LMFDB - Embedded newform 680.2.l.a.101.23

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [680,2,Mod(101,680)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(680, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 1, 0, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("680.101"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 680 = 2^{3} \cdot 5 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	680.l (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [36,0,-4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$5.42982733745$
Analytic rank:	$0$
Dimension:	$36$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			101.23
Character	$\chi$	$=$	680.101
Dual form			680.2.l.a.101.24

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.629773 - 1.26625i) q^{2} -0.528085 q^{3} +(-1.20677 - 1.59490i) q^{4} +1.00000 q^{5} +(-0.332573 + 0.668687i) q^{6} +4.36555i q^{7} +(-2.77953 + 0.523652i) q^{8} -2.72113 q^{9} +(0.629773 - 1.26625i) q^{10} +0.873286 q^{11} +(0.637278 + 0.842241i) q^{12} +6.88027i q^{13} +(5.52788 + 2.74931i) q^{14} -0.528085 q^{15} +(-1.08740 + 3.84936i) q^{16} +(-3.39745 + 2.33609i) q^{17} +(-1.71369 + 3.44562i) q^{18} -3.88862i q^{19} +(-1.20677 - 1.59490i) q^{20} -2.30538i q^{21} +(0.549971 - 1.10580i) q^{22} +4.09430i q^{23} +(1.46783 - 0.276533i) q^{24} +1.00000 q^{25} +(8.71213 + 4.33300i) q^{26} +3.02124 q^{27} +(6.96261 - 5.26823i) q^{28} -6.41784 q^{29} +(-0.332573 + 0.668687i) q^{30} -6.12329i q^{31} +(4.18943 + 3.80114i) q^{32} -0.461169 q^{33} +(0.818452 + 5.77323i) q^{34} +4.36555i q^{35} +(3.28378 + 4.33992i) q^{36} +6.96168 q^{37} +(-4.92396 - 2.44895i) q^{38} -3.63336i q^{39} +(-2.77953 + 0.523652i) q^{40} +12.0257i q^{41} +(-2.91919 - 1.45187i) q^{42} -9.29275i q^{43} +(-1.05386 - 1.39280i) q^{44} -2.72113 q^{45} +(5.18441 + 2.57848i) q^{46} +1.39613 q^{47} +(0.574239 - 2.03279i) q^{48} -12.0581 q^{49} +(0.629773 - 1.26625i) q^{50} +(1.79414 - 1.23365i) q^{51} +(10.9733 - 8.30292i) q^{52} -5.12849i q^{53} +(1.90269 - 3.82564i) q^{54} +0.873286 q^{55} +(-2.28603 - 12.1342i) q^{56} +2.05352i q^{57} +(-4.04178 + 8.12658i) q^{58} +5.18909i q^{59} +(0.637278 + 0.842241i) q^{60} +7.45546 q^{61} +(-7.75362 - 3.85628i) q^{62} -11.8792i q^{63} +(7.45158 - 2.91101i) q^{64} +6.88027i q^{65} +(-0.290432 + 0.583955i) q^{66} -1.10485i q^{67} +(7.82578 + 2.59946i) q^{68} -2.16214i q^{69} +(5.52788 + 2.74931i) q^{70} +8.33370i q^{71} +(7.56345 - 1.42492i) q^{72} +1.86189i q^{73} +(4.38428 - 8.81522i) q^{74} -0.528085 q^{75} +(-6.20195 + 4.69268i) q^{76} +3.81238i q^{77} +(-4.60074 - 2.28819i) q^{78} -3.18110i q^{79} +(-1.08740 + 3.84936i) q^{80} +6.56791 q^{81} +(15.2275 + 7.57344i) q^{82} -4.38088i q^{83} +(-3.67685 + 2.78207i) q^{84} +(-3.39745 + 2.33609i) q^{85} +(-11.7669 - 5.85232i) q^{86} +3.38916 q^{87} +(-2.42732 + 0.457298i) q^{88} +9.98438 q^{89} +(-1.71369 + 3.44562i) q^{90} -30.0362 q^{91} +(6.52999 - 4.94089i) q^{92} +3.23362i q^{93} +(0.879244 - 1.76785i) q^{94} -3.88862i q^{95} +(-2.21238 - 2.00732i) q^{96} +6.33811i q^{97} +(-7.59384 + 15.2685i) q^{98} -2.37632 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 4 q^{3} + 2 q^{4} + 36 q^{5} + 36 q^{9} - 8 q^{11} - 2 q^{12} + 2 q^{14} - 4 q^{15} + 6 q^{16} - 10 q^{18} + 2 q^{20} + 26 q^{24} + 36 q^{25} + 6 q^{26} - 16 q^{27} + 14 q^{28} - 10 q^{32} - 8 q^{33}+ \cdots - 40 q^{99}+O(q^{100}) $ 36 * q - 4 * q^3 + 2 * q^4 + 36 * q^5 + 36 * q^9 - 8 * q^11 - 2 * q^12 + 2 * q^14 - 4 * q^15 + 6 * q^16 - 10 * q^18 + 2 * q^20 + 26 * q^24 + 36 * q^25 + 6 * q^26 - 16 * q^27 + 14 * q^28 - 10 * q^32 - 8 * q^33 - 24 * q^34 + 8 * q^36 - 20 * q^38 - 2 * q^42 + 6 * q^44 + 36 * q^45 + 24 * q^46 + 20 * q^47 - 4 * q^48 - 36 * q^49 + 6 * q^52 - 56 * q^54 - 8 * q^55 + 20 * q^56 - 18 * q^58 - 2 * q^60 - 24 * q^62 + 14 * q^64 - 16 * q^66 - 40 * q^68 + 2 * q^70 - 54 * q^72 + 6 * q^74 - 4 * q^75 + 2 * q^76 - 14 * q^78 + 6 * q^80 + 44 * q^81 + 22 * q^82 - 68 * q^84 - 36 * q^86 + 24 * q^87 - 58 * q^88 - 10 * q^90 - 56 * q^91 - 12 * q^92 + 14 * q^94 - 24 * q^96 + 10 * q^98 - 40 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/680\mathbb{Z}\right)^\times$.

$n$	$137$	$241$	$341$	$511$
$\chi(n)$	$1$	$-1$	$-1$	$1$

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 $

$2$	0.629773	−	1.26625i	0.445316	−	0.895373i
$2$	0.629773	−	1.26625i	0.445316	−	0.895373i
$3$	−0.528085			−0.304890			−0.152445	−	0.988312i	$-0.548715\pi$
$3$	−0.528085			−0.304890			−0.152445	+	0.988312i	$0.548715\pi$
$4$	−1.20677	−	1.59490i	−0.603386	−	0.797449i
$5$	1.00000			0.447214
$5$	1.00000			0.447214
$6$	−0.332573	+	0.668687i	−0.135773	+	0.272990i
$7$			4.36555i			1.65002i	0.565115	+	0.825012i	$0.308832\pi$
$7$			4.36555i			1.65002i	−0.565115	+	0.825012i	$0.691168\pi$
$8$	−2.77953	+	0.523652i	−0.982712	+	0.185139i
$9$	−2.72113			−0.907042
$10$	0.629773	−	1.26625i	0.199152	−	0.400423i
$11$	0.873286			0.263306			0.131653	−	0.991296i	$-0.457972\pi$
$11$	0.873286			0.263306			0.131653	+	0.991296i	$0.457972\pi$
$12$	0.637278	+	0.842241i	0.183966	+	0.243134i
$13$			6.88027i			1.90824i	0.299420	+	0.954121i	$0.403207\pi$
$13$			6.88027i			1.90824i	−0.299420	+	0.954121i	$0.596793\pi$
$14$	5.52788	+	2.74931i	1.47739	+	0.734783i
$15$	−0.528085			−0.136351
$16$	−1.08740	+	3.84936i	−0.271850	+	0.962340i
$17$	−3.39745	+	2.33609i	−0.824003	+	0.566585i
$17$	−3.39745	+	2.33609i	−0.824003	+	0.566585i
$18$	−1.71369	+	3.44562i	−0.403921	+	0.812141i
$19$		−	3.88862i		−	0.892111i	−0.895005	−	0.446056i	$-0.852828\pi$
$19$		−	3.88862i		−	0.892111i	0.895005	−	0.446056i	$-0.147172\pi$
$20$	−1.20677	−	1.59490i	−0.269843	−	0.356630i
$21$		−	2.30538i		−	0.503076i
$22$	0.549971	−	1.10580i	0.117254	−	0.235757i
$23$			4.09430i			0.853721i	0.904317	+	0.426861i	$0.140380\pi$
$23$			4.09430i			0.853721i	−0.904317	+	0.426861i	$0.859620\pi$
$24$	1.46783	−	0.276533i	0.299619	−	0.0564470i
$25$	1.00000			0.200000
$26$	8.71213	+	4.33300i	1.70859	+	0.849772i
$27$	3.02124			0.581438
$28$	6.96261	−	5.26823i	1.31581	−	0.995602i
$29$	−6.41784			−1.19176			−0.595881	−	0.803073i	$-0.703197\pi$
$29$	−6.41784			−1.19176			−0.595881	+	0.803073i	$0.703197\pi$
$30$	−0.332573	+	0.668687i	−0.0607193	+	0.122085i
$31$		−	6.12329i		−	1.09978i	−0.835238	−	0.549888i	$-0.814670\pi$
$31$		−	6.12329i		−	1.09978i	0.835238	−	0.549888i	$-0.185330\pi$
$32$	4.18943	+	3.80114i	0.740594	+	0.671953i
$33$	−0.461169			−0.0802792
$34$	0.818452	+	5.77323i	0.140363	+	0.990100i
$35$			4.36555i			0.737913i
$36$	3.28378	+	4.33992i	0.547297	+	0.723320i
$37$	6.96168			1.14449			0.572247	−	0.820081i	$-0.306072\pi$
$37$	6.96168			1.14449			0.572247	+	0.820081i	$0.306072\pi$
$38$	−4.92396	−	2.44895i	−0.798772	−	0.397272i
$39$		−	3.63336i		−	0.581804i
$40$	−2.77953	+	0.523652i	−0.439482	+	0.0827967i
$41$			12.0257i			1.87810i	0.343786	+	0.939048i	$0.388290\pi$
$41$			12.0257i			1.87810i	−0.343786	+	0.939048i	$0.611710\pi$
$42$	−2.91919	−	1.45187i	−0.450441	−	0.224028i
$43$		−	9.29275i		−	1.41713i	−0.705645	−	0.708566i	$-0.749343\pi$
$43$		−	9.29275i		−	1.41713i	0.705645	−	0.708566i	$-0.250657\pi$
$44$	−1.05386	−	1.39280i	−0.158875	−	0.209973i
$45$	−2.72113			−0.405642
$46$	5.18441	+	2.57848i	0.764399	+	0.380176i
$47$	1.39613			0.203646			0.101823	−	0.994803i	$-0.467532\pi$
$47$	1.39613			0.203646			0.101823	+	0.994803i	$0.467532\pi$
$48$	0.574239	−	2.03279i	0.0828842	−	0.293408i
$49$	−12.0581			−1.72258
$50$	0.629773	−	1.26625i	0.0890633	−	0.179075i
$51$	1.79414	−	1.23365i	0.251230	−	0.172746i
$52$	10.9733	−	8.30292i	1.52173	−	1.15141i
$53$		−	5.12849i		−	0.704452i	−0.935915	−	0.352226i	$-0.885425\pi$
$53$		−	5.12849i		−	0.704452i	0.935915	−	0.352226i	$-0.114575\pi$
$54$	1.90269	−	3.82564i	0.258924	−	0.520604i
$55$	0.873286			0.117754
$56$	−2.28603	−	12.1342i	−0.305484	−	1.62150i
$57$			2.05352i			0.271996i
$58$	−4.04178	+	8.12658i	−0.530711	+	1.06707i
$59$			5.18909i			0.675562i	0.941225	+	0.337781i	$0.109676\pi$
$59$			5.18909i			0.675562i	−0.941225	+	0.337781i	$0.890324\pi$
