LMFDB - Embedded newform 165.4.c.b.34.11

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} + 66x^{12} + 1705x^{10} + 22060x^{8} + 151880x^{6} + 537860x^{4} + 825344x^{2} + 262144 $ x^14 + 66x^12 + 1705x^10 + 22060x^8 + 151880x^6 + 537860x^4 + 825344x^2 + 262144
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{4}\cdot 3^{4}\cdot 5 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			34.11
Root			$1.98683i$ of defining polynomial
Character	$\chi$	$=$	165.34
Dual form			165.4.c.b.34.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.98683i q^{2} +3.00000i q^{3} -0.921158 q^{4} +(7.35339 - 8.42185i) q^{5} -8.96049 q^{6} +6.37827i q^{7} +21.1433i q^{8} -9.00000 q^{9} +O(q^{10})$	\(q+2.98683i q^{2} +3.00000i q^{3} -0.921158 q^{4} +(7.35339 - 8.42185i) q^{5} -8.96049 q^{6} +6.37827i q^{7} +21.1433i q^{8} -9.00000 q^{9} +(25.1547 + 21.9633i) q^{10} +11.0000 q^{11} -2.76347i q^{12} +46.0805i q^{13} -19.0508 q^{14} +(25.2656 + 22.0602i) q^{15} -70.5207 q^{16} +117.372i q^{17} -26.8815i q^{18} +82.9059 q^{19} +(-6.77363 + 7.75786i) q^{20} -19.1348 q^{21} +32.8551i q^{22} -23.1556i q^{23} -63.4299 q^{24} +(-16.8552 - 123.858i) q^{25} -137.635 q^{26} -27.0000i q^{27} -5.87540i q^{28} -218.964 q^{29} +(-65.8900 + 75.4640i) q^{30} -39.0954 q^{31} -41.4871i q^{32} +33.0000i q^{33} -350.571 q^{34} +(53.7169 + 46.9020i) q^{35} +8.29042 q^{36} -277.626i q^{37} +247.626i q^{38} -138.242 q^{39} +(178.066 + 155.475i) q^{40} +311.118 q^{41} -57.1525i q^{42} -406.989i q^{43} -10.1327 q^{44} +(-66.1805 + 75.7967i) q^{45} +69.1618 q^{46} +515.458i q^{47} -211.562i q^{48} +302.318 q^{49} +(369.944 - 50.3437i) q^{50} -352.117 q^{51} -42.4474i q^{52} +177.939i q^{53} +80.6444 q^{54} +(80.8873 - 92.6404i) q^{55} -134.858 q^{56} +248.718i q^{57} -654.008i q^{58} -18.3427 q^{59} +(-23.2736 - 20.3209i) q^{60} +766.183 q^{61} -116.771i q^{62} -57.4045i q^{63} -440.251 q^{64} +(388.083 + 338.848i) q^{65} -98.5654 q^{66} +100.568i q^{67} -108.118i q^{68} +69.4668 q^{69} +(-140.088 + 160.443i) q^{70} -1.02018 q^{71} -190.290i q^{72} -585.922i q^{73} +829.221 q^{74} +(371.575 - 50.5657i) q^{75} -76.3694 q^{76} +70.1610i q^{77} -412.904i q^{78} -658.601 q^{79} +(-518.567 + 593.915i) q^{80} +81.0000 q^{81} +929.256i q^{82} -1258.16i q^{83} +17.6262 q^{84} +(988.492 + 863.084i) q^{85} +1215.61 q^{86} -656.892i q^{87} +232.576i q^{88} +1122.10 q^{89} +(-226.392 - 197.670i) q^{90} -293.914 q^{91} +21.3300i q^{92} -117.286i q^{93} -1539.59 q^{94} +(609.640 - 698.221i) q^{95} +124.461 q^{96} -527.122i q^{97} +902.972i q^{98} -99.0000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q - 26 q^{4} - 14 q^{5} - 30 q^{6} - 126 q^{9}+O(q^{10}) $ 14 * q - 26 * q^4 - 14 * q^5 - 30 * q^6 - 126 * q^9	$ 14 q - 26 q^{4} - 14 q^{5} - 30 q^{6} - 126 q^{9} - 48 q^{10} + 154 q^{11} - 84 q^{14} - 86 q^{16} - 116 q^{19} + 442 q^{20} - 204 q^{21} + 450 q^{24} + 162 q^{25} - 400 q^{26} - 128 q^{29} + 246 q^{30} - 696 q^{31} - 412 q^{34} + 672 q^{35} + 234 q^{36} + 480 q^{39} + 1612 q^{40} - 664 q^{41} - 286 q^{44} + 126 q^{45} - 656 q^{46} + 834 q^{49} + 1908 q^{50} - 972 q^{51} + 270 q^{54} - 154 q^{55} - 3236 q^{56} + 664 q^{59} + 108 q^{60} + 44 q^{61} - 1122 q^{64} - 2328 q^{65} - 330 q^{66} + 1944 q^{69} + 1220 q^{70} - 1032 q^{71} - 3256 q^{74} + 84 q^{75} + 5588 q^{76} - 3492 q^{79} - 510 q^{80} + 1134 q^{81} - 1008 q^{84} - 1068 q^{85} + 2540 q^{86} + 4452 q^{89} + 432 q^{90} + 2144 q^{91} - 9472 q^{94} - 932 q^{95} + 450 q^{96} - 1386 q^{99}+O(q^{100}) $ 14 * q - 26 * q^4 - 14 * q^5 - 30 * q^6 - 126 * q^9 - 48 * q^10 + 154 * q^11 - 84 * q^14 - 86 * q^16 - 116 * q^19 + 442 * q^20 - 204 * q^21 + 450 * q^24 + 162 * q^25 - 400 * q^26 - 128 * q^29 + 246 * q^30 - 696 * q^31 - 412 * q^34 + 672 * q^35 + 234 * q^36 + 480 * q^39 + 1612 * q^40 - 664 * q^41 - 286 * q^44 + 126 * q^45 - 656 * q^46 + 834 * q^49 + 1908 * q^50 - 972 * q^51 + 270 * q^54 - 154 * q^55 - 3236 * q^56 + 664 * q^59 + 108 * q^60 + 44 * q^61 - 1122 * q^64 - 2328 * q^65 - 330 * q^66 + 1944 * q^69 + 1220 * q^70 - 1032 * q^71 - 3256 * q^74 + 84 * q^75 + 5588 * q^76 - 3492 * q^79 - 510 * q^80 + 1134 * q^81 - 1008 * q^84 - 1068 * q^85 + 2540 * q^86 + 4452 * q^89 + 432 * q^90 + 2144 * q^91 - 9472 * q^94 - 932 * q^95 + 450 * 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 $

$2$			2.98683i			1.05600i	0.849243	+	0.528002i	$0.177059\pi$
$2$			2.98683i			1.05600i	−0.849243	+	0.528002i	$0.822941\pi$
$3$			3.00000i			0.577350i
$3$			3.00000i			0.577350i
$4$	−0.921158			−0.115145
$5$	7.35339	−	8.42185i	0.657707	−	0.753273i
$5$	7.35339	−	8.42185i	0.657707	−	0.753273i
$6$	−8.96049			−0.609684
$7$			6.37827i			0.344394i	0.985062	+	0.172197i	$0.0550866\pi$
$7$			6.37827i			0.344394i	−0.985062	+	0.172197i	$0.944913\pi$
$8$			21.1433i			0.934411i
$9$	−9.00000			−0.333333
$10$	25.1547	+	21.9633i	0.795460	+	0.694542i
$11$	11.0000			0.301511
$11$	11.0000			0.301511
$12$		−	2.76347i		−	0.0664788i
$13$			46.0805i			0.983110i	0.870846	+	0.491555i	$0.163571\pi$
$13$			46.0805i			0.983110i	−0.870846	+	0.491555i	$0.836429\pi$
$14$	−19.0508			−0.363682
$15$	25.2656	+	22.0602i	0.434903	+	0.379728i
$16$	−70.5207			−1.10189
$17$			117.372i			1.67453i	0.546800	+	0.837263i	$0.315846\pi$
$17$			117.372i			1.67453i	−0.546800	+	0.837263i	$0.684154\pi$
$18$		−	26.8815i		−	0.352001i
$19$	82.9059			1.00105			0.500524	−	0.865723i	$-0.333141\pi$
$19$	82.9059			1.00105			0.500524	+	0.865723i	$0.333141\pi$
$20$	−6.77363	+	7.75786i	−0.0757315	+	0.0867355i
$21$	−19.1348			−0.198836
$22$			32.8551i			0.318397i
$23$		−	23.1556i		−	0.209925i	−0.994476	−	0.104962i	$-0.966528\pi$
$23$		−	23.1556i		−	0.209925i	0.994476	−	0.104962i	$-0.0334723\pi$
$24$	−63.4299			−0.539482
$25$	−16.8552	−	123.858i	−0.134842	−	0.990867i
$26$	−137.635			−1.03817
$27$		−	27.0000i		−	0.192450i
$28$		−	5.87540i		−	0.0396552i
$29$	−218.964			−1.40209			−0.701044	−	0.713118i	$-0.747283\pi$
$29$	−218.964			−1.40209			−0.701044	+	0.713118i	$0.747283\pi$
$30$	−65.8900	+	75.4640i	−0.400994	+	0.459259i
$31$	−39.0954			−0.226508			−0.113254	−	0.993566i	$-0.536127\pi$
$31$	−39.0954			−0.226508			−0.113254	+	0.993566i	$0.536127\pi$
$32$		−	41.4871i		−	0.229186i
$33$			33.0000i			0.174078i
$34$	−350.571			−1.76831
$35$	53.7169	+	46.9020i	0.259423	+	0.226511i
$36$	8.29042			0.0383816
$37$		−	277.626i		−	1.23355i	−0.787139	−	0.616775i	$-0.788439\pi$
$37$		−	277.626i		−	1.23355i	0.787139	−	0.616775i	$-0.211561\pi$
$38$			247.626i			1.05711i
$39$	−138.242			−0.567599
$40$	178.066	+	155.475i	0.703867	+	0.614569i
$41$	311.118			1.18508			0.592542	−	0.805540i	$-0.298125\pi$
$41$	311.118			1.18508			0.592542	+	0.805540i	$0.298125\pi$
$42$		−	57.1525i		−	0.209972i
$43$		−	406.989i		−	1.44338i	−0.692217	−	0.721689i	$-0.743366\pi$
$43$		−	406.989i		−	1.44338i	0.692217	−	0.721689i	$-0.256634\pi$
$44$	−10.1327			−0.0347174
$45$	−66.1805	+	75.7967i	−0.219236	+	0.251091i
$46$	69.1618			0.221682
$47$			515.458i			1.59973i	0.600180	+	0.799865i	$0.295096\pi$
$47$			515.458i			1.59973i	−0.600180	+	0.799865i	$0.704904\pi$
$48$		−	211.562i		−	0.636174i
$49$	302.318			0.881392
$50$	369.944	−	50.3437i	1.04636	−	0.142393i
$51$	−352.117			−0.966789
$52$		−	42.4474i		−	0.113200i
