LMFDB - Embedded newform 147.3.b.f.50.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [147,3,Mod(50,147)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(147, 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("147.50");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 147 = 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	147.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:	$4.00545988610$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	4.0.65856.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 14x^{2} + 21 $ x^4 + 14*x^2 + 21
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 21)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			50.1
Root			$-3.50592i$ of defining polynomial
Character	$\chi$	$=$	147.50
Dual form			147.3.b.f.50.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-3.50592i q^{2} +(-0.822876 - 2.88494i) q^{3} -8.29150 q^{4} -1.24197i q^{5} +(-10.1144 + 2.88494i) q^{6} +15.0457i q^{8} +(-7.64575 + 4.74789i) q^{9} +O(q^{10})$	\(q-3.50592i q^{2} +(-0.822876 - 2.88494i) q^{3} -8.29150 q^{4} -1.24197i q^{5} +(-10.1144 + 2.88494i) q^{6} +15.0457i q^{8} +(-7.64575 + 4.74789i) q^{9} -4.35425 q^{10} -7.01185i q^{11} +(6.82288 + 23.9205i) q^{12} +11.6458 q^{13} +(-3.58301 + 1.02199i) q^{15} +19.5830 q^{16} -4.52791i q^{17} +(16.6458 + 26.8054i) q^{18} -16.2288 q^{19} +10.2978i q^{20} -24.5830 q^{22} -25.5635i q^{23} +(43.4059 - 12.3807i) q^{24} +23.4575 q^{25} -40.8291i q^{26} +(19.9889 + 18.1506i) q^{27} +9.49579i q^{29} +(3.58301 + 12.5617i) q^{30} -28.7085 q^{31} -8.47380i q^{32} +(-20.2288 + 5.76988i) q^{33} -15.8745 q^{34} +(63.3948 - 39.3672i) q^{36} -33.0405 q^{37} +56.8968i q^{38} +(-9.58301 - 33.5973i) q^{39} +18.6863 q^{40} -67.1946i q^{41} -24.1255 q^{43} +58.1388i q^{44} +(5.89674 + 9.49579i) q^{45} -89.6235 q^{46} +33.0153i q^{47} +(-16.1144 - 56.4958i) q^{48} -82.2403i q^{50} +(-13.0627 + 3.72591i) q^{51} -96.5608 q^{52} -15.1877i q^{53} +(63.6346 - 70.0795i) q^{54} -8.70850 q^{55} +(13.3542 + 46.8190i) q^{57} +33.2915 q^{58} -92.3960i q^{59} +(29.7085 - 8.47380i) q^{60} +57.5203 q^{61} +100.650i q^{62} +48.6235 q^{64} -14.4637i q^{65} +(20.2288 + 70.9205i) q^{66} +15.1660 q^{67} +37.5432i q^{68} +(-73.7490 + 21.0355i) q^{69} -70.5584i q^{71} +(-71.4353 - 115.036i) q^{72} +76.7895 q^{73} +115.838i q^{74} +(-19.3026 - 67.6735i) q^{75} +134.561 q^{76} +(-117.790 + 33.5973i) q^{78} +127.247 q^{79} -24.3215i q^{80} +(35.9150 - 72.6024i) q^{81} -235.579 q^{82} -74.2844i q^{83} -5.62352 q^{85} +84.5821i q^{86} +(27.3948 - 7.81385i) q^{87} +105.498 q^{88} +127.377i q^{89} +(33.2915 - 20.6735i) q^{90} +211.959i q^{92} +(23.6235 + 82.8223i) q^{93} +115.749 q^{94} +20.1556i q^{95} +(-24.4464 + 6.97288i) q^{96} +23.1660 q^{97} +(33.2915 + 53.6108i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{3} - 12 q^{4} - 14 q^{6} - 20 q^{9}+O(q^{10}) $ 4 * q + 2 * q^3 - 12 * q^4 - 14 * q^6 - 20 * q^9	$ 4 q + 2 q^{3} - 12 q^{4} - 14 q^{6} - 20 q^{9} - 28 q^{10} + 22 q^{12} + 36 q^{13} + 28 q^{15} + 36 q^{16} + 56 q^{18} - 12 q^{19} - 56 q^{22} + 126 q^{24} - 12 q^{25} - 10 q^{27} - 28 q^{30} - 136 q^{31} - 28 q^{33} + 116 q^{36} + 16 q^{37} + 4 q^{39} - 84 q^{40} - 160 q^{43} + 140 q^{45} - 168 q^{46} - 38 q^{48} - 84 q^{51} - 164 q^{52} + 154 q^{54} - 56 q^{55} + 64 q^{57} + 112 q^{58} + 140 q^{60} + 156 q^{61} + 4 q^{64} + 28 q^{66} - 24 q^{67} - 168 q^{69} + 32 q^{73} - 146 q^{75} + 316 q^{76} - 196 q^{78} + 128 q^{79} - 68 q^{81} - 392 q^{82} + 168 q^{85} - 28 q^{87} + 168 q^{88} + 112 q^{90} - 96 q^{93} + 336 q^{94} + 98 q^{96} + 8 q^{97} + 112 q^{99}+O(q^{100}) $ 4 * q + 2 * q^3 - 12 * q^4 - 14 * q^6 - 20 * q^9 - 28 * q^10 + 22 * q^12 + 36 * q^13 + 28 * q^15 + 36 * q^16 + 56 * q^18 - 12 * q^19 - 56 * q^22 + 126 * q^24 - 12 * q^25 - 10 * q^27 - 28 * q^30 - 136 * q^31 - 28 * q^33 + 116 * q^36 + 16 * q^37 + 4 * q^39 - 84 * q^40 - 160 * q^43 + 140 * q^45 - 168 * q^46 - 38 * q^48 - 84 * q^51 - 164 * q^52 + 154 * q^54 - 56 * q^55 + 64 * q^57 + 112 * q^58 + 140 * q^60 + 156 * q^61 + 4 * q^64 + 28 * q^66 - 24 * q^67 - 168 * q^69 + 32 * q^73 - 146 * q^75 + 316 * q^76 - 196 * q^78 + 128 * q^79 - 68 * q^81 - 392 * q^82 + 168 * q^85 - 28 * q^87 + 168 * q^88 + 112 * q^90 - 96 * q^93 + 336 * q^94 + 98 * q^96 + 8 * q^97 + 112 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/147\mathbb{Z}\right)^\times$.

$n$	$50$	$52$
$\chi(n)$	$-1$	$1$

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 $

$2$		−	3.50592i		−	1.75296i	−0.481436	−	0.876481i	$-0.659885\pi$
$2$		−	3.50592i		−	1.75296i	0.481436	−	0.876481i	$-0.340115\pi$
$3$	−0.822876	−	2.88494i	−0.274292	−	0.961646i
$3$	−0.822876	−	2.88494i	−0.274292	−	0.961646i
$4$	−8.29150			−2.07288
$5$		−	1.24197i		−	0.248394i	−0.992258	−	0.124197i	$-0.960365\pi$
$5$		−	1.24197i		−	0.248394i	0.992258	−	0.124197i	$-0.0396354\pi$
$6$	−10.1144	+	2.88494i	−1.68573	+	0.480823i
$7$		0			0
$7$		0			0
$8$			15.0457i			1.88071i
$9$	−7.64575	+	4.74789i	−0.849528	+	0.527544i
$10$	−4.35425			−0.435425
$11$		−	7.01185i		−	0.637441i	−0.947849	−	0.318720i	$-0.896747\pi$
$11$		−	7.01185i		−	0.637441i	0.947849	−	0.318720i	$-0.103253\pi$
$12$	6.82288	+	23.9205i	0.568573	+	1.99337i
$13$	11.6458			0.895827			0.447914	−	0.894077i	$-0.352167\pi$
$13$	11.6458			0.895827			0.447914	+	0.894077i	$0.352167\pi$
$14$		0			0
$15$	−3.58301	+	1.02199i	−0.238867	+	0.0681324i
$16$	19.5830			1.22394
$17$		−	4.52791i		−	0.266348i	−0.991093	−	0.133174i	$-0.957483\pi$
$17$		−	4.52791i		−	0.266348i	0.991093	−	0.133174i	$-0.0425169\pi$
$18$	16.6458	+	26.8054i	0.924764	+	1.48919i
$19$	−16.2288			−0.854145			−0.427073	−	0.904217i	$-0.640455\pi$
$19$	−16.2288			−0.854145			−0.427073	+	0.904217i	$0.640455\pi$
$20$			10.2978i			0.514889i
$21$		0			0
$22$	−24.5830			−1.11741
$23$		−	25.5635i		−	1.11145i	−0.831365	−	0.555727i	$-0.812440\pi$
$23$		−	25.5635i		−	1.11145i	0.831365	−	0.555727i	$-0.187560\pi$
$24$	43.4059	−	12.3807i	1.80858	−	0.515864i
$25$	23.4575			0.938301
$26$		−	40.8291i		−	1.57035i
$27$	19.9889	+	18.1506i	0.740329	+	0.672245i
$28$		0			0
$29$			9.49579i			0.327441i	0.986507	+	0.163720i	$0.0523495\pi$
$29$			9.49579i			0.327441i	−0.986507	+	0.163720i	$0.947650\pi$
$30$	3.58301	+	12.5617i	0.119434	+	0.418725i
$31$	−28.7085			−0.926081			−0.463040	−	0.886337i	$-0.653241\pi$
$31$	−28.7085			−0.926081			−0.463040	+	0.886337i	$0.653241\pi$
$32$		−	8.47380i		−	0.264806i
$33$	−20.2288	+	5.76988i	−0.612993	+	0.174845i
$34$	−15.8745			−0.466897
$35$		0			0
$36$	63.3948	−	39.3672i	1.76097	−	1.09353i
$37$	−33.0405			−0.892987			−0.446493	−	0.894787i	$-0.647327\pi$
$37$	−33.0405			−0.892987			−0.446493	+	0.894787i	$0.647327\pi$
$38$			56.8968i			1.49728i
$39$	−9.58301	−	33.5973i	−0.245718	−	0.861469i
$40$	18.6863			0.467157
$41$		−	67.1946i		−	1.63889i	−0.573156	−	0.819446i	$-0.694281\pi$
$41$		−	67.1946i		−	1.63889i	0.573156	−	0.819446i	$-0.305719\pi$
$42$		0			0
$43$	−24.1255			−0.561058			−0.280529	−	0.959846i	$-0.590510\pi$
$43$	−24.1255			−0.561058			−0.280529	+	0.959846i	$0.590510\pi$
$44$			58.1388i			1.32134i
$45$	5.89674	+	9.49579i	0.131039	+	0.211017i
$46$	−89.6235			−1.94834
$47$			33.0153i			0.702452i	0.936291	+	0.351226i	$0.114235\pi$
$47$			33.0153i			0.702452i	−0.936291	+	0.351226i	$0.885765\pi$
$48$	−16.1144	−	56.4958i	−0.335716	−	1.17700i
