LMFDB - Embedded newform 1710.2.l.q.1261.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1710,2,Mod(1261,1710)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1710, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([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("1710.1261");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1710 = 2 \cdot 3^{2} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1710.l (of order $3$, 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:	$13.6544187456$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.29654208.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} + 14x^{4} + 49x^{2} + 12 $ x^6 + 14x^4 + 49x^2 + 12
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 570)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			1261.3
Root			$-0.514306i$ of defining polynomial
Character	$\chi$	$=$	1710.1261
Dual form			1710.2.l.q.1531.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(0.500000 + 0.866025i) q^{5} +3.84469 q^{7} -1.00000 q^{8} +O(q^{10})$	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(0.500000 + 0.866025i) q^{5} +3.84469 q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{10} -5.73549 q^{11} +(-2.36774 + 4.10105i) q^{13} +(1.92234 + 3.32960i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(-3.31315 - 5.73854i) q^{17} +(-4.29009 + 0.771459i) q^{19} -1.00000 q^{20} +(-2.86774 - 4.96708i) q^{22} +(-2.86774 + 4.96708i) q^{23} +(-0.500000 + 0.866025i) q^{25} -4.73549 q^{26} +(-1.92234 + 3.32960i) q^{28} +(-5.15783 + 8.93363i) q^{29} +4.73549 q^{31} +(0.500000 - 0.866025i) q^{32} +(3.31315 - 5.73854i) q^{34} +(1.92234 + 3.32960i) q^{35} -1.00000 q^{37} +(-2.81315 - 3.32960i) q^{38} +(-0.500000 - 0.866025i) q^{40} +(4.39928 + 7.61978i) q^{41} +(-0.523059 - 0.905965i) q^{43} +(2.86774 - 4.96708i) q^{44} -5.73549 q^{46} +(0.890804 - 1.54292i) q^{47} +7.78161 q^{49} -1.00000 q^{50} +(-2.36774 - 4.10105i) q^{52} +(2.55460 - 4.42469i) q^{53} +(-2.86774 - 4.96708i) q^{55} -3.84469 q^{56} -10.3157 q^{58} +(3.00000 + 5.19615i) q^{59} +(0.0545981 - 0.0945666i) q^{61} +(2.36774 + 4.10105i) q^{62} +1.00000 q^{64} -4.73549 q^{65} +(-2.94540 + 5.10159i) q^{67} +6.62629 q^{68} +(-1.92234 + 3.32960i) q^{70} +(-3.31315 - 5.73854i) q^{71} +(3.05460 + 5.29072i) q^{73} +(-0.500000 - 0.866025i) q^{74} +(1.47694 - 4.10105i) q^{76} -22.0512 q^{77} +(3.36774 + 5.83311i) q^{79} +(0.500000 - 0.866025i) q^{80} +(-4.39928 + 7.61978i) q^{82} +16.9420 q^{83} +(3.31315 - 5.73854i) q^{85} +(0.523059 - 0.905965i) q^{86} +5.73549 q^{88} +(-2.55460 + 4.42469i) q^{89} +(-9.10323 + 15.7673i) q^{91} +(-2.86774 - 4.96708i) q^{92} +1.78161 q^{94} +(-2.81315 - 3.32960i) q^{95} +(-4.57766 - 7.92873i) q^{97} +(3.89080 + 6.73907i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 3 q^{2} - 3 q^{4} + 3 q^{5} + 2 q^{7} - 6 q^{8}+O(q^{10}) $ 6 * q + 3 * q^2 - 3 * q^4 + 3 * q^5 + 2 * q^7 - 6 * q^8	$ 6 q + 3 q^{2} - 3 q^{4} + 3 q^{5} + 2 q^{7} - 6 q^{8} - 3 q^{10} - 8 q^{11} - q^{13} + q^{14} - 3 q^{16} - 4 q^{17} - 2 q^{19} - 6 q^{20} - 4 q^{22} - 4 q^{23} - 3 q^{25} - 2 q^{26} - q^{28} + 6 q^{29} + 2 q^{31} + 3 q^{32} + 4 q^{34} + q^{35} - 6 q^{37} - q^{38} - 3 q^{40} + 8 q^{41} - 11 q^{43} + 4 q^{44} - 8 q^{46} + 36 q^{49} - 6 q^{50} - q^{52} + 18 q^{53} - 4 q^{55} - 2 q^{56} + 12 q^{58} + 18 q^{59} + 3 q^{61} + q^{62} + 6 q^{64} - 2 q^{65} - 15 q^{67} + 8 q^{68} - q^{70} - 4 q^{71} + 21 q^{73} - 3 q^{74} + q^{76} - 32 q^{77} + 7 q^{79} + 3 q^{80} - 8 q^{82} - 4 q^{83} + 4 q^{85} + 11 q^{86} + 8 q^{88} - 18 q^{89} - 15 q^{91} - 4 q^{92} - q^{95} - 38 q^{97} + 18 q^{98}+O(q^{100}) $ 6 * q + 3 * q^2 - 3 * q^4 + 3 * q^5 + 2 * q^7 - 6 * q^8 - 3 * q^10 - 8 * q^11 - q^13 + q^14 - 3 * q^16 - 4 * q^17 - 2 * q^19 - 6 * q^20 - 4 * q^22 - 4 * q^23 - 3 * q^25 - 2 * q^26 - q^28 + 6 * q^29 + 2 * q^31 + 3 * q^32 + 4 * q^34 + q^35 - 6 * q^37 - q^38 - 3 * q^40 + 8 * q^41 - 11 * q^43 + 4 * q^44 - 8 * q^46 + 36 * q^49 - 6 * q^50 - q^52 + 18 * q^53 - 4 * q^55 - 2 * q^56 + 12 * q^58 + 18 * q^59 + 3 * q^61 + q^62 + 6 * q^64 - 2 * q^65 - 15 * q^67 + 8 * q^68 - q^70 - 4 * q^71 + 21 * q^73 - 3 * q^74 + q^76 - 32 * q^77 + 7 * q^79 + 3 * q^80 - 8 * q^82 - 4 * q^83 + 4 * q^85 + 11 * q^86 + 8 * q^88 - 18 * q^89 - 15 * q^91 - 4 * q^92 - q^95 - 38 * q^97 + 18 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1710\mathbb{Z}\right)^\times$.

$n$	$191$	$1027$	$1351$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$3$		0			0
$3$		0			0
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$6$		0			0
$7$	3.84469			1.45315			0.726577	−	0.687085i	$-0.241110\pi$
$7$	3.84469			1.45315			0.726577	+	0.687085i	$0.241110\pi$
$8$	−1.00000			−0.353553
$9$		0			0
$10$	−0.500000	+	0.866025i	−0.158114	+	0.273861i
$11$	−5.73549			−1.72932			−0.864658	−	0.502362i	$-0.832465\pi$
$11$	−5.73549			−1.72932			−0.864658	+	0.502362i	$0.832465\pi$
$12$		0			0
$13$	−2.36774	+	4.10105i	−0.656694	+	1.13743i	0.324772	+	0.945792i	$0.394712\pi$
$13$	−2.36774	+	4.10105i	−0.656694	+	1.13743i	−0.981466	+	0.191635i	$0.938621\pi$
$14$	1.92234	+	3.32960i	0.513768	+	0.889872i
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−3.31315	−	5.73854i	−0.803556	−	1.39180i	−0.917262	−	0.398285i	$-0.869605\pi$
$17$	−3.31315	−	5.73854i	−0.803556	−	1.39180i	0.113705	−	0.993515i	$-0.463728\pi$
$18$		0			0
$19$	−4.29009	+	0.771459i	−0.984214	+	0.176985i
$19$	−4.29009	+	0.771459i	−0.984214	+	0.176985i
$20$	−1.00000			−0.223607
$21$		0			0
$22$	−2.86774	−	4.96708i	−0.611405	−	1.05898i
$23$	−2.86774	+	4.96708i	−0.597966	+	1.03571i	0.395155	+	0.918615i	$0.370691\pi$
$23$	−2.86774	+	4.96708i	−0.597966	+	1.03571i	−0.993121	+	0.117093i	$0.962642\pi$
$24$		0			0
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	−4.73549			−0.928706
$27$		0			0
$28$	−1.92234	+	3.32960i	−0.363289	+	0.629234i
$29$	−5.15783	+	8.93363i	−0.957785	+	1.65893i	−0.229924	+	0.973209i	$0.573848\pi$
$29$	−5.15783	+	8.93363i	−0.957785	+	1.65893i	−0.727861	+	0.685724i	$0.759486\pi$
$30$		0			0
$31$	4.73549			0.850519			0.425260	−	0.905071i	$-0.360183\pi$
$31$	4.73549			0.850519			0.425260	+	0.905071i	$0.360183\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$		0			0
$34$	3.31315	−	5.73854i	0.568200	−	0.984151i
$35$	1.92234	+	3.32960i	0.324935	+	0.562804i
$36$		0			0
$37$	−1.00000			−0.164399			−0.0821995	−	0.996616i	$-0.526194\pi$
$37$	−1.00000			−0.164399			−0.0821995	+	0.996616i	$0.526194\pi$
$38$	−2.81315	−	3.32960i	−0.456353	−	0.540132i
$39$		0			0
$40$	−0.500000	−	0.866025i	−0.0790569	−	0.136931i
$41$	4.39928	+	7.61978i	0.687053	+	1.19001i	0.972787	+	0.231701i	$0.0744292\pi$
$41$	4.39928	+	7.61978i	0.687053	+	1.19001i	−0.285734	+	0.958309i	$0.592237\pi$
$42$		0			0
$43$	−0.523059	−	0.905965i	−0.0797658	−	0.138158i	0.823383	−	0.567486i	$-0.192084\pi$
$43$	−0.523059	−	0.905965i	−0.0797658	−	0.138158i	−0.903149	+	0.429328i	$0.858751\pi$
$44$	2.86774	−	4.96708i	0.432329	−	0.748815i
$45$		0			0
$46$	−5.73549			−0.845652
$47$	0.890804	−	1.54292i	0.129937	−	0.225058i	−0.793715	−	0.608290i	$-0.791856\pi$
$47$	0.890804	−	1.54292i	0.129937	−	0.225058i	0.923652	+	0.383232i	$0.125189\pi$
$48$		0			0
$49$	7.78161			1.11166
$50$	−1.00000			−0.141421
$51$		0			0
$52$	−2.36774	−	4.10105i	−0.328347	−	0.568714i
$53$	2.55460	−	4.42469i	0.350901	−	0.607778i	−0.635507	−	0.772095i	$-0.719209\pi$
