LMFDB - Embedded newform 207.2.i.e.82.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [207,2,Mod(55,207)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(207, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 10]))

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

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

chi := DirichletCharacter("207.55");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 207 = 3^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	207.i (of order $11$, degree $10$, 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:	$1.65290332184$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$4$ over $\Q(\zeta_{11})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			82.4
Character	$\chi$	$=$	207.82
Dual form			207.2.i.e.154.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.73622 + 2.00371i) q^{2} +(-0.715745 + 4.97812i) q^{4} +(0.667943 - 1.46259i) q^{5} +(-0.586514 - 0.172216i) q^{7} +(-6.75657 + 4.34219i) q^{8} +O(q^{10})$	\(q+(1.73622 + 2.00371i) q^{2} +(-0.715745 + 4.97812i) q^{4} +(0.667943 - 1.46259i) q^{5} +(-0.586514 - 0.172216i) q^{7} +(-6.75657 + 4.34219i) q^{8} +(4.09030 - 1.20102i) q^{10} +(-2.70958 + 3.12702i) q^{11} +(6.03698 - 1.77262i) q^{13} +(-0.673248 - 1.47421i) q^{14} +(-10.7802 - 3.16536i) q^{16} +(-0.816433 - 5.67841i) q^{17} +(0.729295 - 5.07236i) q^{19} +(6.80287 + 4.37194i) q^{20} -10.9701 q^{22} +(-3.41592 - 3.36623i) q^{23} +(1.58128 + 1.82489i) q^{25} +(14.0333 + 9.01868i) q^{26} +(1.27711 - 2.79647i) q^{28} +(0.438878 + 3.05246i) q^{29} +(-3.31430 + 2.12997i) q^{31} +(-5.70153 - 12.4846i) q^{32} +(9.96037 - 11.4949i) q^{34} +(-0.643639 + 0.742800i) q^{35} +(0.757843 + 1.65944i) q^{37} +(11.4297 - 7.34544i) q^{38} +(1.83784 + 12.7824i) q^{40} +(-0.574040 + 1.25697i) q^{41} +(6.64191 + 4.26849i) q^{43} +(-13.6273 - 15.7268i) q^{44} +(0.814148 - 12.6890i) q^{46} -4.94390 q^{47} +(-5.57443 - 3.58247i) q^{49} +(-0.911101 + 6.33684i) q^{50} +(4.50336 + 31.3215i) q^{52} +(-3.02288 - 0.887597i) q^{53} +(2.76371 + 6.05168i) q^{55} +(4.71062 - 1.38316i) q^{56} +(-5.35425 + 6.17913i) q^{58} +(-3.13323 + 0.920000i) q^{59} +(-6.14413 + 3.94859i) q^{61} +(-10.0222 - 2.94278i) q^{62} +(5.78175 - 12.6603i) q^{64} +(1.43974 - 10.0136i) q^{65} +(-7.53402 - 8.69472i) q^{67} +28.8522 q^{68} -2.60585 q^{70} +(8.68383 + 10.0217i) q^{71} +(0.530112 - 3.68701i) q^{73} +(-2.00926 + 4.39966i) q^{74} +(24.7288 + 7.26103i) q^{76} +(2.12773 - 1.36741i) q^{77} +(-0.348667 + 0.102378i) q^{79} +(-11.8302 + 13.6528i) q^{80} +(-3.51527 + 1.03217i) q^{82} +(-0.462525 - 1.01279i) q^{83} +(-8.85053 - 2.59875i) q^{85} +(2.97901 + 20.7195i) q^{86} +(4.72937 - 32.8935i) q^{88} +(1.39028 + 0.893478i) q^{89} -3.84605 q^{91} +(19.2024 - 14.5955i) q^{92} +(-8.58370 - 9.90612i) q^{94} +(-6.93165 - 4.45470i) q^{95} +(-2.04791 + 4.48430i) q^{97} +(-2.50023 - 17.3895i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 4 q^{4} + 8 q^{7}+O(q^{10}) $ 40 * q - 4 * q^4 + 8 * q^7	$ 40 q - 4 q^{4} + 8 q^{7} - 56 q^{16} - 14 q^{19} - 28 q^{22} - 48 q^{25} - 64 q^{28} - 22 q^{31} - 10 q^{34} + 52 q^{37} + 6 q^{40} + 68 q^{43} + 84 q^{46} + 4 q^{49} + 110 q^{52} + 50 q^{55} + 18 q^{58} + 36 q^{61} + 116 q^{64} - 18 q^{67} + 96 q^{70} + 14 q^{73} + 34 q^{76} - 36 q^{79} - 72 q^{82} - 238 q^{85} - 160 q^{88} - 176 q^{91} - 206 q^{94} - 92 q^{97}+O(q^{100}) $ 40 * q - 4 * q^4 + 8 * q^7 - 56 * q^16 - 14 * q^19 - 28 * q^22 - 48 * q^25 - 64 * q^28 - 22 * q^31 - 10 * q^34 + 52 * q^37 + 6 * q^40 + 68 * q^43 + 84 * q^46 + 4 * q^49 + 110 * q^52 + 50 * q^55 + 18 * q^58 + 36 * q^61 + 116 * q^64 - 18 * q^67 + 96 * q^70 + 14 * q^73 + 34 * q^76 - 36 * q^79 - 72 * q^82 - 238 * q^85 - 160 * q^88 - 176 * q^91 - 206 * q^94 - 92 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/207\mathbb{Z}\right)^\times$.

$n$	$28$	$47$
$\chi(n)$	$e\left(\frac{7}{11}\right)$	$1$

Coefficient data

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

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

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

$2$	1.73622	+	2.00371i	1.22769	+	1.41683i	0.877100	+	0.480307i	$0.159475\pi$
$2$	1.73622	+	2.00371i	1.22769	+	1.41683i	0.350594	+	0.936528i	$0.385980\pi$
$3$		0			0
$3$		0			0
$4$	−0.715745	+	4.97812i	−0.357873	+	2.48906i
$5$	0.667943	−	1.46259i	0.298713	−	0.654090i	−0.699450	−	0.714682i	$-0.746571\pi$
$5$	0.667943	−	1.46259i	0.298713	−	0.654090i	0.998163	+	0.0605916i	$0.0192987\pi$
$6$		0			0
$7$	−0.586514	−	0.172216i	−0.221682	−	0.0650916i	0.169006	−	0.985615i	$-0.445944\pi$
$7$	−0.586514	−	0.172216i	−0.221682	−	0.0650916i	−0.390687	+	0.920524i	$0.627763\pi$
$8$	−6.75657	+	4.34219i	−2.38881	+	1.53519i
$9$		0			0
$10$	4.09030	−	1.20102i	1.29347	−	0.379796i
$11$	−2.70958	+	3.12702i	−0.816969	+	0.942833i	−0.999183	−	0.0404263i	$-0.987128\pi$
$11$	−2.70958	+	3.12702i	−0.816969	+	0.942833i	0.182213	+	0.983259i	$0.441674\pi$
$12$		0			0
$13$	6.03698	−	1.77262i	1.67436	−	0.491635i	0.699531	−	0.714603i	$-0.253392\pi$
$13$	6.03698	−	1.77262i	1.67436	−	0.491635i	0.974826	+	0.222967i	$0.0715743\pi$
$14$	−0.673248	−	1.47421i	−0.179933	−	0.393999i
$15$		0			0
$16$	−10.7802	−	3.16536i	−2.69505	−	0.791339i
$17$	−0.816433	−	5.67841i	−0.198014	−	1.37722i	−0.810037	−	0.586378i	$-0.800553\pi$
$17$	−0.816433	−	5.67841i	−0.198014	−	1.37722i	0.612023	−	0.790840i	$-0.290356\pi$
$18$		0			0
$19$	0.729295	−	5.07236i	0.167312	−	1.16368i	−0.717100	−	0.696971i	$-0.754531\pi$
$19$	0.729295	−	5.07236i	0.167312	−	1.16368i	0.884411	−	0.466708i	$-0.154560\pi$
$20$	6.80287	+	4.37194i	1.52117	+	0.977595i
$21$		0			0
$22$	−10.9701			−2.33883
$23$	−3.41592	−	3.36623i	−0.712268	−	0.701908i
$23$	−3.41592	−	3.36623i	−0.712268	−	0.701908i
$24$		0			0
$25$	1.58128	+	1.82489i	0.316256	+	0.364979i
$26$	14.0333	+	9.01868i	2.75216	+	1.76871i
$27$		0			0
$28$	1.27711	−	2.79647i	0.241350	−	0.528484i
$29$	0.438878	+	3.05246i	0.0814975	+	0.566828i	0.989128	+	0.147058i	$0.0469803\pi$
$29$	0.438878	+	3.05246i	0.0814975	+	0.566828i	−0.907630	+	0.419770i	$0.862111\pi$
$30$		0			0
$31$	−3.31430	+	2.12997i	−0.595265	+	0.382554i	−0.803306	−	0.595566i	$-0.796928\pi$
$31$	−3.31430	+	2.12997i	−0.595265	+	0.382554i	0.208041	+	0.978120i	$0.433291\pi$
$32$	−5.70153	−	12.4846i	−1.00790	−	2.20699i
$33$		0			0
$34$	9.96037	−	11.4949i	1.70819	−	1.97136i
$35$	−0.643639	+	0.742800i	−0.108795	+	0.125556i
$36$		0			0
$37$	0.757843	+	1.65944i	0.124589	+	0.272811i	0.961641	−	0.274312i	$-0.0884502\pi$
$37$	0.757843	+	1.65944i	0.124589	+	0.272811i	−0.837052	+	0.547123i	$0.815723\pi$
$38$	11.4297	−	7.34544i	1.85415	−	1.19159i
$39$		0			0
$40$	1.83784	+	12.7824i	0.290587	+	2.02108i
$41$	−0.574040	+	1.25697i	−0.0896500	+	0.196306i	−0.949146	−	0.314836i	$-0.898050\pi$
$41$	−0.574040	+	1.25697i	−0.0896500	+	0.196306i	0.859496	+	0.511143i	$0.170778\pi$
$42$		0			0
$43$	6.64191	+	4.26849i	1.01288	+	0.650939i	0.938137	−	0.346263i	$-0.112550\pi$
$43$	6.64191	+	4.26849i	1.01288	+	0.650939i	0.0747441	+	0.997203i	$0.476186\pi$
$44$	−13.6273	−	15.7268i	−2.05439	−	2.37090i
$45$		0			0
$46$	0.814148	−	12.6890i	0.120040	−	1.87089i
$47$	−4.94390			−0.721142			−0.360571	−	0.932732i	$-0.617418\pi$
$47$	−4.94390			−0.721142			−0.360571	+	0.932732i	$0.617418\pi$
$48$		0			0
$49$	−5.57443	−	3.58247i	−0.796348	−	0.511782i
$50$	−0.911101	+	6.33684i	−0.128849	+	0.896165i
$51$		0			0
$52$	4.50336	+	31.3215i	0.624503	+	4.34351i
$53$	−3.02288	−	0.887597i	−0.415224	−	0.121921i	0.0674462	−	0.997723i	$-0.478515\pi$
$53$	−3.02288	−	0.887597i	−0.415224	−	0.121921i	−0.482670	+	0.875802i	$0.660333\pi$
$54$		0			0
$55$	2.76371	+	6.05168i	0.372658	+	0.816008i
$56$	4.71062	−	1.38316i	0.629483	−	0.184833i
$57$		0			0
$58$	−5.35425	+	6.17913i	−0.703047	+	0.811360i
$59$	−3.13323	+	0.920000i	−0.407912	+	0.119774i	−0.479250	−	0.877678i	$-0.659091\pi$
