LMFDB - Embedded newform 165.4.c.a.34.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [165,4,Mod(34,165)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(165, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("165.34");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 165 = 3 \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	165.c (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:	$9.73531515095$
Analytic rank:	$0$
Dimension:	$14$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} + 97x^{12} + 3674x^{10} + 68702x^{8} + 656605x^{6} + 2988841x^{4} + 5502384x^{2} + 3385600 $ x^14 + 97x^12 + 3674x^10 + 68702x^8 + 656605x^6 + 2988841x^4 + 5502384x^2 + 3385600
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{4}\cdot 3^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			34.6
Root			$-1.35250i$ of defining polynomial
Character	$\chi$	$=$	165.34
Dual form			165.4.c.a.34.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.35250i q^{2} -3.00000i q^{3} +6.17074 q^{4} +(-4.68011 - 10.1536i) q^{5} -4.05750 q^{6} -5.74924i q^{7} -19.1659i q^{8} -9.00000 q^{9} +O(q^{10})$	\(q-1.35250i q^{2} -3.00000i q^{3} +6.17074 q^{4} +(-4.68011 - 10.1536i) q^{5} -4.05750 q^{6} -5.74924i q^{7} -19.1659i q^{8} -9.00000 q^{9} +(-13.7328 + 6.32986i) q^{10} -11.0000 q^{11} -18.5122i q^{12} +18.0442i q^{13} -7.77585 q^{14} +(-30.4609 + 14.0403i) q^{15} +23.4440 q^{16} -58.2147i q^{17} +12.1725i q^{18} -14.3522 q^{19} +(-28.8798 - 62.6555i) q^{20} -17.2477 q^{21} +14.8775i q^{22} -27.6061i q^{23} -57.4978 q^{24} +(-81.1931 + 95.0404i) q^{25} +24.4048 q^{26} +27.0000i q^{27} -35.4771i q^{28} -88.4751 q^{29} +(18.9896 + 41.1985i) q^{30} -48.3283 q^{31} -185.036i q^{32} +33.0000i q^{33} -78.7355 q^{34} +(-58.3757 + 26.9071i) q^{35} -55.5367 q^{36} +8.79678i q^{37} +19.4113i q^{38} +54.1327 q^{39} +(-194.604 + 89.6988i) q^{40} -53.2829 q^{41} +23.3276i q^{42} -232.057i q^{43} -67.8781 q^{44} +(42.1210 + 91.3828i) q^{45} -37.3373 q^{46} -65.2496i q^{47} -70.3319i q^{48} +309.946 q^{49} +(128.542 + 109.814i) q^{50} -174.644 q^{51} +111.346i q^{52} -205.162i q^{53} +36.5175 q^{54} +(51.4812 + 111.690i) q^{55} -110.190 q^{56} +43.0566i q^{57} +119.663i q^{58} +781.375 q^{59} +(-187.967 + 86.6393i) q^{60} +744.666 q^{61} +65.3641i q^{62} +51.7432i q^{63} -62.7090 q^{64} +(183.215 - 84.4490i) q^{65} +44.6325 q^{66} +603.837i q^{67} -359.228i q^{68} -82.8184 q^{69} +(36.3919 + 78.9533i) q^{70} +771.861 q^{71} +172.493i q^{72} -377.065i q^{73} +11.8977 q^{74} +(285.121 + 243.579i) q^{75} -88.5636 q^{76} +63.2416i q^{77} -73.2145i q^{78} +202.079 q^{79} +(-109.720 - 238.042i) q^{80} +81.0000 q^{81} +72.0652i q^{82} -964.360i q^{83} -106.431 q^{84} +(-591.092 + 272.452i) q^{85} -313.857 q^{86} +265.425i q^{87} +210.825i q^{88} +387.024 q^{89} +(123.595 - 56.9687i) q^{90} +103.741 q^{91} -170.350i q^{92} +144.985i q^{93} -88.2502 q^{94} +(67.1699 + 145.727i) q^{95} -555.107 q^{96} +1221.54i q^{97} -419.203i q^{98} +99.0000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q - 82 q^{4} - 14 q^{5} + 18 q^{6} - 126 q^{9}+O(q^{10}) $ 14 * q - 82 * q^4 - 14 * q^5 + 18 * q^6 - 126 * q^9	$ 14 q - 82 q^{4} - 14 q^{5} + 18 q^{6} - 126 q^{9} - 28 q^{10} - 154 q^{11} - 284 q^{14} + 362 q^{16} - 52 q^{19} + 226 q^{20} + 300 q^{21} - 126 q^{24} - 366 q^{25} + 952 q^{26} - 1144 q^{29} - 582 q^{30} - 280 q^{31} + 1612 q^{34} - 600 q^{35} + 738 q^{36} - 144 q^{39} + 176 q^{40} + 1792 q^{41} + 902 q^{44} + 126 q^{45} - 688 q^{46} - 590 q^{49} + 388 q^{50} + 228 q^{51} - 162 q^{54} + 154 q^{55} + 3044 q^{56} - 2632 q^{59} - 1140 q^{60} - 772 q^{61} - 1738 q^{64} - 904 q^{65} - 198 q^{66} - 1368 q^{69} + 84 q^{70} + 1608 q^{71} + 1496 q^{74} - 300 q^{75} - 3396 q^{76} + 748 q^{79} - 2606 q^{80} + 1134 q^{81} - 5040 q^{84} + 2508 q^{85} - 5068 q^{86} - 1388 q^{89} + 252 q^{90} - 6752 q^{91} + 5840 q^{94} + 1724 q^{95} + 5946 q^{96} + 1386 q^{99}+O(q^{100}) $ 14 * q - 82 * q^4 - 14 * q^5 + 18 * q^6 - 126 * q^9 - 28 * q^10 - 154 * q^11 - 284 * q^14 + 362 * q^16 - 52 * q^19 + 226 * q^20 + 300 * q^21 - 126 * q^24 - 366 * q^25 + 952 * q^26 - 1144 * q^29 - 582 * q^30 - 280 * q^31 + 1612 * q^34 - 600 * q^35 + 738 * q^36 - 144 * q^39 + 176 * q^40 + 1792 * q^41 + 902 * q^44 + 126 * q^45 - 688 * q^46 - 590 * q^49 + 388 * q^50 + 228 * q^51 - 162 * q^54 + 154 * q^55 + 3044 * q^56 - 2632 * q^59 - 1140 * q^60 - 772 * q^61 - 1738 * q^64 - 904 * q^65 - 198 * q^66 - 1368 * q^69 + 84 * q^70 + 1608 * q^71 + 1496 * q^74 - 300 * q^75 - 3396 * q^76 + 748 * q^79 - 2606 * q^80 + 1134 * q^81 - 5040 * q^84 + 2508 * q^85 - 5068 * q^86 - 1388 * q^89 + 252 * q^90 - 6752 * q^91 + 5840 * q^94 + 1724 * q^95 + 5946 * q^96 + 1386 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/165\mathbb{Z}\right)^\times$.

$n$	$46$	$56$	$67$
$\chi(n)$	$1$	$1$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		−	1.35250i		−	0.478181i	−0.970997	−	0.239091i	$-0.923151\pi$
$2$		−	1.35250i		−	0.478181i	0.970997	−	0.239091i	$-0.0768493\pi$
$3$		−	3.00000i		−	0.577350i
$3$		−	3.00000i		−	0.577350i
$4$	6.17074			0.771343
$5$	−4.68011	−	10.1536i	−0.418602	−	0.908170i
$5$	−4.68011	−	10.1536i	−0.418602	−	0.908170i
$6$	−4.05750			−0.276078
$7$		−	5.74924i		−	0.310430i	−0.987881	−	0.155215i	$-0.950393\pi$
$7$		−	5.74924i		−	0.310430i	0.987881	−	0.155215i	$-0.0496070\pi$
$8$		−	19.1659i		−	0.847023i
$9$	−9.00000			−0.333333
$10$	−13.7328	+	6.32986i	−0.434270	+	0.200168i
$11$	−11.0000			−0.301511
$11$	−11.0000			−0.301511
$12$		−	18.5122i		−	0.445335i
$13$			18.0442i			0.384967i	0.981300	+	0.192483i	$0.0616542\pi$
$13$			18.0442i			0.384967i	−0.981300	+	0.192483i	$0.938346\pi$
$14$	−7.77585			−0.148442
$15$	−30.4609	+	14.0403i	−0.524332	+	0.241680i
$16$	23.4440			0.366312
$17$		−	58.2147i		−	0.830538i	−0.909699	−	0.415269i	$-0.863687\pi$
$17$		−	58.2147i		−	0.830538i	0.909699	−	0.415269i	$-0.136313\pi$
$18$			12.1725i			0.159394i
$19$	−14.3522			−0.173296			−0.0866478	−	0.996239i	$-0.527615\pi$
$19$	−14.3522			−0.173296			−0.0866478	+	0.996239i	$0.527615\pi$
$20$	−28.8798	−	62.6555i	−0.322886	−	0.700510i
$21$	−17.2477			−0.179227
$22$			14.8775i			0.144177i
$23$		−	27.6061i		−	0.250273i	−0.992140	−	0.125137i	$-0.960063\pi$
$23$		−	27.6061i		−	0.250273i	0.992140	−	0.125137i	$-0.0399369\pi$
$24$	−57.4978			−0.489029
$25$	−81.1931	+	95.0404i	−0.649545	+	0.760323i
$26$	24.4048			0.184084
$27$			27.0000i			0.192450i
$28$		−	35.4771i		−	0.239448i
$29$	−88.4751			−0.566531			−0.283266	−	0.959041i	$-0.591418\pi$
$29$	−88.4751			−0.566531			−0.283266	+	0.959041i	$0.591418\pi$
$30$	18.9896	+	41.1985i	0.115567	+	0.250726i
$31$	−48.3283			−0.280001			−0.140000	−	0.990151i	$-0.544710\pi$
$31$	−48.3283			−0.280001			−0.140000	+	0.990151i	$0.544710\pi$
$32$		−	185.036i		−	1.02219i
$33$			33.0000i			0.174078i
$34$	−78.7355			−0.397148
$35$	−58.3757	+	26.9071i	−0.281923	+	0.129947i
$36$	−55.5367			−0.257114
$37$			8.79678i			0.0390860i	0.999809	+	0.0195430i	$0.00622112\pi$
$37$			8.79678i			0.0390860i	−0.999809	+	0.0195430i	$0.993779\pi$
$38$			19.4113i			0.0828667i
$39$	54.1327			0.222261
$40$	−194.604	+	89.6988i	−0.769241	+	0.354566i
$41$	−53.2829			−0.202961			−0.101480	−	0.994838i	$-0.532358\pi$
$41$	−53.2829			−0.202961			−0.101480	+	0.994838i	$0.532358\pi$
$42$			23.3276i			0.0857029i
$43$		−	232.057i		−	0.822985i	−0.911413	−	0.411492i	$-0.865008\pi$
