LMFDB - Embedded newform 124.5.b.a.63.12

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			63.12
Character	$\chi$	$=$	124.63
Dual form			124.5.b.a.63.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-3.23786 + 2.34867i) q^{2} -10.1900i q^{3} +(4.96753 - 15.2093i) q^{4} -24.8949 q^{5} +(23.9329 + 32.9938i) q^{6} -72.3138i q^{7} +(19.6374 + 60.9128i) q^{8} -22.8358 q^{9} +O(q^{10})$	\(q+(-3.23786 + 2.34867i) q^{2} -10.1900i q^{3} +(4.96753 - 15.2093i) q^{4} -24.8949 q^{5} +(23.9329 + 32.9938i) q^{6} -72.3138i q^{7} +(19.6374 + 60.9128i) q^{8} -22.8358 q^{9} +(80.6064 - 58.4699i) q^{10} -153.328i q^{11} +(-154.983 - 50.6191i) q^{12} -52.9434 q^{13} +(169.841 + 234.142i) q^{14} +253.679i q^{15} +(-206.647 - 151.106i) q^{16} +129.414 q^{17} +(73.9392 - 53.6336i) q^{18} +147.349i q^{19} +(-123.666 + 378.635i) q^{20} -736.877 q^{21} +(360.116 + 496.455i) q^{22} +966.117i q^{23} +(620.701 - 200.105i) q^{24} -5.24293 q^{25} +(171.424 - 124.346i) q^{26} -592.692i q^{27} +(-1099.84 - 359.221i) q^{28} -695.514 q^{29} +(-595.807 - 821.378i) q^{30} -172.601i q^{31} +(1023.99 + 3.91453i) q^{32} -1562.41 q^{33} +(-419.026 + 303.951i) q^{34} +1800.25i q^{35} +(-113.438 + 347.317i) q^{36} -2476.02 q^{37} +(-346.073 - 477.095i) q^{38} +539.492i q^{39} +(-488.872 - 1516.42i) q^{40} +832.078 q^{41} +(2385.91 - 1730.68i) q^{42} -18.2993i q^{43} +(-2332.02 - 761.662i) q^{44} +568.495 q^{45} +(-2269.09 - 3128.16i) q^{46} -755.674i q^{47} +(-1539.76 + 2105.73i) q^{48} -2828.29 q^{49} +(16.9759 - 12.3139i) q^{50} -1318.73i q^{51} +(-262.998 + 805.233i) q^{52} +4825.00 q^{53} +(1392.04 + 1919.06i) q^{54} +3817.09i q^{55} +(4404.84 - 1420.06i) q^{56} +1501.48 q^{57} +(2251.98 - 1633.53i) q^{58} +6360.00i q^{59} +(3858.28 + 1260.16i) q^{60} +600.977 q^{61} +(405.381 + 558.858i) q^{62} +1651.34i q^{63} +(-3324.74 + 2392.34i) q^{64} +1318.02 q^{65} +(5058.87 - 3669.58i) q^{66} -2048.84i q^{67} +(642.870 - 1968.30i) q^{68} +9844.72 q^{69} +(-4228.18 - 5828.96i) q^{70} +3487.28i q^{71} +(-448.436 - 1390.99i) q^{72} +5117.20 q^{73} +(8017.01 - 5815.34i) q^{74} +53.4253i q^{75} +(2241.07 + 731.959i) q^{76} -11087.7 q^{77} +(-1267.09 - 1746.80i) q^{78} -4235.23i q^{79} +(5144.47 + 3761.76i) q^{80} -7889.23 q^{81} +(-2694.15 + 1954.27i) q^{82} -9258.14i q^{83} +(-3660.46 + 11207.4i) q^{84} -3221.76 q^{85} +(42.9791 + 59.2508i) q^{86} +7087.28i q^{87} +(9339.64 - 3010.97i) q^{88} -13371.0 q^{89} +(-1840.71 + 1335.20i) q^{90} +3828.54i q^{91} +(14694.0 + 4799.22i) q^{92} -1758.80 q^{93} +(1774.83 + 2446.77i) q^{94} -3668.23i q^{95} +(39.8890 - 10434.5i) q^{96} +2111.84 q^{97} +(9157.62 - 6642.71i) q^{98} +3501.36i 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 $

$2$	−3.23786	+	2.34867i	−0.809466	+	0.587167i
$2$	−3.23786	+	2.34867i	−0.809466	+	0.587167i
$3$		−	10.1900i		−	1.13222i	−0.824330	−	0.566110i	$-0.808448\pi$
$3$		−	10.1900i		−	1.13222i	0.824330	−	0.566110i	$-0.191552\pi$
$4$	4.96753	−	15.2093i	0.310471	−	0.950583i
$5$	−24.8949			−0.995797			−0.497898	−	0.867235i	$-0.665895\pi$
$5$	−24.8949			−0.995797			−0.497898	+	0.867235i	$0.665895\pi$
$6$	23.9329	+	32.9938i	0.664802	+	0.916494i
$7$		−	72.3138i		−	1.47579i	−0.674914	−	0.737896i	$-0.735819\pi$
$7$		−	72.3138i		−	1.47579i	0.674914	−	0.737896i	$-0.264181\pi$
$8$	19.6374	+	60.9128i	0.306835	+	0.951763i
$9$	−22.8358			−0.281923
$10$	80.6064	−	58.4699i	0.806064	−	0.584699i
$11$		−	153.328i		−	1.26717i	−0.773672	−	0.633587i	$-0.781582\pi$
$11$		−	153.328i		−	1.26717i	0.773672	−	0.633587i	$-0.218418\pi$
$12$	−154.983	−	50.6191i	−1.07627	−	0.351522i
$13$	−52.9434			−0.313275			−0.156637	−	0.987656i	$-0.550065\pi$
$13$	−52.9434			−0.313275			−0.156637	+	0.987656i	$0.550065\pi$
$14$	169.841	+	234.142i	0.866536	+	1.19460i
$15$			253.679i			1.12746i
$16$	−206.647	−	151.106i	−0.807216	−	0.590257i
$17$	129.414			0.447800			0.223900	−	0.974612i	$-0.428121\pi$
$17$	129.414			0.447800			0.223900	+	0.974612i	$0.428121\pi$
$18$	73.9392	−	53.6336i	0.228207	−	0.165536i
$19$			147.349i			0.408168i	0.978953	+	0.204084i	$0.0654215\pi$
$19$			147.349i			0.408168i	−0.978953	+	0.204084i	$0.934578\pi$
$20$	−123.666	+	378.635i	−0.309166	+	0.946587i
$21$	−736.877			−1.67092
$22$	360.116	+	496.455i	0.744042	+	1.02573i
$23$			966.117i			1.82631i	0.407614	+	0.913154i	$0.366361\pi$
$23$			966.117i			1.82631i	−0.407614	+	0.913154i	$0.633639\pi$
$24$	620.701	−	200.105i	1.07761	−	0.347405i
$25$	−5.24293			−0.00838868
$26$	171.424	−	124.346i	0.253585	−	0.183944i
$27$		−	592.692i		−	0.813021i
$28$	−1099.84	−	359.221i	−1.40286	−	0.458191i
$29$	−695.514			−0.827009			−0.413504	−	0.910502i	$-0.635695\pi$
$29$	−695.514			−0.827009			−0.413504	+	0.910502i	$0.635695\pi$
$30$	−595.807	−	821.378i	−0.662008	−	0.912642i
$31$		−	172.601i		−	0.179605i
$31$		−	172.601i		−	0.179605i
$32$	1023.99	+	3.91453i	0.999993	+	0.00382279i
$33$	−1562.41			−1.43472
$34$	−419.026	+	303.951i	−0.362479	+	0.262933i
$35$			1800.25i			1.46959i
$36$	−113.438	+	347.317i	−0.0875289	+	0.267991i
$37$	−2476.02			−1.80863			−0.904316	−	0.426864i	$-0.859618\pi$
$37$	−2476.02			−1.80863			−0.904316	+	0.426864i	$0.859618\pi$
$38$	−346.073	−	477.095i	−0.239662	−	0.330398i
$39$			539.492i			0.354696i
$40$	−488.872	−	1516.42i	−0.305545	−	0.947762i
$41$	832.078			0.494990			0.247495	−	0.968889i	$-0.420393\pi$
$41$	832.078			0.494990			0.247495	+	0.968889i	$0.420393\pi$
$42$	2385.91	−	1730.68i	1.35256	−	0.981110i
$43$		−	18.2993i		−	0.00989689i	−0.999988	−	0.00494844i	$-0.998425\pi$
$43$		−	18.2993i		−	0.00989689i	0.999988	−	0.00494844i	$-0.00157515\pi$
$44$	−2332.02	−	761.662i	−1.20455	−	0.393420i
$45$	568.495			0.280738
$46$	−2269.09	−	3128.16i	−1.07235	−	1.47834i
$47$		−	755.674i		−	0.342089i	−0.985263	−	0.171044i	$-0.945286\pi$
$47$		−	755.674i		−	0.342089i	0.985263	−	0.171044i	$-0.0547142\pi$
$48$	−1539.76	+	2105.73i	−0.668301	+	0.913946i
$49$	−2828.29			−1.17796
$50$	16.9759	−	12.3139i	0.00679035	−	0.00492555i
$51$		−	1318.73i		−	0.507009i
$52$	−262.998	+	805.233i	−0.0972626	+	0.297793i
$53$	4825.00			1.71769			0.858847	−	0.512233i	$-0.171182\pi$
$53$	4825.00			1.71769			0.858847	+	0.512233i	$0.171182\pi$
$54$	1392.04	+	1919.06i	0.477379	+	0.658113i
$55$			3817.09i			1.26185i
$56$	4404.84	−	1420.06i	1.40460	−	0.452824i
$57$	1501.48			0.462136
$58$	2251.98	−	1633.53i	0.669436	−	0.485592i
$59$			6360.00i			1.82706i	0.406769	+	0.913531i	$0.366655\pi$
$59$			6360.00i			1.82706i	−0.406769	+	0.913531i	$0.633345\pi$
$60$	3858.28	+	1260.16i	1.07175	+	0.350044i
$61$	600.977			0.161509			0.0807547	−	0.996734i	$-0.474267\pi$
$61$	600.977			0.161509			0.0807547	+	0.996734i	$0.474267\pi$
$62$	405.381	+	558.858i	0.105458	+	0.145384i
$63$			1651.34i			0.416060i
$64$	−3324.74	+	2392.34i	−0.811705	+	0.584068i
$65$	1318.02			0.311958
$66$	5058.87	−	3669.58i	1.16136	−	0.842419i
$67$		−	2048.84i		−	0.456413i	−0.973613	−	0.228206i	$-0.926714\pi$
$67$		−	2048.84i		−	0.456413i	0.973613	−	0.228206i	$-0.0732861\pi$
$68$	642.870	−	1968.30i	0.139029	−	0.425671i
$69$	9844.72			2.06778
$70$	−4228.18	−	5828.96i	−0.862894	−	1.18958i
$71$			3487.28i			0.691783i	0.938275	+	0.345891i	$0.112423\pi$
$71$			3487.28i			0.691783i	−0.938275	+	0.345891i	$0.887577\pi$
$72$	−448.436	−	1390.99i	−0.0865038	−	0.268324i
$73$	5117.20			0.960255			0.480128	−	0.877199i	$-0.340590\pi$
$73$	5117.20			0.960255			0.480128	+	0.877199i	$0.340590\pi$
$74$	8017.01	−	5815.34i	1.46403	−	1.06197i
$75$			53.4253i			0.00949784i
$76$	2241.07	+	731.959i	0.387997	+	0.126724i
$77$	−11087.7			−1.87009
$78$	−1267.09	−	1746.80i	−0.208266	−	0.287114i
