LMFDB - Embedded newform 637.2.i.a.489.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [637,2,Mod(489,637)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(637, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1]))

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

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

chi := DirichletCharacter("637.489");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 637 = 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	637.i (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$5.08647060876$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 91)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			489.9
Character	$\chi$	$=$	637.489
Dual form			637.2.i.a.538.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.546480 + 0.546480i) q^{2} -0.487133i q^{3} -1.40272i q^{4} +(1.29040 - 1.29040i) q^{5} +(0.266208 - 0.266208i) q^{6} +(1.85952 - 1.85952i) q^{8} +2.76270 q^{9} +O(q^{10})$	\(q+(0.546480 + 0.546480i) q^{2} -0.487133i q^{3} -1.40272i q^{4} +(1.29040 - 1.29040i) q^{5} +(0.266208 - 0.266208i) q^{6} +(1.85952 - 1.85952i) q^{8} +2.76270 q^{9} +1.41035 q^{10} +(-0.725276 + 0.725276i) q^{11} -0.683311 q^{12} +(-0.266208 - 3.59571i) q^{13} +(-0.628596 - 0.628596i) q^{15} -0.773062 q^{16} -5.20058 q^{17} +(1.50976 + 1.50976i) q^{18} +(-3.71699 + 3.71699i) q^{19} +(-1.81007 - 1.81007i) q^{20} -0.792697 q^{22} -0.843739i q^{23} +(-0.905832 - 0.905832i) q^{24} +1.66974i q^{25} +(1.81951 - 2.11046i) q^{26} -2.80720i q^{27} +10.3454 q^{29} -0.687030i q^{30} +(4.16994 - 4.16994i) q^{31} +(-4.14150 - 4.14150i) q^{32} +(0.353306 + 0.353306i) q^{33} +(-2.84201 - 2.84201i) q^{34} -3.87530i q^{36} +(4.41711 - 4.41711i) q^{37} -4.06252 q^{38} +(-1.75159 + 0.129679i) q^{39} -4.79904i q^{40} +(-0.0927742 + 0.0927742i) q^{41} +7.36681i q^{43} +(1.01736 + 1.01736i) q^{44} +(3.56499 - 3.56499i) q^{45} +(0.461086 - 0.461086i) q^{46} +(-1.59524 - 1.59524i) q^{47} +0.376584i q^{48} +(-0.912480 + 0.912480i) q^{50} +2.53337i q^{51} +(-5.04377 + 0.373416i) q^{52} -6.77180 q^{53} +(1.53408 - 1.53408i) q^{54} +1.87179i q^{55} +(1.81067 + 1.81067i) q^{57} +(5.65353 + 5.65353i) q^{58} +(7.12895 + 7.12895i) q^{59} +(-0.881744 + 0.881744i) q^{60} -1.30682i q^{61} +4.55758 q^{62} -2.98037i q^{64} +(-4.98342 - 4.29639i) q^{65} +0.386149i q^{66} +(3.04544 + 3.04544i) q^{67} +7.29496i q^{68} -0.411013 q^{69} +(-6.02388 - 6.02388i) q^{71} +(5.13729 - 5.13729i) q^{72} +(8.02243 + 8.02243i) q^{73} +4.82772 q^{74} +0.813386 q^{75} +(5.21390 + 5.21390i) q^{76} +(-1.02807 - 0.886341i) q^{78} -10.3248 q^{79} +(-0.997558 + 0.997558i) q^{80} +6.92062 q^{81} -0.101398 q^{82} +(-4.16974 + 4.16974i) q^{83} +(-6.71082 + 6.71082i) q^{85} +(-4.02581 + 4.02581i) q^{86} -5.03957i q^{87} +2.69733i q^{88} +(5.48933 + 5.48933i) q^{89} +3.89639 q^{90} -1.18353 q^{92} +(-2.03132 - 2.03132i) q^{93} -1.74353i q^{94} +9.59280i q^{95} +(-2.01746 + 2.01746i) q^{96} +(2.49152 - 2.49152i) q^{97} +(-2.00372 + 2.00372i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 4 q^{2} - 16 q^{8} - 16 q^{9}+O(q^{10}) $ 32 * q + 4 * q^2 - 16 * q^8 - 16 * q^9	$ 32 q + 4 q^{2} - 16 q^{8} - 16 q^{9} + 20 q^{11} - 44 q^{15} - 24 q^{16} + 8 q^{18} - 8 q^{22} + 16 q^{29} - 8 q^{32} + 16 q^{37} + 12 q^{39} + 84 q^{44} - 24 q^{46} + 88 q^{50} + 24 q^{53} + 40 q^{57} - 52 q^{58} - 32 q^{60} + 16 q^{65} - 32 q^{67} - 36 q^{71} - 44 q^{72} - 24 q^{74} - 176 q^{78} + 64 q^{79} - 32 q^{81} - 84 q^{85} - 84 q^{86} + 48 q^{92} - 12 q^{93} - 24 q^{99}+O(q^{100}) $ 32 * q + 4 * q^2 - 16 * q^8 - 16 * q^9 + 20 * q^11 - 44 * q^15 - 24 * q^16 + 8 * q^18 - 8 * q^22 + 16 * q^29 - 8 * q^32 + 16 * q^37 + 12 * q^39 + 84 * q^44 - 24 * q^46 + 88 * q^50 + 24 * q^53 + 40 * q^57 - 52 * q^58 - 32 * q^60 + 16 * q^65 - 32 * q^67 - 36 * q^71 - 44 * q^72 - 24 * q^74 - 176 * q^78 + 64 * q^79 - 32 * q^81 - 84 * q^85 - 84 * q^86 + 48 * q^92 - 12 * q^93 - 24 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/637\mathbb{Z}\right)^\times$.

$n$	$197$	$248$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$

Coefficient data

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

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

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

$2$	0.546480	+	0.546480i	0.386420	+	0.386420i	0.873408	−	0.486989i	$-0.161905\pi$
$2$	0.546480	+	0.546480i	0.386420	+	0.386420i	−0.486989	+	0.873408i	$0.661905\pi$
$3$		−	0.487133i		−	0.281246i	−0.990063	−	0.140623i	$-0.955089\pi$
$3$		−	0.487133i		−	0.281246i	0.990063	−	0.140623i	$-0.0449106\pi$
$4$		−	1.40272i		−	0.701360i
$5$	1.29040	−	1.29040i	0.577084	−	0.577084i	−0.357015	−	0.934099i	$-0.616205\pi$
$5$	1.29040	−	1.29040i	0.577084	−	0.577084i	0.934099	+	0.357015i	$0.116205\pi$
$6$	0.266208	−	0.266208i	0.108679	−	0.108679i
$7$		0			0
$7$		0			0
$8$	1.85952	−	1.85952i	0.657439	−	0.657439i
$9$	2.76270			0.920901
$10$	1.41035			0.445993
$11$	−0.725276	+	0.725276i	−0.218679	+	0.218679i	−0.807942	−	0.589263i	$-0.799418\pi$
$11$	−0.725276	+	0.725276i	−0.218679	+	0.218679i	0.589263	+	0.807942i	$0.299418\pi$
$12$	−0.683311			−0.197255
$13$	−0.266208	−	3.59571i	−0.0738329	−	0.997271i
$13$	−0.266208	−	3.59571i	−0.0738329	−	0.997271i
$14$		0			0
$15$	−0.628596	−	0.628596i	−0.162303	−	0.162303i
$16$	−0.773062			−0.193266
$17$	−5.20058			−1.26133			−0.630663	−	0.776057i	$-0.717217\pi$
$17$	−5.20058			−1.26133			−0.630663	+	0.776057i	$0.717217\pi$
$18$	1.50976	+	1.50976i	0.355854	+	0.355854i
$19$	−3.71699	+	3.71699i	−0.852736	+	0.852736i	−0.990469	−	0.137733i	$-0.956018\pi$
$19$	−3.71699	+	3.71699i	−0.852736	+	0.852736i	0.137733	+	0.990469i	$0.456018\pi$
$20$	−1.81007	−	1.81007i	−0.404743	−	0.404743i
$21$		0			0
$22$	−0.792697			−0.169004
$23$		−	0.843739i		−	0.175932i	−0.996123	−	0.0879659i	$-0.971963\pi$
$23$		−	0.843739i		−	0.175932i	0.996123	−	0.0879659i	$-0.0280366\pi$
$24$	−0.905832	−	0.905832i	−0.184902	−	0.184902i
$25$			1.66974i			0.333948i
$26$	1.81951	−	2.11046i	0.356834	−	0.413895i
$27$		−	2.80720i		−	0.540246i
$28$		0			0
$29$	10.3454			1.92109			0.960543	−	0.278130i	$-0.0897147\pi$
$29$	10.3454			1.92109			0.960543	+	0.278130i	$0.0897147\pi$
$30$		−	0.687030i		−	0.125434i
$31$	4.16994	−	4.16994i	0.748943	−	0.748943i	−0.225337	−	0.974281i	$-0.572348\pi$
$31$	4.16994	−	4.16994i	0.748943	−	0.748943i	0.974281	+	0.225337i	$0.0723484\pi$
$32$	−4.14150	−	4.14150i	−0.732120	−	0.732120i
$33$	0.353306	+	0.353306i	0.0615026	+	0.0615026i
$34$	−2.84201	−	2.84201i	−0.487401	−	0.487401i
$35$		0			0
$36$		−	3.87530i		−	0.645883i
$37$	4.41711	−	4.41711i	0.726168	−	0.726168i	−0.243686	−	0.969854i	$-0.578357\pi$
$37$	4.41711	−	4.41711i	0.726168	−	0.726168i	0.969854	+	0.243686i	$0.0783566\pi$
$38$	−4.06252			−0.659028
$39$	−1.75159	+	0.129679i	−0.280479	+	0.0207652i
$40$		−	4.79904i		−	0.758795i
$41$	−0.0927742	+	0.0927742i	−0.0144889	+	0.0144889i	−0.714314	−	0.699825i	$-0.753261\pi$
$41$	−0.0927742	+	0.0927742i	−0.0144889	+	0.0144889i	0.699825	+	0.714314i	$0.253261\pi$
$42$		0			0
$43$			7.36681i			1.12343i	0.827331	+	0.561714i	$0.189858\pi$
$43$			7.36681i			1.12343i	−0.827331	+	0.561714i	$0.810142\pi$
$44$	1.01736	+	1.01736i	0.153373	+	0.153373i
$45$	3.56499	−	3.56499i	0.531437	−	0.531437i
$46$	0.461086	−	0.461086i	0.0679835	−	0.0679835i
$47$	−1.59524	−	1.59524i	−0.232689	−	0.232689i	0.581125	−	0.813814i	$-0.302613\pi$
$47$	−1.59524	−	1.59524i	−0.232689	−	0.232689i	−0.813814	+	0.581125i	$0.802613\pi$
$48$			0.376584i			0.0543552i
$49$		0			0
$50$	−0.912480	+	0.912480i	−0.129044	+	0.129044i
$51$			2.53337i			0.354743i
$52$	−5.04377	+	0.373416i	−0.699446	+	0.0517834i
$53$	−6.77180			−0.930178			−0.465089	−	0.885264i	$-0.653978\pi$
$53$	−6.77180			−0.930178			−0.465089	+	0.885264i	$0.653978\pi$
$54$	1.53408	−	1.53408i	0.208762	−	0.208762i
$55$			1.87179i			0.252392i
$56$		0			0
