LMFDB - Embedded newform 105.3.h.a.76.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [105,3,Mod(76,105)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(105, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("105.76");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 105 = 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	105.h (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:	$2.86104277578$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 2 x^{11} + 21 x^{10} - 26 x^{9} + 295 x^{8} - 372 x^{7} + 1704 x^{6} - 1074 x^{5} + 5613 x^{4} + \cdots + 441 $ x^12 - 2x^11 + 21x^10 - 26x^9 + 295x^8 - 372x^7 + 1704x^6 - 1074x^5 + 5613x^4 - 5472x^3 + 4950x^2 - 1638*x + 441
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{10} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			76.1
Root			$1.86875 - 3.23677i$ of defining polynomial
Character	$\chi$	$=$	105.76
Dual form			105.3.h.a.76.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-3.80460 q^{2} -1.73205i q^{3} +10.4750 q^{4} -2.23607i q^{5} +6.58976i q^{6} +(2.44621 + 6.55866i) q^{7} -24.6348 q^{8} -3.00000 q^{9} +O(q^{10})$	\(q-3.80460 q^{2} -1.73205i q^{3} +10.4750 q^{4} -2.23607i q^{5} +6.58976i q^{6} +(2.44621 + 6.55866i) q^{7} -24.6348 q^{8} -3.00000 q^{9} +8.50735i q^{10} +14.4489 q^{11} -18.1432i q^{12} -16.9427i q^{13} +(-9.30684 - 24.9531i) q^{14} -3.87298 q^{15} +51.8255 q^{16} -13.0093i q^{17} +11.4138 q^{18} -18.6908i q^{19} -23.4228i q^{20} +(11.3599 - 4.23695i) q^{21} -54.9723 q^{22} +10.3861 q^{23} +42.6687i q^{24} -5.00000 q^{25} +64.4602i q^{26} +5.19615i q^{27} +(25.6240 + 68.7020i) q^{28} -13.7269 q^{29} +14.7352 q^{30} -42.4383i q^{31} -98.6363 q^{32} -25.0262i q^{33} +49.4951i q^{34} +(14.6656 - 5.46988i) q^{35} -31.4250 q^{36} +28.7434 q^{37} +71.1112i q^{38} -29.3456 q^{39} +55.0850i q^{40} +28.8060i q^{41} +(-43.2200 + 16.1199i) q^{42} -5.84593 q^{43} +151.352 q^{44} +6.70820i q^{45} -39.5151 q^{46} -10.5013i q^{47} -89.7644i q^{48} +(-37.0322 + 32.0877i) q^{49} +19.0230 q^{50} -22.5327 q^{51} -177.475i q^{52} +81.9074 q^{53} -19.7693i q^{54} -32.3087i q^{55} +(-60.2617 - 161.571i) q^{56} -32.3735 q^{57} +52.2254 q^{58} -35.1680i q^{59} -40.5695 q^{60} +68.4826i q^{61} +161.461i q^{62} +(-7.33862 - 19.6760i) q^{63} +167.970 q^{64} -37.8850 q^{65} +95.2149i q^{66} +47.4637 q^{67} -136.272i q^{68} -17.9893i q^{69} +(-55.7968 + 20.8107i) q^{70} +47.6548 q^{71} +73.9043 q^{72} +125.967i q^{73} -109.357 q^{74} +8.66025i q^{75} -195.786i q^{76} +(35.3450 + 94.7655i) q^{77} +111.648 q^{78} -129.527 q^{79} -115.885i q^{80} +9.00000 q^{81} -109.595i q^{82} +42.6906i q^{83} +(118.995 - 44.3820i) q^{84} -29.0896 q^{85} +22.2414 q^{86} +23.7757i q^{87} -355.945 q^{88} -25.5329i q^{89} -25.5220i q^{90} +(111.122 - 41.4453i) q^{91} +108.795 q^{92} -73.5053 q^{93} +39.9533i q^{94} -41.7940 q^{95} +170.843i q^{96} -28.7310i q^{97} +(140.893 - 122.081i) q^{98} -43.3467 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 4 q^{2} + 44 q^{4} - 8 q^{7} + 4 q^{8} - 36 q^{9}+O(q^{10}) $ 12 * q - 4 * q^2 + 44 * q^4 - 8 * q^7 + 4 * q^8 - 36 * q^9	$ 12 q - 4 q^{2} + 44 q^{4} - 8 q^{7} + 4 q^{8} - 36 q^{9} - 16 q^{11} - 40 q^{14} + 92 q^{16} + 12 q^{18} + 36 q^{21} - 88 q^{22} - 64 q^{23} - 60 q^{25} + 88 q^{28} + 104 q^{29} - 228 q^{32} + 60 q^{35} - 132 q^{36} + 32 q^{37} - 24 q^{39} - 60 q^{42} + 152 q^{43} + 192 q^{44} + 200 q^{46} + 60 q^{49} + 20 q^{50} + 24 q^{51} + 176 q^{53} - 368 q^{56} - 240 q^{57} - 400 q^{58} + 24 q^{63} - 20 q^{64} - 240 q^{65} + 168 q^{67} - 60 q^{70} + 32 q^{71} - 12 q^{72} + 184 q^{74} + 8 q^{77} + 456 q^{78} + 120 q^{79} + 108 q^{81} + 108 q^{84} + 120 q^{85} + 400 q^{86} - 536 q^{88} + 24 q^{91} + 192 q^{92} + 48 q^{93} + 884 q^{98} + 48 q^{99}+O(q^{100}) $ 12 * q - 4 * q^2 + 44 * q^4 - 8 * q^7 + 4 * q^8 - 36 * q^9 - 16 * q^11 - 40 * q^14 + 92 * q^16 + 12 * q^18 + 36 * q^21 - 88 * q^22 - 64 * q^23 - 60 * q^25 + 88 * q^28 + 104 * q^29 - 228 * q^32 + 60 * q^35 - 132 * q^36 + 32 * q^37 - 24 * q^39 - 60 * q^42 + 152 * q^43 + 192 * q^44 + 200 * q^46 + 60 * q^49 + 20 * q^50 + 24 * q^51 + 176 * q^53 - 368 * q^56 - 240 * q^57 - 400 * q^58 + 24 * q^63 - 20 * q^64 - 240 * q^65 + 168 * q^67 - 60 * q^70 + 32 * q^71 - 12 * q^72 + 184 * q^74 + 8 * q^77 + 456 * q^78 + 120 * q^79 + 108 * q^81 + 108 * q^84 + 120 * q^85 + 400 * q^86 - 536 * q^88 + 24 * q^91 + 192 * q^92 + 48 * q^93 + 884 * q^98 + 48 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/105\mathbb{Z}\right)^\times$.

$n$	$22$	$31$	$71$
$\chi(n)$	$1$	$-1$	$1$

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 $

$2$	−3.80460			−1.90230			−0.951150	−	0.308728i	$-0.900097\pi$
$2$	−3.80460			−1.90230			−0.951150	+	0.308728i	$0.900097\pi$
$3$		−	1.73205i		−	0.577350i
$3$		−	1.73205i		−	0.577350i
$4$	10.4750			2.61875
$5$		−	2.23607i		−	0.447214i
$5$		−	2.23607i		−	0.447214i
$6$			6.58976i			1.09829i
$7$	2.44621	+	6.55866i	0.349458	+	0.936952i
$7$	2.44621	+	6.55866i	0.349458	+	0.936952i
$8$	−24.6348			−3.07935
$9$	−3.00000			−0.333333
$10$			8.50735i			0.850735i
$11$	14.4489			1.31354			0.656768	−	0.754092i	$-0.271923\pi$
$11$	14.4489			1.31354			0.656768	+	0.754092i	$0.271923\pi$
$12$		−	18.1432i		−	1.51193i
$13$		−	16.9427i		−	1.30329i	−0.758526	−	0.651643i	$-0.774080\pi$
$13$		−	16.9427i		−	1.30329i	0.758526	−	0.651643i	$-0.225920\pi$
$14$	−9.30684	−	24.9531i	−0.664774	−	1.78236i
$15$	−3.87298			−0.258199
$16$	51.8255			3.23909
$17$		−	13.0093i		−	0.765251i	−0.923904	−	0.382625i	$-0.875020\pi$
$17$		−	13.0093i		−	0.765251i	0.923904	−	0.382625i	$-0.124980\pi$
$18$	11.4138			0.634100
$19$		−	18.6908i		−	0.983729i	−0.870672	−	0.491864i	$-0.836316\pi$
$19$		−	18.6908i		−	0.983729i	0.870672	−	0.491864i	$-0.163684\pi$
$20$		−	23.4228i		−	1.17114i
$21$	11.3599	−	4.23695i	0.540950	−	0.201760i
$22$	−54.9723			−2.49874
$23$	10.3861			0.451570			0.225785	−	0.974177i	$-0.427505\pi$
$23$	10.3861			0.451570			0.225785	+	0.974177i	$0.427505\pi$
$24$			42.6687i			1.77786i
$25$	−5.00000			−0.200000
$26$			64.4602i			2.47924i
$27$			5.19615i			0.192450i
$28$	25.6240	+	68.7020i	0.915142	+	2.45364i
$29$	−13.7269			−0.473341			−0.236671	−	0.971590i	$-0.576056\pi$
$29$	−13.7269			−0.473341			−0.236671	+	0.971590i	$0.576056\pi$
$30$	14.7352			0.491172
$31$		−	42.4383i		−	1.36898i	−0.729024	−	0.684488i	$-0.760026\pi$
$31$		−	42.4383i		−	1.36898i	0.729024	−	0.684488i	$-0.239974\pi$
$32$	−98.6363			−3.08238
$33$		−	25.0262i		−	0.758371i
$34$			49.4951i			1.45574i
$35$	14.6656	−	5.46988i	0.419018	−	0.156282i
$36$	−31.4250			−0.872916
$37$	28.7434			0.776850			0.388425	−	0.921480i	$-0.373019\pi$
$37$	28.7434			0.776850			0.388425	+	0.921480i	$0.373019\pi$
$38$			71.1112i			1.87135i
$39$	−29.3456			−0.752452
$40$			55.0850i			1.37713i
$41$			28.8060i			0.702585i	0.936266	+	0.351293i	$0.114258\pi$
$41$			28.8060i			0.702585i	−0.936266	+	0.351293i	$0.885742\pi$
$42$	−43.2200	+	16.1199i	−1.02905	+	0.383807i
$43$	−5.84593			−0.135952			−0.0679759	−	0.997687i	$-0.521654\pi$
$43$	−5.84593			−0.135952			−0.0679759	+	0.997687i	$0.521654\pi$
$44$	151.352			3.43982
$45$			6.70820i			0.149071i
