LMFDB - Embedded newform 912.2.bo.g.289.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [912,2,Mod(289,912)]

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

lf = mfeigenbasis(mf)

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")

//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);

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: f = N[0] # Warning: the index may be different

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} - 3 x^{11} + 27 x^{10} + 309 x^{8} + 42 x^{7} + 2059 x^{6} + 1245 x^{5} + 8226 x^{4} + \cdots + 16129 $ x^12 - 3x^11 + 27x^10 + 309x^8 + 42x^7 + 2059x^6 + 1245x^5 + 8226x^4 + 2250x^3 + 14496x^2 + 6096x + 16129
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 228)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			289.2
Root			$-1.16237 + 2.01328i$ of defining polynomial
Character	$\chi$	$=$	912.289
Dual form			912.2.bo.g.385.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.173648 + 0.984808i) q^{3} +(2.54690 - 2.13710i) q^{5} +(0.596313 - 1.03284i) q^{7} +(-0.939693 + 0.342020i) q^{9} +O(q^{10})$	\(q+(0.173648 + 0.984808i) q^{3} +(2.54690 - 2.13710i) q^{5} +(0.596313 - 1.03284i) q^{7} +(-0.939693 + 0.342020i) q^{9} +(0.647560 + 1.12161i) q^{11} +(0.496083 - 2.81343i) q^{13} +(2.54690 + 2.13710i) q^{15} +(2.08503 + 0.758891i) q^{17} +(2.84913 + 3.29886i) q^{19} +(1.12070 + 0.407902i) q^{21} +(-6.07384 - 5.09656i) q^{23} +(1.05125 - 5.96192i) q^{25} +(-0.500000 - 0.866025i) q^{27} +(4.21893 - 1.53557i) q^{29} +(3.91714 - 6.78468i) q^{31} +(-0.992120 + 0.832488i) q^{33} +(-0.688545 - 3.90493i) q^{35} -7.86729 q^{37} +2.85683 q^{39} +(1.40006 + 7.94015i) q^{41} +(1.37037 - 1.14988i) q^{43} +(-1.66237 + 2.87931i) q^{45} +(5.36453 - 1.95253i) q^{47} +(2.78882 + 4.83038i) q^{49} +(-0.385299 + 2.18514i) q^{51} +(-4.83597 - 4.05786i) q^{53} +(4.04626 + 1.47272i) q^{55} +(-2.75400 + 3.37868i) q^{57} +(-7.41778 - 2.69985i) q^{59} +(11.2096 + 9.40599i) q^{61} +(-0.207097 + 1.17451i) q^{63} +(-4.74910 - 8.22569i) q^{65} +(4.30894 - 1.56833i) q^{67} +(3.96442 - 6.86658i) q^{69} +(-3.20234 + 2.68708i) q^{71} +(0.338056 + 1.91721i) q^{73} +6.05389 q^{75} +1.54460 q^{77} +(1.07749 + 6.11077i) q^{79} +(0.766044 - 0.642788i) q^{81} +(3.91858 - 6.78719i) q^{83} +(6.93220 - 2.52311i) q^{85} +(2.24485 + 3.88819i) q^{87} +(-0.743166 + 4.21470i) q^{89} +(-2.61001 - 2.19006i) q^{91} +(7.36181 + 2.67948i) q^{93} +(14.3064 + 2.31298i) q^{95} +(2.38339 + 0.867483i) q^{97} +(-0.992120 - 0.832488i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 6 q^{5} + 9 q^{7}+O(q^{10}) $ 12 * q - 6 * q^5 + 9 * q^7	$ 12 q - 6 q^{5} + 9 q^{7} + 9 q^{11} - 3 q^{13} - 6 q^{15} + 12 q^{17} - 9 q^{19} + 6 q^{21} - 15 q^{23} + 12 q^{25} - 6 q^{27} - 24 q^{29} + 6 q^{31} - 9 q^{33} + 42 q^{35} + 12 q^{37} - 18 q^{39} + 6 q^{41} + 39 q^{43} - 3 q^{45} + 3 q^{47} - 21 q^{49} + 3 q^{51} + 18 q^{53} - 45 q^{55} + 3 q^{57} + 33 q^{61} - 3 q^{63} - 33 q^{65} + 27 q^{67} + 12 q^{69} - 6 q^{71} - 24 q^{73} + 30 q^{75} - 18 q^{79} - 3 q^{83} + 39 q^{85} + 9 q^{87} - 15 q^{89} - 18 q^{91} - 6 q^{93} + 30 q^{95} - 15 q^{97} - 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 + 6 * q^21 - 15 * q^23 + 12 * q^25 - 6 * q^27 - 24 * q^29 + 6 * q^31 - 9 * q^33 + 42 * q^35 + 12 * q^37 - 18 * q^39 + 6 * q^41 + 39 * q^43 - 3 * q^45 + 3 * q^47 - 21 * q^49 + 3 * q^51 + 18 * q^53 - 45 * q^55 + 3 * q^57 + 33 * q^61 - 3 * q^63 - 33 * q^65 + 27 * q^67 + 12 * q^69 - 6 * q^71 - 24 * q^73 + 30 * q^75 - 18 * q^79 - 3 * q^83 + 39 * q^85 + 9 * q^87 - 15 * q^89 - 18 * q^91 - 6 * q^93 + 30 * q^95 - 15 * q^97 - 9 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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
$5$	2.54690	−	2.13710i	1.13901	−	0.955741i	0.139602	−	0.990208i	$-0.455418\pi$
$5$	2.54690	−	2.13710i	1.13901	−	0.955741i	0.999406	+	0.0344670i	$0.0109734\pi$
$6$		0			0
$7$	0.596313	−	1.03284i	0.225385	−	0.390379i	−0.731050	−	0.682324i	$-0.760969\pi$
$7$	0.596313	−	1.03284i	0.225385	−	0.390379i	0.956435	+	0.291946i	$0.0943026\pi$
$8$		0			0
$9$	−0.939693	+	0.342020i	−0.313231	+	0.114007i
$10$		0			0
$11$	0.647560	+	1.12161i	0.195247	+	0.338177i	0.946981	−	0.321288i	$-0.104116\pi$
$11$	0.647560	+	1.12161i	0.195247	+	0.338177i	−0.751735	+	0.659466i	$0.770783\pi$
$12$		0			0
$13$	0.496083	−	2.81343i	0.137589	−	0.780304i	−0.835433	−	0.549592i	$-0.814783\pi$
$13$	0.496083	−	2.81343i	0.137589	−	0.780304i	0.973022	−	0.230712i	$-0.0741056\pi$
$14$		0			0
$15$	2.54690	+	2.13710i	0.657606	+	0.551797i
$16$		0			0
$17$	2.08503	+	0.758891i	0.505695	+	0.184058i	0.582254	−	0.813007i	$-0.302171\pi$
$17$	2.08503	+	0.758891i	0.505695	+	0.184058i	−0.0765586	+	0.997065i	$0.524393\pi$
$18$		0			0
$19$	2.84913	+	3.29886i	0.653635	+	0.756810i
$19$	2.84913	+	3.29886i	0.653635	+	0.756810i
$20$		0			0
$21$	1.12070	+	0.407902i	0.244557	+	0.0890116i
$22$		0			0
$23$	−6.07384	−	5.09656i	−1.26648	−	1.06271i	−0.994960	−	0.100275i	$-0.968028\pi$
$23$	−6.07384	−	5.09656i	−1.26648	−	1.06271i	−0.271524	−	0.962432i	$-0.587528\pi$
$24$		0			0
$25$	1.05125	−	5.96192i	0.210249	−	1.19238i
$26$		0			0
$27$	−0.500000	−	0.866025i	−0.0962250	−	0.166667i
$28$		0			0
$29$	4.21893	−	1.53557i	0.783436	−	0.285148i	0.0808315	−	0.996728i	$-0.474242\pi$
$29$	4.21893	−	1.53557i	0.783436	−	0.285148i	0.702605	+	0.711580i	$0.252020\pi$
$30$		0			0
$31$	3.91714	−	6.78468i	0.703538	−	1.21856i	−0.263678	−	0.964611i	$-0.584936\pi$
$31$	3.91714	−	6.78468i	0.703538	−	1.21856i	0.967216	−	0.253953i	$-0.0817310\pi$
$32$		0			0
$33$	−0.992120	+	0.832488i	−0.172706	+	0.144918i
$34$		0			0
$35$	−0.688545	−	3.90493i	−0.116385	−	0.660054i
$36$		0			0
$37$	−7.86729			−1.29337			−0.646687	−	0.762755i	$-0.723846\pi$
$37$	−7.86729			−1.29337			−0.646687	+	0.762755i	$0.723846\pi$
$38$		0			0
$39$	2.85683			0.457459
$40$		0			0
$41$	1.40006	+	7.94015i	0.218653	+	1.24004i	0.874454	+	0.485109i	$0.161220\pi$
$41$	1.40006	+	7.94015i	0.218653	+	1.24004i	−0.655801	+	0.754934i	$0.727669\pi$
$42$		0			0
$43$	1.37037	−	1.14988i	0.208980	−	0.175355i	−0.532290	−	0.846562i	$-0.678668\pi$
$43$	1.37037	−	1.14988i	0.208980	−	0.175355i	0.741270	+	0.671207i	$0.234224\pi$
$44$		0			0
$45$	−1.66237	+	2.87931i	−0.247811	+	0.429222i
$46$		0			0
$47$	5.36453	−	1.95253i	0.782497	−	0.284806i	0.0802834	−	0.996772i	$-0.474417\pi$
$47$	5.36453	−	1.95253i	0.782497	−	0.284806i	0.702213	+	0.711967i	$0.252195\pi$
$48$		0			0
$49$	2.78882	+	4.83038i	0.398403	+	0.690054i
$50$		0			0
$51$	−0.385299	+	2.18514i	−0.0539526	+	0.305981i
$52$		0			0
$53$	−4.83597	−	4.05786i	−0.664272	−	0.557390i	0.247092	−	0.968992i	$-0.420525\pi$
$53$	−4.83597	−	4.05786i	−0.664272	−	0.557390i	−0.911364	+	0.411602i	$0.864969\pi$
$54$		0			0
$55$	4.04626	+	1.47272i	0.545598	+	0.198581i
$56$		0			0
$57$	−2.75400	+	3.37868i	−0.364776	+	0.447518i
$58$		0			0
$59$	−7.41778	−	2.69985i	−0.965713	−	0.351491i	−0.189443	−	0.981892i	$-0.560668\pi$
$59$	−7.41778	−	2.69985i	−0.965713	−	0.351491i	−0.776270	+	0.630401i	$0.782891\pi$