$60$	0.637278	+	0.842241i	0.0822723	+	0.108733i
$61$	7.45546			0.954574			0.477287	−	0.878748i	$-0.341620\pi$
$61$	7.45546			0.954574			0.477287	+	0.878748i	$0.341620\pi$
$62$	−7.75362	−	3.85628i	−0.984710	−	0.489748i
$63$		−	11.8792i		−	1.49664i
$64$	7.45158	−	2.91101i	0.931447	−	0.363877i
$65$			6.88027i			0.853392i
$66$	−0.290432	+	0.583955i	−0.0357497	+	0.0718799i
$67$		−	1.10485i		−	0.134978i	−0.997720	−	0.0674892i	$-0.978501\pi$
$67$		−	1.10485i		−	0.134978i	0.997720	−	0.0674892i	$-0.0214988\pi$
$68$	7.82578	+	2.59946i	0.949015	+	0.315230i
$69$		−	2.16214i		−	0.260291i
$70$	5.52788	+	2.74931i	0.660708	+	0.328605i
$71$			8.33370i			0.989028i	0.869170	+	0.494514i	$0.164654\pi$
$71$			8.33370i			0.989028i	−0.869170	+	0.494514i	$0.835346\pi$
$72$	7.56345	−	1.42492i	0.891362	−	0.167929i
$73$			1.86189i			0.217917i	0.994046	+	0.108959i	$0.0347516\pi$
$73$			1.86189i			0.217917i	−0.994046	+	0.108959i	$0.965248\pi$
$74$	4.38428	−	8.81522i	0.509662	−	1.02475i
$75$	−0.528085			−0.0609780
$76$	−6.20195	+	4.69268i	−0.711413	+	0.538288i
$77$			3.81238i			0.434461i
$78$	−4.60074	−	2.28819i	−0.520932	−	0.259087i
$79$		−	3.18110i		−	0.357902i	−0.983858	−	0.178951i	$-0.942730\pi$
$79$		−	3.18110i		−	0.357902i	0.983858	−	0.178951i	$-0.0572704\pi$
$80$	−1.08740	+	3.84936i	−0.121575	+	0.430371i
$81$	6.56791			0.729768
$82$	15.2275	+	7.57344i	1.68160	+	0.836347i
$83$		−	4.38088i		−	0.480864i	−0.970666	−	0.240432i	$-0.922711\pi$
$83$		−	4.38088i		−	0.480864i	0.970666	−	0.240432i	$-0.0772891\pi$
$84$	−3.67685	+	2.78207i	−0.401177	+	0.303549i
$85$	−3.39745	+	2.33609i	−0.368505	+	0.253385i
$86$	−11.7669	−	5.85232i	−1.26886	−	0.631072i
$87$	3.38916			0.363356
$88$	−2.42732	+	0.457298i	−0.258754	+	0.0487481i
$89$	9.98438			1.05834			0.529171	−	0.848515i	$-0.322503\pi$
$89$	9.98438			1.05834			0.529171	+	0.848515i	$0.322503\pi$
$90$	−1.71369	+	3.44562i	−0.180639	+	0.363201i
$91$	−30.0362			−3.14865
$92$	6.52999	−	4.94089i	0.680799	−	0.515124i
$93$			3.23362i			0.335311i
$94$	0.879244	−	1.76785i	0.0906871	−	0.182340i
$95$		−	3.88862i		−	0.398964i
$96$	−2.21238	−	2.00732i	−0.225800	−	0.204872i
$97$			6.33811i			0.643538i	0.946818	+	0.321769i	$0.104277\pi$
$97$			6.33811i			0.643538i	−0.946818	+	0.321769i	$0.895723\pi$
$98$	−7.59384	+	15.2685i	−0.767093	+	1.54235i
$99$	−2.37632			−0.238829
$100$	−1.20677	−	1.59490i	−0.120677	−	0.159490i
$101$			7.56609i			0.752854i	0.926446	+	0.376427i	$0.122847\pi$
$101$			7.56609i			0.752854i	−0.926446	+	0.376427i	$0.877153\pi$
$102$	−0.432212	−	3.04875i	−0.0427954	−	0.301872i
$103$	−7.19929			−0.709368			−0.354684	−	0.934986i	$-0.615411\pi$
$103$	−7.19929			−0.709368			−0.354684	+	0.934986i	$0.615411\pi$
$104$	−3.60287	−	19.1239i	−0.353290	−	1.87525i
$105$		−	2.30538i		−	0.224982i
$106$	−6.49394	−	3.22978i	−0.630747	−	0.313704i
$107$	−17.9909			−1.73925			−0.869624	−	0.493714i	$-0.835639\pi$
$107$	−17.9909			−1.73925			−0.869624	+	0.493714i	$0.835639\pi$
$108$	−3.64595	−	4.81857i	−0.350832	−	0.463667i
$109$	−11.5234			−1.10374			−0.551869	−	0.833931i	$-0.686085\pi$
$109$	−11.5234			−1.10374			−0.551869	+	0.833931i	$0.686085\pi$
$110$	0.549971	−	1.10580i	0.0524377	−	0.105434i
$111$	−3.67636			−0.348945
$112$	−16.8046	−	4.74710i	−1.58788	−	0.448558i
$113$			5.44751i			0.512459i	0.966616	+	0.256229i	$0.0824802\pi$
$113$			5.44751i			0.512459i	−0.966616	+	0.256229i	$0.917520\pi$
$114$	2.60027	+	1.29325i	0.243538	+	0.121124i
$115$			4.09430i			0.381796i
$116$	7.74487	+	10.2358i	0.719093	+	0.950370i
$117$		−	18.7221i		−	1.73086i
$118$	6.57068	+	3.26795i	0.604880	+	0.300839i
$119$	−10.1983	−	14.8318i	−0.934880	−	1.35962i
$120$	1.46783	−	0.276533i	0.133994	−	0.0252439i
$121$	−10.2374			−0.930670
$122$	4.69524	−	9.44047i	0.425087	−	0.854700i
$123$		−	6.35058i		−	0.572613i
$124$	−9.76603	+	7.38943i	−0.877015	+	0.663590i
$125$	1.00000			0.0894427
$126$	−15.0421	−	7.48121i	−1.34005	−	0.666479i
$127$	18.0289			1.59981			0.799903	−	0.600130i	$-0.204884\pi$
$127$	18.0289			1.59981			0.799903	+	0.600130i	$0.204884\pi$
$128$	1.00673	−	11.2688i	0.0889833	−	0.996033i
$129$			4.90736i			0.432069i
$130$	8.71213	+	4.33300i	0.764104	+	0.380030i
$131$	−0.416326			−0.0363746			−0.0181873	−	0.999835i	$-0.505790\pi$
$131$	−0.416326			−0.0363746			−0.0181873	+	0.999835i	$0.505790\pi$
$132$	0.556526	+	0.735517i	0.0484394	+	0.0640186i
$133$	16.9760			1.47201
$134$	−1.39901	−	0.695802i	−0.120856	−	0.0601081i
$135$	3.02124			0.260027
$136$	8.22002	−	8.27232i	0.704861	−	0.709346i
$137$	−2.39871			−0.204936			−0.102468	−	0.994736i	$-0.532674\pi$
$137$	−2.39871			−0.204936			−0.102468	+	0.994736i	$0.532674\pi$
$138$	−2.73781	−	1.36166i	−0.233058	−	0.115912i
$139$	8.52596			0.723163			0.361581	−	0.932341i	$-0.382237\pi$
$139$	8.52596			0.723163			0.361581	+	0.932341i	$0.382237\pi$
$140$	6.96261	−	5.26823i	0.588448	−	0.445247i
$141$	−0.737275			−0.0620897
$142$	10.5525	+	5.24833i	0.885549	+	0.440430i
$143$			6.00844i			0.502451i
$144$	2.95895	−	10.4746i	0.246579	−	0.872883i
$145$	−6.41784			−0.532972
$146$	2.35761	+	1.17257i	0.195117	+	0.0970422i
$147$	6.36768			0.525197
$148$	−8.40117	−	11.1032i	−0.690572	−	0.912675i
$149$		−	7.04895i		−	0.577473i	−0.957409	−	0.288736i	$-0.906765\pi$
$149$		−	7.04895i		−	0.577473i	0.957409	−	0.288736i	$-0.0932351\pi$
$150$	−0.332573	+	0.668687i	−0.0271545	+	0.0545981i
$151$	9.79384			0.797011			0.398506	−	0.917166i	$-0.369529\pi$
$151$	9.79384			0.797011			0.398506	+	0.917166i	$0.369529\pi$
$152$	2.03628	+	10.8085i	0.165165	+	0.876689i
$153$	9.24489	−	6.35680i	0.747405	−	0.513917i
$154$	4.82742	+	2.40093i	0.389004	+	0.193472i
$155$		−	6.12329i		−	0.491835i
$156$	−5.79485	+	4.38465i	−0.463959	+	0.351053i
$157$			1.38378i			0.110438i	0.998474	+	0.0552188i	$0.0175856\pi$
$157$			1.38378i			0.110438i	−0.998474	+	0.0552188i	$0.982414\pi$
$158$	−4.02807	−	2.00337i	−0.320456	−	0.159380i
$159$			2.70828i			0.214780i
$160$	4.18943	+	3.80114i	0.331204	+	0.300506i
$161$	−17.8739			−1.40866
$162$	4.13629	−	8.31661i	0.324978	−	0.653414i
$163$	5.50427			0.431128			0.215564	−	0.976490i	$-0.430841\pi$
$163$	5.50427			0.431128			0.215564	+	0.976490i	$0.430841\pi$
$164$	19.1797	−	14.5123i	1.49769	−	1.13322i
$165$	−0.461169			−0.0359020
$166$	−5.54728	−	2.75896i	−0.430553	−	0.214137i
$167$			13.3312i			1.03160i	0.856710	+	0.515798i	$0.172504\pi$
$167$			13.3312i			1.03160i	−0.856710	+	0.515798i	$0.827496\pi$
$168$	1.20722	+	6.40788i	0.0931389	+	0.494379i
$169$	−34.3381			−2.64139
$170$	0.818452	+	5.77323i	0.0627724	+	0.442786i
$171$			10.5814i			0.809182i
$172$	−14.8210	+	11.2142i	−1.13009	+	0.855078i
$173$	0.0617819			0.00469719			0.00234859	−	0.999997i	$-0.499252\pi$
$173$	0.0617819			0.00469719			0.00234859	+	0.999997i	$0.499252\pi$
$174$	2.13440	−	4.29152i	0.161809	−	0.325340i
$175$			4.36555i			0.330005i
$176$	−0.949609	+	3.36159i	−0.0715795	+	0.253389i
$177$		−	2.74028i		−	0.205972i
$178$	6.28789	−	12.6427i	0.471297	−	0.947611i
$179$			10.4747i			0.782913i	0.920197	+	0.391457i	$0.128029\pi$
$179$			10.4747i			0.782913i	−0.920197	+	0.391457i	$0.871971\pi$
$180$	3.28378	+	4.33992i	0.244759	+	0.323478i
$181$	4.45365			0.331037			0.165518	−	0.986207i	$-0.447070\pi$
$181$	4.45365			0.331037			0.165518	+	0.986207i	$0.447070\pi$
$182$	−18.9160	+	38.0333i	−1.40214	+	2.81921i
$183$	−3.93711			−0.291040
$184$	−2.14399	−	11.3802i	−0.158057	−	0.838962i
$185$	6.96168			0.511833
$186$	4.09457	+	2.03644i	0.300228	+	0.149319i
$187$	−2.96695	+	2.04008i	−0.216965	+	0.149185i
$188$	−1.68481	−	2.22668i	−0.122878	−	0.162398i
$189$			13.1894i			0.959387i
$190$	−4.92396	−	2.44895i	−0.357222	−	0.177665i
$191$	14.0445			1.01622			0.508111	−	0.861292i	$-0.330344\pi$
$191$	14.0445			1.01622			0.508111	+	0.861292i	$0.330344\pi$
$192$	−3.93506	+	1.53726i	−0.283989	+	0.110942i
$193$		−	4.18068i		−	0.300932i	−0.988615	−	0.150466i	$-0.951923\pi$
$193$		−	4.18068i		−	0.300932i	0.988615	−	0.150466i	$-0.0480774\pi$
$194$	8.02563	+	3.99157i	0.576206	+	0.286578i
$195$		−	3.63336i		−	0.260191i