$53$	2.55460	−	4.42469i	0.350901	−	0.607778i	0.986408	+	0.164317i	$0.0525420\pi$
$54$		0			0
$55$	−2.86774	−	4.96708i	−0.386687	−	0.669761i
$56$	−3.84469			−0.513768
$57$		0			0
$58$	−10.3157			−1.35451
$59$	3.00000	+	5.19615i	0.390567	+	0.676481i	0.992524	−	0.122047i	$-0.0389457\pi$
$59$	3.00000	+	5.19615i	0.390567	+	0.676481i	−0.601958	+	0.798528i	$0.705612\pi$
$60$		0			0
$61$	0.0545981	−	0.0945666i	0.00699057	−	0.0121080i	−0.862509	−	0.506042i	$-0.831108\pi$
$61$	0.0545981	−	0.0945666i	0.00699057	−	0.0121080i	0.869500	+	0.493934i	$0.164441\pi$
$62$	2.36774	+	4.10105i	0.300704	+	0.520834i
$63$		0			0
$64$	1.00000			0.125000
$65$	−4.73549			−0.587365
$66$		0			0
$67$	−2.94540	+	5.10159i	−0.359838	+	0.623258i	−0.987934	−	0.154878i	$-0.950501\pi$
$67$	−2.94540	+	5.10159i	−0.359838	+	0.623258i	0.628095	+	0.778136i	$0.283835\pi$
$68$	6.62629			0.803556
$69$		0			0
$70$	−1.92234	+	3.32960i	−0.229764	+	0.397963i
$71$	−3.31315	−	5.73854i	−0.393198	−	0.681039i	0.599671	−	0.800246i	$-0.295298\pi$
$71$	−3.31315	−	5.73854i	−0.393198	−	0.681039i	−0.992869	+	0.119207i	$0.961965\pi$
$72$		0			0
$73$	3.05460	+	5.29072i	0.357514	+	0.619232i	0.987545	−	0.157338i	$-0.0502912\pi$
$73$	3.05460	+	5.29072i	0.357514	+	0.619232i	−0.630031	+	0.776570i	$0.716958\pi$
$74$	−0.500000	−	0.866025i	−0.0581238	−	0.100673i
$75$		0			0
$76$	1.47694	−	4.10105i	0.169417	−	0.470423i
$77$	−22.0512			−2.51296
$78$		0			0
$79$	3.36774	+	5.83311i	0.378901	+	0.656276i	0.990903	−	0.134581i	$-0.0429688\pi$
$79$	3.36774	+	5.83311i	0.378901	+	0.656276i	−0.612002	+	0.790856i	$0.709635\pi$
$80$	0.500000	−	0.866025i	0.0559017	−	0.0968246i
$81$		0			0
$82$	−4.39928	+	7.61978i	−0.485820	+	0.841464i
$83$	16.9420			1.85962			0.929811	−	0.368038i	$-0.119970\pi$
$83$	16.9420			1.85962			0.929811	+	0.368038i	$0.119970\pi$
$84$		0			0
$85$	3.31315	−	5.73854i	0.359361	−	0.622432i
$86$	0.523059	−	0.905965i	0.0564029	−	0.0976927i
$87$		0			0
$88$	5.73549			0.611405
$89$	−2.55460	+	4.42469i	−0.270787	+	0.469017i	−0.969064	−	0.246811i	$-0.920617\pi$
$89$	−2.55460	+	4.42469i	−0.270787	+	0.469017i	0.698277	+	0.715828i	$0.253951\pi$
$90$		0			0
$91$	−9.10323	+	15.7673i	−0.954278	+	1.65286i
$92$	−2.86774	−	4.96708i	−0.298983	−	0.517854i
$93$		0			0
$94$	1.78161			0.183759
$95$	−2.81315	−	3.32960i	−0.288623	−	0.341609i
$96$		0			0
$97$	−4.57766	−	7.92873i	−0.464791	−	0.805041i	0.534401	−	0.845231i	$-0.320537\pi$
$97$	−4.57766	−	7.92873i	−0.464791	−	0.805041i	−0.999192	+	0.0401898i	$0.987204\pi$
$98$	3.89080	+	6.73907i	0.393031	+	0.680749i
$99$		0			0
$100$	−0.500000	−	0.866025i	−0.0500000	−	0.0866025i
$101$	−1.84469	+	3.19509i	−0.183553	+	0.317923i	−0.943088	−	0.332543i	$-0.892093\pi$
$101$	−1.84469	+	3.19509i	−0.183553	+	0.317923i	0.759535	+	0.650467i	$0.225427\pi$
$102$		0			0
$103$	2.06308			0.203281			0.101641	−	0.994821i	$-0.467591\pi$
$103$	2.06308			0.203281			0.101641	+	0.994821i	$0.467591\pi$
$104$	2.36774	−	4.10105i	0.232176	−	0.402141i
$105$		0			0
$106$	5.10920			0.496249
$107$	−14.5341			−1.40506			−0.702530	−	0.711654i	$-0.747946\pi$
$107$	−14.5341			−1.40506			−0.702530	+	0.711654i	$0.747946\pi$
$108$		0			0
$109$	−4.31315	−	7.47059i	−0.413125	−	0.715553i	0.582105	−	0.813114i	$-0.302229\pi$
$109$	−4.31315	−	7.47059i	−0.413125	−	0.715553i	−0.995230	+	0.0975609i	$0.968896\pi$
$110$	2.86774	−	4.96708i	0.273429	−	0.473592i
$111$		0			0
$112$	−1.92234	−	3.32960i	−0.181644	−	0.314617i
$113$	8.53406			0.802817			0.401408	−	0.915899i	$-0.368521\pi$
$113$	8.53406			0.802817			0.401408	+	0.915899i	$0.368521\pi$
$114$		0			0
$115$	−5.73549			−0.534837
$116$	−5.15783	−	8.93363i	−0.478893	−	0.829467i
$117$		0			0
$118$	−3.00000	+	5.19615i	−0.276172	+	0.478345i
$119$	−12.7380	−	22.0629i	−1.16769	−	2.02250i
$120$		0			0
$121$	21.8958			1.99053
$122$	0.109196			0.00988615
$123$		0			0
$124$	−2.36774	+	4.10105i	−0.212630	+	0.368286i
$125$	−1.00000			−0.0894427
$126$		0			0
$127$	−2.33621	+	4.04643i	−0.207305	+	0.359062i	−0.950865	−	0.309607i	$-0.899802\pi$
$127$	−2.33621	+	4.04643i	−0.207305	+	0.359062i	0.743560	+	0.668669i	$0.233136\pi$
$128$	0.500000	+	0.866025i	0.0441942	+	0.0765466i
$129$		0			0
$130$	−2.36774	−	4.10105i	−0.207665	−	0.359686i
$131$	−6.82163	−	11.8154i	−0.596008	−	1.03232i	−0.993404	−	0.114669i	$-0.963419\pi$
$131$	−6.82163	−	11.8154i	−0.596008	−	1.03232i	0.397395	−	0.917647i	$-0.369914\pi$
$132$		0			0
$133$	−16.4940	+	2.96602i	−1.43021	+	0.257186i
$134$	−5.89080			−0.508888
$135$		0			0
$136$	3.31315	+	5.73854i	0.284100	+	0.492076i
$137$	−6.95388	+	12.0445i	−0.594110	+	1.02903i	0.399562	+	0.916706i	$0.369162\pi$
$137$	−6.95388	+	12.0445i	−0.594110	+	1.02903i	−0.993672	+	0.112323i	$0.964171\pi$
$138$		0			0
$139$	0.367745	−	0.636953i	0.0311917	−	0.0540256i	−0.850008	−	0.526770i	$-0.823403\pi$
$139$	0.367745	−	0.636953i	0.0311917	−	0.0540256i	0.881200	+	0.472744i	$0.156736\pi$
$140$	−3.84469			−0.324935
$141$		0			0
$142$	3.31315	−	5.73854i	0.278033	−	0.481567i
$143$	13.5802	−	23.5216i	1.13563	−	1.96697i
$144$		0			0
$145$	−10.3157			−0.856669
$146$	−3.05460	+	5.29072i	−0.252800	+	0.437863i
$147$		0			0
$148$	0.500000	−	0.866025i	0.0410997	−	0.0711868i
$149$	−5.42234	−	9.39177i	−0.444216	−	0.769404i	0.553782	−	0.832662i	$-0.313184\pi$
$149$	−5.42234	−	9.39177i	−0.444216	−	0.769404i	−0.997997	+	0.0632579i	$0.979851\pi$
$150$		0			0
$151$	−0.936922			−0.0762456			−0.0381228	−	0.999273i	$-0.512138\pi$
$151$	−0.936922			−0.0762456			−0.0381228	+	0.999273i	$0.512138\pi$
$152$	4.29009	−	0.771459i	0.347972	−	0.0625736i
$153$		0			0
$154$	−11.0256	−	19.0969i	−0.888466	−	1.53887i
$155$	2.36774	+	4.10105i	0.190182	+	0.329405i
$156$		0			0
$157$	−4.34469	−	7.52522i	−0.346744	−	0.600578i	0.638925	−	0.769269i	$-0.279379\pi$
$157$	−4.34469	−	7.52522i	−0.346744	−	0.600578i	−0.985669	+	0.168691i	$0.946046\pi$
$158$	−3.36774	+	5.83311i	−0.267923	+	0.464057i
$159$		0			0
$160$	1.00000			0.0790569
$161$	−11.0256	+	19.0969i	−0.868937	+	1.50504i
$162$		0			0
$163$	−0.206468			−0.0161719			−0.00808593	−	0.999967i	$-0.502574\pi$
$163$	−0.206468			−0.0161719			−0.00808593	+	0.999967i	$0.502574\pi$
$164$	−8.79857			−0.687053
$165$		0			0
$166$	8.47098	+	14.6722i	0.657475	+	1.13878i
$167$	8.86774	−	15.3594i	0.686207	−	1.18854i	−0.286849	−	0.957976i	$-0.592608\pi$
$167$	8.86774	−	15.3594i	0.686207	−	1.18854i	0.973056	−	0.230569i	$-0.0740588\pi$
$168$		0			0
$169$	−4.71243	−	8.16217i	−0.362495	−	0.627859i
$170$	6.62629			0.508214
$171$		0			0
$172$	1.04612			0.0797658
$173$	0.709912	+	1.22960i	0.0539736	+	0.0934851i	0.891750	−	0.452529i	$-0.149478\pi$
$173$	0.709912	+	1.22960i	0.0539736	+	0.0934851i	−0.837776	+	0.546014i	$0.816145\pi$
$174$		0			0
$175$	−1.92234	+	3.32960i	−0.145315	+	0.251694i
$176$	2.86774	+	4.96708i	0.216164	+	0.374408i
$177$		0			0
$178$	−5.10920			−0.382950
$179$	17.2065			1.28607			0.643036	−	0.765836i	$-0.277675\pi$
$179$	17.2065			1.28607			0.643036	+	0.765836i	$0.277675\pi$
$180$		0			0
$181$	−8.26703	+	14.3189i	−0.614483	+	1.06432i	0.375992	+	0.926623i	$0.377302\pi$
$181$	−8.26703	+	14.3189i	−0.614483	+	1.06432i	−0.990475	+	0.137693i	$0.956031\pi$
$182$	−18.2065			−1.34955
$183$		0			0
$184$	2.86774	−	4.96708i	0.211413	−	0.366178i
$185$	−0.500000	−	0.866025i	−0.0367607	−	0.0636715i
$186$		0			0
$187$	19.0025	+	32.9133i	1.38960	+	2.40686i
$188$	0.890804	+	1.54292i	0.0649685	+	0.112529i
