LMFDB - Embedded newform 165.3.b.a.76.13

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [165,3,Mod(76,165)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("165.76"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(165, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 1])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 165 = 3 \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	165.b (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$4.49592436194$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 36x^{14} + 500x^{12} + 3364x^{10} + 11310x^{8} + 17932x^{6} + 12708x^{4} + 3244x^{2} + 121 $ x^16 + 36x^14 + 500x^12 + 3364x^10 + 11310x^8 + 17932x^6 + 12708x^4 + 3244*x^2 + 121
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{12} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			76.13
Root			$2.33103i$ of defining polynomial
Character	$\chi$	$=$	165.76
Dual form			165.3.b.a.76.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+2.33103i q^{2} -1.73205 q^{3} -1.43371 q^{4} +2.23607 q^{5} -4.03747i q^{6} +6.32430i q^{7} +5.98210i q^{8} +3.00000 q^{9} +5.21235i q^{10} +(-10.3943 - 3.59991i) q^{11} +2.48326 q^{12} +17.3965i q^{13} -14.7421 q^{14} -3.87298 q^{15} -19.6793 q^{16} -12.2603i q^{17} +6.99310i q^{18} +10.6069i q^{19} -3.20588 q^{20} -10.9540i q^{21} +(8.39151 - 24.2294i) q^{22} -9.16729 q^{23} -10.3613i q^{24} +5.00000 q^{25} -40.5519 q^{26} -5.19615 q^{27} -9.06722i q^{28} +0.592304i q^{29} -9.02805i q^{30} +17.1631 q^{31} -21.9447i q^{32} +(18.0034 + 6.23523i) q^{33} +28.5791 q^{34} +14.1416i q^{35} -4.30114 q^{36} +55.3012 q^{37} -24.7249 q^{38} -30.1317i q^{39} +13.3764i q^{40} +13.5046i q^{41} +25.5341 q^{42} +36.0017i q^{43} +(14.9024 + 5.16124i) q^{44} +6.70820 q^{45} -21.3693i q^{46} -19.2531 q^{47} +34.0856 q^{48} +9.00325 q^{49} +11.6552i q^{50} +21.2354i q^{51} -24.9416i q^{52} +70.4442 q^{53} -12.1124i q^{54} +(-23.2423 - 8.04965i) q^{55} -37.8326 q^{56} -18.3716i q^{57} -1.38068 q^{58} +14.9479 q^{59} +5.55274 q^{60} -36.1401i q^{61} +40.0077i q^{62} +18.9729i q^{63} -27.5634 q^{64} +38.8998i q^{65} +(-14.5345 + 41.9665i) q^{66} +127.842 q^{67} +17.5777i q^{68} +15.8782 q^{69} -32.9644 q^{70} -27.8440 q^{71} +17.9463i q^{72} +61.3643i q^{73} +128.909i q^{74} -8.66025 q^{75} -15.2072i q^{76} +(22.7669 - 65.7364i) q^{77} +70.2379 q^{78} -141.550i q^{79} -44.0043 q^{80} +9.00000 q^{81} -31.4798 q^{82} -137.804i q^{83} +15.7049i q^{84} -27.4148i q^{85} -83.9212 q^{86} -1.02590i q^{87} +(21.5350 - 62.1795i) q^{88} +160.353 q^{89} +15.6370i q^{90} -110.021 q^{91} +13.1433 q^{92} -29.7273 q^{93} -44.8797i q^{94} +23.7177i q^{95} +38.0094i q^{96} -57.7240 q^{97} +20.9869i q^{98} +(-31.1828 - 10.7997i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 8 q^{4} + 48 q^{9} - 28 q^{11} - 16 q^{16} + 40 q^{20} - 20 q^{22} + 56 q^{23} + 80 q^{25} - 88 q^{26} - 96 q^{31} - 12 q^{33} - 200 q^{34} - 24 q^{36} + 184 q^{37} + 296 q^{38} - 264 q^{42} + 300 q^{44}+ \cdots - 84 q^{99}+O(q^{100}) $ 16 * q - 8 * q^4 + 48 * q^9 - 28 * q^11 - 16 * q^16 + 40 * q^20 - 20 * q^22 + 56 * q^23 + 80 * q^25 - 88 * q^26 - 96 * q^31 - 12 * q^33 - 200 * q^34 - 24 * q^36 + 184 * q^37 + 296 * q^38 - 264 * q^42 + 300 * q^44 - 200 * q^47 + 96 * q^48 - 496 * q^49 - 80 * q^53 + 20 * q^55 - 32 * q^56 - 16 * q^58 - 136 * q^59 + 456 * q^64 - 180 * q^66 + 256 * q^67 + 168 * q^69 + 216 * q^71 - 248 * q^77 + 240 * q^78 - 160 * q^80 + 144 * q^81 + 232 * q^82 + 192 * q^86 - 116 * q^88 - 336 * q^89 + 256 * q^91 - 440 * q^92 - 144 * q^93 - 144 * q^97 - 84 * q^99

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 $

$2$			2.33103i			1.16552i	0.812646	+	0.582758i	$0.198026\pi$
$2$			2.33103i			1.16552i	−0.812646	+	0.582758i	$0.801974\pi$
$3$	−1.73205			−0.577350
$3$	−1.73205			−0.577350
$4$	−1.43371			−0.358428
$5$	2.23607			0.447214
$5$	2.23607			0.447214
$6$		−	4.03747i		−	0.672911i
$7$			6.32430i			0.903471i	0.892152	+	0.451736i	$0.149195\pi$
$7$			6.32430i			0.903471i	−0.892152	+	0.451736i	$0.850805\pi$
$8$			5.98210i			0.747763i
$9$	3.00000			0.333333
$10$			5.21235i			0.521235i
$11$	−10.3943	−	3.59991i	−0.944933	−	0.327265i
$11$	−10.3943	−	3.59991i	−0.944933	−	0.327265i
$12$	2.48326			0.206938
$13$			17.3965i			1.33820i	0.743175	+	0.669098i	$0.233319\pi$
$13$			17.3965i			1.33820i	−0.743175	+	0.669098i	$0.766681\pi$
$14$	−14.7421			−1.05301
$15$	−3.87298			−0.258199
$16$	−19.6793			−1.22996
$17$		−	12.2603i		−	0.721192i	−0.932722	−	0.360596i	$-0.882573\pi$
$17$		−	12.2603i		−	0.721192i	0.932722	−	0.360596i	$-0.117427\pi$
$18$			6.99310i			0.388505i
$19$			10.6069i			0.558256i	0.960254	+	0.279128i	$0.0900454\pi$
$19$			10.6069i			0.558256i	−0.960254	+	0.279128i	$0.909955\pi$
$20$	−3.20588			−0.160294
$21$		−	10.9540i		−	0.521619i
$22$	8.39151	−	24.2294i	0.381432	−	1.10133i
$23$	−9.16729			−0.398578			−0.199289	−	0.979941i	$-0.563863\pi$
$23$	−9.16729			−0.398578			−0.199289	+	0.979941i	$0.563863\pi$
$24$		−	10.3613i		−	0.431721i
$25$	5.00000			0.200000
$26$	−40.5519			−1.55969
$27$	−5.19615			−0.192450
$28$		−	9.06722i		−	0.323829i
$29$			0.592304i			0.0204243i	0.999948	+	0.0102121i	$0.00325068\pi$
$29$			0.592304i			0.0204243i	−0.999948	+	0.0102121i	$0.996749\pi$
$30$		−	9.02805i		−	0.300935i
$31$	17.1631			0.553648			0.276824	−	0.960921i	$-0.410718\pi$
$31$	17.1631			0.553648			0.276824	+	0.960921i	$0.410718\pi$
$32$		−	21.9447i		−	0.685773i
$33$	18.0034	+	6.23523i	0.545557	+	0.188946i
$34$	28.5791			0.840561
$35$			14.1416i			0.404045i
$36$	−4.30114			−0.119476
$37$	55.3012			1.49463			0.747314	−	0.664472i	$-0.231343\pi$
$37$	55.3012			1.49463			0.747314	+	0.664472i	$0.231343\pi$
$38$	−24.7249			−0.650656
$39$		−	30.1317i		−	0.772607i
$40$			13.3764i			0.334410i
$41$			13.5046i			0.329382i	0.986345	+	0.164691i	$0.0526626\pi$
$41$			13.5046i			0.329382i	−0.986345	+	0.164691i	$0.947337\pi$
$42$	25.5341			0.607956
$43$			36.0017i			0.837249i	0.908159	+	0.418625i	$0.137488\pi$
$43$			36.0017i			0.837249i	−0.908159	+	0.418625i	$0.862512\pi$
$44$	14.9024	+	5.16124i	0.338690	+	0.117301i
$45$	6.70820			0.149071
$46$		−	21.3693i		−	0.464549i
$47$	−19.2531			−0.409641			−0.204821	−	0.978800i	$-0.565661\pi$
$47$	−19.2531			−0.409641			−0.204821	+	0.978800i	$0.565661\pi$
$48$	34.0856			0.710116
$49$	9.00325			0.183740
$50$			11.6552i			0.233103i
$51$			21.2354i			0.416380i
$52$		−	24.9416i		−	0.479646i
$53$	70.4442			1.32914			0.664568	−	0.747228i	$-0.268616\pi$
$53$	70.4442			1.32914			0.664568	+	0.747228i	$0.268616\pi$
$54$		−	12.1124i		−	0.224304i
$55$	−23.2423	−	8.04965i	−0.422587	−	0.146357i
$56$	−37.8326			−0.675582
$57$		−	18.3716i		−	0.322309i
$58$	−1.38068			−0.0238048
$59$	14.9479			0.253354			0.126677	−	0.991944i	$-0.459569\pi$
$59$	14.9479			0.253354			0.126677	+	0.991944i	$0.459569\pi$