$53$			177.939i			0.461166i	0.973053	+	0.230583i	$0.0740633\pi$
$53$			177.939i			0.461166i	−0.973053	+	0.230583i	$0.925937\pi$
$54$	80.6444			0.203228
$55$	80.8873	−	92.6404i	0.198306	−	0.227120i
$56$	−134.858			−0.321806
$57$			248.718i			0.577956i
$58$		−	654.008i		−	1.48061i
$59$	−18.3427			−0.0404750			−0.0202375	−	0.999795i	$-0.506442\pi$
$59$	−18.3427			−0.0404750			−0.0202375	+	0.999795i	$0.506442\pi$
$60$	−23.2736	−	20.3209i	−0.0500767	−	0.0437236i
$61$	766.183			1.60819			0.804096	−	0.594499i	$-0.202650\pi$
$61$	766.183			1.60819			0.804096	+	0.594499i	$0.202650\pi$
$62$		−	116.771i		−	0.239193i
$63$		−	57.4045i		−	0.114798i
$64$	−440.251			−0.859865
$65$	388.083	+	338.848i	0.740551	+	0.646599i
$66$	−98.5654			−0.183827
$67$			100.568i			0.183378i	0.995788	+	0.0916889i	$0.0292265\pi$
$67$			100.568i			0.183378i	−0.995788	+	0.0916889i	$0.970773\pi$
$68$		−	108.118i		−	0.192813i
$69$	69.4668			0.121200
$70$	−140.088	+	160.443i	−0.239196	+	0.273952i
$71$	−1.02018			−0.00170526			−0.000852631	−	1.00000i	$-0.500271\pi$
$71$	−1.02018			−0.00170526			−0.000852631		1.00000i	$0.500271\pi$
$72$		−	190.290i		−	0.311470i
$73$		−	585.922i		−	0.939411i	−0.882823	−	0.469705i	$-0.844360\pi$
$73$		−	585.922i		−	0.939411i	0.882823	−	0.469705i	$-0.155640\pi$
$74$	829.221			1.30263
$75$	371.575	−	50.5657i	0.572077	−	0.0778509i
$76$	−76.3694			−0.115265
$77$			70.1610i			0.103839i
$78$		−	412.904i		−	0.599387i
$79$	−658.601			−0.937955			−0.468978	−	0.883210i	$-0.655377\pi$
$79$	−658.601			−0.937955			−0.468978	+	0.883210i	$0.655377\pi$
$80$	−518.567	+	593.915i	−0.724719	+	0.830022i
$81$	81.0000			0.111111
$82$			929.256i			1.25145i
$83$		−	1258.16i		−	1.66387i	−0.554875	−	0.831934i	$-0.687234\pi$
$83$		−	1258.16i		−	1.66387i	0.554875	−	0.831934i	$-0.312766\pi$
$84$	17.6262			0.0228949
$85$	988.492	+	863.084i	1.26138	+	1.10135i
$86$	1215.61			1.52421
$87$		−	656.892i		−	0.809496i
$88$			232.576i			0.281735i
$89$	1122.10			1.33643			0.668215	−	0.743968i	$-0.267059\pi$
$89$	1122.10			1.33643			0.668215	+	0.743968i	$0.267059\pi$
$90$	−226.392	−	197.670i	−0.265153	−	0.231514i
$91$	−293.914			−0.338578
$92$			21.3300i			0.0241718i
$93$		−	117.286i		−	0.130774i
$94$	−1539.59			−1.68932
$95$	609.640	−	698.221i	0.658397	−	0.754063i
$96$	124.461			0.132320
$97$		−	527.122i		−	0.551765i	−0.961191	−	0.275882i	$-0.911030\pi$
$97$		−	527.122i		−	0.551765i	0.961191	−	0.275882i	$-0.0889700\pi$
$98$			902.972i			0.930754i
$99$	−99.0000			−0.100504
$100$	15.5263	+	114.093i	0.0155263	+	0.114093i
$101$	442.088			0.435538			0.217769	−	0.976000i	$-0.430122\pi$
$101$	442.088			0.435538			0.217769	+	0.976000i	$0.430122\pi$
$102$		−	1051.71i		−	1.02093i
$103$		−	322.216i		−	0.308242i	−0.988052	−	0.154121i	$-0.950745\pi$
$103$		−	322.216i		−	0.308242i	0.988052	−	0.154121i	$-0.0492545\pi$
$104$	−974.294			−0.918629
$105$	−140.706	+	161.151i	−0.130776	+	0.149778i
$106$	−531.473			−0.486993
$107$			1436.99i			1.29831i	0.760658	+	0.649153i	$0.224876\pi$
$107$			1436.99i			1.29831i	−0.760658	+	0.649153i	$0.775124\pi$
$108$			24.8713i			0.0221596i
$109$	313.989			0.275915			0.137957	−	0.990438i	$-0.455946\pi$
$109$	313.989			0.275915			0.137957	+	0.990438i	$0.455946\pi$
$110$	276.701	+	241.597i	0.239840	+	0.209412i
$111$	832.877			0.712191
$112$		−	449.801i		−	0.379484i
$113$		−	1773.00i		−	1.47602i	−0.674792	−	0.738008i	$-0.735767\pi$
$113$		−	1773.00i		−	1.47602i	0.674792	−	0.738008i	$-0.264233\pi$
$114$	−742.878			−0.610324
$115$	−195.013	−	170.272i	−0.158131	−	0.138069i
$116$	201.700			0.161443
$117$		−	414.725i		−	0.327703i
$118$		−	54.7867i		−	0.0427417i
$119$	−748.633			−0.576698
$120$	−466.425	+	534.197i	−0.354822	+	0.406378i
$121$	121.000			0.0909091
$122$			2288.46i			1.69826i
$123$			933.353i			0.684208i
$124$	36.0131			0.0260812
$125$	−1167.06	−	768.827i	−0.835080	−	0.550128i
$126$	171.457			0.121227
$127$		−	630.983i		−	0.440872i	−0.975401	−	0.220436i	$-0.929252\pi$
$127$		−	630.983i		−	0.440872i	0.975401	−	0.220436i	$-0.0707480\pi$
$128$		−	1646.85i		−	1.13721i
$129$	1220.97			0.833335
$130$	−1012.08	+	1159.14i	−0.682811	+	0.782025i
$131$	−2778.06			−1.85283			−0.926414	−	0.376506i	$-0.877125\pi$
$131$	−2778.06			−1.85283			−0.926414	+	0.376506i	$0.877125\pi$
$132$		−	30.3982i		−	0.0200441i
$133$			528.797i			0.344756i
$134$	−300.379			−0.193648
$135$	−227.390	−	198.542i	−0.144968	−	0.126576i
$136$	−2481.64			−1.56470
$137$			795.240i			0.495927i	0.968769	+	0.247963i	$0.0797613\pi$
$137$			795.240i			0.495927i	−0.968769	+	0.247963i	$0.920239\pi$
$138$			207.486i			0.127988i
$139$	−468.568			−0.285924			−0.142962	−	0.989728i	$-0.545663\pi$
$139$	−468.568			−0.285924			−0.142962	+	0.989728i	$0.545663\pi$
$140$	−49.4817	−	43.2041i	−0.0298712	−	0.0260815i
$141$	−1546.38			−0.923605
$142$		−	3.04712i		−	0.00180076i
$143$			506.886i			0.296419i
$144$	634.687			0.367295
$145$	−1610.13	+	1844.08i	−0.922164	+	1.05616i
$146$	1750.05			0.992022
$147$			906.953i			0.508872i
$148$			255.737i			0.142037i
$149$	1993.94			1.09631			0.548153	−	0.836378i	$-0.315331\pi$
$149$	1993.94			1.09631			0.548153	+	0.836378i	$0.315331\pi$
$150$	151.031	+	1109.83i	0.0822109	+	0.604116i
$151$	2105.73			1.13485			0.567424	−	0.823426i	$-0.307940\pi$
$151$	2105.73			1.13485			0.567424	+	0.823426i	$0.307940\pi$
$152$			1752.91i			0.935391i
$153$		−	1056.35i		−	0.558176i
$154$	−209.559			−0.109654
$155$	−287.484	+	329.256i	−0.148976	+	0.170622i
$156$	127.342			0.0653560
$157$		−	1317.28i		−	0.669622i	−0.942285	−	0.334811i	$-0.891328\pi$
$157$		−	1317.28i		−	0.669622i	0.942285	−	0.334811i	$-0.108672\pi$
$158$		−	1967.13i		−	0.990484i
$159$	−533.817			−0.266254
$160$	−349.398	−	305.071i	−0.172640	−	0.150737i
$161$	147.693			0.0722970
$162$			241.933i			0.117334i
$163$		−	1776.83i		−	0.853814i	−0.904295	−	0.426907i	$-0.859603\pi$
$163$		−	1776.83i		−	0.853814i	0.904295	−	0.426907i	$-0.140397\pi$
$164$	−286.588			−0.136456
$165$	277.921	+	242.662i	0.131128	+	0.114492i
$166$	3757.91			1.75705
$167$			984.259i			0.456073i	0.973653	+	0.228037i	$0.0732306\pi$
$167$			984.259i			0.456073i	−0.973653	+	0.228037i	$0.926769\pi$
$168$		−	404.573i		−	0.185795i
$169$	73.5862			0.0334939
$170$	−2577.89	+	2952.46i	−1.16303	+	1.33202i
$171$	−746.153			−0.333683
$172$			374.901i			0.166197i
$173$		−	2878.89i		−	1.26519i	−0.774483	−	0.632595i	$-0.781990\pi$
$173$		−	2878.89i		−	1.26519i	0.774483	−	0.632595i	$-0.218010\pi$
$174$	1962.02			0.854831
$175$	790.003	−	107.507i	0.341249	−	0.0464388i
$176$	−775.728			−0.332231
$177$		−	55.0282i		−	0.0233682i
$178$			3351.52i			1.41128i
$179$	465.925			0.194552			0.0972762	−	0.995257i	$-0.468987\pi$
$179$	465.925			0.194552			0.0972762	+	0.995257i	$0.468987\pi$
$180$	60.9627	−	69.8207i	0.0252438	−	0.0289118i
$181$	−1270.19			−0.521617			−0.260808	−	0.965391i	$-0.583989\pi$
$181$	−1270.19			−0.521617			−0.260808	+	0.965391i	$0.583989\pi$
$182$		−	877.872i		−	0.357540i
$183$			2298.55i			0.928490i
$184$	489.586			0.196156
$185$	−2338.12	−	2041.49i	−0.929201	−	0.811316i
$186$	350.314			0.138098
$187$			1291.10i			0.504889i
$188$		−	474.818i		−	0.184201i
$189$	172.213			0.0662787
$190$	2085.47	+	1820.89i	0.796294	+	0.695270i
$191$	−2060.27			−0.780504			−0.390252	−	0.920708i	$-0.627612\pi$
