LMFDB - Embedded newform 1161.2.f.c.775.6

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			775.6
Character	$\chi$	$=$	1161.775
Dual form			1161.2.f.c.388.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.649321 + 1.12466i) q^{2} +(0.156764 + 0.271524i) q^{4} +(-1.38166 - 2.39311i) q^{5} +(-0.516159 + 0.894013i) q^{7} -3.00445 q^{8} +O(q^{10})$	\(q+(-0.649321 + 1.12466i) q^{2} +(0.156764 + 0.271524i) q^{4} +(-1.38166 - 2.39311i) q^{5} +(-0.516159 + 0.894013i) q^{7} -3.00445 q^{8} +3.58856 q^{10} +(1.47222 - 2.54996i) q^{11} +(1.68562 + 2.91958i) q^{13} +(-0.670305 - 1.16100i) q^{14} +(1.63732 - 2.83592i) q^{16} -1.55106 q^{17} +0.820840 q^{19} +(0.433190 - 0.750307i) q^{20} +(1.91188 + 3.31148i) q^{22} +(4.29584 + 7.44062i) q^{23} +(-1.31797 + 2.28279i) q^{25} -4.37804 q^{26} -0.323661 q^{28} +(-0.623396 + 1.07975i) q^{29} +(0.962734 + 1.66750i) q^{31} +(-0.878152 - 1.52100i) q^{32} +(1.00714 - 1.74442i) q^{34} +2.85262 q^{35} -4.44739 q^{37} +(-0.532989 + 0.923164i) q^{38} +(4.15112 + 7.18996i) q^{40} +(3.13620 + 5.43205i) q^{41} +(-0.500000 + 0.866025i) q^{43} +0.923165 q^{44} -11.1575 q^{46} +(-5.05055 + 8.74780i) q^{47} +(2.96716 + 5.13927i) q^{49} +(-1.71157 - 2.96453i) q^{50} +(-0.528491 + 0.915373i) q^{52} -8.79973 q^{53} -8.13642 q^{55} +(1.55077 - 2.68601i) q^{56} +(-0.809568 - 1.40221i) q^{58} +(3.31596 + 5.74341i) q^{59} +(0.0348705 - 0.0603975i) q^{61} -2.50049 q^{62} +8.83009 q^{64} +(4.65791 - 8.06774i) q^{65} +(5.76481 + 9.98494i) q^{67} +(-0.243152 - 0.421151i) q^{68} +(-1.85227 + 3.20822i) q^{70} +5.88849 q^{71} +1.89767 q^{73} +(2.88779 - 5.00179i) q^{74} +(0.128678 + 0.222878i) q^{76} +(1.51980 + 2.63236i) q^{77} +(-3.49563 + 6.05462i) q^{79} -9.04889 q^{80} -8.14560 q^{82} +(1.50913 - 2.61390i) q^{83} +(2.14304 + 3.71186i) q^{85} +(-0.649321 - 1.12466i) q^{86} +(-4.42320 + 7.66120i) q^{88} +15.2655 q^{89} -3.48019 q^{91} +(-1.34687 + 2.33285i) q^{92} +(-6.55885 - 11.3603i) q^{94} +(-1.13412 - 1.96436i) q^{95} +(1.93718 - 3.35530i) q^{97} -7.70656 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/1161\mathbb{Z}\right)^\times$.

$n$	$433$	$947$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−0.649321	+	1.12466i	−0.459139	+	0.795253i	−0.998916	−	0.0465558i	$-0.985175\pi$
$2$	−0.649321	+	1.12466i	−0.459139	+	0.795253i	0.539776	+	0.841808i	$0.318509\pi$
$3$		0			0
$3$		0			0
$4$	0.156764	+	0.271524i	0.0783822	+	0.135762i
$5$	−1.38166	−	2.39311i	−0.617897	−	1.07023i	−0.989869	−	0.141985i	$-0.954651\pi$
$5$	−1.38166	−	2.39311i	−0.617897	−	1.07023i	0.371972	−	0.928244i	$-0.378682\pi$
$6$		0			0
$7$	−0.516159	+	0.894013i	−0.195090	+	0.337905i	−0.946930	−	0.321440i	$-0.895833\pi$
$7$	−0.516159	+	0.894013i	−0.195090	+	0.337905i	0.751840	+	0.659345i	$0.229166\pi$
$8$	−3.00445			−1.06223
$9$		0			0
$10$	3.58856			1.13480
$11$	1.47222	−	2.54996i	0.443890	−	0.768841i	−0.554084	−	0.832461i	$-0.686931\pi$
$11$	1.47222	−	2.54996i	0.443890	−	0.768841i	0.997974	+	0.0636203i	$0.0202647\pi$
$12$		0			0
$13$	1.68562	+	2.91958i	0.467507	+	0.809747i	0.999311	−	0.0371213i	$-0.0118188\pi$
$13$	1.68562	+	2.91958i	0.467507	+	0.809747i	−0.531803	+	0.846868i	$0.678485\pi$
$14$	−0.670305	−	1.16100i	−0.179147	−	0.310291i
$15$		0			0
$16$	1.63732	−	2.83592i	0.409330	−	0.708981i
$17$	−1.55106			−0.376188			−0.188094	−	0.982151i	$-0.560231\pi$
$17$	−1.55106			−0.376188			−0.188094	+	0.982151i	$0.560231\pi$
$18$		0			0
$19$	0.820840			0.188314			0.0941568	−	0.995557i	$-0.469984\pi$
$19$	0.820840			0.188314			0.0941568	+	0.995557i	$0.469984\pi$
$20$	0.433190	−	0.750307i	0.0968643	−	0.167774i
$21$		0			0
$22$	1.91188	+	3.31148i	0.407615	+	0.706010i
$23$	4.29584	+	7.44062i	0.895745	+	1.55148i	0.832880	+	0.553454i	$0.186691\pi$
$23$	4.29584	+	7.44062i	0.895745	+	1.55148i	0.0628656	+	0.998022i	$0.479976\pi$
$24$		0			0
$25$	−1.31797	+	2.28279i	−0.263594	+	0.456558i
$26$	−4.37804			−0.858604
$27$		0			0
$28$	−0.323661			−0.0611662
$29$	−0.623396	+	1.07975i	−0.115762	+	0.200505i	−0.918084	−	0.396386i	$-0.870264\pi$
$29$	−0.623396	+	1.07975i	−0.115762	+	0.200505i	0.802322	+	0.596891i	$0.203598\pi$
$30$		0			0
$31$	0.962734	+	1.66750i	0.172912	+	0.299493i	0.939437	−	0.342722i	$-0.111349\pi$
$31$	0.962734	+	1.66750i	0.172912	+	0.299493i	−0.766525	+	0.642215i	$0.778016\pi$
$32$	−0.878152	−	1.52100i	−0.155237	−	0.268878i
$33$		0			0
$34$	1.00714	−	1.74442i	0.172723	−	0.299165i
$35$	2.85262			0.482181
$36$		0			0
$37$	−4.44739			−0.731147			−0.365574	−	0.930782i	$-0.619127\pi$
$37$	−4.44739			−0.731147			−0.365574	+	0.930782i	$0.619127\pi$
$38$	−0.532989	+	0.923164i	−0.0864622	+	0.149757i
$39$		0			0
$40$	4.15112	+	7.18996i	0.656350	+	1.13683i
$41$	3.13620	+	5.43205i	0.489792	+	0.848344i	0.999931	−	0.0117476i	$-0.00373948\pi$
$41$	3.13620	+	5.43205i	0.489792	+	0.848344i	−0.510139	+	0.860092i	$0.670406\pi$
$42$		0			0
$43$	−0.500000	+	0.866025i	−0.0762493	+	0.132068i
$43$	−0.500000	+	0.866025i	−0.0762493	+	0.132068i
$44$	0.923165			0.139172
$45$		0			0
$46$	−11.1575			−1.64509
$47$	−5.05055	+	8.74780i	−0.736698	+	1.27600i	0.217276	+	0.976110i	$0.430283\pi$
$47$	−5.05055	+	8.74780i	−0.736698	+	1.27600i	−0.953974	+	0.299888i	$0.903051\pi$
$48$		0			0
$49$	2.96716	+	5.13927i	0.423880	+	0.734182i
$50$	−1.71157	−	2.96453i	−0.242053	−	0.419248i
$51$		0			0
$52$	−0.528491	+	0.915373i	−0.0732885	+	0.126939i
$53$	−8.79973			−1.20874			−0.604368	−	0.796705i	$-0.706574\pi$
$53$	−8.79973			−1.20874			−0.604368	+	0.796705i	$0.706574\pi$
$54$		0			0
$55$	−8.13642			−1.09711
$56$	1.55077	−	2.68601i	0.207230	−	0.358934i
$57$		0			0
$58$	−0.809568	−	1.40221i	−0.106301	−	0.184120i
$59$	3.31596	+	5.74341i	0.431701	+	0.747728i	0.997020	−	0.0771446i	$-0.0245803\pi$
$59$	3.31596	+	5.74341i	0.431701	+	0.747728i	−0.565319	+	0.824872i	$0.691247\pi$
$60$		0			0
$61$	0.0348705	−	0.0603975i	0.00446471	−	0.00773310i	−0.863784	−	0.503862i	$-0.831912\pi$
$61$	0.0348705	−	0.0603975i	0.00446471	−	0.00773310i	0.868249	+	0.496128i	$0.165246\pi$
$62$	−2.50049			−0.317563
$63$		0			0
$64$	8.83009			1.10376
$65$	4.65791	−	8.06774i	0.577743	−	1.00068i
$66$		0			0
$67$	5.76481	+	9.98494i	0.704283	+	1.21985i	0.966950	+	0.254967i	$0.0820647\pi$
$67$	5.76481	+	9.98494i	0.704283	+	1.21985i	−0.262667	+	0.964887i	$0.584602\pi$
$68$	−0.243152	−	0.421151i	−0.0294865	−	0.0510720i
$69$		0			0
$70$	−1.85227	+	3.20822i	−0.221388	+	0.383456i
$71$	5.88849			0.698835			0.349418	−	0.936967i	$-0.386379\pi$
$71$	5.88849			0.698835			0.349418	+	0.936967i	$0.386379\pi$
$72$		0			0
$73$	1.89767			0.222105			0.111053	−	0.993815i	$-0.464578\pi$
$73$	1.89767			0.222105			0.111053	+	0.993815i	$0.464578\pi$
$74$	2.88779	−	5.00179i	0.335698	−	0.581447i
$75$		0			0
$76$	0.128678	+	0.222878i	0.0147604	+	0.0255658i
$77$	1.51980	+	2.63236i	0.173197	+	0.299986i
$78$		0			0
$79$	−3.49563	+	6.05462i	−0.393290	+	0.681198i	−0.992881	−	0.119109i	$-0.961996\pi$
