LMFDB - Embedded newform 171.3.ba.b.91.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [171,3,Mod(10,171)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(171, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 17]))

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

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

chi := DirichletCharacter("171.10");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 171 = 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	171.ba (of order $18$, degree $6$, 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:	$12$
Relative dimension:	$2$ over $\Q(\zeta_{18})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 24x^{10} + 216x^{8} + 905x^{6} + 1770x^{4} + 1395x^{2} + 361 $ x^12 + 24x^10 + 216x^8 + 905x^6 + 1770x^4 + 1395*x^2 + 361
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 19)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			91.1
Root			$1.89323i$ of defining polynomial
Character	$\chi$	$=$	171.91
Dual form			171.3.ba.b.109.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.647524 + 1.77906i) q^{2} +(0.318417 + 0.267183i) q^{4} +(2.13959 - 1.79533i) q^{5} +(-1.20796 + 2.09224i) q^{7} +(-7.23987 + 4.17994i) q^{8} +O(q^{10})$	\(q+(-0.647524 + 1.77906i) q^{2} +(0.318417 + 0.267183i) q^{4} +(2.13959 - 1.79533i) q^{5} +(-1.20796 + 2.09224i) q^{7} +(-7.23987 + 4.17994i) q^{8} +(1.80856 + 4.96897i) q^{10} +(9.60360 + 16.6339i) q^{11} +(14.2961 + 2.52079i) q^{13} +(-2.94004 - 3.50380i) q^{14} +(-2.45965 - 13.9494i) q^{16} +(-16.1226 - 5.86814i) q^{17} +(-13.2208 + 13.6459i) q^{19} +1.16096 q^{20} +(-35.8113 + 6.31450i) q^{22} +(5.84413 + 4.90381i) q^{23} +(-2.98657 + 16.9377i) q^{25} +(-13.7417 + 23.8013i) q^{26} +(-0.943645 + 0.343459i) q^{28} +(-2.81743 - 7.74083i) q^{29} +(5.19837 + 3.00128i) q^{31} +(-6.52208 - 1.15002i) q^{32} +(20.8795 - 24.8832i) q^{34} +(1.17173 + 6.64521i) q^{35} -59.5153i q^{37} +(-15.7160 - 32.3567i) q^{38} +(-7.98598 + 21.9413i) q^{40} +(30.4205 - 5.36396i) q^{41} +(18.8243 - 15.7955i) q^{43} +(-1.38636 + 7.86244i) q^{44} +(-12.5084 + 7.22171i) q^{46} +(68.7602 - 25.0267i) q^{47} +(21.5817 + 37.3806i) q^{49} +(-28.1992 - 16.2808i) q^{50} +(3.87860 + 4.62234i) q^{52} +(18.0172 - 21.4721i) q^{53} +(50.4111 + 18.3482i) q^{55} -20.1968i q^{56} +15.5957 q^{58} +(-3.15174 + 8.65934i) q^{59} +(-47.2307 - 39.6312i) q^{61} +(-8.70552 + 7.30480i) q^{62} +(34.5983 - 59.9260i) q^{64} +(35.1134 - 20.2727i) q^{65} +(-4.12065 - 11.3214i) q^{67} +(-3.56583 - 6.17619i) q^{68} +(-12.5809 - 2.21836i) q^{70} +(-24.7209 - 29.4613i) q^{71} +(8.82556 + 50.0523i) q^{73} +(105.881 + 38.5376i) q^{74} +(-7.85568 + 0.812682i) q^{76} -46.4029 q^{77} +(105.834 - 18.6613i) q^{79} +(-30.3064 - 25.4301i) q^{80} +(-10.1552 + 57.5932i) q^{82} +(35.6336 - 61.7192i) q^{83} +(-45.0309 + 16.3899i) q^{85} +(15.9119 + 43.7175i) q^{86} +(-139.058 - 80.2850i) q^{88} +(-7.98351 - 1.40771i) q^{89} +(-22.5431 + 26.8659i) q^{91} +(0.550653 + 3.12291i) q^{92} +138.534i q^{94} +(-3.78836 + 52.9323i) q^{95} +(40.7412 - 111.936i) q^{97} +(-80.4769 + 14.1902i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 6 q^{2} + 6 q^{5} + 6 q^{7} + 9 q^{8}+O(q^{10}) $ 12 * q + 6 * q^2 + 6 * q^5 + 6 * q^7 + 9 * q^8	$ 12 q + 6 q^{2} + 6 q^{5} + 6 q^{7} + 9 q^{8} + 51 q^{10} + 18 q^{11} + 21 q^{13} - 9 q^{14} - 12 q^{16} + 3 q^{17} - 24 q^{19} + 90 q^{20} - 78 q^{22} + 102 q^{23} - 156 q^{25} - 21 q^{26} + 12 q^{28} - 147 q^{29} + 99 q^{31} - 165 q^{32} + 132 q^{34} - 96 q^{35} - 72 q^{38} - 138 q^{40} + 144 q^{41} - 27 q^{43} + 123 q^{44} - 54 q^{46} + 99 q^{47} - 24 q^{49} - 72 q^{50} + 93 q^{52} - 111 q^{53} + 162 q^{55} - 132 q^{58} - 3 q^{59} + 150 q^{61} - 108 q^{62} + 27 q^{64} - 126 q^{65} + 135 q^{67} + 30 q^{68} + 225 q^{70} + 168 q^{71} - 90 q^{73} + 231 q^{74} + 42 q^{76} - 246 q^{77} - 75 q^{79} - 21 q^{80} - 117 q^{82} + 156 q^{83} - 300 q^{85} + 144 q^{86} - 405 q^{88} + 558 q^{89} - 453 q^{91} - 48 q^{92} + 69 q^{95} + 465 q^{97} - 777 q^{98}+O(q^{100}) $ 12 * q + 6 * q^2 + 6 * q^5 + 6 * q^7 + 9 * q^8 + 51 * q^10 + 18 * q^11 + 21 * q^13 - 9 * q^14 - 12 * q^16 + 3 * q^17 - 24 * q^19 + 90 * q^20 - 78 * q^22 + 102 * q^23 - 156 * q^25 - 21 * q^26 + 12 * q^28 - 147 * q^29 + 99 * q^31 - 165 * q^32 + 132 * q^34 - 96 * q^35 - 72 * q^38 - 138 * q^40 + 144 * q^41 - 27 * q^43 + 123 * q^44 - 54 * q^46 + 99 * q^47 - 24 * q^49 - 72 * q^50 + 93 * q^52 - 111 * q^53 + 162 * q^55 - 132 * q^58 - 3 * q^59 + 150 * q^61 - 108 * q^62 + 27 * q^64 - 126 * q^65 + 135 * q^67 + 30 * q^68 + 225 * q^70 + 168 * q^71 - 90 * q^73 + 231 * q^74 + 42 * q^76 - 246 * q^77 - 75 * q^79 - 21 * q^80 - 117 * q^82 + 156 * q^83 - 300 * q^85 + 144 * q^86 - 405 * q^88 + 558 * q^89 - 453 * q^91 - 48 * q^92 + 69 * q^95 + 465 * q^97 - 777 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$20$	$154$
$\chi(n)$	$1$	$e\left(\frac{11}{18}\right)$

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 $

$2$	−0.647524	+	1.77906i	−0.323762	+	0.889529i	0.665891	+	0.746049i	$0.268052\pi$
$2$	−0.647524	+	1.77906i	−0.323762	+	0.889529i	−0.989653	+	0.143480i	$0.954171\pi$
$3$		0			0
$3$		0			0
$4$	0.318417	+	0.267183i	0.0796042	+	0.0667958i
$5$	2.13959	−	1.79533i	0.427918	−	0.359066i	−0.403248	−	0.915091i	$-0.632119\pi$
$5$	2.13959	−	1.79533i	0.427918	−	0.359066i	0.831165	+	0.556025i	$0.187674\pi$
$6$		0			0
$7$	−1.20796	+	2.09224i	−0.172565	+	0.298892i	−0.939316	−	0.343053i	$-0.888539\pi$
$7$	−1.20796	+	2.09224i	−0.172565	+	0.298892i	0.766751	+	0.641945i	$0.221872\pi$
$8$	−7.23987	+	4.17994i	−0.904984	+	0.522493i
$9$		0			0
$10$	1.80856	+	4.96897i	0.180856	+	0.496897i
$11$	9.60360	+	16.6339i	0.873055	+	1.51218i	0.858821	+	0.512277i	$0.171198\pi$
$11$	9.60360	+	16.6339i	0.873055	+	1.51218i	0.0142343	+	0.999899i	$0.495469\pi$
$12$		0			0
$13$	14.2961	+	2.52079i	1.09970	+	0.193907i	0.693911	−	0.720061i	$-0.255886\pi$
$13$	14.2961	+	2.52079i	1.09970	+	0.193907i	0.405788	+	0.913967i	$0.366997\pi$
$14$	−2.94004	−	3.50380i	−0.210003	−	0.250272i
$15$		0			0
$16$	−2.45965	−	13.9494i	−0.153728	−	0.871836i
$17$	−16.1226	−	5.86814i	−0.948387	−	0.345184i	−0.178914	−	0.983865i	$-0.557258\pi$
$17$	−16.1226	−	5.86814i	−0.948387	−	0.345184i	−0.769472	+	0.638680i	$0.779481\pi$
$18$		0			0
$19$	−13.2208	+	13.6459i	−0.695834	+	0.718203i
$19$	−13.2208	+	13.6459i	−0.695834	+	0.718203i
$20$	1.16096			0.0580481
$21$		0			0
$22$	−35.8113	+	6.31450i	−1.62779	+	0.287023i
$23$	5.84413	+	4.90381i	0.254092	+	0.213209i	0.760932	−	0.648831i	$-0.224742\pi$
$23$	5.84413	+	4.90381i	0.254092	+	0.213209i	−0.506840	+	0.862040i	$0.669186\pi$
$24$		0			0
$25$	−2.98657	+	16.9377i	−0.119463	+	0.677507i
$26$	−13.7417	+	23.8013i	−0.528527	+	0.915435i
$27$		0			0
$28$	−0.943645	+	0.343459i	−0.0337016	+	0.0122664i
$29$	−2.81743	−	7.74083i	−0.0971528	−	0.266925i	0.881590	−	0.472015i	$-0.156473\pi$
$29$	−2.81743	−	7.74083i	−0.0971528	−	0.266925i	−0.978743	+	0.205090i	$0.934251\pi$
$30$		0			0
$31$	5.19837	+	3.00128i	0.167689	+	0.0968155i	0.581496	−	0.813549i	$-0.302468\pi$
$31$	5.19837	+	3.00128i	0.167689	+	0.0968155i	−0.413806	+	0.910365i	$0.635801\pi$
$32$	−6.52208	−	1.15002i	−0.203815	−	0.0359381i
$33$		0			0
$34$	20.8795	−	24.8832i	0.614103	−	0.731860i
$35$	1.17173	+	6.64521i	0.0334780	+	0.189863i
$36$		0			0
$37$		−	59.5153i		−	1.60852i	−0.594277	−	0.804260i	$-0.702562\pi$
$37$		−	59.5153i		−	1.60852i	0.594277	−	0.804260i	$-0.297438\pi$
$38$	−15.7160	−	32.3567i	−0.413578	−	0.851491i
$39$		0			0
$40$	−7.98598	+	21.9413i	−0.199650	+	0.548533i
$41$	30.4205	−	5.36396i	0.741964	−	0.130828i	0.210126	−	0.977674i	$-0.432613\pi$
$41$	30.4205	−	5.36396i	0.741964	−	0.130828i	0.531838	+	0.846846i	$0.321502\pi$
$42$		0			0
$43$	18.8243	−	15.7955i	0.437775	−	0.367337i	−0.397101	−	0.917775i	$-0.629984\pi$
$43$	18.8243	−	15.7955i	0.437775	−	0.367337i	0.834876	+	0.550438i	$0.185539\pi$
$44$	−1.38636	+	7.86244i	−0.0315082	+	0.178692i
$45$		0			0
$46$	−12.5084	+	7.22171i	−0.271921	+	0.156994i
$47$	68.7602	−	25.0267i	1.46298	−	0.532483i	0.516798	−	0.856107i	$-0.327124\pi$
$47$	68.7602	−	25.0267i	1.46298	−	0.532483i	0.946186	+	0.323625i	$0.104901\pi$
