LMFDB - Embedded newform 115.4.b.a.24.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [115,4,Mod(24,115)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(115, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("115.24");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 115 = 5 \cdot 23 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	115.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:	$6.78521965066$
Analytic rank:	$0$
Dimension:	$34$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			24.6
Character	$\chi$	$=$	115.24
Dual form			115.4.b.a.24.29

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-4.24824i q^{2} -2.36809i q^{3} -10.0475 q^{4} +(4.85714 - 10.0702i) q^{5} -10.0602 q^{6} -12.8082i q^{7} +8.69841i q^{8} +21.3922 q^{9} +O(q^{10})$	\(q-4.24824i q^{2} -2.36809i q^{3} -10.0475 q^{4} +(4.85714 - 10.0702i) q^{5} -10.0602 q^{6} -12.8082i q^{7} +8.69841i q^{8} +21.3922 q^{9} +(-42.7805 - 20.6343i) q^{10} -45.1591 q^{11} +23.7934i q^{12} +33.1884i q^{13} -54.4124 q^{14} +(-23.8470 - 11.5021i) q^{15} -43.4273 q^{16} +61.8985i q^{17} -90.8790i q^{18} +144.687 q^{19} +(-48.8023 + 101.180i) q^{20} -30.3310 q^{21} +191.847i q^{22} -23.0000i q^{23} +20.5986 q^{24} +(-77.8163 - 97.8244i) q^{25} +140.992 q^{26} -114.597i q^{27} +128.691i q^{28} -145.728 q^{29} +(-48.8638 + 101.308i) q^{30} +248.907 q^{31} +254.077i q^{32} +106.941i q^{33} +262.959 q^{34} +(-128.981 - 62.2114i) q^{35} -214.938 q^{36} +71.9007i q^{37} -614.665i q^{38} +78.5931 q^{39} +(87.5944 + 42.2494i) q^{40} -330.885 q^{41} +128.853i q^{42} -356.469i q^{43} +453.738 q^{44} +(103.905 - 215.423i) q^{45} -97.7095 q^{46} -338.079i q^{47} +102.840i q^{48} +178.949 q^{49} +(-415.582 + 330.582i) q^{50} +146.581 q^{51} -333.462i q^{52} -464.834i q^{53} -486.835 q^{54} +(-219.344 + 454.760i) q^{55} +111.411 q^{56} -342.631i q^{57} +619.089i q^{58} +645.086 q^{59} +(239.604 + 115.568i) q^{60} +303.402 q^{61} -1057.42i q^{62} -273.996i q^{63} +731.961 q^{64} +(334.213 + 161.201i) q^{65} +454.310 q^{66} +365.094i q^{67} -621.927i q^{68} -54.4660 q^{69} +(-264.289 + 547.942i) q^{70} +6.02613 q^{71} +186.078i q^{72} -319.555i q^{73} +305.451 q^{74} +(-231.657 + 184.276i) q^{75} -1453.75 q^{76} +578.408i q^{77} -333.882i q^{78} -2.86632 q^{79} +(-210.933 + 437.320i) q^{80} +306.213 q^{81} +1405.68i q^{82} +1347.84i q^{83} +304.752 q^{84} +(623.328 + 300.650i) q^{85} -1514.37 q^{86} +345.098i q^{87} -392.813i q^{88} -607.901 q^{89} +(-915.166 - 441.412i) q^{90} +425.085 q^{91} +231.093i q^{92} -589.433i q^{93} -1436.24 q^{94} +(702.765 - 1457.02i) q^{95} +601.677 q^{96} +1096.78i q^{97} -760.220i q^{98} -966.051 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 34 q - 144 q^{4} + 14 q^{5} + 24 q^{6} - 310 q^{9}+O(q^{10}) $ 34 * q - 144 * q^4 + 14 * q^5 + 24 * q^6 - 310 * q^9	$ 34 q - 144 q^{4} + 14 q^{5} + 24 q^{6} - 310 q^{9} + 14 q^{10} - 8 q^{11} + 236 q^{14} + 440 q^{16} + 144 q^{19} - 180 q^{20} - 32 q^{21} + 108 q^{24} + 134 q^{25} - 144 q^{26} + 56 q^{29} - 294 q^{30} - 80 q^{31} + 264 q^{34} + 116 q^{35} + 1864 q^{36} - 1200 q^{39} + 650 q^{40} + 268 q^{41} - 1612 q^{44} - 1346 q^{45} + 184 q^{46} - 1474 q^{49} + 120 q^{50} - 1104 q^{51} + 1564 q^{54} + 1160 q^{55} - 2300 q^{56} - 708 q^{59} - 516 q^{60} + 1100 q^{61} + 100 q^{64} + 1164 q^{65} - 1416 q^{66} - 552 q^{69} + 1144 q^{70} + 1360 q^{71} + 1588 q^{74} - 2064 q^{75} + 108 q^{76} + 3968 q^{79} + 2542 q^{80} + 4914 q^{81} - 1948 q^{84} + 124 q^{85} - 6148 q^{86} + 1196 q^{89} + 2760 q^{90} - 544 q^{91} - 2340 q^{94} + 3920 q^{95} + 2960 q^{96} - 3816 q^{99}+O(q^{100}) $ 34 * q - 144 * q^4 + 14 * q^5 + 24 * q^6 - 310 * q^9 + 14 * q^10 - 8 * q^11 + 236 * q^14 + 440 * q^16 + 144 * q^19 - 180 * q^20 - 32 * q^21 + 108 * q^24 + 134 * q^25 - 144 * q^26 + 56 * q^29 - 294 * q^30 - 80 * q^31 + 264 * q^34 + 116 * q^35 + 1864 * q^36 - 1200 * q^39 + 650 * q^40 + 268 * q^41 - 1612 * q^44 - 1346 * q^45 + 184 * q^46 - 1474 * q^49 + 120 * q^50 - 1104 * q^51 + 1564 * q^54 + 1160 * q^55 - 2300 * q^56 - 708 * q^59 - 516 * q^60 + 1100 * q^61 + 100 * q^64 + 1164 * q^65 - 1416 * q^66 - 552 * q^69 + 1144 * q^70 + 1360 * q^71 + 1588 * q^74 - 2064 * q^75 + 108 * q^76 + 3968 * q^79 + 2542 * q^80 + 4914 * q^81 - 1948 * q^84 + 124 * q^85 - 6148 * q^86 + 1196 * q^89 + 2760 * q^90 - 544 * q^91 - 2340 * q^94 + 3920 * q^95 + 2960 * q^96 - 3816 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/115\mathbb{Z}\right)^\times$.

$n$	$47$	$51$
$\chi(n)$	$-1$	$1$

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 $

$2$		−	4.24824i		−	1.50198i	−0.660314	−	0.750990i	$-0.729577\pi$
$2$		−	4.24824i		−	1.50198i	0.660314	−	0.750990i	$-0.270423\pi$
$3$		−	2.36809i		−	0.455739i	−0.973692	−	0.227869i	$-0.926824\pi$
$3$		−	2.36809i		−	0.455739i	0.973692	−	0.227869i	$-0.0731759\pi$
$4$	−10.0475			−1.25594
$5$	4.85714	−	10.0702i	0.434436	−	0.900703i
$5$	4.85714	−	10.0702i	0.434436	−	0.900703i
$6$	−10.0602			−0.684510
$7$		−	12.8082i		−	0.691579i	−0.938312	−	0.345790i	$-0.887611\pi$
$7$		−	12.8082i		−	0.691579i	0.938312	−	0.345790i	$-0.112389\pi$
$8$			8.69841i			0.384419i
$9$	21.3922			0.792302
$10$	−42.7805	−	20.6343i	−1.35284	−	0.652514i
$11$	−45.1591			−1.23782			−0.618908	−	0.785463i	$-0.712425\pi$
$11$	−45.1591			−1.23782			−0.618908	+	0.785463i	$0.712425\pi$
$12$			23.7934i			0.572381i
$13$			33.1884i			0.708062i	0.935234	+	0.354031i	$0.115189\pi$
$13$			33.1884i			0.708062i	−0.935234	+	0.354031i	$0.884811\pi$
$14$	−54.4124			−1.03874
$15$	−23.8470	−	11.5021i	−0.410485	−	0.197989i
$16$	−43.4273			−0.678552
$17$			61.8985i			0.883093i	0.897238	+	0.441547i	$0.145570\pi$
$17$			61.8985i			0.883093i	−0.897238	+	0.441547i	$0.854430\pi$
$18$		−	90.8790i		−	1.19002i
$19$	144.687			1.74702			0.873512	−	0.486802i	$-0.161837\pi$
$19$	144.687			1.74702			0.873512	+	0.486802i	$0.161837\pi$
$20$	−48.8023	+	101.180i	−0.545626	+	1.13123i
$21$	−30.3310			−0.315179
$22$			191.847i			1.85918i
$23$		−	23.0000i		−	0.208514i
$23$		−	23.0000i		−	0.208514i
$24$	20.5986			0.175195
$25$	−77.8163	−	97.8244i	−0.622531	−	0.782595i
$26$	140.992			1.06349
$27$		−	114.597i		−	0.816822i
$28$			128.691i			0.868583i
$29$	−145.728			−0.933141			−0.466571	−	0.884484i	$-0.654511\pi$
$29$	−145.728			−0.933141			−0.466571	+	0.884484i	$0.654511\pi$
$30$	−48.8638	+	101.308i	−0.297376	+	0.616540i
$31$	248.907			1.44210			0.721048	−	0.692885i	$-0.243661\pi$
$31$	248.907			1.44210			0.721048	+	0.692885i	$0.243661\pi$
$32$			254.077i			1.40359i
$33$			106.941i			0.564121i
$34$	262.959			1.32639
$35$	−128.981	−	62.2114i	−0.622907	−	0.300447i
$36$	−214.938			−0.995085
$37$			71.9007i			0.319470i	0.987160	+	0.159735i	$0.0510640\pi$
$37$			71.9007i			0.319470i	−0.987160	+	0.159735i	$0.948936\pi$
$38$		−	614.665i		−	2.62399i
$39$	78.5931			0.322691
$40$	87.5944	+	42.2494i	0.346247	+	0.167006i
$41$	−330.885			−1.26038			−0.630190	−	0.776441i	$-0.717023\pi$
$41$	−330.885			−1.26038			−0.630190	+	0.776441i	$0.717023\pi$
$42$			128.853i			0.473393i
$43$		−	356.469i		−	1.26421i	−0.774882	−	0.632106i	$-0.782191\pi$
$43$		−	356.469i		−	1.26421i	0.774882	−	0.632106i	$-0.217809\pi$
$44$	453.738			1.55463
$45$	103.905	−	215.423i	0.344205	−	0.713629i
$46$	−97.7095			−0.313184