$59$	−3.13323	+	0.920000i	−0.407912	+	0.119774i	0.0713379	+	0.997452i	$0.477273\pi$
$60$		0			0
$61$	−6.14413	+	3.94859i	−0.786675	+	0.505565i	−0.871243	−	0.490852i	$-0.836685\pi$
$61$	−6.14413	+	3.94859i	−0.786675	+	0.505565i	0.0845677	+	0.996418i	$0.473049\pi$
$62$	−10.0222	−	2.94278i	−1.27282	−	0.373734i
$63$		0			0
$64$	5.78175	−	12.6603i	0.722719	−	1.58253i
$65$	1.43974	−	10.0136i	0.178578	−	1.24204i
$66$		0			0
$67$	−7.53402	−	8.69472i	−0.920427	−	1.06223i	−0.997870	−	0.0652326i	$-0.979221\pi$
$67$	−7.53402	−	8.69472i	−0.920427	−	1.06223i	0.0774431	−	0.996997i	$-0.475324\pi$
$68$	28.8522			3.49884
$69$		0			0
$70$	−2.60585			−0.311459
$71$	8.68383	+	10.0217i	1.03058	+	1.18935i	0.981677	+	0.190550i	$0.0610272\pi$
$71$	8.68383	+	10.0217i	1.03058	+	1.18935i	0.0489034	+	0.998804i	$0.484427\pi$
$72$		0			0
$73$	0.530112	−	3.68701i	0.0620449	−	0.431532i	−0.934996	−	0.354658i	$-0.884597\pi$
$73$	0.530112	−	3.68701i	0.0620449	−	0.431532i	0.997041	−	0.0768733i	$-0.0244937\pi$
$74$	−2.00926	+	4.39966i	−0.233571	+	0.511450i
$75$		0			0
$76$	24.7288	+	7.26103i	2.83659	+	0.832897i
$77$	2.12773	−	1.36741i	0.242477	−	0.155831i
$78$		0			0
$79$	−0.348667	+	0.102378i	−0.0392281	+	0.0115184i	−0.301288	−	0.953533i	$-0.597416\pi$
$79$	−0.348667	+	0.102378i	−0.0392281	+	0.0115184i	0.262060	+	0.965052i	$0.415598\pi$
$80$	−11.8302	+	13.6528i	−1.32265	+	1.52642i
$81$		0			0
$82$	−3.51527	+	1.03217i	−0.388196	+	0.113985i
$83$	−0.462525	−	1.01279i	−0.0507687	−	0.111168i	0.882548	−	0.470223i	$-0.155826\pi$
$83$	−0.462525	−	1.01279i	−0.0507687	−	0.111168i	−0.933317	+	0.359055i	$0.883099\pi$
$84$		0			0
$85$	−8.85053	−	2.59875i	−0.959974	−	0.281874i
$86$	2.97901	+	20.7195i	0.321235	+	2.23424i
$87$		0			0
$88$	4.72937	−	32.8935i	0.504152	−	3.50645i
$89$	1.39028	+	0.893478i	0.147369	+	0.0947085i	0.612248	−	0.790666i	$-0.290266\pi$
$89$	1.39028	+	0.893478i	0.147369	+	0.0947085i	−0.464878	+	0.885375i	$0.653902\pi$
$90$		0			0
$91$	−3.84605			−0.403175
$92$	19.2024	−	14.5955i	2.00199	−	1.52168i
$93$		0			0
$94$	−8.58370	−	9.90612i	−0.885342	−	1.02174i
$95$	−6.93165	−	4.45470i	−0.711173	−	0.457043i
$96$		0			0
$97$	−2.04791	+	4.48430i	−0.207934	+	0.455311i	−0.984650	−	0.174539i	$-0.944156\pi$
$97$	−2.04791	+	4.48430i	−0.207934	+	0.455311i	0.776717	+	0.629850i	$0.216884\pi$
$98$	−2.50023	−	17.3895i	−0.252562	−	1.75660i
$99$		0			0
$100$	−10.2163	+	6.56564i	−1.02163	+	0.656564i
$101$	−5.69461	−	12.4695i	−0.566635	−	1.24076i	−0.948570	−	0.316568i	$-0.897470\pi$
$101$	−5.69461	−	12.4695i	−0.566635	−	1.24076i	0.381935	−	0.924189i	$-0.375258\pi$
$102$		0			0
$103$	−2.90895	+	3.35711i	−0.286627	+	0.330786i	−0.880743	−	0.473594i	$-0.842957\pi$
$103$	−2.90895	+	3.35711i	−0.286627	+	0.330786i	0.594116	+	0.804379i	$0.297502\pi$
$104$	−33.0923	+	38.1905i	−3.24496	+	3.74489i
$105$		0			0
$106$	−3.46990	−	7.59802i	−0.337027	−	0.737985i
$107$	−7.10901	+	4.56868i	−0.687254	+	0.441671i	−0.837109	−	0.547037i	$-0.815756\pi$
$107$	−7.10901	+	4.56868i	−0.687254	+	0.441671i	0.149855	+	0.988708i	$0.452119\pi$
$108$		0			0
$109$	1.35416	+	9.41837i	0.129705	+	0.902117i	0.945927	+	0.324379i	$0.105155\pi$
$109$	1.35416	+	9.41837i	0.129705	+	0.902117i	−0.816222	+	0.577738i	$0.803936\pi$
$110$	−7.32738	+	16.0447i	−0.698638	+	1.52980i
$111$		0			0
$112$	5.77762	+	3.71305i	0.545934	+	0.350850i
$113$	6.97214	+	8.04628i	0.655884	+	0.756930i	0.982099	−	0.188365i	$-0.0603189\pi$
$113$	6.97214	+	8.04628i	0.655884	+	0.756930i	−0.326215	+	0.945295i	$0.605773\pi$
$114$		0			0
$115$	−7.20505	+	2.74764i	−0.671875	+	0.256219i
$116$	−15.5096			−1.44003
$117$		0			0
$118$	−7.28340	−	4.68076i	−0.670491	−	0.430898i
$119$	−0.499065	+	3.47107i	−0.0457492	+	0.318193i
$120$		0			0
$121$	−0.870980	−	6.05780i	−0.0791800	−	0.550709i
$122$	−18.5794	−	5.45540i	−1.68210	−	0.493909i
$123$		0			0
$124$	−8.23105	−	18.0235i	−0.739170	−	1.61856i
$125$	11.4391	−	3.35882i	1.02314	−	0.300422i
$126$		0			0
$127$	5.91009	−	6.82061i	0.524436	−	0.605231i	−0.430300	−	0.902686i	$-0.641592\pi$
$127$	5.91009	−	6.82061i	0.524436	−	0.605231i	0.954736	+	0.297455i	$0.0961377\pi$
$128$	9.06794	−	2.66259i	0.801500	−	0.235342i
$129$		0			0
$130$	22.5641	−	14.5011i	1.97900	−	1.27183i
$131$	7.70511	+	2.26242i	0.673199	+	0.197669i	0.600427	−	0.799680i	$-0.294997\pi$
$131$	7.70511	+	2.26242i	0.673199	+	0.197669i	0.0727717	+	0.997349i	$0.476816\pi$
$132$		0			0
$133$	−1.30128	+	2.84941i	−0.112836	+	0.247075i
$134$	4.34094	−	30.1919i	0.375001	−	2.60819i
$135$		0			0
$136$	30.1730	+	34.8215i	2.58732	+	2.98592i
$137$	17.3960			1.48624			0.743121	−	0.669158i	$-0.233345\pi$
$137$	17.3960			1.48624			0.743121	+	0.669158i	$0.233345\pi$
$138$		0			0
$139$	−1.63378			−0.138576			−0.0692878	−	0.997597i	$-0.522073\pi$
$139$	−1.63378			−0.138576			−0.0692878	+	0.997597i	$0.522073\pi$
$140$	−3.23706	−	3.73577i	−0.273582	−	0.315730i
$141$		0			0
$142$	−5.00344	+	34.7997i	−0.419879	+	2.92033i
$143$	−10.8147	+	23.6808i	−0.904368	+	1.98029i
$144$		0			0
$145$	4.75765	+	1.39697i	0.395101	+	0.116012i
$146$	8.30807	−	5.33927i	0.687581	−	0.441881i
$147$		0			0
$148$	−8.80333	+	2.58489i	−0.723629	+	0.212477i
$149$	13.2184	−	15.2548i	1.08289	−	1.24973i	0.116354	−	0.993208i	$-0.462879\pi$
$149$	13.2184	−	15.2548i	1.08289	−	1.24973i	0.966539	−	0.256518i	$-0.0825754\pi$
$150$		0			0
$151$	2.32717	−	0.683320i	0.189383	−	0.0556078i	−0.185666	−	0.982613i	$-0.559444\pi$
$151$	2.32717	−	0.683320i	0.189383	−	0.0556078i	0.375049	+	0.927005i	$0.377626\pi$
$152$	17.0976	+	37.4385i	1.38680	+	3.03666i
$153$		0			0
$154$	6.43410	+	1.88922i	0.518475	+	0.152238i
$155$	0.901513	+	6.27016i	0.0724112	+	0.503631i
$156$		0			0
$157$	−1.62979	+	11.3355i	−0.130072	+	0.904669i	0.815384	+	0.578920i	$0.196526\pi$
$157$	−1.62979	+	11.3355i	−0.130072	+	0.904669i	−0.945456	+	0.325749i	$0.894383\pi$
$158$	−0.810498	−	0.520875i	−0.0644797	−	0.0414386i
$159$		0			0
$160$	−22.0682			−1.74464
$161$	1.42376	+	2.56262i	0.112208	+	0.201963i
$162$		0			0
$163$	5.39917	+	6.23098i	0.422896	+	0.488048i	0.926717	−	0.375760i	$-0.122618\pi$
$163$	5.39917	+	6.23098i	0.422896	+	0.488048i	−0.503821	+	0.863808i	$0.668073\pi$
$164$	−5.84649	−	3.75731i	−0.456534	−	0.293397i
$165$		0			0
$166$	1.22628	−	2.68519i	0.0951782	−	0.208411i
$167$	−0.0347453	−	0.241659i	−0.00268867	−	0.0187001i	0.988433	−	0.151659i	$-0.0484614\pi$
$167$	−0.0347453	−	0.241659i	−0.00268867	−	0.0187001i	−0.991122	+	0.132958i	$0.957552\pi$
$168$		0			0
$169$	22.3666	−	14.3742i	1.72051	−	1.10571i
$170$	−10.1593	−	22.2459i	−0.779186	−	1.70618i
$171$		0			0
$172$	−26.0030	+	30.0090i	−1.98271	+	2.28817i
$173$	0.351961	−	0.406184i	0.0267591	−	0.0308816i	−0.742212	−	0.670165i	$-0.766223\pi$
$173$	0.351961	−	0.406184i	0.0267591	−	0.0308816i	0.768971	+	0.639283i	$0.220769\pi$
$174$		0			0
$175$	−0.613167	−	1.34265i	−0.0463511	−	0.101495i
$176$	39.1080	−	25.1332i	2.94787	−	1.89448i
$177$		0			0
$178$	0.623565	+	4.33699i	0.0467381	+	0.325071i
$179$	−0.216290	+	0.473609i	−0.0161663	+	0.0353992i	−0.917543	−	0.397637i	$-0.869830\pi$
$179$	−0.216290	+	0.473609i	−0.0161663	+	0.0353992i	0.901377	+	0.433036i	$0.142558\pi$
$180$		0			0
$181$	−16.0652	−	10.3245i	−1.19412	−	0.767414i	−0.216190	−	0.976351i	$-0.569363\pi$
$181$	−16.0652	−	10.3245i	−1.19412	−	0.767414i	−0.977929	+	0.208937i	$0.933000\pi$
$182$	−6.67759	−	7.70635i	−0.494976	−	0.571233i
$183$		0			0
$184$	37.6967	+	7.91163i	2.77904	+	0.583253i
$185$	2.93328			0.215659
$186$		0			0
$187$	19.9687	+	12.8331i	1.46026	+	0.938450i
$188$	3.53857	−	24.6113i	0.258077	−	1.79496i
$189$		0			0
$190$	−3.10897	−	21.6234i	−0.225548	−	1.56872i
$191$	−19.9365	−	5.85389i	−1.44256	−	0.423573i	−0.535483	−	0.844546i	$-0.679870\pi$
$191$	−19.9365	−	5.85389i	−1.44256	−	0.423573i	−0.907073	+	0.420973i	$0.861689\pi$