$79$	−3.49563	+	6.05462i	−0.393290	+	0.681198i	0.599592	+	0.800306i	$0.295330\pi$
$80$	−9.04889			−1.01170
$81$		0			0
$82$	−8.14560			−0.899531
$83$	1.50913	−	2.61390i	0.165649	−	0.286912i	−0.771237	−	0.636549i	$-0.780361\pi$
$83$	1.50913	−	2.61390i	0.165649	−	0.286912i	0.936886	+	0.349636i	$0.113695\pi$
$84$		0			0
$85$	2.14304	+	3.71186i	0.232446	+	0.402608i
$86$	−0.649321	−	1.12466i	−0.0700181	−	0.121275i
$87$		0			0
$88$	−4.42320	+	7.66120i	−0.471514	+	0.816687i
$89$	15.2655			1.61814			0.809071	−	0.587711i	$-0.199971\pi$
$89$	15.2655			1.61814			0.809071	+	0.587711i	$0.199971\pi$
$90$		0			0
$91$	−3.48019			−0.364823
$92$	−1.34687	+	2.33285i	−0.140421	+	0.243216i
$93$		0			0
$94$	−6.55885	−	11.3603i	−0.676494	−	1.17172i
$95$	−1.13412	−	1.96436i	−0.116359	−	0.201539i
$96$		0			0
$97$	1.93718	−	3.35530i	0.196691	−	0.340679i	−0.750763	−	0.660572i	$-0.770314\pi$
$97$	1.93718	−	3.35530i	0.196691	−	0.340679i	0.947454	+	0.319893i	$0.103647\pi$
$98$	−7.70656			−0.778480
$99$		0			0
$100$	−0.826443			−0.0826443
$101$	−5.11490	+	8.85927i	−0.508952	+	0.881530i	0.490994	+	0.871163i	$0.336634\pi$
$101$	−5.11490	+	8.85927i	−0.508952	+	0.881530i	−0.999946	+	0.0103677i	$0.996700\pi$
$102$		0			0
$103$	−6.33977	−	10.9808i	−0.624676	−	1.08197i	−0.988603	−	0.150543i	$-0.951898\pi$
$103$	−6.33977	−	10.9808i	−0.624676	−	1.08197i	0.363927	−	0.931427i	$-0.381436\pi$
$104$	−5.06436	−	8.77173i	−0.496601	−	0.860139i
$105$		0			0
$106$	5.71385	−	9.89668i	0.554978	−	0.961251i
$107$	−10.2054			−0.986597			−0.493298	−	0.869860i	$-0.664209\pi$
$107$	−10.2054			−0.986597			−0.493298	+	0.869860i	$0.664209\pi$
$108$		0			0
$109$	−4.68029			−0.448290			−0.224145	−	0.974556i	$-0.571959\pi$
$109$	−4.68029			−0.448290			−0.224145	+	0.974556i	$0.571959\pi$
$110$	5.28315	−	9.15068i	0.503728	−	0.872483i
$111$		0			0
$112$	1.69023	+	2.92757i	0.159712	+	0.276630i
$113$	−3.43891	−	5.95637i	−0.323505	−	0.560328i	0.657703	−	0.753277i	$-0.271528\pi$
$113$	−3.43891	−	5.95637i	−0.323505	−	0.560328i	−0.981209	+	0.192949i	$0.938195\pi$
$114$		0			0
$115$	11.8708	−	20.5608i	1.10696	−	1.91731i
$116$	−0.390905			−0.0362946
$117$		0			0
$118$	−8.61248			−0.792843
$119$	0.800595	−	1.38667i	0.0733904	−	0.127116i
$120$		0			0
$121$	1.16515	+	2.01810i	0.105923	+	0.183464i
$122$	0.0452843	+	0.0784347i	0.00409985	+	0.00710114i
$123$		0			0
$124$	−0.301845	+	0.522811i	−0.0271065	+	0.0469498i
$125$	−6.53266			−0.584299
$126$		0			0
$127$	6.24851			0.554466			0.277233	−	0.960803i	$-0.410583\pi$
$127$	6.24851			0.554466			0.277233	+	0.960803i	$0.410583\pi$
$128$	−3.97726	+	6.88882i	−0.351544	+	0.608892i
$129$		0			0
$130$	6.04896	+	10.4771i	0.530529	+	0.918903i
$131$	5.77690	+	10.0059i	0.504730	+	0.874219i	0.999985	+	0.00547079i	$0.00174142\pi$
$131$	5.77690	+	10.0059i	0.504730	+	0.874219i	−0.495255	+	0.868748i	$0.664925\pi$
$132$		0			0
$133$	−0.423684	+	0.733842i	−0.0367380	+	0.0636322i
$134$	−14.9728			−1.29346
$135$		0			0
$136$	4.66009			0.399599
$137$	−10.4557	+	18.1097i	−0.893287	+	1.54722i	−0.0573759	+	0.998353i	$0.518273\pi$
$137$	−10.4557	+	18.1097i	−0.893287	+	1.54722i	−0.835911	+	0.548865i	$0.815060\pi$
$138$		0			0
$139$	−11.1311	−	19.2797i	−0.944131	−	1.63528i	−0.757482	−	0.652855i	$-0.773571\pi$
$139$	−11.1311	−	19.2797i	−0.944131	−	1.63528i	−0.186648	−	0.982427i	$-0.559762\pi$
$140$	0.447190	+	0.774555i	0.0377944	+	0.0654619i
$141$		0			0
$142$	−3.82352	+	6.62253i	−0.320863	+	0.555750i
$143$	9.92641			0.830088
$144$		0			0
$145$	3.44528			0.286115
$146$	−1.23220	+	2.13423i	−0.101977	+	0.176630i
$147$		0			0
$148$	−0.697193	−	1.20757i	−0.0573089	−	0.0992619i
$149$	6.32942	+	10.9629i	0.518526	+	0.898114i	0.999768	+	0.0215262i	$0.00685253\pi$
$149$	6.32942	+	10.9629i	0.518526	+	0.898114i	−0.481242	+	0.876588i	$0.659814\pi$
$150$		0			0
$151$	1.88903	−	3.27189i	0.153727	−	0.266262i	−0.778868	−	0.627188i	$-0.784206\pi$
$151$	1.88903	−	3.27189i	0.153727	−	0.266262i	0.932595	+	0.360925i	$0.117539\pi$
$152$	−2.46617			−0.200033
$153$		0			0
$154$	−3.94734			−0.318086
$155$	2.66034	−	4.60785i	0.213684	−	0.370111i
$156$		0			0
$157$	−1.63812	−	2.83730i	−0.130736	−	0.226441i	0.793225	−	0.608929i	$-0.208401\pi$
$157$	−1.63812	−	2.83730i	−0.130736	−	0.226441i	−0.923960	+	0.382488i	$0.875067\pi$
$158$	−4.53958	−	7.86278i	−0.361149	−	0.625529i
$159$		0			0
$160$	−2.42661	+	4.20302i	−0.191841	+	0.332278i
$161$	−8.86935			−0.699002
$162$		0			0
$163$	−2.94951			−0.231023			−0.115512	−	0.993306i	$-0.536851\pi$
$163$	−2.94951			−0.231023			−0.115512	+	0.993306i	$0.536851\pi$
$164$	−0.983288	+	1.70310i	−0.0767819	+	0.132990i
$165$		0			0
$166$	1.95983	+	3.39452i	0.152112	+	0.263466i
$167$	11.9581	+	20.7120i	0.925342	+	1.60274i	0.791011	+	0.611803i	$0.209555\pi$
$167$	11.9581	+	20.7120i	0.925342	+	1.60274i	0.134331	+	0.990936i	$0.457111\pi$
$168$		0			0
$169$	0.817357	−	1.41570i	0.0628736	−	0.108900i
$170$	−5.56609			−0.426900
$171$		0			0
$172$	−0.313529			−0.0239063
$173$	10.9038	−	18.8860i	0.829004	−	1.43588i	−0.0698168	−	0.997560i	$-0.522241\pi$
$173$	10.9038	−	18.8860i	0.829004	−	1.43588i	0.898821	−	0.438317i	$-0.144425\pi$
$174$		0			0
$175$	−1.36056	−	2.35656i	−0.102849	−	0.178139i
$176$	−4.82099	−	8.35019i	−0.363396	−	0.629419i
$177$		0			0
$178$	−9.91223	+	17.1685i	−0.742953	+	1.28683i
$179$	−6.92878			−0.517882			−0.258941	−	0.965893i	$-0.583373\pi$
$179$	−6.92878			−0.517882			−0.258941	+	0.965893i	$0.583373\pi$
$180$		0			0
$181$	−11.0279			−0.819698			−0.409849	−	0.912153i	$-0.634419\pi$
$181$	−11.0279			−0.819698			−0.409849	+	0.912153i	$0.634419\pi$
$182$	2.25976	−	3.91402i	0.167505	−	0.290127i
$183$		0			0
$184$	−12.9066	−	22.3549i	−0.951489	−	1.64803i
$185$	6.14479	+	10.6431i	0.451774	+	0.782495i
$186$		0			0
$187$	−2.28350	+	3.95514i	−0.166986	+	0.289229i
$188$	−3.16698			−0.230976
$189$		0			0
$190$	2.94564			0.213699
$191$	12.6528	−	21.9152i	0.915522	−	1.58573i	0.109386	−	0.993999i	$-0.465112\pi$
$191$	12.6528	−	21.9152i	0.915522	−	1.58573i	0.806136	−	0.591731i	$-0.201555\pi$
$192$		0			0
$193$	10.8578	+	18.8063i	0.781563	+	1.35371i	0.931031	+	0.364940i	$0.118911\pi$
$193$	10.8578	+	18.8063i	0.781563	+	1.35371i	−0.149468	+	0.988767i	$0.547756\pi$
$194$	2.51570	+	4.35733i	0.180617	+	0.312838i
$195$		0			0
$196$	−0.930290	+	1.61131i	−0.0664493	+	0.115094i
$197$	−6.79869			−0.484386			−0.242193	−	0.970228i	$-0.577867\pi$
$197$	−6.79869			−0.484386			−0.242193	+	0.970228i	$0.577867\pi$
$198$		0			0
$199$	27.2806			1.93387			0.966935	−	0.255022i	$-0.0820827\pi$
$199$	27.2806			1.93387			0.966935	+	0.255022i	$0.0820827\pi$
$200$	3.95977	−	6.85852i	0.279998	−	0.484971i
$201$		0			0
$202$	−6.64243	−	11.5050i	−0.467360	−	0.809491i
$203$	−0.643542	−	1.11465i	−0.0451678	−	0.0782329i
$204$		0			0
$205$	8.66632	−	15.0105i	0.605282	−	1.04838i
$206$	16.4662			1.14725
$207$		0			0
$208$	11.0396			0.765460
$209$	1.20846	−	2.09311i	0.0835906	−	0.144783i
$210$		0			0
