LMFDB - Embedded newform 105.4.g.b.104.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [105,4,Mod(104,105)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(105, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("105.104");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 105 = 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	105.g (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:	$6.19520055060$
Analytic rank:	$0$
Dimension:	$40$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			104.16
Character	$\chi$	$=$	105.104
Dual form			105.4.g.b.104.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.24438 q^{2} +(1.06702 + 5.08542i) q^{3} -2.96275 q^{4} +(-8.51335 + 7.24727i) q^{5} +(-2.39479 - 11.4136i) q^{6} +(-12.2768 - 13.8665i) q^{7} +24.6046 q^{8} +(-24.7230 + 10.8524i) q^{9} +O(q^{10})$	\(q-2.24438 q^{2} +(1.06702 + 5.08542i) q^{3} -2.96275 q^{4} +(-8.51335 + 7.24727i) q^{5} +(-2.39479 - 11.4136i) q^{6} +(-12.2768 - 13.8665i) q^{7} +24.6046 q^{8} +(-24.7230 + 10.8524i) q^{9} +(19.1072 - 16.2656i) q^{10} -25.7488i q^{11} +(-3.16130 - 15.0668i) q^{12} +68.2910 q^{13} +(27.5539 + 31.1217i) q^{14} +(-45.9393 - 35.5610i) q^{15} -31.5201 q^{16} +30.6502i q^{17} +(55.4878 - 24.3570i) q^{18} -109.632i q^{19} +(25.2229 - 21.4718i) q^{20} +(57.4174 - 77.2285i) q^{21} +57.7902i q^{22} -152.265 q^{23} +(26.2535 + 125.125i) q^{24} +(19.9543 - 123.397i) q^{25} -153.271 q^{26} +(-81.5690 - 114.147i) q^{27} +(36.3731 + 41.0829i) q^{28} -191.763i q^{29} +(103.105 + 79.8125i) q^{30} -16.4683i q^{31} -126.094 q^{32} +(130.944 - 27.4744i) q^{33} -68.7908i q^{34} +(205.011 + 29.0770i) q^{35} +(73.2479 - 32.1531i) q^{36} +81.9337i q^{37} +246.055i q^{38} +(72.8676 + 347.288i) q^{39} +(-209.468 + 178.316i) q^{40} -372.656 q^{41} +(-128.867 + 173.330i) q^{42} +192.593i q^{43} +76.2873i q^{44} +(131.825 - 271.565i) q^{45} +341.741 q^{46} -0.366739i q^{47} +(-33.6325 - 160.293i) q^{48} +(-41.5595 + 340.473i) q^{49} +(-44.7850 + 276.950i) q^{50} +(-155.869 + 32.7043i) q^{51} -202.329 q^{52} +5.95065 q^{53} +(183.072 + 256.189i) q^{54} +(186.609 + 219.209i) q^{55} +(-302.066 - 341.180i) q^{56} +(557.523 - 116.979i) q^{57} +430.389i q^{58} +198.813 q^{59} +(136.106 + 105.358i) q^{60} -83.5752i q^{61} +36.9613i q^{62} +(454.005 + 209.587i) q^{63} +535.163 q^{64} +(-581.385 + 494.923i) q^{65} +(-293.887 + 61.6631i) q^{66} -1080.15i q^{67} -90.8089i q^{68} +(-162.469 - 774.332i) q^{69} +(-460.123 - 65.2599i) q^{70} -773.288i q^{71} +(-608.298 + 267.020i) q^{72} -448.111 q^{73} -183.891i q^{74} +(648.817 - 30.1909i) q^{75} +324.811i q^{76} +(-357.046 + 316.114i) q^{77} +(-163.543 - 779.447i) q^{78} -1270.27 q^{79} +(268.342 - 228.435i) q^{80} +(493.449 - 536.609i) q^{81} +836.382 q^{82} +429.749i q^{83} +(-170.113 + 228.809i) q^{84} +(-222.130 - 260.936i) q^{85} -432.253i q^{86} +(975.193 - 204.614i) q^{87} -633.540i q^{88} -5.29611 q^{89} +(-295.865 + 609.495i) q^{90} +(-838.395 - 946.956i) q^{91} +451.123 q^{92} +(83.7484 - 17.5720i) q^{93} +0.823102i q^{94} +(794.530 + 933.333i) q^{95} +(-134.544 - 641.238i) q^{96} +435.169 q^{97} +(93.2755 - 764.151i) q^{98} +(279.438 + 636.587i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 184 q^{4} + 4 q^{9}+O(q^{10}) $ 40 * q + 184 * q^4 + 4 * q^9	$ 40 q + 184 q^{4} + 4 q^{9} - 188 q^{15} + 184 q^{16} + 148 q^{21} + 712 q^{25} - 336 q^{30} - 1520 q^{36} + 644 q^{39} - 1488 q^{46} - 1496 q^{49} - 220 q^{51} + 1984 q^{60} + 40 q^{64} - 3000 q^{70} - 1192 q^{79} + 4636 q^{81} - 2192 q^{84} + 4808 q^{85} - 4408 q^{91} + 5276 q^{99}+O(q^{100}) $ 40 * q + 184 * q^4 + 4 * q^9 - 188 * q^15 + 184 * q^16 + 148 * q^21 + 712 * q^25 - 336 * q^30 - 1520 * q^36 + 644 * q^39 - 1488 * q^46 - 1496 * q^49 - 220 * q^51 + 1984 * q^60 + 40 * q^64 - 3000 * q^70 - 1192 * q^79 + 4636 * q^81 - 2192 * q^84 + 4808 * q^85 - 4408 * q^91 + 5276 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/105\mathbb{Z}\right)^\times$.

$n$	$22$	$31$	$71$
$\chi(n)$	$-1$	$-1$	$-1$

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 $

$2$	−2.24438			−0.793509			−0.396754	−	0.917925i	$-0.629864\pi$
$2$	−2.24438			−0.793509			−0.396754	+	0.917925i	$0.629864\pi$
$3$	1.06702	+	5.08542i	0.205347	+	0.978689i
$3$	1.06702	+	5.08542i	0.205347	+	0.978689i
$4$	−2.96275			−0.370344
$5$	−8.51335	+	7.24727i	−0.761457	+	0.648215i
$5$	−8.51335	+	7.24727i	−0.761457	+	0.648215i
$6$	−2.39479	−	11.4136i	−0.162945	−	0.776599i
$7$	−12.2768	−	13.8665i	−0.662886	−	0.748721i
$7$	−12.2768	−	13.8665i	−0.662886	−	0.748721i
$8$	24.6046			1.08738
$9$	−24.7230	+	10.8524i	−0.915665	+	0.401943i
$10$	19.1072	−	16.2656i	0.604223	−	0.514365i
$11$		−	25.7488i		−	0.705779i	−0.935665	−	0.352889i	$-0.885199\pi$
$11$		−	25.7488i		−	0.705779i	0.935665	−	0.352889i	$-0.114801\pi$
$12$	−3.16130	−	15.0668i	−0.0760491	−	0.362451i
$13$	68.2910			1.45696			0.728481	−	0.685066i	$-0.240227\pi$
$13$	68.2910			1.45696			0.728481	+	0.685066i	$0.240227\pi$
$14$	27.5539	+	31.1217i	0.526006	+	0.594116i
$15$	−45.9393	−	35.5610i	−0.790764	−	0.612121i
$16$	−31.5201			−0.492502
$17$			30.6502i			0.437281i	0.975806	+	0.218640i	$0.0701621\pi$
$17$			30.6502i			0.437281i	−0.975806	+	0.218640i	$0.929838\pi$
$18$	55.4878	−	24.3570i	0.726588	−	0.318945i
$19$		−	109.632i		−	1.32375i	−0.749615	−	0.661874i	$-0.769761\pi$
$19$		−	109.632i		−	1.32375i	0.749615	−	0.661874i	$-0.230239\pi$
$20$	25.2229	−	21.4718i	0.282001	−	0.240062i
$21$	57.4174	−	77.2285i	0.596643	−	0.802507i
$22$			57.7902i			0.560042i
$23$	−152.265			−1.38041			−0.690206	−	0.723613i	$-0.742480\pi$
$23$	−152.265			−1.38041			−0.690206	+	0.723613i	$0.742480\pi$
$24$	26.2535	+	125.125i	0.223291	+	1.06421i
$25$	19.9543	−	123.397i	0.159634	−	0.987176i
$26$	−153.271			−1.15611
$27$	−81.5690	−	114.147i	−0.581406	−	0.813613i
$28$	36.3731	+	41.0829i	0.245495	+	0.277284i
$29$		−	191.763i		−	1.22791i	−0.789340	−	0.613956i	$-0.789577\pi$
$29$		−	191.763i		−	1.22791i	0.789340	−	0.613956i	$-0.210423\pi$
$30$	103.105	+	79.8125i	0.627479	+	0.485723i
$31$		−	16.4683i		−	0.0954130i	−0.998861	−	0.0477065i	$-0.984809\pi$
$31$		−	16.4683i		−	0.0954130i	0.998861	−	0.0477065i	$-0.0151912\pi$
$32$	−126.094			−0.696575
$33$	130.944	−	27.4744i	0.690738	−	0.144930i
$34$		−	68.7908i		−	0.346986i
$35$	205.011	+	29.0770i	0.990091	+	0.140426i
$36$	73.2479	−	32.1531i	0.339111	−	0.148857i
$37$			81.9337i			0.364049i	0.983294	+	0.182025i	$0.0582651\pi$
$37$			81.9337i			0.364049i	−0.983294	+	0.182025i	$0.941735\pi$
$38$			246.055i			1.05041i
$39$	72.8676	+	347.288i	0.299183	+	1.42591i
$40$	−209.468	+	178.316i	−0.827993	+	0.704856i
$41$	−372.656			−1.41949			−0.709745	−	0.704459i	$-0.751190\pi$
$41$	−372.656			−1.41949			−0.709745	+	0.704459i	$0.751190\pi$
$42$	−128.867	+	173.330i	−0.473441	+	0.636796i
$43$			192.593i			0.683028i	0.939877	+	0.341514i	$0.110940\pi$
$43$			192.593i			0.683028i	−0.939877	+	0.341514i	$0.889060\pi$
$44$			76.2873i			0.261381i
$45$	131.825	−	271.565i	0.436694	−	0.899610i
$46$	341.741			1.09537
$47$		−	0.366739i		−	0.00113818i	−1.00000		0.000569089i	$-0.999819\pi$
$47$		−	0.366739i		−	0.00113818i	1.00000		0.000569089i	$-0.000181147\pi$
$48$	−33.6325	−	160.293i	−0.101134	−	0.482006i
$49$	−41.5595	+	340.473i	−0.121165	+	0.992632i
$50$	−44.7850	+	276.950i	−0.126671	+	0.783333i
$51$	−155.869	+	32.7043i	−0.427962	+	0.0897944i
$52$	−202.329			−0.539576
$53$	5.95065			0.0154223			0.00771117	−	0.999970i	$-0.497545\pi$
$53$	5.95065			0.0154223			0.00771117	+	0.999970i	$0.497545\pi$
$54$	183.072	+	256.189i	0.461351	+	0.645610i
$55$	186.609	+	219.209i	0.457497	+	0.537420i
$56$	−302.066	−	341.180i	−0.720809	−	0.814144i
$57$	557.523	−	116.979i	1.29554	−	0.271828i
$58$			430.389i			0.974359i
$59$	198.813			0.438699			0.219349	−	0.975646i	$-0.429607\pi$
$59$	198.813			0.438699			0.219349	+	0.975646i	$0.429607\pi$
$60$	136.106	+	105.358i	0.292855	+	0.226695i
$61$		−	83.5752i		−	0.175421i	−0.996146	−	0.0877107i	$-0.972045\pi$
$61$		−	83.5752i		−	0.175421i	0.996146	−	0.0877107i	$-0.0279551\pi$
