LMFDB - Embedded newform 184.5.e.e.45.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [184,5,Mod(45,184)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(184, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("184.45");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 184 = 2^{3} \cdot 23 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	184.e (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:	$19.0200732074$
Analytic rank:	$0$
Dimension:	$84$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			45.13
Character	$\chi$	$=$	184.45
Dual form			184.5.e.e.45.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-3.48223 - 1.96827i) q^{2} -4.47691i q^{3} +(8.25182 + 13.7079i) q^{4} -16.6301 q^{5} +(-8.81177 + 15.5896i) q^{6} -19.2078i q^{7} +(-1.75381 - 63.9760i) q^{8} +60.9573 q^{9} +O(q^{10})$	\(q+(-3.48223 - 1.96827i) q^{2} -4.47691i q^{3} +(8.25182 + 13.7079i) q^{4} -16.6301 q^{5} +(-8.81177 + 15.5896i) q^{6} -19.2078i q^{7} +(-1.75381 - 63.9760i) q^{8} +60.9573 q^{9} +(57.9098 + 32.7326i) q^{10} +13.2510 q^{11} +(61.3692 - 36.9427i) q^{12} +59.9162i q^{13} +(-37.8062 + 66.8861i) q^{14} +74.4515i q^{15} +(-119.815 + 226.231i) q^{16} -390.623i q^{17} +(-212.267 - 119.980i) q^{18} +128.299 q^{19} +(-137.229 - 227.964i) q^{20} -85.9918 q^{21} +(-46.1431 - 26.0816i) q^{22} +(87.5948 - 521.697i) q^{23} +(-286.415 + 7.85166i) q^{24} -348.439 q^{25} +(117.931 - 208.642i) q^{26} -635.530i q^{27} +(263.300 - 158.500i) q^{28} +828.280i q^{29} +(146.541 - 259.257i) q^{30} -23.4866 q^{31} +(862.506 - 551.960i) q^{32} -59.3236i q^{33} +(-768.852 + 1360.24i) q^{34} +319.429i q^{35} +(503.009 + 835.598i) q^{36} -1490.03 q^{37} +(-446.766 - 252.527i) q^{38} +268.239 q^{39} +(29.1661 + 1063.93i) q^{40} -239.228 q^{41} +(299.443 + 169.255i) q^{42} -2981.33 q^{43} +(109.345 + 181.644i) q^{44} -1013.73 q^{45} +(-1331.87 + 1644.26i) q^{46} -2447.37 q^{47} +(1012.82 + 536.400i) q^{48} +2032.06 q^{49} +(1213.35 + 685.823i) q^{50} -1748.79 q^{51} +(-821.327 + 494.418i) q^{52} -4340.56 q^{53} +(-1250.89 + 2213.06i) q^{54} -220.366 q^{55} +(-1228.84 + 33.6870i) q^{56} -574.383i q^{57} +(1630.28 - 2884.26i) q^{58} +1011.86i q^{59} +(-1020.58 + 614.361i) q^{60} -3518.02 q^{61} +(81.7858 + 46.2281i) q^{62} -1170.86i q^{63} +(-4089.85 + 224.404i) q^{64} -996.412i q^{65} +(-116.765 + 206.578i) q^{66} +1813.08 q^{67} +(5354.64 - 3223.35i) q^{68} +(-2335.59 - 392.154i) q^{69} +(628.722 - 1112.32i) q^{70} +4202.62 q^{71} +(-106.908 - 3899.80i) q^{72} -5865.58 q^{73} +(5188.63 + 2932.79i) q^{74} +1559.93i q^{75} +(1058.70 + 1758.71i) q^{76} -254.524i q^{77} +(-934.070 - 527.967i) q^{78} +2415.67i q^{79} +(1992.53 - 3762.24i) q^{80} +2092.33 q^{81} +(833.046 + 470.865i) q^{82} -991.781 q^{83} +(-709.589 - 1178.77i) q^{84} +6496.11i q^{85} +(10381.7 + 5868.06i) q^{86} +3708.13 q^{87} +(-23.2398 - 847.747i) q^{88} -13520.1i q^{89} +(3530.03 + 1995.29i) q^{90} +1150.86 q^{91} +(7874.21 - 3104.21i) q^{92} +105.148i q^{93} +(8522.29 + 4817.08i) q^{94} -2133.63 q^{95} +(-2471.07 - 3861.36i) q^{96} -9360.78i q^{97} +(-7076.09 - 3999.64i) q^{98} +807.746 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 84 q + 4 q^{2} - 32 q^{4} - 120 q^{6} - 212 q^{8} - 2272 q^{9}+O(q^{10}) $ 84 * q + 4 * q^2 - 32 * q^4 - 120 * q^6 - 212 * q^8 - 2272 * q^9	$ 84 q + 4 q^{2} - 32 q^{4} - 120 q^{6} - 212 q^{8} - 2272 q^{9} + 1036 q^{12} - 240 q^{16} - 2392 q^{18} + 2596 q^{23} + 1348 q^{24} + 11996 q^{25} - 1560 q^{26} - 260 q^{31} + 1744 q^{32} - 8600 q^{36} + 18740 q^{39} - 4 q^{41} - 7652 q^{46} - 14732 q^{47} - 10216 q^{48} - 52140 q^{49} - 7264 q^{50} + 18936 q^{52} - 68 q^{54} - 208 q^{55} - 27268 q^{58} - 500 q^{62} - 6536 q^{64} - 16188 q^{70} + 47860 q^{71} + 15584 q^{72} - 4 q^{73} + 37384 q^{78} - 3372 q^{81} + 86300 q^{82} - 34420 q^{87} - 15932 q^{92} - 93956 q^{94} + 109872 q^{95} + 26072 q^{96} + 35848 q^{98}+O(q^{100}) $ 84 * q + 4 * q^2 - 32 * q^4 - 120 * q^6 - 212 * q^8 - 2272 * q^9 + 1036 * q^12 - 240 * q^16 - 2392 * q^18 + 2596 * q^23 + 1348 * q^24 + 11996 * q^25 - 1560 * q^26 - 260 * q^31 + 1744 * q^32 - 8600 * q^36 + 18740 * q^39 - 4 * q^41 - 7652 * q^46 - 14732 * q^47 - 10216 * q^48 - 52140 * q^49 - 7264 * q^50 + 18936 * q^52 - 68 * q^54 - 208 * q^55 - 27268 * q^58 - 500 * q^62 - 6536 * q^64 - 16188 * q^70 + 47860 * q^71 + 15584 * q^72 - 4 * q^73 + 37384 * q^78 - 3372 * q^81 + 86300 * q^82 - 34420 * q^87 - 15932 * q^92 - 93956 * q^94 + 109872 * q^95 + 26072 * q^96 + 35848 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/184\mathbb{Z}\right)^\times$.

$n$	$47$	$93$	$97$
$\chi(n)$	$1$	$-1$	$-1$

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 $

$2$	−3.48223	−	1.96827i	−0.870557	−	0.492068i
$2$	−3.48223	−	1.96827i	−0.870557	−	0.492068i
$3$		−	4.47691i		−	0.497434i	−0.968576	−	0.248717i	$-0.919991\pi$
$3$		−	4.47691i		−	0.497434i	0.968576	−	0.248717i	$-0.0800090\pi$
$4$	8.25182	+	13.7079i	0.515739	+	0.856746i
$5$	−16.6301			−0.665204			−0.332602	−	0.943067i	$-0.607927\pi$
$5$	−16.6301			−0.665204			−0.332602	+	0.943067i	$0.607927\pi$
$6$	−8.81177	+	15.5896i	−0.244771	+	0.433045i
$7$		−	19.2078i		−	0.391997i	−0.980604	−	0.195998i	$-0.937205\pi$
$7$		−	19.2078i		−	0.391997i	0.980604	−	0.195998i	$-0.0627948\pi$
$8$	−1.75381	−	63.9760i	−0.0274033	−	0.999624i
$9$	60.9573			0.752559
$10$	57.9098	+	32.7326i	0.579098	+	0.327326i
$11$	13.2510			0.109513			0.0547563	−	0.998500i	$-0.482562\pi$
$11$	13.2510			0.109513			0.0547563	+	0.998500i	$0.482562\pi$
$12$	61.3692	−	36.9427i	0.426175	−	0.256546i
$13$			59.9162i			0.354533i	0.984163	+	0.177267i	$0.0567255\pi$
$13$			59.9162i			0.354533i	−0.984163	+	0.177267i	$0.943274\pi$
$14$	−37.8062	+	66.8861i	−0.192889	+	0.341256i
$15$			74.4515i			0.330896i
$16$	−119.815	+	226.231i	−0.468027	+	0.883714i
$17$		−	390.623i		−	1.35164i	−0.737068	−	0.675819i	$-0.763790\pi$
$17$		−	390.623i		−	1.35164i	0.737068	−	0.675819i	$-0.236210\pi$
$18$	−212.267	−	119.980i	−0.655145	−	0.370310i
$19$	128.299			0.355399			0.177699	−	0.984085i	$-0.443135\pi$
$19$	128.299			0.355399			0.177699	+	0.984085i	$0.443135\pi$
$20$	−137.229	−	227.964i	−0.343072	−	0.569911i
$21$	−85.9918			−0.194993
$22$	−46.1431	−	26.0816i	−0.0953369	−	0.0538876i
$23$	87.5948	−	521.697i	0.165586	−	0.986195i
$23$	87.5948	−	521.697i	0.165586	−	0.986195i
$24$	−286.415	+	7.85166i	−0.497248	+	0.0136314i
$25$	−348.439			−0.557503
$26$	117.931	−	208.642i	0.174454	−	0.308642i
$27$		−	635.530i		−	0.871783i
$28$	263.300	−	158.500i	0.335842	−	0.202168i
$29$			828.280i			0.984875i	0.870348	+	0.492438i	$0.163894\pi$
$29$			828.280i			0.984875i	−0.870348	+	0.492438i	$0.836106\pi$
$30$	146.541	−	259.257i	0.162823	−	0.288063i
$31$	−23.4866			−0.0244398			−0.0122199	−	0.999925i	$-0.503890\pi$
$31$	−23.4866			−0.0244398			−0.0122199	+	0.999925i	$0.503890\pi$
$32$	862.506	−	551.960i	0.842291	−	0.539023i
$33$		−	59.3236i		−	0.0544753i
$34$	−768.852	+	1360.24i	−0.665097	+	1.17668i
$35$			319.429i			0.260758i
$36$	503.009	+	835.598i	0.388124	+	0.644752i
$37$	−1490.03			−1.08841			−0.544204	−	0.838953i	$-0.683168\pi$
$37$	−1490.03			−1.08841			−0.544204	+	0.838953i	$0.683168\pi$
$38$	−446.766	−	252.527i	−0.309395	−	0.174880i
$39$	268.239			0.176357
$40$	29.1661	+	1063.93i	0.0182288	+	0.664955i
$41$	−239.228			−0.142313			−0.0711564	−	0.997465i	$-0.522669\pi$
$41$	−239.228			−0.142313			−0.0711564	+	0.997465i	$0.522669\pi$
$42$	299.443	+	169.255i	0.169752	+	0.0959496i
$43$	−2981.33			−1.61240			−0.806200	−	0.591643i	$-0.798479\pi$
$43$	−2981.33			−1.61240			−0.806200	+	0.591643i	$0.798479\pi$
$44$	109.345	+	181.644i	0.0564799	+	0.0938244i
$45$	−1013.73			−0.500606
$46$	−1331.87	+	1644.26i	−0.629427	+	0.777060i
$47$	−2447.37			−1.10791			−0.553954	−	0.832548i	$-0.686882\pi$
$47$	−2447.37			−1.10791			−0.553954	+	0.832548i	$0.686882\pi$
$48$	1012.82	+	536.400i	0.439590	+	0.232813i
$49$	2032.06			0.846338
$50$	1213.35	+	685.823i	0.485338	+	0.274329i
$51$	−1748.79			−0.672351
$52$	−821.327	+	494.418i	−0.303745	+	0.182847i
$53$	−4340.56			−1.54523			−0.772617	−	0.634872i	$-0.781053\pi$
$53$	−4340.56			−1.54523			−0.772617	+	0.634872i	$0.781053\pi$
