LMFDB - Embedded newform 783.2.be.a.665.16

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [783,2,Mod(8,783)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(783, base_ring=CyclotomicField(84)) chi = DirichletCharacter(H, H._module([14, 9])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("783.8"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 783 = 3^{3} \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	783.be (of order $84$, degree $24$, not minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$6.25228647827$
Analytic rank:	$0$
Dimension:	$672$
Relative dimension:	$28$ over $\Q(\zeta_{84})$
Twist minimal:	no (minimal twist has level 261)
Sato-Tate group:	$\mathrm{SU}(2)[C_{84}]$

Embedding invariants

Embedding label			665.16
Character	$\chi$	$=$	783.665
Dual form			783.2.be.a.710.16

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.234125 + 0.536620i) q^{2} +(1.12720 - 1.21483i) q^{4} +(1.79123 - 0.269985i) q^{5} +(2.59390 - 2.40679i) q^{7} +(2.02104 + 0.707193i) q^{8} +(0.564252 + 0.898002i) q^{10} +(0.974345 + 0.838491i) q^{11} +(-2.06180 - 3.02410i) q^{13} +(1.89883 + 0.828450i) q^{14} +(-0.154007 - 2.05508i) q^{16} +(2.82385 - 2.82385i) q^{17} +(-5.81575 + 3.65428i) q^{19} +(1.69109 - 2.48037i) q^{20} +(-0.221833 + 0.719165i) q^{22} +(-8.33810 + 3.27246i) q^{23} +(-1.64224 + 0.506563i) q^{25} +(1.14008 - 1.81442i) q^{26} -5.86408i q^{28} +(1.28158 + 5.23045i) q^{29} +(3.72396 + 2.74841i) q^{31} +(4.85287 - 2.56482i) q^{32} +(2.17647 + 0.854200i) q^{34} +(3.99648 - 5.01143i) q^{35} +(2.62155 - 7.49197i) q^{37} +(-3.32257 - 2.26529i) q^{38} +(3.81109 + 0.721097i) q^{40} +(-6.95493 + 1.86357i) q^{41} +(1.32201 + 1.79126i) q^{43} +(2.11691 - 0.238518i) q^{44} +(-3.70823 - 3.70823i) q^{46} +(-1.08573 + 1.26165i) q^{47} +(0.412579 - 5.50549i) q^{49} +(-0.656321 - 0.762658i) q^{50} +(-5.99783 - 0.904027i) q^{52} +(-6.55714 + 5.22915i) q^{53} +(1.97166 + 1.23888i) q^{55} +(6.94443 - 3.02983i) q^{56} +(-2.50671 + 1.91230i) q^{58} +(7.47986 + 4.31850i) q^{59} +(13.5329 + 0.506365i) q^{61} +(-0.602979 + 2.64182i) q^{62} +(-0.709949 - 0.566166i) q^{64} +(-4.50962 - 4.86022i) q^{65} +(10.9354 + 0.819497i) q^{67} +(-0.247461 - 6.61353i) q^{68} +(3.62491 + 0.971292i) q^{70} +(3.89744 + 1.87691i) q^{71} +(0.963648 + 8.55261i) q^{73} +(4.63411 - 0.347279i) q^{74} +(-2.11617 + 11.1843i) q^{76} +(4.54542 - 0.170078i) q^{77} +(0.335835 + 1.77493i) q^{79} +(-0.830703 - 3.63955i) q^{80} +(-2.62835 - 3.29585i) q^{82} +(0.302531 + 0.980782i) q^{83} +(4.29577 - 5.82057i) q^{85} +(-0.651711 + 1.12880i) q^{86} +(1.37622 + 2.38367i) q^{88} +(2.15138 + 0.242402i) q^{89} +(-12.6265 - 2.88191i) q^{91} +(-5.42320 + 13.8181i) q^{92} +(-0.931222 - 0.287244i) q^{94} +(-9.43077 + 8.11583i) q^{95} +(-0.817727 + 1.54721i) q^{97} +(3.05095 - 1.06757i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 672 q + 36 q^{2} - 14 q^{4} + 42 q^{5} - 10 q^{7} - 56 q^{10} + 48 q^{11} - 14 q^{13} + 24 q^{14} - 54 q^{16} - 48 q^{19} + 30 q^{20} - 14 q^{22} + 30 q^{23} + 30 q^{25} - 12 q^{31} - 24 q^{32} - 14 q^{34}+ \cdots - 36 q^{97}+O(q^{100}) $ 672 * q + 36 * q^2 - 14 * q^4 + 42 * q^5 - 10 * q^7 - 56 * q^10 + 48 * q^11 - 14 * q^13 + 24 * q^14 - 54 * q^16 - 48 * q^19 + 30 * q^20 - 14 * q^22 + 30 * q^23 + 30 * q^25 - 12 * q^31 - 24 * q^32 - 14 * q^34 - 48 * q^37 + 42 * q^38 - 2 * q^40 + 24 * q^41 - 12 * q^43 - 64 * q^46 + 42 * q^47 + 22 * q^49 + 66 * q^50 + 22 * q^52 + 76 * q^55 + 42 * q^56 - 42 * q^58 + 132 * q^59 - 308 * q^64 + 66 * q^65 - 14 * q^67 - 60 * q^68 - 14 * q^70 - 48 * q^73 - 66 * q^74 - 28 * q^76 - 30 * q^77 - 12 * q^79 - 136 * q^82 - 246 * q^83 + 34 * q^85 + 8 * q^88 - 56 * q^91 - 462 * q^92 + 26 * q^94 + 246 * q^95 - 36 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/783\mathbb{Z}\right)^\times$.

$n$	$379$	$407$
$\chi(n)$	$e\left(\frac{15}{28}\right)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	0.234125	+	0.536620i	0.165551	+	0.379448i	0.979487	−	0.201507i	$-0.0645840\pi$
$2$	0.234125	+	0.536620i	0.165551	+	0.379448i	−0.813936	+	0.580955i	$0.802679\pi$
$3$		0			0
$3$		0			0
$4$	1.12720	−	1.21483i	0.563599	−	0.607416i
$5$	1.79123	−	0.269985i	0.801064	−	0.120741i	0.264264	−	0.964450i	$-0.414871\pi$
$5$	1.79123	−	0.269985i	0.801064	−	0.120741i	0.536800	+	0.843709i	$0.319633\pi$
$6$		0			0
$7$	2.59390	−	2.40679i	0.980401	−	0.909680i	−0.0155222	−	0.999880i	$-0.504941\pi$
$7$	2.59390	−	2.40679i	0.980401	−	0.909680i	0.995924	+	0.0901999i	$0.0287506\pi$
$8$	2.02104	+	0.707193i	0.714546	+	0.250030i
$9$		0			0
$10$	0.564252	+	0.898002i	0.178432	+	0.283973i
$11$	0.974345	+	0.838491i	0.293776	+	0.252815i	0.786810	−	0.617195i	$-0.211731\pi$
$11$	0.974345	+	0.838491i	0.293776	+	0.252815i	−0.493034	+	0.870010i	$0.664112\pi$
$12$		0			0
$13$	−2.06180	−	3.02410i	−0.571839	−	0.838734i	0.425980	−	0.904732i	$-0.359929\pi$
$13$	−2.06180	−	3.02410i	−0.571839	−	0.838734i	−0.997820	+	0.0659980i	$0.978977\pi$
$14$	1.89883	+	0.828450i	0.507483	+	0.221412i
$15$		0			0
$16$	−0.154007	−	2.05508i	−0.0385017	−	0.513770i
$17$	2.82385	−	2.82385i	0.684884	−	0.684884i	−0.276213	−	0.961096i	$-0.589080\pi$
$17$	2.82385	−	2.82385i	0.684884	−	0.684884i	0.961096	+	0.276213i	$0.0890795\pi$
$18$		0			0
$19$	−5.81575	+	3.65428i	−1.33422	+	0.838349i	−0.994757	−	0.102269i	$-0.967390\pi$
$19$	−5.81575	+	3.65428i	−1.33422	+	0.838349i	−0.339468	+	0.940618i	$0.610247\pi$
$20$	1.69109	−	2.48037i	0.378139	−	0.554629i
$21$		0			0
$22$	−0.221833	+	0.719165i	−0.0472950	+	0.153326i
$23$	−8.33810	+	3.27246i	−1.73861	+	0.682355i	−0.738648	+	0.674092i	$0.764535\pi$
$23$	−8.33810	+	3.27246i	−1.73861	+	0.682355i	−0.999966	+	0.00826369i	$0.997370\pi$
$24$		0			0
$25$	−1.64224	+	0.506563i	−0.328447	+	0.101313i
$26$	1.14008	−	1.81442i	0.223587	−	0.355837i
$27$		0			0
$28$		−	5.86408i		−	1.10821i
$29$	1.28158	+	5.23045i	0.237983	+	0.971269i
$29$	1.28158	+	5.23045i	0.237983	+	0.971269i
$30$		0			0
$31$	3.72396	+	2.74841i	0.668843	+	0.493629i	0.874519	−	0.484992i	$-0.161177\pi$
$31$	3.72396	+	2.74841i	0.668843	+	0.493629i	−0.205676	+	0.978620i	$0.565939\pi$
$32$	4.85287	−	2.56482i	0.857874	−	0.453400i
$33$		0			0
$34$	2.17647	+	0.854200i	0.373261	+	0.146494i
$35$	3.99648	−	5.01143i	0.675529	−	0.847086i
$36$		0			0
$37$	2.62155	−	7.49197i	0.430981	−	1.23167i	−0.499815	−	0.866132i	$-0.666599\pi$
$37$	2.62155	−	7.49197i	0.430981	−	1.23167i	0.930796	−	0.365540i	$-0.119116\pi$
$38$	−3.32257	−	2.26529i	−0.538992	−	0.367479i
$39$		0			0
$40$	3.81109	+	0.721097i	0.602586	+	0.114015i
$41$	−6.95493	+	1.86357i	−1.08618	+	0.291040i	−0.757124	−	0.653271i	$-0.773396\pi$
$41$	−6.95493	+	1.86357i	−1.08618	+	0.291040i	−0.329053	+	0.944311i	$0.606730\pi$
$42$		0			0
$43$	1.32201	+	1.79126i	0.201605	+	0.273165i	0.893723	−	0.448620i	$-0.148084\pi$
$43$	1.32201	+	1.79126i	0.201605	+	0.273165i	−0.692118	+	0.721784i	$0.743322\pi$
$44$	2.11691	−	0.238518i	0.319136	−	0.0359579i
$45$		0			0
$46$	−3.70823	−	3.70823i	−0.546748	−	0.546748i
$47$	−1.08573	+	1.26165i	−0.158371	+	0.184030i	−0.831551	−	0.555448i	$-0.812547\pi$
$47$	−1.08573	+	1.26165i	−0.158371	+	0.184030i	0.673181	+	0.739478i	$0.264928\pi$
$48$		0			0
$49$	0.412579	−	5.50549i	0.0589399	−	0.786499i
$50$	−0.656321	−	0.762658i	−0.0928177	−	0.107856i
$51$		0			0
$52$	−5.99783	−	0.904027i	−0.831749	−	0.125366i
$53$	−6.55714	+	5.22915i	−0.900693	+	0.718278i	−0.960011	−	0.279961i	$-0.909679\pi$
$53$	−6.55714	+	5.22915i	−0.900693	+	0.718278i	0.0593187	+	0.998239i	$0.481107\pi$
$54$		0			0
$55$	1.97166	+	1.23888i	0.265859	+	0.167050i
$56$	6.94443	−	3.02983i	0.927989	−	0.404877i
$57$		0			0
$58$	−2.50671	+	1.91230i	−0.329148	+	0.251097i
$59$	7.47986	+	4.31850i	0.973795	+	0.562221i	0.900391	−	0.435082i	$-0.143281\pi$
$59$	7.47986	+	4.31850i	0.973795	+	0.562221i	0.0734037	+	0.997302i	$0.476614\pi$
$60$		0			0
$61$	13.5329	+	0.506365i	1.73271	+	0.0648334i	0.884989	−	0.465611i	$-0.154165\pi$
$61$	13.5329	+	0.506365i	1.73271	+	0.0648334i	0.847720	+	0.530445i	$0.177975\pi$
