LMFDB - Embedded newform 124.5.b.a.63.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [124,5,Mod(63,124)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(124, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 5, names="a")

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

chi := DirichletCharacter("124.63");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 124 = 2^{2} \cdot 31 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	124.b (of order $2$, degree $1$, 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:	$12.8178754224$
Analytic rank:	$0$
Dimension:	$60$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			63.9
Character	$\chi$	$=$	124.63
Dual form			124.5.b.a.63.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-3.40182 - 2.10420i) q^{2} -9.06141i q^{3} +(7.14471 + 14.3162i) q^{4} +5.08300 q^{5} +(-19.0670 + 30.8253i) q^{6} +38.2255i q^{7} +(5.81911 - 63.7349i) q^{8} -1.10919 q^{9} +O(q^{10})$	\(q+(-3.40182 - 2.10420i) q^{2} -9.06141i q^{3} +(7.14471 + 14.3162i) q^{4} +5.08300 q^{5} +(-19.0670 + 30.8253i) q^{6} +38.2255i q^{7} +(5.81911 - 63.7349i) q^{8} -1.10919 q^{9} +(-17.2914 - 10.6956i) q^{10} -235.972i q^{11} +(129.725 - 64.7411i) q^{12} +95.0688 q^{13} +(80.4341 - 130.036i) q^{14} -46.0592i q^{15} +(-153.906 + 204.570i) q^{16} +18.7043 q^{17} +(3.77325 + 2.33395i) q^{18} -121.361i q^{19} +(36.3166 + 72.7692i) q^{20} +346.377 q^{21} +(-496.532 + 802.734i) q^{22} -274.626i q^{23} +(-577.528 - 52.7294i) q^{24} -599.163 q^{25} +(-323.407 - 200.044i) q^{26} -723.924i q^{27} +(-547.244 + 273.110i) q^{28} -76.7294 q^{29} +(-96.9176 + 156.685i) q^{30} +172.601i q^{31} +(954.017 - 372.060i) q^{32} -2138.24 q^{33} +(-63.6285 - 39.3575i) q^{34} +194.300i q^{35} +(-7.92482 - 15.8793i) q^{36} -1155.74 q^{37} +(-255.366 + 412.846i) q^{38} -861.458i q^{39} +(29.5786 - 323.965i) q^{40} -3108.08 q^{41} +(-1178.31 - 728.846i) q^{42} -466.488i q^{43} +(3378.22 - 1685.95i) q^{44} -5.63801 q^{45} +(-577.867 + 934.227i) q^{46} -1959.04i q^{47} +(1853.69 + 1394.61i) q^{48} +939.809 q^{49} +(2038.24 + 1260.76i) q^{50} -169.487i q^{51} +(679.239 + 1361.02i) q^{52} +1158.91 q^{53} +(-1523.28 + 2462.65i) q^{54} -1199.45i q^{55} +(2436.30 + 222.439i) q^{56} -1099.70 q^{57} +(261.019 + 161.454i) q^{58} -2189.46i q^{59} +(659.392 - 329.079i) q^{60} +5339.17 q^{61} +(363.186 - 587.156i) q^{62} -42.3993i q^{63} +(-4028.28 - 741.761i) q^{64} +483.235 q^{65} +(7273.90 + 4499.28i) q^{66} -3535.96i q^{67} +(133.637 + 267.774i) q^{68} -2488.50 q^{69} +(408.847 - 660.974i) q^{70} +6085.80i q^{71} +(-6.45449 + 70.6940i) q^{72} -3930.57 q^{73} +(3931.60 + 2431.90i) q^{74} +5429.26i q^{75} +(1737.42 - 867.085i) q^{76} +9020.16 q^{77} +(-1812.68 + 2930.52i) q^{78} -5455.71i q^{79} +(-782.307 + 1039.83i) q^{80} -6649.61 q^{81} +(10573.1 + 6540.01i) q^{82} -1343.47i q^{83} +(2474.76 + 4958.80i) q^{84} +95.0739 q^{85} +(-981.583 + 1586.91i) q^{86} +695.277i q^{87} +(-15039.7 - 1373.15i) q^{88} +7689.97 q^{89} +(19.1795 + 11.8635i) q^{90} +3634.05i q^{91} +(3931.60 - 1962.12i) q^{92} +1564.01 q^{93} +(-4122.20 + 6664.29i) q^{94} -616.876i q^{95} +(-3371.39 - 8644.74i) q^{96} +9453.54 q^{97} +(-3197.06 - 1977.54i) q^{98} +261.738i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q + 6 q^{2} - 6 q^{4} + 24 q^{5} + 45 q^{8} - 1732 q^{9}+O(q^{10}) $ 60 * q + 6 * q^2 - 6 * q^4 + 24 * q^5 + 45 * q^8 - 1732 * q^9	$ 60 q + 6 q^{2} - 6 q^{4} + 24 q^{5} + 45 q^{8} - 1732 q^{9} + 53 q^{10} + 130 q^{12} + 120 q^{13} - 231 q^{14} - 590 q^{16} - 648 q^{17} + 230 q^{18} + 1113 q^{20} + 608 q^{21} + 1080 q^{22} - 1028 q^{24} + 8340 q^{25} - 1554 q^{26} - 165 q^{28} - 168 q^{29} - 2238 q^{30} - 1674 q^{32} - 1120 q^{33} + 1844 q^{34} + 1966 q^{36} - 2248 q^{37} - 5055 q^{38} - 1716 q^{40} + 6072 q^{41} + 5794 q^{42} - 120 q^{44} - 4040 q^{45} + 8850 q^{46} + 2276 q^{48} - 17604 q^{49} - 4539 q^{50} + 5896 q^{52} + 3480 q^{53} + 5148 q^{54} - 396 q^{56} - 10912 q^{57} - 7484 q^{58} + 22812 q^{60} + 2200 q^{61} - 19299 q^{64} - 9168 q^{65} - 468 q^{66} - 21930 q^{68} + 6496 q^{69} - 9615 q^{70} - 10079 q^{72} + 13752 q^{73} - 2106 q^{74} + 20099 q^{76} + 16608 q^{77} + 39460 q^{78} - 5787 q^{80} + 20732 q^{81} - 30525 q^{82} - 21760 q^{84} - 21200 q^{85} - 13398 q^{86} + 34690 q^{88} + 22296 q^{89} - 25419 q^{90} - 18852 q^{92} + 3196 q^{94} + 20790 q^{96} + 12120 q^{97} + 21921 q^{98}+O(q^{100}) $ 60 * q + 6 * q^2 - 6 * q^4 + 24 * q^5 + 45 * q^8 - 1732 * q^9 + 53 * q^10 + 130 * q^12 + 120 * q^13 - 231 * q^14 - 590 * q^16 - 648 * q^17 + 230 * q^18 + 1113 * q^20 + 608 * q^21 + 1080 * q^22 - 1028 * q^24 + 8340 * q^25 - 1554 * q^26 - 165 * q^28 - 168 * q^29 - 2238 * q^30 - 1674 * q^32 - 1120 * q^33 + 1844 * q^34 + 1966 * q^36 - 2248 * q^37 - 5055 * q^38 - 1716 * q^40 + 6072 * q^41 + 5794 * q^42 - 120 * q^44 - 4040 * q^45 + 8850 * q^46 + 2276 * q^48 - 17604 * q^49 - 4539 * q^50 + 5896 * q^52 + 3480 * q^53 + 5148 * q^54 - 396 * q^56 - 10912 * q^57 - 7484 * q^58 + 22812 * q^60 + 2200 * q^61 - 19299 * q^64 - 9168 * q^65 - 468 * q^66 - 21930 * q^68 + 6496 * q^69 - 9615 * q^70 - 10079 * q^72 + 13752 * q^73 - 2106 * q^74 + 20099 * q^76 + 16608 * q^77 + 39460 * q^78 - 5787 * q^80 + 20732 * q^81 - 30525 * q^82 - 21760 * q^84 - 21200 * q^85 - 13398 * q^86 + 34690 * q^88 + 22296 * q^89 - 25419 * q^90 - 18852 * q^92 + 3196 * q^94 + 20790 * q^96 + 12120 * q^97 + 21921 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/124\mathbb{Z}\right)^\times$.

$n$	$63$	$65$
$\chi(n)$	$-1$	$1$

Coefficient data

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

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

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

$2$	−3.40182	−	2.10420i	−0.850454	−	0.526049i
$2$	−3.40182	−	2.10420i	−0.850454	−	0.526049i
$3$		−	9.06141i		−	1.00682i	−0.864047	−	0.503412i	$-0.832078\pi$
$3$		−	9.06141i		−	1.00682i	0.864047	−	0.503412i	$-0.167922\pi$
$4$	7.14471	+	14.3162i	0.446544	+	0.894762i
$5$	5.08300			0.203320			0.101660	−	0.994819i	$-0.467585\pi$
$5$	5.08300			0.203320			0.101660	+	0.994819i	$0.467585\pi$
$6$	−19.0670	+	30.8253i	−0.529639	+	0.856257i
$7$			38.2255i			0.780113i	0.920791	+	0.390056i	$0.127544\pi$
$7$			38.2255i			0.780113i	−0.920791	+	0.390056i	$0.872456\pi$
$8$	5.81911	−	63.7349i	0.0909236	−	0.995858i
$9$	−1.10919			−0.0136937
$10$	−17.2914	−	10.6956i	−0.172914	−	0.106956i
$11$		−	235.972i		−	1.95018i	−0.221801	−	0.975092i	$-0.571194\pi$
$11$		−	235.972i		−	1.95018i	0.221801	−	0.975092i	$-0.428806\pi$
$12$	129.725	−	64.7411i	0.900867	−	0.449591i
$13$	95.0688			0.562537			0.281269	−	0.959629i	$-0.409245\pi$
$13$	95.0688			0.562537			0.281269	+	0.959629i	$0.409245\pi$
$14$	80.4341	−	130.036i	0.410378	−	0.663450i
$15$		−	46.0592i		−	0.204708i
$16$	−153.906	+	204.570i	−0.601197	+	0.799101i
$17$	18.7043			0.0647207			0.0323603	−	0.999476i	$-0.489698\pi$
$17$	18.7043			0.0647207			0.0323603	+	0.999476i	$0.489698\pi$
$18$	3.77325	+	2.33395i	0.0116458	+	0.00720355i
$19$		−	121.361i		−	0.336179i	−0.985772	−	0.168089i	$-0.946240\pi$
$19$		−	121.361i		−	0.336179i	0.985772	−	0.168089i	$-0.0537597\pi$
$20$	36.3166	+	72.7692i	0.0907914	+	0.181923i
$21$	346.377			0.785436
$22$	−496.532	+	802.734i	−1.02589	+	1.65854i
$23$		−	274.626i		−	0.519142i	−0.965724	−	0.259571i	$-0.916419\pi$
$23$		−	274.626i		−	0.519142i	0.965724	−	0.259571i	$-0.0835811\pi$
$24$	−577.528	−	52.7294i	−1.00265	−	0.0915440i
$25$	−599.163			−0.958661
$26$	−323.407	−	200.044i	−0.478412	−	0.295922i
$27$		−	723.924i		−	0.993036i
$28$	−547.244	+	273.110i	−0.698015	+	0.348355i
$29$	−76.7294			−0.0912359			−0.0456180	−	0.998959i	$-0.514526\pi$
$29$	−76.7294			−0.0912359			−0.0456180	+	0.998959i	$0.514526\pi$
$30$	−96.9176	+	156.685i	−0.107686	+	0.174094i
$31$			172.601i			0.179605i
$31$			172.601i			0.179605i
$32$	954.017	−	372.060i	0.931657	−	0.363339i
$33$	−2138.24			−1.96349
$34$	−63.6285	−	39.3575i	−0.0550420	−	0.0340463i
$35$			194.300i			0.158613i
$36$	−7.92482	−	15.8793i	−0.00611483	−	0.0122526i
$37$	−1155.74			−0.844219			−0.422110	−	0.906545i	$-0.638710\pi$
$37$	−1155.74			−0.844219			−0.422110	+	0.906545i	$0.638710\pi$
$38$	−255.366	+	412.846i	−0.176847	+	0.285905i
$39$		−	861.458i		−	0.566376i
$40$	29.5786	−	323.965i	0.0184866	−	0.202478i