$60$	5.55274			0.0925457
$61$		−	36.1401i		−	0.592461i	−0.955116	−	0.296231i	$-0.904270\pi$
$61$		−	36.1401i		−	0.592461i	0.955116	−	0.296231i	$-0.0957297\pi$
$62$			40.0077i			0.645285i
$63$			18.9729i			0.301157i
$64$	−27.5634			−0.430678
$65$			38.8998i			0.598459i
$66$	−14.5345	+	41.9665i	−0.220220	+	0.635856i
$67$	127.842			1.90809			0.954046	−	0.299660i	$-0.0968732\pi$
$67$	127.842			1.90809			0.954046	+	0.299660i	$0.0968732\pi$
$68$			17.5777i			0.258495i
$69$	15.8782			0.230119
$70$	−32.9644			−0.470921
$71$	−27.8440			−0.392169			−0.196084	−	0.980587i	$-0.562823\pi$
$71$	−27.8440			−0.392169			−0.196084	+	0.980587i	$0.562823\pi$
$72$			17.9463i			0.249254i
$73$			61.3643i			0.840607i	0.907383	+	0.420304i	$0.138076\pi$
$73$			61.3643i			0.840607i	−0.907383	+	0.420304i	$0.861924\pi$
$74$			128.909i			1.74201i
$75$	−8.66025			−0.115470
$76$		−	15.2072i		−	0.200095i
$77$	22.7669	−	65.7364i	0.295674	−	0.853719i
$78$	70.2379			0.900486
$79$		−	141.550i		−	1.79177i	−0.444289	−	0.895884i	$-0.646544\pi$
$79$		−	141.550i		−	1.79177i	0.444289	−	0.895884i	$-0.353456\pi$
$80$	−44.0043			−0.550054
$81$	9.00000			0.111111
$82$	−31.4798			−0.383900
$83$		−	137.804i		−	1.66028i	−0.557552	−	0.830142i	$-0.688259\pi$
$83$		−	137.804i		−	1.66028i	0.557552	−	0.830142i	$-0.311741\pi$
$84$			15.7049i			0.186963i
$85$		−	27.4148i		−	0.322527i
$86$	−83.9212			−0.975828
$87$		−	1.02590i		−	0.0117920i
$88$	21.5350	−	62.1795i	0.244716	−	0.706585i
$89$	160.353			1.80172			0.900858	−	0.434113i	$-0.142938\pi$
$89$	160.353			1.80172			0.900858	+	0.434113i	$0.142938\pi$
$90$			15.6370i			0.173745i
$91$	−110.021			−1.20902
$92$	13.1433			0.142861
$93$	−29.7273			−0.319649
$94$		−	44.8797i		−	0.477443i
$95$			23.7177i			0.249660i
$96$			38.0094i			0.395931i
$97$	−57.7240			−0.595092			−0.297546	−	0.954707i	$-0.596168\pi$
$97$	−57.7240			−0.595092			−0.297546	+	0.954707i	$0.596168\pi$
$98$			20.9869i			0.214152i
$99$	−31.1828	−	10.7997i	−0.314978	−	0.109088i
$100$	−7.16856			−0.0716856
$101$		−	147.055i		−	1.45599i	−0.685585	−	0.727993i	$-0.740453\pi$
$101$		−	147.055i		−	1.45599i	0.685585	−	0.727993i	$-0.259547\pi$
$102$	−49.5004			−0.485298
$103$	−98.7792			−0.959022			−0.479511	−	0.877536i	$-0.659186\pi$
$103$	−98.7792			−0.959022			−0.479511	+	0.877536i	$0.659186\pi$
$104$	−104.068			−1.00065
$105$		−	24.4939i		−	0.233275i
$106$			164.208i			1.54913i
$107$			107.953i			1.00891i	0.863439	+	0.504453i	$0.168306\pi$
$107$			107.953i			1.00891i	−0.863439	+	0.504453i	$0.831694\pi$
$108$	7.44978			0.0689795
$109$		−	33.0995i		−	0.303666i	−0.988406	−	0.151833i	$-0.951482\pi$
$109$		−	33.0995i		−	0.303666i	0.988406	−	0.151833i	$-0.0485175\pi$
$110$	18.7640	−	54.1785i	0.170582	−	0.492532i
$111$	−95.7845			−0.862923
$112$		−	124.458i		−	1.11123i
$113$	−163.297			−1.44510			−0.722552	−	0.691316i	$-0.757031\pi$
$113$	−163.297			−1.44510			−0.722552	+	0.691316i	$0.757031\pi$
$114$	42.8249			0.375657
$115$	−20.4987			−0.178249
$116$		−	0.849193i		−	0.00732063i
$117$			52.1896i			0.446065i
$118$			34.8441i			0.295289i
$119$	77.5376			0.651576
$120$		−	23.1686i		−	0.193071i
$121$	95.0813	+	74.8369i	0.785795	+	0.618486i
$122$	84.2438			0.690523
$123$		−	23.3907i		−	0.190169i
$124$	−24.6069			−0.198443
$125$	11.1803			0.0894427
$126$	−44.2264			−0.351003
$127$			204.213i			1.60798i	0.594645	+	0.803988i	$0.297293\pi$
$127$			204.213i			1.60798i	−0.594645	+	0.803988i	$0.702707\pi$
$128$		−	152.030i		−	1.18774i
$129$		−	62.3568i		−	0.483386i
$130$	−90.6768			−0.697514
$131$			243.373i			1.85781i	0.370316	+	0.928906i	$0.379249\pi$
$131$			243.373i			1.85781i	−0.370316	+	0.928906i	$0.620751\pi$
$132$	−25.8117	−	8.93953i	−0.195543	−	0.0677237i
$133$	−67.0810			−0.504368
$134$			298.004i			2.22391i
$135$	−11.6190			−0.0860663
$136$	73.3421			0.539280
$137$	68.3154			0.498652			0.249326	−	0.968420i	$-0.419791\pi$
$137$	68.3154			0.498652			0.249326	+	0.968420i	$0.419791\pi$
$138$			37.0126i			0.268208i
$139$			21.5172i			0.154800i	0.997000	+	0.0774001i	$0.0246619\pi$
$139$			21.5172i			0.154800i	−0.997000	+	0.0774001i	$0.975338\pi$
$140$		−	20.2749i		−	0.144821i
$141$	33.3474			0.236506
$142$		−	64.9052i		−	0.457079i
$143$	62.6260	−	180.824i	0.437944	−	1.26450i
$144$	−59.0380			−0.409986
$145$			1.32443i			0.00913401i
$146$	−143.042			−0.979742
$147$	−15.5941			−0.106082
$148$	−79.2860			−0.535716
$149$		−	45.9449i		−	0.308355i	−0.988043	−	0.154178i	$-0.950727\pi$
$149$		−	45.9449i		−	0.308355i	0.988043	−	0.154178i	$-0.0492728\pi$
$150$		−	20.1873i		−	0.134582i
$151$			123.582i			0.818425i	0.912439	+	0.409212i	$0.134197\pi$
$151$			123.582i			0.818425i	−0.912439	+	0.409212i	$0.865803\pi$
$152$	−63.4513			−0.417443
$153$		−	36.7808i		−	0.240397i
$154$	153.234	+	53.0704i	0.995024	+	0.344613i
$155$	38.3778			0.247599
$156$			43.2001i			0.276924i
$157$	65.4047			0.416590			0.208295	−	0.978066i	$-0.433209\pi$
$157$	65.4047			0.416590			0.208295	+	0.978066i	$0.433209\pi$
$158$	329.957			2.08833
$159$	−122.013			−0.767377
$160$		−	49.0699i		−	0.306687i
$161$		−	57.9767i		−	0.360104i
$162$			20.9793i			0.129502i
$163$	−318.348			−1.95305			−0.976527	−	0.215395i	$-0.930896\pi$
$163$	−318.348			−1.95305			−0.976527	+	0.215395i	$0.930896\pi$
$164$		−	19.3618i		−	0.118060i
$165$	40.2568	+	13.9424i	0.243981	+	0.0844994i
$166$	321.225			1.93509
$167$			17.2478i			0.103280i	0.998666	+	0.0516400i	$0.0164448\pi$
$167$			17.2478i			0.103280i	−0.998666	+	0.0516400i	$0.983555\pi$
$168$	65.5280			0.390047
$169$	−133.639			−0.790766
$170$	63.9048			0.375910
$171$			31.8206i			0.186085i
$172$		−	51.6161i		−	0.300094i
$173$		−	322.103i		−	1.86187i	−0.365190	−	0.930933i	$-0.618996\pi$
$173$		−	322.103i		−	1.86187i	0.365190	−	0.930933i	$-0.381004\pi$
$174$	2.39141			0.0137437
$175$			31.6215i			0.180694i
$176$	204.552	+	70.8438i	1.16223	+	0.402522i
$177$	−25.8905			−0.146274
$178$			373.788i			2.09993i
$179$	45.5484			0.254460			0.127230	−	0.991873i	$-0.459391\pi$
$179$	45.5484			0.254460			0.127230	+	0.991873i	$0.459391\pi$
$180$	−9.61763			−0.0534313
$181$	134.271			0.741830			0.370915	−	0.928667i	$-0.379044\pi$
$181$	134.271			0.741830			0.370915	+	0.928667i	$0.379044\pi$
$182$		−	256.462i		−	1.40913i
$183$			62.5965i			0.342058i
$184$		−	54.8397i		−	0.298042i
$185$	123.657			0.668418
$186$		−	69.2954i		−	0.372556i
$187$	−44.1359	+	127.436i	−0.236021	+	0.681478i
$188$	27.6034			0.146827
$189$		−	32.8620i		−	0.173873i
$190$	−55.2867			−0.290982
$191$	−68.0366			−0.356212			−0.178106	−	0.984011i	$-0.556997\pi$
$191$	−68.0366			−0.356212			−0.178106	+	0.984011i	$0.556997\pi$
$192$	47.7412			0.248652
$193$			127.465i			0.660443i	0.943904	+	0.330221i	$0.107123\pi$
$193$			127.465i			0.660443i	−0.943904	+	0.330221i	$0.892877\pi$
$194$		−	134.556i		−	0.693590i
