LMFDB - Embedded newform 1050.3.q.d.199.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1050,3,Mod(199,1050)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1050, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 1]))

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

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

chi := DirichletCharacter("1050.199");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	1050.q (of order $6$, degree $2$, 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:	$28.6104277578$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			199.12
Character	$\chi$	$=$	1050.199
Dual form			1050.3.q.d.649.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.22474 - 0.707107i) q^{2} +(-0.866025 + 1.50000i) q^{3} +(1.00000 - 1.73205i) q^{4} +2.44949i q^{6} +(-6.78392 + 1.72580i) q^{7} -2.82843i q^{8} +(-1.50000 - 2.59808i) q^{9} +O(q^{10})$	\(q+(1.22474 - 0.707107i) q^{2} +(-0.866025 + 1.50000i) q^{3} +(1.00000 - 1.73205i) q^{4} +2.44949i q^{6} +(-6.78392 + 1.72580i) q^{7} -2.82843i q^{8} +(-1.50000 - 2.59808i) q^{9} +(-9.79066 + 16.9579i) q^{11} +(1.73205 + 3.00000i) q^{12} -2.16261 q^{13} +(-7.08825 + 6.91062i) q^{14} +(-2.00000 - 3.46410i) q^{16} +(9.81350 - 16.9975i) q^{17} +(-3.67423 - 2.12132i) q^{18} +(19.8410 - 11.4552i) q^{19} +(3.28635 - 11.6705i) q^{21} +27.6922i q^{22} +(28.1864 - 16.2734i) q^{23} +(4.24264 + 2.44949i) q^{24} +(-2.64865 + 1.52920i) q^{26} +5.19615 q^{27} +(-3.79475 + 13.4759i) q^{28} -27.6922 q^{29} +(-36.3761 - 21.0018i) q^{31} +(-4.89898 - 2.82843i) q^{32} +(-16.9579 - 29.3720i) q^{33} -27.7568i q^{34} -6.00000 q^{36} +(52.3564 - 30.2280i) q^{37} +(16.2001 - 28.0594i) q^{38} +(1.87288 - 3.24392i) q^{39} -66.3893i q^{41} +(-4.22733 - 16.6171i) q^{42} -73.9553i q^{43} +(19.5813 + 33.9159i) q^{44} +(23.0141 - 39.8615i) q^{46} +(30.4450 + 52.7322i) q^{47} +6.92820 q^{48} +(43.0432 - 23.4154i) q^{49} +(16.9975 + 29.4405i) q^{51} +(-2.16261 + 3.74576i) q^{52} +(-80.2145 - 46.3119i) q^{53} +(6.36396 - 3.67423i) q^{54} +(4.88130 + 19.1878i) q^{56} +39.6819i q^{57} +(-33.9159 + 19.5813i) q^{58} +(24.9434 + 14.4011i) q^{59} +(-72.7954 + 42.0285i) q^{61} -59.4020 q^{62} +(14.6596 + 15.0364i) q^{63} -8.00000 q^{64} +(-41.5383 - 23.9821i) q^{66} +(2.81616 + 1.62591i) q^{67} +(-19.6270 - 33.9950i) q^{68} +56.3727i q^{69} -38.9302 q^{71} +(-7.34847 + 4.24264i) q^{72} +(-17.6257 + 30.5285i) q^{73} +(42.7488 - 74.0432i) q^{74} -45.8208i q^{76} +(37.1531 - 131.938i) q^{77} -5.29730i q^{78} +(10.7857 + 18.6813i) q^{79} +(-4.50000 + 7.79423i) q^{81} +(-46.9443 - 81.3099i) q^{82} +40.3650 q^{83} +(-16.9275 - 17.3626i) q^{84} +(-52.2943 - 90.5764i) q^{86} +(23.9821 - 41.5383i) q^{87} +(47.9643 + 27.6922i) q^{88} +(-42.1123 + 24.3136i) q^{89} +(14.6710 - 3.73224i) q^{91} -65.0936i q^{92} +(63.0053 - 36.3761i) q^{93} +(74.5746 + 43.0557i) q^{94} +(8.48528 - 4.89898i) q^{96} -25.2493 q^{97} +(36.1598 - 59.1141i) q^{98} +58.7440 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 24 q^{4} - 36 q^{9}+O(q^{10}) $ 24 * q + 24 * q^4 - 36 * q^9	$ 24 q + 24 q^{4} - 36 q^{9} - 8 q^{11} - 16 q^{14} - 48 q^{16} - 24 q^{19} + 36 q^{21} - 48 q^{26} + 48 q^{29} - 396 q^{31} - 144 q^{36} + 72 q^{39} + 16 q^{44} + 64 q^{46} - 56 q^{49} - 48 q^{51} + 80 q^{56} + 96 q^{59} + 372 q^{61} - 192 q^{64} + 72 q^{66} - 272 q^{71} + 128 q^{74} + 140 q^{79} - 108 q^{81} + 24 q^{84} - 416 q^{86} - 336 q^{89} + 584 q^{91} + 408 q^{94} + 48 q^{99}+O(q^{100}) $ 24 * q + 24 * q^4 - 36 * q^9 - 8 * q^11 - 16 * q^14 - 48 * q^16 - 24 * q^19 + 36 * q^21 - 48 * q^26 + 48 * q^29 - 396 * q^31 - 144 * q^36 + 72 * q^39 + 16 * q^44 + 64 * q^46 - 56 * q^49 - 48 * q^51 + 80 * q^56 + 96 * q^59 + 372 * q^61 - 192 * q^64 + 72 * q^66 - 272 * q^71 + 128 * q^74 + 140 * q^79 - 108 * q^81 + 24 * q^84 - 416 * q^86 - 336 * q^89 + 584 * q^91 + 408 * q^94 + 48 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times$.

$n$	$127$	$451$	$701$
$\chi(n)$	$-1$	$e\left(\frac{1}{6}\right)$	$1$

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 $

$2$	1.22474	−	0.707107i	0.612372	−	0.353553i
$2$	1.22474	−	0.707107i	0.612372	−	0.353553i
$3$	−0.866025	+	1.50000i	−0.288675	+	0.500000i
$3$	−0.866025	+	1.50000i	−0.288675	+	0.500000i
$4$	1.00000	−	1.73205i	0.250000	−	0.433013i
$5$		0			0
$5$		0			0
$6$			2.44949i			0.408248i
$7$	−6.78392	+	1.72580i	−0.969132	+	0.246543i
$7$	−6.78392	+	1.72580i	−0.969132	+	0.246543i
$8$		−	2.82843i		−	0.353553i
$9$	−1.50000	−	2.59808i	−0.166667	−	0.288675i
$10$		0			0
$11$	−9.79066	+	16.9579i	−0.890060	+	1.54163i	−0.0502590	+	0.998736i	$0.516005\pi$
$11$	−9.79066	+	16.9579i	−0.890060	+	1.54163i	−0.839801	+	0.542894i	$0.817329\pi$
$12$	1.73205	+	3.00000i	0.144338	+	0.250000i
$13$	−2.16261			−0.166355			−0.0831775	−	0.996535i	$-0.526507\pi$
$13$	−2.16261			−0.166355			−0.0831775	+	0.996535i	$0.526507\pi$
$14$	−7.08825	+	6.91062i	−0.506303	+	0.493616i
$15$		0			0
$16$	−2.00000	−	3.46410i	−0.125000	−	0.216506i
$17$	9.81350	−	16.9975i	0.577265	−	0.999852i	−0.418527	−	0.908205i	$-0.637453\pi$
$17$	9.81350	−	16.9975i	0.577265	−	0.999852i	0.995792	−	0.0916476i	$-0.0292133\pi$
$18$	−3.67423	−	2.12132i	−0.204124	−	0.117851i
$19$	19.8410	−	11.4552i	1.04426	−	0.602905i	0.123224	−	0.992379i	$-0.460677\pi$
$19$	19.8410	−	11.4552i	1.04426	−	0.602905i	0.921037	+	0.389474i	$0.127343\pi$
$20$		0			0
$21$	3.28635	−	11.6705i	0.156493	−	0.555737i
$22$			27.6922i			1.25874i
$23$	28.1864	−	16.2734i	1.22549	−	0.707539i	0.259410	−	0.965767i	$-0.416472\pi$
$23$	28.1864	−	16.2734i	1.22549	−	0.707539i	0.966084	+	0.258228i	$0.0831387\pi$
$24$	4.24264	+	2.44949i	0.176777	+	0.102062i
$25$		0			0
$26$	−2.64865	+	1.52920i	−0.101871	+	0.0588153i
$27$	5.19615			0.192450
$28$	−3.79475	+	13.4759i	−0.135527	+	0.481282i
$29$	−27.6922			−0.954903			−0.477451	−	0.878658i	$-0.658439\pi$
$29$	−27.6922			−0.954903			−0.477451	+	0.878658i	$0.658439\pi$
$30$		0			0
$31$	−36.3761	−	21.0018i	−1.17342	−	0.677477i	−0.218940	−	0.975738i	$-0.570260\pi$
$31$	−36.3761	−	21.0018i	−1.17342	−	0.677477i	−0.954484	+	0.298262i	$0.903593\pi$
$32$	−4.89898	−	2.82843i	−0.153093	−	0.0883883i
$33$	−16.9579	−	29.3720i	−0.513877	−	0.890060i
$34$		−	27.7568i		−	0.816376i
$35$		0			0
$36$	−6.00000			−0.166667
$37$	52.3564	−	30.2280i	1.41504	−	0.816973i	0.419181	−	0.907902i	$-0.362317\pi$
$37$	52.3564	−	30.2280i	1.41504	−	0.816973i	0.995857	+	0.0909295i	$0.0289838\pi$
$38$	16.2001	−	28.0594i	0.426318	−	0.738405i
$39$	1.87288	−	3.24392i	0.0480225	−	0.0831775i
$40$		0			0
$41$		−	66.3893i		−	1.61925i	−0.586947	−	0.809625i	$-0.699670\pi$
$41$		−	66.3893i		−	1.61925i	0.586947	−	0.809625i	$-0.300330\pi$
$42$	−4.22733	−	16.6171i	−0.100651	−	0.395646i
$43$		−	73.9553i		−	1.71989i	−0.510386	−	0.859945i	$-0.670498\pi$
$43$		−	73.9553i		−	1.71989i	0.510386	−	0.859945i	$-0.329502\pi$
$44$	19.5813	+	33.9159i	0.445030	+	0.770815i
$45$		0			0
$46$	23.0141	−	39.8615i	0.500306	−	0.866555i
$47$	30.4450	+	52.7322i	0.647765	+	1.12196i	0.983655	+	0.180061i	$0.0576296\pi$
$47$	30.4450	+	52.7322i	0.647765	+	1.12196i	−0.335890	+	0.941901i	$0.609037\pi$
$48$	6.92820			0.144338
$49$	43.0432	−	23.4154i	0.878433	−	0.477866i
$50$		0			0
$51$	16.9975	+	29.4405i	0.333284	+	0.577265i
$52$	−2.16261	+	3.74576i	−0.0415887	+	0.0720338i
$53$	−80.2145	−	46.3119i	−1.51348	−	0.873809i	−0.999875	−	0.0157830i	$-0.994976\pi$
$53$	−80.2145	−	46.3119i	−1.51348	−	0.873809i	−0.513606	−	0.858026i	$-0.671691\pi$
$54$	6.36396	−	3.67423i	0.117851	−	0.0680414i
$55$		0			0
$56$	4.88130	+	19.1878i	0.0871662	+	0.342640i
$57$			39.6819i			0.696174i
$58$	−33.9159	+	19.5813i	−0.584756	+	0.337609i
$59$	24.9434	+	14.4011i	0.422770	+	0.244086i	0.696262	−	0.717788i	$-0.254845\pi$
$59$	24.9434	+	14.4011i	0.422770	+	0.244086i	−0.273492	+	0.961874i	$0.588179\pi$
$60$		0			0
$61$	−72.7954	+	42.0285i	−1.19337	+	0.688991i	−0.959069	−	0.283173i	$-0.908613\pi$
$61$	−72.7954	+	42.0285i	−1.19337	+	0.688991i	−0.234299	+	0.972165i	$0.575280\pi$
