LMFDB - Embedded newform 324.3.j.a.199.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [324,3,Mod(19,324)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(324, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 16]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("324.19");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 324 = 2^{2} \cdot 3^{4} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	324.j (of order $18$, degree $6$, not 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:	$8.82836056527$
Analytic rank:	$0$
Dimension:	$204$
Relative dimension:	$34$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 108)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			199.18
Character	$\chi$	$=$	324.199
Dual form			324.3.j.a.127.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.170992 + 1.99268i) q^{2} +(-3.94152 + 0.681463i) q^{4} +(3.81867 - 1.38988i) q^{5} +(5.53905 - 0.976684i) q^{7} +(-2.03190 - 7.73766i) q^{8} +O(q^{10})$	\(q+(0.170992 + 1.99268i) q^{2} +(-3.94152 + 0.681463i) q^{4} +(3.81867 - 1.38988i) q^{5} +(5.53905 - 0.976684i) q^{7} +(-2.03190 - 7.73766i) q^{8} +(3.42255 + 7.37172i) q^{10} +(7.44387 - 20.4519i) q^{11} +(-15.1056 - 12.6751i) q^{13} +(2.89335 + 10.8705i) q^{14} +(15.0712 - 5.37200i) q^{16} +(3.04352 - 5.27153i) q^{17} +(-8.89586 + 5.13603i) q^{19} +(-14.1042 + 8.08054i) q^{20} +(42.0268 + 11.3361i) q^{22} +(25.6005 + 4.51407i) q^{23} +(-6.50063 + 5.45468i) q^{25} +(22.6745 - 32.2680i) q^{26} +(-21.1667 + 7.62428i) q^{28} +(10.0865 - 8.46358i) q^{29} +(37.2448 + 6.56727i) q^{31} +(13.2817 + 29.1135i) q^{32} +(11.0249 + 5.16336i) q^{34} +(19.7943 - 11.4283i) q^{35} +(-13.6566 + 23.6539i) q^{37} +(-11.7556 - 16.8484i) q^{38} +(-18.5136 - 26.7235i) q^{40} +(32.5982 + 27.3531i) q^{41} +(13.6950 - 37.6266i) q^{43} +(-15.4030 + 85.6842i) q^{44} +(-4.61759 + 51.7855i) q^{46} +(18.8590 - 3.32535i) q^{47} +(-16.3178 + 5.93919i) q^{49} +(-11.9810 - 12.0210i) q^{50} +(68.1769 + 39.6654i) q^{52} -84.3059 q^{53} -88.4451i q^{55} +(-18.8121 - 40.8747i) q^{56} +(18.5899 + 18.6519i) q^{58} +(-5.90492 - 16.2236i) q^{59} +(3.64271 + 20.6588i) q^{61} +(-6.71788 + 75.3398i) q^{62} +(-55.7427 + 31.4444i) q^{64} +(-75.3005 - 27.4071i) q^{65} +(-17.2385 + 20.5441i) q^{67} +(-8.40375 + 22.8519i) q^{68} +(26.1575 + 37.4896i) q^{70} +(15.0660 + 8.69838i) q^{71} +(-20.6995 - 35.8526i) q^{73} +(-49.4697 - 23.1685i) q^{74} +(31.5632 - 26.3060i) q^{76} +(21.2570 - 120.554i) q^{77} +(3.44549 + 4.10617i) q^{79} +(50.0856 - 41.4611i) q^{80} +(-48.9319 + 69.6348i) q^{82} +(36.9625 + 44.0502i) q^{83} +(4.29539 - 24.3604i) q^{85} +(77.3193 + 20.8558i) q^{86} +(-173.375 - 16.0419i) q^{88} +(-17.1351 - 29.6789i) q^{89} +(-96.0505 - 55.4548i) q^{91} +(-103.981 - 0.346477i) q^{92} +(9.85110 + 37.0113i) q^{94} +(-26.8319 + 31.9770i) q^{95} +(146.828 + 53.4411i) q^{97} +(-14.6251 - 31.5005i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 204 q + 6 q^{2} - 6 q^{4} + 12 q^{5} + 3 q^{8}+O(q^{10}) $ 204 * q + 6 * q^2 - 6 * q^4 + 12 * q^5 + 3 * q^8	$ 204 q + 6 q^{2} - 6 q^{4} + 12 q^{5} + 3 q^{8} - 3 q^{10} - 12 q^{13} - 39 q^{14} - 6 q^{16} + 6 q^{17} + 69 q^{20} - 6 q^{22} - 12 q^{25} + 174 q^{26} - 12 q^{28} - 60 q^{29} + 96 q^{32} + 6 q^{34} - 6 q^{37} - 72 q^{38} + 69 q^{40} + 192 q^{41} + 219 q^{44} - 3 q^{46} - 12 q^{49} + 165 q^{50} + 21 q^{52} + 24 q^{53} - 99 q^{56} - 141 q^{58} - 12 q^{61} - 294 q^{62} - 3 q^{64} + 156 q^{65} - 375 q^{68} - 165 q^{70} - 6 q^{73} - 447 q^{74} - 54 q^{76} - 132 q^{77} - 798 q^{80} - 12 q^{82} + 138 q^{85} - 606 q^{86} - 198 q^{88} + 114 q^{89} - 723 q^{92} - 357 q^{94} + 168 q^{97} - 510 q^{98}+O(q^{100}) $ 204 * q + 6 * q^2 - 6 * q^4 + 12 * q^5 + 3 * q^8 - 3 * q^10 - 12 * q^13 - 39 * q^14 - 6 * q^16 + 6 * q^17 + 69 * q^20 - 6 * q^22 - 12 * q^25 + 174 * q^26 - 12 * q^28 - 60 * q^29 + 96 * q^32 + 6 * q^34 - 6 * q^37 - 72 * q^38 + 69 * q^40 + 192 * q^41 + 219 * q^44 - 3 * q^46 - 12 * q^49 + 165 * q^50 + 21 * q^52 + 24 * q^53 - 99 * q^56 - 141 * q^58 - 12 * q^61 - 294 * q^62 - 3 * q^64 + 156 * q^65 - 375 * q^68 - 165 * q^70 - 6 * q^73 - 447 * q^74 - 54 * q^76 - 132 * q^77 - 798 * q^80 - 12 * q^82 + 138 * q^85 - 606 * q^86 - 198 * q^88 + 114 * q^89 - 723 * q^92 - 357 * q^94 + 168 * q^97 - 510 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/324\mathbb{Z}\right)^\times$.

$n$	$163$	$245$
$\chi(n)$	$-1$	$e\left(\frac{7}{9}\right)$

Coefficient data

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

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

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

$2$	0.170992	+	1.99268i	0.0854959	+	0.996339i
$2$	0.170992	+	1.99268i	0.0854959	+	0.996339i
$3$		0			0
$3$		0			0
$4$	−3.94152	+	0.681463i	−0.985381	+	0.170366i
$5$	3.81867	−	1.38988i	0.763734	−	0.277977i	0.0693611	−	0.997592i	$-0.477904\pi$
$5$	3.81867	−	1.38988i	0.763734	−	0.277977i	0.694373	+	0.719615i	$0.255682\pi$
$6$		0			0
$7$	5.53905	−	0.976684i	0.791293	−	0.139526i	0.236628	−	0.971600i	$-0.423958\pi$
$7$	5.53905	−	0.976684i	0.791293	−	0.139526i	0.554665	+	0.832074i	$0.312847\pi$
$8$	−2.03190	−	7.73766i	−0.253988	−	0.967207i
$9$		0			0
$10$	3.42255	+	7.37172i	0.342255	+	0.737172i
$11$	7.44387	−	20.4519i	0.676715	−	1.85926i	0.201208	−	0.979549i	$-0.435513\pi$
$11$	7.44387	−	20.4519i	0.676715	−	1.85926i	0.475507	−	0.879712i	$-0.342265\pi$
$12$		0			0
$13$	−15.1056	−	12.6751i	−1.16197	−	0.975011i	−0.162042	−	0.986784i	$-0.551808\pi$
$13$	−15.1056	−	12.6751i	−1.16197	−	0.975011i	−0.999931	+	0.0117728i	$0.996253\pi$
$14$	2.89335	+	10.8705i	0.206668	+	0.776467i
$15$		0			0
$16$	15.0712	−	5.37200i	0.941951	−	0.335750i
$17$	3.04352	−	5.27153i	0.179030	−	0.310090i	−0.762518	−	0.646967i	$-0.776037\pi$
$17$	3.04352	−	5.27153i	0.179030	−	0.310090i	0.941549	+	0.336877i	$0.109371\pi$
$18$		0			0
$19$	−8.89586	+	5.13603i	−0.468203	+	0.270317i	−0.715487	−	0.698626i	$-0.753795\pi$
$19$	−8.89586	+	5.13603i	−0.468203	+	0.270317i	0.247284	+	0.968943i	$0.420462\pi$
$20$	−14.1042	+	8.08054i	−0.705212	+	0.404027i
$21$		0			0
$22$	42.0268	+	11.3361i	1.91031	+	0.515278i
$23$	25.6005	+	4.51407i	1.11307	+	0.196264i	0.699795	−	0.714344i	$-0.253275\pi$
$23$	25.6005	+	4.51407i	1.11307	+	0.196264i	0.413272	+	0.910608i	$0.364386\pi$
$24$		0			0
$25$	−6.50063	+	5.45468i	−0.260025	+	0.218187i
$26$	22.6745	−	32.2680i	0.872097	−	1.24108i
$27$		0			0
$28$	−21.1667	+	7.62428i	−0.755954	+	0.272296i
$29$	10.0865	−	8.46358i	0.347810	−	0.291848i	−0.452100	−	0.891967i	$-0.649325\pi$
$29$	10.0865	−	8.46358i	0.347810	−	0.291848i	0.799910	+	0.600120i	$0.204880\pi$
$30$		0			0
$31$	37.2448	+	6.56727i	1.20145	+	0.211847i	0.738323	−	0.674447i	$-0.235618\pi$
$31$	37.2448	+	6.56727i	1.20145	+	0.211847i	0.463122	+	0.886294i	$0.346729\pi$
$32$	13.2817	+	29.1135i	0.415054	+	0.909797i
$33$		0			0
$34$	11.0249	+	5.16336i	0.324261	+	0.151864i
$35$	19.7943	−	11.4283i	0.565552	−	0.326522i
$36$		0			0
$37$	−13.6566	+	23.6539i	−0.369096	+	0.639294i	−0.989424	−	0.145049i	$-0.953666\pi$
$37$	−13.6566	+	23.6539i	−0.369096	+	0.639294i	0.620328	+	0.784342i	$0.286999\pi$
$38$	−11.7556	−	16.8484i	−0.309357	−	0.443378i
$39$		0			0
$40$	−18.5136	−	26.7235i	−0.462840	−	0.668087i
$41$	32.5982	+	27.3531i	0.795078	+	0.667150i	0.946997	−	0.321243i	$-0.104101\pi$
$41$	32.5982	+	27.3531i	0.795078	+	0.667150i	−0.151919	+	0.988393i	$0.548545\pi$
$42$		0			0
$43$	13.6950	−	37.6266i	0.318487	−	0.875037i	−0.672381	−	0.740205i	$-0.734728\pi$
$43$	13.6950	−	37.6266i	0.318487	−	0.875037i	0.990869	−	0.134832i	$-0.0430494\pi$
$44$	−15.4030	+	85.6842i	−0.350068	+	1.94737i
$45$		0			0
$46$	−4.61759	+	51.7855i	−0.100382	+	1.12577i
$47$	18.8590	−	3.32535i	0.401256	−	0.0707522i	0.0306214	−	0.999531i	$-0.490251\pi$
$47$	18.8590	−	3.32535i	0.401256	−	0.0707522i	0.370634	+	0.928779i	$0.379140\pi$
$48$		0			0
$49$	−16.3178	+	5.93919i	−0.333016	+	0.121208i
$50$	−11.9810	−	12.0210i	−0.239619	−	0.240419i
$51$		0			0
$52$	68.1769	+	39.6654i	1.31109	+	0.762797i