$41$	−3108.08			−1.84895			−0.924473	−	0.381248i	$-0.875494\pi$
$41$	−3108.08			−1.84895			−0.924473	+	0.381248i	$0.875494\pi$
$42$	−1178.31	−	728.846i	−0.667977	−	0.413178i
$43$		−	466.488i		−	0.252292i	−0.992012	−	0.126146i	$-0.959739\pi$
$43$		−	466.488i		−	0.252292i	0.992012	−	0.126146i	$-0.0402608\pi$
$44$	3378.22	−	1685.95i	1.74495	−	0.870843i
$45$	−5.63801			−0.00278420
$46$	−577.867	+	934.227i	−0.273094	+	0.441506i
$47$		−	1959.04i		−	0.886844i	−0.896313	−	0.443422i	$-0.853764\pi$
$47$		−	1959.04i		−	0.886844i	0.896313	−	0.443422i	$-0.146236\pi$
$48$	1853.69	+	1394.61i	0.804554	+	0.605299i
$49$	939.809			0.391424
$50$	2038.24	+	1260.76i	0.815297	+	0.504303i
$51$		−	169.487i		−	0.0651623i
$52$	679.239	+	1361.02i	0.251198	+	0.503337i
$53$	1158.91			0.412569			0.206284	−	0.978492i	$-0.433863\pi$
$53$	1158.91			0.412569			0.206284	+	0.978492i	$0.433863\pi$
$54$	−1523.28	+	2462.65i	−0.522386	+	0.844532i
$55$		−	1199.45i		−	0.396512i
$56$	2436.30	+	222.439i	0.776881	+	0.0709307i
$57$	−1099.70			−0.338473
$58$	261.019	+	161.454i	0.0775920	+	0.0479946i
$59$		−	2189.46i		−	0.628974i	−0.949262	−	0.314487i	$-0.898168\pi$
$59$		−	2189.46i		−	0.628974i	0.949262	−	0.314487i	$-0.101832\pi$
$60$	659.392	−	329.079i	0.183164	−	0.0914109i
$61$	5339.17			1.43487			0.717437	−	0.696624i	$-0.245315\pi$
$61$	5339.17			1.43487			0.717437	+	0.696624i	$0.245315\pi$
$62$	363.186	−	587.156i	0.0944813	−	0.152746i
$63$		−	42.3993i		−	0.0106826i
$64$	−4028.28	−	741.761i	−0.983466	−	0.181094i
$65$	483.235			0.114375
$66$	7273.90	+	4499.28i	1.66986	+	1.03289i
$67$		−	3535.96i		−	0.787695i	−0.919176	−	0.393848i	$-0.871144\pi$
$67$		−	3535.96i		−	0.787695i	0.919176	−	0.393848i	$-0.128856\pi$
$68$	133.637	+	267.774i	0.0289006	+	0.0579096i
$69$	−2488.50			−0.522684
$70$	408.847	−	660.974i	0.0834381	−	0.134893i
$71$			6085.80i			1.20726i	0.797264	+	0.603630i	$0.206280\pi$
$71$			6085.80i			1.20726i	−0.797264	+	0.603630i	$0.793720\pi$
$72$	−6.45449	+	70.6940i	−0.00124508	+	0.0136370i
$73$	−3930.57			−0.737582			−0.368791	−	0.929512i	$-0.620228\pi$
$73$	−3930.57			−0.737582			−0.368791	+	0.929512i	$0.620228\pi$
$74$	3931.60	+	2431.90i	0.717970	+	0.444101i
$75$			5429.26i			0.965202i
$76$	1737.42	−	867.085i	0.300800	−	0.150119i
$77$	9020.16			1.52136
$78$	−1812.68	+	2930.52i	−0.297942	+	0.481677i
$79$		−	5455.71i		−	0.874173i	−0.899420	−	0.437086i	$-0.856010\pi$
$79$		−	5455.71i		−	0.874173i	0.899420	−	0.437086i	$-0.143990\pi$
$80$	−782.307	+	1039.83i	−0.122235	+	0.162473i
$81$	−6649.61			−1.01351
$82$	10573.1	+	6540.01i	1.57244	+	0.972637i
$83$		−	1343.47i		−	0.195016i	−0.995235	−	0.0975081i	$-0.968913\pi$
$83$		−	1343.47i		−	0.195016i	0.995235	−	0.0975081i	$-0.0310872\pi$
$84$	2474.76	+	4958.80i	0.350732	+	0.702778i
$85$	95.0739			0.0131590
$86$	−981.583	+	1586.91i	−0.132718	+	0.214563i
$87$			695.277i			0.0918585i
$88$	−15039.7	−	1373.15i	−1.94211	−	0.177318i
$89$	7689.97			0.970833			0.485417	−	0.874283i	$-0.338668\pi$
$89$	7689.97			0.970833			0.485417	+	0.874283i	$0.338668\pi$
$90$	19.1795	+	11.8635i	0.00236783	+	0.00146463i
$91$			3634.05i			0.438843i
$92$	3931.60	−	1962.12i	0.464508	−	0.231820i
$93$	1564.01			0.180831
$94$	−4122.20	+	6664.29i	−0.466524	+	0.754220i
$95$		−	616.876i		−	0.0683519i
$96$	−3371.39	−	8644.74i	−0.365819	−	0.938014i
$97$	9453.54			1.00473			0.502367	−	0.864655i	$-0.332463\pi$
$97$	9453.54			1.00473			0.502367	+	0.864655i	$0.332463\pi$
$98$	−3197.06	−	1977.54i	−0.332888	−	0.205908i
$99$			261.738i			0.0267052i
$100$	−4280.84	−	8577.73i	−0.428084	−	0.857773i
$101$	1571.06			0.154010			0.0770052	−	0.997031i	$-0.475464\pi$
$101$	1571.06			0.154010			0.0770052	+	0.997031i	$0.475464\pi$
$102$	−356.634	+	576.564i	−0.0342786	+	0.0554175i
$103$		−	15555.0i		−	1.46620i	−0.680119	−	0.733102i	$-0.738072\pi$
$103$		−	15555.0i		−	1.46620i	0.680119	−	0.733102i	$-0.261928\pi$
$104$	553.216	−	6059.20i	0.0511479	−	0.560207i
$105$	1760.64			0.159695
$106$	−3942.38	−	2438.57i	−0.350871	−	0.217031i
$107$		−	19444.1i		−	1.69832i	−0.528132	−	0.849162i	$-0.677107\pi$
$107$		−	19444.1i		−	1.69832i	0.528132	−	0.849162i	$-0.322893\pi$
$108$	10363.8	−	5172.22i	0.888531	−	0.443435i
$109$	−12599.4			−1.06047			−0.530233	−	0.847852i	$-0.677895\pi$
$109$	−12599.4			−1.06047			−0.530233	+	0.847852i	$0.677895\pi$
$110$	−2523.87	+	4080.30i	−0.208585	+	0.337215i
$111$			10472.6i			0.849980i
$112$	−7819.79	−	5883.15i	−0.623389	−	0.469001i
$113$	13568.5			1.06261			0.531305	−	0.847180i	$-0.321702\pi$
$113$	13568.5			1.06261			0.531305	+	0.847180i	$0.321702\pi$
$114$	3740.97	+	2313.98i	0.287855	+	0.178053i
$115$		−	1395.92i		−	0.105552i
$116$	−548.209	−	1098.47i	−0.0407409	−	0.0816344i
$117$	−105.449			−0.00770321
$118$	−4607.05	+	7448.13i	−0.330871	+	0.534913i
$119$			714.981i			0.0504894i
$120$	−2935.58	−	268.024i	−0.203860	−	0.0186127i
$121$	−41041.9			−2.80322
$122$	−18162.9	−	11234.7i	−1.22029	−	0.754814i
$123$			28163.6i			1.86156i
$124$	−2470.98	+	1233.18i	−0.160704	+	0.0802017i
$125$	−6222.43			−0.398235
$126$	−89.2165	+	144.235i	−0.00561958	+	0.00908507i
$127$			19721.6i			1.22274i	0.791345	+	0.611370i	$0.209381\pi$
$127$			19721.6i			1.22274i	−0.791345	+	0.611370i	$0.790619\pi$
$128$	12142.6	+	10999.6i	0.741128	+	0.671364i
$129$	−4227.04			−0.254014
$130$	−1643.88	−	1016.82i	−0.0972708	−	0.0601670i
$131$			28398.1i			1.65481i	0.561608	+	0.827404i	$0.310183\pi$
$131$			28398.1i			1.65481i	−0.561608	+	0.827404i	$0.689817\pi$
$132$	−15277.1	−	30611.5i	−0.876785	−	1.75686i
$133$	4639.07			0.262257
$134$	−7440.37	+	12028.7i	−0.414367	+	0.669898i
$135$		−	3679.71i		−	0.201904i
$136$	108.842	−	1192.12i	0.00588464	−	0.0644526i
$137$	13331.8			0.710310			0.355155	−	0.934807i	$-0.384428\pi$
$137$	13331.8			0.710310			0.355155	+	0.934807i	$0.384428\pi$
$138$	8465.42	+	5236.29i	0.444519	+	0.274958i
$139$		−	6460.99i		−	0.334403i	−0.985923	−	0.167201i	$-0.946527\pi$
$139$		−	6460.99i		−	0.334403i	0.985923	−	0.167201i	$-0.0534730\pi$
$140$	−2781.64	+	1388.22i	−0.141920	+	0.0708275i
$141$	−17751.7			−0.892896
$142$	12805.7	−	20702.8i	0.635079	−	1.02672i
$143$		−	22433.6i		−	1.09705i
$144$	170.711	−	226.906i	0.00823259	−	0.0109426i
$145$	−390.016			−0.0185501
$146$	13371.1	+	8270.70i	0.627279	+	0.388004i
$147$		−	8516.00i		−	0.394095i
$148$	−8257.39	−	16545.7i	−0.376981	−	0.755375i
$149$	13005.6			0.585809			0.292905	−	0.956142i	$-0.405378\pi$
$149$	13005.6			0.585809			0.292905	+	0.956142i	$0.405378\pi$
$150$	11424.2	−	18469.4i	0.507744	−	0.820860i
$151$			39045.7i			1.71245i	0.516600	+	0.856227i	$0.327197\pi$
$151$			39045.7i			1.71245i	−0.516600	+	0.856227i	$0.672803\pi$
$152$	−7734.90	−	706.210i	−0.334786	−	0.0305666i
$153$	−20.7466			−0.000886264
$154$	−30684.9	−	18980.2i	−1.29385	−	0.800312i
$155$			877.330i			0.0365174i
$156$	12332.8	−	6154.86i	0.506771	−	0.252912i
$157$	36517.3			1.48149			0.740746	−	0.671785i	$-0.234472\pi$
$157$	36517.3			1.48149			0.740746	+	0.671785i	$0.234472\pi$
$158$	−11479.9	+	18559.3i	−0.459858	+	0.743444i
$159$		−	10501.3i		−	0.415384i
$160$	4849.27	−	1891.18i	0.189425	−	0.0738742i
$161$	10497.7			0.404989
$162$	22620.8	+	13992.1i	0.861940	+	0.533154i
$163$			17376.4i			0.654011i	0.945022	+	0.327006i	$0.106040\pi$
$163$			17376.4i			0.654011i	−0.945022	+	0.327006i	$0.893960\pi$
$164$	−22206.3	−	44495.8i	−0.825636	−	1.65437i
$165$	−10868.7			−0.399217
$166$	−2826.92	+	4570.22i	−0.102588	+	0.165852i
$167$			21668.4i			0.776950i	0.921459	+	0.388475i	$0.126998\pi$
$167$			21668.4i			0.776950i	−0.921459	+	0.388475i	$0.873002\pi$
$168$	2015.61	−	22076.3i	0.0714147	−	0.782182i
$169$	−19522.9			−0.683552
$170$	−323.424	−	200.054i	−0.0111911	−	0.00692229i
$171$			134.612i			0.00460352i
$172$	6678.33	−	3332.92i	0.225741	−	0.112660i
$173$	42093.7			1.40645			0.703226	−	0.710966i	$-0.251742\pi$
$173$	42093.7			1.40645			0.703226	+	0.710966i	$0.251742\pi$
$174$	1463.00	−	2365.20i	0.0483221	−	0.0781214i
$175$		−	22903.3i		−	0.747864i
$176$	48272.8	+	36317.6i	1.55839	+	1.17244i
$177$	−19839.6			−0.633265
$178$	−26159.9	−	16181.2i	−0.825649	−	0.510706i
$179$			25330.4i			0.790562i	0.918560	+	0.395281i	$0.129353\pi$
$179$			25330.4i			0.790562i	−0.918560	+	0.395281i	$0.870647\pi$
$180$	−40.2819	−	80.7147i	−0.00124327	−	0.00249120i
$181$	−7973.99			−0.243399			−0.121699	−	0.992567i	$-0.538834\pi$