$57$	1.81067	+	1.81067i	0.239829	+	0.239829i
$58$	5.65353	+	5.65353i	0.742345	+	0.742345i
$59$	7.12895	+	7.12895i	0.928110	+	0.928110i	0.997584	−	0.0694735i	$-0.0221319\pi$
$59$	7.12895	+	7.12895i	0.928110	+	0.928110i	−0.0694735	+	0.997584i	$0.522132\pi$
$60$	−0.881744	+	0.881744i	−0.113833	+	0.113833i
$61$		−	1.30682i		−	0.167321i	−0.996494	−	0.0836604i	$-0.973339\pi$
$61$		−	1.30682i		−	0.167321i	0.996494	−	0.0836604i	$-0.0266611\pi$
$62$	4.55758			0.578813
$63$		0			0
$64$		−	2.98037i		−	0.372546i
$65$	−4.98342	−	4.29639i	−0.618117	−	0.532901i
$66$			0.386149i			0.0475316i
$67$	3.04544	+	3.04544i	0.372059	+	0.372059i	0.868227	−	0.496168i	$-0.165260\pi$
$67$	3.04544	+	3.04544i	0.372059	+	0.372059i	−0.496168	+	0.868227i	$0.665260\pi$
$68$			7.29496i			0.884643i
$69$	−0.411013			−0.0494802
$70$		0			0
$71$	−6.02388	−	6.02388i	−0.714903	−	0.714903i	0.252654	−	0.967557i	$-0.418697\pi$
$71$	−6.02388	−	6.02388i	−0.714903	−	0.714903i	−0.967557	+	0.252654i	$0.918697\pi$
$72$	5.13729	−	5.13729i	0.605436	−	0.605436i
$73$	8.02243	+	8.02243i	0.938954	+	0.938954i	0.998241	−	0.0592870i	$-0.0188827\pi$
$73$	8.02243	+	8.02243i	0.938954	+	0.938954i	−0.0592870	+	0.998241i	$0.518883\pi$
$74$	4.82772			0.561211
$75$	0.813386			0.0939218
$76$	5.21390	+	5.21390i	0.598075	+	0.598075i
$77$		0			0
$78$	−1.02807	−	0.886341i	−0.116407	−	0.100358i
$79$	−10.3248			−1.16163			−0.580816	−	0.814035i	$-0.697266\pi$
$79$	−10.3248			−1.16163			−0.580816	+	0.814035i	$0.697266\pi$
$80$	−0.997558	+	0.997558i	−0.111530	+	0.111530i
$81$	6.92062			0.768958
$82$	−0.101398			−0.0111976
$83$	−4.16974	+	4.16974i	−0.457689	+	0.457689i	−0.897896	−	0.440207i	$-0.854905\pi$
$83$	−4.16974	+	4.16974i	−0.457689	+	0.457689i	0.440207	+	0.897896i	$0.354905\pi$
$84$		0			0
$85$	−6.71082	+	6.71082i	−0.727891	+	0.727891i
$86$	−4.02581	+	4.02581i	−0.434115	+	0.434115i
$87$		−	5.03957i		−	0.540299i
$88$			2.69733i			0.287536i
$89$	5.48933	+	5.48933i	0.581868	+	0.581868i	0.935416	−	0.353548i	$-0.115025\pi$
$89$	5.48933	+	5.48933i	0.581868	+	0.581868i	−0.353548	+	0.935416i	$0.615025\pi$
$90$	3.89639			0.410715
$91$		0			0
$92$	−1.18353			−0.123391
$93$	−2.03132	−	2.03132i	−0.210638	−	0.210638i
$94$		−	1.74353i		−	0.179831i
$95$			9.59280i			0.984201i
$96$	−2.01746	+	2.01746i	−0.205906	+	0.205906i
$97$	2.49152	−	2.49152i	0.252976	−	0.252976i	−0.569214	−	0.822189i	$-0.692752\pi$
$97$	2.49152	−	2.49152i	0.252976	−	0.252976i	0.822189	+	0.569214i	$0.192752\pi$
$98$		0			0
$99$	−2.00372	+	2.00372i	−0.201381	+	0.201381i
$100$	2.34218			0.234218
$101$	−2.43372			−0.242164			−0.121082	−	0.992642i	$-0.538636\pi$
$101$	−2.43372			−0.242164			−0.121082	+	0.992642i	$0.538636\pi$
$102$	−1.38444	+	1.38444i	−0.137080	+	0.137080i
$103$	2.73634			0.269620			0.134810	−	0.990871i	$-0.456958\pi$
$103$	2.73634			0.269620			0.134810	+	0.990871i	$0.456958\pi$
$104$	−7.18131	−	6.19127i	−0.704185	−	0.607104i
$105$		0			0
$106$	−3.70065	−	3.70065i	−0.359439	−	0.359439i
$107$	2.25627			0.218122			0.109061	−	0.994035i	$-0.465216\pi$
$107$	2.25627			0.218122			0.109061	+	0.994035i	$0.465216\pi$
$108$	−3.93772			−0.378907
$109$	1.15158	+	1.15158i	0.110301	+	0.110301i	0.760103	−	0.649802i	$-0.225148\pi$
$109$	1.15158	+	1.15158i	0.110301	+	0.110301i	−0.649802	+	0.760103i	$0.725148\pi$
$110$	−1.02290	+	1.02290i	−0.0975292	+	0.0975292i
$111$	−2.15172	−	2.15172i	−0.204232	−	0.204232i
$112$		0			0
$113$	2.63227			0.247623			0.123812	−	0.992306i	$-0.460488\pi$
$113$	2.63227			0.247623			0.123812	+	0.992306i	$0.460488\pi$
$114$			1.97899i			0.185349i
$115$	−1.08876	−	1.08876i	−0.101527	−	0.101527i
$116$		−	14.5117i		−	1.34737i
$117$	−0.735454	−	9.93387i	−0.0679928	−	0.918387i
$118$			7.79165i			0.717280i
$119$		0			0
$120$	−2.33777			−0.213408
$121$			9.94795i			0.904359i
$122$	0.714149	−	0.714149i	0.0646560	−	0.0646560i
$123$	0.0451934	+	0.0451934i	0.00407495	+	0.00407495i
$124$	−5.84926	−	5.84926i	−0.525279	−	0.525279i
$125$	8.60663	+	8.60663i	0.769800	+	0.769800i
$126$		0			0
$127$			11.8104i			1.04801i	0.851716	+	0.524004i	$0.175562\pi$
$127$			11.8104i			1.04801i	−0.851716	+	0.524004i	$0.824438\pi$
$128$	−6.65429	+	6.65429i	−0.588161	+	0.588161i
$129$	3.58862			0.315960
$130$	−0.375448	−	5.07122i	−0.0329290	−	0.444776i
$131$			15.4467i			1.34959i	0.738006	+	0.674794i	$0.235768\pi$
$131$			15.4467i			1.34959i	−0.738006	+	0.674794i	$0.764232\pi$
$132$	0.495589	−	0.495589i	0.0431355	−	0.0431355i
$133$		0			0
$134$			3.32854i			0.287542i
$135$	−3.62241	−	3.62241i	−0.311767	−	0.311767i
$136$	−9.67057	+	9.67057i	−0.829245	+	0.829245i
$137$	−0.724831	+	0.724831i	−0.0619265	+	0.0619265i	−0.737392	−	0.675465i	$-0.763943\pi$
$137$	−0.724831	+	0.724831i	−0.0619265	+	0.0619265i	0.675465	+	0.737392i	$0.263943\pi$
$138$	−0.224610	−	0.224610i	−0.0191201	−	0.0191201i
$139$			11.4028i			0.967171i	0.875297	+	0.483585i	$0.160666\pi$
$139$			11.4028i			0.967171i	−0.875297	+	0.483585i	$0.839334\pi$
$140$		0			0
$141$	−0.777092	+	0.777092i	−0.0654429	+	0.0654429i
$142$		−	6.58385i		−	0.552505i
$143$	2.80096	+	2.41481i	0.234228	+	0.201936i
$144$	−2.13574			−0.177978
$145$	13.3497	−	13.3497i	1.10863	−	1.10863i
$146$			8.76819i			0.725660i
$147$		0			0
$148$	−6.19597	−	6.19597i	−0.509305	−	0.509305i
$149$	−5.40106	−	5.40106i	−0.442472	−	0.442472i	0.450370	−	0.892842i	$-0.351292\pi$
$149$	−5.40106	−	5.40106i	−0.442472	−	0.442472i	−0.892842	+	0.450370i	$0.851292\pi$
$150$	0.444499	+	0.444499i	0.0362932	+	0.0362932i
$151$	4.84411	−	4.84411i	0.394208	−	0.394208i	−0.481976	−	0.876184i	$-0.660081\pi$
$151$	4.84411	−	4.84411i	0.394208	−	0.394208i	0.876184	+	0.481976i	$0.160081\pi$
$152$			13.8236i			1.12124i
$153$	−14.3677			−1.16156
$154$		0			0
$155$		−	10.7618i		−	0.864406i
$156$	0.181903	+	2.45699i	0.0145639	+	0.196717i
$157$		−	12.8475i		−	1.02534i	−0.858586	−	0.512670i	$-0.828657\pi$
$157$		−	12.8475i		−	1.02534i	0.858586	−	0.512670i	$-0.171343\pi$
$158$	−5.64230	−	5.64230i	−0.448877	−	0.448877i
$159$			3.29876i			0.261609i
$160$	−10.6884			−0.844990
$161$		0			0
$162$	3.78198	+	3.78198i	0.297140	+	0.297140i
$163$	−0.694096	+	0.694096i	−0.0543658	+	0.0543658i	−0.733767	−	0.679401i	$-0.762240\pi$
$163$	−0.694096	+	0.694096i	−0.0543658	+	0.0543658i	0.679401	+	0.733767i	$0.262240\pi$
$164$	0.130136	+	0.130136i	0.0101619	+	0.0101619i
$165$	0.911811			0.0709844
$166$	−4.55736			−0.353720
$167$	9.25126	+	9.25126i	0.715884	+	0.715884i	0.967760	−	0.251876i	$-0.0810474\pi$
$167$	9.25126	+	9.25126i	0.715884	+	0.715884i	−0.251876	+	0.967760i	$0.581047\pi$
$168$		0			0
$169$	−12.8583	+	1.91442i	−0.989097	+	0.147263i
$170$	−7.33466			−0.562543
$171$	−10.2689	+	10.2689i	−0.785285	+	0.785285i
$172$	10.3336			0.787927
$173$	−22.1121			−1.68115			−0.840576	−	0.541693i	$-0.817783\pi$
$173$	−22.1121			−1.68115			−0.840576	+	0.541693i	$0.817783\pi$
$174$	2.75402	−	2.75402i	0.208782	−	0.208782i
$175$		0			0
$176$	0.560683	−	0.560683i	0.0422631	−	0.0422631i
$177$	3.47275	−	3.47275i	0.261028	−	0.261028i
$178$			5.99962i			0.449690i
$179$			8.07047i			0.603216i	0.953432	+	0.301608i	$0.0975233\pi$
$179$			8.07047i			0.603216i	−0.953432	+	0.301608i	$0.902477\pi$
$180$	−5.00068	−	5.00068i	−0.372728	−	0.372728i
$181$	20.5622			1.52838			0.764189	−	0.644993i	$-0.223140\pi$
$181$	20.5622			1.52838			0.764189	+	0.644993i	$0.223140\pi$
$182$		0			0
$183$	−0.636594			−0.0470584
$184$	−1.56895	−	1.56895i	−0.115664	−	0.115664i
$185$		−	11.3997i		−	0.838120i
$186$		−	2.22015i		−	0.162789i
$187$	3.77186	−	3.77186i	0.275825	−	0.275825i
$188$	−2.23767	+	2.23767i	−0.163199	+	0.163199i
$189$		0			0
$190$	−5.24227	+	5.24227i	−0.380314	+	0.380314i
$191$	−13.8382			−1.00129			−0.500647	−	0.865651i	$-0.666905\pi$
$191$	−13.8382			−1.00129			−0.500647	+	0.865651i	$0.666905\pi$
$192$	−1.45183			−0.104777
$193$	17.2582	−	17.2582i	1.24227	−	1.24227i	0.283212	−	0.959057i	$-0.408600\pi$