$211$	−7.88503	−	13.6573i	−0.542828	−	0.940206i	−0.998740	−	0.0501808i	$-0.984020\pi$
$211$	−7.88503	−	13.6573i	−0.542828	−	0.940206i	0.455912	−	0.890025i	$-0.349313\pi$
$212$	−1.37948	−	2.38934i	−0.0947434	−	0.164100i
$213$		0			0
$214$	6.62661	−	11.4776i	0.452985	−	0.784594i
$215$	2.76332			0.188457
$216$		0			0
$217$	−1.98769			−0.134933
$218$	3.03901	−	5.26372i	0.205828	−	0.356504i
$219$		0			0
$220$	−1.27550	−	2.20923i	−0.0859942	−	0.148946i
$221$	−2.61451	−	4.52846i	−0.175871	−	0.304617i
$222$		0			0
$223$	−10.5956	+	18.3520i	−0.709531	+	1.22894i	0.255500	+	0.966809i	$0.417760\pi$
$223$	−10.5956	+	18.3520i	−0.709531	+	1.22894i	−0.965031	+	0.262135i	$0.915574\pi$
$224$	1.81306			0.121140
$225$		0			0
$226$	8.93183			0.594136
$227$	0.776999	−	1.34580i	0.0515712	−	0.0893240i	−0.839087	−	0.543997i	$-0.816910\pi$
$227$	0.776999	−	1.34580i	0.0515712	−	0.0893240i	0.890659	+	0.454673i	$0.150244\pi$
$228$		0			0
$229$	−0.990433	−	1.71548i	−0.0654496	−	0.113362i	0.831444	−	0.555609i	$-0.187515\pi$
$229$	−0.990433	−	1.71548i	−0.0654496	−	0.113362i	−0.896893	+	0.442247i	$0.854181\pi$
$230$	15.4159	+	26.7011i	1.01649	+	1.76062i
$231$		0			0
$232$	1.87296	−	3.24406i	0.122966	−	0.212983i
$233$	25.5390			1.67311			0.836557	−	0.547880i	$-0.184565\pi$
$233$	25.5390			1.67311			0.836557	+	0.547880i	$0.184565\pi$
$234$		0			0
$235$	27.9126			1.82081
$236$	−1.03965	+	1.80072i	−0.0676753	+	0.117217i
$237$		0			0
$238$	1.03969	+	1.80079i	0.0673929	+	0.116728i
$239$	−7.98820	−	13.8360i	−0.516714	−	0.894975i	−0.999812	−	0.0194082i	$-0.993822\pi$
$239$	−7.98820	−	13.8360i	−0.516714	−	0.894975i	0.483098	−	0.875566i	$-0.339512\pi$
$240$		0			0
$241$	4.85761	−	8.41363i	0.312906	−	0.541969i	−0.666084	−	0.745877i	$-0.732031\pi$
$241$	4.85761	−	8.41363i	0.312906	−	0.541969i	0.978990	+	0.203907i	$0.0653641\pi$
$242$	−3.02623			−0.194533
$243$		0			0
$244$	0.0218658			0.00139981
$245$	8.19922	−	14.2015i	0.523829	−	0.907298i
$246$		0			0
$247$	1.38363	+	2.39651i	0.0880380	+	0.152486i
$248$	−2.89248	−	5.00993i	−0.183673	−	0.318131i
$249$		0			0
$250$	4.24179	−	7.34700i	0.268274	−	0.464665i
$251$	−5.91101			−0.373100			−0.186550	−	0.982445i	$-0.559731\pi$
$251$	−5.91101			−0.373100			−0.186550	+	0.982445i	$0.559731\pi$
$252$		0			0
$253$	25.2977			1.59045
$254$	−4.05729	+	7.02743i	−0.254577	+	0.440940i
$255$		0			0
$256$	3.66505	+	6.34806i	0.229066	+	0.396754i
$257$	14.1947	+	24.5859i	0.885439	+	1.53363i	0.845210	+	0.534435i	$0.179475\pi$
$257$	14.1947	+	24.5859i	0.885439	+	1.53363i	0.0402290	+	0.999190i	$0.487191\pi$
$258$		0			0
$259$	2.29556	−	3.97603i	0.142639	−	0.247058i
$260$	2.92078			0.181139
$261$		0			0
$262$	−15.0043			−0.926966
$263$	13.1146	−	22.7152i	0.808683	−	1.40068i	−0.105094	−	0.994462i	$-0.533514\pi$
$263$	13.1146	−	22.7152i	0.808683	−	1.40068i	0.913777	−	0.406217i	$-0.133152\pi$
$264$		0			0
$265$	12.1582	+	21.0587i	0.746875	+	1.29362i
$266$	−0.550214	−	0.952998i	−0.0337358	−	0.0584321i
$267$		0			0
$268$	−1.80743	+	3.13056i	−0.110406	+	0.191230i
$269$	−16.9061			−1.03078			−0.515392	−	0.856954i	$-0.672354\pi$
$269$	−16.9061			−1.03078			−0.515392	+	0.856954i	$0.672354\pi$
$270$		0			0
$271$	14.9590			0.908693			0.454347	−	0.890825i	$-0.349873\pi$
$271$	14.9590			0.908693			0.454347	+	0.890825i	$0.349873\pi$
$272$	−2.53959	+	4.39870i	−0.153985	+	0.266710i
$273$		0			0
$274$	−13.5782	−	23.5180i	−0.820286	−	1.42078i
$275$	3.88068	+	6.72153i	0.234014	+	0.405323i
$276$		0			0
$277$	−0.464342	+	0.804265i	−0.0278996	+	0.0483236i	−0.879638	−	0.475644i	$-0.842215\pi$
$277$	−0.464342	+	0.804265i	−0.0278996	+	0.0483236i	0.851738	+	0.523967i	$0.175549\pi$
$278$	28.9107			1.73395
$279$		0			0
$280$	−8.57055			−0.512188
$281$	8.89911	−	15.4137i	0.530876	−	0.919505i	−0.468475	−	0.883477i	$-0.655196\pi$
$281$	8.89911	−	15.4137i	0.530876	−	0.919505i	0.999351	−	0.0360276i	$-0.0114704\pi$
$282$		0			0
$283$	−0.877006	−	1.51902i	−0.0521326	−	0.0902963i	0.838781	−	0.544468i	$-0.183269\pi$
$283$	−0.877006	−	1.51902i	−0.0521326	−	0.0902963i	−0.890914	+	0.454172i	$0.849935\pi$
$284$	0.923105	+	1.59886i	0.0547762	+	0.0948752i
$285$		0			0
$286$	−6.44543	+	11.1638i	−0.381126	+	0.660130i
$287$	−6.47510			−0.382213
$288$		0			0
$289$	−14.5942			−0.858482
$290$	−2.23710	+	3.87476i	−0.131367	+	0.227534i
$291$		0			0
$292$	0.297487	+	0.515262i	0.0174091	+	0.0301534i
$293$	−3.75036	−	6.49581i	−0.219098	−	0.379489i	0.735434	−	0.677596i	$-0.236978\pi$
$293$	−3.75036	−	6.49581i	−0.219098	−	0.379489i	−0.954533	+	0.298107i	$0.903645\pi$
$294$		0			0
$295$	9.16305	−	15.8709i	0.533493	−	0.924038i
$296$	13.3620			0.776648
$297$		0			0
$298$	−16.4393			−0.952303
$299$	−14.4823	+	25.0841i	−0.837535	+	1.45065i
$300$		0			0
$301$	−0.516159	−	0.894013i	−0.0297509	−	0.0515301i
$302$	2.45317	+	4.24901i	0.141164	+	0.244503i
$303$		0			0
$304$	1.34398	−	2.32784i	0.0770825	−	0.133511i
$305$	−0.192717			−0.0110349
$306$		0			0
$307$	24.5577			1.40158			0.700792	−	0.713365i	$-0.252830\pi$
$307$	24.5577			1.40158			0.700792	+	0.713365i	$0.252830\pi$
$308$	−0.476500	+	0.825321i	−0.0271511	+	0.0470271i
$309$		0			0
$310$	3.45483	+	5.98395i	0.196221	+	0.339865i
$311$	−9.36086	−	16.2135i	−0.530806	−	0.919382i	−0.999354	−	0.0359442i	$-0.988556\pi$
$311$	−9.36086	−	16.2135i	−0.530806	−	0.919382i	0.468548	−	0.883438i	$-0.344777\pi$
$312$		0			0
$313$	0.549273	−	0.951369i	0.0310468	−	0.0537746i	−0.850085	−	0.526646i	$-0.823449\pi$
$313$	0.549273	−	0.951369i	0.0310468	−	0.0537746i	0.881131	+	0.472872i	$0.156783\pi$
$314$	4.25466			0.240104
$315$		0			0
$316$	−2.19196			−0.123308
$317$	1.25859	−	2.17995i	0.0706896	−	0.122438i	−0.828514	−	0.559968i	$-0.810813\pi$
$317$	1.25859	−	2.17995i	0.0706896	−	0.122438i	0.899204	+	0.437530i	$0.144147\pi$
$318$		0			0
$319$	1.83555	+	3.17926i	0.102771	+	0.178005i
$320$	−12.2002	−	21.1313i	−0.682011	−	1.18128i
$321$		0			0
$322$	5.75905	−	9.97497i	0.320939	−	0.555883i
$323$	−1.27318			−0.0708414
$324$		0			0
$325$	−8.88639			−0.492928
$326$	1.91518	−	3.31718i	0.106072	−	0.183722i
$327$		0			0
$328$	−9.42253	−	16.3203i	−0.520272	−	0.901138i
$329$	−5.21377	−	9.03051i	−0.287444	−	0.497868i
$330$		0			0
$331$	6.76996	−	11.7259i	0.372111	−	0.644515i	−0.617779	−	0.786352i	$-0.711967\pi$
$331$	6.76996	−	11.7259i	0.372111	−	0.644515i	0.989890	+	0.141837i	$0.0453008\pi$
$332$	0.946314			0.0519357
$333$		0			0
$334$	−31.0585			−1.69944
$335$	15.9300	−	27.5916i	0.870349	−	1.50749i
$336$		0			0
$337$	1.22079	+	2.11448i	0.0665009	+	0.115183i	0.897359	−	0.441302i	$-0.145483\pi$
$337$	1.22079	+	2.11448i	0.0665009	+	0.115183i	−0.830858	+	0.556485i	$0.812150\pi$
$338$	1.06145	+	1.83849i	0.0577355	+	0.100001i
$339$		0			0
$340$	−0.671906	+	1.16377i	−0.0364392	+	0.0631145i
$341$	5.66942			0.307016
$342$		0			0
$343$	−13.3523			−0.720958
$344$	1.50222	−	2.60193i	0.0809944	−	0.140286i
$345$		0			0
$346$	14.1602	+	24.5262i	0.761256	+	1.31853i
$347$	0.939688	+	1.62759i	0.0504451	+	0.0873735i	0.890145	−	0.455677i	$-0.150603\pi$
