LMFDB - Embedded newform 105.3.f.a.29.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [105,3,Mod(29,105)]

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([1, 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("105.29");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 105 = 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	105.f (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:	$24$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			29.1
Character	$\chi$	$=$	105.29
Dual form			105.3.f.a.29.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-3.57140 q^{2} +(2.50375 - 1.65264i) q^{3} +8.75491 q^{4} +(-0.280149 + 4.99215i) q^{5} +(-8.94190 + 5.90225i) q^{6} +2.64575i q^{7} -16.9817 q^{8} +(3.53755 - 8.27561i) q^{9} +O(q^{10})$	\(q-3.57140 q^{2} +(2.50375 - 1.65264i) q^{3} +8.75491 q^{4} +(-0.280149 + 4.99215i) q^{5} +(-8.94190 + 5.90225i) q^{6} +2.64575i q^{7} -16.9817 q^{8} +(3.53755 - 8.27561i) q^{9} +(1.00052 - 17.8290i) q^{10} +2.85975i q^{11} +(21.9201 - 14.4687i) q^{12} +20.2550i q^{13} -9.44904i q^{14} +(7.54881 + 12.9621i) q^{15} +25.6288 q^{16} +25.2668 q^{17} +(-12.6340 + 29.5555i) q^{18} +23.2040 q^{19} +(-2.45268 + 43.7058i) q^{20} +(4.37248 + 6.62430i) q^{21} -10.2133i q^{22} +6.18529 q^{23} +(-42.5179 + 28.0646i) q^{24} +(-24.8430 - 2.79709i) q^{25} -72.3386i q^{26} +(-4.81949 - 26.5664i) q^{27} +23.1633i q^{28} -10.2911i q^{29} +(-26.9598 - 46.2928i) q^{30} -0.392831 q^{31} -23.6039 q^{32} +(4.72615 + 7.16011i) q^{33} -90.2377 q^{34} +(-13.2080 - 0.741205i) q^{35} +(30.9709 - 72.4522i) q^{36} +10.7385i q^{37} -82.8708 q^{38} +(33.4742 + 50.7134i) q^{39} +(4.75740 - 84.7750i) q^{40} +46.2216i q^{41} +(-15.6159 - 23.6580i) q^{42} -35.4569i q^{43} +25.0369i q^{44} +(40.3220 + 19.9783i) q^{45} -22.0902 q^{46} -55.3767 q^{47} +(64.1681 - 42.3552i) q^{48} -7.00000 q^{49} +(88.7244 + 9.98953i) q^{50} +(63.2617 - 41.7569i) q^{51} +177.330i q^{52} -19.7439 q^{53} +(17.2123 + 94.8792i) q^{54} +(-14.2763 - 0.801157i) q^{55} -44.9293i q^{56} +(58.0970 - 38.3479i) q^{57} +36.7538i q^{58} -71.2022i q^{59} +(66.0891 + 113.482i) q^{60} -58.9779 q^{61} +1.40296 q^{62} +(21.8952 + 9.35947i) q^{63} -18.2161 q^{64} +(-101.116 - 5.67441i) q^{65} +(-16.8790 - 25.5716i) q^{66} -95.3915i q^{67} +221.208 q^{68} +(15.4864 - 10.2221i) q^{69} +(47.1710 + 2.64714i) q^{70} +100.533i q^{71} +(-60.0735 + 140.534i) q^{72} +1.93194i q^{73} -38.3514i q^{74} +(-66.8234 + 34.0534i) q^{75} +203.149 q^{76} -7.56620 q^{77} +(-119.550 - 181.118i) q^{78} +40.7290 q^{79} +(-7.17987 + 127.943i) q^{80} +(-55.9715 - 58.5507i) q^{81} -165.076i q^{82} +52.6972 q^{83} +(38.2807 + 57.9952i) q^{84} +(-7.07846 + 126.135i) q^{85} +126.631i q^{86} +(-17.0076 - 25.7664i) q^{87} -48.5634i q^{88} -60.7017i q^{89} +(-144.006 - 71.3507i) q^{90} -53.5896 q^{91} +54.1516 q^{92} +(-0.983551 + 0.649209i) q^{93} +197.773 q^{94} +(-6.50057 + 115.838i) q^{95} +(-59.0983 + 39.0088i) q^{96} -37.6808i q^{97} +24.9998 q^{98} +(23.6662 + 10.1165i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 52 q^{4} - 22 q^{9}+O(q^{10}) $ 24 * q + 52 * q^4 - 22 * q^9	$ 24 q + 52 q^{4} - 22 q^{9} - 24 q^{10} + 26 q^{15} + 4 q^{16} + 72 q^{19} + 14 q^{21} - 156 q^{24} - 64 q^{25} - 32 q^{30} - 40 q^{31} - 144 q^{34} + 36 q^{36} + 62 q^{39} - 40 q^{40} + 120 q^{45} - 104 q^{46} - 168 q^{49} + 70 q^{51} + 60 q^{54} - 16 q^{55} - 348 q^{60} + 432 q^{61} - 364 q^{64} + 284 q^{66} + 404 q^{69} + 140 q^{70} + 204 q^{75} + 152 q^{76} + 108 q^{79} - 158 q^{81} + 112 q^{84} + 196 q^{85} - 152 q^{90} - 84 q^{91} + 808 q^{94} - 516 q^{96} + 582 q^{99}+O(q^{100}) $ 24 * q + 52 * q^4 - 22 * q^9 - 24 * q^10 + 26 * q^15 + 4 * q^16 + 72 * q^19 + 14 * q^21 - 156 * q^24 - 64 * q^25 - 32 * q^30 - 40 * q^31 - 144 * q^34 + 36 * q^36 + 62 * q^39 - 40 * q^40 + 120 * q^45 - 104 * q^46 - 168 * q^49 + 70 * q^51 + 60 * q^54 - 16 * q^55 - 348 * q^60 + 432 * q^61 - 364 * q^64 + 284 * q^66 + 404 * q^69 + 140 * q^70 + 204 * q^75 + 152 * q^76 + 108 * q^79 - 158 * q^81 + 112 * q^84 + 196 * q^85 - 152 * q^90 - 84 * q^91 + 808 * q^94 - 516 * q^96 + 582 * 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 $

$2$	−3.57140			−1.78570			−0.892850	−	0.450354i	$-0.851298\pi$
$2$	−3.57140			−1.78570			−0.892850	+	0.450354i	$0.851298\pi$
$3$	2.50375	−	1.65264i	0.834584	−	0.550881i
$3$	2.50375	−	1.65264i	0.834584	−	0.550881i
$4$	8.75491			2.18873
$5$	−0.280149	+	4.99215i	−0.0560298	+	0.998429i
$5$	−0.280149	+	4.99215i	−0.0560298	+	0.998429i
$6$	−8.94190	+	5.90225i	−1.49032	+	0.983708i
$7$			2.64575i			0.377964i
$7$			2.64575i			0.377964i
$8$	−16.9817			−2.12271
$9$	3.53755	−	8.27561i	0.393061	−	0.919513i
$10$	1.00052	−	17.8290i	0.100052	−	1.78290i
$11$			2.85975i			0.259978i	0.991515	+	0.129989i	$0.0414941\pi$
$11$			2.85975i			0.259978i	−0.991515	+	0.129989i	$0.958506\pi$
$12$	21.9201	−	14.4687i	1.82668	−	1.20573i
$13$			20.2550i			1.55808i	0.626977	+	0.779038i	$0.284292\pi$
$13$			20.2550i			1.55808i	−0.626977	+	0.779038i	$0.715708\pi$
$14$		−	9.44904i		−	0.674931i
$15$	7.54881	+	12.9621i	0.503254	+	0.864139i
$16$	25.6288			1.60180
$17$	25.2668			1.48628			0.743140	−	0.669136i	$-0.233336\pi$
$17$	25.2668			1.48628			0.743140	+	0.669136i	$0.233336\pi$
$18$	−12.6340	+	29.5555i	−0.701889	+	1.64197i
$19$	23.2040			1.22126			0.610631	−	0.791915i	$-0.290916\pi$
$19$	23.2040			1.22126			0.610631	+	0.791915i	$0.290916\pi$
$20$	−2.45268	+	43.7058i	−0.122634	+	2.18529i
$21$	4.37248	+	6.62430i	0.208213	+	0.315443i
$22$		−	10.2133i		−	0.464242i
$23$	6.18529			0.268926			0.134463	−	0.990919i	$-0.457069\pi$
$23$	6.18529			0.268926			0.134463	+	0.990919i	$0.457069\pi$
$24$	−42.5179	+	28.0646i	−1.77158	+	1.16936i
$25$	−24.8430	−	2.79709i	−0.993721	−	0.111884i
$26$		−	72.3386i		−	2.78226i
$27$	−4.81949	−	26.5664i	−0.178500	−	0.983940i
$28$			23.1633i			0.827261i
$29$		−	10.2911i		−	0.354867i	−0.984133	−	0.177433i	$-0.943221\pi$
$29$		−	10.2911i		−	0.354867i	0.984133	−	0.177433i	$-0.0567794\pi$
$30$	−26.9598	−	46.2928i	−0.898661	−	1.54309i
$31$	−0.392831			−0.0126720			−0.00633598	−	0.999980i	$-0.502017\pi$
$31$	−0.392831			−0.0126720			−0.00633598	+	0.999980i	$0.502017\pi$
$32$	−23.6039			−0.737621
$33$	4.72615	+	7.16011i	0.143217	+	0.216973i
$34$	−90.2377			−2.65405
$35$	−13.2080	−	0.741205i	−0.377371	−	0.0211773i
$36$	30.9709	−	72.4522i	0.860302	−	2.01256i
$37$			10.7385i			0.290229i	0.989415	+	0.145115i	$0.0463551\pi$
$37$			10.7385i			0.290229i	−0.989415	+	0.145115i	$0.953645\pi$
$38$	−82.8708			−2.18081
$39$	33.4742	+	50.7134i	0.858314	+	1.30034i
$40$	4.75740	−	84.7750i	0.118935	−	2.11938i
$41$			46.2216i			1.12736i	0.825995	+	0.563678i	$0.190614\pi$
$41$			46.2216i			1.12736i	−0.825995	+	0.563678i	$0.809386\pi$
$42$	−15.6159	−	23.6580i	−0.371807	−	0.563287i
$43$		−	35.4569i		−	0.824578i	−0.911053	−	0.412289i	$-0.864729\pi$
$43$		−	35.4569i		−	0.824578i	0.911053	−	0.412289i	$-0.135271\pi$
$44$			25.0369i			0.569020i
$45$	40.3220	+	19.9783i	0.896045	+	0.443963i
$46$	−22.0902			−0.480221
$47$	−55.3767			−1.17823			−0.589114	−	0.808050i	$-0.700523\pi$
$47$	−55.3767			−1.17823			−0.589114	+	0.808050i	$0.700523\pi$
$48$	64.1681	−	42.3552i	1.33683	−	0.882400i
$49$	−7.00000			−0.142857
$50$	88.7244	+	9.98953i	1.77449	+	0.199791i
$51$	63.2617	−	41.7569i	1.24043	−	0.818763i
$52$			177.330i			3.41020i
$53$	−19.7439			−0.372526			−0.186263	−	0.982500i	$-0.559638\pi$
$53$	−19.7439			−0.372526			−0.186263	+	0.982500i	$0.559638\pi$
$54$	17.2123	+	94.8792i	0.318747	+	1.75702i
$55$	−14.2763	−	0.801157i	−0.259569	−	0.0145665i
$56$		−	44.9293i		−	0.802309i
$57$	58.0970	−	38.3479i	1.01925	−	0.672770i
$58$			36.7538i			0.633686i
$59$		−	71.2022i		−	1.20682i	−0.797432	−	0.603408i	$-0.793809\pi$
$59$		−	71.2022i		−	1.20682i	0.797432	−	0.603408i	$-0.206191\pi$
$60$	66.0891	+	113.482i	1.10149	+	1.89136i
