LMFDB - Embedded newform 1155.2.l.e.1121.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1155,2,Mod(1121,1155)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1155, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0, 0, 1]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("1155.1121");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1155 = 3 \cdot 5 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1155.l (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:	$9.22272143346$
Analytic rank:	$0$
Dimension:	$40$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			1121.1
Character	$\chi$	$=$	1155.1121
Dual form			1155.2.l.e.1121.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.79309 q^{2} +(0.351991 - 1.69591i) q^{3} +5.80135 q^{4} +1.00000i q^{5} +(-0.983141 + 4.73682i) q^{6} -1.00000i q^{7} -10.6175 q^{8} +(-2.75221 - 1.19389i) q^{9} +O(q^{10})$	\(q-2.79309 q^{2} +(0.351991 - 1.69591i) q^{3} +5.80135 q^{4} +1.00000i q^{5} +(-0.983141 + 4.73682i) q^{6} -1.00000i q^{7} -10.6175 q^{8} +(-2.75221 - 1.19389i) q^{9} -2.79309i q^{10} +(1.01781 + 3.15659i) q^{11} +(2.04202 - 9.83855i) q^{12} +1.61455i q^{13} +2.79309i q^{14} +(1.69591 + 0.351991i) q^{15} +18.0529 q^{16} +0.978245 q^{17} +(7.68715 + 3.33463i) q^{18} +0.395037i q^{19} +5.80135i q^{20} +(-1.69591 - 0.351991i) q^{21} +(-2.84283 - 8.81664i) q^{22} -7.12888i q^{23} +(-3.73726 + 18.0063i) q^{24} -1.00000 q^{25} -4.50959i q^{26} +(-2.99347 + 4.24725i) q^{27} -5.80135i q^{28} -7.06734 q^{29} +(-4.73682 - 0.983141i) q^{30} -8.80790 q^{31} -29.1884 q^{32} +(5.71155 - 0.615020i) q^{33} -2.73232 q^{34} +1.00000 q^{35} +(-15.9665 - 6.92615i) q^{36} -6.29015 q^{37} -1.10337i q^{38} +(2.73813 + 0.568307i) q^{39} -10.6175i q^{40} +10.7989 q^{41} +(4.73682 + 0.983141i) q^{42} -10.2461i q^{43} +(5.90466 + 18.3125i) q^{44} +(1.19389 - 2.75221i) q^{45} +19.9116i q^{46} -6.63732i q^{47} +(6.35446 - 30.6161i) q^{48} -1.00000 q^{49} +2.79309 q^{50} +(0.344333 - 1.65901i) q^{51} +9.36657i q^{52} -1.04213i q^{53} +(8.36104 - 11.8629i) q^{54} +(-3.15659 + 1.01781i) q^{55} +10.6175i q^{56} +(0.669946 + 0.139049i) q^{57} +19.7397 q^{58} -2.68958i q^{59} +(9.83855 + 2.04202i) q^{60} -9.03276i q^{61} +24.6012 q^{62} +(-1.19389 + 2.75221i) q^{63} +45.4200 q^{64} -1.61455 q^{65} +(-15.9529 + 1.71780i) q^{66} -10.4405 q^{67} +5.67514 q^{68} +(-12.0899 - 2.50930i) q^{69} -2.79309 q^{70} +3.62237i q^{71} +(29.2215 + 12.6761i) q^{72} +4.53276i q^{73} +17.5690 q^{74} +(-0.351991 + 1.69591i) q^{75} +2.29175i q^{76} +(3.15659 - 1.01781i) q^{77} +(-7.64784 - 1.58733i) q^{78} -11.4024i q^{79} +18.0529i q^{80} +(6.14926 + 6.57165i) q^{81} -30.1622 q^{82} -14.8678 q^{83} +(-9.83855 - 2.04202i) q^{84} +0.978245i q^{85} +28.6184i q^{86} +(-2.48764 + 11.9856i) q^{87} +(-10.8066 - 33.5151i) q^{88} -8.05214i q^{89} +(-3.33463 + 7.68715i) q^{90} +1.61455 q^{91} -41.3571i q^{92} +(-3.10030 + 14.9374i) q^{93} +18.5386i q^{94} -0.395037 q^{95} +(-10.2741 + 49.5009i) q^{96} +9.28996 q^{97} +2.79309 q^{98} +(0.967395 - 9.90273i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 4 q^{2} - 4 q^{3} + 44 q^{4} - 4 q^{6} - 12 q^{8} - 2 q^{9}+O(q^{10}) $ 40 * q - 4 * q^2 - 4 * q^3 + 44 * q^4 - 4 * q^6 - 12 * q^8 - 2 * q^9	$ 40 q - 4 q^{2} - 4 q^{3} + 44 q^{4} - 4 q^{6} - 12 q^{8} - 2 q^{9} - 6 q^{11} + 8 q^{12} + 2 q^{15} + 68 q^{16} + 40 q^{18} - 2 q^{21} - 4 q^{22} - 12 q^{24} - 40 q^{25} + 32 q^{27} - 24 q^{29} - 8 q^{31} + 52 q^{32} - 16 q^{33} + 32 q^{34} + 40 q^{35} - 48 q^{37} + 66 q^{39} - 16 q^{41} + 32 q^{44} + 32 q^{48} - 40 q^{49} + 4 q^{50} - 14 q^{51} - 72 q^{54} + 8 q^{55} - 24 q^{57} - 80 q^{58} + 24 q^{60} + 48 q^{62} + 76 q^{64} + 4 q^{65} - 76 q^{66} - 48 q^{67} - 32 q^{68} - 20 q^{69} - 4 q^{70} + 128 q^{72} + 4 q^{75} - 8 q^{77} - 28 q^{78} + 50 q^{81} - 32 q^{82} - 24 q^{83} - 24 q^{84} - 32 q^{87} - 16 q^{88} + 8 q^{90} - 4 q^{91} - 20 q^{93} - 12 q^{95} + 12 q^{96} + 100 q^{97} + 4 q^{98} - 54 q^{99}+O(q^{100}) $ 40 * q - 4 * q^2 - 4 * q^3 + 44 * q^4 - 4 * q^6 - 12 * q^8 - 2 * q^9 - 6 * q^11 + 8 * q^12 + 2 * q^15 + 68 * q^16 + 40 * q^18 - 2 * q^21 - 4 * q^22 - 12 * q^24 - 40 * q^25 + 32 * q^27 - 24 * q^29 - 8 * q^31 + 52 * q^32 - 16 * q^33 + 32 * q^34 + 40 * q^35 - 48 * q^37 + 66 * q^39 - 16 * q^41 + 32 * q^44 + 32 * q^48 - 40 * q^49 + 4 * q^50 - 14 * q^51 - 72 * q^54 + 8 * q^55 - 24 * q^57 - 80 * q^58 + 24 * q^60 + 48 * q^62 + 76 * q^64 + 4 * q^65 - 76 * q^66 - 48 * q^67 - 32 * q^68 - 20 * q^69 - 4 * q^70 + 128 * q^72 + 4 * q^75 - 8 * q^77 - 28 * q^78 + 50 * q^81 - 32 * q^82 - 24 * q^83 - 24 * q^84 - 32 * q^87 - 16 * q^88 + 8 * q^90 - 4 * q^91 - 20 * q^93 - 12 * q^95 + 12 * q^96 + 100 * q^97 + 4 * q^98 - 54 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1155\mathbb{Z}\right)^\times$.

$n$	$211$	$232$	$386$	$661$
$\chi(n)$	$-1$	$1$	$-1$	$1$

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 $

$2$	−2.79309			−1.97501			−0.987506	−	0.157581i	$-0.949630\pi$
$2$	−2.79309			−1.97501			−0.987506	+	0.157581i	$0.949630\pi$
$3$	0.351991	−	1.69591i	0.203222	−	0.979133i
$3$	0.351991	−	1.69591i	0.203222	−	0.979133i
$4$	5.80135			2.90067
$5$			1.00000i			0.447214i
$5$			1.00000i			0.447214i
$6$	−0.983141	+	4.73682i	−0.401366	+	1.93380i
$7$		−	1.00000i		−	0.377964i
$7$		−	1.00000i		−	0.377964i
$8$	−10.6175			−3.75385
$9$	−2.75221	−	1.19389i	−0.917402	−	0.397963i
$10$		−	2.79309i		−	0.883252i
$11$	1.01781	+	3.15659i	0.306881	+	0.951748i
$11$	1.01781	+	3.15659i	0.306881	+	0.951748i
$12$	2.04202	−	9.83855i	0.589480	−	2.84014i
$13$			1.61455i			0.447796i	0.974613	+	0.223898i	$0.0718783\pi$
$13$			1.61455i			0.447796i	−0.974613	+	0.223898i	$0.928122\pi$
$14$			2.79309i			0.746484i
$15$	1.69591	+	0.351991i	0.437881	+	0.0908836i
$16$	18.0529			4.51323
$17$	0.978245			0.237259			0.118630	−	0.992939i	$-0.462150\pi$
$17$	0.978245			0.237259			0.118630	+	0.992939i	$0.462150\pi$
$18$	7.68715	+	3.33463i	1.81188	+	0.785981i
$19$			0.395037i			0.0906277i	0.998973	+	0.0453139i	$0.0144288\pi$
$19$			0.395037i			0.0906277i	−0.998973	+	0.0453139i	$0.985571\pi$
$20$			5.80135i			1.29722i
$21$	−1.69591	−	0.351991i	−0.370077	−	0.0768107i
$22$	−2.84283	−	8.81664i	−0.606094	−	1.87971i
$23$		−	7.12888i		−	1.48647i	−0.669028	−	0.743237i	$-0.733289\pi$
$23$		−	7.12888i		−	1.48647i	0.669028	−	0.743237i	$-0.266711\pi$
$24$	−3.73726	+	18.0063i	−0.762865	+	3.67552i
$25$	−1.00000			−0.200000
$26$		−	4.50959i		−	0.884403i
$27$	−2.99347	+	4.24725i	−0.576094	+	0.817383i
$28$		−	5.80135i		−	1.09635i
$29$	−7.06734			−1.31237			−0.656186	−	0.754599i	$-0.727832\pi$
$29$	−7.06734			−1.31237			−0.656186	+	0.754599i	$0.727832\pi$
$30$	−4.73682	−	0.983141i	−0.864821	−	0.179496i
$31$	−8.80790			−1.58195			−0.790973	−	0.611852i	$-0.790425\pi$
$31$	−8.80790			−1.58195			−0.790973	+	0.611852i	$0.790425\pi$
$32$	−29.1884			−5.15983
$33$	5.71155	−	0.615020i	0.994252	−	0.107061i
$34$	−2.73232			−0.468590
$35$	1.00000			0.169031
$36$	−15.9665	−	6.92615i	−2.66108	−	1.15436i
$37$	−6.29015			−1.03410			−0.517048	−	0.855957i	$-0.672969\pi$
$37$	−6.29015			−1.03410			−0.517048	+	0.855957i	$0.672969\pi$
$38$		−	1.10337i		−	0.178991i
$39$	2.73813	+	0.568307i	0.438452	+	0.0910020i
$40$		−	10.6175i		−	1.67877i
$41$	10.7989			1.68650			0.843251	−	0.537521i	$-0.180639\pi$
$41$	10.7989			1.68650			0.843251	+	0.537521i	$0.180639\pi$
$42$	4.73682	+	0.983141i	0.730907	+	0.151702i
$43$		−	10.2461i		−	1.56252i	−0.624204	−	0.781261i	$-0.714577\pi$
$43$		−	10.2461i		−	1.56252i	0.624204	−	0.781261i	$-0.285423\pi$
$44$	5.90466	+	18.3125i	0.890161	+	2.76071i
$45$	1.19389	−	2.75221i	0.177974	−	0.410275i
$46$			19.9116i			2.93580i
$47$		−	6.63732i		−	0.968152i	−0.875026	−	0.484076i	$-0.839156\pi$
$47$		−	6.63732i		−	0.968152i	0.875026	−	0.484076i	$-0.160844\pi$
