LMFDB - Embedded newform 43.5.b.b.42.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [43,5,Mod(42,43)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(43, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 5, names="a")

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

chi := DirichletCharacter("43.42");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 43 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	43.b (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$4.44490841261$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 142x^{10} + 7173x^{8} + 157368x^{6} + 1510016x^{4} + 5098688x^{2} + 90352 $ x^12 + 142x^10 + 7173x^8 + 157368x^6 + 1510016x^4 + 5098688*x^2 + 90352
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{8} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			42.2
Root			$-6.72223i$ of defining polynomial
Character	$\chi$	$=$	43.42
Dual form			43.5.b.b.42.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-6.72223i q^{2} -8.31879i q^{3} -29.1884 q^{4} +1.48242i q^{5} -55.9208 q^{6} -13.7963i q^{7} +88.6554i q^{8} +11.7977 q^{9} +O(q^{10})$	\(q-6.72223i q^{2} -8.31879i q^{3} -29.1884 q^{4} +1.48242i q^{5} -55.9208 q^{6} -13.7963i q^{7} +88.6554i q^{8} +11.7977 q^{9} +9.96518 q^{10} -10.2025 q^{11} +242.812i q^{12} +98.4183 q^{13} -92.7416 q^{14} +12.3320 q^{15} +128.948 q^{16} -286.515 q^{17} -79.3069i q^{18} -367.004i q^{19} -43.2695i q^{20} -114.768 q^{21} +68.5838i q^{22} -242.039 q^{23} +737.506 q^{24} +622.802 q^{25} -661.591i q^{26} -771.965i q^{27} +402.691i q^{28} -1147.40i q^{29} -82.8983i q^{30} +895.225 q^{31} +551.669i q^{32} +84.8728i q^{33} +1926.02i q^{34} +20.4519 q^{35} -344.356 q^{36} +2295.69i q^{37} -2467.09 q^{38} -818.722i q^{39} -131.425 q^{40} +1692.26 q^{41} +771.498i q^{42} +(-1546.34 - 1013.73i) q^{43} +297.796 q^{44} +17.4892i q^{45} +1627.04i q^{46} +743.419 q^{47} -1072.69i q^{48} +2210.66 q^{49} -4186.62i q^{50} +2383.46i q^{51} -2872.67 q^{52} +99.3399 q^{53} -5189.33 q^{54} -15.1245i q^{55} +1223.11 q^{56} -3053.03 q^{57} -7713.09 q^{58} +3286.35 q^{59} -359.950 q^{60} +3223.22i q^{61} -6017.91i q^{62} -162.764i q^{63} +5771.61 q^{64} +145.898i q^{65} +570.534 q^{66} +5556.36 q^{67} +8362.90 q^{68} +2013.47i q^{69} -137.482i q^{70} -2953.33i q^{71} +1045.93i q^{72} +3618.34i q^{73} +15432.2 q^{74} -5180.96i q^{75} +10712.3i q^{76} +140.757i q^{77} -5503.64 q^{78} +2380.74 q^{79} +191.155i q^{80} -5466.20 q^{81} -11375.7i q^{82} -6427.91 q^{83} +3349.90 q^{84} -424.736i q^{85} +(-6814.51 + 10394.8i) q^{86} -9544.98 q^{87} -904.510i q^{88} -3293.36i q^{89} +117.566 q^{90} -1357.80i q^{91} +7064.72 q^{92} -7447.19i q^{93} -4997.44i q^{94} +544.055 q^{95} +4589.22 q^{96} -9329.95 q^{97} -14860.6i q^{98} -120.367 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 92 q^{4} + 126 q^{6} - 462 q^{9}+O(q^{10}) $ 12 * q - 92 * q^4 + 126 * q^6 - 462 * q^9	$ 12 q - 92 q^{4} + 126 q^{6} - 462 q^{9} + 182 q^{10} - 180 q^{11} - 216 q^{13} + 732 q^{14} - 92 q^{15} + 1076 q^{16} + 678 q^{17} - 2392 q^{21} + 1566 q^{23} - 4234 q^{24} - 174 q^{25} + 5710 q^{31} + 936 q^{35} + 4210 q^{36} + 1242 q^{38} - 2618 q^{40} + 4878 q^{41} - 1108 q^{43} - 15168 q^{44} - 5526 q^{47} - 8544 q^{49} + 24084 q^{52} + 1212 q^{53} - 10004 q^{54} - 10152 q^{56} - 7692 q^{57} - 4666 q^{58} + 14016 q^{59} + 15848 q^{60} - 15580 q^{64} + 29808 q^{66} - 1088 q^{67} + 15186 q^{68} - 7674 q^{74} - 67708 q^{78} + 24302 q^{79} - 23660 q^{81} - 7032 q^{83} + 37180 q^{84} - 14412 q^{86} + 17850 q^{87} + 4268 q^{90} + 48354 q^{92} + 606 q^{95} + 50546 q^{96} - 5842 q^{97} - 25924 q^{99}+O(q^{100}) $ 12 * q - 92 * q^4 + 126 * q^6 - 462 * q^9 + 182 * q^10 - 180 * q^11 - 216 * q^13 + 732 * q^14 - 92 * q^15 + 1076 * q^16 + 678 * q^17 - 2392 * q^21 + 1566 * q^23 - 4234 * q^24 - 174 * q^25 + 5710 * q^31 + 936 * q^35 + 4210 * q^36 + 1242 * q^38 - 2618 * q^40 + 4878 * q^41 - 1108 * q^43 - 15168 * q^44 - 5526 * q^47 - 8544 * q^49 + 24084 * q^52 + 1212 * q^53 - 10004 * q^54 - 10152 * q^56 - 7692 * q^57 - 4666 * q^58 + 14016 * q^59 + 15848 * q^60 - 15580 * q^64 + 29808 * q^66 - 1088 * q^67 + 15186 * q^68 - 7674 * q^74 - 67708 * q^78 + 24302 * q^79 - 23660 * q^81 - 7032 * q^83 + 37180 * q^84 - 14412 * q^86 + 17850 * q^87 + 4268 * q^90 + 48354 * q^92 + 606 * q^95 + 50546 * q^96 - 5842 * q^97 - 25924 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/43\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$-1$

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 $

$2$		−	6.72223i		−	1.68056i	−0.542154	−	0.840279i	$-0.682391\pi$
$2$		−	6.72223i		−	1.68056i	0.542154	−	0.840279i	$-0.317609\pi$
$3$		−	8.31879i		−	0.924310i	−0.886799	−	0.462155i	$-0.847076\pi$
$3$		−	8.31879i		−	0.924310i	0.886799	−	0.462155i	$-0.152924\pi$
$4$	−29.1884			−1.82427
$5$			1.48242i			0.0592969i	0.999560	+	0.0296484i	$0.00943877\pi$
$5$			1.48242i			0.0592969i	−0.999560	+	0.0296484i	$0.990561\pi$
$6$	−55.9208			−1.55336
$7$		−	13.7963i		−	0.281556i	−0.990041	−	0.140778i	$-0.955040\pi$
$7$		−	13.7963i		−	0.281556i	0.990041	−	0.140778i	$-0.0449604\pi$
$8$			88.6554i			1.38524i
$9$	11.7977			0.145651
$10$	9.96518			0.0996518
$11$	−10.2025			−0.0843185			−0.0421592	−	0.999111i	$-0.513424\pi$
$11$	−10.2025			−0.0843185			−0.0421592	+	0.999111i	$0.513424\pi$
$12$			242.812i			1.68620i
$13$	98.4183			0.582357			0.291179	−	0.956669i	$-0.405953\pi$
$13$	98.4183			0.582357			0.291179	+	0.956669i	$0.405953\pi$
$14$	−92.7416			−0.473172
$15$	12.3320			0.0548087
$16$	128.948			0.503703
$17$	−286.515			−0.991400			−0.495700	−	0.868494i	$-0.665089\pi$
$17$	−286.515			−0.991400			−0.495700	+	0.868494i	$0.665089\pi$
$18$		−	79.3069i		−	0.244775i
$19$		−	367.004i		−	1.01663i	−0.861171	−	0.508316i	$-0.830268\pi$
$19$		−	367.004i		−	1.01663i	0.861171	−	0.508316i	$-0.169732\pi$
$20$		−	43.2695i		−	0.108174i
$21$	−114.768			−0.260245
$22$			68.5838i			0.141702i
$23$	−242.039			−0.457540			−0.228770	−	0.973480i	$-0.573470\pi$
$23$	−242.039			−0.457540			−0.228770	+	0.973480i	$0.573470\pi$
$24$	737.506			1.28039
$25$	622.802			0.996484
$26$		−	661.591i		−	0.978685i
$27$		−	771.965i		−	1.05894i
$28$			402.691i			0.513636i
$29$		−	1147.40i		−	1.36433i	−0.731199	−	0.682164i	$-0.761039\pi$
$29$		−	1147.40i		−	1.36433i	0.731199	−	0.682164i	$-0.238961\pi$
$30$		−	82.8983i		−	0.0921092i
$31$	895.225			0.931556			0.465778	−	0.884902i	$-0.345775\pi$
$31$	895.225			0.931556			0.465778	+	0.884902i	$0.345775\pi$
$32$			551.669i			0.538739i
$33$			84.8728i			0.0779364i
$34$			1926.02i			1.66611i
$35$	20.4519			0.0166954
$36$	−344.356			−0.265707
$37$			2295.69i			1.67691i	0.544969	+	0.838456i	$0.316541\pi$
$37$			2295.69i			1.67691i	−0.544969	+	0.838456i	$0.683459\pi$
$38$	−2467.09			−1.70851
$39$		−	818.722i		−	0.538279i
$40$	−131.425			−0.0821405