$54$	−1250.89	+	2213.06i	−0.428976	+	0.758937i
$55$	−220.366			−0.0728482
$56$	−1228.84	+	33.6870i	−0.391850	+	0.0107420i
$57$		−	574.383i		−	0.176788i
$58$	1630.28	−	2884.26i	0.484625	−	0.857390i
$59$			1011.86i			0.290680i	0.989382	+	0.145340i	$0.0464276\pi$
$59$			1011.86i			0.290680i	−0.989382	+	0.145340i	$0.953572\pi$
$60$	−1020.58	+	614.361i	−0.283493	+	0.170656i
$61$	−3518.02			−0.945450			−0.472725	−	0.881210i	$-0.656730\pi$
$61$	−3518.02			−0.945450			−0.472725	+	0.881210i	$0.656730\pi$
$62$	81.7858	+	46.2281i	0.0212762	+	0.0120260i
$63$		−	1170.86i		−	0.295001i
$64$	−4089.85	+	224.404i	−0.998498	+	0.0547861i
$65$		−	996.412i		−	0.235837i
$66$	−116.765	+	206.578i	−0.0268055	+	0.0474239i
$67$	1813.08			0.403894			0.201947	−	0.979396i	$-0.435273\pi$
$67$	1813.08			0.403894			0.201947	+	0.979396i	$0.435273\pi$
$68$	5354.64	−	3223.35i	1.15801	−	0.697092i
$69$	−2335.59	−	392.154i	−0.490568	−	0.0823680i
$70$	628.722	−	1112.32i	0.128311	−	0.227005i
$71$	4202.62			0.833688			0.416844	−	0.908978i	$-0.363136\pi$
$71$	4202.62			0.833688			0.416844	+	0.908978i	$0.363136\pi$
$72$	−106.908	−	3899.80i	−0.0206226	−	0.752276i
$73$	−5865.58			−1.10069			−0.550345	−	0.834937i	$-0.685504\pi$
$73$	−5865.58			−1.10069			−0.550345	+	0.834937i	$0.685504\pi$
$74$	5188.63	+	2932.79i	0.947522	+	0.535571i
$75$			1559.93i			0.277321i
$76$	1058.70	+	1758.71i	0.183293	+	0.304487i
$77$		−	254.524i		−	0.0429286i
$78$	−934.070	−	527.967i	−0.153529	−	0.0867796i
$79$			2415.67i			0.387065i	0.981094	+	0.193532i	$0.0619945\pi$
$79$			2415.67i			0.387065i	−0.981094	+	0.193532i	$0.938006\pi$
$80$	1992.53	−	3762.24i	0.311333	−	0.587851i
$81$	2092.33			0.318904
$82$	833.046	+	470.865i	0.123891	+	0.0700276i
$83$	−991.781			−0.143966			−0.0719829	−	0.997406i	$-0.522933\pi$
$83$	−991.781			−0.143966			−0.0719829	+	0.997406i	$0.522933\pi$
$84$	−709.589	−	1178.77i	−0.100565	−	0.167059i
$85$			6496.11i			0.899115i
$86$	10381.7	+	5868.06i	1.40369	+	0.793410i
$87$	3708.13			0.489911
$88$	−23.2398	−	847.747i	−0.00300101	−	0.109471i
$89$		−	13520.1i		−	1.70687i	−0.521200	−	0.853435i	$-0.674515\pi$
$89$		−	13520.1i		−	1.70687i	0.521200	−	0.853435i	$-0.325485\pi$
$90$	3530.03	+	1995.29i	0.435806	+	0.246332i
$91$	1150.86			0.138976
$92$	7874.21	−	3104.21i	0.930318	−	0.366755i
$93$			105.148i			0.0121572i
$94$	8522.29	+	4817.08i	0.964496	+	0.545165i
$95$	−2133.63			−0.236413
$96$	−2471.07	−	3861.36i	−0.268129	−	0.418985i
$97$		−	9360.78i		−	0.994876i	−0.867500	−	0.497438i	$-0.834274\pi$
$97$		−	9360.78i		−	0.994876i	0.867500	−	0.497438i	$-0.165726\pi$
$98$	−7076.09	−	3999.64i	−0.736786	−	0.416456i
$99$	807.746			0.0824146
$100$	−2875.26	−	4776.38i	−0.287526	−	0.477638i
$101$		−	12705.5i		−	1.24552i	−0.782415	−	0.622758i	$-0.786012\pi$
$101$		−	12705.5i		−	1.24552i	0.782415	−	0.622758i	$-0.213988\pi$
$102$	6089.67	+	3442.08i	0.585320	+	0.330842i
$103$			4953.33i			0.466899i	0.972369	+	0.233449i	$0.0750013\pi$
$103$			4953.33i			0.466899i	−0.972369	+	0.233449i	$0.924999\pi$
$104$	3833.19	−	105.082i	0.354400	−	0.00971539i
$105$	1430.05			0.129710
$106$	15114.8	+	8543.40i	1.34521	+	0.760360i
$107$	14129.5			1.23412			0.617062	−	0.786915i	$-0.288323\pi$
$107$	14129.5			1.23412			0.617062	+	0.786915i	$0.288323\pi$
$108$	8711.80	−	5244.28i	0.746897	−	0.449613i
$109$	−10694.8			−0.900157			−0.450079	−	0.892989i	$-0.648604\pi$
$109$	−10694.8			−0.900157			−0.450079	+	0.892989i	$0.648604\pi$
$110$	767.364	+	433.740i	0.0634185	+	0.0358462i
$111$			6670.74i			0.541412i
$112$	4345.41	+	2301.39i	0.346413	+	0.183465i
$113$		−	4274.54i		−	0.334759i	−0.985893	−	0.167380i	$-0.946469\pi$
$113$		−	4274.54i		−	0.334759i	0.985893	−	0.167380i	$-0.0535306\pi$
$114$	−1130.54	+	2000.13i	−0.0869915	+	0.153904i
$115$	−1456.71	+	8675.89i	−0.110148	+	0.656022i
$116$	−11354.0	+	6834.82i	−0.843788	+	0.507938i
$117$			3652.33i			0.266807i
$118$	1991.61	−	3523.52i	0.143034	−	0.253053i
$119$	−7503.03			−0.529838
$120$	4763.11	−	130.574i	0.330771	−	0.00906764i
$121$	−14465.4			−0.988007
$122$	12250.5	+	6924.41i	0.823068	+	0.465225i
$123$			1071.00i			0.0707913i
$124$	−193.808	−	321.953i	−0.0126046	−	0.0209387i
$125$	16188.4			1.03606
$126$	−2304.57	+	4077.20i	−0.145160	+	0.256815i
$127$	4278.14			0.265245			0.132623	−	0.991167i	$-0.457660\pi$
$127$	4278.14			0.265245			0.132623	+	0.991167i	$0.457660\pi$
$128$	14683.5	+	7268.50i	0.896208	+	0.443634i
$129$			13347.1i			0.802063i
$130$	−1961.21	+	3469.74i	−0.116048	+	0.205310i
$131$		−	17915.9i		−	1.04399i	−0.852949	−	0.521994i	$-0.825188\pi$
$131$		−	17915.9i		−	1.04399i	0.852949	−	0.521994i	$-0.174812\pi$
$132$	813.204	−	489.528i	0.0466715	−	0.0280950i
$133$		−	2464.35i		−	0.139315i
$134$	−6313.56	−	3568.63i	−0.351613	−	0.198743i
$135$			10568.9i			0.579914i
$136$	−24990.5	+	685.080i	−1.35113	+	0.0370394i
$137$		−	22737.9i		−	1.21146i	−0.795671	−	0.605729i	$-0.792881\pi$
$137$		−	22737.9i		−	1.21146i	0.795671	−	0.605729i	$-0.207119\pi$
$138$	7361.20	+	5962.65i	0.386536	+	0.313098i
$139$		−	11098.7i		−	0.574435i	−0.957865	−	0.287218i	$-0.907270\pi$
$139$		−	11098.7i		−	0.574435i	0.957865	−	0.287218i	$-0.0927303\pi$
$140$	−4378.71	+	2635.87i	−0.223403	+	0.134483i
$141$			10956.6i			0.551111i
$142$	−14634.5	−	8271.90i	−0.725773	−	0.410231i
$143$			793.950i			0.0388259i
$144$	−7303.59	+	13790.4i	−0.352218	+	0.665047i
$145$		−	13774.4i		−	0.655143i
$146$	20425.3	+	11545.0i	0.958213	+	0.541614i
$147$		−	9097.34i		−	0.420998i
$148$	−12295.5	−	20425.3i	−0.561335	−	0.932490i
$149$	1355.94			0.0610756			0.0305378	−	0.999534i	$-0.490278\pi$
$149$	1355.94			0.0610756			0.0305378	+	0.999534i	$0.490278\pi$
$150$	3070.37	−	5432.04i	0.136461	−	0.241424i
$151$	27793.6			1.21897			0.609483	−	0.792799i	$-0.291377\pi$
$151$	27793.6			1.21897			0.609483	+	0.792799i	$0.291377\pi$
$152$	−225.012	−	8208.05i	−0.00973911	−	0.355266i
$153$		−	23811.3i		−	1.01719i
$154$	−500.971	+	886.309i	−0.0211238	+	0.0373718i
$155$	390.585			0.0162575
$156$	2213.46	+	3677.01i	0.0909543	+	0.151093i
$157$	−15374.5			−0.623737			−0.311869	−	0.950125i	$-0.600955\pi$
$157$	−15374.5			−0.623737			−0.311869	+	0.950125i	$0.600955\pi$
$158$	4754.69	−	8411.92i	0.190462	−	0.336962i
$159$			19432.3i			0.768653i
$160$	−14343.6	+	9179.15i	−0.560296	+	0.358560i
$161$	−10020.7	−	1682.51i	−0.386586	−	0.0649091i
$162$	−7285.97	−	4118.27i	−0.277624	−	0.156922i
$163$			27611.5i			1.03924i	0.854398	+	0.519619i	$0.173926\pi$
$163$			27611.5i			1.03924i	−0.854398	+	0.519619i	$0.826074\pi$
$164$	−1974.07	−	3279.32i	−0.0733963	−	0.121926i
$165$			986.558i			0.0362372i
$166$	3453.61	+	1952.09i	0.125330	+	0.0708409i
$167$	−34348.4			−1.23161			−0.615806	−	0.787898i	$-0.711169\pi$
$167$	−34348.4			−1.23161			−0.615806	+	0.787898i	$0.711169\pi$
$168$	150.814	+	5501.41i	0.00534345	+	0.194920i
$169$	24971.1			0.874306
$170$	12786.1	−	22620.9i	0.442426	−	0.782731i
$171$	7820.76			0.267459
$172$	−24601.4	−	40867.8i	−0.831578	−	1.38142i
$173$			26637.2i			0.890012i	0.895528	+	0.445006i	$0.146798\pi$
$173$			26637.2i			0.890012i	−0.895528	+	0.445006i	$0.853202\pi$
$174$	−12912.6	−	7298.61i	−0.426495	−	0.241069i
$175$			6692.77i			0.218539i
$176$	−1587.67	+	2997.79i	−0.0512548	+	0.0967778i
$177$	4529.99			0.144594
$178$	−26611.2	+	47080.1i	−0.839895	+	1.48593i
$179$		−	2923.12i		−	0.0912307i	−0.998959	−	0.0456153i	$-0.985475\pi$
$179$		−	2923.12i		−	0.0912307i	0.998959	−	0.0456153i	$-0.0145249\pi$
$180$	−8365.09	−	13896.1i	−0.258182	−	0.428892i
$181$	−27732.3			−0.846503			−0.423251	−	0.906012i	$-0.639111\pi$
$181$	−27732.3			−0.846503			−0.423251	+	0.906012i	$0.639111\pi$
$182$	−4007.56	−	2265.20i	−0.120987	−	0.0683856i
$183$			15749.9i			0.470299i
$184$	−33529.7	−	4689.00i	−0.990363	−	0.138498i
$185$	24779.4			0.724014
$186$	206.959	−	366.148i	0.00598216	−	0.0105835i
$187$		−	5176.16i		−	0.148021i
$188$	−20195.2	−	33548.3i	−0.571391	−	0.949195i
$189$	−12207.2			−0.341736
$190$	7429.78	+	4199.56i	0.205811	+	0.116331i
$191$			64709.7i			1.77379i	0.461970	+	0.886895i	$0.347143\pi$
$191$			64709.7i			1.77379i	−0.461970	+	0.886895i	$0.652857\pi$
$192$	1004.64	+	18309.9i	0.0272525	+	0.496687i