$191$	−2060.27			−0.780504			−0.390252	+	0.920708i	$0.627612\pi$
$192$		−	1320.75i		−	0.496443i
$193$			2409.42i			0.898622i	0.893375	+	0.449311i	$0.148330\pi$
$193$			2409.42i			0.898622i	−0.893375	+	0.449311i	$0.851670\pi$
$194$	1574.43			0.582666
$195$	−1016.54	+	1164.25i	−0.373314	+	0.427557i
$196$	−278.482			−0.101488
$197$			2893.23i			1.04637i	0.852220	+	0.523183i	$0.175256\pi$
$197$			2893.23i			1.04637i	−0.852220	+	0.523183i	$0.824744\pi$
$198$		−	295.696i		−	0.106132i
$199$	2610.78			0.930018			0.465009	−	0.885306i	$-0.346051\pi$
$199$	2610.78			0.930018			0.465009	+	0.885306i	$0.346051\pi$
$200$	2618.78	−	356.375i	0.925877	−	0.125998i
$201$	−301.704			−0.105873
$202$			1320.44i			0.459930i
$203$		−	1396.61i		−	0.482872i
$204$	324.355			0.111321
$205$	2287.77	−	2620.19i	0.779438	−	0.892692i
$206$	962.405			0.325504
$207$			208.400i			0.0699750i
$208$		−	3249.63i		−	1.08328i
$209$	911.965			0.301827
$210$	−481.330	−	420.265i	−0.158166	−	0.138100i
$211$	−3015.17			−0.983757			−0.491878	−	0.870664i	$-0.663690\pi$
$211$	−3015.17			−0.983757			−0.491878	+	0.870664i	$0.663690\pi$
$212$		−	163.910i		−	0.0531008i
$213$		−	3.06055i		−	0.000984533i
$214$	−4292.03			−1.37102
$215$	−3427.60	−	2992.75i	−1.08726	−	0.949321i
$216$	570.869			0.179827
$217$		−	249.361i		−	0.0780081i
$218$			937.833i			0.291367i
$219$	1757.77			0.542369
$220$	−74.5100	+	85.3364i	−0.0228339	+	0.0261517i
$221$	−5408.57			−1.64624
$222$			2487.66i			0.752077i
$223$		−	3690.02i		−	1.10808i	−0.832490	−	0.554040i	$-0.813085\pi$
$223$		−	3690.02i		−	1.10808i	0.832490	−	0.554040i	$-0.186915\pi$
$224$	264.616			0.0789303
$225$	151.697	+	1114.73i	0.0449473	+	0.330289i
$226$	5295.65			1.55868
$227$		−	5408.08i		−	1.58126i	−0.612292	−	0.790631i	$-0.709752\pi$
$227$		−	5408.08i		−	1.58126i	0.612292	−	0.790631i	$-0.290248\pi$
$228$		−	229.108i		−	0.0665485i
$229$	4292.65			1.23872			0.619358	−	0.785109i	$-0.287393\pi$
$229$	4292.65			1.23872			0.619358	+	0.785109i	$0.287393\pi$
$230$	508.574	−	582.471i	0.145802	−	0.166987i
$231$	−210.483			−0.0599514
$232$		−	4629.62i		−	1.31013i
$233$		−	2481.67i		−	0.697767i	−0.937166	−	0.348884i	$-0.886561\pi$
$233$		−	2481.67i		−	0.697767i	0.937166	−	0.348884i	$-0.113439\pi$
$234$	1238.71			0.346056
$235$	4341.11	+	3790.37i	1.20503	+	1.05215i
$236$	16.8966			0.00466048
$237$		−	1975.80i		−	0.541529i
$238$		−	2236.04i		−	0.608995i
$239$	3821.47			1.03427			0.517134	−	0.855904i	$-0.326999\pi$
$239$	3821.47			1.03427			0.517134	+	0.855904i	$0.326999\pi$
$240$	−1781.75	−	1555.70i	−0.479213	−	0.418417i
$241$	1646.99			0.440217			0.220108	−	0.975475i	$-0.429359\pi$
$241$	1646.99			0.440217			0.220108	+	0.975475i	$0.429359\pi$
$242$			361.407i			0.0960004i
$243$			243.000i			0.0641500i
$244$	−705.776			−0.185175
$245$	2223.06	−	2546.07i	0.579698	−	0.663930i
$246$	−2787.77			−0.722527
$247$			3820.35i			0.984141i
$248$		−	826.607i		−	0.211652i
$249$	3774.48			0.960634
$250$	2296.36	−	3485.81i	0.580937	−	0.881848i
$251$	−7511.56			−1.88895			−0.944473	−	0.328590i	$-0.893427\pi$
$251$	−7511.56			−1.88895			−0.944473	+	0.328590i	$0.893427\pi$
$252$			52.8786i			0.0132184i
$253$		−	254.712i		−	0.0632948i
$254$	1884.64			0.465562
$255$	−2589.25	+	2965.48i	−0.635864	+	0.728256i
$256$	1396.86			0.341030
$257$			494.115i			0.119930i	0.998200	+	0.0599651i	$0.0190990\pi$
$257$			494.115i			0.119930i	−0.998200	+	0.0599651i	$0.980901\pi$
$258$			3646.82i			0.880005i
$259$	1770.77			0.424828
$260$	−357.486	−	312.133i	−0.0852705	−	0.0744525i
$261$	1970.67			0.467363
$262$		−	8297.60i		−	1.95659i
$263$			3850.31i			0.902740i	0.892337	+	0.451370i	$0.149064\pi$
$263$			3850.31i			0.902740i	−0.892337	+	0.451370i	$0.850936\pi$
$264$	−697.729			−0.162660
$265$	1498.58	+	1308.45i	0.347384	+	0.303312i
$266$	−1579.43			−0.364063
$267$			3366.30i			0.771588i
$268$		−	92.6389i		−	0.0211150i
$269$	−8047.29			−1.82399			−0.911993	−	0.410207i	$-0.865457\pi$
$269$	−8047.29			−1.82399			−0.911993	+	0.410207i	$0.865457\pi$
$270$	593.010	−	679.176i	0.133665	−	0.153086i
$271$	514.610			0.115352			0.0576759	−	0.998335i	$-0.481631\pi$
$271$	514.610			0.115352			0.0576759	+	0.998335i	$0.481631\pi$
$272$		−	8277.18i		−	1.84514i
$273$		−	881.743i		−	0.195478i
$274$	−2375.25			−0.523701
$275$	−185.407	−	1362.44i	−0.0406563	−	0.298758i
$276$	−63.9899			−0.0139556
$277$			949.916i			0.206047i	0.994679	+	0.103023i	$0.0328516\pi$
$277$			949.916i			0.206047i	−0.994679	+	0.103023i	$0.967148\pi$
$278$		−	1399.53i		−	0.301937i
$279$	351.859			0.0755027
$280$	−991.662	+	1135.75i	−0.211654	+	0.242408i
$281$	3195.97			0.678491			0.339245	−	0.940698i	$-0.389828\pi$
$281$	3195.97			0.678491			0.339245	+	0.940698i	$0.389828\pi$
$282$		−	4618.76i		−	0.975330i
$283$			1931.31i			0.405669i	0.979213	+	0.202834i	$0.0650153\pi$
$283$			1931.31i			0.405669i	−0.979213	+	0.202834i	$0.934985\pi$
$284$	0.939750			0.000196352
$285$	2094.66	+	1828.92i	0.435359	+	0.380126i
$286$	−1513.98			−0.313020
$287$			1984.39i			0.408136i
$288$			373.384i			0.0763953i
$289$	−8863.25			−1.80404
$290$	−5507.96	−	4809.18i	−1.11531	−	0.973809i
$291$	1581.37			0.318561
$292$			539.727i			0.108168i
$293$			7290.32i			1.45360i	0.686849	+	0.726801i	$0.258994\pi$
$293$			7290.32i			1.45360i	−0.686849	+	0.726801i	$0.741006\pi$
$294$	−2708.91			−0.537371
$295$	−134.881	+	154.480i	−0.0266207	+	0.0304887i
$296$	5869.92			1.15264
$297$		−	297.000i		−	0.0580259i
$298$			5955.55i			1.15770i
$299$	1067.02			0.206379
$300$	−342.279	+	46.5790i	−0.0658717	+	0.00896413i
$301$	2595.89			0.497091
$302$			6289.46i			1.19840i
$303$			1326.26i			0.251458i
$304$	−5846.59			−1.10304
$305$	5634.05	−	6452.68i	1.05772	−	1.21141i
$306$	3155.14			0.589436
$307$			1220.17i			0.226836i	0.993547	+	0.113418i	$0.0361799\pi$
$307$			1220.17i			0.226836i	−0.993547	+	0.113418i	$0.963820\pi$
$308$		−	64.6294i		−	0.0119565i
$309$	966.648			0.177963
$310$	−983.432	−	858.666i	−0.180178	−	0.157319i
$311$	3798.09			0.692507			0.346254	−	0.938141i	$-0.387454\pi$
$311$	3798.09			0.692507			0.346254	+	0.938141i	$0.387454\pi$
$312$		−	2922.88i		−	0.530371i
$313$			1852.83i			0.334595i	0.985906	+	0.167297i	$0.0535040\pi$
$313$			1852.83i			0.334595i	−0.985906	+	0.167297i	$0.946496\pi$
$314$	3934.50			0.707124
$315$	−483.452	−	422.118i	−0.0864744	−	0.0755036i
$316$	606.676			0.108001
$317$			7402.17i			1.31151i	0.754975	+	0.655753i	$0.227649\pi$
$317$			7402.17i			1.31151i	−0.754975	+	0.655753i	$0.772351\pi$
$318$		−	1594.42i		−	0.281166i
$319$	−2408.60			−0.422746
$320$	−3237.34	+	3707.73i	−0.565540	+	0.647714i
$321$	−4310.96			−0.749577
$322$			441.133i			0.0763459i
$323$			9730.86i			1.67628i
$324$	−74.6138			−0.0127939
$325$	5707.46	−	776.697i	0.974132	−	0.132564i
$326$	5307.08			0.901631
$327$			941.968i			0.159299i
$328$			6578.06i			1.10735i
$329$	−3287.74			−0.550938
$330$	−724.790	+	830.103i	−0.120904	+	0.138472i
$331$	−8301.05			−1.37845			−0.689225	−	0.724548i	$-0.742049\pi$
$331$	−8301.05			−1.37845			−0.689225	+	0.724548i	$0.742049\pi$
$332$			1158.96i			0.191586i
$333$			2498.63i			0.411184i
$334$	−2939.81			−0.481615
$335$	846.968	+	739.515i	0.138134	+	0.120609i
$336$	1349.40			0.219095
$337$			4760.81i			0.769548i	0.923011	+	0.384774i	$0.125721\pi$
