LMFDB - Embedded newform 684.2.cf.b.127.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [684,2,Mod(91,684)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(684, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([9, 0, 11])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("684.91"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 684 = 2^{2} \cdot 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	684.cf (of order $18$, degree $6$, minimal)

Newform invariants

comment:select newform

sage:traces = [60,-3] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$5.46176749826$
Analytic rank:	$0$
Dimension:	$60$
Relative dimension:	$10$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 228)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			127.4
Character	$\chi$	$=$	684.127
Dual form			684.2.cf.b.307.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.436096 - 1.34530i) q^{2} +(-1.61964 + 1.17336i) q^{4} +(0.711633 + 4.03587i) q^{5} +(-1.83842 - 1.06142i) q^{7} +(2.28483 + 1.66720i) q^{8} +(5.11910 - 2.71738i) q^{10} +(-3.08105 + 1.77885i) q^{11} +(-0.919976 - 2.52761i) q^{13} +(-0.626188 + 2.93610i) q^{14} +(1.24647 - 3.80083i) q^{16} +(3.54387 - 2.97366i) q^{17} +(-4.35844 + 0.0631645i) q^{19} +(-5.88810 - 5.70166i) q^{20} +(3.73671 + 3.36918i) q^{22} +(-6.47440 - 1.14161i) q^{23} +(-11.0834 + 4.03402i) q^{25} +(-2.99919 + 2.33992i) q^{26} +(4.22301 - 0.438015i) q^{28} +(-3.65007 + 4.34998i) q^{29} +(2.24228 - 3.88374i) q^{31} +(-5.65682 - 0.0193500i) q^{32} +(-5.54592 - 3.47075i) q^{34} +(2.97545 - 8.17498i) q^{35} +1.09818i q^{37} +(1.98567 + 5.83585i) q^{38} +(-5.10265 + 10.4077i) q^{40} +(-1.96417 + 5.39651i) q^{41} +(-4.53199 + 0.799112i) q^{43} +(2.90298 - 6.49626i) q^{44} +(1.28765 + 9.20784i) q^{46} +(5.72037 - 6.81727i) q^{47} +(-1.24680 - 2.15951i) q^{49} +(10.2604 + 13.1512i) q^{50} +(4.45582 + 3.01437i) q^{52} +(-7.11245 - 1.25412i) q^{53} +(-9.37178 - 11.1688i) q^{55} +(-2.43089 - 5.49017i) q^{56} +(7.44379 + 3.01341i) q^{58} +(-5.74836 + 4.82344i) q^{59} +(-0.333289 + 1.89018i) q^{61} +(-6.20262 - 1.32284i) q^{62} +(2.44088 + 7.61854i) q^{64} +(9.54643 - 5.51163i) q^{65} +(8.67038 + 7.27532i) q^{67} +(-2.25064 + 8.97449i) q^{68} +(-12.2954 - 0.437785i) q^{70} +(0.929621 + 5.27214i) q^{71} +(8.23159 + 2.99605i) q^{73} +(1.47738 - 0.478913i) q^{74} +(6.98500 - 5.21630i) q^{76} +7.55238 q^{77} +(3.94216 + 1.43483i) q^{79} +(16.2267 + 2.32581i) q^{80} +(8.11647 + 0.288993i) q^{82} +(4.80400 + 2.77359i) q^{83} +(14.5233 + 12.1865i) q^{85} +(3.05142 + 5.74838i) q^{86} +(-10.0054 - 1.07237i) q^{88} +(-1.59739 - 4.38880i) q^{89} +(-0.991540 + 5.62330i) q^{91} +(11.8257 - 5.74777i) q^{92} +(-11.6659 - 4.72261i) q^{94} +(-3.35653 - 17.5452i) q^{95} +(-0.673146 - 0.802225i) q^{97} +(-2.36146 + 2.61906i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q - 3 q^{2} - 3 q^{4} + 3 q^{8} - 6 q^{10} - 6 q^{13} + 9 q^{14} + 21 q^{16} + 18 q^{19} - 30 q^{20} - 12 q^{22} - 18 q^{28} - 12 q^{31} - 33 q^{32} - 15 q^{34} + 84 q^{38} - 87 q^{40} + 12 q^{41} - 18 q^{43}+ \cdots + 105 q^{98}+O(q^{100}) $ 60 * q - 3 * q^2 - 3 * q^4 + 3 * q^8 - 6 * q^10 - 6 * q^13 + 9 * q^14 + 21 * q^16 + 18 * q^19 - 30 * q^20 - 12 * q^22 - 18 * q^28 - 12 * q^31 - 33 * q^32 - 15 * q^34 + 84 * q^38 - 87 * q^40 + 12 * q^41 - 18 * q^43 + 51 * q^44 - 21 * q^46 + 30 * q^49 + 27 * q^50 - 3 * q^52 - 12 * q^53 - 42 * q^56 - 36 * q^58 - 105 * q^62 + 21 * q^64 + 36 * q^65 + 42 * q^67 + 15 * q^68 - 96 * q^70 - 24 * q^71 + 18 * q^73 - 69 * q^74 + 54 * q^76 + 72 * q^77 + 12 * q^79 + 12 * q^80 + 75 * q^82 - 60 * q^85 - 21 * q^86 + 36 * q^88 + 12 * q^89 - 84 * q^91 - 99 * q^92 + 24 * q^95 + 12 * q^97 + 105 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/684\mathbb{Z}\right)^\times$.

$n$	$325$	$343$	$533$
$\chi(n)$	$e\left(\frac{5}{18}\right)$	$-1$	$1$

Coefficient data

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

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

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

$2$	−0.436096	−	1.34530i	−0.308366	−	0.951268i
$2$	−0.436096	−	1.34530i	−0.308366	−	0.951268i
$3$		0			0
$3$		0			0
$4$	−1.61964	+	1.17336i	−0.809820	+	0.586678i
$5$	0.711633	+	4.03587i	0.318252	+	1.80490i	0.553377	+	0.832931i	$0.313339\pi$
$5$	0.711633	+	4.03587i	0.318252	+	1.80490i	−0.235125	+	0.971965i	$0.575550\pi$
$6$		0			0
$7$	−1.83842	−	1.06142i	−0.694859	−	0.401177i	0.110571	−	0.993868i	$-0.464732\pi$
$7$	−1.83842	−	1.06142i	−0.694859	−	0.401177i	−0.805430	+	0.592691i	$0.798066\pi$
$8$	2.28483	+	1.66720i	0.807809	+	0.589444i
$9$		0			0
$10$	5.11910	−	2.71738i	1.61880	−	0.859312i
$11$	−3.08105	+	1.77885i	−0.928972	+	0.536342i	−0.886486	−	0.462755i	$-0.846861\pi$
$11$	−3.08105	+	1.77885i	−0.928972	+	0.536342i	−0.0424860	+	0.999097i	$0.513528\pi$
$12$		0			0
$13$	−0.919976	−	2.52761i	−0.255155	−	0.701033i	−0.999449	−	0.0331814i	$-0.989436\pi$
$13$	−0.919976	−	2.52761i	−0.255155	−	0.701033i	0.744294	−	0.667852i	$-0.232786\pi$
$14$	−0.626188	+	2.93610i	−0.167356	+	0.784707i
$15$		0			0
$16$	1.24647	−	3.80083i	0.311618	−	0.950207i
$17$	3.54387	−	2.97366i	0.859515	−	0.721219i	−0.102348	−	0.994749i	$-0.532636\pi$
$17$	3.54387	−	2.97366i	0.859515	−	0.721219i	0.961864	+	0.273530i	$0.0881912\pi$
$18$		0			0
$19$	−4.35844	+	0.0631645i	−0.999895	+	0.0144909i
$19$	−4.35844	+	0.0631645i	−0.999895	+	0.0144909i
$20$	−5.88810	−	5.70166i	−1.31662	−	1.27493i
$21$		0			0
$22$	3.73671	+	3.36918i	0.796669	+	0.718312i
$23$	−6.47440	−	1.14161i	−1.35001	−	0.238042i	−0.548561	−	0.836111i	$-0.684824\pi$
$23$	−6.47440	−	1.14161i	−1.35001	−	0.238042i	−0.801445	+	0.598068i	$0.795935\pi$
$24$		0			0
$25$	−11.0834	+	4.03402i	−2.21667	+	0.806803i
$26$	−2.99919	+	2.33992i	−0.588189	+	0.458896i
$27$		0			0
$28$	4.22301	−	0.438015i	0.798073	−	0.0827770i
$29$	−3.65007	+	4.34998i	−0.677801	+	0.807771i	−0.989823	−	0.142303i	$-0.954549\pi$
$29$	−3.65007	+	4.34998i	−0.677801	+	0.807771i	0.312022	+	0.950075i	$0.398994\pi$
$30$		0			0
$31$	2.24228	−	3.88374i	0.402725	−	0.697540i	−0.591329	−	0.806430i	$-0.701397\pi$
$31$	2.24228	−	3.88374i	0.402725	−	0.697540i	0.994054	+	0.108891i	$0.0347298\pi$
$32$	−5.65682	−	0.0193500i	−0.999994	−	0.00342063i
$33$		0			0
$34$	−5.54592	−	3.47075i	−0.951118	−	0.595229i
$35$	2.97545	−	8.17498i	0.502943	−	1.38182i
$36$		0			0
$37$			1.09818i			0.180540i	0.995917	+	0.0902701i	$0.0287730\pi$
$37$			1.09818i			0.180540i	−0.995917	+	0.0902701i	$0.971227\pi$
$38$	1.98567	+	5.83585i	0.322119	+	0.946699i
$39$		0			0
$40$	−5.10265	+	10.4077i	−0.806799	+	1.64560i
$41$	−1.96417	+	5.39651i	−0.306752	+	0.842793i	0.686533	+	0.727099i	$0.259132\pi$
$41$	−1.96417	+	5.39651i	−0.306752	+	0.842793i	−0.993285	+	0.115695i	$0.963091\pi$
$42$		0			0
$43$	−4.53199	+	0.799112i	−0.691122	+	0.121863i	−0.508168	−	0.861258i	$-0.669677\pi$
$43$	−4.53199	+	0.799112i	−0.691122	+	0.121863i	−0.182954	+	0.983121i	$0.558566\pi$
$44$	2.90298	−	6.49626i	0.437641	−	0.979349i
$45$		0			0
$46$	1.28765	+	9.20784i	0.189854	+	1.35762i
$47$	5.72037	−	6.81727i	0.834402	−	0.994402i	−0.165564	−	0.986199i	$-0.552945\pi$
$47$	5.72037	−	6.81727i	0.834402	−	0.994402i	0.999966	−	0.00820263i	$-0.00261101\pi$
$48$		0			0
$49$	−1.24680	−	2.15951i	−0.178114	−	0.308502i
$50$	10.2604	+	13.1512i	1.45103	+	1.85986i
$51$		0			0
$52$	4.45582	+	3.01437i	0.617911	+	0.418017i
$53$	−7.11245	−	1.25412i	−0.976970	−	0.172266i	−0.337704	−	0.941252i	$-0.609650\pi$
$53$	−7.11245	−	1.25412i	−0.976970	−	0.172266i	−0.639266	+	0.768986i	$0.720762\pi$
$54$		0			0
$55$	−9.37178	−	11.1688i	−1.26369	−	1.50601i
$56$	−2.43089	−	5.49017i	−0.324842	−	0.733655i
$57$		0			0
$58$	7.44379	+	3.01341i	0.977418	+	0.395680i
$59$	−5.74836	+	4.82344i	−0.748372	+	0.627959i	−0.935072	−	0.354458i	$-0.884665\pi$
$59$	−5.74836	+	4.82344i	−0.748372	+	0.627959i	0.186700	+	0.982417i	$0.440221\pi$