$46$	−39.5151			−0.859023
$47$		−	10.5013i		−	0.223432i	−0.993740	−	0.111716i	$-0.964365\pi$
$47$		−	10.5013i		−	0.223432i	0.993740	−	0.111716i	$-0.0356347\pi$
$48$		−	89.7644i		−	1.87009i
$49$	−37.0322	+	32.0877i	−0.755758	+	0.654851i
$50$	19.0230			0.380460
$51$	−22.5327			−0.441818
$52$		−	177.475i		−	3.41298i
$53$	81.9074			1.54542			0.772712	−	0.634757i	$-0.218900\pi$
$53$	81.9074			1.54542			0.772712	+	0.634757i	$0.218900\pi$
$54$		−	19.7693i		−	0.366098i
$55$		−	32.3087i		−	0.587432i
$56$	−60.2617	−	161.571i	−1.07610	−	2.88520i
$57$	−32.3735			−0.567956
$58$	52.2254			0.900438
$59$		−	35.1680i		−	0.596067i	−0.954555	−	0.298033i	$-0.903669\pi$
$59$		−	35.1680i		−	0.596067i	0.954555	−	0.298033i	$-0.0963307\pi$
$60$	−40.5695			−0.676158
$61$			68.4826i			1.12267i	0.827590	+	0.561333i	$0.189711\pi$
$61$			68.4826i			1.12267i	−0.827590	+	0.561333i	$0.810289\pi$
$62$			161.461i			2.60421i
$63$	−7.33862	−	19.6760i	−0.116486	−	0.312317i
$64$	167.970			2.62453
$65$	−37.8850			−0.582847
$66$			95.2149i			1.44265i
$67$	47.4637			0.708414			0.354207	−	0.935167i	$-0.384751\pi$
$67$	47.4637			0.708414			0.354207	+	0.935167i	$0.384751\pi$
$68$		−	136.272i		−	2.00400i
$69$		−	17.9893i		−	0.260714i
$70$	−55.7968	+	20.8107i	−0.797098	+	0.297296i
$71$	47.6548			0.671194			0.335597	−	0.942006i	$-0.391062\pi$
$71$	47.6548			0.671194			0.335597	+	0.942006i	$0.391062\pi$
$72$	73.9043			1.02645
$73$			125.967i			1.72557i	0.505569	+	0.862786i	$0.331283\pi$
$73$			125.967i			1.72557i	−0.505569	+	0.862786i	$0.668717\pi$
$74$	−109.357			−1.47780
$75$			8.66025i			0.115470i
$76$		−	195.786i		−	2.57614i
$77$	35.3450	+	94.7655i	0.459026	+	1.23072i
$78$	111.648			1.43139
$79$	−129.527			−1.63958			−0.819790	−	0.572665i	$-0.805910\pi$
$79$	−129.527			−1.63958			−0.819790	+	0.572665i	$0.805910\pi$
$80$		−	115.885i		−	1.44857i
$81$	9.00000			0.111111
$82$		−	109.595i		−	1.33653i
$83$			42.6906i			0.514345i	0.966365	+	0.257173i	$0.0827909\pi$
$83$			42.6906i			0.514345i	−0.966365	+	0.257173i	$0.917209\pi$
$84$	118.995	−	44.3820i	1.41661	−	0.528358i
$85$	−29.0896			−0.342231
$86$	22.2414			0.258621
$87$			23.7757i			0.273284i
$88$	−355.945			−4.04483
$89$		−	25.5329i		−	0.286886i	−0.989659	−	0.143443i	$-0.954183\pi$
$89$		−	25.5329i		−	0.286886i	0.989659	−	0.143443i	$-0.0458174\pi$
$90$		−	25.5220i		−	0.283578i
$91$	111.122	−	41.4453i	1.22112	−	0.455443i
$92$	108.795			1.18255
$93$	−73.5053			−0.790379
$94$			39.9533i			0.425035i
$95$	−41.7940			−0.439937
$96$			170.843i			1.77961i
$97$		−	28.7310i		−	0.296196i	−0.988973	−	0.148098i	$-0.952685\pi$
$97$		−	28.7310i		−	0.296196i	0.988973	−	0.148098i	$-0.0473151\pi$
$98$	140.893	−	122.081i	1.43768	−	1.24572i
$99$	−43.3467			−0.437846
$100$	−52.3750			−0.523750
$101$			12.4609i			0.123375i	0.998096	+	0.0616875i	$0.0196482\pi$
$101$			12.4609i			0.123375i	−0.998096	+	0.0616875i	$0.980352\pi$
$102$	85.7280			0.840470
$103$			38.4795i			0.373587i	0.982399	+	0.186794i	$0.0598096\pi$
$103$			38.4795i			0.373587i	−0.982399	+	0.186794i	$0.940190\pi$
$104$			417.380i			4.01326i
$105$	−9.47411	−	25.4016i	−0.0902296	−	0.241920i
$106$	−311.625			−2.93986
$107$	−87.7985			−0.820547			−0.410273	−	0.911963i	$-0.634567\pi$
$107$	−87.7985			−0.820547			−0.410273	+	0.911963i	$0.634567\pi$
$108$			54.4297i			0.503978i
$109$	130.012			1.19277			0.596386	−	0.802698i	$-0.296603\pi$
$109$	130.012			1.19277			0.596386	+	0.802698i	$0.296603\pi$
$110$			122.922i			1.11747i
$111$		−	49.7851i		−	0.448515i
$112$	126.776	+	339.906i	1.13193	+	3.03487i
$113$	−158.597			−1.40351			−0.701757	−	0.712417i	$-0.747601\pi$
$113$	−158.597			−1.40351			−0.701757	+	0.712417i	$0.747601\pi$
$114$	123.168			1.08042
$115$		−	23.2241i		−	0.201948i
$116$	−143.789			−1.23956
$117$			50.8281i			0.434428i
$118$			133.800i			1.13390i
$119$	85.3234	−	31.8233i	0.717003	−	0.267423i
$120$	95.4100			0.795084
$121$	87.7709			0.725379
$122$		−	260.549i		−	2.13565i
$123$	49.8934			0.405638
$124$		−	444.541i		−	3.58501i
$125$			11.1803i			0.0894427i
$126$	27.9205	+	74.8593i	0.221591	+	0.594122i
$127$	43.0643			0.339089			0.169545	−	0.985523i	$-0.445770\pi$
$127$	43.0643			0.339089			0.169545	+	0.985523i	$0.445770\pi$
$128$	−244.513			−1.91026
$129$			10.1254i			0.0784919i
$130$	144.137			1.10875
$131$			0.686731i			0.00524222i	0.999997	+	0.00262111i	$0.000834326\pi$
$131$			0.686731i			0.00524222i	−0.999997	+	0.00262111i	$0.999166\pi$
$132$		−	262.150i		−	1.98598i
$133$	122.587	−	45.7216i	0.921707	−	0.343772i
$134$	−180.581			−1.34762
$135$	11.6190			0.0860663
$136$			320.480i			2.35647i
$137$	76.2084			0.556266			0.278133	−	0.960543i	$-0.410284\pi$
$137$	76.2084			0.556266			0.278133	+	0.960543i	$0.410284\pi$
$138$			68.4421i			0.495957i
$139$			49.0445i			0.352838i	0.984315	+	0.176419i	$0.0564514\pi$
$139$			49.0445i			0.352838i	−0.984315	+	0.176419i	$0.943549\pi$
$140$	153.622	−	57.2970i	1.09730	−	0.409264i
$141$	−18.1888			−0.128998
$142$	−181.307			−1.27681
$143$		−	244.804i		−	1.71191i
$144$	−155.476			−1.07970
$145$			30.6943i			0.211685i
$146$		−	479.253i		−	3.28256i
$147$	55.5775	+	64.1416i	0.378078	+	0.436337i
$148$	301.087			2.03437
$149$	−242.344			−1.62647			−0.813236	−	0.581934i	$-0.802296\pi$
$149$	−242.344			−1.62647			−0.813236	+	0.581934i	$0.802296\pi$
$150$		−	32.9488i		−	0.219659i
$151$	107.704			0.713271			0.356636	−	0.934244i	$-0.383924\pi$
$151$	107.704			0.713271			0.356636	+	0.934244i	$0.383924\pi$
$152$			460.445i			3.02924i
$153$			39.0278i			0.255084i
$154$	−134.474	−	360.545i	−0.873205	−	2.34120i
$155$	−94.8949			−0.612225
$156$	−307.395			−1.97048
$157$		−	76.1684i		−	0.485149i	−0.970133	−	0.242575i	$-0.922008\pi$
$157$		−	76.1684i		−	0.485149i	0.970133	−	0.242575i	$-0.0779919\pi$
$158$	492.798			3.11897
$159$		−	141.868i		−	0.892250i
$160$			220.557i			1.37848i
$161$	25.4066	+	68.1191i	0.157805	+	0.423100i
$162$	−34.2414			−0.211367
$163$	10.4287			0.0639800			0.0319900	−	0.999488i	$-0.489816\pi$
$163$	10.4287			0.0639800			0.0319900	+	0.999488i	$0.489816\pi$
$164$			301.743i			1.83989i
$165$	−55.9604			−0.339154
$166$		−	162.421i		−	0.978439i
$167$		−	75.7598i		−	0.453652i	−0.973935	−	0.226826i	$-0.927165\pi$
$167$		−	75.7598i		−	0.453652i	0.973935	−	0.226826i	$-0.0728348\pi$
$168$	−279.849	+	104.376i	−1.66577	+	0.621287i
$169$	−118.055			−0.698552
$170$	110.674			0.651025
$171$			56.0725i			0.327910i
$172$	−61.2361			−0.356024
$173$			325.843i			1.88349i	0.336333	+	0.941743i	$0.390813\pi$
$173$			325.843i			1.88349i	−0.336333	+	0.941743i	$0.609187\pi$
$174$		−	90.4570i		−	0.519868i
$175$	−12.2310	−	32.7933i	−0.0698916	−	0.187390i
$176$	748.822			4.25467
$177$	−60.9127			−0.344139
$178$			97.1424i			0.545744i
$179$	−30.9215			−0.172746			−0.0863728	−	0.996263i	$-0.527528\pi$
$179$	−30.9215			−0.172746			−0.0863728	+	0.996263i	$0.527528\pi$
$180$			70.2684i			0.390380i
$181$			211.403i			1.16797i	0.811764	+	0.583985i	$0.198507\pi$
$181$			211.403i			1.16797i	−0.811764	+	0.583985i	$0.801493\pi$
$182$	−422.773	+	157.683i	−2.32293	+	0.866390i
$183$	118.615			0.648171
$184$	−255.860			−1.39054
$185$		−	64.2723i		−	0.347418i