$53$	−84.3059			−1.59068			−0.795339	−	0.606165i	$-0.792707\pi$
$53$	−84.3059			−1.59068			−0.795339	+	0.606165i	$0.792707\pi$
$54$		0			0
$55$		−	88.4451i		−	1.60809i
$56$	−18.8121	−	40.8747i	−0.335930	−	0.729906i
$57$		0			0
$58$	18.5899	+	18.6519i	0.320515	+	0.321585i
$59$	−5.90492	−	16.2236i	−0.100083	−	0.274977i	0.879538	−	0.475828i	$-0.157852\pi$
$59$	−5.90492	−	16.2236i	−0.100083	−	0.274977i	−0.979622	+	0.200851i	$0.935629\pi$
$60$		0			0
$61$	3.64271	+	20.6588i	0.0597166	+	0.338670i	0.999999	−	0.00172713i	$-0.000549762\pi$
$61$	3.64271	+	20.6588i	0.0597166	+	0.338670i	−0.940282	+	0.340397i	$0.889439\pi$
$62$	−6.71788	+	75.3398i	−0.108353	+	1.21516i
$63$		0			0
$64$	−55.7427	+	31.4444i	−0.870980	+	0.491318i
$65$	−75.3005	−	27.4071i	−1.15847	−	0.421648i
$66$		0			0
$67$	−17.2385	+	20.5441i	−0.257292	+	0.306628i	−0.879192	−	0.476469i	$-0.841917\pi$
$67$	−17.2385	+	20.5441i	−0.257292	+	0.306628i	0.621900	+	0.783097i	$0.286361\pi$
$68$	−8.40375	+	22.8519i	−0.123584	+	0.336057i
$69$		0			0
$70$	26.1575	+	37.4896i	0.373679	+	0.535565i
$71$	15.0660	+	8.69838i	0.212198	+	0.122512i	0.602332	−	0.798245i	$-0.294238\pi$
$71$	15.0660	+	8.69838i	0.212198	+	0.122512i	−0.390135	+	0.920758i	$0.627572\pi$
$72$		0			0
$73$	−20.6995	−	35.8526i	−0.283555	−	0.491131i	0.688703	−	0.725043i	$-0.258180\pi$
$73$	−20.6995	−	35.8526i	−0.283555	−	0.491131i	−0.972258	+	0.233913i	$0.924847\pi$
$74$	−49.4697	−	23.1685i	−0.668509	−	0.313088i
$75$		0			0
$76$	31.5632	−	26.3060i	0.415306	−	0.346131i
$77$	21.2570	−	120.554i	0.276064	−	1.56564i
$78$		0			0
$79$	3.44549	+	4.10617i	0.0436138	+	0.0519769i	0.787410	−	0.616429i	$-0.211421\pi$
$79$	3.44549	+	4.10617i	0.0436138	+	0.0519769i	−0.743797	+	0.668406i	$0.766977\pi$
$80$	50.0856	−	41.4611i	0.626070	−	0.518264i
$81$		0			0
$82$	−48.9319	+	69.6348i	−0.596731	+	0.849205i
$83$	36.9625	+	44.0502i	0.445332	+	0.530726i	0.941280	−	0.337626i	$-0.109624\pi$
$83$	36.9625	+	44.0502i	0.445332	+	0.530726i	−0.495949	+	0.868352i	$0.665180\pi$
$84$		0			0
$85$	4.29539	−	24.3604i	0.0505340	−	0.286593i
$86$	77.3193	+	20.8558i	0.899062	+	0.242509i
$87$		0			0
$88$	−173.375	−	16.0419i	−1.97017	−	0.182294i
$89$	−17.1351	−	29.6789i	−0.192529	−	0.333471i	0.753558	−	0.657381i	$-0.228336\pi$
$89$	−17.1351	−	29.6789i	−0.192529	−	0.333471i	−0.946088	+	0.323910i	$0.895002\pi$
$90$		0			0
$91$	−96.0505	−	55.4548i	−1.05550	−	0.609393i
$92$	−103.981	−	0.346477i	−1.13023	−	0.00376605i
$93$		0			0
$94$	9.85110	+	37.0113i	0.104799	+	0.393738i
$95$	−26.8319	+	31.9770i	−0.282441	+	0.336600i
$96$		0			0
$97$	146.828	+	53.4411i	1.51369	+	0.550939i	0.959564	−	0.281491i	$-0.0908291\pi$
$97$	146.828	+	53.4411i	1.51369	+	0.550939i	0.554129	+	0.832431i	$0.313051\pi$
$98$	−14.6251	−	31.5005i	−0.149236	−	0.321434i
$99$		0			0
$100$	21.9052	−	25.9297i	0.219052	−	0.259297i
$101$	3.69583	+	20.9601i	0.0365924	+	0.207526i	0.997622	−	0.0689187i	$-0.0219549\pi$
$101$	3.69583	+	20.9601i	0.0365924	+	0.207526i	−0.961030	+	0.276445i	$0.910844\pi$
$102$		0			0
$103$	−6.44120	−	17.6971i	−0.0625360	−	0.171816i	0.904489	−	0.426496i	$-0.140252\pi$
$103$	−6.44120	−	17.6971i	−0.0625360	−	0.171816i	−0.967025	+	0.254680i	$0.918030\pi$
$104$	−67.3827	+	142.637i	−0.647911	+	1.37151i
$105$		0			0
$106$	−14.4156	−	167.995i	−0.135996	−	1.58485i
$107$		−	45.7984i		−	0.428023i	−0.976831	−	0.214011i	$-0.931347\pi$
$107$		−	45.7984i		−	0.428023i	0.976831	−	0.214011i	$-0.0686530\pi$
$108$		0			0
$109$	15.3619			0.140935			0.0704677	−	0.997514i	$-0.477551\pi$
$109$	15.3619			0.140935			0.0704677	+	0.997514i	$0.477551\pi$
$110$	176.242	−	15.1234i	1.60220	−	0.137485i
$111$		0			0
$112$	78.2335	−	44.4756i	0.698513	−	0.397104i
$113$	178.553	−	64.9880i	1.58012	−	0.575115i	0.604886	−	0.796312i	$-0.293219\pi$
$113$	178.553	−	64.9880i	1.58012	−	0.575115i	0.975229	+	0.221197i	$0.0709964\pi$
$114$		0			0
$115$	104.034	−	18.3440i	0.904644	−	0.159513i
$116$	−33.9886	+	40.2330i	−0.293005	+	0.346836i
$117$		0			0
$118$	31.3188	−	14.5407i	0.265414	−	0.123226i
$119$	11.7096	−	32.1718i	0.0983998	−	0.270351i
$120$		0			0
$121$	−270.176	−	226.705i	−2.23286	−	1.87359i
$122$	−40.5435	+	10.7912i	−0.332324	+	0.0884528i
$123$		0			0
$124$	−151.277	−	0.504069i	−1.21997	−	0.00406508i
$125$	−68.0392	+	117.847i	−0.544314	+	0.942779i
$126$		0			0
$127$	−20.3113	+	11.7267i	−0.159931	+	0.0923364i	−0.577830	−	0.816157i	$-0.696100\pi$
$127$	−20.3113	+	11.7267i	−0.159931	+	0.0923364i	0.417898	+	0.908494i	$0.362767\pi$
$128$	−72.1900	−	105.701i	−0.563984	−	0.825785i
$129$		0			0
$130$	41.7378	−	154.736i	0.321060	−	1.19028i
$131$	−22.5210	−	3.97106i	−0.171916	−	0.0303134i	0.0870275	−	0.996206i	$-0.472263\pi$
$131$	−22.5210	−	3.97106i	−0.171916	−	0.0303134i	−0.258943	+	0.965892i	$0.583374\pi$
$132$		0			0
$133$	−44.2584	+	37.1372i	−0.332770	+	0.279227i
$134$	−43.8854	−	30.8380i	−0.327503	−	0.230134i
$135$		0			0
$136$	−46.9734	−	12.8385i	−0.345393	−	0.0944005i
$137$	−103.052	+	86.4710i	−0.752205	+	0.631175i	−0.936085	−	0.351774i	$-0.885579\pi$
$137$	−103.052	+	86.4710i	−0.752205	+	0.631175i	0.183880	+	0.982949i	$0.441134\pi$
$138$		0			0
$139$	−115.591	−	20.3818i	−0.831588	−	0.146631i	−0.258382	−	0.966043i	$-0.583189\pi$
$139$	−115.591	−	20.3818i	−0.831588	−	0.146631i	−0.573206	+	0.819412i	$0.694300\pi$
$140$	−70.2319	+	58.5339i	−0.501656	+	0.418099i
$141$		0			0
$142$	−14.7569	+	31.5091i	−0.103922	+	0.221895i
$143$	−371.675	+	214.587i	−2.59912	+	1.50061i
$144$		0			0
$145$	26.7536	−	46.3387i	0.184508	−	0.319577i
$146$	67.9031	−	47.3779i	0.465090	−	0.324506i
$147$		0			0
$148$	37.7084	−	102.539i	0.254787	−	0.692829i
$149$	72.4842	+	60.8215i	0.486471	+	0.408198i	0.852760	−	0.522303i	$-0.174927\pi$
$149$	72.4842	+	60.8215i	0.486471	+	0.408198i	−0.366288	+	0.930501i	$0.619372\pi$
$150$		0			0
$151$	−73.2545	+	201.265i	−0.485129	+	1.33288i	0.419915	+	0.907564i	$0.362060\pi$
$151$	−73.2545	+	201.265i	−0.485129	+	1.33288i	−0.905044	+	0.425318i	$0.860162\pi$
$152$	57.8164	+	58.3972i	0.380371	+	0.384192i
$153$		0			0
$154$	243.860	+	21.7445i	1.58351	+	0.141198i
$155$	151.353	−	26.6877i	0.976474	−	0.172179i
$156$		0			0
$157$	140.989	−	51.3158i	0.898019	−	0.326852i	0.148561	−	0.988903i	$-0.452536\pi$
$157$	140.989	−	51.3158i	0.898019	−	0.326852i	0.749459	+	0.662051i	$0.230314\pi$
$158$	−7.59313	+	7.56787i	−0.0480578	+	0.0478979i
$159$		0			0
$160$	91.1829	+	92.7148i	0.569893	+	0.579468i
$161$	146.211			0.908146
$162$		0			0
$163$			125.197i			0.768080i	0.923316	+	0.384040i	$0.125468\pi$
$163$			125.197i			0.768080i	−0.923316	+	0.384040i	$0.874532\pi$
$164$	−147.127	−	85.5986i	−0.897114	−	0.521942i
$165$		0			0
$166$	−81.4576	+	81.1866i	−0.490708	+	0.489076i
$167$	−94.4286	−	259.440i	−0.565441	−	1.55354i	−0.811544	−	0.584292i	$-0.801372\pi$
$167$	−94.4286	−	259.440i	−0.565441	−	1.55354i	0.246103	−	0.969244i	$-0.420850\pi$
$168$		0			0
$169$	38.1748	+	216.500i	0.225886	+	1.28107i
$170$	49.2768	+	4.39390i	0.289864	+	0.0258465i
$171$		0			0
$172$	−28.3379	+	157.639i	−0.164755	+	0.916504i
$173$	133.982	+	48.7655i	0.774463	+	0.281881i	0.698862	−	0.715257i	$-0.253690\pi$
$173$	133.982	+	48.7655i	0.774463	+	0.281881i	0.0756008	+	0.997138i	$0.475913\pi$
$174$		0			0
$175$	−30.6798	+	36.5628i	−0.175313	+	0.208930i
$176$	2.32066	−	348.223i	0.0131855	−	1.97854i
$177$		0			0
$178$	56.2105	−	39.2196i	0.315789	−	0.220335i
$179$	169.609	+	97.9239i	0.947537	+	0.547061i	0.892315	−	0.451413i	$-0.149080\pi$
$179$	169.609	+	97.9239i	0.947537	+	0.547061i	0.0552220	+	0.998474i	$0.482413\pi$
$180$		0			0
$181$	−3.70581	−	6.41865i	−0.0204741	−	0.0354622i	0.855607	−	0.517626i	$-0.173184\pi$
$181$	−3.70581	−	6.41865i	−0.0204741	−	0.0354622i	−0.876081	+	0.482164i	$0.839851\pi$
$182$	94.0797	−	200.880i	0.516921	−	1.10374i
$183$		0			0
$184$	−17.0895	−	207.260i	−0.0928779	−	1.12642i
$185$	−19.2738	+	109.307i	−0.104183	+	0.590851i
$186$		0			0
$187$	−85.1570	−	101.486i	−0.455385	−	0.542707i
$188$	−72.0672	+	25.9587i	−0.383336	+	0.138078i
$189$		0			0
$190$	−68.3079	−	47.9995i	−0.359515	−	0.252629i
