LMFDB - Embedded newform 912.2.bo.j.385.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [912,2,Mod(289,912)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("912.289"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(912, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([0, 0, 0, 2])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 912 = 2^{4} \cdot 3 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	912.bo (of order $9$, degree $6$, not minimal)

Newform invariants

comment:select newform

sage:traces = [12,0,0,0,6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$7.28235666434$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$2$ over $\Q(\zeta_{9})$
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} - 6 x^{11} + 33 x^{10} - 110 x^{9} + 318 x^{8} - 678 x^{7} + 1225 x^{6} - 1698 x^{5} + 1905 x^{4} + \cdots + 57 $ x^12 - 6x^11 + 33x^10 - 110x^9 + 318x^8 - 678x^7 + 1225x^6 - 1698x^5 + 1905x^4 - 1584x^3 + 936x^2 - 342*x + 57
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 57)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			385.1
Root			$0.500000 - 1.80139i$ of defining polynomial
Character	$\chi$	$=$	912.385
Dual form			912.2.bo.j.289.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.173648 + 0.984808i) q^{3} +(1.30800 + 1.09754i) q^{5} +(1.96517 + 3.40377i) q^{7} +(-0.939693 - 0.342020i) q^{9} +(2.21268 - 3.83247i) q^{11} +(0.316842 + 1.79690i) q^{13} +(-1.30800 + 1.09754i) q^{15} +(4.72331 - 1.71914i) q^{17} +(1.33604 + 4.14910i) q^{19} +(-3.69330 + 1.34425i) q^{21} +(-2.64922 + 2.22296i) q^{23} +(-0.361980 - 2.05289i) q^{25} +(0.500000 - 0.866025i) q^{27} +(1.36276 + 0.496003i) q^{29} +(-1.43471 - 2.48499i) q^{31} +(3.39002 + 2.84456i) q^{33} +(-1.16534 + 6.60896i) q^{35} -4.83123 q^{37} -1.82462 q^{39} +(-1.52950 + 8.67423i) q^{41} +(-7.73836 - 6.49325i) q^{43} +(-0.853733 - 1.47871i) q^{45} +(3.22814 + 1.17495i) q^{47} +(-4.22376 + 7.31577i) q^{49} +(0.872832 + 4.95008i) q^{51} +(-1.61814 + 1.35778i) q^{53} +(7.10045 - 2.58435i) q^{55} +(-4.31806 + 0.595259i) q^{57} +(6.01966 - 2.19098i) q^{59} +(0.0587523 - 0.0492990i) q^{61} +(-0.682495 - 3.87062i) q^{63} +(-1.55774 + 2.69809i) q^{65} +(-0.984002 - 0.358147i) q^{67} +(-1.72915 - 2.99498i) q^{69} +(10.3790 + 8.70898i) q^{71} +(0.696538 - 3.95026i) q^{73} +2.08456 q^{75} +17.3931 q^{77} +(-2.94592 + 16.7071i) q^{79} +(0.766044 + 0.642788i) q^{81} +(-6.51259 - 11.2801i) q^{83} +(8.06489 + 2.93538i) q^{85} +(-0.725109 + 1.25592i) q^{87} +(2.14695 + 12.1759i) q^{89} +(-5.49359 + 4.60967i) q^{91} +(2.69638 - 0.981401i) q^{93} +(-2.80626 + 6.89335i) q^{95} +(-0.164685 + 0.0599404i) q^{97} +(-3.39002 + 2.84456i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 6 q^{5} + 9 q^{7} + 9 q^{11} - 3 q^{13} - 6 q^{15} + 12 q^{17} + 9 q^{19} - 9 q^{23} - 12 q^{25} + 6 q^{27} - 9 q^{33} - 30 q^{35} - 12 q^{37} - 6 q^{39} - 18 q^{41} - 15 q^{43} - 9 q^{45} + 9 q^{47}+ \cdots + 9 q^{99}+O(q^{100}) $ 12 * q + 6 * q^5 + 9 * q^7 + 9 * q^11 - 3 * q^13 - 6 * q^15 + 12 * q^17 + 9 * q^19 - 9 * q^23 - 12 * q^25 + 6 * q^27 - 9 * q^33 - 30 * q^35 - 12 * q^37 - 6 * q^39 - 18 * q^41 - 15 * q^43 - 9 * q^45 + 9 * q^47 - 9 * q^49 + 15 * q^51 - 30 * q^53 - 15 * q^55 - 3 * q^57 + 30 * q^59 + 21 * q^61 - 9 * q^63 + 21 * q^65 - 3 * q^67 - 6 * q^69 + 30 * q^71 - 24 * q^73 - 30 * q^75 + 96 * q^77 - 24 * q^79 - 3 * q^83 + 3 * q^85 - 15 * q^87 + 3 * q^89 - 24 * q^91 - 6 * q^93 + 54 * q^95 - 27 * q^97 + 9 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/912\mathbb{Z}\right)^\times$.

$n$	$97$	$229$	$305$	$799$
$\chi(n)$	$e\left(\frac{8}{9}\right)$	$1$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.173648	+	0.984808i	−0.100256	+	0.568579i
$3$	−0.173648	+	0.984808i	−0.100256	+	0.568579i
$4$		0			0
$5$	1.30800	+	1.09754i	0.584953	+	0.490834i	0.886570	−	0.462595i	$-0.153082\pi$
$5$	1.30800	+	1.09754i	0.584953	+	0.490834i	−0.301616	+	0.953429i	$0.597526\pi$
$6$		0			0
$7$	1.96517	+	3.40377i	0.742763	+	1.28650i	0.951233	+	0.308475i	$0.0998185\pi$
$7$	1.96517	+	3.40377i	0.742763	+	1.28650i	−0.208469	+	0.978029i	$0.566848\pi$
$8$		0			0
$9$	−0.939693	−	0.342020i	−0.313231	−	0.114007i
$10$		0			0
$11$	2.21268	−	3.83247i	0.667147	−	1.15553i	−0.311551	−	0.950229i	$-0.600849\pi$
$11$	2.21268	−	3.83247i	0.667147	−	1.15553i	0.978698	−	0.205303i	$-0.0658181\pi$
$12$		0			0
$13$	0.316842	+	1.79690i	0.0878763	+	0.498371i	0.996699	+	0.0811881i	$0.0258714\pi$
$13$	0.316842	+	1.79690i	0.0878763	+	0.498371i	−0.908823	+	0.417183i	$0.863017\pi$
$14$		0			0
$15$	−1.30800	+	1.09754i	−0.337723	+	0.283383i
$16$		0			0
$17$	4.72331	−	1.71914i	1.14557	−	0.416954i	0.301648	−	0.953419i	$-0.402463\pi$
$17$	4.72331	−	1.71914i	1.14557	−	0.416954i	0.843922	+	0.536466i	$0.180241\pi$
$18$		0			0
$19$	1.33604	+	4.14910i	0.306508	+	0.951868i
$19$	1.33604	+	4.14910i	0.306508	+	0.951868i
$20$		0			0
$21$	−3.69330	+	1.34425i	−0.805945	+	0.293340i
$22$		0			0
$23$	−2.64922	+	2.22296i	−0.552400	+	0.463519i	−0.875753	−	0.482760i	$-0.839634\pi$
$23$	−2.64922	+	2.22296i	−0.552400	+	0.463519i	0.323353	+	0.946278i	$0.395190\pi$
$24$		0			0
$25$	−0.361980	−	2.05289i	−0.0723959	−	0.410578i
$26$		0			0
$27$	0.500000	−	0.866025i	0.0962250	−	0.166667i
$28$		0			0
$29$	1.36276	+	0.496003i	0.253058	+	0.0921055i	0.465434	−	0.885082i	$-0.345898\pi$
$29$	1.36276	+	0.496003i	0.253058	+	0.0921055i	−0.212377	+	0.977188i	$0.568120\pi$
$30$		0			0
$31$	−1.43471	−	2.48499i	−0.257682	−	0.446318i	0.707939	−	0.706274i	$-0.249625\pi$
$31$	−1.43471	−	2.48499i	−0.257682	−	0.446318i	−0.965621	+	0.259956i	$0.916292\pi$
$32$		0			0
$33$	3.39002	+	2.84456i	0.590126	+	0.495175i
$34$		0			0
$35$	−1.16534	+	6.60896i	−0.196978	+	1.11712i
$36$		0			0
$37$	−4.83123			−0.794249			−0.397124	−	0.917765i	$-0.629992\pi$
$37$	−4.83123			−0.794249			−0.397124	+	0.917765i	$0.629992\pi$
$38$		0			0
$39$	−1.82462			−0.292173
$40$		0			0
$41$	−1.52950	+	8.67423i	−0.238868	+	1.35469i	0.595445	+	0.803396i	$0.296976\pi$
$41$	−1.52950	+	8.67423i	−0.238868	+	1.35469i	−0.834313	+	0.551291i	$0.814135\pi$
$42$		0			0
$43$	−7.73836	−	6.49325i	−1.18009	−	0.990212i	−0.999978	−	0.00656507i	$-0.997910\pi$
$43$	−7.73836	−	6.49325i	−1.18009	−	0.990212i	−0.180110	−	0.983647i	$-0.557645\pi$
$44$		0			0
$45$	−0.853733	−	1.47871i	−0.127267	−	0.220433i
$46$		0			0
$47$	3.22814	+	1.17495i	0.470872	+	0.171384i	0.566548	−	0.824029i	$-0.308279\pi$
$47$	3.22814	+	1.17495i	0.470872	+	0.171384i	−0.0956751	+	0.995413i	$0.530501\pi$
$48$		0			0
$49$	−4.22376	+	7.31577i	−0.603394	+	1.04511i
$50$		0			0
$51$	0.872832	+	4.95008i	0.122221	+	0.693149i
$52$		0			0
$53$	−1.61814	+	1.35778i	−0.222269	+	0.186506i	−0.747122	−	0.664687i	$-0.768565\pi$
$53$	−1.61814	+	1.35778i	−0.222269	+	0.186506i	0.524853	+	0.851193i	$0.324120\pi$
$54$		0			0
$55$	7.10045	−	2.58435i	0.957425	−	0.348474i
$56$		0			0
$57$	−4.31806	+	0.595259i	−0.571941	+	0.0788440i
$58$		0			0
$59$	6.01966	−	2.19098i	0.783693	−	0.285241i	0.0809810	−	0.996716i	$-0.474195\pi$