$62$			36.9613i			0.0757110i
$63$	454.005	+	209.587i	0.907924	+	0.419135i
$64$	535.163			1.04524
$65$	−581.385	+	494.923i	−1.10941	+	0.944425i
$66$	−293.887	+	61.6631i	−0.548107	+	0.115003i
$67$		−	1080.15i		−	1.96958i	−0.173757	−	0.984789i	$-0.555591\pi$
$67$		−	1080.15i		−	1.96958i	0.173757	−	0.984789i	$-0.444409\pi$
$68$		−	90.8089i		−	0.161944i
$69$	−162.469	−	774.332i	−0.283464	−	1.35099i
$70$	−460.123	−	65.2599i	−0.785646	−	0.111429i
$71$		−	773.288i		−	1.29257i	−0.763097	−	0.646284i	$-0.776322\pi$
$71$		−	773.288i		−	1.29257i	0.763097	−	0.646284i	$-0.223678\pi$
$72$	−608.298	+	267.020i	−0.995676	+	0.437064i
$73$	−448.111			−0.718459			−0.359229	−	0.933249i	$-0.616960\pi$
$73$	−448.111			−0.718459			−0.359229	+	0.933249i	$0.616960\pi$
$74$		−	183.891i		−	0.288876i
$75$	648.817	−	30.1909i	0.998919	−	0.0464820i
$76$			324.811i			0.490242i
$77$	−357.046	+	316.114i	−0.528431	+	0.467851i
$78$	−163.543	−	779.447i	−0.237405	−	1.13147i
$79$	−1270.27			−1.80908			−0.904538	−	0.426393i	$-0.859784\pi$
$79$	−1270.27			−1.80908			−0.904538	+	0.426393i	$0.859784\pi$
$80$	268.342	−	228.435i	0.375019	−	0.319247i
$81$	493.449	−	536.609i	0.676884	−	0.736089i
$82$	836.382			1.12638
$83$			429.749i			0.568327i	0.958776	+	0.284163i	$0.0917158\pi$
$83$			429.749i			0.568327i	−0.958776	+	0.284163i	$0.908284\pi$
$84$	−170.113	+	228.809i	−0.220963	+	0.297203i
$85$	−222.130	−	260.936i	−0.283452	−	0.332971i
$86$		−	432.253i		−	0.541989i
$87$	975.193	−	204.614i	1.20174	−	0.252148i
$88$		−	633.540i		−	0.767450i
$89$	−5.29611			−0.00630772			−0.00315386	−	0.999995i	$-0.501004\pi$
$89$	−5.29611			−0.00630772			−0.00315386	+	0.999995i	$0.501004\pi$
$90$	−295.865	+	609.495i	−0.346521	+	0.713849i
$91$	−838.395	−	946.956i	−0.965799	−	1.09086i
$92$	451.123			0.511227
$93$	83.7484	−	17.5720i	0.0933796	−	0.0195928i
$94$			0.823102i			0.000903154i
$95$	794.530	+	933.333i	0.858074	+	1.00798i
$96$	−134.544	−	641.238i	−0.143040	−	0.681730i
$97$	435.169			0.455513			0.227757	−	0.973718i	$-0.426861\pi$
$97$	435.169			0.455513			0.227757	+	0.973718i	$0.426861\pi$
$98$	93.2755	−	764.151i	0.0961454	−	0.787663i
$99$	279.438	+	636.587i	0.283682	+	0.646257i
$100$	−59.1194	+	365.594i	−0.0591194	+	0.365594i
$101$	−1122.41			−1.10578			−0.552891	−	0.833254i	$-0.686475\pi$
$101$	−1122.41			−1.10578			−0.552891	+	0.833254i	$0.686475\pi$
$102$	349.830	−	73.4009i	0.339592	−	0.0712527i
$103$	−625.230			−0.598114			−0.299057	−	0.954235i	$-0.596672\pi$
$103$	−625.230			−0.598114			−0.299057	+	0.954235i	$0.596672\pi$
$104$	1680.27			1.58427
$105$	70.8815	+	1073.59i	0.0658793	+	0.997828i
$106$	−13.3555			−0.0122378
$107$	988.994			0.893548			0.446774	−	0.894647i	$-0.352573\pi$
$107$	988.994			0.893548			0.446774	+	0.894647i	$0.352573\pi$
$108$	241.669	+	338.188i	0.215320	+	0.301317i
$109$	810.973			0.712634			0.356317	−	0.934365i	$-0.384032\pi$
$109$	810.973			0.712634			0.356317	+	0.934365i	$0.384032\pi$
$110$	−418.821	−	491.988i	−0.363028	−	0.426448i
$111$	−416.667	+	87.4246i	−0.356291	+	0.0747566i
$112$	386.967	+	437.074i	0.326473	+	0.368746i
$113$	−107.711			−0.0896687			−0.0448343	−	0.998994i	$-0.514276\pi$
$113$	−107.711			−0.0896687			−0.0448343	+	0.998994i	$0.514276\pi$
$114$	−1251.29	+	262.545i	−1.02802	+	0.215698i
$115$	1296.29	−	1103.51i	1.05112	−	0.894804i
$116$			568.145i			0.454749i
$117$	−1688.35	+	741.124i	−1.33409	+	0.585615i
$118$	−446.212			−0.348111
$119$	425.011	−	376.287i	0.327401	−	0.289867i
$120$	−1130.32	−	874.964i	−0.859861	−	0.665608i
$121$	667.997			0.501876
$122$			187.575i			0.139199i
$123$	−397.630	−	1895.11i	−0.291488	−	1.38924i
$124$			48.7916i			0.0353356i
$125$	724.414	+	1195.14i	0.518348	+	0.855170i
$126$	−1018.96	−	470.394i	−0.720446	−	0.332587i
$127$		−	33.0601i		−	0.0230993i	−0.999933	−	0.0115496i	$-0.996324\pi$
$127$		−	33.0601i		−	0.0230993i	0.999933	−	0.0115496i	$-0.00367645\pi$
$128$	−192.362			−0.132833
$129$	−979.418	+	205.500i	−0.668472	+	0.140258i
$130$	1304.85	−	1110.80i	0.880330	−	0.749409i
$131$	−997.301			−0.665150			−0.332575	−	0.943077i	$-0.607917\pi$
$131$	−997.301			−0.665150			−0.332575	+	0.943077i	$0.607917\pi$
$132$	−387.953	+	81.3998i	−0.255810	+	0.0536738i
$133$	−1520.21	+	1345.93i	−0.991118	+	0.877494i
$134$			2424.28i			1.56288i
$135$	1521.68	+	380.619i	0.970113	+	0.242655i
$136$			754.136i			0.475490i
$137$	−1373.30			−0.856418			−0.428209	−	0.903680i	$-0.640855\pi$
$137$	−1373.30			−0.856418			−0.428209	+	0.903680i	$0.640855\pi$
$138$	364.643	+	1737.90i	0.224931	+	1.07203i
$139$			1361.65i			0.830891i	0.909618	+	0.415446i	$0.136374\pi$
$139$			1361.65i			0.830891i	−0.909618	+	0.415446i	$0.863626\pi$
$140$	−607.396	−	86.1478i	−0.366674	−	0.0520058i
$141$	1.86502	−	0.391316i	0.00111392	−	0.000233722i
$142$			1735.55i			1.02567i
$143$		−	1758.41i		−	1.02829i
$144$	779.271	−	342.071i	0.450967	−	0.197958i
$145$	1389.76	+	1632.54i	0.795951	+	0.935002i
$146$	1005.73			0.570103
$147$	−1775.79	+	151.942i	−0.996359	+	0.0852517i
$148$		−	242.749i		−	0.134823i
$149$		−	2971.73i		−	1.63392i	−0.576697	−	0.816958i	$-0.695659\pi$
$149$		−	2971.73i		−	1.63392i	0.576697	−	0.816958i	$-0.304341\pi$
$150$	−1456.19	+	67.7600i	−0.792651	+	0.0368839i
$151$	1456.31			0.784851			0.392425	−	0.919784i	$-0.371636\pi$
$151$	1456.31			0.784851			0.392425	+	0.919784i	$0.371636\pi$
$152$		−	2697.44i		−	1.43942i
$153$	−332.630	−	757.764i	−0.175762	−	0.400403i
$154$	801.348	−	709.480i	0.419315	−	0.371244i
$155$	119.350	+	140.201i	0.0618481	+	0.0726529i
$156$	−215.888	−	1028.93i	−0.110801	−	0.528078i
$157$	−2903.14			−1.47577			−0.737885	−	0.674927i	$-0.764175\pi$
$157$	−2903.14			−1.47577			−0.737885	+	0.674927i	$0.764175\pi$
$158$	2850.98			1.43552
$159$	6.34944	+	30.2615i	0.00316694	+	0.0150937i
$160$	1073.48	−	913.834i	0.530412	−	0.451531i
$161$	1869.33	+	2111.38i	0.915056	+	1.03354i
$162$	−1107.49	+	1204.36i	−0.537114	+	0.584093i
$163$			1666.60i			0.800850i	0.916330	+	0.400425i	$0.131137\pi$
$163$			1666.60i			0.800850i	−0.916330	+	0.400425i	$0.868863\pi$
$164$	1104.09			0.525699
$165$	−915.654	+	1182.88i	−0.432022	+	0.558105i
$166$		−	964.522i		−	0.450972i
$167$		−	1688.52i		−	0.782403i	−0.920305	−	0.391201i	$-0.872060\pi$
$167$		−	1688.52i		−	0.782403i	0.920305	−	0.391201i	$-0.127940\pi$
$168$	1412.73	−	1900.18i	0.648777	−	0.872630i
$169$	2466.65			1.12274
$170$	498.545	+	585.640i	0.224922	+	0.264215i
$171$	1189.77	+	2710.42i	0.532071	+	1.21211i
$172$		−	570.606i		−	0.252955i
$173$			719.668i			0.316274i	0.987417	+	0.158137i	$0.0505487\pi$
$173$			719.668i			0.316274i	−0.987417	+	0.158137i	$0.949451\pi$
$174$	−2188.71	+	459.232i	−0.953594	+	0.200082i
$175$	−1956.06	+	1238.23i	−0.844938	+	0.534864i
$176$			811.607i			0.347598i
$177$	212.136	+	1011.05i	0.0900856	+	0.429350i
$178$	11.8865			0.00500523
$179$		−	1130.92i		−	0.472231i	−0.971725	−	0.236115i	$-0.924126\pi$
$179$		−	1130.92i		−	0.472231i	0.971725	−	0.236115i	$-0.0758743\pi$
$180$	−390.563	+	804.577i	−0.161727	+	0.333165i
$181$			1072.04i			0.440243i	0.975472	+	0.220121i	$0.0706453\pi$
$181$			1072.04i			0.440243i	−0.975472	+	0.220121i	$0.929355\pi$
$182$	1881.68	+	2125.33i	0.766370	+	0.865605i
$183$	425.015	−	89.1761i	0.171683	−	0.0360223i
$184$	−3746.42			−1.50103
$185$	−593.796	−	697.530i	−0.235982	−	0.277208i
$186$	−187.963	+	39.4383i	−0.0740976	+	0.0155471i
$187$	789.208			0.308623
$188$			1.08655i			0.000421517i
$189$	−581.409	+	2532.44i	−0.223763	+	0.974644i
$190$	−1783.23	−	2094.75i	−0.680889	−	0.799839i
$191$			1611.22i			0.610386i	0.952291	+	0.305193i	$0.0987209\pi$
$191$			1611.22i			0.610386i	−0.952291	+	0.305193i	$0.901279\pi$
$192$	571.028	+	2721.53i	0.214637	+	1.02297i
$193$			1961.99i			0.731747i	0.930665	+	0.365874i	$0.119230\pi$
$193$			1961.99i			0.731747i	−0.930665	+	0.365874i	$0.880770\pi$
$194$	−976.687			−0.361454
$195$	−3137.24	−	2428.49i	−1.15211	−	0.891836i
$196$	123.130	−	1008.74i	0.0448726	−	0.367615i
$197$	−658.980			−0.238327			−0.119163	−	0.992875i	$-0.538021\pi$
$197$	−658.980			−0.238327			−0.119163	+	0.992875i	$0.538021\pi$