$181$	−7973.99			−0.243399			−0.121699	+	0.992567i	$0.538834\pi$
$182$	7646.77	−	12362.4i	0.230853	−	0.373215i
$183$		−	48380.4i		−	1.44466i
$184$	−17503.3	−	1598.08i	−0.516991	−	0.0472022i
$185$	−5874.61			−0.171647
$186$	−5320.46	−	3290.98i	−0.153788	−	0.0951260i
$187$		−	4413.69i		−	0.126217i
$188$	28046.0	−	13996.8i	0.793514	−	0.396015i
$189$	27672.4			0.774680
$190$	−1298.03	+	2098.50i	−0.0359565	+	0.0581301i
$191$			15523.1i			0.425512i	0.977105	+	0.212756i	$0.0682439\pi$
$191$			15523.1i			0.425512i	−0.977105	+	0.212756i	$0.931756\pi$
$192$	−6721.40	+	36501.9i	−0.182330	+	0.990177i
$193$	61490.1			1.65079			0.825393	−	0.564558i	$-0.190954\pi$
$193$	61490.1			1.65079			0.825393	+	0.564558i	$0.190954\pi$
$194$	−32159.2	−	19892.1i	−0.854480	−	0.528539i
$195$		−	4378.79i		−	0.115156i
$196$	6714.66	+	13454.5i	0.174788	+	0.350231i
$197$	31804.6			0.819517			0.409758	−	0.912194i	$-0.365613\pi$
$197$	31804.6			0.819517			0.409758	+	0.912194i	$0.365613\pi$
$198$	550.748	−	890.383i	0.0140482	−	0.0227115i
$199$			7329.90i			0.185094i	0.995708	+	0.0925469i	$0.0295008\pi$
$199$			7329.90i			0.185094i	−0.995708	+	0.0925469i	$0.970499\pi$
$200$	−3486.60	+	38187.6i	−0.0871649	+	0.954690i
$201$	−32040.8			−0.793070
$202$	−5344.46	−	3305.82i	−0.130979	−	0.0810171i
$203$		−	2933.02i		−	0.0711743i
$204$	2426.41	−	1210.94i	0.0583047	−	0.0290978i
$205$	−15798.4			−0.375928
$206$	−32730.7	+	52915.1i	−0.771296	+	1.24694i
$207$			304.612i			0.00710896i
$208$	−14631.7	+	19448.2i	−0.338196	+	0.449524i
$209$	−28637.7			−0.655610
$210$	−5989.36	−	3704.73i	−0.135813	−	0.0840074i
$211$			19233.2i			0.432002i	0.976393	+	0.216001i	$0.0693015\pi$
$211$			19233.2i			0.432002i	−0.976393	+	0.216001i	$0.930698\pi$
$212$	8280.04	+	16591.1i	0.184230	+	0.369151i
$213$	55146.0			1.21550
$214$	−40914.3	+	66145.3i	−0.893403	+	1.44435i
$215$		−	2371.16i		−	0.0512961i
$216$	−46139.2	−	4212.59i	−0.988923	−	0.0902905i
$217$	−6597.75			−0.140112
$218$	42860.8	+	26511.6i	0.901877	+	0.557857i
$219$			35616.5i			0.742615i
$220$	17171.5	−	8569.70i	0.354783	−	0.177060i
$221$	1778.19			0.0364078
$222$	22036.4	−	35625.9i	0.447131	−	0.722869i
$223$			30305.1i			0.609405i	0.952448	+	0.304702i	$0.0985570\pi$
$223$			30305.1i			0.609405i	−0.952448	+	0.304702i	$0.901443\pi$
$224$	14222.2	+	36467.8i	0.283446	+	0.726797i
$225$	664.584			0.0131276
$226$	−46157.5	−	28550.8i	−0.903702	−	0.558986i
$227$		−	37514.8i		−	0.728033i	−0.931392	−	0.364017i	$-0.881405\pi$
$227$		−	37514.8i		−	0.728033i	0.931392	−	0.364017i	$-0.118595\pi$
$228$	−7857.02	−	15743.5i	−0.151143	−	0.302852i
$229$	−11779.4			−0.224622			−0.112311	−	0.993673i	$-0.535825\pi$
$229$	−11779.4			−0.224622			−0.112311	+	0.993673i	$0.535825\pi$
$230$	−2937.30	+	4748.68i	−0.0555255	+	0.0897671i
$231$		−	81735.4i		−	1.53174i
$232$	−446.497	+	4890.34i	−0.00829550	+	0.0908580i
$233$	−34754.6			−0.640178			−0.320089	−	0.947387i	$-0.603713\pi$
$233$	−34754.6			−0.640178			−0.320089	+	0.947387i	$0.603713\pi$
$234$	358.719	+	221.886i	0.00655122	+	0.00405227i
$235$		−	9957.80i		−	0.180313i
$236$	31344.7	−	15643.0i	0.562781	−	0.280864i
$237$	−49436.4			−0.880138
$238$	1504.46	−	2432.23i	0.0265599	−	0.0429389i
$239$			1860.46i			0.0325705i	0.999867	+	0.0162853i	$0.00518399\pi$
$239$			1860.46i			0.0325705i	−0.999867	+	0.0162853i	$0.994816\pi$
$240$	9422.32	+	7088.80i	0.163582	+	0.123069i
$241$	57575.3			0.991294			0.495647	−	0.868524i	$-0.334931\pi$
$241$	57575.3			0.991294			0.495647	+	0.868524i	$0.334931\pi$
$242$	139617.	+	86360.3i	2.38401	+	1.47463i
$243$			1617.08i			0.0273854i
$244$	38146.8	+	76436.5i	0.640734	+	1.28387i
$245$	4777.05			0.0795844
$246$	59261.7	−	95807.3i	0.979273	−	1.58317i
$247$		−	11537.6i		−	0.189113i
$248$	11000.7	+	1004.38i	0.178861	+	0.0163304i
$249$	−12173.7			−0.196347
$250$	21167.5	+	13093.2i	0.338681	+	0.209491i
$251$			81840.9i			1.29904i	0.760344	+	0.649520i	$0.225030\pi$
$251$			81840.9i			1.29904i	−0.760344	+	0.649520i	$0.774970\pi$
$252$	606.996	−	302.930i	0.00955839	−	0.00477026i
$253$	−64804.1			−1.01242
$254$	41498.1	−	67089.2i	0.643222	−	1.03988i
$255$		−	861.504i		−	0.0132488i
$256$	−18161.7	−	62969.2i	−0.277125	−	0.960834i
$257$	−64719.6			−0.979872			−0.489936	−	0.871758i	$-0.662980\pi$
$257$	−64719.6			−0.979872			−0.489936	+	0.871758i	$0.662980\pi$
$258$	14379.6	+	8894.53i	0.216027	+	0.133624i
$259$		−	44178.6i		−	0.658586i
$260$	3452.57	+	6918.08i	0.0510736	+	0.102339i
$261$	85.1074			0.00124936
$262$	59755.3	−	96605.3i	0.870510	−	1.40734i
$263$		−	99749.6i		−	1.44211i	−0.692876	−	0.721057i	$-0.743657\pi$
$263$		−	99749.6i		−	1.44211i	0.692876	−	0.721057i	$-0.256343\pi$
$264$	−12442.7	+	136281.i	−0.178528	+	1.95536i
$265$	5890.72			0.0838835
$266$	−15781.3	−	9761.52i	−0.223038	−	0.137960i
$267$		−	69682.0i		−	0.977458i
$268$	50621.5	−	25263.4i	0.704799	−	0.351741i
$269$	12046.2			0.166473			0.0832366	−	0.996530i	$-0.473474\pi$
$269$	12046.2			0.166473			0.0832366	+	0.996530i	$0.473474\pi$
$270$	−7742.83	+	12517.7i	−0.106212	+	0.171710i
$271$		−	70285.5i		−	0.957033i	−0.878079	−	0.478516i	$-0.841175\pi$
$271$		−	70285.5i		−	0.957033i	0.878079	−	0.478516i	$-0.158825\pi$
$272$	−2878.71	+	3826.33i	−0.0389099	+	0.0517184i
$273$	32929.7			0.441837
$274$	−45352.4	−	28052.8i	−0.604086	−	0.373658i
$275$			141386.i			1.86956i
$276$	−17779.6	−	35625.8i	−0.233401	−	0.467678i
$277$	13656.6			0.177985			0.0889925	−	0.996032i	$-0.471635\pi$
$277$	13656.6			0.177985			0.0889925	+	0.996032i	$0.471635\pi$
$278$	−13595.2	+	21979.1i	−0.175912	+	0.284394i
$279$		−	191.447i		−	0.00245946i
$280$	12383.7	+	1130.66i	0.157956	+	0.0144216i
$281$	89969.4			1.13942			0.569708	−	0.821848i	$-0.307056\pi$
$281$	89969.4			1.13942			0.569708	+	0.821848i	$0.307056\pi$
$282$	60387.9	+	37353.0i	0.759367	+	0.469707i
$283$			38074.3i			0.475399i	0.971339	+	0.237700i	$0.0763934\pi$
$283$			38074.3i			0.475399i	−0.971339	+	0.237700i	$0.923607\pi$
$284$	−87125.5	+	43481.3i	−1.08021	+	0.539095i
$285$	−5589.77			−0.0688183
$286$	−47204.7	+	76315.0i	−0.577103	+	0.932992i
$287$		−	118808.i		−	1.44239i
$288$	−1058.18	+	412.684i	−0.0127578	+	0.00497545i
$289$	−83171.2			−0.995811
$290$	1326.76	+	820.671i	0.0157760	+	0.00975827i
$291$		−	85662.4i		−	1.01159i
$292$	−28082.8	−	56270.8i	−0.329363	−	0.659960i
$293$	−17756.6			−0.206836			−0.103418	−	0.994638i	$-0.532978\pi$
$293$	−17756.6			−0.206836			−0.103418	+	0.994638i	$0.532978\pi$
$294$	−17919.3	+	28969.9i	−0.207313	+	0.335160i
$295$		−	11129.0i		−	0.127883i
$296$	−6725.36	+	73660.7i	−0.0767594	+	0.840722i
$297$	−170826.			−1.93660
$298$	−44242.5	−	27366.2i	−0.498204	−	0.308165i
$299$		−	26108.4i		−	0.292037i
$300$	−77726.3	+	38790.5i	−0.863626	+	0.431005i
$301$	17831.8			0.196816
$302$	82159.8	−	132826.i	0.900835	−	1.45636i
$303$		−	14236.0i		−	0.155061i
$304$	24826.7	+	18678.2i	0.268641	+	0.202110i
$305$	27139.0			0.291739
$306$	70.5760	+	43.6549i	0.000753727	+	0.000466219i
$307$			96059.5i			1.01921i	0.860408	+	0.509605i	$0.170208\pi$
$307$			96059.5i			1.01921i	−0.860408	+	0.509605i	$0.829792\pi$
$308$	64446.4	+	129134.i	0.679356	+	1.36126i
$309$	−140950.			−1.47621
$310$	1846.08	−	2984.52i	0.0192099	−	0.0310563i
$311$		−	131309.i		−	1.35760i	−0.734322	−	0.678801i	$-0.762500\pi$
$311$		−	131309.i		−	1.35760i	0.734322	−	0.678801i	$-0.237500\pi$
$312$	−54904.9	−	5012.92i	−0.564030	−	0.0514969i
$313$	102222.			1.04342			0.521708	−	0.853124i	$-0.325295\pi$
$313$	102222.			1.04342			0.521708	+	0.853124i	$0.325295\pi$
$314$	−124225.	−	76839.6i	−1.25994	−	0.779338i
$315$		−	215.516i		−	0.00217199i
$316$	78105.0	−	38979.4i	0.782176	−	0.390357i
$317$	−172934.			−1.72092			−0.860461	−	0.509517i	$-0.829824\pi$
$317$	−172934.			−1.72092			−0.860461	+	0.509517i	$0.829824\pi$
$318$	−22096.8	+	35723.6i	−0.218512	+	0.353265i
$319$			18106.0i			0.177927i
$320$	−20475.7	−	3770.37i	−0.199958	−	0.0368201i
$321$	−176191.			−1.70991
$322$	−35711.3	−	22089.3i	−0.344425	−	0.213044i
$323$		−	2269.96i		−	0.0217577i
$324$	−47509.5	−	95197.1i	−0.452575	−	0.906846i
$325$	−56961.7			−0.539283
$326$	36563.4	−	59111.4i	0.344042	−	0.556207i
$327$			114168.i			1.06770i
$328$	−18086.2	+	198093.i	−0.168113	+	1.84129i
$329$	74885.3			0.691838
$330$	36973.3	+	22869.9i	0.339516	+	0.210008i