$43$		−	232.057i		−	0.822985i	0.911413	−	0.411492i	$-0.134992\pi$
$44$	−67.8781			−0.232569
$45$	42.1210	+	91.3828i	0.139534	+	0.302723i
$46$	−37.3373			−0.119676
$47$		−	65.2496i		−	0.202503i	−0.994861	−	0.101251i	$-0.967715\pi$
$47$		−	65.2496i		−	0.202503i	0.994861	−	0.101251i	$-0.0322847\pi$
$48$		−	70.3319i		−	0.211490i
$49$	309.946			0.903633
$50$	128.542	+	109.814i	0.363573	+	0.310600i
$51$	−174.644			−0.479511
$52$			111.346i			0.296941i
$53$		−	205.162i		−	0.531721i	−0.964012	−	0.265860i	$-0.914344\pi$
$53$		−	205.162i		−	0.531721i	0.964012	−	0.265860i	$-0.0856560\pi$
$54$	36.5175			0.0920260
$55$	51.4812	+	111.690i	0.126213	+	0.273823i
$56$	−110.190			−0.262941
$57$			43.0566i			0.100052i
$58$			119.663i			0.270905i
$59$	781.375			1.72418			0.862088	−	0.506759i	$-0.169157\pi$
$59$	781.375			1.72418			0.862088	+	0.506759i	$0.169157\pi$
$60$	−187.967	+	86.6393i	−0.404440	+	0.186418i
$61$	744.666			1.56303			0.781514	−	0.623887i	$-0.214448\pi$
$61$	744.666			1.56303			0.781514	+	0.623887i	$0.214448\pi$
$62$			65.3641i			0.133891i
$63$			51.7432i			0.103477i
$64$	−62.7090			−0.122479
$65$	183.215	−	84.4490i	0.349615	−	0.161148i
$66$	44.6325			0.0832407
$67$			603.837i			1.10105i	0.834818	+	0.550525i	$0.185573\pi$
$67$			603.837i			1.10105i	−0.834818	+	0.550525i	$0.814427\pi$
$68$		−	359.228i		−	0.640629i
$69$	−82.8184			−0.144495
$70$	36.3919	+	78.9533i	0.0621380	+	0.134810i
$71$	771.861			1.29018			0.645092	−	0.764105i	$-0.276819\pi$
$71$	771.861			1.29018			0.645092	+	0.764105i	$0.276819\pi$
$72$			172.493i			0.282341i
$73$		−	377.065i		−	0.604549i	−0.953221	−	0.302275i	$-0.902254\pi$
$73$		−	377.065i		−	0.604549i	0.953221	−	0.302275i	$-0.0977460\pi$
$74$	11.8977			0.0186902
$75$	285.121	+	243.579i	0.438973	+	0.375015i
$76$	−88.5636			−0.133670
$77$			63.2416i			0.0935981i
$78$		−	73.2145i		−	0.106281i
$79$	202.079			0.287793			0.143897	−	0.989593i	$-0.454037\pi$
$79$	202.079			0.287793			0.143897	+	0.989593i	$0.454037\pi$
$80$	−109.720	−	238.042i	−0.153339	−	0.332673i
$81$	81.0000			0.111111
$82$			72.0652i			0.0970520i
$83$		−	964.360i		−	1.27533i	−0.770314	−	0.637664i	$-0.779901\pi$
$83$		−	964.360i		−	1.27533i	0.770314	−	0.637664i	$-0.220099\pi$
$84$	−106.431			−0.138245
$85$	−591.092	+	272.452i	−0.754269	+	0.347665i
$86$	−313.857			−0.393536
$87$			265.425i			0.327087i
$88$			210.825i			0.255387i
$89$	387.024			0.460949			0.230474	−	0.973078i	$-0.425972\pi$
$89$	387.024			0.460949			0.230474	+	0.973078i	$0.425972\pi$
$90$	123.595	−	56.9687i	0.144757	−	0.0667226i
$91$	103.741			0.119505
$92$		−	170.350i		−	0.193046i
$93$			144.985i			0.161659i
$94$	−88.2502			−0.0968331
$95$	67.1699	+	145.727i	0.0725419	+	0.157382i
$96$	−555.107			−0.590160
$97$			1221.54i			1.27864i	0.768939	+	0.639322i	$0.220785\pi$
$97$			1221.54i			1.27864i	−0.768939	+	0.639322i	$0.779215\pi$
$98$		−	419.203i		−	0.432101i
$99$	99.0000			0.100504
$100$	−501.021	+	586.470i	−0.501021	+	0.586470i
$101$	359.145			0.353824			0.176912	−	0.984227i	$-0.443389\pi$
$101$	359.145			0.353824			0.176912	+	0.984227i	$0.443389\pi$
$102$			236.206i			0.229293i
$103$		−	139.352i		−	0.133308i	−0.997776	−	0.0666540i	$-0.978768\pi$
$103$		−	139.352i		−	0.133308i	0.997776	−	0.0666540i	$-0.0212324\pi$
$104$	345.835			0.326076
$105$	80.7213	+	175.127i	0.0750247	+	0.162768i
$106$	−277.482			−0.254259
$107$			1363.52i			1.23193i	0.787772	+	0.615967i	$0.211234\pi$
$107$			1363.52i			1.23193i	−0.787772	+	0.615967i	$0.788766\pi$
$108$			166.610i			0.148445i
$109$	380.307			0.334190			0.167095	−	0.985941i	$-0.446561\pi$
$109$	380.307			0.334190			0.167095	+	0.985941i	$0.446561\pi$
$110$	151.061	−	69.6284i	0.130937	−	0.0603528i
$111$	26.3903			0.0225663
$112$		−	134.785i		−	0.113714i
$113$		−	1835.55i		−	1.52809i	−0.645164	−	0.764044i	$-0.723211\pi$
$113$		−	1835.55i		−	1.52809i	0.645164	−	0.764044i	$-0.276789\pi$
$114$	58.2340			0.0478431
$115$	−280.303	+	129.200i	−0.227290	+	0.104765i
$116$	−545.957			−0.436990
$117$		−	162.398i		−	0.128322i
$118$		−	1056.81i		−	0.824468i
$119$	−334.690			−0.257824
$120$	269.096	+	583.813i	0.204709	+	0.444121i
$121$	121.000			0.0909091
$122$		−	1007.16i		−	0.747411i
$123$			159.849i			0.117179i
$124$	−298.222			−0.215977
$125$	1345.00	+	379.606i	0.962404	+	0.271624i
$126$	69.9827			0.0494806
$127$		−	1122.91i		−	0.784583i	−0.919841	−	0.392291i	$-0.871682\pi$
$127$		−	1122.91i		−	0.784583i	0.919841	−	0.392291i	$-0.128318\pi$
$128$		−	1395.47i		−	0.963620i
$129$	−696.171			−0.475150
$130$	−114.217	−	247.798i	−0.0770579	−	0.167179i
$131$	−871.398			−0.581179			−0.290589	−	0.956848i	$-0.593851\pi$
$131$	−871.398			−0.581179			−0.290589	+	0.956848i	$0.593851\pi$
$132$			203.634i			0.134274i
$133$			82.5142i			0.0537961i
$134$	816.690			0.526502
$135$	274.148	−	126.363i	0.174777	−	0.0805600i
$136$	−1115.74			−0.703485
$137$			2034.32i			1.26864i	0.773070	+	0.634321i	$0.218720\pi$
$137$			2034.32i			1.26864i	−0.773070	+	0.634321i	$0.781280\pi$
$138$			112.012i			0.0690949i
$139$	−529.625			−0.323181			−0.161591	−	0.986858i	$-0.551662\pi$
$139$	−529.625			−0.323181			−0.161591	+	0.986858i	$0.551662\pi$
$140$	−360.222	+	166.037i	−0.217459	+	0.100233i
$141$	−195.749			−0.116915
$142$		−	1043.94i		−	0.616942i
$143$		−	198.487i		−	0.116072i
$144$	−210.996			−0.122104
$145$	414.073	+	898.345i	0.237151	+	0.514507i
$146$	−509.981			−0.289084
$147$		−	929.839i		−	0.521713i
$148$			54.2826i			0.0301487i
$149$	−3116.95			−1.71376			−0.856882	−	0.515513i	$-0.827601\pi$
$149$	−3116.95			−1.71376			−0.856882	+	0.515513i	$0.827601\pi$
$150$	329.441	−	385.627i	0.179325	−	0.209909i
$151$	−3229.83			−1.74066			−0.870331	−	0.492468i	$-0.836095\pi$
$151$	−3229.83			−1.74066			−0.870331	+	0.492468i	$0.836095\pi$
$152$			275.073i			0.146785i
$153$			523.933i			0.276846i
$154$	85.5344			0.0447569
$155$	226.182	+	490.709i	0.117209	+	0.254288i
$156$	334.039			0.171439
$157$		−	824.011i		−	0.418874i	−0.977822	−	0.209437i	$-0.932837\pi$
$157$		−	824.011i		−	0.418874i	0.977822	−	0.209437i	$-0.0671632\pi$
$158$		−	273.312i		−	0.137617i
$159$	−615.487			−0.306989
$160$	−1878.79	+	865.987i	−0.928319	+	0.427889i
$161$	−158.714			−0.0776922
$162$		−	109.553i		−	0.0531313i
$163$		−	2372.29i		−	1.13995i	−0.821661	−	0.569976i	$-0.806952\pi$
$163$		−	2372.29i		−	1.13995i	0.821661	−	0.569976i	$-0.193048\pi$
$164$	−328.795			−0.156552
$165$	335.070	−	154.444i	0.158092	−	0.0728693i
$166$	−1304.30			−0.609838
$167$			2370.18i			1.09826i	0.835736	+	0.549132i	$0.185041\pi$
$167$			2370.18i			1.09826i	−0.835736	+	0.549132i	$0.814959\pi$
$168$			330.569i			0.151809i
$169$	1871.41			0.851801
$170$	368.491	+	799.452i	0.166247	+	0.360678i
$171$	129.170			0.0577652
$172$		−	1431.96i		−	0.634803i
$173$			922.707i			0.405503i	0.979230	+	0.202752i	$0.0649884\pi$
$173$			922.707i			0.405503i	−0.979230	+	0.202752i	$0.935012\pi$
$174$	358.988			0.156407
$175$	546.410	+	466.798i	0.236027	+	0.201638i
$176$	−257.884			−0.110447
$177$		−	2344.12i		−	0.995453i
$178$		−	523.450i		−	0.220417i
$179$	−3707.07			−1.54793			−0.773965	−	0.633229i	$-0.781729\pi$
$179$	−3707.07			−1.54793			−0.773965	+	0.633229i	$0.781729\pi$
$180$	259.918	+	563.900i	0.107629	+	0.233503i
$181$	4141.79			1.70087			0.850433	−	0.526083i	$-0.176340\pi$
$181$	4141.79			1.70087			0.850433	+	0.526083i	$0.176340\pi$