$198$	−627.165	−	1428.75i	−0.225105	−	0.512811i
$199$		−	5062.64i		−	1.80342i	−0.432338	−	0.901712i	$-0.642311\pi$
$199$		−	5062.64i		−	1.80342i	0.432338	−	0.901712i	$-0.357689\pi$
$200$	490.966	−	3036.13i	0.173583	−	1.07344i
$201$	5493.03	−	1152.54i	1.92760	−	0.404447i
$202$	2519.12			0.877447
$203$	−2659.08	+	2354.23i	−0.919362	+	0.813965i
$204$	461.801	−	96.8946i	0.158493	−	0.0332548i
$205$	3172.55	−	2700.74i	1.08088	−	0.920135i
$206$	1403.26			0.474609
$207$	3764.44	−	1652.45i	1.26399	−	0.554846i
$208$	−2152.54			−0.717557
$209$	−2822.89			−0.934274
$210$	−159.085	−	2409.55i	−0.0522758	−	0.791785i
$211$	−3467.27			−1.13126			−0.565631	−	0.824658i	$-0.691368\pi$
$211$	−3467.27			−1.13126			−0.565631	+	0.824658i	$0.691368\pi$
$212$	−17.6303			−0.00571157
$213$	3932.49	−	825.111i	1.26502	−	0.265426i
$214$	−2219.68			−0.709038
$215$	−1395.78	−	1639.61i	−0.442749	−	0.520097i
$216$	−2006.97	−	2808.54i	−0.632209	−	0.884707i
$217$	−228.358	+	202.179i	−0.0714376	+	0.0632479i
$218$	−1820.13			−0.565481
$219$	−478.142	−	2278.83i	−0.147534	−	0.703148i
$220$	−552.875	−	649.461i	−0.169431	−	0.199030i
$221$			2093.13i			0.637101i
$222$	935.161	−	196.214i	0.282720	−	0.0593200i
$223$	2047.08			0.614720			0.307360	−	0.951593i	$-0.400555\pi$
$223$	2047.08			0.614720			0.307360	+	0.951593i	$0.400555\pi$
$224$	1548.03	+	1748.48i	0.461750	+	0.521540i
$225$	845.832	+	3267.29i	0.250617	+	0.968086i
$226$	241.744			0.0711529
$227$			3998.46i			1.16911i	0.811355	+	0.584553i	$0.198730\pi$
$227$			3998.46i			1.16911i	−0.811355	+	0.584553i	$0.801270\pi$
$228$	−1651.80	+	346.579i	−0.479794	+	0.100670i
$229$			3325.60i			0.959659i	0.877362	+	0.479829i	$0.159301\pi$
$229$			3325.60i			0.959659i	−0.877362	+	0.479829i	$0.840699\pi$
$230$	−2909.36	+	2476.69i	−0.834077	+	0.710035i
$231$	−1988.54	−	1478.43i	−0.566392	−	0.421098i
$232$		−	4718.24i		−	1.33521i
$233$	3464.53			0.974116			0.487058	−	0.873370i	$-0.338070\pi$
$233$	3464.53			0.974116			0.487058	+	0.873370i	$0.338070\pi$
$234$	3789.31	−	1663.37i	1.05861	−	0.464691i
$235$	2.65785	+	3.12217i	0.000737784	+	0.000866673i
$236$	−589.032			−0.162469
$237$	−1355.40	−	6459.88i	−0.371489	−	1.77052i
$238$	−953.888	+	844.532i	−0.259796	+	0.230012i
$239$		−	4519.56i		−	1.22321i	−0.791165	−	0.611603i	$-0.790525\pi$
$239$		−	4519.56i		−	1.22321i	0.791165	−	0.611603i	$-0.209475\pi$
$240$	1448.01	+	1120.89i	0.389453	+	0.301471i
$241$			7087.15i			1.89429i	0.320810	+	0.947143i	$0.396045\pi$
$241$			7087.15i			1.89429i	−0.320810	+	0.947143i	$0.603955\pi$
$242$	−1499.24			−0.398243
$243$	3255.40	+	1936.82i	0.859399	+	0.511305i
$244$			247.612i			0.0649662i
$245$	−2113.69	−	3199.76i	−0.551178	−	0.834388i
$246$	892.433	+	4253.35i	0.231299	+	1.10237i
$247$		−	7486.85i		−	1.92865i
$248$		−	405.197i		−	0.103750i
$249$	−2185.46	+	458.550i	−0.556215	+	0.116704i
$250$	−1625.86	−	2682.34i	−0.411314	−	0.678585i
$251$	4749.21			1.19429			0.597146	−	0.802132i	$-0.296301\pi$
$251$	4749.21			1.19429			0.597146	+	0.802132i	$0.296301\pi$
$252$	−1345.10	−	620.954i	−0.336244	−	0.155224i
$253$			3920.65i			0.974266i
$254$			74.1995i			0.0183295i
$255$	1089.95	−	1408.05i	0.267669	−	0.345786i
$256$	−3849.57			−0.939837
$257$		−	1571.33i		−	0.381389i	−0.981649	−	0.190695i	$-0.938926\pi$
$257$		−	1571.33i		−	0.381389i	0.981649	−	0.190695i	$-0.0610740\pi$
$258$	2198.19	−	461.221i	0.530439	−	0.111296i
$259$	1136.13	−	1005.89i	0.272571	−	0.241323i
$260$	1722.50	−	1466.33i	0.410864	−	0.349762i
$261$	2081.09	+	4740.94i	0.493550	+	1.12436i
$262$	2238.33			0.527802
$263$	−5430.48			−1.27322			−0.636612	−	0.771184i	$-0.719665\pi$
$263$	−5430.48			−1.27322			−0.636612	+	0.771184i	$0.719665\pi$
$264$	3221.81	−	675.997i	0.751095	−	0.157594i
$265$	−50.6599	+	43.1259i	−0.0117435	+	0.00999700i
$266$	3411.93	−	3020.78i	0.786461	−	0.696299i
$267$	−5.65104	−	26.9330i	−0.00129527	−	0.00617330i
$268$			3200.22i			0.729420i
$269$	−5118.42			−1.16013			−0.580066	−	0.814570i	$-0.696973\pi$
$269$	−5118.42			−1.16013			−0.580066	+	0.814570i	$0.696973\pi$
$270$	−3415.23	−	854.255i	−0.769793	−	0.192549i
$271$		−	6280.28i		−	1.40775i	−0.710324	−	0.703875i	$-0.751452\pi$
$271$		−	6280.28i		−	1.40775i	0.710324	−	0.703875i	$-0.248548\pi$
$272$		−	966.099i		−	0.215362i
$273$	3921.09	−	5274.01i	0.869286	−	1.16922i
$274$	3082.22			0.679575
$275$	−3177.33	−	513.799i	−0.696728	−	0.112666i
$276$	481.356	+	2294.15i	0.104979	+	0.500332i
$277$			5807.51i			1.25971i	0.776713	+	0.629854i	$0.216885\pi$
$277$			5807.51i			1.25971i	−0.776713	+	0.629854i	$0.783115\pi$
$278$		−	3056.07i		−	0.659320i
$279$	178.722	+	407.146i	0.0383505	+	0.0873663i
$280$	5044.21	+	715.428i	1.07661	+	0.152696i
$281$			201.056i			0.0426833i	0.999772	+	0.0213416i	$0.00679377\pi$
$281$			201.056i			0.0426833i	−0.999772	+	0.0213416i	$0.993206\pi$
$282$	−4.18582	+	0.878263i	−0.000883907	+	0.000185460i
$283$	−4808.75			−1.01007			−0.505036	−	0.863098i	$-0.668521\pi$
$283$	−4808.75			−1.01007			−0.505036	+	0.863098i	$0.668521\pi$
$284$			2291.06i			0.478695i
$285$	−3898.61	+	5036.40i	−0.810294	+	1.04677i
$286$			3946.55i			0.815959i
$287$	4575.03	+	5167.43i	0.940959	+	1.06280i
$288$	3117.40	−	1368.42i	0.637829	−	0.279983i
$289$	3973.56			0.808786
$290$	−3119.14	−	3664.05i	−0.631594	−	0.741932i
$291$	464.333	+	2213.02i	0.0935384	+	0.445806i
$292$	1327.64			0.266076
$293$			6701.42i			1.33618i	0.744080	+	0.668091i	$0.232888\pi$
$293$			6701.42i			1.33618i	−0.744080	+	0.668091i	$0.767112\pi$
$294$	3985.56	−	341.017i	0.790620	−	0.0676480i
$295$	−1692.56	+	1440.85i	−0.334050	+	0.284371i
$296$			2015.95i			0.395860i
$297$	−2939.15	+	2100.31i	−0.574231	+	0.410344i
$298$			6669.69i			1.29653i
$299$	−10398.3			−2.01121
$300$	−1922.28	+	89.4482i	−0.369943	+	0.0172143i
$301$	2670.60	−	2364.43i	0.511397	−	0.452770i
$302$	−3268.51			−0.622786
$303$	−1197.63	−	5707.92i	−0.227069	−	1.08222i
$304$			3455.60i			0.651949i
$305$	605.692	+	711.505i	0.113711	+	0.133576i
$306$	746.549	+	1700.71i	0.139468	+	0.317723i
$307$	1476.12			0.274419			0.137209	−	0.990542i	$-0.456187\pi$
$307$	1476.12			0.274419			0.137209	+	0.990542i	$0.456187\pi$
$308$	1057.84	−	936.566i	0.195701	−	0.173266i
$309$	−667.131	−	3179.56i	−0.122821	−	0.585368i
$310$	−267.868	−	314.664i	−0.0490771	−	0.0576507i
$311$	−2162.00			−0.394199			−0.197100	−	0.980383i	$-0.563152\pi$
$311$	−2162.00			−0.394199			−0.197100	+	0.980383i	$0.563152\pi$
$312$	1792.88	+	8544.88i	0.325326	+	1.55051i
$313$	−1187.83			−0.214505			−0.107253	−	0.994232i	$-0.534205\pi$
$313$	−1187.83			−0.214505			−0.107253	+	0.994232i	$0.534205\pi$
$314$	6515.75			1.17104
$315$	−5384.03	+	1506.00i	−0.963035	+	0.269377i
$316$	3763.50			0.669980
$317$	−4280.71			−0.758450			−0.379225	−	0.925305i	$-0.623809\pi$
$317$	−4280.71			−0.758450			−0.379225	+	0.925305i	$0.623809\pi$
$318$	−14.2506	−	67.9184i	−0.00251299	−	0.0119770i
$319$	−4937.67			−0.866634
$320$	−4556.03	+	3878.47i	−0.795906	+	0.677541i
$321$	1055.27	+	5029.45i	0.183488	+	0.874506i
$322$	−4195.49	−	4738.75i	−0.726105	−	0.820125i
$323$	3360.23			0.578850
$324$	−1461.96	+	1589.84i	−0.250680	+	0.272606i
$325$	1362.69	−	8426.90i	0.232581	−	1.43828i
$326$		−	3740.50i		−	0.635481i
$327$	865.321	+	4124.13i	0.146337	+	0.697447i
$328$	−9169.05			−1.54352
$329$	−5.08538	+	4.50238i	−0.000852177	+	0.000754481i
$330$	2055.08	−	2654.84i	0.342813	−	0.442861i
$331$	4975.22			0.826172			0.413086	−	0.910692i	$-0.364451\pi$
$331$	4975.22			0.826172			0.413086	+	0.910692i	$0.364451\pi$
$332$		−	1273.24i		−	0.210476i
$333$	−889.181	−	2025.64i	−0.146327	−	0.333347i
$334$			3789.67i			0.620843i
$335$	7828.16	+	9195.72i	1.27671	+	1.49975i
$336$	−1809.80	+	2434.25i	−0.293848	+	0.395236i
$337$			8230.66i			1.33042i	0.746655	+	0.665212i	$0.231659\pi$
$337$			8230.66i			1.33042i	−0.746655	+	0.665212i	$0.768341\pi$
$338$	−5536.11			−0.890902
$339$	−114.929	−	547.754i	−0.0184132	−	0.0877578i
$340$	658.116	+	773.088i	0.104975	+	0.123313i
$341$	−424.041			−0.0673404
$342$	−2670.30	−	6083.21i	−0.422203	−	0.961820i
$343$	5231.39	−	3603.64i	0.823523	−	0.567283i