$48$	6.35446	−	30.6161i	0.917187	−	4.41905i
$49$	−1.00000			−0.142857
$50$	2.79309			0.395002
$51$	0.344333	−	1.65901i	0.0482163	−	0.232308i
$52$			9.36657i			1.29891i
$53$		−	1.04213i		−	0.143148i	−0.997435	−	0.0715739i	$-0.977198\pi$
$53$		−	1.04213i		−	0.143148i	0.997435	−	0.0715739i	$-0.0228022\pi$
$54$	8.36104	−	11.8629i	1.13779	−	1.61434i
$55$	−3.15659	+	1.01781i	−0.425635	+	0.137241i
$56$			10.6175i			1.41882i
$57$	0.669946	+	0.139049i	0.0887366	+	0.0184175i
$58$	19.7397			2.59195
$59$		−	2.68958i		−	0.350153i	−0.984555	−	0.175077i	$-0.943983\pi$
$59$		−	2.68958i		−	0.350153i	0.984555	−	0.175077i	$-0.0560174\pi$
$60$	9.83855	+	2.04202i	1.27015	+	0.263624i
$61$		−	9.03276i		−	1.15653i	−0.815850	−	0.578263i	$-0.803731\pi$
$61$		−	9.03276i		−	1.15653i	0.815850	−	0.578263i	$-0.196269\pi$
$62$	24.6012			3.12436
$63$	−1.19389	+	2.75221i	−0.150416	+	0.346745i
$64$	45.4200			5.67750
$65$	−1.61455			−0.200261
$66$	−15.9529	+	1.71780i	−1.96366	+	0.211447i
$67$	−10.4405			−1.27551			−0.637755	−	0.770239i	$-0.720137\pi$
$67$	−10.4405			−1.27551			−0.637755	+	0.770239i	$0.720137\pi$
$68$	5.67514			0.688211
$69$	−12.0899	−	2.50930i	−1.45546	−	0.302084i
$70$	−2.79309			−0.333838
$71$			3.62237i			0.429897i	0.976625	+	0.214948i	$0.0689583\pi$
$71$			3.62237i			0.429897i	−0.976625	+	0.214948i	$0.931042\pi$
$72$	29.2215	+	12.6761i	3.44379	+	1.49389i
$73$			4.53276i			0.530520i	0.964177	+	0.265260i	$0.0854578\pi$
$73$			4.53276i			0.530520i	−0.964177	+	0.265260i	$0.914542\pi$
$74$	17.5690			2.04235
$75$	−0.351991	+	1.69591i	−0.0406444	+	0.195827i
$76$			2.29175i			0.262881i
$77$	3.15659	−	1.01781i	0.359727	−	0.115990i
$78$	−7.64784	−	1.58733i	−0.865948	−	0.179730i
$79$		−	11.4024i		−	1.28287i	−0.767177	−	0.641435i	$-0.778339\pi$
$79$		−	11.4024i		−	1.28287i	0.767177	−	0.641435i	$-0.221661\pi$
$80$			18.0529i			2.01838i
$81$	6.14926	+	6.57165i	0.683252	+	0.730183i
$82$	−30.1622			−3.33086
$83$	−14.8678			−1.63195			−0.815977	−	0.578084i	$-0.803800\pi$
$83$	−14.8678			−1.63195			−0.815977	+	0.578084i	$0.803800\pi$
$84$	−9.83855	−	2.04202i	−1.07347	−	0.222803i
$85$			0.978245i			0.106106i
$86$			28.6184i			3.08600i
$87$	−2.48764	+	11.9856i	−0.266703	+	1.28499i
$88$	−10.8066	−	33.5151i	−1.15199	−	3.57272i
$89$		−	8.05214i		−	0.853525i	−0.904364	−	0.426762i	$-0.859654\pi$
$89$		−	8.05214i		−	0.853525i	0.904364	−	0.426762i	$-0.140346\pi$
$90$	−3.33463	+	7.68715i	−0.351501	+	0.810297i
$91$	1.61455			0.169251
$92$		−	41.3571i		−	4.31178i
$93$	−3.10030	+	14.9374i	−0.321486	+	1.54893i
$94$			18.5386i			1.91211i
$95$	−0.395037			−0.0405299
$96$	−10.2741	+	49.5009i	−1.04859	+	5.05216i
$97$	9.28996			0.943253			0.471626	−	0.881798i	$-0.343667\pi$
$97$	9.28996			0.943253			0.471626	+	0.881798i	$0.343667\pi$
$98$	2.79309			0.282145
$99$	0.967395	−	9.90273i	0.0972268	−	0.995262i
$100$	−5.80135			−0.580135
$101$	−4.72191			−0.469847			−0.234924	−	0.972014i	$-0.575484\pi$
$101$	−4.72191			−0.469847			−0.234924	+	0.972014i	$0.575484\pi$
$102$	−0.961753	+	4.63377i	−0.0952277	+	0.458812i
$103$	1.58051			0.155732			0.0778659	−	0.996964i	$-0.475189\pi$
$103$	1.58051			0.155732			0.0778659	+	0.996964i	$0.475189\pi$
$104$		−	17.1425i		−	1.68096i
$105$	0.351991	−	1.69591i	0.0343508	−	0.165504i
$106$			2.91077i			0.282719i
$107$	−0.467482			−0.0451931			−0.0225966	−	0.999745i	$-0.507193\pi$
$107$	−0.467482			−0.0451931			−0.0225966	+	0.999745i	$0.507193\pi$
$108$	−17.3662	+	24.6398i	−1.67106	+	2.37096i
$109$		−	0.924480i		−	0.0885491i	−0.999019	−	0.0442746i	$-0.985902\pi$
$109$		−	0.924480i		−	0.0885491i	0.999019	−	0.0442746i	$-0.0140976\pi$
$110$	8.81664	−	2.84283i	0.840633	−	0.271053i
$111$	−2.21408	+	10.6675i	−0.210151	+	1.01252i
$112$		−	18.0529i		−	1.70584i
$113$			4.10873i			0.386517i	0.981148	+	0.193258i	$0.0619055\pi$
$113$			4.10873i			0.386517i	−0.981148	+	0.193258i	$0.938094\pi$
$114$	−1.87122	−	0.388377i	−0.175256	−	0.0363749i
$115$	7.12888			0.664772
$116$	−41.0001			−3.80676
$117$	1.92759	−	4.44358i	0.178206	−	0.410809i
$118$			7.51224i			0.691557i
$119$		−	0.978245i		−	0.0896755i
$120$	−18.0063	−	3.73726i	−1.64374	−	0.341164i
$121$	−8.92813	+	6.42561i	−0.811648	+	0.584147i
$122$			25.2293i			2.28415i
$123$	3.80110	−	18.3139i	0.342734	−	1.65131i
$124$	−51.0977			−4.58871
$125$		−	1.00000i		−	0.0894427i
$126$	3.33463	−	7.68715i	0.297073	−	0.684826i
$127$			9.62624i			0.854191i	0.904207	+	0.427095i	$0.140463\pi$
$127$			9.62624i			0.854191i	−0.904207	+	0.427095i	$0.859537\pi$
$128$	−68.4853			−6.05330
$129$	−17.3765	−	3.60655i	−1.52992	−	0.317539i
$130$	4.50959			0.395517
$131$	−10.7484			−0.939096			−0.469548	−	0.882907i	$-0.655583\pi$
$131$	−10.7484			−0.939096			−0.469548	+	0.882907i	$0.655583\pi$
$132$	33.1346	−	3.56794i	2.88400	−	0.310549i
$133$	0.395037			0.0342541
$134$	29.1612			2.51915
$135$	−4.24725	−	2.99347i	−0.365545	−	0.257637i
$136$	−10.3865			−0.890636
$137$		−	1.13790i		−	0.0972174i	−0.998818	−	0.0486087i	$-0.984521\pi$
$137$		−	1.13790i		−	0.0972174i	0.998818	−	0.0486087i	$-0.0154787\pi$
$138$	33.7682	+	7.00870i	2.87454	+	0.596620i
$139$		−	9.88007i		−	0.838017i	−0.907982	−	0.419008i	$-0.862378\pi$
$139$		−	9.88007i		−	0.838017i	0.907982	−	0.419008i	$-0.137622\pi$
$140$	5.80135			0.490303
$141$	−11.2563	−	2.33627i	−0.947949	−	0.196750i
$142$		−	10.1176i		−	0.849051i
$143$	−5.09648	+	1.64331i	−0.426189	+	0.137420i
$144$	−49.6853	−	21.5532i	−4.14044	−	1.79610i
$145$		−	7.06734i		−	0.586911i
$146$		−	12.6604i		−	1.04778i
$147$	−0.351991	+	1.69591i	−0.0290317	+	0.139876i
$148$	−36.4914			−2.99957
$149$	−6.10566			−0.500195			−0.250097	−	0.968221i	$-0.580463\pi$
$149$	−6.10566			−0.500195			−0.250097	+	0.968221i	$0.580463\pi$
$150$	0.983141	−	4.73682i	0.0802732	−	0.386760i
$151$			8.37087i			0.681212i	0.940206	+	0.340606i	$0.110632\pi$
$151$			8.37087i			0.681212i	−0.940206	+	0.340606i	$0.889368\pi$
$152$		−	4.19430i		−	0.340203i
$153$	−2.69233	−	1.16791i	−0.217662	−	0.0944203i
$154$	−8.81664	+	2.84283i	−0.710465	+	0.229082i
$155$		−	8.80790i		−	0.707467i
$156$	15.8848	+	3.29695i	1.27181	+	0.263967i
$157$	−5.57999			−0.445332			−0.222666	−	0.974895i	$-0.571476\pi$
$157$	−5.57999			−0.445332			−0.222666	+	0.974895i	$0.571476\pi$
$158$			31.8479i			2.53368i
$159$	−1.76736	−	0.366821i	−0.140161	−	0.0290908i
$160$		−	29.1884i		−	2.30755i
$161$	−7.12888			−0.561834
$162$	−17.1754	−	18.3552i	−1.34943	−	1.44212i
$163$	6.13168			0.480270			0.240135	−	0.970739i	$-0.422808\pi$
$163$	6.13168			0.480270			0.240135	+	0.970739i	$0.422808\pi$
$164$	62.6480			4.89199
$165$	0.615020	+	5.71155i	0.0478792	+	0.444643i
$166$	41.5271			3.22313
$167$	−13.0190			−1.00744			−0.503722	−	0.863866i	$-0.668036\pi$
$167$	−13.0190			−1.00744			−0.503722	+	0.863866i	$0.668036\pi$
$168$	18.0063	+	3.73726i	1.38922	+	0.288336i
$169$	10.3932			0.799479
$170$		−	2.73232i		−	0.209560i
$171$	0.471630	−	1.08722i	0.0360664	−	0.0831420i
$172$		−	59.4414i		−	4.53237i
$173$	6.69034			0.508657			0.254329	−	0.967118i	$-0.418146\pi$
$173$	6.69034			0.508657			0.254329	+	0.967118i	$0.418146\pi$
$174$	6.94820	−	33.4767i	0.526742	−	2.53787i
$175$			1.00000i			0.0755929i
$176$	18.3744	+	56.9857i	1.38502	+	4.29546i
$177$	−4.56128	−	0.946707i	−0.342847	−	0.0711589i
$178$			22.4903i			1.68572i
$179$		−	5.01629i		−	0.374935i	−0.982271	−	0.187468i	$-0.939972\pi$
$179$		−	5.01629i		−	0.374935i	0.982271	−	0.187468i	$-0.0600280\pi$
$180$	6.92615	−	15.9665i	0.516245	−	1.19007i
$181$	−17.9955			−1.33759			−0.668797	−	0.743445i	$-0.733191\pi$
$181$	−17.9955			−1.33759			−0.668797	+	0.743445i	$0.733191\pi$
$182$	−4.50959			−0.334273
$183$	−15.3187	−	3.17945i	−1.13239	−	0.235032i
$184$			75.6909i			5.58000i
$185$		−	6.29015i		−	0.462461i
$186$	8.65941	−	41.7214i	0.634939	−	3.05916i
$187$	0.995666	+	3.08792i	0.0728103	+	0.225811i