$193$	17.2582	−	17.2582i	1.24227	−	1.24227i	0.959057	−	0.283212i	$-0.0914000\pi$
$194$	2.72313			0.195509
$195$	−2.09291	+	2.42759i	−0.149876	+	0.173843i
$196$		0			0
$197$	−14.3424	−	14.3424i	−1.02185	−	1.02185i	−0.999756	−	0.0220979i	$-0.992965\pi$
$197$	−14.3424	−	14.3424i	−1.02185	−	1.02185i	−0.0220979	−	0.999756i	$-0.507035\pi$
$198$	−2.18999			−0.155635
$199$	14.8160			1.05028			0.525140	−	0.851016i	$-0.324013\pi$
$199$	14.8160			1.05028			0.525140	+	0.851016i	$0.324013\pi$
$200$	3.10491	+	3.10491i	0.219551	+	0.219551i
$201$	1.48353	−	1.48353i	0.104640	−	0.104640i
$202$	−1.32998	−	1.32998i	−0.0935770	−	0.0935770i
$203$		0			0
$204$	3.55361			0.248803
$205$			0.239431i			0.0167226i
$206$	1.49536	+	1.49536i	0.104186	+	0.104186i
$207$		−	2.33100i		−	0.162016i
$208$	0.205796	+	2.77971i	0.0142694	+	0.192738i
$209$		−	5.39169i		−	0.372951i
$210$		0			0
$211$	6.98585			0.480925			0.240463	−	0.970658i	$-0.422701\pi$
$211$	6.98585			0.480925			0.240463	+	0.970658i	$0.422701\pi$
$212$			9.49893i			0.652389i
$213$	−2.93443	+	2.93443i	−0.201064	+	0.201064i
$214$	1.23301	+	1.23301i	0.0842866	+	0.0842866i
$215$	9.50612	+	9.50612i	0.648312	+	0.648312i
$216$	−5.22004	−	5.22004i	−0.355179	−	0.355179i
$217$		0			0
$218$			1.25863i			0.0852451i
$219$	3.90799	−	3.90799i	0.264077	−	0.264077i
$220$	2.62560			0.177018
$221$	1.38444	+	18.6998i	0.0931274	+	1.25788i
$222$		−	2.35174i		−	0.157839i
$223$	19.4291	−	19.4291i	1.30107	−	1.30107i	0.373403	−	0.927669i	$-0.378191\pi$
$223$	19.4291	−	19.4291i	1.30107	−	1.30107i	0.927669	−	0.373403i	$-0.121809\pi$
$224$		0			0
$225$			4.61300i			0.307533i
$226$	1.43848	+	1.43848i	0.0956864	+	0.0956864i
$227$	0.0497885	−	0.0497885i	0.00330458	−	0.00330458i	−0.705453	−	0.708757i	$-0.749256\pi$
$227$	0.0497885	−	0.0497885i	0.00330458	−	0.00330458i	0.708757	+	0.705453i	$0.249256\pi$
$228$	2.53986	−	2.53986i	0.168206	−	0.168206i
$229$	−3.86548	−	3.86548i	−0.255438	−	0.255438i	0.567758	−	0.823196i	$-0.307811\pi$
$229$	−3.86548	−	3.86548i	−0.255438	−	0.255438i	−0.823196	+	0.567758i	$0.807811\pi$
$230$		−	1.18997i		−	0.0784643i
$231$		0			0
$232$	19.2374	−	19.2374i	1.26300	−	1.26300i
$233$		−	1.05440i		−	0.0690762i	−0.999403	−	0.0345381i	$-0.989004\pi$
$233$		−	1.05440i		−	0.0690762i	0.999403	−	0.0345381i	$-0.0109960\pi$
$234$	5.02675	−	5.83057i	0.328609	−	0.381156i
$235$	−4.11698			−0.268562
$236$	9.99992	−	9.99992i	0.650939	−	0.650939i
$237$			5.02955i			0.326705i
$238$		0			0
$239$	18.6963	+	18.6963i	1.20936	+	1.20936i	0.971234	+	0.238127i	$0.0765333\pi$
$239$	18.6963	+	18.6963i	1.20936	+	1.20936i	0.238127	+	0.971234i	$0.423467\pi$
$240$	0.485944	+	0.485944i	0.0313675	+	0.0313675i
$241$	−6.93020	−	6.93020i	−0.446413	−	0.446413i	0.447747	−	0.894160i	$-0.352227\pi$
$241$	−6.93020	−	6.93020i	−0.446413	−	0.446413i	−0.894160	+	0.447747i	$0.852227\pi$
$242$	−5.43635	+	5.43635i	−0.349462	+	0.349462i
$243$		−	11.7929i		−	0.756513i
$244$	−1.83310			−0.117352
$245$		0			0
$246$			0.0493945i			0.00314928i
$247$	14.3547	+	12.3757i	0.913369	+	0.787449i
$248$		−	15.5082i		−	0.984769i
$249$	2.03122	+	2.03122i	0.128723	+	0.128723i
$250$			9.40669i			0.594932i
$251$	−24.9249			−1.57325			−0.786623	−	0.617434i	$-0.788172\pi$
$251$	−24.9249			−1.57325			−0.786623	+	0.617434i	$0.788172\pi$
$252$		0			0
$253$	0.611943	+	0.611943i	0.0384726	+	0.0384726i
$254$	−6.45417	+	6.45417i	−0.404971	+	0.404971i
$255$	3.26906	+	3.26906i	0.204717	+	0.204717i
$256$	−13.2336			−0.827100
$257$	3.96236			0.247165			0.123583	−	0.992334i	$-0.460562\pi$
$257$	3.96236			0.247165			0.123583	+	0.992334i	$0.460562\pi$
$258$	1.96111	+	1.96111i	0.122093	+	0.122093i
$259$		0			0
$260$	−6.02662	+	6.99033i	−0.373755	+	0.433522i
$261$	28.5812			1.76913
$262$	−8.44133	+	8.44133i	−0.521507	+	0.521507i
$263$	−30.9269			−1.90703			−0.953516	−	0.301343i	$-0.902565\pi$
$263$	−30.9269			−1.90703			−0.953516	+	0.301343i	$0.902565\pi$
$264$	1.31396			0.0808684
$265$	−8.73832	+	8.73832i	−0.536791	+	0.536791i
$266$		0			0
$267$	2.67403	−	2.67403i	0.163648	−	0.163648i
$268$	4.27189	−	4.27189i	0.260947	−	0.260947i
$269$			11.0114i			0.671378i	0.941973	+	0.335689i	$0.108969\pi$
$269$			11.0114i			0.671378i	−0.941973	+	0.335689i	$0.891031\pi$
$270$		−	3.95915i		−	0.240946i
$271$	3.54185	+	3.54185i	0.215152	+	0.215152i	0.806452	−	0.591300i	$-0.201385\pi$
$271$	3.54185	+	3.54185i	0.215152	+	0.215152i	−0.591300	+	0.806452i	$0.701385\pi$
$272$	4.02037			0.243771
$273$		0			0
$274$	−0.792211			−0.0478592
$275$	−1.21102	−	1.21102i	−0.0730275	−	0.0730275i
$276$			0.576536i			0.0347034i
$277$			12.2075i			0.733476i	0.930324	+	0.366738i	$0.119525\pi$
$277$			12.2075i			0.733476i	−0.930324	+	0.366738i	$0.880475\pi$
$278$	−6.23139	+	6.23139i	−0.373734	+	0.373734i
$279$	11.5203	−	11.5203i	0.689702	−	0.689702i
$280$		0			0
$281$	−12.8351	+	12.8351i	−0.765677	+	0.765677i	−0.977342	−	0.211665i	$-0.932111\pi$
$281$	−12.8351	+	12.8351i	−0.765677	+	0.765677i	0.211665	+	0.977342i	$0.432111\pi$
$282$	−0.849330			−0.0505768
$283$	−16.8992			−1.00455			−0.502277	−	0.864707i	$-0.667504\pi$
$283$	−16.8992			−1.00455			−0.502277	+	0.864707i	$0.667504\pi$
$284$	−8.44981	+	8.44981i	−0.501404	+	0.501404i
$285$	4.67297			0.276803
$286$	0.211023	+	2.85031i	0.0124780	+	0.168542i
$287$		0			0
$288$	−11.4417	−	11.4417i	−0.674210	−	0.674210i
$289$	10.0460			0.590943
$290$	14.5906			0.856791
$291$	−1.21370	−	1.21370i	−0.0711484	−	0.0711484i
$292$	11.2532	−	11.2532i	0.658545	−	0.658545i
$293$	−11.1183	−	11.1183i	−0.649536	−	0.649536i	0.303345	−	0.952881i	$-0.401897\pi$
$293$	−11.1183	−	11.1183i	−0.649536	−	0.649536i	−0.952881	+	0.303345i	$0.901897\pi$
$294$		0			0
$295$	18.3984			1.07120
$296$		−	16.4274i		−	0.954822i
$297$	2.03600	+	2.03600i	0.118140	+	0.118140i
$298$		−	5.90314i		−	0.341960i
$299$	−3.03384	+	0.224610i	−0.175452	+	0.0129896i
$300$		−	1.14095i		−	0.0658730i
$301$		0			0
$302$	5.29441			0.304659
$303$			1.18555i			0.0681078i
$304$	2.87347	−	2.87347i	0.164805	−	0.164805i
$305$	−1.68632	−	1.68632i	−0.0965582	−	0.0965582i
$306$	−7.85163	−	7.85163i	−0.448848	−	0.448848i
$307$	−14.6604	−	14.6604i	−0.836715	−	0.836715i	0.151710	−	0.988425i	$-0.451522\pi$
$307$	−14.6604	−	14.6604i	−0.836715	−	0.836715i	−0.988425	+	0.151710i	$0.951522\pi$
$308$		0			0
$309$		−	1.33296i		−	0.0758296i
$310$	5.88109	−	5.88109i	0.334024	−	0.334024i
$311$	10.7063			0.607101			0.303550	−	0.952815i	$-0.401828\pi$
$311$	10.7063			0.607101			0.303550	+	0.952815i	$0.401828\pi$
$312$	−3.01597	+	3.49825i	−0.170746	+	0.198049i
$313$			10.7494i			0.607590i	0.952737	+	0.303795i	$0.0982538\pi$
$313$			10.7494i			0.607590i	−0.952737	+	0.303795i	$0.901746\pi$
$314$	7.02088	−	7.02088i	0.396211	−	0.396211i
$315$		0			0
$316$			14.4828i			0.814722i
$317$	8.29001	+	8.29001i	0.465613	+	0.465613i	0.900490	−	0.434877i	$-0.143208\pi$
$317$	8.29001	+	8.29001i	0.465613	+	0.465613i	−0.434877	+	0.900490i	$0.643208\pi$
$318$	−1.80271	+	1.80271i	−0.101091	+	0.101091i
$319$	−7.50325	+	7.50325i	−0.420101	+	0.420101i
$320$	−3.84586	−	3.84586i	−0.214990	−	0.214990i
$321$		−	1.09910i		−	0.0613460i
$322$		0			0
$323$	19.3305	−	19.3305i	1.07558	−	1.07558i
$324$		−	9.70770i		−	0.539316i
$325$	6.00391	−	0.444499i	0.333037	−	0.0246564i
$326$	−0.758619			−0.0420160
$327$	0.560972	−	0.560972i	0.0310218	−	0.0310218i
$328$			0.345031i			0.0190511i
$329$		0			0
$330$	0.498286	+	0.498286i	0.0274297	+	0.0274297i
$331$	−19.1719	−	19.1719i	−1.05378	−	1.05378i	−0.998469	−	0.0553146i	$-0.982384\pi$
$331$	−19.1719	−	19.1719i	−1.05378	−	1.05378i	−0.0553146	−	0.998469i	$-0.517616\pi$
$332$	5.84898	+	5.84898i	0.321005	+	0.321005i
$333$	12.2032	−	12.2032i	0.668729	−	0.668729i
$334$			10.1113i			0.553263i
$335$	7.85966			0.429419
$336$		0			0
$337$		−	20.5911i		−	1.12167i	−0.827927	−	0.560835i	$-0.810480\pi$
$337$		−	20.5911i		−	1.12167i	0.827927	−	0.560835i	$-0.189520\pi$