$189$		0			0
$190$	1.47694	−	4.10105i	0.107149	−	0.297522i
$191$	22.4129			1.62174			0.810872	−	0.585224i	$-0.198993\pi$
$191$	22.4129			1.62174			0.810872	+	0.585224i	$0.198993\pi$
$192$		0			0
$193$	11.5256	+	19.9629i	0.829629	+	1.43696i	0.898329	+	0.439323i	$0.144781\pi$
$193$	11.5256	+	19.9629i	0.829629	+	1.43696i	−0.0687002	+	0.997637i	$0.521885\pi$
$194$	4.57766	−	7.92873i	0.328657	−	0.569250i
$195$		0			0
$196$	−3.89080	+	6.73907i	−0.277915	+	0.481362i
$197$	−2.67241			−0.190401			−0.0952007	−	0.995458i	$-0.530349\pi$
$197$	−2.67241			−0.190401			−0.0952007	+	0.995458i	$0.530349\pi$
$198$		0			0
$199$	5.79009	−	10.0287i	0.410448	−	0.710918i	−0.584490	−	0.811401i	$-0.698706\pi$
$199$	5.79009	−	10.0287i	0.410448	−	0.710918i	0.994939	+	0.100483i	$0.0320388\pi$
$200$	0.500000	−	0.866025i	0.0353553	−	0.0612372i
$201$		0			0
$202$	−3.68937			−0.259583
$203$	−19.8302	+	34.3470i	−1.39181	+	2.41069i
$204$		0			0
$205$	−4.39928	+	7.61978i	−0.307259	+	0.532189i
$206$	1.03154	+	1.78668i	0.0718707	+	0.124484i
$207$		0			0
$208$	4.73549			0.328347
$209$	24.6058	−	4.42469i	1.70202	−	0.306062i
$210$		0			0
$211$	−11.6117	−	20.1121i	−0.799383	−	1.38457i	−0.920018	−	0.391876i	$-0.871826\pi$
$211$	−11.6117	−	20.1121i	−0.799383	−	1.38457i	0.120635	−	0.992697i	$-0.461507\pi$
$212$	2.55460	+	4.42469i	0.175451	+	0.303889i
$213$		0			0
$214$	−7.26703	−	12.5869i	−0.496764	−	0.860420i
$215$	0.523059	−	0.905965i	0.0356723	−	0.0617863i
$216$		0			0
$217$	18.2065			1.23594
$218$	4.31315	−	7.47059i	0.292123	−	0.505972i
$219$		0			0
$220$	5.73549			0.386687
$221$	31.3787			2.11076
$222$		0			0
$223$	7.50252	+	12.9947i	0.502406	+	0.870192i	0.999996	+	0.00278017i	$0.000884956\pi$
$223$	7.50252	+	12.9947i	0.502406	+	0.870192i	−0.497590	+	0.867412i	$0.665782\pi$
$224$	1.92234	−	3.32960i	0.128442	−	0.222468i
$225$		0			0
$226$	4.26703	+	7.39071i	0.283839	+	0.491623i
$227$	20.5341			1.36289			0.681447	−	0.731868i	$-0.261351\pi$
$227$	20.5341			1.36289			0.681447	+	0.731868i	$0.261351\pi$
$228$		0			0
$229$	−13.2645			−0.876544			−0.438272	−	0.898843i	$-0.644409\pi$
$229$	−13.2645			−0.876544			−0.438272	+	0.898843i	$0.644409\pi$
$230$	−2.86774	−	4.96708i	−0.189093	−	0.327520i
$231$		0			0
$232$	5.15783	−	8.93363i	0.338628	−	0.586521i
$233$	9.42486	+	16.3243i	0.617443	+	1.06944i	0.989951	+	0.141414i	$0.0451648\pi$
$233$	9.42486	+	16.3243i	0.617443	+	1.06944i	−0.372507	+	0.928029i	$0.621502\pi$
$234$		0			0
$235$	1.78161			0.116219
$236$	−6.00000			−0.390567
$237$		0			0
$238$	12.7380	−	22.0629i	0.825682	−	1.43012i
$239$	−13.9078			−0.899618			−0.449809	−	0.893125i	$-0.648508\pi$
$239$	−13.9078			−0.899618			−0.449809	+	0.893125i	$0.648508\pi$
$240$		0			0
$241$	15.1032	−	26.1596i	0.972885	−	1.68509i	0.286139	−	0.958188i	$-0.407628\pi$
$241$	15.1032	−	26.1596i	0.972885	−	1.68509i	0.686745	−	0.726898i	$-0.259039\pi$
$242$	10.9479	+	18.9624i	0.703759	+	1.21895i
$243$		0			0
$244$	0.0545981	+	0.0945666i	0.00349528	+	0.00605401i
$245$	3.89080	+	6.73907i	0.248574	+	0.430543i
$246$		0			0
$247$	6.99404	−	19.4205i	0.445020	−	1.23570i
$248$	−4.73549			−0.300704
$249$		0			0
$250$	−0.500000	−	0.866025i	−0.0316228	−	0.0547723i
$251$	−10.5171	+	18.2161i	−0.663833	+	1.14979i	0.315767	+	0.948837i	$0.397738\pi$
$251$	−10.5171	+	18.2161i	−0.663833	+	1.14979i	−0.979600	+	0.200956i	$0.935595\pi$
$252$		0			0
$253$	16.4479	−	28.4886i	1.03407	−	1.79107i
$254$	−4.67241			−0.293173
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	3.00000	−	5.19615i	0.187135	−	0.324127i	−0.757159	−	0.653231i	$-0.773413\pi$
$257$	3.00000	−	5.19615i	0.187135	−	0.324127i	0.944294	+	0.329104i	$0.106747\pi$
$258$		0			0
$259$	−3.84469			−0.238897
$260$	2.36774	−	4.10105i	0.146841	−	0.254337i
$261$		0			0
$262$	6.82163	−	11.8154i	0.421441	−	0.729958i
$263$	−3.39677	−	5.88337i	−0.209454	−	0.362784i	0.742089	−	0.670301i	$-0.233835\pi$
$263$	−3.39677	−	5.88337i	−0.209454	−	0.362784i	−0.951543	+	0.307517i	$0.900502\pi$
$264$		0			0
$265$	5.10920			0.313855
$266$	−10.8157	−	12.8012i	−0.663151	−	0.784895i
$267$		0			0
$268$	−2.94540	−	5.10159i	−0.179919	−	0.311629i
$269$	6.04864	+	10.4765i	0.368792	+	0.638766i	0.989377	−	0.145373i	$-0.0464382\pi$
$269$	6.04864	+	10.4765i	0.368792	+	0.638766i	−0.620585	+	0.784139i	$0.713105\pi$
$270$		0			0
$271$	0.580175	+	1.00489i	0.0352431	+	0.0610429i	0.883109	−	0.469168i	$-0.155446\pi$
$271$	0.580175	+	1.00489i	0.0352431	+	0.0610429i	−0.847866	+	0.530211i	$0.822113\pi$
$272$	−3.31315	+	5.73854i	−0.200889	+	0.347950i
$273$		0			0
$274$	−13.9078			−0.840199
$275$	2.86774	−	4.96708i	0.172932	−	0.299526i
$276$		0			0
$277$	4.83965			0.290786			0.145393	−	0.989374i	$-0.453555\pi$
$277$	4.83965			0.290786			0.145393	+	0.989374i	$0.453555\pi$
$278$	0.735489			0.0441117
$279$		0			0
$280$	−1.92234	−	3.32960i	−0.114882	−	0.198981i
$281$	4.66379	−	8.07793i	0.278219	−	0.481889i	−0.692723	−	0.721203i	$-0.743589\pi$
$281$	4.66379	−	8.07793i	0.278219	−	0.481889i	0.970942	+	0.239314i	$0.0769227\pi$
$282$		0			0
$283$	4.67241	+	8.09285i	0.277746	+	0.481070i	0.970824	−	0.239792i	$-0.0770793\pi$
$283$	4.67241	+	8.09285i	0.277746	+	0.481070i	−0.693078	+	0.720862i	$0.743746\pi$
$284$	6.62629			0.393198
$285$		0			0
$286$	27.1604			1.60603
$287$	16.9139	+	29.2957i	0.998394	+	1.72927i
$288$		0			0
$289$	−13.4539	+	23.3028i	−0.791405	+	1.37075i
$290$	−5.15783	−	8.93363i	−0.302878	−	0.524601i
$291$		0			0
$292$	−6.10920			−0.357514
$293$	−3.20143			−0.187030			−0.0935148	−	0.995618i	$-0.529810\pi$
$293$	−3.20143			−0.187030			−0.0935148	+	0.995618i	$0.529810\pi$
$294$		0			0
$295$	−3.00000	+	5.19615i	−0.174667	+	0.302532i
$296$	1.00000			0.0581238
$297$		0			0
$298$	5.42234	−	9.39177i	0.314108	−	0.544051i
$299$	−13.5802	−	23.5216i	−0.785362	−	1.36029i
$300$		0			0
$301$	−2.01100	−	3.48315i	−0.115912	−	0.200765i
$302$	−0.468461	−	0.811398i	−0.0269569	−	0.0466907i
$303$		0			0
$304$	2.81315	+	3.32960i	0.161345	+	0.190965i
$305$	0.109196			0.00625255
$306$		0			0
$307$	14.1117	+	24.4422i	0.805398	+	1.39499i	0.916022	+	0.401128i	$0.131382\pi$
$307$	14.1117	+	24.4422i	0.805398	+	1.39499i	−0.110624	+	0.993862i	$0.535285\pi$
$308$	11.0256	−	19.0969i	0.628241	−	1.08814i
$309$		0			0
$310$	−2.36774	+	4.10105i	−0.134479	+	0.232924i
$311$	12.8497			0.728641			0.364320	−	0.931274i	$-0.381301\pi$
$311$	12.8497			0.728641			0.364320	+	0.931274i	$0.381301\pi$
$312$		0			0
$313$	−14.5171	+	25.1443i	−0.820555	+	1.42124i	0.0847148	+	0.996405i	$0.473002\pi$
$313$	−14.5171	+	25.1443i	−0.820555	+	1.42124i	−0.905270	+	0.424837i	$0.860331\pi$
$314$	4.34469	−	7.52522i	0.245185	−	0.424673i
$315$		0			0
$316$	−6.73549			−0.378901
$317$	2.22701	−	3.85729i	0.125081	−	0.216647i	−0.796683	−	0.604397i	$-0.793414\pi$
$317$	2.22701	−	3.85729i	0.125081	−	0.216647i	0.921765	+	0.387750i	$0.126747\pi$
$318$		0			0
$319$	29.5827	−	51.2387i	1.65631	−	2.86882i
$320$	0.500000	+	0.866025i	0.0279508	+	0.0484123i
$321$		0			0
$322$	−22.0512			−1.22886
$323$	18.6407	+	22.0629i	1.03720	+	1.22761i
$324$		0			0
$325$	−2.36774	−	4.10105i	−0.131339	−	0.227486i
$326$	−0.103234	−	0.178807i	−0.00571762	−	0.00990320i
$327$		0			0
$328$	−4.39928	−	7.61978i	−0.242910	−	0.420732i
$329$	3.42486	−	5.93203i	0.188819	−	0.327044i
$330$		0			0
$331$	−11.8447			−0.651043			−0.325521	−	0.945535i	$-0.605540\pi$
$331$	−11.8447			−0.651043			−0.325521	+	0.945535i	$0.605540\pi$