$61$	−58.9779			−0.966851			−0.483426	−	0.875385i	$-0.660608\pi$
$61$	−58.9779			−0.966851			−0.483426	+	0.875385i	$0.660608\pi$
$62$	1.40296			0.0226283
$63$	21.8952	+	9.35947i	0.347543	+	0.148563i
$64$	−18.2161			−0.284627
$65$	−101.116	−	5.67441i	−1.55563	−	0.0872986i
$66$	−16.8790	−	25.5716i	−0.255742	−	0.387449i
$67$		−	95.3915i		−	1.42375i	−0.702304	−	0.711877i	$-0.747845\pi$
$67$		−	95.3915i		−	1.42375i	0.702304	−	0.711877i	$-0.252155\pi$
$68$	221.208			3.25306
$69$	15.4864	−	10.2221i	0.224441	−	0.148146i
$70$	47.1710	+	2.64714i	0.673871	+	0.0378163i
$71$			100.533i			1.41596i	0.706232	+	0.707980i	$0.250393\pi$
$71$			100.533i			1.41596i	−0.706232	+	0.707980i	$0.749607\pi$
$72$	−60.0735	+	140.534i	−0.834354	+	1.95186i
$73$			1.93194i			0.0264650i	0.999912	+	0.0132325i	$0.00421216\pi$
$73$			1.93194i			0.0264650i	−0.999912	+	0.0132325i	$0.995788\pi$
$74$		−	38.3514i		−	0.518263i
$75$	−66.8234	+	34.0534i	−0.890978	+	0.454046i
$76$	203.149			2.67301
$77$	−7.56620			−0.0982623
$78$	−119.550	−	181.118i	−1.53269	−	2.32203i
$79$	40.7290			0.515558			0.257779	−	0.966204i	$-0.417009\pi$
$79$	40.7290			0.515558			0.257779	+	0.966204i	$0.417009\pi$
$80$	−7.17987	+	127.943i	−0.0897484	+	1.59928i
$81$	−55.9715	−	58.5507i	−0.691007	−	0.722848i
$82$		−	165.076i		−	2.01312i
$83$	52.6972			0.634906			0.317453	−	0.948274i	$-0.397172\pi$
$83$	52.6972			0.634906			0.317453	+	0.948274i	$0.397172\pi$
$84$	38.2807	+	57.9952i	0.455722	+	0.690419i
$85$	−7.07846	+	126.135i	−0.0832760	+	1.48394i
$86$			126.631i			1.47245i
$87$	−17.0076	−	25.7664i	−0.195489	−	0.296166i
$88$		−	48.5634i		−	0.551857i
$89$		−	60.7017i		−	0.682042i	−0.940056	−	0.341021i	$-0.889227\pi$
$89$		−	60.7017i		−	0.682042i	0.940056	−	0.341021i	$-0.110773\pi$
$90$	−144.006	−	71.3507i	−1.60007	−	0.792785i
$91$	−53.5896			−0.588897
$92$	54.1516			0.588605
$93$	−0.983551	+	0.649209i	−0.0105758	+	0.00698074i
$94$	197.773			2.10396
$95$	−6.50057	+	115.838i	−0.0684271	+	1.21934i
$96$	−59.0983	+	39.0088i	−0.615607	+	0.406342i
$97$		−	37.6808i		−	0.388462i	−0.980956	−	0.194231i	$-0.937779\pi$
$97$		−	37.6808i		−	0.388462i	0.980956	−	0.194231i	$-0.0622211\pi$
$98$	24.9998			0.255100
$99$	23.6662	+	10.1165i	0.239053	+	0.102187i
$100$	−217.498	−	24.4883i	−2.17498	−	0.244883i
$101$		−	114.744i		−	1.13608i	−0.823001	−	0.568040i	$-0.807702\pi$
$101$		−	114.744i		−	1.13608i	0.823001	−	0.568040i	$-0.192298\pi$
$102$	−225.933	+	149.131i	−2.21503	+	1.46207i
$103$		−	75.7875i		−	0.735801i	−0.929865	−	0.367901i	$-0.880077\pi$
$103$		−	75.7875i		−	0.735801i	0.929865	−	0.367901i	$-0.119923\pi$
$104$		−	343.964i		−	3.30734i
$105$	−34.2944	+	19.9723i	−0.326614	+	0.190212i
$106$	70.5133			0.665220
$107$	27.0298			0.252615			0.126307	−	0.991991i	$-0.459687\pi$
$107$	27.0298			0.252615			0.126307	+	0.991991i	$0.459687\pi$
$108$	−42.1942	−	232.586i	−0.390687	−	2.15358i
$109$	−140.887			−1.29254			−0.646270	−	0.763108i	$-0.723672\pi$
$109$	−140.887			−1.29254			−0.646270	+	0.763108i	$0.723672\pi$
$110$	50.9864	+	2.86125i	0.463513	+	0.0260114i
$111$	17.7469	+	26.8865i	0.159882	+	0.242221i
$112$			67.8073i			0.605423i
$113$	−134.480			−1.19009			−0.595046	−	0.803691i	$-0.702866\pi$
$113$	−134.480			−1.19009			−0.595046	+	0.803691i	$0.702866\pi$
$114$	−207.488	+	136.956i	−1.82007	+	1.20137i
$115$	−1.73280	+	30.8779i	−0.0150679	+	0.268503i
$116$		−	90.0979i		−	0.776706i
$117$	167.622	+	71.6529i	1.43267	+	0.612418i
$118$			254.292i			2.15501i
$119$			66.8495i			0.561761i
$120$	−128.191	−	220.118i	−1.06826	−	1.83432i
$121$	112.822			0.932412
$122$	210.634			1.72651
$123$	76.3878	+	115.727i	0.621039	+	0.940873i
$124$	−3.43920			−0.0277355
$125$	20.9232	−	123.236i	0.167386	−	0.985891i
$126$	−78.1966	−	33.4264i	−0.620608	−	0.265289i
$127$			73.8398i			0.581416i	0.956812	+	0.290708i	$0.0938908\pi$
$127$			73.8398i			0.581416i	−0.956812	+	0.290708i	$0.906109\pi$
$128$	159.473			1.24588
$129$	−58.5975	−	88.7752i	−0.454244	−	0.688179i
$130$	361.125	+	20.2656i	2.77789	+	0.155889i
$131$			69.1197i			0.527631i	0.964573	+	0.263816i	$0.0849810\pi$
$131$			69.1197i			0.527631i	−0.964573	+	0.263816i	$0.915019\pi$
$132$	41.3770	+	62.6861i	0.313462	+	0.474895i
$133$			61.3920i			0.461594i
$134$			340.681i			2.54240i
$135$	133.973	−	16.6171i	0.992396	−	0.123089i
$136$	−429.072			−3.15494
$137$	83.3740			0.608569			0.304285	−	0.952581i	$-0.401583\pi$
$137$	83.3740			0.608569			0.304285	+	0.952581i	$0.401583\pi$
$138$	−55.3083	+	36.5071i	−0.400784	+	0.264544i
$139$	67.8361			0.488030			0.244015	−	0.969771i	$-0.421535\pi$
$139$	67.8361			0.488030			0.244015	+	0.969771i	$0.421535\pi$
$140$	−115.635	−	6.48918i	−0.825961	−	0.0463513i
$141$	−138.650	+	91.5179i	−0.983330	+	0.649063i
$142$		−	359.044i		−	2.52848i
$143$	−57.9242			−0.405065
$144$	90.6629	−	212.094i	0.629604	−	1.47287i
$145$	51.3748	+	2.88305i	0.354309	+	0.0198831i
$146$		−	6.89975i		−	0.0472586i
$147$	−17.5263	+	11.5685i	−0.119226	+	0.0786973i
$148$			94.0144i			0.635233i
$149$		−	189.788i		−	1.27374i	−0.770970	−	0.636871i	$-0.780228\pi$
$149$		−	189.788i		−	1.27374i	0.770970	−	0.636871i	$-0.219772\pi$
$150$	238.653	−	121.618i	1.59102	−	0.810790i
$151$	17.7518			0.117562			0.0587810	−	0.998271i	$-0.481279\pi$
$151$	17.7518			0.117562			0.0587810	+	0.998271i	$0.481279\pi$
$152$	−394.043			−2.59239
$153$	89.3823	−	209.098i	0.584198	−	1.36665i
$154$	27.0219			0.175467
$155$	0.110051	−	1.96107i	0.000710007	−	0.0126521i
$156$	293.064	+	443.991i	1.87861	+	2.84610i
$157$		−	189.312i		−	1.20581i	−0.797813	−	0.602905i	$-0.794010\pi$
$157$		−	189.312i		−	1.20581i	0.797813	−	0.602905i	$-0.205990\pi$
$158$	−145.460			−0.920631
$159$	−49.4337	+	32.6296i	−0.310904	+	0.205217i
$160$	6.61261	−	117.834i	0.0413288	−	0.736463i
$161$			16.3647i			0.101644i
$162$	199.897	+	209.108i	1.23393	+	1.29079i
$163$			303.268i			1.86054i	0.366876	+	0.930270i	$0.380427\pi$
$163$			303.268i			1.86054i	−0.366876	+	0.930270i	$0.619573\pi$
$164$			404.666i			2.46747i
$165$	−37.0683	+	21.5877i	−0.224657	+	0.130835i
$166$	−188.203			−1.13375
$167$	111.158			0.665619			0.332809	−	0.942994i	$-0.392003\pi$
$167$	111.158			0.665619			0.332809	+	0.942994i	$0.392003\pi$
$168$	−74.2521	−	112.492i	−0.441977	−	0.669594i
$169$	−241.264			−1.42760
$170$	25.2800	−	450.480i	0.148706	−	2.64988i
$171$	82.0852	−	192.027i	0.480030	−	1.12297i
$172$		−	310.421i		−	1.80478i
$173$	−46.4976			−0.268772			−0.134386	−	0.990929i	$-0.542906\pi$
$173$	−46.4976			−0.268772			−0.134386	+	0.990929i	$0.542906\pi$
$174$	60.7408	+	92.0223i	0.349085	+	0.528864i
$175$	7.40040	−	65.7285i	0.0422880	−	0.375591i
$176$			73.2919i			0.416432i
$177$	−117.672	−	178.273i	−0.664812	−	1.00719i
$178$			216.790i			1.21792i
$179$		−	120.710i		−	0.674358i	−0.941441	−	0.337179i	$-0.890527\pi$
$179$		−	120.710i		−	0.674358i	0.941441	−	0.337179i	$-0.109473\pi$
$180$	353.016	+	174.909i	1.96120	+	0.971714i
$181$	−86.8504			−0.479837			−0.239918	−	0.970793i	$-0.577121\pi$
$181$	−86.8504			−0.479837			−0.239918	+	0.970793i	$0.577121\pi$
$182$	191.390			1.05159
$183$	−147.666	+	97.4694i	−0.806918	+	0.532620i
$184$	−105.037			−0.570851
$185$	−53.6081	−	3.00838i	−0.289773	−	0.0162615i
$186$	3.51265	−	2.31858i	0.0188852	−	0.0124655i
$187$			72.2567i			0.386399i
$188$	−484.818			−2.57882
$189$	70.2880	−	12.7512i	0.371894	−	0.0674666i
$190$	23.2162	−	413.703i	0.122190	−	2.17738i
$191$			22.2683i			0.116588i	0.998299	+	0.0582941i	$0.0185661\pi$
$191$			22.2683i			0.116588i	−0.998299	+	0.0582941i	$0.981434\pi$
$192$	−45.6086	+	30.1047i	−0.237545	+	0.156795i
$193$		−	29.5948i		−	0.153341i	−0.997056	−	0.0766704i	$-0.975571\pi$
$193$		−	29.5948i		−	0.153341i	0.997056	−	0.0766704i	$-0.0244289\pi$
$194$			134.573i			0.693676i
$195$	−262.547	+	152.901i	−1.34639	+	0.784107i
$196$	−61.2843			−0.312675