$41$	1692.26			1.00670			0.503348	−	0.864084i	$-0.332101\pi$
$41$	1692.26			1.00670			0.503348	+	0.864084i	$0.332101\pi$
$42$			771.498i			0.437357i
$43$	−1546.34	−	1013.73i	−0.836310	−	0.548257i
$43$	−1546.34	−	1013.73i	−0.836310	−	0.548257i
$44$	297.796			0.153820
$45$			17.4892i			0.00863663i
$46$			1627.04i			0.768923i
$47$	743.419			0.336541			0.168271	−	0.985741i	$-0.446182\pi$
$47$	743.419			0.336541			0.168271	+	0.985741i	$0.446182\pi$
$48$		−	1072.69i		−	0.465578i
$49$	2210.66			0.920726
$50$		−	4186.62i		−	1.67465i
$51$			2383.46i			0.916361i
$52$	−2872.67			−1.06238
$53$	99.3399			0.0353649			0.0176824	−	0.999844i	$-0.494371\pi$
$53$	99.3399			0.0353649			0.0176824	+	0.999844i	$0.494371\pi$
$54$	−5189.33			−1.77960
$55$		−	15.1245i		−	0.00499982i
$56$	1223.11			0.390023
$57$	−3053.03			−0.939683
$58$	−7713.09			−2.29283
$59$	3286.35			0.944082			0.472041	−	0.881577i	$-0.343517\pi$
$59$	3286.35			0.944082			0.472041	+	0.881577i	$0.343517\pi$
$60$	−359.950			−0.0999861
$61$			3223.22i			0.866225i	0.901340	+	0.433112i	$0.142585\pi$
$61$			3223.22i			0.866225i	−0.901340	+	0.433112i	$0.857415\pi$
$62$		−	6017.91i		−	1.56553i
$63$		−	162.764i		−	0.0410089i
$64$	5771.61			1.40908
$65$			145.898i			0.0345320i
$66$	570.534			0.130977
$67$	5556.36			1.23777			0.618886	−	0.785481i	$-0.287584\pi$
$67$	5556.36			1.23777			0.618886	+	0.785481i	$0.287584\pi$
$68$	8362.90			1.80859
$69$			2013.47i			0.422909i
$70$		−	137.482i		−	0.0280576i
$71$		−	2953.33i		−	0.585861i	−0.956134	−	0.292930i	$-0.905370\pi$
$71$		−	2953.33i		−	0.585861i	0.956134	−	0.292930i	$-0.0946305\pi$
$72$			1045.93i			0.201761i
$73$			3618.34i			0.678991i	0.940608	+	0.339496i	$0.110256\pi$
$73$			3618.34i			0.678991i	−0.940608	+	0.339496i	$0.889744\pi$
$74$	15432.2			2.81815
$75$		−	5180.96i		−	0.921060i
$76$			10712.3i			1.85461i
$77$			140.757i			0.0237404i
$78$	−5503.64			−0.904608
$79$	2380.74			0.381468			0.190734	−	0.981642i	$-0.438913\pi$
$79$	2380.74			0.381468			0.190734	+	0.981642i	$0.438913\pi$
$80$			191.155i			0.0298680i
$81$	−5466.20			−0.833135
$82$		−	11375.7i		−	1.69181i
$83$	−6427.91			−0.933069			−0.466535	−	0.884503i	$-0.654498\pi$
$83$	−6427.91			−0.933069			−0.466535	+	0.884503i	$0.654498\pi$
$84$	3349.90			0.474759
$85$		−	424.736i		−	0.0587869i
$86$	−6814.51	+	10394.8i	−0.921377	+	1.40547i
$87$	−9544.98			−1.26106
$88$		−	904.510i		−	0.116801i
$89$		−	3293.36i		−	0.415776i	−0.978153	−	0.207888i	$-0.933341\pi$
$89$		−	3293.36i		−	0.415776i	0.978153	−	0.207888i	$-0.0666590\pi$
$90$	117.566			0.0145144
$91$		−	1357.80i		−	0.163966i
$92$	7064.72			0.834679
$93$		−	7447.19i		−	0.861046i
$94$		−	4997.44i		−	0.565577i
$95$	544.055			0.0602831
$96$	4589.22			0.497962
$97$	−9329.95			−0.991599			−0.495799	−	0.868437i	$-0.665125\pi$
$97$	−9329.95			−0.991599			−0.495799	+	0.868437i	$0.665125\pi$
$98$		−	14860.6i		−	1.54733i
$99$	−120.367			−0.0122811
$100$	−18178.6			−1.81786
$101$	−13572.8			−1.33054			−0.665270	−	0.746603i	$-0.731683\pi$
$101$	−13572.8			−1.33054			−0.665270	+	0.746603i	$0.731683\pi$
$102$	16022.1			1.54000
$103$	−5527.90			−0.521057			−0.260529	−	0.965466i	$-0.583897\pi$
$103$	−5527.90			−0.521057			−0.260529	+	0.965466i	$0.583897\pi$
$104$			8725.32i			0.806705i
$105$		−	170.135i		−	0.0154317i
$106$		−	667.786i		−	0.0594327i
$107$	−2435.69			−0.212742			−0.106371	−	0.994326i	$-0.533923\pi$
$107$	−2435.69			−0.212742			−0.106371	+	0.994326i	$0.533923\pi$
$108$			22532.4i			1.93179i
$109$	3235.93			0.272362			0.136181	−	0.990684i	$-0.456517\pi$
$109$	3235.93			0.272362			0.136181	+	0.990684i	$0.456517\pi$
$110$	−101.670			−0.00840249
$111$	19097.4			1.54999
$112$		−	1779.00i		−	0.141821i
$113$			14680.9i			1.14973i	0.818247	+	0.574867i	$0.194946\pi$
$113$			14680.9i			1.14973i	−0.818247	+	0.574867i	$0.805054\pi$
$114$			20523.2i			1.57919i
$115$		−	358.803i		−	0.0271307i
$116$			33490.7i			2.48891i
$117$	1161.11			0.0848207
$118$		−	22091.6i		−	1.58658i
$119$			3952.83i			0.279135i
$120$			1093.29i			0.0759233i
$121$	−14536.9			−0.992890
$122$	21667.2			1.45574
$123$		−	14077.5i		−	0.930499i
$124$	−26130.2			−1.69941
$125$			1849.77i			0.118385i
$126$	−1094.14			−0.0689178
$127$	27000.0			1.67400			0.837001	−	0.547201i	$-0.184307\pi$
$127$	27000.0			1.67400			0.837001	+	0.547201i	$0.184307\pi$
$128$		−	29971.4i		−	1.82931i
$129$	−8432.98	+	12863.7i	−0.506759	+	0.773010i
$130$	980.757			0.0580329
$131$			17222.3i			1.00357i	0.864991	+	0.501787i	$0.167324\pi$
$131$			17222.3i			1.00357i	−0.864991	+	0.501787i	$0.832676\pi$
$132$		−	2477.30i		−	0.142177i
$133$	−5063.28			−0.286239
$134$		−	37351.1i		−	2.08015i
$135$	1144.38			0.0627916
$136$		−	25401.1i		−	1.37333i
$137$		−	1880.48i		−	0.100191i	−0.998744	−	0.0500955i	$-0.984047\pi$
$137$		−	1880.48i		−	0.100191i	0.998744	−	0.0500955i	$-0.0159526\pi$
$138$	13535.0			0.710723
$139$	20668.9			1.06977			0.534883	−	0.844926i	$-0.320356\pi$
$139$	20668.9			1.06977			0.534883	+	0.844926i	$0.320356\pi$
$140$	−596.957			−0.0304570
$141$		−	6184.35i		−	0.311068i
$142$	−19852.9			−0.984573
$143$	−1004.12			−0.0491035
$144$	1521.29			0.0733647
$145$	1700.93			0.0809004
$146$	24323.3			1.14108
$147$		−	18390.0i		−	0.851036i
$148$		−	67007.6i		−	3.05915i
$149$		−	13651.5i		−	0.614904i	−0.951564	−	0.307452i	$-0.900524\pi$
$149$		−	13651.5i		−	0.614904i	0.951564	−	0.307452i	$-0.0994763\pi$
$150$	−34827.6			−1.54789
$151$			41870.6i			1.83635i	0.396175	+	0.918175i	$0.370338\pi$
$151$			41870.6i			1.83635i	−0.396175	+	0.918175i	$0.629662\pi$
$152$	32536.9			1.40828
$153$	−3380.22			−0.144398
$154$	946.200			0.0398971
$155$			1327.10i			0.0552383i
$156$			23897.2i			0.981968i
$157$			41348.7i			1.67750i	0.544517	+	0.838750i	$0.316713\pi$
$157$			41348.7i			1.67750i	−0.544517	+	0.838750i	$0.683287\pi$
$158$		−	16003.9i		−	0.641079i
$159$		−	826.388i		−	0.0326881i
$160$	−817.806			−0.0319455
$161$			3339.23i			0.128823i
$162$			36745.1i			1.40013i
$163$		−	6111.31i		−	0.230017i	−0.993365	−	0.115008i	$-0.963311\pi$
$163$		−	6111.31i		−	0.230017i	0.993365	−	0.115008i	$-0.0366895\pi$
$164$	−49394.2			−1.83649
$165$	−125.817			−0.00462139
$166$			43209.9i			1.56808i
$167$	34991.0			1.25465			0.627326	−	0.778757i	$-0.284149\pi$
$167$	34991.0			1.25465			0.627326	+	0.778757i	$0.284149\pi$
$168$		−	10174.8i		−	0.360503i
$169$	−18874.8			−0.660860
$170$	−2855.17			−0.0987949
$171$		−	4329.81i		−	0.148073i
$172$	45135.1	+	29589.1i	1.52566	+	1.00017i
$173$	−4597.15			−0.153602			−0.0768009	−	0.997046i	$-0.524471\pi$
$173$	−4597.15			−0.153602			−0.0768009	+	0.997046i	$0.524471\pi$
$174$			64163.5i			2.11929i
$175$		−	8592.34i		−	0.280566i
$176$	−1315.60			−0.0424715
$177$		−	27338.5i		−	0.872624i
$178$	−22138.7			−0.698736
$179$		−	26315.3i		−	0.821301i	−0.911793	−	0.410650i	$-0.865302\pi$