$62$	−59.4020			−0.958097
$63$	14.6596	+	15.0364i	0.232693	+	0.238674i
$64$	−8.00000			−0.125000
$65$		0			0
$66$	−41.5383	−	23.9821i	−0.629368	−	0.363366i
$67$	2.81616	+	1.62591i	0.0420322	+	0.0242673i	0.520869	−	0.853637i	$-0.325608\pi$
$67$	2.81616	+	1.62591i	0.0420322	+	0.0242673i	−0.478837	+	0.877904i	$0.658941\pi$
$68$	−19.6270	−	33.9950i	−0.288632	−	0.499926i
$69$			56.3727i			0.816996i
$70$		0			0
$71$	−38.9302			−0.548313			−0.274156	−	0.961685i	$-0.588399\pi$
$71$	−38.9302			−0.548313			−0.274156	+	0.961685i	$0.588399\pi$
$72$	−7.34847	+	4.24264i	−0.102062	+	0.0589256i
$73$	−17.6257	+	30.5285i	−0.241447	+	0.418199i	−0.961127	−	0.276107i	$-0.910955\pi$
$73$	−17.6257	+	30.5285i	−0.241447	+	0.418199i	0.719679	+	0.694307i	$0.244289\pi$
$74$	42.7488	−	74.0432i	0.577687	−	1.00058i
$75$		0			0
$76$		−	45.8208i		−	0.602905i
$77$	37.1531	−	131.938i	0.482508	−	1.71348i
$78$		−	5.29730i		−	0.0679141i
$79$	10.7857	+	18.6813i	0.136527	+	0.236472i	0.926180	−	0.377082i	$-0.123073\pi$
$79$	10.7857	+	18.6813i	0.136527	+	0.236472i	−0.789653	+	0.613554i	$0.789739\pi$
$80$		0			0
$81$	−4.50000	+	7.79423i	−0.0555556	+	0.0962250i
$82$	−46.9443	−	81.3099i	−0.572492	−	0.991585i
$83$	40.3650			0.486325			0.243162	−	0.969986i	$-0.421815\pi$
$83$	40.3650			0.486325			0.243162	+	0.969986i	$0.421815\pi$
$84$	−16.9275	−	17.3626i	−0.201518	−	0.206698i
$85$		0			0
$86$	−52.2943	−	90.5764i	−0.608073	−	1.05321i
$87$	23.9821	−	41.5383i	0.275657	−	0.477451i
$88$	47.9643	+	27.6922i	0.545048	+	0.314684i
$89$	−42.1123	+	24.3136i	−0.473172	+	0.273186i	−0.717567	−	0.696490i	$-0.754744\pi$
$89$	−42.1123	+	24.3136i	−0.473172	+	0.273186i	0.244395	+	0.969676i	$0.421411\pi$
$90$		0			0
$91$	14.6710	−	3.73224i	0.161220	−	0.0410137i
$92$		−	65.0936i		−	0.707539i
$93$	63.0053	−	36.3761i	0.677477	−	0.391141i
$94$	74.5746	+	43.0557i	0.793347	+	0.458039i
$95$		0			0
$96$	8.48528	−	4.89898i	0.0883883	−	0.0510310i
$97$	−25.2493			−0.260302			−0.130151	−	0.991494i	$-0.541546\pi$
$97$	−25.2493			−0.260302			−0.130151	+	0.991494i	$0.541546\pi$
$98$	36.1598	−	59.1141i	0.368977	−	0.603205i
$99$	58.7440			0.593374
$100$		0			0
$101$	52.6467	+	30.3956i	0.521255	+	0.300947i	0.737448	−	0.675404i	$-0.236031\pi$
$101$	52.6467	+	30.3956i	0.521255	+	0.300947i	−0.216193	+	0.976351i	$0.569364\pi$
$102$	41.6352	+	24.0381i	0.408188	+	0.235667i
$103$	21.3745	+	37.0217i	0.207519	+	0.359434i	0.950932	−	0.309399i	$-0.100128\pi$
$103$	21.3745	+	37.0217i	0.207519	+	0.359434i	−0.743413	+	0.668832i	$0.766794\pi$
$104$			6.11680i			0.0588153i
$105$		0			0
$106$	−130.990			−1.23575
$107$	132.760	−	76.6488i	1.24074	−	0.716343i	0.271498	−	0.962439i	$-0.412481\pi$
$107$	132.760	−	76.6488i	1.24074	−	0.716343i	0.969246	+	0.246096i	$0.0791477\pi$
$108$	5.19615	−	9.00000i	0.0481125	−	0.0833333i
$109$	28.8885	−	50.0364i	0.265032	−	0.459050i	−0.702540	−	0.711645i	$-0.747951\pi$
$109$	28.8885	−	50.0364i	0.265032	−	0.459050i	0.967572	+	0.252595i	$0.0812840\pi$
$110$		0			0
$111$			104.713i			0.943359i
$112$	19.5462	+	20.0486i	0.174520	+	0.179005i
$113$		−	149.523i		−	1.32322i	−0.749850	−	0.661608i	$-0.769874\pi$
$113$		−	149.523i		−	1.32322i	0.749850	−	0.661608i	$-0.230126\pi$
$114$	28.0594	+	48.6003i	0.246135	+	0.426318i
$115$		0			0
$116$	−27.6922	+	47.9643i	−0.238726	+	0.413485i
$117$	3.24392	+	5.61864i	0.0277258	+	0.0480225i
$118$	40.7325			0.345190
$119$	−37.2398	+	132.246i	−0.312939	+	1.11131i
$120$		0			0
$121$	−131.214	−	227.270i	−1.08442	−	1.87826i
$122$	−59.4372	+	102.948i	−0.487190	+	0.843839i
$123$	99.5839	+	57.4948i	0.809625	+	0.467437i
$124$	−72.7523	+	42.0035i	−0.586712	+	0.338738i
$125$		0			0
$126$	28.5867	+	8.04987i	0.226879	+	0.0638879i
$127$		−	176.212i		−	1.38750i	−0.720217	−	0.693749i	$-0.755958\pi$
$127$		−	176.212i		−	1.38750i	0.720217	−	0.693749i	$-0.244042\pi$
$128$	−9.79796	+	5.65685i	−0.0765466	+	0.0441942i
$129$	110.933	+	64.0472i	0.859945	+	0.496490i
$130$		0			0
$131$	63.0502	−	36.4021i	0.481300	−	0.277878i	−0.239658	−	0.970857i	$-0.577035\pi$
$131$	63.0502	−	36.4021i	0.481300	−	0.277878i	0.720958	+	0.692979i	$0.243702\pi$
$132$	−67.8317			−0.513877
$133$	−114.830	+	111.953i	−0.863385	+	0.841750i
$134$	4.59876			0.0343191
$135$		0			0
$136$	−48.0762	−	27.7568i	−0.353501	−	0.204094i
$137$	−129.472	−	74.7510i	−0.945055	−	0.545628i	−0.0535134	−	0.998567i	$-0.517042\pi$
$137$	−129.472	−	74.7510i	−0.945055	−	0.545628i	−0.891541	+	0.452940i	$0.850375\pi$
$138$	39.8615	+	69.0422i	0.288852	+	0.500306i
$139$			57.4753i			0.413491i	0.978395	+	0.206746i	$0.0662873\pi$
$139$			57.4753i			0.413491i	−0.978395	+	0.206746i	$0.933713\pi$
$140$		0			0
$141$	−105.464			−0.747975
$142$	−47.6796	+	27.5278i	−0.335772	+	0.193858i
$143$	21.1734	−	36.6735i	0.148066	−	0.256458i
$144$	−6.00000	+	10.3923i	−0.0416667	+	0.0721688i
$145$		0			0
$146$			49.8529i			0.341458i
$147$	−2.15340	+	84.8432i	−0.0146490	+	0.577164i
$148$		−	120.912i		−	0.816973i
$149$	−12.5813	−	21.7915i	−0.0844385	−	0.146252i	0.820713	−	0.571340i	$-0.193576\pi$
$149$	−12.5813	−	21.7915i	−0.0844385	−	0.146252i	−0.905152	+	0.425088i	$0.860243\pi$
$150$		0			0
$151$	−11.1332	+	19.2832i	−0.0737296	+	0.127703i	−0.900533	−	0.434787i	$-0.856824\pi$
$151$	−11.1332	+	19.2832i	−0.0737296	+	0.127703i	0.826804	+	0.562491i	$0.190157\pi$
$152$	−32.4002	−	56.1187i	−0.213159	−	0.369202i
$153$	−58.8810			−0.384843
$154$	−47.7912	−	187.862i	−0.310333	−	1.21988i
$155$		0			0
$156$	−3.74576	−	6.48784i	−0.0240113	−	0.0415887i
$157$	140.053	−	242.578i	0.892054	−	1.54508i	0.0546460	−	0.998506i	$-0.482597\pi$
$157$	140.053	−	242.578i	0.892054	−	1.54508i	0.837408	−	0.546578i	$-0.184070\pi$
$158$	26.4193	+	15.2532i	0.167211	+	0.0965393i
$159$	138.936	−	80.2145i	0.873809	−	0.504494i
$160$		0			0
$161$	−163.129	+	159.042i	−1.01323	+	0.987836i
$162$			12.7279i			0.0785674i
$163$	−114.870	+	66.3200i	−0.704722	+	0.406871i	−0.809104	−	0.587666i	$-0.800047\pi$
$163$	−114.870	+	66.3200i	−0.704722	+	0.406871i	0.104382	+	0.994537i	$0.466714\pi$
$164$	−114.990	−	66.3893i	−0.701156	−	0.404813i
$165$		0			0
$166$	49.4368	−	28.5423i	0.297812	−	0.171942i
$167$	119.492			0.715520			0.357760	−	0.933814i	$-0.383541\pi$
$167$	119.492			0.715520			0.357760	+	0.933814i	$0.383541\pi$
$168$	−33.0091	−	9.29519i	−0.196483	−	0.0553285i
$169$	−164.323			−0.972326
$170$		0			0
$171$	−59.5229	−	34.3656i	−0.348087	−	0.200968i
$172$	−128.094	−	73.9553i	−0.744734	−	0.429973i
$173$	126.059	+	218.340i	0.728664	+	1.26208i	0.957448	+	0.288606i	$0.0931916\pi$
$173$	126.059	+	218.340i	0.728664	+	1.26208i	−0.228784	+	0.973477i	$0.573475\pi$
$174$		−	67.8317i		−	0.389837i
$175$		0			0
$176$	78.3253			0.445030
$177$	−43.2033	+	24.9434i	−0.244086	+	0.140923i
$178$	−34.3846	+	59.5558i	−0.193172	+	0.334583i
$179$	20.7738	−	35.9814i	0.116055	−	0.201013i	−0.802146	−	0.597128i	$-0.796308\pi$
$179$	20.7738	−	35.9814i	0.116055	−	0.201013i	0.918201	+	0.396115i	$0.129642\pi$
$180$		0			0
$181$			258.208i			1.42656i	0.700878	+	0.713281i	$0.252792\pi$
$181$			258.208i			1.42656i	−0.700878	+	0.713281i	$0.747208\pi$
$182$	15.3291	−	14.9450i	0.0842261	−	0.0821155i
$183$		−	145.591i		−	0.795579i
$184$	−46.0281	−	79.7230i	−0.250153	−	0.433277i
$185$		0			0
$186$	51.4436	−	89.1030i	0.276579	−	0.479048i
$187$	192.161	+	332.833i	1.02760	+	1.77986i
$188$	121.780			0.647765
$189$	−35.2503	+	8.96753i	−0.186510	+	0.0474472i
$190$		0			0
$191$	45.1850	+	78.2627i	0.236571	+	0.409752i	0.959728	−	0.280931i	$-0.0906432\pi$
$191$	45.1850	+	78.2627i	0.236571	+	0.409752i	−0.723157	+	0.690683i	$0.757310\pi$
$192$	6.92820	−	12.0000i	0.0360844	−	0.0625000i
$193$	−52.7591	−	30.4605i	−0.273363	−	0.157826i	0.357052	−	0.934085i	$-0.383782\pi$
$193$	−52.7591	−	30.4605i	−0.273363	−	0.157826i	−0.630415	+	0.776258i	$0.717115\pi$
$194$	−30.9240	+	17.8540i	−0.159402	+	0.0920307i
$195$		0			0
$196$	2.48653	−	97.9684i	0.0126864	−	0.499839i