$182$		−	140.309i		−	0.0571451i
$183$		−	2234.00i		−	0.902415i
$184$	−529.098			−0.211987
$185$	89.3194	−	41.1699i	0.0354967	−	0.0163615i
$186$	196.092			0.0773021
$187$			640.362i			0.250417i
$188$		−	402.639i		−	0.156199i
$189$	155.229			0.0597422
$190$	197.096	−	90.8473i	0.0752571	−	0.0346882i
$191$	615.308			0.233100			0.116550	−	0.993185i	$-0.462816\pi$
$191$	615.308			0.233100			0.116550	+	0.993185i	$0.462816\pi$
$192$			188.127i			0.0707130i
$193$		−	1244.98i		−	0.464329i	−0.972677	−	0.232164i	$-0.925419\pi$
$193$		−	1244.98i		−	0.464329i	0.972677	−	0.232164i	$-0.0745807\pi$
$194$	1652.13			0.611423
$195$	−253.347	−	549.644i	−0.0930388	−	0.201850i
$196$	1912.60			0.697011
$197$			783.123i			0.283224i	0.989922	+	0.141612i	$0.0452286\pi$
$197$			783.123i			0.283224i	−0.989922	+	0.141612i	$0.954771\pi$
$198$		−	133.898i		−	0.0480590i
$199$	1103.87			0.393221			0.196610	−	0.980482i	$-0.437007\pi$
$199$	1103.87			0.393221			0.196610	+	0.980482i	$0.437007\pi$
$200$	1821.54	+	1556.14i	0.644011	+	0.550179i
$201$	1811.51			0.635692
$202$		−	485.744i		−	0.169192i
$203$			508.664i			0.175868i
$204$	−1077.68			−0.369868
$205$	249.370	+	541.016i	0.0849598	+	0.184323i
$206$	−188.473			−0.0637454
$207$			248.455i			0.0834243i
$208$			423.028i			0.141018i
$209$	157.874			0.0522506
$210$	236.860	−	109.176i	0.0778328	−	0.0358754i
$211$	4359.07			1.42223			0.711115	−	0.703075i	$-0.248190\pi$
$211$	4359.07			1.42223			0.711115	+	0.703075i	$0.248190\pi$
$212$		−	1266.00i		−	0.410139i
$213$		−	2315.58i		−	0.744888i
$214$	1844.17			0.589087
$215$	−2356.22	+	1086.05i	−0.747410	+	0.344503i
$216$	517.480			0.163010
$217$			277.851i			0.0869206i
$218$		−	514.365i		−	0.159804i
$219$	−1131.19			−0.349037
$220$	317.677	+	689.211i	0.0973537	+	0.211212i
$221$	1050.44			0.319730
$222$		−	35.6930i		−	0.0107908i
$223$			2309.64i			0.693564i	0.937946	+	0.346782i	$0.112726\pi$
$223$			2309.64i			0.693564i	−0.937946	+	0.346782i	$0.887274\pi$
$224$	−1063.81			−0.317317
$225$	730.738	−	855.364i	0.216515	−	0.253441i
$226$	−2482.58			−0.730703
$227$			3615.89i			1.05725i	0.848857	+	0.528623i	$0.177292\pi$
$227$			3615.89i			1.05725i	−0.848857	+	0.528623i	$0.822708\pi$
$228$			265.691i			0.0771746i
$229$	4794.63			1.38357			0.691786	−	0.722103i	$-0.256824\pi$
$229$	4794.63			1.38357			0.691786	+	0.722103i	$0.256824\pi$
$230$	174.743	+	379.110i	0.0500966	+	0.108686i
$231$	189.725			0.0540389
$232$			1695.71i			0.479865i
$233$			4221.43i			1.18693i	0.804859	+	0.593466i	$0.202241\pi$
$233$			4221.43i			1.18693i	−0.804859	+	0.593466i	$0.797759\pi$
$234$	−219.644			−0.0613613
$235$	−662.522	+	305.376i	−0.183907	+	0.0847681i
$236$	4821.66			1.32993
$237$		−	606.237i		−	0.166157i
$238$			452.669i			0.123286i
$239$	−6991.16			−1.89214			−0.946068	−	0.323968i	$-0.894983\pi$
$239$	−6991.16			−1.89214			−0.946068	+	0.323968i	$0.894983\pi$
$240$	−714.125	+	329.161i	−0.192069	+	0.0885303i
$241$	476.330			0.127316			0.0636579	−	0.997972i	$-0.479723\pi$
$241$	476.330			0.127316			0.0636579	+	0.997972i	$0.479723\pi$
$242$		−	163.653i		−	0.0434710i
$243$		−	243.000i		−	0.0641500i
$244$	4595.14			1.20563
$245$	−1450.58	−	3147.08i	−0.378263	−	0.820652i
$246$	216.195			0.0560330
$247$		−	258.974i		−	0.0667131i
$248$			926.258i			0.237167i
$249$	−2893.08			−0.736311
$250$	513.417	−	1819.11i	0.129885	−	0.460203i
$251$	898.921			0.226053			0.113027	−	0.993592i	$-0.463945\pi$
$251$	898.921			0.226053			0.113027	+	0.993592i	$0.463945\pi$
$252$			319.294i			0.0798159i
$253$			303.668i			0.0754602i
$254$	−1518.74			−0.375173
$255$	817.355	+	1773.28i	0.200724	+	0.435478i
$256$	−2389.05			−0.583264
$257$			1352.73i			0.328332i	0.986433	+	0.164166i	$0.0524932\pi$
$257$			1352.73i			0.328332i	−0.986433	+	0.164166i	$0.947507\pi$
$258$			941.572i			0.227208i
$259$	50.5748			0.0121335
$260$	1130.57	−	521.113i	0.269673	−	0.124300i
$261$	796.276			0.188844
$262$			1178.57i			0.277909i
$263$			5102.31i			1.19628i	0.801391	+	0.598141i	$0.204094\pi$
$263$			5102.31i			1.19628i	−0.801391	+	0.598141i	$0.795906\pi$
$264$	632.476			0.147448
$265$	−2083.15	+	960.183i	−0.482893	+	0.222579i
$266$	111.600			0.0257243
$267$		−	1161.07i		−	0.266129i
$268$			3726.12i			0.849287i
$269$	2195.98			0.497737			0.248868	−	0.968537i	$-0.419941\pi$
$269$	2195.98			0.497737			0.248868	+	0.968537i	$0.419941\pi$
$270$	−170.906	−	370.786i	−0.0385223	−	0.0835753i
$271$	−7477.46			−1.67610			−0.838050	−	0.545593i	$-0.816304\pi$
$271$	−7477.46			−1.67610			−0.838050	+	0.545593i	$0.816304\pi$
$272$		−	1364.78i		−	0.304236i
$273$		−	311.222i		−	0.0689963i
$274$	2751.42			0.606641
$275$	893.124	−	1045.44i	0.195845	−	0.229246i
$276$	−511.051			−0.111455
$277$			582.644i			0.126381i	0.998001	+	0.0631907i	$0.0201276\pi$
$277$			582.644i			0.126381i	−0.998001	+	0.0631907i	$0.979872\pi$
$278$			716.318i			0.154539i
$279$	434.955			0.0933336
$280$	515.700	+	1118.83i	0.110068	+	0.238795i
$281$	3765.20			0.799335			0.399667	−	0.916660i	$-0.369126\pi$
$281$	3765.20			0.799335			0.399667	+	0.916660i	$0.369126\pi$
$282$			264.751i			0.0559066i
$283$		−	7994.86i		−	1.67931i	−0.543119	−	0.839656i	$-0.682757\pi$
$283$		−	7994.86i		−	1.67931i	0.543119	−	0.839656i	$-0.317243\pi$
$284$	4762.95			0.995173
$285$	437.181	−	201.510i	0.0908645	−	0.0418821i
$286$	−268.453			−0.0555034
$287$			306.336i			0.0630050i
$288$			1665.32i			0.340729i
$289$	1524.05			0.310207
$290$	1215.01	−	560.035i	0.246028	−	0.113401i
$291$	3664.61			0.738225
$292$		−	2326.77i		−	0.466315i
$293$			482.037i			0.0961123i	0.998845	+	0.0480562i	$0.0153026\pi$
$293$			482.037i			0.0961123i	−0.998845	+	0.0480562i	$0.984697\pi$
$294$	−1257.61			−0.249473
$295$	−3656.92	−	7933.80i	−0.721743	−	1.56584i
$296$	168.599			0.0331067
$297$		−	297.000i		−	0.0580259i
$298$			4215.68i			0.819490i
$299$	498.132			0.0963468
$300$	1759.41	+	1503.06i	0.338599	+	0.289265i
$301$	−1334.15			−0.255479
$302$			4368.35i			0.832352i
$303$		−	1077.44i		−	0.204281i
$304$	−336.472			−0.0634803
$305$	−3485.12	−	7561.08i	−0.654287	−	1.41950i
$306$	708.619			0.132383
$307$		−	6400.49i		−	1.18989i	−0.803768	−	0.594943i	$-0.797175\pi$
$307$		−	6400.49i		−	1.18989i	0.803768	−	0.594943i	$-0.202825\pi$
$308$			390.248i			0.0721962i
$309$	−418.055			−0.0769654
$310$	663.684	−	305.912i	0.121596	−	0.0560471i
$311$	−5822.47			−1.06161			−0.530807	−	0.847493i	$-0.678111\pi$
$311$	−5822.47			−1.06161			−0.530807	+	0.847493i	$0.678111\pi$
$312$		−	1037.50i		−	0.188260i
$313$			1921.09i			0.346921i	0.984841	+	0.173461i	$0.0554949\pi$
$313$			1921.09i			0.346921i	−0.984841	+	0.173461i	$0.944505\pi$
$314$	−1114.48			−0.200298
$315$	525.382	−	242.164i	0.0939743	−	0.0433155i
$316$	1246.98			0.221987
$317$			6357.42i			1.12640i	0.826321	+	0.563200i	$0.190430\pi$
$317$			6357.42i			1.12640i	−0.826321	+	0.563200i	$0.809570\pi$
$318$			832.447i			0.146797i
$319$	973.226			0.170816
$320$	293.485	+	636.725i	0.0512698	+	0.111231i
$321$	4090.57			0.711257
$322$			214.661i			0.0371510i
$323$			835.509i			0.143929i
$324$	499.830			0.0857047
$325$	−1714.93	−	1465.07i	−0.292699	−	0.250053i
$326$	−3208.53			−0.545104
$327$		−	1140.92i		−	0.192945i
$328$			1021.22i			0.171912i
$329$	−375.136			−0.0628629
$330$	−208.885	−	453.183i	−0.0348447	−	0.0755967i
$331$	−10068.3			−1.67191			−0.835957	−	0.548795i	$-0.815087\pi$