$338$	−8.07297	−	5.98059i	−0.439112	−	0.325301i
$339$		−	1.28227i		−	0.0696431i
$340$	9.41340	+	9.41340i	0.510513	+	0.510513i
$341$			6.04871i			0.327556i
$342$	−11.2235			−0.606899
$343$		0			0
$344$	13.6987	+	13.6987i	0.738585	+	0.738585i
$345$	−0.530371	+	0.530371i	−0.0285542	+	0.0285542i
$346$	−12.0838	−	12.0838i	−0.649630	−	0.649630i
$347$	14.9791			0.804122			0.402061	−	0.915613i	$-0.368294\pi$
$347$	14.9791			0.804122			0.402061	+	0.915613i	$0.368294\pi$
$348$	−7.06910			−0.378944
$349$	−3.25693	−	3.25693i	−0.174340	−	0.174340i	0.614543	−	0.788883i	$-0.289340\pi$
$349$	−3.25693	−	3.25693i	−0.174340	−	0.174340i	−0.788883	+	0.614543i	$0.789340\pi$
$350$		0			0
$351$	−10.0939	+	0.747300i	−0.538772	+	0.0398879i
$352$	6.00746			0.320198
$353$	−3.94222	+	3.94222i	−0.209823	+	0.209823i	−0.804192	−	0.594369i	$-0.797402\pi$
$353$	−3.94222	+	3.94222i	−0.209823	+	0.209823i	0.594369	+	0.804192i	$0.297402\pi$
$354$	3.79557			0.201732
$355$	−15.5464			−0.825118
$356$	7.70000	−	7.70000i	0.408099	−	0.408099i
$357$		0			0
$358$	−4.41035	+	4.41035i	−0.233094	+	0.233094i
$359$	3.55021	−	3.55021i	0.187373	−	0.187373i	−0.607186	−	0.794559i	$-0.707702\pi$
$359$	3.55021	−	3.55021i	0.187373	−	0.187373i	0.794559	+	0.607186i	$0.207702\pi$
$360$		−	13.2583i		−	0.698774i
$361$		−	8.63206i		−	0.454319i
$362$	11.2368	+	11.2368i	0.590595	+	0.590595i
$363$	4.84597			0.254348
$364$		0			0
$365$	20.7043			1.08371
$366$	−0.347886	−	0.347886i	−0.0181843	−	0.0181843i
$367$			3.07383i			0.160452i	0.996777	+	0.0802262i	$0.0255643\pi$
$367$			3.07383i			0.160452i	−0.996777	+	0.0802262i	$0.974436\pi$
$368$			0.652263i			0.0340015i
$369$	−0.256307	+	0.256307i	−0.0133428	+	0.0133428i
$370$	6.22969	−	6.22969i	0.323866	−	0.323866i
$371$		0			0
$372$	−2.84937	+	2.84937i	−0.147733	+	0.147733i
$373$	23.3509			1.20906			0.604532	−	0.796581i	$-0.293360\pi$
$373$	23.3509			1.20906			0.604532	+	0.796581i	$0.293360\pi$
$374$	4.12248			0.213169
$375$	4.19257	−	4.19257i	0.216503	−	0.216503i
$376$	−5.93273			−0.305957
$377$	−2.75402	−	37.1989i	−0.141839	−	1.91584i
$378$		0			0
$379$	−1.97284	−	1.97284i	−0.101338	−	0.101338i	0.654620	−	0.755958i	$-0.272829\pi$
$379$	−1.97284	−	1.97284i	−0.101338	−	0.101338i	−0.755958	+	0.654620i	$0.772829\pi$
$380$	13.4560			0.690279
$381$	5.75326			0.294748
$382$	−7.56228	−	7.56228i	−0.386920	−	0.386920i
$383$	2.18952	−	2.18952i	0.111879	−	0.111879i	−0.648951	−	0.760830i	$-0.724792\pi$
$383$	2.18952	−	2.18952i	0.111879	−	0.111879i	0.760830	+	0.648951i	$0.224792\pi$
$384$	3.24152	+	3.24152i	0.165418	+	0.165418i
$385$		0			0
$386$	18.8625			0.960074
$387$			20.3523i			1.03457i
$388$	−3.49490	−	3.49490i	−0.177427	−	0.177427i
$389$			11.0113i			0.558295i	0.960248	+	0.279148i	$0.0900519\pi$
$389$			11.0113i			0.558295i	−0.960248	+	0.279148i	$0.909948\pi$
$390$	−2.47036	+	0.182893i	−0.125092	+	0.00926115i
$391$			4.38793i			0.221907i
$392$		0			0
$393$	7.52462			0.379567
$394$		−	15.6757i		−	0.789729i
$395$	−13.3231	+	13.3231i	−0.670359	+	0.670359i
$396$	2.81066	+	2.81066i	0.141241	+	0.141241i
$397$	−27.0816	−	27.0816i	−1.35918	−	1.35918i	−0.874923	−	0.484262i	$-0.839088\pi$
$397$	−27.0816	−	27.0816i	−1.35918	−	1.35918i	−0.484262	−	0.874923i	$-0.660912\pi$
$398$	8.09666	+	8.09666i	0.405849	+	0.405849i
$399$		0			0
$400$		−	1.29081i		−	0.0645407i
$401$	−4.75621	+	4.75621i	−0.237514	+	0.237514i	−0.815820	−	0.578306i	$-0.803714\pi$
$401$	−4.75621	+	4.75621i	−0.237514	+	0.237514i	0.578306	+	0.815820i	$0.303714\pi$
$402$	1.62144			0.0808701
$403$	−16.1040	−	13.8838i	−0.802196	−	0.691603i
$404$			3.41383i			0.169844i
$405$	8.93036	−	8.93036i	0.443753	−	0.443753i
$406$		0			0
$407$			6.40725i			0.317595i
$408$	4.71085	+	4.71085i	0.233222	+	0.233222i
$409$	24.0696	−	24.0696i	1.19017	−	1.19017i	0.213146	−	0.977020i	$-0.431629\pi$
$409$	24.0696	−	24.0696i	1.19017	−	1.19017i	0.977020	−	0.213146i	$-0.0683710\pi$
$410$	−0.130844	+	0.130844i	−0.00646195	+	0.00646195i
$411$	0.353089	+	0.353089i	0.0174166	+	0.0174166i
$412$		−	3.83832i		−	0.189101i
$413$		0			0
$414$	1.27384	−	1.27384i	0.0626060	−	0.0626060i
$415$			10.7613i			0.528250i
$416$	−13.7891	+	15.9941i	−0.676067	+	0.784177i
$417$	5.55467			0.272013
$418$	2.94645	−	2.94645i	0.144116	−	0.144116i
$419$			35.5515i			1.73680i	0.495862	+	0.868401i	$0.334852\pi$
$419$			35.5515i			1.73680i	−0.495862	+	0.868401i	$0.665148\pi$
$420$		0			0
$421$	−10.3166	−	10.3166i	−0.502802	−	0.502802i	0.409505	−	0.912308i	$-0.365701\pi$
$421$	−10.3166	−	10.3166i	−0.502802	−	0.502802i	−0.912308	+	0.409505i	$0.865701\pi$
$422$	3.81762	+	3.81762i	0.185839	+	0.185839i
$423$	−4.40716	−	4.40716i	−0.214283	−	0.214283i
$424$	−12.5923	+	12.5923i	−0.611535	+	0.611535i
$425$		−	8.68363i		−	0.421218i
$426$	−3.20721			−0.155390
$427$		0			0
$428$		−	3.16492i		−	0.152982i
$429$	1.17633	−	1.36444i	0.0567939	−	0.0658757i
$430$			10.3898i			0.501041i
$431$	−25.2499	−	25.2499i	−1.21624	−	1.21624i	−0.968937	−	0.247307i	$-0.920454\pi$
$431$	−25.2499	−	25.2499i	−1.21624	−	1.21624i	−0.247307	−	0.968937i	$-0.579546\pi$
$432$			2.17014i			0.104411i
$433$	−18.6845			−0.897919			−0.448959	−	0.893552i	$-0.648205\pi$
$433$	−18.6845			−0.897919			−0.448959	+	0.893552i	$0.648205\pi$
$434$		0			0
$435$	−6.50305	−	6.50305i	−0.311798	−	0.311798i
$436$	1.61534	−	1.61534i	0.0773608	−	0.0773608i
$437$	3.13617	+	3.13617i	0.150023	+	0.150023i
$438$	4.27127			0.204089
$439$	23.8317			1.13742			0.568712	−	0.822537i	$-0.307442\pi$
$439$	23.8317			1.13742			0.568712	+	0.822537i	$0.307442\pi$
$440$	3.48063	+	3.48063i	0.165932	+	0.165932i
$441$		0			0
$442$	−9.46248	+	10.9756i	−0.450084	+	0.522057i
$443$	−23.3815			−1.11089			−0.555445	−	0.831553i	$-0.687452\pi$
$443$	−23.3815			−1.11089			−0.555445	+	0.831553i	$0.687452\pi$
$444$	−3.01826	+	3.01826i	−0.143240	+	0.143240i
$445$	14.1669			0.671573
$446$	21.2353			1.00552
$447$	−2.63104	+	2.63104i	−0.124444	+	0.124444i
$448$		0			0
$449$	−17.6188	+	17.6188i	−0.831482	+	0.831482i	−0.987720	−	0.156237i	$-0.950063\pi$
$449$	−17.6188	+	17.6188i	−0.831482	+	0.831482i	0.156237	+	0.987720i	$0.450063\pi$
$450$	−2.52091	+	2.52091i	−0.118837	+	0.118837i
$451$		−	0.134574i		−	0.00633683i
$452$		−	3.69234i		−	0.173673i
$453$	−2.35972	−	2.35972i	−0.110869	−	0.110869i
$454$	0.0544168			0.00255391
$455$		0			0
$456$	6.73394			0.315346
$457$	2.86848	+	2.86848i	0.134182	+	0.134182i	0.771008	−	0.636826i	$-0.219753\pi$
$457$	2.86848	+	2.86848i	0.134182	+	0.134182i	−0.636826	+	0.771008i	$0.719753\pi$
$458$		−	4.22481i		−	0.197412i
$459$			14.5991i			0.681427i
$460$	−1.52722	+	1.52722i	−0.0712072	+	0.0712072i
$461$	−7.54874	+	7.54874i	−0.351580	+	0.351580i	−0.860697	−	0.509117i	$-0.829972\pi$
$461$	−7.54874	+	7.54874i	−0.351580	+	0.351580i	0.509117	+	0.860697i	$0.329972\pi$
$462$		0			0
$463$	13.5419	−	13.5419i	0.629344	−	0.629344i	−0.318559	−	0.947903i	$-0.603199\pi$
$463$	13.5419	−	13.5419i	0.629344	−	0.629344i	0.947903	+	0.318559i	$0.103199\pi$
$464$	−7.99761			−0.371280
$465$	−5.24241			−0.243111
$466$	0.576209	−	0.576209i	0.0266924	−	0.0266924i
$467$	36.1267			1.67175			0.835873	−	0.548923i	$-0.184962\pi$
$467$	36.1267			1.67175			0.835873	+	0.548923i	$0.184962\pi$
$468$	−13.9344	+	1.03164i	−0.644120	+	0.0476874i
$469$		0			0
$470$	−2.24985	−	2.24985i	−0.103778	−	0.103778i
$471$	−6.25842			−0.288373
$472$	26.5128			1.22035
$473$	−5.34297	−	5.34297i	−0.245670	−	0.245670i
$474$	−2.74855	+	2.74855i	−0.126245	+	0.126245i
$475$	−6.20642	−	6.20642i	−0.284770	−	0.284770i
$476$		0			0
$477$	−18.7085			−0.856601
$478$			20.4343i			0.934641i
$479$	−23.3427	−	23.3427i	−1.06656	−	1.06656i	−0.997621	−	0.0689350i	$-0.978040\pi$
$479$	−23.3427	−	23.3427i	−1.06656	−	1.06656i	−0.0689350	−	0.997621i	$-0.521960\pi$
$480$			5.20666i			0.237650i
$481$	−17.0585	−	14.7068i	−0.777802	−	0.670571i
$482$		−	7.57443i		−	0.345006i
$483$		0			0
$484$	13.9542			0.634281