$60$		0			0
$61$	11.2096	+	9.40599i	1.43524	+	1.20431i	0.942529	+	0.334123i	$0.108440\pi$
$61$	11.2096	+	9.40599i	1.43524	+	1.20431i	0.492715	+	0.870190i	$0.336004\pi$
$62$		0			0
$63$	−0.207097	+	1.17451i	−0.0260918	+	0.147974i
$64$		0			0
$65$	−4.74910	−	8.22569i	−0.589054	−	1.02027i
$66$		0			0
$67$	4.30894	−	1.56833i	0.526421	−	0.191601i	−0.0651188	−	0.997878i	$-0.520743\pi$
$67$	4.30894	−	1.56833i	0.526421	−	0.191601i	0.591539	+	0.806276i	$0.298520\pi$
$68$		0			0
$69$	3.96442	−	6.86658i	0.477260	−	0.826639i
$70$		0			0
$71$	−3.20234	+	2.68708i	−0.380048	+	0.318898i	−0.812721	−	0.582653i	$-0.802015\pi$
$71$	−3.20234	+	2.68708i	−0.380048	+	0.318898i	0.432674	+	0.901551i	$0.357570\pi$
$72$		0			0
$73$	0.338056	+	1.91721i	0.0395665	+	0.224393i	0.998179	−	0.0603212i	$-0.0192125\pi$
$73$	0.338056	+	1.91721i	0.0395665	+	0.224393i	−0.958613	+	0.284714i	$0.908101\pi$
$74$		0			0
$75$	6.05389			0.699043
$76$		0			0
$77$	1.54460			0.176023
$78$		0			0
$79$	1.07749	+	6.11077i	0.121227	+	0.687515i	0.983477	+	0.181032i	$0.0579437\pi$
$79$	1.07749	+	6.11077i	0.121227	+	0.687515i	−0.862250	+	0.506483i	$0.830945\pi$
$80$		0			0
$81$	0.766044	−	0.642788i	0.0851160	−	0.0714208i
$82$		0			0
$83$	3.91858	−	6.78719i	0.430120	−	0.744990i	−0.566763	−	0.823881i	$-0.691804\pi$
$83$	3.91858	−	6.78719i	0.430120	−	0.744990i	0.996883	+	0.0788906i	$0.0251378\pi$
$84$		0			0
$85$	6.93220	−	2.52311i	0.751902	−	0.273670i
$86$		0			0
$87$	2.24485	+	3.88819i	0.240673	+	0.416858i
$88$		0			0
$89$	−0.743166	+	4.21470i	−0.0787754	+	0.446758i	0.919752	+	0.392501i	$0.128390\pi$
$89$	−0.743166	+	4.21470i	−0.0787754	+	0.446758i	−0.998527	+	0.0542567i	$0.982721\pi$
$90$		0			0
$91$	−2.61001	−	2.19006i	−0.273604	−	0.229581i
$92$		0			0
$93$	7.36181	+	2.67948i	0.763384	+	0.277849i
$94$		0			0
$95$	14.3064	+	2.31298i	1.46781	+	0.237307i
$96$		0			0
$97$	2.38339	+	0.867483i	0.241997	+	0.0880795i	0.460171	−	0.887830i	$-0.347788\pi$
$97$	2.38339	+	0.867483i	0.241997	+	0.0880795i	−0.218175	+	0.975910i	$0.570010\pi$
$98$		0			0
$99$	−0.992120	−	0.832488i	−0.0997118	−	0.0836682i
$100$		0			0
$101$	2.16648	−	12.2867i	0.215573	−	1.22257i	−0.664337	−	0.747434i	$-0.731286\pi$
$101$	2.16648	−	12.2867i	0.215573	−	1.22257i	0.879910	−	0.475141i	$-0.157603\pi$
$102$		0			0
$103$	8.78891	+	15.2228i	0.865997	+	1.49995i	0.866054	+	0.499951i	$0.166649\pi$
$103$	8.78891	+	15.2228i	0.865997	+	1.49995i	−5.70163e−5		1.00000i	$0.500018\pi$
$104$		0			0
$105$	3.72604	−	1.35617i	0.363625	−	0.132349i
$106$		0			0
$107$	−4.35879	+	7.54965i	−0.421381	+	0.729853i	−0.996075	−	0.0885157i	$-0.971788\pi$
$107$	−4.35879	+	7.54965i	−0.421381	+	0.729853i	0.574694	+	0.818368i	$0.305121\pi$
$108$		0			0
$109$	−14.9617	+	12.5544i	−1.43307	+	1.20249i	−0.489204	+	0.872170i	$0.662713\pi$
$109$	−14.9617	+	12.5544i	−1.43307	+	1.20249i	−0.943869	+	0.330321i	$0.892843\pi$
$110$		0			0
$111$	−1.36614	−	7.74777i	−0.129668	−	0.735386i
$112$		0			0
$113$	0.595683			0.0560372			0.0280186	−	0.999607i	$-0.491080\pi$
$113$	0.595683			0.0560372			0.0280186	+	0.999607i	$0.491080\pi$
$114$		0			0
$115$	−26.3613			−2.45821
$116$		0			0
$117$	0.496083	+	2.81343i	0.0458629	+	0.260101i
$118$		0			0
$119$	2.02715	−	1.70098i	0.185829	−	0.155929i
$120$		0			0
$121$	4.66133	−	8.07366i	0.423757	−	0.733969i
$122$		0			0
$123$	−7.57640	+	2.75758i	−0.683141	+	0.248643i
$124$		0			0
$125$	−1.75196	−	3.03448i	−0.156700	−	0.271412i
$126$		0			0
$127$	−1.69849	+	9.63264i	−0.150717	+	0.854758i	0.811881	+	0.583823i	$0.198444\pi$
$127$	−1.69849	+	9.63264i	−0.150717	+	0.854758i	−0.962598	+	0.270935i	$0.912667\pi$
$128$		0			0
$129$	1.37037	+	1.14988i	0.120654	+	0.101241i
$130$		0			0
$131$	−14.7025	−	5.35127i	−1.28456	−	0.467543i	−0.392624	−	0.919699i	$-0.628433\pi$
$131$	−14.7025	−	5.35127i	−1.28456	−	0.467543i	−0.891939	+	0.452156i	$0.850655\pi$
$132$		0			0
$133$	5.10618	−	0.975555i	0.442762	−	0.0845913i
$134$		0			0
$135$	−3.12423	−	1.13713i	−0.268891	−	0.0978684i
$136$		0			0
$137$	−11.8578	−	9.94991i	−1.01308	−	0.850078i	−0.0243410	−	0.999704i	$-0.507749\pi$
$137$	−11.8578	−	9.94991i	−1.01308	−	0.850078i	−0.988743	+	0.149625i	$0.952193\pi$
$138$		0			0
$139$	−2.00473	+	11.3694i	−0.170039	+	0.964338i	0.773677	+	0.633580i	$0.218415\pi$
$139$	−2.00473	+	11.3694i	−0.170039	+	0.964338i	−0.943716	+	0.330758i	$0.892696\pi$
$140$		0			0
$141$	2.85441	+	4.94398i	0.240384	+	0.416358i
$142$		0			0
$143$	3.47680	−	1.26545i	0.290745	−	0.105823i
$144$		0			0
$145$	7.46353	−	12.9272i	0.619813	−	1.07355i
$146$		0			0
$147$	−4.27272	+	3.58524i	−0.352408	+	0.295706i
$148$		0			0
$149$	−4.05008	−	22.9691i	−0.331795	−	1.88170i	−0.456835	−	0.889552i	$-0.651017\pi$
$149$	−4.05008	−	22.9691i	−0.331795	−	1.88170i	0.125040	−	0.992152i	$-0.460094\pi$
$150$		0			0
$151$	3.39770			0.276501			0.138250	−	0.990397i	$-0.455852\pi$
$151$	3.39770			0.276501			0.138250	+	0.990397i	$0.455852\pi$
$152$		0			0
$153$	−2.21885			−0.179383
$154$		0			0
$155$	−4.52300	−	25.6512i	−0.363296	−	2.06035i
$156$		0			0
$157$	−17.4382	+	14.6324i	−1.39172	+	1.16779i	−0.427083	+	0.904213i	$0.640459\pi$
$157$	−17.4382	+	14.6324i	−1.39172	+	1.16779i	−0.964638	+	0.263580i	$0.915097\pi$
$158$		0			0
$159$	3.15646	−	5.46714i	0.250323	−	0.433573i
$160$		0			0
$161$	−8.88587	+	3.23419i	−0.700305	+	0.254890i
$162$		0			0
$163$	−6.53627	−	11.3211i	−0.511960	−	0.886741i	−0.999904	−	0.0138657i	$-0.995586\pi$
$163$	−6.53627	−	11.3211i	−0.511960	−	0.886741i	0.487944	−	0.872875i	$-0.337747\pi$
$164$		0			0
$165$	−0.747719	+	4.24052i	−0.0582098	+	0.330124i
$166$		0			0
$167$	11.6216	+	9.75170i	0.899308	+	0.754609i	0.970055	−	0.242885i	$-0.0780938\pi$
$167$	11.6216	+	9.75170i	0.899308	+	0.754609i	−0.0707468	+	0.997494i	$0.522538\pi$
$168$		0			0
$169$	4.54673	+	1.65488i	0.349749	+	0.127298i
$170$		0			0
$171$	−3.80558	−	2.12545i	−0.291020	−	0.162538i
$172$		0			0
$173$	−15.6934	−	5.71194i	−1.19315	−	0.434271i	−0.332321	−	0.943167i	$-0.607832\pi$
$173$	−15.6934	−	5.71194i	−1.19315	−	0.434271i	−0.860828	+	0.508896i	$0.830054\pi$
$174$		0			0
$175$	−5.53086	−	4.64095i	−0.418094	−	0.350823i
$176$		0			0
$177$	1.37075	−	7.77391i	0.103032	−	0.584323i
$178$		0			0
$179$	6.84712	+	11.8596i	0.511778	+	0.886425i	0.999907	+	0.0136533i	$0.00434612\pi$
$179$	6.84712	+	11.8596i	0.511778	+	0.886425i	−0.488129	+	0.872771i	$0.662321\pi$
$180$		0			0
$181$	−19.1404	+	6.96652i	−1.42269	+	0.517817i	−0.934827	−	0.355102i	$-0.884446\pi$
$181$	−19.1404	+	6.96652i	−1.42269	+	0.517817i	−0.487864	+	0.872920i	$0.662224\pi$
$182$		0			0
$183$	−7.31656	+	12.6727i	−0.540856	+	0.936790i
$184$		0			0
$185$	−20.0372	+	16.8132i	−1.47316	+	1.23613i
$186$		0			0
$187$	0.499009	+	2.83002i	0.0364911	+	0.206951i
$188$		0			0
$189$	−1.19263			−0.0867508
$190$		0			0
$191$	−21.2065			−1.53445			−0.767224	−	0.641380i	$-0.778362\pi$
$191$	−21.2065			−1.53445			−0.767224	+	0.641380i	$0.778362\pi$
$192$		0			0
$193$	2.43434	+	13.8059i	0.175228	+	0.993767i	0.937880	+	0.346958i	$0.112786\pi$
