$	−39.5542	+	121.735i	−0.309017	+	0.951057i
$129$	7.63932			0.0592195
$130$		0			0
$131$			225.609i			1.72221i	0.508428	+	0.861105i	$0.330227\pi$
$131$			225.609i			1.72221i	−0.508428	+	0.861105i	$0.669773\pi$
$132$	8.44582	−	25.9936i	0.0639835	−	0.196921i
$133$	80.0000			0.601504
$134$	−104.472	−	143.794i	−0.779643	−	1.07309i
$135$		0			0
$136$	−59.0557	−	181.755i	−0.434233	−	1.33643i
$137$	52.8328			0.385641			0.192820	−	0.981234i	$-0.438236\pi$
$137$	52.8328			0.385641			0.192820	+	0.981234i	$0.438236\pi$
$138$	99.1935	−	72.0683i	0.718793	−	0.522234i
$139$		−	125.852i		−	0.905407i	−0.891661	−	0.452703i	$-0.850460\pi$
$139$		−	125.852i		−	0.905407i	0.891661	−	0.452703i	$-0.149540\pi$
$140$		0			0
$141$	134.472			0.953703
$142$	−46.3344	−	63.7738i	−0.326298	−	0.449111i
$143$		−	0.848009i		−	0.00593013i
$144$	70.8328	+	51.4631i	0.491895	+	0.357382i
$145$		0			0
$146$	−222.567	+	161.705i	−1.52443	+	1.10757i
$147$			88.8693i			0.604553i
$148$	−32.5836	+	100.282i	−0.220159	+	0.677581i
$149$	132.971			0.892420			0.446210	−	0.894928i	$-0.352773\pi$
$149$	132.971			0.892420			0.446210	+	0.894928i	$0.352773\pi$
$150$		0			0
$151$		−	151.221i		−	1.00146i	−0.865603	−	0.500732i	$-0.833064\pi$
$151$		−	151.221i		−	1.00146i	0.865603	−	0.500732i	$-0.166936\pi$
$152$	−71.5542	+	23.2494i	−0.470751	+	0.152956i
$153$	−130.721			−0.854388
$154$	−24.7214	+	17.9611i	−0.160528	+	0.116631i
$155$		0			0
$156$	6.83282	+	2.22012i	0.0438001	+	0.0142315i
$157$	36.7477			0.234062			0.117031	−	0.993128i	$-0.462662\pi$
$157$	36.7477			0.234062			0.117031	+	0.993128i	$0.462662\pi$
$158$	−133.666	−	183.975i	−0.845985	−	1.16440i
$159$		−	82.3209i		−	0.517741i
$160$		0			0
$161$	−137.082			−0.851441
$162$	−162.297	+	117.916i	−1.00183	+	0.727874i
$163$		−	302.854i		−	1.85800i	−0.370079	−	0.929000i	$-0.620669\pi$
$163$		−	302.854i		−	1.85800i	0.370079	−	0.929000i	$-0.379331\pi$
$164$	−51.1935	+	157.557i	−0.312155	+	0.960716i
$165$		0			0
$166$	−24.9706	−	34.3691i	−0.150425	−	0.207043i
$167$		−	99.3839i		−	0.595113i	−0.954704	−	0.297557i	$-0.903828\pi$
$167$		−	99.3839i		−	0.595113i	0.954704	−	0.297557i	$-0.0961717\pi$
$168$	−80.0000	−	246.215i	−0.476190	−	1.46556i
$169$	−168.777			−0.998681
$170$		0			0
$171$			51.4631i			0.300954i
$172$	7.63932	+	2.48217i	0.0444147	+	0.0144312i
$173$	181.639			1.04994			0.524969	−	0.851121i	$-0.324077\pi$
$173$	181.639			1.04994			0.524969	+	0.851121i	$0.324077\pi$
$174$	−31.0557	−	42.7445i	−0.178481	−	0.245658i
$175$		0			0
$176$	16.8916	−	23.2494i	0.0959753	−	0.132099i
$177$	280.997			1.58755
$178$	109.125	−	79.2837i	0.613060	−	0.445414i
$179$		−	260.907i		−	1.45758i	−0.684735	−	0.728792i	$-0.740082\pi$
$179$		−	260.907i		−	1.45758i	0.684735	−	0.728792i	$-0.259918\pi$
$180$		0			0
$181$	157.777			0.871697			0.435848	−	0.900020i	$-0.356448\pi$
$181$	157.777			0.871697			0.435848	+	0.900020i	$0.356448\pi$
$182$	−4.72136	−	6.49839i	−0.0259415	−	0.0357055i
$183$			99.4340i			0.543355i
$184$	122.610	−	39.8384i	0.666358	−	0.216513i
$185$		0			0
$186$	292.053	−	212.189i	1.57018	−	1.14080i
$187$			42.9065i			0.229447i
$188$	134.472	+	43.6926i	0.715277	+	0.232408i
$189$	114.164			0.604043
$190$		0			0
$191$		−	324.095i		−	1.69683i	−0.529328	−	0.848417i	$-0.677556\pi$
$191$		−	324.095i		−	1.69683i	0.529328	−	0.848417i	$-0.322444\pi$
$192$	143.108	+	196.972i	0.745356	+	1.02589i
$193$	−181.777			−0.941850			−0.470925	−	0.882173i	$-0.656080\pi$
$193$	−181.777			−0.941850			−0.470925	+	0.882173i	$0.656080\pi$
$194$	63.3738	−	46.0438i	0.326669	−	0.237339i
$195$		0			0
$196$	−28.8754	+	88.8693i	−0.147323	+	0.453415i
$197$	−140.525			−0.713324			−0.356662	−	0.934234i	$-0.616085\pi$
$197$	−140.525			−0.713324			−0.356662	+	0.934234i	$0.616085\pi$
$198$	−11.5542	−	15.9030i	−0.0583544	−	0.0803180i
$199$			168.234i			0.845397i	0.906270	+	0.422698i	$0.138917\pi$
$199$			168.234i			0.845397i	−0.906270	+	0.422698i	$0.861083\pi$
$200$		0			0
$201$	−338.079			−1.68198
$202$	161.623	−	117.426i	0.800114	−	0.581317i
$203$			59.0715i			0.290993i
$204$	−345.718	−	112.331i	−1.69470	−	0.550641i
$205$		0			0
$206$	42.0526	+	57.8805i	0.204139	+	0.280973i
$207$		−	88.1833i		−	0.426006i
$208$	6.11146	+	4.44023i	0.0293820	+	0.0213473i
$209$	16.8916			0.0808213
$210$		0			0
$211$			93.9455i			0.445240i	0.974905	+	0.222620i	$0.0714608\pi$
$211$			93.9455i			0.445240i	−0.974905	+	0.222620i	$0.928539\pi$
$212$	26.7477	−	82.3209i	0.126168	−	0.388306i
$213$	−149.941			−0.703949
$214$	142.361	+	195.943i	0.665237	+	0.915620i
$215$		0			0
$216$	−102.111	+	33.1780i	−0.472738	+	0.153602i
$217$	−403.607			−1.85994
$218$	−319.512	+	232.139i	−1.46565	+	1.06486i
$219$			523.287i			2.38944i
$220$		0			0
$221$	−11.2786			−0.0510346
$222$	117.889	+	162.260i	0.531029	+	0.730899i
$223$		−	214.035i		−	0.959797i	−0.877324	−	0.479899i	$-0.840673\pi$
$223$		−	214.035i		−	0.959797i	0.877324	−	0.479899i	$-0.159327\pi$
$224$		−	272.208i		−	1.21522i
$225$		0			0
$226$	−131.512	+	95.5488i	−0.581910	+	0.422782i
$227$			41.4225i			0.182478i	0.995829	+	0.0912389i	$0.0290827\pi$
$227$			41.4225i			0.182478i	−0.995829	+	0.0912389i	$0.970917\pi$
$228$	−44.2229	+	136.104i	−0.193960	+	0.596948i
$229$	73.2786			0.319994			0.159997	−	0.987117i	$-0.448852\pi$
$229$	73.2786			0.319994			0.159997	+	0.987117i	$0.448852\pi$
$230$		0			0
$231$			58.1234i			0.251616i
$232$	−17.1672	−	52.8352i	−0.0739965	−	0.227738i
$233$	307.050			1.31781			0.658905	−	0.752227i	$-0.271020\pi$
$233$	307.050			1.31781			0.658905	+	0.752227i	$0.271020\pi$
$234$	4.18034	−	3.03719i	0.0178647	−	0.0129795i
$235$		0			0
$236$	280.997	+	91.3014i	1.19066	+	0.386870i
$237$	−432.551			−1.82511
$238$	238.885	+	328.798i	1.00372	+	1.38150i
$239$		−	42.9065i		−	0.179525i	−0.995963	−	0.0897625i	$-0.971389\pi$
$239$		−	42.9065i		−	0.179525i	0.995963	−	0.0897625i	$-0.0286108\pi$
$240$		0			0
$241$	−135.082			−0.560506			−0.280253	−	0.959926i	$-0.590418\pi$
$241$	−135.082			−0.560506			−0.280253	+	0.959926i	$0.590418\pi$
$242$	190.562	−	138.452i	0.787448	−	0.572114i
$243$			260.796i			1.07323i