$191$	87.5599	+	104.350i	0.458429	+	0.546334i	0.944899	−	0.327363i	$-0.106160\pi$
$191$	87.5599	+	104.350i	0.458429	+	0.546334i	−0.486470	+	0.873697i	$0.661716\pi$
$192$		0			0
$193$	−47.2377	+	267.898i	−0.244755	+	1.38807i	0.576307	+	0.817234i	$0.304493\pi$
$193$	−47.2377	+	267.898i	−0.244755	+	1.38807i	−0.821061	+	0.570840i	$0.806618\pi$
$194$	−81.3844	+	301.719i	−0.419507	+	1.55525i
$195$		0			0
$196$	60.2696	−	34.5294i	0.307498	−	0.176170i
$197$	−185.008	−	320.442i	−0.939125	−	1.62661i	−0.767108	−	0.641518i	$-0.778305\pi$
$197$	−185.008	−	320.442i	−0.939125	−	1.62661i	−0.172016	−	0.985094i	$-0.555028\pi$
$198$		0			0
$199$	157.019	+	90.6548i	0.789038	+	0.455552i	0.839624	−	0.543168i	$-0.182775\pi$
$199$	157.019	+	90.6548i	0.789038	+	0.455552i	−0.0505855	+	0.998720i	$0.516109\pi$
$200$	55.4151	+	39.2163i	0.277075	+	0.196081i
$201$		0			0
$202$	−41.1348	+	10.9486i	−0.203637	+	0.0542010i
$203$	47.6034	−	56.7315i	0.234499	−	0.279466i
$204$		0			0
$205$	162.499	+	59.1450i	0.792680	+	0.288512i
$206$	34.1631	−	15.8613i	0.165840	−	0.0769966i
$207$		0			0
$208$	−295.751	−	109.882i	−1.42188	−	0.528280i
$209$	38.8217	+	220.169i	0.185750	+	1.05344i
$210$		0			0
$211$	99.8063	+	274.215i	0.473015	+	1.29960i	0.915317	+	0.402733i	$0.131940\pi$
$211$	99.8063	+	274.215i	0.473015	+	1.29960i	−0.442302	+	0.896866i	$0.645838\pi$
$212$	332.294	−	57.4514i	1.56742	−	0.270997i
$213$		0			0
$214$	91.2615	−	7.83116i	0.426456	−	0.0365942i
$215$		−	162.718i		−	0.756828i
$216$		0			0
$217$	212.715			0.980253
$218$	2.62677	+	30.6114i	0.0120494	+	0.140419i
$219$		0			0
$220$	60.2720	+	348.608i	0.273964	+	1.58458i
$221$	−112.792	+	41.0528i	−0.510370	+	0.185759i
$222$		0			0
$223$	325.450	−	57.3856i	1.45942	−	0.257335i	0.613096	−	0.790008i	$-0.289924\pi$
$223$	325.450	−	57.3856i	1.45942	−	0.257335i	0.846321	+	0.532674i	$0.178813\pi$
$224$	102.003	+	148.289i	0.455370	+	0.662005i
$225$		0			0
$226$	160.031	+	344.686i	0.708103	+	1.52516i
$227$	−43.2105	+	118.720i	−0.190355	+	0.522995i	−0.997752	−	0.0670126i	$-0.978653\pi$
$227$	−43.2105	+	118.720i	−0.190355	+	0.522995i	0.807397	+	0.590008i	$0.200875\pi$
$228$		0			0
$229$	99.8093	+	83.7500i	0.435849	+	0.365720i	0.834153	−	0.551533i	$-0.185957\pi$
$229$	99.8093	+	83.7500i	0.435849	+	0.365720i	−0.398305	+	0.917253i	$0.630401\pi$
$230$	54.3427	+	204.170i	0.236273	+	0.887694i
$231$		0			0
$232$	−85.9831	−	60.8487i	−0.370617	−	0.262279i
$233$	−87.7066	+	151.912i	−0.376423	+	0.651984i	−0.990539	−	0.137232i	$-0.956179\pi$
$233$	−87.7066	+	151.912i	−0.376423	+	0.651984i	0.614116	+	0.789216i	$0.289513\pi$
$234$		0			0
$235$	67.3946	−	38.9103i	0.286785	−	0.165576i
$236$	34.3302	+	59.9219i	0.145467	+	0.253906i
$237$		0			0
$238$	66.1103	+	17.8323i	0.277774	+	0.0749256i
$239$	−217.844	−	38.4118i	−0.911483	−	0.160719i	−0.301806	−	0.953369i	$-0.597590\pi$
$239$	−217.844	−	38.4118i	−0.911483	−	0.160719i	−0.609677	+	0.792650i	$0.708701\pi$
$240$		0			0
$241$	−148.174	+	124.333i	−0.614829	+	0.515903i	−0.896173	−	0.443704i	$-0.853664\pi$
$241$	−148.174	+	124.333i	−0.614829	+	0.515903i	0.281344	+	0.959607i	$0.409220\pi$
$242$	405.551	−	577.138i	1.67583	−	2.38487i
$243$		0			0
$244$	−28.4361	−	78.9449i	−0.116541	−	0.323545i
$245$	−54.0575	+	45.3596i	−0.220643	+	0.185141i
$246$		0			0
$247$	199.478	+	35.1733i	0.807602	+	0.142402i
$248$	−24.8626	−	301.532i	−0.100253	−	1.21585i
$249$		0			0
$250$	−246.466	−	115.429i	−0.985864	−	0.461717i
$251$	−190.354	+	109.901i	−0.758383	+	0.437853i	−0.828715	−	0.559671i	$-0.810928\pi$
$251$	−190.354	+	109.901i	−0.758383	+	0.437853i	0.0703317	+	0.997524i	$0.477594\pi$
$252$		0			0
$253$	282.888	−	489.977i	1.11814	−	1.93667i
$254$	−26.8406	−	38.4686i	−0.105672	−	0.151451i
$255$		0			0
$256$	198.283	−	161.925i	0.774543	−	0.632521i
$257$	11.2364	+	9.42849i	0.0437215	+	0.0366867i	0.664387	−	0.747389i	$-0.268693\pi$
$257$	11.2364	+	9.42849i	0.0437215	+	0.0366867i	−0.620665	+	0.784076i	$0.713137\pi$
$258$		0			0
$259$	−52.5420	+	144.358i	−0.202865	+	0.557367i
$260$	315.476	+	56.7114i	1.21337	+	0.218121i
$261$		0			0
$262$	4.06213	−	45.5561i	0.0155043	−	0.173878i
$263$	7.69280	−	1.35645i	0.0292502	−	0.00515760i	−0.159004	−	0.987278i	$-0.550828\pi$
$263$	7.69280	−	1.35645i	0.0292502	−	0.00515760i	0.188254	+	0.982120i	$0.439717\pi$
$264$		0			0
$265$	−321.937	+	117.175i	−1.21486	+	0.442171i
$266$	−81.5702	−	81.8424i	−0.306655	−	0.307678i
$267$		0			0
$268$	53.9461	−	92.7224i	0.201291	−	0.345979i
$269$	−72.1191			−0.268101			−0.134050	−	0.990975i	$-0.542798\pi$
$269$	−72.1191			−0.268101			−0.134050	+	0.990975i	$0.542798\pi$
$270$		0			0
$271$		−	213.834i		−	0.789057i	−0.918884	−	0.394529i	$-0.870908\pi$
$271$		−	213.834i		−	0.789057i	0.918884	−	0.394529i	$-0.129092\pi$
$272$	17.5508	−	95.7981i	0.0645252	−	0.352199i
$273$		0			0
$274$	−189.930	−	190.564i	−0.693174	−	0.695488i
$275$	63.1685	+	173.554i	0.229704	+	0.631105i
$276$		0			0
$277$	−64.3062	−	364.698i	−0.232152	−	1.31660i	−0.848529	−	0.529149i	$-0.822511\pi$
$277$	−64.3062	−	364.698i	−0.232152	−	1.31660i	0.616376	−	0.787452i	$-0.288600\pi$
$278$	20.8492	−	233.820i	0.0749971	−	0.841079i
$279$		0			0
$280$	−128.648	−	129.941i	−0.459458	−	0.464074i
$281$	328.252	+	119.474i	1.16816	+	0.425174i	0.852005	−	0.523534i	$-0.175387\pi$
$281$	328.252	+	119.474i	1.16816	+	0.425174i	0.316152	+	0.948708i	$0.397609\pi$
$282$		0			0
$283$	−246.776	+	294.097i	−0.872001	+	1.03921i	0.126880	+	0.991918i	$0.459504\pi$
$283$	−246.776	+	294.097i	−0.872001	+	1.03921i	−0.998881	+	0.0472925i	$0.984941\pi$
$284$	−65.3107	−	24.0179i	−0.229967	−	0.0845701i
$285$		0			0
$286$	−491.155	−	703.935i	−1.71733	−	2.46131i
$287$	207.278	+	119.672i	0.722224	+	0.416976i
$288$		0			0
$289$	125.974	+	218.193i	0.435896	+	0.754994i
$290$	96.9127	+	45.3878i	0.334182	+	0.156510i
$291$		0			0
$292$	106.020	+	127.208i	0.363081	+	0.435643i
$293$	38.4745	−	218.200i	0.131312	−	0.744709i	−0.846045	−	0.533112i	$-0.821022\pi$
$293$	38.4745	−	218.200i	0.131312	−	0.744709i	0.977357	−	0.211597i	$-0.0678665\pi$
$294$		0			0
$295$	−45.0979	−	53.7456i	−0.152874	−	0.182189i
$296$	210.774	+	57.6074i	0.712075	+	0.194620i
$297$		0			0
$298$	−108.803	+	154.838i	−0.365112	+	0.519589i
$299$	−329.496	−	392.678i	−1.10199	−	1.31331i
$300$		0			0
$301$	39.1078	−	221.791i	0.129926	−	0.736848i
$302$	−413.582	−	111.558i	−1.36948	−	0.369397i
$303$		0			0
$304$	−106.481	+	125.195i	−0.350265	+	0.411825i
$305$	42.6237	+	73.8264i	0.139750	+	0.242054i
$306$		0			0
$307$	−433.287	−	250.158i	−1.41136	−	0.814847i	−0.415841	−	0.909438i	$-0.636513\pi$
$307$	−433.287	−	250.158i	−1.41136	−	0.814847i	−0.995516	+	0.0945902i	$0.969846\pi$
$308$	−1.63157	+	489.653i	−0.00529732	+	1.58978i
$309$		0			0
$310$	79.0602	+	297.035i	0.255033	+	0.958178i
$311$	35.6895	−	42.5330i	0.114757	−	0.136762i	−0.705608	−	0.708603i	$-0.749326\pi$
$311$	35.6895	−	42.5330i	0.114757	−	0.136762i	0.820365	+	0.571840i	$0.193770\pi$
$312$		0			0
$313$	−195.341	−	71.0983i	−0.624092	−	0.227151i	0.0105656	−	0.999944i	$-0.496637\pi$
$313$	−195.341	−	71.0983i	−0.624092	−	0.227151i	−0.634658	+	0.772793i	$0.718859\pi$
$314$	126.364	+	272.171i	0.402433	+	0.866787i
$315$		0			0
$316$	−16.3787	−	13.8366i	−0.0518313	−	0.0437867i
$317$	16.2685	+	92.2635i	0.0513203	+	0.291052i	0.999656	−	0.0262158i	$-0.00834571\pi$
$317$	16.2685	+	92.2635i	0.0513203	+	0.291052i	−0.948336	+	0.317268i	$0.897235\pi$
$318$		0			0
$319$	−98.0134	−	269.289i	−0.307252	−	0.844168i
$320$	−169.159	+	197.552i	−0.528623	+	0.617349i
$321$		0			0
$322$	25.0010	+	291.352i	0.0776428	+	0.904821i
$323$			62.5264i			0.193580i
$324$		0			0
$325$	167.335			0.514877
$326$	−249.477	+	21.4077i	−0.765268	+	0.0656677i
$327$		0			0
$328$	145.413	−	307.813i	0.443332	−	0.938453i
$329$	101.213	−	36.8386i	0.307639	−	0.111971i
$330$		0			0
$331$	274.896	−	48.4715i	0.830501	−	0.146440i	0.257794	−	0.966200i	$-0.417004\pi$
$331$	274.896	−	48.4715i	0.830501	−	0.146440i	0.572707	+	0.819760i	$0.305893\pi$
$332$	−175.707	−	148.436i	−0.529239	−	0.447098i
