LMFDB - Embedded newform 1161.2.f.c.388.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1161,2,Mod(388,1161)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1161, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 0]))

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

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

chi := DirichletCharacter("1161.388");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1161 = 3^{3} \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1161.f (of order $3$, degree $2$, not 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:	$9.27063167467$
Analytic rank:	$0$
Dimension:	$38$
Relative dimension:	$19$ over $\Q(\zeta_{3})$
Twist minimal:	no (minimal twist has level 387)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			388.19
Character	$\chi$	$=$	1161.388
Dual form			1161.2.f.c.775.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.36225 + 2.35949i) q^{2} +(-2.71146 + 4.69638i) q^{4} +(1.18444 - 2.05150i) q^{5} +(-1.93605 - 3.35333i) q^{7} -9.32575 q^{8} +O(q^{10})$	\(q+(1.36225 + 2.35949i) q^{2} +(-2.71146 + 4.69638i) q^{4} +(1.18444 - 2.05150i) q^{5} +(-1.93605 - 3.35333i) q^{7} -9.32575 q^{8} +6.45400 q^{10} +(-2.06096 - 3.56969i) q^{11} +(2.72275 - 4.71594i) q^{13} +(5.27477 - 9.13617i) q^{14} +(-7.28109 - 12.6112i) q^{16} -3.44504 q^{17} +3.07895 q^{19} +(6.42309 + 11.1251i) q^{20} +(5.61510 - 9.72564i) q^{22} +(-2.13956 + 3.70583i) q^{23} +(-0.305775 - 0.529618i) q^{25} +14.8363 q^{26} +20.9981 q^{28} +(-0.411829 - 0.713309i) q^{29} +(1.95997 - 3.39476i) q^{31} +(10.5116 - 18.2067i) q^{32} +(-4.69301 - 8.12854i) q^{34} -9.17250 q^{35} -6.39648 q^{37} +(4.19431 + 7.26476i) q^{38} +(-11.0457 + 19.1318i) q^{40} +(-0.418008 + 0.724011i) q^{41} +(-0.500000 - 0.866025i) q^{43} +22.3529 q^{44} -11.6585 q^{46} +(-1.68757 - 2.92296i) q^{47} +(-3.99657 + 6.92226i) q^{49} +(0.833085 - 1.44295i) q^{50} +(14.7652 + 25.5741i) q^{52} -4.95830 q^{53} -9.76432 q^{55} +(18.0551 + 31.2723i) q^{56} +(1.12203 - 1.94341i) q^{58} +(6.08897 - 10.5464i) q^{59} +(5.51510 + 9.55244i) q^{61} +10.6799 q^{62} +28.1535 q^{64} +(-6.44984 - 11.1714i) q^{65} +(0.723285 - 1.25277i) q^{67} +(9.34109 - 16.1792i) q^{68} +(-12.4952 - 21.6424i) q^{70} +2.22802 q^{71} -1.95911 q^{73} +(-8.71361 - 15.0924i) q^{74} +(-8.34845 + 14.4599i) q^{76} +(-7.98025 + 13.8222i) q^{77} +(-4.27137 - 7.39823i) q^{79} -34.4959 q^{80} -2.27773 q^{82} +(3.41242 + 5.91048i) q^{83} +(-4.08043 + 7.06751i) q^{85} +(1.36225 - 2.35949i) q^{86} +(19.2200 + 33.2901i) q^{88} +11.9116 q^{89} -21.0855 q^{91} +(-11.6027 - 20.0964i) q^{92} +(4.59780 - 7.96362i) q^{94} +(3.64682 - 6.31648i) q^{95} +(3.43122 + 5.94304i) q^{97} -21.7773 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 38 q + 4 q^{2} - 22 q^{4} + 9 q^{5} - 7 q^{7} - 24 q^{8}+O(q^{10}) $ 38 * q + 4 * q^2 - 22 * q^4 + 9 * q^5 - 7 * q^7 - 24 * q^8	$ 38 q + 4 q^{2} - 22 q^{4} + 9 q^{5} - 7 q^{7} - 24 q^{8} - 14 q^{10} + 5 q^{11} + 5 q^{13} + 17 q^{14} - 24 q^{16} - 42 q^{17} - 8 q^{19} + 21 q^{20} + 20 q^{22} + 22 q^{23} - 10 q^{25} - 34 q^{26} - 2 q^{28} + 30 q^{29} + 5 q^{31} + 48 q^{32} + 6 q^{34} - 106 q^{35} - 2 q^{37} + 21 q^{38} - 16 q^{40} + 29 q^{41} - 19 q^{43} - 58 q^{44} + 32 q^{47} + 10 q^{49} - 11 q^{50} - q^{52} - 76 q^{53} + 4 q^{55} + 46 q^{56} - 30 q^{58} + 30 q^{59} + 10 q^{61} - 50 q^{62} + 28 q^{64} + 8 q^{65} - 3 q^{67} + 47 q^{68} - 56 q^{70} - 42 q^{71} + 16 q^{73} + 28 q^{74} + 36 q^{76} + 49 q^{77} - 4 q^{79} - 140 q^{80} - 8 q^{82} + 29 q^{83} + 4 q^{85} + 4 q^{86} + 47 q^{88} - 108 q^{89} + 8 q^{91} + 12 q^{92} + 23 q^{94} + 33 q^{95} + 4 q^{97} - 98 q^{98}+O(q^{100}) $ 38 * q + 4 * q^2 - 22 * q^4 + 9 * q^5 - 7 * q^7 - 24 * q^8 - 14 * q^10 + 5 * q^11 + 5 * q^13 + 17 * q^14 - 24 * q^16 - 42 * q^17 - 8 * q^19 + 21 * q^20 + 20 * q^22 + 22 * q^23 - 10 * q^25 - 34 * q^26 - 2 * q^28 + 30 * q^29 + 5 * q^31 + 48 * q^32 + 6 * q^34 - 106 * q^35 - 2 * q^37 + 21 * q^38 - 16 * q^40 + 29 * q^41 - 19 * q^43 - 58 * q^44 + 32 * q^47 + 10 * q^49 - 11 * q^50 - q^52 - 76 * q^53 + 4 * q^55 + 46 * q^56 - 30 * q^58 + 30 * q^59 + 10 * q^61 - 50 * q^62 + 28 * q^64 + 8 * q^65 - 3 * q^67 + 47 * q^68 - 56 * q^70 - 42 * q^71 + 16 * q^73 + 28 * q^74 + 36 * q^76 + 49 * q^77 - 4 * q^79 - 140 * q^80 - 8 * q^82 + 29 * q^83 + 4 * q^85 + 4 * q^86 + 47 * q^88 - 108 * q^89 + 8 * q^91 + 12 * q^92 + 23 * q^94 + 33 * q^95 + 4 * q^97 - 98 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1161\mathbb{Z}\right)^\times$.

$n$	$433$	$947$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	1.36225	+	2.35949i	0.963257	+	1.66841i	0.714226	+	0.699915i	$0.246779\pi$
$2$	1.36225	+	2.35949i	0.963257	+	1.66841i	0.249031	+	0.968495i	$0.419888\pi$
$3$		0			0
$3$		0			0
$4$	−2.71146	+	4.69638i	−1.35573	+	2.34819i
$5$	1.18444	−	2.05150i	0.529696	−	0.917460i	−0.469704	−	0.882824i	$-0.655639\pi$
$5$	1.18444	−	2.05150i	0.529696	−	0.917460i	0.999400	−	0.0346360i	$-0.0110272\pi$
$6$		0			0
$7$	−1.93605	−	3.35333i	−0.731758	−	1.26744i	−0.956131	−	0.292938i	$-0.905367\pi$
$7$	−1.93605	−	3.35333i	−0.731758	−	1.26744i	0.224374	−	0.974503i	$-0.427966\pi$
$8$	−9.32575			−3.29715
$9$		0			0
$10$	6.45400			2.04093
$11$	−2.06096	−	3.56969i	−0.621404	−	1.07630i	−0.989224	−	0.146407i	$-0.953229\pi$
$11$	−2.06096	−	3.56969i	−0.621404	−	1.07630i	0.367820	−	0.929897i	$-0.380104\pi$
$12$		0			0
$13$	2.72275	−	4.71594i	0.755154	−	1.30797i	−0.190143	−	0.981756i	$-0.560895\pi$
$13$	2.72275	−	4.71594i	0.755154	−	1.30797i	0.945298	−	0.326209i	$-0.105771\pi$
$14$	5.27477	−	9.13617i	1.40974	−	2.44174i
$15$		0			0
$16$	−7.28109	−	12.6112i	−1.82027	−	3.15281i
$17$	−3.44504			−0.835545			−0.417773	−	0.908552i	$-0.637189\pi$
$17$	−3.44504			−0.835545			−0.417773	+	0.908552i	$0.637189\pi$
$18$		0			0
$19$	3.07895			0.706360			0.353180	−	0.935555i	$-0.385100\pi$
$19$	3.07895			0.706360			0.353180	+	0.935555i	$0.385100\pi$
$20$	6.42309	+	11.1251i	1.43625	+	2.48765i
$21$		0			0
$22$	5.61510	−	9.72564i	1.19714	−	2.07351i
$23$	−2.13956	+	3.70583i	−0.446129	+	0.772719i	−0.998130	−	0.0611250i	$-0.980531\pi$
$23$	−2.13956	+	3.70583i	−0.446129	+	0.772719i	0.552001	+	0.833844i	$0.313865\pi$
$24$		0			0
$25$	−0.305775	−	0.529618i	−0.0611550	−	0.105924i
$26$	14.8363			2.90963
$27$		0			0
$28$	20.9981			3.96826
$29$	−0.411829	−	0.713309i	−0.0764748	−	0.132458i	0.825252	−	0.564765i	$-0.191033\pi$
$29$	−0.411829	−	0.713309i	−0.0764748	−	0.132458i	−0.901727	+	0.432307i	$0.857700\pi$
$30$		0			0
$31$	1.95997	−	3.39476i	0.352020	−	0.609717i	−0.634583	−	0.772855i	$-0.718828\pi$
$31$	1.95997	−	3.39476i	0.352020	−	0.609717i	0.986603	+	0.163137i	$0.0521614\pi$
$32$	10.5116	−	18.2067i	1.85821	−	3.21851i
$33$		0			0
$34$	−4.69301	−	8.12854i	−0.804845	−	1.39403i
$35$	−9.17250			−1.55044
$36$		0			0
$37$	−6.39648			−1.05157			−0.525787	−	0.850616i	$-0.676229\pi$
$37$	−6.39648			−1.05157			−0.525787	+	0.850616i	$0.676229\pi$
$38$	4.19431	+	7.26476i	0.680407	+	1.17850i
$39$		0			0
$40$	−11.0457	+	19.1318i	−1.74649	+	3.02500i
$41$	−0.418008	+	0.724011i	−0.0652819	+	0.113072i	−0.896819	−	0.442398i	$-0.854128\pi$
$41$	−0.418008	+	0.724011i	−0.0652819	+	0.113072i	0.831537	+	0.555469i	$0.187461\pi$
$42$		0			0
$43$	−0.500000	−	0.866025i	−0.0762493	−	0.132068i
$43$	−0.500000	−	0.866025i	−0.0762493	−	0.132068i
$44$	22.3529			3.36982
$45$		0			0