$186$	279.658			1.50354
$187$		−	187.970i		−	1.00519i
$188$		−	110.001i		−	0.585112i
$189$	−34.0798	+	12.7109i	−0.180317	+	0.0672532i
$190$	159.010			0.836892
$191$	112.093			0.586874			0.293437	−	0.955978i	$-0.405201\pi$
$191$	112.093			0.586874			0.293437	+	0.955978i	$0.405201\pi$
$192$		−	290.932i		−	1.51527i
$193$	−293.541			−1.52094			−0.760470	−	0.649373i	$-0.775031\pi$
$193$	−293.541			−1.52094			−0.760470	+	0.649373i	$0.775031\pi$
$194$			109.310i			0.563453i
$195$			65.6188i			0.336507i
$196$	−387.912	+	336.118i	−1.97914	+	1.71489i
$197$	−90.7583			−0.460702			−0.230351	−	0.973108i	$-0.573987\pi$
$197$	−90.7583			−0.460702			−0.230351	+	0.973108i	$0.573987\pi$
$198$	164.917			0.832914
$199$			389.421i			1.95689i	0.206505	+	0.978445i	$0.433791\pi$
$199$			389.421i			1.95689i	−0.206505	+	0.978445i	$0.566209\pi$
$200$	123.174			0.615869
$201$		−	82.2096i		−	0.409003i
$202$		−	47.4086i		−	0.234696i
$203$	−33.5788	−	90.0301i	−0.165413	−	0.443498i
$204$	−236.030			−1.15701
$205$	64.4122			0.314206
$206$		−	146.399i		−	0.710676i
$207$	−31.1584			−0.150523
$208$		−	878.064i		−	4.22146i
$209$		−	270.062i		−	1.29216i
$210$	36.0452	+	96.6430i	0.171644	+	0.460205i
$211$	−21.1049			−0.100023			−0.0500115	−	0.998749i	$-0.515926\pi$
$211$	−21.1049			−0.100023			−0.0500115	+	0.998749i	$0.515926\pi$
$212$	857.980			4.04707
$213$		−	82.5405i		−	0.387514i
$214$	334.038			1.56093
$215$			13.0719i			0.0607995i
$216$		−	128.006i		−	0.592620i
$217$	278.338	−	103.813i	1.28267	−	0.478400i
$218$	−494.645			−2.26901
$219$	218.181			0.996259
$220$		−	338.434i		−	1.53834i
$221$	−220.412			−0.997340
$222$			189.413i			0.853209i
$223$		−	293.039i		−	1.31408i	−0.753857	−	0.657039i	$-0.771809\pi$
$223$		−	293.039i		−	1.31408i	0.753857	−	0.657039i	$-0.228191\pi$
$224$	−241.285	−	646.922i	−1.07716	−	2.88805i
$225$	15.0000			0.0666667
$226$	603.398			2.66990
$227$		−	73.9333i		−	0.325697i	−0.986651	−	0.162849i	$-0.947932\pi$
$227$		−	73.9333i		−	0.325697i	0.986651	−	0.162849i	$-0.0520682\pi$
$228$	−339.112			−1.48733
$229$			233.516i			1.01972i	0.860257	+	0.509860i	$0.170303\pi$
$229$			233.516i			1.01972i	−0.860257	+	0.509860i	$0.829697\pi$
$230$			88.3583i			0.384167i
$231$	164.139	−	61.2193i	0.710557	−	0.265019i
$232$	338.159			1.45758
$233$	−385.429			−1.65420			−0.827101	−	0.562054i	$-0.810011\pi$
$233$	−385.429			−1.65420			−0.827101	+	0.562054i	$0.810011\pi$
$234$		−	193.381i		−	0.826413i
$235$	−23.4816			−0.0999218
$236$		−	368.384i		−	1.56095i
$237$			224.347i			0.946611i
$238$	−324.621	+	121.075i	−1.36396	+	0.508719i
$239$	407.373			1.70449			0.852244	−	0.523144i	$-0.175241\pi$
$239$	407.373			1.70449			0.852244	+	0.523144i	$0.175241\pi$
$240$	−200.719			−0.836330
$241$			271.816i			1.12787i	0.825820	+	0.563934i	$0.190713\pi$
$241$			271.816i			1.12787i	−0.825820	+	0.563934i	$0.809287\pi$
$242$	−333.933			−1.37989
$243$		−	15.5885i		−	0.0641500i
$244$			717.355i			2.93998i
$245$	71.7502	+	82.8064i	0.292858	+	0.337985i
$246$	−189.825			−0.771645
$247$	−316.673			−1.28208
$248$			1045.46i			4.21555i
$249$	73.9424			0.296957
$250$		−	42.5367i		−	0.170147i
$251$			442.250i			1.76195i	0.473162	+	0.880976i	$0.343113\pi$
$251$			442.250i			1.76195i	−0.473162	+	0.880976i	$0.656887\pi$
$252$	−76.8719	−	206.106i	−0.305047	−	0.817880i
$253$	150.068			0.593154
$254$	−163.843			−0.645049
$255$			50.3847i			0.197587i
$256$	258.395			1.00935
$257$			390.436i			1.51921i	0.650386	+	0.759604i	$0.274607\pi$
$257$			390.436i			1.51921i	−0.650386	+	0.759604i	$0.725393\pi$
$258$		−	38.5233i		−	0.149315i
$259$	70.3124	+	188.519i	0.271476	+	0.727871i
$260$	−396.846			−1.52633
$261$	41.1807			0.157780
$262$		−	2.61274i		−	0.00997228i
$263$	−1.63279			−0.00620832			−0.00310416	−	0.999995i	$-0.500988\pi$
$263$	−1.63279			−0.00620832			−0.00310416	+	0.999995i	$0.500988\pi$
$264$			616.515i			2.33529i
$265$		−	183.151i		−	0.691134i
$266$	−466.395	+	173.953i	−1.75336	+	0.653957i
$267$	−44.2242			−0.165634
$268$	497.182			1.85516
$269$		−	410.340i		−	1.52543i	−0.646737	−	0.762713i	$-0.723867\pi$
$269$		−	410.340i		−	1.52543i	0.646737	−	0.762713i	$-0.276133\pi$
$270$	−44.2055			−0.163724
$271$		−	470.030i		−	1.73443i	−0.497937	−	0.867213i	$-0.665909\pi$
$271$		−	470.030i		−	1.73443i	0.497937	−	0.867213i	$-0.334091\pi$
$272$		−	674.211i		−	2.47872i
$273$	−71.7854	−	192.468i	−0.262950	−	0.705011i
$274$	−289.943			−1.05818
$275$	−72.2445			−0.262707
$276$		−	188.438i		−	0.682745i
$277$	366.582			1.32340			0.661701	−	0.749768i	$-0.269835\pi$
$277$	366.582			1.32340			0.661701	+	0.749768i	$0.269835\pi$
$278$		−	186.595i		−	0.671204i
$279$			127.315i			0.456326i
$280$	−361.284	+	134.749i	−1.29030	+	0.481247i
$281$	10.1164			0.0360015			0.0180008	−	0.999838i	$-0.494270\pi$
$281$	10.1164			0.0360015			0.0180008	+	0.999838i	$0.494270\pi$
$282$	69.2011			0.245394
$283$			121.896i			0.430729i	0.976534	+	0.215364i	$0.0690939\pi$
$283$			121.896i			0.430729i	−0.976534	+	0.215364i	$0.930906\pi$
$284$	499.183			1.75769
$285$			72.3893i			0.253998i
$286$			931.380i			3.25657i
$287$	−188.929	+	70.4654i	−0.658289	+	0.245524i
$288$	295.909			1.02746
$289$	119.759			0.414391
$290$		−	116.780i		−	0.402688i
$291$	−49.7635			−0.171009
$292$			1319.50i			4.51884i
$293$		−	292.803i		−	0.999327i	−0.866220	−	0.499663i	$-0.833457\pi$
$293$		−	292.803i		−	0.999327i	0.866220	−	0.499663i	$-0.166543\pi$
$294$	−211.450	−	244.033i	−0.719218	−	0.830045i
$295$	−78.6379			−0.266569
$296$	−708.088			−2.39219
$297$			75.0787i			0.252790i
$298$	922.023			3.09404
$299$		−	175.969i		−	0.588525i
$300$			90.7161i			0.302387i
$301$	−14.3003	−	38.3415i	−0.0475095	−	0.127380i
$302$	−409.771			−1.35686
$303$	21.5829			0.0712306
$304$		−	968.662i		−	3.18639i
$305$	153.132			0.502071
$306$		−	148.485i		−	0.485246i
$307$		−	167.855i		−	0.546758i	−0.961906	−	0.273379i	$-0.911859\pi$
$307$		−	167.855i		−	0.546758i	0.961906	−	0.273379i	$-0.0881412\pi$
$308$	370.238	+	992.668i	1.20207	+	3.22295i
$309$	66.6485			0.215691
$310$	361.037			1.16464
$311$		−	303.739i		−	0.976652i	−0.872661	−	0.488326i	$-0.837608\pi$
$311$		−	303.739i		−	0.976652i	0.872661	−	0.488326i	$-0.162392\pi$
$312$	722.923			2.31706
$313$		−	17.2151i		−	0.0550004i	−0.999622	−	0.0275002i	$-0.991245\pi$
$313$		−	17.2151i		−	0.0550004i	0.999622	−	0.0275002i	$-0.00875470\pi$
$314$			289.790i			0.922899i
$315$	−43.9969	+	16.4096i	−0.139673	+	0.0520941i
$316$	−1356.79			−4.29364
$317$	82.8657			0.261406			0.130703	−	0.991422i	$-0.458277\pi$
$317$	82.8657			0.261406			0.130703	+	0.991422i	$0.458277\pi$
$318$			539.750i			1.69733i
$319$	−198.339			−0.621751
$320$		−	375.592i		−	1.17372i
$321$			152.071i			0.473743i
$322$	−96.6619	−	259.166i	−0.300192	−	0.804863i
$323$	−243.154			−0.752799
$324$	94.2749			0.290972
$325$			84.7135i			0.260657i
$326$	−39.6772			−0.121709
$327$		−	225.188i		−	0.688647i
$328$		−	709.629i		−	2.16350i
$329$	68.8745	−	25.6883i	0.209345	−	0.0780800i
$330$	212.907			0.645172
$331$	−451.490			−1.36402			−0.682009	−	0.731343i	$-0.738894\pi$
$331$	−451.490			−1.36402			−0.682009	+	0.731343i	$0.738894\pi$
$332$			447.184i			1.34694i