$192$		0			0
$193$	−4.60565	−	10.0850i	−0.331522	−	0.725932i	0.668317	−	0.743877i	$-0.267015\pi$
$193$	−4.60565	−	10.0850i	−0.331522	−	0.725932i	−0.999839	+	0.0179446i	$0.994288\pi$
$194$	−12.5408	+	3.68232i	−0.900380	+	0.264375i
$195$		0			0
$196$	21.8238	−	25.1860i	1.55885	−	1.79900i
$197$	−13.5839	+	3.98860i	−0.967815	+	0.284176i	−0.727185	−	0.686441i	$-0.759172\pi$
$197$	−13.5839	+	3.98860i	−0.967815	+	0.284176i	−0.240629	+	0.970617i	$0.577354\pi$
$198$		0			0
$199$	−4.58707	+	2.94793i	−0.325169	+	0.208973i	−0.693032	−	0.720907i	$-0.743726\pi$
$199$	−4.58707	+	2.94793i	−0.325169	+	0.208973i	0.367864	+	0.929880i	$0.380089\pi$
$200$	−18.6081	−	5.46382i	−1.31579	−	0.386351i
$201$		0			0
$202$	15.0980	−	33.0601i	1.06229	−	2.32610i
$203$	0.268275	−	1.86589i	0.0188292	−	0.130960i
$204$		0			0
$205$	1.45501	+	1.67917i	0.101622	+	0.117278i
$206$	−11.7772			−0.820559
$207$		0			0
$208$	−70.6909			−4.90153
$209$	13.8853	+	16.0245i	0.960466	+	1.10844i
$210$		0			0
$211$	1.85934	−	12.9320i	0.128002	−	0.890276i	−0.820079	−	0.572250i	$-0.806071\pi$
$211$	1.85934	−	12.9320i	0.128002	−	0.890276i	0.948082	−	0.318026i	$-0.103020\pi$
$212$	6.58217	−	14.4129i	0.452065	−	0.989885i
$213$		0			0
$214$	−21.4971	−	6.31212i	−1.46951	−	0.431488i
$215$	10.6795	−	6.86328i	0.728334	−	0.468072i
$216$		0			0
$217$	2.31070	−	0.678482i	0.156860	−	0.0460584i
$218$	−16.5205	+	19.0657i	−1.11891	+	1.29129i
$219$		0			0
$220$	−32.1041	+	9.42661i	−2.16446	+	0.635542i
$221$	−14.9944	−	32.8332i	−1.00864	−	2.20860i
$222$		0			0
$223$	18.5604	+	5.44982i	1.24290	+	0.364947i	0.836102	−	0.548573i	$-0.184829\pi$
$223$	18.5604	+	5.44982i	1.24290	+	0.364947i	0.406793	+	0.913520i	$0.366647\pi$
$224$	1.19398	+	8.30430i	0.0797760	+	0.554855i
$225$		0			0
$226$	−4.01720	+	27.9402i	−0.267220	+	1.85856i
$227$	19.7071	+	12.6650i	1.30800	+	0.840603i	0.994059	−	0.108839i	$-0.0347132\pi$
$227$	19.7071	+	12.6650i	1.30800	+	0.840603i	0.313944	+	0.949442i	$0.398350\pi$
$228$		0			0
$229$	14.4168			0.952687			0.476344	−	0.879259i	$-0.341962\pi$
$229$	14.4168			0.952687			0.476344	+	0.879259i	$0.341962\pi$
$230$	−18.0150	−	9.66630i	−1.18788	−	0.637377i
$231$		0			0
$232$	−16.2197	−	18.7185i	−1.06487	−	1.22893i
$233$	21.2666	+	13.6672i	1.39322	+	0.895370i	0.999713	−	0.0239509i	$-0.00762455\pi$
$233$	21.2666	+	13.6672i	1.39322	+	0.895370i	0.393509	+	0.919321i	$0.371261\pi$
$234$		0			0
$235$	−3.30224	+	7.23090i	−0.215414	+	0.471692i
$236$	−2.33727	−	16.2561i	−0.152143	−	1.05818i
$237$		0			0
$238$	−7.82150	+	5.02657i	−0.506993	+	0.325824i
$239$	9.30159	+	20.3676i	0.601670	+	1.31747i	0.928128	+	0.372261i	$0.121418\pi$
$239$	9.30159	+	20.3676i	0.601670	+	1.31747i	−0.326458	+	0.945212i	$0.605855\pi$
$240$		0			0
$241$	1.49352	−	1.72362i	0.0962062	−	0.111028i	−0.705605	−	0.708606i	$-0.749325\pi$
$241$	1.49352	−	1.72362i	0.0962062	−	0.111028i	0.801811	+	0.597578i	$0.203870\pi$
$242$	10.6258	−	12.2629i	0.683055	−	0.788287i
$243$		0			0
$244$	−15.2589	−	33.4124i	−0.976852	−	2.13901i
$245$	−8.96309	+	5.76023i	−0.572631	+	0.368008i
$246$		0			0
$247$	−4.58861	−	31.9145i	−0.291966	−	2.03067i
$248$	13.1446	−	28.7826i	0.834681	−	1.82770i
$249$		0			0
$250$	26.5909	+	17.0889i	1.68175	+	1.08080i
$251$	4.62368	+	5.33601i	0.291844	+	0.336806i	0.882670	−	0.469993i	$-0.155743\pi$
$251$	4.62368	+	5.33601i	0.291844	+	0.336806i	−0.590826	+	0.806799i	$0.701198\pi$
$252$		0			0
$253$	19.7820	−	1.56058i	1.24368	−	0.0981128i
$254$	23.9277			1.50136
$255$		0			0
$256$	−2.33814	−	1.50263i	−0.146134	−	0.0939146i
$257$	−1.89122	+	13.1538i	−0.117971	+	0.820509i	0.841813	+	0.539770i	$0.181489\pi$
$257$	−1.89122	+	13.1538i	−0.117971	+	0.820509i	−0.959784	+	0.280739i	$0.909420\pi$
$258$		0			0
$259$	−0.158703	−	1.10380i	−0.00986130	−	0.0685868i
$260$	48.8185	+	14.3344i	3.02760	+	0.888983i
$261$		0			0
$262$	8.84455	+	19.3669i	0.546418	+	1.19649i
$263$	13.5617	−	3.98209i	0.836253	−	0.245546i	0.164552	−	0.986368i	$-0.447382\pi$
$263$	13.5617	−	3.98209i	0.836253	−	0.245546i	0.671701	+	0.740822i	$0.265564\pi$
$264$		0			0
$265$	−3.31730	+	3.82837i	−0.203780	+	0.235175i
$266$	−7.96870	+	2.33982i	−0.488593	+	0.143464i
$267$		0			0
$268$	48.6758	−	31.2820i	2.97335	−	1.91085i
$269$	−12.6925	−	3.72684i	−0.773873	−	0.227230i	−0.129129	−	0.991628i	$-0.541218\pi$
$269$	−12.6925	−	3.72684i	−0.773873	−	0.227230i	−0.644745	+	0.764398i	$0.723036\pi$
$270$		0			0
$271$	3.14909	−	6.89554i	0.191294	−	0.418874i	−0.789546	−	0.613691i	$-0.789684\pi$
$271$	3.14909	−	6.89554i	0.191294	−	0.418874i	0.980840	+	0.194817i	$0.0624112\pi$
$272$	−9.17288	+	63.7988i	−0.556188	+	3.86837i
$273$		0			0
$274$	30.2033	+	34.8565i	1.82465	+	2.10576i
$275$	−9.99109			−0.602485
$276$		0			0
$277$	−12.5567			−0.754461			−0.377230	−	0.926119i	$-0.623123\pi$
$277$	−12.5567			−0.754461			−0.377230	+	0.926119i	$0.623123\pi$
$278$	−2.83661	−	3.27362i	−0.170129	−	0.196339i
$279$		0			0
$280$	1.12342	−	7.81358i	0.0671374	−	0.466951i
$281$	5.07185	−	11.1058i	0.302561	−	0.662517i	−0.695890	−	0.718148i	$-0.744990\pi$
$281$	5.07185	−	11.1058i	0.302561	−	0.662517i	0.998451	+	0.0556313i	$0.0177171\pi$
$282$		0			0
$283$	4.86428	+	1.42828i	0.289152	+	0.0849026i	0.423092	−	0.906087i	$-0.360945\pi$
$283$	4.86428	+	1.42828i	0.289152	+	0.0849026i	−0.133940	+	0.990989i	$0.542763\pi$
$284$	−56.1045	+	36.0561i	−3.32919	+	2.13954i
$285$		0			0
$286$	−66.2261	+	19.4457i	−3.91603	+	1.14985i
$287$	0.553153	−	0.638373i	0.0326516	−	0.0376820i
$288$		0			0
$289$	−15.2665	+	4.48263i	−0.898027	+	0.263684i
$290$	5.46121	+	11.9584i	0.320693	+	0.702220i
$291$		0			0
$292$	17.9749	+	5.27791i	1.05190	+	0.308867i
$293$	−4.34773	−	30.2391i	−0.253997	−	1.76659i	−0.573696	−	0.819068i	$-0.694491\pi$
$293$	−4.34773	−	30.2391i	−0.253997	−	1.76659i	0.319700	−	0.947519i	$-0.396418\pi$
$294$		0			0
$295$	−0.747236	+	5.19714i	−0.0435058	+	0.302589i
$296$	−12.3260	−	7.92146i	−0.716436	−	0.460426i
$297$		0			0
$298$	53.5163			3.10012
$299$	−26.5889	−	14.2667i	−1.53767	−	0.825067i
$300$		0			0
$301$	−3.16047	−	3.64738i	−0.182166	−	0.210231i
$302$	5.40966	+	3.47658i	0.311291	+	0.200055i
$303$		0			0
$304$	−23.9178	+	52.3726i	−1.37178	+	3.00377i
$305$	1.67125	+	11.6238i	0.0956953	+	0.665576i
$306$		0			0
$307$	−20.5592	+	13.2126i	−1.17338	+	0.754084i	−0.974157	−	0.225871i	$-0.927477\pi$
$307$	−20.5592	+	13.2126i	−1.17338	+	0.754084i	−0.199220	+	0.979955i	$0.563841\pi$
$308$	5.28421	+	11.5708i	0.301096	+	0.659308i
$309$		0			0
$310$	−10.9983	+	12.6928i	−0.624663	+	0.720900i
$311$	15.4147	−	17.7895i	0.874088	−	1.00875i	−0.125773	−	0.992059i	$-0.540141\pi$
$311$	15.4147	−	17.7895i	0.874088	−	1.00875i	0.999861	−	0.0166921i	$-0.00531352\pi$
$312$		0			0
$313$	12.0659	+	26.4207i	0.682007	+	1.49339i	0.860502	+	0.509447i	$0.170150\pi$
$313$	12.0659	+	26.4207i	0.682007	+	1.49339i	−0.178495	+	0.983941i	$0.557123\pi$
$314$	−25.5426	+	16.4153i	−1.44145	+	0.926367i
$315$		0			0
$316$	−0.260092	−	1.80898i	−0.0146313	−	0.101763i
$317$	−3.21208	+	7.03347i	−0.180408	+	0.395039i	−0.978132	−	0.207984i	$-0.933310\pi$
$317$	−3.21208	+	7.03347i	−0.180408	+	0.395039i	0.797724	+	0.603023i	$0.206037\pi$
$318$		0			0
$319$	−10.7343	−	6.89851i	−0.601005	−	0.386242i
$320$	−14.6549	−	16.9127i	−0.819234	−	0.945447i
$321$		0			0
$322$	−2.66276	+	7.30208i	−0.148390	+	0.406929i
$323$	−29.3984			−1.63577
$324$		0			0
$325$	12.7810	+	8.21385i	0.708962	+	0.455622i
$326$	−3.11089	+	21.6367i	−0.172296	+	1.19835i
$327$		0			0
$328$	−1.57946	−	10.9854i	−0.0872113	−	0.606568i
$329$	2.89967	+	0.851419i	0.159864	+	0.0469402i
$330$		0			0
$331$	−4.47746	−	9.80426i	−0.246103	−	0.538891i	0.745758	−	0.666217i	$-0.232088\pi$
$331$	−4.47746	−	9.80426i	−0.246103	−	0.538891i	−0.991861	+	0.127326i	$0.959360\pi$
$332$	5.37283	−	1.57760i	0.294872	−	0.0865823i
$333$		0			0
$334$	0.423888	−	0.489193i	0.0231941	−	0.0267675i
