LMFDB - Embedded newform 171.3.p.d.145.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [171,3,Mod(46,171)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(171, base_ring=CyclotomicField(6))

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

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("171.46");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 171 = 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	171.p (of order $6$, degree $2$, 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:	$4.65941252056$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{6})$
Coefficient field:	6.0.6967728.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} + 8x^{4} + 5x^{3} + 50x^{2} - 7x + 1 $ x^6 - x^5 + 8x^4 + 5x^3 + 50x^2 - 7x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 19)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			145.2
Root			$-1.13654 - 1.96854i$ of defining polynomial
Character	$\chi$	$=$	171.145
Dual form			171.3.p.d.46.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.583430 - 0.336844i) q^{2} +(-1.77307 + 3.07105i) q^{4} +(1.55311 + 2.69006i) q^{5} -8.15294 q^{7} +5.08374i q^{8} +O(q^{10})$	\(q+(0.583430 - 0.336844i) q^{2} +(-1.77307 + 3.07105i) q^{4} +(1.55311 + 2.69006i) q^{5} -8.15294 q^{7} +5.08374i q^{8} +(1.81226 + 1.04631i) q^{10} -17.6991 q^{11} +(5.33372 + 3.07942i) q^{13} +(-4.75667 + 2.74626i) q^{14} +(-5.37987 - 9.31820i) q^{16} +(6.91657 + 11.9799i) q^{17} +(3.11375 + 18.7431i) q^{19} -11.0151 q^{20} +(-10.3262 + 5.96182i) q^{22} +(-2.46968 + 4.27760i) q^{23} +(7.67572 - 13.2947i) q^{25} +4.14914 q^{26} +(14.4558 - 25.0381i) q^{28} +(38.2711 + 22.0958i) q^{29} +43.0049i q^{31} +(-23.8881 - 13.7918i) q^{32} +(8.07067 + 4.65960i) q^{34} +(-12.6624 - 21.9319i) q^{35} -30.7849i q^{37} +(8.13016 + 9.88645i) q^{38} +(-13.6756 + 7.89559i) q^{40} +(28.6795 - 16.5581i) q^{41} +(-15.7586 - 27.2946i) q^{43} +(31.3818 - 54.3548i) q^{44} +3.32758i q^{46} +(-8.86404 + 15.3530i) q^{47} +17.4704 q^{49} -10.3421i q^{50} +(-18.9142 + 10.9201i) q^{52} +(-14.6396 - 8.45218i) q^{53} +(-27.4886 - 47.6116i) q^{55} -41.4474i q^{56} +29.7713 q^{58} +(-20.3412 + 11.7440i) q^{59} +(-8.52643 + 14.7682i) q^{61} +(14.4859 + 25.0903i) q^{62} +24.4562 q^{64} +19.1307i q^{65} +(84.9924 + 49.0704i) q^{67} -49.0543 q^{68} +(-14.7752 - 8.53048i) q^{70} +(1.36156 - 0.786099i) q^{71} +(2.85534 + 4.94560i) q^{73} +(-10.3697 - 17.9608i) q^{74} +(-63.0820 - 23.6704i) q^{76} +144.300 q^{77} +(41.9327 - 24.2099i) q^{79} +(16.7110 - 28.9443i) q^{80} +(11.1550 - 19.3210i) q^{82} +74.2729 q^{83} +(-21.4843 + 37.2120i) q^{85} +(-18.3880 - 10.6163i) q^{86} -89.9776i q^{88} +(-81.0798 - 46.8114i) q^{89} +(-43.4855 - 25.1064i) q^{91} +(-8.75783 - 15.1690i) q^{92} +11.9432i q^{94} +(-45.5841 + 37.4862i) q^{95} +(-8.15700 + 4.70945i) q^{97} +(10.1928 - 5.88480i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 3 q^{2} + 5 q^{4} + 2 q^{5}+O(q^{10}) $ 6 * q + 3 * q^2 + 5 * q^4 + 2 * q^5	$ 6 q + 3 q^{2} + 5 q^{4} + 2 q^{5} - 60 q^{10} - 26 q^{11} + 30 q^{13} - 54 q^{14} + q^{16} + 42 q^{17} + 25 q^{19} - 108 q^{20} - 39 q^{22} - 8 q^{23} - 17 q^{25} + 148 q^{26} + 32 q^{28} + 12 q^{29} - 51 q^{32} - 6 q^{34} + 38 q^{35} + 14 q^{38} - 96 q^{40} - 63 q^{41} - 34 q^{43} + 69 q^{44} - 58 q^{47} + 18 q^{49} + 162 q^{52} + 12 q^{53} - 28 q^{55} + 172 q^{58} + 147 q^{59} + 58 q^{61} + 116 q^{62} + 166 q^{64} + 201 q^{67} + 84 q^{68} - 198 q^{70} + 102 q^{71} + 7 q^{73} - 174 q^{74} - 173 q^{76} + 376 q^{77} - 134 q^{80} - 145 q^{82} - 146 q^{83} - 90 q^{85} + 270 q^{86} + 72 q^{89} - 216 q^{91} - 72 q^{92} - 558 q^{95} + 21 q^{97} - 411 q^{98}+O(q^{100}) $ 6 * q + 3 * q^2 + 5 * q^4 + 2 * q^5 - 60 * q^10 - 26 * q^11 + 30 * q^13 - 54 * q^14 + q^16 + 42 * q^17 + 25 * q^19 - 108 * q^20 - 39 * q^22 - 8 * q^23 - 17 * q^25 + 148 * q^26 + 32 * q^28 + 12 * q^29 - 51 * q^32 - 6 * q^34 + 38 * q^35 + 14 * q^38 - 96 * q^40 - 63 * q^41 - 34 * q^43 + 69 * q^44 - 58 * q^47 + 18 * q^49 + 162 * q^52 + 12 * q^53 - 28 * q^55 + 172 * q^58 + 147 * q^59 + 58 * q^61 + 116 * q^62 + 166 * q^64 + 201 * q^67 + 84 * q^68 - 198 * q^70 + 102 * q^71 + 7 * q^73 - 174 * q^74 - 173 * q^76 + 376 * q^77 - 134 * q^80 - 145 * q^82 - 146 * q^83 - 90 * q^85 + 270 * q^86 + 72 * q^89 - 216 * q^91 - 72 * q^92 - 558 * q^95 + 21 * q^97 - 411 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/171\mathbb{Z}\right)^\times$.

$n$	$20$	$154$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$

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 $

$2$	0.583430	−	0.336844i	0.291715	−	0.168422i	−0.347000	−	0.937865i	$-0.612800\pi$
$2$	0.583430	−	0.336844i	0.291715	−	0.168422i	0.638715	+	0.769443i	$0.279466\pi$
$3$		0			0
$3$		0			0
$4$	−1.77307	+	3.07105i	−0.443268	+	0.767763i
$5$	1.55311	+	2.69006i	0.310621	+	0.538012i	0.978497	−	0.206261i	$-0.0661296\pi$
$5$	1.55311	+	2.69006i	0.310621	+	0.538012i	−0.667876	+	0.744273i	$0.732796\pi$
$6$		0			0
$7$	−8.15294			−1.16471			−0.582353	−	0.812936i	$-0.697868\pi$
$7$	−8.15294			−1.16471			−0.582353	+	0.812936i	$0.697868\pi$
$8$			5.08374i			0.635468i
$9$		0			0
$10$	1.81226	+	1.04631i	0.181226	+	0.104631i
$11$	−17.6991			−1.60901			−0.804504	−	0.593947i	$-0.797569\pi$
$11$	−17.6991			−1.60901			−0.804504	+	0.593947i	$0.797569\pi$
$12$		0			0
$13$	5.33372	+	3.07942i	0.410286	+	0.236879i	0.690913	−	0.722938i	$-0.257209\pi$
$13$	5.33372	+	3.07942i	0.410286	+	0.236879i	−0.280627	+	0.959817i	$0.590542\pi$
$14$	−4.75667	+	2.74626i	−0.339762	+	0.196162i
$15$		0			0
$16$	−5.37987	−	9.31820i	−0.336242	−	0.582388i
$17$	6.91657	+	11.9799i	0.406857	+	0.704697i	0.994536	−	0.104397i	$-0.0332914\pi$
$17$	6.91657	+	11.9799i	0.406857	+	0.704697i	−0.587679	+	0.809094i	$0.699958\pi$
$18$		0			0
$19$	3.11375	+	18.7431i	0.163882	+	0.986480i
$19$	3.11375	+	18.7431i	0.163882	+	0.986480i
$20$	−11.0151			−0.550754
$21$		0			0
$22$	−10.3262	+	5.96182i	−0.469372	+	0.270992i
$23$	−2.46968	+	4.27760i	−0.107377	+	0.185983i	−0.914707	−	0.404118i	$-0.867579\pi$
$23$	−2.46968	+	4.27760i	−0.107377	+	0.185983i	0.807330	+	0.590101i	$0.200912\pi$
$24$		0			0
$25$	7.67572	−	13.2947i	0.307029	−	0.531790i
$26$	4.14914			0.159582
$27$		0			0
$28$	14.4558	−	25.0381i	0.516277	−	0.894218i
$29$	38.2711	+	22.0958i	1.31969	+	0.761925i	0.983679	−	0.179933i	$-0.0575880\pi$
$29$	38.2711	+	22.0958i	1.31969	+	0.761925i	0.336013	+	0.941857i	$0.390921\pi$
$30$		0			0
$31$			43.0049i			1.38725i	0.720334	+	0.693627i	$0.243989\pi$
$31$			43.0049i			1.38725i	−0.720334	+	0.693627i	$0.756011\pi$
$32$	−23.8881	−	13.7918i	−0.746505	−	0.430995i
$33$		0			0
$34$	8.07067	+	4.65960i	0.237373	+	0.137047i
$35$	−12.6624	−	21.9319i	−0.361782	−	0.626625i
$36$		0			0
$37$		−	30.7849i		−	0.832024i	−0.909359	−	0.416012i	$-0.863428\pi$
$37$		−	30.7849i		−	0.832024i	0.909359	−	0.416012i	$-0.136572\pi$
$38$	8.13016	+	9.88645i	0.213951	+	0.260170i
$39$		0			0
$40$	−13.6756	+	7.89559i	−0.341889	+	0.197390i
$41$	28.6795	−	16.5581i	0.699501	−	0.403857i	−0.107661	−	0.994188i	$-0.534336\pi$
$41$	28.6795	−	16.5581i	0.699501	−	0.403857i	0.807161	+	0.590331i	$0.201003\pi$
$42$		0			0
$43$	−15.7586	−	27.2946i	−0.366478	−	0.634759i	0.622534	−	0.782593i	$-0.286103\pi$
$43$	−15.7586	−	27.2946i	−0.366478	−	0.634759i	−0.989012	+	0.147834i	$0.952770\pi$
$44$	31.3818	−	54.3548i	0.713222	−	1.23534i
$45$		0			0
$46$			3.32758i			0.0723386i
$47$	−8.86404	+	15.3530i	−0.188597	+	0.326659i	−0.944783	−	0.327698i	$-0.893727\pi$
$47$	−8.86404	+	15.3530i	−0.188597	+	0.326659i	0.756186	+	0.654357i	$0.227061\pi$
$48$		0			0
$49$	17.4704			0.356539