$62$	−0.602979	+	2.64182i	−0.0765784	+	0.335512i
$63$		0			0
$64$	−0.709949	−	0.566166i	−0.0887436	−	0.0707707i
$65$	−4.50962	−	4.86022i	−0.559350	−	0.602836i
$66$		0			0
$67$	10.9354	+	0.819497i	1.33597	+	0.100117i	0.723473	−	0.690352i	$-0.242544\pi$
$67$	10.9354	+	0.819497i	1.33597	+	0.100117i	0.612501	+	0.790470i	$0.290164\pi$
$68$	−0.247461	−	6.61353i	−0.0300091	−	0.802009i
$69$		0			0
$70$	3.62491	+	0.971292i	0.433260	+	0.116092i
$71$	3.89744	+	1.87691i	0.462541	+	0.222748i	0.650616	−	0.759407i	$-0.274511\pi$
$71$	3.89744	+	1.87691i	0.462541	+	0.222748i	−0.188075	+	0.982155i	$0.560225\pi$
$72$		0			0
$73$	0.963648	+	8.55261i	0.112786	+	1.00101i	0.914857	+	0.403778i	$0.132303\pi$
$73$	0.963648	+	8.55261i	0.112786	+	1.00101i	−0.802071	+	0.597229i	$0.796268\pi$
$74$	4.63411	−	0.347279i	0.538705	−	0.0403703i
$75$		0			0
$76$	−2.11617	+	11.1843i	−0.242742	+	1.28292i
$77$	4.54542	−	0.170078i	0.517999	−	0.0193821i
$78$		0			0
$79$	0.335835	+	1.77493i	0.0377844	+	0.199695i	0.996372	−	0.0851015i	$-0.0271214\pi$
$79$	0.335835	+	1.77493i	0.0377844	+	0.199695i	−0.958588	+	0.284797i	$0.908074\pi$
$80$	−0.830703	−	3.63955i	−0.0928754	−	0.406914i
$81$		0			0
$82$	−2.62835	−	3.29585i	−0.290253	−	0.363965i
$83$	0.302531	+	0.980782i	0.0332071	+	0.107655i	0.970659	−	0.240460i	$-0.0772982\pi$
$83$	0.302531	+	0.980782i	0.0332071	+	0.107655i	−0.937452	+	0.348115i	$0.886822\pi$
$84$		0			0
$85$	4.29577	−	5.82057i	0.465942	−	0.631329i
$86$	−0.651711	+	1.12880i	−0.0702758	+	0.121721i
$87$		0			0
$88$	1.37622	+	2.38367i	0.146705	+	0.254101i
$89$	2.15138	+	0.242402i	0.228046	+	0.0256946i	0.225248	−	0.974301i	$-0.427681\pi$
$89$	2.15138	+	0.242402i	0.228046	+	0.0256946i	0.00279797	+	0.999996i	$0.499109\pi$
$90$		0			0
$91$	−12.6265	−	2.88191i	−1.32361	−	0.302106i
$92$	−5.42320	+	13.8181i	−0.565408	+	1.44064i
$93$		0			0
$94$	−0.931222	−	0.287244i	−0.0960482	−	0.0296269i
$95$	−9.43077	+	8.11583i	−0.967576	+	0.832667i
$96$		0			0
$97$	−0.817727	+	1.54721i	−0.0830276	+	0.157096i	−0.922133	−	0.386873i	$-0.873555\pi$
$97$	−0.817727	+	1.54721i	−0.0830276	+	0.157096i	0.839105	+	0.543969i	$0.183079\pi$
$98$	3.05095	−	1.06757i	0.308193	−	0.107841i
$99$		0			0
$100$	−1.23574	+	2.56604i	−0.123574	+	0.256604i
$101$	−1.27105	+	0.938078i	−0.126474	+	0.0933422i	−0.655220	−	0.755438i	$-0.727424\pi$
$101$	−1.27105	+	0.938078i	−0.126474	+	0.0933422i	0.528746	+	0.848780i	$0.322662\pi$
$102$		0			0
$103$	8.55107	−	5.83002i	0.842562	−	0.574449i	−0.0633131	−	0.997994i	$-0.520167\pi$
$103$	8.55107	−	5.83002i	0.842562	−	0.574449i	0.905875	+	0.423545i	$0.139214\pi$
$104$	−2.02835	−	7.56992i	−0.198896	−	0.742291i
$105$		0			0
$106$	−4.34126	−	2.29442i	−0.421660	−	0.222854i
$107$	−1.56083	−	3.24109i	−0.150891	−	0.313328i	0.811798	−	0.583938i	$-0.198489\pi$
$107$	−1.56083	−	3.24109i	−0.150891	−	0.313328i	−0.962689	+	0.270610i	$0.912775\pi$
$108$		0			0
$109$	−15.2545	+	3.48174i	−1.46111	+	0.333490i	−0.877906	−	0.478833i	$-0.841060\pi$
$109$	−15.2545	+	3.48174i	−1.46111	+	0.333490i	−0.583208	+	0.812323i	$0.698203\pi$
$110$	−0.203191	+	1.34808i	−0.0193735	+	0.128535i
$111$		0			0
$112$	−5.34561	−	4.96000i	−0.505113	−	0.468676i
$113$	4.36660	+	8.26201i	0.410775	+	0.777225i	0.999516	−	0.0310970i	$-0.00990006\pi$
$113$	4.36660	+	8.26201i	0.410775	+	0.777225i	−0.588741	+	0.808322i	$0.700376\pi$
$114$		0			0
$115$	−14.0520	+	8.11291i	−1.31035	+	0.756533i
$116$	7.79870	+	4.33885i	0.724091	+	0.402852i
$117$		0			0
$118$	−0.566172	+	5.02491i	−0.0521203	+	0.462581i
$119$	0.528377	−	14.1212i	0.0484362	−	1.29449i
$120$		0			0
$121$	−1.39319	−	9.24318i	−0.126653	−	0.840289i
$122$	2.89666	+	7.38057i	0.262251	+	0.668206i
$123$		0			0
$124$	7.53650	−	1.42598i	0.676797	−	0.128057i
$125$	−10.9652	+	5.28058i	−0.980761	+	0.472310i
$126$		0			0
$127$	−0.619721	−	1.77106i	−0.0549913	−	0.157156i	0.913111	−	0.407711i	$-0.133673\pi$
$127$	−0.619721	−	1.77106i	−0.0549913	−	0.157156i	−0.968103	+	0.250554i	$0.919387\pi$
$128$	2.97889	−	11.1174i	0.263299	−	0.982646i
$129$		0			0
$130$	1.55228	−	3.55785i	0.136144	−	0.312044i
$131$	3.80938	−	8.73120i	0.332828	−	0.762849i	−0.667014	−	0.745045i	$-0.732428\pi$
$131$	3.80938	−	8.73120i	0.332828	−	0.762849i	0.999842	−	0.0178036i	$-0.00566735\pi$
$132$		0			0
$133$	−6.29040	+	23.4761i	−0.545447	+	2.03564i
$134$	2.12050	+	6.06003i	0.183183	+	0.523507i
$135$		0			0
$136$	7.70411	−	3.71010i	0.660622	−	0.318139i
$137$	−1.02757	+	0.194426i	−0.0877910	+	0.0166110i	−0.229622	−	0.973280i	$-0.573749\pi$
$137$	−1.02757	+	0.194426i	−0.0877910	+	0.0166110i	0.141830	+	0.989891i	$0.454701\pi$
$138$		0			0
$139$	−1.26551	−	3.22446i	−0.107339	−	0.273495i	0.867105	−	0.498125i	$-0.165978\pi$
$139$	−1.26551	−	3.22446i	−0.107339	−	0.273495i	−0.974444	+	0.224630i	$0.927883\pi$
$140$	−1.58321	−	10.5039i	−0.133806	−	0.887744i
$141$		0			0
$142$	−0.0946987	+	2.53088i	−0.00794694	+	0.212386i
$143$	0.526781	−	4.67531i	0.0440517	−	0.390969i
$144$		0			0
$145$	3.70775	+	9.02295i	0.307912	+	0.749315i
$146$	−4.36389	+	2.51949i	−0.361158	+	0.208515i
$147$		0			0
$148$	−6.14647	−	11.6297i	−0.505237	−	0.955954i
$149$	−9.95683	−	9.23859i	−0.815696	−	0.756855i	0.157332	−	0.987546i	$-0.449711\pi$
$149$	−9.95683	−	9.23859i	−0.815696	−	0.756855i	−0.973027	+	0.230691i	$0.925901\pi$
$150$		0			0
$151$	−2.55954	+	16.9814i	−0.208292	+	1.38193i	0.603211	+	0.797582i	$0.293888\pi$
$151$	−2.55954	+	16.9814i	−0.208292	+	1.38193i	−0.811503	+	0.584348i	$0.801350\pi$
$152$	−14.3381	+	3.27259i	−1.16298	+	0.265442i
$153$		0			0
$154$	1.15546	+	2.39935i	0.0931099	+	0.193345i
$155$	7.41251	+	3.91763i	0.595387	+	0.314671i
$156$		0			0
$157$	−1.11923	−	4.17702i	−0.0893242	−	0.333362i	0.906774	−	0.421618i	$-0.138538\pi$
$157$	−1.11923	−	4.17702i	−0.0893242	−	0.333362i	−0.996098	+	0.0882552i	$0.971871\pi$
$158$	−0.873837	+	0.595772i	−0.0695187	+	0.0473971i
$159$		0			0
$160$	8.00016	−	5.90439i	0.632469	−	0.466783i
$161$	−13.7521	+	28.5564i	−1.08381	+	2.25056i
$162$		0			0
$163$	−3.67650	+	1.28646i	−0.287966	+	0.100764i	−0.470397	−	0.882455i	$-0.655889\pi$
$163$	−3.67650	+	1.28646i	−0.287966	+	0.100764i	0.182431	+	0.983219i	$0.441603\pi$
$164$	−5.57567	+	10.5497i	−0.435386	+	0.823791i
$165$		0			0
$166$	−0.455477	+	0.391970i	−0.0353519	+	0.0304228i
$167$	9.41264	+	2.90341i	0.728372	+	0.224673i	0.636695	−	0.771116i	$-0.280301\pi$
$167$	9.41264	+	2.90341i	0.728372	+	0.224673i	0.0916769	+	0.995789i	$0.470777\pi$
$168$		0			0
$169$	−0.144743	+	0.368799i	−0.0111341	+	0.0283692i
$170$	4.12918	+	0.942459i	0.316694	+	0.0722833i
$171$		0			0
$172$	3.66625	+	0.413087i	0.279549	+	0.0314976i
$173$	3.25834	+	5.64362i	0.247727	+	0.429076i	0.962895	−	0.269877i	$-0.0869830\pi$
$173$	3.25834	+	5.64362i	0.247727	+	0.429076i	−0.715168	+	0.698953i	$0.753650\pi$
$174$		0			0
$175$	−3.04061	+	5.26648i	−0.229848	+	0.398109i
$176$	1.57311	−	2.13149i	0.118578	−	0.160667i
$177$		0			0
$178$	0.373614	+	1.21123i	0.0280035	+	0.0907853i
$179$	−15.0898	−	18.9220i	−1.12786	−	1.41429i	−0.897403	−	0.441213i	$-0.854548\pi$
$179$	−15.0898	−	18.9220i	−1.12786	−	1.41429i	−0.230460	−	0.973082i	$-0.574023\pi$
$180$		0			0
$181$	−2.36553	−	10.3641i	−0.175828	−	0.770355i	−0.983527	−	0.180759i	$-0.942144\pi$
$181$	−2.36553	−	10.3641i	−0.175828	−	0.770355i	0.807699	−	0.589595i	$-0.200713\pi$
$182$	−1.40968	−	7.45034i	−0.104492	−	0.552256i
$183$		0			0
$184$	−19.1659	+	0.717137i	−1.41293	+	0.0528680i
$185$	2.67310	−	14.1277i	0.196530	−	1.03869i
$186$		0			0
$187$	5.11917	−	0.383629i	0.374351	−	0.0280537i
$188$	0.308849	+	2.74111i	0.0225251	+	0.199916i
$189$		0			0
$190$	−6.56310	−	3.16062i	−0.476137	−	0.229296i
$191$	−6.01366	−	1.61136i	−0.435133	−	0.116594i	0.0346015	−	0.999401i	$-0.488984\pi$
$191$	−6.01366	−	1.61136i	−0.435133	−	0.116594i	−0.469735	+	0.882808i	$0.655650\pi$
$192$		0			0
$193$	−0.614270	−	16.4167i	−0.0442161	−	1.18170i	−0.828022	−	0.560695i	$-0.810534\pi$
$193$	−0.614270	−	16.4167i	−0.0442161	−	1.18170i	0.783806	−	0.621006i	$-0.213276\pi$
$194$	−1.02172	−	0.0765671i	−0.0733550	−	0.00549720i