$47$		−	338.079i		−	1.04923i	−0.851339	−	0.524615i	$-0.824209\pi$
$47$		−	338.079i		−	1.04923i	0.851339	−	0.524615i	$-0.175791\pi$
$48$			102.840i			0.309242i
$49$	178.949			0.521718
$50$	−415.582	+	330.582i	−1.17544	+	0.935028i
$51$	146.581			0.402460
$52$		−	333.462i		−	0.889285i
$53$		−	464.834i		−	1.20471i	−0.798227	−	0.602357i	$-0.794228\pi$
$53$		−	464.834i		−	1.20471i	0.798227	−	0.602357i	$-0.205772\pi$
$54$	−486.835			−1.22685
$55$	−219.344	+	454.760i	−0.537752	+	1.11490i
$56$	111.411			0.265856
$57$		−	342.631i		−	0.796187i
$58$			619.089i			1.40156i
$59$	645.086			1.42344			0.711721	−	0.702462i	$-0.247916\pi$
$59$	645.086			1.42344			0.711721	+	0.702462i	$0.247916\pi$
$60$	239.604	+	115.568i	0.515545	+	0.248663i
$61$	303.402			0.636830			0.318415	−	0.947951i	$-0.396849\pi$
$61$	303.402			0.636830			0.318415	+	0.947951i	$0.396849\pi$
$62$		−	1057.42i		−	2.16600i
$63$		−	273.996i		−	0.547940i
$64$	731.961			1.42961
$65$	334.213	+	161.201i	0.637753	+	0.307608i
$66$	454.310			0.847298
$67$			365.094i			0.665722i	0.942976	+	0.332861i	$0.108014\pi$
$67$			365.094i			0.665722i	−0.942976	+	0.332861i	$0.891986\pi$
$68$		−	621.927i		−	1.10911i
$69$	−54.4660			−0.0950281
$70$	−264.289	+	547.942i	−0.451265	+	0.935594i
$71$	6.02613			0.0100728			0.00503641	−	0.999987i	$-0.498397\pi$
$71$	6.02613			0.0100728			0.00503641	+	0.999987i	$0.498397\pi$
$72$			186.078i			0.304576i
$73$		−	319.555i		−	0.512344i	−0.966631	−	0.256172i	$-0.917539\pi$
$73$		−	319.555i		−	0.512344i	0.966631	−	0.256172i	$-0.0824613\pi$
$74$	305.451			0.479838
$75$	−231.657	+	184.276i	−0.356659	+	0.283711i
$76$	−1453.75			−2.19416
$77$			578.408i			0.856048i
$78$		−	333.882i		−	0.484676i
$79$	−2.86632			−0.00408211			−0.00204106	−	0.999998i	$-0.500650\pi$
$79$	−2.86632			−0.00408211			−0.00204106	+	0.999998i	$0.500650\pi$
$80$	−210.933	+	437.320i	−0.294787	+	0.611174i
$81$	306.213			0.420045
$82$			1405.68i			1.89306i
$83$			1347.84i			1.78247i	0.453542	+	0.891235i	$0.350160\pi$
$83$			1347.84i			1.78247i	−0.453542	+	0.891235i	$0.649840\pi$
$84$	304.752			0.395847
$85$	623.328	+	300.650i	0.795404	+	0.383647i
$86$	−1514.37			−1.89882
$87$			345.098i			0.425269i
$88$		−	392.813i		−	0.475841i
$89$	−607.901			−0.724016			−0.362008	−	0.932175i	$-0.617909\pi$
$89$	−607.901			−0.724016			−0.362008	+	0.932175i	$0.617909\pi$
$90$	−915.166	−	441.412i	−1.07186	−	0.516988i
$91$	425.085			0.489681
$92$			231.093i			0.261882i
$93$		−	589.433i		−	0.657219i
$94$	−1436.24			−1.57592
$95$	702.765	−	1457.02i	0.758970	−	1.57355i
$96$	601.677			0.639671
$97$			1096.78i			1.14805i	0.818837	+	0.574027i	$0.194619\pi$
$97$			1096.78i			1.14805i	−0.818837	+	0.574027i	$0.805381\pi$
$98$		−	760.220i		−	0.783610i
$99$	−966.051			−0.980725
$100$	781.862	+	982.894i	0.781862	+	0.982894i
$101$	1015.77			1.00072			0.500362	−	0.865816i	$-0.333200\pi$
$101$	1015.77			1.00072			0.500362	+	0.865816i	$0.333200\pi$
$102$		−	622.711i		−	0.604486i
$103$		−	500.163i		−	0.478471i	−0.970962	−	0.239236i	$-0.923103\pi$
$103$		−	500.163i		−	0.478471i	0.970962	−	0.239236i	$-0.0768968\pi$
$104$	−288.687			−0.272193
$105$	−147.322	+	305.438i	−0.136925	+	0.283883i
$106$	−1974.73			−1.80946
$107$		−	1242.95i		−	1.12300i	−0.827477	−	0.561499i	$-0.810225\pi$
$107$		−	1242.95i		−	1.12300i	0.827477	−	0.561499i	$-0.189775\pi$
$108$			1151.42i			1.02588i
$109$	−342.605			−0.301060			−0.150530	−	0.988605i	$-0.548098\pi$
$109$	−342.605			−0.301060			−0.150530	+	0.988605i	$0.548098\pi$
$110$	1931.93	+	931.827i	1.67456	+	0.807693i
$111$	170.267			0.145595
$112$			556.227i			0.469272i
$113$			505.551i			0.420870i	0.977608	+	0.210435i	$0.0674880\pi$
$113$			505.551i			0.420870i	−0.977608	+	0.210435i	$0.932512\pi$
$114$	−1455.58			−1.19586
$115$	−231.614	−	111.714i	−0.187809	−	0.0905862i
$116$	1464.21			1.17197
$117$			709.972i			0.560999i
$118$		−	2740.48i		−	2.13798i
$119$	792.810			0.610729
$120$	100.050	−	207.431i	0.0761109	−	0.157798i
$121$	708.345			0.532190
$122$		−	1288.92i		−	0.956506i
$123$			783.565i			0.574404i
$124$	−2500.90			−1.81119
$125$	−1363.07	+	308.476i	−0.975336	+	0.220727i
$126$	−1164.00			−0.822994
$127$			1996.83i			1.39520i	0.716487	+	0.697600i	$0.245749\pi$
$127$			1996.83i			1.39520i	−0.716487	+	0.697600i	$0.754251\pi$
$128$		−	1076.93i		−	0.743657i
$129$	−844.151			−0.576150
$130$	684.820	−	1419.82i	0.462020	−	0.957892i
$131$	2979.17			1.98695			0.993477	−	0.114032i	$-0.0363768\pi$
$131$	2979.17			1.98695			0.993477	+	0.114032i	$0.0363768\pi$
$132$		−	1074.49i		−	0.708503i
$133$		−	1853.18i		−	1.20821i
$134$	1551.01			0.999900
$135$	−1154.01	−	556.613i	−0.735713	−	0.354857i
$136$	−538.419			−0.339478
$137$			582.122i			0.363022i	0.983389	+	0.181511i	$0.0580989\pi$
$137$			582.122i			0.363022i	−0.983389	+	0.181511i	$0.941901\pi$
$138$			231.385i			0.142730i
$139$	−1187.01			−0.724320			−0.362160	−	0.932116i	$-0.617961\pi$
$139$	−1187.01			−0.724320			−0.362160	+	0.932116i	$0.617961\pi$
$140$	1295.94	+	625.071i	0.782335	+	0.377344i
$141$	−800.600			−0.478175
$142$		−	25.6004i		−	0.0151292i
$143$		−	1498.76i		−	0.876451i
$144$	−929.004			−0.537618
$145$	−707.824	+	1467.51i	−0.405390	+	0.840483i
$146$	−1357.55			−0.769529
$147$		−	423.768i		−	0.237767i
$148$		−	722.425i		−	0.401236i
$149$	−2630.96			−1.44656			−0.723278	−	0.690557i	$-0.757365\pi$
$149$	−2630.96			−1.44656			−0.723278	+	0.690557i	$0.757365\pi$
$150$	782.848	+	984.134i	0.426129	+	0.535695i
$151$	500.082			0.269511			0.134755	−	0.990879i	$-0.456975\pi$
$151$	500.082			0.269511			0.134755	+	0.990879i	$0.456975\pi$
$152$			1258.55i			0.671590i
$153$			1324.14i			0.699677i
$154$	2457.22			1.28577
$155$	1208.98	−	2506.53i	0.626499	−	1.29890i
$156$	−789.667			−0.405282
$157$			1466.98i			0.745718i	0.927888	+	0.372859i	$0.121623\pi$
$157$			1466.98i			0.745718i	−0.927888	+	0.372859i	$0.878377\pi$
$158$			12.1768i			0.00613125i
$159$	−1100.77			−0.549035
$160$	2558.60	+	1234.09i	1.26422	+	0.609770i
$161$	−294.589			−0.144204
$162$		−	1300.86i		−	0.630899i
$163$			78.0556i			0.0375079i	0.999824	+	0.0187539i	$0.00596992\pi$
$163$			78.0556i			0.0375079i	−0.999824	+	0.0187539i	$0.994030\pi$
$164$	3324.58			1.58296
$165$	1076.91	+	519.426i	0.508105	+	0.245075i
$166$	5725.96			2.67723
$167$			1813.92i			0.840510i	0.907406	+	0.420255i	$0.138059\pi$
$167$			1813.92i			0.840510i	−0.907406	+	0.420255i	$0.861941\pi$
$168$		−	263.832i		−	0.121161i
$169$	1095.53			0.498648
$170$	1277.23	−	2648.04i	0.576231	−	1.19468i
$171$	3095.17			1.38417
$172$			3581.64i			1.58778i
$173$		−	196.072i		−	0.0861680i	−0.999071	−	0.0430840i	$-0.986282\pi$
$173$		−	196.072i		−	0.0861680i	0.999071	−	0.0430840i	$-0.0137183\pi$
$174$	1466.06			0.638745
$175$	−1252.96	+	996.689i	−0.541227	+	0.430529i
$176$	1961.14			0.839923
$177$		−	1527.62i		−	0.648718i
$178$			2582.51i			1.08746i
$179$	2504.16			1.04564			0.522820	−	0.852443i	$-0.324880\pi$
$179$	2504.16			1.04564			0.522820	+	0.852443i	$0.324880\pi$
$180$	−1043.99	+	2164.47i	−0.432301	+	0.896276i
$181$	−87.4521			−0.0359131			−0.0179565	−	0.999839i	$-0.505716\pi$
$181$	−87.4521			−0.0359131			−0.0179565	+	0.999839i	$0.505716\pi$
$182$		−	1805.86i		−	0.735491i
$183$		−	718.482i		−	0.290228i
$184$	200.064			0.0801570