$244$	−32.3081	+	99.4340i	−0.132410	+	0.407516i
$245$		0			0
$246$	185.220	+	254.933i	0.752926	+	1.03631i
$247$			4.44023i			0.0179767i
$248$	360.997	−	117.295i	1.45563	−	0.472964i
$249$	−80.8065			−0.324524
$250$		0			0
$251$		−	221.169i		−	0.881152i	−0.897715	−	0.440576i	$-0.854774\pi$
$251$		−	221.169i		−	0.881152i	0.897715	−	0.440576i	$-0.145226\pi$
$252$	−177.082	−	57.5374i	−0.702707	−	0.228323i
$253$	−28.9443			−0.114404
$254$	2.17029	+	2.98715i	0.00854445	+	0.0117604i
$255$		0			0
$256$	79.1084	+	243.470i	0.309017	+	0.951057i
$257$	257.056			1.00022			0.500108	−	0.865963i	$-0.333293\pi$
$257$	257.056			1.00022			0.500108	+	0.865963i	$0.333293\pi$
$258$	12.3607	−	8.98056i	0.0479096	−	0.0348084i
$259$		−	224.237i		−	0.865781i
$260$		0			0
$261$	−38.0000			−0.145594
$262$	265.220	+	365.044i	1.01229	+	1.39330i
$263$			164.168i			0.624212i	0.950047	+	0.312106i	$0.101034\pi$
$263$			164.168i			0.624212i	−0.950047	+	0.312106i	$0.898966\pi$
$264$	−16.8916	−	51.9872i	−0.0639835	−	0.196921i
$265$		0			0
$266$	129.443	−	94.0456i	0.486627	−	0.353555i
$267$		−	256.567i		−	0.960926i
$268$	−338.079	−	109.849i	−1.26149	−	0.409882i
$269$	−35.4752			−0.131878			−0.0659391	−	0.997824i	$-0.521004\pi$
$269$	−35.4752			−0.131878			−0.0659391	+	0.997824i	$0.521004\pi$
$270$		0			0
$271$			298.950i			1.10314i	0.834130	+	0.551568i	$0.185970\pi$
$271$			298.950i			1.10314i	−0.834130	+	0.551568i	$0.814030\pi$
$272$	−309.220	−	224.661i	−1.13684	−	0.825961i
$273$	−15.2786			−0.0559657
$274$	85.4853	−	62.1087i	0.311990	−	0.226674i
$275$		0			0
$276$	75.7771	−	233.218i	0.274555	−	0.844992i
$277$	457.246			1.65071			0.825354	−	0.564616i	$-0.190976\pi$
$277$	457.246			1.65071			0.825354	+	0.564616i	$0.190976\pi$
$278$	−147.947	−	203.632i	−0.532185	−	0.732490i
$279$		−	259.635i		−	0.930593i
$280$		0			0
$281$	−5.63932			−0.0200688			−0.0100344	−	0.999950i	$-0.503194\pi$
$281$	−5.63932			−0.0200688			−0.0100344	+	0.999950i	$0.503194\pi$
$282$	217.580	−	158.081i	0.771562	−	0.560573i
$283$			169.918i			0.600418i	0.953874	+	0.300209i	$0.0970563\pi$
$283$			169.918i			0.600418i	−0.953874	+	0.300209i	$0.902944\pi$
$284$	−149.941	−	48.7188i	−0.527962	−	0.171545i
$285$		0			0
$286$	−0.996894	−	1.37211i	−0.00348564	−	0.00479758i
$287$		−	352.309i		−	1.22756i
$288$	175.108			0.608015
$289$	281.663			0.974611
$290$		0			0
$291$		−	149.001i		−	0.512030i
$292$	−170.026	+	523.287i	−0.582282	+	1.79208i
$293$	26.8591			0.0916694			0.0458347	−	0.998949i	$-0.485405\pi$
$293$	26.8591			0.0916694			0.0458347	+	0.998949i	$0.485405\pi$
$294$	104.472	+	143.794i	0.355347	+	0.489094i
$295$		0			0
$296$	65.1672	+	200.564i	0.220159	+	0.677581i
$297$	24.1052			0.0811624
$298$	215.151	−	156.316i	0.721983	−	0.524551i
$299$		−	7.60845i		−	0.0254463i
$300$		0			0
$301$	−17.0820			−0.0567510
$302$	−177.771	−	244.681i	−0.588645	−	0.810201i
$303$		−	379.999i		−	1.25412i
$304$	−88.4458	+	121.735i	−0.290940	+	0.400445i
$305$		0			0
$306$	−211.512	+	153.672i	−0.691214	+	0.502197i
$307$			118.031i			0.384466i	0.981349	+	0.192233i	$0.0615730\pi$
$307$			118.031i			0.384466i	−0.981349	+	0.192233i	$0.938427\pi$
$308$	−18.8854	+	58.1234i	−0.0613164	+	0.188712i
$309$	136.085			0.440405
$310$		0			0
$311$			121.835i			0.391753i	0.980629	+	0.195877i	$0.0627552\pi$
$311$			121.835i			0.391753i	−0.980629	+	0.195877i	$0.937245\pi$
$312$	13.6656	−	4.44023i	0.0438001	−	0.0142315i
$313$	−219.548			−0.701431			−0.350716	−	0.936482i	$-0.614062\pi$
$313$	−219.548			−0.701431			−0.350716	+	0.936482i	$0.614062\pi$
$314$	59.4590	−	43.1995i	0.189360	−	0.137578i
$315$		0			0
$316$	−432.551	−	140.544i	−1.36883	−	0.444761i
$317$	−366.859			−1.15728			−0.578642	−	0.815582i	$-0.696417\pi$
$317$	−366.859			−1.15728			−0.578642	+	0.815582i	$0.696417\pi$
$318$	−96.7740	−	133.198i	−0.304321	−	0.418862i
$319$			12.4727i			0.0390993i
$320$		0			0
$321$	460.689			1.43517
$322$	−221.803	+	161.150i	−0.688830	+	0.500465i
$323$		−	224.661i		−	0.695546i
$324$	−123.984	+	381.583i	−0.382666	+	1.17772i
$325$		0			0
$326$	−356.026	−	490.028i	−1.09211	−	1.50315i
$327$			751.217i			2.29730i
$328$	102.387	+	315.115i	0.312155	+	0.960716i
$329$	−300.689			−0.913948
$330$		0			0
$331$		−	162.846i		−	0.491981i	−0.969272	−	0.245990i	$-0.920887\pi$
$331$		−	162.846i		−	0.491981i	0.969272	−	0.245990i	$-0.0791132\pi$
$332$	−80.8065	−	26.2556i	−0.243393	−	0.0790832i
$333$	144.249			0.433181
$334$	−116.833	−	160.807i	−0.349799	−	0.481457i
$335$		0			0
$336$	−418.885	−	304.338i	−1.24668	−	0.905768i
$337$	−17.1084			−0.0507666			−0.0253833	−	0.999678i	$-0.508081\pi$
$337$	−17.1084			−0.0507666			−0.0253833	+	0.999678i	$0.508081\pi$
$338$	−273.087	+	198.409i	−0.807950	+	0.587010i
$339$			309.202i			0.912101i
$340$		0			0
$341$	−85.2198			−0.249911
$342$	60.4984	+	83.2690i	0.176896	+	0.243477i
$343$			218.101i			0.635863i
$344$	15.2786	−	4.96433i	0.0444147	−	0.0144312i
$345$		0			0
$346$	293.899	−	213.530i	0.849418	−	0.617138i
$347$		−	167.498i		−	0.482703i	−0.970438	−	0.241351i	$-0.922409\pi$
$347$		−	167.498i		−	0.482703i	0.970438	−	0.241351i	$-0.0775906\pi$
$348$	−100.498	−	32.6539i	−0.288789	−	0.0938331i
$349$	−483.495			−1.38537			−0.692687	−	0.721239i	$-0.743573\pi$
$349$	−483.495			−1.38537			−0.692687	+	0.721239i	$0.743573\pi$
$350$		0			0
$351$			6.33644i			0.0180525i
$352$		−	57.4756i		−	0.163283i
$353$	−307.994			−0.872504			−0.436252	−	0.899825i	$-0.643694\pi$
$353$	−307.994			−0.872504			−0.436252	+	0.899825i	$0.643694\pi$
$354$	454.663	−	330.332i	1.28436	−	0.933140i
$355$		0			0
$356$	83.3638	−	256.567i	0.234168	−	0.720695i
$357$	773.050			2.16540
$358$	−306.715	−	422.157i	−0.856746	−	1.17921i
$359$		−	23.2494i		−	0.0647615i	−0.999476	−	0.0323807i	$-0.989691\pi$
$359$		−	23.2494i		−	0.0647615i	0.999476	−	0.0323807i	$-0.0103089\pi$
$360$		0			0
$361$	272.554			0.754998
$362$	255.289	−	185.478i	0.705217	−	0.512370i
$363$		−	448.039i		−	1.23427i
$364$	−15.2786	−	4.96433i	−0.0419743	−	0.0136383i
$365$		0			0
$366$	116.892	+	160.888i	0.319376	+	0.439583i
$367$			517.325i			1.40960i	0.709404	+	0.704802i	$0.248964\pi$