$333$		0			0
$334$	500.834	−	232.528i	1.49950	−	0.696191i
$335$	−37.2744	+	102.411i	−0.111267	+	0.305704i
$336$		0			0
$337$	403.060	+	338.208i	1.19602	+	1.00358i	0.999735	+	0.0230374i	$0.00733369\pi$
$337$	403.060	+	338.208i	1.19602	+	1.00358i	0.196290	+	0.980546i	$0.437111\pi$
$338$	−424.887	+	113.090i	−1.25706	+	0.334585i
$339$		0			0
$340$	−0.329692	+	98.9441i	−0.000969682	+	0.291012i
$341$	411.558	−	712.840i	1.20692	−	2.09044i
$342$		0			0
$343$	−323.261	+	186.635i	−0.942453	+	0.544125i
$344$	−318.968	−	29.5133i	−0.927234	−	0.0857945i
$345$		0			0
$346$	−74.2640	+	275.321i	−0.214636	+	0.795727i
$347$	227.315	+	40.0818i	0.655087	+	0.115510i	0.491306	−	0.870987i	$-0.336520\pi$
$347$	227.315	+	40.0818i	0.655087	+	0.115510i	0.163781	+	0.986497i	$0.447631\pi$
$348$		0			0
$349$	−266.323	+	223.471i	−0.763102	+	0.640319i	−0.938932	−	0.344102i	$-0.888184\pi$
$349$	−266.323	+	223.471i	−0.763102	+	0.640319i	0.175830	+	0.984421i	$0.443739\pi$
$350$	−78.1038	−	54.8830i	−0.223154	−	0.156809i
$351$		0			0
$352$	694.293	−	54.9190i	1.97242	−	0.156020i
$353$	−185.644	+	155.774i	−0.525903	+	0.441285i	−0.866684	−	0.498858i	$-0.833753\pi$
$353$	−185.644	+	155.774i	−0.525903	+	0.441285i	0.340781	+	0.940143i	$0.389309\pi$
$354$		0			0
$355$	69.6219	+	12.2762i	0.196118	+	0.0345809i
$356$	87.7635	+	105.303i	0.246527	+	0.295795i
$357$		0			0
$358$	−166.129	+	354.720i	−0.464047	+	0.990839i
$359$	286.224	−	165.252i	0.797282	−	0.460311i	−0.0452381	−	0.998976i	$-0.514405\pi$
$359$	286.224	−	165.252i	0.797282	−	0.460311i	0.842520	+	0.538665i	$0.181071\pi$
$360$		0			0
$361$	−127.742	+	221.256i	−0.353857	+	0.612898i
$362$	12.1566	−	8.48202i	0.0335819	−	0.0234310i
$363$		0			0
$364$	416.376	+	153.122i	1.14389	+	0.420664i
$365$	−128.875	−	108.139i	−0.353083	−	0.296272i
$366$		0			0
$367$	22.0119	−	60.4772i	0.0599780	−	0.164788i	−0.906084	−	0.423097i	$-0.860943\pi$
$367$	22.0119	−	60.4772i	0.0599780	−	0.164788i	0.966062	+	0.258309i	$0.0831652\pi$
$368$	410.081	−	69.4938i	1.11435	−	0.188842i
$369$		0			0
$370$	−221.110	−	19.7159i	−0.597594	−	0.0532861i
$371$	−466.975	+	82.3403i	−1.25869	+	0.221941i
$372$		0			0
$373$	−242.062	+	88.1032i	−0.648959	+	0.236202i	−0.645462	−	0.763792i	$-0.723335\pi$
$373$	−242.062	+	88.1032i	−0.648959	+	0.236202i	−0.00349656	+	0.999994i	$0.501113\pi$
$374$	187.668	−	187.044i	0.501786	−	0.500117i
$375$		0			0
$376$	−64.0502	−	139.168i	−0.170346	−	0.370127i
$377$	−259.640			−0.688701
$378$		0			0
$379$			299.350i			0.789843i	0.918715	+	0.394921i	$0.129228\pi$
$379$			299.350i			0.789843i	−0.918715	+	0.394921i	$0.870772\pi$
$380$	83.9674	−	144.323i	0.220967	−	0.379798i
$381$		0			0
$382$	−192.963	+	192.321i	−0.505140	+	0.503459i
$383$	94.7246	+	260.254i	0.247323	+	0.679513i	0.999782	+	0.0208747i	$0.00664512\pi$
$383$	94.7246	+	260.254i	0.247323	+	0.679513i	−0.752460	+	0.658639i	$0.771133\pi$
$384$		0			0
$385$	−86.3829	−	489.902i	−0.224371	−	1.27247i
$386$	−541.912	−	48.3210i	−1.40392	−	0.125184i
$387$		0			0
$388$	−615.145	−	110.581i	−1.58543	−	0.285004i
$389$	−346.254	−	126.026i	−0.890114	−	0.323975i	−0.143830	−	0.989602i	$-0.545942\pi$
$389$	−346.254	−	126.026i	−0.890114	−	0.323975i	−0.746284	+	0.665628i	$0.768164\pi$
$390$		0			0
$391$	101.712	−	121.215i	0.260132	−	0.310014i
$392$	79.1116	+	114.194i	0.201815	+	0.291310i
$393$		0			0
$394$	606.904	−	423.453i	1.54036	−	1.07475i
$395$	18.8643	+	10.8913i	0.0477577	+	0.0275729i
$396$		0			0
$397$	−226.740	−	392.726i	−0.571134	−	0.989233i	−0.996450	−	0.0841882i	$-0.973170\pi$
$397$	−226.740	−	392.726i	−0.571134	−	0.989233i	0.425316	−	0.905045i	$-0.360163\pi$
$398$	−153.797	+	328.389i	−0.386424	+	0.825097i
$399$		0			0
$400$	−68.6699	+	117.130i	−0.171675	+	0.292825i
$401$	−81.3303	+	461.247i	−0.202819	+	1.15024i	0.698017	+	0.716081i	$0.254066\pi$
$401$	−81.3303	+	461.247i	−0.202819	+	1.15024i	−0.900836	+	0.434160i	$0.857045\pi$
$402$		0			0
$403$	−479.366	−	571.286i	−1.18949	−	1.41758i
$404$	−28.8508	−	80.0962i	−0.0714127	−	0.198258i
$405$		0			0
$406$	121.187	+	85.1575i	0.298491	+	0.209748i
$407$	382.108	+	455.378i	0.938840	+	1.11887i
$408$		0			0
$409$	4.90627	−	27.8248i	0.0119958	−	0.0680313i	−0.978222	−	0.207560i	$-0.933448\pi$
$409$	4.90627	−	27.8248i	0.0119958	−	0.0680313i	0.990218	+	0.139529i	$0.0445588\pi$
$410$	−90.0707	+	333.922i	−0.219685	+	0.814445i
$411$		0			0
$412$	37.4481	+	65.3640i	0.0908933	+	0.158650i
$413$	−48.5530	−	84.0963i	−0.117562	−	0.203623i
$414$		0			0
$415$	202.372	+	116.840i	0.487644	+	0.281542i
$416$	168.389	−	608.126i	0.404781	−	1.46184i
$417$		0			0
$418$	−432.087	+	115.006i	−1.03370	+	0.275135i
$419$	85.6108	−	102.027i	0.204322	−	0.243501i	−0.654147	−	0.756368i	$-0.726972\pi$
$419$	85.6108	−	102.027i	0.204322	−	0.243501i	0.858468	+	0.512867i	$0.171416\pi$
$420$		0			0
$421$	312.802	+	113.851i	0.742997	+	0.270429i	0.685656	−	0.727926i	$-0.259516\pi$
$421$	312.802	+	113.851i	0.742997	+	0.270429i	0.0573411	+	0.998355i	$0.481738\pi$
$422$	−529.357	+	245.770i	−1.25440	+	0.582394i
$423$		0			0
$424$	171.302	+	652.331i	0.404013	+	1.53852i
$425$	8.96969	+	50.8697i	0.0211052	+	0.119693i
$426$		0			0
$427$	40.3543	+	110.873i	0.0945066	+	0.259655i
$428$	31.2099	+	180.516i	0.0729204	+	0.421766i
$429$		0			0
$430$	324.244	−	27.8234i	0.754057	−	0.0647057i
$431$		−	544.979i		−	1.26445i	−0.774784	−	0.632226i	$-0.782141\pi$
$431$		−	544.979i		−	1.26445i	0.774784	−	0.632226i	$-0.217859\pi$
$432$		0			0
$433$	−750.692			−1.73370			−0.866850	−	0.498568i	$-0.833859\pi$
$433$	−750.692			−1.73370			−0.866850	+	0.498568i	$0.833859\pi$
$434$	36.3725	+	423.872i	0.0838077	+	0.976664i
$435$		0			0
$436$	−60.5495	+	10.4686i	−0.138875	+	0.0240106i
$437$	−250.923	+	91.3286i	−0.574195	+	0.208990i
$438$		0			0
$439$	52.3809	−	9.23616i	0.119319	−	0.0210391i	−0.113670	−	0.993519i	$-0.536261\pi$
$439$	52.3809	−	9.23616i	0.119319	−	0.0210391i	0.232989	+	0.972479i	$0.425150\pi$
$440$	−684.358	+	179.712i	−1.55536	+	0.408436i
$441$		0			0
$442$	−101.091	−	217.738i	−0.228714	−	0.492619i
$443$	141.718	−	389.368i	0.319906	−	0.878934i	−0.670644	−	0.741779i	$-0.733982\pi$
$443$	141.718	−	389.368i	0.319906	−	0.878934i	0.990550	−	0.137154i	$-0.0437957\pi$
$444$		0			0
$445$	−106.684	−	89.5181i	−0.239738	−	0.201164i
$446$	170.000	+	638.704i	0.381167	+	1.43207i
$447$		0			0
$448$	−278.051	+	228.615i	−0.620649	+	0.510301i
$449$	−124.462	+	215.575i	−0.277199	+	0.480122i	−0.970687	−	0.240345i	$-0.922739\pi$
$449$	−124.462	+	215.575i	−0.277199	+	0.480122i	0.693489	+	0.720467i	$0.256073\pi$
$450$		0			0
$451$	802.079	−	463.081i	1.77845	−	1.02679i
$452$	−659.484	+	377.829i	−1.45904	+	0.835905i
$453$		0			0
$454$	−243.959	−	65.8045i	−0.537355	−	0.144944i
$455$	−443.861	−	78.2647i	−0.975519	−	0.172010i
$456$		0			0
$457$	−410.088	+	344.104i	−0.897347	+	0.752964i	−0.969670	−	0.244417i	$-0.921403\pi$
$457$	−410.088	+	344.104i	−0.897347	+	0.752964i	0.0723227	+	0.997381i	$0.476959\pi$
$458$	−149.820	+	213.208i	−0.327118	+	0.465520i
$459$		0			0
$460$	−397.552	+	143.199i	−0.864244	+	0.311302i
$461$	525.136	−	440.641i	1.13912	−	0.955838i	0.139713	−	0.990192i	$-0.455382\pi$
$461$	525.136	−	440.641i	1.13912	−	0.955838i	0.999410	+	0.0343542i	$0.0109374\pi$
$462$		0			0
$463$	−909.043	−	160.289i	−1.96338	−	0.346196i	−0.995499	−	0.0947721i	$-0.969788\pi$
$463$	−909.043	−	160.289i	−1.96338	−	0.346196i	−0.967877	−	0.251424i	$-0.919101\pi$
$464$	106.549	−	181.741i	0.229632	−	0.391683i
$465$		0			0
$466$	−317.709	−	148.795i	−0.681779	−	0.319303i
$467$	129.687	−	74.8750i	0.277703	−	0.160332i	−0.354680	−	0.934988i	$-0.615410\pi$
$467$	129.687	−	74.8750i	0.277703	−	0.160332i	0.632383	+	0.774656i	$0.282077\pi$
$468$		0			0
$469$	−75.4200	+	130.631i	−0.160810	+	0.278532i
$470$	89.0595	+	127.642i	0.189488	+	0.271579i
$471$		0			0
$472$	−113.535	+	78.6552i	−0.240540	+	0.166642i
$473$	−667.590	−	560.175i	−1.41140	−	1.18430i
$474$		0			0
$475$	29.8133	−	81.9115i	0.0627649	−	0.172445i
$476$	−24.2297	+	134.786i	−0.0509027	+	0.283163i