$185$	724.052	+	349.232i	0.287748	+	0.138789i
$186$	−2504.05			−0.987130
$187$		−	2795.28i		−	1.09311i
$188$			3396.86i			1.31777i
$189$	−1467.78			−0.564897
$190$	−6189.77	−	2985.51i	−2.36344	−	1.13996i
$191$	−1559.01			−0.590606			−0.295303	−	0.955404i	$-0.595421\pi$
$191$	−1559.01			−0.590606			−0.295303	+	0.955404i	$0.595421\pi$
$192$		−	1733.35i		−	0.651529i
$193$			1249.77i			0.466117i	0.972463	+	0.233059i	$0.0748734\pi$
$193$			1249.77i			0.466117i	−0.972463	+	0.233059i	$0.925127\pi$
$194$	4659.38			1.72435
$195$	381.738	−	791.445i	0.140189	−	0.290649i
$196$	−1798.00			−0.655248
$197$		−	4555.31i		−	1.64748i	−0.566971	−	0.823738i	$-0.691885\pi$
$197$		−	4555.31i		−	1.64748i	0.566971	−	0.823738i	$-0.308115\pi$
$198$			4104.01i			1.47303i
$199$	−1115.18			−0.397252			−0.198626	−	0.980075i	$-0.563648\pi$
$199$	−1115.18			−0.397252			−0.198626	+	0.980075i	$0.563648\pi$
$200$	850.917	−	676.879i	0.300845	−	0.239313i
$201$	864.575			0.303395
$202$		−	4315.25i		−	1.50307i
$203$			1866.52i			0.645341i
$204$	−1472.78			−0.505466
$205$	−1607.16	+	3332.07i	−0.547554	+	1.13523i
$206$	−2124.81			−0.718654
$207$		−	492.020i		−	0.165206i
$208$		−	1441.28i		−	0.480457i
$209$	−6533.93			−2.16250
$210$	1297.57	+	625.859i	0.426386	+	0.205659i
$211$	−160.283			−0.0522954			−0.0261477	−	0.999658i	$-0.508324\pi$
$211$	−160.283			−0.0522954			−0.0261477	+	0.999658i	$0.508324\pi$
$212$			4670.43i			1.51305i
$213$		−	14.2704i		−	0.00459057i
$214$	−5280.36			−1.68672
$215$	−3589.71	−	1731.42i	−1.13868	−	0.549219i
$216$	996.811			0.314002
$217$		−	3188.06i		−	0.997324i
$218$			1455.47i			0.452186i
$219$	−756.734			−0.233495
$220$	2203.87	−	4569.21i	0.675385	−	1.40026i
$221$	−2054.31			−0.625285
$222$		−	723.336i		−	0.218681i
$223$		−	2162.12i		−	0.649265i	−0.945840	−	0.324633i	$-0.894759\pi$
$223$		−	2162.12i		−	0.649265i	0.945840	−	0.324633i	$-0.105241\pi$
$224$	3254.28			0.970694
$225$	−1664.66	−	2092.68i	−0.493232	−	0.620052i
$226$	2147.70			0.632137
$227$		−	533.687i		−	0.156044i	−0.996952	−	0.0780222i	$-0.975140\pi$
$227$		−	533.687i		−	0.156044i	0.996952	−	0.0780222i	$-0.0248605\pi$
$228$			3442.60i			0.999964i
$229$	3970.00			1.14561			0.572806	−	0.819691i	$-0.305855\pi$
$229$	3970.00			1.14561			0.572806	+	0.819691i	$0.305855\pi$
$230$	−474.589	+	983.950i	−0.136059	+	0.282086i
$231$	1369.72			0.390134
$232$		−	1267.61i		−	0.358717i
$233$			5566.69i			1.56517i	0.622541	+	0.782587i	$0.286100\pi$
$233$			5566.69i			1.56517i	−0.622541	+	0.782587i	$0.713900\pi$
$234$	3016.13			0.842609
$235$	−3404.51	−	1642.10i	−0.945045	−	0.455824i
$236$	−6481.53			−1.78776
$237$			6.78771i			0.00186038i
$238$		−	3368.04i		−	0.917302i
$239$	1140.12			0.308569			0.154284	−	0.988026i	$-0.450693\pi$
$239$	1140.12			0.308569			0.154284	+	0.988026i	$0.450693\pi$
$240$	1035.61	+	499.507i	0.278536	+	0.134346i
$241$	−3893.07			−1.04056			−0.520279	−	0.853996i	$-0.674172\pi$
$241$	−3893.07			−1.04056			−0.520279	+	0.853996i	$0.674172\pi$
$242$		−	3009.22i		−	0.799339i
$243$		−	3819.25i		−	1.00825i
$244$	−3048.44			−0.799822
$245$	869.182	−	1802.05i	0.226653	−	0.469913i
$246$	3328.77			0.862743
$247$			4801.93i			1.23700i
$248$			2165.09i			0.554370i
$249$	3191.81			0.812341
$250$	1310.48	+	5790.66i	0.331528	+	1.46493i
$251$	−7041.05			−1.77063			−0.885313	−	0.464996i	$-0.846056\pi$
$251$	−7041.05			−1.77063			−0.885313	+	0.464996i	$0.846056\pi$
$252$			2752.98i			0.688180i
$253$			1038.66i			0.258103i
$254$	8483.03			2.09556
$255$	711.965	−	1476.09i	0.174843	−	0.362497i
$256$	1280.63			0.312655
$257$			7045.47i			1.71006i	0.518581	+	0.855028i	$0.326460\pi$
$257$			7045.47i			1.71006i	−0.518581	+	0.855028i	$0.673540\pi$
$258$			3586.16i			0.865365i
$259$	920.920			0.220939
$260$	−3358.01	−	1619.67i	−0.800981	−	0.386337i
$261$	−3117.45			−0.739330
$262$		−	12656.2i		−	2.98436i
$263$			2026.02i			0.475018i	0.971385	+	0.237509i	$0.0763309\pi$
$263$			2026.02i			0.475018i	−0.971385	+	0.237509i	$0.923669\pi$
$264$	−930.215			−0.216859
$265$	−4680.95	−	2257.76i	−1.08509	−	0.523371i
$266$	−7872.76			−1.81470
$267$			1439.56i			0.329962i
$268$		−	3668.30i		−	0.836108i
$269$	−2542.68			−0.576320			−0.288160	−	0.957582i	$-0.593043\pi$
$269$	−2542.68			−0.576320			−0.288160	+	0.957582i	$0.593043\pi$
$270$	−2364.63	+	4902.51i	−0.532987	+	1.10503i
$271$	5043.25			1.13046			0.565232	−	0.824932i	$-0.308787\pi$
$271$	5043.25			1.13046			0.565232	+	0.824932i	$0.308787\pi$
$272$		−	2688.09i		−	0.599225i
$273$		−	1006.64i		−	0.223167i
$274$	2473.00			0.545252
$275$	3514.12	+	4417.66i	0.770579	+	0.968710i
$276$	547.249			0.119350
$277$			4892.30i			1.06119i	0.847625	+	0.530596i	$0.178032\pi$
$277$			4892.30i			1.06119i	−0.847625	+	0.530596i	$0.821968\pi$
$278$			5042.69i			1.08791i
$279$	5324.65			1.14258
$280$	541.140	−	1121.93i	0.115498	−	0.239458i
$281$	6380.96			1.35465			0.677324	−	0.735685i	$-0.263139\pi$
$281$	6380.96			1.35465			0.677324	+	0.735685i	$0.263139\pi$
$282$			3401.14i			0.718209i
$283$			399.535i			0.0839218i	0.999119	+	0.0419609i	$0.0133605\pi$
$283$			399.535i			0.0839218i	−0.999119	+	0.0419609i	$0.986640\pi$
$284$	−60.5477			−0.0126509
$285$	−3450.35	−	1664.21i	−0.717127	−	0.345892i
$286$	−6367.09			−1.31641
$287$			4238.05i			0.871653i
$288$			5435.26i			1.11207i
$289$	1081.58			0.220146
$290$	6234.33	+	3007.01i	1.26239	+	0.608888i
$291$	2597.27			0.523212
$292$			3210.74i			0.643474i
$293$		−	7573.01i		−	1.50997i	−0.655745	−	0.754983i	$-0.727645\pi$
$293$		−	7573.01i		−	1.50997i	0.655745	−	0.754983i	$-0.272355\pi$
$294$	−1800.27			−0.357121
$295$	3133.28	−	6496.13i	0.618395	−	1.28210i
$296$	−625.422			−0.122811
$297$			5175.09i			1.01108i
$298$			11177.0i			2.17270i
$299$	763.333			0.147641
$300$	2327.58	−	1851.52i	0.447943	−	0.356325i
$301$	−4565.74			−0.874302
$302$		−	2124.47i		−	0.404799i
$303$		−	2405.44i		−	0.456069i
$304$	−6283.37			−1.18545
$305$	1473.67	−	3055.31i	0.276662	−	0.573595i
$306$	5625.27			1.05090
$307$			2122.08i			0.394507i	0.980353	+	0.197253i	$0.0632022\pi$
$307$			2122.08i			0.394507i	−0.980353	+	0.197253i	$0.936798\pi$
$308$		−	5811.58i		−	1.07515i
$309$	−1184.43			−0.218058
$310$	−10648.3	−	5136.02i	−1.95092	−	0.940988i
$311$	10529.2			1.91980			0.959901	−	0.280340i	$-0.0904473\pi$
$311$	10529.2			1.91980			0.959901	+	0.280340i	$0.0904473\pi$
$312$			683.635i			0.124049i
$313$			233.881i			0.0422356i	0.999777	+	0.0211178i	$0.00672251\pi$
$313$			233.881i			0.0422356i	−0.999777	+	0.0211178i	$0.993277\pi$
$314$	6232.08			1.12005
$315$	−2759.18	−	1330.84i	−0.493531	−	0.238045i
$316$	28.7995			0.00512689
$317$		−	633.262i		−	0.112200i	−0.998425	−	0.0561002i	$-0.982133\pi$
$317$		−	633.262i		−	0.112200i	0.998425	−	0.0561002i	$-0.0178666\pi$
$318$			4676.32i			0.824639i
$319$	6580.97			1.15506
$320$	3555.24	−	7370.97i	0.621075	−	1.28766i
$321$	−2943.42			−0.511794
$322$			1251.49i			0.216592i
$323$			8955.90i			1.54279i
$324$	−3076.68			−0.527552
$325$	3246.64	−	2582.60i	0.554126	−	0.440790i
$326$	331.599			0.0563361
$327$			811.318i			0.137205i
$328$		−	2878.18i		−	0.484514i
$329$	−4330.19			−0.725626
$330$	2206.65	−	4574.97i	0.368097	−	0.763164i
$331$	−1096.66			−0.182108			−0.0910542	−	0.995846i	$-0.529024\pi$