$196$	14.5513	+	19.2314i	1.03938	+	1.37367i
$197$	−7.26818			−0.517836			−0.258918	−	0.965899i	$-0.583366\pi$
$197$	−7.26818			−0.517836			−0.258918	+	0.965899i	$0.583366\pi$
$198$	−1.49654	+	3.00901i	−0.106355	+	0.213841i
$199$		−	17.6226i		−	1.24924i	−0.780930	−	0.624618i	$-0.785255\pi$
$199$		−	17.6226i		−	1.24924i	0.780930	−	0.624618i	$-0.214745\pi$
$200$	−2.77953	+	0.523652i	−0.196542	+	0.0370278i
$201$			0.583453i			0.0411536i
$202$	9.58055	+	4.76491i	0.674085	+	0.335258i
$203$		−	28.0174i		−	1.96644i
$204$	−4.13268	−	1.37273i	−0.289345	−	0.0961105i
$205$			12.0257i			0.839910i
$206$	−4.53392	+	9.11610i	−0.315893	+	0.635149i
$207$		−	11.1411i		−	0.774361i
$208$	−26.4846	−	7.48159i	−1.83638	−	0.518755i
$209$		−	3.39588i		−	0.234898i
$210$	−2.91919	−	1.45187i	−0.201443	−	0.100188i
$211$	17.8735			1.23046			0.615231	−	0.788347i	$-0.289063\pi$
$211$	17.8735			1.23046			0.615231	+	0.788347i	$0.289063\pi$
$212$	−8.17941	+	6.18892i	−0.561764	+	0.425057i
$213$		−	4.40090i		−	0.301545i
$214$	−11.3302	+	22.7810i	−0.774516	+	1.55728i
$215$		−	9.29275i		−	0.633760i
$216$	−8.39763	+	1.58208i	−0.571386	+	0.107647i
$217$	26.7316			1.81466
$218$	−7.25710	+	14.5915i	−0.491513	+	0.988258i
$219$		−	0.983235i		−	0.0664408i
$220$	−1.05386	−	1.39280i	−0.0710511	−	0.0939027i
$221$	−16.0729	−	23.3754i	−1.08118	−	1.57240i
$222$	−2.31527	+	4.65519i	−0.155391	+	0.312436i
$223$	7.40463			0.495851			0.247925	−	0.968779i	$-0.420251\pi$
$223$	7.40463			0.495851			0.247925	+	0.968779i	$0.420251\pi$
$224$	−16.5941	+	18.2892i	−1.10874	+	1.22200i
$225$	−2.72113			−0.181408
$226$	6.89790	+	3.43069i	0.458842	+	0.228206i
$227$	4.35476			0.289036			0.144518	−	0.989502i	$-0.453837\pi$
$227$	4.35476			0.289036			0.144518	+	0.989502i	$0.453837\pi$
$228$	3.27516	−	2.47814i	0.216903	−	0.164119i
$229$			13.1678i			0.870155i	0.900393	+	0.435078i	$0.143279\pi$
$229$			13.1678i			0.870155i	−0.900393	+	0.435078i	$0.856721\pi$
$230$	5.18441	+	2.57848i	0.341850	+	0.170020i
$231$		−	2.01326i		−	0.132463i
$232$	17.8386	−	3.36071i	1.17116	−	0.220642i
$233$			25.3191i			1.65871i	0.558724	+	0.829353i	$0.311291\pi$
$233$			25.3191i			1.65871i	−0.558724	+	0.829353i	$0.688709\pi$
$234$	−23.7068	−	11.7907i	−1.54976	−	0.770779i
$235$	1.39613			0.0910735
$236$	8.27607	−	6.26205i	0.538726	−	0.407625i
$237$			1.67989i			0.109121i
$238$	−25.2033	+	3.57300i	−1.63369	+	0.231603i
$239$	−19.0546			−1.23254			−0.616270	−	0.787535i	$-0.711357\pi$
$239$	−19.0546			−1.23254			−0.616270	+	0.787535i	$0.711357\pi$
$240$	0.574239	−	2.03279i	0.0370669	−	0.131216i
$241$		−	22.7240i		−	1.46378i	−0.681422	−	0.731890i	$-0.738638\pi$
$241$		−	22.7240i		−	1.46378i	0.681422	−	0.731890i	$-0.261362\pi$
$242$	−6.44722	+	12.9631i	−0.414443	+	0.833297i
$243$	−12.5321			−0.803937
$244$	−8.99705	−	11.8907i	−0.575977	−	0.761224i
$245$	−12.0581			−0.770361
$246$	−8.04142	−	3.99942i	−0.512702	−	0.254994i
$247$	26.7548			1.70236
$248$	3.20648	+	17.0199i	0.203611	+	1.08076i
$249$			2.31348i			0.146611i
$250$	0.629773	−	1.26625i	0.0398303	−	0.0800846i
$251$		−	8.04157i		−	0.507579i	−0.967259	−	0.253790i	$-0.918323\pi$
$251$		−	8.04157i		−	0.507579i	0.967259	−	0.253790i	$-0.0816771\pi$
$252$	−18.9461	+	14.3355i	−1.19350	+	0.903053i
$253$			3.57550i			0.224790i
$254$	11.3541	−	22.8291i	0.712420	−	1.43242i
$255$	1.79414	−	1.23365i	0.112354	−	0.0772545i
$256$	−13.6351	−	8.37157i	−0.852196	−	0.523223i
$257$	8.62751			0.538169			0.269085	−	0.963117i	$-0.413279\pi$
$257$	8.62751			0.538169			0.269085	+	0.963117i	$0.413279\pi$
$258$	6.21394	+	3.09052i	0.386863	+	0.192407i
$259$			30.3916i			1.88844i
$260$	10.9733	−	8.30292i	0.680537	−	0.514925i
$261$	17.4637			1.08098
$262$	−0.262191	+	0.527173i	−0.0161982	+	0.0325688i
$263$	28.1526			1.73597			0.867983	−	0.496595i	$-0.165416\pi$
$263$	28.1526			1.73597			0.867983	+	0.496595i	$0.165416\pi$
$264$	1.28183	−	0.241492i	0.0788914	−	0.0148628i
$265$		−	5.12849i		−	0.315040i
$266$	10.6910	−	21.4958i	0.655508	−	1.31799i
$267$	−5.27260			−0.322678
$268$	−1.76212	+	1.33330i	−0.107638	+	0.0814442i
$269$	26.1781			1.59610			0.798052	−	0.602588i	$-0.205864\pi$
$269$	26.1781			1.59610			0.798052	+	0.602588i	$0.205864\pi$
$270$	1.90269	−	3.82564i	0.115794	−	0.232821i
$271$	21.6829			1.31714			0.658571	−	0.752518i	$-0.271161\pi$
$271$	21.6829			1.31714			0.658571	+	0.752518i	$0.271161\pi$
$272$	−5.29807	−	15.6183i	−0.321243	−	0.946997i
$273$	15.8616			0.959991
$274$	−1.51064	+	3.03737i	−0.0912614	+	0.183494i
$275$	0.873286			0.0526611
$276$	−3.44839	+	2.60921i	−0.207569	+	0.157056i
$277$	−1.06364			−0.0639077			−0.0319538	−	0.999489i	$-0.510173\pi$
$277$	−1.06364			−0.0639077			−0.0319538	+	0.999489i	$0.510173\pi$
$278$	5.36942	−	10.7960i	0.322036	−	0.647500i
$279$			16.6623i			0.997543i
$280$	−2.28603	−	12.1342i	−0.136616	−	0.725157i
$281$	−18.1539			−1.08297			−0.541486	−	0.840710i	$-0.682138\pi$
$281$	−18.1539			−1.08297			−0.541486	+	0.840710i	$0.682138\pi$
$282$	−0.464316	+	0.933574i	−0.0276496	+	0.0555935i
$283$	32.5756			1.93642			0.968209	−	0.250142i	$-0.0804774\pi$
$283$	32.5756			1.93642			0.968209	+	0.250142i	$0.0804774\pi$
$284$	13.2914	−	10.0569i	0.788699	−	0.596766i
$285$			2.05352i			0.121640i
$286$	7.60818	+	3.78395i	0.449881	+	0.223750i
$287$	−52.4988			−3.09890
$288$	−11.4000	−	10.3434i	−0.671750	−	0.609489i
$289$	6.08535	−	15.8735i	0.357962	−	0.933736i
$290$	−4.04178	+	8.12658i	−0.237341	+	0.477209i
$291$		−	3.34706i		−	0.196208i
$292$	2.96952	−	2.24688i	0.173778	−	0.131488i
$293$			11.6157i			0.678596i	0.940679	+	0.339298i	$0.110189\pi$
$293$			11.6157i			0.678596i	−0.940679	+	0.339298i	$0.889811\pi$
$294$	4.01019	−	8.06307i	0.233879	−	0.470248i
$295$			5.18909i			0.302121i
$296$	−19.3502	+	3.64550i	−1.12471	+	0.211890i
$297$	2.63841			0.153096
$298$	−8.92573	−	4.43924i	−0.517054	−	0.257158i
$299$	−28.1699			−1.62911
$300$	0.637278	+	0.842241i	0.0367933	+	0.0486268i
$301$	40.5680			2.33830
$302$	6.16789	−	12.4014i	0.354922	−	0.713623i
$303$		−	3.99554i		−	0.229538i
$304$	14.9687	+	4.22848i	0.858514	+	0.242520i
$305$	7.45546			0.426898
$306$	−2.22711	−	15.7097i	−0.127316	−	0.898062i
$307$		−	1.91250i		−	0.109152i	−0.998510	−	0.0545762i	$-0.982619\pi$
$307$		−	1.91250i		−	0.109152i	0.998510	−	0.0545762i	$-0.0173808\pi$
$308$	6.08035	−	4.60067i	0.346460	−	0.262148i
$309$	3.80184			0.216279
$310$	−7.75362	−	3.85628i	−0.440376	−	0.219022i
$311$		−	22.7149i		−	1.28805i	−0.765006	−	0.644023i	$-0.777264\pi$
$311$		−	22.7149i		−	1.28805i	0.765006	−	0.644023i	$-0.222736\pi$
$312$	1.90262	+	10.0990i	0.107715	+	0.571746i
$313$			10.0256i			0.566682i	0.959019	+	0.283341i	$0.0914429\pi$
$313$			10.0256i			0.566682i	−0.959019	+	0.283341i	$0.908557\pi$
$314$	1.75221	+	0.871466i	0.0988828	+	0.0491797i
$315$		−	11.8792i		−	0.669318i
$316$	−5.07353	+	3.83887i	−0.285409	+	0.215953i
$317$	12.0074			0.674403			0.337202	−	0.941432i	$-0.390520\pi$
$317$	12.0074			0.674403			0.337202	+	0.941432i	$0.390520\pi$
$318$	3.42935	+	1.70560i	0.192309	+	0.0956452i
$319$	−5.60461			−0.313798
$320$	7.45158	−	2.91101i	0.416556	−	0.162731i
$321$	9.50073			0.530279
$322$	−11.2565	+	22.6328i	−0.627300	+	1.26128i
$323$	9.08418	+	13.2114i	0.505457	+	0.735102i
$324$	−7.92597	−	10.4751i	−0.440332	−	0.581952i
$325$			6.88027i			0.381649i
$326$	3.46644	−	6.96978i	0.191988	−	0.386020i
$327$	6.08532			0.336519
$328$	−6.29727	−	33.4257i	−0.347709	−	1.84563i
$329$			6.09488i			0.336022i
$330$	−0.290432	+	0.583955i	−0.0159877	+	0.0321456i
$331$			4.89226i			0.268903i	0.990920	+	0.134452i	$0.0429273\pi$
$331$			4.89226i			0.268903i	−0.990920	+	0.134452i	$0.957073\pi$
$332$	−6.98706	+	5.28673i	−0.383464	+	0.290147i
$333$	−18.9436			−1.03810
$334$	16.8806	+	8.39559i	0.923663	+	0.459386i
$335$		−	1.10485i		−	0.0603642i
$336$	8.87425	+	2.50687i	0.484130	+	0.136761i
$337$			27.5016i			1.49811i	0.662509	+	0.749054i	$0.269492\pi$
$337$			27.5016i			1.49811i	−0.662509	+	0.749054i	$0.730508\pi$
$338$	−21.6252	+	43.4806i	−1.17625	+	2.36503i
$339$		−	2.87675i		−	0.156243i