$188$		−	38.5054i		−	2.80829i
$189$	4.24725	+	2.99347i	0.308942	+	0.217743i
$190$	1.10337			0.0800471
$191$		−	5.38943i		−	0.389965i	−0.980807	−	0.194983i	$-0.937535\pi$
$191$		−	5.38943i		−	0.389965i	0.980807	−	0.194983i	$-0.0624650\pi$
$192$	15.9874	−	77.0281i	1.15379	−	5.55903i
$193$			17.9069i			1.28896i	0.764619	+	0.644482i	$0.222927\pi$
$193$			17.9069i			1.28896i	−0.764619	+	0.644482i	$0.777073\pi$
$194$	−25.9477			−1.86294
$195$	−0.568307	+	2.73813i	−0.0406973	+	0.196082i
$196$	−5.80135			−0.414382
$197$	−7.48582			−0.533342			−0.266671	−	0.963788i	$-0.585924\pi$
$197$	−7.48582			−0.533342			−0.266671	+	0.963788i	$0.585924\pi$
$198$	−2.70202	+	27.6592i	−0.192024	+	1.96565i
$199$	−3.65516			−0.259108			−0.129554	−	0.991572i	$-0.541354\pi$
$199$	−3.65516			−0.259108			−0.129554	+	0.991572i	$0.541354\pi$
$200$	10.6175			0.750770
$201$	−3.67496	+	17.7061i	−0.259212	+	1.24889i
$202$	13.1887			0.927954
$203$			7.06734i			0.496030i
$204$	1.99760	−	9.62451i	0.139860	−	0.673850i
$205$			10.7989i			0.754226i
$206$	−4.41449			−0.307572
$207$	−8.51108	+	19.6201i	−0.591561	+	1.36369i
$208$			29.1474i			2.02101i
$209$	−1.24697	+	0.402072i	−0.0862547	+	0.0278119i
$210$	−0.983141	+	4.73682i	−0.0678432	+	0.326872i
$211$		−	0.754319i		−	0.0519295i	−0.999663	−	0.0259647i	$-0.991734\pi$
$211$		−	0.754319i		−	0.0519295i	0.999663	−	0.0259647i	$-0.00826576\pi$
$212$		−	6.04577i		−	0.415225i
$213$	6.14321	+	1.27504i	0.420926	+	0.0873644i
$214$	1.30572			0.0892570
$215$	10.2461			0.698781
$216$	31.7832	−	45.0951i	2.16257	−	3.06834i
$217$			8.80790i			0.597919i
$218$			2.58215i			0.174886i
$219$	7.68715	+	1.59549i	0.519449	+	0.107813i
$220$	−18.3125	+	5.90466i	−1.23463	+	0.398092i
$221$			1.57943i			0.106244i
$222$	6.18411	−	29.7953i	0.415050	−	1.99973i
$223$	−6.79272			−0.454874			−0.227437	−	0.973793i	$-0.573035\pi$
$223$	−6.79272			−0.454874			−0.227437	+	0.973793i	$0.573035\pi$
$224$			29.1884i			1.95023i
$225$	2.75221	+	1.19389i	0.183480	+	0.0795925i
$226$		−	11.4760i		−	0.763375i
$227$	6.20452			0.411808			0.205904	−	0.978572i	$-0.433986\pi$
$227$	6.20452			0.411808			0.205904	+	0.978572i	$0.433986\pi$
$228$	3.88659	+	0.806673i	0.257396	+	0.0534233i
$229$	1.52273			0.100625			0.0503124	−	0.998734i	$-0.483978\pi$
$229$	1.52273			0.100625			0.0503124	+	0.998734i	$0.483978\pi$
$230$	−19.9116			−1.31293
$231$	−0.615020	−	5.71155i	−0.0404653	−	0.375792i
$232$	75.0375			4.92645
$233$	−6.47307			−0.424065			−0.212032	−	0.977263i	$-0.568008\pi$
$233$	−6.47307			−0.424065			−0.212032	+	0.977263i	$0.568008\pi$
$234$	−5.38394	+	12.4113i	−0.351959	+	0.811353i
$235$	6.63732			0.432971
$236$		−	15.6032i		−	1.01568i
$237$	−19.3374	−	4.01354i	−1.25610	−	0.260707i
$238$			2.73232i			0.177110i
$239$	12.0335			0.778380			0.389190	−	0.921158i	$-0.372755\pi$
$239$	12.0335			0.778380			0.389190	+	0.921158i	$0.372755\pi$
$240$	30.6161	+	6.35446i	1.97626	+	0.410179i
$241$			4.99219i			0.321575i	0.986989	+	0.160788i	$0.0514035\pi$
$241$			4.99219i			0.321575i	−0.986989	+	0.160788i	$0.948597\pi$
$242$	24.9371	−	17.9473i	1.60301	−	1.15370i
$243$	13.3094	−	8.11543i	0.853798	−	0.520605i
$244$		−	52.4022i		−	3.35471i
$245$		−	1.00000i		−	0.0638877i
$246$	−10.6168	+	51.1523i	−0.676904	+	3.26135i
$247$	−0.637808			−0.0405827
$248$	93.5178			5.93839
$249$	−5.23333	+	25.2144i	−0.331649	+	1.59790i
$250$			2.79309i			0.176650i
$251$			23.0855i			1.45715i	0.684968	+	0.728573i	$0.259816\pi$
$251$			23.0855i			1.45715i	−0.684968	+	0.728573i	$0.740184\pi$
$252$	−6.92615	+	15.9665i	−0.436307	+	1.00579i
$253$	22.5030	−	7.25584i	1.41475	−	0.456171i
$254$		−	26.8869i		−	1.68704i
$255$	1.65901	+	0.344333i	0.103891	+	0.0215630i
$256$	100.445			6.27784
$257$			21.7167i			1.35465i	0.735684	+	0.677324i	$0.236861\pi$
$257$			21.7167i			1.35465i	−0.735684	+	0.677324i	$0.763139\pi$
$258$	48.5342	+	10.0734i	3.02161	+	0.627143i
$259$			6.29015i			0.390851i
$260$	−9.36657			−0.580890
$261$	19.4508	+	8.43762i	1.20397	+	0.522275i
$262$	30.0214			1.85473
$263$	2.86791			0.176843			0.0884215	−	0.996083i	$-0.471818\pi$
$263$	2.86791			0.176843			0.0884215	+	0.996083i	$0.471818\pi$
$264$	−60.6423	+	6.52997i	−3.73228	+	0.401892i
$265$	1.04213			0.0640176
$266$	−1.10337			−0.0676522
$267$	−13.6557	−	2.83428i	−0.835714	−	0.173455i
$268$	−60.5690			−3.69984
$269$		−	25.7337i		−	1.56901i	−0.620123	−	0.784505i	$-0.712917\pi$
$269$		−	25.7337i		−	1.56901i	0.620123	−	0.784505i	$-0.287083\pi$
$270$	11.8629	+	8.36104i	0.721956	+	0.508837i
$271$		−	18.6787i		−	1.13465i	−0.823493	−	0.567326i	$-0.807978\pi$
$271$		−	18.6787i		−	1.13465i	0.823493	−	0.567326i	$-0.192022\pi$
$272$	17.6602			1.07081
$273$	0.568307	−	2.73813i	0.0343955	−	0.165719i
$274$			3.17826i			0.192005i
$275$	−1.01781	−	3.15659i	−0.0613762	−	0.190350i
$276$	−70.1378	−	14.5573i	−4.22180	−	0.876247i
$277$			4.86592i			0.292365i	0.989258	+	0.146182i	$0.0466986\pi$
$277$			4.86592i			0.292365i	−0.989258	+	0.146182i	$0.953301\pi$
$278$			27.5959i			1.65509i
$279$	24.2411	+	10.5156i	1.45128	+	0.629555i
$280$	−10.6175			−0.634517
$281$	−13.7597			−0.820835			−0.410417	−	0.911898i	$-0.634617\pi$
$281$	−13.7597			−0.820835			−0.410417	+	0.911898i	$0.634617\pi$
$282$	31.4398	+	6.52542i	1.87221	+	0.388583i
$283$		−	14.2787i		−	0.848783i	−0.905479	−	0.424392i	$-0.860488\pi$
$283$		−	14.2787i		−	0.848783i	0.905479	−	0.424392i	$-0.139512\pi$
$284$			21.0146i			1.24699i
$285$	−0.139049	+	0.669946i	−0.00823657	+	0.0396842i
$286$	14.2349	−	4.58990i	0.841729	−	0.271406i
$287$		−	10.7989i		−	0.637437i
$288$	80.3325	+	34.8477i	4.73364	+	2.05342i
$289$	−16.0430			−0.943708
$290$			19.7397i			1.15916i
$291$	3.26998	−	15.7549i	0.191690	−	0.923570i
$292$			26.2961i			1.53886i
$293$	−17.5529			−1.02545			−0.512726	−	0.858552i	$-0.671364\pi$
$293$	−17.5529			−1.02545			−0.512726	+	0.858552i	$0.671364\pi$
$294$	0.983141	−	4.73682i	0.0573380	−	0.276257i
$295$	2.68958			0.156593
$296$	66.7857			3.88184
$297$	−16.4536	−	5.12628i	−0.954735	−	0.297457i
$298$	17.0536			0.987891
$299$	11.5099			0.665638
$300$	−2.04202	+	9.83855i	−0.117896	+	0.568029i
$301$	−10.2461			−0.590578
$302$		−	23.3806i		−	1.34540i
$303$	−1.66207	+	8.00792i	−0.0954833	+	0.460043i
$304$			7.13157i			0.409024i
$305$	9.03276			0.517215
$306$	7.51992	+	3.26209i	0.429885	+	0.186481i
$307$		−	16.3306i		−	0.932037i	−0.884775	−	0.466018i	$-0.845688\pi$
$307$		−	16.3306i		−	0.932037i	0.884775	−	0.466018i	$-0.154312\pi$
$308$	18.3125	−	5.90466i	1.04345	−	0.336449i
$309$	0.556323	−	2.68039i	0.0316481	−	0.152482i
$310$			24.6012i			1.39726i
$311$			1.89148i			0.107256i	0.998561	+	0.0536279i	$0.0170785\pi$
$311$			1.89148i			0.107256i	−0.998561	+	0.0536279i	$0.982922\pi$
$312$	−29.0721	−	6.03400i	−1.64588	−	0.341608i
$313$	−27.1821			−1.53642			−0.768212	−	0.640195i	$-0.778853\pi$
$313$	−27.1821			−1.53642			−0.768212	+	0.640195i	$0.778853\pi$
$314$	15.5854			0.879536
$315$	−2.75221	−	1.19389i	−0.155069	−	0.0672679i
$316$		−	66.1493i		−	3.72119i
$317$			4.15856i			0.233568i	0.993157	+	0.116784i	$0.0372585\pi$
$317$			4.15856i			0.233568i	−0.993157	+	0.116784i	$0.962741\pi$
$318$	4.93639	+	1.02456i	0.276819	+	0.0574546i
$319$	−7.19321	−	22.3087i	−0.402742	−	1.24905i
$320$			45.4200i			2.53906i
$321$	−0.164549	+	0.792805i	−0.00918424	+	0.0442501i
$322$	19.9116			1.10963
$323$			0.386443i			0.0215023i
$324$	35.6740	+	38.1244i	1.98189	+	2.11802i
$325$		−	1.61455i		−	0.0895592i
$326$	−17.1263			−0.948540
$327$	−1.56783	−	0.325408i	−0.0867013	−	0.0179951i
$328$	−114.657			−6.33087
$329$	−6.63732			−0.365927
$330$	−1.71780	−	15.9529i	−0.0945620	−	0.878176i
$331$	12.2660			0.674201			0.337101	−	0.941469i	$-0.390554\pi$
$331$	12.2660			0.674201			0.337101	+	0.941469i	$0.390554\pi$
$332$	−86.2533			−4.73377
