LMFDB - Embedded newform 1638.2.bj.g.1135.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1638,2,Mod(127,1638)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1638, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 5]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("1638.127");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1638 = 2 \cdot 3^{2} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1638.bj (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$13.0794958511$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
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} + 39 x^{10} - 140 x^{9} + 460 x^{8} - 1066 x^{7} + 2127 x^{6} - 3172 x^{5} + \cdots + 169 $ x^12 - 6x^11 + 39x^10 - 140x^9 + 460x^8 - 1066x^7 + 2127x^6 - 3172x^5 + 3842x^4 - 3394x^3 + 2141x^2 - 832*x + 169
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 182)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			1135.2
Root			$0.500000 + 3.15681i$ of defining polynomial
Character	$\chi$	$=$	1638.1135
Dual form			1638.2.bj.g.127.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} -0.901839i q^{5} +(0.866025 - 0.500000i) q^{7} -1.00000i q^{8} +O(q^{10})$	\(q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} -0.901839i q^{5} +(0.866025 - 0.500000i) q^{7} -1.00000i q^{8} +(-0.450919 + 0.781015i) q^{10} +(3.75609 + 2.16858i) q^{11} +(-0.426876 + 3.58019i) q^{13} -1.00000 q^{14} +(-0.500000 + 0.866025i) q^{16} +(-2.53296 - 4.38722i) q^{17} +(5.34544 - 3.08619i) q^{19} +(0.781015 - 0.450919i) q^{20} +(-2.16858 - 3.75609i) q^{22} +(-4.22559 + 7.31893i) q^{23} +4.18669 q^{25} +(2.15978 - 2.88710i) q^{26} +(0.866025 + 0.500000i) q^{28} +(-1.09643 + 1.89907i) q^{29} +0.873062i q^{31} +(0.866025 - 0.500000i) q^{32} +5.06592i q^{34} +(-0.450919 - 0.781015i) q^{35} +(0.124973 + 0.0721531i) q^{37} -6.17238 q^{38} -0.901839 q^{40} +(3.46110 + 1.99827i) q^{41} +(3.85426 + 6.67577i) q^{43} +4.33716i q^{44} +(7.31893 - 4.22559i) q^{46} +2.92115i q^{47} +(0.500000 - 0.866025i) q^{49} +(-3.62578 - 2.09334i) q^{50} +(-3.31398 + 1.42041i) q^{52} -1.69699 q^{53} +(1.95571 - 3.38739i) q^{55} +(-0.500000 - 0.866025i) q^{56} +(1.89907 - 1.09643i) q^{58} +(7.40394 - 4.27467i) q^{59} +(-4.16720 - 7.21780i) q^{61} +(0.436531 - 0.756094i) q^{62} -1.00000 q^{64} +(3.22876 + 0.384973i) q^{65} +(-8.99180 - 5.19142i) q^{67} +(2.53296 - 4.38722i) q^{68} +0.901839i q^{70} +(2.83932 - 1.63928i) q^{71} +0.539023i q^{73} +(-0.0721531 - 0.124973i) q^{74} +(5.34544 + 3.08619i) q^{76} +4.33716 q^{77} +6.53349 q^{79} +(0.781015 + 0.450919i) q^{80} +(-1.99827 - 3.46110i) q^{82} +13.2348i q^{83} +(-3.95656 + 2.28432i) q^{85} -7.70851i q^{86} +(2.16858 - 3.75609i) q^{88} +(6.74790 + 3.89590i) q^{89} +(1.42041 + 3.31398i) q^{91} -8.45117 q^{92} +(1.46057 - 2.52979i) q^{94} +(-2.78325 - 4.82072i) q^{95} +(10.1378 - 5.85305i) q^{97} +(-0.866025 + 0.500000i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 6 q^{4}+O(q^{10}) $ 12 * q + 6 * q^4	$ 12 q + 6 q^{4} - 2 q^{10} + 18 q^{11} - 8 q^{13} - 12 q^{14} - 6 q^{16} - 4 q^{17} + 12 q^{19} - 2 q^{22} + 6 q^{23} - 24 q^{25} + 14 q^{26} + 10 q^{29} - 2 q^{35} - 6 q^{37} - 8 q^{38} - 4 q^{40} + 24 q^{41} + 26 q^{43} - 6 q^{46} + 6 q^{49} + 12 q^{50} - 4 q^{52} - 36 q^{53} - 6 q^{55} - 6 q^{56} + 24 q^{58} - 6 q^{59} - 28 q^{61} + 2 q^{62} - 12 q^{64} + 34 q^{65} - 42 q^{67} + 4 q^{68} - 48 q^{71} + 12 q^{76} + 4 q^{77} + 44 q^{79} + 6 q^{82} + 54 q^{85} + 2 q^{88} - 12 q^{89} - 16 q^{91} + 12 q^{92} + 8 q^{94} - 32 q^{95} + 60 q^{97}+O(q^{100}) $ 12 * q + 6 * q^4 - 2 * q^10 + 18 * q^11 - 8 * q^13 - 12 * q^14 - 6 * q^16 - 4 * q^17 + 12 * q^19 - 2 * q^22 + 6 * q^23 - 24 * q^25 + 14 * q^26 + 10 * q^29 - 2 * q^35 - 6 * q^37 - 8 * q^38 - 4 * q^40 + 24 * q^41 + 26 * q^43 - 6 * q^46 + 6 * q^49 + 12 * q^50 - 4 * q^52 - 36 * q^53 - 6 * q^55 - 6 * q^56 + 24 * q^58 - 6 * q^59 - 28 * q^61 + 2 * q^62 - 12 * q^64 + 34 * q^65 - 42 * q^67 + 4 * q^68 - 48 * q^71 + 12 * q^76 + 4 * q^77 + 44 * q^79 + 6 * q^82 + 54 * q^85 + 2 * q^88 - 12 * q^89 - 16 * q^91 + 12 * q^92 + 8 * q^94 - 32 * q^95 + 60 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1638\mathbb{Z}\right)^\times$.

$n$	$379$	$703$	$911$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$	$1$

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 $

$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$3$		0			0
$3$		0			0
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$		−	0.901839i		−	0.403315i	−0.979456	−	0.201657i	$-0.935367\pi$
$5$		−	0.901839i		−	0.403315i	0.979456	−	0.201657i	$-0.0646327\pi$
$6$		0			0
$7$	0.866025	−	0.500000i	0.327327	−	0.188982i
$7$	0.866025	−	0.500000i	0.327327	−	0.188982i
$8$		−	1.00000i		−	0.353553i
$9$		0			0
$10$	−0.450919	+	0.781015i	−0.142593	+	0.246979i
$11$	3.75609	+	2.16858i	1.13251	+	0.653852i	0.944564	−	0.328328i	$-0.106485\pi$
$11$	3.75609	+	2.16858i	1.13251	+	0.653852i	0.187941	+	0.982180i	$0.439819\pi$
$12$		0			0
$13$	−0.426876	+	3.58019i	−0.118394	+	0.992967i
$13$	−0.426876	+	3.58019i	−0.118394	+	0.992967i
$14$	−1.00000			−0.267261
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−2.53296	−	4.38722i	−0.614333	−	1.06406i	−0.990501	−	0.137505i	$-0.956092\pi$
$17$	−2.53296	−	4.38722i	−0.614333	−	1.06406i	0.376168	−	0.926551i	$-0.377242\pi$
$18$		0			0
$19$	5.34544	−	3.08619i	1.22633	−	0.708021i	0.260068	−	0.965590i	$-0.416255\pi$
$19$	5.34544	−	3.08619i	1.22633	−	0.708021i	0.966260	+	0.257570i	$0.0829217\pi$
$20$	0.781015	−	0.450919i	0.174640	−	0.100829i
$21$		0			0
$22$	−2.16858	−	3.75609i	−0.462343	−	0.800802i
$23$	−4.22559	+	7.31893i	−0.881096	+	1.52610i	−0.0309711	+	0.999520i	$0.509860\pi$
$23$	−4.22559	+	7.31893i	−0.881096	+	1.52610i	−0.850124	+	0.526582i	$0.823473\pi$
$24$		0			0
$25$	4.18669			0.837337
$26$	2.15978	−	2.88710i	0.423568	−	0.566207i
$27$		0			0
$28$	0.866025	+	0.500000i	0.163663	+	0.0944911i
$29$	−1.09643	+	1.89907i	−0.203602	+	0.352649i	−0.949686	−	0.313203i	$-0.898598\pi$
$29$	−1.09643	+	1.89907i	−0.203602	+	0.352649i	0.746085	+	0.665851i	$0.231931\pi$
$30$		0			0
$31$			0.873062i			0.156807i	0.996922	+	0.0784033i	$0.0249822\pi$
$31$			0.873062i			0.156807i	−0.996922	+	0.0784033i	$0.975018\pi$
$32$	0.866025	−	0.500000i	0.153093	−	0.0883883i
$33$		0			0
$34$			5.06592i			0.868798i
$35$	−0.450919	−	0.781015i	−0.0762193	−	0.132016i
$36$		0			0
$37$	0.124973	+	0.0721531i	0.0205454	+	0.0118619i	0.510238	−	0.860034i	$-0.329557\pi$
$37$	0.124973	+	0.0721531i	0.0205454	+	0.0118619i	−0.489692	+	0.871895i	$0.662891\pi$
$38$	−6.17238			−1.00129
$39$		0			0
$40$	−0.901839			−0.142593
$41$	3.46110	+	1.99827i	0.540533	+	0.312077i	0.745295	−	0.666735i	$-0.232309\pi$
$41$	3.46110	+	1.99827i	0.540533	+	0.312077i	−0.204762	+	0.978812i	$0.565642\pi$
$42$		0			0
$43$	3.85426	+	6.67577i	0.587768	+	1.01804i	0.994524	+	0.104508i	$0.0333267\pi$
$43$	3.85426	+	6.67577i	0.587768	+	1.01804i	−0.406756	+	0.913537i	$0.633340\pi$
$44$			4.33716i			0.653852i
$45$		0			0
$46$	7.31893	−	4.22559i	1.07912	−	0.623029i
$47$			2.92115i			0.426093i	0.977042	+	0.213047i	$0.0683387\pi$
$47$			2.92115i			0.426093i	−0.977042	+	0.213047i	$0.931661\pi$
$48$		0			0
$49$	0.500000	−	0.866025i	0.0714286	−	0.123718i
$50$	−3.62578	−	2.09334i	−0.512762	−	0.296043i
$51$		0			0
$52$	−3.31398	+	1.42041i	−0.459566	+	0.196976i
$53$	−1.69699			−0.233099			−0.116549	−	0.993185i	$-0.537183\pi$
$53$	−1.69699			−0.233099			−0.116549	+	0.993185i	$0.537183\pi$
$54$		0			0
$55$	1.95571	−	3.38739i	0.263708	−	0.456756i
$56$	−0.500000	−	0.866025i	−0.0668153	−	0.115728i