$79$		−	4235.23i		−	0.678614i	−0.940676	−	0.339307i	$-0.889808\pi$
$79$		−	4235.23i		−	0.678614i	0.940676	−	0.339307i	$-0.110192\pi$
$80$	5144.47	+	3761.76i	0.803823	+	0.587776i
$81$	−7889.23			−1.20244
$82$	−2694.15	+	1954.27i	−0.400677	+	0.290641i
$83$		−	9258.14i		−	1.34390i	−0.740596	−	0.671951i	$-0.765456\pi$
$83$		−	9258.14i		−	1.34390i	0.740596	−	0.671951i	$-0.234544\pi$
$84$	−3660.46	+	11207.4i	−0.518773	+	1.58835i
$85$	−3221.76			−0.445918
$86$	42.9791	+	59.2508i	0.00581112	+	0.00801120i
$87$			7087.28i			0.936356i
$88$	9339.64	−	3010.97i	1.20605	−	0.388813i
$89$	−13371.0			−1.68805			−0.844023	−	0.536307i	$-0.819819\pi$
$89$	−13371.0			−1.68805			−0.844023	+	0.536307i	$0.819819\pi$
$90$	−1840.71	+	1335.20i	−0.227248	+	0.164840i
$91$			3828.54i			0.462328i
$92$	14694.0	+	4799.22i	1.73606	+	0.567016i
$93$	−1758.80			−0.203353
$94$	1774.83	+	2446.77i	0.200863	+	0.276909i
$95$		−	3668.23i		−	0.406452i
$96$	39.8890	−	10434.5i	0.00432824	−	1.13221i
$97$	2111.84			0.224449			0.112225	−	0.993683i	$-0.464202\pi$
$97$	2111.84			0.224449			0.112225	+	0.993683i	$0.464202\pi$
$98$	9157.62	−	6642.71i	0.953522	−	0.691661i
$99$			3501.36i			0.357246i
$100$	−26.0444	+	79.7414i	−0.00260444	+	0.00797414i
$101$	−3999.04			−0.392024			−0.196012	−	0.980602i	$-0.562799\pi$
$101$	−3999.04			−0.392024			−0.196012	+	0.980602i	$0.562799\pi$
$102$	3097.25	+	4269.87i	0.297698	+	0.410406i
$103$		−	12212.9i		−	1.15118i	−0.817737	−	0.575591i	$-0.804772\pi$
$103$		−	12212.9i		−	1.15118i	0.817737	−	0.575591i	$-0.195228\pi$
$104$	−1039.67	−	3224.93i	−0.0961235	−	0.298163i
$105$	18344.5			1.66390
$106$	−15622.7	+	11332.3i	−1.39041	+	1.00857i
$107$		−	14617.8i		−	1.27677i	−0.769716	−	0.638387i	$-0.779602\pi$
$107$		−	14617.8i		−	1.27677i	0.769716	−	0.638387i	$-0.220398\pi$
$108$	−9014.45	−	2944.22i	−0.772844	−	0.252419i
$109$	−9026.32			−0.759728			−0.379864	−	0.925042i	$-0.624029\pi$
$109$	−9026.32			−0.759728			−0.379864	+	0.925042i	$0.624029\pi$
$110$	−8965.07	−	12359.2i	−0.740914	−	1.02142i
$111$			25230.6i			2.04777i
$112$	−10927.0	+	14943.5i	−0.871096	+	1.19128i
$113$	10264.0			0.803823			0.401912	−	0.915678i	$-0.368346\pi$
$113$	10264.0			0.803823			0.401912	+	0.915678i	$0.368346\pi$
$114$	−4861.59	+	3526.47i	−0.374083	+	0.271351i
$115$		−	24051.4i		−	1.81863i
$116$	−3454.99	+	10578.3i	−0.256762	+	0.786140i
$117$	1209.00			0.0883193
$118$	−14937.5	−	20592.8i	−1.07279	−	1.47894i
$119$		−	9358.44i		−	0.660860i
$120$	−15452.3	+	4981.60i	−1.07308	+	0.345944i
$121$	−8868.47			−0.605728
$122$	−1945.88	+	1411.49i	−0.130736	+	0.0948329i
$123$		−	8478.86i		−	0.560437i
$124$	−2625.14	−	857.400i	−0.170730	−	0.0557622i
$125$	15689.8			1.00415
$126$	−3878.45	−	5346.82i	−0.244297	−	0.336787i
$127$			16896.2i			1.04757i	0.851851	+	0.523784i	$0.175480\pi$
$127$			16896.2i			1.04757i	−0.851851	+	0.523784i	$0.824520\pi$
$128$	5146.26	−	15554.8i	0.314103	−	0.949389i
$129$	−186.470			−0.0112055
$130$	−4267.58	+	3095.59i	−0.252519	+	0.183171i
$131$		−	6142.39i		−	0.357927i	−0.983856	−	0.178964i	$-0.942726\pi$
$131$		−	6142.39i		−	0.357927i	0.983856	−	0.178964i	$-0.0572744\pi$
$132$	−7761.32	+	23763.2i	−0.445439	+	1.36382i
$133$	10655.3			0.602371
$134$	4812.03	+	6633.86i	0.267990	+	0.369451i
$135$			14755.0i			0.809604i
$136$	2541.36	+	7882.99i	0.137401	+	0.426200i
$137$	2395.57			0.127634			0.0638172	−	0.997962i	$-0.479673\pi$
$137$	2395.57			0.127634			0.0638172	+	0.997962i	$0.479673\pi$
$138$	−31875.9	+	23122.0i	−1.67380	+	1.21413i
$139$			8782.69i			0.454567i	0.973829	+	0.227284i	$0.0729844\pi$
$139$			8782.69i			0.454567i	−0.973829	+	0.227284i	$0.927016\pi$
$140$	27380.5	+	8942.79i	1.39697	+	0.456265i
$141$	−7700.31			−0.387320
$142$	−8190.45	−	11291.3i	−0.406192	−	0.559975i
$143$			8117.70i			0.396973i
$144$	4718.95	+	3450.62i	0.227573	+	0.166407i
$145$	17314.8			0.823533
$146$	−16568.8	+	12018.6i	−0.777294	+	0.563830i
$147$			28820.2i			1.33371i
$148$	−12299.7	+	37658.6i	−0.561528	+	1.71925i
$149$	−26072.9			−1.17440			−0.587201	−	0.809441i	$-0.699770\pi$
$149$	−26072.9			−1.17440			−0.587201	+	0.809441i	$0.699770\pi$
$150$	−125.478	−	172.984i	−0.00557681	−	0.00768818i
$151$		−	25638.0i		−	1.12442i	−0.826993	−	0.562212i	$-0.809950\pi$
$151$		−	25638.0i		−	1.12442i	0.826993	−	0.562212i	$-0.190050\pi$
$152$	−8975.42	+	2893.55i	−0.388479	+	0.125240i
$153$	−2955.28			−0.126245
$154$	35900.6	−	26041.4i	1.51377	−	1.09805i
$155$			4296.88i			0.178850i
$156$	8205.31	+	2679.95i	0.337168	+	0.110123i
$157$	−32156.5			−1.30458			−0.652289	−	0.757971i	$-0.726191\pi$
$157$	−32156.5			−1.30458			−0.652289	+	0.757971i	$0.726191\pi$
$158$	9947.13	+	13713.1i	0.398459	+	0.549315i
$159$		−	49166.7i		−	1.94481i
$160$	−25492.2	−	97.4520i	−0.995790	−	0.00380672i
$161$	69863.7			2.69525
$162$	25544.2	−	18529.2i	0.973337	−	0.706034i
$163$		−	28835.7i		−	1.08531i	−0.839955	−	0.542657i	$-0.817418\pi$
$163$		−	28835.7i		−	1.08531i	0.839955	−	0.542657i	$-0.182582\pi$
$164$	4133.37	−	12655.3i	0.153680	−	0.470529i
$165$	38896.1			1.42869
$166$	21744.3	+	29976.6i	0.789094	+	1.08784i
$167$			26032.7i			0.933440i	0.884405	+	0.466720i	$0.154564\pi$
$167$			26032.7i			0.933440i	−0.884405	+	0.466720i	$0.845436\pi$
$168$	−14470.4	−	44885.2i	−0.512697	−	1.59032i
$169$	−25758.0			−0.901859
$170$	10431.6	−	7566.83i	0.360956	−	0.261828i
$171$		−	3364.82i		−	0.115072i
$172$	−278.321	−	90.9026i	−0.00940781	−	0.00307270i
$173$	−49848.7			−1.66557			−0.832783	−	0.553600i	$-0.813254\pi$
$173$	−49848.7			−1.66557			−0.832783	+	0.553600i	$0.813254\pi$
$174$	−16645.7	−	22947.7i	−0.549797	−	0.757949i
$175$			379.136i			0.0123800i
$176$	−23168.7	+	31684.8i	−0.747958	+	1.02288i
$177$	64808.3			2.06864
$178$	43293.5	−	31404.0i	1.36642	−	0.991164i
$179$		−	2731.10i		−	0.0852377i	−0.999091	−	0.0426189i	$-0.986430\pi$
$179$		−	2731.10i		−	0.0852377i	0.999091	−	0.0426189i	$-0.0135701\pi$
$180$	2824.02	−	8646.42i	0.0871611	−	0.266865i
$181$	−2723.46			−0.0831312			−0.0415656	−	0.999136i	$-0.513235\pi$
$181$	−2723.46			−0.0831312			−0.0415656	+	0.999136i	$0.513235\pi$
$182$	−8991.96	−	12396.3i	−0.271464	−	0.374239i
$183$		−	6123.94i		−	0.182864i
$184$	−58848.9	+	18972.1i	−1.73821	+	0.560375i
$185$	61640.3			1.80103
$186$	5694.75	−	4130.83i	0.164607	−	0.119402i
$187$		−	19842.8i		−	0.567440i
$188$	−11493.3	−	3753.84i	−0.325184	−	0.106209i
$189$	−42859.9			−1.19985
$190$	8615.45	+	11877.2i	0.238655	+	0.329009i
$191$			10232.6i			0.280492i	0.990117	+	0.140246i	$0.0447894\pi$
$191$			10232.6i			0.280492i	−0.990117	+	0.140246i	$0.955211\pi$
$192$	24377.9	+	33879.1i	0.661294	+	0.919029i
$193$	−22632.2			−0.607591			−0.303795	−	0.952737i	$-0.598254\pi$
$193$	−22632.2			−0.607591			−0.303795	+	0.952737i	$0.598254\pi$
$194$	−6837.87	+	4960.02i	−0.181684	+	0.131789i
$195$		−	13430.6i		−	0.353205i
$196$	−14049.6	+	43016.4i	−0.365724	+	1.11975i
$197$	−41844.8			−1.07822			−0.539112	−	0.842234i	$-0.681240\pi$
$197$	−41844.8			−1.07822			−0.539112	+	0.842234i	$0.681240\pi$
$198$	−8223.53	−	11336.9i	−0.209763	−	0.289178i
$199$		−	34389.0i		−	0.868388i	−0.900819	−	0.434194i	$-0.857033\pi$
$199$		−	34389.0i		−	0.868388i	0.900819	−	0.434194i	$-0.142967\pi$
$200$	−102.958	−	319.361i	−0.00257394	−	0.00798404i
$201$	−20877.6			−0.516760
$202$	12948.3	−	9392.40i	0.317330	−	0.230183i
$203$			50295.3i			1.22049i
$204$	−20057.0	−	6550.83i	−0.481954	−	0.157411i
$205$	−20714.5			−0.492909
$206$	28684.0	+	39543.7i	0.675936	+	0.931844i
$207$		−	22062.0i		−	0.514879i
$208$	10940.6	+	8000.05i	0.252880	+	0.184912i
$209$	22592.7			0.517219
$210$	−59397.0	+	43085.1i	−1.34687	+	0.976986i
