LMFDB - Embedded newform 165.4.c.b.34.13

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			34.13
Root			$2.70507i$ of defining polynomial
Character	$\chi$	$=$	165.34
Dual form			165.4.c.b.34.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+3.70507i q^{2} +3.00000i q^{3} -5.72754 q^{4} +(-10.6368 - 3.44353i) q^{5} -11.1152 q^{6} +30.9104i q^{7} +8.41961i q^{8} -9.00000 q^{9} +O(q^{10})$	\(q+3.70507i q^{2} +3.00000i q^{3} -5.72754 q^{4} +(-10.6368 - 3.44353i) q^{5} -11.1152 q^{6} +30.9104i q^{7} +8.41961i q^{8} -9.00000 q^{9} +(12.7585 - 39.4102i) q^{10} +11.0000 q^{11} -17.1826i q^{12} -39.2828i q^{13} -114.525 q^{14} +(10.3306 - 31.9105i) q^{15} -77.0156 q^{16} -83.0298i q^{17} -33.3456i q^{18} -49.6019 q^{19} +(60.9229 + 19.7230i) q^{20} -92.7312 q^{21} +40.7558i q^{22} -10.7536i q^{23} -25.2588 q^{24} +(101.284 + 73.2564i) q^{25} +145.545 q^{26} -27.0000i q^{27} -177.041i q^{28} -198.890 q^{29} +(118.231 + 38.2755i) q^{30} +229.071 q^{31} -217.991i q^{32} +33.0000i q^{33} +307.631 q^{34} +(106.441 - 328.789i) q^{35} +51.5479 q^{36} +348.562i q^{37} -183.778i q^{38} +117.848 q^{39} +(28.9931 - 89.5579i) q^{40} -459.643 q^{41} -343.576i q^{42} +461.300i q^{43} -63.0030 q^{44} +(95.7315 + 30.9917i) q^{45} +39.8427 q^{46} +272.390i q^{47} -231.047i q^{48} -612.453 q^{49} +(-271.420 + 375.265i) q^{50} +249.089 q^{51} +224.994i q^{52} -360.420i q^{53} +100.037 q^{54} +(-117.005 - 37.8788i) q^{55} -260.253 q^{56} -148.806i q^{57} -736.901i q^{58} +215.424 q^{59} +(-59.1689 + 182.769i) q^{60} +367.967 q^{61} +848.723i q^{62} -278.194i q^{63} +191.548 q^{64} +(-135.271 + 417.844i) q^{65} -122.267 q^{66} +929.374i q^{67} +475.557i q^{68} +32.2607 q^{69} +(1218.18 + 394.371i) q^{70} +126.531 q^{71} -75.7765i q^{72} -509.402i q^{73} -1291.45 q^{74} +(-219.769 + 303.853i) q^{75} +284.097 q^{76} +340.014i q^{77} +436.636i q^{78} -719.755 q^{79} +(819.202 + 265.205i) q^{80} +81.0000 q^{81} -1703.01i q^{82} +865.128i q^{83} +531.122 q^{84} +(-285.915 + 883.173i) q^{85} -1709.15 q^{86} -596.670i q^{87} +92.6157i q^{88} -528.684 q^{89} +(-114.827 + 354.692i) q^{90} +1214.25 q^{91} +61.5915i q^{92} +687.212i q^{93} -1009.22 q^{94} +(527.607 + 170.805i) q^{95} +653.974 q^{96} +858.037i q^{97} -2269.18i q^{98} -99.0000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$			3.70507i			1.30994i	0.755655	+	0.654970i	$0.227319\pi$
$2$			3.70507i			1.30994i	−0.755655	+	0.654970i	$0.772681\pi$
$3$			3.00000i			0.577350i
$3$			3.00000i			0.577350i
$4$	−5.72754			−0.715943
$5$	−10.6368	−	3.44353i	−0.951387	−	0.307998i
$5$	−10.6368	−	3.44353i	−0.951387	−	0.307998i
$6$	−11.1152			−0.756294
$7$			30.9104i			1.66900i	0.551004	+	0.834502i	$0.314245\pi$
$7$			30.9104i			1.66900i	−0.551004	+	0.834502i	$0.685755\pi$
$8$			8.41961i			0.372098i
$9$	−9.00000			−0.333333
$10$	12.7585	−	39.4102i	0.403459	−	1.24626i
$11$	11.0000			0.301511
$11$	11.0000			0.301511
$12$		−	17.1826i		−	0.413350i
$13$		−	39.2828i		−	0.838083i	−0.907967	−	0.419042i	$-0.862366\pi$
$13$		−	39.2828i		−	0.838083i	0.907967	−	0.419042i	$-0.137634\pi$
$14$	−114.525			−2.18630
$15$	10.3306	−	31.9105i	0.177823	−	0.549283i
$16$	−77.0156			−1.20337
$17$		−	83.0298i		−	1.18457i	−0.805729	−	0.592285i	$-0.798226\pi$
$17$		−	83.0298i		−	1.18457i	0.805729	−	0.592285i	$-0.201774\pi$
$18$		−	33.3456i		−	0.436647i
$19$	−49.6019			−0.598918			−0.299459	−	0.954109i	$-0.596806\pi$
$19$	−49.6019			−0.598918			−0.299459	+	0.954109i	$0.596806\pi$
$20$	60.9229	+	19.7230i	0.681139	+	0.220509i
$21$	−92.7312			−0.963600
$22$			40.7558i			0.394962i
$23$		−	10.7536i		−	0.0974902i	−0.998811	−	0.0487451i	$-0.984478\pi$
$23$		−	10.7536i		−	0.0974902i	0.998811	−	0.0487451i	$-0.0155222\pi$
$24$	−25.2588			−0.214831
$25$	101.284	+	73.2564i	0.810274	+	0.586051i
$26$	145.545			1.09784
$27$		−	27.0000i		−	0.192450i
$28$		−	177.041i		−	1.19491i
$29$	−198.890			−1.27355			−0.636775	−	0.771050i	$-0.719732\pi$
$29$	−198.890			−1.27355			−0.636775	+	0.771050i	$0.719732\pi$
$30$	118.231	+	38.2755i	0.719528	+	0.232937i
$31$	229.071			1.32717			0.663586	−	0.748100i	$-0.269034\pi$
$31$	229.071			1.32717			0.663586	+	0.748100i	$0.269034\pi$
$32$		−	217.991i		−	1.20424i
$33$			33.0000i			0.174078i
$34$	307.631			1.55171
$35$	106.441	−	328.789i	0.514051	−	1.58787i
$36$	51.5479			0.238648
$37$			348.562i			1.54874i	0.632736	+	0.774368i	$0.281932\pi$
$37$			348.562i			1.54874i	−0.632736	+	0.774368i	$0.718068\pi$
$38$		−	183.778i		−	0.784547i
$39$	117.848			0.483867
$40$	28.9931	−	89.5579i	0.114605	−	0.354009i
$41$	−459.643			−1.75083			−0.875416	−	0.483370i	$-0.839413\pi$
$41$	−459.643			−1.75083			−0.875416	+	0.483370i	$0.839413\pi$
$42$		−	343.576i		−	1.26226i
$43$			461.300i			1.63599i	0.575226	+	0.817995i	$0.304914\pi$
$43$			461.300i			1.63599i	−0.575226	+	0.817995i	$0.695086\pi$
$44$	−63.0030			−0.215865
$45$	95.7315	+	30.9917i	0.317129	+	0.102666i
$46$	39.8427			0.127706
$47$			272.390i			0.845365i	0.906278	+	0.422682i	$0.138911\pi$
$47$			272.390i			0.845365i	−0.906278	+	0.422682i	$0.861089\pi$
$48$		−	231.047i		−	0.694765i
$49$	−612.453			−1.78558
$50$	−271.420	+	375.265i	−0.767692	+	1.06141i
$51$	249.089			0.683911
$52$			224.994i			0.600020i
$53$		−	360.420i		−	0.934104i	−0.884230	−	0.467052i	$-0.845316\pi$
$53$		−	360.420i		−	0.934104i	0.884230	−	0.467052i	$-0.154684\pi$
$54$	100.037			0.252098
$55$	−117.005	−	37.8788i	−0.286854	−	0.0928650i
$56$	−260.253			−0.621033
$57$		−	148.806i		−	0.345786i
$58$		−	736.901i		−	1.66827i
$59$	215.424			0.475352			0.237676	−	0.971345i	$-0.423614\pi$
$59$	215.424			0.475352			0.237676	+	0.971345i	$0.423614\pi$
$60$	−59.1689	+	182.769i	−0.127311	+	0.393256i
$61$	367.967			0.772350			0.386175	−	0.922426i	$-0.373796\pi$
$61$	367.967			0.772350			0.386175	+	0.922426i	$0.373796\pi$
$62$			848.723i			1.73851i
$63$		−	278.194i		−	0.556335i
$64$	191.548			0.374118
$65$	−135.271	+	417.844i	−0.258128	+	0.797341i
$66$	−122.267			−0.228031
$67$			929.374i			1.69464i	0.531079	+	0.847322i	$0.321787\pi$
$67$			929.374i			1.69464i	−0.531079	+	0.847322i	$0.678213\pi$
$68$			475.557i			0.848084i
$69$	32.2607			0.0562860
$70$	1218.18	+	394.371i	2.08001	+	0.673376i
$71$	126.531			0.211499			0.105750	−	0.994393i	$-0.466276\pi$
$71$	126.531			0.211499			0.105750	+	0.994393i	$0.466276\pi$
$72$		−	75.7765i		−	0.124033i
$73$		−	509.402i		−	0.816726i	−0.912820	−	0.408363i	$-0.866100\pi$
$73$		−	509.402i		−	0.816726i	0.912820	−	0.408363i	$-0.133900\pi$
$74$	−1291.45			−2.02875
$75$	−219.769	+	303.853i	−0.338357	+	0.467812i
$76$	284.097			0.428791
$77$			340.014i			0.503224i
$78$			436.636i			0.633837i
$79$	−719.755			−1.02505			−0.512524	−	0.858673i	$-0.671289\pi$
$79$	−719.755			−1.02505			−0.512524	+	0.858673i	$0.671289\pi$
$80$	819.202	+	265.205i	1.14487	+	0.370636i