$197$			74.1310i			0.376299i	0.982140	+	0.188150i	$0.0602490\pi$
$197$			74.1310i			0.376299i	−0.982140	+	0.188150i	$0.939751\pi$
$198$	71.9464	−	41.5383i	0.363366	−	0.209789i
$199$	−77.5575	−	44.7778i	−0.389736	−	0.225014i	0.292310	−	0.956324i	$-0.405576\pi$
$199$	−77.5575	−	44.7778i	−0.389736	−	0.225014i	−0.682046	+	0.731309i	$0.738910\pi$
$200$		0			0
$201$	−4.87773	+	2.81616i	−0.0242673	+	0.0140107i
$202$	85.9717			0.425603
$203$	187.862	−	47.7912i	0.925427	−	0.235425i
$204$	67.9899			0.333284
$205$		0			0
$206$	52.3565	+	30.2281i	0.254158	+	0.146738i
$207$	−84.5591	−	48.8202i	−0.408498	−	0.235846i
$208$	4.32523	+	7.49151i	0.0207944	+	0.0360169i
$209$			448.616i			2.14649i
$210$		0			0
$211$	69.8647			0.331112			0.165556	−	0.986200i	$-0.447058\pi$
$211$	69.8647			0.331112			0.165556	+	0.986200i	$0.447058\pi$
$212$	−160.429	+	92.6238i	−0.756741	+	0.436905i
$213$	33.7145	−	58.3953i	0.158284	−	0.274156i
$214$	108.398	−	187.750i	0.506531	−	0.877338i
$215$		0			0
$216$		−	14.6969i		−	0.0680414i
$217$	283.018	+	79.6964i	1.30423	+	0.367265i
$218$		−	81.7091i		−	0.374812i
$219$	−30.5285	−	52.8770i	−0.139400	−	0.241447i
$220$		0			0
$221$	−21.2228	+	36.7590i	−0.0960309	+	0.166330i
$222$	74.0432	+	128.247i	0.333528	+	0.577687i
$223$	−389.679			−1.74744			−0.873719	−	0.486430i	$-0.838299\pi$
$223$	−389.679			−1.74744			−0.873719	+	0.486430i	$0.838299\pi$
$224$	38.1156	+	10.7332i	0.170159	+	0.0479159i
$225$		0			0
$226$	−105.729	−	183.128i	−0.467828	−	0.810301i
$227$	3.73645	−	6.47172i	0.0164601	−	0.0285098i	−0.857678	−	0.514187i	$-0.828094\pi$
$227$	3.73645	−	6.47172i	0.0164601	−	0.0285098i	0.874138	+	0.485677i	$0.161427\pi$
$228$	68.7311	+	39.6819i	0.301452	+	0.174044i
$229$	86.8317	−	50.1323i	0.379178	−	0.218918i	−0.298283	−	0.954478i	$-0.596414\pi$
$229$	86.8317	−	50.1323i	0.379178	−	0.218918i	0.677460	+	0.735559i	$0.263080\pi$
$230$		0			0
$231$	165.732	+	169.991i	0.717452	+	0.735893i
$232$			78.3253i			0.337609i
$233$	294.424	−	169.986i	1.26362	−	0.729552i	0.289848	−	0.957073i	$-0.406395\pi$
$233$	294.424	−	169.986i	1.26362	−	0.729552i	0.973773	+	0.227520i	$0.0730618\pi$
$234$	7.94595	+	4.58760i	0.0339571	+	0.0196051i
$235$		0			0
$236$	49.8869	−	28.8022i	0.211385	−	0.122043i
$237$	−37.3626			−0.157648
$238$	47.9027	+	188.300i	0.201272	+	0.791176i
$239$	−37.7094			−0.157780			−0.0788899	−	0.996883i	$-0.525138\pi$
$239$	−37.7094			−0.157780			−0.0788899	+	0.996883i	$0.525138\pi$
$240$		0			0
$241$	−258.515	−	149.254i	−1.07268	−	0.619310i	−0.143765	−	0.989612i	$-0.545921\pi$
$241$	−258.515	−	149.254i	−1.07268	−	0.619310i	−0.928912	+	0.370301i	$0.879254\pi$
$242$	−321.408	−	185.565i	−1.32813	−	0.766797i
$243$	−7.79423	−	13.5000i	−0.0320750	−	0.0555556i
$244$			168.114i			0.688991i
$245$		0			0
$246$	162.620			0.661056
$247$	−42.9084	+	24.7732i	−0.173718	+	0.100296i
$248$	−59.4020	+	102.887i	−0.239524	+	0.414868i
$249$	−34.9571	+	60.5474i	−0.140390	+	0.243162i
$250$		0			0
$251$		−	251.129i		−	1.00051i	−0.865877	−	0.500257i	$-0.833239\pi$
$251$		−	251.129i		−	1.00051i	0.865877	−	0.500257i	$-0.166761\pi$
$252$	40.7035	−	10.3548i	0.161522	−	0.0410905i
$253$			637.310i			2.51901i
$254$	−124.601	−	215.815i	−0.490554	−	0.849665i
$255$		0			0
$256$	−8.00000	+	13.8564i	−0.0312500	+	0.0541266i
$257$	29.8336	+	51.6733i	0.116084	+	0.201063i	0.918213	−	0.396088i	$-0.129632\pi$
$257$	29.8336	+	51.6733i	0.116084	+	0.201063i	−0.802129	+	0.597151i	$0.796299\pi$
$258$	181.153			0.702142
$259$	−303.014	+	295.421i	−1.16994	+	1.14062i
$260$		0			0
$261$	41.5383	+	71.9464i	0.159150	+	0.275657i
$262$	51.4803	−	89.1665i	0.196490	−	0.340330i
$263$	−108.087	−	62.4039i	−0.410976	−	0.237277i	0.280233	−	0.959932i	$-0.409588\pi$
$263$	−108.087	−	62.4039i	−0.410976	−	0.237277i	−0.691209	+	0.722655i	$0.742922\pi$
$264$	−83.0765	+	47.9643i	−0.314684	+	0.181683i
$265$		0			0
$266$	−61.4752	+	218.311i	−0.231110	+	0.820717i
$267$		−	84.2246i		−	0.315448i
$268$	5.63231	−	3.25182i	0.0210161	−	0.0121336i
$269$	180.299	+	104.096i	0.670257	+	0.386973i	0.796174	−	0.605068i	$-0.206854\pi$
$269$	180.299	+	104.096i	0.670257	+	0.386973i	−0.125917	+	0.992041i	$0.540187\pi$
$270$		0			0
$271$	17.1857	−	9.92217i	0.0634159	−	0.0366132i	−0.467957	−	0.883751i	$-0.655010\pi$
$271$	17.1857	−	9.92217i	0.0634159	−	0.0366132i	0.531373	+	0.847138i	$0.321676\pi$
$272$	−78.5080			−0.288632
$273$	−7.10710	+	25.2387i	−0.0260333	+	0.0924496i
$274$	−211.428			−0.771634
$275$		0			0
$276$	97.6404	+	56.3727i	0.353770	+	0.204249i
$277$	75.3576	+	43.5077i	0.272049	+	0.157068i	0.629818	−	0.776742i	$-0.283129\pi$
$277$	75.3576	+	43.5077i	0.272049	+	0.157068i	−0.357769	+	0.933810i	$0.616463\pi$
$278$	40.6412	+	70.3926i	0.146191	+	0.253211i
$279$			126.011i			0.451651i
$280$		0			0
$281$	145.993			0.519549			0.259774	−	0.965669i	$-0.416352\pi$
$281$	145.993			0.519549			0.259774	+	0.965669i	$0.416352\pi$
$282$	−129.167	+	74.5746i	−0.458039	+	0.264449i
$283$	−176.873	+	306.352i	−0.624991	+	1.08252i	0.363551	+	0.931574i	$0.381564\pi$
$283$	−176.873	+	306.352i	−0.624991	+	1.08252i	−0.988543	+	0.150943i	$0.951769\pi$
$284$	−38.9302	+	67.4291i	−0.137078	+	0.237426i
$285$		0			0
$286$		−	59.8875i		−	0.209397i
$287$	114.575	+	450.380i	0.399215	+	1.56927i
$288$			16.9706i			0.0589256i
$289$	−48.1097	−	83.3284i	−0.166470	−	0.288334i
$290$		0			0
$291$	21.8665	−	37.8740i	0.0751428	−	0.130151i
$292$	35.2513	+	61.0571i	0.120724	+	0.209100i
$293$	−118.997			−0.406135			−0.203067	−	0.979165i	$-0.565091\pi$
$293$	−118.997			−0.406135			−0.203067	+	0.979165i	$0.565091\pi$
$294$	57.3558	+	105.434i	0.195088	+	0.358619i
$295$		0			0
$296$	−85.4977	−	148.086i	−0.288844	−	0.500292i
$297$	−50.8738	+	88.1160i	−0.171292	+	0.296687i
$298$	−30.8179	−	17.7927i	−0.103416	−	0.0597071i
$299$	−60.9562	+	35.1931i	−0.203867	+	0.117703i
$300$		0			0
$301$	127.632	+	501.707i	0.424027	+	1.66680i
$302$			31.4894i			0.104269i
$303$	−91.1868	+	52.6467i	−0.300947	+	0.173752i
$304$	−79.3639	−	45.8208i	−0.261065	−	0.150726i
$305$		0			0
$306$	−72.1142	+	41.6352i	−0.235667	+	0.136063i
$307$	−481.700			−1.56905			−0.784527	−	0.620095i	$-0.787094\pi$
$307$	−481.700			−1.56905			−0.784527	+	0.620095i	$0.787094\pi$
$308$	−191.370	−	196.289i	−0.621332	−	0.637302i
$309$	−74.0433			−0.239622
$310$		0			0
$311$	498.665	+	287.904i	1.60343	+	0.925738i	0.990795	+	0.135368i	$0.0432216\pi$
$311$	498.665	+	287.904i	1.60343	+	0.925738i	0.612630	+	0.790370i	$0.290112\pi$
$312$	−9.17519	−	5.29730i	−0.0294077	−	0.0169785i
$313$	−213.139	−	369.168i	−0.680957	−	1.17945i	−0.974689	−	0.223564i	$-0.928231\pi$
$313$	−213.139	−	369.168i	−0.680957	−	1.17945i	0.293733	−	0.955888i	$-0.405102\pi$
$314$		−	396.128i		−	1.26156i
$315$		0			0
$316$	43.1426			0.136527
$317$	21.8410	−	12.6099i	0.0688990	−	0.0397789i	−0.465155	−	0.885229i	$-0.654001\pi$
$317$	21.8410	−	12.6099i	0.0688990	−	0.0397789i	0.534054	+	0.845451i	$0.320668\pi$
$318$	113.440	−	196.485i	0.356731	−	0.617876i
$319$	271.125	−	469.602i	0.849921	−	1.47211i
$320$		0			0
$321$			265.519i			0.827162i
$322$	−87.3325	+	310.135i	−0.271219	+	0.963153i
$323$		−	449.662i		−	1.39214i
$324$	9.00000	+	15.5885i	0.0277778	+	0.0481125i
$325$		0			0
$326$	−93.7907	+	162.450i	−0.287701	+	0.498313i
$327$	50.0364	+	86.6656i	0.153017	+	0.265032i
$328$	−187.777			−0.572492
$329$	−297.542	−	305.189i	−0.904382	−	0.927627i
$330$		0			0
$331$	0.955424	+	1.65484i	0.00288648	+	0.00499953i	0.867465	−	0.497498i	$-0.165748\pi$
$331$	0.955424	+	1.65484i	0.00288648	+	0.00499953i	−0.864579	+	0.502498i	$0.832415\pi$
$332$	40.3650	−	69.9142i	0.121581	−	0.210585i
$333$	−157.069	−	90.6840i	−0.471680	−	0.272324i
$334$	146.347	−	84.4935i	0.438165	−	0.252975i
$335$		0			0
$336$	−47.0004	+	11.9567i	−0.139882	+	0.0355854i
$337$			337.622i			1.00184i	0.865492	+	0.500922i	$0.167006\pi$
$337$			337.622i			1.00184i	−0.865492	+	0.500922i	$0.832994\pi$
$338$	−201.254	+	116.194i	−0.595426	+	0.343769i
$339$	224.285	+	129.491i	0.661608	+	0.381980i