$179$		−	26315.3i		−	0.821301i	0.911793	−	0.410650i	$-0.134698\pi$
$180$		−	510.481i		−	0.0157556i
$181$	48133.4			1.46923			0.734614	−	0.678485i	$-0.237363\pi$
$181$	48133.4			1.46923			0.734614	+	0.678485i	$0.237363\pi$
$182$	−9127.48			−0.275555
$183$	26813.3			0.800660
$184$		−	21458.0i		−	0.633803i
$185$	−3403.19			−0.0994357
$186$	−50061.7			−1.44704
$187$	2923.18			0.0835934
$188$	−21699.2			−0.613943
$189$	−10650.2			−0.298150
$190$		−	3657.26i		−	0.101309i
$191$		−	46954.1i		−	1.28708i	−0.765411	−	0.643542i	$-0.777464\pi$
$191$		−	46954.1i		−	1.28708i	0.765411	−	0.643542i	$-0.222536\pi$
$192$		−	48012.8i		−	1.30243i
$193$	18967.8			0.509215			0.254608	−	0.967044i	$-0.418054\pi$
$193$	18967.8			0.509215			0.254608	+	0.967044i	$0.418054\pi$
$194$			62718.1i			1.66644i
$195$	1213.69			0.0319182
$196$	−64525.7			−1.67966
$197$	−77177.1			−1.98864			−0.994320	−	0.106435i	$-0.966056\pi$
$197$	−77177.1			−1.98864			−0.994320	+	0.106435i	$0.966056\pi$
$198$			809.132i			0.0206390i
$199$			2250.86i			0.0568385i	0.999596	+	0.0284192i	$0.00904734\pi$
$199$			2250.86i			0.0568385i	−0.999596	+	0.0284192i	$0.990953\pi$
$200$			55214.8i			1.38037i
$201$		−	46222.2i		−	1.14409i
$202$			91239.7i			2.23605i
$203$	−15829.8			−0.384135
$204$		−	69569.3i		−	1.67169i
$205$			2508.64i			0.0596939i
$206$			37159.8i			0.875667i
$207$	−2855.50			−0.0666411
$208$	12690.8			0.293335
$209$			3744.37i			0.0857208i
$210$	−1143.69			−0.0259339
$211$		−	64198.9i		−	1.44199i	−0.692939	−	0.720996i	$-0.743685\pi$
$211$		−	64198.9i		−	1.44199i	0.692939	−	0.720996i	$-0.256315\pi$
$212$	−2899.57			−0.0645152
$213$	−24568.1			−0.541517
$214$			16373.2i			0.357526i
$215$	1502.77	−	2292.32i	0.0325099	−	0.0495906i
$216$	68438.9			1.46688
$217$		−	12350.8i		−	0.262285i
$218$		−	21752.7i		−	0.457720i
$219$	30100.2			0.627598
$220$			441.459i			0.00912105i
$221$	−28198.3			−0.577349
$222$		−	128377.i		−	2.60484i
$223$			53407.6i			1.07397i	0.843591	+	0.536987i	$0.180437\pi$
$223$			53407.6i			1.07397i	−0.843591	+	0.536987i	$0.819563\pi$
$224$	7610.96			0.151685
$225$	7347.64			0.145139
$226$	98688.7			1.93219
$227$		−	43494.8i		−	0.844084i	−0.906576	−	0.422042i	$-0.861313\pi$
$227$		−	43494.8i		−	0.844084i	0.906576	−	0.422042i	$-0.138687\pi$
$228$	89113.0			1.71424
$229$	67145.4			1.28040			0.640199	−	0.768209i	$-0.278852\pi$
$229$	67145.4			1.28040			0.640199	+	0.768209i	$0.278852\pi$
$230$	−2411.96			−0.0455947
$231$	1170.93			0.0219435
$232$	101723.			1.88992
$233$			76734.0i			1.41344i	0.707496	+	0.706718i	$0.249825\pi$
$233$			76734.0i			1.41344i	−0.707496	+	0.706718i	$0.750175\pi$
$234$		−	7805.26i		−	0.142546i
$235$			1102.06i			0.0199558i
$236$	−95923.2			−1.72226
$237$		−	19804.9i		−	0.352595i
$238$	26571.8			0.469103
$239$	−26767.6			−0.468613			−0.234307	−	0.972163i	$-0.575282\pi$
$239$	−26767.6			−0.468613			−0.234307	+	0.972163i	$0.575282\pi$
$240$	1590.18			0.0276073
$241$			100445.i			1.72939i	0.502297	+	0.864695i	$0.332488\pi$
$241$			100445.i			1.72939i	−0.502297	+	0.864695i	$0.667512\pi$
$242$			97720.5i			1.66861i
$243$		−	17057.0i		−	0.288861i
$244$		−	94080.7i		−	1.58023i
$245$			3277.14i			0.0545962i
$246$	−94632.4			−1.56376
$247$		−	36119.9i		−	0.592043i
$248$			79366.5i			1.29043i
$249$			53472.5i			0.862445i
$250$	12434.6			0.198953
$251$	−71737.6			−1.13867			−0.569337	−	0.822104i	$-0.692800\pi$
$251$	−71737.6			−1.13867			−0.569337	+	0.822104i	$0.692800\pi$
$252$			4750.83i			0.0748115i
$253$	2469.41			0.0385791
$254$		−	181500.i		−	2.81326i
$255$	−3533.29			−0.0543374
$256$	−109129.			−1.66518
$257$		−	7267.88i		−	0.110038i	−0.998485	−	0.0550189i	$-0.982478\pi$
$257$		−	7267.88i		−	0.110038i	0.998485	−	0.0550189i	$-0.0175219\pi$
$258$	86472.5	+	56688.5i	1.29909	+	0.851638i
$259$	31672.0			0.472145
$260$		−	4258.51i		−	0.0629958i
$261$		−	13536.7i		−	0.198715i
$262$	115773.			1.68656
$263$			73838.4i			1.06751i	0.845640	+	0.533754i	$0.179219\pi$
$263$			73838.4i			1.06751i	−0.845640	+	0.533754i	$0.820781\pi$
$264$	−7524.43			−0.107961
$265$			147.264i			0.00209703i
$266$			34036.6i			0.481041i
$267$	−27396.8			−0.384306
$268$	−162181.			−2.25804
$269$	127266.			1.75877			0.879384	−	0.476113i	$-0.157955\pi$
$269$	127266.			1.75877			0.879384	+	0.476113i	$0.157955\pi$
$270$		−	7692.77i		−	0.105525i
$271$	44182.9			0.601610			0.300805	−	0.953686i	$-0.402745\pi$
$271$	44182.9			0.601610			0.300805	+	0.953686i	$0.402745\pi$
$272$	−36945.5			−0.499371
$273$	−11295.3			−0.151556
$274$	−12641.0			−0.168377
$275$	−6354.17			−0.0840220
$276$		−	58769.9i		−	0.771502i
$277$		−	31197.7i		−	0.406596i	−0.979117	−	0.203298i	$-0.934834\pi$
$277$		−	31197.7i		−	0.406596i	0.979117	−	0.203298i	$-0.0651660\pi$
$278$		−	138941.i		−	1.79780i
$279$	10561.6			0.135682
$280$			1813.17i			0.0231272i
$281$	−140212.			−1.77572			−0.887859	−	0.460116i	$-0.847808\pi$
$281$	−140212.			−1.77572			−0.887859	+	0.460116i	$0.847808\pi$
$282$	−41572.6			−0.522768
$283$	2024.17			0.0252740			0.0126370	−	0.999920i	$-0.495977\pi$
$283$	2024.17			0.0252740			0.0126370	+	0.999920i	$0.495977\pi$
$284$			86202.8i			1.06877i
$285$		−	4525.88i		−	0.0557203i
$286$			6749.91i			0.0825212i
$287$		−	23346.8i		−	0.283442i
$288$			6508.43i			0.0784677i
$289$	−1430.31			−0.0171252
$290$		−	11434.0i		−	0.135958i
$291$			77613.9i			0.916545i
$292$		−	105614.i		−	1.23867i
$293$	75732.9			0.882164			0.441082	−	0.897467i	$-0.354595\pi$
$293$	75732.9			0.882164			0.441082	+	0.897467i	$0.354595\pi$
$294$	−123622.			−1.43022
$295$			4871.76i			0.0559811i
$296$	−203526.			−2.32293
$297$			7876.00i			0.0892879i
$298$	−91768.4			−1.03338
$299$	−23821.0			−0.266452
$300$			151224.i			1.68027i
$301$	−13985.6	+	21333.7i	−0.154365	+	0.235468i
$302$	281464.			3.08609
$303$			112910.i			1.22983i
$304$		−	47324.4i		−	0.512080i
$305$	−4778.18			−0.0513644
$306$			22722.6i			0.242670i
$307$	−158838.			−1.68530			−0.842652	−	0.538458i	$-0.819007\pi$
$307$	−158838.			−1.68530			−0.842652	+	0.538458i	$0.819007\pi$
$308$		−	4108.47i		−	0.0433090i
$309$			45985.4i			0.481619i
$310$	8921.08			0.0928312
$311$	−49344.1			−0.510169			−0.255085	−	0.966919i	$-0.582103\pi$
$311$	−49344.1			−0.510169			−0.255085	+	0.966919i	$0.582103\pi$
$312$	72584.1			0.745645
$313$		−	66350.6i		−	0.677261i	−0.940919	−	0.338631i	$-0.890036\pi$
$313$		−	66350.6i		−	0.677261i	0.940919	−	0.338631i	$-0.109964\pi$
$314$	277955.			2.81914
$315$	241.285			0.00243170
$316$	−69490.0			−0.695903
$317$	15717.4			0.156409			0.0782046	−	0.996937i	$-0.475081\pi$
$317$	15717.4			0.156409			0.0782046	+	0.996937i	$0.475081\pi$
$318$	−5555.17			−0.0549342
$319$			11706.4i			0.115038i
$320$			8555.96i			0.0835543i
$321$			20262.0i			0.196640i
$322$	22447.1			0.216495
$323$			105152.i			1.00789i
$324$	159550.			1.51987
$325$	61295.2			0.580309
$326$	−41081.6			−0.386556
