LMFDB - Embedded newform 819.2.o.h.568.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [819,2,Mod(568,819)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(819, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 4]))

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

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

chi := DirichletCharacter("819.568");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 819 = 3^{2} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	819.o (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:	$6.53974792554$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + 7x^{6} + 38x^{4} - 16x^{3} + 15x^{2} + 3x + 1 $ x^8 - x^7 + 7x^6 + 38x^4 - 16x^3 + 15x^2 + 3*x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 91)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			568.4
Root			$-1.11000 + 1.92258i$ of defining polynomial
Character	$\chi$	$=$	819.568
Dual form			819.2.o.h.757.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.11000 - 1.92258i) q^{2} +(-1.46422 - 2.53610i) q^{4} +4.22001 q^{5} +(0.500000 + 0.866025i) q^{7} -2.06113 q^{8} +O(q^{10})$	\(q+(1.11000 - 1.92258i) q^{2} +(-1.46422 - 2.53610i) q^{4} +4.22001 q^{5} +(0.500000 + 0.866025i) q^{7} -2.06113 q^{8} +(4.68423 - 8.11332i) q^{10} +(-0.274776 + 0.475925i) q^{11} +(-2.95900 + 2.06017i) q^{13} +2.22001 q^{14} +(0.640570 - 1.10950i) q^{16} +(-1.18944 - 2.06017i) q^{17} +(1.80534 + 3.12694i) q^{19} +(-6.17901 - 10.7024i) q^{20} +(0.610004 + 1.05656i) q^{22} +(2.90945 - 5.03931i) q^{23} +12.8085 q^{25} +(0.676353 + 7.97573i) q^{26} +(1.46422 - 2.53610i) q^{28} +(-1.79945 + 3.11673i) q^{29} -5.14844 q^{31} +(-3.48320 - 6.03308i) q^{32} -5.28114 q^{34} +(2.11000 + 3.65463i) q^{35} +(0.164772 - 0.285393i) q^{37} +8.01574 q^{38} -8.69799 q^{40} +(-3.14579 + 5.44866i) q^{41} +(-1.61000 - 2.78861i) q^{43} +1.60932 q^{44} +(-6.45900 - 11.1873i) q^{46} -8.20957 q^{47} +(-0.500000 + 0.866025i) q^{49} +(14.2174 - 24.6253i) q^{50} +(9.55742 + 4.48778i) q^{52} -2.65866 q^{53} +(-1.15956 + 2.00841i) q^{55} +(-1.03057 - 1.78499i) q^{56} +(3.99478 + 6.91917i) q^{58} +(-0.903765 - 1.56537i) q^{59} +(-0.304662 - 0.527691i) q^{61} +(-5.71479 + 9.89831i) q^{62} -12.9032 q^{64} +(-12.4870 + 8.69395i) q^{65} +(-5.18490 + 8.98052i) q^{67} +(-3.48320 + 6.03308i) q^{68} +9.36845 q^{70} +(-5.59889 - 9.69756i) q^{71} +4.90621 q^{73} +(-0.365794 - 0.633574i) q^{74} +(5.28682 - 9.15705i) q^{76} -0.549551 q^{77} -14.0171 q^{79} +(2.70321 - 4.68210i) q^{80} +(6.98367 + 12.0961i) q^{82} +5.73159 q^{83} +(-5.01945 - 8.69395i) q^{85} -7.14844 q^{86} +(0.566349 - 0.980945i) q^{88} +(-3.73378 + 6.46709i) q^{89} +(-3.26366 - 1.53248i) q^{91} -17.0403 q^{92} +(-9.11266 + 15.7836i) q^{94} +(7.61856 + 13.1957i) q^{95} +(3.42035 + 5.92422i) q^{97} +(1.11000 + 1.92258i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - q^{2} - 5 q^{4} + 14 q^{5} + 4 q^{7} + 12 q^{8}+O(q^{10}) $ 8 * q - q^2 - 5 * q^4 + 14 * q^5 + 4 * q^7 + 12 * q^8	$ 8 q - q^{2} - 5 q^{4} + 14 q^{5} + 4 q^{7} + 12 q^{8} + 11 q^{10} - q^{11} + 4 q^{13} - 2 q^{14} - 19 q^{16} - 4 q^{17} - q^{19} - 2 q^{20} - 5 q^{22} - 2 q^{23} + 10 q^{25} - 12 q^{26} + 5 q^{28} + q^{29} - 8 q^{31} - 33 q^{32} + 6 q^{34} + 7 q^{35} + 10 q^{37} + 46 q^{38} - 34 q^{40} - 22 q^{41} - 3 q^{43} + 24 q^{44} - 24 q^{46} - 4 q^{47} - 4 q^{49} + 43 q^{50} + 65 q^{52} - 4 q^{53} + 3 q^{55} + 6 q^{56} + 11 q^{58} - 8 q^{59} - 8 q^{61} - 5 q^{62} + 28 q^{64} - 7 q^{65} + 6 q^{67} - 33 q^{68} + 22 q^{70} - 14 q^{71} - 16 q^{73} + 20 q^{74} - 32 q^{76} - 2 q^{77} - 52 q^{79} + 7 q^{80} + 14 q^{82} - 5 q^{85} - 24 q^{86} - 3 q^{88} - q^{89} - 4 q^{91} - 24 q^{92} - 33 q^{94} + 21 q^{95} - 3 q^{97} - q^{98}+O(q^{100}) $ 8 * q - q^2 - 5 * q^4 + 14 * q^5 + 4 * q^7 + 12 * q^8 + 11 * q^10 - q^11 + 4 * q^13 - 2 * q^14 - 19 * q^16 - 4 * q^17 - q^19 - 2 * q^20 - 5 * q^22 - 2 * q^23 + 10 * q^25 - 12 * q^26 + 5 * q^28 + q^29 - 8 * q^31 - 33 * q^32 + 6 * q^34 + 7 * q^35 + 10 * q^37 + 46 * q^38 - 34 * q^40 - 22 * q^41 - 3 * q^43 + 24 * q^44 - 24 * q^46 - 4 * q^47 - 4 * q^49 + 43 * q^50 + 65 * q^52 - 4 * q^53 + 3 * q^55 + 6 * q^56 + 11 * q^58 - 8 * q^59 - 8 * q^61 - 5 * q^62 + 28 * q^64 - 7 * q^65 + 6 * q^67 - 33 * q^68 + 22 * q^70 - 14 * q^71 - 16 * q^73 + 20 * q^74 - 32 * q^76 - 2 * q^77 - 52 * q^79 + 7 * q^80 + 14 * q^82 - 5 * q^85 - 24 * q^86 - 3 * q^88 - q^89 - 4 * q^91 - 24 * q^92 - 33 * q^94 + 21 * q^95 - 3 * q^97 - q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/819\mathbb{Z}\right)^\times$.

$n$	$92$	$379$	$703$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$1$

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 $

$2$	1.11000	−	1.92258i	0.784891	−	1.35947i	−0.144173	−	0.989553i	$-0.546052\pi$
$2$	1.11000	−	1.92258i	0.784891	−	1.35947i	0.929064	−	0.369919i	$-0.120615\pi$
$3$		0			0
$3$		0			0
$4$	−1.46422	−	2.53610i	−0.732109	−	1.26805i
$5$	4.22001			1.88724			0.943622	−	0.331024i	$-0.107394\pi$
$5$	4.22001			1.88724			0.943622	+	0.331024i	$0.107394\pi$
$6$		0			0
$7$	0.500000	+	0.866025i	0.188982	+	0.327327i
$7$	0.500000	+	0.866025i	0.188982	+	0.327327i
$8$	−2.06113			−0.728720
$9$		0			0
$10$	4.68423	−	8.11332i	1.48128	−	2.56566i
$11$	−0.274776	+	0.475925i	−0.0828480	+	0.143497i	−0.904472	−	0.426533i	$-0.859735\pi$
$11$	−0.274776	+	0.475925i	−0.0828480	+	0.143497i	0.821624	+	0.570030i	$0.193068\pi$
$12$		0			0
$13$	−2.95900	+	2.06017i	−0.820679	+	0.571389i
$13$	−2.95900	+	2.06017i	−0.820679	+	0.571389i
$14$	2.22001			0.593322
$15$		0			0
$16$	0.640570	−	1.10950i	0.160142	−	0.277375i
$17$	−1.18944	−	2.06017i	−0.288482	−	0.499665i	0.684966	−	0.728575i	$-0.259817\pi$
$17$	−1.18944	−	2.06017i	−0.288482	−	0.499665i	−0.973448	+	0.228910i	$0.926484\pi$
$18$		0			0
$19$	1.80534	+	3.12694i	0.414174	+	0.717370i	0.995341	−	0.0964139i	$-0.0307372\pi$
$19$	1.80534	+	3.12694i	0.414174	+	0.717370i	−0.581168	+	0.813784i	$0.697404\pi$
$20$	−6.17901	−	10.7024i	−1.38167	−	2.39312i
$21$		0			0
$22$	0.610004	+	1.05656i	0.130053	+	0.225259i
$23$	2.90945	−	5.03931i	0.606662	−	1.05077i	−0.385124	−	0.922865i	$-0.625841\pi$
$23$	2.90945	−	5.03931i	0.606662	−	1.05077i	0.991786	−	0.127905i	$-0.0408253\pi$
$24$		0			0
$25$	12.8085			2.56169
$26$	0.676353	+	7.97573i	0.132644	+	1.56417i
$27$		0			0
$28$	1.46422	−	2.53610i	0.276711	−	0.479278i
$29$	−1.79945	+	3.11673i	−0.334149	+	0.578762i	−0.983321	−	0.181879i	$-0.941782\pi$
$29$	−1.79945	+	3.11673i	−0.334149	+	0.578762i	0.649172	+	0.760641i	$0.275115\pi$
$30$		0			0
$31$	−5.14844			−0.924688			−0.462344	−	0.886701i	$-0.652991\pi$
$31$	−5.14844			−0.924688			−0.462344	+	0.886701i	$0.652991\pi$
$32$	−3.48320	−	6.03308i	−0.615749	−	1.06651i
$33$		0			0
$34$	−5.28114			−0.905708
$35$	2.11000	+	3.65463i	0.356656	+	0.617746i
$36$		0			0
$37$	0.164772	−	0.285393i	0.0270883	−	0.0469183i	−0.852163	−	0.523276i	$-0.824710\pi$
$37$	0.164772	−	0.285393i	0.0270883	−	0.0469183i	0.879252	+	0.476357i	$0.158043\pi$
$38$	8.01574			1.30033
$39$		0			0
$40$	−8.69799			−1.37527
$41$	−3.14579	+	5.44866i	−0.491289	+	0.850938i	−0.999950	−	0.0100292i	$-0.996808\pi$
$41$	−3.14579	+	5.44866i	−0.491289	+	0.850938i	0.508660	+	0.860967i	$0.330141\pi$
$42$		0			0
$43$	−1.61000	−	2.78861i	−0.245523	−	0.425259i	0.716755	−	0.697325i	$-0.245626\pi$
$43$	−1.61000	−	2.78861i	−0.245523	−	0.425259i	−0.962279	+	0.272066i	$0.912293\pi$
$44$	1.60932			0.242615
$45$		0			0
$46$	−6.45900	−	11.1873i	−0.952328	−	1.64948i
$47$	−8.20957			−1.19749			−0.598745	−	0.800940i	$-0.704334\pi$
$47$	−8.20957			−1.19749			−0.598745	+	0.800940i	$0.704334\pi$