$211$		−	20118.9i		−	0.451898i	−0.974139	−	0.225949i	$-0.927452\pi$
$211$		−	20118.9i		−	0.451898i	0.974139	−	0.225949i	$-0.0725483\pi$
$212$	23968.4	−	73385.0i	0.533294	−	1.63281i
$213$	35535.3			0.783251
$214$	34332.3	+	47330.4i	0.749679	+	1.03351i
$215$			455.561i			0.00985529i
$216$	36102.6	−	11639.0i	0.773803	−	0.249463i
$217$	−12481.4			−0.265060
$218$	29226.0	−	21199.8i	0.614974	−	0.446087i
$219$		−	52144.2i		−	1.08722i
$220$	58055.3	+	18961.5i	1.19949	+	0.391767i
$221$	−6851.63			−0.140284
$222$	−59258.2	−	81693.2i	−1.20238	−	1.65760i
$223$			43114.5i			0.866989i	0.901156	+	0.433495i	$0.142720\pi$
$223$			43114.5i			0.866989i	−0.901156	+	0.433495i	$0.857280\pi$
$224$	283.075	−	74048.8i	0.00564164	−	1.47578i
$225$	119.726			0.00236496
$226$	−33233.5	+	24106.8i	−0.650668	+	0.471978i
$227$		−	82478.6i		−	1.60062i	−0.599584	−	0.800312i	$-0.704667\pi$
$227$		−	82478.6i		−	1.60062i	0.599584	−	0.800312i	$-0.295333\pi$
$228$	7458.65	−	22836.5i	0.143480	−	0.439298i
$229$	−18516.8			−0.353098			−0.176549	−	0.984292i	$-0.556493\pi$
$229$	−18516.8			−0.353098			−0.176549	+	0.984292i	$0.556493\pi$
$230$	56488.7	+	77875.2i	1.06784	+	1.47212i
$231$			112984.i			2.11735i
$232$	−13658.1	−	42365.7i	−0.253755	−	0.787116i
$233$	86558.6			1.59440			0.797202	−	0.603713i	$-0.206313\pi$
$233$	86558.6			1.59440			0.797202	+	0.603713i	$0.206313\pi$
$234$	−3914.59	+	2839.55i	−0.0714915	+	0.0518582i
$235$			18812.4i			0.340651i
$236$	96731.4	+	31593.5i	1.73677	+	0.567250i
$237$	−43156.9			−0.768340
$238$	21979.9	+	30301.4i	0.388035	+	0.534944i
$239$		−	78590.3i		−	1.37586i	−0.725779	−	0.687928i	$-0.758521\pi$
$239$		−	78590.3i		−	1.37586i	0.725779	−	0.687928i	$-0.241479\pi$
$240$	38332.3	−	52422.0i	0.665492	−	0.910105i
$241$	−81006.8			−1.39472			−0.697360	−	0.716721i	$-0.745642\pi$
$241$	−81006.8			−1.39472			−0.697360	+	0.716721i	$0.745642\pi$
$242$	28714.9	−	20829.1i	0.490317	−	0.355663i
$243$			32383.0i			0.548409i
$244$	2985.37	−	9140.45i	0.0501440	−	0.153528i
$245$	70410.1			1.17301
$246$	19914.0	+	27453.4i	0.329070	+	0.453655i
$247$		−	7801.13i		−	0.127869i
$248$	10513.6	−	3389.43i	0.170942	−	0.0551092i
$249$	−94340.3			−1.52159
$250$	−50801.6	+	36850.2i	−0.812826	+	0.589603i
$251$		−	25243.3i		−	0.400681i	−0.979726	−	0.200340i	$-0.935795\pi$
$251$		−	25243.3i		−	0.400681i	0.979726	−	0.200340i	$-0.0642048\pi$
$252$	25115.8	+	8203.10i	0.395500	+	0.129175i
$253$	148133.			2.31425
$254$	−39683.6	−	54707.7i	−0.615097	−	0.847971i
$255$			32829.7i			0.504877i
$256$	19870.1	+	62451.1i	0.303194	+	0.952929i
$257$	38812.4			0.587630			0.293815	−	0.955862i	$-0.405075\pi$
$257$	38812.4			0.587630			0.293815	+	0.955862i	$0.405075\pi$
$258$	603.765	−	437.956i	0.00907044	−	0.00657947i
$259$			179050.i			2.66917i
$260$	6547.32	−	20046.2i	0.0968538	−	0.296542i
$261$	15882.6			0.233153
$262$	14426.4	+	19888.2i	0.210163	+	0.289730i
$263$			88485.0i			1.27926i	0.768684	+	0.639629i	$0.220912\pi$
$263$			88485.0i			1.27926i	−0.768684	+	0.639629i	$0.779088\pi$
$264$	−30681.7	−	95170.8i	−0.440222	−	1.36551i
$265$	−120118.			−1.71047
$266$	−34500.5	+	25025.8i	−0.487599	+	0.353692i
$267$			136250.i			1.91124i
$268$	−31161.4	−	10177.7i	−0.433858	−	0.141703i
$269$	−59385.2			−0.820680			−0.410340	−	0.911933i	$-0.634590\pi$
$269$	−59385.2			−0.820680			−0.410340	+	0.911933i	$0.634590\pi$
$270$	−34654.6	−	47774.8i	−0.475372	−	0.655347i
$271$			79890.9i			1.08782i	0.839142	+	0.543912i	$0.183057\pi$
$271$			79890.9i			1.08782i	−0.839142	+	0.543912i	$0.816943\pi$
$272$	−26743.1	−	19555.2i	−0.361471	−	0.264317i
$273$	39012.8			0.523457
$274$	−7756.53	+	5626.40i	−0.103316	+	0.0749427i
$275$			803.887i			0.0106299i
$276$	48904.0	−	149732.i	0.641987	−	1.96560i
$277$	110068.			1.43450			0.717252	−	0.696814i	$-0.245400\pi$
$277$	110068.			1.43450			0.717252	+	0.696814i	$0.245400\pi$
$278$	−20627.6	−	28437.2i	−0.266907	−	0.367957i
$279$			3941.47i			0.0506349i
$280$	−109658.	+	35352.2i	−1.39870	+	0.450921i
$281$	−58132.0			−0.736212			−0.368106	−	0.929784i	$-0.619994\pi$
$281$	−58132.0			−0.736212			−0.368106	+	0.929784i	$0.619994\pi$
$282$	24932.6	−	18085.5i	0.313522	−	0.227421i
$283$			8268.13i			0.103237i	0.998667	+	0.0516184i	$0.0164380\pi$
$283$			8268.13i			0.103237i	−0.998667	+	0.0516184i	$0.983562\pi$
$284$	53039.1	+	17323.2i	0.657597	+	0.214778i
$285$	−37379.2			−0.460193
$286$	−19065.8	−	26284.0i	−0.233089	−	0.321336i
$287$		−	60170.7i		−	0.730502i
$288$	−23383.7	−	89.3914i	−0.281921	−	0.00107773i
$289$	−66773.0			−0.799475
$290$	−56062.9	+	40666.6i	−0.666622	+	0.483551i
$291$		−	21519.7i		−	0.254126i
$292$	25419.9	−	77829.2i	0.298131	−	0.912802i
$293$	5326.36			0.0620433			0.0310217	−	0.999519i	$-0.490124\pi$
$293$	5326.36			0.0620433			0.0310217	+	0.999519i	$0.490124\pi$
$294$	−67689.1	−	93316.0i	−0.783113	−	1.07960i
$295$		−	158332.i		−	1.81938i
$296$	−48622.6	−	150821.i	−0.554951	−	1.72139i
$297$	−90876.3			−1.03024
$298$	84420.4	−	61236.5i	0.950638	−	0.689569i
$299$		−	51149.5i		−	0.572136i
$300$	812.563	+	265.392i	0.00902848	+	0.00294880i
$301$	−1323.30			−0.0146058
$302$	60215.1	+	83012.4i	0.660224	+	0.910183i
$303$			40750.1i			0.443857i
$304$	22265.2	−	30449.2i	0.240924	−	0.329479i
$305$	−14961.3			−0.160831
$306$	9568.78	−	6940.95i	0.102191	−	0.0741270i
$307$		−	101763.i		−	1.07972i	−0.841753	−	0.539862i	$-0.818476\pi$
$307$		−	101763.i		−	1.07972i	0.841753	−	0.539862i	$-0.181524\pi$
$308$	−55078.7	+	168637.i	−0.580607	+	1.77767i
$309$	−124449.			−1.30339
$310$	−10091.9	−	13912.7i	−0.105015	−	0.144773i
$311$			179161.i			1.85234i	0.377102	+	0.926172i	$0.376921\pi$
$311$			179161.i			1.85234i	−0.377102	+	0.926172i	$0.623079\pi$
$312$	−32862.0	+	10594.2i	−0.337586	+	0.108833i
$313$	43952.4			0.448636			0.224318	−	0.974516i	$-0.427985\pi$
$313$	43952.4			0.448636			0.224318	+	0.974516i	$0.427985\pi$
$314$	104118.	−	75524.9i	1.05601	−	0.766004i
$315$		−	41110.0i		−	0.414311i
$316$	−64414.9	−	21038.6i	−0.645078	−	0.210690i
$317$	94646.3			0.941857			0.470929	−	0.882171i	$-0.343919\pi$
$317$	94646.3			0.941857			0.470929	+	0.882171i	$0.343919\pi$
$318$	115476.	+	159195.i	1.14193	+	1.57426i
$319$			106642.i			1.04796i
$320$	82769.2	−	59557.2i	0.808293	−	0.581613i
$321$	−148955.			−1.44559
$322$	−226209.	+	164086.i	−2.18172	+	1.58256i
$323$			19069.0i			0.182778i
$324$	−39190.0	+	119990.i	−0.373323	+	1.14302i
$325$	277.578			0.00262796
$326$	67725.4	+	93366.1i	0.637260	+	0.878525i
$327$			91978.1i			0.860179i
$328$	16339.9	+	50684.2i	0.151880	+	0.471113i
$329$	−54645.7			−0.504852
$330$	−125940.	+	91353.9i	−1.15648	+	0.838879i
$331$		−	156370.i		−	1.42724i	−0.700532	−	0.713621i	$-0.747054\pi$
$331$		−	156370.i		−	1.42724i	0.700532	−	0.713621i	$-0.252946\pi$
$332$	−140810.	−	45990.1i	−1.27749	−	0.417243i
$333$	56541.8			0.509895
$334$	−61142.1	−	84290.4i	−0.548085	−	0.755588i
$335$			51005.6i			0.454494i
$336$	152274.	+	111346.i	1.34879	+	0.986273i
$337$	124028.			1.09209			0.546046	−	0.837755i	$-0.316132\pi$
$337$	124028.			1.09209			0.546046	+	0.837755i	$0.316132\pi$
$338$	83400.9	−	60496.9i	0.730024	−	0.529541i
$339$		−	104590.i		−	0.910105i
$340$	−16004.2	+	49000.8i	−0.138445	+	0.423882i
$341$	−26464.5			−0.227591
$342$	7902.84	+	10894.8i	0.0675664	+	0.0931469i
$343$			30899.1i			0.262638i
$344$	1114.66	−	359.352i	0.00941949	−	0.00303671i
$345$	−245084.			−2.05909
$346$	161403.	−	117078.i	1.34822	−	0.977964i
$347$			123524.i			1.02587i	0.858427	+	0.512936i	$0.171442\pi$
$347$			123524.i			1.02587i	−0.858427	+	0.512936i	$0.828558\pi$
$348$	107793.	+	35206.3i	0.890084	+	0.290711i