$331$	−1096.66			−0.182108			−0.0910542	+	0.995846i	$0.529024\pi$
$332$		−	13542.5i		−	2.23868i
$333$			1538.11i			0.253117i
$334$	7705.96			1.26243
$335$	3676.56	+	1773.31i	0.599617	+	0.289213i
$336$	1317.19			0.213866
$337$			8262.07i			1.33550i	0.744385	+	0.667750i	$0.232743\pi$
$337$			8262.07i			1.33550i	−0.744385	+	0.667750i	$0.767257\pi$
$338$		−	4654.07i		−	0.748959i
$339$	1197.19			0.191807
$340$	−6262.91	−	3020.79i	−0.998982	−	0.481839i
$341$	−11240.4			−1.78505
$342$		−	13149.0i		−	2.07900i
$343$		−	6685.25i		−	1.05239i
$344$	3100.72			0.485987
$345$	−264.549	+	548.482i	−0.0412836	+	0.0855921i
$346$	−832.960			−0.129423
$347$		−	453.251i		−	0.0701205i	−0.999385	−	0.0350602i	$-0.988838\pi$
$347$		−	453.251i		−	0.0701205i	0.999385	−	0.0350602i	$-0.0111623\pi$
$348$		−	3467.38i		−	0.534113i
$349$	5010.89			0.768558			0.384279	−	0.923217i	$-0.374450\pi$
$349$	5010.89			0.768558			0.384279	+	0.923217i	$0.374450\pi$
$350$	4234.17	+	5322.86i	0.646646	+	0.812911i
$351$	3803.29			0.578360
$352$		−	11473.9i		−	1.73739i
$353$		−	3768.90i		−	0.568266i	−0.958785	−	0.284133i	$-0.908294\pi$
$353$		−	3768.90i		−	0.568266i	0.958785	−	0.284133i	$-0.0917058\pi$
$354$	−6489.70			−0.974361
$355$	29.2697	−	60.6841i	0.00437599	−	0.00907261i
$356$	6107.91			0.909322
$357$		−	1877.44i		−	0.278333i
$358$		−	10638.3i		−	1.57053i
$359$	2618.64			0.384977			0.192488	−	0.981299i	$-0.438344\pi$
$359$	2618.64			0.384977			0.192488	+	0.981299i	$0.438344\pi$
$360$	1873.83	+	903.807i	0.274333	+	0.132319i
$361$	14075.3			2.05209
$362$			371.517i			0.0539407i
$363$		−	1677.42i		−	0.242540i
$364$	−4271.05			−0.615011
$365$	−3217.97	−	1552.12i	−0.461469	−	0.222581i
$366$	−3052.29			−0.435917
$367$			5485.76i			0.780258i	0.920760	+	0.390129i	$0.127570\pi$
$367$			5485.76i			0.780258i	−0.920760	+	0.390129i	$0.872430\pi$
$368$			998.829i			0.141488i
$369$	−7078.35			−0.998602
$370$	1483.62	−	3075.94i	0.208459	−	0.432191i
$371$	−5953.70			−0.833155
$372$			5922.35i			0.825429i
$373$			7784.54i			1.08061i	0.841469	+	0.540306i	$0.181692\pi$
$373$			7784.54i			1.08061i	−0.841469	+	0.540306i	$0.818308\pi$
$374$	−11875.0			−1.64182
$375$	730.498	+	3227.88i	0.100594	+	0.444498i
$376$	2940.75			0.403345
$377$		−	4836.50i		−	0.660722i
$378$			6235.49i			0.848463i
$379$	2956.81			0.400742			0.200371	−	0.979720i	$-0.435785\pi$
$379$	2956.81			0.400742			0.200371	+	0.979720i	$0.435785\pi$
$380$	−7061.06	+	14639.5i	−0.953222	+	1.97629i
$381$	4728.68			0.635847
$382$			6623.03i			0.887077i
$383$			5707.61i			0.761476i	0.924683	+	0.380738i	$0.124330\pi$
$383$			5707.61i			0.761476i	−0.924683	+	0.380738i	$0.875670\pi$
$384$	−2550.26			−0.338913
$385$	5824.66	+	2809.41i	0.771045	+	0.371898i
$386$	5309.34			0.700099
$387$		−	7625.65i		−	1.00164i
$388$		−	11019.9i		−	1.44189i
$389$	3237.19			0.421933			0.210966	−	0.977493i	$-0.432339\pi$
$389$	3237.19			0.421933			0.210966	+	0.977493i	$0.432339\pi$
$390$	−3362.25	−	1621.71i	−0.436549	−	0.210561i
$391$	1423.66			0.184138
$392$			1556.58i			0.200559i
$393$		−	7054.93i		−	0.905532i
$394$	−19352.1			−2.47447
$395$	−13.9221	+	28.8644i	−0.00177342	+	0.00367677i
$396$	9706.43			1.23173
$397$			4346.35i			0.549464i	0.961521	+	0.274732i	$0.0885892\pi$
$397$			4346.35i			0.549464i	−0.961521	+	0.274732i	$0.911411\pi$
$398$			4737.55i			0.596664i
$399$	−4388.50			−0.550626
$400$	3379.36	+	4248.25i	0.422419	+	0.531032i
$401$	−13341.6			−1.66146			−0.830731	−	0.556674i	$-0.812077\pi$
$401$	−13341.6			−1.66146			−0.830731	+	0.556674i	$0.812077\pi$
$402$		−	3672.92i		−	0.455693i
$403$			8260.82i			1.02109i
$404$	−10206.0			−1.25685
$405$	1487.32	−	3083.61i	0.182483	−	0.378336i
$406$	7929.44			0.969289
$407$		−	3246.97i		−	0.395446i
$408$			1275.02i			0.154713i
$409$	−3839.43			−0.464174			−0.232087	−	0.972695i	$-0.574555\pi$
$409$	−3839.43			−0.464174			−0.232087	+	0.972695i	$0.574555\pi$
$410$	14155.4	+	6827.58i	1.70509	+	0.822415i
$411$	1378.52			0.165443
$412$			5025.41i			0.600932i
$413$		−	8262.41i		−	0.984423i
$414$	−2090.22			−0.248137
$415$	13573.0	+	6546.67i	1.60548	+	0.774369i
$416$	−8432.41			−0.993829
$417$			2810.93i			0.330101i
$418$			27757.7i			3.24802i
$419$	4009.29			0.467462			0.233731	−	0.972301i	$-0.424907\pi$
$419$	4009.29			0.467462			0.233731	+	0.972301i	$0.424907\pi$
$420$	1480.22	−	3068.90i	0.171970	−	0.356541i
$421$	2837.80			0.328518			0.164259	−	0.986417i	$-0.447477\pi$
$421$	2837.80			0.328518			0.164259	+	0.986417i	$0.447477\pi$
$422$			680.920i			0.0785466i
$423$		−	7232.23i		−	0.831308i
$424$	4043.32			0.463115
$425$	6055.18	−	4816.71i	0.691105	−	0.549753i
$426$	−60.6241			−0.00689494
$427$		−	3886.04i		−	0.440418i
$428$			12488.6i			1.41042i
$429$	−3549.19			−0.399433
$430$	−7355.50	+	15249.9i	−0.824915	+	1.71027i
$431$	−12034.9			−1.34502			−0.672508	−	0.740090i	$-0.734783\pi$
$431$	−12034.9			−1.34502			−0.672508	+	0.740090i	$0.734783\pi$
$432$			4976.64i			0.554256i
$433$			1764.15i			0.195796i	0.995196	+	0.0978980i	$0.0312119\pi$
$433$			1764.15i			0.195796i	−0.995196	+	0.0978980i	$0.968788\pi$
$434$	−13543.6			−1.49796
$435$	3475.19	+	1676.19i	0.383041	+	0.184752i
$436$	3442.33			0.378114
$437$		−	3327.80i		−	0.364280i
$438$			3214.79i			0.350704i
$439$	1799.49			0.195637			0.0978186	−	0.995204i	$-0.468813\pi$
$439$	1799.49			0.195637			0.0978186	+	0.995204i	$0.468813\pi$
$440$	−3955.69	−	1907.95i	−0.428591	−	0.206722i
$441$	3828.11			0.413358
$442$			8727.21i			0.939165i
$443$		−	14559.6i		−	1.56150i	−0.624842	−	0.780751i	$-0.714837\pi$
$443$		−	14559.6i		−	1.56150i	0.624842	−	0.780751i	$-0.285163\pi$
$444$	−1710.77			−0.182859
$445$	−2952.66	+	6121.67i	−0.314539	+	0.652123i
$446$	−9185.19			−0.975183
$447$			6230.35i			0.659251i
$448$		−	9375.12i		−	0.988690i
$449$	−7008.95			−0.736688			−0.368344	−	0.929690i	$-0.620075\pi$
$449$	−7008.95			−0.736688			−0.368344	+	0.929690i	$0.620075\pi$
$450$	−8890.19	+	7071.87i	−0.931305	+	0.740825i
$451$	14942.5			1.56012
$452$		−	5079.54i		−	0.528588i
$453$		−	1184.24i		−	0.122826i
$454$	−2267.23			−0.234375
$455$	2064.70	−	4280.67i	0.212735	−	0.441057i
$456$	2980.35			0.306069
$457$			12350.3i			1.26416i	0.774901	+	0.632082i	$0.217800\pi$
$457$			12350.3i			1.26416i	−0.774901	+	0.632082i	$0.782200\pi$
$458$		−	16865.5i		−	1.72068i
$459$	7093.37			0.721330
$460$	2327.15	+	1122.45i	0.235878	+	0.113771i
$461$	−15666.5			−1.58278			−0.791391	−	0.611310i	$-0.790643\pi$
$461$	−15666.5			−1.58278			−0.791391	+	0.611310i	$0.790643\pi$
$462$		−	5818.90i		−	0.585974i
$463$		−	11781.2i		−	1.18254i	−0.806472	−	0.591272i	$-0.798626\pi$
$463$		−	11781.2i		−	1.18254i	0.806472	−	0.591272i	$-0.201374\pi$
$464$	6328.60			0.633185
$465$	−5935.69	−	2862.96i	−0.591959	−	0.285520i
$466$	23648.6			2.35086
$467$		−	15588.3i		−	1.54463i	−0.635241	−	0.772314i	$-0.719099\pi$
$467$		−	15588.3i		−	1.54463i	0.635241	−	0.772314i	$-0.280901\pi$
$468$		−	7133.46i		−	0.704582i
$469$	4676.21			0.460399
$470$	−6976.02	+	14463.2i	−0.684638	+	1.41944i
$471$	3473.94			0.339853
$472$			5611.23i			0.547199i
$473$			16097.8i			1.56486i
$474$	28.8358			0.00279425
$475$	−11259.0	−	14153.9i	−1.08758	−	1.36721i
$476$	−7965.78			−0.767040
$477$		−	9943.80i		−	0.954497i
$478$		−	4843.49i		−	0.463464i
$479$	−10048.7			−0.958531			−0.479265	−	0.877670i	$-0.659097\pi$