$347$	0.939688	+	1.62759i	0.0504451	+	0.0873735i	−0.839700	+	0.543050i	$0.817269\pi$
$348$		0			0
$349$	−12.0684	+	20.9031i	−0.646006	+	1.11892i	0.338062	+	0.941124i	$0.390229\pi$
$349$	−12.0684	+	20.9031i	−0.646006	+	1.11892i	−0.984068	+	0.177792i	$0.943105\pi$
$350$	3.53377			0.188888
$351$		0			0
$352$	−5.17132			−0.275632
$353$	−6.77717	+	11.7384i	−0.360712	+	0.624772i	−0.988078	−	0.153953i	$-0.950800\pi$
$353$	−6.77717	+	11.7384i	−0.360712	+	0.624772i	0.627366	+	0.778724i	$0.284133\pi$
$354$		0			0
$355$	−8.13589	−	14.0918i	−0.431808	−	0.747914i
$356$	2.39309	+	4.14495i	0.126834	+	0.219682i
$357$		0			0
$358$	4.49900	−	7.79250i	0.237780	−	0.411847i
$359$	3.49289			0.184348			0.0921739	−	0.995743i	$-0.470618\pi$
$359$	3.49289			0.184348			0.0921739	+	0.995743i	$0.470618\pi$
$360$		0			0
$361$	−18.3262			−0.964538
$362$	7.16065	−	12.4026i	0.376355	−	0.651867i
$363$		0			0
$364$	−0.545570	−	0.944955i	−0.0285957	−	0.0495291i
$365$	−2.62193	−	4.54132i	−0.137238	−	0.237704i
$366$		0			0
$367$	−14.5976	+	25.2838i	−0.761989	+	1.31980i	0.179834	+	0.983697i	$0.442444\pi$
$367$	−14.5976	+	25.2838i	−0.761989	+	1.31980i	−0.941824	+	0.336107i	$0.890890\pi$
$368$	28.1347			1.46662
$369$		0			0
$370$	−15.9598			−0.829708
$371$	4.54206	−	7.86707i	0.235812	−	0.408438i
$372$		0			0
$373$	2.95796	+	5.12334i	0.153157	+	0.265276i	0.932387	−	0.361463i	$-0.117723\pi$
$373$	2.95796	+	5.12334i	0.153157	+	0.265276i	−0.779229	+	0.626739i	$0.784389\pi$
$374$	−2.96545	−	5.13632i	−0.153340	−	0.265593i
$375$		0			0
$376$	15.1741	−	26.2823i	0.782544	−	1.35541i
$377$	−4.20324			−0.216478
$378$		0			0
$379$	8.06235			0.414135			0.207067	−	0.978327i	$-0.433608\pi$
$379$	8.06235			0.414135			0.207067	+	0.978327i	$0.433608\pi$
$380$	0.355580	−	0.615882i	0.0182409	−	0.0315941i
$381$		0			0
$382$	16.4314	+	28.4600i	0.840704	+	1.45614i
$383$	2.31912	+	4.01683i	0.118501	+	0.205250i	0.919174	−	0.393852i	$-0.128858\pi$
$383$	2.31912	+	4.01683i	0.118501	+	0.205250i	−0.800673	+	0.599102i	$0.795524\pi$
$384$		0			0
$385$	4.19968	−	7.27406i	0.214036	−	0.370721i
$386$	−28.2008			−1.43539
$387$		0			0
$388$	1.21472			0.0616683
$389$	−9.06993	+	15.7096i	−0.459864	+	0.796507i	−0.998953	−	0.0457413i	$-0.985435\pi$
$389$	−9.06993	+	15.7096i	−0.459864	+	0.796507i	0.539090	+	0.842248i	$0.318768\pi$
$390$		0			0
$391$	−6.66313	−	11.5409i	−0.336969	−	0.583647i
$392$	−8.91467	−	15.4407i	−0.450259	−	0.779871i
$393$		0			0
$394$	4.41453	−	7.64619i	0.222401	−	0.385210i
$395$	19.3191			0.972050
$396$		0			0
$397$	32.4912			1.63069			0.815343	−	0.578979i	$-0.196549\pi$
$397$	32.4912			1.63069			0.815343	+	0.578979i	$0.196549\pi$
$398$	−17.7139	+	30.6813i	−0.887916	+	1.53792i
$399$		0			0
$400$	4.31588	+	7.47532i	0.215794	+	0.373766i
$401$	2.47708	+	4.29042i	0.123699	+	0.214254i	0.921224	−	0.389033i	$-0.127191\pi$
$401$	2.47708	+	4.29042i	0.123699	+	0.214254i	−0.797524	+	0.603287i	$0.793857\pi$
$402$		0			0
$403$	−3.24561	+	5.62156i	−0.161675	+	0.280030i
$404$	−3.20734			−0.159571
$405$		0			0
$406$	1.67146			0.0829533
$407$	−6.54753	+	11.3407i	−0.324549	+	0.562136i
$408$		0			0
$409$	−13.5836	−	23.5274i	−0.671664	−	1.16336i	−0.977432	−	0.211250i	$-0.932247\pi$
$409$	−13.5836	−	23.5274i	−0.671664	−	1.16336i	0.305768	−	0.952106i	$-0.401087\pi$
$410$	11.2544	+	19.4933i	0.555817	+	0.962704i
$411$		0			0
$412$	1.98770	−	3.44280i	0.0979269	−	0.169614i
$413$	−6.84624			−0.336881
$414$		0			0
$415$	−8.34044			−0.409416
$416$	2.96046	−	5.12767i	0.145149	−	0.251405i
$417$		0			0
$418$	1.56935	+	2.71820i	0.0767595	+	0.132951i
$419$	0.591184	+	1.02396i	0.0288812	+	0.0500238i	0.880105	−	0.474780i	$-0.157472\pi$
$419$	0.591184	+	1.02396i	0.0288812	+	0.0500238i	−0.851224	+	0.524803i	$0.824139\pi$
$420$		0			0
$421$	−12.8870	+	22.3209i	−0.628072	+	1.08785i	0.359867	+	0.933004i	$0.382822\pi$
$421$	−12.8870	+	22.3209i	−0.628072	+	1.08785i	−0.987938	+	0.154848i	$0.950511\pi$
$422$	20.4797			0.996935
$423$		0			0
$424$	26.4383			1.28396
$425$	2.04426	−	3.54075i	0.0991610	−	0.171752i
$426$		0			0
$427$	0.0359974	+	0.0623493i	0.00174204	+	0.00301730i
$428$	−1.59985	−	2.77102i	−0.0773316	−	0.133942i
$429$		0			0
$430$	−1.79428	+	3.10779i	−0.0865280	+	0.149871i
$431$	9.39722			0.452648			0.226324	−	0.974052i	$-0.427329\pi$
$431$	9.39722			0.452648			0.226324	+	0.974052i	$0.427329\pi$
$432$		0			0
$433$	−21.5740			−1.03678			−0.518391	−	0.855144i	$-0.673469\pi$
$433$	−21.5740			−1.03678			−0.518391	+	0.855144i	$0.673469\pi$
$434$	1.29065	−	2.23547i	0.0619533	−	0.107306i
$435$		0			0
$436$	−0.733702	−	1.27081i	−0.0351380	−	0.0608607i
$437$	3.52620	+	6.10756i	0.168681	+	0.292164i
$438$		0			0
$439$	−1.04927	+	1.81739i	−0.0500790	+	0.0867395i	−0.889978	−	0.456003i	$-0.849281\pi$
$439$	−1.04927	+	1.81739i	−0.0500790	+	0.0867395i	0.839899	+	0.542742i	$0.182614\pi$
$440$	24.4454			1.16539
$441$		0			0
$442$	6.79062			0.322997
$443$	18.2063	−	31.5342i	0.865007	−	1.49824i	−0.00203309	−	0.999998i	$-0.500647\pi$
$443$	18.2063	−	31.5342i	0.865007	−	1.49824i	0.867040	−	0.498238i	$-0.166020\pi$
$444$		0			0
$445$	−21.0918	−	36.5320i	−0.999846	−	1.73178i
$446$	−13.7598	−	23.8327i	−0.651547	−	1.12851i
$447$		0			0
$448$	−4.55773	+	7.89422i	−0.215332	+	0.372967i
$449$	−7.78784			−0.367531			−0.183765	−	0.982970i	$-0.558829\pi$
$449$	−7.78784			−0.367531			−0.183765	+	0.982970i	$0.558829\pi$
$450$		0			0
$451$	18.4687			0.869655
$452$	1.07820	−	1.86749i	0.0507141	−	0.0878394i
$453$		0			0
$454$	1.00904	+	1.74771i	0.0473567	+	0.0820243i
$455$	4.80844	+	8.32847i	0.225423	+	0.390445i
$456$		0			0
$457$	11.8008	−	20.4395i	0.552016	−	0.956120i	−0.446113	−	0.894977i	$-0.647192\pi$
$457$	11.8008	−	20.4395i	0.552016	−	0.956120i	0.998129	−	0.0611431i	$-0.0194746\pi$
$458$	2.57243			0.120202
$459$		0			0
$460$	7.44367			0.347063
$461$	0.177184	−	0.306891i	0.00825227	−	0.0142933i	−0.861870	−	0.507130i	$-0.830707\pi$
$461$	0.177184	−	0.306891i	0.00825227	−	0.0142933i	0.870122	+	0.492836i	$0.164040\pi$
$462$		0			0
$463$	5.49903	+	9.52459i	0.255561	+	0.442645i	0.965048	−	0.262074i	$-0.0844064\pi$
$463$	5.49903	+	9.52459i	0.255561	+	0.442645i	−0.709486	+	0.704719i	$0.751073\pi$
$464$	2.04140	+	3.53581i	0.0947695	+	0.164146i
$465$		0			0
$466$	−16.5830	+	28.7226i	−0.768192	+	1.33055i
$467$	−0.429641			−0.0198814			−0.00994072	−	0.999951i	$-0.503164\pi$
$467$	−0.429641			−0.0198814			−0.00994072	+	0.999951i	$0.503164\pi$
$468$		0			0
$469$	−11.9022			−0.549593
$470$	−18.1242	+	31.3921i	−0.836008	+	1.44801i
$471$		0			0
$472$	−9.96261	−	17.2557i	−0.458566	−	0.794260i
$473$	1.47222	+	2.54996i	0.0676926	+	0.117247i
$474$		0			0
$475$	−1.08184	+	1.87381i	−0.0496383	+	0.0859761i
$476$	0.502019			0.0230100
$477$		0			0
$478$	20.7476			0.948975
$479$	−0.666231	+	1.15395i	−0.0304409	+	0.0527252i	−0.880845	−	0.473406i	$-0.843024\pi$
$479$	−0.666231	+	1.15395i	−0.0304409	+	0.0527252i	0.850404	+	0.526131i	$0.176358\pi$