$331$			21732.4i			0.198359i	0.995070	+	0.0991793i	$0.0316217\pi$
$331$			21732.4i			0.198359i	−0.995070	+	0.0991793i	$0.968378\pi$
$332$	19233.3	−	9598.67i	0.174493	−	0.0870833i
$333$	1281.93			0.0115605
$334$	45594.5	−	73711.7i	0.408714	−	0.660760i
$335$		−	17973.3i		−	0.160154i
$336$	−53309.7	+	70858.3i	−0.472201	+	0.627643i
$337$	105964.			0.933037			0.466518	−	0.884511i	$-0.345508\pi$
$337$	105964.			0.933037			0.466518	+	0.884511i	$0.345508\pi$
$338$	66413.4	+	41080.1i	0.581329	+	0.359582i
$339$		−	122950.i		−	1.06986i
$340$	679.275	+	1361.10i	0.00587608	+	0.0117742i
$341$	40729.0			0.350263
$342$	283.249	−	457.924i	0.00242168	−	0.00391508i
$343$			127704.i			1.08547i
$344$	−29731.6	−	2714.55i	−0.251247	−	0.0229393i
$345$	−12649.0			−0.106272
$346$	−143195.	−	88573.5i	−1.19612	−	0.739863i
$347$		−	21022.7i		−	0.174594i	−0.996182	−	0.0872970i	$-0.972177\pi$
$347$		−	21022.7i		−	0.174594i	0.996182	−	0.0872970i	$-0.0278229\pi$
$348$	−9953.71	+	4967.55i	−0.0821915	+	0.0410189i
$349$	−94655.6			−0.777133			−0.388567	−	0.921421i	$-0.627030\pi$
$349$	−94655.6			−0.777133			−0.388567	+	0.921421i	$0.627030\pi$
$350$	−48193.1	+	77912.9i	−0.393413	+	0.636024i
$351$		−	68822.6i		−	0.558620i
$352$	−87795.7	−	225121.i	−0.708579	−	1.81690i
$353$	144765.			1.16175			0.580876	−	0.813992i	$-0.302710\pi$
$353$	144765.			1.16175			0.580876	+	0.813992i	$0.302710\pi$
$354$	67490.6	+	41746.4i	0.538563	+	0.333129i
$355$			30934.1i			0.245460i
$356$	54942.6	+	110091.i	0.433520	+	0.868664i
$357$	6478.73			0.0508339
$358$	53300.2	−	86169.3i	0.415875	−	0.672337i
$359$		−	112860.i		−	0.875692i	−0.899050	−	0.437846i	$-0.855742\pi$
$359$		−	112860.i		−	0.875692i	0.899050	−	0.437846i	$-0.144258\pi$
$360$	−32.8082	+	359.338i	−0.000253150	+	0.00277267i
$361$	115593.			0.886984
$362$	27126.0	+	16778.8i	0.206999	+	0.128040i
$363$			371898.i			2.82234i
$364$	−52025.8	+	25964.3i	−0.392659	+	0.195963i
$365$	−19979.1			−0.149965
$366$	−101802.	+	164581.i	−0.759965	+	1.22862i
$367$		−	144950.i		−	1.07618i	−0.842887	−	0.538091i	$-0.819146\pi$
$367$		−	144950.i		−	1.07618i	0.842887	−	0.538091i	$-0.180854\pi$
$368$	56180.2	+	42266.7i	0.414847	+	0.312106i
$369$	3447.44			0.0253189
$370$	19984.3	+	12361.3i	0.145978	+	0.0902947i
$371$			44299.8i			0.321850i
$372$	11174.4	+	22390.6i	0.0807489	+	0.161801i
$373$	170556.			1.22588			0.612942	−	0.790128i	$-0.289986\pi$
$373$	170556.			1.22588			0.612942	+	0.790128i	$0.289986\pi$
$374$	−9287.28	+	15014.6i	−0.0663965	+	0.107342i
$375$			56384.0i			0.400953i
$376$	−124859.	−	11399.9i	−0.883171	−	0.0806351i
$377$	−7294.58			−0.0513236
$378$	−94136.3	−	58228.1i	−0.658830	−	0.407520i
$379$			31427.3i			0.218791i	0.993998	+	0.109395i	$0.0348914\pi$
$379$			31427.3i			0.218791i	−0.993998	+	0.109395i	$0.965109\pi$
$380$	8831.31	−	4407.40i	0.0611587	−	0.0305221i
$381$	178705.			1.23108
$382$	32663.7	−	52806.7i	0.223840	−	0.361878i
$383$		−	113173.i		−	0.771515i	−0.922600	−	0.385757i	$-0.873940\pi$
$383$		−	113173.i		−	0.771515i	0.922600	−	0.385757i	$-0.126060\pi$
$384$	99672.1	−	110029.i	0.675945	−	0.746185i
$385$	45849.5			0.309324
$386$	−209178.	−	129387.i	−1.40392	−	0.868395i
$387$			517.423i			0.00345481i
$388$	67542.7	+	135339.i	0.448658	+	0.898997i
$389$	221991.			1.46702			0.733511	−	0.679677i	$-0.237880\pi$
$389$	221991.			1.46702			0.733511	+	0.679677i	$0.237880\pi$
$390$	−9213.84	+	14895.8i	−0.0605775	+	0.0979346i
$391$		−	5136.68i		−	0.0335992i
$392$	5468.86	−	59898.7i	0.0355897	−	0.389803i
$393$	257327.			1.66610
$394$	−108193.	−	66923.2i	−0.696961	−	0.431106i
$395$		−	27731.4i		−	0.177737i
$396$	−3747.08	+	1870.04i	−0.0238948	+	0.0119250i
$397$	−246192.			−1.56204			−0.781021	−	0.624504i	$-0.785301\pi$
$397$	−246192.			−1.56204			−0.781021	+	0.624504i	$0.785301\pi$
$398$	15423.6	−	24935.0i	0.0973685	−	0.157414i
$399$		−	42036.5i		−	0.264047i
$400$	92215.0	−	122571.i	0.576344	−	0.766067i
$401$	−87458.9			−0.543895			−0.271948	−	0.962312i	$-0.587668\pi$
$401$	−87458.9			−0.543895			−0.271948	+	0.962312i	$0.587668\pi$
$402$	108997.	+	67420.2i	0.674470	+	0.417194i
$403$			16408.9i			0.101035i
$404$	11224.8	+	22491.6i	0.0687724	+	0.137803i
$405$	−33800.0			−0.206066
$406$	−6171.66	+	9977.60i	−0.0374412	+	0.0605305i
$407$			272722.i			1.64638i
$408$	−10802.2	−	986.265i	−0.0648924	−	0.00592479i
$409$	323731.			1.93525			0.967625	−	0.252392i	$-0.0812172\pi$
$409$	323731.			1.93525			0.967625	+	0.252392i	$0.0812172\pi$
$410$	53743.1	+	33242.9i	0.319709	+	0.197757i
$411$		−	120805.i		−	0.715157i
$412$	222688.	−	111136.i	1.31190	−	0.654725i
$413$	83693.1			0.490670
$414$	640.963	−	1036.23i	0.00373966	−	0.00604584i
$415$		−	6828.84i		−	0.0396507i
$416$	90697.2	−	35371.3i	0.524092	−	0.204392i
$417$	−58545.7			−0.336684
$418$	97420.2	+	60259.4i	0.557566	+	0.344883i
$419$			50438.9i			0.287301i	0.989628	+	0.143651i	$0.0458841\pi$
$419$			50438.9i			0.287301i	−0.989628	+	0.143651i	$0.954116\pi$
$420$	12579.2	+	25205.6i	0.0713108	+	0.142889i
$421$	182618.			1.03034			0.515168	−	0.857089i	$-0.327729\pi$
$421$	182618.			1.03034			0.515168	+	0.857089i	$0.327729\pi$
$422$	40470.4	−	65427.7i	0.227255	−	0.367398i
$423$			2172.94i			0.0121442i
$424$	6743.80	−	73862.7i	0.0375122	−	0.410860i
$425$	−11206.9			−0.0620452
$426$	−187596.	−	116038.i	−1.03373	−	0.639412i
$427$			204092.i			1.11936i
$428$	278366.	−	138923.i	1.51960	−	0.758377i
$429$	−203280.			−1.10454
$430$	−4989.39	+	8066.25i	−0.0269843	+	0.0436250i
$431$			319392.i			1.71937i	0.510822	+	0.859687i	$0.329341\pi$
$431$			319392.i			1.71937i	−0.510822	+	0.859687i	$0.670659\pi$
$432$	148093.	+	111416.i	0.793536	+	0.597010i
$433$	−48045.5			−0.256258			−0.128129	−	0.991758i	$-0.540897\pi$
$433$	−48045.5			−0.256258			−0.128129	+	0.991758i	$0.540897\pi$
$434$	22444.3	+	13883.0i	0.119159	+	0.0737060i
$435$			3534.10i			0.0186767i
$436$	−90018.9	−	180375.i	−0.473545	−	0.948864i
$437$	−33328.7			−0.174524
$438$	74944.2	−	121161.i	0.390652	−	0.631560i
$439$			310010.i			1.60860i	0.594226	+	0.804298i	$0.297459\pi$
$439$			310010.i			1.60860i	−0.594226	+	0.804298i	$0.702541\pi$
$440$	−76446.7	−	6979.72i	−0.394869	−	0.0360523i
$441$	−1042.43			−0.00536004
$442$	−6049.09	−	3741.67i	−0.0309632	−	0.0191523i
$443$		−	71440.8i		−	0.364031i	−0.983296	−	0.182016i	$-0.941738\pi$
$443$		−	71440.8i		−	0.364031i	0.983296	−	0.182016i	$-0.0582621\pi$
$444$	−149928.	+	74823.6i	−0.760529	+	0.379553i
$445$	39088.1			0.197390
$446$	63767.9	−	103092.i	0.320577	−	0.518271i
$447$		−	117849.i		−	0.589807i
$448$	28354.2	−	153983.i	0.141274	−	0.767214i
$449$	−300174.			−1.48895			−0.744474	−	0.667651i	$-0.767300\pi$
$449$	−300174.			−1.48895			−0.744474	+	0.667651i	$0.767300\pi$
$450$	−2260.79	−	1398.42i	−0.0111644	−	0.00690576i
$451$			733420.i			3.60578i
$452$	96942.8	+	194249.i	0.474503	+	0.950783i
$453$	353809.			1.72414
$454$	−78938.6	+	127619.i	−0.382981	+	0.619159i
$455$			18471.9i			0.0892255i
$456$	−6399.26	+	70089.1i	−0.0307752	+	0.337071i
$457$	67598.3			0.323671			0.161835	−	0.986818i	$-0.448259\pi$
$457$	67598.3			0.323671			0.161835	+	0.986818i	$0.448259\pi$
$458$	40071.3	+	24786.2i	0.191030	+	0.118162i
$459$		−	13540.5i		−	0.0642700i
$460$	19984.3	−	9973.47i	0.0944438	−	0.0471336i
$461$	−351014.			−1.65167			−0.825834	−	0.563913i	$-0.809295\pi$
$461$	−351014.			−1.65167			−0.825834	+	0.563913i	$0.809295\pi$
$462$	−171987.	+	278049.i	−0.805773	+	1.30268i
$463$		−	384210.i		−	1.79229i	−0.443766	−	0.896143i	$-0.646358\pi$
$463$		−	384210.i		−	1.79229i	0.443766	−	0.896143i	$-0.353642\pi$
$464$	11809.1	−	15696.5i	0.0548508	−	0.0729067i
$465$	7949.85			0.0367666
$466$	118229.	+	73130.6i	0.544442	+	0.336765i
$467$			115656.i			0.530315i	0.964205	+	0.265157i	$0.0854239\pi$
$467$			115656.i			0.530315i	−0.964205	+	0.265157i	$0.914576\pi$
$468$	−753.403	−	1509.63i	−0.00343982	−	0.00689253i
$469$	135164.			0.614491
$470$	−20953.2	+	33874.6i	−0.0948537	+	0.153348i
$471$		−	330898.i		−	1.49160i
$472$	−139545.	−	12740.7i	−0.626368	−	0.0571886i
$473$	−110078.			−0.492016
$474$	168174.	+	104024.i	0.748517	+	0.462996i
$475$			72714.7i			0.322281i
$476$	−10235.8	+	5108.33i	−0.0451760	+	0.0225458i
$477$	−1285.44			−0.00564958
$478$	3914.78	−	6328.95i	0.0171337	−	0.0276997i
$479$		−	163462.i		−	0.712436i	−0.934403	−	0.356218i	$-0.884066\pi$