$344$			4738.68i			0.742711i
$345$	6994.95	+	5414.70i	1.09158	+	0.844979i
$346$		−	1615.21i		−	0.250966i
$347$	−864.297			−0.133712			−0.0668558	−	0.997763i	$-0.521297\pi$
$347$	−864.297			−0.133712			−0.0668558	+	0.997763i	$0.521297\pi$
$348$	−2889.25	+	606.219i	−0.445058	+	0.0933815i
$349$		−	4811.80i		−	0.738022i	−0.929425	−	0.369011i	$-0.879696\pi$
$349$		−	4811.80i		−	0.738022i	0.929425	−	0.369011i	$-0.120304\pi$
$350$	4390.14	−	2779.06i	0.670466	−	0.424419i
$351$	−5570.43	−	7795.19i	−0.847086	−	1.18540i
$352$			3246.76i			0.491628i
$353$		−	1206.50i		−	0.181913i	−0.995855	−	0.0909565i	$-0.971008\pi$
$353$		−	1206.50i		−	0.181913i	0.995855	−	0.0909565i	$-0.0289924\pi$
$354$	−476.115	−	2269.17i	−0.0714837	−	0.340693i
$355$	5604.22	+	6583.27i	0.837863	+	0.984236i
$356$	15.6911			0.00233602
$357$	2367.07	+	1759.86i	0.350921	+	0.260900i
$358$			2538.23i			0.374719i
$359$			7589.54i			1.11577i	0.829919	+	0.557884i	$0.188387\pi$
$359$			7589.54i			1.11577i	−0.829919	+	0.557884i	$0.811613\pi$
$360$	3243.49	−	6681.74i	0.474853	−	0.978218i
$361$	−5160.10			−0.752310
$362$		−	2406.06i		−	0.349337i
$363$	712.764	+	3397.05i	0.103059	+	0.491181i
$364$	2483.95	+	2805.59i	0.357678	+	0.403992i
$365$	3814.93	−	3247.58i	0.547075	−	0.465716i
$366$	−953.896	+	200.145i	−0.136232	+	0.0285840i
$367$	6905.34			0.982168			0.491084	−	0.871112i	$-0.336601\pi$
$367$	6905.34			0.982168			0.491084	+	0.871112i	$0.336601\pi$
$368$	4799.42			0.679856
$369$	9213.15	−	4044.23i	1.29978	−	0.570553i
$370$	1332.70	+	1565.52i	0.187254	+	0.219967i
$371$	−73.0550	−	82.5146i	−0.0102233	−	0.0115470i
$372$	−248.126	+	52.0614i	−0.0345825	+	0.00725607i
$373$		−	11871.0i		−	1.64788i	−0.566678	−	0.823939i	$-0.691772\pi$
$373$		−	11871.0i		−	1.64788i	0.566678	−	0.823939i	$-0.308228\pi$
$374$	−1771.28			−0.244895
$375$	−5304.80	+	4959.18i	−0.730504	+	0.682909i
$376$		−	9.02346i		−	0.00123763i
$377$		−	13095.7i		−	1.78902i
$378$	1304.90	−	5683.75i	0.177558	−	0.773388i
$379$	−4071.94			−0.551877			−0.275938	−	0.961175i	$-0.588989\pi$
$379$	−4071.94			−0.551877			−0.275938	+	0.961175i	$0.588989\pi$
$380$	−2353.99	−	2765.23i	−0.317782	−	0.373298i
$381$	168.124	−	35.2757i	0.0226070	−	0.00474338i
$382$		−	3616.19i		−	0.484346i
$383$		−	9559.09i		−	1.27532i	−0.770319	−	0.637659i	$-0.779903\pi$
$383$		−	9559.09i		−	1.27532i	0.770319	−	0.637659i	$-0.220097\pi$
$384$	−205.254	−	978.243i	−0.0272768	−	0.130002i
$385$	748.699	−	5278.80i	0.0991096	−	0.698785i
$386$		−	4403.46i		−	0.580648i
$387$	−2090.11	−	4761.48i	−0.274538	−	0.625425i
$388$	−1289.30			−0.168696
$389$		−	6559.03i		−	0.854899i	−0.904039	−	0.427450i	$-0.859412\pi$
$389$		−	6559.03i		−	0.854899i	0.904039	−	0.427450i	$-0.140588\pi$
$390$	7041.16	+	5450.47i	0.914212	+	0.707680i
$391$		−	4666.96i		−	0.603628i
$392$	−1022.56	+	8377.20i	−0.131752	+	1.07937i
$393$	−1064.14	−	5071.69i	−0.136587	−	0.650975i
$394$	1479.00			0.189115
$395$	10814.3	−	9206.02i	1.37753	−	1.17267i
$396$	−827.904	−	1886.05i	−0.105060	−	0.239337i
$397$	−3903.80			−0.493516			−0.246758	−	0.969077i	$-0.579365\pi$
$397$	−3903.80			−0.493516			−0.246758	+	0.969077i	$0.579365\pi$
$398$			11362.5i			1.43103i
$399$	−8466.69	−	6294.76i	−1.06232	−	0.789805i
$400$	−628.961	+	3889.49i	−0.0786201	+	0.486186i
$401$		−	3085.45i		−	0.384239i	−0.981372	−	0.192120i	$-0.938464\pi$
$401$		−	3085.45i		−	0.384239i	0.981372	−	0.192120i	$-0.0615362\pi$
$402$	−12328.5	+	2586.74i	−1.52957	+	0.320933i
$403$		−	1124.64i		−	0.139013i
$404$	3325.42			0.409519
$405$	−311.953	+	8144.50i	−0.0382742	+	0.999267i
$406$	5967.98	−	5283.80i	0.729522	−	0.645889i
$407$	2109.70			0.256938
$408$	−3835.10	+	804.676i	−0.465357	+	0.0976407i
$409$		−	254.304i		−	0.0307446i	−0.999882	−	0.0153723i	$-0.995107\pi$
$409$		−	254.304i		−	0.0307446i	0.999882	−	0.0153723i	$-0.00489335\pi$
$410$	−7120.41	+	6061.48i	−0.857688	+	0.730135i
$411$	−1465.34	−	6983.82i	−0.175863	−	0.838167i
$412$	1852.40			0.221508
$413$	−2440.79	−	2756.84i	−0.290807	−	0.328463i
$414$	−8448.85	+	3708.73i	−1.00299	+	0.440275i
$415$	−3114.51	−	3658.61i	−0.368398	−	0.432756i
$416$	−8611.05			−1.01488
$417$	−6924.57	+	1452.91i	−0.813184	+	0.170621i
$418$	6335.64			0.741355
$419$	1777.00			0.207189			0.103594	−	0.994620i	$-0.466966\pi$
$419$	1777.00			0.207189			0.103594	+	0.994620i	$0.466966\pi$
$420$	−210.004	−	3180.78i	−0.0243980	−	0.369539i
$421$	−6856.09			−0.793695			−0.396847	−	0.917885i	$-0.629896\pi$
$421$	−6856.09			−0.793695			−0.396847	+	0.917885i	$0.629896\pi$
$422$	7781.87			0.897667
$423$	3.98001	+	9.06686i	0.000457482	+	0.00104219i
$424$	146.413			0.0167699
$425$	3782.15	+	611.602i	0.431673	+	0.0698049i
$426$	−8826.02	+	1851.86i	−1.00381	+	0.210618i
$427$	−1158.90	+	1026.04i	−0.131342	+	0.116284i
$428$	−2930.14			−0.330920
$429$	8942.26	−	1876.25i	1.00638	−	0.211157i
$430$	3132.65	+	3679.92i	0.351325	+	0.412701i
$431$			1425.61i			0.159325i	0.996822	+	0.0796625i	$0.0253842\pi$
$431$			1425.61i			0.159325i	−0.996822	+	0.0796625i	$0.974616\pi$
$432$	2571.07	+	3597.92i	0.286344	+	0.400706i
$433$	−5863.42			−0.650757			−0.325379	−	0.945584i	$-0.605492\pi$
$433$	−5863.42			−0.650757			−0.325379	+	0.945584i	$0.605492\pi$
$434$	512.523	−	453.767i	0.0566864	−	0.0501878i
$435$	−6819.27	+	8809.44i	−0.751630	+	0.970989i
$436$	−2402.71			−0.263919
$437$			16693.1i			1.82732i
$438$	1073.13	+	5114.57i	0.117069	+	0.557954i
$439$		−	9688.48i		−	1.05332i	−0.850077	−	0.526658i	$-0.823445\pi$
$439$		−	9688.48i		−	1.05332i	0.850077	−	0.526658i	$-0.176555\pi$
$440$	4591.43	+	5393.55i	0.497473	+	0.584380i
$441$	−2667.49	−	8868.52i	−0.288035	−	0.957620i
$442$		−	4697.79i		−	0.505546i
$443$	17681.9			1.89637			0.948185	−	0.317719i	$-0.102917\pi$
$443$	17681.9			1.89637			0.948185	+	0.317719i	$0.102917\pi$
$444$	1234.48	−	259.017i	0.131950	−	0.0276856i
$445$	45.0877	−	38.3824i	0.00480306	−	0.00408876i
$446$	−4594.42			−0.487785
$447$	15112.5	−	3170.88i	1.59910	−	0.335520i
$448$	−6570.10	−	7420.84i	−0.692875	−	0.782593i
$449$			5275.90i			0.554533i	0.960793	+	0.277266i	$0.0894285\pi$
$449$			5275.90i			0.554533i	−0.960793	+	0.277266i	$0.910572\pi$
$450$	−1898.37	−	7333.05i	−0.198867	−	0.768185i
$451$			9595.45i			1.00185i
$452$	319.119			0.0332082
$453$	1553.90	+	7405.92i	0.161167	+	0.768125i
$454$		−	8974.08i		−	0.927697i
$455$	14000.4	+	1985.69i	1.44252	+	0.204595i
$456$	13717.6	−	2878.22i	1.40874	−	0.295581i
$457$		−	696.329i		−	0.0712755i	−0.999365	−	0.0356378i	$-0.988654\pi$
$457$		−	696.329i		−	0.0712755i	0.999365	−	0.0356378i	$-0.0113463\pi$
$458$		−	7463.92i		−	0.761498i
$459$	3498.63	−	2500.11i	0.355777	−	0.254238i
$460$	−3840.57	+	3269.41i	−0.389277	+	0.331385i
$461$	−7690.68			−0.776986			−0.388493	−	0.921452i	$-0.627004\pi$
$461$	−7690.68			−0.776986			−0.388493	+	0.921452i	$0.627004\pi$
$462$	4463.05	+	3318.16i	0.449437	+	0.334145i
$463$			4517.49i			0.453446i	0.973959	+	0.226723i	$0.0728012\pi$
$463$			4517.49i			0.453446i	−0.973959	+	0.226723i	$0.927199\pi$
$464$			6044.38i			0.604749i
$465$	−585.631	+	756.544i	−0.0584042	+	0.0754492i
$466$	−7775.73			−0.772970
$467$		−	17707.4i		−	1.75461i	−0.479934	−	0.877304i	$-0.659339\pi$
$467$		−	17707.4i		−	1.75461i	0.479934	−	0.877304i	$-0.340661\pi$
$468$	5002.17	−	2195.76i	0.494071	−	0.216879i
$469$	−14977.9	+	13260.8i	−1.47466	+	1.30560i
$470$	−5.96524	−	7.00735i	−0.000585438	−	0.000687713i
$471$	−3097.70	−	14763.7i	−0.303045	−	1.44432i
$472$	4891.71			0.477032
$473$	4959.05			0.482067
$474$	3042.04	+	14498.4i	0.294780	+	1.40493i
$475$	−13528.2	−	2187.62i	−1.30677	−	0.211315i
$476$	−1259.20	+	1114.84i	−0.121251	+	0.107350i
$477$	−147.118	+	64.5791i	−0.0141217	+	0.00619890i
$478$			10143.6i			0.970624i
$479$	12707.4			1.21214			0.606072	−	0.795410i	$-0.292744\pi$
$479$	12707.4			1.21214			0.606072	+	0.795410i	$0.292744\pi$
$480$	5792.65	+	4484.01i	0.550827	+	0.426388i
$481$			5595.33i			0.530406i
$482$		−	15906.3i		−	1.50313i
$483$	−8742.67	+	11759.2i	−0.823613	+	1.10779i
$484$	−1979.11			−0.185867
$485$	−3704.75	+	3153.79i	−0.346854	+	0.295271i