$48$		0			0
$49$	−0.500000	+	0.866025i	−0.0714286	+	0.123718i
$50$	14.2174	−	24.6253i	2.01065	−	3.48255i
$51$		0			0
$52$	9.55742	+	4.48778i	1.32538	+	0.622343i
$53$	−2.65866			−0.365196			−0.182598	−	0.983188i	$-0.558451\pi$
$53$	−2.65866			−0.365196			−0.182598	+	0.983188i	$0.558451\pi$
$54$		0			0
$55$	−1.15956	+	2.00841i	−0.156354	+	0.270814i
$56$	−1.03057	−	1.78499i	−0.137715	−	0.238530i
$57$		0			0
$58$	3.99478	+	6.91917i	0.524541	+	0.908531i
$59$	−0.903765	−	1.56537i	−0.117660	−	0.203793i	0.801180	−	0.598424i	$-0.204206\pi$
$59$	−0.903765	−	1.56537i	−0.117660	−	0.203793i	−0.918840	+	0.394630i	$0.870873\pi$
$60$		0			0
$61$	−0.304662	−	0.527691i	−0.0390080	−	0.0675639i	0.845862	−	0.533401i	$-0.179086\pi$
$61$	−0.304662	−	0.527691i	−0.0390080	−	0.0675639i	−0.884870	+	0.465838i	$0.845753\pi$
$62$	−5.71479	+	9.89831i	−0.725779	+	1.25709i
$63$		0			0
$64$	−12.9032			−1.61290
$65$	−12.4870	+	8.69395i	−1.54882	+	1.07835i
$66$		0			0
$67$	−5.18490	+	8.98052i	−0.633437	+	1.09714i	0.353407	+	0.935470i	$0.385023\pi$
$67$	−5.18490	+	8.98052i	−0.633437	+	1.09714i	−0.986844	+	0.161675i	$0.948310\pi$
$68$	−3.48320	+	6.03308i	−0.422400	+	0.731619i
$69$		0			0
$70$	9.36845			1.11974
$71$	−5.59889	−	9.69756i	−0.664466	−	1.15089i	−0.979430	−	0.201785i	$-0.935326\pi$
$71$	−5.59889	−	9.69756i	−0.664466	−	1.15089i	0.314964	−	0.949104i	$-0.398008\pi$
$72$		0			0
$73$	4.90621			0.574228			0.287114	−	0.957896i	$-0.407304\pi$
$73$	4.90621			0.574228			0.287114	+	0.957896i	$0.407304\pi$
$74$	−0.365794	−	0.633574i	−0.0425227	−	0.0736515i
$75$		0			0
$76$	5.28682	−	9.15705i	0.606440	−	1.05039i
$77$	−0.549551			−0.0626272
$78$		0			0
$79$	−14.0171			−1.57705			−0.788524	−	0.615004i	$-0.789154\pi$
$79$	−14.0171			−1.57705			−0.788524	+	0.615004i	$0.789154\pi$
$80$	2.70321	−	4.68210i	0.302228	−	0.523474i
$81$		0			0
$82$	6.98367	+	12.0961i	0.771217	+	1.33579i
$83$	5.73159			0.629124			0.314562	−	0.949237i	$-0.398142\pi$
$83$	5.73159			0.629124			0.314562	+	0.949237i	$0.398142\pi$
$84$		0			0
$85$	−5.01945	−	8.69395i	−0.544436	−	0.942991i
$86$	−7.14844			−0.770836
$87$		0			0
$88$	0.566349	−	0.980945i	0.0603730	−	0.104569i
$89$	−3.73378	+	6.46709i	−0.395779	+	0.685510i	−0.993200	−	0.116418i	$-0.962859\pi$
$89$	−3.73378	+	6.46709i	−0.395779	+	0.685510i	0.597421	+	0.801928i	$0.296192\pi$
$90$		0			0
$91$	−3.26366	−	1.53248i	−0.342125	−	0.160648i
$92$	−17.0403			−1.77657
$93$		0			0
$94$	−9.11266	+	15.7836i	−0.939899	+	1.62795i
$95$	7.61856	+	13.1957i	0.781647	+	1.35385i
$96$		0			0
$97$	3.42035	+	5.92422i	0.347284	+	0.601514i	0.985766	−	0.168123i	$-0.0537706\pi$
$97$	3.42035	+	5.92422i	0.347284	+	0.601514i	−0.638482	+	0.769637i	$0.720437\pi$
$98$	1.11000	+	1.92258i	0.112127	+	0.194210i
$99$		0			0
$100$	−18.7544	−	32.4835i	−1.87544	−	3.24835i
$101$	2.87956	−	4.98755i	0.286527	−	0.496280i	−0.686451	−	0.727176i	$-0.740832\pi$
$101$	2.87956	−	4.98755i	0.286527	−	0.496280i	0.972978	+	0.230896i	$0.0741658\pi$
$102$		0			0
$103$	0.571776			0.0563388			0.0281694	−	0.999603i	$-0.491032\pi$
$103$	0.571776			0.0563388			0.0281694	+	0.999603i	$0.491032\pi$
$104$	6.09889	−	4.24629i	0.598045	−	0.416383i
$105$		0			0
$106$	−2.95113	+	5.11150i	−0.286639	+	0.496473i
$107$	2.03578	−	3.52608i	0.196807	−	0.340879i	−0.750685	−	0.660661i	$-0.770276\pi$
$107$	2.03578	−	3.52608i	0.196807	−	0.340879i	0.947491	+	0.319782i	$0.103610\pi$
$108$		0			0
$109$	15.3087			1.46631			0.733153	−	0.680064i	$-0.238048\pi$
$109$	15.3087			1.46631			0.733153	+	0.680064i	$0.238048\pi$
$110$	2.57422	+	4.45868i	0.245442	+	0.425119i
$111$		0			0
$112$	1.28114			0.121056
$113$	6.08846	+	10.5455i	0.572754	+	0.992039i	0.996282	+	0.0861558i	$0.0274583\pi$
$113$	6.08846	+	10.5455i	0.572754	+	0.992039i	−0.423528	+	0.905883i	$0.639208\pi$
$114$		0			0
$115$	12.2779	−	21.2659i	1.14492	−	1.98306i
$116$	10.5391			0.978533
$117$		0			0
$118$	−4.01273			−0.369402
$119$	1.18944	−	2.06017i	0.109036	−	0.188856i
$120$		0			0
$121$	5.34900	+	9.26473i	0.486272	+	0.842249i
$122$	−1.35271			−0.122468
$123$		0			0
$124$	7.53844	+	13.0570i	0.676972	+	1.17255i
$125$	32.9518			2.94730
$126$		0			0
$127$	−0.980336	+	1.69799i	−0.0869907	+	0.150672i	−0.906238	−	0.422768i	$-0.861058\pi$
$127$	−0.980336	+	1.69799i	−0.0869907	+	0.150672i	0.819247	+	0.573441i	$0.194392\pi$
$128$	−7.35619	+	12.7413i	−0.650201	+	1.12618i
$129$		0			0
$130$	2.85421	+	33.6576i	0.250331	+	2.95197i
$131$	6.50021			0.567926			0.283963	−	0.958835i	$-0.408351\pi$
$131$	6.50021			0.567926			0.283963	+	0.958835i	$0.408351\pi$
$132$		0			0
$133$	−1.80534	+	3.12694i	−0.156543	+	0.271140i
$134$	11.5105	+	19.9368i	0.994358	+	1.72228i
$135$		0			0
$136$	2.45160	+	4.24629i	0.210223	+	0.364116i
$137$	−7.62878	−	13.2134i	−0.651770	−	1.12890i	−0.982693	−	0.185242i	$-0.940693\pi$
$137$	−7.62878	−	13.2134i	−0.651770	−	1.12890i	0.330923	−	0.943658i	$-0.392640\pi$
$138$		0			0
$139$	8.74801	+	15.1520i	0.741997	+	1.28518i	0.951585	+	0.307386i	$0.0994544\pi$
$139$	8.74801	+	15.1520i	0.741997	+	1.28518i	−0.209588	+	0.977790i	$0.567212\pi$
$140$	6.17901	−	10.7024i	0.522222	−	0.904514i
$141$		0			0
$142$	−24.8592			−2.08613
$143$	−0.167428	−	1.97435i	−0.0140010	−	0.165103i
$144$		0			0
$145$	−7.59367	+	13.1526i	−0.630620	+	1.09227i
$146$	5.44591	−	9.43260i	0.450707	−	0.780647i
$147$		0			0
$148$	−0.965046			−0.0793263
$149$	2.27743	+	3.94463i	0.186574	+	0.323156i	0.944106	−	0.329642i	$-0.106928\pi$
$149$	2.27743	+	3.94463i	0.186574	+	0.323156i	−0.757531	+	0.652799i	$0.773595\pi$
$150$		0			0
$151$	−6.32912			−0.515057			−0.257528	−	0.966271i	$-0.582908\pi$
$151$	−6.32912			−0.515057			−0.257528	+	0.966271i	$0.582908\pi$
$152$	−3.72105	−	6.44504i	−0.301817	−	0.522762i
$153$		0			0
$154$	−0.610004	+	1.05656i	−0.0491555	+	0.0851398i
$155$	−21.7265			−1.74511
$156$		0			0
$157$	16.3100			1.30168			0.650841	−	0.759214i	$-0.274416\pi$
$157$	16.3100			1.30168			0.650841	+	0.759214i	$0.274416\pi$
$158$	−15.5590	+	26.9490i	−1.23781	+	2.14395i
$159$		0			0
$160$	−14.6991	−	25.4597i	−1.16207	−	2.01276i
$161$	5.81890			0.458593
$162$		0			0
$163$	−11.7999	−	20.4381i	−0.924241	−	1.60083i	−0.792778	−	0.609511i	$-0.791366\pi$
$163$	−11.7999	−	20.4381i	−0.924241	−	1.60083i	−0.131463	−	0.991321i	$-0.541967\pi$
$164$	18.4245			1.43871
$165$		0			0
$166$	6.36209	−	11.0195i	0.493794	−	0.855276i
$167$	−8.91513	+	15.4415i	−0.689874	+	1.19490i	0.282005	+	0.959413i	$0.409001\pi$
$167$	−8.91513	+	15.4415i	−0.689874	+	1.19490i	−0.971878	+	0.235483i	$0.924333\pi$
$168$		0			0
$169$	4.51137	−	12.1921i	0.347028	−	0.937855i
$170$	−22.2865			−1.70929
$171$		0			0
$172$	−4.71479	+	8.16626i	−0.359499	+	0.622671i
$173$	−3.78568	−	6.55699i	−0.287820	−	0.498518i	0.685469	−	0.728101i	$-0.259597\pi$
$173$	−3.78568	−	6.55699i	−0.287820	−	0.498518i	−0.973289	+	0.229583i	$0.926264\pi$
$174$		0			0
$175$	6.40423	+	11.0925i	0.484115	+	0.838511i
$176$	0.352026	+	0.609727i	0.0265350	+	0.0459599i
$177$		0			0
$178$	8.28901	+	14.3570i	0.621288	+	1.07610i
$179$	−11.4017	+	19.7483i	−0.852201	+	1.47606i	0.0270166	+	0.999635i	$0.491399\pi$
$179$	−11.4017	+	19.7483i	−0.852201	+	1.47606i	−0.879218	+	0.476420i	$0.841934\pi$
$180$		0			0
$181$	13.9294			1.03536			0.517681	−	0.855574i	$-0.326795\pi$
$181$	13.9294			1.03536			0.517681	+	0.855574i	$0.326795\pi$
$182$	−6.56900	+	4.57360i	−0.486927	+	0.339018i
$183$		0			0
$184$	−5.99676	+	10.3867i	−0.442087	+	0.765717i
$185$	0.695338	−	1.20436i	0.0511222	−	0.0885463i
$186$		0			0
$187$	1.30732			0.0956006
$188$	12.0206	+	20.8203i	0.876692	+	1.51848i
$189$		0			0
$190$	33.8265			2.45403