$340$		0			0
$341$	712.293	−	411.243i	2.08884	−	1.20599i
$342$	−97.2005			−0.284212
$343$	−251.591	+	233.132i	−0.733503	+	0.679686i
$344$	−209.177			−0.608073
$345$		0			0
$346$	308.780	+	178.274i	0.892427	+	0.515243i
$347$	−256.776	−	148.250i	−0.739988	−	0.427232i	0.0820768	−	0.996626i	$-0.473845\pi$
$347$	−256.776	−	148.250i	−0.739988	−	0.427232i	−0.822065	+	0.569394i	$0.807178\pi$
$348$	−47.9643	−	83.0765i	−0.137828	−	0.238726i
$349$		−	367.499i		−	1.05300i	−0.850174	−	0.526502i	$-0.823503\pi$
$349$		−	367.499i		−	1.05300i	0.850174	−	0.526502i	$-0.176497\pi$
$350$		0			0
$351$	−11.2373			−0.0320150
$352$	95.9285	−	55.3844i	0.272524	−	0.157342i
$353$	−263.651	+	456.656i	−0.746886	+	1.29364i	0.202423	+	0.979298i	$0.435118\pi$
$353$	−263.651	+	456.656i	−0.746886	+	1.29364i	−0.949309	+	0.314346i	$0.898215\pi$
$354$	−35.2753	+	61.0987i	−0.0996479	+	0.172595i
$355$		0			0
$356$			97.2542i			0.273186i
$357$	−166.118	−	170.388i	−0.465317	−	0.477277i
$358$		−	58.7573i		−	0.164127i
$359$	294.338	+	509.809i	0.819884	+	1.42008i	0.905767	+	0.423775i	$0.139295\pi$
$359$	294.338	+	509.809i	0.819884	+	1.42008i	−0.0858836	+	0.996305i	$0.527371\pi$
$360$		0			0
$361$	81.9428	−	141.929i	0.226988	−	0.393155i
$362$	182.580	+	316.239i	0.504366	+	0.873587i
$363$	454.539			1.25217
$364$	8.20657	−	29.1432i	0.0225455	−	0.0800637i
$365$		0			0
$366$	−102.948	−	178.312i	−0.281280	−	0.487190i
$367$	170.503	−	295.319i	0.464585	−	0.804685i	−0.534598	−	0.845107i	$-0.679537\pi$
$367$	170.503	−	295.319i	0.464585	−	0.804685i	0.999183	+	0.0404219i	$0.0128702\pi$
$368$	−112.745	−	65.0936i	−0.306373	−	0.176885i
$369$	−172.484	+	99.5839i	−0.467437	+	0.269875i
$370$		0			0
$371$	624.094	+	175.742i	1.68219	+	0.473698i
$372$		−	145.505i		−	0.391141i
$373$	−101.621	+	58.6711i	−0.272443	+	0.157295i	−0.629998	−	0.776597i	$-0.716944\pi$
$373$	−101.621	+	58.6711i	−0.272443	+	0.157295i	0.357554	+	0.933892i	$0.383611\pi$
$374$	470.697	+	271.757i	1.25855	+	0.726624i
$375$		0			0
$376$	149.149	−	86.1114i	0.396674	−	0.229020i
$377$	59.8875			0.158853
$378$	−36.8316	+	35.9087i	−0.0974381	+	0.0949965i
$379$	188.135			0.496398			0.248199	−	0.968709i	$-0.420161\pi$
$379$	188.135			0.496398			0.248199	+	0.968709i	$0.420161\pi$
$380$		0			0
$381$	264.318	+	152.604i	0.693749	+	0.400536i
$382$	110.680	+	63.9012i	0.289739	+	0.167281i
$383$	134.462	+	232.895i	0.351076	+	0.608081i	0.986438	−	0.164133i	$-0.0524827\pi$
$383$	134.462	+	232.895i	0.351076	+	0.608081i	−0.635363	+	0.772214i	$0.719149\pi$
$384$		−	19.5959i		−	0.0510310i
$385$		0			0
$386$	−86.1552			−0.223200
$387$	−192.141	+	110.933i	−0.496490	+	0.286648i
$388$	−25.2493	+	43.7331i	−0.0650755	+	0.112714i
$389$	148.182	−	256.658i	0.380930	−	0.659790i	−0.610265	−	0.792197i	$-0.708937\pi$
$389$	148.182	−	256.658i	0.380930	−	0.659790i	0.991195	+	0.132407i	$0.0422705\pi$
$390$		0			0
$391$		−	638.796i		−	1.63375i
$392$	−66.2288	−	121.745i	−0.168951	−	0.310573i
$393$			126.100i			0.320866i
$394$	52.4185	+	90.7915i	0.133042	+	0.230435i
$395$		0			0
$396$	58.7440	−	101.748i	0.148343	−	0.256938i
$397$	9.43705	+	16.3455i	0.0237709	+	0.0411724i	0.877666	−	0.479273i	$-0.159099\pi$
$397$	9.43705	+	16.3455i	0.0237709	+	0.0411724i	−0.853895	+	0.520445i	$0.825766\pi$
$398$	−126.651			−0.318218
$399$	−68.4832	−	269.199i	−0.171637	−	0.674685i
$400$		0			0
$401$	−171.967	−	297.856i	−0.428845	−	0.742782i	0.567925	−	0.823080i	$-0.307746\pi$
$401$	−171.967	−	297.856i	−0.428845	−	0.742782i	−0.996771	+	0.0802979i	$0.974413\pi$
$402$	−3.98265	+	6.89815i	−0.00990708	+	0.0171596i
$403$	78.6675	+	45.4187i	0.195205	+	0.112702i
$404$	105.293	−	60.7912i	0.260627	−	0.150473i
$405$		0			0
$406$	196.289	−	191.370i	0.483471	−	0.471355i
$407$			1183.81i			2.90862i
$408$	83.2703	−	48.0762i	0.204094	−	0.117834i
$409$	−376.358	−	217.291i	−0.920192	−	0.531273i	−0.0364954	−	0.999334i	$-0.511619\pi$
$409$	−376.358	−	217.291i	−0.920192	−	0.531273i	−0.883696	+	0.468061i	$0.844953\pi$
$410$		0			0
$411$	224.253	−	129.472i	0.545628	−	0.315018i
$412$	85.4978			0.207519
$413$	−194.068	−	54.6485i	−0.469898	−	0.132321i
$414$	−138.084			−0.333537
$415$		0			0
$416$	10.5946	+	6.11680i	0.0254678	+	0.0147038i
$417$	−86.2129	−	49.7751i	−0.206746	−	0.119365i
$418$	317.219	+	549.440i	0.758898	+	1.31445i
$419$		−	319.236i		−	0.761899i	−0.924596	−	0.380949i	$-0.875597\pi$
$419$		−	319.236i		−	0.761899i	0.924596	−	0.380949i	$-0.124403\pi$
$420$		0			0
$421$	−663.506			−1.57602			−0.788012	−	0.615660i	$-0.788889\pi$
$421$	−663.506			−1.57602			−0.788012	+	0.615660i	$0.788889\pi$
$422$	85.5664	−	49.4018i	0.202764	−	0.117066i
$423$	91.3349	−	158.197i	0.215922	−	0.373987i
$424$	−130.990	+	226.881i	−0.308938	+	0.535097i
$425$		0			0
$426$		−	95.3591i		−	0.223848i
$427$	421.306	−	410.748i	0.986665	−	0.961940i
$428$		−	306.595i		−	0.716343i
$429$	36.6735	+	63.5203i	0.0854859	+	0.148066i
$430$		0			0
$431$	50.5285	−	87.5179i	0.117235	−	0.203058i	−0.801436	−	0.598081i	$-0.795930\pi$
$431$	50.5285	−	87.5179i	0.117235	−	0.203058i	0.918671	+	0.395023i	$0.129263\pi$
$432$	−10.3923	−	18.0000i	−0.0240563	−	0.0416667i
$433$	−490.183			−1.13206			−0.566031	−	0.824384i	$-0.691522\pi$
$433$	−490.183			−1.13206			−0.566031	+	0.824384i	$0.691522\pi$
$434$	402.978	−	102.516i	0.928522	−	0.236212i
$435$		0			0
$436$	−57.7771	−	100.073i	−0.132516	−	0.229525i
$437$	372.830	−	645.760i	0.853157	−	1.47771i
$438$	−74.7793	−	43.1739i	−0.170729	−	0.0985705i
$439$	−399.753	+	230.797i	−0.910599	+	0.525735i	−0.880624	−	0.473816i	$-0.842876\pi$
$439$	−399.753	+	230.797i	−0.910599	+	0.525735i	−0.0299751	+	0.999551i	$0.509543\pi$
$440$		0			0
$441$	−125.400	−	76.7064i	−0.284353	−	0.173937i
$442$			60.0272i			0.135808i
$443$	173.245	−	100.023i	0.391073	−	0.225786i	−0.291552	−	0.956555i	$-0.594172\pi$
$443$	173.245	−	100.023i	0.391073	−	0.225786i	0.682625	+	0.730769i	$0.260838\pi$
$444$	181.368	+	104.713i	0.408487	+	0.235840i
$445$		0			0
$446$	−477.257	+	275.545i	−1.07008	+	0.617813i
$447$	43.5830			0.0975012
$448$	54.2714	−	13.8064i	0.121141	−	0.0308179i
$449$	75.8015			0.168823			0.0844115	−	0.996431i	$-0.473099\pi$
$449$	75.8015			0.168823			0.0844115	+	0.996431i	$0.473099\pi$
$450$		0			0
$451$	1125.82	+	649.995i	2.49629	+	1.44123i
$452$	−258.982	−	149.523i	−0.572970	−	0.330804i
$453$	−19.2832	−	33.3995i	−0.0425678	−	0.0737296i
$454$		−	10.5683i		−	0.0232781i
$455$		0			0
$456$	112.237			0.246135
$457$	356.062	−	205.573i	0.779129	−	0.449831i	−0.0569922	−	0.998375i	$-0.518151\pi$
$457$	356.062	−	205.573i	0.779129	−	0.449831i	0.836122	+	0.548544i	$0.184818\pi$
$458$	70.8978	−	122.799i	0.154799	−	0.268119i
$459$	50.9925	−	88.3215i	0.111095	−	0.192422i
$460$		0			0
$461$			278.002i			0.603041i	0.953460	+	0.301521i	$0.0974942\pi$
$461$			278.002i			0.603041i	−0.953460	+	0.301521i	$0.902506\pi$
$462$	323.181	+	91.0061i	0.699526	+	0.196983i
$463$		−	492.573i		−	1.06387i	−0.846784	−	0.531936i	$-0.821465\pi$
$463$		−	492.573i		−	1.06387i	0.846784	−	0.531936i	$-0.178535\pi$
$464$	55.3844	+	95.9285i	0.119363	+	0.206743i
$465$		0			0
$466$	240.396	−	416.378i	0.515871	−	0.893515i
$467$	161.500	+	279.726i	0.345824	+	0.598985i	0.985503	−	0.169657i	$-0.0542659\pi$
$467$	161.500	+	279.726i	0.345824	+	0.598985i	−0.639679	+	0.768642i	$0.720933\pi$
$468$	12.9757			0.0277258
$469$	−21.9106	−	6.16991i	−0.0467177	−	0.0131555i
$470$		0			0
$471$	242.578	+	420.158i	0.515028	+	0.892054i
$472$	40.7325	−	70.5507i	0.0862976	−	0.149472i
$473$	1254.13	+	724.072i	2.65143	+	1.53081i
$474$	−45.7597	+	26.4193i	−0.0965393	+	0.0557370i
$475$		0			0
$476$	191.817	+	196.747i	0.402976	+	0.413334i
$477$			277.871i			0.582539i
$478$	−46.1844	+	26.6646i	−0.0966200	+	0.0557836i
$479$	267.845	+	154.641i	0.559176	+	0.322841i	0.752815	−	0.658232i	$-0.228696\pi$
$479$	267.845	+	154.641i	0.559176	+	0.322841i	−0.193639	+	0.981073i	$0.562029\pi$
$480$		0			0
$481$	−113.227	+	65.3715i	−0.235399	+	0.135907i
$482$	−422.154			−0.875837