$332$	−8.47098	+	14.6722i	−0.464905	+	0.805240i
$333$		0			0
$334$	17.7355			0.970443
$335$	−5.89080			−0.321849
$336$		0			0
$337$	−3.58614	−	6.21137i	−0.195349	−	0.338355i	0.751666	−	0.659544i	$-0.229251\pi$
$337$	−3.58614	−	6.21137i	−0.195349	−	0.338355i	−0.947015	+	0.321189i	$0.895917\pi$
$338$	4.71243	−	8.16217i	0.256322	−	0.443963i
$339$		0			0
$340$	3.31315	+	5.73854i	0.179681	+	0.311216i
$341$	−27.1604			−1.47082
$342$		0			0
$343$	3.00504			0.162257
$344$	0.523059	+	0.905965i	0.0282015	+	0.0488464i
$345$		0			0
$346$	−0.709912	+	1.22960i	−0.0381651	+	0.0661039i
$347$	11.2065	+	19.4102i	0.601595	+	1.04199i	0.992580	+	0.121596i	$0.0388011\pi$
$347$	11.2065	+	19.4102i	0.601595	+	1.04199i	−0.390985	+	0.920397i	$0.627866\pi$
$348$		0			0
$349$	−24.3037			−1.30095			−0.650475	−	0.759528i	$-0.725430\pi$
$349$	−24.3037			−1.30095			−0.650475	+	0.759528i	$0.725430\pi$
$350$	−3.84469			−0.205507
$351$		0			0
$352$	−2.86774	+	4.96708i	−0.152851	+	0.264746i
$353$	−32.7286			−1.74197			−0.870984	−	0.491312i	$-0.836518\pi$
$353$	−32.7286			−1.74197			−0.870984	+	0.491312i	$0.836518\pi$
$354$		0			0
$355$	3.31315	−	5.73854i	0.175844	−	0.304570i
$356$	−2.55460	−	4.42469i	−0.135393	−	0.234508i
$357$		0			0
$358$	8.60323	+	14.9012i	0.454695	+	0.787555i
$359$	−0.577657	−	1.00053i	−0.0304876	−	0.0528060i	0.850379	−	0.526171i	$-0.176373\pi$
$359$	−0.577657	−	1.00053i	−0.0304876	−	0.0528060i	−0.880867	+	0.473365i	$0.843039\pi$
$360$		0			0
$361$	17.8097	−	6.61925i	0.937353	−	0.348382i
$362$	−16.5341			−0.869011
$363$		0			0
$364$	−9.10323	−	15.7673i	−0.477139	−	0.826429i
$365$	−3.05460	+	5.29072i	−0.159885	+	0.276929i
$366$		0			0
$367$	−13.8387	+	23.9694i	−0.722375	+	1.25119i	0.237670	+	0.971346i	$0.423616\pi$
$367$	−13.8387	+	23.9694i	−0.722375	+	1.25119i	−0.960045	+	0.279845i	$0.909717\pi$
$368$	5.73549			0.298983
$369$		0			0
$370$	0.500000	−	0.866025i	0.0259938	−	0.0450225i
$371$	9.82163	−	17.0116i	0.509913	−	0.883196i
$372$		0			0
$373$	−23.5171			−1.21767			−0.608835	−	0.793297i	$-0.708363\pi$
$373$	−23.5171			−1.21767			−0.608835	+	0.793297i	$0.708363\pi$
$374$	−19.0025	+	32.9133i	−0.982597	+	1.70191i
$375$		0			0
$376$	−0.890804	+	1.54292i	−0.0459397	+	0.0795699i
$377$	−24.4249	−	42.3051i	−1.25794	−	2.17882i
$378$		0			0
$379$	8.29870			0.426276			0.213138	−	0.977022i	$-0.431632\pi$
$379$	8.29870			0.426276			0.213138	+	0.977022i	$0.431632\pi$
$380$	4.29009	−	0.771459i	0.220077	−	0.0395750i
$381$		0			0
$382$	11.2065	+	19.4102i	0.573373	+	0.993111i
$383$	6.89080	+	11.9352i	0.352104	+	0.609861i	0.986618	−	0.163050i	$-0.0521331\pi$
$383$	6.89080	+	11.9352i	0.352104	+	0.609861i	−0.634514	+	0.772911i	$0.718800\pi$
$384$		0			0
$385$	−11.0256	−	19.0969i	−0.561915	−	0.973266i
$386$	−11.5256	+	19.9629i	−0.586636	+	1.01608i
$387$		0			0
$388$	9.15531			0.464791
$389$	−0.842168	+	1.45868i	−0.0426996	+	0.0739579i	−0.886585	−	0.462565i	$-0.846929\pi$
$389$	−0.842168	+	1.45868i	−0.0426996	+	0.0739579i	0.843886	+	0.536523i	$0.180263\pi$
$390$		0			0
$391$	38.0050			1.92200
$392$	−7.78161			−0.393031
$393$		0			0
$394$	−1.33621	−	2.31438i	−0.0673171	−	0.116597i
$395$	−3.36774	+	5.83311i	−0.169450	+	0.293495i
$396$		0			0
$397$	−7.28161	−	12.6121i	−0.365453	−	0.632984i	0.623395	−	0.781907i	$-0.285753\pi$
$397$	−7.28161	−	12.6121i	−0.365453	−	0.632984i	−0.988849	+	0.148923i	$0.952419\pi$
$398$	11.5802			0.580462
$399$		0			0
$400$	1.00000			0.0500000
$401$	10.7816	+	18.6743i	0.538408	+	0.932550i	0.998990	+	0.0449326i	$0.0143073\pi$
$401$	10.7816	+	18.6743i	0.538408	+	0.932550i	−0.460582	+	0.887617i	$0.652359\pi$
$402$		0			0
$403$	−11.2124	+	19.4205i	−0.558531	+	0.967404i
$404$	−1.84469	−	3.19509i	−0.0917765	−	0.158962i
$405$		0			0
$406$	−39.6605			−1.96832
$407$	5.73549			0.284298
$408$		0			0
$409$	6.64935	−	11.5170i	0.328789	−	0.569480i	−0.653483	−	0.756942i	$-0.726693\pi$
$409$	6.64935	−	11.5170i	0.328789	−	0.569480i	0.982272	+	0.187462i	$0.0600261\pi$
$410$	−8.79857			−0.434530
$411$		0			0
$412$	−1.03154	+	1.78668i	−0.0508203	+	0.0880233i
$413$	11.5341	+	19.9776i	0.567554	+	0.983032i
$414$		0			0
$415$	8.47098	+	14.6722i	0.415824	+	0.720228i
$416$	2.36774	+	4.10105i	0.116088	+	0.201071i
$417$		0			0
$418$	16.1348	+	19.0969i	0.789178	+	0.934058i
$419$	36.9881			1.80699			0.903493	−	0.428603i	$-0.140994\pi$
$419$	36.9881			1.80699			0.903493	+	0.428603i	$0.140994\pi$
$420$		0			0
$421$	1.68685	+	2.92172i	0.0822122	+	0.142396i	0.904200	−	0.427110i	$-0.140468\pi$
$421$	1.68685	+	2.92172i	0.0822122	+	0.142396i	−0.821988	+	0.569505i	$0.807135\pi$
$422$	11.6117	−	20.1121i	0.565249	−	0.979041i
$423$		0			0
$424$	−2.55460	+	4.42469i	−0.124062	+	0.214882i
$425$	6.62629			0.321422
$426$		0			0
$427$	0.209912	−	0.363579i	0.0101584	−	0.0175948i
$428$	7.26703	−	12.5869i	0.351265	−	0.608409i
$429$		0			0
$430$	1.04612			0.0504483
$431$	11.5827	−	20.0618i	0.557919	−	0.966344i	−0.439751	−	0.898120i	$-0.644933\pi$
$431$	11.5827	−	20.0618i	0.557919	−	0.966344i	0.997670	−	0.0682240i	$-0.0217332\pi$
$432$		0			0
$433$	−0.836206	+	1.44835i	−0.0401855	+	0.0696033i	−0.885419	−	0.464794i	$-0.846128\pi$
$433$	−0.836206	+	1.44835i	−0.0401855	+	0.0696033i	0.845233	+	0.534398i	$0.179462\pi$
$434$	9.10323	+	15.7673i	0.436969	+	0.756853i
$435$		0			0
$436$	8.62629			0.413125
$437$	8.47098	−	23.5216i	0.405222	−	1.12519i
$438$		0			0
$439$	13.3703	+	23.1580i	0.638128	+	1.10527i	0.985843	+	0.167670i	$0.0536242\pi$
$439$	13.3703	+	23.1580i	0.638128	+	1.10527i	−0.347715	+	0.937600i	$0.613042\pi$
$440$	2.86774	+	4.96708i	0.136714	+	0.236796i
$441$		0			0
$442$	15.6894	+	27.1748i	0.746267	+	1.29257i
$443$	3.04864	−	5.28039i	0.144845	−	0.250879i	−0.784470	−	0.620167i	$-0.787065\pi$
$443$	3.04864	−	5.28039i	0.144845	−	0.250879i	0.929315	+	0.369288i	$0.120398\pi$
$444$		0			0
$445$	−5.10920			−0.242199
$446$	−7.50252	+	12.9947i	−0.355255	+	0.615319i
$447$		0			0
$448$	3.84469			0.181644
$449$	5.10920			0.241118			0.120559	−	0.992706i	$-0.461531\pi$
$449$	5.10920			0.241118			0.120559	+	0.992706i	$0.461531\pi$
$450$		0			0
$451$	−25.2320	−	43.7032i	−1.18813	−	2.05790i
$452$	−4.26703	+	7.39071i	−0.200704	+	0.347630i
$453$		0			0
$454$	10.2670	+	17.7830i	0.481856	+	0.834598i
$455$	−18.2065			−0.853532
$456$		0			0
$457$	−34.3960			−1.60898			−0.804488	−	0.593969i	$-0.797560\pi$
$457$	−34.3960			−1.60898			−0.804488	+	0.593969i	$0.797560\pi$
$458$	−6.63226	−	11.4874i	−0.309905	−	0.536771i
$459$		0			0
$460$	2.86774	−	4.96708i	0.133709	−	0.231591i
$461$	−5.73549	−	9.93416i	−0.267128	−	0.462680i	0.700991	−	0.713170i	$-0.252741\pi$
$461$	−5.73549	−	9.93416i	−0.267128	−	0.462680i	−0.968119	+	0.250491i	$0.919408\pi$
$462$		0			0
$463$	1.93692			0.0900164			0.0450082	−	0.998987i	$-0.485669\pi$
$463$	1.93692			0.0900164			0.0450082	+	0.998987i	$0.485669\pi$
$464$	10.3157			0.478893
$465$		0			0
$466$	−9.42486	+	16.3243i	−0.436598	+	0.756210i
$467$	9.78664			0.452872			0.226436	−	0.974026i	$-0.427293\pi$
$467$	9.78664			0.452872			0.226436	+	0.974026i	$0.427293\pi$
$468$		0			0
$469$	−11.3241	+	19.6140i	−0.522900	+	0.905690i
$470$	0.890804	+	1.54292i	0.0410897	+	0.0711695i
$471$		0			0
$472$	−3.00000	−	5.19615i	−0.138086	−	0.239172i
$473$	3.00000	+	5.19615i	0.137940	+	0.238919i
$474$		0			0
$475$	1.47694	−	4.10105i	0.0677667	−	0.188169i
$476$	25.4760			1.16769
$477$		0			0