$57$		0			0
$58$	1.89907	−	1.09643i	0.249360	−	0.143968i
$59$	7.40394	−	4.27467i	0.963911	−	0.556514i	0.0665363	−	0.997784i	$-0.478805\pi$
$59$	7.40394	−	4.27467i	0.963911	−	0.556514i	0.897374	+	0.441270i	$0.145472\pi$
$60$		0			0
$61$	−4.16720	−	7.21780i	−0.533555	−	0.924145i	−0.999232	−	0.0391900i	$-0.987522\pi$
$61$	−4.16720	−	7.21780i	−0.533555	−	0.924145i	0.465676	−	0.884955i	$-0.345811\pi$
$62$	0.436531	−	0.756094i	0.0554395	−	0.0960241i
$63$		0			0
$64$	−1.00000			−0.125000
$65$	3.22876	+	0.384973i	0.400478	+	0.0477501i
$66$		0			0
$67$	−8.99180	−	5.19142i	−1.09852	−	0.634233i	−0.162691	−	0.986677i	$-0.552017\pi$
$67$	−8.99180	−	5.19142i	−1.09852	−	0.634233i	−0.935833	+	0.352444i	$0.885351\pi$
$68$	2.53296	−	4.38722i	0.307167	−	0.532028i
$69$		0			0
$70$			0.901839i			0.107790i
$71$	2.83932	−	1.63928i	0.336965	−	0.194547i	−0.321964	−	0.946752i	$-0.604343\pi$
$71$	2.83932	−	1.63928i	0.336965	−	0.194547i	0.658929	+	0.752205i	$0.271010\pi$
$72$		0			0
$73$			0.539023i			0.0630879i	0.999502	+	0.0315439i	$0.0100424\pi$
$73$			0.539023i			0.0630879i	−0.999502	+	0.0315439i	$0.989958\pi$
$74$	−0.0721531	−	0.124973i	−0.00838763	−	0.0145278i
$75$		0			0
$76$	5.34544	+	3.08619i	0.613164	+	0.354010i
$77$	4.33716			0.494266
$78$		0			0
$79$	6.53349			0.735075			0.367537	−	0.930009i	$-0.380201\pi$
$79$	6.53349			0.735075			0.367537	+	0.930009i	$0.380201\pi$
$80$	0.781015	+	0.450919i	0.0873202	+	0.0504143i
$81$		0			0
$82$	−1.99827	−	3.46110i	−0.220672	−	0.382215i
$83$			13.2348i			1.45271i	0.687319	+	0.726356i	$0.258788\pi$
$83$			13.2348i			1.45271i	−0.687319	+	0.726356i	$0.741212\pi$
$84$		0			0
$85$	−3.95656	+	2.28432i	−0.429149	+	0.247769i
$86$		−	7.70851i		−	0.831230i
$87$		0			0
$88$	2.16858	−	3.75609i	0.231172	−	0.400401i
$89$	6.74790	+	3.89590i	0.715276	+	0.412965i	0.813011	−	0.582248i	$-0.197827\pi$
$89$	6.74790	+	3.89590i	0.715276	+	0.412965i	−0.0977357	+	0.995212i	$0.531160\pi$
$90$		0			0
$91$	1.42041	+	3.31398i	0.148900	+	0.347399i
$92$	−8.45117			−0.881096
$93$		0			0
$94$	1.46057	−	2.52979i	0.150647	−	0.260928i
$95$	−2.78325	−	4.82072i	−0.285555	−	0.494596i
$96$		0			0
$97$	10.1378	−	5.85305i	1.02934	−	0.594287i	0.112541	−	0.993647i	$-0.464101\pi$
$97$	10.1378	−	5.85305i	1.02934	−	0.594287i	0.916794	+	0.399360i	$0.130768\pi$
$98$	−0.866025	+	0.500000i	−0.0874818	+	0.0505076i
$99$		0			0
$100$	2.09334	+	3.62578i	0.209334	+	0.362578i
$101$	5.37145	−	9.30362i	0.534479	−	0.925745i	−0.464709	−	0.885463i	$-0.653841\pi$
$101$	5.37145	−	9.30362i	0.534479	−	0.925745i	0.999188	−	0.0402814i	$-0.0128254\pi$
$102$		0			0
$103$	4.81099			0.474041			0.237021	−	0.971505i	$-0.423829\pi$
$103$	4.81099			0.474041			0.237021	+	0.971505i	$0.423829\pi$
$104$	3.58019	+	0.426876i	0.351067	+	0.0418586i
$105$		0			0
$106$	1.46963	+	0.848493i	0.142743	+	0.0824129i
$107$	6.82652	−	11.8239i	0.659944	−	1.14306i	−0.320686	−	0.947186i	$-0.603913\pi$
$107$	6.82652	−	11.8239i	0.659944	−	1.14306i	0.980630	−	0.195871i	$-0.0627534\pi$
$108$		0			0
$109$			5.11747i			0.490165i	0.969502	+	0.245082i	$0.0788150\pi$
$109$			5.11747i			0.490165i	−0.969502	+	0.245082i	$0.921185\pi$
$110$	−3.38739	+	1.95571i	−0.322975	+	0.186470i
$111$		0			0
$112$			1.00000i			0.0944911i
$113$	8.96603	+	15.5296i	0.843453	+	1.46090i	0.886958	+	0.461850i	$0.152814\pi$
$113$	8.96603	+	15.5296i	0.843453	+	1.46090i	−0.0435052	+	0.999053i	$0.513853\pi$
$114$		0			0
$115$	6.60049	+	3.81080i	0.615499	+	0.355359i
$116$	−2.19286			−0.203602
$117$		0			0
$118$	−8.54933			−0.787030
$119$	−4.38722	−	2.53296i	−0.402175	−	0.232196i
$120$		0			0
$121$	3.90550	+	6.76452i	0.355045	+	0.614956i
$122$			8.33440i			0.754561i
$123$		0			0
$124$	−0.756094	+	0.436531i	−0.0678993	+	0.0392017i
$125$		−	8.28491i		−	0.741025i
$126$		0			0
$127$	−9.75681	+	16.8993i	−0.865777	+	1.49957i	0.000496195		1.00000i	$0.499842\pi$
$127$	−9.75681	+	16.8993i	−0.865777	+	1.49957i	−0.866273	+	0.499570i	$0.833491\pi$
$128$	0.866025	+	0.500000i	0.0765466	+	0.0441942i
$129$		0			0
$130$	−2.60370	−	1.94777i	−0.228359	−	0.170831i
$131$	20.6496			1.80417			0.902083	−	0.431562i	$-0.142037\pi$
$131$	20.6496			1.80417			0.902083	+	0.431562i	$0.142037\pi$
$132$		0			0
$133$	3.08619	−	5.34544i	0.267607	−	0.463508i
$134$	5.19142	+	8.99180i	0.448470	+	0.776773i
$135$		0			0
$136$	−4.38722	+	2.53296i	−0.376201	+	0.217200i
$137$	−2.76224	+	1.59478i	−0.235994	+	0.136251i	−0.613334	−	0.789823i	$-0.710172\pi$
$137$	−2.76224	+	1.59478i	−0.235994	+	0.136251i	0.377340	+	0.926075i	$0.376839\pi$
$138$		0			0
$139$	0.297855	+	0.515900i	0.0252637	+	0.0437581i	0.878381	−	0.477961i	$-0.158624\pi$
$139$	0.297855	+	0.515900i	0.0252637	+	0.0437581i	−0.853117	+	0.521719i	$0.825291\pi$
$140$	0.450919	−	0.781015i	0.0381096	−	0.0660078i
$141$		0			0
$142$	−3.27856			−0.275131
$143$	−9.36733	+	12.5218i	−0.783335	+	1.04713i
$144$		0			0
$145$	1.71266	+	0.988802i	0.142228	+	0.0821155i
$146$	0.269511	−	0.466808i	0.0223049	−	0.0386333i
$147$		0			0
$148$			0.144306i			0.0118619i
$149$	−9.70783	+	5.60482i	−0.795297	+	0.459165i	−0.841824	−	0.539752i	$-0.818518\pi$
$149$	−9.70783	+	5.60482i	−0.795297	+	0.459165i	0.0465273	+	0.998917i	$0.485185\pi$
$150$		0			0
$151$		−	13.0731i		−	1.06387i	−0.846785	−	0.531935i	$-0.821465\pi$
$151$		−	13.0731i		−	1.06387i	0.846785	−	0.531935i	$-0.178535\pi$
$152$	−3.08619	−	5.34544i	−0.250323	−	0.433572i
$153$		0			0
$154$	−3.75609	−	2.16858i	−0.302675	−	0.174749i
$155$	0.787362			0.0632424
$156$		0			0
$157$	17.9245			1.43053			0.715266	−	0.698853i	$-0.246306\pi$
$157$	17.9245			1.43053			0.715266	+	0.698853i	$0.246306\pi$
$158$	−5.65817	−	3.26674i	−0.450139	−	0.259888i
$159$		0			0
$160$	−0.450919	−	0.781015i	−0.0356483	−	0.0617447i
$161$			8.45117i			0.666046i
$162$		0			0
$163$	17.5958	−	10.1589i	1.37821	−	0.795710i	0.386266	−	0.922387i	$-0.373765\pi$
$163$	17.5958	−	10.1589i	1.37821	−	0.795710i	0.991944	+	0.126677i	$0.0404312\pi$
$164$			3.99654i			0.312077i
$165$		0			0
$166$	6.61742	−	11.4617i	0.513611	−	0.889601i
$167$	2.79770	+	1.61525i	0.216493	+	0.124992i	0.604325	−	0.796738i	$-0.293443\pi$
$167$	2.79770	+	1.61525i	0.216493	+	0.124992i	−0.387833	+	0.921730i	$0.626776\pi$
$168$		0			0
$169$	−12.6356	−	3.05660i	−0.971966	−	0.235123i
$170$	4.56864			0.350399
$171$		0			0
$172$	−3.85426	+	6.67577i	−0.293884	+	0.509022i
$173$	4.58522	+	7.94183i	0.348608	+	0.603806i	0.986002	−	0.166731i	$-0.0533212\pi$
$173$	4.58522	+	7.94183i	0.348608	+	0.603806i	−0.637395	+	0.770538i	$0.719988\pi$
$174$		0			0
$175$	3.62578	−	2.09334i	0.274083	−	0.158242i
$176$	−3.75609	+	2.16858i	−0.283126	+	0.163463i
$177$		0			0
$178$	−3.89590	−	6.74790i	−0.292010	−	0.505776i
$179$	8.47747	−	14.6834i	0.633636	−	1.09749i	−0.353166	−	0.935561i	$-0.614895\pi$
$179$	8.47747	−	14.6834i	0.633636	−	1.09749i	0.986802	−	0.161929i	$-0.0517717\pi$
$180$		0			0
$181$	−2.65743			−0.197525			−0.0987626	−	0.995111i	$-0.531488\pi$
$181$	−2.65743			−0.197525			−0.0987626	+	0.995111i	$0.531488\pi$
$182$	0.426876	−	3.58019i	0.0316421	−	0.265382i
$183$		0			0
$184$	7.31893	+	4.22559i	0.539559	+	0.311514i
$185$	0.0650705	−	0.112705i	0.00478408	−	0.00828627i
$186$		0			0
$187$		−	21.9717i		−	1.60673i
$188$	−2.52979	+	1.46057i	−0.184504	+	0.106523i
$189$		0			0
$190$			5.56649i			0.403836i
$191$	−12.2430	−	21.2056i	−0.885875	−	1.53438i	−0.844708	−	0.535228i	$-0.820226\pi$
$191$	−12.2430	−	21.2056i	−0.885875	−	1.53438i	−0.0411671	−	0.999152i	$-0.513108\pi$
$192$		0			0
$193$	10.6009	+	6.12046i	0.763072	+	0.440560i	0.830398	−	0.557171i	$-0.188113\pi$