$333$	17.3118	+	7.50974i	0.948680	+	0.411531i
$334$	36.3633			1.98971
$335$		−	10.4405i		−	0.570426i
$336$	−30.6161	−	6.35446i	−1.67024	−	0.346664i
$337$			28.2675i			1.53983i	0.638149	+	0.769913i	$0.279700\pi$
$337$			28.2675i			1.53983i	−0.638149	+	0.769913i	$0.720300\pi$
$338$	−29.0292			−1.57898
$339$	6.96802	+	1.44623i	0.378451	+	0.0785486i
$340$			5.67514i			0.307777i
$341$	−8.96476	−	27.8029i	−0.485469	−	1.50561i
$342$	−1.31730	+	3.03671i	−0.0712316	+	0.164206i
$343$			1.00000i			0.0539949i
$344$			108.788i			5.86548i
$345$	2.50930	−	12.0899i	0.135096	−	0.650900i
$346$	−18.6867			−1.00460
$347$	10.3963			0.558104			0.279052	−	0.960276i	$-0.409980\pi$
$347$	10.3963			0.558104			0.279052	+	0.960276i	$0.409980\pi$
$348$	−14.4317	+	69.5324i	−0.773618	+	3.72733i
$349$			5.17490i			0.277006i	0.990362	+	0.138503i	$0.0442291\pi$
$349$			5.17490i			0.277006i	−0.990362	+	0.138503i	$0.955771\pi$
$350$		−	2.79309i		−	0.149297i
$351$	−6.85740	−	4.83312i	−0.366021	−	0.257973i
$352$	−29.7082	−	92.1359i	−1.58345	−	4.91086i
$353$		−	11.0865i		−	0.590074i	−0.955486	−	0.295037i	$-0.904668\pi$
$353$		−	11.0865i		−	0.590074i	0.955486	−	0.295037i	$-0.0953320\pi$
$354$	12.7401	+	2.64424i	0.677126	+	0.140540i
$355$	−3.62237			−0.192256
$356$		−	46.7132i		−	2.47580i
$357$	−1.65901	−	0.344333i	−0.0878043	−	0.0182240i
$358$			14.0110i			0.740502i
$359$	29.4548			1.55457			0.777284	−	0.629150i	$-0.216597\pi$
$359$	29.4548			1.55457			0.777284	+	0.629150i	$0.216597\pi$
$360$	−12.6761	+	29.2215i	−0.668089	+	1.54011i
$361$	18.8439			0.991787
$362$	50.2630			2.64176
$363$	7.75463	+	17.4030i	0.407012	+	0.913423i
$364$	9.36657			0.490942
$365$	−4.53276			−0.237256
$366$	42.7866	+	8.88048i	2.23649	+	0.464190i
$367$	32.3772			1.69007			0.845037	−	0.534708i	$-0.179578\pi$
$367$	32.3772			1.69007			0.845037	+	0.534708i	$0.179578\pi$
$368$		−	128.697i		−	6.70880i
$369$	−29.7207	−	12.8926i	−1.54720	−	0.671164i
$370$			17.5690i			0.913367i
$371$	−1.04213			−0.0541048
$372$	−17.9859	+	86.6569i	−0.932526	+	4.49295i
$373$			3.49916i			0.181180i	0.995888	+	0.0905898i	$0.0288752\pi$
$373$			3.49916i			0.181180i	−0.995888	+	0.0905898i	$0.971125\pi$
$374$	−2.78099	−	8.62483i	−0.143801	−	0.445979i
$375$	−1.69591	−	0.351991i	−0.0875763	−	0.0181767i
$376$			70.4717i			3.63430i
$377$		−	11.4106i		−	0.587676i
$378$	−11.8629	−	8.36104i	−0.610164	−	0.430045i
$379$	−12.4760			−0.640848			−0.320424	−	0.947274i	$-0.603825\pi$
$379$	−12.4760			−0.640848			−0.320424	+	0.947274i	$0.603825\pi$
$380$	−2.29175			−0.117564
$381$	16.3252	+	3.38835i	0.836366	+	0.173590i
$382$			15.0531i			0.770186i
$383$			20.0294i			1.02346i	0.859148	+	0.511728i	$0.170994\pi$
$383$			20.0294i			1.02346i	−0.859148	+	0.511728i	$0.829006\pi$
$384$	−24.1062	+	116.145i	−1.23016	+	5.92698i
$385$	1.01781	+	3.15659i	0.0518724	+	0.160875i
$386$		−	50.0155i		−	2.54572i
$387$	−12.2327	+	28.1995i	−0.621826	+	1.43346i
$388$	53.8943			2.73607
$389$		−	29.8331i		−	1.51260i	−0.654225	−	0.756300i	$-0.727005\pi$
$389$		−	29.8331i		−	1.51260i	0.654225	−	0.756300i	$-0.272995\pi$
$390$	1.58733	−	7.64784i	0.0803777	−	0.387264i
$391$		−	6.97379i		−	0.352680i
$392$	10.6175			0.536265
$393$	−3.78335	+	18.2284i	−0.190845	+	0.919500i
$394$	20.9086			1.05336
$395$	11.4024			0.573717
$396$	5.61219	−	57.4492i	0.282023	−	2.88693i
$397$	25.8678			1.29827			0.649133	−	0.760675i	$-0.275132\pi$
$397$	25.8678			1.29827			0.649133	+	0.760675i	$0.275132\pi$
$398$	10.2092			0.511741
$399$	0.139049	−	0.669946i	0.00696118	−	0.0335393i
$400$	−18.0529			−0.902646
$401$		−	20.5045i		−	1.02395i	−0.859001	−	0.511974i	$-0.828915\pi$
$401$		−	20.5045i		−	1.02395i	0.859001	−	0.511974i	$-0.171085\pi$
$402$	10.2645	−	49.4548i	0.511946	−	2.46658i
$403$		−	14.2208i		−	0.708389i
$404$	−27.3934			−1.36287
$405$	−6.57165	+	6.14926i	−0.326548	+	0.305559i
$406$		−	19.7397i		−	0.979666i
$407$	−6.40218	−	19.8554i	−0.317344	−	0.984198i
$408$	−3.65596	+	17.6146i	−0.180997	+	0.872051i
$409$			25.0112i			1.23673i	0.785893	+	0.618363i	$0.212204\pi$
$409$			25.0112i			1.23673i	−0.785893	+	0.618363i	$0.787796\pi$
$410$		−	30.1622i		−	1.48961i
$411$	−1.92977	−	0.400530i	−0.0951887	−	0.0197567i
$412$	9.16906			0.451727
$413$	−2.68958			−0.132346
$414$	23.7722	−	54.8008i	1.16834	−	2.69331i
$415$		−	14.8678i		−	0.729832i
$416$		−	47.1262i		−	2.31055i
$417$	−16.7557	−	3.47769i	−0.820529	−	0.170303i
$418$	3.48290	−	1.12302i	0.170354	−	0.0549289i
$419$		−	16.0284i		−	0.783039i	−0.920170	−	0.391519i	$-0.871950\pi$
$419$		−	16.0284i		−	0.783039i	0.920170	−	0.391519i	$-0.128050\pi$
$420$	2.04202	−	9.83855i	0.0996404	−	0.480072i
$421$	14.3788			0.700779			0.350389	−	0.936604i	$-0.386049\pi$
$421$	14.3788			0.700779			0.350389	+	0.936604i	$0.386049\pi$
$422$			2.10688i			0.102561i
$423$	−7.92421	+	18.2673i	−0.385288	+	0.888184i
$424$			11.0648i			0.537356i
$425$	−0.978245			−0.0474518
$426$	−17.1585	−	3.56131i	−0.831334	−	0.172546i
$427$	−9.03276			−0.437126
$428$	−2.71202			−0.131091
$429$	0.992981	+	9.22159i	0.0479416	+	0.445222i
$430$	−28.6184			−1.38010
$431$	13.1819			0.634951			0.317476	−	0.948266i	$-0.397165\pi$
$431$	13.1819			0.634951			0.317476	+	0.948266i	$0.397165\pi$
$432$	−54.0409	+	76.6752i	−2.60005	+	3.68904i
$433$	7.38090			0.354704			0.177352	−	0.984148i	$-0.443247\pi$
$433$	7.38090			0.354704			0.177352	+	0.984148i	$0.443247\pi$
$434$		−	24.6012i		−	1.18090i
$435$	−11.9856	−	2.48764i	−0.574664	−	0.119273i
$436$		−	5.36323i		−	0.256852i
$437$	2.81617			0.134716
$438$	−21.4709	−	4.45635i	−1.02592	−	0.212933i
$439$		−	30.5545i		−	1.45828i	−0.684362	−	0.729142i	$-0.739919\pi$
$439$		−	30.5545i		−	1.45828i	0.684362	−	0.729142i	$-0.260081\pi$
$440$	33.5151	−	10.8066i	1.59777	−	0.515184i
$441$	2.75221	+	1.19389i	0.131057	+	0.0568518i
$442$		−	4.41148i		−	0.209833i
$443$		−	30.1068i		−	1.43042i	−0.698911	−	0.715208i	$-0.746332\pi$
$443$		−	30.1068i		−	1.43042i	0.698911	−	0.715208i	$-0.253668\pi$
$444$	−12.8446	+	61.8860i	−0.609579	+	2.93698i
$445$	8.05214			0.381708
$446$	18.9727			0.898382
$447$	−2.14913	+	10.3546i	−0.101651	+	0.489757i
$448$		−	45.4200i		−	2.14589i
$449$		−	11.4414i		−	0.539954i	−0.962867	−	0.269977i	$-0.912984\pi$
$449$		−	11.4414i		−	0.539954i	0.962867	−	0.269977i	$-0.0870162\pi$
$450$	−7.68715	−	3.33463i	−0.362376	−	0.157196i
$451$	10.9912	+	34.0876i	0.517555	+	1.60512i
$452$			23.8361i			1.12116i
$453$	14.1962	+	2.94647i	0.666997	+	0.138437i
$454$	−17.3298			−0.813326
$455$			1.61455i			0.0756914i
$456$	−7.11315	−	1.47636i	−0.333104	−	0.0691367i
$457$			17.5847i			0.822579i	0.911505	+	0.411289i	$0.134921\pi$
$457$			17.5847i			0.822579i	−0.911505	+	0.411289i	$0.865079\pi$
$458$	−4.25312			−0.198735
$459$	−2.92835	+	4.15485i	−0.136684	+	0.193932i
$460$	41.3571			1.92828
$461$	−17.1269			−0.797680			−0.398840	−	0.917021i	$-0.630587\pi$
$461$	−17.1269			−0.797680			−0.398840	+	0.917021i	$0.630587\pi$
$462$	1.71780	+	15.9529i	0.0799195	+	0.742194i
$463$	38.7490			1.80082			0.900410	−	0.435043i	$-0.143267\pi$
$463$	38.7490			1.80082			0.900410	+	0.435043i	$0.143267\pi$
$464$	−127.586			−5.92304
$465$	−14.9374	−	3.10030i	−0.692704	−	0.143773i
$466$	18.0799			0.837533
$467$			3.28084i			0.151819i	0.997115	+	0.0759095i	$0.0241860\pi$
$467$			3.28084i			0.151819i	−0.997115	+	0.0759095i	$0.975814\pi$
$468$	11.1826	−	25.7787i	0.516918	−	1.19162i
$469$			10.4405i			0.482098i
$470$	−18.5386			−0.855122
$471$	−1.96411	+	9.46316i	−0.0905013	+	0.436039i
$472$			28.5566i			1.31442i
$473$	32.3429	−	10.4286i	1.48713	−	0.479509i
$474$	54.0111	+	11.2102i	2.48081	+	0.514900i
$475$		−	0.395037i		−	0.0181255i
$476$		−	5.67514i		−	0.260119i
$477$	−1.24419	+	2.86816i	−0.0569675	+	0.131324i
$478$	−33.6105			−1.53731
$479$	20.3560			0.930089			0.465044	−	0.885287i	$-0.346038\pi$