$193$	−16236.5			−0.435891			−0.217945	−	0.975961i	$-0.569935\pi$
$193$	−16236.5			−0.435891			−0.217945	+	0.975961i	$0.569935\pi$
$194$	−18424.6	+	32596.4i	−0.489546	+	0.866096i
$195$	−4460.85			−0.117314
$196$	16768.2	+	27855.3i	0.436490	+	0.725097i
$197$		−	20892.1i		−	0.538331i	−0.963094	−	0.269166i	$-0.913252\pi$
$197$		−	20892.1i		−	0.538331i	0.963094	−	0.269166i	$-0.0867479\pi$
$198$	−2812.76	−	1589.86i	−0.0717466	−	0.0405536i
$199$			69996.3i			1.76754i	0.467923	+	0.883769i	$0.345003\pi$
$199$			69996.3i			1.76754i	−0.467923	+	0.883769i	$0.654997\pi$
$200$	611.097	+	22291.7i	0.0152774	+	0.557294i
$201$		−	8117.00i		−	0.200911i
$202$	−25007.9	+	44243.5i	−0.612878	+	1.08429i
$203$	15909.5			0.386068
$204$	−14430.7	−	23972.2i	−0.346758	−	0.576034i
$205$	3978.39			0.0946672
$206$	9749.49	−	17248.6i	0.229746	−	0.406462i
$207$	5339.54	−	31801.3i	0.124613	−	0.742170i
$208$	−13554.9	−	7178.84i	−0.313306	−	0.165931i
$209$	1700.09			0.0389206
$210$	−4979.77	−	2814.73i	−0.112920	−	0.0638261i
$211$		−	14655.2i		−	0.329176i	−0.986362	−	0.164588i	$-0.947371\pi$
$211$		−	14655.2i		−	0.329176i	0.986362	−	0.164588i	$-0.0526295\pi$
$212$	−35817.6	−	59500.2i	−0.796938	−	1.32387i
$213$		−	18814.8i		−	0.414705i
$214$	−49202.1	−	27810.7i	−1.07438	−	0.607272i
$215$	49579.8			1.07258
$216$	−40658.6	+	1114.60i	−0.871456	+	0.0238898i
$217$			451.128i			0.00958032i
$218$	37241.6	+	21050.2i	0.783638	+	0.442938i
$219$			26259.7i			0.547521i
$220$	−1818.42	−	3020.76i	−0.0375707	−	0.0624124i
$221$	23404.6			0.479201
$222$	13129.8	−	23229.0i	0.266411	−	0.471330i
$223$	12242.8			0.246190			0.123095	−	0.992395i	$-0.460718\pi$
$223$	12242.8			0.246190			0.123095	+	0.992395i	$0.460718\pi$
$224$	−10602.0	−	16566.9i	−0.211295	−	0.330176i
$225$	−21239.9			−0.419554
$226$	−8413.46	+	14884.9i	−0.164724	+	0.291427i
$227$	77803.3			1.50989			0.754947	−	0.655786i	$-0.227663\pi$
$227$	77803.3			1.50989			0.754947	+	0.655786i	$0.227663\pi$
$228$	7873.61	−	4739.71i	0.151462	−	0.0911763i
$229$	10831.1			0.206538			0.103269	−	0.994653i	$-0.467070\pi$
$229$	10831.1			0.206538			0.103269	+	0.994653i	$0.467070\pi$
$230$	22149.1	−	27344.2i	0.418697	−	0.516904i
$231$	−1139.48			−0.0213542
$232$	52990.0	−	1452.65i	0.984505	−	0.0269888i
$233$	−58770.8			−1.08255			−0.541277	−	0.840844i	$-0.682059\pi$
$233$	−58770.8			−1.08255			−0.541277	+	0.840844i	$0.682059\pi$
$234$	7188.76	−	12718.2i	0.131287	−	0.232271i
$235$	40700.0			0.736985
$236$	−13870.5	+	8349.66i	−0.249039	+	0.149915i
$237$	10814.7			0.192539
$238$	26127.3	+	14768.0i	0.461254	+	0.260716i
$239$	−39730.9			−0.695557			−0.347779	−	0.937577i	$-0.613064\pi$
$239$	−39730.9			−0.695557			−0.347779	+	0.937577i	$0.613064\pi$
$240$	−16843.2	−	8920.39i	−0.292417	−	0.154868i
$241$			155.179i			0.00267177i	0.999999	+	0.00133589i	$0.000425226\pi$
$241$			155.179i			0.00267177i	−0.999999	+	0.00133589i	$0.999575\pi$
$242$	50371.9	+	28471.8i	0.860116	+	0.486166i
$243$		−	60845.1i		−	1.03042i
$244$	−29030.1	−	48224.8i	−0.487605	−	0.810010i
$245$	−33793.4			−0.562988
$246$	2108.02	−	3729.47i	0.0348341	−	0.0616279i
$247$			7687.18i			0.126001i
$248$	41.1912	+	1502.58i	0.000669731	+	0.0244306i
$249$			4440.11i			0.0716136i
$250$	−56371.7	−	31863.2i	−0.901947	−	0.509811i
$251$	59911.9			0.950968			0.475484	−	0.879725i	$-0.342273\pi$
$251$	59911.9			0.950968			0.475484	+	0.879725i	$0.342273\pi$
$252$	16050.0	−	9661.72i	0.252741	−	0.152143i
$253$	1160.72	−	6913.02i	0.0181337	−	0.108001i
$254$	−14897.5	−	8420.54i	−0.230911	−	0.130519i
$255$	29082.5			0.447251
$256$	−36824.8	−	54211.6i	−0.561902	−	0.827204i
$257$	−10721.1			−0.162321			−0.0811603	−	0.996701i	$-0.525863\pi$
$257$	−10721.1			−0.162321			−0.0811603	+	0.996701i	$0.525863\pi$
$258$	26270.8	−	46477.8i	0.394669	−	0.698242i
$259$			28620.3i			0.426653i
$260$	13658.8	−	8222.22i	0.202053	−	0.121630i
$261$			50489.7i			0.741177i
$262$	−35263.3	+	62387.2i	−0.513713	+	0.908852i
$263$		−	65164.6i		−	0.942107i	−0.882105	−	0.471054i	$-0.843874\pi$
$263$		−	65164.6i		−	0.942107i	0.882105	−	0.471054i	$-0.156126\pi$
$264$	−3795.28	+	104.042i	−0.0544548	+	0.00149280i
$265$	72184.1			1.02790
$266$	−4850.50	+	8581.42i	−0.0685525	+	0.121282i
$267$	−60528.3			−0.849056
$268$	14961.2	+	24853.6i	0.208304	+	0.346034i
$269$		−	4484.18i		−	0.0619695i	−0.999520	−	0.0309848i	$-0.990136\pi$
$269$		−	4484.18i		−	0.0619695i	0.999520	−	0.0309848i	$-0.00986434\pi$
$270$	20802.5	−	36803.4i	0.285357	−	0.504848i
$271$	−5342.73			−0.0727486			−0.0363743	−	0.999338i	$-0.511581\pi$
$271$	−5342.73			−0.0727486			−0.0363743	+	0.999338i	$0.511581\pi$
$272$	88371.0	+	46802.5i	1.19446	+	0.632602i
$273$		−	5152.30i		−	0.0691315i
$274$	−44754.3	+	79178.4i	−0.596120	+	1.05464i
$275$	−4617.18			−0.0610536
$276$	−13897.3	−	35252.1i	−0.182436	−	0.462772i
$277$		−	125955.i		−	1.64156i	−0.571247	−	0.820778i	$-0.693540\pi$
$277$		−	125955.i		−	1.64156i	0.571247	−	0.820778i	$-0.306460\pi$
$278$	−21845.2	+	38648.1i	−0.282661	+	0.500079i
$279$	−1431.68			−0.0183924
$280$	20435.8	−	560.218i	0.260660	−	0.00714564i
$281$			49011.9i			0.620711i	0.950621	+	0.310355i	$0.100448\pi$
$281$			49011.9i			0.620711i	−0.950621	+	0.310355i	$0.899552\pi$
$282$	21565.6	−	38153.5i	0.271184	−	0.479774i
$283$	62632.4			0.782035			0.391017	−	0.920383i	$-0.372123\pi$
$283$	62632.4			0.782035			0.391017	+	0.920383i	$0.372123\pi$
$284$	34679.3	+	57609.3i	0.429965	+	0.714259i
$285$			9552.06i			0.117600i
$286$	1562.71	−	2764.71i	0.0191049	−	0.0338001i
$287$			4595.05i			0.0557862i
$288$	52576.0	−	33645.9i	0.633874	−	0.405647i
$289$	−69065.6			−0.826924
$290$	−27111.7	+	47965.6i	−0.322375	+	0.570340i
$291$	−41907.4			−0.494885
$292$	−48401.7	−	80404.9i	−0.567669	−	0.943011i
$293$	90924.1			1.05912			0.529559	−	0.848273i	$-0.322358\pi$
$293$	90924.1			1.05912			0.529559	+	0.848273i	$0.322358\pi$
$294$	−17906.0	+	31679.0i	−0.207159	+	0.366503i
$295$		−	16827.3i		−	0.193362i
$296$	2613.24	+	95326.2i	0.0298260	+	1.08800i
$297$		−	8421.42i		−	0.0954712i
$298$	−4721.69	−	2668.85i	−0.0531698	−	0.0300533i
$299$	31258.1	+	5248.35i	0.349639	+	0.0587057i
$300$	−21383.4	+	12872.3i	−0.237594	+	0.143025i
$301$			57264.9i			0.632056i
$302$	−96783.8	−	54705.4i	−1.06118	−	0.599814i
$303$	−56881.4			−0.619562
$304$	−15372.1	+	29025.2i	−0.166336	+	0.314071i
$305$	58505.0			0.628917
$306$	−46867.1	+	82916.5i	−0.500525	+	0.885519i
$307$			124670.i			1.32277i	0.750046	+	0.661386i	$0.230032\pi$
$307$			124670.i			1.32277i	−0.750046	+	0.661386i	$0.769968\pi$
$308$	3488.99	−	2100.28i	0.0367789	−	0.0221399i
$309$	22175.6			0.232252
$310$	−1360.11	−	768.778i	−0.0141530	−	0.00799977i
$311$	44384.3			0.458890			0.229445	−	0.973322i	$-0.426309\pi$
$311$	44384.3			0.458890			0.229445	+	0.973322i	$0.426309\pi$
$312$	−470.441	−	17160.9i	−0.00483277	−	0.176291i
$313$			118023.i			1.20470i	0.798231	+	0.602351i	$0.205769\pi$
$313$			118023.i			1.20470i	−0.798231	+	0.602351i	$0.794231\pi$
$314$	53537.5	+	30261.2i	0.542999	+	0.306921i
$315$			19471.5i			0.196236i
$316$	−33113.9	+	19933.7i	−0.331616	+	0.199624i
$317$			89983.7i			0.895458i	0.894169	+	0.447729i	$0.147767\pi$
$317$			89983.7i			0.895458i	−0.894169	+	0.447729i	$0.852233\pi$
$318$	38248.0	−	67667.7i	0.378229	−	0.669156i
$319$			10975.6i			0.107856i
$320$	68014.6	−	3731.86i	0.664205	−	0.0364439i
$321$		−	63256.4i		−	0.613896i
$322$	31582.7	+	25582.3i	0.304605	+	0.246733i
$323$		−	50116.6i		−	0.480371i
$324$	17265.5	+	28681.5i	0.164471	+	0.273220i
$325$		−	20877.2i		−	0.197653i
$326$	54346.9	−	96149.6i	0.511375	−	0.904716i
$327$			47879.5i			0.447769i
$328$	419.561	+	15304.8i	0.00389985	+	0.142259i
$329$			47008.7i			0.434296i
$330$	1941.81	−	3435.42i	0.0178312	−	0.0315466i
$331$		−	135290.i		−	1.23484i	−0.786634	−	0.617419i	$-0.788178\pi$
$331$		−	135290.i		−	1.23484i	0.786634	−	0.617419i	$-0.211822\pi$
$332$	−8184.00	−	13595.3i	−0.0742488	−	0.123342i
$333$	−90828.3			−0.819092
$334$	119609.	+	67607.0i	1.07219	+	0.606036i
$335$	−30151.7			−0.268672
$336$	10303.1	−	19454.0i	0.0912618	−	0.172318i
$337$		−	79768.9i		−	0.702383i	−0.936304	−	0.351191i	$-0.885777\pi$
$337$		−	79768.9i		−	0.702383i	0.936304	−	0.351191i	$-0.114223\pi$