$478$	−6.95388	−	12.0445i	−0.318063	−	0.550902i
$479$	13.2040	−	22.8699i	0.603304	−	1.04495i	−0.389013	−	0.921232i	$-0.627184\pi$
$479$	13.2040	−	22.8699i	0.603304	−	1.04495i	0.992317	−	0.123721i	$-0.0394827\pi$
$480$		0			0
$481$	2.36774	−	4.10105i	0.107960	−	0.186992i
$482$	30.2065			1.37587
$483$		0			0
$484$	−10.9479	+	18.9624i	−0.497633	+	0.861925i
$485$	4.57766	−	7.92873i	0.207861	−	0.360025i
$486$		0			0
$487$	39.3377			1.78256			0.891280	−	0.453454i	$-0.149808\pi$
$487$	39.3377			1.78256			0.891280	+	0.453454i	$0.149808\pi$
$488$	−0.0545981	+	0.0945666i	−0.00247154	+	0.00428083i
$489$		0			0
$490$	−3.89080	+	6.73907i	−0.175769	+	0.304440i
$491$	5.33872	+	9.24694i	0.240933	+	0.417309i	0.960980	−	0.276617i	$-0.0892132\pi$
$491$	5.33872	+	9.24694i	0.240933	+	0.417309i	−0.720047	+	0.693925i	$0.755880\pi$
$492$		0			0
$493$	68.3546			3.07854
$494$	20.3157	−	3.65323i	0.914045	−	0.164367i
$495$		0			0
$496$	−2.36774	−	4.10105i	−0.106315	−	0.184143i
$497$	−12.7380	−	22.0629i	−0.571378	−	0.989655i
$498$		0			0
$499$	−12.7670	−	22.1131i	−0.571531	−	0.989920i	−0.996409	−	0.0846697i	$-0.973016\pi$
$499$	−12.7670	−	22.1131i	−0.571531	−	0.989920i	0.424878	−	0.905250i	$-0.360317\pi$
$500$	0.500000	−	0.866025i	0.0223607	−	0.0387298i
$501$		0			0
$502$	−21.0342			−0.938802
$503$	−11.3387	+	19.6392i	−0.505569	+	0.875671i	0.494411	+	0.869229i	$0.335384\pi$
$503$	−11.3387	+	19.6392i	−0.505569	+	0.875671i	−0.999979	+	0.00644217i	$0.997949\pi$
$504$		0			0
$505$	−3.68937			−0.164175
$506$	32.8958			1.46240
$507$		0			0
$508$	−2.33621	−	4.04643i	−0.103652	−	0.179531i
$509$	12.3618	−	21.4112i	0.547926	−	0.949036i	−0.450490	−	0.892781i	$-0.648751\pi$
$509$	12.3618	−	21.4112i	0.547926	−	0.949036i	0.998416	−	0.0562549i	$-0.0179159\pi$
$510$		0			0
$511$	11.7440	+	20.3412i	0.519523	+	0.899840i
$512$	−1.00000			−0.0441942
$513$		0			0
$514$	6.00000			0.264649
$515$	1.03154	+	1.78668i	0.0454550	+	0.0787304i
$516$		0			0
$517$	−5.10920	+	8.84939i	−0.224702	+	0.389196i
$518$	−1.92234	−	3.32960i	−0.0844629	−	0.146294i
$519$		0			0
$520$	4.73549			0.207665
$521$	−21.1604			−0.927052			−0.463526	−	0.886083i	$-0.653416\pi$
$521$	−21.1604			−0.927052			−0.463526	+	0.886083i	$0.653416\pi$
$522$		0			0
$523$	3.11768	−	5.39997i	0.136326	−	0.236124i	−0.789777	−	0.613394i	$-0.789804\pi$
$523$	3.11768	−	5.39997i	0.136326	−	0.236124i	0.926103	+	0.377270i	$0.123137\pi$
$524$	13.6433			0.596008
$525$		0			0
$526$	3.39677	−	5.88337i	0.148106	−	0.256527i
$527$	−15.6894	−	27.1748i	−0.683440	−	1.18375i
$528$		0			0
$529$	−4.94792	−	8.57005i	−0.215127	−	0.372611i
$530$	2.55460	+	4.42469i	0.110965	+	0.192196i
$531$		0			0
$532$	5.67837	−	15.7673i	0.246189	−	0.683598i
$533$	−41.6655			−1.80473
$534$		0			0
$535$	−7.26703	−	12.5869i	−0.314181	−	0.544178i
$536$	2.94540	−	5.10159i	0.127222	−	0.220355i
$537$		0			0
$538$	−6.04864	+	10.4765i	−0.260775	+	0.451676i
$539$	−44.6313			−1.92241
$540$		0			0
$541$	−20.2636	+	35.0976i	−0.871200	+	1.50896i	−0.0104427	+	0.999945i	$0.503324\pi$
$541$	−20.2636	+	35.0976i	−0.871200	+	1.50896i	−0.860757	+	0.509016i	$0.830009\pi$
$542$	−0.580175	+	1.00489i	−0.0249207	+	0.0431638i
$543$		0			0
$544$	−6.62629			−0.284100
$545$	4.31315	−	7.47059i	0.184755	−	0.320005i
$546$		0			0
$547$	0.632255	−	1.09510i	0.0270333	−	0.0468230i	−0.852192	−	0.523229i	$-0.824727\pi$
$547$	0.632255	−	1.09510i	0.0270333	−	0.0468230i	0.879226	+	0.476406i	$0.158061\pi$
$548$	−6.95388	−	12.0445i	−0.297055	−	0.514515i
$549$		0			0
$550$	5.73549			0.244562
$551$	15.2356	−	42.3051i	0.649060	−	1.80226i
$552$		0			0
$553$	12.9479	+	22.4265i	0.550602	+	0.953670i
$554$	2.41982	+	4.19126i	0.102809	+	0.178070i
$555$		0			0
$556$	0.367745	+	0.636953i	0.0155959	+	0.0270128i
$557$	−10.3362	+	17.9028i	−0.437959	+	0.758567i	−0.997532	−	0.0702137i	$-0.977632\pi$
$557$	−10.3362	+	17.9028i	−0.437959	+	0.758567i	0.559573	+	0.828781i	$0.310965\pi$
$558$		0			0
$559$	4.95388			0.209527
$560$	1.92234	−	3.32960i	0.0812338	−	0.140701i
$561$		0			0
$562$	9.32759			0.393461
$563$	−9.03419			−0.380746			−0.190373	−	0.981712i	$-0.560970\pi$
$563$	−9.03419			−0.380746			−0.190373	+	0.981712i	$0.560970\pi$
$564$		0			0
$565$	4.26703	+	7.39071i	0.179515	+	0.310930i
$566$	−4.67241	+	8.09285i	−0.196396	+	0.340168i
$567$		0			0
$568$	3.31315	+	5.73854i	0.139017	+	0.240784i
$569$	−25.7405			−1.07910			−0.539549	−	0.841954i	$-0.681405\pi$
$569$	−25.7405			−1.07910			−0.539549	+	0.841954i	$0.681405\pi$
$570$		0			0
$571$	15.5513			0.650801			0.325401	−	0.945576i	$-0.394501\pi$
$571$	15.5513			0.650801			0.325401	+	0.945576i	$0.394501\pi$
$572$	13.5802	+	23.5216i	0.567816	+	0.983486i
$573$		0			0
$574$	−16.9139	+	29.2957i	−0.705971	+	1.22278i
$575$	−2.86774	−	4.96708i	−0.119593	−	0.207142i
$576$		0			0
$577$	−38.3157			−1.59510			−0.797551	−	0.603252i	$-0.793872\pi$
$577$	−38.3157			−1.59510			−0.797551	+	0.603252i	$0.793872\pi$
$578$	−26.9078			−1.11922
$579$		0			0
$580$	5.15783	−	8.93363i	0.214167	−	0.370949i
$581$	65.1365			2.70232
$582$		0			0
$583$	−14.6519	+	25.3778i	−0.606818	+	1.05104i
$584$	−3.05460	−	5.29072i	−0.126400	−	0.218932i
$585$		0			0
$586$	−1.60072	−	2.77252i	−0.0661250	−	0.114532i
$587$	15.3618	+	26.6074i	0.634049	+	1.09820i	0.986716	+	0.162456i	$0.0519414\pi$
$587$	15.3618	+	26.6074i	0.634049	+	1.09820i	−0.352667	+	0.935749i	$0.614725\pi$
$588$		0			0
$589$	−20.3157	+	3.65323i	−0.837092	+	0.150529i
$590$	−6.00000			−0.247016
$591$		0			0
$592$	0.500000	+	0.866025i	0.0205499	+	0.0355934i
$593$	5.98556	−	10.3673i	0.245797	−	0.425734i	−0.716558	−	0.697527i	$-0.754284\pi$
$593$	5.98556	−	10.3673i	0.245797	−	0.425734i	0.962356	+	0.271794i	$0.0876169\pi$
$594$		0			0
$595$	12.7380	−	22.0629i	0.522207	−	0.904490i
$596$	10.8447			0.444216
$597$		0			0
$598$	13.5802	−	23.5216i	0.555335	−	0.961868i
$599$	−4.33011	+	7.49996i	−0.176923	+	0.306440i	−0.940825	−	0.338892i	$-0.889948\pi$
$599$	−4.33011	+	7.49996i	−0.176923	+	0.306440i	0.763902	+	0.645332i	$0.223281\pi$
$600$		0			0
$601$	−44.3787			−1.81025			−0.905123	−	0.425149i	$-0.860222\pi$
$601$	−44.3787			−1.81025			−0.905123	+	0.425149i	$0.860222\pi$
$602$	2.01100	−	3.48315i	0.0819622	−	0.141963i
$603$		0			0
$604$	0.468461	−	0.811398i	0.0190614	−	0.0330153i
$605$	10.9479	+	18.9624i	0.445096	+	0.770929i
$606$		0			0
$607$	−24.6944			−1.00232			−0.501158	−	0.865356i	$-0.667092\pi$
$607$	−24.6944			−1.00232			−0.501158	+	0.865356i	$0.667092\pi$
$608$	−1.47694	+	4.10105i	−0.0598979	+	0.166320i
$609$		0			0
$610$	0.0545981	+	0.0945666i	0.00221061	+	0.00382889i
$611$	4.21839	+	7.30647i	0.170658	+	0.295588i
$612$		0			0
$613$	9.18341	+	15.9061i	0.370914	+	0.642443i	0.989706	−	0.143112i	$-0.0457110\pi$
$613$	9.18341	+	15.9061i	0.370914	+	0.642443i	−0.618792	+	0.785555i	$0.712378\pi$
$614$	−14.1117	+	24.4422i	−0.569502	+	0.986407i
$615$		0			0
$616$	22.0512			0.888466
$617$	−6.00000	+	10.3923i	−0.241551	+	0.418378i	−0.961156	−	0.276005i	$-0.910989\pi$
$617$	−6.00000	+	10.3923i	−0.241551	+	0.418378i	0.719605	+	0.694383i	$0.244323\pi$
$618$		0			0
$619$	8.46594			0.340275			0.170137	−	0.985420i	$-0.445579\pi$
$619$	8.46594			0.340275			0.170137	+	0.985420i	$0.445579\pi$
$620$	−4.73549			−0.190182
$621$		0			0
$622$	6.42486	+	11.1282i	0.257613	+	0.446200i
$623$	−9.82163	+	17.0116i	−0.393495	+	0.681554i
$624$		0			0
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	−29.0342			−1.16044