$59$	6.01966	−	2.19098i	0.783693	−	0.285241i	0.702712	+	0.711475i	$0.251972\pi$
$60$		0			0
$61$	0.0587523	−	0.0492990i	0.00752246	−	0.00631209i	−0.639019	−	0.769191i	$-0.720659\pi$
$61$	0.0587523	−	0.0492990i	0.00752246	−	0.00631209i	0.646541	+	0.762879i	$0.276215\pi$
$62$		0			0
$63$	−0.682495	−	3.87062i	−0.0859863	−	0.487653i
$64$		0			0
$65$	−1.55774	+	2.69809i	−0.193214	+	0.334656i
$66$		0			0
$67$	−0.984002	−	0.358147i	−0.120215	−	0.0437547i	0.281212	−	0.959646i	$-0.409264\pi$
$67$	−0.984002	−	0.358147i	−0.120215	−	0.0437547i	−0.401427	+	0.915891i	$0.631486\pi$
$68$		0			0
$69$	−1.72915	−	2.99498i	−0.208166	−	0.360553i
$70$		0			0
$71$	10.3790	+	8.70898i	1.23176	+	1.03357i	0.998123	+	0.0612406i	$0.0195057\pi$
$71$	10.3790	+	8.70898i	1.23176	+	1.03357i	0.233632	+	0.972325i	$0.424939\pi$
$72$		0			0
$73$	0.696538	−	3.95026i	0.0815236	−	0.462343i	−0.916529	−	0.399968i	$-0.869021\pi$
$73$	0.696538	−	3.95026i	0.0815236	−	0.462343i	0.998053	−	0.0623753i	$-0.0198676\pi$
$74$		0			0
$75$	2.08456			0.240704
$76$		0			0
$77$	17.3931			1.98213
$78$		0			0
$79$	−2.94592	+	16.7071i	−0.331442	+	1.87970i	0.128438	+	0.991718i	$0.459004\pi$
$79$	−2.94592	+	16.7071i	−0.331442	+	1.87970i	−0.459880	+	0.887981i	$0.652107\pi$
$80$		0			0
$81$	0.766044	+	0.642788i	0.0851160	+	0.0714208i
$82$		0			0
$83$	−6.51259	−	11.2801i	−0.714850	−	1.23816i	−0.963017	−	0.269440i	$-0.913162\pi$
$83$	−6.51259	−	11.2801i	−0.714850	−	1.23816i	0.248167	−	0.968717i	$-0.420172\pi$
$84$		0			0
$85$	8.06489	+	2.93538i	0.874760	+	0.318387i
$86$		0			0
$87$	−0.725109	+	1.25592i	−0.0777398	+	0.134649i
$88$		0			0
$89$	2.14695	+	12.1759i	0.227576	+	1.29065i	0.857699	+	0.514152i	$0.171893\pi$
$89$	2.14695	+	12.1759i	0.227576	+	1.29065i	−0.630123	+	0.776496i	$0.716995\pi$
$90$		0			0
$91$	−5.49359	+	4.60967i	−0.575885	+	0.483225i
$92$		0			0
$93$	2.69638	−	0.981401i	0.279601	−	0.101767i
$94$		0			0
$95$	−2.80626	+	6.89335i	−0.287916	+	0.707243i
$96$		0			0
$97$	−0.164685	+	0.0599404i	−0.0167212	+	0.00608603i	−0.350367	−	0.936612i	$-0.613943\pi$
$97$	−0.164685	+	0.0599404i	−0.0167212	+	0.00608603i	0.333646	+	0.942698i	$0.391721\pi$
$98$		0			0
$99$	−3.39002	+	2.84456i	−0.340710	+	0.285889i
$100$		0			0
$101$	−1.94720	−	11.0431i	−0.193754	−	1.09883i	−0.914183	−	0.405303i	$-0.867166\pi$
$101$	−1.94720	−	11.0431i	−0.193754	−	1.09883i	0.720429	−	0.693529i	$-0.243945\pi$
$102$		0			0
$103$	4.76005	−	8.24465i	0.469022	−	0.812369i	−0.530351	−	0.847778i	$-0.677940\pi$
$103$	4.76005	−	8.24465i	0.469022	−	0.812369i	0.999373	+	0.0354087i	$0.0112733\pi$
$104$		0			0
$105$	−6.30620	−	2.29527i	−0.615422	−	0.223995i
$106$		0			0
$107$	−5.13450	−	8.89322i	−0.496371	−	0.859740i	0.503620	−	0.863925i	$-0.332001\pi$
$107$	−5.13450	−	8.89322i	−0.496371	−	0.859740i	−0.999991	+	0.00418546i	$0.998668\pi$
$108$		0			0
$109$	−1.56399	−	1.31234i	−0.149803	−	0.125700i	0.564806	−	0.825224i	$-0.308951\pi$
$109$	−1.56399	−	1.31234i	−0.149803	−	0.125700i	−0.714609	+	0.699524i	$0.753395\pi$
$110$		0			0
$111$	0.838934	−	4.75783i	0.0796281	−	0.451593i
$112$		0			0
$113$	−13.9973			−1.31675			−0.658375	−	0.752690i	$-0.728756\pi$
$113$	−13.9973			−1.31675			−0.658375	+	0.752690i	$0.728756\pi$
$114$		0			0
$115$	−5.90494			−0.550639
$116$		0			0
$117$	0.316842	−	1.79690i	0.0292921	−	0.166124i
$118$		0			0
$119$	15.1337	+	12.6986i	1.38730	+	1.16408i
$120$		0			0
$121$	−4.29187	−	7.43374i	−0.390170	−	0.675795i
$122$		0			0
$123$	−8.27685	−	3.01253i	−0.746299	−	0.271631i
$124$		0			0
$125$	6.04832	−	10.4760i	0.540978	−	0.937002i
$126$		0			0
$127$	−0.340225	−	1.92951i	−0.0301901	−	0.171216i	0.965985	−	0.258599i	$-0.0832608\pi$
$127$	−0.340225	−	1.92951i	−0.0301901	−	0.171216i	−0.996175	+	0.0873827i	$0.972150\pi$
$128$		0			0
$129$	7.73836	−	6.49325i	0.681324	−	0.571699i
$130$		0			0
$131$	−1.46596	+	0.533566i	−0.128082	+	0.0466179i	−0.405266	−	0.914199i	$-0.632821\pi$
$131$	−1.46596	+	0.533566i	−0.128082	+	0.0466179i	0.277184	+	0.960817i	$0.410599\pi$
$132$		0			0
$133$	−11.4970	+	12.7012i	−0.996918	+	1.10134i
$134$		0			0
$135$	1.60449	−	0.583988i	0.138093	−	0.0502617i
$136$		0			0
$137$	11.7678	−	9.87434i	1.00539	−	0.843622i	0.0176677	−	0.999844i	$-0.494376\pi$
$137$	11.7678	−	9.87434i	1.00539	−	0.843622i	0.987722	+	0.156222i	$0.0499314\pi$
$138$		0			0
$139$	−1.61632	−	9.16662i	−0.137095	−	0.777502i	−0.973378	−	0.229205i	$-0.926387\pi$
$139$	−1.61632	−	9.16662i	−0.137095	−	0.777502i	0.836284	−	0.548297i	$-0.184724\pi$
$140$		0			0
$141$	−1.71766	+	2.97507i	−0.144653	+	0.250546i
$142$		0			0
$143$	7.58764	+	2.76167i	0.634510	+	0.230943i
$144$		0			0
$145$	1.23810	+	2.14445i	0.102818	+	0.178087i
$146$		0			0
$147$	−6.47117	−	5.42996i	−0.533733	−	0.447856i
$148$		0			0
$149$	0.900217	−	5.10538i	0.0737487	−	0.418249i	−0.925473	−	0.378813i	$-0.876332\pi$
$149$	0.900217	−	5.10538i	0.0737487	−	0.418249i	0.999222	−	0.0394368i	$-0.0125564\pi$
$150$		0			0
$151$	−13.0922			−1.06543			−0.532713	−	0.846296i	$-0.678827\pi$
$151$	−13.0922			−1.06543			−0.532713	+	0.846296i	$0.678827\pi$
$152$		0			0
$153$	−5.02644			−0.406364
$154$		0			0
$155$	0.850780	−	4.82501i	0.0683363	−	0.387554i
$156$		0			0
$157$	−5.64550	−	4.73714i	−0.450560	−	0.378065i	0.389084	−	0.921202i	$-0.372792\pi$
$157$	−5.64550	−	4.73714i	−0.450560	−	0.378065i	−0.839644	+	0.543138i	$0.817236\pi$
$158$		0			0
$159$	−1.05617	−	1.82934i	−0.0837596	−	0.145076i
$160$		0			0
$161$	−12.7726	−	4.64884i	−1.00662	−	0.366380i
$162$		0			0
$163$	−8.01404	+	13.8807i	−0.627708	+	1.08722i	0.360302	+	0.932836i	$0.382674\pi$
$163$	−8.01404	+	13.8807i	−0.627708	+	1.08722i	−0.988010	+	0.154387i	$0.950660\pi$
$164$		0			0
$165$	1.31211	+	7.44135i	0.102148	+	0.579308i
$166$		0			0
$167$	10.0561	−	8.43808i	0.778165	−	0.652958i	−0.164621	−	0.986357i	$-0.552640\pi$
$167$	10.0561	−	8.43808i	0.778165	−	0.652958i	0.942786	+	0.333399i	$0.108196\pi$
$168$		0			0
$169$	9.08754	−	3.30759i	0.699041	−	0.254430i
$170$		0			0
$171$	0.163608	−	4.35583i	0.0125114	−	0.333098i
$172$		0			0
$173$	17.3580	−	6.31781i	1.31971	−	0.480334i	0.416342	−	0.909208i	$-0.363312\pi$
$173$	17.3580	−	6.31781i	1.31971	−	0.480334i	0.903364	+	0.428874i	$0.141090\pi$
$174$		0			0
$175$	6.27621	−	5.26636i	0.474437	−	0.398100i
$176$		0			0
$177$	1.11239	+	6.30866i	0.0836122	+	0.474188i
$178$		0			0
$179$	5.92941	−	10.2700i	0.443185	−	0.767619i	−0.554739	−	0.832024i	$-0.687182\pi$
$179$	5.92941	−	10.2700i	0.443185	−	0.767619i	0.997924	+	0.0644059i	$0.0205152\pi$
$180$		0			0
$181$	−0.257216	−	0.0936191i	−0.0191187	−	0.00695866i	0.332443	−	0.943123i	$-0.392127\pi$
$181$	−0.257216	−	0.0936191i	−0.0191187	−	0.00695866i	−0.351562	+	0.936165i	$0.614349\pi$
$182$		0			0
$183$	0.0383478	+	0.0664204i	0.00283475	+	0.00490994i
$184$		0			0
$185$	−6.31922	−	5.30246i	−0.464599	−	0.389844i
$186$		0			0
$187$	3.86259	−	21.9058i	0.282461	−	1.60191i
$188$		0			0
$189$	3.93033			0.285890
$190$		0			0
$191$	12.1649			0.880218			0.440109	−	0.897944i	$-0.354940\pi$
$191$	12.1649			0.880218			0.440109	+	0.897944i	$0.354940\pi$