$327$		−	26919.1i		−	0.251747i
$328$			150028.i			1.39452i
$329$		−	10256.4i		−	0.0947553i
$330$			845.773i			0.00776651i
$331$		−	85452.6i		−	0.779954i	−0.920825	−	0.389977i	$-0.872483\pi$
$331$		−	85452.6i		−	0.779954i	0.920825	−	0.389977i	$-0.127517\pi$
$332$	187620.			1.70217
$333$			27083.9i			0.244244i
$334$		−	235218.i		−	2.10852i
$335$			8236.87i			0.0733960i
$336$	−14799.1			−0.131086
$337$	−146925.			−1.29371			−0.646855	−	0.762613i	$-0.723916\pi$
$337$	−146925.			−1.29371			−0.646855	+	0.762613i	$0.723916\pi$
$338$			126881.i			1.11061i
$339$	122128.			1.06271
$340$			12397.4i			0.107244i
$341$	−9133.57			−0.0785474
$342$	−29106.0			−0.248845
$343$		−	63623.7i		−	0.540793i
$344$	89872.4	−	137091.i	0.759468	−	1.15849i
$345$	−2984.81			−0.0250772
$346$			30903.1i			0.258137i
$347$		−	78623.4i		−	0.652969i	−0.945203	−	0.326485i	$-0.894136\pi$
$347$		−	78623.4i		−	0.652969i	0.945203	−	0.326485i	$-0.105864\pi$
$348$	278603.			2.30052
$349$		−	165981.i		−	1.36273i	−0.731945	−	0.681363i	$-0.761387\pi$
$349$		−	165981.i		−	1.36273i	0.731945	−	0.681363i	$-0.238613\pi$
$350$	−57759.7			−0.471508
$351$		−	75975.5i		−	0.616679i
$352$		−	5628.42i		−	0.0454257i
$353$	53106.9			0.426188			0.213094	−	0.977032i	$-0.431646\pi$
$353$	53106.9			0.426188			0.213094	+	0.977032i	$0.431646\pi$
$354$	−183775.			−1.46650
$355$	4378.07			0.0347397
$356$			96127.9i			0.758490i
$357$	32882.8			0.258007
$358$	−176897.			−1.38024
$359$	−120101.			−0.931879			−0.465939	−	0.884817i	$-0.654284\pi$
$359$	−120101.			−0.931879			−0.465939	+	0.884817i	$0.654284\pi$
$360$	−1550.51			−0.0119638
$361$	−4370.92			−0.0335396
$362$		−	323564.i		−	2.46912i
$363$			120930.i			0.917739i
$364$			39632.1i			0.299120i
$365$	−5363.91			−0.0402620
$366$		−	180245.i		−	1.34556i
$367$	−37702.0			−0.279919			−0.139959	−	0.990157i	$-0.544697\pi$
$367$	−37702.0			−0.279919			−0.139959	+	0.990157i	$0.544697\pi$
$368$	−31210.4			−0.230464
$369$	19964.7			0.146626
$370$			22877.0i			0.167107i
$371$		−	1370.52i		−	0.00995720i
$372$			217371.i			1.57078i
$373$		−	139388.i		−	1.00186i	−0.865488	−	0.500930i	$-0.832991\pi$
$373$		−	139388.i		−	1.00186i	0.865488	−	0.500930i	$-0.167009\pi$
$374$		−	19650.3i		−	0.140484i
$375$	15387.8			0.109425
$376$			65908.1i			0.466190i
$377$		−	112925.i		−	0.794526i
$378$			71593.3i			0.501059i
$379$	−88126.5			−0.613519			−0.306759	−	0.951787i	$-0.599245\pi$
$379$	−88126.5			−0.613519			−0.306759	+	0.951787i	$0.599245\pi$
$380$	−15880.1			−0.109973
$381$		−	224607.i		−	1.54730i
$382$	−315636.			−2.16302
$383$			250818.i			1.70986i	0.518743	+	0.854930i	$0.326400\pi$
$383$			250818.i			1.70986i	−0.518743	+	0.854930i	$0.673600\pi$
$384$	−249326.			−1.69085
$385$	−208.661			−0.00140773
$386$		−	127506.i		−	0.855766i
$387$	−18243.2	−	11959.7i	−0.121809	−	0.0798540i
$388$	272326.			1.80895
$389$			34015.7i			0.224792i	0.993664	+	0.112396i	$0.0358524\pi$
$389$			34015.7i			0.224792i	−0.993664	+	0.112396i	$0.964148\pi$
$390$		−	8158.71i		−	0.0536404i
$391$	69347.7			0.453605
$392$			195987.i			1.27543i
$393$	143269.			0.927614
$394$			518802.i			3.34202i
$395$			3529.26i			0.0226199i
$396$	3513.31			0.0224040
$397$	206559.			1.31058			0.655291	−	0.755377i	$-0.272546\pi$
$397$	206559.			1.31058			0.655291	+	0.755377i	$0.272546\pi$
$398$	15130.8			0.0955203
$399$			42120.4i			0.264574i
$400$	80309.1			0.501932
$401$	85162.0			0.529611			0.264806	−	0.964302i	$-0.414692\pi$
$401$	85162.0			0.529611			0.264806	+	0.964302i	$0.414692\pi$
$402$	−310716.			−1.92270
$403$	88106.5			0.542498
$404$	396169.			2.42727
$405$		−	8103.21i		−	0.0494023i
$406$			106412.i			0.645561i
$407$		−	23421.9i		−	0.141395i
$408$	−211306.			−1.26938
$409$			216421.i			1.29375i	0.762594	+	0.646877i	$0.223925\pi$
$409$			216421.i			1.29375i	−0.762594	+	0.646877i	$0.776075\pi$
$410$	16863.6			0.100319
$411$	−15643.3			−0.0926075
$412$	161350.			0.950552
$413$		−	45339.3i		−	0.265812i
$414$			19195.3i			0.111994i
$415$		−	9528.88i		−	0.0553281i
$416$			54294.3i			0.313738i
$417$		−	171941.i		−	0.988795i
$418$	25170.5			0.144059
$419$			195727.i			1.11487i	0.830222	+	0.557433i	$0.188214\pi$
$419$			195727.i			1.11487i	−0.830222	+	0.557433i	$0.811786\pi$
$420$			4965.96i			0.0281517i
$421$		−	216454.i		−	1.22124i	−0.791924	−	0.610620i	$-0.790920\pi$
$421$		−	216454.i		−	1.22124i	0.791924	−	0.610620i	$-0.209080\pi$
$422$	−431560.			−2.42335
$423$	8770.65			0.0490175
$424$			8807.02i			0.0489889i
$425$	−178442.			−0.987915
$426$			165152.i			0.910051i
$427$	44468.4			0.243891
$428$	71093.8			0.388100
$429$			8353.04i			0.0453868i
$430$	−15409.5	−	10102.0i	−0.0833398	−	0.0546348i
$431$	−219971.			−1.18416			−0.592082	−	0.805878i	$-0.701694\pi$
$431$	−219971.			−1.18416			−0.592082	+	0.805878i	$0.701694\pi$
$432$		−	99543.3i		−	0.533390i
$433$			141123.i			0.752699i	0.926478	+	0.376349i	$0.122821\pi$
$433$			141123.i			0.752699i	−0.926478	+	0.376349i	$0.877179\pi$
$434$	−83024.6			−0.440786
$435$		−	14149.7i		−	0.0747770i
$436$	−94451.7			−0.496863
$437$			88829.2i			0.465150i
$438$		−	202341.i		−	1.05472i
$439$	−18660.8			−0.0968279			−0.0484139	−	0.998827i	$-0.515417\pi$
$439$	−18660.8			−0.0968279			−0.0484139	+	0.998827i	$0.515417\pi$
$440$	1340.87			0.00692596
$441$	26080.8			0.134104
$442$			189556.i			0.970268i
$443$	21366.2			0.108873			0.0544366	−	0.998517i	$-0.482664\pi$
$443$	21366.2			0.108873			0.0544366	+	0.998517i	$0.482664\pi$
$444$	−557422.			−2.82760
$445$	4882.15			0.0246542
$446$	359018.			1.80487
$447$	−113564.			−0.568362
$448$		−	79626.7i		−	0.396737i
$449$			101517.i			0.503553i	0.967785	+	0.251777i	$0.0810148\pi$
$449$			101517.i			0.503553i	−0.967785	+	0.251777i	$0.918985\pi$
$450$		−	49392.6i		−	0.243914i
$451$	−17265.3			−0.0848831
$452$		−	428513.i		−	2.09743i
$453$	348313.			1.69736
$454$	−292382.			−1.41853
$455$	2012.84			0.00972269
$456$		−	270668.i		−	1.30169i
$457$		−	308003.i		−	1.47477i	−0.675475	−	0.737383i	$-0.736061\pi$
$457$		−	308003.i		−	1.47477i	0.675475	−	0.737383i	$-0.263939\pi$
$458$		−	451367.i		−	2.15178i
$459$			221179.i			1.04983i
$460$			10472.9i			0.0494938i
$461$	156343.			0.735660			0.367830	−	0.929893i	$-0.380101\pi$
$461$	156343.			0.735660			0.367830	+	0.929893i	$0.380101\pi$
$462$		−	7871.24i		−	0.0368773i
$463$		−	203393.i		−	0.948800i	−0.880309	−	0.474400i	$-0.842665\pi$
$463$		−	203393.i		−	0.948800i	0.880309	−	0.474400i	$-0.157335\pi$
$464$		−	147955.i		−	0.687216i
$465$	11039.9			0.0510573
$466$	515824.			2.37536
$467$		−	208975.i		−	0.958209i	−0.877758	−	0.479104i	$-0.840962\pi$
$467$		−	208975.i		−	0.958209i	0.877758	−	0.479104i	$-0.159038\pi$
$468$	−33891.0			−0.154736
$469$		−	76657.0i		−	0.348503i
$470$	7408.31			0.0335369
$471$	343971.			1.55053
$472$			291353.i			1.30778i
$473$	15776.6	+	10342.6i	0.0705164	+	0.0462282i