$335$	−17.7491	+	5.21161i	−0.969738	+	0.284741i
$336$		0			0
$337$	−13.9303	+	8.95249i	−0.758834	+	0.487673i	−0.861948	−	0.506996i	$-0.830756\pi$
$337$	−13.9303	+	8.95249i	−0.758834	+	0.487673i	0.103114	+	0.994670i	$0.467119\pi$
$338$	67.6351	+	19.8595i	3.67886	+	1.08021i
$339$		0			0
$340$	19.2716	−	42.1989i	1.04515	−	2.28856i
$341$	2.31989	−	16.1352i	0.125629	−	0.873770i
$342$		0			0
$343$	5.45463	+	6.29497i	0.294522	+	0.339897i
$344$	−63.4111			−3.41890
$345$		0			0
$346$	1.42496			0.0766061
$347$	8.40950	+	9.70508i	0.451446	+	0.520996i	0.935158	−	0.354231i	$-0.115257\pi$
$347$	8.40950	+	9.70508i	0.451446	+	0.520996i	−0.483712	+	0.875227i	$0.660712\pi$
$348$		0			0
$349$	2.18120	−	15.1706i	0.116757	−	0.812062i	−0.844332	−	0.535821i	$-0.820002\pi$
$349$	2.18120	−	15.1706i	0.116757	−	0.812062i	0.961088	−	0.276241i	$-0.0890887\pi$
$350$	1.62568	−	3.55974i	0.0868962	−	0.190276i
$351$		0			0
$352$	54.4885	+	15.9993i	2.90424	+	0.852763i
$353$	14.1770	−	9.11098i	0.754564	−	0.484929i	−0.105940	−	0.994373i	$-0.533785\pi$
$353$	14.1770	−	9.11098i	0.754564	−	0.484929i	0.860504	+	0.509444i	$0.170149\pi$
$354$		0			0
$355$	20.4579	−	6.00698i	1.08579	−	0.318818i
$356$	−5.44292	+	6.28147i	−0.288474	+	0.332917i
$357$		0			0
$358$	−1.32450	+	0.388909i	−0.0700021	+	0.0205545i
$359$	−1.96069	−	4.29331i	−0.103481	−	0.226592i	0.850808	−	0.525476i	$-0.176113\pi$
$359$	−1.96069	−	4.29331i	−0.103481	−	0.226592i	−0.954289	+	0.298884i	$0.903386\pi$
$360$		0			0
$361$	−6.96657	−	2.04557i	−0.366661	−	0.107661i
$362$	−7.20554	−	50.1156i	−0.378715	−	2.63402i
$363$		0			0
$364$	2.75279	−	19.1461i	0.144285	−	1.00353i
$365$	−5.03850	−	3.23805i	−0.263727	−	0.169487i
$366$		0			0
$367$	−26.2863			−1.37213			−0.686066	−	0.727539i	$-0.740664\pi$
$367$	−26.2863			−1.37213			−0.686066	+	0.727539i	$0.740664\pi$
$368$	26.1690	+	47.1013i	1.36415	+	2.45532i
$369$		0			0
$370$	5.09283	+	5.87744i	0.264764	+	0.305554i
$371$	1.62010	+	1.04118i	0.0841115	+	0.0540552i
$372$		0			0
$373$	−3.60024	+	7.88343i	−0.186414	+	0.408189i	−0.979647	−	0.200729i	$-0.935669\pi$
$373$	−3.60024	+	7.88343i	−0.186414	+	0.408189i	0.793233	+	0.608918i	$0.208396\pi$
$374$	8.95632	+	62.2926i	0.463120	+	3.22107i
$375$		0			0
$376$	33.4038	−	21.4673i	1.72267	−	1.10709i
$377$	8.06034	+	17.6497i	0.415129	+	0.909005i
$378$		0			0
$379$	−9.25610	+	10.6821i	−0.475454	+	0.548703i	−0.941921	−	0.335836i	$-0.890981\pi$
$379$	−9.25610	+	10.6821i	−0.475454	+	0.548703i	0.466467	+	0.884539i	$0.345527\pi$
$380$	27.1373	−	31.3181i	1.39212	−	1.60659i
$381$		0			0
$382$	−22.8847	−	50.1106i	−1.17089	−	2.56388i
$383$	0.857567	−	0.551125i	0.0438196	−	0.0281612i	−0.518548	−	0.855049i	$-0.673527\pi$
$383$	0.857567	−	0.551125i	0.0438196	−	0.0281612i	0.562367	+	0.826888i	$0.309891\pi$
$384$		0			0
$385$	−0.578758	−	4.02535i	−0.0294962	−	0.205151i
$386$	12.2109	−	26.7381i	0.621518	−	1.36093i
$387$		0			0
$388$	−20.8576	−	13.4043i	−1.05888	−	0.680503i
$389$	6.05906	+	6.99252i	0.307206	+	0.354535i	0.888269	−	0.459324i	$-0.151908\pi$
$389$	6.05906	+	6.99252i	0.307206	+	0.354535i	−0.581063	+	0.813859i	$0.697363\pi$
$390$		0			0
$391$	−16.3260	+	22.1453i	−0.825641	+	1.11994i
$392$	53.2198			2.68801
$393$		0			0
$394$	−31.5767	−	20.2931i	−1.59081	−	1.02235i
$395$	−0.0831526	+	0.578339i	−0.00418386	+	0.0290994i
$396$		0			0
$397$	−2.01011	−	13.9806i	−0.100884	−	0.701667i	−0.976003	−	0.217758i	$-0.930126\pi$
$397$	−2.01011	−	13.9806i	−0.100884	−	0.701667i	0.875118	−	0.483909i	$-0.160783\pi$
$398$	−13.8710	−	4.07288i	−0.695288	−	0.204155i
$399$		0			0
$400$	−11.2701	−	24.6781i	−0.563505	−	1.23390i
$401$	−24.6671	+	7.24291i	−1.23182	+	0.361694i	−0.831935	−	0.554873i	$-0.812767\pi$
$401$	−24.6671	+	7.24291i	−1.23182	+	0.361694i	−0.399881	+	0.916567i	$0.630949\pi$
$402$		0			0
$403$	−16.2327	+	18.7336i	−0.808610	+	0.933185i
$404$	66.1503	−	19.4235i	3.29110	−	0.966354i
$405$		0			0
$406$	4.20449	−	2.70206i	0.208665	−	0.134101i
$407$	−7.24256	−	2.12661i	−0.359000	−	0.105412i
$408$		0			0
$409$	−10.3198	+	22.5971i	−0.510279	+	1.11735i	0.462711	+	0.886509i	$0.346877\pi$
$409$	−10.3198	+	22.5971i	−0.510279	+	1.11735i	−0.972990	+	0.230846i	$0.925851\pi$
$410$	−0.838346	+	5.83083i	−0.0414030	+	0.287964i
$411$		0			0
$412$	−14.6300	−	16.8839i	−0.720769	−	0.831811i
$413$	1.99612			0.0982228
$414$		0			0
$415$	−1.79023			−0.0878792
$416$	−56.5505	−	65.2627i	−2.77262	−	3.19977i
$417$		0			0
$418$	−8.00041	+	55.6441i	−0.391313	+	2.72164i
$419$	0.275458	−	0.603169i	0.0134570	−	0.0294667i	−0.902784	−	0.430094i	$-0.858480\pi$
$419$	0.275458	−	0.603169i	0.0134570	−	0.0294667i	0.916241	+	0.400627i	$0.131208\pi$
$420$		0			0
$421$	−15.3580	−	4.50951i	−0.748503	−	0.219780i	−0.114834	−	0.993385i	$-0.536634\pi$
$421$	−15.3580	−	4.50951i	−0.748503	−	0.219780i	−0.633669	+	0.773604i	$0.718452\pi$
$422$	29.1402	−	18.7273i	1.41852	−	0.911629i
$423$		0			0
$424$	24.2784	−	7.12878i	1.17906	−	0.346204i
$425$	9.07150	−	10.4691i	0.440032	−	0.507824i
$426$		0			0
$427$	4.28363	−	1.25779i	0.207299	−	0.0608686i
$428$	−17.6552	−	38.6595i	−0.853396	−	1.86868i
$429$		0			0
$430$	32.2939	+	9.48236i	1.55735	+	0.457280i
$431$	0.224178	+	1.55919i	0.0107983	+	0.0751036i	0.994508	−	0.104661i	$-0.0333756\pi$
$431$	0.224178	+	1.55919i	0.0107983	+	0.0751036i	−0.983710	+	0.179764i	$0.942467\pi$
$432$		0			0
$433$	4.84193	−	33.6764i	0.232688	−	1.61838i	−0.453705	−	0.891152i	$-0.649898\pi$
$433$	4.84193	−	33.6764i	0.232688	−	1.61838i	0.686393	−	0.727230i	$-0.259193\pi$
$434$	5.37136	+	3.45197i	0.257834	+	0.165700i
$435$		0			0
$436$	−47.8550			−2.29184
$437$	−19.5659	+	14.8718i	−0.935965	+	0.711414i
$438$		0			0
$439$	−11.5518	−	13.3314i	−0.551335	−	0.636275i	0.409859	−	0.912149i	$-0.365578\pi$
$439$	−11.5518	−	13.3314i	−0.551335	−	0.636275i	−0.961194	+	0.275875i	$0.911033\pi$
$440$	−44.9507	−	28.8881i	−2.14294	−	1.37718i
$441$		0			0
$442$	39.7545	−	87.0503i	1.89093	−	4.14056i
$443$	−2.03800	−	14.1746i	−0.0968285	−	0.673457i	−0.979199	−	0.202902i	$-0.934963\pi$
$443$	−2.03800	−	14.1746i	−0.0968285	−	0.673457i	0.882371	−	0.470555i	$-0.155946\pi$
$444$		0			0
$445$	2.23542	−	1.43662i	0.105969	−	0.0681022i
$446$	21.3051	+	46.6517i	1.00883	+	2.20902i
$447$		0			0
$448$	−5.57138	+	6.42971i	−0.263223	+	0.303775i
$449$	9.62013	−	11.1022i	0.454002	−	0.523946i	−0.481891	−	0.876231i	$-0.660050\pi$
$449$	9.62013	−	11.1022i	0.454002	−	0.523946i	0.935893	+	0.352285i	$0.114595\pi$
$450$		0			0
$451$	−2.37517	−	5.20090i	−0.111843	−	0.244901i
$452$	−45.0456	+	28.9490i	−2.11877	+	1.36165i
$453$		0			0
$454$	8.83896	+	61.4763i	0.414833	+	2.88523i
$455$	−2.56894	+	5.62519i	−0.120434	+	0.263713i
$456$		0			0
$457$	6.29300	+	4.04427i	0.294374	+	0.189183i	0.679489	−	0.733686i	$-0.262202\pi$
$457$	6.29300	+	4.04427i	0.294374	+	0.189183i	−0.385114	+	0.922869i	$0.625838\pi$
$458$	25.0307	+	28.8870i	1.16961	+	1.34980i
$459$		0			0
$460$	−8.52109	−	37.8342i	−0.397298	−	1.76403i
$461$	−21.0428			−0.980061			−0.490031	−	0.871705i	$-0.663014\pi$
$461$	−21.0428			−0.980061			−0.490031	+	0.871705i	$0.663014\pi$
$462$		0			0
$463$	16.0046	+	10.2855i	0.743795	+	0.478008i	0.856840	−	0.515582i	$-0.172424\pi$
$463$	16.0046	+	10.2855i	0.743795	+	0.478008i	−0.113045	+	0.993590i	$0.536061\pi$
$464$	4.93093	−	34.2954i	0.228913	−	1.59212i
$465$		0			0
$466$	9.53845	+	66.3414i	0.441860	+	3.07321i
$467$	−11.8100	−	3.46773i	−0.546503	−	0.160468i	−0.00318504	−	0.999995i	$-0.501014\pi$
$467$	−11.8100	−	3.46773i	−0.546503	−	0.160468i	−0.543318	+	0.839527i	$0.682832\pi$
$468$		0			0
$469$	2.92144	+	6.39706i	0.134899	+	0.295389i
$470$	−20.2220	+	5.93772i	−0.932772	+	0.273887i
$471$		0			0
$472$	17.1751	−	19.8211i	0.790548	−	0.912341i
$473$	−31.3445	+	9.20356i	−1.44122	+	0.423180i
$474$		0			0
$475$	10.4097	−	6.68993i	0.477631	−	0.306955i