$60$		0			0
$61$	−0.333289	+	1.89018i	−0.0426733	+	0.242012i	−0.998682	−	0.0513263i	$-0.983655\pi$
$61$	−0.333289	+	1.89018i	−0.0426733	+	0.242012i	0.956009	+	0.293338i	$0.0947663\pi$
$62$	−6.20262	−	1.32284i	−0.787734	−	0.168001i
$63$		0			0
$64$	2.44088	+	7.61854i	0.305111	+	0.952317i
$65$	9.54643	−	5.51163i	1.18409	−	0.683634i
$66$		0			0
$67$	8.67038	+	7.27532i	1.05926	+	0.888821i	0.994036	−	0.109050i	$-0.0347807\pi$
$67$	8.67038	+	7.27532i	1.05926	+	0.888821i	0.0652198	+	0.997871i	$0.479225\pi$
$68$	−2.25064	+	8.97449i	−0.272930	+	1.08832i
$69$		0			0
$70$	−12.2954	−	0.437785i	−1.46958	−	0.0523253i
$71$	0.929621	+	5.27214i	0.110326	+	0.625688i	0.988959	+	0.148191i	$0.0473449\pi$
$71$	0.929621	+	5.27214i	0.110326	+	0.625688i	−0.878633	+	0.477497i	$0.841544\pi$
$72$		0			0
$73$	8.23159	+	2.99605i	0.963434	+	0.350661i	0.775378	−	0.631497i	$-0.217559\pi$
$73$	8.23159	+	2.99605i	0.963434	+	0.350661i	0.188056	+	0.982158i	$0.439781\pi$
$74$	1.47738	−	0.478913i	0.171742	−	0.0556725i
$75$		0			0
$76$	6.98500	−	5.21630i	0.801234	−	0.598351i
$77$	7.55238			0.860673
$78$		0			0
$79$	3.94216	+	1.43483i	0.443527	+	0.161431i	0.554123	−	0.832435i	$-0.313054\pi$
$79$	3.94216	+	1.43483i	0.443527	+	0.161431i	−0.110596	+	0.993865i	$0.535276\pi$
$80$	16.2267	+	2.32581i	1.81420	+	0.260034i
$81$		0			0
$82$	8.11647	+	0.288993i	0.896314	+	0.0319139i
$83$	4.80400	+	2.77359i	0.527308	+	0.304441i	0.739920	−	0.672695i	$-0.234864\pi$
$83$	4.80400	+	2.77359i	0.527308	+	0.304441i	−0.212612	+	0.977137i	$0.568197\pi$
$84$		0			0
$85$	14.5233	+	12.1865i	1.57527	+	1.32181i
$86$	3.05142	+	5.74838i	0.329043	+	0.619863i
$87$		0			0
$88$	−10.0054	−	1.07237i	−1.06658	−	0.114315i
$89$	−1.59739	−	4.38880i	−0.169323	−	0.465212i	0.825787	−	0.563982i	$-0.190731\pi$
$89$	−1.59739	−	4.38880i	−0.169323	−	0.465212i	−0.995110	+	0.0987701i	$0.968509\pi$
$90$		0			0
$91$	−0.991540	+	5.62330i	−0.103942	+	0.589482i
$92$	11.8257	−	5.74777i	1.23292	−	0.599247i
$93$		0			0
$94$	−11.6659	−	4.72261i	−1.20324	−	0.487100i
$95$	−3.35653	−	17.5452i	−0.344373	−	1.80010i
$96$		0			0
$97$	−0.673146	−	0.802225i	−0.0683477	−	0.0814536i	0.730787	−	0.682605i	$-0.239153\pi$
$97$	−0.673146	−	0.802225i	−0.0683477	−	0.0814536i	−0.799135	+	0.601152i	$0.794709\pi$
$98$	−2.36146	+	2.61906i	−0.238544	+	0.264565i
$99$		0			0
$100$	13.2177	−	19.5384i	1.32177	−	1.95384i
$101$	−12.9780	+	4.72361i	−1.29136	+	0.470016i	−0.894173	−	0.447721i	$-0.852236\pi$
$101$	−12.9780	+	4.72361i	−1.29136	+	0.470016i	−0.397187	+	0.917738i	$0.630013\pi$
$102$		0			0
$103$	−5.73664	−	9.93615i	−0.565248	−	0.979038i	−0.997027	−	0.0770585i	$-0.975447\pi$
$103$	−5.73664	−	9.93615i	−0.565248	−	0.979038i	0.431779	−	0.901980i	$-0.357886\pi$
$104$	2.11205	−	7.30894i	0.207104	−	0.716701i
$105$		0			0
$106$	1.41455	+	10.1153i	0.137393	+	0.982481i
$107$	−7.21066	+	12.4892i	−0.697080	+	1.20738i	0.272394	+	0.962186i	$0.412185\pi$
$107$	−7.21066	+	12.4892i	−0.697080	+	1.20738i	−0.969474	+	0.245193i	$0.921149\pi$
$108$		0			0
$109$	1.35889	−	0.239609i	0.130158	−	0.0229504i	−0.108190	−	0.994130i	$-0.534505\pi$
$109$	1.35889	−	0.239609i	0.130158	−	0.0229504i	0.238348	+	0.971180i	$0.423394\pi$
$110$	−10.9384	+	17.4785i	−1.04294	+	1.66651i
$111$		0			0
$112$	−6.32581	+	5.66451i	−0.597732	+	0.535246i
$113$			7.65796i			0.720401i	0.932875	+	0.360200i	$0.117292\pi$
$113$			7.65796i			0.720401i	−0.932875	+	0.360200i	$0.882708\pi$
$114$		0			0
$115$		−	26.9423i		−	2.51238i
$116$	0.807725	−	11.3282i	0.0749953	−	1.05180i
$117$		0			0
$118$	8.99579	+	5.62975i	0.828130	+	0.518261i
$119$	−9.67143	+	1.70533i	−0.886579	+	0.156328i
$120$		0			0
$121$	0.828591	−	1.43516i	0.0753265	−	0.130469i
$122$	2.68819	−	0.375925i	0.243377	−	0.0340347i
$123$		0			0
$124$	0.925321	+	8.92125i	0.0830963	+	0.801152i
$125$	−13.9227	−	24.1149i	−1.24529	−	2.15690i
$126$		0			0
$127$	−2.38904	+	0.869540i	−0.211993	+	0.0771592i	−0.445834	−	0.895116i	$-0.647093\pi$
$127$	−2.38904	+	0.869540i	−0.211993	+	0.0771592i	0.233841	+	0.972275i	$0.424871\pi$
$128$	9.18472	−	6.60612i	0.811823	−	0.583904i
$129$		0			0
$130$	−11.5779	−	10.4392i	−1.01545	−	0.915576i
$131$	3.85394	+	4.59295i	0.336720	+	0.401288i	0.907661	−	0.419703i	$-0.137866\pi$
$131$	3.85394	+	4.59295i	0.336720	+	0.401288i	−0.570941	+	0.820991i	$0.693421\pi$
$132$		0			0
$133$	8.07971	+	4.50999i	0.700600	+	0.391066i
$134$	6.00633	−	14.8370i	0.518868	−	1.28172i
$135$		0			0
$136$	13.0548	−	0.885962i	1.11944	−	0.0759706i
$137$	0.598106	−	3.39202i	0.0510996	−	0.289800i	−0.948540	−	0.316658i	$-0.897439\pi$
$137$	0.598106	−	3.39202i	0.0510996	−	0.289800i	0.999639	+	0.0268581i	$0.00855024\pi$
$138$		0			0
$139$	3.02967	+	8.32394i	0.256973	+	0.706028i	0.999350	+	0.0360455i	$0.0114761\pi$
$139$	3.02967	+	8.32394i	0.256973	+	0.706028i	−0.742377	+	0.669982i	$0.766302\pi$
$140$	4.77300	+	16.7318i	0.403392	+	1.41410i
$141$		0			0
$142$	6.68719	−	3.54977i	0.561176	−	0.297890i
$143$	7.33073	+	6.15121i	0.613026	+	0.514390i
$144$		0			0
$145$	−20.1535	−	11.6356i	−1.67365	−	0.966285i
$146$	0.440816	−	12.3805i	0.0364822	−	1.02462i
$147$		0			0
$148$	−1.28856	−	1.77866i	−0.105919	−	0.146205i
$149$	−13.8652	−	5.04652i	−1.13588	−	0.413427i	−0.295457	−	0.955356i	$-0.595472\pi$
$149$	−13.8652	−	5.04652i	−1.13588	−	0.413427i	−0.840424	+	0.541929i	$0.817694\pi$
$150$		0			0
$151$	0.105578			0.00859181			0.00429591	−	0.999991i	$-0.498633\pi$
$151$	0.105578			0.00859181			0.00429591	+	0.999991i	$0.498633\pi$
$152$	−10.0636	−	7.12208i	−0.816266	−	0.577677i
$153$		0			0
$154$	−3.29356	−	10.1602i	−0.265403	−	0.818731i
$155$	17.2699	+	6.28574i	1.38716	+	0.504883i
$156$		0			0
$157$	−2.85909	−	16.2147i	−0.228180	−	1.29408i	−0.856511	−	0.516129i	$-0.827373\pi$
$157$	−2.85909	−	16.2147i	−0.228180	−	1.29408i	0.628330	−	0.777947i	$-0.283739\pi$
$158$	0.211110	−	5.92909i	0.0167950	−	0.471693i
$159$		0			0
$160$	−3.94749	−	22.8440i	−0.312076	−	1.80597i
$161$	10.6910	+	8.97079i	0.842567	+	0.706998i
$162$		0			0
$163$	−15.6449	+	9.03261i	−1.22541	+	0.707488i	−0.966065	−	0.258298i	$-0.916838\pi$
$163$	−15.6449	+	9.03261i	−1.22541	+	0.707488i	−0.259340	+	0.965786i	$0.583505\pi$
$164$	−3.15078	−	11.0451i	−0.246034	−	0.862476i
$165$		0			0
$166$	1.63630	−	7.67236i	0.127001	−	0.595490i
$167$	0.866864	−	4.91623i	0.0670799	−	0.380429i	−0.932723	−	0.360593i	$-0.882574\pi$
$167$	0.866864	−	4.91623i	0.0670799	−	0.380429i	0.999803	−	0.0198363i	$-0.00631450\pi$
$168$		0			0
$169$	4.41611	−	3.70556i	0.339701	−	0.285043i
$170$	10.0609	−	24.8525i	0.771633	−	1.90610i
$171$		0			0
$172$	6.40255	−	6.61191i	0.488190	−	0.504153i
$173$	15.5466	+	18.5277i	1.18198	+	1.40863i	0.892260	+	0.451522i	$0.149119\pi$
$173$	15.5466	+	18.5277i	1.18198	+	1.40863i	0.289723	+	0.957110i	$0.406437\pi$
$174$		0			0
$175$	24.6577	+	4.34782i	1.86395	+	0.328664i
$176$	2.92064	+	13.9278i	0.220152	+	1.04985i
$177$		0			0
$178$	−5.20762	+	4.06291i	−0.390328	+	0.304528i
$179$	−3.04930	−	5.28154i	−0.227915	−	0.394761i	0.729275	−	0.684221i	$-0.239858\pi$
$179$	−3.04930	−	5.28154i	−0.227915	−	0.394761i	−0.957190	+	0.289460i	$0.906524\pi$
$180$		0			0
$181$	−0.110871	+	0.132131i	−0.00824100	+	0.00982125i	−0.770149	−	0.637864i	$-0.779818\pi$
$181$	−0.110871	+	0.132131i	−0.00824100	+	0.00982125i	0.761908	+	0.647685i	$0.224263\pi$
$182$	7.99741	−	1.11838i	0.592807	−	0.0829001i
$183$		0			0
$184$	−12.8896	−	13.4025i	−0.950234	−	0.988046i
$185$	−4.43213	+	0.781504i	−0.325856	+	0.0574573i
$186$		0			0
$187$	−5.62917	+	15.4660i	−0.411646	+	1.13099i
$188$	−1.26586	+	17.7536i	−0.0923225	+	1.29481i
$189$		0			0
$190$	−22.1397	+	12.1669i	−1.60618	+	0.882680i
$191$			7.77180i			0.562348i	0.959657	+	0.281174i	$0.0907238\pi$
$191$			7.77180i			0.562348i	−0.959657	+	0.281174i	$0.909276\pi$
$192$		0			0
$193$	−1.92679	+	5.29382i	−0.138693	+	0.381057i	−0.989521	−	0.144388i	$-0.953879\pi$