$338$	−86954.9	−	49149.8i	−0.761133	−	0.430218i
$339$	−19136.7			−0.166521
$340$	−89048.2	+	53604.7i	−0.770313	+	0.463709i
$341$	−311.222			−0.00267646
$342$	−27233.7	−	15393.4i	−0.232838	−	0.131608i
$343$		−	85149.5i		−	0.723759i
$344$	5228.69	+	190733.i	0.0441851	+	1.61179i
$345$	38841.2	+	6521.57i	0.326328	+	0.0547916i
$346$	52429.2	−	92756.7i	0.437946	−	0.774806i
$347$		−	86659.5i		−	0.719710i	−0.933008	−	0.359855i	$-0.882826\pi$
$347$		−	86659.5i		−	0.719710i	0.933008	−	0.359855i	$-0.117174\pi$
$348$	30598.9	+	50830.9i	0.252666	+	0.419729i
$349$		−	69799.7i		−	0.573064i	−0.958071	−	0.286532i	$-0.907498\pi$
$349$		−	69799.7i		−	0.573064i	0.958071	−	0.286532i	$-0.0925024\pi$
$350$	13173.2	−	23305.8i	0.107536	−	0.190251i
$351$	38078.5			0.309076
$352$	11429.1	−	7314.02i	0.0922414	−	0.0590298i
$353$	210507.			1.68934			0.844671	−	0.535285i	$-0.179796\pi$
$353$	210507.			1.68934			0.844671	+	0.535285i	$0.179796\pi$
$354$	−15774.5	−	8916.25i	−0.125878	−	0.0711501i
$355$	−69890.1			−0.554573
$356$	185333.	−	111566.i	1.46235	−	0.880299i
$357$			33590.4i			0.263560i
$358$	−5753.50	+	10179.0i	−0.0448917	+	0.0794215i
$359$		−	48815.6i		−	0.378765i	−0.981903	−	0.189382i	$-0.939351\pi$
$359$		−	48815.6i		−	0.378765i	0.981903	−	0.189382i	$-0.0606485\pi$
$360$	1777.89	+	64854.1i	0.0137183	+	0.500418i
$361$	−113860.			−0.873692
$362$	96570.1	+	54584.6i	0.736929	+	0.416537i
$363$			64760.3i			0.491469i
$364$	9496.70	+	15775.9i	0.0716754	+	0.119067i
$365$	97545.2			0.732184
$366$	31000.0	−	54844.6i	0.231419	−	0.409422i
$367$		−	75081.0i		−	0.557440i	−0.960372	−	0.278720i	$-0.910090\pi$
$367$		−	75081.0i		−	0.557440i	0.960372	−	0.278720i	$-0.0899101\pi$
$368$	107529.	+	82323.7i	0.794017	+	0.607896i
$369$	−14582.7			−0.107099
$370$	−86287.5	−	48772.5i	−0.630296	−	0.356264i
$371$			83372.9i			0.605727i
$372$	−1441.36	+	867.659i	−0.0104156	+	0.00626994i
$373$	58268.0			0.418806			0.209403	−	0.977829i	$-0.432848\pi$
$373$	58268.0			0.418806			0.209403	+	0.977829i	$0.432848\pi$
$374$	−10188.1	+	18024.6i	−0.0728365	+	0.128861i
$375$		−	72474.0i		−	0.515371i
$376$	4292.22	+	156573.i	0.0303603	+	1.10749i
$377$	−49627.4			−0.349171
$378$	42508.1	+	24027.0i	0.297501	+	0.168157i
$379$	−56816.9			−0.395548			−0.197774	−	0.980248i	$-0.563371\pi$
$379$	−56816.9			−0.395548			−0.197774	+	0.980248i	$0.563371\pi$
$380$	−17606.3	−	29247.6i	−0.121927	−	0.202546i
$381$		−	19152.9i		−	0.131942i
$382$	127366.	−	225334.i	0.872825	−	1.54419i
$383$		−	109132.i		−	0.743970i	−0.928239	−	0.371985i	$-0.878677\pi$
$383$		−	109132.i		−	0.743970i	0.928239	−	0.371985i	$-0.121323\pi$
$384$	32540.4	−	65736.6i	0.220679	−	0.445805i
$385$			4232.75i			0.0285563i
$386$	56539.2	+	31957.8i	0.379468	+	0.214488i
$387$	−181734.			−1.21343
$388$	128317.	−	77243.5i	0.852355	−	0.513096i
$389$	−51510.4			−0.340405			−0.170202	−	0.985409i	$-0.554442\pi$
$389$	−51510.4			−0.340405			−0.170202	+	0.985409i	$0.554442\pi$
$390$	15533.7	+	8780.16i	0.102128	+	0.0577262i
$391$	−203787.	−	34216.6i	−1.33298	−	0.223812i
$392$	−3563.85	−	130003.i	−0.0231925	−	0.846021i
$393$	−80207.8			−0.519316
$394$	−41121.3	+	72751.0i	−0.264895	+	0.468648i
$395$		−	40172.9i		−	0.257477i
$396$	6665.38	+	11072.5i	0.0425044	+	0.0706084i
$397$			76081.0i			0.482720i	0.970436	+	0.241360i	$0.0775934\pi$
$397$			76081.0i			0.482720i	−0.970436	+	0.241360i	$0.922407\pi$
$398$	137772.	−	243743.i	0.869749	−	1.53874i
$399$	−11032.7			−0.0693002
$400$	41748.2	−	78827.7i	0.260926	−	0.492673i
$401$		−	48197.7i		−	0.299735i	−0.988706	−	0.149868i	$-0.952115\pi$
$401$		−	48197.7i		−	0.299735i	0.988706	−	0.149868i	$-0.0478848\pi$
$402$	−15976.4	+	28265.2i	−0.0988617	+	0.174904i
$403$		−	1407.23i		−	0.00866472i
$404$	174166.	−	104844.i	1.06709	−	0.642361i
$405$	−34795.7			−0.212136
$406$	−55400.4	−	31314.2i	−0.336094	−	0.189972i
$407$	−19744.4			−0.119194
$408$	3067.04	+	111880.i	0.0184247	+	0.672099i
$409$	24835.8			0.148468			0.0742338	−	0.997241i	$-0.476349\pi$
$409$	24835.8			0.148468			0.0742338	+	0.997241i	$0.476349\pi$
$410$	−13853.7	−	7830.54i	−0.0824132	−	0.0465826i
$411$	−101795.			−0.602621
$412$	−67899.9	+	40874.0i	−0.400014	+	0.240798i
$413$	19435.6			0.113946
$414$	−81187.0	+	100230.i	−0.473681	+	0.584783i
$415$	16493.4			0.0957667
$416$	33071.3	+	51678.0i	0.191102	+	0.298620i
$417$	−49687.7			−0.285744
$418$	−5920.11	−	3346.24i	−0.0338826	−	0.0191516i
$419$	−319188.			−1.81810			−0.909051	−	0.416685i	$-0.863192\pi$
$419$	−319188.			−1.81810			−0.909051	+	0.416685i	$0.863192\pi$
$420$	11800.5	+	19603.1i	0.0668965	+	0.111129i
$421$	−101043.			−0.570087			−0.285043	−	0.958515i	$-0.592008\pi$
$421$	−101043.			−0.570087			−0.285043	+	0.958515i	$0.592008\pi$
$422$	−28845.5	+	51032.9i	−0.161977	+	0.286567i
$423$	−149185.			−0.833766
$424$	7612.53	+	277692.i	0.0423446	+	1.54465i
$425$			136109.i			0.753542i
$426$	−37032.5	+	65517.3i	−0.204063	+	0.361024i
$427$			67573.6i			0.370613i
$428$	116594.	+	193686.i	0.636486	+	1.05733i
$429$	3554.44			0.0193133
$430$	−172648.	−	97586.5i	−0.933738	−	0.527780i
$431$		−	289564.i		−	1.55880i	−0.626529	−	0.779398i	$-0.715525\pi$
$431$		−	289564.i		−	1.55880i	0.626529	−	0.779398i	$-0.284475\pi$
$432$	143776.	+	76145.9i	0.770407	+	0.408018i
$433$			173675.i			0.926320i	0.886275	+	0.463160i	$0.153284\pi$
$433$			173675.i			0.926320i	−0.886275	+	0.463160i	$0.846716\pi$
$434$	887.941	−	1570.93i	0.00471417	−	0.00834022i
$435$	−61666.7			−0.325891
$436$	−88251.3	−	146603.i	−0.464246	−	0.771206i
$437$	11238.3	−	66933.3i	0.0588490	−	0.350493i
$438$	51686.1	−	91442.1i	0.269417	−	0.476648i
$439$	210043.			1.08988			0.544941	−	0.838475i	$-0.316552\pi$
$439$	210043.			1.08988			0.544941	+	0.838475i	$0.316552\pi$
$440$	386.480	+	14098.1i	0.00199628	+	0.0728209i
$441$	123869.			0.636920
$442$	−81500.3	−	46066.7i	−0.417172	−	0.235799i
$443$			109897.i			0.559986i	0.960002	+	0.279993i	$0.0903322\pi$
$443$			109897.i			0.559986i	−0.960002	+	0.279993i	$0.909668\pi$
$444$	−91442.0	+	55045.8i	−0.463853	+	0.279227i
$445$			224841.i			1.13542i
$446$	−42632.1	−	24097.1i	−0.214322	−	0.121142i
$447$		−	6070.42i		−	0.0303811i
$448$	4310.31	+	78557.2i	0.0214760	+	0.391408i
$449$	−42370.3			−0.210169			−0.105085	−	0.994463i	$-0.533511\pi$
$449$	−42370.3			−0.210169			−0.105085	+	0.994463i	$0.533511\pi$
$450$	73962.2	+	41805.9i	0.365246	+	0.206449i
$451$	−3170.01			−0.0155850
$452$	58595.1	−	35272.8i	0.286804	−	0.172648i
$453$		−	124430.i		−	0.606356i
$454$	−270929.	−	153138.i	−1.31445	−	0.742970i
$455$	−19138.9			−0.0924475
$456$	−36746.7	+	1007.36i	−0.176721	+	0.00484457i
$457$			229397.i			1.09839i	0.835695	+	0.549193i	$0.185065\pi$
$457$			229397.i			1.09839i	−0.835695	+	0.549193i	$0.814935\pi$
$458$	−37716.2	−	21318.5i	−0.179803	−	0.101631i
$459$	−248253.			−1.17834
$460$	−130949.	+	51623.4i	−0.618852	+	0.243967i
$461$		−	272746.i		−	1.28339i	−0.766962	−	0.641693i	$-0.778232\pi$
$461$		−	272746.i		−	1.28339i	0.766962	−	0.641693i	$-0.221768\pi$
$462$	3967.93	+	2242.80i	0.0185900	+	0.0105077i
$463$	174386.			0.813484			0.406742	−	0.913543i	$-0.366665\pi$
$463$	174386.			0.813484			0.406742	+	0.913543i	$0.366665\pi$
$464$	−187383.	−	99240.2i	−0.870348	−	0.460948i
$465$		−	1748.62i		−	0.00808702i
$466$	204653.	+	115677.i	0.942425	+	0.532690i
$467$	−178953.			−0.820551			−0.410276	−	0.911962i	$-0.634568\pi$
$467$	−178953.			−0.820551			−0.410276	+	0.911962i	$0.634568\pi$
$468$	−50065.8	+	30138.3i	−0.228586	+	0.137603i
$469$		−	34825.4i		−	0.158325i
$470$	−141727.	−	80108.6i	−0.641587	−	0.362646i
$471$			68830.3i			0.310268i
$472$	64734.5	−	1774.61i	0.290571	−	0.00796560i
$473$	−39505.6			−0.176578
$474$	−37659.4	−	21286.3i	−0.167616	−	0.0947424i
$475$	−44704.4			−0.198136
$476$	−61913.7	−	102851.i	−0.273258	−	0.453936i
$477$	−264589.			−1.16288
$478$	138352.	+	78201.2i	0.605522	+	0.342261i
$479$		−	111903.i		−	0.487720i	−0.969810	−	0.243860i	$-0.921586\pi$
$479$		−	111903.i		−	0.487720i	0.969810	−	0.243860i	$-0.0784137\pi$
$480$	41094.2	+	64214.9i	0.178360	+	0.278710i
$481$		−	89277.0i		−	0.385877i
$482$	305.435	−	540.370i	0.00131469	−	0.00232593i
$483$	−7532.44	+	44861.7i	−0.0322880	+	0.192301i