$50$		−	10.3421i		−	0.206841i
$51$		0			0
$52$	−18.9142	+	10.9201i	−0.363734	+	0.210002i
$53$	−14.6396	−	8.45218i	−0.276219	−	0.159475i	0.355492	−	0.934679i	$-0.384313\pi$
$53$	−14.6396	−	8.45218i	−0.276219	−	0.159475i	−0.631710	+	0.775204i	$0.717647\pi$
$54$		0			0
$55$	−27.4886	−	47.6116i	−0.499792	−	0.865665i
$56$		−	41.4474i		−	0.740133i
$57$		0			0
$58$	29.7713			0.513299
$59$	−20.3412	+	11.7440i	−0.344766	+	0.199050i	−0.662377	−	0.749170i	$-0.730452\pi$
$59$	−20.3412	+	11.7440i	−0.344766	+	0.199050i	0.317612	+	0.948221i	$0.397119\pi$
$60$		0			0
$61$	−8.52643	+	14.7682i	−0.139777	+	0.242102i	−0.927412	−	0.374041i	$-0.877972\pi$
$61$	−8.52643	+	14.7682i	−0.139777	+	0.242102i	0.787635	+	0.616142i	$0.211305\pi$
$62$	14.4859	+	25.0903i	0.233644	+	0.404683i
$63$		0			0
$64$	24.4562			0.382128
$65$			19.1307i			0.294318i
$66$		0			0
$67$	84.9924	+	49.0704i	1.26854	+	0.732393i	0.974712	−	0.223464i	$-0.0717365\pi$
$67$	84.9924	+	49.0704i	1.26854	+	0.732393i	0.293831	+	0.955858i	$0.405070\pi$
$68$	−49.0543			−0.721387
$69$		0			0
$70$	−14.7752	−	8.53048i	−0.211075	−	0.121864i
$71$	1.36156	−	0.786099i	0.0191769	−	0.0110718i	−0.490381	−	0.871508i	$-0.663142\pi$
$71$	1.36156	−	0.786099i	0.0191769	−	0.0110718i	0.509558	+	0.860436i	$0.329809\pi$
$72$		0			0
$73$	2.85534	+	4.94560i	0.0391143	+	0.0677479i	0.884920	−	0.465743i	$-0.154213\pi$
$73$	2.85534	+	4.94560i	0.0391143	+	0.0677479i	−0.845806	+	0.533491i	$0.820880\pi$
$74$	−10.3697	−	17.9608i	−0.140131	−	0.242714i
$75$		0			0
$76$	−63.0820	−	23.6704i	−0.830026	−	0.311453i
$77$	144.300			1.87402
$78$		0			0
$79$	41.9327	−	24.2099i	0.530794	−	0.306454i	−0.210546	−	0.977584i	$-0.567524\pi$
$79$	41.9327	−	24.2099i	0.530794	−	0.306454i	0.741340	+	0.671130i	$0.234191\pi$
$80$	16.7110	−	28.9443i	0.208888	−	0.361804i
$81$		0			0
$82$	11.1550	−	19.3210i	0.136037	−	0.235622i
$83$	74.2729			0.894854			0.447427	−	0.894320i	$-0.352340\pi$
$83$	74.2729			0.894854			0.447427	+	0.894320i	$0.352340\pi$
$84$		0			0
$85$	−21.4843	+	37.2120i	−0.252757	+	0.437788i
$86$	−18.3880	−	10.6163i	−0.213815	−	0.123446i
$87$		0			0
$88$		−	89.9776i		−	1.02247i
$89$	−81.0798	−	46.8114i	−0.911008	−	0.525971i	−0.0302530	−	0.999542i	$-0.509631\pi$
$89$	−81.0798	−	46.8114i	−0.911008	−	0.525971i	−0.880755	+	0.473571i	$0.842965\pi$
$90$		0			0
$91$	−43.4855	−	25.1064i	−0.477863	−	0.275894i
$92$	−8.75783	−	15.1690i	−0.0951938	−	0.164881i
$93$		0			0
$94$			11.9432i			0.127055i
$95$	−45.5841	+	37.4862i	−0.479833	+	0.394592i
$96$		0			0
$97$	−8.15700	+	4.70945i	−0.0840928	+	0.0485510i	−0.541457	−	0.840729i	$-0.682127\pi$
$97$	−8.15700	+	4.70945i	−0.0840928	+	0.0485510i	0.457364	+	0.889280i	$0.348794\pi$
$98$	10.1928	−	5.88480i	0.104008	−	0.0600489i
$99$		0			0
$100$	27.2192	+	47.1451i	0.272192	+	0.471451i
$101$	−66.5604	+	115.286i	−0.659014	+	1.14145i	0.321858	+	0.946788i	$0.395693\pi$
$101$	−66.5604	+	115.286i	−0.659014	+	1.14145i	−0.980871	+	0.194657i	$0.937641\pi$
$102$		0			0
$103$			92.7893i			0.900867i	0.892810	+	0.450433i	$0.148731\pi$
$103$			92.7893i			0.900867i	−0.892810	+	0.450433i	$0.851269\pi$
$104$	−15.6550	+	27.1153i	−0.150529	+	0.260724i
$105$		0			0
$106$	−11.3882			−0.107436
$107$			139.410i			1.30289i	0.758695	+	0.651446i	$0.225837\pi$
$107$			139.410i			1.30289i	−0.758695	+	0.651446i	$0.774163\pi$
$108$		0			0
$109$	−112.823	+	65.1381i	−1.03507	+	0.597597i	−0.918433	−	0.395577i	$-0.870545\pi$
$109$	−112.823	+	65.1381i	−1.03507	+	0.597597i	−0.116636	+	0.993175i	$0.537211\pi$
$110$	−32.0753	−	18.5187i	−0.291594	−	0.168352i
$111$		0			0
$112$	43.8617	+	75.9707i	0.391623	+	0.678310i
$113$		−	19.1195i		−	0.169199i	−0.996415	−	0.0845997i	$-0.973039\pi$
$113$		−	19.1195i		−	0.169199i	0.996415	−	0.0845997i	$-0.0269612\pi$
$114$		0			0
$115$	−15.3427			−0.133415
$116$	−135.715	+	78.3550i	−1.16996	+	0.675474i
$117$		0			0
$118$	−7.91177	+	13.7036i	−0.0670489	+	0.116132i
$119$	−56.3904	−	97.6710i	−0.473869	−	0.820765i
$120$		0			0
$121$	192.258			1.58891
$122$			11.4883i			0.0941663i
$123$		0			0
$124$	−132.070	−	76.2508i	−1.06508	−	0.614926i
$125$	125.340			1.00272
$126$		0			0
$127$	−21.1332	−	12.2013i	−0.166403	−	0.0960730i	0.414486	−	0.910056i	$-0.363962\pi$
$127$	−21.1332	−	12.2013i	−0.166403	−	0.0960730i	−0.580889	+	0.813983i	$0.697295\pi$
$128$	109.821	−	63.4052i	0.857977	−	0.495353i
$129$		0			0
$130$	6.44405	+	11.1614i	0.0495696	+	0.0858571i
$131$	38.0958	+	65.9839i	0.290808	+	0.503694i	0.974001	−	0.226544i	$-0.0727426\pi$
$131$	38.0958	+	65.9839i	0.290808	+	0.503694i	−0.683193	+	0.730238i	$0.739409\pi$
$132$		0			0
$133$	−25.3862	−	152.812i	−0.190874	−	1.14896i
$134$	66.1161			0.493404
$135$		0			0
$136$	−60.9025	+	35.1620i	−0.447812	+	0.258544i
$137$	−118.616	+	205.449i	−0.865811	+	1.49963i	0.000428189		1.00000i	$0.499864\pi$
$137$	−118.616	+	205.449i	−0.865811	+	1.49963i	−0.866239	+	0.499629i	$0.833470\pi$
$138$		0			0
$139$	−10.0402	+	17.3902i	−0.0722320	+	0.125110i	−0.899879	−	0.436139i	$-0.856346\pi$
$139$	−10.0402	+	17.3902i	−0.0722320	+	0.125110i	0.827647	+	0.561249i	$0.189679\pi$
$140$	89.8053			0.641466
$141$		0			0
$142$	0.529585	−	0.917267i	0.00372947	−	0.00645963i
$143$	−94.4020	−	54.5030i	−0.660154	−	0.381140i
$144$		0			0
$145$			137.269i			0.946680i
$146$	3.33178	+	1.92361i	0.0228204	+	0.0131754i
$147$		0			0
$148$	94.5419	+	54.5838i	0.638797	+	0.368810i
$149$	−77.8489	−	134.838i	−0.522476	−	0.904954i	−0.999658	−	0.0261500i	$-0.991675\pi$
$149$	−77.8489	−	134.838i	−0.522476	−	0.904954i	0.477182	−	0.878804i	$-0.341658\pi$
$150$		0			0
$151$		−	41.4678i		−	0.274621i	−0.990528	−	0.137310i	$-0.956154\pi$
$151$		−	41.4678i		−	0.274621i	0.990528	−	0.137310i	$-0.0438458\pi$
$152$	−95.2852	+	15.8295i	−0.626876	+	0.104142i
$153$		0			0
$154$	84.1887	−	48.6064i	0.546680	−	0.315626i
$155$	−115.686	+	66.7912i	−0.746359	+	0.430911i
$156$		0			0
$157$	39.5539	+	68.5094i	0.251936	+	0.436366i	0.964059	−	0.265689i	$-0.0855994\pi$
$157$	39.5539	+	68.5094i	0.251936	+	0.436366i	−0.712123	+	0.702055i	$0.752266\pi$
$158$	16.3099	−	28.2495i	0.103227	−	0.178794i
$159$		0			0
$160$		−	85.6807i		−	0.535504i
$161$	20.1351	−	34.8751i	0.125063	−	0.216615i
$162$		0			0
$163$	−135.441			−0.830926			−0.415463	−	0.909610i	$-0.636380\pi$
$163$	−135.441			−0.830926			−0.415463	+	0.909610i	$0.636380\pi$
$164$			117.435i			0.716068i
$165$		0			0
$166$	43.3330	−	25.0183i	0.261042	−	0.150713i
$167$	−54.3880	−	31.4010i	−0.325677	−	0.188030i	0.328243	−	0.944593i	$-0.393543\pi$
$167$	−54.3880	−	31.4010i	−0.325677	−	0.188030i	−0.653920	+	0.756564i	$0.726877\pi$
$168$		0			0
$169$	−65.5343	−	113.509i	−0.387777	−	0.671649i
$170$			28.9474i			0.170279i
$171$		0			0
$172$	111.764			0.649793
$173$	282.606	−	163.162i	1.63356	−	0.943135i	0.650574	−	0.759442i	$-0.274528\pi$
$173$	282.606	−	163.162i	1.63356	−	0.943135i	0.982984	−	0.183693i	$-0.0588052\pi$
$174$		0			0
$175$	−62.5797	+	108.391i	−0.357598	+	0.619378i
$176$	95.2187	+	164.924i	0.541015	+	0.937066i
$177$		0			0
$178$	−63.0725			−0.354340
$179$		−	266.546i		−	1.48909i	−0.667575	−	0.744543i	$-0.732668\pi$
$179$		−	266.546i		−	1.48909i	0.667575	−	0.744543i	$-0.267332\pi$
$180$		0			0
$181$	129.999	+	75.0548i	0.718225	+	0.414667i	0.814099	−	0.580726i	$-0.197231\pi$
$181$	129.999	+	75.0548i	0.718225	+	0.414667i	−0.0958743	+	0.995393i	$0.530565\pi$
$182$	−33.8277			−0.185866
$183$		0			0
$184$	−21.7462	−	12.5552i	−0.118186	−	0.0682347i
$185$	82.8131	−	47.8122i	0.447638	−	0.258444i
$186$		0			0
$187$	−122.417	−	212.032i	−0.654636	−	1.13386i
$188$	−31.4332	−	54.4439i	−0.167198	−	0.289595i
$189$		0			0
$190$	−13.9681	+	37.2253i	−0.0735165	+	0.195923i