$193$	−1.92679	+	5.29382i	−0.138693	+	0.381057i	0.850828	+	0.525445i	$0.176101\pi$
$194$	−0.785673	+	1.25543i	−0.0564080	+	0.0901345i
$195$		0			0
$196$	4.55324	+	2.03470i	0.325231	+	0.145336i
$197$	11.0193	−	19.0861i	0.785096	−	1.35983i	−0.143846	−	0.989600i	$-0.545947\pi$
$197$	11.0193	−	19.0861i	0.785096	−	1.35983i	0.928942	−	0.370225i	$-0.120720\pi$
$198$		0			0
$199$	6.60433	−	7.87073i	0.468168	−	0.557941i	−0.479358	−	0.877620i	$-0.659130\pi$
$199$	6.60433	−	7.87073i	0.468168	−	0.557941i	0.947526	+	0.319678i	$0.103575\pi$
$200$	−32.0491	−	9.26116i	−2.26622	−	0.654863i
$201$		0			0
$202$	12.0143	+	15.3993i	0.845323	+	1.08349i
$203$	11.3275	−	4.12288i	0.795035	−	0.289369i
$204$		0			0
$205$	−23.1774	−	4.08680i	−1.61878	−	0.285434i
$206$	−10.8653	+	12.0506i	−0.757024	+	0.839604i
$207$		0			0
$208$	−10.7537	+	0.346068i	−0.745638	+	0.0239955i
$209$	13.3162	−	7.94761i	0.921103	−	0.549748i
$210$		0			0
$211$	−2.27879	+	1.91213i	−0.156879	+	0.131637i	−0.717848	−	0.696200i	$-0.754873\pi$
$211$	−2.27879	+	1.91213i	−0.156879	+	0.131637i	0.560970	+	0.827836i	$0.310428\pi$
$212$	12.9911	−	6.31421i	0.892235	−	0.433662i
$213$		0			0
$214$	19.9462	+	4.25397i	1.36350	+	0.290795i
$215$	−6.45023	−	17.7218i	−0.439902	−	1.20862i
$216$		0			0
$217$	−8.24451	+	4.75997i	−0.559674	+	0.323128i
$218$	−0.914951	−	1.72362i	−0.0619683	−	0.116738i
$219$		0			0
$220$	28.2839	+	7.09310i	1.90690	+	0.478217i
$221$	−10.7765	−	6.22184i	−0.724908	−	0.418526i
$222$		0			0
$223$	2.27484	+	12.9013i	0.152335	+	0.863932i	0.961182	+	0.275914i	$0.0889805\pi$
$223$	2.27484	+	12.9013i	0.152335	+	0.863932i	−0.808848	+	0.588018i	$0.799908\pi$
$224$	10.3791	+	6.03981i	0.693483	+	0.403552i
$225$		0			0
$226$	10.3022	−	3.33961i	0.685294	−	0.222147i
$227$	−19.5224			−1.29575			−0.647873	−	0.761749i	$-0.724341\pi$
$227$	−19.5224			−1.29575			−0.647873	+	0.761749i	$0.724341\pi$
$228$		0			0
$229$	−3.65697			−0.241660			−0.120830	−	0.992673i	$-0.538556\pi$
$229$	−3.65697			−0.241660			−0.120830	+	0.992673i	$0.538556\pi$
$230$	−36.2453	+	11.7494i	−2.38994	+	0.774733i
$231$		0			0
$232$	−15.5921	+	3.85357i	−1.02367	+	0.252999i
$233$	3.63030	+	20.5885i	0.237829	+	1.34879i	0.836574	+	0.547855i	$0.184555\pi$
$233$	3.63030	+	20.5885i	0.237829	+	1.34879i	−0.598745	+	0.800940i	$0.704334\pi$
$234$		0			0
$235$	31.5844	+	18.2353i	2.06034	+	1.18954i
$236$	3.65066	−	14.5571i	0.237638	−	0.947587i
$237$		0			0
$238$	6.51185	+	12.2672i	0.422101	+	0.795167i
$239$	5.20862	−	3.00720i	0.336917	−	0.194519i	−0.321991	−	0.946743i	$-0.604352\pi$
$239$	5.20862	−	3.00720i	0.336917	−	0.194519i	0.658908	+	0.752224i	$0.271019\pi$
$240$		0			0
$241$	4.03800	+	11.0943i	0.260111	+	0.714648i	0.999159	+	0.0409961i	$0.0130531\pi$
$241$	4.03800	+	11.0943i	0.260111	+	0.714648i	−0.739049	+	0.673652i	$0.764725\pi$
$242$	−2.29206	−	0.488832i	−0.147339	−	0.0314233i
$243$		0			0
$244$	−1.67804	−	3.45247i	−0.107425	−	0.221022i
$245$	7.82826	−	6.56869i	0.500129	−	0.419658i
$246$		0			0
$247$	4.16931	+	10.9583i	0.265287	+	0.697262i
$248$	11.5982	−	5.13535i	0.736486	−	0.326095i
$249$		0			0
$250$	−26.3700	+	29.2466i	−1.66779	+	1.84972i
$251$	25.1628	+	4.43689i	1.58826	+	0.280054i	0.896827	−	0.442382i	$-0.145866\pi$
$251$	25.1628	+	4.43689i	1.58826	+	0.280054i	0.691438	+	0.722436i	$0.256978\pi$
$252$		0			0
$253$	21.9787	−	7.99960i	1.38179	−	0.502931i
$254$	2.21164	+	2.83476i	0.138771	+	0.177869i
$255$		0			0
$256$	−12.8926	−	9.47527i	−0.805788	−	0.592204i
$257$	9.65399	−	11.5052i	0.602199	−	0.717673i	−0.375702	−	0.926741i	$-0.622598\pi$
$257$	9.65399	−	11.5052i	0.602199	−	0.717673i	0.977901	+	0.209067i	$0.0670428\pi$
$258$		0			0
$259$	1.16563	−	2.01893i	0.0724286	−	0.125450i
$260$	−8.99468	+	20.1282i	−0.557827	+	1.24830i
$261$		0			0
$262$	4.49818	−	7.18765i	0.277899	−	0.444055i
$263$	−6.98652	+	19.1953i	−0.430807	+	1.18363i	0.514511	+	0.857484i	$0.327974\pi$
$263$	−6.98652	+	19.1953i	−0.430807	+	1.18363i	−0.945318	+	0.326150i	$0.894249\pi$
$264$		0			0
$265$		−	29.5974i		−	1.81815i
$266$	2.54375	−	12.8364i	0.155967	−	0.787049i
$267$		0			0
$268$	−22.5794	−	1.60996i	−1.37926	−	0.0983438i
$269$	−4.70144	+	12.9171i	−0.286652	+	0.787569i	0.709877	+	0.704325i	$0.248750\pi$
$269$	−4.70144	+	12.9171i	−0.286652	+	0.787569i	−0.996529	+	0.0832439i	$0.973472\pi$
$270$		0			0
$271$	−9.89960	+	1.74557i	−0.601358	+	0.106036i	−0.466035	−	0.884766i	$-0.654318\pi$
$271$	−9.89960	+	1.74557i	−0.601358	+	0.106036i	−0.135322	+	0.990802i	$0.543207\pi$
$272$	−6.88504	−	17.1762i	−0.417467	−	1.04146i
$273$		0			0
$274$	−4.82411	+	0.674619i	−0.291435	+	0.0407552i
$275$	26.9726	−	32.1446i	1.62651	−	1.93839i
$276$		0			0
$277$	−6.28070	−	10.8785i	−0.377370	−	0.653625i	0.613308	−	0.789844i	$-0.289838\pi$
$277$	−6.28070	−	10.8785i	−0.377370	−	0.653625i	−0.990679	+	0.136219i	$0.956505\pi$
$278$	9.87694	−	7.70584i	0.592380	−	0.462165i
$279$		0			0
$280$	20.4277	−	13.7178i	1.22079	−	0.819793i
$281$	15.9346	+	2.80969i	0.950576	+	0.167612i	0.627374	−	0.778718i	$-0.284130\pi$
$281$	15.9346	+	2.80969i	0.950576	+	0.167612i	0.323202	+	0.946330i	$0.395241\pi$
$282$		0			0
$283$	0.116039	+	0.138290i	0.00689780	+	0.00822048i	0.769482	−	0.638668i	$-0.220514\pi$
$283$	0.116039	+	0.138290i	0.00689780	+	0.00822048i	−0.762585	+	0.646889i	$0.776070\pi$
$284$	−7.69175	−	7.44820i	−0.456421	−	0.441969i
$285$		0			0
$286$	5.07830	−	12.5445i	0.300286	−	0.741773i
$287$	9.33891	−	7.83628i	0.551259	−	0.462561i
$288$		0			0
$289$	0.764346	−	4.33482i	0.0449615	−	0.254990i
$290$	−6.86450	+	32.1866i	−0.403097	+	1.89006i
$291$		0			0
$292$	−16.8477	+	4.80605i	−0.985934	+	0.281253i
$293$	5.02365	−	2.90040i	0.293485	−	0.169443i	−0.346028	−	0.938224i	$-0.612470\pi$
$293$	5.02365	−	2.90040i	0.293485	−	0.169443i	0.639512	+	0.768781i	$0.279136\pi$
$294$		0			0
$295$	−23.5575	−	19.7671i	−1.37157	−	1.15089i
$296$	−1.83089	+	2.50916i	−0.106418	+	0.145842i
$297$		0			0
$298$	−0.742506	+	20.8535i	−0.0430122	+	1.20801i
$299$	3.07074	+	17.4150i	0.177585	+	1.00714i
$300$		0			0
$301$	9.17991	+	3.34121i	0.529121	+	0.192584i
$302$	−0.0460421	−	0.142034i	−0.00264943	−	0.00817311i
$303$		0			0
$304$	−5.19260	+	16.6444i	−0.297816	+	0.954623i
$305$	−7.86568			−0.450388
$306$		0			0
$307$	27.7415	+	10.0971i	1.58329	+	0.576271i	0.975916	−	0.218145i	$-0.0700006\pi$
$307$	27.7415	+	10.0971i	1.58329	+	0.576271i	0.607374	+	0.794416i	$0.292223\pi$
$308$	−12.2321	+	8.86163i	−0.696991	+	0.504938i
$309$		0			0
$310$	0.924837	−	25.9744i	0.0525272	−	1.47524i
$311$	−17.8231	−	10.2902i	−1.01065	−	0.583502i	−0.0992714	−	0.995060i	$-0.531651\pi$
$311$	−17.8231	−	10.2902i	−1.01065	−	0.583502i	−0.911383	+	0.411559i	$0.864985\pi$
$312$		0			0
$313$	16.9322	+	14.2078i	0.957062	+	0.803071i	0.980473	−	0.196655i	$-0.0630080\pi$
$313$	16.9322	+	14.2078i	0.957062	+	0.803071i	−0.0234104	+	0.999726i	$0.507452\pi$
$314$	−20.5668	+	10.9175i	−1.16065	+	0.616110i
$315$		0			0
$316$	−8.06844	+	2.30165i	−0.453885	+	0.129478i
$317$	5.33653	+	14.6620i	0.299729	+	0.823500i	0.994545	+	0.104312i	$0.0332639\pi$
$317$	5.33653	+	14.6620i	0.299729	+	0.823500i	−0.694815	+	0.719188i	$0.744514\pi$
$318$		0			0
$319$	3.50810	−	19.8954i	0.196416	−	1.11393i
$320$	−29.0104	+	15.2727i	−1.62173	+	0.853770i
$321$		0			0
$322$	7.40608	−	18.2946i	0.412725	−	1.01952i
$323$	−15.2579	+	13.1844i	−0.848974	+	0.733598i
$324$		0			0
$325$	20.3929	+	24.3033i	1.13119	+	1.34810i
$326$	18.9742	+	17.1080i	1.05088	+	0.947523i
$327$		0			0
$328$	−13.4849	+	9.05544i	−0.744577	+	0.500003i
$329$	−17.7524	+	6.46136i	−0.978723	+	0.356226i
$330$		0			0
$331$	−12.2363	−	21.1939i	−0.672567	−	1.16492i	−0.977174	−	0.212442i	$-0.931858\pi$
$331$	−12.2363	−	21.1939i	−0.672567	−	1.16492i	0.304606	−	0.952478i	$-0.401475\pi$
$332$	−11.0352	+	1.14458i	−0.605634	+	0.0628170i
$333$		0			0
$334$	−6.99182	+	0.977758i	−0.382575	+	0.0535006i
$335$	−23.1921	+	40.1699i	−1.26712	+	2.19472i
$336$		0			0