$479$		−	163462.i		−	0.712436i	0.934403	−	0.356218i	$-0.115934\pi$
$480$	−17136.8	−	43941.2i	−0.0743783	−	0.190717i
$481$	−109874.			−0.474905
$482$	−195861.	−	121150.i	−0.843050	−	0.521469i
$483$		−	95124.2i		−	0.407752i
$484$	−293232.	−	587563.i	−1.25176	−	2.50821i
$485$	48052.4			0.204283
$486$	3402.66	−	5501.02i	0.0144061	−	0.0232901i
$487$			43275.5i			0.182467i	0.995830	+	0.0912335i	$0.0290810\pi$
$487$			43275.5i			0.182467i	−0.995830	+	0.0912335i	$0.970919\pi$
$488$	31069.2	−	340291.i	0.130464	−	1.42893i
$489$	157455.			0.658474
$490$	−16250.7	−	10051.9i	−0.0676829	−	0.0418653i
$491$		−	59784.2i		−	0.247984i	−0.992283	−	0.123992i	$-0.960430\pi$
$491$		−	59784.2i		−	0.247984i	0.992283	−	0.123992i	$-0.0395697\pi$
$492$	−403195.	+	201220.i	−1.66565	+	0.831269i
$493$	−1435.17			−0.00590485
$494$	−24277.4	+	39248.8i	−0.0994828	+	0.160832i
$495$			1330.41i			0.00542970i
$496$	−35308.9	−	26564.3i	−0.143523	−	0.107978i
$497$	−232633.			−0.941799
$498$	41412.7	+	25615.9i	0.166984	+	0.103288i
$499$		−	6482.63i		−	0.0260346i	−0.999915	−	0.0130173i	$-0.995856\pi$
$499$		−	6482.63i		−	0.0260346i	0.999915	−	0.0130173i	$-0.00414365\pi$
$500$	−44457.4	−	89081.4i	−0.177830	−	0.356326i
$501$	196346.			0.782251
$502$	172209.	−	278408.i	0.683360	−	1.10477i
$503$		−	116729.i		−	0.461362i	−0.973029	−	0.230681i	$-0.925905\pi$
$503$		−	116729.i		−	0.461362i	0.973029	−	0.230681i	$-0.0740954\pi$
$504$	−2702.31	−	246.726i	−0.0106384	−	0.000971302i
$505$	7985.70			0.0313134
$506$	220452.	+	136361.i	0.861018	+	0.532584i
$507$			176905.i			0.688216i
$508$	−282338.	+	140905.i	−1.09406	+	0.546008i
$509$	−377140.			−1.45568			−0.727842	−	0.685744i	$-0.759477\pi$
$509$	−377140.			−1.45568			−0.727842	+	0.685744i	$0.759477\pi$
$510$	−1812.77	+	2930.68i	−0.00696953	+	0.0112675i
$511$		−	150248.i		−	0.575397i
$512$	−70717.0	+	252425.i	−0.269764	+	0.962926i
$513$	−87855.7			−0.333838
$514$	220164.	+	136183.i	0.833337	+	0.515461i
$515$		−	79065.9i		−	0.298109i
$516$	−30201.0	−	60515.1i	−0.113428	−	0.227282i
$517$	−462279.			−1.72951
$518$	−92960.5	+	150288.i	−0.346449	+	0.560097i
$519$		−	381428.i		−	1.41605i
$520$	2812.00	−	30798.9i	0.0103994	−	0.113901i
$521$	9345.20			0.0344281			0.0172141	−	0.999852i	$-0.494520\pi$
$521$	9345.20			0.0344281			0.0172141	+	0.999852i	$0.494520\pi$
$522$	−289.520	−	179.083i	−0.00106252	−	0.000657223i
$523$			257853.i			0.942690i	0.881949	+	0.471345i	$0.156231\pi$
$523$			257853.i			0.942690i	−0.881949	+	0.471345i	$0.843769\pi$
$524$	−406553.	+	202896.i	−1.48066	+	0.738944i
$525$	−207536.			−0.752967
$526$	−209893.	+	339330.i	−0.758623	+	1.22645i
$527$			3228.37i			0.0116242i
$528$	329089.	−	437420.i	1.18044	−	1.56903i
$529$	204422.			0.730492
$530$	−20039.1	−	12395.2i	−0.0713391	−	0.0441269i
$531$			2428.52i			0.00861296i
$532$	33144.8	+	66413.8i	0.117109	+	0.234658i
$533$	−295481.			−1.04010
$534$	−146625.	+	237045.i	−0.514191	+	0.831283i
$535$		−	98834.5i		−	0.345304i
$536$	−225364.	−	20576.2i	−0.784432	−	0.0716201i
$537$	229529.			0.795956
$538$	−40978.9	−	25347.5i	−0.141578	−	0.0875731i
$539$		−	221769.i		−	0.763349i
$540$	52679.4	−	26290.4i	0.180656	−	0.0901592i
$541$	138137.			0.471970			0.235985	−	0.971757i	$-0.424168\pi$
$541$	138137.			0.471970			0.235985	+	0.971757i	$0.424168\pi$
$542$	−147894.	+	239098.i	−0.503447	+	0.813913i
$543$			72255.6i			0.245060i
$544$	17844.2	−	6959.11i	0.0602975	−	0.0235156i
$545$	−64042.7			−0.215614
$546$	−112021.	−	69290.5i	−0.375762	−	0.232428i
$547$		−	158234.i		−	0.528843i	−0.964407	−	0.264421i	$-0.914819\pi$
$547$		−	158234.i		−	0.528843i	0.964407	−	0.264421i	$-0.0851809\pi$
$548$	95251.8	+	190861.i	0.317185	+	0.635558i
$549$	−5922.14			−0.0196487
$550$	297504.	−	480969.i	0.983483	−	1.58998i
$551$			9311.92i			0.0306716i
$552$	−14480.9	+	158604.i	−0.0475243	+	0.520519i
$553$	208547.			0.681953
$554$	−46457.3	−	28736.2i	−0.151368	−	0.0936289i
$555$			53232.3i			0.172818i
$556$	92496.8	−	46161.9i	0.299211	−	0.149326i
$557$	34714.7			0.111893			0.0559466	−	0.998434i	$-0.482182\pi$
$557$	34714.7			0.111893			0.0559466	+	0.998434i	$0.482182\pi$
$558$	−402.841	+	651.266i	−0.00129380	+	0.00209166i
$559$		−	44348.5i		−	0.141924i
$560$	−39748.0	−	29904.1i	−0.126748	−	0.0953574i
$561$	−39994.3			−0.127078
$562$	−306059.	−	189313.i	−0.969020	−	0.599389i
$563$			303850.i			0.958610i	0.877648	+	0.479305i	$0.159111\pi$
$563$			303850.i			0.958610i	−0.877648	+	0.479305i	$0.840889\pi$
$564$	−126830.	−	254136.i	−0.398717	−	0.798929i
$565$	68968.6			0.216050
$566$	80115.8	−	129522.i	0.250084	−	0.404305i
$567$		−	254185.i		−	0.790649i
$568$	387878.	+	35414.0i	1.20226	+	0.109769i
$569$	624380.			1.92852			0.964261	−	0.264953i	$-0.0853564\pi$
$569$	624380.			1.92852			0.964261	+	0.264953i	$0.0853564\pi$
$570$	19015.4	+	11762.0i	0.0585268	+	0.0362018i
$571$		−	327175.i		−	1.00348i	−0.865019	−	0.501738i	$-0.832694\pi$
$571$		−	327175.i		−	1.00348i	0.865019	−	0.501738i	$-0.167306\pi$
$572$	321164.	−	160281.i	0.981599	−	0.489882i
$573$	140661.			0.428415
$574$	−249995.	+	404163.i	−0.758766	+	1.22668i
$575$			164546.i			0.497681i
$576$	4468.11	+	822.752i	0.0134673	+	0.00247984i
$577$	−521336.			−1.56591			−0.782953	−	0.622080i	$-0.786288\pi$
$577$	−521336.			−1.56591			−0.782953	+	0.622080i	$0.786288\pi$
$578$	282933.	+	175009.i	0.846892	+	0.523846i
$579$		−	557187.i		−	1.66205i
$580$	−2786.55	−	5583.54i	−0.00828344	−	0.0165979i
$581$	51354.7			0.152135
$582$	−180251.	+	291408.i	−0.532146	+	0.860310i
$583$		−	273469.i		−	0.804585i
$584$	−22872.4	+	250515.i	−0.0670636	+	0.734527i
$585$	−535.999			−0.00156622
$586$	60404.8	+	37363.5i	0.175904	+	0.108806i
$587$		−	266538.i		−	0.773539i	−0.922176	−	0.386769i	$-0.873591\pi$
$587$		−	266538.i		−	0.773539i	0.922176	−	0.386769i	$-0.126409\pi$
$588$	121917.	−	60844.3i	0.352621	−	0.175981i
$589$	20946.9			0.0603795
$590$	−23417.7	+	37858.9i	−0.0672728	+	0.108759i
$591$		−	288195.i		−	0.825109i
$592$	177875.	−	236429.i	0.507542	−	0.674616i
$593$	294179.			0.836569			0.418285	−	0.908316i	$-0.362631\pi$
$593$	294179.			0.836569			0.418285	+	0.908316i	$0.362631\pi$
$594$	581118.	+	359451.i	1.64699	+	1.01875i
$595$			3634.25i			0.0102655i
$596$	92920.8	+	186190.i	0.261590	+	0.524160i
$597$	66419.2			0.186357
$598$	−54937.2	+	88815.8i	−0.153626	+	0.248364i
$599$		−	638612.i		−	1.77985i	−0.456106	−	0.889925i	$-0.650756\pi$
$599$		−	638612.i		−	1.77985i	0.456106	−	0.889925i	$-0.349244\pi$
$600$	346034.	+	31593.5i	0.961204	+	0.0877597i
$601$	−221143.			−0.612242			−0.306121	−	0.951993i	$-0.599031\pi$
$601$	−221143.			−0.612242			−0.306121	+	0.951993i	$0.599031\pi$
$602$	−60660.4	−	37521.5i	−0.167383	−	0.103535i
$603$			3922.05i			0.0107864i
$604$	−558985.	+	278970.i	−1.53224	+	0.764686i
$605$	−208616.			−0.569950
$606$	−29955.4	+	48428.3i	−0.0815699	+	0.131873i
$607$			489560.i			1.32870i	0.747420	+	0.664352i	$0.231292\pi$
$607$			489560.i			1.32870i	−0.747420	+	0.664352i	$0.768708\pi$
$608$	−45153.3	−	115780.i	−0.122147	−	0.313203i
$609$	−26577.3			−0.0716600
$610$	−92321.9	−	57105.8i	−0.248110	−	0.153469i
$611$		−	186243.i		−	0.498883i
$612$	−148.228	−	297.012i	−0.000395756	−	0.000792995i
$613$	−174637.			−0.464746			−0.232373	−	0.972627i	$-0.574649\pi$
$613$	−174637.			−0.464746			−0.232373	+	0.972627i	$0.574649\pi$
$614$	202128.	−	326777.i	0.536155	−	0.866791i
$615$			143156.i			0.378493i
$616$	52489.3	−	574899.i	0.138328	−	1.51506i
$617$	−263127.			−0.691186			−0.345593	−	0.938384i	$-0.612322\pi$
$617$	−263127.			−0.691186			−0.345593	+	0.938384i	$0.612322\pi$
$618$	479486.	+	296586.i	1.25545	+	0.776559i
$619$			556188.i			1.45158i	0.687918	+	0.725789i	$0.258525\pi$
$619$			556188.i			1.45158i	−0.687918	+	0.725789i	$0.741475\pi$
$620$	−12560.0	+	6268.26i	−0.0326743	+	0.0163066i
$621$	−198808.			−0.515527
$622$	−276299.	+	446688.i	−0.714166	+	1.15458i
$623$			293953.i			0.757359i
$624$	176228.	+	132584.i	0.452592	+	0.340503i
$625$	342848.			0.877692
$626$	−347742.	−	215096.i	−0.887377	−	0.548888i
$627$			259498.i			0.660084i
$628$	260905.	+	522788.i	0.661551	+	1.32558i
$629$	−21617.2			−0.0546384
$630$	−453.488	+	733.145i	−0.00114257	+	0.00184718i
$631$			451189.i			1.13318i	0.823999	+	0.566591i	$0.191738\pi$
$631$			451189.i			1.13318i	−0.823999	+	0.566591i	$0.808262\pi$