$333$	−86.2303			−0.258950
$334$			288.236i			0.862982i
$335$		−	106.132i		−	0.316812i
$336$	588.734	−	219.582i	1.75219	−	0.653518i
$337$	204.157			0.605808			0.302904	−	0.953021i	$-0.402044\pi$
$337$	204.157			0.605808			0.302904	+	0.953021i	$0.402044\pi$
$338$	449.153			1.32886
$339$			274.698i			0.810319i
$340$	−304.713			−0.896215
$341$		−	613.187i		−	1.79820i
$342$		−	213.334i		−	0.623783i
$343$	−301.041	−	164.388i	−0.877669	−	0.479267i
$344$	144.013			0.418643
$345$	−40.2253			−0.116595
$346$		−	1239.70i		−	3.58296i
$347$	146.593			0.422458			0.211229	−	0.977437i	$-0.432253\pi$
$347$	146.593			0.422458			0.211229	+	0.977437i	$0.432253\pi$
$348$			249.050i			0.715661i
$349$			11.4454i			0.0327947i	0.999866	+	0.0163974i	$0.00521968\pi$
$349$			11.4454i			0.0327947i	−0.999866	+	0.0163974i	$0.994780\pi$
$350$	46.5342	+	124.766i	0.132955	+	0.356473i
$351$	88.0369			0.250817
$352$	−1425.19			−4.04882
$353$			177.817i			0.503730i	0.967762	+	0.251865i	$0.0810439\pi$
$353$			177.817i			0.503730i	−0.967762	+	0.251865i	$0.918956\pi$
$354$	231.748			0.654657
$355$		−	106.559i		−	0.300167i
$356$		−	267.457i		−	0.751283i
$357$	−55.1196	−	147.784i	−0.154397	−	0.413962i
$358$	117.644			0.328614
$359$	653.079			1.81916			0.909581	−	0.415526i	$-0.136402\pi$
$359$	653.079			1.81916			0.909581	+	0.415526i	$0.136402\pi$
$360$		−	165.255i		−	0.459042i
$361$	11.6523			0.0322780
$362$		−	804.303i		−	2.22183i
$363$		−	152.024i		−	0.418798i
$364$	1164.00	−	434.140i	3.19779	−	1.19269i
$365$	281.670			0.771699
$366$	−451.284			−1.23302
$367$		−	466.632i		−	1.27148i	−0.771905	−	0.635738i	$-0.780696\pi$
$367$		−	466.632i		−	1.27148i	0.771905	−	0.635738i	$-0.219304\pi$
$368$	538.266			1.46268
$369$		−	86.4180i		−	0.234195i
$370$			244.530i			0.660893i
$371$	200.362	+	537.203i	0.540060	+	1.44799i
$372$	−769.967			−2.06980
$373$	−452.082			−1.21202			−0.606008	−	0.795459i	$-0.707230\pi$
$373$	−452.082			−1.21202			−0.606008	+	0.795459i	$0.707230\pi$
$374$			715.149i			1.91216i
$375$	19.3649			0.0516398
$376$			258.697i			0.688024i
$377$			232.571i			0.616899i
$378$	129.660	−	48.3597i	0.343016	−	0.127936i
$379$	326.478			0.861420			0.430710	−	0.902490i	$-0.358263\pi$
$379$	326.478			0.861420			0.430710	+	0.902490i	$0.358263\pi$
$380$	−437.792			−1.15208
$381$		−	74.5896i		−	0.195773i
$382$	−426.469			−1.11641
$383$			381.262i			0.995462i	0.867331	+	0.497731i	$0.165833\pi$
$383$			381.262i			0.995462i	−0.867331	+	0.497731i	$0.834167\pi$
$384$			423.509i			1.10289i
$385$	211.902	−	79.0338i	0.550395	−	0.205283i
$386$	1116.81			2.89329
$387$	17.5378			0.0453173
$388$		−	300.957i		−	0.775662i
$389$	−68.8443			−0.176978			−0.0884888	−	0.996077i	$-0.528204\pi$
$389$	−68.8443			−0.176978			−0.0884888	+	0.996077i	$0.528204\pi$
$390$		−	249.653i		−	0.640137i
$391$		−	135.116i		−	0.345565i
$392$	912.278	−	790.472i	2.32724	−	2.01651i
$393$	1.18945			0.00302660
$394$	345.299			0.876394
$395$			289.631i			0.733242i
$396$	−454.056			−1.14661
$397$		−	370.531i		−	0.933328i	−0.884435	−	0.466664i	$-0.845456\pi$
$397$		−	370.531i		−	0.933328i	0.884435	−	0.466664i	$-0.154544\pi$
$398$		−	1481.59i		−	3.72259i
$399$	−79.1922	−	212.327i	−0.198477	−	0.532148i
$400$	−259.127			−0.647819
$401$	8.95073			0.0223210			0.0111605	−	0.999938i	$-0.496447\pi$
$401$	8.95073			0.0223210			0.0111605	+	0.999938i	$0.496447\pi$
$402$			312.775i			0.778047i
$403$	−719.019			−1.78417
$404$			130.528i			0.323088i
$405$		−	20.1246i		−	0.0496904i
$406$	127.754	+	342.529i	0.314665	+	0.843667i
$407$	415.311			1.02042
$408$	555.088			1.36051
$409$			63.1330i			0.154359i	0.997017	+	0.0771797i	$0.0245915\pi$
$409$			63.1330i			0.154359i	−0.997017	+	0.0771797i	$0.975408\pi$
$410$	−245.063			−0.597714
$411$		−	131.997i		−	0.321160i
$412$			403.072i			0.978331i
$413$	230.655	−	86.0280i	0.558486	−	0.208300i
$414$	118.545			0.286341
$415$	95.4592			0.230022
$416$			1671.17i			4.01722i
$417$	84.9475			0.203711
$418$			1027.48i			2.45808i
$419$			3.58774i			0.00856263i	0.999991	+	0.00428131i	$0.00136279\pi$
$419$			3.58774i			0.00856263i	−0.999991	+	0.00428131i	$0.998637\pi$
$420$	−99.2412	−	266.082i	−0.236289	−	0.633527i
$421$	119.594			0.284071			0.142035	−	0.989862i	$-0.454635\pi$
$421$	119.594			0.284071			0.142035	+	0.989862i	$0.454635\pi$
$422$	80.2956			0.190274
$423$			31.5039i			0.0744773i
$424$	−2017.77			−4.75889
$425$			65.0463i			0.153050i
$426$			314.034i			0.737168i
$427$	−449.154	+	167.523i	−1.05188	+	0.392324i
$428$	−919.689			−2.14881
$429$	−424.012			−0.988373
$430$		−	49.7334i		−	0.115659i
$431$	−404.488			−0.938488			−0.469244	−	0.883069i	$-0.655473\pi$
$431$	−404.488			−0.938488			−0.469244	+	0.883069i	$0.655473\pi$
$432$			269.293i			0.623364i
$433$			116.085i			0.268094i	0.990975	+	0.134047i	$0.0427974\pi$
$433$			116.085i			0.268094i	−0.990975	+	0.134047i	$0.957203\pi$
$434$	−1058.97	+	394.966i	−2.44002	+	0.910060i
$435$	53.1641			0.122216
$436$	1361.88			3.12357
$437$		−	194.125i		−	0.444223i
$438$	−830.091			−1.89519
$439$			58.4183i			0.133071i	0.997784	+	0.0665357i	$0.0211946\pi$
$439$			58.4183i			0.133071i	−0.997784	+	0.0665357i	$0.978805\pi$
$440$			795.918i			1.80890i
$441$	111.096	−	96.2630i	0.251919	−	0.218284i
$442$	838.580			1.89724
$443$	267.301			0.603388			0.301694	−	0.953405i	$-0.402448\pi$
$443$	267.301			0.603388			0.301694	+	0.953405i	$0.402448\pi$
$444$		−	521.499i		−	1.17455i
$445$	−57.0932			−0.128299
$446$			1114.90i			2.49977i
$447$			419.753i			0.939044i
$448$	410.888	+	1101.66i	0.917162	+	2.45906i
$449$	296.478			0.660307			0.330154	−	0.943927i	$-0.392899\pi$
$449$	296.478			0.660307			0.330154	+	0.943927i	$0.392899\pi$
$450$	−57.0690			−0.126820
$451$			416.215i			0.922872i
$452$	−1661.30			−3.67545
$453$		−	186.549i		−	0.411807i
$454$			281.287i			0.619574i
$455$	−92.6746	−	248.475i	−0.203680	−	0.546100i
$456$	797.513			1.74893
$457$	12.1251			0.0265320			0.0132660	−	0.999912i	$-0.495777\pi$
$457$	12.1251			0.0265320			0.0132660	+	0.999912i	$0.495777\pi$
$458$		−	888.435i		−	1.93981i
$459$	67.5981			0.147273
$460$		−	243.272i		−	0.528852i
$461$		−	103.948i		−	0.225483i	−0.993624	−	0.112741i	$-0.964037\pi$
$461$		−	103.948i		−	0.225483i	0.993624	−	0.112741i	$-0.0359632\pi$
$462$	−624.482	+	232.915i	−1.35169	+	0.504145i
$463$	498.831			1.07739			0.538694	−	0.842501i	$-0.318918\pi$
$463$	498.831			1.07739			0.538694	+	0.842501i	$0.318918\pi$
$464$	−711.403			−1.53320
$465$			164.363i			0.353468i
$466$	1466.40			3.14679
$467$			597.683i			1.27983i	0.768444	+	0.639917i	$0.221031\pi$
$467$			597.683i			1.27983i	−0.768444	+	0.639917i	$0.778969\pi$
$468$			532.424i			1.13766i
$469$	116.106	+	311.299i	0.247561	+	0.663750i
$470$	89.3382			0.190081
$471$	−131.928			−0.280101
$472$			866.354i			1.83550i
$473$	−84.4673			−0.178578
$474$		−	853.551i		−	1.80074i
$475$			93.4542i			0.196746i
$476$	893.762	−	333.349i	1.87765	−	0.700313i
$477$	−245.722			−0.515141
$478$	−1549.89			−3.24245
$479$		−	276.703i		−	0.577669i	−0.957379	−	0.288834i	$-0.906732\pi$
$479$		−	276.703i		−	0.577669i	0.957379	−	0.288834i	$-0.0932677\pi$
$480$	382.017			0.795868