$191$	−6.33591	−	10.9741i	−0.458450	−	0.794059i	0.540429	−	0.841390i	$-0.318262\pi$
$191$	−6.33591	−	10.9741i	−0.458450	−	0.794059i	−0.998879	+	0.0473305i	$0.984929\pi$
$192$		0			0
$193$	2.07746	−	3.59827i	0.149539	−	0.259009i	−0.781518	−	0.623882i	$-0.785554\pi$
$193$	2.07746	−	3.59827i	0.149539	−	0.259009i	0.931057	+	0.364873i	$0.118888\pi$
$194$	15.1864			1.09032
$195$		0			0
$196$	2.92843			0.209174
$197$	−3.42510	+	5.93245i	−0.244028	+	0.422669i	−0.961858	−	0.273549i	$-0.911802\pi$
$197$	−3.42510	+	5.93245i	−0.244028	+	0.422669i	0.717830	+	0.696219i	$0.245136\pi$
$198$		0			0
$199$	0.406794	+	0.704587i	0.0288368	+	0.0499469i	0.880084	−	0.474819i	$-0.157486\pi$
$199$	0.406794	+	0.704587i	0.0288368	+	0.0499469i	−0.851247	+	0.524766i	$0.824153\pi$
$200$	−26.3999			−1.86676
$201$		0			0
$202$	−6.39265	−	11.0724i	−0.449785	−	0.779051i
$203$	−3.59889			−0.252593
$204$		0			0
$205$	−13.2752	+	22.9934i	−0.927183	+	1.60593i
$206$	0.634674	−	1.09929i	0.0442198	−	0.0765910i
$207$		0			0
$208$	0.390315	+	4.60270i	0.0270635	+	0.319140i
$209$	−1.98426			−0.137254
$210$		0			0
$211$	6.98670	−	12.1013i	0.480984	−	0.833089i	−0.518778	−	0.854909i	$-0.673613\pi$
$211$	6.98670	−	12.1013i	0.480984	−	0.833089i	0.999762	+	0.0218200i	$0.00694608\pi$
$212$	3.89286	+	6.74264i	0.267363	+	0.463086i
$213$		0			0
$214$	−4.51945	−	7.82792i	−0.308943	−	0.535106i
$215$	−6.79423	−	11.7679i	−0.463363	−	0.802568i
$216$		0			0
$217$	−2.57422	−	4.45868i	−0.174750	−	0.302675i
$218$	16.9927	−	29.4322i	1.15089	−	1.99340i
$219$		0			0
$220$	6.79136			0.457874
$221$	7.76387	+	3.64560i	0.522255	+	0.245229i
$222$		0			0
$223$	6.76700	−	11.7208i	0.453152	−	0.784882i	−0.545428	−	0.838158i	$-0.683633\pi$
$223$	6.76700	−	11.7208i	0.453152	−	0.784882i	0.998580	+	0.0532758i	$0.0169662\pi$
$224$	3.48320	−	6.03308i	0.232731	−	0.403102i
$225$		0			0
$226$	27.0328			1.79820
$227$	−2.68376	−	4.64840i	−0.178127	−	0.308525i	0.763112	−	0.646266i	$-0.223671\pi$
$227$	−2.68376	−	4.64840i	−0.178127	−	0.308525i	−0.941239	+	0.337741i	$0.890337\pi$
$228$		0			0
$229$	3.09910			0.204794			0.102397	−	0.994744i	$-0.467349\pi$
$229$	3.09910			0.204794			0.102397	+	0.994744i	$0.467349\pi$
$230$	−27.2570	−	47.2106i	−1.79728	−	3.11297i
$231$		0			0
$232$	3.70890	−	6.42399i	0.243501	−	0.421756i
$233$	20.3712			1.33456			0.667280	−	0.744807i	$-0.267459\pi$
$233$	20.3712			1.33456			0.667280	+	0.744807i	$0.267459\pi$
$234$		0			0
$235$	−34.6445			−2.25996
$236$	−2.64662	+	4.58407i	−0.172280	+	0.298398i
$237$		0			0
$238$	−2.64057	−	4.57360i	−0.171163	−	0.296463i
$239$	1.29157			0.0835449			0.0417725	−	0.999127i	$-0.486700\pi$
$239$	1.29157			0.0835449			0.0417725	+	0.999127i	$0.486700\pi$
$240$		0			0
$241$	−1.06635	−	1.84697i	−0.0686896	−	0.118974i	0.829635	−	0.558306i	$-0.188548\pi$
$241$	−1.06635	−	1.84697i	−0.0686896	−	0.118974i	−0.898325	+	0.439332i	$0.855215\pi$
$242$	23.7496			1.52668
$243$		0			0
$244$	−0.892184	+	1.54531i	−0.0571162	+	0.0989282i
$245$	−2.11000	+	3.65463i	−0.134803	+	0.233486i
$246$		0			0
$247$	−11.7841	−	5.53331i	−0.749801	−	0.352076i
$248$	10.6116			0.673839
$249$		0			0
$250$	36.5766	−	63.3525i	2.31331	−	4.00677i
$251$	−15.3856	−	26.6486i	−0.971128	−	1.68204i	−0.692164	−	0.721741i	$-0.743342\pi$
$251$	−15.3856	−	26.6486i	−0.971128	−	1.68204i	−0.278964	−	0.960302i	$-0.589991\pi$
$252$		0			0
$253$	1.59889	+	2.76936i	0.100521	+	0.174108i
$254$	2.17635	+	3.76955i	0.136557	+	0.236523i
$255$		0			0
$256$	3.42761	+	5.93679i	0.214225	+	0.371049i
$257$	−0.736805	+	1.27618i	−0.0459607	+	0.0796062i	−0.888091	−	0.459669i	$-0.847968\pi$
$257$	−0.736805	+	1.27618i	−0.0459607	+	0.0796062i	0.842130	+	0.539275i	$0.181302\pi$
$258$		0			0
$259$	0.329543			0.0204768
$260$	40.3324	+	18.9385i	2.50131	+	1.17451i
$261$		0			0
$262$	7.21526	−	12.4972i	0.445760	−	0.772079i
$263$	3.33847	−	5.78240i	0.205859	−	0.356558i	−0.744547	−	0.667570i	$-0.767335\pi$
$263$	3.33847	−	5.78240i	0.205859	−	0.356558i	0.950406	+	0.311012i	$0.100668\pi$
$264$		0			0
$265$	−11.2196			−0.689214
$266$	4.00787	+	6.94184i	0.245738	+	0.425631i
$267$		0			0
$268$	30.3673			1.85498
$269$	3.78786	+	6.56077i	0.230950	+	0.400017i	0.958088	−	0.286474i	$-0.0924832\pi$
$269$	3.78786	+	6.56077i	0.230950	+	0.400017i	−0.727138	+	0.686492i	$0.759150\pi$
$270$		0			0
$271$	−10.2840	+	17.8124i	−0.624709	+	1.08203i	0.363888	+	0.931443i	$0.381449\pi$
$271$	−10.2840	+	17.8124i	−0.624709	+	1.08203i	−0.988597	+	0.150585i	$0.951884\pi$
$272$	−3.04768			−0.184793
$273$		0			0
$274$	−33.8719			−2.04628
$275$	−3.51945	+	6.09587i	−0.212231	+	0.367595i
$276$		0			0
$277$	−2.85271	−	4.94103i	−0.171402	−	0.296878i	0.767508	−	0.641039i	$-0.221497\pi$
$277$	−2.85271	−	4.94103i	−0.171402	−	0.296878i	−0.938910	+	0.344162i	$0.888163\pi$
$278$	38.8413			2.32955
$279$		0			0
$280$	−4.34900	−	7.53268i	−0.259902	−	0.450164i
$281$	6.37315			0.380190			0.190095	−	0.981766i	$-0.439120\pi$
$281$	6.37315			0.380190			0.190095	+	0.981766i	$0.439120\pi$
$282$		0			0
$283$	−13.5097	+	23.3995i	−0.803068	+	1.39096i	0.114519	+	0.993421i	$0.463467\pi$
$283$	−13.5097	+	23.3995i	−0.803068	+	1.39096i	−0.917587	+	0.397534i	$0.869866\pi$
$284$	−16.3960	+	28.3987i	−0.972923	+	1.68515i
$285$		0			0
$286$	−3.98169	−	1.86964i	−0.235443	−	0.110554i
$287$	−6.29157			−0.371380
$288$		0			0
$289$	5.67046	−	9.82152i	0.333556	−	0.577736i
$290$	16.8580	+	29.1989i	0.989937	+	1.71462i
$291$		0			0
$292$	−7.18376	−	12.4426i	−0.420398	−	0.728150i
$293$	−2.43736	−	4.22163i	−0.142392	−	0.246630i	0.786005	−	0.618220i	$-0.212146\pi$
$293$	−2.43736	−	4.22163i	−0.142392	−	0.246630i	−0.928397	+	0.371590i	$0.878813\pi$
$294$		0			0
$295$	−3.81389	−	6.60586i	−0.222053	−	0.384608i
$296$	−0.339616	+	0.588232i	−0.0197398	+	0.0341903i
$297$		0			0
$298$	10.1118			0.585763
$299$	1.77280	+	20.9053i	0.102524	+	1.20899i
$300$		0			0
$301$	1.61000	−	2.78861i	0.0927991	−	0.160733i
$302$	−7.02535	+	12.1683i	−0.404263	+	0.700205i
$303$		0			0
$304$	4.62579			0.265307
$305$	−1.28568	−	2.22686i	−0.0736177	−	0.127510i
$306$		0			0
$307$	16.1760			0.923212			0.461606	−	0.887085i	$-0.347273\pi$
$307$	16.1760			0.923212			0.461606	+	0.887085i	$0.347273\pi$
$308$	0.804662	+	1.39372i	0.0458499	+	0.0794143i
$309$		0			0
$310$	−24.1165	+	41.7709i	−1.36972	+	2.37243i
$311$	1.30806			0.0741735			0.0370868	−	0.999312i	$-0.488192\pi$
$311$	1.30806			0.0741735			0.0370868	+	0.999312i	$0.488192\pi$
$312$		0			0
$313$	13.1978			0.745983			0.372991	−	0.927835i	$-0.378332\pi$
$313$	13.1978			0.745983			0.372991	+	0.927835i	$0.378332\pi$
$314$	18.1042	−	31.3574i	1.02168	−	1.76960i
$315$		0			0
$316$	20.5241	+	35.5488i	1.15457	+	1.99977i
$317$	8.07552			0.453566			0.226783	−	0.973945i	$-0.427179\pi$
$317$	8.07552			0.453566			0.226783	+	0.973945i	$0.427179\pi$
$318$		0			0
$319$	−0.988887	−	1.71280i	−0.0553671	−	0.0958986i
$320$	−54.4516			−3.04394
$321$		0			0
$322$	6.45900	−	11.1873i	0.359946	−	0.623445i
$323$	4.29470	−	7.43863i	0.238963	−	0.413897i
$324$		0			0
$325$	−37.9003	+	26.3877i	−2.10233	+	1.46372i
$326$	−52.3918			−2.90171
$327$		0			0
$328$	6.48388	−	11.2304i	0.358012	−	0.620096i
$329$	−4.10479	−	7.10970i	−0.226304	−	0.391970i
$330$		0			0
$331$	7.47256	+	12.9429i	0.410729	+	0.711403i	0.994970	−	0.100177i	$-0.0319409\pi$
$331$	7.47256	+	12.9429i	0.410729	+	0.711403i	−0.584241	+	0.811580i	$0.698608\pi$
$332$	−8.39229	−	14.5359i	−0.460587	−	0.797760i
$333$		0			0
$334$	19.7917	+	34.2802i	1.08295	+	1.87573i
$335$	−21.8803	+	37.8979i	−1.19545	+	2.07058i
$336$		0			0
$337$	−17.1695			−0.935282			−0.467641	−	0.883918i	$-0.654896\pi$