$486$	−7306.36	−	4346.97i	−0.681941	−	0.405725i
$487$		−	224.275i		−	0.0208684i	−0.999946	−	0.0104342i	$-0.996679\pi$
$487$		−	224.275i		−	0.0208684i	0.999946	−	0.0104342i	$-0.00332136\pi$
$488$		−	2056.33i		−	0.190750i
$489$	−8475.38	+	1778.29i	−0.783783	+	0.164452i
$490$	4743.92	+	7181.48i	0.437364	+	0.662094i
$491$			6605.29i			0.607113i	0.952813	+	0.303557i	$0.0981742\pi$
$491$			6605.29i			0.607113i	−0.952813	+	0.303557i	$0.901826\pi$
$492$	1178.08	+	5614.74i	0.107951	+	0.514496i
$493$	5877.57			0.536942
$494$			16803.4i			1.53040i
$495$	−6992.47	−	3394.33i	−0.634926	−	0.308210i
$496$			519.084i			0.0469911i
$497$	−10722.8	+	9493.51i	−0.967773	+	0.856826i
$498$	4905.00	−	1029.16i	0.441362	−	0.0926060i
$499$	14083.4			1.26344			0.631722	−	0.775195i	$-0.282349\pi$
$499$	14083.4			1.26344			0.631722	+	0.775195i	$0.282349\pi$
$500$	−2146.26	−	3540.89i	−0.191967	−	0.316707i
$501$	8586.81	−	1801.67i	0.765729	−	0.160664i
$502$	−10659.0			−0.947682
$503$			23.1056i			0.00204816i	0.999999	+	0.00102408i	$0.000325975\pi$
$503$			23.1056i			0.00204816i	−0.999999	+	0.00102408i	$0.999674\pi$
$504$	11170.6	+	5156.81i	0.987258	+	0.455759i
$505$	9555.46	−	8134.40i	0.842005	−	0.716784i
$506$		−	8799.44i		−	0.773088i
$507$	2631.96	+	12544.0i	0.230551	+	1.09881i
$508$			97.9487i			0.00855467i
$509$	−3934.85			−0.342650			−0.171325	−	0.985215i	$-0.554805\pi$
$509$	−3934.85			−0.342650			−0.171325	+	0.985215i	$0.554805\pi$
$510$	−2446.27	+	3160.20i	−0.212397	+	0.274384i
$511$	5501.38	+	6213.74i	0.476256	+	0.537925i
$512$	10178.8			0.878602
$513$	−12514.1	+	8942.55i	−1.07702	+	0.769636i
$514$			3526.67i			0.302636i
$515$	5322.81	−	4531.21i	0.455438	−	0.387707i
$516$	2901.77	−	608.845i	0.247564	−	0.0519437i
$517$	−9.44309			−0.000803301
$518$	−2549.92	+	2257.59i	−0.216288	+	0.191492i
$519$	−3659.81	+	767.897i	−0.309533	+	0.0649459i
$520$	−14304.7	+	12177.4i	−1.20635	+	1.02695i
$521$	8113.65			0.682275			0.341138	−	0.940013i	$-0.389188\pi$
$521$	8113.65			0.682275			0.341138	+	0.940013i	$0.389188\pi$
$522$	−4670.77	−	10640.5i	−0.391636	−	0.892186i
$523$	−5518.74			−0.461410			−0.230705	−	0.973024i	$-0.574103\pi$
$523$	−5518.74			−0.461410			−0.230705	+	0.973024i	$0.574103\pi$
$524$	2954.75			0.246334
$525$	−8384.05	−	8626.17i	−0.696971	−	0.717099i
$526$	12188.1			1.01031
$527$	504.759			0.0417223
$528$	−4127.36	+	865.998i	−0.340190	+	0.0713782i
$529$	11017.7			0.905537
$530$	113.700	−	96.7911i	0.00931854	−	0.00793271i
$531$	−4915.24	+	2157.61i	−0.401701	+	0.176332i
$532$	4503.99	−	3987.64i	0.367054	−	0.324974i
$533$	−25449.0			−2.06814
$534$	12.6831	+	60.4478i	0.00102781	+	0.00489857i
$535$	−8419.65	+	7167.50i	−0.680398	+	0.579211i
$536$		−	26576.7i		−	2.14168i
$537$	5751.22	−	1206.72i	0.462167	−	0.0969713i
$538$	11487.7			0.920575
$539$	8766.78	+	1070.11i	0.700579	+	0.0855156i
$540$	−4508.35	−	1127.68i	−0.359275	−	0.0898659i
$541$	3915.43			0.311160			0.155580	−	0.987823i	$-0.450275\pi$
$541$	3915.43			0.311160			0.155580	+	0.987823i	$0.450275\pi$
$542$			14095.4i			1.11706i
$543$	−5451.76	+	1143.88i	−0.430861	+	0.0904027i
$544$		−	3864.80i		−	0.304599i
$545$	−6904.09	+	5877.33i	−0.542640	+	0.461940i
$546$	−8800.42	+	11836.9i	−0.689786	+	0.927788i
$547$			5022.18i			0.392564i	0.980547	+	0.196282i	$0.0628869\pi$
$547$			5022.18i			0.392564i	−0.980547	+	0.196282i	$0.937113\pi$
$548$	4068.75			0.317169
$549$	906.996	+	2066.23i	0.0705093	+	0.160627i
$550$	7131.14	+	1153.16i	0.552860	+	0.0894017i
$551$	−21023.3			−1.62545
$552$	−3997.49	−	19052.1i	−0.308233	−	1.46904i
$553$	15594.9	+	17614.3i	1.19921	+	1.35449i
$554$		−	13034.3i		−	0.999590i
$555$	2913.64	−	3763.97i	0.222842	−	0.287877i
$556$		−	4034.23i		−	0.307715i
$557$	13585.5			1.03346			0.516729	−	0.856149i	$-0.327149\pi$
$557$	13585.5			1.03346			0.516729	+	0.856149i	$0.327149\pi$
$558$	−401.120	−	913.791i	−0.0304315	−	0.0693259i
$559$			13152.4i			0.995146i
$560$	−6461.98	−	916.510i	−0.487622	−	0.0691601i
$561$	842.097	+	4013.45i	0.0633750	+	0.302046i
$562$		−	451.247i		−	0.0338696i
$563$		−	12293.5i		−	0.920267i	−0.887850	−	0.460133i	$-0.847802\pi$
$563$		−	12293.5i		−	0.920267i	0.887850	−	0.460133i	$-0.152198\pi$
$564$	−5.52558	+	1.15937i	−0.000412534	+	8.65573e-5i
$565$	916.978	−	780.608i	0.0682789	−	0.0581246i
$566$	10792.7			0.801502
$567$	−13498.9	−	254.555i	−0.999822	−	0.0188542i
$568$		−	19026.4i		−	1.40551i
$569$		−	10764.9i		−	0.793123i	−0.918008	−	0.396562i	$-0.870203\pi$
$569$		−	10764.9i		−	0.793123i	0.918008	−	0.396562i	$-0.129797\pi$
$570$	8749.97	−	11303.6i	0.642975	−	0.830624i
$571$	14290.9			1.04738			0.523690	−	0.851909i	$-0.324555\pi$
$571$	14290.9			1.04738			0.523690	+	0.851909i	$0.324555\pi$
$572$			5209.73i			0.380822i
$573$	−8193.72	+	1719.20i	−0.597378	+	0.125341i
$574$	−10268.1	−	11597.7i	−0.746660	−	0.843342i
$575$	−3038.34	+	18789.1i	−0.220361	+	1.36271i
$576$	−13230.8	+	5807.83i	−0.957090	+	0.420127i
$577$	−25946.6			−1.87205			−0.936024	−	0.351937i	$-0.885523\pi$
$577$	−25946.6			−1.87205			−0.936024	+	0.351937i	$0.885523\pi$
$578$	−8918.20			−0.641779
$579$	−9977.55	+	2093.48i	−0.716153	+	0.150262i
$580$	−4117.49	−	4836.81i	−0.294775	−	0.346272i
$581$	5959.12	−	5275.95i	0.425518	−	0.376736i
$582$	−1042.14	−	4966.86i	−0.0742236	−	0.353751i
$583$		−	153.222i		−	0.0108848i
$584$	−11025.6			−0.781237
$585$	9002.42	−	18545.4i	0.636247	−	1.31070i
$586$		−	15040.6i		−	1.06027i
$587$		−	18044.2i		−	1.26876i	−0.773020	−	0.634382i	$-0.781255\pi$
$587$		−	18044.2i		−	1.26876i	0.773020	−	0.634382i	$-0.218745\pi$
$588$	5261.22	−	450.167i	0.368995	−	0.0315724i
$589$	−1805.45			−0.126303
$590$	3798.76	−	3233.82i	0.265072	−	0.225651i
$591$	−703.143	−	3351.19i	−0.0489398	−	0.233248i
$592$		−	2582.56i		−	0.179295i
$593$			14485.3i			1.00310i	0.865129	+	0.501550i	$0.167237\pi$
$593$			14485.3i			1.00310i	−0.865129	+	0.501550i	$0.832763\pi$
$594$	6596.57	−	4713.89i	0.455658	−	0.325612i
$595$	−891.216	+	6283.64i	−0.0614056	+	0.432948i
$596$			8804.48i			0.605110i
$597$	25745.7	−	5401.92i	1.76499	−	0.370328i
$598$	23337.8			1.59591
$599$			2982.21i			0.203422i	0.994814	+	0.101711i	$0.0324317\pi$
$599$			2982.21i			0.203422i	−0.994814	+	0.101711i	$0.967568\pi$
$600$	15963.9	−	742.836i	1.08620	−	0.0505436i
$601$		−	15274.2i		−	1.03668i	−0.855174	−	0.518341i	$-0.826550\pi$
$601$		−	15274.2i		−	1.03668i	0.855174	−	0.518341i	$-0.173450\pi$
$602$	−5993.84	+	5306.69i	−0.405798	+	0.359277i
$603$	11722.3	+	26704.6i	0.791657	+	1.80347i
$604$	−4314.67			−0.290664
$605$	−5686.90	+	4841.16i	−0.382157	+	0.325324i
$606$	2687.94	+	12810.8i	0.180182	+	0.858748i
$607$	14554.3			0.973214			0.486607	−	0.873621i	$-0.338234\pi$
$607$	14554.3			0.973214			0.486607	+	0.873621i	$0.338234\pi$
$608$			13823.8i			0.922090i
$609$	−14809.5	−	11010.5i	−0.985407	−	0.732625i
$610$	−1359.40	−	1596.89i	−0.0902306	−	0.105994i
$611$		−	25.0449i		−	0.00165828i
$612$	985.499	+	2245.06i	0.0650922	+	0.148287i
$613$		−	18176.4i		−	1.19761i	−0.800893	−	0.598807i	$-0.795642\pi$
$613$		−	18176.4i		−	1.19761i	0.800893	−	0.598807i	$-0.204358\pi$
$614$	−3312.98			−0.217754
$615$	17119.5	+	13252.0i	1.12248	+	0.868899i
$616$	−8784.98	+	7777.85i	−0.574605	+	0.508731i
$617$	7001.54			0.456842			0.228421	−	0.973562i	$-0.426644\pi$
$617$	7001.54			0.456842			0.228421	+	0.973562i	$0.426644\pi$
$618$	1497.30	+	7136.14i	0.0974597	+	0.464495i
$619$			382.714i			0.0248507i	0.999923	+	0.0124253i	$0.00395521\pi$
$619$			382.714i			0.0248507i	−0.999923	+	0.0124253i	$0.996045\pi$
$620$	−353.605	−	415.380i	−0.0229051	−	0.0269065i
$621$	12420.1	+	17380.6i	0.802580	+	1.12312i
$622$	4852.36			0.312801
$623$	65.0194	+	73.4386i	0.00418130	+	0.00472272i
$624$	−2296.80	−	10946.6i	−0.147348	−	0.702265i
$625$	−14828.7	−	4924.59i	−0.949034	−	0.315174i
$626$	2665.95			0.170212
$627$	−3012.07	−	14355.6i	−0.191851	−	0.914364i
$628$	8601.27			0.546542
$629$	−2511.29			−0.159192
$630$	12083.8	−	3380.05i	0.764177	−	0.213753i
$631$	−20481.5			−1.29217			−0.646083	−	0.763267i	$-0.723594\pi$