$632$	−347719.	−	31747.4i	−0.870552	−	0.0794829i
$633$	174280.			0.434950
$634$	588288.	+	363887.i	1.46356	+	0.905289i
$635$			100245.i			0.248608i
$636$	150339.	−	75028.8i	0.371670	−	0.185487i
$637$	89346.6			0.220191
$638$	38098.6	−	61593.3i	0.0935983	−	0.151319i
$639$		−	6750.30i		−	0.0165318i
$640$	61721.1	+	55911.1i	0.150686	+	0.136502i
$641$	−605473.			−1.47360			−0.736799	−	0.676112i	$-0.763663\pi$
$641$	−605473.			−1.47360			−0.736799	+	0.676112i	$0.763663\pi$
$642$	599370.	+	370741.i	1.45420	+	0.899499i
$643$			194487.i			0.470402i	0.971947	+	0.235201i	$0.0755748\pi$
$643$			194487.i			0.470402i	−0.971947	+	0.235201i	$0.924425\pi$
$644$	75003.1	+	150287.i	0.180845	+	0.362369i
$645$	−21486.1			−0.0516461
$646$	−4776.45	+	7721.99i	−0.0114456	+	0.0185039i
$647$		−	350201.i		−	0.836582i	−0.908313	−	0.418291i	$-0.862629\pi$
$647$		−	350201.i		−	0.836582i	0.908313	−	0.418291i	$-0.137371\pi$
$648$	−38694.8	+	423813.i	−0.0921516	+	1.00931i
$649$	−516651.			−1.22661
$650$	193773.	+	119859.i	0.458635	+	0.283689i
$651$			59784.9i			0.141068i
$652$	−248764.	+	124149.i	−0.585184	+	0.292045i
$653$	−89726.9			−0.210425			−0.105212	−	0.994450i	$-0.533552\pi$
$653$	−89726.9			−0.210425			−0.105212	+	0.994450i	$0.533552\pi$
$654$	240233.	−	388379.i	0.561664	−	0.908031i
$655$			144348.i			0.336456i
$656$	478353.	−	635819.i	1.11158	−	1.47749i
$657$	4359.74			0.0101002
$658$	−254746.	−	157573.i	−0.588377	−	0.363941i
$659$		−	101738.i		−	0.234269i	−0.993116	−	0.117134i	$-0.962629\pi$
$659$		−	101738.i		−	0.234269i	0.993116	−	0.117134i	$-0.0373708\pi$
$660$	−77653.6	−	155598.i	−0.178268	−	0.357204i
$661$	−10409.2			−0.0238241			−0.0119120	−	0.999929i	$-0.503792\pi$
$661$	−10409.2			−0.0238241			−0.0119120	+	0.999929i	$0.503792\pi$
$662$	45729.2	−	73929.5i	0.104346	−	0.168695i
$663$		−	16112.9i		−	0.0366562i
$664$	−85625.7	−	7817.78i	−0.194208	−	0.0177316i
$665$	23580.4			0.0533222
$666$	−4360.88	−	2697.43i	−0.00983164	−	0.00608138i
$667$			21071.9i			0.0473644i
$668$	−310208.	+	154814.i	−0.695185	+	0.346942i
$669$	274607.			0.613563
$670$	−37819.4	+	61141.9i	−0.0842491	+	0.136204i
$671$		−	1.25989e6i		−	2.79827i
$672$	330450.	−	128873.i	0.731757	−	0.285380i
$673$	−393442.			−0.868661			−0.434330	−	0.900754i	$-0.643015\pi$
$673$	−393442.			−0.868661			−0.434330	+	0.900754i	$0.643015\pi$
$674$	−360470.	−	222969.i	−0.793505	−	0.490823i
$675$			433748.i			0.951985i
$676$	−139486.	−	279494.i	−0.305236	−	0.611616i
$677$	566478.			1.23596			0.617982	−	0.786192i	$-0.287950\pi$
$677$	566478.			1.23596			0.617982	+	0.786192i	$0.287950\pi$
$678$	−258710.	+	418252.i	−0.562800	+	0.909868i
$679$			361366.i			0.783805i
$680$	553.246	−	6059.53i	0.00119647	−	0.0131045i
$681$	−339937.			−0.733001
$682$	−138552.	−	85701.8i	−0.297883	−	0.184256i
$683$		−	570234.i		−	1.22240i	−0.791478	−	0.611198i	$-0.790688\pi$
$683$		−	570234.i		−	1.22240i	0.791478	−	0.611198i	$-0.209312\pi$
$684$	−1927.12	+	961.760i	−0.00411906	+	0.00205568i
$685$	67765.6			0.144420
$686$	268715.	−	434426.i	0.571010	−	0.923140i
$687$			106738.i			0.226154i
$688$	95429.4	+	71795.5i	0.201607	+	0.151677i
$689$	110176.			0.232085
$690$	43029.7	+	26616.1i	0.0903796	+	0.0559044i
$691$			297310.i			0.622664i	0.950301	+	0.311332i	$0.100775\pi$
$691$			297310.i			0.622664i	−0.950301	+	0.311332i	$0.899225\pi$
$692$	300747.	+	602621.i	0.628043	+	1.25844i
$693$	−10005.1			−0.0208331
$694$	−44235.9	+	71515.4i	−0.0918451	+	0.148484i
$695$		−	32841.3i		−	0.0679908i
$696$	44313.4	+	4045.89i	0.0914780	+	0.00835211i
$697$	−58134.3			−0.119665
$698$	322001.	+	199174.i	0.660916	+	0.408810i
$699$			314926.i			0.644546i
$700$	327888.	−	163637.i	0.669160	−	0.333954i
$701$	580709.			1.18174			0.590871	−	0.806766i	$-0.298784\pi$
$701$	580709.			1.18174			0.590871	+	0.806766i	$0.298784\pi$
$702$	−144816.	+	234122.i	−0.293862	+	0.475081i
$703$			140261.i			0.283808i
$704$	−175035.	+	950561.i	−0.353167	+	1.91794i
$705$	−90231.7			−0.181544
$706$	−492463.	−	304614.i	−0.988017	−	0.611139i
$707$			60054.6i			0.120145i
$708$	−141748.	−	284027.i	−0.282781	−	0.566622i
$709$	328971.			0.654434			0.327217	−	0.944949i	$-0.393889\pi$
$709$	328971.			0.654434			0.327217	+	0.944949i	$0.393889\pi$
$710$	65091.6	−	105232.i	0.129124	−	0.208753i
$711$			6051.41i			0.0119706i
$712$	44748.8	−	490119.i	0.0882716	−	0.966812i
$713$	47400.6			0.0932406
$714$	−22039.5	−	13632.5i	−0.0432319	−	0.0267412i
$715$		−	114030.i		−	0.223053i
$716$	−362635.	+	180978.i	−0.707364	+	0.353021i
$717$	16858.4			0.0327928
$718$	−237480.	+	383929.i	−0.460657	+	0.744736i
$719$		−	661643.i		−	1.27987i	−0.768429	−	0.639935i	$-0.778961\pi$
$719$		−	661643.i		−	1.27987i	0.768429	−	0.639935i	$-0.221039\pi$
$720$	867.725	−	1153.37i	0.00167385	−	0.00222486i
$721$	594597.			1.14380
$722$	−393225.	−	243230.i	−0.754339	−	0.466597i
$723$		−	521714.i		−	0.998058i
$724$	−56971.8	−	114157.i	−0.108688	−	0.217784i
$725$	45973.4			0.0874643
$726$	782546.	−	1.26513e6i	1.48469	−	2.40027i
$727$		−	617142.i		−	1.16766i	−0.811876	−	0.583830i	$-0.801554\pi$
$727$		−	617142.i		−	1.16766i	0.811876	−	0.583830i	$-0.198446\pi$
$728$	231616.	+	21147.0i	0.437025	+	0.0399011i
$729$	−523966.			−0.985934
$730$	67965.3	+	42040.0i	0.127539	+	0.0788891i
$731$		−	8725.32i		−	0.0163285i
$732$	692622.	−	345664.i	1.29263	−	0.645106i
$733$	631236.			1.17485			0.587426	−	0.809278i	$-0.300141\pi$
$733$	631236.			1.17485			0.587426	+	0.809278i	$0.300141\pi$
$734$	−305003.	+	493093.i	−0.566125	+	0.915244i
$735$		−	43286.9i		−	0.0801275i
$736$	−102177.	−	261998.i	−0.188625	−	0.483662i
$737$	−834389.			−1.53615
$738$	−11727.6	−	7254.10i	−0.0215325	−	0.0133190i
$739$			785739.i			1.43876i	0.694615	+	0.719382i	$0.255575\pi$
$739$			785739.i			1.43876i	−0.694615	+	0.719382i	$0.744425\pi$
$740$	−41972.4	−	84102.0i	−0.0766478	−	0.153583i
$741$	−104547.			−0.190404
$742$	93215.5	−	150700.i	0.169309	−	0.273719i
$743$			1.07760e6i			1.95200i	0.217771	+	0.976000i	$0.430121\pi$
$743$			1.07760e6i			1.95200i	−0.217771	+	0.976000i	$0.569879\pi$
$744$	9101.12	−	99681.8i	0.0164418	−	0.180082i
$745$	66107.3			0.119107
$746$	−580200.	−	358883.i	−1.04256	−	0.644875i
$747$			1490.16i			0.00267049i
$748$	63187.2	−	31534.5i	0.112934	−	0.0563615i
$749$	743262.			1.32488
$750$	118643.	−	191808.i	0.210921	−	0.340992i
$751$			730398.i			1.29503i	0.762053	+	0.647515i	$0.224192\pi$
$751$			730398.i			1.29503i	−0.762053	+	0.647515i	$0.775808\pi$
$752$	400760.	+	301509.i	0.708678	+	0.533168i
$753$	741594.			1.30791
$754$	24814.8	+	15349.2i	0.0436484	+	0.0269988i
$755$			198469.i			0.348176i
$756$	197711.	+	396163.i	0.345929	+	0.693154i
$757$	388468.			0.677897			0.338949	−	0.940805i	$-0.389929\pi$
$757$	388468.			0.677897			0.338949	+	0.940805i	$0.389929\pi$
$758$	66129.2	−	106910.i	0.115095	−	0.186071i
$759$			587217.i			1.01933i
$760$	−39316.5	−	3589.67i	−0.0680688	−	0.00621480i
$761$	−1.10422e6			−1.90672			−0.953362	−	0.301831i	$-0.902402\pi$
$761$	−1.10422e6			−1.90672			−0.953362	+	0.301831i	$0.902402\pi$
$762$	−607923.	−	376032.i	−1.04698	−	0.647611i
$763$		−	481618.i		−	0.827283i
$764$	−222232.	+	110908.i	−0.380732	+	0.190010i
$765$	−105.455			−0.000180195
$766$	−238138.	+	384993.i	−0.405855	+	0.656138i
$767$		−	208149.i		−	0.353821i
$768$	−570590.	+	164570.i	−0.967390	+	0.279016i
$769$	−891596.			−1.50770			−0.753851	−	0.657046i	$-0.771806\pi$
$769$	−891596.			−1.50770			−0.753851	+	0.657046i	$0.771806\pi$
$770$	−155972.	−	96476.4i	−0.263066	−	0.162720i
$771$			586451.i			0.986559i
$772$	439329.	+	880304.i	0.737149	+	1.47706i
$773$	75342.1			0.126089			0.0630447	−	0.998011i	$-0.479919\pi$
$773$	75342.1			0.126089			0.0630447	+	0.998011i	$0.479919\pi$
$774$	1088.76	−	1760.18i	0.00181740	−	0.00293816i
$775$		−	103416.i		−	0.172181i
$776$	55011.2	−	602520.i	0.0913540	−	1.00057i
$777$	−400321.			−0.663080
$778$	−755174.	−	467114.i	−1.24764	−	0.771726i
$779$			377198.i			0.621576i
$780$	62687.6	−	31285.2i	0.103037	−	0.0514221i
$781$	1.43608e6			2.35438
$782$	−10808.6	+	17474.0i	−0.0176748	+	0.0285746i
$783$			55546.2i			0.0906006i
$784$	−144643.	+	192257.i	−0.235323	+	0.312787i
$785$	185618.			0.301217
$786$	−875380.	−	541468.i	−1.41694	−	0.876450i
$787$		−	649432.i		−	1.04854i	−0.851553	−	0.524269i	$-0.824339\pi$