$191$	99.5798			0.521360			0.260680	−	0.965425i	$-0.416053\pi$
$191$	99.5798			0.521360			0.260680	+	0.965425i	$0.416053\pi$
$192$		0			0
$193$	−42.4195	+	24.4909i	−0.219790	+	0.126896i	−0.605853	−	0.795577i	$-0.707168\pi$
$193$	−42.4195	+	24.4909i	−0.219790	+	0.126896i	0.386063	+	0.922472i	$0.373835\pi$
$194$	−3.17269	+	5.49527i	−0.0163541	+	0.0283261i
$195$		0			0
$196$	−30.9763	+	53.6526i	−0.158042	+	0.273738i
$197$	167.819			0.851875			0.425938	−	0.904753i	$-0.359944\pi$
$197$	167.819			0.851875			0.425938	+	0.904753i	$0.359944\pi$
$198$		0			0
$199$	46.2601	−	80.1249i	0.232463	−	0.402638i	−0.726069	−	0.687621i	$-0.758655\pi$
$199$	46.2601	−	80.1249i	0.232463	−	0.402638i	0.958532	+	0.284984i	$0.0919882\pi$
$200$	67.5870	+	39.0214i	0.337935	+	0.195107i
$201$		0			0
$202$			89.6818i			0.443969i
$203$	−312.022	−	180.146i	−1.53705	−	0.887418i
$204$		0			0
$205$	89.0847	+	51.4331i	0.434559	+	0.250893i
$206$	31.2555	+	54.1361i	0.151726	+	0.262796i
$207$		0			0
$208$		−	66.2676i		−	0.318594i
$209$	−55.1106	−	331.736i	−0.263687	−	1.58725i
$210$		0			0
$211$	−54.4067	+	31.4117i	−0.257852	+	0.148871i	−0.623354	−	0.781940i	$-0.714231\pi$
$211$	−54.4067	+	31.4117i	−0.257852	+	0.148871i	0.365502	+	0.930810i	$0.380897\pi$
$212$	51.9142	−	29.9726i	0.244878	−	0.141380i
$213$		0			0
$214$	46.9592	+	81.3357i	0.219436	+	0.380073i
$215$	48.9495	−	84.7830i	0.227672	−	0.394339i
$216$		0			0
$217$		−	350.616i		−	1.61574i
$218$	−43.8827	+	76.0071i	−0.201297	+	0.348656i
$219$		0			0
$220$	194.957			0.886168
$221$			85.1962i			0.385503i
$222$		0			0
$223$	371.890	−	214.711i	1.66767	−	0.962830i	0.698781	−	0.715336i	$-0.253726\pi$
$223$	371.890	−	214.711i	1.66767	−	0.962830i	0.968889	−	0.247494i	$-0.0796071\pi$
$224$	194.759	+	112.444i	0.869458	+	0.501982i
$225$		0			0
$226$	−6.44029	−	11.1549i	−0.0284969	−	0.0493580i
$227$		−	246.184i		−	1.08451i	−0.840213	−	0.542256i	$-0.817570\pi$
$227$		−	246.184i		−	1.08451i	0.840213	−	0.542256i	$-0.182430\pi$
$228$		0			0
$229$	−31.8783			−0.139207			−0.0696033	−	0.997575i	$-0.522173\pi$
$229$	−31.8783			−0.139207			−0.0696033	+	0.997575i	$0.522173\pi$
$230$	−8.95138	+	5.16808i	−0.0389190	+	0.0224699i
$231$		0			0
$232$	−112.329	+	194.560i	−0.484178	+	0.838622i
$233$	184.933	+	320.313i	0.793704	+	1.37474i	0.923659	+	0.383216i	$0.125183\pi$
$233$	184.933	+	320.313i	0.793704	+	1.37474i	−0.129955	+	0.991520i	$0.541483\pi$
$234$		0			0
$235$	−55.0672			−0.234329
$236$		−	83.2917i		−	0.352931i
$237$		0			0
$238$	−65.7997	−	37.9895i	−0.276469	−	0.159620i
$239$	−106.567			−0.445887			−0.222944	−	0.974831i	$-0.571567\pi$
$239$	−106.567			−0.445887			−0.222944	+	0.974831i	$0.571567\pi$
$240$		0			0
$241$	−11.9695	−	6.91062i	−0.0496662	−	0.0286748i	0.474961	−	0.880007i	$-0.342462\pi$
$241$	−11.9695	−	6.91062i	−0.0496662	−	0.0286748i	−0.524627	+	0.851332i	$0.675795\pi$
$242$	112.169	−	64.7607i	0.463508	−	0.267606i
$243$		0			0
$244$	−30.2359	−	52.3702i	−0.123918	−	0.214632i
$245$	27.1334	+	46.9964i	0.110749	+	0.191822i
$246$		0			0
$247$	−41.1101	+	109.559i	−0.166438	+	0.443559i
$248$	−218.626			−0.881555
$249$		0			0
$250$	73.1272	−	42.2200i	0.292509	−	0.168880i
$251$	−61.3921	+	106.334i	−0.244590	+	0.423642i	−0.962016	−	0.272992i	$-0.911987\pi$
$251$	−61.3921	+	106.334i	−0.244590	+	0.423642i	0.717426	+	0.696635i	$0.245320\pi$
$252$		0			0
$253$	43.7110	−	75.7097i	0.172771	−	0.299248i
$254$	−16.4397			−0.0647231
$255$		0			0
$256$	−6.19708	+	10.7337i	−0.0242073	+	0.0419283i
$257$	343.131	+	198.107i	1.33514	+	0.770843i	0.986082	−	0.166258i	$-0.0531684\pi$
$257$	343.131	+	198.107i	1.33514	+	0.770843i	0.349058	+	0.937101i	$0.386502\pi$
$258$		0			0
$259$			250.987i			0.969062i
$260$	−58.7514	−	33.9201i	−0.225967	−	0.130462i
$261$		0			0
$262$	44.4525	+	25.6647i	0.169666	+	0.0979568i
$263$	−26.7480	−	46.3289i	−0.101704	−	0.176156i	0.810683	−	0.585485i	$-0.199096\pi$
$263$	−26.7480	−	46.3289i	−0.101704	−	0.176156i	−0.912387	+	0.409330i	$0.865763\pi$
$264$		0			0
$265$		−	52.5085i		−	0.198145i
$266$	−66.2847	−	80.6036i	−0.249190	−	0.303021i
$267$		0			0
$268$	−301.395	+	174.011i	−1.12461	+	0.649293i
$269$	−316.357	+	182.649i	−1.17605	+	0.678993i	−0.955098	−	0.296292i	$-0.904250\pi$
$269$	−316.357	+	182.649i	−1.17605	+	0.678993i	−0.220953	+	0.975285i	$0.570917\pi$
$270$		0			0
$271$	−87.1835	−	151.006i	−0.321710	−	0.557219i	0.659131	−	0.752028i	$-0.270924\pi$
$271$	−87.1835	−	151.006i	−0.321710	−	0.557219i	−0.980841	+	0.194810i	$0.937591\pi$
$272$	74.4204	−	128.900i	0.273605	−	0.473897i
$273$		0			0
$274$			159.820i			0.583286i
$275$	−135.853	+	235.305i	−0.494012	+	0.855654i
$276$		0			0
$277$	93.2815			0.336756			0.168378	−	0.985722i	$-0.446147\pi$
$277$	93.2815			0.336756			0.168378	+	0.985722i	$0.446147\pi$
$278$			13.5280i			0.0486618i
$279$		0			0
$280$	111.496	−	64.3723i	0.398200	−	0.229901i
$281$	−325.337	−	187.834i	−1.15778	−	0.668447i	−0.207013	−	0.978338i	$-0.566374\pi$
$281$	−325.337	−	187.834i	−1.15778	−	0.668447i	−0.950772	+	0.309891i	$0.899707\pi$
$282$		0			0
$283$	32.0728	+	55.5518i	0.113332	+	0.196296i	0.917112	−	0.398631i	$-0.130514\pi$
$283$	32.0728	+	55.5518i	0.113332	+	0.196296i	−0.803780	+	0.594927i	$0.797181\pi$
$284$			5.57524i			0.0196311i
$285$		0			0
$286$	−73.4359			−0.256769
$287$	−233.822	+	134.997i	−0.814712	+	0.470374i
$288$		0			0
$289$	48.8221	−	84.5624i	0.168935	−	0.292603i
$290$	46.2380	+	80.0866i	0.159442	+	0.276161i
$291$		0			0
$292$	−20.2509			−0.0693524
$293$		−	111.814i		−	0.381618i	−0.981627	−	0.190809i	$-0.938889\pi$
$293$		−	111.814i		−	0.381618i	0.981627	−	0.190809i	$-0.0611112\pi$
$294$		0			0
$295$	−63.1840	−	36.4793i	−0.214183	−	0.123659i
$296$	156.502			0.528724
$297$		0			0
$298$	−90.8387	−	52.4458i	−0.304828	−	0.175993i
$299$	−26.3451	+	15.2104i	−0.0881108	+	0.0508708i
$300$		0			0
$301$	128.479	+	222.532i	0.426839	+	0.739308i
$302$	−13.9681	−	24.1935i	−0.0462521	−	0.0801110i
$303$		0			0
$304$	157.901	−	129.850i	0.519410	−	0.427138i
$305$	−52.9698			−0.173671
$306$		0			0
$307$	−297.331	+	171.664i	−0.968503	+	0.559166i	−0.898780	−	0.438401i	$-0.855545\pi$
$307$	−297.331	+	171.664i	−0.968503	+	0.559166i	−0.0697237	+	0.997566i	$0.522212\pi$
$308$	−255.854	+	443.151i	−0.830694	+	1.43880i
$309$		0			0
$310$	−44.9963	+	77.9360i	−0.145150	+	0.251406i
$311$	251.722			0.809397			0.404698	−	0.914450i	$-0.367376\pi$
$311$	251.722			0.809397			0.404698	+	0.914450i	$0.367376\pi$
$312$		0			0
$313$	−243.143	+	421.136i	−0.776814	+	1.34548i	0.156955	+	0.987606i	$0.449832\pi$
$313$	−243.143	+	421.136i	−0.776814	+	1.34548i	−0.933769	+	0.357876i	$0.883501\pi$
$314$	46.1539	+	26.6470i	0.146987	+	0.0848630i
$315$		0			0
$316$			171.703i			0.543365i
$317$	240.229	+	138.696i	0.757819	+	0.437527i	0.828512	−	0.559971i	$-0.189188\pi$
$317$	240.229	+	138.696i	0.757819	+	0.437527i	−0.0706929	+	0.997498i	$0.522521\pi$
$318$		0			0
$319$	−677.363	−	391.076i	−2.12340	−	1.22594i
$320$	37.9830	+	65.7886i	0.118697	+	0.205589i
$321$		0			0
$322$		−	27.1295i		−	0.0842532i
$323$	−203.003	+	166.940i	−0.628493	+	0.516843i
$324$		0			0
$325$	81.8803	−	47.2736i	0.251939	−	0.145457i
$326$	−79.0203	+	45.6224i	−0.242394	+	0.139946i
$327$		0			0
$328$	84.1772	+	145.799i	0.256638	+	0.444510i
$329$	72.2680	−	125.172i	0.219660	−	0.380462i
$330$		0			0
$331$			110.480i			0.333776i	0.985976	+	0.166888i	$0.0533719\pi$
$331$			110.480i			0.333776i	−0.985976	+	0.166888i	$0.946628\pi$
$332$	−131.691	+	228.096i	−0.396660	+	0.687036i
$333$		0			0
$334$	−42.3088			−0.126673
$335$			304.846i			0.909988i
$336$		0			0