$476$	−16.9222	−	4.96881i	−0.775628	−	0.227745i
$477$		0			0
$478$	−24.6612	+	54.0004i	−1.12797	+	2.46992i
$479$	3.55643	−	24.7355i	0.162497	−	1.13019i	−0.731409	−	0.681940i	$-0.761137\pi$
$479$	3.55643	−	24.7355i	0.162497	−	1.13019i	0.893906	−	0.448255i	$-0.147954\pi$
$480$		0			0
$481$	7.51664	+	8.67467i	0.342729	+	0.395531i
$482$	6.04671			0.275420
$483$		0			0
$484$	30.7798			1.39908
$485$	5.19080	+	5.99051i	0.235702	+	0.272015i
$486$		0			0
$487$	2.55530	−	17.7725i	0.115792	−	0.805350i	−0.846316	−	0.532681i	$-0.821185\pi$
$487$	2.55530	−	17.7725i	0.115792	−	0.805350i	0.962108	−	0.272669i	$-0.0879064\pi$
$488$	24.3677	−	53.3579i	1.10308	−	2.41540i
$489$		0			0
$490$	−27.1037	−	7.95837i	−1.22442	−	0.359523i
$491$	21.7817	−	13.9983i	0.982996	−	0.631733i	0.0527258	−	0.998609i	$-0.483209\pi$
$491$	21.7817	−	13.9983i	0.982996	−	0.631733i	0.930270	+	0.366876i	$0.119573\pi$
$492$		0			0
$493$	16.9748	−	4.98426i	0.764508	−	0.224480i
$494$	55.9804	−	64.6048i	2.51868	−	2.90671i
$495$		0			0
$496$	42.4709	−	12.4706i	1.90700	−	0.559946i
$497$	−3.36730	−	7.37335i	−0.151044	−	0.330740i
$498$		0			0
$499$	−29.1237	−	8.55149i	−1.30376	−	0.382817i	−0.445151	−	0.895455i	$-0.646850\pi$
$499$	−29.1237	−	8.55149i	−1.30376	−	0.382817i	−0.858605	+	0.512638i	$0.828668\pi$
$500$	8.53312	+	59.3492i	0.381613	+	2.65418i
$501$		0			0
$502$	−2.66407	+	18.5290i	−0.118903	+	0.826990i
$503$	−23.8586	−	15.3330i	−1.06380	−	0.683664i	−0.113042	−	0.993590i	$-0.536059\pi$
$503$	−23.8586	−	15.3330i	−1.06380	−	0.683664i	−0.950761	+	0.309926i	$0.899696\pi$
$504$		0			0
$505$	−22.0414			−0.980828
$506$	37.4728	+	36.9278i	1.66587	+	1.64164i
$507$		0			0
$508$	29.7237	+	34.3029i	1.31877	+	1.52195i
$509$	−21.1039	−	13.5626i	−0.935412	−	0.601153i	−0.0183217	−	0.999832i	$-0.505832\pi$
$509$	−21.1039	−	13.5626i	−0.935412	−	0.601153i	−0.917090	+	0.398679i	$0.869469\pi$
$510$		0			0
$511$	−0.945880	+	2.07119i	−0.0418433	+	0.0916240i
$512$	−3.73867	−	26.0030i	−0.165227	−	1.14918i
$513$		0			0
$514$	−29.6399	+	19.0484i	−1.30736	+	0.840188i
$515$	2.96706	+	6.49696i	0.130744	+	0.286290i
$516$		0			0
$517$	13.3959	−	15.4597i	0.589151	−	0.679916i
$518$	1.93615	−	2.23444i	0.0850695	−	0.0981755i
$519$		0			0
$520$	33.7533	+	73.9095i	1.48018	+	3.24115i
$521$	−20.7529	+	13.3370i	−0.909199	+	0.584307i	−0.909505	−	0.415693i	$-0.863539\pi$
$521$	−20.7529	+	13.3370i	−0.909199	+	0.584307i	0.000305900		1.00000i	$0.499903\pi$
$522$		0			0
$523$	2.48731	+	17.2996i	0.108762	+	0.756460i	0.969088	+	0.246715i	$0.0793511\pi$
$523$	2.48731	+	17.2996i	0.108762	+	0.756460i	−0.860326	+	0.509745i	$0.829740\pi$
$524$	−16.7775	+	36.7376i	−0.732929	+	1.60489i
$525$		0			0
$526$	31.5251	+	20.2600i	1.37456	+	0.883377i
$527$	14.8008	+	17.0810i	0.644731	+	0.744059i
$528$		0			0
$529$	0.336986	+	22.9975i	0.0146515	+	0.999893i
$530$	−13.4305			−0.583383
$531$		0			0
$532$	−13.2533	−	8.51739i	−0.574604	−	0.369276i
$533$	−1.23734	+	8.60587i	−0.0535950	+	0.372762i
$534$		0			0
$535$	1.93370	+	13.4492i	0.0836012	+	0.581459i
$536$	88.6583	+	26.0324i	3.82945	+	1.12443i
$537$		0			0
$538$	−14.5694	−	31.9026i	−0.628133	−	1.37542i
$539$	26.3068	−	7.72439i	1.13312	−	0.332713i
$540$		0			0
$541$	7.81295	−	9.01662i	0.335905	−	0.387655i	−0.562519	−	0.826784i	$-0.690168\pi$
$541$	7.81295	−	9.01662i	0.335905	−	0.387655i	0.898424	+	0.439130i	$0.144713\pi$
$542$	19.2842	−	5.66234i	0.828326	−	0.243218i
$543$		0			0
$544$	−66.2379	+	42.5685i	−2.83993	+	1.82511i
$545$	14.6797	+	4.31036i	0.628810	+	0.184635i
$546$		0			0
$547$	9.49728	−	20.7961i	0.406074	−	0.889178i	−0.590544	−	0.807006i	$-0.701087\pi$
$547$	9.49728	−	20.7961i	0.406074	−	0.889178i	0.996618	−	0.0821729i	$-0.0261860\pi$
$548$	−12.4511	+	86.5993i	−0.531885	+	3.69934i
$549$		0			0
$550$	−17.3468	−	20.0192i	−0.739668	−	0.853622i
$551$	15.8032			0.673241
$552$		0			0
$553$	0.222129			0.00944589
$554$	−21.8013	−	25.1600i	−0.926247	−	1.06895i
$555$		0			0
$556$	1.16937	−	8.13316i	0.0495924	−	0.344923i
$557$	−9.15661	+	20.0502i	−0.387978	+	0.849553i	0.610371	+	0.792115i	$0.291020\pi$
$557$	−9.15661	+	20.0502i	−0.387978	+	0.849553i	−0.998349	+	0.0574375i	$0.981707\pi$
$558$		0			0
$559$	47.6635	+	13.9953i	2.01595	+	0.591936i
$560$	9.28979	−	5.97019i	0.392565	−	0.252286i
$561$		0			0
$562$	31.0587	−	9.11964i	1.31013	−	0.384689i
$563$	19.3485	−	22.3294i	0.815442	−	0.941070i	−0.183679	−	0.982986i	$-0.558801\pi$
$563$	19.3485	−	22.3294i	0.815442	−	0.941070i	0.999121	+	0.0419160i	$0.0133462\pi$
$564$		0			0
$565$	16.4254	−	4.82293i	0.691022	−	0.202902i
$566$	5.58362	+	12.2264i	0.234697	+	0.513914i
$567$		0			0
$568$	−102.189	−	30.0054i	−4.28775	−	1.25900i
$569$	3.61600	+	25.1499i	0.151591	+	1.05434i	0.913554	+	0.406717i	$0.133326\pi$
$569$	3.61600	+	25.1499i	0.151591	+	1.05434i	−0.761963	+	0.647620i	$0.775764\pi$
$570$		0			0
$571$	4.62566	−	32.1721i	0.193578	−	1.34636i	−0.628865	−	0.777515i	$-0.716480\pi$
$571$	4.62566	−	32.1721i	0.193578	−	1.34636i	0.822443	−	0.568848i	$-0.192611\pi$
$572$	−110.145	−	70.7861i	−4.60541	−	2.95972i
$573$		0			0
$574$	2.23951			0.0934753
$575$	0.741493	−	11.5566i	0.0309224	−	0.481945i
$576$		0			0
$577$	4.24934	+	4.90400i	0.176902	+	0.204156i	0.837275	−	0.546782i	$-0.184147\pi$
$577$	4.24934	+	4.90400i	0.176902	+	0.204156i	−0.660373	+	0.750938i	$0.729602\pi$
$578$	−35.4878	−	22.8066i	−1.47610	−	0.948631i
$579$		0			0
$580$	−10.3595	+	22.6842i	−0.430157	+	0.941912i
$581$	0.0968590	+	0.673669i	0.00401839	+	0.0279485i
$582$		0			0
$583$	10.9663	−	7.04759i	0.454176	−	0.291881i
$584$	12.4279	+	27.2134i	0.514272	+	1.12610i
$585$		0			0
$586$	53.0417	−	61.2134i	2.19113	−	2.52870i
$587$	18.2208	−	21.0279i	0.752053	−	0.867915i	−0.242713	−	0.970098i	$-0.578037\pi$
$587$	18.2208	−	21.0279i	0.752053	−	0.867915i	0.994766	+	0.102183i	$0.0325828\pi$
$588$		0			0
$589$	8.38687	+	18.3647i	0.345575	+	0.756703i
$590$	−11.7109	+	7.52615i	−0.482131	+	0.309847i
$591$		0			0
$592$	−2.91697	−	20.2880i	−0.119887	−	0.833832i
$593$	−17.3299	+	37.9473i	−0.711655	+	1.55831i	0.113587	+	0.993528i	$0.463766\pi$
$593$	−17.3299	+	37.9473i	−0.711655	+	1.55831i	−0.825242	+	0.564779i	$0.808961\pi$
$594$		0			0
$595$	4.74341	+	3.04841i	0.194461	+	0.124972i
$596$	66.4794	+	76.7213i	2.72310	+	3.14263i
$597$		0			0
$598$	−17.5778	−	78.0465i	−0.718809	−	3.19156i
$599$	36.3784			1.48638			0.743191	−	0.669079i	$-0.233311\pi$
$599$	36.3784			1.48638			0.743191	+	0.669079i	$0.233311\pi$
$600$		0			0
$601$	−0.585322	−	0.376163i	−0.0238758	−	0.0153440i	0.528648	−	0.848841i	$-0.322699\pi$
$601$	−0.585322	−	0.376163i	−0.0238758	−	0.0153440i	−0.552524	+	0.833497i	$0.686335\pi$
$602$	1.82100	−	12.6653i	0.0742183	−	0.516199i
$603$		0			0
$604$	1.73598	+	12.0740i	0.0706361	+	0.491285i
$605$	−9.44185	−	2.77238i	−0.383866	−	0.112713i
$606$		0			0
$607$	15.2919	+	33.4847i	0.620681	+	1.35910i	0.915023	+	0.403402i	$0.132172\pi$
$607$	15.2919	+	33.4847i	0.620681	+	1.35910i	−0.294342	+	0.955700i	$0.595101\pi$
$608$	−67.4845	+	19.8153i	−2.73686	+	0.803615i
$609$		0			0
$610$	−20.3890	+	23.5301i	−0.825526	+	0.952708i
$611$	−29.8462	+	8.76364i	−1.20745	+	0.354539i
$612$		0			0
$613$	−21.8242	+	14.0256i	−0.881470	+	0.566487i	−0.901241	−	0.433318i	$-0.857343\pi$
$613$	−21.8242	+	14.0256i	−0.881470	+	0.566487i	0.0197707	+	0.999805i	$0.493706\pi$
$614$	−62.1696	−	18.2546i	−2.50896	−	0.736697i
$615$		0			0
$616$	−8.43862	+	18.4780i	−0.340002	+	0.744500i
$617$	4.33998	−	30.1852i	0.174721	−	1.21521i	−0.694024	−	0.719952i	$-0.744164\pi$
$617$	4.33998	−	30.1852i	0.174721	−	1.21521i	0.868745	−	0.495260i	$-0.164927\pi$
$618$		0			0
$619$	−26.1063	−	30.1283i	−1.04930	−	1.21096i	−0.976925	−	0.213583i	$-0.931487\pi$
$619$	−26.1063	−	30.1283i	−1.04930	−	1.21096i	−0.0723776	−	0.997377i	$-0.523059\pi$
$620$	−31.8588			−1.27948
$621$		0			0
$622$	62.4083			2.50235