$331$	−10068.3			−1.67191			−0.835957	+	0.548795i	$0.815087\pi$
$332$		−	5950.82i		−	0.983715i
$333$		−	79.1710i		−	0.0130287i
$334$	3205.67			0.525169
$335$	6131.14	−	2826.02i	0.999941	−	0.460902i
$336$	−404.355			−0.0656529
$337$		−	3795.60i		−	0.613529i	−0.951785	−	0.306765i	$-0.900754\pi$
$337$		−	3795.60i		−	0.613529i	0.951785	−	0.306765i	$-0.0992465\pi$
$338$		−	2531.08i		−	0.407315i
$339$	−5506.65			−0.882242
$340$	−3647.47	+	1681.23i	−0.581800	+	0.268169i
$341$	531.612			0.0844234
$342$		−	174.702i		−	0.0276222i
$343$		−	3753.94i		−	0.590944i
$344$	−4447.59			−0.697087
$345$	387.600	+	840.909i	0.0604860	+	0.131226i
$346$	1247.96			0.193904
$347$		−	6852.81i		−	1.06017i	−0.847945	−	0.530084i	$-0.822160\pi$
$347$		−	6852.81i		−	1.06017i	0.847945	−	0.530084i	$-0.177840\pi$
$348$			1637.87i			0.252296i
$349$	1322.51			0.202843			0.101421	−	0.994844i	$-0.467661\pi$
$349$	1322.51			0.202843			0.101421	+	0.994844i	$0.467661\pi$
$350$	631.345	−	739.020i	0.0964195	−	0.112864i
$351$	−487.194			−0.0740869
$352$			2035.39i			0.308201i
$353$			3094.70i			0.466612i	0.972403	+	0.233306i	$0.0749544\pi$
$353$			3094.70i			0.466612i	−0.972403	+	0.233306i	$0.925046\pi$
$354$	−3170.43			−0.476007
$355$	−3612.40	−	7837.20i	−0.540073	−	1.17171i
$356$	2388.22			0.355550
$357$			1004.07i			0.148855i
$358$			5013.82i			0.740191i
$359$	−13000.6			−1.91127			−0.955635	−	0.294555i	$-0.904829\pi$
$359$	−13000.6			−1.91127			−0.955635	+	0.294555i	$0.904829\pi$
$360$	1751.44	−	807.289i	0.256414	−	0.118189i
$361$	−6653.01			−0.969969
$362$		−	5601.77i		−	0.813322i
$363$		−	363.000i		−	0.0524864i
$364$	640.156			0.0921794
$365$	−3828.58	+	1764.71i	−0.549034	+	0.253066i
$366$	−3021.49			−0.431518
$367$			11082.4i			1.57629i	0.615492	+	0.788143i	$0.288957\pi$
$367$			11082.4i			1.57629i	−0.615492	+	0.788143i	$0.711043\pi$
$368$		−	647.198i		−	0.0916780i
$369$	479.546			0.0676536
$370$	−55.6824	−	120.805i	−0.00782375	−	0.0169739i
$371$	−1179.53			−0.165062
$372$			894.665i			0.124694i
$373$			2349.02i			0.326080i	0.986619	+	0.163040i	$0.0521300\pi$
$373$			2349.02i			0.326080i	−0.986619	+	0.163040i	$0.947870\pi$
$374$	866.090			0.119745
$375$	1138.82	−	4035.00i	0.156822	−	0.555644i
$376$	−1250.57			−0.171525
$377$		−	1596.46i		−	0.218096i
$378$		−	209.948i		−	0.0285676i
$379$	5717.72			0.774932			0.387466	−	0.921884i	$-0.373350\pi$
$379$	5717.72			0.774932			0.387466	+	0.921884i	$0.373350\pi$
$380$	414.488	+	899.244i	0.0559547	+	0.121395i
$381$	−3368.73			−0.452979
$382$		−	832.205i		−	0.111464i
$383$			2803.10i			0.373973i	0.982363	+	0.186986i	$0.0598720\pi$
$383$			2803.10i			0.373973i	−0.982363	+	0.186986i	$0.940128\pi$
$384$	−4186.41			−0.556346
$385$	642.133	−	295.978i	0.0850030	−	0.0391804i
$386$	−1683.83			−0.222033
$387$			2088.51i			0.274328i
$388$			7537.79i			0.986272i
$389$	3757.31			0.489725			0.244863	−	0.969558i	$-0.421257\pi$
$389$	3757.31			0.489725			0.244863	+	0.969558i	$0.421257\pi$
$390$	−743.394	+	342.652i	−0.0965211	+	0.0444894i
$391$	−1607.08			−0.207861
$392$		−	5940.41i		−	0.765398i
$393$			2614.20i			0.335544i
$394$	1059.17			0.135433
$395$	−945.753	−	2051.84i	−0.120471	−	0.261365i
$396$	610.903			0.0775228
$397$		−	2391.63i		−	0.302349i	−0.988507	−	0.151175i	$-0.951694\pi$
$397$		−	2391.63i		−	0.302349i	0.988507	−	0.151175i	$-0.0483056\pi$
$398$		−	1492.98i		−	0.188031i
$399$	247.542			0.0310592
$400$	−1903.49	+	2228.12i	−0.237936	+	0.278516i
$401$	1714.87			0.213557			0.106779	−	0.994283i	$-0.465946\pi$
$401$	1714.87			0.213557			0.106779	+	0.994283i	$0.465946\pi$
$402$		−	2450.07i		−	0.303976i
$403$		−	872.048i		−	0.107791i
$404$	2216.19			0.272920
$405$	−379.089	−	822.445i	−0.0465113	−	0.100908i
$406$	687.969			0.0840969
$407$		−	96.7646i		−	0.0117849i
$408$			3347.22i			0.406157i
$409$	11896.9			1.43830			0.719148	−	0.694857i	$-0.244532\pi$
$409$	11896.9			1.43830			0.719148	+	0.694857i	$0.244532\pi$
$410$	731.724	−	337.273i	0.0881397	−	0.0406262i
$411$	6102.97			0.732450
$412$		−	859.903i		−	0.102826i
$413$		−	4492.31i		−	0.535235i
$414$	336.036			0.0398920
$415$	−9791.77	+	4513.31i	−1.15821	+	0.533855i
$416$	3338.82			0.393508
$417$			1588.87i			0.186589i
$418$		−	213.525i		−	0.0249853i
$419$	14479.8			1.68827			0.844135	−	0.536131i	$-0.180115\pi$
$419$	14479.8			1.68827			0.844135	+	0.536131i	$0.180115\pi$
$420$	498.110	+	1080.66i	0.0578697	+	0.125550i
$421$	−4412.32			−0.510792			−0.255396	−	0.966837i	$-0.582206\pi$
$421$	−4412.32			−0.510792			−0.255396	+	0.966837i	$0.582206\pi$
$422$		−	5895.65i		−	0.680084i
$423$			587.247i			0.0675010i
$424$	−3932.13			−0.450380
$425$	5532.75	+	4726.63i	0.631478	+	0.539471i
$426$	−3131.83			−0.356191
$427$		−	4281.27i		−	0.485211i
$428$			8413.95i			0.950242i
$429$	−595.460			−0.0670141
$430$	1468.89	+	3186.79i	0.164735	+	0.357397i
$431$	−5137.37			−0.574149			−0.287075	−	0.957908i	$-0.592683\pi$
$431$	−5137.37			−0.574149			−0.287075	+	0.957908i	$0.592683\pi$
$432$			632.987i			0.0704968i
$433$			17693.7i			1.96375i	0.189532	+	0.981875i	$0.439303\pi$
$433$			17693.7i			1.96375i	−0.189532	+	0.981875i	$0.560697\pi$
$434$	375.794			0.0415638
$435$	2695.03	−	1242.22i	0.297051	−	0.136919i
$436$	2346.77			0.257775
$437$			396.209i			0.0433712i
$438$			1529.94i			0.166903i
$439$	−7.74474			−0.000841996			−0.000420998	−	1.00000i	$-0.500134\pi$
$439$	−7.74474			−0.000841996			−0.000420998		1.00000i	$0.500134\pi$
$440$	2140.65	−	986.687i	0.231935	−	0.106906i
$441$	−2789.52			−0.301211
$442$		−	1420.72i		−	0.152889i
$443$			6920.57i			0.742226i	0.928588	+	0.371113i	$0.121024\pi$
$443$			6920.57i			0.742226i	−0.928588	+	0.371113i	$0.878976\pi$
$444$	162.848			0.0174064
$445$	−1811.32	−	3929.70i	−0.192954	−	0.418620i
$446$	3123.79			0.331649
$447$			9350.86i			0.989442i
$448$			360.529i			0.0380210i
$449$	−1401.13			−0.147268			−0.0736342	−	0.997285i	$-0.523460\pi$
$449$	−1401.13			−0.147268			−0.0736342	+	0.997285i	$0.523460\pi$
$450$	−1156.88	−	988.324i	−0.121191	−	0.103533i
$451$	586.112			0.0611950
$452$		−	11326.7i		−	1.17868i
$453$			9689.49i			1.00497i
$454$	4890.49			0.505556
$455$	−485.518	−	1053.35i	−0.0500251	−	0.108531i
$456$	825.220			0.0847466
$457$			16586.6i			1.69779i	0.528564	+	0.848893i	$0.322731\pi$
$457$			16586.6i			1.69779i	−0.528564	+	0.848893i	$0.677269\pi$
$458$		−	6484.74i		−	0.661598i
$459$	1571.80			0.159837
$460$	−1729.68	+	797.259i	−0.175319	+	0.0808096i
$461$	15640.7			1.58017			0.790085	−	0.612997i	$-0.210036\pi$
$461$	15640.7			1.58017			0.790085	+	0.612997i	$0.210036\pi$
$462$		−	256.603i		−	0.0258404i
$463$		−	11044.9i		−	1.10864i	−0.832302	−	0.554322i	$-0.812978\pi$
$463$		−	11044.9i		−	1.10864i	0.832302	−	0.554322i	$-0.187022\pi$
$464$	−2074.21			−0.207527
$465$	1472.13	−	678.546i	0.146813	−	0.0676706i
$466$	5709.49			0.567569
$467$		−	793.129i		−	0.0785903i	−0.999228	−	0.0392951i	$-0.987489\pi$
$467$		−	793.129i		−	0.0785903i	0.999228	−	0.0392951i	$-0.0125112\pi$
$468$		−	1002.12i		−	0.0989804i
$469$	3471.60			0.341799
$470$	413.021	+	896.061i	0.0405345	+	0.0879409i
$471$	−2472.03			−0.241837
$472$		−	14975.8i		−	1.46042i
$473$			2552.63i			0.248139i
$474$	−819.936			−0.0794534
$475$	1165.30	−	1364.04i	0.112563	−	0.131761i
$476$	−2065.29			−0.198870
$477$			1846.46i			0.177240i
$478$			9455.55i			0.904784i
$479$	−5157.94			−0.492009			−0.246005	−	0.969269i	$-0.579118\pi$