$195$		−	67.3765i		−	0.345520i
$196$	−12.9081			−0.0658575
$197$			148.516i			0.753888i	0.926236	+	0.376944i	$0.123025\pi$
$197$			148.516i			0.753888i	−0.926236	+	0.376944i	$0.876975\pi$
$198$	25.1745	−	72.6881i	0.127144	−	0.367111i
$199$	63.0543			0.316856			0.158428	−	0.987371i	$-0.449357\pi$
$199$	63.0543			0.316856			0.158428	+	0.987371i	$0.449357\pi$
$200$			29.9105i			0.149553i
$201$	−221.429			−1.10164
$202$	342.789			1.69697
$203$	−3.74591			−0.0184527
$204$		−	30.4454i		−	0.149242i
$205$			30.1973i			0.147304i
$206$		−	230.258i		−	1.11776i
$207$	−27.5019			−0.132859
$208$		−	342.352i		−	1.64592i
$209$	38.1838	−	110.250i	0.182698	−	0.527514i
$210$	57.0961			0.271886
$211$		−	228.972i		−	1.08517i	−0.840000	−	0.542587i	$-0.817445\pi$
$211$		−	228.972i		−	1.08517i	0.840000	−	0.542587i	$-0.182555\pi$
$212$	−100.997			−0.476400
$213$	48.2272			0.226419
$214$	−251.642			−1.17590
$215$			80.5023i			0.374429i
$216$		−	31.0839i		−	0.143907i
$217$			108.544i			0.500205i
$218$	77.1561			0.353927
$219$		−	106.286i		−	0.485325i
$220$	33.3227	+	11.5409i	0.151467	+	0.0524585i
$221$	213.286			0.965096
$222$		−	223.277i		−	1.00575i
$223$	−101.764			−0.456339			−0.228169	−	0.973621i	$-0.573274\pi$
$223$	−101.764			−0.456339			−0.228169	+	0.973621i	$0.573274\pi$
$224$	138.785			0.619576
$225$	15.0000			0.0666667
$226$		−	380.650i		−	1.68429i
$227$		−	351.517i		−	1.54853i	−0.632861	−	0.774266i	$-0.718119\pi$
$227$		−	351.517i		−	1.54853i	0.632861	−	0.774266i	$-0.281881\pi$
$228$			26.3396i			0.115525i
$229$	141.322			0.617125			0.308563	−	0.951204i	$-0.400152\pi$
$229$	141.322			0.617125			0.308563	+	0.951204i	$0.400152\pi$
$230$		−	47.7831i		−	0.207753i
$231$	−39.4335	+	113.859i	−0.170708	+	0.492895i
$232$	−3.54322			−0.0152725
$233$			370.243i			1.58903i	0.607246	+	0.794514i	$0.292274\pi$
$233$			370.243i			1.58903i	−0.607246	+	0.794514i	$0.707726\pi$
$234$	−121.656			−0.519896
$235$	−43.0513			−0.183197
$236$	−21.4310			−0.0908093
$237$			245.171i			1.03448i
$238$			180.743i			0.759423i
$239$			68.3043i			0.285792i	0.989738	+	0.142896i	$0.0456414\pi$
$239$			68.3043i			0.285792i	−0.989738	+	0.142896i	$0.954359\pi$
$240$	76.2177			0.317574
$241$		−	200.283i		−	0.831052i	−0.909581	−	0.415526i	$-0.863598\pi$
$241$		−	200.283i		−	0.831052i	0.909581	−	0.415526i	$-0.136402\pi$
$242$	−174.447	+	221.637i	−0.720856	+	0.915857i
$243$	−15.5885			−0.0641500
$244$			51.8145i			0.212355i
$245$	20.1319			0.0821709
$246$	54.5246			0.221645
$247$	−184.523			−0.747055
$248$			102.671i			0.413997i
$249$			238.683i			0.958565i
$250$			26.0617i			0.104247i
$251$	213.104			0.849019			0.424510	−	0.905423i	$-0.360447\pi$
$251$	213.104			0.849019			0.424510	+	0.905423i	$0.360447\pi$
$252$		−	27.2017i		−	0.107943i
$253$	95.2872	+	33.0015i	0.376629	+	0.130441i
$254$	−476.027			−1.87412
$255$			47.4838i			0.186211i
$256$	244.133			0.953646
$257$	−30.3594			−0.118130			−0.0590650	−	0.998254i	$-0.518812\pi$
$257$	−30.3594			−0.118130			−0.0590650	+	0.998254i	$0.518812\pi$
$258$	145.356			0.563394
$259$			349.741i			1.35035i
$260$		−	55.7712i		−	0.214504i
$261$			1.77691i			0.00680809i
$262$	−567.311			−2.16531
$263$			359.742i			1.36784i	0.729557	+	0.683920i	$0.239726\pi$
$263$			359.742i			1.36784i	−0.729557	+	0.683920i	$0.760274\pi$
$264$	−37.2998	+	107.698i	−0.141287	+	0.407947i
$265$	157.518			0.594408
$266$		−	156.368i		−	0.587849i
$267$	−277.739			−1.04022
$268$	−183.289			−0.683914
$269$	−320.990			−1.19327			−0.596637	−	0.802512i	$-0.703497\pi$
$269$	−320.990			−1.19327			−0.596637	+	0.802512i	$0.703497\pi$
$270$		−	27.0841i		−	0.100312i
$271$		−	419.497i		−	1.54796i	−0.633211	−	0.773979i	$-0.718264\pi$
$271$		−	419.497i		−	1.54796i	0.633211	−	0.773979i	$-0.281736\pi$
$272$			241.274i			0.887036i
$273$	190.562			0.698028
$274$			159.245i			0.581187i
$275$	−51.9713	−	17.9996i	−0.188987	−	0.0654530i
$276$	−22.7648			−0.0824811
$277$		−	86.8213i		−	0.313434i	−0.987644	−	0.156717i	$-0.949909\pi$
$277$		−	86.8213i		−	0.313434i	0.987644	−	0.156717i	$-0.0500911\pi$
$278$	−50.1574			−0.180422
$279$	51.4892			0.184549
$280$	−84.5962			−0.302129
$281$			300.755i			1.07030i	0.844756	+	0.535152i	$0.179745\pi$
$281$			300.755i			1.07030i	−0.844756	+	0.535152i	$0.820255\pi$
$282$			77.7339i			0.275652i
$283$		−	319.781i		−	1.12997i	−0.825102	−	0.564984i	$-0.808882\pi$
$283$		−	319.781i		−	1.12997i	0.825102	−	0.564984i	$-0.191118\pi$
$284$	39.9202			0.140564
$285$		−	41.0802i		−	0.144141i
$286$	421.507	+	145.983i	1.47380	+	0.510431i
$287$	−85.4074			−0.297587
$288$		−	65.8342i		−	0.228591i
$289$	138.686			0.479882
$290$	−3.08729			−0.0106458
$291$	99.9808			0.343577
$292$		−	87.9788i		−	0.301297i
$293$			421.749i			1.43942i	0.694276	+	0.719709i	$0.255725\pi$
$293$			421.749i			1.43942i	−0.694276	+	0.719709i	$0.744275\pi$
$294$		−	36.3503i		−	0.123641i
$295$	33.4245			0.113304
$296$			330.817i			1.11763i
$297$	54.0102	+	18.7057i	0.181852	+	0.0629821i
$298$	107.099			0.359393
$299$		−	159.479i		−	0.533375i
$300$	12.4163			0.0413877
$301$	−227.686			−0.756431
$302$	−288.074			−0.953887
$303$			254.706i			0.840614i
$304$		−	208.736i		−	0.686631i
$305$		−	80.8118i		−	0.264957i
$306$	85.7372			0.280187
$307$		−	65.1772i		−	0.212303i	−0.994350	−	0.106152i	$-0.966147\pi$
$307$		−	65.1772i		−	0.212303i	0.994350	−	0.106152i	$-0.0338529\pi$
$308$	−32.6412	+	94.2470i	−0.105978	+	0.305997i
$309$	171.091			0.553691
$310$			89.4599i			0.288580i
$311$	−296.311			−0.952768			−0.476384	−	0.879237i	$-0.658053\pi$
$311$	−296.311			−0.952768			−0.476384	+	0.879237i	$0.658053\pi$
$312$	180.251			0.577727
$313$	−430.760			−1.37623			−0.688115	−	0.725601i	$-0.741562\pi$
$313$	−430.760			−1.37623			−0.688115	+	0.725601i	$0.741562\pi$
$314$			152.460i			0.485543i
$315$			42.4247i			0.134682i
$316$			202.941i			0.642219i
$317$	−248.606			−0.784246			−0.392123	−	0.919913i	$-0.628259\pi$
$317$	−248.606			−0.784246			−0.392123	+	0.919913i	$0.628259\pi$
$318$		−	284.416i		−	0.894391i
$319$	2.13224	−	6.15656i	0.00668414	−	0.0192996i
$320$	−61.6337			−0.192605
$321$		−	186.980i		−	0.582492i
$322$	135.146			0.419707
$323$	130.043			0.402610
$324$	−12.9034			−0.0398253
$325$			86.9827i			0.267639i
$326$		−	742.079i		−	2.27632i
$327$			57.3301i			0.175321i
$328$	−80.7862			−0.246299
$329$		−	121.763i		−	0.370099i
$330$	−32.5002	+	93.8399i	−0.0984854	+	0.284363i
$331$	−379.595			−1.14681			−0.573406	−	0.819271i	$-0.694378\pi$
$331$	−379.595			−1.14681			−0.573406	+	0.819271i	$0.694378\pi$
$332$			197.571i			0.595092i
$333$	165.904			0.498209
$334$	−40.2051			−0.120375
$335$	285.864			0.853325
$336$			215.567i			0.641570i
$337$		−	528.010i		−	1.56680i	−0.621521	−	0.783398i	$-0.713485\pi$
$337$		−	528.010i		−	1.56680i	0.621521	−	0.783398i	$-0.286515\pi$
$338$		−	311.518i		−	0.921651i