$481$		−	486.992i		−	1.01246i
$482$		−	1034.15i		−	2.14554i
$483$	117.986	−	44.0055i	0.244277	−	0.0911087i
$484$	919.399			1.89958
$485$	−64.2444			−0.132463
$486$			59.3079i			0.122033i
$487$	−542.653			−1.11428			−0.557138	−	0.830420i	$-0.688101\pi$
$487$	−542.653			−1.11428			−0.557138	+	0.830420i	$0.688101\pi$
$488$		−	1687.05i		−	3.45708i
$489$		−	18.0631i		−	0.0369389i
$490$	−272.981	−	315.045i	−0.557104	−	0.642950i
$491$	574.817			1.17071			0.585353	−	0.810778i	$-0.300956\pi$
$491$	574.817			1.17071			0.585353	+	0.810778i	$0.300956\pi$
$492$	522.633			1.06226
$493$			178.577i			0.362225i
$494$	1204.82			2.43890
$495$			96.9262i			0.195811i
$496$		−	2199.38i		−	4.43424i
$497$	116.573	+	312.552i	0.234554	+	0.628877i
$498$	−281.321			−0.564902
$499$	−549.967			−1.10214			−0.551070	−	0.834459i	$-0.685780\pi$
$499$	−549.967			−1.10214			−0.551070	+	0.834459i	$0.685780\pi$
$500$			117.114i			0.234228i
$501$	−131.220			−0.261916
$502$		−	1682.58i		−	3.35176i
$503$			397.053i			0.789369i	0.918817	+	0.394685i	$0.129146\pi$
$503$			397.053i			0.789369i	−0.918817	+	0.394685i	$0.870854\pi$
$504$	180.785	+	484.713i	0.358701	+	0.961733i
$505$	27.8634			0.0551750
$506$	−570.949			−1.12836
$507$			204.478i			0.403309i
$508$	451.098			0.887989
$509$			557.813i			1.09590i	0.836511	+	0.547950i	$0.184592\pi$
$509$			557.813i			1.09590i	−0.836511	+	0.547950i	$0.815408\pi$
$510$		−	191.694i		−	0.375870i
$511$	−826.174	+	308.141i	−1.61678	+	0.603015i
$512$	−5.03806			−0.00983995
$513$	97.1205			0.189319
$514$		−	1485.45i		−	2.88999i
$515$	86.0428			0.167073
$516$			106.064i			0.205550i
$517$		−	151.732i		−	0.293486i
$518$	−267.511	−	717.238i	−0.516430	−	1.38463i
$519$	564.377			1.08743
$520$	933.289			1.79479
$521$		−	287.300i		−	0.551439i	−0.961238	−	0.275719i	$-0.911084\pi$
$521$		−	287.300i		−	0.551439i	0.961238	−	0.275719i	$-0.0889161\pi$
$522$	−156.676			−0.300146
$523$			1012.28i			1.93553i	0.251853	+	0.967766i	$0.418960\pi$
$523$			1012.28i			1.93553i	−0.251853	+	0.967766i	$0.581040\pi$
$524$			7.19350i			0.0137281i
$525$	−56.7997	+	21.1848i	−0.108190	+	0.0403519i
$526$	6.21211			0.0118101
$527$	−552.091			−1.04761
$528$		−	1297.00i		−	2.45643i
$529$	−421.128			−0.796084
$530$			696.815i			1.31475i
$531$			105.504i			0.198689i
$532$	1284.10	−	478.934i	2.41372	−	0.900252i
$533$	488.051			0.915669
$534$	168.256			0.315085
$535$			196.323i			0.366960i
$536$	−1169.26			−2.18145
$537$			53.5575i			0.0997347i
$538$			1561.18i			2.90182i
$539$	−535.074	+	463.632i	−0.992716	+	0.860170i
$540$	121.708			0.225386
$541$	526.853			0.973851			0.486925	−	0.873444i	$-0.338118\pi$
$541$	526.853			0.973851			0.486925	+	0.873444i	$0.338118\pi$
$542$			1788.28i			3.29940i
$543$	366.160			0.674328
$544$			1283.19i			2.35880i
$545$		−	290.716i		−	0.533424i
$546$	273.115	+	732.265i	0.500211	+	1.34114i
$547$	−250.549			−0.458042			−0.229021	−	0.973421i	$-0.573553\pi$
$547$	−250.549			−0.458042			−0.229021	+	0.973421i	$0.573553\pi$
$548$	798.282			1.45672
$549$		−	205.448i		−	0.374222i
$550$	274.862			0.499748
$551$			256.567i			0.465640i
$552$			443.162i			0.802829i
$553$	−316.849	−	849.522i	−0.572964	−	1.53621i
$554$	−1394.70			−2.51751
$555$	−111.323			−0.200582
$556$			513.741i			0.923994i
$557$	−64.1496			−0.115170			−0.0575849	−	0.998341i	$-0.518340\pi$
$557$	−64.1496			−0.115170			−0.0575849	+	0.998341i	$0.518340\pi$
$558$		−	484.382i		−	0.868069i
$559$			99.0459i			0.177184i
$560$	760.053	−	283.479i	1.35724	−	0.506213i
$561$	−325.573			−0.580344
$562$	−38.4890			−0.0684857
$563$		−	17.3869i		−	0.0308826i	−0.999881	−	0.0154413i	$-0.995085\pi$
$563$		−	17.3869i		−	0.0308826i	0.999881	−	0.0154413i	$-0.00491531\pi$
$564$	−190.527			−0.337814
$565$			354.634i			0.627670i
$566$		−	463.767i		−	0.819376i
$567$	22.0158	+	59.0280i	0.0388287	+	0.104106i
$568$	−1173.96			−2.06684
$569$	174.914			0.307405			0.153703	−	0.988117i	$-0.450880\pi$
$569$	174.914			0.307405			0.153703	+	0.988117i	$0.450880\pi$
$570$		−	275.413i		−	0.483180i
$571$	−376.637			−0.659609			−0.329805	−	0.944049i	$-0.606983\pi$
$571$	−376.637			−0.659609			−0.329805	+	0.944049i	$0.606983\pi$
$572$		−	2564.32i		−	4.48307i
$573$		−	194.151i		−	0.338832i
$574$	718.799	−	268.093i	1.25226	−	0.467060i
$575$	−51.9306			−0.0903141
$576$	−503.909			−0.874842
$577$			448.775i			0.777773i	0.921286	+	0.388886i	$0.127140\pi$
$577$			448.775i			0.777773i	−0.921286	+	0.388886i	$0.872860\pi$
$578$	−455.636			−0.788297
$579$			508.429i			0.878115i
$580$			321.522i			0.554349i
$581$	−279.994	+	104.430i	−0.481917	+	0.179742i
$582$	189.330			0.325310
$583$	1183.47			2.02997
$584$		−	3103.16i		−	5.31363i
$585$	113.655			0.194282
$586$			1114.00i			1.90102i
$587$			275.916i			0.470044i	0.971990	+	0.235022i	$0.0755162\pi$
$587$			275.916i			0.470044i	−0.971990	+	0.235022i	$0.924484\pi$
$588$	582.174	+	671.883i	0.990091	+	1.14266i
$589$	−793.207			−1.34670
$590$	299.186			0.507095
$591$			157.198i			0.265986i
$592$	1489.64			2.51629
$593$			893.938i			1.50748i	0.657171	+	0.753742i	$0.271753\pi$
$593$			893.938i			1.50748i	−0.657171	+	0.753742i	$0.728247\pi$
$594$		−	285.645i		−	0.480883i
$595$	−71.1591	−	190.789i	−0.119595	−	0.320654i
$596$	−2538.55			−4.25932
$597$	674.497			1.12981
$598$			669.492i			1.11955i
$599$	−122.407			−0.204352			−0.102176	−	0.994766i	$-0.532581\pi$
$599$	−122.407			−0.204352			−0.102176	+	0.994766i	$0.532581\pi$
$600$		−	213.343i		−	0.355572i
$601$		−	594.921i		−	0.989885i	−0.868926	−	0.494943i	$-0.835189\pi$
$601$		−	594.921i		−	0.989885i	0.868926	−	0.494943i	$-0.164811\pi$
$602$	54.4071	+	145.874i	0.0903773	+	0.242316i
$603$	−142.391			−0.236138
$604$	1128.20			1.86788
$605$		−	196.262i		−	0.324399i
$606$	−82.1142			−0.135502
$607$		−	539.772i		−	0.889246i	−0.895718	−	0.444623i	$-0.853338\pi$
$607$		−	539.772i		−	0.889246i	0.895718	−	0.444623i	$-0.146662\pi$
$608$			1843.60i			3.03223i
$609$	−155.937	+	58.1602i	−0.256054	+	0.0955012i
$610$	−582.605			−0.955091
$611$	−177.920			−0.291195
$612$			408.816i			0.668000i
$613$	1180.07			1.92508			0.962540	−	0.271140i	$-0.0874006\pi$
$613$	1180.07			1.92508			0.962540	+	0.271140i	$0.0874006\pi$
$614$			638.620i			1.04010i
$615$		−	111.565i		−	0.181407i
$616$	−870.715	−	2334.53i	−1.41350	−	3.78982i
$617$	−777.688			−1.26043			−0.630217	−	0.776419i	$-0.717034\pi$
$617$	−777.688			−1.26043			−0.630217	+	0.776419i	$0.717034\pi$
$618$	−253.571			−0.410309
$619$			285.107i			0.460592i	0.973121	+	0.230296i	$0.0739695\pi$
$619$			285.107i			0.460592i	−0.973121	+	0.230296i	$0.926030\pi$
$620$	−994.023			−1.60326
$621$			53.9679i			0.0869048i
$622$			1155.60i			1.85789i
$623$	167.462	−	62.4586i	0.268799	−	0.100255i
$624$	−1520.85			−2.43726
$625$	25.0000			0.0400000
$626$			65.4967i			0.104627i
$627$	−467.762			−0.746031
$628$		−	797.863i		−	1.27048i
$629$		−	373.931i		−	0.594485i
$630$	167.391	−	62.4322i	0.265699	−	0.0990987i
$631$	506.946			0.803401			0.401700	−	0.915771i	$-0.368419\pi$
$631$	506.946			0.803401			0.401700	+	0.915771i	$0.368419\pi$
$632$	3190.86			5.04883
$633$			36.5547i			0.0577483i
$634$	−315.271			−0.497273