$337$			4760.81i			0.769548i	−0.923011	+	0.384774i	$0.874279\pi$
$338$			219.790i			0.0353697i
$339$	5319.00			0.852178
$340$	−910.557	−	795.037i	−0.145241	−	0.126815i
$341$	−430.050			−0.0682947
$342$		−	2228.63i		−	0.352370i
$343$			4116.01i			0.647941i
$344$	8605.10			1.34871
$345$	510.817	−	585.039i	0.0797143	−	0.0912969i
$346$	8598.75			1.33605
$347$		−	1211.41i		−	0.187412i	−0.995600	−	0.0937060i	$-0.970129\pi$
$347$		−	1211.41i		−	0.187412i	0.995600	−	0.0937060i	$-0.0298714\pi$
$348$			605.101i			0.0932092i
$349$	−2102.90			−0.322537			−0.161269	−	0.986911i	$-0.551559\pi$
$349$	−2102.90			−0.322537			−0.161269	+	0.986911i	$0.551559\pi$
$350$	321.106	+	2359.60i	0.0490395	+	0.360361i
$351$	1244.17			0.189200
$352$		−	456.358i		−	0.0691021i
$353$		−	4888.60i		−	0.737093i	−0.929609	−	0.368546i	$-0.879856\pi$
$353$		−	4888.60i		−	0.737093i	0.929609	−	0.368546i	$-0.120144\pi$
$354$	164.360			0.0246769
$355$	−7.50181	+	8.59184i	−0.00112156	+	0.00128453i
$356$	−1033.63			−0.153883
$357$		−	2245.90i		−	0.332957i
$358$			1391.64i			0.205448i
$359$	−10187.1			−1.49765			−0.748825	−	0.662768i	$-0.769382\pi$
$359$	−10187.1			−1.49765			−0.748825	+	0.662768i	$0.769382\pi$
$360$	−1602.59	−	1399.28i	−0.234622	−	0.204856i
$361$	14.3915			0.00209820
$362$		−	3793.85i		−	0.550830i
$363$			363.000i			0.0524864i
$364$	270.741			0.0389854
$365$	−4934.55	−	4308.51i	−0.707633	−	0.617857i
$366$	−6865.38			−0.980490
$367$			10674.3i			1.51824i	0.650952	+	0.759118i	$0.274370\pi$
$367$			10674.3i			1.51824i	−0.650952	+	0.759118i	$0.725630\pi$
$368$			1632.95i			0.231314i
$369$	−2800.06			−0.395028
$370$	6097.59	−	6983.58i	0.856753	−	0.981240i
$371$	−1134.94			−0.158823
$372$			108.039i			0.0150580i
$373$			1674.87i			0.232498i	0.993220	+	0.116249i	$0.0370870\pi$
$373$			1674.87i			0.232498i	−0.993220	+	0.116249i	$0.962913\pi$
$374$	−3856.28			−0.533165
$375$	2306.48	−	3501.18i	0.317617	−	0.482134i
$376$	−10898.5			−1.49481
$377$		−	10090.0i		−	1.37841i
$378$			514.372i			0.0699906i
$379$	−13912.2			−1.88555			−0.942776	−	0.333428i	$-0.891795\pi$
$379$	−13912.2			−1.88555			−0.942776	+	0.333428i	$0.891795\pi$
$380$	−561.574	+	643.172i	−0.0758109	+	0.0868264i
$381$	1892.95			0.254537
$382$		−	6153.69i		−	0.824215i
$383$			5368.14i			0.716185i	0.933686	+	0.358093i	$0.116573\pi$
$383$			5368.14i			0.716185i	−0.933686	+	0.358093i	$0.883427\pi$
$384$	4940.56			0.656567
$385$	590.886	+	515.922i	0.0782190	+	0.0682956i
$386$	−7196.54			−0.948949
$387$			3662.90i			0.481126i
$388$			485.563i			0.0635328i
$389$	13523.6			1.76265			0.881326	−	0.472509i	$-0.156652\pi$
$389$	13523.6			1.76265			0.881326	+	0.472509i	$0.156652\pi$
$390$	−3477.42	−	3036.25i	−0.451502	−	0.394221i
$391$	2717.82			0.351525
$392$			6391.99i			0.823583i
$393$		−	8334.19i		−	1.06973i
$394$	−8641.59			−1.10497
$395$	−4842.95	+	5546.64i	−0.616900	+	0.706537i
$396$	91.1946			0.0115725
$397$		−	7522.12i		−	0.950944i	−0.879731	−	0.475472i	$-0.842277\pi$
$397$		−	7522.12i		−	0.950944i	0.879731	−	0.475472i	$-0.157723\pi$
$398$			7797.97i			0.982103i
$399$	−1586.39			−0.199045
$400$	1188.64	+	8734.58i	0.148580	+	1.09182i
$401$	−6909.62			−0.860474			−0.430237	−	0.902716i	$-0.641570\pi$
$401$	−6909.62			−0.860474			−0.430237	+	0.902716i	$0.641570\pi$
$402$		−	901.137i		−	0.111803i
$403$		−	1801.54i		−	0.222682i
$404$	−407.232			−0.0501499
$405$	595.625	−	682.170i	0.0730786	−	0.0836971i
$406$	4171.44			0.509914
$407$		−	3053.88i		−	0.371930i
$408$		−	7444.91i		−	0.903378i
$409$	−12852.7			−1.55385			−0.776925	−	0.629594i	$-0.783221\pi$
$409$	−12852.7			−1.55385			−0.776925	+	0.629594i	$0.783221\pi$
$410$	7826.06	+	6833.18i	0.942686	+	0.823090i
$411$	−2385.72			−0.286323
$412$			296.812i			0.0354924i
$413$		−	116.995i		−	0.0139394i
$414$	−622.457			−0.0738939
$415$	−10596.0	−	9251.74i	−1.25335	−	1.09434i
$416$	1911.74			0.225315
$417$		−	1405.70i		−	0.165078i
$418$			2723.89i			0.318731i
$419$	−4750.89			−0.553929			−0.276964	−	0.960880i	$-0.589328\pi$
$419$	−4750.89			−0.553929			−0.276964	+	0.960880i	$0.589328\pi$
$420$	129.612	−	148.445i	0.0150582	−	0.0172462i
$421$	6277.43			0.726706			0.363353	−	0.931652i	$-0.381632\pi$
$421$	6277.43			0.726706			0.363353	+	0.931652i	$0.381632\pi$
$422$		−	9005.80i		−	1.03885i
$423$		−	4639.13i		−	0.533243i
$424$	−3762.22			−0.430918
$425$	14537.5	−	1978.34i	1.65923	−	0.225796i
$426$	9.14135			0.00103967
$427$			4886.93i			0.553852i
$428$		−	1323.69i		−	0.149493i
$429$	−1520.66			−0.171138
$430$	8938.84	−	10237.7i	1.00249	−	1.14815i
$431$	11831.0			1.32222			0.661112	−	0.750288i	$-0.270085\pi$
$431$	11831.0			1.32222			0.661112	+	0.750288i	$0.270085\pi$
$432$			1904.06i			0.212058i
$433$			6675.54i			0.740891i	0.928854	+	0.370446i	$0.120795\pi$
$433$			6675.54i			0.740891i	−0.928854	+	0.370446i	$0.879205\pi$
$434$	744.800			0.0823769
$435$	−5532.24	−	4830.38i	−0.609772	−	0.532412i
$436$	−289.234			−0.0317701
$437$		−	1919.74i		−	0.210145i
$438$			5250.15i			0.572744i
$439$	−16289.0			−1.77091			−0.885455	−	0.464725i	$-0.846153\pi$
$439$	−16289.0			−1.77091			−0.885455	+	0.464725i	$0.846153\pi$
$440$	1958.72	+	1710.23i	0.212224	+	0.185300i
$441$	−2720.86			−0.293797
$442$		−	16154.5i		−	1.73844i
$443$		−	15833.7i		−	1.69815i	−0.528272	−	0.849075i	$-0.677160\pi$
$443$		−	15833.7i		−	1.69815i	0.528272	−	0.849075i	$-0.322840\pi$
$444$	−767.211			−0.0820050
$445$	8251.24	−	9450.15i	0.878980	−	1.00670i
$446$	11021.5			1.17014
$447$			5981.81i			0.632953i
$448$		−	2808.04i		−	0.296133i
$449$	12865.7			1.35227			0.676135	−	0.736778i	$-0.263654\pi$
$449$	12865.7			1.35227			0.676135	+	0.736778i	$0.263654\pi$
$450$	−3329.50	+	453.093i	−0.348787	+	0.0474645i
$451$	3422.29			0.357316
$452$			1633.21i			0.169955i
$453$			6317.19i			0.655204i
$454$	16153.0			1.66982
$455$	−2161.27	+	2475.30i	−0.222685	+	0.255042i
$456$	−5258.72			−0.540048
$457$			24.2151i			0.00247863i	0.999999	+	0.00123932i	$0.000394487\pi$
$457$			24.2151i			0.00247863i	−0.999999	+	0.00123932i	$0.999606\pi$
$458$			12821.4i			1.30809i
$459$	3169.05			0.322263
$460$	179.638	+	156.848i	0.0182079	+	0.0158979i
$461$	2731.66			0.275978			0.137989	−	0.990434i	$-0.455936\pi$
$461$	2731.66			0.275978			0.137989	+	0.990434i	$0.455936\pi$
$462$		−	628.677i		−	0.0633089i
$463$		−	1298.92i		−	0.130380i	−0.997873	−	0.0651901i	$-0.979235\pi$
$463$		−	1298.92i		−	0.130380i	0.997873	−	0.0651901i	$-0.0207654\pi$
$464$	15441.5			1.54494
$465$	−987.768	−	862.452i	−0.0985089	−	0.0860113i
$466$	7412.34			0.736845
$467$			2009.42i			0.199111i	0.995032	+	0.0995557i	$0.0317422\pi$
$467$			2009.42i			0.199111i	−0.995032	+	0.0995557i	$0.968258\pi$
$468$			382.027i			0.0377333i
$469$	−641.449			−0.0631543
$470$	−11321.2	+	12966.2i	−1.11108	+	1.27252i
$471$	3951.85			0.386606
$472$		−	387.826i		−	0.0378202i
$473$		−	4476.88i		−	0.435195i
$474$	5901.39			0.571856
$475$	−1397.40	−	10268.6i	−0.134983	−	0.991906i
$476$	689.609			0.0664037
$477$		−	1601.45i		−	0.153722i
$478$			11414.1i			1.09219i
$479$	−7137.51			−0.680837			−0.340419	−	0.940274i	$-0.610569\pi$
$479$	−7137.51			−0.680837			−0.340419	+	0.940274i	$0.610569\pi$
$480$	915.212	−	1048.19i	0.0870282	−	0.0996735i
$481$	12793.1			1.21272
$482$			4919.29i			0.464871i