$81$	81.0000			0.111111
$82$		−	1703.01i		−	2.29349i
$83$			865.128i			1.14410i	0.820220	+	0.572049i	$0.193851\pi$
$83$			865.128i			1.14410i	−0.820220	+	0.572049i	$0.806149\pi$
$84$	531.122			0.689883
$85$	−285.915	+	883.173i	−0.364845	+	1.12698i
$86$	−1709.15			−2.14305
$87$		−	596.670i		−	0.735284i
$88$			92.6157i			0.112192i
$89$	−528.684			−0.629668			−0.314834	−	0.949147i	$-0.601949\pi$
$89$	−528.684			−0.629668			−0.314834	+	0.949147i	$0.601949\pi$
$90$	−114.827	+	354.692i	−0.134486	+	0.415420i
$91$	1214.25			1.39876
$92$			61.5915i			0.0697974i
$93$			687.212i			0.766243i
$94$	−1009.22			−1.10738
$95$	527.607	+	170.805i	0.569803	+	0.184466i
$96$	653.974			0.695270
$97$			858.037i			0.898149i	0.893494	+	0.449075i	$0.148246\pi$
$97$			858.037i			0.898149i	−0.893494	+	0.449075i	$0.851754\pi$
$98$		−	2269.18i		−	2.33900i
$99$	−99.0000			−0.100504
$100$	−580.110	−	419.579i	−0.580110	−	0.419579i
$101$	−48.7808			−0.0480582			−0.0240291	−	0.999711i	$-0.507649\pi$
$101$	−48.7808			−0.0480582			−0.0240291	+	0.999711i	$0.507649\pi$
$102$			922.893i			0.895883i
$103$		−	525.103i		−	0.502329i	−0.967944	−	0.251165i	$-0.919186\pi$
$103$		−	525.103i		−	0.502329i	0.967944	−	0.251165i	$-0.0808136\pi$
$104$	330.746			0.311849
$105$	986.366	+	319.322i	0.916757	+	0.296787i
$106$	1335.38			1.22362
$107$			986.489i			0.891285i	0.895211	+	0.445643i	$0.147025\pi$
$107$			986.489i			0.891285i	−0.895211	+	0.445643i	$0.852975\pi$
$108$			154.644i			0.137783i
$109$	55.2903			0.0485858			0.0242929	−	0.999705i	$-0.492267\pi$
$109$	55.2903			0.0485858			0.0242929	+	0.999705i	$0.492267\pi$
$110$	140.344	−	433.512i	0.121648	−	0.375761i
$111$	−1045.69			−0.894163
$112$		−	2380.58i		−	2.00843i
$113$		−	459.760i		−	0.382748i	−0.981517	−	0.191374i	$-0.938706\pi$
$113$		−	459.760i		−	0.382748i	0.981517	−	0.191374i	$-0.0612944\pi$
$114$	551.335			0.452959
$115$	−37.0302	+	114.384i	−0.0300268	+	0.0927509i
$116$	1139.15			0.911789
$117$			353.545i			0.279361i
$118$			798.160i			0.622683i
$119$	2566.48			1.97705
$120$	268.674	+	86.9794i	0.204387	+	0.0661675i
$121$	121.000			0.0909091
$122$			1363.34i			1.01173i
$123$		−	1378.93i		−	1.01084i
$124$	−1312.01			−0.950179
$125$	−825.083	−	1127.99i	−0.590381	−	0.807125i
$126$	1030.73			0.728765
$127$		−	1959.31i		−	1.36898i	−0.729020	−	0.684492i	$-0.760024\pi$
$127$		−	1959.31i		−	1.36898i	0.729020	−	0.684492i	$-0.239976\pi$
$128$		−	1034.23i		−	0.714171i
$129$	−1383.90			−0.944539
$130$	−1548.14	−	501.190i	−1.04447	−	0.338133i
$131$	16.2654			0.0108482			0.00542412	−	0.999985i	$-0.498273\pi$
$131$	16.2654			0.0108482			0.00542412	+	0.999985i	$0.498273\pi$
$132$		−	189.009i		−	0.124630i
$133$		−	1533.21i		−	0.999598i
$134$	−3443.40			−2.21988
$135$	−92.9752	+	287.194i	−0.0592743	+	0.183094i
$136$	699.078			0.440775
$137$			941.492i			0.587132i	0.955939	+	0.293566i	$0.0948421\pi$
$137$			941.492i			0.587132i	−0.955939	+	0.293566i	$0.905158\pi$
$138$			119.528i			0.0737313i
$139$	1975.04			1.20518			0.602591	−	0.798050i	$-0.294135\pi$
$139$	1975.04			1.20518			0.602591	+	0.798050i	$0.294135\pi$
$140$	−609.644	+	1883.15i	−0.368031	+	1.13682i
$141$	−817.169			−0.488072
$142$			468.805i			0.277051i
$143$		−	432.110i		−	0.252692i
$144$	693.140			0.401123
$145$	2115.56	+	684.883i	1.21164	+	0.392251i
$146$	1887.37			1.06986
$147$		−	1837.36i		−	1.03090i
$148$		−	1996.40i		−	1.10881i
$149$	2958.51			1.62665			0.813325	−	0.581810i	$-0.197655\pi$
$149$	2958.51			1.62665			0.813325	+	0.581810i	$0.197655\pi$
$150$	−1125.80	−	814.260i	−0.612806	−	0.443227i
$151$	−3453.22			−1.86105			−0.930526	−	0.366227i	$-0.880650\pi$
$151$	−3453.22			−1.86105			−0.930526	+	0.366227i	$0.880650\pi$
$152$		−	417.628i		−	0.222856i
$153$			747.268i			0.394856i
$154$	−1259.78			−0.659193
$155$	−2436.59	−	788.811i	−1.26265	−	0.408767i
$156$	−674.981			−0.346422
$157$			738.890i			0.375604i	0.982207	+	0.187802i	$0.0601364\pi$
$157$			738.890i			0.375604i	−0.982207	+	0.187802i	$0.939864\pi$
$158$		−	2666.74i		−	1.34275i
$159$	1081.26			0.539305
$160$	−750.659	+	2318.74i	−0.370905	+	1.14570i
$161$	332.397			0.162712
$162$			300.111i			0.145549i
$163$		−	242.527i		−	0.116541i	−0.998301	−	0.0582705i	$-0.981441\pi$
$163$		−	242.527i		−	0.116541i	0.998301	−	0.0582705i	$-0.0185586\pi$
$164$	2632.62			1.25350
$165$	113.636	−	351.015i	0.0536156	−	0.165615i
$166$	−3205.36			−1.49870
$167$			2447.06i			1.13389i	0.823756	+	0.566944i	$0.191874\pi$
$167$			2447.06i			1.13389i	−0.823756	+	0.566944i	$0.808126\pi$
$168$		−	780.760i		−	0.358553i
$169$	653.864			0.297617
$170$	−3272.22	−	1059.34i	−1.47628	−	0.477926i
$171$	446.417			0.199639
$172$		−	2642.11i		−	1.17127i
$173$			878.419i			0.386040i	0.981195	+	0.193020i	$0.0618282\pi$
$173$			878.419i			0.386040i	−0.981195	+	0.193020i	$0.938172\pi$
$174$	2210.70			0.963178
$175$	−2264.38	+	3130.74i	−0.978122	+	1.35235i
$176$	−847.172			−0.362829
$177$			646.271i			0.274445i
$178$		−	1958.81i		−	0.824827i
$179$	2473.19			1.03271			0.516354	−	0.856375i	$-0.327289\pi$
$179$	2473.19			1.03271			0.516354	+	0.856375i	$0.327289\pi$
$180$	−548.306	−	177.507i	−0.227046	−	0.0735031i
$181$	49.4762			0.0203179			0.0101589	−	0.999948i	$-0.496766\pi$
$181$	49.4762			0.0203179			0.0101589	+	0.999948i	$0.496766\pi$
$182$			4498.87i			1.83230i
$183$			1103.90i			0.445916i
$184$	90.5408			0.0362759
$185$	1200.28	−	3707.59i	0.477008	−	1.47345i
$186$	−2546.17			−1.00373
$187$		−	913.327i		−	0.357161i
$188$		−	1560.12i		−	0.605233i
$189$	834.581			0.321200
$190$	−632.846	+	1954.82i	−0.241639	+	0.746408i
$191$	−1945.54			−0.737037			−0.368518	−	0.929620i	$-0.620135\pi$
$191$	−1945.54			−0.737037			−0.368518	+	0.929620i	$0.620135\pi$
$192$			574.645i			0.215997i
$193$			3064.50i			1.14294i	0.820623	+	0.571470i	$0.193627\pi$
$193$			3064.50i			1.14294i	−0.820623	+	0.571470i	$0.806373\pi$
$194$	−3179.09			−1.17652
$195$	−1253.53	−	405.814i	−0.460345	−	0.149030i
$196$	3507.85			1.27837
$197$		−	1659.71i		−	0.600251i	−0.953900	−	0.300125i	$-0.902971\pi$
$197$		−	1659.71i		−	0.600251i	0.953900	−	0.300125i	$-0.0970285\pi$
$198$		−	366.802i		−	0.131654i
$199$	3230.11			1.15063			0.575317	−	0.817930i	$-0.304879\pi$
$199$	3230.11			1.15063			0.575317	+	0.817930i	$0.304879\pi$
$200$	−616.790	+	852.774i	−0.218068	+	0.301501i
$201$	−2788.12			−0.978403
$202$		−	180.736i		−	0.0629533i
$203$		−	6147.77i		−	2.12556i
$204$	−1426.67			−0.489642
$205$	4889.14	+	1582.79i	1.66572	+	0.539254i
$206$	1945.54			0.658021
$207$			96.7821i			0.0324967i
$208$			3025.39i			1.00852i
$209$	−545.621			−0.180581
$210$	−1183.11	+	3654.55i	−0.388774	+	1.20090i
$211$	−2543.86			−0.829983			−0.414991	−	0.909825i	$-0.636215\pi$
$211$	−2543.86			−0.829983			−0.414991	+	0.909825i	$0.636215\pi$
$212$			2064.32i			0.668766i