$623$	−0.661547	−	0.763466i	−0.0265043	−	0.0305876i
$624$		0			0
$625$	1.00985	−	7.02368i	0.0403941	−	0.280947i
$626$	−31.9902	+	70.0489i	−1.27859	+	2.79972i
$627$		0			0
$628$	−55.2628	−	16.2266i	−2.20522	−	0.647512i
$629$	8.80429	−	5.65817i	0.351050	−	0.225606i
$630$		0			0
$631$	−5.91973	+	1.73819i	−0.235661	+	0.0691962i	−0.397430	−	0.917632i	$-0.630098\pi$
$631$	−5.91973	+	1.73819i	−0.235661	+	0.0691962i	0.161770	+	0.986829i	$0.448280\pi$
$632$	1.91125	−	2.20570i	0.0760254	−	0.0877380i
$633$		0			0
$634$	−19.6699	+	5.77560i	−0.781191	+	0.229378i
$635$	−6.02816	−	13.1998i	−0.239220	−	0.523819i
$636$		0			0
$637$	−40.0031	−	11.7460i	−1.58498	−	0.465392i
$638$	−4.81452	−	33.4857i	−0.190609	−	1.32571i
$639$		0			0
$640$	2.16259	−	15.0411i	0.0854838	−	0.594553i
$641$	30.5941	+	19.6616i	1.20840	+	0.776588i	0.980389	−	0.197071i	$-0.0631431\pi$
$641$	30.5941	+	19.6616i	1.20840	+	0.776588i	0.228006	+	0.973660i	$0.426779\pi$
$642$		0			0
$643$	42.0938			1.66002			0.830008	−	0.557751i	$-0.188336\pi$
$643$	42.0938			1.66002			0.830008	+	0.557751i	$0.188336\pi$
$644$	−13.7761	+	5.25349i	−0.542853	+	0.207016i
$645$		0			0
$646$	−51.0421	−	58.9057i	−2.00822	−	2.31761i
$647$	−3.01789	−	1.93948i	−0.118645	−	0.0762488i	0.479972	−	0.877284i	$-0.340647\pi$
$647$	−3.01789	−	1.93948i	−0.118645	−	0.0762488i	−0.598618	+	0.801035i	$0.704283\pi$
$648$		0			0
$649$	5.61288	−	12.2905i	0.220325	−	0.482444i
$650$	5.73250	+	39.8704i	0.224847	+	1.56385i
$651$		0			0
$652$	−34.8829	+	22.4179i	−1.36612	+	0.877953i
$653$	−6.49135	−	14.2141i	−0.254026	−	0.556240i	0.739058	−	0.673642i	$-0.235271\pi$
$653$	−6.49135	−	14.2141i	−0.254026	−	0.556240i	−0.993085	+	0.117402i	$0.962544\pi$
$654$		0			0
$655$	8.45557	−	9.75825i	0.330387	−	0.381286i
$656$	10.1670	−	11.7334i	0.396956	−	0.458112i
$657$		0			0
$658$	3.32847	+	7.28833i	0.129757	+	0.284129i
$659$	−31.7833	+	20.4259i	−1.23810	+	0.795679i	−0.985133	−	0.171796i	$-0.945043\pi$
$659$	−31.7833	+	20.4259i	−1.23810	+	0.795679i	−0.252968	+	0.967475i	$0.581407\pi$
$660$		0			0
$661$	−2.52574	−	17.5669i	−0.0982398	−	0.683273i	−0.978115	−	0.208067i	$-0.933283\pi$
$661$	−2.52574	−	17.5669i	−0.0982398	−	0.683273i	0.879875	−	0.475206i	$-0.157626\pi$
$662$	11.8710	−	25.9939i	0.461380	−	1.01028i
$663$		0			0
$664$	7.52280	+	4.83461i	0.291941	+	0.187619i
$665$	3.29834	+	3.80649i	0.127904	+	0.147609i
$666$		0			0
$667$	8.77612	−	11.9043i	0.339813	−	0.460937i
$668$	1.22788			0.0475079
$669$		0			0
$670$	−41.2589	−	26.5155i	−1.59397	−	1.02438i
$671$	4.30068	−	29.9119i	0.166026	−	1.15473i
$672$		0			0
$673$	2.99142	+	20.8058i	0.115311	+	0.802003i	0.962611	+	0.270889i	$0.0873176\pi$
$673$	2.99142	+	20.8058i	0.115311	+	0.802003i	−0.847300	+	0.531115i	$0.821773\pi$
$674$	−42.1243	−	12.3688i	−1.62257	−	0.476429i
$675$		0			0
$676$	55.5475	+	121.632i	2.13644	+	4.67815i
$677$	−14.9365	+	4.38574i	−0.574055	+	0.168558i	−0.555859	−	0.831277i	$-0.687610\pi$
$677$	−14.9365	+	4.38574i	−0.574055	+	0.168558i	−0.0181960	+	0.999834i	$0.505792\pi$
$678$		0			0
$679$	1.97340	−	2.27742i	0.0757320	−	0.0873994i
$680$	71.0835	−	20.8720i	2.72593	−	0.800404i
$681$		0			0
$682$	36.3581	−	23.3659i	1.39222	−	0.894727i
$683$	40.0075	+	11.7472i	1.53084	+	0.449496i	0.935308	−	0.353834i	$-0.115122\pi$
$683$	40.0075	+	11.7472i	1.53084	+	0.449496i	0.595534	+	0.803330i	$0.296940\pi$
$684$		0			0
$685$	11.6195	−	25.4432i	0.443960	−	0.972136i
$686$	−3.14284	+	21.8589i	−0.119994	+	0.834578i
$687$		0			0
$688$	−58.0899	−	67.0393i	−2.21465	−	2.55585i
$689$	−19.8224			−0.755174
$690$		0			0
$691$	9.19006			0.349606			0.174803	−	0.984603i	$-0.444071\pi$
$691$	9.19006			0.349606			0.174803	+	0.984603i	$0.444071\pi$
$692$	1.77012	+	2.04283i	0.0672898	+	0.0776566i
$693$		0			0
$694$	−4.84538	+	33.7004i	−0.183928	+	1.27925i
$695$	−1.09127	+	2.38956i	−0.0413944	+	0.0906410i
$696$		0			0
$697$	7.60628	+	2.23340i	0.288108	+	0.0845962i
$698$	34.1844	−	21.9690i	1.29390	−	0.831538i
$699$		0			0
$700$	7.12273	−	2.09142i	0.269214	−	0.0790483i
$701$	−8.99829	+	10.3846i	−0.339861	+	0.392220i	−0.899792	−	0.436319i	$-0.856282\pi$
$701$	−8.99829	+	10.3846i	−0.339861	+	0.392220i	0.559931	+	0.828539i	$0.310827\pi$
$702$		0			0
$703$	8.96999	−	2.63383i	0.338309	−	0.0993366i
$704$	23.9228	+	52.3837i	0.901625	+	1.97428i
$705$		0			0
$706$	42.8701	+	12.5878i	1.61344	+	0.473748i
$707$	1.19253	+	8.29421i	0.0448496	+	0.311936i
$708$		0			0
$709$	0.411479	−	2.86190i	0.0154534	−	0.107481i	−0.980635	−	0.195845i	$-0.937255\pi$
$709$	0.411479	−	2.86190i	0.0154534	−	0.107481i	0.996088	+	0.0883645i	$0.0281640\pi$
$710$	47.5557	+	30.5622i	1.78473	+	1.14698i
$711$		0			0
$712$	−13.2732			−0.497433
$713$	18.4913	+	3.88089i	0.692506	+	0.145340i
$714$		0			0
$715$	27.4118	+	31.6349i	1.02514	+	1.18308i
$716$	−2.20287	−	1.41570i	−0.0823253	−	0.0529072i
$717$		0			0
$718$	5.19834	−	11.3828i	0.194000	−	0.424802i
$719$	4.64212	+	32.2866i	0.173122	+	1.20409i	0.872239	+	0.489081i	$0.162668\pi$
$719$	4.64212	+	32.2866i	0.173122	+	1.20409i	−0.699117	+	0.715007i	$0.746423\pi$
$720$		0			0
$721$	2.28429	−	1.46802i	0.0850714	−	0.0546720i
$722$	−7.99679	−	17.5105i	−0.297610	−	0.651674i
$723$		0			0
$724$	62.8952	−	72.5849i	2.33748	−	2.69760i
$725$	−4.87643	+	5.62770i	−0.181106	+	0.209008i
$726$		0			0
$727$	−1.23427	−	2.70267i	−0.0457764	−	0.100236i	0.885362	−	0.464902i	$-0.153911\pi$
$727$	−1.23427	−	2.70267i	−0.0457764	−	0.100236i	−0.931138	+	0.364666i	$0.881183\pi$
$728$	25.9861	−	16.7003i	0.963109	−	0.618952i
$729$		0			0
$730$	−2.25986	−	15.7176i	−0.0836410	−	0.581736i
$731$	18.8156	−	41.2004i	0.695921	−	1.52385i
$732$		0			0
$733$	22.2268	+	14.2843i	0.820964	+	0.527602i	0.882395	−	0.470510i	$-0.155930\pi$
$733$	22.2268	+	14.2843i	0.820964	+	0.527602i	−0.0614306	+	0.998111i	$0.519566\pi$
$734$	−45.6388	−	52.6700i	−1.68456	−	1.94408i
$735$		0			0
$736$	−22.5501	+	61.8391i	−0.831209	+	2.27942i
$737$	47.6026			1.75347
$738$		0			0
$739$	5.67451	+	3.64678i	0.208740	+	0.134149i	0.640834	−	0.767680i	$-0.278589\pi$
$739$	5.67451	+	3.64678i	0.208740	+	0.134149i	−0.432094	+	0.901829i	$0.642225\pi$
$740$	−2.09948	+	14.6022i	−0.0771785	+	0.536788i
$741$		0			0
$742$	0.726644	+	5.05392i	0.0266759	+	0.185535i
$743$	−2.88104	−	0.845950i	−0.105695	−	0.0310349i	0.228457	−	0.973554i	$-0.426632\pi$
$743$	−2.88104	−	0.845950i	−0.105695	−	0.0310349i	−0.334152	+	0.942519i	$0.608450\pi$
$744$		0			0
$745$	−13.4825	−	29.5225i	−0.493959	−	1.08162i
$746$	−22.0469	+	6.47356i	−0.807195	+	0.237014i
$747$		0			0
$748$	−78.1773	+	90.2214i	−2.85844	+	3.29882i
$749$	4.95634	−	1.45531i	0.181101	−	0.0531759i
$750$		0			0
$751$	−45.3199	+	29.1253i	−1.65375	+	1.06280i	−0.727340	+	0.686278i	$0.759243\pi$
$751$	−45.3199	+	29.1253i	−1.65375	+	1.06280i	−0.926408	+	0.376521i	$0.877120\pi$
$752$	53.2963	+	15.6492i	1.94351	+	0.570667i
$753$		0			0
$754$	−21.3703	+	46.7943i	−0.778259	+	1.70415i
$755$	0.555001	−	3.86012i	0.0201986	−	0.140484i
$756$		0			0
$757$	1.30984	+	1.51163i	0.0476068	+	0.0549412i	0.779054	−	0.626957i	$-0.215700\pi$
$757$	1.30984	+	1.51163i	0.0476068	+	0.0549412i	−0.731447	+	0.681899i	$0.761155\pi$
$758$	−37.4745			−1.36113
$759$		0			0
$760$	66.1774			2.40051
$761$	18.5654	+	21.4256i	0.672994	+	0.776677i	0.984842	−	0.173456i	$-0.0554933\pi$
$761$	18.5654	+	21.4256i	0.672994	+	0.776677i	−0.311848	+	0.950132i	$0.600948\pi$
$762$		0			0
$763$	0.827763	−	5.75722i	0.0299670	−	0.208425i
$764$	43.4108	−	95.0564i	1.57055	−	3.43902i
$765$		0			0
$766$	2.59322	+	0.761438i	0.0936968	+	0.0275119i
$767$	−17.2845	+	11.1080i	−0.624105	+	0.401088i
$768$		0			0
$769$	1.51762	−	0.445612i	0.0547266	−	0.0160692i	−0.254255	−	0.967137i	$-0.581830\pi$
$769$	1.51762	−	0.445612i	0.0547266	−	0.0160692i	0.308981	+	0.951068i	$0.400012\pi$
$770$	7.06077	−	8.14856i	0.254452	−	0.293654i