$48$		0			0
$49$	21.5817	+	37.3806i	0.440443	+	0.762869i
$50$	−28.1992	−	16.2808i	−0.563984	−	0.325617i
$51$		0			0
$52$	3.87860	+	4.62234i	0.0745885	+	0.0888911i
$53$	18.0172	−	21.4721i	0.339947	−	0.405133i	−0.568803	−	0.822474i	$-0.692593\pi$
$53$	18.0172	−	21.4721i	0.339947	−	0.405133i	0.908750	+	0.417341i	$0.137038\pi$
$54$		0			0
$55$	50.4111	+	18.3482i	0.916566	+	0.333603i
$56$		−	20.1968i		−	0.360656i
$57$		0			0
$58$	15.5957			0.268892
$59$	−3.15174	+	8.65934i	−0.0534194	+	0.146769i	−0.963532	−	0.267591i	$-0.913772\pi$
$59$	−3.15174	+	8.65934i	−0.0534194	+	0.146769i	0.910113	+	0.414360i	$0.135995\pi$
$60$		0			0
$61$	−47.2307	−	39.6312i	−0.774273	−	0.649692i	0.167526	−	0.985868i	$-0.446422\pi$
$61$	−47.2307	−	39.6312i	−0.774273	−	0.649692i	−0.941799	+	0.336175i	$0.890867\pi$
$62$	−8.70552	+	7.30480i	−0.140412	+	0.117819i
$63$		0			0
$64$	34.5983	−	59.9260i	0.540598	−	0.936344i
$65$	35.1134	−	20.2727i	0.540206	−	0.311888i
$66$		0			0
$67$	−4.12065	−	11.3214i	−0.0615023	−	0.168976i	0.905136	−	0.425123i	$-0.139769\pi$
$67$	−4.12065	−	11.3214i	−0.0615023	−	0.168976i	−0.966638	+	0.256147i	$0.917547\pi$
$68$	−3.56583	−	6.17619i	−0.0524386	−	0.0908264i
$69$		0			0
$70$	−12.5809	−	2.21836i	−0.179728	−	0.0316909i
$71$	−24.7209	−	29.4613i	−0.348182	−	0.414948i	0.563322	−	0.826237i	$-0.309523\pi$
$71$	−24.7209	−	29.4613i	−0.348182	−	0.414948i	−0.911505	+	0.411290i	$0.865078\pi$
$72$		0			0
$73$	8.82556	+	50.0523i	0.120898	+	0.685647i	0.983660	+	0.180037i	$0.0576217\pi$
$73$	8.82556	+	50.0523i	0.120898	+	0.685647i	−0.862762	+	0.505611i	$0.831267\pi$
$74$	105.881	+	38.5376i	1.43083	+	0.520778i
$75$		0			0
$76$	−7.85568	+	0.812682i	−0.103364	+	0.0106932i
$77$	−46.4029			−0.602635
$78$		0			0
$79$	105.834	−	18.6613i	1.33967	−	0.236219i	0.542538	−	0.840031i	$-0.317463\pi$
$79$	105.834	−	18.6613i	1.33967	−	0.236219i	0.797127	+	0.603812i	$0.206352\pi$
$80$	−30.3064	−	25.4301i	−0.378830	−	0.317876i
$81$		0			0
$82$	−10.1552	+	57.5932i	−0.123844	+	0.702356i
$83$	35.6336	−	61.7192i	0.429321	−	0.743605i	−0.567492	−	0.823379i	$-0.692086\pi$
$83$	35.6336	−	61.7192i	0.429321	−	0.743605i	0.996813	+	0.0797735i	$0.0254197\pi$
$84$		0			0
$85$	−45.0309	+	16.3899i	−0.529775	+	0.192822i
$86$	15.9119	+	43.7175i	0.185022	+	0.508343i
$87$		0			0
$88$	−139.058	−	80.2850i	−1.58020	−	0.912330i
$89$	−7.98351	−	1.40771i	−0.0897024	−	0.0158169i	0.128617	−	0.991694i	$-0.458946\pi$
$89$	−7.98351	−	1.40771i	−0.0897024	−	0.0158169i	−0.218319	+	0.975877i	$0.570057\pi$
$90$		0			0
$91$	−22.5431	+	26.8659i	−0.247727	+	0.295229i
$92$	0.550653	+	3.12291i	0.00598535	+	0.0339446i
$93$		0			0
$94$			138.534i			1.47376i
$95$	−3.78836	+	52.9323i	−0.0398775	+	0.557182i
$96$		0			0
$97$	40.7412	−	111.936i	0.420013	−	1.15398i	−0.531686	−	0.846941i	$-0.678441\pi$
$97$	40.7412	−	111.936i	0.420013	−	1.15398i	0.951699	−	0.307034i	$-0.0993364\pi$
$98$	−80.4769	+	14.1902i	−0.821193	+	0.144798i
$99$		0			0
$100$	−5.47643	+	4.59527i	−0.0547643	+	0.0459527i
$101$	−22.8186	+	129.411i	−0.225926	+	1.28129i	0.634980	+	0.772529i	$0.281008\pi$
$101$	−22.8186	+	129.411i	−0.225926	+	1.28129i	−0.860906	+	0.508764i	$0.830103\pi$
$102$		0			0
$103$	11.4431	−	6.60670i	0.111098	−	0.0641427i	−0.443421	−	0.896313i	$-0.646235\pi$
$103$	11.4431	−	6.60670i	0.111098	−	0.0641427i	0.554520	+	0.832171i	$0.312902\pi$
$104$	−114.039	+	41.5067i	−1.09653	+	0.399102i
$105$		0			0
$106$	26.5335	+	45.9573i	0.250316	+	0.433560i
$107$	−94.8683	−	54.7722i	−0.886620	−	0.511890i	−0.0137844	−	0.999905i	$-0.504388\pi$
$107$	−94.8683	−	54.7722i	−0.886620	−	0.511890i	−0.872835	+	0.488015i	$0.837721\pi$
$108$		0			0
$109$	−132.479	−	157.882i	−1.21540	−	1.44846i	−0.857331	−	0.514766i	$-0.827879\pi$
$109$	−132.479	−	157.882i	−1.21540	−	1.44846i	−0.358071	−	0.933694i	$-0.616565\pi$
$110$	−65.2849	+	77.8035i	−0.593499	+	0.707304i
$111$		0			0
$112$	32.1566	+	11.7041i	0.287113	+	0.104500i
$113$		−	18.3671i		−	0.162541i	−0.996692	−	0.0812705i	$-0.974102\pi$
$113$		−	18.3671i		−	0.162541i	0.996692	−	0.0812705i	$-0.0258978\pi$
$114$		0			0
$115$	21.3080			0.185287
$116$	1.17110	−	3.21758i	0.0100957	−	0.0277377i
$117$		0			0
$118$	−13.3646	−	11.2143i	−0.113260	−	0.0950362i
$119$	31.7529	−	26.6439i	0.266831	−	0.223898i
$120$		0			0
$121$	−123.958	+	214.702i	−1.02445	+	1.77440i
$122$	101.089	−	58.3639i	0.828601	−	0.478393i
$123$		0			0
$124$	0.853356	+	2.34458i	0.00688190	+	0.0189079i
$125$	58.9316	+	102.072i	0.471453	+	0.816580i
$126$		0			0
$127$	−11.1586	−	1.96757i	−0.0878634	−	0.0154927i	0.129544	−	0.991574i	$-0.458649\pi$
$127$	−11.1586	−	1.96757i	−0.0878634	−	0.0154927i	−0.217407	+	0.976081i	$0.569760\pi$
$128$	67.1807	+	80.0628i	0.524849	+	0.625491i
$129$		0			0
$130$	13.3296	+	75.5959i	0.102535	+	0.581507i
$131$	10.5473	+	3.83890i	0.0805137	+	0.0293046i	0.381963	−	0.924178i	$-0.375248\pi$
$131$	10.5473	+	3.83890i	0.0805137	+	0.0293046i	−0.301449	+	0.953482i	$0.597470\pi$
$132$		0			0
$133$	−12.5802	−	44.1448i	−0.0945883	−	0.331916i
$134$	22.8097			0.170221
$135$		0			0
$136$	141.254	−	24.9069i	1.03863	−	0.183139i
$137$	−123.899	−	103.964i	−0.904374	−	0.758860i	0.0666667	−	0.997775i	$-0.478764\pi$
$137$	−123.899	−	103.964i	−0.904374	−	0.758860i	−0.971040	+	0.238916i	$0.923208\pi$
$138$		0			0
$139$	−33.3504	+	189.139i	−0.239931	+	1.36071i	0.592046	+	0.805904i	$0.298320\pi$
$139$	−33.3504	+	189.139i	−0.239931	+	1.36071i	−0.831977	+	0.554810i	$0.812791\pi$
$140$	−1.40239	+	2.42901i	−0.0100171	+	0.0173501i
$141$		0			0
$142$	68.4208	−	24.9031i	0.481836	−	0.175374i
$143$	95.3634	+	262.009i	0.666877	+	1.83223i
$144$		0			0
$145$	−19.9255	−	11.5040i	−0.137417	−	0.0793378i
$146$	−94.7607	−	16.7089i	−0.649046	−	0.114444i
$147$		0			0
$148$	15.9015	−	18.9506i	0.107442	−	0.128045i
$149$	−24.4090	−	138.430i	−0.163819	−	0.929063i	−0.950274	−	0.311415i	$-0.899197\pi$
$149$	−24.4090	−	138.430i	−0.163819	−	0.929063i	0.786455	−	0.617648i	$-0.211914\pi$
$150$		0			0
$151$		−	101.605i		−	0.672880i	−0.941705	−	0.336440i	$-0.890777\pi$
$151$		−	101.605i		−	0.672880i	0.941705	−	0.336440i	$-0.109223\pi$
$152$	38.6783	−	154.057i	0.254462	−	1.01353i
$153$		0			0
$154$	30.0470	−	82.5535i	0.195111	−	0.536062i
$155$	16.5107	−	2.91127i	0.106520	−	0.0187824i
$156$		0			0
$157$	128.198	−	107.571i	0.816551	−	0.685167i	−0.135611	−	0.990762i	$-0.543300\pi$
$157$	128.198	−	107.571i	0.816551	−	0.685167i	0.952162	+	0.305595i	$0.0988553\pi$
$158$	−35.3302	+	200.368i	−0.223609	+	1.26815i
$159$		0			0
$160$	−16.0192	+	9.24871i	−0.100120	+	0.0578044i
$161$	−17.3194	+	6.30374i	−0.107574	+	0.0391537i
$162$		0			0
$163$	16.9195	+	29.3054i	0.103801	+	0.179788i	0.913248	−	0.407405i	$-0.133566\pi$
$163$	16.9195	+	29.3054i	0.103801	+	0.179788i	−0.809447	+	0.587193i	$0.800233\pi$
$164$	11.1196	+	6.41988i	0.0678022	+	0.0391456i
$165$		0			0
$166$	86.7285	+	103.359i	0.522461	+	0.622644i
$167$	31.0323	−	36.9829i	0.185822	−	0.221454i	−0.665089	−	0.746764i	$-0.731606\pi$
$167$	31.0323	−	36.9829i	0.185822	−	0.221454i	0.850911	+	0.525310i	$0.176051\pi$
$168$		0			0
$169$	39.2157	+	14.2733i	0.232046	+	0.0844577i
$170$		−	90.7255i		−	0.533679i
$171$		0			0
$172$	10.2143			0.0593852
$173$	−17.6894	+	48.6013i	−0.102251	+	0.280932i	−0.980260	−	0.197711i	$-0.936649\pi$
$173$	−17.6894	+	48.6013i	−0.102251	+	0.280932i	0.878009	+	0.478643i	$0.158871\pi$
$174$		0			0
$175$	−31.8300	−	26.7086i	−0.181886	−	0.152620i
$176$	208.411	−	174.878i	1.18416	−	0.993625i
$177$		0			0
$178$	7.67391	−	13.2916i	0.0431119	−	0.0746719i
$179$	200.919	−	116.001i	1.12245	−	0.648048i	0.180426	−	0.983589i	$-0.442252\pi$
$179$	200.919	−	116.001i	1.12245	−	0.648048i	0.942026	+	0.335541i	$0.108919\pi$
$180$		0			0
$181$	92.4816	+	254.091i	0.510948	+	1.40382i	0.880251	+	0.474509i	$0.157374\pi$
$181$	92.4816	+	254.091i	0.510948	+	1.40382i	−0.369303	+	0.929309i	$0.620404\pi$
$182$	−33.1987	−	57.5019i	−0.182411	−	0.315944i
$183$		0			0
$184$	−62.8084	−	11.0748i	−0.341350	−	0.0601892i
$185$	−106.849	−	127.338i	−0.577564	−	0.688315i
$186$		0			0
$187$	−57.2246	−	324.537i	−0.306014	−	1.73549i
$188$	28.5811	+	10.4027i	0.152027	+	0.0553334i
$189$		0			0
$190$	−91.7166	−	41.0146i	−0.482719	−	0.215867i