$337$	−17.1695			−0.935282			−0.467641	+	0.883918i	$0.654896\pi$
$338$	−18.4327	−	22.2068i	−1.00261	−	1.20789i
$339$		0			0
$340$	−14.6991	+	25.4597i	−0.797173	+	1.38074i
$341$	1.41467	−	2.45027i	0.0766085	−	0.132690i
$342$		0			0
$343$	−1.00000			−0.0539949
$344$	3.31843	+	5.74769i	0.178918	+	0.309895i
$345$		0			0
$346$	−16.8085			−0.903629
$347$	−1.96922	−	3.41079i	−0.105713	−	0.183101i	0.808316	−	0.588749i	$-0.200379\pi$
$347$	−1.96922	−	3.41079i	−0.105713	−	0.183101i	−0.914029	+	0.405648i	$0.867046\pi$
$348$		0			0
$349$	−8.58883	+	14.8763i	−0.459750	+	0.796310i	−0.998947	−	0.0458695i	$-0.985394\pi$
$349$	−8.58883	+	14.8763i	−0.459750	+	0.796310i	0.539198	+	0.842179i	$0.318728\pi$
$350$	28.4349			1.51991
$351$		0			0
$352$	3.82840			0.204054
$353$	−9.09821	+	15.7586i	−0.484249	+	0.838744i	−0.999836	−	0.0180932i	$-0.994240\pi$
$353$	−9.09821	+	15.7586i	−0.484249	+	0.838744i	0.515587	+	0.856837i	$0.327574\pi$
$354$		0			0
$355$	−23.6274	−	40.9238i	−1.25401	−	2.17201i
$356$	21.8682			1.15901
$357$		0			0
$358$	25.3118	+	43.8413i	1.33777	+	2.31709i
$359$	−16.3126			−0.860948			−0.430474	−	0.902603i	$-0.641654\pi$
$359$	−16.3126			−0.860948			−0.430474	+	0.902603i	$0.641654\pi$
$360$		0			0
$361$	2.98148	−	5.16408i	0.156920	−	0.271794i
$362$	15.4617	−	26.7804i	0.812647	−	1.40755i
$363$		0			0
$364$	0.892184	+	10.5209i	0.0467631	+	0.551443i
$365$	20.7042			1.08371
$366$		0			0
$367$	18.0982	−	31.3469i	0.944716	−	1.63630i	0.188398	−	0.982093i	$-0.439671\pi$
$367$	18.0982	−	31.3469i	0.944716	−	1.63630i	0.756319	−	0.654203i	$-0.226996\pi$
$368$	−3.72741	−	6.45607i	−0.194305	−	0.336546i
$369$		0			0
$370$	−1.54366	−	2.67369i	−0.0802508	−	0.138998i
$371$	−1.32933	−	2.30247i	−0.0690155	−	0.119538i
$372$		0			0
$373$	−4.89892	−	8.48518i	−0.253657	−	0.439346i	0.710873	−	0.703320i	$-0.248300\pi$
$373$	−4.89892	−	8.48518i	−0.253657	−	0.439346i	−0.964530	+	0.263974i	$0.914967\pi$
$374$	1.45113	−	2.51343i	0.0750361	−	0.129966i
$375$		0			0
$376$	16.9210			0.872635
$377$	−1.09645	−	12.9296i	−0.0564699	−	0.665907i
$378$		0			0
$379$	−6.53275	+	11.3151i	−0.335565	+	0.581216i	−0.983593	−	0.180401i	$-0.942261\pi$
$379$	−6.53275	+	11.3151i	−0.335565	+	0.581216i	0.648028	+	0.761616i	$0.275594\pi$
$380$	22.3104	−	38.6428i	1.14450	−	1.98233i
$381$		0			0
$382$	−28.1315			−1.43933
$383$	13.8965	+	24.0694i	0.710076	+	1.22989i	0.964828	+	0.262881i	$0.0846726\pi$
$383$	13.8965	+	24.0694i	0.710076	+	1.22989i	−0.254753	+	0.967006i	$0.581994\pi$
$384$		0			0
$385$	−2.31911			−0.118193
$386$	−4.61198	−	7.98818i	−0.234744	−	0.406588i
$387$		0			0
$388$	10.0163	−	17.3487i	0.508499	−	0.880747i
$389$	−13.7047			−0.694854			−0.347427	−	0.937707i	$-0.612945\pi$
$389$	−13.7047			−0.694854			−0.347427	+	0.937707i	$0.612945\pi$
$390$		0			0
$391$	−13.8425			−0.700044
$392$	1.03057	−	1.78499i	0.0520514	−	0.0901557i
$393$		0			0
$394$	7.60375	+	13.1701i	0.383071	+	0.663499i
$395$	−59.1523			−2.97627
$396$		0			0
$397$	−3.95597	−	6.85194i	−0.198545	−	0.343889i	0.749512	−	0.661991i	$-0.230288\pi$
$397$	−3.95597	−	6.85194i	−0.198545	−	0.343889i	−0.948057	+	0.318101i	$0.896955\pi$
$398$	1.80617			0.0905351
$399$		0			0
$400$	8.20472	−	14.2110i	0.410236	−	0.710549i
$401$	−8.27212	+	14.3277i	−0.413090	+	0.715493i	−0.995226	−	0.0975987i	$-0.968884\pi$
$401$	−8.27212	+	14.3277i	−0.413090	+	0.715493i	0.582136	+	0.813092i	$0.302217\pi$
$402$		0			0
$403$	15.2342	−	10.6067i	0.758872	−	0.528357i
$404$	−16.8652			−0.839076
$405$		0			0
$406$	−3.99478	+	6.91917i	−0.198258	+	0.343393i
$407$	0.0905505	+	0.156838i	0.00448842	+	0.00777417i
$408$		0			0
$409$	−12.8909	−	22.3278i	−0.637416	−	1.10404i	−0.985998	−	0.166758i	$-0.946670\pi$
$409$	−12.8909	−	22.3278i	−0.637416	−	1.10404i	0.348582	−	0.937278i	$-0.386663\pi$
$410$	29.4711	+	51.0455i	1.45548	+	2.52096i
$411$		0			0
$412$	−0.837205	−	1.45008i	−0.0412461	−	0.0714404i
$413$	0.903765	−	1.56537i	0.0444713	−	0.0770266i
$414$		0			0
$415$	24.1873			1.18731
$416$	22.7360	+	10.6759i	1.11472	+	0.523429i
$417$		0			0
$418$	−2.20253	+	3.81490i	−0.107729	+	0.186593i
$419$	11.8436	−	20.5137i	0.578596	−	1.00216i	−0.417044	−	0.908886i	$-0.636934\pi$
$419$	11.8436	−	20.5137i	0.578596	−	1.00216i	0.995641	−	0.0932720i	$-0.0297326\pi$
$420$		0			0
$421$	−20.8246			−1.01493			−0.507465	−	0.861672i	$-0.669417\pi$
$421$	−20.8246			−1.01493			−0.507465	+	0.861672i	$0.669417\pi$
$422$	−15.5105	−	26.8650i	−0.755041	−	1.30777i
$423$		0			0
$424$	5.47986			0.266125
$425$	−15.2349	−	26.3877i	−0.739002	−	1.27999i
$426$		0			0
$427$	0.304662	−	0.527691i	0.0147436	−	0.0255367i
$428$	−11.9233			−0.576335
$429$		0			0
$430$	−30.1665			−1.45476
$431$	9.97521	−	17.2776i	0.480489	−	0.832232i	−0.519260	−	0.854616i	$-0.673792\pi$
$431$	9.97521	−	17.2776i	0.480489	−	0.832232i	0.999749	+	0.0223845i	$0.00712581\pi$
$432$		0			0
$433$	−0.00834083	−	0.0144467i	−0.000400835	−	0.000694266i	0.865825	−	0.500347i	$-0.166794\pi$
$433$	−0.00834083	−	0.0144467i	−0.000400835	−	0.000694266i	−0.866226	+	0.499653i	$0.833461\pi$
$434$	−11.4296			−0.548638
$435$		0			0
$436$	−22.4152	−	38.8243i	−1.07349	−	1.85935i
$437$	21.0102			1.00505
$438$		0			0
$439$	−6.74801	+	11.6879i	−0.322065	+	0.557833i	−0.980914	−	0.194442i	$-0.937710\pi$
$439$	−6.74801	+	11.6879i	−0.322065	+	0.557833i	0.658849	+	0.752275i	$0.271044\pi$
$440$	2.39000	−	4.13959i	0.113939	−	0.197347i
$441$		0			0
$442$	15.6269	−	10.8801i	0.743296	−	0.517512i
$443$	15.0110			0.713196			0.356598	−	0.934258i	$-0.383937\pi$
$443$	15.0110			0.713196			0.356598	+	0.934258i	$0.383937\pi$
$444$		0			0
$445$	−15.7566	+	27.2912i	−0.746933	+	1.29373i
$446$	−15.0228	−	26.0202i	−0.711350	−	1.23209i
$447$		0			0
$448$	−6.45160	−	11.1745i	−0.304809	−	0.527945i
$449$	−11.8918	−	20.5972i	−0.561210	−	0.972044i	−0.997391	−	0.0721852i	$-0.977003\pi$
$449$	−11.8918	−	20.5972i	−0.561210	−	0.972044i	0.436181	−	0.899859i	$-0.356331\pi$
$450$		0			0
$451$	−1.72877	−	2.99432i	−0.0814046	−	0.140997i
$452$	17.8297	−	30.8819i	0.838636	−	1.45256i
$453$		0			0
$454$	−11.9159			−0.559242
$455$	−13.7727	−	6.46709i	−0.645673	−	0.303182i
$456$		0			0
$457$	−9.06567	+	15.7022i	−0.424074	+	0.734518i	−0.996333	−	0.0855548i	$-0.972734\pi$
$457$	−9.06567	+	15.7022i	−0.424074	+	0.734518i	0.572259	+	0.820073i	$0.306067\pi$
$458$	3.44002	−	5.95828i	0.160741	−	0.278412i
$459$		0			0
$460$	−71.9101			−3.35282
$461$	−3.03980	−	5.26508i	−0.141577	−	0.245219i	0.786513	−	0.617573i	$-0.211884\pi$
$461$	−3.03980	−	5.26508i	−0.141577	−	0.245219i	−0.928091	+	0.372354i	$0.878551\pi$
$462$		0			0
$463$	5.19289			0.241334			0.120667	−	0.992693i	$-0.461497\pi$
$463$	5.19289			0.241334			0.120667	+	0.992693i	$0.461497\pi$
$464$	2.30534	+	3.99297i	0.107023	+	0.185369i
$465$		0			0
$466$	22.6121	−	39.1653i	1.04748	−	1.81430i
$467$	8.69968			0.402573			0.201287	−	0.979532i	$-0.435488\pi$
$467$	8.69968			0.402573			0.201287	+	0.979532i	$0.435488\pi$
$468$		0			0
$469$	−10.3698			−0.478833
$470$	−38.4555	+	66.6069i	−1.77382	+	3.07235i
$471$		0			0
$472$	1.86278	+	3.22643i	0.0857413	+	0.148508i
$473$	1.76956			0.0813644
$474$		0			0
$475$	23.1237	+	40.0513i	1.06099	+	1.83768i
$476$	−6.96640			−0.319305
$477$		0			0
$478$	1.43365	−	2.48316i	0.0655737	−	0.113577i
$479$	12.1094	−	20.9741i	0.553294	−	0.958332i	−0.444741	−	0.895659i	$-0.646704\pi$
$479$	12.1094	−	20.9741i	0.553294	−	0.958332i	0.998034	−	0.0626730i	$-0.0199625\pi$
$480$		0			0
$481$	0.100399	+	1.18394i	0.00457782	+	0.0539828i
$482$	−4.73461			−0.215655
$483$		0			0
$484$	15.6642	−	27.1312i	0.712009	−	1.23323i
$485$	14.4339	+	25.0003i	0.655410	+	1.13520i