$192$		0			0
$193$	4.00715	−	22.7257i	0.288441	−	1.63583i	−0.404288	−	0.914632i	$-0.632481\pi$
$193$	4.00715	−	22.7257i	0.288441	−	1.63583i	0.692729	−	0.721198i	$-0.256408\pi$
$194$		0			0
$195$	−2.38660	−	2.00259i	−0.170908	−	0.143409i
$196$		0			0
$197$	−3.23436	−	5.60208i	−0.230439	−	0.399132i	0.727498	−	0.686109i	$-0.240683\pi$
$197$	−3.23436	−	5.60208i	−0.230439	−	0.399132i	−0.957937	+	0.286978i	$0.907349\pi$
$198$		0			0
$199$	0.288569	+	0.105030i	0.0204561	+	0.00744541i	0.352228	−	0.935914i	$-0.385424\pi$
$199$	0.288569	+	0.105030i	0.0204561	+	0.00744541i	−0.331772	+	0.943360i	$0.607646\pi$
$200$		0			0
$201$	0.523576	−	0.906861i	0.0369302	−	0.0639650i
$202$		0			0
$203$	0.989766	+	5.61324i	0.0694680	+	0.393972i
$204$		0			0
$205$	−11.5209	+	9.66717i	−0.804653	+	0.675184i
$206$		0			0
$207$	3.24975	−	1.18281i	0.225873	−	0.0822110i
$208$		0			0
$209$	18.8575	+	4.06028i	1.30440	+	0.280855i
$210$		0			0
$211$	9.94719	−	3.62048i	0.684793	−	0.249244i	0.0238889	−	0.999715i	$-0.492395\pi$
$211$	9.94719	−	3.62048i	0.684793	−	0.249244i	0.660904	+	0.750470i	$0.270173\pi$
$212$		0			0
$213$	−10.3790	+	8.70898i	−0.711154	+	0.596729i
$214$		0			0
$215$	−2.99514	−	16.9863i	−0.204267	−	1.15846i
$216$		0			0
$217$	5.63890	−	9.76686i	0.382793	−	0.663018i
$218$		0			0
$219$	3.76929	+	1.37191i	0.254705	+	0.0927052i
$220$		0			0
$221$	4.58568	+	7.94263i	0.308466	+	0.534279i
$222$		0			0
$223$	−5.69559	−	4.77917i	−0.381405	−	0.320037i	0.431849	−	0.901946i	$-0.357861\pi$
$223$	−5.69559	−	4.77917i	−0.381405	−	0.320037i	−0.813254	+	0.581909i	$0.802306\pi$
$224$		0			0
$225$	−0.361980	+	2.05289i	−0.0241320	+	0.136859i
$226$		0			0
$227$	−3.54389			−0.235216			−0.117608	−	0.993060i	$-0.537523\pi$
$227$	−3.54389			−0.235216			−0.117608	+	0.993060i	$0.537523\pi$
$228$		0			0
$229$	−11.3492			−0.749973			−0.374987	−	0.927030i	$-0.622353\pi$
$229$	−11.3492			−0.749973			−0.374987	+	0.927030i	$0.622353\pi$
$230$		0			0
$231$	−3.02028	+	17.1289i	−0.198720	+	1.12700i
$232$		0			0
$233$	−4.54086	−	3.81024i	−0.297482	−	0.249617i	0.481813	−	0.876274i	$-0.339978\pi$
$233$	−4.54086	−	3.81024i	−0.297482	−	0.249617i	−0.779295	+	0.626657i	$0.784423\pi$
$234$		0			0
$235$	2.93284	+	5.07983i	0.191317	+	0.331372i
$236$		0			0
$237$	−15.9418	−	5.80232i	−1.03553	−	0.376901i
$238$		0			0
$239$	7.58422	−	13.1363i	0.490583	−	0.849714i	−0.509359	−	0.860554i	$-0.670117\pi$
$239$	7.58422	−	13.1363i	0.490583	−	0.849714i	0.999941	+	0.0108402i	$0.00345063\pi$
$240$		0			0
$241$	1.53896	+	8.72790i	0.0991334	+	0.562214i	0.993402	+	0.114683i	$0.0365853\pi$
$241$	1.53896	+	8.72790i	0.0991334	+	0.562214i	−0.894269	+	0.447530i	$0.852304\pi$
$242$		0			0
$243$	−0.766044	+	0.642788i	−0.0491418	+	0.0412348i
$244$		0			0
$245$	−13.5540	+	4.93325i	−0.865933	+	0.315174i
$246$		0			0
$247$	−7.03221	+	3.71534i	−0.447449	+	0.236401i
$248$		0			0
$249$	12.2397	−	4.45488i	0.775658	−	0.282316i
$250$		0			0
$251$	−8.96819	+	7.52520i	−0.566067	+	0.474987i	−0.880338	−	0.474347i	$-0.842684\pi$
$251$	−8.96819	+	7.52520i	−0.566067	+	0.474987i	0.314271	+	0.949333i	$0.398240\pi$
$252$		0			0
$253$	2.65755	+	15.0717i	0.167079	+	0.947551i
$254$		0			0
$255$	−4.29124	+	7.43264i	−0.268728	+	0.465450i
$256$		0			0
$257$	9.31797	+	3.39146i	0.581239	+	0.211554i	0.615872	−	0.787846i	$-0.288804\pi$
$257$	9.31797	+	3.39146i	0.581239	+	0.211554i	−0.0346328	+	0.999400i	$0.511026\pi$
$258$		0			0
$259$	−9.49417	−	16.4444i	−0.589939	−	1.02180i
$260$		0			0
$261$	−1.11093	−	0.932182i	−0.0687649	−	0.0577006i
$262$		0			0
$263$	1.17020	−	6.63654i	0.0721577	−	0.409227i	−0.927238	−	0.374472i	$-0.877824\pi$
$263$	1.17020	−	6.63654i	0.0721577	−	0.409227i	0.999396	−	0.0347546i	$-0.0110650\pi$
$264$		0			0
$265$	−3.60674			−0.221560
$266$		0			0
$267$	−12.3638			−0.756651
$268$		0			0
$269$	0.124730	−	0.707378i	0.00760491	−	0.0431296i	−0.980769	−	0.195171i	$-0.937474\pi$
$269$	0.124730	−	0.707378i	0.00760491	−	0.0431296i	0.988374	+	0.152042i	$0.0485848\pi$
$270$		0			0
$271$	22.0935	+	18.5387i	1.34209	+	1.12614i	0.981085	+	0.193579i	$0.0620097\pi$
$271$	22.0935	+	18.5387i	1.34209	+	1.12614i	0.361002	+	0.932565i	$0.382435\pi$
$272$		0			0
$273$	−3.58569	−	6.21059i	−0.217016	−	0.375882i
$274$		0			0
$275$	−8.66857	−	3.15510i	−0.522735	−	0.190260i
$276$		0			0
$277$	1.91567	−	3.31804i	0.115101	−	0.199361i	−0.802719	−	0.596358i	$-0.796614\pi$
$277$	1.91567	−	3.31804i	0.115101	−	0.199361i	0.917820	+	0.396996i	$0.129947\pi$
$278$		0			0
$279$	0.498270	+	2.82583i	0.0298307	+	0.169178i
$280$		0			0
$281$	−16.9236	+	14.2006i	−1.00957	+	0.847134i	−0.988282	−	0.152639i	$-0.951223\pi$
$281$	−16.9236	+	14.2006i	−1.00957	+	0.847134i	−0.0212929	+	0.999773i	$0.506778\pi$
$282$		0			0
$283$	−23.6300	+	8.60061i	−1.40466	+	0.511253i	−0.929557	−	0.368678i	$-0.879810\pi$
$283$	−23.6300	+	8.60061i	−1.40466	+	0.511253i	−0.475100	+	0.879932i	$0.657588\pi$
$284$		0			0
$285$	−6.30133	−	3.96064i	−0.373258	−	0.234608i
$286$		0			0
$287$	−32.5308	+	11.8402i	−1.92023	+	0.698907i
$288$		0			0
$289$	6.33143	−	5.31270i	0.372437	−	0.312512i
$290$		0			0
$291$	−0.0304326	−	0.172592i	−0.00178399	−	0.0101175i
$292$		0			0
$293$	2.96356	−	5.13304i	0.173133	−	0.299875i	−0.766381	−	0.642387i	$-0.777944\pi$
$293$	2.96356	−	5.13304i	0.173133	−	0.299875i	0.939514	+	0.342512i	$0.111278\pi$
$294$		0			0
$295$	10.2784	+	3.74102i	0.598429	+	0.217811i
$296$		0			0
$297$	−2.21268	−	3.83247i	−0.128393	−	0.222382i
$298$		0			0
$299$	−4.83382	−	4.05606i	−0.279547	−	0.234568i
$300$		0			0
$301$	6.89437	−	39.0999i	0.397385	−	2.25368i
$302$		0			0
$303$	11.2135			0.644197
$304$		0			0
$305$	0.130955			0.00749848
$306$		0			0
$307$	3.05347	−	17.3171i	0.174271	−	0.988339i	−0.764711	−	0.644373i	$-0.777118\pi$
$307$	3.05347	−	17.3171i	0.174271	−	0.988339i	0.938982	−	0.343966i	$-0.111771\pi$
$308$		0			0
$309$	7.29282	+	6.11940i	0.414874	+	0.348121i
$310$		0			0
$311$	−3.01433	−	5.22097i	−0.170927	−	0.296054i	0.767817	−	0.640669i	$-0.221343\pi$
$311$	−3.01433	−	5.22097i	−0.170927	−	0.296054i	−0.938744	+	0.344615i	$0.888010\pi$
$312$		0			0
$313$	−15.6910	−	5.71107i	−0.886909	−	0.322809i	−0.141914	−	0.989879i	$-0.545326\pi$
$313$	−15.6910	−	5.71107i	−0.886909	−	0.322809i	−0.744995	+	0.667070i	$0.767548\pi$
$314$		0			0
$315$	3.35546	−	5.81182i	0.189059	−	0.327459i
$316$		0			0
$317$	−0.380819	−	2.15973i	−0.0213889	−	0.121303i	0.972244	−	0.233970i	$-0.0751717\pi$
$317$	−0.380819	−	2.15973i	−0.0213889	−	0.121303i	−0.993633	+	0.112667i	$0.964061\pi$
$318$		0			0
$319$	4.91626	−	4.12523i	0.275258	−	0.230969i
$320$		0			0
$321$	9.64970	−	3.51221i	0.538594	−	0.196032i
$322$		0			0
$323$	13.4434	+	17.3006i	0.748012	+	0.962632i
$324$		0			0
$325$	3.57415	−	1.30088i	0.198258	−	0.0721601i
$326$		0			0
$327$	1.56399	−	1.31234i	0.0864888	−	0.0725727i
$328$		0			0
$329$	2.34458	+	13.2968i	0.129261	+	0.733076i
$330$		0			0
$331$	7.77039	−	13.4587i	0.427099	−	0.739758i	−0.569515	−	0.821981i	$-0.692869\pi$