$46$	−11.6585			−1.71895
$47$	−1.68757	−	2.92296i	−0.246158	−	0.426358i	0.716299	−	0.697794i	$-0.245835\pi$
$47$	−1.68757	−	2.92296i	−0.246158	−	0.426358i	−0.962457	+	0.271436i	$0.912501\pi$
$48$		0			0
$49$	−3.99657	+	6.92226i	−0.570938	+	0.988894i
$50$	0.833085	−	1.44295i	0.117816	−	0.204063i
$51$		0			0
$52$	14.7652	+	25.5741i	2.04757	+	3.54649i
$53$	−4.95830			−0.681074			−0.340537	−	0.940231i	$-0.610609\pi$
$53$	−4.95830			−0.681074			−0.340537	+	0.940231i	$0.610609\pi$
$54$		0			0
$55$	−9.76432			−1.31662
$56$	18.0551	+	31.2723i	2.41271	+	4.17894i
$57$		0			0
$58$	1.12203	−	1.94341i	0.147330	−	0.255183i
$59$	6.08897	−	10.5464i	0.792717	−	1.37303i	−0.131562	−	0.991308i	$-0.541999\pi$
$59$	6.08897	−	10.5464i	0.792717	−	1.37303i	0.924279	−	0.381718i	$-0.124667\pi$
$60$		0			0
$61$	5.51510	+	9.55244i	0.706137	+	1.22306i	0.966280	+	0.257495i	$0.0828970\pi$
$61$	5.51510	+	9.55244i	0.706137	+	1.22306i	−0.260143	+	0.965570i	$0.583770\pi$
$62$	10.6799			1.35635
$63$		0			0
$64$	28.1535			3.51919
$65$	−6.44984	−	11.1714i	−0.800004	−	1.38565i
$66$		0			0
$67$	0.723285	−	1.25277i	0.0883633	−	0.153050i	−0.818456	−	0.574569i	$-0.805170\pi$
$67$	0.723285	−	1.25277i	0.0883633	−	0.153050i	0.906819	+	0.421519i	$0.138503\pi$
$68$	9.34109	−	16.1792i	1.13277	−	1.96202i
$69$		0			0
$70$	−12.4952	−	21.6424i	−1.49347	−	2.58676i
$71$	2.22802			0.264417			0.132208	−	0.991222i	$-0.457793\pi$
$71$	2.22802			0.264417			0.132208	+	0.991222i	$0.457793\pi$
$72$		0			0
$73$	−1.95911			−0.229296			−0.114648	−	0.993406i	$-0.536574\pi$
$73$	−1.95911			−0.229296			−0.114648	+	0.993406i	$0.536574\pi$
$74$	−8.71361	−	15.0924i	−1.01294	−	1.75446i
$75$		0			0
$76$	−8.34845	+	14.4599i	−0.957633	+	1.65867i
$77$	−7.98025	+	13.8222i	−0.909434	+	1.57519i
$78$		0			0
$79$	−4.27137	−	7.39823i	−0.480567	−	0.832366i	0.519185	−	0.854662i	$-0.326236\pi$
$79$	−4.27137	−	7.39823i	−0.480567	−	0.832366i	−0.999751	+	0.0222960i	$0.992902\pi$
$80$	−34.4959			−3.85676
$81$		0			0
$82$	−2.27773			−0.251533
$83$	3.41242	+	5.91048i	0.374562	+	0.648760i	0.990261	−	0.139221i	$-0.0444599\pi$
$83$	3.41242	+	5.91048i	0.374562	+	0.648760i	−0.615700	+	0.787981i	$0.711127\pi$
$84$		0			0
$85$	−4.08043	+	7.06751i	−0.442585	+	0.766579i
$86$	1.36225	−	2.35949i	0.146895	−	0.254430i
$87$		0			0
$88$	19.2200	+	33.2901i	2.04886	+	3.54873i
$89$	11.9116			1.26263			0.631314	−	0.775527i	$-0.282516\pi$
$89$	11.9116			1.26263			0.631314	+	0.775527i	$0.282516\pi$
$90$		0			0
$91$	−21.0855			−2.21036
$92$	−11.6027	−	20.0964i	−1.20966	−	2.09519i
$93$		0			0
$94$	4.59780	−	7.96362i	0.474227	−	0.821385i
$95$	3.64682	−	6.31648i	0.374156	−	0.648057i
$96$		0			0
$97$	3.43122	+	5.94304i	0.348387	+	0.603425i	0.985963	−	0.166963i	$-0.0533960\pi$
$97$	3.43122	+	5.94304i	0.348387	+	0.603425i	−0.637576	+	0.770388i	$0.720063\pi$
$98$	−21.7773			−2.19984
$99$		0			0
$100$	3.31638			0.331638
$101$	−0.267052	−	0.462547i	−0.0265726	−	0.0460252i	0.852433	−	0.522836i	$-0.175126\pi$
$101$	−0.267052	−	0.462547i	−0.0265726	−	0.0460252i	−0.879006	+	0.476811i	$0.841793\pi$
$102$		0			0
$103$	5.75481	−	9.96763i	0.567039	−	0.982140i	−0.429818	−	0.902915i	$-0.641422\pi$
$103$	5.75481	−	9.96763i	0.567039	−	0.982140i	0.996857	−	0.0792243i	$-0.0252443\pi$
$104$	−25.3916	+	43.9796i	−2.48986	+	4.31256i
$105$		0			0
$106$	−6.75445	−	11.6990i	−0.656050	−	1.13631i
$107$	−2.26151			−0.218629			−0.109314	−	0.994007i	$-0.534866\pi$
$107$	−2.26151			−0.218629			−0.109314	+	0.994007i	$0.534866\pi$
$108$		0			0
$109$	4.89727			0.469074			0.234537	−	0.972107i	$-0.424643\pi$
$109$	4.89727			0.469074			0.234537	+	0.972107i	$0.424643\pi$
$110$	−13.3015	−	23.0388i	−1.26824	−	2.19666i
$111$		0			0
$112$	−28.1931	+	48.8319i	−2.66400	+	4.61418i
$113$	−0.0409584	+	0.0709420i	−0.00385304	+	0.00667366i	−0.867945	−	0.496659i	$-0.834560\pi$
$113$	−0.0409584	+	0.0709420i	−0.00385304	+	0.00667366i	0.864092	+	0.503333i	$0.167893\pi$
$114$		0			0
$115$	5.06834	+	8.77863i	0.472625	+	0.818611i
$116$	4.46663			0.414716
$117$		0			0
$118$	33.1788			3.05436
$119$	6.66977	+	11.5524i	0.611417	+	1.05900i
$120$		0			0
$121$	−2.99515	+	5.18775i	−0.272286	+	0.471613i
$122$	−15.0259	+	26.0257i	−1.36038	+	2.35625i
$123$		0			0
$124$	10.6287	+	18.4095i	0.954489	+	1.65322i
$125$	10.3957			0.929817
$126$		0			0
$127$	−11.2447			−0.997804			−0.498902	−	0.866658i	$-0.666263\pi$
$127$	−11.2447			−0.997804			−0.498902	+	0.866658i	$0.666263\pi$
$128$	17.3289	+	30.0145i	1.53167	+	2.65293i
$129$		0			0
$130$	17.5726	−	30.4366i	1.54122	−	2.66947i
$131$	−5.66102	+	9.80518i	−0.494606	+	0.856683i	−0.999981	−	0.00621725i	$-0.998021\pi$
$131$	−5.66102	+	9.80518i	−0.494606	+	0.856683i	0.505375	+	0.862900i	$0.331354\pi$
$132$		0			0
$133$	−5.96100	−	10.3248i	−0.516884	−	0.895270i
$134$	3.94118			0.340466
$135$		0			0
$136$	32.1276			2.75492
$137$	8.13854	+	14.0964i	0.695322	+	1.20433i	0.970072	+	0.242817i	$0.0780716\pi$
$137$	8.13854	+	14.0964i	0.695322	+	1.20433i	−0.274750	+	0.961516i	$0.588595\pi$
$138$		0			0
$139$	3.37149	−	5.83960i	0.285966	−	0.495308i	−0.686877	−	0.726774i	$-0.741019\pi$
$139$	3.37149	−	5.83960i	0.285966	−	0.495308i	0.972843	+	0.231466i	$0.0743521\pi$
$140$	24.8708	−	43.0776i	2.10197	−	3.64072i
$141$		0			0
$142$	3.03512	+	5.25698i	0.254701	+	0.441156i
$143$	−22.4459			−1.87702
$144$		0			0
$145$	−1.95114			−0.162033
$146$	−2.66880	−	4.62249i	−0.220871	−	0.382560i
$147$		0			0
$148$	17.3438	−	30.0403i	1.42565	−	2.46930i
$149$	11.0432	−	19.1273i	0.904692	−	1.56697i	0.0833616	−	0.996519i	$-0.473434\pi$
$149$	11.0432	−	19.1273i	0.904692	−	1.56697i	0.821330	−	0.570453i	$-0.193232\pi$
$150$		0			0
$151$	−3.38688	−	5.86625i	−0.275621	−	0.477389i	0.694671	−	0.719328i	$-0.255550\pi$
$151$	−3.38688	−	5.86625i	−0.275621	−	0.477389i	−0.970292	+	0.241939i	$0.922217\pi$
$152$	−28.7135			−2.32898
$153$		0			0
$154$	−43.4844			−3.50408
$155$	−4.64291	−	8.04175i	−0.372927	−	0.645929i
$156$		0			0
$157$	−8.68723	+	15.0467i	−0.693316	+	1.20086i	0.277429	+	0.960746i	$0.410518\pi$
$157$	−8.68723	+	15.0467i	−0.693316	+	1.20086i	−0.970745	+	0.240113i	$0.922816\pi$
$158$	11.6374	−	20.1565i	0.925819	−	1.60357i
$159$		0			0
$160$	−24.9007	−	43.1292i	−1.96857	−	3.40966i
$161$	16.5692			1.30583
$162$		0			0
$163$	8.27231			0.647938			0.323969	−	0.946068i	$-0.394983\pi$
$163$	8.27231			0.647938			0.323969	+	0.946068i	$0.394983\pi$
$164$	−2.26682	−	3.92625i	−0.177009	−	0.306589i
$165$		0			0
$166$	−9.29715	+	16.1031i	−0.721599	+	1.24985i
$167$	3.44049	−	5.95911i	0.266233	−	0.461130i	−0.701653	−	0.712519i	$-0.747554\pi$
$167$	3.44049	−	5.95911i	0.266233	−	0.461130i	0.967886	+	0.251389i	$0.0808875\pi$
$168$		0			0
$169$	−8.32670	−	14.4223i	−0.640516	−	1.10941i
$170$	−22.2343			−1.70529
$171$		0			0
$172$	5.42292			0.413493
$173$	4.79186	+	8.29974i	0.364318	+	0.631018i	0.988666	−	0.150128i	$-0.0479687\pi$
$173$	4.79186	+	8.29974i	0.364318	+	0.631018i	−0.624348	+	0.781146i	$0.714635\pi$
$174$		0			0
$175$	−1.18399	+	2.05073i	−0.0895013	+	0.155021i
$176$	−30.0121	+	51.9826i	−2.26225	+	3.91833i
$177$		0			0
$178$	16.2266	+	28.1053i	1.21624	+	2.10658i
$179$	11.2071			0.837655			0.418828	−	0.908066i	$-0.362441\pi$
$179$	11.2071			0.837655			0.418828	+	0.908066i	$0.362441\pi$
$180$		0			0
$181$	17.3136			1.28691			0.643456	−	0.765483i	$-0.277500\pi$
$181$	17.3136			1.28691			0.643456	+	0.765483i	$0.277500\pi$