$191$	−81.4552			−0.426467			−0.213233	−	0.977001i	$-0.568399\pi$
$191$	−81.4552			−0.426467			−0.213233	+	0.977001i	$0.568399\pi$
$192$		0			0
$193$	−29.3774	+	5.18002i	−0.152214	+	0.0268395i	−0.249236	−	0.968443i	$-0.580179\pi$
$193$	−29.3774	+	5.18002i	−0.152214	+	0.0268395i	0.0970217	+	0.995282i	$0.469068\pi$
$194$	172.759	+	144.962i	0.890510	+	0.747227i
$195$		0			0
$196$	−3.11550	+	17.6689i	−0.0158954	+	0.0901472i
$197$	−90.0191	+	155.918i	−0.456950	+	0.791461i	−0.998798	−	0.0490159i	$-0.984391\pi$
$197$	−90.0191	+	155.918i	−0.456950	+	0.791461i	0.541848	+	0.840476i	$0.317725\pi$
$198$		0			0
$199$	−103.486	+	37.6658i	−0.520030	+	0.189276i	−0.588681	−	0.808365i	$-0.700353\pi$
$199$	−103.486	+	37.6658i	−0.520030	+	0.189276i	0.0686510	+	0.997641i	$0.478130\pi$
$200$	−49.1761	−	135.110i	−0.245880	−	0.675551i
$201$		0			0
$202$	−215.453	−	124.392i	−1.06660	−	0.615802i
$203$	19.5990	+	3.45583i	0.0965468	+	0.0170238i
$204$		0			0
$205$	55.4573	−	66.0915i	0.270524	−	0.322397i
$206$	4.34399	+	24.6360i	0.0210874	+	0.119592i
$207$		0			0
$208$		−	205.622i		−	0.988566i
$209$	−353.952	−	88.8650i	−1.69355	−	0.425192i
$210$		0			0
$211$	−52.6404	+	144.628i	−0.249480	+	0.685442i	0.750225	+	0.661182i	$0.229945\pi$
$211$	−52.6404	+	144.628i	−0.249480	+	0.685442i	−0.999706	+	0.0242596i	$0.992277\pi$
$212$	11.4740	−	2.02317i	0.0541224	−	0.00954324i
$213$		0			0
$214$	158.873	−	133.310i	0.742395	−	0.622944i
$215$	11.9182	−	67.5916i	0.0554336	−	0.314380i
$216$		0			0
$217$	−12.5588	+	7.25083i	−0.0578747	+	0.0334140i
$218$	366.665	−	133.455i	1.68195	−	0.612179i
$219$		0			0
$220$	11.1494	+	19.3114i	0.0506792	+	0.0877789i
$221$	−215.697	−	124.533i	−0.976006	−	0.563497i
$222$		0			0
$223$	100.038	+	119.221i	0.448602	+	0.534623i	0.942193	−	0.335071i	$-0.108760\pi$
$223$	100.038	+	119.221i	0.448602	+	0.534623i	−0.493591	+	0.869694i	$0.664316\pi$
$224$	10.2845	−	12.2566i	0.0459129	−	0.0547169i
$225$		0			0
$226$	32.6762	+	11.8932i	0.144585	+	0.0526247i
$227$			67.0830i			0.295520i	0.989023	+	0.147760i	$0.0472063\pi$
$227$			67.0830i			0.295520i	−0.989023	+	0.147760i	$0.952794\pi$
$228$		0			0
$229$	69.2740			0.302506			0.151253	−	0.988495i	$-0.451669\pi$
$229$	69.2740			0.302506			0.151253	+	0.988495i	$0.451669\pi$
$230$	−13.7974	+	37.9081i	−0.0599888	+	0.164818i
$231$		0			0
$232$	52.7541	+	44.2659i	0.227388	+	0.190801i
$233$	125.028	−	104.911i	0.536601	−	0.450261i	−0.333773	−	0.942654i	$-0.608322\pi$
$233$	125.028	−	104.911i	0.536601	−	0.450261i	0.870373	+	0.492392i	$0.163877\pi$
$234$		0			0
$235$	102.188	−	176.994i	0.434841	−	0.753166i
$236$	−3.31720	+	1.91519i	−0.0140559	+	0.00811519i
$237$		0			0
$238$	26.8402	+	73.7428i	0.112774	+	0.309844i
$239$	152.816	+	264.685i	0.639397	+	1.10747i	0.985565	+	0.169296i	$0.0541492\pi$
$239$	152.816	+	264.685i	0.639397	+	1.10747i	−0.346168	+	0.938172i	$0.612517\pi$
$240$		0			0
$241$	−236.403	−	41.6842i	−0.980925	−	0.172963i	−0.339881	−	0.940468i	$-0.610387\pi$
$241$	−236.403	−	41.6842i	−0.980925	−	0.172963i	−0.641043	+	0.767505i	$0.721498\pi$
$242$	−301.702	−	359.554i	−1.24670	−	1.48576i
$243$		0			0
$244$	−4.45023	−	25.2385i	−0.0182386	−	0.103436i
$245$	113.286	+	41.2329i	0.462393	+	0.168297i
$246$		0			0
$247$	−223.405	+	161.755i	−0.904472	+	0.654881i
$248$	−50.1807			−0.202342
$249$		0			0
$250$	−219.753	+	38.7483i	−0.879010	+	0.154993i
$251$	244.652	+	205.287i	0.974708	+	0.817877i	0.983283	−	0.182086i	$-0.0582849\pi$
$251$	244.652	+	205.287i	0.974708	+	0.817877i	−0.00857425	+	0.999963i	$0.502729\pi$
$252$		0			0
$253$	−25.4449	+	144.305i	−0.100573	+	0.570375i
$254$	10.7259	−	18.5778i	0.0422280	−	0.0731411i
$255$		0			0
$256$	74.1565	−	26.9908i	0.289674	−	0.105433i
$257$	−39.3775	−	108.189i	−0.153220	−	0.420968i	0.839206	−	0.543814i	$-0.183020\pi$
$257$	−39.3775	−	108.189i	−0.153220	−	0.420968i	−0.992426	+	0.122846i	$0.960798\pi$
$258$		0			0
$259$	124.520	+	71.8918i	0.480773	+	0.277575i
$260$	16.5972	+	2.92654i	0.0638355	+	0.0112559i
$261$		0			0
$262$	−13.6593	+	16.2785i	−0.0521346	+	0.0621315i
$263$	3.94528	+	22.3748i	0.0150011	+	0.0850752i	0.991389	−	0.130949i	$-0.0418023\pi$
$263$	3.94528	+	22.3748i	0.0150011	+	0.0850752i	−0.976388	+	0.216024i	$0.930691\pi$
$264$		0			0
$265$		−	78.2882i		−	0.295427i
$266$	86.6822	+	6.20384i	0.325873	+	0.0233227i
$267$		0			0
$268$	1.71280	−	4.70589i	0.00639106	−	0.0175593i
$269$	273.598	−	48.2428i	1.01709	−	0.179341i	0.359843	−	0.933013i	$-0.382830\pi$
$269$	273.598	−	48.2428i	1.01709	−	0.179341i	0.657251	+	0.753672i	$0.271719\pi$
$270$		0			0
$271$	2.59209	−	2.17502i	0.00956490	−	0.00802590i	−0.637993	−	0.770042i	$-0.720235\pi$
$271$	2.59209	−	2.17502i	0.00956490	−	0.00802590i	0.647558	+	0.762017i	$0.275791\pi$
$272$	−42.2009	+	239.333i	−0.155151	+	0.879902i
$273$		0			0
$274$	265.185	−	153.105i	0.967830	−	0.558777i
$275$	−310.422	+	112.984i	−1.12881	+	0.410852i
$276$		0			0
$277$	67.8848	+	117.580i	0.245072	+	0.424476i	0.962152	−	0.272514i	$-0.0878552\pi$
$277$	67.8848	+	117.580i	0.245072	+	0.424476i	−0.717080	+	0.696991i	$0.754522\pi$
$278$	−314.895	−	181.804i	−1.13271	−	0.653973i
$279$		0			0
$280$	−36.2598	−	43.2127i	−0.129499	−	0.154331i
$281$	−317.040	+	377.834i	−1.12826	+	1.34460i	−0.196932	+	0.980417i	$0.563098\pi$
$281$	−317.040	+	377.834i	−1.12826	+	1.34460i	−0.931326	+	0.364188i	$0.881347\pi$
$282$		0			0
$283$	352.072	+	128.144i	1.24407	+	0.452804i	0.878393	−	0.477938i	$-0.158616\pi$
$283$	352.072	+	128.144i	1.24407	+	0.452804i	0.365676	+	0.930742i	$0.380838\pi$
$284$		−	15.9860i		−	0.0562887i
$285$		0			0
$286$	−527.879			−1.84573
$287$	−25.5240	+	70.1265i	−0.0889336	+	0.244343i
$288$		0			0
$289$	4.11543	+	3.45325i	0.0142402	+	0.0119490i
$290$	33.3685	−	27.9995i	0.115064	−	0.0965499i
$291$		0			0
$292$	−10.5629	+	18.2955i	−0.0361744	+	0.0626559i
$293$	63.5500	−	36.6906i	0.216894	−	0.125224i	−0.387617	−	0.921820i	$-0.626702\pi$
$293$	63.5500	−	36.6906i	0.216894	−	0.125224i	0.604511	+	0.796597i	$0.293368\pi$
$294$		0			0
$295$	8.80293	+	24.1859i	0.0298404	+	0.0819859i
$296$	248.770	+	430.883i	0.840440	+	1.45569i
$297$		0			0
$298$	262.081	+	46.2120i	0.879467	+	0.155074i
$299$	71.1867	+	84.8370i	0.238083	+	0.283736i
$300$		0			0
$301$	10.3090	+	58.4652i	0.0342492	+	0.194237i
$302$	180.761	+	65.7916i	0.598547	+	0.217853i
$303$		0			0
$304$	222.870	+	150.858i	0.733125	+	0.496245i
$305$	−172.205			−0.564607
$306$		0			0
$307$	−91.0288	+	16.0508i	−0.296511	+	0.0522829i	−0.319925	−	0.947443i	$-0.603658\pi$
$307$	−91.0288	+	16.0508i	−0.296511	+	0.0522829i	0.0234138	+	0.999726i	$0.492546\pi$
$308$	−14.7755	−	12.3981i	−0.0479723	−	0.0402535i
$309$		0			0
$310$	−5.51173	+	31.2585i	−0.0177798	+	0.100834i
$311$	99.6155	−	172.539i	0.320307	−	0.554788i	−0.660244	−	0.751051i	$-0.729547\pi$
$311$	99.6155	−	172.539i	0.320307	−	0.554788i	0.980551	+	0.196263i	$0.0628806\pi$
$312$		0			0
$313$	−28.7523	+	10.4650i	−0.0918605	+	0.0334345i	−0.387542	−	0.921852i	$-0.626676\pi$
$313$	−28.7523	+	10.4650i	−0.0918605	+	0.0334345i	0.295681	+	0.955287i	$0.404453\pi$
$314$	108.364	+	297.728i	0.345108	+	0.948177i
$315$		0			0
$316$	38.6852	+	22.3349i	0.122421	+	0.0706800i
$317$	−561.248	−	98.9631i	−1.77050	−	0.312186i	−0.809166	−	0.587581i	$-0.800081\pi$
$317$	−561.248	−	98.9631i	−1.77050	−	0.312186i	−0.961331	+	0.275394i	$0.911192\pi$
$318$		0			0
$319$	101.703	−	121.205i	0.318818	−	0.379952i
$320$	−33.5607	−	190.332i	−0.104877	−	0.594789i
$321$		0			0
$322$		−	34.8940i		−	0.108367i
$323$	293.230	−	142.425i	0.907832	−	0.440943i
$324$		0			0
$325$	−85.3924	+	234.614i	−0.262746	+	0.721889i
$326$	−63.0919	+	11.1248i	−0.193533	+	0.0341251i
$327$		0			0
$328$	−197.820	+	165.990i	−0.603109	+	0.506068i
$329$	−30.6975	+	174.094i	−0.0933055	+	0.529162i
$330$		0			0
$331$	383.016	−	221.134i	1.15715	−	0.668079i	0.206529	−	0.978441i	$-0.433783\pi$
$331$	383.016	−	221.134i	1.15715	−	0.668079i	0.950619	+	0.310361i	$0.100450\pi$
$332$	27.8367	−	10.1317i	0.0838454	−	0.0305172i
$333$		0			0
$334$	45.7005	+	79.1556i	0.136828	+	0.236993i
$335$	−29.1421	−	16.8252i	−0.0869915	−	0.0502245i
$336$		0			0