$213$			379.592i			0.122109i
$214$	−3655.01			−1.16753
$215$	1588.50	−	4906.76i	0.503882	−	1.55646i
$216$	227.329			0.0716102
$217$			7080.67i			2.21506i
$218$			204.854i			0.0636445i
$219$	1528.21			0.471537
$220$	670.152	+	216.952i	0.205371	+	0.0664861i
$221$	−3261.64			−0.992767
$222$		−	3874.34i		−	1.17130i
$223$		−	1189.64i		−	0.357240i	−0.983918	−	0.178620i	$-0.942837\pi$
$223$		−	1189.64i		−	0.357240i	0.983918	−	0.178620i	$-0.0571632\pi$
$224$	6738.20			2.00989
$225$	−911.558	−	659.308i	−0.270091	−	0.195350i
$226$	1703.44			0.501378
$227$			4897.90i			1.43209i	0.698053	+	0.716047i	$0.254050\pi$
$227$			4897.90i			1.43209i	−0.698053	+	0.716047i	$0.745950\pi$
$228$			852.291i			0.247563i
$229$	2415.61			0.697065			0.348533	−	0.937297i	$-0.386680\pi$
$229$	2415.61			0.697065			0.348533	+	0.937297i	$0.386680\pi$
$230$	−423.800	−	137.199i	−0.121498	−	0.0393333i
$231$	−1020.04			−0.290536
$232$		−	1674.58i		−	0.473885i
$233$			524.258i			0.147405i	0.997280	+	0.0737023i	$0.0234815\pi$
$233$			524.258i			0.147405i	−0.997280	+	0.0737023i	$0.976519\pi$
$234$	−1309.91			−0.365946
$235$	937.982	−	2897.36i	0.260371	−	0.804269i
$236$	−1233.85			−0.340325
$237$		−	2159.27i		−	0.591812i
$238$			9509.00i			2.58982i
$239$	4165.12			1.12728			0.563638	−	0.826022i	$-0.309401\pi$
$239$	4165.12			1.12728			0.563638	+	0.826022i	$0.309401\pi$
$240$	−795.616	+	2457.60i	−0.213987	+	0.660990i
$241$	1908.80			0.510194			0.255097	−	0.966915i	$-0.417893\pi$
$241$	1908.80			0.510194			0.255097	+	0.966915i	$0.417893\pi$
$242$			448.313i			0.119085i
$243$			243.000i			0.0641500i
$244$	−2107.55			−0.552958
$245$	6514.56	+	2109.00i	1.69877	+	0.549955i
$246$	5109.03			1.32414
$247$			1948.50i			0.501943i
$248$			1928.69i			0.493837i
$249$	−2595.38			−0.660545
$250$	4179.29	−	3056.99i	1.05728	−	0.773364i
$251$	2503.63			0.629592			0.314796	−	0.949159i	$-0.398064\pi$
$251$	2503.63			0.629592			0.314796	+	0.949159i	$0.398064\pi$
$252$			1593.37i			0.398304i
$253$		−	118.289i		−	0.0293944i
$254$	7259.39			1.79329
$255$	−2649.52	−	857.746i	−0.650664	−	0.210644i
$256$	5364.28			1.30964
$257$		−	2985.91i		−	0.724731i	−0.932036	−	0.362365i	$-0.881969\pi$
$257$		−	2985.91i		−	0.724731i	0.932036	−	0.362365i	$-0.118031\pi$
$258$		−	5127.44i		−	1.23729i
$259$	−10774.2			−2.58485
$260$	774.772	−	2393.22i	0.184805	−	0.570851i
$261$	1790.01			0.424517
$262$			60.2646i			0.0142105i
$263$		−	2213.20i		−	0.518903i	−0.965756	−	0.259452i	$-0.916458\pi$
$263$		−	2213.20i		−	0.518903i	0.965756	−	0.259452i	$-0.0835418\pi$
$264$	−277.847			−0.0647739
$265$	−1241.12	+	3833.73i	−0.287703	+	0.888695i
$266$	5680.66			1.30941
$267$		−	1586.05i		−	0.363539i
$268$		−	5323.03i		−	1.21327i
$269$	630.921			0.143003			0.0715017	−	0.997440i	$-0.477221\pi$
$269$	630.921			0.143003			0.0715017	+	0.997440i	$0.477221\pi$
$270$	−1064.08	−	344.480i	−0.239843	−	0.0776458i
$271$	−5781.90			−1.29603			−0.648017	−	0.761626i	$-0.724402\pi$
$271$	−5781.90			−1.29603			−0.648017	+	0.761626i	$0.724402\pi$
$272$			6394.59i			1.42547i
$273$			3642.74i			0.807577i
$274$	−3488.29			−0.769108
$275$	1114.13	+	805.820i	0.244307	+	0.176701i
$276$	−184.775			−0.0402976
$277$		−	3365.10i		−	0.729925i	−0.931022	−	0.364962i	$-0.881082\pi$
$277$		−	3365.10i		−	0.729925i	0.931022	−	0.364962i	$-0.118918\pi$
$278$			7317.64i			1.57872i
$279$	−2061.64			−0.442390
$280$	2768.27	+	896.190i	0.590842	+	0.191277i
$281$	622.308			0.132113			0.0660566	−	0.997816i	$-0.478958\pi$
$281$	622.308			0.132113			0.0660566	+	0.997816i	$0.478958\pi$
$282$		−	3027.67i		−	0.639344i
$283$			1629.44i			0.342263i	0.985248	+	0.171131i	$0.0547423\pi$
$283$			1629.44i			0.342263i	−0.985248	+	0.171131i	$0.945258\pi$
$284$	−724.710			−0.151421
$285$	−512.416	+	1582.82i	−0.106501	+	0.328976i
$286$	1601.00			0.331011
$287$		−	14207.7i		−	2.92215i
$288$			1961.92i			0.401414i
$289$	−1980.94			−0.403204
$290$	−2537.54	+	7838.29i	−0.513826	+	1.58717i
$291$	−2574.11			−0.518547
$292$			2917.62i			0.584729i
$293$			5845.09i			1.16544i	0.812673	+	0.582720i	$0.198012\pi$
$293$			5845.09i			1.16544i	−0.812673	+	0.582720i	$0.801988\pi$
$294$	6807.54			1.35042
$295$	−2291.42	−	741.817i	−0.452244	−	0.146408i
$296$	−2934.75			−0.576281
$297$		−	297.000i		−	0.0580259i
$298$			10961.5i			2.13081i
$299$	−422.430			−0.0817049
$300$	1258.74	−	1740.33i	0.242244	−	0.334927i
$301$	−14259.0			−2.73047
$302$		−	12794.4i		−	2.43787i
$303$		−	146.343i		−	0.0277464i
$304$	3820.12			0.720720
$305$	−3914.00	−	1267.10i	−0.734803	−	0.237883i
$306$	−2768.68			−0.517238
$307$		−	4452.12i		−	0.827674i	−0.910351	−	0.413837i	$-0.864188\pi$
$307$		−	4452.12i		−	0.827674i	0.910351	−	0.413837i	$-0.135812\pi$
$308$		−	1947.45i		−	0.360280i
$309$	1575.31			0.290020
$310$	2922.60	−	9027.72i	0.535460	−	1.65400i
$311$	−7340.61			−1.33842			−0.669209	−	0.743074i	$-0.733367\pi$
$311$	−7340.61			−1.33842			−0.669209	+	0.743074i	$0.733367\pi$
$312$			992.237i			0.180046i
$313$		−	4302.99i		−	0.777059i	−0.921436	−	0.388530i	$-0.872983\pi$
$313$		−	4302.99i		−	0.777059i	0.921436	−	0.388530i	$-0.127017\pi$
$314$	−2737.64			−0.492019
$315$	−957.967	+	2959.10i	−0.171350	+	0.529290i
$316$	4122.43			0.733876
$317$			5631.72i			0.997821i	0.866654	+	0.498910i	$0.166266\pi$
$317$			5631.72i			0.997821i	−0.866654	+	0.498910i	$0.833734\pi$
$318$			4006.15i			0.706458i
$319$	−2187.79			−0.383990
$320$	−2037.47	−	659.602i	−0.355931	−	0.115228i
$321$	−2959.47			−0.514584
$322$			1231.55i			0.213142i
$323$			4118.43i			0.709460i
$324$	−463.931			−0.0795492
$325$	2877.71	−	3978.73i	0.491160	−	0.679077i
$326$	898.579			0.152662
$327$			165.871i			0.0280510i
$328$		−	3870.01i		−	0.651481i
$329$	−8419.68			−1.41092
$330$	1300.54	+	421.031i	0.216946	+	0.0702333i
$331$	11290.4			1.87485			0.937424	−	0.348190i	$-0.113204\pi$
$331$	11290.4			1.87485			0.937424	+	0.348190i	$0.113204\pi$
$332$		−	4955.06i		−	0.819109i
$333$		−	3137.06i		−	0.516245i
$334$	−9066.53			−1.48533
$335$	3200.33	−	9885.60i	0.521948	−	1.61226i
$336$	7141.75			1.15957
$337$		−	4323.61i		−	0.698878i	−0.936959	−	0.349439i	$-0.886372\pi$
$337$		−	4323.61i		−	0.698878i	0.936959	−	0.349439i	$-0.113628\pi$
$338$			2422.61i			0.389860i
$339$	1379.28			0.220980
$340$	1637.59	−	5058.42i	0.261209	−	0.806856i
$341$	2519.78			0.400157
$342$			1654.01i			0.261516i
$343$		−	8328.90i		−	1.31113i
$344$	−3883.96			−0.608748
$345$	−343.152	−	111.091i	−0.0535497	−	0.0173360i
$346$	−3254.60			−0.505689
$347$			7693.25i			1.19019i	0.803656	+	0.595094i	$0.202885\pi$
$347$			7693.25i			1.19019i	−0.803656	+	0.595094i	$0.797115\pi$
$348$			3417.45i			0.526422i
$349$	−2791.91			−0.428217			−0.214108	−	0.976810i	$-0.568685\pi$
$349$	−2791.91			−0.428217			−0.214108	+	0.976810i	$0.568685\pi$