$627$		0			0
$628$	8.68937			0.346744
$629$	3.31315	+	5.73854i	0.132104	+	0.228811i
$630$		0			0
$631$	−10.2611	+	17.7727i	−0.408487	+	0.707520i	−0.994720	−	0.102622i	$-0.967277\pi$
$631$	−10.2611	+	17.7727i	−0.408487	+	0.707520i	0.586234	+	0.810142i	$0.300610\pi$
$632$	−3.36774	−	5.83311i	−0.133962	−	0.232028i
$633$		0			0
$634$	4.45402			0.176892
$635$	−4.67241			−0.185419
$636$		0			0
$637$	−18.4249	+	31.9128i	−0.730020	+	1.26443i
$638$	59.1654			2.34238
$639$		0			0
$640$	−0.500000	+	0.866025i	−0.0197642	+	0.0342327i
$641$	14.1434	+	24.4971i	0.558630	+	0.967576i	0.997611	+	0.0690797i	$0.0220063\pi$
$641$	14.1434	+	24.4971i	0.558630	+	0.967576i	−0.438981	+	0.898496i	$0.644660\pi$
$642$		0			0
$643$	15.4795	+	26.8112i	0.610450	+	1.05733i	0.991165	+	0.132638i	$0.0423448\pi$
$643$	15.4795	+	26.8112i	0.610450	+	1.05733i	−0.380714	+	0.924693i	$0.624322\pi$
$644$	−11.0256	−	19.0969i	−0.434469	−	0.752522i
$645$		0			0
$646$	−9.78664	+	27.1748i	−0.385050	+	1.06918i
$647$	33.0220			1.29823			0.649114	−	0.760691i	$-0.275140\pi$
$647$	33.0220			1.29823			0.649114	+	0.760691i	$0.275140\pi$
$648$		0			0
$649$	−17.2065	−	29.8025i	−0.675413	−	1.16985i
$650$	2.36774	−	4.10105i	0.0928706	−	0.160857i
$651$		0			0
$652$	0.103234	−	0.178807i	0.00404297	−	0.00700262i
$653$	−33.1193			−1.29606			−0.648029	−	0.761616i	$-0.724406\pi$
$653$	−33.1193			−1.29606			−0.648029	+	0.761616i	$0.724406\pi$
$654$		0			0
$655$	6.82163	−	11.8154i	0.266543	−	0.461666i
$656$	4.39928	−	7.61978i	0.171763	−	0.297503i
$657$		0			0
$658$	6.84972			0.267030
$659$	−6.55712	+	11.3573i	−0.255429	+	0.442416i	−0.965012	−	0.262206i	$-0.915550\pi$
$659$	−6.55712	+	11.3573i	−0.255429	+	0.442416i	0.709583	+	0.704622i	$0.248883\pi$
$660$		0			0
$661$	−3.17227	+	5.49454i	−0.123387	+	0.213713i	−0.921101	−	0.389323i	$-0.872709\pi$
$661$	−3.17227	+	5.49454i	−0.123387	+	0.213713i	0.797714	+	0.603036i	$0.206042\pi$
$662$	−5.92234	−	10.2578i	−0.230178	−	0.398681i
$663$		0			0
$664$	−16.9420			−0.657475
$665$	−10.8157	−	12.8012i	−0.419413	−	0.496411i
$666$		0			0
$667$	−29.5827	−	51.2387i	−1.14545	−	1.98397i
$668$	8.86774	+	15.3594i	0.343103	+	0.594272i
$669$		0			0
$670$	−2.94540	−	5.10159i	−0.113791	−	0.197091i
$671$	−0.313147	+	0.542386i	−0.0120889	+	0.0209386i
$672$		0			0
$673$	32.2987			1.24502			0.622512	−	0.782610i	$-0.286112\pi$
$673$	32.2987			1.24502			0.622512	+	0.782610i	$0.286112\pi$
$674$	3.58614	−	6.21137i	0.138133	−	0.239253i
$675$		0			0
$676$	9.42486			0.362495
$677$	−1.54598			−0.0594169			−0.0297084	−	0.999559i	$-0.509458\pi$
$677$	−1.54598			−0.0594169			−0.0297084	+	0.999559i	$0.509458\pi$
$678$		0			0
$679$	−17.5997	−	30.4835i	−0.675413	−	1.16985i
$680$	−3.31315	+	5.73854i	−0.127053	+	0.220063i
$681$		0			0
$682$	−13.5802	−	23.5216i	−0.520012	−	0.900687i
$683$	14.5341			0.556130			0.278065	−	0.960562i	$-0.410307\pi$
$683$	14.5341			0.556130			0.278065	+	0.960562i	$0.410307\pi$
$684$		0			0
$685$	−13.9078			−0.531388
$686$	1.50252	+	2.60244i	0.0573664	+	0.0993615i
$687$		0			0
$688$	−0.523059	+	0.905965i	−0.0199414	+	0.0345396i
$689$	12.0973	+	20.9531i	0.460869	+	0.798249i
$690$		0			0
$691$	8.48794			0.322896			0.161448	−	0.986881i	$-0.448384\pi$
$691$	8.48794			0.322896			0.161448	+	0.986881i	$0.448384\pi$
$692$	−1.41982			−0.0539736
$693$		0			0
$694$	−11.2065	+	19.4102i	−0.425392	+	0.736800i
$695$	0.735489			0.0278987
$696$		0			0
$697$	29.1509	−	50.4909i	1.10417	−	1.91248i
$698$	−12.1519	−	21.0477i	−0.459955	−	0.796666i
$699$		0			0
$700$	−1.92234	−	3.32960i	−0.0726577	−	0.125847i
$701$	−9.29870	−	16.1058i	−0.351207	−	0.608309i	0.635254	−	0.772303i	$-0.280895\pi$
$701$	−9.29870	−	16.1058i	−0.351207	−	0.608309i	−0.986461	+	0.163994i	$0.947562\pi$
$702$		0			0
$703$	4.29009	−	0.771459i	0.161804	−	0.0290961i
$704$	−5.73549			−0.216164
$705$		0			0
$706$	−16.3643	−	28.3438i	−0.615879	−	1.06673i
$707$	−7.09224	+	12.2841i	−0.266731	+	0.461992i
$708$		0			0
$709$	−3.96236	+	6.86301i	−0.148810	+	0.257746i	−0.930788	−	0.365560i	$-0.880877\pi$
$709$	−3.96236	+	6.86301i	−0.148810	+	0.257746i	0.781978	+	0.623306i	$0.214211\pi$
$710$	6.62629			0.248680
$711$		0			0
$712$	2.55460	−	4.42469i	0.0957376	−	0.165822i
$713$	−13.5802	+	23.5216i	−0.508582	+	0.880889i
$714$		0			0
$715$	27.1604			1.01574
$716$	−8.60323	+	14.9012i	−0.321518	+	0.556885i
$717$		0			0
$718$	0.577657	−	1.00053i	0.0215580	−	0.0373395i
$719$	−14.8328	−	25.6911i	−0.553169	−	0.958116i	−0.998043	−	0.0625235i	$-0.980085\pi$
$719$	−14.8328	−	25.6911i	−0.553169	−	0.958116i	0.444875	−	0.895593i	$-0.353248\pi$
$720$		0			0
$721$	7.93189			0.295399
$722$	14.6373	+	12.1140i	0.544744	+	0.450837i
$723$		0			0
$724$	−8.26703	−	14.3189i	−0.307242	−	0.532158i
$725$	−5.15783	−	8.93363i	−0.191557	−	0.331787i
$726$		0			0
$727$	7.25855	+	12.5722i	0.269205	+	0.466276i	0.968657	−	0.248403i	$-0.0799059\pi$
$727$	7.25855	+	12.5722i	0.269205	+	0.466276i	−0.699452	+	0.714680i	$0.746573\pi$
$728$	9.10323	−	15.7673i	0.337388	−	0.584374i
$729$		0			0
$730$	−6.10920			−0.226111
$731$	−3.46594	+	6.00319i	−0.128193	+	0.222036i
$732$		0			0
$733$	25.7355			0.950562			0.475281	−	0.879834i	$-0.342346\pi$
$733$	25.7355			0.950562			0.475281	+	0.879834i	$0.342346\pi$
$734$	−27.6774			−1.02159
$735$		0			0
$736$	2.86774	+	4.96708i	0.105706	+	0.183089i
$737$	16.8933	−	29.2601i	0.622274	−	1.07781i
$738$		0			0
$739$	2.23297	+	3.86762i	0.0821412	+	0.142273i	0.904169	−	0.427174i	$-0.140491\pi$
$739$	2.23297	+	3.86762i	0.0821412	+	0.142273i	−0.822028	+	0.569447i	$0.807157\pi$
$740$	1.00000			0.0367607
$741$		0			0
$742$	19.6433			0.721127
$743$	5.04002	+	8.72957i	0.184900	+	0.320257i	0.943543	−	0.331250i	$-0.107470\pi$
$743$	5.04002	+	8.72957i	0.184900	+	0.320257i	−0.758643	+	0.651507i	$0.774137\pi$
$744$		0			0
$745$	5.42234	−	9.39177i	0.198659	−	0.344088i
$746$	−11.7585	−	20.3664i	−0.430511	−	0.745667i
$747$		0			0
$748$	−38.0050			−1.38960
$749$	−55.8789			−2.04177
$750$		0			0
$751$	1.94792	−	3.37390i	0.0710806	−	0.123115i	−0.828295	−	0.560293i	$-0.810689\pi$
$751$	1.94792	−	3.37390i	0.0710806	−	0.123115i	0.899375	+	0.437178i	$0.144022\pi$
$752$	−1.78161			−0.0649685
$753$		0			0
$754$	24.4249	−	42.3051i	0.889501	−	1.54066i
$755$	−0.468461	−	0.811398i	−0.0170490	−	0.0295298i
$756$		0			0
$757$	−18.2866	−	31.6734i	−0.664639	−	1.15119i	−0.979383	−	0.202012i	$-0.935252\pi$
$757$	−18.2866	−	31.6734i	−0.664639	−	1.15119i	0.314744	−	0.949177i	$-0.398081\pi$
$758$	4.14935	+	7.18689i	0.150711	+	0.261040i
$759$		0			0
$760$	2.81315	+	3.32960i	0.102044	+	0.120777i
$761$	−29.9589			−1.08601			−0.543005	−	0.839729i	$-0.682714\pi$
$761$	−29.9589			−1.08601			−0.543005	+	0.839729i	$0.682714\pi$
$762$		0			0
$763$	−16.5827	−	28.7221i	−0.600334	−	1.03981i
$764$	−11.2065	+	19.4102i	−0.405436	+	0.702235i
$765$		0			0
$766$	−6.89080	+	11.9352i	−0.248975	+	0.431237i
$767$	−28.4129			−1.02593
$768$		0			0
$769$	24.9940	−	43.2909i	0.901308	−	1.56111i	0.0755103	−	0.997145i	$-0.475941\pi$
$769$	24.9940	−	43.2909i	0.901308	−	1.56111i	0.825798	−	0.563966i	$-0.190725\pi$
$770$	11.0256	−	19.0969i	0.397334	−	0.688203i
$771$		0			0
$772$	−23.0512			−0.829629
$773$	−14.3532	+	24.8604i	−0.516247	+	0.894167i	0.483575	+	0.875303i	$0.339338\pi$
$773$	−14.3532	+	24.8604i	−0.516247	+	0.894167i	−0.999822	+	0.0188637i	$0.993995\pi$
$774$		0			0