$477$		0			0
$478$	39.2928	−	440.662i	0.0822025	−	0.921886i
$479$	560.418	−	98.8168i	1.16997	−	0.206298i	0.445295	−	0.895384i	$-0.353099\pi$
$479$	560.418	−	98.8168i	1.16997	−	0.206298i	0.724680	+	0.689086i	$0.241988\pi$
$480$		0			0
$481$	506.107	−	184.208i	1.05220	−	0.382969i
$482$	−273.091	−	274.003i	−0.566579	−	0.568471i
$483$		0			0
$484$	1219.40	+	709.447i	2.51941	+	1.46580i
$485$	634.966			1.30921
$486$		0			0
$487$		−	75.8835i		−	0.155818i	−0.996960	−	0.0779091i	$-0.975176\pi$
$487$		−	75.8835i		−	0.155818i	0.996960	−	0.0779091i	$-0.0248244\pi$
$488$	152.449	−	70.1628i	0.312396	−	0.143776i
$489$		0			0
$490$	−99.6305	−	99.9630i	−0.203327	−	0.204006i
$491$	−16.9685	−	46.6205i	−0.0345590	−	0.0949502i	0.921213	−	0.389058i	$-0.127200\pi$
$491$	−16.9685	−	46.6205i	−0.0345590	−	0.0949502i	−0.955772	+	0.294108i	$0.904977\pi$
$492$		0			0
$493$	−13.9175	−	78.9303i	−0.0282303	−	0.160102i
$494$	−35.9800	+	403.509i	−0.0728339	+	0.816820i
$495$		0			0
$496$	596.604	−	101.103i	1.20283	−	0.203836i
$497$	91.9470	+	33.4660i	0.185004	+	0.0673360i
$498$		0			0
$499$	541.294	−	645.089i	1.08476	−	1.29276i	0.131266	−	0.991347i	$-0.458096\pi$
$499$	541.294	−	645.089i	1.08476	−	1.29276i	0.953492	−	0.301417i	$-0.0974597\pi$
$500$	187.870	−	510.865i	0.375739	−	1.02173i
$501$		0			0
$502$	−251.546	−	360.522i	−0.501088	−	0.718172i
$503$	262.850	+	151.757i	0.522565	+	0.301703i	0.737984	−	0.674819i	$-0.235778\pi$
$503$	262.850	+	151.757i	0.522565	+	0.301703i	−0.215418	+	0.976522i	$0.569111\pi$
$504$		0			0
$505$	43.2453	+	74.9030i	0.0856342	+	0.148323i
$506$	1024.74	+	479.923i	2.02517	+	0.948464i
$507$		0			0
$508$	72.0660	−	60.0625i	0.141862	−	0.118233i
$509$	18.5379	−	105.133i	0.0364202	−	0.206549i	−0.961168	−	0.275965i	$-0.911003\pi$
$509$	18.5379	−	105.133i	0.0364202	−	0.206549i	0.997588	+	0.0694162i	$0.0221136\pi$
$510$		0			0
$511$	−149.672	−	178.372i	−0.292900	−	0.349065i
$512$	356.570	+	367.426i	0.696425	+	0.717630i
$513$		0			0
$514$	−16.8666	+	24.0028i	−0.0328144	+	0.0466980i
$515$	−49.1937	−	58.6268i	−0.0955217	−	0.113838i
$516$		0			0
$517$	72.3744	−	410.456i	0.139989	−	0.793918i
$518$	−296.643	−	80.0152i	−0.572670	−	0.154470i
$519$		0			0
$520$	−59.0637	+	638.338i	−0.113584	+	1.22757i
$521$	227.354	+	393.788i	0.436380	+	0.755832i	0.997407	−	0.0719656i	$-0.0229272\pi$
$521$	227.354	+	393.788i	0.436380	+	0.755832i	−0.561028	+	0.827797i	$0.689594\pi$
$522$		0			0
$523$	508.326	+	293.482i	0.971943	+	0.561152i	0.899828	−	0.436245i	$-0.143692\pi$
$523$	508.326	+	293.482i	0.971943	+	0.561152i	0.0721152	+	0.997396i	$0.477025\pi$
$524$	91.4732	+	0.304798i	0.174567	+	0.000581676i
$525$		0			0
$526$	4.01837	+	15.0973i	0.00763948	+	0.0287021i
$527$	147.975	−	176.349i	0.280787	−	0.334629i
$528$		0			0
$529$	137.914	+	50.1965i	0.260706	+	0.0948894i
$530$	−288.541	−	621.480i	−0.544417	−	1.17260i
$531$		0			0
$532$	149.138	−	176.537i	0.280334	−	0.331837i
$533$	−145.712	−	826.374i	−0.273381	−	1.55042i
$534$		0			0
$535$	−63.6545	−	174.889i	−0.118980	−	0.326896i
$536$	193.990	+	91.6423i	0.361922	+	0.170974i
$537$		0			0
$538$	−12.3318	−	143.710i	−0.0229215	−	0.267119i
$539$			377.940i			0.701187i
$540$		0			0
$541$	408.236			0.754595			0.377297	−	0.926092i	$-0.376853\pi$
$541$	408.236			0.754595			0.377297	+	0.926092i	$0.376853\pi$
$542$	426.103	−	36.5639i	0.786168	−	0.0674612i
$543$		0			0
$544$	193.896	+	18.5925i	0.356426	+	0.0341773i
$545$	58.6622	−	21.3513i	0.107637	−	0.0391767i
$546$		0			0
$547$	332.257	−	58.5859i	0.607417	−	0.107104i	0.138524	−	0.990359i	$-0.455764\pi$
$547$	332.257	−	58.5859i	0.607417	−	0.107104i	0.468893	+	0.883255i	$0.344653\pi$
$548$	347.255	−	411.053i	0.633678	−	0.750098i
$549$		0			0
$550$	−335.036	+	155.551i	−0.609156	+	0.282819i
$551$	−46.2589	+	127.095i	−0.0839545	+	0.230663i
$552$		0			0
$553$	23.0952	+	19.3791i	0.0417634	+	0.0350437i
$554$	715.730	−	190.502i	1.29193	−	0.343866i
$555$		0			0
$556$	469.493	+	1.56440i	0.844411	+	0.00281367i
$557$	−460.391	+	797.421i	−0.826555	+	1.43164i	0.0741701	+	0.997246i	$0.476369\pi$
$557$	−460.391	+	797.421i	−0.826555	+	1.43164i	−0.900725	+	0.434390i	$0.856964\pi$
$558$		0			0
$559$	−683.794	+	394.788i	−1.22324	+	0.706240i
$560$	236.932	−	278.573i	0.423093	−	0.497452i
$561$		0			0
$562$	−181.945	+	674.529i	−0.323745	+	1.20023i
$563$	587.386	+	103.572i	1.04332	+	0.183965i	0.668943	−	0.743314i	$-0.266747\pi$
$563$	587.386	+	103.572i	1.04332	+	0.183965i	0.374372	+	0.927278i	$0.377858\pi$
$564$		0			0
$565$	591.510	−	496.336i	1.04692	−	0.878470i
$566$	−628.236	−	441.457i	−1.10996	−	0.779960i
$567$		0			0
$568$	36.6923	−	134.250i	0.0645992	−	0.236356i
$569$	349.724	−	293.453i	0.614629	−	0.515735i	−0.281481	−	0.959567i	$-0.590826\pi$
$569$	349.724	−	293.453i	0.614629	−	0.515735i	0.896110	+	0.443832i	$0.146381\pi$
$570$		0			0
$571$	518.842	+	91.4859i	0.908656	+	0.160221i	0.608393	−	0.793636i	$-0.291815\pi$
$571$	518.842	+	91.4859i	0.908656	+	0.160221i	0.300263	+	0.953857i	$0.402926\pi$
$572$	1318.73	−	1099.08i	2.30548	−	1.92147i
$573$		0			0
$574$	−203.025	+	433.502i	−0.353702	+	0.755230i
$575$	−191.042	+	110.298i	−0.332248	+	0.191823i
$576$		0			0
$577$	−529.613	+	917.317i	−0.917873	+	1.58980i	−0.115234	+	0.993338i	$0.536762\pi$
$577$	−529.613	+	917.317i	−0.917873	+	1.58980i	−0.802639	+	0.596465i	$0.796571\pi$
$578$	−413.248	+	288.335i	−0.714963	+	0.498849i
$579$		0			0
$580$	−73.8720	+	200.877i	−0.127366	+	0.346339i
$581$	247.760	+	207.896i	0.426438	+	0.357824i
$582$		0			0
$583$	−627.562	+	1724.21i	−1.07644	+	2.95748i
$584$	−235.355	+	233.014i	−0.403006	+	0.398997i
$585$		0			0
$586$	441.381	+	39.3569i	0.753209	+	0.0671619i
$587$	−254.912	+	44.9479i	−0.434262	+	0.0765722i	−0.386506	−	0.922287i	$-0.626318\pi$
$587$	−254.912	+	44.9479i	−0.434262	+	0.0765722i	−0.0477562	+	0.998859i	$0.515207\pi$
$588$		0			0
$589$	−365.054	+	132.869i	−0.619787	+	0.225584i
$590$	99.3863	−	99.0557i	0.168451	−	0.167891i
$591$		0			0
$592$	−78.7524	+	429.856i	−0.133028	+	0.726107i
$593$	676.112			1.14015			0.570077	−	0.821591i	$-0.306913\pi$
$593$	676.112			1.14015			0.570077	+	0.821591i	$0.306913\pi$
$594$		0			0
$595$		−	139.128i		−	0.233829i
$596$	−327.146	−	190.334i	−0.548903	−	0.319352i
$597$		0			0
$598$	726.140	−	723.725i	1.21428	−	1.21024i
$599$	55.7448	+	153.158i	0.0930631	+	0.255689i	0.977487	−	0.210996i	$-0.0676706\pi$
$599$	55.7448	+	153.158i	0.0930631	+	0.255689i	−0.884424	+	0.466684i	$0.845448\pi$
$600$		0			0
$601$	−87.8381	−	498.155i	−0.146153	−	0.828876i	−0.966434	−	0.256915i	$-0.917294\pi$
$601$	−87.8381	−	498.155i	−0.146153	−	0.828876i	0.820281	−	0.571961i	$-0.193817\pi$
$602$	448.645	+	40.0047i	0.745258	+	0.0664529i
$603$		0			0
$604$	151.580	−	843.212i	0.250960	−	1.39605i
$605$	−1346.81	−	490.198i	−2.22613	−	0.810244i
$606$		0			0
$607$	702.863	−	837.639i	1.15793	−	1.37997i	0.246176	−	0.969225i	$-0.420826\pi$
$607$	702.863	−	837.639i	1.15793	−	1.37997i	0.911752	−	0.410740i	$-0.134730\pi$
$608$	−267.680	−	190.774i	−0.440263	−	0.313774i
$609$		0			0
$610$	−139.824	+	97.5590i	−0.229219	+	0.159933i
$611$	−327.027	−	188.809i	−0.535233	−	0.309017i
$612$		0			0
$613$	123.629	+	214.132i	0.201679	+	0.349318i	0.949070	−	0.315067i	$-0.102027\pi$
$613$	123.629	+	214.132i	0.201679	+	0.349318i	−0.747391	+	0.664385i	$0.768694\pi$
$614$	424.396	−	906.175i	0.691198	−	1.47586i
$615$		0			0
$616$	−975.999	+	80.4755i	−1.58441	+	0.130642i
$617$	−18.2921	+	103.739i	−0.0296468	+	0.168135i	−0.996036	−	0.0889467i	$-0.971650\pi$
$617$	−18.2921	+	103.739i	−0.0296468	+	0.168135i	0.966390	+	0.257082i	$0.0827610\pi$
$618$		0			0
$619$	−181.659	−	216.492i	−0.293471	−	0.349746i	0.599082	−	0.800688i	$-0.295532\pi$
$619$	−181.659	−	216.492i	−0.293471	−	0.349746i	−0.892553	+	0.450942i	$0.851088\pi$
$620$	−578.376	+	208.332i	−0.932865	+	0.336019i
$621$		0			0
$622$	90.8572	+	63.8448i	0.146073	+	0.102644i
$623$	−123.899	−	147.657i	−0.198875	−	0.237010i
$624$		0			0
$625$	−59.1861	+	335.661i	−0.0946977	+	0.537057i
$626$	108.274	−	401.409i	0.172962	−	0.641228i