$331$	7.77039	−	13.4587i	0.427099	−	0.739758i	0.996614	+	0.0822234i	$0.0262021\pi$
$332$		0			0
$333$	4.53987	+	1.65238i	0.248783	+	0.0905497i
$334$		0			0
$335$	−0.893989	−	1.54843i	−0.0488439	−	0.0846000i
$336$		0			0
$337$	9.48108	+	7.95557i	0.516467	+	0.433368i	0.863398	−	0.504523i	$-0.168332\pi$
$337$	9.48108	+	7.95557i	0.516467	+	0.433368i	−0.346931	+	0.937891i	$0.612776\pi$
$338$		0			0
$339$	2.43060	−	13.7846i	0.132012	−	0.748677i
$340$		0			0
$341$	−12.6982			−0.687647
$342$		0			0
$343$	−5.68923			−0.307189
$344$		0			0
$345$	1.02538	−	5.81523i	0.0552047	−	0.313082i
$346$		0			0
$347$	17.0105	+	14.2735i	0.913171	+	0.766241i	0.972720	−	0.231984i	$-0.0745217\pi$
$347$	17.0105	+	14.2735i	0.913171	+	0.766241i	−0.0595486	+	0.998225i	$0.518966\pi$
$348$		0			0
$349$	9.96461	+	17.2592i	0.533393	+	0.923864i	0.999239	+	0.0389982i	$0.0124167\pi$
$349$	9.96461	+	17.2592i	0.533393	+	0.923864i	−0.465846	+	0.884866i	$0.654250\pi$
$350$		0			0
$351$	1.71458	+	0.624058i	0.0915177	+	0.0333097i
$352$		0			0
$353$	2.60302	−	4.50856i	0.138545	−	0.239966i	−0.788401	−	0.615161i	$-0.789091\pi$
$353$	2.60302	−	4.50856i	0.138545	−	0.239966i	0.926946	+	0.375195i	$0.122424\pi$
$354$		0			0
$355$	4.01719	+	22.7826i	0.213210	+	1.20918i
$356$		0			0
$357$	−15.1337	+	12.6986i	−0.800958	+	0.672083i
$358$		0			0
$359$	−4.85658	+	1.76765i	−0.256320	+	0.0932930i	−0.466984	−	0.884266i	$-0.654660\pi$
$359$	−4.85658	+	1.76765i	−0.256320	+	0.0932930i	0.210664	+	0.977559i	$0.432437\pi$
$360$		0			0
$361$	−15.4300	+	11.0867i	−0.812105	+	0.583511i
$362$		0			0
$363$	8.06609	−	2.93581i	0.423360	−	0.154090i
$364$		0			0
$365$	5.24663	−	4.40245i	0.274621	−	0.230435i
$366$		0			0
$367$	1.05270	+	5.97015i	0.0549504	+	0.311639i	0.999878	−	0.0156413i	$-0.00497898\pi$
$367$	1.05270	+	5.97015i	0.0549504	+	0.311639i	−0.944927	+	0.327280i	$0.893868\pi$
$368$		0			0
$369$	4.40402	−	7.62799i	0.229264	−	0.397097i
$370$		0			0
$371$	−7.80150	−	2.83951i	−0.405034	−	0.147420i
$372$		0			0
$373$	−4.99273	−	8.64766i	−0.258514	−	0.447759i	0.707330	−	0.706883i	$-0.249899\pi$
$373$	−4.99273	−	8.64766i	−0.258514	−	0.447759i	−0.965844	+	0.259124i	$0.916566\pi$
$374$		0			0
$375$	9.26657	+	7.77557i	0.478524	+	0.401529i
$376$		0			0
$377$	−0.459490	+	2.60590i	−0.0236649	+	0.134211i
$378$		0			0
$379$	13.7799			0.707826			0.353913	−	0.935278i	$-0.384851\pi$
$379$	13.7799			0.707826			0.353913	+	0.935278i	$0.384851\pi$
$380$		0			0
$381$	1.95928			0.100377
$382$		0			0
$383$	−2.83262	+	16.0646i	−0.144740	+	0.820861i	0.822836	+	0.568279i	$0.192391\pi$
$383$	−2.83262	+	16.0646i	−0.144740	+	0.820861i	−0.967576	+	0.252582i	$0.918720\pi$
$384$		0			0
$385$	22.7501	+	19.0896i	1.15945	+	0.972896i
$386$		0			0
$387$	5.05085	+	8.74833i	0.256749	+	0.444703i
$388$		0			0
$389$	10.7795	+	3.92341i	0.546541	+	0.198925i	0.600509	−	0.799618i	$-0.294965\pi$
$389$	10.7795	+	3.92341i	0.546541	+	0.198925i	−0.0539681	+	0.998543i	$0.517187\pi$
$390$		0			0
$391$	−8.69149	+	15.0541i	−0.439547	+	0.761318i
$392$		0			0
$393$	−0.270899	−	1.53634i	−0.0136650	−	0.0774982i
$394$		0			0
$395$	−22.1900	+	18.6196i	−1.11650	+	0.936853i
$396$		0			0
$397$	0.421085	−	0.153262i	0.0211336	−	0.00769201i	−0.331432	−	0.943479i	$-0.607532\pi$
$397$	0.421085	−	0.153262i	0.0211336	−	0.00769201i	0.352565	+	0.935787i	$0.385309\pi$
$398$		0			0
$399$	−10.5118	−	13.5279i	−0.526250	−	0.677242i
$400$		0			0
$401$	−13.6316	+	4.96149i	−0.680729	+	0.247765i	−0.659160	−	0.752002i	$-0.729088\pi$
$401$	−13.6316	+	4.96149i	−0.680729	+	0.247765i	−0.0215682	+	0.999767i	$0.506866\pi$
$402$		0			0
$403$	4.01072	−	3.36539i	0.199788	−	0.167642i
$404$		0			0
$405$	0.296498	+	1.68153i	0.0147331	+	0.0835557i
$406$		0			0
$407$	−10.6899	+	18.5155i	−0.529881	+	0.917781i
$408$		0			0
$409$	12.4030	+	4.51431i	0.613287	+	0.223218i	0.629941	−	0.776643i	$-0.283079\pi$
$409$	12.4030	+	4.51431i	0.613287	+	0.223218i	−0.0166536	+	0.999861i	$0.505301\pi$
$410$		0			0
$411$	7.68088	+	13.3037i	0.378870	+	0.656222i
$412$		0			0
$413$	19.2872	+	16.1839i	0.949061	+	0.796357i
$414$		0			0
$415$	3.86195	−	21.9022i	0.189576	−	1.07514i
$416$		0			0
$417$	9.30803			0.455816
$418$		0			0
$419$	−11.4229			−0.558047			−0.279024	−	0.960284i	$-0.590011\pi$
$419$	−11.4229			−0.558047			−0.279024	+	0.960284i	$0.590011\pi$
$420$		0			0
$421$	−2.87973	+	16.3318i	−0.140349	+	0.795961i	0.830635	+	0.556818i	$0.187978\pi$
$421$	−2.87973	+	16.3318i	−0.140349	+	0.795961i	−0.970984	+	0.239144i	$0.923133\pi$
$422$		0			0
$423$	−2.63160	−	2.20818i	−0.127953	−	0.107365i
$424$		0			0
$425$	−5.23895	−	9.07413i	−0.254126	−	0.440160i
$426$		0			0
$427$	0.283261	+	0.103098i	0.0137079	+	0.00498928i
$428$		0			0
$429$	−4.03730	+	6.99281i	−0.194923	+	0.337616i
$430$		0			0
$431$	−4.94875	−	28.0658i	−0.238373	−	1.35188i	−0.835393	−	0.549654i	$-0.814760\pi$
$431$	−4.94875	−	28.0658i	−0.238373	−	1.35188i	0.597020	−	0.802227i	$-0.296351\pi$
$432$		0			0
$433$	10.7227	−	8.99743i	0.515301	−	0.432389i	−0.347689	−	0.937610i	$-0.613034\pi$
$433$	10.7227	−	8.99743i	0.515301	−	0.432389i	0.862990	+	0.505221i	$0.168589\pi$
$434$		0			0
$435$	−2.32686	+	0.846909i	−0.111565	+	0.0406062i
$436$		0			0
$437$	−12.7627	−	8.02190i	−0.610524	−	0.383739i
$438$		0			0
$439$	−25.2111	+	9.17609i	−1.20326	+	0.437951i	−0.864361	−	0.502871i	$-0.832277\pi$
$439$	−25.2111	+	9.17609i	−1.20326	+	0.437951i	−0.338900	+	0.940823i	$0.610055\pi$
$440$		0			0
$441$	6.47117	−	5.42996i	0.308151	−	0.258570i
$442$		0			0
$443$	2.41688	+	13.7068i	0.114829	+	0.651230i	0.986834	+	0.161733i	$0.0517085\pi$
$443$	2.41688	+	13.7068i	0.114829	+	0.651230i	−0.872005	+	0.489497i	$0.837180\pi$
$444$		0			0
$445$	−10.5554	+	18.2824i	−0.500373	+	0.866671i
$446$		0			0
$447$	4.87150	+	1.77308i	0.230414	+	0.0838639i
$448$		0			0
$449$	−10.6420	−	18.4326i	−0.502229	−	0.869887i	−0.999997	−	0.00257601i	$-0.999180\pi$
$449$	−10.6420	−	18.4326i	−0.502229	−	0.869887i	0.497767	−	0.867311i	$-0.334153\pi$
$450$		0			0
$451$	29.8594	+	25.0550i	1.40603	+	1.17980i
$452$		0			0
$453$	2.27343	−	12.8933i	0.106815	−	0.605779i
$454$		0			0
$455$	−12.2449			−0.574049
$456$		0			0
$457$	−0.745738			−0.0348842			−0.0174421	−	0.999848i	$-0.505552\pi$
$457$	−0.745738			−0.0348842			−0.0174421	+	0.999848i	$0.505552\pi$
$458$		0			0
$459$	0.872832	−	4.95008i	0.0407403	−	0.231050i
$460$		0			0
$461$	21.5980	+	18.1229i	1.00592	+	0.844068i	0.987794	−	0.155768i	$-0.0497852\pi$
$461$	21.5980	+	18.1229i	1.00592	+	0.844068i	0.0181272	+	0.999836i	$0.494230\pi$
$462$		0			0
$463$	4.42852	+	7.67043i	0.205811	+	0.356475i	0.950391	−	0.311058i	$-0.100683\pi$
$463$	4.42852	+	7.67043i	0.205811	+	0.356475i	−0.744580	+	0.667533i	$0.767350\pi$
$464$		0			0
$465$	4.60397	+	1.67571i	0.213504	+	0.0777092i
$466$		0			0
$467$	18.6388	−	32.2833i	0.862500	−	1.49389i	−0.00700866	−	0.999975i	$-0.502231\pi$
$467$	18.6388	−	32.2833i	0.862500	−	1.49389i	0.869508	−	0.493918i	$-0.164436\pi$
$468$		0			0
$469$	−0.714677	−	4.05313i	−0.0330007	−	0.187156i
$470$		0			0
$471$	5.64550	−	4.73714i	0.260131	−	0.218276i