$483$	−97.2881	−	382.428i	−0.201425	−	0.791777i
$484$	−524.857			−1.08442
$485$		0			0
$486$	−19.0919	−	11.0227i	−0.0392837	−	0.0226805i
$487$	−489.918	−	282.854i	−1.00599	−	0.580809i	−0.0959758	−	0.995384i	$-0.530597\pi$
$487$	−489.918	−	282.854i	−1.00599	−	0.580809i	−0.910015	+	0.414574i	$0.863930\pi$
$488$	118.874	+	205.897i	0.243595	+	0.421919i
$489$		−	229.739i		−	0.469814i
$490$		0			0
$491$	−379.335			−0.772577			−0.386288	−	0.922378i	$-0.626243\pi$
$491$	−379.335			−0.772577			−0.386288	+	0.922378i	$0.626243\pi$
$492$	199.168	−	114.990i	0.404813	−	0.233719i
$493$	−271.757	+	470.697i	−0.551232	+	0.954762i
$494$	−35.0345	+	60.6816i	−0.0709201	+	0.122837i
$495$		0			0
$496$			168.014i			0.338738i
$497$	264.099	−	67.1858i	0.531387	−	0.135183i
$498$			98.8736i			0.198541i
$499$	−271.332	−	469.961i	−0.543751	−	0.941805i	−0.998684	−	0.0512794i	$-0.983670\pi$
$499$	−271.332	−	469.961i	−0.543751	−	0.941805i	0.454933	−	0.890526i	$-0.349663\pi$
$500$		0			0
$501$	−103.483	+	179.238i	−0.206553	+	0.357760i
$502$	−177.575	−	307.569i	−0.353735	−	0.612687i
$503$	281.628			0.559896			0.279948	−	0.960015i	$-0.409683\pi$
$503$	281.628			0.559896			0.279948	+	0.960015i	$0.409683\pi$
$504$	42.5295	−	41.4637i	0.0843839	−	0.0822693i
$505$		0			0
$506$	450.646	+	780.542i	0.890605	+	1.54257i
$507$	142.308	−	246.485i	0.280686	−	0.486163i
$508$	−305.208	−	176.212i	−0.600804	−	0.346874i
$509$	8.88432	−	5.12937i	0.0174545	−	0.0100773i	−0.491247	−	0.871020i	$-0.663459\pi$
$509$	8.88432	−	5.12937i	0.0174545	−	0.0100773i	0.508702	+	0.860943i	$0.330126\pi$
$510$		0			0
$511$	66.8849	−	237.522i	0.130890	−	0.464817i
$512$			22.6274i			0.0441942i
$513$	103.097	−	59.5229i	0.200968	−	0.116029i
$514$	73.0771	+	42.1911i	0.142173	+	0.0820838i
$515$		0			0
$516$	221.866	−	128.094i	0.429973	−	0.248245i
$517$	−1192.31			−2.30620
$518$	−162.221	+	576.079i	−0.313168	+	1.11212i
$519$	−436.681			−0.841389
$520$		0			0
$521$	−666.970	−	385.075i	−1.28017	−	0.739108i	−0.303292	−	0.952898i	$-0.598086\pi$
$521$	−666.970	−	385.075i	−1.28017	−	0.739108i	−0.976880	+	0.213790i	$0.931419\pi$
$522$	101.748	+	58.7440i	0.194919	+	0.112536i
$523$	−150.678	−	260.981i	−0.288102	−	0.499008i	0.685254	−	0.728304i	$-0.259691\pi$
$523$	−150.678	−	260.981i	−0.288102	−	0.499008i	−0.973357	+	0.229296i	$0.926358\pi$
$524$		−	145.608i		−	0.277878i
$525$		0			0
$526$	−176.505			−0.335561
$527$	−713.955	+	412.202i	−1.35475	+	0.782167i
$528$	−67.8317	+	117.488i	−0.128469	+	0.222515i
$529$	265.147	−	459.248i	0.501223	−	0.868144i
$530$		0			0
$531$		−	86.4066i		−	0.162724i
$532$	79.0776	+	310.845i	0.148642	+	0.584294i
$533$			143.574i			0.269370i
$534$	−59.5558	−	103.154i	−0.111528	−	0.193172i
$535$		0			0
$536$	4.59876	−	7.96529i	0.00857978	−	0.0148606i
$537$	35.9814	+	62.3215i	0.0670044	+	0.116055i
$538$	294.427			0.547263
$539$	−24.3448	+	959.176i	−0.0451666	+	1.77955i
$540$		0			0
$541$	−488.481	−	846.074i	−0.902922	−	1.56391i	−0.823682	−	0.567052i	$-0.808084\pi$
$541$	−488.481	−	846.074i	−0.902922	−	1.56391i	−0.0792400	−	0.996856i	$-0.525249\pi$
$542$	14.0321	−	24.3042i	0.0258894	−	0.0448418i
$543$	−387.311	−	223.614i	−0.713281	−	0.411813i
$544$	−96.1523	+	55.5136i	−0.176751	+	0.102047i
$545$		0			0
$546$	9.14209	+	35.9365i	0.0167438	+	0.0658177i
$547$		−	231.665i		−	0.423520i	−0.977322	−	0.211760i	$-0.932080\pi$
$547$		−	231.665i		−	0.423520i	0.977322	−	0.211760i	$-0.0679195\pi$
$548$	−258.945	+	149.502i	−0.472527	+	0.272814i
$549$	218.386	+	126.085i	0.397789	+	0.229664i
$550$		0			0
$551$	−549.440	+	317.219i	−0.997168	+	0.575715i
$552$	159.446			0.288852
$553$	−105.409	−	108.119i	−0.190613	−	0.195513i
$554$	123.058			0.222127
$555$		0			0
$556$	99.5501	+	57.4753i	0.179047	+	0.103373i
$557$	160.044	+	92.4015i	0.287332	+	0.165891i	0.636738	−	0.771080i	$-0.280283\pi$
$557$	160.044	+	92.4015i	0.287332	+	0.165891i	−0.349406	+	0.936971i	$0.613617\pi$
$558$	89.1030	+	154.331i	0.159683	+	0.276579i
$559$			159.937i			0.286112i
$560$		0			0
$561$	−665.667			−1.18657
$562$	178.804	−	103.233i	0.318157	−	0.183688i
$563$	20.4134	−	35.3570i	0.0362582	−	0.0628011i	−0.847327	−	0.531072i	$-0.821789\pi$
$563$	20.4134	−	35.3570i	0.0362582	−	0.0628011i	0.883585	+	0.468271i	$0.155123\pi$
$564$	−105.464	+	182.670i	−0.186994	+	0.323883i
$565$		0			0
$566$			500.271i			0.883871i
$567$	17.0764	−	60.6416i	0.0301170	−	0.106952i
$568$			110.111i			0.193858i
$569$	−300.722	−	520.866i	−0.528509	−	0.915405i	−0.999447	−	0.0332389i	$-0.989418\pi$
$569$	−300.722	−	520.866i	−0.528509	−	0.915405i	0.470938	−	0.882166i	$-0.343916\pi$
$570$		0			0
$571$	−434.599	+	752.747i	−0.761119	+	1.31830i	0.181156	+	0.983454i	$0.442016\pi$
$571$	−434.599	+	752.747i	−0.761119	+	1.31830i	−0.942274	+	0.334842i	$0.891317\pi$
$572$	−42.3469	−	73.3469i	−0.0740330	−	0.128229i
$573$	−156.525			−0.273168
$574$	458.791	+	470.584i	0.799288	+	0.819832i
$575$		0			0
$576$	12.0000	+	20.7846i	0.0208333	+	0.0360844i
$577$	31.3112	−	54.2326i	0.0542655	−	0.0939906i	−0.837617	−	0.546259i	$-0.816052\pi$
$577$	31.3112	−	54.2326i	0.0542655	−	0.0939906i	0.891882	+	0.452268i	$0.149385\pi$
$578$	−117.844	−	68.0374i	−0.203883	−	0.117712i
$579$	91.3814	−	52.7591i	0.157826	−	0.0911210i
$580$		0			0
$581$	−273.833	+	69.6619i	−0.471313	+	0.119900i
$582$		−	61.8479i		−	0.106268i
$583$	1570.71	−	906.848i	2.69418	−	1.55549i
$584$	86.3477	+	49.8529i	0.147856	+	0.0853645i
$585$		0			0
$586$	−145.741	+	84.1439i	−0.248706	+	0.143590i
$587$	−112.217			−0.191170			−0.0955852	−	0.995421i	$-0.530472\pi$
$587$	−112.217			−0.191170			−0.0955852	+	0.995421i	$0.530472\pi$
$588$	144.799	+	88.5730i	0.246257	+	0.150634i
$589$	−962.317			−1.63382
$590$		0			0
$591$	−111.196	−	64.1993i	−0.188150	−	0.108628i
$592$	−209.426	−	120.912i	−0.353760	−	0.204243i
$593$	259.803	+	449.992i	0.438117	+	0.758841i	0.997544	−	0.0700388i	$-0.0223123\pi$
$593$	259.803	+	449.992i	0.438117	+	0.758841i	−0.559427	+	0.828879i	$0.688979\pi$
$594$			143.893i			0.242244i
$595$		0			0
$596$	−50.3254			−0.0844385
$597$	134.334	−	77.5575i	0.225014	−	0.129912i
$598$	−49.7705	+	86.2051i	−0.0832283	+	0.144156i
$599$	−123.317	+	213.591i	−0.205871	+	0.356579i	−0.950410	−	0.311000i	$-0.899336\pi$
$599$	−123.317	+	213.591i	−0.205871	+	0.356579i	0.744539	+	0.667579i	$0.232669\pi$
$600$		0			0
$601$		−	244.671i		−	0.407106i	−0.979064	−	0.203553i	$-0.934751\pi$
$601$		−	244.671i		−	0.407106i	0.979064	−	0.203553i	$-0.0652489\pi$
$602$	511.077	+	524.214i	0.848966	+	0.870787i
$603$		−	9.75545i		−	0.0161782i
$604$	22.2663	+	38.5664i	0.0368648	+	0.0638517i
$605$		0			0
$606$	−74.4537	+	128.958i	−0.122861	+	0.212801i
$607$	20.2975	+	35.1564i	0.0334391	+	0.0579183i	0.882261	−	0.470761i	$-0.156021\pi$
$607$	20.2975	+	35.1564i	0.0334391	+	0.0579183i	−0.848822	+	0.528680i	$0.822687\pi$
$608$	−129.601			−0.213159
$609$	−91.0061	+	323.181i	−0.149435	+	0.530675i
$610$		0			0
$611$	−65.8407	−	114.039i	−0.107759	−	0.186644i
$612$	−58.8810	+	101.985i	−0.0962108	+	0.166642i
$613$	−95.2330	−	54.9828i	−0.155356	−	0.0896946i	0.420307	−	0.907382i	$-0.361922\pi$
$613$	−95.2330	−	54.9828i	−0.155356	−	0.0896946i	−0.575662	+	0.817687i	$0.695256\pi$
$614$	−589.959	+	340.613i	−0.960845	+	0.554744i
$615$		0			0
$616$	−373.177	−	105.085i	−0.605807	−	0.170592i
$617$		−	168.842i		−	0.273650i	−0.990595	−	0.136825i	$-0.956310\pi$
$617$		−	168.842i		−	0.273650i	0.990595	−	0.136825i	$-0.0436898\pi$
$618$	−90.6842	+	52.3565i	−0.146738	+	0.0847193i
$619$	607.202	+	350.568i	0.980940	+	0.566346i	0.902554	−	0.430577i	$-0.141690\pi$
$619$	607.202	+	350.568i	0.980940	+	0.566346i	0.0783859	+	0.996923i	$0.475023\pi$
$620$		0			0
$621$	146.461	−	84.5591i	0.235846	−	0.136166i
$622$	814.317			1.30919
$623$	243.726	−	237.619i	0.391214	−	0.381411i
$624$	−14.9830			−0.0240113
$625$		0			0
$626$	−522.083	−	301.425i	−0.833998	−	0.481509i
$627$	−672.924	−	388.513i	−1.07324	−	0.619637i
$628$	−280.105	−	485.156i	−0.446027	−	0.772542i