$337$	23.9735	−	13.8411i	0.0711380	−	0.0410716i	−0.464009	−	0.885830i	$-0.653590\pi$
$337$	23.9735	−	13.8411i	0.0711380	−	0.0410716i	0.535147	+	0.844759i	$0.320256\pi$
$338$	−76.4694	−	44.1496i	−0.226241	−	0.130620i
$339$		0			0
$340$	−76.1866	−	131.959i	−0.224078	−	0.388115i
$341$		−	761.147i		−	2.23210i
$342$		0			0
$343$	257.059			0.749443
$344$	138.759	−	80.1125i	0.403369	−	0.232885i
$345$		0			0
$346$	109.920	−	190.388i	0.317689	−	0.550254i
$347$	129.243	+	223.856i	0.372459	+	0.645118i	0.989943	−	0.141465i	$-0.0451813\pi$
$347$	129.243	+	223.856i	0.372459	+	0.645118i	−0.617484	+	0.786583i	$0.711848\pi$
$348$		0			0
$349$	502.852			1.44084			0.720419	−	0.693539i	$-0.243950\pi$
$349$	502.852			1.44084			0.720419	+	0.693539i	$0.243950\pi$
$350$			84.3183i			0.240909i
$351$		0			0
$352$	422.798	+	244.103i	1.20113	+	0.693474i
$353$	−54.1066			−0.153277			−0.0766383	−	0.997059i	$-0.524419\pi$
$353$	−54.1066			−0.153277			−0.0766383	+	0.997059i	$0.524419\pi$
$354$		0			0
$355$	4.22930	+	2.44179i	0.0119135	+	0.00687828i
$356$	287.521	−	166.000i	0.807642	−	0.466292i
$357$		0			0
$358$	−89.7844	−	155.511i	−0.250794	−	0.434389i
$359$	−218.686	−	378.775i	−0.609152	−	1.05508i	−0.991380	−	0.131015i	$-0.958176\pi$
$359$	−218.686	−	378.775i	−0.609152	−	1.05508i	0.382228	−	0.924068i	$-0.375157\pi$
$360$		0			0
$361$	−341.609	+	116.723i	−0.946286	+	0.323332i
$362$	101.127			0.279356
$363$		0			0
$364$	154.206	−	89.0308i	0.423643	−	0.244590i
$365$	−8.86930	+	15.3621i	−0.0242994	+	0.0420879i
$366$		0			0
$367$	48.1329	−	83.3687i	0.131152	−	0.227163i	−0.792969	−	0.609262i	$-0.791466\pi$
$367$	48.1329	−	83.3687i	0.131152	−	0.227163i	0.924121	+	0.382100i	$0.124799\pi$
$368$	53.1461			0.144419
$369$		0			0
$370$	32.2104	−	55.7901i	0.0870553	−	0.150784i
$371$	119.356	+	68.9101i	0.321714	+	0.185741i
$372$		0			0
$373$		−	598.561i		−	1.60472i	−0.596840	−	0.802360i	$-0.703577\pi$
$373$		−	598.561i		−	1.60472i	0.596840	−	0.802360i	$-0.296423\pi$
$374$	−142.843	−	82.4707i	−0.381934	−	0.220510i
$375$		0			0
$376$	−78.0505	−	45.0625i	−0.207581	−	0.119847i
$377$	136.085	+	235.706i	0.360968	+	0.625214i
$378$		0			0
$379$		−	161.020i		−	0.424855i	−0.977177	−	0.212427i	$-0.931863\pi$
$379$		−	161.020i		−	0.424855i	0.977177	−	0.212427i	$-0.0681369\pi$
$380$	−34.2983	−	206.457i	−0.0902586	−	0.543308i
$381$		0			0
$382$	58.0979	−	33.5428i	0.152089	−	0.0878084i
$383$	−200.487	+	115.751i	−0.523464	+	0.302222i	−0.738351	−	0.674417i	$-0.764395\pi$
$383$	−200.487	+	115.751i	−0.523464	+	0.302222i	0.214887	+	0.976639i	$0.431062\pi$
$384$		0			0
$385$	224.113	+	388.174i	0.582111	+	1.00825i
$386$	−16.4992	+	28.5775i	−0.0427440	+	0.0740348i
$387$		0			0
$388$		−	33.4008i		−	0.0860845i
$389$	40.5074	−	70.1609i	0.104132	−	0.180362i	−0.809251	−	0.587463i	$-0.800127\pi$
$389$	40.5074	−	70.1609i	0.104132	−	0.180362i	0.913383	+	0.407101i	$0.133460\pi$
$390$		0			0
$391$	−68.3268			−0.174749
$392$			88.8151i			0.226569i
$393$		0			0
$394$	97.9109	−	56.5289i	0.248505	−	0.143474i
$395$	130.252	+	75.2010i	0.329752	+	0.190382i
$396$		0			0
$397$	341.051	+	590.718i	0.859071	+	1.48796i	0.872816	+	0.488050i	$0.162291\pi$
$397$	341.051	+	590.718i	0.859071	+	1.48796i	−0.0137446	+	0.999906i	$0.504375\pi$
$398$		−	62.3297i		−	0.156607i
$399$		0			0
$400$	−165.177			−0.412944
$401$	82.6912	−	47.7418i	0.206213	−	0.119057i	−0.393337	−	0.919394i	$-0.628680\pi$
$401$	82.6912	−	47.7418i	0.206213	−	0.119057i	0.599550	+	0.800337i	$0.295346\pi$
$402$		0			0
$403$	−132.430	+	229.376i	−0.328611	+	0.569171i
$404$	−236.033	−	408.821i	−0.584240	−	1.01193i
$405$		0			0
$406$	−242.724			−0.597842
$407$			544.864i			1.33873i
$408$		0			0
$409$	−169.330	−	97.7625i	−0.414009	−	0.239028i	0.278502	−	0.960436i	$-0.410162\pi$
$409$	−169.330	−	97.7625i	−0.414009	−	0.239028i	−0.692511	+	0.721408i	$0.743495\pi$
$410$	69.2996			0.169023
$411$		0			0
$412$	−284.961	−	164.522i	−0.691652	−	0.399326i
$413$	165.840	−	95.7479i	0.401550	−	0.231835i
$414$		0			0
$415$	115.354	+	199.798i	0.277961	+	0.481442i
$416$	−84.9418	−	147.124i	−0.204187	−	0.353662i
$417$		0			0
$418$	−143.896	−	174.981i	−0.344250	−	0.418615i
$419$	388.318			0.926773			0.463387	−	0.886156i	$-0.346634\pi$
$419$	388.318			0.926773			0.463387	+	0.886156i	$0.346634\pi$
$420$		0			0
$421$	225.968	−	130.463i	0.536742	−	0.309888i	−0.207015	−	0.978338i	$-0.566375\pi$
$421$	225.968	−	130.463i	0.536742	−	0.309888i	0.743758	+	0.668449i	$0.233042\pi$
$422$	−21.1617	+	36.6531i	−0.0501462	+	0.0868557i
$423$		0			0
$424$	42.9687	−	74.4239i	0.101341	−	0.175528i
$425$	212.359			0.499667
$426$		0			0
$427$	69.5154	−	120.404i	0.162800	−	0.281977i
$428$	−428.134	−	247.183i	−1.00031	−	0.577531i
$429$		0			0
$430$		−	65.9533i		−	0.153380i
$431$	−496.682	−	286.760i	−1.15239	−	0.665335i	−0.202925	−	0.979194i	$-0.565045\pi$
$431$	−496.682	−	286.760i	−1.15239	−	0.665335i	−0.949470	+	0.313859i	$0.898378\pi$
$432$		0			0
$433$	216.750	+	125.141i	0.500578	+	0.289009i	0.728952	−	0.684565i	$-0.240008\pi$
$433$	216.750	+	125.141i	0.500578	+	0.289009i	−0.228374	+	0.973573i	$0.573341\pi$
$434$	−118.103	−	204.560i	−0.272126	−	0.471337i
$435$		0			0
$436$		−	461.978i		−	1.05958i
$437$	−87.8656	−	32.9700i	−0.201065	−	0.0754463i
$438$		0			0
$439$	406.897	−	234.922i	0.926872	−	0.535130i	0.0410511	−	0.999157i	$-0.486929\pi$
$439$	406.897	−	234.922i	0.926872	−	0.535130i	0.885821	+	0.464027i	$0.153596\pi$
$440$	242.045	−	139.745i	0.550102	−	0.317602i
$441$		0			0
$442$	28.6978	+	49.7060i	0.0649271	+	0.112457i
$443$	360.119	−	623.744i	0.812909	−	1.40800i	−0.0979100	−	0.995195i	$-0.531216\pi$
$443$	360.119	−	623.744i	0.812909	−	1.40800i	0.910819	−	0.412805i	$-0.135451\pi$
$444$		0			0
$445$		−	290.812i		−	0.653511i
$446$	144.648	−	250.538i	0.324323	−	0.561744i
$447$		0			0
$448$	−199.390			−0.445066
$449$			726.910i			1.61895i	0.587151	+	0.809477i	$0.300249\pi$
$449$			726.910i			1.61895i	−0.587151	+	0.809477i	$0.699751\pi$
$450$		0			0
$451$	−507.601	+	293.064i	−1.12550	+	0.649809i
$452$	58.7171	+	33.9003i	0.129905	+	0.0750007i
$453$		0			0
$454$	−82.9256	−	143.631i	−0.182655	−	0.316369i
$455$		−	155.971i		−	0.342794i
$456$		0			0
$457$	114.104			0.249681			0.124841	−	0.992177i	$-0.460158\pi$
$457$	114.104			0.249681			0.124841	+	0.992177i	$0.460158\pi$
$458$	−18.5988	+	10.7380i	−0.0406087	+	0.0234454i
$459$		0			0
$460$	27.2037	−	47.1182i	0.0591385	−	0.102431i
$461$	−157.029	−	271.982i	−0.340626	−	0.589982i	0.643923	−	0.765090i	$-0.277306\pi$
$461$	−157.029	−	271.982i	−0.340626	−	0.589982i	−0.984549	+	0.175108i	$0.943972\pi$
$462$		0			0
$463$	402.830			0.870044			0.435022	−	0.900420i	$-0.356741\pi$
$463$	402.830			0.870044			0.435022	+	0.900420i	$0.356741\pi$
$464$		−	475.490i		−	1.02476i
$465$		0			0
$466$	215.791	+	124.587i	0.463071	+	0.267354i
$467$	759.715			1.62680			0.813399	−	0.581706i	$-0.197614\pi$
$467$	759.715			1.62680			0.813399	+	0.581706i	$0.197614\pi$
$468$		0			0
$469$	−692.938	−	400.068i	−1.47748	−	0.853023i
$470$	−32.1279	+	18.5490i	−0.0683572	+	0.0394660i
$471$		0			0
$472$	−59.7033	−	103.409i	−0.126490	−	0.219087i
$473$	278.912	+	483.090i	0.589667	+	1.02133i
$474$		0			0
$475$	273.085	+	102.470i	0.574916	+	0.215727i
$476$	399.937			0.840204
$477$		0			0
$478$	−62.1744	+	35.8964i	−0.130072	+	0.0750971i
$479$	−14.1426	+	24.4957i	−0.0295253	+	0.0511393i	−0.880411	−	0.474212i	$-0.842733\pi$
$479$	−14.1426	+	24.4957i	−0.0295253	+	0.0511393i	0.850885	+	0.525352i	$0.176066\pi$
$480$		0			0
$481$	94.7997	−	164.198i	0.197089	−	0.341368i
$482$	−9.31119			−0.0193178
$483$		0			0
$484$	−340.887	+	590.433i	−0.704311	+	1.21990i