$627$		0			0
$628$	−520.742	+	298.341i	−0.829207	+	0.475066i
$629$	83.1280	+	143.982i	0.132159	+	0.228906i
$630$		0			0
$631$	205.862	+	118.855i	0.326248	+	0.188359i	0.654174	−	0.756344i	$-0.273016\pi$
$631$	205.862	+	118.855i	0.326248	+	0.188359i	−0.327926	+	0.944703i	$0.606350\pi$
$632$	24.7713	−	35.0034i	0.0391951	−	0.0553851i
$633$		0			0
$634$	−181.070	+	48.1942i	−0.285599	+	0.0760162i
$635$	−61.2633	+	73.0108i	−0.0964777	+	0.114978i
$636$		0			0
$637$	321.771	+	117.115i	0.505135	+	0.183854i
$638$	519.847	−	241.355i	0.814808	−	0.378300i
$639$		0			0
$640$	−422.581	−	303.300i	−0.660283	−	0.473906i
$641$	−30.6876	−	174.038i	−0.0478746	−	0.271510i	0.951469	−	0.307746i	$-0.0995746\pi$
$641$	−30.6876	−	174.038i	−0.0478746	−	0.271510i	−0.999343	+	0.0362352i	$0.988463\pi$
$642$		0			0
$643$	−158.986	−	436.809i	−0.247256	−	0.679330i	−0.999784	−	0.0207704i	$-0.993388\pi$
$643$	−158.986	−	436.809i	−0.247256	−	0.679330i	0.752528	−	0.658560i	$-0.228834\pi$
$644$	−576.296	+	99.6377i	−0.894870	+	0.154717i
$645$		0			0
$646$	−124.595	+	10.6915i	−0.192871	+	0.0165503i
$647$		−	932.596i		−	1.44142i	−0.693239	−	0.720708i	$-0.743817\pi$
$647$		−	932.596i		−	1.44142i	0.693239	−	0.720708i	$-0.256183\pi$
$648$		0			0
$649$	−375.759			−0.578982
$650$	28.6129	+	333.445i	0.0440199	+	0.512992i
$651$		0			0
$652$	−85.3172	−	493.467i	−0.130855	−	0.756852i
$653$	−81.2175	+	29.5607i	−0.124376	+	0.0452691i	−0.403458	−	0.914998i	$-0.632192\pi$
$653$	−81.2175	+	29.5607i	−0.124376	+	0.0452691i	0.279082	+	0.960267i	$0.409970\pi$
$654$		0			0
$655$	−91.5196	+	16.1374i	−0.139725	+	0.0246372i
$656$	638.236	+	237.127i	0.972920	+	0.361475i
$657$		0			0
$658$	90.7141	+	195.386i	0.137863	+	0.296940i
$659$	62.6424	−	172.109i	0.0950568	−	0.261166i	−0.883047	−	0.469285i	$-0.844512\pi$
$659$	62.6424	−	172.109i	0.0950568	−	0.261166i	0.978104	+	0.208119i	$0.0667340\pi$
$660$		0			0
$661$	854.686	+	717.167i	1.29302	+	1.08497i	0.991306	+	0.131574i	$0.0420031\pi$
$661$	854.686	+	717.167i	1.29302	+	1.08497i	0.301714	+	0.953399i	$0.402441\pi$
$662$	143.593	+	539.490i	0.216908	+	0.814940i
$663$		0			0
$664$	265.741	−	375.509i	0.400213	−	0.565526i
$665$	−117.392	+	203.329i	−0.176529	+	0.305757i
$666$		0			0
$667$	296.425	−	171.141i	0.444415	−	0.256583i
$668$	548.991	+	958.241i	0.821844	+	1.43449i
$669$		0			0
$670$	−210.445	−	56.7645i	−0.314097	−	0.0847232i
$671$	449.628	+	79.2815i	0.670086	+	0.118154i
$672$		0			0
$673$	−284.180	+	238.456i	−0.422259	+	0.354317i	−0.829022	−	0.559216i	$-0.811102\pi$
$673$	−284.180	+	238.456i	−0.422259	+	0.354317i	0.406763	+	0.913534i	$0.366658\pi$
$674$	−605.019	+	860.999i	−0.897654	+	1.27745i
$675$		0			0
$676$	−298.004	−	827.325i	−0.440834	−	1.22385i
$677$	−286.716	+	240.583i	−0.423509	+	0.355367i	−0.829496	−	0.558512i	$-0.811372\pi$
$677$	−286.716	+	240.583i	−0.423509	+	0.355367i	0.405987	+	0.913879i	$0.366928\pi$
$678$		0			0
$679$	865.484	+	152.608i	1.27464	+	0.224754i
$680$	−197.220	+	16.2617i	−0.290029	+	0.0239142i
$681$		0			0
$682$	1490.83	+	698.213i	2.18597	+	1.02377i
$683$	−4.35578	+	2.51481i	−0.00637743	+	0.00368201i	−0.503185	−	0.864179i	$-0.667839\pi$
$683$	−4.35578	+	2.51481i	−0.00637743	+	0.00368201i	0.496808	+	0.867861i	$0.334505\pi$
$684$		0			0
$685$	−273.338	+	473.434i	−0.399033	+	0.691145i
$686$	−427.178	−	612.242i	−0.622709	−	0.892481i
$687$		0			0
$688$	4.26946	−	640.648i	0.00620561	−	0.931174i
$689$	1273.50	+	1068.59i	1.84833	+	1.55093i
$690$		0			0
$691$	−312.035	+	857.308i	−0.451570	+	1.24068i	0.480049	+	0.877241i	$0.340619\pi$
$691$	−312.035	+	857.308i	−0.451570	+	1.24068i	−0.931619	+	0.363436i	$0.881604\pi$
$692$	−561.325	−	100.906i	−0.811163	−	0.145819i
$693$		0			0
$694$	−41.0010	+	459.819i	−0.0590793	+	0.662564i
$695$	−469.731	+	82.8263i	−0.675872	+	0.119174i
$696$		0			0
$697$	243.406	−	88.5925i	0.349219	−	0.127105i
$698$	−490.845	−	492.483i	−0.703217	−	0.705564i
$699$		0			0
$700$	96.0091	−	165.020i	0.137156	−	0.235743i
$701$	−540.204			−0.770619			−0.385310	−	0.922787i	$-0.625905\pi$
$701$	−540.204			−0.770619			−0.385310	+	0.922787i	$0.625905\pi$
$702$		0			0
$703$		−	280.562i		−	0.399092i
$704$	228.154	+	1374.11i	0.324083	+	1.95186i
$705$		0			0
$706$	−342.150	−	343.292i	−0.484632	−	0.486249i
$707$	40.9428	+	112.489i	0.0579106	+	0.159108i
$708$		0			0
$709$	−166.509	−	944.318i	−0.234850	−	1.33190i	−0.842929	−	0.538025i	$-0.819171\pi$
$709$	−166.509	−	944.318i	−0.234850	−	1.33190i	0.608079	−	0.793877i	$-0.291940\pi$
$710$	−12.5578	+	140.833i	−0.0176870	+	0.198357i
$711$		0			0
$712$	−194.828	+	192.890i	−0.273635	+	0.270913i
$713$	923.842	+	336.251i	1.29571	+	0.471600i
$714$		0			0
$715$	−1121.05	+	1336.02i	−1.56791	+	1.86856i
$716$	−735.250	−	270.387i	−1.02689	−	0.377635i
$717$		0			0
$718$	378.235	+	542.096i	0.526790	+	0.755008i
$719$	−209.447	−	120.924i	−0.291303	−	0.168184i	0.347226	−	0.937781i	$-0.387124\pi$
$719$	−209.447	−	120.924i	−0.291303	−	0.168184i	−0.638529	+	0.769598i	$0.720457\pi$
$720$		0			0
$721$	−52.9626	−	91.7339i	−0.0734571	−	0.127231i
$722$	−462.735	−	216.716i	−0.640908	−	0.300161i
$723$		0			0
$724$	18.9806	+	22.7739i	0.0262163	+	0.0314557i
$725$	−19.4025	+	110.037i	−0.0267621	+	0.151775i
$726$		0			0
$727$	−181.466	−	216.263i	−0.249610	−	0.297473i	0.626661	−	0.779292i	$-0.284421\pi$
$727$	−181.466	−	216.263i	−0.249610	−	0.297473i	−0.876271	+	0.481818i	$0.839976\pi$
$728$	−233.925	+	855.885i	−0.321325	+	1.17567i
$729$		0			0
$730$	193.450	−	275.298i	0.265000	−	0.377120i
$731$	−156.669	−	186.710i	−0.214321	−	0.255418i
$732$		0			0
$733$	200.749	−	1138.50i	0.273873	−	1.55321i	−0.468645	−	0.883387i	$-0.655258\pi$
$733$	200.749	−	1138.50i	0.273873	−	1.55321i	0.742518	−	0.669826i	$-0.233631\pi$
$734$	124.275	+	33.5215i	0.169313	+	0.0456696i
$735$		0			0
$736$	208.599	+	805.276i	0.283423	+	1.09413i
$737$	291.844	+	505.488i	0.395988	+	0.685872i
$738$		0			0
$739$	628.641	+	362.946i	0.850664	+	0.491131i	0.860875	−	0.508817i	$-0.169917\pi$
$739$	628.641	+	362.946i	0.850664	+	0.491131i	−0.0102107	+	0.999948i	$0.503250\pi$
$740$	1.47936	−	443.972i	0.00199914	−	0.599962i
$741$		0			0
$742$	−243.926	−	916.450i	−0.328742	−	1.23511i
$743$	−819.405	+	976.528i	−1.10283	+	1.31430i	−0.157748	+	0.987479i	$0.550423\pi$
$743$	−819.405	+	976.528i	−1.10283	+	1.31430i	−0.945085	+	0.326825i	$0.894021\pi$
$744$		0			0
$745$	361.328	+	131.513i	0.485004	+	0.176527i
$746$	−216.952	−	467.286i	−0.290820	−	0.626388i
$747$		0			0
$748$	404.807	+	341.979i	0.541186	+	0.457191i
$749$	−44.7306	−	253.680i	−0.0597204	−	0.338691i
$750$		0			0
$751$	184.174	+	506.015i	0.245239	+	0.673789i	0.999845	+	0.0176103i	$0.00560584\pi$
$751$	184.174	+	506.015i	0.245239	+	0.673789i	−0.754606	+	0.656178i	$0.772172\pi$
$752$	266.365	−	151.428i	0.354208	−	0.201367i
$753$		0			0
$754$	−44.3964	−	517.379i	−0.0588811	−	0.686179i
$755$			870.381i			1.15282i
$756$		0			0
$757$	−616.583			−0.814509			−0.407254	−	0.913315i	$-0.633514\pi$
$757$	−616.583			−0.814509			−0.407254	+	0.913315i	$0.633514\pi$
$758$	−596.508	+	51.1865i	−0.786951	+	0.0675283i
$759$		0			0
$760$	301.947	+	142.642i	0.397299	+	0.187687i
$761$	−883.018	+	321.392i	−1.16034	+	0.422329i	−0.849218	−	0.528042i	$-0.822926\pi$
$761$	−883.018	+	321.392i	−1.16034	+	0.422329i	−0.311120	+	0.950371i	$0.600704\pi$
$762$		0			0
$763$	85.0906	−	15.0038i	0.111521	−	0.0196642i
$764$	−416.230	−	351.628i	−0.544803	−	0.460246i
$765$		0			0
$766$	−502.404	+	233.257i	−0.655880	+	0.304513i
$767$	−116.439	+	319.914i	−0.151811	+	0.417098i
$768$		0			0
$769$	−359.959	−	302.041i	−0.468087	−	0.392771i	0.378009	−	0.925802i	$-0.376609\pi$
$769$	−359.959	−	302.041i	−0.468087	−	0.392771i	−0.846096	+	0.533030i	$0.821053\pi$
$770$	961.445	−	255.902i	1.24863	−	0.332341i
$771$		0			0
$772$	3.62572	−	1088.12i	0.00469653	−	1.40948i
$773$	28.5783	−	49.4991i	0.0369707	−	0.0640351i	−0.846948	−	0.531676i	$-0.821563\pi$
$773$	28.5783	−	49.4991i	0.0369707	−	0.0640351i	0.883919	+	0.467641i	$0.154896\pi$
$774$		0			0