$631$	−20481.5			−1.29217			−0.646083	+	0.763267i	$0.723594\pi$
$632$	−31254.6			−1.96715
$633$	−3699.63	−	17632.5i	−0.232302	−	1.10715i
$634$	9607.55			0.601837
$635$	239.595	+	281.452i	0.0149733	+	0.0175891i
$636$	−18.8118	−	89.6573i	−0.00117286	−	0.00558985i
$637$	−2838.14	+	23251.2i	−0.176533	+	1.44623i
$638$	11082.0			0.687682
$639$	8392.07	+	19118.0i	0.519538	+	1.18356i
$640$	1637.65	−	1394.10i	0.101146	−	0.0861042i
$641$			28510.2i			1.75676i	0.477962	+	0.878380i	$0.341376\pi$
$641$			28510.2i			1.75676i	−0.477962	+	0.878380i	$0.658624\pi$
$642$	−2368.43	−	11288.0i	−0.145599	−	0.693928i
$643$	−1013.84			−0.0621802			−0.0310901	−	0.999517i	$-0.509898\pi$
$643$	−1013.84			−0.0621802			−0.0310901	+	0.999517i	$0.509898\pi$
$644$	−5538.36	−	6255.50i	−0.338885	−	0.382766i
$645$	6848.81	−	8847.60i	0.418096	−	0.540114i
$646$	−7541.65			−0.459322
$647$			9793.59i			0.595094i	0.954707	+	0.297547i	$0.0961685\pi$
$647$			9793.59i			0.595094i	−0.954707	+	0.297547i	$0.903832\pi$
$648$	12141.1	−	13203.1i	0.736031	−	0.800409i
$649$		−	5119.20i		−	0.309624i
$650$	−3058.41	+	18913.2i	−0.184555	+	1.14129i
$651$	−1271.83	−	945.569i	−0.0765696	−	0.0569275i
$652$		−	4937.73i		−	0.296590i
$653$	9713.50			0.582111			0.291056	−	0.956706i	$-0.405994\pi$
$653$	9713.50			0.582111			0.291056	+	0.956706i	$0.405994\pi$
$654$	−1942.11	−	9256.13i	−0.116120	−	0.553430i
$655$	8490.38	−	7227.71i	0.506483	−	0.431160i
$656$	11746.2			0.699101
$657$	11078.6	−	4863.11i	0.657867	−	0.288779i
$658$	11.4135	−	10.1051i	0.000676210	−	0.000598688i
$659$		−	14730.6i		−	0.870745i	−0.900250	−	0.435373i	$-0.856617\pi$
$659$		−	14730.6i		−	0.870745i	0.900250	−	0.435373i	$-0.143383\pi$
$660$	2712.85	−	3504.58i	0.159996	−	0.206691i
$661$		−	23656.2i		−	1.39201i	−0.718036	−	0.696006i	$-0.754959\pi$
$661$		−	23656.2i		−	1.39201i	0.718036	−	0.696006i	$-0.245041\pi$
$662$	−11166.3			−0.655575
$663$	−10644.5	+	2233.41i	−0.623524	+	0.130827i
$664$			10573.8i			0.617987i
$665$	3187.76	−	22475.7i	0.185889	−	1.31063i
$666$	1995.66	+	4546.32i	0.116112	+	0.264514i
$667$			29198.8i			1.69502i
$668$			5002.65i			0.289758i
$669$	2184.27	+	10410.2i	0.126231	+	0.601619i
$670$	−17569.4	−	20638.7i	−1.01308	−	1.19006i
$671$	−2151.96			−0.123809
$672$	−7239.96	+	9738.02i	−0.415606	+	0.559006i
$673$		−	23206.9i		−	1.32921i	−0.747194	−	0.664606i	$-0.768600\pi$
$673$		−	23206.9i		−	1.32921i	0.747194	−	0.664606i	$-0.231400\pi$
$674$		−	18472.7i		−	1.05570i
$675$	−15713.0	+	7787.66i	−0.895992	+	0.444070i
$676$	−7308.08			−0.415799
$677$		−	2008.10i		−	0.113999i	−0.998374	−	0.0569997i	$-0.981847\pi$
$677$		−	2008.10i		−	0.113999i	0.998374	−	0.0569997i	$-0.0181534\pi$
$678$	257.945	+	1229.37i	0.0146111	+	0.0696366i
$679$	−5342.50	−	6034.28i	−0.301953	−	0.341052i
$680$	−5465.43	−	6420.23i	−0.308220	−	0.362065i
$681$	−20333.8	+	4266.42i	−1.14419	+	0.240073i
$682$	951.709			0.0534352
$683$	9344.15			0.523491			0.261745	−	0.965137i	$-0.415702\pi$
$683$	9344.15			0.523491			0.261745	+	0.965137i	$0.415702\pi$
$684$	−3524.99	−	8030.29i	−0.197049	−	0.448897i
$685$	11691.4	−	9952.70i	0.652125	−	0.555143i
$686$	−11741.2	+	8087.94i	−0.653473	+	0.450144i
$687$	−16912.1	+	3548.47i	−0.939208	+	0.197063i
$688$		−	6070.57i		−	0.336393i
$689$	406.375			0.0224698
$690$	−15699.3	−	12152.7i	−0.866179	−	0.670498i
$691$			28869.6i			1.58937i	0.607025	+	0.794683i	$0.292363\pi$
$691$			28869.6i			1.58937i	−0.607025	+	0.794683i	$0.707637\pi$
$692$		−	2132.19i		−	0.117130i
$693$	5396.63	−	11690.1i	0.295817	−	0.640793i
$694$	1939.81			0.106101
$695$	−9868.26	−	11592.2i	−0.538596	−	0.632688i
$696$	23994.2	−	5034.44i	1.30675	−	0.274181i
$697$		−	11422.0i		−	0.620715i
$698$			10799.5i			0.585627i
$699$	3696.71	+	17618.6i	0.200032	+	0.953357i
$700$	5795.31	−	3668.56i	0.312917	−	0.198083i
$701$		−	3198.20i		−	0.172317i	−0.996281	−	0.0861585i	$-0.972541\pi$
$701$		−	3198.20i		−	0.172317i	0.996281	−	0.0861585i	$-0.0274592\pi$
$702$	12502.2	+	17495.4i	0.672171	+	0.940628i
$703$	8982.53			0.481910
$704$		−	13779.8i		−	0.737709i
$705$	−13.0416	+	16.8477i	−0.000696702	+	0.000900030i
$706$			2707.84i			0.144350i
$707$	13779.6	+	15563.9i	0.733007	+	0.827921i
$708$	−628.507	−	2995.48i	−0.0333626	−	0.159007i
$709$	−5643.25			−0.298923			−0.149462	−	0.988768i	$-0.547754\pi$
$709$	−5643.25			−0.298923			−0.149462	+	0.988768i	$0.547754\pi$
$710$	−12578.0	−	14775.4i	−0.664852	−	0.781000i
$711$	31404.9	−	13785.6i	1.65651	−	0.727145i
$712$	−130.309			−0.00685889
$713$			2507.55i			0.131709i
$714$	−5312.61	−	3949.79i	−0.278459	−	0.207027i
$715$	12743.7	+	14970.0i	0.666555	+	0.783001i
$716$			3350.65i			0.174888i
$717$	22983.9	−	4822.44i	1.19714	−	0.251182i
$718$		−	17033.8i		−	0.885372i
$719$	31212.4			1.61895			0.809475	−	0.587154i	$-0.199752\pi$
$719$	31212.4			1.61895			0.809475	+	0.587154i	$0.199752\pi$
$720$	−4155.13	+	8559.75i	−0.215073	+	0.443060i
$721$	7675.84	+	8669.76i	0.396482	+	0.447821i
$722$	11581.2			0.596965
$723$	−36041.1	+	7562.10i	−1.85392	+	0.388987i
$724$		−	3176.18i		−	0.163041i
$725$	−23662.9	−	3826.48i	−1.21217	−	0.196016i
$726$	−1599.71	−	7624.27i	−0.0817782	−	0.389756i
$727$	−34019.5			−1.73551			−0.867753	−	0.496995i	$-0.834437\pi$
$727$	−34019.5			−1.73551			−0.867753	+	0.496995i	$0.834437\pi$
$728$	−20628.4	−	23299.5i	−1.05019	−	1.18618i
$729$	−6375.99	+	18621.7i	−0.323934	+	0.946080i
$730$	−8562.16	+	7288.82i	−0.434109	+	0.369550i
$731$	−5903.03			−0.298675
$732$	−1259.21	+	264.206i	−0.0635817	+	0.0133406i
$733$	−7823.52			−0.394227			−0.197113	−	0.980381i	$-0.563157\pi$
$733$	−7823.52			−0.394227			−0.197113	+	0.980381i	$0.563157\pi$
$734$	−15498.2			−0.779359
$735$	14016.8	−	14163.2i	0.703424	−	0.710771i
$736$	19199.7			0.961561
$737$	−27812.7			−1.39009
$738$	−20677.8	+	9076.79i	−1.03138	+	0.452739i
$739$	14767.9			0.735107			0.367554	−	0.930002i	$-0.380195\pi$
$739$	14767.9			0.735107			0.367554	+	0.930002i	$0.380195\pi$
$740$	1759.27	+	2066.61i	0.0873945	+	0.102662i
$741$	38073.8	−	7988.59i	1.88755	−	0.396043i
$742$	163.963	+	185.194i	0.00811224	+	0.00916267i
$743$	−13145.6			−0.649077			−0.324539	−	0.945872i	$-0.605209\pi$
$743$	−13145.6			−0.649077			−0.324539	+	0.945872i	$0.605209\pi$
$744$	2060.60	−	432.352i	0.101539	−	0.0213048i
$745$	21536.9	+	25299.4i	1.05913	+	1.24416i
$746$			26643.1i			1.30761i
$747$	−4663.83	−	10624.7i	−0.228435	−	0.520397i
$748$	−2338.22			−0.114297
$749$	−12141.7	−	13713.9i	−0.592320	−	0.669018i
$750$	11906.0	−	11130.3i	0.579661	−	0.541894i
$751$	326.336			0.0158564			0.00792821	−	0.999969i	$-0.497476\pi$
$751$	326.336			0.0158564			0.00792821	+	0.999969i	$0.497476\pi$
$752$			11.5596i			0.000560555i
$753$	5067.48	+	24151.7i	0.245245	+	1.16884i
$754$			29391.7i			1.41960i
$755$	−12398.0	+	10554.2i	−0.597630	+	0.508752i
$756$	1722.57	−	7502.97i	0.0828693	−	0.360953i
$757$			361.891i			0.0173754i	0.999962	+	0.00868769i	$0.00276541\pi$
$757$			361.891i			0.0173754i	−0.999962	+	0.00868769i	$0.997235\pi$
$758$	9138.98			0.437919
$759$	−19938.1	+	4183.40i	−0.953503	+	0.200063i
$760$	19549.1	+	22964.3i	0.933052	+	1.09605i
$761$	31708.0			1.51040			0.755199	−	0.655495i	$-0.227540\pi$
$761$	31708.0			1.51040			0.755199	+	0.655495i	$0.227540\pi$
$762$	−377.335	+	79.1721i	−0.0179389	+	0.00376391i
$763$	−9956.16	−	11245.4i	−0.472395	−	0.533564i
$764$		−	4773.63i		−	0.226052i
$765$	8323.51	+	4040.45i	0.393382	+	0.190958i
$766$			21454.3i			1.01198i
$767$	13577.1			0.639167
$768$	−4107.55	−	19576.7i	−0.192993	−	0.919808i
$769$			4392.75i			0.205990i	0.994682	+	0.102995i	$0.0328426\pi$
$769$			4392.75i			0.205990i	−0.994682	+	0.102995i	$0.967157\pi$
$770$	−1680.37	+	11847.6i	−0.0786444	+	0.554492i
$771$	7990.89	−	1676.64i	0.373262	−	0.0783173i
$772$		−	5812.89i		−	0.270998i
$773$		−	11252.2i		−	0.523563i	−0.965127	−	0.261782i	$-0.915690\pi$
$773$		−	11252.2i		−	0.523563i	0.965127	−	0.261782i	$-0.0843100\pi$
$774$	4691.00	+	10686.6i	0.217848	+	0.496280i
$775$	−2032.14	−	328.613i	−0.0941894	−	0.0152312i
$776$	10707.2			0.495316
$777$	6327.62	+	4704.42i	0.292152	+	0.217207i