$485$	−25.3374	−	14.6285i	−0.0522420	−	0.0301620i
$486$		0			0
$487$			918.051i			1.88511i	0.334045	+	0.942557i	$0.391586\pi$
$487$			918.051i			1.88511i	−0.334045	+	0.942557i	$0.608414\pi$
$488$	−75.0777	−	43.3461i	−0.153848	−	0.0888241i
$489$		0			0
$490$	31.6609	+	18.2794i	0.0646141	+	0.0373050i
$491$	20.5361	+	35.5696i	0.0418250	+	0.0724431i	0.886180	−	0.463341i	$-0.153349\pi$
$491$	20.5361	+	35.5696i	0.0418250	+	0.0724431i	−0.844355	+	0.535784i	$0.820016\pi$
$492$		0			0
$493$			611.309i			1.23998i
$494$	12.9194	+	77.7678i	0.0261526	+	0.157425i
$495$		0			0
$496$	400.728	−	231.361i	0.807920	−	0.466453i
$497$	−11.1007	+	6.40901i	−0.0223355	+	0.0128954i
$498$		0			0
$499$	−324.374	−	561.832i	−0.650047	−	1.12592i	−0.983111	−	0.183011i	$-0.941416\pi$
$499$	−324.374	−	561.832i	−0.650047	−	1.12592i	0.333063	−	0.942904i	$-0.391918\pi$
$500$	−222.237	+	384.926i	−0.444474	+	0.769852i
$501$		0			0
$502$			82.7181i			0.164777i
$503$	205.525	−	355.979i	0.408598	−	0.707712i	−0.586135	−	0.810213i	$-0.699351\pi$
$503$	205.525	−	355.979i	0.408598	−	0.707712i	0.994733	+	0.102501i	$0.0326846\pi$
$504$		0			0
$505$	−413.501			−0.818815
$506$		−	58.8951i		−	0.116393i
$507$		0			0
$508$	74.9414	−	43.2675i	0.147523	−	0.0851722i
$509$	19.2779	+	11.1301i	0.0378740	+	0.0218666i	0.518817	−	0.854885i	$-0.326372\pi$
$509$	19.2779	+	11.1301i	0.0378740	+	0.0218666i	−0.480943	+	0.876752i	$0.659706\pi$
$510$		0			0
$511$	−23.2794	−	40.3211i	−0.0455566	−	0.0789064i
$512$			515.592i			1.00701i
$513$		0			0
$514$	266.924			0.519307
$515$	−249.609	+	144.112i	−0.484677	+	0.279828i
$516$		0			0
$517$	156.885	−	271.734i	0.303454	−	0.525597i
$518$	84.5434	+	146.433i	0.163211	+	0.282690i
$519$		0			0
$520$	−97.2555			−0.187030
$521$			87.1316i			0.167239i	0.996498	+	0.0836196i	$0.0266481\pi$
$521$			87.1316i			0.167239i	−0.996498	+	0.0836196i	$0.973352\pi$
$522$		0			0
$523$	−342.658	−	197.833i	−0.655177	−	0.378267i	0.135260	−	0.990810i	$-0.456813\pi$
$523$	−342.658	−	197.833i	−0.655177	−	0.378267i	−0.790437	+	0.612544i	$0.790146\pi$
$524$	−270.187			−0.515624
$525$		0			0
$526$	−31.2112	−	18.0198i	−0.0593369	−	0.0342582i
$527$	−515.192	+	297.446i	−0.977594	+	0.564414i
$528$		0			0
$529$	252.301	+	436.999i	0.476940	+	0.826085i
$530$	−17.6872	−	30.6350i	−0.0333720	−	0.0578020i
$531$		0			0
$532$	514.304	+	192.983i	0.966736	+	0.362751i
$533$	203.958			0.382661
$534$		0			0
$535$	−375.020	+	216.518i	−0.700972	+	0.404706i
$536$	−249.461	+	432.079i	−0.465412	+	0.806118i
$537$		0			0
$538$	−123.048	+	213.126i	−0.228714	+	0.396145i
$539$	−309.210			−0.573674
$540$		0			0
$541$	509.586	−	882.629i	0.941933	−	1.63148i	0.180155	−	0.983638i	$-0.442340\pi$
$541$	509.586	−	882.629i	0.941933	−	1.63148i	0.761778	−	0.647838i	$-0.224327\pi$
$542$	−101.731	−	58.7344i	−0.187696	−	0.108366i
$543$		0			0
$544$		−	381.569i		−	0.701413i
$545$	−350.451	−	202.333i	−0.643029	−	0.371253i
$546$		0			0
$547$	582.402	+	336.250i	1.06472	+	0.614717i	0.926734	−	0.375717i	$-0.122604\pi$
$547$	582.402	+	336.250i	1.06472	+	0.614717i	0.137986	+	0.990434i	$0.455937\pi$
$548$	−420.630	−	728.553i	−0.767573	−	1.32948i
$549$		0			0
$550$			183.045i			0.332809i
$551$	−294.978	+	786.120i	−0.535350	+	1.42672i
$552$		0			0
$553$	−341.875	+	197.382i	−0.618219	+	0.356929i
$554$	54.4232	−	31.4213i	0.0982369	−	0.0567171i
$555$		0			0
$556$	−35.6042	−	61.6683i	−0.0640363	−	0.110914i
$557$	−108.576	+	188.060i	−0.194931	+	0.337630i	−0.946878	−	0.321594i	$-0.895781\pi$
$557$	−108.576	+	188.060i	−0.194931	+	0.337630i	0.751947	+	0.659223i	$0.229115\pi$
$558$		0			0
$559$		−	194.109i		−	0.347244i
$560$	−136.244	+	235.981i	−0.243293	+	0.421395i
$561$		0			0
$562$	−253.082			−0.450324
$563$		−	571.551i		−	1.01519i	−0.861596	−	0.507594i	$-0.830535\pi$
$563$		−	571.551i		−	1.01519i	0.861596	−	0.507594i	$-0.169465\pi$
$564$		0			0
$565$	51.4327	−	29.6947i	0.0910313	−	0.0525570i
$566$	37.4245	+	21.6071i	0.0661211	+	0.0381750i
$567$		0			0
$568$	3.99632	+	6.92183i	0.00703578	+	0.0121863i
$569$			411.891i			0.723886i	0.932200	+	0.361943i	$0.117886\pi$
$569$			411.891i			0.723886i	−0.932200	+	0.361943i	$0.882114\pi$
$570$		0			0
$571$	746.121			1.30669			0.653346	−	0.757060i	$-0.273365\pi$
$571$	746.121			1.30669			0.653346	+	0.757060i	$0.273365\pi$
$572$	334.763	−	193.276i	0.585250	−	0.337894i
$573$		0			0
$574$	−90.9460	+	157.523i	−0.158443	+	0.274431i
$575$	37.9131	+	65.6674i	0.0659358	+	0.114204i
$576$		0			0
$577$	−877.551			−1.52089			−0.760443	−	0.649405i	$-0.775018\pi$
$577$	−877.551			−1.52089			−0.760443	+	0.649405i	$0.775018\pi$
$578$		−	65.7817i		−	0.113809i
$579$		0			0
$580$	−421.559	−	243.387i	−0.726826	−	0.419633i
$581$	−605.542			−1.04224
$582$		0			0
$583$	259.107	+	149.596i	0.444438	+	0.256597i
$584$	−25.1421	+	14.5158i	−0.0430516	+	0.0248558i
$585$		0			0
$586$	−37.6639	−	65.2358i	−0.0642728	−	0.111324i
$587$	0.899138	+	1.55735i	0.00153175	+	0.00265307i	0.866790	−	0.498673i	$-0.166179\pi$
$587$	0.899138	+	1.55735i	0.00153175	+	0.00265307i	−0.865259	+	0.501326i	$0.832846\pi$
$588$		0			0
$589$	−806.046	+	133.907i	−1.36850	+	0.227346i
$590$	−49.1513			−0.0833072
$591$		0			0
$592$	−286.860	+	165.618i	−0.484560	+	0.279761i
$593$	5.61476	−	9.72504i	0.00946839	−	0.0163997i	−0.861252	−	0.508177i	$-0.830319\pi$
$593$	5.61476	−	9.72504i	0.00946839	−	0.0163997i	0.870721	+	0.491778i	$0.163653\pi$
$594$		0			0
$595$	175.160	−	303.387i	0.294387	−	0.509894i
$596$	552.127			0.926387
$597$		0			0
$598$	−10.2470	+	17.7484i	−0.0171355	+	0.0296795i
$599$	391.707	+	226.152i	0.653934	+	0.377549i	0.789962	−	0.613156i	$-0.210100\pi$
$599$	391.707	+	226.152i	0.653934	+	0.377549i	−0.136028	+	0.990705i	$0.543434\pi$
$600$		0			0
$601$			32.0350i			0.0533029i	0.999645	+	0.0266514i	$0.00848442\pi$
$601$			32.0350i			0.0533029i	−0.999645	+	0.0266514i	$0.991516\pi$
$602$	149.917	+	86.5544i	0.249031	+	0.143778i
$603$		0			0
$604$	127.350	+	73.5253i	0.210844	+	0.121731i
$605$	298.596	+	517.184i	0.493548	+	0.854850i
$606$		0			0
$607$		−	161.891i		−	0.266706i	−0.991069	−	0.133353i	$-0.957426\pi$
$607$		−	161.891i		−	0.266706i	0.991069	−	0.133353i	$-0.0425745\pi$
$608$	184.120	−	490.683i	0.302829	−	0.807044i
$609$		0			0
$610$	−30.9042	+	17.8425i	−0.0506626	+	0.0292500i
$611$	−94.5567	+	54.5923i	−0.154757	+	0.0893491i
$612$		0			0
$613$	−9.10873	−	15.7768i	−0.0148593	−	0.0257370i	0.858500	−	0.512813i	$-0.171397\pi$
$613$	−9.10873	−	15.7768i	−0.0148593	−	0.0257370i	−0.873359	+	0.487076i	$0.838063\pi$
$614$	−115.648	+	200.308i	−0.188351	+	0.326234i
$615$		0			0
$616$			733.582i			1.19088i
$617$	−355.912	+	616.457i	−0.576842	+	0.999120i	0.418997	+	0.907988i	$0.362382\pi$
$617$	−355.912	+	616.457i	−0.576842	+	0.999120i	−0.995839	+	0.0911323i	$0.970951\pi$
$618$		0			0
$619$	1039.82			1.67984			0.839918	−	0.542713i	$-0.182603\pi$
$619$	1039.82			1.67984			0.839918	+	0.542713i	$0.182603\pi$
$620$		−	473.702i		−	0.764036i
$621$		0			0
$622$	146.862	−	84.7911i	0.236113	−	0.136320i
$623$	661.038	+	381.651i	1.06106	+	0.612601i
$624$		0			0
$625$	2.77356	+	4.80394i	0.00443769	+	0.00768631i
$626$			327.604i			0.523330i
$627$		0			0
$628$	−280.528			−0.446701
$629$	368.798	−	212.926i	0.586325	−	0.338515i
$630$		0			0
$631$	−417.964	+	723.935i	−0.662383	+	1.14728i	0.317604	+	0.948223i	$0.397122\pi$
$631$	−417.964	+	723.935i	−0.662383	+	1.14728i	−0.979988	+	0.199058i	$0.936212\pi$
$632$	123.077	+	213.175i	0.194742	+	0.337302i
$633$		0			0
$634$	186.876			0.294756
$635$		−	75.7994i		−	0.119369i
$636$		0			0
$637$	93.1823	+	53.7988i	0.146283	+	0.0844566i
$638$	−526.925			−0.825902
$639$		0			0