$337$	−284.270	−	338.780i	−0.843531	−	1.00528i	−0.999846	−	0.0175740i	$-0.994406\pi$
$337$	−284.270	−	338.780i	−0.843531	−	1.00528i	0.156314	−	0.987707i	$-0.450039\pi$
$338$	−50.7862	+	60.5247i	−0.150255	+	0.179067i
$339$		0			0
$340$	−18.7177	−	6.81269i	−0.0550521	−	0.0200373i
$341$			115.292i			0.338101i
$342$		0			0
$343$	−222.659			−0.649150
$344$	−70.2614	+	193.042i	−0.204248	+	0.561168i
$345$		0			0
$346$	−75.0102	−	62.9410i	−0.216792	−	0.181910i
$347$	−2.68547	+	2.25337i	−0.00773910	+	0.00649387i	−0.646649	−	0.762788i	$-0.723830\pi$
$347$	−2.68547	+	2.25337i	−0.00773910	+	0.00649387i	0.638910	+	0.769282i	$0.279386\pi$
$348$		0			0
$349$	−44.1774	+	76.5174i	−0.126583	+	0.219248i	−0.922350	−	0.386354i	$-0.873734\pi$
$349$	−44.1774	+	76.5174i	−0.126583	+	0.219248i	0.795768	+	0.605602i	$0.207068\pi$
$350$	68.1268	−	39.3330i	0.194648	−	0.112380i
$351$		0			0
$352$	−43.5061	−	119.532i	−0.123597	−	0.339580i
$353$	−62.9423	−	109.019i	−0.178307	−	0.308837i	0.762994	−	0.646406i	$-0.223729\pi$
$353$	−62.9423	−	109.019i	−0.178307	−	0.308837i	−0.941301	+	0.337569i	$0.890395\pi$
$354$		0			0
$355$	−105.785	−	18.6528i	−0.297987	−	0.0525431i
$356$	−2.16597	−	2.58130i	−0.00608418	−	0.00725084i
$357$		0			0
$358$	76.2719	+	432.559i	0.213050	+	1.20827i
$359$	−56.5579	−	20.5854i	−0.157543	−	0.0573409i	0.262045	−	0.965056i	$-0.415603\pi$
$359$	−56.5579	−	20.5854i	−0.157543	−	0.0573409i	−0.419588	+	0.907715i	$0.637825\pi$
$360$		0			0
$361$	−11.4190	−	360.819i	−0.0316314	−	0.999500i
$362$	−511.927			−1.41416
$363$		0			0
$364$	−14.3562	+	2.53139i	−0.0394402	+	0.00695437i
$365$	108.743	+	91.2465i	0.297927	+	0.249990i
$366$		0			0
$367$	26.6342	−	151.050i	0.0725729	−	0.411581i	−0.926780	−	0.375605i	$-0.877435\pi$
$367$	26.6342	−	151.050i	0.0725729	−	0.411581i	0.999353	−	0.0359761i	$-0.0114540\pi$
$368$	54.0305	−	93.5836i	0.146822	−	0.254303i
$369$		0			0
$370$	295.730	−	107.637i	0.799269	−	0.290910i
$371$	23.1607	+	63.6336i	0.0624279	+	0.171519i
$372$		0			0
$373$	−230.727	−	133.210i	−0.618571	−	0.357132i	0.157741	−	0.987480i	$-0.449579\pi$
$373$	−230.727	−	133.210i	−0.618571	−	0.357132i	−0.776313	+	0.630348i	$0.782912\pi$
$374$	614.425	+	108.340i	1.64285	+	0.289678i
$375$		0			0
$376$	−393.205	+	468.604i	−1.04576	+	1.24629i
$377$	−20.7653	−	117.766i	−0.0550803	−	0.312376i
$378$		0			0
$379$			670.093i			1.76806i	0.467435	+	0.884028i	$0.345178\pi$
$379$			670.093i			1.76806i	−0.467435	+	0.884028i	$0.654822\pi$
$380$	−15.3489	+	15.8423i	−0.0403918	+	0.0416903i
$381$		0			0
$382$	52.7442	−	144.914i	0.138074	−	0.379355i
$383$	−679.414	+	119.799i	−1.77393	+	0.312791i	−0.962423	−	0.271556i	$-0.912462\pi$
$383$	−679.414	+	119.799i	−1.77393	+	0.312791i	−0.811504	+	0.584347i	$0.801351\pi$
$384$		0			0
$385$	−99.2832	+	83.3085i	−0.257878	+	0.216386i
$386$	9.80699	−	55.6182i	0.0254067	−	0.144089i
$387$		0			0
$388$	42.8800	−	24.7568i	0.110515	−	0.0638061i
$389$	212.211	−	77.2383i	0.545528	−	0.198556i	−0.0545302	−	0.998512i	$-0.517366\pi$
$389$	212.211	−	77.2383i	0.545528	−	0.198556i	0.600059	+	0.799956i	$0.295144\pi$
$390$		0			0
$391$	−65.4462	−	113.356i	−0.167381	−	0.289913i
$392$	−312.497	−	180.420i	−0.797187	−	0.460256i
$393$		0			0
$394$	−219.097	−	261.110i	−0.556084	−	0.662715i
$395$	192.937	−	229.934i	0.488448	−	0.582110i
$396$		0			0
$397$	−568.125	−	206.781i	−1.43105	−	0.520858i	−0.493815	−	0.869567i	$-0.664398\pi$
$397$	−568.125	−	206.781i	−1.43105	−	0.520858i	−0.937231	+	0.348709i	$0.886620\pi$
$398$		−	208.497i		−	0.523862i
$399$		0			0
$400$	243.616			0.609039
$401$	110.875	−	304.626i	0.276495	−	0.759665i	−0.721258	−	0.692667i	$-0.756436\pi$
$401$	110.875	−	304.626i	0.276495	−	0.759665i	0.997753	−	0.0669980i	$-0.0213421\pi$
$402$		0			0
$403$	66.7508	+	56.0105i	0.165635	+	0.138984i
$404$	−41.8421	+	35.1097i	−0.103570	+	0.0869053i
$405$		0			0
$406$	−18.8390	+	32.6300i	−0.0464014	+	0.0803696i
$407$	989.972	−	571.561i	2.43236	−	1.40433i
$408$		0			0
$409$	−89.4166	−	245.670i	−0.218623	−	0.600660i	0.781095	−	0.624412i	$-0.214661\pi$
$409$	−89.4166	−	245.670i	−0.218623	−	0.600660i	−0.999718	+	0.0237513i	$0.992439\pi$
$410$	81.6706	+	141.458i	0.199197	+	0.345019i
$411$		0			0
$412$	5.40889	+	0.953733i	0.0131284	+	0.00231489i
$413$	−14.3103	−	17.0543i	−0.0346496	−	0.0412937i
$414$		0			0
$415$	−34.5650	−	196.028i	−0.0832891	−	0.472356i
$416$	−90.3412	−	32.8815i	−0.217166	−	0.0790421i
$417$		0			0
$418$	387.289	−	572.159i	0.926528	−	1.36880i
$419$	242.808			0.579495			0.289747	−	0.957103i	$-0.406429\pi$
$419$	242.808			0.579495			0.289747	+	0.957103i	$0.406429\pi$
$420$		0			0
$421$	547.350	−	96.5126i	1.30012	−	0.229246i	0.519617	−	0.854399i	$-0.326075\pi$
$421$	547.350	−	96.5126i	1.30012	−	0.229246i	0.780502	+	0.625154i	$0.214964\pi$
$422$	−223.216	−	187.301i	−0.528948	−	0.443840i
$423$		0			0
$424$	−40.6902	+	230.766i	−0.0959676	+	0.544259i
$425$	147.544	−	255.553i	0.347162	−	0.601301i
$426$		0			0
$427$	139.971	−	50.9452i	0.327800	−	0.119309i
$428$	−15.5734	−	42.7876i	−0.0363865	−	0.0999711i
$429$		0			0
$430$	112.532	+	64.9704i	0.261703	+	0.151094i
$431$	−6.30702	−	1.11210i	−0.0146335	−	0.00258028i	0.166327	−	0.986071i	$-0.446809\pi$
$431$	−6.30702	−	1.11210i	−0.0146335	−	0.00258028i	−0.180960	+	0.983490i	$0.557920\pi$
$432$		0			0
$433$	−36.8103	+	43.8687i	−0.0850121	+	0.101314i	−0.806874	−	0.590724i	$-0.798842\pi$
$433$	−36.8103	+	43.8687i	−0.0850121	+	0.101314i	0.721862	+	0.692037i	$0.243287\pi$
$434$	−4.76752	−	27.0379i	−0.0109851	−	0.0622994i
$435$		0			0
$436$		−	85.6684i		−	0.196487i
$437$	−144.181	+	14.9157i	−0.329933	+	0.0341321i
$438$		0			0
$439$	−179.069	+	491.987i	−0.407901	+	1.12070i	0.550391	+	0.834907i	$0.314479\pi$
$439$	−179.069	+	491.987i	−0.407901	+	1.12070i	−0.958292	+	0.285792i	$0.907744\pi$
$440$	−441.664	+	77.8774i	−1.00378	+	0.176994i
$441$		0			0
$442$	361.221	−	303.100i	0.817241	−	0.685747i
$443$	−75.4553	+	427.928i	−0.170328	+	0.965978i	0.773071	+	0.634319i	$0.218719\pi$
$443$	−75.4553	+	427.928i	−0.170328	+	0.965978i	−0.943399	+	0.331659i	$0.892392\pi$
$444$		0			0
$445$	−19.6087	+	11.3211i	−0.0440646	+	0.0254407i
$446$	−276.878	+	100.775i	−0.620803	+	0.225954i
$447$		0			0
$448$	83.5864	+	144.776i	0.186577	+	0.323161i
$449$	272.280	+	157.201i	0.606415	+	0.350114i	0.771561	−	0.636155i	$-0.219476\pi$
$449$	272.280	+	157.201i	0.606415	+	0.350114i	−0.165146	+	0.986269i	$0.552810\pi$
$450$		0			0
$451$	381.370	+	454.499i	0.845610	+	1.00776i
$452$	4.90739	−	5.84840i	0.0108571	−	0.0129389i
$453$		0			0
$454$	−119.345	−	43.4379i	−0.262873	−	0.0956781i
$455$			97.9543i			0.215284i
$456$		0			0
$457$	525.189			1.14921			0.574606	−	0.818431i	$-0.305155\pi$
$457$	525.189			1.14921			0.574606	+	0.818431i	$0.305155\pi$
$458$	−44.8566	+	123.242i	−0.0979401	+	0.269088i
$459$		0			0
$460$	6.78481	+	5.69313i	0.0147496	+	0.0123764i
$461$	466.982	−	391.845i	1.01298	−	0.849988i	0.0242478	−	0.999706i	$-0.492281\pi$
$461$	466.982	−	391.845i	1.01298	−	0.849988i	0.988729	+	0.149718i	$0.0478365\pi$
$462$		0			0
$463$	381.720	−	661.158i	0.824449	−	1.42799i	−0.0778909	−	0.996962i	$-0.524819\pi$
$463$	381.720	−	661.158i	0.824449	−	1.42799i	0.902340	−	0.431025i	$-0.141848\pi$
$464$	−101.050	+	58.3411i	−0.217780	+	0.125735i
$465$		0			0
$466$	105.684	+	290.364i	0.226790	+	0.623099i
$467$	−224.311	−	388.519i	−0.480324	−	0.831946i	0.519421	−	0.854519i	$-0.326148\pi$
$467$	−224.311	−	388.519i	−0.480324	−	0.831946i	−0.999745	+	0.0225724i	$0.992814\pi$
$468$		0			0
$469$	28.6647	+	5.05436i	0.0611187	+	0.0107769i
$470$	248.714	+	296.406i	0.529178	+	0.630650i
$471$		0			0
$472$	−13.3773	−	75.8667i	−0.0283418	−	0.160734i
$473$	443.522	+	161.429i	0.937678	+	0.341287i
$474$		0			0
$475$	−191.644	−	264.684i	−0.403461	−	0.557230i
$476$	17.2294			0.0361963
$477$		0			0
$478$	−569.842	+	100.478i	−1.19214	+	0.210206i
$479$	533.676	+	447.807i	1.11415	+	0.934879i	0.998294	−	0.0583874i	$-0.0185959\pi$
$479$	533.676	+	447.807i	1.11415	+	0.934879i	0.115852	+	0.993267i	$0.463040\pi$
$480$		0			0
$481$	150.025	−	850.835i	0.311903	−	1.76889i
$482$	227.235	−	393.583i	0.471442	−	0.816562i
$483$		0			0
$484$	−96.8353	+	35.2451i	−0.200073	+	0.0728206i