$193$	2.43434	+	13.8059i	0.175228	+	0.993767i	−0.762653	+	0.646808i	$0.776103\pi$
$194$		0			0
$195$	7.27605	−	6.10533i	0.521049	−	0.437212i
$196$		0			0
$197$	−2.84138	+	4.92142i	−0.202440	+	0.350637i	−0.949314	−	0.314329i	$-0.898220\pi$
$197$	−2.84138	+	4.92142i	−0.202440	+	0.350637i	0.746874	+	0.664966i	$0.231554\pi$
$198$		0			0
$199$	10.0943	−	3.67403i	0.715567	−	0.260445i	0.0415244	−	0.999137i	$-0.486779\pi$
$199$	10.0943	−	3.67403i	0.715567	−	0.260445i	0.674043	+	0.738692i	$0.264556\pi$
$200$		0			0
$201$	2.29274	+	3.97114i	0.161717	+	0.280103i
$202$		0			0
$203$	0.929804	−	5.27318i	0.0652595	−	0.370105i
$204$		0			0
$205$	20.5347	+	17.2307i	1.43421	+	1.20344i
$206$		0			0
$207$	7.45067	+	2.71182i	0.517858	+	0.188485i
$208$		0			0
$209$	−1.85504	+	5.33181i	−0.128316	+	0.368809i
$210$		0			0
$211$	−18.9123	−	6.88351i	−1.30198	−	0.473880i	−0.404336	−	0.914610i	$-0.632497\pi$
$211$	−18.9123	−	6.88351i	−1.30198	−	0.473880i	−0.897640	+	0.440730i	$0.854720\pi$
$212$		0			0
$213$	−3.20234	−	2.68708i	−0.219421	−	0.184116i
$214$		0			0
$215$	1.03279	−	5.85725i	0.0704357	−	0.399461i
$216$		0			0
$217$	−4.67168	−	8.09159i	−0.317134	−	0.549293i
$218$		0			0
$219$	−1.82938	+	0.665841i	−0.123618	+	0.0449933i
$220$		0			0
$221$	3.16943	−	5.48962i	0.213199	−	0.369272i
$222$		0			0
$223$	−2.60127	+	2.18272i	−0.174194	+	0.146166i	−0.725716	−	0.687994i	$-0.758492\pi$
$223$	−2.60127	+	2.18272i	−0.174194	+	0.146166i	0.551523	+	0.834160i	$0.314047\pi$
$224$		0			0
$225$	1.05125	+	5.96192i	0.0700831	+	0.397461i
$226$		0			0
$227$	−11.7293			−0.778503			−0.389251	−	0.921132i	$-0.627266\pi$
$227$	−11.7293			−0.778503			−0.389251	+	0.921132i	$0.627266\pi$
$228$		0			0
$229$	7.83401			0.517686			0.258843	−	0.965919i	$-0.416659\pi$
$229$	7.83401			0.517686			0.258843	+	0.965919i	$0.416659\pi$
$230$		0			0
$231$	0.268216	+	1.52113i	0.0176473	+	0.100083i
$232$		0			0
$233$	−2.10168	+	1.76352i	−0.137685	+	0.115532i	−0.709029	−	0.705179i	$-0.750867\pi$
$233$	−2.10168	+	1.76352i	−0.137685	+	0.115532i	0.571344	+	0.820711i	$0.306422\pi$
$234$		0			0
$235$	9.49015	−	16.4374i	0.619069	−	1.07226i
$236$		0			0
$237$	−5.83083	+	2.12225i	−0.378753	+	0.137855i
$238$		0			0
$239$	8.54354	+	14.7978i	0.552636	+	0.957193i	0.998083	+	0.0618851i	$0.0197112\pi$
$239$	8.54354	+	14.7978i	0.552636	+	0.957193i	−0.445448	+	0.895308i	$0.646955\pi$
$240$		0			0
$241$	0.561919	−	3.18680i	0.0361964	−	0.205280i	−0.961346	−	0.275342i	$-0.911209\pi$
$241$	0.561919	−	3.18680i	0.0361964	−	0.205280i	0.997543	+	0.0700625i	$0.0223199\pi$
$242$		0			0
$243$	0.766044	+	0.642788i	0.0491418	+	0.0412348i
$244$		0			0
$245$	17.4259	+	6.34249i	1.11330	+	0.405207i
$246$		0			0
$247$	10.6945	−	6.37931i	0.680475	−	0.405906i
$248$		0			0
$249$	7.36453	+	2.68047i	0.466708	+	0.169868i
$250$		0			0
$251$	−5.06837	−	4.25287i	−0.319913	−	0.268439i	0.468662	−	0.883378i	$-0.344736\pi$
$251$	−5.06837	−	4.25287i	−0.319913	−	0.268439i	−0.788575	+	0.614939i	$0.789181\pi$
$252$		0			0
$253$	1.78316	−	10.1128i	0.112106	−	0.635786i
$254$		0			0
$255$	3.68854	+	6.38875i	0.230986	+	0.400079i
$256$		0			0
$257$	−13.6959	+	4.98492i	−0.854330	+	0.310951i	−0.731804	−	0.681515i	$-0.761322\pi$
$257$	−13.6959	+	4.98492i	−0.854330	+	0.310951i	−0.122525	+	0.992465i	$0.539099\pi$
$258$		0			0
$259$	−4.69137	+	8.12569i	−0.291507	+	0.504906i
$260$		0			0
$261$	−3.43931	+	2.88592i	−0.212888	+	0.178634i
$262$		0			0
$263$	−1.70600	−	9.67520i	−0.105196	−	0.596598i	−0.991142	−	0.132809i	$-0.957600\pi$
$263$	−1.70600	−	9.67520i	−0.105196	−	0.596598i	0.885945	−	0.463790i	$-0.153511\pi$
$264$		0			0
$265$	−20.9888			−1.28933
$266$		0			0
$267$	−4.27972			−0.261915
$268$		0			0
$269$	3.75753	+	21.3100i	0.229101	+	1.29929i	0.854689	+	0.519141i	$0.173748\pi$
$269$	3.75753	+	21.3100i	0.229101	+	1.29929i	−0.625588	+	0.780154i	$0.715141\pi$
$270$		0			0
$271$	4.66583	−	3.91509i	0.283429	−	0.237825i	−0.489978	−	0.871735i	$-0.662995\pi$
$271$	4.66583	−	3.91509i	0.283429	−	0.237825i	0.773407	+	0.633910i	$0.218551\pi$
$272$		0			0
$273$	1.70356	−	2.95066i	0.103104	−	0.178582i
$274$		0			0
$275$	7.36768	−	2.68162i	0.444288	−	0.161708i
$276$		0			0
$277$	−8.11381	−	14.0535i	−0.487512	−	0.844395i	0.512385	−	0.858756i	$-0.328762\pi$
$277$	−8.11381	−	14.0535i	−0.487512	−	0.844395i	−0.999897	+	0.0143607i	$0.995429\pi$
$278$		0			0
$279$	−1.36041	+	7.71525i	−0.0814454	+	0.461900i
$280$		0			0
$281$	3.15528	+	2.64760i	0.188228	+	0.157942i	0.732032	−	0.681270i	$-0.238572\pi$
$281$	3.15528	+	2.64760i	0.188228	+	0.157942i	−0.543804	+	0.839212i	$0.683016\pi$
$282$		0			0
$283$	25.3540	+	9.22811i	1.50714	+	0.548554i	0.957898	−	0.287109i	$-0.0926941\pi$
$283$	25.3540	+	9.22811i	1.50714	+	0.548554i	0.549242	+	0.835663i	$0.314916\pi$
$284$		0			0
$285$	0.206445	+	14.4907i	0.0122287	+	0.858357i
$286$		0			0
$287$	9.03582	+	3.28877i	0.533367	+	0.194130i
$288$		0			0
$289$	−9.25130	−	7.76276i	−0.544194	−	0.456633i
$290$		0			0
$291$	−0.440433	+	2.49782i	−0.0258186	+	0.146425i
$292$		0			0
$293$	−3.12397	−	5.41088i	−0.182504	−	0.316107i	0.760228	−	0.649656i	$-0.225087\pi$
$293$	−3.12397	−	5.41088i	−0.182504	−	0.316107i	−0.942733	+	0.333549i	$0.891754\pi$
$294$		0			0
$295$	−24.6622	+	8.97630i	−1.43589	+	0.522621i
$296$		0			0
$297$	0.647560	−	1.12161i	0.0375753	−	0.0650823i
$298$		0			0
$299$	−17.3519	+	14.5600i	−1.00349	+	0.842026i
$300$		0			0
$301$	−0.370475	−	2.10107i	−0.0213538	−	0.121104i
$302$		0			0
$303$	12.4763			0.716743
$304$		0			0
$305$	48.6513			2.78577
$306$		0			0
$307$	2.08041	+	11.7986i	0.118735	+	0.673381i	0.984833	+	0.173506i	$0.0555096\pi$
$307$	2.08041	+	11.7986i	0.118735	+	0.673381i	−0.866098	+	0.499875i	$0.833379\pi$
$308$		0			0
$309$	−13.4654	+	11.2988i	−0.766019	+	0.642766i
$310$		0			0
$311$	−4.54108	+	7.86538i	−0.257501	+	0.446005i	−0.965572	−	0.260137i	$-0.916232\pi$
$311$	−4.54108	+	7.86538i	−0.257501	+	0.446005i	0.708071	+	0.706141i	$0.249566\pi$
$312$		0			0
$313$	15.5136	−	5.64648i	0.876878	−	0.319158i	0.135929	−	0.990719i	$-0.456598\pi$
$313$	15.5136	−	5.64648i	0.876878	−	0.319158i	0.740949	+	0.671561i	$0.234376\pi$
$314$		0			0
$315$	1.98259	+	3.43394i	0.111706	+	0.193481i
$316$		0			0
$317$	3.37258	−	19.1269i	0.189423	−	1.07427i	−0.730716	−	0.682681i	$-0.760814\pi$
$317$	3.37258	−	19.1269i	0.189423	−	1.07427i	0.920139	−	0.391591i	$-0.128075\pi$
$318$		0			0
$319$	4.45432	+	3.73762i	0.249394	+	0.209266i
$320$		0			0
$321$	−8.19185	−	2.98159i	−0.457225	−	0.166416i
$322$		0			0
$323$	3.43706	+	9.04041i	0.191243	+	0.503022i
$324$		0			0
$325$	−16.2519	−	5.91521i	−0.901494	−	0.328117i
$326$		0			0
$327$	−14.9617	−	12.5544i	−0.827385	−	0.694258i
$328$		0			0
$329$	1.18228	−	6.70504i	0.0651812	−	0.369661i
$330$		0			0
$331$	−7.48454	−	12.9636i	−0.411387	−	0.712544i	0.583654	−	0.812002i	$-0.301622\pi$
$331$	−7.48454	−	12.9636i	−0.411387	−	0.712544i	−0.995042	+	0.0994585i	$0.968289\pi$
$332$		0			0
$333$	7.39283	−	2.69077i	0.405125	−	0.147453i
$334$		0			0
$335$	7.62276	−	13.2030i	0.416476	−	0.721357i
$336$		0			0