$367$			517.325i			1.40960i	−0.709404	+	0.704802i	$0.751036\pi$
$368$	151.554	−	208.596i	0.411832	−	0.566838i
$369$	226.636			0.614190
$370$		0			0
$371$			184.075i			0.496159i
$372$	223.108	−	686.657i	0.599754	−	1.84585i
$373$	88.3545			0.236875			0.118438	−	0.992961i	$-0.462211\pi$
$373$	88.3545			0.236875			0.118438	+	0.992961i	$0.462211\pi$
$374$	50.4396	+	69.4242i	0.134865	+	0.185626i
$375$		0			0
$376$	268.944	−	87.3853i	0.715277	−	0.232408i
$377$	−3.27864			−0.00869666
$378$	184.721	−	134.208i	0.488681	−	0.355047i
$379$			19.3332i			0.0510112i	0.999675	+	0.0255056i	$0.00811956\pi$
$379$			19.3332i			0.0510112i	−0.999675	+	0.0255056i	$0.991880\pi$
$380$		0			0
$381$	7.02321			0.0184336
$382$	−380.997	−	524.397i	−0.997374	−	1.37277i
$383$			431.612i			1.12692i	0.826142	+	0.563462i	$0.190531\pi$
$383$			431.612i			1.12692i	−0.826142	+	0.563462i	$0.809469\pi$
$384$	463.108	+	150.473i	1.20601	+	0.391857i
$385$		0			0
$386$	−294.122	+	213.692i	−0.761973	+	0.553606i
$387$		−	10.9887i		−	0.0283945i
$388$	48.4133	−	149.001i	0.124777	−	0.384023i
$389$	−296.354			−0.761837			−0.380918	−	0.924609i	$-0.624392\pi$
$389$	−296.354			−0.761837			−0.380918	+	0.924609i	$0.624392\pi$
$390$		0			0
$391$			384.963i			0.984560i
$392$	57.7508	+	177.739i	0.147323	+	0.453415i
$393$	858.269			2.18389
$394$	−227.374	+	165.197i	−0.577091	+	0.419281i
$395$		0			0
$396$	−37.3901	−	12.1488i	−0.0944194	−	0.0306787i
$397$	86.1904			0.217104			0.108552	−	0.994091i	$-0.465379\pi$
$397$	86.1904			0.217104			0.108552	+	0.994091i	$0.465379\pi$
$398$	197.771	+	272.208i	0.496912	+	0.683940i
$399$		−	304.338i		−	0.762752i
$400$		0			0
$401$	442.997			1.10473			0.552365	−	0.833602i	$-0.313725\pi$
$401$	442.997			1.10473			0.552365	+	0.833602i	$0.313725\pi$
$402$	−547.023	+	397.436i	−1.36075	+	0.988646i
$403$		−	22.4014i		−	0.0555865i
$404$	123.469	−	379.999i	0.305616	−	0.940591i
$405$		0			0
$406$	69.4427	+	95.5797i	0.171041	+	0.235418i
$407$		−	47.3467i		−	0.116331i
$408$	−691.437	+	224.661i	−1.69470	+	0.550641i
$409$	63.4102			0.155037			0.0775186	−	0.996991i	$-0.475300\pi$
$409$	63.4102			0.155037			0.0775186	+	0.996991i	$0.475300\pi$
$410$		0			0
$411$		−	200.988i		−	0.489022i
$412$	136.085	+	44.2167i	0.330304	+	0.107322i
$413$	−628.328			−1.52138
$414$	−103.666	−	142.684i	−0.250400	−	0.344646i
$415$		0			0
$416$	15.1084			0.0363182
$417$	−478.768			−1.14812
$418$	27.3313	−	19.8573i	0.0653858	−	0.0475056i
$419$		−	435.678i		−	1.03980i	−0.854226	−	0.519902i	$-0.825968\pi$
$419$		−	435.678i		−	1.03980i	0.854226	−	0.519902i	$-0.174032\pi$
$420$		0			0
$421$	−582.912			−1.38459			−0.692294	−	0.721615i	$-0.743400\pi$
$421$	−582.912			−1.38459			−0.692294	+	0.721615i	$0.743400\pi$
$422$	110.440	+	152.007i	0.261705	+	0.360206i
$423$		−	193.430i		−	0.457280i
$424$	−53.4953	−	164.642i	−0.126168	−	0.388306i
$425$		0			0
$426$	−242.610	+	176.266i	−0.569507	+	0.413771i
$427$		−	222.341i		−	0.520705i
$428$	460.689	+	149.687i	1.07638	+	0.349736i
$429$	−3.22602			−0.00751986
$430$		0			0
$431$			375.882i			0.872117i	0.899918	+	0.436058i	$0.143626\pi$
$431$			375.882i			0.872117i	−0.899918	+	0.436058i	$0.856374\pi$
$432$	−126.217	+	173.722i	−0.292168	+	0.402135i
$433$	368.164			0.850263			0.425132	−	0.905131i	$-0.360228\pi$
$433$	368.164			0.850263			0.425132	+	0.905131i	$0.360228\pi$
$434$	−653.050	+	474.468i	−1.50472	+	1.09324i
$435$		0			0
$436$	−244.085	+	751.217i	−0.559828	+	1.72297i
$437$	151.554			0.346806
$438$	615.161	+	846.696i	1.40448	+	1.93310i
$439$			483.549i			1.10148i	0.834677	+	0.550739i	$0.185654\pi$
$439$			483.549i			1.10148i	−0.834677	+	0.550739i	$0.814346\pi$
$440$		0			0
$441$	127.833			0.289870
$442$	−18.2492	+	13.2588i	−0.0412878	+	0.0299974i
$443$			279.181i			0.630205i	0.949058	+	0.315102i	$0.102039\pi$
$443$			279.181i			0.630205i	−0.949058	+	0.315102i	$0.897961\pi$
$444$	381.495	+	123.955i	0.859224	+	0.279179i
$445$		0			0
$446$	−251.613	−	346.316i	−0.564155	−	0.776492i
$447$		−	505.850i		−	1.13166i
$448$	−320.000	−	440.442i	−0.714286	−	0.983130i
$449$	756.079			1.68392			0.841959	−	0.539542i	$-0.181403\pi$
$449$	756.079			1.68392			0.841959	+	0.539542i	$0.181403\pi$
$450$		0			0
$451$		−	74.3885i		−	0.164941i
$452$	−100.466	+	309.202i	−0.222270	+	0.684076i
$453$	−575.279			−1.26993
$454$	48.6950	+	67.0230i	0.107258	+	0.147628i
$455$		0			0
$456$	88.4458	+	272.208i	0.193960	+	0.596948i
$457$	−285.672			−0.625103			−0.312551	−	0.949901i	$-0.601184\pi$
$457$	−285.672			−0.625103			−0.312551	+	0.949901i	$0.601184\pi$
$458$	118.567	−	86.1442i	0.258881	−	0.188088i
$459$		−	320.603i		−	0.698482i
$460$		0			0
$461$	−99.1146			−0.214999			−0.107500	−	0.994205i	$-0.534284\pi$
$461$	−99.1146			−0.214999			−0.107500	+	0.994205i	$0.534284\pi$
$462$	68.3282	+	94.0456i	0.147896	+	0.203562i
$463$			630.603i			1.36199i	0.732286	+	0.680997i	$0.238453\pi$
$463$			630.603i			1.36199i	−0.732286	+	0.680997i	$0.761547\pi$
$464$	−89.8885	−	65.3078i	−0.193725	−	0.140750i
$465$		0			0
$466$	496.817	−	360.958i	1.06613	−	0.774589i
$467$		−	496.010i		−	1.06212i	−0.847334	−	0.531060i	$-0.821794\pi$
$467$		−	496.010i		−	1.06212i	0.847334	−	0.531060i	$-0.178206\pi$
$468$	3.19350	−	9.82857i	0.00682371	−	0.0210012i
$469$	755.967			1.61187
$470$		0			0
$471$		−	139.796i		−	0.296808i
$472$	561.994	−	182.603i	1.19066	−	0.386870i
$473$	−3.60680			−0.00762537
$474$	−699.882	+	508.494i	−1.47655	+	1.07277i
$475$		0			0
$476$	773.050	+	251.179i	1.62405	+	0.527687i
$477$	−118.413			−0.248246
$478$	−50.4396	−	69.4242i	−0.105522	−	0.145239i
$479$			579.090i			1.20896i	0.796621	+	0.604478i	$0.206618\pi$
$479$			579.090i			1.20896i	−0.796621	+	0.604478i	$0.793382\pi$
$480$		0			0
$481$	12.4458			0.0258749
$482$	−218.567	+	158.798i	−0.453459	+	0.329457i
$483$			521.491i			1.07969i
$484$	145.577	−	448.039i	0.300778	−	0.925700i
$485$		0			0
$486$	306.584	+	421.976i	0.630830	+	0.868264i
$487$		−	626.363i		−	1.28617i	−0.765796	−	0.643084i	$-0.777655\pi$
$487$		−	626.363i		−	1.28617i	0.765796	−	0.643084i	$-0.222345\pi$