$337$	−24.3074	+	4.28605i	−1.32411	+	0.233476i	−0.790607	−	0.612324i	$-0.790235\pi$
$337$	−24.3074	+	4.28605i	−1.32411	+	0.233476i	−0.533500	+	0.845800i	$0.679124\pi$
$338$	−6.91092	−	4.32500i	−0.375904	−	0.235249i
$339$		0			0
$340$	−37.8215	−	2.69674i	−2.05116	−	0.146251i
$341$			15.9547i			0.863994i
$342$		0			0
$343$			20.1533i			1.08818i
$344$	−11.6871	−	5.72990i	−0.630126	−	0.308936i
$345$		0			0
$346$	18.1454	−	28.9946i	0.975503	−	1.55876i
$347$	18.6375	−	3.28629i	1.00051	−	0.176417i	0.350680	−	0.936495i	$-0.385951\pi$
$347$	18.6375	−	3.28629i	1.00051	−	0.176417i	0.649832	+	0.760078i	$0.274839\pi$
$348$		0			0
$349$	−0.0843926	+	0.146172i	−0.00451743	+	0.00782442i	−0.868275	−	0.496083i	$-0.834771\pi$
$349$	−0.0843926	+	0.146172i	−0.00451743	+	0.00782442i	0.863758	+	0.503907i	$0.168105\pi$
$350$	−4.90402	−	35.0680i	−0.262131	−	1.87446i
$351$		0			0
$352$	17.4634	−	10.0030i	0.930802	−	0.533162i
$353$	−16.9470	−	29.3530i	−0.901996	−	1.56230i	−0.824900	−	0.565279i	$-0.808768\pi$
$353$	−16.9470	−	29.3530i	−0.901996	−	1.56230i	−0.0770963	−	0.997024i	$-0.524565\pi$
$354$		0			0
$355$	−20.6161	+	7.50366i	−1.09419	+	0.398253i
$356$	7.73683	+	5.23397i	0.410051	+	0.277400i
$357$		0			0
$358$	−5.77545	+	6.40547i	−0.305242	+	0.338540i
$359$	0.215220	+	0.256489i	0.0113589	+	0.0135370i	0.771694	−	0.635994i	$-0.219410\pi$
$359$	0.215220	+	0.256489i	0.0113589	+	0.0135370i	−0.760335	+	0.649531i	$0.774965\pi$
$360$		0			0
$361$	18.9920	−	0.550597i	0.999580	−	0.0289788i
$362$	0.226106	+	0.0915328i	0.0118839	+	0.00481086i
$363$		0			0
$364$	−4.99219	−	10.2712i	−0.261662	−	0.538355i
$365$	−6.23381	+	35.3537i	−0.326293	+	1.85050i
$366$		0			0
$367$	7.82567	+	21.5009i	0.408497	+	1.12234i	0.957981	+	0.286831i	$0.0926020\pi$
$367$	7.82567	+	21.5009i	0.408497	+	1.12234i	−0.549484	+	0.835504i	$0.685176\pi$
$368$	−12.4092	+	23.1851i	−0.646876	+	1.20861i
$369$		0			0
$370$	2.98419	+	5.62171i	0.155140	+	0.292259i
$371$	11.7446	+	9.85486i	0.609747	+	0.511639i
$372$		0			0
$373$	4.29467	+	2.47953i	0.222369	+	0.128385i	0.607047	−	0.794666i	$-0.292354\pi$
$373$	4.29467	+	2.47953i	0.222369	+	0.128385i	−0.384677	+	0.923051i	$0.625687\pi$
$374$	23.2612	+	0.828233i	1.20281	+	0.0428269i
$375$		0			0
$376$	24.4358	−	6.03930i	1.26018	−	0.311453i
$377$	14.3530	+	5.22408i	0.739219	+	0.269054i
$378$		0			0
$379$	31.6774			1.62716			0.813579	−	0.581454i	$-0.197516\pi$
$379$	31.6774			1.62716			0.813579	+	0.581454i	$0.197516\pi$
$380$	26.0231	+	24.4784i	1.33496	+	1.25572i
$381$		0			0
$382$	10.4554	−	3.38925i	0.534943	−	0.173409i
$383$	−31.5696	−	11.4904i	−1.61313	−	0.587131i	−0.631074	−	0.775722i	$-0.717386\pi$
$383$	−31.5696	−	11.4904i	−1.61313	−	0.587131i	−0.982056	+	0.188591i	$0.939608\pi$
$384$		0			0
$385$	5.37452	+	30.4804i	0.273911	+	1.55343i
$386$	7.96201	+	0.283493i	0.405256	+	0.0144294i
$387$		0			0
$388$	2.03155	+	0.509476i	0.103136	+	0.0258647i
$389$	−8.60011	−	7.21635i	−0.436043	−	0.365883i	0.398183	−	0.917306i	$-0.369641\pi$
$389$	−8.60011	−	7.21635i	−0.436043	−	0.365883i	−0.834226	+	0.551422i	$0.814085\pi$
$390$		0			0
$391$	−26.3392	+	15.2070i	−1.33203	+	0.769049i
$392$	0.751628	−	7.01278i	0.0379629	−	0.354199i
$393$		0			0
$394$	−30.4819	−	6.50092i	−1.53566	−	0.327512i
$395$	−2.98541	+	16.9311i	−0.150212	+	0.851897i
$396$		0			0
$397$	10.1113	−	8.48436i	0.507470	−	0.425818i	−0.352768	−	0.935711i	$-0.614759\pi$
$397$	10.1113	−	8.48436i	0.507470	−	0.425818i	0.860238	+	0.509893i	$0.170315\pi$
$398$	−13.4686	−	5.45238i	−0.675119	−	0.273303i
$399$		0			0
$400$	1.51748	+	47.1543i	0.0758740	+	2.35771i
$401$	−22.0701	−	26.3021i	−1.10213	−	1.31346i	−0.945433	−	0.325816i	$-0.894361\pi$
$401$	−22.0701	−	26.3021i	−1.10213	−	1.31346i	−0.156693	−	0.987647i	$-0.550083\pi$
$402$		0			0
$403$	−11.8794	−	2.09466i	−0.591756	−	0.104343i
$404$	15.4772	−	22.8784i	0.770021	−	1.13824i
$405$		0			0
$406$	−10.4864	−	13.4409i	−0.520430	−	0.667060i
$407$	−1.95350	−	3.38356i	−0.0968314	−	0.167717i
$408$		0			0
$409$	−17.6689	+	21.0569i	−0.873669	+	1.04120i	0.125127	+	0.992141i	$0.460066\pi$
$409$	−17.6689	+	21.0569i	−0.873669	+	1.04120i	−0.998796	+	0.0490573i	$0.984378\pi$
$410$	4.60961	+	32.9627i	0.227652	+	1.62791i
$411$		0			0
$412$	20.9499	+	9.36188i	1.03213	+	0.461227i
$413$	15.6876	−	2.76615i	0.771936	−	0.136113i
$414$		0			0
$415$	−7.77518	+	21.3621i	−0.381668	+	1.04863i
$416$	5.15523	+	14.3161i	0.252756	+	0.701902i
$417$		0			0
$418$	−16.4990	−	14.4483i	−0.806994	−	0.706692i
$419$			8.73341i			0.426655i	0.976981	+	0.213327i	$0.0684301\pi$
$419$			8.73341i			0.426655i	−0.976981	+	0.213327i	$0.931570\pi$
$420$		0			0
$421$	7.08553	−	19.4673i	0.345328	−	0.948780i	−0.638494	−	0.769627i	$-0.720442\pi$
$421$	7.08553	−	19.4673i	0.345328	−	0.948780i	0.983821	−	0.179153i	$-0.0573356\pi$
$422$	3.56616	+	2.23178i	0.173598	+	0.108641i
$423$		0			0
$424$	−14.1599	−	14.7233i	−0.687664	−	0.715028i
$425$	−27.2822	+	47.2542i	−1.32338	+	2.29217i
$426$		0			0
$427$	2.61899	−	3.12119i	0.126742	−	0.151045i
$428$	−2.97562	−	28.6887i	−0.143832	−	1.38672i
$429$		0			0
$430$	−21.0282	+	16.4059i	−1.01407	+	0.791162i
$431$	−14.7071	+	5.35294i	−0.708416	+	0.257842i	−0.671000	−	0.741458i	$-0.734135\pi$
$431$	−14.7071	+	5.35294i	−0.708416	+	0.257842i	−0.0374160	+	0.999300i	$0.511913\pi$
$432$		0			0
$433$	21.2295	+	3.74334i	1.02023	+	0.179893i	0.658650	−	0.752449i	$-0.271128\pi$
$433$	21.2295	+	3.74334i	1.02023	+	0.179893i	0.361576	+	0.932343i	$0.382239\pi$
$434$	9.99897	+	9.01551i	0.479966	+	0.432758i
$435$		0			0
$436$	−1.91977	+	1.98254i	−0.0919401	+	0.0949465i
$437$	28.2904	+	4.56670i	1.35331	+	0.218455i
$438$		0			0
$439$	−18.2798	+	15.3386i	−0.872447	+	0.732070i	−0.964612	−	0.263674i	$-0.915066\pi$
$439$	−18.2798	+	15.3386i	−0.872447	+	0.732070i	0.0921648	+	0.995744i	$0.470621\pi$
$440$	−2.79219	−	41.1435i	−0.133113	−	1.96144i
$441$		0			0
$442$	−3.67061	+	17.2109i	−0.174593	+	0.818641i
$443$	1.19994	+	3.29680i	0.0570107	+	0.156636i	0.964929	−	0.262512i	$-0.0845511\pi$
$443$	1.19994	+	3.29680i	0.0570107	+	0.156636i	−0.907918	+	0.419148i	$0.862329\pi$
$444$		0			0
$445$	16.5759	−	9.57009i	0.785772	−	0.453666i
$446$	16.3640	−	8.68651i	0.774856	−	0.411318i
$447$		0			0
$448$	3.59905	−	16.5969i	0.170039	−	0.784130i
$449$	−5.94492	−	3.43230i	−0.280558	−	0.161980i	0.353118	−	0.935579i	$-0.385121\pi$
$449$	−5.94492	−	3.43230i	−0.280558	−	0.161980i	−0.633676	+	0.773598i	$0.718455\pi$
$450$		0			0
$451$	−3.54786	−	20.1209i	−0.167062	−	0.947456i
$452$	−8.98551	−	12.4032i	−0.422643	−	0.583395i
$453$		0			0
$454$	8.51362	+	26.2634i	0.399564	+	1.23260i
$455$	−23.4005			−1.09703
$456$		0			0
$457$	−23.0184			−1.07675			−0.538377	−	0.842704i	$-0.680962\pi$
$457$	−23.0184			−1.07675			−0.538377	+	0.842704i	$0.680962\pi$
$458$	1.59479	+	4.91971i	0.0745197	+	0.229883i
$459$		0			0
$460$	31.6128	+	43.6368i	1.47396	+	2.03458i
$461$	−5.44422	−	30.8757i	−0.253563	−	1.43803i	−0.799735	−	0.600353i	$-0.795027\pi$
$461$	−5.44422	−	30.8757i	−0.253563	−	1.43803i	0.546173	−	0.837673i	$-0.316084\pi$
$462$		0			0
$463$	12.4250	+	7.17355i	0.577436	+	0.333383i	0.760114	−	0.649790i	$-0.225143\pi$
$463$	12.4250	+	7.17355i	0.577436	+	0.333383i	−0.182677	+	0.983173i	$0.558476\pi$
$464$	11.9838	+	19.2954i	0.556335	+	0.895768i
$465$		0			0
$466$	26.1144	−	13.8624i	1.20973	−	0.642162i
$467$	−14.8365	+	8.56586i	−0.686552	+	0.396381i	−0.802319	−	0.596895i	$-0.796401\pi$
$467$	−14.8365	+	8.56586i	−0.686552	+	0.396381i	0.115767	+	0.993276i	$0.463067\pi$
$468$		0			0
$469$	−8.21772	−	22.5780i	−0.379459	−	1.04256i
$470$	10.7580	−	50.4427i	0.496230	−	2.32675i
$471$		0			0
$472$	−21.1757	+	1.43708i	−0.974689	+	0.0661469i
$473$	12.5418	−	10.5238i	0.576673	−	0.483886i
$474$		0			0
$475$	48.0514	−	18.2821i	2.20475	−	0.838840i
$476$	13.6633	−	14.1101i	0.626256	−	0.646733i
$477$		0			0
$478$	−6.31702	−	5.69570i	−0.288934	−	0.260515i