$350$	−11599.6	−	8389.71i	−1.77150	−	1.28128i
$351$	−1060.63			−0.161289
$352$		−	2397.90i		−	0.363093i
$353$			5310.27i			0.800672i	0.916368	+	0.400336i	$0.131107\pi$
$353$			5310.27i			0.800672i	−0.916368	+	0.400336i	$0.868893\pi$
$354$	−2394.48			−0.359506
$355$	−1345.89	−	435.712i	−0.201217	−	0.0651414i
$356$	3028.06			0.450806
$357$			7699.45i			1.14145i
$358$			9163.33i			1.35278i
$359$	−7008.05			−1.03028			−0.515140	−	0.857106i	$-0.672260\pi$
$359$	−7008.05			−1.03028			−0.515140	+	0.857106i	$0.672260\pi$
$360$	−260.938	+	806.021i	−0.0382018	+	0.118003i
$361$	−4398.65			−0.641297
$362$			183.313i			0.0266152i
$363$			363.000i			0.0524864i
$364$	−6954.65			−1.00144
$365$	−1754.14	+	5418.42i	−0.251550	+	0.777022i
$366$	−4090.03			−0.584124
$367$			2101.70i			0.298932i	0.988767	+	0.149466i	$0.0477555\pi$
$367$			2101.70i			0.298932i	−0.988767	+	0.149466i	$0.952245\pi$
$368$			828.192i			0.117317i
$369$	4136.78			0.583611
$370$	13736.9	+	4447.13i	1.93013	+	0.624852i
$371$	11140.7			1.55902
$372$		−	3936.04i		−	0.548586i
$373$		−	8782.22i		−	1.21910i	−0.792746	−	0.609552i	$-0.791349\pi$
$373$		−	8782.22i		−	1.21910i	0.792746	−	0.609552i	$-0.208651\pi$
$374$	3383.94			0.467860
$375$	3383.97	−	2475.25i	0.465994	−	0.340857i
$376$	−2293.42			−0.314558
$377$			7812.95i			1.06734i
$378$			3092.18i			0.420753i
$379$	−3038.99			−0.411879			−0.205940	−	0.978565i	$-0.566025\pi$
$379$	−3038.99			−0.411879			−0.205940	+	0.978565i	$0.566025\pi$
$380$	−3021.89	−	978.295i	−0.407947	−	0.132067i
$381$	5877.94			0.790383
$382$		−	7208.35i		−	0.965474i
$383$		−	14611.0i		−	1.94932i	−0.223700	−	0.974658i	$-0.571814\pi$
$383$		−	14611.0i		−	1.94932i	0.223700	−	0.974658i	$-0.428186\pi$
$384$	3102.69			0.412327
$385$	1170.85	−	3616.68i	0.154992	−	0.478761i
$386$	−11354.2			−1.49718
$387$		−	4151.70i		−	0.545330i
$388$		−	4914.45i		−	0.643024i
$389$	173.498			0.0226136			0.0113068	−	0.999936i	$-0.496401\pi$
$389$	173.498			0.0226136			0.0113068	+	0.999936i	$0.496401\pi$
$390$	1503.57	−	4644.42i	0.195221	−	0.603025i
$391$	−892.866			−0.115484
$392$		−	5156.61i		−	0.664409i
$393$			48.7963i			0.00626323i
$394$	6149.34			0.786292
$395$	7655.91	+	2478.50i	0.975217	+	0.315713i
$396$	567.027			0.0719550
$397$			1369.79i			0.173168i	0.996245	+	0.0865841i	$0.0275951\pi$
$397$			1369.79i			0.173168i	−0.996245	+	0.0865841i	$0.972405\pi$
$398$			11967.8i			1.50726i
$399$	4599.64			0.577118
$400$	−7800.47	−	5641.89i	−0.975058	−	0.705236i
$401$	14595.4			1.81760			0.908801	−	0.417230i	$-0.136999\pi$
$401$	14595.4			1.81760			0.908801	+	0.417230i	$0.136999\pi$
$402$		−	10330.2i		−	1.28165i
$403$		−	8998.53i		−	1.11228i
$404$	279.394			0.0344069
$405$	−861.583	−	278.926i	−0.105710	−	0.0342220i
$406$	22777.9			2.78436
$407$			3834.18i			0.466961i
$408$			2097.23i			0.254482i
$409$	9903.11			1.19726			0.598628	−	0.801027i	$-0.295713\pi$
$409$	9903.11			1.19726			0.598628	+	0.801027i	$0.295713\pi$
$410$	−5864.36	+	18114.6i	−0.706390	+	2.18199i
$411$	−2824.48			−0.338981
$412$			3007.55i			0.359639i
$413$			6658.83i			0.793365i
$414$	−358.584			−0.0425688
$415$	2979.09	−	9202.21i	0.352380	−	1.08848i
$416$	−8563.30			−1.00926
$417$			5925.11i			0.695812i
$418$		−	2021.56i		−	0.236550i
$419$	10648.7			1.24159			0.620794	−	0.783974i	$-0.286810\pi$
$419$	10648.7			1.24159			0.620794	+	0.783974i	$0.286810\pi$
$420$	−5649.45	−	1828.93i	−0.656346	−	0.212483i
$421$	14573.7			1.68713			0.843563	−	0.537030i	$-0.180454\pi$
$421$	14573.7			1.68713			0.843563	+	0.537030i	$0.180454\pi$
$422$		−	9425.17i		−	1.08723i
$423$		−	2451.51i		−	0.281788i
$424$	3034.60			0.347578
$425$	6082.46	−	8409.61i	0.694218	−	0.959826i
$426$	−1406.42			−0.159956
$427$			11374.0i			1.28906i
$428$		−	5650.16i		−	0.638110i
$429$	1296.33			0.145892
$430$	18179.9	+	5885.49i	2.03887	+	0.660055i
$431$	−2825.70			−0.315799			−0.157899	−	0.987455i	$-0.550472\pi$
$431$	−2825.70			−0.315799			−0.157899	+	0.987455i	$0.550472\pi$
$432$			2079.42i			0.231588i
$433$			14814.8i			1.64423i	0.569320	+	0.822116i	$0.307206\pi$
$433$			14814.8i			1.64423i	−0.569320	+	0.822116i	$0.692794\pi$
$434$	−26234.4			−2.90159
$435$	−2054.65	+	6346.68i	−0.226466	+	0.699540i
$436$	−316.678			−0.0347847
$437$			533.397i			0.0583887i
$438$			5662.11i			0.617685i
$439$	−12452.4			−1.35381			−0.676904	−	0.736071i	$-0.736679\pi$
$439$	−12452.4			−1.35381			−0.676904	+	0.736071i	$0.736679\pi$
$440$	318.925	−	985.137i	0.0345548	−	0.106738i
$441$	5512.08			0.595192
$442$		−	12084.6i		−	1.30047i
$443$			7989.73i			0.856892i	0.903567	+	0.428446i	$0.140939\pi$
$443$			7989.73i			0.856892i	−0.903567	+	0.428446i	$0.859061\pi$
$444$	5989.21			0.640170
$445$	5623.52	+	1820.54i	0.599057	+	0.193937i
$446$	4407.71			0.467963
$447$			8875.54i			0.939147i
$448$			5920.83i			0.624404i
$449$	−7874.23			−0.827635			−0.413817	−	0.910360i	$-0.635805\pi$
$449$	−7874.23			−0.827635			−0.413817	+	0.910360i	$0.635805\pi$
$450$	2442.78	−	3377.39i	0.255897	−	0.353803i
$451$	−5056.07			−0.527896
$452$			2633.30i			0.274026i
$453$		−	10359.6i		−	1.07448i
$454$	−18147.1			−1.87596
$455$	−12915.7	−	4181.29i	−1.33077	−	0.430817i
$456$	1252.88			0.128666
$457$		−	10376.8i		−	1.06216i	−0.847323	−	0.531078i	$-0.821787\pi$
$457$		−	10376.8i		−	1.06216i	0.847323	−	0.531078i	$-0.178213\pi$
$458$			8950.00i			0.913114i
$459$	−2241.80			−0.227970
$460$	212.092	−	655.139i	0.0214975	−	0.0664043i
$461$	−7935.15			−0.801685			−0.400843	−	0.916147i	$-0.631283\pi$
$461$	−7935.15			−0.801685			−0.400843	+	0.916147i	$0.631283\pi$
$462$		−	3779.33i		−	0.380585i
$463$			4036.46i			0.405163i	0.979265	+	0.202581i	$0.0649331\pi$
$463$			4036.46i			0.405163i	−0.979265	+	0.202581i	$0.935067\pi$
$464$	15317.6			1.53255
$465$	2366.43	−	7309.76i	0.236002	−	0.728993i
$466$	−1942.41			−0.193091
$467$		−	9548.40i		−	0.946140i	−0.881025	−	0.473070i	$-0.843146\pi$
$467$		−	9548.40i		−	0.946140i	0.881025	−	0.473070i	$-0.156854\pi$
$468$		−	2024.94i		−	0.200007i
$469$	−28727.3			−2.82837
$470$	10734.9	+	3475.29i	1.05354	+	0.341070i
$471$	−2216.67			−0.216855
$472$			1813.78i			0.176877i
$473$			5074.30i			0.493269i
$474$	8000.23			0.775238
$475$	−5023.89	−	3633.65i	−0.485288	−	0.350997i
$476$	−14699.6			−1.41546
$477$			3243.78i			0.311368i
$478$			15432.1i			1.47667i
$479$	15208.5			1.45072			0.725358	−	0.688372i	$-0.241674\pi$
$479$	15208.5			1.45072			0.725358	+	0.688372i	$0.241674\pi$
$480$	−6956.21	−	2251.98i	−0.661471	−	0.214142i
$481$	13692.5			1.29797
$482$			7072.25i			0.668324i
$483$			997.191i			0.0939416i
$484$	−693.033			−0.0650857
$485$	2954.67	−	9126.79i	0.276629	−	0.854487i
$486$	−900.332			−0.0840327
$487$			12284.0i			1.14300i	0.820601	+	0.571502i	$0.193639\pi$
$487$			12284.0i			1.14300i	−0.820601	+	0.571502i	$0.806361\pi$
$488$			3098.14i			0.287390i