$787$		−	649432.i		−	1.04854i	0.851553	−	0.524269i	$-0.175661\pi$
$788$	227235.	+	455321.i	0.365950	+	0.733272i
$789$	−903872.			−1.45195
$790$	−58352.3	+	94337.1i	−0.0934984	+	0.151157i
$791$			518662.i			0.828956i
$792$	16681.8	+	1523.08i	0.0265946	+	0.00242813i
$793$	507588.			0.807170
$794$	837500.	+	518037.i	1.32845	+	0.821712i
$795$		−	53378.2i		−	0.0844559i
$796$	−104936.	+	52370.0i	−0.165615	+	0.0826525i
$797$	−1.00353e6			−1.57985			−0.789923	−	0.613206i	$-0.789879\pi$
$797$	−1.00353e6			−1.57985			−0.789923	+	0.613206i	$0.789879\pi$
$798$	−88453.1	+	143000.i	−0.138902	+	0.224560i
$799$		−	36642.4i		−	0.0573972i
$800$	−571612.	+	222924.i	−0.893143	+	0.348319i
$801$	−8529.62			−0.0132943
$802$	297519.	+	184031.i	0.462558	+	0.286116i
$803$			927506.i			1.43842i
$804$	−228922.	−	458702.i	−0.354141	−	0.709609i
$805$	53359.9			0.0823424
$806$	34527.7	−	55820.2i	0.0531492	−	0.0859254i
$807$		−	109155.i		−	0.167609i
$808$	9142.17	−	100131.i	0.0140032	−	0.153372i
$809$	904407.			1.38187			0.690935	−	0.722917i	$-0.257199\pi$
$809$	904407.			1.38187			0.690935	+	0.722917i	$0.257199\pi$
$810$	114981.	+	71121.9i	0.175250	+	0.108401i
$811$		−	1.08327e6i		−	1.64700i	−0.567313	−	0.823502i	$-0.692017\pi$
$811$		−	1.08327e6i		−	1.64700i	0.567313	−	0.823502i	$-0.307983\pi$
$812$	41989.7	−	20955.6i	0.0636840	−	0.0317825i
$813$	−636885.			−0.963563
$814$	573860.	−	927749.i	0.866078	−	1.40017i
$815$			88324.5i			0.132974i
$816$	34672.0	+	26085.2i	0.0520713	+	0.0391754i
$817$	−56613.2			−0.0848153
$818$	−1.10127e6	−	681193.i	−1.64584	−	1.01804i
$819$		−	4030.85i		−	0.00600937i
$820$	−112875.	−	226172.i	−0.167868	−	0.336366i
$821$	688285.			1.02113			0.510566	−	0.859839i	$-0.329436\pi$
$821$	688285.			1.02113			0.510566	+	0.859839i	$0.329436\pi$
$822$	−254198.	+	410956.i	−0.376208	+	0.608208i
$823$			982689.i			1.45083i	0.688312	+	0.725415i	$0.258352\pi$
$823$			982689.i			1.45083i	−0.688312	+	0.725415i	$0.741648\pi$
$824$	−991394.	−	90516.1i	−1.46013	−	0.133313i
$825$	1.28116e6			1.88232
$826$	−284709.	−	176107.i	−0.417293	−	0.258117i
$827$		−	1.15658e6i		−	1.69109i	−0.533905	−	0.845545i	$-0.679276\pi$
$827$		−	1.15658e6i		−	1.69109i	0.533905	−	0.845545i	$-0.320724\pi$
$828$	−4360.88	+	2176.36i	−0.00636082	+	0.00317446i
$829$	1.21032e6			1.76113			0.880567	−	0.473922i	$-0.157162\pi$
$829$	1.21032e6			1.76113			0.880567	+	0.473922i	$0.157162\pi$
$830$	−14369.2	+	23230.5i	−0.0208582	+	0.0337211i
$831$		−	123748.i		−	0.179199i
$832$	−382963.	−	70518.3i	−0.553236	−	0.101872i
$833$	17578.5			0.0253332
$834$	199162.	+	123192.i	0.286335	+	0.177113i
$835$			110140.i			0.157970i
$836$	−204608.	−	409983.i	−0.292759	−	0.586615i
$837$	124950.			0.178355
$838$	106133.	−	171584.i	0.151135	−	0.244336i
$839$			386105.i			0.548507i	0.961657	+	0.274253i	$0.0884307\pi$
$839$			386105.i			0.548507i	−0.961657	+	0.274253i	$0.911569\pi$
$840$	10245.3	−	112214.i	0.0145200	−	0.159033i
$841$	−701394.			−0.991676
$842$	−621232.	−	384264.i	−0.876254	−	0.542008i
$843$		−	815249.i		−	1.14719i
$844$	−275346.	+	137415.i	−0.386539	+	0.192908i
$845$	−99235.1			−0.138980
$846$	4572.30	−	7391.95i	0.00638843	−	0.0103280i
$847$		−	1.56885e6i		−	2.18682i
$848$	−178363.	+	237077.i	−0.248035	+	0.329684i
$849$	345007.			0.478643
$850$	38123.9	+	23581.6i	0.0527666	+	0.0326388i
$851$			317395.i			0.438269i
$852$	394002.	+	789480.i	0.542774	+	1.08758i
$853$	490204.			0.673719			0.336859	−	0.941555i	$-0.390635\pi$
$853$	490204.			0.673719			0.336859	+	0.941555i	$0.390635\pi$
$854$	429451.	−	694285.i	0.588840	−	0.951967i
$855$			684.231i			0.000935989i
$856$	−1.23927e6	−	113147.i	−1.69129	−	0.154418i
$857$	65235.1			0.0888218			0.0444109	−	0.999013i	$-0.485859\pi$
$857$	65235.1			0.0888218			0.0444109	+	0.999013i	$0.485859\pi$
$858$	691521.	+	427741.i	0.939358	+	0.581041i
$859$			73562.9i			0.0996947i	0.998757	+	0.0498474i	$0.0158735\pi$
$859$			73562.9i			0.0996947i	−0.998757	+	0.0498474i	$0.984127\pi$
$860$	33946.0	−	16941.2i	0.0458978	−	0.0229060i
$861$	−1.07657e6			−1.45223
$862$	672065.	−	1.08651e6i	0.904475	−	1.46225i
$863$		−	472142.i		−	0.633945i	−0.948435	−	0.316972i	$-0.897334\pi$
$863$		−	472142.i		−	0.633945i	0.948435	−	0.316972i	$-0.102666\pi$
$864$	−269343.	−	690635.i	−0.360809	−	0.925169i
$865$	213962.			0.285960
$866$	163442.	+	101097.i	0.217936	+	0.134804i
$867$			753648.i			1.00261i
$868$	−47139.0	−	94454.6i	−0.0625664	−	0.125367i
$869$	−1.28740e6			−1.70480
$870$	7436.43	−	12022.3i	0.00982486	−	0.0158837i
$871$		−	336160.i		−	0.443108i
$872$	−73317.3	+	803021.i	−0.0964214	+	1.05607i
$873$	−10485.7			−0.0137585
$874$	113378.	+	70130.3i	0.148425	+	0.0918084i
$875$		−	237855.i		−	0.310668i
$876$	−509893.	+	254470.i	−0.664463	+	0.331610i
$877$	424190.			0.551521			0.275760	−	0.961226i	$-0.411070\pi$
$877$	424190.			0.551521			0.275760	+	0.961226i	$0.411070\pi$
$878$	652323.	−	1.05460e6i	0.846201	−	1.36804i
$879$			160900.i			0.208247i
$880$	245371.	+	184603.i	0.316853	+	0.238382i
$881$	−361012.			−0.465125			−0.232563	−	0.972581i	$-0.574711\pi$
$881$	−361012.			−0.465125			−0.232563	+	0.972581i	$0.574711\pi$
$882$	3546.14	+	2193.47i	0.00455846	+	0.00281964i
$883$			695616.i			0.892171i	0.894990	+	0.446086i	$0.147182\pi$
$883$			695616.i			0.892171i	−0.894990	+	0.446086i	$0.852818\pi$
$884$	12704.7	+	25456.9i	0.0162577	+	0.0325763i
$885$	−100845.			−0.128756
$886$	−150325.	+	243028.i	−0.191498	+	0.309592i
$887$			765966.i			0.973559i	0.873525	+	0.486780i	$0.161828\pi$
$887$			765966.i			0.973559i	−0.873525	+	0.486780i	$0.838172\pi$
$888$	667470.	+	60941.2i	0.846459	+	0.0772832i
$889$	−753868.			−0.953876
$890$	−132971.	−	82249.2i	−0.167871	−	0.103837i
$891$			1.56912e6i			1.97652i
$892$	−433853.	+	216521.i	−0.545272	+	0.272126i
$893$	−237750.			−0.298138
$894$	−247977.	+	400899.i	−0.310267	+	0.501603i
$895$			128754.i			0.160737i
$896$	−420466.	+	464159.i	−0.523739	+	0.578163i
$897$	−236579.			−0.294029
$898$	1.02114e6	+	631625.i	1.26628	+	0.783261i
$899$		−	13243.6i		−	0.0163865i
$900$	4748.26	+	9514.31i	0.00586205	+	0.0117461i
$901$	21676.5			0.0267017
$902$	1.54326e6	−	2.49496e6i	1.89682	−	3.06655i
$903$		−	161581.i		−	0.198159i
$904$	78956.5	−	864786.i	0.0966164	−	1.05821i
$905$	−40531.8			−0.0494879
$906$	−1.20359e6	−	744484.i	−1.46630	−	0.906982i
$907$			791052.i			0.961591i	0.876833	+	0.480796i	$0.159652\pi$
$907$			791052.i			0.961591i	−0.876833	+	0.480796i	$0.840348\pi$
$908$	537069.	−	268032.i	0.651416	−	0.325099i
$909$	−1742.60			−0.00210897
$910$	38868.6	−	62838.1i	0.0469370	−	0.0758822i
$911$			1.05307e6i			1.26888i	0.772974	+	0.634438i	$0.218768\pi$
$911$			1.05307e6i			1.26888i	−0.772974	+	0.634438i	$0.781232\pi$
$912$	169250.	−	224965.i	0.203489	−	0.270474i
$913$	−317021.			−0.380317
$914$	−229957.	−	142240.i	−0.275267	−	0.170267i
$915$		−	245918.i		−	0.293729i
$916$	−84160.3	−	168636.i	−0.100303	−	0.200983i
$917$	−1.08553e6			−1.29094
$918$	−28491.8	+	46062.2i	−0.0338092	+	0.0546587i
$919$		−	1.14547e6i		−	1.35629i	−0.734929	−	0.678144i	$-0.762785\pi$
$919$		−	1.14547e6i		−	1.35629i	0.734929	−	0.678144i	$-0.237215\pi$
$920$	−88969.1	−	8123.04i	−0.105115	−	0.00959716i
$921$	870435.			1.02616
$922$	1.19409e6	+	738603.i	1.40467	+	0.868859i
$923$			578570.i			0.679129i
$924$	1.17014e6	−	583975.i	1.37055	−	0.683991i
$925$	692474.			0.809320
$926$	−808455.	+	1.30701e6i	−0.942831	+	1.52426i
$927$			17253.4i			0.0200777i
$928$	−73201.1	+	28547.9i	−0.0850006	+	0.0331496i
$929$	−4598.47			−0.00532822			−0.00266411	−	0.999996i	$-0.500848\pi$
$929$	−4598.47			−0.00532822			−0.00266411	+	0.999996i	$0.500848\pi$
$930$	−27043.9	−	16728.1i	−0.0312683	−	0.0193410i
$931$		−	114056.i		−	0.131588i
$932$	−248311.	−	497554.i	−0.285868	−	0.572807i
$933$	−1.18984e6			−1.36687
$934$	243363.	−	393440.i	0.278972	−	0.451008i
$935$		−	22434.8i		−	0.0256625i
$936$	−613.620	+	6720.79i	−0.000700403	+	0.00767130i
$937$	412980.			0.470381			0.235191	−	0.971949i	$-0.424429\pi$
$937$	412980.			0.470381			0.235191	+	0.971949i	$0.424429\pi$
$938$	−459803.	−	284412.i	−0.522596	−	0.323253i
$939$		−	926280.i		−	1.05054i
$940$	142558.	−	71145.6i	0.161337	−	0.0805178i
$941$	−1.37923e6			−1.55760			−0.778802	−	0.627270i	$-0.784172\pi$
$941$	−1.37923e6			−1.55760			−0.778802	+	0.627270i	$0.784172\pi$
$942$	−696275.	+	1.12566e6i	−0.784656	+	1.26854i