$339$	282.838			0.834332
$340$			39.3049i			0.115603i
$341$	−178.398	−	61.7856i	−0.523160	−	0.181189i
$342$	−74.1748			−0.216885
$343$			366.830i			1.06947i
$344$	−215.366			−0.626064
$345$	35.5048			0.102912
$346$	750.832			2.17004
$347$			35.7638i			0.103066i	0.998671	+	0.0515328i	$0.0164107\pi$
$347$			35.7638i			0.103066i	−0.998671	+	0.0515328i	$0.983589\pi$
$348$			1.47084i			0.00422657i
$349$		−	453.183i		−	1.29852i	−0.760568	−	0.649259i	$-0.775079\pi$
$349$		−	453.183i		−	1.29852i	0.760568	−	0.649259i	$-0.224921\pi$
$350$	−73.7107			−0.210602
$351$		−	90.3951i		−	0.257536i
$352$	−78.9991	+	228.099i	−0.224429	+	0.648009i
$353$	−76.8798			−0.217790			−0.108895	−	0.994053i	$-0.534731\pi$
$353$	−76.8798			−0.217790			−0.108895	+	0.994053i	$0.534731\pi$
$354$		−	60.3517i		−	0.170485i
$355$	−62.2610			−0.175383
$356$	−229.900			−0.645786
$357$	−134.299			−0.376188
$358$			106.175i			0.296577i
$359$		−	406.327i		−	1.13183i	−0.824463	−	0.565915i	$-0.808523\pi$
$359$		−	406.327i		−	1.13183i	0.824463	−	0.565915i	$-0.191477\pi$
$360$			40.1292i			0.111470i
$361$	248.494			0.688350
$362$			312.991i			0.864615i
$363$	−164.686	−	129.621i	−0.453679	−	0.357083i
$364$	157.738			0.433347
$365$			137.215i			0.375931i
$366$	−145.915			−0.398674
$367$	−287.030			−0.782098			−0.391049	−	0.920370i	$-0.627888\pi$
$367$	−287.030			−0.782098			−0.391049	+	0.920370i	$0.627888\pi$
$368$	180.406			0.490234
$369$			40.5139i			0.109794i
$370$			288.249i			0.779051i
$371$			445.510i			1.20084i
$372$	42.6204			0.114571
$373$		−	359.705i		−	0.964356i	−0.876073	−	0.482178i	$-0.839846\pi$
$373$		−	359.705i		−	0.964356i	0.876073	−	0.482178i	$-0.160154\pi$
$374$	−297.058	−	102.882i	−0.794274	−	0.275086i
$375$	−19.3649			−0.0516398
$376$		−	115.174i		−	0.306314i
$377$	−10.3040			−0.0273316
$378$	76.6024			0.202652
$379$	94.3980			0.249071			0.124536	−	0.992215i	$-0.460256\pi$
$379$	94.3980			0.249071			0.124536	+	0.992215i	$0.460256\pi$
$380$		−	34.0043i		−	0.0894850i
$381$		−	353.707i		−	0.928366i
$382$		−	158.595i		−	0.415171i
$383$	−92.3643			−0.241160			−0.120580	−	0.992704i	$-0.538475\pi$
$383$	−92.3643			−0.241160			−0.120580	+	0.992704i	$0.538475\pi$
$384$			263.324i			0.685739i
$385$	50.9084	−	146.991i	0.132230	−	0.381795i
$386$	−297.126			−0.769757
$387$			108.005i			0.279083i
$388$	82.7595			0.213298
$389$	126.237			0.324517			0.162259	−	0.986748i	$-0.448122\pi$
$389$	126.237			0.324517			0.162259	+	0.986748i	$0.448122\pi$
$390$	157.057			0.402710
$391$			112.393i			0.287451i
$392$			53.8583i			0.137394i
$393$		−	421.535i		−	1.07261i
$394$	−346.195			−0.878668
$395$		−	316.515i		−	0.801303i
$396$	44.7071	+	15.4837i	0.112897	+	0.0391003i
$397$	732.111			1.84411			0.922054	−	0.387060i	$-0.126509\pi$
$397$	732.111			1.84411			0.922054	+	0.387060i	$0.126509\pi$
$398$			146.982i			0.369300i
$399$	116.188			0.291197
$400$	−98.3966			−0.245991
$401$	288.306			0.718966			0.359483	−	0.933152i	$-0.382953\pi$
$401$	288.306			0.718966			0.359483	+	0.933152i	$0.382953\pi$
$402$		−	516.158i		−	1.28398i
$403$			298.578i			0.740889i
$404$			210.834i			0.521866i
$405$	20.1246			0.0496904
$406$		−	8.73183i		−	0.0215070i
$407$	−574.815	−	199.080i	−1.41232	−	0.489139i
$408$	−127.032			−0.311354
$409$		−	536.385i		−	1.31146i	−0.754997	−	0.655728i	$-0.772362\pi$
$409$		−	536.385i		−	1.31146i	0.754997	−	0.655728i	$-0.227638\pi$
$410$	−70.3909			−0.171685
$411$	−118.326			−0.287897
$412$	141.621			0.343740
$413$			94.5350i			0.228898i
$414$		−	64.1078i		−	0.154850i
$415$		−	308.138i		−	0.742501i
$416$	381.762			0.917697
$417$		−	37.2689i		−	0.0893739i
$418$	256.997	+	89.0076i	0.614826	+	0.212937i
$419$	772.235			1.84304			0.921521	−	0.388328i	$-0.126947\pi$
$419$	772.235			1.84304			0.921521	+	0.388328i	$0.126947\pi$
$420$			35.1172i			0.0836124i
$421$	530.329			1.25969			0.629844	−	0.776721i	$-0.283119\pi$
$421$	530.329			1.25969			0.629844	+	0.776721i	$0.283119\pi$
$422$	533.740			1.26479
$423$	−57.7594			−0.136547
$424$			421.405i			0.993879i
$425$		−	61.3013i		−	0.144238i
$426$			112.419i			0.263895i
$427$	228.561			0.535272
$428$		−	154.773i		−	0.361620i
$429$	−108.471	+	313.197i	−0.252847	+	0.730062i
$430$	−187.653			−0.436403
$431$			98.0885i			0.227584i	0.993505	+	0.113792i	$0.0362997\pi$
$431$			98.0885i			0.227584i	−0.993505	+	0.113792i	$0.963700\pi$
$432$	102.257			0.236705
$433$	−467.819			−1.08041			−0.540206	−	0.841533i	$-0.681654\pi$
$433$	−467.819			−1.08041			−0.540206	+	0.841533i	$0.681654\pi$
$434$	−253.021			−0.582997
$435$		−	2.29398i		−	0.00527352i
$436$			47.4552i			0.108842i
$437$		−	97.2362i		−	0.222509i
$438$	247.756			0.565654
$439$			732.331i			1.66818i	0.551628	+	0.834090i	$0.314007\pi$
$439$			732.331i			1.66818i	−0.551628	+	0.834090i	$0.685993\pi$
$440$	48.1538	−	139.038i	0.109440	−	0.315995i
$441$	27.0097			0.0612466
$442$			497.177i			1.12483i
$443$	522.885			1.18033			0.590164	−	0.807284i	$-0.299063\pi$
$443$	522.885			1.18033			0.590164	+	0.807284i	$0.299063\pi$
$444$	137.327			0.309296
$445$	358.560			0.805752
$446$		−	237.214i		−	0.531870i
$447$			79.5790i			0.178029i
$448$		−	174.319i		−	0.389105i
$449$	119.788			0.266788			0.133394	−	0.991063i	$-0.457412\pi$
$449$	119.788			0.266788			0.133394	+	0.991063i	$0.457412\pi$
$450$			34.9655i			0.0777011i
$451$	48.6156	−	140.371i	0.107795	−	0.311243i
$452$	234.121			0.517966
$453$		−	214.051i		−	0.472518i
$454$	819.397			1.80484
$455$	−246.014			−0.540691
$456$	109.901			0.241011
$457$		−	4.81549i		−	0.0105372i	−0.999986	−	0.00526859i	$-0.998323\pi$
$457$		−	4.81549i		−	0.0105372i	0.999986	−	0.00526859i	$-0.00167705\pi$
$458$			329.425i			0.719269i
$459$			63.7062i			0.138793i
$460$	29.3892			0.0638896
$461$			570.680i			1.23792i	0.785424	+	0.618958i	$0.212445\pi$
$461$			570.680i			1.23792i	−0.785424	+	0.618958i	$0.787555\pi$
$462$	−265.409	−	91.9207i	−0.574477	−	0.198963i
$463$	131.935			0.284956			0.142478	−	0.989798i	$-0.454493\pi$
$463$	131.935			0.284956			0.142478	+	0.989798i	$0.454493\pi$
$464$		−	11.6561i		−	0.0251210i
$465$	−66.4723			−0.142951
$466$	−863.050			−1.85204
$467$	−89.8728			−0.192447			−0.0962235	−	0.995360i	$-0.530676\pi$
$467$	−89.8728			−0.192447			−0.0962235	+	0.995360i	$0.530676\pi$
$468$		−	74.8249i		−	0.159882i
$469$			808.512i			1.72391i
$470$		−	100.354i		−	0.213519i
$471$	−113.284			−0.240518
$472$			89.4199i			0.189449i
$473$	129.603	−	374.211i	0.274002	−	0.791144i
$474$	−571.502			−1.20570
$475$			53.0343i			0.111651i
$476$	−111.167			−0.233543
$477$	211.333			0.443045
$478$	−159.219			−0.333095
$479$		−	717.047i		−	1.49697i	−0.663153	−	0.748484i	$-0.730782\pi$
$479$		−	717.047i		−	1.49697i	0.663153	−	0.748484i	$-0.269218\pi$
$480$			84.9915i			0.177066i
$481$			962.049i			2.00010i
$482$	466.867			0.968604