$479$	−22.0097	−	3.88090i	−1.00565	−	0.177323i	−0.353516	−	0.935428i	$-0.615014\pi$
$479$	−22.0097	−	3.88090i	−1.00565	−	0.177323i	−0.652132	+	0.758105i	$0.726125\pi$
$480$		0			0
$481$	2.77578	−	1.01030i	0.126565	−	0.0460658i
$482$	13.1642	−	10.2705i	0.599612	−	0.467808i
$483$		0			0
$484$	0.341935	+	3.29668i	0.0155425	+	0.149849i
$485$	2.75864	−	3.28762i	0.125263	−	0.149283i
$486$		0			0
$487$	11.3250	−	19.6155i	0.513185	−	0.888862i	−0.486698	−	0.873570i	$-0.661799\pi$
$487$	11.3250	−	19.6155i	0.513185	−	0.888862i	0.999883	−	0.0152921i	$-0.00486782\pi$
$488$	−3.91281	+	3.76307i	−0.177125	+	0.170346i
$489$		0			0
$490$	−12.2507	−	7.66675i	−0.553430	−	0.346348i
$491$	8.60271	−	23.6357i	0.388235	−	1.06667i	−0.579561	−	0.814929i	$-0.696776\pi$
$491$	8.60271	−	23.6357i	0.388235	−	1.06667i	0.967796	−	0.251737i	$-0.0810019\pi$
$492$		0			0
$493$			26.2698i			1.18313i
$494$	12.9240	−	10.3878i	0.581478	−	0.467371i
$495$		0			0
$496$	−11.9665	−	13.3635i	−0.537311	−	0.600038i
$497$	3.88689	−	10.6792i	0.174351	−	0.479025i
$498$		0			0
$499$	27.0863	−	4.77605i	1.21255	−	0.213805i	0.469434	−	0.882967i	$-0.344458\pi$
$499$	27.0863	−	4.77605i	1.21255	−	0.213805i	0.743117	+	0.669162i	$0.233347\pi$
$500$	50.8452	+	22.7211i	2.27387	+	1.01612i
$501$		0			0
$502$	−5.00448	−	35.7864i	−0.223361	−	1.59722i
$503$	−11.8240	+	14.0913i	−0.527207	+	0.628301i	−0.962269	−	0.272099i	$-0.912282\pi$
$503$	−11.8240	+	14.0913i	−0.527207	+	0.628301i	0.435062	+	0.900401i	$0.356726\pi$
$504$		0			0
$505$	−28.2994	−	49.0161i	−1.25931	−	2.18119i
$506$	−20.3467	−	26.0793i	−0.904519	−	1.15937i
$507$		0			0
$508$	2.84911	−	4.21154i	0.126409	−	0.186857i
$509$	−39.6174	−	6.98562i	−1.75601	−	0.309632i	−0.799356	−	0.600857i	$-0.794826\pi$
$509$	−39.6174	−	6.98562i	−1.75601	−	0.309632i	−0.956654	+	0.291225i	$0.905937\pi$
$510$		0			0
$511$	−11.9531	−	14.2451i	−0.528774	−	0.630168i
$512$	−7.12462	+	21.4765i	−0.314867	+	0.949136i
$513$		0			0
$514$	−19.6879	−	7.97011i	−0.868397	−	0.351546i
$515$	36.0186	−	30.2232i	1.58717	−	1.33179i
$516$		0			0
$517$	−5.49788	+	31.1800i	−0.241797	+	1.37130i
$518$	−3.22438	−	0.687669i	−0.141671	−	0.0302144i
$519$		0			0
$520$	31.0010	+	3.32268i	1.35948	+	0.145709i
$521$	12.8556	−	7.42221i	0.563216	−	0.325173i	−0.191219	−	0.981547i	$-0.561244\pi$
$521$	12.8556	−	7.42221i	0.563216	−	0.325173i	0.754435	+	0.656374i	$0.227911\pi$
$522$		0			0
$523$	7.26433	+	6.09550i	0.317647	+	0.266538i	0.787644	−	0.616130i	$-0.211301\pi$
$523$	7.26433	+	6.09550i	0.317647	+	0.266538i	−0.469997	+	0.882668i	$0.655745\pi$
$524$	−11.6312	−	2.91688i	−0.508110	−	0.127425i
$525$		0			0
$526$	28.8702	+	1.02794i	1.25880	+	0.0448205i
$527$	−3.60258	−	20.4312i	−0.156931	−	0.889999i
$528$		0			0
$529$	19.0017	+	6.91604i	0.826159	+	0.300697i
$530$	−39.8172	+	12.9073i	−1.72955	+	0.560657i
$531$		0			0
$532$	−18.3781	+	2.17580i	−0.796790	+	0.0943331i
$533$	15.4473			0.669096
$534$		0			0
$535$	−55.5362	−	20.2135i	−2.40104	−	0.873907i
$536$	7.68093	+	31.0781i	0.331766	+	1.34237i
$537$		0			0
$538$	19.4276	+	0.691734i	0.837583	+	0.0298228i
$539$	7.68289	+	4.43572i	0.330926	+	0.191060i
$540$		0			0
$541$	−26.1459	−	21.9390i	−1.12410	−	0.943231i	−0.125294	−	0.992120i	$-0.539987\pi$
$541$	−26.1459	−	21.9390i	−1.12410	−	0.943231i	−0.998804	+	0.0488891i	$0.984432\pi$
$542$	6.66548	+	12.5567i	0.286307	+	0.539354i
$543$		0			0
$544$	−20.1046	+	16.7529i	−0.861977	+	0.718275i
$545$	1.93406	+	5.31379i	0.0828461	+	0.227618i
$546$		0			0
$547$	−2.00888	+	11.3929i	−0.0858937	+	0.487127i	0.911266	+	0.411817i	$0.135106\pi$
$547$	−2.00888	+	11.3929i	−0.0858937	+	0.487127i	−0.997160	+	0.0753101i	$0.976005\pi$
$548$	3.01133	+	6.19565i	0.128638	+	0.264665i
$549$		0			0
$550$	−55.0067	−	22.2679i	−2.34549	−	0.949507i
$551$	15.6338	−	19.1897i	0.666024	−	0.817508i
$552$		0			0
$553$	−5.72441	−	6.82209i	−0.243427	−	0.290105i
$554$	−11.8958	+	13.1935i	−0.505404	+	0.560536i
$555$		0			0
$556$	−14.6739	−	9.92692i	−0.622313	−	0.420995i
$557$	6.50467	−	2.36750i	0.275612	−	0.100314i	−0.200517	−	0.979690i	$-0.564262\pi$
$557$	6.50467	−	2.36750i	0.275612	−	0.100314i	0.476128	+	0.879376i	$0.342040\pi$
$558$		0			0
$559$	6.18916	+	10.7199i	0.261774	+	0.453405i
$560$	−27.3629	−	21.4991i	−1.15629	−	0.908502i
$561$		0			0
$562$	−3.16913	−	22.6620i	−0.133681	−	0.955938i
$563$	12.2842	−	21.2769i	0.517718	−	0.896713i	−0.482071	−	0.876132i	$-0.660115\pi$
$563$	12.2842	−	21.2769i	0.517718	−	0.896713i	0.999788	−	0.0205807i	$-0.00655150\pi$
$564$		0			0
$565$	−30.9066	+	5.44966i	−1.30025	+	0.229269i
$566$	0.135437	−	0.216414i	0.00569283	−	0.00909658i
$567$		0			0
$568$	−6.66569	+	13.5958i	−0.279686	+	0.570467i
$569$		−	34.0797i		−	1.42870i	−0.699790	−	0.714348i	$-0.746723\pi$
$569$		−	34.0797i		−	1.42870i	0.699790	−	0.714348i	$-0.253277\pi$
$570$		0			0
$571$		−	9.62744i		−	0.402896i	−0.979499	−	0.201448i	$-0.935435\pi$
$571$		−	9.62744i		−	0.402896i	0.979499	−	0.201448i	$-0.0645647\pi$
$572$	−19.0907	−	1.36120i	−0.798222	−	0.0569148i
$573$		0			0
$574$	−14.6148	−	9.14623i	−0.610009	−	0.381756i
$575$	76.3635	−	13.4649i	3.18458	−	0.561527i
$576$		0			0
$577$	−0.894022	+	1.54849i	−0.0372186	+	0.0644646i	−0.884035	−	0.467421i	$-0.845183\pi$
$577$	−0.894022	+	1.54849i	−0.0372186	+	0.0644646i	0.846816	+	0.531886i	$0.178516\pi$
$578$	−6.16495	+	0.862126i	−0.256428	+	0.0358597i
$579$		0			0
$580$	46.2941	−	4.80167i	1.92226	−	0.199379i
$581$	−5.88787	−	10.1981i	−0.244270	−	0.423088i
$582$		0			0
$583$	24.1447	−	8.78796i	0.999972	−	0.363960i
$584$	13.8127	+	20.5692i	0.571575	+	0.851158i
$585$		0			0
$586$	−6.09269	−	5.49344i	−0.251687	−	0.226932i
$587$	19.6664	+	23.4375i	0.811719	+	0.967369i	0.999891	−	0.0147675i	$-0.00470082\pi$
$587$	19.6664	+	23.4375i	0.811719	+	0.967369i	−0.188172	+	0.982136i	$0.560256\pi$
$588$		0			0
$589$	−9.52752	+	17.0687i	−0.392575	+	0.703302i
$590$	−16.3193	+	40.3122i	−0.671853	+	1.65963i
$591$		0			0
$592$	4.17401	+	1.36886i	0.171551	+	0.0562597i
$593$	−0.892954	+	5.06419i	−0.0366692	+	0.207962i	−0.997638	−	0.0686968i	$-0.978116\pi$
$593$	−0.892954	+	5.06419i	−0.0366692	+	0.207962i	0.960968	+	0.276658i	$0.0892270\pi$
$594$		0			0
$595$	−13.7650	−	37.8191i	−0.564311	−	1.55043i
$596$	28.3780	−	8.09525i	1.16241	−	0.331594i
$597$		0			0
$598$	22.0892	−	11.7257i	0.903296	−	0.479498i
$599$	18.9579	+	15.9076i	0.774600	+	0.649966i	0.941882	−	0.335943i	$-0.109055\pi$
$599$	18.9579	+	15.9076i	0.774600	+	0.649966i	−0.167283	+	0.985909i	$0.553499\pi$
$600$		0			0
$601$	1.99259	+	1.15042i	0.0812794	+	0.0469267i	0.540089	−	0.841608i	$-0.318391\pi$
$601$	1.99259	+	1.15042i	0.0812794	+	0.0469267i	−0.458809	+	0.888535i	$0.651724\pi$
$602$	0.491601	−	13.8068i	0.0200362	−	0.562722i
$603$		0			0
$604$	−0.170998	+	0.123880i	−0.00695783	+	0.00504062i
$605$	6.38178	+	2.32278i	0.259456	+	0.0944344i
$606$		0			0
$607$	−33.4906			−1.35934			−0.679671	−	0.733517i	$-0.737877\pi$
$607$	−33.4906			−1.35934			−0.679671	+	0.733517i	$0.737877\pi$
$608$	24.6561	−	0.272974i	0.999939	−	0.0110706i
$609$		0			0
$610$	3.43019	+	10.5817i	0.138884	+	0.428439i
$611$	−22.4940	−	8.18716i	−0.910011	−	0.331217i
$612$		0			0
$613$	3.19791	+	18.1363i	0.129163	+	0.732517i	0.978748	+	0.205066i	$0.0657410\pi$
$613$	3.19791	+	18.1363i	0.129163	+	0.732517i	−0.849586	+	0.527451i	$0.823148\pi$
$614$	1.48561	−	41.7238i	0.0599542	−	1.68384i
$615$		0			0
$616$	17.2559	+	12.5913i	0.695260	+	0.507319i
$617$	5.51004	+	4.62348i	0.221826	+	0.186134i	0.746927	−	0.664906i	$-0.231528\pi$
$617$	5.51004	+	4.62348i	0.221826	+	0.186134i	−0.525102	+	0.851040i	$0.675973\pi$
$618$		0			0
$619$	−22.0539	+	12.7328i	−0.886421	+	0.511775i	−0.872770	−	0.488131i	$-0.837679\pi$
$619$	−22.0539	+	12.7328i	−0.886421	+	0.511775i	−0.0136509	+	0.999907i	$0.504345\pi$
$620$	−35.3465	+	10.0831i	−1.41955	+	0.404948i
$621$		0			0
$622$	−6.07074	+	28.4648i	−0.243415	+	1.14134i