$479$	−5157.94			−0.492009			−0.246005	+	0.969269i	$0.579118\pi$
$480$	2597.96	+	5636.36i	0.247042	+	0.535965i
$481$	−158.731			−0.0150468
$482$		−	644.237i		−	0.0608801i
$483$			476.143i			0.0448556i
$484$	746.660			0.0701221
$485$	12403.1	−	5716.94i	1.16123	−	0.535243i
$486$	−328.658			−0.0306753
$487$		−	5443.47i		−	0.506504i	−0.967400	−	0.253252i	$-0.918500\pi$
$487$		−	5443.47i		−	0.506504i	0.967400	−	0.253252i	$-0.0815001\pi$
$488$		−	14272.2i		−	1.32392i
$489$	−7116.88			−0.658152
$490$	−4256.44	+	1961.92i	−0.392421	+	0.180878i
$491$	2105.11			0.193488			0.0967438	−	0.995309i	$-0.469157\pi$
$491$	2105.11			0.193488			0.0967438	+	0.995309i	$0.469157\pi$
$492$			986.385i			0.0903855i
$493$			5150.55i			0.470526i
$494$	−350.263			−0.0319009
$495$	−463.331	−	1005.21i	−0.0420711	−	0.0912745i
$496$	−1133.01			−0.102568
$497$		−	4437.61i		−	0.400511i
$498$			3912.89i			0.352090i
$499$	2553.34			0.229065			0.114532	−	0.993420i	$-0.463463\pi$
$499$	2553.34			0.229065			0.114532	+	0.993420i	$0.463463\pi$
$500$	8299.64	+	2342.45i	0.742343	+	0.209515i
$501$	7110.54			0.634083
$502$		−	1215.79i		−	0.108095i
$503$		−	11389.3i		−	1.00959i	−0.863240	−	0.504794i	$-0.831569\pi$
$503$		−	11389.3i		−	1.00959i	0.863240	−	0.504794i	$-0.168431\pi$
$504$	991.706			0.0876470
$505$	−1680.84	−	3646.63i	−0.148112	−	0.321333i
$506$	410.711			0.0360836
$507$		−	5614.22i		−	0.491787i
$508$		−	6929.18i		−	0.605182i
$509$	9084.20			0.791061			0.395530	−	0.918453i	$-0.370561\pi$
$509$	9084.20			0.791061			0.395530	+	0.918453i	$0.370561\pi$
$510$	2398.36	−	1105.47i	0.208237	−	0.0959827i
$511$	−2167.84			−0.187670
$512$		−	7932.57i		−	0.684714i
$513$		−	387.509i		−	0.0333508i
$514$	1829.58			0.157002
$515$	−1414.93	+	652.181i	−0.121066	+	0.0558030i
$516$	−4295.89			−0.366504
$517$			717.746i			0.0610569i
$518$		−	68.4025i		−	0.00580199i
$519$	2768.12			0.234117
$520$	−1618.55	−	3511.48i	−0.136496	−	0.296132i
$521$	−5185.78			−0.436072			−0.218036	−	0.975941i	$-0.569965\pi$
$521$	−5185.78			−0.436072			−0.218036	+	0.975941i	$0.569965\pi$
$522$		−	1076.96i		−	0.0903016i
$523$			16846.8i			1.40853i	0.709939	+	0.704263i	$0.248722\pi$
$523$			16846.8i			1.40853i	−0.709939	+	0.704263i	$0.751278\pi$
$524$	−5377.17			−0.448288
$525$	1400.40	−	1639.23i	0.116416	−	0.136270i
$526$	6900.88			0.572039
$527$			2813.42i			0.232551i
$528$			773.651i			0.0637667i
$529$	11404.9			0.937363
$530$	1298.65	+	2817.46i	0.106433	+	0.230910i
$531$	−7032.37			−0.574725
$532$			509.173i			0.0414952i
$533$		−	961.449i		−	0.0781331i
$534$	−1570.35			−0.127258
$535$	13844.7	−	6381.45i	1.11880	−	0.515690i
$536$	11573.1			0.932615
$537$			11121.2i			0.893698i
$538$		−	2970.06i		−	0.238008i
$539$	−3409.41			−0.272456
$540$	1691.70	−	779.754i	0.134813	−	0.0621394i
$541$	9817.00			0.780159			0.390079	−	0.920781i	$-0.372448\pi$
$541$	9817.00			0.780159			0.390079	+	0.920781i	$0.372448\pi$
$542$			10113.3i			0.801480i
$543$		−	12425.4i		−	0.981995i
$544$	−10771.8			−0.848965
$545$	−1779.88	−	3861.50i	−0.139893	−	0.303502i
$546$	−420.928			−0.0329928
$547$			21899.3i			1.71178i	0.517157	+	0.855891i	$0.326990\pi$
$547$			21899.3i			1.71178i	−0.517157	+	0.855891i	$0.673010\pi$
$548$			12553.3i			0.978557i
$549$	−6702.00			−0.521010
$550$	−1413.97	−	1207.95i	−0.109621	−	0.0936495i
$551$	1269.81			0.0981774
$552$			1587.29i			0.122391i
$553$		−	1161.80i		−	0.0893396i
$554$	788.026			0.0604333
$555$	−123.510	−	267.958i	−0.00944630	−	0.0204940i
$556$	−3268.18			−0.249283
$557$			6655.17i			0.506263i	0.967432	+	0.253131i	$0.0814605\pi$
$557$			6655.17i			0.506263i	−0.967432	+	0.253131i	$0.918539\pi$
$558$		−	588.277i		−	0.0446304i
$559$	4187.29			0.316822
$560$	−1368.56	+	630.809i	−0.103272	+	0.0476010i
$561$	1921.09			0.144578
$562$		−	5092.44i		−	0.382227i
$563$		−	3634.71i		−	0.272087i	−0.990703	−	0.136043i	$-0.956561\pi$
$563$		−	3634.71i		−	0.272087i	0.990703	−	0.136043i	$-0.0434387\pi$
$564$	−1207.92			−0.0901816
$565$	−18637.5	+	8590.58i	−1.38776	+	0.639661i
$566$	−10813.1			−0.803016
$567$		−	465.688i		−	0.0344922i
$568$		−	14793.4i		−	1.09281i
$569$	−13019.5			−0.959240			−0.479620	−	0.877476i	$-0.659225\pi$
$569$	−13019.5			−0.959240			−0.479620	+	0.877476i	$0.659225\pi$
$570$	−272.542	−	591.288i	−0.0200272	−	0.0434497i
$571$	18165.0			1.33132			0.665659	−	0.746256i	$-0.268151\pi$
$571$	18165.0			1.33132			0.665659	+	0.746256i	$0.268151\pi$
$572$		−	1224.81i		−	0.0895312i
$573$		−	1845.92i		−	0.134580i
$574$	414.320			0.0301278
$575$	2623.70	+	2241.43i	0.190288	+	0.162564i
$576$	564.381			0.0408262
$577$			21192.9i			1.52907i	0.644583	+	0.764534i	$0.277031\pi$
$577$			21192.9i			1.52907i	−0.644583	+	0.764534i	$0.722969\pi$
$578$		−	2061.27i		−	0.148335i
$579$	−3734.93			−0.268080
$580$	2555.14	+	5543.45i	0.182925	+	0.396861i
$581$	−5544.34			−0.395900
$582$		−	4956.39i		−	0.353005i
$583$			2256.79i			0.160320i
$584$	−7226.80			−0.512067
$585$	−1648.93	+	760.041i	−0.116538	+	0.0537160i
$586$	651.956			0.0459591
$587$			5287.35i			0.371775i	0.982571	+	0.185888i	$0.0595161\pi$
$587$			5287.35i			0.371775i	−0.982571	+	0.185888i	$0.940484\pi$
$588$		−	5737.79i		−	0.402419i
$589$	693.617			0.0485229
$590$	−10730.5	+	4945.99i	−0.748757	+	0.345124i
$591$	2349.37			0.163520
$592$			206.231i			0.0143177i
$593$			15923.6i			1.10270i	0.834273	+	0.551351i	$0.185888\pi$
$593$			15923.6i			1.10270i	−0.834273	+	0.551351i	$0.814112\pi$
$594$	−401.693			−0.0277469
$595$	1566.39	+	3398.33i	0.107926	+	0.234148i
$596$	−19233.9			−1.32190
$597$		−	3311.60i		−	0.227026i
$598$		−	673.724i		−	0.0460713i
$599$	−11778.8			−0.803455			−0.401728	−	0.915759i	$-0.631590\pi$
$599$	−11778.8			−0.803455			−0.401728	+	0.915759i	$0.631590\pi$
$600$	4668.43	−	5464.62i	0.317646	−	0.371820i
$601$	11465.4			0.778176			0.389088	−	0.921201i	$-0.372790\pi$
$601$	11465.4			0.778176			0.389088	+	0.921201i	$0.372790\pi$
$602$			1804.44i			0.122165i
$603$		−	5434.53i		−	0.367017i
$604$	−19930.4			−1.34265
$605$	−566.294	−	1228.59i	−0.0380547	−	0.0825609i
$606$	−1457.23			−0.0976832
$607$		−	20121.6i		−	1.34549i	−0.739875	−	0.672745i	$-0.765115\pi$
$607$		−	20121.6i		−	1.34549i	0.739875	−	0.672745i	$-0.234885\pi$
$608$			2655.66i			0.177140i
$609$	1525.99			0.101538
$610$	−10226.4	+	4713.63i	−0.678776	+	0.312868i
$611$	1177.38			0.0779569
$612$			3233.05i			0.213543i
$613$		−	13322.5i		−	0.877797i	−0.898537	−	0.438899i	$-0.855369\pi$
$613$		−	13322.5i		−	0.877797i	0.898537	−	0.438899i	$-0.144631\pi$
$614$	−8656.67			−0.568981
$615$	1623.05	−	748.110i	0.106419	−	0.0490515i
$616$	1212.09			0.0792797
$617$			8363.01i			0.545676i	0.962060	+	0.272838i	$0.0879623\pi$
$617$			8363.01i			0.545676i	−0.962060	+	0.272838i	$0.912038\pi$
$618$			565.420i			0.0368034i
$619$	5307.02			0.344599			0.172300	−	0.985045i	$-0.444880\pi$
$619$	5307.02			0.344599			0.172300	+	0.985045i	$0.444880\pi$
$620$	1395.71	+	3028.04i	0.0904082	+	0.196143i
$621$	745.366			0.0481651
$622$			7874.89i			0.507644i
$623$		−	2225.09i		−	0.143092i
$624$	1269.08			0.0814168
$625$	−2440.37	−	15433.3i	−0.156184	−	0.987728i
$626$	2598.27			0.165891
$627$		−	473.622i		−	0.0301669i
$628$		−	5084.76i		−	0.323096i
$629$	512.102			0.0324624
$630$	−327.527	−	710.579i	−0.0207127	−	0.0449368i
$631$	−23400.0			−1.47629			−0.738144	−	0.674643i	$-0.764298\pi$
$631$	−23400.0			−1.47629			−0.738144	+	0.674643i	$0.764298\pi$