$485$		−	6.43011i		−	0.291976i
$486$	6.44456	−	6.44456i	0.292331	−	0.292331i
$487$	−4.37289	−	4.37289i	−0.198155	−	0.198155i	0.601054	−	0.799209i	$-0.294748\pi$
$487$	−4.37289	−	4.37289i	−0.198155	−	0.198155i	−0.799209	+	0.601054i	$0.794748\pi$
$488$	−2.43005	−	2.43005i	−0.110003	−	0.110003i
$489$	0.338117	+	0.338117i	0.0152902	+	0.0152902i
$490$		0			0
$491$		−	33.4149i		−	1.50799i	−0.656879	−	0.753996i	$-0.728124\pi$
$491$		−	33.4149i		−	1.50799i	0.656879	−	0.753996i	$-0.271876\pi$
$492$	0.0633936	−	0.0633936i	0.00285801	−	0.00285801i
$493$	−53.8019			−2.42312
$494$	1.08148	+	14.6077i	0.0486580	+	0.657229i
$495$			5.17120i			0.232428i
$496$	−3.22362	+	3.22362i	−0.144745	+	0.144745i
$497$		0			0
$498$			2.22004i			0.0994824i
$499$	−10.5085	−	10.5085i	−0.470427	−	0.470427i	0.431626	−	0.902053i	$-0.357940\pi$
$499$	−10.5085	−	10.5085i	−0.470427	−	0.470427i	−0.902053	+	0.431626i	$0.857940\pi$
$500$	12.0727	−	12.0727i	0.539907	−	0.539907i
$501$	4.50659	−	4.50659i	0.201340	−	0.201340i
$502$	−13.6210	−	13.6210i	−0.607933	−	0.607933i
$503$			24.9299i			1.11157i	0.831327	+	0.555784i	$0.187582\pi$
$503$			24.9299i			1.11157i	−0.831327	+	0.555784i	$0.812418\pi$
$504$		0			0
$505$	−3.14047	+	3.14047i	−0.139749	+	0.139749i
$506$			0.668829i			0.0297331i
$507$	0.932575	+	6.26369i	0.0414171	+	0.278180i
$508$	16.5667			0.735030
$509$	1.34716	−	1.34716i	0.0597116	−	0.0597116i	−0.676620	−	0.736332i	$-0.736556\pi$
$509$	1.34716	−	1.34716i	0.0597116	−	0.0597116i	0.736332	+	0.676620i	$0.236556\pi$
$510$			3.57295i			0.158213i
$511$		0			0
$512$	6.07668	+	6.07668i	0.268554	+	0.268554i
$513$	10.4343	+	10.4343i	0.460688	+	0.460688i
$514$	2.16535	+	2.16535i	0.0955094	+	0.0955094i
$515$	3.53098	−	3.53098i	0.155593	−	0.155593i
$516$		−	5.03382i		−	0.221602i
$517$	2.31397			0.101768
$518$		0			0
$519$			10.7715i			0.472818i
$520$	−17.2560	+	1.27754i	−0.756724	+	0.0560240i
$521$			10.8700i			0.476222i	0.971238	+	0.238111i	$0.0765283\pi$
$521$			10.8700i			0.476222i	−0.971238	+	0.238111i	$0.923472\pi$
$522$	15.6190	+	15.6190i	0.683626	+	0.683626i
$523$			23.3792i			1.02230i	0.859491	+	0.511151i	$0.170781\pi$
$523$			23.3792i			1.02230i	−0.859491	+	0.511151i	$0.829219\pi$
$524$	21.6675			0.946547
$525$		0			0
$526$	−16.9009	−	16.9009i	−0.736914	−	0.736914i
$527$	−21.6861	+	21.6861i	−0.944662	+	0.944662i
$528$	−0.273127	−	0.273127i	−0.0118863	−	0.0118863i
$529$	22.2881			0.969048
$530$	−9.55063			−0.414853
$531$	19.6952	+	19.6952i	0.854697	+	0.854697i
$532$		0			0
$533$	0.358286	+	0.308892i	0.0155191	+	0.0133796i
$534$	2.92261			0.126474
$535$	2.91149	−	2.91149i	0.125875	−	0.125875i
$536$	11.3261			0.489212
$537$	3.93139			0.169652
$538$	−6.01752	+	6.01752i	−0.259434	+	0.259434i
$539$		0			0
$540$	−5.08123	+	5.08123i	−0.218661	+	0.218661i
$541$	−4.80784	+	4.80784i	−0.206705	+	0.206705i	−0.802865	−	0.596160i	$-0.796692\pi$
$541$	−4.80784	+	4.80784i	−0.206705	+	0.206705i	0.596160	+	0.802865i	$0.296692\pi$
$542$			3.87110i			0.166278i
$543$		−	10.0165i		−	0.429850i
$544$	21.5382	+	21.5382i	0.923442	+	0.923442i
$545$	2.97199			0.127306
$546$		0			0
$547$	−14.2303			−0.608446			−0.304223	−	0.952601i	$-0.598397\pi$
$547$	−14.2303			−0.608446			−0.304223	+	0.952601i	$0.598397\pi$
$548$	1.01673	+	1.01673i	0.0434328	+	0.0434328i
$549$		−	3.61035i		−	0.154086i
$550$		−	1.32360i		−	0.0564385i
$551$	−38.4537	+	38.4537i	−1.63818	+	1.63818i
$552$	−0.764286	+	0.764286i	−0.0325302	+	0.0325302i
$553$		0			0
$554$	−6.67114	+	6.67114i	−0.283429	+	0.283429i
$555$	−5.55315			−0.235718
$556$	15.9949			0.678335
$557$	5.73436	−	5.73436i	0.242973	−	0.242973i	−0.575106	−	0.818079i	$-0.695039\pi$
$557$	5.73436	−	5.73436i	0.242973	−	0.242973i	0.818079	+	0.575106i	$0.195039\pi$
$558$	12.5912			0.533029
$559$	26.4889	−	1.96111i	1.12036	−	0.0829459i
$560$		0			0
$561$	−1.83739	−	1.83739i	−0.0775749	−	0.0775749i
$562$	−14.0282			−0.591745
$563$	−35.5046			−1.49634			−0.748170	−	0.663507i	$-0.769067\pi$
$563$	−35.5046			−1.49634			−0.748170	+	0.663507i	$0.769067\pi$
$564$	1.09004	+	1.09004i	0.0458990	+	0.0458990i
$565$	3.39668	−	3.39668i	0.142899	−	0.142899i
$566$	−9.23508	−	9.23508i	−0.388179	−	0.388179i
$567$		0			0
$568$	−22.4030			−0.940009
$569$		−	31.7463i		−	1.33087i	−0.746454	−	0.665437i	$-0.768245\pi$
$569$		−	31.7463i		−	1.33087i	0.746454	−	0.665437i	$-0.231755\pi$
$570$	2.55368	+	2.55368i	0.106962	+	0.106962i
$571$			8.26604i			0.345923i	0.984929	+	0.172961i	$0.0553336\pi$
$571$			8.26604i			0.345923i	−0.984929	+	0.172961i	$0.944666\pi$
$572$	3.38730	−	3.92896i	0.141630	−	0.164278i
$573$			6.74103i			0.281611i
$574$		0			0
$575$	1.40883			0.0587521
$576$		−	8.23386i		−	0.343077i
$577$	2.38091	−	2.38091i	0.0991186	−	0.0991186i	−0.655809	−	0.754927i	$-0.727672\pi$
$577$	2.38091	−	2.38091i	0.0991186	−	0.0991186i	0.754927	+	0.655809i	$0.227672\pi$
$578$	5.48996	+	5.48996i	0.228352	+	0.228352i
$579$	−8.40702	−	8.40702i	−0.349384	−	0.349384i
$580$	−18.7258	−	18.7258i	−0.777547	−	0.777547i
$581$		0			0
$582$		−	1.32653i		−	0.0549863i
$583$	4.91142	−	4.91142i	0.203410	−	0.203410i
$584$	29.8357			1.23461
$585$	−13.7677	−	11.8696i	−0.569224	−	0.490749i
$586$		−	12.1518i		−	0.501987i
$587$	−3.33097	+	3.33097i	−0.137484	+	0.137484i	−0.772499	−	0.635016i	$-0.780994\pi$
$587$	−3.33097	+	3.33097i	−0.137484	+	0.137484i	0.635016	+	0.772499i	$0.280994\pi$
$588$		0			0
$589$			30.9993i			1.27730i
$590$	10.0543	+	10.0543i	0.413931	+	0.413931i
$591$	−6.98666	+	6.98666i	−0.287393	+	0.287393i
$592$	−3.41470	+	3.41470i	−0.140343	+	0.140343i
$593$	−10.6290	−	10.6290i	−0.436480	−	0.436480i	0.454345	−	0.890826i	$-0.349873\pi$
$593$	−10.6290	−	10.6290i	−0.436480	−	0.436480i	−0.890826	+	0.454345i	$0.849873\pi$
$594$			2.22526i			0.0913035i
$595$		0			0
$596$	−7.57618	+	7.57618i	−0.310332	+	0.310332i
$597$		−	7.21737i		−	0.295387i
$598$	−1.78068	−	1.53519i	−0.0728173	−	0.0627785i
$599$	7.27545			0.297267			0.148633	−	0.988892i	$-0.452513\pi$
$599$	7.27545			0.297267			0.148633	+	0.988892i	$0.452513\pi$
$600$	1.51251	−	1.51251i	0.0617478	−	0.0617478i
$601$		−	2.83288i		−	0.115555i	−0.998329	−	0.0577777i	$-0.981599\pi$
$601$		−	2.83288i		−	0.115555i	0.998329	−	0.0577777i	$-0.0184015\pi$
$602$		0			0
$603$	8.41363	+	8.41363i	0.342630	+	0.342630i
$604$	−6.79492	−	6.79492i	−0.276481	−	0.276481i
$605$	12.8368	+	12.8368i	0.521891	+	0.521891i
$606$	−0.647877	+	0.647877i	−0.0263182	+	0.0263182i
$607$			27.5502i			1.11823i	0.829091	+	0.559114i	$0.188859\pi$
$607$			27.5502i			1.11823i	−0.829091	+	0.559114i	$0.811141\pi$
$608$	30.7878			1.24861
$609$		0			0
$610$		−	1.84308i		−	0.0746239i
$611$	−5.31134	+	6.16067i	−0.214874	+	0.249234i
$612$			20.1538i			0.814669i
$613$	−17.3792	−	17.3792i	−0.701941	−	0.701941i	0.262886	−	0.964827i	$-0.415326\pi$
$613$	−17.3792	−	17.3792i	−0.701941	−	0.701941i	−0.964827	+	0.262886i	$0.915326\pi$
$614$		−	16.0233i		−	0.646646i
$615$	0.116635			0.00470318
$616$		0			0
$617$	−10.3106	−	10.3106i	−0.415090	−	0.415090i	0.468417	−	0.883507i	$-0.344824\pi$
$617$	−10.3106	−	10.3106i	−0.415090	−	0.415090i	−0.883507	+	0.468417i	$0.844824\pi$
$618$	0.728438	−	0.728438i	0.0293021	−	0.0293021i
$619$	21.4347	+	21.4347i	0.861532	+	0.861532i	0.991516	−	0.129984i	$-0.0414925\pi$
$619$	21.4347	+	21.4347i	0.861532	+	0.861532i	−0.129984	+	0.991516i	$0.541492\pi$
$620$	−15.0958			−0.606260
$621$	−2.36855			−0.0950465
$622$	5.85080	+	5.85080i	0.234596	+	0.234596i
$623$		0			0
$624$	1.35409	−	0.100250i	0.0542069	−	0.00401320i
$625$	13.8633			0.554530
$626$	−5.87431	+	5.87431i	−0.234785	+	0.234785i
$627$	−2.62647			−0.104891
$628$	−18.0214			−0.719132
$629$	−22.9715	+	22.9715i	−0.915935	+	0.915935i
$630$		0			0
$631$	−9.56348	+	9.56348i	−0.380716	+	0.380716i	−0.871360	−	0.490644i	$-0.836762\pi$
$631$	−9.56348	+	9.56348i	−0.380716	+	0.380716i	0.490644	+	0.871360i	$0.336762\pi$
$632$	−19.1992	+	19.1992i	−0.763701	+	0.763701i