$337$	12.3718	−	10.3812i	0.673934	−	0.565498i	−0.240293	−	0.970700i	$-0.577243\pi$
$337$	12.3718	−	10.3812i	0.673934	−	0.565498i	0.914227	+	0.405203i	$0.132799\pi$
$338$		0			0
$339$	0.103439	+	0.586634i	0.00561805	+	0.0318616i
$340$		0			0
$341$	10.1463			0.549454
$342$		0			0
$343$	15.0004			0.809947
$344$		0			0
$345$	−4.57760	−	25.9608i	−0.246449	−	1.39768i
$346$		0			0
$347$	−24.3637	+	20.4436i	−1.30791	+	1.09747i	−0.319194	+	0.947689i	$0.603412\pi$
$347$	−24.3637	+	20.4436i	−1.30791	+	1.09747i	−0.988719	+	0.149780i	$0.952143\pi$
$348$		0			0
$349$	1.77710	−	3.07803i	0.0951261	−	0.164763i	−0.814535	−	0.580114i	$-0.803008\pi$
$349$	1.77710	−	3.07803i	0.0951261	−	0.164763i	0.909661	+	0.415351i	$0.136341\pi$
$350$		0			0
$351$	−2.68454	+	0.977093i	−0.143290	+	0.0521534i
$352$		0			0
$353$	15.7010	+	27.1949i	0.835678	+	1.44744i	0.893477	+	0.449109i	$0.148259\pi$
$353$	15.7010	+	27.1949i	0.835678	+	1.44744i	−0.0577986	+	0.998328i	$0.518408\pi$
$354$		0			0
$355$	−2.41347	+	13.6874i	−0.128093	+	0.726454i
$356$		0			0
$357$	2.02715	+	1.70098i	0.107288	+	0.0900255i
$358$		0			0
$359$	−15.9000	−	5.78713i	−0.839171	−	0.305433i	−0.113554	−	0.993532i	$-0.536223\pi$
$359$	−15.9000	−	5.78713i	−0.839171	−	0.305433i	−0.725617	+	0.688099i	$0.758446\pi$
$360$		0			0
$361$	−2.76493	+	18.7977i	−0.145523	+	0.989355i
$362$		0			0
$363$	8.76044	+	3.18854i	0.459804	+	0.167355i
$364$		0			0
$365$	4.95827	+	4.16048i	0.259528	+	0.217770i
$366$		0			0
$367$	−1.65004	+	9.35784i	−0.0861314	+	0.488475i	0.910975	+	0.412461i	$0.135331\pi$
$367$	−1.65004	+	9.35784i	−0.0861314	+	0.488475i	−0.997107	+	0.0760144i	$0.975780\pi$
$368$		0			0
$369$	−4.03132	−	6.98245i	−0.209862	−	0.363492i
$370$		0			0
$371$	−7.07490	+	2.57505i	−0.367310	+	0.133690i
$372$		0			0
$373$	11.6964	−	20.2588i	0.605619	−	1.04896i	−0.386334	−	0.922359i	$-0.626259\pi$
$373$	11.6964	−	20.2588i	0.605619	−	1.04896i	0.991953	−	0.126604i	$-0.0404078\pi$
$374$		0			0
$375$	2.68415	−	2.25227i	0.138609	−	0.116307i
$376$		0			0
$377$	−2.22726	−	12.6314i	−0.114710	−	0.650552i
$378$		0			0
$379$	22.1013			1.13527			0.567634	−	0.823281i	$-0.307859\pi$
$379$	22.1013			1.13527			0.567634	+	0.823281i	$0.307859\pi$
$380$		0			0
$381$	−9.78123			−0.501108
$382$		0			0
$383$	−3.13998	−	17.8077i	−0.160446	−	0.909932i	−0.953637	−	0.300960i	$-0.902693\pi$
$383$	−3.13998	−	17.8077i	−0.160446	−	0.909932i	0.793191	−	0.608973i	$-0.208418\pi$
$384$		0			0
$385$	3.93393	−	3.30096i	0.200492	−	0.168232i
$386$		0			0
$387$	−0.894447	+	1.54923i	−0.0454673	+	0.0787516i
$388$		0			0
$389$	−31.8516	+	11.5930i	−1.61494	+	0.587791i	−0.982409	−	0.186742i	$-0.940207\pi$
$389$	−31.8516	+	11.5930i	−1.61494	+	0.587791i	−0.632533	+	0.774533i	$0.717985\pi$
$390$		0			0
$391$	−8.79644	−	15.2359i	−0.444855	−	0.770512i
$392$		0			0
$393$	2.71691	−	15.4084i	0.137050	−	0.777249i
$394$		0			0
$395$	15.8036	+	13.2608i	0.795165	+	0.667223i
$396$		0			0
$397$	16.4034	+	5.97033i	0.823261	+	0.299642i	0.719090	−	0.694917i	$-0.244559\pi$
$397$	16.4034	+	5.97033i	0.823261	+	0.299642i	0.104171	+	0.994559i	$0.466781\pi$
$398$		0			0
$399$	1.84741	+	4.85920i	0.0924863	+	0.243264i
$400$		0			0
$401$	30.9170	+	11.2529i	1.54392	+	0.561941i	0.966981	−	0.254847i	$-0.0820250\pi$
$401$	30.9170	+	11.2529i	1.54392	+	0.561941i	0.576938	+	0.816788i	$0.304247\pi$
$402$		0			0
$403$	−17.1450	−	14.3863i	−0.854052	−	0.716634i
$404$		0			0
$405$	0.577335	−	3.27423i	0.0286880	−	0.162698i
$406$		0			0
$407$	−5.09455	−	8.82401i	−0.252527	−	0.437390i
$408$		0			0
$409$	−7.26825	+	2.64543i	−0.359392	+	0.130808i	−0.515404	−	0.856947i	$-0.672358\pi$
$409$	−7.26825	+	2.64543i	−0.359392	+	0.130808i	0.156013	+	0.987755i	$0.450136\pi$
$410$		0			0
$411$	7.73966	−	13.4055i	0.381769	−	0.661243i
$412$		0			0
$413$	−7.21185	+	6.05146i	−0.354872	+	0.297773i
$414$		0			0
$415$	−4.52467	−	25.6607i	−0.222107	−	1.25963i
$416$		0			0
$417$	−11.5448			−0.565350
$418$		0			0
$419$	26.4903			1.29414			0.647068	−	0.762432i	$-0.275995\pi$
$419$	26.4903			1.29414			0.647068	+	0.762432i	$0.275995\pi$
$420$		0			0
$421$	1.83547	+	10.4095i	0.0894554	+	0.507327i	0.996306	+	0.0858746i	$0.0273684\pi$
$421$	1.83547	+	10.4095i	0.0894554	+	0.507327i	−0.906851	+	0.421452i	$0.861520\pi$
$422$		0			0
$423$	−4.37320	+	3.66955i	−0.212632	+	0.178420i
$424$		0			0
$425$	6.71633	−	11.6330i	0.325790	−	0.564285i
$426$		0			0
$427$	16.3994	−	5.96888i	0.793621	−	0.288855i
$428$		0			0
$429$	1.84997	+	3.20424i	0.0893173	+	0.154702i
$430$		0			0
$431$	−2.61415	+	14.8256i	−0.125919	+	0.714123i	0.854838	+	0.518894i	$0.173656\pi$
$431$	−2.61415	+	14.8256i	−0.125919	+	0.714123i	−0.980758	+	0.195229i	$0.937455\pi$
$432$		0			0
$433$	−29.7556	−	24.9679i	−1.42996	−	1.19988i	−0.945735	−	0.324939i	$-0.894656\pi$
$433$	−29.7556	−	24.9679i	−1.42996	−	1.19988i	−0.484228	−	0.874942i	$-0.660899\pi$
$434$		0			0
$435$	14.0269	+	5.10536i	0.672536	+	0.244783i
$436$		0			0
$437$	−0.492330	−	34.5575i	−0.0235513	−	1.65311i
$438$		0			0
$439$	0.955140	+	0.347643i	0.0455864	+	0.0165921i	0.364713	−	0.931120i	$-0.381167\pi$
$439$	0.955140	+	0.347643i	0.0455864	+	0.0165921i	−0.319126	+	0.947712i	$0.603389\pi$
$440$		0			0
$441$	−4.27272	−	3.58524i	−0.203463	−	0.170726i
$442$		0			0
$443$	2.08139	−	11.8042i	0.0988900	−	0.560833i	−0.894596	−	0.446876i	$-0.852536\pi$
$443$	2.08139	−	11.8042i	0.0988900	−	0.560833i	0.993486	−	0.113957i	$-0.0363525\pi$
$444$		0			0
$445$	7.11448	+	12.3226i	0.337259	+	0.584149i
$446$		0			0
$447$	21.9169	−	7.97709i	1.03663	−	0.377303i
$448$		0			0
$449$	−15.7291	+	27.2436i	−0.742301	+	1.28570i	0.209144	+	0.977885i	$0.432932\pi$
$449$	−15.7291	+	27.2436i	−0.742301	+	1.28570i	−0.951445	+	0.307818i	$0.900401\pi$
$450$		0			0
$451$	−7.99910	+	6.71205i	−0.376663	+	0.316058i
$452$		0			0
$453$	0.590004	+	3.34608i	0.0277208	+	0.157213i
$454$		0			0
$455$	−11.3278			−0.531056
$456$		0			0
$457$	−5.25795			−0.245956			−0.122978	−	0.992409i	$-0.539245\pi$
$457$	−5.25795			−0.245956			−0.122978	+	0.992409i	$0.539245\pi$
$458$		0			0
$459$	−0.385299	−	2.18514i	−0.0179842	−	0.101994i
$460$		0			0
$461$	12.8528	−	10.7848i	0.598616	−	0.502299i	−0.292384	−	0.956301i	$-0.594449\pi$
$461$	12.8528	−	10.7848i	0.598616	−	0.502299i	0.891001	+	0.454002i	$0.150004\pi$
$462$		0			0
$463$	4.73299	−	8.19777i	0.219961	−	0.380983i	−0.734835	−	0.678246i	$-0.762740\pi$
$463$	4.73299	−	8.19777i	0.219961	−	0.380983i	0.954796	+	0.297263i	$0.0960738\pi$
$464$		0			0
$465$	24.4761	−	8.90857i	1.13505	−	0.413125i
$466$		0			0
$467$	−9.27914	−	16.0719i	−0.429387	−	0.743721i	0.567432	−	0.823421i	$-0.307937\pi$
$467$	−9.27914	−	16.0719i	−0.429387	−	0.743721i	−0.996819	+	0.0796999i	$0.974604\pi$
$468$		0			0
$469$	0.949640	−	5.38568i	0.0438503	−	0.248687i
$470$		0			0
$471$	−17.4382	−	14.6324i	−0.803510	−	0.674225i
$472$		0			0
$473$	2.17711	+	0.792404i	0.100104	+	0.0364348i
$474$		0			0
$475$	22.6627	−	13.5184i	1.03983	−	0.620265i
$476$		0			0
$477$	5.93220	+	2.15914i	0.271617	+	0.0988604i
$478$		0			0
$479$	5.52763	+	4.63823i	0.252564	+	0.211926i	0.760275	−	0.649601i	$-0.225064\pi$