$485$	−113.792	−	312.640i	−0.234622	−	0.644619i
$486$		0			0
$487$	16.8247	+	9.71373i	0.0345476	+	0.0199461i	0.517174	−	0.855880i	$-0.326984\pi$
$487$	16.8247	+	9.71373i	0.0345476	+	0.0199461i	−0.482627	+	0.875826i	$0.660317\pi$
$488$	507.600	+	89.5036i	1.04016	+	0.183409i
$489$		0			0
$490$	−146.711	+	174.844i	−0.299411	+	0.356824i
$491$	−115.016	−	652.286i	−0.234248	−	1.32848i	−0.844192	−	0.536041i	$-0.819919\pi$
$491$	−115.016	−	652.286i	−0.234248	−	1.32848i	0.609944	−	0.792444i	$-0.291192\pi$
$492$		0			0
$493$			141.335i			0.286684i
$494$	−143.113	−	502.190i	−0.289702	−	1.01658i
$495$		0			0
$496$	29.0798	−	79.8961i	0.0586287	−	0.161081i
$497$	91.5019	−	16.1343i	0.184109	−	0.0324633i
$498$		0			0
$499$	−102.346	+	85.8785i	−0.205102	+	0.172101i	−0.739553	−	0.673098i	$-0.764963\pi$
$499$	−102.346	+	85.8785i	−0.205102	+	0.172101i	0.534451	+	0.845200i	$0.320519\pi$
$500$	−8.50727	+	48.2471i	−0.0170145	+	0.0964942i
$501$		0			0
$502$	−523.636	+	302.321i	−1.04310	+	0.602234i
$503$	−305.161	+	111.070i	−0.606682	+	0.220814i	−0.627051	−	0.778978i	$-0.715738\pi$
$503$	−305.161	+	111.070i	−0.606682	+	0.220814i	0.0203686	+	0.999793i	$0.493516\pi$
$504$		0			0
$505$	183.512	+	317.852i	0.363390	+	0.629410i
$506$	−240.251	−	138.709i	−0.474804	−	0.274128i
$507$		0			0
$508$	−3.02740	−	3.60791i	−0.00595944	−	0.00710219i
$509$	−314.036	+	374.253i	−0.616966	+	0.735271i	−0.980545	−	0.196292i	$-0.937110\pi$
$509$	−314.036	+	374.253i	−0.616966	+	0.735271i	0.363580	+	0.931563i	$0.381554\pi$
$510$		0			0
$511$	−115.382	−	41.9957i	−0.225797	−	0.0821834i
$512$			567.464i			1.10833i
$513$		0			0
$514$	217.972			0.424070
$515$	12.6224	−	34.6798i	0.0245096	−	0.0673395i
$516$		0			0
$517$	1076.64	+	903.407i	2.08247	+	1.74740i
$518$	−208.530	+	174.977i	−0.402567	+	0.337794i
$519$		0			0
$520$	−169.478	+	293.544i	−0.325919	+	0.564508i
$521$	−539.718	+	311.606i	−1.03593	+	0.598093i	−0.918677	−	0.395010i	$-0.870741\pi$
$521$	−539.718	+	311.606i	−1.03593	+	0.598093i	−0.117250	+	0.993102i	$0.537408\pi$
$522$		0			0
$523$	−224.813	−	617.668i	−0.429853	−	1.18101i	−0.945902	−	0.324452i	$-0.894820\pi$
$523$	−224.813	−	617.668i	−0.429853	−	1.18101i	0.516050	−	0.856559i	$-0.327402\pi$
$524$	2.33274	+	4.04043i	0.00445180	+	0.00771074i
$525$		0			0
$526$	−42.3607	−	7.46933i	−0.0805336	−	0.0142003i
$527$	−66.1992	−	78.8931i	−0.125615	−	0.149702i
$528$		0			0
$529$	−81.7534	−	463.646i	−0.154543	−	0.876458i
$530$	139.279	+	50.6935i	0.262791	+	0.0956481i
$531$		0			0
$532$	7.78899	−	17.4177i	0.0146410	−	0.0327400i
$533$	448.416			0.841305
$534$		0			0
$535$	−301.313	+	53.1297i	−0.563203	+	0.0993078i
$536$	77.1558	+	64.7414i	0.143947	+	0.120786i
$537$		0			0
$538$	−91.3349	+	517.986i	−0.169767	+	0.962799i
$539$	−414.524	+	717.976i	−0.769061	+	1.33205i
$540$		0			0
$541$	−84.0065	+	30.5759i	−0.155280	+	0.0565173i	−0.418491	−	0.908221i	$-0.637441\pi$
$541$	−84.0065	+	30.5759i	−0.155280	+	0.0565173i	0.263211	+	0.964738i	$0.415219\pi$
$542$	2.19105	+	6.01985i	0.00404252	+	0.0111067i
$543$		0			0
$544$	98.4042	+	56.8137i	0.180890	+	0.104437i
$545$	−566.901	−	99.9599i	−1.04018	−	0.183413i
$546$		0			0
$547$	−450.474	+	536.854i	−0.823535	+	0.981451i	−0.999996	−	0.00285665i	$-0.999091\pi$
$547$	−450.474	+	536.854i	−0.823535	+	0.981451i	0.176461	+	0.984308i	$0.443535\pi$
$548$	−11.6742	−	66.2076i	−0.0213033	−	0.120817i
$549$		0			0
$550$		−	625.418i		−	1.13712i
$551$	142.879	+	63.8939i	0.259309	+	0.115960i
$552$		0			0
$553$	−88.7983	+	243.971i	−0.160576	+	0.441178i
$554$	−253.139	+	44.6352i	−0.456929	+	0.0805689i
$555$		0			0
$556$	−61.1541	+	51.3144i	−0.109989	+	0.0922921i
$557$	36.5801	−	207.456i	0.0656733	−	0.372452i	−0.934203	−	0.356741i	$-0.883888\pi$
$557$	36.5801	−	207.456i	0.0656733	−	0.372452i	0.999877	−	0.0157108i	$-0.00500111\pi$
$558$		0			0
$559$	308.931	−	178.361i	0.552649	−	0.319072i
$560$	89.8146	−	32.6898i	0.160383	−	0.0583747i
$561$		0			0
$562$	−466.897	−	808.690i	−0.830778	−	1.43895i
$563$	461.855	+	266.652i	0.820347	+	0.473627i	0.850536	−	0.525917i	$-0.176278\pi$
$563$	461.855	+	266.652i	0.820347	+	0.473627i	−0.0301894	+	0.999544i	$0.509611\pi$
$564$		0			0
$565$	−32.9751	−	39.2981i	−0.0583629	−	0.0695542i
$566$	−455.950	+	543.380i	−0.805565	+	0.960035i
$567$		0			0
$568$	302.123	+	109.964i	0.531907	+	0.193598i
$569$		−	610.046i		−	1.07214i	−0.844174	−	0.536068i	$-0.819909\pi$
$569$		−	610.046i		−	1.07214i	0.844174	−	0.536068i	$-0.180091\pi$
$570$		0			0
$571$	−678.976			−1.18910			−0.594550	−	0.804059i	$-0.702670\pi$
$571$	−678.976			−1.18910			−0.594550	+	0.804059i	$0.702670\pi$
$572$	−39.6391	+	108.907i	−0.0692991	+	0.190398i
$573$		0			0
$574$	−108.232	−	90.8172i	−0.188557	−	0.158218i
$575$	−100.513	+	84.3403i	−0.174805	+	0.146679i
$576$		0			0
$577$	−363.669	+	629.894i	−0.630276	+	1.09167i	0.357219	+	0.934021i	$0.383725\pi$
$577$	−363.669	+	629.894i	−0.630276	+	1.09167i	−0.987495	+	0.157649i	$0.949608\pi$
$578$	−8.80838	+	5.08552i	−0.0152394	+	0.00879847i
$579$		0			0
$580$	−3.27093	−	8.98681i	−0.00563954	−	0.0154945i
$581$	86.0877	+	149.108i	0.148172	+	0.256641i
$582$		0			0
$583$	530.195	+	93.4876i	0.909425	+	0.160356i
$584$	−273.112	−	325.482i	−0.467657	−	0.557332i
$585$		0			0
$586$	24.1246	+	136.817i	0.0411682	+	0.233477i
$587$	−920.712	−	335.112i	−1.56850	−	0.570889i	−0.595840	−	0.803103i	$-0.703181\pi$
$587$	−920.712	−	335.112i	−1.56850	−	0.570889i	−0.972665	+	0.232214i	$0.925403\pi$
$588$		0			0
$589$	−109.682	+	31.2568i	−0.186217	+	0.0530676i
$590$	−48.7282			−0.0825901
$591$		0			0
$592$	−830.201	+	146.387i	−1.40237	+	0.247275i
$593$	267.014	+	224.051i	0.450277	+	0.377827i	0.839538	−	0.543300i	$-0.182825\pi$
$593$	267.014	+	224.051i	0.450277	+	0.377827i	−0.389262	+	0.921127i	$0.627270\pi$
$594$		0			0
$595$	20.1037	−	114.014i	0.0337878	−	0.191620i
$596$	29.2140	−	50.6002i	0.0490169	−	0.0848997i
$597$		0			0
$598$	−197.025	+	71.7113i	−0.329473	+	0.119919i
$599$	144.781	+	397.783i	0.241705	+	0.664078i	0.999927	+	0.0120820i	$0.00384592\pi$
$599$	144.781	+	397.783i	0.241705	+	0.664078i	−0.758222	+	0.651996i	$0.773932\pi$
$600$		0			0
$601$	437.051	+	252.331i	0.727206	+	0.419853i	0.817399	−	0.576072i	$-0.195415\pi$
$601$	437.051	+	252.331i	0.727206	+	0.419853i	−0.0901931	+	0.995924i	$0.528748\pi$
$602$	−110.688	−	19.5173i	−0.183868	−	0.0324208i
$603$		0			0
$604$	27.1471	−	32.3527i	0.0449456	−	0.0535641i
$605$	120.241	+	681.921i	0.198745	+	1.12714i
$606$		0			0
$607$		−	73.0072i		−	0.120275i	−0.998190	−	0.0601377i	$-0.980846\pi$
$607$		−	73.0072i		−	0.120275i	0.998190	−	0.0601377i	$-0.0191540\pi$
$608$	101.920	−	73.7952i	0.167632	−	0.121374i
$609$		0			0
$610$	111.507	−	306.363i	0.182799	−	0.502235i
$611$	1046.09	−	184.454i	1.71209	−	0.301888i
$612$		0			0
$613$	−786.854	+	660.249i	−1.28361	+	1.07708i	−0.290876	+	0.956761i	$0.593947\pi$
$613$	−786.854	+	660.249i	−1.28361	+	1.07708i	−0.992735	+	0.120317i	$0.961609\pi$
$614$	30.3880	−	172.339i	0.0494919	−	0.280682i
$615$		0			0
$616$	335.951	−	193.962i	0.545376	−	0.314873i
$617$	398.587	−	145.074i	0.646007	−	0.235127i	0.00182377	−	0.999998i	$-0.499419\pi$
$617$	398.587	−	145.074i	0.646007	−	0.235127i	0.644184	+	0.764871i	$0.277197\pi$
$618$		0			0
$619$	−164.352	−	284.665i	−0.265512	−	0.459879i	0.702186	−	0.711994i	$-0.252208\pi$
$619$	−164.352	−	284.665i	−0.265512	−	0.459879i	−0.967698	+	0.252114i	$0.918874\pi$
$620$	6.03511	+	3.48437i	0.00973405	+	0.00561996i
$621$		0			0
$622$	242.454	+	288.945i	0.389797	+	0.464542i
$623$	12.5890	−	15.0030i	0.0202071	−	0.0240818i
$624$		0			0
$625$	−94.7002	−	34.4681i	−0.151520	−	0.0551489i
$626$		−	57.9284i		−	0.0925375i
$627$		0			0
$628$	69.5618			0.110767
$629$	−349.244	+	959.539i	−0.555236	+	1.52550i
$630$		0			0
$631$	90.2242	+	75.7071i	0.142986	+	0.119980i	0.711475	−	0.702711i	$-0.248027\pi$
$631$	90.2242	+	75.7071i	0.142986	+	0.119980i	−0.568489	+	0.822691i	$0.692472\pi$
$632$	−688.218	+	577.484i	−1.08895	+	0.913740i
$633$		0			0
$634$	539.483	−	934.411i	0.850919	−	1.47383i
$635$	−27.4074	+	15.8236i	−0.0431612	+	0.0249191i
$636$		0			0
$637$	214.305	+	588.799i	0.336429	+	0.924331i
$638$	149.775	+	259.418i	0.234757	+	0.406612i