$629$		−	1186.57i		−	1.88644i
$630$		0			0
$631$	−465.556			−0.737807			−0.368903	−	0.929468i	$-0.620267\pi$
$631$	−465.556			−0.737807			−0.368903	+	0.929468i	$0.620267\pi$
$632$	52.8387	−	30.5064i	0.0836055	−	0.0482697i
$633$	−60.5046	+	104.797i	−0.0955838	+	0.165556i
$634$	17.8331	−	30.8878i	0.0281279	−	0.0487189i
$635$		0			0
$636$		−	320.858i		−	0.504494i
$637$	−93.0859	+	50.6385i	−0.146132	+	0.0794953i
$638$		−	766.857i		−	1.20197i
$639$	58.3953	+	101.144i	0.0913854	+	0.158284i
$640$		0			0
$641$	615.260	−	1065.66i	0.959844	−	1.66250i	0.236973	−	0.971516i	$-0.423845\pi$
$641$	615.260	−	1065.66i	0.959844	−	1.66250i	0.722871	−	0.690983i	$-0.242822\pi$
$642$	187.750	+	325.193i	0.292446	+	0.506531i
$643$	322.975			0.502293			0.251147	−	0.967949i	$-0.419192\pi$
$643$	322.975			0.502293			0.251147	+	0.967949i	$0.419192\pi$
$644$	112.339	+	441.590i	0.174439	+	0.685699i
$645$		0			0
$646$	−317.959	−	550.721i	−0.492197	−	0.852510i
$647$	592.243	−	1025.79i	0.915368	−	1.58546i	0.109006	−	0.994041i	$-0.465233\pi$
$647$	592.243	−	1025.79i	0.915368	−	1.58546i	0.806362	−	0.591422i	$-0.201433\pi$
$648$	22.0454	+	12.7279i	0.0340207	+	0.0196419i
$649$	−488.426	+	281.993i	−0.752582	+	0.434503i
$650$		0			0
$651$	−364.645	+	355.508i	−0.560131	+	0.546095i
$652$			265.280i			0.406871i
$653$	228.041	−	131.660i	0.349221	−	0.201623i	−0.315121	−	0.949052i	$-0.602045\pi$
$653$	228.041	−	131.660i	0.349221	−	0.201623i	0.664342	+	0.747429i	$0.268712\pi$
$654$	122.564	+	70.7622i	0.187406	+	0.108199i
$655$		0			0
$656$	−229.979	+	132.779i	−0.350578	+	0.202406i
$657$	105.754			0.160965
$658$	−580.214	−	163.385i	−0.881784	−	0.248306i
$659$	1199.70			1.82049			0.910246	−	0.414069i	$-0.135893\pi$
$659$	1199.70			1.82049			0.910246	+	0.414069i	$0.135893\pi$
$660$		0			0
$661$	497.702	+	287.349i	0.752954	+	0.434718i	0.826760	−	0.562555i	$-0.190181\pi$
$661$	497.702	+	287.349i	0.752954	+	0.434718i	−0.0738065	+	0.997273i	$0.523515\pi$
$662$	2.34030	+	1.35117i	0.00353520	+	0.00204105i
$663$	−36.7590	−	63.6685i	−0.0554434	−	0.0960309i
$664$		−	114.169i		−	0.171942i
$665$		0			0
$666$	−256.493			−0.385125
$667$	−780.542	+	450.646i	−1.17023	+	0.675631i
$668$	119.492	−	206.966i	0.178880	−	0.309829i
$669$	337.472	−	584.518i	0.504442	−	0.873719i
$670$		0			0
$671$		−	1645.95i		−	2.45298i
$672$	−49.1088	+	47.8782i	−0.0730786	+	0.0712473i
$673$			958.817i			1.42469i	0.701829	+	0.712346i	$0.252367\pi$
$673$			958.817i			1.42469i	−0.701829	+	0.712346i	$0.747633\pi$
$674$	238.735	+	413.500i	0.354206	+	0.613502i
$675$		0			0
$676$	−164.323	+	284.616i	−0.243082	+	0.421030i
$677$	227.961	+	394.839i	0.336722	+	0.583219i	0.983814	−	0.179192i	$-0.0573485\pi$
$677$	227.961	+	394.839i	0.336722	+	0.583219i	−0.647092	+	0.762412i	$0.724015\pi$
$678$	366.256			0.540201
$679$	171.289	−	43.5753i	0.252267	−	0.0641757i
$680$		0			0
$681$	6.47172	+	11.2093i	0.00950325	+	0.0164601i
$682$	581.585	−	1007.33i	0.852764	−	1.47703i
$683$	−200.015	−	115.479i	−0.292848	−	0.169076i	0.346378	−	0.938095i	$-0.387412\pi$
$683$	−200.015	−	115.479i	−0.292848	−	0.169076i	−0.639225	+	0.769019i	$0.720745\pi$
$684$	−119.046	+	68.7311i	−0.174044	+	0.100484i
$685$		0			0
$686$	−143.286	+	463.430i	−0.208872	+	0.675554i
$687$			173.663i			0.252785i
$688$	−256.189	+	147.911i	−0.372367	+	0.214986i
$689$	173.473	+	100.155i	0.251775	+	0.145362i
$690$		0			0
$691$	−92.1832	+	53.2220i	−0.133405	+	0.0770217i	−0.565217	−	0.824942i	$-0.691208\pi$
$691$	−92.1832	+	53.2220i	−0.133405	+	0.0770217i	0.431812	+	0.901964i	$0.357874\pi$
$692$	504.235			0.728664
$693$	−398.515	+	101.380i	−0.575057	+	0.146292i
$694$	−419.313			−0.604198
$695$		0			0
$696$	−117.488	−	67.8317i	−0.168805	−	0.0974594i
$697$	−1128.45	−	651.511i	−1.61901	−	0.934737i
$698$	−259.861	−	450.092i	−0.372293	−	0.644831i
$699$			588.848i			0.842414i
$700$		0			0
$701$	−623.489			−0.889429			−0.444714	−	0.895672i	$-0.646695\pi$
$701$	−623.489			−0.889429			−0.444714	+	0.895672i	$0.646695\pi$
$702$	−13.7628	+	7.94595i	−0.0196051	+	0.0113190i
$703$	692.535	−	1199.51i	0.985114	−	1.70627i
$704$	78.3253	−	135.663i	0.111258	−	0.192704i
$705$		0			0
$706$			745.717i			1.05626i
$707$	−409.608	−	115.344i	−0.579361	−	0.163145i
$708$			99.7737i			0.140923i
$709$	397.184	+	687.943i	0.560203	+	0.970300i	0.997478	+	0.0709721i	$0.0226101\pi$
$709$	397.184	+	687.943i	0.560203	+	0.970300i	−0.437275	+	0.899328i	$0.644057\pi$
$710$		0			0
$711$	32.3570	−	56.0439i	0.0455091	−	0.0788240i
$712$	68.7691	+	119.112i	0.0965858	+	0.167292i
$713$	−1367.08			−1.91736
$714$	−323.935	−	91.2184i	−0.453690	−	0.127757i
$715$		0			0
$716$	−41.5477	−	71.9627i	−0.0580275	−	0.100507i
$717$	32.6573	−	56.5641i	0.0455471	−	0.0788899i
$718$	720.979	+	416.257i	1.00415	+	0.579745i
$719$	33.4178	−	19.2938i	0.0464782	−	0.0268342i	−0.476581	−	0.879131i	$-0.658124\pi$
$719$	33.4178	−	19.2938i	0.0464782	−	0.0268342i	0.523059	+	0.852296i	$0.324791\pi$
$720$		0			0
$721$	−208.895	−	214.264i	−0.289729	−	0.297176i
$722$		−	231.769i		−	0.321010i
$723$	447.761	−	258.515i	0.619310	−	0.357559i
$724$	447.229	+	258.208i	0.617719	+	0.356640i
$725$		0			0
$726$	556.695	−	321.408i	0.766797	−	0.442711i
$727$	867.980			1.19392			0.596960	−	0.802271i	$-0.296375\pi$
$727$	867.980			1.19392			0.596960	+	0.802271i	$0.296375\pi$
$728$	−10.5564	−	41.4959i	−0.0145005	−	0.0569998i
$729$	27.0000			0.0370370
$730$		0			0
$731$	−1257.05	−	725.761i	−1.71964	−	0.992832i
$732$	−252.171	−	145.591i	−0.344496	−	0.198895i
$733$	−163.869	−	283.830i	−0.223560	−	0.387217i	0.732327	−	0.680954i	$-0.238434\pi$
$733$	−163.869	−	283.830i	−0.223560	−	0.387217i	−0.955886	+	0.293737i	$0.905101\pi$
$734$		−	482.254i		−	0.657022i
$735$		0			0
$736$	−184.112			−0.250153
$737$	−55.1441	+	31.8375i	−0.0748224	+	0.0431987i
$738$	−140.833	+	243.930i	−0.190831	+	0.330528i
$739$	598.500	−	1036.63i	0.809878	−	1.40275i	−0.103070	−	0.994674i	$-0.532866\pi$
$739$	598.500	−	1036.63i	0.809878	−	1.40275i	0.912948	−	0.408076i	$-0.133800\pi$
$740$		0			0
$741$		−	85.8167i		−	0.115812i
$742$	888.625	−	226.062i	1.19761	−	0.304666i
$743$			685.246i			0.922269i	0.887330	+	0.461135i	$0.152557\pi$
$743$			685.246i			0.922269i	−0.887330	+	0.461135i	$0.847443\pi$
$744$	−102.887	−	178.206i	−0.138289	−	0.239524i
$745$		0			0
$746$	−82.9735	+	143.714i	−0.111225	+	0.192647i
$747$	−60.5474	−	104.871i	−0.0810541	−	0.140390i
$748$	768.646			1.02760
$749$	−768.350	+	749.096i	−1.02583	+	1.00013i
$750$		0			0
$751$	−40.2714	−	69.7521i	−0.0536237	−	0.0928789i	0.837968	−	0.545720i	$-0.183744\pi$
$751$	−40.2714	−	69.7521i	−0.0536237	−	0.0928789i	−0.891591	+	0.452841i	$0.850410\pi$
$752$	121.780	−	210.929i	0.161941	−	0.280491i
$753$	376.694	+	217.484i	0.500257	+	0.288824i
$754$	73.3469	−	42.3469i	0.0972771	−	0.0561629i
$755$		0			0
$756$	−19.7181	+	70.0228i	−0.0260821	+	0.0926228i
$757$			978.106i			1.29208i	0.763303	+	0.646041i	$0.223576\pi$
$757$			978.106i			1.29208i	−0.763303	+	0.646041i	$0.776424\pi$
$758$	230.417	−	133.031i	0.303981	−	0.175503i
$759$	−955.964	−	551.926i	−1.25951	−	0.727176i
$760$		0			0
$761$	−514.781	+	297.209i	−0.676453	+	0.390550i	−0.798517	−	0.601972i	$-0.794382\pi$
$761$	−514.781	+	297.209i	−0.676453	+	0.390550i	0.122064	+	0.992522i	$0.461049\pi$
$762$	431.630			0.566443
$763$	−109.625	+	389.299i	−0.143676	+	0.510221i
$764$	180.740			0.236571
$765$		0			0
$766$	329.363	+	190.158i	0.429978	+	0.248248i
$767$	−53.9430	−	31.1440i	−0.0703299	−	0.0406050i
$768$	−13.8564	−	24.0000i	−0.0180422	−	0.0312500i
$769$			1475.89i			1.91923i	0.281321	+	0.959614i	$0.409228\pi$
$769$			1475.89i			1.91923i	−0.281321	+	0.959614i	$0.590772\pi$
$770$		0			0
$771$	−103.347			−0.134042
$772$	−105.518	+	60.9209i	−0.136682	+	0.0789131i
$773$	19.6389	−	34.0155i	0.0254060	−	0.0440045i	−0.853043	−	0.521841i	$-0.825245\pi$
$773$	19.6389	−	34.0155i	0.0254060	−	0.0440045i	0.878449	+	0.477836i	$0.158579\pi$
$774$	−156.883	+	271.729i	−0.202691	+	0.351071i