$479$	20.3560			0.930089			0.465044	+	0.885287i	$0.346038\pi$
$480$	−49.5009	−	10.2741i	−2.25939	−	0.468944i
$481$		−	10.1558i		−	0.463064i
$482$		−	13.9436i		−	0.635115i
$483$	−2.50930	+	12.0899i	−0.114177	+	0.550110i
$484$	−51.7952	+	37.2772i	−2.35433	+	1.69442i
$485$			9.28996i			0.421836i
$486$	−37.1743	+	22.6671i	−1.68626	+	1.02820i
$487$	6.40137			0.290074			0.145037	−	0.989426i	$-0.453670\pi$
$487$	6.40137			0.290074			0.145037	+	0.989426i	$0.453670\pi$
$488$			95.9053i			4.34143i
$489$	2.15830	−	10.3988i	0.0976015	−	0.470248i
$490$			2.79309i			0.126179i
$491$	40.9267			1.84699			0.923497	−	0.383606i	$-0.125318\pi$
$491$	40.9267			1.84699			0.923497	+	0.383606i	$0.125318\pi$
$492$	22.0515	−	106.245i	0.994159	−	4.78990i
$493$	−6.91359			−0.311373
$494$	1.78145			0.0801514
$495$	9.90273	+	0.967395i	0.445095	+	0.0434812i
$496$	−159.008			−7.13968
$497$	3.62237			0.162486
$498$	14.6172	−	70.4261i	0.655011	−	3.15587i
$499$	−17.7913			−0.796447			−0.398224	−	0.917288i	$-0.630373\pi$
$499$	−17.7913			−0.796447			−0.398224	+	0.917288i	$0.630373\pi$
$500$		−	5.80135i		−	0.259444i
$501$	−4.58258	+	22.0791i	−0.204735	+	0.986421i
$502$		−	64.4800i		−	2.87788i
$503$	−22.6998			−1.01213			−0.506066	−	0.862495i	$-0.668901\pi$
$503$	−22.6998			−1.01213			−0.506066	+	0.862495i	$0.668901\pi$
$504$	12.6761	−	29.2215i	0.564638	−	1.30163i
$505$		−	4.72191i		−	0.210122i
$506$	−62.8528	+	20.2662i	−2.79415	+	0.900943i
$507$	3.65832	−	17.6259i	0.162472	−	0.782796i
$508$			55.8451i			2.47773i
$509$		−	32.6377i		−	1.44664i	−0.690512	−	0.723321i	$-0.742615\pi$
$509$		−	32.6377i		−	1.44664i	0.690512	−	0.723321i	$-0.257385\pi$
$510$	−4.63377	−	0.961753i	−0.205187	−	0.0425871i
$511$	4.53276			0.200518
$512$	−143.583			−6.34551
$513$	−1.67782	−	1.18253i	−0.0740776	−	0.0522101i
$514$		−	60.6566i		−	2.67545i
$515$			1.58051i			0.0696454i
$516$	−100.807	−	20.9228i	−4.43779	−	0.921077i
$517$	20.9513	−	6.75552i	0.921437	−	0.297107i
$518$		−	17.5690i		−	0.771936i
$519$	2.35494	−	11.3462i	0.103370	−	0.498043i
$520$	17.1425			0.751748
$521$			24.9611i			1.09356i	0.837275	+	0.546782i	$0.184147\pi$
$521$			24.9611i			1.09356i	−0.837275	+	0.546782i	$0.815853\pi$
$522$	−54.3278	−	23.5670i	−2.37786	−	1.03150i
$523$		−	30.3151i		−	1.32559i	−0.748803	−	0.662793i	$-0.769371\pi$
$523$		−	30.3151i		−	1.32559i	0.748803	−	0.662793i	$-0.230629\pi$
$524$	−62.3555			−2.72401
$525$	1.69591	+	0.351991i	0.0740155	+	0.0153621i
$526$	−8.01033			−0.349267
$527$	−8.61628			−0.375331
$528$	103.110	−	11.1029i	4.48729	−	0.483192i
$529$	−27.8209			−1.20961
$530$	−2.91077			−0.126436
$531$	−3.21106	+	7.40227i	−0.139348	+	0.321231i
$532$	2.29175			0.0993598
$533$			17.4353i			0.755209i
$534$	38.1415	+	7.91639i	1.65055	+	0.342576i
$535$		−	0.467482i		−	0.0202110i
$536$	110.852			4.78808
$537$	−8.50717	−	1.76569i	−0.367112	−	0.0761951i
$538$			71.8764i			3.09881i
$539$	−1.01781	−	3.15659i	−0.0438401	−	0.135964i
$540$	−24.6398	−	17.3662i	−1.06033	−	0.747321i
$541$		−	37.2597i		−	1.60192i	−0.598719	−	0.800959i	$-0.704323\pi$
$541$		−	37.2597i		−	1.60192i	0.598719	−	0.800959i	$-0.295677\pi$
$542$			52.1714i			2.24095i
$543$	−6.33425	+	30.5187i	−0.271829	+	1.30968i
$544$	−28.5534			−1.22422
$545$	0.924480			0.0396004
$546$	−1.58733	+	7.64784i	−0.0679316	+	0.327297i
$547$		−	15.7536i		−	0.673573i	−0.941581	−	0.336787i	$-0.890660\pi$
$547$		−	15.7536i		−	0.673573i	0.941581	−	0.336787i	$-0.109340\pi$
$548$		−	6.60135i		−	0.281996i
$549$	−10.7841	+	24.8600i	−0.460254	+	1.06100i
$550$	2.84283	+	8.81664i	0.121219	+	0.375943i
$551$		−	2.79186i		−	0.118937i
$552$	128.365	+	26.6425i	5.46356	+	1.13398i
$553$	−11.4024			−0.484879
$554$		−	13.5909i		−	0.577424i
$555$	−10.6675	−	2.21408i	−0.452811	−	0.0939823i
$556$		−	57.3177i		−	2.43081i
$557$	−13.3993			−0.567747			−0.283873	−	0.958862i	$-0.591619\pi$
$557$	−13.3993			−0.567747			−0.283873	+	0.958862i	$0.591619\pi$
$558$	−67.7077	−	29.3711i	−2.86629	−	1.24338i
$559$	16.5429			0.699692
$560$	18.0529			0.762875
$561$	5.58729	−	0.601640i	0.235896	−	0.0254012i
$562$	38.4321			1.62116
$563$	−16.8012			−0.708086			−0.354043	−	0.935229i	$-0.615193\pi$
$563$	−16.8012			−0.708086			−0.354043	+	0.935229i	$0.615193\pi$
$564$	−65.3015	−	13.5535i	−2.74969	−	0.570707i
$565$	−4.10873			−0.172855
$566$			39.8818i			1.67636i
$567$	6.57165	−	6.14926i	0.275983	−	0.258245i
$568$		−	38.4605i		−	1.61377i
$569$	32.3634			1.35674			0.678371	−	0.734719i	$-0.262686\pi$
$569$	32.3634			1.35674			0.678371	+	0.734719i	$0.262686\pi$
$570$	0.388377	−	1.87122i	0.0162673	−	0.0783768i
$571$			44.7809i			1.87402i	0.349297	+	0.937012i	$0.386420\pi$
$571$			44.7809i			1.87402i	−0.349297	+	0.937012i	$0.613580\pi$
$572$	−29.5664	+	9.53339i	−1.23624	+	0.398611i
$573$	−9.13997	−	1.89703i	−0.381828	−	0.0792495i
$574$			30.1622i			1.25895i
$575$			7.12888i			0.297295i
$576$	−125.005	−	54.2264i	−5.20855	−	2.25943i
$577$	−16.4375			−0.684302			−0.342151	−	0.939645i	$-0.611156\pi$
$577$	−16.4375			−0.684302			−0.342151	+	0.939645i	$0.611156\pi$
$578$	44.8096			1.86383
$579$	30.3684	+	6.30305i	1.26207	+	0.261946i
$580$		−	41.0001i		−	1.70244i
$581$			14.8678i			0.616821i
$582$	−9.13335	+	44.0049i	−0.378589	+	1.82406i
$583$	3.28958	−	1.06069i	0.136241	−	0.0439293i
$584$		−	48.1266i		−	1.99149i
$585$	4.44358	+	1.92759i	0.183719	+	0.0796962i
$586$	49.0268			2.02528
$587$		−	3.92954i		−	0.162189i	−0.996706	−	0.0810947i	$-0.974158\pi$
$587$		−	3.92954i		−	0.162189i	0.996706	−	0.0810947i	$-0.0258416\pi$
$588$	−2.04202	+	9.83855i	−0.0842115	+	0.405735i
$589$		−	3.47945i		−	0.143368i
$590$	−7.51224			−0.309274
$591$	−2.63494	+	12.6953i	−0.108387	+	0.522213i
$592$	−113.556			−4.66711
$593$	−14.1574			−0.581375			−0.290688	−	0.956818i	$-0.593884\pi$
$593$	−14.1574			−0.581375			−0.290688	+	0.956818i	$0.593884\pi$
$594$	45.9564	+	14.3182i	1.88561	+	0.587481i
$595$	0.978245			0.0401041
$596$	−35.4210			−1.45090
$597$	−1.28658	+	6.19882i	−0.0526564	+	0.253701i
$598$	−32.1483			−1.31464
$599$			35.7844i			1.46211i	0.682317	+	0.731056i	$0.260972\pi$
$599$			35.7844i			1.46211i	−0.682317	+	0.731056i	$0.739028\pi$
$600$	3.73726	−	18.0063i	0.152573	−	0.735104i
$601$			36.5050i			1.48907i	0.667584	+	0.744534i	$0.267328\pi$
$601$			36.5050i			1.48907i	−0.667584	+	0.744534i	$0.732672\pi$
$602$	28.6184			1.16640
$603$	28.7344	+	12.4648i	1.17016	+	0.507605i
$604$			48.5623i			1.97597i
$605$	−6.42561	−	8.92813i	−0.261238	−	0.362980i
$606$	4.64230	−	22.3668i	0.188581	−	0.908590i
$607$		−	37.7732i		−	1.53317i	−0.642145	−	0.766583i	$-0.721955\pi$
$607$		−	37.7732i		−	1.53317i	0.642145	−	0.766583i	$-0.278045\pi$
$608$		−	11.5305i		−	0.467624i
$609$	11.9856	+	2.48764i	0.485680	+	0.100804i
$610$	−25.2293			−1.02150
$611$	10.7163			0.433535
$612$	−15.6191	−	6.77547i	−0.631366	−	0.273882i
$613$			22.2930i			0.900406i	0.892926	+	0.450203i	$0.148648\pi$
$613$			22.2930i			0.900406i	−0.892926	+	0.450203i	$0.851352\pi$
$614$			45.6128i			1.84078i
$615$	18.3139	+	3.80110i	0.738488	+	0.153275i
$616$	−33.5151	+	10.8066i	−1.35036	+	0.435410i
$617$			38.2785i			1.54103i	0.637420	+	0.770517i	$0.280002\pi$
$617$			38.2785i			1.54103i	−0.637420	+	0.770517i	$0.719998\pi$
$618$	−1.55386	+	7.48657i	−0.0625054	+	0.301154i
$619$	18.0790			0.726658			0.363329	−	0.931661i	$-0.381640\pi$
$619$	18.0790			0.726658			0.363329	+	0.931661i	$0.381640\pi$
$620$		−	51.0977i		−	2.05213i
$621$	30.2781	+	21.3401i	1.21502	+	0.856349i
$622$		−	5.28306i		−	0.211832i
$623$	−8.05214			−0.322602
$624$	49.4313	+	10.2596i	1.97883	+	0.410713i
$625$	1.00000			0.0400000
$626$	75.9221			3.03446
$627$	0.242956	+	2.25627i	0.00970271	+	0.0901068i
$628$	−32.3715			−1.29176
$629$	−6.15331			−0.245349
$630$	7.68715	+	3.33463i	0.306264	+	0.132855i
$631$	−6.42461			−0.255760			−0.127880	−	0.991790i	$-0.540817\pi$