$349$	156067.			1.28133			0.640663	−	0.767823i	$-0.278660\pi$
$349$	156067.			1.28133			0.640663	+	0.767823i	$0.278660\pi$
$350$	−890.464	−	1227.59i	−0.00726910	−	0.0100212i
$351$			31379.2i			0.254699i
$352$	600.208	−	157007.i	0.00484413	−	1.26716i
$353$	−29134.2			−0.233805			−0.116902	−	0.993143i	$-0.537296\pi$
$353$	−29134.2			−0.233805			−0.116902	+	0.993143i	$0.537296\pi$
$354$	−209841.	+	152213.i	−1.67449	+	1.21463i
$355$		−	86815.5i		−	0.688875i
$356$	−66420.9	+	203364.i	−0.524089	+	1.60463i
$357$	−95362.4			−0.748239
$358$	6414.45	+	8842.94i	0.0500487	+	0.0689971i
$359$		−	16202.4i		−	0.125716i	−0.998022	−	0.0628581i	$-0.979978\pi$
$359$		−	16202.4i		−	0.125716i	0.998022	−	0.0628581i	$-0.0200216\pi$
$360$	11163.8	+	34628.6i	0.0861402	+	0.267196i
$361$	108609.			0.833399
$362$	8818.20	−	6396.50i	0.0672919	−	0.0488119i
$363$			90369.6i			0.685818i
$364$	58229.5	+	19018.4i	0.439481	+	0.143539i
$365$	−127392.			−0.956219
$366$	14383.1	+	19828.5i	0.107372	+	0.148022i
$367$		−	116180.i		−	0.862577i	−0.902214	−	0.431288i	$-0.858059\pi$
$367$		−	116180.i		−	0.862577i	0.902214	−	0.431288i	$-0.141941\pi$
$368$	145986.	−	199645.i	1.07799	−	1.47423i
$369$	−19001.1			−0.139549
$370$	−199583.	+	144772.i	−1.45787	+	1.05750i
$371$		−	348914.i		−	2.53496i
$372$	−8736.89	+	26750.1i	−0.0631351	+	0.193304i
$373$	−147034.			−1.05682			−0.528411	−	0.848989i	$-0.677212\pi$
$373$	−147034.			−1.05682			−0.528411	+	0.848989i	$0.677212\pi$
$374$	46604.2	+	64248.4i	0.333182	+	0.459324i
$375$		−	159879.i		−	1.13692i
$376$	46030.2	−	14839.5i	0.325587	−	0.104965i
$377$	36822.9			0.259081
$378$	138774.	−	100664.i	0.971239	−	0.704512i
$379$		−	205935.i		−	1.43368i	−0.697239	−	0.716838i	$-0.745589\pi$
$379$		−	205935.i		−	1.43368i	0.697239	−	0.716838i	$-0.254411\pi$
$380$	−55791.3	−	18222.1i	−0.386366	−	0.126192i
$381$	172172.			1.18608
$382$	−24033.1	−	33131.9i	−0.164696	−	0.227049i
$383$		−	84354.1i		−	0.575054i	−0.957773	−	0.287527i	$-0.907167\pi$
$383$		−	84354.1i		−	0.575054i	0.957773	−	0.287527i	$-0.0928331\pi$
$384$	−158503.	−	52440.3i	−1.07492	−	0.355633i
$385$	276028.			1.86222
$386$	73279.8	−	53155.4i	0.491824	−	0.356757i
$387$			417.880i			0.00279016i
$388$	10490.7	−	32119.7i	0.0696850	−	0.213358i
$389$	−156642.			−1.03517			−0.517583	−	0.855633i	$-0.673168\pi$
$389$	−156642.			−1.03517			−0.517583	+	0.855633i	$0.673168\pi$
$390$	31544.0	+	43486.5i	0.207390	+	0.285907i
$391$			125029.i			0.817821i
$392$	−55540.4	−	172279.i	−0.361440	−	1.12114i
$393$	−62590.8			−0.405252
$394$	135488.	−	98279.5i	0.872787	−	0.633098i
$395$			105436.i			0.675761i
$396$	53253.4	+	17393.1i	0.339592	+	0.110914i
$397$	196457.			1.24648			0.623241	−	0.782030i	$-0.285815\pi$
$397$	196457.			1.24648			0.623241	+	0.782030i	$0.285815\pi$
$398$	80768.4	+	111347.i	0.509888	+	0.702931i
$399$		−	108578.i		−	0.682017i
$400$	1083.44	+	792.236i	0.00677148	+	0.00495148i
$401$	−159939.			−0.994639			−0.497319	−	0.867568i	$-0.665682\pi$
$401$	−159939.			−0.994639			−0.497319	+	0.867568i	$0.665682\pi$
$402$	67598.9	−	49034.5i	0.418300	−	0.303424i
$403$			9138.07i			0.0562658i
$404$	−19865.3	+	60822.6i	−0.121712	+	0.372651i
$405$	196402.			1.19739
$406$	−118127.	−	162849.i	−0.716633	−	0.987948i
$407$			379643.i			2.29185i
$408$	80327.5	−	25896.4i	0.482552	−	0.155568i
$409$	93337.3			0.557967			0.278983	−	0.960296i	$-0.410003\pi$
$409$	93337.3			0.557967			0.278983	+	0.960296i	$0.410003\pi$
$410$	67070.8	−	48651.5i	0.398993	−	0.289420i
$411$		−	24410.8i		−	0.144510i
$412$	−185750.	−	60668.0i	−1.09429	−	0.357409i
$413$	459916.			2.69636
$414$	51816.4	+	71433.9i	0.302320	+	0.416777i
$415$			230481.i			1.33825i
$416$	−54213.6	−	207.249i	−0.313272	−	0.00119758i
$417$	89495.5			0.514670
$418$	−73152.0	+	53062.6i	−0.418672	+	0.303694i
$419$		−	305072.i		−	1.73770i	−0.495075	−	0.868850i	$-0.664859\pi$
$419$		−	305072.i		−	1.73770i	0.495075	−	0.868850i	$-0.335141\pi$
$420$	91126.9	−	279007.i	0.516592	−	1.58167i
$421$	302106.			1.70449			0.852246	−	0.523141i	$-0.175240\pi$
$421$	302106.			1.70449			0.852246	+	0.523141i	$0.175240\pi$
$422$	47252.7	+	65142.4i	0.265339	+	0.365796i
$423$			17256.4i			0.0964428i
$424$	94750.6	+	293904.i	0.527048	+	1.63484i
$425$	−678.509			−0.00375645
$426$	−115058.	+	83460.6i	−0.634015	+	0.459899i
$427$		−	43458.9i		−	0.238354i
$428$	−222327.	−	72614.3i	−1.21368	−	0.396401i
$429$	82719.3			0.449461
$430$	−1069.96	−	1475.04i	−0.00578670	−	0.00797752i
$431$		−	77178.0i		−	0.415469i	−0.978185	−	0.207735i	$-0.933391\pi$
$431$		−	77178.0i		−	0.415469i	0.978185	−	0.207735i	$-0.0666090\pi$
$432$	−89559.2	+	122478.i	−0.479891	+	0.656283i
$433$	−10452.0			−0.0557471			−0.0278735	−	0.999611i	$-0.508874\pi$
$433$	−10452.0			−0.0557471			−0.0278735	+	0.999611i	$0.508874\pi$
$434$	40413.1	−	29314.7i	0.214557	−	0.155634i
$435$		−	176437.i		−	0.932421i
$436$	−44838.6	+	137284.i	−0.235873	+	0.722184i
$437$	−142356.			−0.745440
$438$	122469.	+	168836.i	0.638379	+	0.880068i
$439$			132395.i			0.686978i	0.939157	+	0.343489i	$0.111609\pi$
$439$			132395.i			0.686978i	−0.939157	+	0.343489i	$0.888391\pi$
$440$	−232510.	+	74957.8i	−1.20098	+	0.387179i
$441$	64586.2			0.332095
$442$	22184.6	−	16092.2i	0.113555	−	0.0823703i
$443$		−	165537.i		−	0.843506i	−0.906711	−	0.421753i	$-0.861415\pi$
$443$		−	165537.i		−	0.843506i	0.906711	−	0.421753i	$-0.138585\pi$
$444$	383740.	+	125334.i	1.94658	+	0.635773i
$445$	332870.			1.68095
$446$	−101262.	−	139599.i	−0.509067	−	0.701798i
$447$			265682.i			1.32968i
$448$	172999.	+	240425.i	0.861963	+	1.19791i
$449$	356427.			1.76798			0.883991	−	0.467504i	$-0.154847\pi$
$449$	356427.			1.76798			0.883991	+	0.467504i	$0.154847\pi$
$450$	−387.658	+	281.197i	−0.00191436	+	0.00138863i
$451$		−	127581.i		−	0.627238i
$452$	50986.9	−	156109.i	0.249564	−	0.764101i
$453$	−261251.			−1.27310
$454$	193715.	+	267054.i	0.939833	+	1.29565i
$455$		−	95311.2i		−	0.460385i
$456$	29485.2	+	91459.4i	0.141799	+	0.439844i
$457$	−146481.			−0.701375			−0.350688	−	0.936493i	$-0.614052\pi$
$457$	−146481.			−0.701375			−0.350688	+	0.936493i	$0.614052\pi$
$458$	59955.0	−	43489.8i	0.285821	−	0.207327i
$459$		−	76702.9i		−	0.364071i
$460$	−365806.	−	119476.i	−1.72876	−	0.564633i
$461$	−359443.			−1.69133			−0.845665	−	0.533714i	$-0.820796\pi$
$461$	−359443.			−1.69133			−0.845665	+	0.533714i	$0.820796\pi$
$462$	−265361.	−	365826.i	−1.24324	−	1.71392i
$463$		−	302942.i		−	1.41318i	−0.707622	−	0.706591i	$-0.750232\pi$
$463$		−	302942.i		−	1.41318i	0.707622	−	0.706591i	$-0.249768\pi$
$464$	143726.	+	105096.i	0.667574	+	0.488147i
$465$	43785.1			0.202498
$466$	−280265.	+	203297.i	−1.29062	+	0.936181i
$467$			326415.i			1.49671i	0.663300	+	0.748353i	$0.269155\pi$
$467$			326415.i			1.49671i	−0.663300	+	0.748353i	$0.730845\pi$
$468$	6005.77	−	18388.1i	0.0274206	−	0.0839549i
$469$	−148159.			−0.673571
$470$	−44184.2	−	60912.2i	−0.200019	−	0.275745i
$471$			327675.i			1.47707i
$472$	−387406.	+	124894.i	−1.73893	+	0.560606i
$473$	−2805.80			−0.0125411
$474$	139736.	−	101361.i	0.621945	−	0.451144i
$475$		−	772.538i		−	0.00342399i
$476$	−142336.	−	46488.4i	−0.628202	−	0.205178i
$477$	−110183.			−0.484258
$478$	184582.	+	254465.i	0.807856	+	1.11371i
$479$			433227.i			1.88818i	0.329683	+	0.944092i	$0.393058\pi$
$479$			433227.i			1.88818i	−0.329683	+	0.944092i	$0.606942\pi$
$480$	−993.035	+	259765.i	−0.00431005	+	1.12745i
$481$	131089.			0.566598
$482$	262289.	−	190258.i	1.12898	−	0.818933i
$483$		−	711910.i		−	3.05162i
$484$	−44054.4	+	134883.i	−0.188061	+	0.575795i
$485$	−52574.2			−0.223506
$486$	−76056.8	−	104852.i	−0.322007	−	0.443918i