$197$	−114.282			−0.580114			−0.290057	−	0.957009i	$-0.593674\pi$
$197$	−114.282			−0.580114			−0.290057	+	0.957009i	$0.593674\pi$
$198$	−84.5215	−	36.1301i	−0.426876	−	0.182475i
$199$	377.846			1.89872			0.949361	−	0.314187i	$-0.101732\pi$
$199$	377.846			1.89872			0.949361	+	0.314187i	$0.101732\pi$
$200$	421.876	+	47.4993i	2.10938	+	0.237496i
$201$	−157.648	−	238.837i	−0.784319	−	1.18824i
$202$			409.797i			2.02870i
$203$	27.2278			0.134127
$204$	553.850	−	365.578i	2.71495	−	1.79205i
$205$	−230.745	−	12.9489i	−1.12559	−	0.0631655i
$206$			270.668i			1.31392i
$207$	21.8807	−	51.1871i	0.105704	−	0.247281i
$208$			519.110i			2.49572i
$209$			66.3577i			0.317501i
$210$	122.479	−	71.3290i	0.583234	−	0.339662i
$211$	290.180			1.37526			0.687631	−	0.726061i	$-0.258651\pi$
$211$	290.180			1.37526			0.687631	+	0.726061i	$0.258651\pi$
$212$	−172.856			−0.815357
$213$	166.145	+	251.710i	0.780025	+	1.18174i
$214$	−96.5342			−0.451094
$215$	177.006	+	9.93320i	0.823283	+	0.0462009i
$216$	81.8431	+	451.142i	0.378903	+	2.08862i
$217$		−	1.03933i		−	0.00478955i
$218$	503.164			2.30809
$219$	3.19281	+	4.83711i	0.0145791	+	0.0220873i
$220$	−124.988	−	7.01406i	−0.568126	−	0.0318821i
$221$			511.777i			2.31574i
$222$	−63.3812	−	96.0225i	−0.285501	−	0.432534i
$223$		−	291.102i		−	1.30539i	−0.757622	−	0.652694i	$-0.773639\pi$
$223$		−	291.102i		−	1.30539i	0.757622	−	0.652694i	$-0.226361\pi$
$224$		−	62.4500i		−	0.278795i
$225$	−111.031	+	195.696i	−0.493471	+	0.869762i
$226$	480.284			2.12515
$227$	−117.918			−0.519463			−0.259731	−	0.965681i	$-0.583634\pi$
$227$	−117.918			−0.519463			−0.259731	+	0.965681i	$0.583634\pi$
$228$	508.634	−	335.732i	2.23085	−	1.47251i
$229$	450.593			1.96766			0.983829	−	0.179113i	$-0.0573227\pi$
$229$	450.593			1.96766			0.983829	+	0.179113i	$0.0573227\pi$
$230$	6.18853	−	110.277i	0.0269067	−	0.479466i
$231$	−18.9439	+	12.5042i	−0.0820081	+	0.0541308i
$232$			174.761i			0.753279i
$233$	−148.921			−0.639145			−0.319572	−	0.947562i	$-0.603539\pi$
$233$	−148.921			−0.639145			−0.319572	+	0.947562i	$0.603539\pi$
$234$	−598.647	−	255.901i	−2.55832	−	1.09360i
$235$	15.5137	−	276.449i	0.0660159	−	1.17638i
$236$		−	623.368i		−	2.64139i
$237$	101.975	−	67.3106i	0.430276	−	0.284011i
$238$		−	238.747i		−	1.00314i
$239$		−	286.082i		−	1.19700i	−0.801124	−	0.598499i	$-0.795764\pi$
$239$		−	286.082i		−	1.19700i	0.801124	−	0.598499i	$-0.204236\pi$
$240$	193.467	+	332.202i	0.806111	+	1.38418i
$241$	−264.148			−1.09605			−0.548025	−	0.836462i	$-0.684620\pi$
$241$	−264.148			−1.09605			−0.548025	+	0.836462i	$0.684620\pi$
$242$	−402.932			−1.66501
$243$	−236.902	−	54.0955i	−0.974906	−	0.222615i
$244$	−516.346			−2.11617
$245$	1.96104	−	34.9450i	0.00800426	−	0.142633i
$246$	−272.811	−	413.309i	−1.10899	−	1.68012i
$247$			469.996i			1.90282i
$248$	6.67093			0.0268989
$249$	131.941	−	87.0896i	0.529882	−	0.349757i
$250$	−74.7252	+	440.127i	−0.298901	+	1.76051i
$251$			122.313i			0.487302i	0.969863	+	0.243651i	$0.0783452\pi$
$251$			122.313i			0.487302i	−0.969863	+	0.243651i	$0.921655\pi$
$252$	191.691	+	81.9412i	0.760677	+	0.325164i
$253$			17.6884i			0.0699146i
$254$		−	263.712i		−	1.03823i
$255$	190.734	+	327.510i	0.747976	+	1.28435i
$256$	−496.676			−1.94014
$257$	−118.674			−0.461766			−0.230883	−	0.972982i	$-0.574161\pi$
$257$	−118.674			−0.461766			−0.230883	+	0.972982i	$0.574161\pi$
$258$	209.275	+	317.052i	0.811144	+	1.22888i
$259$	−28.4114			−0.109696
$260$	−885.259	−	49.6789i	−3.40484	−	0.191073i
$261$	−85.1654	−	36.4053i	−0.326304	−	0.139484i
$262$		−	246.854i		−	0.942191i
$263$	175.268			0.666417			0.333208	−	0.942853i	$-0.391869\pi$
$263$	175.268			0.666417			0.333208	+	0.942853i	$0.391869\pi$
$264$	−80.2580	−	121.591i	−0.304007	−	0.460571i
$265$	5.53123	−	98.5643i	0.0208725	−	0.371941i
$266$		−	219.255i		−	0.824268i
$267$	−100.318	−	151.982i	−0.375724	−	0.569221i
$268$		−	835.144i		−	3.11621i
$269$		−	38.6352i		−	0.143625i	−0.997418	−	0.0718127i	$-0.977122\pi$
$269$		−	38.6352i		−	0.143625i	0.997418	−	0.0718127i	$-0.0228784\pi$
$270$	−478.473	+	59.3462i	−1.77212	+	0.219801i
$271$	54.6721			0.201742			0.100871	−	0.994900i	$-0.467837\pi$
$271$	54.6721			0.201742			0.100871	+	0.994900i	$0.467837\pi$
$272$	647.556			2.38072
$273$	−134.175	+	88.5645i	−0.491484	+	0.324412i
$274$	−297.762			−1.08672
$275$	7.99898	−	71.0449i	0.0290872	−	0.258345i
$276$	135.582	−	89.4933i	0.491240	−	0.324251i
$277$			119.112i			0.430008i	0.976613	+	0.215004i	$0.0689764\pi$
$277$			119.112i			0.430008i	−0.976613	+	0.215004i	$0.931024\pi$
$278$	−242.270			−0.871475
$279$	−1.38966	+	3.25091i	−0.00498085	+	0.0116520i
$280$	224.294	+	12.5869i	0.801049	+	0.0449532i
$281$			284.613i			1.01286i	0.862282	+	0.506429i	$0.169035\pi$
$281$			284.613i			1.01286i	−0.862282	+	0.506429i	$0.830965\pi$
$282$	495.173	−	326.847i	1.75593	−	1.15903i
$283$		−	217.996i		−	0.770304i	−0.922853	−	0.385152i	$-0.874149\pi$
$283$		−	217.996i		−	0.770304i	0.922853	−	0.385152i	$-0.125851\pi$
$284$			880.159i			3.09915i
$285$	175.162	+	300.772i	0.614605	+	1.05534i
$286$	206.871			0.723324
$287$	−122.291			−0.426101
$288$	−83.4998	+	195.337i	−0.289930	+	0.678252i
$289$	349.409			1.20903
$290$	−183.480	−	10.2965i	−0.632690	−	0.0355053i
$291$	−62.2729	−	94.3433i	−0.213996	−	0.324204i
$292$			16.9140i			0.0579246i
$293$	−475.423			−1.62260			−0.811302	−	0.584627i	$-0.801241\pi$
$293$	−475.423			−1.62260			−0.811302	+	0.584627i	$0.801241\pi$
$294$	62.5933	−	41.3157i	0.212902	−	0.140530i
$295$	355.452	+	19.9472i	1.20492	+	0.0676177i
$296$		−	182.357i		−	0.616073i
$297$	75.9733	−	13.7826i	0.255802	−	0.0464059i
$298$			677.808i			2.27452i
$299$			125.283i			0.419006i
$300$	−585.032	+	298.135i	−1.95011	+	0.993782i
$301$	93.8100			0.311661
$302$	−63.3990			−0.209930
$303$	−189.631	−	287.291i	−0.625845	−	0.948154i
$304$	594.690			1.95622
$305$	16.5226	−	294.426i	0.0541725	−	0.965332i
$306$	−319.220	+	746.772i	−1.04320	+	2.44043i
$307$			167.830i			0.546676i	0.961918	+	0.273338i	$0.0881278\pi$
$307$			167.830i			0.546676i	−0.961918	+	0.273338i	$0.911872\pi$
$308$	−66.2413			−0.215069
$309$	−125.250	−	189.753i	−0.405339	−	0.614088i
$310$	−0.393037	+	7.00376i	−0.00126786	+	0.0225928i
$311$		−	231.810i		−	0.745370i	−0.927958	−	0.372685i	$-0.878437\pi$
$311$		−	231.810i		−	0.745370i	0.927958	−	0.372685i	$-0.121563\pi$
$312$	−568.449	−	861.199i	−1.82195	−	2.76025i
$313$		−	333.644i		−	1.06596i	−0.846129	−	0.532978i	$-0.821073\pi$
$313$		−	333.644i		−	1.06596i	0.846129	−	0.532978i	$-0.178927\pi$
$314$			676.109i			2.15321i
$315$	−52.8577	+	106.682i	−0.167802	+	0.338673i
$316$	356.579			1.12841
$317$	120.686			0.380714			0.190357	−	0.981715i	$-0.439035\pi$
$317$	120.686			0.380714			0.190357	+	0.981715i	$0.439035\pi$
$318$	176.548	−	116.533i	0.555182	−	0.366457i
$319$	29.4301			0.0922574
$320$	5.10323	−	90.9375i	0.0159476	−	0.284180i
$321$	67.6758	−	44.6705i	0.210828	−	0.139161i
$322$		−	58.4451i		−	0.181506i
$323$	586.289			1.81514
$324$	−490.026	−	512.606i	−1.51242	−	1.58212i
$325$	56.6550	−	503.195i	0.174323	−	1.54829i
$326$		−	1083.09i		−	3.32237i
$327$	−352.746	+	232.836i	−1.07873	+	0.712036i
$328$		−	784.920i		−	2.39305i
$329$		−	146.513i		−	0.445328i
$330$	132.386	−	77.0984i	0.401170	−	0.233632i
$331$	−381.774			−1.15340			−0.576698	−	0.816958i	$-0.695659\pi$
$331$	−381.774			−1.15340			−0.576698	+	0.816958i	$0.695659\pi$
$332$	461.359			1.38964
$333$	88.8675	+	37.9879i	0.266869	+	0.114078i
$334$	−396.991			−1.18860
$335$	476.208	+	26.7238i	1.42152	+	0.0797726i
$336$	112.061	+	169.773i	0.333516	+	0.505276i
$337$			360.117i			1.06860i	0.845296	+	0.534298i	$0.179424\pi$
$337$			360.117i			1.06860i	−0.845296	+	0.534298i	$0.820576\pi$
$338$	861.651			2.54926
$339$	−336.706	+	222.248i	−0.993232	+	0.655599i
$340$	−61.9712	+	1104.30i	−0.182268	+	3.24795i
$341$		−	1.12340i		−	0.00329442i