$49$		0			0
$50$		−	82.2403i		−	1.64481i
$51$	−13.0627	+	3.72591i	−0.256132	+	0.0730570i
$52$	−96.5608			−1.85694
$53$		−	15.1877i		−	0.286561i	−0.989682	−	0.143281i	$-0.954235\pi$
$53$		−	15.1877i		−	0.286561i	0.989682	−	0.143281i	$-0.0457651\pi$
$54$	63.6346	−	70.0795i	1.17842	−	1.29777i
$55$	−8.70850			−0.158336
$56$		0			0
$57$	13.3542	+	46.8190i	0.234285	+	0.821386i
$58$	33.2915			0.573991
$59$		−	92.3960i		−	1.56603i	−0.622000	−	0.783017i	$-0.713680\pi$
$59$		−	92.3960i		−	1.56603i	0.622000	−	0.783017i	$-0.286320\pi$
$60$	29.7085	−	8.47380i	0.495142	−	0.141230i
$61$	57.5203			0.942955			0.471478	−	0.881878i	$-0.343721\pi$
$61$	57.5203			0.942955			0.471478	+	0.881878i	$0.343721\pi$
$62$			100.650i			1.62338i
$63$		0			0
$64$	48.6235			0.759743
$65$		−	14.4637i		−	0.222518i
$66$	20.2288	+	70.9205i	0.306496	+	1.07455i
$67$	15.1660			0.226358			0.113179	−	0.993575i	$-0.463897\pi$
$67$	15.1660			0.226358			0.113179	+	0.993575i	$0.463897\pi$
$68$			37.5432i			0.552106i
$69$	−73.7490	+	21.0355i	−1.06883	+	0.304863i
$70$		0			0
$71$		−	70.5584i		−	0.993781i	−0.867813	−	0.496890i	$-0.834475\pi$
$71$		−	70.5584i		−	0.993781i	0.867813	−	0.496890i	$-0.165525\pi$
$72$	−71.4353	−	115.036i	−0.992157	−	1.59772i
$73$	76.7895			1.05191			0.525956	−	0.850512i	$-0.323708\pi$
$73$	76.7895			1.05191			0.525956	+	0.850512i	$0.323708\pi$
$74$			115.838i			1.56537i
$75$	−19.3026	−	67.6735i	−0.257368	−	0.902313i
$76$	134.561			1.77054
$77$		0			0
$78$	−117.790	+	33.5973i	−1.51012	+	0.430734i
$79$	127.247			1.61072			0.805361	−	0.592785i	$-0.201971\pi$
$79$	127.247			1.61072			0.805361	+	0.592785i	$0.201971\pi$
$80$		−	24.3215i		−	0.304019i
$81$	35.9150	−	72.6024i	0.443395	−	0.896326i
$82$	−235.579			−2.87292
$83$		−	74.2844i		−	0.894992i	−0.894286	−	0.447496i	$-0.852316\pi$
$83$		−	74.2844i		−	0.894992i	0.894286	−	0.447496i	$-0.147684\pi$
$84$		0			0
$85$	−5.62352			−0.0661591
$86$			84.5821i			0.983513i
$87$	27.3948	−	7.81385i	0.314882	−	0.0898144i
$88$	105.498			1.19884
$89$			127.377i			1.43121i	0.698507	+	0.715603i	$0.253848\pi$
$89$			127.377i			1.43121i	−0.698507	+	0.715603i	$0.746152\pi$
$90$	33.2915	−	20.6735i	0.369906	−	0.229706i
$91$		0			0
$92$			211.959i			2.30391i
$93$	23.6235	+	82.8223i	0.254016	+	0.890562i
$94$	115.749			1.23137
$95$			20.1556i			0.212164i
$96$	−24.4464	+	6.97288i	−0.254650	+	0.0726342i
$97$	23.1660			0.238825			0.119412	−	0.992845i	$-0.461899\pi$
$97$	23.1660			0.238825			0.119412	+	0.992845i	$0.461899\pi$
$98$		0			0
$99$	33.2915	+	53.6108i	0.336278	+	0.541524i
$100$	−194.498			−1.94498
$101$			134.907i			1.33571i	0.744290	+	0.667857i	$0.232788\pi$
$101$			134.907i			1.33571i	−0.744290	+	0.667857i	$0.767212\pi$
$102$	13.0627	+	45.7970i	0.128066	+	0.448990i
$103$	119.749			1.16261			0.581306	−	0.813685i	$-0.302542\pi$
$103$	119.749			1.16261			0.581306	+	0.813685i	$0.302542\pi$
$104$			175.218i			1.68479i
$105$		0			0
$106$	−53.2470			−0.502331
$107$		−	77.8544i		−	0.727611i	−0.931475	−	0.363806i	$-0.881477\pi$
$107$		−	77.8544i		−	0.727611i	0.931475	−	0.363806i	$-0.118523\pi$
$108$	−165.738	−	150.496i	−1.53461	−	1.39348i
$109$	−36.5385			−0.335216			−0.167608	−	0.985854i	$-0.553604\pi$
$109$	−36.5385			−0.335216			−0.167608	+	0.985854i	$0.553604\pi$
$110$			30.5313i			0.277558i
$111$	27.1882	+	95.3199i	0.244939	+	0.858738i
$112$		0			0
$113$			21.7596i			0.192563i	0.995354	+	0.0962815i	$0.0306949\pi$
$113$			21.7596i			0.192563i	−0.995354	+	0.0962815i	$0.969305\pi$
$114$	164.144	−	46.8190i	1.43986	−	0.410693i
$115$	−31.7490			−0.276078
$116$		−	78.7343i		−	0.678744i
$117$	−89.0405	+	55.2928i	−0.761030	+	0.472588i
$118$	−323.933			−2.74520
$119$		0			0
$120$	−15.3765	−	53.9088i	−0.128137	−	0.449240i
$121$	71.8340			0.593669
$122$		−	201.662i		−	1.65296i
$123$	−193.852	+	55.2928i	−1.57603	+	0.449535i
$124$	238.037			1.91965
$125$		−	60.1827i		−	0.481462i
$126$		0			0
$127$	−15.4170			−0.121394			−0.0606968	−	0.998156i	$-0.519332\pi$
$127$	−15.4170			−0.121394			−0.0606968	+	0.998156i	$0.519332\pi$
$128$		−	204.366i		−	1.59661i
$129$	19.8523	+	69.6006i	0.153894	+	0.539539i
$130$	−50.7085			−0.390065
$131$		−	183.110i		−	1.39779i	−0.715226	−	0.698893i	$-0.753676\pi$
$131$		−	183.110i		−	1.39779i	0.715226	−	0.698893i	$-0.246324\pi$
$132$	167.727	−	47.8410i	1.27066	−	0.362432i
$133$		0			0
$134$		−	53.1709i		−	0.396798i
$135$	22.5425	−	24.8256i	0.166981	−	0.183893i
$136$	68.1255			0.500923
$137$			33.0153i			0.240987i	0.992714	+	0.120494i	$0.0384477\pi$
$137$			33.0153i			0.240987i	−0.992714	+	0.120494i	$0.961552\pi$
$138$	73.7490	+	258.558i	0.534413	+	1.87361i
$139$	−64.6418			−0.465049			−0.232525	−	0.972591i	$-0.574699\pi$
$139$	−64.6418			−0.465049			−0.232525	+	0.972591i	$0.574699\pi$
$140$		0			0
$141$	95.2470	−	27.1675i	0.675511	−	0.192677i
$142$	−247.373			−1.74206
$143$		−	81.6582i		−	0.571037i
$144$	−149.727	+	92.9780i	−1.03977	+	0.645681i
$145$	11.7935			0.0813343
$146$		−	269.218i		−	1.84396i
$147$		0			0
$148$	273.956			1.85105
$149$			195.736i			1.31366i	0.754037	+	0.656832i	$0.228104\pi$
$149$			195.736i			1.31366i	−0.754037	+	0.656832i	$0.771896\pi$
$150$	−237.258	+	67.6735i	−1.58172	+	0.451157i
$151$	102.251			0.677159			0.338579	−	0.940938i	$-0.390054\pi$
$151$	102.251			0.677159			0.338579	+	0.940938i	$0.390054\pi$
$152$		−	244.173i		−	1.60640i
$153$	21.4980	+	34.6193i	0.140510	+	0.226270i
$154$		0			0
$155$			35.6551i			0.230033i
$156$	79.4575	+	278.572i	0.509343	+	1.78572i
$157$	−104.723			−0.667025			−0.333512	−	0.942746i	$-0.608234\pi$
$157$	−104.723			−0.667025			−0.333512	+	0.942746i	$0.608234\pi$
$158$		−	446.118i		−	2.82353i
$159$	−43.8157	+	12.4976i	−0.275570	+	0.0786014i
$160$	−10.5242			−0.0657762
$161$		0			0
$162$	−254.539	−	125.915i	−1.57123	−	0.777255i
$163$	−70.9595			−0.435334			−0.217667	−	0.976023i	$-0.569845\pi$
$163$	−70.9595			−0.435334			−0.217667	+	0.976023i	$0.569845\pi$
$164$			557.144i			3.39722i
$165$	7.16601	+	25.1235i	0.0434304	+	0.152264i
$166$	−260.435			−1.56889
$167$			206.992i			1.23947i	0.784811	+	0.619735i	$0.212760\pi$
$167$			206.992i			1.23947i	−0.784811	+	0.619735i	$0.787240\pi$
$168$		0			0
$169$	−33.3765			−0.197494
$170$			19.7156i			0.115974i
$171$	124.081	−	77.0524i	0.725620	−	0.450599i
$172$	200.037			1.16300
$173$		−	108.464i		−	0.626958i	−0.949595	−	0.313479i	$-0.898506\pi$
$173$		−	108.464i		−	0.626958i	0.949595	−	0.313479i	$-0.101494\pi$
$174$	−27.3948	−	96.0440i	−0.157441	−	0.551977i
$175$		0			0
$176$		−	137.313i		−	0.780188i
$177$	−266.557	+	76.0304i	−1.50597	+	0.429550i
$178$	446.575			2.50885
$179$			159.357i			0.890261i	0.895466	+	0.445131i	$0.146843\pi$
$179$			159.357i			0.890261i	−0.895466	+	0.445131i	$0.853157\pi$
$180$	−48.8928	−	78.7343i	−0.271627	−	0.437413i
$181$	233.889			1.29220			0.646102	−	0.763251i	$-0.276398\pi$
$181$	233.889			1.29220			0.646102	+	0.763251i	$0.276398\pi$
$182$		0			0
$183$	−47.3320	−	165.942i	−0.258645	−	0.906789i
$184$	384.620			2.09032
$185$			41.0353i			0.221812i
$186$	290.369	−	82.8223i	1.56112	−	0.445281i
$187$	−31.7490			−0.169781
$188$		−	273.746i		−	1.45610i
$189$		0			0
$190$	70.6640			0.371916
$191$		−	288.210i		−	1.50895i	−0.656328	−	0.754476i	$-0.727891\pi$
$191$		−	288.210i		−	1.50895i	0.656328	−	0.754476i	$-0.272109\pi$
$192$	−40.0111	−	140.276i	−0.208391	−	0.730604i