$771$		0			0
$772$	53.5006	−	15.7092i	1.92553	−	0.565387i
$773$	−5.53350	−	12.1167i	−0.199026	−	0.435806i	0.783634	−	0.621223i	$-0.213364\pi$
$773$	−5.53350	−	12.1167i	−0.199026	−	0.435806i	−0.982660	+	0.185417i	$0.940637\pi$
$774$		0			0
$775$	−9.12780	−	2.68016i	−0.327880	−	0.0962744i
$776$	−5.63480	−	39.1909i	−0.202277	−	1.40687i
$777$		0			0
$778$	−3.49110	+	24.2811i	−0.125162	+	0.870521i
$779$	5.95717	+	3.82844i	0.213438	+	0.137168i
$780$		0			0
$781$	−54.8675			−1.96331
$782$	−72.7182	+	5.73666i	−2.60040	+	0.205143i
$783$		0			0
$784$	48.7538	+	56.2649i	1.74121	+	2.00946i
$785$	15.4905	+	9.95517i	0.552881	+	0.355315i
$786$		0			0
$787$	−20.1798	+	44.1876i	−0.719331	+	1.57512i	0.0955074	+	0.995429i	$0.469553\pi$
$787$	−20.1798	+	44.1876i	−0.719331	+	1.57512i	−0.814839	+	0.579688i	$0.803175\pi$
$788$	−10.1331	−	70.4772i	−0.360976	−	2.51065i
$789$		0			0
$790$	−1.30319	+	0.837511i	−0.0463655	+	0.0297973i
$791$	−2.70356	−	5.91997i	−0.0961275	−	0.210490i
$792$		0			0
$793$	−30.0926	+	34.7288i	−1.06862	+	1.23325i
$794$	24.5231	−	28.3011i	0.870291	−	1.00437i
$795$		0			0
$796$	−11.3920	−	24.9449i	−0.403777	−	0.884149i
$797$	−9.29577	+	5.97403i	−0.329273	+	0.211611i	−0.694823	−	0.719181i	$-0.744517\pi$
$797$	−9.29577	+	5.97403i	−0.329273	+	0.211611i	0.365550	+	0.930792i	$0.380881\pi$
$798$		0			0
$799$	4.03636	+	28.0735i	0.142796	+	0.993169i
$800$	13.7674	−	30.1464i	0.486751	−	1.06584i
$801$		0			0
$802$	−57.3402	−	36.8503i	−2.02475	−	1.30123i
$803$	10.0930	+	11.6479i	0.356173	+	0.411046i
$804$		0			0
$805$	4.69905	−	0.370703i	0.165620	−	0.0130656i
$806$	−65.7202			−2.31489
$807$		0			0
$808$	92.6207	+	59.5237i	3.25839	+	2.09404i
$809$	−6.94029	+	48.2708i	−0.244007	+	1.69711i	0.387605	+	0.921825i	$0.373302\pi$
$809$	−6.94029	+	48.2708i	−0.244007	+	1.69711i	−0.631613	+	0.775284i	$0.717607\pi$
$810$		0			0
$811$	−2.50051	−	17.3915i	−0.0878049	−	0.610697i	−0.985448	−	0.169974i	$-0.945632\pi$
$811$	−2.50051	−	17.3915i	−0.0878049	−	0.610697i	0.897644	−	0.440722i	$-0.145278\pi$
$812$	9.09662	+	2.67101i	0.319229	+	0.0937340i
$813$		0			0
$814$	−8.31359	−	18.2042i	−0.291391	−	0.638058i
$815$	12.7197	−	3.73484i	0.445552	−	0.130826i
$816$		0			0
$817$	26.4952	−	30.5771i	0.926951	−	1.06976i
$818$	−63.1954	+	18.5558i	−2.20957	+	0.648789i
$819$		0			0
$820$	−9.40053	+	6.04135i	−0.328281	+	0.210973i
$821$	−10.7462	−	3.15538i	−0.375047	−	0.110124i	0.0887762	−	0.996052i	$-0.471704\pi$
$821$	−10.7462	−	3.15538i	−0.375047	−	0.110124i	−0.463823	+	0.885928i	$0.653523\pi$
$822$		0			0
$823$	12.8172	−	28.0658i	0.446780	−	0.978312i	−0.543524	−	0.839394i	$-0.682910\pi$
$823$	12.8172	−	28.0658i	0.446780	−	0.978312i	0.990304	−	0.138918i	$-0.0443625\pi$
$824$	5.07735	−	35.3138i	0.176878	−	1.23021i
$825$		0			0
$826$	3.46571	+	3.99965i	0.120588	+	0.139166i
$827$	6.07065			0.211097			0.105549	−	0.994414i	$-0.466340\pi$
$827$	6.07065			0.211097			0.105549	+	0.994414i	$0.466340\pi$
$828$		0			0
$829$	−30.4401			−1.05723			−0.528615	−	0.848862i	$-0.677288\pi$
$829$	−30.4401			−1.05723			−0.528615	+	0.848862i	$0.677288\pi$
$830$	−3.10824	−	3.58711i	−0.107889	−	0.124510i
$831$		0			0
$832$	12.4625	−	86.6786i	0.432059	−	3.00504i
$833$	−15.7916	+	34.5788i	−0.547147	+	1.19808i
$834$		0			0
$835$	−0.376656	−	0.110596i	−0.0130347	−	0.00382734i
$836$	−89.7100	+	57.6531i	−3.10269	+	1.99398i
$837$		0			0
$838$	1.68683	−	0.495298i	0.0582706	−	0.0171098i
$839$	−9.99142	+	11.5307i	−0.344942	+	0.398084i	−0.901539	−	0.432699i	$-0.857561\pi$
$839$	−9.99142	+	11.5307i	−0.344942	+	0.398084i	0.556597	+	0.830783i	$0.312107\pi$
$840$		0			0
$841$	18.7004	−	5.49093i	0.644841	−	0.189342i
$842$	−17.6291	−	38.6024i	−0.607540	−	1.33033i
$843$		0			0
$844$	63.0462	+	18.5120i	2.17014	+	0.637211i
$845$	−6.08389	−	42.3144i	−0.209292	−	1.45566i
$846$		0			0
$847$	−0.532408	+	3.70298i	−0.0182938	+	0.127236i
$848$	29.7777	+	19.1370i	1.02257	+	0.657166i
$849$		0			0
$850$	36.7271			1.25973
$851$	2.99734	−	8.21960i	0.102748	−	0.281764i
$852$		0			0
$853$	30.8250	+	35.5739i	1.05543	+	1.21803i	0.975217	+	0.221251i	$0.0710139\pi$
$853$	30.8250	+	35.5739i	1.05543	+	1.21803i	0.0802108	+	0.996778i	$0.474441\pi$
$854$	9.95757	+	6.39934i	0.340741	+	0.218981i
$855$		0			0
$856$	28.1945	−	61.7373i	0.963667	−	2.11014i
$857$	−4.30423	−	29.9366i	−0.147030	−	1.02262i	−0.921047	−	0.389451i	$-0.872665\pi$
$857$	−4.30423	−	29.9366i	−0.147030	−	1.02262i	0.774017	−	0.633164i	$-0.218244\pi$
$858$		0			0
$859$	18.9529	−	12.1803i	0.646665	−	0.415586i	−0.175781	−	0.984429i	$-0.556245\pi$
$859$	18.9529	−	12.1803i	0.646665	−	0.415586i	0.822446	+	0.568843i	$0.192609\pi$
$860$	26.5224	+	58.0760i	0.904407	+	1.98038i
$861$		0			0
$862$	−2.73494	+	3.15629i	−0.0931524	+	0.107504i
$863$	15.2041	−	17.5465i	0.517554	−	0.597290i	−0.435462	−	0.900207i	$-0.643415\pi$
$863$	15.2041	−	17.5465i	0.517554	−	0.597290i	0.953017	+	0.302917i	$0.0979606\pi$
$864$		0			0
$865$	−0.358992	−	0.786082i	−0.0122061	−	0.0267276i
$866$	75.8842	−	48.7678i	2.57865	−	1.65720i
$867$		0			0
$868$	1.72369	+	11.9885i	0.0585059	+	0.406918i
$869$	0.624603	−	1.36769i	0.0211882	−	0.0463957i
$870$		0			0
$871$	−60.8951	−	39.1349i	−2.06335	−	1.32604i
$872$	−50.0458	−	57.7559i	−1.69476	−	1.95586i
$873$		0			0
$874$	−63.7695	−	13.3837i	−2.15703	−	0.452710i
$875$	−7.28763			−0.246367
$876$		0			0
$877$	7.53656	+	4.84345i	0.254491	+	0.163552i	0.661666	−	0.749799i	$-0.269850\pi$
$877$	7.53656	+	4.84345i	0.254491	+	0.163552i	−0.407175	+	0.913350i	$0.633486\pi$
$878$	6.65588	−	46.2926i	0.224625	−	1.56230i
$879$		0			0
$880$	−10.6376	−	73.9865i	−0.358595	−	2.49408i
$881$	18.1213	+	5.32088i	0.610521	+	0.179265i	0.572354	−	0.820006i	$-0.306030\pi$
$881$	18.1213	+	5.32088i	0.610521	+	0.179265i	0.0381664	+	0.999271i	$0.487848\pi$
$882$		0			0
$883$	−22.0576	−	48.2995i	−0.742299	−	1.62541i	−0.779736	−	0.626109i	$-0.784647\pi$
$883$	−22.0576	−	48.2995i	−0.742299	−	1.62541i	0.0374372	−	0.999299i	$-0.488081\pi$
$884$	174.180	−	51.1438i	5.85830	−	1.72015i
$885$		0			0
$886$	24.8634	−	28.6939i	0.835301	−	0.963989i
$887$	13.8115	−	4.05542i	0.463745	−	0.136168i	−0.0415099	−	0.999138i	$-0.513217\pi$
$887$	13.8115	−	4.05542i	0.463745	−	0.136168i	0.505254	+	0.862970i	$0.331399\pi$
$888$		0			0
$889$	−4.64097	+	2.98257i	−0.155653	+	0.100032i
$890$	6.75974	+	1.98484i	0.226587	+	0.0665320i
$891$		0			0
$892$	−40.4143	+	88.4951i	−1.35317	+	2.96303i
$893$	−3.60556	+	25.0772i	−0.120655	+	0.839177i
$894$		0			0
$895$	0.548227	+	0.632688i	0.0183252	+	0.0211484i
$896$	−5.77702			−0.192997
$897$		0			0
$898$	38.9483			1.29972
$899$	−7.95622	−	9.18197i	−0.265355	−	0.306236i
$900$		0			0
$901$	−2.57217	+	17.8898i	−0.0856913	+	0.595996i
$902$	6.29726	−	13.7891i	0.209676	−	0.459126i
$903$		0			0
$904$	−82.0462	−	24.0909i	−2.72882	−	0.801253i
$905$	−25.8312	+	16.6007i	−0.858657	+	0.551825i
$906$		0			0
$907$	−49.9438	+	14.6648i	−1.65836	+	0.486937i	−0.970939	−	0.239327i	$-0.923073\pi$
$907$	−49.9438	+	14.6648i	−1.65836	+	0.486937i	−0.687416	+	0.726264i	$0.741255\pi$
$908$	−77.1529	+	89.0391i	−2.56041	+	2.95487i
$909$		0			0
$910$	−15.7315	+	4.61918i	−0.521494	+	0.153124i
$911$	4.69511	+	10.2809i	0.155556	+	0.340620i	0.971324	−	0.237759i	$-0.0764128\pi$
$911$	4.69511	+	10.2809i	0.155556	+	0.340620i	−0.815768	+	0.578379i	$0.803686\pi$
$912$		0			0
$913$	4.42026	+	1.29791i	0.146289	+	0.0429544i
$914$	2.82252	+	19.6311i	0.0933608	+	0.649339i
$915$		0			0
$916$	−10.3187	+	71.7684i	−0.340941	+	2.37129i
$917$	−4.12953	−	2.65389i	−0.136369	−	0.0876391i
$918$		0			0
$919$	−16.8713			−0.556533			−0.278266	−	0.960504i	$-0.589760\pi$
$919$	−16.8713			−0.556533			−0.278266	+	0.960504i	$0.589760\pi$
$920$	36.7507	−	49.8503i	1.21164	−	1.64352i
$921$		0			0
$922$	−36.5350	−	42.1636i	−1.20322	−	1.38858i
$923$	70.1887	+	45.1075i	2.31029	+	1.48473i