$633$		−	3.40304i		−	0.135259i
$634$			9.06065i			0.359844i
$635$	15.2402	+	15.2402i	0.604788	+	0.604788i
$636$	4.62724			0.183482
$637$		0			0
$638$	−8.20074			−0.324671
$639$	−16.6422	−	16.6422i	−0.658354	−	0.658354i
$640$			17.1734i			0.678837i
$641$		−	27.3055i		−	1.07850i	−0.842145	−	0.539251i	$-0.818708\pi$
$641$		−	27.3055i		−	1.07850i	0.842145	−	0.539251i	$-0.181292\pi$
$642$	0.600638	−	0.600638i	0.0237053	−	0.0237053i
$643$	−17.4331	+	17.4331i	−0.687495	+	0.687495i	−0.961678	−	0.274183i	$-0.911593\pi$
$643$	−17.4331	+	17.4331i	−0.687495	+	0.687495i	0.274183	+	0.961678i	$0.411593\pi$
$644$		0			0
$645$	4.63075	−	4.63075i	0.182335	−	0.182335i
$646$	21.1275			0.831249
$647$	19.2142			0.755386			0.377693	−	0.925931i	$-0.376717\pi$
$647$	19.2142			0.755386			0.377693	+	0.925931i	$0.376717\pi$
$648$	12.8690	−	12.8690i	0.505543	−	0.505543i
$649$	−10.3409			−0.405916
$650$	3.52392	+	3.03810i	0.138220	+	0.119164i
$651$		0			0
$652$	0.973622	+	0.973622i	0.0381300	+	0.0381300i
$653$	−18.1628			−0.710765			−0.355383	−	0.934721i	$-0.615649\pi$
$653$	−18.1628			−0.710765			−0.355383	+	0.934721i	$0.615649\pi$
$654$	0.613119			0.0239749
$655$	19.9325	+	19.9325i	0.778826	+	0.778826i
$656$	0.0717202	−	0.0717202i	0.00280020	−	0.00280020i
$657$	22.1636	+	22.1636i	0.864683	+	0.864683i
$658$		0			0
$659$	−36.6851			−1.42905			−0.714525	−	0.699610i	$-0.753357\pi$
$659$	−36.6851			−1.42905			−0.714525	+	0.699610i	$0.753357\pi$
$660$		−	1.27901i		−	0.0497856i
$661$	−1.78106	−	1.78106i	−0.0692752	−	0.0692752i	0.671620	−	0.740895i	$-0.265599\pi$
$661$	−1.78106	−	1.78106i	−0.0692752	−	0.0692752i	−0.740895	+	0.671620i	$0.765599\pi$
$662$		−	20.9541i		−	0.814405i
$663$	9.10928	−	0.674405i	0.353775	−	0.0261917i
$664$			15.5074i			0.601805i
$665$		0			0
$666$	13.3376			0.516820
$667$		−	8.72879i		−	0.337980i
$668$	12.9769	−	12.9769i	0.502092	−	0.502092i
$669$	−9.46458	−	9.46458i	−0.365922	−	0.365922i
$670$	4.29514	+	4.29514i	0.165936	+	0.165936i
$671$	0.947803	+	0.947803i	0.0365895	+	0.0365895i
$672$		0			0
$673$		−	3.52257i		−	0.135785i	−0.997693	−	0.0678925i	$-0.978373\pi$
$673$		−	3.52257i		−	0.135785i	0.997693	−	0.0678925i	$-0.0216275\pi$
$674$	11.2526	−	11.2526i	0.433436	−	0.433436i
$675$	4.68730			0.180414
$676$	2.68539	+	18.0365i	0.103284	+	0.693713i
$677$		−	21.2972i		−	0.818518i	−0.912418	−	0.409259i	$-0.865787\pi$
$677$		−	21.2972i		−	0.818518i	0.912418	−	0.409259i	$-0.134213\pi$
$678$	0.700732	−	0.700732i	0.0269115	−	0.0269115i
$679$		0			0
$680$			24.9578i			0.957087i
$681$	−0.0242536	−	0.0242536i	−0.000929400	−	0.000929400i
$682$	−3.30550	+	3.30550i	−0.126574	+	0.126574i
$683$	1.42970	−	1.42970i	0.0547060	−	0.0547060i	−0.679225	−	0.733931i	$-0.737684\pi$
$683$	1.42970	−	1.42970i	0.0547060	−	0.0547060i	0.733931	+	0.679225i	$0.237684\pi$
$684$	14.4044	+	14.4044i	0.550768	+	0.550768i
$685$			1.87064i			0.0714736i
$686$		0			0
$687$	−1.88300	+	1.88300i	−0.0718410	+	0.0718410i
$688$		−	5.69500i		−	0.217120i
$689$	1.80271	+	24.3494i	0.0686777	+	0.927639i
$690$	−0.579674			−0.0220678
$691$	−0.899585	+	0.899585i	−0.0342218	+	0.0342218i	−0.724011	−	0.689789i	$-0.757703\pi$
$691$	−0.899585	+	0.899585i	−0.0342218	+	0.0342218i	0.689789	+	0.724011i	$0.257703\pi$
$692$			31.0171i			1.17909i
$693$		0			0
$694$	8.18579	+	8.18579i	0.310728	+	0.310728i
$695$	14.7141	+	14.7141i	0.558139	+	0.558139i
$696$	−9.37117	−	9.37117i	−0.355213	−	0.355213i
$697$	0.482480	−	0.482480i	0.0182752	−	0.0182752i
$698$		−	3.55970i		−	0.134737i
$699$	−0.513634			−0.0194274
$700$		0			0
$701$		−	2.12113i		−	0.0801138i	−0.999197	−	0.0400569i	$-0.987246\pi$
$701$		−	2.12113i		−	0.0801138i	0.999197	−	0.0400569i	$-0.0127539\pi$
$702$	−5.92449	−	5.10772i	−0.223605	−	0.192778i
$703$			32.8367i			1.23846i
$704$	2.16159	+	2.16159i	0.0814679	+	0.0814679i
$705$			2.00552i			0.0755321i
$706$	−4.30869			−0.162160
$707$		0			0
$708$	−4.87129	−	4.87129i	−0.183074	−	0.183074i
$709$	−0.990630	+	0.990630i	−0.0372039	+	0.0372039i	−0.725464	−	0.688260i	$-0.758375\pi$
$709$	−0.990630	+	0.990630i	−0.0372039	+	0.0372039i	0.688260	+	0.725464i	$0.258375\pi$
$710$	−8.49580	−	8.49580i	−0.318842	−	0.318842i
$711$	−28.5244			−1.06975
$712$	20.4150			0.765085
$713$	−3.51834	−	3.51834i	−0.131763	−	0.131763i
$714$		0			0
$715$	6.73041	−	0.498286i	0.251703	−	0.0186348i
$716$	11.3206			0.423071
$717$	9.10757	−	9.10757i	0.340128	−	0.340128i
$718$	3.88024			0.144809
$719$	−33.0502			−1.23256			−0.616281	−	0.787526i	$-0.711362\pi$
$719$	−33.0502			−1.23256			−0.616281	+	0.787526i	$0.711362\pi$
$720$	−2.75596	+	2.75596i	−0.102708	+	0.102708i
$721$		0			0
$722$	4.71725	−	4.71725i	0.175558	−	0.175558i
$723$	−3.37593	+	3.37593i	−0.125552	+	0.125552i
$724$		−	28.8430i		−	1.07194i
$725$			17.2741i			0.641544i
$726$	2.64823	+	2.64823i	0.0982849	+	0.0982849i
$727$	−33.8896			−1.25689			−0.628447	−	0.777852i	$-0.716309\pi$
$727$	−33.8896			−1.25689			−0.628447	+	0.777852i	$0.716309\pi$
$728$		0			0
$729$	15.0172			0.556192
$730$	11.3145	+	11.3145i	0.418767	+	0.418767i
$731$		−	38.3117i		−	1.41701i
$732$			0.892963i			0.0330049i
$733$	27.8480	−	27.8480i	1.02859	−	1.02859i	0.0290099	−	0.999579i	$-0.490765\pi$
$733$	27.8480	−	27.8480i	1.02859	−	1.02859i	0.999579	−	0.0290099i	$-0.00923543\pi$
$734$	−1.67978	+	1.67978i	−0.0620020	+	0.0620020i
$735$		0			0
$736$	−3.49434	+	3.49434i	−0.128803	+	0.128803i
$737$	−4.41756			−0.162723
$738$	−0.280134			−0.0103119
$739$	−26.6484	+	26.6484i	−0.980277	+	0.980277i	−0.999809	−	0.0195327i	$-0.993782\pi$
$739$	−26.6484	+	26.6484i	−0.980277	+	0.980277i	0.0195327	+	0.999809i	$0.493782\pi$
$740$	−15.9905			−0.587824
$741$	6.02863	−	6.99266i	0.221467	−	0.256882i
$742$		0			0
$743$	−31.2340	−	31.2340i	−1.14587	−	1.14587i	−0.987358	−	0.158508i	$-0.949332\pi$
$743$	−31.2340	−	31.2340i	−1.14587	−	1.14587i	−0.158508	−	0.987358i	$-0.550668\pi$
$744$	−7.55453			−0.276963
$745$	−13.9390			−0.510687
$746$	12.7608	+	12.7608i	0.467206	+	0.467206i
$747$	−11.5198	+	11.5198i	−0.421486	+	0.421486i
$748$	−5.29086	−	5.29086i	−0.193453	−	0.193453i
$749$		0			0
$750$	4.58231			0.167322
$751$			18.0891i			0.660080i	0.943967	+	0.330040i	$0.107062\pi$
$751$			18.0891i			0.660080i	−0.943967	+	0.330040i	$0.892938\pi$
$752$	1.23322	+	1.23322i	0.0449708	+	0.0449708i
$753$			12.1417i			0.442470i
$754$	18.8235	−	21.8335i	0.685510	−	0.795129i
$755$		−	12.5017i		−	0.454982i
$756$		0			0
$757$	4.04733			0.147103			0.0735514	−	0.997291i	$-0.476567\pi$
$757$	4.04733			0.147103			0.0735514	+	0.997291i	$0.476567\pi$
$758$		−	2.15623i		−	0.0783180i
$759$	0.298098	−	0.298098i	0.0108203	−	0.0108203i
$760$	17.8380	+	17.8380i	0.647052	+	0.647052i
$761$	27.1193	+	27.1193i	0.983073	+	0.983073i	0.999859	−	0.0167862i	$-0.00534346\pi$
$761$	27.1193	+	27.1193i	0.983073	+	0.983073i	−0.0167862	+	0.999859i	$0.505343\pi$
$762$	3.14404	+	3.14404i	0.113897	+	0.113897i
$763$		0			0
$764$			19.4111i			0.702268i
$765$	−18.5400	+	18.5400i	−0.670315	+	0.670315i
$766$	2.39305			0.0864645
$767$	23.7359	−	27.5314i	0.857052	−	0.994102i
$768$			6.44652i			0.232619i
$769$	24.8051	−	24.8051i	0.894496	−	0.894496i	−0.100446	−	0.994942i	$-0.532027\pi$
$769$	24.8051	−	24.8051i	0.894496	−	0.894496i	0.994942	+	0.100446i	$0.0320271\pi$
$770$		0			0
$771$		−	1.93020i		−	0.0695143i
$772$	−24.2084	−	24.2084i	−0.871278	−	0.871278i
$773$	−21.3049	+	21.3049i	−0.766284	+	0.766284i	−0.977450	−	0.211166i	$-0.932274\pi$
$773$	−21.3049	+	21.3049i	−0.766284	+	0.766284i	0.211166	+	0.977450i	$0.432274\pi$
$774$	−11.1221	+	11.1221i	−0.399776	+	0.399776i
$775$	6.96273	+	6.96273i	0.250108	+	0.250108i
$776$		−	9.26605i		−	0.332632i
$777$		0			0
$778$	−6.01745	+	6.01745i	−0.215736	+	0.215736i
$779$		−	0.689682i		−	0.0247104i
$780$	3.40522	+	2.93577i	0.121927	+	0.105117i
$781$	8.73794			0.312668
$782$	−2.39792	+	2.39792i	−0.0857493	+	0.0857493i
$783$		−	29.0415i		−	1.03786i