$483$			443.078i			0.0417407i
$484$	−111.460			−0.0104677
$485$	−4439.35	−	3876.14i	−0.415630	−	0.362900i
$486$	−725.800			−0.0677427
$487$			17766.0i			1.65309i	0.562868	+	0.826547i	$0.309698\pi$
$487$			17766.0i			1.65309i	−0.562868	+	0.826547i	$0.690302\pi$
$488$			16199.6i			1.50271i
$489$	5330.48			0.492950
$490$	7604.69	+	6639.90i	0.701112	+	0.612164i
$491$	4139.76			0.380498			0.190249	−	0.981736i	$-0.439070\pi$
$491$	4139.76			0.380498			0.190249	+	0.981736i	$0.439070\pi$
$492$		−	859.765i		−	0.0787830i
$493$		−	25700.3i		−	2.34784i
$494$	−11410.7			−1.03926
$495$	−727.986	+	833.763i	−0.0661021	+	0.0757068i
$496$	2757.04			0.249586
$497$		−	6.50701i		−	0.000587283i
$498$			11273.7i			1.01443i
$499$	12017.3			1.07809			0.539047	−	0.842275i	$-0.318784\pi$
$499$	12017.3			1.07809			0.539047	+	0.842275i	$0.318784\pi$
$500$	1075.05	+	708.211i	0.0961551	+	0.0633443i
$501$	−2952.78			−0.263314
$502$		−	22435.8i		−	1.99473i
$503$			5223.09i			0.462994i	0.972836	+	0.231497i	$0.0743623\pi$
$503$			5223.09i			0.462994i	−0.972836	+	0.231497i	$0.925638\pi$
$504$	1213.72			0.107269
$505$	3250.84	−	3723.20i	0.286457	−	0.328079i
$506$	760.780			0.0668395
$507$			220.759i			0.0193377i
$508$			581.235i			0.0507641i
$509$	15072.3			1.31251			0.656257	−	0.754537i	$-0.272139\pi$
$509$	15072.3			1.31251			0.656257	+	0.754537i	$0.272139\pi$
$510$	−8857.38	−	7733.66i	−0.769042	−	0.671475i
$511$	3737.17			0.323528
$512$		−	9002.63i		−	0.777078i
$513$		−	2238.46i		−	0.192652i
$514$	−1475.84			−0.126647
$515$	−2713.66	−	2369.38i	−0.232190	−	0.202733i
$516$	−1124.70			−0.0959541
$517$			5670.04i			0.482337i
$518$			5289.00i			0.448620i
$519$	8636.66			0.730457
$520$	−7164.37	+	8205.36i	−0.604189	+	0.691979i
$521$	−5083.74			−0.427491			−0.213745	−	0.976889i	$-0.568566\pi$
$521$	−5083.74			−0.427491			−0.213745	+	0.976889i	$0.568566\pi$
$522$			5886.07i			0.493537i
$523$			3566.03i			0.298148i	0.988826	+	0.149074i	$0.0476293\pi$
$523$			3566.03i			0.298148i	−0.988826	+	0.149074i	$0.952371\pi$
$524$	2559.03			0.213343
$525$	322.522	+	2370.01i	0.0268114	+	0.197020i
$526$	−11500.2			−0.953297
$527$		−	4588.72i		−	0.379294i
$528$		−	2327.18i		−	0.191814i
$529$	11630.8			0.955931
$530$	−3908.13	+	4475.99i	−0.320299	+	0.366839i
$531$	165.085			0.0134917
$532$		−	487.105i		−	0.0396968i
$533$			14336.5i			1.16507i
$534$	−10054.6			−0.814800
$535$	12102.1	+	10566.7i	0.977979	+	0.853905i
$536$	−2126.34			−0.171350
$537$			1397.77i			0.112325i
$538$		−	24035.9i		−	1.92614i
$539$	3325.49			0.265750
$540$	209.462	+	182.888i	0.0166922	+	0.0145745i
$541$	−12123.4			−0.963448			−0.481724	−	0.876323i	$-0.659989\pi$
$541$	−12123.4			−0.963448			−0.481724	+	0.876323i	$0.659989\pi$
$542$			1537.05i			0.121812i
$543$		−	3810.58i		−	0.301156i
$544$	4869.43			0.383778
$545$	2308.89	−	2644.37i	0.181471	−	0.207839i
$546$	2633.62			0.206426
$547$		−	4883.04i		−	0.381689i	−0.981620	−	0.190844i	$-0.938877\pi$
$547$		−	4883.04i		−	0.381689i	0.981620	−	0.190844i	$-0.0611226\pi$
$548$		−	732.542i		−	0.0571034i
$549$	−6895.65			−0.536064
$550$	4069.38	−	553.781i	0.315489	−	0.0429333i
$551$	−18153.4			−1.40356
$552$			1468.76i			0.113251i
$553$		−	4200.74i		−	0.323027i
$554$	−2837.24			−0.217586
$555$	6124.47	−	7014.37i	0.468413	−	0.536475i
$556$	431.625			0.0329226
$557$			7572.07i			0.576013i	0.957629	+	0.288006i	$0.0929924\pi$
$557$			7572.07i			0.576013i	−0.957629	+	0.288006i	$0.907008\pi$
$558$			1050.94i			0.0797311i
$559$	18754.3			1.41900
$560$	−3788.15	−	3307.56i	−0.285855	−	0.249589i
$561$	−3873.29			−0.291498
$562$			9545.83i			0.716489i
$563$		−	5697.55i		−	0.426506i	−0.976997	−	0.213253i	$-0.931594\pi$
$563$		−	5697.55i		−	0.426506i	0.976997	−	0.213253i	$-0.0684059\pi$
$564$	1424.46			0.106348
$565$	−14931.9	−	13037.6i	−1.11184	−	0.970787i
$566$	−5768.49			−0.428388
$567$			516.640i			0.0382661i
$568$		−	21.5701i		−	0.00159341i
$569$	1611.88			0.118758			0.0593791	−	0.998236i	$-0.481088\pi$
$569$	1611.88			0.118758			0.0593791	+	0.998236i	$0.481088\pi$
$570$	−5462.67	+	6256.41i	−0.401414	+	0.459741i
$571$	8711.54			0.638470			0.319235	−	0.947676i	$-0.396574\pi$
$571$	8711.54			0.638470			0.319235	+	0.947676i	$0.396574\pi$
$572$		−	466.922i		−	0.0341311i
$573$		−	6180.82i		−	0.450624i
$574$	−5927.05			−0.430993
$575$	−2868.01	+	390.293i	−0.208008	+	0.0283067i
$576$	3962.26			0.286622
$577$		−	22988.8i		−	1.65864i	−0.558774	−	0.829320i	$-0.688728\pi$
$577$		−	22988.8i		−	1.65864i	0.558774	−	0.829320i	$-0.311272\pi$
$578$		−	26473.0i		−	1.90507i
$579$	−7228.27			−0.518820
$580$	1483.18	−	1698.69i	0.106182	−	0.121611i
$581$	8024.89			0.573027
$582$			4723.28i			0.336402i
$583$			1957.33i			0.139047i
$584$	12388.3			0.877796
$585$	−3492.75	−	3049.63i	−0.246850	−	0.215533i
$586$	−21775.0			−1.53501
$587$		−	8179.42i		−	0.575129i	−0.957761	−	0.287565i	$-0.907154\pi$
$587$		−	8179.42i		−	0.575129i	0.957761	−	0.287565i	$-0.0928456\pi$
$588$		−	835.447i		−	0.0585939i
$589$	−3241.24			−0.226745
$590$	−461.405	−	402.868i	−0.0321962	−	0.0281115i
$591$	−8679.70			−0.604120
$592$			19578.4i			1.35923i
$593$			9229.06i			0.639110i	0.947568	+	0.319555i	$0.103533\pi$
$593$			9229.06i			0.639110i	−0.947568	+	0.319555i	$0.896467\pi$
$594$	887.089			0.0612756
$595$	−5504.99	+	6304.87i	−0.379298	+	0.434411i
$596$	−1836.73			−0.126234
$597$			7832.35i			0.536946i
$598$			3187.01i			0.217938i
$599$	−17455.2			−1.19065			−0.595325	−	0.803485i	$-0.702977\pi$
$599$	−17455.2			−1.19065			−0.595325	+	0.803485i	$0.702977\pi$
$600$	1069.13	+	7856.33i	0.0727448	+	0.534555i
$601$	−1414.61			−0.0960122			−0.0480061	−	0.998847i	$-0.515287\pi$
$601$	−1414.61			−0.0960122			−0.0480061	+	0.998847i	$0.515287\pi$
$602$			7753.48i			0.524931i
$603$		−	905.111i		−	0.0611260i
$604$	−1939.71			−0.130672
$605$	889.761	−	1019.04i	0.0597916	−	0.0684794i
$606$	−3961.32			−0.265541
$607$			9733.00i			0.650824i	0.945572	+	0.325412i	$0.105503\pi$
$607$			9733.00i			0.650824i	−0.945572	+	0.325412i	$0.894497\pi$
$608$		−	3439.52i		−	0.229426i
$609$	4189.84			0.278786
$610$	19273.1	+	16827.9i	1.27925	+	1.11696i
$611$	−23752.6			−1.57271
$612$			973.065i			0.0642710i
$613$			24361.4i			1.60513i	0.596561	+	0.802567i	$0.296533\pi$
$613$			24361.4i			1.60513i	−0.596561	+	0.802567i	$0.703467\pi$
$614$	−3644.43			−0.239539
$615$	7860.56	+	6863.31i	0.515396	+	0.450009i
$616$	−1483.44			−0.0970281
$617$		−	8275.57i		−	0.539971i	−0.962864	−	0.269985i	$-0.912981\pi$
$617$		−	8275.57i		−	0.539971i	0.962864	−	0.269985i	$-0.0870189\pi$
$618$			2887.21i			0.187930i
$619$	−16003.0			−1.03912			−0.519560	−	0.854434i	$-0.673904\pi$
$619$	−16003.0			−1.03912			−0.519560	+	0.854434i	$0.673904\pi$
$620$	264.818	−	303.297i	0.0171538	−	0.0196463i
$621$	−625.201			−0.0404001
$622$			11344.2i			0.731291i
$623$			7157.06i			0.460259i
$624$	9748.89			0.625430
$625$	−15056.8	+	4175.32i	−0.963635	+	0.267221i
$626$	−5534.09			−0.353334
$627$			2735.90i			0.174260i
$628$			1213.43i			0.0771034i
$629$	32585.6			2.06561
$630$	1260.79	−	1443.99i	0.0797321	−	0.0913173i
$631$	21324.5			1.34535			0.672674	−	0.739939i	$-0.265146\pi$
$631$	21324.5			1.34535			0.672674	+	0.739939i	$0.265146\pi$
$632$		−	13925.0i		−	0.876435i
$633$		−	9045.50i		−	0.567972i
$634$	−22109.0			−1.38496