$479$	−10048.7			−0.958531			−0.479265	+	0.877670i	$0.659097\pi$
$480$	2922.43	−	6058.98i	0.277896	−	0.576153i
$481$	−2386.27			−0.226205
$482$			16538.7i			1.56290i
$483$			697.613i			0.0657195i
$484$	−7117.12			−0.668400
$485$	11044.8	+	5327.22i	1.03405	+	0.498756i
$486$	−16225.1			−1.51437
$487$		−	13513.2i		−	1.25738i	−0.777656	−	0.628690i	$-0.783592\pi$
$487$		−	13513.2i		−	1.25738i	0.777656	−	0.628690i	$-0.216408\pi$
$488$			2639.12i			0.244810i
$489$	184.843			0.0170938
$490$	−7655.53	−	3692.49i	−0.705800	−	0.340428i
$491$	−7071.37			−0.649952			−0.324976	−	0.945722i	$-0.605356\pi$
$491$	−7071.37			−0.649952			−0.324976	+	0.945722i	$0.605356\pi$
$492$		−	7872.90i		−	0.721418i
$493$		−	9020.37i		−	0.824051i
$494$	20399.7			1.85795
$495$	−4692.25	+	9728.29i	−0.426062	+	0.883342i
$496$	−10809.4			−0.978537
$497$		−	77.1840i		−	0.00696615i
$498$		−	13559.6i		−	1.22012i
$499$	−17583.8			−1.57747			−0.788734	−	0.614734i	$-0.789263\pi$
$499$	−17583.8			−1.57747			−0.788734	+	0.614734i	$0.789263\pi$
$500$	13695.5	−	3099.42i	1.22496	−	0.277221i
$501$	4295.52			0.383053
$502$			29912.0i			2.65944i
$503$			5960.79i			0.528386i	0.964470	+	0.264193i	$0.0851057\pi$
$503$			5960.79i			0.528386i	−0.964470	+	0.264193i	$0.914894\pi$
$504$	2383.33			0.210639
$505$	4933.75	−	10229.0i	0.434751	−	0.901355i
$506$	4412.47			0.387665
$507$		−	2594.31i		−	0.227253i
$508$		−	20063.3i		−	1.75229i
$509$	17522.7			1.52590			0.762948	−	0.646460i	$-0.223751\pi$
$509$	17522.7			1.52590			0.762948	+	0.646460i	$0.223751\pi$
$510$	−6270.80	−	3024.60i	−0.544462	−	0.262611i
$511$	−4092.93			−0.354326
$512$		−	14055.9i		−	1.21326i
$513$		−	16580.7i		−	1.42701i
$514$	29930.9			2.56847
$515$	−5036.72	−	2429.36i	−0.430960	−	0.207865i
$516$	8481.64			0.723611
$517$			15267.3i			1.29876i
$518$		−	3912.29i		−	0.331846i
$519$	−464.315			−0.0392701
$520$	−1402.19	+	2907.12i	−0.118250	+	0.245165i
$521$	−21064.8			−1.77133			−0.885667	−	0.464320i	$-0.846299\pi$
$521$	−21064.8			−1.77133			−0.885667	+	0.464320i	$0.846299\pi$
$522$			13243.7i			1.11046i
$523$			11064.7i			0.925097i	0.886594	+	0.462549i	$0.153065\pi$
$523$			11064.7i			0.925097i	−0.886594	+	0.462549i	$0.846935\pi$
$524$	−29933.3			−2.49550
$525$	2360.25	+	2967.11i	0.196209	+	0.246658i
$526$	8607.02			0.713467
$527$			15407.0i			1.27351i
$528$		−	4644.15i		−	0.382785i
$529$	−529.000			−0.0434783
$530$	−9591.52	+	19885.8i	−0.786093	+	1.62978i
$531$	13799.8			1.12780
$532$			18619.9i			1.51744i
$533$		−	10981.5i		−	0.892427i
$534$	6115.61			0.495596
$535$	−12516.7	−	6037.20i	−1.01149	−	0.487871i
$536$	−3175.74			−0.255916
$537$		−	5930.06i		−	0.476538i
$538$			10801.9i			0.865620i
$539$	−8081.19			−0.645791
$540$	11594.9	+	5592.59i	0.924013	+	0.445679i
$541$	18341.7			1.45762			0.728808	−	0.684718i	$-0.240075\pi$
$541$	18341.7			1.45762			0.728808	+	0.684718i	$0.240075\pi$
$542$		−	21424.9i		−	1.69793i
$543$			207.094i			0.0163670i
$544$	−15727.0			−1.23950
$545$	−1664.08	+	3450.08i	−0.130791	+	0.271166i
$546$	−4276.44			−0.335192
$547$		−	1764.25i		−	0.137905i	−0.997620	−	0.0689524i	$-0.978034\pi$
$547$		−	1764.25i		−	0.137905i	0.997620	−	0.0689524i	$-0.0219657\pi$
$548$		−	5848.90i		−	0.455935i
$549$	6490.42			0.504562
$550$	18767.3	−	14928.8i	1.45498	−	1.15739i
$551$	−21085.0			−1.63022
$552$		−	473.768i		−	0.0365306i
$553$			36.7125i			0.00282310i
$554$	20783.7			1.59389
$555$	827.012	−	1714.62i	0.0632517	−	0.131138i
$556$	11926.5			0.909704
$557$			21849.9i			1.66214i	0.556172	+	0.831068i	$0.312270\pi$
$557$			21849.9i			1.66214i	−0.556172	+	0.831068i	$0.687730\pi$
$558$		−	22620.4i		−	1.71613i
$559$	11830.7			0.895140
$560$	5601.30	+	2701.67i	0.422675	+	0.203869i
$561$	−6619.47			−0.498171
$562$		−	27107.9i		−	2.03465i
$563$		−	16177.4i		−	1.21101i	−0.795842	−	0.605504i	$-0.792972\pi$
$563$		−	16177.4i		−	1.21101i	0.795842	−	0.605504i	$-0.207028\pi$
$564$	8044.06			0.600560
$565$	5090.98	+	2455.53i	0.379078	+	0.182841i
$566$	1697.32			0.126049
$567$		−	3922.04i		−	0.290494i
$568$			52.4177i			0.00387218i
$569$	13874.3			1.02222			0.511109	−	0.859516i	$-0.329235\pi$
$569$	13874.3			1.02222			0.511109	+	0.859516i	$0.329235\pi$
$570$	−7069.96	+	14657.9i	−0.519523	+	1.07711i
$571$	4404.68			0.322820			0.161410	−	0.986887i	$-0.448396\pi$
$571$	4404.68			0.322820			0.161410	+	0.986887i	$0.448396\pi$
$572$			15058.8i			1.10077i
$573$			3691.86i			0.269162i
$574$	18004.3			1.30920
$575$	−2249.96	+	1789.78i	−0.163182	+	0.129807i
$576$	15658.2			1.13268
$577$		−	3986.38i		−	0.287617i	−0.989606	−	0.143809i	$-0.954065\pi$
$577$		−	3986.38i		−	0.287617i	0.989606	−	0.143809i	$-0.0459349\pi$
$578$		−	4594.81i		−	0.330655i
$579$	2959.57			0.212428
$580$	7111.89	−	14744.9i	0.509146	−	1.05560i
$581$	17263.5			1.23272
$582$		−	11033.8i		−	0.785854i
$583$			20991.5i			1.49122i
$584$	2779.62			0.196955
$585$	7149.53	+	3448.43i	0.505293	+	0.243718i
$586$	−32172.0			−2.26794
$587$		−	12208.0i		−	0.858394i	−0.903211	−	0.429197i	$-0.858797\pi$
$587$		−	12208.0i		−	0.858394i	0.903211	−	0.429197i	$-0.141203\pi$
$588$			4257.82i			0.298622i
$589$	36013.6			2.51938
$590$	−27597.1	−	13310.9i	−1.92569	−	0.928816i
$591$	−10787.4			−0.750818
$592$		−	3122.46i		−	0.216777i
$593$			7654.56i			0.530076i	0.964238	+	0.265038i	$0.0853845\pi$
$593$			7654.56i			0.530076i	−0.964238	+	0.265038i	$0.914615\pi$
$594$	21985.0			1.51861
$595$	3850.79	−	7983.72i	0.265323	−	0.550085i
$596$	26434.7			1.81679
$597$			2640.85i			0.181043i
$598$		−	3242.82i		−	0.221754i
$599$	−17448.9			−1.19022			−0.595111	−	0.803644i	$-0.702892\pi$
$599$	−17448.9			−1.19022			−0.595111	+	0.803644i	$0.702892\pi$
$600$	−1602.91	−	2015.05i	−0.109064	−	0.137107i
$601$	−21666.0			−1.47051			−0.735253	−	0.677792i	$-0.762937\pi$
$601$	−21666.0			−1.47051			−0.735253	+	0.677792i	$0.762937\pi$
$602$			19396.4i			1.31318i
$603$			7810.15i			0.527453i
$604$	−5024.59			−0.338490
$605$	3440.53	−	7133.15i	0.231203	−	0.479345i
$606$	−10218.9			−0.685006
$607$			16606.1i			1.11041i	0.831713	+	0.555205i	$0.187360\pi$
$607$			16606.1i			1.11041i	−0.831713	+	0.555205i	$0.812640\pi$
$608$			36761.6i			2.45211i
$609$	4420.09			0.294107
$610$	−12979.7	−	6260.49i	−0.861527	−	0.415540i
$611$	11220.3			0.742921
$612$		−	13304.4i		−	0.878753i
$613$			8834.87i			0.582116i	0.956705	+	0.291058i	$0.0940072\pi$
$613$			8834.87i			0.582116i	−0.956705	+	0.291058i	$0.905993\pi$
$614$	9015.11			0.592541
$615$	7890.63	+	3805.89i	0.517367	+	0.249542i
$616$	−5031.23			−0.329081
$617$			25353.4i			1.65428i	0.561996	+	0.827140i	$0.310034\pi$
$617$			25353.4i			1.65428i	−0.561996	+	0.827140i	$0.689966\pi$
$618$			5031.74i			0.327518i
$619$	−14879.3			−0.966156			−0.483078	−	0.875577i	$-0.660481\pi$
$619$	−14879.3			−0.966156			−0.483078	+	0.875577i	$0.660481\pi$
$620$	−12147.2	+	25184.5i	−0.786846	+	1.63134i
$621$	−2635.73			−0.170319
$622$		−	44730.7i		−	2.88350i
$623$			7786.14i			0.500714i
$624$	−3413.09			−0.218963
$625$	−3514.24	+	15224.7i	−0.224911	+	0.974379i
$626$	993.584			0.0634371
$627$			15472.9i			0.985533i
$628$		−	14739.5i		−	0.936579i
$629$	−4450.54			−0.282122
$630$	−5653.71	+	11721.7i	−0.357538	+	0.741273i
$631$	−21128.2			−1.33296			−0.666481	−	0.745522i	$-0.732200\pi$