$340$	7.82578	+	2.59946i	0.424413	+	0.140975i
$341$		−	5.34739i		−	0.289577i
$342$	13.3987	+	6.66390i	0.724520	+	0.360342i
$343$		−	22.0812i		−	1.19228i
$344$	4.86617	+	25.8295i	0.262366	+	1.39263i
$345$		−	2.16214i		−	0.116406i
$346$	0.0389085	−	0.0782312i	0.00209174	−	0.00420574i
$347$	−0.154619			−0.00830038			−0.00415019	−	0.999991i	$-0.501321\pi$
$347$	−0.154619			−0.00830038			−0.00415019	+	0.999991i	$0.501321\pi$
$348$	−4.08995	−	5.40537i	−0.219244	−	0.289758i
$349$			20.5204i			1.09843i	0.835680	+	0.549216i	$0.185074\pi$
$349$			20.5204i			1.09843i	−0.835680	+	0.549216i	$0.814926\pi$
$350$	5.52788	+	2.74931i	0.295478	+	0.146957i
$351$			20.7869i			1.10952i
$352$	3.65857	+	3.31948i	0.195003	+	0.176929i
$353$	8.41354			0.447808			0.223904	−	0.974611i	$-0.428120\pi$
$353$	8.41354			0.447808			0.223904	+	0.974611i	$0.428120\pi$
$354$	−3.46988	−	1.72575i	−0.184422	−	0.0917228i
$355$			8.33370i			0.442307i
$356$	−12.0489	−	15.9241i	−0.638589	−	0.843974i
$357$	5.38559	+	7.83243i	0.285035	+	0.414536i
$358$	13.2635	+	6.59666i	0.700999	+	0.348644i
$359$	7.54413			0.398164			0.199082	−	0.979983i	$-0.436204\pi$
$359$	7.54413			0.398164			0.199082	+	0.979983i	$0.436204\pi$
$360$	7.56345	−	1.42492i	0.398629	−	0.0751001i
$361$	3.87862			0.204138
$362$	2.80478	−	5.63942i	0.147416	−	0.296402i
$363$	5.40620			0.283752
$364$	36.2468	+	47.9046i	1.89985	+	2.51089i
$365$			1.86189i			0.0974556i
$366$	−2.47949	+	4.98537i	−0.129605	+	0.260589i
$367$		−	22.1579i		−	1.15664i	−0.815812	−	0.578318i	$-0.803709\pi$
$367$		−	22.1579i		−	1.15664i	0.815812	−	0.578318i	$-0.196291\pi$
$368$	−15.7604	−	4.45214i	−0.821570	−	0.232084i
$369$		−	32.7234i		−	1.70351i
$370$	4.38428	−	8.81522i	0.227928	−	0.458282i
$371$	22.3887			1.16236
$372$	5.15729	−	3.90224i	0.267393	−	0.202322i
$373$			6.34772i			0.328672i	0.986404	+	0.164336i	$0.0525482\pi$
$373$			6.34772i			0.328672i	−0.986404	+	0.164336i	$0.947452\pi$
$374$	0.714743	+	5.04168i	0.0369585	+	0.260699i
$375$	−0.528085			−0.0272702
$376$	−3.88058	+	0.731086i	−0.200126	+	0.0377029i
$377$		−	44.1564i		−	2.27417i
$378$	16.7010	+	8.30631i	0.859009	+	0.427231i
$379$	−6.11516			−0.314115			−0.157057	−	0.987589i	$-0.550201\pi$
$379$	−6.11516			−0.314115			−0.157057	+	0.987589i	$0.550201\pi$
$380$	−6.20195	+	4.69268i	−0.318154	+	0.240730i
$381$	−9.52078			−0.487765
$382$	8.84481	−	17.7838i	0.452540	−	0.909897i
$383$	−18.2832			−0.934230			−0.467115	−	0.884197i	$-0.654707\pi$
$383$	−18.2832			−0.934230			−0.467115	+	0.884197i	$0.654707\pi$
$384$	−0.531640	+	5.95090i	−0.0271301	+	0.303680i
$385$			3.81238i			0.194297i
$386$	−5.29378	−	2.63288i	−0.269446	−	0.134010i
$387$			25.2868i			1.28540i
$388$	10.1086	−	7.64866i	0.513188	−	0.388302i
$389$			2.01710i			0.102271i	0.998692	+	0.0511355i	$0.0162840\pi$
$389$			2.01710i			0.102271i	−0.998692	+	0.0511355i	$0.983716\pi$
$390$	−4.60074	−	2.28819i	−0.232968	−	0.115867i
$391$	−9.56467	−	13.9102i	−0.483706	−	0.703469i
$392$	33.5158	−	6.31423i	1.69280	−	0.318917i
$393$	0.219856			0.0110903
$394$	−4.57730	+	9.20332i	−0.230601	+	0.463657i
$395$		−	3.18110i		−	0.160059i
$396$	2.86768	+	3.78999i	0.144106	+	0.190454i
$397$	−23.2575			−1.16726			−0.583631	−	0.812019i	$-0.698368\pi$
$397$	−23.2575			−1.16726			−0.583631	+	0.812019i	$0.698368\pi$
$398$	−22.3147	−	11.0983i	−1.11853	−	0.556306i
$399$	−8.96476			−0.448799
$400$	−1.08740	+	3.84936i	−0.0543699	+	0.192468i
$401$		−	8.22710i		−	0.410842i	−0.978674	−	0.205421i	$-0.934144\pi$
$401$		−	8.22710i		−	0.410842i	0.978674	−	0.205421i	$-0.0658563\pi$
$402$	0.738796	+	0.367442i	0.0368478	+	0.0183264i
$403$	42.1299			2.09864
$404$	12.0671	−	9.13055i	0.600362	−	0.454262i
$405$	6.56791			0.326362
$406$	−35.4770	−	17.6446i	−1.76070	−	0.875687i
$407$	6.07954			0.301352
$408$	−4.34087	+	4.36849i	−0.214905	+	0.216272i
$409$	18.3658			0.908130			0.454065	−	0.890969i	$-0.349973\pi$
$409$	18.3658			0.908130			0.454065	+	0.890969i	$0.349973\pi$
$410$	15.2275	+	7.57344i	0.752033	+	0.374026i
$411$	1.26672			0.0624829
$412$	8.68791	+	11.4821i	0.428023	+	0.565684i
$413$	−22.6533			−1.11469
$414$	−14.1074	−	7.01637i	−0.693342	−	0.344836i
$415$		−	4.38088i		−	0.215049i
$416$	−26.1528	+	28.8244i	−1.28225	+	1.41323i
$417$	−4.50243			−0.220485
$418$	−4.30003	−	2.13863i	−0.210321	−	0.104604i
$419$	−18.1101			−0.884738			−0.442369	−	0.896833i	$-0.645862\pi$
$419$	−18.1101			−0.884738			−0.442369	+	0.896833i	$0.645862\pi$
$420$	−3.67685	+	2.78207i	−0.179412	+	0.135751i
$421$		−	36.7654i		−	1.79184i	−0.444219	−	0.895918i	$-0.646519\pi$
$421$		−	36.7654i		−	1.79184i	0.444219	−	0.895918i	$-0.353481\pi$
$422$	11.2562	−	22.6323i	0.547945	−	1.10172i
$423$	−3.79905			−0.184716
$424$	2.68554	+	14.2548i	0.130421	+	0.692274i
$425$	−3.39745	+	2.33609i	−0.164801	+	0.113317i
$426$	−5.57263	−	2.77157i	−0.269995	−	0.134283i
$427$			32.5472i			1.57507i
$428$	21.7110	+	28.6937i	1.04944	+	1.38696i
$429$		−	3.17297i		−	0.153192i
$430$	−11.7669	−	5.85232i	−0.567452	−	0.282224i
$431$			25.4830i			1.22747i	0.789512	+	0.613735i	$0.210334\pi$
$431$			25.4830i			1.22747i	−0.789512	+	0.613735i	$0.789666\pi$
$432$	−3.28529	+	11.6298i	−0.158064	+	0.559541i
$433$	−8.52916			−0.409885			−0.204943	−	0.978774i	$-0.565701\pi$
$433$	−8.52916			−0.409885			−0.204943	+	0.978774i	$0.565701\pi$
$434$	16.8348	−	33.8488i	0.808097	−	1.62480i
$435$	3.38916			0.162498
$436$	13.9061	+	18.3786i	0.665981	+	0.880175i
$437$	15.9212			0.761614
$438$	−1.24502	−	0.619214i	−0.0594893	−	0.0295872i
$439$			7.77824i			0.371235i	0.982622	+	0.185618i	$0.0594286\pi$
$439$			7.77824i			0.371235i	−0.982622	+	0.185618i	$0.940571\pi$
$440$	−2.42732	+	0.457298i	−0.115718	+	0.0218008i
$441$	32.8115			1.56245
$442$	−39.7213	+	5.63117i	−1.88935	+	0.267847i
$443$		−	17.4505i		−	0.829098i	−0.910027	−	0.414549i	$-0.863939\pi$
$443$		−	17.4505i		−	0.829098i	0.910027	−	0.414549i	$-0.136061\pi$
$444$	4.43653	+	5.86342i	0.210548	+	0.278265i
$445$	9.98438			0.473305
$446$	4.66323	−	9.37610i	0.220810	−	0.443971i
$447$			3.72244i			0.176066i
$448$	12.7082	+	32.5303i	0.600405	+	1.53691i
$449$		−	28.7365i		−	1.35616i	−0.734988	−	0.678080i	$-0.762812\pi$
$449$		−	28.7365i		−	1.35616i	0.734988	−	0.678080i	$-0.237188\pi$
$450$	−1.71369	+	3.44562i	−0.0807842	+	0.162428i
$451$			10.5019i			0.494513i
$452$	8.68822	−	6.57391i	0.408660	−	0.309211i
$453$	−5.17198			−0.243001
$454$	2.74251	−	5.51421i	0.128712	−	0.258795i
$455$	−30.0362			−1.40812
$456$	−1.07533	−	5.70783i	−0.0503570	−	0.267294i
$457$	10.9671			0.513021			0.256510	−	0.966541i	$-0.417427\pi$
$457$	10.9671			0.513021			0.256510	+	0.966541i	$0.417427\pi$
$458$	16.6738	+	8.29274i	0.779114	+	0.387494i
$459$	−10.2645	+	7.05789i	−0.479107	+	0.329434i
$460$	6.52999	−	4.94089i	0.304463	−	0.230370i
$461$		−	33.5453i		−	1.56236i	−0.624307	−	0.781179i	$-0.714618\pi$
$461$		−	33.5453i		−	1.56236i	0.624307	−	0.781179i	$-0.285382\pi$
$462$	−2.54929	−	1.26789i	−0.118604	−	0.0589878i
$463$	−26.2145			−1.21829			−0.609145	−	0.793059i	$-0.708487\pi$
$463$	−26.2145			−1.21829			−0.609145	+	0.793059i	$0.708487\pi$
$464$	6.97874	−	24.7046i	0.323980	−	1.14688i
$465$			3.23362i			0.149955i
$466$	32.0602	+	15.9453i	1.48516	+	0.738650i
$467$		−	13.2337i		−	0.612380i	−0.951970	−	0.306190i	$-0.900946\pi$
$467$		−	13.2337i		−	0.612380i	0.951970	−	0.306190i	$-0.0990544\pi$
$468$	−29.8598	+	22.5933i	−1.38027	+	1.04438i
$469$	4.82327			0.222718
$470$	0.879244	−	1.76785i	0.0405565	−	0.0815447i
$471$		−	0.730752i		−	0.0336713i
$472$	−2.71728	−	14.4232i	−0.125073	−	0.663883i
$473$		−	8.11523i		−	0.373139i
$474$	2.12716	+	1.05795i	0.0977038	+	0.0485933i
$475$		−	3.88862i		−	0.178422i
$476$	−11.3481	+	34.1639i	−0.520138	+	1.56590i
$477$			13.9553i			0.638968i
$478$	−12.0001	+	24.1279i	−0.548871	+	1.10358i
$479$			27.1795i			1.24186i	0.783865	+	0.620931i	$0.213245\pi$
$479$			27.1795i			1.24186i	−0.783865	+	0.620931i	$0.786755\pi$
$480$	−2.21238	−	2.00732i	−0.100981	−	0.0916213i
$481$			47.8982i			2.18397i
$482$	−28.7742	−	14.3109i	−1.31063	−	0.651846i