$474$	−133133.			−0.592556
$475$		−	228571.i		−	1.01306i
$476$		−	115377.i		−	0.509219i
$477$	1171.98			0.00515092
$478$			179938.i			0.787531i
$479$	98547.6			0.429512			0.214756	−	0.976668i	$-0.431104\pi$
$479$	98547.6			0.429512			0.214756	+	0.976668i	$0.431104\pi$
$480$			6803.16i			0.0295276i
$481$			225938.i			0.976562i
$482$	675212.			2.90634
$483$	27778.3			0.119073
$484$	424309.			1.81130
$485$		−	13830.9i		−	0.0587987i
$486$	−114661.			−0.485448
$487$	−319902.			−1.34884			−0.674418	−	0.738350i	$-0.735605\pi$
$487$	−319902.			−1.34884			−0.674418	+	0.738350i	$0.735605\pi$
$488$	−285756.			−1.19993
$489$	−50838.7			−0.212607
$490$	22029.7			0.0917520
$491$			454263.i			1.88428i	0.335226	+	0.942138i	$0.391187\pi$
$491$			454263.i			1.88428i	−0.335226	+	0.942138i	$0.608813\pi$
$492$			410900.i			1.69749i
$493$			328747.i			1.35260i
$494$	−242806.			−0.994962
$495$		−	178.434i		−	0.000728228i
$496$	115437.			0.469227
$497$	−40744.8			−0.164953
$498$	359454.			1.44939
$499$			336510.i			1.35144i	0.737158	+	0.675720i	$0.236167\pi$
$499$			336510.i			1.35144i	−0.737158	+	0.675720i	$0.763833\pi$
$500$		−	53991.8i		−	0.215967i
$501$		−	291083.i		−	1.15969i
$502$			482237.i			1.91361i
$503$		−	313054.i		−	1.23732i	−0.785658	−	0.618661i	$-0.787675\pi$
$503$		−	313054.i		−	1.23732i	0.785658	−	0.618661i	$-0.212325\pi$
$504$	14429.9			0.0568072
$505$		−	20120.7i		−	0.0788968i
$506$		−	16599.9i		−	0.0648344i
$507$			157016.i			0.610840i
$508$	−788086.			−3.05384
$509$	406043.			1.56724			0.783621	−	0.621239i	$-0.213370\pi$
$509$	406043.			1.56724			0.783621	+	0.621239i	$0.213370\pi$
$510$			23751.6i			0.0913171i
$511$	49919.6			0.191174
$512$			254048.i			0.969114i
$513$	−283314.			−1.07655
$514$	−48856.4			−0.184925
$515$		−	8194.68i		−	0.0308971i
$516$	246145.	−	375469.i	0.924468	−	1.41018i
$517$	−7584.76			−0.0283766
$518$		−	212906.i		−	0.793467i
$519$			38242.7i			0.141976i
$520$	−12934.6			−0.0478351
$521$			221529.i			0.816122i	0.912955	+	0.408061i	$0.133795\pi$
$521$			221529.i			0.816122i	−0.912955	+	0.408061i	$0.866205\pi$
$522$	−90996.8			−0.333953
$523$			146666.i			0.536199i	0.963391	+	0.268099i	$0.0863955\pi$
$523$			146666.i			0.536199i	−0.963391	+	0.268099i	$0.913604\pi$
$524$		−	502692.i		−	1.83080i
$525$	−71477.9			−0.259330
$526$	496359.			1.79401
$527$	−256495.			−0.923545
$528$			10944.2i			0.0392568i
$529$	−221258.			−0.790657
$530$	989.940			0.00352417
$531$	38771.4			0.137506
$532$	147789.			0.522179
$533$	166549.			0.586257
$534$			184168.i			0.645848i
$535$		−	3610.71i		−	0.0126150i
$536$			492601.i			1.71461i
$537$	−218911.			−0.759137
$538$		−	855513.i		−	2.95571i
$539$	−22554.4			−0.0776342
$540$	−33402.5			−0.114549
$541$	38164.1			0.130395			0.0651974	−	0.997872i	$-0.479232\pi$
$541$	38164.1			0.130395			0.0651974	+	0.997872i	$0.479232\pi$
$542$		−	297007.i		−	1.01104i
$543$		−	400411.i		−	1.35802i
$544$		−	158061.i		−	0.534106i
$545$			4797.02i			0.0161502i
$546$			75929.6i			0.254698i
$547$	105758.			0.353459			0.176730	−	0.984259i	$-0.443448\pi$
$547$	105758.			0.353459			0.176730	+	0.984259i	$0.443448\pi$
$548$			54888.3i			0.182776i
$549$			38026.6i			0.126166i
$550$			42714.2i			0.141204i
$551$	−421100.			−1.38702
$552$	−178505.			−0.585831
$553$		−	32845.3i		−	0.107405i
$554$	−209718.			−0.683308
$555$			28310.4i			0.0919094i
$556$	−603293.			−1.95155
$557$	280135.			0.902936			0.451468	−	0.892287i	$-0.350900\pi$
$557$	280135.			0.902936			0.451468	+	0.892287i	$0.350900\pi$
$558$		−	70997.5i		−	0.228021i
$559$	−152188.	−	99769.3i	−0.487031	−	0.319281i
$560$	2637.23			0.00840953
$561$		−	24317.3i		−	0.0772662i
$562$			942541.i			2.98420i
$563$	−403332.			−1.27247			−0.636233	−	0.771497i	$-0.719508\pi$
$563$	−403332.			−1.27247			−0.636233	+	0.771497i	$0.719508\pi$
$564$			180511.i			0.567474i
$565$	−21763.3			−0.0681756
$566$		−	13606.9i		−	0.0424744i
$567$			75413.1i			0.234574i
$568$	261828.			0.811559
$569$	−72865.2			−0.225059			−0.112529	−	0.993648i	$-0.535895\pi$
$569$	−72865.2			−0.225059			−0.112529	+	0.993648i	$0.535895\pi$
$570$	−30424.0			−0.0936411
$571$		−	280074.i		−	0.859015i	−0.903063	−	0.429507i	$-0.858687\pi$
$571$		−	280074.i		−	0.859015i	0.903063	−	0.429507i	$-0.141313\pi$
$572$	29308.6			0.0895782
$573$	−390601.			−1.18966
$574$	−156943.			−0.476340
$575$	−150742.			−0.455931
$576$	68091.8			0.205234
$577$			205999.i			0.618748i	0.950940	+	0.309374i	$0.100119\pi$
$577$			205999.i			0.618748i	−0.950940	+	0.309374i	$0.899881\pi$
$578$			9614.89i			0.0287799i
$579$		−	157789.i		−	0.470673i
$580$	−49647.4			−0.147584
$581$			88681.2i			0.262712i
$582$	521739.			1.54031
$583$	−1013.52			−0.00298191
$584$	−320786.			−0.940566
$585$			1721.26i			0.00502960i
$586$		−	509094.i		−	1.48253i
$587$		−	466185.i		−	1.35295i	−0.736464	−	0.676476i	$-0.763506\pi$
$587$		−	466185.i		−	1.35295i	0.736464	−	0.676476i	$-0.236494\pi$
$588$			536776.i			1.55252i
$589$		−	328551.i		−	0.947049i
$590$	32749.1			0.0940795
$591$			642020.i			1.83812i
$592$			296025.i			0.844666i
$593$			284311.i			0.808507i	0.914647	+	0.404253i	$0.132469\pi$
$593$			284311.i			0.808507i	−0.914647	+	0.404253i	$0.867531\pi$
$594$	52944.3			0.150054
$595$	−5859.76			−0.0165518
$596$			398465.i			1.12175i
$597$	18724.4			0.0525364
$598$			160131.i			0.447787i
$599$	438880.			1.22318			0.611592	−	0.791173i	$-0.290529\pi$
$599$	438880.			1.22318			0.611592	+	0.791173i	$0.290529\pi$
$600$	459320.			1.27589
$601$			52157.2i			0.144399i	0.997390	+	0.0721997i	$0.0230019\pi$
$601$			52157.2i			0.144399i	−0.997390	+	0.0721997i	$0.976998\pi$
$602$	143410.	+	94014.7i	0.395718	+	0.259420i
$603$	65552.3			0.180282
$604$		−	1.22214e6i		−	3.35001i
$605$		−	21549.8i		−	0.0588753i
$606$	759004.			2.06680
$607$		−	328500.i		−	0.891575i	−0.895139	−	0.445788i	$-0.852924\pi$
$607$		−	328500.i		−	0.891575i	0.895139	−	0.445788i	$-0.147076\pi$
$608$	202465.			0.547699
$609$			131685.i			0.355060i
$610$			32120.0i			0.0863209i
$611$	73166.1			0.195987
$612$	98663.1			0.263422
$613$	−194249.			−0.516937			−0.258468	−	0.966020i	$-0.583218\pi$
$613$	−194249.			−0.516937			−0.258468	+	0.966020i	$0.583218\pi$
$614$			1.06775e6i			2.83225i
$615$	20868.8			0.0551757
$616$	−12478.9			−0.0328862
$617$	−203384.			−0.534253			−0.267126	−	0.963662i	$-0.586074\pi$
$617$	−203384.			−0.534253			−0.267126	+	0.963662i	$0.586074\pi$
$618$	309125.			0.809388
$619$	504248.			1.31602			0.658011	−	0.753008i	$-0.271398\pi$
$619$	504248.			1.31602			0.658011	+	0.753008i	$0.271398\pi$
$620$		−	38735.9i		−	0.100770i
$621$			186845.i			0.484506i
$622$			331702.i			0.857369i
$623$	−45436.1			−0.117064
$624$		−	105572.i		−	0.271133i
$625$	386509.			0.989464
$626$	−446024.			−1.13818
$627$	31148.6			0.0792326
$628$		−	1.20690e6i		−	3.06022i