$775$	−277.937	+	160.467i	−0.358629	+	0.207054i
$776$	115.168	−	1244.69i	0.148413	−	1.60399i
$777$		0			0
$778$	191.923	−	711.522i	0.246688	−	0.914553i
$779$	−430.476	−	75.9045i	−0.552600	−	0.0974383i
$780$		0			0
$781$	290.048	−	243.379i	0.371380	−	0.311625i
$782$	258.935	+	181.952i	0.331119	+	0.232675i
$783$		0			0
$784$	−214.024	+	177.170i	−0.272989	+	0.225982i
$785$	467.068	−	391.917i	0.594991	−	0.499257i
$786$		0			0
$787$	−886.857	−	156.377i	−1.12688	−	0.198700i	−0.421022	−	0.907050i	$-0.638329\pi$
$787$	−886.857	−	156.377i	−1.12688	−	0.198700i	−0.705861	+	0.708350i	$0.749440\pi$
$788$	947.581	+	1136.96i	1.20251	+	1.44284i
$789$		0			0
$790$	−18.4772	+	39.4528i	−0.0233889	+	0.0499402i
$791$	925.541	−	534.361i	1.17009	−	0.675552i
$792$		0			0
$793$	206.828	−	358.237i	0.260818	−	0.451749i
$794$	743.805	−	518.973i	0.936782	−	0.653618i
$795$		0			0
$796$	−680.671	−	250.315i	−0.855114	−	0.314467i
$797$	−585.520	−	491.310i	−0.734655	−	0.616449i	0.196741	−	0.980455i	$-0.436964\pi$
$797$	−585.520	−	491.310i	−0.734655	−	0.616449i	−0.931396	+	0.364006i	$0.881409\pi$
$798$		0			0
$799$	39.8681	−	109.537i	0.0498975	−	0.137092i
$800$	−245.144	−	116.809i	−0.306430	−	0.146011i
$801$		0			0
$802$	−933.023	−	83.1955i	−1.16337	−	0.103735i
$803$	−887.336	+	156.461i	−1.10503	+	0.194846i
$804$		0			0
$805$	558.334	−	203.217i	0.693582	−	0.252443i
$806$	1056.42	−	1052.91i	1.31070	−	1.30634i
$807$		0			0
$808$	154.673	−	71.1860i	0.191426	−	0.0881015i
$809$	−388.814			−0.480610			−0.240305	−	0.970697i	$-0.577247\pi$
$809$	−388.814			−0.480610			−0.240305	+	0.970697i	$0.577247\pi$
$810$		0			0
$811$			1206.55i			1.48774i	0.668326	+	0.743869i	$0.267011\pi$
$811$			1206.55i			1.48774i	−0.668326	+	0.743869i	$0.732989\pi$
$812$	−148.969	+	256.048i	−0.183460	+	0.315331i
$813$		0			0
$814$	−842.085	+	839.284i	−1.03450	+	1.03106i
$815$	174.009	+	478.087i	0.213508	+	0.586609i
$816$		0			0
$817$	71.4228	+	405.059i	0.0874208	+	0.495788i
$818$	56.2848	+	5.01879i	0.0688078	+	0.00613544i
$819$		0			0
$820$	−680.801	−	122.384i	−0.830245	−	0.149249i
$821$	979.566	+	356.533i	1.19314	+	0.434266i	0.860824	−	0.508903i	$-0.169949\pi$
$821$	979.566	+	356.533i	1.19314	+	0.434266i	0.332313	+	0.943169i	$0.392171\pi$
$822$		0			0
$823$	−136.341	+	162.485i	−0.165663	+	0.197430i	−0.842489	−	0.538713i	$-0.818911\pi$
$823$	−136.341	+	162.485i	−0.165663	+	0.197430i	0.676826	+	0.736143i	$0.263355\pi$
$824$	−123.846	+	85.7986i	−0.150298	+	0.104124i
$825$		0			0
$826$	159.275	−	111.130i	0.192826	−	0.134540i
$827$	−1235.32	−	713.212i	−1.49373	−	0.862408i	−0.493761	−	0.869598i	$-0.664378\pi$
$827$	−1235.32	−	713.212i	−1.49373	−	0.862408i	−0.999974	+	0.00718959i	$0.997711\pi$
$828$		0			0
$829$	363.827	+	630.168i	0.438875	+	0.760154i	0.997603	−	0.0691970i	$-0.0220437\pi$
$829$	363.827	+	630.168i	0.438875	+	0.760154i	−0.558728	+	0.829351i	$0.688710\pi$
$830$	−198.220	+	423.242i	−0.238819	+	0.509930i
$831$		0			0
$832$	1240.59	+	231.560i	1.49110	+	0.278317i
$833$	−18.3549	+	104.096i	−0.0220347	+	0.124965i
$834$		0			0
$835$	−721.183	−	859.473i	−0.863693	−	1.02931i
$836$	−303.054	−	841.345i	−0.362504	−	1.00639i
$837$		0			0
$838$	217.946	+	153.149i	0.260078	+	0.182755i
$839$	−499.135	−	594.846i	−0.594916	−	0.708994i	0.381627	−	0.924317i	$-0.375364\pi$
$839$	−499.135	−	594.846i	−0.594916	−	0.708994i	−0.976543	+	0.215323i	$0.930920\pi$
$840$		0			0
$841$	−115.933	+	657.488i	−0.137851	+	0.781793i
$842$	−173.381	+	642.780i	−0.205915	+	0.763397i
$843$		0			0
$844$	−580.256	−	1012.81i	−0.687508	−	1.20001i
$845$	446.687	+	773.684i	0.528623	+	0.915602i
$846$		0			0
$847$	−1717.94	−	991.852i	−2.02826	−	1.17102i
$848$	−1270.59	+	452.892i	−1.49834	+	0.534071i
$849$		0			0
$850$	−99.8331	+	26.5720i	−0.117451	+	0.0312612i
$851$	−456.391	+	543.905i	−0.536299	+	0.639136i
$852$		0			0
$853$	128.733	+	46.8551i	0.150918	+	0.0549298i	0.416375	−	0.909193i	$-0.363300\pi$
$853$	128.733	+	46.8551i	0.150918	+	0.0549298i	−0.265456	+	0.964123i	$0.585523\pi$
$854$	−214.033	+	99.3714i	−0.250624	+	0.116360i
$855$		0			0
$856$	−354.373	+	93.0580i	−0.413987	+	0.108713i
$857$	−177.241	−	1005.19i	−0.206816	−	1.17291i	−0.894556	−	0.446955i	$-0.852508\pi$
$857$	−177.241	−	1005.19i	−0.206816	−	1.17291i	0.687740	−	0.725957i	$-0.258603\pi$
$858$		0			0
$859$	3.67086	+	10.0856i	0.00427341	+	0.0117411i	0.941811	−	0.336143i	$-0.109123\pi$
$859$	3.67086	+	10.0856i	0.00427341	+	0.0117411i	−0.937538	+	0.347884i	$0.886900\pi$
$860$	110.886	+	641.357i	0.128938	+	0.745764i
$861$		0			0
$862$	1085.97	−	93.1869i	1.25982	−	0.108105i
$863$			761.949i			0.882907i	0.897284	+	0.441454i	$0.145537\pi$
$863$			761.949i			0.882907i	−0.897284	+	0.441454i	$0.854463\pi$
$864$		0			0
$865$	579.412			0.669840
$866$	−128.362	−	1495.89i	−0.148224	−	1.72735i
$867$		0			0
$868$	−838.421	+	144.957i	−0.965923	+	0.167002i
$869$	109.627	−	39.9009i	0.126153	−	0.0459158i
$870$		0			0
$871$	520.799	−	91.8309i	0.597932	−	0.105432i
$872$	−31.2140	−	118.866i	−0.0357959	−	0.136314i
$873$		0			0
$874$	−224.894	−	484.393i	−0.257316	−	0.554225i
$875$	−261.773	+	719.215i	−0.299169	+	0.821960i
$876$		0			0
$877$	11.1243	+	9.33437i	0.0126845	+	0.0106435i	0.649108	−	0.760696i	$-0.275142\pi$
$877$	11.1243	+	9.33437i	0.0126845	+	0.0106435i	−0.636423	+	0.771340i	$0.719587\pi$
$878$	27.3614	+	102.799i	0.0311633	+	0.117083i
$879$		0			0
$880$	−475.127	−	1332.97i	−0.539917	−	1.51474i
$881$	357.397	−	619.030i	0.405672	−	0.702645i	−0.588727	−	0.808332i	$-0.700371\pi$
$881$	357.397	−	619.030i	0.405672	−	0.702645i	0.994399	+	0.105687i	$0.0337042\pi$
$882$		0			0
$883$	−396.493	+	228.915i	−0.449029	+	0.259247i	−0.707420	−	0.706793i	$-0.750141\pi$
$883$	−396.493	+	228.915i	−0.449029	+	0.259247i	0.258391	+	0.966040i	$0.416808\pi$
$884$	416.595	−	238.674i	0.471261	−	0.269993i
$885$		0			0
$886$	800.117	+	215.820i	0.903066	+	0.243589i
$887$	384.736	+	67.8393i	0.433749	+	0.0764817i	0.386260	−	0.922390i	$-0.373767\pi$
$887$	384.736	+	67.8393i	0.433749	+	0.0764817i	0.0474895	+	0.998872i	$0.484878\pi$
$888$		0			0
$889$	−101.052	+	84.7926i	−0.113669	+	0.0953797i
$890$	160.139	−	227.893i	0.179931	−	0.256059i
$891$		0			0
$892$	−1243.66	+	447.969i	−1.39424	+	0.502207i
$893$	−150.688	+	126.442i	−0.168744	+	0.141593i
$894$		0			0
$895$	783.784	+	138.202i	0.875737	+	0.154416i
$896$	−503.100	−	514.974i	−0.561496	−	0.574747i
$897$		0			0
$898$	−450.853	−	211.151i	−0.502064	−	0.235135i
$899$	431.252	−	248.984i	0.479702	−	0.276956i
$900$		0			0
$901$	−256.587	+	444.421i	−0.284780	+	0.493253i
$902$	1059.92	+	1519.10i	1.17508	+	1.68415i
$903$		0			0
$904$	−865.657	−	1249.53i	−0.957586	−	1.38223i
$905$	−23.0724	−	19.3601i	−0.0254944	−	0.0213924i
$906$		0			0
$907$	237.421	−	652.309i	0.261765	−	0.719194i	−0.737283	−	0.675584i	$-0.763892\pi$
$907$	237.421	−	652.309i	0.261765	−	0.719194i	0.999049	−	0.0436106i	$-0.0138861\pi$
$908$	89.4121	−	497.384i	0.0984715	−	0.547780i
$909$		0			0
$910$	80.0596	−	897.855i	0.0879776	−	0.986653i
$911$	662.597	−	116.834i	0.727329	−	0.128248i	0.202290	−	0.979326i	$-0.435162\pi$
$911$	662.597	−	116.834i	0.727329	−	0.128248i	0.525039	+	0.851078i	$0.324051\pi$
$912$		0			0
$913$	1176.05	−	428.048i	1.28812	−	0.468837i
$914$	−755.811	−	758.333i	−0.826926	−	0.829686i
$915$		0			0
$916$	−450.473	−	262.086i	−0.491783	−	0.286120i
$917$	−128.623			−0.140265
$918$		0			0
$919$			128.381i			0.139696i	0.997558	+	0.0698481i	$0.0222514\pi$
$919$			128.381i			0.139696i	−0.997558	+	0.0698481i	$0.977749\pi$
$920$	−353.327	−	767.707i	−0.384051	−	0.834464i
$921$		0			0
$922$	967.850	+	971.080i	1.04973	+	1.05323i
$923$	−117.329	−	322.359i	−0.127117	−	0.349251i
$924$		0			0
$925$	−40.2479	−	228.257i	−0.0435112	−	0.246765i
$926$	163.965	−	1838.84i	0.177068	−	1.98579i
$927$		0			0
$928$	380.370	+	181.242i	0.409882	+	0.195304i
$929$	−1149.47	−	418.374i	−1.23732	−	0.450349i	−0.361223	−	0.932479i	$-0.617641\pi$
$929$	−1149.47	−	418.374i	−1.23732	−	0.450349i	−0.876099	+	0.482131i	$0.839863\pi$
$930$		0			0
$931$	114.657	−	136.643i	0.123155	−	0.146770i