$193$	10.6009	+	6.12046i	0.763072	+	0.440560i	−0.0673254	+	0.997731i	$0.521447\pi$
$194$	−11.7061			−0.840449
$195$		0			0
$196$	1.00000			0.0714286
$197$	−4.72634	−	2.72876i	−0.336738	−	0.194416i	0.322091	−	0.946709i	$-0.395614\pi$
$197$	−4.72634	−	2.72876i	−0.336738	−	0.194416i	−0.658829	+	0.752293i	$0.728948\pi$
$198$		0			0
$199$	−6.40832	−	11.0995i	−0.454274	−	0.786825i	0.544372	−	0.838844i	$-0.316768\pi$
$199$	−6.40832	−	11.0995i	−0.454274	−	0.786825i	−0.998646	+	0.0520184i	$0.983435\pi$
$200$		−	4.18669i		−	0.296043i
$201$		0			0
$202$	−9.30362	+	5.37145i	−0.654600	+	0.377934i
$203$			2.19286i			0.153908i
$204$		0			0
$205$	1.80212	−	3.12136i	0.125865	−	0.218005i
$206$	−4.16644	−	2.40550i	−0.290290	−	0.167599i
$207$		0			0
$208$	−2.88710	−	2.15978i	−0.200184	−	0.149754i
$209$	26.7706			1.85176
$210$		0			0
$211$	9.65552	−	16.7239i	0.664713	−	1.15132i	−0.314649	−	0.949208i	$-0.601887\pi$
$211$	9.65552	−	16.7239i	0.664713	−	1.15132i	0.979363	−	0.202110i	$-0.0647797\pi$
$212$	−0.848493	−	1.46963i	−0.0582747	−	0.100935i
$213$		0			0
$214$	−11.8239	+	6.82652i	−0.808263	+	0.466651i
$215$	6.02046	−	3.47592i	0.410592	−	0.237056i
$216$		0			0
$217$	0.436531	+	0.756094i	0.0296337	+	0.0513270i
$218$	2.55874	−	4.43186i	0.173299	−	0.300163i
$219$		0			0
$220$	3.91142			0.263708
$221$	16.7883	−	7.19569i	1.12931	−	0.484034i
$222$		0			0
$223$	−9.21079	−	5.31785i	−0.616800	−	0.356110i	0.158822	−	0.987307i	$-0.449230\pi$
$223$	−9.21079	−	5.31785i	−0.616800	−	0.356110i	−0.775622	+	0.631197i	$0.782564\pi$
$224$	0.500000	−	0.866025i	0.0334077	−	0.0578638i
$225$		0			0
$226$		−	17.9321i		−	1.19282i
$227$	−19.6776	+	11.3609i	−1.30605	+	0.754047i	−0.981434	−	0.191800i	$-0.938567\pi$
$227$	−19.6776	+	11.3609i	−1.30605	+	0.754047i	−0.324613	+	0.945847i	$0.605234\pi$
$228$		0			0
$229$			20.3094i			1.34208i	0.741420	+	0.671042i	$0.234153\pi$
$229$			20.3094i			1.34208i	−0.741420	+	0.671042i	$0.765847\pi$
$230$	−3.81080	−	6.60049i	−0.251277	−	0.435224i
$231$		0			0
$232$	1.89907	+	1.09643i	0.124680	+	0.0719841i
$233$	−10.6446			−0.697352			−0.348676	−	0.937243i	$-0.613369\pi$
$233$	−10.6446			−0.697352			−0.348676	+	0.937243i	$0.613369\pi$
$234$		0			0
$235$	2.63441			0.171850
$236$	7.40394	+	4.27467i	0.481955	+	0.278257i
$237$		0			0
$238$	2.53296	+	4.38722i	0.164187	+	0.284381i
$239$			0.311564i			0.0201534i	0.999949	+	0.0100767i	$0.00320757\pi$
$239$			0.311564i			0.0201534i	−0.999949	+	0.0100767i	$0.996792\pi$
$240$		0			0
$241$	−21.9100	+	12.6498i	−1.41135	+	0.814843i	−0.995516	−	0.0945983i	$-0.969843\pi$
$241$	−21.9100	+	12.6498i	−1.41135	+	0.814843i	−0.415833	+	0.909441i	$0.636510\pi$
$242$		−	7.81099i		−	0.502110i
$243$		0			0
$244$	4.16720	−	7.21780i	0.266778	−	0.462073i
$245$	−0.781015	−	0.450919i	−0.0498972	−	0.0288082i
$246$		0			0
$247$	8.76732	+	20.4551i	0.557851	+	1.30153i
$248$	0.873062			0.0554395
$249$		0			0
$250$	−4.14246	+	7.17494i	−0.261992	+	0.453783i
$251$	−4.02015	−	6.96311i	−0.253750	−	0.439507i	0.710805	−	0.703389i	$-0.248331\pi$
$251$	−4.02015	−	6.96311i	−0.253750	−	0.439507i	−0.964555	+	0.263881i	$0.914997\pi$
$252$		0			0
$253$	−31.7434	+	18.3271i	−1.99569	+	1.15221i
$254$	16.8993	−	9.75681i	1.06036	−	0.612197i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	8.46634	−	14.6641i	0.528116	−	0.914723i	−0.471347	−	0.881948i	$-0.656232\pi$
$257$	8.46634	−	14.6641i	0.528116	−	0.914723i	0.999463	−	0.0327753i	$-0.0104346\pi$
$258$		0			0
$259$	0.144306			0.00896676
$260$	1.28098	+	2.98867i	0.0794431	+	0.185350i
$261$		0			0
$262$	−17.8831	−	10.3248i	−1.10482	−	0.637869i
$263$	5.16045	−	8.93817i	0.318207	−	0.551151i	−0.661907	−	0.749586i	$-0.730253\pi$
$263$	5.16045	−	8.93817i	0.318207	−	0.551151i	0.980114	+	0.198435i	$0.0635859\pi$
$264$		0			0
$265$			1.53041i			0.0940122i
$266$	−5.34544	+	3.08619i	−0.327750	+	0.189226i
$267$		0			0
$268$		−	10.3828i		−	0.634233i
$269$	−3.06999	−	5.31738i	−0.187181	−	0.324207i	0.757128	−	0.653266i	$-0.226602\pi$
$269$	−3.06999	−	5.31738i	−0.187181	−	0.324207i	−0.944309	+	0.329059i	$0.893268\pi$
$270$		0			0
$271$	9.24673	+	5.33860i	0.561699	+	0.324297i	0.753827	−	0.657073i	$-0.228206\pi$
$271$	9.24673	+	5.33860i	0.561699	+	0.324297i	−0.192128	+	0.981370i	$0.561539\pi$
$272$	5.06592			0.307167
$273$		0			0
$274$	3.18956			0.192689
$275$	15.7256	+	9.07917i	0.948289	+	0.547495i
$276$		0			0
$277$	10.9545	+	18.9737i	0.658191	+	1.14002i	0.981084	+	0.193585i	$0.0620114\pi$
$277$	10.9545	+	18.9737i	0.658191	+	1.14002i	−0.322892	+	0.946436i	$0.604655\pi$
$278$		−	0.595710i		−	0.0357283i
$279$		0			0
$280$	−0.781015	+	0.450919i	−0.0466746	+	0.0269476i
$281$			25.7719i			1.53743i	0.639594	+	0.768713i	$0.279102\pi$
$281$			25.7719i			1.53743i	−0.639594	+	0.768713i	$0.720898\pi$
$282$		0			0
$283$	−5.66344	+	9.80937i	−0.336657	+	0.583107i	−0.983802	−	0.179260i	$-0.942630\pi$
$283$	−5.66344	+	9.80937i	−0.336657	+	0.583107i	0.647145	+	0.762367i	$0.275963\pi$
$284$	2.83932	+	1.63928i	0.168482	+	0.0972733i
$285$		0			0
$286$	14.3733	−	6.16055i	0.849908	−	0.364281i
$287$	3.99654			0.235908
$288$		0			0
$289$	−4.33177	+	7.50285i	−0.254810	+	0.441344i
$290$	−0.988802	−	1.71266i	−0.0580645	−	0.100571i
$291$		0			0
$292$	−0.466808	+	0.269511i	−0.0273178	+	0.0157720i
$293$	−20.5646	+	11.8730i	−1.20140	+	0.693626i	−0.960865	−	0.277016i	$-0.910655\pi$
$293$	−20.5646	+	11.8730i	−1.20140	+	0.693626i	−0.240530	+	0.970642i	$0.577321\pi$
$294$		0			0
$295$	−3.85506	−	6.67716i	−0.224450	−	0.388759i
$296$	0.0721531	−	0.124973i	0.00419382	−	0.00726390i
$297$		0			0
$298$	11.2096			0.649357
$299$	−24.3994	−	18.2527i	−1.41105	−	1.05558i
$300$		0			0
$301$	6.67577	+	3.85426i	0.384785	+	0.222156i
$302$	−6.53653	+	11.3216i	−0.376135	+	0.651485i
$303$		0			0
$304$			6.17238i			0.354010i
$305$	−6.50930	+	3.75814i	−0.372721	+	0.215191i
$306$		0			0
$307$		−	6.68810i		−	0.381710i	−0.981618	−	0.190855i	$-0.938874\pi$
$307$		−	6.68810i		−	0.381710i	0.981618	−	0.190855i	$-0.0611261\pi$
$308$	2.16858	+	3.75609i	0.123566	+	0.214023i
$309$		0			0
$310$	−0.681875	−	0.393681i	−0.0387279	−	0.0223596i
$311$	−9.18724			−0.520961			−0.260480	−	0.965479i	$-0.583881\pi$
$311$	−9.18724			−0.520961			−0.260480	+	0.965479i	$0.583881\pi$
$312$		0			0
$313$	−17.1631			−0.970118			−0.485059	−	0.874481i	$-0.661202\pi$
$313$	−17.1631			−0.970118			−0.485059	+	0.874481i	$0.661202\pi$
$314$	−15.5231	−	8.96225i	−0.876018	−	0.505769i
$315$		0			0
$316$	3.26674	+	5.65817i	0.183769	+	0.318297i
$317$			3.76247i			0.211322i	0.994402	+	0.105661i	$0.0336958\pi$
$317$			3.76247i			0.211322i	−0.994402	+	0.105661i	$0.966304\pi$
$318$		0			0
$319$	−8.23658	+	4.75539i	−0.461160	+	0.266251i
$320$			0.901839i			0.0504143i
$321$		0			0
$322$	4.22559	−	7.31893i	0.235483	−	0.407868i
$323$	−27.0796	−	15.6344i	−1.50675	−	0.869921i
$324$		0			0
$325$	−1.78720	+	14.9891i	−0.0991358	+	0.831448i
$326$	−20.3179			−1.12530
$327$		0			0
$328$	1.99827	−	3.46110i	0.110336	−	0.191107i
$329$	1.46057	+	2.52979i	0.0805241	+	0.139472i
$330$		0			0
$331$	−27.9083	+	16.1129i	−1.53398	+	0.885643i	−0.534806	+	0.844975i	$0.679615\pi$
$331$	−27.9083	+	16.1129i	−1.53398	+	0.885643i	−0.999173	+	0.0406683i	$0.987051\pi$
$332$	−11.4617	+	6.61742i	−0.629043	+	0.363178i
$333$		0			0
$334$	−1.61525	−	2.79770i	−0.0883827	−	0.153083i
$335$	−4.68182	+	8.10916i	−0.255795	+	0.443051i
$336$		0			0
$337$	−3.01703			−0.164348			−0.0821740	−	0.996618i	$-0.526186\pi$
$337$	−3.01703			−0.164348			−0.0821740	+	0.996618i	$0.526186\pi$
$338$	9.41441	+	8.96487i	0.512077	+	0.487624i
$339$		0			0