$629$		−	657750.i		−	1.66249i
$630$		−	1621.98i		−	0.00408661i
$631$		−	612948.i		−	1.53945i	−0.638376	−	0.769724i	$-0.720394\pi$
$631$		−	612948.i		−	1.53945i	0.638376	−	0.769724i	$-0.279606\pi$
$632$			211066.i			0.528425i
$633$	−534057.			−1.33285
$634$		−	105656.i		−	0.262855i
$635$			40025.4i			0.0992631i
$636$			24120.9i			0.0596321i
$637$	217570.			0.536191
$638$	78693.0			0.193328
$639$		−	34842.5i		−	0.0853311i
$640$	44430.3			0.108472
$641$			571747.i			1.39151i	0.718277	+	0.695757i	$0.244931\pi$
$641$			571747.i			1.39151i	−0.718277	+	0.695757i	$0.755069\pi$
$642$	136206.			0.330465
$643$	−530650.			−1.28347			−0.641736	−	0.766926i	$-0.721785\pi$
$643$	−530650.			−1.28347			−0.641736	+	0.766926i	$0.721785\pi$
$644$		−	97466.7i		−	0.235009i
$645$	−19069.4	−	12501.2i	−0.0458371	−	0.0300492i
$646$	706856.			1.69382
$647$			481379.i			1.14995i	0.818171	+	0.574975i	$0.194988\pi$
$647$			481379.i			1.14995i	−0.818171	+	0.574975i	$0.805012\pi$
$648$		−	484608.i		−	1.15409i
$649$	−33529.1			−0.0796036
$650$		−	412040.i		−	0.975244i
$651$	−102743.			−0.242433
$652$			178379.i			0.419613i
$653$			293363.i			0.687984i	0.938973	+	0.343992i	$0.111779\pi$
$653$			293363.i			0.687984i	−0.938973	+	0.343992i	$0.888221\pi$
$654$	−180956.			−0.423076
$655$	−25530.8			−0.0595088
$656$	218213.			0.507076
$657$			42688.2i			0.0988956i
$658$	−68945.9			−0.159242
$659$	657906.			1.51493			0.757466	−	0.652875i	$-0.226437\pi$
$659$	657906.			1.51493			0.757466	+	0.652875i	$0.226437\pi$
$660$	3672.40			0.00843068
$661$	−267844.			−0.613026			−0.306513	−	0.951866i	$-0.599162\pi$
$661$	−267844.			−0.613026			−0.306513	+	0.951866i	$0.599162\pi$
$662$	−574432.			−1.31076
$663$			234576.i			0.533650i
$664$		−	569869.i		−	1.29253i
$665$		−	7505.92i		−	0.0169731i
$666$	182064.			0.410465
$667$			277715.i			0.624235i
$668$	−1.02133e6			−2.28883
$669$	444287.			0.992685
$670$	55370.1			0.123346
$671$		−	32885.0i		−	0.0730388i
$672$		−	63314.0i		−	0.140204i
$673$		−	48089.2i		−	0.106174i	−0.998590	−	0.0530869i	$-0.983094\pi$
$673$		−	48089.2i		−	0.106174i	0.998590	−	0.0530869i	$-0.0169060\pi$
$674$			987667.i			2.17416i
$675$		−	480782.i		−	1.05521i
$676$	550926.			1.20559
$677$			84879.3i			0.185193i	0.995704	+	0.0925964i	$0.0295166\pi$
$677$			84879.3i			0.185193i	−0.995704	+	0.0925964i	$0.970483\pi$
$678$		−	820971.i		−	1.78595i
$679$			128718.i			0.279191i
$680$	37655.1			0.0814341
$681$	−361824.			−0.780195
$682$			61397.9i			0.132003i
$683$	−707010.			−1.51560			−0.757799	−	0.652488i	$-0.773725\pi$
$683$	−707010.			−1.51560			−0.757799	+	0.652488i	$0.773725\pi$
$684$			126380.i			0.270126i
$685$	2787.67			0.00594101
$686$	−427693.			−0.908833
$687$		−	558568.i		−	1.18348i
$688$	−199397.	−	130718.i	−0.421252	−	0.276159i
$689$	9776.87			0.0205950
$690$			20064.6i			0.0421436i
$691$			316021.i			0.661851i	0.943657	+	0.330925i	$0.107361\pi$
$691$			316021.i			0.661851i	−0.943657	+	0.330925i	$0.892639\pi$
$692$	134183.			0.280212
$693$			1660.61i			0.00345781i
$694$	−528525.			−1.09735
$695$			30640.1i			0.0634338i
$696$		−	846214.i		−	1.74687i
$697$	−484856.			−0.998039
$698$	−1.11577e6			−2.29014
$699$	638334.			1.30645
$700$			250797.i			0.511830i
$701$	790342.			1.60835			0.804173	−	0.594396i	$-0.202609\pi$
$701$	790342.			1.60835			0.804173	+	0.594396i	$0.202609\pi$
$702$	−510725.			−1.03637
$703$	842529.			1.70480
$704$	−58885.1			−0.118812
$705$	9167.81			0.0184454
$706$		−	356997.i		−	0.716234i
$707$			187254.i			0.374622i
$708$			797965.i			1.59191i
$709$	218246.			0.434165			0.217082	−	0.976153i	$-0.430346\pi$
$709$	218246.			0.434165			0.217082	+	0.976153i	$0.430346\pi$
$710$		−	29430.4i		−	0.0583821i
$711$	28087.3			0.0555611
$712$	291974.			0.575950
$713$	−216679.			−0.426224
$714$		−	221046.i		−	0.433596i
$715$		−	1488.52i		−	0.00291168i
$716$			768101.i			1.49828i
$717$			222674.i			0.433144i
$718$			807350.i			1.56608i
$719$	733807.			1.41946			0.709732	−	0.704472i	$-0.248816\pi$
$719$	733807.			1.41946			0.709732	+	0.704472i	$0.248816\pi$
$720$			2255.19i			0.00435030i
$721$			76264.3i			0.146707i
$722$			29382.3i			0.0563653i
$723$	835578.			1.59849
$724$	−1.40494e6			−2.68027
$725$		−	714603.i		−	1.35953i
$726$	812916.			1.54231
$727$			250259.i			0.473501i	0.971570	+	0.236750i	$0.0760824\pi$
$727$			250259.i			0.473501i	−0.971570	+	0.236750i	$0.923918\pi$
$728$	120377.			0.227133
$729$	−584656.			−1.10013
$730$			36057.5i			0.0676627i
$731$	443048.	+	290448.i	0.829118	+	0.543542i
$732$	−782638.			−1.46062
$733$			610120.i			1.13555i	0.823183	+	0.567776i	$0.192196\pi$
$733$			610120.i			1.13555i	−0.823183	+	0.567776i	$0.807804\pi$
$734$			253441.i			0.470419i
$735$	27261.8			0.0504638
$736$		−	133525.i		−	0.246495i
$737$	−56689.0			−0.104367
$738$		−	134208.i		−	0.246414i
$739$			67964.4i			0.124449i	0.998062	+	0.0622246i	$0.0198195\pi$
$739$			67964.4i			0.124449i	−0.998062	+	0.0622246i	$0.980180\pi$
$740$	99333.5			0.181398
$741$	−300474.			−0.547231
$742$	−9212.95			−0.0167337
$743$		−	707585.i		−	1.28174i	−0.767648	−	0.640871i	$-0.778573\pi$
$743$		−	707585.i		−	1.28174i	0.767648	−	0.640871i	$-0.221427\pi$
$744$	660234.			1.19276
$745$	20237.3			0.0364619
$746$	−936998.			−1.68368
$747$	−75834.7			−0.135902
$748$	−85322.8			−0.152497
$749$			33603.4i			0.0598989i
$750$		−	103441.i		−	0.183895i
$751$			613506.i			1.08778i	0.839158	+	0.543888i	$0.183048\pi$
$751$			613506.i			1.08778i	−0.839158	+	0.543888i	$0.816952\pi$
$752$	95862.4			0.169517
$753$			596770.i			1.05249i
$754$	−759109.			−1.33525
$755$	−62069.9			−0.108890
$756$	310863.			0.543908
$757$			132879.i			0.231880i	0.993256	+	0.115940i	$0.0369881\pi$
$757$			132879.i			0.231880i	−0.993256	+	0.115940i	$0.963012\pi$
$758$			592406.i			1.03105i
$759$		−	20542.5i		−	0.0356590i
$760$			48233.4i			0.0835066i
$761$		−	790123.i		−	1.36435i	−0.731190	−	0.682174i	$-0.761035\pi$
$761$		−	790123.i		−	1.36435i	0.731190	−	0.682174i	$-0.238965\pi$
$762$	−1.50986e6			−2.60032
$763$		−	44643.8i		−	0.0766853i
$764$			1.37051e6i			2.34799i
$765$		−	5010.91i		−	0.00856236i
$766$	1.68605e6			2.87352
$767$	323437.			0.549793
$768$			907821.i			1.53914i
$769$	−204245.			−0.345382			−0.172691	−	0.984976i	$-0.555246\pi$
$769$	−204245.			−0.345382			−0.172691	+	0.984976i	$0.555246\pi$
$770$			1402.67i			0.00236577i
$771$	−60460.0			−0.101709
$772$	−553638.			−0.928948
$773$		−	824077.i		−	1.37914i	−0.724218	−	0.689571i	$-0.757799\pi$
$773$		−	824077.i		−	1.37914i	0.724218	−	0.689571i	$-0.242201\pi$
$774$	−80395.6	+	122635.i	−0.134199	+	0.204707i
$775$	557548.			0.928280
$776$		−	827151.i		−	1.37360i
$777$		−	263473.i		−	0.436409i
$778$	228661.			0.377775
$779$		−	621065.i		−	1.02344i
$780$	−35425.7			−0.0582276
$781$			30131.4i			0.0493989i
$782$		−	466171.i		−	0.762310i
$783$	−885752.			−1.44474