$778$			14721.0i			0.678370i
$779$			40854.9i			1.87905i
$780$	9294.84	+	7195.02i	0.426678	+	0.330286i
$781$	−19911.3			−0.912268
$782$			10474.4i			0.478984i
$783$	−21889.1	+	15641.9i	−0.999045	+	0.713915i
$784$	1309.96	−	10731.8i	0.0596739	−	0.488874i
$785$	24715.4	−	21039.8i	1.12373	−	0.956616i
$786$	2388.33	+	11382.8i	0.108383	+	0.516554i
$787$	−10540.6			−0.477421			−0.238711	−	0.971091i	$-0.576725\pi$
$787$	−10540.6			−0.477421			−0.238711	+	0.971091i	$0.576725\pi$
$788$	1952.39			0.0882628
$789$	−5794.41	−	27616.3i	−0.261453	−	1.24609i
$790$	−24271.4	+	20661.8i	−1.09309	+	0.930525i
$791$	1322.34	+	1493.57i	0.0594401	+	0.0671368i
$792$	6875.46	+	15663.0i	0.308471	+	0.702727i
$793$		−	5707.43i		−	0.255582i
$794$	8761.61			0.391609
$795$	−273.368	−	211.611i	−0.0121954	−	0.00944033i
$796$			14999.3i			0.667886i
$797$		−	34322.0i		−	1.52540i	−0.646750	−	0.762702i	$-0.723872\pi$
$797$		−	34322.0i		−	1.52540i	0.646750	−	0.762702i	$-0.276128\pi$
$798$	19002.5	+	14127.9i	0.842958	+	0.626717i
$799$	11.2406			0.000497703
$800$	−2516.10	+	15559.6i	−0.111197	+	0.687642i
$801$	130.936	−	57.4758i	0.00577576	−	0.00253534i
$802$			6924.93i			0.304897i
$803$			11538.3i			0.507073i
$804$	−16274.5	+	3414.69i	−0.713876	+	0.149785i
$805$	−31216.0	−	4427.41i	−1.36673	−	0.193846i
$806$			2524.12i			0.110308i
$807$	−5461.43	−	26029.3i	−0.238230	−	1.13541i
$808$	−27616.4			−1.20240
$809$		−	32097.4i		−	1.39491i	−0.716627	−	0.697457i	$-0.754315\pi$
$809$		−	32097.4i		−	1.39491i	0.716627	−	0.697457i	$-0.245685\pi$
$810$	700.141	−	18279.4i	0.0303709	−	0.792928i
$811$			15356.6i			0.664910i	0.943119	+	0.332455i	$0.107877\pi$
$811$			15356.6i			0.664910i	−0.943119	+	0.332455i	$0.892123\pi$
$812$	7878.18	−	6975.01i	0.340480	−	0.301447i
$813$	31937.9	−	6701.16i	1.37775	−	0.289078i
$814$	−4734.97			−0.203883
$815$	−12078.3	−	14188.4i	−0.519123	−	0.609813i
$816$	4913.02	−	1030.84i	0.210772	−	0.0442240i
$817$	21114.3			0.904158
$818$			570.756i			0.0243961i
$819$	31004.4	+	14312.9i	1.32281	+	0.610664i
$820$	−9399.47	+	8001.60i	−0.400297	+	0.340766i
$821$			38785.8i			1.64876i	0.566035	+	0.824381i	$0.308477\pi$
$821$			38785.8i			1.64876i	−0.566035	+	0.824381i	$0.691523\pi$
$822$	3288.78	+	15674.4i	0.139549	+	0.665093i
$823$		−	21905.2i		−	0.927787i	−0.885891	−	0.463894i	$-0.846452\pi$
$823$		−	21905.2i		−	0.927787i	0.885891	−	0.463894i	$-0.153548\pi$
$824$	−15383.5			−0.650378
$825$	−777.382	−	16706.3i	−0.0328060	−	0.705016i
$826$	5478.06	+	6187.40i	0.230758	+	0.260638i
$827$	−14660.5			−0.616438			−0.308219	−	0.951315i	$-0.599733\pi$
$827$	−14660.5			−0.616438			−0.308219	+	0.951315i	$0.599733\pi$
$828$	−11153.1	+	4895.79i	−0.468112	+	0.205484i
$829$		−	6485.45i		−	0.271712i	−0.990729	−	0.135856i	$-0.956622\pi$
$829$		−	6485.45i		−	0.271712i	0.990729	−	0.135856i	$-0.0433784\pi$
$830$	6990.15	+	8211.31i	0.292327	+	0.343396i
$831$	−29533.6	+	6196.71i	−1.23286	+	0.258678i
$832$	36546.8			1.52288
$833$	−10435.6	−	1273.81i	−0.434059	−	0.0529831i
$834$	15541.4	−	3260.88i	0.645269	−	0.135390i
$835$	12237.1	+	14374.9i	0.507165	+	0.595766i
$836$	8363.51			0.346002
$837$	−1879.81	+	1343.31i	−0.0776293	+	0.0554737i
$838$	−3988.27			−0.164406
$839$	10919.1			0.449306			0.224653	−	0.974439i	$-0.427875\pi$
$839$	10919.1			0.449306			0.224653	+	0.974439i	$0.427875\pi$
$840$	1744.01	+	26415.3i	0.0716358	+	1.08502i
$841$	−12383.9			−0.507766
$842$	15387.7			0.629804
$843$	−1022.45	+	214.530i	−0.0417736	+	0.00876490i
$844$	10272.6			0.418956
$845$	−20999.5	+	17876.5i	−0.854916	+	0.727775i
$846$	−8.93267	−	20.3495i	−0.000363016	−	0.000826986i
$847$	−8200.88	−	9262.78i	−0.332687	−	0.375765i
$848$	−187.565			−0.00759554
$849$	−5131.01	−	24454.5i	−0.207416	−	0.988547i
$850$	−8488.58	−	1372.67i	−0.342536	−	0.0553908i
$851$		−	12475.7i		−	0.502538i
$852$	−11651.0	+	2444.60i	−0.468493	+	0.0982987i
$853$	33026.1			1.32567			0.662833	−	0.748768i	$-0.269354\pi$
$853$	33026.1			1.32567			0.662833	+	0.748768i	$0.269354\pi$
$854$	2601.00	−	2302.82i	0.104221	−	0.0922727i
$855$	−29772.1	−	14452.1i	−1.19086	−	0.578074i
$856$	24333.8			0.971626
$857$			25463.0i			1.01494i	0.861671	+	0.507468i	$0.169418\pi$
$857$			25463.0i			1.01494i	−0.861671	+	0.507468i	$0.830582\pi$
$858$	−20069.9	+	4211.03i	−0.798571	+	0.167555i
$859$		−	16073.2i		−	0.638429i	−0.947682	−	0.319215i	$-0.896581\pi$
$859$		−	16073.2i		−	0.638429i	0.947682	−	0.319215i	$-0.103419\pi$
$860$	4135.33	+	4857.77i	0.163969	+	0.192614i
$861$	−21396.9	+	28779.7i	−0.846928	+	1.13915i
$862$		−	3199.61i		−	0.126426i
$863$	17723.7			0.699099			0.349549	−	0.936918i	$-0.386335\pi$
$863$	17723.7			0.699099			0.349549	+	0.936918i	$0.386335\pi$
$864$	10285.3	+	14393.2i	0.404993	+	0.566743i
$865$	−5215.62	−	6126.78i	−0.205013	−	0.240829i
$866$	13159.8			0.516382
$867$	4239.86	+	20207.2i	0.166082	+	0.791550i
$868$	676.568	−	599.005i	0.0264565	−	0.0234235i
$869$			32708.1i			1.27681i
$870$	15305.0	−	19771.7i	0.596425	−	0.770488i
$871$		−	73764.7i		−	2.86960i
$872$	19953.7			0.774904
$873$	−10758.7	+	4722.65i	−0.417097	+	0.183090i
$874$		−	37465.6i		−	1.44999i
$875$	7678.86	−	24717.5i	0.296677	−	0.954978i
$876$	1416.61	+	6751.61i	0.0546381	+	0.260406i
$877$		−	24096.5i		−	0.927802i	−0.885887	−	0.463901i	$-0.846449\pi$
$877$		−	24096.5i		−	0.927802i	0.885887	−	0.463901i	$-0.153551\pi$
$878$			21744.6i			0.835816i
$879$	−34079.5	+	7150.53i	−1.30771	+	0.274381i
$880$	−5881.93	−	6909.49i	−0.225318	−	0.264681i
$881$	−22774.5			−0.870934			−0.435467	−	0.900205i	$-0.643417\pi$
$881$	−22774.5			−0.870934			−0.435467	+	0.900205i	$0.643417\pi$
$882$	5986.87	+	19904.3i	0.228558	+	0.759880i
$883$			739.337i			0.0281774i	0.999901	+	0.0140887i	$0.00448472\pi$
$883$			739.337i			0.0281774i	−0.999901	+	0.0140887i	$0.995515\pi$
$884$		−	6201.43i		−	0.235946i
$885$	−9133.31	−	7069.98i	−0.346907	−	0.268536i
$886$	−39684.9			−1.50479
$887$		−	2411.83i		−	0.0912979i	−0.998958	−	0.0456490i	$-0.985464\pi$
$887$		−	2411.83i		−	0.0912979i	0.998958	−	0.0456490i	$-0.0145356\pi$
$888$	−10251.9	+	2151.05i	−0.387424	+	0.0812888i
$889$	−458.428	+	405.873i	−0.0172949	+	0.0153122i
$890$	−101.194	+	86.1447i	−0.00381127	+	0.00324447i
$891$	−13817.1	−	12705.7i	−0.519516	−	0.477731i
$892$	−6064.98			−0.227657
$893$	−40.2062			−0.00150666
$894$	−33918.2	+	7116.67i	−1.26890	+	0.266238i
$895$	8196.11	+	9627.96i	0.306107	+	0.359583i
$896$	2361.60	+	2667.39i	0.0880529	+	0.0994546i
$897$	−11095.2	−	52879.9i	−0.412996	−	1.96835i
$898$		−	11841.1i		−	0.440027i
$899$	−3158.01			−0.117159
$900$	−2505.99	−	9680.16i	−0.0928143	−	0.358525i
$901$			182.389i			0.00674389i
$902$		−	21535.9i		−	0.794973i
$903$	14873.7	+	11058.2i	0.548135	+	0.407524i
$904$	−2650.18			−0.0975039
$905$	−7769.34	−	9126.63i	−0.285372	−	0.335226i
$906$	−3487.55	−	16621.7i	−0.127888	−	0.609514i
$907$			21835.5i			0.799379i	0.916651	+	0.399690i	$0.130882\pi$
$907$			21835.5i			0.799379i	−0.916651	+	0.399690i	$0.869118\pi$
$908$		−	11846.4i		−	0.432971i
$909$	27749.3	−	12180.9i	1.01253	−	0.444461i
$910$	−31422.2	−	4456.66i	−1.14466	−	0.162348i
$911$		−	25167.1i		−	0.915282i	−0.889137	−	0.457641i	$-0.848694\pi$
$911$		−	25167.1i		−	0.915282i	0.889137	−	0.457641i	$-0.151306\pi$
$912$	−17573.2	+	3687.19i	−0.638055	+	0.133876i
$913$	11065.5			0.401113
$914$			1562.83i			0.0565577i
$915$	−2972.02	+	3839.38i	−0.107379	+	0.138717i
$916$		−	9852.92i		−	0.355403i
$917$	12243.7	+	13829.1i	0.440918	+	0.498011i
$918$	−7852.25	+	5611.20i	−0.282313	+	0.201740i
$919$	−30919.9			−1.10985			−0.554925	−	0.831900i	$-0.687253\pi$
$919$	−30919.9			−1.10985			−0.554925	+	0.831900i	$0.687253\pi$
$920$	31894.6	−	27151.3i	1.14297	−	0.972992i
$921$	1575.04	+	7506.68i	0.0563512	+	0.268571i
$922$	17260.8			0.616546
$923$		−	52808.6i		−	1.88322i
$924$	5891.56	+	4380.22i	0.209760	+	0.155951i
$925$	10110.4	+	1634.93i	0.359381	+	0.0581146i
$926$		−	10139.0i		−	0.359813i
$927$	15457.5	−	6785.28i	0.547672	−	0.240408i
$928$			24180.0i			0.855332i
$929$	27897.3			0.985230			0.492615	−	0.870247i	$-0.336041\pi$