$195$		0			0
$196$	−6.22318	−	6.70700i	−0.444513	−	0.479071i
$197$	−8.02113	−	6.39664i	−0.571482	−	0.455741i	0.294616	−	0.955616i	$-0.404808\pi$
$197$	−8.02113	−	6.39664i	−0.571482	−	0.455741i	−0.866098	+	0.499874i	$0.833380\pi$
$198$		0			0
$199$	−4.26586	+	18.6900i	−0.302399	+	1.32490i	0.564096	+	0.825709i	$0.309225\pi$
$199$	−4.26586	+	18.6900i	−0.302399	+	1.32490i	−0.866494	+	0.499187i	$0.833632\pi$
$200$	−3.67726	−	0.137594i	−0.260022	−	0.00972933i
$201$		0			0
$202$	−0.800976	−	0.462444i	−0.0563565	−	0.0325374i
$203$	15.9128	+	10.4828i	1.11686	+	0.735746i
$204$		0			0
$205$	−11.9548	+	5.21581i	−0.834957	+	0.364288i
$206$	5.13053	+	3.22372i	0.357461	+	0.224608i
$207$		0			0
$208$	−5.89723	+	4.70288i	−0.408899	+	0.326086i
$209$	−8.73062	−	1.31593i	−0.603910	−	0.0910248i
$210$		0			0
$211$	8.93001	+	10.3769i	0.614767	+	0.714372i	0.975919	−	0.218135i	$-0.0699973\pi$
$211$	8.93001	+	10.3769i	0.614767	+	0.714372i	−0.361152	+	0.932507i	$0.617616\pi$
$212$	−1.03867	+	13.8601i	−0.0713363	+	0.951916i
$213$		0			0
$214$	1.37381	−	1.59639i	0.0939114	−	0.109127i
$215$	2.85164	+	2.85164i	0.194480	+	0.194480i
$216$		0			0
$217$	16.2744	−	1.83369i	1.10478	−	0.124479i
$218$	−5.43982	−	7.37070i	−0.368431	−	0.499207i
$219$		0			0
$220$	3.72748	−	0.998775i	0.251306	−	0.0673374i
$221$	−14.3618	−	2.71740i	−0.966079	−	0.182792i
$222$		0			0
$223$	17.7860	+	12.1263i	1.19104	+	0.812035i	0.986004	−	0.166721i	$-0.0533178\pi$
$223$	17.7860	+	12.1263i	1.19104	+	0.812035i	0.205032	+	0.978755i	$0.434270\pi$
$224$	6.41489	−	18.3327i	0.428613	−	1.22490i
$225$		0			0
$226$	−3.41123	+	4.27755i	−0.226912	+	0.284538i
$227$	−25.1369	−	9.86550i	−1.66839	−	0.654796i	−0.672072	−	0.740486i	$-0.734595\pi$
$227$	−25.1369	−	9.86550i	−1.66839	−	0.654796i	−0.996322	+	0.0856896i	$0.972691\pi$
$228$		0			0
$229$	−14.6405	+	7.73771i	−0.967469	+	0.511322i	−0.874858	−	0.484380i	$-0.839045\pi$
$229$	−14.6405	+	7.73771i	−0.967469	+	0.511322i	−0.0926110	+	0.995702i	$0.529521\pi$
$230$	−7.64347	−	5.64114i	−0.503995	−	0.371965i
$231$		0			0
$232$	−1.10882	+	11.4773i	−0.0727973	+	0.753519i
$233$		−	18.9493i		−	1.24141i	−0.784044	−	0.620705i	$-0.786846\pi$
$233$		−	18.9493i		−	1.24141i	0.784044	−	0.620705i	$-0.213154\pi$
$234$		0			0
$235$	−1.60418	+	2.55303i	−0.104645	+	0.166542i
$236$	13.6775	−	4.21896i	0.890332	−	0.274631i
$237$		0			0
$238$	7.70141	−	3.02258i	0.499208	−	0.195925i
$239$	−2.90929	+	9.43170i	−0.188187	+	0.610086i	0.811483	+	0.584376i	$0.198661\pi$
$239$	−2.90929	+	9.43170i	−0.188187	+	0.610086i	−0.999669	+	0.0257096i	$0.991815\pi$
$240$		0			0
$241$	1.80931	−	2.65377i	0.116548	−	0.170944i	−0.763532	−	0.645770i	$-0.776537\pi$
$241$	1.80931	−	2.65377i	0.116548	−	0.170944i	0.880080	+	0.474826i	$0.157489\pi$
$242$	4.63390	−	2.91167i	0.297878	−	0.187169i
$243$		0			0
$244$	15.8694	−	15.8694i	1.01593	−	1.01593i
$245$	−0.747374	−	9.97301i	−0.0477480	−	0.637152i
$246$		0			0
$247$	23.0418	+	10.0530i	1.46611	+	0.639659i
$248$	5.58262	+	8.18820i	0.354497	+	0.519951i
$249$		0			0
$250$	−5.40090	−	4.64785i	−0.341583	−	0.293956i
$251$	−1.44426	−	2.29853i	−0.0911610	−	0.145082i	0.798031	−	0.602617i	$-0.205875\pi$
$251$	−1.44426	−	2.29853i	−0.0911610	−	0.145082i	−0.889192	+	0.457535i	$0.848732\pi$
$252$		0			0
$253$	−10.8681	−	3.80292i	−0.683272	−	0.239087i
$254$	0.805295	−	0.747204i	0.0505287	−	0.0468838i
$255$		0			0
$256$	4.86741	−	0.733644i	0.304213	−	0.0458527i
$257$	−0.730713	+	0.787521i	−0.0455806	+	0.0491242i	−0.755431	−	0.655229i	$-0.772572\pi$
$257$	−0.730713	+	0.787521i	−0.0455806	+	0.0491242i	0.709850	+	0.704353i	$0.248763\pi$
$258$		0			0
$259$	−11.2315	−	25.7429i	−0.697893	−	1.59959i
$260$	−10.9876			−0.681421
$261$		0			0
$262$	5.57721			0.344561
$263$	7.21655	+	16.5405i	0.444992	+	1.01993i	0.984087	+	0.177687i	$0.0568614\pi$
$263$	7.21655	+	16.5405i	0.444992	+	1.01993i	−0.539096	+	0.842245i	$0.681234\pi$
$264$		0			0
$265$	−10.3336	+	11.1370i	−0.634787	+	0.684138i
$266$	−14.0705	+	2.12078i	−0.862717	+	0.130034i
$267$		0			0
$268$	13.3219	−	12.3610i	0.813767	−	0.755066i
$269$	−4.38546	−	1.53454i	−0.267386	−	0.0935625i	0.193256	−	0.981148i	$-0.438095\pi$
$269$	−4.38546	−	1.53454i	−0.267386	−	0.0935625i	−0.460642	+	0.887586i	$0.652381\pi$
$270$		0			0
$271$	1.36275	+	2.16881i	0.0827813	+	0.131746i	0.885549	−	0.464547i	$-0.153783\pi$
$271$	1.36275	+	2.16881i	0.0827813	+	0.131746i	−0.802767	+	0.596292i	$0.796640\pi$
$272$	−6.23812	−	5.36833i	−0.378241	−	0.325503i
$273$		0			0
$274$	−0.344912	−	0.505894i	−0.0208369	−	0.0305621i
$275$	−2.02485	−	0.883434i	−0.122103	−	0.0532731i
$276$		0			0
$277$	−0.222034	−	2.96284i	−0.0133407	−	0.178020i	−0.999894	−	0.0145781i	$-0.995359\pi$
$277$	−0.222034	−	2.96284i	−0.0133407	−	0.178020i	0.986553	−	0.163442i	$-0.0522596\pi$
$278$	1.43402	−	1.43402i	0.0860071	−	0.0860071i
$279$		0			0
$280$	11.6211	−	7.30202i	0.694494	−	0.436379i
$281$	−2.90516	+	4.26109i	−0.173308	+	0.254195i	−0.903058	−	0.429518i	$-0.858684\pi$
$281$	−2.90516	+	4.26109i	−0.173308	+	0.254195i	0.729751	+	0.683713i	$0.239636\pi$
$282$		0			0
$283$	−4.73199	+	15.3407i	−0.281287	+	0.911911i	0.699132	+	0.714992i	$0.253570\pi$
$283$	−4.73199	+	15.3407i	−0.281287	+	0.911911i	−0.980420	+	0.196919i	$0.936906\pi$
$284$	6.67332	−	2.61908i	0.395988	−	0.155414i
$285$		0			0
$286$	2.63220	−	0.811927i	0.155645	−	0.0480102i
$287$	−13.5552	+	21.5729i	−0.800136	+	1.27341i
$288$		0			0
$289$			1.05178i			0.0618692i
$290$	−3.97382	+	4.10215i	−0.233351	+	0.240886i
$291$		0			0
$292$	11.4762	+	8.46982i	0.671594	+	0.495659i
$293$	18.5869	−	9.82349i	1.08586	−	0.573894i	0.174147	−	0.984720i	$-0.444283\pi$
$293$	18.5869	−	9.82349i	1.08586	−	0.573894i	0.911714	+	0.410826i	$0.134759\pi$
$294$		0			0
$295$	14.5641	+	5.71599i	0.847955	+	0.332798i
$296$	10.5965	−	13.2876i	0.615911	−	0.772328i
$297$		0			0
$298$	2.62647	−	7.50602i	0.152147	−	0.434812i
$299$	27.0877	+	18.4681i	1.56652	+	1.06804i
$300$		0			0
$301$	7.74034	+	1.46455i	0.446146	+	0.0844153i
$302$	−9.71183	+	2.60228i	−0.558853	+	0.149744i
$303$		0			0
$304$	8.40549	+	11.3890i	0.482088	+	0.653206i
$305$	24.3773	−	2.74666i	1.39584	−	0.157273i
$306$		0			0
$307$	−1.65888	−	1.65888i	−0.0946772	−	0.0946772i	0.658182	−	0.752859i	$-0.271326\pi$
$307$	−1.65888	−	1.65888i	−0.0946772	−	0.0946772i	−0.752859	+	0.658182i	$0.771326\pi$
$308$	4.91698	−	5.71363i	0.280171	−	0.325564i
$309$		0			0
$310$	−0.366824	+	4.89492i	−0.0208342	+	0.278013i
$311$	4.21991	+	4.90363i	0.239289	+	0.278059i	0.864757	−	0.502191i	$-0.167473\pi$
$311$	4.21991	+	4.90363i	0.239289	+	0.278059i	−0.625467	+	0.780250i	$0.715092\pi$
$312$		0			0
$313$	−19.8385	−	2.99017i	−1.12134	−	0.169014i	−0.437900	−	0.899024i	$-0.644278\pi$
$313$	−19.8385	−	2.99017i	−1.12134	−	0.169014i	−0.683437	+	0.730009i	$0.739516\pi$
$314$	1.97943	−	1.57855i	0.111706	−	0.0890825i
$315$		0			0
$316$	2.53480	+	1.59272i	0.142593	+	0.0895974i
$317$	10.4430	−	4.55625i	0.586539	−	0.255904i	−0.0855997	−	0.996330i	$-0.527281\pi$
$317$	10.4430	−	4.55625i	0.586539	−	0.255904i	0.672139	+	0.740425i	$0.265376\pi$
$318$		0			0
$319$	−3.13699	+	6.17085i	−0.175638	+	0.345501i
$320$	−1.42454	−	0.822459i	−0.0796343	−	0.0459769i
$321$		0			0
$322$	−18.5437	−	0.693855i	−1.03340	−	0.0386670i
$323$	−6.10367	+	26.7419i	−0.339617	+	1.48796i
$324$		0			0
$325$	4.91785	+	3.92186i	0.272793	+	0.217546i
$326$	−1.55110	−	1.67169i	−0.0859076	−	0.0925864i
$327$		0			0
$328$	−15.3741	−	1.15213i	−0.848892	−	0.0636157i
$329$	0.220228	+	5.88571i	0.0121415	+	0.324490i
$330$		0			0
$331$	2.13003	+	0.570739i	0.117077	+	0.0313706i	0.316882	−	0.948465i	$-0.397364\pi$
$331$	2.13003	+	0.570739i	0.117077	+	0.0313706i	−0.199805	+	0.979836i	$0.564031\pi$
$332$	1.53250	+	0.738012i	0.0841067	+	0.0405037i
$333$		0			0
$334$	0.645703	+	5.73077i	0.0353313	+	0.313574i
$335$	19.8092	−	1.48449i	1.08229	−	0.0811064i
$336$		0			0
$337$	6.29336	−	33.2612i	0.342821	−	1.81185i	−0.209027	−	0.977910i	$-0.567030\pi$
$337$	6.29336	−	33.2612i	0.342821	−	1.81185i	0.551849	−	0.833944i	$-0.313923\pi$