$784$	285061.			0.463772
$785$	−61296.2			−0.0994705
$786$		−	963088.i		−	1.55891i
$787$	347326.			0.560774			0.280387	−	0.959887i	$-0.409537\pi$
$787$	347326.			0.560774			0.280387	+	0.959887i	$0.409537\pi$
$788$	2.25268e6			3.62782
$789$	614246.			0.986708
$790$	23724.5			0.0380140
$791$	202542.			0.323715
$792$		−	10671.2i		−	0.0170122i
$793$			317224.i			0.504452i
$794$		−	1.38854e6i		−	2.20251i
$795$	1225.06			0.00193830
$796$		−	65699.0i		−	0.103689i
$797$	−550267.			−0.866278			−0.433139	−	0.901327i	$-0.642594\pi$
$797$	−550267.			−0.866278			−0.433139	+	0.901327i	$0.642594\pi$
$798$	283143.			0.444631
$799$	−213001.			−0.333647
$800$			343581.i			0.536845i
$801$		−	38854.1i		−	0.0605581i
$802$		−	572479.i		−	0.890042i
$803$		−	36916.3i		−	0.0572515i
$804$			1.34915e6i			2.08713i
$805$	−4950.15			−0.00763882
$806$		−	592273.i		−	0.911699i
$807$		−	1.05870e6i		−	1.62565i
$808$		−	1.20331e6i		−	1.84312i
$809$	−237489.			−0.362866			−0.181433	−	0.983403i	$-0.558074\pi$
$809$	−237489.			−0.362866			−0.181433	+	0.983403i	$0.558074\pi$
$810$	−54471.7			−0.0830234
$811$		−	1.00555e6i		−	1.52884i	−0.644717	−	0.764422i	$-0.723025\pi$
$811$		−	1.00555e6i		−	1.52884i	0.644717	−	0.764422i	$-0.276975\pi$
$812$	462047.			0.700768
$813$		−	367548.i		−	0.556074i
$814$	−157447.			−0.237622
$815$	9059.54			0.0136393
$816$			307342.i			0.461574i
$817$	−372042.	+	567512.i	−0.557375	+	0.850219i
$818$	1.45483e6			2.17423
$819$		−	16019.0i		−	0.0238818i
$820$		−	73223.1i		−	0.108898i
$821$	−259037.			−0.384305			−0.192152	−	0.981365i	$-0.561547\pi$
$821$	−259037.			−0.384305			−0.192152	+	0.981365i	$0.561547\pi$
$822$			105158.i			0.155632i
$823$	−70048.9			−0.103419			−0.0517097	−	0.998662i	$-0.516467\pi$
$823$	−70048.9			−0.103419			−0.0517097	+	0.998662i	$0.516467\pi$
$824$		−	490078.i		−	0.721790i
$825$			52859.0i			0.0776624i
$826$	−304781.			−0.446713
$827$	−771588.			−1.12817			−0.564085	−	0.825717i	$-0.690771\pi$
$827$	−771588.			−1.12817			−0.564085	+	0.825717i	$0.690771\pi$
$828$	83347.5			0.121572
$829$		−	131193.i		−	0.190898i	−0.995434	−	0.0954489i	$-0.969571\pi$
$829$		−	131193.i		−	0.190898i	0.995434	−	0.0954489i	$-0.0304286\pi$
$830$	−64055.3			−0.0929821
$831$	−259527.			−0.375821
$832$	568033.			0.820591
$833$	−633388.			−0.912808
$834$	−1.15582e6			−1.66173
$835$			51871.4i			0.0743970i
$836$		−	109292.i		−	0.156378i
$837$		−	691082.i		−	0.986458i
$838$	1.31572e6			1.87360
$839$			473423.i			0.672552i	0.941764	+	0.336276i	$0.109167\pi$
$839$			473423.i			0.672552i	−0.941764	+	0.336276i	$0.890833\pi$
$840$	15083.4			0.0213767
$841$	−609245.			−0.861390
$842$	−1.45505e6			−2.05236
$843$			1.16640e6i			1.64131i
$844$			1.87386e6i			2.63059i
$845$		−	27980.5i		−	0.0391869i
$846$		−	58958.3i		−	0.0823767i
$847$			200555.i			0.279555i
$848$	12809.7			0.0178134
$849$		−	16838.6i		−	0.0233610i
$850$			1.19953e6i			1.66025i
$851$		−	555647.i		−	0.767255i
$852$	717103.			0.987876
$853$	−535509.			−0.735985			−0.367992	−	0.929829i	$-0.619955\pi$
$853$	−535509.			−0.735985			−0.367992	+	0.929829i	$0.619955\pi$
$854$		−	298927.i		−	0.409873i
$855$	6418.60			0.00878027
$856$		−	215937.i		−	0.294699i
$857$	1.28191e6			1.74540			0.872699	−	0.488258i	$-0.162368\pi$
$857$	1.28191e6			1.74540			0.872699	+	0.488258i	$0.162368\pi$
$858$	56151.1			0.0762752
$859$			683886.i			0.926825i	0.886143	+	0.463412i	$0.153375\pi$
$859$			683886.i			0.926825i	−0.886143	+	0.463412i	$0.846625\pi$
$860$	−43863.5	+	66909.3i	−0.0593070	+	0.0904668i
$861$	−194217.			−0.261988
$862$			1.47870e6i			1.99005i
$863$			423128.i			0.568134i	0.958804	+	0.284067i	$0.0916838\pi$
$863$			423128.i			0.568134i	−0.958804	+	0.284067i	$0.908316\pi$
$864$	425869.			0.570490
$865$		−	6814.91i		−	0.00910810i
$866$	948660.			1.26495
$867$			11898.5i			0.0158290i
$868$			360499.i			0.478480i
$869$	−24289.6			−0.0321648
$870$	−95117.4			−0.125667
$871$	546848.			0.720825
$872$			286883.i			0.377287i
$873$	−110072.			−0.144427
$874$	597130.			0.781711
$875$	25519.9			0.0333321
$876$	−878578.			−1.14491
$877$	543060.			0.706071			0.353036	−	0.935610i	$-0.385149\pi$
$877$	543060.			0.706071			0.353036	+	0.935610i	$0.385149\pi$
$878$			125442.i			0.162725i
$879$		−	630006.i		−	0.815393i
$880$		−	1950.27i		−	0.00251843i
$881$	−747183.			−0.962665			−0.481333	−	0.876538i	$-0.659847\pi$
$881$	−747183.			−0.962665			−0.481333	+	0.876538i	$0.659847\pi$
$882$		−	175321.i		−	0.225370i
$883$	908500.			1.16521			0.582604	−	0.812756i	$-0.302034\pi$
$883$	908500.			1.16521			0.582604	+	0.812756i	$0.302034\pi$
$884$	823063.			1.05324
$885$	40527.1			0.0517439
$886$		−	143629.i		−	0.182968i
$887$		−	283934.i		−	0.360886i	−0.983585	−	0.180443i	$-0.942247\pi$
$887$		−	283934.i		−	0.360886i	0.983585	−	0.180443i	$-0.0577531\pi$
$888$			1.69309e6i			2.14711i
$889$		−	372499.i		−	0.471326i
$890$		−	32819.0i		−	0.0414328i
$891$	55769.1			0.0702487
$892$		−	1.55888e6i		−	1.95922i
$893$		−	272838.i		−	0.342138i
$894$			763402.i			0.955165i
$895$	39010.4			0.0487006
$896$	−413493.			−0.515054
$897$			198162.i			0.246284i
$898$	682420.			0.846250
$899$		−	1.02718e6i		−	1.27095i
$900$	−214466.			−0.264773
$901$	−28462.3			−0.0350607
$902$			116061.i			0.142651i
$903$	177470.	+	116344.i	0.217646	+	0.142681i
$904$	−1.30155e6			−1.59266
$905$			71354.0i			0.0871206i
$906$		−	2.34144e6i		−	2.85251i
$907$	−329783.			−0.400880			−0.200440	−	0.979706i	$-0.564237\pi$
$907$	−329783.			−0.400880			−0.200440	+	0.979706i	$0.564237\pi$
$908$			1.26954e6i			1.53984i
$909$	−160128.			−0.193794
$910$		−	13530.8i		−	0.0163395i
$911$			1.20039e6i			1.44639i	0.690642	+	0.723197i	$0.257328\pi$
$911$			1.20039e6i			1.44639i	−0.690642	+	0.723197i	$0.742672\pi$
$912$	−393682.			−0.473321
$913$	65581.0			0.0786750
$914$	−2.07047e6			−2.47843
$915$			39748.6i			0.0474767i
$916$	−1.95986e6			−2.33580
$917$	237604.			0.282563
$918$	1.48682e6			1.76430
$919$	−775338.			−0.918037			−0.459018	−	0.888427i	$-0.651799\pi$
$919$	−775338.			−0.918037			−0.459018	+	0.888427i	$0.651799\pi$
$920$	31809.9			0.0375826
$921$			1.32134e6i			1.55774i
$922$		−	1.05098e6i		−	1.23632i
$923$		−	290661.i		−	0.341180i
$924$	−34177.5			−0.0400310
$925$			1.42976e6i			1.67102i
$926$	−1.36726e6			−1.59451
$927$	−65216.5			−0.0758924
$928$	632985.			0.735017
$929$			763445.i			0.884599i	0.896867	+	0.442300i	$0.145837\pi$
$929$			763445.i			0.884599i	−0.896867	+	0.442300i	$0.854163\pi$
$930$		−	74212.6i		−	0.0858048i
$931$		−	811322.i		−	0.936039i
$932$		−	2.23974e6i		−	2.57849i
$933$			410483.i			0.471555i
$934$	−1.40478e6			−1.61033
$935$			4333.38i			0.00495683i
$936$			102939.i			0.117497i
$937$			1.72023e6i			1.95932i	0.200654	+	0.979662i	$0.435693\pi$
$937$			1.72023e6i			1.95932i	−0.200654	+	0.979662i	$0.564307\pi$
$938$	−515306.			−0.585679