$488$	64.6161	+	198.868i	0.132410	+	0.407516i
$489$	−1152.13			−2.35608
$490$		0			0
$491$			22.3013i			0.0454201i	0.999742	+	0.0227100i	$0.00722945\pi$
$491$			22.3013i			0.0454201i	−0.999742	+	0.0227100i	$0.992771\pi$
$492$	599.384	+	194.752i	1.21826	+	0.395837i
$493$	165.889			0.336488
$494$	5.21981	+	7.18445i	0.0105664	+	0.0145434i
$495$		0			0
$496$	446.217	−	614.165i	0.899630	−	1.23824i
$497$	335.279			0.674605
$498$	−130.748	+	94.9937i	−0.262546	+	0.190750i
$499$			627.362i			1.25724i	0.777714	+	0.628619i	$0.216379\pi$
$499$			627.362i			1.25724i	−0.777714	+	0.628619i	$0.783621\pi$
$500$		0			0
$501$	−378.079			−0.754649
$502$	−260.000	−	357.859i	−0.517928	−	0.712867i
$503$		−	780.853i		−	1.55239i	−0.630492	−	0.776196i	$-0.717147\pi$
$503$		−	780.853i		−	1.55239i	0.630492	−	0.776196i	$-0.282853\pi$
$504$	−354.164	+	115.075i	−0.702707	+	0.228323i
$505$		0			0
$506$	−46.8328	+	34.0260i	−0.0925550	+	0.0672451i
$507$			642.066i			1.26640i
$508$	7.02321	+	2.28198i	0.0138252	+	0.00449208i
$509$	−288.950			−0.567683			−0.283841	−	0.958871i	$-0.591609\pi$
$509$	−288.950			−0.567683			−0.283841	+	0.958871i	$0.591609\pi$
$510$		0			0
$511$		−	1170.11i		−	2.28984i
$512$	414.217	+	300.946i	0.809017	+	0.587785i
$513$	−126.217			−0.246036
$514$	415.925	−	302.187i	0.809192	−	0.587913i
$515$		0			0
$516$	9.44272	−	29.0617i	0.0182998	−	0.0563211i
$517$	−63.4891			−0.122803
$518$	−263.607	−	362.824i	−0.508893	−	0.700432i
$519$		−	690.997i		−	1.33140i
$520$		0			0
$521$	−602.984			−1.15736			−0.578680	−	0.815555i	$-0.696432\pi$
$521$	−602.984			−1.15736			−0.578680	+	0.815555i	$0.696432\pi$
$522$	−61.4853	+	44.6717i	−0.117788	+	0.0855779i
$523$		−	367.962i		−	0.703560i	−0.936083	−	0.351780i	$-0.885577\pi$
$523$		−	367.962i		−	0.703560i	0.936083	−	0.351780i	$-0.114423\pi$
$524$	858.269	+	278.869i	1.63792	+	0.532192i
$525$		0			0
$526$	192.991	+	265.629i	0.366902	+	0.504998i
$527$			1133.44i			2.15073i
$528$	−88.4458	−	64.2597i	−0.167511	−	0.121704i
$529$	269.308			0.509089
$530$		0			0
$531$		−	404.196i		−	0.761198i
$532$	98.8854	−	304.338i	0.185875	−	0.572064i
$533$	19.5542			0.0366870
$534$	−301.613	−	415.135i	−0.564818	−	0.777406i
$535$		0			0
$536$	−676.158	+	219.697i	−1.26149	+	0.409882i
$537$	−992.551			−1.84833
$538$	−57.4001	+	41.7036i	−0.106692	+	0.0775161i
$539$		−	41.9584i		−	0.0778449i
$540$		0			0
$541$	−616.885			−1.14027			−0.570134	−	0.821551i	$-0.693109\pi$
$541$	−616.885			−1.14027			−0.570134	+	0.821551i	$0.693109\pi$
$542$	351.437	+	483.711i	0.648407	+	0.892455i
$543$		−	600.220i		−	1.10538i
$544$	−764.433			−1.40521
$545$		0			0
$546$	−24.7214	+	17.9611i	−0.0452772	+	0.0328958i
$547$			97.8499i			0.178885i	0.995992	+	0.0894423i	$0.0285085\pi$
$547$			97.8499i			0.178885i	−0.995992	+	0.0894423i	$0.971492\pi$
$548$	65.3050	−	200.988i	0.119170	−	0.366766i
$549$	143.029			0.260527
$550$		0			0
$551$		−	65.3078i		−	0.118526i
$552$	−151.554	−	466.436i	−0.274555	−	0.844992i
$553$	967.214			1.74903
$554$	739.840	−	537.525i	1.33545	−	0.970262i
$555$		0			0
$556$	−478.768	−	155.561i	−0.861093	−	0.279786i
$557$	−896.302			−1.60916			−0.804580	−	0.593845i	$-0.797609\pi$
$557$	−896.302			−1.60916			−0.804580	+	0.593845i	$0.797609\pi$
$558$	−305.220	−	420.099i	−0.546989	−	0.752866i
$559$		−	0.948103i		−	0.00169607i
$560$		0			0
$561$	163.226			0.290955
$562$	−9.12461	+	6.62942i	−0.0162360	+	0.0117961i
$563$		−	771.186i		−	1.36978i	−0.728647	−	0.684890i	$-0.759850\pi$
$563$		−	771.186i		−	1.36978i	0.728647	−	0.684890i	$-0.240150\pi$
$564$	166.217	−	511.562i	0.294710	−	0.907026i
$565$		0			0
$566$	199.751	+	274.933i	0.352917	+	0.485748i
$567$		−	853.245i		−	1.50484i
$568$	−299.882	+	97.4377i	−0.527962	+	0.171545i
$569$	8.74767			0.0153738			0.00768688	−	0.999970i	$-0.497553\pi$
$569$	8.74767			0.0153738			0.00768688	+	0.999970i	$0.497553\pi$
$570$		0			0
$571$			511.138i			0.895164i	0.894243	+	0.447582i	$0.147715\pi$
$571$			511.138i			0.895164i	−0.894243	+	0.447582i	$0.852285\pi$
$572$	−3.22602	−	1.04820i	−0.00563989	−	0.00183251i
$573$	−1232.93			−2.15171
$574$	−414.164	−	570.048i	−0.721540	−	0.993115i
$575$		0			0
$576$	283.331	−	205.852i	0.491895	−	0.357382i
$577$	713.712			1.23694			0.618468	−	0.785810i	$-0.287754\pi$
$577$	713.712			1.23694			0.618468	+	0.785810i	$0.287754\pi$
$578$	455.740	−	331.114i	0.788477	−	0.572862i
$579$			691.521i			1.19434i
$580$		0			0
$581$	180.689			0.310996
$582$	−175.161	−	241.088i	−0.300964	−	0.414241i
$583$			38.8666i			0.0666666i
$584$	340.053	+	1046.57i	0.582282	+	1.79208i
$585$		0			0
$586$	43.4590	−	31.5748i	0.0741621	−	0.0538819i
$587$			422.169i			0.719198i	0.933107	+	0.359599i	$0.117086\pi$
$587$			422.169i			0.719198i	−0.933107	+	0.359599i	$0.882914\pi$
$588$	338.079	+	109.849i	0.574964	+	0.186817i
$589$	446.217			0.757584
$590$		0			0
$591$			534.588i			0.904548i
$592$	341.220	+	247.911i	0.576385	+	0.418768i
$593$	308.663			0.520510			0.260255	−	0.965540i	$-0.416193\pi$
$593$	308.663			0.520510			0.260255	+	0.965540i	$0.416193\pi$
$594$	39.0031	−	28.3374i	0.0656618	−	0.0477061i
$595$		0			0
$596$	164.361	−	505.850i	0.275773	−	0.848742i
$597$	640.000			1.07203
$598$	−8.94427	−	12.3107i	−0.0149570	−	0.0205865i
$599$		−	462.196i		−	0.771612i	−0.922580	−	0.385806i	$-0.873923\pi$
$599$		−	462.196i		−	0.771612i	0.922580	−	0.385806i	$-0.126077\pi$
$600$		0			0
$601$	355.358			0.591277			0.295639	−	0.955300i	$-0.404468\pi$
$601$	355.358			0.591277			0.295639	+	0.955300i	$0.404468\pi$
$602$	−27.6393	+	20.0811i	−0.0459125	+	0.0333574i
$603$			486.305i			0.806476i
$604$	−575.279	−	186.919i	−0.952448	−	0.309469i
$605$		0			0
$606$	−446.715	−	614.851i	−0.737154	−	1.01461i
$607$		−	630.403i		−	1.03856i	−0.854605	−	0.519278i	$-0.826201\pi$
$607$		−	630.403i		−	1.03856i	0.854605	−	0.519278i	$-0.173799\pi$
$608$			300.946i			0.494977i
$609$	224.721			0.369001
$610$		0			0
$611$		−	16.6891i		−	0.0273144i
$612$	−161.580	+	497.294i	−0.264020	+	0.812571i
$613$	−812.525			−1.32549			−0.662745	−	0.748846i	$-0.730608\pi$
$613$	−812.525			−1.32549			−0.662745	+	0.748846i	$0.730608\pi$