$472$		0			0
$473$	−42.0077	+	15.2895i	−1.93151	+	0.703014i
$474$		0			0
$475$	8.03401	−	4.24463i	0.368626	−	0.194757i
$476$		0			0
$477$	1.98495	−	0.722461i	0.0908844	−	0.0330792i
$478$		0			0
$479$	22.8704	−	19.1905i	1.04498	−	0.876838i	0.0524190	−	0.998625i	$-0.483307\pi$
$479$	22.8704	−	19.1905i	1.04498	−	0.876838i	0.992556	+	0.121787i	$0.0388624\pi$
$480$		0			0
$481$	−1.53074	−	8.68124i	−0.0697956	−	0.395831i
$482$		0			0
$483$	6.79615	−	11.7713i	0.309235	−	0.535612i
$484$		0			0
$485$	−0.281194	−	0.102346i	−0.0127684	−	0.00464731i
$486$		0			0
$487$	15.4404	+	26.7435i	0.699671	+	1.21187i	0.968581	+	0.248700i	$0.0800034\pi$
$487$	15.4404	+	26.7435i	0.699671	+	1.21187i	−0.268910	+	0.963165i	$0.586663\pi$
$488$		0			0
$489$	−12.2782	−	10.3027i	−0.555240	−	0.465902i
$490$		0			0
$491$	−1.75863	+	9.97370i	−0.0793660	+	0.450107i	0.919065	+	0.394107i	$0.128946\pi$
$491$	−1.75863	+	9.97370i	−0.0793660	+	0.450107i	−0.998431	+	0.0560004i	$0.982165\pi$
$492$		0			0
$493$	7.28943			0.328299
$494$		0			0
$495$	−7.55614			−0.339623
$496$		0			0
$497$	−9.24697	+	52.4422i	−0.414783	+	2.35235i
$498$		0			0
$499$	−6.58385	−	5.52450i	−0.294734	−	0.247311i	0.483415	−	0.875391i	$-0.339396\pi$
$499$	−6.58385	−	5.52450i	−0.294734	−	0.247311i	−0.778148	+	0.628081i	$0.783841\pi$
$500$		0			0
$501$	6.56366	+	11.3686i	0.293243	+	0.507911i
$502$		0			0
$503$	−16.9775	−	6.17930i	−0.756989	−	0.275521i	−0.0654451	−	0.997856i	$-0.520847\pi$
$503$	−16.9775	−	6.17930i	−0.756989	−	0.275521i	−0.691543	+	0.722335i	$0.743069\pi$
$504$		0			0
$505$	9.57332	−	16.5815i	0.426007	−	0.737866i
$506$		0			0
$507$	1.67931	+	9.52383i	0.0745807	+	0.422968i
$508$		0			0
$509$	24.0894	−	20.2134i	1.06774	−	0.895942i	0.0728963	−	0.997340i	$-0.476776\pi$
$509$	24.0894	−	20.2134i	1.06774	−	0.895942i	0.994846	+	0.101397i	$0.0323314\pi$
$510$		0			0
$511$	14.8146	−	5.39207i	0.655359	−	0.238531i
$512$		0			0
$513$	4.26124	+	0.917504i	0.188138	+	0.0405088i
$514$		0			0
$515$	15.2749	−	5.55962i	0.673094	−	0.244986i
$516$		0			0
$517$	11.6458	−	9.77196i	0.512180	−	0.429770i
$518$		0			0
$519$	3.20763	+	18.1914i	0.140800	+	0.798514i
$520$		0			0
$521$	−9.97505	+	17.2773i	−0.437015	+	0.756932i	−0.997458	−	0.0712610i	$-0.977298\pi$
$521$	−9.97505	+	17.2773i	−0.437015	+	0.756932i	0.560443	+	0.828193i	$0.310631\pi$
$522$		0			0
$523$	2.97141	+	1.08150i	0.129931	+	0.0472909i	0.406167	−	0.913799i	$-0.366865\pi$
$523$	2.97141	+	1.08150i	0.129931	+	0.0472909i	−0.276236	+	0.961090i	$0.589087\pi$
$524$		0			0
$525$	4.09650	+	7.09535i	0.178786	+	0.309667i
$526$		0			0
$527$	−11.0487	−	9.27092i	−0.481287	−	0.403848i
$528$		0			0
$529$	−1.91710	+	10.8724i	−0.0833520	+	0.472713i
$530$		0			0
$531$	−6.40598			−0.277996
$532$		0			0
$533$	−16.0714			−0.696128
$534$		0			0
$535$	3.04474	−	17.2676i	0.131636	−	0.746543i
$536$		0			0
$537$	9.08438	+	7.62270i	0.392020	+	0.328944i
$538$		0			0
$539$	18.6916	+	32.3748i	0.805105	+	1.39448i
$540$		0			0
$541$	−0.558559	−	0.203299i	−0.0240143	−	0.00874050i	0.329985	−	0.943986i	$-0.392956\pi$
$541$	−0.558559	−	0.203299i	−0.0240143	−	0.00874050i	−0.353999	+	0.935246i	$0.615179\pi$
$542$		0			0
$543$	0.136862	−	0.237052i	0.00587331	−	0.0101729i
$544$		0			0
$545$	−0.605344	−	3.43308i	−0.0259301	−	0.147057i
$546$		0			0
$547$	−20.3567	+	17.0813i	−0.870392	+	0.730345i	−0.964181	−	0.265247i	$-0.914547\pi$
$547$	−20.3567	+	17.0813i	−0.870392	+	0.730345i	0.0937888	+	0.995592i	$0.470102\pi$
$548$		0			0
$549$	−0.0720704	+	0.0262315i	−0.00307589	+	0.00111953i
$550$		0			0
$551$	−0.237267	+	6.31690i	−0.0101079	+	0.269109i
$552$		0			0
$553$	−62.6564	+	22.8051i	−2.66442	+	0.969770i
$554$		0			0
$555$	6.31922	−	5.30246i	0.268236	−	0.225077i
$556$		0			0
$557$	5.93387	+	33.6527i	0.251426	+	1.42591i	0.805082	+	0.593163i	$0.202121\pi$
$557$	5.93387	+	33.6527i	0.251426	+	1.42591i	−0.553656	+	0.832745i	$0.686768\pi$
$558$		0			0
$559$	9.21590	−	15.9624i	0.389791	−	0.675138i
$560$		0			0
$561$	20.9023	+	7.60782i	0.882496	+	0.321202i
$562$		0			0
$563$	−15.0358	−	26.0427i	−0.633683	−	1.09757i	−0.986793	−	0.161989i	$-0.948209\pi$
$563$	−15.0358	−	26.0427i	−0.633683	−	1.09757i	0.353110	−	0.935582i	$-0.385124\pi$
$564$		0			0
$565$	−18.3083	−	15.3625i	−0.770238	−	0.646306i
$566$		0			0
$567$	−0.682495	+	3.87062i	−0.0286621	+	0.162551i
$568$		0			0
$569$	−24.7511			−1.03762			−0.518809	−	0.854890i	$-0.673624\pi$
$569$	−24.7511			−1.03762			−0.518809	+	0.854890i	$0.673624\pi$
$570$		0			0
$571$	−31.5869			−1.32187			−0.660934	−	0.750444i	$-0.729840\pi$
$571$	−31.5869			−1.32187			−0.660934	+	0.750444i	$0.729840\pi$
$572$		0			0
$573$	−2.11241	+	11.9800i	−0.0882470	+	0.500474i
$574$		0			0
$575$	5.52245	+	4.63388i	0.230302	+	0.193246i
$576$		0			0
$577$	15.4054	+	26.6830i	0.641337	+	1.11083i	0.985135	+	0.171784i	$0.0549531\pi$
$577$	15.4054	+	26.6830i	0.641337	+	1.11083i	−0.343798	+	0.939044i	$0.611714\pi$
$578$		0			0
$579$	21.6846	+	7.89254i	0.901180	+	0.328003i
$580$		0			0
$581$	25.5967	−	44.3347i	1.06193	−	1.83931i
$582$		0			0
$583$	1.62323	+	9.20582i	0.0672275	+	0.381266i
$584$		0			0
$585$	2.38660	−	2.00259i	0.0986737	−	0.0827970i
$586$		0			0
$587$	−13.2728	+	4.83091i	−0.547828	+	0.199393i	−0.601081	−	0.799188i	$-0.705263\pi$
$587$	−13.2728	+	4.83091i	−0.547828	+	0.199393i	0.0532531	+	0.998581i	$0.483041\pi$
$588$		0			0
$589$	8.39365	−	9.27281i	0.345854	−	0.382080i
$590$		0			0
$591$	6.07861	−	2.21243i	0.250041	−	0.0910074i
$592$		0			0
$593$	28.8915	−	24.2428i	1.18643	−	0.995533i	0.186516	−	0.982452i	$-0.440280\pi$
$593$	28.8915	−	24.2428i	1.18643	−	0.995533i	0.999914	−	0.0130812i	$-0.00416400\pi$
$594$		0			0
$595$	5.85750	+	33.2195i	0.240134	+	1.36187i
$596$		0			0
$597$	−0.153544	+	0.265946i	−0.00628414	+	0.0108845i
$598$		0			0
$599$	0.0872028	+	0.0317392i	0.00356301	+	0.00129683i	0.343801	−	0.939043i	$-0.388285\pi$
$599$	0.0872028	+	0.0317392i	0.00356301	+	0.00129683i	−0.340238	+	0.940339i	$0.610508\pi$
$600$		0			0
$601$	11.5190	+	19.9515i	0.469870	+	0.813839i	0.999406	−	0.0344482i	$-0.0109674\pi$
$601$	11.5190	+	19.9515i	0.469870	+	0.813839i	−0.529536	+	0.848287i	$0.677634\pi$
$602$		0			0
$603$	0.802166	+	0.673097i	0.0326667	+	0.0274106i
$604$		0			0
$605$	2.54507	−	14.4338i	0.103472	−	0.586817i
$606$		0			0
$607$	−31.9363			−1.29625			−0.648127	−	0.761532i	$-0.724447\pi$
$607$	−31.9363			−1.29625			−0.648127	+	0.761532i	$0.724447\pi$
$608$		0			0
$609$	−5.69984			−0.230969
$610$		0			0
$611$	−1.08845	+	6.17292i	−0.0440341	+	0.249730i
$612$		0			0
$613$	33.4848	+	28.0971i	1.35244	+	1.13483i	0.978239	+	0.207482i	$0.0665269\pi$
$613$	33.4848	+	28.0971i	1.35244	+	1.13483i	0.374199	+	0.927348i	$0.377918\pi$
$614$		0			0
$615$	−7.51972	−	13.0245i	−0.303224	−	0.525200i
$616$		0			0
$617$	12.6034	+	4.58726i	0.507394	+	0.184676i	0.583016	−	0.812460i	$-0.301872\pi$
$617$	12.6034	+	4.58726i	0.507394	+	0.184676i	−0.0756229	+	0.997136i	$0.524095\pi$
$618$		0			0
$619$	11.4670	−	19.8615i	0.460899	−	0.798300i	−0.538107	−	0.842876i	$-0.680861\pi$