$640$	341.128	+	196.950i	0.533012	+	0.307735i
$641$	−504.690	+	291.383i	−0.787347	+	0.454575i	−0.839028	−	0.544089i	$-0.816876\pi$
$641$	−504.690	+	291.383i	−0.787347	+	0.454575i	0.0516806	+	0.998664i	$0.483542\pi$
$642$		0			0
$643$	−238.122	−	412.439i	−0.370330	−	0.641430i	0.619286	−	0.785165i	$-0.287422\pi$
$643$	−238.122	−	412.439i	−0.370330	−	0.641430i	−0.989616	+	0.143735i	$0.954089\pi$
$644$	71.4021	+	123.672i	0.110873	+	0.192037i
$645$		0			0
$646$	−62.2054	+	165.778i	−0.0962932	+	0.256623i
$647$	304.985			0.471383			0.235691	−	0.971828i	$-0.424265\pi$
$647$	304.985			0.471383			0.235691	+	0.971828i	$0.424265\pi$
$648$		0			0
$649$	360.020	−	207.858i	0.554730	−	0.320274i
$650$	31.8476	−	55.1617i	0.0489963	−	0.0848642i
$651$		0			0
$652$	240.147	−	415.946i	0.368323	−	0.637954i
$653$	−123.278			−0.188787			−0.0943937	−	0.995535i	$-0.530091\pi$
$653$	−123.278			−0.188787			−0.0943937	+	0.995535i	$0.530091\pi$
$654$		0			0
$655$	−118.334	+	204.960i	−0.180662	+	0.312916i
$656$	−308.584	−	178.161i	−0.470402	−	0.271587i
$657$		0			0
$658$		−	97.3721i		−	0.147982i
$659$	−749.625	−	432.796i	−1.13752	−	0.656747i	−0.191704	−	0.981453i	$-0.561401\pi$
$659$	−749.625	−	432.796i	−1.13752	−	0.656747i	−0.945815	+	0.324706i	$0.894735\pi$
$660$		0			0
$661$	−572.988	−	330.815i	−0.866850	−	0.500476i	−0.000549974	−	1.00000i	$-0.500175\pi$
$661$	−572.988	−	330.815i	−0.866850	−	0.500476i	−0.866300	+	0.499524i	$0.833508\pi$
$662$	37.2145	+	64.4573i	0.0562152	+	0.0973676i
$663$		0			0
$664$			377.584i			0.568651i
$665$	371.644	−	305.623i	0.558864	−	0.459583i
$666$		0			0
$667$	−189.034	+	109.139i	−0.283410	+	0.163627i
$668$	192.868	−	111.352i	0.288724	−	0.166695i
$669$		0			0
$670$	102.685	+	177.856i	0.153262	+	0.265457i
$671$	150.910	−	261.384i	0.224903	−	0.389543i
$672$		0			0
$673$			104.231i			0.154875i	0.996997	+	0.0774373i	$0.0246737\pi$
$673$			104.231i			0.154875i	−0.996997	+	0.0774373i	$0.975326\pi$
$674$	9.32458	−	16.1506i	0.0138347	−	0.0239624i
$675$		0			0
$676$	464.788			0.687557
$677$		−	863.985i		−	1.27620i	−0.769955	−	0.638099i	$-0.779721\pi$
$677$		−	863.985i		−	1.27620i	0.769955	−	0.638099i	$-0.220279\pi$
$678$		0			0
$679$	66.5036	−	38.3958i	0.0979434	−	0.0565476i
$680$	−189.176	−	109.221i	−0.278200	−	0.160619i
$681$		0			0
$682$	−256.388	−	444.076i	−0.375935	−	0.651138i
$683$		−	34.9808i		−	0.0512165i	−0.999672	−	0.0256082i	$-0.991848\pi$
$683$		−	34.9808i		−	0.0512165i	0.999672	−	0.0256082i	$-0.00815224\pi$
$684$		0			0
$685$	−736.894			−1.07576
$686$	149.976	−	86.5886i	0.218624	−	0.126222i
$687$		0			0
$688$	−169.558	+	293.683i	−0.246451	+	0.426865i
$689$	−52.0557	−	90.1631i	−0.0755525	−	0.130861i
$690$		0			0
$691$	−346.797			−0.501876			−0.250938	−	0.968003i	$-0.580739\pi$
$691$	−346.797			−0.501876			−0.250938	+	0.968003i	$0.580739\pi$
$692$			1157.20i			1.67225i
$693$		0			0
$694$	150.809	+	87.0696i	0.217304	+	0.125461i
$695$	−62.3743			−0.0897472
$696$		0			0
$697$	396.728	+	229.051i	0.569193	+	0.328624i
$698$	293.379	−	169.383i	0.420314	−	0.242668i
$699$		0			0
$700$	−221.917	−	384.371i	−0.317024	−	0.549101i
$701$	320.881	+	555.783i	0.457748	+	0.792843i	0.998842	−	0.0481197i	$-0.0153229\pi$
$701$	320.881	+	555.783i	0.457748	+	0.792843i	−0.541094	+	0.840962i	$0.681990\pi$
$702$		0			0
$703$	577.005	−	95.8565i	0.820775	−	0.136354i
$704$	−432.852			−0.614847
$705$		0			0
$706$	−31.5674	+	18.2255i	−0.0447131	+	0.0258151i
$707$	542.663	−	939.920i	0.767557	−	1.32945i
$708$		0			0
$709$	−277.968	+	481.454i	−0.392056	+	0.679061i	−0.992721	−	0.120440i	$-0.961569\pi$
$709$	−277.968	+	481.454i	−0.392056	+	0.679061i	0.600665	+	0.799501i	$0.294903\pi$
$710$	3.29000			0.00463381
$711$		0			0
$712$	237.977	−	412.188i	0.334238	−	0.578916i
$713$	−183.958	−	106.208i	−0.258006	−	0.148960i
$714$		0			0
$715$		−	338.596i		−	0.473561i
$716$	818.578	+	472.606i	1.14326	+	0.660064i
$717$		0			0
$718$	−255.176	−	147.326i	−0.355398	−	0.205189i
$719$	−120.548	−	208.795i	−0.167661	−	0.290397i	0.769936	−	0.638121i	$-0.220288\pi$
$719$	−120.548	−	208.795i	−0.167661	−	0.290397i	−0.937597	+	0.347724i	$0.886955\pi$
$720$		0			0
$721$		−	756.505i		−	1.04924i
$722$	−159.988	+	183.168i	−0.221590	+	0.253696i
$723$		0			0
$724$	−460.994	+	266.155i	−0.636732	+	0.367618i
$725$	587.516	−	339.203i	0.810367	−	0.467866i
$726$		0			0
$727$	−495.032	−	857.420i	−0.680924	−	1.17939i	−0.974699	−	0.223520i	$-0.928245\pi$
$727$	−495.032	−	857.420i	−0.680924	−	1.17939i	0.293776	−	0.955874i	$-0.405088\pi$
$728$	127.634	−	221.069i	0.175322	−	0.303666i
$729$		0			0
$730$			11.9503i			0.0163702i
$731$	217.991	−	377.571i	0.298209	−	0.516513i
$732$		0			0
$733$	748.994			1.02182			0.510910	−	0.859634i	$-0.329309\pi$
$733$	748.994			1.02182			0.510910	+	0.859634i	$0.329309\pi$
$734$		−	64.8531i		−	0.0883557i
$735$		0			0
$736$	117.992	−	68.1227i	0.160315	−	0.0925580i
$737$	−1504.29	−	868.501i	−2.04110	−	1.17843i
$738$		0			0
$739$	−123.521	−	213.945i	−0.167147	−	0.289506i	0.770269	−	0.637719i	$-0.220122\pi$
$739$	−123.521	−	213.945i	−0.167147	−	0.289506i	−0.937415	+	0.348213i	$0.886789\pi$
$740$			339.098i			0.458240i
$741$		0			0
$742$	92.8477			0.125132
$743$	−278.718	+	160.918i	−0.375126	+	0.216579i	−0.675695	−	0.737181i	$-0.736157\pi$
$743$	−278.718	+	160.918i	−0.375126	+	0.216579i	0.300570	+	0.953760i	$0.402823\pi$
$744$		0			0
$745$	241.815	−	418.836i	0.324584	−	0.562196i
$746$	−201.621	−	349.218i	−0.270270	−	0.468121i
$747$		0			0
$748$	868.217			1.16072
$749$		−	1136.60i		−	1.51749i
$750$		0			0
$751$	−165.099	−	95.3199i	−0.219839	−	0.126924i	0.386037	−	0.922483i	$-0.373844\pi$
$751$	−165.099	−	95.3199i	−0.219839	−	0.126924i	−0.605876	+	0.795559i	$0.707177\pi$
$752$	190.749			0.253656
$753$		0			0
$754$	158.792	+	91.6786i	0.210599	+	0.121590i
$755$	111.551	−	64.4038i	0.147749	−	0.0853031i
$756$		0			0
$757$	292.845	+	507.222i	0.386849	+	0.670042i	0.992024	−	0.126050i	$-0.0402301\pi$
$757$	292.845	+	507.222i	0.386849	+	0.670042i	−0.605175	+	0.796093i	$0.706897\pi$
$758$	−54.2385	−	93.9439i	−0.0715548	−	0.123936i
$759$		0			0
$760$	−190.570	−	231.738i	−0.250750	−	0.304918i
$761$	−581.690			−0.764376			−0.382188	−	0.924085i	$-0.624829\pi$
$761$	−581.690			−0.764376			−0.382188	+	0.924085i	$0.624829\pi$
$762$		0			0
$763$	919.835	−	531.067i	1.20555	−	0.696025i
$764$	−176.562	+	305.815i	−0.231102	+	0.400281i
$765$		0			0
$766$	−77.9799	+	135.065i	−0.101801	+	0.176325i
$767$	−144.659			−0.188603
$768$		0			0
$769$	−642.973	+	1113.66i	−0.836116	+	1.44820i	0.0570025	+	0.998374i	$0.481846\pi$
$769$	−642.973	+	1113.66i	−0.836116	+	1.44820i	−0.893119	+	0.449821i	$0.851488\pi$
$770$	261.508	+	150.982i	0.339621	+	0.196080i
$771$		0			0
$772$		−	173.697i		−	0.224996i
$773$	1069.34	+	617.384i	1.38336	+	0.798686i	0.992556	−	0.121786i	$-0.0388621\pi$
$773$	1069.34	+	617.384i	1.38336	+	0.798686i	0.390809	+	0.920472i	$0.372195\pi$
$774$		0			0
$775$	571.739	+	330.094i	0.737728	+	0.425927i
$776$	−23.9416	−	41.4681i	−0.0308526	−	0.0534383i
$777$		0			0
$778$		−	54.5786i		−	0.0701525i
$779$	399.652	+	485.986i	0.513032	+	0.623859i
$780$		0			0
$781$	−24.0984	+	13.9132i	−0.0308558	+	0.0178146i
$782$	−39.8639	+	23.0154i	−0.0509768	+	0.0294315i
$783$		0			0
$784$	−93.9885	−	162.793i	−0.119883	−	0.207644i
$785$	−122.863	+	212.805i	−0.156513	+	0.271089i
$786$		0			0
$787$			543.258i			0.690289i	0.938550	+	0.345145i	$0.112170\pi$
$787$			543.258i			0.690289i	−0.938550	+	0.345145i	$0.887830\pi$
$788$	−297.556	+	515.382i	−0.377609	+	0.654038i
$789$		0			0
$790$	101.324			0.128258
$791$			155.880i			0.197068i
$792$		0			0
$793$	−90.9551	+	52.5130i	−0.114698	+	0.0662206i