$483$			100.419i			0.207906i
$484$	−136.319	−	107.294i	−0.281651	−	0.221683i
$485$	−129.075			−0.266133
$486$		−	36.3372i		−	0.0747679i
$487$	916.798			1.88254			0.941271	−	0.337653i	$-0.109633\pi$
$487$	916.798			1.88254			0.941271	+	0.337653i	$0.109633\pi$
$488$	216.194			0.443020
$489$	551.395			1.12760
$490$			46.9280i			0.0957715i
$491$			302.142i			0.615361i	0.951490	+	0.307680i	$0.0995527\pi$
$491$			302.142i			0.615361i	−0.951490	+	0.307680i	$0.900447\pi$
$492$			33.5356i			0.0681617i
$493$	7.26180			0.0147298
$494$		−	430.128i		−	0.870705i
$495$	−69.7268	−	24.1489i	−0.140862	−	0.0487858i
$496$	−337.758			−0.680963
$497$		−	176.094i		−	0.354313i
$498$	−556.377			−1.11722
$499$	−102.798			−0.206008			−0.103004	−	0.994681i	$-0.532846\pi$
$499$	−102.798			−0.206008			−0.103004	+	0.994681i	$0.532846\pi$
$500$	−16.0294			−0.0320588
$501$		−	29.8740i		−	0.0596287i
$502$			496.752i			0.989545i
$503$		−	567.728i		−	1.12868i	−0.825541	−	0.564342i	$-0.809130\pi$
$503$		−	567.728i		−	1.12868i	0.825541	−	0.564342i	$-0.190870\pi$
$504$	−113.498			−0.225194
$505$		−	328.824i		−	0.651137i
$506$	−76.9275	+	222.118i	−0.152031	+	0.438968i
$507$	231.470			0.456549
$508$		−	292.783i		−	0.576344i
$509$	−423.197			−0.831428			−0.415714	−	0.909495i	$-0.636468\pi$
$509$	−423.197			−0.831428			−0.415714	+	0.909495i	$0.636468\pi$
$510$	−110.686			−0.217032
$511$	−388.086			−0.759465
$512$		−	39.0375i		−	0.0762451i
$513$		−	55.1149i		−	0.107436i
$514$		−	70.7687i		−	0.137682i
$515$	−220.877			−0.428887
$516$			89.4017i			0.173259i
$517$	200.122	+	69.3096i	0.387083	+	0.134061i
$518$	−815.258			−1.57386
$519$			557.898i			1.07495i
$520$	−232.703			−0.447505
$521$	−658.340			−1.26361			−0.631805	−	0.775128i	$-0.717685\pi$
$521$	−658.340			−1.26361			−0.631805	+	0.775128i	$0.717685\pi$
$522$	−4.14204			−0.00793494
$523$		−	568.723i		−	1.08743i	−0.839272	−	0.543713i	$-0.817018\pi$
$523$		−	568.723i		−	1.08743i	0.839272	−	0.543713i	$-0.182982\pi$
$524$		−	348.927i		−	0.665892i
$525$		−	54.7700i		−	0.104324i
$526$	−838.570			−1.59424
$527$		−	210.424i		−	0.399286i
$528$	−354.294	−	122.705i	−0.671012	−	0.232396i
$529$	−444.961			−0.841136
$530$			367.180i			0.692792i
$531$	44.8437			0.0844515
$532$	96.1748			0.180780
$533$	−234.934			−0.440777
$534$		−	647.419i		−	1.21240i
$535$			241.390i			0.451197i
$536$			764.765i			1.42680i
$537$	−78.8921			−0.146913
$538$		−	748.239i		−	1.39078i
$539$	−93.5821	−	32.4109i	−0.173622	−	0.0601316i
$540$	16.6582			0.0308486
$541$		−	451.918i		−	0.835339i	−0.908599	−	0.417669i	$-0.862847\pi$
$541$		−	451.918i		−	0.835339i	0.908599	−	0.417669i	$-0.137153\pi$
$542$	977.860			1.80417
$543$	−232.565			−0.428296
$544$	−269.048			−0.494574
$545$		−	74.0128i		−	0.135803i
$546$			444.206i			0.813563i
$547$		−	149.931i		−	0.274097i	−0.990564	−	0.137048i	$-0.956238\pi$
$547$		−	149.931i		−	0.274097i	0.990564	−	0.137048i	$-0.0437615\pi$
$548$	−97.9446			−0.178731
$549$		−	108.420i		−	0.197487i
$550$	41.9576	−	121.147i	0.0762865	−	0.220267i
$551$	−6.28248			−0.0114020
$552$			94.9851i			0.172074i
$553$	895.202			1.61881
$554$	202.383			0.365313
$555$	−214.181			−0.385911
$556$		−	30.8495i		−	0.0554847i
$557$			14.5869i			0.0261883i	0.999914	+	0.0130941i	$0.00416812\pi$
$557$			14.5869i			0.0261883i	−0.999914	+	0.0130941i	$0.995832\pi$
$558$			120.023i			0.215095i
$559$	−626.305			−1.12040
$560$		−	278.296i		−	0.496958i
$561$	76.4456	−	220.726i	0.136267	−	0.393451i
$562$	−701.070			−1.24746
$563$			123.461i			0.219291i	0.993971	+	0.109645i	$0.0349715\pi$
$563$			123.461i			0.219291i	−0.993971	+	0.109645i	$0.965028\pi$
$564$	−47.8106			−0.0847705
$565$	−365.143			−0.646270
$566$	745.420			1.31700
$567$			56.9187i			0.100386i
$568$		−	166.565i		−	0.293249i
$569$			849.647i			1.49323i	0.665257	+	0.746614i	$0.268322\pi$
$569$			849.647i			1.49323i	−0.665257	+	0.746614i	$0.731678\pi$
$570$	95.7593			0.167999
$571$			607.460i			1.06385i	0.846791	+	0.531926i	$0.178532\pi$
$571$			607.460i			1.06385i	−0.846791	+	0.531926i	$0.821468\pi$
$572$	−89.7876	+	259.250i	−0.156971	+	0.453234i
$573$	117.843			0.205659
$574$		−	199.087i		−	0.346842i
$575$	−45.8365			−0.0797156
$576$	−82.6902			−0.143559
$577$	−345.393			−0.598602			−0.299301	−	0.954159i	$-0.596754\pi$
$577$	−345.393			−0.598602			−0.299301	+	0.954159i	$0.596754\pi$
$578$			323.281i			0.559310i
$579$		−	220.777i		−	0.381307i
$580$		−	1.89885i		−	0.00327388i
$581$	871.511			1.50002
$582$			233.059i			0.400444i
$583$	−732.216	−	253.593i	−1.25594	−	0.434980i
$584$	−367.088			−0.628575
$585$			116.700i			0.199486i
$586$	−983.111			−1.67766
$587$	800.135			1.36309			0.681546	−	0.731775i	$-0.261308\pi$
$587$	800.135			1.36309			0.681546	+	0.731775i	$0.261308\pi$
$588$	22.3574			0.0380228
$589$			182.046i			0.309077i
$590$			77.9137i			0.132057i
$591$		−	257.237i		−	0.435257i
$592$	−1088.29			−1.83833
$593$		−	157.850i		−	0.266189i	−0.991103	−	0.133094i	$-0.957509\pi$
$593$		−	157.850i		−	0.266189i	0.991103	−	0.133094i	$-0.0424913\pi$
$594$	−43.6036	+	125.899i	−0.0734067	+	0.211952i
$595$	173.379			0.291394
$596$			65.8718i			0.110523i
$597$	−109.213			−0.182937
$598$	371.751			0.621657
$599$	623.613			1.04109			0.520545	−	0.853834i	$-0.325729\pi$
$599$	623.613			1.04109			0.520545	+	0.853834i	$0.325729\pi$
$600$		−	51.8065i		−	0.0863442i
$601$		−	140.001i		−	0.232947i	−0.993194	−	0.116474i	$-0.962841\pi$
$601$		−	140.001i		−	0.232947i	0.993194	−	0.116474i	$-0.0371591\pi$
$602$		−	530.743i		−	0.881632i
$603$	383.527			0.636031
$604$		−	177.181i		−	0.293346i
$605$	212.608	+	167.340i	0.351418	+	0.276596i
$606$	−593.728			−0.979749
$607$		−	758.571i		−	1.24971i	−0.780743	−	0.624853i	$-0.785159\pi$
$607$		−	758.571i		−	1.24971i	0.780743	−	0.624853i	$-0.214841\pi$
$608$	232.765			0.382837
$609$	6.48810			0.0106537
$610$	188.375			0.308811
$611$		−	334.938i		−	0.548180i
$612$			52.7331i			0.0861651i
$613$			487.490i			0.795253i	0.917547	+	0.397627i	$0.130166\pi$
$613$			487.490i			0.795253i	−0.917547	+	0.397627i	$0.869834\pi$
$614$	151.930			0.247443
$615$		−	52.3033i		−	0.0850460i
$616$	393.242	+	136.194i	0.638380	+	0.221094i
$617$	−773.785			−1.25411			−0.627054	−	0.778975i	$-0.715740\pi$
$617$	−773.785			−1.25411			−0.627054	+	0.778975i	$0.715740\pi$
$618$			398.818i			0.645336i
$619$	1182.12			1.90972			0.954859	−	0.297059i	$-0.0960058\pi$
$619$	1182.12			1.90972			0.954859	+	0.297059i	$0.0960058\pi$
$620$	−55.0227			−0.0887463
$621$	47.6347			0.0767064
$622$		−	690.710i		−	1.11047i
$623$			1014.12i			1.62780i
$624$			592.971i			0.950274i
$625$	25.0000			0.0400000
$626$		−	1004.12i		−	1.60402i
$627$	−66.1363	+	190.959i	−0.105480	+	0.304561i
$628$	−93.7714			−0.149318
$629$		−	678.007i		−	1.07791i
$630$	−98.8933			−0.156974
$631$	−1089.91			−1.72727			−0.863634	−	0.504120i	$-0.831817\pi$
