LMFDB - Embedded newform 136.4.c.b.69.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [136,4,Mod(69,136)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(136, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("136.69");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 136 = 2^{3} \cdot 17 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	136.c (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:	$8.02425976078$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			69.13
Character	$\chi$	$=$	136.69
Dual form			136.4.c.b.69.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.705834 - 2.73894i) q^{2} +9.36589i q^{3} +(-7.00360 - 3.86648i) q^{4} -7.78969i q^{5} +(25.6526 + 6.61076i) q^{6} +32.6671 q^{7} +(-15.5334 + 16.4533i) q^{8} -60.7198 q^{9} +O(q^{10})$	\(q+(0.705834 - 2.73894i) q^{2} +9.36589i q^{3} +(-7.00360 - 3.86648i) q^{4} -7.78969i q^{5} +(25.6526 + 6.61076i) q^{6} +32.6671 q^{7} +(-15.5334 + 16.4533i) q^{8} -60.7198 q^{9} +(-21.3355 - 5.49823i) q^{10} +63.1812i q^{11} +(36.2130 - 65.5949i) q^{12} +14.6588i q^{13} +(23.0576 - 89.4733i) q^{14} +72.9573 q^{15} +(34.1007 + 54.1585i) q^{16} +17.0000 q^{17} +(-42.8581 + 166.308i) q^{18} +102.287i q^{19} +(-30.1187 + 54.5558i) q^{20} +305.957i q^{21} +(173.050 + 44.5954i) q^{22} +25.9454 q^{23} +(-154.100 - 145.484i) q^{24} +64.3207 q^{25} +(40.1495 + 10.3467i) q^{26} -315.816i q^{27} +(-228.787 - 126.307i) q^{28} +34.7232i q^{29} +(51.4958 - 199.826i) q^{30} -7.62186 q^{31} +(172.406 - 55.1729i) q^{32} -591.748 q^{33} +(11.9992 - 46.5620i) q^{34} -254.467i q^{35} +(425.257 + 234.772i) q^{36} -150.046i q^{37} +(280.158 + 72.1975i) q^{38} -137.292 q^{39} +(128.166 + 121.001i) q^{40} -105.949 q^{41} +(837.997 + 215.955i) q^{42} -267.704i q^{43} +(244.289 - 442.495i) q^{44} +472.989i q^{45} +(18.3131 - 71.0628i) q^{46} -342.854 q^{47} +(-507.242 + 319.383i) q^{48} +724.141 q^{49} +(45.3998 - 176.171i) q^{50} +159.220i q^{51} +(56.6778 - 102.664i) q^{52} -95.6101i q^{53} +(-865.002 - 222.914i) q^{54} +492.162 q^{55} +(-507.432 + 537.483i) q^{56} -958.007 q^{57} +(95.1047 + 24.5088i) q^{58} +255.897i q^{59} +(-510.964 - 282.088i) q^{60} -847.927i q^{61} +(-5.37977 + 20.8758i) q^{62} -1983.54 q^{63} +(-29.4251 - 511.154i) q^{64} +114.187 q^{65} +(-417.676 + 1620.76i) q^{66} -117.059i q^{67} +(-119.061 - 65.7301i) q^{68} +243.001i q^{69} +(-696.969 - 179.611i) q^{70} +777.152 q^{71} +(943.187 - 999.044i) q^{72} +802.416 q^{73} +(-410.968 - 105.908i) q^{74} +602.421i q^{75} +(395.490 - 716.376i) q^{76} +2063.95i q^{77} +(-96.9056 + 376.036i) q^{78} -858.679 q^{79} +(421.878 - 265.634i) q^{80} +1318.46 q^{81} +(-74.7821 + 290.187i) q^{82} -519.209i q^{83} +(1182.97 - 2142.80i) q^{84} -132.425i q^{85} +(-733.226 - 188.955i) q^{86} -325.213 q^{87} +(-1039.54 - 981.420i) q^{88} -360.044 q^{89} +(1295.49 + 333.852i) q^{90} +478.860i q^{91} +(-181.711 - 100.317i) q^{92} -71.3854i q^{93} +(-241.998 + 939.057i) q^{94} +796.783 q^{95} +(516.743 + 1614.74i) q^{96} +850.341 q^{97} +(511.124 - 1983.38i) q^{98} -3836.35i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + q^{2} + 5 q^{4} + 40 q^{6} + 84 q^{7} + 13 q^{8} - 216 q^{9}+O(q^{10}) $ 24 * q + q^2 + 5 * q^4 + 40 * q^6 + 84 * q^7 + 13 * q^8 - 216 * q^9	$ 24 q + q^{2} + 5 q^{4} + 40 q^{6} + 84 q^{7} + 13 q^{8} - 216 q^{9} - 16 q^{10} - 18 q^{12} + 26 q^{14} - 180 q^{15} - 103 q^{16} + 408 q^{17} - 5 q^{18} - 24 q^{20} + 172 q^{22} + 624 q^{23} - 310 q^{24} - 600 q^{25} - 180 q^{26} - 132 q^{28} - 80 q^{30} - 744 q^{31} - 39 q^{32} - 280 q^{33} + 17 q^{34} + 791 q^{36} - 162 q^{38} + 1236 q^{39} - 1396 q^{40} + 1132 q^{42} + 886 q^{44} - 1246 q^{46} - 956 q^{47} - 2226 q^{48} + 1688 q^{49} + 2505 q^{50} + 2544 q^{52} - 3264 q^{54} + 1684 q^{55} - 1100 q^{56} - 168 q^{57} + 2800 q^{58} + 2520 q^{60} - 1946 q^{62} - 2520 q^{63} - 2143 q^{64} - 72 q^{65} + 3660 q^{66} + 85 q^{68} - 5084 q^{70} + 1532 q^{71} - 2277 q^{72} + 216 q^{73} + 2188 q^{74} + 2094 q^{76} - 4748 q^{78} - 3176 q^{79} + 116 q^{80} + 2040 q^{81} + 3198 q^{82} + 5916 q^{84} - 2066 q^{86} - 236 q^{87} - 3598 q^{88} - 424 q^{89} + 2180 q^{90} + 1940 q^{92} - 2156 q^{94} - 1248 q^{95} - 4674 q^{96} - 1304 q^{97} + 3705 q^{98}+O(q^{100}) $ 24 * q + q^2 + 5 * q^4 + 40 * q^6 + 84 * q^7 + 13 * q^8 - 216 * q^9 - 16 * q^10 - 18 * q^12 + 26 * q^14 - 180 * q^15 - 103 * q^16 + 408 * q^17 - 5 * q^18 - 24 * q^20 + 172 * q^22 + 624 * q^23 - 310 * q^24 - 600 * q^25 - 180 * q^26 - 132 * q^28 - 80 * q^30 - 744 * q^31 - 39 * q^32 - 280 * q^33 + 17 * q^34 + 791 * q^36 - 162 * q^38 + 1236 * q^39 - 1396 * q^40 + 1132 * q^42 + 886 * q^44 - 1246 * q^46 - 956 * q^47 - 2226 * q^48 + 1688 * q^49 + 2505 * q^50 + 2544 * q^52 - 3264 * q^54 + 1684 * q^55 - 1100 * q^56 - 168 * q^57 + 2800 * q^58 + 2520 * q^60 - 1946 * q^62 - 2520 * q^63 - 2143 * q^64 - 72 * q^65 + 3660 * q^66 + 85 * q^68 - 5084 * q^70 + 1532 * q^71 - 2277 * q^72 + 216 * q^73 + 2188 * q^74 + 2094 * q^76 - 4748 * q^78 - 3176 * q^79 + 116 * q^80 + 2040 * q^81 + 3198 * q^82 + 5916 * q^84 - 2066 * q^86 - 236 * q^87 - 3598 * q^88 - 424 * q^89 + 2180 * q^90 + 1940 * q^92 - 2156 * q^94 - 1248 * q^95 - 4674 * q^96 - 1304 * q^97 + 3705 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/136\mathbb{Z}\right)^\times$.

$n$	$69$	$103$	$105$
$\chi(n)$	$-1$	$1$	$1$

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 $

$2$	0.705834	−	2.73894i	0.249550	−	0.968362i
$2$	0.705834	−	2.73894i	0.249550	−	0.968362i
$3$			9.36589i			1.80247i	0.433335	+	0.901233i	$0.357337\pi$
$3$			9.36589i			1.80247i	−0.433335	+	0.901233i	$0.642663\pi$
$4$	−7.00360	−	3.86648i	−0.875449	−	0.483310i
$5$		−	7.78969i		−	0.696731i	−0.937359	−	0.348366i	$-0.886737\pi$
$5$		−	7.78969i		−	0.696731i	0.937359	−	0.348366i	$-0.113263\pi$
$6$	25.6526	+	6.61076i	1.74544	+	0.449805i
$7$	32.6671			1.76386			0.881929	−	0.471381i	$-0.156244\pi$
$7$	32.6671			1.76386			0.881929	+	0.471381i	$0.156244\pi$
$8$	−15.5334	+	16.4533i	−0.686487	+	0.727142i
$9$	−60.7198			−2.24888
$10$	−21.3355	−	5.49823i	−0.674688	−	0.173869i
$11$			63.1812i			1.73180i	0.500214	+	0.865902i	$0.333255\pi$
$11$			63.1812i			1.73180i	−0.500214	+	0.865902i	$0.666745\pi$
$12$	36.2130	−	65.5949i	0.871149	−	1.57797i
$13$			14.6588i			0.312739i	0.987699	+	0.156370i	$0.0499791\pi$
$13$			14.6588i			0.312739i	−0.987699	+	0.156370i	$0.950021\pi$
$14$	23.0576	−	89.4733i	0.440171	−	1.70805i
$15$	72.9573			1.25583
$16$	34.1007	+	54.1585i	0.532824	+	0.846226i
$17$	17.0000			0.242536
$17$	17.0000			0.242536
$18$	−42.8581	+	166.308i	−0.561209	+	2.17773i
$19$			102.287i			1.23506i	0.786546	+	0.617532i	$0.211867\pi$
$19$			102.287i			1.23506i	−0.786546	+	0.617532i	$0.788133\pi$
$20$	−30.1187	+	54.5558i	−0.336737	+	0.609953i
$21$			305.957i			3.17930i
$22$	173.050	+	44.5954i	1.67701	+	0.432172i
$23$	25.9454			0.235217			0.117608	−	0.993060i	$-0.462477\pi$
$23$	25.9454			0.235217			0.117608	+	0.993060i	$0.462477\pi$
$24$	−154.100	−	145.484i	−1.31065	−	1.23737i
$25$	64.3207			0.514566
$26$	40.1495	+	10.3467i	0.302845	+	0.0780441i
$27$		−	315.816i		−	2.25107i
$28$	−228.787	−	126.307i	−1.54417	−	0.852490i
$29$			34.7232i			0.222342i	0.993801	+	0.111171i	$0.0354602\pi$
$29$			34.7232i			0.222342i	−0.993801	+	0.111171i	$0.964540\pi$
$30$	51.4958	−	199.826i	0.313393	−	1.21610i
$31$	−7.62186			−0.0441589			−0.0220794	−	0.999756i	$-0.507029\pi$
$31$	−7.62186			−0.0441589			−0.0220794	+	0.999756i	$0.507029\pi$
$32$	172.406	−	55.1729i	0.952419	−	0.304790i
$33$	−591.748			−3.12152
$34$	11.9992	−	46.5620i	0.0605248	−	0.234862i
$35$		−	254.467i		−	1.22894i
$36$	425.257	+	234.772i	1.96878	+	1.08691i
$37$		−	150.046i		−	0.666689i	−0.942805	−	0.333344i	$-0.891823\pi$
$37$		−	150.046i		−	0.666689i	0.942805	−	0.333344i	$-0.108177\pi$
$38$	280.158	+	72.1975i	1.19599	+	0.308210i
$39$	−137.292			−0.563702
$40$	128.166	+	121.001i	0.506622	+	0.478297i
$41$	−105.949			−0.403570			−0.201785	−	0.979430i	$-0.564674\pi$
$41$	−105.949			−0.403570			−0.201785	+	0.979430i	$0.564674\pi$
$42$	837.997	+	215.955i	3.07871	+	0.793393i
$43$		−	267.704i		−	0.949407i	−0.880146	−	0.474704i	$-0.842555\pi$
$43$		−	267.704i		−	0.949407i	0.880146	−	0.474704i	$-0.157445\pi$