$480$		0			0
$481$	−7.49663	−	12.9845i	−0.341817	−	0.592044i
$482$	6.30830	+	10.9263i	0.287335	+	0.497679i
$483$		0			0
$484$	−0.365308	+	0.632732i	−0.0166049	+	0.0287606i
$485$	−10.7061			−0.486139
$486$		0			0
$487$	−17.8776			−0.810113			−0.405057	−	0.914292i	$-0.632748\pi$
$487$	−17.8776			−0.810113			−0.405057	+	0.914292i	$0.632748\pi$
$488$	−0.104767	+	0.181461i	−0.00474256	+	0.00821435i
$489$		0			0
$490$	10.6478	+	18.4426i	0.481021	+	0.833152i
$491$	−11.4781	−	19.8806i	−0.517998	−	0.897199i	−0.999781	−	0.0209087i	$-0.993344\pi$
$491$	−11.4781	−	19.8806i	−0.517998	−	0.897199i	0.481783	−	0.876290i	$-0.339989\pi$
$492$		0			0
$493$	0.966927	−	1.67477i	0.0435482	−	0.0754277i
$494$	−3.59367			−0.161687
$495$		0			0
$496$	6.30522			0.283113
$497$	−3.03939	+	5.26439i	−0.136335	+	0.236140i
$498$		0			0
$499$	−4.72216	−	8.17902i	−0.211393	−	0.366143i	0.740758	−	0.671772i	$-0.234467\pi$
$499$	−4.72216	−	8.17902i	−0.211393	−	0.366143i	−0.952151	+	0.305629i	$0.901133\pi$
$500$	−1.02409	−	1.77377i	−0.0457986	−	0.0793255i
$501$		0			0
$502$	3.83815	−	6.64786i	0.171305	−	0.296709i
$503$	−44.4176			−1.98048			−0.990241	−	0.139366i	$-0.955493\pi$
$503$	−44.4176			−1.98048			−0.990241	+	0.139366i	$0.955493\pi$
$504$		0			0
$505$	28.2682			1.25792
$506$	−16.4263	+	28.4512i	−0.730238	+	1.26481i
$507$		0			0
$508$	0.979544	+	1.69662i	0.0434602	+	0.0752753i
$509$	21.3394	+	36.9609i	0.945852	+	1.63826i	0.754037	+	0.656832i	$0.228104\pi$
$509$	21.3394	+	36.9609i	0.945852	+	1.63826i	0.191815	+	0.981431i	$0.438563\pi$
$510$		0			0
$511$	−0.979498	+	1.69654i	−0.0433304	+	0.0750505i
$512$	−25.4282			−1.12378
$513$		0			0
$514$	−36.8676			−1.62616
$515$	−17.5188	+	30.3435i	−0.771971	+	1.33709i
$516$		0			0
$517$	14.8710	+	25.7573i	0.654026	+	1.13281i
$518$	2.98111	+	5.16344i	0.130983	+	0.226868i
$519$		0			0
$520$	−13.9944	+	24.2391i	−0.613697	+	1.06295i
$521$	30.0291			1.31560			0.657799	−	0.753194i	$-0.271488\pi$
$521$	30.0291			1.31560			0.657799	+	0.753194i	$0.271488\pi$
$522$		0			0
$523$	−20.0700			−0.877599			−0.438799	−	0.898585i	$-0.644596\pi$
$523$	−20.0700			−0.877599			−0.438799	+	0.898585i	$0.644596\pi$
$524$	−1.81122	+	3.13713i	−0.0791237	+	0.137046i
$525$		0			0
$526$	17.0312	+	29.4989i	0.742596	+	1.28621i
$527$	−1.49326	−	2.58641i	−0.0650475	−	0.112666i
$528$		0			0
$529$	−25.4085	+	44.0089i	−1.10472	+	1.91343i
$530$	−31.5784			−1.37168
$531$		0			0
$532$	−0.265674			−0.0115184
$533$	−10.5729	+	18.3128i	−0.457963	+	0.793214i
$534$		0			0
$535$	14.1004	+	24.4227i	0.609615	+	1.05588i
$536$	−17.3200	−	29.9992i	−0.748112	−	1.29577i
$537$		0			0
$538$	10.9775	−	19.0136i	0.473274	−	0.819734i
$539$	17.4732			0.752625
$540$		0			0
$541$	25.4769			1.09534			0.547669	−	0.836695i	$-0.315515\pi$
$541$	25.4769			1.09534			0.547669	+	0.836695i	$0.315515\pi$
$542$	−9.71318	+	16.8237i	−0.417217	+	0.722641i
$543$		0			0
$544$	1.36207	+	2.35917i	0.0583982	+	0.101149i
$545$	6.46656	+	11.2004i	0.276997	+	0.479773i
$546$		0			0
$547$	12.7230	−	22.0368i	0.543994	−	0.942226i	−0.454675	−	0.890657i	$-0.650245\pi$
$547$	12.7230	−	22.0368i	0.543994	−	0.942226i	0.998669	−	0.0515683i	$-0.0164220\pi$
$548$	−6.55629			−0.280071
$549$		0			0
$550$	−10.0792			−0.429779
$551$	−0.511708	+	0.886305i	−0.0217995	+	0.0377579i
$552$		0			0
$553$	−3.60860	−	6.25028i	−0.153453	−	0.265789i
$554$	−0.603015	−	1.04445i	−0.0256196	−	0.0443745i
$555$		0			0
$556$	3.48993	−	6.04474i	0.148006	−	0.256354i
$557$	−43.3451			−1.83659			−0.918295	−	0.395898i	$-0.870433\pi$
$557$	−43.3451			−1.83659			−0.918295	+	0.395898i	$0.870433\pi$
$558$		0			0
$559$	−3.37124			−0.142588
$560$	4.67066	−	8.08982i	0.197371	−	0.341857i
$561$		0			0
$562$	11.5568	+	20.0169i	0.487492	+	0.844361i
$563$	−19.1697	−	33.2028i	−0.807905	−	1.39933i	−0.914312	−	0.405010i	$-0.867268\pi$
$563$	−19.1697	−	33.2028i	−0.807905	−	1.39933i	0.106407	−	0.994323i	$-0.466065\pi$
$564$		0			0
$565$	−9.50281	+	16.4593i	−0.399786	+	0.692450i
$566$	2.27783			0.0957445
$567$		0			0
$568$	−17.6916			−0.742325
$569$	−2.85151	+	4.93897i	−0.119542	+	0.207052i	−0.919586	−	0.392888i	$-0.871476\pi$
$569$	−2.85151	+	4.93897i	−0.119542	+	0.207052i	0.800044	+	0.599941i	$0.204809\pi$
$570$		0			0
$571$	−21.5962	−	37.4056i	−0.903771	−	1.56538i	−0.822559	−	0.568680i	$-0.807454\pi$
$571$	−21.5962	−	37.4056i	−0.903771	−	1.56538i	−0.0812121	−	0.996697i	$-0.525879\pi$
$572$	1.55611	+	2.69526i	0.0650641	+	0.112694i
$573$		0			0
$574$	4.20442	−	7.28227i	0.175489	−	0.303956i
$575$	−22.6472			−0.944452
$576$		0			0
$577$	1.62734			0.0677469			0.0338735	−	0.999426i	$-0.489216\pi$
$577$	1.62734			0.0677469			0.0338735	+	0.999426i	$0.489216\pi$
$578$	9.47632	−	16.4135i	0.394163	−	0.682710i
$579$		0			0
$580$	0.540098	+	0.935477i	0.0224263	+	0.0388436i
$581$	1.55791	+	2.69837i	0.0646328	+	0.111947i
$582$		0			0
$583$	−12.9551	+	22.4389i	−0.536546	+	0.929325i
$584$	−5.70144			−0.235927
$585$		0			0
$586$	9.74075			0.402387
$587$	−22.8904	+	39.6473i	−0.944786	+	1.63642i	−0.188607	+	0.982053i	$0.560397\pi$
$587$	−22.8904	+	39.6473i	−0.944786	+	1.63642i	−0.756179	+	0.654365i	$0.772936\pi$
$588$		0			0
$589$	0.790251	+	1.36876i	0.0325617	+	0.0563986i
$590$	11.8995	+	20.6106i	0.489896	+	0.848524i
$591$		0			0
$592$	−7.28181	+	12.6125i	−0.299281	+	0.518369i
$593$	−22.1612			−0.910051			−0.455026	−	0.890478i	$-0.650370\pi$
$593$	−22.1612			−0.910051			−0.455026	+	0.890478i	$0.650370\pi$
$594$		0			0
$595$	−4.42460			−0.181391
$596$	−1.98446	+	3.43718i	−0.0812865	+	0.140792i
$597$		0			0
$598$	−18.8074	−	32.5753i	−0.769091	−	1.33210i
$599$	−16.3016	−	28.2351i	−0.666063	−	1.15366i	−0.978996	−	0.203880i	$-0.934645\pi$
$599$	−16.3016	−	28.2351i	−0.666063	−	1.15366i	0.312932	−	0.949775i	$-0.398689\pi$
$600$		0			0
$601$	−0.818207	+	1.41718i	−0.0333753	+	0.0578078i	−0.882231	−	0.470818i	$-0.843959\pi$
$601$	−0.818207	+	1.41718i	−0.0333753	+	0.0578078i	0.848855	+	0.528625i	$0.177292\pi$
$602$	1.34061			0.0546392
$603$		0			0
$604$	1.18453			0.0481977
$605$	3.21968	−	5.57666i	0.130899	−	0.226723i
$606$		0			0
$607$	−4.95802	−	8.58754i	−0.201240	−	0.348557i	0.747688	−	0.664050i	$-0.231164\pi$
$607$	−4.95802	−	8.58754i	−0.201240	−	0.348557i	−0.948928	+	0.315492i	$0.897830\pi$
$608$	−0.720822	−	1.24850i	−0.0292332	−	0.0506334i
$609$		0			0
$610$	0.125135	−	0.216740i	0.00506657	−	0.00877555i
$611$	−34.0533			−1.37765
$612$		0			0
$613$	26.3963			1.06614			0.533068	−	0.846072i	$-0.321039\pi$
$613$	26.3963			1.06614			0.533068	+	0.846072i	$0.321039\pi$
$614$	−15.9459	+	27.6190i	−0.643523	+	1.11461i
$615$		0			0
$616$	−4.56614	−	7.90879i	−0.183975	−	0.318654i
$617$	−9.98736	−	17.2986i	−0.402076	−	0.696416i	0.591900	−	0.806011i	$-0.298378\pi$
$617$	−9.98736	−	17.2986i	−0.402076	−	0.696416i	−0.993976	+	0.109595i	$0.965045\pi$
$618$		0			0
$619$	−18.0421	+	31.2499i	−0.725174	+	1.25604i	0.233728	+	0.972302i	$0.424907\pi$