$619$	11.4670	−	19.8615i	0.460899	−	0.798300i	0.999006	+	0.0445765i	$0.0141938\pi$
$620$		0			0
$621$	0.600529	+	3.40577i	0.0240984	+	0.136669i
$622$		0			0
$623$	−37.2250	+	31.2355i	−1.49139	+	1.25142i
$624$		0			0
$625$	9.61478	−	3.49949i	0.384591	−	0.139980i
$626$		0			0
$627$	−7.27317	+	17.8660i	−0.290462	+	0.713497i
$628$		0			0
$629$	−22.8194	+	8.30557i	−0.909868	+	0.331165i
$630$		0			0
$631$	16.3606	−	13.7282i	0.651306	−	0.546510i	−0.256161	−	0.966634i	$-0.582458\pi$
$631$	16.3606	−	13.7282i	0.651306	−	0.546510i	0.907467	+	0.420124i	$0.138013\pi$
$632$		0			0
$633$	1.83817	+	10.4248i	0.0730606	+	0.414347i
$634$		0			0
$635$	1.67270	−	2.89720i	0.0663790	−	0.114972i
$636$		0			0
$637$	−14.4840	−	5.27174i	−0.573876	−	0.208874i
$638$		0			0
$639$	−6.77438	−	11.7336i	−0.267990	−	0.464173i
$640$		0			0
$641$	−22.5997	−	18.9634i	−0.892634	−	0.749009i	0.0761030	−	0.997100i	$-0.475752\pi$
$641$	−22.5997	−	18.9634i	−0.892634	−	0.749009i	−0.968737	+	0.248091i	$0.920197\pi$
$642$		0			0
$643$	−1.18655	+	6.72928i	−0.0467931	+	0.265377i	−0.999224	−	0.0393763i	$-0.987463\pi$
$643$	−1.18655	+	6.72928i	−0.0467931	+	0.265377i	0.952431	+	0.304753i	$0.0985740\pi$
$644$		0			0
$645$	17.2483			0.679152
$646$		0			0
$647$	18.9452			0.744812			0.372406	−	0.928070i	$-0.378533\pi$
$647$	18.9452			0.744812			0.372406	+	0.928070i	$0.378533\pi$
$648$		0			0
$649$	4.92271	−	27.9181i	0.193233	−	1.09588i
$650$		0			0
$651$	8.63929	+	7.24923i	0.338601	+	0.284120i
$652$		0			0
$653$	−13.5699	−	23.5038i	−0.531033	−	0.919776i	−0.999344	−	0.0362124i	$-0.988471\pi$
$653$	−13.5699	−	23.5038i	−0.531033	−	0.919776i	0.468311	−	0.883564i	$-0.344863\pi$
$654$		0			0
$655$	−2.50308	−	0.911046i	−0.0978034	−	0.0355975i
$656$		0			0
$657$	−2.00560	+	3.47380i	−0.0782459	+	0.135526i
$658$		0			0
$659$	6.92986	+	39.3012i	0.269949	+	1.53096i	0.754562	+	0.656228i	$0.227849\pi$
$659$	6.92986	+	39.3012i	0.269949	+	1.53096i	−0.484613	+	0.874729i	$0.661040\pi$
$660$		0			0
$661$	−38.5678	+	32.3622i	−1.50011	+	1.25874i	−0.619415	+	0.785064i	$0.712630\pi$
$661$	−38.5678	+	32.3622i	−1.50011	+	1.25874i	−0.880697	+	0.473680i	$0.842925\pi$
$662$		0			0
$663$	−8.61825	+	3.13679i	−0.334705	+	0.121823i
$664$		0			0
$665$	−28.9781	+	3.99473i	−1.12372	+	0.154909i
$666$		0			0
$667$	−4.71284	+	1.71533i	−0.182482	+	0.0664179i
$668$		0			0
$669$	5.69559	−	4.77917i	0.220204	−	0.184773i
$670$		0			0
$671$	−0.0589371	−	0.334249i	−0.00227524	−	0.0129035i
$672$		0			0
$673$	23.9052	−	41.4050i	0.921477	−	1.59605i	0.124347	−	0.992239i	$-0.460317\pi$
$673$	23.9052	−	41.4050i	0.921477	−	1.59605i	0.797131	−	0.603807i	$-0.206350\pi$
$674$		0			0
$675$	−1.95884	−	0.712961i	−0.0753959	−	0.0274419i
$676$		0			0
$677$	−20.6305	−	35.7331i	−0.792894	−	1.37333i	−0.924168	−	0.381987i	$-0.875240\pi$
$677$	−20.6305	−	35.7331i	−0.792894	−	1.37333i	0.131274	−	0.991346i	$-0.458093\pi$
$678$		0			0
$679$	−0.527657	−	0.442757i	−0.0202496	−	0.0169914i
$680$		0			0
$681$	0.615390	−	3.49005i	0.0235818	−	0.133739i
$682$		0			0
$683$	17.8805			0.684178			0.342089	−	0.939668i	$-0.388866\pi$
$683$	17.8805			0.684178			0.342089	+	0.939668i	$0.388866\pi$
$684$		0			0
$685$	26.2297			1.00218
$686$		0			0
$687$	1.97076	−	11.1767i	0.0751892	−	0.426419i
$688$		0			0
$689$	−2.95250	−	2.47744i	−0.112481	−	0.0943830i
$690$		0			0
$691$	−5.66655	−	9.81476i	−0.215566	−	0.373371i	0.737882	−	0.674930i	$-0.235826\pi$
$691$	−5.66655	−	9.81476i	−0.215566	−	0.373371i	−0.953447	+	0.301559i	$0.902493\pi$
$692$		0			0
$693$	−16.3442	−	5.94879i	−0.620864	−	0.225976i
$694$		0			0
$695$	7.94657	−	13.7639i	0.301431	−	0.522093i
$696$		0			0
$697$	7.68794	+	43.6005i	0.291202	+	1.65149i
$698$		0			0
$699$	4.54086	−	3.81024i	0.171751	−	0.144116i
$700$		0			0
$701$	−6.47788	+	2.35776i	−0.244666	+	0.0890512i	−0.461443	−	0.887170i	$-0.652668\pi$
$701$	−6.47788	+	2.35776i	−0.244666	+	0.0890512i	0.216776	+	0.976221i	$0.430446\pi$
$702$		0			0
$703$	−6.45471	−	20.0452i	−0.243444	−	0.756020i
$704$		0			0
$705$	−5.51194	+	2.00618i	−0.207592	+	0.0755572i
$706$		0			0
$707$	33.7616	−	28.3294i	1.26974	−	1.06544i
$708$		0			0
$709$	−8.79501	−	49.8790i	−0.330304	−	1.87325i	−0.469429	−	0.882970i	$-0.655540\pi$
$709$	−8.79501	−	49.8790i	−0.330304	−	1.87325i	0.139125	−	0.990275i	$-0.455571\pi$
$710$		0			0
$711$	8.48243	−	14.6920i	0.318116	−	0.550993i
$712$		0			0
$713$	9.32490	+	3.39399i	0.349220	+	0.127106i
$714$		0			0
$715$	6.89355	+	11.9400i	0.257804	+	0.446530i
$716$		0			0
$717$	11.6197	+	9.75009i	0.433946	+	0.364124i
$718$		0			0
$719$	−3.41095	+	19.3445i	−0.127207	+	0.721427i	0.852765	+	0.522294i	$0.174924\pi$
$719$	−3.41095	+	19.3445i	−0.127207	+	0.721427i	−0.979972	+	0.199133i	$0.936187\pi$
$720$		0			0
$721$	37.4172			1.39349
$722$		0			0
$723$	−8.86254			−0.329602
$724$		0			0
$725$	0.524949	−	2.97713i	0.0194961	−	0.110568i
$726$		0			0
$727$	13.6886	+	11.4861i	0.507684	+	0.425997i	0.860313	−	0.509766i	$-0.170268\pi$
$727$	13.6886	+	11.4861i	0.507684	+	0.425997i	−0.352630	+	0.935763i	$0.614712\pi$
$728$		0			0
$729$	−0.500000	−	0.866025i	−0.0185185	−	0.0320750i
$730$		0			0
$731$	−47.7135	−	17.3663i	−1.76475	−	0.642315i
$732$		0			0
$733$	−19.5736	+	33.9025i	−0.722968	+	1.25222i	0.236837	+	0.971549i	$0.423889\pi$
$733$	−19.5736	+	33.9025i	−0.722968	+	1.25222i	−0.959805	+	0.280668i	$0.909444\pi$
$734$		0			0
$735$	−2.50468	−	14.2047i	−0.0923864	−	0.523949i
$736$		0			0
$737$	−3.54987	+	2.97869i	−0.130761	+	0.109722i
$738$		0			0
$739$	29.1001	−	10.5916i	1.07046	−	0.389617i	0.254113	−	0.967175i	$-0.418216\pi$
$739$	29.1001	−	10.5916i	1.07046	−	0.389617i	0.816350	+	0.577558i	$0.195994\pi$
$740$		0			0
$741$	−2.43777	−	7.57053i	−0.0895536	−	0.278110i
$742$		0			0
$743$	−11.5042	+	4.18720i	−0.422050	+	0.153614i	−0.544309	−	0.838885i	$-0.683208\pi$
$743$	−11.5042	+	4.18720i	−0.422050	+	0.153614i	0.122259	+	0.992498i	$0.460986\pi$
$744$		0			0
$745$	6.78084	−	5.68980i	0.248431	−	0.208458i
$746$		0			0
$747$	2.26180	+	12.8273i	0.0827549	+	0.469327i
$748$		0			0
$749$	20.1803	−	34.9533i	0.737372	−	1.27717i
$750$		0			0
$751$	−42.2047	−	15.3613i	−1.54007	−	0.560541i	−0.574010	−	0.818848i	$-0.694613\pi$
$751$	−42.2047	−	15.3613i	−1.54007	−	0.560541i	−0.966063	+	0.258308i	$0.916835\pi$
$752$		0			0
$753$	−5.85357	−	10.1387i	−0.213316	−	0.369474i
$754$		0			0
$755$	−17.1245	−	14.3692i	−0.623224	−	0.522947i
$756$		0			0
$757$	−2.64469	+	14.9988i	−0.0961228	+	0.545139i	0.898275	+	0.439434i	$0.144821\pi$
$757$	−2.64469	+	14.9988i	−0.0961228	+	0.545139i	−0.994398	+	0.105705i	$0.966290\pi$
$758$		0			0
$759$	−15.3042			−0.555508
$760$		0			0
$761$	−32.2300			−1.16834			−0.584169	−	0.811632i	$-0.698579\pi$
$761$	−32.2300			−1.16834			−0.584169	+	0.811632i	$0.698579\pi$
$762$		0			0
$763$	1.39341	−	7.90243i	0.0504449	−	0.286087i
$764$		0			0
$765$	−6.57456	−	5.51671i	−0.237704	−	0.199457i
$766$		0			0
$767$	5.84425	+	10.1225i	0.211024	+	0.365504i
$768$		0			0
$769$	−10.0805	−	3.66902i	−0.363514	−	0.132308i	0.153804	−	0.988101i	$-0.450847\pi$