$484$	−119366.	−	198291.i	−0.509554	−	0.846471i
$485$			155671.i			0.661796i
$486$	−119760.	+	211876.i	−0.507035	+	0.897037i
$487$	33278.0			0.140313			0.0701566	−	0.997536i	$-0.477650\pi$
$487$	33278.0			0.140313			0.0701566	+	0.997536i	$0.477650\pi$
$488$	6169.95	+	225069.i	0.0259085	+	0.945095i
$489$	123614.			0.516953
$490$	117676.	+	66514.5i	0.490113	+	0.277028i
$491$			395933.i			1.64232i	0.570697	+	0.821161i	$0.306673\pi$
$491$			395933.i			1.64232i	−0.570697	+	0.821161i	$0.693327\pi$
$492$	−14681.2	+	8837.72i	−0.0606502	+	0.0365098i
$493$	323545.			1.33119
$494$	15130.5	−	26768.5i	0.0620009	−	0.109691i
$495$	−13432.9			−0.0548226
$496$	2814.05	−	5313.40i	0.0114385	−	0.0215978i
$497$		−	80723.3i		−	0.326803i
$498$	8739.34	−	15461.5i	0.0352387	−	0.0623437i
$499$		−	261241.i		−	1.04916i	−0.851362	−	0.524578i	$-0.824223\pi$
$499$		−	261241.i		−	1.04916i	0.851362	−	0.524578i	$-0.175777\pi$
$500$	133584.	+	221910.i	0.534335	+	0.887638i
$501$			153775.i			0.612646i
$502$	−208627.	−	117923.i	−0.827871	−	0.467940i
$503$		−	413190.i		−	1.63310i	−0.577273	−	0.816551i	$-0.695883\pi$
$503$		−	413190.i		−	1.63310i	0.577273	−	0.816551i	$-0.304117\pi$
$504$	−74906.8	+	2053.47i	−0.294890	+	0.00808400i
$505$			211294.i			0.828522i
$506$	−17648.6	+	21788.1i	−0.0689301	+	0.0850978i
$507$		−	111793.i		−	0.434910i
$508$	35302.5	+	58644.5i	0.136797	+	0.227248i
$509$			97081.6i			0.374715i	0.982292	+	0.187358i	$0.0599924\pi$
$509$			97081.6i			0.374715i	−0.982292	+	0.187358i	$0.940008\pi$
$510$	−101272.	−	57242.2i	−0.389357	−	0.220078i
$511$			112665.i			0.431467i
$512$	21529.3	+	261258.i	0.0821276	+	0.996622i
$513$		−	81537.9i		−	0.309831i
$514$	37333.4	+	21102.1i	0.141309	+	0.0798727i
$515$		−	82374.4i		−	0.310583i
$516$	−182962.	+	110138.i	−0.687164	+	0.413655i
$517$	−32430.1			−0.121330
$518$	56332.5	−	99662.4i	0.209942	−	0.371426i
$519$	119252.			0.442723
$520$	−63746.4	+	1747.52i	−0.235749	+	0.00646272i
$521$			249872.i			0.920540i	0.887779	+	0.460270i	$0.152247\pi$
$521$			249872.i			0.920540i	−0.887779	+	0.460270i	$0.847753\pi$
$522$	99377.4	−	175817.i	0.364709	−	0.645237i
$523$	180097.			0.658422			0.329211	−	0.944256i	$-0.393217\pi$
$523$	180097.			0.658422			0.329211	+	0.944256i	$0.393217\pi$
$524$	245590.	−	147839.i	0.894433	−	0.538426i
$525$	29962.9			0.108709
$526$	−128262.	+	226918.i	−0.463581	+	0.820158i
$527$			9174.43i			0.0330337i
$528$	13420.8	+	7107.85i	0.0481406	+	0.0254959i
$529$	−264495.	−	91396.0i	−0.945163	−	0.326600i
$530$	−251361.	−	142078.i	−0.894843	−	0.505795i
$531$			61680.0i			0.218754i
$532$	33781.1	−	20335.4i	0.119358	−	0.0718503i
$533$		−	14333.6i		−	0.0504547i
$534$	210773.	+	119136.i	0.739151	+	0.417793i
$535$	−234975.			−0.820945
$536$	−3179.80	−	115994.i	−0.0110680	−	0.403742i
$537$	−13086.6			−0.0453813
$538$	−8826.07	+	15614.9i	−0.0304932	+	0.0539480i
$539$	26926.8			0.0926847
$540$	−144878.	+	87213.0i	−0.496839	+	0.299084i
$541$		−	542150.i		−	1.85236i	−0.377085	−	0.926179i	$-0.623073\pi$
$541$		−	542150.i		−	1.85236i	0.377085	−	0.926179i	$-0.376927\pi$
$542$	18604.6	+	10515.9i	0.0633318	+	0.0357972i
$543$			124155.i			0.421080i
$544$	−215608.	−	336915.i	−0.728564	−	1.13847i
$545$	177855.			0.598789
$546$	−10141.1	+	17941.5i	−0.0340174	+	0.0601829i
$547$			268881.i			0.898640i	0.893371	+	0.449320i	$0.148334\pi$
$547$			268881.i			0.898640i	−0.893371	+	0.449320i	$0.851666\pi$
$548$	311689.	−	187629.i	1.03791	−	0.624796i
$549$	−214449.			−0.711507
$550$	16078.1	+	9087.85i	0.0531506	+	0.0300425i
$551$			106268.i			0.350024i
$552$	−20992.2	+	150110.i	−0.0688939	+	0.492640i
$553$	46399.8			0.151728
$554$	−247913.	+	438604.i	−0.807756	+	1.42907i
$555$		−	110935.i		−	0.360150i
$556$	152140.	−	91584.2i	0.492145	−	0.296259i
$557$	136208.			0.439027			0.219513	−	0.975610i	$-0.429553\pi$
$557$	136208.			0.439027			0.219513	+	0.975610i	$0.429553\pi$
$558$	4985.44	+	2817.94i	0.0160116	+	0.00905030i
$559$		−	178630.i		−	0.571650i
$560$	−72264.6	−	38272.3i	−0.230436	−	0.122042i
$561$	−23173.2			−0.0736309
$562$	96468.7	−	170671.i	0.305432	−	0.540364i
$563$	505002.			1.59322			0.796610	−	0.604493i	$-0.206624\pi$
$563$	505002.			1.59322			0.796610	+	0.604493i	$0.206624\pi$
$564$	−150193.	+	90412.3i	−0.472162	+	0.284230i
$565$			71086.1i			0.222683i
$566$	−218100.	−	123277.i	−0.680806	−	0.384814i
$567$		−	40189.1i		−	0.125009i
$568$	−7370.61	−	268867.i	−0.0228458	−	0.833375i
$569$			52065.8i			0.160816i	0.996762	+	0.0804078i	$0.0256223\pi$
$569$			52065.8i			0.160816i	−0.996762	+	0.0804078i	$0.974378\pi$
$570$	18801.0	−	33262.4i	0.0578671	−	0.102377i
$571$	500314.			1.53451			0.767257	−	0.641340i	$-0.221621\pi$
$571$	500314.			1.53451			0.767257	+	0.641340i	$0.221621\pi$
$572$	−10883.4	+	6551.53i	−0.0332639	+	0.0200240i
$573$	289699.			0.882345
$574$	9044.31	−	16001.0i	0.0274506	−	0.0485651i
$575$	−30521.5	+	181780.i	−0.0923145	+	0.549807i
$576$	−249306.	+	13679.0i	−0.751429	+	0.0412297i
$577$	81158.1			0.243770			0.121885	−	0.992544i	$-0.461106\pi$
$577$	81158.1			0.243770			0.121885	+	0.992544i	$0.461106\pi$
$578$	240502.	+	135940.i	0.719885	+	0.406903i
$579$			72689.3i			0.216827i
$580$	188818.	−	113664.i	0.561291	−	0.337883i
$581$			19050.0i			0.0564342i
$582$	145931.	+	82485.1i	0.430826	+	0.243517i
$583$	−57516.9			−0.169223
$584$	10287.1	+	375256.i	0.0301626	+	1.10028i
$585$		−	60738.6i		−	0.177481i
$586$	−316619.	−	178963.i	−0.922022	−	0.521157i
$587$		−	498760.i		−	1.44749i	−0.690068	−	0.723744i	$-0.742420\pi$
$587$		−	498760.i		−	1.44749i	0.690068	−	0.723744i	$-0.257580\pi$
$588$	124706.	−	75069.7i	0.360688	−	0.217125i
$589$	−3013.31			−0.00868588
$590$	−33120.7	+	58596.5i	−0.0951470	+	0.168332i
$591$	−93532.0			−0.267784
$592$	178528.	−	337091.i	0.509404	−	0.961843i
$593$	−321893.			−0.915381			−0.457690	−	0.889112i	$-0.651323\pi$
$593$	−321893.			−0.915381			−0.457690	+	0.889112i	$0.651323\pi$
$594$	−16575.6	+	29325.3i	−0.0469783	+	0.0831131i
$595$	124776.			0.352450
$596$	11189.0	+	18587.1i	0.0314991	+	0.0523262i
$597$	313367.			0.879235
$598$	−98517.7	−	79800.3i	−0.275494	−	0.223153i
$599$	−338938.			−0.944639			−0.472320	−	0.881427i	$-0.656583\pi$
$599$	−338938.			−0.944639			−0.472320	+	0.881427i	$0.656583\pi$
$600$	99798.1	−	2735.83i	0.277217	−	0.00759952i
$601$	594089.			1.64476			0.822380	−	0.568938i	$-0.192646\pi$
$601$	594089.			1.64476			0.822380	+	0.568938i	$0.192646\pi$
$602$	112713.	−	199409.i	0.311014	−	0.550241i
$603$	110520.			0.303954
$604$	229348.	+	380993.i	0.628668	+	1.04434i
$605$	240561.			0.657227
$606$	198074.	+	111958.i	0.539364	+	0.304866i
$607$	62131.7			0.168630			0.0843152	−	0.996439i	$-0.473130\pi$
$607$	62131.7			0.168630			0.0843152	+	0.996439i	$0.473130\pi$
$608$	110659.	−	70815.9i	0.299349	−	0.191568i
$609$		−	71225.3i		−	0.192044i
$610$	−203728.	−	115154.i	−0.547508	−	0.309470i
$611$		−	146637.i		−	0.392790i
$612$	326404.	−	196487.i	0.871471	−	0.524603i
$613$	718755.			1.91276			0.956379	−	0.292127i	$-0.0943631\pi$
$613$	718755.			1.91276			0.956379	+	0.292127i	$0.0943631\pi$
$614$	245384.	−	434129.i	0.650893	−	1.15155i
$615$		−	17810.9i		−	0.0470907i
$616$	−16283.4	+	446.386i	−0.0429125	+	0.00117639i
$617$			337214.i			0.885800i	0.896571	+	0.442900i	$0.146050\pi$
$617$			337214.i			0.885800i	−0.896571	+	0.442900i	$0.853950\pi$
$618$	−77220.5	−	43647.6i	−0.202188	−	0.114283i
$619$	260680.			0.680340			0.340170	−	0.940364i	$-0.389515\pi$
$619$	260680.			0.680340			0.340170	+	0.940364i	$0.389515\pi$
$620$	3223.04	+	5354.12i	0.00838460	+	0.0139285i
$621$	−331554.	−	55669.1i	−0.859749	−	0.144355i
$622$	−154556.	−	87360.4i	−0.399490	−	0.225805i
$623$	−259692.			−0.669088
$624$	−32139.0	+	60684.0i	−0.0825399	+	0.155849i
$625$	−51440.4			−0.131687
$626$	232302.	−	410984.i	0.592795	−	1.04876i
$627$		−	7611.16i		−	0.0193605i
$628$	−126868.	−	210753.i	−0.321686	−	0.534384i
$629$			582041.i			1.47113i
$630$	38325.2	−	67804.2i	0.0965613	−	0.170834i
$631$			410811.i			1.03177i	0.856658	+	0.515885i	$0.172537\pi$
$631$			410811.i			1.03177i	−0.856658	+	0.515885i	$0.827463\pi$
$632$	154545.	−	4236.63i	0.386919	−	0.0106069i
$633$	−65610.2			−0.163744
$634$	177112.	−	313344.i	0.440626	−	0.779547i