$193$	77.1216			0.399594			0.199797	−	0.979837i	$-0.435972\pi$
$193$	77.1216			0.399594			0.199797	+	0.979837i	$0.435972\pi$
$194$		−	81.2183i		−	0.418651i
$195$	−41.7268	+	11.9018i	−0.213984	+	0.0610348i
$196$		0			0
$197$		−	136.433i		−	0.692554i	−0.938132	−	0.346277i	$-0.887446\pi$
$197$		−	136.433i		−	0.692554i	0.938132	−	0.346277i	$-0.112554\pi$
$198$	187.956	−	116.717i	0.949270	−	0.589482i
$199$	−86.5830			−0.435090			−0.217545	−	0.976050i	$-0.569805\pi$
$199$	−86.5830			−0.435090			−0.217545	+	0.976050i	$0.569805\pi$
$200$			352.934i			1.76467i
$201$	−12.4797	−	43.7530i	−0.0620883	−	0.217677i
$202$	472.974			2.34145
$203$		0			0
$204$	108.310	−	30.8934i	0.530930	−	0.151438i
$205$	−83.4536			−0.407091
$206$		−	419.831i		−	2.03801i
$207$	121.373	+	195.452i	0.586341	+	0.944212i
$208$	228.059			1.09644
$209$			113.794i			0.544467i
$210$		0			0
$211$	19.4170			0.0920237			0.0460118	−	0.998941i	$-0.485349\pi$
$211$	19.4170			0.0920237			0.0460118	+	0.998941i	$0.485349\pi$
$212$			125.929i			0.594005i
$213$	−203.557	+	58.0608i	−0.955666	+	0.272586i
$214$	−272.952			−1.27547
$215$			29.9631i			0.139363i
$216$	−273.088	+	300.746i	−1.26430	+	1.39234i
$217$		0			0
$218$			128.101i			0.587621i
$219$	−63.1882	−	221.533i	−0.288531	−	1.01157i
$220$	72.2065			0.328211
$221$		−	52.7309i		−	0.238601i
$222$	334.184	−	95.3199i	1.50533	−	0.429369i
$223$	−175.041			−0.784935			−0.392468	−	0.919766i	$-0.628378\pi$
$223$	−175.041			−0.784935			−0.392468	+	0.919766i	$0.628378\pi$
$224$		0			0
$225$	−179.350	+	111.374i	−0.797112	+	0.494994i
$226$	76.2876			0.337556
$227$			177.574i			0.782264i	0.920335	+	0.391132i	$0.127916\pi$
$227$			177.574i			0.782264i	−0.920335	+	0.391132i	$0.872084\pi$
$228$	−110.727	−	388.200i	−0.485644	−	1.70263i
$229$	−40.8118			−0.178217			−0.0891087	−	0.996022i	$-0.528402\pi$
$229$	−40.8118			−0.178217			−0.0891087	+	0.996022i	$0.528402\pi$
$230$			111.310i			0.483955i
$231$		0			0
$232$	−142.871			−0.615821
$233$			387.696i			1.66393i	0.554828	+	0.831965i	$0.312784\pi$
$233$			387.696i			1.66393i	−0.554828	+	0.831965i	$0.687216\pi$
$234$	193.852	+	312.169i	0.828429	+	1.33406i
$235$	41.0039			0.174485
$236$			766.102i			3.24619i
$237$	−104.708	−	367.100i	−0.441808	−	1.54895i
$238$		0			0
$239$		−	49.5229i		−	0.207209i	−0.994619	−	0.103604i	$-0.966962\pi$
$239$		−	49.5229i		−	0.207209i	0.994619	−	0.103604i	$-0.0330376\pi$
$240$	−70.1660	+	20.0136i	−0.292358	+	0.0833898i
$241$	−325.247			−1.34957			−0.674786	−	0.738013i	$-0.735764\pi$
$241$	−325.247			−1.34957			−0.674786	+	0.738013i	$0.735764\pi$
$242$		−	251.845i		−	1.04068i
$243$	−239.007	−	43.8699i	−0.983569	−	0.180535i
$244$	−476.929			−1.95463
$245$		0			0
$246$	193.852	+	679.631i	0.788017	+	2.76273i
$247$	−188.996			−0.765166
$248$		−	431.939i		−	1.74169i
$249$	−214.306	+	61.1268i	−0.860666	+	0.245489i
$250$	−210.996			−0.843984
$251$			263.732i			1.05073i	0.850878	+	0.525364i	$0.176071\pi$
$251$			263.732i			1.05073i	−0.850878	+	0.525364i	$0.823929\pi$
$252$		0			0
$253$	−179.247			−0.708486
$254$			54.0508i			0.212798i
$255$	4.62746	+	16.2235i	0.0181469	+	0.0636217i
$256$	−521.996			−2.03905
$257$			151.181i			0.588252i	0.955767	+	0.294126i	$0.0950286\pi$
$257$			151.181i			0.588252i	−0.955767	+	0.294126i	$0.904971\pi$
$258$	244.014	−	69.6006i	0.945792	−	0.269770i
$259$		0			0
$260$			119.925i			0.461252i
$261$	−45.0850	−	72.6024i	−0.172739	−	0.278170i
$262$	−641.970			−2.45027
$263$			114.389i			0.434941i	0.976067	+	0.217470i	$0.0697805\pi$
$263$			114.389i			0.434941i	−0.976067	+	0.217470i	$0.930219\pi$
$264$	−86.8118	−	304.355i	−0.328832	−	1.15286i
$265$	−18.8627			−0.0711800
$266$		0			0
$267$	367.476	−	104.816i	1.37631	−	0.392568i
$268$	−125.749			−0.469213
$269$		−	4.76170i		−	0.0177015i	−0.999961	−	0.00885074i	$-0.997183\pi$
$269$		−	4.76170i		−	0.0177015i	0.999961	−	0.00885074i	$-0.00281731\pi$
$270$	−87.0366	−	79.0322i	−0.322358	−	0.292712i
$271$	518.701			1.91402			0.957012	−	0.290048i	$-0.0936711\pi$
$271$	518.701			1.91402			0.957012	+	0.290048i	$0.0936711\pi$
$272$		−	88.6701i		−	0.325993i
$273$		0			0
$274$	115.749			0.422442
$275$		−	164.481i		−	0.598111i
$276$	611.490	−	174.416i	2.21554	−	0.631943i
$277$	−121.085			−0.437130			−0.218565	−	0.975822i	$-0.570138\pi$
$277$	−121.085			−0.437130			−0.218565	+	0.975822i	$0.570138\pi$
$278$			226.629i			0.815213i
$279$	219.498	−	136.305i	0.786731	−	0.488548i
$280$		0			0
$281$			407.255i			1.44931i	0.689113	+	0.724654i	$0.258000\pi$
$281$			407.255i			1.44931i	−0.689113	+	0.724654i	$0.742000\pi$
$282$	−95.2470	−	333.929i	−0.337755	−	1.18415i
$283$	398.634			1.40860			0.704300	−	0.709902i	$-0.251261\pi$
$283$	398.634			1.40860			0.704300	+	0.709902i	$0.251261\pi$
$284$			585.036i			2.05998i
$285$	58.1477	−	16.5856i	0.204027	−	0.0581950i
$286$	−286.288			−1.00101
$287$		0			0
$288$	40.2327	+	64.7886i	0.139697	+	0.224960i
$289$	268.498			0.929059
$290$		−	41.3470i		−	0.142576i
$291$	−19.0627	−	66.8325i	−0.0655077	−	0.229665i
$292$	−636.701			−2.18048
$293$		−	2.53426i		−	0.00864935i	−0.999991	−	0.00432468i	$-0.998623\pi$
$293$		−	2.53426i		−	0.00864935i	0.999991	−	0.00432468i	$-0.00137659\pi$
$294$		0			0
$295$	−114.753			−0.388993
$296$		−	497.117i		−	1.67945i
$297$	127.269	−	140.159i	0.428516	−	0.471916i
$298$	686.235			2.30280
$299$		−	297.706i		−	0.995671i
$300$	160.048	+	561.115i	0.533492	+	1.87038i
$301$		0			0
$302$		−	358.484i		−	1.18703i
$303$	389.199	−	111.012i	1.28448	−	0.366375i
$304$	−317.808			−1.04542
$305$		−	71.4384i		−	0.234224i
$306$	121.373	−	75.3705i	0.396642	−	0.246309i
$307$	−86.2366			−0.280901			−0.140451	−	0.990088i	$-0.544855\pi$
$307$	−86.2366			−0.280901			−0.140451	+	0.990088i	$0.544855\pi$
$308$		0			0
$309$	−98.5385	−	345.469i	−0.318895	−	1.11802i
$310$	125.004			0.403239
$311$		−	151.777i		−	0.488028i	−0.969772	−	0.244014i	$-0.921536\pi$
$311$		−	151.777i		−	0.488028i	0.969772	−	0.244014i	$-0.0784643\pi$
$312$	505.494	−	144.183i	1.62017	−	0.462125i
$313$	−318.118			−1.01635			−0.508175	−	0.861254i	$-0.669680\pi$
$313$	−318.118			−1.01635			−0.508175	+	0.861254i	$0.669680\pi$
$314$			367.150i			1.16927i
$315$		0			0
$316$	−1055.07			−3.33883
$317$			364.020i			1.14833i	0.818740	+	0.574164i	$0.194673\pi$
$317$			364.020i			1.14833i	−0.818740	+	0.574164i	$0.805327\pi$
$318$	43.8157	+	153.615i	0.137785	+	0.483064i
$319$	66.5830			0.208724
$320$		−	60.3889i		−	0.188715i
$321$	−224.605	+	64.0645i	−0.699705	+	0.199578i
$322$		0			0
$323$			73.4823i			0.227500i
$324$	−297.790	+	601.983i	−0.919104	+	1.85797i
$325$	273.180			0.840555
$326$			248.779i			0.763124i
$327$	30.0667	+	105.412i	0.0919470	+	0.322359i
$328$	1010.99			3.08228
$329$		0			0
$330$	88.0810	−	25.1235i	0.266912	−	0.0761318i
$331$	154.369			0.466370			0.233185	−	0.972432i	$-0.425085\pi$
$331$	154.369			0.466370			0.233185	+	0.972432i	$0.425085\pi$
$332$			615.929i			1.85521i
$333$	252.620	−	156.873i	0.758617	−	0.471090i
$334$	725.697			2.17274
$335$		−	18.8357i		−	0.0562260i
$336$		0			0
$337$	403.041			1.19597			0.597983	−	0.801509i	$-0.295969\pi$
$337$	403.041			1.19597			0.597983	+	0.801509i	$0.295969\pi$
$338$			117.015i			0.346199i
$339$	62.7752	−	17.9055i	0.185178	−	0.0528185i
$340$	46.6275			0.137140
$341$			201.300i			0.590321i
$342$	−270.140	−	435.019i	−0.789883	−	1.27198i