$635$		−	96.2947i		−	0.151645i
$636$		−	1486.06i		−	2.33658i
$637$	543.652	+	627.425i	0.853457	+	0.984969i
$638$	754.600			1.18276
$639$	−142.964			−0.223731
$640$			546.747i			0.854293i
$641$	537.896			0.839152			0.419576	−	0.907720i	$-0.362179\pi$
$641$	537.896			0.839152			0.419576	+	0.907720i	$0.362179\pi$
$642$		−	578.571i		−	0.901202i
$643$		−	673.330i		−	1.04717i	−0.851973	−	0.523585i	$-0.824594\pi$
$643$		−	673.330i		−	1.04717i	0.851973	−	0.523585i	$-0.175406\pi$
$644$	266.134	+	713.547i	0.413251	+	1.10799i
$645$	22.6412			0.0351026
$646$	925.104			1.43205
$647$		−	1082.21i		−	1.67266i	−0.548224	−	0.836332i	$-0.684696\pi$
$647$		−	1082.21i		−	1.67266i	0.548224	−	0.836332i	$-0.315304\pi$
$648$	−221.713			−0.342149
$649$		−	508.138i		−	0.782956i
$650$		−	322.301i		−	0.495848i
$651$	−179.809	−	482.096i	−0.276204	−	0.740547i
$652$	109.241			0.167547
$653$	−491.429			−0.752571			−0.376285	−	0.926504i	$-0.622799\pi$
$653$	−491.429			−0.752571			−0.376285	+	0.926504i	$0.622799\pi$
$654$			856.749i			1.31001i
$655$	1.53558			0.00234439
$656$			1492.88i			2.27574i
$657$		−	377.900i		−	0.575191i
$658$	−262.040	+	97.7339i	−0.398237	+	0.148532i
$659$	248.373			0.376893			0.188447	−	0.982083i	$-0.439655\pi$
$659$	248.373			0.376893			0.188447	+	0.982083i	$0.439655\pi$
$660$	−586.184			−0.888158
$661$			681.545i			1.03108i	0.856865	+	0.515541i	$0.172409\pi$
$661$			681.545i			1.03108i	−0.856865	+	0.515541i	$0.827591\pi$
$662$	1717.74			2.59477
$663$			381.765i			0.575814i
$664$		−	1051.67i		−	1.58385i
$665$	−102.237	−	274.113i	−0.153739	−	0.412200i
$666$	328.072			0.492601
$667$	−142.569			−0.213747
$668$		−	793.584i		−	1.18800i
$669$	−507.559			−0.758683
$670$			403.791i			0.602672i
$671$			989.499i			1.47466i
$672$	−1120.50	+	417.917i	−1.66741	+	0.621900i
$673$	86.1498			0.128009			0.0640043	−	0.997950i	$-0.479613\pi$
$673$	86.1498			0.128009			0.0640043	+	0.997950i	$0.479613\pi$
$674$	−776.737			−1.15243
$675$		−	25.9808i		−	0.0384900i
$676$	−1236.63			−1.82933
$677$		−	793.846i		−	1.17259i	−0.810096	−	0.586297i	$-0.800585\pi$
$677$		−	793.846i		−	1.17259i	0.810096	−	0.586297i	$-0.199415\pi$
$678$		−	1045.12i		−	1.54147i
$679$	188.437	−	70.2819i	0.277521	−	0.103508i
$680$	716.615			1.05385
$681$	−128.056			−0.188041
$682$			2332.93i			3.42072i
$683$	−186.736			−0.273406			−0.136703	−	0.990612i	$-0.543651\pi$
$683$	−186.736			−0.273406			−0.136703	+	0.990612i	$0.543651\pi$
$684$			587.359i			0.858712i
$685$		−	170.407i		−	0.248770i
$686$	1145.34	+	625.433i	1.66959	+	0.911709i
$687$	404.461			0.588736
$688$	−302.968			−0.440361
$689$		−	1387.73i		−	2.01413i
$690$	153.041			0.221799
$691$		−	1030.46i		−	1.49126i	−0.666361	−	0.745630i	$-0.732149\pi$
$691$		−	1030.46i		−	1.49126i	0.666361	−	0.745630i	$-0.267851\pi$
$692$			3413.20i			4.93238i
$693$	−106.035	−	284.297i	−0.153009	−	0.410240i
$694$	−557.727			−0.803642
$695$	109.667			0.157794
$696$		−	585.709i		−	0.841535i
$697$	374.745			0.537654
$698$		−	43.5450i		−	0.0623854i
$699$			667.582i			0.955054i
$700$	−128.120	−	343.510i	−0.183028	−	0.490728i
$701$	−1143.88			−1.63179			−0.815893	−	0.578203i	$-0.803754\pi$
$701$	−1143.88			−1.63179			−0.815893	+	0.578203i	$0.803754\pi$
$702$	−334.945			−0.477130
$703$		−	537.239i		−	0.764210i
$704$	2426.98			3.44741
$705$			40.6714i			0.0576899i
$706$		−	676.521i		−	0.958246i
$707$	−81.7267	+	30.4818i	−0.115596	+	0.0431143i
$708$	−638.060			−0.901214
$709$	−316.757			−0.446766			−0.223383	−	0.974731i	$-0.571710\pi$
$709$	−316.757			−0.446766			−0.223383	+	0.974731i	$0.571710\pi$
$710$			405.416i			0.571008i
$711$	388.580			0.546526
$712$			628.996i			0.883422i
$713$		−	440.769i		−	0.618190i
$714$	209.708	+	562.261i	0.293709	+	0.787480i
$715$	−547.397			−0.765591
$716$	−323.902			−0.452377
$717$		−	705.590i		−	0.984087i
$718$	−2484.71			−3.46059
$719$		−	1145.95i		−	1.59381i	−0.604104	−	0.796906i	$-0.706469\pi$
$719$		−	1145.95i		−	1.59381i	0.604104	−	0.796906i	$-0.293531\pi$
$720$			347.656i			0.482855i
$721$	−252.374	+	94.1288i	−0.350034	+	0.130553i
$722$	−44.3325			−0.0614024
$723$	470.799			0.651174
$724$			2214.44i			3.05862i
$725$	68.6345			0.0946683
$726$			578.389i			0.796679i
$727$		−	149.829i		−	0.206093i	−0.994677	−	0.103046i	$-0.967141\pi$
$727$		−	149.829i		−	0.206093i	0.994677	−	0.103046i	$-0.0328590\pi$
$728$	−2737.45	+	1021.00i	−3.76024	+	1.40247i
$729$	−27.0000			−0.0370370
$730$	−1071.64			−1.46800
$731$			76.0512i			0.104037i
$732$	1242.49			1.69740
$733$		−	70.3231i		−	0.0959388i	−0.998849	−	0.0479694i	$-0.984725\pi$
$733$		−	70.3231i		−	0.0959388i	0.998849	−	0.0479694i	$-0.0152750\pi$
$734$			1775.35i			2.41873i
$735$	143.425	−	124.275i	0.195136	−	0.169082i
$736$	−1024.45			−1.39191
$737$	685.799			0.930528
$738$			328.786i			0.445509i
$739$	774.145			1.04756			0.523779	−	0.851854i	$-0.324522\pi$
$739$	774.145			1.04756			0.523779	+	0.851854i	$0.324522\pi$
$740$		−	673.252i		−	0.909800i
$741$			548.495i			0.740209i
$742$	−762.299	−	2043.84i	−1.02736	−	2.75451i
$743$	1071.79			1.44252			0.721260	−	0.692665i	$-0.243563\pi$
$743$	1071.79			1.44252			0.721260	+	0.692665i	$0.243563\pi$
$744$	1810.78			2.43385
$745$			541.898i			0.727380i
$746$	1719.99			2.30562
$747$		−	128.072i		−	0.171448i
$748$		−	1968.98i		−	2.63233i
$749$	−214.773	−	575.841i	−0.286747	−	0.768813i
$750$	−73.6758			−0.0982344
$751$	361.789			0.481742			0.240871	−	0.970557i	$-0.422567\pi$
$751$	361.789			0.481742			0.240871	+	0.970557i	$0.422567\pi$
$752$		−	544.235i		−	0.723717i
$753$	765.999			1.01726
$754$		−	884.839i		−	1.17353i
$755$		−	240.833i		−	0.318985i
$756$	−356.986	+	133.146i	−0.472203	+	0.176119i
$757$	812.552			1.07338			0.536692	−	0.843778i	$-0.319674\pi$
$757$	812.552			1.07338			0.536692	+	0.843778i	$0.319674\pi$
$758$	−1242.12			−1.63868
$759$		−	259.926i		−	0.342458i
$760$	1029.59			1.35472
$761$		−	728.812i		−	0.957703i	−0.877896	−	0.478851i	$-0.841053\pi$
$761$		−	728.812i		−	0.957703i	0.877896	−	0.478851i	$-0.158947\pi$
$762$			283.784i			0.372419i
$763$	318.036	+	852.706i	0.416824	+	1.11757i
$764$	1174.17			1.53688
$765$	87.2688			0.114077
$766$		−	1450.55i		−	1.89367i
$767$	−595.840			−0.776845
$768$		−	447.553i		−	0.582751i
$769$		−	624.378i		−	0.811935i	−0.913888	−	0.405967i	$-0.866935\pi$
$769$		−	624.378i		−	0.811935i	0.913888	−	0.405967i	$-0.133065\pi$
$770$	−806.203	+	300.692i	−1.04702	+	0.390509i
$771$	676.255			0.877115
$772$	−3074.84			−3.98296
$773$			34.6106i			0.0447744i	0.999749	+	0.0223872i	$0.00712666\pi$
$773$			34.6106i			0.0447744i	−0.999749	+	0.0223872i	$0.992873\pi$
$774$	−66.7243			−0.0862071
$775$			212.191i			0.273795i
$776$			707.781i			0.912089i
$777$	326.524	−	121.785i	0.420237	−	0.156737i
$778$	261.925			0.336665
$779$	538.408			0.691153
$780$			687.357i			0.881226i
$781$	688.559			0.881638
$782$			514.062i			0.657368i
$783$		−	71.3271i		−	0.0910946i
$784$	−1919.21	+	1662.96i	−2.44797	+	2.12112i
$785$	−170.318			−0.216965
$786$	−4.52539			−0.00575750
$787$			563.953i			0.716586i	0.933609	+	0.358293i	$0.116641\pi$
$787$			563.953i			0.716586i	−0.933609	+	0.358293i	$0.883359\pi$
$788$	−950.692			−1.20646