$479$	5.52763	+	4.63823i	0.252564	+	0.211926i	−0.507712	+	0.861527i	$0.669508\pi$
$480$		0			0
$481$	−3.90283	+	22.1340i	−0.177954	+	1.00923i
$482$		0			0
$483$	−4.72807	−	8.18926i	−0.215135	−	0.372624i
$484$		0			0
$485$	7.92415	−	2.88415i	0.359817	−	0.130963i
$486$		0			0
$487$	2.32705	−	4.03057i	0.105449	−	0.182642i	−0.808473	−	0.588534i	$-0.799705\pi$
$487$	2.32705	−	4.03057i	0.105449	−	0.182642i	0.913921	+	0.405891i	$0.133039\pi$
$488$		0			0
$489$	10.0141	−	8.40286i	0.452855	−	0.379991i
$490$		0			0
$491$	−0.690291	−	3.91483i	−0.0311524	−	0.176674i	0.965262	−	0.261285i	$-0.0841463\pi$
$491$	−0.690291	−	3.91483i	−0.0311524	−	0.176674i	−0.996414	+	0.0846112i	$0.973035\pi$
$492$		0			0
$493$	9.96195			0.448664
$494$		0			0
$495$	−4.30594			−0.193538
$496$		0			0
$497$	0.865741	+	4.90986i	0.0388338	+	0.220237i
$498$		0			0
$499$	−0.215315	+	0.180670i	−0.00963881	+	0.00808792i	−0.647594	−	0.761985i	$-0.724225\pi$
$499$	−0.215315	+	0.180670i	−0.00963881	+	0.00808792i	0.637955	+	0.770073i	$0.279780\pi$
$500$		0			0
$501$	−7.58548	+	13.1384i	−0.338894	+	0.586982i
$502$		0			0
$503$	34.6506	−	12.6118i	1.54499	−	0.562332i	0.577757	−	0.816208i	$-0.303928\pi$
$503$	34.6506	−	12.6118i	1.54499	−	0.562332i	0.967237	+	0.253877i	$0.0817057\pi$
$504$		0			0
$505$	−20.7402	−	35.9230i	−0.922925	−	1.59855i
$506$		0			0
$507$	−0.840202	+	4.76502i	−0.0373147	+	0.211622i
$508$		0			0
$509$	19.9516	+	16.7413i	0.884338	+	0.742047i	0.967066	−	0.254525i	$-0.0819191\pi$
$509$	19.9516	+	16.7413i	0.884338	+	0.742047i	−0.0827287	+	0.996572i	$0.526364\pi$
$510$		0			0
$511$	2.18177	+	0.794099i	0.0965158	+	0.0351289i
$512$		0			0
$513$	1.43233	−	4.11685i	0.0632390	−	0.181763i
$514$		0			0
$515$	54.9172	+	19.9882i	2.41994	+	0.880786i
$516$		0			0
$517$	5.66383	+	4.75252i	0.249095	+	0.209015i
$518$		0			0
$519$	2.90003	−	16.4469i	0.127297	−	0.721937i
$520$		0			0
$521$	−4.97112	−	8.61023i	−0.217789	−	0.377221i	0.736343	−	0.676608i	$-0.236551\pi$
$521$	−4.97112	−	8.61023i	−0.217789	−	0.377221i	−0.954132	+	0.299387i	$0.903218\pi$
$522$		0			0
$523$	−35.3037	+	12.8495i	−1.54373	+	0.561870i	−0.966935	−	0.255022i	$-0.917917\pi$
$523$	−35.3037	+	12.8495i	−1.54373	+	0.561870i	−0.576790	+	0.816892i	$0.695695\pi$
$524$		0			0
$525$	3.61002	−	6.25273i	0.157554	−	0.272892i
$526$		0			0
$527$	13.3162	−	11.1736i	0.580062	−	0.486730i
$528$		0			0
$529$	6.92275	+	39.2608i	0.300989	+	1.70699i
$530$		0			0
$531$	7.89384			0.342563
$532$		0			0
$533$	23.0336			0.997695
$534$		0			0
$535$	5.03297	+	28.5434i	0.217594	+	1.23404i
$536$		0			0
$537$	−10.4904	+	8.80248i	−0.452694	+	0.379855i
$538$		0			0
$539$	−3.61186	+	6.25593i	−0.155574	+	0.269462i
$540$		0			0
$541$	2.50545	−	0.911911i	0.107718	−	0.0392061i	−0.287599	−	0.957751i	$-0.592857\pi$
$541$	2.50545	−	0.911911i	0.107718	−	0.0392061i	0.395317	+	0.918545i	$0.370635\pi$
$542$		0			0
$543$	−10.1844	−	17.6398i	−0.437053	−	0.756998i
$544$		0			0
$545$	−11.2760	+	63.9494i	−0.483011	+	2.73929i
$546$		0			0
$547$	17.5767	+	14.7486i	0.751526	+	0.630605i	0.935906	−	0.352250i	$-0.114583\pi$
$547$	17.5767	+	14.7486i	0.751526	+	0.630605i	−0.184380	+	0.982855i	$0.559028\pi$
$548$		0			0
$549$	−13.7506	−	5.00482i	−0.586863	−	0.213601i
$550$		0			0
$551$	17.0859	+	9.54264i	0.727884	+	0.406530i
$552$		0			0
$553$	6.95400	+	2.53105i	0.295714	+	0.107631i
$554$		0			0
$555$	−20.0372	−	16.8132i	−0.850531	−	0.713680i
$556$		0			0
$557$	−1.26779	+	7.18999i	−0.0537180	+	0.304650i	−0.999815	−	0.0192335i	$-0.993877\pi$
$557$	−1.26779	+	7.18999i	−0.0537180	+	0.304650i	0.946097	+	0.323883i	$0.104989\pi$
$558$		0			0
$559$	−2.55528	−	4.42588i	−0.108077	−	0.187195i
$560$		0			0
$561$	−2.70037	+	0.982855i	−0.114010	+	0.0414962i
$562$		0			0
$563$	21.1345	−	36.6060i	0.890712	−	1.54276i	0.0516876	−	0.998663i	$-0.483540\pi$
$563$	21.1345	−	36.6060i	0.890712	−	1.54276i	0.839024	−	0.544094i	$-0.183127\pi$
$564$		0			0
$565$	1.51714	−	1.27304i	0.0638268	−	0.0535570i
$566$		0			0
$567$	−0.207097	−	1.17451i	−0.00869727	−	0.0493247i
$568$		0			0
$569$	15.0782			0.632112			0.316056	−	0.948741i	$-0.397641\pi$
$569$	15.0782			0.632112			0.316056	+	0.948741i	$0.397641\pi$
$570$		0			0
$571$	42.7731			1.79000			0.894998	−	0.446070i	$-0.147177\pi$
$571$	42.7731			1.79000			0.894998	+	0.446070i	$0.147177\pi$
$572$		0			0
$573$	−3.68247	−	20.8843i	−0.153837	−	0.872455i
$574$		0			0
$575$	−36.7704	+	30.8540i	−1.53343	+	1.28670i
$576$		0			0
$577$	−11.6399	+	20.1609i	−0.484576	+	0.839311i	−0.999843	−	0.0177189i	$-0.994360\pi$
$577$	−11.6399	+	20.1609i	−0.484576	+	0.839311i	0.515267	+	0.857030i	$0.327693\pi$
$578$		0			0
$579$	−13.1734	+	4.79472i	−0.547467	+	0.199262i
$580$		0			0
$581$	−4.67341	−	8.09458i	−0.193886	−	0.335820i
$582$		0			0
$583$	1.41974	−	8.05177i	0.0587998	−	0.333470i
$584$		0			0
$585$	7.27605	+	6.10533i	0.300828	+	0.252424i
$586$		0			0
$587$	20.5574	+	7.48229i	0.848496	+	0.308827i	0.729427	−	0.684059i	$-0.239787\pi$
$587$	20.5574	+	7.48229i	0.848496	+	0.308827i	0.119069	+	0.992886i	$0.462009\pi$
$588$		0			0
$589$	33.5421	−	6.40834i	1.38208	−	0.264051i
$590$		0			0
$591$	−5.34005	−	1.94362i	−0.219660	−	0.0799499i
$592$		0			0
$593$	−25.1385	−	21.0937i	−1.03231	−	0.866213i	−0.0411885	−	0.999151i	$-0.513114\pi$
$593$	−25.1385	−	21.0937i	−1.03231	−	0.866213i	−0.991124	+	0.132938i	$0.957559\pi$
$594$		0			0
$595$	1.52778	−	8.66445i	0.0626327	−	0.355208i
$596$		0			0
$597$	5.37107	+	9.30297i	0.219823	+	0.380745i
$598$		0			0
$599$	−6.49512	+	2.36403i	−0.265384	+	0.0965917i	−0.471285	−	0.881981i	$-0.656210\pi$
$599$	−6.49512	+	2.36403i	−0.265384	+	0.0965917i	0.205901	+	0.978573i	$0.433987\pi$
$600$		0			0
$601$	17.0005	−	29.4457i	0.693465	−	1.20112i	−0.277231	−	0.960803i	$-0.589417\pi$
$601$	17.0005	−	29.4457i	0.693465	−	1.20112i	0.970696	−	0.240313i	$-0.0772500\pi$
$602$		0			0
$603$	−3.51268	+	2.94749i	−0.143047	+	0.120031i
$604$		0			0
$605$	−5.38230	−	30.5245i	−0.218822	−	1.24100i
$606$		0			0
$607$	−21.1493			−0.858424			−0.429212	−	0.903204i	$-0.641209\pi$
$607$	−21.1493			−0.858424			−0.429212	+	0.903204i	$0.641209\pi$
$608$		0			0
$609$	5.35453			0.216977
$610$		0			0
$611$	−2.83204	−	16.0613i	−0.114572	−	0.649772i
$612$		0			0
$613$	−3.92762	+	3.29566i	−0.158635	+	0.133111i	−0.718650	−	0.695372i	$-0.755240\pi$
$613$	−3.92762	+	3.29566i	−0.158635	+	0.133111i	0.560015	+	0.828482i	$0.310795\pi$
$614$		0			0
$615$	−13.4031	+	23.2148i	−0.540464	+	0.936112i
$616$		0			0
$617$	25.5654	−	9.30504i	1.02922	−	0.374607i	0.228439	−	0.973558i	$-0.426638\pi$
$617$	25.5654	−	9.30504i	1.02922	−	0.374607i	0.800785	+	0.598951i	$0.204416\pi$
$618$		0			0
$619$	−5.74222	−	9.94582i	−0.230799	−	0.399756i	0.727244	−	0.686379i	$-0.240801\pi$
$619$	−5.74222	−	9.94582i	−0.230799	−	0.399756i	−0.958044	+	0.286623i	$0.907467\pi$
$620$		0			0
$621$	−1.37683	+	7.80838i	−0.0552502	+	0.313340i
$622$		0			0
$623$	3.90997	+	3.28086i	0.156650	+	0.131445i
$624$		0			0
$625$	17.4969	+	6.36837i	0.699878	+	0.254735i
$626$		0			0