$489$	727.581			0.0672849
$490$	−7813.99	+	24136.9i	−0.720408	+	2.22529i
$491$	−15310.6			−1.40725			−0.703623	−	0.710574i	$-0.748436\pi$
$491$	−15310.6			−1.40725			−0.703623	+	0.710574i	$0.748436\pi$
$492$			7897.87i			0.723707i
$493$			16513.8i			1.50861i
$494$	−7219.32			−0.657516
$495$	1053.05	+	340.909i	0.0956180	+	0.0309550i
$496$	−17642.0			−1.59708
$497$			3911.12i			0.352993i
$498$		−	9616.08i		−	0.865274i
$499$	−2024.99			−0.181665			−0.0908325	−	0.995866i	$-0.528953\pi$
$499$	−2024.99			−0.181665			−0.0908325	+	0.995866i	$0.528953\pi$
$500$	4725.70	+	6460.62i	0.422679	+	0.577855i
$501$	−7341.18			−0.654651
$502$			9276.11i			0.824728i
$503$			9262.81i			0.821090i	0.911840	+	0.410545i	$0.134661\pi$
$503$			9262.81i			0.821090i	−0.911840	+	0.410545i	$0.865339\pi$
$504$	2342.28			0.207011
$505$	518.873	+	167.978i	0.0457219	+	0.0148018i
$506$	438.270			0.0385049
$507$			1961.59i			0.171829i
$508$			11222.1i			0.980115i
$509$	15354.4			1.33707			0.668537	−	0.743679i	$-0.266921\pi$
$509$	15354.4			1.33707			0.668537	+	0.743679i	$0.266921\pi$
$510$	3178.01	−	9816.66i	0.275931	−	0.852331i
$511$	15745.8			1.36312
$512$			11601.2i			1.00138i
$513$			1339.25i			0.115262i
$514$	11063.0			0.949354
$515$	−1808.21	+	5585.43i	−0.154717	+	0.477910i
$516$	7926.34			0.676236
$517$			2996.29i			0.254887i
$518$		−	39919.1i		−	3.38599i
$519$	−2635.26			−0.222880
$520$	−3518.08	−	1138.93i	−0.296689	−	0.0960489i
$521$	−1155.39			−0.0971562			−0.0485781	−	0.998819i	$-0.515469\pi$
$521$	−1155.39			−0.0971562			−0.0485781	+	0.998819i	$0.515469\pi$
$522$			6632.11i			0.556091i
$523$		−	3705.49i		−	0.309808i	−0.987930	−	0.154904i	$-0.950493\pi$
$523$		−	3705.49i		−	0.309808i	0.987930	−	0.154904i	$-0.0495069\pi$
$524$	−93.1611			−0.00776672
$525$	−9392.21	−	6793.15i	−0.780780	−	0.564719i
$526$	8200.05			0.679732
$527$		−	19019.7i		−	1.57213i
$528$		−	2541.51i		−	0.209480i
$529$	12051.4			0.990496
$530$	−14204.2	−	4598.43i	−1.16414	−	0.376873i
$531$	−1938.81			−0.158451
$532$			8781.55i			0.715655i
$533$			18056.0i			1.46734i
$534$	5876.44			0.476214
$535$	3397.00	−	10493.1i	0.274514	−	0.847957i
$536$	−7824.97			−0.630573
$537$			7419.56i			0.596234i
$538$			2337.61i			0.187326i
$539$	−6736.98			−0.538372
$540$	532.520	−	1644.92i	0.0424370	−	0.131085i
$541$	13354.8			1.06131			0.530653	−	0.847589i	$-0.321947\pi$
$541$	13354.8			1.06131			0.530653	+	0.847589i	$0.321947\pi$
$542$		−	21422.3i		−	1.69773i
$543$			148.429i			0.0117305i
$544$	−18099.8			−1.42651
$545$	−588.114	−	190.394i	−0.0462239	−	0.0149643i
$546$	−13496.6			−1.05788
$547$			18996.8i			1.48491i	0.669897	+	0.742454i	$0.266338\pi$
$547$			18996.8i			1.48491i	−0.669897	+	0.742454i	$0.733662\pi$
$548$		−	5392.44i		−	0.420353i
$549$	−3311.70			−0.257450
$550$	−2985.62	+	4127.92i	−0.231468	+	0.320027i
$551$	9865.31			0.762752
$552$			271.622i			0.0209439i
$553$		−	22247.9i		−	1.71081i
$554$	12467.9			0.956158
$555$	11122.8	+	3600.85i	0.850695	+	0.275401i
$556$	−11312.1			−0.862842
$557$			8518.26i			0.647990i	0.946059	+	0.323995i	$0.105026\pi$
$557$			8518.26i			0.647990i	−0.946059	+	0.323995i	$0.894974\pi$
$558$		−	7638.51i		−	0.579505i
$559$	18121.1			1.37109
$560$	−8197.60	+	25321.9i	−0.618593	+	1.91079i
$561$	2739.98			0.206207
$562$			2305.70i			0.173060i
$563$			10311.5i			0.771900i	0.922520	+	0.385950i	$0.126126\pi$
$563$			10311.5i			0.771900i	−0.922520	+	0.385950i	$0.873874\pi$
$564$	4680.37			0.349431
$565$	−1583.20	+	4890.39i	−0.117886	+	0.364142i
$566$	−6037.20			−0.448344
$567$			2503.74i			0.185445i
$568$			1065.34i			0.0786983i
$569$	14997.9			1.10500			0.552498	−	0.833514i	$-0.313675\pi$
$569$	14997.9			1.10500			0.552498	+	0.833514i	$0.313675\pi$
$570$	−5864.46	−	1898.54i	−0.430939	−	0.139511i
$571$	12160.9			0.891274			0.445637	−	0.895214i	$-0.352977\pi$
$571$	12160.9			0.891274			0.445637	+	0.895214i	$0.352977\pi$
$572$			2474.93i			0.180913i
$573$		−	5836.61i		−	0.425528i
$574$	52640.7			3.82784
$575$	787.768	−	1089.17i	0.0571342	−	0.0789937i
$576$	−1723.93			−0.124706
$577$		−	16898.7i		−	1.21924i	−0.792694	−	0.609619i	$-0.791322\pi$
$577$		−	16898.7i		−	1.21924i	0.792694	−	0.609619i	$-0.208678\pi$
$578$		−	7339.53i		−	0.528174i
$579$	−9193.50			−0.659877
$580$	−12117.0	−	3922.70i	−0.867464	−	0.280830i
$581$	−26741.4			−1.90950
$582$		−	9537.26i		−	0.679265i
$583$		−	3964.62i		−	0.281643i
$584$	4288.96			0.303902
$585$	1217.44	−	3760.60i	0.0860427	−	0.265780i
$586$	−21656.5			−1.52666
$587$		−	18702.0i		−	1.31502i	−0.753448	−	0.657508i	$-0.771611\pi$
$587$		−	18702.0i		−	1.31502i	0.753448	−	0.657508i	$-0.228389\pi$
$588$			10523.6i			0.738068i
$589$	−11362.3			−0.794867
$590$	2748.48	−	8489.89i	0.191785	−	0.592412i
$591$	4979.13			0.346555
$592$		−	26844.7i		−	1.86370i
$593$			198.418i			0.0137404i	0.999976	+	0.00687019i	$0.00218687\pi$
$593$			198.418i			0.0137404i	−0.999976	+	0.00687019i	$0.997813\pi$
$594$	1100.41			0.0760104
$595$	−27299.2	−	8837.75i	−1.88094	−	0.608929i
$596$	−16945.0			−1.16459
$597$			9690.32i			0.664319i
$598$		−	1565.13i		−	0.107028i
$599$	−13958.3			−0.952119			−0.476060	−	0.879413i	$-0.657935\pi$
$599$	−13958.3			−0.952119			−0.476060	+	0.879413i	$0.657935\pi$
$600$	−2558.32	−	1850.37i	−0.174072	−	0.125902i
$601$	14279.5			0.969173			0.484587	−	0.874743i	$-0.338970\pi$
$601$	14279.5			0.969173			0.484587	+	0.874743i	$0.338970\pi$
$602$		−	52830.4i		−	3.57676i
$603$		−	8364.37i		−	0.564881i
$604$	19778.4			1.33241
$605$	−1287.06	−	416.667i	−0.0864897	−	0.0279999i
$606$	542.209			0.0363461
$607$		−	435.160i		−	0.0290982i	−0.999894	−	0.0145491i	$-0.995369\pi$
$607$		−	435.160i		−	0.0290982i	0.999894	−	0.0145491i	$-0.00463128\pi$
$608$			10812.8i			0.721243i
$609$	18443.3			1.22719
$610$	4694.71	−	14501.6i	0.311612	−	0.962549i
$611$	10700.2			0.708486
$612$		−	4280.01i		−	0.282695i
$613$		−	1032.63i		−	0.0680384i	−0.999421	−	0.0340192i	$-0.989169\pi$
$613$		−	1032.63i		−	0.0680384i	0.999421	−	0.0340192i	$-0.0108307\pi$
$614$	16495.4			1.08420
$615$	−4748.38	+	14667.4i	−0.311338	+	0.961703i
$616$	−2862.79			−0.187248
$617$			1793.68i			0.117035i	0.998286	+	0.0585176i	$0.0186374\pi$
$617$			1793.68i			0.117035i	−0.998286	+	0.0585176i	$0.981363\pi$
$618$			5836.63i			0.379909i
$619$	21282.0			1.38190			0.690948	−	0.722904i	$-0.257193\pi$
$619$	21282.0			1.38190			0.690948	+	0.722904i	$0.257193\pi$
$620$	13955.7	+	4517.95i	0.903988	+	0.292654i
$621$	−290.346			−0.0187620
$622$		−	27197.5i		−	1.75325i
$623$		−	16341.8i		−	1.05092i
$624$	−9076.16			−0.582271
$625$	4892.00	+	14839.4i	0.313088	+	0.949724i
$626$	15942.9			1.01790
$627$		−	1636.86i		−	0.104258i
$628$		−	4232.03i		−	0.268911i
$629$	28941.0			1.83458
$630$	−10963.7	−	3549.34i	−0.693338	−	0.224459i