$487$		−	362697.i		−	1.52928i	−0.644460	−	0.764638i	$-0.722918\pi$
$487$		−	362697.i		−	1.52928i	0.644460	−	0.764638i	$-0.277082\pi$
$488$	11801.6	+	36607.2i	0.0495567	+	0.153719i
$489$	−293835.			−1.22881
$490$	−227978.	+	165370.i	−0.949514	+	0.688754i
$491$			81321.4i			0.337320i	0.985674	+	0.168660i	$0.0539440\pi$
$491$			81321.4i			0.337320i	−0.985674	+	0.168660i	$0.946056\pi$
$492$	−128958.	−	42119.0i	−0.532742	−	0.174000i
$493$	−90009.5			−0.370335
$494$	18322.3	+	25259.0i	0.0750801	+	0.103505i
$495$		−	87166.2i		−	0.355744i
$496$	−26080.9	+	35667.5i	−0.106013	+	0.144980i
$497$	252178.			1.02093
$498$	305461.	−	221574.i	1.23168	−	0.893429i
$499$		−	111106.i		−	0.446206i	−0.974795	−	0.223103i	$-0.928381\pi$
$499$		−	111106.i		−	0.446206i	0.974795	−	0.223103i	$-0.0716186\pi$
$500$	77939.9	−	238632.i	0.311759	−	0.954528i
$501$	265273.			1.05686
$502$	59288.1	+	81734.4i	0.235266	+	0.324338i
$503$		−	88040.8i		−	0.347975i	−0.984748	−	0.173987i	$-0.944335\pi$
$503$		−	88040.8i		−	0.347975i	0.984748	−	0.173987i	$-0.0556652\pi$
$504$	−100588.	+	32428.1i	−0.395991	+	0.127662i
$505$	99555.7			0.390376
$506$	−479634.	+	347915.i	−1.87331	+	1.35885i
$507$			262474.i			1.02110i
$508$	256980.	+	83932.6i	0.995801	+	0.325240i
$509$	−306244.			−1.18204			−0.591019	−	0.806658i	$-0.701274\pi$
$509$	−306244.			−1.18204			−0.591019	+	0.806658i	$0.701274\pi$
$510$	−77105.9	−	106298.i	−0.296447	−	0.408681i
$511$		−	370044.i		−	1.41714i
$512$	−211014.	−	155540.i	−0.804953	−	0.593338i
$513$	87332.4			0.331849
$514$	−125669.	+	91157.3i	−0.475666	+	0.345037i
$515$			304039.i			1.14634i
$516$	−926.296	+	2836.08i	−0.00347897	+	0.0106517i
$517$	−115866.			−0.433486
$518$	−420529.	−	579741.i	−1.56724	−	2.16060i
$519$			507958.i			1.88579i
$520$	25882.5	+	80284.4i	0.0957195	+	0.296910i
$521$	−96690.4			−0.356211			−0.178106	−	0.984011i	$-0.556997\pi$
$521$	−96690.4			−0.356211			−0.178106	+	0.984011i	$0.556997\pi$
$522$	−51425.7	+	37303.0i	−0.188729	+	0.136900i
$523$		−	48389.7i		−	0.176909i	−0.996080	−	0.0884545i	$-0.971807\pi$
$523$		−	48389.7i		−	0.176909i	0.996080	−	0.0884545i	$-0.0281928\pi$
$524$	−93421.6	−	30512.5i	−0.340239	−	0.111126i
$525$	3863.39			0.0140168
$526$	−207822.	−	286502.i	−0.751137	−	1.03552i
$527$		−	22337.0i		−	0.0804273i
$528$	322868.	+	236089.i	1.15813	+	0.846853i
$529$	−653542.			−2.33540
$530$	388926.	−	282117.i	1.38457	−	1.00433i
$531$		−	145236.i		−	0.515091i
$532$	52930.8	−	162061.i	0.187019	−	0.572604i
$533$	−44053.0			−0.155068
$534$	−320007.	−	441160.i	−1.12222	−	1.54708i
$535$			363909.i			1.27141i
$536$	124800.	−	40233.9i	0.434397	−	0.140043i
$537$	−27829.9			−0.0965079
$538$	192281.	−	139476.i	0.664313	−	0.481876i
$539$			433656.i			1.49268i
$540$	224414.	+	73296.1i	0.769596	+	0.251358i
$541$	−321785.			−1.09944			−0.549719	−	0.835350i	$-0.685265\pi$
$541$	−321785.			−1.09944			−0.549719	+	0.835350i	$0.685265\pi$
$542$	−187637.	−	258676.i	−0.638734	−	0.880557i
$543$			27752.0i			0.0941229i
$544$	132519.	+	506.596i	0.447797	+	0.00171184i
$545$	224710.			0.756534
$546$	−126318.	+	91628.0i	−0.423721	+	0.307357i
$547$		−	255441.i		−	0.853722i	−0.904317	−	0.426861i	$-0.859619\pi$
$547$		−	255441.i		−	0.853722i	0.904317	−	0.426861i	$-0.140381\pi$
$548$	11900.1	−	36435.0i	0.0396268	−	0.121327i
$549$	−13723.8			−0.0455333
$550$	−1888.06	−	2602.88i	−0.00624153	−	0.00860456i
$551$		−	102483.i		−	0.337558i
$552$	193325.	+	599670.i	0.634468	+	1.96804i
$553$	−306266.			−1.00149
$554$	−356385.	+	258513.i	−1.16118	+	0.842293i
$555$		−	628113.i		−	2.03916i
$556$	133579.	+	43628.3i	0.432104	+	0.141130i
$557$	97319.4			0.313681			0.156841	−	0.987624i	$-0.449869\pi$
$557$	97319.4			0.313681			0.156841	+	0.987624i	$0.449869\pi$
$558$	−9257.20	−	12762.0i	−0.0297311	−	0.0409872i
$559$			968.830i			0.00310044i
$560$	272028.	−	372016.i	0.867435	−	1.18628i
$561$	−202198.			−0.642468
$562$	188224.	−	136533.i	0.595939	−	0.432279i
$563$			185399.i			0.584912i	0.956279	+	0.292456i	$0.0944725\pi$
$563$			185399.i			0.584912i	−0.956279	+	0.292456i	$0.905528\pi$
$564$	−38251.5	+	117116.i	−0.120252	+	0.368180i
$565$	−255522.			−0.800445
$566$	−19419.1	−	26771.1i	−0.0606172	−	0.0835667i
$567$			570500.i			1.77456i
$568$	−212420.	+	68481.1i	−0.658413	+	0.212263i
$569$	−486829.			−1.50367			−0.751834	−	0.659352i	$-0.770831\pi$
$569$	−486829.			−1.50367			−0.751834	+	0.659352i	$0.770831\pi$
$570$	121029.	−	87791.3i	0.372511	−	0.270210i
$571$			219913.i			0.674496i	0.941416	+	0.337248i	$0.109496\pi$
$571$			219913.i			0.674496i	−0.941416	+	0.337248i	$0.890504\pi$
$572$	123465.	+	40325.0i	0.377356	+	0.123249i
$573$	104270.			0.317579
$574$	141321.	+	194825.i	0.428926	+	0.591317i
$575$		−	5065.28i		−	0.0153203i
$576$	75923.1	−	54631.0i	0.228838	−	0.164662i
$577$	123975.			0.372377			0.186189	−	0.982514i	$-0.440386\pi$
$577$	123975.			0.372377			0.186189	+	0.982514i	$0.440386\pi$
$578$	216202.	−	156827.i	0.647148	−	0.469425i
$579$			230621.i			0.687927i
$580$	86011.7	−	263346.i	0.255683	−	0.782836i
$581$	−669492.			−1.98332
$582$	50542.5	+	69677.8i	0.149214	+	0.205707i
$583$		−	739807.i		−	2.17661i
$584$	100489.	+	311703.i	0.294640	+	0.913935i
$585$	−30098.0			−0.0879481
$586$	−17246.0	+	12509.8i	−0.0502220	+	0.0364298i
$587$			282593.i			0.820135i	0.912055	+	0.410067i	$0.134495\pi$
$587$			282593.i			0.820135i	−0.912055	+	0.410067i	$0.865505\pi$
$588$	438336.	+	143166.i	1.26781	+	0.414080i
$589$	25432.5			0.0733091
$590$	371868.	+	512657.i	1.06828	+	1.47273i
$591$			426398.i			1.22079i
$592$	511662.	+	374140.i	1.45996	+	1.06756i
$593$	391544.			1.11345			0.556726	−	0.830696i	$-0.312057\pi$
$593$	391544.			1.11345			0.556726	+	0.830696i	$0.312057\pi$
$594$	294245.	−	213438.i	0.833944	−	0.604922i
$595$			232978.i			0.658082i
$596$	−129518.	+	396551.i	−0.364617	+	1.11637i
$597$	−350424.			−0.983207
$598$	120133.	+	165615.i	0.335939	+	0.463125i
$599$		−	548193.i		−	1.52785i	−0.645307	−	0.763924i	$-0.723270\pi$
$599$		−	548193.i		−	1.52785i	0.645307	−	0.763924i	$-0.276730\pi$
$600$	−3254.29	+	1049.14i	−0.00903969	+	0.00291427i
$601$	571965.			1.58351			0.791755	−	0.610839i	$-0.209168\pi$
$601$	571965.			1.58351			0.791755	+	0.610839i	$0.209168\pi$
$602$	4284.65	−	3107.98i	0.0118229	−	0.00857601i
$603$			46786.8i			0.128673i
$604$	−389937.	−	127358.i	−1.06886	−	0.349101i
$605$	220780.			0.603182
$606$	−95708.4	−	131943.i	−0.260618	−	0.359288i
$607$			228130.i			0.619162i	0.950873	+	0.309581i	$0.100189\pi$
$607$			228130.i			0.619162i	−0.950873	+	0.309581i	$0.899811\pi$
$608$	−576.801	+	150884.i	−0.00156034	+	0.408165i
$609$	512508.			1.38187
$610$	48442.5	−	35139.0i	0.130187	−	0.0944343i
$611$			40008.0i			0.107168i
$612$	−14680.4	+	44947.7i	−0.0391955	+	0.120007i
$613$	473166.			1.25919			0.629597	−	0.776922i	$-0.283220\pi$
$613$	473166.			1.25919			0.629597	+	0.776922i	$0.283220\pi$
$614$	239007.	+	329495.i	0.633978	+	0.874001i
$615$			211081.i			0.558082i
$616$	−217735.	−	675385.i	−0.573807	−	1.77988i
$617$	−256962.			−0.674993			−0.337496	−	0.941327i	$-0.609580\pi$
$617$	−256962.			−0.674993			−0.337496	+	0.941327i	$0.609580\pi$
$618$	402950.	−	292290.i	1.05505	−	0.765309i
$619$			299079.i			0.780557i	0.920697	+	0.390278i	$0.127621\pi$
$619$			299079.i			0.780557i	−0.920697	+	0.390278i	$0.872379\pi$
$620$	65352.7	+	21344.9i	0.170012	+	0.0555278i
$621$	572611.			1.48483
$622$	−420788.	−	580098.i	−1.08763	−	1.49941i
$623$			966909.i			2.49121i
$624$	81520.4	−	111485.i	0.209362	−	0.286316i
$625$	−387321.			−0.991541
$626$	−142312.	+	103230.i	−0.363156	+	0.263424i
$627$		−	230219.i		−	0.585606i