$340$	−3.95656	−	2.28432i	−0.214575	−	0.123885i
$341$	−1.89331	+	3.27931i	−0.102528	+	0.177584i
$342$		0			0
$343$		−	1.00000i		−	0.0539949i
$344$	6.67577	−	3.85426i	0.359933	−	0.207808i
$345$		0			0
$346$		−	9.17044i		−	0.493006i
$347$	0.234270	+	0.405768i	0.0125763	+	0.0217828i	0.872245	−	0.489069i	$-0.162663\pi$
$347$	0.234270	+	0.405768i	0.0125763	+	0.0217828i	−0.859669	+	0.510852i	$0.829330\pi$
$348$		0			0
$349$	−27.9044	−	16.1106i	−1.49369	−	0.862380i	−0.493712	−	0.869625i	$-0.664360\pi$
$349$	−27.9044	−	16.1106i	−1.49369	−	0.862380i	−0.999974	+	0.00724565i	$0.997694\pi$
$350$	−4.18669			−0.223788
$351$		0			0
$352$	4.33716			0.231172
$353$	11.3583	+	6.55771i	0.604540	+	0.349031i	0.770826	−	0.637046i	$-0.219844\pi$
$353$	11.3583	+	6.55771i	0.604540	+	0.349031i	−0.166285	+	0.986078i	$0.553177\pi$
$354$		0			0
$355$	−1.47837	−	2.56060i	−0.0784635	−	0.135903i
$356$			7.79180i			0.412965i
$357$		0			0
$358$	−14.6834	+	8.47747i	−0.776043	+	0.448048i
$359$		−	4.37981i		−	0.231157i	−0.993298	−	0.115579i	$-0.963128\pi$
$359$		−	4.37981i		−	0.231157i	0.993298	−	0.115579i	$-0.0368722\pi$
$360$		0			0
$361$	9.54914	−	16.5396i	0.502586	−	0.870505i
$362$	2.30140	+	1.32871i	0.120959	+	0.0698357i
$363$		0			0
$364$	−2.15978	+	2.88710i	−0.113203	+	0.151325i
$365$	0.486112			0.0254443
$366$		0			0
$367$	−12.9094	+	22.3597i	−0.673865	+	1.16717i	0.302934	+	0.953011i	$0.402034\pi$
$367$	−12.9094	+	22.3597i	−0.673865	+	1.16717i	−0.976799	+	0.214157i	$0.931300\pi$
$368$	−4.22559	−	7.31893i	−0.220274	−	0.381526i
$369$		0			0
$370$	−0.112705	+	0.0650705i	−0.00585928	+	0.00338285i
$371$	−1.46963	+	0.848493i	−0.0762995	+	0.0440515i
$372$		0			0
$373$	−15.3143	−	26.5251i	−0.792942	−	1.37342i	−0.924138	−	0.382059i	$-0.875215\pi$
$373$	−15.3143	−	26.5251i	−0.792942	−	1.37342i	0.131196	−	0.991356i	$-0.458118\pi$
$374$	−10.9859	+	19.0281i	−0.568065	+	0.983918i
$375$		0			0
$376$	2.92115			0.150647
$377$	−6.33100	−	4.73609i	−0.326063	−	0.243921i
$378$		0			0
$379$	−33.0409	−	19.0762i	−1.69720	−	0.979877i	−0.948400	−	0.317076i	$-0.897299\pi$
$379$	−33.0409	−	19.0762i	−1.69720	−	0.979877i	−0.748796	−	0.662801i	$-0.769368\pi$
$380$	2.78325	−	4.82072i	0.142778	−	0.247298i
$381$		0			0
$382$			24.4861i			1.25282i
$383$	27.6783	−	15.9801i	1.41430	−	0.816544i	0.418507	−	0.908214i	$-0.362554\pi$
$383$	27.6783	−	15.9801i	1.41430	−	0.816544i	0.995790	+	0.0916693i	$0.0292203\pi$
$384$		0			0
$385$		−	3.91142i		−	0.199345i
$386$	−6.12046	−	10.6009i	−0.311523	−	0.539574i
$387$		0			0
$388$	10.1378	+	5.85305i	0.514668	+	0.297144i
$389$	−5.24585			−0.265975			−0.132988	−	0.991118i	$-0.542457\pi$
$389$	−5.24585			−0.265975			−0.132988	+	0.991118i	$0.542457\pi$
$390$		0			0
$391$	42.8130			2.16514
$392$	−0.866025	−	0.500000i	−0.0437409	−	0.0252538i
$393$		0			0
$394$	2.72876	+	4.72634i	0.137473	+	0.238110i
$395$		−	5.89215i		−	0.296466i
$396$		0			0
$397$	21.2432	−	12.2648i	1.06617	−	0.615552i	0.139035	−	0.990287i	$-0.455600\pi$
$397$	21.2432	−	12.2648i	1.06617	−	0.615552i	0.927132	+	0.374736i	$0.122266\pi$
$398$			12.8166i			0.642440i
$399$		0			0
$400$	−2.09334	+	3.62578i	−0.104667	+	0.181289i
$401$	−3.69916	−	2.13571i	−0.184727	−	0.106652i	0.404784	−	0.914412i	$-0.367347\pi$
$401$	−3.69916	−	2.13571i	−0.184727	−	0.106652i	−0.589512	+	0.807760i	$0.700680\pi$
$402$		0			0
$403$	−3.12573	−	0.372689i	−0.155704	−	0.0185650i
$404$	10.7429			0.534479
$405$		0			0
$406$	1.09643	−	1.89907i	0.0544149	−	0.0942493i
$407$	0.312940	+	0.542028i	0.0155119	+	0.0268673i
$408$		0			0
$409$	−1.39990	+	0.808235i	−0.0692208	+	0.0399646i	−0.534211	−	0.845351i	$-0.679391\pi$
$409$	−1.39990	+	0.808235i	−0.0692208	+	0.0399646i	0.464990	+	0.885316i	$0.346058\pi$
$410$	−3.12136	+	1.80212i	−0.154153	+	0.0890001i
$411$		0			0
$412$	2.40550	+	4.16644i	0.118510	+	0.205266i
$413$	4.27467	−	7.40394i	0.210343	−	0.364324i
$414$		0			0
$415$	11.9357			0.585900
$416$	1.42041	+	3.31398i	0.0696414	+	0.162481i
$417$		0			0
$418$	−23.1840	−	13.3853i	−1.13397	−	0.654697i
$419$	−13.0156	+	22.5437i	−0.635854	+	1.10133i	0.350480	+	0.936570i	$0.386018\pi$
$419$	−13.0156	+	22.5437i	−0.635854	+	1.10133i	−0.986334	+	0.164761i	$0.947315\pi$
$420$		0			0
$421$			37.5391i			1.82954i	0.403971	+	0.914772i	$0.367630\pi$
$421$			37.5391i			1.82954i	−0.403971	+	0.914772i	$0.632370\pi$
$422$	−16.7239	+	9.65552i	−0.814104	+	0.470023i
$423$		0			0
$424$			1.69699i			0.0824129i
$425$	−10.6047	−	18.3679i	−0.514404	−	0.890974i
$426$		0			0
$427$	−7.21780	−	4.16720i	−0.349294	−	0.201665i
$428$	13.6530			0.659944
$429$		0			0
$430$	−6.95183			−0.335247
$431$	−18.6662	−	10.7769i	−0.899118	−	0.519106i	−0.0222041	−	0.999753i	$-0.507068\pi$
$431$	−18.6662	−	10.7769i	−0.899118	−	0.519106i	−0.876914	+	0.480647i	$0.840402\pi$
$432$		0			0
$433$	1.59958	+	2.77056i	0.0768710	+	0.133145i	0.901898	−	0.431948i	$-0.142174\pi$
$433$	1.59958	+	2.77056i	0.0768710	+	0.133145i	−0.825027	+	0.565093i	$0.808840\pi$
$434$		−	0.873062i		−	0.0419083i
$435$		0			0
$436$	−4.43186	+	2.55874i	−0.212248	+	0.122541i
$437$			52.1638i			2.49534i
$438$		0			0
$439$	13.3114	−	23.0560i	0.635317	−	1.10040i	−0.351131	−	0.936326i	$-0.614203\pi$
$439$	13.3114	−	23.0560i	0.635317	−	1.10040i	0.986448	−	0.164075i	$-0.0524638\pi$
$440$	−3.38739	−	1.95571i	−0.161488	−	0.0932349i
$441$		0			0
$442$	−18.1370	−	2.16252i	−0.862688	−	0.102861i
$443$	−9.09867			−0.432291			−0.216145	−	0.976361i	$-0.569348\pi$
$443$	−9.09867			−0.432291			−0.216145	+	0.976361i	$0.569348\pi$
$444$		0			0
$445$	3.51347	−	6.08551i	0.166555	−	0.288481i
$446$	5.31785	+	9.21079i	0.251808	+	0.436144i
$447$		0			0
$448$	−0.866025	+	0.500000i	−0.0409159	+	0.0236228i
$449$	−6.08550	+	3.51346i	−0.287192	+	0.165811i	−0.636675	−	0.771132i	$-0.719691\pi$
$449$	−6.08550	+	3.51346i	−0.287192	+	0.165811i	0.349483	+	0.936943i	$0.386357\pi$
$450$		0			0
$451$	8.66681	+	15.0114i	0.408104	+	0.706858i
$452$	−8.96603	+	15.5296i	−0.421726	+	0.730452i
$453$		0			0
$454$	22.7217			1.06638
$455$	2.98867	−	1.28098i	0.140111	−	0.0600533i
$456$		0			0
$457$	−16.5853	−	9.57556i	−0.775830	−	0.447926i	0.0591204	−	0.998251i	$-0.481170\pi$
$457$	−16.5853	−	9.57556i	−0.775830	−	0.447926i	−0.834950	+	0.550325i	$0.814504\pi$
$458$	10.1547	−	17.5885i	0.474498	−	0.821855i
$459$		0			0
$460$			7.62159i			0.355359i
$461$	2.82026	−	1.62828i	0.131353	−	0.0758365i	−0.432884	−	0.901450i	$-0.642504\pi$
$461$	2.82026	−	1.62828i	0.131353	−	0.0758365i	0.564236	+	0.825613i	$0.309171\pi$
$462$		0			0
$463$			21.2761i			0.988786i	0.869238	+	0.494393i	$0.164610\pi$
$463$			21.2761i			0.988786i	−0.869238	+	0.494393i	$0.835390\pi$
$464$	−1.09643	−	1.89907i	−0.0509004	−	0.0881621i
$465$		0			0
$466$	9.21851	+	5.32231i	0.427039	+	0.246551i
$467$	3.33171			0.154173			0.0770866	−	0.997024i	$-0.475438\pi$
$467$	3.33171			0.154173			0.0770866	+	0.997024i	$0.475438\pi$
$468$		0			0
$469$	−10.3828			−0.479435
$470$	−2.28146	−	1.31720i	−0.105236	−	0.0607580i
$471$		0			0
$472$	−4.27467	−	7.40394i	−0.196757	−	0.340794i
$473$			33.4331i			1.53725i
$474$		0			0
$475$	22.3797	−	12.9209i	1.02685	−	0.592852i
$476$		−	5.06592i		−	0.232196i
$477$		0			0
$478$	0.155782	−	0.269822i	0.00712530	−	0.0123414i
$479$	0.160402	+	0.0926079i	0.00732894	+	0.00423136i	0.503660	−	0.863902i	$-0.331986\pi$
$479$	0.160402	+	0.0926079i	0.00732894	+	0.00423136i	−0.496331	+	0.868133i	$0.665320\pi$
$480$		0			0
$481$	−0.311670	+	0.416627i	−0.0142109	+	0.0189965i
$482$	25.2995			1.15236
$483$		0			0
$484$	−3.90550	+	6.76452i	−0.177523	+	0.307478i
$485$	−5.27851	−	9.14264i	−0.239685	−	0.415146i