$631$	−20393.2			−1.28660			−0.643298	−	0.765616i	$-0.722434\pi$
$631$	−20393.2			−1.28660			−0.643298	+	0.765616i	$0.722434\pi$
$632$		−	6060.06i		−	0.381418i
$633$		−	7631.57i		−	0.479191i
$634$	−20865.9			−1.30709
$635$	−6746.95	+	20840.9i	−0.421645	+	1.30243i
$636$	−6192.97			−0.386112
$637$			24058.8i			1.49646i
$638$		−	8105.91i		−	0.503003i
$639$	−1138.78			−0.0704997
$640$	−3561.40	+	11000.9i	−0.219964	+	0.679453i
$641$	−1068.76			−0.0658559			−0.0329280	−	0.999458i	$-0.510483\pi$
$641$	−1068.76			−0.0658559			−0.0329280	+	0.999458i	$0.510483\pi$
$642$		−	10965.0i		−	0.674074i
$643$		−	6293.52i		−	0.385991i	−0.981200	−	0.192995i	$-0.938180\pi$
$643$		−	6293.52i		−	0.385991i	0.981200	−	0.192995i	$-0.0618203\pi$
$644$	−1903.82			−0.116492
$645$	14720.3	+	4765.49i	0.898622	+	0.290916i
$646$	−15259.1			−0.929351
$647$			14233.7i			0.864888i	0.901661	+	0.432444i	$0.142349\pi$
$647$			14233.7i			0.864888i	−0.901661	+	0.432444i	$0.857651\pi$
$648$			681.988i			0.0413442i
$649$	2369.66			0.143324
$650$	14741.5	+	10662.1i	0.889550	+	0.643390i
$651$	−21242.0			−1.27886
$652$			1389.08i			0.0834367i
$653$			7671.06i			0.459712i	0.973225	+	0.229856i	$0.0738255\pi$
$653$			7671.06i			0.459712i	−0.973225	+	0.229856i	$0.926175\pi$
$654$	−614.563			−0.0367452
$655$	−173.013	−	56.0105i	−0.0103209	−	0.00334124i
$656$	35399.7			2.10690
$657$			4584.62i			0.272242i
$658$		−	31195.5i		−	1.84822i
$659$	−18783.6			−1.11033			−0.555165	−	0.831741i	$-0.687345\pi$
$659$	−18783.6			−1.11033			−0.555165	+	0.831741i	$0.687345\pi$
$660$	−650.857	+	2010.46i	−0.0383857	+	0.118571i
$661$	−21814.3			−1.28363			−0.641815	−	0.766859i	$-0.721818\pi$
$661$	−21814.3			−1.28363			−0.641815	+	0.766859i	$0.721818\pi$
$662$			41831.6i			2.45594i
$663$		−	9784.92i		−	0.573175i
$664$	−7284.04			−0.425716
$665$	−5279.66	+	16308.5i	−0.307874	+	0.951004i
$666$	11623.0			0.676250
$667$			2138.78i			0.124159i
$668$		−	14015.7i		−	0.811799i
$669$	3568.93			0.206252
$670$	36626.8	+	11857.4i	2.11197	+	0.683720i
$671$	4047.64			0.232872
$672$			20214.6i			1.16041i
$673$		−	4320.84i		−	0.247483i	−0.992314	−	0.123742i	$-0.960511\pi$
$673$		−	4320.84i		−	0.247483i	0.992314	−	0.123742i	$-0.0394894\pi$
$674$	16019.3			0.915488
$675$	1977.92	−	2734.67i	0.112786	−	0.155937i
$676$	−3745.03			−0.213077
$677$		−	8173.49i		−	0.464007i	−0.972715	−	0.232004i	$-0.925472\pi$
$677$		−	8173.49i		−	0.464007i	0.972715	−	0.232004i	$-0.0745281\pi$
$678$			5110.33i			0.289470i
$679$	−26522.3			−1.49902
$680$	−7435.97	−	2407.29i	−0.419348	−	0.135758i
$681$	−14693.7			−0.826819
$682$			9335.95i			0.524182i
$683$			11387.1i			0.637945i	0.947764	+	0.318973i	$0.103338\pi$
$683$			11387.1i			0.637945i	−0.947764	+	0.318973i	$0.896662\pi$
$684$	−2556.87			−0.142930
$685$	3242.05	−	10014.5i	0.180836	−	0.558590i
$686$	30859.2			1.71750
$687$			7246.83i			0.402451i
$688$		−	35527.3i		−	1.96870i
$689$	−14158.3			−0.782857
$690$	411.598	−	1271.40i	0.0227091	−	0.0701469i
$691$	7445.76			0.409913			0.204957	−	0.978771i	$-0.434295\pi$
$691$	7445.76			0.409913			0.204957	+	0.978771i	$0.434295\pi$
$692$		−	5031.18i		−	0.276383i
$693$		−	3060.13i		−	0.167741i
$694$	−28504.0			−1.55907
$695$	−21008.1	−	6801.09i	−1.14659	−	0.371194i
$696$	5023.73			0.273598
$697$			38164.0i			2.07398i
$698$		−	10344.2i		−	0.560938i
$699$	−1572.77			−0.0851041
$700$	12969.4	−	17931.4i	0.700280	−	0.968206i
$701$	−35574.7			−1.91674			−0.958372	−	0.285523i	$-0.907833\pi$
$701$	−35574.7			−1.91674			−0.958372	+	0.285523i	$0.907833\pi$
$702$		−	3929.73i		−	0.211279i
$703$		−	17289.3i		−	0.927566i
$704$	2107.03			0.112801
$705$	8692.09	+	2813.94i	0.464345	+	0.150325i
$706$	−19674.9			−1.04883
$707$		−	1507.84i		−	0.0802093i
$708$		−	3701.54i		−	0.196487i
$709$	−12878.9			−0.682199			−0.341099	−	0.940027i	$-0.610799\pi$
$709$	−12878.9			−0.682199			−0.341099	+	0.940027i	$0.610799\pi$
$710$	1614.34	−	4986.60i	0.0853313	−	0.263583i
$711$	6477.80			0.341683
$712$		−	4451.31i		−	0.234298i
$713$		−	2463.33i		−	0.129386i
$714$	−28527.0			−1.49523
$715$	−1487.98	+	4596.29i	−0.0778286	+	0.240407i
$716$	−14165.3			−0.739359
$717$			12495.4i			0.650834i
$718$		−	25965.3i		−	1.34961i
$719$	19103.3			0.990867			0.495434	−	0.868646i	$-0.335009\pi$
$719$	19103.3			0.990867			0.495434	+	0.868646i	$0.335009\pi$
$720$	−7372.81	−	2386.85i	−0.381623	−	0.123545i
$721$	16231.1			0.838390
$722$		−	16297.3i		−	0.840060i
$723$			5726.41i			0.294561i
$724$	−283.377			−0.0145465
$725$	−20144.4	−	14570.0i	−1.03192	−	0.746365i
$726$	−1344.94			−0.0687540
$727$		−	1059.06i		−	0.0540281i	−0.999635	−	0.0270141i	$-0.991400\pi$
$727$		−	1059.06i		−	0.0540281i	0.999635	−	0.0270141i	$-0.00859989\pi$
$728$			10223.5i			0.520477i
$729$	−729.000			−0.0370370
$730$	−20075.6	−	6499.21i	−1.01785	−	0.329516i
$731$	38301.6			1.93794
$732$		−	6322.64i		−	0.319251i
$733$			24503.8i			1.23475i	0.786670	+	0.617373i	$0.211803\pi$
$733$			24503.8i			1.23475i	−0.786670	+	0.617373i	$0.788197\pi$
$734$	−7786.96			−0.391583
$735$	−6326.99	+	19543.7i	−0.317517	+	0.980788i
$736$	−2344.18			−0.117402
$737$			10223.1i			0.510954i
$738$			15327.1i			0.764495i
$739$	−23488.3			−1.16919			−0.584595	−	0.811325i	$-0.698747\pi$
$739$	−23488.3			−1.16919			−0.584595	+	0.811325i	$0.698747\pi$
$740$	−6874.67	+	21235.4i	−0.341511	+	1.05490i
$741$	−5845.50			−0.289797
$742$			41277.2i			2.04223i
$743$		−	33500.5i		−	1.65413i	−0.562109	−	0.827063i	$-0.690010\pi$
$743$		−	33500.5i		−	1.65413i	0.562109	−	0.827063i	$-0.309990\pi$
$744$	−5786.06			−0.285117
$745$	−31469.2	−	10187.7i	−1.54757	−	0.501006i
$746$	32538.7			1.59695
$747$		−	7786.15i		−	0.381366i
$748$			5231.12i			0.255707i
$749$	−30492.8			−1.48756
$750$	9170.97	+	12537.9i	0.446502	+	0.610424i
$751$	−26937.5			−1.30887			−0.654436	−	0.756117i	$-0.727094\pi$
$751$	−26937.5			−1.30887			−0.654436	+	0.756117i	$0.727094\pi$
$752$		−	20978.3i		−	1.01729i
$753$			7510.88i			0.363495i
$754$	−28947.5			−1.39815
$755$	36731.3	+	11891.2i	1.77058	+	0.573201i
$756$	−4780.10			−0.229961
$757$			8869.39i			0.425843i	0.977069	+	0.212922i	$0.0682979\pi$
$757$			8869.39i			0.425843i	−0.977069	+	0.212922i	$0.931702\pi$
$758$		−	11259.7i		−	0.539537i
$759$	354.868			0.0169709
$760$	−1438.11	+	4442.24i	−0.0686393	+	0.212022i
$761$	12433.6			0.592271			0.296135	−	0.955146i	$-0.404302\pi$
$761$	12433.6			0.592271			0.296135	+	0.955146i	$0.404302\pi$
$762$			21778.2i			1.03535i
$763$			1709.05i			0.0810899i
$764$	11143.1			0.527676
$765$	2573.24	−	7948.56i	0.121615	−	0.375661i
$766$	54134.8			2.55349
$767$		−	8462.44i		−	0.398384i
$768$			16092.8i			0.756121i
$769$	−24551.5			−1.15130			−0.575650	−	0.817696i	$-0.695251\pi$
$769$	−24551.5			−1.15130			−0.575650	+	0.817696i	$0.695251\pi$
$770$	13400.0	+	4338.08i	0.627148	+	0.203030i