$631$	−21128.2			−1.33296			−0.666481	+	0.745522i	$0.732200\pi$
$632$		−	24.9325i		−	0.00156924i
$633$			379.564i			0.0238330i
$634$	−2690.25			−0.168523
$635$	20108.4	+	9698.91i	1.25666	+	0.606125i
$636$	11060.0			0.689556
$637$			5939.04i			0.369409i
$638$		−	27957.5i		−	1.73487i
$639$	128.912			0.00798071
$640$	−10844.9	−	5230.80i	−0.669814	−	0.323071i
$641$	−1682.51			−0.103674			−0.0518372	−	0.998656i	$-0.516508\pi$
$641$	−1682.51			−0.103674			−0.0518372	+	0.998656i	$0.516508\pi$
$642$			12504.4i			0.768704i
$643$		−	4463.95i		−	0.273781i	−0.990586	−	0.136890i	$-0.956289\pi$
$643$		−	4463.95i		−	0.273781i	0.990586	−	0.136890i	$-0.0437108\pi$
$644$	2959.90			0.181112
$645$	−4100.16	+	8500.74i	−0.250300	+	0.518940i
$646$	38046.8			2.31723
$647$			1751.79i			0.106445i	0.998583	+	0.0532225i	$0.0169493\pi$
$647$			1751.79i			0.106445i	−0.998583	+	0.0532225i	$0.983051\pi$
$648$			2663.57i			0.161473i
$649$	−29131.5			−1.76196
$650$	−10971.5	−	13792.5i	−0.662058	−	0.832286i
$651$	−7549.60			−0.454519
$652$		−	784.266i		−	0.0471077i
$653$		−	3142.57i		−	0.188328i	−0.995557	−	0.0941641i	$-0.969982\pi$
$653$		−	3142.57i		−	0.188328i	0.995557	−	0.0941641i	$-0.0300178\pi$
$654$	3446.67			0.206079
$655$	14470.2	−	30000.7i	0.863204	−	1.78965i
$656$	14369.5			0.855233
$657$		−	6835.97i		−	0.405931i
$658$			18395.7i			1.08988i
$659$	−3491.07			−0.206362			−0.103181	−	0.994663i	$-0.532902\pi$
$659$	−3491.07			−0.206362			−0.103181	+	0.994663i	$0.532902\pi$
$660$	−10820.3	−	5218.96i	−0.638151	−	0.307799i
$661$	−27662.3			−1.62774			−0.813871	−	0.581046i	$-0.802644\pi$
$661$	−27662.3			−1.62774			−0.813871	+	0.581046i	$0.802644\pi$
$662$			4658.87i			0.273523i
$663$			4864.79i			0.284967i
$664$	−11724.1			−0.685216
$665$	−18661.9	−	9001.17i	−1.08823	−	0.524888i
$666$	6534.26			0.380177
$667$			3351.75i			0.194573i
$668$		−	18225.4i		−	1.05563i
$669$	−5120.09			−0.295895
$670$	7533.46	−	15618.9i	0.434393	−	0.900613i
$671$	−13701.4			−0.788279
$672$		−	7706.41i		−	0.442383i
$673$		−	30526.7i		−	1.74846i	−0.485508	−	0.874232i	$-0.661365\pi$
$673$		−	30526.7i		−	1.74846i	0.485508	−	0.874232i	$-0.338635\pi$
$674$	35099.2			2.00589
$675$	−11210.4	+	8917.51i	−0.639241	+	0.508497i
$676$	−11007.4			−0.626273
$677$		−	17328.8i		−	0.983753i	−0.870665	−	0.491876i	$-0.836311\pi$
$677$		−	17328.8i		−	0.983753i	0.870665	−	0.491876i	$-0.163689\pi$
$678$		−	5085.95i		−	0.288090i
$679$	14047.8			0.793970
$680$	−2615.18	+	5421.96i	−0.147481	+	0.305769i
$681$	−1263.82			−0.0711154
$682$			47752.0i			2.68111i
$683$			15668.1i			0.877781i	0.898541	+	0.438890i	$0.144628\pi$
$683$			15668.1i			0.877781i	−0.898541	+	0.438890i	$0.855372\pi$
$684$	−31098.8			−1.73844
$685$	5862.07	+	2827.45i	0.326975	+	0.157710i
$686$	−28400.5			−1.58067
$687$		−	9401.31i		−	0.522099i
$688$			15480.5i			0.857833i
$689$	15427.1			0.853012
$690$	2330.08	+	1123.87i	0.128558	+	0.0620072i
$691$	−15744.3			−0.866773			−0.433386	−	0.901208i	$-0.642681\pi$
$691$	−15744.3			−0.866773			−0.433386	+	0.901208i	$0.642681\pi$
$692$			1970.04i			0.108222i
$693$			12373.4i			0.678249i
$694$	−1925.52			−0.105319
$695$	−5765.46	+	11953.3i	−0.314671	+	0.652397i
$696$	−3001.80			−0.163481
$697$		−	20481.3i		−	1.11303i
$698$		−	21287.5i		−	1.15436i
$699$	13182.4			0.713311
$700$	12589.1	−	10014.3i	0.679749	−	0.540720i
$701$	20506.1			1.10486			0.552428	−	0.833561i	$-0.313702\pi$
$701$	20506.1			1.10486			0.552428	+	0.833561i	$0.313702\pi$
$702$		−	16157.3i		−	0.868685i
$703$			10403.1i			0.558122i
$704$	−33054.7			−1.76960
$705$	−3888.63	+	8062.17i	−0.207737	+	0.430694i
$706$	−16011.2			−0.853524
$707$		−	13010.3i		−	0.692080i
$708$			15348.8i			0.814752i
$709$	11473.8			0.607767			0.303883	−	0.952709i	$-0.401717\pi$
$709$	11473.8			0.607767			0.303883	+	0.952709i	$0.401717\pi$
$710$	−257.800	−	124.345i	−0.0136269	−	0.00657265i
$711$	−61.3169			−0.00323427
$712$		−	5287.78i		−	0.278326i
$713$		−	5724.86i		−	0.300698i
$714$	−7975.83			−0.418050
$715$	−15092.7	−	7279.68i	−0.789422	−	0.380762i
$716$	−25160.6			−1.31326
$717$		−	2699.90i		−	0.140627i
$718$		−	11124.6i		−	0.578227i
$719$	9129.49			0.473536			0.236768	−	0.971566i	$-0.423912\pi$
$719$	9129.49			0.473536			0.236768	+	0.971566i	$0.423912\pi$
$720$	−4512.31	+	9355.22i	−0.233561	+	0.484234i
$721$	−6406.20			−0.330901
$722$		−	59795.3i		−	3.08220i
$723$			9219.13i			0.474223i
$724$	878.678			0.0451047
$725$	11340.1	+	14255.8i	0.580909	+	0.730272i
$726$	−7126.10			−0.364290
$727$		−	25602.8i		−	1.30613i	−0.757302	−	0.653065i	$-0.773483\pi$
$727$		−	25602.8i		−	1.30613i	0.757302	−	0.653065i	$-0.226517\pi$
$728$			3697.56i			0.188243i
$729$	−776.588			−0.0394548
$730$	−6593.79	+	13670.7i	−0.334311	+	0.693117i
$731$	22064.9			1.11642
$732$			7218.98i			0.364510i
$733$		−	28934.2i		−	1.45800i	−0.684516	−	0.728998i	$-0.739987\pi$
$733$		−	28934.2i		−	1.45800i	0.684516	−	0.728998i	$-0.260013\pi$
$734$	23304.8			1.17193
$735$	−4267.41	−	2058.30i	−0.214158	−	0.103295i
$736$	5843.77			0.292669
$737$		−	16487.3i		−	0.824041i
$738$			30070.5i			1.49988i
$739$	−15934.2			−0.793163			−0.396582	−	0.917999i	$-0.629804\pi$
$739$	−15934.2			−0.793163			−0.396582	+	0.917999i	$0.629804\pi$
$740$	−7274.93	−	3508.92i	−0.361394	−	0.174311i
$741$	11371.4			0.563750
$742$			25292.7i			1.25138i
$743$			32769.8i			1.61804i	0.587779	+	0.809022i	$0.300003\pi$
$743$			32769.8i			1.61804i	−0.587779	+	0.809022i	$0.699997\pi$
$744$	5127.14			0.252648
$745$	−12779.0	+	26494.2i	−0.628436	+	1.30292i
$746$	33070.6			1.62306
$747$			28833.3i			1.41225i
$748$			28085.7i			1.37288i
$749$	−15920.0			−0.776642
$750$	13712.8	−	3103.33i	0.667627	−	0.151090i
$751$	14662.7			0.712451			0.356226	−	0.934400i	$-0.384063\pi$
$751$	14662.7			0.712451			0.356226	+	0.934400i	$0.384063\pi$
$752$			14681.9i			0.711958i
$753$			16673.8i			0.806943i
$754$	−20546.6			−0.992391
$755$	2428.97	−	5035.91i	0.117085	−	0.242749i
$756$	14747.6			0.709478
$757$		−	22632.4i		−	1.08664i	−0.839525	−	0.543321i	$-0.817167\pi$
$757$		−	22632.4i		−	1.08664i	0.839525	−	0.543321i	$-0.182833\pi$
$758$		−	12561.2i		−	0.601906i
$759$	2459.64			0.117627
$760$	12673.8	+	6112.94i	0.604903	+	0.291763i
$761$	−5408.08			−0.257612			−0.128806	−	0.991670i	$-0.541114\pi$
$761$	−5408.08			−0.257612			−0.128806	+	0.991670i	$0.541114\pi$
$762$		−	20088.6i		−	0.955029i
$763$			4388.16i			0.208207i
$764$	15664.2			0.741766
$765$	13334.3	+	6431.55i	0.630201	+	0.303965i
$766$	24247.3			1.14372
$767$			21409.4i			1.00789i
$768$		−	3032.65i		−	0.142489i
$769$	−21697.9			−1.01748			−0.508742	−	0.860919i	$-0.669889\pi$
$769$	−21697.9			−1.01748			−0.508742	+	0.860919i	$0.669889\pi$
$770$	11935.0	−	24744.6i	0.558583	−	1.15809i
$771$	16684.3			0.779339
$772$		−	12557.1i		−	0.585416i
$773$		−	27736.1i		−	1.29055i	−0.763949	−	0.645276i	$-0.776742\pi$
$773$		−	27736.1i		−	1.29055i	0.763949	−	0.645276i	$-0.223258\pi$
$774$	−32395.6			−1.50444
$775$	−19369.0	−	24349.2i	−0.897749	−	1.12858i
$776$	−9540.25			−0.441334
$777$		−	2180.82i		−	0.100690i
$778$		−	13752.3i		−	0.633734i
$779$	−47874.8			−2.20191
$780$	−3835.52	+	7952.07i	−0.176069	+	0.365038i
$781$	−272.134			−0.0124683
$782$		−	6048.07i		−	0.276571i
$783$			16700.0i			0.762210i