$343$		0			0
$344$		−	362.984i		−	1.05519i
$345$	26.1255	+	91.5940i	0.0757261	+	0.265490i
$346$	−380.265			−1.09903
$347$		−	471.242i		−	1.35805i	−0.734117	−	0.679023i	$-0.762404\pi$
$347$		−	471.242i		−	1.35805i	0.734117	−	0.679023i	$-0.237596\pi$
$348$	−227.144	+	64.7886i	−0.652712	+	0.186174i
$349$	364.516			1.04446			0.522230	−	0.852805i	$-0.325100\pi$
$349$	364.516			1.04446			0.522230	+	0.852805i	$0.325100\pi$
$350$		0			0
$351$	232.786	+	211.377i	0.663207	+	0.602215i
$352$	−59.4170			−0.168798
$353$			86.3420i			0.244595i	0.992493	+	0.122297i	$0.0390262\pi$
$353$			86.3420i			0.244595i	−0.992493	+	0.122297i	$0.960974\pi$
$354$	266.557	+	934.528i	0.752985	+	2.63991i
$355$	−87.6314			−0.246849
$356$		−	1056.15i		−	2.96671i
$357$		0			0
$358$	558.693			1.56059
$359$			372.068i			1.03640i	0.855259	+	0.518200i	$0.173398\pi$
$359$			372.068i			1.03640i	−0.855259	+	0.518200i	$0.826602\pi$
$360$	−142.871	+	88.7204i	−0.396863	+	0.246446i
$361$	−97.6275			−0.270436
$362$		−	819.997i		−	2.26518i
$363$	−59.1104	−	207.237i	−0.162839	−	0.570900i
$364$		0			0
$365$		−	95.3702i		−	0.261288i
$366$	−581.782	+	165.942i	−1.58957	+	0.453395i
$367$	161.786			0.440833			0.220416	−	0.975406i	$-0.429258\pi$
$367$	161.786			0.440833			0.220416	+	0.975406i	$0.429258\pi$
$368$		−	500.609i		−	1.36035i
$369$	319.033	+	513.753i	0.864587	+	1.39228i
$370$	143.867			0.388829
$371$		0			0
$372$	−195.875	−	686.721i	−0.526544	−	1.84602i
$373$	378.251			1.01408			0.507039	−	0.861923i	$-0.330740\pi$
$373$	378.251			1.01408			0.507039	+	0.861923i	$0.330740\pi$
$374$			111.310i			0.297619i
$375$	−173.624	+	49.5229i	−0.462996	+	0.132061i
$376$	−496.737			−1.32111
$377$			110.586i			0.293330i
$378$		0			0
$379$	−50.7974			−0.134030			−0.0670151	−	0.997752i	$-0.521348\pi$
$379$	−50.7974			−0.134030			−0.0670151	+	0.997752i	$0.521348\pi$
$380$		−	167.120i		−	0.439790i
$381$	12.6863	+	44.4771i	0.0332973	+	0.116738i
$382$	−1010.44			−2.64514
$383$		−	113.381i		−	0.296034i	−0.988985	−	0.148017i	$-0.952711\pi$
$383$		−	113.381i		−	0.296034i	0.988985	−	0.148017i	$-0.0472891\pi$
$384$	−589.582	+	168.167i	−1.53537	+	0.437936i
$385$		0			0
$386$		−	270.382i		−	0.700472i
$387$	184.458	−	114.545i	0.476634	−	0.295983i
$388$	−192.081			−0.495054
$389$		−	725.584i		−	1.86526i	−0.360841	−	0.932628i	$-0.617510\pi$
$389$		−	725.584i		−	1.86526i	0.360841	−	0.932628i	$-0.382490\pi$
$390$	41.7268	+	146.291i	0.106992	+	0.375105i
$391$	−115.749			−0.296033
$392$		0			0
$393$	−528.261	+	150.677i	−1.34418	+	0.383402i
$394$	−478.324			−1.21402
$395$		−	158.037i		−	0.400093i
$396$	−276.037	−	444.514i	−0.697062	−	1.12251i
$397$	94.3464			0.237648			0.118824	−	0.992915i	$-0.462088\pi$
$397$	94.3464			0.237648			0.118824	+	0.992915i	$0.462088\pi$
$398$			303.553i			0.762697i
$399$		0			0
$400$	459.369			1.14842
$401$		−	677.665i		−	1.68994i	−0.534815	−	0.844969i	$-0.679619\pi$
$401$		−	677.665i		−	1.68994i	0.534815	−	0.844969i	$-0.320381\pi$
$402$	−153.395	+	43.7530i	−0.381579	+	0.108838i
$403$	−334.332			−0.829608
$404$		−	1118.58i		−	2.76877i
$405$	−90.1699	−	44.6053i	−0.222642	−	0.110137i
$406$		0			0
$407$			231.675i			0.569226i
$408$	−56.0588	−	196.538i	−0.137399	−	0.481711i
$409$	−17.3647			−0.0424564			−0.0212282	−	0.999775i	$-0.506758\pi$
$409$	−17.3647			−0.0424564			−0.0212282	+	0.999775i	$0.506758\pi$
$410$			292.582i			0.713614i
$411$	95.2470	−	27.1675i	0.231745	−	0.0661009i
$412$	−992.899			−2.40995
$413$		0			0
$414$	685.239	−	425.523i	1.65517	−	1.02783i
$415$	−92.2589			−0.222311
$416$		−	98.6838i		−	0.237221i
$417$	53.1922	+	186.488i	0.127559	+	0.447213i
$418$	398.952			0.954430
$419$		−	136.071i		−	0.324752i	−0.986729	−	0.162376i	$-0.948084\pi$
$419$		−	136.071i		−	0.324752i	0.986729	−	0.162376i	$-0.0519157\pi$
$420$		0			0
$421$	423.992			1.00711			0.503554	−	0.863964i	$-0.332026\pi$
$421$	423.992			1.00711			0.503554	+	0.863964i	$0.332026\pi$
$422$		−	68.0745i		−	0.161314i
$423$	−156.753	−	252.427i	−0.370574	−	0.596753i
$424$	228.510			0.538938
$425$		−	106.214i		−	0.249914i
$426$	203.557	+	713.655i	0.477833	+	1.67525i
$427$		0			0
$428$			645.530i			1.50825i
$429$	−235.579	+	67.1946i	−0.549135	+	0.156631i
$430$	105.048			0.244299
$431$			340.244i			0.789430i	0.918804	+	0.394715i	$0.129157\pi$
$431$			340.244i			0.789430i	−0.918804	+	0.394715i	$0.870843\pi$
$432$	391.442	+	355.443i	0.906117	+	0.822786i
$433$	−159.166			−0.367589			−0.183794	−	0.982965i	$-0.558838\pi$
$433$	−159.166			−0.367589			−0.183794	+	0.982965i	$0.558838\pi$
$434$		0			0
$435$	−9.70456	−	34.0235i	−0.0223093	−	0.0782148i
$436$	302.959			0.694861
$437$			414.863i			0.949343i
$438$	−776.678	+	221.533i	−1.77324	+	0.505783i
$439$	−128.073			−0.291738			−0.145869	−	0.989304i	$-0.546598\pi$
$439$	−128.073			−0.291738			−0.145869	+	0.989304i	$0.546598\pi$
$440$		−	131.025i		−	0.297785i
$441$		0			0
$442$	−184.871			−0.418259
$443$		−	197.340i		−	0.445463i	−0.974880	−	0.222731i	$-0.928503\pi$
$443$		−	197.340i		−	0.445463i	0.974880	−	0.222731i	$-0.0714973\pi$
$444$	−225.431	−	790.345i	−0.507728	−	1.78006i
$445$	158.199			0.355503
$446$			613.679i			1.37596i
$447$	564.686	−	161.066i	1.26328	−	0.360327i
$448$		0			0
$449$			148.101i			0.329847i	0.986306	+	0.164923i	$0.0527377\pi$
$449$			148.101i			0.329847i	−0.986306	+	0.164923i	$0.947262\pi$
$450$	390.468	+	628.789i	0.867707	+	1.39731i
$451$	−471.158			−1.04470
$452$		−	180.420i		−	0.399159i
$453$	−84.1398	−	294.988i	−0.185739	−	0.651187i
$454$	622.561			1.37128
$455$		0			0
$456$	−704.423	+	200.924i	−1.54479	+	0.440622i
$457$	−122.214			−0.267428			−0.133714	−	0.991020i	$-0.542690\pi$
$457$	−122.214			−0.267428			−0.133714	+	0.991020i	$0.542690\pi$
$458$			143.083i			0.312408i
$459$	82.1843	−	90.5079i	0.179051	−	0.197185i
$460$	263.247			0.572276
$461$		−	602.089i		−	1.30605i	−0.757337	−	0.653025i	$-0.773500\pi$
$461$		−	602.089i		−	1.30605i	0.757337	−	0.653025i	$-0.226500\pi$
$462$		0			0
$463$	−637.061			−1.37594			−0.687971	−	0.725738i	$-0.741498\pi$
$463$	−637.061			−1.37594			−0.687971	+	0.725738i	$0.741498\pi$
$464$			185.956i			0.400767i
$465$	102.863	−	29.3397i	0.221210	−	0.0630961i
$466$	1359.23			2.91681
$467$			767.706i			1.64391i	0.569553	+	0.821955i	$0.307116\pi$
$467$			767.706i			1.64391i	−0.569553	+	0.821955i	$0.692884\pi$
$468$	738.280	−	458.460i	1.57752	−	0.979616i
$469$		0			0
$470$		−	143.757i		−	0.305865i
$471$	86.1739	+	302.119i	0.182959	+	0.641442i
$472$	1390.16			2.94526
$473$			169.164i			0.357641i
$474$	−1287.02	+	367.100i	−2.71524	+	0.774473i
$475$	−380.686			−0.801445
$476$		0			0
$477$	72.1097	+	116.122i	0.151173	+	0.243442i
$478$	−173.624			−0.363229
$479$		−	393.855i		−	0.822245i	−0.911580	−	0.411122i	$-0.865137\pi$
$479$		−	393.855i		−	0.822245i	0.911580	−	0.411122i	$-0.134863\pi$
$480$	8.66010	+	30.3617i	0.0180419	+	0.0632535i
$481$	−384.782			−0.799962
$482$			1140.29i			2.36575i
$483$		0			0
$484$	−595.612			−1.23060
$485$		−	28.7715i		−	0.0593226i
$486$	−153.805	+	837.941i	−0.316470	+	1.72416i
$487$	573.409			1.17743			0.588716	−	0.808340i	$-0.299634\pi$
$487$	573.409			1.17743			0.588716	+	0.808340i	$0.299634\pi$
$488$			865.432i			1.77343i
$489$	58.3908	+	204.714i	0.119409	+	0.418638i
$490$		0			0
$491$		−	170.796i		−	0.347853i	−0.984759	−	0.173927i	$-0.944354\pi$