$771$	8957.72			0.418424
$772$		−	17552.1i		−	0.818280i
$773$		−	21858.5i		−	1.01707i	−0.861041	−	0.508535i	$-0.830187\pi$
$773$		−	21858.5i		−	1.01707i	0.861041	−	0.508535i	$-0.169813\pi$
$774$	15382.3			0.714349
$775$	23201.3	+	16780.9i	1.07537	+	0.777790i
$776$	−7224.34			−0.334199
$777$		−	32322.6i		−	1.49236i
$778$			642.821i			0.0296224i
$779$	22799.1			1.04861
$780$	7179.66	+	2324.32i	0.329581	+	0.106697i
$781$	1391.84			0.0637694
$782$		−	3308.13i		−	0.151277i
$783$			5370.03i			0.245095i
$784$	47168.4			2.14871
$785$	2544.39	−	7859.45i	0.115685	−	0.357345i
$786$	−180.794			−0.00820446
$787$			3488.56i			0.158010i	0.996874	+	0.0790048i	$0.0251743\pi$
$787$			3488.56i			0.158010i	−0.996874	+	0.0790048i	$0.974826\pi$
$788$			9506.06i			0.429745i
$789$	6639.59			0.299589
$790$	−9183.00	+	28365.7i	−0.413565	+	1.27748i
$791$	14211.4			0.638809
$792$		−	833.541i		−	0.0373972i
$793$		−	14454.8i		−	0.647293i
$794$	−5075.16			−0.226840
$795$	−11501.2	−	3723.35i	−0.513088	−	0.166105i
$796$	−18500.6			−0.823789
$797$			19467.5i			0.865212i	0.901583	+	0.432606i	$0.142406\pi$
$797$			19467.5i			0.865212i	−0.901583	+	0.432606i	$0.857594\pi$
$798$			17042.0i			0.755990i
$799$	22616.5			1.00139
$800$	15969.3	−	22079.1i	0.705748	−	0.975767i
$801$	4758.16			0.209889
$802$			54076.9i			2.38095i
$803$		−	5603.42i		−	0.246252i
$804$	15969.1			0.700481
$805$	−3535.65	−	1144.62i	−0.154802	−	0.0501149i
$806$	33340.2			1.45702
$807$			1892.76i			0.0825631i
$808$		−	410.716i		−	0.0178823i
$809$	3078.16			0.133773			0.0668866	−	0.997761i	$-0.478693\pi$
$809$	3078.16			0.133773			0.0668866	+	0.997761i	$0.478693\pi$
$810$	1033.44	−	3192.23i	0.0448288	−	0.138473i
$811$	31711.1			1.37303			0.686516	−	0.727115i	$-0.259139\pi$
$811$	31711.1			1.37303			0.686516	+	0.727115i	$0.259139\pi$
$812$			35211.6i			1.52178i
$813$		−	17345.7i		−	0.748266i
$814$	−14205.9			−0.611691
$815$	−835.148	+	2579.72i	−0.0358944	+	0.110876i
$816$	−19183.8			−0.822998
$817$		−	22881.3i		−	0.979824i
$818$			36691.7i			1.56833i
$819$	−10928.2			−0.466255
$820$	−28002.8	−	9065.51i	−1.19256	−	0.386075i
$821$	−31485.7			−1.33844			−0.669219	−	0.743065i	$-0.733371\pi$
$821$	−31485.7			−1.33844			−0.669219	+	0.743065i	$0.733371\pi$
$822$		−	10464.9i		−	0.444045i
$823$		−	19306.7i		−	0.817726i	−0.912596	−	0.408863i	$-0.865925\pi$
$823$		−	19306.7i		−	0.817726i	0.912596	−	0.408863i	$-0.134075\pi$
$824$	4421.16			0.186916
$825$	−2417.46	+	3342.38i	−0.102018	+	0.141051i
$826$	−24671.4			−1.03926
$827$			7147.76i			0.300546i	0.988645	+	0.150273i	$0.0480153\pi$
$827$			7147.76i			0.300546i	−0.988645	+	0.150273i	$0.951985\pi$
$828$		−	554.324i		−	0.0232658i
$829$	35630.4			1.49276			0.746378	−	0.665522i	$-0.231791\pi$
$829$	35630.4			1.49276			0.746378	+	0.665522i	$0.231791\pi$
$830$	34094.8	+	11037.7i	1.42584	+	0.461597i
$831$	10095.3			0.421422
$832$		−	7524.55i		−	0.313542i
$833$			50851.8i			2.11514i
$834$	−21952.9			−0.911472
$835$	8426.52	−	26029.0i	0.349236	−	1.07877i
$836$	3125.07			0.129285
$837$		−	6184.91i		−	0.255414i
$838$			39454.3i			1.62640i
$839$	−27513.3			−1.13214			−0.566070	−	0.824357i	$-0.691537\pi$
$839$	−27513.3			−1.13214			−0.566070	+	0.824357i	$0.691537\pi$
$840$	−2688.57	+	8304.81i	−0.110434	+	0.341123i
$841$	15168.2			0.621929
$842$			53996.7i			2.21003i
$843$			1866.92i			0.0762756i
$844$	14570.1			0.594220
$845$	−6955.04	−	2251.60i	−0.283149	−	0.0916655i
$846$	9083.01			0.369126
$847$			3740.16i			0.151728i
$848$			27758.0i			1.12407i
$849$	−4888.33			−0.197605
$850$	31158.2	+	22536.0i	1.25731	+	0.909384i
$851$	3748.28			0.150986
$852$		−	2174.13i		−	0.0874231i
$853$			21498.2i			0.862935i	0.902129	+	0.431467i	$0.142004\pi$
$853$			21498.2i			0.862935i	−0.902129	+	0.431467i	$0.857996\pi$
$854$	−42141.5			−1.68859
$855$	−4748.46	−	1537.25i	−0.189934	−	0.0614886i
$856$	−8305.85			−0.331645
$857$		−	7144.96i		−	0.284792i	−0.989810	−	0.142396i	$-0.954519\pi$
$857$		−	7144.96i		−	0.284792i	0.989810	−	0.142396i	$-0.0454807\pi$
$858$			4803.00i			0.191109i
$859$	5734.28			0.227766			0.113883	−	0.993494i	$-0.463671\pi$
$859$	5734.28			0.227766			0.113883	+	0.993494i	$0.463671\pi$
$860$	−9098.19	+	28103.7i	−0.360751	+	1.11434i
$861$	42623.2			1.68710
$862$		−	10469.4i		−	0.413677i
$863$			5032.50i			0.198503i	0.995062	+	0.0992516i	$0.0316449\pi$
$863$			5032.50i			0.198503i	−0.995062	+	0.0992516i	$0.968355\pi$
$864$	−5885.76			−0.231757
$865$	3024.86	−	9343.59i	0.118900	−	0.367273i
$866$	−54889.8			−2.15385
$867$		−	5942.83i		−	0.232790i
$868$		−	40554.8i		−	1.58585i
$869$	−7917.31			−0.309064
$870$	−23514.9	−	7612.62i	−0.916355	−	0.296657i
$871$	36508.4			1.42025
$872$			465.523i			0.0180787i
$873$		−	7722.33i		−	0.299383i
$874$	−1976.27			−0.0764856
$875$	34866.7	−	25503.6i	1.34709	−	0.985349i
$876$	−8752.86			−0.337593
$877$		−	29097.4i		−	1.12035i	−0.828373	−	0.560177i	$-0.810733\pi$
$877$		−	29097.4i		−	1.12035i	0.828373	−	0.560177i	$-0.189267\pi$
$878$		−	46137.1i		−	1.77341i
$879$	−17535.3			−0.672867
$880$	9011.22	+	2917.26i	0.345191	+	0.111751i
$881$	6899.21			0.263837			0.131918	−	0.991261i	$-0.457886\pi$
$881$	6899.21			0.263837			0.131918	+	0.991261i	$0.457886\pi$
$882$			20422.6i			0.779666i
$883$			13094.5i			0.499054i	0.968368	+	0.249527i	$0.0802752\pi$
$883$			13094.5i			0.499054i	−0.968368	+	0.249527i	$0.919725\pi$
$884$	18681.2			0.710765
$885$	2225.45	−	6874.27i	0.0845285	−	0.261103i
$886$	−29602.5			−1.12248
$887$		−	27043.9i		−	1.02373i	−0.859067	−	0.511863i	$-0.828956\pi$
$887$		−	27043.9i		−	1.02373i	0.859067	−	0.511863i	$-0.171044\pi$
$888$		−	8804.26i		−	0.332716i
$889$	60563.2			2.28484
$890$	−6745.22	+	20835.5i	−0.254045	+	0.784729i
$891$	891.000			0.0335013
$892$			6813.74i			0.255763i
$893$		−	13511.0i		−	0.506304i
$894$	−32884.5			−1.23023
$895$	−26306.9	−	8516.48i	−0.982504	−	0.318072i
$896$	31968.5			1.19196
$897$		−	1267.29i		−	0.0471723i
$898$		−	29174.6i		−	1.08415i
$899$	−45559.9			−1.69022
$900$	5220.99	+	3776.21i	0.193370	+	0.139860i
$901$	−29925.6			−1.10651
$902$		−	18733.1i		−	0.691512i
$903$		−	42776.9i		−	1.57644i
$904$	3871.00			0.142420
$905$	−526.270	−	170.373i	−0.0193302	−	0.00625788i
$906$	38383.2			1.40750
$907$		−	375.753i		−	0.0137560i	−0.999976	−	0.00687799i	$-0.997811\pi$
$907$		−	375.753i		−	0.0137560i	0.999976	−	0.00687799i	$-0.00218935\pi$
$908$		−	28052.9i		−	1.02530i
$909$	439.028			0.0160194
$910$	15492.0	−	47853.7i	0.564345	−	1.74322i
$911$	7303.70			0.265623			0.132811	−	0.991141i	$-0.457600\pi$
$911$	7303.70			0.265623			0.132811	+	0.991141i	$0.457600\pi$
$912$			11460.4i			0.416108i
$913$			9516.40i			0.344958i
$914$	38446.7			1.39136
$915$	3801.31	−	11742.0i	0.137342	−	0.424239i
$916$	−13835.5			−0.499059
$917$			502.772i			0.0181058i
$918$		−	8306.04i		−	0.298628i