$614$	138.754	+	190.978i	0.225984	+	0.311040i
$615$		0			0
$616$	37.7709	+	116.247i	0.0613164	+	0.188712i
$617$	437.935			0.709781			0.354891	−	0.934908i	$-0.384518\pi$
$617$	437.935			0.709781			0.354891	+	0.934908i	$0.384518\pi$
$618$	220.190	−	159.978i	0.356295	−	0.258864i
$619$		−	770.250i		−	1.24435i	−0.782880	−	0.622173i	$-0.786250\pi$
$619$		−	770.250i		−	1.24435i	0.782880	−	0.622173i	$-0.213750\pi$
$620$		0			0
$621$	216.276			0.348270
$622$	143.226	+	197.134i	0.230267	+	0.316935i
$623$			573.702i			0.920870i
$624$	16.8916	−	23.2494i	0.0270700	−	0.0372586i
$625$		0			0
$626$	−355.236	+	258.094i	−0.567470	+	0.412291i
$627$		−	64.2597i		−	0.102487i
$628$	45.4226	−	139.796i	0.0723290	−	0.222606i
$629$	−629.718			−1.00114
$630$		0			0
$631$		−	875.496i		−	1.38747i	−0.720228	−	0.693737i	$-0.755963\pi$
$631$		−	875.496i		−	1.38747i	0.720228	−	0.693737i	$-0.244037\pi$
$632$	−865.102	+	281.089i	−1.36883	+	0.444761i
$633$	357.390			0.564597
$634$	−593.591	+	431.269i	−0.936263	+	0.680235i
$635$		0			0
$636$	−313.167	−	101.754i	−0.492401	−	0.159991i
$637$	11.0294			0.0173146
$638$	14.6625	+	20.1812i	0.0229820	+	0.0316320i
$639$			215.681i			0.337529i
$640$		0			0
$641$	842.571			1.31446			0.657232	−	0.753689i	$-0.271727\pi$
$641$	842.571			1.31446			0.657232	+	0.753689i	$0.271727\pi$
$642$	745.410	−	541.572i	1.16108	−	0.843570i
$643$			1153.20i			1.79348i	0.442563	+	0.896738i	$0.354069\pi$
$643$			1153.20i			1.79348i	−0.442563	+	0.896738i	$0.645931\pi$
$644$	−169.443	+	521.491i	−0.263110	+	0.809769i
$645$		0			0
$646$	−264.105	−	363.510i	−0.408832	−	0.562708i
$647$			355.751i			0.549847i	0.961466	+	0.274924i	$0.0886526\pi$
$647$			355.751i			0.549847i	−0.961466	+	0.274924i	$0.911347\pi$
$648$	247.967	+	763.165i	0.382666	+	1.17772i
$649$	−132.669			−0.204420
$650$		0			0
$651$			1535.41i			2.35854i
$652$	−1152.13	−	374.348i	−1.76706	−	0.574154i
$653$	557.915			0.854387			0.427194	−	0.904160i	$-0.359502\pi$
$653$	557.915			0.854387			0.427194	+	0.904160i	$0.359502\pi$
$654$	883.108	+	1215.49i	1.35032	+	1.85855i
$655$		0			0
$656$	536.105	+	389.503i	0.817234	+	0.593755i
$657$	752.715			1.14569
$658$	−486.525	+	353.481i	−0.739399	+	0.537205i
$659$			284.157i			0.431194i	0.976482	+	0.215597i	$0.0691697\pi$
$659$			284.157i			0.431194i	−0.976482	+	0.215597i	$0.930830\pi$
$660$		0			0
$661$	716.735			1.08432			0.542160	−	0.840275i	$-0.317607\pi$
$661$	716.735			1.08432			0.542160	+	0.840275i	$0.317607\pi$
$662$	−191.437	−	263.490i	−0.289179	−	0.398021i
$663$			42.9065i			0.0647157i
$664$	−161.613	+	52.5112i	−0.243393	+	0.0790832i
$665$		0			0
$666$	233.400	−	169.575i	0.350451	−	0.254617i
$667$			111.907i			0.167776i
$668$	−378.079	−	122.845i	−0.565986	−	0.183900i
$669$	−814.237			−1.21710
$670$		0			0
$671$		−	46.9464i		−	0.0699648i
$672$	−1035.54			−1.54098
$673$	695.378			1.03325			0.516625	−	0.856212i	$-0.327188\pi$
$673$	695.378			1.03325			0.516625	+	0.856212i	$0.327188\pi$
$674$	−27.6819	+	20.1121i	−0.0410711	+	0.0298399i
$675$		0			0
$676$	−208.620	+	642.066i	−0.308609	+	0.949802i
$677$	820.237			1.21158			0.605788	−	0.795626i	$-0.292858\pi$
$677$	820.237			1.21158			0.605788	+	0.795626i	$0.292858\pi$
$678$	363.489	+	500.300i	0.536120	+	0.737905i
$679$			333.176i			0.490686i
$680$		0			0
$681$	157.580			0.231396
$682$	−137.889	+	100.182i	−0.202183	+	0.146894i
$683$		−	335.508i		−	0.491227i	−0.969368	−	0.245613i	$-0.921011\pi$
$683$		−	335.508i		−	0.491227i	0.969368	−	0.245613i	$-0.0789894\pi$
$684$	195.777	+	63.6118i	0.286224	+	0.0929998i
$685$		0			0
$686$	256.393	+	352.895i	0.373751	+	0.514424i
$687$		−	278.769i		−	0.405777i
$688$	18.8854	−	25.9936i	0.0274498	−	0.0377814i
$689$	−10.2167			−0.0148283
$690$		0			0
$691$			336.568i			0.487074i	0.969892	+	0.243537i	$0.0783077\pi$
$691$			336.568i			0.487074i	−0.969892	+	0.243537i	$0.921692\pi$
$692$	224.519	−	690.997i	0.324449	−	0.998551i
$693$	83.6068			0.120645
$694$	−196.906	−	271.017i	−0.283726	−	0.390515i
$695$		0			0
$696$	−200.997	+	65.3078i	−0.288789	+	0.0938331i
$697$	−989.378			−1.41948
$698$	−782.312	+	568.383i	−1.12079	+	0.814302i
$699$		−	1168.09i		−	1.67108i
$700$		0			0
$701$	−429.364			−0.612502			−0.306251	−	0.951951i	$-0.599075\pi$
$701$	−429.364			−0.612502			−0.306251	+	0.951951i	$0.599075\pi$
$702$	7.44893	+	10.2526i	0.0106110	+	0.0146048i
$703$			247.911i			0.352647i
$704$	−67.5666	−	92.9974i	−0.0959753	−	0.132099i
$705$		0			0
$706$	−498.344	+	362.068i	−0.705870	+	0.512845i
$707$			849.703i			1.20184i
$708$	347.331	−	1068.98i	0.490581	−	1.50985i
$709$	1224.60			1.72722			0.863609	−	0.504162i	$-0.168199\pi$
$709$	1224.60			1.72722			0.863609	+	0.504162i	$0.168199\pi$
$710$		0			0
$711$			622.197i			0.875101i
$712$	−166.728	−	513.135i	−0.234168	−	0.720695i
$713$	−764.604			−1.07238
$714$	1250.82	−	908.774i	1.75185	−	1.27279i
$715$		0			0
$716$	−992.551	−	322.499i	−1.38624	−	0.450418i
$717$	−163.226			−0.227651
$718$	−27.3313	−	37.6183i	−0.0380658	−	0.0523931i
$719$			496.022i			0.689877i	0.938625	+	0.344939i	$0.112100\pi$
$719$			496.022i			0.689877i	−0.938625	+	0.344939i	$0.887900\pi$
$720$		0			0
$721$	−304.296			−0.422047
$722$	441.002	−	320.407i	0.610806	−	0.443777i
$723$			513.883i			0.710764i
$724$	195.023	−	600.220i	0.269369	−	0.829033i
$725$		0			0
$726$	−526.701	−	724.942i	−0.725484	−	0.998543i
$727$			152.843i			0.210238i	0.994460	+	0.105119i	$0.0335224\pi$
$727$			152.843i			0.210238i	−0.994460	+	0.105119i	$0.966478\pi$
$728$	−30.5573	+	9.92866i	−0.0419743	+	0.0136383i
$729$	89.3808			0.122607
$730$		0			0
$731$			47.9709i			0.0656237i
$732$	378.269	+	122.907i	0.516761	+	0.167906i
$733$	761.286			1.03859			0.519295	−	0.854595i	$-0.326195\pi$
$733$	761.286			1.03859			0.519295	+	0.854595i	$0.326195\pi$
$734$	608.152	+	837.049i	0.828544	+	1.14039i
$735$		0			0
$736$		−	515.679i		−	0.700650i
$737$	159.619			0.216580
$738$	366.705	−	266.427i	0.496890	−	0.361012i
$739$		−	183.975i		−	0.248951i	−0.992223	−	0.124476i	$-0.960275\pi$
$739$		−	183.975i		−	0.248951i	0.992223	−	0.124476i	$-0.0397249\pi$