$342$	−293.159	+	685.806i	−0.857190	+	2.00528i
$343$		−	18.5203i		−	0.0539949i
$344$			602.117i			1.75034i
$345$	46.6916	+	80.1742i	0.135338	+	0.232389i
$346$	166.062			0.479947
$347$	−154.887			−0.446360			−0.223180	−	0.974777i	$-0.571644\pi$
$347$	−154.887			−0.446360			−0.223180	+	0.974777i	$0.571644\pi$
$348$	−148.900	−	225.583i	−0.427872	−	0.648226i
$349$	−6.04733			−0.0173276			−0.00866380	−	0.999962i	$-0.502758\pi$
$349$	−6.04733			−0.0173276			−0.00866380	+	0.999962i	$0.502758\pi$
$350$	−26.4298	+	234.743i	−0.0755137	+	0.670694i
$351$	538.101	−	97.6187i	1.53305	−	0.278116i
$352$		−	67.5013i		−	0.191765i
$353$	534.849			1.51515			0.757577	−	0.652746i	$-0.226383\pi$
$353$	534.849			1.51515			0.757577	+	0.652746i	$0.226383\pi$
$354$	420.253	+	636.683i	1.18716	+	1.79854i
$355$	−501.876	−	28.1643i	−1.41374	−	0.0793360i
$356$		−	531.438i		−	1.49280i
$357$	110.478	+	167.375i	0.309463	+	0.468837i
$358$			431.104i			1.20420i
$359$			700.942i			1.95249i	0.216681	+	0.976243i	$0.430477\pi$
$359$			700.942i			1.95249i	−0.216681	+	0.976243i	$0.569523\pi$
$360$	−684.736	−	339.266i	−1.90204	−	0.942405i
$361$	177.425			0.491482
$362$	310.178			0.856845
$363$	282.478	−	186.454i	0.778176	−	0.513648i
$364$	−469.172			−1.28893
$365$	−9.64455	−	0.541232i	−0.0264234	−	0.00148283i
$366$	527.375	−	348.102i	1.44091	−	0.951099i
$367$			229.545i			0.625464i	0.949841	+	0.312732i	$0.101244\pi$
$367$			229.545i			0.625464i	−0.949841	+	0.312732i	$0.898756\pi$
$368$	158.521			0.430765
$369$	382.512	+	163.511i	1.03662	+	0.443119i
$370$	191.456	+	10.7441i	0.517448	+	0.0290381i
$371$		−	52.2374i		−	0.140802i
$372$	−8.61089	+	5.68376i	−0.0231476	+	0.0152789i
$373$			200.492i			0.537511i	0.963208	+	0.268756i	$0.0866124\pi$
$373$			200.492i			0.537511i	−0.963208	+	0.268756i	$0.913388\pi$
$374$		−	258.058i		−	0.689994i
$375$	−151.279	−	343.132i	−0.403411	−	0.915019i
$376$	940.390			2.50104
$377$	208.447			0.552909
$378$	−251.027	+	45.5396i	−0.664092	+	0.120475i
$379$	−628.729			−1.65891			−0.829457	−	0.558570i	$-0.811350\pi$
$379$	−628.729			−1.65891			−0.829457	+	0.558570i	$0.811350\pi$
$380$	−56.9119	+	1014.15i	−0.149768	+	2.66881i
$381$	122.031	+	184.877i	0.320291	+	0.485240i
$382$		−	79.5292i		−	0.208192i
$383$	48.3499			0.126240			0.0631200	−	0.998006i	$-0.479895\pi$
$383$	48.3499			0.126240			0.0631200	+	0.998006i	$0.479895\pi$
$384$	399.280	−	263.551i	1.03979	−	0.686331i
$385$	2.11966	−	37.7715i	0.00550562	−	0.0981079i
$386$			105.695i			0.273821i
$387$	−293.427	−	125.430i	−0.758210	−	0.324109i
$388$		−	329.892i		−	0.850237i
$389$		−	88.9021i		−	0.228540i	−0.993450	−	0.114270i	$-0.963547\pi$
$389$		−	88.9021i		−	0.228540i	0.993450	−	0.114270i	$-0.0364529\pi$
$390$	937.659	−	546.071i	2.40425	−	1.40018i
$391$	156.282			0.399699
$392$	118.872			0.303244
$393$	114.230	+	173.058i	0.290662	+	0.440352i
$394$	408.148			1.03591
$395$	−11.4102	+	203.325i	−0.0288866	+	0.514748i
$396$	207.195	+	88.5691i	0.523221	+	0.223659i
$397$			223.013i			0.561746i	0.959745	+	0.280873i	$0.0906239\pi$
$397$			223.013i			0.561746i	−0.959745	+	0.280873i	$0.909376\pi$
$398$	−1349.44			−3.39055
$399$	101.459	+	153.710i	0.254283	+	0.385239i
$400$	−636.696	−	71.6859i	−1.59174	−	0.179215i
$401$			448.262i			1.11786i	0.829215	+	0.558931i	$0.188788\pi$
$401$			448.262i			1.11786i	−0.829215	+	0.558931i	$0.811212\pi$
$402$	563.024	+	852.981i	1.40056	+	2.12184i
$403$		−	7.95678i		−	0.0197439i
$404$		−	1004.57i		−	2.48657i
$405$	307.974	−	263.015i	0.760430	−	0.649420i
$406$	−97.2413			−0.239511
$407$	−30.7094			−0.0754531
$408$	−1074.29	+	709.102i	−2.63306	+	1.73800i
$409$	−412.884			−1.00950			−0.504749	−	0.863266i	$-0.668415\pi$
$409$	−412.884			−1.00950			−0.504749	+	0.863266i	$0.668415\pi$
$410$	824.083	+	46.2458i	2.00996	+	0.112795i
$411$	208.748	−	137.787i	0.507902	−	0.335249i
$412$		−	663.513i		−	1.61047i
$413$	188.383			0.456134
$414$	−78.1449	+	182.810i	−0.188756	+	0.441569i
$415$	−14.7631	+	263.072i	−0.0355737	+	0.633909i
$416$		−	478.096i		−	1.14927i
$417$	169.845	−	112.109i	0.407302	−	0.268846i
$418$		−	236.990i		−	0.566961i
$419$		−	496.934i		−	1.18600i	−0.805203	−	0.592999i	$-0.797944\pi$
$419$		−	496.934i		−	1.18600i	0.805203	−	0.592999i	$-0.202056\pi$
$420$	−300.245	+	174.855i	−0.714868	+	0.416322i
$421$	−258.161			−0.613209			−0.306604	−	0.951837i	$-0.599193\pi$
$421$	−258.161			−0.613209			−0.306604	+	0.951837i	$0.599193\pi$
$422$	−1036.35			−2.45581
$423$	−195.898	+	458.276i	−0.463115	+	1.08340i
$424$	335.284			0.790764
$425$	−627.703	−	70.6734i	−1.47695	−	0.166290i
$426$	−593.372	−	898.958i	−1.39289	−	2.11023i
$427$		−	156.041i		−	0.365435i
$428$	236.643			0.552905
$429$	−145.028	+	95.7280i	−0.338060	+	0.223142i
$430$	−632.159	−	35.4754i	−1.47014	−	0.0825010i
$431$		−	55.4708i		−	0.128703i	−0.997927	−	0.0643513i	$-0.979502\pi$
$431$		−	55.4708i		−	0.128703i	0.997927	−	0.0643513i	$-0.0204978\pi$
$432$	−123.518	−	680.864i	−0.285921	−	1.57607i
$433$			379.997i			0.877591i	0.898587	+	0.438796i	$0.144595\pi$
$433$			379.997i			0.877591i	−0.898587	+	0.438796i	$0.855405\pi$
$434$			3.71187i			0.00855270i
$435$	133.394	−	77.6858i	0.306654	−	0.178588i
$436$	−1233.45			−2.82902
$437$	143.523			0.328429
$438$	−11.4028	−	17.2753i	−0.0260338	−	0.0394412i
$439$	−339.273			−0.772832			−0.386416	−	0.922325i	$-0.626287\pi$
$439$	−339.273			−0.772832			−0.386416	+	0.922325i	$0.626287\pi$
$440$	242.436	+	13.6050i	0.550990	+	0.0309204i
$441$	−24.7628	+	57.9293i	−0.0561515	+	0.131359i
$442$		−	1827.76i		−	4.13521i
$443$	−76.0497			−0.171670			−0.0858349	−	0.996309i	$-0.527356\pi$
$443$	−76.0497			−0.171670			−0.0858349	+	0.996309i	$0.527356\pi$
$444$	155.372	+	235.389i	0.349937	+	0.530155i
$445$	303.032	+	17.0055i	0.680970	+	0.0382147i
$446$			1039.64i			2.33103i
$447$	−313.651	−	475.181i	−0.701680	−	1.06304i
$448$		−	48.1953i		−	0.107579i
$449$		−	646.472i		−	1.43980i	−0.694076	−	0.719901i	$-0.744187\pi$
$449$		−	646.472i		−	1.43980i	0.694076	−	0.719901i	$-0.255813\pi$
$450$	396.536	−	698.911i	0.881192	−	1.55313i
$451$	−132.182			−0.293087
$452$	−1177.36			−2.60479
$453$	44.4462	−	29.3375i	0.0981153	−	0.0647626i
$454$	421.133			0.927605
$455$	15.0131	−	267.527i	0.0329958	−	0.587972i
$456$	−986.585	+	651.212i	−2.16356	+	1.42810i
$457$			496.581i			1.08661i	0.839535	+	0.543305i	$0.182827\pi$
$457$			496.581i			1.08661i	−0.839535	+	0.543305i	$0.817173\pi$
$458$	−1609.25			−3.51365
$459$	−121.773	−	671.246i	−0.265301	−	1.46241i
$460$	−15.1705	+	270.333i	−0.0329794	+	0.587680i
$461$		−	311.434i		−	0.675562i	−0.941225	−	0.337781i	$-0.890324\pi$
$461$		−	311.434i		−	0.675562i	0.941225	−	0.337781i	$-0.109676\pi$
$462$	67.6562	−	44.6576i	0.146442	−	0.0966614i
$463$		−	561.365i		−	1.21245i	−0.795293	−	0.606226i	$-0.792683\pi$
$463$		−	561.365i		−	1.21245i	0.795293	−	0.606226i	$-0.207317\pi$
$464$		−	263.749i		−	0.568425i
$465$	−2.96540	−	5.09190i	−0.00637721	−	0.0109503i
$466$	531.856			1.14132
$467$	538.798			1.15374			0.576871	−	0.816835i	$-0.304273\pi$
$467$	538.798			1.15374			0.576871	+	0.816835i	$0.304273\pi$
$468$	1467.52	+	627.314i	3.13572	+	1.34042i
$469$	252.382			0.538128
$470$	−55.4058	+	987.309i	−0.117885	+	2.10066i
$471$	−312.865	−	473.991i	−0.664257	−	1.00635i
$472$			1209.13i			2.56172i
$473$	101.398			0.214372
$474$	−364.195	+	240.393i	−0.768344	+	0.507158i
$475$	−576.457	−	64.9036i	−1.21359	−	0.136639i
$476$			585.262i			1.22954i
$477$	−69.8448	+	163.393i	−0.146425	+	0.342542i
$478$			1021.71i			2.13748i
$479$		−	49.2437i		−	0.102805i	−0.998678	−	0.0514026i	$-0.983631\pi$
$479$		−	49.2437i		−	0.102805i	0.998678	−	0.0514026i	$-0.0163692\pi$
$480$	−178.181	−	305.955i	−0.371211	−	0.637407i
$481$	−217.508			−0.452199
$482$	943.379			1.95722
$483$	27.0451	+	40.9732i	0.0559939	+	0.0848307i
$484$	987.744			2.04079