$639$		0			0
$640$	287.478	+	50.6902i	0.449185	+	0.0792034i
$641$	−47.8317	−	57.0036i	−0.0746204	−	0.0889292i	0.727443	−	0.686168i	$-0.240709\pi$
$641$	−47.8317	−	57.0036i	−0.0746204	−	0.0889292i	−0.802063	+	0.597239i	$0.796264\pi$
$642$		0			0
$643$	−85.6026	−	485.476i	−0.133130	−	0.755018i	−0.976144	−	0.217126i	$-0.930332\pi$
$643$	−85.6026	−	485.476i	−0.133130	−	0.755018i	0.843014	−	0.537892i	$-0.180779\pi$
$644$	−7.19904	−	2.62024i	−0.0111786	−	0.00406869i
$645$		0			0
$646$	63.5085	+	613.896i	0.0983103	+	0.950304i
$647$	−989.083			−1.52872			−0.764361	−	0.644789i	$-0.776945\pi$
$647$	−989.083			−1.52872			−0.764361	+	0.644789i	$0.776945\pi$
$648$		0			0
$649$	−174.307	+	30.7350i	−0.268578	+	0.0473575i
$650$	−362.098	−	303.836i	−0.557074	−	0.467440i
$651$		0			0
$652$	−2.44247	+	13.8519i	−0.00374612	+	0.0212453i
$653$	−79.5099	+	137.715i	−0.121761	+	0.210896i	−0.920462	−	0.390832i	$-0.872187\pi$
$653$	−79.5099	+	137.715i	−0.121761	+	0.210896i	0.798701	+	0.601728i	$0.205521\pi$
$654$		0			0
$655$	29.4590	−	10.7222i	0.0449755	−	0.0163697i
$656$	−149.648	−	411.154i	−0.228122	−	0.626759i
$657$		0			0
$658$	−289.846	−	167.343i	−0.440496	−	0.254320i
$659$	−733.027	−	129.252i	−1.11233	−	0.196134i	−0.412860	−	0.910794i	$-0.635470\pi$
$659$	−733.027	−	129.252i	−1.11233	−	0.196134i	−0.699472	+	0.714660i	$0.746581\pi$
$660$		0			0
$661$	492.719	−	587.200i	0.745414	−	0.888350i	−0.251418	−	0.967879i	$-0.580897\pi$
$661$	492.719	−	587.200i	0.745414	−	0.888350i	0.996833	+	0.0795282i	$0.0253414\pi$
$662$	145.399	+	824.597i	0.219636	+	1.24562i
$663$		0			0
$664$			595.786i			0.897268i
$665$	−106.171	−	71.8660i	−0.159656	−	0.108069i
$666$		0			0
$667$	21.4941	−	59.0545i	0.0322250	−	0.0885375i
$668$	19.7624	−	3.48465i	0.0295845	−	0.00521654i
$669$		0			0
$670$	48.8033	−	40.9508i	0.0728407	−	0.0611206i
$671$	205.639	−	1166.23i	0.306466	−	1.73805i
$672$		0			0
$673$	695.119	−	401.327i	1.03287	−	0.596326i	0.115062	−	0.993358i	$-0.463293\pi$
$673$	695.119	−	401.327i	1.03287	−	0.596326i	0.917804	+	0.397033i	$0.129960\pi$
$674$	786.781	−	286.365i	1.16733	−	0.424874i
$675$		0			0
$676$	8.67333	+	15.0227i	0.0128304	+	0.0222229i
$677$	432.884	+	249.926i	0.639415	+	0.369166i	0.784389	−	0.620269i	$-0.212977\pi$
$677$	432.884	+	249.926i	0.639415	+	0.369166i	−0.144974	+	0.989435i	$0.546310\pi$
$678$		0			0
$679$	184.983	+	220.454i	0.272434	+	0.324674i
$680$	257.509	−	306.888i	0.378690	−	0.451305i
$681$		0			0
$682$	−205.112	−	74.6546i	−0.300751	−	0.109464i
$683$		−	52.2603i		−	0.0765159i	−0.999268	−	0.0382579i	$-0.987819\pi$
$683$		−	52.2603i		−	0.0765159i	0.999268	−	0.0382579i	$-0.0121808\pi$
$684$		0			0
$685$	−451.742			−0.659478
$686$	144.177	−	396.123i	0.210170	−	0.577438i
$687$		0			0
$688$	−266.638	−	223.736i	−0.387556	−	0.325198i
$689$	311.702	−	261.549i	0.452398	−	0.379607i
$690$		0			0
$691$	130.083	−	225.311i	0.188253	−	0.326065i	−0.756415	−	0.654093i	$-0.773051\pi$
$691$	130.083	−	225.311i	0.188253	−	0.326065i	0.944668	+	0.328028i	$0.106384\pi$
$692$	−18.6180	+	10.7491i	−0.0269047	+	0.0155334i
$693$		0			0
$694$	−2.26998	−	6.23672i	−0.00327086	−	0.00898662i
$695$	268.211	+	464.555i	0.385915	+	0.668425i
$696$		0			0
$697$	−521.933	−	92.0309i	−0.748828	−	0.132039i
$698$	−107.523	−	128.141i	−0.154044	−	0.183583i
$699$		0			0
$700$	−2.99913	−	17.0089i	−0.00428447	−	0.0242984i
$701$	451.101	+	164.187i	0.643511	+	0.234219i	0.643101	−	0.765781i	$-0.277647\pi$
$701$	451.101	+	164.187i	0.643511	+	0.234219i	0.000409474		1.00000i	$0.499870\pi$
$702$		0			0
$703$	812.137	+	786.841i	1.15524	+	1.11926i
$704$	1329.07			1.88789
$705$		0			0
$706$	234.708	−	41.3854i	0.332448	−	0.0586196i
$707$	−243.194	−	204.064i	−0.343981	−	0.288634i
$708$		0			0
$709$	73.9347	−	419.305i	0.104280	−	0.591403i	−0.887225	−	0.461337i	$-0.847370\pi$
$709$	73.9347	−	419.305i	0.104280	−	0.591403i	0.991505	−	0.130066i	$-0.0415189\pi$
$710$	101.683	−	176.120i	0.143216	−	0.248057i
$711$		0			0
$712$	63.6837	−	23.1790i	0.0894435	−	0.0325548i
$713$	15.6622	+	43.0317i	0.0219667	+	0.0603530i
$714$		0			0
$715$	674.430	+	389.382i	0.943259	+	0.544591i
$716$	94.9693	+	16.7456i	0.132639	+	0.0233878i
$717$		0			0
$718$	73.2452	−	87.2903i	0.102013	−	0.121574i
$719$	−97.6030	−	553.534i	−0.135748	−	0.769866i	−0.974336	−	0.225100i	$-0.927729\pi$
$719$	−97.6030	−	553.534i	−0.135748	−	0.769866i	0.838588	−	0.544767i	$-0.183382\pi$
$720$		0			0
$721$			31.9224i			0.0442752i
$722$	649.313	+	213.324i	0.899325	+	0.295463i
$723$		0			0
$724$	−38.4412	+	105.616i	−0.0530956	+	0.145879i
$725$	139.526	−	24.6022i	0.192450	−	0.0339341i
$726$		0			0
$727$	203.608	−	170.848i	0.280067	−	0.235004i	−0.491923	−	0.870638i	$-0.663706\pi$
$727$	203.608	−	170.848i	0.280067	−	0.235004i	0.771990	+	0.635635i	$0.219262\pi$
$728$	50.9117	−	288.735i	0.0699336	−	0.396613i
$729$		0			0
$730$	−232.747	+	134.376i	−0.318831	+	0.184077i
$731$	−396.186	+	144.200i	−0.541978	+	0.197264i
$732$		0			0
$733$	354.455	+	613.934i	0.483567	+	0.837563i	0.999822	−	0.0188721i	$-0.00600753\pi$
$733$	354.455	+	613.934i	0.483567	+	0.837563i	−0.516255	+	0.856435i	$0.672674\pi$
$734$	251.481	+	145.193i	0.342617	+	0.197810i
$735$		0			0
$736$	−32.4764	−	38.7039i	−0.0441255	−	0.0525868i
$737$	148.746	−	177.269i	0.201827	−	0.240528i
$738$		0			0
$739$	584.475	+	212.732i	0.790901	+	0.287864i	0.705710	−	0.708500i	$-0.250628\pi$
$739$	584.475	+	212.732i	0.790901	+	0.287864i	0.0851902	+	0.996365i	$0.472850\pi$
$740$		−	69.0950i		−	0.0933716i
$741$		0			0
$742$	−128.205			−0.172783
$743$	174.096	−	478.325i	0.234315	−	0.643775i	−0.765685	−	0.643216i	$-0.777600\pi$
$743$	174.096	−	478.325i	0.234315	−	0.643775i	1.00000		0.000559205i	$-0.000178000\pi$
$744$		0			0
$745$	−300.753	−	252.362i	−0.403696	−	0.338741i
$746$	386.390	−	324.220i	0.517950	−	0.434611i
$747$		0			0
$748$	68.4896	−	118.627i	0.0915636	−	0.158593i
$749$	229.194	−	132.325i	0.305999	−	0.176669i
$750$		0			0
$751$	−185.743	−	510.324i	−0.247327	−	0.679525i	−0.999782	−	0.0208816i	$-0.993353\pi$
$751$	−185.743	−	510.324i	−0.247327	−	0.679525i	0.752455	−	0.658644i	$-0.228870\pi$
$752$	−518.233	−	897.606i	−0.689140	−	1.19362i
$753$		0			0
$754$	222.958	+	39.3135i	0.295700	+	0.0521399i
$755$	−182.414	−	217.393i	−0.241608	−	0.287937i
$756$		0			0
$757$	−106.917	−	606.358i	−0.141238	−	0.801001i	−0.970311	−	0.241860i	$-0.922242\pi$
$757$	−106.917	−	606.358i	−0.141238	−	0.801001i	0.829073	−	0.559140i	$-0.188869\pi$
$758$	−1192.13	−	433.901i	−1.57274	−	0.572429i
$759$		0			0
$760$	−193.827	−	399.058i	−0.255035	−	0.525076i
$761$	−841.391			−1.10564			−0.552819	−	0.833301i	$-0.686448\pi$
$761$	−841.391			−1.10564			−0.552819	+	0.833301i	$0.686448\pi$
$762$		0			0
$763$	490.356	−	86.4630i	0.642669	−	0.113320i
$764$	−25.9367	−	21.7635i	−0.0339485	−	0.0284862i
$765$		0			0
$766$	226.808	−	1286.29i	0.296093	−	1.67923i
$767$	−66.8860	+	115.850i	−0.0872046	+	0.151043i
$768$		0			0
$769$	−735.497	+	267.699i	−0.956434	+	0.348113i	−0.772635	−	0.634851i	$-0.781062\pi$
$769$	−735.497	+	267.699i	−0.956434	+	0.348113i	−0.183799	+	0.982964i	$0.558839\pi$
$770$	−83.9224	−	230.575i	−0.108990	−	0.299448i
$771$		0			0
$772$	−10.7383	−	6.19973i	−0.0139097	−	0.00803074i
$773$	950.278	+	167.560i	1.22934	+	0.216765i	0.750341	−	0.661051i	$-0.229889\pi$
$773$	950.278	+	167.560i	1.22934	+	0.216765i	0.478997	+	0.877816i	$0.341000\pi$
$774$		0			0
$775$	−66.3600	+	79.0847i	−0.0856257	+	0.102045i
$776$	172.923	+	980.695i	0.222839	+	1.26378i
$777$		0			0
$778$			427.549i			0.549548i
$779$	−328.989	+	486.030i	−0.422322	+	0.623915i
$780$		0			0
$781$	252.647	−	694.141i	0.323491	−	0.888785i
$782$	244.045	−	43.0317i	0.312078	−	0.0550278i
$783$		0			0
$784$	468.352	−	392.994i	0.597388	−	0.501268i
$785$	81.1662	−	460.317i	0.103396	−	0.586391i
$786$		0			0
$787$	−1163.29	+	671.627i	−1.47814	+	0.853402i	−0.999694	−	0.0247177i	$-0.992131\pi$
$787$	−1163.29	+	671.627i	−1.47814	+	0.853402i	−0.478441	+	0.878120i	$0.658798\pi$
$788$	−70.3222	+	25.5952i	−0.0892414	+	0.0324812i
$789$		0			0
$790$	284.134	+	492.134i	0.359663	+	0.622954i
$791$	38.4285	+	22.1867i	0.0485822	+	0.0280489i
$792$		0			0