$775$	−2.36774	+	4.10105i	−0.0850519	+	0.147314i
$776$	4.57766	+	7.92873i	0.164328	+	0.284625i
$777$		0			0
$778$	−1.68434			−0.0603863
$779$	−24.7517	−	29.2957i	−0.886820	−	1.04963i
$780$		0			0
$781$	19.0025	+	32.9133i	0.679964	+	1.17773i
$782$	19.0025	+	32.9133i	0.679529	+	1.17698i
$783$		0			0
$784$	−3.89080	−	6.73907i	−0.138957	−	0.240681i
$785$	4.34469	−	7.52522i	0.155068	−	0.268586i
$786$		0			0
$787$	14.3960			0.513161			0.256581	−	0.966523i	$-0.417404\pi$
$787$	14.3960			0.513161			0.256581	+	0.966523i	$0.417404\pi$
$788$	1.33621	−	2.31438i	0.0476004	−	0.0824462i
$789$		0			0
$790$	−6.73549			−0.239638
$791$	32.8108			1.16662
$792$		0			0
$793$	0.258549	+	0.447819i	0.00918133	+	0.0159025i
$794$	7.28161	−	12.6121i	0.258415	−	0.447587i
$795$		0			0
$796$	5.79009	+	10.0287i	0.205224	+	0.355459i
$797$	35.8328			1.26926			0.634631	−	0.772815i	$-0.281152\pi$
$797$	35.8328			1.26926			0.634631	+	0.772815i	$0.281152\pi$
$798$		0			0
$799$	−11.8055			−0.417647
$800$	0.500000	+	0.866025i	0.0176777	+	0.0306186i
$801$		0			0
$802$	−10.7816	+	18.6743i	−0.380712	+	0.659412i
$803$	−17.5196	−	30.3449i	−0.618254	−	1.07085i
$804$		0			0
$805$	−22.0512			−0.777201
$806$	−22.4249			−0.789882
$807$		0			0
$808$	1.84469	−	3.19509i	0.0648958	−	0.112403i
$809$	28.2184			0.992106			0.496053	−	0.868292i	$-0.334782\pi$
$809$	28.2184			0.992106			0.496053	+	0.868292i	$0.334782\pi$
$810$		0			0
$811$	8.24397	−	14.2790i	0.289485	−	0.501403i	−0.684202	−	0.729293i	$-0.739849\pi$
$811$	8.24397	−	14.2790i	0.289485	−	0.501403i	0.973687	+	0.227890i	$0.0731827\pi$
$812$	−19.8302	−	34.3470i	−0.695905	−	1.20534i
$813$		0			0
$814$	2.86774	+	4.96708i	0.100514	+	0.174096i
$815$	−0.103234	−	0.178807i	−0.00361614	−	0.00626333i
$816$		0			0
$817$	2.94288	+	3.48315i	0.102958	+	0.121860i
$818$	13.2987			0.464978
$819$		0			0
$820$	−4.39928	−	7.61978i	−0.153630	−	0.266094i
$821$	−26.4710	+	45.8491i	−0.923844	+	1.60014i	−0.130433	+	0.991457i	$0.541637\pi$
$821$	−26.4710	+	45.8491i	−0.923844	+	1.60014i	−0.793411	+	0.608687i	$0.791697\pi$
$822$		0			0
$823$	−0.916381	+	1.58722i	−0.0319430	+	0.0553270i	−0.881555	−	0.472081i	$-0.843503\pi$
$823$	−0.916381	+	1.58722i	−0.0319430	+	0.0553270i	0.849612	+	0.527408i	$0.176836\pi$
$824$	−2.06308			−0.0718707
$825$		0			0
$826$	−11.5341	+	19.9776i	−0.401321	+	0.695109i
$827$	−3.73801	+	6.47442i	−0.129983	+	0.225138i	−0.923670	−	0.383189i	$-0.874826\pi$
$827$	−3.73801	+	6.47442i	−0.129983	+	0.225138i	0.793687	+	0.608327i	$0.208159\pi$
$828$		0			0
$829$	24.7116			0.858271			0.429135	−	0.903240i	$-0.358818\pi$
$829$	24.7116			0.858271			0.429135	+	0.903240i	$0.358818\pi$
$830$	−8.47098	+	14.6722i	−0.294032	+	0.509278i
$831$		0			0
$832$	−2.36774	+	4.10105i	−0.0820868	+	0.142178i
$833$	−25.7816	−	44.6551i	−0.893280	−	1.54721i
$834$		0			0
$835$	17.7355			0.613762
$836$	−8.47098	+	23.5216i	−0.292975	+	0.813510i
$837$		0			0
$838$	18.4940	+	32.0326i	0.638866	+	1.10655i
$839$	−17.8328	−	30.8872i	−0.615655	−	1.06635i	−0.990269	−	0.139165i	$-0.955558\pi$
$839$	−17.8328	−	30.8872i	−0.615655	−	1.06635i	0.374614	−	0.927181i	$-0.377775\pi$
$840$		0			0
$841$	−38.7065	−	67.0416i	−1.33471	−	2.31178i
$842$	−1.68685	+	2.92172i	−0.0581328	+	0.100689i
$843$		0			0
$844$	23.2234			0.799383
$845$	4.71243	−	8.16217i	0.162113	−	0.280787i
$846$		0			0
$847$	84.1826			2.89255
$848$	−5.10920			−0.175451
$849$		0			0
$850$	3.31315	+	5.73854i	0.113640	+	0.196830i
$851$	2.86774	−	4.96708i	0.0983050	−	0.170269i
$852$		0			0
$853$	−5.99404	−	10.3820i	−0.205232	−	0.355472i	0.744975	−	0.667093i	$-0.232462\pi$
$853$	−5.99404	−	10.3820i	−0.205232	−	0.355472i	−0.950207	+	0.311621i	$0.899128\pi$
$854$	0.419825			0.0143661
$855$		0			0
$856$	14.5341			0.496764
$857$	16.2184	+	28.0911i	0.554010	+	0.959573i	0.997980	+	0.0635314i	$0.0202363\pi$
$857$	16.2184	+	28.0911i	0.554010	+	0.959573i	−0.443970	+	0.896042i	$0.646430\pi$
$858$		0			0
$859$	0.548636	−	0.950266i	0.0187192	−	0.0324226i	−0.856514	−	0.516124i	$-0.827374\pi$
$859$	0.548636	−	0.950266i	0.0187192	−	0.0324226i	0.875233	+	0.483701i	$0.160708\pi$
$860$	0.523059	+	0.905965i	0.0178362	+	0.0308931i
$861$		0			0
$862$	23.1654			0.789016
$863$	−22.8036			−0.776244			−0.388122	−	0.921608i	$-0.626876\pi$
$863$	−22.8036			−0.776244			−0.388122	+	0.921608i	$0.626876\pi$
$864$		0			0
$865$	−0.709912	+	1.22960i	−0.0241377	+	0.0418078i
$866$	−1.67241			−0.0568309
$867$		0			0
$868$	−9.10323	+	15.7673i	−0.308984	+	0.535176i
$869$	−19.3157	−	33.4557i	−0.655239	−	1.13491i
$870$		0			0
$871$	−13.9479	−	24.1585i	−0.472607	−	0.818580i
$872$	4.31315	+	7.47059i	0.146062	+	0.252986i
$873$		0			0
$874$	24.6058	−	4.42469i	0.832302	−	0.149667i
$875$	−3.84469			−0.129974
$876$		0			0
$877$	8.54612	+	14.8023i	0.288582	+	0.499839i	0.973471	−	0.228808i	$-0.0734829\pi$
$877$	8.54612	+	14.8023i	0.288582	+	0.499839i	−0.684890	+	0.728647i	$0.740150\pi$
$878$	−13.3703	+	23.1580i	−0.451225	+	0.781544i
$879$		0			0
$880$	−2.86774	+	4.96708i	−0.0966717	+	0.167440i
$881$	−41.9589			−1.41363			−0.706816	−	0.707398i	$-0.749869\pi$
$881$	−41.9589			−1.41363			−0.706816	+	0.707398i	$0.749869\pi$
$882$		0			0
$883$	18.3122	−	31.7177i	0.616255	−	1.06739i	−0.373908	−	0.927466i	$-0.621982\pi$
$883$	18.3122	−	31.7177i	0.616255	−	1.06739i	0.990163	−	0.139920i	$-0.0446844\pi$
$884$	−15.6894	+	27.1748i	−0.527691	+	0.913987i
$885$		0			0
$886$	6.09727			0.204842
$887$	−5.20647	+	9.01787i	−0.174816	+	0.302790i	−0.940098	−	0.340905i	$-0.889266\pi$
$887$	−5.20647	+	9.01787i	−0.174816	+	0.302790i	0.765282	+	0.643696i	$0.222600\pi$
$888$		0			0
$889$	−8.98198	+	15.5572i	−0.301246	+	0.521773i
$890$	−2.55460	−	4.42469i	−0.0856303	−	0.148316i
$891$		0			0
$892$	−15.0050			−0.502406
$893$	−2.63133	+	7.30647i	−0.0880541	+	0.244502i
$894$		0			0
$895$	8.60323	+	14.9012i	0.287574	+	0.498093i
$896$	1.92234	+	3.32960i	0.0642210	+	0.111234i
$897$		0			0
$898$	2.55460	+	4.42469i	0.0852480	+	0.147654i
$899$	−24.4249	+	42.3051i	−0.814615	+	1.41095i
$900$		0			0
$901$	−33.8550			−1.12787
$902$	25.2320	−	43.7032i	0.840135	−	1.45516i
$903$		0			0
$904$	−8.53406			−0.283839
$905$	−16.5341			−0.549611
$906$		0			0
$907$	−2.48290	−	4.30051i	−0.0824434	−	0.142796i	0.821856	−	0.569696i	$-0.192939\pi$
$907$	−2.48290	−	4.30051i	−0.0824434	−	0.142796i	−0.904299	+	0.426900i	$0.859606\pi$
$908$	−10.2670	+	17.7830i	−0.340723	+	0.590150i
$909$		0			0
$910$	−9.10323	−	15.7673i	−0.301769	−	0.522680i
$911$	−1.18420			−0.0392342			−0.0196171	−	0.999808i	$-0.506245\pi$
$911$	−1.18420			−0.0392342			−0.0196171	+	0.999808i	$0.506245\pi$
$912$		0			0
$913$	−97.1704			−3.21587
$914$	−17.1980	−	29.7878i	−0.568859	−	0.985293i
$915$		0			0
$916$	6.63226	−	11.4874i	0.219136	−	0.379554i
$917$	−26.2270	−	45.4265i	−0.866092	−	1.50012i
$918$		0			0
$919$	17.3618			0.572712			0.286356	−	0.958123i	$-0.407556\pi$
$919$	17.3618			0.572712			0.286356	+	0.958123i	$0.407556\pi$
$920$	5.73549			0.189093
$921$		0			0
$922$	5.73549	−	9.93416i	0.188888	−	0.327164i
$923$	31.3787			1.03284
$924$		0			0
$925$	0.500000	−	0.866025i	0.0164399	−	0.0284747i
$926$	0.968461	+	1.67742i	0.0318256	+	0.0551236i
$927$		0			0
$928$	5.15783	+	8.93363i	0.169314	+	0.293261i
$929$	22.2951	+	38.6163i	0.731479	+	1.26696i	0.956251	+	0.292548i	$0.0945031\pi$
$929$	22.2951	+	38.6163i	0.731479	+	1.26696i	−0.224772	+	0.974411i	$0.572164\pi$
$930$		0			0