$486$		0			0
$487$	−27.0466	+	15.6154i	−1.22560	+	0.707601i	−0.966106	−	0.258144i	$-0.916889\pi$
$487$	−27.0466	+	15.6154i	−1.22560	+	0.707601i	−0.259494	+	0.965745i	$0.583556\pi$
$488$	−7.21780	+	4.16720i	−0.326735	+	0.188640i
$489$		0			0
$490$	0.450919	+	0.781015i	0.0203705	+	0.0352827i
$491$	−13.4236	+	23.2504i	−0.605799	+	1.04927i	0.386126	+	0.922446i	$0.373813\pi$
$491$	−13.4236	+	23.2504i	−0.605799	+	1.04927i	−0.991925	+	0.126829i	$0.959520\pi$
$492$		0			0
$493$	11.1088			0.500317
$494$	2.63484	−	22.0983i	0.118547	−	0.994250i
$495$		0			0
$496$	−0.756094	−	0.436531i	−0.0339496	−	0.0196008i
$497$	1.63928	−	2.83932i	0.0735317	−	0.127361i
$498$		0			0
$499$		−	15.2869i		−	0.684337i	−0.939639	−	0.342168i	$-0.888839\pi$
$499$		−	15.2869i		−	0.684337i	0.939639	−	0.342168i	$-0.111161\pi$
$500$	7.17494	−	4.14246i	0.320873	−	0.185256i
$501$		0			0
$502$			8.04030i			0.358856i
$503$	−13.0551	−	22.6121i	−0.582097	−	1.00822i	−0.995230	−	0.0975513i	$-0.968899\pi$
$503$	−13.0551	−	22.6121i	−0.582097	−	1.00822i	0.413133	−	0.910671i	$-0.364434\pi$
$504$		0			0
$505$	−8.39036	−	4.84418i	−0.373366	−	0.215563i
$506$	36.6541			1.62947
$507$		0			0
$508$	−19.5136			−0.865777
$509$	−14.7459	−	8.51357i	−0.653602	−	0.377357i	0.136233	−	0.990677i	$-0.456500\pi$
$509$	−14.7459	−	8.51357i	−0.653602	−	0.377357i	−0.789835	+	0.613320i	$0.789834\pi$
$510$		0			0
$511$	0.269511	+	0.466808i	0.0119225	+	0.0206504i
$512$			1.00000i			0.0441942i
$513$		0			0
$514$	−14.6641	+	8.46634i	−0.646807	+	0.373434i
$515$		−	4.33874i		−	0.191188i
$516$		0			0
$517$	−6.33475	+	10.9721i	−0.278602	+	0.482553i
$518$	−0.124973	−	0.0721531i	−0.00549099	−	0.00317023i
$519$		0			0
$520$	0.384973	−	3.22876i	0.0168822	−	0.141590i
$521$	18.7760			0.822593			0.411297	−	0.911502i	$-0.365076\pi$
$521$	18.7760			0.822593			0.411297	+	0.911502i	$0.365076\pi$
$522$		0			0
$523$	1.51624	−	2.62620i	0.0663004	−	0.114836i	−0.830970	−	0.556318i	$-0.812214\pi$
$523$	1.51624	−	2.62620i	0.0663004	−	0.114836i	0.897270	+	0.441482i	$0.145547\pi$
$524$	10.3248	+	17.8831i	0.451042	+	0.781227i
$525$		0			0
$526$	−8.93817	+	5.16045i	−0.389723	+	0.225006i
$527$	3.83031	−	2.21143i	0.166851	−	0.0963315i
$528$		0			0
$529$	−24.2111	−	41.9349i	−1.05266	−	1.82326i
$530$	0.765204	−	1.32537i	0.0332383	−	0.0575705i
$531$		0			0
$532$	6.17238			0.267607
$533$	−8.63164	+	11.5384i	−0.373878	+	0.499783i
$534$		0			0
$535$	−10.6632	−	6.15642i	−0.461011	−	0.266165i
$536$	−5.19142	+	8.99180i	−0.224235	+	0.388387i
$537$		0			0
$538$			6.13999i			0.264714i
$539$	3.75609	−	2.16858i	0.161786	−	0.0934074i
$540$		0			0
$541$			6.11845i			0.263053i	0.991313	+	0.131526i	$0.0419878\pi$
$541$			6.11845i			0.263053i	−0.991313	+	0.131526i	$0.958012\pi$
$542$	−5.33860	−	9.24673i	−0.229313	−	0.397181i
$543$		0			0
$544$	−4.38722	−	2.53296i	−0.188100	−	0.108600i
$545$	4.61513			0.197691
$546$		0			0
$547$	−37.4754			−1.60233			−0.801166	−	0.598442i	$-0.795786\pi$
$547$	−37.4754			−1.60233			−0.801166	+	0.598442i	$0.795786\pi$
$548$	−2.76224	−	1.59478i	−0.117997	−	0.0681257i
$549$		0			0
$550$	−9.07917	−	15.7256i	−0.387137	−	0.670541i
$551$			13.5352i			0.576617i
$552$		0			0
$553$	5.65817	−	3.26674i	0.240610	−	0.138916i
$554$		−	21.9090i		−	0.930823i
$555$		0			0
$556$	−0.297855	+	0.515900i	−0.0126319	+	0.0218790i
$557$	7.69941	+	4.44526i	0.326234	+	0.188352i	0.654168	−	0.756349i	$-0.273019\pi$
$557$	7.69941	+	4.44526i	0.326234	+	0.188352i	−0.327934	+	0.944701i	$0.606352\pi$
$558$		0			0
$559$	−25.5458	+	10.9493i	−1.08047	+	0.463104i
$560$	0.901839			0.0381096
$561$		0			0
$562$	12.8860	−	22.3192i	0.543562	−	0.941477i
$563$	−8.89598	−	15.4083i	−0.374921	−	0.649382i	0.615394	−	0.788219i	$-0.288997\pi$
$563$	−8.89598	−	15.4083i	−0.374921	−	0.649382i	−0.990315	+	0.138838i	$0.955663\pi$
$564$		0			0
$565$	14.0052	−	8.08591i	0.589204	−	0.340177i
$566$	9.80937	−	5.66344i	0.412319	−	0.238052i
$567$		0			0
$568$	−1.63928	−	2.83932i	−0.0687826	−	0.119135i
$569$	−5.58684	+	9.67669i	−0.234212	+	0.405668i	−0.959044	−	0.283259i	$-0.908584\pi$
$569$	−5.58684	+	9.67669i	−0.234212	+	0.405668i	0.724831	+	0.688927i	$0.241918\pi$
$570$		0			0
$571$	−16.7239			−0.699873			−0.349936	−	0.936773i	$-0.613797\pi$
$571$	−16.7239			−0.699873			−0.349936	+	0.936773i	$0.613797\pi$
$572$	−15.5279	−	1.85143i	−0.649253	−	0.0774122i
$573$		0			0
$574$	−3.46110	−	1.99827i	−0.144464	−	0.0834061i
$575$	−17.6912	+	30.6421i	−0.737774	+	1.27786i
$576$		0			0
$577$			0.798887i			0.0332581i	0.999862	+	0.0166291i	$0.00529344\pi$
$577$			0.798887i			0.0332581i	−0.999862	+	0.0166291i	$0.994707\pi$
$578$	7.50285	−	4.33177i	0.312078	−	0.180178i
$579$		0			0
$580$			1.97760i			0.0821155i
$581$	6.61742	+	11.4617i	0.274537	+	0.475512i
$582$		0			0
$583$	−6.37404	−	3.68005i	−0.263986	−	0.152412i
$584$	0.539023			0.0223049
$585$		0			0
$586$	23.7459			0.980935
$587$	−6.94921	−	4.01213i	−0.286825	−	0.165598i	0.349684	−	0.936868i	$-0.386289\pi$
$587$	−6.94921	−	4.01213i	−0.286825	−	0.165598i	−0.636509	+	0.771269i	$0.719622\pi$
$588$		0			0
$589$	2.69444	+	4.66690i	0.111022	+	0.192296i
$590$			7.71012i			0.317421i
$591$		0			0
$592$	−0.124973	+	0.0721531i	−0.00513635	+	0.00296548i
$593$			4.93120i			0.202500i	0.994861	+	0.101250i	$0.0322842\pi$
$593$			4.93120i			0.202500i	−0.994861	+	0.101250i	$0.967716\pi$
$594$		0			0
$595$	−2.28432	+	3.95656i	−0.0936481	+	0.162203i
$596$	−9.70783	−	5.60482i	−0.397648	−	0.229582i
$597$		0			0
$598$	12.0041	+	28.0070i	0.490886	+	1.14529i
$599$	17.8249			0.728306			0.364153	−	0.931339i	$-0.381358\pi$
$599$	17.8249			0.728306			0.364153	+	0.931339i	$0.381358\pi$
$600$		0			0
$601$	0.0809165	−	0.140152i	0.00330065	−	0.00571690i	−0.864370	−	0.502856i	$-0.832283\pi$
$601$	0.0809165	−	0.140152i	0.00330065	−	0.00571690i	0.867671	+	0.497139i	$0.165616\pi$
$602$	−3.85426	−	6.67577i	−0.157088	−	0.272084i
$603$		0			0
$604$	11.3216	−	6.53653i	0.460670	−	0.265968i
$605$	6.10050	−	3.52213i	0.248021	−	0.143195i
$606$		0			0
$607$	−3.09423	−	5.35937i	−0.125591	−	0.217530i	0.796373	−	0.604806i	$-0.206749\pi$
$607$	−3.09423	−	5.35937i	−0.125591	−	0.217530i	−0.921964	+	0.387276i	$0.873416\pi$
$608$	3.08619	−	5.34544i	0.125162	−	0.216786i
$609$		0			0
$610$	7.51629			0.304326
$611$	−10.4583	−	1.24697i	−0.423097	−	0.0504469i
$612$		0			0
$613$	32.2269	+	18.6062i	1.30163	+	0.751497i	0.980684	−	0.195600i	$-0.0626654\pi$
$613$	32.2269	+	18.6062i	1.30163	+	0.751497i	0.320947	+	0.947097i	$0.395999\pi$
$614$	−3.34405	+	5.79207i	−0.134955	+	0.233749i
$615$		0			0
$616$		−	4.33716i		−	0.174749i
$617$	5.78536	−	3.34018i	0.232910	−	0.134471i	−0.379004	−	0.925395i	$-0.623733\pi$
$617$	5.78536	−	3.34018i	0.232910	−	0.134471i	0.611914	+	0.790924i	$0.290400\pi$
$618$		0			0
$619$		−	23.7344i		−	0.953965i	−0.878913	−	0.476982i	$-0.841731\pi$
$619$		−	23.7344i		−	0.953965i	0.878913	−	0.476982i	$-0.158269\pi$
$620$	0.393681	+	0.681875i	0.0158106	+	0.0273848i
$621$		0			0
$622$	7.95639	+	4.59362i	0.319022	+	0.184187i
$623$	7.79180			0.312172
$624$		0			0
$625$	13.4618			0.538471
$626$	14.8637	+	8.58157i	0.594074	+	0.342989i
$627$		0			0
$628$	8.96225	+	15.5231i	0.357633	+	0.619438i
$629$		−	0.731044i		−	0.0291486i
$630$		0			0
$631$	19.9348	−	11.5093i	0.793590	−	0.458180i	−0.0476346	−	0.998865i	$-0.515168\pi$
$631$	19.9348	−	11.5093i	0.793590	−	0.458180i	0.841225	+	0.540685i	$0.181835\pi$
$632$		−	6.53349i		−	0.259888i
$633$		0			0
$634$	1.88124	−	3.25840i	0.0747135	−	0.129408i
$635$	15.2404	+	8.79907i	0.604798	+	0.349181i
$636$		0			0