$632$		−	3873.03i		−	0.243767i
$633$		−	13077.2i		−	0.821125i
$634$	8598.42			0.538623
$635$	−11401.6	+	5255.34i	−0.712534	+	0.328428i
$636$	−3798.01			−0.236794
$637$			5592.74i			0.347869i
$638$		−	1316.29i		−	0.0816809i
$639$	−6946.75			−0.430061
$640$	−14169.1	+	6530.96i	−0.875130	+	0.403373i
$641$	22448.6			1.38326			0.691628	−	0.722254i	$-0.256894\pi$
$641$	22448.6			1.38326			0.691628	+	0.722254i	$0.256894\pi$
$642$		−	5532.50i		−	0.340110i
$643$		−	25043.3i		−	1.53594i	−0.640485	−	0.767970i	$-0.721267\pi$
$643$		−	25043.3i		−	1.53594i	0.640485	−	0.767970i	$-0.278733\pi$
$644$	−979.385			−0.0599273
$645$	3258.16	+	7068.67i	0.198899	+	0.431517i
$646$	1130.03			0.0688240
$647$		−	669.423i		−	0.0406766i	−0.999793	−	0.0203383i	$-0.993526\pi$
$647$		−	669.423i		−	0.0406766i	0.999793	−	0.0203383i	$-0.00647433\pi$
$648$		−	1552.44i		−	0.0941137i
$649$	−8595.12			−0.519858
$650$	−1981.50	+	2319.45i	−0.119571	+	0.139963i
$651$	833.554			0.0501836
$652$		−	14638.8i		−	0.879294i
$653$		−	25102.4i		−	1.50434i	−0.658971	−	0.752168i	$-0.729008\pi$
$653$		−	25102.4i		−	1.50434i	0.658971	−	0.752168i	$-0.270992\pi$
$654$	−1543.09			−0.0922627
$655$	4078.24	+	8847.87i	0.243283	+	0.527809i
$656$	−1249.16			−0.0743469
$657$			3393.58i			0.201516i
$658$			507.372i			0.0300599i
$659$	−3954.72			−0.233770			−0.116885	−	0.993145i	$-0.537291\pi$
$659$	−3954.72			−0.233770			−0.116885	+	0.993145i	$0.537291\pi$
$660$	2067.63	−	953.032i	0.121943	−	0.0562072i
$661$	−5847.99			−0.344115			−0.172058	−	0.985087i	$-0.555042\pi$
$661$	−5847.99			−0.344115			−0.172058	+	0.985087i	$0.555042\pi$
$662$			13617.4i			0.799478i
$663$		−	3151.32i		−	0.184596i
$664$	−18482.9			−1.08023
$665$	837.820	−	386.176i	0.0488560	−	0.0225192i
$666$	−107.079			−0.00623006
$667$			2442.46i			0.141788i
$668$			14625.8i			0.847137i
$669$	6928.91			0.400429
$670$	−3822.20	−	8292.38i	−0.220395	−	0.478153i
$671$	−8191.33			−0.471271
$672$			3191.44i			0.183203i
$673$		−	33260.5i		−	1.90505i	−0.304462	−	0.952524i	$-0.598477\pi$
$673$		−	33260.5i		−	1.90505i	0.304462	−	0.952524i	$-0.401523\pi$
$674$	−5133.55			−0.293378
$675$	−2566.09	−	2192.21i	−0.146324	−	0.125005i
$676$	11548.0			0.657030
$677$		−	14942.0i		−	0.848252i	−0.905603	−	0.424126i	$-0.860581\pi$
$677$		−	14942.0i		−	0.848252i	0.905603	−	0.424126i	$-0.139419\pi$
$678$			7447.75i			0.421872i
$679$	7022.91			0.396929
$680$	5221.79	+	11328.8i	0.294480	+	0.638884i
$681$	10847.7			0.610401
$682$		−	719.005i		−	0.0403697i
$683$			15799.2i			0.885125i	0.896738	+	0.442562i	$0.145930\pi$
$683$			15799.2i			0.885125i	−0.896738	+	0.442562i	$0.854070\pi$
$684$	797.073			0.0445568
$685$	20655.8	−	9520.86i	1.15214	−	0.531056i
$686$	−5077.21			−0.282579
$687$		−	14383.9i		−	0.798805i
$688$		−	5440.33i		−	0.301469i
$689$	3702.00			0.204695
$690$	1137.33	−	524.229i	0.0627499	−	0.0289233i
$691$	−9432.09			−0.519267			−0.259633	−	0.965707i	$-0.583602\pi$
$691$	−9432.09			−0.519267			−0.259633	+	0.965707i	$0.583602\pi$
$692$			5693.78i			0.312782i
$693$		−	569.175i		−	0.0311994i
$694$	−9268.43			−0.506952
$695$	2478.70	+	5377.62i	0.135284	+	0.293503i
$696$	5087.13			0.277050
$697$			3101.85i			0.168567i
$698$		−	1788.69i		−	0.0969957i
$699$	12664.3			0.685276
$700$	3371.76	+	2880.49i	0.182058	+	0.155532i
$701$	21441.3			1.15525			0.577624	−	0.816303i	$-0.303980\pi$
$701$	21441.3			1.15525			0.577624	+	0.816303i	$0.303980\pi$
$702$			658.931i			0.0354270i
$703$		−	126.253i		−	0.00677343i
$704$	689.799			0.0369287
$705$	916.127	+	1987.57i	0.0489409	+	0.106179i
$706$	4185.58			0.223125
$707$		−	2064.81i		−	0.109838i
$708$		−	14465.0i		−	0.767835i
$709$	−33984.4			−1.80016			−0.900078	−	0.435728i	$-0.856491\pi$
$709$	−33984.4			−1.80016			−0.900078	+	0.435728i	$0.856491\pi$
$710$	−10599.8	+	4885.77i	−0.560288	+	0.258253i
$711$	−1818.71			−0.0959311
$712$		−	7417.68i		−	0.390434i
$713$			1334.16i			0.0700767i
$714$	1358.01			0.0711795
$715$	−2015.36	+	928.939i	−0.105413	+	0.0485879i
$716$	−22875.4			−1.19398
$717$			20973.5i			1.09243i
$718$			17583.3i			0.913933i
$719$	12029.9			0.623978			0.311989	−	0.950086i	$-0.399005\pi$
$719$	12029.9			0.623978			0.311989	+	0.950086i	$0.399005\pi$
$720$	987.484	+	2142.38i	0.0511130	+	0.110891i
$721$	−801.166			−0.0413828
$722$			8998.21i			0.463821i
$723$		−	1428.99i		−	0.0735058i
$724$	25557.9			1.31195
$725$	7183.56	−	8408.71i	0.367987	−	0.430747i
$726$	−490.958			−0.0250980
$727$			28766.2i			1.46751i	0.679415	+	0.733754i	$0.262233\pi$
$727$			28766.2i			1.46751i	−0.679415	+	0.733754i	$0.737767\pi$
$728$		−	1988.29i		−	0.101224i
$729$	−729.000			−0.0370370
$730$	2386.77	+	5178.16i	0.121011	+	0.262538i
$731$	−13509.1			−0.683520
$732$		−	13785.4i		−	0.696071i
$733$		−	35648.2i		−	1.79631i	−0.439679	−	0.898155i	$-0.644908\pi$
$733$		−	35648.2i		−	1.79631i	0.439679	−	0.898155i	$-0.355092\pi$
$734$	14989.0			0.753750
$735$	−9441.25	+	4351.75i	−0.473804	+	0.218390i
$736$	−5108.12			−0.255826
$737$		−	6642.20i		−	0.331979i
$738$		−	648.586i		−	0.0323507i
$739$	16407.4			0.816718			0.408359	−	0.912821i	$-0.366101\pi$
$739$	16407.4			0.816718			0.408359	+	0.912821i	$0.366101\pi$
$740$	551.167	−	254.049i	0.0273801	−	0.0126203i
$741$	−776.922			−0.0385168
$742$			1595.31i			0.0789296i
$743$		−	11405.7i		−	0.563168i	−0.959537	−	0.281584i	$-0.909140\pi$
$743$		−	11405.7i		−	0.563168i	0.959537	−	0.281584i	$-0.0908598\pi$
$744$	2778.77			0.136929
$745$	14587.7	+	31648.4i	0.717385	+	1.55639i
$746$	3177.06			0.155925
$747$			8679.24i			0.425110i
$748$			3951.51i			0.193157i
$749$	7839.23			0.382429
$750$	−5457.34	−	1540.25i	−0.265699	−	0.0749894i
$751$	−7363.93			−0.357808			−0.178904	−	0.983867i	$-0.557255\pi$
$751$	−7363.93			−0.357808			−0.178904	+	0.983867i	$0.557255\pi$
$752$		−	1529.71i		−	0.0741792i
$753$		−	2696.76i		−	0.130512i
$754$	−2159.22			−0.104289
$755$	15116.0	+	32794.6i	0.728645	+	1.58082i
$756$	957.881			0.0460817
$757$		−	35739.0i		−	1.71592i	−0.513713	−	0.857962i	$-0.671730\pi$
$757$		−	35739.0i		−	1.71592i	0.513713	−	0.857962i	$-0.328270\pi$
$758$		−	7733.22i		−	0.370558i
$759$	911.003			0.0435669
$760$	2793.00	−	1287.37i	0.133306	−	0.0614447i
$761$	−34213.7			−1.62976			−0.814879	−	0.579631i	$-0.803197\pi$
$761$	−34213.7			−1.62976			−0.814879	+	0.579631i	$0.803197\pi$
$762$			4556.21i			0.216606i
$763$		−	2186.47i		−	0.103743i
$764$	3796.90			0.179800
$765$	5319.83	−	2452.06i	0.251423	−	0.115888i
$766$	3791.19			0.178827
$767$			14099.3i			0.663750i
$768$			7167.14i			0.336747i
$769$	15177.7			0.711731			0.355866	−	0.934537i	$-0.384186\pi$
$769$	15177.7			0.711731			0.355866	+	0.934537i	$0.384186\pi$
$770$	−400.311	−	868.486i	−0.0187353	−	0.0406468i
$771$	4058.20			0.189562
$772$		−	7682.44i		−	0.358157i
$773$			26576.1i			1.23658i	0.785950	+	0.618290i	$0.212174\pi$
$773$			26576.1i			1.23658i	−0.785950	+	0.618290i	$0.787826\pi$
$774$	2824.71			0.131179
$775$	3923.93	−	4593.15i	0.181873	−	0.212891i
$776$	23411.9			1.08304
$777$		−	151.724i		−	0.00700525i
$778$		−	5081.76i		−	0.234177i
$779$	764.726			0.0351722
$780$	−1563.34	−	3391.71i	−0.0717648	−	0.155696i
$781$	−8490.47			−0.389005
$782$			2173.58i			0.0993954i
$783$		−	2388.83i		−	0.109029i
$784$	7266.37			0.331012
$785$	−8366.72	+	3856.47i	−0.380409	+	0.175342i
$786$	3535.70			0.160451
$787$			31856.8i			1.44291i	0.692459	+	0.721457i	$0.256527\pi$