$931$	−33.3838	+	6.00319i	−1.09411	+	0.196747i
$932$	−18.8497			−0.617443
$933$		0			0
$934$	4.89332	+	8.47548i	0.160114	+	0.277326i
$935$	−19.0025	+	32.9133i	−0.621449	+	1.07638i
$936$		0			0
$937$	−14.0888	+	24.4025i	−0.460261	+	0.797195i	−0.998974	−	0.0452943i	$-0.985577\pi$
$937$	−14.0888	+	24.4025i	−0.460261	+	0.797195i	0.538713	+	0.842489i	$0.318911\pi$
$938$	−22.6483			−0.739493
$939$		0			0
$940$	−0.890804	+	1.54292i	−0.0290548	+	0.0503244i
$941$	15.2501	−	26.4139i	0.497138	−	0.861068i	−0.502857	−	0.864370i	$-0.667718\pi$
$941$	15.2501	−	26.4139i	0.497138	−	0.861068i	0.999995	+	0.00330157i	$0.00105092\pi$
$942$		0			0
$943$	−50.4641			−1.64334
$944$	3.00000	−	5.19615i	0.0976417	−	0.169120i
$945$		0			0
$946$	−3.00000	+	5.19615i	−0.0975384	+	0.168941i
$947$	−7.46846	−	12.9358i	−0.242692	−	0.420356i	0.718788	−	0.695229i	$-0.244697\pi$
$947$	−7.46846	−	12.9358i	−0.242692	−	0.420356i	−0.961480	+	0.274874i	$0.911364\pi$
$948$		0			0
$949$	−28.9300			−0.939109
$950$	4.29009	−	0.771459i	0.139189	−	0.0250294i
$951$		0			0
$952$	12.7380	+	22.0629i	0.412841	+	0.715062i
$953$	13.3787	+	23.1727i	0.433380	+	0.750636i	0.997162	−	0.0752876i	$-0.0239875\pi$
$953$	13.3787	+	23.1727i	0.433380	+	0.750636i	−0.563782	+	0.825924i	$0.690654\pi$
$954$		0			0
$955$	11.2065	+	19.4102i	0.362633	+	0.628098i
$956$	6.95388	−	12.0445i	0.224905	−	0.389546i
$957$		0			0
$958$	26.4079			0.853201
$959$	−26.7355	+	46.3072i	−0.863334	+	1.49534i
$960$		0			0
$961$	−8.57514			−0.276617
$962$	4.73549			0.152678
$963$		0			0
$964$	15.1032	+	26.1596i	0.486442	+	0.842543i
$965$	−11.5256	+	19.9629i	−0.371021	+	0.642628i
$966$		0			0
$967$	−20.3677	−	35.2780i	−0.654983	−	1.13446i	−0.981898	−	0.189409i	$-0.939343\pi$
$967$	−20.3677	−	35.2780i	−0.654983	−	1.13446i	0.326916	−	0.945054i	$-0.393991\pi$
$968$	−21.8958			−0.703759
$969$		0			0
$970$	9.15531			0.293959
$971$	−2.67241	−	4.62875i	−0.0857618	−	0.148544i	0.819954	−	0.572430i	$-0.193999\pi$
$971$	−2.67241	−	4.62875i	−0.0857618	−	0.148544i	−0.905716	+	0.423886i	$0.860666\pi$
$972$		0			0
$973$	1.41386	−	2.44888i	0.0453264	−	0.0785076i
$974$	19.6688	+	34.0674i	0.630230	+	1.09159i
$975$		0			0
$976$	−0.109196			−0.00349528
$977$	42.6947			1.36592			0.682962	−	0.730454i	$-0.260691\pi$
$977$	42.6947			1.36592			0.682962	+	0.730454i	$0.260691\pi$
$978$		0			0
$979$	14.6519	−	25.3778i	0.468276	−	0.811077i
$980$	−7.78161			−0.248574
$981$		0			0
$982$	−5.33872	+	9.24694i	−0.170366	+	0.295082i
$983$	−7.28757	−	12.6224i	−0.232437	−	0.402593i	0.726087	−	0.687602i	$-0.241337\pi$
$983$	−7.28757	−	12.6224i	−0.232437	−	0.402593i	−0.958525	+	0.285009i	$0.908003\pi$
$984$		0			0
$985$	−1.33621	−	2.31438i	−0.0425751	−	0.0737422i
$986$	34.1773	+	59.1968i	1.08843	+	1.88521i
$987$		0			0
$988$	13.3216	+	15.7673i	0.423817	+	0.501623i
$989$	6.00000			0.190789
$990$		0			0
$991$	21.5425	+	37.3128i	0.684321	+	1.18528i	0.973650	+	0.228049i	$0.0732347\pi$
$991$	21.5425	+	37.3128i	0.684321	+	1.18528i	−0.289328	+	0.957230i	$0.593432\pi$
$992$	2.36774	−	4.10105i	0.0751760	−	0.130209i
$993$		0			0
$994$	12.7380	−	22.0629i	0.404025	−	0.699792i
$995$	11.5802			0.367116
$996$		0			0
$997$	20.1144	−	34.8391i	0.637028	−	1.10337i	−0.349053	−	0.937103i	$-0.613497\pi$
$997$	20.1144	−	34.8391i	0.637028	−	1.10337i	0.986081	−	0.166263i	$-0.0531700\pi$
$998$	12.7670	−	22.1131i	0.404133	−	0.699979i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1710.2.l.q.1261.3		6
3.2	odd	2		570.2.i.j.121.3	✓	6
19.11	even	3	inner	1710.2.l.q.1531.3		6
57.11	odd	6		570.2.i.j.391.3	yes	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.i.j.121.3	✓	6	3.2	odd	2
570.2.i.j.391.3	yes	6	57.11	odd	6
1710.2.l.q.1261.3		6	1.1	even	1	trivial
1710.2.l.q.1531.3		6	19.11	even	3	inner

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:	\( N \)	\(=\)	\( 1710 = 2 \cdot 3^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1710.l (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(0.500000 + 0.866025i) q^{5} +3.84469 q^{7} -1.00000 q^{8} +O(q^{10})\)	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(0.500000 + 0.866025i) q^{5} +3.84469 q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{10} -5.73549 q^{11} +(-2.36774 + 4.10105i) q^{13} +(1.92234 + 3.32960i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(-3.31315 - 5.73854i) q^{17} +(-4.29009 + 0.771459i) q^{19} -1.00000 q^{20} +(-2.86774 - 4.96708i) q^{22} +(-2.86774 + 4.96708i) q^{23} +(-0.500000 + 0.866025i) q^{25} -4.73549 q^{26} +(-1.92234 + 3.32960i) q^{28} +(-5.15783 + 8.93363i) q^{29} +4.73549 q^{31} +(0.500000 - 0.866025i) q^{32} +(3.31315 - 5.73854i) q^{34} +(1.92234 + 3.32960i) q^{35} -1.00000 q^{37} +(-2.81315 - 3.32960i) q^{38} +(-0.500000 - 0.866025i) q^{40} +(4.39928 + 7.61978i) q^{41} +(-0.523059 - 0.905965i) q^{43} +(2.86774 - 4.96708i) q^{44} -5.73549 q^{46} +(0.890804 - 1.54292i) q^{47} +7.78161 q^{49} -1.00000 q^{50} +(-2.36774 - 4.10105i) q^{52} +(2.55460 - 4.42469i) q^{53} +(-2.86774 - 4.96708i) q^{55} -3.84469 q^{56} -10.3157 q^{58} +(3.00000 + 5.19615i) q^{59} +(0.0545981 - 0.0945666i) q^{61} +(2.36774 + 4.10105i) q^{62} +1.00000 q^{64} -4.73549 q^{65} +(-2.94540 + 5.10159i) q^{67} +6.62629 q^{68} +(-1.92234 + 3.32960i) q^{70} +(-3.31315 - 5.73854i) q^{71} +(3.05460 + 5.29072i) q^{73} +(-0.500000 - 0.866025i) q^{74} +(1.47694 - 4.10105i) q^{76} -22.0512 q^{77} +(3.36774 + 5.83311i) q^{79} +(0.500000 - 0.866025i) q^{80} +(-4.39928 + 7.61978i) q^{82} +16.9420 q^{83} +(3.31315 - 5.73854i) q^{85} +(0.523059 - 0.905965i) q^{86} +5.73549 q^{88} +(-2.55460 + 4.42469i) q^{89} +(-9.10323 + 15.7673i) q^{91} +(-2.86774 - 4.96708i) q^{92} +1.78161 q^{94} +(-2.81315 - 3.32960i) q^{95} +(-4.57766 - 7.92873i) q^{97} +(3.89080 + 6.73907i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 3 q^{2} - 3 q^{4} + 3 q^{5} + 2 q^{7} - 6 q^{8}+O(q^{10}) \) 6 * q + 3 * q^2 - 3 * q^4 + 3 * q^5 + 2 * q^7 - 6 * q^8	\( 6 q + 3 q^{2} - 3 q^{4} + 3 q^{5} + 2 q^{7} - 6 q^{8} - 3 q^{10} - 8 q^{11} - q^{13} + q^{14} - 3 q^{16} - 4 q^{17} - 2 q^{19} - 6 q^{20} - 4 q^{22} - 4 q^{23} - 3 q^{25} - 2 q^{26} - q^{28} + 6 q^{29} + 2 q^{31} + 3 q^{32} + 4 q^{34} + q^{35} - 6 q^{37} - q^{38} - 3 q^{40} + 8 q^{41} - 11 q^{43} + 4 q^{44} - 8 q^{46} + 36 q^{49} - 6 q^{50} - q^{52} + 18 q^{53} - 4 q^{55} - 2 q^{56} + 12 q^{58} + 18 q^{59} + 3 q^{61} + q^{62} + 6 q^{64} - 2 q^{65} - 15 q^{67} + 8 q^{68} - q^{70} - 4 q^{71} + 21 q^{73} - 3 q^{74} + q^{76} - 32 q^{77} + 7 q^{79} + 3 q^{80} - 8 q^{82} - 4 q^{83} + 4 q^{85} + 11 q^{86} + 8 q^{88} - 18 q^{89} - 15 q^{91} - 4 q^{92} - q^{95} - 38 q^{97} + 18 q^{98}+O(q^{100}) \) 6 * q + 3 * q^2 - 3 * q^4 + 3 * q^5 + 2 * q^7 - 6 * q^8 - 3 * q^10 - 8 * q^11 - q^13 + q^14 - 3 * q^16 - 4 * q^17 - 2 * q^19 - 6 * q^20 - 4 * q^22 - 4 * q^23 - 3 * q^25 - 2 * q^26 - q^28 + 6 * q^29 + 2 * q^31 + 3 * q^32 + 4 * q^34 + q^35 - 6 * q^37 - q^38 - 3 * q^40 + 8 * q^41 - 11 * q^43 + 4 * q^44 - 8 * q^46 + 36 * q^49 - 6 * q^50 - q^52 + 18 * q^53 - 4 * q^55 - 2 * q^56 + 12 * q^58 + 18 * q^59 + 3 * q^61 + q^62 + 6 * q^64 - 2 * q^65 - 15 * q^67 + 8 * q^68 - q^70 - 4 * q^71 + 21 * q^73 - 3 * q^74 + q^76 - 32 * q^77 + 7 * q^79 + 3 * q^80 - 8 * q^82 - 4 * q^83 + 4 * q^85 + 11 * q^86 + 8 * q^88 - 18 * q^89 - 15 * q^91 - 4 * q^92 - q^95 - 38 * q^97 + 18 * q^98

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