$182$	−28.7237	−	49.7510i	−2.12914	−	3.68779i
$183$		0			0
$184$	19.9530	−	34.5596i	1.47095	−	2.54777i
$185$	−7.57622	+	13.1224i	−0.557014	+	0.964777i
$186$		0			0
$187$	7.10011	+	12.2977i	0.519211	+	0.899300i
$188$	18.3031			1.33489
$189$		0			0
$190$	19.8716			1.44163
$191$	−6.74538	−	11.6833i	−0.488079	−	0.845377i	0.511827	−	0.859088i	$-0.328969\pi$
$191$	−6.74538	−	11.6833i	−0.488079	−	0.845377i	−0.999906	+	0.0137113i	$0.995635\pi$
$192$		0			0
$193$	−7.75879	+	13.4386i	−0.558490	+	0.967333i	0.439133	+	0.898422i	$0.355286\pi$
$193$	−7.75879	+	13.4386i	−0.558490	+	0.967333i	−0.997623	+	0.0689106i	$0.978048\pi$
$194$	−9.34836	+	16.1918i	−0.671173	+	1.16251i
$195$		0			0
$196$	−21.6730	−	37.5388i	−1.54807	−	2.68134i
$197$	4.03681			0.287611			0.143805	−	0.989606i	$-0.454066\pi$
$197$	4.03681			0.287611			0.143805	+	0.989606i	$0.454066\pi$
$198$		0			0
$199$	−22.8794			−1.62188			−0.810939	−	0.585131i	$-0.801043\pi$
$199$	−22.8794			−1.62188			−0.810939	+	0.585131i	$0.801043\pi$
$200$	2.85158	+	4.93908i	0.201637	+	0.349246i
$201$		0			0
$202$	0.727583	−	1.26021i	0.0511926	−	0.0886681i
$203$	−1.59464	+	2.76200i	−0.111922	+	0.193855i
$204$		0			0
$205$	0.990207	+	1.71509i	0.0691590	+	0.119787i
$206$	31.3580			2.18482
$207$		0			0
$208$	−79.2983			−5.49835
$209$	−6.34561	−	10.9909i	−0.438935	−	0.760258i
$210$		0			0
$211$	4.17030	−	7.22316i	0.287095	−	0.497263i	−0.686020	−	0.727583i	$-0.740644\pi$
$211$	4.17030	−	7.22316i	0.287095	−	0.497263i	0.973115	+	0.230320i	$0.0739771\pi$
$212$	13.4442	−	23.2861i	0.923352	−	1.59929i
$213$		0			0
$214$	−3.08075	−	5.33602i	−0.210596	−	0.364763i
$215$	−2.36887			−0.161556
$216$		0			0
$217$	−15.1784			−1.03037
$218$	6.67132	+	11.5551i	0.451839	+	0.782608i
$219$		0			0
$220$	26.4755	−	45.8570i	1.78498	−	3.09168i
$221$	−9.37998	+	16.2466i	−0.630966	+	1.09286i
$222$		0			0
$223$	−8.17474	−	14.1591i	−0.547421	−	0.948161i	−0.998450	−	0.0556521i	$-0.982276\pi$
$223$	−8.17474	−	14.1591i	−0.547421	−	0.948161i	0.451029	−	0.892509i	$-0.351057\pi$
$224$	−81.4040			−5.43903
$225$		0			0
$226$	−0.223182			−0.0148459
$227$	3.41252	+	5.91066i	0.226497	+	0.392304i	0.956767	−	0.290854i	$-0.0939393\pi$
$227$	3.41252	+	5.91066i	0.226497	+	0.392304i	−0.730271	+	0.683158i	$0.760606\pi$
$228$		0			0
$229$	0.302595	−	0.524110i	0.0199961	−	0.0346342i	−0.855854	−	0.517217i	$-0.826968\pi$
$229$	0.302595	−	0.524110i	0.0199961	−	0.0346342i	0.875850	+	0.482583i	$0.160301\pi$
$230$	−13.8087	+	23.9174i	−0.910520	+	1.57707i
$231$		0			0
$232$	3.84062	+	6.65214i	0.252149	+	0.436734i
$233$	24.3172			1.59307			0.796537	−	0.604589i	$-0.206663\pi$
$233$	24.3172			1.59307			0.796537	+	0.604589i	$0.206663\pi$
$234$		0			0
$235$	−7.99529			−0.521555
$236$	33.0200	+	57.1923i	2.14942	+	3.72290i
$237$		0			0
$238$	−18.1718	+	31.4745i	−1.17790	+	2.04019i
$239$	11.1069	−	19.2378i	0.718447	−	1.24439i	−0.243168	−	0.969984i	$-0.578187\pi$
$239$	11.1069	−	19.2378i	0.718447	−	1.24439i	0.961615	−	0.274402i	$-0.0884800\pi$
$240$		0			0
$241$	−8.13506	−	14.0903i	−0.524025	−	0.907638i	−0.999609	−	0.0279677i	$-0.991096\pi$
$241$	−8.13506	−	14.0903i	−0.524025	−	0.907638i	0.475584	−	0.879670i	$-0.342237\pi$
$242$	−16.3206			−1.04913
$243$		0			0
$244$	−59.8159			−3.82932
$245$	9.46735	+	16.3979i	0.604847	+	1.04763i
$246$		0			0
$247$	8.38321	−	14.5201i	0.533411	−	0.923895i
$248$	−18.2782	+	31.6587i	−1.16066	+	2.01033i
$249$		0			0
$250$	14.1615	+	24.5285i	0.895653	+	1.55132i
$251$	−22.3094			−1.40816			−0.704078	−	0.710122i	$-0.748640\pi$
$251$	−22.3094			−1.40816			−0.704078	+	0.710122i	$0.748640\pi$
$252$		0			0
$253$	17.6382			1.10891
$254$	−15.3181	−	26.5317i	−0.961142	−	1.66475i
$255$		0			0
$256$	−19.0591	+	33.0114i	−1.19120	+	2.06321i
$257$	8.70029	−	15.0694i	0.542709	−	0.940000i	−0.456038	−	0.889960i	$-0.650732\pi$
$257$	8.70029	−	15.0694i	0.542709	−	0.940000i	0.998747	−	0.0500400i	$-0.0159349\pi$
$258$		0			0
$259$	12.3839	+	21.4495i	0.769498	+	1.33281i
$260$	69.9538			4.33835
$261$		0			0
$262$	−30.8470			−1.90573
$263$	−3.78238	−	6.55127i	−0.233231	−	0.403968i	0.725526	−	0.688195i	$-0.241597\pi$
$263$	−3.78238	−	6.55127i	−0.233231	−	0.403968i	−0.958757	+	0.284226i	$0.908263\pi$
$264$		0			0
$265$	−5.87278	+	10.1720i	−0.360762	+	0.624858i
$266$	16.2408	−	28.1298i	0.995785	−	1.72475i
$267$		0			0
$268$	3.92231	+	6.79365i	0.239593	+	0.414988i
$269$	−18.6824			−1.13909			−0.569543	−	0.821962i	$-0.692880\pi$
$269$	−18.6824			−1.13909			−0.569543	+	0.821962i	$0.692880\pi$
$270$		0			0
$271$	25.3148			1.53777			0.768883	−	0.639389i	$-0.220813\pi$
$271$	25.3148			1.53777			0.768883	+	0.639389i	$0.220813\pi$
$272$	25.0837	+	43.4462i	1.52092	+	2.63431i
$273$		0			0
$274$	−22.1735	+	38.4056i	−1.33955	+	2.32017i
$275$	−1.26038	+	2.18305i	−0.0760040	+	0.131643i
$276$		0			0
$277$	9.35755	+	16.2078i	0.562241	+	0.973830i	0.997301	+	0.0734281i	$0.0233939\pi$
$277$	9.35755	+	16.2078i	0.562241	+	0.973830i	−0.435060	+	0.900402i	$0.643273\pi$
$278$	18.3713			1.10184
$279$		0			0
$280$	85.5404			5.11202
$281$	−2.86714	−	4.96603i	−0.171039	−	0.296248i	0.767744	−	0.640756i	$-0.221379\pi$
$281$	−2.86714	−	4.96603i	−0.171039	−	0.296248i	−0.938783	+	0.344508i	$0.888046\pi$
$282$		0			0
$283$	4.64686	−	8.04860i	0.276227	−	0.478439i	−0.694217	−	0.719766i	$-0.744249\pi$
$283$	4.64686	−	8.04860i	0.276227	−	0.478439i	0.970444	+	0.241326i	$0.0775825\pi$
$284$	−6.04117	+	10.4636i	−0.358478	+	0.620901i
$285$		0			0
$286$	−30.5770	−	52.9609i	−1.80806	−	3.13165i
$287$	3.23713			0.191082
$288$		0			0
$289$	−5.13169			−0.301864
$290$	−2.65794	−	4.60370i	−0.156080	−	0.270338i
$291$		0			0
$292$	5.31204	−	9.20072i	0.310863	−	0.538431i
$293$	14.8149	−	25.6602i	0.865498	−	1.49909i	−0.00105318	−	0.999999i	$-0.500335\pi$
$293$	14.8149	−	25.6602i	0.865498	−	1.49909i	0.866552	−	0.499088i	$-0.166331\pi$
$294$		0			0
$295$	−14.4240	−	24.9831i	−0.839797	−	1.45457i
$296$	59.6519			3.46720
$297$		0			0
$298$	60.1743			3.48580
$299$	11.6510	+	20.1801i	0.673793	+	1.16704i
$300$		0			0
$301$	−1.93605	+	3.35333i	−0.111592	+	0.193283i
$302$	9.22757	−	15.9826i	0.530987	−	0.919697i
$303$		0			0
$304$	−22.4181	−	38.8294i	−1.28577	−	2.22702i
$305$	26.1291			1.49615
$306$		0			0
$307$	7.82610			0.446659			0.223330	−	0.974743i	$-0.428307\pi$
$307$	7.82610			0.446659			0.223330	+	0.974743i	$0.428307\pi$
$308$	−43.2762	−	74.9567i	−2.46589	−	4.27105i
$309$		0			0
$310$	12.6496	−	21.9098i	0.718450	−	1.24439i
$311$	3.94391	−	6.83106i	0.223639	−	0.387354i	−0.732271	−	0.681013i	$-0.761540\pi$
$311$	3.94391	−	6.83106i	0.223639	−	0.387354i	0.955910	+	0.293659i	$0.0948730\pi$
$312$		0			0
$313$	11.0261	+	19.0978i	0.623233	+	1.07947i	0.988880	+	0.148717i	$0.0475143\pi$
$313$	11.0261	+	19.0978i	0.623233	+	1.07947i	−0.365647	+	0.930754i	$0.619152\pi$
$314$	−47.3368			−2.67137
$315$		0			0
$316$	46.3266			2.60607
$317$	3.10977	+	5.38627i	0.174662	+	0.302523i	0.940044	−	0.341053i	$-0.110783\pi$
$317$	3.10977	+	5.38627i	0.174662	+	0.302523i	−0.765382	+	0.643576i	$0.777450\pi$
$318$		0			0
$319$	−1.69753	+	2.94021i	−0.0950435	+	0.164620i
$320$	33.3460	−	57.7569i	1.86410	−	3.22871i
$321$		0			0
$322$	22.5714	+	39.0948i	1.25785	+	2.17867i
$323$	−10.6071			−0.590196
$324$		0			0
$325$	−3.33019			−0.184726
$326$	11.2690	+	19.5184i	0.624131	+	1.08103i
$327$		0			0
$328$	3.89824	−	6.75194i	0.215244	−	0.372814i