$635$	−5314.05	−	4639.87i	−0.332097	−	0.289965i
$636$	491.729			0.0306578
$637$			13931.0i			0.866506i
$638$		−	7194.09i		−	0.446421i
$639$	9.18166			0.000568421
$640$	−13869.5	−	12109.9i	−0.856628	−	0.747950i
$641$	−21660.7			−1.33471			−0.667353	−	0.744741i	$-0.732573\pi$
$641$	−21660.7			−1.33471			−0.667353	+	0.744741i	$0.732573\pi$
$642$		−	12876.1i		−	0.791556i
$643$		−	13379.3i		−	0.820575i	−0.911956	−	0.410287i	$-0.865428\pi$
$643$		−	13379.3i		−	0.820575i	0.911956	−	0.410287i	$-0.134572\pi$
$644$	−136.048			−0.00832462
$645$	8978.25	−	10282.8i	0.548091	−	0.627729i
$646$	−29064.4			−1.77016
$647$		−	14817.4i		−	0.900359i	−0.892938	−	0.450179i	$-0.851360\pi$
$647$		−	14817.4i		−	0.900359i	0.892938	−	0.450179i	$-0.148640\pi$
$648$			1712.61i			0.103823i
$649$	−201.770			−0.0122037
$650$	2319.86	+	17047.2i	0.139989	+	1.02869i
$651$	748.084			0.0450380
$652$			1636.74i			0.0983122i
$653$		−	8214.45i		−	0.492276i	−0.969235	−	0.246138i	$-0.920838\pi$
$653$		−	8214.45i		−	0.492276i	0.969235	−	0.246138i	$-0.0791617\pi$
$654$	−2813.50			−0.168221
$655$	−20428.2	+	23396.4i	−1.21862	+	1.39569i
$656$	−21940.2			−1.30583
$657$			5273.30i			0.313137i
$658$		−	9819.91i		−	0.581793i
$659$	14461.5			0.854843			0.427421	−	0.904053i	$-0.359422\pi$
$659$	14461.5			0.854843			0.427421	+	0.904053i	$0.359422\pi$
$660$	−256.009	−	223.530i	−0.0150987	−	0.0131832i
$661$	3311.80			0.194878			0.0974389	−	0.995242i	$-0.468935\pi$
$661$	3311.80			0.194878			0.0974389	+	0.995242i	$0.468935\pi$
$662$		−	24793.8i		−	1.45565i
$663$		−	16225.7i		−	0.950460i
$664$	26601.7			1.55474
$665$	4453.45	+	3888.45i	0.259695	+	0.226748i
$666$	−7462.99			−0.434212
$667$			5070.24i			0.294333i
$668$		−	906.657i		−	0.0525144i
$669$	11070.1			0.639750
$670$	−2208.81	+	2529.75i	−0.127364	+	0.145870i
$671$	8428.02			0.484888
$672$			793.848i			0.0455704i
$673$		−	17154.8i		−	0.982571i	−0.870999	−	0.491286i	$-0.836527\pi$
$673$		−	17154.8i		−	0.982571i	0.870999	−	0.491286i	$-0.163473\pi$
$674$	−14219.7			−0.812646
$675$	−3344.18	+	455.091i	−0.190692	+	0.0259503i
$676$	−67.7845			−0.00385665
$677$			9967.23i			0.565837i	0.959144	+	0.282919i	$0.0913026\pi$
$677$			9967.23i			0.565837i	−0.959144	+	0.282919i	$0.908697\pi$
$678$			15886.9i			0.899904i
$679$	3362.13			0.190025
$680$	−18248.5	+	20900.0i	−1.02911	+	1.17864i
$681$	16224.2			0.912942
$682$		−	1284.49i		−	0.0721195i
$683$		−	6859.68i		−	0.384302i	−0.981365	−	0.192151i	$-0.938454\pi$
$683$		−	6859.68i		−	0.384302i	0.981365	−	0.192151i	$-0.0615463\pi$
$684$	687.325			0.0384218
$685$	6697.40	+	5847.72i	0.373569	+	0.326175i
$686$	−12293.8			−0.684229
$687$			12877.9i			0.715173i
$688$			28701.2i			1.59044i
$689$	−8199.52			−0.453377
$690$	1747.41	+	1525.72i	0.0964099	+	0.0841786i
$691$	10609.4			0.584080			0.292040	−	0.956406i	$-0.405666\pi$
$691$	10609.4			0.584080			0.292040	+	0.956406i	$0.405666\pi$
$692$			2651.91i			0.145680i
$693$		−	631.449i		−	0.0346129i
$694$	3618.28			0.197908
$695$	−3445.57	+	3946.21i	−0.188054	+	0.215379i
$696$	13888.9			0.756402
$697$			36516.6i			1.98445i
$698$		−	6281.00i		−	0.340601i
$699$	7445.02			0.402856
$700$	−727.717	+	99.0311i	−0.0392930	+	0.00534718i
$701$	35711.5			1.92411			0.962057	−	0.272850i	$-0.0879664\pi$
$701$	35711.5			1.92411			0.962057	+	0.272850i	$0.0879664\pi$
$702$			3716.14i			0.199796i
$703$		−	23016.8i		−	1.23484i
$704$	−4842.76			−0.259259
$705$	−11371.1	+	13023.3i	−0.607462	+	0.695727i
$706$	14601.4			0.778373
$707$			2819.76i			0.149997i
$708$			50.6897i			0.00269073i
$709$	−8876.90			−0.470210			−0.235105	−	0.971970i	$-0.575543\pi$
$709$	−8876.90			−0.470210			−0.235105	+	0.971970i	$0.575543\pi$
$710$	−25.6624	−	22.4066i	−0.00135647	−	0.00118438i
$711$	5927.41			0.312652
$712$			23724.9i			1.24877i
$713$			905.278i			0.0475497i
$714$	6708.12			0.351604
$715$	4268.92	+	3727.33i	0.223285	+	0.194957i
$716$	−429.190			−0.0224017
$717$			11464.4i			0.597135i
$718$		−	30427.2i		−	1.58152i
$719$	−29427.3			−1.52636			−0.763181	−	0.646185i	$-0.776363\pi$
$719$	−29427.3			−1.52636			−0.763181	+	0.646185i	$0.776363\pi$
$720$	4667.10	−	5345.24i	0.241573	−	0.276674i
$721$	2055.18			0.106157
$722$			42.9851i			0.00221571i
$723$			4940.98i			0.254159i
$724$	1170.05			0.0600614
$725$	3690.69	+	27120.5i	0.189060	+	1.38928i
$726$	−1084.22			−0.0554258
$727$			15630.1i			0.797368i	0.917088	+	0.398684i	$0.130533\pi$
$727$			15630.1i			0.797368i	−0.917088	+	0.398684i	$0.869467\pi$
$728$		−	6214.32i		−	0.316371i
$729$	−729.000			−0.0370370
$730$	12868.8	−	14738.7i	0.652460	−	0.747264i
$731$	47769.2			2.41698
$732$		−	2117.33i		−	0.106911i
$733$		−	10487.2i		−	0.528451i	−0.964461	−	0.264226i	$-0.914884\pi$
$733$		−	10487.2i		−	0.528451i	0.964461	−	0.264226i	$-0.0851164\pi$
$734$	−31882.3			−1.60326
$735$	7638.22	+	6669.18i	0.383320	+	0.334689i
$736$	−960.657			−0.0481118
$737$			1106.25i			0.0552905i
$738$		−	8363.30i		−	0.417151i
$739$	18169.9			0.904454			0.452227	−	0.891903i	$-0.350630\pi$
$739$	18169.9			0.904454			0.452227	+	0.891903i	$0.350630\pi$
$740$	2153.78	+	1880.54i	0.106993	+	0.0934187i
$741$	−11461.0			−0.568194
$742$		−	3389.88i		−	0.167718i
$743$			2297.97i			0.113465i	0.998389	+	0.0567324i	$0.0180682\pi$
$743$			2297.97i			0.113465i	−0.998389	+	0.0567324i	$0.981932\pi$
$744$	2479.82			0.122197
$745$	14662.2	−	16792.6i	0.721049	−	0.825819i
$746$	−5002.56			−0.245519
$747$			11323.4i			0.554622i
$748$		−	1189.30i		−	0.0581353i
$749$	−9165.49			−0.447129
$750$	10457.4	+	6889.07i	0.509135	+	0.335404i
$751$	−6345.74			−0.308335			−0.154167	−	0.988045i	$-0.549269\pi$
$751$	−6345.74			−0.308335			−0.154167	+	0.988045i	$0.549269\pi$
$752$		−	36350.5i		−	1.76272i
$753$		−	22534.7i		−	1.09058i
$754$	30137.0			1.45560
$755$	15484.3	−	17734.2i	0.746398	−	0.854850i
$756$	−158.636			−0.00763165
$757$		−	23466.2i		−	1.12668i	−0.826227	−	0.563338i	$-0.809517\pi$
$757$		−	23466.2i		−	1.12668i	0.826227	−	0.563338i	$-0.190483\pi$
$758$		−	41553.5i		−	1.99115i
$759$	764.135			0.0365433
$760$	14762.7	+	12889.8i	0.704605	+	0.615213i
$761$	4503.87			0.214541			0.107270	−	0.994230i	$-0.465789\pi$
$761$	4503.87			0.214541			0.107270	+	0.994230i	$0.465789\pi$
$762$			5653.92i			0.268793i
$763$			2002.71i			0.0950235i
$764$	1897.84			0.0898709
$765$	−8896.43	−	7767.76i	−0.420459	−	0.367116i
$766$	−16033.7			−0.756295
$767$		−	845.243i		−	0.0397914i
$768$			4190.58i			0.196894i
$769$	−18535.4			−0.869183			−0.434592	−	0.900628i	$-0.643107\pi$
$769$	−18535.4			−0.869183			−0.434592	+	0.900628i	$0.643107\pi$
$770$	−1540.97	+	1764.88i	−0.0721204	+	0.0825996i
$771$	−1482.35			−0.0692418
$772$		−	2219.46i		−	0.103472i
$773$			11175.3i			0.519982i	0.965611	+	0.259991i	$0.0837196\pi$
$773$			11175.3i			0.519982i	−0.965611	+	0.259991i	$0.916280\pi$
$774$	−10940.5			−0.508071
$775$	658.962	+	4842.30i	0.0305427	+	0.224439i
$776$	11145.1			0.515575
$777$			5312.32i			0.245275i
$778$			40392.6i			1.86137i
$779$	25793.5			1.18633
$780$	936.398	−	1072.46i	0.0429852	−	0.0492310i
$781$	−11.2220			−0.000514156
$782$			8117.68i			0.371212i
$783$			5912.02i			0.269832i
$784$	−21319.7			−0.971194
$785$	−11094.0	−	9686.50i	−0.504408	−	0.440415i
$786$	24892.8			1.12964