$483$	9.43893			0.429486
$484$	12.3542	+	16.3276i	0.561554	+	0.742162i
$485$			6.33811i			0.287799i
$486$	−7.89239	+	15.8688i	−0.358006	+	0.719823i
$487$			16.8533i			0.763694i	0.924226	+	0.381847i	$0.124712\pi$
$487$			16.8533i			0.763694i	−0.924226	+	0.381847i	$0.875288\pi$
$488$	−20.7227	+	3.90407i	−0.938071	+	0.176729i
$489$	−2.90672			−0.131447
$490$	−7.59384	+	15.2685i	−0.343055	+	0.689761i
$491$			35.5251i			1.60323i	0.597842	+	0.801614i	$0.296025\pi$
$491$			35.5251i			1.60323i	−0.597842	+	0.801614i	$0.703975\pi$
$492$	−10.1285	+	7.66371i	−0.456629	+	0.345507i
$493$	21.8043	−	14.9927i	0.982016	−	0.675235i
$494$	16.8494	−	33.8782i	0.758091	−	1.52425i
$495$	−2.37632			−0.106808
$496$	23.5708	+	6.65846i	1.05836	+	0.298974i
$497$	−36.3812			−1.63192
$498$	2.92944	+	1.45696i	0.131271	+	0.0652881i
$499$	13.8837			0.621519			0.310759	−	0.950489i	$-0.399417\pi$
$499$	13.8837			0.621519			0.310759	+	0.950489i	$0.399417\pi$
$500$	−1.20677	−	1.59490i	−0.0539685	−	0.0713260i
$501$		−	7.03998i		−	0.314523i
$502$	−10.1826	−	5.06436i	−0.454473	−	0.226033i
$503$			18.5408i			0.826692i	0.910574	+	0.413346i	$0.135640\pi$
$503$			18.5408i			0.826692i	−0.910574	+	0.413346i	$0.864360\pi$
$504$	6.22058	+	33.0187i	0.277087	+	1.47077i
$505$			7.56609i			0.336686i
$506$	4.52747	+	2.25175i	0.201271	+	0.100102i
$507$	18.1334			0.805333
$508$	−21.7568	−	28.7542i	−0.965301	−	1.27576i
$509$			1.95559i			0.0866798i	0.999060	+	0.0433399i	$0.0137998\pi$
$509$			1.95559i			0.0866798i	−0.999060	+	0.0433399i	$0.986200\pi$
$510$	−0.432212	−	3.04875i	−0.0191387	−	0.135001i
$511$	−8.12817			−0.359569
$512$	−19.1875	+	11.9933i	−0.847977	+	0.530033i
$513$		−	11.7485i		−	0.518707i
$514$	5.43337	−	10.9246i	0.239656	−	0.481862i
$515$	−7.19929			−0.317239
$516$	7.82674	−	5.92207i	0.344553	−	0.260705i
$517$	1.21922			0.0536212
$518$	38.4833	+	19.1398i	1.69086	+	0.840955i
$519$	−0.0326261			−0.00143213
$520$	−3.60287	−	19.1239i	−0.157996	−	0.838639i
$521$		−	1.28044i		−	0.0560971i	−0.999607	−	0.0280485i	$-0.991071\pi$
$521$		−	1.28044i		−	0.0560971i	0.999607	−	0.0280485i	$-0.00892929\pi$
$522$	10.9982	−	22.1135i	0.481378	−	0.967879i
$523$		−	27.2314i		−	1.19075i	−0.803449	−	0.595374i	$-0.797004\pi$
$523$		−	27.2314i		−	1.19075i	0.803449	−	0.595374i	$-0.202996\pi$
$524$	0.502411	+	0.663998i	0.0219479	+	0.0290069i
$525$		−	2.30538i		−	0.100615i
$526$	17.7298	−	35.6482i	0.773054	−	1.55434i
$527$	14.3046	+	20.8036i	0.623117	+	0.906219i
$528$	0.501474	−	1.77520i	0.0218239	−	0.0772559i
$529$	6.23669			0.271160
$530$	−6.49394	−	3.22978i	−0.282079	−	0.140293i
$531$		−	14.1202i		−	0.612763i
$532$	−20.4862	−	27.0750i	−0.888188	−	1.17385i
$533$	−82.7399			−3.58386
$534$	−3.32054	+	6.67642i	−0.143694	+	0.288917i
$535$	−17.9909			−0.777815
$536$	0.578555	+	3.07095i	0.0249898	+	0.132645i
$537$		−	5.53151i		−	0.238702i
$538$	16.4862	−	33.1479i	0.710772	−	1.42911i
$539$	−10.5301			−0.453565
$540$	−3.64595	−	4.81857i	−0.156897	−	0.207358i
$541$	−6.70395			−0.288225			−0.144113	−	0.989561i	$-0.546033\pi$
$541$	−6.70395			−0.288225			−0.144113	+	0.989561i	$0.546033\pi$
$542$	13.6553	−	27.4560i	0.586545	−	1.17933i
$543$	−2.35190			−0.100930
$544$	−23.1132	−	3.12728i	−0.990970	−	0.134081i
$545$	−11.5234			−0.493607
$546$	9.98923	−	20.0848i	0.427500	−	0.859550i
$547$	24.6055			1.05206			0.526028	−	0.850467i	$-0.323681\pi$
$547$	24.6055			1.05206			0.526028	+	0.850467i	$0.323681\pi$
$548$	2.89470	+	3.82570i	0.123656	+	0.163426i
$549$	−20.2872			−0.865838
$550$	0.549971	−	1.10580i	0.0234509	−	0.0471514i
$551$			24.9565i			1.06318i
$552$	1.13221	+	6.00973i	0.0481900	+	0.255791i
$553$	13.8873			0.590547
$554$	−0.669848	+	1.34683i	−0.0284591	+	0.0572212i
$555$	−3.67636			−0.156053
$556$	−10.2889	−	13.5980i	−0.436346	−	0.576685i
$557$			18.7515i			0.794528i	0.917704	+	0.397264i	$0.130040\pi$
$557$			18.7515i			0.794528i	−0.917704	+	0.397264i	$0.869960\pi$
$558$	21.0986	+	10.4934i	0.893174	+	0.444222i
$559$	63.9366			2.70423
$560$	−16.8046	−	4.74710i	−0.710123	−	0.200601i
$561$	1.56680	−	1.07733i	0.0661503	−	0.0454850i
$562$	−11.4328	+	22.9874i	−0.482265	+	0.969664i
$563$		−	18.6069i		−	0.784188i	−0.919925	−	0.392094i	$-0.871751\pi$
$563$		−	18.6069i		−	0.784188i	0.919925	−	0.392094i	$-0.128249\pi$
$564$	0.889723	+	1.17588i	0.0374641	+	0.0495134i
$565$			5.44751i			0.229179i
$566$	20.5152	−	41.2488i	0.862319	−	1.73382i
$567$			28.6726i			1.20413i
$568$	−4.36396	−	23.1638i	−0.183108	−	0.971930i
$569$	−20.0128			−0.838979			−0.419490	−	0.907760i	$-0.637791\pi$
$569$	−20.0128			−0.838979			−0.419490	+	0.907760i	$0.637791\pi$
$570$	2.60027	+	1.29325i	0.108913	+	0.0541684i
$571$	−26.4577			−1.10722			−0.553609	−	0.832777i	$-0.686750\pi$
$571$	−26.4577			−1.10722			−0.553609	+	0.832777i	$0.686750\pi$
$572$	9.58285	−	7.25082i	0.400679	−	0.303172i
$573$	−7.41667			−0.309836
$574$	−33.0623	+	66.4765i	−1.37999	+	2.77468i
$575$			4.09430i			0.170744i
$576$	−20.2767	+	7.92123i	−0.844862	+	0.330051i
$577$	−25.9220			−1.07915			−0.539573	−	0.841939i	$-0.681414\pi$
$577$	−25.9220			−1.07915			−0.539573	+	0.841939i	$0.681414\pi$
$578$	−16.2674	−	17.7023i	−0.676636	−	0.736318i
$579$			2.20775i			0.0917511i
$580$	7.74487	+	10.2358i	0.321588	+	0.425018i
$581$	19.1250			0.793437
$582$	−4.23821	−	2.10789i	−0.175680	−	0.0873747i
$583$		−	4.47863i		−	0.185486i
$584$	−0.974981	−	5.17517i	−0.0403450	−	0.214150i
$585$		−	18.7221i		−	0.774063i
$586$	14.7083	+	7.31524i	0.607596	+	0.302190i
$587$		−	10.0183i		−	0.413500i	−0.978394	−	0.206750i	$-0.933711\pi$
$587$		−	10.0183i		−	0.413500i	0.978394	−	0.206750i	$-0.0662886\pi$
$588$	−7.68434	−	10.1558i	−0.316897	−	0.418818i
$589$	−23.8112			−0.981123
$590$	6.57068	+	3.26795i	0.270511	+	0.134539i
$591$	3.83821			0.157883
$592$	−7.57012	+	26.7980i	−0.311130	+	1.10139i
$593$	26.4028			1.08423			0.542116	−	0.840303i	$-0.317623\pi$
$593$	26.4028			1.08423			0.542116	+	0.840303i	$0.317623\pi$
$594$	1.66160	−	3.34088i	0.0681761	−	0.137078i
$595$	−10.1983	−	14.8318i	−0.418091	−	0.608043i
$596$	−11.2424	+	8.50648i	−0.460505	+	0.348439i
$597$			9.30625i			0.380880i
$598$	−17.7406	+	35.6701i	−0.725468	+	1.45866i
$599$	−29.1150			−1.18960			−0.594802	−	0.803872i	$-0.702770\pi$
$599$	−29.1150			−1.18960			−0.594802	+	0.803872i	$0.702770\pi$
$600$	1.46783	−	0.276533i	0.0599238	−	0.0112894i
$601$		−	29.3695i		−	1.19801i	−0.800746	−	0.599004i	$-0.795563\pi$
$601$		−	29.3695i		−	1.19801i	0.800746	−	0.599004i	$-0.204437\pi$
$602$	25.5486	−	51.3692i	1.04128	−	2.09365i
$603$			3.00643i			0.122431i
$604$	−11.8189	−	15.6202i	−0.480906	−	0.635576i
$605$	−10.2374			−0.416208
$606$	−5.05934	−	2.51628i	−0.205522	−	0.102217i
$607$			9.38687i			0.381001i	0.981687	+	0.190501i	$0.0610111\pi$
$607$			9.38687i			0.381001i	−0.981687	+	0.190501i	$0.938989\pi$
$608$	14.7812	−	16.2911i	0.599456	−	0.660692i
$609$			14.7956i			0.599547i
$610$	4.69524	−	9.44047i	0.190105	−	0.382233i
$611$			9.60575i			0.388607i
$612$	−21.2949	−	7.07345i	−0.860797	−	0.285927i
$613$			12.9115i			0.521492i	0.965407	+	0.260746i	$0.0839685\pi$
$613$			12.9115i			0.521492i	−0.965407	+	0.260746i	$0.916031\pi$
$614$	−2.42171	−	1.20444i	−0.0977321	−	0.0486073i
$615$		−	6.35058i		−	0.256080i
$616$	−1.99636	−	10.5966i	−0.0804356	−	0.426950i
$617$			14.3911i			0.579362i	0.957123	+	0.289681i	$0.0935493\pi$
$617$			14.3911i			0.579362i	−0.957123	+	0.289681i	$0.906451\pi$
$618$	2.39429	−	4.81407i	0.0963126	−	0.193650i
$619$	−41.8855			−1.68352			−0.841759	−	0.539853i	$-0.818480\pi$
$619$	−41.8855			−1.68352			−0.841759	+	0.539853i	$0.818480\pi$
$620$	−9.76603	+	7.38943i	−0.392213	+	0.296766i
$621$			12.3699i			0.496386i
$622$	−28.7628	−	14.3052i	−1.15328	−	0.573588i
$623$			43.5873i			1.74629i
$624$	13.9861	+	3.95091i	0.559893	+	0.158163i
$625$	1.00000			0.0400000
$626$	12.6949	+	6.31387i	0.507392	+	0.252353i
$627$			1.79331i			0.0716180i
$628$	2.20699	−	1.66991i	0.0880683	−	0.0666365i
$629$	−23.6520	+	16.2631i	−0.943066	+	0.648454i
$630$	−15.0421	−	7.48121i	−0.599290	−	0.298059i