$338$	−0.231793	+	0.00867309i	−0.0126079	+	0.000471754i
$339$		0			0
$340$	−2.22882	−	11.7796i	−0.120875	−	0.638837i
$341$	1.32390	+	5.80041i	0.0716935	+	0.314110i
$342$		0			0
$343$	3.26315	+	4.09186i	0.176193	+	0.220940i
$344$	1.40507	+	4.55512i	0.0757563	+	0.245596i
$345$		0			0
$346$	−2.26562	+	3.06981i	−0.121800	+	0.165034i
$347$	1.41886	−	2.45753i	0.0761683	−	0.131927i	−0.825425	−	0.564511i	$-0.809065\pi$
$347$	1.41886	−	2.45753i	0.0761683	−	0.131927i	0.901594	+	0.432584i	$0.142398\pi$
$348$		0			0
$349$	−13.2134	−	22.8862i	−0.707295	−	1.22507i	−0.965857	−	0.259076i	$-0.916582\pi$
$349$	−13.2134	−	22.8862i	−0.707295	−	1.22507i	0.258562	−	0.965995i	$-0.416751\pi$
$350$	−3.53798	−	0.398635i	−0.189113	−	0.0213079i
$351$		0			0
$352$	6.87895	+	1.57007i	0.366649	+	0.0836852i
$353$	−1.72127	+	4.38573i	−0.0916142	+	0.233429i	−0.969335	−	0.245743i	$-0.920968\pi$
$353$	−1.72127	+	4.38573i	−0.0916142	+	0.233429i	0.877721	+	0.479172i	$0.159063\pi$
$354$		0			0
$355$	7.48796	+	2.30973i	0.397420	+	0.122588i
$356$	2.71951	−	2.34033i	0.144134	−	0.124037i
$357$		0			0
$358$	6.62102	−	12.5276i	0.349932	−	0.662103i
$359$	12.5299	−	4.38440i	0.661303	−	0.231400i	0.0213010	−	0.999773i	$-0.493219\pi$
$359$	12.5299	−	4.38440i	0.661303	−	0.231400i	0.640002	+	0.768373i	$0.278933\pi$
$360$		0			0
$361$	12.2254	−	25.3863i	0.643442	−	1.33612i
$362$	5.00773	−	3.69588i	0.263201	−	0.194251i
$363$		0			0
$364$	−17.7336	+	12.0905i	−0.929491	+	0.633716i
$365$	4.03520	+	15.0596i	0.211212	+	0.788253i
$366$		0			0
$367$	−18.6655	−	9.86501i	−0.974332	−	0.514950i	−0.0972343	−	0.995262i	$-0.531000\pi$
$367$	−18.6655	−	9.86501i	−0.974332	−	0.514950i	−0.877098	+	0.480312i	$0.840523\pi$
$368$	8.00929	+	16.6315i	0.417513	+	0.866975i
$369$		0			0
$370$	8.20702	−	1.87320i	0.426663	−	0.0973830i
$371$	−4.42312	+	29.3455i	−0.229637	+	1.52354i
$372$		0			0
$373$	−0.342406	−	0.317706i	−0.0177291	−	0.0164502i	0.671258	−	0.741223i	$-0.265754\pi$
$373$	−0.342406	−	0.317706i	−0.0177291	−	0.0164502i	−0.688988	+	0.724773i	$0.741945\pi$
$374$	1.40439	+	2.65723i	0.0726192	+	0.137402i
$375$		0			0
$376$	−3.08654	+	1.78201i	−0.159176	+	0.0919003i
$377$	13.1750	−	14.6597i	0.678549	−	0.755014i
$378$		0			0
$379$	1.42454	−	12.6431i	0.0731737	−	0.649435i	−0.902574	−	0.430535i	$-0.858325\pi$
$379$	1.42454	−	12.6431i	0.0731737	−	0.649435i	0.975747	−	0.218899i	$-0.0702466\pi$
$380$	−0.770983	+	20.6049i	−0.0395506	+	1.05701i
$381$		0			0
$382$	−0.543262	−	3.60431i	−0.0277957	−	0.184413i
$383$	4.00297	+	10.1994i	0.204542	+	0.521165i	0.995928	−	0.0901518i	$-0.0287352\pi$
$383$	4.00297	+	10.1994i	0.204542	+	0.521165i	−0.791386	+	0.611317i	$0.790640\pi$
$384$		0			0
$385$	8.09599	−	1.53184i	0.412610	−	0.0780700i
$386$	8.66573	−	4.17319i	0.441074	−	0.212410i
$387$		0			0
$388$	0.957864	+	2.73742i	0.0486282	+	0.138971i
$389$	4.93448	−	18.4157i	0.250188	−	0.933715i	−0.720516	−	0.693438i	$-0.756095\pi$
$389$	4.93448	−	18.4157i	0.250188	−	0.933715i	0.970704	−	0.240277i	$-0.0772383\pi$
$390$		0			0
$391$	−14.3046	+	32.7864i	−0.723414	+	1.65808i
$392$	4.72728	−	10.8350i	0.238764	−	0.547252i
$393$		0			0
$394$	1.55462	−	5.80191i	0.0783205	−	0.292296i
$395$	1.08076	+	3.08865i	0.0543792	+	0.155407i
$396$		0			0
$397$	−17.4974	+	8.42630i	−0.878169	+	0.422904i	−0.817955	−	0.575282i	$-0.804892\pi$
$397$	−17.4974	+	8.42630i	−0.878169	+	0.422904i	−0.0602137	+	0.998186i	$0.519178\pi$
$398$	−11.0282	+	2.08664i	−0.552791	+	0.104594i
$399$		0			0
$400$	1.29394	+	3.29691i	0.0646971	+	0.164846i
$401$	−5.30567	−	35.2008i	−0.264952	−	1.75784i	−0.585557	−	0.810631i	$-0.699124\pi$
$401$	−5.30567	−	35.2008i	−0.264952	−	1.75784i	0.320605	−	0.947213i	$-0.396114\pi$
$402$		0			0
$403$	0.633412	−	16.9283i	0.0315525	−	0.843258i
$404$	−0.293120	+	2.60151i	−0.0145833	+	0.129430i
$405$		0			0
$406$	−1.89967	+	10.9934i	−0.0942790	+	0.545595i
$407$	8.83625	−	5.10161i	0.437997	−	0.252878i
$408$		0			0
$409$	5.87118	+	11.1088i	0.290311	+	0.549296i	0.985530	−	0.169503i	$-0.0542162\pi$
$409$	5.87118	+	11.1088i	0.290311	+	0.549296i	−0.695218	+	0.718798i	$0.744692\pi$
$410$	−5.59782	−	5.19402i	−0.276457	−	0.256514i
$411$		0			0
$412$	2.55626	−	16.9597i	0.125938	−	0.835545i
$413$	29.7957	−	6.80067i	1.46615	−	0.334639i
$414$		0			0
$415$	0.806700	+	1.67513i	0.0395994	+	0.0822289i
$416$	−17.7619	−	9.38743i	−0.870848	−	0.460257i
$417$		0			0
$418$	−1.33790	−	4.99312i	−0.0654390	−	0.244222i
$419$	−8.10443	+	5.52551i	−0.395927	+	0.269939i	−0.744876	−	0.667203i	$-0.767491\pi$
$419$	−8.10443	+	5.52551i	−0.395927	+	0.269939i	0.348948	+	0.937142i	$0.386539\pi$
$420$		0			0
$421$	−3.24358	+	2.39387i	−0.158083	+	0.116670i	−0.669989	−	0.742371i	$-0.733701\pi$
$421$	−3.24358	+	2.39387i	−0.158083	+	0.116670i	0.511907	+	0.859041i	$0.328939\pi$
$422$	−3.47769	+	7.22150i	−0.169291	+	0.351537i
$423$		0			0
$424$	−16.9503	+	5.93115i	−0.823177	+	0.288042i
$425$	−3.20697	+	6.06788i	−0.155561	+	0.294335i
$426$		0			0
$427$	36.3217	−	31.2573i	1.75773	−	1.51265i
$428$	−5.69674	−	1.75721i	−0.275362	−	0.0849380i
$429$		0			0
$430$	−0.862608	+	2.19789i	−0.0415987	+	0.105992i
$431$	−30.2968	−	6.91504i	−1.45934	−	0.333086i	−0.582095	−	0.813121i	$-0.697767\pi$
$431$	−30.2968	−	6.91504i	−1.45934	−	0.333086i	−0.877249	+	0.480035i	$0.840624\pi$
$432$		0			0
$433$	−17.4126	−	1.96193i	−0.836797	−	0.0942844i	−0.316843	−	0.948478i	$-0.602623\pi$
$433$	−17.4126	−	1.96193i	−0.836797	−	0.0942844i	−0.519955	+	0.854194i	$0.674051\pi$
$434$	4.79424	+	8.30386i	0.230131	+	0.398598i
$435$		0			0
$436$	−12.9651	+	22.4562i	−0.620916	+	1.07546i
$437$	36.5338	−	49.5015i	1.74765	−	2.36798i
$438$		0			0
$439$	2.94163	+	9.53652i	0.140396	+	0.455153i	0.998276	−	0.0586975i	$-0.0186947\pi$
$439$	2.94163	+	9.53652i	0.140396	+	0.455153i	−0.857880	+	0.513851i	$0.828219\pi$
$440$	3.10868	+	3.89816i	0.148200	+	0.185838i
$441$		0			0
$442$	−1.90424	−	8.34304i	−0.0905757	−	0.396838i
$443$	2.02742	+	10.7152i	0.0963257	+	0.509094i	0.997185	+	0.0749821i	$0.0238900\pi$
$443$	2.02742	+	10.7152i	0.0963257	+	0.509094i	−0.900859	+	0.434111i	$0.857062\pi$
$444$		0			0
$445$	3.91907	−	0.146641i	0.185782	−	0.00695146i
$446$	−2.34306	+	12.3834i	−0.110947	+	0.586370i
$447$		0			0
$448$	−3.20418	+	0.240120i	−0.151383	+	0.0113446i
$449$	−0.405760	−	3.60122i	−0.0191490	−	0.169952i	0.980498	−	0.196530i	$-0.0629674\pi$
$449$	−0.405760	−	3.60122i	−0.0191490	−	0.169952i	−0.999647	+	0.0265783i	$0.991539\pi$
$450$		0			0
$451$	−8.33908	−	4.01589i	−0.392672	−	0.189101i
$452$	14.9590	+	4.00825i	0.703611	+	0.188532i
$453$		0			0
$454$	−0.591146	−	15.7987i	−0.0277439	−	0.741471i
$455$	−23.3950	−	1.75321i	−1.09677	−	0.0821919i
$456$		0			0
$457$	9.09607	+	9.80323i	0.425496	+	0.458576i	0.909018	−	0.416756i	$-0.136833\pi$
$457$	9.09607	+	9.80323i	0.425496	+	0.458576i	−0.483522	+	0.875332i	$0.660643\pi$
$458$	−7.57991	−	6.04477i	−0.354186	−	0.282454i
$459$		0			0
$460$	−5.98355	+	26.2156i	−0.278984	+	1.22231i
$461$	−18.6864	−	0.699194i	−0.870311	−	0.0325647i	−0.401496	−	0.915861i	$-0.631509\pi$
$461$	−18.6864	−	0.699194i	−0.870311	−	0.0325647i	−0.468815	+	0.883296i	$0.655319\pi$
$462$		0			0
$463$	−9.86520	−	5.69568i	−0.458475	−	0.264701i	0.252928	−	0.967485i	$-0.418606\pi$
$463$	−9.86520	−	5.69568i	−0.458475	−	0.264701i	−0.711403	+	0.702785i	$0.751940\pi$
$464$	10.5516	−	3.43926i	0.489846	−	0.159664i
$465$		0			0
$466$	10.1686	−	4.43651i	0.471051	−	0.205517i
$467$	17.6805	+	11.1094i	0.818158	+	0.514083i	0.874898	−	0.484306i	$-0.160928\pi$
$467$	17.6805	+	11.1094i	0.818158	+	0.514083i	−0.0567408	+	0.998389i	$0.518071\pi$
$468$		0			0
$469$	30.3377	−	24.1935i	1.40087	−	1.11715i
$470$	−1.74559	−	0.263105i	−0.0805180	−	0.0121361i
$471$		0			0
$472$	12.0631	+	14.0176i	0.555249	+	0.645210i
$473$	−0.213863	+	2.85380i	−0.00983342	+	0.131218i
$474$		0			0
$475$	7.69971	−	8.94723i	0.353287	−	0.410527i
$476$	−16.5593	−	16.5593i	−0.758992	−	0.758992i
$477$		0			0
$478$	−5.74238	+	0.647011i	−0.262650	+	0.0295936i