$787$			9832.48i			0.445349i	0.974893	+	0.222675i	$0.0714788\pi$
$787$			9832.48i			0.445349i	−0.974893	+	0.222675i	$0.928521\pi$
$788$		−	2665.12i		−	0.120484i
$789$	−11550.9			−0.521197
$790$	−16566.9	−	14465.1i	−0.746106	−	0.651449i
$791$	11308.7			0.508332
$792$		−	2093.19i		−	0.0939118i
$793$			35306.1i			1.58103i
$794$	22467.3			1.00420
$795$	−3925.36	+	4495.73i	−0.175117	+	0.200562i
$796$	−2404.94			−0.107087
$797$		−	16910.3i		−	0.751562i	−0.926708	−	0.375781i	$-0.877374\pi$
$797$		−	16910.3i		−	0.751562i	0.926708	−	0.375781i	$-0.122626\pi$
$798$		−	4738.28i		−	0.210192i
$799$	−60500.5			−2.67879
$800$	−5138.52	+	699.274i	−0.227093	+	0.0309038i
$801$	−10098.9			−0.445477
$802$		−	20637.9i		−	0.908664i
$803$		−	6445.14i		−	0.283243i
$804$	277.917			0.0121907
$805$	1086.04	−	1243.85i	0.0475503	−	0.0544594i
$806$	5380.89			0.235153
$807$		−	24141.9i		−	1.05308i
$808$			9347.19i			0.406972i
$809$	−5452.73			−0.236969			−0.118485	−	0.992956i	$-0.537804\pi$
$809$	−5452.73			−0.236969			−0.118485	+	0.992956i	$0.537804\pi$
$810$	2037.53	+	1779.03i	0.0883844	+	0.0771713i
$811$	24896.6			1.07798			0.538988	−	0.842313i	$-0.318807\pi$
$811$	24896.6			1.07798			0.538988	+	0.842313i	$0.318807\pi$
$812$			1286.50i			0.0556001i
$813$			1543.83i			0.0665983i
$814$	9121.43			0.392759
$815$	−14964.2	−	13065.7i	−0.643156	−	0.561560i
$816$	24831.5			1.06529
$817$		−	33741.8i		−	1.44489i
$818$		−	38388.8i		−	1.64087i
$819$	2645.23			0.112859
$820$	−2107.40	+	2413.61i	−0.0897482	+	0.102789i
$821$	−21112.2			−0.897469			−0.448734	−	0.893665i	$-0.648125\pi$
$821$	−21112.2			−0.897469			−0.448734	+	0.893665i	$0.648125\pi$
$822$		−	7125.75i		−	0.302359i
$823$		−	45743.4i		−	1.93744i	−0.248153	−	0.968721i	$-0.579824\pi$
$823$		−	45743.4i		−	1.93744i	0.248153	−	0.968721i	$-0.420176\pi$
$824$	6812.71			0.288024
$825$	4087.33	−	556.222i	0.172488	−	0.0234729i
$826$	349.445			0.0147200
$827$			17332.8i			0.728805i	0.931242	+	0.364402i	$0.118727\pi$
$827$			17332.8i			0.728805i	−0.931242	+	0.364402i	$0.881273\pi$
$828$		−	191.970i		−	0.00805725i
$829$	29411.6			1.23221			0.616107	−	0.787662i	$-0.288709\pi$
$829$	29411.6			1.23221			0.616107	+	0.787662i	$0.288709\pi$
$830$	27633.4	−	31648.6i	1.15563	−	1.32354i
$831$	−2849.75			−0.118961
$832$		−	20287.0i		−	0.845343i
$833$			35483.7i			1.47592i
$834$	4198.60			0.174323
$835$	8289.28	+	7237.64i	0.343548	+	0.299963i
$836$	−840.064			−0.0347538
$837$			1055.58i			0.0435915i
$838$		−	14190.1i		−	0.584951i
$839$	−32036.3			−1.31825			−0.659127	−	0.752031i	$-0.729074\pi$
$839$	−32036.3			−1.31825			−0.659127	+	0.752031i	$0.729074\pi$
$840$	−3407.26	−	2974.99i	−0.139954	−	0.122199i
$841$	23556.2			0.965853
$842$			18749.6i			0.767405i
$843$			9587.92i			0.391727i
$844$	2777.45			0.113274
$845$	541.108	−	619.732i	0.0220292	−	0.0252301i
$846$	13856.3			0.563107
$847$			771.771i			0.0313086i
$848$		−	12548.4i		−	0.508152i
$849$	−5793.92			−0.234213
$850$	5908.95	+	43421.2i	0.238442	+	1.75216i
$851$	−6428.59			−0.258953
$852$			2.81925i			0.000113364i
$853$		−	30906.3i		−	1.24058i	−0.784373	−	0.620289i	$-0.787015\pi$
$853$		−	30906.3i		−	1.24058i	0.784373	−	0.620289i	$-0.212985\pi$
$854$	−14596.4			−0.584871
$855$	−5486.76	+	6283.99i	−0.219466	+	0.251354i
$856$	−30382.6			−1.21315
$857$			44000.0i			1.75380i	0.480669	+	0.876902i	$0.340394\pi$
$857$			44000.0i			1.75380i	−0.480669	+	0.876902i	$0.659606\pi$
$858$		−	4541.94i		−	0.180722i
$859$	25896.0			1.02859			0.514295	−	0.857613i	$-0.328054\pi$
$859$	25896.0			1.02859			0.514295	+	0.857613i	$0.328054\pi$
$860$	3157.36	+	2756.80i	0.125192	+	0.109309i
$861$	−5953.18			−0.235638
$862$			35337.1i			1.39627i
$863$		−	39792.0i		−	1.56956i	−0.619772	−	0.784782i	$-0.712775\pi$
$863$		−	39792.0i		−	1.56956i	0.619772	−	0.784782i	$-0.287225\pi$
$864$	−1120.15			−0.0441068
$865$	−24245.6	−	21169.6i	−0.953033	−	0.832124i
$866$	−19938.7			−0.782384
$867$		−	26589.8i		−	1.04156i
$868$			229.701i			0.00898222i
$869$	−7244.62			−0.282804
$870$	14427.5	−	16523.9i	0.562229	−	0.643922i
$871$	−4634.22			−0.180281
$872$			6638.77i			0.257818i
$873$			4744.10i			0.183922i
$874$	5733.93			0.221914
$875$	4903.79	−	7443.83i	0.189461	−	0.287597i
$876$	−1619.18			−0.0624509
$877$			19424.4i			0.747908i	0.927447	+	0.373954i	$0.121998\pi$
$877$			19424.4i			0.747908i	−0.927447	+	0.373954i	$0.878002\pi$
$878$		−	48652.3i		−	1.87009i
$879$	−21871.0			−0.839237
$880$	−5704.23	+	6533.07i	−0.218511	+	0.250261i
$881$	35113.0			1.34278			0.671388	−	0.741106i	$-0.265698\pi$
$881$	35113.0			1.34278			0.671388	+	0.741106i	$0.265698\pi$
$882$		−	8126.74i		−	0.310251i
$883$			2370.67i			0.0903503i	0.998979	+	0.0451751i	$0.0143846\pi$
$883$			2370.67i			0.0903503i	−0.998979	+	0.0451751i	$0.985615\pi$
$884$	4982.15			0.189556
$885$	−463.440	−	404.644i	−0.0176027	−	0.0153695i
$886$	47292.5			1.79325
$887$		−	7629.61i		−	0.288813i	−0.989518	−	0.144407i	$-0.953873\pi$
$887$		−	7629.61i		−	0.288813i	0.989518	−	0.144407i	$-0.0461273\pi$
$888$			17609.8i			0.665479i
$889$	4024.58			0.151834
$890$	28226.0	+	24645.0i	1.06308	+	0.928206i
$891$	891.000			0.0335013
$892$			3399.09i			0.127590i
$893$			42734.5i			1.60141i
$894$	−17866.7			−0.668401
$895$	3426.13	−	3923.95i	0.127959	−	0.146551i
$896$	10504.1			0.391648
$897$			3201.06i			0.119153i
$898$			38427.6i			1.42800i
$899$	8560.49			0.317584
$900$	−139.737	−	1026.84i	−0.00517544	−	0.0380310i
$901$	−20885.1			−0.772235
$902$			10221.8i			0.377327i
$903$			7787.67i			0.286996i
$904$	37487.1			1.37921
$905$	−9340.23	+	10697.4i	−0.343071	+	0.392920i
$906$	−18868.4			−0.691899
$907$		−	32420.3i		−	1.18688i	−0.804878	−	0.593440i	$-0.797769\pi$
$907$		−	32420.3i		−	1.18688i	0.804878	−	0.593440i	$-0.202231\pi$
$908$			4981.69i			0.182074i
$909$	−3978.79			−0.145179
$910$	−7393.31	−	6455.34i	−0.269325	−	0.235156i
$911$	−23172.8			−0.842754			−0.421377	−	0.906886i	$-0.638453\pi$
$911$	−23172.8			−0.842754			−0.421377	+	0.906886i	$0.638453\pi$
$912$		−	17539.8i		−	0.636841i
$913$		−	13839.8i		−	0.501675i
$914$	−72.3264			−0.00261744
$915$	19358.1	+	16902.1i	0.699407	+	0.610675i
$916$	−3954.20			−0.142632
$917$		−	17719.2i		−	0.638104i
$918$			9465.42i			0.340311i
$919$	−25499.5			−0.915288			−0.457644	−	0.889136i	$-0.651307\pi$
$919$	−25499.5			−0.915288			−0.457644	+	0.889136i	$0.651307\pi$
$920$	3600.12	−	4123.22i	0.129013	−	0.147759i
$921$	−3660.50			−0.130964
$922$			8159.00i			0.291434i
$923$		−	47.0106i		−	0.00167646i
$924$	193.888			0.00690308
$925$	−34386.3	+	4679.44i	−1.22228	+	0.166334i
$926$	3879.66			0.137682
$927$			2899.94i			0.102747i
$928$			9084.17i			0.321339i
$929$	−43633.2			−1.54097			−0.770483	−	0.637460i	$-0.779985\pi$
$929$	−43633.2			−1.54097			−0.770483	+	0.637460i	$0.779985\pi$
$930$	2576.00	−	2950.30i	0.0908283	−	0.104026i
$931$	25063.9			0.882317
$932$			2286.01i			0.0803442i
$933$			11394.3i			0.399819i
$934$	−6001.81			−0.210263
$935$	10873.4	+	9493.93i	0.380319	+	0.332069i
$936$	8768.65			0.306210
$937$		−	50755.0i		−	1.76958i	−0.465994	−	0.884788i	$-0.654303\pi$
$937$		−	50755.0i		−	1.76958i	0.465994	−	0.884788i	$-0.345697\pi$
$938$		−	1915.90i		−	0.0666912i
$939$	−5558.49			−0.193178
$940$	−3998.85	−	3491.53i	−0.138753	−	0.121150i
$941$	−42883.6			−1.48562			−0.742809	−	0.669503i	$-0.766507\pi$