$623$	−1.72165	+	9.76398i	−0.0689766	+	0.391186i
$624$		0			0
$625$	42.2405	−	35.4440i	1.68962	−	1.41776i
$626$	11.7296	−	28.9747i	0.468809	−	1.15806i
$627$		0			0
$628$	23.6563	+	22.9073i	0.943990	+	0.914100i
$629$	3.26563	+	3.89182i	0.130209	+	0.155177i
$630$		0			0
$631$	34.1843	+	6.02761i	1.36085	+	0.239955i	0.805962	−	0.591967i	$-0.201649\pi$
$631$	34.1843	+	6.02761i	1.36085	+	0.239955i	0.554892	+	0.831923i	$0.312760\pi$
$632$	6.61501	+	9.85070i	0.263131	+	0.391840i
$633$		0			0
$634$	17.3975	−	13.5732i	0.690942	−	0.539063i
$635$	−5.20947	−	9.02307i	−0.206731	−	0.358069i
$636$		0			0
$637$	−4.31139	+	5.13812i	−0.170824	+	0.203580i
$638$	−28.2951	+	3.95688i	−1.12021	+	0.156654i
$639$		0			0
$640$	33.1976	+	32.3672i	1.31225	+	1.27943i
$641$	−15.5563	+	2.74300i	−0.614437	+	0.108342i	−0.472201	−	0.881491i	$-0.656540\pi$
$641$	−15.5563	+	2.74300i	−0.614437	+	0.108342i	−0.142236	+	0.989833i	$0.545429\pi$
$642$		0			0
$643$	7.88997	−	21.6775i	0.311150	−	0.854878i	−0.681275	−	0.732027i	$-0.738574\pi$
$643$	7.88997	−	21.6775i	0.311150	−	0.854878i	0.992425	−	0.122850i	$-0.0392035\pi$
$644$	−27.8415	−	1.98515i	−1.09711	−	0.0782259i
$645$		0			0
$646$	24.3908	+	14.7768i	0.959643	+	0.581384i
$647$		−	10.0700i		−	0.395891i	−0.980213	−	0.197946i	$-0.936573\pi$
$647$		−	10.0700i		−	0.395891i	0.980213	−	0.197946i	$-0.0634269\pi$
$648$		0			0
$649$	9.13082	−	25.0867i	0.358416	−	0.984740i
$650$	23.8018	−	38.0330i	0.933585	−	1.49178i
$651$		0			0
$652$	14.7407	−	32.9866i	0.577291	−	1.29186i
$653$	−4.15147	+	7.19055i	−0.162459	+	0.281388i	−0.935750	−	0.352664i	$-0.885276\pi$
$653$	−4.15147	+	7.19055i	−0.162459	+	0.281388i	0.773291	+	0.634052i	$0.218609\pi$
$654$		0			0
$655$	−15.7940	+	18.8225i	−0.617121	+	0.735456i
$656$	18.0629	+	14.1921i	0.705239	+	0.554108i
$657$		0			0
$658$	16.4342	+	21.0645i	0.640672	+	0.821180i
$659$	26.1053	−	9.50156i	1.01692	−	0.370128i	0.220833	−	0.975312i	$-0.429123\pi$
$659$	26.1053	−	9.50156i	1.01692	−	0.370128i	0.796086	+	0.605184i	$0.206900\pi$
$660$		0			0
$661$	−23.2420	−	4.09819i	−0.904008	−	0.159401i	−0.297727	−	0.954651i	$-0.596228\pi$
$661$	−23.2420	−	4.09819i	−0.904008	−	0.159401i	−0.606281	+	0.795250i	$0.707340\pi$
$662$	−23.1758	+	25.7040i	−0.900754	+	0.999014i
$663$		0			0
$664$	6.35219	+	14.3464i	0.246513	+	0.556749i
$665$	−12.4520	+	35.8181i	−0.482866	+	1.38897i
$666$		0			0
$667$	28.5980	−	23.9966i	1.10732	−	0.929151i
$668$	4.36448	+	8.97966i	0.168867	+	0.347434i
$669$		0			0
$670$	64.1544	+	13.6823i	2.47850	+	0.528594i
$671$	−2.33545	−	6.41660i	−0.0901591	−	0.247710i
$672$		0			0
$673$	−6.45808	+	3.72857i	−0.248941	+	0.143726i	−0.619279	−	0.785171i	$-0.712575\pi$
$673$	−6.45808	+	3.72857i	−0.248941	+	0.143726i	0.370338	+	0.928897i	$0.379242\pi$
$674$	16.3663	+	30.8315i	0.630408	+	1.18758i
$675$		0			0
$676$	−2.80458	+	11.1833i	−0.107868	+	0.430128i
$677$	25.0349	+	14.4539i	0.962171	+	0.555510i	0.896841	−	0.442354i	$-0.145857\pi$
$677$	25.0349	+	14.4539i	0.962171	+	0.555510i	0.0653305	+	0.997864i	$0.479190\pi$
$678$		0			0
$679$	0.386036	+	2.18932i	0.0148147	+	0.0840183i
$680$	12.8659	+	52.0571i	0.493384	+	1.99630i
$681$		0			0
$682$	21.4637	−	6.95776i	0.821889	−	0.266426i
$683$	−48.0254			−1.83764			−0.918821	−	0.394676i	$-0.870857\pi$
$683$	−48.0254			−1.83764			−0.918821	+	0.394676i	$0.870857\pi$
$684$		0			0
$685$	14.1154			0.539322
$686$	27.1121	−	8.78876i	1.03515	−	0.335556i
$687$		0			0
$688$	−2.61172	+	18.2214i	−0.0995708	+	0.694684i
$689$	3.37336	+	19.1313i	0.128515	+	0.728843i
$690$		0			0
$691$	−23.6640	−	13.6624i	−0.900221	−	0.519743i	−0.0229489	−	0.999737i	$-0.507306\pi$
$691$	−23.6640	−	13.6624i	−0.900221	−	0.519743i	−0.877272	+	0.479994i	$0.840639\pi$
$692$	−46.9194	−	11.7665i	−1.78361	−	0.447296i
$693$		0			0
$694$	−12.5487	−	23.6398i	−0.476344	−	0.897353i
$695$	−31.4384	+	18.1509i	−1.19252	+	0.688505i
$696$		0			0
$697$	9.08663	+	24.9653i	0.344181	+	0.945629i
$698$	0.233448	+	0.0497879i	0.00883614	+	0.00188450i
$699$		0			0
$700$	−45.0382	+	21.8904i	−1.70228	+	0.827378i
$701$	−16.8471	+	14.1364i	−0.636306	+	0.533924i	−0.902881	−	0.429890i	$-0.858552\pi$
$701$	−16.8471	+	14.1364i	−0.636306	+	0.533924i	0.266575	+	0.963814i	$0.414108\pi$
$702$		0			0
$703$	−0.0693662	−	4.78637i	−0.00261619	−	0.180521i
$704$	−21.0727	−	19.1312i	−0.794207	−	0.721032i
$705$		0			0
$706$	−32.0980	+	35.5994i	−1.20802	+	1.33980i
$707$	28.8728	+	5.09105i	1.08587	+	0.191469i
$708$		0			0
$709$	−14.0920	+	5.12907i	−0.529236	+	0.192626i	−0.592797	−	0.805352i	$-0.701976\pi$
$709$	−14.0920	+	5.12907i	−0.529236	+	0.192626i	0.0635610	+	0.997978i	$0.479754\pi$
$710$	19.0853	+	24.4625i	0.716257	+	0.918061i
$711$		0			0
$712$	3.66724	−	12.6908i	0.137436	−	0.475609i
$713$	−18.9511	+	22.5851i	−0.709725	+	0.845817i
$714$		0			0
$715$	−19.6087	+	33.9633i	−0.733324	+	1.27015i
$716$	11.1359	+	4.97629i	0.416168	+	0.185973i
$717$		0			0
$718$	0.251197	−	0.401388i	0.00937458	−	0.0149797i
$719$	5.86251	−	16.1071i	0.218635	−	0.600693i	−0.781084	−	0.624426i	$-0.785333\pi$
$719$	5.86251	−	16.1071i	0.218635	−	0.600693i	0.999718	+	0.0237327i	$0.00755507\pi$
$720$		0			0
$721$			24.3558i			0.907058i
$722$	−9.02306	−	25.3098i	−0.335803	−	0.941932i
$723$		0			0
$724$	0.0245348	−	0.344097i	0.000911827	−	0.0127883i
$725$	22.9072	−	62.9369i	0.850750	−	2.33742i
$726$		0			0
$727$	−6.63741	+	1.17035i	−0.246168	+	0.0434060i	−0.295371	−	0.955383i	$-0.595443\pi$
$727$	−6.63741	+	1.17035i	−0.246168	+	0.0434060i	0.0492027	+	0.998789i	$0.484332\pi$
$728$	−11.6407	+	11.1952i	−0.431432	+	0.414921i
$729$		0			0
$730$	50.2797	−	7.03128i	1.86094	−	0.260239i
$731$	−13.6845	+	16.3086i	−0.506140	+	0.603194i
$732$		0			0
$733$	−5.86925	−	10.1658i	−0.216786	−	0.375484i	0.737038	−	0.675851i	$-0.236224\pi$
$733$	−5.86925	−	10.1658i	−0.216786	−	0.375484i	−0.953823	+	0.300368i	$0.902891\pi$
$734$	25.5123	−	19.9043i	0.941675	−	0.734680i
$735$		0			0
$736$	36.6024	+	6.58317i	1.34918	+	0.242659i
$737$	−39.6556	−	6.99235i	−1.46073	−	0.257567i
$738$		0			0
$739$	−9.52966	−	11.3570i	−0.350554	−	0.417774i	0.561737	−	0.827316i	$-0.310133\pi$
$739$	−9.52966	−	11.3570i	−0.350554	−	0.417774i	−0.912292	+	0.409541i	$0.865689\pi$
$740$	6.26147	−	6.46622i	0.230176	−	0.237703i
$741$		0			0
$742$	8.13594	−	20.0976i	0.298680	−	0.737805i
$743$	−37.9130	+	31.8128i	−1.39089	+	1.16710i	−0.425916	+	0.904763i	$0.640048\pi$
$743$	−37.9130	+	31.8128i	−1.39089	+	1.16710i	−0.964977	+	0.262335i	$0.915507\pi$
$744$		0			0
$745$	10.5002	−	59.5494i	0.384696	−	2.18172i
$746$	1.46281	−	6.85891i	0.0535573	−	0.251123i
$747$		0			0
$748$	−9.02990	−	31.6544i	−0.330166	−	1.15740i
$749$	26.5125	−	15.3070i	0.968746	−	0.559306i
$750$		0			0
$751$	−15.5215	−	13.0241i	−0.566388	−	0.475256i	0.314057	−	0.949404i	$-0.398312\pi$
$751$	−15.5215	−	13.0241i	−0.566388	−	0.475256i	−0.880445	+	0.474148i	$0.842756\pi$
$752$	−18.7810	−	30.2397i	−0.684873	−	1.10273i
$753$		0			0
$754$	0.768631	−	21.5873i	0.0279919	−	0.786162i
$755$	0.0751328	+	0.426099i	0.00273436	+	0.0155073i
$756$		0			0
$757$	−45.5910	−	16.5938i	−1.65703	−	0.603111i	−0.667141	−	0.744931i	$-0.732482\pi$
$757$	−45.5910	−	16.5938i	−1.65703	−	0.603111i	−0.989892	+	0.141820i	$0.954705\pi$
$758$	−13.8144	−	42.6155i	−0.501761	−	1.54786i
$759$		0			0
$760$	21.5822	−	45.6837i	0.782868	−	1.65712i
$761$	−2.39951			−0.0869822			−0.0434911	−	0.999054i	$-0.513848\pi$
$761$	−2.39951			−0.0869822			−0.0434911	+	0.999054i	$0.513848\pi$
$762$		0			0
$763$	−2.75254	−	1.00184i	−0.0996487	−	0.0362691i
$764$	−9.11909	−	12.5875i	−0.329917	−	0.455401i
$765$		0			0
$766$	−1.69061	+	47.4813i	−0.0610842	+	1.71557i
$767$	17.4801	+	10.0922i	0.631171	+	0.364407i
$768$		0			0
$769$	21.1512	+	17.7480i	0.762732	+	0.640008i	0.938836	−	0.344364i	$-0.111905\pi$
$769$	21.1512	+	17.7480i	0.762732	+	0.640008i	−0.176105	+	0.984371i	$0.556350\pi$