$479$	7.60424	+	10.3034i	0.347446	+	0.470773i	0.943120	−	0.332454i	$-0.107877\pi$
$479$	7.60424	+	10.3034i	0.347446	+	0.470773i	−0.595673	+	0.803227i	$0.703115\pi$
$480$		0			0
$481$	−28.0616	+	7.51908i	−1.27950	+	0.342840i
$482$	1.84767	+	0.349598i	0.0841591	+	0.0159238i
$483$		0			0
$484$	−12.7993	−	8.72642i	−0.581786	−	0.396655i
$485$	−1.04701	+	2.99220i	−0.0475425	+	0.135869i
$486$		0			0
$487$	16.0848	−	20.1697i	0.728873	−	0.913978i	−0.269930	−	0.962880i	$-0.587001\pi$
$487$	16.0848	−	20.1697i	0.728873	−	0.913978i	0.998804	+	0.0489019i	$0.0155722\pi$
$488$	26.9924	+	10.5937i	1.22189	+	0.479556i
$489$		0			0
$490$	5.17674	−	2.73599i	0.233861	−	0.123599i
$491$	−25.5288	−	18.8411i	−1.15210	−	0.850287i	−0.161470	−	0.986878i	$-0.551623\pi$
$491$	−25.5288	−	18.8411i	−1.15210	−	0.850287i	−0.990628	+	0.136591i	$0.956385\pi$
$492$		0			0
$493$	18.3890	+	11.1510i	0.828197	+	0.502216i
$494$			14.7184i			0.662210i
$495$		0			0
$496$	5.07468	−	8.07630i	0.227860	−	0.362637i
$497$	14.6269	−	4.51180i	0.656105	−	0.202382i
$498$		0			0
$499$	−6.47222	+	2.54016i	−0.289736	+	0.113713i	−0.505758	−	0.862676i	$-0.668787\pi$
$499$	−6.47222	+	2.54016i	−0.289736	+	0.113713i	0.216022	+	0.976389i	$0.430692\pi$
$500$	−5.94499	+	19.2732i	−0.265868	+	0.861923i
$501$		0			0
$502$	0.895300	−	1.31316i	0.0399592	−	0.0586093i
$503$	20.7948	−	13.0663i	0.927197	−	0.582596i	0.0183977	−	0.999831i	$-0.494144\pi$
$503$	20.7948	−	13.0663i	0.927197	−	0.582596i	0.908799	+	0.417235i	$0.137001\pi$
$504$		0			0
$505$	−2.02348	+	2.02348i	−0.0900438	+	0.0900438i
$506$	−0.503775	−	6.72241i	−0.0223955	−	0.298847i
$507$		0			0
$508$	−2.85009	−	1.24348i	−0.126452	−	0.0551705i
$509$	22.6715	+	33.2529i	1.00489	+	1.47391i	0.876035	+	0.482247i	$0.160179\pi$
$509$	22.6715	+	33.2529i	1.00489	+	1.47391i	0.128859	+	0.991663i	$0.458868\pi$
$510$		0			0
$511$	23.0839	+	19.8653i	1.02117	+	0.878790i
$512$	−10.7136	−	17.0506i	−0.473480	−	0.753539i
$513$		0			0
$514$	−0.593678	−	0.207737i	−0.0261860	−	0.00916289i
$515$	13.7430	−	12.7516i	0.605587	−	0.561903i
$516$		0			0
$517$	−2.11576	+	0.318899i	−0.0930509	+	0.0140252i
$518$	11.1846	−	12.0541i	0.491423	−	0.529628i
$519$		0			0
$520$	−5.67702	−	13.0119i	−0.248954	−	0.570608i
$521$	−3.70615			−0.162370			−0.0811848	−	0.996699i	$-0.525870\pi$
$521$	−3.70615			−0.162370			−0.0811848	+	0.996699i	$0.525870\pi$
$522$		0			0
$523$	21.1827			0.926256			0.463128	−	0.886291i	$-0.346727\pi$
$523$	21.1827			0.926256			0.463128	+	0.886291i	$0.346727\pi$
$524$	−6.31300	−	14.4696i	−0.275785	−	0.632106i
$525$		0			0
$526$	−7.18640	+	7.74509i	−0.313342	+	0.337702i
$527$	18.2770	−	2.75481i	0.796158	−	0.120001i
$528$		0			0
$529$	41.9547	−	38.9282i	1.82412	−	1.69253i
$530$	−8.39567	−	2.93777i	−0.364684	−	0.127609i
$531$		0			0
$532$	21.4290	+	34.1040i	0.929063	+	1.47860i
$533$	19.9753	+	17.1901i	0.865225	+	0.744586i
$534$		0			0
$535$	−3.67085	−	5.38415i	−0.158705	−	0.232777i
$536$	21.5214	+	9.38968i	0.929582	+	0.405573i
$537$		0			0
$538$	−0.203281	−	2.71260i	−0.00876408	−	0.116949i
$539$	5.01830	−	5.01830i	0.216154	−	0.216154i
$540$		0			0
$541$	−33.4037	+	20.9889i	−1.43614	+	0.902385i	−0.436140	+	0.899879i	$0.643655\pi$
$541$	−33.4037	+	20.9889i	−1.43614	+	0.902385i	−0.999997	+	0.00250608i	$0.999202\pi$
$542$	−0.844771	+	1.23905i	−0.0362860	+	0.0532218i
$543$		0			0
$544$	6.46111	−	20.9464i	0.277018	−	0.898070i
$545$	−26.3843	+	10.3551i	−1.13018	+	0.443563i
$546$		0			0
$547$	2.92690	−	0.902828i	0.125145	−	0.0386021i	−0.231550	−	0.972823i	$-0.574380\pi$
$547$	2.92690	−	0.902828i	0.125145	−	0.0386021i	0.356695	+	0.934221i	$0.383904\pi$
$548$	−0.922078	+	1.46748i	−0.0393892	+	0.0626876i
$549$		0			0
$550$		−	1.29341i		−	0.0551512i
$551$	−26.5668	−	25.7357i	−1.13178	−	1.09638i
$552$		0			0
$553$	5.14300	+	3.79571i	0.218703	+	0.161410i
$554$	1.53794	−	0.812823i	0.0653407	−	0.0345336i
$555$		0			0
$556$	−5.34366	−	2.09723i	−0.226622	−	0.0889424i
$557$	−9.78635	+	12.2717i	−0.414661	+	0.519969i	−0.944669	−	0.328024i	$-0.893617\pi$
$557$	−9.78635	+	12.2717i	−0.414661	+	0.519969i	0.530008	+	0.847992i	$0.322189\pi$
$558$		0			0
$559$	2.69123	−	7.69110i	0.113827	−	0.325299i
$560$	−10.9144	−	7.44129i	−0.461216	−	0.314452i
$561$		0			0
$562$	−2.96676	−	0.561341i	−0.125145	−	0.0236787i
$563$	−26.3568	+	7.06228i	−1.11081	+	0.297640i	−0.767157	−	0.641459i	$-0.778330\pi$
$563$	−26.3568	+	7.06228i	−1.11081	+	0.297640i	−0.343648	+	0.939098i	$0.611663\pi$
$564$		0			0
$565$	10.0522	+	13.6203i	0.422900	+	0.573009i
$566$	−9.34002	+	1.05237i	−0.392590	+	0.0442343i
$567$		0			0
$568$	6.54955	+	6.54955i	0.274813	+	0.274813i
$569$	19.7647	−	22.9671i	0.828581	−	0.962829i	−0.171167	−	0.985242i	$-0.554754\pi$
$569$	19.7647	−	22.9671i	0.828581	−	0.962829i	0.999749	+	0.0224130i	$0.00713486\pi$
$570$		0			0
$571$	−0.146362	+	1.95307i	−0.00612506	+	0.0817333i	−0.999429	−	0.0338007i	$-0.989239\pi$
$571$	−0.146362	+	1.95307i	−0.00612506	+	0.0817333i	0.993304	+	0.115534i	$0.0368579\pi$
$572$	−5.08593	−	5.90996i	−0.212653	−	0.247108i
$573$		0			0
$574$	−14.7501	−	2.22322i	−0.615656	−	0.0927952i
$575$	12.0354	−	9.59793i	0.501912	−	0.400261i
$576$		0			0
$577$	13.6071	+	8.54991i	0.566471	+	0.355937i	0.784619	−	0.619978i	$-0.212859\pi$
$577$	13.6071	+	8.54991i	0.566471	+	0.355937i	−0.218148	+	0.975916i	$0.570002\pi$
$578$	−0.564404	+	0.246247i	−0.0234761	+	0.0102425i
$579$		0			0
$580$	15.1407	+	5.66637i	0.628684	+	0.235283i
$581$	3.14527	+	1.81592i	0.130488	+	0.0753371i
$582$		0			0
$583$	−10.7735	−	0.403116i	−0.446193	−	0.0166954i
$584$	−4.10077	+	17.9667i	−0.169691	+	0.743465i
$585$		0			0
$586$	9.62315	+	7.67421i	0.397529	+	0.317019i
$587$	−9.97283	−	10.7482i	−0.411623	−	0.443624i	0.492876	−	0.870099i	$-0.335945\pi$
$587$	−9.97283	−	10.7482i	−0.411623	−	0.443624i	−0.904499	+	0.426476i	$0.859755\pi$
$588$		0			0
$589$	−31.7011	−	2.37567i	−1.30622	−	0.0978876i
$590$	0.342505	+	9.15365i	0.0141007	+	0.376850i
$591$		0			0
$592$	−15.8003	−	4.23368i	−0.649389	−	0.174003i
$593$	−3.15432	−	1.51904i	−0.129533	−	0.0623796i	0.367995	−	0.929828i	$-0.380044\pi$
$593$	−3.15432	−	1.51904i	−0.129533	−	0.0623796i	−0.497527	+	0.867448i	$0.665759\pi$
$594$		0			0
$595$	−2.86606	−	25.4370i	−0.117497	−	1.04281i
$596$	−22.4467	+	1.68214i	−0.919451	+	0.0689033i
$597$		0			0
$598$	−3.56844	+	18.8597i	−0.145924	+	0.771229i
$599$	−43.8025	+	1.63897i	−1.78972	+	0.0669666i	−0.911503	−	0.411294i	$-0.865077\pi$
$599$	−43.8025	+	1.63897i	−1.78972	+	0.0669666i	−0.878218	+	0.478261i	$0.841267\pi$
$600$		0			0
$601$	−4.34605	−	22.9694i	−0.177279	−	0.936942i	−0.952336	−	0.305051i	$-0.901327\pi$
$601$	−4.34605	−	22.9694i	−0.177279	−	0.936942i	0.775057	−	0.631891i	$-0.217721\pi$
$602$	1.02630	+	4.49651i	0.0418288	+	0.183264i
$603$		0			0
$604$	17.7445	+	22.2509i	0.722012	+	0.905375i
$605$	−4.99104	−	16.1806i	−0.202915	−	0.657833i
$606$		0			0
$607$	20.2804	−	27.4790i	0.823157	−	1.11534i	−0.168407	−	0.985718i	$-0.553862\pi$
$607$	20.2804	−	27.4790i	0.823157	−	1.11534i	0.991564	−	0.129620i	$-0.0413759\pi$
$608$	−18.8505	+	32.6501i	−0.764490	+	1.32413i
$609$		0			0
$610$	7.18125	+	12.4383i	0.290760	+	0.503611i
$611$	6.05390	+	0.682111i	0.244915	+	0.0275953i
$612$		0			0
$613$	16.5394	+	3.77501i	0.668020	+	0.152471i	0.543064	−	0.839691i	$-0.317264\pi$
$613$	16.5394	+	3.77501i	0.668020	+	0.152471i	0.124955	+	0.992162i	$0.460121\pi$
$614$	0.501803	−	1.27857i	0.0202511	−	0.0515990i
$615$		0			0
$616$	9.30676	+	2.87075i	0.374980	+	0.115666i
$617$	−27.2867	+	23.4821i	−1.09852	+	0.945354i	−0.998766	−	0.0496578i	$-0.984187\pi$
$617$	−27.2867	+	23.4821i	−1.09852	+	0.945354i	−0.0997552	+	0.995012i	$0.531806\pi$
$618$		0			0
$619$	−13.2327	+	25.0374i	−0.531865	+	1.00634i	0.461034	+	0.887382i	$0.347479\pi$
$619$	−13.2327	+	25.0374i	−0.531865	+	1.00634i	−0.992900	+	0.118956i	$0.962045\pi$
$620$	13.1146	−	4.58901i	0.526696	−	0.184299i
$621$		0			0
$622$	−1.64340	+	3.41255i	−0.0658943	+	0.136831i
$623$	6.16387	−	4.54914i	0.246950	−	0.182258i
$624$		0			0
$625$	−11.1158	+	7.57863i	−0.444632	+	0.303145i