$769$	−10.0805	−	3.66902i	−0.363514	−	0.132308i	−0.517318	+	0.855793i	$0.673070\pi$
$770$		0			0
$771$	−4.95799	+	8.58749i	−0.178558	+	0.309271i
$772$		0			0
$773$	0.143553	+	0.814127i	0.00516323	+	0.0292821i	0.987281	−	0.158988i	$-0.0508231\pi$
$773$	0.143553	+	0.814127i	0.00516323	+	0.0292821i	−0.982117	+	0.188270i	$0.939712\pi$
$774$		0			0
$775$	−4.58208	+	3.84482i	−0.164593	+	0.138110i
$776$		0			0
$777$	17.8432	−	6.49439i	0.640121	−	0.232985i
$778$		0			0
$779$	−38.0337	+	5.24307i	−1.36270	+	0.187852i
$780$		0			0
$781$	56.3422	−	20.5069i	2.01608	−	0.733793i
$782$		0			0
$783$	1.11093	−	0.932182i	0.0397014	−	0.0333135i
$784$		0			0
$785$	−2.18510	−	12.3923i	−0.0779895	−	0.442300i
$786$		0			0
$787$	−6.51330	+	11.2814i	−0.232174	+	0.402137i	−0.958448	−	0.285269i	$-0.907917\pi$
$787$	−6.51330	+	11.2814i	−0.232174	+	0.402137i	0.726274	+	0.687406i	$0.241251\pi$
$788$		0			0
$789$	6.33252	+	2.30485i	0.225444	+	0.0820547i
$790$		0			0
$791$	−27.5069	−	47.6434i	−0.978034	−	1.69400i
$792$		0			0
$793$	0.107201	+	0.0899521i	0.00380681	+	0.00319429i
$794$		0			0
$795$	0.626304	−	3.55195i	0.0222127	−	0.125975i
$796$		0			0
$797$	−47.0808			−1.66769			−0.833844	−	0.552000i	$-0.813865\pi$
$797$	−47.0808			−1.66769			−0.833844	+	0.552000i	$0.813865\pi$
$798$		0			0
$799$	17.2674			0.610877
$800$		0			0
$801$	2.14695	−	12.1759i	0.0758587	−	0.430216i
$802$		0			0
$803$	−13.5980	−	11.4101i	−0.479864	−	0.402654i
$804$		0			0
$805$	−11.6042	−	20.0991i	−0.408994	−	0.708399i
$806$		0			0
$807$	0.674972	+	0.245670i	0.0237601	+	0.00864799i
$808$		0			0
$809$	5.00748	−	8.67320i	0.176053	−	0.304934i	−0.764472	−	0.644657i	$-0.777000\pi$
$809$	5.00748	−	8.67320i	0.176053	−	0.304934i	0.940525	+	0.339724i	$0.110333\pi$
$810$		0			0
$811$	5.47946	+	31.0756i	0.192410	+	1.09121i	0.916059	+	0.401043i	$0.131352\pi$
$811$	5.47946	+	31.0756i	0.192410	+	1.09121i	−0.723649	+	0.690168i	$0.757537\pi$
$812$		0			0
$813$	−22.0935	+	18.5387i	−0.774854	+	0.650180i
$814$		0			0
$815$	−25.7170	+	9.36021i	−0.900826	+	0.327874i
$816$		0			0
$817$	16.6024	−	40.7824i	0.580844	−	1.42680i
$818$		0			0
$819$	6.73889	−	2.45275i	0.235476	−	0.0857062i
$820$		0			0
$821$	−29.3751	+	24.6487i	−1.02520	+	0.860244i	−0.990272	−	0.139146i	$-0.955564\pi$
$821$	−29.3751	+	24.6487i	−1.02520	+	0.860244i	−0.0349269	+	0.999390i	$0.511120\pi$
$822$		0			0
$823$	−8.53261	−	48.3909i	−0.297428	−	1.68680i	−0.657166	−	0.753746i	$-0.728245\pi$
$823$	−8.53261	−	48.3909i	−0.297428	−	1.68680i	0.359738	−	0.933053i	$-0.382866\pi$
$824$		0			0
$825$	4.61245	−	7.98900i	0.160585	−	0.278141i
$826$		0			0
$827$	15.0574	+	5.48045i	0.523597	+	0.190574i	0.590277	−	0.807201i	$-0.299018\pi$
$827$	15.0574	+	5.48045i	0.523597	+	0.190574i	−0.0666799	+	0.997774i	$0.521241\pi$
$828$		0			0
$829$	−17.2476	−	29.8737i	−0.599033	−	1.03756i	−0.992964	−	0.118416i	$-0.962218\pi$
$829$	−17.2476	−	29.8737i	−0.599033	−	1.03756i	0.393931	−	0.919140i	$-0.371115\pi$
$830$		0			0
$831$	2.93498	+	2.46274i	0.101813	+	0.0854314i
$832$		0			0
$833$	−7.37326	+	41.8159i	−0.255468	+	1.44883i
$834$		0			0
$835$	22.4145			0.775685
$836$		0			0
$837$	−2.86943			−0.0991818
$838$		0			0
$839$	2.95759	−	16.7733i	0.102107	−	0.579080i	−0.890229	−	0.455514i	$-0.849456\pi$
$839$	2.95759	−	16.7733i	0.102107	−	0.579080i	0.992336	−	0.123567i	$-0.0394333\pi$
$840$		0			0
$841$	−20.6042	−	17.2890i	−0.710490	−	0.596172i
$842$		0			0
$843$	−11.0461	−	19.1324i	−0.380447	−	0.658953i
$844$		0			0
$845$	15.5167	+	5.64760i	0.533789	+	0.194283i
$846$		0			0
$847$	16.8685	−	29.2171i	0.579608	−	1.00391i
$848$		0			0
$849$	−4.36665	−	24.7645i	−0.149863	−	0.849915i
$850$		0			0
$851$	12.7990	−	10.7396i	0.438743	−	0.368149i
$852$		0			0
$853$	−32.1506	+	11.7019i	−1.10082	+	0.400664i	−0.827617	−	0.561293i	$-0.810304\pi$
$853$	−32.1506	+	11.7019i	−1.10082	+	0.400664i	−0.273199	+	0.961957i	$0.588082\pi$
$854$		0			0
$855$	4.99469	−	5.51784i	0.170815	−	0.188706i
$856$		0			0
$857$	−7.76834	+	2.82745i	−0.265362	+	0.0965837i	−0.471274	−	0.881987i	$-0.656206\pi$
$857$	−7.76834	+	2.82745i	−0.265362	+	0.0965837i	0.205913	+	0.978570i	$0.433984\pi$
$858$		0			0
$859$	38.6809	−	32.4571i	1.31977	−	1.10742i	0.333421	−	0.942778i	$-0.391797\pi$
$859$	38.6809	−	32.4571i	1.31977	−	1.10742i	0.986353	−	0.164643i	$-0.0526473\pi$
$860$		0			0
$861$	−6.01145	−	34.0926i	−0.204870	−	1.16187i
$862$		0			0
$863$	−16.5035	+	28.5849i	−0.561785	+	0.973040i	0.435556	+	0.900162i	$0.356552\pi$
$863$	−16.5035	+	28.5849i	−0.561785	+	0.973040i	−0.997341	+	0.0728785i	$0.976781\pi$
$864$		0			0
$865$	29.6383	+	10.7874i	1.00773	+	0.366784i
$866$		0			0
$867$	4.13255	+	7.15778i	0.140349	+	0.243091i
$868$		0			0
$869$	57.5112	+	48.2576i	1.95093	+	1.63703i
$870$		0			0
$871$	0.331782	−	1.88163i	0.0112420	−	0.0637566i
$872$		0			0
$873$	0.175254			0.00593145
$874$		0			0
$875$	47.5438			1.60728
$876$		0			0
$877$	0.367446	−	2.08389i	0.0124078	−	0.0703680i	−0.977975	−	0.208721i	$-0.933070\pi$
$877$	0.367446	−	2.08389i	0.0124078	−	0.0703680i	0.990383	+	0.138353i	$0.0441810\pi$
$878$		0			0
$879$	4.54044	+	3.80988i	0.153145	+	0.128504i
$880$		0			0
$881$	26.5203	+	45.9345i	0.893492	+	1.54757i	0.835660	+	0.549246i	$0.185085\pi$
$881$	26.5203	+	45.9345i	0.893492	+	1.54757i	0.0578312	+	0.998326i	$0.481581\pi$
$882$		0			0
$883$	16.1473	+	5.87714i	0.543401	+	0.197782i	0.599112	−	0.800665i	$-0.295520\pi$
$883$	16.1473	+	5.87714i	0.543401	+	0.197782i	−0.0557114	+	0.998447i	$0.517743\pi$
$884$		0			0
$885$	−5.46900	+	9.47259i	−0.183839	+	0.318418i
$886$		0			0
$887$	0.676465	+	3.83642i	0.0227135	+	0.128814i	0.994056	−	0.108869i	$-0.0347230\pi$
$887$	0.676465	+	3.83642i	0.0227135	+	0.128814i	−0.971343	+	0.237684i	$0.923612\pi$
$888$		0			0
$889$	5.89901	−	4.94985i	0.197846	−	0.166013i
$890$		0			0
$891$	4.15847	−	1.51356i	0.139314	−	0.0507062i
$892$		0			0
$893$	−0.562045	+	14.9636i	−0.0188081	+	0.500739i
$894$		0			0
$895$	19.0274	−	6.92541i	0.636016	−	0.231491i
$896$		0			0
$897$	4.83382	−	4.05606i	0.161397	−	0.135428i
$898$		0			0
$899$	−0.722600	−	4.09807i	−0.0241001	−	0.136678i
$900$		0			0
$901$	−5.30876	+	9.19505i	−0.176861	+	0.306331i
$902$		0			0
$903$	37.3087	+	13.5792i	1.24156	+	0.451889i
$904$		0			0
$905$	−0.233687	−	0.404758i	−0.00776803	−	0.0134546i
$906$		0			0
$907$	6.77309	+	5.68329i	0.224897	+	0.188711i	0.748273	−	0.663391i	$-0.230883\pi$
$907$	6.77309	+	5.68329i	0.224897	+	0.188711i	−0.523376	+	0.852102i	$0.675328\pi$
$908$		0			0
$909$	−1.94720	+	11.0431i	−0.0645845	+	0.366277i
$910$		0			0
$911$	−18.4416			−0.610997			−0.305498	−	0.952193i	$-0.598823\pi$
$911$	−18.4416			−0.610997			−0.305498	+	0.952193i	$0.598823\pi$
$912$		0			0
$913$	−57.6411			−1.90764
$914$		0			0
$915$	−0.0227402	+	0.128966i	−0.000751766	+	0.00426348i
$916$		0			0
$917$	−4.69699	−	3.94124i	−0.155108	−	0.130151i
$918$		0			0
$919$	−22.7681	−	39.4355i	−0.751051	−	1.30086i	−0.947314	−	0.320307i	$-0.896214\pi$
$919$	−22.7681	−	39.4355i	−0.751051	−	1.30086i	0.196263	−	0.980551i	$-0.437119\pi$