$637$	2.88710	+	2.15978i	0.114391	+	0.0855737i
$638$	9.51078			0.376536
$639$		0			0
$640$	0.450919	−	0.781015i	0.0178242	−	0.0308723i
$641$	−6.32539	−	10.9559i	−0.249838	−	0.432732i	0.713643	−	0.700510i	$-0.247044\pi$
$641$	−6.32539	−	10.9559i	−0.249838	−	0.432732i	−0.963481	+	0.267778i	$0.913711\pi$
$642$		0			0
$643$	−13.1971	+	7.61938i	−0.520445	+	0.300479i	−0.737117	−	0.675766i	$-0.763813\pi$
$643$	−13.1971	+	7.61938i	−0.520445	+	0.300479i	0.216672	+	0.976244i	$0.430480\pi$
$644$	−7.31893	+	4.22559i	−0.288406	+	0.166511i
$645$		0			0
$646$	15.6344	+	27.0796i	0.615127	+	1.06543i
$647$	14.6821	−	25.4301i	0.577213	−	0.999762i	−0.418585	−	0.908178i	$-0.637474\pi$
$647$	14.6821	−	25.4301i	0.577213	−	0.999762i	0.995797	−	0.0915840i	$-0.0291930\pi$
$648$		0			0
$649$	37.0799			1.45551
$650$	9.04233	−	12.0874i	0.354669	−	0.474106i
$651$		0			0
$652$	17.5958	+	10.1589i	0.689105	+	0.397855i
$653$	−14.5106	+	25.1330i	−0.567842	+	0.983532i	0.428937	+	0.903335i	$0.358888\pi$
$653$	−14.5106	+	25.1330i	−0.567842	+	0.983532i	−0.996779	+	0.0801974i	$0.974445\pi$
$654$		0			0
$655$		−	18.6226i		−	0.727647i
$656$	−3.46110	+	1.99827i	−0.135133	+	0.0780192i
$657$		0			0
$658$		−	2.92115i		−	0.113878i
$659$	3.98651	+	6.90484i	0.155293	+	0.268975i	0.933166	−	0.359447i	$-0.117035\pi$
$659$	3.98651	+	6.90484i	0.155293	+	0.268975i	−0.777873	+	0.628422i	$0.783701\pi$
$660$		0			0
$661$	3.40668	+	1.96685i	0.132505	+	0.0765015i	0.564787	−	0.825237i	$-0.308958\pi$
$661$	3.40668	+	1.96685i	0.132505	+	0.0765015i	−0.432282	+	0.901738i	$0.642292\pi$
$662$	32.2257			1.25249
$663$		0			0
$664$	13.2348			0.513611
$665$	−4.82072	−	2.78325i	−0.186940	−	0.107930i
$666$		0			0
$667$	−9.26611	−	16.0494i	−0.358785	−	0.621434i
$668$			3.23051i			0.124992i
$669$		0			0
$670$	8.10916	−	4.68182i	0.313284	−	0.180875i
$671$		−	36.1477i		−	1.39547i
$672$		0			0
$673$	18.1599	−	31.4539i	0.700014	−	1.21246i	−0.268447	−	0.963295i	$-0.586510\pi$
$673$	18.1599	−	31.4539i	0.700014	−	1.21246i	0.968461	−	0.249166i	$-0.0801563\pi$
$674$	2.61282	+	1.50851i	0.100642	+	0.0581058i
$675$		0			0
$676$	−3.67069	−	12.4710i	−0.141180	−	0.479654i
$677$	21.1068			0.811201			0.405600	−	0.914051i	$-0.367062\pi$
$677$	21.1068			0.811201			0.405600	+	0.914051i	$0.367062\pi$
$678$		0			0
$679$	5.85305	−	10.1378i	0.224619	−	0.389052i
$680$	2.28432	+	3.95656i	0.0875997	+	0.151727i
$681$		0			0
$682$	3.27931	−	1.89331i	0.125571	−	0.0724985i
$683$	22.8854	−	13.2129i	0.875685	−	0.505577i	0.00645161	−	0.999979i	$-0.497946\pi$
$683$	22.8854	−	13.2129i	0.875685	−	0.505577i	0.869233	+	0.494402i	$0.164613\pi$
$684$		0			0
$685$	1.43824	+	2.49110i	0.0549522	+	0.0951799i
$686$	−0.500000	+	0.866025i	−0.0190901	+	0.0330650i
$687$		0			0
$688$	−7.70851			−0.293884
$689$	0.724402	−	6.07553i	0.0275975	−	0.231459i
$690$		0			0
$691$	0.675291	+	0.389880i	0.0256893	+	0.0148317i	0.512790	−	0.858514i	$-0.328612\pi$
$691$	0.675291	+	0.389880i	0.0256893	+	0.0148317i	−0.487100	+	0.873346i	$0.661945\pi$
$692$	−4.58522	+	7.94183i	−0.174304	+	0.301903i
$693$		0			0
$694$		−	0.468540i		−	0.0177855i
$695$	0.465259	−	0.268617i	0.0176483	−	0.0101892i
$696$		0			0
$697$		−	20.2461i		−	0.766877i
$698$	16.1106	+	27.9044i	0.609795	+	1.05620i
$699$		0			0
$700$	3.62578	+	2.09334i	0.137041	+	0.0791209i
$701$	−21.5491			−0.813899			−0.406950	−	0.913451i	$-0.633408\pi$
$701$	−21.5491			−0.813899			−0.406950	+	0.913451i	$0.633408\pi$
$702$		0			0
$703$	0.890713			0.0335939
$704$	−3.75609	−	2.16858i	−0.141563	−	0.0817315i
$705$		0			0
$706$	−6.55771	−	11.3583i	−0.246803	−	0.427474i
$707$		−	10.7429i		−	0.404028i
$708$		0			0
$709$	−3.92952	+	2.26871i	−0.147576	+	0.0852031i	−0.571970	−	0.820275i	$-0.693821\pi$
$709$	−3.92952	+	2.26871i	−0.147576	+	0.0852031i	0.424394	+	0.905478i	$0.360487\pi$
$710$			2.95673i			0.110964i
$711$		0			0
$712$	3.89590	−	6.74790i	0.146005	−	0.252888i
$713$	−6.38988	−	3.68920i	−0.239303	−	0.138162i
$714$		0			0
$715$	11.2927	+	8.44782i	0.422322	+	0.315931i
$716$	16.9549			0.633636
$717$		0			0
$718$	−2.18990	+	3.79302i	−0.0817265	+	0.141554i
$719$	7.30036	+	12.6446i	0.272258	+	0.471564i	0.969440	−	0.245330i	$-0.0788964\pi$
$719$	7.30036	+	12.6446i	0.272258	+	0.471564i	−0.697182	+	0.716894i	$0.745563\pi$
$720$		0			0
$721$	4.16644	−	2.40550i	0.155166	−	0.0895854i
$722$	−16.5396	+	9.54914i	−0.615540	+	0.355382i
$723$		0			0
$724$	−1.32871	−	2.30140i	−0.0493813	−	0.0855309i
$725$	−4.59040	+	7.95081i	−0.170483	+	0.295286i
$726$		0			0
$727$	30.6315			1.13606			0.568030	−	0.823008i	$-0.307706\pi$
$727$	30.6315			1.13606			0.568030	+	0.823008i	$0.307706\pi$
$728$	3.31398	−	1.42041i	0.122824	−	0.0526439i
$729$		0			0
$730$	−0.420985	−	0.243056i	−0.0155814	−	0.00899590i
$731$	19.5254	−	33.8189i	0.722171	−	1.25084i
$732$		0			0
$733$			17.7195i			0.654484i	0.944941	+	0.327242i	$0.106119\pi$
$733$			17.7195i			0.654484i	−0.944941	+	0.327242i	$0.893881\pi$
$734$	22.3597	−	12.9094i	0.825313	−	0.476495i
$735$		0			0
$736$			8.45117i			0.311514i
$737$	−22.5160	−	38.9989i	−0.829389	−	1.43654i
$738$		0			0
$739$	−9.05014	−	5.22510i	−0.332915	−	0.192208i	0.324220	−	0.945982i	$-0.394898\pi$
$739$	−9.05014	−	5.22510i	−0.332915	−	0.192208i	−0.657134	+	0.753773i	$0.728232\pi$
$740$	0.130141			0.00478408
$741$		0			0
$742$	1.69699			0.0622983
$743$	−42.0103	−	24.2547i	−1.54121	−	0.889818i	−0.998763	−	0.0497278i	$-0.984165\pi$
$743$	−42.0103	−	24.2547i	−1.54121	−	0.889818i	−0.542447	−	0.840090i	$-0.682502\pi$
$744$		0			0
$745$	5.05464	+	8.75490i	0.185188	+	0.320755i
$746$			30.6285i			1.12139i
$747$		0			0
$748$	19.0281	−	10.9859i	0.695735	−	0.401683i
$749$		−	13.6530i		−	0.498871i
$750$		0			0
$751$	15.7278	−	27.2413i	0.573914	−	0.994049i	−0.422244	−	0.906482i	$-0.638758\pi$
$751$	15.7278	−	27.2413i	0.573914	−	0.994049i	0.996159	−	0.0875667i	$-0.0279091\pi$
$752$	−2.52979	−	1.46057i	−0.0922519	−	0.0532617i
$753$		0			0
$754$	3.11476	+	7.26708i	0.113433	+	0.264651i
$755$	−11.7898			−0.429075
$756$		0			0
$757$	−24.3442	+	42.1654i	−0.884805	+	1.53253i	−0.0388676	+	0.999244i	$0.512375\pi$
$757$	−24.3442	+	42.1654i	−0.884805	+	1.53253i	−0.845937	+	0.533283i	$0.820958\pi$
$758$	19.0762	+	33.0409i	0.692877	+	1.20010i
$759$		0			0
$760$	−4.82072	+	2.78325i	−0.174866	+	0.100959i
$761$	40.3350	−	23.2874i	1.46214	−	0.844169i	0.463033	−	0.886341i	$-0.346761\pi$
$761$	40.3350	−	23.2874i	1.46214	−	0.844169i	0.999110	+	0.0421718i	$0.0134277\pi$
$762$		0			0
$763$	2.55874	+	4.43186i	0.0926325	+	0.160444i
$764$	12.2430	−	21.2056i	0.442937	−	0.767190i
$765$		0			0
$766$	−31.9602			−1.15477
$767$	12.1436	+	28.3323i	0.438479	+	1.02302i
$768$		0			0
$769$	−24.1069	−	13.9181i	−0.869315	−	0.501899i	−0.00219468	−	0.999998i	$-0.500699\pi$
$769$	−24.1069	−	13.9181i	−0.869315	−	0.501899i	−0.867121	+	0.498098i	$0.834032\pi$
$770$	−1.95571	+	3.38739i	−0.0704789	+	0.122073i
$771$		0			0
$772$			12.2409i			0.440560i
$773$	−24.6578	+	14.2362i	−0.886880	+	0.512040i	−0.872921	−	0.487862i	$-0.837777\pi$
$773$	−24.6578	+	14.2362i	−0.886880	+	0.512040i	−0.0139594	+	0.999903i	$0.504444\pi$
$774$		0			0
$775$			3.65524i			0.131300i
$776$	−5.85305	−	10.1378i	−0.210112	−	0.363925i
$777$		0			0
$778$	4.54304	+	2.62292i	0.162876	+	0.0940364i
$779$	24.6681			0.883828
$780$		0			0
$781$	14.2196			0.508819
$782$	−37.0771	−	21.4065i	−1.32587	−	0.765494i
$783$		0			0
$784$	0.500000	+	0.866025i	0.0178571	+	0.0309295i
$785$		−	16.1650i		−	0.576954i
$786$		0			0
$787$	13.1046	−	7.56594i	0.467128	−	0.269697i	−0.247908	−	0.968783i	$-0.579743\pi$
$787$	13.1046	−	7.56594i	0.467128	−	0.269697i	0.715037	+	0.699087i	$0.246410\pi$