$44$	244.289	−	442.495i	0.836997	−	1.51611i
$45$			472.989i			1.56687i
$46$	18.3131	−	71.0628i	0.0586983	−	0.227775i
$47$	−342.854			−1.06405			−0.532026	−	0.846728i	$-0.678569\pi$
$47$	−342.854			−1.06405			−0.532026	+	0.846728i	$0.678569\pi$
$48$	−507.242	+	319.383i	−1.52529	+	0.960396i
$49$	724.141			2.11120
$50$	45.3998	−	176.171i	0.128410	−	0.498286i
$51$			159.220i			0.437162i
$52$	56.6778	−	102.664i	0.151150	−	0.273787i
$53$		−	95.6101i		−	0.247794i	−0.992295	−	0.123897i	$-0.960461\pi$
$53$		−	95.6101i		−	0.247794i	0.992295	−	0.123897i	$-0.0395392\pi$
$54$	−865.002	−	222.914i	−2.17985	−	0.561754i
$55$	492.162			1.20660
$56$	−507.432	+	537.483i	−1.21087	+	1.28258i
$57$	−958.007			−2.22616
$58$	95.1047	+	24.5088i	0.215308	+	0.0554856i
$59$			255.897i			0.564661i	0.959317	+	0.282330i	$0.0911075\pi$
$59$			255.897i			0.564661i	−0.959317	+	0.282330i	$0.908893\pi$
$60$	−510.964	−	282.088i	−1.09942	−	0.606957i
$61$		−	847.927i		−	1.77977i	−0.456185	−	0.889885i	$-0.650784\pi$
$61$		−	847.927i		−	1.77977i	0.456185	−	0.889885i	$-0.349216\pi$
$62$	−5.37977	+	20.8758i	−0.0110199	+	0.0427618i
$63$	−1983.54			−3.96671
$64$	−29.4251	−	511.154i	−0.0574709	−	0.998347i
$65$	114.187			0.217895
$66$	−417.676	+	1620.76i	−0.778975	+	3.02276i
$67$		−	117.059i		−	0.213448i	−0.994289	−	0.106724i	$-0.965964\pi$
$67$		−	117.059i		−	0.213448i	0.994289	−	0.106724i	$-0.0340361\pi$
$68$	−119.061	−	65.7301i	−0.212328	−	0.117220i
$69$			243.001i			0.423970i
$70$	−696.969	−	179.611i	−1.19005	−	0.306681i
$71$	777.152			1.29903			0.649514	−	0.760350i	$-0.274972\pi$
$71$	777.152			1.29903			0.649514	+	0.760350i	$0.274972\pi$
$72$	943.187	−	999.044i	1.54383	−	1.63526i
$73$	802.416			1.28652			0.643258	−	0.765650i	$-0.277582\pi$
$73$	802.416			1.28652			0.643258	+	0.765650i	$0.277582\pi$
$74$	−410.968	−	105.908i	−0.645596	−	0.166372i
$75$			602.421i			0.927487i
$76$	395.490	−	716.376i	0.596918	−	1.08124i
$77$			2063.95i			3.05466i
$78$	−96.9056	+	376.036i	−0.140672	+	0.545867i
$79$	−858.679			−1.22290			−0.611449	−	0.791284i	$-0.709413\pi$
$79$	−858.679			−1.22290			−0.611449	+	0.791284i	$0.709413\pi$
$80$	421.878	−	265.634i	0.589592	−	0.371235i
$81$	1318.46			1.80859
$82$	−74.7821	+	290.187i	−0.100711	+	0.390802i
$83$		−	519.209i		−	0.686633i	−0.939220	−	0.343317i	$-0.888450\pi$
$83$		−	519.209i		−	0.686633i	0.939220	−	0.343317i	$-0.111550\pi$
$84$	1182.97	−	2142.80i	1.53658	−	2.78331i
$85$		−	132.425i		−	0.168982i
$86$	−733.226	−	188.955i	−0.919370	−	0.236925i
$87$	−325.213			−0.400765
$88$	−1039.54	−	981.420i	−1.25927	−	1.18886i
$89$	−360.044			−0.428815			−0.214408	−	0.976744i	$-0.568782\pi$
$89$	−360.044			−0.428815			−0.214408	+	0.976744i	$0.568782\pi$
$90$	1295.49	+	333.852i	1.51729	+	0.391012i
$91$			478.860i			0.551628i
$92$	−181.711	−	100.317i	−0.205920	−	0.113682i
$93$		−	71.3854i		−	0.0795949i
$94$	−241.998	+	939.057i	−0.265534	+	1.03039i
$95$	796.783			0.860507
$96$	516.743	+	1614.74i	0.549374	+	1.71670i
$97$	850.341			0.890094			0.445047	−	0.895507i	$-0.353187\pi$
$97$	850.341			0.890094			0.445047	+	0.895507i	$0.353187\pi$
$98$	511.124	−	1983.38i	0.526850	−	2.04440i
$99$		−	3836.35i		−	3.89462i
$100$	−450.476	−	248.695i	−0.450476	−	0.248695i
$101$			1339.84i			1.31999i	0.751269	+	0.659997i	$0.229442\pi$
$101$			1339.84i			1.31999i	−0.751269	+	0.659997i	$0.770558\pi$
$102$	436.094	+	112.383i	0.423331	+	0.109094i
$103$	595.015			0.569209			0.284605	−	0.958645i	$-0.408138\pi$
$103$	595.015			0.569209			0.284605	+	0.958645i	$0.408138\pi$
$104$	−241.186	−	227.701i	−0.227406	−	0.214691i
$105$	2383.31			2.21511
$106$	−261.870	−	67.4849i	−0.239954	−	0.0618369i
$107$			120.295i			0.108685i	0.998522	+	0.0543427i	$0.0173063\pi$
$107$			120.295i			0.108685i	−0.998522	+	0.0543427i	$0.982694\pi$
$108$	−1221.10	+	2211.85i	−1.08796	+	1.97070i
$109$		−	211.820i		−	0.186135i	−0.995660	−	0.0930673i	$-0.970333\pi$
$109$		−	211.820i		−	0.186135i	0.995660	−	0.0930673i	$-0.0296672\pi$
$110$	347.385	−	1348.00i	0.301108	−	1.16843i
$111$	1405.32			1.20168
$112$	1113.97	+	1769.20i	0.939826	+	1.49262i
$113$	−431.349			−0.359097			−0.179548	−	0.983749i	$-0.557464\pi$
$113$	−431.349			−0.359097			−0.179548	+	0.983749i	$0.557464\pi$
$114$	−676.194	+	2623.92i	−0.555538	+	2.15573i
$115$		−	202.106i		−	0.163883i
$116$	134.256	−	243.187i	0.107460	−	0.194650i
$117$		−	890.078i		−	0.703314i
$118$	700.888	+	180.621i	0.546796	+	0.140911i
$119$	555.341			0.427799
$120$	−1133.28	+	1200.39i	−0.862114	+	0.913169i
$121$	−2660.86			−1.99914
$122$	−2322.42	−	598.496i	−1.72346	−	0.444142i
$123$		−	992.302i		−	0.727422i
$124$	53.3804	+	29.4697i	0.0386589	+	0.0213424i
$125$		−	1474.75i		−	1.05525i
$126$	−1400.05	+	5432.81i	−0.989893	+	3.84121i
$127$	1379.78			0.964062			0.482031	−	0.876154i	$-0.339899\pi$
$127$	1379.78			0.964062			0.482031	+	0.876154i	$0.339899\pi$
$128$	−1420.79	−	280.196i	−0.981103	−	0.193485i
$129$	2507.29			1.71127
$130$	80.5972	−	312.752i	0.0543757	−	0.211001i
$131$		−	1517.31i		−	1.01197i	−0.862543	−	0.505983i	$-0.831130\pi$
$131$		−	1517.31i		−	1.01197i	0.862543	−	0.505983i	$-0.168870\pi$
$132$	4144.36	+	2287.98i	2.73273	+	1.50866i
$133$			3341.42i			2.17848i
$134$	−320.617	−	82.6241i	−0.206695	−	0.0532659i
$135$	−2460.11			−1.56839
$136$	−264.068	+	279.707i	−0.166498	+	0.176358i
$137$	−3027.04			−1.88772			−0.943860	−	0.330347i	$-0.892834\pi$
$137$	−3027.04			−1.88772			−0.943860	+	0.330347i	$0.892834\pi$
$138$	665.566	+	171.519i	0.410556	+	0.105802i
$139$			1119.59i			0.683182i	0.939849	+	0.341591i	$0.110966\pi$
$139$			1119.59i			0.683182i	−0.939849	+	0.341591i	$0.889034\pi$
$140$	−983.890	+	1782.18i	−0.593956	+	1.07587i
$141$		−	3211.13i		−	1.91792i
$142$	548.540	−	2128.57i	0.324173	−	1.25793i
$143$	−926.158			−0.541603
$144$	−2070.59	−	3288.49i	−1.19826	−	1.90306i
$145$	270.483			0.154913
$146$	566.372	−	2197.77i	0.321050	−	1.24581i
$147$			6782.22i			3.80536i
$148$	−580.151	+	1050.86i	−0.322217	+	0.583652i
$149$		−	117.894i		−	0.0648207i	−0.999475	−	0.0324104i	$-0.989682\pi$
$149$		−	117.894i		−	0.0648207i	0.999475	−	0.0324104i	$-0.0103183\pi$
$150$	1649.99	+	425.209i	0.898143	+	0.231455i
$151$	959.155			0.516920			0.258460	−	0.966022i	$-0.416785\pi$
$151$	959.155			0.516920			0.258460	+	0.966022i	$0.416785\pi$
$152$	−1682.96	−	1588.87i	−0.898066	−	0.847855i
$153$	−1032.24			−0.545434
$154$	5653.03	+	1456.80i	2.95801	+	0.762290i
$155$			59.3719i			0.0307669i
$156$	961.540	+	530.838i	0.493492	+	0.272442i
$157$		−	2974.89i		−	1.51224i	−0.654431	−	0.756122i	$-0.727092\pi$
$157$		−	2974.89i		−	1.51224i	0.654431	−	0.756122i	$-0.272908\pi$
$158$	−606.085	+	2351.87i	−0.305174	+	1.18421i
$159$	895.473			0.446639
$160$	−429.780	−	1342.99i	−0.212357	−	0.663580i
$161$	847.561			0.414889
$162$	930.616	−	3611.19i	0.451334	−	1.75137i
$163$			172.904i			0.0830851i	0.999137	+	0.0415425i	$0.0132272\pi$
$163$			172.904i			0.0830851i	−0.999137	+	0.0415425i	$0.986773\pi$
$164$	742.021	+	409.648i	0.353305	+	0.195049i
$165$			4609.53i			2.17486i
$166$	−1422.08	−	366.475i	−0.664910	−	0.171349i
$167$	−855.309			−0.396322			−0.198161	−	0.980169i	$-0.563497\pi$
$167$	−855.309			−0.396322			−0.198161	+	0.980169i	$0.563497\pi$
$168$	−5034.01	−	4752.56i	−2.31180	−	2.18255i
$169$	1982.12			0.902194
$170$	−362.704	−	93.4699i	−0.163636	−	0.0421695i
$171$		−	6210.84i		−	2.77751i
$172$	−1035.07	+	1874.89i	−0.458858	+	0.831158i
$173$			1208.93i			0.531292i	0.964071	+	0.265646i	$0.0855852\pi$
$173$			1208.93i			0.531292i	−0.964071	+	0.265646i	$0.914415\pi$
$174$	−229.547	+	890.740i	−0.100011	+	0.388085i
$175$	2101.17			0.907622
$176$	−3421.80	+	2154.52i	−1.46550	+	0.922746i
$177$	−2396.71			−1.01778
$178$	−254.131	+	986.139i	−0.107011	+	0.415248i
$179$		−	2198.91i		−	0.918178i	−0.888390	−	0.459089i	$-0.848176\pi$
$179$		−	2198.91i		−	0.918178i	0.888390	−	0.459089i	$-0.151824\pi$
$180$	1828.80	−	3312.62i	0.757282	−	1.37171i
$181$			4766.84i			1.95755i	0.204936	+	0.978775i	$0.434301\pi$
$181$			4766.84i			1.95755i	−0.204936	+	0.978775i	$0.565699\pi$
$182$	1311.57	+	337.996i	0.534175	+	0.137659i
$183$	7941.59			3.20797
$184$	−403.021	+	426.888i	−0.161473	+	0.171036i