$486$		0			0
$487$	−0.886967	−	1.53627i	−0.0401923	−	0.0696151i	0.845229	−	0.534404i	$-0.179464\pi$
$487$	−0.886967	−	1.53627i	−0.0401923	−	0.0696151i	−0.885422	+	0.464788i	$0.846130\pi$
$488$	0.627949	+	1.08764i	0.0284259	+	0.0492351i
$489$		0			0
$490$	4.68423	+	8.11332i	0.211612	+	0.366522i
$491$	−3.34483	+	5.79342i	−0.150950	+	0.261453i	−0.931577	−	0.363544i	$-0.881567\pi$
$491$	−3.34483	+	5.79342i	−0.150950	+	0.261453i	0.780627	+	0.624997i	$0.214900\pi$
$492$		0			0
$493$	8.56134			0.385584
$494$	−23.7186	+	16.5138i	−1.06715	+	0.742992i
$495$		0			0
$496$	−3.29794	+	5.71220i	−0.148082	+	0.256485i
$497$	5.59889	−	9.69756i	0.251145	−	0.434995i
$498$		0			0
$499$	24.6387			1.10298			0.551491	−	0.834181i	$-0.314059\pi$
$499$	24.6387			1.10298			0.551491	+	0.834181i	$0.314059\pi$
$500$	−48.2486	−	83.5690i	−2.15774	−	3.73732i
$501$		0			0
$502$	−68.3121			−3.04892
$503$	16.5726	+	28.7046i	0.738936	+	1.27987i	0.952975	+	0.303049i	$0.0980046\pi$
$503$	16.5726	+	28.7046i	0.738936	+	1.27987i	−0.214039	+	0.976825i	$0.568662\pi$
$504$		0			0
$505$	12.1518	−	21.0475i	0.540747	−	0.936601i
$506$	7.09910			0.315594
$507$		0			0
$508$	5.74170			0.254747
$509$	−13.8290	+	23.9526i	−0.612961	+	1.06168i	0.377778	+	0.925896i	$0.376688\pi$
$509$	−13.8290	+	23.9526i	−0.612961	+	1.06168i	−0.990739	+	0.135783i	$0.956645\pi$
$510$		0			0
$511$	2.45310	+	4.24890i	0.108519	+	0.187960i
$512$	−14.2061			−0.627828
$513$		0			0
$514$	1.63571	+	2.83314i	0.0721482	+	0.124964i
$515$	2.41290			0.106325
$516$		0			0
$517$	2.25579	−	3.90714i	0.0992096	−	0.171836i
$518$	0.365794	−	0.633574i	0.0160721	−	0.0278377i
$519$		0			0
$520$	25.7374	−	17.9194i	1.12866	−	0.785817i
$521$	−1.42217			−0.0623062			−0.0311531	−	0.999515i	$-0.509918\pi$
$521$	−1.42217			−0.0623062			−0.0311531	+	0.999515i	$0.509918\pi$
$522$		0			0
$523$	1.68089	−	2.91139i	0.0735002	−	0.127306i	−0.826933	−	0.562301i	$-0.809916\pi$
$523$	1.68089	−	2.91139i	0.0735002	−	0.127306i	0.900433	+	0.434995i	$0.143250\pi$
$524$	−9.51772	−	16.4852i	−0.415784	−	0.720158i
$525$		0			0
$526$	−7.41143	−	12.8370i	−0.323154	−	0.559718i
$527$	6.12377	+	10.6067i	0.266756	+	0.462034i
$528$		0			0
$529$	−5.42979	−	9.40468i	−0.236078	−	0.408899i
$530$	−12.4538	+	21.5706i	−0.540958	+	0.936966i
$531$		0			0
$532$	10.5736			0.458426
$533$	−1.91681	−	22.6035i	−0.0830260	−	0.979065i
$534$		0			0
$535$	8.59102	−	14.8801i	0.371422	−	0.643322i
$536$	10.6868	−	18.5100i	0.461598	−	0.799512i
$537$		0			0
$538$	16.8182			0.725083
$539$	−0.274776	−	0.475925i	−0.0118354	−	0.0204996i
$540$		0			0
$541$	7.76289			0.333753			0.166876	−	0.985978i	$-0.446632\pi$
$541$	7.76289			0.333753			0.166876	+	0.985978i	$0.446632\pi$
$542$	22.8306	+	39.5437i	0.980657	+	1.69855i
$543$		0			0
$544$	−8.28613	+	14.3520i	−0.355265	+	0.615337i
$545$	64.6027			2.76728
$546$		0			0
$547$	−6.19247			−0.264771			−0.132385	−	0.991198i	$-0.542264\pi$
$547$	−6.19247			−0.264771			−0.132385	+	0.991198i	$0.542264\pi$
$548$	−22.3404	+	38.6947i	−0.954334	+	1.65295i
$549$		0			0
$550$	7.81321	+	13.5329i	0.333157	+	0.577044i
$551$	−12.9945			−0.553582
$552$		0			0
$553$	−7.00855	−	12.1392i	−0.298034	−	0.516210i
$554$	−12.6661			−0.538129
$555$		0			0
$556$	25.6180	−	44.3717i	1.08644	−	1.88178i
$557$	14.7729	−	25.5874i	0.625948	−	1.08417i	−0.362409	−	0.932019i	$-0.618046\pi$
$557$	14.7729	−	25.5874i	0.625948	−	1.08417i	0.988357	−	0.152154i	$-0.0486210\pi$
$558$		0			0
$559$	10.5090	+	4.93461i	0.444484	+	0.208712i
$560$	5.40642			0.228463
$561$		0			0
$562$	7.07422	−	12.2529i	0.298408	−	0.516858i
$563$	3.23368	+	5.60090i	0.136283	+	0.236050i	0.926087	−	0.377310i	$-0.123151\pi$
$563$	3.23368	+	5.60090i	0.136283	+	0.236050i	−0.789804	+	0.613360i	$0.789818\pi$
$564$		0			0
$565$	25.6933	+	44.5022i	1.08093	+	1.87222i
$566$	29.9916	+	51.9470i	1.26064	+	2.18350i
$567$		0			0
$568$	11.5401	+	19.9880i	0.484210	+	0.838676i
$569$	10.8478	−	18.7889i	0.454763	−	0.787673i	−0.543911	−	0.839143i	$-0.683057\pi$
$569$	10.8478	−	18.7889i	0.454763	−	0.787673i	0.998675	+	0.0514697i	$0.0163906\pi$
$570$		0			0
$571$	−16.6418			−0.696436			−0.348218	−	0.937414i	$-0.613213\pi$
$571$	−16.6418			−0.696436			−0.348218	+	0.937414i	$0.613213\pi$
$572$	−4.76199	+	3.31549i	−0.199109	+	0.138628i
$573$		0			0
$574$	−6.98367	+	12.0961i	−0.291493	+	0.504880i
$575$	37.2656	−	64.5459i	1.55408	−	2.69175i
$576$		0			0
$577$	−2.64240			−0.110005			−0.0550024	−	0.998486i	$-0.517517\pi$
$577$	−2.64240			−0.110005			−0.0550024	+	0.998486i	$0.517517\pi$
$578$	−12.5885	−	21.8038i	−0.523611	−	0.906921i
$579$		0			0
$580$	44.4752			1.84673
$581$	2.86579	+	4.96370i	0.118893	+	0.205929i
$582$		0			0
$583$	0.730536	−	1.26533i	0.0302557	−	0.0524044i
$584$	−10.1123			−0.418452
$585$		0			0
$586$	−10.8219			−0.447049
$587$	3.69407	−	6.39832i	0.152471	−	0.264087i	−0.779664	−	0.626198i	$-0.784610\pi$
$587$	3.69407	−	6.39832i	0.152471	−	0.264087i	0.932135	+	0.362110i	$0.117944\pi$
$588$		0			0
$589$	−9.29470	−	16.0989i	−0.382981	−	0.663343i
$590$	−16.9337			−0.697151
$591$		0			0
$592$	−0.211096	−	0.365628i	−0.00867597	−	0.0150272i
$593$	−46.9030			−1.92607			−0.963037	−	0.269370i	$-0.913185\pi$
$593$	−46.9030			−1.92607			−0.963037	+	0.269370i	$0.913185\pi$
$594$		0			0
$595$	5.01945	−	8.69395i	0.205778	−	0.356417i
$596$	6.66931	−	11.5516i	0.273186	−	0.473171i
$597$		0			0
$598$	42.1600	+	19.7966i	1.72405	+	0.809544i
$599$	−1.62290			−0.0663098			−0.0331549	−	0.999450i	$-0.510555\pi$
$599$	−1.62290			−0.0663098			−0.0331549	+	0.999450i	$0.510555\pi$
$600$		0			0
$601$	23.5174	−	40.7333i	0.959293	−	1.66154i	0.235070	−	0.971978i	$-0.424468\pi$
$601$	23.5174	−	40.7333i	0.959293	−	1.66154i	0.724223	−	0.689566i	$-0.242199\pi$
$602$	−3.57422	−	6.19073i	−0.145674	−	0.252315i
$603$		0			0
$604$	9.26721	+	16.0513i	0.377077	+	0.653117i
$605$	22.5728	+	39.0973i	0.917715	+	1.58953i
$606$		0			0
$607$	14.1935	+	24.5838i	0.576095	+	0.997825i	0.995922	+	0.0902211i	$0.0287574\pi$
$607$	14.1935	+	24.5838i	0.576095	+	0.997825i	−0.419827	+	0.907604i	$0.637909\pi$
$608$	12.5767	−	21.7836i	0.510054	−	0.883440i
$609$		0			0
$610$	−5.70843			−0.231127
$611$	24.2921	−	16.9131i	0.982755	−	0.684233i
$612$		0			0
$613$	23.7782	−	41.1851i	0.960393	−	1.66345i	0.238878	−	0.971050i	$-0.423220\pi$
$613$	23.7782	−	41.1851i	0.960393	−	1.66345i	0.721514	−	0.692399i	$-0.243446\pi$
$614$	17.9554	−	31.0997i	0.724621	−	1.25508i
$615$		0			0
$616$	1.13270			0.0456377
$617$	−8.24338	−	14.2780i	−0.331866	−	0.574809i	0.651012	−	0.759068i	$-0.274345\pi$
$617$	−8.24338	−	14.2780i	−0.331866	−	0.574809i	−0.982878	+	0.184259i	$0.941012\pi$
$618$		0			0
$619$	−31.9412			−1.28382			−0.641912	−	0.766778i	$-0.721859\pi$
$619$	−31.9412			−1.28382			−0.641912	+	0.766778i	$0.721859\pi$
$620$	31.8123	+	55.1005i	1.27761	+	2.21289i
$621$		0			0
$622$	1.45196	−	2.51486i	0.0582182	−	0.100837i
$623$	−7.46755			−0.299181
$624$		0			0
$625$	75.0145			3.00058
$626$	14.6496	−	25.3738i	0.585515	−	1.01414i
$627$		0			0
$628$	−23.8814	−	41.3639i	−0.952973	−	1.65060i
$629$	−0.783945			−0.0312579
$630$		0			0
$631$	−6.59577	−	11.4242i	−0.262573	−	0.454790i	0.704352	−	0.709851i	$-0.251238\pi$
$631$	−6.59577	−	11.4242i	−0.262573	−	0.454790i	−0.966925	+	0.255061i	$0.917905\pi$
$632$	28.8911			1.14923
$633$		0			0
$634$	8.96386	−	15.5259i	0.356000	−	0.616610i
$635$	−4.13702	+	7.16554i	−0.164173	+	0.284356i
$636$		0			0
$637$	−0.304662	−	3.59266i	−0.0120712	−	0.142346i
$638$	−4.39068			−0.173829
$639$		0			0
$640$	−31.0432	+	53.7684i	−1.22709	+	2.12538i
$641$	−23.5814	−	40.8441i	−0.931408	−	1.61325i	−0.780918	−	0.624634i	$-0.785248\pi$