$626$	−3.04010	−	11.3458i	−0.121507	−	0.453469i
$627$		0			0
$628$	−6.33597	−	3.34866i	−0.252833	−	0.133626i
$629$	−13.7533	−	28.5590i	−0.548380	−	1.13872i
$630$		0			0
$631$	1.09042	−	0.248881i	0.0434088	−	0.00990778i	−0.200761	−	0.979640i	$-0.564342\pi$
$631$	1.09042	−	0.248881i	0.0434088	−	0.00990778i	0.244170	+	0.969732i	$0.421484\pi$
$632$	−0.576482	+	3.82471i	−0.0229312	+	0.152139i
$633$		0			0
$634$	4.88995	+	4.53721i	0.194205	+	0.180196i
$635$	−1.58822	−	3.00507i	−0.0630268	−	0.119252i
$636$		0			0
$637$	−17.4998	+	10.1035i	−0.693368	+	0.400316i
$638$	−4.04585	−	0.238621i	−0.160177	−	0.00944709i
$639$		0			0
$640$	2.33437	−	20.7181i	0.0922739	−	0.818954i
$641$	−1.69467	+	45.2909i	−0.0669353	+	1.78888i	0.412152	+	0.911115i	$0.364777\pi$
$641$	−1.69467	+	45.2909i	−0.0669353	+	1.78888i	−0.479087	+	0.877767i	$0.659032\pi$
$642$		0			0
$643$	1.46511	+	9.72037i	0.0577783	+	0.383334i	0.998967	+	0.0454513i	$0.0144726\pi$
$643$	1.46511	+	9.72037i	0.0577783	+	0.383334i	−0.941188	+	0.337883i	$0.890289\pi$
$644$	19.1900	+	48.8952i	0.756190	+	1.92674i
$645$		0			0
$646$	−15.7793	+	2.98560i	−0.620827	+	0.117467i
$647$	−19.9433	+	9.60419i	−0.784052	+	0.377580i	−0.782684	−	0.622420i	$-0.786150\pi$
$647$	−19.9433	+	9.60419i	−0.784052	+	0.377580i	−0.00136817	+	0.999999i	$0.500436\pi$
$648$		0			0
$649$	3.66694	+	10.4795i	0.143940	+	0.411356i
$650$	−0.953156	+	3.55723i	−0.0373858	+	0.139526i
$651$		0			0
$652$	−2.58131	+	5.91643i	−0.101092	+	0.231705i
$653$	14.9925	−	34.3631i	0.586701	−	1.34473i	−0.329554	−	0.944137i	$-0.606898\pi$
$653$	14.9925	−	34.3631i	0.586701	−	1.34473i	0.916255	−	0.400596i	$-0.131197\pi$
$654$		0			0
$655$	4.46621	−	16.6681i	0.174509	−	0.651277i
$656$	4.90088	+	14.0059i	0.191347	+	0.546839i
$657$		0			0
$658$	−3.10683	+	1.49617i	−0.121117	+	0.0583268i
$659$	−34.7249	+	6.57030i	−1.35269	+	0.255943i	−0.811202	−	0.584766i	$-0.801186\pi$
$659$	−34.7249	+	6.57030i	−1.35269	+	0.255943i	−0.541488	+	0.840709i	$0.682139\pi$
$660$		0			0
$661$	−7.47190	−	19.0381i	−0.290623	−	0.740496i	−0.999386	−	0.0350489i	$-0.988841\pi$
$661$	−7.47190	−	19.0381i	−0.290623	−	0.740496i	0.708762	−	0.705447i	$-0.249254\pi$
$662$	0.192422	+	1.27664i	0.00747871	+	0.0496180i
$663$		0			0
$664$	−0.0821740	+	2.19615i	−0.00318897	+	0.0852270i
$665$	−4.92938	+	43.7495i	−0.191153	+	1.69653i
$666$		0			0
$667$	−27.8023	−	39.4181i	−1.07651	−	1.52627i
$668$	14.1371	−	8.16204i	0.546980	−	0.315799i
$669$		0			0
$670$	5.43443	+	10.2824i	0.209950	+	0.397245i
$671$	12.7611	+	11.8406i	0.492637	+	0.457101i
$672$		0			0
$673$	−0.605378	+	4.01642i	−0.0233356	+	0.154822i	−0.997464	−	0.0711740i	$-0.977325\pi$
$673$	−0.605378	+	4.01642i	−0.0233356	+	0.154822i	0.974128	+	0.225996i	$0.0725635\pi$
$674$	19.3221	−	4.41014i	0.744259	−	0.169872i
$675$		0			0
$676$	0.284875	+	0.591549i	0.0109567	+	0.0227519i
$677$	−42.7466	−	22.5923i	−1.64289	−	0.868291i	−0.994237	−	0.107204i	$-0.965810\pi$
$677$	−42.7466	−	22.5923i	−1.64289	−	0.868291i	−0.648650	−	0.761087i	$-0.724666\pi$
$678$		0			0
$679$	1.60271	+	5.98141i	0.0615065	+	0.229545i
$680$	12.7982	−	8.72566i	0.490788	−	0.334614i
$681$		0			0
$682$	−2.80266	+	2.06845i	−0.107319	+	0.0792052i
$683$	19.0377	−	39.5323i	0.728459	−	1.51266i	−0.125372	−	0.992110i	$-0.540012\pi$
$683$	19.0377	−	39.5323i	0.728459	−	1.51266i	0.853831	−	0.520551i	$-0.174273\pi$
$684$		0			0
$685$	−1.78812	+	0.625691i	−0.0683206	+	0.0239064i
$686$	−1.43179	+	2.70908i	−0.0546660	+	0.103433i
$687$		0			0
$688$	3.47758	−	2.99270i	0.132582	−	0.114096i
$689$	29.3330	+	9.04802i	1.11750	+	0.344702i
$690$		0			0
$691$	−6.47640	+	16.5016i	−0.246374	+	0.627750i	−0.999548	−	0.0300710i	$-0.990427\pi$
$691$	−6.47640	+	16.5016i	−0.246374	+	0.627750i	0.753174	+	0.657822i	$0.228522\pi$
$692$	10.5288	+	2.40314i	0.400247	+	0.0913537i
$693$		0			0
$694$	1.65095	+	0.186018i	0.0626693	+	0.00706113i
$695$	−3.13738	−	5.43410i	−0.119008	−	0.206127i
$696$		0			0
$697$	−14.3772	+	24.9021i	−0.544576	+	0.943234i
$698$	9.18762	−	12.4488i	0.347757	−	0.471194i
$699$		0			0
$700$	2.97052	+	9.63020i	0.112275	+	0.363987i
$701$	−28.4724	−	35.7032i	−1.07539	−	1.34849i	−0.933487	−	0.358611i	$-0.883251\pi$
$701$	−28.4724	−	35.7032i	−1.07539	−	1.34849i	−0.141899	−	0.989881i	$-0.545321\pi$
$702$		0			0
$703$	12.1314	+	53.1513i	0.457546	+	2.00464i
$704$	−0.217010	−	1.14693i	−0.00817888	−	0.0432264i
$705$		0			0
$706$	−2.75647	+	0.103140i	−0.103741	+	0.00388171i
$707$	−1.03922	+	5.49243i	−0.0390840	+	0.206564i
$708$		0			0
$709$	−25.9681	+	1.94604i	−0.975253	+	0.0730851i	−0.552812	−	0.833306i	$-0.686445\pi$
$709$	−25.9681	+	1.94604i	−0.975253	+	0.0730851i	−0.422440	+	0.906391i	$0.638826\pi$
$710$	0.513671	+	4.55896i	0.0192777	+	0.171095i
$711$		0			0
$712$	4.17660	+	2.01134i	0.156525	+	0.0753783i
$713$	−40.0448	−	10.7300i	−1.49969	−	0.401841i
$714$		0			0
$715$	−0.318676	−	8.51681i	−0.0119178	−	0.318510i
$716$	−39.9962	−	2.99730i	−1.49473	−	0.112014i
$717$		0			0
$718$	5.28632	+	5.69730i	0.197284	+	0.212621i
$719$	−17.9950	−	14.3506i	−0.671101	−	0.535185i	0.227596	−	0.973756i	$-0.426914\pi$
$719$	−17.9950	−	14.3506i	−0.671101	−	0.535185i	−0.898697	+	0.438570i	$0.855485\pi$
$720$		0			0
$721$	8.14900	−	35.7031i	0.303485	−	1.32965i
$722$	16.4851	+	0.616828i	0.613511	+	0.0229560i
$723$		0			0
$724$	−15.2570	−	8.80864i	−0.567022	−	0.327370i
$725$	−4.75420	−	7.94043i	−0.176567	−	0.294900i
$726$		0			0
$727$	25.5756	−	11.1585i	0.948547	−	0.413847i	0.132080	−	0.991239i	$-0.457834\pi$
$727$	25.5756	−	11.1585i	0.948547	−	0.413847i	0.816467	+	0.577392i	$0.195930\pi$
$728$	−23.4805	−	14.7538i	−0.870245	−	0.546811i
$729$		0			0
$730$	−7.13652	+	5.69119i	−0.264135	+	0.210640i
$731$	8.79140	+	1.32509i	0.325162	+	0.0490102i
$732$		0			0
$733$	−24.3536	−	28.2994i	−0.899520	−	1.04526i	−0.998739	−	0.0501960i	$-0.984015\pi$
$733$	−24.3536	−	28.2994i	−0.899520	−	1.04526i	0.0992190	−	0.995066i	$-0.468366\pi$
$734$	0.923701	−	12.3259i	0.0340944	−	0.454959i
$735$		0			0
$736$	−32.0704	+	37.2665i	−1.18213	+	1.37366i
$737$	9.96773	+	9.96773i	0.367166	+	0.367166i
$738$		0			0
$739$	2.57887	−	0.290569i	0.0948654	−	0.0106888i	−0.0644041	−	0.997924i	$-0.520515\pi$
$739$	2.57887	−	0.290569i	0.0948654	−	0.0106888i	0.159270	+	0.987235i	$0.449086\pi$
$740$	−14.1496	−	19.1720i	−0.520150	−	0.704778i
$741$		0			0
$742$	−16.7830	+	4.49698i	−0.616122	+	0.165089i
$743$	−4.49542	−	0.850580i	−0.164921	−	0.0312048i	0.102795	−	0.994703i	$-0.467221\pi$
$743$	−4.49542	−	0.850580i	−0.164921	−	0.0312048i	−0.267716	+	0.963498i	$0.586269\pi$
$744$		0			0
$745$	−20.3293	−	13.8603i	−0.744808	−	0.507801i
$746$	0.0903218	−	0.258125i	0.00330692	−	0.00945063i
$747$		0			0
$748$	5.30428	−	6.65136i	0.193944	−	0.243198i
$749$	−11.8492	−	4.65048i	−0.432962	−	0.169925i
$750$		0			0
$751$	25.0618	−	13.2455i	0.914517	−	0.483337i	0.0573382	−	0.998355i	$-0.481739\pi$
$751$	25.0618	−	13.2455i	0.914517	−	0.483337i	0.857179	+	0.515018i	$0.172215\pi$
$752$	2.75999	+	2.03697i	0.100646	+	0.0742805i
$753$		0			0
$754$	10.9513	+	3.63778i	0.398823	+	0.132480i
$755$			31.1088i			1.13216i
$756$		0			0
$757$	−6.75132	+	10.7447i	−0.245381	+	0.390521i	−0.946593	−	0.322432i	$-0.895500\pi$
$757$	−6.75132	+	10.7447i	−0.245381	+	0.390521i	0.701212	+	0.712953i	$0.252643\pi$
$758$	7.11809	−	2.19564i	0.258541	−	0.0797492i
$759$		0			0
$760$	−24.7994	+	9.73305i	−0.899569	+	0.353055i
$761$	13.8324	−	44.8437i	0.501425	−	1.62558i	−0.251772	−	0.967787i	$-0.581013\pi$
$761$	13.8324	−	44.8437i	0.501425	−	1.62558i	0.753197	−	0.657795i	$-0.228511\pi$
$762$		0			0
$763$	−31.1888	+	45.7455i	−1.12911	+	1.65610i
$764$	−8.73612	+	5.48927i	−0.316062	+	0.198595i
$765$		0			0
$766$	−4.53601	+	4.53601i	−0.163893	+	0.163893i
$767$	−2.36238	−	31.5237i	−0.0853004	−	1.13826i
$768$		0			0
$769$	10.5381	+	4.59771i	0.380012	+	0.165798i	0.581211	−	0.813753i	$-0.302579\pi$
$769$	10.5381	+	4.59771i	0.380012	+	0.165798i	−0.201199	+	0.979550i	$0.564484\pi$
$770$	2.71749	+	3.98583i	0.0979317	+	0.143639i
$771$		0			0