$619$	−18.0421	+	31.2499i	−0.725174	+	1.25604i	−0.958902	+	0.283737i	$0.908426\pi$
$620$	1.66819			0.0669960
$621$		0			0
$622$	24.3128			0.974855
$623$	−7.87943	+	13.6476i	−0.315683	+	0.546779i
$624$		0			0
$625$	15.6158	+	27.0473i	0.624630	+	1.08189i
$626$	0.713309	+	1.23549i	0.0285096	+	0.0493800i
$627$		0			0
$628$	0.513597	−	0.889576i	0.0204947	−	0.0354979i
$629$	6.89819			0.275049
$630$		0			0
$631$	−46.6716			−1.85797			−0.928984	−	0.370120i	$-0.879317\pi$
$631$	−46.6716			−1.85797			−0.928984	+	0.370120i	$0.879317\pi$
$632$	10.5024	−	18.1908i	0.417765	−	0.723590i
$633$		0			0
$634$	1.63446	+	2.83097i	0.0649128	+	0.112432i
$635$	−8.63332	−	14.9534i	−0.342603	−	0.593406i
$636$		0			0
$637$	−10.0030	+	17.3257i	−0.396334	+	0.686471i
$638$	−4.76744			−0.188745
$639$		0			0
$640$	21.9809			0.868871
$641$	−0.383789	+	0.664742i	−0.0151588	+	0.0262557i	−0.873505	−	0.486815i	$-0.838159\pi$
$641$	−0.383789	+	0.664742i	−0.0151588	+	0.0262557i	0.858347	+	0.513070i	$0.171492\pi$
$642$		0			0
$643$	−14.4053	−	24.9507i	−0.568090	−	0.983960i	−0.996755	−	0.0804966i	$-0.974349\pi$
$643$	−14.4053	−	24.9507i	−0.568090	−	0.983960i	0.428665	−	0.903463i	$-0.358984\pi$
$644$	−1.39040	−	2.40824i	−0.0547893	−	0.0948979i
$645$		0			0
$646$	0.826700	−	1.43189i	0.0325261	−	0.0563368i
$647$	5.46805			0.214971			0.107486	−	0.994207i	$-0.465720\pi$
$647$	5.46805			0.214971			0.107486	+	0.994207i	$0.465720\pi$
$648$		0			0
$649$	19.5272			0.766511
$650$	5.77012	−	9.99415i	0.226323	−	0.392003i
$651$		0			0
$652$	−0.462378	−	0.800861i	−0.0181081	−	0.0313642i
$653$	2.85758	+	4.94948i	0.111826	+	0.193688i	0.916506	−	0.400020i	$-0.130997\pi$
$653$	2.85758	+	4.94948i	0.111826	+	0.193688i	−0.804681	+	0.593708i	$0.797663\pi$
$654$		0			0
$655$	15.9634	−	27.6495i	0.623743	−	1.08035i
$656$	20.5398			0.801946
$657$		0			0
$658$	13.5416			0.527908
$659$	18.2149	−	31.5491i	0.709552	−	1.22898i	−0.255471	−	0.966817i	$-0.582231\pi$
$659$	18.2149	−	31.5491i	0.709552	−	1.22898i	0.965023	−	0.262163i	$-0.0844360\pi$
$660$		0			0
$661$	9.85404	+	17.0677i	0.383278	+	0.663856i	0.991529	−	0.129888i	$-0.0414619\pi$
$661$	9.85404	+	17.0677i	0.383278	+	0.663856i	−0.608251	+	0.793745i	$0.708129\pi$
$662$	8.79176	+	15.2278i	0.341701	+	0.591844i
$663$		0			0
$664$	−4.53411	+	7.85331i	−0.175958	+	0.304768i
$665$	2.34155			0.0908013
$666$		0			0
$667$	−10.7120			−0.414772
$668$	−3.74919	+	6.49379i	−0.145061	+	0.251252i
$669$		0			0
$670$	20.6874	+	35.8316i	0.799223	+	1.38429i
$671$	−0.102674	−	0.177836i	−0.00396368	−	0.00686530i
$672$		0			0
$673$	1.68997	−	2.92712i	0.0651437	−	0.112832i	−0.831614	−	0.555354i	$-0.812583\pi$
$673$	1.68997	−	2.92712i	0.0651437	−	0.112832i	0.896758	+	0.442522i	$0.145916\pi$
$674$	−3.17075			−0.122133
$675$		0			0
$676$	0.512530			0.0197127
$677$	−8.48897	+	14.7033i	−0.326258	+	0.565095i	−0.981766	−	0.190093i	$-0.939121\pi$
$677$	−8.48897	+	14.7033i	−0.326258	+	0.565095i	0.655508	+	0.755188i	$0.272454\pi$
$678$		0			0
$679$	1.99979	+	3.46373i	0.0767447	+	0.132926i
$680$	−6.43866	−	11.1521i	−0.246911	−	0.427663i
$681$		0			0
$682$	−3.68127	+	6.37615i	−0.140963	+	0.244155i
$683$	10.3202			0.394890			0.197445	−	0.980314i	$-0.436736\pi$
$683$	10.3202			0.394890			0.197445	+	0.980314i	$0.436736\pi$
$684$		0			0
$685$	57.7846			2.20784
$686$	8.66994	−	15.0168i	0.331020	−	0.573343i
$687$		0			0
$688$	1.63732	+	2.83592i	0.0624223	+	0.108119i
$689$	−14.8330	−	25.6915i	−0.565093	−	0.978770i
$690$		0			0
$691$	−2.11921	+	3.67057i	−0.0806184	+	0.139635i	−0.903516	−	0.428555i	$-0.859023\pi$
$691$	−2.11921	+	3.67057i	−0.0806184	+	0.139635i	0.822897	+	0.568190i	$0.192356\pi$
$692$	6.83733			0.259916
$693$		0			0
$694$	−2.44064			−0.0926453
$695$	−30.7589	+	53.2760i	−1.16675	+	2.02087i
$696$		0			0
$697$	−4.86444	−	8.42546i	−0.184254	−	0.319137i
$698$	−15.6725	−	27.1456i	−0.593214	−	1.02748i
$699$		0			0
$700$	0.426576	−	0.738850i	0.0161230	−	0.0279259i
$701$	4.89904			0.185034			0.0925171	−	0.995711i	$-0.470509\pi$
$701$	4.89904			0.185034			0.0925171	+	0.995711i	$0.470509\pi$
$702$		0			0
$703$	−3.65060			−0.137685
$704$	12.9998	−	22.5163i	0.489949	−	0.848617i
$705$		0			0
$706$	−8.80111	−	15.2440i	−0.331234	−	0.573715i
$707$	−5.28020	−	9.14558i	−0.198582	−	0.343955i
$708$		0			0
$709$	17.1625	−	29.7264i	0.644552	−	1.11640i	−0.339853	−	0.940479i	$-0.610377\pi$
$709$	17.1625	−	29.7264i	0.644552	−	1.11640i	0.984405	−	0.175918i	$-0.0562894\pi$
$710$	21.1312			0.793041
$711$		0			0
$712$	−45.8644			−1.71884
$713$	−8.27151	+	14.3267i	−0.309770	+	0.536538i
$714$		0			0
$715$	−13.7149	−	23.7549i	−0.512909	−	0.888385i
$716$	−1.08619	−	1.88133i	−0.0405927	−	0.0703086i
$717$		0			0
$718$	−2.26801	+	3.92831i	−0.0846413	+	0.146603i
$719$	13.6554			0.509260			0.254630	−	0.967039i	$-0.418046\pi$
$719$	13.6554			0.509260			0.254630	+	0.967039i	$0.418046\pi$
$720$		0			0
$721$	13.0893			0.487471
$722$	11.8996	−	20.6107i	0.442857	−	0.767051i
$723$		0			0
$724$	−1.72878	−	2.99434i	−0.0642497	−	0.111284i
$725$	−1.64323	−	2.84616i	−0.0610282	−	0.105704i
$726$		0			0
$727$	−19.1619	+	33.1895i	−0.710677	+	1.23093i	0.253926	+	0.967224i	$0.418278\pi$
$727$	−19.1619	+	33.1895i	−0.710677	+	1.23093i	−0.964603	+	0.263705i	$0.915055\pi$
$728$	10.4561			0.387527
$729$		0			0
$730$	6.80990			0.252046
$731$	0.775532	−	1.34326i	0.0286841	−	0.0496823i
$732$		0			0
$733$	−2.13197	−	3.69269i	−0.0787463	−	0.136393i	0.823963	−	0.566644i	$-0.191758\pi$
$733$	−2.13197	−	3.69269i	−0.0787463	−	0.136393i	−0.902709	+	0.430251i	$0.858425\pi$
$734$	−18.9571	−	32.8346i	−0.699718	−	1.21195i
$735$		0			0
$736$	7.54480	−	13.0680i	0.278105	−	0.481692i
$737$	33.9482			1.25050
$738$		0			0
$739$	−33.6314			−1.23715			−0.618576	−	0.785725i	$-0.712290\pi$
$739$	−33.6314			−1.23715			−0.618576	+	0.785725i	$0.712290\pi$
$740$	−1.92657	+	3.33691i	−0.0708220	+	0.122667i
$741$		0			0
$742$	5.89851	+	10.2165i	0.216541	+	0.375060i
$743$	8.45867	+	14.6508i	0.310318	+	0.537487i	0.978431	−	0.206573i	$-0.0662310\pi$
$743$	8.45867	+	14.6508i	0.310318	+	0.537487i	−0.668113	+	0.744060i	$0.732898\pi$
$744$		0			0
$745$	17.4902	−	30.2939i	0.640792	−	1.10988i
$746$	−7.68266			−0.281282
$747$		0			0
$748$	−1.43189			−0.0523550
$749$	5.26762	−	9.12379i	0.192475	−	0.333376i
$750$		0			0
$751$	4.64235	+	8.04079i	0.169402	+	0.293412i	0.938210	−	0.346067i	$-0.112483\pi$
$751$	4.64235	+	8.04079i	0.169402	+	0.293412i	−0.768808	+	0.639480i	$0.779150\pi$
$752$	16.5387	+	28.6459i	0.603106	+	1.04461i
$753$		0			0
$754$	2.72925	−	4.72720i	0.0993935	−	0.172155i
$755$	−10.4400			−0.379949
$756$		0			0
$757$	−34.5024			−1.25401			−0.627005	−	0.779015i	$-0.715719\pi$
$757$	−34.5024			−1.25401			−0.627005	+	0.779015i	$0.715719\pi$
$758$	−5.23505	+	9.06737i	−0.190146	+	0.329342i
$759$		0			0
$760$	3.40741	+	5.90181i	0.123600	+	0.214081i
$761$	−7.97924	−	13.8204i	−0.289247	−	0.500991i	0.684383	−	0.729123i	$-0.260072\pi$