$924$		0			0
$925$	−1.82995	+	4.00703i	−0.0601684	+	0.131750i
$926$	7.17833	+	49.9264i	0.235894	+	1.64068i
$927$		0			0
$928$	35.6065	−	22.8829i	1.16884	−	0.751169i
$929$	15.4444	+	33.8184i	0.506713	+	1.10955i	0.974229	+	0.225562i	$0.0724217\pi$
$929$	15.4444	+	33.8184i	0.506713	+	1.10955i	−0.467516	+	0.883985i	$0.654851\pi$
$930$		0			0
$931$	−22.2370	+	25.6628i	−0.728788	+	0.841066i
$932$	−83.2585	+	96.0854i	−2.72722	+	3.14738i
$933$		0			0
$934$	−13.5565	−	29.6846i	−0.443582	−	0.971309i
$935$	32.1076	−	20.6343i	1.05003	−	0.674813i
$936$		0			0
$937$	−1.91802	−	13.3401i	−0.0626589	−	0.435802i	−0.996868	−	0.0790775i	$-0.974803\pi$
$937$	−1.91802	−	13.3401i	−0.0626589	−	0.435802i	0.934210	−	0.356725i	$-0.116107\pi$
$938$	−7.74556	+	16.9604i	−0.252902	+	0.553777i
$939$		0			0
$940$	−33.6327	−	21.6144i	−1.09698	−	0.704985i
$941$	−12.8182	−	14.7930i	−0.417863	−	0.482239i	0.507322	−	0.861757i	$-0.330635\pi$
$941$	−12.8182	−	14.7930i	−0.417863	−	0.482239i	−0.925185	+	0.379517i	$0.876090\pi$
$942$		0			0
$943$	6.19213	−	2.36136i	0.201644	−	0.0768966i
$944$	36.6890			1.19413
$945$		0			0
$946$	−72.8622	−	46.8257i	−2.36895	−	1.52243i
$947$	−0.614955	+	4.27711i	−0.0199833	+	0.138987i	−0.997371	−	0.0724700i	$-0.976912\pi$
$947$	−0.614955	+	4.27711i	−0.0199833	+	0.138987i	0.977387	+	0.211457i	$0.0678209\pi$
$948$		0			0
$949$	−3.33538	−	23.1981i	−0.108271	−	0.753041i
$950$	31.4783	+	9.24285i	1.02129	+	0.299878i
$951$		0			0
$952$	−11.7001	−	25.6196i	−0.379202	−	0.830336i
$953$	−3.12989	+	0.919018i	−0.101387	+	0.0297699i	−0.332033	−	0.943268i	$-0.607734\pi$
$953$	−3.12989	+	0.919018i	−0.101387	+	0.0297699i	0.230646	+	0.973038i	$0.425916\pi$
$954$		0			0
$955$	−21.8783	+	25.2489i	−0.707965	+	0.817035i
$956$	−108.050	+	31.7264i	−3.49459	+	1.02610i
$957$		0			0
$958$	55.7375	−	35.8203i	1.80080	−	1.15730i
$959$	−10.2030	−	2.99587i	−0.329472	−	0.0967418i
$960$		0			0
$961$	−6.43007	+	14.0799i	−0.207422	+	0.454190i
$962$	−4.33093	+	30.1223i	−0.139635	+	0.971182i
$963$		0			0
$964$	7.51138	+	8.66859i	0.241925	+	0.279197i
$965$	−17.8265			−0.573855
$966$		0			0
$967$	−13.9480			−0.448536			−0.224268	−	0.974527i	$-0.571999\pi$
$967$	−13.9480			−0.448536			−0.224268	+	0.974527i	$0.571999\pi$
$968$	32.1889	+	37.1480i	1.03459	+	1.19398i
$969$		0			0
$970$	−2.99083	+	20.8017i	−0.0960298	+	0.667902i
$971$	23.9480	−	52.4388i	0.768527	−	1.68284i	0.0386585	−	0.999252i	$-0.487692\pi$
$971$	23.9480	−	52.4388i	0.768527	−	1.68284i	0.729869	−	0.683587i	$-0.239581\pi$
$972$		0			0
$973$	0.958237	+	0.281364i	0.0307197	+	0.00902011i
$974$	40.0475	−	25.7370i	1.28320	−	0.824666i
$975$		0			0
$976$	78.7337	−	23.1183i	2.52020	−	0.739999i
$977$	−9.12746	+	10.5336i	−0.292013	+	0.337001i	−0.882732	−	0.469876i	$-0.844299\pi$
$977$	−9.12746	+	10.5336i	−0.292013	+	0.337001i	0.590719	+	0.806877i	$0.298844\pi$
$978$		0			0
$979$	−6.56100	+	1.92648i	−0.209690	+	0.0615707i
$980$	−22.2598	−	48.7422i	−0.711063	−	1.55701i
$981$		0			0
$982$	65.8663	+	19.3401i	2.10188	+	0.617167i
$983$	−4.19855	−	29.2016i	−0.133913	−	0.931385i	−0.940385	−	0.340112i	$-0.889535\pi$
$983$	−4.19855	−	29.2016i	−0.133913	−	0.931385i	0.806472	−	0.591273i	$-0.201374\pi$
$984$		0			0
$985$	−3.23960	+	22.5319i	−0.103222	+	0.717925i
$986$	39.4591	+	25.3588i	1.25663	+	0.807589i
$987$		0			0
$988$	162.158			5.15894
$989$	−8.31947	−	36.9390i	−0.264544	−	1.17459i
$990$		0			0
$991$	−9.09873	−	10.5005i	−0.289031	−	0.333559i	0.592602	−	0.805495i	$-0.298101\pi$
$991$	−9.09873	−	10.5005i	−0.289031	−	0.333559i	−0.881633	+	0.471936i	$0.843555\pi$
$992$	45.4884	+	29.2337i	1.44426	+	0.928169i
$993$		0			0
$994$	8.92766	−	19.5488i	0.283168	−	0.620052i
$995$	1.24772	+	8.67805i	0.0395552	+	0.275113i
$996$		0			0
$997$	13.1364	−	8.44226i	0.416034	−	0.267369i	−0.315835	−	0.948814i	$-0.602285\pi$
$997$	13.1364	−	8.44226i	0.416034	−	0.267369i	0.731869	+	0.681445i	$0.238648\pi$
$998$	−33.4305	−	73.2026i	−1.05822	−	2.31719i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	207.2.i.e.82.4	yes	40
3.2	odd	2	inner	207.2.i.e.82.1	✓	40
23.4	even	11		4761.2.a.bw.1.1		20
23.16	even	11	inner	207.2.i.e.154.4	yes	40
23.19	odd	22		4761.2.a.bx.1.1		20
69.50	odd	22		4761.2.a.bw.1.20		20
69.62	odd	22	inner	207.2.i.e.154.1	yes	40
69.65	even	22		4761.2.a.bx.1.20		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
207.2.i.e.82.1	✓	40	3.2	odd	2	inner
207.2.i.e.82.4	yes	40	1.1	even	1	trivial
207.2.i.e.154.1	yes	40	69.62	odd	22	inner
207.2.i.e.154.4	yes	40	23.16	even	11	inner
4761.2.a.bw.1.1		20	23.4	even	11
4761.2.a.bw.1.20		20	69.50	odd	22
4761.2.a.bx.1.1		20	23.19	odd	22
4761.2.a.bx.1.20		20	69.65	even	22

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:	\( N \)	\(=\)	\( 207 = 3^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	207.i (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(1.73622 + 2.00371i) q^{2} +(-0.715745 + 4.97812i) q^{4} +(0.667943 - 1.46259i) q^{5} +(-0.586514 - 0.172216i) q^{7} +(-6.75657 + 4.34219i) q^{8} +O(q^{10})\)	\(q+(1.73622 + 2.00371i) q^{2} +(-0.715745 + 4.97812i) q^{4} +(0.667943 - 1.46259i) q^{5} +(-0.586514 - 0.172216i) q^{7} +(-6.75657 + 4.34219i) q^{8} +(4.09030 - 1.20102i) q^{10} +(-2.70958 + 3.12702i) q^{11} +(6.03698 - 1.77262i) q^{13} +(-0.673248 - 1.47421i) q^{14} +(-10.7802 - 3.16536i) q^{16} +(-0.816433 - 5.67841i) q^{17} +(0.729295 - 5.07236i) q^{19} +(6.80287 + 4.37194i) q^{20} -10.9701 q^{22} +(-3.41592 - 3.36623i) q^{23} +(1.58128 + 1.82489i) q^{25} +(14.0333 + 9.01868i) q^{26} +(1.27711 - 2.79647i) q^{28} +(0.438878 + 3.05246i) q^{29} +(-3.31430 + 2.12997i) q^{31} +(-5.70153 - 12.4846i) q^{32} +(9.96037 - 11.4949i) q^{34} +(-0.643639 + 0.742800i) q^{35} +(0.757843 + 1.65944i) q^{37} +(11.4297 - 7.34544i) q^{38} +(1.83784 + 12.7824i) q^{40} +(-0.574040 + 1.25697i) q^{41} +(6.64191 + 4.26849i) q^{43} +(-13.6273 - 15.7268i) q^{44} +(0.814148 - 12.6890i) q^{46} -4.94390 q^{47} +(-5.57443 - 3.58247i) q^{49} +(-0.911101 + 6.33684i) q^{50} +(4.50336 + 31.3215i) q^{52} +(-3.02288 - 0.887597i) q^{53} +(2.76371 + 6.05168i) q^{55} +(4.71062 - 1.38316i) q^{56} +(-5.35425 + 6.17913i) q^{58} +(-3.13323 + 0.920000i) q^{59} +(-6.14413 + 3.94859i) q^{61} +(-10.0222 - 2.94278i) q^{62} +(5.78175 - 12.6603i) q^{64} +(1.43974 - 10.0136i) q^{65} +(-7.53402 - 8.69472i) q^{67} +28.8522 q^{68} -2.60585 q^{70} +(8.68383 + 10.0217i) q^{71} +(0.530112 - 3.68701i) q^{73} +(-2.00926 + 4.39966i) q^{74} +(24.7288 + 7.26103i) q^{76} +(2.12773 - 1.36741i) q^{77} +(-0.348667 + 0.102378i) q^{79} +(-11.8302 + 13.6528i) q^{80} +(-3.51527 + 1.03217i) q^{82} +(-0.462525 - 1.01279i) q^{83} +(-8.85053 - 2.59875i) q^{85} +(2.97901 + 20.7195i) q^{86} +(4.72937 - 32.8935i) q^{88} +(1.39028 + 0.893478i) q^{89} -3.84605 q^{91} +(19.2024 - 14.5955i) q^{92} +(-8.58370 - 9.90612i) q^{94} +(-6.93165 - 4.45470i) q^{95} +(-2.04791 + 4.48430i) q^{97} +(-2.50023 - 17.3895i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 4 q^{4} + 8 q^{7}+O(q^{10}) \) 40 * q - 4 * q^4 + 8 * q^7	\( 40 q - 4 q^{4} + 8 q^{7} - 56 q^{16} - 14 q^{19} - 28 q^{22} - 48 q^{25} - 64 q^{28} - 22 q^{31} - 10 q^{34} + 52 q^{37} + 6 q^{40} + 68 q^{43} + 84 q^{46} + 4 q^{49} + 110 q^{52} + 50 q^{55} + 18 q^{58} + 36 q^{61} + 116 q^{64} - 18 q^{67} + 96 q^{70} + 14 q^{73} + 34 q^{76} - 36 q^{79} - 72 q^{82} - 238 q^{85} - 160 q^{88} - 176 q^{91} - 206 q^{94} - 92 q^{97}+O(q^{100}) \) 40 * q - 4 * q^4 + 8 * q^7 - 56 * q^16 - 14 * q^19 - 28 * q^22 - 48 * q^25 - 64 * q^28 - 22 * q^31 - 10 * q^34 + 52 * q^37 + 6 * q^40 + 68 * q^43 + 84 * q^46 + 4 * q^49 + 110 * q^52 + 50 * q^55 + 18 * q^58 + 36 * q^61 + 116 * q^64 - 18 * q^67 + 96 * q^70 + 14 * q^73 + 34 * q^76 - 36 * q^79 - 72 * q^82 - 238 * q^85 - 160 * q^88 - 176 * q^91 - 206 * q^94 - 92 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more