$794$	397.959	+	229.762i	0.501208	+	0.289373i
$795$		0			0
$796$	164.045	+	284.134i	0.206087	+	0.356953i
$797$		−	942.119i		−	1.18208i	−0.806642	−	0.591041i	$-0.798717\pi$
$797$		−	942.119i		−	1.18208i	0.806642	−	0.591041i	$-0.201283\pi$
$798$		0			0
$799$	−245.235			−0.306928
$800$	−366.718	+	211.724i	−0.458397	+	0.264656i
$801$		0			0
$802$	32.1630	−	55.7080i	0.0401035	−	0.0694614i
$803$	−50.5369	−	87.5325i	−0.0629352	−	0.109007i
$804$		0			0
$805$	125.088			0.155389
$806$			178.433i			0.221381i
$807$		0			0
$808$	−586.084	−	338.376i	−0.725352	−	0.418782i
$809$	374.800			0.463288			0.231644	−	0.972801i	$-0.425590\pi$
$809$	374.800			0.463288			0.231644	+	0.972801i	$0.425590\pi$
$810$		0			0
$811$	−145.337	−	83.9101i	−0.179207	−	0.103465i	0.407713	−	0.913110i	$-0.366326\pi$
$811$	−145.337	−	83.9101i	−0.179207	−	0.103465i	−0.586920	+	0.809645i	$0.699660\pi$
$812$	1106.47	−	638.823i	1.36265	−	0.786728i
$813$		0			0
$814$	183.534	+	317.890i	0.225472	+	0.390528i
$815$	−210.354	−	364.344i	−0.258103	−	0.447048i
$816$		0			0
$817$	462.518	−	380.354i	0.566118	−	0.465549i
$818$	−131.723			−0.161030
$819$		0			0
$820$	−315.907	+	182.389i	−0.385253	+	0.222426i
$821$	628.725	−	1088.98i	0.765804	−	1.32641i	−0.174016	−	0.984743i	$-0.555675\pi$
$821$	628.725	−	1088.98i	0.765804	−	1.32641i	0.939820	−	0.341669i	$-0.110992\pi$
$822$		0			0
$823$	225.462	−	390.511i	0.273951	−	0.474497i	−0.695919	−	0.718120i	$-0.745003\pi$
$823$	225.462	−	390.511i	0.273951	−	0.474497i	0.969870	+	0.243623i	$0.0783361\pi$
$824$	−471.717			−0.572472
$825$		0			0
$826$	64.5041	−	111.724i	0.0780922	−	0.135260i
$827$	349.235	+	201.631i	0.422292	+	0.243810i	0.696057	−	0.717986i	$-0.254936\pi$
$827$	349.235	+	201.631i	0.422292	+	0.243810i	−0.273766	+	0.961796i	$0.588269\pi$
$828$		0			0
$829$		−	676.543i		−	0.816096i	−0.912961	−	0.408048i	$-0.866210\pi$
$829$		−	676.543i		−	0.816096i	0.912961	−	0.408048i	$-0.133790\pi$
$830$	134.602	+	77.7123i	0.162171	+	0.0936293i
$831$		0			0
$832$	130.442	+	75.3110i	0.156782	+	0.0905180i
$833$	120.835	+	209.293i	0.145060	+	0.251252i
$834$		0			0
$835$		−	195.076i		−	0.233624i
$836$	1116.49	+	418.945i	1.33552	+	0.501130i
$837$		0			0
$838$	226.556	−	130.802i	0.270354	−	0.156089i
$839$	1311.19	−	757.016i	1.56280	−	0.902284i	0.565830	−	0.824522i	$-0.308556\pi$
$839$	1311.19	−	757.016i	1.56280	−	0.902284i	0.996972	−	0.0777621i	$-0.0247775\pi$
$840$		0			0
$841$	555.950	+	962.934i	0.661058	+	1.14499i
$842$	87.8912	−	152.232i	0.104384	−	0.180798i
$843$		0			0
$844$		−	222.781i		−	0.263959i
$845$	203.563	−	352.582i	0.240903	−	0.417257i
$846$		0			0
$847$	−1567.46			−1.85061
$848$			181.886i			0.214489i
$849$		0			0
$850$	123.896	−	71.5316i	0.145761	−	0.0841549i
$851$	131.686	+	76.0287i	0.154742	+	0.0893404i
$852$		0			0
$853$	−533.457	−	923.975i	−0.625389	−	1.08321i	−0.988465	−	0.151447i	$-0.951607\pi$
$853$	−533.457	−	923.975i	−0.625389	−	1.08321i	0.363076	−	0.931760i	$-0.381727\pi$
$854$		−	93.6633i		−	0.109676i
$855$		0			0
$856$	−708.722			−0.827946
$857$	−1171.55	+	676.397i	−1.36704	+	0.789261i	−0.990549	−	0.137158i	$-0.956203\pi$
$857$	−1171.55	+	676.397i	−1.36704	+	0.789261i	−0.376492	+	0.926420i	$0.622870\pi$
$858$		0			0
$859$	419.232	−	726.131i	0.488046	−	0.845321i	−0.511859	−	0.859069i	$-0.671043\pi$
$859$	419.232	−	726.131i	0.488046	−	0.845321i	0.999905	+	0.0137483i	$0.00437635\pi$
$860$	173.582	+	300.653i	0.201839	+	0.349596i
$861$		0			0
$862$	−386.372			−0.448228
$863$		−	61.7364i		−	0.0715369i	−0.999360	−	0.0357685i	$-0.988612\pi$
$863$		−	61.7364i		−	0.0715369i	0.999360	−	0.0357685i	$-0.0113879\pi$
$864$		0			0
$865$	877.833	+	506.817i	1.01484	+	0.585916i
$866$	168.612			0.194702
$867$		0			0
$868$	1076.76	+	621.668i	1.24051	+	0.716208i
$869$	−742.171	+	428.492i	−0.854051	+	0.493087i
$870$		0			0
$871$	302.217	+	523.455i	0.346977	+	0.600982i
$872$	−331.145	−	573.560i	−0.379754	−	0.657753i
$873$		0			0
$874$	−62.3692	+	10.3613i	−0.0713606	+	0.0118550i
$875$	−1021.89			−1.16788
$876$		0			0
$877$	−411.522	+	237.592i	−0.469239	+	0.270915i	−0.715921	−	0.698181i	$-0.753993\pi$
$877$	−411.522	+	237.592i	−0.469239	+	0.270915i	0.246682	+	0.969096i	$0.420660\pi$
$878$	158.264	−	274.121i	0.180255	−	0.312211i
$879$		0			0
$880$	−295.770	+	512.288i	−0.336102	+	0.582145i
$881$	−1656.73			−1.88051			−0.940253	−	0.340477i	$-0.889412\pi$
$881$	−1656.73			−1.88051			−0.940253	+	0.340477i	$0.889412\pi$
$882$		0			0
$883$	3.24702	−	5.62400i	0.00367726	−	0.00636920i	−0.864181	−	0.503181i	$-0.832163\pi$
$883$	3.24702	−	5.62400i	0.00367726	−	0.00636920i	0.867858	+	0.496812i	$0.165496\pi$
$884$	−261.642	−	151.059i	−0.295975	−	0.170881i
$885$		0			0
$886$		−	485.215i		−	0.547647i
$887$	517.144	+	298.573i	0.583026	+	0.336610i	0.762335	−	0.647183i	$-0.224053\pi$
$887$	517.144	+	298.573i	0.583026	+	0.336610i	−0.179309	+	0.983793i	$0.557386\pi$
$888$		0			0
$889$	172.298	+	99.4762i	0.193811	+	0.111897i
$890$	−97.9583	−	169.669i	−0.110065	−	0.190639i
$891$		0			0
$892$			1522.79i			1.70717i
$893$	−315.363	−	118.334i	−0.353150	−	0.132513i
$894$		0			0
$895$	717.025	−	413.975i	0.801145	−	0.462542i
$896$	−895.364	+	516.939i	−0.999291	+	0.576941i
$897$		0			0
$898$	244.855	+	424.101i	0.272667	+	0.472273i
$899$	−950.228	+	1645.84i	−1.05698	+	1.83075i
$900$		0			0
$901$		−	233.840i		−	0.259534i
$902$	−197.433	+	341.964i	−0.218884	+	0.379118i
$903$		0			0
$904$	97.1988			0.107521
$905$			466.272i			0.515218i
$906$		0			0
$907$	−1415.50	+	817.238i	−1.56064	+	0.901034i	−0.563445	+	0.826154i	$0.690524\pi$
$907$	−1415.50	+	817.238i	−1.56064	+	0.901034i	−0.997192	+	0.0748809i	$0.976142\pi$
$908$	756.045	+	436.503i	0.832649	+	0.480730i
$909$		0			0
$910$	−52.5380	−	90.9984i	−0.0577340	−	0.0999983i
$911$			1326.40i			1.45598i	0.685587	+	0.727991i	$0.259546\pi$
$911$			1326.40i			1.45598i	−0.685587	+	0.727991i	$0.740454\pi$
$912$		0			0
$913$	−1314.56			−1.43983
$914$	66.5719	−	38.4353i	0.0728358	−	0.0420518i
$915$		0			0
$916$	56.5226	−	97.9000i	0.0617059	−	0.106878i
$917$	−310.593	−	537.963i	−0.338706	−	0.586655i
$918$		0			0
$919$	−1155.93			−1.25782			−0.628908	−	0.777479i	$-0.716498\pi$
$919$	−1155.93			−1.25782			−0.628908	+	0.777479i	$0.716498\pi$
$920$		−	77.9982i		−	0.0847807i
$921$		0			0
$922$	−183.231	−	105.788i	−0.198732	−	0.114738i
$923$	9.68293			0.0104907
$924$		0			0
$925$	−409.277	−	236.296i	−0.442461	−	0.255455i
$926$	235.023	−	135.691i	0.253805	−	0.146534i
$927$		0			0
$928$	−609.483	−	1055.66i	−0.656771	−	1.13756i
$929$	24.9510	+	43.2164i	0.0268579	+	0.0465192i	0.879142	−	0.476560i	$-0.158117\pi$
$929$	24.9510	+	43.2164i	0.0268579	+	0.0465192i	−0.852284	+	0.523079i	$0.824783\pi$
$930$		0			0
$931$	54.3986	+	327.450i	0.0584303	+	0.351719i
$932$	−1311.60			−1.40729
$933$		0			0
$934$	443.241	−	255.905i	0.474562	−	0.273988i
$935$	380.253	−	658.618i	0.406688	−	0.704404i
$936$		0			0
$937$	261.663	−	453.214i	0.279256	−	0.483686i	−0.691944	−	0.721951i	$-0.743245\pi$
$937$	261.663	−	453.214i	0.279256	−	0.483686i	0.971200	+	0.238265i	$0.0765788\pi$
$938$	−539.041			−0.574670
$939$		0			0
$940$	97.6382	−	169.114i	0.103870	−	0.179909i
$941$	−528.450	−	305.101i	−0.561583	−	0.324230i	0.192197	−	0.981356i	$-0.438439\pi$
$941$	−528.450	−	305.101i	−0.561583	−	0.324230i	−0.753781	+	0.657126i	$0.771772\pi$
$942$		0			0
$943$			163.573i			0.173460i
$944$	218.865	+	126.362i	0.231849	+	0.133858i
$945$		0			0
$946$	325.452	+	187.900i	0.344029	+	0.198625i
$947$	727.100	+	1259.37i	0.767794	+	1.32986i	0.938757	+	0.344580i	$0.111979\pi$
$947$	727.100	+	1259.37i	0.767794	+	1.32986i	−0.170963	+	0.985277i	$0.554688\pi$