$932$	242.175	−	658.534i	0.259844	−	0.706582i
$933$		0			0
$934$	171.377	+	245.622i	0.183487	+	0.262979i
$935$	−466.241	−	269.184i	−0.498653	−	0.287897i
$936$		0			0
$937$	−274.344	−	475.177i	−0.292789	−	0.507126i	0.681679	−	0.731652i	$-0.261250\pi$
$937$	−274.344	−	475.177i	−0.292789	−	0.507126i	−0.974468	+	0.224525i	$0.927917\pi$
$938$	−273.202	−	127.951i	−0.291260	−	0.136408i
$939$		0			0
$940$	−239.121	+	199.293i	−0.254384	+	0.212013i
$941$	124.148	−	704.078i	0.131932	−	0.748224i	−0.845015	−	0.534742i	$-0.820409\pi$
$941$	124.148	−	704.078i	0.131932	−	0.748224i	0.976947	−	0.213481i	$-0.0684802\pi$
$942$		0			0
$943$	711.058	+	847.406i	0.754038	+	0.898627i
$944$	−176.148	−	212.789i	−0.186597	−	0.225412i
$945$		0			0
$946$	1002.09	−	1426.08i	1.05930	−	1.50748i
$947$	−406.774	−	484.775i	−0.429540	−	0.511906i	0.507250	−	0.861799i	$-0.330662\pi$
$947$	−406.774	−	484.775i	−0.429540	−	0.511906i	−0.936789	+	0.349894i	$0.886218\pi$
$948$		0			0
$949$	−141.757	+	803.945i	−0.149375	+	0.847150i
$950$	168.321	+	45.4022i	0.177180	+	0.0477918i
$951$		0			0
$952$	−272.727	−	25.2347i	−0.286478	−	0.0265070i
$953$	−31.0794	−	53.8310i	−0.0326121	−	0.0564859i	0.849259	−	0.527977i	$-0.177049\pi$
$953$	−31.0794	−	53.8310i	−0.0326121	−	0.0564859i	−0.881871	+	0.471491i	$0.843716\pi$
$954$		0			0
$955$	479.396	+	276.780i	0.501986	+	0.289822i
$956$	884.815	+	2.94830i	0.925539	+	0.00308399i
$957$		0			0
$958$	292.737	+	1099.84i	0.305571	+	1.14805i
$959$	−486.356	+	579.616i	−0.507149	+	0.604396i
$960$		0			0
$961$	441.002	+	160.512i	0.458899	+	0.167026i
$962$	453.607	+	977.010i	0.471525	+	1.01560i
$963$		0			0
$964$	499.303	−	591.035i	0.517949	−	0.613107i
$965$	191.962	+	1088.67i	0.198924	+	1.12816i
$966$		0			0
$967$	−311.692	−	856.368i	−0.322329	−	0.885592i	−0.989991	−	0.141128i	$-0.954927\pi$
$967$	−311.692	−	856.368i	−0.322329	−	0.885592i	0.667662	−	0.744464i	$-0.267295\pi$
$968$	−1205.19	+	2551.17i	−1.24503	+	2.63551i
$969$		0			0
$970$	108.574	+	1265.28i	0.111932	+	1.30441i
$971$			1749.90i			1.80216i	0.433655	+	0.901079i	$0.357224\pi$
$971$			1749.90i			1.80216i	−0.433655	+	0.901079i	$0.642776\pi$
$972$		0			0
$973$	−660.169			−0.678488
$974$	151.211	−	12.9755i	0.155248	−	0.0133218i
$975$		0			0
$976$	165.879	+	291.785i	0.169958	+	0.298960i
$977$	342.599	−	124.696i	0.350664	−	0.127631i	−0.160682	−	0.987006i	$-0.551369\pi$
$977$	342.599	−	124.696i	0.350664	−	0.127631i	0.511346	+	0.859375i	$0.329147\pi$
$978$		0			0
$979$	−734.540	+	129.519i	−0.750296	+	0.132297i
$980$	182.158	−	215.624i	0.185875	−	0.220025i
$981$		0			0
$982$	89.9982	−	41.7844i	0.0916479	−	0.0425503i
$983$	−29.4082	+	80.7983i	−0.0299168	+	0.0821956i	−0.953752	−	0.300595i	$-0.902815\pi$
$983$	−29.4082	+	80.7983i	−0.0299168	+	0.0821956i	0.923835	+	0.382791i	$0.125037\pi$
$984$		0			0
$985$	−1151.86	−	966.526i	−1.16940	−	0.981245i
$986$	154.903	−	41.2296i	0.157102	−	0.0418150i
$987$		0			0
$988$	−810.215	−	2.69972i	−0.820056	−	0.00273251i
$989$	520.447	−	901.441i	0.526236	−	0.911467i
$990$		0			0
$991$	576.512	−	332.849i	0.581747	−	0.335872i	−0.180080	−	0.983652i	$-0.557636\pi$
$991$	576.512	−	332.849i	0.581747	−	0.335872i	0.761828	+	0.647780i	$0.224302\pi$
$992$	303.479	+	1171.55i	0.305927	+	1.18100i
$993$		0			0
$994$	−50.9647	+	188.943i	−0.0512723	+	0.190084i
$995$	725.602	+	127.943i	0.729248	+	0.128586i
$996$		0			0
$997$	−389.011	+	326.419i	−0.390181	+	0.327401i	−0.816684	−	0.577085i	$-0.804190\pi$
$997$	−389.011	+	326.419i	−0.390181	+	0.327401i	0.426503	+	0.904486i	$0.359746\pi$
$998$	1378.01	+	968.320i	1.38077	+	0.970260i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	324.3.j.a.199.18		204
3.2	odd	2		108.3.j.a.103.17	yes	204
4.3	odd	2	inner	324.3.j.a.199.3		204
12.11	even	2		108.3.j.a.103.32	yes	204
27.11	odd	18		108.3.j.a.43.32	yes	204
27.16	even	9	inner	324.3.j.a.127.3		204
108.11	even	18		108.3.j.a.43.17	✓	204
108.43	odd	18	inner	324.3.j.a.127.18		204

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
108.3.j.a.43.17	✓	204	108.11	even	18
108.3.j.a.43.32	yes	204	27.11	odd	18
108.3.j.a.103.17	yes	204	3.2	odd	2
108.3.j.a.103.32	yes	204	12.11	even	2
324.3.j.a.127.3		204	27.16	even	9	inner
324.3.j.a.127.18		204	108.43	odd	18	inner
324.3.j.a.199.3		204	4.3	odd	2	inner
324.3.j.a.199.18		204	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 324 = 2^{2} \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	324.j (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.170992 + 1.99268i) q^{2} +(-3.94152 + 0.681463i) q^{4} +(3.81867 - 1.38988i) q^{5} +(5.53905 - 0.976684i) q^{7} +(-2.03190 - 7.73766i) q^{8} +O(q^{10})\)	\(q+(0.170992 + 1.99268i) q^{2} +(-3.94152 + 0.681463i) q^{4} +(3.81867 - 1.38988i) q^{5} +(5.53905 - 0.976684i) q^{7} +(-2.03190 - 7.73766i) q^{8} +(3.42255 + 7.37172i) q^{10} +(7.44387 - 20.4519i) q^{11} +(-15.1056 - 12.6751i) q^{13} +(2.89335 + 10.8705i) q^{14} +(15.0712 - 5.37200i) q^{16} +(3.04352 - 5.27153i) q^{17} +(-8.89586 + 5.13603i) q^{19} +(-14.1042 + 8.08054i) q^{20} +(42.0268 + 11.3361i) q^{22} +(25.6005 + 4.51407i) q^{23} +(-6.50063 + 5.45468i) q^{25} +(22.6745 - 32.2680i) q^{26} +(-21.1667 + 7.62428i) q^{28} +(10.0865 - 8.46358i) q^{29} +(37.2448 + 6.56727i) q^{31} +(13.2817 + 29.1135i) q^{32} +(11.0249 + 5.16336i) q^{34} +(19.7943 - 11.4283i) q^{35} +(-13.6566 + 23.6539i) q^{37} +(-11.7556 - 16.8484i) q^{38} +(-18.5136 - 26.7235i) q^{40} +(32.5982 + 27.3531i) q^{41} +(13.6950 - 37.6266i) q^{43} +(-15.4030 + 85.6842i) q^{44} +(-4.61759 + 51.7855i) q^{46} +(18.8590 - 3.32535i) q^{47} +(-16.3178 + 5.93919i) q^{49} +(-11.9810 - 12.0210i) q^{50} +(68.1769 + 39.6654i) q^{52} -84.3059 q^{53} -88.4451i q^{55} +(-18.8121 - 40.8747i) q^{56} +(18.5899 + 18.6519i) q^{58} +(-5.90492 - 16.2236i) q^{59} +(3.64271 + 20.6588i) q^{61} +(-6.71788 + 75.3398i) q^{62} +(-55.7427 + 31.4444i) q^{64} +(-75.3005 - 27.4071i) q^{65} +(-17.2385 + 20.5441i) q^{67} +(-8.40375 + 22.8519i) q^{68} +(26.1575 + 37.4896i) q^{70} +(15.0660 + 8.69838i) q^{71} +(-20.6995 - 35.8526i) q^{73} +(-49.4697 - 23.1685i) q^{74} +(31.5632 - 26.3060i) q^{76} +(21.2570 - 120.554i) q^{77} +(3.44549 + 4.10617i) q^{79} +(50.0856 - 41.4611i) q^{80} +(-48.9319 + 69.6348i) q^{82} +(36.9625 + 44.0502i) q^{83} +(4.29539 - 24.3604i) q^{85} +(77.3193 + 20.8558i) q^{86} +(-173.375 - 16.0419i) q^{88} +(-17.1351 - 29.6789i) q^{89} +(-96.0505 - 55.4548i) q^{91} +(-103.981 - 0.346477i) q^{92} +(9.85110 + 37.0113i) q^{94} +(-26.8319 + 31.9770i) q^{95} +(146.828 + 53.4411i) q^{97} +(-14.6251 - 31.5005i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 204 q + 6 q^{2} - 6 q^{4} + 12 q^{5} + 3 q^{8}+O(q^{10}) \) 204 * q + 6 * q^2 - 6 * q^4 + 12 * q^5 + 3 * q^8	\( 204 q + 6 q^{2} - 6 q^{4} + 12 q^{5} + 3 q^{8} - 3 q^{10} - 12 q^{13} - 39 q^{14} - 6 q^{16} + 6 q^{17} + 69 q^{20} - 6 q^{22} - 12 q^{25} + 174 q^{26} - 12 q^{28} - 60 q^{29} + 96 q^{32} + 6 q^{34} - 6 q^{37} - 72 q^{38} + 69 q^{40} + 192 q^{41} + 219 q^{44} - 3 q^{46} - 12 q^{49} + 165 q^{50} + 21 q^{52} + 24 q^{53} - 99 q^{56} - 141 q^{58} - 12 q^{61} - 294 q^{62} - 3 q^{64} + 156 q^{65} - 375 q^{68} - 165 q^{70} - 6 q^{73} - 447 q^{74} - 54 q^{76} - 132 q^{77} - 798 q^{80} - 12 q^{82} + 138 q^{85} - 606 q^{86} - 198 q^{88} + 114 q^{89} - 723 q^{92} - 357 q^{94} + 168 q^{97} - 510 q^{98}+O(q^{100}) \) 204 * q + 6 * q^2 - 6 * q^4 + 12 * q^5 + 3 * q^8 - 3 * q^10 - 12 * q^13 - 39 * q^14 - 6 * q^16 + 6 * q^17 + 69 * q^20 - 6 * q^22 - 12 * q^25 + 174 * q^26 - 12 * q^28 - 60 * q^29 + 96 * q^32 + 6 * q^34 - 6 * q^37 - 72 * q^38 + 69 * q^40 + 192 * q^41 + 219 * q^44 - 3 * q^46 - 12 * q^49 + 165 * q^50 + 21 * q^52 + 24 * q^53 - 99 * q^56 - 141 * q^58 - 12 * q^61 - 294 * q^62 - 3 * q^64 + 156 * q^65 - 375 * q^68 - 165 * q^70 - 6 * q^73 - 447 * q^74 - 54 * q^76 - 132 * q^77 - 798 * q^80 - 12 * q^82 + 138 * q^85 - 606 * q^86 - 198 * q^88 + 114 * q^89 - 723 * q^92 - 357 * q^94 + 168 * q^97 - 510 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more