$761$	−7.97924	−	13.8204i	−0.289247	−	0.500991i	−0.973630	+	0.228132i	$0.926738\pi$
$762$		0			0
$763$	2.41577	−	4.18424i	0.0874567	−	0.151480i
$764$	7.93401			0.287042
$765$		0			0
$766$	−6.02341			−0.217635
$767$	−11.1789	+	19.3624i	−0.403647	+	0.699136i
$768$		0			0
$769$	7.85906	+	13.6123i	0.283405	+	0.490872i	0.972221	−	0.234064i	$-0.0752026\pi$
$769$	7.85906	+	13.6123i	0.283405	+	0.490872i	−0.688816	+	0.724936i	$0.741869\pi$
$770$	5.45388	+	9.44640i	0.196544	+	0.340425i
$771$		0			0
$772$	−3.40424	+	5.89631i	−0.122521	+	0.212213i
$773$	−0.818514			−0.0294399			−0.0147200	−	0.999892i	$-0.504686\pi$
$773$	−0.818514			−0.0294399			−0.0147200	+	0.999892i	$0.504686\pi$
$774$		0			0
$775$	−5.07542			−0.182314
$776$	−5.82016	+	10.0808i	−0.208931	+	0.361880i
$777$		0			0
$778$	−11.7786	−	20.4011i	−0.422283	−	0.731415i
$779$	2.57432	+	4.45885i	0.0922345	+	0.159755i
$780$		0			0
$781$	8.66914	−	15.0154i	0.310206	−	0.537293i
$782$	17.3060			0.618863
$783$		0			0
$784$	19.4328			0.694028
$785$	−4.52664	+	7.84037i	−0.161563	+	0.279835i
$786$		0			0
$787$	−18.3210	−	31.7329i	−0.653074	−	1.13116i	−0.982373	−	0.186932i	$-0.940146\pi$
$787$	−18.3210	−	31.7329i	−0.653074	−	1.13116i	0.329299	−	0.944226i	$-0.393188\pi$
$788$	−1.06579	−	1.84601i	−0.0379673	−	0.0657612i
$789$		0			0
$790$	−12.5443	+	21.7274i	−0.446306	+	0.773025i
$791$	7.10009			0.252450
$792$		0			0
$793$	0.235114			0.00834914
$794$	−21.0972	+	36.5414i	−0.748712	+	1.29681i
$795$		0			0
$796$	4.27663	+	7.40733i	0.151581	+	0.262546i
$797$	6.01770	+	10.4230i	0.213158	+	0.369200i	0.952701	−	0.303909i	$-0.0982918\pi$
$797$	6.01770	+	10.4230i	0.213158	+	0.369200i	−0.739543	+	0.673109i	$0.764958\pi$
$798$		0			0
$799$	7.83372	−	13.5684i	0.277137	−	0.480016i
$800$	4.62951			0.163678
$801$		0			0
$802$	−6.43367			−0.227181
$803$	2.79378	−	4.83897i	0.0985904	−	0.170764i
$804$		0			0
$805$	12.2544	+	21.2253i	0.431912	+	0.748093i
$806$	−4.21489	−	7.30040i	−0.148463	−	0.257146i
$807$		0			0
$808$	15.3674	−	26.6172i	0.540625	−	0.936390i
$809$	8.87248			0.311940			0.155970	−	0.987762i	$-0.450150\pi$
$809$	8.87248			0.311940			0.155970	+	0.987762i	$0.450150\pi$
$810$		0			0
$811$	9.69230			0.340343			0.170171	−	0.985414i	$-0.445568\pi$
$811$	9.69230			0.340343			0.170171	+	0.985414i	$0.445568\pi$
$812$	0.201769	−	0.349474i	0.00708070	−	0.0122641i
$813$		0			0
$814$	−8.50290	−	14.7275i	−0.298027	−	0.516197i
$815$	4.07522	+	7.05848i	0.142749	+	0.247248i
$816$		0			0
$817$	−0.410420	+	0.710869i	−0.0143588	+	0.0248701i
$818$	35.2804			1.23355
$819$		0			0
$820$	5.43428			0.189773
$821$	5.13985	−	8.90248i	0.179382	−	0.310699i	−0.762287	−	0.647239i	$-0.775924\pi$
$821$	5.13985	−	8.90248i	0.179382	−	0.310699i	0.941669	+	0.336540i	$0.109257\pi$
$822$		0			0
$823$	−20.9587	−	36.3015i	−0.730573	−	1.26539i	−0.956639	−	0.291277i	$-0.905920\pi$
$823$	−20.9587	−	36.3015i	−0.730573	−	1.26539i	0.226066	−	0.974112i	$-0.427413\pi$
$824$	19.0475	+	32.9912i	0.663551	+	1.14930i
$825$		0			0
$826$	4.44541	−	7.69967i	0.154675	−	0.267906i
$827$	−27.5477			−0.957927			−0.478963	−	0.877835i	$-0.658987\pi$
$827$	−27.5477			−0.957927			−0.478963	+	0.877835i	$0.658987\pi$
$828$		0			0
$829$	−23.3262			−0.810154			−0.405077	−	0.914283i	$-0.632755\pi$
$829$	−23.3262			−0.810154			−0.405077	+	0.914283i	$0.632755\pi$
$830$	5.41562	−	9.38014i	0.187979	−	0.325589i
$831$		0			0
$832$	14.8842	+	25.7802i	0.516017	+	0.893767i
$833$	−4.60226	−	7.97134i	−0.159459	−	0.276191i
$834$		0			0
$835$	33.0439	−	57.2338i	1.14353	−	1.98066i
$836$	0.757771			0.0262081
$837$		0			0
$838$	−1.53547			−0.0530421
$839$	4.31079	−	7.46651i	0.148825	−	0.257773i	−0.781968	−	0.623318i	$-0.785784\pi$
$839$	4.31079	−	7.46651i	0.148825	−	0.257773i	0.930793	+	0.365545i	$0.119118\pi$
$840$		0			0
$841$	13.7228	+	23.7685i	0.473198	+	0.819604i
$842$	−16.7355	−	28.9868i	−0.576745	−	0.998951i
$843$		0			0
$844$	2.47218	−	4.28195i	0.0850961	−	0.147391i
$845$	−4.51724			−0.155398
$846$		0			0
$847$	−2.40561			−0.0826577
$848$	−14.4080	+	24.9554i	−0.494772	+	0.856971i
$849$		0			0
$850$	2.65476	+	4.59817i	0.0910574	+	0.157716i
$851$	−19.1053	−	33.0914i	−0.654922	−	1.13436i
$852$		0			0
$853$	−21.3858	+	37.0412i	−0.732235	+	1.26827i	0.223691	+	0.974660i	$0.428189\pi$
$853$	−21.3858	+	37.0412i	−0.732235	+	1.26827i	−0.955926	+	0.293608i	$0.905144\pi$
$854$	−0.0934955			−0.00319935
$855$		0			0
$856$	30.6617			1.04799
$857$	22.2710	−	38.5744i	0.760762	−	1.31768i	−0.181697	−	0.983355i	$-0.558159\pi$
$857$	22.2710	−	38.5744i	0.760762	−	1.31768i	0.942458	−	0.334323i	$-0.108508\pi$
$858$		0			0
$859$	15.9851	+	27.6871i	0.545406	+	0.944671i	0.998581	+	0.0532497i	$0.0169579\pi$
$859$	15.9851	+	27.6871i	0.545406	+	0.944671i	−0.453175	+	0.891422i	$0.649709\pi$
$860$	0.433190	+	0.750307i	0.0147717	+	0.0255853i
$861$		0			0
$862$	−6.10181	+	10.5687i	−0.207829	+	0.359970i
$863$	39.0037			1.32770			0.663851	−	0.747865i	$-0.268921\pi$
$863$	39.0037			1.32770			0.663851	+	0.747865i	$0.268921\pi$
$864$		0			0
$865$	−60.2616			−2.04896
$866$	14.0085	−	24.2634i	0.476028	−	0.824504i
$867$		0			0
$868$	−0.311600	−	0.539706i	−0.0105764	−	0.0183188i
$869$	10.2927	+	17.8274i	0.349155	+	0.604754i
$870$		0			0
$871$	−19.4346	+	33.6617i	−0.658515	+	1.14058i
$872$	14.0617			0.476188
$873$		0			0
$874$	−9.15855			−0.309792
$875$	3.37189	−	5.84028i	0.113991	−	0.197437i
$876$		0			0
$877$	25.0560	+	43.3983i	0.846082	+	1.46546i	0.884678	+	0.466202i	$0.154378\pi$
$877$	25.0560	+	43.3983i	0.846082	+	1.46546i	−0.0385964	+	0.999255i	$0.512289\pi$
$878$	−1.36263	−	2.36014i	−0.0459865	−	0.0796510i
$879$		0			0
$880$	−13.3219	+	23.0743i	−0.449082	+	0.777833i
$881$	30.9354			1.04224			0.521120	−	0.853483i	$-0.325514\pi$
$881$	30.9354			1.04224			0.521120	+	0.853483i	$0.325514\pi$
$882$		0			0
$883$	35.3840			1.19077			0.595383	−	0.803442i	$-0.297000\pi$
$883$	35.3840			1.19077			0.595383	+	0.803442i	$0.297000\pi$
$884$	0.819723	−	1.41980i	0.0275703	−	0.0477531i
$885$		0			0
$886$	23.6435	+	40.9517i	0.794318	+	1.37580i
$887$	24.4733	+	42.3890i	0.821733	+	1.42328i	0.904391	+	0.426705i	$0.140326\pi$
$887$	24.4733	+	42.3890i	0.821733	+	1.42328i	−0.0826579	+	0.996578i	$0.526341\pi$
$888$		0			0
$889$	−3.22522	+	5.58625i	−0.108171	+	0.187357i
$890$	54.7813			1.83627
$891$		0			0
$892$	−6.64402			−0.222458
$893$	−4.14569	+	7.18055i	−0.138730	+	0.240288i
$894$		0			0
$895$	9.57322	+	16.5813i	0.319998	+	0.554252i
$896$	−4.10580	−	7.11145i	−0.137165	−	0.237577i
$897$		0			0
$898$	5.05681	−	8.75865i	0.168748	−	0.292280i
$899$	−2.40066			−0.0800664
$900$		0			0
$901$	13.6489			0.454712
$902$	−11.9921	+	20.7709i	−0.399293	+	0.691596i
$903$		0			0
$904$	10.3320	+	17.8956i	0.343638	+	0.595198i
$905$	15.2368	+	26.3909i	0.506489	+	0.877265i
$906$		0			0
$907$	−14.1919	+	24.5811i	−0.471234	+	0.816202i	−0.999459	−	0.0329029i	$-0.989525\pi$
$907$	−14.1919	+	24.5811i	−0.471234	+	0.816202i	0.528224	+	0.849105i	$0.322858\pi$