$628$	−159739.	+	489079.i	−0.405033	+	1.24011i
$629$	−320432.			−0.809906
$630$	96553.8	+	133109.i	0.243270	+	0.335371i
$631$		−	568459.i		−	1.42771i	−0.700293	−	0.713856i	$-0.746947\pi$
$631$		−	568459.i		−	1.42771i	0.700293	−	0.713856i	$-0.253053\pi$
$632$	257980.	−	83169.0i	0.645879	−	0.208222i
$633$	−205012.			−0.511648
$634$	−306452.	+	222293.i	−0.762401	+	0.553027i
$635$		−	420630.i		−	1.04317i
$636$	−747792.	−	244237.i	−1.84870	−	0.603806i
$637$	149739.			0.369026
$638$	−250466.	−	345292.i	−0.615329	−	0.848291i
$639$		−	79634.7i		−	0.195030i
$640$	−128116.	+	387235.i	−0.312782	+	0.945399i
$641$	229580.			0.558750			0.279375	−	0.960182i	$-0.409873\pi$
$641$	229580.			0.558750			0.279375	+	0.960182i	$0.409873\pi$
$642$	482296.	−	349846.i	1.17016	−	0.848802i
$643$			206201.i			0.498734i	0.968409	+	0.249367i	$0.0802226\pi$
$643$			206201.i			0.498734i	−0.968409	+	0.249367i	$0.919777\pi$
$644$	347050.	−	1.06258e6i	0.836798	−	2.56206i
$645$	4642.16			0.0111584
$646$	−44786.7	−	61742.9i	−0.107321	−	0.147952i
$647$			625446.i			1.49411i	0.664765	+	0.747053i	$0.268532\pi$
$647$			625446.i			1.49411i	−0.664765	+	0.747053i	$0.731468\pi$
$648$	−154924.	−	480555.i	−0.368951	−	1.14444i
$649$	975166.			2.31520
$650$	−898.761	+	651.939i	−0.00212725	+	0.00154305i
$651$			127185.i			0.300107i
$652$	−438571.	−	143242.i	−1.03168	−	0.336958i
$653$	−358912.			−0.841709			−0.420855	−	0.907128i	$-0.638270\pi$
$653$	−358912.			−0.841709			−0.420855	+	0.907128i	$0.638270\pi$
$654$	−216026.	−	297813.i	−0.505068	−	0.696286i
$655$			152914.i			0.356423i
$656$	−171947.	−	125732.i	−0.399563	−	0.292171i
$657$	−116855.			−0.270718
$658$	176935.	−	128345.i	0.408661	−	0.296432i
$659$			843.217i			0.00194164i	1.00000		0.000970819i	$0.000309021\pi$
$659$			843.217i			0.00194164i	−1.00000		0.000970819i	$0.999691\pi$
$660$	193218.	−	591583.i	0.443566	−	1.35809i
$661$	182593.			0.417908			0.208954	−	0.977925i	$-0.432994\pi$
$661$	182593.			0.417908			0.208954	+	0.977925i	$0.432994\pi$
$662$	367261.	+	506305.i	0.838029	+	1.15530i
$663$			69818.0i			0.158833i
$664$	563940.	−	181806.i	1.27908	−	0.412356i
$665$	−265264.			−0.599839
$666$	−183075.	+	132798.i	−0.412743	+	0.299393i
$667$		−	671949.i		−	1.51037i
$668$	395940.	+	129318.i	0.887312	+	0.289806i
$669$	439336.			0.981623
$670$	−119795.	−	165149.i	−0.266864	−	0.367898i
$671$		−	92146.5i		−	0.204660i
$672$	−754556.	−	2884.53i	−1.67091	−	0.00638758i
$673$	174089.			0.384362			0.192181	−	0.981360i	$-0.438444\pi$
$673$	174089.			0.384362			0.192181	+	0.981360i	$0.438444\pi$
$674$	−401586.	+	291300.i	−0.884012	+	0.641240i
$675$			3107.44i			0.00682018i
$676$	−127954.	+	391762.i	−0.280001	+	0.857292i
$677$	446572.			0.974347			0.487174	−	0.873305i	$-0.338028\pi$
$677$	446572.			0.974347			0.487174	+	0.873305i	$0.338028\pi$
$678$	245647.	+	338649.i	0.534383	+	0.736699i
$679$		−	152716.i		−	0.331241i
$680$	−63267.0	−	196246.i	−0.136823	−	0.424408i
$681$	−840455.			−1.81226
$682$	85688.5	−	62156.3i	0.184227	−	0.133634i
$683$		−	580771.i		−	1.24498i	−0.782627	−	0.622491i	$-0.786121\pi$
$683$		−	580771.i		−	1.24498i	0.782627	−	0.622491i	$-0.213879\pi$
$684$	−51176.6	−	16714.9i	−0.109385	−	0.0357265i
$685$	−59637.5			−0.127098
$686$	−72571.6	−	100047.i	−0.154212	−	0.212596i
$687$			188686.i			0.399785i
$688$	−2765.14	+	3781.51i	−0.00584170	+	0.00798892i
$689$	−255452.			−0.538109
$690$	793547.	−	575619.i	1.66677	−	1.20903i
$691$			588160.i			1.23180i	0.787825	+	0.615899i	$0.211207\pi$
$691$			588160.i			1.23180i	−0.787825	+	0.615899i	$0.788793\pi$
$692$	−247625.	+	758165.i	−0.517110	+	1.58326i
$693$	253197.			0.527220
$694$	−290117.	−	399955.i	−0.602357	−	0.830408i
$695$		−	218644.i		−	0.452657i
$696$	−431706.	+	139176.i	−0.891189	+	0.287307i
$697$	107683.			0.221656
$698$	−505323.	+	366549.i	−1.03719	+	0.752351i
$699$		−	882031.i		−	1.80522i
$700$	5766.41	+	1883.37i	0.0117682	+	0.00384362i
$701$	773222.			1.57350			0.786752	−	0.617269i	$-0.211761\pi$
$701$	773222.			1.57350			0.786752	+	0.617269i	$0.211761\pi$
$702$	−73699.2	−	101601.i	−0.149551	−	0.206170i
$703$		−	364838.i		−	0.738225i
$704$	366813.	+	509776.i	0.740115	+	1.02857i
$705$	191699.			0.385692
$706$	94332.5	−	68426.4i	0.189257	−	0.137282i
$707$			289186.i			0.578546i
$708$	321938.	−	985691.i	0.642252	−	1.96641i
$709$	−132132.			−0.262855			−0.131428	−	0.991326i	$-0.541956\pi$
$709$	−132132.			−0.262855			−0.131428	+	0.991326i	$0.541956\pi$
$710$	203901.	+	281097.i	0.404484	+	0.557621i
$711$			96714.7i			0.191317i
$712$	−262572.	−	814466.i	−0.517951	−	1.60662i
$713$	166753.			0.328015
$714$	308770.	−	223974.i	0.605674	−	0.439341i
$715$		−	202090.i		−	0.395305i
$716$	−41538.2	−	13566.8i	−0.0810255	−	0.0264638i
$717$	−800833.			−1.55777
$718$	38054.1	+	52461.3i	0.0738164	+	0.101763i
$719$			933016.i			1.80481i	0.430890	+	0.902405i	$0.358200\pi$
$719$			933016.i			1.80481i	−0.430890	+	0.902405i	$0.641800\pi$
$720$	−117478.	−	85902.8i	−0.226616	−	0.165708i
$721$	−883162.			−1.69891
$722$	−351663.	+	255087.i	−0.674608	+	0.489344i
$723$			825458.i			1.57913i
$724$	−13528.9	+	41422.0i	−0.0258098	+	0.0790231i
$725$	3646.53			0.00693751
$726$	−212248.	−	292604.i	−0.402689	−	0.555147i
$727$		−	15987.8i		−	0.0302497i	−0.999886	−	0.0151248i	$-0.995185\pi$
$727$		−	15987.8i		−	0.0302497i	0.999886	−	0.0151248i	$-0.00481457\pi$
$728$	−233207.	+	75182.7i	−0.440027	+	0.141858i
$729$	−309045.			−0.581523
$730$	412479.	−	299202.i	0.774027	−	0.561460i
$731$		−	2368.20i		−	0.00443183i
$732$	−93141.0	−	30420.9i	−0.173828	−	0.0567740i
$733$	854378.			1.59016			0.795082	−	0.606501i	$-0.207428\pi$
$733$	854378.			1.59016			0.795082	+	0.606501i	$0.207428\pi$
$734$	272867.	+	376174.i	0.506476	+	0.698227i
$735$		−	717478.i		−	1.32811i
$736$	−3781.90	+	989297.i	−0.00698159	+	1.82630i
$737$	−314144.			−0.578354
$738$	61523.1	−	44627.3i	0.112960	−	0.0819385i
$739$			34036.8i			0.0623247i	0.999514	+	0.0311623i	$0.00992089\pi$
$739$			34036.8i			0.0623247i	−0.999514	+	0.0311623i	$0.990079\pi$
$740$	306200.	−	937507.i	0.559167	−	1.71203i
$741$	−79493.4			−0.144775
$742$	819483.	+	1.12974e6i	1.48844	+	2.05196i
$743$		−	702217.i		−	1.27202i	−0.771681	−	0.636010i	$-0.780584\pi$
$743$		−	702217.i		−	1.27202i	0.771681	−	0.636010i	$-0.219416\pi$
$744$	−34538.3	−	107133.i	−0.0623957	−	0.193544i
$745$	649082.			1.16946
$746$	476078.	−	345335.i	0.855461	−	0.620530i
$747$			211417.i			0.378877i
$748$	−301796.	−	98569.9i	−0.539399	−	0.176174i
$749$	−1.05707e6			−1.88425
$750$	375503.	+	517668.i	0.667561	+	0.920298i
$751$			195616.i			0.346835i	0.984848	+	0.173418i	$0.0554811\pi$
$751$			195616.i			0.346835i	−0.984848	+	0.173418i	$0.944519\pi$
$752$	−114187.	+	156158.i	−0.201920	+	0.276139i
$753$	−257229.			−0.453659
$754$	−119228.	+	86484.7i	−0.209717	+	0.152124i
$755$			638256.i			1.11970i
$756$	−212908.	+	651870.i	−0.372519	+	1.14056i
$757$	−651866.			−1.13754			−0.568770	−	0.822497i	$-0.692581\pi$
$757$	−651866.			−1.13754			−0.568770	+	0.822497i	$0.692581\pi$
$758$	483672.	+	666789.i	0.841807	+	1.16051i
$759$		−	1.50947e6i		−	2.62024i
$760$	223442.	−	72034.6i	0.386846	−	0.124714i
$761$	62603.7			0.108101			0.0540506	−	0.998538i	$-0.482787\pi$
$761$	62603.7			0.108101			0.0540506	+	0.998538i	$0.482787\pi$
$762$	−557471.	+	404375.i	−0.960091	+	0.696426i
$763$			652728.i			1.12120i
$764$	155632.	+	50831.0i	0.266631	+	0.0870847i
$765$	73571.3			0.125715
$766$	198120.	+	273127.i	0.337652	+	0.465487i
$767$		−	336720.i		−	0.572372i
$768$	636376.	−	202476.i	1.07893	−	0.343283i
$769$	−64238.0			−0.108627			−0.0543137	−	0.998524i	$-0.517297\pi$