$631$	−6.42461			−0.255760			−0.127880	+	0.991790i	$0.540817\pi$
$632$			121.065i			4.81570i
$633$	−1.27926	−	0.265513i	−0.0508458	−	0.0105532i
$634$		−	11.6152i		−	0.461300i
$635$	−9.62624			−0.382006
$636$	−10.2531	−	2.12805i	−0.406560	−	0.0843828i
$637$		−	1.61455i		−	0.0639709i
$638$	20.0913	+	62.3102i	0.795421	+	2.46689i
$639$	4.32471	−	9.96951i	0.171083	−	0.394388i
$640$		−	68.4853i		−	2.70712i
$641$			14.2895i			0.564403i	0.959355	+	0.282201i	$0.0910646\pi$
$641$			14.2895i			0.564403i	−0.959355	+	0.282201i	$0.908935\pi$
$642$	0.459600	−	2.21438i	0.0181390	−	0.0873945i
$643$	23.2944			0.918643			0.459322	−	0.888270i	$-0.348093\pi$
$643$	23.2944			0.918643			0.459322	+	0.888270i	$0.348093\pi$
$644$	−41.3571			−1.62970
$645$	3.60655	−	17.3765i	0.142008	−	0.684200i
$646$		−	1.07937i		−	0.0424672i
$647$		−	6.27095i		−	0.246536i	−0.992373	−	0.123268i	$-0.960662\pi$
$647$		−	6.27095i		−	0.246536i	0.992373	−	0.123268i	$-0.0393375\pi$
$648$	−65.2898	−	69.7744i	−2.56483	−	2.74100i
$649$	8.48990	−	2.73748i	0.333258	−	0.107455i
$650$			4.50959i			0.176881i
$651$	14.9374	+	3.10030i	0.585442	+	0.121510i
$652$	35.5720			1.39311
$653$			17.2078i			0.673395i	0.941613	+	0.336697i	$0.109310\pi$
$653$			17.2078i			0.673395i	−0.941613	+	0.336697i	$0.890690\pi$
$654$	4.37909	+	0.908894i	0.171236	+	0.0355406i
$655$		−	10.7484i		−	0.419977i
$656$	194.951			7.61157
$657$	5.41161	−	12.4751i	0.211127	−	0.486700i
$658$	18.5386			0.722710
$659$	−11.2786			−0.439351			−0.219675	−	0.975573i	$-0.570500\pi$
$659$	−11.2786			−0.439351			−0.219675	+	0.975573i	$0.570500\pi$
$660$	3.56794	+	33.1346i	0.138882	+	1.28976i
$661$	17.8112			0.692774			0.346387	−	0.938092i	$-0.387408\pi$
$661$	17.8112			0.692774			0.346387	+	0.938092i	$0.387408\pi$
$662$	−34.2601			−1.33156
$663$	2.67856	+	0.555944i	0.104027	+	0.0215911i
$664$	157.859			6.12611
$665$			0.395037i			0.0153189i
$666$	−48.3534	−	20.9754i	−1.87366	−	0.812779i
$667$			50.3823i			1.95081i
$668$	−75.5279			−2.92226
$669$	−2.39098	+	11.5198i	−0.0924404	+	0.445382i
$670$			29.1612i			1.12660i
$671$	28.5127	−	9.19363i	1.10072	−	0.354916i
$672$	49.5009	+	10.2741i	1.90954	+	0.396330i
$673$		−	50.7390i		−	1.95585i	−0.208966	−	0.977923i	$-0.567010\pi$
$673$		−	50.7390i		−	1.95585i	0.208966	−	0.977923i	$-0.432990\pi$
$674$		−	78.9535i		−	3.04118i
$675$	2.99347	−	4.24725i	0.115219	−	0.163477i
$676$	60.2947			2.31903
$677$	−22.5241			−0.865672			−0.432836	−	0.901473i	$-0.642487\pi$
$677$	−22.5241			−0.865672			−0.432836	+	0.901473i	$0.642487\pi$
$678$	−19.4623	−	4.03946i	−0.747445	−	0.155135i
$679$		−	9.28996i		−	0.356516i
$680$		−	10.3865i		−	0.398304i
$681$	2.18393	−	10.5223i	0.0836885	−	0.403215i
$682$	25.0394	+	77.6561i	0.958807	+	2.97360i
$683$			39.0405i			1.49384i	0.664912	+	0.746922i	$0.268469\pi$
$683$			39.0405i			1.49384i	−0.664912	+	0.746922i	$0.731531\pi$
$684$	2.73609	−	6.30736i	0.104617	−	0.241168i
$685$	1.13790			0.0434769
$686$		−	2.79309i		−	0.106641i
$687$	0.535987	−	2.58241i	0.0204492	−	0.0985250i
$688$		−	184.973i		−	7.05202i
$689$	1.68258			0.0641010
$690$	−7.00870	+	33.7682i	−0.266817	+	1.28553i
$691$	−6.07285			−0.231022			−0.115511	−	0.993306i	$-0.536851\pi$
$691$	−6.07285			−0.231022			−0.115511	+	0.993306i	$0.536851\pi$
$692$	38.8130			1.47545
$693$	−9.90273	−	0.967395i	−0.376174	−	0.0367483i
$694$	−29.0379			−1.10226
$695$	9.88007			0.374772
$696$	26.4125	−	127.257i	1.00116	−	4.82365i
$697$	10.5639			0.400138
$698$		−	14.4540i		−	0.547090i
$699$	−2.27846	+	10.9777i	−0.0861793	+	0.415216i
$700$			5.80135i			0.219270i
$701$	8.73966			0.330092			0.165046	−	0.986286i	$-0.447223\pi$
$701$	8.73966			0.330092			0.165046	+	0.986286i	$0.447223\pi$
$702$	19.1533	+	13.4993i	0.722896	+	0.509499i
$703$		−	2.48484i		−	0.0937177i
$704$	46.2289	+	143.372i	1.74232	+	5.40355i
$705$	2.33627	−	11.2563i	0.0879892	−	0.423936i
$706$			30.9655i			1.16540i
$707$			4.72191i			0.177586i
$708$	−26.4616	−	5.49218i	−0.994486	−	0.206409i
$709$	−17.5568			−0.659358			−0.329679	−	0.944093i	$-0.606941\pi$
$709$	−17.5568			−0.659358			−0.329679	+	0.944093i	$0.606941\pi$
$710$	10.1176			0.379707
$711$	−13.6132	+	31.3817i	−0.510534	+	1.17691i
$712$			85.4935i			3.20401i
$713$			62.7905i			2.35152i
$714$	4.63377	+	0.961753i	0.173414	+	0.0359927i
$715$	−1.64331	−	5.09648i	−0.0614562	−	0.190598i
$716$		−	29.1013i		−	1.08756i
$717$	4.23567	−	20.4076i	0.158184	−	0.762137i
$718$	−82.2700			−3.07029
$719$		−	29.6860i		−	1.10710i	−0.832816	−	0.553550i	$-0.813273\pi$
$719$		−	29.6860i		−	1.10710i	0.832816	−	0.553550i	$-0.186727\pi$
$720$	21.5532	−	49.6853i	0.803239	−	1.85166i
$721$		−	1.58051i		−	0.0588611i
$722$	−52.6328			−1.95879
$723$	8.46630	+	1.75721i	0.314865	+	0.0653512i
$724$	−104.398			−3.87992
$725$	7.06734			0.262475
$726$	−21.6594	−	48.6082i	−0.803855	−	1.80402i
$727$	−3.54441			−0.131455			−0.0657274	−	0.997838i	$-0.520937\pi$
$727$	−3.54441			−0.131455			−0.0657274	+	0.997838i	$0.520937\pi$
$728$	−17.1425			−0.635343
$729$	−9.07823	−	25.4281i	−0.336231	−	0.941780i
$730$	12.6604			0.468583
$731$		−	10.0232i		−	0.370723i
$732$	−88.8693	−	18.4451i	−3.28470	−	0.681750i
$733$		−	20.6329i		−	0.762095i	−0.924555	−	0.381047i	$-0.875563\pi$
$733$		−	20.6329i		−	0.762095i	0.924555	−	0.381047i	$-0.124437\pi$
$734$	−90.4323			−3.33792
$735$	−1.69591	−	0.351991i	−0.0625545	−	0.0129834i
$736$			208.081i			7.66996i
$737$	−10.6264	−	32.9564i	−0.391430	−	1.21396i
$738$	83.0126	+	36.0103i	3.05574	+	1.32556i
$739$		−	2.54454i		−	0.0936026i	−0.998904	−	0.0468013i	$-0.985097\pi$
$739$		−	2.54454i		−	0.0936026i	0.998904	−	0.0468013i	$-0.0149028\pi$
$740$		−	36.4914i		−	1.34145i
$741$	−0.224502	+	1.08166i	−0.00824730	+	0.0397359i
$742$	2.91077			0.106858
$743$	27.0239			0.991411			0.495706	−	0.868491i	$-0.334909\pi$
$743$	27.0239			0.991411			0.495706	+	0.868491i	$0.334909\pi$
$744$	32.9174	−	158.598i	1.20681	−	5.81447i
$745$		−	6.10566i		−	0.223694i
$746$		−	9.77346i		−	0.357832i
$747$	40.9193	+	17.7505i	1.49716	+	0.649457i
$748$	5.77621	+	17.9141i	0.211199	+	0.655004i
$749$			0.467482i			0.0170814i
$750$	4.73682	+	0.983141i	0.172964	+	0.0358993i
$751$	18.7563			0.684426			0.342213	−	0.939622i	$-0.388824\pi$
$751$	18.7563			0.684426			0.342213	+	0.939622i	$0.388824\pi$
$752$		−	119.823i		−	4.36949i
$753$	39.1509	+	8.12590i	1.42674	+	0.296124i
$754$			31.8708i			1.16067i
$755$	−8.37087			−0.304647
$756$	24.6398	+	17.3662i	0.896139	+	0.631602i
$757$	36.8368			1.33886			0.669429	−	0.742876i	$-0.266539\pi$
$757$	36.8368			1.33886			0.669429	+	0.742876i	$0.266539\pi$
$758$	34.8465			1.26568
$759$	−4.38440	−	40.7169i	−0.159144	−	1.47793i
$760$	4.19430			0.152143
$761$	−33.9015			−1.22893			−0.614463	−	0.788945i	$-0.710627\pi$
$761$	−33.9015			−1.22893			−0.614463	+	0.788945i	$0.710627\pi$
$762$	−45.5978	−	9.46395i	−1.65183	−	0.342843i
$763$	−0.924480			−0.0334684
$764$		−	31.2659i		−	1.13116i
$765$	1.16791	−	2.69233i	0.0422260	−	0.0973414i
$766$		−	55.9439i		−	2.02134i
$767$	4.34247			0.156797
$768$	35.3559	−	170.346i	1.27580	−	6.14684i
$769$		−	41.4811i		−	1.49585i	−0.663785	−	0.747924i	$-0.731051\pi$
$769$		−	41.4811i		−	1.49585i	0.663785	−	0.747924i	$-0.268949\pi$
$770$	−2.84283	−	8.81664i	−0.102449	−	0.317730i
$771$	36.8295	+	7.64407i	1.32638	+	0.275294i
$772$			103.884i			3.73886i
$773$		−	41.1606i		−	1.48044i	−0.672363	−	0.740222i	$-0.734721\pi$
$773$		−	41.1606i		−	1.48044i	0.672363	−	0.740222i	$-0.265279\pi$
$774$	34.1672	−	78.7637i	1.22811	−	2.83110i
$775$	8.80790			0.316389
$776$	−98.6362			−3.54083
$777$	10.6675	+	2.21408i	0.382695	+	0.0794295i
$778$			83.3266i			2.98740i
$779$			4.26596i			0.152844i
$780$	−3.29695	+	15.8848i	−0.118050	+	0.568769i
$781$	−11.4344	+	3.68689i	−0.409153	+	0.131927i
$782$			19.4784i			0.696547i
$783$	21.1559	−	30.0168i	0.756051	−	1.07271i