$185$	−1168.81			−0.464503
$186$	−195.520	−	50.3863i	−0.0770767	−	0.0198629i
$187$			1074.08i			0.420024i
$188$	2401.21	+	1325.64i	0.931523	+	0.514266i
$189$		−	10316.8i		−	3.97057i
$190$	562.396	−	2182.34i	0.214740	−	0.833282i
$191$	−2491.05			−0.943696			−0.471848	−	0.881680i	$-0.656413\pi$
$191$	−2491.05			−0.943696			−0.471848	+	0.881680i	$0.656413\pi$
$192$	4787.41	−	275.592i	1.79949	−	0.103589i
$193$	180.000			0.0671330			0.0335665	−	0.999436i	$-0.489313\pi$
$193$	180.000			0.0671330			0.0335665	+	0.999436i	$0.489313\pi$
$194$	600.200	−	2329.04i	0.222123	−	0.861933i
$195$			1069.46i			0.392748i
$196$	−5071.59	−	2799.87i	−1.84825	−	1.02036i
$197$		−	3605.38i		−	1.30392i	−0.758252	−	0.651961i	$-0.773946\pi$
$197$		−	3605.38i		−	1.30392i	0.758252	−	0.651961i	$-0.226054\pi$
$198$	−10507.5	−	2707.83i	−3.77141	−	0.971904i
$199$	3143.54			1.11980			0.559899	−	0.828561i	$-0.310840\pi$
$199$	3143.54			1.11980			0.559899	+	0.828561i	$0.310840\pi$
$200$	−999.122	+	1058.29i	−0.353243	+	0.374162i
$201$	1096.36			0.384733
$202$	3669.75	+	945.707i	1.27823	+	0.329404i
$203$			1134.31i			0.392181i
$204$	615.621	−	1115.11i	0.211285	−	0.382713i
$205$			825.306i			0.281180i
$206$	419.982	−	1629.71i	0.142046	−	0.551201i
$207$	−1575.40			−0.528975
$208$	−793.896	+	499.874i	−0.264648	+	0.166635i
$209$	−6462.60			−2.13889
$210$	1682.22	−	6527.74i	0.552782	−	2.14503i
$211$		−	784.005i		−	0.255797i	−0.991787	−	0.127898i	$-0.959177\pi$
$211$		−	784.005i		−	0.255797i	0.991787	−	0.127898i	$-0.0408232\pi$
$212$	−369.674	+	669.615i	−0.119761	+	0.216931i
$213$			7278.72i			2.34145i
$214$	329.480	+	84.9082i	0.105247	+	0.0271224i
$215$	−2085.33			−0.661482
$216$	5196.23	+	4905.71i	1.63685	+	1.54533i
$217$	−248.984			−0.0778901
$218$	−580.162	−	149.510i	−0.180246	−	0.0464499i
$219$			7515.33i			2.31890i
$220$	−3446.90	−	1902.93i	−1.05632	−	0.583162i
$221$			249.199i			0.0758504i
$222$	991.921	−	3849.08i	0.299880	−	1.16366i
$223$	−2215.62			−0.665333			−0.332666	−	0.943045i	$-0.607948\pi$
$223$	−2215.62			−0.665333			−0.332666	+	0.943045i	$0.607948\pi$
$224$	5632.02	−	1802.34i	1.67993	−	0.537607i
$225$	−3905.54			−1.15720
$226$	−304.461	+	1181.44i	−0.0896126	+	0.347735i
$227$			2974.47i			0.869702i	0.900502	+	0.434851i	$0.143199\pi$
$227$			2974.47i			0.869702i	−0.900502	+	0.434851i	$0.856801\pi$
$228$	6709.49	+	3704.11i	1.94889	+	1.07592i
$229$			1244.87i			0.359228i	0.983737	+	0.179614i	$0.0574848\pi$
$229$			1244.87i			0.359228i	−0.983737	+	0.179614i	$0.942515\pi$
$230$	−553.557	−	142.654i	−0.158698	−	0.0408970i
$231$	−19330.7			−5.50592
$232$	−571.312	−	539.370i	−0.161675	−	0.152635i
$233$	3001.75			0.843997			0.421999	−	0.906597i	$-0.361329\pi$
$233$	3001.75			0.843997			0.421999	+	0.906597i	$0.361329\pi$
$234$	−2437.87	−	628.247i	−0.681062	−	0.175512i
$235$			2670.73i			0.741357i
$236$	989.421	−	1792.20i	0.272906	−	0.494332i
$237$		−	8042.29i		−	2.20423i
$238$	391.979	−	1521.05i	0.106757	−	0.414264i
$239$	1672.47			0.452649			0.226324	−	0.974052i	$-0.427329\pi$
$239$	1672.47			0.452649			0.226324	+	0.974052i	$0.427329\pi$
$240$	2487.90	+	3951.26i	0.669138	+	1.06272i
$241$	−1943.95			−0.519588			−0.259794	−	0.965664i	$-0.583655\pi$
$241$	−1943.95			−0.519588			−0.259794	+	0.965664i	$0.583655\pi$
$242$	−1878.13	+	7287.94i	−0.498887	+	1.93590i
$243$			3821.54i			1.00885i
$244$	−3278.49	+	5938.54i	−0.860180	+	1.55810i
$245$		−	5640.83i		−	1.47094i
$246$	−2717.86	−	700.401i	−0.704408	−	0.181528i
$247$	−1499.40			−0.386253
$248$	118.394	−	125.405i	0.0303145	−	0.0321098i
$249$	4862.85			1.23763
$250$	−4039.25	−	1040.93i	−1.02186	−	0.263336i
$251$			2011.45i			0.505824i	0.967489	+	0.252912i	$0.0813882\pi$
$251$			2011.45i			0.505824i	−0.967489	+	0.252912i	$0.918612\pi$
$252$	13891.9	+	7669.32i	3.47266	+	1.91715i
$253$			1639.26i			0.407349i
$254$	973.898	−	3779.14i	0.240582	−	0.933561i
$255$	1240.27			0.304584
$256$	−1770.28	+	3693.69i	−0.432198	+	0.901779i
$257$	5643.22			1.36971			0.684853	−	0.728681i	$-0.259866\pi$
$257$	5643.22			1.36971			0.684853	+	0.728681i	$0.259866\pi$
$258$	1769.73	−	6867.31i	0.427049	−	1.65713i
$259$		−	4901.58i		−	1.17594i
$260$	−799.721	−	441.502i	−0.190756	−	0.105311i
$261$		−	2108.38i		−	0.500022i
$262$	−4155.81	−	1070.97i	−0.979949	−	0.252536i
$263$	5057.40			1.18575			0.592876	−	0.805294i	$-0.297993\pi$
$263$	5057.40			1.18575			0.592876	+	0.805294i	$0.297993\pi$
$264$	9191.87	−	9736.23i	2.14288	−	2.26979i
$265$	−744.773			−0.172645
$266$	9151.94	+	2358.49i	2.10955	+	0.543639i
$267$		−	3372.13i		−	0.772925i
$268$	−452.605	+	819.833i	−0.103161	+	0.186863i
$269$			1124.80i			0.254946i	0.991842	+	0.127473i	$0.0406866\pi$
$269$			1124.80i			0.254946i	−0.991842	+	0.127473i	$0.959313\pi$
$270$	−1736.43	+	6738.10i	−0.391392	+	1.51877i
$271$	7536.44			1.68932			0.844660	−	0.535303i	$-0.179802\pi$
$271$	7536.44			1.68932			0.844660	+	0.535303i	$0.179802\pi$
$272$	579.712	+	920.694i	0.129229	+	0.205240i
$273$	−4484.95			−0.994290
$274$	−2136.59	+	8290.89i	−0.471081	+	1.82800i
$275$			4063.86i			0.891127i
$276$	939.559	−	1701.88i	0.204909	−	0.371164i
$277$		−	2139.45i		−	0.464068i	−0.972708	−	0.232034i	$-0.925462\pi$
$277$		−	2139.45i		−	0.464068i	0.972708	−	0.232034i	$-0.0745381\pi$
$278$	3066.49	+	790.244i	0.661567	+	0.170488i
$279$	462.798			0.0993082
$280$	4186.83	+	3952.74i	0.893610	+	0.843648i
$281$	−3080.33			−0.653941			−0.326970	−	0.945035i	$-0.606028\pi$
$281$	−3080.33			−0.653941			−0.326970	+	0.945035i	$0.606028\pi$
$282$	−8795.10	−	2266.53i	−1.85724	−	0.478616i
$283$		−	3522.95i		−	0.739991i	−0.929033	−	0.369996i	$-0.879359\pi$
$283$		−	3522.95i		−	0.739991i	0.929033	−	0.369996i	$-0.120641\pi$
$284$	−5442.86	−	3004.84i	−1.13723	−	0.627833i
$285$			7462.57i			1.55103i
$286$	−653.714	+	2536.69i	−0.135157	+	0.524468i
$287$	−3461.03			−0.711841
$288$	−10468.5	+	3350.09i	−2.14188	+	0.685438i
$289$	289.000			0.0588235
$290$	190.916	−	740.836i	0.0386585	−	0.150012i
$291$			7964.20i			1.60436i
$292$	−5619.79	−	3102.52i	−1.12628	−	0.621785i
$293$		−	3403.81i		−	0.678678i	−0.940664	−	0.339339i	$-0.889797\pi$
$293$		−	3403.81i		−	0.678678i	0.940664	−	0.339339i	$-0.110203\pi$
$294$	18576.1	+	4787.13i	3.68497	+	0.949629i
$295$	1993.36			0.393417
$296$	2468.77	+	2330.74i	0.484777	+	0.457673i
$297$	19953.6			3.89841
$298$	−322.906	−	83.2140i	−0.0627699	−	0.0161760i
$299$			380.327i			0.0735615i
$300$	2329.25	−	4219.11i	0.448264	−	0.811968i
$301$		−	8745.13i		−	1.67462i
$302$	677.004	−	2627.07i	0.128997	−	0.500566i
$303$	−12548.8			−2.37924
$304$	−5539.70	+	3488.05i	−1.04514	+	0.658071i
$305$	−6605.09			−1.24002
$306$	−728.588	+	2827.24i	−0.136113	+	0.528178i
$307$		−	10233.1i		−	1.90240i	−0.308581	−	0.951198i	$-0.599854\pi$
$307$		−	10233.1i		−	1.90240i	0.308581	−	0.951198i	$-0.400146\pi$
$308$	7980.21	−	14455.1i	1.47635	−	2.67420i
$309$			5572.84i			1.02598i
$310$	162.616	+	41.9067i	0.0297935	+	0.00767788i
$311$	2974.39			0.542322			0.271161	−	0.962534i	$-0.412592\pi$
$311$	2974.39			0.542322			0.271161	+	0.962534i	$0.412592\pi$
$312$	2132.62	−	2258.92i	0.386974	−	0.409891i
$313$	−15.6178			−0.00282035			−0.00141018	−	0.999999i	$-0.500449\pi$
$313$	−15.6178			−0.00282035			−0.00141018	+	0.999999i	$0.500449\pi$
$314$	−8148.05	−	2099.78i	−1.46440	−	0.377381i
$315$			15451.2i			2.76373i
$316$	6013.84	+	3320.06i	1.07059	+	0.591038i
$317$		−	7346.91i		−	1.30171i	−0.759200	−	0.650857i	$-0.774410\pi$
$317$		−	7346.91i		−	1.30171i	0.759200	−	0.650857i	$-0.225590\pi$
$318$	632.056	−	2452.65i	0.111459	−	0.432509i
$319$	−2193.85			−0.385053
$320$	−3981.73	+	229.212i	−0.695579	+	0.0400418i
$321$	−1126.67			−0.195902
$322$	598.237	−	2321.42i	0.103536	−	0.401763i
$323$			1738.88i			0.299547i
$324$	−9233.98	−	5097.80i	−1.58333	−	0.874109i
$325$			942.862i			0.160925i
$326$	473.573	+	122.041i	0.0804564	+	0.0207339i
$327$	1983.88			0.335501
$328$	1645.74	−	1743.21i	0.277046	−	0.293453i
$329$	−11200.1			−1.87684
$330$	12625.2	+	3253.57i	2.10605	+	0.542736i
$331$			9999.36i			1.66047i	0.557416	+	0.830234i	$0.311793\pi$
$331$			9999.36i			1.66047i	−0.557416	+	0.830234i	$0.688207\pi$
$332$	−2007.51	+	3636.33i	−0.331856	+	0.601113i
$333$			9110.79i			1.49930i