$491$		−	170.796i		−	0.347853i	0.984759	−	0.173927i	$-0.0556455\pi$
$492$	1607.33	−	458.460i	3.26692	−	0.931830i
$493$	42.9961			0.0872131
$494$			662.606i			1.34131i
$495$	66.5830	−	41.3470i	0.134511	−	0.0835293i
$496$	−562.199			−1.13347
$497$		0			0
$498$	214.306	+	751.340i	0.430333	+	1.50871i
$499$	−847.814			−1.69903			−0.849513	−	0.527567i	$-0.823104\pi$
$499$	−847.814			−1.69903			−0.849513	+	0.527567i	$0.823104\pi$
$500$			499.005i			0.998010i
$501$	597.158	−	170.328i	1.19193	−	0.339977i
$502$	924.626			1.84188
$503$		−	197.624i		−	0.392891i	−0.980515	−	0.196445i	$-0.937060\pi$
$503$		−	197.624i		−	0.392891i	0.980515	−	0.196445i	$-0.0629398\pi$
$504$		0			0
$505$	167.550			0.331783
$506$			628.427i			1.24195i
$507$	27.4647	+	96.2891i	0.0541710	+	0.189919i
$508$	127.830			0.251634
$509$		−	491.448i		−	0.965516i	−0.875754	−	0.482758i	$-0.839635\pi$
$509$		−	491.448i		−	0.965516i	0.875754	−	0.482758i	$-0.160365\pi$
$510$	56.8784	−	16.2235i	0.111526	−	0.0318108i
$511$		0			0
$512$			1012.62i			1.97777i
$513$	−324.395	−	294.562i	−0.632348	−	0.574194i
$514$	530.029			1.03118
$515$		−	148.725i		−	0.288786i
$516$	−164.605	−	577.093i	−0.319002	−	1.11840i
$517$	231.498			0.447772
$518$		0			0
$519$	−312.911	+	89.2521i	−0.602912	+	0.171969i
$520$	217.616			0.418492
$521$		−	870.010i		−	1.66988i	−0.550338	−	0.834942i	$-0.685501\pi$
$521$		−	870.010i		−	1.66988i	0.550338	−	0.834942i	$-0.314499\pi$
$522$	−254.539	+	158.064i	−0.487622	+	0.302806i
$523$	−798.707			−1.52716			−0.763582	−	0.645710i	$-0.776561\pi$
$523$	−798.707			−1.52716			−0.763582	+	0.645710i	$0.776561\pi$
$524$			1518.26i			2.89744i
$525$		0			0
$526$	401.041			0.762434
$527$			129.989i			0.246659i
$528$	−396.140	+	112.992i	−0.750265	+	0.213999i
$529$	−124.490			−0.235331
$530$			66.1312i			0.124776i
$531$	438.686	+	706.437i	0.826151	+	1.33039i
$532$		0			0
$533$		−	782.531i		−	1.46816i
$534$	−367.476	−	1288.34i	−0.688157	−	2.41263i
$535$	−96.6927			−0.180734
$536$			228.183i			0.425714i
$537$	459.735	−	131.131i	0.856117	−	0.244191i
$538$	−16.6941			−0.0310300
$539$		0			0
$540$	−186.911	+	205.841i	−0.346132	+	0.381188i
$541$	−736.243			−1.36089			−0.680446	−	0.732798i	$-0.738214\pi$
$541$	−736.243			−1.36089			−0.680446	+	0.732798i	$0.738214\pi$
$542$		−	1818.52i		−	3.35521i
$543$	−192.461	−	674.755i	−0.354441	−	1.24264i
$544$	−38.3686			−0.0705305
$545$			45.3797i			0.0832656i
$546$		0			0
$547$	−228.952			−0.418559			−0.209279	−	0.977856i	$-0.567112\pi$
$547$	−228.952			−0.418559			−0.209279	+	0.977856i	$0.567112\pi$
$548$		−	273.746i		−	0.499537i
$549$	−439.786	+	273.100i	−0.801067	+	0.497450i
$550$	−576.656			−1.04847
$551$		−	154.105i		−	0.279682i
$552$	−316.494	−	1109.60i	−0.573359	−	2.01015i
$553$		0			0
$554$			424.515i			0.766272i
$555$	118.384	−	33.7669i	0.213305	−	0.0608413i
$556$	535.978			0.963989
$557$			906.288i			1.62709i	0.581503	+	0.813544i	$0.302465\pi$
$557$			906.288i			1.62709i	−0.581503	+	0.813544i	$0.697535\pi$
$558$	−477.875	−	769.543i	−0.856406	−	1.37911i
$559$	−280.959			−0.502611
$560$		0			0
$561$	26.1255	+	91.5940i	0.0465695	+	0.163269i
$562$	1427.81			2.54058
$563$			458.616i			0.814593i	0.913296	+	0.407297i	$0.133529\pi$
$563$			458.616i			0.814593i	−0.913296	+	0.407297i	$0.866471\pi$
$564$	−789.741	+	225.259i	−1.40025	+	0.399396i
$565$	27.0248			0.0478315
$566$		−	1397.58i		−	2.46922i
$567$		0			0
$568$	1061.60			1.86901
$569$		−	577.428i		−	1.01481i	−0.861707	−	0.507406i	$-0.830605\pi$
$569$		−	577.428i		−	1.01481i	0.861707	−	0.507406i	$-0.169395\pi$
$570$	−58.1477	−	203.861i	−0.102014	−	0.357652i
$571$	−103.122			−0.180598			−0.0902991	−	0.995915i	$-0.528782\pi$
$571$	−103.122			−0.180598			−0.0902991	+	0.995915i	$0.528782\pi$
$572$			677.069i			1.18369i
$573$	−831.468	+	237.161i	−1.45108	+	0.413893i
$574$		0			0
$575$		−	599.655i		−	1.04288i
$576$	−371.763	+	230.859i	−0.645423	+	0.400797i
$577$	676.583			1.17259			0.586294	−	0.810099i	$-0.300586\pi$
$577$	676.583			1.17259			0.586294	+	0.810099i	$0.300586\pi$
$578$		−	941.334i		−	1.62860i
$579$	−63.4615	−	222.491i	−0.109605	−	0.384268i
$580$	−97.7856			−0.168596
$581$		0			0
$582$	−234.310	+	66.8325i	−0.402594	+	0.114833i
$583$	−106.494			−0.182666
$584$			1155.35i			1.97834i
$585$	68.6719	+	110.586i	0.117388	+	0.189035i
$586$	−8.88492			−0.0151620
$587$		−	158.683i		−	0.270329i	−0.990823	−	0.135164i	$-0.956844\pi$
$587$		−	158.683i		−	0.270329i	0.990823	−	0.135164i	$-0.0431563\pi$
$588$		0			0
$589$	465.903			0.791007
$590$			402.315i			0.681890i
$591$	−393.601	+	112.267i	−0.665992	+	0.189962i
$592$	−647.033			−1.09296
$593$			935.371i			1.57735i	0.614807	+	0.788677i	$0.289234\pi$
$593$			935.371i			1.57735i	−0.614807	+	0.788677i	$0.710766\pi$
$594$	−491.387	−	446.196i	−0.827251	−	0.751172i
$595$		0			0
$596$		−	1622.94i		−	2.72306i
$597$	71.2470	+	249.787i	0.119342	+	0.418403i
$598$	−1043.73			−1.74537
$599$			73.7665i			0.123149i	0.998102	+	0.0615747i	$0.0196122\pi$
$599$			73.7665i			0.123149i	−0.998102	+	0.0615747i	$0.980388\pi$
$600$	1018.19	−	290.421i	1.69699	−	0.484035i
$601$	934.280			1.55454			0.777271	−	0.629166i	$-0.216603\pi$
$601$	934.280			1.55454			0.777271	+	0.629166i	$0.216603\pi$
$602$		0			0
$603$	−115.956	+	72.0066i	−0.192298	+	0.119414i
$604$	−847.814			−1.40367
$605$		−	89.2156i		−	0.147464i
$606$	−389.199	−	1364.50i	−0.642242	−	2.25165i
$607$	181.608			0.299189			0.149595	−	0.988747i	$-0.452203\pi$
$607$	181.608			0.299189			0.149595	+	0.988747i	$0.452203\pi$
$608$			137.519i			0.226183i
$609$		0			0
$610$	−250.458			−0.410586
$611$			384.488i			0.629276i
$612$	−178.251	−	287.046i	−0.291260	−	0.469029i
$613$	−897.940			−1.46483			−0.732414	−	0.680859i	$-0.761606\pi$
$613$	−897.940			−1.46483			−0.732414	+	0.680859i	$0.761606\pi$
$614$			302.339i			0.492409i
$615$	68.6719	+	240.759i	0.111662	+	0.391477i
$616$		0			0
$617$			1169.69i			1.89576i	0.318622	+	0.947882i	$0.396780\pi$
$617$			1169.69i			1.89576i	−0.318622	+	0.947882i	$0.603220\pi$
$618$	−1211.19	+	345.469i	−1.95985	+	0.559011i
$619$	−1208.97			−1.95310			−0.976548	−	0.215301i	$-0.930927\pi$
$619$	−1208.97			−1.95310			−0.976548	+	0.215301i	$0.930927\pi$
$620$		−	295.634i		−	0.476829i
$621$	463.992	−	510.985i	0.747169	−	0.822842i
$622$	−532.118			−0.855495
$623$		0			0
$624$	−187.664	−	657.936i	−0.300744	−	1.05438i
$625$	511.693			0.818708
$626$			1115.30i			1.78162i
$627$	328.288	−	93.6380i	0.523585	−	0.149343i
$628$	868.310			1.38266
$629$			149.604i			0.237845i
$630$		0			0
$631$	901.223			1.42825			0.714123	−	0.700020i	$-0.246826\pi$
$631$	901.223			1.42825			0.714123	+	0.700020i	$0.246826\pi$
$632$			1914.52i			3.02930i
$633$	−15.9778	−	56.0169i	−0.0252413	−	0.0884942i
$634$	1276.23			2.01298
$635$			19.1474i			0.0301534i
$636$	363.298	−	103.624i	0.571223	−	0.162931i
$637$		0			0
$638$		−	233.435i		−	0.365886i
$639$	335.004	+	539.472i	0.524263	+	0.844245i
$640$	−253.816			−0.396587
$641$			528.629i			0.824694i	0.911027	+	0.412347i	$0.135291\pi$
$641$			528.629i			0.824694i	−0.911027	+	0.412347i	$0.864709\pi$
$642$	224.605	+	787.449i	0.349852	+	1.22656i
$643$	−33.4392			−0.0520050			−0.0260025	−	0.999662i	$-0.508278\pi$
$643$	−33.4392			−0.0520050			−0.0260025	+	0.999662i	$0.508278\pi$
$644$		0			0
$645$	86.4418	−	24.6559i	0.134018	−	0.0382262i
$646$	257.624			0.398798