$929$	27897.3			0.985230			0.492615	+	0.870247i	$0.336041\pi$
$930$	1314.38	−	1697.97i	0.0463443	−	0.0598696i
$931$	37326.6	+	4556.24i	1.31400	+	0.160392i
$932$	−10264.5			−0.360758
$933$	−2306.89	−	10994.7i	−0.0809478	−	0.385798i
$934$			39742.3i			1.39230i
$935$	−6718.80	+	5719.60i	−0.235004	+	0.200054i
$936$	−41541.3	+	18235.1i	−1.45066	+	0.636786i
$937$	28956.4			1.00957			0.504784	−	0.863246i	$-0.331572\pi$
$937$	28956.4			1.00957			0.504784	+	0.863246i	$0.331572\pi$
$938$	33616.2	−	29762.4i	1.17016	−	1.03601i
$939$	−1267.43	−	6040.61i	−0.0440481	−	0.209934i
$940$	−7.87455	−	9.25022i	−0.000273233	−	0.000320967i
$941$	38808.0			1.34442			0.672212	−	0.740358i	$-0.265344\pi$
$941$	38808.0			1.34442			0.672212	+	0.740358i	$0.265344\pi$
$942$	6952.42	+	33135.3i	0.240469	+	1.14608i
$943$	56742.5			1.95948
$944$	−6266.61			−0.216060
$945$	−13403.5	−	25773.1i	−0.461393	−	0.887196i
$946$	−11130.0			−0.382524
$947$	19164.9			0.657629			0.328814	−	0.944395i	$-0.393351\pi$
$947$	19164.9			0.657629			0.328814	+	0.944395i	$0.393351\pi$
$948$	4015.72	+	19139.0i	0.137579	+	0.655702i
$949$	−30602.0			−1.04677
$950$	30362.5	+	4909.85i	1.03694	+	0.167681i
$951$	−4567.59	−	21769.2i	−0.155746	−	0.742287i
$952$	10457.2	−	9258.40i	0.356009	−	0.315196i
$953$	3621.39			0.123094			0.0615469	−	0.998104i	$-0.480397\pi$
$953$	3621.39			0.123094			0.0615469	+	0.998104i	$0.480397\pi$
$954$	330.188	−	144.940i	0.0112057	−	0.00491888i
$955$	−11676.9	−	13716.9i	−0.395661	−	0.464782i
$956$			13390.3i			0.453006i
$957$	−5268.57	−	25110.1i	−0.177961	−	0.848165i
$958$	−28520.3			−0.961848
$959$	16859.8	+	19042.9i	0.567707	+	0.641217i
$960$	−24585.0	−	19030.9i	−0.826539	−	0.639813i
$961$	29519.8			0.990896
$962$		−	12558.1i		−	0.420882i
$963$	−24450.8	+	10733.0i	−0.818190	+	0.359155i
$964$		−	20997.4i		−	0.701537i
$965$	−14219.1	−	16703.1i	−0.474330	−	0.557194i
$966$	19621.9	−	26392.2i	0.653544	−	0.879041i
$967$			9516.35i			0.316469i	0.987402	+	0.158234i	$0.0505801\pi$
$967$			9516.35i			0.316469i	−0.987402	+	0.158234i	$0.949420\pi$
$968$	16435.8			0.545730
$969$	3585.43	+	17088.2i	0.118865	+	0.566514i
$970$	8314.88	−	7078.31i	0.275231	−	0.234300i
$971$	−1539.07			−0.0508661			−0.0254331	−	0.999677i	$-0.508096\pi$
$971$	−1539.07			−0.0508661			−0.0254331	+	0.999677i	$0.508096\pi$
$972$	−9644.93	−	5738.32i	−0.318273	−	0.189359i
$973$	18881.4	−	16716.8i	0.622105	−	0.550786i
$974$			503.360i			0.0165592i
$975$	44308.3	−	2061.77i	1.45539	−	0.0677225i
$976$			2634.30i			0.0863954i
$977$	−20070.0			−0.657213			−0.328607	−	0.944467i	$-0.606579\pi$
$977$	−20070.0			−0.657213			−0.328607	+	0.944467i	$0.606579\pi$
$978$	19022.0	−	3991.17i	0.621939	−	0.130494i
$979$			136.369i			0.00445185i
$980$	6262.32	+	9480.08i	0.204125	+	0.309010i
$981$	−20049.6	+	8801.04i	−0.652534	+	0.286438i
$982$		−	14824.8i		−	0.481750i
$983$			7463.49i			0.242165i	0.992642	+	0.121083i	$0.0386366\pi$
$983$			7463.49i			0.242165i	−0.992642	+	0.121083i	$0.961363\pi$
$984$	−9783.52	−	46628.4i	−0.316959	−	1.51063i
$985$	5610.13	−	4775.81i	0.181476	−	0.154487i
$986$	−13191.5			−0.426068
$987$	−28.3227	−	21.0572i	−0.000913395	−	0.000679085i
$988$			22181.7i			0.714263i
$989$		−	29325.3i		−	0.942860i
$990$	15693.8	+	7618.17i	0.503819	+	0.244567i
$991$	−21807.0			−0.699014			−0.349507	−	0.936934i	$-0.613651\pi$
$991$	−21807.0			−0.699014			−0.349507	+	0.936934i	$0.613651\pi$
$992$			2076.55i			0.0664623i
$993$	5308.64	+	25301.1i	0.169652	+	0.808566i
$994$	24066.1	−	21307.1i	0.767936	−	0.679899i
$995$	36690.3	+	43100.1i	1.16901	+	1.37323i
$996$	6474.95	−	1358.57i	0.205991	−	0.0432207i
$997$	−34022.7			−1.08075			−0.540377	−	0.841423i	$-0.681718\pi$
$997$	−34022.7			−1.08075			−0.540377	+	0.841423i	$0.681718\pi$
$998$	−31608.5			−1.00255
$999$	9352.47	−	6683.25i	0.296195	−	0.211660i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	105.4.g.b.104.16	yes	40
3.2	odd	2	inner	105.4.g.b.104.27	yes	40
5.4	even	2	inner	105.4.g.b.104.25	yes	40
7.6	odd	2	inner	105.4.g.b.104.13	✓	40
15.14	odd	2	inner	105.4.g.b.104.14	yes	40
21.20	even	2	inner	105.4.g.b.104.26	yes	40
35.34	odd	2	inner	105.4.g.b.104.28	yes	40
105.104	even	2	inner	105.4.g.b.104.15	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.4.g.b.104.13	✓	40	7.6	odd	2	inner
105.4.g.b.104.14	yes	40	15.14	odd	2	inner
105.4.g.b.104.15	yes	40	105.104	even	2	inner
105.4.g.b.104.16	yes	40	1.1	even	1	trivial
105.4.g.b.104.25	yes	40	5.4	even	2	inner
105.4.g.b.104.26	yes	40	21.20	even	2	inner
105.4.g.b.104.27	yes	40	3.2	odd	2	inner
105.4.g.b.104.28	yes	40	35.34	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 105 = 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	105.g (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-2.24438 q^{2} +(1.06702 + 5.08542i) q^{3} -2.96275 q^{4} +(-8.51335 + 7.24727i) q^{5} +(-2.39479 - 11.4136i) q^{6} +(-12.2768 - 13.8665i) q^{7} +24.6046 q^{8} +(-24.7230 + 10.8524i) q^{9} +O(q^{10})\)	\(q-2.24438 q^{2} +(1.06702 + 5.08542i) q^{3} -2.96275 q^{4} +(-8.51335 + 7.24727i) q^{5} +(-2.39479 - 11.4136i) q^{6} +(-12.2768 - 13.8665i) q^{7} +24.6046 q^{8} +(-24.7230 + 10.8524i) q^{9} +(19.1072 - 16.2656i) q^{10} -25.7488i q^{11} +(-3.16130 - 15.0668i) q^{12} +68.2910 q^{13} +(27.5539 + 31.1217i) q^{14} +(-45.9393 - 35.5610i) q^{15} -31.5201 q^{16} +30.6502i q^{17} +(55.4878 - 24.3570i) q^{18} -109.632i q^{19} +(25.2229 - 21.4718i) q^{20} +(57.4174 - 77.2285i) q^{21} +57.7902i q^{22} -152.265 q^{23} +(26.2535 + 125.125i) q^{24} +(19.9543 - 123.397i) q^{25} -153.271 q^{26} +(-81.5690 - 114.147i) q^{27} +(36.3731 + 41.0829i) q^{28} -191.763i q^{29} +(103.105 + 79.8125i) q^{30} -16.4683i q^{31} -126.094 q^{32} +(130.944 - 27.4744i) q^{33} -68.7908i q^{34} +(205.011 + 29.0770i) q^{35} +(73.2479 - 32.1531i) q^{36} +81.9337i q^{37} +246.055i q^{38} +(72.8676 + 347.288i) q^{39} +(-209.468 + 178.316i) q^{40} -372.656 q^{41} +(-128.867 + 173.330i) q^{42} +192.593i q^{43} +76.2873i q^{44} +(131.825 - 271.565i) q^{45} +341.741 q^{46} -0.366739i q^{47} +(-33.6325 - 160.293i) q^{48} +(-41.5595 + 340.473i) q^{49} +(-44.7850 + 276.950i) q^{50} +(-155.869 + 32.7043i) q^{51} -202.329 q^{52} +5.95065 q^{53} +(183.072 + 256.189i) q^{54} +(186.609 + 219.209i) q^{55} +(-302.066 - 341.180i) q^{56} +(557.523 - 116.979i) q^{57} +430.389i q^{58} +198.813 q^{59} +(136.106 + 105.358i) q^{60} -83.5752i q^{61} +36.9613i q^{62} +(454.005 + 209.587i) q^{63} +535.163 q^{64} +(-581.385 + 494.923i) q^{65} +(-293.887 + 61.6631i) q^{66} -1080.15i q^{67} -90.8089i q^{68} +(-162.469 - 774.332i) q^{69} +(-460.123 - 65.2599i) q^{70} -773.288i q^{71} +(-608.298 + 267.020i) q^{72} -448.111 q^{73} -183.891i q^{74} +(648.817 - 30.1909i) q^{75} +324.811i q^{76} +(-357.046 + 316.114i) q^{77} +(-163.543 - 779.447i) q^{78} -1270.27 q^{79} +(268.342 - 228.435i) q^{80} +(493.449 - 536.609i) q^{81} +836.382 q^{82} +429.749i q^{83} +(-170.113 + 228.809i) q^{84} +(-222.130 - 260.936i) q^{85} -432.253i q^{86} +(975.193 - 204.614i) q^{87} -633.540i q^{88} -5.29611 q^{89} +(-295.865 + 609.495i) q^{90} +(-838.395 - 946.956i) q^{91} +451.123 q^{92} +(83.7484 - 17.5720i) q^{93} +0.823102i q^{94} +(794.530 + 933.333i) q^{95} +(-134.544 - 641.238i) q^{96} +435.169 q^{97} +(93.2755 - 764.151i) q^{98} +(279.438 + 636.587i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 184 q^{4} + 4 q^{9}+O(q^{10}) \) 40 * q + 184 * q^4 + 4 * q^9	\( 40 q + 184 q^{4} + 4 q^{9} - 188 q^{15} + 184 q^{16} + 148 q^{21} + 712 q^{25} - 336 q^{30} - 1520 q^{36} + 644 q^{39} - 1488 q^{46} - 1496 q^{49} - 220 q^{51} + 1984 q^{60} + 40 q^{64} - 3000 q^{70} - 1192 q^{79} + 4636 q^{81} - 2192 q^{84} + 4808 q^{85} - 4408 q^{91} + 5276 q^{99}+O(q^{100}) \) 40 * q + 184 * q^4 + 4 * q^9 - 188 * q^15 + 184 * q^16 + 148 * q^21 + 712 * q^25 - 336 * q^30 - 1520 * q^36 + 644 * q^39 - 1488 * q^46 - 1496 * q^49 - 220 * q^51 + 1984 * q^60 + 40 * q^64 - 3000 * q^70 - 1192 * q^79 + 4636 * q^81 - 2192 * q^84 + 4808 * q^85 - 4408 * q^91 + 5276 * q^99

Introduction

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