$740$		0			0
$741$	16.8916			0.0227957
$742$	216.393	+	297.840i	0.291635	+	0.401401i
$743$		−	495.247i		−	0.666551i	−0.942830	−	0.333275i	$-0.891846\pi$
$743$		−	495.247i		−	0.666551i	0.942830	−	0.333275i	$-0.108154\pi$
$744$	−446.217	−	1373.31i	−0.599754	−	1.84585i
$745$		0			0
$746$	142.961	−	103.867i	0.191636	−	0.139232i
$747$			116.235i			0.155602i
$748$	163.226	+	53.0353i	0.218217	+	0.0709029i
$749$	−1030.13			−1.37534
$750$		0			0
$751$			800.059i			1.06533i	0.846328	+	0.532663i	$0.178809\pi$
$751$			800.059i			1.06533i	−0.846328	+	0.532663i	$0.821191\pi$
$752$	332.433	−	457.555i	0.442066	−	0.608451i
$753$	−841.378			−1.11737
$754$	−5.30495	+	3.85427i	−0.00703574	+	0.00511177i
$755$		0			0
$756$	141.115	−	434.306i	0.186659	−	0.574479i
$757$	276.367			0.365082			0.182541	−	0.983198i	$-0.441568\pi$
$757$	276.367			0.365082			0.182541	+	0.983198i	$0.441568\pi$
$758$	22.7276	+	31.2818i	0.0299836	+	0.0412689i
$759$			110.111i			0.145073i
$760$		0			0
$761$	891.207			1.17110			0.585550	−	0.810636i	$-0.300879\pi$
$761$	891.207			1.17110			0.585550	+	0.810636i	$0.300879\pi$
$762$	11.3638	−	8.25627i	0.0149131	−	0.0108350i
$763$		−	1679.77i		−	2.20154i
$764$	−1232.93	−	400.604i	−1.61379	−	0.524351i
$765$		0			0
$766$	507.390	+	698.363i	0.662389	+	0.911700i
$767$		−	34.8740i		−	0.0454681i
$768$	926.217	−	300.946i	1.20601	−	0.391857i
$769$	−835.430			−1.08639			−0.543193	−	0.839608i	$-0.682785\pi$
$769$	−835.430			−1.08639			−0.543193	+	0.839608i	$0.682785\pi$
$770$		0			0
$771$		−	977.898i		−	1.26835i
$772$	−224.689	+	691.521i	−0.291048	+	0.895753i
$773$	−213.522			−0.276225			−0.138112	−	0.990417i	$-0.544103\pi$
$773$	−213.522			−0.276225			−0.138112	+	0.990417i	$0.544103\pi$
$774$	−12.9180	−	17.7800i	−0.0166899	−	0.0229716i
$775$		0			0
$776$	−96.8266	−	298.002i	−0.124777	−	0.384023i
$777$	−853.050			−1.09788
$778$	−479.512	+	348.386i	−0.616339	+	0.447796i
$779$			389.503i			0.500004i
$780$		0			0
$781$	70.7926			0.0906436
$782$	452.551	+	622.883i	0.578710	+	0.796526i
$783$		−	93.1976i		−	0.119026i
$784$	302.387	+	219.697i	0.385698	+	0.280226i
$785$		0			0
$786$	1388.71	−	1008.96i	1.76681	−	1.28366i
$787$			370.182i			0.470371i	0.971951	+	0.235185i	$0.0755697\pi$
$787$			370.182i			0.470371i	−0.971951	+	0.235185i	$0.924430\pi$
$788$	−173.698	+	534.588i	−0.220429	+	0.678411i
$789$	624.531			0.791547
$790$		0			0
$791$		−	691.397i		−	0.874080i
$792$	−74.7802	+	24.2976i	−0.0944194	+	0.0306787i
$793$	12.3406			0.0155619
$794$	139.459	−	101.323i	0.175641	−	0.127611i
$795$		0			0
$796$	640.000	+	207.949i	0.804020	+	0.261242i
$797$	−274.426			−0.344323			−0.172162	−	0.985069i	$-0.555075\pi$
$797$	−274.426			−0.344323			−0.172162	+	0.985069i	$0.555075\pi$
$798$	−357.771	−	492.429i	−0.448334	−	0.617079i
$799$			844.414i			1.05684i
$800$		0			0
$801$	−369.056			−0.460744
$802$	716.784	−	520.774i	0.893746	−	0.649344i
$803$		−	247.063i		−	0.307675i
$804$	−417.889	+	1286.13i	−0.519762	+	1.59966i
$805$		0			0
$806$	−26.3344	−	36.2461i	−0.0326729	−	0.0449704i
$807$			134.956i			0.167232i
$808$	−246.938	−	759.997i	−0.305616	−	0.940591i
$809$	665.214			0.822266			0.411133	−	0.911575i	$-0.365133\pi$
$809$	665.214			0.822266			0.411133	+	0.911575i	$0.365133\pi$
$810$		0			0
$811$		−	360.665i		−	0.444717i	−0.974965	−	0.222358i	$-0.928624\pi$
$811$		−	360.665i		−	0.444717i	0.974965	−	0.222358i	$-0.0713755\pi$
$812$	224.721	+	73.0164i	0.276750	+	0.0899217i
$813$	1137.27			1.39886
$814$	−55.6594	−	76.6086i	−0.0683777	−	0.0941138i
$815$		0			0
$816$	−854.663	+	1176.34i	−1.04738	+	1.44160i
$817$	18.8854			0.0231156
$818$	102.600	−	74.5432i	0.125428	−	0.0911286i
$819$			21.9773i			0.0268344i
$820$		0			0
$821$	−666.899			−0.812301			−0.406151	−	0.913806i	$-0.633129\pi$
$821$	−666.899			−0.812301			−0.406151	+	0.913806i	$0.633129\pi$
$822$	−236.276	−	325.205i	−0.287440	−	0.395627i
$823$			122.433i			0.148764i	0.997230	+	0.0743822i	$0.0236985\pi$
$823$			122.433i			0.148764i	−0.997230	+	0.0743822i	$0.976302\pi$
$824$	272.170	−	88.4335i	0.330304	−	0.107322i
$825$		0			0
$826$	−1016.66	+	738.644i	−1.23082	+	0.894242i
$827$		−	1532.98i		−	1.85366i	−0.375477	−	0.926832i	$-0.622521\pi$
$827$		−	1532.98i		−	1.85366i	0.375477	−	0.926832i	$-0.377479\pi$
$828$	−335.469	−	109.000i	−0.405156	−	0.131643i
$829$	−195.475			−0.235796			−0.117898	−	0.993026i	$-0.537616\pi$
$829$	−195.475			−0.235796			−0.117898	+	0.993026i	$0.537616\pi$
$830$		0			0
$831$		−	1739.47i		−	2.09322i
$832$	24.4458	−	17.7609i	0.0293820	−	0.0213473i
$833$	−558.053			−0.669931
$834$	−774.663	+	562.825i	−0.928852	+	0.674850i
$835$		0			0
$836$	20.8792	−	64.2597i	0.0249752	−	0.0768656i
$837$	636.774			0.760781
$838$	−512.170	−	704.942i	−0.611182	−	0.841219i
$839$		−	1325.97i		−	1.58041i	−0.612840	−	0.790207i	$-0.709973\pi$
$839$		−	1325.97i		−	1.58041i	0.612840	−	0.790207i	$-0.290027\pi$
$840$		0			0
$841$	−792.777			−0.942660
$842$	−943.171	+	685.254i	−1.12016	+	0.813841i
$843$			21.4532i			0.0254487i
$844$	357.390	+	116.123i	0.423448	+	0.137587i
$845$		0			0
$846$	−227.390	−	312.976i	−0.268783	−	0.369948i
$847$			1001.85i			1.18282i
$848$	−280.105	−	203.508i	−0.330313	−	0.239986i
$849$	646.407			0.761375
$850$		0			0
$851$		−	424.801i		−	0.499179i
$852$	−185.337	+	570.410i	−0.217532	+	0.669495i
$853$	−1055.28			−1.23714			−0.618570	−	0.785730i	$-0.712288\pi$
$853$	−1055.28			−1.23714			−0.618570	+	0.785730i	$0.712288\pi$
$854$	−261.378	−	359.756i	−0.306063	−	0.421259i
$855$		0			0
$856$	921.378	−	299.374i	1.07638	−	0.349736i
$857$	−155.378			−0.181304			−0.0906521	−	0.995883i	$-0.528895\pi$
$857$	−155.378			−0.181304			−0.0906521	+	0.995883i	$0.528895\pi$
$858$	−5.21981	+	3.79241i	−0.00608369	+	0.00442006i
$859$			226.033i			0.263136i	0.991307	+	0.131568i	$0.0420011\pi$
$859$			226.033i			0.263136i	−0.991307	+	0.131568i	$0.957999\pi$
$860$		0			0
$861$	−1340.26			−1.55664
$862$	441.876	+	608.190i	0.512617	+	0.705557i
$863$			930.702i			1.07845i	0.842162	+	0.539225i	$0.181283\pi$
$863$			930.702i			1.07845i	−0.842162	+	0.539225i	$0.818717\pi$