$631$	−1089.91			−1.72727			−0.863634	+	0.504120i	$0.831817\pi$
$632$	846.764			1.33982
$633$			396.590i			0.626525i
$634$		−	579.509i		−	0.914051i
$635$			456.634i			0.719109i
$636$	174.931			0.275049
$637$			156.625i			0.245880i
$638$	14.3511	+	4.97032i	0.0224939	+	0.00779048i
$639$	−83.5319			−0.130723
$640$		−	339.950i		−	0.531171i
$641$	−661.586			−1.03212			−0.516058	−	0.856554i	$-0.672601\pi$
$641$	−661.586			−1.03212			−0.516058	+	0.856554i	$0.672601\pi$
$642$	435.856			0.678904
$643$	700.467			1.08937			0.544687	−	0.838639i	$-0.316648\pi$
$643$	700.467			1.08937			0.544687	+	0.838639i	$0.316648\pi$
$644$			83.1219i			0.129071i
$645$		−	139.434i		−	0.216177i
$646$			303.134i			0.469248i
$647$	128.968			0.199332			0.0996658	−	0.995021i	$-0.468223\pi$
$647$	128.968			0.199332			0.0996658	+	0.995021i	$0.468223\pi$
$648$			53.8389i			0.0830847i
$649$	−155.372	−	53.8112i	−0.239403	−	0.0829140i
$650$	−202.759			−0.311938
$651$		−	188.005i		−	0.288793i
$652$	456.419			0.700029
$653$	−828.659			−1.26900			−0.634502	−	0.772921i	$-0.718795\pi$
$653$	−828.659			−1.26900			−0.634502	+	0.772921i	$0.718795\pi$
$654$	−133.638			−0.204340
$655$			544.199i			0.830839i
$656$		−	265.762i		−	0.405125i
$657$			184.093i			0.280202i
$658$	283.832			0.431356
$659$			216.327i			0.328265i	0.986438	+	0.164133i	$0.0524825\pi$
$659$			216.327i			0.328265i	−0.986438	+	0.164133i	$0.947517\pi$
$660$	−57.7166	−	19.9894i	−0.0874494	−	0.0302869i
$661$	114.149			0.172691			0.0863457	−	0.996265i	$-0.472481\pi$
$661$	114.149			0.172691			0.0863457	+	0.996265i	$0.472481\pi$
$662$		−	884.848i		−	1.33663i
$663$	−369.422			−0.557198
$664$	824.355			1.24150
$665$	−149.998			−0.225560
$666$			386.727i			0.580671i
$667$		−	5.42982i		−	0.00814066i
$668$		−	24.7283i		−	0.0370184i
$669$	176.260			0.263467
$670$			666.358i			0.994564i
$671$	−130.101	+	375.650i	−0.193892	+	0.559836i
$672$	−240.383			−0.357712
$673$			1173.35i			1.74346i	0.489989	+	0.871729i	$0.337001\pi$
$673$			1173.35i			1.74346i	−0.489989	+	0.871729i	$0.662999\pi$
$674$	1230.81			1.82613
$675$	−25.9808			−0.0384900
$676$	191.600			0.283433
$677$			145.079i			0.214297i	0.994243	+	0.107148i	$0.0341720\pi$
$677$			145.079i			0.214297i	−0.994243	+	0.107148i	$0.965828\pi$
$678$			659.305i			0.972427i
$679$		−	365.064i		−	0.537649i
$680$	163.998			0.241174
$681$			608.845i			0.894045i
$682$	144.024	−	415.850i	0.211179	−	0.609751i
$683$	542.580			0.794407			0.397204	−	0.917731i	$-0.369981\pi$
$683$	542.580			0.794407			0.397204	+	0.917731i	$0.369981\pi$
$684$		−	45.6216i		−	0.0666982i
$685$	152.758			0.223004
$686$	−855.092			−1.24649
$687$	−244.776			−0.356297
$688$		−	708.489i		−	1.02978i
$689$			1225.49i			1.77864i
$690$			82.7628i			0.119946i
$691$	−190.564			−0.275780			−0.137890	−	0.990448i	$-0.544032\pi$
$691$	−190.564			−0.275780			−0.137890	+	0.990448i	$0.544032\pi$
$692$			461.803i			0.667345i
$693$	68.3008	−	197.209i	0.0985581	−	0.284573i
$694$	−83.3665			−0.120125
$695$			48.1140i			0.0692288i
$696$	6.13704			0.00881758
$697$	165.571			0.237547
$698$	1056.38			1.51344
$699$		−	641.281i		−	0.917426i
$700$		−	45.3361i		−	0.0647659i
$701$		−	149.736i		−	0.213603i	−0.994280	−	0.106801i	$-0.965939\pi$
$701$		−	149.736i		−	0.213603i	0.994280	−	0.106801i	$-0.0340609\pi$
$702$	210.714			0.300162
$703$			586.572i			0.834385i
$704$	286.501	+	99.2259i	0.406962	+	0.140946i
$705$	74.5671			0.105769
$706$		−	179.209i		−	0.253838i
$707$	930.017			1.31544
$708$	37.1196			0.0524288
$709$	−225.902			−0.318621			−0.159310	−	0.987229i	$-0.550927\pi$
$709$	−225.902			−0.318621			−0.159310	+	0.987229i	$0.550927\pi$
$710$		−	145.132i		−	0.204412i
$711$		−	424.649i		−	0.597256i
$712$			959.247i			1.34726i
$713$	−157.339			−0.220672
$714$		−	313.055i		−	0.438453i
$715$	140.036	−	404.335i	0.195855	−	0.565503i
$716$	−65.3032			−0.0912056
$717$		−	118.306i		−	0.165002i
$718$	947.162			1.31917
$719$	508.963			0.707877			0.353938	−	0.935269i	$-0.384842\pi$
$719$	508.963			0.707877			0.353938	+	0.935269i	$0.384842\pi$
$720$	−132.013			−0.183351
$721$		−	624.709i		−	0.866448i
$722$			579.249i			0.802283i
$723$			346.901i			0.479808i
$724$	−192.506			−0.265893
$725$			2.96152i			0.00408485i
$726$	302.151	−	383.887i	0.416186	−	0.528770i
$727$	−155.888			−0.214426			−0.107213	−	0.994236i	$-0.534193\pi$
$727$	−155.888			−0.214426			−0.107213	+	0.994236i	$0.534193\pi$
$728$		−	658.156i		−	0.904061i
$729$	27.0000			0.0370370
$730$	−319.852			−0.438154
$731$	441.391			0.603818
$732$		−	89.7454i		−	0.122603i
$733$		−	393.332i		−	0.536605i	−0.963335	−	0.268303i	$-0.913537\pi$
$733$		−	393.332i		−	0.536605i	0.963335	−	0.268303i	$-0.0864627\pi$
$734$		−	669.076i		−	0.911548i
$735$	−34.8694			−0.0474414
$736$			201.174i			0.273334i
$737$	−1328.82	−	460.221i	−1.80302	−	0.624451i
$738$	−94.4393			−0.127967
$739$		−	224.197i		−	0.303379i	−0.988428	−	0.151689i	$-0.951529\pi$
$739$		−	224.197i		−	0.303379i	0.988428	−	0.151689i	$-0.0484713\pi$
$740$	−177.289			−0.239580
$741$	319.603			0.431313
$742$	−1038.50			−1.39959
$743$			115.127i			0.154948i	0.996994	+	0.0774741i	$0.0246855\pi$
$743$			115.127i			0.154948i	−0.996994	+	0.0774741i	$0.975314\pi$
$744$		−	177.832i		−	0.239021i
$745$		−	102.736i		−	0.137901i
$746$	838.484			1.12397
$747$		−	413.411i		−	0.553428i
$748$	63.2781	−	182.707i	0.0845964	−	0.244261i
$749$	−682.727			−0.911518
$750$		−	45.1402i		−	0.0601870i
$751$	−494.453			−0.658392			−0.329196	−	0.944262i	$-0.606778\pi$
$751$	−494.453			−0.658392			−0.329196	+	0.944262i	$0.606778\pi$
$752$	378.888			0.503841
$753$	−369.107			−0.490181
$754$		−	24.0190i		−	0.0318555i
$755$			276.338i			0.366011i
$756$			47.1147i			0.0623210i
$757$	531.890			0.702629			0.351314	−	0.936258i	$-0.385735\pi$
$757$	531.890			0.702629			0.351314	+	0.936258i	$0.385735\pi$
$758$			220.045i			0.290297i
$759$	−165.042	−	57.1602i	−0.217447	−	0.0753099i
$760$	−141.881			−0.186686
$761$		−	1343.41i		−	1.76532i	−0.470013	−	0.882660i	$-0.655751\pi$
$761$		−	1343.41i		−	1.76532i	0.470013	−	0.882660i	$-0.344249\pi$
$762$	824.503			1.08203
$763$	209.331			0.274353
$764$	97.5448			0.127676
$765$		−	82.2444i		−	0.107509i
$766$		−	215.304i		−	0.281076i
$767$			260.042i			0.339038i
$768$	−422.851			−0.550588
$769$			735.802i			0.956830i	0.878134	+	0.478415i	$0.158788\pi$
$769$			735.802i			0.956830i	−0.878134	+	0.478415i	$0.841212\pi$
$770$	342.641	+	118.669i	0.444988	+	0.154116i
$771$	52.5840			0.0682023
$772$		−	182.749i		−	0.236721i
$773$	−1135.40			−1.46882			−0.734410	−	0.678706i	$-0.762541\pi$
$773$	−1135.40			−1.46882			−0.734410	+	0.678706i	$0.762541\pi$
$774$	−251.764			−0.325276
$775$	85.8154			0.110730
$776$		−	345.311i		−	0.444988i
$777$		−	605.770i		−	0.779626i
$778$			294.263i			0.378230i
$779$	−143.242			−0.183879