$485$	188.108	+	10.5562i	0.387851	+	0.0217654i
$486$	846.073	+	193.197i	1.74089	+	0.397524i
$487$		−	360.453i		−	0.740150i	−0.929002	−	0.370075i	$-0.879332\pi$
$487$		−	360.453i		−	0.740150i	0.929002	−	0.370075i	$-0.120668\pi$
$488$	1001.54			2.05234
$489$	501.194	+	759.308i	1.02494	+	1.55278i
$490$	−7.00367	+	124.803i	−0.0142932	+	0.254699i
$491$		−	284.994i		−	0.580436i	−0.956961	−	0.290218i	$-0.906272\pi$
$491$		−	284.994i		−	0.580436i	0.956961	−	0.290218i	$-0.0937278\pi$
$492$	668.768	+	1013.18i	1.35928	+	2.05931i
$493$		−	260.023i		−	0.527431i
$494$		−	1678.55i		−	3.39786i
$495$	−57.1331	+	115.311i	−0.115420	+	0.232952i
$496$	−10.0678			−0.0202979
$497$	−265.986			−0.535183
$498$	−471.213	+	311.032i	−0.946211	+	0.624562i
$499$	−478.846			−0.959610			−0.479805	−	0.877375i	$-0.659293\pi$
$499$	−478.846			−0.959610			−0.479805	+	0.877375i	$0.659293\pi$
$500$	183.181	−	1078.92i	0.366362	−	2.15785i
$501$	278.313	−	183.705i	0.555515	−	0.366677i
$502$		−	436.828i		−	0.870176i
$503$	167.887			0.333771			0.166885	−	0.985976i	$-0.446629\pi$
$503$	167.887			0.333771			0.166885	+	0.985976i	$0.446629\pi$
$504$	−371.818	−	158.939i	−0.737733	−	0.315356i
$505$	572.819	+	32.1454i	1.13430	+	0.0636543i
$506$		−	63.1724i		−	0.124847i
$507$	−604.065	+	398.723i	−1.19145	+	0.786436i
$508$			646.461i			1.27256i
$509$			690.227i			1.35605i	0.735041	+	0.678023i	$0.237163\pi$
$509$			690.227i			1.35605i	−0.735041	+	0.678023i	$0.762837\pi$
$510$	−681.187	−	1169.67i	−1.33566	−	2.29347i
$511$	−5.11144			−0.0100028
$512$	1135.94			2.21863
$513$	−111.831	−	616.446i	−0.217995	−	1.20165i
$514$	423.832			0.824576
$515$	378.342	+	21.2318i	0.734645	+	0.0412268i
$516$	−513.016	−	777.218i	−0.994216	−	1.50624i
$517$		−	158.364i		−	0.306313i
$518$	101.468			0.195885
$519$	−116.419	+	76.8439i	−0.224313	+	0.148062i
$520$	1717.12	+	96.3610i	3.30215	+	0.185310i
$521$			754.960i			1.44906i	0.689244	+	0.724529i	$0.257943\pi$
$521$			754.960i			1.44906i	−0.689244	+	0.724529i	$0.742057\pi$
$522$	304.160	+	130.018i	0.582682	+	0.249077i
$523$			531.600i			1.01644i	0.861226	+	0.508222i	$0.169697\pi$
$523$			531.600i			1.01644i	−0.861226	+	0.508222i	$0.830303\pi$
$524$			605.136i			1.15484i
$525$	−90.0969	−	176.798i	−0.171613	−	0.336758i
$526$	−625.951			−1.19002
$527$	−9.92556			−0.0188341
$528$	121.125	+	183.505i	0.229404	+	0.347547i
$529$	−490.742			−0.927679
$530$	−19.7542	+	352.013i	−0.0372721	+	0.664175i
$531$	−589.242	−	251.881i	−1.10968	−	0.474352i
$532$			537.481i			1.01030i
$533$	−936.217			−1.75651
$534$	358.277	+	542.789i	0.670930	+	1.01646i
$535$	−7.57236	+	134.937i	−0.0141540	+	0.252218i
$536$			1619.91i			3.02222i
$537$	−199.490	−	302.228i	−0.371491	−	0.562808i
$538$			137.982i			0.256472i
$539$		−	20.0183i		−	0.0371397i
$540$	1172.92	−	145.481i	2.17208	−	0.269409i
$541$	−265.520			−0.490795			−0.245398	−	0.969422i	$-0.578919\pi$
$541$	−265.520			−0.490795			−0.245398	+	0.969422i	$0.578919\pi$
$542$	−195.256			−0.360251
$543$	−217.452	+	143.533i	−0.400464	+	0.264333i
$544$	−596.394			−1.09631
$545$	39.4693	−	703.328i	0.0724208	−	1.29051i
$546$	479.193	−	316.299i	0.877643	−	0.579303i
$547$			665.944i			1.21745i	0.793382	+	0.608724i	$0.208318\pi$
$547$			665.944i			1.21745i	−0.793382	+	0.608724i	$0.791682\pi$
$548$	729.932			1.33199
$549$	−208.637	+	488.078i	−0.380031	+	0.889032i
$550$	−28.5676	+	253.730i	−0.0519411	+	0.461327i
$551$		−	238.795i		−	0.433385i
$552$	−262.986	+	173.588i	−0.476423	+	0.314471i
$553$			107.759i			0.194862i
$554$		−	425.397i		−	0.767865i
$555$	−139.193	+	81.0627i	−0.250798	+	0.146059i
$556$	593.899			1.06816
$557$	−679.746			−1.22037			−0.610185	−	0.792259i	$-0.708905\pi$
$557$	−679.746			−1.22037			−0.610185	+	0.792259i	$0.708905\pi$
$558$	4.96302	−	11.6103i	0.00889430	−	0.0208070i
$559$	718.178			1.28475
$560$	−338.504	−	18.9962i	−0.604472	−	0.0339217i
$561$	119.414	+	180.913i	0.212860	+	0.322483i
$562$		−	1016.47i		−	1.80866i
$563$	−246.198			−0.437297			−0.218649	−	0.975804i	$-0.570165\pi$
$563$	−246.198			−0.437297			−0.218649	+	0.975804i	$0.570165\pi$
$564$	−1213.86	+	801.231i	−2.15224	+	1.42062i
$565$	37.6746	−	671.346i	0.0666807	−	1.18822i
$566$			778.552i			1.37553i
$567$	154.911	−	148.087i	0.273211	−	0.261176i
$568$		−	1707.22i		−	3.00567i
$569$		−	124.085i		−	0.218076i	−0.994038	−	0.109038i	$-0.965223\pi$
$569$		−	124.085i		−	0.218076i	0.994038	−	0.109038i	$-0.0347770\pi$
$570$	−625.575	−	1074.18i	−1.09750	−	1.88452i
$571$	460.191			0.805939			0.402969	−	0.915213i	$-0.367978\pi$
$571$	460.191			0.805939			0.402969	+	0.915213i	$0.367978\pi$
$572$	−507.121			−0.886576
$573$	36.8016	+	55.7544i	0.0642262	+	0.0973026i
$574$	436.750			0.760888
$575$	−153.661	−	17.3008i	−0.267237	−	0.0300884i
$576$	−64.4403	+	150.750i	−0.111876	+	0.261718i
$577$		−	517.238i		−	0.896427i	−0.893927	−	0.448213i	$-0.852060\pi$
$577$		−	517.238i		−	0.896427i	0.893927	−	0.448213i	$-0.147940\pi$
$578$	−1247.88			−2.15896
$579$	−48.9096	−	74.0980i	−0.0844725	−	0.127976i
$580$	449.782	+	25.2408i	0.775486	+	0.0435187i
$581$			139.424i			0.239972i
$582$	222.401	+	336.938i	0.382133	+	0.578931i
$583$		−	56.4626i		−	0.0968483i
$584$		−	32.8077i		−	0.0561775i
$585$	−404.661	+	816.722i	−0.691728	+	1.39611i
$586$	1697.93			2.89749
$587$	61.0908			0.104073			0.0520365	−	0.998645i	$-0.483429\pi$
$587$	61.0908			0.104073			0.0520365	+	0.998645i	$0.483429\pi$
$588$	−153.441	+	101.281i	−0.260954	+	0.172247i
$589$	−9.11524			−0.0154758
$590$	−1269.46	−	71.2395i	−2.15163	−	0.120745i
$591$	−286.135	+	188.868i	−0.484154	+	0.319574i
$592$			275.214i			0.464889i
$593$	755.915			1.27473			0.637365	−	0.770562i	$-0.280024\pi$
$593$	755.915			1.27473			0.637365	+	0.770562i	$0.280024\pi$
$594$	−271.331	+	49.2231i	−0.456786	+	0.0828671i
$595$	−333.723	−	18.7278i	−0.560878	−	0.0314754i
$596$		−	1661.57i		−	2.78787i
$597$	946.032	−	624.444i	1.58464	−	1.04597i
$598$		−	447.436i		−	0.748220i
$599$			837.936i			1.39889i	0.714686	+	0.699445i	$0.246570\pi$
$599$			837.936i			1.39889i	−0.714686	+	0.699445i	$0.753430\pi$
$600$	1134.77	−	578.285i	1.89129	−	0.963808i
$601$	−211.613			−0.352102			−0.176051	−	0.984381i	$-0.556332\pi$
$601$	−211.613			−0.352102			−0.176051	+	0.984381i	$0.556332\pi$
$602$	−335.033			−0.556534
$603$	−789.423	−	337.452i	−1.30916	−	0.559621i
$604$	155.416			0.257311
$605$	−31.6069	+	563.223i	−0.0522428	+	0.930947i
$606$	677.248	+	1026.03i	1.11757	+	1.69312i
$607$		−	784.186i		−	1.29190i	−0.763378	−	0.645952i	$-0.776461\pi$
$607$		−	784.186i		−	1.29190i	0.763378	−	0.645952i	$-0.223539\pi$
$608$	−547.704			−0.900829
$609$	68.1716	−	44.9978i	0.111940	−	0.0738880i
$610$	−59.0089	+	1051.51i	−0.0967358	+	1.72379i
$611$		−	1121.65i		−	1.83577i
$612$	782.534	−	1830.63i	1.27865	−	2.99123i
$613$		−	790.592i		−	1.28971i	−0.764305	−	0.644855i	$-0.776918\pi$
$613$		−	790.592i		−	1.28971i	0.764305	−	0.644855i	$-0.223082\pi$
$614$		−	599.387i		−	0.976200i
$615$	−599.128	+	348.918i	−0.974192	+	0.567346i
$616$	128.487			0.208582
$617$	−314.657			−0.509978			−0.254989	−	0.966944i	$-0.582072\pi$
$617$	−314.657			−0.509978			−0.254989	+	0.966944i	$0.582072\pi$
$618$	447.317	+	677.685i	0.723814	+	1.09658i
$619$	−952.388			−1.53859			−0.769296	−	0.638893i	$-0.779393\pi$
$619$	−952.388			−1.53859			−0.769296	+	0.638893i	$0.779393\pi$
$620$	0.963487	−	17.1690i	0.00155401	−	0.0276919i
$621$	−29.8100	−	164.321i	−0.0480032	−	0.264607i
$622$			827.887i			1.33101i
$623$	160.602			0.257788
$624$	857.903	+	1299.72i	1.37485	+	2.08289i
$625$	609.353	+	138.976i	0.974964	+	0.222362i
$626$			1191.58i			1.90348i
$627$	109.666	+	166.143i	0.174905	+	0.264981i
$628$		−	1657.41i		−	2.63919i
$629$			271.327i			0.431362i
$630$	188.776	−	381.004i	0.299645	−	0.604769i
$631$	783.866			1.24226			0.621130	−	0.783708i	$-0.286674\pi$
$631$	783.866			1.24226			0.621130	+	0.783708i	$0.286674\pi$