$948$		0			0
$949$			35.1712i			0.0370614i
$950$	193.843	−	32.2027i	0.204045	−	0.0338975i
$951$		0			0
$952$	496.534	−	286.674i	0.521569	−	0.301128i
$953$	−1408.40	+	813.142i	−1.47786	+	0.853244i	−0.999687	−	0.0250198i	$-0.992035\pi$
$953$	−1408.40	+	813.142i	−1.47786	+	0.853244i	−0.478176	+	0.878264i	$0.658702\pi$
$954$		0			0
$955$	154.658	+	267.876i	0.161946	+	0.280498i
$956$	188.951	−	327.273i	0.197648	−	0.342336i
$957$		0			0
$958$			19.0554i			0.0198908i
$959$	967.070	−	1675.01i	1.00842	−	1.74663i
$960$		0			0
$961$	−888.421			−0.924475
$962$		−	127.731i		−	0.132776i
$963$		0			0
$964$	42.4457	−	24.5061i	0.0440309	−	0.0254212i
$965$	−131.764	−	76.0739i	−0.136543	−	0.0788331i
$966$		0			0
$967$	716.252	+	1240.59i	0.740695	+	1.28292i	0.952179	+	0.305540i	$0.0988370\pi$
$967$	716.252	+	1240.59i	0.740695	+	1.28292i	−0.211484	+	0.977381i	$0.567830\pi$
$968$			977.388i			1.00970i
$969$		0			0
$970$	−19.7101			−0.0203197
$971$	870.744	−	502.724i	0.896749	−	0.517738i	0.0206051	−	0.999788i	$-0.493441\pi$
$971$	870.744	−	502.724i	0.896749	−	0.517738i	0.876144	+	0.482049i	$0.160107\pi$
$972$		0			0
$973$	81.8575	−	141.781i	0.0841290	−	0.145716i
$974$	309.239	+	535.618i	0.317494	+	0.549916i
$975$		0			0
$976$	183.484			0.187996
$977$			1459.45i			1.49381i	0.664931	+	0.746905i	$0.268461\pi$
$977$			1459.45i			1.49381i	−0.664931	+	0.746905i	$0.731539\pi$
$978$		0			0
$979$	1435.04	+	828.519i	1.46582	+	0.846291i
$980$	−192.438			−0.196365
$981$		0			0
$982$	23.9628	+	13.8349i	0.0244020	+	0.0140885i
$983$	−447.660	+	258.456i	−0.455401	+	0.262926i	−0.710109	−	0.704092i	$-0.751354\pi$
$983$	−447.660	+	258.456i	−0.455401	+	0.262926i	0.254707	+	0.967018i	$0.418021\pi$
$984$		0			0
$985$	260.641	+	451.444i	0.264611	+	0.458319i
$986$	205.915	+	356.656i	0.208839	+	0.361720i
$987$		0			0
$988$	−263.571	−	320.508i	−0.266772	−	0.324401i
$989$	155.674			0.157406
$990$		0			0
$991$	−333.382	+	192.478i	−0.336410	+	0.194226i	−0.658683	−	0.752420i	$-0.728886\pi$
$991$	−333.382	+	192.478i	−0.336410	+	0.194226i	0.322274	+	0.946647i	$0.395553\pi$
$992$	593.116	−	1027.31i	0.597899	−	1.03559i
$993$		0			0
$994$	−4.31767	+	7.47842i	−0.00434373	+	0.00752357i
$995$	287.388			0.288832
$996$		0			0
$997$	532.640	−	922.560i	0.534243	−	0.925336i	−0.464957	−	0.885333i	$-0.653930\pi$
$997$	532.640	−	922.560i	0.534243	−	0.925336i	0.999200	−	0.0400025i	$-0.0127366\pi$
$998$	−378.499	−	218.526i	−0.379257	−	0.218964i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	171.3.p.d.145.2		6
3.2	odd	2		19.3.d.a.12.2	yes	6
12.11	even	2		304.3.r.b.145.1		6
19.8	odd	6	inner	171.3.p.d.46.2		6
57.2	even	18		361.3.f.h.333.2		18
57.5	odd	18		361.3.f.i.262.2		18
57.8	even	6		19.3.d.a.8.2	✓	6
57.11	odd	6		361.3.d.c.293.2		6
57.14	even	18		361.3.f.h.262.2		18
57.17	odd	18		361.3.f.i.333.2		18
57.23	odd	18		361.3.f.h.116.2		18
57.26	odd	6		361.3.b.b.360.3		6
57.29	even	18		361.3.f.i.307.2		18
57.32	even	18		361.3.f.i.299.2		18
57.35	odd	18		361.3.f.i.127.2		18
57.41	even	18		361.3.f.h.127.2		18
57.44	odd	18		361.3.f.h.299.2		18
57.47	odd	18		361.3.f.h.307.2		18
57.50	even	6		361.3.b.b.360.4		6
57.53	even	18		361.3.f.i.116.2		18
57.56	even	2		361.3.d.c.69.2		6
228.179	odd	6		304.3.r.b.65.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
19.3.d.a.8.2	✓	6	57.8	even	6
19.3.d.a.12.2	yes	6	3.2	odd	2
171.3.p.d.46.2		6	19.8	odd	6	inner
171.3.p.d.145.2		6	1.1	even	1	trivial
304.3.r.b.65.1		6	228.179	odd	6
304.3.r.b.145.1		6	12.11	even	2
361.3.b.b.360.3		6	57.26	odd	6
361.3.b.b.360.4		6	57.50	even	6
361.3.d.c.69.2		6	57.56	even	2
361.3.d.c.293.2		6	57.11	odd	6
361.3.f.h.116.2		18	57.23	odd	18
361.3.f.h.127.2		18	57.41	even	18
361.3.f.h.262.2		18	57.14	even	18
361.3.f.h.299.2		18	57.44	odd	18
361.3.f.h.307.2		18	57.47	odd	18
361.3.f.h.333.2		18	57.2	even	18
361.3.f.i.116.2		18	57.53	even	18
361.3.f.i.127.2		18	57.35	odd	18
361.3.f.i.262.2		18	57.5	odd	18
361.3.f.i.299.2		18	57.32	even	18
361.3.f.i.307.2		18	57.29	even	18
361.3.f.i.333.2		18	57.17	odd	18

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:	\( N \)	\(=\)	\( 171 = 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	171.p (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.583430 - 0.336844i) q^{2} +(-1.77307 + 3.07105i) q^{4} +(1.55311 + 2.69006i) q^{5} -8.15294 q^{7} +5.08374i q^{8} +O(q^{10})\)	\(q+(0.583430 - 0.336844i) q^{2} +(-1.77307 + 3.07105i) q^{4} +(1.55311 + 2.69006i) q^{5} -8.15294 q^{7} +5.08374i q^{8} +(1.81226 + 1.04631i) q^{10} -17.6991 q^{11} +(5.33372 + 3.07942i) q^{13} +(-4.75667 + 2.74626i) q^{14} +(-5.37987 - 9.31820i) q^{16} +(6.91657 + 11.9799i) q^{17} +(3.11375 + 18.7431i) q^{19} -11.0151 q^{20} +(-10.3262 + 5.96182i) q^{22} +(-2.46968 + 4.27760i) q^{23} +(7.67572 - 13.2947i) q^{25} +4.14914 q^{26} +(14.4558 - 25.0381i) q^{28} +(38.2711 + 22.0958i) q^{29} +43.0049i q^{31} +(-23.8881 - 13.7918i) q^{32} +(8.07067 + 4.65960i) q^{34} +(-12.6624 - 21.9319i) q^{35} -30.7849i q^{37} +(8.13016 + 9.88645i) q^{38} +(-13.6756 + 7.89559i) q^{40} +(28.6795 - 16.5581i) q^{41} +(-15.7586 - 27.2946i) q^{43} +(31.3818 - 54.3548i) q^{44} +3.32758i q^{46} +(-8.86404 + 15.3530i) q^{47} +17.4704 q^{49} -10.3421i q^{50} +(-18.9142 + 10.9201i) q^{52} +(-14.6396 - 8.45218i) q^{53} +(-27.4886 - 47.6116i) q^{55} -41.4474i q^{56} +29.7713 q^{58} +(-20.3412 + 11.7440i) q^{59} +(-8.52643 + 14.7682i) q^{61} +(14.4859 + 25.0903i) q^{62} +24.4562 q^{64} +19.1307i q^{65} +(84.9924 + 49.0704i) q^{67} -49.0543 q^{68} +(-14.7752 - 8.53048i) q^{70} +(1.36156 - 0.786099i) q^{71} +(2.85534 + 4.94560i) q^{73} +(-10.3697 - 17.9608i) q^{74} +(-63.0820 - 23.6704i) q^{76} +144.300 q^{77} +(41.9327 - 24.2099i) q^{79} +(16.7110 - 28.9443i) q^{80} +(11.1550 - 19.3210i) q^{82} +74.2729 q^{83} +(-21.4843 + 37.2120i) q^{85} +(-18.3880 - 10.6163i) q^{86} -89.9776i q^{88} +(-81.0798 - 46.8114i) q^{89} +(-43.4855 - 25.1064i) q^{91} +(-8.75783 - 15.1690i) q^{92} +11.9432i q^{94} +(-45.5841 + 37.4862i) q^{95} +(-8.15700 + 4.70945i) q^{97} +(10.1928 - 5.88480i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 3 q^{2} + 5 q^{4} + 2 q^{5}+O(q^{10}) \) 6 * q + 3 * q^2 + 5 * q^4 + 2 * q^5	\( 6 q + 3 q^{2} + 5 q^{4} + 2 q^{5} - 60 q^{10} - 26 q^{11} + 30 q^{13} - 54 q^{14} + q^{16} + 42 q^{17} + 25 q^{19} - 108 q^{20} - 39 q^{22} - 8 q^{23} - 17 q^{25} + 148 q^{26} + 32 q^{28} + 12 q^{29} - 51 q^{32} - 6 q^{34} + 38 q^{35} + 14 q^{38} - 96 q^{40} - 63 q^{41} - 34 q^{43} + 69 q^{44} - 58 q^{47} + 18 q^{49} + 162 q^{52} + 12 q^{53} - 28 q^{55} + 172 q^{58} + 147 q^{59} + 58 q^{61} + 116 q^{62} + 166 q^{64} + 201 q^{67} + 84 q^{68} - 198 q^{70} + 102 q^{71} + 7 q^{73} - 174 q^{74} - 173 q^{76} + 376 q^{77} - 134 q^{80} - 145 q^{82} - 146 q^{83} - 90 q^{85} + 270 q^{86} + 72 q^{89} - 216 q^{91} - 72 q^{92} - 558 q^{95} + 21 q^{97} - 411 q^{98}+O(q^{100}) \) 6 * q + 3 * q^2 + 5 * q^4 + 2 * q^5 - 60 * q^10 - 26 * q^11 + 30 * q^13 - 54 * q^14 + q^16 + 42 * q^17 + 25 * q^19 - 108 * q^20 - 39 * q^22 - 8 * q^23 - 17 * q^25 + 148 * q^26 + 32 * q^28 + 12 * q^29 - 51 * q^32 - 6 * q^34 + 38 * q^35 + 14 * q^38 - 96 * q^40 - 63 * q^41 - 34 * q^43 + 69 * q^44 - 58 * q^47 + 18 * q^49 + 162 * q^52 + 12 * q^53 - 28 * q^55 + 172 * q^58 + 147 * q^59 + 58 * q^61 + 116 * q^62 + 166 * q^64 + 201 * q^67 + 84 * q^68 - 198 * q^70 + 102 * q^71 + 7 * q^73 - 174 * q^74 - 173 * q^76 + 376 * q^77 - 134 * q^80 - 145 * q^82 - 146 * q^83 - 90 * q^85 + 270 * q^86 + 72 * q^89 - 216 * q^91 - 72 * q^92 - 558 * q^95 + 21 * q^97 - 411 * q^98

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