$334$	−603.707	+	2342.64i	−0.0989023	+	0.383783i
$335$	−911.852			−0.148716
$336$	−16570.1	+	10433.3i	−2.69040	+	1.69400i
$337$	4238.34			0.685095			0.342547	−	0.939501i	$-0.388710\pi$
$337$	4238.34			0.685095			0.342547	+	0.939501i	$0.388710\pi$
$338$	1399.05	−	5428.91i	0.225143	−	0.873650i
$339$		−	4039.97i		−	0.647259i
$340$	−512.017	+	927.449i	−0.0816707	+	0.147935i
$341$		−	481.558i		−	0.0764745i
$342$	−17011.1	−	4383.82i	−2.68964	−	0.693129i
$343$	12450.8			1.96000
$344$	4404.63	+	4158.37i	0.690354	+	0.651756i
$345$	1892.91			0.295393
$346$	3311.20	+	853.307i	0.514483	+	0.132584i
$347$			3743.20i			0.579094i	0.957164	+	0.289547i	$0.0935046\pi$
$347$			3743.20i			0.579094i	−0.957164	+	0.289547i	$0.906495\pi$
$348$	2277.66	+	1257.43i	0.350849	+	0.193693i
$349$		−	5018.19i		−	0.769678i	−0.922984	−	0.384839i	$-0.874257\pi$
$349$		−	5018.19i		−	0.769678i	0.922984	−	0.384839i	$-0.125743\pi$
$350$	1483.08	−	5754.99i	0.226497	−	0.878906i
$351$	4629.47			0.703997
$352$	3485.89	+	10892.8i	0.527837	+	1.64940i
$353$	−7492.60			−1.12972			−0.564860	−	0.825187i	$-0.691070\pi$
$353$	−7492.60			−1.12972			−0.564860	+	0.825187i	$0.691070\pi$
$354$	−1691.68	+	6564.43i	−0.253988	+	0.985581i
$355$		−	6053.77i		−	0.905073i
$356$	2521.60	+	1392.10i	0.375406	+	0.207251i
$357$			5201.26i			0.771092i
$358$	−6022.67	−	1552.06i	−0.889129	−	0.229131i
$359$	3415.31			0.502098			0.251049	−	0.967974i	$-0.419225\pi$
$359$	3415.31			0.502098			0.251049	+	0.967974i	$0.419225\pi$
$360$	−7782.25	−	7347.14i	−1.13933	−	1.07563i
$361$	−3603.59			−0.525382
$362$	13056.1	+	3364.60i	1.89562	+	0.488507i
$363$		−	24921.3i		−	3.60339i
$364$	1851.50	−	3353.74i	0.266607	−	0.482922i
$365$		−	6250.57i		−	0.896355i
$366$	5605.45	−	21751.5i	0.800550	−	3.10648i
$367$	598.367			0.0851076			0.0425538	−	0.999094i	$-0.486451\pi$
$367$	598.367			0.0851076			0.0425538	+	0.999094i	$0.486451\pi$
$368$	884.756	+	1405.16i	0.125329	+	0.199047i
$369$	6433.18			0.907582
$370$	−824.990	+	3201.32i	−0.115917	+	0.449807i
$371$		−	3123.31i		−	0.437073i
$372$	−276.010	+	499.955i	−0.0384690	+	0.0696813i
$373$			7446.74i			1.03372i	0.856070	+	0.516860i	$0.172899\pi$
$373$			7446.74i			1.03372i	−0.856070	+	0.516860i	$0.827101\pi$
$374$	2941.84	+	758.123i	0.406735	+	0.104817i
$375$	13812.3			1.90204
$376$	5325.70	−	5641.10i	0.730457	−	0.773716i
$377$	−508.999			−0.0695352
$378$	−28257.1	−	7281.95i	−3.84495	−	0.990855i
$379$		−	5008.53i		−	0.678815i	−0.940639	−	0.339407i	$-0.889774\pi$
$379$		−	5008.53i		−	0.678815i	0.940639	−	0.339407i	$-0.110226\pi$
$380$	−5580.34	−	3080.74i	−0.753330	−	0.415891i
$381$			12922.9i			1.73769i
$382$	−1758.27	+	6822.84i	−0.235500	+	0.913840i
$383$	11686.5			1.55915			0.779573	−	0.626311i	$-0.215436\pi$
$383$	11686.5			1.55915			0.779573	+	0.626311i	$0.215436\pi$
$384$	2624.29	−	13307.0i	0.348750	−	1.76840i
$385$	16077.5			2.12827
$386$	127.050	−	493.009i	0.0167530	−	0.0650090i
$387$			16255.0i			2.13511i
$388$	−5955.45	−	3287.83i	−0.779232	−	0.430191i
$389$		−	10415.2i		−	1.35752i	−0.734362	−	0.678758i	$-0.762518\pi$
$389$		−	10415.2i		−	1.35752i	0.734362	−	0.678758i	$-0.237482\pi$
$390$	2929.20	+	754.865i	0.380323	+	0.0980104i
$391$	441.071			0.0570484
$392$	−11248.4	+	11914.5i	−1.44931	+	1.53514i
$393$	14210.9			1.82403
$394$	−9874.93	−	2544.80i	−1.26267	−	0.325394i
$395$			6688.84i			0.852031i
$396$	−14833.2	+	26868.3i	−1.88231	+	3.40955i
$397$			4188.56i			0.529515i	0.964315	+	0.264758i	$0.0852920\pi$
$397$			4188.56i			0.529515i	−0.964315	+	0.264758i	$0.914708\pi$
$398$	2218.82	−	8609.98i	0.279446	−	1.08437i
$399$	−31295.3			−3.92663
$400$	2193.38	+	3483.51i	0.274173	+	0.435439i
$401$	−9121.17			−1.13588			−0.567942	−	0.823069i	$-0.692260\pi$
$401$	−9121.17			−1.13588			−0.567942	+	0.823069i	$0.692260\pi$
$402$	773.848	−	3002.86i	0.0960100	−	0.372560i
$403$		−	111.727i		−	0.0138102i
$404$	5180.47	−	9383.72i	0.637965	−	1.15559i
$405$		−	10270.4i		−	1.26010i
$406$	3106.80	+	800.632i	0.379773	+	0.0978687i
$407$	9480.11			1.15457
$408$	−2619.70	−	2473.23i	−0.317879	−	0.300106i
$409$	−14442.7			−1.74607			−0.873037	−	0.487655i	$-0.837853\pi$
$409$	−14442.7			−1.74607			−0.873037	+	0.487655i	$0.837853\pi$
$410$	2260.47	+	582.530i	0.272284	+	0.0701685i
$411$		−	28350.9i		−	3.40255i
$412$	−4167.24	−	2300.61i	−0.498314	−	0.275104i
$413$			8359.43i			0.995982i
$414$	−1111.97	+	4314.92i	−0.132006	+	0.512239i
$415$	−4044.48			−0.478399
$416$	808.767	+	2527.26i	0.0953199	+	0.297859i
$417$	−10485.9			−1.23141
$418$	−4561.53	+	17700.7i	−0.533760	+	2.07122i
$419$		−	3114.49i		−	0.363133i	−0.983379	−	0.181566i	$-0.941883\pi$
$419$		−	3114.49i		−	0.363133i	0.983379	−	0.181566i	$-0.0581167\pi$
$420$	−16691.7	−	9215.00i	−1.93922	−	1.07059i
$421$			3368.55i			0.389960i	0.980807	+	0.194980i	$0.0624641\pi$
$421$			3368.55i			0.389960i	−0.980807	+	0.194980i	$0.937536\pi$
$422$	−2147.34	−	553.378i	−0.247704	−	0.0638341i
$423$	20818.0			2.39293
$424$	1573.11	+	1485.15i	0.180181	+	0.170107i
$425$	1093.45			0.124801
$426$	19936.0	+	5137.57i	2.26737	+	0.584310i
$427$		−	27699.3i		−	3.13926i
$428$	465.117	−	842.496i	0.0525287	−	0.0951485i
$429$		−	8674.29i		−	0.976221i
$430$	−1471.90	+	5711.60i	−0.165073	+	0.640554i
$431$	−7526.50			−0.841157			−0.420578	−	0.907256i	$-0.638173\pi$
$431$	−7526.50			−0.841157			−0.420578	+	0.907256i	$0.638173\pi$
$432$	17104.1	−	10769.6i	1.90491	−	1.19942i
$433$	10118.7			1.12304			0.561519	−	0.827464i	$-0.310217\pi$
$433$	10118.7			1.12304			0.561519	+	0.827464i	$0.310217\pi$
$434$	−175.742	+	681.953i	−0.0194375	+	0.0754258i
$435$			2533.31i			0.279225i
$436$	−818.997	+	1483.50i	−0.0899606	+	0.162951i
$437$			2653.87i			0.290507i
$438$	20584.1	+	5304.58i	2.24553	+	0.578682i
$439$	−6469.04			−0.703304			−0.351652	−	0.936131i	$-0.614380\pi$
$439$	−6469.04			−0.703304			−0.351652	+	0.936131i	$0.614380\pi$
$440$	−7644.96	+	8097.71i	−0.828316	+	0.877371i
$441$	−43969.7			−4.74784
$442$	682.541	+	175.893i	0.0734506	+	0.0189285i
$443$			7990.89i			0.857018i	0.903538	+	0.428509i	$0.140961\pi$
$443$			7990.89i			0.857018i	−0.903538	+	0.428509i	$0.859039\pi$
$444$	−9842.28	−	5433.63i	−1.05201	−	0.580785i
$445$			2804.63i			0.298769i
$446$	−1563.86	+	6068.46i	−0.166034	+	0.644283i
$447$	1104.19			0.116837
$448$	−961.233	−	16697.9i	−0.101371	−	1.76094i
$449$	−3117.79			−0.327700			−0.163850	−	0.986485i	$-0.552391\pi$
$449$	−3117.79			−0.327700			−0.163850	+	0.986485i	$0.552391\pi$
$450$	−2756.67	+	10697.1i	−0.288779	+	1.12059i
$451$		−	6693.96i		−	0.698905i
$452$	3020.99	+	1667.80i	0.314371	+	0.173555i
$453$			8983.33i			0.931730i
$454$	8146.89	+	2099.48i	0.842186	+	0.217034i
$455$	3730.17			0.384336
$456$	14881.1	−	15762.4i	1.52823	−	1.61873i
$457$	11407.3			1.16764			0.583819	−	0.811884i	$-0.301558\pi$
$457$	11407.3			1.16764			0.583819	+	0.811884i	$0.301558\pi$
$458$	3409.62	+	878.670i	0.347862	+	0.0896453i
$459$		−	5368.87i		−	0.545964i
$460$	−781.440	+	1415.47i	−0.0792061	+	0.143471i
$461$			10506.7i			1.06149i	0.847531	+	0.530745i	$0.178088\pi$
$461$			10506.7i			1.06149i	−0.847531	+	0.530745i	$0.821912\pi$
$462$	−13644.3	+	52945.6i	−1.37400	+	5.33172i
$463$	−843.127			−0.0846295			−0.0423147	−	0.999104i	$-0.513473\pi$
$463$	−843.127			−0.0846295			−0.0423147	+	0.999104i	$0.513473\pi$
$464$	−1880.55	+	1184.08i	−0.188152	+	0.118469i
$465$	−556.070			−0.0554562
$466$	2118.74	−	8221.62i	0.210620	−	0.817295i
$467$			2325.28i			0.230410i	0.993342	+	0.115205i	$0.0367524\pi$
$467$			2325.28i			0.230410i	−0.993342	+	0.115205i	$0.963248\pi$
$468$	−3441.46	+	6233.74i	−0.339918	+	0.615716i
$469$		−	3823.97i		−	0.376492i
$470$	7314.96	+	1885.09i	0.717902	+	0.185006i
$471$	27862.5			2.72577
$472$	−4210.37	−	3974.96i	−0.410589	−	0.387632i
$473$	16913.9			1.64419
$474$	−22027.4	−	5676.52i	−2.13449	−	0.550066i
$475$			6579.16i			0.635522i
$476$	−3889.38	−	2147.21i	−0.374516	−	0.206759i
$477$			5805.43i			0.557259i
$478$	1180.49	−	4580.79i	0.112959	−	0.438328i
$479$	−13560.1			−1.29348			−0.646742	−	0.762709i	$-0.723869\pi$
$479$	−13560.1			−1.29348			−0.646742	+	0.762709i	$0.723869\pi$
$480$	12578.3	−	4025.27i	1.19608	−	0.382766i
$481$	2199.49			0.208500