$631$	1.87504			0.0746443			0.0373221	−	0.999303i	$-0.488117\pi$
$631$	1.87504			0.0746443			0.0373221	+	0.999303i	$0.488117\pi$
$632$	1.66579	+	8.84197i	0.0662616	+	0.351715i
$633$	−9.43872			−0.375155
$634$	7.56194	−	15.2044i	0.300323	−	0.603842i
$635$	18.0289			0.715455
$636$	4.31942	−	3.26827i	0.171276	−	0.129596i
$637$		−	82.9627i		−	3.28710i
$638$	−3.52963	+	7.09683i	−0.139739	+	0.280966i
$639$		−	22.6770i		−	0.897090i
$640$	1.00673	−	11.2688i	0.0397946	−	0.445440i
$641$		−	15.3284i		−	0.605436i	−0.953080	−	0.302718i	$-0.902106\pi$
$641$		−	15.3284i		−	0.605436i	0.953080	−	0.302718i	$-0.0978940\pi$
$642$	5.98330	−	12.0303i	0.236142	−	0.474798i
$643$	−27.6479			−1.09033			−0.545164	−	0.838329i	$-0.683533\pi$
$643$	−27.6479			−1.09033			−0.545164	+	0.838329i	$0.683533\pi$
$644$	21.5697	+	28.5070i	0.849967	+	1.12333i
$645$			4.90736i			0.193227i
$646$	22.4499	−	3.18265i	0.883279	−	0.125220i
$647$	26.4175			1.03858			0.519289	−	0.854599i	$-0.326197\pi$
$647$	26.4175			1.03858			0.519289	+	0.854599i	$0.326197\pi$
$648$	−18.2557	+	3.43930i	−0.717152	+	0.135108i
$649$			4.53156i			0.177879i
$650$	8.71213	+	4.33300i	0.341718	+	0.169954i
$651$	−14.1165			−0.553271
$652$	−6.64240	−	8.77875i	−0.260137	−	0.343802i
$653$	41.1531			1.61044			0.805222	−	0.592974i	$-0.202046\pi$
$653$	41.1531			1.61044			0.805222	+	0.592974i	$0.202046\pi$
$654$	3.83237	−	7.70553i	0.149857	−	0.301310i
$655$	−0.416326			−0.0162672
$656$	−46.2912	−	13.0767i	−1.80737	−	0.510560i
$657$		−	5.06643i		−	0.197660i
$658$	7.71764	+	3.83839i	0.300865	+	0.149636i
$659$		−	41.4752i		−	1.61564i	−0.589427	−	0.807822i	$-0.700646\pi$
$659$		−	41.4752i		−	1.61564i	0.589427	−	0.807822i	$-0.299354\pi$
$660$	0.556526	+	0.735517i	0.0216628	+	0.0286300i
$661$			13.3874i			0.520711i	0.965513	+	0.260356i	$0.0838398\pi$
$661$			13.3874i			0.520711i	−0.965513	+	0.260356i	$0.916160\pi$
$662$	6.19482	+	3.08101i	0.240769	+	0.119747i
$663$	8.48787	+	12.3442i	0.329642	+	0.479408i
$664$	2.29406	+	12.1768i	0.0890267	+	0.472551i
$665$	16.9760			0.658301
$666$	−11.9302	+	23.9873i	−0.462285	+	0.929491i
$667$		−	26.2766i		−	1.01743i
$668$	21.2618	−	16.0877i	0.822645	−	0.622451i
$669$	−3.91027			−0.151180
$670$	−1.39901	−	0.695802i	−0.0540485	−	0.0268812i
$671$	6.51075			0.251345
$672$	8.76308	−	9.65825i	0.338043	−	0.372575i
$673$			37.1662i			1.43265i	0.697767	+	0.716325i	$0.254177\pi$
$673$			37.1662i			1.43265i	−0.697767	+	0.716325i	$0.745823\pi$
$674$	34.8239	+	17.3198i	1.34137	+	0.667132i
$675$	3.02124			0.116288
$676$	41.4383	+	54.7657i	1.59378	+	2.10637i
$677$	−12.9242			−0.496717			−0.248358	−	0.968668i	$-0.579891\pi$
$677$	−12.9242			−0.496717			−0.248358	+	0.968668i	$0.579891\pi$
$678$	−3.64268	−	1.81170i	−0.139896	−	0.0695778i
$679$	−27.6694			−1.06185
$680$	8.22002	−	8.27232i	0.315223	−	0.317229i
$681$	−2.29968			−0.0881241
$682$	−6.77112	−	3.36764i	−0.259280	−	0.128953i
$683$	17.2012			0.658185			0.329092	−	0.944298i	$-0.393257\pi$
$683$	17.2012			0.658185			0.329092	+	0.944298i	$0.393257\pi$
$684$	16.8763	−	12.7694i	0.645282	−	0.488250i
$685$	−2.39871			−0.0916501
$686$	−27.9604	−	13.9062i	−1.06753	−	0.530940i
$687$		−	6.95374i		−	0.265302i
$688$	35.7711	+	10.1049i	1.36376	+	0.385247i
$689$	35.2854			1.34427
$690$	−2.73781	−	1.36166i	−0.104227	−	0.0518374i
$691$	−25.6782			−0.976846			−0.488423	−	0.872607i	$-0.662428\pi$
$691$	−25.6782			−0.976846			−0.488423	+	0.872607i	$0.662428\pi$
$692$	−0.0745567	−	0.0985358i	−0.00283422	−	0.00374577i
$693$		−	10.3740i		−	0.394074i
$694$	−0.0973748	+	0.195786i	−0.00369630	+	0.00743194i
$695$	8.52596			0.323408
$696$	−9.42028	+	1.77474i	−0.357075	+	0.0672714i
$697$	−28.0931	−	40.8567i	−1.06410	−	1.54756i
$698$	25.9839	+	12.9232i	0.983507	+	0.489150i
$699$		−	13.3706i		−	0.505723i
$700$	6.96261	−	5.26823i	0.263162	−	0.199120i
$701$		−	29.0433i		−	1.09695i	−0.836167	−	0.548475i	$-0.815209\pi$
$701$		−	29.0433i		−	1.09695i	0.836167	−	0.548475i	$-0.184791\pi$
$702$	26.3214	+	13.0910i	0.993439	+	0.494090i
$703$		−	27.0714i		−	1.02102i
$704$	6.50736	−	2.54215i	0.245255	−	0.0958107i
$705$	−0.737275			−0.0277674
$706$	5.29862	−	10.6536i	0.199416	−	0.400955i
$707$	−33.0302			−1.24223
$708$	−4.37047	+	3.30690i	−0.164252	+	0.124281i
$709$	26.2551			0.986032			0.493016	−	0.870020i	$-0.335894\pi$
$709$	26.2551			0.986032			0.493016	+	0.870020i	$0.335894\pi$
$710$	10.5525	+	5.24833i	0.396030	+	0.196966i
$711$			8.65618i			0.324632i
$712$	−27.7519	+	5.22834i	−1.04005	+	0.195940i
$713$	25.0706			0.938902
$714$	13.3095	−	1.88685i	0.498095	−	0.0706134i
$715$			6.00844i			0.224703i
$716$	16.7060	−	12.6405i	0.624333	−	0.472399i
$717$	10.0625			0.375789
$718$	4.75109	−	9.55275i	0.177309	−	0.356505i
$719$			21.7421i			0.810843i	0.914130	+	0.405421i	$0.132875\pi$
$719$			21.7421i			0.810843i	−0.914130	+	0.405421i	$0.867125\pi$
$720$	2.95895	−	10.4746i	0.110273	−	0.390365i
$721$		−	31.4289i		−	1.17047i
$722$	2.44265	−	4.91130i	0.0909059	−	0.182780i
$723$			12.0002i			0.446292i
$724$	−5.37454	−	7.10311i	−0.199743	−	0.263985i
$725$	−6.41784			−0.238352
$726$	3.40468	−	6.84560i	0.126359	−	0.254064i
$727$	−52.0930			−1.93202			−0.966011	−	0.258499i	$-0.916772\pi$
$727$	−52.0930			−1.93202			−0.966011	+	0.258499i	$0.916772\pi$
$728$	83.4865	−	15.7285i	3.09421	−	0.582937i
$729$	−13.0857			−0.484655
$730$	2.35761	+	1.17257i	0.0872592	+	0.0433986i
$731$	21.7087	+	31.5717i	0.802926	+	1.16772i
$732$	4.75120	+	6.27930i	0.175610	+	0.232089i
$733$			6.56217i			0.242379i	0.992629	+	0.121190i	$0.0386709\pi$
$733$			6.56217i			0.242379i	−0.992629	+	0.121190i	$0.961329\pi$
$734$	−28.0575	−	13.9545i	−1.03562	−	0.515069i
$735$	6.36768			0.234875
$736$	−15.5630	+	17.1528i	−0.573660	+	0.632261i
$737$		−	0.964847i		−	0.0355406i
$738$	−41.4360	−	20.6083i	−1.52528	−	0.758602i
$739$			30.8831i			1.13605i	0.823010	+	0.568026i	$0.192293\pi$
$739$			30.8831i			1.13605i	−0.823010	+	0.568026i	$0.807707\pi$
$740$	−8.40117	−	11.1032i	−0.308833	−	0.408161i
$741$	−14.1288			−0.519034
$742$	14.0998	−	28.3497i	0.517619	−	1.04075i
$743$		−	34.7514i		−	1.27490i	−0.770490	−	0.637452i	$-0.779988\pi$
$743$		−	34.7514i		−	1.27490i	0.770490	−	0.637452i	$-0.220012\pi$
$744$	−1.69329	−	8.98794i	−0.0620791	−	0.329514i
$745$		−	7.04895i		−	0.258254i
$746$	8.03779	+	3.99762i	0.294284	+	0.146363i
$747$			11.9209i			0.436164i
$748$	6.83414	+	2.27007i	0.249881	+	0.0830019i
$749$		−	78.5403i		−	2.86980i
$750$	−0.332573	+	0.668687i	−0.0121439	+	0.0244170i
$751$		−	8.49846i		−	0.310113i	−0.987906	−	0.155057i	$-0.950444\pi$
$751$		−	8.49846i		−	0.310113i	0.987906	−	0.155057i	$-0.0495560\pi$
$752$	−1.51815	+	5.37420i	−0.0553612	+	0.195977i
$753$			4.24663i			0.154756i
$754$	−55.9130	−	27.8085i	−2.03623	−	1.01273i
$755$	9.79384			0.356434
$756$	21.0357	−	15.9166i	0.765062	−	0.578881i
$757$		−	17.5911i		−	0.639358i	−0.947526	−	0.319679i	$-0.896425\pi$
$757$		−	17.5911i		−	0.639358i	0.947526	−	0.319679i	$-0.103575\pi$
$758$	−3.85116	+	7.74332i	−0.139880	+	0.281250i
$759$		−	1.88817i		−	0.0685361i
$760$	2.03628	+	10.8085i	0.0738638	+	0.392067i
$761$	−16.4486			−0.596262			−0.298131	−	0.954525i	$-0.596363\pi$
$761$	−16.4486			−0.596262			−0.298131	+	0.954525i	$0.596363\pi$
$762$	−5.99593	+	12.0557i	−0.217210	+	0.436731i
$763$		−	50.3059i		−	1.82120i
$764$	−16.9485	−	22.3995i	−0.613174	−	0.810385i
$765$	9.24489	−	6.35680i	0.334250	−	0.229831i
$766$	−11.5143	+	23.1511i	−0.416028	+	0.836485i
$767$	−35.7023			−1.28914
$768$	7.20051	+	4.42090i	0.259826	+	0.159526i
$769$	45.5271			1.64175			0.820874	−	0.571110i	$-0.193487\pi$
$769$	45.5271			1.64175			0.820874	+	0.571110i	$0.193487\pi$
$770$	4.82742	+	2.40093i	0.173968	+	0.0865235i
$771$	−4.55605			−0.164082
$772$	−6.66776	+	5.04513i	−0.239978	+	0.181578i
$773$			48.9953i			1.76224i	0.472895	+	0.881119i	$0.343209\pi$
$773$			48.9953i			1.76224i	−0.472895	+	0.881119i	$0.656791\pi$
$774$	32.0193	+	15.9249i	1.15091	+	0.572409i
$775$		−	6.12329i		−	0.219955i
$776$	−3.31896	−	17.6170i	−0.119144	−	0.632412i