$772$	−20.6359	−	17.7587i	−0.742704	−	0.639149i
$773$	23.2548	+	37.0098i	0.836416	+	1.33115i	0.941613	+	0.336698i	$0.109310\pi$
$773$	23.2548	+	37.0098i	0.836416	+	1.33115i	−0.105196	+	0.994451i	$0.533547\pi$
$774$		0			0
$775$	−7.50787	−	2.62712i	−0.269691	−	0.0943688i
$776$	−2.74684	+	2.54869i	−0.0986057	+	0.0914927i
$777$		0			0
$778$	11.0375	−	1.66364i	0.395715	−	0.0596445i
$779$	33.6381	−	36.2533i	1.20521	−	1.29891i
$780$		0			0
$781$	2.22368	+	5.09673i	0.0795695	+	0.182375i
$782$	−20.9429			−0.748918
$783$		0			0
$784$	−11.3778			−0.406348
$785$	−3.13253	−	7.17984i	−0.111805	−	0.256260i
$786$		0			0
$787$	6.05694	−	6.52783i	0.215906	−	0.232692i	−0.615807	−	0.787897i	$-0.711170\pi$
$787$	6.05694	−	6.52783i	0.215906	−	0.232692i	0.831713	+	0.555205i	$0.187360\pi$
$788$	−16.8122	+	2.53404i	−0.598911	+	0.0902713i
$789$		0			0
$790$	−1.40440	+	1.30309i	−0.0499662	+	0.0463619i
$791$	31.2114	+	10.9213i	1.10975	+	0.388318i
$792$		0			0
$793$	−26.3708	−	41.9688i	−0.936453	−	1.49036i
$794$	−8.61830	−	7.41665i	−0.305852	−	0.263207i
$795$		0			0
$796$	17.8967	+	26.2496i	0.634331	+	0.930392i
$797$	36.7249	+	16.0229i	1.30086	+	0.567560i	0.932180	−	0.361996i	$-0.117905\pi$
$797$	36.7249	+	16.0229i	1.30086	+	0.567560i	0.368682	+	0.929556i	$0.379809\pi$
$798$		0			0
$799$	0.496748	+	6.62864i	0.0175737	+	0.234504i
$800$	−6.67032	+	6.67032i	−0.235831	+	0.235831i
$801$		0			0
$802$	17.6473	−	11.0885i	0.623147	−	0.391549i
$803$	−6.23237	+	9.14120i	−0.219935	+	0.322586i
$804$		0			0
$805$	−16.9233	+	54.8641i	−0.596470	+	1.93371i
$806$	9.23236	−	3.62343i	0.325196	−	0.127630i
$807$		0			0
$808$	−3.23225	+	0.997016i	−0.113710	+	0.0350749i
$809$	−0.548274	+	0.872572i	−0.0192763	+	0.0306780i	−0.856223	−	0.516606i	$-0.827195\pi$
$809$	−0.548274	+	0.872572i	−0.0192763	+	0.0306780i	0.836947	+	0.547284i	$0.184338\pi$
$810$		0			0
$811$			5.29060i			0.185778i	0.995676	+	0.0928891i	$0.0296102\pi$
$811$			5.29060i			0.185778i	−0.995676	+	0.0928891i	$0.970390\pi$
$812$	30.6717	−	7.51526i	1.07637	−	0.263734i
$813$		0			0
$814$	4.80642	+	3.54730i	0.168465	+	0.124333i
$815$	−6.23815	+	3.29696i	−0.218513	+	0.115487i
$816$		0			0
$817$	−14.2342	−	5.58653i	−0.497993	−	0.195448i
$818$	−4.58663	+	5.75145i	−0.160368	+	0.201095i
$819$		0			0
$820$	−7.13907	+	20.4023i	−0.249307	+	0.712479i
$821$	29.0659	+	19.8168i	1.01441	+	0.691611i	0.951892	−	0.306433i	$-0.0991355\pi$
$821$	29.0659	+	19.8168i	1.01441	+	0.691611i	0.0625149	+	0.998044i	$0.480088\pi$
$822$		0			0
$823$	13.1045	+	2.47951i	0.456795	+	0.0864303i	0.409217	−	0.912437i	$-0.365802\pi$
$823$	13.1045	+	2.47951i	0.456795	+	0.0864303i	0.0475784	+	0.998868i	$0.484850\pi$
$824$	21.4050	−	5.73546i	0.745679	−	0.199804i
$825$		0			0
$826$	10.6253	+	14.3968i	0.369701	+	0.500928i
$827$	47.5270	−	5.35500i	1.65267	−	0.186212i	0.764149	−	0.645039i	$-0.223159\pi$
$827$	47.5270	−	5.35500i	1.65267	−	0.186212i	0.888525	+	0.458828i	$0.151730\pi$
$828$		0			0
$829$	39.4991	+	39.4991i	1.37186	+	1.37186i	0.857686	+	0.514174i	$0.171902\pi$
$829$	39.4991	+	39.4991i	1.37186	+	1.37186i	0.514174	+	0.857686i	$0.328098\pi$
$830$	−0.710040	+	0.825082i	−0.0246459	+	0.0286390i
$831$		0			0
$832$	−0.248371	+	3.31428i	−0.00861070	+	0.114902i
$833$	−14.3816	−	16.7117i	−0.498293	−	0.579027i
$834$		0			0
$835$	17.6441	+	2.65942i	0.610600	+	0.0920331i
$836$	−11.4398	+	9.12292i	−0.395653	+	0.315523i
$837$		0			0
$838$	−4.86255	−	3.05534i	−0.167974	−	0.105545i
$839$	−18.2703	+	7.97124i	−0.630760	+	0.275198i	−0.690853	−	0.722995i	$-0.742765\pi$
$839$	−18.2703	+	7.97124i	−0.630760	+	0.275198i	0.0600932	+	0.998193i	$0.480860\pi$
$840$		0			0
$841$	−25.7151	+	13.4064i	−0.886728	+	0.462291i
$842$	−2.04401	−	1.18011i	−0.0704411	−	0.0406692i
$843$		0			0
$844$	22.6720	+	0.848327i	0.780403	+	0.0292006i
$845$	−0.159698	+	0.699684i	−0.00549379	+	0.0240699i
$846$		0			0
$847$	−25.8601	−	20.6228i	−0.888565	−	0.708607i
$848$	11.7561	+	12.6701i	0.403708	+	0.435094i
$849$		0			0
$850$	−4.00698	−	0.300282i	−0.137438	−	0.0102996i
$851$	2.65842	+	71.0477i	0.0911294	+	2.43548i
$852$		0			0
$853$	1.54122	+	0.412969i	0.0527704	+	0.0141398i	0.285108	−	0.958496i	$-0.407971\pi$
$853$	1.54122	+	0.412969i	0.0527704	+	0.0141398i	−0.232337	+	0.972635i	$0.574637\pi$
$854$	25.2771	+	12.1728i	0.864965	+	0.416545i
$855$		0			0
$856$	−0.862419	−	7.65418i	−0.0294769	−	0.261614i
$857$	4.58909	−	0.343904i	0.156760	−	0.0117476i	0.00388120	−	0.999992i	$-0.498765\pi$
$857$	4.58909	−	0.343904i	0.156760	−	0.0117476i	0.152879	+	0.988245i	$0.451146\pi$
$858$		0			0
$859$	7.08136	−	37.4259i	0.241613	−	1.27696i	−0.626042	−	0.779789i	$-0.715326\pi$
$859$	7.08136	−	37.4259i	0.241613	−	1.27696i	0.867655	−	0.497166i	$-0.165626\pi$
$860$	6.67863	−	0.249897i	0.227740	−	0.00852141i
$861$		0			0
$862$	−3.38248	−	17.8768i	−0.115208	−	0.608888i
$863$	1.48533	+	6.50765i	0.0505612	+	0.221523i	0.993896	−	0.110319i	$-0.0351872\pi$
$863$	1.48533	+	6.50765i	0.0505612	+	0.221523i	−0.943335	+	0.331842i	$0.892330\pi$
$864$		0			0
$865$	7.36015	+	9.22934i	0.250253	+	0.313807i
$866$	−3.02392	−	9.80331i	−0.102757	−	0.333130i
$867$		0			0
$868$	16.1169	−	21.8376i	0.547042	−	0.741216i
$869$	−1.16105	+	2.01099i	−0.0393858	+	0.0682182i
$870$		0			0
$871$	−20.0684	−	34.7594i	−0.679991	−	1.17778i
$872$	−33.2922	−	3.75113i	−1.12742	−	0.127029i
$873$		0			0
$874$	35.1170	+	8.01523i	1.18785	+	0.271119i
$875$	−15.7335	+	40.0883i	−0.531889	+	1.35523i
$876$		0			0
$877$	−22.2970	−	6.87772i	−0.752916	−	0.232244i	−0.105541	−	0.994415i	$-0.533657\pi$
$877$	−22.2970	−	6.87772i	−0.752916	−	0.232244i	−0.647376	+	0.762171i	$0.724134\pi$
$878$	−4.42878	+	3.81127i	−0.149464	+	0.128624i
$879$		0			0
$880$	2.24234	−	4.24271i	0.0755892	−	0.143022i
$881$	−5.99551	+	2.09792i	−0.201994	+	0.0706808i	−0.429380	−	0.903124i	$-0.641268\pi$
$881$	−5.99551	+	2.09792i	−0.201994	+	0.0706808i	0.227386	+	0.973805i	$0.426982\pi$
$882$		0			0
$883$	−13.4568	+	27.9434i	−0.452859	+	0.940371i	0.542121	+	0.840300i	$0.317621\pi$
$883$	−13.4568	+	27.9434i	−0.452859	+	0.940371i	−0.994980	+	0.100071i	$0.968093\pi$
$884$	−19.4898	+	14.3841i	−0.655512	+	0.483790i
$885$		0			0
$886$	−5.27531	+	3.59665i	−0.177228	+	0.120832i
$887$	7.38642	+	27.5665i	0.248012	+	0.925592i	0.971846	+	0.235618i	$0.0757115\pi$
$887$	7.38642	+	27.5665i	0.248012	+	0.925592i	−0.723834	+	0.689974i	$0.757622\pi$
$888$		0			0
$889$	−5.87006	−	3.10242i	−0.196875	−	0.104052i
$890$	0.996243	+	2.06872i	0.0333941	+	0.0693437i
$891$		0			0
$892$	34.7797	−	7.93824i	1.16451	−	0.265792i
$893$	1.70395	−	11.3050i	0.0570206	−	0.378307i
$894$		0			0
$895$	−32.1380	−	29.8197i	−1.07425	−	0.996762i
$896$	−19.0302	−	36.0069i	−0.635754	−	1.20291i
$897$		0			0
$898$	1.83749	−	1.06088i	0.0613178	−	0.0354019i
$899$	−9.60286	+	23.0003i	−0.320273	+	0.767102i
$900$		0			0
$901$	−3.75006	+	33.2827i	−0.124933	+	1.10881i
$902$	0.202620	−	5.41514i	0.00674652	−	0.180304i
$903$		0			0
$904$	2.98224	+	19.7859i	0.0991879	+	0.658069i
$905$	−7.03536	−	17.9258i	−0.233863	−	0.595874i
$906$		0			0
$907$	−31.4200	+	5.94498i	−1.04328	+	0.197400i	−0.679190	−	0.733962i	$-0.737669\pi$
$907$	−31.4200	+	5.94498i	−1.04328	+	0.197400i	−0.364094	+	0.931362i	$0.618621\pi$
$908$	−40.3192	+	19.4167i	−1.33804	+	0.644366i
$909$		0			0
$910$	−4.53655	−	12.9647i	−0.150385	−	0.429776i
$911$	−8.67377	+	32.3709i	−0.287375	+	1.07250i	0.659712	+	0.751519i	$0.270678\pi$
$911$	−8.67377	+	32.3709i	−0.287375	+	1.07250i	−0.947086	+	0.320979i	$0.895988\pi$
$912$		0			0
$913$	−0.527608	+	1.20929i	−0.0174613	+	0.0400216i
$914$	−3.13099	+	7.17631i	−0.103564	+	0.237371i
$915$		0			0
$916$	−7.10269	+	26.5076i	−0.234680	+	0.875836i
$917$	−11.1330	−	31.8162i	−0.367643	−	1.05066i
$918$		0			0
$919$	2.37687	−	1.14464i	0.0784057	−	0.0377582i	−0.394270	−	0.918995i	$-0.629003\pi$
$919$	2.37687	−	1.14464i	0.0784057	−	0.0377582i	0.472676	+	0.881236i	$0.343288\pi$
$920$	−34.1370	+	6.45907i	−1.12546	+	0.212949i
$921$		0			0
$922$	−3.99974	−	10.1912i	−0.131725	−	0.335629i