$789$			2.82807i			0.00358437i
$790$		−	1101.93i		−	1.39485i
$791$	−387.961	−	1040.18i	−0.490469	−	1.31502i
$792$	1067.84			1.34828
$793$	1160.28			1.46315
$794$			1409.72i			1.77547i
$795$	−317.226			−0.399027
$796$			4079.18i			5.12460i
$797$			887.777i			1.11390i	0.830546	+	0.556949i	$0.188028\pi$
$797$			887.777i			1.11390i	−0.830546	+	0.556949i	$0.811972\pi$
$798$	301.295	+	807.819i	0.377562	+	1.01230i
$799$	−136.614			−0.170981
$800$	493.181			0.616477
$801$			76.5986i			0.0956287i
$802$	−34.0540			−0.0424613
$803$			1820.08i			2.26660i
$804$		−	861.145i		−	1.07108i
$805$	152.319	−	56.8108i	0.189216	−	0.0705725i
$806$	2735.58			3.39402
$807$	−710.729			−0.880706
$808$		−	306.971i		−	0.379914i
$809$	−1338.15			−1.65408			−0.827041	−	0.562142i	$-0.809977\pi$
$809$	−1338.15			−1.65408			−0.827041	+	0.562142i	$0.809977\pi$
$810$			76.5661i			0.0945261i
$811$			1002.03i			1.23555i	0.786353	+	0.617777i	$0.211967\pi$
$811$			1002.03i			1.23555i	−0.786353	+	0.617777i	$0.788033\pi$
$812$	−351.738	−	943.065i	−0.433175	−	1.16141i
$813$	−814.115			−1.00137
$814$	−1580.09			−1.94115
$815$		−	23.3194i		−	0.0286127i
$816$	−1167.77			−1.43109
$817$			109.265i			0.133740i
$818$		−	240.196i		−	0.293638i
$819$	−333.365	+	124.336i	−0.407039	+	0.151814i
$820$	674.717			0.822825
$821$	−519.980			−0.633349			−0.316675	−	0.948534i	$-0.602566\pi$
$821$	−519.980			−0.633349			−0.316675	+	0.948534i	$0.602566\pi$
$822$			502.195i			0.610943i
$823$	−35.2676			−0.0428524			−0.0214262	−	0.999770i	$-0.506821\pi$
$823$	−35.2676			−0.0428524			−0.0214262	+	0.999770i	$0.506821\pi$
$824$		−	947.933i		−	1.15040i
$825$			125.131i			0.151674i
$826$	−877.550	+	327.302i	−1.06241	+	0.396250i
$827$	−1047.83			−1.26703			−0.633514	−	0.773731i	$-0.718388\pi$
$827$	−1047.83			−1.26703			−0.633514	+	0.773731i	$0.718388\pi$
$828$	−326.384			−0.394183
$829$		−	125.947i		−	0.151926i	−0.997111	−	0.0759632i	$-0.975797\pi$
$829$		−	125.947i		−	0.151926i	0.997111	−	0.0759632i	$-0.0242031\pi$
$830$	−363.184			−0.437571
$831$		−	634.939i		−	0.764067i
$832$		−	2845.86i		−	3.42051i
$833$	417.437	+	481.761i	0.501125	+	0.578345i
$834$	−323.192			−0.387520
$835$	−169.404			−0.202879
$836$		−	2828.90i		−	3.38385i
$837$	220.516			0.263460
$838$		−	13.6499i		−	0.0162887i
$839$		−	456.709i		−	0.544349i	−0.962248	−	0.272174i	$-0.912257\pi$
$839$		−	456.709i		−	0.544349i	0.962248	−	0.272174i	$-0.0877427\pi$
$840$	233.393	+	625.762i	0.277848	+	0.744955i
$841$	−652.572			−0.775948
$842$	−455.007			−0.540388
$843$		−	17.5222i		−	0.0207855i
$844$	−221.073			−0.261935
$845$			263.980i			0.312402i
$846$		−	119.860i		−	0.141678i
$847$	214.706	+	575.660i	0.253489	+	0.679645i
$848$	4244.89			5.00577
$849$	211.131			0.248681
$850$		−	247.475i		−	0.291147i
$851$	298.533			0.350802
$852$		−	864.611i		−	1.01480i
$853$		−	815.418i		−	0.955941i	−0.878376	−	0.477971i	$-0.841373\pi$
$853$		−	815.418i		−	0.955941i	0.878376	−	0.477971i	$-0.158627\pi$
$854$	1708.85	−	637.356i	2.00100	−	0.746319i
$855$	125.382			0.146646
$856$	2162.90			2.52675
$857$		−	609.807i		−	0.711560i	−0.934570	−	0.355780i	$-0.884215\pi$
$857$		−	609.807i		−	0.711560i	0.934570	−	0.355780i	$-0.115785\pi$
$858$	1613.20			1.88018
$859$			136.971i			0.159454i	0.996817	+	0.0797272i	$0.0254049\pi$
$859$			136.971i			0.159454i	−0.996817	+	0.0797272i	$0.974595\pi$
$860$			136.928i			0.159219i
$861$	122.050	+	327.234i	0.141753	+	0.380063i
$862$	1538.92			1.78529
$863$	305.240			0.353696			0.176848	−	0.984238i	$-0.443410\pi$
$863$	305.240			0.353696			0.176848	+	0.984238i	$0.443410\pi$
$864$		−	512.529i		−	0.593205i
$865$	728.607			0.842321
$866$		−	441.657i		−	0.509996i
$867$		−	207.429i		−	0.239249i
$868$	2915.59	−	1087.44i	3.35898	−	1.25281i
$869$	−1871.52			−2.15365
$870$	−202.268			−0.232492
$871$		−	804.164i		−	0.923266i
$872$	−3202.82			−3.67296
$873$			86.1929i			0.0987319i
$874$			738.570i			0.845045i
$875$	−73.3281	+	27.3494i	−0.0838035	+	0.0312565i
$876$	2285.44			2.60895
$877$	621.320			0.708461			0.354231	−	0.935158i	$-0.384743\pi$
$877$	621.320			0.708461			0.354231	+	0.935158i	$0.384743\pi$
$878$		−	222.258i		−	0.253142i
$879$	−507.149			−0.576962
$880$		−	1674.42i		−	1.90275i
$881$			739.549i			0.839443i	0.907653	+	0.419721i	$0.137872\pi$
$881$			739.549i			0.839443i	−0.907653	+	0.419721i	$0.862128\pi$
$882$	−422.678	+	366.242i	−0.479227	+	0.415241i
$883$	643.821			0.729129			0.364564	−	0.931178i	$-0.381218\pi$
$883$	643.821			0.729129			0.364564	+	0.931178i	$0.381218\pi$
$884$	−2308.82			−2.61178
$885$			136.205i			0.153904i
$886$	−1016.97			−1.14782
$887$		−	926.753i		−	1.04482i	−0.852695	−	0.522409i	$-0.825034\pi$
$887$		−	926.753i		−	1.04482i	0.852695	−	0.522409i	$-0.174966\pi$
$888$			1226.44i			1.38113i
$889$	105.344	+	282.444i	0.118497	+	0.317710i
$890$	217.217			0.244064
$891$	130.040			0.145949
$892$		−	3069.58i		−	3.44124i
$893$	−196.278			−0.219796
$894$		−	1596.99i		−	1.78634i
$895$			69.1425i			0.0772542i
$896$	−598.128	−	1603.68i	−0.667554	−	1.78982i
$897$	−304.787			−0.339785
$898$	−1127.98			−1.25610
$899$			582.546i			0.647994i
$900$	157.125			0.174583
$901$		−	1065.56i		−	1.18264i
$902$		−	1583.53i		−	1.75558i
$903$	−66.4094	+	24.7689i	−0.0735431	+	0.0274296i
$904$	3907.00			4.32190
$905$	472.711			0.522332
$906$			709.744i			0.783382i
$907$	−1540.97			−1.69898			−0.849489	−	0.527607i	$-0.823090\pi$
$907$	−1540.97			−1.69898			−0.849489	+	0.527607i	$0.823090\pi$
$908$		−	774.450i		−	0.852919i
$909$		−	37.3826i		−	0.0411250i
$910$	352.590	+	945.349i	0.387461	+	1.03885i
$911$	−1187.49			−1.30350			−0.651748	−	0.758435i	$-0.725964\pi$
$911$	−1187.49			−1.30350			−0.651748	+	0.758435i	$0.725964\pi$
$912$	−1677.77			−1.83966
$913$			616.833i			0.675611i
$914$	−46.1312			−0.0504718
$915$		−	265.232i		−	0.289871i
$916$			2446.08i			2.67039i
$917$	−4.50404	+	1.67988i	−0.00491171	+	0.00183194i
$918$	−257.184			−0.280157
$919$	223.009			0.242665			0.121333	−	0.992612i	$-0.461283\pi$
$919$	223.009			0.242665			0.121333	+	0.992612i	$0.461283\pi$
$920$			572.120i			0.621869i
$921$	−290.733			−0.315671
$922$			395.479i			0.428936i
$923$		−	807.401i		−	0.874757i
$924$	1719.35	−	641.272i	1.86077	−	0.694017i
$925$	−143.717			−0.155370
$926$	−1897.85			−2.04952
$927$		−	115.439i		−	0.124529i
$928$	1353.97			1.45902
$929$			1482.17i			1.59545i	0.603024	+	0.797723i	$0.293962\pi$
$929$			1482.17i			1.59545i	−0.603024	+	0.797723i	$0.706038\pi$
$930$		−	625.335i		−	0.672403i
$931$	599.746	+	692.162i	0.644195	+	0.743461i
$932$	−4037.36			−4.33194
$933$	−526.091			−0.563870
$934$		−	2273.95i		−	2.43463i
$935$	−420.313			−0.449532
$936$		−	1252.14i		−	1.33775i
$937$			836.508i			0.892751i	0.894846	+	0.446376i	$0.147285\pi$
$937$			836.508i			0.892751i	−0.894846	+	0.446376i	$0.852715\pi$
$938$	−441.737	−	1184.37i	−0.470935	−	1.26265i
$939$	−29.8175			−0.0317545
$940$	−245.970			−0.261670
$941$			1637.85i			1.74055i	0.492569	+	0.870273i	$0.336058\pi$
$941$			1637.85i			1.74055i	−0.492569	+	0.870273i	$0.663942\pi$
$942$	501.932			0.532836
$943$			299.183i			0.317267i
$944$		−	1822.60i		−	1.93072i