$482$	−1372.11	+	5324.36i	−0.129663	+	0.503150i
$483$			7938.16i			0.747823i
$484$	18635.6	+	10288.2i	1.75015	+	0.966206i
$485$		−	6623.90i		−	0.620156i
$486$	10467.0	+	2697.37i	0.976936	+	0.251760i
$487$	−20615.6			−1.91824			−0.959121	−	0.282996i	$-0.908672\pi$
$487$	−20615.6			−1.91824			−0.959121	+	0.282996i	$0.908672\pi$
$488$	13951.2	+	13171.2i	1.29415	+	1.22179i
$489$	−1619.40			−0.149758
$490$	−15449.9	−	3981.49i	−1.42440	−	0.367073i
$491$		−	10318.4i		−	0.948398i	−0.880418	−	0.474199i	$-0.842738\pi$
$491$		−	10318.4i		−	0.948398i	0.880418	−	0.474199i	$-0.157262\pi$
$492$	−3836.71	+	6949.68i	−0.351570	+	0.636821i
$493$			590.294i			0.0539260i
$494$	−1058.33	+	4106.76i	−0.0963894	+	0.374032i
$495$	−29884.0			−2.71351
$496$	−259.911	−	412.788i	−0.0235289	−	0.0373684i
$497$	25387.3			2.29130
$498$	3432.37	−	13319.1i	0.308851	−	1.19848i
$499$			14010.0i			1.25686i	0.777865	+	0.628431i	$0.216303\pi$
$499$			14010.0i			1.25686i	−0.777865	+	0.628431i	$0.783697\pi$
$500$	−5702.09	+	10328.6i	−0.510010	+	0.923814i
$501$		−	8010.73i		−	0.714357i
$502$	5509.25	+	1419.75i	0.489820	+	0.126228i
$503$	−19285.7			−1.70956			−0.854778	−	0.518994i	$-0.826307\pi$
$503$	−19285.7			−1.70956			−0.854778	+	0.518994i	$0.826307\pi$
$504$	30811.2	−	32635.9i	2.72310	−	2.88436i
$505$	10437.0			0.919680
$506$	4489.83	+	1157.05i	0.394461	+	0.101654i
$507$			18564.3i			1.62617i
$508$	−9663.44	−	5334.90i	−0.843988	−	0.465941i
$509$		−	2991.31i		−	0.260486i	−0.991482	−	0.130243i	$-0.958424\pi$
$509$		−	2991.31i		−	0.260486i	0.991482	−	0.130243i	$-0.0415757\pi$
$510$	875.429	−	3397.04i	0.0760091	−	0.294948i
$511$	26212.6			2.26923
$512$	8867.26	+	7455.83i	0.765393	+	0.643563i
$513$	32303.8			2.78021
$514$	3983.18	−	15456.5i	0.341811	−	1.32637i
$515$		−	4634.98i		−	0.396586i
$516$	−17560.0	−	9694.37i	−1.49813	−	0.827075i
$517$		−	21661.9i		−	1.84273i
$518$	−13425.2	−	3459.71i	−1.13874	−	0.293457i
$519$	−11322.7			−0.957636
$520$	−1773.72	+	1878.76i	−0.149582	+	0.158441i
$521$	10155.8			0.854002			0.427001	−	0.904251i	$-0.359570\pi$
$521$	10155.8			0.854002			0.427001	+	0.904251i	$0.359570\pi$
$522$	−5774.74	−	1488.17i	−0.484202	−	0.124781i
$523$		−	16855.3i		−	1.40924i	−0.709586	−	0.704619i	$-0.751118\pi$
$523$		−	16855.3i		−	1.40924i	0.709586	−	0.704619i	$-0.248882\pi$
$524$	−5866.63	+	10626.6i	−0.489093	+	0.885925i
$525$			19679.4i			1.63596i
$526$	3569.68	−	13851.9i	0.295904	−	1.14824i
$527$	−129.572			−0.0107101
$528$	−20179.0	−	32048.2i	−1.66322	−	2.64151i
$529$	−11493.8			−0.944673
$530$	−525.686	+	2039.89i	−0.0430837	+	0.167183i
$531$		−	15538.0i		−	1.26986i
$532$	12919.5	−	23401.9i	1.05288	−	1.90715i
$533$		−	1553.07i		−	0.126212i
$534$	−9236.06	−	2380.16i	−0.748471	−	0.192883i
$535$	937.059			0.0757245
$536$	1926.01	+	1818.32i	0.155207	+	0.146529i
$537$	20594.7			1.65498
$538$	3080.77	+	793.925i	0.246880	+	0.0636218i
$539$			45752.1i			3.65618i
$540$	17229.6	+	9511.96i	1.37305	+	0.758017i
$541$		−	2898.06i		−	0.230309i	−0.993348	−	0.115155i	$-0.963264\pi$
$541$		−	2898.06i		−	0.230309i	0.993348	−	0.115155i	$-0.0367364\pi$
$542$	5319.47	−	20641.9i	0.421570	−	1.63587i
$543$	−44645.7			−3.52842
$544$	2930.91	−	937.940i	0.230996	−	0.0739225i
$545$	−1650.01			−0.129686
$546$	−3165.63	+	12284.0i	−0.248125	+	0.962833i
$547$			89.4625i			0.00699294i	0.999994	+	0.00349647i	$0.00111296\pi$
$547$			89.4625i			0.00699294i	−0.999994	+	0.00349647i	$0.998887\pi$
$548$	21200.2	+	11704.0i	1.65260	+	0.912353i
$549$			51486.0i			4.00249i
$550$	11130.7	+	2868.41i	0.862934	+	0.222381i
$551$	−3551.72			−0.274607
$552$	−3998.19	−	3774.64i	−0.308286	−	0.291050i
$553$	−28050.6			−2.15702
$554$	−5859.82	−	1510.09i	−0.449386	−	0.115808i
$555$		−	10947.0i		−	0.837250i
$556$	4328.86	−	7841.15i	0.330188	−	0.598091i
$557$			18747.8i			1.42616i	0.701082	+	0.713080i	$0.252700\pi$
$557$			18747.8i			1.42616i	−0.701082	+	0.713080i	$0.747300\pi$
$558$	326.659	−	1267.58i	0.0247824	−	0.0961662i
$559$	3924.21			0.296917
$560$	13781.5	−	8677.50i	1.03996	−	0.654806i
$561$	−10059.7			−0.757079
$562$	−2174.21	+	8436.85i	−0.163191	+	0.633251i
$563$			7865.98i			0.588831i	0.955678	+	0.294415i	$0.0951249\pi$
$563$			7865.98i			0.588831i	−0.955678	+	0.294415i	$0.904875\pi$
$564$	−12415.8	+	22489.5i	−0.926947	+	1.67904i
$565$			3360.08i			0.250194i
$566$	−9649.15	−	2486.62i	−0.716579	−	0.184665i
$567$	43070.4			3.19010
$568$	−12071.8	+	12786.7i	−0.891766	+	0.944578i
$569$	−3193.28			−0.235271			−0.117635	−	0.993057i	$-0.537531\pi$
$569$	−3193.28			−0.235271			−0.117635	+	0.993057i	$0.537531\pi$
$570$	20439.6	+	5267.34i	1.50196	+	0.387061i
$571$		−	2014.35i		−	0.147632i	−0.997272	−	0.0738161i	$-0.976482\pi$
$571$		−	2014.35i		−	0.147632i	0.997272	−	0.0738161i	$-0.0235178\pi$
$572$	6486.44	+	3580.97i	0.474146	+	0.261762i
$573$		−	23330.9i		−	1.70098i
$574$	−2442.92	+	9479.57i	−0.177640	+	0.689320i
$575$	1668.83			0.121034
$576$	1786.69	+	31037.2i	0.129245	+	2.24517i
$577$	11539.0			0.832541			0.416271	−	0.909241i	$-0.363337\pi$
$577$	11539.0			0.832541			0.416271	+	0.909241i	$0.363337\pi$
$578$	203.986	−	791.554i	0.0146794	−	0.0569625i
$579$			1685.86i			0.121005i
$580$	−1894.35	−	1045.82i	−0.135618	−	0.0748709i
$581$		−	16961.1i		−	1.21112i
$582$	21813.5	+	5621.41i	1.55360	+	0.400369i
$583$	6040.76			0.429130
$584$	−12464.3	+	13202.4i	−0.883176	+	0.935480i
$585$	−6933.43			−0.490021
$586$	−9322.83	−	2402.52i	−0.657206	−	0.169364i
$587$			11151.6i			0.784118i	0.919940	+	0.392059i	$0.128237\pi$
$587$			11151.6i			0.784118i	−0.919940	+	0.392059i	$0.871763\pi$
$588$	26223.3	−	47499.9i	1.83917	−	3.33140i
$589$		−	779.615i		−	0.0545390i
$590$	1406.98	−	5459.70i	0.0981772	−	0.380970i
$591$	33767.6			2.35028
$592$	8126.29	−	5116.69i	0.564169	−	0.355227i
$593$	17143.1			1.18716			0.593578	−	0.804776i	$-0.297715\pi$
$593$	17143.1			1.18716			0.593578	+	0.804776i	$0.297715\pi$
$594$	14084.0	−	54651.8i	0.972848	−	3.77507i
$595$		−	4325.93i		−	0.298061i
$596$	−455.836	+	825.685i	−0.0313285	+	0.0567473i
$597$			29442.1i			2.01840i
$598$	1041.69	+	268.448i	0.0712341	+	0.0183573i
$599$	−17637.9			−1.20311			−0.601555	−	0.798831i	$-0.705452\pi$
$599$	−17637.9			−1.20311			−0.601555	+	0.798831i	$0.705452\pi$
$600$	−9911.84	−	9357.66i	−0.674415	−	0.636708i
$601$	−7397.45			−0.502077			−0.251038	−	0.967977i	$-0.580772\pi$
$601$	−7397.45			−0.502077			−0.251038	+	0.967977i	$0.580772\pi$
$602$	−23952.4	−	6172.61i	−1.62164	−	0.417902i
$603$			7107.79i			0.480019i
$604$	−6717.53	−	3708.55i	−0.452537	−	0.249832i
$605$			20727.3i			1.39287i
$606$	−8857.38	+	34370.5i	−0.593740	+	2.30397i
$607$	−18032.2			−1.20577			−0.602885	−	0.797828i	$-0.705982\pi$
$607$	−18032.2			−1.20577			−0.602885	+	0.797828i	$0.705982\pi$
$608$	5643.46	+	17634.9i	0.376435	+	1.17630i
$609$	−10623.8			−0.706892
$610$	−4662.10	+	18091.0i	−0.309447	+	1.20079i
$611$		−	5025.82i		−	0.332770i
$612$	7229.37	+	3991.12i	0.477500	+	0.263614i
$613$			20487.4i			1.34988i	0.737873	+	0.674940i	$0.235831\pi$
$613$			20487.4i			1.34988i	−0.737873	+	0.674940i	$0.764169\pi$
$614$	−28027.9	−	7222.89i	−1.84221	−	0.474743i
$615$	−7729.73			−0.506817
$616$	−33958.8	−	32060.2i	−2.22117	−	2.09698i
$617$	−23179.5			−1.51244			−0.756218	−	0.654320i	$-0.772955\pi$
$617$	−23179.5			−1.51244			−0.756218	+	0.654320i	$0.772955\pi$
$618$	15263.7	+	3933.50i	0.993520	+	0.256033i
$619$			11447.4i			0.743311i	0.928371	+	0.371656i	$0.121210\pi$
$619$			11447.4i			0.743311i	−0.928371	+	0.371656i	$0.878790\pi$
$620$	229.560	−	415.817i	0.0148699	−	0.0269348i
$621$		−	8193.97i		−	0.529489i
$622$	2099.43	−	8146.67i	0.135336	−	0.525164i
$623$	−11761.6			−0.756370
$624$	−4681.77	−	7435.54i	−0.300354	−	0.477019i
$625$	−3447.75			−0.220656
$626$	−11.0236	+	42.7762i	−0.000703819	+	0.00273112i
$627$		−	60528.0i		−	3.85527i
$628$	−11502.4	+	20834.9i	−0.730882	+	1.32389i
$629$		−	2550.79i		−	0.161696i
$630$	42319.9	+	10906.0i	2.67629	+	0.689689i
$631$	−6531.80			−0.412087			−0.206044	−	0.978543i	$-0.566059\pi$
$631$	−6531.80			−0.412087			−0.206044	+	0.978543i	$0.566059\pi$
$632$	13338.2	−	14128.1i	0.839503	−	0.889220i
$633$	7342.90			0.461065
$634$	−20122.8	−	5185.70i	−1.26053	−	0.324843i