$788$		−	5.45751i		−	0.194416i
$789$		0			0
$790$	−2.94608	+	5.10275i	−0.104817	+	0.181548i
$791$	15.5296	+	8.96603i	0.552170	+	0.318795i
$792$		0			0
$793$	27.6200	−	11.8383i	0.980815	−	0.420389i
$794$	−24.5296			−0.870522
$795$		0			0
$796$	6.40832	−	11.0995i	0.227137	−	0.393413i
$797$	−6.97234	−	12.0764i	−0.246973	−	0.427770i	0.715712	−	0.698396i	$-0.246103\pi$
$797$	−6.97234	−	12.0764i	−0.246973	−	0.427770i	−0.962684	+	0.270626i	$0.912769\pi$
$798$		0			0
$799$	12.8157	−	7.39916i	0.453387	−	0.261763i
$800$	3.62578	−	2.09334i	0.128191	−	0.0740109i
$801$		0			0
$802$	2.13571	+	3.69916i	0.0754147	+	0.130622i
$803$	−1.16892	+	2.02462i	−0.0412501	+	0.0714473i
$804$		0			0
$805$	7.62159			0.268626
$806$	2.52062	+	1.88562i	0.0887850	+	0.0664183i
$807$		0			0
$808$	−9.30362	−	5.37145i	−0.327300	−	0.188967i
$809$	−10.8714	+	18.8299i	−0.382220	+	0.662024i	−0.991379	−	0.131024i	$-0.958174\pi$
$809$	−10.8714	+	18.8299i	−0.382220	+	0.662024i	0.609159	+	0.793048i	$0.291507\pi$
$810$		0			0
$811$			21.1256i			0.741819i	0.928669	+	0.370910i	$0.120954\pi$
$811$			21.1256i			0.741819i	−0.928669	+	0.370910i	$0.879046\pi$
$812$	−1.89907	+	1.09643i	−0.0666443	+	0.0384771i
$813$		0			0
$814$		−	0.625880i		−	0.0219371i
$815$	−9.16173	−	15.8686i	−0.320921	−	0.555852i
$816$		0			0
$817$	41.2054	+	23.7899i	1.44159	+	0.832304i
$818$	1.61647			0.0565185
$819$		0			0
$820$	3.60423			0.125865
$821$	14.0933	+	8.13678i	0.491860	+	0.283976i	0.725346	−	0.688385i	$-0.241680\pi$
$821$	14.0933	+	8.13678i	0.491860	+	0.283976i	−0.233486	+	0.972360i	$0.575013\pi$
$822$		0			0
$823$	9.32713	+	16.1551i	0.325123	+	0.563130i	0.981537	−	0.191271i	$-0.0612609\pi$
$823$	9.32713	+	16.1551i	0.325123	+	0.563130i	−0.656414	+	0.754401i	$0.727928\pi$
$824$		−	4.81099i		−	0.167599i
$825$		0			0
$826$	−7.40394	+	4.27467i	−0.257616	+	0.148735i
$827$		−	47.3361i		−	1.64604i	−0.568015	−	0.823018i	$-0.692288\pi$
$827$		−	47.3361i		−	1.64604i	0.568015	−	0.823018i	$-0.307712\pi$
$828$		0			0
$829$	0.460988	−	0.798454i	0.0160108	−	0.0277315i	−0.857909	−	0.513802i	$-0.828237\pi$
$829$	0.460988	−	0.798454i	0.0160108	−	0.0277315i	0.873920	+	0.486070i	$0.161570\pi$
$830$	−10.3366	−	5.96784i	−0.358789	−	0.207147i
$831$		0			0
$832$	0.426876	−	3.58019i	0.0147993	−	0.124121i
$833$	−5.06592			−0.175524
$834$		0			0
$835$	1.45670	−	2.52307i	0.0504111	−	0.0873146i
$836$	13.3853	+	23.1840i	0.462941	+	0.801837i
$837$		0			0
$838$	22.5437	−	13.0156i	0.778758	−	0.449616i
$839$	14.3894	−	8.30775i	0.496779	−	0.286815i	−0.230604	−	0.973048i	$-0.574070\pi$
$839$	14.3894	−	8.30775i	0.496779	−	0.286815i	0.727382	+	0.686232i	$0.240737\pi$
$840$		0			0
$841$	12.0957	+	20.9503i	0.417093	+	0.722426i
$842$	18.7696	−	32.5098i	0.646841	−	1.12036i
$843$		0			0
$844$	19.3110			0.664713
$845$	−2.75656	+	11.3952i	−0.0948284	+	0.392008i
$846$		0			0
$847$	6.76452	+	3.90550i	0.232432	+	0.134194i
$848$	0.848493	−	1.46963i	0.0291374	−	0.0504674i
$849$		0			0
$850$			21.2094i			0.727477i
$851$	−1.05617	+	0.609779i	−0.0362050	+	0.0209029i
$852$		0			0
$853$		−	26.3277i		−	0.901445i	−0.892664	−	0.450722i	$-0.851166\pi$
$853$		−	26.3277i		−	0.901445i	0.892664	−	0.450722i	$-0.148834\pi$
$854$	4.16720	+	7.21780i	0.142599	+	0.246988i
$855$		0			0
$856$	−11.8239	−	6.82652i	−0.404132	−	0.233325i
$857$	−14.1058			−0.481845			−0.240923	−	0.970544i	$-0.577450\pi$
$857$	−14.1058			−0.481845			−0.240923	+	0.970544i	$0.577450\pi$
$858$		0			0
$859$	23.4719			0.800850			0.400425	−	0.916329i	$-0.368862\pi$
$859$	23.4719			0.800850			0.400425	+	0.916329i	$0.368862\pi$
$860$	6.02046	+	3.47592i	0.205296	+	0.118528i
$861$		0			0
$862$	10.7769	+	18.6662i	0.367063	+	0.635772i
$863$		−	11.9484i		−	0.406727i	−0.979103	−	0.203364i	$-0.934813\pi$
$863$		−	11.9484i		−	0.406727i	0.979103	−	0.203364i	$-0.0651874\pi$
$864$		0			0
$865$	7.16225	−	4.13513i	0.243524	−	0.140599i
$866$		−	3.19917i		−	0.108712i
$867$		0			0
$868$	−0.436531	+	0.756094i	−0.0148168	+	0.0256635i
$869$	24.5404	+	14.1684i	0.832476	+	0.480630i
$870$		0			0
$871$	22.4247	−	29.9763i	0.759831	−	1.01571i
$872$	5.11747			0.173299
$873$		0			0
$874$	26.0819	−	45.1752i	0.882234	−	1.52807i
$875$	−4.14246	−	7.17494i	−0.140041	−	0.242557i
$876$		0			0
$877$	−28.3486	+	16.3671i	−0.957264	+	0.552677i	−0.895330	−	0.445403i	$-0.853060\pi$
$877$	−28.3486	+	16.3671i	−0.957264	+	0.552677i	−0.0619342	+	0.998080i	$0.519727\pi$
$878$	−23.0560	+	13.3114i	−0.778101	+	0.449237i
$879$		0			0
$880$	1.95571	+	3.38739i	0.0659270	+	0.114189i
$881$	5.29540	−	9.17190i	0.178407	−	0.309009i	−0.762928	−	0.646483i	$-0.776239\pi$
$881$	5.29540	−	9.17190i	0.178407	−	0.309009i	0.941335	+	0.337474i	$0.109572\pi$
$882$		0			0
$883$	−38.6713			−1.30139			−0.650696	−	0.759338i	$-0.725523\pi$
$883$	−38.6713			−1.30139			−0.650696	+	0.759338i	$0.725523\pi$
$884$	14.6258	+	10.9413i	0.491919	+	0.367995i
$885$		0			0
$886$	7.87968	+	4.54933i	0.264723	+	0.152838i
$887$	2.36082	−	4.08906i	0.0792685	−	0.137297i	−0.823666	−	0.567075i	$-0.808075\pi$
$887$	2.36082	−	4.08906i	0.0792685	−	0.137297i	0.902935	+	0.429778i	$0.141408\pi$
$888$		0			0
$889$			19.5136i			0.654466i
$890$	−6.08551	+	3.51347i	−0.203987	+	0.117772i
$891$		0			0
$892$		−	10.6357i		−	0.356110i
$893$	9.01522	+	15.6148i	0.301683	+	0.522530i
$894$		0			0
$895$	−13.2421	−	7.64531i	−0.442634	−	0.255555i
$896$	1.00000			0.0334077
$897$		0			0
$898$	7.02693			0.234492
$899$	−1.65801	−	0.957251i	−0.0552976	−	0.0319261i
$900$		0			0
$901$	4.29840	+	7.44504i	0.143200	+	0.248030i
$902$		−	17.3336i		−	0.577147i
$903$		0			0
$904$	15.5296	−	8.96603i	0.516507	−	0.298206i
$905$			2.39657i			0.0796648i
$906$		0			0
$907$	−20.9654	+	36.3132i	−0.696146	+	1.20576i	0.273646	+	0.961830i	$0.411770\pi$
$907$	−20.9654	+	36.3132i	−0.696146	+	1.20576i	−0.969793	+	0.243930i	$0.921563\pi$
$908$	−19.6776	−	11.3609i	−0.653023	−	0.377023i
$909$		0			0
$910$	−3.22876	−	0.384973i	−0.107032	−	0.0127617i
$911$	54.1425			1.79382			0.896910	−	0.442213i	$-0.145806\pi$
$911$	54.1425			1.79382			0.896910	+	0.442213i	$0.145806\pi$
$912$		0			0
$913$	−28.7008	+	49.7113i	−0.949859	+	1.64520i
$914$	9.57556	+	16.5853i	0.316731	+	0.548595i
$915$		0			0
$916$	−17.5885	+	10.1547i	−0.581139	+	0.335521i
$917$	17.8831	−	10.3248i	0.590552	−	0.340956i
$918$		0			0
$919$	12.9117	+	22.3636i	0.425916	+	0.737708i	0.996506	−	0.0835271i	$-0.0266185\pi$
$919$	12.9117	+	22.3636i	0.425916	+	0.737708i	−0.570589	+	0.821236i	$0.693285\pi$
$920$	3.81080	−	6.60049i	0.125638	−	0.217612i
$921$		0			0
$922$	−3.25656			−0.107249
$923$	4.65690	+	10.8651i	0.153284	+	0.357628i
$924$		0			0
$925$	0.523222	+	0.302083i	0.0172034	+	0.00993241i
$926$	10.6381	−	18.4257i	0.349589	−	0.605506i
$927$		0			0
$928$			2.19286i			0.0719841i
$929$	−13.8843	+	8.01610i	−0.455529	+	0.263000i	−0.710162	−	0.704038i	$-0.751379\pi$
$929$	−13.8843	+	8.01610i	−0.455529	+	0.263000i	0.254633	+	0.967038i	$0.418045\pi$
$930$		0			0
$931$		−	6.17238i		−	0.202292i
$932$	−5.32231	−	9.21851i	−0.174338	−	0.301962i
$933$		0			0
$934$	−2.88535	−	1.66586i	−0.0944115	−	0.0545085i
$935$	−19.8150			−0.648018
$936$		0			0
$937$	47.0232			1.53618			0.768091	−	0.640340i	$-0.221207\pi$
$937$	47.0232			1.53618			0.768091	+	0.640340i	$0.221207\pi$
$938$	8.99180	+	5.19142i	0.293593	+	0.169506i
$939$		0			0
$940$	1.31720	+	2.28146i	0.0429624	+	0.0744131i
$941$			52.8569i			1.72308i	0.507686	+	0.861542i	$0.330501\pi$
$941$			52.8569i			1.72308i	−0.507686	+	0.861542i	$0.669499\pi$
$942$		0			0
$943$	−29.2504	+	16.8877i	−0.952523	+	0.549939i