$769$	−64238.0			−0.108627			−0.0543137	+	0.998524i	$0.517297\pi$
$770$	−893742.	+	648298.i	−1.50741	+	1.09344i
$771$		−	395497.i		−	0.665327i
$772$	−112426.	+	344220.i	−0.188639	+	0.577565i
$773$	−522482.			−0.874404			−0.437202	−	0.899363i	$-0.644031\pi$
$773$	−522482.			−0.874404			−0.437202	+	0.899363i	$0.644031\pi$
$774$	−981.460	−	1353.04i	−0.00163829	−	0.00225854i
$775$			904.933i			0.00150665i
$776$	41471.2	+	128638.i	0.0688689	+	0.213623i
$777$	1.82452e6			3.02208
$778$	507186.	−	367900.i	0.837931	−	0.607814i
$779$			122605.i			0.202039i
$780$	−204271.	−	66717.1i	−0.335751	−	0.109660i
$781$	534697.			0.876609
$782$	−293652.	−	404828.i	−0.480197	−	0.661999i
$783$			412226.i			0.672376i
$784$	584458.	+	427371.i	0.950871	+	0.695301i
$785$	800534.			1.29909
$786$	202661.	−	147005.i	0.328038	−	0.237951i
$787$		−	839298.i		−	1.35509i	−0.735483	−	0.677543i	$-0.763045\pi$
$787$		−	839298.i		−	1.35509i	0.735483	−	0.677543i	$-0.236955\pi$
$788$	−207866.	+	636432.i	−0.334757	+	1.02494i
$789$	901660.			1.44840
$790$	−247633.	−	341386.i	−0.396784	−	0.547006i
$791$		−	742231.i		−	1.18628i
$792$	−213278.	+	68757.8i	−0.340013	+	0.109615i
$793$	−31817.7			−0.0505968
$794$	−636101.	+	461412.i	−1.00899	+	0.731893i
$795$			1.22400e6i			1.93663i
$796$	−523034.	−	170829.i	−0.825475	−	0.269609i
$797$	−815691.			−1.28413			−0.642065	−	0.766650i	$-0.721922\pi$
$797$	−815691.			−1.28413			−0.642065	+	0.766650i	$0.721922\pi$
$798$	255013.	+	351560.i	0.400457	+	0.552069i
$799$		−	97795.0i		−	0.153187i
$800$	−5368.72	−	20.5236i	−0.00838862	−	3.20682e-5i
$801$	305337.			0.475899
$802$	517861.	−	375643.i	0.805127	−	0.584019i
$803$		−	784610.i		−	1.21681i
$804$	−103710.	+	317534.i	−0.160439	+	0.491223i
$805$	−1.73925e6			−2.68392
$806$	−21462.3	−	29587.8i	−0.0330374	−	0.0455452i
$807$			605134.i			0.929190i
$808$	−78530.8	−	243593.i	−0.120287	−	0.373114i
$809$	5626.97			0.00859760			0.00429880	−	0.999991i	$-0.498632\pi$
$809$	5626.97			0.00859760			0.00429880	+	0.999991i	$0.498632\pi$
$810$	−635922.	+	461282.i	−0.969245	+	0.703066i
$811$		−	49129.3i		−	0.0746963i	−0.999302	−	0.0373481i	$-0.988109\pi$
$811$		−	49129.3i		−	0.0746963i	0.999302	−	0.0373481i	$-0.0118910\pi$
$812$	764958.	+	249844.i	1.16018	+	0.378928i
$813$	814087.			1.23166
$814$	−891654.	−	1.22923e6i	−1.34570	−	1.85518i
$815$			717862.i			1.08075i
$816$	−199267.	+	272512.i	−0.299265	+	0.409265i
$817$	2696.38			0.00403959
$818$	−302213.	+	219218.i	−0.451655	+	0.327620i
$819$		−	87427.7i		−	0.130341i
$820$	−102900.	+	315054.i	−0.153034	+	0.468551i
$821$	−1.04729e6			−1.55375			−0.776874	−	0.629656i	$-0.783196\pi$
$821$	−1.04729e6			−1.55375			−0.776874	+	0.629656i	$0.783196\pi$
$822$	57332.9	+	79039.0i	0.0848516	+	0.116976i
$823$		−	463250.i		−	0.683936i	−0.939712	−	0.341968i	$-0.888907\pi$
$823$		−	463250.i		−	0.683936i	0.939712	−	0.341968i	$-0.111093\pi$
$824$	743922.	−	239830.i	1.09565	−	0.353223i
$825$	8191.60			0.0120354
$826$	−1.48915e6	+	1.08019e6i	−2.18262	+	1.58322i
$827$			52507.2i			0.0767728i	0.999263	+	0.0383864i	$0.0122218\pi$
$827$			52507.2i			0.0767728i	−0.999263	+	0.0383864i	$0.987778\pi$
$828$	−335549.	−	109594.i	−0.489435	−	0.159855i
$829$	142541.			0.207411			0.103705	−	0.994608i	$-0.466930\pi$
$829$	142541.			0.207411			0.103705	+	0.994608i	$0.466930\pi$
$830$	−541322.	−	746265.i	−0.785778	−	1.08327i
$831$		−	1.12159e6i		−	1.62417i
$832$	176023.	−	126659.i	0.254286	−	0.182974i
$833$	−366021.			−0.527492
$834$	−289774.	+	210195.i	−0.416608	+	0.302197i
$835$		−	648082.i		−	0.929516i
$836$	112230.	−	343619.i	0.160582	−	0.491660i
$837$	−102299.			−0.146023
$838$	716513.	+	987783.i	1.02032	+	1.40661i
$839$		−	326237.i		−	0.463457i	−0.972780	−	0.231729i	$-0.925562\pi$
$839$		−	326237.i		−	0.463457i	0.972780	−	0.231729i	$-0.0744381\pi$
$840$	360239.	+	1.11741e6i	0.510542	+	1.58364i
$841$	−223541.			−0.316056
$842$	−978178.	+	709546.i	−1.37973	+	1.00082i
$843$			592365.i			0.833554i
$844$	−305996.	−	99941.6i	−0.429566	−	0.140301i
$845$	641243.			0.898068
$846$	−40529.5	−	55873.9i	−0.0566280	−	0.0780672i
$847$			641313.i			0.893930i
$848$	−997073.	−	729085.i	−1.38655	−	1.01388i
$849$	84252.1			0.116887
$850$	2196.92	−	1593.59i	0.00304072	−	0.00220566i
$851$		−	2.39212e6i		−	3.30312i
$852$	176523.	−	540468.i	0.243177	−	0.744545i
$853$	766385.			1.05329			0.526646	−	0.850085i	$-0.323449\pi$
$853$	766385.			1.05329			0.526646	+	0.850085i	$0.323449\pi$
$854$	102070.	+	140714.i	0.139954	+	0.192940i
$855$			83766.9i			0.114588i
$856$	890410.	−	287056.i	1.21519	−	0.391759i
$857$	799521.			1.08860			0.544300	−	0.838891i	$-0.316795\pi$
$857$	799521.			1.08860			0.544300	+	0.838891i	$0.316795\pi$
$858$	−267834.	+	194280.i	−0.363824	+	0.263909i
$859$			326976.i			0.443129i	0.975146	+	0.221564i	$0.0711163\pi$
$859$			326976.i			0.443129i	−0.975146	+	0.221564i	$0.928884\pi$
$860$	6928.77	+	2263.01i	0.00936827	+	0.00305978i
$861$	−613139.			−0.827089
$862$	181265.	+	249892.i	0.243950	+	0.336308i
$863$		−	206376.i		−	0.277101i	−0.990355	−	0.138551i	$-0.955756\pi$
$863$		−	206376.i		−	0.277101i	0.990355	−	0.138551i	$-0.0442443\pi$
$864$	2320.12	−	606913.i	0.00310801	−	0.813015i
$865$	1.24098e6			1.65857
$866$	33842.0	−	24548.2i	0.0451254	−	0.0327328i
$867$			680415.i			0.905182i
$868$	−62001.9	+	189834.i	−0.0822935	+	0.251962i
$869$	−649379.			−0.859921
$870$	414392.	+	571280.i	0.547486	+	0.754763i
$871$			108472.i			0.142982i
$872$	−177254.	−	549819.i	−0.233111	−	0.723080i
$873$	−48225.6			−0.0632775
$874$	460929.	−	334347.i	0.603409	−	0.437698i
$875$		−	1.13459e6i		−	1.48192i
$876$	−793078.	−	259028.i	−1.03349	−	0.337550i
$877$	10327.6			0.0134277			0.00671385	−	0.999977i	$-0.497863\pi$
$877$	10327.6			0.0134277			0.00671385	+	0.999977i	$0.497863\pi$
$878$	−310952.	−	428677.i	−0.403371	−	0.556086i
$879$		−	54275.5i		−	0.0702467i
$880$	576784.	−	788791.i	0.744814	−	1.01858i
$881$	27290.0			0.0351602			0.0175801	−	0.999845i	$-0.494404\pi$
$881$	27290.0			0.0351602			0.0175801	+	0.999845i	$0.494404\pi$
$882$	−209121.	+	151691.i	−0.268820	+	0.194995i
$883$		−	552360.i		−	0.708437i	−0.935163	−	0.354218i	$-0.884747\pi$
$883$		−	552360.i		−	0.708437i	0.935163	−	0.354218i	$-0.115253\pi$
$884$	−34035.7	+	104209.i	−0.0435542	+	0.133352i
$885$	−1.61340e6			−2.05994
$886$	388792.	+	535987.i	0.495278	+	0.682789i
$887$			1.20853e6i			1.53607i	0.640408	+	0.768035i	$0.278765\pi$
$887$			1.20853e6i			1.53607i	−0.640408	+	0.768035i	$0.721235\pi$
$888$	−1.53687e6	+	495464.i	−1.94899	+	0.628327i
$889$	1.22183e6			1.54599
$890$	−1.07779e6	+	781801.i	−1.36067	+	0.986998i
$891$			1.20964e6i			1.52370i
$892$	655742.	+	214173.i	0.824145	+	0.269175i
$893$	111348.			0.139630
$894$	−623999.	−	860243.i	−0.780744	−	1.07633i
$895$			67990.6i			0.0848795i
$896$	−1.12483e6	−	372145.i	−1.40110	−	0.463550i
$897$	−521213.			−0.647784
$898$	−1.15406e6	+	837128.i	−1.43112	+	1.03810i
$899$			120046.i			0.148535i
$900$	594.745	−	1820.96i	0.000734253	−	0.00224809i
$901$	624424.			0.769183
$902$	299645.	+	413089.i	0.368293	+	0.507728i
$903$			13484.4i			0.0165369i
$904$	201559.	+	625210.i	0.246641	+	0.765049i
$905$	67800.4			0.0827818
$906$	845895.	−	613591.i	1.03053	−	0.747520i
$907$			493541.i			0.599942i	0.953948	+	0.299971i	$0.0969770\pi$
$907$			493541.i			0.599942i	−0.953948	+	0.299971i	$0.903023\pi$
$908$	−1.25444e6	−	409715.i	−1.52153	−	0.496947i
$909$	91321.1			0.110521
$910$	223854.	+	308605.i	0.270323	+	0.372666i
$911$		−	662065.i		−	0.797744i	−0.917007	−	0.398872i	$-0.869402\pi$
$911$		−	662065.i		−	0.797744i	0.917007	−	0.398872i	$-0.130598\pi$