$908$	0.487223			0.0161691
$909$		0			0
$910$	−12.4889			−0.414003
$911$	2.89932	−	5.02177i	0.0960588	−	0.166379i	−0.813991	−	0.580877i	$-0.802710\pi$
$911$	2.89932	−	5.02177i	0.0960588	−	0.166379i	0.910050	+	0.414499i	$0.136043\pi$
$912$		0			0
$913$	−4.44355	−	7.69645i	−0.147060	−	0.254715i
$914$	15.3250	+	26.5436i	0.506905	+	0.877984i
$915$		0			0
$916$	0.310529	−	0.537852i	0.0102602	−	0.0177711i
$917$	−11.9272			−0.393871
$918$		0			0
$919$	−46.2912			−1.52701			−0.763503	−	0.645804i	$-0.776522\pi$
$919$	−46.2912			−1.52701			−0.763503	+	0.645804i	$0.776522\pi$
$920$	−35.6651	+	61.7738i	−1.17585	+	2.03662i
$921$		0			0
$922$	0.230098	+	0.398542i	0.00757788	+	0.0131253i
$923$	9.92577	+	17.1919i	0.326711	+	0.565879i
$924$		0			0
$925$	5.86153	−	10.1525i	0.192726	−	0.333811i
$926$	−14.2825			−0.469353
$927$		0			0
$928$	2.18974			0.0718819
$929$	21.1201	−	36.5811i	0.692928	−	1.20019i	−0.277947	−	0.960596i	$-0.589654\pi$
$929$	21.1201	−	36.5811i	0.692928	−	1.20019i	0.970874	−	0.239589i	$-0.0770128\pi$
$930$		0			0
$931$	2.43557	+	4.21852i	0.0798224	+	0.138256i
$932$	4.00360	+	6.93444i	0.131142	+	0.227145i
$933$		0			0
$934$	0.278975	−	0.483199i	0.00912835	−	0.0158108i
$935$	12.6201			0.412722
$936$		0			0
$937$	34.2767			1.11977			0.559886	−	0.828570i	$-0.310845\pi$
$937$	34.2767			1.11977			0.559886	+	0.828570i	$0.310845\pi$
$938$	7.72836	−	13.3859i	0.252340	−	0.437066i
$939$		0			0
$940$	4.37569	+	7.57892i	0.142719	+	0.247197i
$941$	−15.2021	−	26.3309i	−0.495576	−	0.858362i	0.504411	−	0.863463i	$-0.331709\pi$
$941$	−15.2021	−	26.3309i	−0.495576	−	0.858362i	−0.999987	+	0.00510142i	$0.998376\pi$
$942$		0			0
$943$	−26.9452	+	46.6705i	−0.877457	+	1.51980i
$944$	21.7171			0.706833
$945$		0			0
$946$	−3.82377			−0.124321
$947$	18.1345	−	31.4099i	0.589293	−	1.02068i	−0.405033	−	0.914302i	$-0.632740\pi$
$947$	18.1345	−	31.4099i	0.589293	−	1.02068i	0.994325	−	0.106383i	$-0.0339268\pi$
$948$		0			0
$949$	3.19875	+	5.54040i	0.103836	+	0.179849i
$950$	−1.40493	−	2.43340i	−0.0455818	−	0.0789501i
$951$		0			0
$952$	−2.40534	+	4.16618i	−0.0779577	+	0.135027i
$953$	21.1687			0.685722			0.342861	−	0.939386i	$-0.388604\pi$
$953$	21.1687			0.685722			0.342861	+	0.939386i	$0.388604\pi$
$954$		0			0
$955$	−69.9273			−2.26279
$956$	2.50453	−	4.33797i	0.0810023	−	0.140300i
$957$		0			0
$958$	−0.865196	−	1.49856i	−0.0279532	−	0.0484164i
$959$	−10.7936	−	18.6950i	−0.348542	−	0.603692i
$960$		0			0
$961$	13.6463	−	23.6361i	0.440203	−	0.762454i
$962$	19.4709			0.627766
$963$		0			0
$964$	3.04600			0.0981051
$965$	30.0036	−	51.9678i	0.965851	−	1.67290i
$966$		0			0
$967$	1.59049	+	2.75482i	0.0511468	+	0.0885889i	0.890465	−	0.455051i	$-0.150379\pi$
$967$	1.59049	+	2.75482i	0.0511468	+	0.0885889i	−0.839318	+	0.543640i	$0.817046\pi$
$968$	−3.50063	−	6.06327i	−0.112515	−	0.194881i
$969$		0			0
$970$	6.95170	−	12.0407i	0.223206	−	0.386603i
$971$	23.4998			0.754145			0.377072	−	0.926184i	$-0.376931\pi$
$971$	23.4998			0.754145			0.377072	+	0.926184i	$0.376931\pi$
$972$		0			0
$973$	22.9817			0.736760
$974$	11.6083	−	20.1062i	0.371955	−	0.644245i
$975$		0			0
$976$	−0.114188	−	0.197780i	−0.00365508	−	0.00633079i
$977$	20.2314	+	35.0418i	0.647260	+	1.12109i	0.983775	+	0.179409i	$0.0574184\pi$
$977$	20.2314	+	35.0418i	0.647260	+	1.12109i	−0.336515	+	0.941678i	$0.609248\pi$
$978$		0			0
$979$	22.4742	−	38.9264i	0.718278	−	1.24409i
$980$	5.14138			0.164235
$981$		0			0
$982$	29.8118			0.951333
$983$	20.9320	−	36.2552i	0.667626	−	1.15636i	−0.310940	−	0.950430i	$-0.600644\pi$
$983$	20.9320	−	36.2552i	0.667626	−	1.15636i	0.978566	−	0.205933i	$-0.0660229\pi$
$984$		0			0
$985$	9.39348	+	16.2700i	0.299301	+	0.518405i
$986$	1.25569	+	2.17492i	0.0399894	+	0.0692636i
$987$		0			0
$988$	−0.433807	+	0.751375i	−0.0138012	+	0.0239044i
$989$	−8.59169			−0.273200
$990$		0			0
$991$	−18.0897			−0.574638			−0.287319	−	0.957835i	$-0.592764\pi$
$991$	−18.0897			−0.574638			−0.287319	+	0.957835i	$0.592764\pi$
$992$	1.69085	−	2.92864i	0.0536846	−	0.0929845i
$993$		0			0
$994$	−3.94709	−	6.83655i	−0.125194	−	0.216842i
$995$	−37.6925	−	65.2854i	−1.19493	−	2.06968i
$996$		0			0
$997$	18.6698	−	32.3370i	0.591278	−	1.02412i	−0.402783	−	0.915296i	$-0.631957\pi$
$997$	18.6698	−	32.3370i	0.591278	−	1.02412i	0.994061	−	0.108828i	$-0.0347096\pi$
$998$	12.2648			0.388235
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1161.2.f.c.775.6		38
3.2	odd	2		387.2.f.c.259.14	yes	38
9.2	odd	6		3483.2.a.s.1.6		19
9.4	even	3	inner	1161.2.f.c.388.6		38
9.5	odd	6		387.2.f.c.130.14	✓	38
9.7	even	3		3483.2.a.r.1.14		19

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
387.2.f.c.130.14	✓	38	9.5	odd	6
387.2.f.c.259.14	yes	38	3.2	odd	2
1161.2.f.c.388.6		38	9.4	even	3	inner
1161.2.f.c.775.6		38	1.1	even	1	trivial
3483.2.a.r.1.14		19	9.7	even	3
3483.2.a.s.1.6		19	9.2	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)

\(f(q)\)	\(=\)	\(q+(-0.649321 + 1.12466i) q^{2} +(0.156764 + 0.271524i) q^{4} +(-1.38166 - 2.39311i) q^{5} +(-0.516159 + 0.894013i) q^{7} -3.00445 q^{8} +O(q^{10})\)	\(q+(-0.649321 + 1.12466i) q^{2} +(0.156764 + 0.271524i) q^{4} +(-1.38166 - 2.39311i) q^{5} +(-0.516159 + 0.894013i) q^{7} -3.00445 q^{8} +3.58856 q^{10} +(1.47222 - 2.54996i) q^{11} +(1.68562 + 2.91958i) q^{13} +(-0.670305 - 1.16100i) q^{14} +(1.63732 - 2.83592i) q^{16} -1.55106 q^{17} +0.820840 q^{19} +(0.433190 - 0.750307i) q^{20} +(1.91188 + 3.31148i) q^{22} +(4.29584 + 7.44062i) q^{23} +(-1.31797 + 2.28279i) q^{25} -4.37804 q^{26} -0.323661 q^{28} +(-0.623396 + 1.07975i) q^{29} +(0.962734 + 1.66750i) q^{31} +(-0.878152 - 1.52100i) q^{32} +(1.00714 - 1.74442i) q^{34} +2.85262 q^{35} -4.44739 q^{37} +(-0.532989 + 0.923164i) q^{38} +(4.15112 + 7.18996i) q^{40} +(3.13620 + 5.43205i) q^{41} +(-0.500000 + 0.866025i) q^{43} +0.923165 q^{44} -11.1575 q^{46} +(-5.05055 + 8.74780i) q^{47} +(2.96716 + 5.13927i) q^{49} +(-1.71157 - 2.96453i) q^{50} +(-0.528491 + 0.915373i) q^{52} -8.79973 q^{53} -8.13642 q^{55} +(1.55077 - 2.68601i) q^{56} +(-0.809568 - 1.40221i) q^{58} +(3.31596 + 5.74341i) q^{59} +(0.0348705 - 0.0603975i) q^{61} -2.50049 q^{62} +8.83009 q^{64} +(4.65791 - 8.06774i) q^{65} +(5.76481 + 9.98494i) q^{67} +(-0.243152 - 0.421151i) q^{68} +(-1.85227 + 3.20822i) q^{70} +5.88849 q^{71} +1.89767 q^{73} +(2.88779 - 5.00179i) q^{74} +(0.128678 + 0.222878i) q^{76} +(1.51980 + 2.63236i) q^{77} +(-3.49563 + 6.05462i) q^{79} -9.04889 q^{80} -8.14560 q^{82} +(1.50913 - 2.61390i) q^{83} +(2.14304 + 3.71186i) q^{85} +(-0.649321 - 1.12466i) q^{86} +(-4.42320 + 7.66120i) q^{88} +15.2655 q^{89} -3.48019 q^{91} +(-1.34687 + 2.33285i) q^{92} +(-6.55885 - 11.3603i) q^{94} +(-1.13412 - 1.96436i) q^{95} +(1.93718 - 3.35530i) q^{97} -7.70656 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 38 q + 4 q^{2} - 22 q^{4} + 9 q^{5} - 7 q^{7} - 24 q^{8}+O(q^{10}) \) 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