$780$			96.5985i			0.123844i
$781$	289.417	+	100.236i	0.370573	+	0.128343i
$782$	−261.993			−0.335029
$783$		−	3.07770i		−	0.00393065i
$784$	−177.178			−0.225992
$785$	146.249			0.186305
$786$	982.612			1.25014
$787$		−	115.155i		−	0.146321i	−0.997320	−	0.0731605i	$-0.976691\pi$
$787$		−	115.155i		−	0.146321i	0.997320	−	0.0731605i	$-0.0233085\pi$
$788$		−	212.929i		−	0.270214i
$789$		−	623.091i		−	0.789723i
$790$	737.806			0.933931
$791$		−	1032.74i		−	1.30561i
$792$	64.6051	−	186.539i	0.0815721	−	0.235528i
$793$	628.713			0.792828
$794$			1706.57i			2.14934i
$795$	−272.829			−0.343182
$796$	−90.4017			−0.113570
$797$	−1486.27			−1.86483			−0.932416	−	0.361387i	$-0.882303\pi$
$797$	−1486.27			−1.86483			−0.932416	+	0.361387i	$0.882303\pi$
$798$			270.837i			0.339395i
$799$			236.049i			0.295430i
$800$		−	109.724i		−	0.137155i
$801$	481.058			0.600572
$802$			672.049i			0.837967i
$803$	220.906	−	637.837i	0.275101	−	0.794317i
$804$	317.466			0.394858
$805$		−	129.640i		−	0.161043i
$806$	−695.995			−0.863518
$807$	555.972			0.688937
$808$	879.695			1.08873
$809$		−	546.514i		−	0.675543i	−0.941228	−	0.337771i	$-0.890327\pi$
$809$		−	546.514i		−	0.675543i	0.941228	−	0.337771i	$-0.109673\pi$
$810$			46.9111i			0.0579150i
$811$		−	1066.45i		−	1.31499i	−0.753460	−	0.657494i	$-0.771617\pi$
$811$		−	1066.45i		−	1.31499i	0.753460	−	0.657494i	$-0.228383\pi$
$812$	5.37055			0.00661398
$813$			726.589i			0.893714i
$814$	464.061	−	1339.91i	0.570099	−	1.64608i
$815$	−711.847			−0.873432
$816$		−	417.898i		−	0.512130i
$817$	−381.865			−0.467399
$818$	1250.33			1.52852
$819$	−330.063			−0.403007
$820$		−	43.2942i		−	0.0527978i
$821$			1206.66i			1.46974i	0.678207	+	0.734871i	$0.262757\pi$
$821$			1206.66i			1.46974i	−0.678207	+	0.734871i	$0.737243\pi$
$822$		−	275.821i		−	0.335549i
$823$	312.518			0.379730			0.189865	−	0.981810i	$-0.439195\pi$
$823$	312.518			0.379730			0.189865	+	0.981810i	$0.439195\pi$
$824$		−	590.907i		−	0.717120i
$825$	90.0169	+	31.1762i	0.109111	+	0.0377893i
$826$	−220.364			−0.266785
$827$		−	1166.37i		−	1.41036i	−0.709029	−	0.705180i	$-0.750866\pi$
$827$		−	1166.37i		−	1.41036i	0.709029	−	0.705180i	$-0.249134\pi$
$828$	39.4298			0.0476205
$829$	−205.935			−0.248413			−0.124207	−	0.992256i	$-0.539639\pi$
$829$	−205.935			−0.248413			−0.124207	+	0.992256i	$0.539639\pi$
$830$	718.280			0.865397
$831$			150.379i			0.180961i
$832$		−	479.508i		−	0.576332i
$833$		−	110.382i		−	0.132512i
$834$	86.8751			0.104167
$835$			38.5672i			0.0461882i
$836$	−54.7445	+	158.067i	−0.0654839	+	0.189076i
$837$	−89.1820			−0.106550
$838$			1800.10i			2.14810i
$839$	−619.889			−0.738843			−0.369422	−	0.929262i	$-0.620444\pi$
$839$	−619.889			−0.738843			−0.369422	+	0.929262i	$0.620444\pi$
$840$	146.525			0.174435
$841$	840.649			0.999583
$842$			1236.21i			1.46819i
$843$		−	520.923i		−	0.617940i
$844$			328.279i			0.388956i
$845$	−298.827			−0.353641
$846$		−	134.639i		−	0.159148i
$847$	−473.291	+	601.322i	−0.558785	+	0.709944i
$848$	−1386.29			−1.63478
$849$			553.877i			0.652387i
$850$	142.895			0.168112
$851$	−506.962			−0.595725
$852$	−69.1439			−0.0811548
$853$		−	1067.19i		−	1.25110i	−0.780185	−	0.625549i	$-0.784875\pi$
$853$		−	1067.19i		−	1.25110i	0.780185	−	0.625549i	$-0.215125\pi$
$854$			532.783i			0.623868i
$855$			71.1530i			0.0832199i
$856$	−645.786			−0.754422
$857$		−	135.288i		−	0.157862i	−0.996880	−	0.0789310i	$-0.974849\pi$
$857$		−	135.288i		−	0.157862i	0.996880	−	0.0789310i	$-0.0251507\pi$
$858$	−730.071	−	252.850i	−0.850899	−	0.294697i
$859$	−88.1149			−0.102578			−0.0512892	−	0.998684i	$-0.516333\pi$
$859$	−88.1149			−0.102578			−0.0512892	+	0.998684i	$0.516333\pi$
$860$		−	115.417i		−	0.134206i
$861$	147.930			0.171812
$862$	−228.648			−0.265252
$863$	−1506.50			−1.74566			−0.872830	−	0.488024i	$-0.837718\pi$
$863$	−1506.50			−1.74566			−0.872830	+	0.488024i	$0.837718\pi$
$864$			114.028i			0.131977i
$865$		−	720.244i		−	0.832652i
$866$		−	1090.50i		−	1.25924i
$867$	−240.211			−0.277060
$868$		−	155.621i		−	0.179287i
$869$	−509.566	+	1471.30i	−0.586382	+	1.69310i
$870$	5.34735			0.00614638
$871$			2224.01i			2.55340i
$872$	198.005			0.227070
$873$	−173.172			−0.198364
$874$	226.661			0.259337
$875$			70.7078i			0.0808089i
$876$			152.384i			0.173954i
$877$			874.405i			0.997041i	0.866878	+	0.498521i	$0.166123\pi$
$877$			874.405i			0.997041i	−0.866878	+	0.498521i	$0.833877\pi$
$878$	−1707.09			−1.94429
$879$		−	730.491i		−	0.831048i
$880$	457.392	+	158.412i	0.519764	+	0.180013i
$881$	628.003			0.712830			0.356415	−	0.934328i	$-0.383999\pi$
$881$	628.003			0.712830			0.356415	+	0.934328i	$0.383999\pi$
$882$			62.9606i			0.0713839i
$883$	1234.85			1.39848			0.699238	−	0.714889i	$-0.253523\pi$
$883$	1234.85			1.39848			0.699238	+	0.714889i	$0.253523\pi$
$884$	−305.791			−0.345917
$885$	−57.8930			−0.0654158
$886$			1218.86i			1.37569i
$887$			282.840i			0.318872i	0.987208	+	0.159436i	$0.0509676\pi$
$887$			282.840i			0.318872i	−0.987208	+	0.159436i	$0.949032\pi$
$888$		−	572.992i		−	0.645262i
$889$	−1291.50			−1.45276
$890$			835.814i			0.939117i
$891$	−93.5483	−	32.3992i	−0.104993	−	0.0363628i
$892$	145.900			0.163565
$893$		−	204.215i		−	0.228685i
$894$	−185.501			−0.207496
$895$	101.849			0.113798
$896$	961.484			1.07308
$897$			276.226i			0.307944i
$898$			279.229i			0.310946i
$899$			10.1658i			0.0113078i
$900$	−21.5057			−0.0238952
$901$		−	863.665i		−	0.958563i
$902$	327.209	+	113.324i	0.362759	+	0.125637i
$903$	394.363			0.436725
$904$		−	976.858i		−	1.08060i
$905$	300.240			0.331757
$906$	498.959			0.550727
$907$	604.942			0.666970			0.333485	−	0.942755i	$-0.391775\pi$
$907$	604.942			0.666970			0.333485	+	0.942755i	$0.391775\pi$
$908$			503.974i			0.555037i
$909$		−	441.164i		−	0.485329i
$910$		−	573.467i		−	0.630184i
$911$	339.992			0.373208			0.186604	−	0.982435i	$-0.440252\pi$
$911$	339.992			0.373208			0.186604	+	0.982435i	$0.440252\pi$
$912$			361.541i			0.396427i
$913$	−496.081	+	1432.37i	−0.543352	+	1.56886i
$914$	11.2251			0.0122813
$915$			139.970i			0.152973i
$916$	−202.615			−0.221195
$917$	−1539.17			−1.67848
$918$	−148.501			−0.161766
$919$			885.348i			0.963382i	0.876341	+	0.481691i	$0.159977\pi$
$919$			885.348i			0.963382i	−0.876341	+	0.481691i	$0.840023\pi$
$920$		−	122.625i		−	0.133288i
$921$			112.890i			0.122573i
$922$	−1330.27			−1.44281
$923$		−	484.389i		−	0.524798i
$924$	56.5362	−	163.241i	0.0611864	−	0.176667i
$925$	276.506			0.298925
$926$			307.544i			0.332121i
$927$	−296.338			−0.319674
$928$	12.9979			0.0140064
$929$	−821.063			−0.883814			−0.441907	−	0.897061i	$-0.645698\pi$
$929$	−821.063			−0.883814			−0.441907	+	0.897061i	$0.645698\pi$
$930$		−	154.949i		−	0.166612i
$931$			95.4962i			0.102574i
$932$		−	530.822i		−	0.569552i