$864$			429.465i			0.497066i
$865$		0			0
$866$	595.702	−	432.803i	0.687878	−	0.499772i
$867$		−	1071.51i		−	1.23588i
$868$	−498.885	+	1535.41i	−0.574753	+	1.76891i
$869$	204.223			0.235009
$870$		0			0
$871$			41.9584i			0.0481727i
$872$	488.170	+	1502.43i	0.559828	+	1.72297i
$873$	−214.328			−0.245508
$874$	245.220	−	178.163i	0.280572	−	0.203847i
$875$		0			0
$876$	1990.70	+	646.819i	2.27249	+	0.738377i
$877$	33.5217			0.0382231			0.0191115	−	0.999817i	$-0.493916\pi$
$877$	33.5217			0.0382231			0.0191115	+	0.999817i	$0.493916\pi$
$878$	568.446	+	782.399i	0.647433	+	0.891115i
$879$		−	102.178i		−	0.116244i
$880$		0			0
$881$	−933.850			−1.05999			−0.529994	−	0.848001i	$-0.677806\pi$
$881$	−933.850			−1.05999			−0.529994	+	0.848001i	$0.677806\pi$
$882$	206.838	−	150.276i	0.234510	−	0.170382i
$883$			542.308i			0.614166i	0.951683	+	0.307083i	$0.0993529\pi$
$883$			542.308i			0.614166i	−0.951683	+	0.307083i	$0.900647\pi$
$884$	−13.9412	+	42.9065i	−0.0157706	+	0.0485368i
$885$		0			0
$886$	328.197	+	451.724i	0.370425	+	0.509846i
$887$		−	714.720i		−	0.805773i	−0.915250	−	0.402886i	$-0.868007\pi$
$887$		−	714.720i		−	0.805773i	0.915250	−	0.402886i	$-0.131993\pi$
$888$	762.991	−	247.911i	0.859224	−	0.279179i
$889$	−15.7044			−0.0176652
$890$		0			0
$891$		−	180.159i		−	0.202199i
$892$	−814.237	−	264.562i	−0.912822	−	0.296594i
$893$	332.433			0.372266
$894$	−594.663	−	818.483i	−0.665171	−	0.915529i
$895$		0			0
$896$	−1035.54	−	336.468i	−1.15574	−	0.375522i
$897$	−28.9443			−0.0322679
$898$	1223.36	−	888.824i	1.36232	−	0.989782i
$899$			329.484i			0.366500i
$900$		0			0
$901$	516.932			0.573731
$902$	−87.4489	−	120.363i	−0.0969500	−	0.133440i
$903$			64.9839i			0.0719645i
$904$	200.932	+	618.405i	0.222270	+	0.684076i
$905$		0			0
$906$	−930.820	+	676.281i	−1.02740	+	0.746447i
$907$		−	347.233i		−	0.382837i	−0.981509	−	0.191418i	$-0.938691\pi$
$907$		−	347.233i		−	0.382837i	0.981509	−	0.191418i	$-0.0613087\pi$
$908$	157.580	+	51.2010i	0.173547	+	0.0563888i
$909$	−546.604			−0.601324
$910$		0			0
$911$			1427.54i			1.56701i	0.621386	+	0.783504i	$0.286570\pi$
$911$			1427.54i			1.56701i	−0.621386	+	0.783504i	$0.713430\pi$
$912$	463.108	+	336.468i	0.507794	+	0.368934i
$913$	38.1517			0.0417871
$914$	−462.227	+	335.827i	−0.505719	+	0.367426i
$915$		0			0
$916$	90.5774	−	278.769i	0.0988836	−	0.304332i
$917$	−1919.15			−2.09286
$918$	−376.892	−	518.747i	−0.410557	−	0.565084i
$919$		−	569.162i		−	0.619327i	−0.950846	−	0.309664i	$-0.899784\pi$
$919$		−	569.162i		−	0.619327i	0.950846	−	0.309664i	$-0.100216\pi$
$920$		0			0
$921$	449.017			0.487532
$922$	−160.371	+	116.516i	−0.173938	+	0.126373i
$923$			18.6089i			0.0201614i
$924$	221.115	+	71.8445i	0.239301	+	0.0777538i
$925$		0			0
$926$	741.319	+	1020.34i	0.800560	+	1.10188i
$927$		−	195.750i		−	0.211165i
$928$	−222.217			−0.239458
$929$	1535.96			1.65335			0.826675	−	0.562680i	$-0.190230\pi$
$929$	1535.96			1.65335			0.826675	+	0.562680i	$0.190230\pi$
$930$		0			0
$931$			219.697i			0.235980i
$932$	379.534	−	1168.09i	0.407225	−	1.25331i
$933$	463.489			0.496773
$934$	−583.094	−	802.561i	−0.624298	−	0.859273i
$935$		0			0
$936$	−6.38699	−	19.6571i	−0.00682371	−	0.0210012i
$937$	−338.721			−0.361496			−0.180748	−	0.983529i	$-0.557852\pi$
$937$	−338.721			−0.361496			−0.180748	+	0.983529i	$0.557852\pi$
$938$	1223.18	−	888.693i	1.30403	−	0.947434i
$939$			835.210i			0.889468i
$940$		0			0
$941$	1439.77			1.53004			0.765022	−	0.644004i	$-0.222728\pi$
$941$	1439.77			1.53004			0.765022	+	0.644004i	$0.222728\pi$
$942$	−164.341	−	226.195i	−0.174459	−	0.240123i
$943$		−	667.424i		−	0.707766i
$944$	694.663	−	956.121i	0.735871	−	1.01284i
$945$		0			0
$946$	−5.83592	+	4.24005i	−0.00616905	+	0.00448208i
$947$		−	656.135i		−	0.692856i	−0.938077	−	0.346428i	$-0.887394\pi$
$947$		−	656.135i		−	0.692856i	0.938077	−	0.346428i	$-0.112606\pi$
$948$	−534.663	+	1645.52i	−0.563990	+	1.73578i
$949$	64.9443			0.0684344
$950$		0			0
$951$			1395.62i			1.46752i
$952$	1546.10	−	502.358i	1.62405	−	0.527687i
$953$	−436.675			−0.458211			−0.229105	−	0.973402i	$-0.573580\pi$
$953$	−436.675			−0.458211			−0.229105	+	0.973402i	$0.573580\pi$
$954$	−191.597	+	139.203i	−0.200835	+	0.145915i
$955$		0			0
$956$	−163.226	−	53.0353i	−0.170739	−	0.0554763i
$957$	47.4489			0.0495809
$958$	680.762	+	936.988i	0.710607	+	0.978067i
$959$			449.423i			0.468637i
$960$		0			0
$961$	−1290.20			−1.34256
$962$	20.1378	−	14.6309i	0.0209332	−	0.0152089i
$963$		−	662.671i		−	0.688132i
$964$	−166.971	+	513.883i	−0.173206	+	0.533073i
$965$		0			0
$966$	613.050	+	843.790i	0.634627	+	0.873489i
$967$			903.436i			0.934267i	0.884187	+	0.467133i	$0.154713\pi$
$967$			903.436i			0.934267i	−0.884187	+	0.467133i	$0.845287\pi$
$968$	−291.153	−	896.078i	−0.300778	−	0.925700i
$969$	−854.663			−0.882005
$970$		0			0
$971$		−	1866.89i		−	1.92265i	−0.275420	−	0.961324i	$-0.588817\pi$
$971$		−	1866.89i		−	1.92265i	0.275420	−	0.961324i	$-0.411183\pi$
$972$	992.125	+	322.361i	1.02071	+	0.331647i
$973$	1070.56			1.10026
$974$	−736.334	−	1013.48i	−0.755990	−	1.04053i
$975$		0			0
$976$	338.334	+	245.814i	0.346654	+	0.251859i
$977$	1073.95			1.09923			0.549615	−	0.835418i	$-0.314774\pi$
$977$	1073.95			1.09923			0.549615	+	0.835418i	$0.314774\pi$
$978$	−1864.18	+	1354.40i	−1.90611	+	1.38487i
$979$			121.135i			0.123733i
$980$		0			0
$981$	1080.58			1.10151
$982$	26.2167	+	36.0842i	0.0266973	+	0.0367456i
$983$		−	534.114i		−	0.543351i	−0.962389	−	0.271675i	$-0.912422\pi$
$983$		−	534.114i		−	0.543351i	0.962389	−	0.271675i	$-0.0875777\pi$
$984$	1198.77	−	389.503i	1.21826	−	0.395837i
$985$		0			0
$986$	268.413	−	195.014i	0.272224	−	0.197783i
$987$			1143.89i			1.15895i
$988$	16.8916	+	5.48843i	0.0170968	+	0.00555509i
$989$	−32.3607			−0.0327206
$990$		0			0
$991$			520.419i			0.525146i	0.964912	+	0.262573i	$0.0845710\pi$
$991$			520.419i			0.525146i	−0.964912	+	0.262573i	$0.915429\pi$
$992$		−	1518.30i		−	1.53054i
$993$	−619.502			−0.623869
$994$	542.492	−	394.144i	0.545767	−	0.396523i
$995$		0			0
$996$	−99.8823	+	307.406i	−0.100283	+	0.308641i