$632$	−691.648			−1.09438
$633$	726.539	−	479.564i	1.14777	−	0.757605i
$634$	−431.019			−0.679841
$635$	−368.619	−	20.6862i	−0.580503	−	0.0325766i
$636$	−432.788	+	285.669i	−0.680484	+	0.449165i
$637$		−	141.785i		−	0.222582i
$638$	−105.107			−0.164744
$639$	831.974	+	355.641i	1.30199	+	0.556558i
$640$	−44.6761	+	796.110i	−0.0698064	+	1.24392i
$641$			258.089i			0.402635i	0.979526	+	0.201317i	$0.0645223\pi$
$641$			258.089i			0.402635i	−0.979526	+	0.201317i	$0.935478\pi$
$642$	−241.698	+	159.536i	−0.376476	+	0.248499i
$643$		−	322.611i		−	0.501728i	−0.968022	−	0.250864i	$-0.919285\pi$
$643$		−	322.611i		−	0.501728i	0.968022	−	0.250864i	$-0.0807147\pi$
$644$			143.272i			0.222472i
$645$	459.594	−	267.657i	0.712550	−	0.414972i
$646$	−2093.87			−3.24129
$647$	632.810			0.978068			0.489034	−	0.872265i	$-0.337349\pi$
$647$	632.810			0.978068			0.489034	+	0.872265i	$0.337349\pi$
$648$	950.491	+	994.290i	1.46681	+	1.53440i
$649$	203.621			0.313745
$650$	−202.338	+	1797.11i	−0.311289	+	2.76479i
$651$	−1.71764	−	2.60223i	−0.00263847	−	0.00399728i
$652$			2655.08i			4.07221i
$653$	−25.8462			−0.0395807			−0.0197903	−	0.999804i	$-0.506300\pi$
$653$	−25.8462			−0.0395807			−0.0197903	+	0.999804i	$0.506300\pi$
$654$	1259.80	−	831.550i	1.92630	−	1.27148i
$655$	−345.055	−	19.3638i	−0.526802	−	0.0295631i
$656$			1184.60i			1.80580i
$657$	15.9880	+	6.83434i	0.0243349	+	0.0104023i
$658$			523.257i			0.795223i
$659$		−	819.617i		−	1.24373i	−0.783125	−	0.621864i	$-0.786376\pi$
$659$		−	819.617i		−	1.24373i	0.783125	−	0.621864i	$-0.213624\pi$
$660$	−324.530	+	188.999i	−0.491712	+	0.286361i
$661$	331.772			0.501924			0.250962	−	0.967997i	$-0.419253\pi$
$661$	331.772			0.501924			0.250962	+	0.967997i	$0.419253\pi$
$662$	1363.47			2.05962
$663$	845.785	+	1281.36i	1.27569	+	1.93268i
$664$	−894.887			−1.34772
$665$	−306.478	−	17.1989i	−0.460869	−	0.0258630i
$666$	−317.382	−	135.670i	−0.476549	−	0.203709i
$667$		−	63.6536i		−	0.0954327i
$668$	973.181			1.45686
$669$	−481.087	−	728.846i	−0.719113	−	1.08946i
$670$	−1700.73	−	95.4415i	−2.53840	−	0.142450i
$671$		−	168.662i		−	0.251360i
$672$	−103.208	−	156.359i	−0.153583	−	0.232678i
$673$			881.421i			1.30969i	0.755764	+	0.654845i	$0.227266\pi$
$673$			881.421i			1.30969i	−0.755764	+	0.654845i	$0.772734\pi$
$674$		−	1286.12i		−	1.90819i
$675$	45.4223	+	673.470i	0.0672923	+	0.997733i
$676$	−2112.24			−3.12462
$677$	−38.4488			−0.0567929			−0.0283965	−	0.999597i	$-0.509040\pi$
$677$	−38.4488			−0.0567929			−0.0283965	+	0.999597i	$0.509040\pi$
$678$	1202.51	−	793.737i	1.77362	−	1.17070i
$679$	99.6940			0.146825
$680$	120.204	−	2141.99i	0.176771	−	3.14998i
$681$	−295.237	+	194.876i	−0.433535	+	0.286162i
$682$			4.01211i			0.00588286i
$683$	221.067			0.323671			0.161836	−	0.986818i	$-0.448259\pi$
$683$	221.067			0.323671			0.161836	+	0.986818i	$0.448259\pi$
$684$	718.648	−	1681.18i	1.05065	−	2.45787i
$685$	−23.3571	+	416.215i	−0.0340980	+	0.607613i
$686$			66.1433i			0.0964188i
$687$	1128.17	−	744.670i	1.64217	−	1.08394i
$688$		−	908.715i		−	1.32081i
$689$		−	399.912i		−	0.580423i
$690$	−166.754	−	286.334i	−0.241673	−	0.414977i
$691$	−431.071			−0.623837			−0.311918	−	0.950109i	$-0.600972\pi$
$691$	−431.071			−0.623837			−0.311918	+	0.950109i	$0.600972\pi$
$692$	−407.082			−0.588269
$693$	−26.7658	+	62.6149i	−0.0386230	+	0.0903534i
$694$	553.163			0.797065
$695$	−19.0042	+	338.648i	−0.0273442	+	0.487263i
$696$	288.817	+	437.557i	0.414967	+	0.628674i
$697$			1167.87i			1.67557i
$698$	21.5974			0.0309419
$699$	−372.861	+	246.113i	−0.533420	+	0.352093i
$700$	64.7898	−	575.447i	0.0925569	−	0.822067i
$701$			718.274i			1.02464i	0.858794	+	0.512321i	$0.171214\pi$
$701$			718.274i			1.02464i	−0.858794	+	0.512321i	$0.828786\pi$
$702$	−1921.78	+	348.636i	−2.73757	+	0.496632i
$703$			249.176i			0.354446i
$704$		−	52.0936i		−	0.0739966i
$705$	−418.028	−	717.798i	−0.592948	−	1.01815i
$706$	−1910.16			−2.70561
$707$	303.584			0.429398
$708$	−1030.21	−	1560.76i	−1.45509	−	2.20446i
$709$	1301.82			1.83614			0.918071	−	0.396416i	$-0.129746\pi$
$709$	1301.82			1.83614			0.918071	+	0.396416i	$0.129746\pi$
$710$	1792.40	+	100.586i	2.52451	+	0.141670i
$711$	144.081	−	337.058i	0.202645	−	0.474062i
$712$			1030.82i			1.44778i
$713$	−2.42977			−0.00340781
$714$	−394.563	−	597.762i	−0.552609	−	0.837202i
$715$	16.2274	−	289.166i	0.0226957	−	0.404428i
$716$		−	1056.80i		−	1.47598i
$717$	−472.792	−	716.279i	−0.659403	−	0.998995i
$718$		−	2503.35i		−	3.48655i
$719$			602.954i			0.838601i	0.907847	+	0.419301i	$0.137725\pi$
$719$			602.954i			0.838601i	−0.907847	+	0.419301i	$0.862275\pi$
$720$	1033.40	+	512.020i	1.43528	+	0.711139i
$721$	200.515			0.278107
$722$	−633.656			−0.877640
$723$	−661.361	+	436.542i	−0.914746	+	0.603793i
$724$	−760.368			−1.05023
$725$	−28.7852	+	255.663i	−0.0397037	+	0.352639i
$726$	−1008.84	+	665.902i	−1.38959	+	0.917221i
$727$			543.467i			0.747547i	0.927520	+	0.373773i	$0.121936\pi$
$727$			543.467i			0.747547i	−0.927520	+	0.373773i	$0.878064\pi$
$728$	910.042			1.25006
$729$	−682.545	+	256.073i	−0.936276	+	0.351266i
$730$	34.4446	+	1.93296i	0.0471843	+	0.00264789i
$731$		−	895.879i		−	1.22555i
$732$	−1292.80	+	853.336i	−1.76612	+	1.16576i
$733$			668.850i			0.912483i	0.889856	+	0.456241i	$0.150805\pi$
$733$			668.850i			0.912483i	−0.889856	+	0.456241i	$0.849195\pi$
$734$		−	819.798i		−	1.11689i
$735$	−52.8417	−	90.7346i	−0.0718934	−	0.123448i
$736$	−145.997			−0.198365
$737$	272.796			0.370144
$738$	−1366.10	−	583.963i	−1.85109	−	0.791278i
$739$	833.682			1.12812			0.564061	−	0.825733i	$-0.309238\pi$
$739$	833.682			1.12812			0.564061	+	0.825733i	$0.309238\pi$
$740$	−469.334	−	26.3380i	−0.634235	−	0.0355920i
$741$	776.736	+	1176.75i	1.04823	+	1.58806i
$742$			186.561i			0.251429i
$743$	378.505			0.509428			0.254714	−	0.967016i	$-0.418019\pi$
$743$	378.505			0.509428			0.254714	+	0.967016i	$0.418019\pi$
$744$	16.7023	−	11.0247i	0.0224494	−	0.0148181i
$745$	947.447	+	53.1688i	1.27174	+	0.0713675i
$746$		−	716.036i		−	0.959834i
$747$	186.419	−	436.102i	0.249556	−	0.583804i
$748$			632.600i			0.845723i
$749$			71.5141i			0.0954794i
$750$	540.279	+	1225.46i	0.720372	+	1.63395i
$751$	917.810			1.22212			0.611058	−	0.791586i	$-0.290744\pi$
$751$	917.810			1.22212			0.611058	+	0.791586i	$0.290744\pi$
$752$	−1419.24			−1.88728
$753$	202.139	+	306.241i	0.268445	+	0.406695i
$754$	−744.447			−0.987330
$755$	−4.97316	+	88.6198i	−0.00658697	+	0.117377i
$756$	615.365	−	111.635i	0.813975	−	0.147666i
$757$		−	785.695i		−	1.03791i	−0.854803	−	0.518953i	$-0.826322\pi$
$757$		−	785.695i		−	1.03791i	0.854803	−	0.518953i	$-0.173678\pi$
$758$	2245.44			2.96233
$759$	29.2326	+	44.2874i	0.0385146	+	0.0583496i
$760$	110.391	−	1967.12i	0.145251	−	2.58831i
$761$			871.596i			1.14533i	0.819789	+	0.572665i	$0.194090\pi$
$761$			871.596i			1.14533i	−0.819789	+	0.572665i	$0.805910\pi$
$762$	−435.821	−	660.269i	−0.571944	−	0.866494i
$763$		−	372.752i		−	0.488535i
$764$			194.957i			0.255180i
$765$	1018.81	+	504.788i	1.33177	+	0.659854i
$766$	−172.677			−0.225427
$767$	1442.20			1.88031
$768$	−1243.55	+	820.828i	−1.61921	+	1.06879i
$769$	853.562			1.10996			0.554982	−	0.831863i	$-0.312725\pi$
$769$	853.562			1.10996			0.554982	+	0.831863i	$0.312725\pi$
$770$	−7.57016	+	134.897i	−0.00983138	+	0.175191i
$771$	−297.130	+	196.125i	−0.385382	+	0.254378i
$772$		−	259.099i		−	0.335621i
$773$	−1395.30			−1.80505			−0.902526	−	0.430636i	$-0.858289\pi$
$773$	−1395.30			−1.80505			−0.902526	+	0.430636i	$0.858289\pi$
$774$	1047.95	+	447.962i	1.35394	+	0.578762i
$775$	9.75911	+	1.09878i	0.0125924	+	0.00141778i
$776$			639.883i			0.824592i
$777$	−71.1350	+	46.9538i	−0.0915508	+	0.0604296i
$778$			317.505i			0.408104i
$779$			1072.53i			1.37680i
$780$	−2298.57	+	1338.63i	−2.94689	+	1.71620i
$781$	−287.500			−0.368118