$641$	−23.5814	−	40.8441i	−0.931408	−	1.61325i	−0.150490	−	0.988612i	$-0.548085\pi$
$642$		0			0
$643$	1.40679	+	2.43664i	0.0554785	+	0.0960916i	0.892431	−	0.451184i	$-0.148998\pi$
$643$	1.40679	+	2.43664i	0.0554785	+	0.0960916i	−0.836952	+	0.547276i	$0.815665\pi$
$644$	−8.52013	−	14.7573i	−0.335740	−	0.581519i
$645$		0			0
$646$	−9.53426	−	16.5138i	−0.375121	−	0.649728i
$647$	12.9891	−	22.4979i	0.510656	−	0.884482i	−0.489268	−	0.872134i	$-0.662736\pi$
$647$	12.9891	−	22.4979i	0.510656	−	0.884482i	0.999924	−	0.0123485i	$-0.00393074\pi$
$648$		0			0
$649$	0.993330			0.0389916
$650$	8.66304	+	102.157i	0.339792	+	4.00692i
$651$		0			0
$652$	−34.5553	+	59.8515i	−1.35329	+	2.34397i
$653$	−13.4213	+	23.2464i	−0.525216	+	0.909700i	0.474353	+	0.880335i	$0.342682\pi$
$653$	−13.4213	+	23.2464i	−0.525216	+	0.909700i	−0.999569	+	0.0293654i	$0.990651\pi$
$654$		0			0
$655$	27.4309			1.07182
$656$	4.03019	+	6.98050i	0.157353	+	0.272543i
$657$		0			0
$658$	−18.2253			−0.710497
$659$	7.78666	+	13.4869i	0.303325	+	0.525375i	0.976887	−	0.213756i	$-0.0685698\pi$
$659$	7.78666	+	13.4869i	0.303325	+	0.525375i	−0.673562	+	0.739131i	$0.735236\pi$
$660$		0			0
$661$	−16.6902	+	28.9083i	−0.649174	+	1.12440i	0.334146	+	0.942521i	$0.391552\pi$
$661$	−16.6902	+	28.9083i	−0.649174	+	1.12440i	−0.983320	+	0.181881i	$0.941781\pi$
$662$	33.1783			1.28951
$663$		0			0
$664$	−11.8136			−0.458455
$665$	−7.61856	+	13.1957i	−0.295435	+	0.511708i
$666$		0			0
$667$	10.4708	+	18.1359i	0.405431	+	0.702227i
$668$	52.2148			2.02025
$669$		0			0
$670$	48.5745	+	84.1335i	1.87660	+	3.25036i
$671$	0.334855			0.0129269
$672$		0			0
$673$	−0.427076	+	0.739717i	−0.0164626	+	0.0285140i	−0.874139	−	0.485675i	$-0.838574\pi$
$673$	−0.427076	+	0.739717i	−0.0164626	+	0.0285140i	0.857677	+	0.514189i	$0.171907\pi$
$674$	−19.0582	+	33.0098i	−0.734095	+	1.27149i
$675$		0			0
$676$	−37.5260	+	6.41062i	−1.44331	+	0.246562i
$677$	24.5449			0.943339			0.471669	−	0.881775i	$-0.343652\pi$
$677$	24.5449			0.943339			0.471669	+	0.881775i	$0.343652\pi$
$678$		0			0
$679$	−3.42035	+	5.92422i	−0.131261	+	0.227351i
$680$	10.3458	+	17.9194i	0.396742	+	0.687177i
$681$		0			0
$682$	−3.14057	−	5.43963i	−0.120259	−	0.208294i
$683$	−21.5186	−	37.2714i	−0.823387	−	1.42615i	−0.903146	−	0.429334i	$-0.858748\pi$
$683$	−21.5186	−	37.2714i	−0.823387	−	1.42615i	0.0797583	−	0.996814i	$-0.474585\pi$
$684$		0			0
$685$	−32.1935	−	55.7608i	−1.23005	−	2.13051i
$686$	−1.11000	+	1.92258i	−0.0423801	+	0.0734046i
$687$		0			0
$688$	−4.12528			−0.157275
$689$	7.86699	−	5.47731i	0.299708	−	0.208669i
$690$		0			0
$691$	12.9098	−	22.3604i	0.491110	−	0.850628i	−0.508837	−	0.860863i	$-0.669925\pi$
$691$	12.9098	−	22.3604i	0.491110	−	0.850628i	0.999948	+	0.0102348i	$0.00325788\pi$
$692$	−11.0861	+	19.2017i	−0.421431	+	0.729939i
$693$		0			0
$694$	−8.74338			−0.331894
$695$	36.9167	+	63.9416i	1.40033	+	2.42544i
$696$		0			0
$697$	14.9669			0.566913
$698$	19.0673	+	33.0255i	0.721707	+	1.25003i
$699$		0			0
$700$	18.7544	−	32.4835i	0.708849	−	1.22776i
$701$	−16.3178			−0.616313			−0.308156	−	0.951336i	$-0.599712\pi$
$701$	−16.3178			−0.616313			−0.308156	+	0.951336i	$0.599712\pi$
$702$		0			0
$703$	1.18988			0.0448770
$704$	3.54548	−	6.14096i	0.133625	−	0.231446i
$705$		0			0
$706$	20.1981	+	34.9841i	0.760166	+	1.31665i
$707$	5.75913			0.216594
$708$		0			0
$709$	11.1897	+	19.3811i	0.420238	+	0.727874i	0.995963	−	0.0897702i	$-0.0286133\pi$
$709$	11.1897	+	19.3811i	0.420238	+	0.727874i	−0.575725	+	0.817644i	$0.695280\pi$
$710$	−104.906			−3.93705
$711$		0			0
$712$	7.69581	−	13.3295i	0.288413	−	0.499545i
$713$	−14.9791	+	25.9446i	−0.560973	+	0.971634i
$714$		0			0
$715$	−0.706545	−	8.33177i	−0.0264233	−	0.311590i
$716$	66.7781			2.49561
$717$		0			0
$718$	−18.1071	+	31.3624i	−0.675750	+	1.17043i
$719$	−11.3723	−	19.6973i	−0.424113	−	0.734586i	0.572224	−	0.820098i	$-0.306081\pi$
$719$	−11.3723	−	19.6973i	−0.424113	−	0.734586i	−0.996337	+	0.0855115i	$0.972748\pi$
$720$		0			0
$721$	0.285888	+	0.495173i	0.0106470	+	0.0184412i
$722$	−6.61892	−	11.4643i	−0.246331	−	0.426657i
$723$		0			0
$724$	−20.3956	−	35.3263i	−0.757997	−	1.31289i
$725$	−23.0481	+	39.9205i	−0.855986	+	1.48261i
$726$		0			0
$727$	18.7274			0.694561			0.347280	−	0.937761i	$-0.387105\pi$
$727$	18.7274			0.694561			0.347280	+	0.937761i	$0.387105\pi$
$728$	6.72684	+	3.15865i	0.249313	+	0.117067i
$729$		0			0
$730$	22.9818	−	39.8056i	0.850594	−	1.47327i
$731$	−3.83001	+	6.63377i	−0.141658	+	0.245359i
$732$		0			0
$733$	−1.69268			−0.0625206			−0.0312603	−	0.999511i	$-0.509952\pi$
$733$	−1.69268			−0.0625206			−0.0312603	+	0.999511i	$0.509952\pi$
$734$	−40.1781	−	69.5904i	−1.48300	−	2.56863i
$735$		0			0
$736$	−40.5368			−1.49421
$737$	−2.84937	−	4.93525i	−0.104958	−	0.181792i
$738$		0			0
$739$	−23.4581	+	40.6305i	−0.862919	+	1.49462i	0.00618065	+	0.999981i	$0.498033\pi$
$739$	−23.4581	+	40.6305i	−0.862919	+	1.49462i	−0.869099	+	0.494638i	$0.835301\pi$
$740$	−4.07250			−0.149708
$741$		0			0
$742$	−5.90226			−0.216679
$743$	6.44831	−	11.1688i	0.236566	−	0.409744i	−0.723161	−	0.690680i	$-0.757312\pi$
$743$	6.44831	−	11.1688i	0.236566	−	0.409744i	0.959727	+	0.280936i	$0.0906449\pi$
$744$		0			0
$745$	9.61078	+	16.6464i	0.352112	+	0.609875i
$746$	−21.7513			−0.796371
$747$		0			0
$748$	−1.91420	−	3.31549i	−0.0699900	−	0.121226i
$749$	4.07157			0.148772
$750$		0			0
$751$	22.8166	−	39.5196i	0.832591	−	1.44209i	−0.0633855	−	0.997989i	$-0.520190\pi$
$751$	22.8166	−	39.5196i	0.832591	−	1.44209i	0.895977	−	0.444101i	$-0.146477\pi$
$752$	−5.25881	+	9.10852i	−0.191769	+	0.332154i
$753$		0			0
$754$	−26.0753	−	12.2439i	−0.949605	−	0.445896i
$755$	−26.7089			−0.972038
$756$		0			0
$757$	19.0782	−	33.0445i	0.693410	−	1.20102i	−0.277303	−	0.960782i	$-0.589441\pi$
$757$	19.0782	−	33.0445i	0.693410	−	1.20102i	0.970714	−	0.240239i	$-0.0772260\pi$
$758$	14.5028	+	25.1195i	0.526764	+	0.912382i
$759$		0			0
$760$	−15.7028	−	27.1981i	−0.569602	−	0.986580i
$761$	21.3672	+	37.0092i	0.774562	+	1.34158i	0.935040	+	0.354542i	$0.115363\pi$
$761$	21.3672	+	37.0092i	0.774562	+	1.34158i	−0.160478	+	0.987039i	$0.551304\pi$
$762$		0			0
$763$	7.65434	+	13.2577i	0.277106	+	0.479961i
$764$	−18.5543	+	32.1370i	−0.671271	+	1.16267i
$765$		0			0
$766$	61.7005			2.22933
$767$	5.89917	+	2.77001i	0.213007	+	0.100019i
$768$		0			0
$769$	−10.8088	+	18.7215i	−0.389777	+	0.675113i	−0.992419	−	0.122898i	$-0.960781\pi$
$769$	−10.8088	+	18.7215i	−0.389777	+	0.675113i	0.602643	+	0.798011i	$0.294114\pi$
$770$	−2.57422	+	4.45868i	−0.0927685	+	0.160680i
$771$		0			0
$772$	−12.1674			−0.437915
$773$	5.00056	+	8.66123i	0.179858	+	0.311523i	0.941832	−	0.336085i	$-0.109103\pi$
$773$	5.00056	+	8.66123i	0.179858	+	0.311523i	−0.761974	+	0.647608i	$0.775770\pi$
$774$		0			0
$775$	−65.9436			−2.36877
$776$	−7.04980	−	12.2106i	−0.253073	−	0.438335i
$777$		0			0
$778$	−15.2122	+	26.3484i	−0.545385	+	0.944634i
$779$	−22.7169			−0.813917
$780$		0			0
$781$	6.15375			0.220199
$782$	−15.3652	+	26.6133i	−0.549459	+	0.951691i
$783$		0			0
$784$	0.640570	+	1.10950i	0.0228775	+	0.0396250i
$785$	68.8285			2.45659
$786$		0			0
$787$	−20.8939	−	36.1893i	−0.744787	−	1.29001i	−0.950294	−	0.311353i	$-0.899218\pi$
$787$	−20.8939	−	36.1893i	−0.744787	−	1.29001i	0.205507	−	0.978656i	$-0.434116\pi$
$788$	20.0604			0.714621
$789$		0			0
$790$	−65.6593	+	113.725i	−2.33605	+	4.04616i
$791$	−6.08846	+	10.5455i	−0.216481	+	0.374955i
$792$		0			0
$793$	1.98863	+	0.933780i	0.0706183	+	0.0331595i
$794$	−17.5646			−0.623343
$795$		0			0