$912$	−310277.	−	226882.i	−0.373043	−	0.272779i
$913$	−1.41953e6			−1.70296
$914$	474287.	−	344036.i	0.567739	−	0.411824i
$915$			152455.i			0.182096i
$916$	−91982.9	+	281628.i	−0.109627	+	0.335649i
$917$	−444180.			−0.528226
$918$	180149.	+	248353.i	0.213770	+	0.294703i
$919$			766410.i			0.907466i	0.891138	+	0.453733i	$0.149908\pi$
$919$			766410.i			0.907466i	−0.891138	+	0.453733i	$0.850092\pi$
$920$	1.46504e6	−	472308.i	1.73091	−	0.558020i
$921$	−1.03696e6			−1.22249
$922$	1.16383e6	−	844212.i	1.36907	−	0.993093i
$923$		−	184628.i		−	0.216718i
$924$	1.71841e6	+	561251.i	2.01272	+	0.657375i
$925$	12981.6			0.0151720
$926$	711510.	+	980886.i	0.829773	+	1.14392i
$927$			278891.i			0.324545i
$928$	−712202.	−	2722.61i	−0.827003	−	0.00316148i
$929$	470408.			0.545058			0.272529	−	0.962148i	$-0.412140\pi$
$929$	470408.			0.545058			0.272529	+	0.962148i	$0.412140\pi$
$930$	−141770.	+	102837.i	−0.163915	+	0.118900i
$931$		−	416745.i		−	0.480807i
$932$	429983.	−	1.31650e6i	0.495016	−	1.51561i
$933$	1.82564e6			2.09726
$934$	−766640.	−	1.05689e6i	−0.878816	−	1.21153i
$935$			493986.i			0.565055i
$936$	23741.7	+	73643.8i	0.0270994	+	0.0840591i
$937$	−794757.			−0.905222			−0.452611	−	0.891708i	$-0.649507\pi$
$937$	−794757.			−0.905222			−0.452611	+	0.891708i	$0.649507\pi$
$938$	479720.	−	347977.i	0.545233	−	0.395498i
$939$		−	447874.i		−	0.507955i
$940$	286125.	+	93451.5i	0.323817	+	0.105762i
$941$	−639415.			−0.722111			−0.361055	−	0.932544i	$-0.617583\pi$
$941$	−639415.			−0.722111			−0.361055	+	0.932544i	$0.617583\pi$
$942$	−769598.	−	1.06097e6i	−0.867286	−	1.19564i
$943$			803885.i			0.904004i
$944$	961033.	−	1.31428e6i	1.07844	−	1.47483i
$945$	1.06699e6			1.19481
$946$	9084.81	−	6589.89i	0.0101516	−	0.00736370i
$947$			24436.7i			0.0272485i	0.999907	+	0.0136243i	$0.00433687\pi$
$947$			24436.7i			0.0272485i	−0.999907	+	0.0136243i	$0.995663\pi$
$948$	−214383.	+	656387.i	−0.238547	+	0.730371i
$949$	−270922.			−0.300823
$950$	1814.43	+	2501.37i	0.00201045	+	0.00277160i
$951$		−	964444.i		−	1.06639i
$952$	570049.	−	183776.i	0.628982	−	0.202775i
$953$	−63398.9			−0.0698065			−0.0349033	−	0.999391i	$-0.511112\pi$
$953$	−63398.9			−0.0698065			−0.0349033	+	0.999391i	$0.511112\pi$
$954$	356756.	−	258782.i	0.391990	−	0.284340i
$955$		−	254741.i		−	0.279313i
$956$	−1.19530e6	−	390400.i	−1.30786	−	0.427163i
$957$	1.08668e6			1.18653
$958$	−1.01751e6	−	1.40273e6i	−1.10868	−	1.52842i
$959$		−	173233.i		−	0.188362i
$960$	−606887.	−	843417.i	−0.658514	−	0.915166i
$961$	−29791.0			−0.0322581
$962$	−424448.	+	307884.i	−0.458642	+	0.332688i
$963$			333808.i			0.359952i
$964$	−402404.	+	1.23206e6i	−0.433020	+	1.32580i
$965$	563426.			0.605037
$966$	1.67204e6	+	2.30507e6i	1.79181	+	2.47018i
$967$		−	700573.i		−	0.749205i	−0.927186	−	0.374602i	$-0.877779\pi$
$967$		−	700573.i		−	0.749205i	0.927186	−	0.374602i	$-0.122221\pi$
$968$	−174154.	−	540203.i	−0.185859	−	0.576510i
$969$	194313.			0.206945
$970$	170228.	−	123479.i	0.180921	−	0.131235i
$971$			641959.i			0.680877i	0.940267	+	0.340439i	$0.110576\pi$
$971$			641959.i			0.680877i	−0.940267	+	0.340439i	$0.889424\pi$
$972$	492523.	+	160864.i	0.521308	+	0.170265i
$973$	635110.			0.670847
$974$	851853.	+	1.17436e6i	0.897939	+	1.23790i
$975$		−	2828.52i		−	0.00297543i
$976$	−124190.	−	90811.0i	−0.130373	−	0.0953320i
$977$	−701993.			−0.735434			−0.367717	−	0.929938i	$-0.619860\pi$
$977$	−701993.			−0.735434			−0.367717	+	0.929938i	$0.619860\pi$
$978$	951399.	−	690121.i	0.994683	−	0.721519i
$979$			2.05015e6i			2.13905i
$980$	349765.	−	1.07089e6i	0.364186	−	1.11505i
$981$	206123.			0.214185
$982$	−190997.	−	263308.i	−0.198063	−	0.273049i
$983$		−	776417.i		−	0.803504i	−0.915748	−	0.401752i	$-0.868401\pi$
$983$		−	776417.i		−	0.803504i	0.915748	−	0.401752i	$-0.131599\pi$
$984$	516471.	−	166503.i	0.533404	−	0.171962i
$985$	1.04172e6			1.07369
$986$	291438.	−	211402.i	0.299773	−	0.217448i
$987$			556839.i			0.571604i
$988$	−118650.	−	38752.4i	−0.121550	−	0.0396995i
$989$	17679.3			0.0180748
$990$	204724.	+	282232.i	0.208881	+	0.287963i
$991$		−	981286.i		−	0.999190i	−0.866259	−	0.499595i	$-0.833482\pi$
$991$		−	981286.i		−	0.999190i	0.866259	−	0.499595i	$-0.166518\pi$
$992$	675.651	−	176742.i	0.000686593	−	0.179604i
$993$	−1.59341e6			−1.61595
$994$	−816520.	+	592283.i	−0.826407	+	0.599455i
$995$			856112.i			0.864738i
$996$	−468639.	+	1.43485e6i	−0.472411	+	1.44640i
$997$	−393553.			−0.395925			−0.197963	−	0.980210i	$-0.563432\pi$
$997$	−393553.			−0.395925			−0.197963	+	0.980210i	$0.563432\pi$
$998$	260950.	+	359745.i	0.261997	+	0.361188i
$999$			1.46752e6i			1.47046i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	124.5.b.a.63.12	yes	60
4.3	odd	2	inner	124.5.b.a.63.11	✓	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
124.5.b.a.63.11	✓	60	4.3	odd	2	inner
124.5.b.a.63.12	yes	60	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 124 = 2^{2} \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	124.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-3.23786 + 2.34867i) q^{2} -10.1900i q^{3} +(4.96753 - 15.2093i) q^{4} -24.8949 q^{5} +(23.9329 + 32.9938i) q^{6} -72.3138i q^{7} +(19.6374 + 60.9128i) q^{8} -22.8358 q^{9} +O(q^{10})\)	\(q+(-3.23786 + 2.34867i) q^{2} -10.1900i q^{3} +(4.96753 - 15.2093i) q^{4} -24.8949 q^{5} +(23.9329 + 32.9938i) q^{6} -72.3138i q^{7} +(19.6374 + 60.9128i) q^{8} -22.8358 q^{9} +(80.6064 - 58.4699i) q^{10} -153.328i q^{11} +(-154.983 - 50.6191i) q^{12} -52.9434 q^{13} +(169.841 + 234.142i) q^{14} +253.679i q^{15} +(-206.647 - 151.106i) q^{16} +129.414 q^{17} +(73.9392 - 53.6336i) q^{18} +147.349i q^{19} +(-123.666 + 378.635i) q^{20} -736.877 q^{21} +(360.116 + 496.455i) q^{22} +966.117i q^{23} +(620.701 - 200.105i) q^{24} -5.24293 q^{25} +(171.424 - 124.346i) q^{26} -592.692i q^{27} +(-1099.84 - 359.221i) q^{28} -695.514 q^{29} +(-595.807 - 821.378i) q^{30} -172.601i q^{31} +(1023.99 + 3.91453i) q^{32} -1562.41 q^{33} +(-419.026 + 303.951i) q^{34} +1800.25i q^{35} +(-113.438 + 347.317i) q^{36} -2476.02 q^{37} +(-346.073 - 477.095i) q^{38} +539.492i q^{39} +(-488.872 - 1516.42i) q^{40} +832.078 q^{41} +(2385.91 - 1730.68i) q^{42} -18.2993i q^{43} +(-2332.02 - 761.662i) q^{44} +568.495 q^{45} +(-2269.09 - 3128.16i) q^{46} -755.674i q^{47} +(-1539.76 + 2105.73i) q^{48} -2828.29 q^{49} +(16.9759 - 12.3139i) q^{50} -1318.73i q^{51} +(-262.998 + 805.233i) q^{52} +4825.00 q^{53} +(1392.04 + 1919.06i) q^{54} +3817.09i q^{55} +(4404.84 - 1420.06i) q^{56} +1501.48 q^{57} +(2251.98 - 1633.53i) q^{58} +6360.00i q^{59} +(3858.28 + 1260.16i) q^{60} +600.977 q^{61} +(405.381 + 558.858i) q^{62} +1651.34i q^{63} +(-3324.74 + 2392.34i) q^{64} +1318.02 q^{65} +(5058.87 - 3669.58i) q^{66} -2048.84i q^{67} +(642.870 - 1968.30i) q^{68} +9844.72 q^{69} +(-4228.18 - 5828.96i) q^{70} +3487.28i q^{71} +(-448.436 - 1390.99i) q^{72} +5117.20 q^{73} +(8017.01 - 5815.34i) q^{74} +53.4253i q^{75} +(2241.07 + 731.959i) q^{76} -11087.7 q^{77} +(-1267.09 - 1746.80i) q^{78} -4235.23i q^{79} +(5144.47 + 3761.76i) q^{80} -7889.23 q^{81} +(-2694.15 + 1954.27i) q^{82} -9258.14i q^{83} +(-3660.46 + 11207.4i) q^{84} -3221.76 q^{85} +(42.9791 + 59.2508i) q^{86} +7087.28i q^{87} +(9339.64 - 3010.97i) q^{88} -13371.0 q^{89} +(-1840.71 + 1335.20i) q^{90} +3828.54i q^{91} +(14694.0 + 4799.22i) q^{92} -1758.80 q^{93} +(1774.83 + 2446.77i) q^{94} -3668.23i q^{95} +(39.8890 - 10434.5i) q^{96} +2111.84 q^{97} +(9157.62 - 6642.71i) q^{98} +3501.36i 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

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