$784$		0			0
$785$	−16.5784	−	16.5784i	−0.591707	−	0.591707i
$786$	4.11205	+	4.11205i	0.146672	+	0.146672i
$787$	−6.86137	−	6.86137i	−0.244581	−	0.244581i	0.574161	−	0.818742i	$-0.305328\pi$
$787$	−6.86137	−	6.86137i	−0.244581	−	0.244581i	−0.818742	+	0.574161i	$0.805328\pi$
$788$	−20.1184	+	20.1184i	−0.716687	+	0.716687i
$789$			15.0655i			0.536346i
$790$	−14.5616			−0.518079
$791$		0			0
$792$			7.45191i			0.264792i
$793$	−4.69894	+	0.347886i	−0.166864	+	0.0123538i
$794$		−	29.5991i		−	1.05043i
$795$	4.25672	+	4.25672i	0.150970	+	0.150970i
$796$		−	20.7827i		−	0.736624i
$797$	9.46979			0.335437			0.167719	−	0.985835i	$-0.446360\pi$
$797$	9.46979			0.335437			0.167719	+	0.985835i	$0.446360\pi$
$798$		0			0
$799$	8.29615	+	8.29615i	0.293497	+	0.293497i
$800$	6.91523	−	6.91523i	0.244490	−	0.244490i
$801$	15.1654	+	15.1654i	0.535843	+	0.535843i
$802$	−5.19835			−0.183560
$803$	−11.6369			−0.410659
$804$	−2.08098	−	2.08098i	−0.0733905	−	0.0733905i
$805$		0			0
$806$	−1.21326	−	16.3877i	−0.0427354	−	0.577233i
$807$	5.36402			0.188823
$808$	−4.52555	+	4.52555i	−0.159208	+	0.159208i
$809$	23.7060			0.833458			0.416729	−	0.909031i	$-0.363176\pi$
$809$	23.7060			0.833458			0.416729	+	0.909031i	$0.363176\pi$
$810$	9.76053			0.342950
$811$	29.4470	−	29.4470i	1.03403	−	1.03403i	0.0346248	−	0.999400i	$-0.488976\pi$
$811$	29.4470	−	29.4470i	1.03403	−	1.03403i	0.999400	−	0.0346248i	$-0.0110236\pi$
$812$		0			0
$813$	1.72535	−	1.72535i	0.0605108	−	0.0605108i
$814$	−3.50143	+	3.50143i	−0.122725	+	0.122725i
$815$			1.79132i			0.0627473i
$816$		−	1.95846i		−	0.0685597i
$817$	−27.3824	−	27.3824i	−0.957988	−	0.957988i
$818$	26.3071			0.919807
$819$		0			0
$820$	0.335855			0.0117286
$821$	15.1774	+	15.1774i	0.529696	+	0.529696i	0.920482	−	0.390786i	$-0.127797\pi$
$821$	15.1774	+	15.1774i	0.529696	+	0.529696i	−0.390786	+	0.920482i	$0.627797\pi$
$822$			0.385912i			0.0134602i
$823$		−	18.9392i		−	0.660178i	−0.943950	−	0.330089i	$-0.892921\pi$
$823$		−	18.9392i		−	0.660178i	0.943950	−	0.330089i	$-0.107079\pi$
$824$	5.08828	−	5.08828i	0.177259	−	0.177259i
$825$	−0.589929	+	0.589929i	−0.0205387	+	0.0205387i
$826$		0			0
$827$	0.174463	−	0.174463i	0.00606667	−	0.00606667i	−0.704067	−	0.710134i	$-0.748635\pi$
$827$	0.174463	−	0.174463i	0.00606667	−	0.00606667i	0.710134	+	0.704067i	$0.248635\pi$
$828$	−3.26974			−0.113631
$829$	17.0844			0.593365			0.296682	−	0.954976i	$-0.404120\pi$
$829$	17.0844			0.593365			0.296682	+	0.954976i	$0.404120\pi$
$830$	−5.88081	+	5.88081i	−0.204126	+	0.204126i
$831$	5.94666			0.206287
$832$	−10.7165	+	0.793398i	−0.371529	+	0.0275061i
$833$		0			0
$834$	3.03551	+	3.03551i	0.105111	+	0.105111i
$835$	23.8756			0.826250
$836$	−7.56303			−0.261573
$837$	−11.7059	−	11.7059i	−0.404614	−	0.404614i
$838$	−19.4282	+	19.4282i	−0.671134	+	0.671134i
$839$	−22.4787	−	22.4787i	−0.776052	−	0.776052i	0.203105	−	0.979157i	$-0.434897\pi$
$839$	−22.4787	−	22.4787i	−0.776052	−	0.776052i	−0.979157	+	0.203105i	$0.934897\pi$
$840$		0			0
$841$	78.0266			2.69057
$842$		−	11.2757i		−	0.388585i
$843$	6.25240	+	6.25240i	0.215344	+	0.215344i
$844$		−	9.79918i		−	0.337302i
$845$	−14.1219	+	19.0627i	−0.485809	+	0.655775i
$846$		−	4.81685i		−	0.165607i
$847$		0			0
$848$	5.23502			0.179771
$849$			8.23216i			0.282527i
$850$	4.74543	−	4.74543i	0.162767	−	0.162767i
$851$	−3.72689	−	3.72689i	−0.127756	−	0.127756i
$852$	4.11618	+	4.11618i	0.141018	+	0.141018i
$853$	−3.63231	−	3.63231i	−0.124368	−	0.124368i	0.642183	−	0.766551i	$-0.278029\pi$
$853$	−3.63231	−	3.63231i	−0.124368	−	0.124368i	−0.766551	+	0.642183i	$0.778029\pi$
$854$		0			0
$855$			26.5021i			0.906351i
$856$	4.19558	−	4.19558i	0.143402	−	0.143402i
$857$	−48.1799			−1.64579			−0.822897	−	0.568190i	$-0.807644\pi$
$857$	−48.1799			−1.64579			−0.822897	+	0.568190i	$0.807644\pi$
$858$	1.38848	−	0.102796i	0.0474019	−	0.00350940i
$859$			3.08901i			0.105396i	0.998611	+	0.0526978i	$0.0167820\pi$
$859$			3.08901i			0.105396i	−0.998611	+	0.0526978i	$0.983218\pi$
$860$	13.3344	−	13.3344i	0.454700	−	0.454700i
$861$		0			0
$862$		−	27.5971i		−	0.939961i
$863$	18.1969	+	18.1969i	0.619430	+	0.619430i	0.945385	−	0.325955i	$-0.105686\pi$
$863$	18.1969	+	18.1969i	0.619430	+	0.619430i	−0.325955	+	0.945385i	$0.605686\pi$
$864$	−11.6260	+	11.6260i	−0.395525	+	0.395525i
$865$	−28.5334	+	28.5334i	−0.970166	+	0.970166i
$866$	−10.2107	−	10.2107i	−0.346973	−	0.346973i
$867$		−	4.89375i		−	0.166201i
$868$		0			0
$869$	7.48833	−	7.48833i	0.254024	−	0.254024i
$870$		−	7.10758i		−	0.240969i
$871$	10.1398	−	11.7612i	0.343574	−	0.398514i
$872$	4.28276			0.145033
$873$	6.88333	−	6.88333i	0.232965	−	0.232965i
$874$			3.42771i			0.115944i
$875$		0			0
$876$	−5.48181	−	5.48181i	−0.185213	−	0.185213i
$877$	0.845403	+	0.845403i	0.0285472	+	0.0285472i	0.721236	−	0.692689i	$-0.243574\pi$
$877$	0.845403	+	0.845403i	0.0285472	+	0.0285472i	−0.692689	+	0.721236i	$0.743574\pi$
$878$	13.0235	+	13.0235i	0.439523	+	0.439523i
$879$	−5.41608	+	5.41608i	−0.182680	+	0.182680i
$880$		−	1.44701i		−	0.0487787i
$881$	−20.3067			−0.684151			−0.342075	−	0.939672i	$-0.611130\pi$
$881$	−20.3067			−0.684151			−0.342075	+	0.939672i	$0.611130\pi$
$882$		0			0
$883$		−	28.8309i		−	0.970238i	−0.874448	−	0.485119i	$-0.838776\pi$
$883$		−	28.8309i		−	0.970238i	0.874448	−	0.485119i	$-0.161224\pi$
$884$	26.2306	−	1.94198i	0.882229	−	0.0653158i
$885$		−	8.96246i		−	0.301270i
$886$	−12.7775	−	12.7775i	−0.429270	−	0.429270i
$887$		−	1.59150i		−	0.0534373i	−0.999643	−	0.0267186i	$-0.991494\pi$
$887$		−	1.59150i		−	0.0534373i	0.999643	−	0.0267186i	$-0.00850582\pi$
$888$	−8.00232			−0.268540
$889$		0			0
$890$	7.74190	+	7.74190i	0.259509	+	0.259509i
$891$	−5.01936	+	5.01936i	−0.168155	+	0.168155i
$892$	−27.2537	−	27.2537i	−0.912520	−	0.912520i
$893$	11.8590			0.396845
$894$	−2.87562			−0.0961750
$895$	10.4141	+	10.4141i	0.348106	+	0.348106i
$896$		0			0
$897$	0.109415	+	1.47788i	0.00365326	+	0.0493451i
$898$	−19.2566			−0.642602
$899$	43.1396	−	43.1396i	1.43879	−	1.43879i
$900$	6.47074			0.215691
$901$	35.2173			1.17326
$902$	0.0735418	−	0.0735418i	0.00244868	−	0.00244868i
$903$		0			0
$904$	4.89475	−	4.89475i	0.162797	−	0.162797i
$905$	26.5335	−	26.5335i	0.882002	−	0.882002i
$906$		−	2.57908i		−	0.0856843i
$907$			0.116742i			0.00387636i	0.999998	+	0.00193818i	$0.000616942\pi$
$907$			0.116742i			0.00387636i	−0.999998	+	0.00193818i	$0.999383\pi$
$908$	−0.0698392	−	0.0698392i	−0.00231770	−	0.00231770i
$909$	−6.72364			−0.223009
$910$		0			0
$911$	19.0003			0.629507			0.314753	−	0.949173i	$-0.398078\pi$
$911$	19.0003			0.629507			0.314753	+	0.949173i	$0.398078\pi$
$912$	−1.39976	−	1.39976i	−0.0463507	−	0.0463507i
$913$		−	6.04843i		−	0.200174i
$914$			3.13513i			0.103701i
$915$	−0.821460	+	0.821460i	−0.0271566	+	0.0271566i
$916$	−5.42218	+	5.42218i	−0.179154	+	0.179154i
$917$		0			0
$918$	−7.97810	+	7.97810i	−0.263317	+	0.263317i
$919$	−11.6437			−0.384089			−0.192045	−	0.981386i	$-0.561512\pi$
$919$	−11.6437			−0.384089			−0.192045	+	0.981386i	$0.561512\pi$
$920$	−4.04914			−0.133496
$921$	−7.14158	+	7.14158i	−0.235323	+	0.235323i
$922$	−8.25047			−0.271715
$923$	−20.0565	+	23.2637i	−0.660168	+	0.765735i
$924$		0			0
$925$	7.37543	+	7.37543i	0.242503	+	0.242503i
$926$	14.8007			0.486382
$927$	7.55970			0.248293
$928$	−42.8453	−	42.8453i	−1.40647	−	1.40647i
$929$	36.5980	−	36.5980i	1.20074	−	1.20074i	0.226802	−	0.973941i	$-0.427173\pi$
$929$	36.5980	−	36.5980i	1.20074	−	1.20074i	0.973941	−	0.226802i	$-0.0728271\pi$
$930$	−2.86487	−	2.86487i	−0.0939429	−	0.0939429i
$931$		0			0
$932$	−1.47903			−0.0484473
$933$		−	5.21541i		−	0.170745i
$934$	19.7425	+	19.7425i	0.645995	+	0.645995i
$935$		−	9.73439i		−	0.318349i
$936$	−19.8398	−	17.1046i	−0.648484	−	0.559082i
$937$			47.9005i			1.56484i	0.622751	+	0.782420i	$0.286015\pi$
$937$			47.9005i			1.56484i	−0.622751	+	0.782420i	$0.713985\pi$