$635$	−71146.0			−0.176442
$636$	−266377.	+	160352.i	−0.658540	+	0.396424i
$637$			121753.i			0.300055i
$638$	21602.9	−	38219.4i	0.0530725	−	0.0938949i
$639$	256180.			0.627399
$640$	−244188.	−	120876.i	−0.596162	−	0.295107i
$641$			339552.i			0.826400i	0.910640	+	0.413200i	$0.135589\pi$
$641$			339552.i			0.826400i	−0.910640	+	0.413200i	$0.864411\pi$
$642$	−124506.	+	220273.i	−0.302078	+	0.534431i
$643$	546710.			1.32232			0.661158	−	0.750247i	$-0.270065\pi$
$643$	546710.			1.32232			0.661158	+	0.750247i	$0.270065\pi$
$644$	−59625.2	−	151247.i	−0.143767	−	0.364682i
$645$		−	221964.i		−	0.533536i
$646$	−98643.0	+	174517.i	−0.236375	+	0.418190i
$647$	807329.			1.92860			0.964299	−	0.264815i	$-0.0853109\pi$
$647$	807329.			1.92860			0.964299	+	0.264815i	$0.0853109\pi$
$648$	−3669.55	−	133859.i	−0.00873903	−	0.318784i
$649$			13408.1i			0.0318331i
$650$	−41091.9	+	72699.0i	−0.0972589	+	0.172069i
$651$	2019.66			0.00476558
$652$	−378497.	+	227845.i	−0.890363	+	0.535975i
$653$		−	283319.i		−	0.664431i	−0.943204	−	0.332215i	$-0.892204\pi$
$653$		−	283319.i		−	0.664431i	0.943204	−	0.332215i	$-0.107796\pi$
$654$	94239.8	−	166727.i	0.220333	−	0.389809i
$655$			297943.i			0.694466i
$656$	28663.1	−	54120.7i	0.0666062	−	0.125764i
$657$	−357550.			−0.828334
$658$	92525.7	−	163695.i	0.213703	−	0.378080i
$659$	−241404.			−0.555871			−0.277935	−	0.960600i	$-0.589650\pi$
$659$	−241404.			−0.555871			−0.277935	+	0.960600i	$0.589650\pi$
$660$	−13523.7	+	8140.90i	−0.0310461	+	0.0186889i
$661$	544622.			1.24650			0.623250	−	0.782023i	$-0.285812\pi$
$661$	544622.			1.24650			0.623250	+	0.782023i	$0.285812\pi$
$662$	−266287.	+	471111.i	−0.607624	+	1.07500i
$663$		−	104780.i		−	0.238371i
$664$	1739.40	+	63450.1i	0.00394514	+	0.143912i
$665$			40982.4i			0.0926732i
$666$	316285.	+	178775.i	0.713066	+	0.403049i
$667$	432112.	+	72553.0i	0.971279	+	0.163081i
$668$	−283437.	−	470846.i	−0.635190	−	1.05518i
$669$		−	54809.8i		−	0.122463i
$670$	104995.	+	59346.7i	0.233894	+	0.132205i
$671$	−46617.3			−0.103539
$672$	−74168.5	+	47464.0i	−0.164241	+	0.105106i
$673$	314656.			0.694714			0.347357	−	0.937733i	$-0.387079\pi$
$673$	314656.			0.694714			0.347357	+	0.937733i	$0.387079\pi$
$674$	−157007.	+	277773.i	−0.345620	+	0.611464i
$675$			221444.i			0.486022i
$676$	206057.	+	342302.i	0.450914	+	0.749058i
$677$	−406996.			−0.888000			−0.444000	−	0.896027i	$-0.646441\pi$
$677$	−406996.			−0.888000			−0.444000	+	0.896027i	$0.646441\pi$
$678$	66638.5	+	37666.3i	0.144966	+	0.0819395i
$679$	−179801.			−0.389988
$680$	415595.	−	11393.0i	0.898778	−	0.0246387i
$681$		−	348318.i		−	0.751073i
$682$	1083.75	+	612.569i	0.00233001	+	0.00131700i
$683$		−	683402.i		−	1.46499i	−0.680772	−	0.732496i	$-0.738355\pi$
$683$		−	683402.i		−	1.46499i	0.680772	−	0.732496i	$-0.261645\pi$
$684$	64535.5	+	107206.i	0.137939	+	0.229144i
$685$			378133.i			0.805868i
$686$	−167597.	+	296510.i	−0.356138	+	0.630073i
$687$		−	48489.7i		−	0.102739i
$688$	357207.	−	674468.i	0.754646	−	1.42490i
$689$		−	260070.i		−	0.547837i
$690$	−122418.	−	99159.5i	−0.257126	−	0.208274i
$691$		−	697150.i		−	1.46006i	−0.683416	−	0.730029i	$-0.739506\pi$
$691$		−	697150.i		−	1.46006i	0.683416	−	0.730029i	$-0.260494\pi$
$692$	−365141.	+	219805.i	−0.762514	+	0.459014i
$693$		−	15515.1i		−	0.0323063i
$694$	−170569.	+	301768.i	−0.354146	+	0.626548i
$695$			184572.i			0.382117i
$696$	−6503.37	−	237232.i	−0.0134252	−	0.489727i
$697$			93448.0i			0.192355i
$698$	−137385.	+	243059.i	−0.281986	+	0.498885i
$699$			263111.i			0.538500i
$700$	−91744.1	+	55227.6i	−0.187233	+	0.112709i
$701$	−551797.			−1.12291			−0.561453	−	0.827509i	$-0.689757\pi$
$701$	−551797.			−1.12291			−0.561453	+	0.827509i	$0.689757\pi$
$702$	−132598.	−	74948.8i	−0.269069	−	0.152086i
$703$	−191170.			−0.386819
$704$	−54194.6	+	2973.58i	−0.109348	+	0.00599976i
$705$		−	182210.i		−	0.366602i
$706$	−733034.	−	414335.i	−1.47067	−	0.831271i
$707$	−244045.			−0.488238
$708$	37380.7	+	62096.8i	0.0745729	+	0.123880i
$709$	−201602.			−0.401053			−0.200526	−	0.979688i	$-0.564265\pi$
$709$	−201602.			−0.401053			−0.200526	+	0.979688i	$0.564265\pi$
$710$	243373.	+	137563.i	0.482787	+	0.272887i
$711$			147253.i			0.291289i
$712$	−864962.	+	23711.7i	−1.70623	+	0.0467739i
$713$	−2057.31	+	12252.9i	−0.00404688	+	0.0241024i
$714$	66115.0	−	116969.i	0.129689	−	0.229444i
$715$		−	13203.5i		−	0.0258271i
$716$	40070.0	−	24121.1i	0.0781615	−	0.0470512i
$717$			177872.i			0.345994i
$718$	−96082.2	+	169987.i	−0.186378	+	0.329736i
$719$	355494.			0.687661			0.343830	−	0.939032i	$-0.388275\pi$
$719$	355494.			0.687661			0.343830	+	0.939032i	$0.388275\pi$
$720$	121459.	−	229336.i	0.234297	−	0.442392i
$721$	95142.8			0.183023
$722$	396488.	+	224108.i	0.760598	+	0.429915i
$723$	694.724			0.00132903
$724$	−228842.	−	380152.i	−0.436574	−	0.725238i
$725$		−	288605.i		−	0.549071i
$726$	127466.	−	225510.i	0.241836	−	0.427852i
$727$			450474.i			0.852317i	0.904649	+	0.426158i	$0.140133\pi$
$727$			450474.i			0.852317i	−0.904649	+	0.426158i	$0.859867\pi$
$728$	−2018.39	−	73627.4i	−0.00380840	−	0.138924i
$729$	−102919.			−0.193661
$730$	−339675.	−	191995.i	−0.637408	−	0.360284i
$731$			1.16458e6i			2.17938i
$732$	−215898.	+	129965.i	−0.402927	+	0.242552i
$733$	−137605.			−0.256109			−0.128054	−	0.991767i	$-0.540873\pi$
$733$	−137605.			−0.256109			−0.128054	+	0.991767i	$0.540873\pi$
$734$	−147780.	+	261449.i	−0.274298	+	0.485283i
$735$			151290.i			0.280050i
$736$	−212405.	−	498316.i	−0.392111	−	0.919918i
$737$	24025.2			0.0442315
$738$	50780.2	+	28702.7i	0.0932356	+	0.0526999i
$739$			293388.i			0.537221i	0.963249	+	0.268610i	$0.0865644\pi$
$739$			293388.i			0.537221i	−0.963249	+	0.268610i	$0.913436\pi$
$740$	204475.	+	339674.i	0.373402	+	0.620296i
$741$	34414.8			0.0626772
$742$	164100.	−	290323.i	0.298059	−	0.527320i
$743$			411394.i			0.745214i	0.927989	+	0.372607i	$0.121536\pi$
$743$			411394.i			0.745214i	−0.927989	+	0.372607i	$0.878464\pi$
$744$	6726.92	−	184.409i	0.0121526	−	0.000333147i
$745$	−22549.4			−0.0406277
$746$	−202902.	−	114687.i	−0.364594	−	0.206081i
$747$	−60456.3			−0.108343
$748$	70954.4	−	42712.7i	0.126817	−	0.0763403i
$749$		−	271397.i		−	0.483773i
$750$	−142648.	+	252371.i	−0.253597	+	0.448660i
$751$			388022.i			0.687982i	0.938973	+	0.343991i	$0.111779\pi$
$751$			388022.i			0.687982i	−0.938973	+	0.343991i	$0.888221\pi$
$752$	293231.	−	553670.i	0.518530	−	0.979074i
$753$		−	268220.i		−	0.473044i
$754$	172814.	+	97680.1i	0.303973	+	0.171816i
$755$	−462211.			−0.810861
$756$	−100731.	−	167335.i	−0.176247	−	0.292781i
$757$	−1.14104e6			−1.99117			−0.995586	−	0.0938540i	$-0.970081\pi$
$757$	−1.14104e6			−1.99117			−0.995586	+	0.0938540i	$0.970081\pi$
$758$	197849.	+	111831.i	0.344347	+	0.194636i
$759$	−30949.0	−	5196.44i	−0.0537233	−	0.00902033i
$760$	3741.98	+	136501.i	0.00647850	+	0.236324i
$761$	−358751.			−0.619475			−0.309738	−	0.950822i	$-0.600241\pi$
$761$	−358751.			−0.619475			−0.309738	+	0.950822i	$0.600241\pi$
$762$	−37698.0	+	66694.6i	−0.0649245	+	0.114863i
$763$			205423.i			0.352859i
$764$	−887036.	+	533973.i	−1.51969	+	0.914813i
$765$			395985.i			0.676637i
$766$	−214802.	+	380023.i	−0.366083	+	0.647668i
$767$	−60626.6			−0.103056
$768$	−242701.	+	164861.i	−0.411480	+	0.279509i
$769$		−	746083.i		−	1.26164i	−0.775930	−	0.630819i	$-0.782719\pi$
$769$		−	746083.i		−	1.26164i	0.775930	−	0.630819i	$-0.217281\pi$
$770$	8331.21	−	14739.4i	0.0140516	−	0.0248599i
$771$			47997.5i			0.0807439i
$772$	−133981.	−	222569.i	−0.224806	−	0.373448i
$773$	162387.			0.271764			0.135882	−	0.990725i	$-0.456613\pi$
$773$	162387.			0.271764			0.135882	+	0.990725i	$0.456613\pi$
$774$	632838.	+	357701.i	1.05636	+	0.597088i
$775$	8183.67			0.0136253
$776$	−598865.	+	16417.1i	−0.994502	+	0.0272629i
$777$	128131.			0.212232
$778$	179371.	+	101386.i	0.296342	+	0.167502i
$779$	−30692.7			−0.0505778
$780$	−36810.1	−	61149.0i	−0.0605032	−	0.100508i
$781$	55689.0			0.0912993
$782$	642286.	+	520258.i	1.05030	+	0.850757i
$783$	526397.			0.858598
$784$	−243471.	+	459714.i	−0.396109	+	0.747921i
$785$	255680.			0.414913
$786$	279302.	+	157871.i	0.452094	+	0.255539i