$647$			786.308i			1.21531i	0.794200	+	0.607657i	$0.207890\pi$
$647$			786.308i			1.21531i	−0.794200	+	0.607657i	$0.792110\pi$
$648$	1092.35	+	540.366i	1.68573	+	0.833898i
$649$	−647.867			−0.998254
$650$		−	957.750i		−	1.47346i
$651$		0			0
$652$	588.361			0.902394
$653$		−	385.807i		−	0.590823i	−0.955370	−	0.295412i	$-0.904543\pi$
$653$		−	385.807i		−	0.590823i	0.955370	−	0.295412i	$-0.0954568\pi$
$654$	369.565	−	105.412i	0.565084	−	0.161180i
$655$	−227.417			−0.347202
$656$		−	1315.87i		−	2.00590i
$657$	−587.114	+	364.588i	−0.893628	+	0.554929i
$658$		0			0
$659$		−	97.2583i		−	0.147585i	−0.997274	−	0.0737924i	$-0.976490\pi$
$659$		−	97.2583i		−	0.147585i	0.997274	−	0.0737924i	$-0.0235102\pi$
$660$	−59.4170	−	208.311i	−0.0900257	−	0.315623i
$661$	961.505			1.45462			0.727311	−	0.686309i	$-0.240770\pi$
$661$	961.505			1.45462			0.727311	+	0.686309i	$0.240770\pi$
$662$		−	541.205i		−	0.817530i
$663$	−152.125	+	43.3910i	−0.229450	+	0.0654464i
$664$	1117.66			1.68322
$665$		0			0
$666$	−549.984	−	885.665i	−0.825802	−	1.32983i
$667$	242.745			0.363936
$668$		−	1716.27i		−	2.56927i
$669$	144.037	+	504.981i	0.215301	+	0.754830i
$670$	−66.0366			−0.0985621
$671$		−	403.323i		−	0.601078i
$672$		0			0
$673$	−1089.81			−1.61933			−0.809663	−	0.586895i	$-0.800350\pi$
$673$	−1089.81			−1.61933			−0.809663	+	0.586895i	$0.800350\pi$
$674$		−	1413.03i		−	2.09648i
$675$	468.890	+	425.768i	0.694651	+	0.630767i
$676$	276.741			0.409380
$677$		−	1252.56i		−	1.85016i	−0.379771	−	0.925080i	$-0.623997\pi$
$677$		−	1252.56i		−	1.85016i	0.379771	−	0.925080i	$-0.376003\pi$
$678$	−62.7752	−	220.085i	−0.0925888	−	0.324609i
$679$		0			0
$680$		−	84.6097i		−	0.124426i
$681$	512.290	−	146.121i	0.752262	−	0.214569i
$682$	705.741			1.03481
$683$			341.097i			0.499409i	0.968322	+	0.249705i	$0.0803335\pi$
$683$			341.097i			0.499409i	−0.968322	+	0.249705i	$0.919666\pi$
$684$	−1028.82	+	638.880i	−1.50412	+	0.934035i
$685$	41.0039			0.0598598
$686$		0			0
$687$	33.5830	+	117.739i	0.0488836	+	0.171382i
$688$	−472.450			−0.686700
$689$		−	176.873i		−	0.256709i
$690$	321.122	−	91.5940i	0.465394	−	0.132745i
$691$	783.667			1.13411			0.567053	−	0.823682i	$-0.308084\pi$
$691$	783.667			1.13411			0.567053	+	0.823682i	$0.308084\pi$
$692$			899.327i			1.29961i
$693$		0			0
$694$	−1652.14			−2.38060
$695$			80.2831i			0.115515i
$696$	117.565	+	412.173i	0.168915	+	0.592203i
$697$	−304.251			−0.436515
$698$		−	1277.97i		−	1.83090i
$699$	1118.48	−	319.025i	1.60011	−	0.456402i
$700$		0			0
$701$		−	1331.76i		−	1.89979i	−0.312562	−	0.949897i	$-0.601187\pi$
$701$		−	1331.76i		−	1.89979i	0.312562	−	0.949897i	$-0.398813\pi$
$702$	741.073	−	816.129i	1.05566	−	1.16258i
$703$	536.207			0.762740
$704$		−	340.941i		−	0.484291i
$705$	−33.7411	−	118.294i	−0.0478598	−	0.167793i
$706$	302.708			0.428766
$707$		0			0
$708$	2210.16	−	630.406i	3.12169	−	0.890404i
$709$	763.963			1.07752			0.538761	−	0.842459i	$-0.318893\pi$
$709$	763.963			1.07752			0.538761	+	0.842459i	$0.318893\pi$
$710$			307.229i			0.432717i
$711$	−972.899	+	604.155i	−1.36835	+	0.849726i
$712$	−1916.48			−2.69168
$713$			733.888i			1.02930i
$714$		0			0
$715$	−101.417			−0.141842
$716$		−	1321.31i		−	1.84540i
$717$	−142.871	+	40.7512i	−0.199262	+	0.0568357i
$718$	1304.44			1.81677
$719$			623.715i			0.867476i	0.901039	+	0.433738i	$0.142806\pi$
$719$			623.715i			0.867476i	−0.901039	+	0.433738i	$0.857194\pi$
$720$	115.476	+	185.956i	0.160383	+	0.258272i
$721$		0			0
$722$			342.274i			0.474064i
$723$	267.638	+	938.318i	0.370177	+	1.29781i
$724$	−1939.29			−2.67858
$725$			222.748i			0.307238i
$726$	−726.556	+	207.237i	−1.00077	+	0.285450i
$727$	−678.494			−0.933279			−0.466640	−	0.884448i	$-0.654536\pi$
$727$	−678.494			−0.933279			−0.466640	+	0.884448i	$0.654536\pi$
$728$		0			0
$729$	70.1111	+	725.621i	0.0961744	+	0.995364i
$730$	−334.361			−0.458028
$731$			109.238i			0.149436i
$732$	392.454	+	1375.91i	0.536139	+	1.87966i
$733$	394.966			0.538835			0.269417	−	0.963023i	$-0.413169\pi$
$733$	394.966			0.538835			0.269417	+	0.963023i	$0.413169\pi$
$734$		−	567.208i		−	0.772763i
$735$		0			0
$736$	−216.620			−0.294320
$737$		−	106.342i		−	0.144290i
$738$	1801.18	−	1118.50i	2.44062	−	1.51559i
$739$	292.199			0.395397			0.197699	−	0.980263i	$-0.436653\pi$
$739$	292.199			0.395397			0.197699	+	0.980263i	$0.436653\pi$
$740$		−	340.244i		−	0.459790i
$741$	155.520	+	545.242i	0.209879	+	0.735819i
$742$		0			0
$743$			383.452i			0.516086i	0.966133	+	0.258043i	$0.0830776\pi$
$743$			383.452i			0.516086i	−0.966133	+	0.258043i	$0.916922\pi$
$744$	−1246.12	+	355.432i	−1.67489	+	0.477731i
$745$	243.098			0.326306
$746$		−	1326.12i		−	1.77764i
$747$	352.694	+	567.960i	0.472147	+	0.760321i
$748$	263.247			0.351935
$749$		0			0
$750$	173.624	+	608.711i	0.231498	+	0.811614i
$751$	−696.332			−0.927206			−0.463603	−	0.886043i	$-0.653444\pi$
$751$	−696.332			−0.927206			−0.463603	+	0.886043i	$0.653444\pi$
$752$			646.538i			0.859758i
$753$	760.852	−	217.019i	1.01043	−	0.288206i
$754$	387.705			0.514197
$755$		−	126.993i		−	0.168202i
$756$		0			0
$757$	967.357			1.27788			0.638941	−	0.769256i	$-0.279373\pi$
$757$	967.357			1.27788			0.638941	+	0.769256i	$0.279373\pi$
$758$			178.092i			0.234950i
$759$	147.498	+	517.117i	0.194332	+	0.681313i
$760$	−303.255			−0.399020
$761$		−	89.7059i		−	0.117879i	−0.998262	−	0.0589395i	$-0.981228\pi$
$761$		−	89.7059i		−	0.117879i	0.998262	−	0.0589395i	$-0.0187719\pi$
$762$	155.933	−	44.4771i	0.204637	−	0.0583689i
$763$		0			0
$764$			2389.69i			3.12787i
$765$	42.9961	−	26.6999i	0.0562040	−	0.0349018i
$766$	−397.506			−0.518937
$767$		−	1076.02i		−	1.40290i
$768$	429.538	+	1505.93i	0.559294	+	1.96084i
$769$	−926.219			−1.20445			−0.602223	−	0.798328i	$-0.705718\pi$
$769$	−926.219			−1.20445			−0.602223	+	0.798328i	$0.705718\pi$
$770$		0			0
$771$	436.148	−	124.403i	0.565691	−	0.161353i
$772$	−639.454			−0.828308
$773$			424.125i			0.548674i	0.961634	+	0.274337i	$0.0884584\pi$
$773$			424.125i			0.548674i	−0.961634	+	0.274337i	$0.911542\pi$
$774$	−401.587	−	646.694i	−0.518846	−	0.835522i
$775$	−673.430			−0.868942
$776$			348.548i			0.449160i
$777$		0			0
$778$	−2543.84			−3.26972
$779$			1090.48i			1.39985i
$780$	345.978	−	98.6838i	0.443561	−	0.126518i
$781$	−494.745			−0.633476
$782$			405.807i			0.518935i
$783$	−172.354	+	189.810i	−0.220120	+	0.242414i
$784$		0			0
$785$			130.063i			0.165685i
$786$	528.261	+	1852.04i	0.672088	+	2.35629i
$787$	155.889			0.198080			0.0990399	−	0.995083i	$-0.468423\pi$
$787$	155.889			0.198080			0.0990399	+	0.995083i	$0.468423\pi$
$788$			1131.24i			1.43558i
$789$	330.006	−	94.1282i	0.418259	−	0.119301i
$790$	−554.065			−0.701348
$791$		0			0
$792$	−806.612	+	500.893i	−1.01845	+	0.632441i
$793$	669.867			0.844725
$794$		−	330.771i		−	0.416588i
$795$	15.5217	+	54.4177i	0.0195241	+	0.0684500i
$796$	717.903			0.901888
$797$		−	719.191i		−	0.902373i	−0.892430	−	0.451186i	$-0.851001\pi$
$797$		−	719.191i		−	0.902373i	0.892430	−	0.451186i	$-0.148999\pi$
$798$		0			0
$799$	149.490			0.187097
$800$		−	198.774i		−	0.248468i
$801$	−604.774	−	973.895i	−0.755023	−	1.21585i
$802$	−2375.84			−2.96240
$803$		−	538.437i		−	0.670531i
$804$	103.476	+	362.778i	0.128701	+	0.451217i
$805$		0			0
$806$			1172.14i			1.45427i
$807$	−13.7372	+	3.91828i	−0.0170226	+	0.00485537i