$329$	−6.53445	+	11.3180i	−0.360256	+	0.623981i
$330$		0			0
$331$	12.8852	+	22.3178i	0.708234	+	1.22670i	0.965512	+	0.260359i	$0.0838411\pi$
$331$	12.8852	+	22.3178i	0.708234	+	1.22670i	−0.257278	+	0.966337i	$0.582826\pi$
$332$	−37.0105			−2.03122
$333$		0			0
$334$	18.7473			1.02581
$335$	−1.71337	−	2.96764i	−0.0936113	−	0.162140i
$336$		0			0
$337$	−14.1881	+	24.5745i	−0.772874	+	1.33866i	0.163107	+	0.986608i	$0.447848\pi$
$337$	−14.1881	+	24.5745i	−0.772874	+	1.33866i	−0.935982	+	0.352049i	$0.885485\pi$
$338$	22.6861	−	39.2935i	1.23396	−	2.13729i
$339$		0			0
$340$	−22.1278	−	38.3265i	−1.20005	−	2.07855i
$341$	−16.1577			−0.874988
$342$		0			0
$343$	3.84551			0.207638
$344$	4.66287	+	8.07633i	0.251405	+	0.435447i
$345$		0			0
$346$	−13.0554	+	22.6127i	−0.701864	+	1.21566i
$347$	−12.1320	+	21.0133i	−0.651280	+	1.12805i	0.331532	+	0.943444i	$0.392434\pi$
$347$	−12.1320	+	21.0133i	−0.651280	+	1.12805i	−0.982812	+	0.184607i	$0.940899\pi$
$348$		0			0
$349$	−10.3359	−	17.9022i	−0.553266	−	0.958285i	−0.998036	−	0.0626403i	$-0.980048\pi$
$349$	−10.3359	−	17.9022i	−0.553266	−	0.958285i	0.444770	−	0.895645i	$-0.353285\pi$
$350$	−6.45157			−0.344851
$351$		0			0
$352$	−86.6563			−4.61879
$353$	7.04608	+	12.2042i	0.375025	+	0.649562i	0.990331	−	0.138726i	$-0.0443008\pi$
$353$	7.04608	+	12.2042i	0.375025	+	0.649562i	−0.615306	+	0.788288i	$0.710967\pi$
$354$		0			0
$355$	2.63894	−	4.57078i	0.140060	−	0.242592i
$356$	−32.2978	+	55.9415i	−1.71178	+	2.96489i
$357$		0			0
$358$	15.2668	+	26.4429i	0.806877	+	1.39755i
$359$	−1.18550			−0.0625682			−0.0312841	−	0.999511i	$-0.509960\pi$
$359$	−1.18550			−0.0625682			−0.0312841	+	0.999511i	$0.509960\pi$
$360$		0			0
$361$	−9.52005			−0.501055
$362$	23.5855	+	40.8513i	1.23963	+	2.14710i
$363$		0			0
$364$	57.1724	−	99.0255i	2.99665	−	5.19035i
$365$	−2.32044	+	4.01911i	−0.121457	+	0.210370i
$366$		0			0
$367$	−2.56413	−	4.44121i	−0.133847	−	0.231829i	0.791310	−	0.611416i	$-0.209400\pi$
$367$	−2.56413	−	4.44121i	−0.133847	−	0.231829i	−0.925156	+	0.379587i	$0.876066\pi$
$368$	62.3134			3.24831
$369$		0			0
$370$	−41.2828			−2.14619
$371$	9.59950	+	16.6268i	0.498381	+	0.863222i
$372$		0			0
$373$	7.60600	−	13.1740i	0.393824	−	0.682123i	−0.599126	−	0.800655i	$-0.704485\pi$
$373$	7.60600	−	13.1740i	0.393824	−	0.682123i	0.992950	+	0.118531i	$0.0378186\pi$
$374$	−19.3443	+	33.5052i	−1.00027	+	1.73252i
$375$		0			0
$376$	15.7379	+	27.2588i	0.811619	+	1.40577i
$377$	−4.48523			−0.231001
$378$		0			0
$379$	−16.5992			−0.852644			−0.426322	−	0.904571i	$-0.640191\pi$
$379$	−16.5992			−0.852644			−0.426322	+	0.904571i	$0.640191\pi$
$380$	19.7764	+	34.2537i	1.01451	+	1.75718i
$381$		0			0
$382$	18.3778	−	31.8313i	0.940291	−	1.62863i
$383$	0.826132	−	1.43090i	0.0422134	−	0.0731157i	−0.844147	−	0.536112i	$-0.819892\pi$
$383$	0.826132	−	1.43090i	0.0422134	−	0.0731157i	0.886360	+	0.462996i	$0.153226\pi$
$384$		0			0
$385$	18.9042	+	32.7430i	0.963447	+	1.66874i
$386$	−42.2777			−2.15188
$387$		0			0
$388$	−37.2144			−1.88928
$389$	−1.80738	−	3.13047i	−0.0916376	−	0.158721i	0.816563	−	0.577257i	$-0.195877\pi$
$389$	−1.80738	−	3.13047i	−0.0916376	−	0.158721i	−0.908200	+	0.418536i	$0.862543\pi$
$390$		0			0
$391$	7.37088	−	12.7667i	0.372761	−	0.645641i
$392$	37.2710	−	64.5552i	1.88247	−	3.26053i
$393$		0			0
$394$	5.49915	+	9.52480i	0.277043	+	0.479853i
$395$	−20.2367			−1.01822
$396$		0			0
$397$	−26.2385			−1.31687			−0.658436	−	0.752637i	$-0.728782\pi$
$397$	−26.2385			−1.31687			−0.658436	+	0.752637i	$0.728782\pi$
$398$	−31.1675	−	53.9837i	−1.56229	−	2.70596i
$399$		0			0
$400$	−4.45275	+	7.71240i	−0.222638	+	0.385620i
$401$	−2.36439	+	4.09525i	−0.118072	+	0.204507i	−0.919004	−	0.394249i	$-0.871005\pi$
$401$	−2.36439	+	4.09525i	−0.118072	+	0.204507i	0.800932	+	0.598756i	$0.204338\pi$
$402$		0			0
$403$	−10.6730	−	18.4862i	−0.531659	−	0.920861i
$404$	2.89640			0.144101
$405$		0			0
$406$	−8.68922			−0.431239
$407$	13.1829	+	22.8335i	0.653453	+	1.13181i
$408$		0			0
$409$	8.09906	−	14.0280i	0.400473	−	0.693639i	−0.593310	−	0.804974i	$-0.702179\pi$
$409$	8.09906	−	14.0280i	0.400473	−	0.693639i	0.993783	+	0.111335i	$0.0355126\pi$
$410$	−2.69782	+	4.67276i	−0.133236	+	0.230771i
$411$		0			0
$412$	31.2079	+	54.0536i	1.53750	+	2.66303i
$413$	−47.1542			−2.32031
$414$		0			0
$415$	16.1672			0.793615
$416$	−57.2409	−	99.1442i	−2.80647	−	4.86095i
$417$		0			0
$418$	17.2886	−	29.9448i	0.845615	−	1.46465i
$419$	9.20851	−	15.9496i	0.449865	−	0.779189i	−0.548512	−	0.836143i	$-0.684805\pi$
$419$	9.20851	−	15.9496i	0.449865	−	0.779189i	0.998377	+	0.0569535i	$0.0181387\pi$
$420$		0			0
$421$	13.6306	+	23.6090i	0.664317	+	1.15063i	0.979470	+	0.201589i	$0.0646106\pi$
$421$	13.6306	+	23.6090i	0.664317	+	1.15063i	−0.315154	+	0.949041i	$0.602056\pi$
$422$	22.7240			1.10619
$423$		0			0
$424$	46.2398			2.24560
$425$	1.05341	+	1.82456i	0.0510978	+	0.0885040i
$426$		0			0
$427$	21.3550	−	36.9880i	1.03344	−	1.78997i
$428$	6.13200	−	10.6209i	0.296401	−	0.513382i
$429$		0			0
$430$	−3.22700	−	5.58932i	−0.155620	−	0.269541i
$431$	−32.1317			−1.54773			−0.773865	−	0.633351i	$-0.781679\pi$
$431$	−32.1317			−1.54773			−0.773865	+	0.633351i	$0.781679\pi$
$432$		0			0
$433$	−31.8836			−1.53223			−0.766113	−	0.642706i	$-0.777812\pi$
$433$	−31.8836			−1.53223			−0.766113	+	0.642706i	$0.777812\pi$
$434$	−20.6767	−	35.8132i	−0.992516	−	1.71909i
$435$		0			0
$436$	−13.2788	+	22.9995i	−0.635937	+	1.10148i
$437$	−6.58761	+	11.4101i	−0.315128	+	0.545818i
$438$		0			0
$439$	15.2651	+	26.4399i	0.728563	+	1.26191i	0.957491	+	0.288465i	$0.0931448\pi$
$439$	15.2651	+	26.4399i	0.728563	+	1.26191i	−0.228928	+	0.973443i	$0.573522\pi$
$440$	91.0595			4.34109
$441$		0			0
$442$	−51.1116			−2.43113
$443$	16.0146	+	27.7381i	0.760878	+	1.31788i	0.942399	+	0.334492i	$0.108565\pi$
$443$	16.0146	+	27.7381i	0.760878	+	1.31788i	−0.181521	+	0.983387i	$0.558102\pi$
$444$		0			0
$445$	14.1085	−	24.4367i	0.668809	−	1.15841i
$446$	22.2721	−	38.5764i	1.05461	−	1.82665i
$447$		0			0
$448$	−54.5065	−	94.4080i	−2.57519	−	4.46036i
$449$	−7.78474			−0.367385			−0.183692	−	0.982984i	$-0.558805\pi$
$449$	−7.78474			−0.367385			−0.183692	+	0.982984i	$0.558805\pi$
$450$		0			0
$451$	3.44600			0.162266
$452$	−0.222114	−	0.384712i	−0.0104474	−	0.0180954i
$453$		0			0
$454$	−9.29742	+	16.1036i	−0.436350	+	0.755780i
$455$	−24.9744	+	43.2569i	−1.17082	+	2.02792i
$456$		0			0
$457$	−10.5994	−	18.3587i	−0.495820	−	0.858785i	0.504168	−	0.863605i	$-0.331799\pi$
$457$	−10.5994	−	18.3587i	−0.495820	−	0.858785i	−0.999988	+	0.00481994i	$0.998466\pi$
$458$	1.64884			0.0770454
$459$		0			0
$460$	−54.9704			−2.56301
$461$	6.84089	+	11.8488i	0.318612	+	0.551852i	0.980199	−	0.198017i	$-0.0634500\pi$
$461$	6.84089	+	11.8488i	0.318612	+	0.551852i	−0.661587	+	0.749869i	$0.730117\pi$
$462$		0			0
$463$	13.4757	−	23.3406i	0.626269	−	1.08473i	−0.362025	−	0.932168i	$-0.617914\pi$
$463$	13.4757	−	23.3406i	0.626269	−	1.08473i	0.988294	−	0.152561i	$-0.0487522\pi$
$464$	−5.99714	+	10.3873i	−0.278410	+	0.482220i
$465$		0			0
$466$	33.1262	+	57.3762i	1.53454	+	2.65790i
$467$	8.28254			0.383270			0.191635	−	0.981466i	$-0.438621\pi$
$467$	8.28254			0.383270			0.191635	+	0.981466i	$0.438621\pi$
$468$		0			0
$469$	−5.60126			−0.258642
$470$	−10.8916	−	18.8648i	−0.502392	−	0.870168i
$471$		0			0
$472$	−56.7842	+	98.3531i	−2.61371	+	4.52707i