$787$	−82216.9			−0.132743			−0.0663715	−	0.997795i	$-0.521142\pi$
$787$	−82216.9			−0.132743			−0.0663715	+	0.997795i	$0.521142\pi$
$788$	286387.	−	172398.i	0.461213	−	0.277638i
$789$	−291736.			−0.468637
$790$	−79071.1	+	139891.i	−0.126696	+	0.224149i
$791$	−82104.8			−0.131225
$792$	−1416.63	−	51676.3i	−0.00225843	−	0.0823837i
$793$		−	210786.i		−	0.335194i
$794$	149748.	−	264931.i	0.237531	−	0.420235i
$795$		−	323162.i		−	0.511311i
$796$	−959505.	+	577597.i	−1.51433	+	0.911589i
$797$	−601586.			−0.947068			−0.473534	−	0.880775i	$-0.657022\pi$
$797$	−601586.			−0.947068			−0.473534	+	0.880775i	$0.657022\pi$
$798$	38418.3	+	21715.3i	0.0603298	+	0.0341004i
$799$			955999.i			1.49749i
$800$	−300531.	+	192324.i	−0.469580	+	0.300507i
$801$		−	824149.i		−	1.28452i
$802$	−94866.2	+	167835.i	−0.147490	+	0.260937i
$803$	−77724.9			−0.120539
$804$	111267.	−	66980.0i	0.172129	−	0.103618i
$805$	166645.	+	27980.3i	0.257158	+	0.0431778i
$806$	−2769.81	+	4900.29i	−0.00426363	+	0.00754314i
$807$	−20075.3			−0.0308258
$808$	−812847.	+	22283.1i	−1.24505	+	0.0341313i
$809$	−811457.			−1.23985			−0.619924	−	0.784662i	$-0.712837\pi$
$809$	−811457.			−1.23985			−0.619924	+	0.784662i	$0.712837\pi$
$810$	121166.	+	68487.3i	0.184677	+	0.104385i
$811$		−	841724.i		−	1.27976i	−0.768475	−	0.639879i	$-0.778984\pi$
$811$		−	841724.i		−	1.27976i	0.768475	−	0.639879i	$-0.221016\pi$
$812$	131282.	+	218086.i	0.199110	+	0.330762i
$813$			23918.9i			0.0361876i
$814$	68754.6	+	38862.4i	0.103766	+	0.0586517i
$815$		−	459183.i		−	0.691306i
$816$	209530.	−	395629.i	0.314678	−	0.594166i
$817$	−382501.			−0.573045
$818$	−86483.9	−	48883.6i	−0.129249	−	0.0730561i
$819$	70153.3			0.104588
$820$	32828.9	+	54535.5i	0.0488235	+	0.0811057i
$821$		−	76581.1i		−	0.113615i	−0.998385	−	0.0568075i	$-0.981908\pi$
$821$		−	76581.1i		−	0.113615i	0.998385	−	0.0568075i	$-0.0180921\pi$
$822$	354475.	+	200361.i	0.524616	+	0.296530i
$823$	432517.			0.638563			0.319281	−	0.947660i	$-0.396559\pi$
$823$	432517.			0.638563			0.319281	+	0.947660i	$0.396559\pi$
$824$	316894.	−	8687.21i	0.466723	−	0.0127946i
$825$			20670.7i			0.0303701i
$826$	−67679.2	−	38254.5i	−0.0991962	−	0.0560690i
$827$	−1.01192e6			−1.47958			−0.739788	−	0.672840i	$-0.765074\pi$
$827$	−1.01192e6			−1.47958			−0.739788	+	0.672840i	$0.765074\pi$
$828$	479990.	−	189224.i	0.700119	−	0.276004i
$829$		−	854987.i		−	1.24409i	−0.782983	−	0.622043i	$-0.786303\pi$
$829$		−	854987.i		−	1.24409i	0.782983	−	0.622043i	$-0.213697\pi$
$830$	−57433.9	−	32463.5i	−0.0833704	−	0.0471237i
$831$	−563889.			−0.816566
$832$	−13445.4	−	245048.i	−0.0194235	−	0.354001i
$833$		−	793769.i		−	1.14394i
$834$	173024.	+	97798.8i	0.248756	+	0.140605i
$835$	571218.			0.819274
$836$	14028.9	+	23304.8i	0.0200729	+	0.0333451i
$837$			14926.5i			0.0213062i
$838$	1.11148e6	+	628248.i	1.58276	+	0.894629i
$839$		−	812222.i		−	1.15385i	−0.816796	−	0.576927i	$-0.804252\pi$
$839$		−	812222.i		−	1.15385i	0.816796	−	0.576927i	$-0.195748\pi$
$840$	−2508.05	−	91489.0i	−0.00355449	−	0.129661i
$841$	21233.2			0.0300209
$842$	351854.	+	198879.i	0.496293	+	0.280521i
$843$	219422.			0.308763
$844$	200893.	−	120933.i	0.282020	−	0.169769i
$845$	−415271.			−0.581592
$846$	519496.	+	293636.i	0.725840	+	0.410269i
$847$			277849.i			0.387296i
$848$	520064.	−	981969.i	0.723211	−	1.36555i
$849$		−	280400.i		−	0.389011i
$850$	267898.	−	473961.i	0.370794	−	0.656001i
$851$	−130519.	+	777346.i	−0.180225	+	1.07338i
$852$	257911.	−	155256.i	0.355297	−	0.213880i
$853$			623609.i			0.857066i	0.903526	+	0.428533i	$0.140969\pi$
$853$			623609.i			0.857066i	−0.903526	+	0.428533i	$0.859031\pi$
$854$	133003.	−	235307.i	0.182367	−	0.322640i
$855$	−130060.			−0.177915
$856$	−24780.5	−	903948.i	−0.0338191	−	1.23366i
$857$	−346156.			−0.471314			−0.235657	−	0.971836i	$-0.575724\pi$
$857$	−346156.			−0.471314			−0.235657	+	0.971836i	$0.575724\pi$
$858$	−12377.4	−	6996.10i	−0.0168133	−	0.00950346i
$859$			677228.i			0.917801i	0.888488	+	0.458901i	$0.151757\pi$
$859$			677228.i			0.917801i	−0.888488	+	0.458901i	$0.848243\pi$
$860$	409124.	+	679637.i	0.553169	+	0.918925i
$861$	20571.6			0.0277500
$862$	−569939.	+	1.00833e6i	−0.767033	+	1.35702i
$863$	208506.			0.279961			0.139980	−	0.990154i	$-0.455296\pi$
$863$	208506.			0.279961			0.139980	+	0.990154i	$0.455296\pi$
$864$	−350787.	−	548148.i	−0.469911	−	0.734295i
$865$		−	442979.i		−	0.592040i
$866$	341839.	−	604775.i	0.455812	−	0.806414i
$867$			309200.i			0.411341i
$868$	−6184.03	+	3722.63i	−0.00820790	+	0.00494095i
$869$			32010.1i			0.0423884i
$870$	214737.	+	121377.i	0.283707	+	0.160360i
$871$			108633.i			0.143194i
$872$	18756.6	+	684208.i	0.0246673	+	0.899819i
$873$		−	570608.i		−	0.748703i
$874$	−170877.	+	210957.i	−0.223698	+	0.276166i
$875$		−	310944.i		−	0.406132i
$876$	−359966.	+	216690.i	−0.469086	+	0.282378i
$877$		−	643468.i		−	0.836619i	−0.908305	−	0.418309i	$-0.862623\pi$
$877$		−	643468.i		−	0.836619i	0.908305	−	0.418309i	$-0.137377\pi$
$878$	−731418.	−	413422.i	−0.948804	−	0.536295i
$879$		−	407059.i		−	0.526841i
$880$	26403.1	−	49853.6i	0.0340949	−	0.0643770i
$881$		−	444673.i		−	0.572913i	−0.958093	−	0.286457i	$-0.907523\pi$
$881$		−	444673.i		−	0.572913i	0.958093	−	0.286457i	$-0.0924774\pi$
$882$	−431339.	−	243807.i	−0.554475	−	0.313407i
$883$		−	730574.i		−	0.937007i	−0.883462	−	0.468504i	$-0.844793\pi$
$883$		−	730574.i		−	0.937007i	0.883462	−	0.468504i	$-0.155207\pi$
$884$	193131.	+	320829.i	0.247143	+	0.410553i
$885$	−75334.3			−0.0961847
$886$	216307.	−	382686.i	0.275551	−	0.487500i
$887$	−1.08807e6			−1.38296			−0.691479	−	0.722397i	$-0.743040\pi$
$887$	−1.08807e6			−1.38296			−0.691479	+	0.722397i	$0.743040\pi$
$888$	426767.	−	11699.2i	0.541209	−	0.0148365i
$889$		−	82173.9i		−	0.103975i
$890$	442548.	−	782948.i	0.558702	−	0.988445i
$891$	27725.5			0.0349240
$892$	101025.	+	167823.i	0.126970	+	0.210922i
$893$	−313995.			−0.393749
$894$	−11948.2	+	21138.6i	−0.0149496	+	0.0264485i
$895$			48611.9i			0.0606871i
$896$	139612.	−	282038.i	0.173903	−	0.351311i
$897$	23496.4	−	139940.i	0.0292022	−	0.173923i
$898$	147543.	+	83396.2i	0.182964	+	0.103417i
$899$		−	19453.5i		−	0.0240701i
$900$	−175268.	−	291155.i	−0.216380	−	0.359451i
$901$			1.69553e6i			2.08860i
$902$	11038.7	+	6239.44i	0.0135677	+	0.00766889i
$903$	256370.			0.314406
$904$	−273468.	+	7496.75i	−0.334634	+	0.00917352i
$905$	461191.			0.563097
$906$	−244911.	+	433292.i	−0.298368	+	0.527867i
$907$	−914545.			−1.11171			−0.555854	−	0.831280i	$-0.687609\pi$
$907$	−914545.			−1.11171			−0.555854	+	0.831280i	$0.687609\pi$
$908$	642019.	+	1.06652e6i	0.778711	+	1.29360i
$909$		−	774493.i		−	0.937324i
$910$	66646.1	+	37670.6i	0.0804808	+	0.0454904i
$911$		−	712356.i		−	0.858342i	−0.903223	−	0.429171i	$-0.858806\pi$
$911$		−	712356.i		−	0.858342i	0.903223	−	0.429171i	$-0.141194\pi$
$912$	129943.	+	68819.6i	0.156230	+	0.0827413i
$913$	−13142.1			−0.0157661
$914$	451515.	−	798812.i	0.540480	−	0.956208i
$915$		−	261922.i		−	0.312845i
$916$	89376.0	+	148471.i	0.106520	+	0.176951i
$917$	−344126.			−0.409240
$918$	864473.	+	488629.i	1.02581	+	0.579820i
$919$			862614.i			1.02138i	0.859766	+	0.510688i	$0.170609\pi$
$919$			862614.i			1.02138i	−0.859766	+	0.510688i	$0.829391\pi$
$920$	557603.	+	77978.7i	0.658794	+	0.0921298i
$921$	558136.			0.657993
$922$	−536839.	+	949765.i	−0.631512	+	1.11726i
$923$			251805.i			0.295570i
$924$	−9402.78	−	15619.9i	−0.0110132	−	0.0182951i
$925$	519186.			0.606791
$926$	−607251.	−	343238.i	−0.708184	−	0.400289i
$927$			301941.i			0.351369i
$928$	457177.	+	714397.i	0.530870	+	0.829552i
$929$	1.19416e6			1.38366			0.691831	−	0.722059i	$-0.256804\pi$
$929$	1.19416e6			1.38366			0.691831	+	0.722059i	$0.256804\pi$
$930$	−3441.75	+	6089.08i	−0.00397936	+	0.00704021i
$931$	260711.			0.300788
$932$	−484966.	−	805626.i	−0.558315	−	0.927473i
$933$		−	198705.i		−	0.228268i
$934$	623156.	+	352228.i	0.714337	+	0.403767i
$935$			86080.0i			0.0984644i
$936$	233661.	−	6405.49i	0.266707	−	0.00731141i
$937$			1.18532e6i			1.35007i	0.737785	+	0.675036i	$0.235872\pi$
$937$			1.18532e6i			1.35007i	−0.737785	+	0.675036i	$0.764128\pi$