$920$		0			0
$921$	16.5238	+	6.01417i	0.544477	+	0.198174i
$922$		0			0
$923$	−12.3607	+	21.4093i	−0.406857	+	0.704697i
$924$		0			0
$925$	1.74881	+	9.91797i	0.0575004	+	0.326101i
$926$		0			0
$927$	−7.29282	+	6.11940i	−0.239528	+	0.200988i
$928$		0			0
$929$	1.42489	−	0.518618i	0.0467492	−	0.0170153i	−0.318540	−	0.947910i	$-0.603192\pi$
$929$	1.42489	−	0.518618i	0.0467492	−	0.0170153i	0.365289	+	0.930894i	$0.380970\pi$
$930$		0			0
$931$	−35.9969	−	7.75063i	−1.17975	−	0.254017i
$932$		0			0
$933$	5.66509	−	2.06192i	0.185467	−	0.0675044i
$934$		0			0
$935$	29.0947	−	24.4134i	0.951500	−	0.798403i
$936$		0			0
$937$	1.23932	+	7.02855i	0.0404869	+	0.229613i	0.998336	−	0.0576578i	$-0.0183632\pi$
$937$	1.23932	+	7.02855i	0.0404869	+	0.229613i	−0.957849	+	0.287271i	$0.907252\pi$
$938$		0			0
$939$	8.34902	−	14.4609i	0.272460	−	0.471914i
$940$		0			0
$941$	−46.7927	−	17.0311i	−1.52540	−	0.555200i	−0.562909	−	0.826519i	$-0.690318\pi$
$941$	−46.7927	−	17.0311i	−1.52540	−	0.555200i	−0.962489	+	0.271319i	$0.912540\pi$
$942$		0			0
$943$	−15.2305	−	26.3799i	−0.495972	−	0.859049i
$944$		0			0
$945$	5.14086	+	4.31369i	0.167232	+	0.140324i
$946$		0			0
$947$	0.0606990	−	0.344241i	0.00197245	−	0.0111863i	−0.983806	−	0.179239i	$-0.942637\pi$
$947$	0.0606990	−	0.344241i	0.00197245	−	0.0111863i	0.985778	+	0.168052i	$0.0537477\pi$
$948$		0			0
$949$	7.31892			0.237582
$950$		0			0
$951$	2.19305			0.0711146
$952$		0			0
$953$	3.64810	−	20.6894i	0.118174	−	0.670195i	−0.866956	−	0.498384i	$-0.833927\pi$
$953$	3.64810	−	20.6894i	0.118174	−	0.670195i	0.985130	−	0.171811i	$-0.0549619\pi$
$954$		0			0
$955$	15.9116	+	13.3514i	0.514887	+	0.432041i
$956$		0			0
$957$	3.20886	+	5.55791i	0.103728	+	0.179662i
$958$		0			0
$959$	56.7356	+	20.6501i	1.83209	+	0.666826i
$960$		0			0
$961$	11.3832	−	19.7163i	0.367200	−	0.636009i
$962$		0			0
$963$	1.78319	+	10.1130i	0.0574626	+	0.325887i
$964$		0			0
$965$	30.1836	−	25.3271i	0.971645	−	0.815307i
$966$		0			0
$967$	−34.6193	+	12.6004i	−1.11328	+	0.405201i	−0.832196	−	0.554482i	$-0.812916\pi$
$967$	−34.6193	+	12.6004i	−1.11328	+	0.405201i	−0.281085	+	0.959683i	$0.590694\pi$
$968$		0			0
$969$	−19.3722	+	10.2350i	−0.622325	+	0.328794i
$970$		0			0
$971$	5.06606	−	1.84390i	0.162578	−	0.0591735i	−0.259449	−	0.965757i	$-0.583541\pi$
$971$	5.06606	−	1.84390i	0.162578	−	0.0591735i	0.422027	+	0.906583i	$0.361319\pi$
$972$		0			0
$973$	28.0247	−	23.5155i	0.898430	−	0.753873i
$974$		0			0
$975$	0.660476	+	3.74575i	0.0211522	+	0.119960i
$976$		0			0
$977$	20.3591	−	35.2630i	0.651345	−	1.12816i	−0.331451	−	0.943472i	$-0.607538\pi$
$977$	20.3591	−	35.2630i	0.651345	−	1.12816i	0.982797	−	0.184691i	$-0.0591283\pi$
$978$		0			0
$979$	51.4144	+	18.7133i	1.64321	+	0.598080i
$980$		0			0
$981$	1.02082	+	1.76812i	0.0325923	+	0.0564516i
$982$		0			0
$983$	−33.6989	−	28.2767i	−1.07483	−	0.901887i	−0.0793458	−	0.996847i	$-0.525283\pi$
$983$	−33.6989	−	28.2767i	−1.07483	−	0.901887i	−0.995481	+	0.0949603i	$0.969728\pi$
$984$		0			0
$985$	1.91797	−	10.8773i	0.0611115	−	0.346581i
$986$		0			0
$987$	−13.5019			−0.429771
$988$		0			0
$989$	34.9348			1.11086
$990$		0			0
$991$	−5.77639	+	32.7595i	−0.183493	+	1.04064i	0.744383	+	0.667752i	$0.232744\pi$
$991$	−5.77639	+	32.7595i	−0.183493	+	1.04064i	−0.927876	+	0.372888i	$0.878368\pi$
$992$		0			0
$993$	11.9049	+	9.98942i	0.377792	+	0.317005i
$994$		0			0
$995$	0.262172	+	0.454094i	0.00831140	+	0.0143958i
$996$		0			0
$997$	−25.4469	−	9.26192i	−0.805912	−	0.293328i	−0.0939778	−	0.995574i	$-0.529958\pi$
$997$	−25.4469	−	9.26192i	−0.805912	−	0.293328i	−0.711934	+	0.702246i	$0.752180\pi$
$998$		0			0
$999$	−2.41561	+	4.18397i	−0.0764266	+	0.132375i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	912.2.bo.j.385.1		12
4.3	odd	2		57.2.i.b.43.2	yes	12
12.11	even	2		171.2.u.e.100.1		12
19.4	even	9	inner	912.2.bo.j.289.1		12
76.23	odd	18		57.2.i.b.4.2	✓	12
76.55	odd	18		1083.2.a.q.1.3		6
76.59	even	18		1083.2.a.p.1.4		6
228.23	even	18		171.2.u.e.118.1		12
228.59	odd	18		3249.2.a.bg.1.3		6
228.131	even	18		3249.2.a.bh.1.4		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
57.2.i.b.4.2	✓	12	76.23	odd	18
57.2.i.b.43.2	yes	12	4.3	odd	2
171.2.u.e.100.1		12	12.11	even	2
171.2.u.e.118.1		12	228.23	even	18
912.2.bo.j.289.1		12	19.4	even	9	inner
912.2.bo.j.385.1		12	1.1	even	1	trivial
1083.2.a.p.1.4		6	76.59	even	18
1083.2.a.q.1.3		6	76.55	odd	18
3249.2.a.bg.1.3		6	228.59	odd	18
3249.2.a.bh.1.4		6	228.131	even	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 912 = 2^{4} \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	912.bo (of order \(9\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.173648 + 0.984808i) q^{3} +(1.30800 + 1.09754i) q^{5} +(1.96517 + 3.40377i) q^{7} +(-0.939693 - 0.342020i) q^{9} +(2.21268 - 3.83247i) q^{11} +(0.316842 + 1.79690i) q^{13} +(-1.30800 + 1.09754i) q^{15} +(4.72331 - 1.71914i) q^{17} +(1.33604 + 4.14910i) q^{19} +(-3.69330 + 1.34425i) q^{21} +(-2.64922 + 2.22296i) q^{23} +(-0.361980 - 2.05289i) q^{25} +(0.500000 - 0.866025i) q^{27} +(1.36276 + 0.496003i) q^{29} +(-1.43471 - 2.48499i) q^{31} +(3.39002 + 2.84456i) q^{33} +(-1.16534 + 6.60896i) q^{35} -4.83123 q^{37} -1.82462 q^{39} +(-1.52950 + 8.67423i) q^{41} +(-7.73836 - 6.49325i) q^{43} +(-0.853733 - 1.47871i) q^{45} +(3.22814 + 1.17495i) q^{47} +(-4.22376 + 7.31577i) q^{49} +(0.872832 + 4.95008i) q^{51} +(-1.61814 + 1.35778i) q^{53} +(7.10045 - 2.58435i) q^{55} +(-4.31806 + 0.595259i) q^{57} +(6.01966 - 2.19098i) q^{59} +(0.0587523 - 0.0492990i) q^{61} +(-0.682495 - 3.87062i) q^{63} +(-1.55774 + 2.69809i) q^{65} +(-0.984002 - 0.358147i) q^{67} +(-1.72915 - 2.99498i) q^{69} +(10.3790 + 8.70898i) q^{71} +(0.696538 - 3.95026i) q^{73} +2.08456 q^{75} +17.3931 q^{77} +(-2.94592 + 16.7071i) q^{79} +(0.766044 + 0.642788i) q^{81} +(-6.51259 - 11.2801i) q^{83} +(8.06489 + 2.93538i) q^{85} +(-0.725109 + 1.25592i) q^{87} +(2.14695 + 12.1759i) q^{89} +(-5.49359 + 4.60967i) q^{91} +(2.69638 - 0.981401i) q^{93} +(-2.80626 + 6.89335i) q^{95} +(-0.164685 + 0.0599404i) q^{97} +(-3.39002 + 2.84456i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 6 q^{5} + 9 q^{7} + 9 q^{11} - 3 q^{13} - 6 q^{15} + 12 q^{17} + 9 q^{19} - 9 q^{23} - 12 q^{25} + 6 q^{27} - 9 q^{33} - 30 q^{35} - 12 q^{37} - 6 q^{39} - 18 q^{41} - 15 q^{43} - 9 q^{45} + 9 q^{47}+ \cdots + 9 q^{99}+O(q^{100}) \) 12 * q + 6 * q^5 + 9 * q^7 + 9 * q^11 - 3 * q^13 - 6 * q^15 + 12 * q^17 + 9 * q^19 - 9 * q^23 - 12 * q^25 + 6 * q^27 - 9 * q^33 - 30 * q^35 - 12 * q^37 - 6 * q^39 - 18 * q^41 - 15 * q^43 - 9 * q^45 + 9 * q^47 - 9 * q^49 + 15 * q^51 - 30 * q^53 - 15 * q^55 - 3 * q^57 + 30 * q^59 + 21 * q^61 - 9 * q^63 + 21 * q^65 - 3 * q^67 - 6 * q^69 + 30 * q^71 - 24 * q^73 - 30 * q^75 + 96 * q^77 - 24 * q^79 - 3 * q^83 + 3 * q^85 - 15 * q^87 + 3 * q^89 - 24 * q^91 - 6 * q^93 + 54 * q^95 - 27 * q^97 + 9 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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