$784$	−7771.29			−0.354013
$785$	14772.7	+	7125.33i	0.671670	+	0.323967i
$786$	−29971.0			−1.36009
$787$			16195.2i			0.733539i	0.930312	+	0.366770i	$0.119536\pi$
$787$			16195.2i			0.733539i	−0.930312	+	0.366770i	$0.880464\pi$
$788$			45769.7i			2.06913i
$789$	4797.80			0.216484
$790$	122.623	+	59.1446i	0.00552243	+	0.00266363i
$791$	6475.22			0.291065
$792$		−	8403.11i		−	0.377010i
$793$			10069.4i			0.450915i
$794$	18464.4			0.825284
$795$	−5346.58	+	11084.9i	−0.238521	+	0.494517i
$796$	11204.8			0.498925
$797$			33094.7i			1.47086i	0.677602	+	0.735429i	$0.263019\pi$
$797$			33094.7i			1.47086i	−0.677602	+	0.735429i	$0.736981\pi$
$798$			18643.4i			0.827029i
$799$	20926.6			0.926569
$800$	24854.9	−	19771.3i	1.09844	−	0.873778i
$801$	−13004.3			−0.573639
$802$			56678.2i			2.49548i
$803$			14430.8i			0.634187i
$804$	−8686.85			−0.381047
$805$	−1430.86	+	2966.56i	−0.0626475	+	0.129885i
$806$	35093.9			1.53366
$807$			6021.29i			0.262651i
$808$			8835.62i			0.384698i
$809$	−25432.3			−1.10526			−0.552629	−	0.833428i	$-0.686375\pi$
$809$	−25432.3			−1.10526			−0.552629	+	0.833428i	$0.686375\pi$
$810$	−13099.9	−	6318.49i	−0.568252	−	0.274085i
$811$	6421.64			0.278045			0.139022	−	0.990289i	$-0.455604\pi$
$811$	6421.64			0.278045			0.139022	+	0.990289i	$0.455604\pi$
$812$		−	18754.0i		−	0.810511i
$813$		−	11942.9i		−	0.515196i
$814$	−13793.9			−0.593951
$815$	786.033	+	379.127i	0.0337835	+	0.0162948i
$816$	−6365.62			−0.273090
$817$		−	51576.5i		−	2.20861i
$818$			16310.8i			0.697180i
$819$	9093.48			0.387975
$820$	16148.0	−	33479.1i	0.687696	−	1.42578i
$821$	41129.4			1.74839			0.874195	−	0.485576i	$-0.161390\pi$
$821$	41129.4			1.74839			0.874195	+	0.485576i	$0.161390\pi$
$822$		−	5856.27i		−	0.248493i
$823$		−	8574.46i		−	0.363168i	−0.983375	−	0.181584i	$-0.941878\pi$
$823$		−	8574.46i		−	0.363168i	0.983375	−	0.181584i	$-0.0581224\pi$
$824$	4350.63			0.183934
$825$	10461.4	−	8321.74i	0.441479	−	0.351183i
$826$	−35100.7			−1.47858
$827$			9063.58i			0.381102i	0.981677	+	0.190551i	$0.0610275\pi$
$827$			9063.58i			0.381102i	−0.981677	+	0.190551i	$0.938972\pi$
$828$			4943.58i			0.207490i
$829$	28331.5			1.18696			0.593482	−	0.804847i	$-0.297753\pi$
$829$	28331.5			1.18696			0.593482	+	0.804847i	$0.297753\pi$
$830$	27811.8	−	57661.3i	1.16309	−	2.41139i
$831$	11585.4			0.483626
$832$			24292.6i			1.01225i
$833$			11076.7i			0.460726i
$834$	11941.5			0.495805
$835$	18266.4	+	8810.46i	0.757050	+	0.365148i
$836$	65649.9			2.71597
$837$		−	28524.0i		−	1.17794i
$838$		−	17032.4i		−	0.702118i
$839$	−18180.7			−0.748115			−0.374058	−	0.927405i	$-0.622034\pi$
$839$	−18180.7			−0.748115			−0.374058	+	0.927405i	$0.622034\pi$
$840$	−2656.83	−	1281.47i	−0.109130	−	0.0526367i
$841$	−3152.21			−0.129247
$842$		−	12055.7i		−	0.493427i
$843$		−	15110.7i		−	0.617366i
$844$	1610.45			0.0656800
$845$	5321.14	−	11032.2i	0.216631	−	0.449134i
$846$	−30724.3			−1.24861
$847$		−	9072.65i		−	0.368052i
$848$			20186.5i			0.817461i
$849$	946.133			0.0382464
$850$	−20462.5	−	25723.9i	−0.825717	−	1.03802i
$851$	1653.72			0.0666142
$852$			143.382i			0.00576549i
$853$		−	35109.3i		−	1.40928i	−0.709563	−	0.704642i	$-0.751108\pi$
$853$		−	35109.3i		−	1.40928i	0.709563	−	0.704642i	$-0.248892\pi$
$854$	−16508.8			−0.661499
$855$	15033.7	−	31168.8i	0.601334	−	1.24673i
$856$	10811.7			0.431702
$857$			43608.5i			1.73820i	0.494635	+	0.869101i	$0.335302\pi$
$857$			43608.5i			1.73820i	−0.494635	+	0.869101i	$0.664698\pi$
$858$			15077.8i			0.599940i
$859$	−28107.2			−1.11642			−0.558210	−	0.829700i	$-0.688512\pi$
$859$	−28107.2			−1.11642			−0.558210	+	0.829700i	$0.688512\pi$
$860$	36067.7	+	17396.5i	1.43011	+	0.689787i
$861$	10036.1			0.397246
$862$			51127.2i			2.02019i
$863$		−	2495.15i		−	0.0984195i	−0.998788	−	0.0492097i	$-0.984330\pi$
$863$		−	2495.15i		−	0.0984195i	0.998788	−	0.0492097i	$-0.0156703\pi$
$864$	29116.4			1.14648
$865$	−1974.47	−	952.348i	−0.0776117	−	0.0374345i
$866$	7494.54			0.294082
$867$		−	2561.27i		−	0.100329i
$868$			32032.1i			1.25258i
$869$	129.441			0.00505290
$870$	7120.85	−	14763.4i	0.277494	−	0.575319i
$871$	−12116.9			−0.471372
$872$		−	2980.12i		−	0.115733i
$873$			23462.5i			0.909605i
$874$	−14137.3			−0.547141
$875$	3951.03	+	17458.5i	0.152651	+	0.674522i
$876$	7603.31			0.293256
$877$		−	8858.57i		−	0.341086i	−0.985350	−	0.170543i	$-0.945448\pi$
$877$		−	8858.57i		−	0.341086i	0.985350	−	0.170543i	$-0.0545522\pi$
$878$		−	7644.64i		−	0.293843i
$879$	−17933.6			−0.688150
$880$	9525.53	−	19749.0i	0.364893	−	0.756521i
$881$	2511.07			0.0960274			0.0480137	−	0.998847i	$-0.484711\pi$
$881$	2511.07			0.0960274			0.0480137	+	0.998847i	$0.484711\pi$
$882$		−	16262.7i		−	0.620856i
$883$			34908.4i			1.33042i	0.746656	+	0.665210i	$0.231658\pi$
$883$			34908.4i			1.33042i	−0.746656	+	0.665210i	$0.768342\pi$
$884$	20640.8			0.785321
$885$	−15383.4	−	7419.88i	−0.584302	−	0.281826i
$886$	−61852.5			−2.34534
$887$		−	3735.01i		−	0.141386i	−0.997498	−	0.0706930i	$-0.977479\pi$
$887$		−	3735.01i		−	0.141386i	0.997498	−	0.0706930i	$-0.0225211\pi$
$888$			1481.05i			0.0559695i
$889$	25575.9			0.964891
$890$	26006.3	+	12543.6i	0.979475	+	0.472430i
$891$	−13828.3			−0.519939
$892$			21724.0i			0.815439i
$893$		−	48915.6i		−	1.83303i
$894$	26468.0			0.990182
$895$	12163.0	−	25217.3i	0.454263	−	0.941810i
$896$	−13793.6			−0.514297
$897$		−	1807.64i		−	0.0672858i
$898$			29775.7i			1.10649i
$899$	−36272.8			−1.34568
$900$	16725.7	+	21026.2i	0.619471	+	0.778749i
$901$	28772.5			1.06387
$902$		−	63479.2i		−	2.34327i
$903$			10812.1i			0.398453i
$904$	−4397.49			−0.161790
$905$	−424.767	+	880.657i	−0.0156019	+	0.0323470i
$906$	−5030.93			−0.184483
$907$		−	47690.8i		−	1.74592i	−0.487794	−	0.872958i	$-0.662198\pi$
$907$		−	47690.8i		−	1.74592i	0.487794	−	0.872958i	$-0.337802\pi$
$908$			5362.24i			0.195983i
$909$	21729.6			0.792876
$910$	−18185.3	−	8771.32i	−0.662459	−	0.319524i
$911$	−3741.08			−0.136056			−0.0680282	−	0.997683i	$-0.521671\pi$
$911$	−3741.08			−0.136056			−0.0680282	+	0.997683i	$0.521671\pi$
$912$			14879.6i			0.540254i
$913$		−	60867.4i		−	2.20637i
$914$	52467.1			1.89875
$915$	−7235.24	−	3489.77i	−0.261409	−	0.126086i
$916$	−39888.7			−1.43882
$917$		−	38157.8i		−	1.37414i
$918$		−	30134.3i		−	1.08342i
$919$	−22203.8			−0.796993			−0.398496	−	0.917170i	$-0.630468\pi$
$919$	−22203.8			−0.796993			−0.398496	+	0.917170i	$0.630468\pi$
$920$	971.737	−	2014.67i	0.0348231	−	0.0721976i
$921$	5025.27			0.179792
$922$			66555.1i			2.37731i
$923$			199.997i			0.00713218i
$924$	−13762.3			−0.489986
$925$	7033.64	−	5595.05i	0.250016	−	0.198880i
$926$	−50049.2			−1.77616
$927$		−	10699.6i		−	0.379094i
$928$		−	37026.3i		−	1.30975i
$929$	−31609.9			−1.11635			−0.558173	−	0.829724i	$-0.688498\pi$
$929$	−31609.9			−1.11635			−0.558173	+	0.829724i	$0.688498\pi$
$930$	−12162.5	+	25216.2i	−0.428845	+	0.889110i
$931$	25891.6			0.911454
$932$		−	55931.5i		−	1.96577i
$933$		−	24934.2i		−	0.874928i
$934$	−66222.9			−2.32000
$935$	−28148.9	−	13577.1i	−0.984565	−	0.474885i
$936$	−6175.63			−0.215659
$937$			47341.7i			1.65057i	0.564715	+	0.825286i	$0.308986\pi$
$937$			47341.7i			1.65057i	−0.564715	+	0.825286i	$0.691014\pi$
$938$		−	19865.7i		−	0.691510i