$808$	−2029.77			−2.51209
$809$			212.244i			0.262353i	0.991359	+	0.131176i	$0.0418755\pi$
$809$			212.244i			0.262353i	−0.991359	+	0.131176i	$0.958125\pi$
$810$	−156.383	+	316.129i	−0.193065	+	0.390283i
$811$	−1058.66			−1.30538			−0.652690	−	0.757625i	$-0.726359\pi$
$811$	−1058.66			−1.30538			−0.652690	+	0.757625i	$0.726359\pi$
$812$		0			0
$813$	−426.826	−	1496.42i	−0.525001	−	1.84061i
$814$	812.235			0.997832
$815$			88.1295i			0.108134i
$816$	−255.808	+	72.9645i	−0.313490	+	0.0894172i
$817$	391.527			0.479225
$818$			60.8792i			0.0744244i
$819$		0			0
$820$	691.956			0.843848
$821$		−	818.571i		−	0.997042i	−0.866878	−	0.498521i	$-0.833877\pi$
$821$		−	818.571i		−	0.997042i	0.866878	−	0.498521i	$-0.166123\pi$
$822$	−95.2470	−	333.929i	−0.115872	−	0.406240i
$823$	206.850			0.251336			0.125668	−	0.992072i	$-0.459893\pi$
$823$	206.850			0.251336			0.125668	+	0.992072i	$0.459893\pi$
$824$			1801.71i			2.18654i
$825$	−474.516	+	135.347i	−0.575171	+	0.164057i
$826$		0			0
$827$			438.639i			0.530398i	0.964194	+	0.265199i	$0.0854376\pi$
$827$			438.639i			0.530398i	−0.964194	+	0.265199i	$0.914562\pi$
$828$	−1006.36	−	1620.59i	−1.21541	−	1.95723i
$829$	−654.804			−0.789872			−0.394936	−	0.918709i	$-0.629233\pi$
$829$	−654.804			−0.789872			−0.394936	+	0.918709i	$0.629233\pi$
$830$			323.453i			0.389702i
$831$	99.6379	+	349.323i	0.119901	+	0.420364i
$832$	566.257			0.680598
$833$		0			0
$834$	653.812	−	186.488i	0.783947	−	0.223606i
$835$	257.077			0.307877
$836$		−	943.520i		−	1.12861i
$837$	−573.851	−	521.077i	−0.685604	−	0.622553i
$838$	−477.055			−0.569278
$839$			50.9710i			0.0607521i	0.999539	+	0.0303761i	$0.00967049\pi$
$839$			50.9710i			0.0607521i	−0.999539	+	0.0303761i	$0.990330\pi$
$840$		0			0
$841$	750.830			0.892782
$842$		−	1486.48i		−	1.76542i
$843$	1174.91	−	335.121i	1.39372	−	0.397533i
$844$	−160.996			−0.190754
$845$			41.4525i			0.0490563i
$846$	−884.988	+	549.564i	−1.04609	+	0.649603i
$847$		0			0
$848$		−	297.422i		−	0.350733i
$849$	−328.026	−	1150.03i	−0.386368	−	1.35458i
$850$	−372.376			−0.438090
$851$			844.630i			0.992514i
$852$	1687.79	−	481.411i	1.98098	−	0.565037i
$853$	883.941			1.03627			0.518137	−	0.855298i	$-0.326626\pi$
$853$	883.941			1.03627			0.518137	+	0.855298i	$0.326626\pi$
$854$		0			0
$855$	−95.6967	−	154.105i	−0.111926	−	0.180240i
$856$	1171.37			1.36843
$857$		−	556.521i		−	0.649382i	−0.945820	−	0.324691i	$-0.894740\pi$
$857$		−	556.521i		−	0.649382i	0.945820	−	0.324691i	$-0.105260\pi$
$858$	235.579	+	825.922i	0.274568	+	0.962613i
$859$	643.078			0.748636			0.374318	−	0.927300i	$-0.377877\pi$
$859$	643.078			0.748636			0.374318	+	0.927300i	$0.377877\pi$
$860$		−	248.439i		−	0.288883i
$861$		0			0
$862$	1192.87			1.38384
$863$			204.892i			0.237419i	0.992929	+	0.118709i	$0.0378757\pi$
$863$			204.892i			0.237419i	−0.992929	+	0.118709i	$0.962124\pi$
$864$	153.805	−	169.382i	0.178015	−	0.196044i
$865$	−134.708			−0.155732
$866$			558.024i			0.644369i
$867$	−220.940	−	774.601i	−0.254833	−	0.893426i
$868$		0			0
$869$		−	892.237i		−	1.02674i
$870$	−119.284	+	34.0235i	−0.137108	+	0.0391074i
$871$	176.620			0.202778
$872$		−	549.747i		−	0.630444i
$873$	−177.122	+	109.990i	−0.202888	+	0.125991i
$874$	1454.48			1.66416
$875$		0			0
$876$	523.925	+	1836.84i	0.598088	+	2.09685i
$877$	−207.210			−0.236272			−0.118136	−	0.992997i	$-0.537692\pi$
$877$	−207.210			−0.236272			−0.118136	+	0.992997i	$0.537692\pi$
$878$			449.015i			0.511406i
$879$	−7.31119	+	2.08538i	−0.00831762	+	0.00237245i
$880$	−170.539			−0.193794
$881$			1391.37i			1.57931i	0.613552	+	0.789654i	$0.289740\pi$
$881$			1391.37i			1.57931i	−0.613552	+	0.789654i	$0.710260\pi$
$882$		0			0
$883$	−1091.99			−1.23668			−0.618342	−	0.785909i	$-0.712195\pi$
$883$	−1091.99			−1.23668			−0.618342	+	0.785909i	$0.712195\pi$
$884$			437.219i			0.494591i
$885$	94.4274	+	331.055i	0.106698	+	0.374074i
$886$	−691.859			−0.780879
$887$		−	149.449i		−	0.168488i	−0.996445	−	0.0842439i	$-0.973153\pi$
$887$		−	149.449i		−	0.168488i	0.996445	−	0.0842439i	$-0.0268475\pi$
$888$	−1434.15	+	409.066i	−1.61504	+	0.460659i
$889$		0			0
$890$		−	554.632i		−	0.623183i
$891$	−509.077	−	251.831i	−0.571355	−	0.282638i
$892$	1451.35			1.62707
$893$		−	535.797i		−	0.599996i
$894$	−564.686	−	1979.75i	−0.631640	−	2.21448i
$895$	197.916			0.221135
$896$		0			0
$897$	−858.863	+	244.975i	−0.957483	+	0.273104i
$898$	519.231			0.578209
$899$		−	272.610i		−	0.303237i
$900$	1487.08	−	923.456i	1.65232	−	1.02606i
$901$	−68.7687			−0.0763249
$902$			1651.84i			1.83131i
$903$		0			0
$904$	−327.388			−0.362155
$905$		−	290.483i		−	0.320975i
$906$	−1034.21	+	294.988i	−1.14151	+	0.325594i
$907$	593.718			0.654595			0.327297	−	0.944921i	$-0.393862\pi$
$907$	593.718			0.654595			0.327297	+	0.944921i	$0.393862\pi$
$908$		−	1472.35i		−	1.62154i
$909$	−640.524	−	1031.47i	−0.704647	−	1.13473i
$910$		0			0
$911$			1133.75i			1.24451i	0.782815	+	0.622254i	$0.213783\pi$
$911$			1133.75i			1.24451i	−0.782815	+	0.622254i	$0.786217\pi$
$912$	261.516	+	916.856i	0.286750	+	1.00532i
$913$	−520.871			−0.570504
$914$			428.474i			0.468790i
$915$	−206.095	+	58.7849i	−0.225241	+	0.0642458i
$916$	338.391			0.369422
$917$		0			0
$918$	−317.314	−	288.132i	−0.345658	−	0.313869i
$919$	−684.988			−0.745363			−0.372681	−	0.927959i	$-0.621562\pi$
$919$	−684.988			−0.745363			−0.372681	+	0.927959i	$0.621562\pi$
$920$		−	477.686i		−	0.519223i
$921$	70.9620	+	248.787i	0.0770489	+	0.270128i
$922$	−2110.88			−2.28945
$923$		−	821.706i		−	0.890256i
$924$		0			0
$925$	−775.048			−0.837890
$926$			2233.49i			2.41197i
$927$	−915.571	+	568.556i	−0.987671	+	0.613328i
$928$	80.4654			0.0867084
$929$			192.317i			0.207015i	0.994629	+	0.103507i	$0.0330066\pi$
$929$			192.317i			0.207015i	−0.994629	+	0.103507i	$0.966993\pi$
$930$	−102.863	−	360.629i	−0.110605	−	0.387773i
$931$		0			0
$932$		−	3214.58i		−	3.44912i
$933$	−437.867	+	124.893i	−0.469310	+	0.133862i
$934$	2691.52			2.88171
$935$			39.4313i			0.0421725i
$936$	−831.918	−	1339.68i	−0.888801	−	1.43128i
$937$	1270.28			1.35569			0.677844	−	0.735206i	$-0.262914\pi$
$937$	1270.28			1.35569			0.677844	+	0.735206i	$0.262914\pi$
$938$		0			0
$939$	261.771	+	917.750i	0.278777	+	0.977370i
$940$	−339.984			−0.361685
$941$		−	156.951i		−	0.166791i	−0.996517	−	0.0833957i	$-0.973423\pi$
$941$		−	156.951i		−	0.166791i	0.996517	−	0.0833957i	$-0.0265766\pi$
$942$	1059.21	−	302.119i	1.12442	−	0.320721i
$943$	−1717.73			−1.82155
$944$		−	1809.39i		−	1.91673i
$945$		0			0
$946$	593.077			0.626931
$947$			879.945i			0.929193i	0.885523	+	0.464596i	$0.153801\pi$
$947$			879.945i			0.929193i	−0.885523	+	0.464596i	$0.846199\pi$
$948$	868.191	+	3043.81i	0.915813	+	3.21077i
$949$	894.272			0.942331
$950$			1334.66i			1.40490i
$951$	1050.18	−	299.543i	1.10429	−	0.314977i
$952$		0			0
$953$			563.276i			0.591056i	0.955334	+	0.295528i	$0.0954955\pi$
$953$			563.276i			0.591056i	−0.955334	+	0.295528i	$0.904505\pi$
$954$	407.114	−	252.811i	0.426744	−	0.265001i
$955$	−357.948			−0.374814
$956$			410.619i			0.429518i
$957$	−54.7895	−	192.088i	−0.0572513	−	0.200719i
$958$	−1380.83			−1.44136
$959$		0			0
$960$	−174.218	+	49.6926i	−0.181477	+	0.0517631i
$961$	−136.822			−0.142375
$962$			1349.02i			1.40230i
$963$	369.644	+	595.255i	0.383847	+	0.618126i
$964$	2696.79			2.79750