$635$		−	10748.1i		−	0.671692i
$636$	−6271.53	−	3462.33i	−0.391010	−	0.215865i
$637$			10615.0i			0.660254i
$638$	−1548.50	+	6008.83i	−0.0960901	+	0.372871i
$639$	−47188.5			−2.92136
$640$	−2182.64	+	11067.5i	−0.134807	+	0.683565i
$641$	−25251.3			−1.55595			−0.777977	−	0.628293i	$-0.783754\pi$
$641$	−25251.3			−1.55595			−0.777977	+	0.628293i	$0.783754\pi$
$642$	−795.240	+	3085.87i	−0.0488873	+	0.189704i
$643$			14486.6i			0.888486i	0.895906	+	0.444243i	$0.146527\pi$
$643$			14486.6i			0.888486i	−0.895906	+	0.444243i	$0.853473\pi$
$644$	−5935.97	−	3277.07i	−0.363214	−	0.200520i
$645$		−	19531.0i		−	1.19230i
$646$	4762.68	+	1227.36i	0.290070	+	0.0747520i
$647$	−5874.77			−0.356972			−0.178486	−	0.983942i	$-0.557120\pi$
$647$	−5874.77			−0.356972			−0.178486	+	0.983942i	$0.557120\pi$
$648$	−20480.2	+	21693.1i	−1.24157	+	1.31510i
$649$	−16167.9			−0.977882
$650$	2582.44	+	665.505i	0.155834	+	0.0401588i
$651$		−	2331.96i		−	0.140394i
$652$	668.528	−	1210.95i	0.0401558	−	0.0727368i
$653$		−	1232.11i		−	0.0738380i	−0.999318	−	0.0369190i	$-0.988246\pi$
$653$		−	1232.11i		−	0.0738380i	0.999318	−	0.0369190i	$-0.0117544\pi$
$654$	1400.29	−	5433.73i	0.0837243	−	0.324886i
$655$	−11819.3			−0.705068
$656$	−3612.92	−	5738.01i	−0.215032	−	0.341512i
$657$	−48722.5			−2.89322
$658$	−7905.38	+	30676.3i	−0.468365	+	1.81746i
$659$			9007.08i			0.532422i	0.963915	+	0.266211i	$0.0857718\pi$
$659$			9007.08i			0.532422i	−0.963915	+	0.266211i	$0.914228\pi$
$660$	17822.6	−	32283.3i	1.05113	−	1.90398i
$661$		−	25240.0i		−	1.48521i	−0.669730	−	0.742605i	$-0.733590\pi$
$661$		−	25240.0i		−	1.48521i	0.669730	−	0.742605i	$-0.266410\pi$
$662$	27387.7	+	7057.89i	1.60793	+	0.414370i
$663$	−2333.97			−0.136718
$664$	8542.72	+	8065.09i	0.499280	+	0.471365i
$665$	26028.6			1.51781
$666$	24953.9	+	6430.71i	1.45187	+	0.374152i
$667$			900.905i			0.0522986i
$668$	5990.24	+	3307.03i	0.346960	+	0.191546i
$669$		−	20751.3i		−	1.19924i
$670$	−643.616	+	2497.51i	−0.0371120	+	0.144011i
$671$	53573.0			3.08221
$672$	16880.5	+	52748.9i	0.969018	+	3.02802i
$673$	18781.8			1.07576			0.537878	−	0.843023i	$-0.319226\pi$
$673$	18781.8			1.07576			0.537878	+	0.843023i	$0.319226\pi$
$674$	2991.56	−	11608.6i	0.170966	−	0.663420i
$675$		−	20313.5i		−	1.15832i
$676$	−13882.0	−	7663.82i	−0.789825	−	0.436039i
$677$		−	6984.94i		−	0.396533i	−0.980148	−	0.198267i	$-0.936469\pi$
$677$		−	6984.94i		−	0.396533i	0.980148	−	0.198267i	$-0.0635312\pi$
$678$	−11065.2	−	2851.55i	−0.626781	−	0.161524i
$679$	27778.2			1.57000
$680$	2178.83	+	2057.01i	0.122874	+	0.116004i
$681$	−27858.5			−1.56761
$682$	−1318.96	−	339.900i	−0.0740550	−	0.0190842i
$683$		−	16547.6i		−	0.927053i	−0.886083	−	0.463527i	$-0.846584\pi$
$683$		−	16547.6i		−	0.927053i	0.886083	−	0.463527i	$-0.153416\pi$
$684$	−24014.1	+	43498.2i	−1.34240	+	2.43157i
$685$			23579.7i			1.31523i
$686$	8788.19	−	34102.0i	0.489117	−	1.89799i
$687$	−11659.3			−0.647495
$688$	14498.5	−	9128.91i	0.803414	−	0.505867i
$689$	1401.53			0.0774948
$690$	1336.08	−	5184.56i	0.0737154	−	0.286047i
$691$			4557.98i			0.250932i	0.992098	+	0.125466i	$0.0400426\pi$
$691$			4557.98i			0.250932i	−0.992098	+	0.125466i	$0.959957\pi$
$692$	4674.31	−	8466.88i	0.256779	−	0.465119i
$693$		−	125323.i		−	6.86957i
$694$	10252.4	+	2642.08i	0.560773	+	0.144513i
$695$	8721.25			0.475994
$696$	5051.68	−	5350.85i	0.275120	−	0.291413i
$697$	−1801.13			−0.0978802
$698$	−13744.5	−	3542.01i	−0.745327	−	0.192073i
$699$			28114.1i			1.52128i
$700$	−14715.8	−	8124.14i	−0.794577	−	0.438662i
$701$		−	3013.14i		−	0.162347i	−0.996700	−	0.0811733i	$-0.974133\pi$
$701$		−	3013.14i		−	0.162347i	0.996700	−	0.0811733i	$-0.0258667\pi$
$702$	3267.64	−	12679.9i	0.175683	−	0.681724i
$703$	15347.8			0.823403
$704$	32295.3	−	1859.11i	1.72894	−	0.0995283i
$705$	−25013.7			−1.33627
$706$	−5288.53	+	20521.8i	−0.281922	+	1.09398i
$707$			43768.8i			2.32828i
$708$	16785.6	+	9266.81i	0.891017	+	0.491904i
$709$		−	1356.75i		−	0.0718670i	−0.999354	−	0.0359335i	$-0.988560\pi$
$709$		−	1356.75i		−	0.0718670i	0.999354	−	0.0359335i	$-0.0114404\pi$
$710$	−16580.9	−	4272.96i	−0.876438	−	0.225861i
$711$	52138.8			2.75015
$712$	5592.71	−	5923.92i	0.294376	−	0.311810i
$713$	−197.752			−0.0103869
$714$	14245.9	+	3671.23i	0.746696	+	0.192426i
$715$			7214.48i			0.377352i
$716$	−8502.02	+	15400.2i	−0.443764	+	0.803819i
$717$			15664.2i			0.815884i
$718$	2410.64	−	9354.33i	0.125298	−	0.486212i
$719$	26972.2			1.39902			0.699508	−	0.714625i	$-0.253402\pi$
$719$	26972.2			1.39902			0.699508	+	0.714625i	$0.253402\pi$
$720$	−25616.3	+	16129.3i	−1.32592	+	0.834863i
$721$	19437.4			1.00400
$722$	−2543.54	+	9870.03i	−0.131109	+	0.508760i
$723$		−	18206.8i		−	0.936540i
$724$	18430.9	−	33385.0i	0.946103	−	1.71374i
$725$			2233.42i			0.114410i
$726$	−68258.0	−	17590.3i	−3.48939	−	0.899226i
$727$	1509.74			0.0770197			0.0385098	−	0.999258i	$-0.487739\pi$
$727$	1509.74			0.0770197			0.0385098	+	0.999258i	$0.487739\pi$
$728$	−7878.84	−	7438.33i	−0.401112	−	0.378685i
$729$	−193.579			−0.00983484
$730$	−17119.9	−	4411.87i	−0.867996	−	0.223686i
$731$		−	4550.97i		−	0.230265i
$732$	−55619.7	−	30706.0i	−2.80842	−	1.55044i
$733$		−	27371.2i		−	1.37923i	−0.724175	−	0.689617i	$-0.757779\pi$
$733$		−	27371.2i		−	1.37923i	0.724175	−	0.689617i	$-0.242221\pi$
$734$	422.348	−	1638.89i	0.0212386	−	0.0824150i
$735$	52831.4			2.65131
$736$	4473.15	−	1431.48i	0.224025	−	0.0716917i
$737$	7395.91			0.369650
$738$	4540.76	−	17620.1i	0.226487	−	0.878868i
$739$		−	23080.3i		−	1.14888i	−0.818547	−	0.574440i	$-0.805220\pi$
$739$		−	23080.3i		−	1.14888i	0.818547	−	0.574440i	$-0.194780\pi$
$740$	8185.91	+	4519.20i	0.406649	+	0.224499i
$741$		−	14043.2i		−	0.696207i
$742$	−8554.55	−	2204.54i	−0.423245	−	0.109072i
$743$	−18872.7			−0.931859			−0.465929	−	0.884822i	$-0.654280\pi$
$743$	−18872.7			−0.931859			−0.465929	+	0.884822i	$0.654280\pi$
$744$	1174.53	+	1108.86i	0.0578768	+	0.0546409i
$745$	−918.361			−0.0451626
$746$	20396.2	+	5256.17i	1.00102	+	0.257965i
$747$			31526.3i			1.54416i
$748$	4152.91	−	7522.42i	0.203002	−	0.367710i
$749$			3929.68i			0.191706i
$750$	9749.22	−	37831.2i	0.474655	−	1.84187i
$751$	−14246.9			−0.692247			−0.346124	−	0.938189i	$-0.612502\pi$
$751$	−14246.9			−0.692247			−0.346124	+	0.938189i	$0.612502\pi$
$752$	−11691.6	−	18568.5i	−0.566952	−	0.900428i
$753$	−18839.0			−0.911730
$754$	−359.269	+	1394.12i	−0.0173525	+	0.0673352i
$755$		−	7471.52i		−	0.360154i
$756$	−39889.7	+	72254.7i	−1.91901	+	3.47603i
$757$			87.9429i			0.00422238i	0.999998	+	0.00211119i	$0.000672013\pi$
$757$			87.9429i			0.00422238i	−0.999998	+	0.00211119i	$0.999328\pi$
$758$	−13718.1	−	3535.19i	−0.657338	−	0.169398i
$759$	−15353.1			−0.734233
$760$	−12376.8	+	13109.7i	−0.590727	+	0.625711i
$761$	22286.7			1.06162			0.530810	−	0.847491i	$-0.321888\pi$
$761$	22286.7			1.06162			0.530810	+	0.847491i	$0.321888\pi$
$762$	35395.0	+	9121.42i	1.68271	+	0.433641i
$763$		−	6919.55i		−	0.328315i
$764$	17446.3	+	9631.58i	0.826159	+	0.456098i
$765$			8040.81i			0.380021i
$766$	8248.74	−	32008.7i	0.389085	−	1.50982i
$767$	−3751.14			−0.176592
$768$	−34594.6	−	16580.3i	−1.62543	−	0.779022i
$769$	14125.8			0.662405			0.331202	−	0.943560i	$-0.392546\pi$
$769$	14125.8			0.662405			0.331202	+	0.943560i	$0.392546\pi$
$770$	11348.1	−	44035.4i	0.531111	−	2.06094i
$771$			52853.8i			2.46885i
$772$	−1260.65	−	695.965i	−0.0587716	−	0.0324460i
$773$		−	25171.1i		−	1.17121i	−0.810598	−	0.585603i	$-0.800858\pi$
$773$		−	25171.1i		−	1.17121i	0.810598	−	0.585603i	$-0.199142\pi$
$774$	44521.4	+	11473.3i	2.06756	+	0.532816i
$775$	−490.243			−0.0227227
$776$	−13208.7	+	13991.0i	−0.611038	+	0.647225i
$777$	45907.7			2.11960
$778$	−28526.7	−	7351.44i	−1.31457	−	0.338768i
$779$		−	10837.1i		−	0.498435i
$780$	4135.06	−	7490.10i	0.189819	−	0.343831i
$781$			49101.4i			2.24966i
$782$	311.323	−	1208.07i	0.0142364	−	0.0552435i
$783$	10966.1			0.500508
$784$	24693.7	+	39218.4i	1.12490	+	1.78655i
$785$	−23173.5			−1.05363
$786$	10030.5	−	38922.8i	0.455188	−	1.76633i
$787$			29767.0i			1.34826i	0.738613	+	0.674130i	$0.235481\pi$
$787$			29767.0i			1.34826i	−0.738613	+	0.674130i	$0.764519\pi$