$782$	−558.146			−0.713742
$783$	−273.398	+	49.5981i	−0.349167	+	0.0633436i
$784$	−179.401			−0.228828
$785$	945.074	+	53.0356i	1.20392	+	0.0675613i
$786$	−407.962	−	618.061i	−0.519035	−	0.786338i
$787$			933.326i			1.18593i	0.805228	+	0.592965i	$0.202043\pi$
$787$			933.326i			1.18593i	−0.805228	+	0.592965i	$0.797957\pi$
$788$	−1000.53			−1.26971
$789$	438.827	−	289.655i	0.556181	−	0.367116i
$790$	40.7504	−	726.156i	0.0515828	−	0.919185i
$791$		−	355.802i		−	0.449813i
$792$	−401.892	−	171.795i	−0.507439	−	0.216913i
$793$		−	1194.60i		−	1.50643i
$794$		−	796.469i		−	1.00311i
$795$	−149.043	−	255.922i	−0.187475	−	0.321914i
$796$	3308.00			4.15578
$797$	−766.294			−0.961473			−0.480736	−	0.876865i	$-0.659631\pi$
$797$	−766.294			−0.961473			−0.480736	+	0.876865i	$0.659631\pi$
$798$	−362.351	−	548.961i	−0.454074	−	0.687921i
$799$	−1399.19			−1.75118
$800$	586.392	+	66.0222i	0.732990	+	0.0825277i
$801$	−502.344	−	214.735i	−0.627146	−	0.268084i
$802$		−	1600.92i		−	1.99617i
$803$	−5.52488			−0.00688030
$804$	−1380.19	−	2090.99i	−1.71666	−	2.60074i
$805$	−81.6952	−	4.58457i	−0.101485	−	0.00569511i
$806$			28.4168i			0.0352566i
$807$	−63.8503	−	96.7331i	−0.0791205	−	0.119867i
$808$			1948.55i			2.41157i
$809$			797.510i			0.985798i	0.870087	+	0.492899i	$0.164063\pi$
$809$			797.510i			0.985798i	−0.870087	+	0.492899i	$0.835937\pi$
$810$	−1099.90	+	939.333i	−1.35790	+	1.15967i
$811$	−290.228			−0.357864			−0.178932	−	0.983861i	$-0.557264\pi$
$811$	−290.228			−0.357864			−0.178932	+	0.983861i	$0.557264\pi$
$812$	238.377			0.293567
$813$	136.885	−	90.3535i	0.168371	−	0.111136i
$814$	109.676			0.134737
$815$	−1513.96	−	84.9602i	−1.85762	−	0.104246i
$816$	1621.32	−	1070.18i	1.98691	−	1.31149i
$817$		−	822.740i		−	1.00703i
$818$	1474.58			1.80266
$819$	−189.576	+	443.487i	−0.231472	+	0.541498i
$820$	−2020.15	−	113.367i	−2.46360	−	0.138252i
$821$		−	655.358i		−	0.798244i	−0.916898	−	0.399122i	$-0.869315\pi$
$821$		−	655.358i		−	0.798244i	0.916898	−	0.399122i	$-0.130685\pi$
$822$	−745.522	+	492.094i	−0.906961	+	0.598655i
$823$			371.417i			0.451297i	0.974209	+	0.225648i	$0.0724501\pi$
$823$			371.417i			0.451297i	−0.974209	+	0.225648i	$0.927550\pi$
$824$			1287.00i			1.56189i
$825$	−97.3844	−	191.098i	−0.118042	−	0.231634i
$826$	−672.792			−0.814518
$827$	192.502			0.232771			0.116386	−	0.993204i	$-0.462869\pi$
$827$	192.502			0.232771			0.116386	+	0.993204i	$0.462869\pi$
$828$	191.564	−	448.138i	0.231357	−	0.541229i
$829$	−1096.32			−1.32246			−0.661228	−	0.750185i	$-0.729965\pi$
$829$	−1096.32			−1.32246			−0.661228	+	0.750185i	$0.729965\pi$
$830$	52.7248	−	939.536i	0.0635239	−	1.13197i
$831$	196.850	+	298.227i	0.236883	+	0.358877i
$832$		−	368.967i		−	0.443470i
$833$	−176.867			−0.212326
$834$	−606.584	+	400.386i	−0.727319	+	0.480079i
$835$	−31.1409	+	554.919i	−0.0372945	+	0.664573i
$836$			580.955i			0.694923i
$837$	1.89325	+	10.4361i	0.00226194	+	0.0124684i
$838$			1774.75i			2.11784i
$839$			614.544i			0.732472i	0.930522	+	0.366236i	$0.119354\pi$
$839$			614.544i			0.732472i	−0.930522	+	0.366236i	$0.880646\pi$
$840$	582.377	−	339.163i	0.693306	−	0.403765i
$841$	735.093			0.874070
$842$	921.996			1.09501
$843$	470.364	+	712.601i	0.557964	+	0.845315i
$844$	2540.50			3.01007
$845$	67.5899	−	1204.43i	0.0799880	−	1.42536i
$846$	699.629	−	1636.69i	0.826985	−	1.93462i
$847$			298.498i			0.352418i
$848$	−506.011			−0.596711
$849$	−360.270	−	545.808i	−0.424346	−	0.642884i
$850$	2241.78	+	252.403i	2.63739	+	0.296945i
$851$			66.4206i			0.0780501i
$852$	1454.59	+	2203.70i	1.70726	+	2.58650i
$853$			1275.30i			1.49508i	0.664216	+	0.747541i	$0.268766\pi$
$853$			1275.30i			1.49508i	−0.664216	+	0.747541i	$0.731234\pi$
$854$			557.285i			0.652558i
$855$	935.632	+	463.577i	1.09431	+	0.542196i
$856$	−459.011			−0.536228
$857$	750.090			0.875251			0.437625	−	0.899157i	$-0.355820\pi$
$857$	750.090			0.875251			0.437625	+	0.899157i	$0.355820\pi$
$858$	517.953	−	341.883i	0.603675	−	0.398465i
$859$	690.198			0.803490			0.401745	−	0.915752i	$-0.368404\pi$
$859$	690.198			0.803490			0.401745	+	0.915752i	$0.368404\pi$
$860$	1549.67	+	86.9643i	1.80194	+	0.101121i
$861$	−306.186	+	202.103i	−0.355617	+	0.234731i
$862$			198.108i			0.229824i
$863$	−1331.83			−1.54326			−0.771628	−	0.636075i	$-0.780557\pi$
$863$	−1331.83			−1.54326			−0.771628	+	0.636075i	$0.780557\pi$
$864$	113.759	+	627.070i	0.131665	+	0.725775i
$865$	13.0263	−	232.123i	0.0150593	−	0.268350i
$866$		−	1357.12i		−	1.56712i
$867$	874.833	−	577.448i	1.00903	−	0.666030i
$868$		−	9.09926i		−	0.0104830i
$869$			116.475i			0.134033i
$870$	−476.405	+	277.447i	−0.547592	+	0.318905i
$871$	1932.15			2.21831
$872$	2392.50			2.74369
$873$	−311.832	−	133.297i	−0.357195	−	0.152689i
$874$	−512.580			−0.586476
$875$	326.053	+	55.3577i	0.372632	+	0.0632659i
$876$	27.9528	+	42.3484i	0.0319096	+	0.0483430i
$877$		−	400.529i		−	0.456704i	−0.973579	−	0.228352i	$-0.926666\pi$
$877$		−	400.529i		−	0.456704i	0.973579	−	0.228352i	$-0.0733337\pi$
$878$	1211.68			1.38005
$879$	−1190.34	+	785.704i	−1.35420	+	0.893862i
$880$	−365.884	−	20.5327i	−0.415777	−	0.0233326i
$881$		−	1039.59i		−	1.18001i	−0.807399	−	0.590006i	$-0.799125\pi$
$881$		−	1039.59i		−	1.18001i	0.807399	−	0.590006i	$-0.200875\pi$
$882$	88.4380	−	206.889i	0.100270	−	0.234568i
$883$		−	978.741i		−	1.10843i	−0.832375	−	0.554213i	$-0.813019\pi$
$883$		−	978.741i		−	1.10843i	0.832375	−	0.554213i	$-0.186981\pi$
$884$			4480.56i			5.06851i
$885$	922.928	−	537.492i	1.04286	−	0.607335i
$886$	271.604			0.306551
$887$	−1416.18			−1.59659			−0.798296	−	0.602265i	$-0.794265\pi$
$887$	−1416.18			−1.59659			−0.798296	+	0.602265i	$0.794265\pi$
$888$	−301.372	−	456.578i	−0.339383	−	0.514164i
$889$	−195.362			−0.219755
$890$	−1082.25	−	60.7336i	−1.21601	−	0.0682399i
$891$	167.441	−	160.065i	0.187924	−	0.179646i
$892$		−	2548.57i		−	2.85714i
$893$	−1284.96			−1.43893
$894$	1120.17	+	1697.06i	1.25299	+	1.89828i
$895$	602.602	+	33.8168i	0.673298	+	0.0377841i
$896$			421.925i			0.470898i
$897$	207.048	+	313.677i	0.230823	+	0.349696i
$898$			2308.81i			2.57106i
$899$			4.04267i			0.00449685i
$900$	−972.066	+	1713.30i	−1.08007	+	1.90367i
$901$	−498.863			−0.553677
$902$	472.076			0.523366
$903$	234.877	−	155.034i	0.260107	−	0.171688i
$904$	2283.70			2.52622
$905$	24.3311	−	433.570i	0.0268852	−	0.479083i
$906$	−158.735	+	104.776i	−0.175205	+	0.115647i
$907$		−	1289.84i		−	1.42210i	−0.703142	−	0.711050i	$-0.748220\pi$
$907$		−	1289.84i		−	1.42210i	0.703142	−	0.711050i	$-0.251780\pi$
$908$	−1032.36			−1.13696
$909$	−949.578	−	405.912i	−1.04464	−	0.446548i
$910$	−53.6177	+	955.447i	−0.0589206	+	1.04994i
$911$		−	73.9117i		−	0.0811325i	−0.999177	−	0.0405663i	$-0.987084\pi$
$911$		−	73.9117i		−	0.0811325i	0.999177	−	0.0405663i	$-0.0129162\pi$
$912$	1488.96	−	982.809i	1.63263	−	1.07764i
$913$			150.701i			0.165061i
$914$		−	1773.49i		−	1.94036i
$915$	−445.213	−	764.476i	−0.486572	−	0.835493i
$916$	3944.90			4.30666
$917$	−182.873			−0.199426
$918$	434.900	+	2397.29i	0.473747	+	2.61143i
$919$	−852.388			−0.927517			−0.463758	−	0.885962i	$-0.653499\pi$
$919$	−852.388			−0.927517			−0.463758	+	0.885962i	$0.653499\pi$
$920$	29.4259	−	524.358i	0.0319847	−	0.569954i
$921$	277.362	+	420.204i	0.301153	+	0.456247i
$922$			1112.26i			1.20635i
$923$	−2036.30			−2.20617
$924$	−165.852	+	109.473i	−0.179493	+	0.118478i
$925$	30.0365	−	266.776i	0.0324719	−	0.288407i
$926$			2004.86i			2.16507i
$927$	−627.188	−	268.102i	−0.676579	−	0.289215i
$928$			242.911i			0.261757i
$929$			848.480i			0.913326i	0.889640	+	0.456663i	$0.150956\pi$
$929$			848.480i			0.913326i	−0.889640	+	0.456663i	$0.849044\pi$
$930$	10.5906	+	18.1852i	0.0113878	+	0.0195540i
$931$	−162.428			−0.174466
$932$	−1303.79			−1.39891
$933$	−383.099	−	580.395i	−0.410610	−	0.622074i