$796$	1.19127	−	2.06334i	0.0422234	−	0.0731331i
$797$	−11.3856	−	19.7204i	−0.403297	−	0.698531i	0.590825	−	0.806800i	$-0.298803\pi$
$797$	−11.3856	−	19.7204i	−0.403297	−	0.698531i	−0.994122	+	0.108269i	$0.965469\pi$
$798$		0			0
$799$	9.76481	+	16.9131i	0.345454	+	0.598344i
$800$	−44.6145	−	77.2745i	−1.57736	−	2.73207i
$801$		0			0
$802$	18.3642	+	31.8077i	0.648461	+	1.12317i
$803$	−1.34811	+	2.33499i	−0.0475736	+	0.0824000i
$804$		0			0
$805$	24.5558			0.865478
$806$	−3.48216	−	41.0626i	−0.122654	−	1.44637i
$807$		0			0
$808$	−5.93516	+	10.2800i	−0.208798	+	0.361649i
$809$	−18.7851	+	32.5367i	−0.660449	+	1.14393i	0.320049	+	0.947401i	$0.396301\pi$
$809$	−18.7851	+	32.5367i	−0.660449	+	1.14393i	−0.980498	+	0.196530i	$0.937033\pi$
$810$		0			0
$811$	11.5936			0.407106			0.203553	−	0.979064i	$-0.434751\pi$
$811$	11.5936			0.407106			0.203553	+	0.979064i	$0.434751\pi$
$812$	5.26956	+	9.12714i	0.184925	+	0.320300i
$813$		0			0
$814$	0.402045			0.0140917
$815$	−49.7957	−	86.2487i	−1.74427	−	3.02116i
$816$		0			0
$817$	5.81321	−	10.0688i	0.203379	−	0.352262i
$818$	−57.2359			−2.00121
$819$		0			0
$820$	77.7514			2.71520
$821$	15.5121	−	26.8678i	0.541378	−	0.937693i	−0.457448	−	0.889237i	$-0.651236\pi$
$821$	15.5121	−	26.8678i	0.541378	−	0.937693i	0.998825	−	0.0484569i	$-0.0154304\pi$
$822$		0			0
$823$	−14.5387	−	25.1818i	−0.506789	−	0.877784i	−0.999969	−	0.00785682i	$-0.997499\pi$
$823$	−14.5387	−	25.1818i	−0.506789	−	0.877784i	0.493180	−	0.869927i	$-0.335834\pi$
$824$	−1.17851			−0.0410552
$825$		0			0
$826$	−2.00636	−	3.47512i	−0.0698103	−	0.120915i
$827$	−14.8920			−0.517846			−0.258923	−	0.965898i	$-0.583368\pi$
$827$	−14.8920			−0.517846			−0.258923	+	0.965898i	$0.583368\pi$
$828$		0			0
$829$	2.18594	−	3.78617i	0.0759210	−	0.131499i	−0.825565	−	0.564306i	$-0.809144\pi$
$829$	2.18594	−	3.78617i	0.0759210	−	0.131499i	0.901486	+	0.432807i	$0.142477\pi$
$830$	26.8481	−	46.5022i	0.931909	−	1.61411i
$831$		0			0
$832$	38.1806	−	26.5828i	1.32367	−	0.921593i
$833$	2.37888			0.0824234
$834$		0			0
$835$	−37.6219	+	65.1631i	−1.30196	+	2.25506i
$836$	2.90538	+	5.03227i	0.100485	+	0.174045i
$837$		0			0
$838$	−26.2928	−	45.5405i	−0.908270	−	1.57317i
$839$	11.4109	+	19.7643i	0.393948	+	0.682338i	0.992966	−	0.118397i	$-0.0377756\pi$
$839$	11.4109	+	19.7643i	0.393948	+	0.682338i	−0.599018	+	0.800735i	$0.704442\pi$
$840$		0			0
$841$	8.02399	+	13.8980i	0.276689	+	0.479240i
$842$	−23.1154	+	40.0371i	−0.796610	+	1.37977i
$843$		0			0
$844$	−40.9202			−1.40853
$845$	19.0380	−	51.4508i	0.654928	−	1.76996i
$846$		0			0
$847$	−5.34900	+	9.26473i	−0.183794	+	0.318340i
$848$	−1.70306	+	2.94979i	−0.0584833	+	0.101296i
$849$		0			0
$850$	−67.6433			−2.32015
$851$	−0.958790	−	1.66067i	−0.0328669	−	0.0569271i
$852$		0			0
$853$	23.3549			0.799656			0.399828	−	0.916590i	$-0.369070\pi$
$853$	23.3549			0.799656			0.399828	+	0.916590i	$0.369070\pi$
$854$	−0.676353	−	1.17148i	−0.0231443	−	0.0400871i
$855$		0			0
$856$	−4.19602	+	7.26771i	−0.143417	+	0.248405i
$857$	43.5306			1.48698			0.743488	−	0.668750i	$-0.233170\pi$
$857$	43.5306			1.48698			0.743488	+	0.668750i	$0.233170\pi$
$858$		0			0
$859$	20.5113			0.699838			0.349919	−	0.936780i	$-0.386209\pi$
$859$	20.5113			0.699838			0.349919	+	0.936780i	$0.386209\pi$
$860$	−19.8965	+	34.4617i	−0.678464	+	1.17513i
$861$		0			0
$862$	−22.1451	−	38.3564i	−0.754263	−	1.30642i
$863$	50.6678			1.72475			0.862376	−	0.506268i	$-0.168975\pi$
$863$	50.6678			1.72475			0.862376	+	0.506268i	$0.168975\pi$
$864$		0			0
$865$	−15.9756	−	27.6705i	−0.543186	−	0.940826i
$866$	−0.0370334			−0.00125845
$867$		0			0
$868$	−7.53844	+	13.0570i	−0.255871	+	0.443182i
$869$	3.85156	−	6.67109i	0.130655	−	0.226301i
$870$		0			0
$871$	−3.15929	−	37.2552i	−0.107048	−	1.26234i
$872$	−31.5532			−1.06853
$873$		0			0
$874$	23.3214	−	40.3939i	0.788858	−	1.36634i
$875$	16.4759	+	28.5371i	0.556987	+	0.964730i
$876$		0			0
$877$	23.5180	+	40.7344i	0.794148	+	1.37550i	0.923379	+	0.383890i	$0.125416\pi$
$877$	23.5180	+	40.7344i	0.794148	+	1.37550i	−0.129231	+	0.991615i	$0.541251\pi$
$878$	14.9806	+	25.9472i	0.505572	+	0.875677i
$879$		0			0
$880$	1.48555	+	2.57305i	0.0500780	+	0.0867376i
$881$	−8.05674	+	13.9547i	−0.271439	+	0.470145i	−0.969230	−	0.246155i	$-0.920833\pi$
$881$	−8.05674	+	13.9547i	−0.271439	+	0.470145i	0.697792	+	0.716301i	$0.254166\pi$
$882$		0			0
$883$	42.0733			1.41588			0.707940	−	0.706273i	$-0.249625\pi$
$883$	42.0733			1.41588			0.707940	+	0.706273i	$0.249625\pi$
$884$	−2.12240	−	25.0279i	−0.0713841	−	0.841779i
$885$		0			0
$886$	16.6623	−	28.8600i	0.559782	−	0.969570i
$887$	−20.8814	+	36.1676i	−0.701128	+	1.21439i	0.266942	+	0.963713i	$0.413987\pi$
$887$	−20.8814	+	36.1676i	−0.701128	+	1.21439i	−0.968071	+	0.250678i	$0.919347\pi$
$888$		0			0
$889$	−1.96067			−0.0657588
$890$	34.9797	+	60.5866i	1.17252	+	2.03087i
$891$		0			0
$892$	−39.6334			−1.32703
$893$	−14.8211	−	25.6709i	−0.495969	−	0.859043i
$894$		0			0
$895$	−48.1151	+	83.3379i	−1.60831	+	2.78568i
$896$	−14.7124			−0.491506
$897$		0			0
$898$	−52.7999			−1.76195
$899$	9.26434	−	16.0463i	0.308983	−	0.535174i
$900$		0			0
$901$	3.16233	+	5.47731i	0.105352	+	0.182476i
$902$	−7.67577			−0.255575
$903$		0			0
$904$	−12.5491	−	21.7357i	−0.417377	−	0.722919i
$905$	58.7821			1.95398
$906$		0			0
$907$	7.71125	−	13.3563i	0.256048	−	0.443488i	−0.709132	−	0.705076i	$-0.750913\pi$
$907$	7.71125	−	13.3563i	0.256048	−	0.443488i	0.965180	+	0.261588i	$0.0842463\pi$
$908$	−7.85921	+	13.6125i	−0.260817	+	0.451748i
$909$		0			0
$910$	−27.7213	+	19.3006i	−0.918951	+	0.639810i
$911$	−37.5462			−1.24396			−0.621981	−	0.783033i	$-0.713672\pi$
$911$	−37.5462			−1.24396			−0.621981	+	0.783033i	$0.713672\pi$
$912$		0			0
$913$	−1.57490	+	2.72781i	−0.0521216	+	0.0902773i
$914$	20.1259	+	34.8590i	0.665704	+	1.15303i
$915$		0			0
$916$	−4.53776	−	7.85963i	−0.149932	−	0.259689i
$917$	3.25011	+	5.62935i	0.107328	+	0.185897i
$918$		0			0
$919$	4.73732	+	8.20528i	0.156270	+	0.270667i	0.933521	−	0.358524i	$-0.116720\pi$
$919$	4.73732	+	8.20528i	0.156270	+	0.270667i	−0.777251	+	0.629191i	$0.783386\pi$
$920$	−25.3064	+	43.8319i	−0.834326	+	1.44510i
$921$		0			0
$922$	−13.4967			−0.444492
$923$	36.5458	+	17.1604i	1.20292	+	0.564842i
$924$		0			0
$925$	2.11047	−	3.65545i	0.0693919	−	0.120190i
$926$	5.76413	−	9.98377i	0.189421	−	0.328087i
$927$		0			0
$928$	25.0713			0.823007
$929$	17.9220	+	31.0418i	0.588001	+	1.01845i	0.994494	+	0.104793i	$0.0334181\pi$
$929$	17.9220	+	31.0418i	0.588001	+	1.01845i	−0.406493	+	0.913654i	$0.633249\pi$
$930$		0			0
$931$	−3.61068			−0.118335
$932$	−29.8278	−	51.6633i	−0.977043	−	1.69229i
$933$		0			0
$934$	9.65668	−	16.7259i	0.315976	−	0.547287i
$935$	5.51689			0.180422
$936$		0			0
$937$	−31.3709			−1.02484			−0.512422	−	0.858734i	$-0.671252\pi$
$937$	−31.3709			−1.02484			−0.512422	+	0.858734i	$0.671252\pi$
$938$	−11.5105	+	19.9368i	−0.375832	+	0.650960i
$939$		0			0
$940$	50.7270	+	87.8618i	1.65453	+	2.86574i
$941$	−44.7844			−1.45993			−0.729964	−	0.683486i	$-0.760463\pi$
$941$	−44.7844			−1.45993			−0.729964	+	0.683486i	$0.760463\pi$
$942$		0			0
$943$	18.3050	+	31.7052i	0.596093	+	1.03246i
$944$	−2.31570			−0.0753695
$945$		0			0
$946$	1.96422	−	3.40212i	0.0638622	−	0.110613i
$947$	−17.5337	+	30.3692i	−0.569768	+	0.986868i	0.426820	+	0.904337i	$0.359634\pi$
$947$	−17.5337	+	30.3692i	−0.569768	+	0.986868i	−0.996588	+	0.0825312i	$0.973700\pi$
$948$		0			0
$949$	−14.5175	+	10.1076i	−0.471257	+	0.328108i
$950$	102.669			3.33104
$951$		0			0
$952$	−2.45160	+	4.24629i	−0.0794567	+	0.137623i