$945$	28.4223	+	76.2048i	0.0300765	+	0.0806400i
$946$	321.364			0.339709
$947$	748.381			0.790265			0.395133	−	0.918624i	$-0.370699\pi$
$947$	748.381			0.790265			0.395133	+	0.918624i	$0.370699\pi$
$948$			2350.03i			2.47894i
$949$	2134.22			2.24891
$950$		−	355.556i		−	0.374270i
$951$		−	143.528i		−	0.150923i
$952$	−2101.92	+	783.960i	−2.20790	+	0.823487i
$953$	−942.124			−0.988588			−0.494294	−	0.869295i	$-0.664573\pi$
$953$	−942.124			−0.988588			−0.494294	+	0.869295i	$0.664573\pi$
$954$	934.875			0.979953
$955$		−	250.648i		−	0.262458i
$956$	4267.23			4.46362
$957$			343.533i			0.358968i
$958$			1052.75i			1.09890i
$959$	186.421	+	499.825i	0.194391	+	0.521194i
$960$	−650.544			−0.677650
$961$	−840.008			−0.874098
$962$			1852.81i			1.92600i
$963$	263.396			0.273516
$964$			2847.27i			2.95360i
$965$			656.379i			0.680185i
$966$	−448.889	+	167.423i	−0.464688	+	0.173316i
$967$	−1654.90			−1.71138			−0.855690	−	0.517489i	$-0.826867\pi$
$967$	−1654.90			−1.71138			−0.855690	+	0.517489i	$0.826867\pi$
$968$	−2162.21			−2.23369
$969$			421.155i			0.434629i
$970$	244.424			0.251984
$971$		−	354.436i		−	0.365022i	−0.983204	−	0.182511i	$-0.941578\pi$
$971$		−	354.436i		−	0.365022i	0.983204	−	0.182511i	$-0.0584224\pi$
$972$		−	163.289i		−	0.167993i
$973$	−321.666	+	119.973i	−0.330592	+	0.123302i
$974$	2064.58			2.11969
$975$	146.728			0.150490
$976$			3549.14i			3.63642i
$977$	1726.63			1.76727			0.883637	−	0.468173i	$-0.155088\pi$
$977$	1726.63			1.76727			0.883637	+	0.468173i	$0.155088\pi$
$978$			68.7229i			0.0702688i
$979$		−	368.922i		−	0.376836i
$980$	751.583	+	867.397i	0.766922	+	0.885099i
$981$	−390.037			−0.397591
$982$	−2186.95			−2.22704
$983$			1635.34i			1.66362i	0.555062	+	0.831809i	$0.312694\pi$
$983$			1635.34i			1.66362i	−0.555062	+	0.831809i	$0.687306\pi$
$984$	−1229.11			−1.24910
$985$			202.942i			0.206032i
$986$		−	679.414i		−	0.689061i
$987$	−44.4935	−	119.294i	−0.0450795	−	0.120865i
$988$	−3317.15			−3.35744
$989$	−60.7165			−0.0613919
$990$		−	368.766i		−	0.372490i
$991$	−313.579			−0.316427			−0.158213	−	0.987405i	$-0.550573\pi$
$991$	−313.579			−0.316427			−0.158213	+	0.987405i	$0.550573\pi$
$992$			4185.95i			4.21971i
$993$			782.004i			0.787517i
$994$	−443.515	−	1189.13i	−0.446192	−	1.19631i
$995$	870.772			0.875148
$996$	774.546			0.777656
$997$			17.3708i			0.0174231i	0.999962	+	0.00871155i	$0.00277301\pi$
$997$			17.3708i			0.0174231i	−0.999962	+	0.00871155i	$0.997227\pi$
$998$	2092.41			2.09660
$999$			149.355i			0.149505i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	105.3.h.a.76.1	✓	12
3.2	odd	2		315.3.h.d.181.12		12
4.3	odd	2		1680.3.s.c.1441.8		12
5.2	odd	4		525.3.e.c.349.11		24
5.3	odd	4		525.3.e.c.349.4		24
5.4	even	2		525.3.h.d.76.12		12
7.6	odd	2	inner	105.3.h.a.76.2	yes	12
21.20	even	2		315.3.h.d.181.11		12
28.27	even	2		1680.3.s.c.1441.5		12
35.13	even	4		525.3.e.c.349.12		24
35.27	even	4		525.3.e.c.349.3		24
35.34	odd	2		525.3.h.d.76.11		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.3.h.a.76.1	✓	12	1.1	even	1	trivial
105.3.h.a.76.2	yes	12	7.6	odd	2	inner
315.3.h.d.181.11		12	21.20	even	2
315.3.h.d.181.12		12	3.2	odd	2
525.3.e.c.349.3		24	35.27	even	4
525.3.e.c.349.4		24	5.3	odd	4
525.3.e.c.349.11		24	5.2	odd	4
525.3.e.c.349.12		24	35.13	even	4
525.3.h.d.76.11		12	35.34	odd	2
525.3.h.d.76.12		12	5.4	even	2
1680.3.s.c.1441.5		12	28.27	even	2
1680.3.s.c.1441.8		12	4.3	odd	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:	\( N \)	\(=\)	\( 105 = 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	105.h (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-3.80460 q^{2} -1.73205i q^{3} +10.4750 q^{4} -2.23607i q^{5} +6.58976i q^{6} +(2.44621 + 6.55866i) q^{7} -24.6348 q^{8} -3.00000 q^{9} +O(q^{10})\)	\(q-3.80460 q^{2} -1.73205i q^{3} +10.4750 q^{4} -2.23607i q^{5} +6.58976i q^{6} +(2.44621 + 6.55866i) q^{7} -24.6348 q^{8} -3.00000 q^{9} +8.50735i q^{10} +14.4489 q^{11} -18.1432i q^{12} -16.9427i q^{13} +(-9.30684 - 24.9531i) q^{14} -3.87298 q^{15} +51.8255 q^{16} -13.0093i q^{17} +11.4138 q^{18} -18.6908i q^{19} -23.4228i q^{20} +(11.3599 - 4.23695i) q^{21} -54.9723 q^{22} +10.3861 q^{23} +42.6687i q^{24} -5.00000 q^{25} +64.4602i q^{26} +5.19615i q^{27} +(25.6240 + 68.7020i) q^{28} -13.7269 q^{29} +14.7352 q^{30} -42.4383i q^{31} -98.6363 q^{32} -25.0262i q^{33} +49.4951i q^{34} +(14.6656 - 5.46988i) q^{35} -31.4250 q^{36} +28.7434 q^{37} +71.1112i q^{38} -29.3456 q^{39} +55.0850i q^{40} +28.8060i q^{41} +(-43.2200 + 16.1199i) q^{42} -5.84593 q^{43} +151.352 q^{44} +6.70820i q^{45} -39.5151 q^{46} -10.5013i q^{47} -89.7644i q^{48} +(-37.0322 + 32.0877i) q^{49} +19.0230 q^{50} -22.5327 q^{51} -177.475i q^{52} +81.9074 q^{53} -19.7693i q^{54} -32.3087i q^{55} +(-60.2617 - 161.571i) q^{56} -32.3735 q^{57} +52.2254 q^{58} -35.1680i q^{59} -40.5695 q^{60} +68.4826i q^{61} +161.461i q^{62} +(-7.33862 - 19.6760i) q^{63} +167.970 q^{64} -37.8850 q^{65} +95.2149i q^{66} +47.4637 q^{67} -136.272i q^{68} -17.9893i q^{69} +(-55.7968 + 20.8107i) q^{70} +47.6548 q^{71} +73.9043 q^{72} +125.967i q^{73} -109.357 q^{74} +8.66025i q^{75} -195.786i q^{76} +(35.3450 + 94.7655i) q^{77} +111.648 q^{78} -129.527 q^{79} -115.885i q^{80} +9.00000 q^{81} -109.595i q^{82} +42.6906i q^{83} +(118.995 - 44.3820i) q^{84} -29.0896 q^{85} +22.2414 q^{86} +23.7757i q^{87} -355.945 q^{88} -25.5329i q^{89} -25.5220i q^{90} +(111.122 - 41.4453i) q^{91} +108.795 q^{92} -73.5053 q^{93} +39.9533i q^{94} -41.7940 q^{95} +170.843i q^{96} -28.7310i q^{97} +(140.893 - 122.081i) q^{98} -43.3467 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 4 q^{2} + 44 q^{4} - 8 q^{7} + 4 q^{8} - 36 q^{9}+O(q^{10}) \) 12 * q - 4 * q^2 + 44 * q^4 - 8 * q^7 + 4 * q^8 - 36 * q^9	\( 12 q - 4 q^{2} + 44 q^{4} - 8 q^{7} + 4 q^{8} - 36 q^{9} - 16 q^{11} - 40 q^{14} + 92 q^{16} + 12 q^{18} + 36 q^{21} - 88 q^{22} - 64 q^{23} - 60 q^{25} + 88 q^{28} + 104 q^{29} - 228 q^{32} + 60 q^{35} - 132 q^{36} + 32 q^{37} - 24 q^{39} - 60 q^{42} + 152 q^{43} + 192 q^{44} + 200 q^{46} + 60 q^{49} + 20 q^{50} + 24 q^{51} + 176 q^{53} - 368 q^{56} - 240 q^{57} - 400 q^{58} + 24 q^{63} - 20 q^{64} - 240 q^{65} + 168 q^{67} - 60 q^{70} + 32 q^{71} - 12 q^{72} + 184 q^{74} + 8 q^{77} + 456 q^{78} + 120 q^{79} + 108 q^{81} + 108 q^{84} + 120 q^{85} + 400 q^{86} - 536 q^{88} + 24 q^{91} + 192 q^{92} + 48 q^{93} + 884 q^{98} + 48 q^{99}+O(q^{100}) \) 12 * q - 4 * q^2 + 44 * q^4 - 8 * q^7 + 4 * q^8 - 36 * q^9 - 16 * q^11 - 40 * q^14 + 92 * q^16 + 12 * q^18 + 36 * q^21 - 88 * q^22 - 64 * q^23 - 60 * q^25 + 88 * q^28 + 104 * q^29 - 228 * q^32 + 60 * q^35 - 132 * q^36 + 32 * q^37 - 24 * q^39 - 60 * q^42 + 152 * q^43 + 192 * q^44 + 200 * q^46 + 60 * q^49 + 20 * q^50 + 24 * q^51 + 176 * q^53 - 368 * q^56 - 240 * q^57 - 400 * q^58 + 24 * q^63 - 20 * q^64 - 240 * q^65 + 168 * q^67 - 60 * q^70 + 32 * q^71 - 12 * q^72 + 184 * q^74 + 8 * q^77 + 456 * q^78 + 120 * q^79 + 108 * q^81 + 108 * q^84 + 120 * q^85 + 400 * q^86 - 536 * q^88 + 24 * q^91 + 192 * q^92 + 48 * q^93 + 884 * q^98 + 48 * q^99

Introduction

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