$775$		0			0
$776$			71.4158i			0.0920307i
$777$	−180.714	−	710.364i	−0.232579	−	0.914239i
$778$		−	419.121i		−	0.538716i
$779$	−760.502	−	1317.23i	−0.976254	−	1.69092i
$780$		0			0
$781$	381.153	−	660.176i	0.488031	−	0.845295i
$782$	−451.697	−	782.362i	−0.577618	−	1.00046i
$783$	−143.893			−0.183771
$784$	−167.200	−	102.275i	−0.213265	−	0.130453i
$785$		0			0
$786$	89.1665	+	154.441i	0.113443	+	0.196490i
$787$	−444.246	+	769.456i	−0.564480	+	0.977708i	0.432618	+	0.901577i	$0.357590\pi$
$787$	−444.246	+	769.456i	−0.564480	+	0.977708i	−0.997098	+	0.0761308i	$0.975743\pi$
$788$	128.399	+	74.1310i	0.162942	+	0.0940749i
$789$	187.212	−	108.087i	0.237277	−	0.136992i
$790$		0			0
$791$	258.048	+	1014.36i	0.326230	+	1.28237i
$792$		−	166.153i		−	0.209789i
$793$	157.428	−	90.8914i	0.198523	−	0.114617i
$794$	23.1160	+	13.3460i	0.0291133	+	0.0168086i
$795$		0			0
$796$	−155.115	+	89.5557i	−0.194868	+	0.112507i
$797$	340.067			0.426684			0.213342	−	0.976978i	$-0.431565\pi$
$797$	340.067			0.426684			0.213342	+	0.976978i	$0.431565\pi$
$798$	−274.227	−	281.275i	−0.343643	−	0.352476i
$799$	1195.09			1.49573
$800$		0			0
$801$	126.337	+	72.9407i	0.157724	+	0.0910620i
$802$	−421.231	−	243.198i	−0.525226	−	0.303240i
$803$	−345.134	−	597.789i	−0.429806	−	0.744445i
$804$			11.2646i			0.0140107i
$805$		0			0
$806$	128.464			0.159384
$807$	−312.287	+	180.299i	−0.386973	+	0.223419i
$808$	85.9717	−	148.907i	0.106401	−	0.184291i
$809$	−17.5840	+	30.4564i	−0.0217355	+	0.0376470i	−0.876689	−	0.481058i	$-0.840253\pi$
$809$	−17.5840	+	30.4564i	−0.0217355	+	0.0376470i	0.854953	+	0.518705i	$0.173586\pi$
$810$		0			0
$811$			1408.87i			1.73720i	0.495511	+	0.868602i	$0.334981\pi$
$811$			1408.87i			1.73720i	−0.495511	+	0.868602i	$0.665019\pi$
$812$	105.085	−	373.177i	0.129415	−	0.459578i
$813$			34.3714i			0.0422772i
$814$	837.079	+	1449.86i	1.02835	+	1.78116i
$815$		0			0
$816$	67.9899	−	117.762i	0.0833210	−	0.144316i
$817$	−847.172	−	1467.35i	−1.03693	−	1.79602i
$818$	−614.591			−0.751333
$819$	−31.7032	−	32.5180i	−0.0387096	−	0.0397046i
$820$		0			0
$821$	−218.908	−	379.160i	−0.266636	−	0.461827i	0.701355	−	0.712812i	$-0.252579\pi$
$821$	−218.908	−	379.160i	−0.266636	−	0.461827i	−0.967991	+	0.250985i	$0.919245\pi$
$822$	183.102	−	317.141i	0.222751	−	0.385817i
$823$	682.642	+	394.124i	0.829456	+	0.478887i	0.853666	−	0.520820i	$-0.174374\pi$
$823$	682.642	+	394.124i	0.829456	+	0.478887i	−0.0242104	+	0.999707i	$0.507707\pi$
$824$	104.713	−	60.4561i	0.127079	−	0.0733691i
$825$		0			0
$826$	−276.326	+	70.2962i	−0.334535	+	0.0851043i
$827$			45.9270i			0.0555345i	0.999614	+	0.0277673i	$0.00883973\pi$
$827$			45.9270i			0.0555345i	−0.999614	+	0.0277673i	$0.991160\pi$
$828$	−169.118	+	97.6404i	−0.204249	+	0.117923i
$829$	−519.195	−	299.757i	−0.626290	−	0.361589i	0.153024	−	0.988223i	$-0.451099\pi$
$829$	−519.195	−	299.757i	−0.626290	−	0.361589i	−0.779314	+	0.626634i	$0.784432\pi$
$830$		0			0
$831$	−130.523	+	75.3576i	−0.157068	+	0.0906830i
$832$	17.3009			0.0207944
$833$	24.4016	−	961.414i	0.0292936	−	1.15416i
$834$	−140.785			−0.168807
$835$		0			0
$836$	777.025	+	448.616i	0.929456	+	0.536622i
$837$	−189.016	−	109.128i	−0.225826	−	0.130380i
$838$	−225.734	−	390.982i	−0.269372	−	0.466566i
$839$			933.368i			1.11248i	0.831023	+	0.556238i	$0.187756\pi$
$839$			933.368i			1.11248i	−0.831023	+	0.556238i	$0.812244\pi$
$840$		0			0
$841$	−74.1431			−0.0881606
$842$	−812.626	+	469.170i	−0.965114	+	0.557209i
$843$	−126.434	+	218.990i	−0.149981	+	0.259774i
$844$	69.8647	−	121.009i	0.0827780	−	0.143376i
$845$		0			0
$846$		−	258.334i		−	0.305359i
$847$	1282.37	+	1315.33i	1.51401	+	1.55293i
$848$			370.495i			0.436905i
$849$	−306.352	−	530.618i	−0.360839	−	0.624991i
$850$		0			0
$851$	983.825	−	1704.03i	1.15608	−	2.00239i
$852$	−67.4291	−	116.791i	−0.0791421	−	0.137078i
$853$	1336.84			1.56722			0.783608	−	0.621255i	$-0.213377\pi$
$853$	1336.84			1.56722			0.783608	+	0.621255i	$0.213377\pi$
$854$	225.549	−	800.970i	0.264109	−	0.937904i
$855$		0			0
$856$	−216.795	−	375.501i	−0.253266	−	0.438669i
$857$	603.883	−	1045.96i	0.704647	−	1.22049i	−0.262171	−	0.965021i	$-0.584439\pi$
$857$	603.883	−	1045.96i	0.704647	−	1.22049i	0.966819	−	0.255464i	$-0.0822281\pi$
$858$	89.8313	+	51.8641i	0.104698	+	0.0604477i
$859$	1377.37	−	795.223i	1.60345	−	0.925755i	0.612665	−	0.790343i	$-0.290098\pi$
$859$	1377.37	−	795.223i	1.60345	−	0.925755i	0.990789	−	0.135412i	$-0.0432358\pi$
$860$		0			0
$861$	−774.794	−	218.178i	−0.899877	−	0.253401i
$862$		−	142.916i		−	0.165796i
$863$	50.2209	−	28.9950i	0.0581934	−	0.0335980i	−0.470621	−	0.882335i	$-0.655970\pi$
$863$	50.2209	−	28.9950i	0.0581934	−	0.0335980i	0.528814	+	0.848737i	$0.322637\pi$
$864$	−25.4558	−	14.6969i	−0.0294628	−	0.0170103i
$865$		0			0
$866$	−600.349	+	346.612i	−0.693243	+	0.400244i
$867$	166.657			0.192222
$868$	421.056	−	410.505i	0.485088	−	0.472932i
$869$	−422.395			−0.486070
$870$		0			0
$871$	−6.09026	−	3.51621i	−0.00699226	−	0.00403698i
$872$	−141.524	−	81.7091i	−0.162299	−	0.0937031i
$873$	37.8740	+	65.5996i	0.0433837	+	0.0751428i
$874$		−	1054.52i		−	1.20655i
$875$		0			0
$876$	−122.114			−0.139400
$877$	442.389	−	255.414i	0.504435	−	0.291236i	−0.226108	−	0.974102i	$-0.572600\pi$
$877$	442.389	−	255.414i	0.504435	−	0.291236i	0.730543	+	0.682867i	$0.239267\pi$
$878$	−326.397	+	565.336i	−0.371750	+	0.643891i
$879$	103.055	−	178.496i	0.117241	−	0.203067i
$880$		0			0
$881$		−	631.045i		−	0.716282i	−0.933667	−	0.358141i	$-0.883411\pi$
$881$		−	631.045i		−	0.716282i	0.933667	−	0.358141i	$-0.116589\pi$
$882$	−207.822	−	5.27473i	−0.235626	−	0.00598042i
$883$		−	918.874i		−	1.04063i	−0.853975	−	0.520314i	$-0.825815\pi$
$883$		−	918.874i		−	1.04063i	0.853975	−	0.520314i	$-0.174185\pi$
$884$	42.4456	+	73.5180i	0.0480154	+	0.0831652i
$885$		0			0
$886$	141.454	−	245.006i	0.159655	−	0.276530i
$887$	−48.5981	−	84.1745i	−0.0547893	−	0.0948979i	0.837330	−	0.546698i	$-0.184115\pi$
$887$	−48.5981	−	84.1745i	−0.0547893	−	0.0948979i	−0.892119	+	0.451800i	$0.850782\pi$
$888$	296.173			0.333528
$889$	304.107	+	1195.41i	0.342078	+	1.34467i
$890$		0			0
$891$	−88.1160	−	152.621i	−0.0988956	−	0.171292i
$892$	−389.679	+	674.944i	−0.436860	+	0.756663i
$893$	1208.12	+	697.506i	1.35287	+	0.781082i
$894$	53.3781	−	30.8179i	0.0597071	−	0.0344719i
$895$		0			0
$896$	56.7060	−	55.2850i	0.0632879	−	0.0617020i
$897$		−	121.912i		−	0.135911i
$898$	92.8375	−	53.5998i	0.103383	−	0.0596880i
$899$	1007.33	+	581.585i	1.12051	+	0.646924i
$900$		0			0
$901$	−1574.37	+	908.964i	−1.74736	+	1.00884i
$902$	1838.46			2.03821
$903$	−863.093	−	243.043i	−0.955806	−	0.269150i
$904$	−422.916			−0.467828
$905$		0			0
$906$	−47.2340	−	27.2706i	−0.0521347	−	0.0301000i
$907$	−509.032	−	293.890i	−0.561226	−	0.324024i	0.192412	−	0.981314i	$-0.438369\pi$
$907$	−509.032	−	293.890i	−0.561226	−	0.324024i	−0.753637	+	0.657291i	$0.771702\pi$
$908$	−7.47289	−	12.9434i	−0.00823006	−	0.0142549i
$909$		−	182.374i		−	0.200631i
$910$		0			0
$911$	−406.902			−0.446654			−0.223327	−	0.974744i	$-0.571692\pi$
$911$	−406.902			−0.446654			−0.223327	+	0.974744i	$0.571692\pi$
$912$	137.462	−	79.3639i	0.150726	−	0.0870218i
$913$	−395.200	+	684.506i	−0.432858	+	0.749733i
$914$	290.724	−	503.548i	0.318078	−	0.550928i
$915$		0			0
$916$		−	200.529i		−	0.218918i
$917$	−364.905	+	355.761i	−0.397934	+	0.387962i
$918$		−	144.228i		−	0.157112i
$919$	−480.514	−	832.275i	−0.522866	−	0.905631i	−0.999646	−	0.0266079i	$-0.991529\pi$
$919$	−480.514	−	832.275i	−0.522866	−	0.905631i	0.476780	−	0.879023i	$-0.341804\pi$
$920$		0			0
$921$	417.164	−	722.549i	0.452947	−	0.784527i
$922$	196.577	+	340.481i	0.213207	+	0.369286i
$923$	84.1910			0.0912145
$924$	460.165	−	117.064i	0.498014	−	0.126693i
$925$		0			0
$926$	−348.302	−	603.276i	−0.376136	−	0.651486i
$927$	64.1234	−	111.065i	0.0691730	−	0.119811i
$928$	135.663	+	78.3253i	0.146189	+	0.0844023i