$938$	−68545.7	+	121270.i	−0.0779067	+	0.137831i
$939$	528380.			0.599260
$940$	335849.	+	557913.i	0.380092	+	0.631409i
$941$	43346.7			0.0489527			0.0244763	−	0.999700i	$-0.492208\pi$
$941$	43346.7			0.0489527			0.0244763	+	0.999700i	$0.492208\pi$
$942$	135477.	−	239683.i	0.152673	−	0.270106i
$943$	−20955.1	+	124805.i	−0.0235650	+	0.140348i
$944$	−228913.	−	121235.i	−0.256878	−	0.136046i
$945$	203006.			0.227325
$946$	137568.	+	77757.7i	0.153721	+	0.0868883i
$947$			1.18797e6i			1.32466i	0.749212	+	0.662330i	$0.230432\pi$
$947$			1.18797e6i			1.32466i	−0.749212	+	0.662330i	$0.769568\pi$
$948$	89241.3	+	148248.i	0.0993000	+	0.164957i
$949$		−	351443.i		−	0.390231i
$950$	155671.	+	87990.4i	0.172489	+	0.0974963i
$951$	402849.			0.445432
$952$	13158.9	+	480014.i	0.0145193	+	0.529639i
$953$			1.23050e6i			1.35487i	0.735584	+	0.677434i	$0.236908\pi$
$953$			1.23050e6i			1.35487i	−0.735584	+	0.677434i	$0.763092\pi$
$954$	921359.	+	520783.i	1.01235	+	0.572216i
$955$		−	1.07613e6i		−	1.17993i
$956$	−327853.	−	544629.i	−0.358726	−	0.595916i
$957$	49136.6			0.0536514
$958$	−220255.	+	389671.i	−0.239991	+	0.424588i
$959$	−436746.			−0.474888
$960$	−16707.2	−	304495.i	−0.0181285	−	0.330399i
$961$	−922969.			−0.999403
$962$	−175721.	+	310883.i	−0.189878	+	0.335928i
$963$	861295.			0.928751
$964$	−2127.19	+	1280.51i	−0.00228903	+	0.00137794i
$965$	270015.			0.289957
$966$	114530.	−	141393.i	0.122734	−	0.151521i
$967$	1.61264e6			1.72458			0.862290	−	0.506415i	$-0.169030\pi$
$967$	1.61264e6			1.72458			0.862290	+	0.506415i	$0.169030\pi$
$968$	25369.6	+	925439.i	0.0270747	+	0.987636i
$969$	−224367.			−0.238953
$970$	306402.	−	542082.i	0.325648	−	0.576131i
$971$	−461953.			−0.489959			−0.244979	−	0.969528i	$-0.578781\pi$
$971$	−461953.			−0.489959			−0.244979	+	0.969528i	$0.578781\pi$
$972$	834060.	−	502083.i	0.882805	−	0.531426i
$973$	−213181.			−0.225177
$974$	−115881.	−	65500.0i	−0.122151	−	0.0690436i
$975$	−93465.1			−0.0983197
$976$	421511.	−	795884.i	0.442496	−	0.835508i
$977$		−	601336.i		−	0.629982i	−0.949095	−	0.314991i	$-0.897998\pi$
$977$		−	601336.i		−	0.629982i	0.949095	−	0.314991i	$-0.102002\pi$
$978$	−430453.	−	243306.i	−0.450037	−	0.254376i
$979$		−	179155.i		−	0.186924i
$980$	−278857.	−	463237.i	−0.290355	−	0.482338i
$981$	−651924.			−0.677421
$982$	779302.	−	1.37873e6i	0.808133	−	1.42973i
$983$		−	772345.i		−	0.799290i	−0.916670	−	0.399645i	$-0.869133\pi$
$983$		−	772345.i		−	0.799290i	0.916670	−	0.399645i	$-0.130867\pi$
$984$	68518.4	−	1878.34i	0.0707647	−	0.00193992i
$985$			347438.i			0.358100i
$986$	−1.12666e6	−	636825.i	−1.15888	−	0.655038i
$987$	210454.			0.216034
$988$	−105375.	+	63433.3i	−0.107951	+	0.0649835i
$989$	−261149.	+	1.55535e6i	−0.266990	+	1.59014i
$990$	46776.4	+	26439.6i	0.0477262	+	0.0269764i
$991$	137244.			0.139748			0.0698739	−	0.997556i	$-0.477740\pi$
$991$	137244.			0.139748			0.0698739	+	0.997556i	$0.477740\pi$
$992$	−20257.4	+	12963.7i	−0.0205854	+	0.0131736i
$993$	−605681.			−0.614251
$994$	−158885.	+	281097.i	−0.160809	+	0.284501i
$995$		−	1.16405e6i		−	1.17577i
$996$	−60864.8	+	36639.0i	−0.0613546	+	0.0369339i
$997$			935088.i			0.940724i	0.882474	+	0.470362i	$0.155877\pi$
$997$			935088.i			0.940724i	−0.882474	+	0.470362i	$0.844123\pi$
$998$	−514193.	+	909701.i	−0.516256	+	0.913350i
$999$			946960.i			0.948857i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	184.5.e.e.45.13	✓	84
4.3	odd	2		736.5.e.e.689.54		84
8.3	odd	2		736.5.e.e.689.31		84
8.5	even	2	inner	184.5.e.e.45.16	yes	84
23.22	odd	2	inner	184.5.e.e.45.14	yes	84
92.91	even	2		736.5.e.e.689.32		84
184.45	odd	2	inner	184.5.e.e.45.15	yes	84
184.91	even	2		736.5.e.e.689.53		84

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
184.5.e.e.45.13	✓	84	1.1	even	1	trivial
184.5.e.e.45.14	yes	84	23.22	odd	2	inner
184.5.e.e.45.15	yes	84	184.45	odd	2	inner
184.5.e.e.45.16	yes	84	8.5	even	2	inner
736.5.e.e.689.31		84	8.3	odd	2
736.5.e.e.689.32		84	92.91	even	2
736.5.e.e.689.53		84	184.91	even	2
736.5.e.e.689.54		84	4.3	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:	\( N \)	\(=\)	\( 184 = 2^{3} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	184.e (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-3.48223 - 1.96827i) q^{2} -4.47691i q^{3} +(8.25182 + 13.7079i) q^{4} -16.6301 q^{5} +(-8.81177 + 15.5896i) q^{6} -19.2078i q^{7} +(-1.75381 - 63.9760i) q^{8} +60.9573 q^{9} +O(q^{10})\)	\(q+(-3.48223 - 1.96827i) q^{2} -4.47691i q^{3} +(8.25182 + 13.7079i) q^{4} -16.6301 q^{5} +(-8.81177 + 15.5896i) q^{6} -19.2078i q^{7} +(-1.75381 - 63.9760i) q^{8} +60.9573 q^{9} +(57.9098 + 32.7326i) q^{10} +13.2510 q^{11} +(61.3692 - 36.9427i) q^{12} +59.9162i q^{13} +(-37.8062 + 66.8861i) q^{14} +74.4515i q^{15} +(-119.815 + 226.231i) q^{16} -390.623i q^{17} +(-212.267 - 119.980i) q^{18} +128.299 q^{19} +(-137.229 - 227.964i) q^{20} -85.9918 q^{21} +(-46.1431 - 26.0816i) q^{22} +(87.5948 - 521.697i) q^{23} +(-286.415 + 7.85166i) q^{24} -348.439 q^{25} +(117.931 - 208.642i) q^{26} -635.530i q^{27} +(263.300 - 158.500i) q^{28} +828.280i q^{29} +(146.541 - 259.257i) q^{30} -23.4866 q^{31} +(862.506 - 551.960i) q^{32} -59.3236i q^{33} +(-768.852 + 1360.24i) q^{34} +319.429i q^{35} +(503.009 + 835.598i) q^{36} -1490.03 q^{37} +(-446.766 - 252.527i) q^{38} +268.239 q^{39} +(29.1661 + 1063.93i) q^{40} -239.228 q^{41} +(299.443 + 169.255i) q^{42} -2981.33 q^{43} +(109.345 + 181.644i) q^{44} -1013.73 q^{45} +(-1331.87 + 1644.26i) q^{46} -2447.37 q^{47} +(1012.82 + 536.400i) q^{48} +2032.06 q^{49} +(1213.35 + 685.823i) q^{50} -1748.79 q^{51} +(-821.327 + 494.418i) q^{52} -4340.56 q^{53} +(-1250.89 + 2213.06i) q^{54} -220.366 q^{55} +(-1228.84 + 33.6870i) q^{56} -574.383i q^{57} +(1630.28 - 2884.26i) q^{58} +1011.86i q^{59} +(-1020.58 + 614.361i) q^{60} -3518.02 q^{61} +(81.7858 + 46.2281i) q^{62} -1170.86i q^{63} +(-4089.85 + 224.404i) q^{64} -996.412i q^{65} +(-116.765 + 206.578i) q^{66} +1813.08 q^{67} +(5354.64 - 3223.35i) q^{68} +(-2335.59 - 392.154i) q^{69} +(628.722 - 1112.32i) q^{70} +4202.62 q^{71} +(-106.908 - 3899.80i) q^{72} -5865.58 q^{73} +(5188.63 + 2932.79i) q^{74} +1559.93i q^{75} +(1058.70 + 1758.71i) q^{76} -254.524i q^{77} +(-934.070 - 527.967i) q^{78} +2415.67i q^{79} +(1992.53 - 3762.24i) q^{80} +2092.33 q^{81} +(833.046 + 470.865i) q^{82} -991.781 q^{83} +(-709.589 - 1178.77i) q^{84} +6496.11i q^{85} +(10381.7 + 5868.06i) q^{86} +3708.13 q^{87} +(-23.2398 - 847.747i) q^{88} -13520.1i q^{89} +(3530.03 + 1995.29i) q^{90} +1150.86 q^{91} +(7874.21 - 3104.21i) q^{92} +105.148i q^{93} +(8522.29 + 4817.08i) q^{94} -2133.63 q^{95} +(-2471.07 - 3861.36i) q^{96} -9360.78i q^{97} +(-7076.09 - 3999.64i) q^{98} +807.746 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 84 q + 4 q^{2} - 32 q^{4} - 120 q^{6} - 212 q^{8} - 2272 q^{9}+O(q^{10}) \) 84 * q + 4 * q^2 - 32 * q^4 - 120 * q^6 - 212 * q^8 - 2272 * q^9	\( 84 q + 4 q^{2} - 32 q^{4} - 120 q^{6} - 212 q^{8} - 2272 q^{9} + 1036 q^{12} - 240 q^{16} - 2392 q^{18} + 2596 q^{23} + 1348 q^{24} + 11996 q^{25} - 1560 q^{26} - 260 q^{31} + 1744 q^{32} - 8600 q^{36} + 18740 q^{39} - 4 q^{41} - 7652 q^{46} - 14732 q^{47} - 10216 q^{48} - 52140 q^{49} - 7264 q^{50} + 18936 q^{52} - 68 q^{54} - 208 q^{55} - 27268 q^{58} - 500 q^{62} - 6536 q^{64} - 16188 q^{70} + 47860 q^{71} + 15584 q^{72} - 4 q^{73} + 37384 q^{78} - 3372 q^{81} + 86300 q^{82} - 34420 q^{87} - 15932 q^{92} - 93956 q^{94} + 109872 q^{95} + 26072 q^{96} + 35848 q^{98}+O(q^{100}) \) 84 * q + 4 * q^2 - 32 * q^4 - 120 * q^6 - 212 * q^8 - 2272 * q^9 + 1036 * q^12 - 240 * q^16 - 2392 * q^18 + 2596 * q^23 + 1348 * q^24 + 11996 * q^25 - 1560 * q^26 - 260 * q^31 + 1744 * q^32 - 8600 * q^36 + 18740 * q^39 - 4 * q^41 - 7652 * q^46 - 14732 * q^47 - 10216 * q^48 - 52140 * q^49 - 7264 * q^50 + 18936 * q^52 - 68 * q^54 - 208 * q^55 - 27268 * q^58 - 500 * q^62 - 6536 * q^64 - 16188 * q^70 + 47860 * q^71 + 15584 * q^72 - 4 * q^73 + 37384 * q^78 - 3372 * q^81 + 86300 * q^82 - 34420 * q^87 - 15932 * q^92 - 93956 * q^94 + 109872 * q^95 + 26072 * q^96 + 35848 * q^98

Introduction

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