$938$		0			0
$939$	5.23637			0.170882
$940$			5.77497i			0.188359i
$941$	−22.2959	+	22.2959i	−0.726825	+	0.726825i	−0.969986	−	0.243161i	$-0.921816\pi$
$941$	−22.2959	+	22.2959i	−0.726825	+	0.726825i	0.243161	+	0.969986i	$0.421816\pi$
$942$	−3.42010	−	3.42010i	−0.111433	−	0.111433i
$943$	0.0782772	+	0.0782772i	0.00254906	+	0.00254906i
$944$	−5.51112	−	5.51112i	−0.179372	−	0.179372i
$945$		0			0
$946$		−	5.83965i		−	0.189863i
$947$	19.4568	−	19.4568i	0.632261	−	0.632261i	−0.316374	−	0.948635i	$-0.602465\pi$
$947$	19.4568	−	19.4568i	0.632261	−	0.632261i	0.948635	+	0.316374i	$0.102465\pi$
$948$	7.05505			0.229137
$949$	26.7107	−	30.9820i	0.867066	−	1.00572i
$950$		−	6.78336i		−	0.220081i
$951$	4.03834	−	4.03834i	0.130952	−	0.130952i
$952$		0			0
$953$		−	16.2238i		−	0.525541i	−0.964858	−	0.262771i	$-0.915364\pi$
$953$		−	16.2238i		−	0.525541i	0.964858	−	0.262771i	$-0.0846362\pi$
$954$	−10.2238	−	10.2238i	−0.331007	−	0.331007i
$955$	−17.8568	+	17.8568i	−0.577831	+	0.577831i
$956$	26.2256	−	26.2256i	0.848197	−	0.848197i
$957$	3.65508	+	3.65508i	0.118152	+	0.118152i
$958$		−	25.5127i		−	0.824276i
$959$		0			0
$960$	−1.87344	+	1.87344i	−0.0604652	+	0.0604652i
$961$		−	3.77681i		−	0.121833i
$962$	−1.28518	−	17.3591i	−0.0414359	−	0.559680i
$963$	6.23341			0.200869
$964$	−9.72113	+	9.72113i	−0.313097	+	0.313097i
$965$		−	44.5398i		−	1.43379i
$966$		0			0
$967$	18.2029	+	18.2029i	0.585366	+	0.585366i	0.936373	−	0.351007i	$-0.114161\pi$
$967$	18.2029	+	18.2029i	0.585366	+	0.585366i	−0.351007	+	0.936373i	$0.614161\pi$
$968$	18.4984	+	18.4984i	0.594561	+	0.594561i
$969$	−9.41653	−	9.41653i	−0.302503	−	0.302503i
$970$	3.51392	−	3.51392i	0.112825	−	0.112825i
$971$		−	41.8891i		−	1.34428i	−0.740422	−	0.672142i	$-0.765374\pi$
$971$		−	41.8891i		−	1.34428i	0.740422	−	0.672142i	$-0.234626\pi$
$972$	−16.5421			−0.530588
$973$		0			0
$974$		−	4.77939i		−	0.153142i
$975$	−0.216530	−	2.92470i	−0.00693452	−	0.0936654i
$976$			1.01025i			0.0323374i
$977$	−10.4217	−	10.4217i	−0.333420	−	0.333420i	0.520464	−	0.853884i	$-0.325759\pi$
$977$	−10.4217	−	10.4217i	−0.333420	−	0.333420i	−0.853884	+	0.520464i	$0.825759\pi$
$978$			0.369548i			0.0118169i
$979$	−7.96256			−0.254485
$980$		0			0
$981$	3.18147	+	3.18147i	0.101576	+	0.101576i
$982$	18.2605	−	18.2605i	0.582717	−	0.582717i
$983$	−14.2126	−	14.2126i	−0.453312	−	0.453312i	0.443140	−	0.896452i	$-0.353864\pi$
$983$	−14.2126	−	14.2126i	−0.453312	−	0.453312i	−0.896452	+	0.443140i	$0.853864\pi$
$984$	0.168076			0.00535806
$985$	−37.0148			−1.17939
$986$	−29.4017	−	29.4017i	−0.936340	−	0.936340i
$987$		0			0
$988$	17.3597	−	20.1357i	0.552285	−	0.640600i
$989$	6.21566			0.197647
$990$	−2.82595	+	2.82595i	−0.0898147	+	0.0898147i
$991$	−27.0650			−0.859747			−0.429873	−	0.902889i	$-0.641442\pi$
$991$	−27.0650			−0.859747			−0.429873	+	0.902889i	$0.641442\pi$
$992$	−34.5396			−1.09663
$993$	−9.33927	+	9.33927i	−0.296373	+	0.296373i
$994$		0			0
$995$	19.1186	−	19.1186i	0.606100	−	0.606100i
$996$	2.84923	−	2.84923i	0.0902814	−	0.0902814i
$997$		−	28.3372i		−	0.897449i	−0.893670	−	0.448725i	$-0.851878\pi$
$997$		−	28.3372i		−	0.897449i	0.893670	−	0.448725i	$-0.148122\pi$
$998$		−	11.4854i		−	0.363564i
$999$	−12.3997	−	12.3997i	−0.392310	−	0.392310i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	637.2.i.a.489.9		32
7.2	even	3		637.2.bc.b.619.5		32
7.3	odd	6		637.2.bc.b.411.4		32
7.4	even	3		91.2.bb.a.47.4	yes	32
7.5	odd	6		91.2.bb.a.73.5	yes	32
7.6	odd	2	inner	637.2.i.a.489.10		32
13.5	odd	4	inner	637.2.i.a.538.9		32
21.5	even	6		819.2.fn.e.73.4		32
21.11	odd	6		819.2.fn.e.775.5		32
91.5	even	12		91.2.bb.a.31.4	yes	32
91.18	odd	12		91.2.bb.a.5.5	✓	32
91.31	even	12		637.2.bc.b.460.5		32
91.44	odd	12		637.2.bc.b.31.4		32
91.83	even	4	inner	637.2.i.a.538.10		32
273.5	odd	12		819.2.fn.e.577.5		32
273.200	even	12		819.2.fn.e.460.4		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.bb.a.5.5	✓	32	91.18	odd	12
91.2.bb.a.31.4	yes	32	91.5	even	12
91.2.bb.a.47.4	yes	32	7.4	even	3
91.2.bb.a.73.5	yes	32	7.5	odd	6
637.2.i.a.489.9		32	1.1	even	1	trivial
637.2.i.a.489.10		32	7.6	odd	2	inner
637.2.i.a.538.9		32	13.5	odd	4	inner
637.2.i.a.538.10		32	91.83	even	4	inner
637.2.bc.b.31.4		32	91.44	odd	12
637.2.bc.b.411.4		32	7.3	odd	6
637.2.bc.b.460.5		32	91.31	even	12
637.2.bc.b.619.5		32	7.2	even	3
819.2.fn.e.73.4		32	21.5	even	6
819.2.fn.e.460.4		32	273.200	even	12
819.2.fn.e.577.5		32	273.5	odd	12
819.2.fn.e.775.5		32	21.11	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 637 = 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	637.i (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.546480 + 0.546480i) q^{2} -0.487133i q^{3} -1.40272i q^{4} +(1.29040 - 1.29040i) q^{5} +(0.266208 - 0.266208i) q^{6} +(1.85952 - 1.85952i) q^{8} +2.76270 q^{9} +O(q^{10})\)	\(q+(0.546480 + 0.546480i) q^{2} -0.487133i q^{3} -1.40272i q^{4} +(1.29040 - 1.29040i) q^{5} +(0.266208 - 0.266208i) q^{6} +(1.85952 - 1.85952i) q^{8} +2.76270 q^{9} +1.41035 q^{10} +(-0.725276 + 0.725276i) q^{11} -0.683311 q^{12} +(-0.266208 - 3.59571i) q^{13} +(-0.628596 - 0.628596i) q^{15} -0.773062 q^{16} -5.20058 q^{17} +(1.50976 + 1.50976i) q^{18} +(-3.71699 + 3.71699i) q^{19} +(-1.81007 - 1.81007i) q^{20} -0.792697 q^{22} -0.843739i q^{23} +(-0.905832 - 0.905832i) q^{24} +1.66974i q^{25} +(1.81951 - 2.11046i) q^{26} -2.80720i q^{27} +10.3454 q^{29} -0.687030i q^{30} +(4.16994 - 4.16994i) q^{31} +(-4.14150 - 4.14150i) q^{32} +(0.353306 + 0.353306i) q^{33} +(-2.84201 - 2.84201i) q^{34} -3.87530i q^{36} +(4.41711 - 4.41711i) q^{37} -4.06252 q^{38} +(-1.75159 + 0.129679i) q^{39} -4.79904i q^{40} +(-0.0927742 + 0.0927742i) q^{41} +7.36681i q^{43} +(1.01736 + 1.01736i) q^{44} +(3.56499 - 3.56499i) q^{45} +(0.461086 - 0.461086i) q^{46} +(-1.59524 - 1.59524i) q^{47} +0.376584i q^{48} +(-0.912480 + 0.912480i) q^{50} +2.53337i q^{51} +(-5.04377 + 0.373416i) q^{52} -6.77180 q^{53} +(1.53408 - 1.53408i) q^{54} +1.87179i q^{55} +(1.81067 + 1.81067i) q^{57} +(5.65353 + 5.65353i) q^{58} +(7.12895 + 7.12895i) q^{59} +(-0.881744 + 0.881744i) q^{60} -1.30682i q^{61} +4.55758 q^{62} -2.98037i q^{64} +(-4.98342 - 4.29639i) q^{65} +0.386149i q^{66} +(3.04544 + 3.04544i) q^{67} +7.29496i q^{68} -0.411013 q^{69} +(-6.02388 - 6.02388i) q^{71} +(5.13729 - 5.13729i) q^{72} +(8.02243 + 8.02243i) q^{73} +4.82772 q^{74} +0.813386 q^{75} +(5.21390 + 5.21390i) q^{76} +(-1.02807 - 0.886341i) q^{78} -10.3248 q^{79} +(-0.997558 + 0.997558i) q^{80} +6.92062 q^{81} -0.101398 q^{82} +(-4.16974 + 4.16974i) q^{83} +(-6.71082 + 6.71082i) q^{85} +(-4.02581 + 4.02581i) q^{86} -5.03957i q^{87} +2.69733i q^{88} +(5.48933 + 5.48933i) q^{89} +3.89639 q^{90} -1.18353 q^{92} +(-2.03132 - 2.03132i) q^{93} -1.74353i q^{94} +9.59280i q^{95} +(-2.01746 + 2.01746i) q^{96} +(2.49152 - 2.49152i) q^{97} +(-2.00372 + 2.00372i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 4 q^{2} - 16 q^{8} - 16 q^{9}+O(q^{10}) \) 32 * q + 4 * q^2 - 16 * q^8 - 16 * q^9	\( 32 q + 4 q^{2} - 16 q^{8} - 16 q^{9} + 20 q^{11} - 44 q^{15} - 24 q^{16} + 8 q^{18} - 8 q^{22} + 16 q^{29} - 8 q^{32} + 16 q^{37} + 12 q^{39} + 84 q^{44} - 24 q^{46} + 88 q^{50} + 24 q^{53} + 40 q^{57} - 52 q^{58} - 32 q^{60} + 16 q^{65} - 32 q^{67} - 36 q^{71} - 44 q^{72} - 24 q^{74} - 176 q^{78} + 64 q^{79} - 32 q^{81} - 84 q^{85} - 84 q^{86} + 48 q^{92} - 12 q^{93} - 24 q^{99}+O(q^{100}) \) 32 * q + 4 * q^2 - 16 * q^8 - 16 * q^9 + 20 * q^11 - 44 * q^15 - 24 * q^16 + 8 * q^18 - 8 * q^22 + 16 * q^29 - 8 * q^32 + 16 * q^37 + 12 * q^39 + 84 * q^44 - 24 * q^46 + 88 * q^50 + 24 * q^53 + 40 * q^57 - 52 * q^58 - 32 * q^60 + 16 * q^65 - 32 * q^67 - 36 * q^71 - 44 * q^72 - 24 * q^74 - 176 * q^78 + 64 * q^79 - 32 * q^81 - 84 * q^85 - 84 * q^86 + 48 * q^92 - 12 * q^93 - 24 * q^99

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