$793$	−575.312	−	685.630i	−0.725488	−	0.864603i
$794$	735.750	−	876.833i	0.926637	−	1.10432i
$795$		0			0
$796$	−43.0154	−	15.6563i	−0.0540394	−	0.0196687i
$797$			1393.79i			1.74880i	0.485209	+	0.874398i	$0.338743\pi$
$797$			1393.79i			1.74880i	−0.485209	+	0.874398i	$0.661257\pi$
$798$		0			0
$799$	−1255.45			−1.57128
$800$	38.9572	−	107.034i	0.0486966	−	0.133793i
$801$		0			0
$802$	470.153	+	394.505i	0.586225	+	0.491901i
$803$	−747.809	+	627.486i	−0.931268	+	0.781427i
$804$		0			0
$805$	−25.7391	+	44.5814i	−0.0319740	+	0.0553806i
$806$	−142.869	+	82.4853i	−0.177257	+	0.102339i
$807$		0			0
$808$	−375.725	−	1032.30i	−0.465006	−	1.27759i
$809$	−650.512	−	1126.72i	−0.804095	−	1.39273i	−0.916901	−	0.399116i	$-0.869317\pi$
$809$	−650.512	−	1126.72i	−0.804095	−	1.39273i	0.112806	−	0.993617i	$-0.464016\pi$
$810$		0			0
$811$	−1454.46	−	256.460i	−1.79341	−	0.316227i	−0.824917	−	0.565254i	$-0.808778\pi$
$811$	−1454.46	−	256.460i	−1.79341	−	0.316227i	−0.968497	+	0.249027i	$0.919889\pi$
$812$	5.31731	+	6.33692i	0.00654841	+	0.00780409i
$813$		0			0
$814$	375.809	+	2131.32i	0.461682	+	2.61833i
$815$	88.8136	+	32.3255i	0.108974	+	0.0396632i
$816$		0			0
$817$	−33.3303	+	465.703i	−0.0407960	+	0.570016i
$818$	494.961			0.605087
$819$		0			0
$820$	35.3171	−	6.22735i	0.0430696	−	0.00759433i
$821$	91.1195	+	76.4583i	0.110986	+	0.0931283i	0.696592	−	0.717468i	$-0.254699\pi$
$821$	91.1195	+	76.4583i	0.110986	+	0.0931283i	−0.585606	+	0.810596i	$0.699143\pi$
$822$		0			0
$823$	−182.307	+	1033.92i	−0.221516	+	1.25628i	0.647720	+	0.761879i	$0.275723\pi$
$823$	−182.307	+	1033.92i	−0.221516	+	1.25628i	−0.869235	+	0.494398i	$0.835388\pi$
$824$	−55.2313	+	95.6634i	−0.0670282	+	0.116096i
$825$		0			0
$826$	39.6069	−	14.4157i	0.0479502	−	0.0174524i
$827$	−125.480	−	344.754i	−0.151729	−	0.416873i	0.840419	−	0.541937i	$-0.182309\pi$
$827$	−125.480	−	344.754i	−0.151729	−	0.416873i	−0.992149	+	0.125064i	$0.960086\pi$
$828$		0			0
$829$	290.861	+	167.929i	0.350858	+	0.202568i	0.665063	−	0.746787i	$-0.268405\pi$
$829$	290.861	+	167.929i	0.350858	+	0.202568i	−0.314205	+	0.949355i	$0.601738\pi$
$830$	371.127	+	65.4396i	0.447141	+	0.0788429i
$831$		0			0
$832$	645.681	−	769.492i	0.776059	−	0.924871i
$833$	−128.598	−	729.315i	−0.154379	−	0.875528i
$834$		0			0
$835$		−	134.841i		−	0.161487i
$836$	−88.9609	−	122.866i	−0.106413	−	0.146969i
$837$		0			0
$838$	−157.224	+	431.970i	−0.187619	+	0.515478i
$839$	−1038.92	+	183.189i	−1.23828	+	0.218342i	−0.754178	−	0.656670i	$-0.771965\pi$
$839$	−1038.92	+	183.189i	−1.23828	+	0.218342i	−0.484102	+	0.875012i	$0.660853\pi$
$840$		0			0
$841$	592.261	−	496.966i	0.704234	−	0.590923i
$842$	−182.721	+	1036.26i	−0.217008	+	1.23071i
$843$		0			0
$844$	−55.4038	+	31.9874i	−0.0656443	+	0.0378998i
$845$	109.531	−	39.8660i	0.129622	−	0.0471787i
$846$		0			0
$847$	−299.473	−	518.702i	−0.353569	−	0.612399i
$848$	−343.838	−	198.515i	−0.405469	−	0.234098i
$849$		0			0
$850$	359.106	+	427.966i	0.422477	+	0.503489i
$851$	291.851	−	347.815i	0.342951	−	0.408713i
$852$		0			0
$853$	−504.478	−	183.615i	−0.591417	−	0.215258i	0.0289358	−	0.999581i	$-0.490788\pi$
$853$	−504.478	−	183.615i	−0.591417	−	0.215258i	−0.620352	+	0.784323i	$0.713010\pi$
$854$			282.004i			0.330216i
$855$		0			0
$856$	915.780			1.06984
$857$	426.906	−	1172.91i	0.498140	−	1.36863i	−0.394930	−	0.918711i	$-0.629231\pi$
$857$	426.906	−	1172.91i	0.498140	−	1.36863i	0.893070	−	0.449917i	$-0.148546\pi$
$858$		0			0
$859$	−387.840	−	325.436i	−0.451502	−	0.378855i	0.388491	−	0.921453i	$-0.372996\pi$
$859$	−387.840	−	325.436i	−0.451502	−	0.378855i	−0.839993	+	0.542598i	$0.817441\pi$
$860$	21.8543	−	18.3379i	0.0254120	−	0.0213232i
$861$		0			0
$862$	6.06244	−	10.5005i	0.00703299	−	0.0121815i
$863$	−1102.47	+	636.511i	−1.27748	+	0.737556i	−0.976385	−	0.216037i	$-0.930687\pi$
$863$	−1102.47	+	636.511i	−1.27748	+	0.737556i	−0.301099	+	0.953593i	$0.597354\pi$
$864$		0			0
$865$	49.4072	+	135.745i	0.0571181	+	0.156931i
$866$	−54.2095	−	93.8937i	−0.0625976	−	0.108422i
$867$		0			0
$868$	−5.93623	−	1.04672i	−0.00683898	−	0.00120590i
$869$	1326.79	+	1581.21i	1.52681	+	1.81958i
$870$		0			0
$871$	−30.3704	−	172.239i	−0.0348684	−	0.197749i
$872$	1619.07	+	589.293i	1.85673	+	0.675794i
$873$		0			0
$874$	66.8247	−	266.165i	0.0764584	−	0.304536i
$875$	−284.747			−0.325425
$876$		0			0
$877$	303.148	−	53.4532i	0.345665	−	0.0609500i	0.00187921	−	0.999998i	$-0.499402\pi$
$877$	303.148	−	53.4532i	0.345665	−	0.0609500i	0.343785	+	0.939048i	$0.388291\pi$
$878$	−759.322	−	637.147i	−0.864831	−	0.725680i
$879$		0			0
$880$	131.951	−	748.334i	0.149945	−	0.850380i
$881$	117.273	−	203.123i	0.133113	−	0.230559i	−0.791762	−	0.610830i	$-0.790836\pi$
$881$	117.273	−	203.123i	0.133113	−	0.230559i	0.924875	+	0.380271i	$0.124169\pi$
$882$		0			0
$883$	258.816	−	94.2012i	0.293110	−	0.106683i	−0.191280	−	0.981535i	$-0.561264\pi$
$883$	258.816	−	94.2012i	0.293110	−	0.106683i	0.484390	+	0.874852i	$0.339042\pi$
$884$	−35.4085	−	97.2841i	−0.0400549	−	0.110050i
$885$		0			0
$886$	−712.450	−	411.333i	−0.804120	−	0.464259i
$887$	−332.187	−	58.5735i	−0.374506	−	0.0660355i	−0.0167728	−	0.999859i	$-0.505339\pi$
$887$	−332.187	−	58.5735i	−0.374506	−	0.0660355i	−0.357733	+	0.933824i	$0.616450\pi$
$888$		0			0
$889$	17.5958	−	20.9698i	0.0197928	−	0.0235881i
$890$	−7.44378	−	42.2158i	−0.00836380	−	0.0474334i
$891$		0			0
$892$			64.6905i			0.0725230i
$893$	−567.557	+	1269.17i	−0.635563	+	1.42124i
$894$		0			0
$895$	221.625	−	608.909i	0.247625	−	0.680345i
$896$	−248.662	+	43.8458i	−0.277525	+	0.0489351i
$897$		0			0
$898$	−455.978	+	382.611i	−0.507770	+	0.426070i
$899$	8.58634	−	48.6956i	0.00955099	−	0.0541664i
$900$		0			0
$901$	−416.485	+	240.457i	−0.462247	+	0.266878i
$902$	−1055.53	+	384.181i	−1.17021	+	0.425921i
$903$		0			0
$904$	76.7736	+	132.976i	0.0849266	+	0.147097i
$905$	654.049	+	377.616i	0.722706	+	0.417255i
$906$		0			0
$907$	−164.258	−	195.755i	−0.181100	−	0.215827i	0.667855	−	0.744291i	$-0.267212\pi$
$907$	−164.258	−	195.755i	−0.181100	−	0.215827i	−0.848956	+	0.528464i	$0.822768\pi$
$908$	−17.9235	+	21.3603i	−0.0197395	+	0.0235246i
$909$		0			0
$910$	−174.266	−	63.4278i	−0.191501	−	0.0697008i
$911$		−	598.961i		−	0.657477i	−0.944421	−	0.328738i	$-0.893377\pi$
$911$		−	598.961i		−	0.657477i	0.944421	−	0.328738i	$-0.106623\pi$
$912$		0			0
$913$	1368.84			1.49928
$914$	−340.073	+	934.343i	−0.372071	+	1.02226i
$915$		0			0
$916$	22.0580	+	18.5088i	0.0240808	+	0.0202062i
$917$	−20.7726	+	17.4303i	−0.0226527	+	0.0190079i
$918$		0			0
$919$	−724.843	+	1255.46i	−0.788730	+	1.36612i	0.138015	+	0.990430i	$0.455928\pi$
$919$	−724.843	+	1255.46i	−0.788730	+	1.36612i	−0.926745	+	0.375691i	$0.877406\pi$
$920$	−154.267	+	89.0661i	−0.167682	+	0.0968110i
$921$		0			0
$922$	394.732	+	1084.52i	0.428126	+	1.17627i
$923$	−279.147	−	483.497i	−0.302435	−	0.523832i
$924$		0			0
$925$	1008.05	+	177.746i	1.08978	+	0.192158i
$926$	929.066	+	1107.22i	1.00331	+	1.19570i
$927$		0			0
$928$	9.47341	+	53.7264i	0.0102084	+	0.0578948i
$929$	−1664.16	−	605.703i	−1.79134	−	0.651995i	−0.999128	−	0.0417491i	$-0.986707\pi$
$929$	−1664.16	−	605.703i	−1.79134	−	0.651995i	−0.792212	−	0.610246i	$-0.791071\pi$
$930$		0			0
$931$	−795.418	−	199.702i	−0.854369	−	0.214503i
$932$	67.8414			0.0727912
$933$		0			0
$934$	836.445	−	147.488i	0.895551	−	0.157910i
$935$	−705.088	−	591.639i	−0.754104	−	0.632769i
$936$		0			0
$937$	−112.461	+	637.796i	−0.120022	+	0.680678i	0.864119	+	0.503288i	$0.167877\pi$
$937$	−112.461	+	637.796i	−0.120022	+	0.680678i	−0.984141	+	0.177390i	$0.943235\pi$
$938$	−27.5531	+	47.7233i	−0.0293743	+	0.0508777i
$939$		0			0
$940$	79.8281	−	29.0550i	0.0849235	−	0.0309096i
$941$	463.502	+	1273.46i	0.492563	+	1.35331i	0.898327	+	0.439328i	$0.144783\pi$
$941$	463.502	+	1273.46i	0.492563	+	1.35331i	−0.405764	+	0.913978i	$0.632995\pi$
$942$		0			0
$943$	204.085	+	117.829i	0.216421	+	0.124951i
$944$	128.545	+	22.6659i	0.136170	+	0.0240105i
$945$		0			0
$946$	−574.382	+	684.522i	−0.607170	+	0.723597i
$947$	55.2366	+	313.263i	0.0583280	+	0.330795i	0.999983	−	0.00578427i	$-0.00184120\pi$