$784$	−18.0529			−0.644747
$785$		−	5.57999i		−	0.199159i
$786$	10.5672	−	50.9135i	0.376921	−	1.81602i
$787$			3.10764i			0.110775i	0.998465	+	0.0553877i	$0.0176395\pi$
$787$			3.10764i			0.110775i	−0.998465	+	0.0553877i	$0.982361\pi$
$788$	−43.4278			−1.54705
$789$	1.00948	−	4.86371i	0.0359384	−	0.173153i
$790$	−31.8479			−1.13310
$791$	4.10873			0.146090
$792$	−10.2713	+	105.142i	−0.364975	+	3.73607i
$793$	14.5839			0.517888
$794$	−72.2509			−2.56409
$795$	0.366821	−	1.76736i	0.0130098	−	0.0626818i
$796$	−21.2049			−0.751586
$797$			20.7244i			0.734095i	0.930202	+	0.367047i	$0.119631\pi$
$797$			20.7244i			0.734095i	−0.930202	+	0.367047i	$0.880369\pi$
$798$	−0.388377	+	1.87122i	−0.0137484	+	0.0662405i
$799$		−	6.49292i		−	0.229703i
$800$	29.1884			1.03197
$801$	−9.61335	+	22.1611i	−0.339671	+	0.783025i
$802$			57.2710i			2.02231i
$803$	−14.3081	+	4.61349i	−0.504921	+	0.162807i
$804$	−21.3197	+	102.719i	−0.751888	+	3.62263i
$805$		−	7.12888i		−	0.251260i
$806$			39.7200i			1.39908i
$807$	−43.6419	−	9.05802i	−1.53627	−	0.318857i
$808$	50.1348			1.76374
$809$	10.9192			0.383898			0.191949	−	0.981405i	$-0.438519\pi$
$809$	10.9192			0.383898			0.191949	+	0.981405i	$0.438519\pi$
$810$	18.3552	−	17.1754i	0.644936	−	0.603484i
$811$			21.8350i			0.766730i	0.923597	+	0.383365i	$0.125235\pi$
$811$			21.8350i			0.766730i	−0.923597	+	0.383365i	$0.874765\pi$
$812$			41.0001i			1.43882i
$813$	−31.6774	−	6.57474i	−1.11098	−	0.230586i
$814$	17.8818	+	55.4580i	0.626759	+	1.94380i
$815$			6.13168i			0.214783i
$816$	6.21622	−	29.9500i	0.217611	−	1.04846i
$817$	4.04761			0.141608
$818$		−	69.8586i		−	2.44255i
$819$	−4.44358	−	1.92759i	−0.155271	−	0.0673556i
$820$			62.6480i			2.18776i
$821$	−17.3306			−0.604842			−0.302421	−	0.953175i	$-0.597795\pi$
$821$	−17.3306			−0.604842			−0.302421	+	0.953175i	$0.597795\pi$
$822$	5.39003	+	1.11872i	0.187999	+	0.0390197i
$823$	−16.3188			−0.568837			−0.284419	−	0.958700i	$-0.591801\pi$
$823$	−16.3188			−0.568837			−0.284419	+	0.958700i	$0.591801\pi$
$824$	−16.7810			−0.584594
$825$	−5.71155	+	0.615020i	−0.198850	+	0.0214122i
$826$	7.51224			0.261384
$827$	40.7311			1.41636			0.708179	−	0.706033i	$-0.249517\pi$
$827$	40.7311			1.41636			0.708179	+	0.706033i	$0.249517\pi$
$828$	−49.3757	+	113.823i	−1.71593	+	3.95563i
$829$	9.19341			0.319300			0.159650	−	0.987174i	$-0.448963\pi$
$829$	9.19341			0.319300			0.159650	+	0.987174i	$0.448963\pi$
$830$			41.5271i			1.44143i
$831$	8.25215	+	1.71276i	0.286264	+	0.0594150i
$832$			73.3330i			2.54236i
$833$	−0.978245			−0.0338942
$834$	46.8001	+	9.71351i	1.62056	+	0.336351i
$835$		−	13.0190i		−	0.450542i
$836$	−7.23410	+	2.33256i	−0.250197	+	0.0806733i
$837$	26.3662	−	37.4093i	0.911350	−	1.29306i
$838$			44.7688i			1.54651i
$839$			3.38362i			0.116816i	0.998293	+	0.0584078i	$0.0186024\pi$
$839$			3.38362i			0.116816i	−0.998293	+	0.0584078i	$0.981398\pi$
$840$	−3.73726	+	18.0063i	−0.128948	+	0.621276i
$841$	20.9474			0.722323
$842$	−40.1612			−1.38405
$843$	−4.84329	+	23.3352i	−0.166812	+	0.803706i
$844$		−	4.37607i		−	0.150630i
$845$			10.3932i			0.357538i
$846$	22.1330	−	51.0221i	0.760949	−	1.75417i
$847$	6.42561	+	8.92813i	0.220787	+	0.306774i
$848$		−	18.8135i		−	0.646059i
$849$	−24.2154	−	5.02599i	−0.831072	−	0.172491i
$850$	2.73232			0.0937180
$851$			44.8418i			1.53716i
$852$	35.6389	+	7.39696i	1.22097	+	0.253416i
$853$		−	28.1668i		−	0.964412i	−0.876058	−	0.482206i	$-0.839836\pi$
$853$		−	28.1668i		−	0.964412i	0.876058	−	0.482206i	$-0.160164\pi$
$854$	25.2293			0.863329
$855$	1.08722	+	0.471630i	0.0371822	+	0.0161294i
$856$	4.96348			0.169648
$857$	42.6131			1.45563			0.727817	−	0.685771i	$-0.240535\pi$
$857$	42.6131			1.45563			0.727817	+	0.685771i	$0.240535\pi$
$858$	−2.77348	−	25.7567i	−0.0946852	−	0.879320i
$859$	−53.4234			−1.82278			−0.911392	−	0.411540i	$-0.864991\pi$
$859$	−53.4234			−1.82278			−0.911392	+	0.411540i	$0.864991\pi$
$860$	59.4414			2.02694
$861$	−18.3139	−	3.80110i	−0.624136	−	0.129541i
$862$	−36.8183			−1.25404
$863$			30.9333i			1.05298i	0.850181	+	0.526491i	$0.176493\pi$
$863$			30.9333i			1.05298i	−0.850181	+	0.526491i	$0.823507\pi$
$864$	87.3748	−	123.970i	2.97255	−	4.21756i
$865$			6.69034i			0.227478i
$866$	−20.6155			−0.700544
$867$	−5.64700	+	27.2075i	−0.191782	+	0.924015i
$868$			51.0977i			1.73437i
$869$	35.9927	−	11.6055i	1.22097	−	0.393689i
$870$	33.4767	+	6.94820i	1.13497	+	0.235566i
$871$		−	16.8567i		−	0.571169i
$872$			9.81566i			0.332400i
$873$	−25.5679	−	11.0912i	−0.865342	−	0.375379i
$874$	−7.86582			−0.266065
$875$	−1.00000			−0.0338062
$876$	44.5958	+	9.25600i	1.50675	+	0.312731i
$877$			19.5951i			0.661679i	0.943687	+	0.330839i	$0.107332\pi$
$877$			19.5951i			0.661679i	−0.943687	+	0.330839i	$0.892668\pi$
$878$			85.3413i			2.88013i
$879$	−6.17846	+	29.7681i	−0.208394	+	1.00405i
$880$	−56.9857	+	18.3744i	−1.92099	+	0.619402i
$881$		−	30.2490i		−	1.01911i	−0.860437	−	0.509557i	$-0.829809\pi$
$881$		−	30.2490i		−	1.01911i	0.860437	−	0.509557i	$-0.170191\pi$
$882$	−7.68715	−	3.33463i	−0.258840	−	0.112283i
$883$	−39.6717			−1.33506			−0.667530	−	0.744583i	$-0.732648\pi$
$883$	−39.6717			−1.33506			−0.667530	+	0.744583i	$0.732648\pi$
$884$			9.16280i			0.308178i
$885$	0.946707	−	4.56128i	0.0318232	−	0.153326i
$886$			84.0909i			2.82509i
$887$	−18.6826			−0.627301			−0.313651	−	0.949538i	$-0.601552\pi$
$887$	−18.6826			−0.627301			−0.313651	+	0.949538i	$0.601552\pi$
$888$	23.5079	−	113.262i	0.788875	−	3.80084i
$889$	9.62624			0.322854
$890$	−22.4903			−0.753878
$891$	−14.4852	+	26.0994i	−0.485273	+	0.874363i
$892$	−39.4069			−1.31944
$893$	2.62199			0.0877414
$894$	6.00272	−	28.9214i	0.200761	−	0.967276i
$895$	5.01629			0.167676
$896$			68.4853i			2.28793i
$897$	4.05140	−	19.5198i	0.135272	−	0.651747i
$898$			31.9569i			1.06642i
$899$	62.2485			2.07610
$900$	15.9665	+	6.92615i	0.532216	+	0.230872i
$901$		−	1.01946i		−	0.0339631i
$902$	−30.6994	−	95.2098i	−1.02218	−	3.17014i
$903$	−3.60655	+	17.3765i	−0.120018	+	0.578254i
$904$		−	43.6244i		−	1.45093i
$905$		−	17.9955i		−	0.598190i
$906$	−39.6513	−	8.22975i	−1.31733	−	0.273415i
$907$	−26.2014			−0.870004			−0.435002	−	0.900429i	$-0.643252\pi$
$907$	−26.2014			−0.870004			−0.435002	+	0.900429i	$0.643252\pi$
$908$	35.9946			1.19452
$909$	12.9957	+	5.63743i	0.431039	+	0.186982i
$910$		−	4.50959i		−	0.149491i
$911$			9.73533i			0.322546i	0.986910	+	0.161273i	$0.0515600\pi$
$911$			9.73533i			0.322546i	−0.986910	+	0.161273i	$0.948440\pi$
$912$	12.0945	+	2.51025i	0.400488	+	0.0831226i
$913$	−15.1326	−	46.9316i	−0.500816	−	1.55321i
$914$		−	49.1157i		−	1.62460i
$915$	3.17945	−	15.3187i	0.105109	−	0.506422i
$916$	8.83388			0.291880
$917$			10.7484i			0.354945i
$918$	8.17914	−	11.6049i	0.269952	−	0.383017i
$919$			18.3036i			0.603781i	0.953343	+	0.301891i	$0.0976178\pi$
$919$			18.3036i			0.603781i	−0.953343	+	0.301891i	$0.902382\pi$
$920$	−75.6909			−2.49545
$921$	−27.6952	−	5.74822i	−0.912588	−	0.189410i
$922$	47.8370			1.57543
$923$	−5.84851			−0.192506
$924$	−3.56794	−	33.1346i	−0.117377	−	1.09005i
$925$	6.29015			0.206819
$926$	−108.229			−3.55664
$927$	−4.34987	−	1.88695i	−0.142869	−	0.0619754i
$928$	206.285			6.77162
$929$		−	3.40185i		−	0.111611i	−0.998442	−	0.0558055i	$-0.982227\pi$
$929$		−	3.40185i		−	0.111611i	0.998442	−	0.0558055i	$-0.0177727\pi$
$930$	41.7214	+	8.65941i	1.36810	+	0.283953i
$931$		−	0.395037i		−	0.0129468i
$932$	−37.5525			−1.23007
$933$	3.20777	+	0.665782i	0.105018	+	0.0217967i
$934$		−	9.16367i		−	0.299844i
$935$	−3.08792	+	0.995666i	−0.100986	+	0.0325618i
$936$	−20.4662	+	47.1797i	−0.668959	+	1.54212i
$937$			0.534100i			0.0174483i	0.999962	+	0.00872414i	$0.00277701\pi$
$937$			0.534100i			0.0174483i	−0.999962	+	0.00872414i	$0.997223\pi$