$919$	−3492.12			−0.125348			−0.0626738	−	0.998034i	$-0.519963\pi$
$919$	−3492.12			−0.125348			−0.0626738	+	0.998034i	$0.519963\pi$
$920$	−963.067	−	311.780i	−0.0345124	−	0.0111729i
$921$	13356.4			0.477858
$922$		−	29400.3i		−	1.05016i
$923$		−	4970.48i		−	0.177254i
$924$	5842.34			0.208008
$925$	−25534.4	+	35303.8i	−0.907638	+	1.25490i
$926$	−14955.4			−0.530739
$927$			4725.93i			0.167443i
$928$			43356.3i			1.53366i
$929$	−16961.2			−0.599009			−0.299504	−	0.954095i	$-0.596821\pi$
$929$	−16961.2			−0.599009			−0.299504	+	0.954095i	$0.596821\pi$
$930$	27083.2	+	8767.80i	0.954938	+	0.309148i
$931$	30378.8			1.06941
$932$		−	3002.71i		−	0.105533i
$933$		−	22021.8i		−	0.772736i
$934$	35377.5			1.23939
$935$	−3145.07	+	9714.91i	−0.110005	+	0.339798i
$936$	−2976.71			−0.103950
$937$			3401.53i			0.118595i	0.998240	+	0.0592973i	$0.0188860\pi$
$937$			3401.53i			0.118595i	−0.998240	+	0.0592973i	$0.981114\pi$
$938$		−	106437.i		−	3.70499i
$939$	12909.0			0.448635
$940$	−5372.33	+	16594.8i	−0.186411	+	0.575811i
$941$	−39517.5			−1.36901			−0.684503	−	0.729010i	$-0.739981\pi$
$941$	−39517.5			−1.36901			−0.684503	+	0.729010i	$0.739981\pi$
$942$		−	8212.92i		−	0.284067i
$943$			4942.80i			0.170689i
$944$	−16591.0			−0.572024
$945$	−8877.29	−	2873.90i	−0.305586	−	0.0989291i
$946$	−18800.6			−0.646153
$947$			39781.6i			1.36508i	0.730850	+	0.682538i	$0.239124\pi$
$947$			39781.6i			1.36508i	−0.730850	+	0.682538i	$0.760876\pi$
$948$			12367.3i			0.423703i
$949$	−20010.7			−0.684484
$950$	13462.9	−	18613.9i	0.459785	−	0.635698i
$951$	−16895.2			−0.576092
$952$			21608.8i			0.735656i
$953$			19941.5i			0.677826i	0.940818	+	0.338913i	$0.110059\pi$
$953$			19941.5i			0.677826i	−0.940818	+	0.338913i	$0.889941\pi$
$954$	−12018.4			−0.407874
$955$	20694.3	+	6699.51i	0.701207	+	0.227006i
$956$	−23855.9			−0.807066
$957$		−	6563.37i		−	0.221697i
$958$			56348.5i			1.90035i
$959$	−29101.9			−0.979926
$960$	1978.81	−	6112.40i	0.0665267	−	0.205497i
$961$	22682.4			0.761384
$962$			50731.6i			1.70026i
$963$		−	8878.41i		−	0.297095i
$964$	−10932.8			−0.365270
$965$	10552.7	−	32596.6i	0.352024	−	1.08738i
$966$	−3694.66			−0.123058
$967$			22672.9i			0.753992i	0.926215	+	0.376996i	$0.123043\pi$
$967$			22672.9i			0.753992i	−0.926215	+	0.376996i	$0.876957\pi$
$968$			1018.77i			0.0338271i
$969$	−12355.3			−0.409607
$970$	33815.4	+	10947.3i	1.11933	+	0.362367i
$971$	15739.4			0.520186			0.260093	−	0.965584i	$-0.416247\pi$
$971$	15739.4			0.520186			0.260093	+	0.965584i	$0.416247\pi$
$972$		−	1391.79i		−	0.0459278i
$973$			61049.1i			2.01145i
$974$	−45513.2			−1.49727
$975$	11936.2	+	8633.14i	0.392065	+	0.283571i
$976$	−28339.2			−0.929422
$977$		−	55085.0i		−	1.80381i	−0.431933	−	0.901906i	$-0.642168\pi$
$977$		−	55085.0i		−	1.80381i	0.431933	−	0.901906i	$-0.357832\pi$
$978$			2695.74i			0.0881392i
$979$	−5815.53			−0.189852
$980$	−37312.4	−	12079.4i	−1.21623	−	0.393736i
$981$	−497.613			−0.0161953
$982$		−	56726.8i		−	1.84341i
$983$		−	3826.41i		−	0.124154i	−0.998071	−	0.0620770i	$-0.980228\pi$
$983$		−	3826.41i		−	0.124154i	0.998071	−	0.0620770i	$-0.0197724\pi$
$984$	11610.0			0.376133
$985$	−5715.25	+	17654.0i	−0.184876	+	0.571071i
$986$	−61184.7			−1.97619
$987$		−	25259.0i		−	0.814594i
$988$		−	11160.1i		−	0.359363i
$989$	4960.62			0.159493
$990$	−1263.09	+	3901.61i	−0.0405492	+	0.125254i
$991$	10873.3			0.348538			0.174269	−	0.984698i	$-0.444244\pi$
$991$	10873.3			0.348538			0.174269	+	0.984698i	$0.444244\pi$
$992$		−	49935.4i		−	1.59824i
$993$			33871.1i			1.08244i
$994$	−14491.0			−0.462400
$995$	−34358.1	−	11123.0i	−1.09470	−	0.354394i
$996$	14865.2			0.472913
$997$		−	40064.9i		−	1.27269i	−0.771406	−	0.636343i	$-0.780446\pi$
$997$		−	40064.9i		−	1.27269i	0.771406	−	0.636343i	$-0.219554\pi$
$998$		−	7502.72i		−	0.237970i
$999$	9411.17			0.298054

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	165.4.c.b.34.13	yes	14
3.2	odd	2		495.4.c.d.199.2		14
5.2	odd	4		825.4.a.ba.1.2		7
5.3	odd	4		825.4.a.bd.1.6		7
5.4	even	2	inner	165.4.c.b.34.2	✓	14
15.2	even	4		2475.4.a.bs.1.6		7
15.8	even	4		2475.4.a.bo.1.2		7
15.14	odd	2		495.4.c.d.199.13		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
165.4.c.b.34.2	✓	14	5.4	even	2	inner
165.4.c.b.34.13	yes	14	1.1	even	1	trivial
495.4.c.d.199.2		14	3.2	odd	2
495.4.c.d.199.13		14	15.14	odd	2
825.4.a.ba.1.2		7	5.2	odd	4
825.4.a.bd.1.6		7	5.3	odd	4
2475.4.a.bo.1.2		7	15.8	even	4
2475.4.a.bs.1.6		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)

\(f(q)\)	\(=\)	\(q+3.70507i q^{2} +3.00000i q^{3} -5.72754 q^{4} +(-10.6368 - 3.44353i) q^{5} -11.1152 q^{6} +30.9104i q^{7} +8.41961i q^{8} -9.00000 q^{9} +O(q^{10})\)	\(q+3.70507i q^{2} +3.00000i q^{3} -5.72754 q^{4} +(-10.6368 - 3.44353i) q^{5} -11.1152 q^{6} +30.9104i q^{7} +8.41961i q^{8} -9.00000 q^{9} +(12.7585 - 39.4102i) q^{10} +11.0000 q^{11} -17.1826i q^{12} -39.2828i q^{13} -114.525 q^{14} +(10.3306 - 31.9105i) q^{15} -77.0156 q^{16} -83.0298i q^{17} -33.3456i q^{18} -49.6019 q^{19} +(60.9229 + 19.7230i) q^{20} -92.7312 q^{21} +40.7558i q^{22} -10.7536i q^{23} -25.2588 q^{24} +(101.284 + 73.2564i) q^{25} +145.545 q^{26} -27.0000i q^{27} -177.041i q^{28} -198.890 q^{29} +(118.231 + 38.2755i) q^{30} +229.071 q^{31} -217.991i q^{32} +33.0000i q^{33} +307.631 q^{34} +(106.441 - 328.789i) q^{35} +51.5479 q^{36} +348.562i q^{37} -183.778i q^{38} +117.848 q^{39} +(28.9931 - 89.5579i) q^{40} -459.643 q^{41} -343.576i q^{42} +461.300i q^{43} -63.0030 q^{44} +(95.7315 + 30.9917i) q^{45} +39.8427 q^{46} +272.390i q^{47} -231.047i q^{48} -612.453 q^{49} +(-271.420 + 375.265i) q^{50} +249.089 q^{51} +224.994i q^{52} -360.420i q^{53} +100.037 q^{54} +(-117.005 - 37.8788i) q^{55} -260.253 q^{56} -148.806i q^{57} -736.901i q^{58} +215.424 q^{59} +(-59.1689 + 182.769i) q^{60} +367.967 q^{61} +848.723i q^{62} -278.194i q^{63} +191.548 q^{64} +(-135.271 + 417.844i) q^{65} -122.267 q^{66} +929.374i q^{67} +475.557i q^{68} +32.2607 q^{69} +(1218.18 + 394.371i) q^{70} +126.531 q^{71} -75.7765i q^{72} -509.402i q^{73} -1291.45 q^{74} +(-219.769 + 303.853i) q^{75} +284.097 q^{76} +340.014i q^{77} +436.636i q^{78} -719.755 q^{79} +(819.202 + 265.205i) q^{80} +81.0000 q^{81} -1703.01i q^{82} +865.128i q^{83} +531.122 q^{84} +(-285.915 + 883.173i) q^{85} -1709.15 q^{86} -596.670i q^{87} +92.6157i q^{88} -528.684 q^{89} +(-114.827 + 354.692i) q^{90} +1214.25 q^{91} +61.5915i q^{92} +687.212i q^{93} -1009.22 q^{94} +(527.607 + 170.805i) q^{95} +653.974 q^{96} +858.037i q^{97} -2269.18i q^{98} -99.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - 26 q^{4} - 14 q^{5} - 30 q^{6} - 126 q^{9}+O(q^{10}) \) 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

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