$947$	55.2366	+	313.263i	0.0583280	+	0.330795i	−0.941655	+	0.336579i	$0.890730\pi$
$948$		0			0
$949$			737.799i			0.777449i
$950$	594.983	−	169.556i	0.626298	−	0.178480i
$951$		0			0
$952$	−118.517	+	325.624i	−0.124493	+	0.342042i
$953$	904.106	−	159.418i	0.948694	−	0.167280i	0.322170	−	0.946682i	$-0.395588\pi$
$953$	904.106	−	159.418i	0.948694	−	0.167280i	0.626525	+	0.779401i	$0.284477\pi$
$954$		0			0
$955$	−174.281	+	146.239i	−0.182493	+	0.153130i
$956$	−22.0602	+	125.110i	−0.0230756	+	0.130868i
$957$		0			0
$958$	−1142.24	+	659.474i	−1.19232	+	0.688387i
$959$	367.182	−	133.643i	0.382880	−	0.139357i
$960$		0			0
$961$	−462.485	−	801.047i	−0.481254	−	0.833556i
$962$	1416.54	+	817.840i	1.47250	+	0.850146i
$963$		0			0
$964$	−64.1373	−	76.4358i	−0.0665324	−	0.0792903i
$965$	−53.5556	+	63.8251i	−0.0554981	+	0.0661400i
$966$		0			0
$967$	−368.728	−	134.206i	−0.381311	−	0.138786i	0.144251	−	0.989541i	$-0.453923\pi$
$967$	−368.728	−	134.206i	−0.381311	−	0.138786i	−0.525562	+	0.850755i	$0.676145\pi$
$968$		−	2072.56i		−	2.14107i
$969$		0			0
$970$	629.888			0.649369
$971$	−161.114	+	442.657i	−0.165926	+	0.455877i	−0.994591	−	0.103867i	$-0.966878\pi$
$971$	−161.114	+	442.657i	−0.165926	+	0.455877i	0.828666	+	0.559744i	$0.189101\pi$
$972$		0			0
$973$	−355.439	−	298.249i	−0.365302	−	0.306525i
$974$	−28.1757	+	23.6422i	−0.0289278	+	0.0242733i
$975$		0			0
$976$	−436.660	+	756.317i	−0.447398	+	0.774915i
$977$	−170.882	+	98.6590i	−0.174905	+	0.100982i	−0.584897	−	0.811108i	$-0.698865\pi$
$977$	−170.882	+	98.6590i	−0.174905	+	0.100982i	0.409991	+	0.912089i	$0.365532\pi$
$978$		0			0
$979$	−53.2547	−	146.316i	−0.0543971	−	0.149455i
$980$	25.0555	+	43.3974i	0.0255669	+	0.0442831i
$981$		0			0
$982$	1234.93	+	217.752i	1.25757	+	0.221743i
$983$	494.260	+	589.036i	0.502808	+	0.599223i	0.956427	−	0.291973i	$-0.0943117\pi$
$983$	494.260	+	589.036i	0.502808	+	0.599223i	−0.453619	+	0.891196i	$0.649867\pi$
$984$		0			0
$985$	87.3196	+	495.214i	0.0886493	+	0.502755i
$986$	−251.443	−	91.5179i	−0.255014	−	0.0928173i
$987$		0			0
$988$	−114.354	−	8.18431i	−0.115743	−	0.00828372i
$989$	187.470			0.189555
$990$		0			0
$991$	1718.71	−	303.054i	1.73431	−	0.305806i	0.784851	−	0.619685i	$-0.212740\pi$
$991$	1718.71	−	303.054i	1.73431	−	0.305806i	0.949463	+	0.313878i	$0.101628\pi$
$992$	−30.4526	−	25.5528i	−0.0306982	−	0.0257589i
$993$		0			0
$994$	−30.5459	+	173.235i	−0.0307303	+	0.174280i
$995$	−153.795	+	266.381i	−0.154568	+	0.267719i
$996$		0			0
$997$	1158.78	−	421.762i	1.16227	−	0.423031i	0.312362	−	0.949963i	$-0.398880\pi$
$997$	1158.78	−	421.762i	1.16227	−	0.423031i	0.849908	+	0.526932i	$0.176658\pi$
$998$	−86.5114	−	237.688i	−0.0866847	−	0.238164i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	171.3.ba.b.91.1		12
3.2	odd	2		19.3.f.a.15.2	yes	12
12.11	even	2		304.3.z.a.129.2		12
19.14	odd	18	inner	171.3.ba.b.109.1		12
57.2	even	18		361.3.f.e.307.2		12
57.5	odd	18		361.3.f.g.299.1		12
57.8	even	6		361.3.f.b.333.2		12
57.11	odd	6		361.3.f.f.333.1		12
57.14	even	18		19.3.f.a.14.2	✓	12
57.17	odd	18		361.3.f.c.307.1		12
57.23	odd	18		361.3.d.f.69.5		12
57.26	odd	6		361.3.f.e.127.2		12
57.29	even	18		361.3.b.c.360.4		12
57.32	even	18		361.3.d.f.293.5		12
57.35	odd	18		361.3.f.b.116.2		12
57.41	even	18		361.3.f.f.116.1		12
57.44	odd	18		361.3.d.d.293.2		12
57.47	odd	18		361.3.b.c.360.9		12
57.50	even	6		361.3.f.c.127.1		12
57.53	even	18		361.3.d.d.69.2		12
57.56	even	2		361.3.f.g.262.1		12
228.71	odd	18		304.3.z.a.33.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
19.3.f.a.14.2	✓	12	57.14	even	18
19.3.f.a.15.2	yes	12	3.2	odd	2
171.3.ba.b.91.1		12	1.1	even	1	trivial
171.3.ba.b.109.1		12	19.14	odd	18	inner
304.3.z.a.33.2		12	228.71	odd	18
304.3.z.a.129.2		12	12.11	even	2
361.3.b.c.360.4		12	57.29	even	18
361.3.b.c.360.9		12	57.47	odd	18
361.3.d.d.69.2		12	57.53	even	18
361.3.d.d.293.2		12	57.44	odd	18
361.3.d.f.69.5		12	57.23	odd	18
361.3.d.f.293.5		12	57.32	even	18
361.3.f.b.116.2		12	57.35	odd	18
361.3.f.b.333.2		12	57.8	even	6
361.3.f.c.127.1		12	57.50	even	6
361.3.f.c.307.1		12	57.17	odd	18
361.3.f.e.127.2		12	57.26	odd	6
361.3.f.e.307.2		12	57.2	even	18
361.3.f.f.116.1		12	57.41	even	18
361.3.f.f.333.1		12	57.11	odd	6
361.3.f.g.262.1		12	57.56	even	2
361.3.f.g.299.1		12	57.5	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.ba (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.647524 + 1.77906i) q^{2} +(0.318417 + 0.267183i) q^{4} +(2.13959 - 1.79533i) q^{5} +(-1.20796 + 2.09224i) q^{7} +(-7.23987 + 4.17994i) q^{8} +O(q^{10})\)	\(q+(-0.647524 + 1.77906i) q^{2} +(0.318417 + 0.267183i) q^{4} +(2.13959 - 1.79533i) q^{5} +(-1.20796 + 2.09224i) q^{7} +(-7.23987 + 4.17994i) q^{8} +(1.80856 + 4.96897i) q^{10} +(9.60360 + 16.6339i) q^{11} +(14.2961 + 2.52079i) q^{13} +(-2.94004 - 3.50380i) q^{14} +(-2.45965 - 13.9494i) q^{16} +(-16.1226 - 5.86814i) q^{17} +(-13.2208 + 13.6459i) q^{19} +1.16096 q^{20} +(-35.8113 + 6.31450i) q^{22} +(5.84413 + 4.90381i) q^{23} +(-2.98657 + 16.9377i) q^{25} +(-13.7417 + 23.8013i) q^{26} +(-0.943645 + 0.343459i) q^{28} +(-2.81743 - 7.74083i) q^{29} +(5.19837 + 3.00128i) q^{31} +(-6.52208 - 1.15002i) q^{32} +(20.8795 - 24.8832i) q^{34} +(1.17173 + 6.64521i) q^{35} -59.5153i q^{37} +(-15.7160 - 32.3567i) q^{38} +(-7.98598 + 21.9413i) q^{40} +(30.4205 - 5.36396i) q^{41} +(18.8243 - 15.7955i) q^{43} +(-1.38636 + 7.86244i) q^{44} +(-12.5084 + 7.22171i) q^{46} +(68.7602 - 25.0267i) q^{47} +(21.5817 + 37.3806i) q^{49} +(-28.1992 - 16.2808i) q^{50} +(3.87860 + 4.62234i) q^{52} +(18.0172 - 21.4721i) q^{53} +(50.4111 + 18.3482i) q^{55} -20.1968i q^{56} +15.5957 q^{58} +(-3.15174 + 8.65934i) q^{59} +(-47.2307 - 39.6312i) q^{61} +(-8.70552 + 7.30480i) q^{62} +(34.5983 - 59.9260i) q^{64} +(35.1134 - 20.2727i) q^{65} +(-4.12065 - 11.3214i) q^{67} +(-3.56583 - 6.17619i) q^{68} +(-12.5809 - 2.21836i) q^{70} +(-24.7209 - 29.4613i) q^{71} +(8.82556 + 50.0523i) q^{73} +(105.881 + 38.5376i) q^{74} +(-7.85568 + 0.812682i) q^{76} -46.4029 q^{77} +(105.834 - 18.6613i) q^{79} +(-30.3064 - 25.4301i) q^{80} +(-10.1552 + 57.5932i) q^{82} +(35.6336 - 61.7192i) q^{83} +(-45.0309 + 16.3899i) q^{85} +(15.9119 + 43.7175i) q^{86} +(-139.058 - 80.2850i) q^{88} +(-7.98351 - 1.40771i) q^{89} +(-22.5431 + 26.8659i) q^{91} +(0.550653 + 3.12291i) q^{92} +138.534i q^{94} +(-3.78836 + 52.9323i) q^{95} +(40.7412 - 111.936i) q^{97} +(-80.4769 + 14.1902i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 6 q^{2} + 6 q^{5} + 6 q^{7} + 9 q^{8}+O(q^{10}) \) 12 * q + 6 * q^2 + 6 * q^5 + 6 * q^7 + 9 * q^8	\( 12 q + 6 q^{2} + 6 q^{5} + 6 q^{7} + 9 q^{8} + 51 q^{10} + 18 q^{11} + 21 q^{13} - 9 q^{14} - 12 q^{16} + 3 q^{17} - 24 q^{19} + 90 q^{20} - 78 q^{22} + 102 q^{23} - 156 q^{25} - 21 q^{26} + 12 q^{28} - 147 q^{29} + 99 q^{31} - 165 q^{32} + 132 q^{34} - 96 q^{35} - 72 q^{38} - 138 q^{40} + 144 q^{41} - 27 q^{43} + 123 q^{44} - 54 q^{46} + 99 q^{47} - 24 q^{49} - 72 q^{50} + 93 q^{52} - 111 q^{53} + 162 q^{55} - 132 q^{58} - 3 q^{59} + 150 q^{61} - 108 q^{62} + 27 q^{64} - 126 q^{65} + 135 q^{67} + 30 q^{68} + 225 q^{70} + 168 q^{71} - 90 q^{73} + 231 q^{74} + 42 q^{76} - 246 q^{77} - 75 q^{79} - 21 q^{80} - 117 q^{82} + 156 q^{83} - 300 q^{85} + 144 q^{86} - 405 q^{88} + 558 q^{89} - 453 q^{91} - 48 q^{92} + 69 q^{95} + 465 q^{97} - 777 q^{98}+O(q^{100}) \) 12 * q + 6 * q^2 + 6 * q^5 + 6 * q^7 + 9 * q^8 + 51 * q^10 + 18 * q^11 + 21 * q^13 - 9 * q^14 - 12 * q^16 + 3 * q^17 - 24 * q^19 + 90 * q^20 - 78 * q^22 + 102 * q^23 - 156 * q^25 - 21 * q^26 + 12 * q^28 - 147 * q^29 + 99 * q^31 - 165 * q^32 + 132 * q^34 - 96 * q^35 - 72 * q^38 - 138 * q^40 + 144 * q^41 - 27 * q^43 + 123 * q^44 - 54 * q^46 + 99 * q^47 - 24 * q^49 - 72 * q^50 + 93 * q^52 - 111 * q^53 + 162 * q^55 - 132 * q^58 - 3 * q^59 + 150 * q^61 - 108 * q^62 + 27 * q^64 - 126 * q^65 + 135 * q^67 + 30 * q^68 + 225 * q^70 + 168 * q^71 - 90 * q^73 + 231 * q^74 + 42 * q^76 - 246 * q^77 - 75 * q^79 - 21 * q^80 - 117 * q^82 + 156 * q^83 - 300 * q^85 + 144 * q^86 - 405 * q^88 + 558 * q^89 - 453 * q^91 - 48 * q^92 + 69 * q^95 + 465 * q^97 - 777 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more