$627$	−5.57294	−	0.901000i	−0.222562	−	0.0359825i
$628$		0			0
$629$	−16.4036	−	5.97041i	−0.654053	−	0.238056i
$630$		0			0
$631$	−2.74578	−	2.30398i	−0.109308	−	0.0917201i	0.586496	−	0.809952i	$-0.300507\pi$
$631$	−2.74578	−	2.30398i	−0.109308	−	0.0917201i	−0.695803	+	0.718232i	$0.744952\pi$
$632$		0			0
$633$	3.49485	−	19.8203i	0.138908	−	0.787785i
$634$		0			0
$635$	16.2600	+	28.1632i	0.645259	+	1.11762i
$636$		0			0
$637$	14.9734	−	5.44987i	0.593268	−	0.215932i
$638$		0			0
$639$	2.09018	−	3.62029i	0.0826862	−	0.143217i
$640$		0			0
$641$	3.30991	−	2.77734i	0.130734	−	0.109698i	−0.575076	−	0.818100i	$-0.695028\pi$
$641$	3.30991	−	2.77734i	0.130734	−	0.109698i	0.705810	+	0.708401i	$0.250583\pi$
$642$		0			0
$643$	3.16436	+	17.9460i	0.124790	+	0.707720i	0.981432	+	0.191809i	$0.0614354\pi$
$643$	3.16436	+	17.9460i	0.124790	+	0.707720i	−0.856642	+	0.515911i	$0.827453\pi$
$644$		0			0
$645$	5.94760			0.234187
$646$		0			0
$647$	26.4490			1.03982			0.519910	−	0.854221i	$-0.325966\pi$
$647$	26.4490			1.03982			0.519910	+	0.854221i	$0.325966\pi$
$648$		0			0
$649$	−1.77529	−	10.0682i	−0.0696862	−	0.395210i
$650$		0			0
$651$	7.15743	−	6.00580i	0.280522	−	0.235386i
$652$		0			0
$653$	0.435379	−	0.754099i	0.0170377	−	0.0295102i	−0.857381	−	0.514683i	$-0.827910\pi$
$653$	0.435379	−	0.754099i	0.0170377	−	0.0295102i	0.874419	+	0.485172i	$0.161243\pi$
$654$		0			0
$655$	−48.8820	+	17.7916i	−1.90998	+	0.695175i
$656$		0			0
$657$	−0.973394	−	1.68597i	−0.0379757	−	0.0657759i
$658$		0			0
$659$	−4.71041	+	26.7141i	−0.183492	+	1.04063i	0.744387	+	0.667749i	$0.232742\pi$
$659$	−4.71041	+	26.7141i	−0.183492	+	1.04063i	−0.927878	+	0.372884i	$0.878369\pi$
$660$		0			0
$661$	2.42547	+	2.03521i	0.0943398	+	0.0791605i	0.688738	−	0.725011i	$-0.258165\pi$
$661$	2.42547	+	2.03521i	0.0943398	+	0.0791605i	−0.594398	+	0.804171i	$0.702610\pi$
$662$		0			0
$663$	5.95659	+	2.16802i	0.231335	+	0.0841989i
$664$		0			0
$665$	10.9201	−	13.3971i	0.423462	−	0.519516i
$666$		0			0
$667$	−33.4513	−	12.1753i	−1.29524	−	0.471428i
$668$		0			0
$669$	−2.60127	−	2.18272i	−0.100571	−	0.0843890i
$670$		0			0
$671$	−3.29092	+	18.6637i	−0.127045	+	0.720506i
$672$		0			0
$673$	4.92701	+	8.53384i	0.189922	+	0.328955i	0.945224	−	0.326422i	$-0.105843\pi$
$673$	4.92701	+	8.53384i	0.189922	+	0.328955i	−0.755302	+	0.655377i	$0.772510\pi$
$674$		0			0
$675$	−5.68880	+	2.07055i	−0.218962	+	0.0796956i
$676$		0			0
$677$	−0.247613	+	0.428878i	−0.00951653	+	0.0164831i	−0.870744	−	0.491736i	$-0.836363\pi$
$677$	−0.247613	+	0.428878i	−0.00951653	+	0.0164831i	0.861228	+	0.508219i	$0.169696\pi$
$678$		0			0
$679$	2.31722	−	1.94438i	0.0889268	−	0.0746185i
$680$		0			0
$681$	−2.03678	−	11.5511i	−0.0780494	−	0.442640i
$682$		0			0
$683$	−11.8365			−0.452910			−0.226455	−	0.974022i	$-0.572714\pi$
$683$	−11.8365			−0.452910			−0.226455	+	0.974022i	$0.572714\pi$
$684$		0			0
$685$	−51.4647			−1.96636
$686$		0			0
$687$	1.36036	+	7.71499i	0.0519010	+	0.294345i
$688$		0			0
$689$	−13.8155	+	11.5926i	−0.526330	+	0.441643i
$690$		0			0
$691$	−9.11315	+	15.7844i	−0.346680	+	0.600468i	−0.985658	−	0.168758i	$-0.946024\pi$
$691$	−9.11315	+	15.7844i	−0.346680	+	0.600468i	0.638977	+	0.769226i	$0.279358\pi$
$692$		0			0
$693$	−1.45145	+	0.528283i	−0.0551358	+	0.0200678i
$694$		0			0
$695$	19.1917	+	33.2409i	0.727982	+	1.26090i
$696$		0			0
$697$	−3.10652	+	17.6180i	−0.117668	+	0.667328i
$698$		0			0
$699$	−2.10168	−	1.76352i	−0.0794927	−	0.0667023i
$700$		0			0
$701$	−15.5323	−	5.65330i	−0.586648	−	0.213522i	0.0316067	−	0.999500i	$-0.489938\pi$
$701$	−15.5323	−	5.65330i	−0.586648	−	0.213522i	−0.618254	+	0.785978i	$0.712160\pi$
$702$		0			0
$703$	−22.4149	−	25.9531i	−0.845395	−	0.978839i
$704$		0			0
$705$	17.8357	+	6.49165i	0.671730	+	0.244490i
$706$		0			0
$707$	−11.3984	−	9.56438i	−0.428680	−	0.359705i
$708$		0			0
$709$	−3.27055	+	18.5482i	−0.122828	+	0.696593i	0.859746	+	0.510722i	$0.170622\pi$
$709$	−3.27055	+	18.5482i	−0.122828	+	0.696593i	−0.982574	+	0.185871i	$0.940489\pi$
$710$		0			0
$711$	−3.10252	−	5.37372i	−0.116354	−	0.201530i
$712$		0			0
$713$	−58.3706	+	21.2452i	−2.18600	+	0.795637i
$714$		0			0
$715$	6.15066	−	10.6533i	0.230022	−	0.398409i
$716$		0			0
$717$	−13.0895	+	10.9834i	−0.488835	+	0.410181i
$718$		0			0
$719$	6.17486	+	35.0194i	0.230283	+	1.30600i	0.852323	+	0.523016i	$0.175193\pi$
$719$	6.17486	+	35.0194i	0.230283	+	1.30600i	−0.622039	+	0.782986i	$0.713696\pi$
$720$		0			0
$721$	20.9638			0.780732
$722$		0			0
$723$	3.23596			0.120347
$724$		0			0
$725$	−4.71978	−	26.7672i	−0.175288	−	0.994109i
$726$		0			0
$727$	7.02657	−	5.89599i	0.260601	−	0.218670i	−0.503120	−	0.864216i	$-0.667815\pi$
$727$	7.02657	−	5.89599i	0.260601	−	0.218670i	0.763721	+	0.645546i	$0.223370\pi$
$728$		0			0
$729$	−0.500000	+	0.866025i	−0.0185185	+	0.0320750i
$730$		0			0
$731$	3.72990	−	1.35757i	0.137955	−	0.0502117i
$732$		0			0
$733$	−5.77022	−	9.99431i	−0.213128	−	0.369148i	0.739564	−	0.673086i	$-0.235032\pi$
$733$	−5.77022	−	9.99431i	−0.213128	−	0.369148i	−0.952692	+	0.303938i	$0.901698\pi$
$734$		0			0
$735$	−3.22017	+	18.2625i	−0.118778	+	0.673622i
$736$		0			0
$737$	4.54934	+	3.81735i	0.167577	+	0.140614i
$738$		0			0
$739$	−9.08882	−	3.30806i	−0.334338	−	0.121689i	0.169396	−	0.985548i	$-0.445818\pi$
$739$	−9.08882	−	3.30806i	−0.334338	−	0.121689i	−0.503733	+	0.863859i	$0.668041\pi$
$740$		0			0
$741$	8.13947	+	9.42427i	0.299011	+	0.346209i
$742$		0			0
$743$	−21.9925	−	8.00463i	−0.806828	−	0.293662i	−0.0945153	−	0.995523i	$-0.530130\pi$
$743$	−21.9925	−	8.00463i	−0.806828	−	0.293662i	−0.712313	+	0.701862i	$0.752352\pi$
$744$		0			0
$745$	−59.4025	−	49.8446i	−2.17634	−	1.82616i
$746$		0			0
$747$	−1.36091	+	7.71810i	−0.0497931	+	0.282391i
$748$		0			0
$749$	5.19841	+	9.00392i	0.189946	+	0.328996i
$750$		0			0
$751$	−2.60159	+	0.946900i	−0.0949332	+	0.0345529i	−0.389050	−	0.921217i	$-0.627197\pi$
$751$	−2.60159	+	0.946900i	−0.0949332	+	0.0345529i	0.294117	+	0.955769i	$0.404974\pi$
$752$		0			0
$753$	3.30814	−	5.72987i	0.120555	−	0.208808i
$754$		0			0
$755$	8.65359	−	7.26123i	0.314936	−	0.264263i
$756$		0			0
$757$	−3.87344	−	21.9673i	−0.140782	−	0.798417i	−0.970657	−	0.240467i	$-0.922699\pi$
$757$	−3.87344	−	21.9673i	−0.140782	−	0.798417i	0.829875	−	0.557950i	$-0.188412\pi$
$758$		0			0
$759$	10.2688			0.372734
$760$		0			0
$761$	−0.666605			−0.0241644			−0.0120822	−	0.999927i	$-0.503846\pi$
$761$	−0.666605			−0.0241644			−0.0120822	+	0.999927i	$0.503846\pi$
$762$		0			0
$763$	4.04485	+	22.9395i	0.146433	+	0.830464i
$764$		0			0
$765$	−5.65118	+	4.74190i	−0.204319	+	0.171444i
$766$		0			0
$767$	−11.2757	+	19.5300i	−0.407141	+	0.705189i
$768$		0			0
$769$	18.5010	−	6.73381i	0.667162	−	0.242827i	0.0138367	−	0.999904i	$-0.495595\pi$
$769$	18.5010	−	6.73381i	0.667162	−	0.242827i	0.653326	+	0.757077i	$0.273373\pi$
$770$		0			0
$771$	−7.28746	−	12.6223i	−0.262452	−	0.454579i
$772$		0			0
$773$	−8.57404	+	48.6258i	−0.308387	+	1.74895i	0.298733	+	0.954337i	$0.403436\pi$