$473$	−2.06096	+	3.56969i	−0.0947632	+	0.164135i
$474$		0			0
$475$	−0.941467	−	1.63067i	−0.0431975	−	0.0748202i
$476$	−72.3392			−3.31566
$477$		0			0
$478$	60.5217			2.76820
$479$	16.8577	+	29.1984i	0.770248	+	1.33411i	0.937427	+	0.348182i	$0.113201\pi$
$479$	16.8577	+	29.1984i	0.770248	+	1.33411i	−0.167179	+	0.985927i	$0.553466\pi$
$480$		0			0
$481$	−17.4160	+	30.1654i	−0.794101	+	1.37542i
$482$	22.1640	−	38.3892i	1.00954	−	1.74858i
$483$		0			0
$484$	−16.2424	−	28.1327i	−0.738292	−	1.27876i
$485$	16.2562			0.738157
$486$		0			0
$487$	−2.95600			−0.133949			−0.0669746	−	0.997755i	$-0.521335\pi$
$487$	−2.95600			−0.133949			−0.0669746	+	0.997755i	$0.521335\pi$
$488$	−51.4325	−	89.0836i	−2.32824	−	4.03263i
$489$		0			0
$490$	−25.7938	+	44.6762i	−1.16525	+	2.01827i
$491$	−18.2795	+	31.6611i	−0.824944	+	1.42885i	0.0770177	+	0.997030i	$0.475460\pi$
$491$	−18.2795	+	31.6611i	−0.824944	+	1.42885i	−0.901962	+	0.431816i	$0.857873\pi$
$492$		0			0
$493$	1.41877	+	2.45738i	0.0638982	+	0.110675i
$494$	45.6802			2.05525
$495$		0			0
$496$	−57.0828			−2.56309
$497$	−4.31355	−	7.47128i	−0.193489	−	0.335133i
$498$		0			0
$499$	14.4582	−	25.0423i	0.647236	−	1.12105i	−0.336544	−	0.941668i	$-0.609258\pi$
$499$	14.4582	−	25.0423i	0.647236	−	1.12105i	0.983780	−	0.179378i	$-0.0574086\pi$
$500$	−28.1874	+	48.8221i	−1.26058	+	2.18339i
$501$		0			0
$502$	−30.3910	−	52.6388i	−1.35642	−	2.34938i
$503$	−3.49351			−0.155768			−0.0778841	−	0.996962i	$-0.524816\pi$
$503$	−3.49351			−0.155768			−0.0778841	+	0.996962i	$0.524816\pi$
$504$		0			0
$505$	−1.26522			−0.0563016
$506$	24.0277	+	41.6172i	1.06816	+	1.85011i
$507$		0			0
$508$	30.4895	−	52.8093i	1.35275	−	2.34304i
$509$	3.05899	−	5.29832i	0.135587	−	0.234844i	−0.790234	−	0.612805i	$-0.790041\pi$
$509$	3.05899	−	5.29832i	0.135587	−	0.234844i	0.925822	+	0.377961i	$0.123375\pi$
$510$		0			0
$511$	3.79293	+	6.56954i	0.167789	+	0.290619i
$512$	−34.5378			−1.52637
$513$		0			0
$514$	47.4080			2.09108
$515$	−13.6324	−	23.6120i	−0.600716	−	1.04047i
$516$		0			0
$517$	−6.95606	+	12.0482i	−0.305927	+	0.529881i
$518$	−33.7399	+	58.4393i	−1.48245	+	2.56768i
$519$		0			0
$520$	60.1495	+	104.182i	2.63773	+	4.56869i
$521$	9.62448			0.421656			0.210828	−	0.977523i	$-0.432384\pi$
$521$	9.62448			0.421656			0.210828	+	0.977523i	$0.432384\pi$
$522$		0			0
$523$	−17.2618			−0.754805			−0.377403	−	0.926049i	$-0.623183\pi$
$523$	−17.2618			−0.754805			−0.377403	+	0.926049i	$0.623183\pi$
$524$	−30.6993	−	53.1727i	−1.34110	−	2.32286i
$525$		0			0
$526$	10.3051	−	17.8489i	0.449323	−	0.778251i
$527$	−6.75217	+	11.6951i	−0.294129	+	0.509446i
$528$		0			0
$529$	2.34456	+	4.06090i	0.101937	+	0.176561i
$530$	−32.0008			−1.39003
$531$		0			0
$532$	64.6520			2.80302
$533$	2.27626	+	3.94260i	0.0985957	+	0.170773i
$534$		0			0
$535$	−2.67862	+	4.63950i	−0.115807	+	0.200583i
$536$	−6.74517	+	11.6830i	−0.291347	+	0.504628i
$537$		0			0
$538$	−25.4501	−	44.0809i	−1.09723	−	1.90046i
$539$	32.9471			1.41913
$540$		0			0
$541$	−38.1110			−1.63852			−0.819259	−	0.573424i	$-0.805615\pi$
$541$	−38.1110			−1.63852			−0.819259	+	0.573424i	$0.805615\pi$
$542$	34.4852	+	59.7301i	1.48126	+	2.56563i
$543$		0			0
$544$	−36.2130	+	62.7227i	−1.55262	+	2.68921i
$545$	5.80051	−	10.0468i	0.248466	−	0.430356i
$546$		0			0
$547$	12.9324	+	22.3996i	0.552950	+	0.957738i	0.998060	+	0.0622621i	$0.0198315\pi$
$547$	12.9324	+	22.3996i	0.552950	+	0.957738i	−0.445109	+	0.895476i	$0.646835\pi$
$548$	−88.2692			−3.77067
$549$		0			0
$550$	−6.86783			−0.292845
$551$	−1.26800	−	2.19625i	−0.0540188	−	0.0935632i
$552$		0			0
$553$	−16.5392	+	28.6467i	−0.703317	+	1.21818i
$554$	−25.4947	+	44.1581i	−1.08317	+	1.87610i
$555$		0			0
$556$	18.2833	+	31.6676i	0.775386	+	1.34301i
$557$	21.3539			0.904792			0.452396	−	0.891817i	$-0.350569\pi$
$557$	21.3539			0.904792			0.452396	+	0.891817i	$0.350569\pi$
$558$		0			0
$559$	−5.44549			−0.230320
$560$	66.7858	+	115.676i	2.82222	+	4.88822i
$561$		0			0
$562$	7.81152	−	13.5300i	0.329509	−	0.570727i
$563$	17.3760	−	30.0962i	0.732312	−	1.26840i	−0.223580	−	0.974685i	$-0.571775\pi$
$563$	17.3760	−	30.0962i	0.732312	−	1.26840i	0.955893	−	0.293716i	$-0.0948921\pi$
$564$		0			0
$565$	0.0970251	+	0.168052i	0.00408188	+	0.00707002i
$566$	25.3208			1.06431
$567$		0			0
$568$	−20.7779			−0.871822
$569$	3.44115	+	5.96024i	0.144260	+	0.249866i	0.929097	−	0.369837i	$-0.120586\pi$
$569$	3.44115	+	5.96024i	0.144260	+	0.249866i	−0.784836	+	0.619703i	$0.787253\pi$
$570$		0			0
$571$	−1.00685	+	1.74391i	−0.0421352	+	0.0729804i	−0.886324	−	0.463066i	$-0.846749\pi$
$571$	−1.00685	+	1.74391i	−0.0421352	+	0.0729804i	0.844189	+	0.536046i	$0.180083\pi$
$572$	60.8612	−	105.415i	2.54474	−	4.40761i
$573$		0			0
$574$	4.40979	+	7.63798i	0.184061	+	0.318803i
$575$	2.61690			0.109132
$576$		0			0
$577$	32.3262			1.34576			0.672879	−	0.739752i	$-0.265057\pi$
$577$	32.3262			1.34576			0.672879	+	0.739752i	$0.265057\pi$
$578$	−6.99065	−	12.1082i	−0.290773	−	0.503633i
$579$		0			0
$580$	5.29044	−	9.16331i	0.219673	−	0.380486i
$581$	13.2132	−	22.8860i	0.548177	−	0.949470i
$582$		0			0
$583$	10.2189	+	17.6996i	0.423222	+	0.733043i
$584$	18.2701			0.756023
$585$		0			0
$586$	80.7267			3.33479
$587$	−13.8900	−	24.0582i	−0.573301	−	0.992986i	−0.996224	−	0.0868206i	$-0.972329\pi$
$587$	−13.8900	−	24.0582i	−0.573301	−	0.992986i	0.422923	−	0.906166i	$-0.361004\pi$
$588$		0			0
$589$	6.03465	−	10.4523i	0.248653	−	0.430680i
$590$	39.2982	−	68.0665i	1.61788	−	2.80225i
$591$		0			0
$592$	46.5734	+	80.6674i	1.91415	+	3.31541i
$593$	18.5663			0.762428			0.381214	−	0.924487i	$-0.375506\pi$
$593$	18.5663			0.762428			0.381214	+	0.924487i	$0.375506\pi$
$594$		0			0
$595$	31.5996			1.29546
$596$	59.8862	+	103.726i	2.45303	+	4.24878i
$597$		0			0
$598$	−31.7431	+	54.9806i	−1.29807	+	2.24833i
$599$	−3.32626	+	5.76125i	−0.135907	+	0.235398i	−0.925944	−	0.377662i	$-0.876728\pi$
$599$	−3.32626	+	5.76125i	−0.135907	+	0.235398i	0.790036	+	0.613060i	$0.210062\pi$
$600$		0			0
$601$	2.23361	+	3.86872i	0.0911107	+	0.157808i	0.907979	−	0.419016i	$-0.137625\pi$
$601$	2.23361	+	3.86872i	0.0911107	+	0.157808i	−0.816868	+	0.576825i	$0.804292\pi$
$602$	−10.5495			−0.429967
$603$		0			0
$604$	36.7336			1.49467
$605$	7.09512	+	12.2891i	0.288458	+	0.499623i
$606$		0			0
$607$	9.32524	−	16.1518i	0.378500	−	0.655581i	−0.612345	−	0.790591i	$-0.709773\pi$
$607$	9.32524	−	16.1518i	0.378500	−	0.655581i	0.990844	+	0.135010i	$0.0431068\pi$
$608$	32.3648	−	56.0574i	1.31256	−	2.27343i
$609$		0			0
$610$	35.5945	+	61.6514i	1.44118	+	2.49619i
$611$	−18.3793			−0.743549
$612$		0			0
$613$	47.9290			1.93583			0.967917	−	0.251271i	$-0.0808484\pi$
$613$	47.9290			1.93583			0.967917	+	0.251271i	$0.0808484\pi$
$614$	10.6611	+	18.4656i	0.430248	+	0.745211i
$615$		0			0
$616$	74.4218	−	128.902i	2.99854	−	5.19362i
$617$	−13.3991	+	23.2080i	−0.539429	+	0.934318i	0.459506	+	0.888175i	$0.348026\pi$
$617$	−13.3991	+	23.2080i	−0.539429	+	0.934318i	−0.998935	+	0.0461433i	$0.985307\pi$
$618$		0			0
$619$	4.10239	+	7.10554i	0.164889	+	0.285596i	0.936616	−	0.350358i	$-0.113940\pi$
$619$	4.10239	+	7.10554i	0.164889	+	0.285596i	−0.771727	+	0.635954i	$0.780607\pi$
$620$	50.3562			2.02235
$621$		0			0
$622$	21.4904			0.861687
$623$	−23.0615	−	39.9436i	−0.923938	−	1.60031i
$624$		0			0
$625$	13.8419	−	23.9748i	0.553675	−	0.958993i