$939$	−551957.			−0.625999
$940$		−	32167.4i		−	0.0364049i
$941$	657189.			0.742183			0.371092	−	0.928596i	$-0.378984\pi$
$941$	657189.			0.742183			0.371092	+	0.928596i	$0.378984\pi$
$942$		−	2.31225e6i		−	2.60576i
$943$	−409591.			−0.460604
$944$	423768.			0.475537
$945$		−	15788.1i		−	0.0176794i
$946$	69525.3	−	106054.i	0.0776891	−	0.118507i
$947$	−829200.			−0.924612			−0.462306	−	0.886721i	$-0.652978\pi$
$947$	−829200.			−0.924612			−0.462306	+	0.886721i	$0.652978\pi$
$948$			578073.i			0.643230i
$949$			356111.i			0.395415i
$950$	−1.53651e6			−1.70250
$951$		−	130750.i		−	0.144571i
$952$	−350440.			−0.386669
$953$		−	1.33377e6i		−	1.46858i	−0.678838	−	0.734288i	$-0.737516\pi$
$953$		−	1.33377e6i		−	1.46858i	0.678838	−	0.734288i	$-0.262484\pi$
$954$		−	7878.34i		−	0.00865642i
$955$	69605.8			0.0763200
$956$	781305.			0.854879
$957$	97383.0			0.106331
$958$		−	662460.i		−	0.721819i
$959$	−25943.6			−0.0282094
$960$	71175.3			0.0772301
$961$	−122093.			−0.132204
$962$	1.51881e6			1.64117
$963$	−28735.5			−0.0309861
$964$		−	2.93182e6i		−	3.15488i
$965$			28118.2i			0.0301949i
$966$		−	186732.i		−	0.200109i
$967$	788889.			0.843652			0.421826	−	0.906677i	$-0.361389\pi$
$967$	788889.			0.843652			0.421826	+	0.906677i	$0.361389\pi$
$968$		−	1.28878e6i		−	1.37539i
$969$	874738.			0.931602
$970$	−92974.7			−0.0988146
$971$	−1.20251e6			−1.27541			−0.637704	−	0.770282i	$-0.720115\pi$
$971$	−1.20251e6			−1.27541			−0.637704	+	0.770282i	$0.720115\pi$
$972$			497866.i			0.526962i
$973$		−	285154.i		−	0.301199i
$974$			2.15046e6i			2.26680i
$975$		−	509902.i		−	0.536386i
$976$			415628.i			0.436320i
$977$	634645.			0.664878			0.332439	−	0.943125i	$-0.392128\pi$
$977$	634645.			0.664878			0.332439	+	0.943125i	$0.392128\pi$
$978$			341750.i			0.357298i
$979$			33600.7i			0.0350576i
$980$		−	95654.3i		−	0.0995984i
$981$	38176.6			0.0396698
$982$	3.05366e6			3.16663
$983$			1.63591e6i			1.69298i	0.532403	+	0.846491i	$0.321289\pi$
$983$			1.63591e6i			1.69298i	−0.532403	+	0.846491i	$0.678711\pi$
$984$	1.24805e6			1.28897
$985$		−	114409.i		−	0.117920i
$986$	2.20991e6			2.27311
$987$	−85320.9			−0.0875832
$988$			1.05428e6i			1.08005i
$989$	374273.	+	245361.i	0.382645	+	0.250849i
$990$	−1199.48			−0.00122383
$991$			1.20041e6i			1.22231i	0.791510	+	0.611156i	$0.209295\pi$
$991$			1.20041e6i			1.22231i	−0.791510	+	0.611156i	$0.790705\pi$
$992$			493868.i			0.501865i
$993$	−710862.			−0.720920
$994$			273896.i			0.277213i
$995$	−3336.72			−0.00337034
$996$		−	1.56078e6i		−	1.57334i
$997$			1.25293e6i			1.26048i	0.776401	+	0.630239i	$0.217043\pi$
$997$			1.25293e6i			1.26048i	−0.776401	+	0.630239i	$0.782957\pi$
$998$	2.26210e6			2.27117
$999$	1.77219e6			1.77574

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	43.5.b.b.42.2	✓	12
3.2	odd	2		387.5.b.c.343.11		12
4.3	odd	2		688.5.b.d.257.9		12
43.42	odd	2	inner	43.5.b.b.42.11	yes	12
129.128	even	2		387.5.b.c.343.2		12
172.171	even	2		688.5.b.d.257.4		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.5.b.b.42.2	✓	12	1.1	even	1	trivial
43.5.b.b.42.11	yes	12	43.42	odd	2	inner
387.5.b.c.343.2		12	129.128	even	2
387.5.b.c.343.11		12	3.2	odd	2
688.5.b.d.257.4		12	172.171	even	2
688.5.b.d.257.9		12	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 43 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	43.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-6.72223i q^{2} -8.31879i q^{3} -29.1884 q^{4} +1.48242i q^{5} -55.9208 q^{6} -13.7963i q^{7} +88.6554i q^{8} +11.7977 q^{9} +O(q^{10})\)	\(q-6.72223i q^{2} -8.31879i q^{3} -29.1884 q^{4} +1.48242i q^{5} -55.9208 q^{6} -13.7963i q^{7} +88.6554i q^{8} +11.7977 q^{9} +9.96518 q^{10} -10.2025 q^{11} +242.812i q^{12} +98.4183 q^{13} -92.7416 q^{14} +12.3320 q^{15} +128.948 q^{16} -286.515 q^{17} -79.3069i q^{18} -367.004i q^{19} -43.2695i q^{20} -114.768 q^{21} +68.5838i q^{22} -242.039 q^{23} +737.506 q^{24} +622.802 q^{25} -661.591i q^{26} -771.965i q^{27} +402.691i q^{28} -1147.40i q^{29} -82.8983i q^{30} +895.225 q^{31} +551.669i q^{32} +84.8728i q^{33} +1926.02i q^{34} +20.4519 q^{35} -344.356 q^{36} +2295.69i q^{37} -2467.09 q^{38} -818.722i q^{39} -131.425 q^{40} +1692.26 q^{41} +771.498i q^{42} +(-1546.34 - 1013.73i) q^{43} +297.796 q^{44} +17.4892i q^{45} +1627.04i q^{46} +743.419 q^{47} -1072.69i q^{48} +2210.66 q^{49} -4186.62i q^{50} +2383.46i q^{51} -2872.67 q^{52} +99.3399 q^{53} -5189.33 q^{54} -15.1245i q^{55} +1223.11 q^{56} -3053.03 q^{57} -7713.09 q^{58} +3286.35 q^{59} -359.950 q^{60} +3223.22i q^{61} -6017.91i q^{62} -162.764i q^{63} +5771.61 q^{64} +145.898i q^{65} +570.534 q^{66} +5556.36 q^{67} +8362.90 q^{68} +2013.47i q^{69} -137.482i q^{70} -2953.33i q^{71} +1045.93i q^{72} +3618.34i q^{73} +15432.2 q^{74} -5180.96i q^{75} +10712.3i q^{76} +140.757i q^{77} -5503.64 q^{78} +2380.74 q^{79} +191.155i q^{80} -5466.20 q^{81} -11375.7i q^{82} -6427.91 q^{83} +3349.90 q^{84} -424.736i q^{85} +(-6814.51 + 10394.8i) q^{86} -9544.98 q^{87} -904.510i q^{88} -3293.36i q^{89} +117.566 q^{90} -1357.80i q^{91} +7064.72 q^{92} -7447.19i q^{93} -4997.44i q^{94} +544.055 q^{95} +4589.22 q^{96} -9329.95 q^{97} -14860.6i q^{98} -120.367 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 92 q^{4} + 126 q^{6} - 462 q^{9}+O(q^{10}) \) 12 * q - 92 * q^4 + 126 * q^6 - 462 * q^9	\( 12 q - 92 q^{4} + 126 q^{6} - 462 q^{9} + 182 q^{10} - 180 q^{11} - 216 q^{13} + 732 q^{14} - 92 q^{15} + 1076 q^{16} + 678 q^{17} - 2392 q^{21} + 1566 q^{23} - 4234 q^{24} - 174 q^{25} + 5710 q^{31} + 936 q^{35} + 4210 q^{36} + 1242 q^{38} - 2618 q^{40} + 4878 q^{41} - 1108 q^{43} - 15168 q^{44} - 5526 q^{47} - 8544 q^{49} + 24084 q^{52} + 1212 q^{53} - 10004 q^{54} - 10152 q^{56} - 7692 q^{57} - 4666 q^{58} + 14016 q^{59} + 15848 q^{60} - 15580 q^{64} + 29808 q^{66} - 1088 q^{67} + 15186 q^{68} - 7674 q^{74} - 67708 q^{78} + 24302 q^{79} - 23660 q^{81} - 7032 q^{83} + 37180 q^{84} - 14412 q^{86} + 17850 q^{87} + 4268 q^{90} + 48354 q^{92} + 606 q^{95} + 50546 q^{96} - 5842 q^{97} - 25924 q^{99}+O(q^{100}) \) 12 * q - 92 * q^4 + 126 * q^6 - 462 * q^9 + 182 * q^10 - 180 * q^11 - 216 * q^13 + 732 * q^14 - 92 * q^15 + 1076 * q^16 + 678 * q^17 - 2392 * q^21 + 1566 * q^23 - 4234 * q^24 - 174 * q^25 + 5710 * q^31 + 936 * q^35 + 4210 * q^36 + 1242 * q^38 - 2618 * q^40 + 4878 * q^41 - 1108 * q^43 - 15168 * q^44 - 5526 * q^47 - 8544 * q^49 + 24084 * q^52 + 1212 * q^53 - 10004 * q^54 - 10152 * q^56 - 7692 * q^57 - 4666 * q^58 + 14016 * q^59 + 15848 * q^60 - 15580 * q^64 + 29808 * q^66 - 1088 * q^67 + 15186 * q^68 - 7674 * q^74 - 67708 * q^78 + 24302 * q^79 - 23660 * q^81 - 7032 * q^83 + 37180 * q^84 - 14412 * q^86 + 17850 * q^87 + 4268 * q^90 + 48354 * q^92 + 606 * q^95 + 50546 * q^96 - 5842 * q^97 - 25924 * q^99

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