$773$	−8.57404	+	48.6258i	−0.308387	+	1.74895i	−0.607119	+	0.794611i	$0.707675\pi$
$774$		0			0
$775$	−36.3318	−	30.4860i	−1.30508	−	1.09509i
$776$		0			0
$777$	−8.81689	−	3.20909i	−0.316304	−	0.115125i
$778$		0			0
$779$	−22.2045	+	27.2411i	−0.795558	+	0.976014i
$780$		0			0
$781$	−5.08756	−	1.85172i	−0.182047	−	0.0662597i
$782$		0			0
$783$	−3.43931	−	2.88592i	−0.122911	−	0.103134i
$784$		0			0
$785$	−13.1424	+	74.5344i	−0.469073	+	2.66025i
$786$		0			0
$787$	−20.9273	−	36.2472i	−0.745978	−	1.29207i	−0.949737	−	0.313050i	$-0.898649\pi$
$787$	−20.9273	−	36.2472i	−0.745978	−	1.29207i	0.203759	−	0.979021i	$-0.434684\pi$
$788$		0			0
$789$	9.23197	−	3.36016i	0.328667	−	0.119625i
$790$		0			0
$791$	0.355214	−	0.615248i	0.0126300	−	0.0218757i
$792$		0			0
$793$	32.0240	−	26.8713i	1.13720	−	0.954228i
$794$		0			0
$795$	−3.64466	−	20.6699i	−0.129263	−	0.733087i
$796$		0			0
$797$	50.2358			1.77944			0.889722	−	0.456503i	$-0.150898\pi$
$797$	50.2358			1.77944			0.889722	+	0.456503i	$0.150898\pi$
$798$		0			0
$799$	12.6670			0.448126
$800$		0			0
$801$	−0.743166	−	4.21470i	−0.0262585	−	0.148919i
$802$		0			0
$803$	−1.93145	+	1.62068i	−0.0681593	+	0.0571925i
$804$		0			0
$805$	−15.7196	+	27.2272i	−0.554043	+	0.959631i
$806$		0			0
$807$	−20.3338	+	7.40089i	−0.715783	+	0.260524i
$808$		0			0
$809$	−4.91982	−	8.52138i	−0.172972	−	0.299596i	0.766486	−	0.642261i	$-0.222004\pi$
$809$	−4.91982	−	8.52138i	−0.172972	−	0.299596i	−0.939458	+	0.342665i	$0.888670\pi$
$810$		0			0
$811$	4.97290	−	28.2027i	0.174622	−	0.990331i	−0.763957	−	0.645267i	$-0.776746\pi$
$811$	4.97290	−	28.2027i	0.174622	−	0.990331i	0.938579	−	0.345064i	$-0.112143\pi$
$812$		0			0
$813$	4.66583	+	3.91509i	0.163638	+	0.137308i
$814$		0			0
$815$	−40.8416	−	14.8651i	−1.43062	−	0.520703i
$816$		0			0
$817$	7.69765	+	1.24451i	0.269307	+	0.0435399i
$818$		0			0
$819$	3.20165	+	1.16531i	0.111875	+	0.0407191i
$820$		0			0
$821$	−36.3403	−	30.4931i	−1.26829	−	1.06422i	−0.994748	−	0.102356i	$-0.967362\pi$
$821$	−36.3403	−	30.4931i	−1.26829	−	1.06422i	−0.273537	−	0.961861i	$-0.588194\pi$
$822$		0			0
$823$	−7.04848	+	39.9739i	−0.245695	+	1.39340i	0.573179	+	0.819430i	$0.305710\pi$
$823$	−7.04848	+	39.9739i	−0.245695	+	1.39340i	−0.818874	+	0.573974i	$0.805401\pi$
$824$		0			0
$825$	3.92026	+	6.79009i	0.136486	+	0.236401i
$826$		0			0
$827$	−1.74185	+	0.633981i	−0.0605700	+	0.0220457i	−0.372127	−	0.928182i	$-0.621372\pi$
$827$	−1.74185	+	0.633981i	−0.0605700	+	0.0220457i	0.311557	+	0.950227i	$0.399149\pi$
$828$		0			0
$829$	15.4767	−	26.8065i	0.537529	−	0.931028i	−0.461507	−	0.887136i	$-0.652691\pi$
$829$	15.4767	−	26.8065i	0.537529	−	0.931028i	0.999036	−	0.0438911i	$-0.0139755\pi$
$830$		0			0
$831$	12.4311	−	10.4309i	0.431229	−	0.361844i
$832$		0			0
$833$	2.14906	+	12.1879i	0.0744605	+	0.422286i
$834$		0			0
$835$	50.4395			1.74553
$836$		0			0
$837$	−7.83427			−0.270792
$838$		0			0
$839$	−5.44892	−	30.9024i	−0.188118	−	1.06687i	−0.921884	−	0.387466i	$-0.873350\pi$
$839$	−5.44892	−	30.9024i	−0.188118	−	1.06687i	0.733766	−	0.679402i	$-0.237761\pi$
$840$		0			0
$841$	−6.77385	+	5.68394i	−0.233581	+	0.195998i
$842$		0			0
$843$	−2.05946	+	3.56710i	−0.0709317	+	0.122857i
$844$		0			0
$845$	15.1167	−	5.50203i	0.520030	−	0.189276i
$846$		0			0
$847$	−5.55923	−	9.62886i	−0.191017	−	0.330852i
$848$		0			0
$849$	−4.68523	+	26.5713i	−0.160797	+	0.911924i
$850$		0			0
$851$	47.7847	+	40.0961i	1.63804	+	1.37448i
$852$		0			0
$853$	−26.6764	−	9.70940i	−0.913381	−	0.332444i	−0.157779	−	0.987474i	$-0.550433\pi$
$853$	−26.6764	−	9.70940i	−0.913381	−	0.332444i	−0.755602	+	0.655031i	$0.772656\pi$
$854$		0			0
$855$	−14.2347	+	2.71960i	−0.486818	+	0.0930083i
$856$		0			0
$857$	6.11088	+	2.22418i	0.208744	+	0.0759765i	0.444276	−	0.895890i	$-0.353461\pi$
$857$	6.11088	+	2.22418i	0.208744	+	0.0759765i	−0.235532	+	0.971867i	$0.575683\pi$
$858$		0			0
$859$	12.5436	+	10.5253i	0.427982	+	0.359119i	0.831190	−	0.555989i	$-0.187660\pi$
$859$	12.5436	+	10.5253i	0.427982	+	0.359119i	−0.403208	+	0.915108i	$0.632105\pi$
$860$		0			0
$861$	−1.66975	+	9.46963i	−0.0569050	+	0.322724i
$862$		0			0
$863$	−24.5642	−	42.5464i	−0.836174	−	1.44829i	−0.893071	−	0.449915i	$-0.851454\pi$
$863$	−24.5642	−	42.5464i	−0.836174	−	1.44829i	0.0568979	−	0.998380i	$-0.481879\pi$
$864$		0			0
$865$	−52.1765	+	18.9907i	−1.77406	+	0.645703i
$866$		0			0
$867$	6.03836	−	10.4587i	0.205073	−	0.355198i
$868$		0			0
$869$	−6.15614	+	5.16562i	−0.208833	+	0.175232i
$870$		0			0
$871$	−2.27478	−	12.9009i	−0.0770779	−	0.437130i
$872$		0			0
$873$	−2.53635			−0.0858425
$874$		0			0
$875$	−4.17886			−0.141271
$876$		0			0
$877$	−2.24069	−	12.7076i	−0.0756628	−	0.429105i	−0.998984	−	0.0450756i	$-0.985647\pi$
$877$	−2.24069	−	12.7076i	−0.0756628	−	0.429105i	0.923321	−	0.384030i	$-0.125464\pi$
$878$		0			0
$879$	4.78620	−	4.01610i	0.161435	−	0.135460i
$880$		0			0
$881$	18.6390	−	32.2837i	0.627965	−	1.08767i	−0.359995	−	0.932954i	$-0.617222\pi$
$881$	18.6390	−	32.2837i	0.627965	−	1.08767i	0.987960	−	0.154712i	$-0.0494451\pi$
$882$		0			0
$883$	7.29529	−	2.65527i	0.245506	−	0.0893570i	−0.216336	−	0.976319i	$-0.569411\pi$
$883$	7.29529	−	2.65527i	0.245506	−	0.0893570i	0.461842	+	0.886962i	$0.347189\pi$
$884$		0			0
$885$	−13.1225	−	22.7288i	−0.441107	−	0.764020i
$886$		0			0
$887$	7.14167	−	40.5024i	0.239794	−	1.35994i	−0.592485	−	0.805581i	$-0.701853\pi$
$887$	7.14167	−	40.5024i	0.239794	−	1.35994i	0.832279	−	0.554357i	$-0.187036\pi$
$888$		0			0
$889$	8.93618	+	7.49835i	0.299710	+	0.251487i
$890$		0			0
$891$	1.21702	+	0.442957i	0.0407716	+	0.0148396i
$892$		0			0
$893$	21.7253	+	12.1338i	0.727011	+	0.406043i
$894$		0			0
$895$	42.7840	+	15.5721i	1.43011	+	0.520518i
$896$		0			0
$897$	−17.3519	−	14.5600i	−0.579364	−	0.486144i
$898$		0			0
$899$	6.10781	−	34.6391i	0.203707	−	1.15528i
$900$		0			0
$901$	−7.00369	−	12.1308i	−0.233327	−	0.404134i
$902$		0			0
$903$	2.00482	−	0.729694i	0.0667161	−	0.0242827i
$904$		0			0
$905$	−33.8604	+	58.6479i	−1.12556	+	1.94952i
$906$		0			0
$907$	25.5449	−	21.4347i	0.848206	−	0.711729i	−0.111188	−	0.993799i	$-0.535466\pi$
$907$	25.5449	−	21.4347i	0.848206	−	0.711729i	0.959394	+	0.282070i	$0.0910211\pi$
$908$		0			0
$909$	2.16648	+	12.2867i	0.0718576	+	0.407525i
$910$		0			0
$911$	−26.6721			−0.883687			−0.441844	−	0.897092i	$-0.645675\pi$
$911$	−26.6721			−0.883687			−0.441844	+	0.897092i	$0.645675\pi$
$912$		0			0
$913$	10.1501			0.335919
$914$		0			0
$915$	8.44821	+	47.9122i	0.279289	+	1.58393i
$916$		0			0
$917$	−14.2943	+	11.9944i	−0.472040	+	0.396089i
$918$		0			0
$919$	−1.49951	+	2.59722i	−0.0494642	+	0.0856745i	−0.889697	−	0.456551i	$-0.849085\pi$
$919$	−1.49951	+	2.59722i	−0.0494642	+	0.0856745i	0.840233	+	0.542225i	$0.182418\pi$
$920$		0			0
$921$	−11.2581	+	4.09761i	−0.370967	+	0.135021i
$922$		0			0
$923$	5.97128	+	10.3426i	0.196547	+	0.340429i
$924$		0			0
$925$	−8.27047	+	46.9041i	−0.271931	+	1.54220i
$926$		0			0
$927$	−13.4654	−	11.2988i	−0.442261	−	0.371101i
$928$		0			0