$787$			31856.8i			1.44291i	−0.692459	+	0.721457i	$0.743473\pi$
$788$			4832.45i			0.218463i
$789$	15306.9			0.690673
$790$	−2775.11	+	1279.13i	−0.124980	+	0.0576069i
$791$	−10553.0			−0.474364
$792$		−	1897.43i		−	0.0851290i
$793$			13436.9i			0.601714i
$794$	−3234.69			−0.144578
$795$	2880.55	+	6249.44i	0.128506	+	0.278798i
$796$	6811.67			0.303308
$797$		−	24033.2i		−	1.06813i	−0.845444	−	0.534064i	$-0.820664\pi$
$797$		−	24033.2i		−	1.06813i	0.845444	−	0.534064i	$-0.179336\pi$
$798$		−	334.801i		−	0.0148519i
$799$	−3798.49			−0.168186
$800$	17585.9	+	15023.6i	0.777192	+	0.663956i
$801$	−3483.22			−0.153650
$802$		−	2319.36i		−	0.102119i
$803$			4147.71i			0.182279i
$804$	11178.4			0.490336
$805$	742.801	+	1611.53i	0.0325221	+	0.0705577i
$806$	−1179.45			−0.0515437
$807$		−	6587.93i		−	0.287368i
$808$		−	6883.35i		−	0.299697i
$809$	39382.0			1.71149			0.855747	−	0.517395i	$-0.173098\pi$
$809$	39382.0			1.71149			0.855747	+	0.517395i	$0.173098\pi$
$810$	−1112.36	+	512.719i	−0.0482522	+	0.0222409i
$811$	−9798.88			−0.424273			−0.212136	−	0.977240i	$-0.568042\pi$
$811$	−9798.88			−0.424273			−0.212136	+	0.977240i	$0.568042\pi$
$812$			3138.84i			0.135655i
$813$			22432.4i			0.967697i
$814$	−130.874			−0.00563530
$815$	−24087.4	+	11102.6i	−1.03527	+	0.477187i
$816$	−4094.35			−0.175651
$817$			3330.52i			0.142620i
$818$		−	16090.5i		−	0.687766i
$819$	−933.665			−0.0398351
$820$	1538.80	+	3338.47i	0.0655331	+	0.142176i
$821$	26436.8			1.12381			0.561906	−	0.827201i	$-0.310068\pi$
$821$	26436.8			1.12381			0.561906	+	0.827201i	$0.310068\pi$
$822$		−	8254.27i		−	0.350244i
$823$		−	13086.4i		−	0.554268i	−0.960831	−	0.277134i	$-0.910615\pi$
$823$		−	13086.4i		−	0.554268i	0.960831	−	0.277134i	$-0.0893846\pi$
$824$	−2670.80			−0.112915
$825$	−3136.33	−	2679.37i	−0.132355	−	0.113071i
$826$	−6075.86			−0.255940
$827$			31317.4i			1.31682i	0.752658	+	0.658411i	$0.228771\pi$
$827$			31317.4i			1.31682i	−0.752658	+	0.658411i	$0.771229\pi$
$828$			1533.15i			0.0643487i
$829$	−11163.4			−0.467698			−0.233849	−	0.972273i	$-0.575132\pi$
$829$	−11163.4			−0.467698			−0.233849	+	0.972273i	$0.575132\pi$
$830$	6104.26	+	13243.4i	0.255280	+	0.553837i
$831$	1747.93			0.0729664
$832$		−	1131.54i		−	0.0471502i
$833$		−	18043.4i		−	0.750502i
$834$	2148.95			0.0892233
$835$	24066.0	−	11092.7i	0.997410	−	0.459735i
$836$	974.200			0.0403031
$837$		−	1304.87i		−	0.0538862i
$838$		−	19584.0i		−	0.807299i
$839$	−10001.0			−0.411531			−0.205765	−	0.978601i	$-0.565968\pi$
$839$	−10001.0			−0.411531			−0.205765	+	0.978601i	$0.565968\pi$
$840$	3356.48	−	1547.10i	0.137868	−	0.0635476i
$841$	−16561.2			−0.679042
$842$			5967.67i			0.244251i
$843$		−	11295.6i		−	0.461496i
$844$	26898.7			1.09703
$845$	−8758.39	−	19001.6i	−0.356565	−	0.773579i
$846$	794.252			0.0322777
$847$		−	695.658i		−	0.0282209i
$848$		−	4809.82i		−	0.194776i
$849$	−23984.6			−0.969551
$850$	6392.78	−	7483.06i	0.257965	−	0.301961i
$851$	242.845			0.00978217
$852$		−	14288.9i		−	0.574564i
$853$			43331.6i			1.73933i	0.493646	+	0.869663i	$0.335664\pi$
$853$			43331.6i			1.73933i	−0.493646	+	0.869663i	$0.664336\pi$
$854$	−5790.42			−0.232019
$855$	−604.529	−	1311.54i	−0.0241806	−	0.0524606i
$856$	26133.2			1.04348
$857$			2343.88i			0.0934254i	0.998908	+	0.0467127i	$0.0148745\pi$
$857$			2343.88i			0.0934254i	−0.998908	+	0.0467127i	$0.985125\pi$
$858$			805.360i			0.0320449i
$859$	−1084.52			−0.0430771			−0.0215385	−	0.999768i	$-0.506856\pi$
$859$	−1084.52			−0.0430771			−0.0215385	+	0.999768i	$0.506856\pi$
$860$	−14539.6	+	6701.75i	−0.576509	+	0.265730i
$861$	919.008			0.0363760
$862$			6948.30i			0.274547i
$863$		−	32370.6i		−	1.27684i	−0.769690	−	0.638418i	$-0.779589\pi$
$863$		−	32370.6i		−	1.27684i	0.769690	−	0.638418i	$-0.220411\pi$
$864$	4995.96			0.196720
$865$	9368.84	−	4318.37i	0.368266	−	0.169745i
$866$	23930.7			0.939028
$867$		−	4572.14i		−	0.179098i
$868$			1714.55i			0.0670456i
$869$	−2222.87			−0.0867729
$870$	−1680.10	−	3645.04i	−0.0654723	−	0.142044i
$871$	−10895.8			−0.423868
$872$		−	7288.93i		−	0.283067i
$873$		−	10993.8i		−	0.426214i
$874$	535.873			0.0207393
$875$	2182.44	−	7732.73i	0.0843201	−	0.298759i
$876$	−6980.31			−0.269227
$877$		−	8691.24i		−	0.334643i	−0.985902	−	0.167322i	$-0.946488\pi$
$877$		−	8691.24i		−	0.334643i	0.985902	−	0.167322i	$-0.0535119\pi$
$878$			10.4748i			0.000402627i
$879$	1446.11			0.0554905
$880$	1206.92	+	2618.46i	0.0462334	+	0.100305i
$881$	19564.0			0.748158			0.374079	−	0.927397i	$-0.377959\pi$
$881$	19564.0			0.748158			0.374079	+	0.927397i	$0.377959\pi$
$882$			3772.82i			0.144034i
$883$			21023.0i			0.801223i	0.916248	+	0.400612i	$0.131202\pi$
$883$			21023.0i			0.801223i	−0.916248	+	0.400612i	$0.868798\pi$
$884$	6481.99			0.246621
$885$	−23801.4	+	10970.8i	−0.904040	+	0.416699i
$886$	9360.08			0.354919
$887$			18263.8i			0.691364i	0.938352	+	0.345682i	$0.112352\pi$
$887$			18263.8i			0.691364i	−0.938352	+	0.345682i	$0.887648\pi$
$888$		−	505.796i		−	0.0191142i
$889$	−6455.87			−0.243558
$890$	−5314.93	+	2449.81i	−0.200176	+	0.0922671i
$891$	−891.000			−0.0335013
$892$			14252.2i			0.534975i
$893$			936.475i			0.0350929i
$894$	12647.0			0.473133
$895$	17349.5	+	37640.3i	0.647967	+	1.40578i
$896$	−8022.89			−0.299136
$897$		−	1494.40i		−	0.0556259i
$898$			1895.03i			0.0704210i
$899$	4275.85			0.158629
$900$	4509.19	−	5278.23i	0.167007	−	0.195490i
$901$	−11943.5			−0.441614
$902$		−	792.717i		−	0.0292623i
$903$			4002.45i			0.147501i
$904$	−35180.0			−1.29433
$905$	−19384.0	−	42054.3i	−0.711986	−	1.54468i
$906$	13105.0			0.480559
$907$		−	12919.6i		−	0.472977i	−0.971634	−	0.236488i	$-0.924003\pi$
$907$		−	12919.6i		−	0.472977i	0.971634	−	0.236488i	$-0.0759965\pi$
$908$			22312.7i			0.815499i
$909$	−3232.31			−0.117941
$910$	−1424.65	+	656.663i	−0.0518975	+	0.0239211i
$911$	−24240.5			−0.881583			−0.440792	−	0.897609i	$-0.645302\pi$
$911$	−24240.5			−0.881583			−0.440792	+	0.897609i	$0.645302\pi$
$912$			1009.42i			0.0366504i
$913$			10608.0i			0.384526i
$914$	22433.4			0.811850
$915$	−22683.2	+	10455.4i	−0.819546	+	0.377753i
$916$	29586.4			1.06721
$917$			5009.88i			0.180415i
$918$		−	2125.86i		−	0.0764311i
$919$	−3954.04			−0.141928			−0.0709639	−	0.997479i	$-0.522608\pi$
$919$	−3954.04			−0.141928			−0.0709639	+	0.997479i	$0.522608\pi$
$920$	2476.24	+	5372.27i	0.0887382	+	0.192520i
$921$	−19201.5			−0.686981
$922$		−	21154.0i		−	0.755608i
$923$			13927.6i			0.496678i
$924$	1170.74			0.0416825
$925$	−836.050	−	714.238i	−0.0297180	−	0.0253881i
$926$	−14938.3			−0.530133
$927$			1254.16i			0.0444360i
$928$			16371.0i			0.579101i
$929$	−52632.8			−1.85880			−0.929401	−	0.369071i	$-0.879676\pi$
$929$	−52632.8			−1.85880			−0.929401	+	0.369071i	$0.879676\pi$
$930$	−917.735	−	1991.05i	−0.0323588	−	0.0702034i
$931$	−4448.41			−0.156596
$932$			26049.4i			0.915532i
$933$			17467.4i			0.612923i
$934$	−1072.71			−0.0375804
$935$	6502.01	−	2996.97i	0.227421	−	0.104825i
$936$	−3112.51			−0.108692
$937$		−	255.763i		−	0.00891719i	−0.999990	−	0.00445860i	$-0.998581\pi$
$937$		−	255.763i		−	0.00891719i	0.999990	−	0.00445860i	$-0.00141922\pi$
$938$		−	4695.35i		−	0.163442i
$939$	5763.26			0.200295
$940$	−4088.25	+	1884.39i	−0.141855	+	0.0653853i
$941$	25842.2			0.895251			0.447626	−	0.894221i	$-0.352270\pi$