$944$			8.54933i			0.278257i
$945$		0			0
$946$	16.7165	−	28.9539i	0.543502	−	0.941372i
$947$	33.4029	+	19.2852i	1.08545	+	0.626684i	0.932361	−	0.361528i	$-0.117745\pi$
$947$	33.4029	+	19.2852i	1.08545	+	0.626684i	0.153088	+	0.988213i	$0.451078\pi$
$948$		0			0
$949$	−1.92981	−	0.230096i	−0.0626441	−	0.00746923i
$950$	−25.8418			−0.838419
$951$		0			0
$952$	−2.53296	+	4.38722i	−0.0820937	+	0.142190i
$953$	−13.6505	−	23.6433i	−0.442182	−	0.765882i	0.555669	−	0.831404i	$-0.312462\pi$
$953$	−13.6505	−	23.6433i	−0.442182	−	0.765882i	−0.997851	+	0.0655217i	$0.979129\pi$
$954$		0			0
$955$	−19.1240	+	11.0412i	−0.618838	+	0.357286i
$956$	−0.269822	+	0.155782i	−0.00872668	+	0.00503835i
$957$		0			0
$958$	−0.0926079	−	0.160402i	−0.00299203	−	0.00518234i
$959$	−1.59478	+	2.76224i	−0.0514982	+	0.0891975i
$960$		0			0
$961$	30.2378			0.975412
$962$	0.478227	−	0.204974i	0.0154187	−	0.00660863i
$963$		0			0
$964$	−21.9100	−	12.6498i	−0.705674	−	0.407421i
$965$	5.51966	−	9.56034i	0.177684	−	0.307758i
$966$		0			0
$967$		−	25.2494i		−	0.811966i	−0.913881	−	0.405983i	$-0.866929\pi$
$967$		−	25.2494i		−	0.811966i	0.913881	−	0.405983i	$-0.133071\pi$
$968$	6.76452	−	3.90550i	0.217420	−	0.125527i
$969$		0			0
$970$			10.5570i			0.338965i
$971$	−3.28682	−	5.69294i	−0.105479	−	0.182695i	0.808455	−	0.588558i	$-0.200304\pi$
$971$	−3.28682	−	5.69294i	−0.105479	−	0.182695i	−0.913934	+	0.405863i	$0.866971\pi$
$972$		0			0
$973$	0.515900	+	0.297855i	0.0165390	+	0.00954879i
$974$	31.2308			1.00070
$975$		0			0
$976$	8.33440			0.266778
$977$	−12.0773	−	6.97285i	−0.386388	−	0.223081i	0.294206	−	0.955742i	$-0.404945\pi$
$977$	−12.0773	−	6.97285i	−0.386388	−	0.223081i	−0.680594	+	0.732661i	$0.738278\pi$
$978$		0			0
$979$	16.8972	+	29.2667i	0.540036	+	0.935369i
$980$		−	0.901839i		−	0.0288082i
$981$		0			0
$982$	23.2504	−	13.4236i	0.741949	−	0.428365i
$983$		−	47.1390i		−	1.50350i	−0.659449	−	0.751750i	$-0.729210\pi$
$983$		−	47.1390i		−	1.50350i	0.659449	−	0.751750i	$-0.270790\pi$
$984$		0			0
$985$	−2.46090	+	4.26240i	−0.0784107	+	0.135811i
$986$	−9.62054	−	5.55442i	−0.306380	−	0.176889i
$987$		0			0
$988$	−13.3310	+	17.8203i	−0.424115	+	0.566939i
$989$	−65.1459			−2.07152
$990$		0			0
$991$	−4.70805	+	8.15458i	−0.149556	+	0.259039i	−0.931063	−	0.364857i	$-0.881118\pi$
$991$	−4.70805	+	8.15458i	−0.149556	+	0.259039i	0.781507	+	0.623896i	$0.214451\pi$
$992$	0.436531	+	0.756094i	0.0138599	+	0.0240060i
$993$		0			0
$994$	−2.83932	+	1.63928i	−0.0900576	+	0.0519948i
$995$	−10.0100	+	5.77927i	−0.317338	+	0.183215i
$996$		0			0
$997$	−20.2607	−	35.0926i	−0.641664	−	1.11139i	−0.985061	−	0.172204i	$-0.944911\pi$
$997$	−20.2607	−	35.0926i	−0.641664	−	1.11139i	0.343398	−	0.939190i	$-0.388422\pi$
$998$	−7.64346	+	13.2389i	−0.241950	+	0.419069i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1638.2.bj.g.1135.2		12
3.2	odd	2		182.2.m.b.43.4	✓	12
12.11	even	2		1456.2.cc.d.225.5		12
13.10	even	6	inner	1638.2.bj.g.127.2		12
21.2	odd	6		1274.2.o.d.459.1		12
21.5	even	6		1274.2.o.e.459.3		12
21.11	odd	6		1274.2.v.e.667.3		12
21.17	even	6		1274.2.v.d.667.1		12
21.20	even	2		1274.2.m.c.589.6		12
39.17	odd	6		2366.2.d.r.337.11		12
39.20	even	12		2366.2.a.bh.1.5		6
39.23	odd	6		182.2.m.b.127.4	yes	12
39.32	even	12		2366.2.a.bf.1.5		6
39.35	odd	6		2366.2.d.r.337.5		12
156.23	even	6		1456.2.cc.d.673.5		12
273.23	odd	6		1274.2.v.e.361.3		12
273.62	even	6		1274.2.m.c.491.6		12
273.101	even	6		1274.2.o.e.569.6		12
273.179	odd	6		1274.2.o.d.569.4		12
273.257	even	6		1274.2.v.d.361.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
182.2.m.b.43.4	✓	12	3.2	odd	2
182.2.m.b.127.4	yes	12	39.23	odd	6
1274.2.m.c.491.6		12	273.62	even	6
1274.2.m.c.589.6		12	21.20	even	2
1274.2.o.d.459.1		12	21.2	odd	6
1274.2.o.d.569.4		12	273.179	odd	6
1274.2.o.e.459.3		12	21.5	even	6
1274.2.o.e.569.6		12	273.101	even	6
1274.2.v.d.361.1		12	273.257	even	6
1274.2.v.d.667.1		12	21.17	even	6
1274.2.v.e.361.3		12	273.23	odd	6
1274.2.v.e.667.3		12	21.11	odd	6
1456.2.cc.d.225.5		12	12.11	even	2
1456.2.cc.d.673.5		12	156.23	even	6
1638.2.bj.g.127.2		12	13.10	even	6	inner
1638.2.bj.g.1135.2		12	1.1	even	1	trivial
2366.2.a.bf.1.5		6	39.32	even	12
2366.2.a.bh.1.5		6	39.20	even	12
2366.2.d.r.337.5		12	39.35	odd	6
2366.2.d.r.337.11		12	39.17	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1638 = 2 \cdot 3^{2} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1638.bj (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} -0.901839i q^{5} +(0.866025 - 0.500000i) q^{7} -1.00000i q^{8} +O(q^{10})\)	\(q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} -0.901839i q^{5} +(0.866025 - 0.500000i) q^{7} -1.00000i q^{8} +(-0.450919 + 0.781015i) q^{10} +(3.75609 + 2.16858i) q^{11} +(-0.426876 + 3.58019i) q^{13} -1.00000 q^{14} +(-0.500000 + 0.866025i) q^{16} +(-2.53296 - 4.38722i) q^{17} +(5.34544 - 3.08619i) q^{19} +(0.781015 - 0.450919i) q^{20} +(-2.16858 - 3.75609i) q^{22} +(-4.22559 + 7.31893i) q^{23} +4.18669 q^{25} +(2.15978 - 2.88710i) q^{26} +(0.866025 + 0.500000i) q^{28} +(-1.09643 + 1.89907i) q^{29} +0.873062i q^{31} +(0.866025 - 0.500000i) q^{32} +5.06592i q^{34} +(-0.450919 - 0.781015i) q^{35} +(0.124973 + 0.0721531i) q^{37} -6.17238 q^{38} -0.901839 q^{40} +(3.46110 + 1.99827i) q^{41} +(3.85426 + 6.67577i) q^{43} +4.33716i q^{44} +(7.31893 - 4.22559i) q^{46} +2.92115i q^{47} +(0.500000 - 0.866025i) q^{49} +(-3.62578 - 2.09334i) q^{50} +(-3.31398 + 1.42041i) q^{52} -1.69699 q^{53} +(1.95571 - 3.38739i) q^{55} +(-0.500000 - 0.866025i) q^{56} +(1.89907 - 1.09643i) q^{58} +(7.40394 - 4.27467i) q^{59} +(-4.16720 - 7.21780i) q^{61} +(0.436531 - 0.756094i) q^{62} -1.00000 q^{64} +(3.22876 + 0.384973i) q^{65} +(-8.99180 - 5.19142i) q^{67} +(2.53296 - 4.38722i) q^{68} +0.901839i q^{70} +(2.83932 - 1.63928i) q^{71} +0.539023i q^{73} +(-0.0721531 - 0.124973i) q^{74} +(5.34544 + 3.08619i) q^{76} +4.33716 q^{77} +6.53349 q^{79} +(0.781015 + 0.450919i) q^{80} +(-1.99827 - 3.46110i) q^{82} +13.2348i q^{83} +(-3.95656 + 2.28432i) q^{85} -7.70851i q^{86} +(2.16858 - 3.75609i) q^{88} +(6.74790 + 3.89590i) q^{89} +(1.42041 + 3.31398i) q^{91} -8.45117 q^{92} +(1.46057 - 2.52979i) q^{94} +(-2.78325 - 4.82072i) q^{95} +(10.1378 - 5.85305i) q^{97} +(-0.866025 + 0.500000i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 6 q^{4}+O(q^{10}) \) 12 * q + 6 * q^4	\( 12 q + 6 q^{4} - 2 q^{10} + 18 q^{11} - 8 q^{13} - 12 q^{14} - 6 q^{16} - 4 q^{17} + 12 q^{19} - 2 q^{22} + 6 q^{23} - 24 q^{25} + 14 q^{26} + 10 q^{29} - 2 q^{35} - 6 q^{37} - 8 q^{38} - 4 q^{40} + 24 q^{41} + 26 q^{43} - 6 q^{46} + 6 q^{49} + 12 q^{50} - 4 q^{52} - 36 q^{53} - 6 q^{55} - 6 q^{56} + 24 q^{58} - 6 q^{59} - 28 q^{61} + 2 q^{62} - 12 q^{64} + 34 q^{65} - 42 q^{67} + 4 q^{68} - 48 q^{71} + 12 q^{76} + 4 q^{77} + 44 q^{79} + 6 q^{82} + 54 q^{85} + 2 q^{88} - 12 q^{89} - 16 q^{91} + 12 q^{92} + 8 q^{94} - 32 q^{95} + 60 q^{97}+O(q^{100}) \) 12 * q + 6 * q^4 - 2 * q^10 + 18 * q^11 - 8 * q^13 - 12 * q^14 - 6 * q^16 - 4 * q^17 + 12 * q^19 - 2 * q^22 + 6 * q^23 - 24 * q^25 + 14 * q^26 + 10 * q^29 - 2 * q^35 - 6 * q^37 - 8 * q^38 - 4 * q^40 + 24 * q^41 + 26 * q^43 - 6 * q^46 + 6 * q^49 + 12 * q^50 - 4 * q^52 - 36 * q^53 - 6 * q^55 - 6 * q^56 + 24 * q^58 - 6 * q^59 - 28 * q^61 + 2 * q^62 - 12 * q^64 + 34 * q^65 - 42 * q^67 + 4 * q^68 - 48 * q^71 + 12 * q^76 + 4 * q^77 + 44 * q^79 + 6 * q^82 + 54 * q^85 + 2 * q^88 - 12 * q^89 - 16 * q^91 + 12 * q^92 + 8 * q^94 - 32 * q^95 + 60 * q^97

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