$997$	−457.680			−0.459057			−0.229528	−	0.973302i	$-0.573718\pi$
$997$	−457.680			−0.459057			−0.229528	+	0.973302i	$0.573718\pi$
$998$	737.508	+	1015.09i	0.738986	+	1.01713i
$999$			353.781i			0.354135i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	100.3.b.f.51.3		4
3.2	odd	2		900.3.c.k.451.2		4
4.3	odd	2	inner	100.3.b.f.51.4		4
5.2	odd	4		100.3.d.b.99.6		8
5.3	odd	4		100.3.d.b.99.3		8
5.4	even	2		20.3.b.a.11.2	yes	4
8.3	odd	2		1600.3.b.s.1151.1		4
8.5	even	2		1600.3.b.s.1151.4		4
12.11	even	2		900.3.c.k.451.1		4
15.2	even	4		900.3.f.e.199.3		8
15.8	even	4		900.3.f.e.199.6		8
15.14	odd	2		180.3.c.a.91.3		4
20.3	even	4		100.3.d.b.99.5		8
20.7	even	4		100.3.d.b.99.4		8
20.19	odd	2		20.3.b.a.11.1	✓	4
40.3	even	4		1600.3.h.n.1599.8		8
40.13	odd	4		1600.3.h.n.1599.1		8
40.19	odd	2		320.3.b.c.191.4		4
40.27	even	4		1600.3.h.n.1599.2		8
40.29	even	2		320.3.b.c.191.1		4
40.37	odd	4		1600.3.h.n.1599.7		8
60.23	odd	4		900.3.f.e.199.4		8
60.47	odd	4		900.3.f.e.199.5		8
60.59	even	2		180.3.c.a.91.4		4
80.19	odd	4		1280.3.g.e.1151.7		8
80.29	even	4		1280.3.g.e.1151.1		8
80.59	odd	4		1280.3.g.e.1151.2		8
80.69	even	4		1280.3.g.e.1151.8		8
120.29	odd	2		2880.3.e.e.2431.3		4
120.59	even	2		2880.3.e.e.2431.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
20.3.b.a.11.1	✓	4	20.19	odd	2
20.3.b.a.11.2	yes	4	5.4	even	2
100.3.b.f.51.3		4	1.1	even	1	trivial
100.3.b.f.51.4		4	4.3	odd	2	inner
100.3.d.b.99.3		8	5.3	odd	4
100.3.d.b.99.4		8	20.7	even	4
100.3.d.b.99.5		8	20.3	even	4
100.3.d.b.99.6		8	5.2	odd	4
180.3.c.a.91.3		4	15.14	odd	2
180.3.c.a.91.4		4	60.59	even	2
320.3.b.c.191.1		4	40.29	even	2
320.3.b.c.191.4		4	40.19	odd	2
900.3.c.k.451.1		4	12.11	even	2
900.3.c.k.451.2		4	3.2	odd	2
900.3.f.e.199.3		8	15.2	even	4
900.3.f.e.199.4		8	60.23	odd	4
900.3.f.e.199.5		8	60.47	odd	4
900.3.f.e.199.6		8	15.8	even	4
1280.3.g.e.1151.1		8	80.29	even	4
1280.3.g.e.1151.2		8	80.59	odd	4
1280.3.g.e.1151.7		8	80.19	odd	4
1280.3.g.e.1151.8		8	80.69	even	4
1600.3.b.s.1151.1		4	8.3	odd	2
1600.3.b.s.1151.4		4	8.5	even	2
1600.3.h.n.1599.1		8	40.13	odd	4
1600.3.h.n.1599.2		8	40.27	even	4
1600.3.h.n.1599.7		8	40.37	odd	4
1600.3.h.n.1599.8		8	40.3	even	4
2880.3.e.e.2431.3		4	120.29	odd	2
2880.3.e.e.2431.4		4	120.59	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 100 = 2^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	100.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(1.61803 - 1.17557i) q^{2} -3.80423i q^{3} +(1.23607 - 3.80423i) q^{4} +(-4.47214 - 6.15537i) q^{6} +8.50651i q^{7} +(-2.47214 - 7.60845i) q^{8} -5.47214 q^{9} +O(q^{10})\)	\(q+(1.61803 - 1.17557i) q^{2} -3.80423i q^{3} +(1.23607 - 3.80423i) q^{4} +(-4.47214 - 6.15537i) q^{6} +8.50651i q^{7} +(-2.47214 - 7.60845i) q^{8} -5.47214 q^{9} +1.79611i q^{11} +(-14.4721 - 4.70228i) q^{12} -0.472136 q^{13} +(10.0000 + 13.7638i) q^{14} +(-12.9443 - 9.40456i) q^{16} +23.8885 q^{17} +(-8.85410 + 6.43288i) q^{18} -9.40456i q^{19} +32.3607 q^{21} +(2.11146 + 2.90617i) q^{22} +16.1150i q^{23} +(-28.9443 + 9.40456i) q^{24} +(-0.763932 + 0.555029i) q^{26} -13.4208i q^{27} +(32.3607 + 10.5146i) q^{28} +6.94427 q^{29} +47.4468i q^{31} -32.0000 q^{32} +6.83282 q^{33} +(38.6525 - 28.0827i) q^{34} +(-6.76393 + 20.8172i) q^{36} -26.3607 q^{37} +(-11.0557 - 15.2169i) q^{38} +1.79611i q^{39} -41.4164 q^{41} +(52.3607 - 38.0423i) q^{42} +2.00811i q^{43} +(6.83282 + 2.22012i) q^{44} +(18.9443 + 26.0746i) q^{46} +35.3481i q^{47} +(-35.7771 + 49.2429i) q^{48} -23.3607 q^{49} -90.8774i q^{51} +(-0.583592 + 1.79611i) q^{52} +21.6393 q^{53} +(-15.7771 - 21.7153i) q^{54} +(64.7214 - 21.0292i) q^{56} -35.7771 q^{57} +(11.2361 - 8.16348i) q^{58} +73.8644i q^{59} -26.1378 q^{61} +(55.7771 + 76.7706i) q^{62} -46.5488i q^{63} +(-51.7771 + 37.6183i) q^{64} +(11.0557 - 8.03246i) q^{66} -88.8693i q^{67} +(29.5279 - 90.8774i) q^{68} +61.3050 q^{69} -39.4144i q^{71} +(13.5279 + 41.6345i) q^{72} -137.554 q^{73} +(-42.6525 + 30.9888i) q^{74} +(-35.7771 - 11.6247i) q^{76} -15.2786 q^{77} +(2.11146 + 2.90617i) q^{78} -113.703i q^{79} -100.305 q^{81} +(-67.0132 + 48.6879i) q^{82} -21.2412i q^{83} +(40.0000 - 123.107i) q^{84} +(2.36068 + 3.24920i) q^{86} -26.4176i q^{87} +(13.6656 - 4.44023i) q^{88} +67.4427 q^{89} -4.01623i q^{91} +(61.3050 + 19.9192i) q^{92} +180.498 q^{93} +(41.5542 + 57.1944i) q^{94} +121.735i q^{96} +39.1672 q^{97} +(-37.7984 + 27.4621i) q^{98} -9.82857i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{2} - 4 q^{4} + 8 q^{8} - 4 q^{9}+O(q^{10}) \) 4 * q + 2 * q^2 - 4 * q^4 + 8 * q^8 - 4 * q^9	\( 4 q + 2 q^{2} - 4 q^{4} + 8 q^{8} - 4 q^{9} - 40 q^{12} + 16 q^{13} + 40 q^{14} - 16 q^{16} + 24 q^{17} - 22 q^{18} + 40 q^{21} + 80 q^{22} - 80 q^{24} - 12 q^{26} + 40 q^{28} - 8 q^{29} - 128 q^{32} - 80 q^{33} + 92 q^{34} - 36 q^{36} - 16 q^{37} - 80 q^{38} - 112 q^{41} + 120 q^{42} - 80 q^{44} + 40 q^{46} - 4 q^{49} - 56 q^{52} + 176 q^{53} + 80 q^{54} + 80 q^{56} + 36 q^{58} + 128 q^{61} + 80 q^{62} - 64 q^{64} + 80 q^{66} + 136 q^{68} + 120 q^{69} + 72 q^{72} - 264 q^{73} - 108 q^{74} - 240 q^{77} + 80 q^{78} - 276 q^{81} - 116 q^{82} + 160 q^{84} - 80 q^{86} - 160 q^{88} - 88 q^{89} + 120 q^{92} + 400 q^{93} - 120 q^{94} + 264 q^{97} - 102 q^{98}+O(q^{100}) \) 4 * q + 2 * q^2 - 4 * q^4 + 8 * q^8 - 4 * q^9 - 40 * q^12 + 16 * q^13 + 40 * q^14 - 16 * q^16 + 24 * q^17 - 22 * q^18 + 40 * q^21 + 80 * q^22 - 80 * q^24 - 12 * q^26 + 40 * q^28 - 8 * q^29 - 128 * q^32 - 80 * q^33 + 92 * q^34 - 36 * q^36 - 16 * q^37 - 80 * q^38 - 112 * q^41 + 120 * q^42 - 80 * q^44 + 40 * q^46 - 4 * q^49 - 56 * q^52 + 176 * q^53 + 80 * q^54 + 80 * q^56 + 36 * q^58 + 128 * q^61 + 80 * q^62 - 64 * q^64 + 80 * q^66 + 136 * q^68 + 120 * q^69 + 72 * q^72 - 264 * q^73 - 108 * q^74 - 240 * q^77 + 80 * q^78 - 276 * q^81 - 116 * q^82 + 160 * q^84 - 80 * q^86 - 160 * q^88 - 88 * q^89 + 120 * q^92 + 400 * q^93 - 120 * q^94 + 264 * q^97 - 102 * q^98

Introduction

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Modular forms

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