$941$	25842.2			0.895251			0.447626	+	0.894221i	$0.352270\pi$
$942$			3343.43i			0.115642i
$943$			1470.94i			0.0507956i
$944$	18318.5			0.631586
$945$	−726.492	−	1576.15i	−0.0250082	−	0.0542561i
$946$	3452.43			0.118656
$947$		−	13239.2i		−	0.454293i	−0.973861	−	0.227147i	$-0.927060\pi$
$947$		−	13239.2i		−	0.454293i	0.973861	−	0.227147i	$-0.0729396\pi$
$948$		−	3740.93i		−	0.128164i
$949$	6803.85			0.232731
$950$	−1844.86	−	1576.07i	−0.0630055	−	0.0538257i
$951$	19072.3			0.650327
$952$			6414.66i			0.218383i
$953$		−	43415.2i		−	1.47571i	−0.674957	−	0.737857i	$-0.735838\pi$
$953$		−	43415.2i		−	1.47571i	0.674957	−	0.737857i	$-0.264162\pi$
$954$	2497.34			0.0847530
$955$	−2879.71	−	6247.62i	−0.0975762	−	0.211694i
$956$	−43140.6			−1.45949
$957$		−	2919.68i		−	0.0986205i
$958$			6976.12i			0.235270i
$959$	11695.8			0.393824
$960$	1910.18	−	880.456i	0.0642195	−	0.0296006i
$961$	−27455.4			−0.921600
$962$			214.684i			0.00719510i
$963$		−	12271.7i		−	0.410644i
$964$	2939.31			0.0982041
$965$	−12641.1	+	5826.64i	−0.421689	+	0.194369i
$966$	643.984			0.0214491
$967$		−	10591.0i		−	0.352207i	−0.984372	−	0.176104i	$-0.943651\pi$
$967$		−	10591.0i		−	0.352207i	0.984372	−	0.176104i	$-0.0563494\pi$
$968$		−	2319.08i		−	0.0770021i
$969$	2506.53			0.0830972
$970$	−7732.16	−	16775.2i	−0.255943	−	0.555276i
$971$	13910.5			0.459741			0.229870	−	0.973221i	$-0.426170\pi$
$971$	13910.5			0.459741			0.229870	+	0.973221i	$0.426170\pi$
$972$		−	1499.49i		−	0.0494817i
$973$			3044.94i			0.100325i
$974$	−7362.30			−0.242201
$975$	−4395.20	+	5144.79i	−0.144368	+	0.168990i
$976$	17457.9			0.572556
$977$		−	36037.3i		−	1.18008i	−0.807375	−	0.590038i	$-0.799113\pi$
$977$		−	36037.3i		−	1.18008i	0.807375	−	0.590038i	$-0.200887\pi$
$978$			9625.59i			0.314716i
$979$	−4257.26			−0.138981
$980$	−8951.17	−	19419.8i	−0.291770	−	0.633004i
$981$	−3422.76			−0.111397
$982$		−	2847.17i		−	0.0925222i
$983$		−	39661.0i		−	1.28687i	−0.765502	−	0.643433i	$-0.777509\pi$
$983$		−	39661.0i		−	1.28687i	0.765502	−	0.643433i	$-0.222491\pi$
$984$	3063.65			0.0992537
$985$	7951.55	−	3665.10i	0.257216	−	0.118558i
$986$	6966.13			0.224997
$987$			1125.41i			0.0362939i
$988$		−	1598.06i		−	0.0514586i
$989$	−6406.20			−0.205971
$990$	−1359.55	+	626.656i	−0.0436458	+	0.0201176i
$991$	26337.9			0.844249			0.422125	−	0.906538i	$-0.361285\pi$
$991$	26337.9			0.844249			0.422125	+	0.906538i	$0.361285\pi$
$992$			8942.46i			0.286213i
$993$			30204.9i			0.965280i
$994$	−6001.88			−0.191517
$995$	−5166.21	−	11208.3i	−0.164603	−	0.357111i
$996$	−17852.4			−0.567948
$997$		−	4539.45i		−	0.144198i	−0.997397	−	0.0720992i	$-0.977030\pi$
$997$		−	4539.45i		−	0.144198i	0.997397	−	0.0720992i	$-0.0229698\pi$
$998$		−	3453.40i		−	0.109535i
$999$	−237.513			−0.00752210

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	165.4.c.a.34.6	✓	14
3.2	odd	2		495.4.c.c.199.9		14
5.2	odd	4		825.4.a.bb.1.5		7
5.3	odd	4		825.4.a.bc.1.3		7
5.4	even	2	inner	165.4.c.a.34.9	yes	14
15.2	even	4		2475.4.a.br.1.3		7
15.8	even	4		2475.4.a.bq.1.5		7
15.14	odd	2		495.4.c.c.199.6		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
165.4.c.a.34.6	✓	14	1.1	even	1	trivial
165.4.c.a.34.9	yes	14	5.4	even	2	inner
495.4.c.c.199.6		14	15.14	odd	2
495.4.c.c.199.9		14	3.2	odd	2
825.4.a.bb.1.5		7	5.2	odd	4
825.4.a.bc.1.3		7	5.3	odd	4
2475.4.a.bq.1.5		7	15.8	even	4
2475.4.a.br.1.3		7	15.2	even	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:	\( N \)	\(=\)	\( 165 = 3 \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	165.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.35250i q^{2} -3.00000i q^{3} +6.17074 q^{4} +(-4.68011 - 10.1536i) q^{5} -4.05750 q^{6} -5.74924i q^{7} -19.1659i q^{8} -9.00000 q^{9} +O(q^{10})\)	\(q-1.35250i q^{2} -3.00000i q^{3} +6.17074 q^{4} +(-4.68011 - 10.1536i) q^{5} -4.05750 q^{6} -5.74924i q^{7} -19.1659i q^{8} -9.00000 q^{9} +(-13.7328 + 6.32986i) q^{10} -11.0000 q^{11} -18.5122i q^{12} +18.0442i q^{13} -7.77585 q^{14} +(-30.4609 + 14.0403i) q^{15} +23.4440 q^{16} -58.2147i q^{17} +12.1725i q^{18} -14.3522 q^{19} +(-28.8798 - 62.6555i) q^{20} -17.2477 q^{21} +14.8775i q^{22} -27.6061i q^{23} -57.4978 q^{24} +(-81.1931 + 95.0404i) q^{25} +24.4048 q^{26} +27.0000i q^{27} -35.4771i q^{28} -88.4751 q^{29} +(18.9896 + 41.1985i) q^{30} -48.3283 q^{31} -185.036i q^{32} +33.0000i q^{33} -78.7355 q^{34} +(-58.3757 + 26.9071i) q^{35} -55.5367 q^{36} +8.79678i q^{37} +19.4113i q^{38} +54.1327 q^{39} +(-194.604 + 89.6988i) q^{40} -53.2829 q^{41} +23.3276i q^{42} -232.057i q^{43} -67.8781 q^{44} +(42.1210 + 91.3828i) q^{45} -37.3373 q^{46} -65.2496i q^{47} -70.3319i q^{48} +309.946 q^{49} +(128.542 + 109.814i) q^{50} -174.644 q^{51} +111.346i q^{52} -205.162i q^{53} +36.5175 q^{54} +(51.4812 + 111.690i) q^{55} -110.190 q^{56} +43.0566i q^{57} +119.663i q^{58} +781.375 q^{59} +(-187.967 + 86.6393i) q^{60} +744.666 q^{61} +65.3641i q^{62} +51.7432i q^{63} -62.7090 q^{64} +(183.215 - 84.4490i) q^{65} +44.6325 q^{66} +603.837i q^{67} -359.228i q^{68} -82.8184 q^{69} +(36.3919 + 78.9533i) q^{70} +771.861 q^{71} +172.493i q^{72} -377.065i q^{73} +11.8977 q^{74} +(285.121 + 243.579i) q^{75} -88.5636 q^{76} +63.2416i q^{77} -73.2145i q^{78} +202.079 q^{79} +(-109.720 - 238.042i) q^{80} +81.0000 q^{81} +72.0652i q^{82} -964.360i q^{83} -106.431 q^{84} +(-591.092 + 272.452i) q^{85} -313.857 q^{86} +265.425i q^{87} +210.825i q^{88} +387.024 q^{89} +(123.595 - 56.9687i) q^{90} +103.741 q^{91} -170.350i q^{92} +144.985i q^{93} -88.2502 q^{94} +(67.1699 + 145.727i) q^{95} -555.107 q^{96} +1221.54i q^{97} -419.203i q^{98} +99.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - 82 q^{4} - 14 q^{5} + 18 q^{6} - 126 q^{9}+O(q^{10}) \) 14 * q - 82 * q^4 - 14 * q^5 + 18 * q^6 - 126 * q^9	\( 14 q - 82 q^{4} - 14 q^{5} + 18 q^{6} - 126 q^{9} - 28 q^{10} - 154 q^{11} - 284 q^{14} + 362 q^{16} - 52 q^{19} + 226 q^{20} + 300 q^{21} - 126 q^{24} - 366 q^{25} + 952 q^{26} - 1144 q^{29} - 582 q^{30} - 280 q^{31} + 1612 q^{34} - 600 q^{35} + 738 q^{36} - 144 q^{39} + 176 q^{40} + 1792 q^{41} + 902 q^{44} + 126 q^{45} - 688 q^{46} - 590 q^{49} + 388 q^{50} + 228 q^{51} - 162 q^{54} + 154 q^{55} + 3044 q^{56} - 2632 q^{59} - 1140 q^{60} - 772 q^{61} - 1738 q^{64} - 904 q^{65} - 198 q^{66} - 1368 q^{69} + 84 q^{70} + 1608 q^{71} + 1496 q^{74} - 300 q^{75} - 3396 q^{76} + 748 q^{79} - 2606 q^{80} + 1134 q^{81} - 5040 q^{84} + 2508 q^{85} - 5068 q^{86} - 1388 q^{89} + 252 q^{90} - 6752 q^{91} + 5840 q^{94} + 1724 q^{95} + 5946 q^{96} + 1386 q^{99}+O(q^{100}) \) 14 * q - 82 * q^4 - 14 * q^5 + 18 * q^6 - 126 * q^9 - 28 * q^10 - 154 * q^11 - 284 * q^14 + 362 * q^16 - 52 * q^19 + 226 * q^20 + 300 * q^21 - 126 * q^24 - 366 * q^25 + 952 * q^26 - 1144 * q^29 - 582 * q^30 - 280 * q^31 + 1612 * q^34 - 600 * q^35 + 738 * q^36 - 144 * q^39 + 176 * q^40 + 1792 * q^41 + 902 * q^44 + 126 * q^45 - 688 * q^46 - 590 * q^49 + 388 * q^50 + 228 * q^51 - 162 * q^54 + 154 * q^55 + 3044 * q^56 - 2632 * q^59 - 1140 * q^60 - 772 * q^61 - 1738 * q^64 - 904 * q^65 - 198 * q^66 - 1368 * q^69 + 84 * q^70 + 1608 * q^71 + 1496 * q^74 - 300 * q^75 - 3396 * q^76 + 748 * q^79 - 2606 * q^80 + 1134 * q^81 - 5040 * q^84 + 2508 * q^85 - 5068 * q^86 - 1388 * q^89 + 252 * q^90 - 6752 * q^91 + 5840 * q^94 + 1724 * q^95 + 5946 * q^96 + 1386 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more