$626$	−30.0407	+	52.0320i	−1.20067	+	2.07962i
$627$		0			0
$628$	−47.1101	−	81.5971i	−1.87990	−	3.25608i
$629$	22.0361			0.878638
$630$		0			0
$631$	−4.21035			−0.167611			−0.0838056	−	0.996482i	$-0.526707\pi$
$631$	−4.21035			−0.167611			−0.0838056	+	0.996482i	$0.526707\pi$
$632$	39.8337	+	68.9940i	1.58450	+	2.74444i
$633$		0			0
$634$	−8.47257	+	14.6749i	−0.336489	+	0.582815i
$635$	−13.3186	+	23.0685i	−0.528533	+	0.915445i
$636$		0			0
$637$	21.7633	+	37.6951i	0.862293	+	1.49353i
$638$	−9.24986			−0.366205
$639$		0			0
$640$	82.0998			3.24528
$641$	−22.5416	−	39.0432i	−0.890340	−	1.54211i	−0.839468	−	0.543410i	$-0.817133\pi$
$641$	−22.5416	−	39.0432i	−0.890340	−	1.54211i	−0.0508726	−	0.998705i	$-0.516200\pi$
$642$		0			0
$643$	−25.2911	+	43.8054i	−0.997382	+	1.72752i	−0.436068	+	0.899914i	$0.643629\pi$
$643$	−25.2911	+	43.8054i	−0.997382	+	1.72752i	−0.561314	+	0.827603i	$0.689704\pi$
$644$	−44.9266	+	77.8152i	−1.77036	+	3.06635i
$645$		0			0
$646$	−14.4496	−	25.0274i	−0.568511	−	0.984689i
$647$	−1.23511			−0.0485570			−0.0242785	−	0.999705i	$-0.507729\pi$
$647$	−1.23511			−0.0485570			−0.0242785	+	0.999705i	$0.507729\pi$
$648$		0			0
$649$	−50.1966			−1.97039
$650$	−4.53656	−	7.85755i	−0.177939	−	0.308199i
$651$		0			0
$652$	−22.4300	+	38.8499i	−0.878428	+	1.52148i
$653$	5.47255	−	9.47874i	0.214157	−	0.370932i	−0.738854	−	0.673865i	$-0.764633\pi$
$653$	5.47255	−	9.47874i	0.214157	−	0.370932i	0.953012	+	0.302934i	$0.0979661\pi$
$654$		0			0
$655$	13.4102	+	23.2272i	0.523981	+	0.907562i
$656$	12.1742			0.475323
$657$		0			0
$658$	−35.6062			−1.38808
$659$	−14.2844	−	24.7413i	−0.556441	−	0.963783i	−0.997790	−	0.0664479i	$-0.978833\pi$
$659$	−14.2844	−	24.7413i	−0.556441	−	0.963783i	0.441349	−	0.897335i	$-0.354500\pi$
$660$		0			0
$661$	−16.1079	+	27.8997i	−0.626524	+	1.08517i	0.361720	+	0.932287i	$0.382190\pi$
$661$	−16.1079	+	27.8997i	−0.626524	+	1.08517i	−0.988244	+	0.152885i	$0.951144\pi$
$662$	−35.1057	+	60.8049i	−1.36442	+	2.36325i
$663$		0			0
$664$	−31.8234	−	55.1197i	−1.23499	−	2.13906i
$665$	−28.2417			−1.09517
$666$		0			0
$667$	3.52454			0.136471
$668$	18.6575	+	32.3158i	0.721881	+	1.25033i
$669$		0			0
$670$	4.66808	−	8.08535i	0.180344	−	0.312364i
$671$	22.7329	−	39.3745i	0.877593	−	1.52003i
$672$		0			0
$673$	17.9482	+	31.0872i	0.691852	+	1.19832i	0.971230	+	0.238142i	$0.0765383\pi$
$673$	17.9482	+	31.0872i	0.691852	+	1.19832i	−0.279378	+	0.960181i	$0.590128\pi$
$674$	−77.3109			−2.97791
$675$		0			0
$676$	90.3100			3.47346
$677$	14.9738	+	25.9354i	0.575490	+	0.996779i	0.995988	+	0.0894851i	$0.0285222\pi$
$677$	14.9738	+	25.9354i	0.575490	+	0.996779i	−0.420498	+	0.907294i	$0.638145\pi$
$678$		0			0
$679$	13.2860	−	23.0120i	0.509870	−	0.883121i
$680$	38.0530	−	65.9098i	1.45927	−	2.52753i
$681$		0			0
$682$	−22.0108	−	38.1239i	−0.842838	−	1.45984i
$683$	13.9614			0.534218			0.267109	−	0.963666i	$-0.413932\pi$
$683$	13.9614			0.534218			0.267109	+	0.963666i	$0.413932\pi$
$684$		0			0
$685$	38.5583			1.47324
$686$	5.23856	+	9.07344i	0.200009	+	0.346426i
$687$		0			0
$688$	−7.28109	+	12.6112i	−0.277589	+	0.480798i
$689$	−13.5002	+	23.3830i	−0.514316	+	0.890822i
$690$		0			0
$691$	−15.7519	−	27.2831i	−0.599230	−	1.03790i	−0.992935	−	0.118661i	$-0.962140\pi$
$691$	−15.7519	−	27.2831i	−0.599230	−	1.03790i	0.393704	−	0.919237i	$-0.371193\pi$
$692$	−51.9717			−1.97567
$693$		0			0
$694$	−66.1074			−2.50940
$695$	−7.98663	−	13.8333i	−0.302950	−	0.524725i
$696$		0			0
$697$	1.44005	−	2.49425i	0.0545460	−	0.0944764i
$698$	28.1601	−	48.7747i	1.06588	−	1.84615i
$699$		0			0
$700$	−6.42068	−	11.1209i	−0.242679	−	0.420332i
$701$	25.7639			0.973088			0.486544	−	0.873656i	$-0.338257\pi$
$701$	25.7639			0.973088			0.486544	+	0.873656i	$0.338257\pi$
$702$		0			0
$703$	−19.6945			−0.742790
$704$	−58.0233	−	100.499i	−2.18684	−	3.78771i
$705$		0			0
$706$	−19.1971	+	33.2503i	−0.722491	+	1.25139i
$707$	−1.03405	+	1.79103i	−0.0388895	+	0.0673585i
$708$		0			0
$709$	−19.9104	−	34.4859i	−0.747752	−	1.29515i	−0.948898	−	0.315584i	$-0.897800\pi$
$709$	−19.9104	−	34.4859i	−0.747752	−	1.29515i	0.201145	−	0.979561i	$-0.435534\pi$
$710$	14.3796			0.539657
$711$		0			0
$712$	−111.085			−4.16307
$713$	8.38694	+	14.5266i	0.314093	+	0.544025i
$714$		0			0
$715$	−26.5858	+	46.0479i	−0.994251	+	1.72209i
$716$	−30.3875	+	52.6327i	−1.13563	+	1.96697i
$717$		0			0
$718$	−1.61495	−	2.79717i	−0.0602693	−	0.104389i
$719$	47.8875			1.78590			0.892952	−	0.450152i	$-0.148630\pi$
$719$	47.8875			1.78590			0.892952	+	0.450152i	$0.148630\pi$
$720$		0			0
$721$	−44.5664			−1.65974
$722$	−12.9687	−	22.4624i	−0.482645	−	0.835966i
$723$		0			0
$724$	−46.9452	+	81.3115i	−1.74470	+	3.02192i
$725$	−0.251854	+	0.436224i	−0.00935363	+	0.0162010i
$726$		0			0
$727$	13.4309	+	23.2630i	0.498124	+	0.862776i	0.999998	−	0.00216520i	$-0.000689204\pi$
$727$	13.4309	+	23.2630i	0.498124	+	0.862776i	−0.501874	+	0.864941i	$0.667356\pi$
$728$	196.638			7.28788
$729$		0			0
$730$	−12.6441			−0.467978
$731$	1.72252	+	2.98349i	0.0637097	+	0.110348i
$732$		0			0
$733$	−1.15702	+	2.00401i	−0.0427354	+	0.0740198i	−0.886602	−	0.462533i	$-0.846941\pi$
$733$	−1.15702	+	2.00401i	−0.0427354	+	0.0740198i	0.843867	+	0.536553i	$0.180274\pi$
$734$	6.98598	−	12.1001i	0.257857	−	0.446622i
$735$		0			0
$736$	44.9805	+	77.9085i	1.65800	+	2.87174i
$737$	−5.96266			−0.219637
$738$		0			0
$739$	30.1874			1.11046			0.555232	−	0.831696i	$-0.312630\pi$
$739$	30.1874			1.11046			0.555232	+	0.831696i	$0.312630\pi$
$740$	−41.0852	−	71.1616i	−1.51032	−	2.61595i
$741$		0			0
$742$	−26.1539	+	45.2998i	−0.960139	+	1.66301i
$743$	−5.27571	+	9.13781i	−0.193547	+	0.335234i	−0.946423	−	0.322929i	$-0.895333\pi$
$743$	−5.27571	+	9.13781i	−0.193547	+	0.335234i	0.752876	+	0.658162i	$0.228666\pi$
$744$		0			0
$745$	−26.1599	−	45.3102i	−0.958423	−	1.66004i
$746$	41.4452			1.51742
$747$		0			0
$748$	−77.0066			−2.81564
$749$	4.37840	+	7.58361i	0.159983	+	0.277099i
$750$		0			0
$751$	−6.47677	+	11.2181i	−0.236341	+	0.409354i	−0.959661	−	0.281158i	$-0.909281\pi$
$751$	−6.47677	+	11.2181i	−0.236341	+	0.409354i	0.723321	+	0.690512i	$0.242615\pi$
$752$	−24.5748	+	42.5647i	−0.896149	+	1.55218i
$753$		0			0
$754$	−6.11001	−	10.5828i	−0.222513	−	0.385405i
$755$	−16.0462			−0.583980
$756$		0			0
$757$	−43.0070			−1.56312			−0.781558	−	0.623833i	$-0.785575\pi$
$757$	−43.0070			−1.56312			−0.781558	+	0.623833i	$0.785575\pi$
$758$	−22.6123	−	39.1657i	−0.821316	−	1.42256i
$759$		0			0
$760$	−34.0093	+	58.9059i	−1.23365	+	2.13674i
$761$	6.39939	−	11.0841i	0.231978	−	0.401797i	−0.726412	−	0.687259i	$-0.758814\pi$
$761$	6.39939	−	11.0841i	0.231978	−	0.401797i	0.958390	+	0.285462i	$0.0921470\pi$
$762$		0			0
$763$	−9.48136	−	16.4222i	−0.343248	−	0.594523i
$764$	73.1593			2.64681
$765$		0			0
$766$	4.50160			0.162649
$767$	−33.1575	−	57.4304i	−1.19725	−	2.07369i
$768$		0			0
$769$	1.34641	−	2.33204i	0.0485526	−	0.0840956i	−0.840728	−	0.541458i	$-0.817872\pi$
$769$	1.34641	−	2.33204i	0.0485526	−	0.0840956i	0.889280	+	0.457362i	$0.151206\pi$
$770$	−51.5045	+	89.2085i	−1.85609	+	3.21485i
$771$		0			0
$772$	−42.0753	−	72.8765i	−1.51432	−	2.62288i
$773$	−43.8593			−1.57751			−0.788755	−	0.614708i	$-0.789274\pi$
$773$	−43.8593			−1.57751			−0.788755	+	0.614708i	$0.789274\pi$
$774$		0			0
$775$	−2.39724			−0.0861113
$776$	−31.9987	−	55.4233i	−1.14869	−	1.98958i