$788$	−13940.1	+	25250.6i	−0.630198	+	1.14152i
$789$			47367.0i			2.13728i
$790$	18320.3	+	4721.21i	0.825074	+	0.212624i
$791$	−14090.9			−0.633396
$792$	63120.8	+	59591.7i	2.83194	+	2.67361i
$793$	12429.6			0.556604
$794$	11472.2	+	2956.43i	0.512762	+	0.132141i
$795$		−	6975.46i		−	0.311187i
$796$	−22016.1	−	12154.4i	−0.980327	−	0.541209i
$797$			34089.8i			1.51509i	0.652785	+	0.757543i	$0.273600\pi$
$797$			34089.8i			1.51509i	−0.652785	+	0.757543i	$0.726400\pi$
$798$	−22089.3	+	85716.0i	−0.979891	+	3.80240i
$799$	−5828.52			−0.258070
$800$	11089.3	−	3548.76i	0.490083	−	0.156835i
$801$	21861.8			0.964355
$802$	−6438.03	+	24982.3i	−0.283460	+	1.09995i
$803$			50697.6i			2.22799i
$804$	−7678.46	−	4239.05i	−0.336814	−	0.185945i
$805$		−	6602.23i		−	0.289066i
$806$	−306.014	−	78.8607i	−0.0133733	−	0.00344634i
$807$	−10534.8			−0.459532
$808$	−22044.9	−	20812.4i	−0.959823	−	0.906158i
$809$	−24027.9			−1.04422			−0.522111	−	0.852877i	$-0.674855\pi$
$809$	−24027.9			−1.04422			−0.522111	+	0.852877i	$0.674855\pi$
$810$	−28130.1	−	7249.21i	−1.22023	−	0.314458i
$811$		−	27707.3i		−	1.19968i	−0.800122	−	0.599838i	$-0.795232\pi$
$811$		−	27707.3i		−	1.19968i	0.800122	−	0.599838i	$-0.204768\pi$
$812$	4385.77	−	7944.22i	0.189545	−	0.343334i
$813$			70585.4i			3.04494i
$814$	6691.39	−	25965.5i	0.288124	−	1.11805i
$815$	1346.87			0.0578879
$816$	−8623.12	+	5429.52i	−0.369938	+	0.232930i
$817$	27382.6			1.17258
$818$	−10194.1	+	39557.6i	−0.435733	+	1.69083i
$819$		−	29076.3i		−	1.24055i
$820$	3191.03	−	5780.11i	0.135897	−	0.246159i
$821$		−	29951.2i		−	1.27321i	−0.771191	−	0.636603i	$-0.780339\pi$
$821$		−	29951.2i		−	1.27321i	0.771191	−	0.636603i	$-0.219661\pi$
$822$	−77651.5	−	20011.1i	−3.29490	−	0.849107i
$823$	21290.6			0.901755			0.450878	−	0.892586i	$-0.351111\pi$
$823$	21290.6			0.901755			0.450878	+	0.892586i	$0.351111\pi$
$824$	−9242.62	+	9789.99i	−0.390755	+	0.413896i
$825$	−38061.7			−1.60623
$826$	22896.0	+	5900.37i	0.964471	+	0.248547i
$827$			37461.5i			1.57517i	0.616206	+	0.787585i	$0.288669\pi$
$827$			37461.5i			1.57517i	−0.616206	+	0.787585i	$0.711331\pi$
$828$	11033.5	+	6091.24i	0.463091	+	0.255659i
$829$		−	4257.81i		−	0.178384i	−0.996014	−	0.0891918i	$-0.971572\pi$
$829$		−	4257.81i		−	0.178384i	0.996014	−	0.0891918i	$-0.0284284\pi$
$830$	−2854.73	+	11077.6i	−0.119384	+	0.463263i
$831$	20037.8			0.836467
$832$	7492.88	−	431.336i	0.312222	−	0.0179734i
$833$	12310.4			0.512041
$834$	−7401.34	+	28720.4i	−0.307299	+	1.19245i
$835$			6662.59i			0.276130i
$836$	45261.5	+	24987.5i	1.87249	+	1.03374i
$837$			2407.10i			0.0994047i
$838$	−8530.40	−	2198.31i	−0.351644	−	0.0906198i
$839$	41692.0			1.71558			0.857788	−	0.514003i	$-0.171838\pi$
$839$	41692.0			1.71558			0.857788	+	0.514003i	$0.171838\pi$
$840$	−37020.9	+	39213.4i	−1.52065	+	1.61070i
$841$	23183.3			0.950564
$842$	9226.26	+	2377.64i	0.377622	+	0.0973145i
$843$		−	28850.1i		−	1.17871i
$844$	−3031.34	+	5490.86i	−0.123629	+	0.223937i
$845$		−	15440.1i		−	0.628587i
$846$	14694.1	−	57019.4i	0.597155	−	2.31722i
$847$	−86922.7			−3.52621
$848$	5178.10	−	3260.37i	0.209689	−	0.132030i
$849$	32995.5			1.33381
$850$	771.796	−	2994.90i	0.0311440	−	0.120852i
$851$		−	3893.01i		−	0.156816i
$852$	28143.0	−	50977.2i	1.13165	−	2.04982i
$853$			12550.7i			0.503782i	0.967756	+	0.251891i	$0.0810525\pi$
$853$			12550.7i			0.503782i	−0.967756	+	0.251891i	$0.918947\pi$
$854$	−75866.9	−	19551.1i	−3.03994	−	0.783403i
$855$	−48380.5			−1.93518
$856$	−1979.25	−	1868.59i	−0.0790297	−	0.0746111i
$857$	35835.9			1.42839			0.714196	−	0.699946i	$-0.246792\pi$
$857$	35835.9			1.42839			0.714196	+	0.699946i	$0.246792\pi$
$858$	−23758.4	−	6122.61i	−0.945335	−	0.243616i
$859$		−	2957.24i		−	0.117462i	−0.998274	−	0.0587309i	$-0.981295\pi$
$859$		−	2957.24i		−	0.117462i	0.998274	−	0.0587309i	$-0.0187054\pi$
$860$	14604.8	+	8062.89i	0.579094	+	0.319700i
$861$		−	32415.7i		−	1.28307i
$862$	−5312.46	+	20614.6i	−0.209911	+	0.814544i
$863$	−38694.5			−1.52628			−0.763138	−	0.646235i	$-0.776342\pi$
$863$	−38694.5			−1.52628			−0.763138	+	0.646235i	$0.776342\pi$
$864$	−17424.5	−	54448.7i	−0.686104	−	2.14396i
$865$	9417.22			0.370168
$866$	7142.15	−	27714.6i	0.280254	−	1.08751i
$867$			2706.74i			0.106027i
$868$	1743.78	+	962.691i	0.0681888	+	0.0376450i
$869$		−	54252.3i		−	2.11782i
$870$	6938.59	+	1788.10i	0.270391	+	0.0696807i
$871$	1715.94			0.0667535
$872$	3485.15	+	3290.29i	0.135346	+	0.127779i
$873$	−51632.6			−2.00172
$874$	7268.79	+	1873.19i	0.281316	+	0.0724962i
$875$		−	48175.8i		−	1.86130i
$876$	29057.9	−	52634.4i	1.12075	−	2.03008i
$877$			9719.92i			0.374251i	0.982336	+	0.187126i	$0.0599172\pi$
$877$			9719.92i			0.374251i	−0.982336	+	0.187126i	$0.940083\pi$
$878$	−4566.07	+	17718.3i	−0.175510	+	0.681053i
$879$	31879.7			1.22329
$880$	16783.1	+	26654.7i	0.642906	+	1.02106i
$881$	−9693.62			−0.370700			−0.185350	−	0.982673i	$-0.559342\pi$
$881$	−9693.62			−0.370700			−0.185350	+	0.982673i	$0.559342\pi$
$882$	−31035.3	+	120430.i	−1.18482	+	4.59762i
$883$		−	31483.3i		−	1.19988i	−0.800044	−	0.599942i	$-0.795190\pi$
$883$		−	31483.3i		−	1.19988i	0.800044	−	0.599942i	$-0.204810\pi$
$884$	963.522	−	1745.29i	0.0366592	−	0.0664032i
$885$			18669.6i			0.709120i
$886$	21886.6	+	5640.25i	0.829903	+	0.213869i
$887$	11444.3			0.433214			0.216607	−	0.976259i	$-0.430501\pi$
$887$	11444.3			0.433214			0.216607	+	0.976259i	$0.430501\pi$
$888$	−21829.4	+	23122.2i	−0.824940	+	0.873794i
$889$	45073.5			1.70047
$890$	7681.71	+	1979.60i	0.289316	+	0.0745578i
$891$			83302.0i			3.13212i
$892$	15517.3	+	8566.66i	0.582465	+	0.321562i
$893$		−	35069.4i		−	1.31417i
$894$	779.372	−	3024.30i	0.0291567	−	0.113141i
$895$	−17128.8			−0.639723
$896$	−46413.1	−	9153.20i	−1.73053	−	0.341280i
$897$	−3562.10			−0.132592
$898$	−2200.64	+	8539.44i	−0.0817777	+	0.317333i
$899$		−	264.655i		−	0.00981840i
$900$	27352.9	+	15100.7i	1.01307	+	0.559285i
$901$		−	1625.37i		−	0.0600988i
$902$	−18334.3	−	4724.82i	−0.676793	−	0.174412i
$903$	81905.9			3.01845
$904$	6700.33	−	7097.13i	0.246515	−	0.261114i
$905$	37132.2			1.36389
$906$	24604.8	+	6340.75i	0.902252	+	0.232513i
$907$			34567.2i			1.26547i	0.774367	+	0.632736i	$0.218068\pi$
$907$			34567.2i			1.26547i	−0.774367	+	0.632736i	$0.781932\pi$
$908$	11500.7	−	20832.0i	0.420335	−	0.761380i
$909$		−	81355.0i		−	2.96851i
$910$	2632.88	−	10216.7i	0.0959111	−	0.372177i
$911$	11288.6			0.410548			0.205274	−	0.978705i	$-0.434191\pi$
$911$	11288.6			0.410548			0.205274	+	0.978705i	$0.434191\pi$
$912$	−32668.7	−	51884.2i	−1.18615	−	1.88383i
$913$	32804.2			1.18911
$914$	8051.65	−	31243.9i	0.291384	−	1.13070i
$915$		−	61862.5i		−	2.23510i
$916$	4813.25	−	8718.54i	0.173618	−	0.314486i
$917$		−	49566.0i		−	1.78497i
$918$	−14705.0	−	3789.54i	−0.528691	−	0.136245i
$919$	−24704.1			−0.886738			−0.443369	−	0.896339i	$-0.646217\pi$
$919$	−24704.1			−0.886738			−0.443369	+	0.896339i	$0.646217\pi$
$920$	3325.33	+	3139.40i	0.119166	+	0.112503i
$921$	95842.3			3.42900
$922$	28777.3	+	7416.01i	1.02791	+	0.264895i
$923$			11392.1i			0.406257i
$924$	135384.	+	74741.7i	4.82015	+	2.66106i
$925$		−	9651.10i		−	0.343055i
$926$	−595.108	+	2309.28i	−0.0211193	+	0.0819520i
$927$	−36129.2			−1.28008
$928$	1915.78	+	5986.49i	0.0677678	+	0.211763i
$929$	−19015.5			−0.671559			−0.335780	−	0.941941i	$-0.609000\pi$
$929$	−19015.5			−0.671559			−0.335780	+	0.941941i	$0.609000\pi$
$930$	−392.494	+	1523.04i	−0.0138391	+	0.0537017i
$931$			74070.1i			2.60746i
$932$	−21023.1	−	11606.2i	−0.738877	−	0.407912i
$933$			27857.8i			0.977517i
$934$	6368.81	+	1641.26i	0.223120	+	0.0574987i
$935$	8366.75			0.292644
$936$	14644.8	+	13826.0i	0.511409	+	0.482816i
$937$	−48300.8			−1.68401			−0.842006	−	0.539468i	$-0.818625\pi$
$937$	−48300.8			−1.68401			−0.842006	+	0.539468i	$0.818625\pi$
$938$	−10473.6	−	2699.09i	−0.364581	−	0.0939536i
$939$		−	146.275i		−	0.00508359i
$940$	10326.3	−	18704.7i	0.358305	−	0.649021i
$941$		−	45387.5i		−	1.57236i	−0.617999	−	0.786179i	$-0.712056\pi$
$941$		−	45387.5i		−	1.57236i	0.617999	−	0.786179i	$-0.287944\pi$
$942$	19666.3	−	76313.8i	0.680215	−	2.63953i
$943$	−2748.87			−0.0949265
$944$	−13859.0	+	8726.28i	−0.477831	+	0.300865i