$777$		−	16.0493i		−	0.575767i
$778$	2.55415	+	1.27031i	0.0915706	+	0.0455429i
$779$	46.7633			1.67547
$780$	−5.79485	+	4.38465i	−0.207489	+	0.156996i
$781$			7.27770i			0.260416i
$782$	−23.6373	+	3.35099i	−0.845269	+	0.119831i
$783$	−19.3898			−0.692936
$784$	13.1119	−	46.4158i	0.468283	−	1.65771i
$785$			1.38378i			0.0493892i
$786$	0.138459	−	0.278392i	0.00493867	−	0.00992991i
$787$	23.0782			0.822648			0.411324	−	0.911489i	$-0.365066\pi$
$787$	23.0782			0.822648			0.411324	+	0.911489i	$0.365066\pi$
$788$	8.77104	+	11.5920i	0.312455	+	0.412948i
$789$	−14.8670			−0.529278
$790$	−4.02807	−	2.00337i	−0.143312	−	0.0712768i
$791$	−23.7814			−0.845569
$792$	6.60506	−	1.24437i	0.234700	−	0.0442166i
$793$			51.2955i			1.82156i
$794$	−14.6469	+	29.4498i	−0.519801	+	1.04513i
$795$			2.70828i			0.0960527i
$796$	−28.1063	+	21.2665i	−0.996202	+	0.753772i
$797$		−	30.6176i		−	1.08453i	−0.840207	−	0.542265i	$-0.817567\pi$
$797$		−	30.6176i		−	1.08453i	0.840207	−	0.542265i	$-0.182433\pi$
$798$	−5.64576	+	11.3516i	−0.199858	+	0.401843i
$799$	−4.74328	+	3.26149i	−0.167805	+	0.115383i
$800$	4.18943	+	3.80114i	0.148119	+	0.134391i
$801$	−27.1688			−0.959961
$802$	−10.4176	−	5.18120i	−0.367857	−	0.182955i
$803$			1.62596i			0.0573789i
$804$	0.930547	−	0.704095i	0.0328179	−	0.0248315i
$805$	−17.8739			−0.629972
$806$	26.5323	−	53.3469i	0.934559	−	1.87907i
$807$	−13.8242			−0.486636
$808$	−3.96200	−	21.0302i	−0.139383	−	0.739839i
$809$			33.7864i			1.18787i	0.804514	+	0.593933i	$0.202426\pi$
$809$			33.7864i			1.18787i	−0.804514	+	0.593933i	$0.797574\pi$
$810$	4.13629	−	8.31661i	0.145334	−	0.292216i
$811$	−39.0651			−1.37176			−0.685880	−	0.727714i	$-0.740583\pi$
$811$	−39.0651			−1.37176			−0.685880	+	0.727714i	$0.740583\pi$
$812$	−44.6849	+	33.8107i	−1.56813	+	1.18652i
$813$	−11.4504			−0.401584
$814$	3.82873	−	7.69821i	0.134197	−	0.269822i
$815$	5.50427			0.192806
$816$	2.79783	+	8.24777i	0.0979437	+	0.288730i
$817$	−36.1360			−1.26424
$818$	11.5663	−	23.2557i	0.404405	−	0.813115i
$819$	81.7322			2.85596
$820$	19.1797	−	14.5123i	0.669785	−	0.506790i
$821$	−42.3273			−1.47723			−0.738617	−	0.674125i	$-0.764521\pi$
$821$	−42.3273			−1.47723			−0.738617	+	0.674125i	$0.764521\pi$
$822$	0.797748	−	1.60399i	0.0278247	−	0.0559455i
$823$			56.0530i			1.95388i	0.213505	+	0.976942i	$0.431512\pi$
$823$			56.0530i			1.95388i	−0.213505	+	0.976942i	$0.568488\pi$
$824$	20.0107	−	3.76993i	0.697104	−	0.131332i
$825$	−0.461169			−0.0160558
$826$	−14.2664	+	28.6847i	−0.496392	+	0.998067i
$827$	−52.6744			−1.83167			−0.915834	−	0.401556i	$-0.868469\pi$
$827$	−52.6744			−1.83167			−0.915834	+	0.401556i	$0.868469\pi$
$828$	−17.7689	+	13.4448i	−0.617513	+	0.467239i
$829$			44.0897i			1.53130i	0.643259	+	0.765649i	$0.277582\pi$
$829$			44.0897i			1.53130i	−0.643259	+	0.765649i	$0.722418\pi$
$830$	−5.54728	−	2.75896i	−0.192549	−	0.0957648i
$831$	0.561690			0.0194848
$832$	20.0285	+	51.2688i	0.694365	+	1.77743i
$833$	40.9667	−	28.1687i	1.41941	−	0.975989i
$834$	−2.83551	+	5.70120i	−0.0981856	+	0.197416i
$835$			13.3312i			0.461344i
$836$	−5.41608	+	4.09805i	−0.187319	+	0.141734i
$837$		−	18.4999i		−	0.639452i
$838$	−11.4053	+	22.9320i	−0.393989	+	0.792171i
$839$			39.6273i			1.36809i	0.729442	+	0.684043i	$0.239780\pi$
$839$			39.6273i			1.36809i	−0.729442	+	0.684043i	$0.760220\pi$
$840$	1.20722	+	6.40788i	0.0416530	+	0.221093i
$841$	12.1886			0.420298
$842$	−46.5542	−	23.1539i	−1.60436	−	0.797935i
$843$	9.58681			0.330187
$844$	−21.5692	−	28.5064i	−0.742444	−	0.981230i
$845$	−34.3381			−1.18127
$846$	−2.39253	+	4.81054i	−0.0822570	+	0.165390i
$847$		−	44.6918i		−	1.53563i
$848$	19.7414	+	5.57671i	0.677922	+	0.191505i
$849$	−17.2027			−0.590394
$850$	0.818452	+	5.77323i	0.0280727	+	0.198020i
$851$			28.5032i			0.977078i
$852$	−7.01898	+	5.31088i	−0.240466	+	0.181948i
$853$	−19.0981			−0.653905			−0.326953	−	0.945041i	$-0.606022\pi$
$853$	−19.0981			−0.653905			−0.326953	+	0.945041i	$0.606022\pi$
$854$	41.2129	+	20.4973i	1.41028	+	0.701405i
$855$			10.5814i			0.361877i
$856$	50.0063	−	9.42098i	1.70918	−	0.322003i
$857$		−	4.23888i		−	0.144798i	−0.997376	−	0.0723988i	$-0.976935\pi$
$857$		−	4.23888i		−	0.144798i	0.997376	−	0.0723988i	$-0.0230654\pi$
$858$	−4.01776	−	1.99825i	−0.137164	−	0.0682190i
$859$		−	33.5933i		−	1.14619i	−0.819490	−	0.573094i	$-0.805743\pi$
$859$		−	33.5933i		−	1.14619i	0.819490	−	0.573094i	$-0.194257\pi$
$860$	−14.8210	+	11.2142i	−0.505392	+	0.382402i
$861$	27.7238			0.944825
$862$	32.2678	+	16.0485i	1.09904	+	0.546613i
$863$	35.9961			1.22532			0.612661	−	0.790346i	$-0.290099\pi$
$863$	35.9961			1.22532			0.612661	+	0.790346i	$0.290099\pi$
$864$	12.6573	+	11.4841i	0.430610	+	0.390699i
$865$	0.0617819			0.00210065
$866$	−5.37143	+	10.8000i	−0.182529	+	0.367000i
$867$	−3.21358	+	8.38256i	−0.109139	+	0.284687i
$868$	−32.2589	−	42.6341i	−1.09494	−	1.44710i
$869$		−	2.77801i		−	0.0942376i
$870$	2.13440	−	4.29152i	0.0723630	−	0.145496i
$871$	7.60164			0.257572
$872$	32.0296	−	6.03424i	1.08466	−	0.204345i
$873$		−	17.2468i		−	0.583716i
$874$	10.0267	−	20.1602i	0.339159	−	0.681929i
$875$			4.36555i			0.147583i
$876$	−1.56816	+	1.18654i	−0.0529832	+	0.0400895i
$877$	32.2329			1.08843			0.544214	−	0.838947i	$-0.316828\pi$
$877$	32.2329			1.08843			0.544214	+	0.838947i	$0.316828\pi$
$878$	9.84919	+	4.89852i	0.332394	+	0.165317i
$879$		−	6.13407i		−	0.206897i
$880$	−0.949609	+	3.36159i	−0.0320113	+	0.113319i
$881$		−	0.697366i		−	0.0234949i	−0.999931	−	0.0117474i	$-0.996261\pi$
$881$		−	0.697366i		−	0.0234949i	0.999931	−	0.0117474i	$-0.00373941\pi$
$882$	20.6638	−	41.5475i	0.695786	−	1.39898i
$883$			16.4181i			0.552514i	0.961084	+	0.276257i	$0.0890941\pi$
$883$			16.4181i			0.552514i	−0.961084	+	0.276257i	$0.910906\pi$
$884$	−17.8849	+	53.8435i	−0.601536	+	1.81095i
$885$		−	2.74028i		−	0.0921135i
$886$	−22.0967	−	10.9898i	−0.742352	−	0.369211i
$887$		−	25.9180i		−	0.870240i	−0.900373	−	0.435120i	$-0.856706\pi$
$887$		−	25.9180i		−	0.870240i	0.900373	−	0.435120i	$-0.143294\pi$
$888$	10.2186	−	1.92513i	0.342912	−	0.0646032i
$889$			78.7061i			2.63972i
$890$	6.28789	−	12.6427i	0.210771	−	0.423785i
$891$	5.73566			0.192152
$892$	−8.93570	−	11.8096i	−0.299189	−	0.395415i
$893$		−	5.42902i		−	0.181675i
$894$	4.71354	+	2.34429i	0.157644	+	0.0784049i
$895$			10.4747i			0.350129i
$896$	49.1947	+	4.39494i	1.64348	+	0.146825i
$897$	14.8761			0.496698
$898$	−36.3876	−	18.0975i	−1.21427	−	0.603920i
$899$			39.2983i			1.31067i
$900$	3.28378	+	4.33992i	0.109459	+	0.144664i
$901$	11.9806	+	17.4238i	0.399132	+	0.580470i
$902$	13.2980	+	6.61378i	0.442774	+	0.220215i
$903$	−21.4234			−0.712925
$904$	−2.85260	−	15.1415i	−0.0948761	−	0.503600i
$905$	4.45365			0.148044
$906$	−3.25717	+	6.54901i	−0.108212	+	0.217576i
$907$	−50.7214			−1.68418			−0.842089	−	0.539339i	$-0.818674\pi$
$907$	−50.7214			−1.68418			−0.842089	+	0.539339i	$0.818674\pi$
$908$	−5.25521	−	6.94540i	−0.174400	−	0.230491i
$909$		−	20.5883i		−	0.682870i
$910$	−18.9160	+	38.0333i	−0.627058	+	1.26079i
$911$		−	15.5598i		−	0.515519i	−0.966209	−	0.257759i	$-0.917016\pi$
$911$		−	15.5598i		−	0.515519i	0.966209	−	0.257759i	$-0.0829842\pi$
$912$	−7.90474	−	2.23300i	−0.261752	−	0.0739419i
$913$		−	3.82576i		−	0.126614i
$914$	6.90680	−	13.8871i	0.228457	−	0.459345i
$915$	−3.93711			−0.130157
$916$	21.0014	−	15.8906i	0.693904	−	0.525040i
$917$		−	1.81750i		−	0.0600190i
$918$	2.47274	+	17.4423i	0.0816126	+	0.575682i
$919$	−14.7019			−0.484971			−0.242486	−	0.970155i	$-0.577963\pi$
$919$	−14.7019			−0.484971			−0.242486	+	0.970155i	$0.577963\pi$
$920$	−2.14399	−	11.3802i	−0.0706852	−	0.375195i
$921$			1.00996i			0.0332794i
$922$	−42.4767	−	21.1259i	−1.39889	−	0.695744i
$923$	−57.3380			−1.88730
$924$	−3.21094	+	2.42955i	−0.105632	+	0.0799262i
$925$	6.96168			0.228899
$926$	−16.5091	+	33.1940i	−0.542524	+	1.09082i
$927$	19.5902			0.643426
$928$	−26.8871	−	24.3951i	−0.882612	−	0.800808i
$929$		−	2.30440i		−	0.0756050i	−0.999285	−	0.0378025i	$-0.987964\pi$