$929$	6.32189	+	2.30098i	0.207415	+	0.0754927i	0.443638	−	0.896206i	$-0.353688\pi$
$929$	6.32189	+	2.30098i	0.207415	+	0.0754927i	−0.236224	+	0.971699i	$0.575910\pi$
$930$		0			0
$931$	−7.98903	+	22.9623i	−0.261830	+	0.752559i
$932$		0			0
$933$	−8.53444	−	3.10628i	−0.279405	−	0.101695i
$934$		0			0
$935$	7.31896	+	6.14134i	0.239356	+	0.200843i
$936$		0			0
$937$	−2.73192	+	15.4935i	−0.0892481	+	0.506151i	0.907111	+	0.420892i	$0.138283\pi$
$937$	−2.73192	+	15.4935i	−0.0892481	+	0.506151i	−0.996359	+	0.0852590i	$0.972828\pi$
$938$		0			0
$939$	8.25460	+	14.2974i	0.269379	+	0.466577i
$940$		0			0
$941$	−4.49945	+	1.63766i	−0.146678	+	0.0533864i	−0.414316	−	0.910133i	$-0.635979\pi$
$941$	−4.49945	+	1.63766i	−0.146678	+	0.0533864i	0.267638	+	0.963520i	$0.413757\pi$
$942$		0			0
$943$	31.9637	−	55.3627i	1.04088	−	1.80286i
$944$		0			0
$945$	−3.03750	+	2.54876i	−0.0988098	+	0.0829113i
$946$		0			0
$947$	5.17749	+	29.3630i	0.168246	+	0.954169i	0.945654	+	0.325173i	$0.105423\pi$
$947$	5.17749	+	29.3630i	0.168246	+	0.954169i	−0.777409	+	0.628996i	$0.783466\pi$
$948$		0			0
$949$	5.56164			0.180538
$950$		0			0
$951$	19.4219			0.629799
$952$		0			0
$953$	−0.728873	−	4.13365i	−0.0236105	−	0.133902i	0.970724	−	0.240197i	$-0.0772122\pi$
$953$	−0.728873	−	4.13365i	−0.0236105	−	0.133902i	−0.994335	+	0.106295i	$0.966101\pi$
$954$		0			0
$955$	−54.0108	+	45.3204i	−1.74775	+	1.46653i
$956$		0			0
$957$	−2.90735	+	5.03568i	−0.0939813	+	0.162780i
$958$		0			0
$959$	−17.3477	+	6.31405i	−0.560187	+	0.203891i
$960$		0			0
$961$	−15.1879	−	26.3062i	−0.489932	−	0.848588i
$962$		0			0
$963$	1.51379	−	8.58515i	0.0487813	−	0.276653i
$964$		0			0
$965$	35.7045	+	29.9597i	1.14937	+	0.964435i
$966$		0			0
$967$	7.76004	+	2.82442i	0.249546	+	0.0908274i	0.463765	−	0.885958i	$-0.346498\pi$
$967$	7.76004	+	2.82442i	0.249546	+	0.0908274i	−0.214219	+	0.976786i	$0.568721\pi$
$968$		0			0
$969$	−8.30623	+	4.95469i	−0.266834	+	0.159168i
$970$		0			0
$971$	11.3878	+	4.14480i	0.365450	+	0.133013i	0.518217	−	0.855249i	$-0.326596\pi$
$971$	11.3878	+	4.14480i	0.365450	+	0.133013i	−0.152767	+	0.988262i	$0.548818\pi$
$972$		0			0
$973$	10.5474	+	8.85028i	0.338133	+	0.283727i
$974$		0			0
$975$	3.00323	−	17.0322i	0.0961804	−	0.545466i
$976$		0			0
$977$	−14.8156	−	25.6614i	−0.473994	−	0.820982i	0.525562	−	0.850755i	$-0.323855\pi$
$977$	−14.8156	−	25.6614i	−0.473994	−	0.820982i	−0.999557	+	0.0297727i	$0.990522\pi$
$978$		0			0
$979$	−5.20849	+	1.89573i	−0.166464	+	0.0605879i
$980$		0			0
$981$	9.76557	−	16.9145i	0.311791	−	0.540037i
$982$		0			0
$983$	−27.4542	+	23.0368i	−0.875652	+	0.734759i	−0.965280	−	0.261216i	$-0.915876\pi$
$983$	−27.4542	+	23.0368i	−0.875652	+	0.734759i	0.0896287	+	0.995975i	$0.471432\pi$
$984$		0			0
$985$	3.28086	+	18.6067i	0.104537	+	0.592858i
$986$		0			0
$987$	6.80848			0.216716
$988$		0			0
$989$	−14.1838			−0.451020
$990$		0			0
$991$	2.48372	+	14.0859i	0.0788980	+	0.447453i	0.998507	+	0.0546185i	$0.0173943\pi$
$991$	2.48372	+	14.0859i	0.0788980	+	0.447453i	−0.919609	+	0.392834i	$0.871495\pi$
$992$		0			0
$993$	11.4670	−	9.62193i	0.363893	−	0.305343i
$994$		0			0
$995$	17.8574	−	30.9300i	0.566118	−	0.980546i
$996$		0			0
$997$	2.44915	−	0.891419i	0.0775654	−	0.0282315i	−0.302946	−	0.953008i	$-0.597970\pi$
$997$	2.44915	−	0.891419i	0.0775654	−	0.0282315i	0.380511	+	0.924776i	$0.375748\pi$
$998$		0			0
$999$	3.93364	+	6.81327i	0.124455	+	0.215562i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	912.2.bo.g.289.2		12
4.3	odd	2		228.2.q.b.61.2	✓	12
12.11	even	2		684.2.bo.e.289.1		12
19.5	even	9	inner	912.2.bo.g.385.2		12
76.43	odd	18		228.2.q.b.157.2	yes	12
76.47	odd	18		4332.2.a.t.1.5		6
76.67	even	18		4332.2.a.u.1.5		6
228.119	even	18		684.2.bo.e.613.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
228.2.q.b.61.2	✓	12	4.3	odd	2
228.2.q.b.157.2	yes	12	76.43	odd	18
684.2.bo.e.289.1		12	12.11	even	2
684.2.bo.e.613.1		12	228.119	even	18
912.2.bo.g.289.2		12	1.1	even	1	trivial
912.2.bo.g.385.2		12	19.5	even	9	inner
4332.2.a.t.1.5		6	76.47	odd	18
4332.2.a.u.1.5		6	76.67	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 $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(0.173648 + 0.984808i) q^{3} +(2.54690 - 2.13710i) q^{5} +(0.596313 - 1.03284i) q^{7} +(-0.939693 + 0.342020i) q^{9} +O(q^{10})\)	\(q+(0.173648 + 0.984808i) q^{3} +(2.54690 - 2.13710i) q^{5} +(0.596313 - 1.03284i) q^{7} +(-0.939693 + 0.342020i) q^{9} +(0.647560 + 1.12161i) q^{11} +(0.496083 - 2.81343i) q^{13} +(2.54690 + 2.13710i) q^{15} +(2.08503 + 0.758891i) q^{17} +(2.84913 + 3.29886i) q^{19} +(1.12070 + 0.407902i) q^{21} +(-6.07384 - 5.09656i) q^{23} +(1.05125 - 5.96192i) q^{25} +(-0.500000 - 0.866025i) q^{27} +(4.21893 - 1.53557i) q^{29} +(3.91714 - 6.78468i) q^{31} +(-0.992120 + 0.832488i) q^{33} +(-0.688545 - 3.90493i) q^{35} -7.86729 q^{37} +2.85683 q^{39} +(1.40006 + 7.94015i) q^{41} +(1.37037 - 1.14988i) q^{43} +(-1.66237 + 2.87931i) q^{45} +(5.36453 - 1.95253i) q^{47} +(2.78882 + 4.83038i) q^{49} +(-0.385299 + 2.18514i) q^{51} +(-4.83597 - 4.05786i) q^{53} +(4.04626 + 1.47272i) q^{55} +(-2.75400 + 3.37868i) q^{57} +(-7.41778 - 2.69985i) q^{59} +(11.2096 + 9.40599i) q^{61} +(-0.207097 + 1.17451i) q^{63} +(-4.74910 - 8.22569i) q^{65} +(4.30894 - 1.56833i) q^{67} +(3.96442 - 6.86658i) q^{69} +(-3.20234 + 2.68708i) q^{71} +(0.338056 + 1.91721i) q^{73} +6.05389 q^{75} +1.54460 q^{77} +(1.07749 + 6.11077i) q^{79} +(0.766044 - 0.642788i) q^{81} +(3.91858 - 6.78719i) q^{83} +(6.93220 - 2.52311i) q^{85} +(2.24485 + 3.88819i) q^{87} +(-0.743166 + 4.21470i) q^{89} +(-2.61001 - 2.19006i) q^{91} +(7.36181 + 2.67948i) q^{93} +(14.3064 + 2.31298i) q^{95} +(2.38339 + 0.867483i) q^{97} +(-0.992120 - 0.832488i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 6 q^{5} + 9 q^{7}+O(q^{10}) \) 12 * q - 6 * q^5 + 9 * q^7	\( 12 q - 6 q^{5} + 9 q^{7} + 9 q^{11} - 3 q^{13} - 6 q^{15} + 12 q^{17} - 9 q^{19} + 6 q^{21} - 15 q^{23} + 12 q^{25} - 6 q^{27} - 24 q^{29} + 6 q^{31} - 9 q^{33} + 42 q^{35} + 12 q^{37} - 18 q^{39} + 6 q^{41} + 39 q^{43} - 3 q^{45} + 3 q^{47} - 21 q^{49} + 3 q^{51} + 18 q^{53} - 45 q^{55} + 3 q^{57} + 33 q^{61} - 3 q^{63} - 33 q^{65} + 27 q^{67} + 12 q^{69} - 6 q^{71} - 24 q^{73} + 30 q^{75} - 18 q^{79} - 3 q^{83} + 39 q^{85} + 9 q^{87} - 15 q^{89} - 18 q^{91} - 6 q^{93} + 30 q^{95} - 15 q^{97} - 9 q^{99}+O(q^{100}) \) 12 * q - 6 * q^5 + 9 * q^7 + 9 * q^11 - 3 * q^13 - 6 * q^15 + 12 * q^17 - 9 * q^19 + 6 * q^21 - 15 * q^23 + 12 * q^25 - 6 * q^27 - 24 * q^29 + 6 * q^31 - 9 * q^33 + 42 * q^35 + 12 * q^37 - 18 * q^39 + 6 * q^41 + 39 * q^43 - 3 * q^45 + 3 * q^47 - 21 * q^49 + 3 * q^51 + 18 * q^53 - 45 * q^55 + 3 * q^57 + 33 * q^61 - 3 * q^63 - 33 * q^65 + 27 * q^67 + 12 * q^69 - 6 * q^71 - 24 * q^73 + 30 * q^75 - 18 * q^79 - 3 * q^83 + 39 * q^85 + 9 * q^87 - 15 * q^89 - 18 * q^91 - 6 * q^93 + 30 * q^95 - 15 * q^97 - 9 * q^99

Introduction

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Database

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