$941$	−42883.6			−1.48562			−0.742809	+	0.669503i	$0.766507\pi$
$942$			11803.5i			0.408258i
$943$		−	7204.11i		−	0.248779i
$944$	1293.54			0.0445988
$945$	1266.35	−	1450.36i	0.0435920	−	0.0499260i
$946$	13371.7			0.459568
$947$			20928.0i			0.718130i	0.933313	+	0.359065i	$0.116904\pi$
$947$			20928.0i			0.718130i	−0.933313	+	0.359065i	$0.883096\pi$
$948$			1820.03i			0.0623542i
$949$	26999.6			0.923544
$950$	30670.6	−	4173.79i	1.04746	−	0.142543i
$951$	−22206.5			−0.757198
$952$		−	15828.6i		−	0.538873i
$953$			22216.4i			0.755153i	0.925978	+	0.377576i	$0.123242\pi$
$953$			22216.4i			0.755153i	−0.925978	+	0.377576i	$0.876758\pi$
$954$	4783.26			0.162331
$955$	−15150.0	+	17351.3i	−0.513343	+	0.587933i
$956$	−3520.17			−0.119091
$957$		−	7225.81i		−	0.244072i
$958$		−	21318.5i		−	0.718967i
$959$	−5072.26			−0.170794
$960$	−11123.2	−	9712.02i	−0.373958	−	0.326515i
$961$	−28262.5			−0.948694
$962$			38210.9i			1.28063i
$963$		−	12932.9i		−	0.432769i
$964$	−1517.14			−0.0506886
$965$	20291.8	+	17717.4i	0.676908	+	0.591030i
$966$	−1323.40			−0.0440783
$967$			38687.0i			1.28654i	0.765637	+	0.643272i	$0.222424\pi$
$967$			38687.0i			1.28654i	−0.765637	+	0.643272i	$0.777576\pi$
$968$			2558.34i			0.0849464i
$969$	−29192.6			−0.967802
$970$	11577.4	−	13259.6i	0.383224	−	0.438907i
$971$	17290.0			0.571434			0.285717	−	0.958314i	$-0.407768\pi$
$971$	17290.0			0.571434			0.285717	+	0.958314i	$0.407768\pi$
$972$		−	223.841i		−	0.00738654i
$973$		−	2988.66i		−	0.0984707i
$974$	−53064.2			−1.74567
$975$	2330.09	+	17122.4i	0.0765361	+	0.562415i
$976$	−54031.8			−1.77205
$977$			34072.2i			1.11573i	0.829932	+	0.557864i	$0.188379\pi$
$977$			34072.2i			1.11573i	−0.829932	+	0.557864i	$0.811621\pi$
$978$			15921.2i			0.520557i
$979$	12343.1			0.402949
$980$	−2047.79	+	2345.34i	−0.0667492	+	0.0764480i
$981$	−2825.90			−0.0919716
$982$			12364.8i			0.401808i
$983$			30568.9i			0.991857i	0.868363	+	0.495928i	$0.165172\pi$
$983$			30568.9i			0.991857i	−0.868363	+	0.495928i	$0.834828\pi$
$984$	−19734.2			−0.639332
$985$	24366.4	+	21275.1i	0.788200	+	0.688203i
$986$	76762.4			2.47932
$987$		−	9863.21i		−	0.318084i
$988$		−	3519.14i		−	0.113319i
$989$	−9424.08			−0.303001
$990$	−2490.31	−	2174.37i	−0.0799467	−	0.0698041i
$991$	−1838.61			−0.0589358			−0.0294679	−	0.999566i	$-0.509381\pi$
$991$	−1838.61			−0.0589358			−0.0294679	+	0.999566i	$0.509381\pi$
$992$			1621.95i			0.0519124i
$993$		−	24903.1i		−	0.795848i
$994$	19.4353			0.000620173
$995$	19198.1	−	21987.6i	0.611680	−	0.700558i
$996$	−3476.89			−0.110612
$997$		−	44103.1i		−	1.40096i	−0.713671	−	0.700482i	$-0.752969\pi$
$997$		−	44103.1i		−	1.40096i	0.713671	−	0.700482i	$-0.247031\pi$
$998$			35893.7i			1.13847i
$999$	−7495.89			−0.237397

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	165.4.c.b.34.11	yes	14
3.2	odd	2		495.4.c.d.199.4		14
5.2	odd	4		825.4.a.ba.1.3		7
5.3	odd	4		825.4.a.bd.1.5		7
5.4	even	2	inner	165.4.c.b.34.4	✓	14
15.2	even	4		2475.4.a.bs.1.5		7
15.8	even	4		2475.4.a.bo.1.3		7
15.14	odd	2		495.4.c.d.199.11		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
165.4.c.b.34.4	✓	14	5.4	even	2	inner
165.4.c.b.34.11	yes	14	1.1	even	1	trivial
495.4.c.d.199.4		14	3.2	odd	2
495.4.c.d.199.11		14	15.14	odd	2
825.4.a.ba.1.3		7	5.2	odd	4
825.4.a.bd.1.5		7	5.3	odd	4
2475.4.a.bo.1.3		7	15.8	even	4
2475.4.a.bs.1.5		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)

\(f(q)\)	\(=\)	\(q+2.98683i q^{2} +3.00000i q^{3} -0.921158 q^{4} +(7.35339 - 8.42185i) q^{5} -8.96049 q^{6} +6.37827i q^{7} +21.1433i q^{8} -9.00000 q^{9} +O(q^{10})\)	\(q+2.98683i q^{2} +3.00000i q^{3} -0.921158 q^{4} +(7.35339 - 8.42185i) q^{5} -8.96049 q^{6} +6.37827i q^{7} +21.1433i q^{8} -9.00000 q^{9} +(25.1547 + 21.9633i) q^{10} +11.0000 q^{11} -2.76347i q^{12} +46.0805i q^{13} -19.0508 q^{14} +(25.2656 + 22.0602i) q^{15} -70.5207 q^{16} +117.372i q^{17} -26.8815i q^{18} +82.9059 q^{19} +(-6.77363 + 7.75786i) q^{20} -19.1348 q^{21} +32.8551i q^{22} -23.1556i q^{23} -63.4299 q^{24} +(-16.8552 - 123.858i) q^{25} -137.635 q^{26} -27.0000i q^{27} -5.87540i q^{28} -218.964 q^{29} +(-65.8900 + 75.4640i) q^{30} -39.0954 q^{31} -41.4871i q^{32} +33.0000i q^{33} -350.571 q^{34} +(53.7169 + 46.9020i) q^{35} +8.29042 q^{36} -277.626i q^{37} +247.626i q^{38} -138.242 q^{39} +(178.066 + 155.475i) q^{40} +311.118 q^{41} -57.1525i q^{42} -406.989i q^{43} -10.1327 q^{44} +(-66.1805 + 75.7967i) q^{45} +69.1618 q^{46} +515.458i q^{47} -211.562i q^{48} +302.318 q^{49} +(369.944 - 50.3437i) q^{50} -352.117 q^{51} -42.4474i q^{52} +177.939i q^{53} +80.6444 q^{54} +(80.8873 - 92.6404i) q^{55} -134.858 q^{56} +248.718i q^{57} -654.008i q^{58} -18.3427 q^{59} +(-23.2736 - 20.3209i) q^{60} +766.183 q^{61} -116.771i q^{62} -57.4045i q^{63} -440.251 q^{64} +(388.083 + 338.848i) q^{65} -98.5654 q^{66} +100.568i q^{67} -108.118i q^{68} +69.4668 q^{69} +(-140.088 + 160.443i) q^{70} -1.02018 q^{71} -190.290i q^{72} -585.922i q^{73} +829.221 q^{74} +(371.575 - 50.5657i) q^{75} -76.3694 q^{76} +70.1610i q^{77} -412.904i q^{78} -658.601 q^{79} +(-518.567 + 593.915i) q^{80} +81.0000 q^{81} +929.256i q^{82} -1258.16i q^{83} +17.6262 q^{84} +(988.492 + 863.084i) q^{85} +1215.61 q^{86} -656.892i q^{87} +232.576i q^{88} +1122.10 q^{89} +(-226.392 - 197.670i) q^{90} -293.914 q^{91} +21.3300i q^{92} -117.286i q^{93} -1539.59 q^{94} +(609.640 - 698.221i) q^{95} +124.461 q^{96} -527.122i q^{97} +902.972i q^{98} -99.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - 26 q^{4} - 14 q^{5} - 30 q^{6} - 126 q^{9}+O(q^{10}) \) 14 * q - 26 * q^4 - 14 * q^5 - 30 * q^6 - 126 * q^9	\( 14 q - 26 q^{4} - 14 q^{5} - 30 q^{6} - 126 q^{9} - 48 q^{10} + 154 q^{11} - 84 q^{14} - 86 q^{16} - 116 q^{19} + 442 q^{20} - 204 q^{21} + 450 q^{24} + 162 q^{25} - 400 q^{26} - 128 q^{29} + 246 q^{30} - 696 q^{31} - 412 q^{34} + 672 q^{35} + 234 q^{36} + 480 q^{39} + 1612 q^{40} - 664 q^{41} - 286 q^{44} + 126 q^{45} - 656 q^{46} + 834 q^{49} + 1908 q^{50} - 972 q^{51} + 270 q^{54} - 154 q^{55} - 3236 q^{56} + 664 q^{59} + 108 q^{60} + 44 q^{61} - 1122 q^{64} - 2328 q^{65} - 330 q^{66} + 1944 q^{69} + 1220 q^{70} - 1032 q^{71} - 3256 q^{74} + 84 q^{75} + 5588 q^{76} - 3492 q^{79} - 510 q^{80} + 1134 q^{81} - 1008 q^{84} - 1068 q^{85} + 2540 q^{86} + 4452 q^{89} + 432 q^{90} + 2144 q^{91} - 9472 q^{94} - 932 q^{95} + 450 q^{96} - 1386 q^{99}+O(q^{100}) \) 14 * q - 26 * q^4 - 14 * q^5 - 30 * q^6 - 126 * q^9 - 48 * q^10 + 154 * q^11 - 84 * q^14 - 86 * q^16 - 116 * q^19 + 442 * q^20 - 204 * q^21 + 450 * q^24 + 162 * q^25 - 400 * q^26 - 128 * q^29 + 246 * q^30 - 696 * q^31 - 412 * q^34 + 672 * q^35 + 234 * q^36 + 480 * q^39 + 1612 * q^40 - 664 * q^41 - 286 * q^44 + 126 * q^45 - 656 * q^46 + 834 * q^49 + 1908 * q^50 - 972 * q^51 + 270 * q^54 - 154 * q^55 - 3236 * q^56 + 664 * q^59 + 108 * q^60 + 44 * q^61 - 1122 * q^64 - 2328 * q^65 - 330 * q^66 + 1944 * q^69 + 1220 * q^70 - 1032 * q^71 - 3256 * q^74 + 84 * q^75 + 5588 * q^76 - 3492 * q^79 - 510 * q^80 + 1134 * q^81 - 1008 * q^84 - 1068 * q^85 + 2540 * q^86 + 4452 * q^89 + 432 * q^90 + 2144 * q^91 - 9472 * q^94 - 932 * q^95 + 450 * q^96 - 1386 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more