$933$	513.225			0.550081
$934$		−	209.496i		−	0.224300i
$935$	−98.6908	+	284.956i	−0.105552	+	0.304766i
$936$	−312.203			−0.333551
$937$			1507.89i			1.60927i	0.593768	+	0.804636i	$0.297639\pi$
$937$			1507.89i			1.60927i	−0.593768	+	0.804636i	$0.702361\pi$
$938$	−1884.67			−2.00924
$939$	746.099			0.794567
$940$	61.7232			0.0656629
$941$		−	138.310i		−	0.146982i	−0.997296	−	0.0734909i	$-0.976586\pi$
$941$		−	138.310i		−	0.146982i	0.997296	−	0.0734909i	$-0.0234140\pi$
$942$		−	264.069i		−	0.280328i
$943$		−	123.801i		−	0.131284i
$944$	−294.165			−0.311615
$945$		−	73.4817i		−	0.0777584i
$946$	872.298	+	302.109i	0.922091	+	0.319354i
$947$	1559.87			1.64717			0.823586	−	0.567192i	$-0.191970\pi$
$947$	1559.87			1.64717			0.823586	+	0.567192i	$0.191970\pi$
$948$		−	351.505i		−	0.370786i
$949$	−1067.53			−1.12490
$950$	−123.625			−0.130131
$951$	430.598			0.452785
$952$			463.838i			0.487224i
$953$		−	1073.64i		−	1.12659i	−0.826255	−	0.563296i	$-0.809533\pi$
$953$		−	1073.64i		−	1.12659i	0.826255	−	0.563296i	$-0.190467\pi$
$954$			492.623i			0.516377i
$955$	−152.134			−0.159303
$956$		−	97.9286i		−	0.102436i
$957$	−3.69315	+	10.6635i	−0.00385909	+	0.0111426i
$958$	1671.46			1.74474
$959$			432.047i			0.450518i
$960$	106.753			0.111201
$961$	−666.429			−0.693474
$962$	−2242.57			−2.33115
$963$			323.859i			0.336302i
$964$			287.149i			0.297872i
$965$			285.021i			0.295359i
$966$	−234.079			−0.242318
$967$		−	1403.40i		−	1.45130i	−0.688066	−	0.725648i	$-0.741540\pi$
$967$		−	1403.40i		−	1.45130i	0.688066	−	0.725648i	$-0.258460\pi$
$968$	−447.682	+	568.786i	−0.462481	+	0.587588i
$969$	−225.241			−0.232447
$970$		−	300.877i		−	0.310183i
$971$	724.260			0.745891			0.372945	−	0.927853i	$-0.378348\pi$
$971$	724.260			0.745891			0.372945	+	0.927853i	$0.378348\pi$
$972$	22.3494			0.0229932
$973$	−136.081			−0.139858
$974$			2137.09i			2.19413i
$975$		−	150.658i		−	0.154521i
$976$			711.213i			0.728702i
$977$	943.252			0.965458			0.482729	−	0.875770i	$-0.339646\pi$
$977$	943.252			0.965458			0.482729	+	0.875770i	$0.339646\pi$
$978$			1285.32i			1.31423i
$979$	−1666.75	−	577.256i	−1.70250	−	0.589639i
$980$	−28.8633			−0.0294523
$981$		−	99.2986i		−	0.101222i
$982$	−704.303			−0.717213
$983$	1101.28			1.12033			0.560163	−	0.828383i	$-0.310739\pi$
$983$	1101.28			1.12033			0.560163	+	0.828383i	$0.310739\pi$
$984$	139.926			0.142201
$985$			332.092i			0.337149i
$986$			16.9275i			0.0171678i
$987$			210.899i			0.213677i
$988$	264.552			0.267766
$989$		−	330.038i		−	0.333709i
$990$	56.2920	−	162.535i	0.0568606	−	0.164177i
$991$	−639.463			−0.645271			−0.322635	−	0.946523i	$-0.604569\pi$
$991$	−639.463			−0.645271			−0.322635	+	0.946523i	$0.604569\pi$
$992$		−	376.639i		−	0.379676i
$993$	657.478			0.662112
$994$	410.480			0.412958
$995$	140.994			0.141702
$996$		−	342.202i		−	0.343577i
$997$		−	351.666i		−	0.352724i	−0.984325	−	0.176362i	$-0.943567\pi$
$997$		−	351.666i		−	0.352724i	0.984325	−	0.176362i	$-0.0564329\pi$
$998$		−	239.626i		−	0.240106i
$999$	−287.353			−0.287641

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	165.3.b.a.76.13	yes	16
3.2	odd	2		495.3.b.c.406.4		16
4.3	odd	2		2640.3.c.c.241.14		16
5.2	odd	4		825.3.h.b.274.7		32
5.3	odd	4		825.3.h.b.274.25		32
5.4	even	2		825.3.b.d.76.4		16
11.10	odd	2	inner	165.3.b.a.76.4	✓	16
33.32	even	2		495.3.b.c.406.13		16
44.43	even	2		2640.3.c.c.241.15		16
55.32	even	4		825.3.h.b.274.26		32
55.43	even	4		825.3.h.b.274.8		32
55.54	odd	2		825.3.b.d.76.13		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
165.3.b.a.76.4	✓	16	11.10	odd	2	inner
165.3.b.a.76.13	yes	16	1.1	even	1	trivial
495.3.b.c.406.4		16	3.2	odd	2
495.3.b.c.406.13		16	33.32	even	2
825.3.b.d.76.4		16	5.4	even	2
825.3.b.d.76.13		16	55.54	odd	2
825.3.h.b.274.7		32	5.2	odd	4
825.3.h.b.274.8		32	55.43	even	4
825.3.h.b.274.25		32	5.3	odd	4
825.3.h.b.274.26		32	55.32	even	4
2640.3.c.c.241.14		16	4.3	odd	2
2640.3.c.c.241.15		16	44.43	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 165 = 3 \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	165.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+2.33103i q^{2} -1.73205 q^{3} -1.43371 q^{4} +2.23607 q^{5} -4.03747i q^{6} +6.32430i q^{7} +5.98210i q^{8} +3.00000 q^{9} +5.21235i q^{10} +(-10.3943 - 3.59991i) q^{11} +2.48326 q^{12} +17.3965i q^{13} -14.7421 q^{14} -3.87298 q^{15} -19.6793 q^{16} -12.2603i q^{17} +6.99310i q^{18} +10.6069i q^{19} -3.20588 q^{20} -10.9540i q^{21} +(8.39151 - 24.2294i) q^{22} -9.16729 q^{23} -10.3613i q^{24} +5.00000 q^{25} -40.5519 q^{26} -5.19615 q^{27} -9.06722i q^{28} +0.592304i q^{29} -9.02805i q^{30} +17.1631 q^{31} -21.9447i q^{32} +(18.0034 + 6.23523i) q^{33} +28.5791 q^{34} +14.1416i q^{35} -4.30114 q^{36} +55.3012 q^{37} -24.7249 q^{38} -30.1317i q^{39} +13.3764i q^{40} +13.5046i q^{41} +25.5341 q^{42} +36.0017i q^{43} +(14.9024 + 5.16124i) q^{44} +6.70820 q^{45} -21.3693i q^{46} -19.2531 q^{47} +34.0856 q^{48} +9.00325 q^{49} +11.6552i q^{50} +21.2354i q^{51} -24.9416i q^{52} +70.4442 q^{53} -12.1124i q^{54} +(-23.2423 - 8.04965i) q^{55} -37.8326 q^{56} -18.3716i q^{57} -1.38068 q^{58} +14.9479 q^{59} +5.55274 q^{60} -36.1401i q^{61} +40.0077i q^{62} +18.9729i q^{63} -27.5634 q^{64} +38.8998i q^{65} +(-14.5345 + 41.9665i) q^{66} +127.842 q^{67} +17.5777i q^{68} +15.8782 q^{69} -32.9644 q^{70} -27.8440 q^{71} +17.9463i q^{72} +61.3643i q^{73} +128.909i q^{74} -8.66025 q^{75} -15.2072i q^{76} +(22.7669 - 65.7364i) q^{77} +70.2379 q^{78} -141.550i q^{79} -44.0043 q^{80} +9.00000 q^{81} -31.4798 q^{82} -137.804i q^{83} +15.7049i q^{84} -27.4148i q^{85} -83.9212 q^{86} -1.02590i q^{87} +(21.5350 - 62.1795i) q^{88} +160.353 q^{89} +15.6370i q^{90} -110.021 q^{91} +13.1433 q^{92} -29.7273 q^{93} -44.8797i q^{94} +23.7177i q^{95} +38.0094i q^{96} -57.7240 q^{97} +20.9869i q^{98} +(-31.1828 - 10.7997i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 8 q^{4} + 48 q^{9} - 28 q^{11} - 16 q^{16} + 40 q^{20} - 20 q^{22} + 56 q^{23} + 80 q^{25} - 88 q^{26} - 96 q^{31} - 12 q^{33} - 200 q^{34} - 24 q^{36} + 184 q^{37} + 296 q^{38} - 264 q^{42} + 300 q^{44}+ \cdots - 84 q^{99}+O(q^{100}) \) 16 * q - 8 * q^4 + 48 * q^9 - 28 * q^11 - 16 * q^16 + 40 * q^20 - 20 * q^22 + 56 * q^23 + 80 * q^25 - 88 * q^26 - 96 * q^31 - 12 * q^33 - 200 * q^34 - 24 * q^36 + 184 * q^37 + 296 * q^38 - 264 * q^42 + 300 * q^44 - 200 * q^47 + 96 * q^48 - 496 * q^49 - 80 * q^53 + 20 * q^55 - 32 * q^56 - 16 * q^58 - 136 * q^59 + 456 * q^64 - 180 * q^66 + 256 * q^67 + 168 * q^69 + 216 * q^71 - 248 * q^77 + 240 * q^78 - 160 * q^80 + 144 * q^81 + 232 * q^82 + 192 * q^86 - 116 * q^88 - 336 * q^89 + 256 * q^91 - 440 * q^92 - 144 * q^93 - 144 * q^97 - 84 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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