$939$	553.852			0.0192484
$940$	34206.9	+	16499.0i	1.18692	+	0.572488i
$941$	17602.5			0.609803			0.304901	−	0.952384i	$-0.401377\pi$
$941$	17602.5			0.609803			0.304901	+	0.952384i	$0.401377\pi$
$942$		−	14758.1i		−	0.510452i
$943$			7610.36i			0.262807i
$944$	−28014.4			−0.965880
$945$	−7129.23	+	14780.8i	−0.245412	+	0.508804i
$946$	68387.5			2.35039
$947$			10159.6i			0.348619i	0.984691	+	0.174310i	$0.0557693\pi$
$947$			10159.6i			0.348619i	−0.984691	+	0.174310i	$0.944231\pi$
$948$		−	68.1997i		−	0.00233652i
$949$	10605.5			0.362771
$950$	−60129.2	+	47831.0i	−2.05353	+	1.63352i
$951$	−1499.62			−0.0511341
$952$			6896.19i			0.234776i
$953$			20880.0i			0.709728i	0.934918	+	0.354864i	$0.115473\pi$
$953$			20880.0i			0.709728i	−0.934918	+	0.354864i	$0.884527\pi$
$954$	−42243.6			−1.43364
$955$	−7572.31	+	15699.4i	−0.256580	+	0.531960i
$956$	−11455.4			−0.387545
$957$		−	15584.3i		−	0.526405i
$958$			42689.2i			1.43969i
$959$	7455.96			0.251059
$960$	−17455.1	−	8419.12i	−0.586834	−	0.283048i
$961$	32163.6			1.07964
$962$			10137.4i			0.339755i
$963$		−	26589.5i		−	0.889754i
$964$	39115.7			1.30688
$965$	12585.4	+	6070.33i	0.419833	+	0.202498i
$966$	2963.63			0.0987093
$967$		−	16972.4i		−	0.564423i	−0.959352	−	0.282211i	$-0.908932\pi$
$967$		−	16972.4i		−	0.564423i	0.959352	−	0.282211i	$-0.0910679\pi$
$968$			6161.48i			0.204584i
$969$	21208.4			0.703107
$970$	22631.3	−	46920.8i	0.749121	−	1.55313i
$971$	−11675.5			−0.385876			−0.192938	−	0.981211i	$-0.561802\pi$
$971$	−11675.5			−0.385876			−0.192938	+	0.981211i	$0.561802\pi$
$972$			38374.1i			1.26631i
$973$			15203.4i			0.500925i
$974$	−57407.5			−1.88856
$975$	−6115.82	−	7688.32i	−0.200885	−	0.252537i
$976$	−13175.9			−0.432122
$977$			7742.47i			0.253535i	0.991932	+	0.126767i	$0.0404602\pi$
$977$			7742.47i			0.253535i	−0.991932	+	0.126767i	$0.959540\pi$
$978$		−	785.255i		−	0.0256745i
$979$	27452.3			0.896199
$980$	−8733.14	+	18106.1i	−0.284663	+	0.590183i
$981$	−7329.05			−0.238531
$982$			30040.9i			0.976214i
$983$			18779.1i			0.609318i	0.952461	+	0.304659i	$0.0985426\pi$
$983$			18779.1i			0.609318i	−0.952461	+	0.304659i	$0.901457\pi$
$984$	−6815.77			−0.220812
$985$	−45872.7	−	22125.8i	−1.48389	−	0.715723i
$986$	−38320.7			−1.23771
$987$			10254.3i			0.330696i
$988$		−	48247.5i		−	1.55360i
$989$	−8198.80			−0.263606
$990$	41328.1	+	19933.8i	1.32676	+	0.639937i
$991$	−41515.6			−1.33076			−0.665381	−	0.746504i	$-0.731731\pi$
$991$	−41515.6			−1.33076			−0.665381	+	0.746504i	$0.731731\pi$
$992$			63241.5i			2.02411i
$993$			2596.99i			0.0829939i
$994$	−327.896			−0.0104630
$995$	−5416.59	+	11230.1i	−0.172580	+	0.357806i
$996$	−32069.8			−1.02025
$997$			3363.67i			0.106849i	0.998572	+	0.0534245i	$0.0170136\pi$
$997$			3363.67i			0.106849i	−0.998572	+	0.0534245i	$0.982986\pi$
$998$			74700.0i			2.36933i
$999$	8239.60			0.260950

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	115.4.b.a.24.6	✓	34
5.2	odd	4		575.4.a.q.1.15		17
5.3	odd	4		575.4.a.r.1.3		17
5.4	even	2	inner	115.4.b.a.24.29	yes	34

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
115.4.b.a.24.6	✓	34	1.1	even	1	trivial
115.4.b.a.24.29	yes	34	5.4	even	2	inner
575.4.a.q.1.15		17	5.2	odd	4
575.4.a.r.1.3		17	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:	\( N \)	\(=\)	\( 115 = 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	115.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-4.24824i q^{2} -2.36809i q^{3} -10.0475 q^{4} +(4.85714 - 10.0702i) q^{5} -10.0602 q^{6} -12.8082i q^{7} +8.69841i q^{8} +21.3922 q^{9} +O(q^{10})\)	\(q-4.24824i q^{2} -2.36809i q^{3} -10.0475 q^{4} +(4.85714 - 10.0702i) q^{5} -10.0602 q^{6} -12.8082i q^{7} +8.69841i q^{8} +21.3922 q^{9} +(-42.7805 - 20.6343i) q^{10} -45.1591 q^{11} +23.7934i q^{12} +33.1884i q^{13} -54.4124 q^{14} +(-23.8470 - 11.5021i) q^{15} -43.4273 q^{16} +61.8985i q^{17} -90.8790i q^{18} +144.687 q^{19} +(-48.8023 + 101.180i) q^{20} -30.3310 q^{21} +191.847i q^{22} -23.0000i q^{23} +20.5986 q^{24} +(-77.8163 - 97.8244i) q^{25} +140.992 q^{26} -114.597i q^{27} +128.691i q^{28} -145.728 q^{29} +(-48.8638 + 101.308i) q^{30} +248.907 q^{31} +254.077i q^{32} +106.941i q^{33} +262.959 q^{34} +(-128.981 - 62.2114i) q^{35} -214.938 q^{36} +71.9007i q^{37} -614.665i q^{38} +78.5931 q^{39} +(87.5944 + 42.2494i) q^{40} -330.885 q^{41} +128.853i q^{42} -356.469i q^{43} +453.738 q^{44} +(103.905 - 215.423i) q^{45} -97.7095 q^{46} -338.079i q^{47} +102.840i q^{48} +178.949 q^{49} +(-415.582 + 330.582i) q^{50} +146.581 q^{51} -333.462i q^{52} -464.834i q^{53} -486.835 q^{54} +(-219.344 + 454.760i) q^{55} +111.411 q^{56} -342.631i q^{57} +619.089i q^{58} +645.086 q^{59} +(239.604 + 115.568i) q^{60} +303.402 q^{61} -1057.42i q^{62} -273.996i q^{63} +731.961 q^{64} +(334.213 + 161.201i) q^{65} +454.310 q^{66} +365.094i q^{67} -621.927i q^{68} -54.4660 q^{69} +(-264.289 + 547.942i) q^{70} +6.02613 q^{71} +186.078i q^{72} -319.555i q^{73} +305.451 q^{74} +(-231.657 + 184.276i) q^{75} -1453.75 q^{76} +578.408i q^{77} -333.882i q^{78} -2.86632 q^{79} +(-210.933 + 437.320i) q^{80} +306.213 q^{81} +1405.68i q^{82} +1347.84i q^{83} +304.752 q^{84} +(623.328 + 300.650i) q^{85} -1514.37 q^{86} +345.098i q^{87} -392.813i q^{88} -607.901 q^{89} +(-915.166 - 441.412i) q^{90} +425.085 q^{91} +231.093i q^{92} -589.433i q^{93} -1436.24 q^{94} +(702.765 - 1457.02i) q^{95} +601.677 q^{96} +1096.78i q^{97} -760.220i q^{98} -966.051 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 34 q - 144 q^{4} + 14 q^{5} + 24 q^{6} - 310 q^{9}+O(q^{10}) \) 34 * q - 144 * q^4 + 14 * q^5 + 24 * q^6 - 310 * q^9	\( 34 q - 144 q^{4} + 14 q^{5} + 24 q^{6} - 310 q^{9} + 14 q^{10} - 8 q^{11} + 236 q^{14} + 440 q^{16} + 144 q^{19} - 180 q^{20} - 32 q^{21} + 108 q^{24} + 134 q^{25} - 144 q^{26} + 56 q^{29} - 294 q^{30} - 80 q^{31} + 264 q^{34} + 116 q^{35} + 1864 q^{36} - 1200 q^{39} + 650 q^{40} + 268 q^{41} - 1612 q^{44} - 1346 q^{45} + 184 q^{46} - 1474 q^{49} + 120 q^{50} - 1104 q^{51} + 1564 q^{54} + 1160 q^{55} - 2300 q^{56} - 708 q^{59} - 516 q^{60} + 1100 q^{61} + 100 q^{64} + 1164 q^{65} - 1416 q^{66} - 552 q^{69} + 1144 q^{70} + 1360 q^{71} + 1588 q^{74} - 2064 q^{75} + 108 q^{76} + 3968 q^{79} + 2542 q^{80} + 4914 q^{81} - 1948 q^{84} + 124 q^{85} - 6148 q^{86} + 1196 q^{89} + 2760 q^{90} - 544 q^{91} - 2340 q^{94} + 3920 q^{95} + 2960 q^{96} - 3816 q^{99}+O(q^{100}) \) 34 * q - 144 * q^4 + 14 * q^5 + 24 * q^6 - 310 * q^9 + 14 * q^10 - 8 * q^11 + 236 * q^14 + 440 * q^16 + 144 * q^19 - 180 * q^20 - 32 * q^21 + 108 * q^24 + 134 * q^25 - 144 * q^26 + 56 * q^29 - 294 * q^30 - 80 * q^31 + 264 * q^34 + 116 * q^35 + 1864 * q^36 - 1200 * q^39 + 650 * q^40 + 268 * q^41 - 1612 * q^44 - 1346 * q^45 + 184 * q^46 - 1474 * q^49 + 120 * q^50 - 1104 * q^51 + 1564 * q^54 + 1160 * q^55 - 2300 * q^56 - 708 * q^59 - 516 * q^60 + 1100 * q^61 + 100 * q^64 + 1164 * q^65 - 1416 * q^66 - 552 * q^69 + 1144 * q^70 + 1360 * q^71 + 1588 * q^74 - 2064 * q^75 + 108 * q^76 + 3968 * q^79 + 2542 * q^80 + 4914 * q^81 - 1948 * q^84 + 124 * q^85 - 6148 * q^86 + 1196 * q^89 + 2760 * q^90 - 544 * q^91 - 2340 * q^94 + 3920 * q^95 + 2960 * q^96 - 3816 * q^99

Introduction

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