$770$	38.6614	−	20.5227i	1.39326	−	0.739587i
$771$		0			0
$772$	−3.09082	−	10.8349i	−0.111241	−	0.389956i
$773$	4.96066	+	13.6293i	0.178423	+	0.490212i	0.996375	−	0.0850744i	$-0.0271128\pi$
$773$	4.96066	+	13.6293i	0.178423	+	0.490212i	−0.817952	+	0.575286i	$0.804891\pi$
$774$		0			0
$775$	−9.18492	+	52.0903i	−0.329932	+	1.87114i
$776$	−0.200555	−	2.95522i	−0.00719950	−	0.106086i
$777$		0			0
$778$	−5.95765	+	14.7167i	−0.213592	+	0.527620i
$779$	8.21985	−	23.6444i	0.294507	−	0.847150i
$780$		0			0
$781$	−12.2425	−	14.5901i	−0.438073	−	0.522075i
$782$	31.9443	+	28.8023i	1.14232	+	1.02997i
$783$		0			0
$784$	−9.76204	+	2.04708i	−0.348644	+	0.0731101i
$785$	63.4059	−	23.0779i	2.26305	−	0.823684i
$786$		0			0
$787$	10.2360	+	17.7292i	0.364873	+	0.631979i	0.988756	−	0.149539i	$-0.0477790\pi$
$787$	10.2360	+	17.7292i	0.364873	+	0.631979i	−0.623883	+	0.781518i	$0.714446\pi$
$788$	4.54736	+	43.8422i	0.161993	+	1.56181i
$789$		0			0
$790$	24.0793	−	3.36732i	0.856702	−	0.119804i
$791$	8.12828	−	14.0786i	0.289008	−	0.500577i
$792$		0			0
$793$	5.08425	−	0.896490i	0.180547	−	0.0318353i
$794$	−15.8235	−	9.90265i	−0.561553	−	0.351432i
$795$		0			0
$796$	−1.46147	+	20.4970i	−0.0518006	+	0.726496i
$797$			6.95943i			0.246516i	0.992375	+	0.123258i	$0.0393342\pi$
$797$			6.95943i			0.246516i	−0.992375	+	0.123258i	$0.960666\pi$
$798$		0			0
$799$		−	41.1700i		−	1.45649i
$800$	62.7747	−	22.6053i	2.21942	−	0.799216i
$801$		0			0
$802$	−25.7594	+	41.1610i	−0.909596	+	1.45344i
$803$	−30.6915	+	5.41173i	−1.08308	+	0.190976i
$804$		0			0
$805$	−28.5969	+	49.5313i	−1.00791	+	1.74575i
$806$	2.36262	+	16.8948i	0.0832199	+	0.595094i
$807$		0			0
$808$	−37.5277	−	10.8443i	−1.32022	−	0.381501i
$809$	−2.02094	−	3.50038i	−0.0710526	−	0.123067i	0.828310	−	0.560270i	$-0.189302\pi$
$809$	−2.02094	−	3.50038i	−0.0710526	−	0.123067i	−0.899363	+	0.437203i	$0.855969\pi$
$810$		0			0
$811$	−23.4470	+	8.53402i	−0.823336	+	0.299670i	−0.719121	−	0.694885i	$-0.755455\pi$
$811$	−23.4470	+	8.53402i	−0.823336	+	0.299670i	−0.104215	+	0.994555i	$0.533233\pi$
$812$	−13.5089	+	19.9688i	−0.474069	+	0.700767i
$813$		0			0
$814$	−3.69998	+	4.10359i	−0.129684	+	0.143831i
$815$	−47.5879	−	56.7130i	−1.66693	−	1.98657i
$816$		0			0
$817$	19.7019	−	3.76914i	0.689283	−	0.131866i
$818$	36.0331	+	14.5870i	1.25987	+	0.510023i
$819$		0			0
$820$	42.3343	−	20.5762i	1.47838	−	0.718551i
$821$	1.97173	−	11.1822i	0.0688138	−	0.390262i	−0.930876	−	0.365337i	$-0.880954\pi$
$821$	1.97173	−	11.1822i	0.0688138	−	0.390262i	0.999689	−	0.0249259i	$-0.00793497\pi$
$822$		0			0
$823$	−10.6234	−	29.1877i	−0.370310	−	1.01742i	−0.975242	−	0.221141i	$-0.929022\pi$
$823$	−10.6234	−	29.1877i	−0.370310	−	1.01742i	0.604932	−	0.796277i	$-0.293200\pi$
$824$	3.45832	−	32.2665i	0.120476	−	1.12406i
$825$		0			0
$826$	−10.5626	−	19.8981i	−0.367519	−	0.692345i
$827$	−2.30858	−	1.93713i	−0.0802772	−	0.0673606i	0.601766	−	0.798672i	$-0.294464\pi$
$827$	−2.30858	−	1.93713i	−0.0802772	−	0.0673606i	−0.682043	+	0.731312i	$0.738908\pi$
$828$		0			0
$829$	44.7506	+	25.8368i	1.55425	+	0.897348i	0.997788	+	0.0664763i	$0.0211757\pi$
$829$	44.7506	+	25.8368i	1.55425	+	0.897348i	0.556464	+	0.830872i	$0.312158\pi$
$830$	32.1291	+	1.14398i	1.11522	+	0.0397081i
$831$		0			0
$832$	17.0111	−	13.1785i	0.589755	−	0.456881i
$833$	−10.8402	−	3.94549i	−0.375589	−	0.136703i
$834$		0			0
$835$	20.4582			0.707984
$836$	−12.2421	+	28.4969i	−0.423403	+	0.985588i
$837$		0			0
$838$	11.7490	−	3.80860i	0.405863	−	0.131566i
$839$	5.56173	+	2.02430i	0.192012	+	0.0698867i	0.436236	−	0.899832i	$-0.356311\pi$
$839$	5.56173	+	2.02430i	0.192012	+	0.0698867i	−0.244224	+	0.969719i	$0.578533\pi$
$840$		0			0
$841$	−0.563547	−	3.19603i	−0.0194327	−	0.110208i
$842$	−29.2793	−	1.04251i	−1.00903	−	0.0359273i
$843$		0			0
$844$	1.44721	−	5.77081i	0.0498151	−	0.198639i
$845$	18.0978	+	15.1859i	0.622583	+	0.522409i
$846$		0			0
$847$	−3.04661	+	1.75896i	−0.104683	+	0.0604385i
$848$	−13.6322	+	25.4700i	−0.468130	+	0.874643i
$849$		0			0
$850$	75.4686	+	16.0953i	2.58855	+	0.552065i
$851$	1.25370	−	7.11008i	0.0429763	−	0.243730i
$852$		0			0
$853$	−10.5042	+	8.81406i	−0.359657	+	0.301788i	−0.804654	−	0.593744i	$-0.797649\pi$
$853$	−10.5042	+	8.81406i	−0.359657	+	0.301788i	0.444997	+	0.895532i	$0.353205\pi$
$854$	−5.34105	−	2.16218i	−0.182767	−	0.0739881i
$855$		0			0
$856$	−37.2972	+	16.5141i	−1.27479	+	0.564441i
$857$	20.4136	+	24.3280i	0.697315	+	0.831027i	0.992220	−	0.124499i	$-0.0397325\pi$
$857$	20.4136	+	24.3280i	0.697315	+	0.831027i	−0.294905	+	0.955527i	$0.595288\pi$
$858$		0			0
$859$	−21.7695	−	3.83856i	−0.742767	−	0.130970i	−0.210556	−	0.977582i	$-0.567528\pi$
$859$	−21.7695	−	3.83856i	−0.742767	−	0.130970i	−0.532211	+	0.846612i	$0.678639\pi$
$860$	31.2411	+	21.1346i	1.06531	+	0.720685i
$861$		0			0
$862$	13.6150	+	17.4510i	0.463729	+	0.594383i
$863$	0.298949	+	0.517795i	0.0101763	+	0.0176259i	0.871069	−	0.491161i	$-0.163427\pi$
$863$	0.298949	+	0.517795i	0.0101763	+	0.0176259i	−0.860892	+	0.508787i	$0.830094\pi$
$864$		0			0
$865$	−63.7118	+	75.9288i	−2.16627	+	2.58166i
$866$	−4.22221	−	30.1924i	−0.143477	−	1.02598i
$867$		0			0
$868$	7.76801	−	17.3832i	0.263664	−	0.590024i
$869$	−14.6983	+	2.59171i	−0.498607	+	0.0879178i
$870$		0			0
$871$	10.4126	−	28.6085i	0.352819	−	0.969361i
$872$	3.50431	+	1.71808i	0.118671	+	0.0581814i
$873$		0			0
$874$	−6.19377	−	40.0505i	−0.209507	−	1.35473i
$875$			59.1112i			1.99832i
$876$		0			0
$877$	15.7951	−	43.3968i	0.533364	−	1.46541i	−0.321679	−	0.946849i	$-0.604247\pi$
$877$	15.7951	−	43.3968i	0.533364	−	1.46541i	0.855043	−	0.518557i	$-0.173531\pi$
$878$	28.6067	+	17.9026i	0.965428	+	0.604185i
$879$		0			0
$880$	−54.1326	+	21.6988i	−1.82481	+	0.731468i
$881$	−1.08289	+	1.87562i	−0.0364835	+	0.0631913i	−0.883691	−	0.468071i	$-0.844949\pi$
$881$	−1.08289	+	1.87562i	−0.0364835	+	0.0631913i	0.847207	+	0.531263i	$0.178282\pi$
$882$		0			0
$883$	−0.285489	+	0.340233i	−0.00960747	+	0.0114497i	−0.770827	−	0.637045i	$-0.780157\pi$
$883$	−0.285489	+	0.340233i	−0.00960747	+	0.0114497i	0.761219	+	0.648495i	$0.224601\pi$
$884$	24.7546	−	2.56757i	0.832586	−	0.0863567i
$885$		0			0
$886$	3.91188	−	3.05199i	0.131422	−	0.102534i
$887$	12.1025	−	4.40495i	0.406363	−	0.147904i	−0.130748	−	0.991416i	$-0.541738\pi$
$887$	12.1025	−	4.40495i	0.406363	−	0.147904i	0.537111	+	0.843512i	$0.319516\pi$
$888$		0			0
$889$	5.31501	+	0.937180i	0.178260	+	0.0314320i
$890$	−20.1033	−	18.1260i	−0.673863	−	0.607585i
$891$		0			0
$892$	−18.8222	−	18.2262i	−0.630213	−	0.610259i
$893$	−24.5013	+	30.0740i	−0.819905	+	1.00639i
$894$		0			0
$895$	19.1456	−	16.0651i	0.639968	−	0.536997i
$896$	−23.8973	+	2.39606i	−0.798351	+	0.0800466i
$897$		0			0
$898$	−2.02491	+	9.49449i	−0.0675720	+	0.316835i
$899$	8.70972	+	23.9298i	0.290486	+	0.798102i
$900$		0			0
$901$	−28.9349	+	16.7056i	−0.963962	+	0.556544i
$902$	−25.5213	+	13.5476i	−0.849768	+	0.451084i
$903$		0			0
$904$	−12.7674	+	17.4971i	−0.424636	+	0.581946i
$905$	−0.612165	−	0.353434i	−0.0203490	−	0.0117485i
$906$		0			0
$907$	7.19674	+	40.8147i	0.238964	+	1.35523i	0.834103	+	0.551609i	$0.185986\pi$
$907$	7.19674	+	40.8147i	0.238964	+	1.35523i	−0.595139	+	0.803623i	$0.702903\pi$
$908$	31.6192	−	22.9067i	1.04932	−	0.760185i
$909$		0			0
$910$	10.2049	+	31.4806i	0.338288	+	1.04357i
$911$	−4.19282			−0.138914			−0.0694571	−	0.997585i	$-0.522127\pi$
$911$	−4.19282			−0.138914			−0.0694571	+	0.997585i	$0.522127\pi$
$912$		0			0
$913$	−19.7352			−0.653139
$914$	10.0382	+	30.9665i	0.332035	+	1.02428i
$915$		0			0
$916$	5.92298	−	4.29093i	0.195701	−	0.141776i
$917$	−2.21016	−	12.5344i	−0.0729858	−	0.413923i
$918$		0			0
$919$	−35.7443	−	20.6370i	−1.17910	−	0.680752i	−0.223291	−	0.974752i	$-0.571680\pi$
$919$	−35.7443	−	20.6370i	−1.17910	−	0.680752i	−0.955805	+	0.294000i	$0.905013\pi$
$920$	44.9181	−	61.5584i	1.48091	−	2.02952i