$965$		−	95.7826i		−	0.0992566i
$966$		0			0
$967$	237.676			0.245787			0.122893	−	0.992420i	$-0.460783\pi$
$967$	237.676			0.245787			0.122893	+	0.992420i	$0.460783\pi$
$968$			1080.79i			1.11652i
$969$	211.992	−	60.4668i	0.218774	−	0.0624013i
$970$	−100.871			−0.103990
$971$			1355.00i			1.39546i	0.716359	+	0.697732i	$0.245808\pi$
$971$			1355.00i			1.39546i	−0.716359	+	0.697732i	$0.754192\pi$
$972$	1981.73	+	363.748i	2.03882	+	0.374226i
$973$		0			0
$974$		−	2010.33i		−	2.06399i
$975$	−224.793	−	788.109i	−0.230557	−	0.808317i
$976$	1126.42			1.15412
$977$		−	493.726i		−	0.505349i	−0.967551	−	0.252674i	$-0.918690\pi$
$977$		−	493.726i		−	0.505349i	0.967551	−	0.252674i	$-0.0813101\pi$
$978$	717.711	−	204.714i	0.733856	−	0.209319i
$979$	893.150			0.912309
$980$		0			0
$981$	279.365	−	173.481i	0.284775	−	0.176841i
$982$	−598.797			−0.609773
$983$			1538.05i			1.56465i	0.622870	+	0.782325i	$0.285966\pi$
$983$			1538.05i			1.56465i	−0.622870	+	0.782325i	$0.714034\pi$
$984$	−831.918	−	2916.64i	−0.845445	−	2.96406i
$985$	−169.446			−0.172026
$986$		−	150.741i		−	0.152881i
$987$		0			0
$988$	1567.06			1.58609
$989$			616.731i			0.623590i
$990$	−144.959	−	233.435i	−0.146424	−	0.235793i
$991$	1514.73			1.52849			0.764243	−	0.644929i	$-0.223113\pi$
$991$	1514.73			1.52849			0.764243	+	0.644929i	$0.223113\pi$
$992$			243.270i			0.245232i
$993$	−127.026	−	445.344i	−0.127922	−	0.448483i
$994$		0			0
$995$			107.533i			0.108074i
$996$	1776.92	−	506.833i	1.78405	−	0.508868i
$997$	−1826.43			−1.83193			−0.915964	−	0.401260i	$-0.868572\pi$
$997$	−1826.43			−1.83193			−0.915964	+	0.401260i	$0.868572\pi$
$998$			2972.37i			2.97833i
$999$	−660.443	−	599.705i	−0.661104	−	0.600306i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	147.3.b.f.50.1		4
3.2	odd	2	inner	147.3.b.f.50.4		4
7.2	even	3		147.3.h.c.116.1		8
7.3	odd	6		147.3.h.e.128.4		8
7.4	even	3		147.3.h.c.128.4		8
7.5	odd	6		147.3.h.e.116.1		8
7.6	odd	2		21.3.b.a.8.1	✓	4
21.2	odd	6		147.3.h.c.116.4		8
21.5	even	6		147.3.h.e.116.4		8
21.11	odd	6		147.3.h.c.128.1		8
21.17	even	6		147.3.h.e.128.1		8
21.20	even	2		21.3.b.a.8.4	yes	4
28.27	even	2		336.3.d.c.113.1		4
35.13	even	4		525.3.f.a.449.2		8
35.27	even	4		525.3.f.a.449.7		8
35.34	odd	2		525.3.c.a.176.4		4
56.13	odd	2		1344.3.d.f.449.1		4
56.27	even	2		1344.3.d.b.449.4		4
63.13	odd	6		567.3.r.c.512.4		8
63.20	even	6		567.3.r.c.134.4		8
63.34	odd	6		567.3.r.c.134.1		8
63.41	even	6		567.3.r.c.512.1		8
84.83	odd	2		336.3.d.c.113.2		4
105.62	odd	4		525.3.f.a.449.1		8
105.83	odd	4		525.3.f.a.449.8		8
105.104	even	2		525.3.c.a.176.1		4
168.83	odd	2		1344.3.d.b.449.3		4
168.125	even	2		1344.3.d.f.449.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
21.3.b.a.8.1	✓	4	7.6	odd	2
21.3.b.a.8.4	yes	4	21.20	even	2
147.3.b.f.50.1		4	1.1	even	1	trivial
147.3.b.f.50.4		4	3.2	odd	2	inner
147.3.h.c.116.1		8	7.2	even	3
147.3.h.c.116.4		8	21.2	odd	6
147.3.h.c.128.1		8	21.11	odd	6
147.3.h.c.128.4		8	7.4	even	3
147.3.h.e.116.1		8	7.5	odd	6
147.3.h.e.116.4		8	21.5	even	6
147.3.h.e.128.1		8	21.17	even	6
147.3.h.e.128.4		8	7.3	odd	6
336.3.d.c.113.1		4	28.27	even	2
336.3.d.c.113.2		4	84.83	odd	2
525.3.c.a.176.1		4	105.104	even	2
525.3.c.a.176.4		4	35.34	odd	2
525.3.f.a.449.1		8	105.62	odd	4
525.3.f.a.449.2		8	35.13	even	4
525.3.f.a.449.7		8	35.27	even	4
525.3.f.a.449.8		8	105.83	odd	4
567.3.r.c.134.1		8	63.34	odd	6
567.3.r.c.134.4		8	63.20	even	6
567.3.r.c.512.1		8	63.41	even	6
567.3.r.c.512.4		8	63.13	odd	6
1344.3.d.b.449.3		4	168.83	odd	2
1344.3.d.b.449.4		4	56.27	even	2
1344.3.d.f.449.1		4	56.13	odd	2
1344.3.d.f.449.2		4	168.125	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:	\( N \)	\(=\)	\( 147 = 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	147.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-3.50592i q^{2} +(-0.822876 - 2.88494i) q^{3} -8.29150 q^{4} -1.24197i q^{5} +(-10.1144 + 2.88494i) q^{6} +15.0457i q^{8} +(-7.64575 + 4.74789i) q^{9} +O(q^{10})\)	\(q-3.50592i q^{2} +(-0.822876 - 2.88494i) q^{3} -8.29150 q^{4} -1.24197i q^{5} +(-10.1144 + 2.88494i) q^{6} +15.0457i q^{8} +(-7.64575 + 4.74789i) q^{9} -4.35425 q^{10} -7.01185i q^{11} +(6.82288 + 23.9205i) q^{12} +11.6458 q^{13} +(-3.58301 + 1.02199i) q^{15} +19.5830 q^{16} -4.52791i q^{17} +(16.6458 + 26.8054i) q^{18} -16.2288 q^{19} +10.2978i q^{20} -24.5830 q^{22} -25.5635i q^{23} +(43.4059 - 12.3807i) q^{24} +23.4575 q^{25} -40.8291i q^{26} +(19.9889 + 18.1506i) q^{27} +9.49579i q^{29} +(3.58301 + 12.5617i) q^{30} -28.7085 q^{31} -8.47380i q^{32} +(-20.2288 + 5.76988i) q^{33} -15.8745 q^{34} +(63.3948 - 39.3672i) q^{36} -33.0405 q^{37} +56.8968i q^{38} +(-9.58301 - 33.5973i) q^{39} +18.6863 q^{40} -67.1946i q^{41} -24.1255 q^{43} +58.1388i q^{44} +(5.89674 + 9.49579i) q^{45} -89.6235 q^{46} +33.0153i q^{47} +(-16.1144 - 56.4958i) q^{48} -82.2403i q^{50} +(-13.0627 + 3.72591i) q^{51} -96.5608 q^{52} -15.1877i q^{53} +(63.6346 - 70.0795i) q^{54} -8.70850 q^{55} +(13.3542 + 46.8190i) q^{57} +33.2915 q^{58} -92.3960i q^{59} +(29.7085 - 8.47380i) q^{60} +57.5203 q^{61} +100.650i q^{62} +48.6235 q^{64} -14.4637i q^{65} +(20.2288 + 70.9205i) q^{66} +15.1660 q^{67} +37.5432i q^{68} +(-73.7490 + 21.0355i) q^{69} -70.5584i q^{71} +(-71.4353 - 115.036i) q^{72} +76.7895 q^{73} +115.838i q^{74} +(-19.3026 - 67.6735i) q^{75} +134.561 q^{76} +(-117.790 + 33.5973i) q^{78} +127.247 q^{79} -24.3215i q^{80} +(35.9150 - 72.6024i) q^{81} -235.579 q^{82} -74.2844i q^{83} -5.62352 q^{85} +84.5821i q^{86} +(27.3948 - 7.81385i) q^{87} +105.498 q^{88} +127.377i q^{89} +(33.2915 - 20.6735i) q^{90} +211.959i q^{92} +(23.6235 + 82.8223i) q^{93} +115.749 q^{94} +20.1556i q^{95} +(-24.4464 + 6.97288i) q^{96} +23.1660 q^{97} +(33.2915 + 53.6108i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{3} - 12 q^{4} - 14 q^{6} - 20 q^{9}+O(q^{10}) \) 4 * q + 2 * q^3 - 12 * q^4 - 14 * q^6 - 20 * q^9	\( 4 q + 2 q^{3} - 12 q^{4} - 14 q^{6} - 20 q^{9} - 28 q^{10} + 22 q^{12} + 36 q^{13} + 28 q^{15} + 36 q^{16} + 56 q^{18} - 12 q^{19} - 56 q^{22} + 126 q^{24} - 12 q^{25} - 10 q^{27} - 28 q^{30} - 136 q^{31} - 28 q^{33} + 116 q^{36} + 16 q^{37} + 4 q^{39} - 84 q^{40} - 160 q^{43} + 140 q^{45} - 168 q^{46} - 38 q^{48} - 84 q^{51} - 164 q^{52} + 154 q^{54} - 56 q^{55} + 64 q^{57} + 112 q^{58} + 140 q^{60} + 156 q^{61} + 4 q^{64} + 28 q^{66} - 24 q^{67} - 168 q^{69} + 32 q^{73} - 146 q^{75} + 316 q^{76} - 196 q^{78} + 128 q^{79} - 68 q^{81} - 392 q^{82} + 168 q^{85} - 28 q^{87} + 168 q^{88} + 112 q^{90} - 96 q^{93} + 336 q^{94} + 98 q^{96} + 8 q^{97} + 112 q^{99}+O(q^{100}) \) 4 * q + 2 * q^3 - 12 * q^4 - 14 * q^6 - 20 * q^9 - 28 * q^10 + 22 * q^12 + 36 * q^13 + 28 * q^15 + 36 * q^16 + 56 * q^18 - 12 * q^19 - 56 * q^22 + 126 * q^24 - 12 * q^25 - 10 * q^27 - 28 * q^30 - 136 * q^31 - 28 * q^33 + 116 * q^36 + 16 * q^37 + 4 * q^39 - 84 * q^40 - 160 * q^43 + 140 * q^45 - 168 * q^46 - 38 * q^48 - 84 * q^51 - 164 * q^52 + 154 * q^54 - 56 * q^55 + 64 * q^57 + 112 * q^58 + 140 * q^60 + 156 * q^61 + 4 * q^64 + 28 * q^66 - 24 * q^67 - 168 * q^69 + 32 * q^73 - 146 * q^75 + 316 * q^76 - 196 * q^78 + 128 * q^79 - 68 * q^81 - 392 * q^82 + 168 * q^85 - 28 * q^87 + 168 * q^88 + 112 * q^90 - 96 * q^93 + 336 * q^94 + 98 * q^96 + 8 * q^97 + 112 * q^99

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