$777$		0			0
$778$	4.92420	−	8.52896i	0.176541	−	0.305778i
$779$	−1.28703	+	2.22920i	−0.0461125	+	0.0798692i
$780$		0			0
$781$	−4.59186	−	7.95334i	−0.164310	−	0.284593i
$782$	40.1639			1.43626
$783$		0			0
$784$	116.398			4.15705
$785$	20.5789	+	35.6437i	0.734493	+	1.27218i
$786$		0			0
$787$	−5.22766	+	9.05457i	−0.186346	+	0.322761i	−0.944029	−	0.329862i	$-0.892998\pi$
$787$	−5.22766	+	9.05457i	−0.186346	+	0.322761i	0.757683	+	0.652622i	$0.226331\pi$
$788$	−10.9456	+	18.9584i	−0.389922	+	0.675365i
$789$		0			0
$790$	−27.5674	−	47.7482i	−0.980805	−	1.69880i
$791$	0.317190			0.0112780
$792$		0			0
$793$	60.0649			2.13297
$794$	−35.7434	−	61.9094i	−1.26849	−	2.19708i
$795$		0			0
$796$	62.0365	−	107.450i	2.19883	−	3.80848i
$797$	12.0676	−	20.9017i	0.427456	−	0.740376i	−0.569190	−	0.822206i	$-0.692743\pi$
$797$	12.0676	−	20.9017i	0.427456	−	0.740376i	0.996646	+	0.0818301i	$0.0260765\pi$
$798$		0			0
$799$	5.81376	+	10.0697i	0.205676	+	0.356241i
$800$	−12.8568			−0.454555
$801$		0			0
$802$	−12.8836			−0.454935
$803$	4.03765	+	6.99341i	0.142486	+	0.246792i
$804$		0			0
$805$	19.6251	−	33.9917i	0.691694	−	1.19805i
$806$	29.0786	−	50.3656i	1.02425	−	1.77405i
$807$		0			0
$808$	2.49046	+	4.31360i	0.0876139	+	0.151752i
$809$	−23.5605			−0.828342			−0.414171	−	0.910199i	$-0.635929\pi$
$809$	−23.5605			−0.828342			−0.414171	+	0.910199i	$0.635929\pi$
$810$		0			0
$811$	30.9321			1.08617			0.543087	−	0.839677i	$-0.317255\pi$
$811$	30.9321			1.08617			0.543087	+	0.839677i	$0.317255\pi$
$812$	−8.64762	−	14.9781i	−0.303472	−	0.525629i
$813$		0			0
$814$	−35.9169	+	62.2099i	−1.25889	+	2.18045i
$815$	9.79802	−	16.9707i	0.343210	−	0.594457i
$816$		0			0
$817$	−1.53948	−	2.66645i	−0.0538595	−	0.0932873i
$818$	44.1318			1.54303
$819$		0			0
$820$	−10.7396			−0.375044
$821$	19.5949	+	33.9393i	0.683866	+	1.18449i	0.973792	+	0.227441i	$0.0730359\pi$
$821$	19.5949	+	33.9393i	0.683866	+	1.18449i	−0.289926	+	0.957049i	$0.593631\pi$
$822$		0			0
$823$	−6.35307	+	11.0038i	−0.221454	+	0.383569i	−0.955250	−	0.295801i	$-0.904414\pi$
$823$	−6.35307	+	11.0038i	−0.221454	+	0.383569i	0.733796	+	0.679370i	$0.237747\pi$
$824$	−53.6679	+	92.9556i	−1.86961	+	3.23826i
$825$		0			0
$826$	−64.2359	−	111.260i	−2.23505	−	3.87122i
$827$	−5.03431			−0.175060			−0.0875300	−	0.996162i	$-0.527897\pi$
$827$	−5.03431			−0.175060			−0.0875300	+	0.996162i	$0.527897\pi$
$828$		0			0
$829$	36.3613			1.26288			0.631439	−	0.775425i	$-0.282464\pi$
$829$	36.3613			1.26288			0.631439	+	0.775425i	$0.282464\pi$
$830$	22.0237	+	38.1462i	0.764455	+	1.32408i
$831$		0			0
$832$	76.6548	−	132.770i	2.65753	−	4.60297i
$833$	13.7683	−	23.8475i	0.477045	−	0.826266i
$834$		0			0
$835$	−8.15009	−	14.1164i	−0.282045	−	0.488517i
$836$	68.8235			2.38031
$837$		0			0
$838$	50.1772			1.73334
$839$	−24.5196	−	42.4691i	−0.846509	−	1.46620i	−0.884304	−	0.466912i	$-0.845367\pi$
$839$	−24.5196	−	42.4691i	−0.846509	−	1.46620i	0.0377943	−	0.999286i	$-0.487967\pi$
$840$		0			0
$841$	14.1608	−	24.5272i	0.488303	−	0.845766i
$842$	−37.1367	+	64.3227i	−1.27982	+	2.21671i
$843$		0			0
$844$	22.6152	+	39.1706i	0.778446	+	1.34831i
$845$	−39.4498			−1.35711
$846$		0			0
$847$	23.1950			0.796990
$848$	36.1018	+	62.5302i	1.23974	+	2.14730i
$849$		0			0
$850$	−2.87001	+	4.97101i	−0.0984406	+	0.170504i
$851$	13.6857	−	23.7042i	0.469138	−	0.812571i
$852$		0			0
$853$	−7.06487	−	12.2367i	−0.241897	−	0.418977i	0.719358	−	0.694640i	$-0.244436\pi$
$853$	−7.06487	−	12.2367i	−0.241897	−	0.418977i	−0.961255	+	0.275662i	$0.911103\pi$
$854$	116.364			3.98188
$855$		0			0
$856$	21.0903			0.720852
$857$	0.797123	+	1.38066i	0.0272292	+	0.0471624i	0.879319	−	0.476233i	$-0.157998\pi$
$857$	0.797123	+	1.38066i	0.0272292	+	0.0471624i	−0.852090	+	0.523396i	$0.824665\pi$
$858$		0			0
$859$	12.3404	−	21.3743i	0.421050	−	0.729280i	−0.574992	−	0.818159i	$-0.694995\pi$
$859$	12.3404	−	21.3743i	0.421050	−	0.729280i	0.996042	+	0.0888786i	$0.0283283\pi$
$860$	6.42309	−	11.1251i	0.219026	−	0.379364i
$861$		0			0
$862$	−43.7715	−	75.8144i	−1.49086	−	2.58225i
$863$	−39.9282			−1.35917			−0.679585	−	0.733596i	$-0.737840\pi$
$863$	−39.9282			−1.35917			−0.679585	+	0.733596i	$0.737840\pi$
$864$		0			0
$865$	22.7026			0.771911
$866$	−43.4334	−	75.2289i	−1.47593	−	2.55638i
$867$		0			0
$868$	41.1555	−	71.2834i	1.39691	−	2.41952i
$869$	−17.6063	+	30.4950i	−0.597252	+	1.03447i
$870$		0			0
$871$	−3.93864	−	6.82193i	−0.133456	−	0.231152i
$872$	−45.6707			−1.54661
$873$		0			0
$874$	−35.8959			−1.21420
$875$	−20.1265	−	34.8602i	−0.680401	−	1.17849i
$876$		0			0
$877$	26.0193	−	45.0668i	0.878610	−	1.52180i	0.0257432	−	0.999669i	$-0.491805\pi$
$877$	26.0193	−	45.0668i	0.878610	−	1.52180i	0.852867	−	0.522129i	$-0.174862\pi$
$878$	−41.5898	+	72.0356i	−1.40359	+	2.43108i
$879$		0			0
$880$	71.0949	+	123.140i	2.39661	+	4.15105i
$881$	6.56038			0.221025			0.110512	−	0.993875i	$-0.464751\pi$
$881$	6.56038			0.221025			0.110512	+	0.993875i	$0.464751\pi$
$882$		0			0
$883$	−13.3395			−0.448910			−0.224455	−	0.974484i	$-0.572060\pi$
$883$	−13.3395			−0.448910			−0.224455	+	0.974484i	$0.572060\pi$
$884$	−50.8668	−	88.1039i	−1.71084	−	2.96326i
$885$		0			0
$886$	−43.6319	+	75.5727i	−1.46584	+	2.53891i
$887$	6.85452	−	11.8724i	0.230152	−	0.398635i	−0.727701	−	0.685895i	$-0.759411\pi$
$887$	6.85452	−	11.8724i	0.230152	−	0.398635i	0.957853	+	0.287260i	$0.0927443\pi$
$888$		0			0
$889$	21.7703	+	37.7072i	0.730151	+	1.26466i
$890$	76.8775			2.57694
$891$		0			0
$892$	88.6619			2.96862
$893$	−5.19596	−	8.99966i	−0.173876	−	0.301162i
$894$		0			0
$895$	13.2740	−	22.9913i	0.443702	−	0.768515i
$896$	67.0991	−	116.219i	2.24163	−	3.88261i
$897$		0			0
$898$	−10.6048	−	18.3680i	−0.353886	−	0.612948i
$899$	−3.22869			−0.107683
$900$		0			0
$901$	17.0815			0.569069
$902$	4.69431	+	8.13079i	0.156304	+	0.270726i
$903$		0			0
$904$	0.381967	−	0.661587i	0.0127040	−	0.0220041i
$905$	20.5069	−	35.5190i	0.681672	−	1.18069i
$906$		0			0
$907$	−15.2871	−	26.4781i	−0.507601	−	0.879191i	−0.999961	−	0.00879920i	$-0.997199\pi$
$907$	−15.2871	−	26.4781i	−0.507601	−	0.879191i	0.492360	−	0.870391i	$-0.336134\pi$
$908$	−37.0116			−1.22827
$909$		0			0
$910$	−136.086			−4.51119
$911$	15.5598	+	26.9504i	0.515519	+	0.892905i	0.999838	+	0.0180135i	$0.00573418\pi$
$911$	15.5598	+	26.9504i	0.515519	+	0.892905i	−0.484319	+	0.874892i	$0.660932\pi$
$912$		0			0
$913$	14.0657	−	24.3626i	0.465508	−	0.806284i
$914$	28.8782	−	50.0184i	0.955204	−	1.65446i
$915$		0			0
$916$	1.64095	+	2.84221i	0.0542185	+	0.0939091i
$917$	43.8401			1.44773
$918$		0			0
$919$	49.9506			1.64772			0.823859	−	0.566795i	$-0.191817\pi$
$919$	49.9506			1.64772			0.823859	+	0.566795i	$0.191817\pi$
$920$	−47.2661	−	81.8673i	−1.55832	−	2.69908i
$921$		0			0
$922$	−18.6380	+	32.2820i	−0.613810	+	1.06315i
$923$	6.06632	−	10.5072i	0.199675	−	0.345848i
$924$		0			0
$925$	1.95588	+	3.38769i	0.0643090	+	0.111387i
$926$	73.4292			2.41303
$927$		0			0
$928$	−17.3160			−0.568424
$929$	17.5644	+	30.4225i	0.576271	+	0.998130i	0.995902	+	0.0904359i	$0.0288260\pi$
$929$	17.5644	+	30.4225i	0.576271	+	0.998130i	−0.419631	+	0.907695i	$0.637841\pi$
$930$		0			0
$931$	−12.3052	+	21.3133i	−0.403288	+	0.698515i
$932$	−65.9351	+	114.203i	−2.15978	+	3.74084i
$933$		0			0
$934$	11.2829	+	19.5426i	0.369188	+	0.639452i
$935$	33.6385			1.10010
$936$		0			0