$929$	−1072.91	+	619.447i	−1.15491	+	0.666789i	−0.950079	−	0.312009i	$-0.898998\pi$
$929$	−1072.91	+	619.447i	−1.15491	+	0.666789i	−0.204832	+	0.978797i	$0.565665\pi$
$930$		0			0
$931$	585.791	−	957.653i	0.629206	−	1.02863i
$932$		−	679.943i		−	0.729552i
$933$	−863.713	+	498.665i	−0.925738	+	0.534475i
$934$	395.593	+	228.395i	0.423547	+	0.244535i
$935$		0			0
$936$	15.8919	−	9.17519i	0.0169785	−	0.00980256i
$937$	219.917			0.234703			0.117351	−	0.993090i	$-0.462560\pi$
$937$	219.917			0.234703			0.117351	+	0.993090i	$0.462560\pi$
$938$	−31.1977	+	7.93656i	−0.0332598	+	0.00846115i
$939$	738.337			0.786301
$940$		0			0
$941$	1070.33	+	617.954i	1.13744	+	0.656700i	0.945795	−	0.324765i	$-0.105285\pi$
$941$	1070.33	+	617.954i	1.13744	+	0.656700i	0.191642	+	0.981465i	$0.438619\pi$
$942$	594.193	+	343.057i	0.630778	+	0.364180i
$943$	−1080.38	−	1871.27i	−1.14568	−	1.98438i
$944$		−	115.209i		−	0.122043i
$945$		0			0
$946$	2047.98			2.16489
$947$	499.231	−	288.231i	0.527172	−	0.304363i	−0.212692	−	0.977119i	$-0.568223\pi$
$947$	499.231	−	288.231i	0.527172	−	0.304363i	0.739864	+	0.672757i	$0.234890\pi$
$948$	−37.3626	+	64.7139i	−0.0394120	+	0.0682636i
$949$	38.1175	−	66.0214i	0.0401660	−	0.0695695i
$950$		0			0
$951$			43.6820i			0.0459327i
$952$	374.048	+	105.330i	0.392907	+	0.110641i
$953$		−	976.945i		−	1.02513i	−0.858650	−	0.512563i	$-0.828696\pi$
$953$		−	976.945i		−	1.02513i	0.858650	−	0.512563i	$-0.171304\pi$
$954$	196.485	+	340.321i	0.205959	+	0.356731i
$955$		0			0
$956$	−37.7094	+	65.3145i	−0.0394449	+	0.0683207i
$957$	469.602	+	813.375i	0.490702	+	0.849921i
$958$	437.390			0.456566
$959$	1007.34	+	283.661i	1.05040	+	0.295788i
$960$		0			0
$961$	401.649	+	695.676i	0.417949	+	0.723909i
$962$	−92.4493	+	160.127i	−0.0961011	+	0.166452i
$963$	−398.279	−	229.946i	−0.413581	−	0.238781i
$964$	−517.030	+	298.508i	−0.536339	+	0.309655i
$965$		0			0
$966$	−389.571	−	399.584i	−0.403282	−	0.413648i
$967$			805.489i			0.832978i	0.909141	+	0.416489i	$0.136740\pi$
$967$			805.489i			0.832978i	−0.909141	+	0.416489i	$0.863260\pi$
$968$	−642.816	+	371.130i	−0.664066	+	0.383399i
$969$	674.493	+	389.419i	0.696072	+	0.401877i
$970$		0			0
$971$	1332.28	−	769.192i	1.37207	−	0.792165i	0.380881	−	0.924624i	$-0.375621\pi$
$971$	1332.28	−	769.192i	1.37207	−	0.792165i	0.991188	+	0.132459i	$0.0422873\pi$
$972$	−31.1769			−0.0320750
$973$	−99.1910	−	389.908i	−0.101943	−	0.400728i
$974$	−800.032			−0.821388
$975$		0			0
$976$	291.182	+	168.114i	0.298342	+	0.172248i
$977$	−1013.26	−	585.004i	−1.03711	−	0.598775i	−0.118096	−	0.993002i	$-0.537679\pi$
$977$	−1013.26	−	585.004i	−1.03711	−	0.598775i	−0.919013	+	0.394227i	$0.871012\pi$
$978$	−162.450	−	281.372i	−0.166104	−	0.287701i
$979$		−	952.183i		−	0.972608i
$980$		0			0
$981$	−173.331			−0.176688
$982$	−464.589	+	268.230i	−0.473105	+	0.273147i
$983$	221.534	−	383.708i	0.225365	−	0.390344i	−0.731064	−	0.682309i	$-0.760976\pi$
$983$	221.534	−	383.708i	0.225365	−	0.390344i	0.956429	+	0.291965i	$0.0943091\pi$
$984$	162.620	−	281.666i	0.165264	−	0.286246i
$985$		0			0
$986$			768.646i			0.779560i
$987$	715.463	−	182.011i	0.724886	−	0.184408i
$988$			99.0926i			0.100296i
$989$	−1203.50	−	2084.53i	−1.21689	−	2.10771i
$990$		0			0
$991$	−72.4829	+	125.544i	−0.0731411	+	0.126684i	−0.900276	−	0.435319i	$-0.856636\pi$
$991$	−72.4829	+	125.544i	−0.0731411	+	0.126684i	0.827135	+	0.562003i	$0.189969\pi$
$992$	118.804	+	205.775i	0.119762	+	0.207434i
$993$	−3.30969			−0.00333302
$994$	275.947	−	269.032i	0.277613	−	0.270656i
$995$		0			0
$996$	69.9142	+	121.095i	0.0701949	+	0.121581i
$997$	451.437	−	781.912i	0.452796	−	0.784265i	−0.545763	−	0.837940i	$-0.683760\pi$
$997$	451.437	−	781.912i	0.452796	−	0.784265i	0.998558	+	0.0536748i	$0.0170934\pi$
$998$	−664.625	−	383.721i	−0.665957	−	0.384490i
$999$	272.052	−	157.069i	0.272324	−	0.157227i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1050.3.q.d.199.12		24
5.2	odd	4		1050.3.p.f.451.5	yes	12
5.3	odd	4		1050.3.p.e.451.2	✓	12
5.4	even	2	inner	1050.3.q.d.199.5		24
7.5	odd	6	inner	1050.3.q.d.649.5		24
35.12	even	12		1050.3.p.f.901.5	yes	12
35.19	odd	6	inner	1050.3.q.d.649.12		24
35.33	even	12		1050.3.p.e.901.2	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1050.3.p.e.451.2	✓	12	5.3	odd	4
1050.3.p.e.901.2	yes	12	35.33	even	12
1050.3.p.f.451.5	yes	12	5.2	odd	4
1050.3.p.f.901.5	yes	12	35.12	even	12
1050.3.q.d.199.5		24	5.4	even	2	inner
1050.3.q.d.199.12		24	1.1	even	1	trivial
1050.3.q.d.649.5		24	7.5	odd	6	inner
1050.3.q.d.649.12		24	35.19	odd	6	inner

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:	\( N \)	\(=\)	\( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	1050.q (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.22474 - 0.707107i) q^{2} +(-0.866025 + 1.50000i) q^{3} +(1.00000 - 1.73205i) q^{4} +2.44949i q^{6} +(-6.78392 + 1.72580i) q^{7} -2.82843i q^{8} +(-1.50000 - 2.59808i) q^{9} +O(q^{10})\)	\(q+(1.22474 - 0.707107i) q^{2} +(-0.866025 + 1.50000i) q^{3} +(1.00000 - 1.73205i) q^{4} +2.44949i q^{6} +(-6.78392 + 1.72580i) q^{7} -2.82843i q^{8} +(-1.50000 - 2.59808i) q^{9} +(-9.79066 + 16.9579i) q^{11} +(1.73205 + 3.00000i) q^{12} -2.16261 q^{13} +(-7.08825 + 6.91062i) q^{14} +(-2.00000 - 3.46410i) q^{16} +(9.81350 - 16.9975i) q^{17} +(-3.67423 - 2.12132i) q^{18} +(19.8410 - 11.4552i) q^{19} +(3.28635 - 11.6705i) q^{21} +27.6922i q^{22} +(28.1864 - 16.2734i) q^{23} +(4.24264 + 2.44949i) q^{24} +(-2.64865 + 1.52920i) q^{26} +5.19615 q^{27} +(-3.79475 + 13.4759i) q^{28} -27.6922 q^{29} +(-36.3761 - 21.0018i) q^{31} +(-4.89898 - 2.82843i) q^{32} +(-16.9579 - 29.3720i) q^{33} -27.7568i q^{34} -6.00000 q^{36} +(52.3564 - 30.2280i) q^{37} +(16.2001 - 28.0594i) q^{38} +(1.87288 - 3.24392i) q^{39} -66.3893i q^{41} +(-4.22733 - 16.6171i) q^{42} -73.9553i q^{43} +(19.5813 + 33.9159i) q^{44} +(23.0141 - 39.8615i) q^{46} +(30.4450 + 52.7322i) q^{47} +6.92820 q^{48} +(43.0432 - 23.4154i) q^{49} +(16.9975 + 29.4405i) q^{51} +(-2.16261 + 3.74576i) q^{52} +(-80.2145 - 46.3119i) q^{53} +(6.36396 - 3.67423i) q^{54} +(4.88130 + 19.1878i) q^{56} +39.6819i q^{57} +(-33.9159 + 19.5813i) q^{58} +(24.9434 + 14.4011i) q^{59} +(-72.7954 + 42.0285i) q^{61} -59.4020 q^{62} +(14.6596 + 15.0364i) q^{63} -8.00000 q^{64} +(-41.5383 - 23.9821i) q^{66} +(2.81616 + 1.62591i) q^{67} +(-19.6270 - 33.9950i) q^{68} +56.3727i q^{69} -38.9302 q^{71} +(-7.34847 + 4.24264i) q^{72} +(-17.6257 + 30.5285i) q^{73} +(42.7488 - 74.0432i) q^{74} -45.8208i q^{76} +(37.1531 - 131.938i) q^{77} -5.29730i q^{78} +(10.7857 + 18.6813i) q^{79} +(-4.50000 + 7.79423i) q^{81} +(-46.9443 - 81.3099i) q^{82} +40.3650 q^{83} +(-16.9275 - 17.3626i) q^{84} +(-52.2943 - 90.5764i) q^{86} +(23.9821 - 41.5383i) q^{87} +(47.9643 + 27.6922i) q^{88} +(-42.1123 + 24.3136i) q^{89} +(14.6710 - 3.73224i) q^{91} -65.0936i q^{92} +(63.0053 - 36.3761i) q^{93} +(74.5746 + 43.0557i) q^{94} +(8.48528 - 4.89898i) q^{96} -25.2493 q^{97} +(36.1598 - 59.1141i) q^{98} +58.7440 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 24 q^{4} - 36 q^{9}+O(q^{10}) \) 24 * q + 24 * q^4 - 36 * q^9	\( 24 q + 24 q^{4} - 36 q^{9} - 8 q^{11} - 16 q^{14} - 48 q^{16} - 24 q^{19} + 36 q^{21} - 48 q^{26} + 48 q^{29} - 396 q^{31} - 144 q^{36} + 72 q^{39} + 16 q^{44} + 64 q^{46} - 56 q^{49} - 48 q^{51} + 80 q^{56} + 96 q^{59} + 372 q^{61} - 192 q^{64} + 72 q^{66} - 272 q^{71} + 128 q^{74} + 140 q^{79} - 108 q^{81} + 24 q^{84} - 416 q^{86} - 336 q^{89} + 584 q^{91} + 408 q^{94} + 48 q^{99}+O(q^{100}) \) 24 * q + 24 * q^4 - 36 * q^9 - 8 * q^11 - 16 * q^14 - 48 * q^16 - 24 * q^19 + 36 * q^21 - 48 * q^26 + 48 * q^29 - 396 * q^31 - 144 * q^36 + 72 * q^39 + 16 * q^44 + 64 * q^46 - 56 * q^49 - 48 * q^51 + 80 * q^56 + 96 * q^59 + 372 * q^61 - 192 * q^64 + 72 * q^66 - 272 * q^71 + 128 * q^74 + 140 * q^79 - 108 * q^81 + 24 * q^84 - 416 * q^86 - 336 * q^89 + 584 * q^91 + 408 * q^94 + 48 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more