$953$	29.4852	+	51.0699i	0.955120	+	1.65432i	0.734093	+	0.679048i	$0.237607\pi$
$953$	29.4852	+	51.0699i	0.955120	+	1.65432i	0.221027	+	0.975268i	$0.429059\pi$
$954$		0			0
$955$	−26.7376	−	46.3108i	−0.865208	−	1.49858i
$956$	−1.89114	−	3.27556i	−0.0611640	−	0.105939i
$957$		0			0
$958$	−26.8830	−	46.5627i	−0.868550	−	1.50437i
$959$	7.62878	−	13.2134i	0.246346	−	0.426684i
$960$		0			0
$961$	−4.49354			−0.144953
$962$	2.38766	+	1.12115i	0.0769812	+	0.0361472i
$963$		0			0
$964$	−3.12273	+	5.40873i	−0.100576	+	0.174204i
$965$	8.76690	−	15.1847i	0.282217	−	0.488813i
$966$		0			0
$967$	30.3671			0.976540			0.488270	−	0.872693i	$-0.337628\pi$
$967$	30.3671			0.976540			0.488270	+	0.872693i	$0.337628\pi$
$968$	−11.0250	−	19.0958i	−0.354357	−	0.613764i
$969$		0			0
$970$	64.0868			2.05770
$971$	−24.7588	−	42.8834i	−0.794546	−	1.37619i	−0.923127	−	0.384495i	$-0.874375\pi$
$971$	−24.7588	−	42.8834i	−0.794546	−	1.37619i	0.128581	−	0.991699i	$-0.458958\pi$
$972$		0			0
$973$	−8.74801	+	15.1520i	−0.280448	+	0.485751i
$974$	−3.93815			−0.126186
$975$		0			0
$976$	−0.780630			−0.0249874
$977$	−5.43356	+	9.41120i	−0.173835	+	0.301091i	−0.939757	−	0.341842i	$-0.888949\pi$
$977$	−5.43356	+	9.41120i	−0.173835	+	0.301091i	0.765923	+	0.642933i	$0.222283\pi$
$978$		0			0
$979$	−2.05190	−	3.55400i	−0.0655790	−	0.113586i
$980$	12.3580			0.394762
$981$		0			0
$982$	7.42555	+	12.8614i	0.236959	+	0.410425i
$983$	−2.34833			−0.0749001			−0.0374501	−	0.999299i	$-0.511924\pi$
$983$	−2.34833			−0.0749001			−0.0374501	+	0.999299i	$0.511924\pi$
$984$		0			0
$985$	−14.4539	+	25.0350i	−0.460541	+	0.797680i
$986$	9.50312	−	16.4599i	0.302641	−	0.524190i
$987$		0			0
$988$	3.22139	+	37.9875i	0.102486	+	1.20854i
$989$	−18.7369			−0.595799
$990$		0			0
$991$	−12.2408	+	21.2016i	−0.388841	+	0.673492i	−0.992294	−	0.123907i	$-0.960458\pi$
$991$	−12.2408	+	21.2016i	−0.388841	+	0.673492i	0.603453	+	0.797398i	$0.293791\pi$
$992$	17.9331	+	31.0610i	0.569375	+	0.986187i
$993$		0			0
$994$	−12.4296	−	21.5287i	−0.394242	−	0.682848i
$995$	1.71667	+	2.97336i	0.0544222	+	0.0942620i
$996$		0			0
$997$	3.31171	+	5.73604i	0.104883	+	0.181662i	0.913690	−	0.406411i	$-0.133220\pi$
$997$	3.31171	+	5.73604i	0.104883	+	0.181662i	−0.808808	+	0.588073i	$0.799887\pi$
$998$	27.3491	−	47.3700i	0.865720	−	1.49947i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	819.2.o.h.568.4		8
3.2	odd	2		91.2.f.c.22.1	✓	8
12.11	even	2		1456.2.s.q.113.2		8
13.3	even	3	inner	819.2.o.h.757.4		8
21.2	odd	6		637.2.h.h.165.4		8
21.5	even	6		637.2.h.i.165.4		8
21.11	odd	6		637.2.g.k.373.1		8
21.17	even	6		637.2.g.j.373.1		8
21.20	even	2		637.2.f.i.295.1		8
39.17	odd	6		1183.2.a.l.1.1		4
39.20	even	12		1183.2.c.g.337.7		8
39.29	odd	6		91.2.f.c.29.1	yes	8
39.32	even	12		1183.2.c.g.337.2		8
39.35	odd	6		1183.2.a.k.1.4		4
156.107	even	6		1456.2.s.q.1121.2		8
273.68	even	6		637.2.g.j.263.1		8
273.107	odd	6		637.2.g.k.263.1		8
273.146	even	6		637.2.f.i.393.1		8
273.185	even	6		637.2.h.i.471.4		8
273.230	even	6		8281.2.a.bp.1.4		4
273.251	even	6		8281.2.a.bt.1.1		4
273.263	odd	6		637.2.h.h.471.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.f.c.22.1	✓	8	3.2	odd	2
91.2.f.c.29.1	yes	8	39.29	odd	6
637.2.f.i.295.1		8	21.20	even	2
637.2.f.i.393.1		8	273.146	even	6
637.2.g.j.263.1		8	273.68	even	6
637.2.g.j.373.1		8	21.17	even	6
637.2.g.k.263.1		8	273.107	odd	6
637.2.g.k.373.1		8	21.11	odd	6
637.2.h.h.165.4		8	21.2	odd	6
637.2.h.h.471.4		8	273.263	odd	6
637.2.h.i.165.4		8	21.5	even	6
637.2.h.i.471.4		8	273.185	even	6
819.2.o.h.568.4		8	1.1	even	1	trivial
819.2.o.h.757.4		8	13.3	even	3	inner
1183.2.a.k.1.4		4	39.35	odd	6
1183.2.a.l.1.1		4	39.17	odd	6
1183.2.c.g.337.2		8	39.32	even	12
1183.2.c.g.337.7		8	39.20	even	12
1456.2.s.q.113.2		8	12.11	even	2
1456.2.s.q.1121.2		8	156.107	even	6
8281.2.a.bp.1.4		4	273.230	even	6
8281.2.a.bt.1.1		4	273.251	even	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:	\( N \)	\(=\)	\( 819 = 3^{2} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	819.o (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.11000 - 1.92258i) q^{2} +(-1.46422 - 2.53610i) q^{4} +4.22001 q^{5} +(0.500000 + 0.866025i) q^{7} -2.06113 q^{8} +O(q^{10})\)	\(q+(1.11000 - 1.92258i) q^{2} +(-1.46422 - 2.53610i) q^{4} +4.22001 q^{5} +(0.500000 + 0.866025i) q^{7} -2.06113 q^{8} +(4.68423 - 8.11332i) q^{10} +(-0.274776 + 0.475925i) q^{11} +(-2.95900 + 2.06017i) q^{13} +2.22001 q^{14} +(0.640570 - 1.10950i) q^{16} +(-1.18944 - 2.06017i) q^{17} +(1.80534 + 3.12694i) q^{19} +(-6.17901 - 10.7024i) q^{20} +(0.610004 + 1.05656i) q^{22} +(2.90945 - 5.03931i) q^{23} +12.8085 q^{25} +(0.676353 + 7.97573i) q^{26} +(1.46422 - 2.53610i) q^{28} +(-1.79945 + 3.11673i) q^{29} -5.14844 q^{31} +(-3.48320 - 6.03308i) q^{32} -5.28114 q^{34} +(2.11000 + 3.65463i) q^{35} +(0.164772 - 0.285393i) q^{37} +8.01574 q^{38} -8.69799 q^{40} +(-3.14579 + 5.44866i) q^{41} +(-1.61000 - 2.78861i) q^{43} +1.60932 q^{44} +(-6.45900 - 11.1873i) q^{46} -8.20957 q^{47} +(-0.500000 + 0.866025i) q^{49} +(14.2174 - 24.6253i) q^{50} +(9.55742 + 4.48778i) q^{52} -2.65866 q^{53} +(-1.15956 + 2.00841i) q^{55} +(-1.03057 - 1.78499i) q^{56} +(3.99478 + 6.91917i) q^{58} +(-0.903765 - 1.56537i) q^{59} +(-0.304662 - 0.527691i) q^{61} +(-5.71479 + 9.89831i) q^{62} -12.9032 q^{64} +(-12.4870 + 8.69395i) q^{65} +(-5.18490 + 8.98052i) q^{67} +(-3.48320 + 6.03308i) q^{68} +9.36845 q^{70} +(-5.59889 - 9.69756i) q^{71} +4.90621 q^{73} +(-0.365794 - 0.633574i) q^{74} +(5.28682 - 9.15705i) q^{76} -0.549551 q^{77} -14.0171 q^{79} +(2.70321 - 4.68210i) q^{80} +(6.98367 + 12.0961i) q^{82} +5.73159 q^{83} +(-5.01945 - 8.69395i) q^{85} -7.14844 q^{86} +(0.566349 - 0.980945i) q^{88} +(-3.73378 + 6.46709i) q^{89} +(-3.26366 - 1.53248i) q^{91} -17.0403 q^{92} +(-9.11266 + 15.7836i) q^{94} +(7.61856 + 13.1957i) q^{95} +(3.42035 + 5.92422i) q^{97} +(1.11000 + 1.92258i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - q^{2} - 5 q^{4} + 14 q^{5} + 4 q^{7} + 12 q^{8}+O(q^{10}) \) 8 * q - q^2 - 5 * q^4 + 14 * q^5 + 4 * q^7 + 12 * q^8	\( 8 q - q^{2} - 5 q^{4} + 14 q^{5} + 4 q^{7} + 12 q^{8} + 11 q^{10} - q^{11} + 4 q^{13} - 2 q^{14} - 19 q^{16} - 4 q^{17} - q^{19} - 2 q^{20} - 5 q^{22} - 2 q^{23} + 10 q^{25} - 12 q^{26} + 5 q^{28} + q^{29} - 8 q^{31} - 33 q^{32} + 6 q^{34} + 7 q^{35} + 10 q^{37} + 46 q^{38} - 34 q^{40} - 22 q^{41} - 3 q^{43} + 24 q^{44} - 24 q^{46} - 4 q^{47} - 4 q^{49} + 43 q^{50} + 65 q^{52} - 4 q^{53} + 3 q^{55} + 6 q^{56} + 11 q^{58} - 8 q^{59} - 8 q^{61} - 5 q^{62} + 28 q^{64} - 7 q^{65} + 6 q^{67} - 33 q^{68} + 22 q^{70} - 14 q^{71} - 16 q^{73} + 20 q^{74} - 32 q^{76} - 2 q^{77} - 52 q^{79} + 7 q^{80} + 14 q^{82} - 5 q^{85} - 24 q^{86} - 3 q^{88} - q^{89} - 4 q^{91} - 24 q^{92} - 33 q^{94} + 21 q^{95} - 3 q^{97} - q^{98}+O(q^{100}) \) 8 * q - q^2 - 5 * q^4 + 14 * q^5 + 4 * q^7 + 12 * q^8 + 11 * q^10 - q^11 + 4 * q^13 - 2 * q^14 - 19 * q^16 - 4 * q^17 - q^19 - 2 * q^20 - 5 * q^22 - 2 * q^23 + 10 * q^25 - 12 * q^26 + 5 * q^28 + q^29 - 8 * q^31 - 33 * q^32 + 6 * q^34 + 7 * q^35 + 10 * q^37 + 46 * q^38 - 34 * q^40 - 22 * q^41 - 3 * q^43 + 24 * q^44 - 24 * q^46 - 4 * q^47 - 4 * q^49 + 43 * q^50 + 65 * q^52 - 4 * q^53 + 3 * q^55 + 6 * q^56 + 11 * q^58 - 8 * q^59 - 8 * q^61 - 5 * q^62 + 28 * q^64 - 7 * q^65 + 6 * q^67 - 33 * q^68 + 22 * q^70 - 14 * q^71 - 16 * q^73 + 20 * q^74 - 32 * q^76 - 2 * q^77 - 52 * q^79 + 7 * q^80 + 14 * q^82 - 5 * q^85 - 24 * q^86 - 3 * q^88 - q^89 - 4 * q^91 - 24 * q^92 - 33 * q^94 + 21 * q^95 - 3 * q^97 - q^98

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