$945$	−80364.7			−2.76642
$946$	11938.4	−	46326.1i	0.410307	−	1.59217i
$947$		−	8787.33i		−	0.301531i	−0.988570	−	0.150766i	$-0.951826\pi$
$947$		−	8787.33i		−	0.301531i	0.988570	−	0.150766i	$-0.0481739\pi$
$948$	−31095.3	+	56324.9i	−1.06533	+	1.92969i
$949$			11762.4i			0.402344i
$950$	18019.9	+	4643.80i	0.615415	+	0.158594i
$951$	68810.3			2.34630
$952$	−8626.35	+	9137.22i	−0.293678	+	0.311070i
$953$	−2944.50			−0.100086			−0.0500429	−	0.998747i	$-0.515936\pi$
$953$	−2944.50			−0.100086			−0.0500429	+	0.998747i	$0.515936\pi$
$954$	15900.7	+	4097.67i	0.539628	+	0.139064i
$955$			19404.5i			0.657503i
$956$	−11713.3	−	6466.56i	−0.396271	−	0.218769i
$957$		−	20547.4i		−	0.694046i
$958$	−9571.21	+	37140.4i	−0.322789	+	1.25256i
$959$	−98884.7			−3.32967
$960$	−2146.78	−	37292.4i	−0.0721739	−	1.25376i
$961$	−29732.9			−0.998050
$962$	1552.48	−	6024.29i	0.0520311	−	0.201903i
$963$		−	7304.28i		−	0.244421i
$964$	13614.6	+	7516.24i	0.454873	+	0.251122i
$965$		−	1402.14i		−	0.0467737i
$966$	21742.1	+	5603.02i	0.724163	+	0.186619i
$967$	−50768.0			−1.68830			−0.844152	−	0.536104i	$-0.819896\pi$
$967$	−50768.0			−1.68830			−0.844152	+	0.536104i	$0.819896\pi$
$968$	41332.3	−	43780.1i	1.37239	−	1.45366i
$969$	−16286.1			−0.539923
$970$	−18142.5	−	4675.37i	−0.600535	−	0.154760i
$971$			14369.7i			0.474917i	0.971398	+	0.237458i	$0.0763143\pi$
$971$			14369.7i			0.474917i	−0.971398	+	0.237458i	$0.923686\pi$
$972$	14775.9	−	26764.5i	0.487589	−	0.883201i
$973$			36573.8i			1.20504i
$974$	−14551.2	+	56465.0i	−0.478698	+	1.85755i
$975$	−8830.74			−0.290062
$976$	45922.5	−	28914.9i	1.50609	−	0.948303i
$977$	−17456.1			−0.571619			−0.285809	−	0.958287i	$-0.592262\pi$
$977$	−17456.1			−0.571619			−0.285809	+	0.958287i	$0.592262\pi$
$978$	−1143.03	+	4435.43i	−0.0373721	+	0.145020i
$979$		−	22748.0i		−	0.742624i
$980$	−21810.2	+	39506.1i	−0.710918	+	1.28773i
$981$			12861.7i			0.418595i
$982$	−28261.5	−	7283.09i	−0.918393	−	0.236673i
$983$	49621.1			1.61004			0.805019	−	0.593249i	$-0.202155\pi$
$983$	49621.1			1.61004			0.805019	+	0.593249i	$0.202155\pi$
$984$	16326.7	+	15413.9i	0.528939	+	0.499366i
$985$	−28084.8			−0.908484
$986$	1616.78	+	416.650i	0.0522198	+	0.0134572i
$987$		−	104898.i		−	3.38293i
$988$	10501.2	+	5797.39i	0.338145	+	0.186680i
$989$		−	6945.69i		−	0.223316i
$990$	−21093.1	+	81850.5i	−0.677155	+	2.62766i
$991$	−42593.5			−1.36531			−0.682657	−	0.730739i	$-0.739176\pi$
$991$	−42593.5			−1.36531			−0.682657	+	0.730739i	$0.739176\pi$
$992$	−1314.06	+	420.520i	−0.0420578	+	0.0134592i
$993$	−93652.9			−2.99294
$994$	17919.2	−	69534.4i	0.571795	−	2.21881i
$995$		−	24487.2i		−	0.780198i
$996$	−34057.4	−	18802.1i	−1.08349	−	0.598160i
$997$		−	6552.38i		−	0.208140i	−0.994570	−	0.104070i	$-0.966813\pi$
$997$		−	6552.38i		−	0.208140i	0.994570	−	0.104070i	$-0.0331867\pi$
$998$	38372.6	+	9888.75i	1.21710	+	0.313650i
$999$	−47387.1			−1.50076

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	136.4.c.b.69.13	✓	24
4.3	odd	2		544.4.c.a.273.1		24
8.3	odd	2		544.4.c.a.273.24		24
8.5	even	2	inner	136.4.c.b.69.14	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
136.4.c.b.69.13	✓	24	1.1	even	1	trivial
136.4.c.b.69.14	yes	24	8.5	even	2	inner
544.4.c.a.273.1		24	4.3	odd	2
544.4.c.a.273.24		24	8.3	odd	2

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:	\( N \)	\(=\)	\( 136 = 2^{3} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	136.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(0.705834 - 2.73894i) q^{2} +9.36589i q^{3} +(-7.00360 - 3.86648i) q^{4} -7.78969i q^{5} +(25.6526 + 6.61076i) q^{6} +32.6671 q^{7} +(-15.5334 + 16.4533i) q^{8} -60.7198 q^{9} +O(q^{10})\)	\(q+(0.705834 - 2.73894i) q^{2} +9.36589i q^{3} +(-7.00360 - 3.86648i) q^{4} -7.78969i q^{5} +(25.6526 + 6.61076i) q^{6} +32.6671 q^{7} +(-15.5334 + 16.4533i) q^{8} -60.7198 q^{9} +(-21.3355 - 5.49823i) q^{10} +63.1812i q^{11} +(36.2130 - 65.5949i) q^{12} +14.6588i q^{13} +(23.0576 - 89.4733i) q^{14} +72.9573 q^{15} +(34.1007 + 54.1585i) q^{16} +17.0000 q^{17} +(-42.8581 + 166.308i) q^{18} +102.287i q^{19} +(-30.1187 + 54.5558i) q^{20} +305.957i q^{21} +(173.050 + 44.5954i) q^{22} +25.9454 q^{23} +(-154.100 - 145.484i) q^{24} +64.3207 q^{25} +(40.1495 + 10.3467i) q^{26} -315.816i q^{27} +(-228.787 - 126.307i) q^{28} +34.7232i q^{29} +(51.4958 - 199.826i) q^{30} -7.62186 q^{31} +(172.406 - 55.1729i) q^{32} -591.748 q^{33} +(11.9992 - 46.5620i) q^{34} -254.467i q^{35} +(425.257 + 234.772i) q^{36} -150.046i q^{37} +(280.158 + 72.1975i) q^{38} -137.292 q^{39} +(128.166 + 121.001i) q^{40} -105.949 q^{41} +(837.997 + 215.955i) q^{42} -267.704i q^{43} +(244.289 - 442.495i) q^{44} +472.989i q^{45} +(18.3131 - 71.0628i) q^{46} -342.854 q^{47} +(-507.242 + 319.383i) q^{48} +724.141 q^{49} +(45.3998 - 176.171i) q^{50} +159.220i q^{51} +(56.6778 - 102.664i) q^{52} -95.6101i q^{53} +(-865.002 - 222.914i) q^{54} +492.162 q^{55} +(-507.432 + 537.483i) q^{56} -958.007 q^{57} +(95.1047 + 24.5088i) q^{58} +255.897i q^{59} +(-510.964 - 282.088i) q^{60} -847.927i q^{61} +(-5.37977 + 20.8758i) q^{62} -1983.54 q^{63} +(-29.4251 - 511.154i) q^{64} +114.187 q^{65} +(-417.676 + 1620.76i) q^{66} -117.059i q^{67} +(-119.061 - 65.7301i) q^{68} +243.001i q^{69} +(-696.969 - 179.611i) q^{70} +777.152 q^{71} +(943.187 - 999.044i) q^{72} +802.416 q^{73} +(-410.968 - 105.908i) q^{74} +602.421i q^{75} +(395.490 - 716.376i) q^{76} +2063.95i q^{77} +(-96.9056 + 376.036i) q^{78} -858.679 q^{79} +(421.878 - 265.634i) q^{80} +1318.46 q^{81} +(-74.7821 + 290.187i) q^{82} -519.209i q^{83} +(1182.97 - 2142.80i) q^{84} -132.425i q^{85} +(-733.226 - 188.955i) q^{86} -325.213 q^{87} +(-1039.54 - 981.420i) q^{88} -360.044 q^{89} +(1295.49 + 333.852i) q^{90} +478.860i q^{91} +(-181.711 - 100.317i) q^{92} -71.3854i q^{93} +(-241.998 + 939.057i) q^{94} +796.783 q^{95} +(516.743 + 1614.74i) q^{96} +850.341 q^{97} +(511.124 - 1983.38i) q^{98} -3836.35i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + q^{2} + 5 q^{4} + 40 q^{6} + 84 q^{7} + 13 q^{8} - 216 q^{9}+O(q^{10}) \) 24 * q + q^2 + 5 * q^4 + 40 * q^6 + 84 * q^7 + 13 * q^8 - 216 * q^9	\( 24 q + q^{2} + 5 q^{4} + 40 q^{6} + 84 q^{7} + 13 q^{8} - 216 q^{9} - 16 q^{10} - 18 q^{12} + 26 q^{14} - 180 q^{15} - 103 q^{16} + 408 q^{17} - 5 q^{18} - 24 q^{20} + 172 q^{22} + 624 q^{23} - 310 q^{24} - 600 q^{25} - 180 q^{26} - 132 q^{28} - 80 q^{30} - 744 q^{31} - 39 q^{32} - 280 q^{33} + 17 q^{34} + 791 q^{36} - 162 q^{38} + 1236 q^{39} - 1396 q^{40} + 1132 q^{42} + 886 q^{44} - 1246 q^{46} - 956 q^{47} - 2226 q^{48} + 1688 q^{49} + 2505 q^{50} + 2544 q^{52} - 3264 q^{54} + 1684 q^{55} - 1100 q^{56} - 168 q^{57} + 2800 q^{58} + 2520 q^{60} - 1946 q^{62} - 2520 q^{63} - 2143 q^{64} - 72 q^{65} + 3660 q^{66} + 85 q^{68} - 5084 q^{70} + 1532 q^{71} - 2277 q^{72} + 216 q^{73} + 2188 q^{74} + 2094 q^{76} - 4748 q^{78} - 3176 q^{79} + 116 q^{80} + 2040 q^{81} + 3198 q^{82} + 5916 q^{84} - 2066 q^{86} - 236 q^{87} - 3598 q^{88} - 424 q^{89} + 2180 q^{90} + 1940 q^{92} - 2156 q^{94} - 1248 q^{95} - 4674 q^{96} - 1304 q^{97} + 3705 q^{98}+O(q^{100}) \) 24 * q + q^2 + 5 * q^4 + 40 * q^6 + 84 * q^7 + 13 * q^8 - 216 * q^9 - 16 * q^10 - 18 * q^12 + 26 * q^14 - 180 * q^15 - 103 * q^16 + 408 * q^17 - 5 * q^18 - 24 * q^20 + 172 * q^22 + 624 * q^23 - 310 * q^24 - 600 * q^25 - 180 * q^26 - 132 * q^28 - 80 * q^30 - 744 * q^31 - 39 * q^32 - 280 * q^33 + 17 * q^34 + 791 * q^36 - 162 * q^38 + 1236 * q^39 - 1396 * q^40 + 1132 * q^42 + 886 * q^44 - 1246 * q^46 - 956 * q^47 - 2226 * q^48 + 1688 * q^49 + 2505 * q^50 + 2544 * q^52 - 3264 * q^54 + 1684 * q^55 - 1100 * q^56 - 168 * q^57 + 2800 * q^58 + 2520 * q^60 - 1946 * q^62 - 2520 * q^63 - 2143 * q^64 - 72 * q^65 + 3660 * q^66 + 85 * q^68 - 5084 * q^70 + 1532 * q^71 - 2277 * q^72 + 216 * q^73 + 2188 * q^74 + 2094 * q^76 - 4748 * q^78 - 3176 * q^79 + 116 * q^80 + 2040 * q^81 + 3198 * q^82 + 5916 * q^84 - 2066 * q^86 - 236 * q^87 - 3598 * q^88 - 424 * q^89 + 2180 * q^90 + 1940 * q^92 - 2156 * q^94 - 1248 * q^95 - 4674 * q^96 - 1304 * q^97 + 3705 * q^98

Introduction

L-functions

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