$937$	50.6512			1.65470			0.827351	−	0.561686i	$-0.189847\pi$
$937$	50.6512			1.65470			0.827351	+	0.561686i	$0.189847\pi$
$938$	−7.63032	−	13.2161i	−0.249139	−	0.431521i
$939$		0			0
$940$	21.6789	−	37.5489i	0.707087	−	1.22471i
$941$	19.6932	−	34.1096i	0.641979	−	1.11194i	−0.343012	−	0.939331i	$-0.611447\pi$
$941$	19.6932	−	34.1096i	0.641979	−	1.11194i	0.984990	−	0.172609i	$-0.0552196\pi$
$942$		0			0
$943$	−1.78871	−	3.09813i	−0.0582483	−	0.100889i
$944$	−177.338			−5.77184
$945$		0			0
$946$	−11.2302			−0.365126
$947$	15.0264	+	26.0265i	0.488293	+	0.845749i	0.999909	−	0.0134654i	$-0.00428630\pi$
$947$	15.0264	+	26.0265i	0.488293	+	0.845749i	−0.511616	+	0.859214i	$0.670953\pi$
$948$		0			0
$949$	−5.33415	+	9.23902i	−0.173154	+	0.299911i
$950$	2.56503	−	4.44276i	0.0832206	−	0.144142i
$951$		0			0
$952$	−62.2006	−	107.735i	−2.01593	−	3.49170i
$953$	−33.5633			−1.08722			−0.543612	−	0.839337i	$-0.682944\pi$
$953$	−33.5633			−1.08722			−0.543612	+	0.839337i	$0.682944\pi$
$954$		0			0
$955$	−31.9579			−1.03413
$956$	60.2319	+	104.325i	1.94804	+	3.37410i
$957$		0			0
$958$	−45.9288	+	79.5511i	−1.48389	+	2.57018i
$959$	31.5132	−	54.5825i	1.01761	−	1.76256i
$960$		0			0
$961$	7.81706	+	13.5395i	0.252163	+	0.436759i
$962$	−94.8998			−3.05969
$963$		0			0
$964$	88.2315			2.84174
$965$	18.3796	+	31.8343i	0.591659	+	1.02478i
$966$		0			0
$967$	18.1872	−	31.5012i	0.584862	−	1.01301i	−0.410031	−	0.912072i	$-0.634482\pi$
$967$	18.1872	−	31.5012i	0.584862	−	1.01301i	0.994893	−	0.100939i	$-0.0321846\pi$
$968$	27.9320	−	48.3796i	0.897768	−	1.55498i
$969$		0			0
$970$	22.1451	+	38.3564i	0.711035	+	1.23155i
$971$	−12.8615			−0.412745			−0.206372	−	0.978474i	$-0.566166\pi$
$971$	−12.8615			−0.412745			−0.206372	+	0.978474i	$0.566166\pi$
$972$		0			0
$973$	−26.1095			−0.837032
$974$	−4.02682	−	6.97465i	−0.129028	−	0.223482i
$975$		0			0
$976$	80.3120	−	139.104i	2.57072	−	4.45262i
$977$	−9.38786	+	16.2602i	−0.300344	+	0.520211i	−0.976214	−	0.216810i	$-0.930435\pi$
$977$	−9.38786	+	16.2602i	−0.300344	+	0.520211i	0.675870	+	0.737021i	$0.263768\pi$
$978$		0			0
$979$	−24.5494	−	42.5208i	−0.784603	−	1.35897i
$980$	−102.681			−3.28003
$981$		0			0
$982$	−99.6053			−3.17853
$983$	−5.70454	−	9.88055i	−0.181946	−	0.315140i	0.760597	−	0.649224i	$-0.224906\pi$
$983$	−5.70454	−	9.88055i	−0.181946	−	0.315140i	−0.942543	+	0.334084i	$0.891573\pi$
$984$		0			0
$985$	4.78134	−	8.28152i	0.152346	−	0.263871i
$986$	−3.86544	+	6.69514i	−0.123101	+	0.213217i
$987$		0			0
$988$	45.4615	+	78.7415i	1.44632	+	2.50510i
$989$	4.27912			0.136068
$990$		0			0
$991$	−15.7239			−0.499487			−0.249743	−	0.968312i	$-0.580346\pi$
$991$	−15.7239			−0.499487			−0.249743	+	0.968312i	$0.580346\pi$
$992$	−41.2048	−	71.3689i	−1.30826	−	2.26596i
$993$		0			0
$994$	11.7523	−	20.3555i	0.372759	−	0.645638i
$995$	−27.0992	+	46.9372i	−0.859102	+	1.48801i
$996$		0			0
$997$	−2.48825	−	4.30977i	−0.0788035	−	0.136492i	0.823930	−	0.566691i	$-0.191777\pi$
$997$	−2.48825	−	4.30977i	−0.0788035	−	0.136492i	−0.902734	+	0.430199i	$0.858443\pi$
$998$	78.7826			2.49382
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1161.2.f.c.388.19		38
3.2	odd	2		387.2.f.c.130.1	✓	38
9.2	odd	6		387.2.f.c.259.1	yes	38
9.4	even	3		3483.2.a.r.1.1		19
9.5	odd	6		3483.2.a.s.1.19		19
9.7	even	3	inner	1161.2.f.c.775.19		38

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
387.2.f.c.130.1	✓	38	3.2	odd	2
387.2.f.c.259.1	yes	38	9.2	odd	6
1161.2.f.c.388.19		38	1.1	even	1	trivial
1161.2.f.c.775.19		38	9.7	even	3	inner
3483.2.a.r.1.1		19	9.4	even	3
3483.2.a.s.1.19		19	9.5	odd	6

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:	\( N \)	\(=\)	\( 1161 = 3^{3} \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1161.f (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.36225 + 2.35949i) q^{2} +(-2.71146 + 4.69638i) q^{4} +(1.18444 - 2.05150i) q^{5} +(-1.93605 - 3.35333i) q^{7} -9.32575 q^{8} +O(q^{10})\)	\(q+(1.36225 + 2.35949i) q^{2} +(-2.71146 + 4.69638i) q^{4} +(1.18444 - 2.05150i) q^{5} +(-1.93605 - 3.35333i) q^{7} -9.32575 q^{8} +6.45400 q^{10} +(-2.06096 - 3.56969i) q^{11} +(2.72275 - 4.71594i) q^{13} +(5.27477 - 9.13617i) q^{14} +(-7.28109 - 12.6112i) q^{16} -3.44504 q^{17} +3.07895 q^{19} +(6.42309 + 11.1251i) q^{20} +(5.61510 - 9.72564i) q^{22} +(-2.13956 + 3.70583i) q^{23} +(-0.305775 - 0.529618i) q^{25} +14.8363 q^{26} +20.9981 q^{28} +(-0.411829 - 0.713309i) q^{29} +(1.95997 - 3.39476i) q^{31} +(10.5116 - 18.2067i) q^{32} +(-4.69301 - 8.12854i) q^{34} -9.17250 q^{35} -6.39648 q^{37} +(4.19431 + 7.26476i) q^{38} +(-11.0457 + 19.1318i) q^{40} +(-0.418008 + 0.724011i) q^{41} +(-0.500000 - 0.866025i) q^{43} +22.3529 q^{44} -11.6585 q^{46} +(-1.68757 - 2.92296i) q^{47} +(-3.99657 + 6.92226i) q^{49} +(0.833085 - 1.44295i) q^{50} +(14.7652 + 25.5741i) q^{52} -4.95830 q^{53} -9.76432 q^{55} +(18.0551 + 31.2723i) q^{56} +(1.12203 - 1.94341i) q^{58} +(6.08897 - 10.5464i) q^{59} +(5.51510 + 9.55244i) q^{61} +10.6799 q^{62} +28.1535 q^{64} +(-6.44984 - 11.1714i) q^{65} +(0.723285 - 1.25277i) q^{67} +(9.34109 - 16.1792i) q^{68} +(-12.4952 - 21.6424i) q^{70} +2.22802 q^{71} -1.95911 q^{73} +(-8.71361 - 15.0924i) q^{74} +(-8.34845 + 14.4599i) q^{76} +(-7.98025 + 13.8222i) q^{77} +(-4.27137 - 7.39823i) q^{79} -34.4959 q^{80} -2.27773 q^{82} +(3.41242 + 5.91048i) q^{83} +(-4.08043 + 7.06751i) q^{85} +(1.36225 - 2.35949i) q^{86} +(19.2200 + 33.2901i) q^{88} +11.9116 q^{89} -21.0855 q^{91} +(-11.6027 - 20.0964i) q^{92} +(4.59780 - 7.96362i) q^{94} +(3.64682 - 6.31648i) q^{95} +(3.43122 + 5.94304i) q^{97} -21.7773 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 38 q + 4 q^{2} - 22 q^{4} + 9 q^{5} - 7 q^{7} - 24 q^{8}+O(q^{10}) \) 38 * q + 4 * q^2 - 22 * q^4 + 9 * q^5 - 7 * q^7 - 24 * q^8	\( 38 q + 4 q^{2} - 22 q^{4} + 9 q^{5} - 7 q^{7} - 24 q^{8} - 14 q^{10} + 5 q^{11} + 5 q^{13} + 17 q^{14} - 24 q^{16} - 42 q^{17} - 8 q^{19} + 21 q^{20} + 20 q^{22} + 22 q^{23} - 10 q^{25} - 34 q^{26} - 2 q^{28} + 30 q^{29} + 5 q^{31} + 48 q^{32} + 6 q^{34} - 106 q^{35} - 2 q^{37} + 21 q^{38} - 16 q^{40} + 29 q^{41} - 19 q^{43} - 58 q^{44} + 32 q^{47} + 10 q^{49} - 11 q^{50} - q^{52} - 76 q^{53} + 4 q^{55} + 46 q^{56} - 30 q^{58} + 30 q^{59} + 10 q^{61} - 50 q^{62} + 28 q^{64} + 8 q^{65} - 3 q^{67} + 47 q^{68} - 56 q^{70} - 42 q^{71} + 16 q^{73} + 28 q^{74} + 36 q^{76} + 49 q^{77} - 4 q^{79} - 140 q^{80} - 8 q^{82} + 29 q^{83} + 4 q^{85} + 4 q^{86} + 47 q^{88} - 108 q^{89} + 8 q^{91} + 12 q^{92} + 23 q^{94} + 33 q^{95} + 4 q^{97} - 98 q^{98}+O(q^{100}) \) 38 * q + 4 * q^2 - 22 * q^4 + 9 * q^5 - 7 * q^7 - 24 * q^8 - 14 * q^10 + 5 * q^11 + 5 * q^13 + 17 * q^14 - 24 * q^16 - 42 * q^17 - 8 * q^19 + 21 * q^20 + 20 * q^22 + 22 * q^23 - 10 * q^25 - 34 * q^26 - 2 * q^28 + 30 * q^29 + 5 * q^31 + 48 * q^32 + 6 * q^34 - 106 * q^35 - 2 * q^37 + 21 * q^38 - 16 * q^40 + 29 * q^41 - 19 * q^43 - 58 * q^44 + 32 * q^47 + 10 * q^49 - 11 * q^50 - q^52 - 76 * q^53 + 4 * q^55 + 46 * q^56 - 30 * q^58 + 30 * q^59 + 10 * q^61 - 50 * q^62 + 28 * q^64 + 8 * q^65 - 3 * q^67 + 47 * q^68 - 56 * q^70 - 42 * q^71 + 16 * q^73 + 28 * q^74 + 36 * q^76 + 49 * q^77 - 4 * q^79 - 140 * q^80 - 8 * q^82 + 29 * q^83 + 4 * q^85 + 4 * q^86 + 47 * q^88 - 108 * q^89 + 8 * q^91 + 12 * q^92 + 23 * q^94 + 33 * q^95 + 4 * q^97 - 98 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more