$943$			853559.i			0.959865i
$944$	447897.	+	336971.i	0.502613	+	0.378137i
$945$	140659.			0.157508
$946$	374466.	+	231626.i	0.418437	+	0.258825i
$947$		−	1.39922e6i		−	1.56022i	−0.625641	−	0.780111i	$-0.715162\pi$
$947$		−	1.39922e6i		−	1.56022i	0.625641	−	0.780111i	$-0.284838\pi$
$948$	−353209.	−	707741.i	−0.393020	−	0.787513i
$949$	−373675.			−0.414917
$950$	153006.	−	247362.i	0.169536	−	0.274086i
$951$			1.56702e6i			1.73266i
$952$	45569.2	+	4160.55i	0.0502803	+	0.00459068i
$953$	70654.9			0.0777959			0.0388980	−	0.999243i	$-0.487615\pi$
$953$	70654.9			0.0777959			0.0388980	+	0.999243i	$0.487615\pi$
$954$	4372.84	+	2704.83i	0.00480471	+	0.00297196i
$955$			78904.0i			0.0865151i
$956$	−26634.7	+	13292.4i	−0.0291429	+	0.0145442i
$957$	164066.			0.179141
$958$	−343956.	+	556068.i	−0.374777	+	0.605894i
$959$			509615.i			0.554122i
$960$	−34164.9	+	185539.i	−0.0370713	+	0.201323i
$961$	−29791.0			−0.0322581
$962$	373773.	+	231198.i	0.403885	+	0.249823i
$963$			21567.2i			0.0232563i
$964$	411359.	+	824259.i	0.442656	+	0.886972i
$965$	312555.			0.335638
$966$	−200160.	+	323595.i	−0.214498	+	0.346775i
$967$			345692.i			0.369689i	0.982768	+	0.184844i	$0.0591781\pi$
$967$			345692.i			0.369689i	−0.982768	+	0.184844i	$0.940822\pi$
$968$	−238827.	+	2.61580e6i	−0.254879	+	2.79161i
$969$	−20569.0			−0.0219062
$970$	−163465.	−	101112.i	−0.173733	−	0.107463i
$971$		−	541195.i		−	0.574004i	−0.957930	−	0.287002i	$-0.907341\pi$
$971$		−	541195.i		−	0.574004i	0.957930	−	0.287002i	$-0.0926587\pi$
$972$	−23150.5	+	11553.6i	−0.0245034	+	0.0122288i
$973$	246975.			0.260872
$974$	91060.2	−	147215.i	0.0959866	−	0.155180i
$975$			516154.i			0.542962i
$976$	−821732.	+	1.09223e6i	−0.862641	+	1.14661i
$977$	795301.			0.833187			0.416594	−	0.909093i	$-0.363224\pi$
$977$	795301.			0.833187			0.416594	+	0.909093i	$0.363224\pi$
$978$	−535633.	−	331316.i	−0.560002	−	0.346390i
$979$		−	1.81462e6i		−	1.89330i
$980$	34130.6	+	68389.2i	0.0355380	+	0.0712091i
$981$	13975.1			0.0145217
$982$	−125798.	+	203375.i	−0.130452	+	0.210899i
$983$		−	326723.i		−	0.338121i	−0.985606	−	0.169061i	$-0.945927\pi$
$983$		−	326723.i		−	0.338121i	0.985606	−	0.169061i	$-0.0540733\pi$
$984$	1.79500e6	+	163887.i	1.85385	+	0.169260i
$985$	161663.			0.166624
$986$	4882.18	+	3019.88i	0.00502181	+	0.00310624i
$987$		−	678566.i		−	0.696559i
$988$	165174.	−	82432.7i	0.169211	−	0.0844473i
$989$	−128110.			−0.130975
$990$	2799.45	−	4525.82i	0.00285629	−	0.00461771i
$991$			336741.i			0.342885i	0.985194	+	0.171442i	$0.0548427\pi$
$991$			336741.i			0.342885i	−0.985194	+	0.171442i	$0.945157\pi$
$992$	64217.7	+	164664.i	0.0652577	+	0.167331i
$993$	196926.			0.199712
$994$	791374.	+	489506.i	0.800957	+	0.495433i
$995$			37257.9i			0.0376333i
$996$	−86977.5	−	174281.i	−0.0876775	−	0.175684i
$997$	−349952.			−0.352061			−0.176031	−	0.984385i	$-0.556326\pi$
$997$	−349952.			−0.352061			−0.176031	+	0.984385i	$0.556326\pi$
$998$	−13640.7	+	22052.7i	−0.0136955	+	0.0221412i
$999$			836665.i			0.838340i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	124.5.b.a.63.9	✓	60
4.3	odd	2	inner	124.5.b.a.63.10	yes	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
124.5.b.a.63.9	✓	60	1.1	even	1	trivial
124.5.b.a.63.10	yes	60	4.3	odd	2	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:	\( N \)	\(=\)	\( 124 = 2^{2} \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	124.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-3.40182 - 2.10420i) q^{2} -9.06141i q^{3} +(7.14471 + 14.3162i) q^{4} +5.08300 q^{5} +(-19.0670 + 30.8253i) q^{6} +38.2255i q^{7} +(5.81911 - 63.7349i) q^{8} -1.10919 q^{9} +O(q^{10})\)	\(q+(-3.40182 - 2.10420i) q^{2} -9.06141i q^{3} +(7.14471 + 14.3162i) q^{4} +5.08300 q^{5} +(-19.0670 + 30.8253i) q^{6} +38.2255i q^{7} +(5.81911 - 63.7349i) q^{8} -1.10919 q^{9} +(-17.2914 - 10.6956i) q^{10} -235.972i q^{11} +(129.725 - 64.7411i) q^{12} +95.0688 q^{13} +(80.4341 - 130.036i) q^{14} -46.0592i q^{15} +(-153.906 + 204.570i) q^{16} +18.7043 q^{17} +(3.77325 + 2.33395i) q^{18} -121.361i q^{19} +(36.3166 + 72.7692i) q^{20} +346.377 q^{21} +(-496.532 + 802.734i) q^{22} -274.626i q^{23} +(-577.528 - 52.7294i) q^{24} -599.163 q^{25} +(-323.407 - 200.044i) q^{26} -723.924i q^{27} +(-547.244 + 273.110i) q^{28} -76.7294 q^{29} +(-96.9176 + 156.685i) q^{30} +172.601i q^{31} +(954.017 - 372.060i) q^{32} -2138.24 q^{33} +(-63.6285 - 39.3575i) q^{34} +194.300i q^{35} +(-7.92482 - 15.8793i) q^{36} -1155.74 q^{37} +(-255.366 + 412.846i) q^{38} -861.458i q^{39} +(29.5786 - 323.965i) q^{40} -3108.08 q^{41} +(-1178.31 - 728.846i) q^{42} -466.488i q^{43} +(3378.22 - 1685.95i) q^{44} -5.63801 q^{45} +(-577.867 + 934.227i) q^{46} -1959.04i q^{47} +(1853.69 + 1394.61i) q^{48} +939.809 q^{49} +(2038.24 + 1260.76i) q^{50} -169.487i q^{51} +(679.239 + 1361.02i) q^{52} +1158.91 q^{53} +(-1523.28 + 2462.65i) q^{54} -1199.45i q^{55} +(2436.30 + 222.439i) q^{56} -1099.70 q^{57} +(261.019 + 161.454i) q^{58} -2189.46i q^{59} +(659.392 - 329.079i) q^{60} +5339.17 q^{61} +(363.186 - 587.156i) q^{62} -42.3993i q^{63} +(-4028.28 - 741.761i) q^{64} +483.235 q^{65} +(7273.90 + 4499.28i) q^{66} -3535.96i q^{67} +(133.637 + 267.774i) q^{68} -2488.50 q^{69} +(408.847 - 660.974i) q^{70} +6085.80i q^{71} +(-6.45449 + 70.6940i) q^{72} -3930.57 q^{73} +(3931.60 + 2431.90i) q^{74} +5429.26i q^{75} +(1737.42 - 867.085i) q^{76} +9020.16 q^{77} +(-1812.68 + 2930.52i) q^{78} -5455.71i q^{79} +(-782.307 + 1039.83i) q^{80} -6649.61 q^{81} +(10573.1 + 6540.01i) q^{82} -1343.47i q^{83} +(2474.76 + 4958.80i) q^{84} +95.0739 q^{85} +(-981.583 + 1586.91i) q^{86} +695.277i q^{87} +(-15039.7 - 1373.15i) q^{88} +7689.97 q^{89} +(19.1795 + 11.8635i) q^{90} +3634.05i q^{91} +(3931.60 - 1962.12i) q^{92} +1564.01 q^{93} +(-4122.20 + 6664.29i) q^{94} -616.876i q^{95} +(-3371.39 - 8644.74i) q^{96} +9453.54 q^{97} +(-3197.06 - 1977.54i) q^{98} +261.738i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q + 6 q^{2} - 6 q^{4} + 24 q^{5} + 45 q^{8} - 1732 q^{9}+O(q^{10}) \) 60 * q + 6 * q^2 - 6 * q^4 + 24 * q^5 + 45 * q^8 - 1732 * q^9	\( 60 q + 6 q^{2} - 6 q^{4} + 24 q^{5} + 45 q^{8} - 1732 q^{9} + 53 q^{10} + 130 q^{12} + 120 q^{13} - 231 q^{14} - 590 q^{16} - 648 q^{17} + 230 q^{18} + 1113 q^{20} + 608 q^{21} + 1080 q^{22} - 1028 q^{24} + 8340 q^{25} - 1554 q^{26} - 165 q^{28} - 168 q^{29} - 2238 q^{30} - 1674 q^{32} - 1120 q^{33} + 1844 q^{34} + 1966 q^{36} - 2248 q^{37} - 5055 q^{38} - 1716 q^{40} + 6072 q^{41} + 5794 q^{42} - 120 q^{44} - 4040 q^{45} + 8850 q^{46} + 2276 q^{48} - 17604 q^{49} - 4539 q^{50} + 5896 q^{52} + 3480 q^{53} + 5148 q^{54} - 396 q^{56} - 10912 q^{57} - 7484 q^{58} + 22812 q^{60} + 2200 q^{61} - 19299 q^{64} - 9168 q^{65} - 468 q^{66} - 21930 q^{68} + 6496 q^{69} - 9615 q^{70} - 10079 q^{72} + 13752 q^{73} - 2106 q^{74} + 20099 q^{76} + 16608 q^{77} + 39460 q^{78} - 5787 q^{80} + 20732 q^{81} - 30525 q^{82} - 21760 q^{84} - 21200 q^{85} - 13398 q^{86} + 34690 q^{88} + 22296 q^{89} - 25419 q^{90} - 18852 q^{92} + 3196 q^{94} + 20790 q^{96} + 12120 q^{97} + 21921 q^{98}+O(q^{100}) \) 60 * q + 6 * q^2 - 6 * q^4 + 24 * q^5 + 45 * q^8 - 1732 * q^9 + 53 * q^10 + 130 * q^12 + 120 * q^13 - 231 * q^14 - 590 * q^16 - 648 * q^17 + 230 * q^18 + 1113 * q^20 + 608 * q^21 + 1080 * q^22 - 1028 * q^24 + 8340 * q^25 - 1554 * q^26 - 165 * q^28 - 168 * q^29 - 2238 * q^30 - 1674 * q^32 - 1120 * q^33 + 1844 * q^34 + 1966 * q^36 - 2248 * q^37 - 5055 * q^38 - 1716 * q^40 + 6072 * q^41 + 5794 * q^42 - 120 * q^44 - 4040 * q^45 + 8850 * q^46 + 2276 * q^48 - 17604 * q^49 - 4539 * q^50 + 5896 * q^52 + 3480 * q^53 + 5148 * q^54 - 396 * q^56 - 10912 * q^57 - 7484 * q^58 + 22812 * q^60 + 2200 * q^61 - 19299 * q^64 - 9168 * q^65 - 468 * q^66 - 21930 * q^68 + 6496 * q^69 - 9615 * q^70 - 10079 * q^72 + 13752 * q^73 - 2106 * q^74 + 20099 * q^76 + 16608 * q^77 + 39460 * q^78 - 5787 * q^80 + 20732 * q^81 - 30525 * q^82 - 21760 * q^84 - 21200 * q^85 - 13398 * q^86 + 34690 * q^88 + 22296 * q^89 - 25419 * q^90 - 18852 * q^92 + 3196 * q^94 + 20790 * q^96 + 12120 * q^97 + 21921 * q^98

Introduction

L-functions

Modular forms

Varieties

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Database

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