$921$		0			0
$922$	−39.1628	+	20.7889i	−1.28976	+	0.684645i
$923$	12.4707	−	7.19996i	0.410478	−	0.236990i
$924$		0			0
$925$	−4.43009	−	12.1716i	−0.145661	−	0.400199i
$926$	4.23208	−	19.8436i	0.139075	−	0.652101i
$927$		0			0
$928$	20.7320	−	24.5364i	0.680560	−	0.805448i
$929$	−17.9323	+	15.0470i	−0.588339	+	0.493675i	−0.887674	−	0.460473i	$-0.847680\pi$
$929$	−17.9323	+	15.0470i	−0.588339	+	0.493675i	0.299334	+	0.954148i	$0.403235\pi$
$930$		0			0
$931$	5.57049	+	9.33336i	0.182566	+	0.305889i
$932$	−30.0374	−	29.0863i	−0.983907	−	0.952753i
$933$		0			0
$934$	17.9938	+	16.2240i	0.588774	+	0.530864i
$935$	−66.4247	−	11.7125i	−2.17232	−	0.383039i
$936$		0			0
$937$	56.8850	−	20.7045i	1.85835	−	0.676385i	0.878151	−	0.478383i	$-0.158777\pi$
$937$	56.8850	−	20.7045i	1.85835	−	0.676385i	0.980202	−	0.198002i	$-0.0634453\pi$
$938$	−26.7904	+	20.9014i	−0.874737	+	0.682456i
$939$		0			0
$940$	−72.5519	+	7.52516i	−2.36638	+	0.245444i
$941$	−8.15425	+	9.71786i	−0.265821	+	0.316793i	−0.882400	−	0.470500i	$-0.844074\pi$
$941$	−8.15425	+	9.71786i	−0.265821	+	0.316793i	0.616579	+	0.787293i	$0.288518\pi$
$942$		0			0
$943$	18.8775	−	32.6969i	0.614737	−	1.06476i
$944$	11.1679	+	27.8608i	0.363485	+	0.906792i
$945$		0			0
$946$	−19.6271	−	12.2830i	−0.638131	−	0.399356i
$947$	17.5275	−	48.1565i	0.569569	−	1.56488i	−0.235612	−	0.971847i	$-0.575709\pi$
$947$	17.5275	−	48.1565i	0.569569	−	1.56488i	0.805180	−	0.593030i	$-0.202068\pi$
$948$		0			0
$949$		−	23.5626i		−	0.764873i
$950$	−45.5499	−	56.6706i	−1.47783	−	1.83864i
$951$		0			0
$952$	−24.9407	−	12.2278i	−0.808333	−	0.396306i
$953$	−2.10699	+	5.78891i	−0.0682522	+	0.187521i	−0.969129	−	0.246553i	$-0.920702\pi$
$953$	−2.10699	+	5.78891i	−0.0682522	+	0.187521i	0.900877	+	0.434074i	$0.142924\pi$
$954$		0			0
$955$	−31.3660	+	5.53067i	−1.01498	+	0.178968i
$956$	−4.90758	+	10.9821i	−0.158722	+	0.355188i
$957$		0			0
$958$	4.37737	+	31.3020i	0.141426	+	1.01132i
$959$	−4.69992	+	5.60114i	−0.151768	+	0.180870i
$960$		0			0
$961$	5.44439	+	9.42996i	0.175626	+	0.304192i
$962$	−2.56966	−	3.29366i	−0.0828492	−	0.106192i
$963$		0			0
$964$	−19.5577	−	13.2308i	−0.629911	−	0.426136i
$965$	−22.7363	−	4.00903i	−0.731908	−	0.129055i
$966$		0			0
$967$	4.44136	+	5.29300i	0.142824	+	0.170211i	0.832714	−	0.553703i	$-0.186786\pi$
$967$	4.44136	+	5.29300i	0.142824	+	0.170211i	−0.689890	+	0.723914i	$0.742341\pi$
$968$	4.28589	−	1.89767i	0.137754	−	0.0609935i
$969$		0			0
$970$	−5.62586	−	2.27747i	−0.180635	−	0.0731252i
$971$	−37.1841	+	31.2011i	−1.19329	+	1.00129i	−0.193497	+	0.981101i	$0.561983\pi$
$971$	−37.1841	+	31.2011i	−1.19329	+	1.00129i	−0.999796	+	0.0201908i	$0.993573\pi$
$972$		0			0
$973$	3.26534	−	18.5187i	0.104682	−	0.593682i
$974$	−31.3274	−	6.68125i	−1.00379	−	0.214081i
$975$		0			0
$976$	6.76880	+	3.62283i	0.216664	+	0.115964i
$977$	−45.9065	+	26.5041i	−1.46868	+	0.847942i	−0.999384	−	0.0351002i	$-0.988825\pi$
$977$	−45.9065	+	26.5041i	−1.46868	+	0.847942i	−0.469294	+	0.883042i	$0.655492\pi$
$978$		0			0
$979$	12.7287	+	10.6806i	0.406810	+	0.341354i
$980$	−4.97156	+	19.8243i	−0.158811	+	0.633263i
$981$		0			0
$982$	−35.5487	−	1.26574i	−1.13440	−	0.0403913i
$983$	−3.45333	−	19.5848i	−0.110144	−	0.624659i	−0.989040	−	0.147646i	$-0.952830\pi$
$983$	−3.45333	−	19.5848i	−0.110144	−	0.624659i	0.878896	−	0.477013i	$-0.158281\pi$
$984$		0			0
$985$	84.8706	+	30.8904i	2.70420	+	0.984249i
$986$	35.3407	−	11.4562i	1.12548	−	0.364839i
$987$		0			0
$988$	−19.6108	−	12.8565i	−0.623903	−	0.409019i
$989$	30.2542			0.962027
$990$		0			0
$991$	−13.1289	−	4.77853i	−0.417053	−	0.151795i	0.124966	−	0.992161i	$-0.460118\pi$
$991$	−13.1289	−	4.77853i	−0.417053	−	0.151795i	−0.542019	+	0.840366i	$0.682340\pi$
$992$	−12.7593	+	21.9262i	−0.405108	+	0.696158i
$993$		0			0
$994$	−16.0617	−	0.571888i	−0.509445	−	0.0181392i
$995$	36.4651	+	21.0531i	1.15602	+	0.667430i
$996$		0			0
$997$	−7.05984	−	5.92391i	−0.223587	−	0.187612i	0.524112	−	0.851649i	$-0.324397\pi$
$997$	−7.05984	−	5.92391i	−0.223587	−	0.187612i	−0.747700	+	0.664037i	$0.768842\pi$
$998$	−18.2374	−	34.3563i	−0.577296	−	1.08753i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	684.2.cf.b.127.4		60
3.2	odd	2		228.2.w.b.127.7	yes	60
4.3	odd	2		684.2.cf.c.127.2		60
12.11	even	2		228.2.w.a.127.9	yes	60
19.3	odd	18		684.2.cf.c.307.2		60
57.41	even	18		228.2.w.a.79.9	✓	60
76.3	even	18	inner	684.2.cf.b.307.4		60
228.155	odd	18		228.2.w.b.79.7	yes	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
228.2.w.a.79.9	✓	60	57.41	even	18
228.2.w.a.127.9	yes	60	12.11	even	2
228.2.w.b.79.7	yes	60	228.155	odd	18
228.2.w.b.127.7	yes	60	3.2	odd	2
684.2.cf.b.127.4		60	1.1	even	1	trivial
684.2.cf.b.307.4		60	76.3	even	18	inner
684.2.cf.c.127.2		60	4.3	odd	2
684.2.cf.c.307.2		60	19.3	odd	18

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 684 = 2^{2} \cdot 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	684.cf (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.436096 - 1.34530i) q^{2} +(-1.61964 + 1.17336i) q^{4} +(0.711633 + 4.03587i) q^{5} +(-1.83842 - 1.06142i) q^{7} +(2.28483 + 1.66720i) q^{8} +(5.11910 - 2.71738i) q^{10} +(-3.08105 + 1.77885i) q^{11} +(-0.919976 - 2.52761i) q^{13} +(-0.626188 + 2.93610i) q^{14} +(1.24647 - 3.80083i) q^{16} +(3.54387 - 2.97366i) q^{17} +(-4.35844 + 0.0631645i) q^{19} +(-5.88810 - 5.70166i) q^{20} +(3.73671 + 3.36918i) q^{22} +(-6.47440 - 1.14161i) q^{23} +(-11.0834 + 4.03402i) q^{25} +(-2.99919 + 2.33992i) q^{26} +(4.22301 - 0.438015i) q^{28} +(-3.65007 + 4.34998i) q^{29} +(2.24228 - 3.88374i) q^{31} +(-5.65682 - 0.0193500i) q^{32} +(-5.54592 - 3.47075i) q^{34} +(2.97545 - 8.17498i) q^{35} +1.09818i q^{37} +(1.98567 + 5.83585i) q^{38} +(-5.10265 + 10.4077i) q^{40} +(-1.96417 + 5.39651i) q^{41} +(-4.53199 + 0.799112i) q^{43} +(2.90298 - 6.49626i) q^{44} +(1.28765 + 9.20784i) q^{46} +(5.72037 - 6.81727i) q^{47} +(-1.24680 - 2.15951i) q^{49} +(10.2604 + 13.1512i) q^{50} +(4.45582 + 3.01437i) q^{52} +(-7.11245 - 1.25412i) q^{53} +(-9.37178 - 11.1688i) q^{55} +(-2.43089 - 5.49017i) q^{56} +(7.44379 + 3.01341i) q^{58} +(-5.74836 + 4.82344i) q^{59} +(-0.333289 + 1.89018i) q^{61} +(-6.20262 - 1.32284i) q^{62} +(2.44088 + 7.61854i) q^{64} +(9.54643 - 5.51163i) q^{65} +(8.67038 + 7.27532i) q^{67} +(-2.25064 + 8.97449i) q^{68} +(-12.2954 - 0.437785i) q^{70} +(0.929621 + 5.27214i) q^{71} +(8.23159 + 2.99605i) q^{73} +(1.47738 - 0.478913i) q^{74} +(6.98500 - 5.21630i) q^{76} +7.55238 q^{77} +(3.94216 + 1.43483i) q^{79} +(16.2267 + 2.32581i) q^{80} +(8.11647 + 0.288993i) q^{82} +(4.80400 + 2.77359i) q^{83} +(14.5233 + 12.1865i) q^{85} +(3.05142 + 5.74838i) q^{86} +(-10.0054 - 1.07237i) q^{88} +(-1.59739 - 4.38880i) q^{89} +(-0.991540 + 5.62330i) q^{91} +(11.8257 - 5.74777i) q^{92} +(-11.6659 - 4.72261i) q^{94} +(-3.35653 - 17.5452i) q^{95} +(-0.673146 - 0.802225i) q^{97} +(-2.36146 + 2.61906i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q - 3 q^{2} - 3 q^{4} + 3 q^{8} - 6 q^{10} - 6 q^{13} + 9 q^{14} + 21 q^{16} + 18 q^{19} - 30 q^{20} - 12 q^{22} - 18 q^{28} - 12 q^{31} - 33 q^{32} - 15 q^{34} + 84 q^{38} - 87 q^{40} + 12 q^{41} - 18 q^{43}+ \cdots + 105 q^{98}+O(q^{100}) \) 60 * q - 3 * q^2 - 3 * q^4 + 3 * q^8 - 6 * q^10 - 6 * q^13 + 9 * q^14 + 21 * q^16 + 18 * q^19 - 30 * q^20 - 12 * q^22 - 18 * q^28 - 12 * q^31 - 33 * q^32 - 15 * q^34 + 84 * q^38 - 87 * q^40 + 12 * q^41 - 18 * q^43 + 51 * q^44 - 21 * q^46 + 30 * q^49 + 27 * q^50 - 3 * q^52 - 12 * q^53 - 42 * q^56 - 36 * q^58 - 105 * q^62 + 21 * q^64 + 36 * q^65 + 42 * q^67 + 15 * q^68 - 96 * q^70 - 24 * q^71 + 18 * q^73 - 69 * q^74 + 54 * q^76 + 72 * q^77 + 12 * q^79 + 12 * q^80 + 75 * q^82 - 60 * q^85 - 21 * q^86 + 36 * q^88 + 12 * q^89 - 84 * q^91 - 99 * q^92 + 24 * q^95 + 12 * q^97 + 105 * q^98

Introduction

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