$938$		−	29.1612i		−	0.952149i
$939$	−9.56786	+	46.0984i	−0.312235	+	1.50436i
$940$	38.5054			1.25591
$941$	−27.7277			−0.903898			−0.451949	−	0.892044i	$-0.649271\pi$
$941$	−27.7277			−0.903898			−0.451949	+	0.892044i	$0.649271\pi$
$942$	5.48592	−	26.4314i	0.178741	−	0.861183i
$943$		−	76.9839i		−	2.50694i
$944$		−	48.5548i		−	1.58032i
$945$	−2.99347	+	4.24725i	−0.0973777	+	0.138163i
$946$	−90.3366	+	29.1281i	−2.93710	+	0.947035i
$947$			44.0022i			1.42988i	0.699186	+	0.714940i	$0.253546\pi$
$947$			44.0022i			1.42988i	−0.699186	+	0.714940i	$0.746454\pi$
$948$	−112.183	−	23.2839i	−3.64354	−	0.756227i
$949$	−7.31838			−0.237565
$950$			1.10337i			0.0357982i
$951$	7.05253	+	1.46377i	0.228694	+	0.0474661i
$952$			10.3865i			0.336629i
$953$	−34.3690			−1.11332			−0.556660	−	0.830740i	$-0.687917\pi$
$953$	−34.3690			−1.11332			−0.556660	+	0.830740i	$0.687917\pi$
$954$	3.47513	−	8.01103i	0.112511	−	0.259367i
$955$	5.38943			0.174398
$956$	69.8102			2.25782
$957$	−40.3655	+	4.34656i	−1.30483	+	0.140504i
$958$	−56.8561			−1.83694
$959$	−1.13790			−0.0367447
$960$	77.0281	+	15.9874i	2.48607	+	0.515992i
$961$	46.5791			1.50255
$962$			28.3660i			0.914557i
$963$	1.28661	+	0.558120i	0.0414603	+	0.0179852i
$964$			28.9614i			0.932785i
$965$	−17.9069			−0.576442
$966$	7.00870	−	33.7682i	0.225501	−	1.08647i
$967$		−	14.1092i		−	0.453720i	−0.973927	−	0.226860i	$-0.927154\pi$
$967$		−	14.1092i		−	0.453720i	0.973927	−	0.226860i	$-0.0728460\pi$
$968$	94.7944	−	68.2239i	3.04681	−	2.19280i
$969$	0.655371	+	0.136024i	0.0210536	+	0.00436973i
$970$		−	25.9477i		−	0.833130i
$971$		−	40.4514i		−	1.29815i	−0.760726	−	0.649074i	$-0.775157\pi$
$971$		−	40.4514i		−	1.29815i	0.760726	−	0.649074i	$-0.224843\pi$
$972$	77.2124	−	47.0804i	2.47659	−	1.51010i
$973$	−9.88007			−0.316740
$974$	−17.8796			−0.572899
$975$	−2.73813	−	0.568307i	−0.0876904	−	0.0182004i
$976$		−	163.068i		−	5.21967i
$977$		−	29.4790i		−	0.943116i	−0.881835	−	0.471558i	$-0.843692\pi$
$977$		−	29.4790i		−	0.943116i	0.881835	−	0.471558i	$-0.156308\pi$
$978$	−6.02831	+	29.0447i	−0.192764	+	0.928746i
$979$	25.4173	−	8.19554i	0.812340	−	0.261931i
$980$		−	5.80135i		−	0.185317i
$981$	−1.10372	+	2.54436i	−0.0352392	+	0.0812351i
$982$	−114.312			−3.64784
$983$		−	46.1126i		−	1.47076i	−0.677654	−	0.735381i	$-0.737003\pi$
$983$		−	46.1126i		−	1.47076i	0.677654	−	0.735381i	$-0.262997\pi$
$984$	−40.3582	+	194.448i	−1.28657	+	6.19877i
$985$		−	7.48582i		−	0.238518i
$986$	19.3103			0.614965
$987$	−2.33627	+	11.2563i	−0.0743644	+	0.358291i
$988$	−3.70014			−0.117717
$989$	−73.0436			−2.32265
$990$	−27.6592	−	2.70202i	−0.879068	−	0.0858758i
$991$	−8.28076			−0.263047			−0.131524	−	0.991313i	$-0.541987\pi$
$991$	−8.28076			−0.263047			−0.131524	+	0.991313i	$0.541987\pi$
$992$	257.089			8.16257
$993$	4.31752	−	20.8020i	0.137012	−	0.660132i
$994$	−10.1176			−0.320911
$995$		−	3.65516i		−	0.115876i
$996$	−30.3604	+	146.278i	−0.962005	+	4.63498i
$997$		−	44.3712i		−	1.40525i	−0.711561	−	0.702624i	$-0.752012\pi$
$997$		−	44.3712i		−	1.40525i	0.711561	−	0.702624i	$-0.247988\pi$
$998$	49.6926			1.57299
$999$	18.8294	−	26.7158i	0.595736	−	0.845252i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1155.2.l.e.1121.1	✓	40
3.2	odd	2		1155.2.l.f.1121.40	yes	40
11.10	odd	2		1155.2.l.f.1121.39	yes	40
33.32	even	2	inner	1155.2.l.e.1121.2	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1155.2.l.e.1121.1	✓	40	1.1	even	1	trivial
1155.2.l.e.1121.2	yes	40	33.32	even	2	inner
1155.2.l.f.1121.39	yes	40	11.10	odd	2
1155.2.l.f.1121.40	yes	40	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1155 = 3 \cdot 5 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1155.l (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-2.79309 q^{2} +(0.351991 - 1.69591i) q^{3} +5.80135 q^{4} +1.00000i q^{5} +(-0.983141 + 4.73682i) q^{6} -1.00000i q^{7} -10.6175 q^{8} +(-2.75221 - 1.19389i) q^{9} +O(q^{10})\)	\(q-2.79309 q^{2} +(0.351991 - 1.69591i) q^{3} +5.80135 q^{4} +1.00000i q^{5} +(-0.983141 + 4.73682i) q^{6} -1.00000i q^{7} -10.6175 q^{8} +(-2.75221 - 1.19389i) q^{9} -2.79309i q^{10} +(1.01781 + 3.15659i) q^{11} +(2.04202 - 9.83855i) q^{12} +1.61455i q^{13} +2.79309i q^{14} +(1.69591 + 0.351991i) q^{15} +18.0529 q^{16} +0.978245 q^{17} +(7.68715 + 3.33463i) q^{18} +0.395037i q^{19} +5.80135i q^{20} +(-1.69591 - 0.351991i) q^{21} +(-2.84283 - 8.81664i) q^{22} -7.12888i q^{23} +(-3.73726 + 18.0063i) q^{24} -1.00000 q^{25} -4.50959i q^{26} +(-2.99347 + 4.24725i) q^{27} -5.80135i q^{28} -7.06734 q^{29} +(-4.73682 - 0.983141i) q^{30} -8.80790 q^{31} -29.1884 q^{32} +(5.71155 - 0.615020i) q^{33} -2.73232 q^{34} +1.00000 q^{35} +(-15.9665 - 6.92615i) q^{36} -6.29015 q^{37} -1.10337i q^{38} +(2.73813 + 0.568307i) q^{39} -10.6175i q^{40} +10.7989 q^{41} +(4.73682 + 0.983141i) q^{42} -10.2461i q^{43} +(5.90466 + 18.3125i) q^{44} +(1.19389 - 2.75221i) q^{45} +19.9116i q^{46} -6.63732i q^{47} +(6.35446 - 30.6161i) q^{48} -1.00000 q^{49} +2.79309 q^{50} +(0.344333 - 1.65901i) q^{51} +9.36657i q^{52} -1.04213i q^{53} +(8.36104 - 11.8629i) q^{54} +(-3.15659 + 1.01781i) q^{55} +10.6175i q^{56} +(0.669946 + 0.139049i) q^{57} +19.7397 q^{58} -2.68958i q^{59} +(9.83855 + 2.04202i) q^{60} -9.03276i q^{61} +24.6012 q^{62} +(-1.19389 + 2.75221i) q^{63} +45.4200 q^{64} -1.61455 q^{65} +(-15.9529 + 1.71780i) q^{66} -10.4405 q^{67} +5.67514 q^{68} +(-12.0899 - 2.50930i) q^{69} -2.79309 q^{70} +3.62237i q^{71} +(29.2215 + 12.6761i) q^{72} +4.53276i q^{73} +17.5690 q^{74} +(-0.351991 + 1.69591i) q^{75} +2.29175i q^{76} +(3.15659 - 1.01781i) q^{77} +(-7.64784 - 1.58733i) q^{78} -11.4024i q^{79} +18.0529i q^{80} +(6.14926 + 6.57165i) q^{81} -30.1622 q^{82} -14.8678 q^{83} +(-9.83855 - 2.04202i) q^{84} +0.978245i q^{85} +28.6184i q^{86} +(-2.48764 + 11.9856i) q^{87} +(-10.8066 - 33.5151i) q^{88} -8.05214i q^{89} +(-3.33463 + 7.68715i) q^{90} +1.61455 q^{91} -41.3571i q^{92} +(-3.10030 + 14.9374i) q^{93} +18.5386i q^{94} -0.395037 q^{95} +(-10.2741 + 49.5009i) q^{96} +9.28996 q^{97} +2.79309 q^{98} +(0.967395 - 9.90273i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 4 q^{2} - 4 q^{3} + 44 q^{4} - 4 q^{6} - 12 q^{8} - 2 q^{9}+O(q^{10}) \) 40 * q - 4 * q^2 - 4 * q^3 + 44 * q^4 - 4 * q^6 - 12 * q^8 - 2 * q^9	\( 40 q - 4 q^{2} - 4 q^{3} + 44 q^{4} - 4 q^{6} - 12 q^{8} - 2 q^{9} - 6 q^{11} + 8 q^{12} + 2 q^{15} + 68 q^{16} + 40 q^{18} - 2 q^{21} - 4 q^{22} - 12 q^{24} - 40 q^{25} + 32 q^{27} - 24 q^{29} - 8 q^{31} + 52 q^{32} - 16 q^{33} + 32 q^{34} + 40 q^{35} - 48 q^{37} + 66 q^{39} - 16 q^{41} + 32 q^{44} + 32 q^{48} - 40 q^{49} + 4 q^{50} - 14 q^{51} - 72 q^{54} + 8 q^{55} - 24 q^{57} - 80 q^{58} + 24 q^{60} + 48 q^{62} + 76 q^{64} + 4 q^{65} - 76 q^{66} - 48 q^{67} - 32 q^{68} - 20 q^{69} - 4 q^{70} + 128 q^{72} + 4 q^{75} - 8 q^{77} - 28 q^{78} + 50 q^{81} - 32 q^{82} - 24 q^{83} - 24 q^{84} - 32 q^{87} - 16 q^{88} + 8 q^{90} - 4 q^{91} - 20 q^{93} - 12 q^{95} + 12 q^{96} + 100 q^{97} + 4 q^{98} - 54 q^{99}+O(q^{100}) \) 40 * q - 4 * q^2 - 4 * q^3 + 44 * q^4 - 4 * q^6 - 12 * q^8 - 2 * q^9 - 6 * q^11 + 8 * q^12 + 2 * q^15 + 68 * q^16 + 40 * q^18 - 2 * q^21 - 4 * q^22 - 12 * q^24 - 40 * q^25 + 32 * q^27 - 24 * q^29 - 8 * q^31 + 52 * q^32 - 16 * q^33 + 32 * q^34 + 40 * q^35 - 48 * q^37 + 66 * q^39 - 16 * q^41 + 32 * q^44 + 32 * q^48 - 40 * q^49 + 4 * q^50 - 14 * q^51 - 72 * q^54 + 8 * q^55 - 24 * q^57 - 80 * q^58 + 24 * q^60 + 48 * q^62 + 76 * q^64 + 4 * q^65 - 76 * q^66 - 48 * q^67 - 32 * q^68 - 20 * q^69 - 4 * q^70 + 128 * q^72 + 4 * q^75 - 8 * q^77 - 28 * q^78 + 50 * q^81 - 32 * q^82 - 24 * q^83 - 24 * q^84 - 32 * q^87 - 16 * q^88 + 8 * q^90 - 4 * q^91 - 20 * q^93 - 12 * q^95 + 12 * q^96 + 100 * q^97 + 4 * q^98 - 54 * q^99

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