$929$		−	2.30440i		−	0.0756050i	0.999285	−	0.0378025i	$-0.0120358\pi$
$930$	4.09457	+	2.03644i	0.134266	+	0.0667777i
$931$			46.8892i			1.53673i
$932$	40.3813	−	30.5544i	1.32273	−	1.00084i
$933$			11.9954i			0.392712i
$934$	−16.7571	−	8.33419i	−0.548309	−	0.272703i
$935$	−2.96695	+	2.04008i	−0.0970295	+	0.0667176i
$936$	9.80385	+	52.0386i	0.320449	+	1.70093i
$937$	28.9950			0.947225			0.473612	−	0.880733i	$-0.342950\pi$
$937$	28.9950			0.947225			0.473612	+	0.880733i	$0.342950\pi$
$938$	3.03756	−	6.10746i	0.0991799	−	0.199416i
$939$		−	5.29439i		−	0.172776i
$940$	−1.68481	−	2.22668i	−0.0549525	−	0.0726264i
$941$	−36.3601			−1.18531			−0.592653	−	0.805458i	$-0.701919\pi$
$941$	−36.3601			−1.18531			−0.592653	+	0.805458i	$0.701919\pi$
$942$	−0.925315	−	0.460208i	−0.0301484	−	0.0149944i
$943$	−49.2368			−1.60337
$944$	−19.9747	−	5.64261i	−0.650120	−	0.183651i
$945$			13.1894i			0.429051i
$946$	−10.2759	−	5.11075i	−0.334098	−	0.166165i
$947$	10.9938			0.357251			0.178625	−	0.983917i	$-0.442835\pi$
$947$	10.9938			0.357251			0.178625	+	0.983917i	$0.442835\pi$
$948$	2.67926	−	2.02725i	0.0870182	−	0.0658420i
$949$	−12.8103			−0.415839
$950$	−4.92396	−	2.44895i	−0.159754	−	0.0794544i
$951$	−6.34093			−0.205619
$952$	36.1133	+	35.8849i	1.17044	+	1.16304i
$953$	18.8369			0.610187			0.305093	−	0.952322i	$-0.401312\pi$
$953$	18.8369			0.610187			0.305093	+	0.952322i	$0.401312\pi$
$954$	17.6708	+	8.78864i	0.572114	+	0.284543i
$955$	14.0445			0.454468
$956$	22.9946	+	30.3902i	0.743698	+	0.982888i
$957$	2.95971			0.0956738
$958$	34.4160	+	17.1169i	1.11193	+	0.553022i
$959$		−	10.4717i		−	0.338149i
$960$	−3.93506	+	1.53726i	−0.127004	+	0.0496149i
$961$	−6.49474			−0.209508
$962$	60.6511	+	30.1650i	1.95547	+	0.972559i
$963$	48.9556			1.57757
$964$	−36.2424	+	27.4227i	−1.16729	+	0.883226i
$965$		−	4.18068i		−	0.134581i
$966$	5.94438	−	11.9520i	0.191257	−	0.384551i
$967$	17.2985			0.556282			0.278141	−	0.960540i	$-0.410282\pi$
$967$	17.2985			0.556282			0.278141	+	0.960540i	$0.410282\pi$
$968$	28.4551	−	5.36082i	0.914581	−	0.172303i
$969$	−4.79722	−	6.97674i	−0.154109	−	0.224125i
$970$	8.02563	+	3.99157i	0.257687	+	0.128162i
$971$		−	37.7748i		−	1.21225i	−0.795370	−	0.606125i	$-0.792723\pi$
$971$		−	37.7748i		−	1.21225i	0.795370	−	0.606125i	$-0.207277\pi$
$972$	15.1234	+	19.9875i	0.485085	+	0.641098i
$973$			37.2205i			1.19324i
$974$	21.3404	+	10.6137i	0.683791	+	0.340086i
$975$		−	3.63336i		−	0.116361i
$976$	−8.10705	+	28.6987i	−0.259500	+	0.918624i
$977$	5.78792			0.185172			0.0925859	−	0.995705i	$-0.470487\pi$
$977$	5.78792			0.185172			0.0925859	+	0.995705i	$0.470487\pi$
$978$	−1.83057	+	3.68063i	−0.0585353	+	0.117694i
$979$	8.71922			0.278667
$980$	14.5513	+	19.2314i	0.464826	+	0.614324i
$981$	31.3565			1.00114
$982$	44.9837	+	22.3728i	1.43549	+	0.713944i
$983$			9.58334i			0.305661i	0.988252	+	0.152830i	$0.0488389\pi$
$983$			9.58334i			0.305661i	−0.988252	+	0.152830i	$0.951161\pi$
$984$	3.32549	+	17.6516i	0.106013	+	0.562713i
$985$	−7.26818			−0.231583
$986$	−5.25269	−	37.0516i	−0.167280	−	1.17996i
$987$		−	3.21861i		−	0.102450i
$988$	−32.2869	−	42.6711i	−1.02718	−	1.35755i
$989$	38.0473			1.20984
$990$	−1.49654	+	3.00901i	−0.0475632	+	0.0956327i
$991$			38.7288i			1.23026i	0.788425	+	0.615131i	$0.210897\pi$
$991$			38.7288i			1.23026i	−0.788425	+	0.615131i	$0.789103\pi$
$992$	23.2755	−	25.6531i	0.738997	−	0.814488i
$993$		−	2.58353i		−	0.0819858i
$994$	−22.9119	+	46.0677i	−0.726721	+	1.46118i
$995$		−	17.6226i		−	0.558675i
$996$	3.68976	−	2.79184i	0.116914	−	0.0884628i
$997$	30.4509			0.964388			0.482194	−	0.876064i	$-0.339840\pi$
$997$	30.4509			0.964388			0.482194	+	0.876064i	$0.339840\pi$
$998$	8.74356	−	17.5802i	0.276773	−	0.556491i
$999$	21.0329			0.665452

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	680.2.l.a.101.23	✓	36
4.3	odd	2		2720.2.l.b.2481.20		36
8.3	odd	2		2720.2.l.a.2481.18		36
8.5	even	2		680.2.l.b.101.24	yes	36
17.16	even	2		680.2.l.b.101.23	yes	36
68.67	odd	2		2720.2.l.a.2481.17		36
136.67	odd	2		2720.2.l.b.2481.19		36
136.101	even	2	inner	680.2.l.a.101.24	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
680.2.l.a.101.23	✓	36	1.1	even	1	trivial
680.2.l.a.101.24	yes	36	136.101	even	2	inner
680.2.l.b.101.23	yes	36	17.16	even	2
680.2.l.b.101.24	yes	36	8.5	even	2
2720.2.l.a.2481.17		36	68.67	odd	2
2720.2.l.a.2481.18		36	8.3	odd	2
2720.2.l.b.2481.19		36	136.67	odd	2
2720.2.l.b.2481.20		36	4.3	odd	2

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:	\( N \)	\(=\)	\( 680 = 2^{3} \cdot 5 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	680.l (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(0.629773 - 1.26625i) q^{2} -0.528085 q^{3} +(-1.20677 - 1.59490i) q^{4} +1.00000 q^{5} +(-0.332573 + 0.668687i) q^{6} +4.36555i q^{7} +(-2.77953 + 0.523652i) q^{8} -2.72113 q^{9} +(0.629773 - 1.26625i) q^{10} +0.873286 q^{11} +(0.637278 + 0.842241i) q^{12} +6.88027i q^{13} +(5.52788 + 2.74931i) q^{14} -0.528085 q^{15} +(-1.08740 + 3.84936i) q^{16} +(-3.39745 + 2.33609i) q^{17} +(-1.71369 + 3.44562i) q^{18} -3.88862i q^{19} +(-1.20677 - 1.59490i) q^{20} -2.30538i q^{21} +(0.549971 - 1.10580i) q^{22} +4.09430i q^{23} +(1.46783 - 0.276533i) q^{24} +1.00000 q^{25} +(8.71213 + 4.33300i) q^{26} +3.02124 q^{27} +(6.96261 - 5.26823i) q^{28} -6.41784 q^{29} +(-0.332573 + 0.668687i) q^{30} -6.12329i q^{31} +(4.18943 + 3.80114i) q^{32} -0.461169 q^{33} +(0.818452 + 5.77323i) q^{34} +4.36555i q^{35} +(3.28378 + 4.33992i) q^{36} +6.96168 q^{37} +(-4.92396 - 2.44895i) q^{38} -3.63336i q^{39} +(-2.77953 + 0.523652i) q^{40} +12.0257i q^{41} +(-2.91919 - 1.45187i) q^{42} -9.29275i q^{43} +(-1.05386 - 1.39280i) q^{44} -2.72113 q^{45} +(5.18441 + 2.57848i) q^{46} +1.39613 q^{47} +(0.574239 - 2.03279i) q^{48} -12.0581 q^{49} +(0.629773 - 1.26625i) q^{50} +(1.79414 - 1.23365i) q^{51} +(10.9733 - 8.30292i) q^{52} -5.12849i q^{53} +(1.90269 - 3.82564i) q^{54} +0.873286 q^{55} +(-2.28603 - 12.1342i) q^{56} +2.05352i q^{57} +(-4.04178 + 8.12658i) q^{58} +5.18909i q^{59} +(0.637278 + 0.842241i) q^{60} +7.45546 q^{61} +(-7.75362 - 3.85628i) q^{62} -11.8792i q^{63} +(7.45158 - 2.91101i) q^{64} +6.88027i q^{65} +(-0.290432 + 0.583955i) q^{66} -1.10485i q^{67} +(7.82578 + 2.59946i) q^{68} -2.16214i q^{69} +(5.52788 + 2.74931i) q^{70} +8.33370i q^{71} +(7.56345 - 1.42492i) q^{72} +1.86189i q^{73} +(4.38428 - 8.81522i) q^{74} -0.528085 q^{75} +(-6.20195 + 4.69268i) q^{76} +3.81238i q^{77} +(-4.60074 - 2.28819i) q^{78} -3.18110i q^{79} +(-1.08740 + 3.84936i) q^{80} +6.56791 q^{81} +(15.2275 + 7.57344i) q^{82} -4.38088i q^{83} +(-3.67685 + 2.78207i) q^{84} +(-3.39745 + 2.33609i) q^{85} +(-11.7669 - 5.85232i) q^{86} +3.38916 q^{87} +(-2.42732 + 0.457298i) q^{88} +9.98438 q^{89} +(-1.71369 + 3.44562i) q^{90} -30.0362 q^{91} +(6.52999 - 4.94089i) q^{92} +3.23362i q^{93} +(0.879244 - 1.76785i) q^{94} -3.88862i q^{95} +(-2.21238 - 2.00732i) q^{96} +6.33811i q^{97} +(-7.59384 + 15.2685i) q^{98} -2.37632 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 4 q^{3} + 2 q^{4} + 36 q^{5} + 36 q^{9} - 8 q^{11} - 2 q^{12} + 2 q^{14} - 4 q^{15} + 6 q^{16} - 10 q^{18} + 2 q^{20} + 26 q^{24} + 36 q^{25} + 6 q^{26} - 16 q^{27} + 14 q^{28} - 10 q^{32} - 8 q^{33}+ \cdots - 40 q^{99}+O(q^{100}) \) 36 * q - 4 * q^3 + 2 * q^4 + 36 * q^5 + 36 * q^9 - 8 * q^11 - 2 * q^12 + 2 * q^14 - 4 * q^15 + 6 * q^16 - 10 * q^18 + 2 * q^20 + 26 * q^24 + 36 * q^25 + 6 * q^26 - 16 * q^27 + 14 * q^28 - 10 * q^32 - 8 * q^33 - 24 * q^34 + 8 * q^36 - 20 * q^38 - 2 * q^42 + 6 * q^44 + 36 * q^45 + 24 * q^46 + 20 * q^47 - 4 * q^48 - 36 * q^49 + 6 * q^52 - 56 * q^54 - 8 * q^55 + 20 * q^56 - 18 * q^58 - 2 * q^60 - 24 * q^62 + 14 * q^64 - 16 * q^66 - 40 * q^68 + 2 * q^70 - 54 * q^72 + 6 * q^74 - 4 * q^75 + 2 * q^76 - 14 * q^78 + 6 * q^80 + 44 * q^81 + 22 * q^82 - 68 * q^84 - 36 * q^86 + 24 * q^87 - 58 * q^88 - 10 * q^90 - 56 * q^91 - 12 * q^92 + 14 * q^94 - 24 * q^96 + 10 * q^98 - 40 * q^99

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