$923$	−2.35977	−	15.6561i	−0.0776728	−	0.515325i
$924$		0			0
$925$	−0.510057	+	13.6316i	−0.0167706	+	0.448203i
$926$	0.746725	−	6.62737i	0.0245389	−	0.217789i
$927$		0			0
$928$	19.6345	+	22.0957i	0.644533	+	0.725326i
$929$	8.30673	−	4.79589i	0.272535	−	0.157348i	−0.357504	−	0.933912i	$-0.616372\pi$
$929$	8.30673	−	4.79589i	0.272535	−	0.157348i	0.630039	+	0.776563i	$0.283039\pi$
$930$		0			0
$931$	17.7191	+	33.5262i	0.580721	+	1.09878i
$932$	−23.0202	−	21.3596i	−0.754052	−	0.699658i
$933$		0			0
$934$	−1.82208	+	12.0887i	−0.0596204	+	0.395555i
$935$	9.06606	−	2.06927i	0.296492	−	0.0676723i
$936$		0			0
$937$	−5.49690	−	11.4144i	−0.179576	−	0.372893i	0.791678	−	0.610938i	$-0.209208\pi$
$937$	−5.49690	−	11.4144i	−0.179576	−	0.372893i	−0.971254	+	0.238045i	$0.923493\pi$
$938$	20.0856	+	10.6155i	0.655817	+	0.346609i
$939$		0			0
$940$	1.29328	+	4.82658i	0.0421821	+	0.157426i
$941$	−27.9758	+	19.0736i	−0.911986	+	0.621781i	−0.925755	−	0.378124i	$-0.876569\pi$
$941$	−27.9758	+	19.0736i	−0.911986	+	0.621781i	0.0137692	+	0.999905i	$0.495617\pi$
$942$		0			0
$943$	51.8924	−	38.2983i	1.68985	−	1.24717i
$944$	7.72290	−	16.0368i	0.251359	−	0.521952i
$945$		0			0
$946$	−1.58148	+	0.553383i	−0.0514182	+	0.0179920i
$947$	−0.835381	+	1.58062i	−0.0271462	+	0.0513632i	−0.897315	−	0.441390i	$-0.854486\pi$
$947$	−0.835381	+	1.58062i	−0.0271462	+	0.0513632i	0.870169	+	0.492753i	$0.164009\pi$
$948$		0			0
$949$	23.8771	−	20.5479i	0.775084	−	0.667013i
$950$	6.60396	+	2.03705i	0.214261	+	0.0660907i
$951$		0			0
$952$	11.0543	−	28.1658i	0.358270	−	0.912858i
$953$	−12.7383	−	2.90744i	−0.412635	−	0.0941812i	0.0111637	−	0.999938i	$-0.496446\pi$
$953$	−12.7383	−	2.90744i	−0.412635	−	0.0941812i	−0.423799	+	0.905756i	$0.639304\pi$
$954$		0			0
$955$	−11.2069	−	1.26272i	−0.362647	−	0.0408605i
$956$	8.17857	+	14.1657i	0.264514	+	0.458151i
$957$		0			0
$958$	−3.74866	+	6.49287i	−0.121114	+	0.209775i
$959$	−2.19746	+	2.97746i	−0.0709598	+	0.0961471i
$960$		0			0
$961$	−2.82327	−	9.15283i	−0.0910733	−	0.295253i
$962$	−10.6048	−	13.2980i	−0.341913	−	0.428745i
$963$		0			0
$964$	−1.18443	−	5.18933i	−0.0381480	−	0.167137i
$965$	−5.53257	−	29.2403i	−0.178100	−	0.941280i
$966$		0			0
$967$	−17.2340	+	0.644851i	−0.554208	+	0.0207370i	−0.313029	−	0.949744i	$-0.601344\pi$
$967$	−17.2340	+	0.644851i	−0.554208	+	0.0207370i	−0.241179	+	0.970481i	$0.577534\pi$
$968$	3.72102	−	19.6661i	0.119598	−	0.632092i
$969$		0			0
$970$	−1.85081	+	0.138699i	−0.0594258	+	0.00445335i
$971$	2.65467	+	23.5608i	0.0851923	+	0.756102i	0.961585	+	0.274506i	$0.0885143\pi$
$971$	2.65467	+	23.5608i	0.0851923	+	0.756102i	−0.876393	+	0.481596i	$0.840057\pi$
$972$		0			0
$973$	−11.0432	−	5.31812i	−0.354029	−	0.170491i
$974$	14.5893	+	3.90920i	0.467473	+	0.125259i
$975$		0			0
$976$	−1.04354	−	27.8891i	−0.0334028	−	0.892709i
$977$	45.2855	+	3.39368i	1.44881	+	0.108573i	0.775763	−	0.631024i	$-0.217365\pi$
$977$	45.2855	+	3.39368i	1.44881	+	0.108573i	0.673049	+	0.739598i	$0.264984\pi$
$978$		0			0
$979$	1.89293	+	2.04010i	0.0604984	+	0.0652018i
$980$	−12.9580	−	10.3336i	−0.413927	−	0.330096i
$981$		0			0
$982$	4.13359	−	18.1104i	0.131908	−	0.577927i
$983$	41.2564	+	1.54371i	1.31587	+	0.0492366i	0.686081	−	0.727526i	$-0.259330\pi$
$983$	41.2564	+	1.54371i	1.31587	+	0.0492366i	0.629794	+	0.776762i	$0.283139\pi$
$984$		0			0
$985$	−16.0947	−	9.29229i	−0.512820	−	0.296077i
$986$	−1.67854	+	12.4786i	−0.0534556	+	0.397400i
$987$		0			0
$988$	38.1854	−	16.6601i	1.21484	−	0.530029i
$989$	−16.8849	−	10.6095i	−0.536908	−	0.337362i
$990$		0			0
$991$	−15.2058	+	12.1262i	−0.483028	+	0.385202i	−0.834510	−	0.550993i	$-0.814249\pi$
$991$	−15.2058	+	12.1262i	−0.483028	+	0.385202i	0.351482	+	0.936195i	$0.385678\pi$
$992$	25.1211	+	3.78639i	0.797595	+	0.120218i
$993$		0			0
$994$	5.84564	+	6.79276i	0.185412	+	0.215453i
$995$	−2.59515	+	34.6298i	−0.0822716	+	1.09784i
$996$		0			0
$997$	−6.74063	+	7.83275i	−0.213478	+	0.248066i	−0.854494	−	0.519462i	$-0.826132\pi$
$997$	−6.74063	+	7.83275i	−0.213478	+	0.248066i	0.641016	+	0.767528i	$0.278513\pi$
$998$	−2.87841	−	2.87841i	−0.0911144	−	0.0911144i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	783.2.be.a.665.16		672
3.2	odd	2		261.2.x.a.230.13	yes	672
9.2	odd	6	inner	783.2.be.a.143.13		672
9.7	even	3		261.2.x.a.56.16	yes	672
29.14	odd	28	inner	783.2.be.a.449.13		672
87.14	even	28		261.2.x.a.14.16	✓	672
261.43	odd	84		261.2.x.a.101.13	yes	672
261.101	even	84	inner	783.2.be.a.710.16		672

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
261.2.x.a.14.16	✓	672	87.14	even	28
261.2.x.a.56.16	yes	672	9.7	even	3
261.2.x.a.101.13	yes	672	261.43	odd	84
261.2.x.a.230.13	yes	672	3.2	odd	2
783.2.be.a.143.13		672	9.2	odd	6	inner
783.2.be.a.449.13		672	29.14	odd	28	inner
783.2.be.a.665.16		672	1.1	even	1	trivial
783.2.be.a.710.16		672	261.101	even	84	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 783 = 3^{3} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	783.be (of order \(84\), degree \(24\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.234125 + 0.536620i) q^{2} +(1.12720 - 1.21483i) q^{4} +(1.79123 - 0.269985i) q^{5} +(2.59390 - 2.40679i) q^{7} +(2.02104 + 0.707193i) q^{8} +(0.564252 + 0.898002i) q^{10} +(0.974345 + 0.838491i) q^{11} +(-2.06180 - 3.02410i) q^{13} +(1.89883 + 0.828450i) q^{14} +(-0.154007 - 2.05508i) q^{16} +(2.82385 - 2.82385i) q^{17} +(-5.81575 + 3.65428i) q^{19} +(1.69109 - 2.48037i) q^{20} +(-0.221833 + 0.719165i) q^{22} +(-8.33810 + 3.27246i) q^{23} +(-1.64224 + 0.506563i) q^{25} +(1.14008 - 1.81442i) q^{26} -5.86408i q^{28} +(1.28158 + 5.23045i) q^{29} +(3.72396 + 2.74841i) q^{31} +(4.85287 - 2.56482i) q^{32} +(2.17647 + 0.854200i) q^{34} +(3.99648 - 5.01143i) q^{35} +(2.62155 - 7.49197i) q^{37} +(-3.32257 - 2.26529i) q^{38} +(3.81109 + 0.721097i) q^{40} +(-6.95493 + 1.86357i) q^{41} +(1.32201 + 1.79126i) q^{43} +(2.11691 - 0.238518i) q^{44} +(-3.70823 - 3.70823i) q^{46} +(-1.08573 + 1.26165i) q^{47} +(0.412579 - 5.50549i) q^{49} +(-0.656321 - 0.762658i) q^{50} +(-5.99783 - 0.904027i) q^{52} +(-6.55714 + 5.22915i) q^{53} +(1.97166 + 1.23888i) q^{55} +(6.94443 - 3.02983i) q^{56} +(-2.50671 + 1.91230i) q^{58} +(7.47986 + 4.31850i) q^{59} +(13.5329 + 0.506365i) q^{61} +(-0.602979 + 2.64182i) q^{62} +(-0.709949 - 0.566166i) q^{64} +(-4.50962 - 4.86022i) q^{65} +(10.9354 + 0.819497i) q^{67} +(-0.247461 - 6.61353i) q^{68} +(3.62491 + 0.971292i) q^{70} +(3.89744 + 1.87691i) q^{71} +(0.963648 + 8.55261i) q^{73} +(4.63411 - 0.347279i) q^{74} +(-2.11617 + 11.1843i) q^{76} +(4.54542 - 0.170078i) q^{77} +(0.335835 + 1.77493i) q^{79} +(-0.830703 - 3.63955i) q^{80} +(-2.62835 - 3.29585i) q^{82} +(0.302531 + 0.980782i) q^{83} +(4.29577 - 5.82057i) q^{85} +(-0.651711 + 1.12880i) q^{86} +(1.37622 + 2.38367i) q^{88} +(2.15138 + 0.242402i) q^{89} +(-12.6265 - 2.88191i) q^{91} +(-5.42320 + 13.8181i) q^{92} +(-0.931222 - 0.287244i) q^{94} +(-9.43077 + 8.11583i) q^{95} +(-0.817727 + 1.54721i) q^{97} +(3.05095 - 1.06757i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 672 q + 36 q^{2} - 14 q^{4} + 42 q^{5} - 10 q^{7} - 56 q^{10} + 48 q^{11} - 14 q^{13} + 24 q^{14} - 54 q^{16} - 48 q^{19} + 30 q^{20} - 14 q^{22} + 30 q^{23} + 30 q^{25} - 12 q^{31} - 24 q^{32} - 14 q^{34}+ \cdots - 36 q^{97}+O(q^{100}) \) 672 * q + 36 * q^2 - 14 * q^4 + 42 * q^5 - 10 * q^7 - 56 * q^10 + 48 * q^11 - 14 * q^13 + 24 * q^14 - 54 * q^16 - 48 * q^19 + 30 * q^20 - 14 * q^22 + 30 * q^23 + 30 * q^25 - 12 * q^31 - 24 * q^32 - 14 * q^34 - 48 * q^37 + 42 * q^38 - 2 * q^40 + 24 * q^41 - 12 * q^43 - 64 * q^46 + 42 * q^47 + 22 * q^49 + 66 * q^50 + 22 * q^52 + 76 * q^55 + 42 * q^56 - 42 * q^58 + 132 * q^59 - 308 * q^64 + 66 * q^65 - 14 * q^67 - 60 * q^68 - 14 * q^70 - 48 * q^73 - 66 * q^74 - 28 * q^76 - 30 * q^77 - 12 * q^79 - 136 * q^82 - 246 * q^83 + 34 * q^85 + 8 * q^88 - 56 * q^91 - 462 * q^92 + 26 * q^94 + 246 * q^95 - 36 * q^97

Introduction

L-functions

Modular forms

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