$934$	−1924.26			−2.06024
$935$	−360.716	−	20.2426i	−0.385792	−	0.0216499i
$936$	−2846.51	−	1216.79i	−3.04114	−	1.29999i
$937$			1349.04i			1.43975i	0.694106	+	0.719873i	$0.255800\pi$
$937$			1349.04i			1.43975i	−0.694106	+	0.719873i	$0.744200\pi$
$938$	−901.358			−0.960936
$939$	−551.394	−	835.362i	−0.587214	−	0.889629i
$940$	135.821	−	2420.28i	0.144491	−	2.57477i
$941$		−	1436.19i		−	1.52624i	−0.646257	−	0.763120i	$-0.723667\pi$
$941$		−	1436.19i		−	1.52624i	0.646257	−	0.763120i	$-0.276333\pi$
$942$	1117.37	+	1692.81i	1.18616	+	1.79704i
$943$			285.894i			0.303175i
$944$		−	1824.82i		−	1.93308i
$945$	43.9646	+	354.460i	0.0465234	+	0.375090i
$946$	−362.132			−0.382804
$947$	647.132			0.683349			0.341675	−	0.939818i	$-0.389006\pi$
$947$	647.132			0.683349			0.341675	+	0.939818i	$0.389006\pi$
$948$	892.785	−	589.298i	0.941757	−	0.621622i
$949$	−39.1315			−0.0412344
$950$	2058.76	+	231.797i	2.16712	+	0.243997i
$951$	302.168	−	199.451i	0.317738	−	0.209728i
$952$		−	1135.22i		−	1.19246i
$953$	1806.71			1.89581			0.947906	−	0.318552i	$-0.103196\pi$
$953$	1806.71			1.89581			0.947906	+	0.318552i	$0.103196\pi$
$954$	249.444	−	583.541i	0.261472	−	0.611678i
$955$	−111.167	−	6.23846i	−0.116405	−	0.00653241i
$956$		−	2504.62i		−	2.61990i
$957$	73.6857	−	48.6374i	0.0769965	−	0.0508228i
$958$			175.869i			0.183579i
$959$			220.587i			0.230018i
$960$	−137.510	−	236.119i	−0.143240	−	0.245957i
$961$	−960.846			−0.999839
$962$	776.807			0.807492
$963$	95.6190	−	223.688i	0.0992929	−	0.232282i
$964$	−2312.59			−2.39895
$965$	147.741	+	8.29095i	0.153100	+	0.00859165i
$966$	−96.5888	−	146.332i	−0.0999884	−	0.151482i
$967$		−	1053.97i		−	1.08994i	−0.838455	−	0.544970i	$-0.816541\pi$
$967$		−	1053.97i		−	1.08994i	0.838455	−	0.544970i	$-0.183459\pi$
$968$	−1915.90			−1.97924
$969$	1467.92	−	968.927i	1.51488	−	0.999925i
$970$	−671.809	−	37.7006i	−0.692587	−	0.0388665i
$971$		−	1151.47i		−	1.18586i	−0.805255	−	0.592928i	$-0.797972\pi$
$971$		−	1151.47i		−	1.18586i	0.805255	−	0.592928i	$-0.202028\pi$
$972$	−2074.06	−	473.601i	−2.13380	−	0.487244i
$973$			179.478i			0.184458i
$974$			1287.32i			1.32169i
$975$	−689.752	−	1353.51i	−0.707437	−	1.38821i
$976$	−1511.53			−1.54870
$977$	−1419.64			−1.45306			−0.726530	−	0.687134i	$-0.758868\pi$
$977$	−1419.64			−1.45306			−0.726530	+	0.687134i	$0.758868\pi$
$978$	−1789.96	−	2711.79i	−1.83023	−	2.77279i
$979$	173.592			0.177316
$980$	17.1687	−	305.940i	0.0175191	−	0.312184i
$981$	−498.394	+	1165.93i	−0.508047	+	1.18851i
$982$			1017.83i			1.03648i
$983$	841.041			0.855586			0.427793	−	0.903877i	$-0.359291\pi$
$983$	841.041			0.855586			0.427793	+	0.903877i	$0.359291\pi$
$984$	−1297.19	−	1965.25i	−1.31829	−	1.99720i
$985$	32.0161	−	570.514i	0.0325037	−	0.579202i
$986$			928.648i			0.941834i
$987$	−242.134	−	366.832i	−0.245323	−	0.371664i
$988$			4114.77i			4.16475i
$989$		−	219.311i		−	0.221750i
$990$	204.045	−	411.822i	0.206106	−	0.415982i
$991$	−684.530			−0.690747			−0.345373	−	0.938465i	$-0.612248\pi$
$991$	−684.530			−0.690747			−0.345373	+	0.938465i	$0.612248\pi$
$992$	9.27233			0.00934711
$993$	−955.867	+	630.936i	−0.962605	+	0.635383i
$994$	949.942			0.955676
$995$	−105.853	+	1886.26i	−0.106385	+	1.89574i
$996$	1155.13	−	762.461i	1.15977	−	0.765524i
$997$		−	1023.09i		−	1.02617i	−0.858337	−	0.513086i	$-0.828502\pi$
$997$		−	1023.09i		−	1.02617i	0.858337	−	0.513086i	$-0.171498\pi$
$998$	1710.15			1.71358
$999$	285.283	−	51.7541i	0.285568	−	0.0518059i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	105.3.f.a.29.1	✓	24
3.2	odd	2	inner	105.3.f.a.29.23	yes	24
5.2	odd	4		525.3.c.e.176.1		24
5.3	odd	4		525.3.c.e.176.24		24
5.4	even	2	inner	105.3.f.a.29.24	yes	24
15.2	even	4		525.3.c.e.176.23		24
15.8	even	4		525.3.c.e.176.2		24
15.14	odd	2	inner	105.3.f.a.29.2	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.3.f.a.29.1	✓	24	1.1	even	1	trivial
105.3.f.a.29.2	yes	24	15.14	odd	2	inner
105.3.f.a.29.23	yes	24	3.2	odd	2	inner
105.3.f.a.29.24	yes	24	5.4	even	2	inner
525.3.c.e.176.1		24	5.2	odd	4
525.3.c.e.176.2		24	15.8	even	4
525.3.c.e.176.23		24	15.2	even	4
525.3.c.e.176.24		24	5.3	odd	4

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.f (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-3.57140 q^{2} +(2.50375 - 1.65264i) q^{3} +8.75491 q^{4} +(-0.280149 + 4.99215i) q^{5} +(-8.94190 + 5.90225i) q^{6} +2.64575i q^{7} -16.9817 q^{8} +(3.53755 - 8.27561i) q^{9} +O(q^{10})\)	\(q-3.57140 q^{2} +(2.50375 - 1.65264i) q^{3} +8.75491 q^{4} +(-0.280149 + 4.99215i) q^{5} +(-8.94190 + 5.90225i) q^{6} +2.64575i q^{7} -16.9817 q^{8} +(3.53755 - 8.27561i) q^{9} +(1.00052 - 17.8290i) q^{10} +2.85975i q^{11} +(21.9201 - 14.4687i) q^{12} +20.2550i q^{13} -9.44904i q^{14} +(7.54881 + 12.9621i) q^{15} +25.6288 q^{16} +25.2668 q^{17} +(-12.6340 + 29.5555i) q^{18} +23.2040 q^{19} +(-2.45268 + 43.7058i) q^{20} +(4.37248 + 6.62430i) q^{21} -10.2133i q^{22} +6.18529 q^{23} +(-42.5179 + 28.0646i) q^{24} +(-24.8430 - 2.79709i) q^{25} -72.3386i q^{26} +(-4.81949 - 26.5664i) q^{27} +23.1633i q^{28} -10.2911i q^{29} +(-26.9598 - 46.2928i) q^{30} -0.392831 q^{31} -23.6039 q^{32} +(4.72615 + 7.16011i) q^{33} -90.2377 q^{34} +(-13.2080 - 0.741205i) q^{35} +(30.9709 - 72.4522i) q^{36} +10.7385i q^{37} -82.8708 q^{38} +(33.4742 + 50.7134i) q^{39} +(4.75740 - 84.7750i) q^{40} +46.2216i q^{41} +(-15.6159 - 23.6580i) q^{42} -35.4569i q^{43} +25.0369i q^{44} +(40.3220 + 19.9783i) q^{45} -22.0902 q^{46} -55.3767 q^{47} +(64.1681 - 42.3552i) q^{48} -7.00000 q^{49} +(88.7244 + 9.98953i) q^{50} +(63.2617 - 41.7569i) q^{51} +177.330i q^{52} -19.7439 q^{53} +(17.2123 + 94.8792i) q^{54} +(-14.2763 - 0.801157i) q^{55} -44.9293i q^{56} +(58.0970 - 38.3479i) q^{57} +36.7538i q^{58} -71.2022i q^{59} +(66.0891 + 113.482i) q^{60} -58.9779 q^{61} +1.40296 q^{62} +(21.8952 + 9.35947i) q^{63} -18.2161 q^{64} +(-101.116 - 5.67441i) q^{65} +(-16.8790 - 25.5716i) q^{66} -95.3915i q^{67} +221.208 q^{68} +(15.4864 - 10.2221i) q^{69} +(47.1710 + 2.64714i) q^{70} +100.533i q^{71} +(-60.0735 + 140.534i) q^{72} +1.93194i q^{73} -38.3514i q^{74} +(-66.8234 + 34.0534i) q^{75} +203.149 q^{76} -7.56620 q^{77} +(-119.550 - 181.118i) q^{78} +40.7290 q^{79} +(-7.17987 + 127.943i) q^{80} +(-55.9715 - 58.5507i) q^{81} -165.076i q^{82} +52.6972 q^{83} +(38.2807 + 57.9952i) q^{84} +(-7.07846 + 126.135i) q^{85} +126.631i q^{86} +(-17.0076 - 25.7664i) q^{87} -48.5634i q^{88} -60.7017i q^{89} +(-144.006 - 71.3507i) q^{90} -53.5896 q^{91} +54.1516 q^{92} +(-0.983551 + 0.649209i) q^{93} +197.773 q^{94} +(-6.50057 + 115.838i) q^{95} +(-59.0983 + 39.0088i) q^{96} -37.6808i q^{97} +24.9998 q^{98} +(23.6662 + 10.1165i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 52 q^{4} - 22 q^{9}+O(q^{10}) \) 24 * q + 52 * q^4 - 22 * q^9	\( 24 q + 52 q^{4} - 22 q^{9} - 24 q^{10} + 26 q^{15} + 4 q^{16} + 72 q^{19} + 14 q^{21} - 156 q^{24} - 64 q^{25} - 32 q^{30} - 40 q^{31} - 144 q^{34} + 36 q^{36} + 62 q^{39} - 40 q^{40} + 120 q^{45} - 104 q^{46} - 168 q^{49} + 70 q^{51} + 60 q^{54} - 16 q^{55} - 348 q^{60} + 432 q^{61} - 364 q^{64} + 284 q^{66} + 404 q^{69} + 140 q^{70} + 204 q^{75} + 152 q^{76} + 108 q^{79} - 158 q^{81} + 112 q^{84} + 196 q^{85} - 152 q^{90} - 84 q^{91} + 808 q^{94} - 516 q^{96} + 582 q^{99}+O(q^{100}) \) 24 * q + 52 * q^4 - 22 * q^9 - 24 * q^10 + 26 * q^15 + 4 * q^16 + 72 * q^19 + 14 * q^21 - 156 * q^24 - 64 * q^25 - 32 * q^30 - 40 * q^31 - 144 * q^34 + 36 * q^36 + 62 * q^39 - 40 * q^40 + 120 * q^45 - 104 * q^46 - 168 * q^49 + 70 * q^51 + 60 * q^54 - 16 * q^55 - 348 * q^60 + 432 * q^61 - 364 * q^64 + 284 * q^66 + 404 * q^69 + 140 * q^70 + 204 * q^75 + 152 * q^76 + 108 * q^79 - 158 * q^81 + 112 * q^84 + 196 * q^85 - 152 * q^90 - 84 * q^91 + 808 * q^94 - 516 * q^96 + 582 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more